id	sid	tid	token	lemma	pos
ejpam-3763	1	1	european	european	PROPN
ejpam-3763	1	2	journal	journal	PROPN
ejpam-3763	1	3	of	of	ADP
ejpam-3763	1	4	pure	pure	ADJ
ejpam-3763	1	5	and	and	CCONJ
ejpam-3763	1	6	applied	apply	VERB
ejpam-3763	1	7	mathematics	mathematic	NOUN
ejpam-3763	1	8	vol	vol	NOUN
ejpam-3763	1	9	.	.	PROPN
ejpam-3763	2	1	13	13	NUM
ejpam-3763	2	2	,	,	PUNCT
ejpam-3763	2	3	no	no	INTJ
ejpam-3763	2	4	.	.	NOUN
ejpam-3763	2	5	3	3	NUM
ejpam-3763	2	6	,	,	PUNCT
ejpam-3763	2	7	2020	2020	NUM
ejpam-3763	2	8	,	,	PUNCT
ejpam-3763	2	9	529	529	NUM
ejpam-3763	2	10	-	-	SYM
ejpam-3763	2	11	548	548	NUM
ejpam-3763	2	12	issn	issn	PROPN
ejpam-3763	2	13	1307	1307	NUM
ejpam-3763	2	14	-	-	SYM
ejpam-3763	2	15	5543	5543	NUM
ejpam-3763	2	16	–	–	PUNCT
ejpam-3763	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3763	2	18	published	publish	VERB
ejpam-3763	2	19	by	by	ADP
ejpam-3763	2	20	new	new	PROPN
ejpam-3763	2	21	york	york	PROPN
ejpam-3763	2	22	business	business	PROPN
ejpam-3763	2	23	global	global	PROPN
ejpam-3763	2	24	more	more	ADV
ejpam-3763	2	25	on	on	ADP
ejpam-3763	2	26	perfect	perfect	ADJ
ejpam-3763	2	27	roman	roman	ADJ
ejpam-3763	2	28	domination	domination	NOUN
ejpam-3763	2	29	in	in	ADP
ejpam-3763	2	30	graphs	graph	NOUN
ejpam-3763	2	31	leonard	leonard	PROPN
ejpam-3763	2	32	mijares	mijares	PROPN
ejpam-3763	2	33	paleta1,∗	paleta1,∗	PROPN
ejpam-3763	2	34	,	,	PUNCT
ejpam-3763	2	35	ferdinand	ferdinand	PROPN
ejpam-3763	2	36	p.	p.	PROPN
ejpam-3763	3	1	jamil2	jamil2	PROPN
ejpam-3763	4	1	1	1	NUM
ejpam-3763	4	2	department	department	NOUN
ejpam-3763	4	3	of	of	ADP
ejpam-3763	4	4	mathematics	mathematic	NOUN
ejpam-3763	4	5	,	,	PUNCT
ejpam-3763	4	6	college	college	NOUN
ejpam-3763	4	7	of	of	ADP
ejpam-3763	4	8	science	science	NOUN
ejpam-3763	4	9	and	and	CCONJ
ejpam-3763	4	10	mathematics	mathematic	NOUN
ejpam-3763	4	11	,	,	PUNCT
ejpam-3763	4	12	university	university	NOUN
ejpam-3763	4	13	of	of	ADP
ejpam-3763	4	14	southern	southern	ADJ
ejpam-3763	4	15	mindanao	mindanao	PROPN
ejpam-3763	4	16	,	,	PUNCT
ejpam-3763	4	17	kabacan	kabacan	NOUN
ejpam-3763	4	18	9407	9407	NUM
ejpam-3763	4	19	,	,	PUNCT
ejpam-3763	4	20	north	north	NOUN
ejpam-3763	4	21	cotabato	cotabato	PROPN
ejpam-3763	4	22	,	,	PUNCT
ejpam-3763	4	23	philippines	philippine	NOUN
ejpam-3763	4	24	2	2	NUM
ejpam-3763	4	25	department	department	NOUN
ejpam-3763	4	26	of	of	ADP
ejpam-3763	4	27	mathematics	mathematic	NOUN
ejpam-3763	4	28	and	and	CCONJ
ejpam-3763	4	29	statistics	statistic	NOUN
ejpam-3763	4	30	,	,	PUNCT
ejpam-3763	4	31	college	college	NOUN
ejpam-3763	4	32	of	of	ADP
ejpam-3763	4	33	science	science	NOUN
ejpam-3763	4	34	and	and	CCONJ
ejpam-3763	4	35	mathematics	mathematic	NOUN
ejpam-3763	4	36	.	.	PUNCT
ejpam-3763	5	1	center	center	NOUN
ejpam-3763	5	2	for	for	ADP
ejpam-3763	5	3	graph	graph	NOUN
ejpam-3763	5	4	theory	theory	NOUN
ejpam-3763	5	5	,	,	PUNCT
ejpam-3763	5	6	algebra	algebra	NOUN
ejpam-3763	5	7	and	and	CCONJ
ejpam-3763	5	8	analysis	analysis	NOUN
ejpam-3763	5	9	,	,	PUNCT
ejpam-3763	5	10	premier	premier	ADJ
ejpam-3763	5	11	research	research	NOUN
ejpam-3763	5	12	of	of	ADP
ejpam-3763	5	13	institute	institute	PROPN
ejpam-3763	5	14	of	of	ADP
ejpam-3763	5	15	science	science	NOUN
ejpam-3763	5	16	and	and	CCONJ
ejpam-3763	5	17	mathematics	mathematic	NOUN
ejpam-3763	5	18	,	,	PUNCT
ejpam-3763	5	19	mindanao	mindanao	PROPN
ejpam-3763	5	20	state	state	PROPN
ejpam-3763	5	21	university	university	PROPN
ejpam-3763	5	22	-	-	PUNCT
ejpam-3763	5	23	iligan	iligan	PROPN
ejpam-3763	5	24	institute	institute	PROPN
ejpam-3763	5	25	of	of	ADP
ejpam-3763	5	26	technology	technology	PROPN
ejpam-3763	5	27	,	,	PUNCT
ejpam-3763	5	28	9200	9200	NUM
ejpam-3763	5	29	iligan	iligan	ADJ
ejpam-3763	5	30	city	city	NOUN
ejpam-3763	5	31	,	,	PUNCT
ejpam-3763	5	32	philippines	philippine	NOUN
ejpam-3763	5	33	abstract	abstract	ADJ
ejpam-3763	5	34	.	.	PUNCT
ejpam-3763	6	1	a	a	DET
ejpam-3763	6	2	perfect	perfect	ADJ
ejpam-3763	6	3	roman	roman	ADJ
ejpam-3763	6	4	dominating	dominating	NOUN
ejpam-3763	6	5	function	function	NOUN
ejpam-3763	6	6	on	on	ADP
ejpam-3763	6	7	a	a	DET
ejpam-3763	6	8	graph	graph	NOUN
ejpam-3763	6	9	g	g	NOUN
ejpam-3763	6	10	=	=	PUNCT
ejpam-3763	6	11	(	(	PUNCT
ejpam-3763	6	12	v	v	NOUN
ejpam-3763	6	13	(	(	PUNCT
ejpam-3763	6	14	g	g	NOUN
ejpam-3763	6	15	)	)	PUNCT
ejpam-3763	6	16	,	,	PUNCT
ejpam-3763	6	17	e(g	e(g	PROPN
ejpam-3763	6	18	)	)	PUNCT
ejpam-3763	6	19	)	)	PUNCT
ejpam-3763	6	20	is	be	AUX
ejpam-3763	6	21	a	a	DET
ejpam-3763	6	22	function	function	NOUN
ejpam-3763	6	23	f	f	NOUN
ejpam-3763	6	24	:	:	PUNCT
ejpam-3763	6	25	v	v	X
ejpam-3763	6	26	(	(	PUNCT
ejpam-3763	6	27	g	g	NOUN
ejpam-3763	6	28	)	)	PUNCT
ejpam-3763	6	29	→	→	SYM
ejpam-3763	6	30	{	{	PUNCT
ejpam-3763	6	31	0	0	NUM
ejpam-3763	6	32	,	,	PUNCT
ejpam-3763	6	33	1	1	NUM
ejpam-3763	6	34	,	,	PUNCT
ejpam-3763	6	35	2	2	NUM
ejpam-3763	6	36	}	}	PUNCT
ejpam-3763	6	37	for	for	ADP
ejpam-3763	6	38	which	which	PRON
ejpam-3763	6	39	each	each	DET
ejpam-3763	6	40	u	u	PROPN
ejpam-3763	6	41	∈	∈	PROPN
ejpam-3763	6	42	v	v	NOUN
ejpam-3763	6	43	(	(	PUNCT
ejpam-3763	6	44	g	g	NOUN
ejpam-3763	6	45	)	)	PUNCT
ejpam-3763	6	46	with	with	ADP
ejpam-3763	6	47	f(u	f(u	PROPN
ejpam-3763	6	48	)	)	PUNCT
ejpam-3763	7	1	=	=	SYM
ejpam-3763	7	2	0	0	NUM
ejpam-3763	7	3	is	be	AUX
ejpam-3763	7	4	adjacent	adjacent	ADJ
ejpam-3763	7	5	to	to	ADP
ejpam-3763	7	6	exactly	exactly	ADV
ejpam-3763	7	7	one	one	NUM
ejpam-3763	7	8	vertex	vertex	NOUN
ejpam-3763	7	9	v	v	ADP
ejpam-3763	7	10	∈	∈	NOUN
ejpam-3763	7	11	v	v	NOUN
ejpam-3763	7	12	(	(	PUNCT
ejpam-3763	7	13	g	g	NOUN
ejpam-3763	7	14	)	)	PUNCT
ejpam-3763	7	15	with	with	ADP
ejpam-3763	7	16	f(v	f(v	NOUN
ejpam-3763	7	17	)	)	PUNCT
ejpam-3763	7	18	=	=	SYM
ejpam-3763	8	1	2	2	X
ejpam-3763	8	2	.	.	PUNCT
ejpam-3763	8	3	the	the	DET
ejpam-3763	8	4	weight	weight	NOUN
ejpam-3763	8	5	of	of	ADP
ejpam-3763	8	6	a	a	DET
ejpam-3763	8	7	perfect	perfect	ADJ
ejpam-3763	8	8	roman	roman	ADJ
ejpam-3763	8	9	dominating	dominating	NOUN
ejpam-3763	8	10	function	function	NOUN
ejpam-3763	8	11	f	f	PROPN
ejpam-3763	8	12	is	be	AUX
ejpam-3763	8	13	the	the	DET
ejpam-3763	8	14	value	value	NOUN
ejpam-3763	8	15	ωg(f	ωg(f	PRON
ejpam-3763	8	16	)	)	PUNCT
ejpam-3763	8	17	=	=	SYM
ejpam-3763	8	18	∑	∑	PUNCT
ejpam-3763	8	19	v∈v	v∈v	PROPN
ejpam-3763	8	20	(	(	PUNCT
ejpam-3763	8	21	g	g	NOUN
ejpam-3763	8	22	)	)	PUNCT
ejpam-3763	8	23	f(v	f(v	NOUN
ejpam-3763	8	24	)	)	PUNCT
ejpam-3763	8	25	.	.	PUNCT
ejpam-3763	9	1	the	the	DET
ejpam-3763	9	2	perfect	perfect	ADJ
ejpam-3763	9	3	roman	roman	ADJ
ejpam-3763	9	4	domination	domination	NOUN
ejpam-3763	9	5	number	number	NOUN
ejpam-3763	9	6	of	of	ADP
ejpam-3763	9	7	g	g	PROPN
ejpam-3763	9	8	is	be	AUX
ejpam-3763	9	9	the	the	DET
ejpam-3763	9	10	minimum	minimum	ADJ
ejpam-3763	9	11	weight	weight	NOUN
ejpam-3763	9	12	of	of	ADP
ejpam-3763	9	13	a	a	DET
ejpam-3763	9	14	perfect	perfect	ADJ
ejpam-3763	9	15	roman	roman	ADJ
ejpam-3763	9	16	dominating	dominating	NOUN
ejpam-3763	9	17	function	function	NOUN
ejpam-3763	9	18	on	on	ADP
ejpam-3763	9	19	g.	g.	PROPN
ejpam-3763	9	20	in	in	ADP
ejpam-3763	9	21	this	this	DET
ejpam-3763	9	22	paper	paper	NOUN
ejpam-3763	9	23	,	,	PUNCT
ejpam-3763	9	24	we	we	PRON
ejpam-3763	9	25	study	study	VERB
ejpam-3763	9	26	the	the	DET
ejpam-3763	9	27	perfect	perfect	ADJ
ejpam-3763	9	28	roman	roman	ADJ
ejpam-3763	9	29	domination	domination	NOUN
ejpam-3763	9	30	numbers	number	NOUN
ejpam-3763	9	31	of	of	ADP
ejpam-3763	9	32	graphs	graph	NOUN
ejpam-3763	9	33	under	under	ADP
ejpam-3763	9	34	some	some	DET
ejpam-3763	9	35	binary	binary	ADJ
ejpam-3763	9	36	operations	operation	NOUN
ejpam-3763	9	37	.	.	PUNCT
ejpam-3763	10	1	2020	2020	NUM
ejpam-3763	10	2	mathematics	mathematic	NOUN
ejpam-3763	10	3	subject	subject	NOUN
ejpam-3763	10	4	classifications	classification	NOUN
ejpam-3763	10	5	:	:	PUNCT
ejpam-3763	10	6	05c22	05c22	NOUN
ejpam-3763	10	7	,	,	PUNCT
ejpam-3763	10	8	05c69,05c76	05c69,05c76	PRON
ejpam-3763	10	9	key	key	ADJ
ejpam-3763	10	10	words	word	NOUN
ejpam-3763	10	11	and	and	CCONJ
ejpam-3763	10	12	phrases	phrase	NOUN
ejpam-3763	10	13	:	:	PUNCT
ejpam-3763	10	14	roman	roman	ADJ
ejpam-3763	10	15	dominating	dominating	NOUN
ejpam-3763	10	16	function	function	NOUN
ejpam-3763	10	17	,	,	PUNCT
ejpam-3763	10	18	perfect	perfect	ADJ
ejpam-3763	10	19	roman	roman	ADJ
ejpam-3763	10	20	dominating	dominating	NOUN
ejpam-3763	10	21	function	function	NOUN
ejpam-3763	10	22	,	,	PUNCT
ejpam-3763	10	23	roman	roman	ADJ
ejpam-3763	10	24	domination	domination	NOUN
ejpam-3763	10	25	number	number	NOUN
ejpam-3763	10	26	,	,	PUNCT
ejpam-3763	10	27	perfect	perfect	ADJ
ejpam-3763	10	28	roman	roman	ADJ
ejpam-3763	10	29	domination	domination	NOUN
ejpam-3763	10	30	number	number	NOUN
ejpam-3763	10	31	1	1	NUM
ejpam-3763	10	32	.	.	PUNCT
ejpam-3763	10	33	introduction	introduction	NOUN
ejpam-3763	10	34	throughout	throughout	ADP
ejpam-3763	10	35	this	this	DET
ejpam-3763	10	36	paper	paper	NOUN
ejpam-3763	10	37	,	,	PUNCT
ejpam-3763	10	38	all	all	DET
ejpam-3763	10	39	graphs	graph	NOUN
ejpam-3763	10	40	considered	consider	VERB
ejpam-3763	10	41	are	be	AUX
ejpam-3763	10	42	finite	finite	ADJ
ejpam-3763	10	43	,	,	PUNCT
ejpam-3763	10	44	simple	simple	ADJ
ejpam-3763	10	45	and	and	CCONJ
ejpam-3763	10	46	undirected	undirected	ADJ
ejpam-3763	10	47	.	.	PUNCT
ejpam-3763	11	1	let	let	VERB
ejpam-3763	11	2	g	g	PROPN
ejpam-3763	11	3	=	=	SYM
ejpam-3763	11	4	(	(	PUNCT
ejpam-3763	11	5	v	v	NOUN
ejpam-3763	11	6	(	(	PUNCT
ejpam-3763	11	7	g	g	NOUN
ejpam-3763	11	8	)	)	PUNCT
ejpam-3763	11	9	,	,	PUNCT
ejpam-3763	11	10	e(g	e(g	PROPN
ejpam-3763	11	11	)	)	PUNCT
ejpam-3763	11	12	be	be	AUX
ejpam-3763	11	13	a	a	DET
ejpam-3763	11	14	graph	graph	NOUN
ejpam-3763	11	15	.	.	PUNCT
ejpam-3763	12	1	the	the	DET
ejpam-3763	12	2	sets	set	NOUN
ejpam-3763	12	3	v	v	ADP
ejpam-3763	12	4	(	(	PUNCT
ejpam-3763	12	5	g	g	NOUN
ejpam-3763	12	6	)	)	PUNCT
ejpam-3763	12	7	and	and	CCONJ
ejpam-3763	12	8	e(g	e(g	PROPN
ejpam-3763	12	9	)	)	PUNCT
ejpam-3763	12	10	are	be	AUX
ejpam-3763	12	11	the	the	DET
ejpam-3763	12	12	vertex	vertex	NOUN
ejpam-3763	12	13	set	set	NOUN
ejpam-3763	12	14	and	and	CCONJ
ejpam-3763	12	15	edge	edge	NOUN
ejpam-3763	12	16	set	set	NOUN
ejpam-3763	12	17	,	,	PUNCT
ejpam-3763	12	18	respectively	respectively	ADV
ejpam-3763	12	19	,	,	PUNCT
ejpam-3763	12	20	of	of	ADP
ejpam-3763	12	21	g.	g.	NOUN
ejpam-3763	12	22	for	for	ADP
ejpam-3763	12	23	s	s	PROPN
ejpam-3763	12	24	⊆	⊆	NUM
ejpam-3763	12	25	v	v	NOUN
ejpam-3763	12	26	(	(	PUNCT
ejpam-3763	12	27	g	g	NOUN
ejpam-3763	12	28	)	)	PUNCT
ejpam-3763	12	29	,	,	PUNCT
ejpam-3763	12	30	|s|	|s|	PROPN
ejpam-3763	12	31	is	be	AUX
ejpam-3763	12	32	the	the	DET
ejpam-3763	12	33	cardinality	cardinality	NOUN
ejpam-3763	12	34	of	of	ADP
ejpam-3763	12	35	s.	s.	PROPN
ejpam-3763	12	36	in	in	ADP
ejpam-3763	12	37	particular	particular	ADJ
ejpam-3763	12	38	,	,	PUNCT
ejpam-3763	12	39	|v	|v	PROPN
ejpam-3763	12	40	(	(	PUNCT
ejpam-3763	12	41	g)|	g)|	PROPN
ejpam-3763	12	42	is	be	AUX
ejpam-3763	12	43	called	call	VERB
ejpam-3763	12	44	the	the	DET
ejpam-3763	12	45	order	order	NOUN
ejpam-3763	12	46	of	of	ADP
ejpam-3763	12	47	g.	g.	PROPN
ejpam-3763	12	48	for	for	ADP
ejpam-3763	12	49	notation	notation	NOUN
ejpam-3763	12	50	and	and	CCONJ
ejpam-3763	12	51	terminology	terminology	NOUN
ejpam-3763	12	52	not	not	PART
ejpam-3763	12	53	given	give	VERB
ejpam-3763	12	54	here	here	ADV
ejpam-3763	12	55	,	,	PUNCT
ejpam-3763	12	56	see	see	VERB
ejpam-3763	12	57	[	[	X
ejpam-3763	12	58	5	5	NUM
ejpam-3763	12	59	]	]	PUNCT
ejpam-3763	12	60	.	.	PUNCT
ejpam-3763	13	1	vertices	vertice	VERB
ejpam-3763	13	2	u	u	NOUN
ejpam-3763	13	3	and	and	CCONJ
ejpam-3763	13	4	v	v	NOUN
ejpam-3763	13	5	of	of	ADP
ejpam-3763	13	6	g	g	PROPN
ejpam-3763	13	7	are	be	AUX
ejpam-3763	13	8	neighbors	neighbor	NOUN
ejpam-3763	13	9	if	if	SCONJ
ejpam-3763	13	10	uv	uv	PROPN
ejpam-3763	13	11	∈	∈	PROPN
ejpam-3763	13	12	e(g	e(g	PROPN
ejpam-3763	13	13	)	)	PUNCT
ejpam-3763	13	14	.	.	PUNCT
ejpam-3763	14	1	the	the	DET
ejpam-3763	14	2	open	open	ADJ
ejpam-3763	14	3	neighborhood	neighborhood	NOUN
ejpam-3763	14	4	of	of	ADP
ejpam-3763	14	5	v	v	NOUN
ejpam-3763	14	6	refers	refer	VERB
ejpam-3763	14	7	to	to	ADP
ejpam-3763	14	8	the	the	DET
ejpam-3763	14	9	set	set	NOUN
ejpam-3763	14	10	ng(v	ng(v	PUNCT
ejpam-3763	14	11	)	)	PUNCT
ejpam-3763	14	12	consisting	consist	VERB
ejpam-3763	14	13	of	of	ADP
ejpam-3763	14	14	all	all	DET
ejpam-3763	14	15	neighbors	neighbor	NOUN
ejpam-3763	14	16	of	of	ADP
ejpam-3763	14	17	v.	v.	ADP
ejpam-3763	14	18	the	the	DET
ejpam-3763	14	19	closed	closed	ADJ
ejpam-3763	14	20	neighborhood	neighborhood	NOUN
ejpam-3763	14	21	of	of	ADP
ejpam-3763	14	22	v	v	NOUN
ejpam-3763	14	23	is	be	AUX
ejpam-3763	14	24	the	the	DET
ejpam-3763	14	25	set	set	NOUN
ejpam-3763	14	26	ng[v	ng[v	NOUN
ejpam-3763	14	27	]	]	X
ejpam-3763	14	28	=	=	SYM
ejpam-3763	14	29	ng(v	ng(v	X
ejpam-3763	14	30	)	)	PUNCT
ejpam-3763	14	31	∪	∪	ADP
ejpam-3763	14	32	{	{	PUNCT
ejpam-3763	14	33	v	v	NOUN
ejpam-3763	14	34	}	}	PUNCT
ejpam-3763	14	35	.	.	PUNCT
ejpam-3763	15	1	the	the	DET
ejpam-3763	15	2	degree	degree	NOUN
ejpam-3763	15	3	of	of	ADP
ejpam-3763	15	4	v	v	NOUN
ejpam-3763	15	5	,	,	PUNCT
ejpam-3763	15	6	denoted	denote	VERB
ejpam-3763	15	7	degg(v	degg(v	PROPN
ejpam-3763	15	8	)	)	PUNCT
ejpam-3763	15	9	,	,	PUNCT
ejpam-3763	15	10	refers	refer	VERB
ejpam-3763	15	11	to	to	ADP
ejpam-3763	15	12	the	the	DET
ejpam-3763	15	13	value	value	NOUN
ejpam-3763	15	14	|ng(v)|	|ng(v)|	NOUN
ejpam-3763	15	15	,	,	PUNCT
ejpam-3763	15	16	and	and	CCONJ
ejpam-3763	15	17	we	we	PRON
ejpam-3763	15	18	define	define	VERB
ejpam-3763	15	19	∆(g	∆(g	NOUN
ejpam-3763	15	20	)	)	PUNCT
ejpam-3763	15	21	=	=	PUNCT
ejpam-3763	15	22	max{degg(v	max{degg(v	NOUN
ejpam-3763	15	23	)	)	PUNCT
ejpam-3763	15	24	:	:	PUNCT
ejpam-3763	16	1	v	v	X
ejpam-3763	16	2	∈	∈	PROPN
ejpam-3763	16	3	v	v	NOUN
ejpam-3763	16	4	(	(	PUNCT
ejpam-3763	16	5	g	g	NOUN
ejpam-3763	16	6	)	)	PUNCT
ejpam-3763	16	7	}	}	PUNCT
ejpam-3763	16	8	.	.	PUNCT
ejpam-3763	17	1	vertex	vertex	NOUN
ejpam-3763	17	2	v	v	NOUN
ejpam-3763	17	3	is	be	AUX
ejpam-3763	17	4	an	an	DET
ejpam-3763	17	5	endvertex	endvertex	NOUN
ejpam-3763	17	6	if	if	SCONJ
ejpam-3763	17	7	degg(v	degg(v	VERB
ejpam-3763	17	8	)	)	PUNCT
ejpam-3763	17	9	=	=	SYM
ejpam-3763	17	10	1	1	NUM
ejpam-3763	17	11	,	,	PUNCT
ejpam-3763	17	12	and	and	CCONJ
ejpam-3763	17	13	end(g	end(g	NUM
ejpam-3763	17	14	)	)	PUNCT
ejpam-3763	17	15	is	be	AUX
ejpam-3763	17	16	the	the	DET
ejpam-3763	17	17	set	set	NOUN
ejpam-3763	17	18	of	of	ADP
ejpam-3763	17	19	all	all	DET
ejpam-3763	17	20	endvertices	endvertice	NOUN
ejpam-3763	17	21	of	of	ADP
ejpam-3763	17	22	g.	g.	PROPN
ejpam-3763	17	23	vertex	vertex	PROPN
ejpam-3763	17	24	v	v	PROPN
ejpam-3763	17	25	is	be	AUX
ejpam-3763	17	26	an	an	DET
ejpam-3763	17	27	isolated	isolated	ADJ
ejpam-3763	17	28	vertex	vertex	NOUN
ejpam-3763	17	29	if	if	SCONJ
ejpam-3763	17	30	degg(v	degg(v	VERB
ejpam-3763	17	31	)	)	PUNCT
ejpam-3763	17	32	=	=	SYM
ejpam-3763	17	33	0	0	X
ejpam-3763	17	34	.	.	PUNCT
ejpam-3763	18	1	we	we	PRON
ejpam-3763	18	2	denote	denote	VERB
ejpam-3763	18	3	by	by	ADP
ejpam-3763	18	4	iso(g	iso(g	NOUN
ejpam-3763	18	5	)	)	PUNCT
ejpam-3763	18	6	the	the	DET
ejpam-3763	18	7	set	set	NOUN
ejpam-3763	18	8	of	of	ADP
ejpam-3763	18	9	all	all	DET
ejpam-3763	18	10	isolated	isolated	ADJ
ejpam-3763	18	11	vertices	vertex	NOUN
ejpam-3763	18	12	of	of	ADP
ejpam-3763	18	13	g.	g.	NOUN
ejpam-3763	18	14	for	for	ADP
ejpam-3763	18	15	s	s	PROPN
ejpam-3763	18	16	⊆	⊆	NUM
ejpam-3763	18	17	v	v	NOUN
ejpam-3763	18	18	(	(	PUNCT
ejpam-3763	18	19	g	g	NOUN
ejpam-3763	18	20	)	)	PUNCT
ejpam-3763	18	21	,	,	PUNCT
ejpam-3763	18	22	ng(s	ng(s	NUM
ejpam-3763	18	23	)	)	PUNCT
ejpam-3763	18	24	=	=	SYM
ejpam-3763	18	25	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-3763	18	26	)	)	PUNCT
ejpam-3763	18	27	,	,	PUNCT
ejpam-3763	18	28	and	and	CCONJ
ejpam-3763	18	29	ng[s	ng[s	PROPN
ejpam-3763	18	30	]	]	PUNCT
ejpam-3763	19	1	=	=	SYM
ejpam-3763	19	2	s	s	NOUN
ejpam-3763	19	3	∪ng(s	∪ng(s	NOUN
ejpam-3763	19	4	)	)	PUNCT
ejpam-3763	19	5	.	.	PUNCT
ejpam-3763	20	1	∗corresponding	∗corresponde	VERB
ejpam-3763	20	2	author	author	NOUN
ejpam-3763	20	3	.	.	PUNCT
ejpam-3763	21	1	doi	doi	NOUN
ejpam-3763	21	2	:	:	PUNCT
ejpam-3763	21	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3763	https://doi.org/10.29020/nybg.ejpam.v13i3.3763	ADJ
ejpam-3763	21	4	email	email	NOUN
ejpam-3763	21	5	addresses	address	NOUN
ejpam-3763	21	6	:	:	PUNCT
ejpam-3763	21	7	leonard.paleta@g.msuiit.edu.ph	leonard.paleta@g.msuiit.edu.ph	PROPN
ejpam-3763	21	8	(	(	PUNCT
ejpam-3763	21	9	l.	l.	PROPN
ejpam-3763	21	10	paleta	paleta	PROPN
ejpam-3763	21	11	)	)	PUNCT
ejpam-3763	21	12	,	,	PUNCT
ejpam-3763	21	13	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-3763	21	14	(	(	PUNCT
ejpam-3763	21	15	f.	f.	PROPN
ejpam-3763	21	16	jamil	jamil	PROPN
ejpam-3763	21	17	)	)	PUNCT
ejpam-3763	21	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3763	22	1	529	529	NUM
ejpam-3763	22	2	c	c	NOUN
ejpam-3763	22	3	©	©	NOUN
ejpam-3763	22	4	2020	2020	NUM
ejpam-3763	22	5	ejpam	ejpam	VERB
ejpam-3763	22	6	all	all	DET
ejpam-3763	22	7	rights	right	NOUN
ejpam-3763	22	8	reserved	reserve	VERB
ejpam-3763	22	9	.	.	PUNCT
ejpam-3763	23	1	l.	l.	PROPN
ejpam-3763	23	2	paleta	paleta	PROPN
ejpam-3763	23	3	,	,	PUNCT
ejpam-3763	23	4	f.	f.	PROPN
ejpam-3763	23	5	jamil	jamil	PROPN
ejpam-3763	23	6	/	/	SYM
ejpam-3763	23	7	eur	eur	PROPN
ejpam-3763	23	8	.	.	PUNCT
ejpam-3763	24	1	j.	j.	PROPN
ejpam-3763	24	2	pure	pure	PROPN
ejpam-3763	24	3	appl	appl	PROPN
ejpam-3763	24	4	.	.	PROPN
ejpam-3763	24	5	math	math	PROPN
ejpam-3763	24	6	,	,	PUNCT
ejpam-3763	24	7	13	13	NUM
ejpam-3763	24	8	(	(	PUNCT
ejpam-3763	24	9	3	3	NUM
ejpam-3763	24	10	)	)	PUNCT
ejpam-3763	24	11	(	(	PUNCT
ejpam-3763	24	12	2020	2020	NUM
ejpam-3763	24	13	)	)	PUNCT
ejpam-3763	24	14	,	,	PUNCT
ejpam-3763	24	15	529	529	NUM
ejpam-3763	24	16	-	-	SYM
ejpam-3763	24	17	548	548	NUM
ejpam-3763	24	18	530	530	NUM
ejpam-3763	24	19	let	let	VERB
ejpam-3763	24	20	g	g	NOUN
ejpam-3763	24	21	and	and	CCONJ
ejpam-3763	24	22	h	h	NOUN
ejpam-3763	24	23	be	be	AUX
ejpam-3763	24	24	graphs	graph	NOUN
ejpam-3763	24	25	with	with	ADP
ejpam-3763	24	26	disjoint	disjoint	ADJ
ejpam-3763	24	27	vertex	vertex	NOUN
ejpam-3763	24	28	sets	set	NOUN
ejpam-3763	24	29	.	.	PUNCT
ejpam-3763	25	1	the	the	DET
ejpam-3763	25	2	disjoint	disjoint	PROPN
ejpam-3763	25	3	union	union	NOUN
ejpam-3763	25	4	of	of	ADP
ejpam-3763	25	5	g	g	PROPN
ejpam-3763	25	6	and	and	CCONJ
ejpam-3763	25	7	h	h	NOUN
ejpam-3763	25	8	is	be	AUX
ejpam-3763	25	9	the	the	DET
ejpam-3763	25	10	graph	graph	NOUN
ejpam-3763	25	11	g∪h	g∪h	NOUN
ejpam-3763	25	12	with	with	ADP
ejpam-3763	25	13	v	v	NOUN
ejpam-3763	25	14	(	(	PUNCT
ejpam-3763	25	15	g∪h	g∪h	NOUN
ejpam-3763	25	16	)	)	PUNCT
ejpam-3763	25	17	=	=	SYM
ejpam-3763	25	18	v	v	X
ejpam-3763	25	19	(	(	PUNCT
ejpam-3763	25	20	g)∪v	g)∪v	NOUN
ejpam-3763	25	21	(	(	PUNCT
ejpam-3763	25	22	h	h	NOUN
ejpam-3763	25	23	)	)	PUNCT
ejpam-3763	25	24	and	and	CCONJ
ejpam-3763	25	25	e(g∪h	e(g∪h	NOUN
ejpam-3763	25	26	)	)	PUNCT
ejpam-3763	25	27	=	=	PUNCT
ejpam-3763	25	28	e(g)∪e(h	e(g)∪e(h	PROPN
ejpam-3763	25	29	)	)	PUNCT
ejpam-3763	25	30	.	.	PUNCT
ejpam-3763	26	1	the	the	DET
ejpam-3763	26	2	join	join	NOUN
ejpam-3763	26	3	of	of	ADP
ejpam-3763	26	4	g	g	PROPN
ejpam-3763	26	5	and	and	CCONJ
ejpam-3763	26	6	h	h	NOUN
ejpam-3763	26	7	is	be	AUX
ejpam-3763	26	8	the	the	DET
ejpam-3763	26	9	graph	graph	NOUN
ejpam-3763	26	10	g+h	g+h	PROPN
ejpam-3763	26	11	with	with	ADP
ejpam-3763	26	12	vertex	vertex	NOUN
ejpam-3763	26	13	set	set	VERB
ejpam-3763	26	14	v	v	NOUN
ejpam-3763	26	15	(	(	PUNCT
ejpam-3763	26	16	g)∪v	g)∪v	X
ejpam-3763	26	17	(	(	PUNCT
ejpam-3763	26	18	h	h	NOUN
ejpam-3763	26	19	)	)	PUNCT
ejpam-3763	26	20	and	and	CCONJ
ejpam-3763	26	21	edge	edge	NOUN
ejpam-3763	26	22	set	set	VERB
ejpam-3763	26	23	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	NOUN
ejpam-3763	26	24	:	:	PUNCT
ejpam-3763	26	25	u	u	PROPN
ejpam-3763	26	26	∈	∈	PROPN
ejpam-3763	26	27	v	v	NOUN
ejpam-3763	26	28	(	(	PUNCT
ejpam-3763	26	29	g	g	NOUN
ejpam-3763	26	30	)	)	PUNCT
ejpam-3763	26	31	,	,	PUNCT
ejpam-3763	26	32	v	v	X
ejpam-3763	26	33	∈	∈	PROPN
ejpam-3763	26	34	v	v	NOUN
ejpam-3763	26	35	(	(	PUNCT
ejpam-3763	26	36	h	h	NOUN
ejpam-3763	26	37	)	)	PUNCT
ejpam-3763	26	38	}	}	PUNCT
ejpam-3763	26	39	.	.	PUNCT
ejpam-3763	27	1	the	the	DET
ejpam-3763	27	2	corona	corona	NOUN
ejpam-3763	27	3	of	of	ADP
ejpam-3763	27	4	g	g	PROPN
ejpam-3763	27	5	and	and	CCONJ
ejpam-3763	27	6	h	h	NOUN
ejpam-3763	27	7	is	be	AUX
ejpam-3763	27	8	the	the	DET
ejpam-3763	27	9	graph	graph	NOUN
ejpam-3763	27	10	g	g	PROPN
ejpam-3763	27	11	◦	◦	NOUN
ejpam-3763	27	12	h	h	NOUN
ejpam-3763	27	13	obtained	obtain	VERB
ejpam-3763	27	14	by	by	ADP
ejpam-3763	27	15	taking	take	VERB
ejpam-3763	27	16	one	one	NUM
ejpam-3763	27	17	copy	copy	NOUN
ejpam-3763	27	18	of	of	ADP
ejpam-3763	27	19	g	g	PROPN
ejpam-3763	27	20	and	and	CCONJ
ejpam-3763	27	21	|v	|v	PROPN
ejpam-3763	27	22	(	(	PUNCT
ejpam-3763	27	23	g)|	g)|	NOUN
ejpam-3763	27	24	copies	copy	NOUN
ejpam-3763	27	25	of	of	ADP
ejpam-3763	27	26	h	h	NOUN
ejpam-3763	27	27	,	,	PUNCT
ejpam-3763	27	28	and	and	CCONJ
ejpam-3763	27	29	then	then	ADV
ejpam-3763	27	30	joining	join	VERB
ejpam-3763	27	31	the	the	DET
ejpam-3763	27	32	ith	ith	PROPN
ejpam-3763	27	33	vertex	vertex	NOUN
ejpam-3763	27	34	of	of	ADP
ejpam-3763	27	35	g	g	NOUN
ejpam-3763	27	36	to	to	ADP
ejpam-3763	27	37	every	every	DET
ejpam-3763	27	38	vertex	vertex	NOUN
ejpam-3763	27	39	in	in	ADP
ejpam-3763	27	40	the	the	DET
ejpam-3763	27	41	ith	ith	PROPN
ejpam-3763	27	42	copy	copy	NOUN
ejpam-3763	27	43	of	of	ADP
ejpam-3763	27	44	h.	h.	PROPN
ejpam-3763	27	45	the	the	DET
ejpam-3763	27	46	edge	edge	NOUN
ejpam-3763	27	47	corona	corona	NOUN
ejpam-3763	27	48	of	of	ADP
ejpam-3763	27	49	g	g	PROPN
ejpam-3763	27	50	and	and	CCONJ
ejpam-3763	27	51	h	h	NOUN
ejpam-3763	27	52	is	be	AUX
ejpam-3763	27	53	the	the	DET
ejpam-3763	27	54	graph	graph	NOUN
ejpam-3763	27	55	g	g	PROPN
ejpam-3763	27	56	�	�	PROPN
ejpam-3763	27	57	h	h	PROPN
ejpam-3763	27	58	obtained	obtain	VERB
ejpam-3763	27	59	by	by	ADP
ejpam-3763	27	60	taking	take	VERB
ejpam-3763	27	61	one	one	NUM
ejpam-3763	27	62	copy	copy	NOUN
ejpam-3763	27	63	of	of	ADP
ejpam-3763	27	64	g	g	PROPN
ejpam-3763	27	65	and	and	CCONJ
ejpam-3763	27	66	|e(g)|	|e(g)|	ADJ
ejpam-3763	27	67	copies	copy	NOUN
ejpam-3763	27	68	of	of	ADP
ejpam-3763	27	69	h	h	NOUN
ejpam-3763	27	70	and	and	CCONJ
ejpam-3763	27	71	joining	join	VERB
ejpam-3763	27	72	each	each	PRON
ejpam-3763	27	73	of	of	ADP
ejpam-3763	27	74	the	the	DET
ejpam-3763	27	75	end	end	NOUN
ejpam-3763	27	76	vertices	vertice	VERB
ejpam-3763	27	77	u	u	NOUN
ejpam-3763	27	78	and	and	CCONJ
ejpam-3763	27	79	v	v	NOUN
ejpam-3763	27	80	of	of	ADP
ejpam-3763	27	81	each	each	DET
ejpam-3763	27	82	edge	edge	NOUN
ejpam-3763	27	83	uv	uv	NOUN
ejpam-3763	27	84	of	of	ADP
ejpam-3763	27	85	g	g	NOUN
ejpam-3763	27	86	to	to	ADP
ejpam-3763	27	87	every	every	DET
ejpam-3763	27	88	vertex	vertex	NOUN
ejpam-3763	27	89	of	of	ADP
ejpam-3763	27	90	the	the	DET
ejpam-3763	27	91	copy	copy	NOUN
ejpam-3763	27	92	huv	huv	PROPN
ejpam-3763	27	93	of	of	ADP
ejpam-3763	27	94	h.	h.	PROPN
ejpam-3763	27	95	the	the	DET
ejpam-3763	27	96	composition	composition	NOUN
ejpam-3763	27	97	g[h	g[h	PROPN
ejpam-3763	27	98	]	]	PUNCT
ejpam-3763	27	99	of	of	ADP
ejpam-3763	27	100	g	g	PROPN
ejpam-3763	27	101	and	and	CCONJ
ejpam-3763	27	102	h	h	NOUN
ejpam-3763	27	103	is	be	AUX
ejpam-3763	27	104	the	the	DET
ejpam-3763	27	105	graph	graph	NOUN
ejpam-3763	27	106	with	with	ADP
ejpam-3763	27	107	v	v	NOUN
ejpam-3763	27	108	(	(	PUNCT
ejpam-3763	27	109	g[h	g[h	PROPN
ejpam-3763	27	110	]	]	PUNCT
ejpam-3763	27	111	)	)	PUNCT
ejpam-3763	27	112	=	=	SYM
ejpam-3763	27	113	v	v	X
ejpam-3763	27	114	(	(	PUNCT
ejpam-3763	27	115	g	g	NOUN
ejpam-3763	27	116	)	)	PUNCT
ejpam-3763	27	117	×	×	NOUN
ejpam-3763	27	118	v	v	NOUN
ejpam-3763	27	119	(	(	PUNCT
ejpam-3763	27	120	h	h	NOUN
ejpam-3763	27	121	)	)	PUNCT
ejpam-3763	27	122	and	and	CCONJ
ejpam-3763	27	123	(	(	PUNCT
ejpam-3763	27	124	u	u	NOUN
ejpam-3763	27	125	,	,	PUNCT
ejpam-3763	27	126	v)(u′	v)(u′	NOUN
ejpam-3763	27	127	,	,	PUNCT
ejpam-3763	27	128	v′	v′	NOUN
ejpam-3763	27	129	)	)	PUNCT
ejpam-3763	27	130	∈	∈	NOUN
ejpam-3763	27	131	e(g[h	e(g[h	NOUN
ejpam-3763	27	132	]	]	PUNCT
ejpam-3763	27	133	)	)	PUNCT
ejpam-3763	27	134	if	if	SCONJ
ejpam-3763	27	135	and	and	CCONJ
ejpam-3763	27	136	only	only	ADV
ejpam-3763	27	137	if	if	SCONJ
ejpam-3763	27	138	either	either	CCONJ
ejpam-3763	27	139	uu′	uu′	PROPN
ejpam-3763	27	140	∈	∈	PROPN
ejpam-3763	27	141	e(g	e(g	PROPN
ejpam-3763	27	142	)	)	PUNCT
ejpam-3763	27	143	or	or	CCONJ
ejpam-3763	27	144	u	u	X
ejpam-3763	27	145	=	=	PUNCT
ejpam-3763	27	146	u′	u′	PROPN
ejpam-3763	27	147	and	and	CCONJ
ejpam-3763	27	148	vv′	vv′	NOUN
ejpam-3763	27	149	∈	∈	PROPN
ejpam-3763	27	150	e(h	e(h	PROPN
ejpam-3763	27	151	)	)	PUNCT
ejpam-3763	27	152	.	.	PUNCT
ejpam-3763	28	1	the	the	DET
ejpam-3763	28	2	complementary	complementary	ADJ
ejpam-3763	28	3	prism	prism	NOUN
ejpam-3763	28	4	,	,	PUNCT
ejpam-3763	28	5	denoted	denote	VERB
ejpam-3763	28	6	gg	gg	NOUN
ejpam-3763	28	7	,	,	PUNCT
ejpam-3763	28	8	is	be	AUX
ejpam-3763	28	9	the	the	DET
ejpam-3763	28	10	graph	graph	NOUN
ejpam-3763	28	11	formed	form	VERB
ejpam-3763	28	12	from	from	ADP
ejpam-3763	28	13	the	the	DET
ejpam-3763	28	14	disjoint	disjoint	PROPN
ejpam-3763	28	15	union	union	NOUN
ejpam-3763	28	16	of	of	ADP
ejpam-3763	28	17	g	g	PROPN
ejpam-3763	28	18	and	and	CCONJ
ejpam-3763	28	19	its	its	PRON
ejpam-3763	28	20	complement	complement	NOUN
ejpam-3763	28	21	g	g	NOUN
ejpam-3763	28	22	by	by	ADP
ejpam-3763	28	23	adding	add	VERB
ejpam-3763	28	24	a	a	DET
ejpam-3763	28	25	perfect	perfect	ADJ
ejpam-3763	28	26	matching	matching	NOUN
ejpam-3763	28	27	between	between	ADP
ejpam-3763	28	28	corresponding	corresponding	ADJ
ejpam-3763	28	29	vertices	vertex	NOUN
ejpam-3763	28	30	of	of	ADP
ejpam-3763	28	31	g	g	PROPN
ejpam-3763	28	32	and	and	CCONJ
ejpam-3763	28	33	g.	g.	PROPN
ejpam-3763	28	34	for	for	ADP
ejpam-3763	28	35	the	the	DET
ejpam-3763	28	36	complementary	complementary	ADJ
ejpam-3763	28	37	prism	prism	NOUN
ejpam-3763	28	38	,	,	PUNCT
ejpam-3763	28	39	v	v	PROPN
ejpam-3763	28	40	(	(	PUNCT
ejpam-3763	28	41	gg	gg	NOUN
ejpam-3763	28	42	)	)	PUNCT
ejpam-3763	28	43	=	=	NOUN
ejpam-3763	28	44	v	v	X
ejpam-3763	28	45	(	(	PUNCT
ejpam-3763	28	46	g	g	NOUN
ejpam-3763	28	47	)	)	PUNCT
ejpam-3763	28	48	∪	∪	NOUN
ejpam-3763	28	49	v	v	NOUN
ejpam-3763	28	50	(	(	PUNCT
ejpam-3763	28	51	g	g	NOUN
ejpam-3763	28	52	)	)	PUNCT
ejpam-3763	28	53	and	and	CCONJ
ejpam-3763	28	54	e(gg	e(gg	NUM
ejpam-3763	28	55	)	)	PUNCT
ejpam-3763	28	56	=	=	SYM
ejpam-3763	28	57	e(g	e(g	PROPN
ejpam-3763	28	58	)	)	PUNCT
ejpam-3763	28	59	∪e(g	∪e(g	PROPN
ejpam-3763	28	60	)	)	PUNCT
ejpam-3763	28	61	∪	∪	NOUN
ejpam-3763	28	62	{	{	PUNCT
ejpam-3763	28	63	vv	vv	NOUN
ejpam-3763	28	64	:	:	PUNCT
ejpam-3763	28	65	v	v	NUM
ejpam-3763	28	66	∈	∈	PROPN
ejpam-3763	28	67	v	v	NOUN
ejpam-3763	28	68	(	(	PUNCT
ejpam-3763	28	69	g	g	NOUN
ejpam-3763	28	70	)	)	PUNCT
ejpam-3763	28	71	}	}	PUNCT
ejpam-3763	28	72	,	,	PUNCT
ejpam-3763	28	73	where	where	SCONJ
ejpam-3763	28	74	v	v	NOUN
ejpam-3763	28	75	is	be	AUX
ejpam-3763	28	76	the	the	DET
ejpam-3763	28	77	vertex	vertex	NOUN
ejpam-3763	28	78	in	in	ADP
ejpam-3763	28	79	g	g	PROPN
ejpam-3763	28	80	corresponding	correspond	VERB
ejpam-3763	28	81	to	to	ADP
ejpam-3763	28	82	v	v	ADP
ejpam-3763	28	83	∈	∈	PROPN
ejpam-3763	28	84	v	v	NOUN
ejpam-3763	28	85	(	(	PUNCT
ejpam-3763	28	86	g	g	NOUN
ejpam-3763	28	87	)	)	PUNCT
ejpam-3763	28	88	in	in	ADP
ejpam-3763	28	89	the	the	DET
ejpam-3763	28	90	perfect	perfect	ADJ
ejpam-3763	28	91	matching	matching	NOUN
ejpam-3763	28	92	.	.	PUNCT
ejpam-3763	29	1	a	a	DET
ejpam-3763	29	2	subset	subset	NOUN
ejpam-3763	29	3	s	s	VERB
ejpam-3763	29	4	⊆	⊆	NUM
ejpam-3763	29	5	v	v	NOUN
ejpam-3763	29	6	(	(	PUNCT
ejpam-3763	29	7	g	g	NOUN
ejpam-3763	29	8	)	)	PUNCT
ejpam-3763	29	9	is	be	AUX
ejpam-3763	29	10	a	a	DET
ejpam-3763	29	11	dominating	dominating	NOUN
ejpam-3763	29	12	set	set	NOUN
ejpam-3763	29	13	of	of	ADP
ejpam-3763	29	14	g	g	PROPN
ejpam-3763	29	15	if	if	SCONJ
ejpam-3763	29	16	ng[s	ng[	NOUN
ejpam-3763	29	17	]	]	PUNCT
ejpam-3763	29	18	=	=	SYM
ejpam-3763	29	19	v	v	NOUN
ejpam-3763	29	20	(	(	PUNCT
ejpam-3763	29	21	g	g	NOUN
ejpam-3763	29	22	)	)	PUNCT
ejpam-3763	29	23	.	.	PUNCT
ejpam-3763	30	1	the	the	DET
ejpam-3763	30	2	minimum	minimum	ADJ
ejpam-3763	30	3	cardinality	cardinality	NOUN
ejpam-3763	30	4	of	of	ADP
ejpam-3763	30	5	a	a	DET
ejpam-3763	30	6	dominating	dominating	NOUN
ejpam-3763	30	7	set	set	NOUN
ejpam-3763	30	8	is	be	AUX
ejpam-3763	30	9	the	the	DET
ejpam-3763	30	10	domination	domination	NOUN
ejpam-3763	30	11	number	number	NOUN
ejpam-3763	30	12	of	of	ADP
ejpam-3763	30	13	g	g	NOUN
ejpam-3763	30	14	,	,	PUNCT
ejpam-3763	30	15	denoted	denote	VERB
ejpam-3763	30	16	by	by	ADP
ejpam-3763	30	17	γ(g	γ(g	PROPN
ejpam-3763	30	18	)	)	PUNCT
ejpam-3763	30	19	.	.	PUNCT
ejpam-3763	31	1	for	for	ADP
ejpam-3763	31	2	more	more	ADJ
ejpam-3763	31	3	details	detail	NOUN
ejpam-3763	31	4	and	and	CCONJ
ejpam-3763	31	5	results	result	NOUN
ejpam-3763	31	6	on	on	ADP
ejpam-3763	31	7	domination	domination	NOUN
ejpam-3763	31	8	number	number	NOUN
ejpam-3763	31	9	,	,	PUNCT
ejpam-3763	31	10	we	we	PRON
ejpam-3763	31	11	refer	refer	VERB
ejpam-3763	31	12	to	to	ADP
ejpam-3763	31	13	[	[	X
ejpam-3763	31	14	4	4	NUM
ejpam-3763	31	15	,	,	PUNCT
ejpam-3763	31	16	9–11	9–11	NOUN
ejpam-3763	31	17	,	,	PUNCT
ejpam-3763	31	18	13	13	NUM
ejpam-3763	31	19	]	]	PUNCT
ejpam-3763	31	20	.	.	PUNCT
ejpam-3763	32	1	in	in	ADP
ejpam-3763	32	2	particular	particular	ADJ
ejpam-3763	32	3	,	,	PUNCT
ejpam-3763	32	4	if	if	SCONJ
ejpam-3763	32	5	γ(g	γ(g	PROPN
ejpam-3763	32	6	)	)	PUNCT
ejpam-3763	33	1	=	=	SYM
ejpam-3763	33	2	1	1	NUM
ejpam-3763	33	3	and	and	CCONJ
ejpam-3763	33	4	ng[v	ng[v	PROPN
ejpam-3763	33	5	]	]	X
ejpam-3763	33	6	=	=	SYM
ejpam-3763	33	7	v	v	X
ejpam-3763	33	8	(	(	PUNCT
ejpam-3763	33	9	g	g	NOUN
ejpam-3763	33	10	)	)	PUNCT
ejpam-3763	33	11	,	,	PUNCT
ejpam-3763	33	12	then	then	ADV
ejpam-3763	33	13	v	v	NOUN
ejpam-3763	33	14	is	be	AUX
ejpam-3763	33	15	said	say	VERB
ejpam-3763	33	16	to	to	PART
ejpam-3763	33	17	be	be	AUX
ejpam-3763	33	18	a	a	DET
ejpam-3763	33	19	dominating	dominating	NOUN
ejpam-3763	33	20	vertex	vertex	NOUN
ejpam-3763	33	21	of	of	ADP
ejpam-3763	33	22	g.	g.	PROPN
ejpam-3763	33	23	in	in	ADP
ejpam-3763	33	24	this	this	DET
ejpam-3763	33	25	case	case	NOUN
ejpam-3763	33	26	,	,	PUNCT
ejpam-3763	33	27	dom(g	dom(g	NOUN
ejpam-3763	33	28	)	)	PUNCT
ejpam-3763	33	29	denotes	denote	VERB
ejpam-3763	33	30	the	the	DET
ejpam-3763	33	31	set	set	NOUN
ejpam-3763	33	32	of	of	ADP
ejpam-3763	33	33	all	all	DET
ejpam-3763	33	34	dominating	dominating	NOUN
ejpam-3763	33	35	vertices	vertex	NOUN
ejpam-3763	33	36	of	of	ADP
ejpam-3763	33	37	g.	g.	NOUN
ejpam-3763	33	38	any	any	DET
ejpam-3763	33	39	dominating	dominating	NOUN
ejpam-3763	33	40	set	set	NOUN
ejpam-3763	33	41	of	of	ADP
ejpam-3763	33	42	g	g	PROPN
ejpam-3763	33	43	of	of	ADP
ejpam-3763	33	44	cardinality	cardinality	PROPN
ejpam-3763	33	45	γ(g	γ(g	PROPN
ejpam-3763	33	46	)	)	PUNCT
ejpam-3763	33	47	is	be	AUX
ejpam-3763	33	48	called	call	VERB
ejpam-3763	33	49	γ	γ	NOUN
ejpam-3763	33	50	-	-	PUNCT
ejpam-3763	33	51	set	set	NOUN
ejpam-3763	33	52	of	of	ADP
ejpam-3763	33	53	g.	g.	PROPN
ejpam-3763	33	54	a	a	DET
ejpam-3763	33	55	dominating	dominating	NOUN
ejpam-3763	33	56	set	set	NOUN
ejpam-3763	33	57	s	s	NOUN
ejpam-3763	33	58	of	of	ADP
ejpam-3763	33	59	g	g	PROPN
ejpam-3763	33	60	is	be	AUX
ejpam-3763	33	61	a	a	DET
ejpam-3763	33	62	perfect	perfect	ADJ
ejpam-3763	33	63	dominating	dominating	NOUN
ejpam-3763	33	64	set	set	VERB
ejpam-3763	33	65	if	if	SCONJ
ejpam-3763	33	66	for	for	ADP
ejpam-3763	33	67	every	every	PRON
ejpam-3763	33	68	v	v	NUM
ejpam-3763	33	69	∈	∈	NOUN
ejpam-3763	33	70	v	v	NOUN
ejpam-3763	33	71	(	(	PUNCT
ejpam-3763	33	72	g	g	NOUN
ejpam-3763	33	73	)	)	PUNCT
ejpam-3763	33	74	\	\	PROPN
ejpam-3763	34	1	s	s	X
ejpam-3763	34	2	,	,	PUNCT
ejpam-3763	34	3	there	there	PRON
ejpam-3763	34	4	exists	exist	VERB
ejpam-3763	34	5	exactly	exactly	ADV
ejpam-3763	34	6	one	one	NUM
ejpam-3763	34	7	u	u	NOUN
ejpam-3763	34	8	∈	∈	NOUN
ejpam-3763	34	9	s	s	X
ejpam-3763	34	10	for	for	ADP
ejpam-3763	34	11	which	which	PRON
ejpam-3763	34	12	uv	uv	NOUN
ejpam-3763	34	13	∈	∈	PROPN
ejpam-3763	34	14	e(g	e(g	PROPN
ejpam-3763	34	15	)	)	PUNCT
ejpam-3763	35	1	[	[	X
ejpam-3763	35	2	16	16	NUM
ejpam-3763	35	3	]	]	PUNCT
ejpam-3763	35	4	.	.	PUNCT
ejpam-3763	36	1	the	the	DET
ejpam-3763	36	2	minimum	minimum	ADJ
ejpam-3763	36	3	cardinality	cardinality	NOUN
ejpam-3763	36	4	of	of	ADP
ejpam-3763	36	5	a	a	DET
ejpam-3763	36	6	perfect	perfect	ADJ
ejpam-3763	36	7	dominating	dominating	NOUN
ejpam-3763	36	8	set	set	NOUN
ejpam-3763	36	9	is	be	AUX
ejpam-3763	36	10	the	the	DET
ejpam-3763	36	11	perfect	perfect	ADJ
ejpam-3763	36	12	domination	domination	NOUN
ejpam-3763	36	13	number	number	NOUN
ejpam-3763	36	14	of	of	ADP
ejpam-3763	36	15	g	g	NOUN
ejpam-3763	36	16	,	,	PUNCT
ejpam-3763	36	17	which	which	PRON
ejpam-3763	36	18	is	be	AUX
ejpam-3763	36	19	denoted	denote	VERB
ejpam-3763	36	20	by	by	ADP
ejpam-3763	36	21	γp	γp	PROPN
ejpam-3763	36	22	(	(	PUNCT
ejpam-3763	36	23	g	g	NOUN
ejpam-3763	36	24	)	)	PUNCT
ejpam-3763	36	25	.	.	PUNCT
ejpam-3763	37	1	since	since	SCONJ
ejpam-3763	37	2	perfect	perfect	ADJ
ejpam-3763	37	3	dominating	dominating	NOUN
ejpam-3763	37	4	sets	set	NOUN
ejpam-3763	37	5	are	be	AUX
ejpam-3763	37	6	dominating	dominate	VERB
ejpam-3763	37	7	sets	set	NOUN
ejpam-3763	37	8	,	,	PUNCT
ejpam-3763	37	9	γ(g	γ(g	PROPN
ejpam-3763	37	10	)	)	PUNCT
ejpam-3763	37	11	≤	≤	NUM
ejpam-3763	38	1	γp	γp	NOUN
ejpam-3763	39	1	(	(	PUNCT
ejpam-3763	40	1	g	g	NOUN
ejpam-3763	40	2	)	)	PUNCT
ejpam-3763	40	3	for	for	ADP
ejpam-3763	40	4	any	any	DET
ejpam-3763	40	5	graph	graph	NOUN
ejpam-3763	40	6	g.	g.	NOUN
ejpam-3763	40	7	a	a	DET
ejpam-3763	40	8	roman	roman	ADJ
ejpam-3763	40	9	dominating	dominating	NOUN
ejpam-3763	40	10	function	function	NOUN
ejpam-3763	40	11	on	on	ADP
ejpam-3763	40	12	g	g	PROPN
ejpam-3763	40	13	is	be	AUX
ejpam-3763	40	14	a	a	DET
ejpam-3763	40	15	function	function	NOUN
ejpam-3763	40	16	f	f	NOUN
ejpam-3763	40	17	:	:	PUNCT
ejpam-3763	40	18	v	v	X
ejpam-3763	40	19	(	(	PUNCT
ejpam-3763	40	20	g	g	NOUN
ejpam-3763	40	21	)	)	PUNCT
ejpam-3763	40	22	→	→	SYM
ejpam-3763	40	23	{	{	PUNCT
ejpam-3763	40	24	0	0	NUM
ejpam-3763	40	25	,	,	PUNCT
ejpam-3763	40	26	1	1	NUM
ejpam-3763	40	27	,	,	PUNCT
ejpam-3763	40	28	2	2	NUM
ejpam-3763	40	29	}	}	PUNCT
ejpam-3763	40	30	satisfying	satisfy	VERB
ejpam-3763	40	31	the	the	DET
ejpam-3763	40	32	condition	condition	NOUN
ejpam-3763	40	33	that	that	SCONJ
ejpam-3763	40	34	for	for	ADP
ejpam-3763	40	35	each	each	DET
ejpam-3763	40	36	u	u	PROPN
ejpam-3763	40	37	∈	∈	PROPN
ejpam-3763	40	38	v	v	NOUN
ejpam-3763	40	39	(	(	PUNCT
ejpam-3763	40	40	g	g	NOUN
ejpam-3763	40	41	)	)	PUNCT
ejpam-3763	40	42	for	for	ADP
ejpam-3763	40	43	which	which	PRON
ejpam-3763	40	44	f(u	f(u	PROPN
ejpam-3763	40	45	)	)	PUNCT
ejpam-3763	40	46	=	=	SYM
ejpam-3763	40	47	0	0	NUM
ejpam-3763	40	48	,	,	PUNCT
ejpam-3763	40	49	there	there	PRON
ejpam-3763	40	50	exists	exist	VERB
ejpam-3763	40	51	v	v	ADP
ejpam-3763	40	52	∈	∈	PROPN
ejpam-3763	40	53	v	v	NOUN
ejpam-3763	40	54	(	(	PUNCT
ejpam-3763	40	55	g	g	NOUN
ejpam-3763	40	56	)	)	PUNCT
ejpam-3763	40	57	such	such	ADJ
ejpam-3763	40	58	that	that	SCONJ
ejpam-3763	40	59	f(v	f(v	NOUN
ejpam-3763	40	60	)	)	PUNCT
ejpam-3763	41	1	=	=	SYM
ejpam-3763	41	2	2	2	NUM
ejpam-3763	41	3	and	and	CCONJ
ejpam-3763	41	4	uv	uv	NOUN
ejpam-3763	41	5	∈	∈	PROPN
ejpam-3763	41	6	e(g	e(g	PROPN
ejpam-3763	41	7	)	)	PUNCT
ejpam-3763	41	8	.	.	PUNCT
ejpam-3763	42	1	the	the	DET
ejpam-3763	42	2	weight	weight	NOUN
ejpam-3763	42	3	of	of	ADP
ejpam-3763	42	4	f	f	PROPN
ejpam-3763	42	5	is	be	AUX
ejpam-3763	42	6	the	the	DET
ejpam-3763	42	7	value	value	NOUN
ejpam-3763	42	8	ωg(f	ωg(f	PRON
ejpam-3763	42	9	)	)	PUNCT
ejpam-3763	42	10	=	=	SYM
ejpam-3763	42	11	∑	∑	PUNCT
ejpam-3763	42	12	v∈v	v∈v	PROPN
ejpam-3763	42	13	(	(	PUNCT
ejpam-3763	42	14	g	g	NOUN
ejpam-3763	42	15	)	)	PUNCT
ejpam-3763	42	16	f(v	f(v	NOUN
ejpam-3763	42	17	)	)	PUNCT
ejpam-3763	42	18	.	.	PUNCT
ejpam-3763	43	1	the	the	DET
ejpam-3763	43	2	roman	roman	ADJ
ejpam-3763	43	3	domination	domination	NOUN
ejpam-3763	43	4	number	number	NOUN
ejpam-3763	43	5	of	of	ADP
ejpam-3763	43	6	g	g	NOUN
ejpam-3763	43	7	,	,	PUNCT
ejpam-3763	43	8	denoted	denote	VERB
ejpam-3763	43	9	by	by	ADP
ejpam-3763	43	10	γr(g	γr(g	PROPN
ejpam-3763	43	11	)	)	PUNCT
ejpam-3763	43	12	,	,	PUNCT
ejpam-3763	43	13	is	be	AUX
ejpam-3763	43	14	the	the	DET
ejpam-3763	43	15	minimum	minimum	ADJ
ejpam-3763	43	16	weight	weight	NOUN
ejpam-3763	43	17	of	of	ADP
ejpam-3763	43	18	a	a	DET
ejpam-3763	43	19	function	function	NOUN
ejpam-3763	43	20	f	f	PROPN
ejpam-3763	43	21	on	on	ADP
ejpam-3763	43	22	g.	g.	PROPN
ejpam-3763	43	23	we	we	PRON
ejpam-3763	43	24	refer	refer	VERB
ejpam-3763	43	25	to	to	ADP
ejpam-3763	43	26	[	[	X
ejpam-3763	43	27	2	2	NUM
ejpam-3763	43	28	,	,	PUNCT
ejpam-3763	43	29	3	3	NUM
ejpam-3763	43	30	,	,	PUNCT
ejpam-3763	43	31	7	7	NUM
ejpam-3763	43	32	,	,	PUNCT
ejpam-3763	43	33	8	8	NUM
ejpam-3763	43	34	,	,	PUNCT
ejpam-3763	43	35	12	12	NUM
ejpam-3763	43	36	,	,	PUNCT
ejpam-3763	43	37	17	17	NUM
ejpam-3763	43	38	,	,	PUNCT
ejpam-3763	43	39	18	18	NUM
ejpam-3763	43	40	]	]	PUNCT
ejpam-3763	43	41	for	for	ADP
ejpam-3763	43	42	the	the	DET
ejpam-3763	43	43	history	history	NOUN
ejpam-3763	43	44	,	,	PUNCT
ejpam-3763	43	45	introduction	introduction	NOUN
ejpam-3763	43	46	,	,	PUNCT
ejpam-3763	43	47	importance	importance	NOUN
ejpam-3763	43	48	and	and	CCONJ
ejpam-3763	43	49	for	for	ADP
ejpam-3763	43	50	some	some	PRON
ejpam-3763	43	51	of	of	ADP
ejpam-3763	43	52	the	the	DET
ejpam-3763	43	53	recent	recent	ADJ
ejpam-3763	43	54	developments	development	NOUN
ejpam-3763	43	55	of	of	ADP
ejpam-3763	43	56	the	the	DET
ejpam-3763	43	57	study	study	NOUN
ejpam-3763	43	58	of	of	ADP
ejpam-3763	43	59	roman	roman	ADJ
ejpam-3763	43	60	domination	domination	NOUN
ejpam-3763	43	61	in	in	ADP
ejpam-3763	43	62	graphs	graph	NOUN
ejpam-3763	43	63	.	.	PUNCT
ejpam-3763	44	1	customarily	customarily	ADV
ejpam-3763	44	2	,	,	PUNCT
ejpam-3763	44	3	we	we	PRON
ejpam-3763	44	4	write	write	VERB
ejpam-3763	44	5	f	f	PROPN
ejpam-3763	44	6	=	=	SYM
ejpam-3763	44	7	(	(	PUNCT
ejpam-3763	44	8	v0	v0	PROPN
ejpam-3763	44	9	,	,	PUNCT
ejpam-3763	44	10	v1	v1	NOUN
ejpam-3763	44	11	,	,	PUNCT
ejpam-3763	44	12	v2	v2	PROPN
ejpam-3763	44	13	)	)	PUNCT
ejpam-3763	44	14	for	for	ADP
ejpam-3763	44	15	a	a	DET
ejpam-3763	44	16	roman	roman	ADJ
ejpam-3763	44	17	dominating	dominating	NOUN
ejpam-3763	44	18	function	function	NOUN
ejpam-3763	44	19	f	f	PROPN
ejpam-3763	44	20	on	on	ADP
ejpam-3763	44	21	g	g	PROPN
ejpam-3763	44	22	,	,	PUNCT
ejpam-3763	44	23	where	where	SCONJ
ejpam-3763	44	24	vk	vk	VERB
ejpam-3763	44	25	=	=	SYM
ejpam-3763	44	26	{	{	PUNCT
ejpam-3763	44	27	v	v	NUM
ejpam-3763	44	28	∈	∈	NOUN
ejpam-3763	44	29	v	v	NOUN
ejpam-3763	44	30	(	(	PUNCT
ejpam-3763	44	31	g	g	NOUN
ejpam-3763	44	32	)	)	PUNCT
ejpam-3763	44	33	:	:	PUNCT
ejpam-3763	44	34	f(v	f(v	NOUN
ejpam-3763	44	35	)	)	PUNCT
ejpam-3763	44	36	=	=	SYM
ejpam-3763	45	1	k	k	NOUN
ejpam-3763	45	2	}	}	PUNCT
ejpam-3763	45	3	.	.	PUNCT
ejpam-3763	46	1	with	with	ADP
ejpam-3763	46	2	this	this	DET
ejpam-3763	46	3	convention	convention	NOUN
ejpam-3763	46	4	,	,	PUNCT
ejpam-3763	46	5	ωg(f	ωg(f	X
ejpam-3763	46	6	)	)	PUNCT
ejpam-3763	46	7	=	=	PUNCT
ejpam-3763	46	8	|v1|+	|v1|+	PRON
ejpam-3763	46	9	2|v2|	2|v2|	NUM
ejpam-3763	46	10	and	and	CCONJ
ejpam-3763	46	11	v1	v1	VERB
ejpam-3763	46	12	∪	∪	NOUN
ejpam-3763	46	13	v2	v2	NOUN
ejpam-3763	46	14	is	be	AUX
ejpam-3763	46	15	a	a	DET
ejpam-3763	46	16	dominating	dominating	NOUN
ejpam-3763	46	17	set	set	NOUN
ejpam-3763	46	18	of	of	ADP
ejpam-3763	46	19	g.	g.	PROPN
ejpam-3763	46	20	in	in	ADP
ejpam-3763	46	21	[	[	X
ejpam-3763	46	22	8	8	NUM
ejpam-3763	46	23	]	]	PUNCT
ejpam-3763	46	24	,	,	PUNCT
ejpam-3763	46	25	it	it	PRON
ejpam-3763	46	26	is	be	AUX
ejpam-3763	46	27	known	know	VERB
ejpam-3763	46	28	that	that	SCONJ
ejpam-3763	46	29	for	for	ADP
ejpam-3763	46	30	any	any	DET
ejpam-3763	46	31	graph	graph	NOUN
ejpam-3763	46	32	g	g	PROPN
ejpam-3763	46	33	,	,	PUNCT
ejpam-3763	46	34	γ(g	γ(g	PROPN
ejpam-3763	46	35	)	)	PUNCT
ejpam-3763	46	36	≤	≤	NOUN
ejpam-3763	46	37	γr(g	γr(g	NUM
ejpam-3763	46	38	)	)	PUNCT
ejpam-3763	46	39	≤	≤	NUM
ejpam-3763	46	40	2γ(g	2γ(g	NUM
ejpam-3763	46	41	)	)	PUNCT
ejpam-3763	46	42	.	.	PUNCT
ejpam-3763	47	1	a	a	DET
ejpam-3763	47	2	perfect	perfect	ADJ
ejpam-3763	47	3	roman	roman	ADJ
ejpam-3763	47	4	dominating	dominating	NOUN
ejpam-3763	47	5	function	function	NOUN
ejpam-3763	47	6	(	(	PUNCT
ejpam-3763	47	7	or	or	CCONJ
ejpam-3763	47	8	prd	prd	NOUN
ejpam-3763	47	9	-	-	PUNCT
ejpam-3763	47	10	function	function	NOUN
ejpam-3763	47	11	)	)	PUNCT
ejpam-3763	47	12	on	on	ADP
ejpam-3763	47	13	g	g	PROPN
ejpam-3763	47	14	is	be	AUX
ejpam-3763	47	15	a	a	DET
ejpam-3763	47	16	roman	roman	ADJ
ejpam-3763	47	17	domination	domination	NOUN
ejpam-3763	47	18	function	function	NOUN
ejpam-3763	47	19	f	f	PROPN
ejpam-3763	47	20	=	=	SYM
ejpam-3763	47	21	(	(	PUNCT
ejpam-3763	47	22	v0	v0	PROPN
ejpam-3763	47	23	,	,	PUNCT
ejpam-3763	47	24	v1	v1	NOUN
ejpam-3763	47	25	,	,	PUNCT
ejpam-3763	47	26	v2	v2	PROPN
ejpam-3763	47	27	)	)	PUNCT
ejpam-3763	47	28	on	on	ADP
ejpam-3763	47	29	g	g	PROPN
ejpam-3763	47	30	such	such	ADJ
ejpam-3763	47	31	that	that	PRON
ejpam-3763	47	32	for	for	ADP
ejpam-3763	47	33	each	each	DET
ejpam-3763	47	34	u	u	PROPN
ejpam-3763	47	35	∈	∈	PROPN
ejpam-3763	47	36	v0	v0	NOUN
ejpam-3763	47	37	there	there	PRON
ejpam-3763	47	38	exists	exist	VERB
ejpam-3763	47	39	exactly	exactly	ADV
ejpam-3763	47	40	one	one	NUM
ejpam-3763	47	41	v	v	NOUN
ejpam-3763	47	42	∈	∈	NOUN
ejpam-3763	47	43	v2	v2	NOUN
ejpam-3763	47	44	for	for	ADP
ejpam-3763	47	45	which	which	PRON
ejpam-3763	47	46	uv	uv	NOUN
ejpam-3763	47	47	∈	∈	PROPN
ejpam-3763	47	48	e(g	e(g	PROPN
ejpam-3763	47	49	)	)	PUNCT
ejpam-3763	47	50	.	.	PUNCT
ejpam-3763	48	1	in	in	ADP
ejpam-3763	48	2	other	other	ADJ
ejpam-3763	48	3	words	word	NOUN
ejpam-3763	48	4	,	,	PUNCT
ejpam-3763	48	5	a	a	DET
ejpam-3763	48	6	prd	prd	NOUN
ejpam-3763	48	7	-	-	PUNCT
ejpam-3763	48	8	function	function	NOUN
ejpam-3763	48	9	on	on	ADP
ejpam-3763	48	10	g	g	PROPN
ejpam-3763	48	11	is	be	AUX
ejpam-3763	48	12	a	a	DET
ejpam-3763	48	13	colouring	colouring	NOUN
ejpam-3763	48	14	of	of	ADP
ejpam-3763	48	15	the	the	DET
ejpam-3763	48	16	vertices	vertex	NOUN
ejpam-3763	48	17	of	of	ADP
ejpam-3763	48	18	g	g	NOUN
ejpam-3763	48	19	using	use	VERB
ejpam-3763	48	20	colours	colour	NOUN
ejpam-3763	48	21	0	0	NUM
ejpam-3763	48	22	,	,	PUNCT
ejpam-3763	48	23	1	1	NUM
ejpam-3763	48	24	and	and	CCONJ
ejpam-3763	48	25	2	2	NUM
ejpam-3763	48	26	such	such	ADJ
ejpam-3763	48	27	that	that	SCONJ
ejpam-3763	48	28	each	each	DET
ejpam-3763	48	29	vertex	vertex	NOUN
ejpam-3763	48	30	coloured	colour	VERB
ejpam-3763	48	31	0	0	NUM
ejpam-3763	48	32	is	be	AUX
ejpam-3763	48	33	adjacent	adjacent	ADJ
ejpam-3763	48	34	to	to	ADP
ejpam-3763	48	35	exactly	exactly	ADV
ejpam-3763	48	36	one	one	NUM
ejpam-3763	48	37	vertex	vertex	NOUN
ejpam-3763	48	38	coloured	colour	VERB
ejpam-3763	48	39	2	2	NUM
ejpam-3763	48	40	.	.	PUNCT
ejpam-3763	49	1	the	the	DET
ejpam-3763	49	2	perfect	perfect	ADJ
ejpam-3763	49	3	roman	roman	ADJ
ejpam-3763	49	4	domination	domination	NOUN
ejpam-3763	49	5	number	number	NOUN
ejpam-3763	49	6	of	of	ADP
ejpam-3763	49	7	g	g	NOUN
ejpam-3763	49	8	,	,	PUNCT
ejpam-3763	49	9	denoted	denote	VERB
ejpam-3763	49	10	by	by	ADP
ejpam-3763	49	11	γpr(g	γpr(g	PROPN
ejpam-3763	49	12	)	)	PUNCT
ejpam-3763	49	13	,	,	PUNCT
ejpam-3763	49	14	is	be	AUX
ejpam-3763	49	15	the	the	DET
ejpam-3763	49	16	minimum	minimum	ADJ
ejpam-3763	49	17	weight	weight	NOUN
ejpam-3763	49	18	of	of	ADP
ejpam-3763	49	19	a	a	DET
ejpam-3763	49	20	prd	prd	NOUN
ejpam-3763	49	21	-	-	PUNCT
ejpam-3763	49	22	function	function	NOUN
ejpam-3763	49	23	on	on	ADP
ejpam-3763	49	24	g.	g.	PROPN
ejpam-3763	49	25	a	a	DET
ejpam-3763	49	26	prd	prd	NOUN
ejpam-3763	49	27	-	-	PUNCT
ejpam-3763	49	28	function	function	NOUN
ejpam-3763	49	29	f	f	NOUN
ejpam-3763	49	30	with	with	ADP
ejpam-3763	49	31	ωg(f	ωg(f	NOUN
ejpam-3763	49	32	)	)	PUNCT
ejpam-3763	49	33	=	=	SYM
ejpam-3763	49	34	γpr(g	γpr(g	PROPN
ejpam-3763	49	35	)	)	PUNCT
ejpam-3763	49	36	is	be	AUX
ejpam-3763	49	37	called	call	VERB
ejpam-3763	49	38	γpr	γpr	PRON
ejpam-3763	49	39	-function	-function	NOUN
ejpam-3763	49	40	of	of	ADP
ejpam-3763	49	41	g.	g.	NOUN
ejpam-3763	49	42	the	the	DET
ejpam-3763	49	43	perfect	perfect	ADJ
ejpam-3763	49	44	roman	roman	ADJ
ejpam-3763	49	45	domination	domination	NOUN
ejpam-3763	49	46	,	,	PUNCT
ejpam-3763	49	47	a	a	DET
ejpam-3763	49	48	variation	variation	NOUN
ejpam-3763	49	49	of	of	ADP
ejpam-3763	49	50	the	the	DET
ejpam-3763	49	51	roman	roman	ADJ
ejpam-3763	49	52	domination	domination	NOUN
ejpam-3763	49	53	,	,	PUNCT
ejpam-3763	49	54	was	be	AUX
ejpam-3763	49	55	introduced	introduce	VERB
ejpam-3763	49	56	and	and	CCONJ
ejpam-3763	49	57	first	first	ADV
ejpam-3763	49	58	investigated	investigate	VERB
ejpam-3763	49	59	in	in	ADP
ejpam-3763	49	60	2018	2018	NUM
ejpam-3763	49	61	by	by	ADP
ejpam-3763	49	62	henning	henning	PROPN
ejpam-3763	49	63	et	et	PROPN
ejpam-3763	49	64	al	al	PROPN
ejpam-3763	49	65	.	.	PUNCT
ejpam-3763	50	1	[	[	X
ejpam-3763	50	2	15	15	NUM
ejpam-3763	50	3	]	]	X
ejpam-3763	50	4	,	,	PUNCT
ejpam-3763	50	5	particularly	particularly	ADV
ejpam-3763	50	6	in	in	ADP
ejpam-3763	50	7	trees	tree	NOUN
ejpam-3763	50	8	.	.	PUNCT
ejpam-3763	51	1	it	it	PRON
ejpam-3763	51	2	is	be	AUX
ejpam-3763	51	3	further	far	ADV
ejpam-3763	51	4	studied	study	VERB
ejpam-3763	51	5	in	in	ADP
ejpam-3763	51	6	[	[	X
ejpam-3763	51	7	14	14	NUM
ejpam-3763	51	8	]	]	PUNCT
ejpam-3763	51	9	for	for	ADP
ejpam-3763	51	10	regular	regular	ADJ
ejpam-3763	51	11	graphs	graph	NOUN
ejpam-3763	51	12	.	.	PUNCT
ejpam-3763	52	1	more	more	ADJ
ejpam-3763	52	2	recent	recent	ADJ
ejpam-3763	52	3	studies	study	NOUN
ejpam-3763	52	4	on	on	ADP
ejpam-3763	52	5	the	the	DET
ejpam-3763	52	6	concept	concept	NOUN
ejpam-3763	52	7	include	include	VERB
ejpam-3763	52	8	[	[	X
ejpam-3763	52	9	1	1	NUM
ejpam-3763	52	10	,	,	PUNCT
ejpam-3763	52	11	19	19	NUM
ejpam-3763	52	12	,	,	PUNCT
ejpam-3763	52	13	20	20	NUM
ejpam-3763	52	14	]	]	PUNCT
ejpam-3763	52	15	.	.	PUNCT
ejpam-3763	53	1	l.	l.	PROPN
ejpam-3763	53	2	paleta	paleta	PROPN
ejpam-3763	53	3	,	,	PUNCT
ejpam-3763	53	4	f.	f.	PROPN
ejpam-3763	53	5	jamil	jamil	PROPN
ejpam-3763	53	6	/	/	SYM
ejpam-3763	53	7	eur	eur	PROPN
ejpam-3763	53	8	.	.	PUNCT
ejpam-3763	54	1	j.	j.	PROPN
ejpam-3763	54	2	pure	pure	PROPN
ejpam-3763	54	3	appl	appl	PROPN
ejpam-3763	54	4	.	.	PROPN
ejpam-3763	54	5	math	math	PROPN
ejpam-3763	54	6	,	,	PUNCT
ejpam-3763	54	7	13	13	NUM
ejpam-3763	54	8	(	(	PUNCT
ejpam-3763	54	9	3	3	NUM
ejpam-3763	54	10	)	)	PUNCT
ejpam-3763	54	11	(	(	PUNCT
ejpam-3763	54	12	2020	2020	NUM
ejpam-3763	54	13	)	)	PUNCT
ejpam-3763	54	14	,	,	PUNCT
ejpam-3763	54	15	529	529	NUM
ejpam-3763	54	16	-	-	SYM
ejpam-3763	54	17	548	548	NUM
ejpam-3763	54	18	531	531	NUM
ejpam-3763	54	19	in	in	ADP
ejpam-3763	54	20	this	this	DET
ejpam-3763	54	21	present	present	ADJ
ejpam-3763	54	22	paper	paper	NOUN
ejpam-3763	55	1	,	,	PUNCT
ejpam-3763	55	2	we	we	PRON
ejpam-3763	55	3	continue	continue	VERB
ejpam-3763	55	4	the	the	DET
ejpam-3763	55	5	study	study	NOUN
ejpam-3763	55	6	of	of	ADP
ejpam-3763	55	7	perfect	perfect	ADJ
ejpam-3763	55	8	roman	roman	ADJ
ejpam-3763	55	9	domination	domination	NOUN
ejpam-3763	55	10	,	,	PUNCT
ejpam-3763	55	11	specifically	specifically	ADV
ejpam-3763	55	12	on	on	ADP
ejpam-3763	55	13	the	the	DET
ejpam-3763	55	14	join	join	NOUN
ejpam-3763	55	15	,	,	PUNCT
ejpam-3763	55	16	corona	corona	PROPN
ejpam-3763	55	17	,	,	PUNCT
ejpam-3763	55	18	complementary	complementary	ADJ
ejpam-3763	55	19	prism	prism	NOUN
ejpam-3763	55	20	,	,	PUNCT
ejpam-3763	55	21	edge	edge	NOUN
ejpam-3763	55	22	corona	corona	NOUN
ejpam-3763	55	23	and	and	CCONJ
ejpam-3763	55	24	composition	composition	NOUN
ejpam-3763	55	25	of	of	ADP
ejpam-3763	55	26	graphs	graph	NOUN
ejpam-3763	55	27	.	.	PUNCT
ejpam-3763	56	1	the	the	DET
ejpam-3763	56	2	following	follow	VERB
ejpam-3763	56	3	bounds	bound	NOUN
ejpam-3763	56	4	are	be	AUX
ejpam-3763	56	5	established	establish	VERB
ejpam-3763	56	6	in	in	ADP
ejpam-3763	56	7	the	the	DET
ejpam-3763	56	8	referred	refer	VERB
ejpam-3763	56	9	articles	article	NOUN
ejpam-3763	56	10	above	above	ADV
ejpam-3763	56	11	.	.	PUNCT
ejpam-3763	57	1	theorem	theorem	VERB
ejpam-3763	57	2	1.1	1.1	NUM
ejpam-3763	57	3	.	.	PUNCT
ejpam-3763	58	1	(	(	PUNCT
ejpam-3763	58	2	i)[15	i)[15	NOUN
ejpam-3763	58	3	]	]	X
ejpam-3763	58	4	if	if	SCONJ
ejpam-3763	58	5	t	t	PROPN
ejpam-3763	58	6	is	be	AUX
ejpam-3763	58	7	a	a	DET
ejpam-3763	58	8	tree	tree	NOUN
ejpam-3763	58	9	of	of	ADP
ejpam-3763	58	10	order	order	NOUN
ejpam-3763	58	11	n	n	PRON
ejpam-3763	58	12	≥	≥	NOUN
ejpam-3763	58	13	3	3	NUM
ejpam-3763	58	14	,	,	PUNCT
ejpam-3763	58	15	then	then	ADV
ejpam-3763	58	16	γpr(t	γpr(t	PROPN
ejpam-3763	58	17	)	)	PUNCT
ejpam-3763	58	18	≤	≤	NUM
ejpam-3763	58	19	4	4	NUM
ejpam-3763	58	20	5n	5n	NUM
ejpam-3763	58	21	;	;	PUNCT
ejpam-3763	58	22	(	(	PUNCT
ejpam-3763	58	23	ii	ii	NOUN
ejpam-3763	58	24	)	)	PUNCT
ejpam-3763	59	1	[	[	X
ejpam-3763	59	2	14	14	NUM
ejpam-3763	59	3	]	]	X
ejpam-3763	59	4	if	if	SCONJ
ejpam-3763	59	5	g	g	PROPN
ejpam-3763	59	6	is	be	AUX
ejpam-3763	59	7	a	a	DET
ejpam-3763	59	8	k	k	ADJ
ejpam-3763	59	9	-	-	ADJ
ejpam-3763	59	10	regular	regular	ADJ
ejpam-3763	59	11	graph	graph	NOUN
ejpam-3763	59	12	of	of	ADP
ejpam-3763	59	13	order	order	NOUN
ejpam-3763	59	14	n	n	NOUN
ejpam-3763	59	15	with	with	ADP
ejpam-3763	59	16	k	k	PROPN
ejpam-3763	59	17	≥	≥	NUM
ejpam-3763	59	18	4	4	NUM
ejpam-3763	59	19	,	,	PUNCT
ejpam-3763	59	20	then	then	ADV
ejpam-3763	59	21	γpr(g	γpr(g	PROPN
ejpam-3763	59	22	)	)	PUNCT
ejpam-3763	59	23	≤	≤	NOUN
ejpam-3763	59	24	(	(	PUNCT
ejpam-3763	59	25	k2+k+3	k2+k+3	NUM
ejpam-3763	59	26	k2	k2	X
ejpam-3763	59	27	+	+	PROPN
ejpam-3763	59	28	3k+1	3k+1	PROPN
ejpam-3763	59	29	)	)	PUNCT
ejpam-3763	59	30	n	n	CCONJ
ejpam-3763	59	31	;	;	PUNCT
ejpam-3763	59	32	(	(	PUNCT
ejpam-3763	59	33	iii	iii	X
ejpam-3763	59	34	)	)	PUNCT
ejpam-3763	59	35	[	[	X
ejpam-3763	59	36	19	19	NUM
ejpam-3763	59	37	]	]	X
ejpam-3763	59	38	if	if	SCONJ
ejpam-3763	59	39	g	g	PROPN
ejpam-3763	59	40	is	be	AUX
ejpam-3763	59	41	a	a	DET
ejpam-3763	59	42	graph	graph	NOUN
ejpam-3763	59	43	of	of	ADP
ejpam-3763	59	44	order	order	NOUN
ejpam-3763	59	45	n	n	CCONJ
ejpam-3763	59	46	,	,	PUNCT
ejpam-3763	59	47	then	then	ADV
ejpam-3763	59	48	γpr(g	γpr(g	PROPN
ejpam-3763	59	49	)	)	PUNCT
ejpam-3763	59	50	≤	≤	NUM
ejpam-3763	59	51	n+	n+	PUNCT
ejpam-3763	59	52	1−∆(g	1−∆(g	NUM
ejpam-3763	59	53	)	)	PUNCT
ejpam-3763	59	54	.	.	PUNCT
ejpam-3763	60	1	(	(	PUNCT
ejpam-3763	60	2	iv	iv	X
ejpam-3763	60	3	)	)	PUNCT
ejpam-3763	61	1	[	[	X
ejpam-3763	61	2	19	19	NUM
ejpam-3763	61	3	]	]	PUNCT
ejpam-3763	61	4	for	for	ADP
ejpam-3763	61	5	paths	path	NOUN
ejpam-3763	61	6	pn	pn	PROPN
ejpam-3763	61	7	and	and	CCONJ
ejpam-3763	61	8	cycles	cycle	NOUN
ejpam-3763	61	9	cn	cn	PROPN
ejpam-3763	61	10	on	on	ADP
ejpam-3763	61	11	n	n	NUM
ejpam-3763	61	12	≥	≥	NUM
ejpam-3763	61	13	3	3	NUM
ejpam-3763	61	14	vertices	vertex	NOUN
ejpam-3763	61	15	,	,	PUNCT
ejpam-3763	61	16	γpr(pn	γpr(pn	NOUN
ejpam-3763	61	17	)	)	PUNCT
ejpam-3763	61	18	=	=	SYM
ejpam-3763	61	19	γpr(cn	γpr(cn	NOUN
ejpam-3763	61	20	)	)	PUNCT
ejpam-3763	61	21	=	=	PUNCT
ejpam-3763	62	1	d2n3	d2n3	PROPN
ejpam-3763	62	2	e.	e.	PROPN
ejpam-3763	62	3	for	for	ADP
ejpam-3763	62	4	convenience	convenience	NOUN
ejpam-3763	62	5	,	,	PUNCT
ejpam-3763	62	6	we	we	PRON
ejpam-3763	62	7	adapt	adapt	VERB
ejpam-3763	62	8	the	the	DET
ejpam-3763	62	9	symbol	symbol	NOUN
ejpam-3763	62	10	prd(g	prd(g	NUM
ejpam-3763	62	11	)	)	PUNCT
ejpam-3763	62	12	to	to	PART
ejpam-3763	62	13	denote	denote	VERB
ejpam-3763	62	14	the	the	DET
ejpam-3763	62	15	set	set	NOUN
ejpam-3763	62	16	of	of	ADP
ejpam-3763	62	17	all	all	DET
ejpam-3763	62	18	perfect	perfect	ADJ
ejpam-3763	62	19	roman	roman	ADJ
ejpam-3763	62	20	dominating	dominating	NOUN
ejpam-3763	62	21	functions	function	NOUN
ejpam-3763	62	22	on	on	ADP
ejpam-3763	62	23	the	the	DET
ejpam-3763	62	24	graph	graph	NOUN
ejpam-3763	62	25	g.	g.	PROPN
ejpam-3763	62	26	2	2	NUM
ejpam-3763	62	27	.	.	PUNCT
ejpam-3763	62	28	results	result	VERB
ejpam-3763	62	29	the	the	DET
ejpam-3763	62	30	following	follow	VERB
ejpam-3763	62	31	proposition	proposition	NOUN
ejpam-3763	62	32	plays	play	VERB
ejpam-3763	62	33	an	an	DET
ejpam-3763	62	34	important	important	ADJ
ejpam-3763	62	35	role	role	NOUN
ejpam-3763	62	36	in	in	ADP
ejpam-3763	62	37	proving	prove	VERB
ejpam-3763	62	38	the	the	DET
ejpam-3763	62	39	desired	desire	VERB
ejpam-3763	62	40	results	result	NOUN
ejpam-3763	62	41	.	.	PUNCT
ejpam-3763	63	1	proposition	proposition	NOUN
ejpam-3763	63	2	2.1	2.1	NUM
ejpam-3763	63	3	.	.	PUNCT
ejpam-3763	64	1	if	if	SCONJ
ejpam-3763	64	2	f	f	PROPN
ejpam-3763	64	3	=	=	SYM
ejpam-3763	64	4	(	(	PUNCT
ejpam-3763	64	5	v0	v0	PROPN
ejpam-3763	64	6	,	,	PUNCT
ejpam-3763	64	7	v1	v1	NOUN
ejpam-3763	64	8	,	,	PUNCT
ejpam-3763	64	9	v2	v2	PROPN
ejpam-3763	64	10	)	)	PUNCT
ejpam-3763	64	11	is	be	AUX
ejpam-3763	64	12	a	a	DET
ejpam-3763	64	13	γpr	γpr	NOUN
ejpam-3763	64	14	-function	-function	NOUN
ejpam-3763	64	15	of	of	ADP
ejpam-3763	64	16	g	g	NOUN
ejpam-3763	64	17	,	,	PUNCT
ejpam-3763	64	18	then	then	ADV
ejpam-3763	64	19	|ng(v	|ng(v	NOUN
ejpam-3763	64	20	)	)	PUNCT
ejpam-3763	64	21	∩	∩	ADJ
ejpam-3763	64	22	v2|	v2|	X
ejpam-3763	64	23	6=	6=	ADP
ejpam-3763	64	24	1	1	NUM
ejpam-3763	64	25	for	for	ADP
ejpam-3763	64	26	each	each	DET
ejpam-3763	64	27	v	v	ADP
ejpam-3763	64	28	∈	∈	PROPN
ejpam-3763	64	29	v1	v1	NOUN
ejpam-3763	64	30	.	.	PUNCT
ejpam-3763	65	1	proof	proof	NOUN
ejpam-3763	65	2	:	:	PUNCT
ejpam-3763	65	3	suppose	suppose	VERB
ejpam-3763	65	4	that	that	SCONJ
ejpam-3763	65	5	there	there	PRON
ejpam-3763	65	6	exists	exist	VERB
ejpam-3763	65	7	v	v	ADP
ejpam-3763	65	8	∈	∈	NOUN
ejpam-3763	65	9	v1	v1	NOUN
ejpam-3763	65	10	for	for	ADP
ejpam-3763	65	11	which	which	PRON
ejpam-3763	65	12	|ng(v)∩v2|	|ng(v)∩v2|	NOUN
ejpam-3763	65	13	=	=	SYM
ejpam-3763	65	14	1	1	X
ejpam-3763	65	15	.	.	X
ejpam-3763	65	16	consider	consider	VERB
ejpam-3763	65	17	,	,	PUNCT
ejpam-3763	65	18	in	in	ADP
ejpam-3763	65	19	particular	particular	ADJ
ejpam-3763	65	20	,	,	PUNCT
ejpam-3763	65	21	the	the	DET
ejpam-3763	65	22	function	function	NOUN
ejpam-3763	65	23	f∗	f∗	NOUN
ejpam-3763	65	24	=	=	SYM
ejpam-3763	65	25	(	(	PUNCT
ejpam-3763	65	26	v	v	NOUN
ejpam-3763	65	27	∗0	∗0	PROPN
ejpam-3763	65	28	,	,	PUNCT
ejpam-3763	65	29	v	v	NOUN
ejpam-3763	65	30	∗	∗	NOUN
ejpam-3763	65	31	1	1	NUM
ejpam-3763	65	32	,	,	PUNCT
ejpam-3763	65	33	v	v	NOUN
ejpam-3763	65	34	∗	∗	NOUN
ejpam-3763	65	35	2	2	NUM
ejpam-3763	65	36	)	)	PUNCT
ejpam-3763	65	37	given	give	VERB
ejpam-3763	65	38	by	by	ADP
ejpam-3763	65	39	f∗(v	f∗(v	PROPN
ejpam-3763	65	40	)	)	PUNCT
ejpam-3763	65	41	=	=	SYM
ejpam-3763	65	42	0	0	NUM
ejpam-3763	65	43	and	and	CCONJ
ejpam-3763	65	44	f∗(x	f∗(x	PROPN
ejpam-3763	65	45	)	)	PUNCT
ejpam-3763	66	1	=	=	SYM
ejpam-3763	66	2	f(x	f(x	PROPN
ejpam-3763	66	3	)	)	PUNCT
ejpam-3763	66	4	for	for	ADP
ejpam-3763	66	5	all	all	PRON
ejpam-3763	66	6	x	x	SYM
ejpam-3763	66	7	6=	6=	NUM
ejpam-3763	66	8	v.	v.	CCONJ
ejpam-3763	66	9	we	we	PRON
ejpam-3763	66	10	have	have	VERB
ejpam-3763	66	11	f∗	f∗	NOUN
ejpam-3763	66	12	∈	∈	PROPN
ejpam-3763	66	13	prd(g	prd(g	PROPN
ejpam-3763	66	14	)	)	PUNCT
ejpam-3763	66	15	with	with	ADP
ejpam-3763	66	16	v	v	NUM
ejpam-3763	66	17	∗0	∗0	PROPN
ejpam-3763	66	18	=	=	SYM
ejpam-3763	66	19	v0∪{v	v0∪{v	PROPN
ejpam-3763	66	20	}	}	PUNCT
ejpam-3763	66	21	,	,	PUNCT
ejpam-3763	66	22	v	v	X
ejpam-3763	66	23	∗1	∗1	PROPN
ejpam-3763	66	24	=	=	PUNCT
ejpam-3763	66	25	v1\{v	v1\{v	PROPN
ejpam-3763	66	26	}	}	PUNCT
ejpam-3763	66	27	and	and	CCONJ
ejpam-3763	66	28	v	v	ADP
ejpam-3763	66	29	∗2	∗2	PROPN
ejpam-3763	66	30	=	=	SYM
ejpam-3763	66	31	v2	v2	PROPN
ejpam-3763	66	32	.	.	PUNCT
ejpam-3763	67	1	thus	thus	ADV
ejpam-3763	67	2	,	,	PUNCT
ejpam-3763	67	3	ωg(f∗	ωg(f∗	NUM
ejpam-3763	67	4	)	)	PUNCT
ejpam-3763	67	5	=	=	SYM
ejpam-3763	67	6	γpr(g)−1	γpr(g)−1	NOUN
ejpam-3763	67	7	,	,	PUNCT
ejpam-3763	67	8	a	a	DET
ejpam-3763	67	9	contradiction	contradiction	NOUN
ejpam-3763	67	10	.	.	PUNCT
ejpam-3763	68	1	�	�	PROPN
ejpam-3763	68	2	proposition	proposition	NOUN
ejpam-3763	68	3	2.2	2.2	NUM
ejpam-3763	68	4	.	.	PUNCT
ejpam-3763	69	1	for	for	ADP
ejpam-3763	69	2	a	a	DET
ejpam-3763	69	3	nontrivial	nontrivial	ADJ
ejpam-3763	69	4	connected	connect	VERB
ejpam-3763	69	5	graph	graph	NOUN
ejpam-3763	69	6	g	g	NOUN
ejpam-3763	69	7	of	of	ADP
ejpam-3763	69	8	order	order	NOUN
ejpam-3763	69	9	n	n	CCONJ
ejpam-3763	69	10	,	,	PUNCT
ejpam-3763	69	11	max{2	max{2	PROPN
ejpam-3763	69	12	,	,	PUNCT
ejpam-3763	69	13	γ(g	γ(g	PROPN
ejpam-3763	69	14	)	)	PUNCT
ejpam-3763	69	15	}	}	PUNCT
ejpam-3763	69	16	≤	≤	NUM
ejpam-3763	69	17	γpr(g	γpr(g	PROPN
ejpam-3763	69	18	)	)	PUNCT
ejpam-3763	69	19	≤	≤	NUM
ejpam-3763	69	20	min{n+	min{n+	VERB
ejpam-3763	69	21	1−∆(g	1−∆(g	NUM
ejpam-3763	69	22	)	)	PUNCT
ejpam-3763	69	23	,	,	PUNCT
ejpam-3763	69	24	2γp	2γp	NOUN
ejpam-3763	69	25	(	(	PUNCT
ejpam-3763	69	26	g	g	NOUN
ejpam-3763	69	27	)	)	PUNCT
ejpam-3763	69	28	}	}	PUNCT
ejpam-3763	69	29	.	.	PUNCT
ejpam-3763	70	1	proof	proof	NOUN
ejpam-3763	70	2	:	:	PUNCT
ejpam-3763	70	3	since	since	SCONJ
ejpam-3763	70	4	a	a	DET
ejpam-3763	70	5	perfect	perfect	ADJ
ejpam-3763	70	6	roman	roman	ADJ
ejpam-3763	70	7	domination	domination	NOUN
ejpam-3763	70	8	is	be	AUX
ejpam-3763	70	9	a	a	DET
ejpam-3763	70	10	roman	roman	ADJ
ejpam-3763	70	11	domination	domination	NOUN
ejpam-3763	70	12	,	,	PUNCT
ejpam-3763	70	13	γ(g	γ(g	PROPN
ejpam-3763	70	14	)	)	PUNCT
ejpam-3763	70	15	≤	≤	PUNCT
ejpam-3763	70	16	γpr(g	γpr(g	PROPN
ejpam-3763	70	17	)	)	PUNCT
ejpam-3763	70	18	.	.	PUNCT
ejpam-3763	71	1	let	let	VERB
ejpam-3763	71	2	f	f	PROPN
ejpam-3763	71	3	=	=	SYM
ejpam-3763	71	4	(	(	PUNCT
ejpam-3763	71	5	v0	v0	PROPN
ejpam-3763	71	6	,	,	PUNCT
ejpam-3763	71	7	v1	v1	NOUN
ejpam-3763	71	8	,	,	PUNCT
ejpam-3763	71	9	v2	v2	PROPN
ejpam-3763	71	10	)	)	PUNCT
ejpam-3763	71	11	be	be	AUX
ejpam-3763	71	12	a	a	DET
ejpam-3763	71	13	γpr	γpr	NOUN
ejpam-3763	71	14	-function	-function	NOUN
ejpam-3763	71	15	of	of	ADP
ejpam-3763	71	16	g.	g.	NOUN
ejpam-3763	72	1	if	if	SCONJ
ejpam-3763	72	2	v0	v0	NOUN
ejpam-3763	72	3	=	=	SYM
ejpam-3763	72	4	∅	∅	NOUN
ejpam-3763	72	5	,	,	PUNCT
ejpam-3763	72	6	then	then	ADV
ejpam-3763	72	7	γpr(g	γpr(g	PRON
ejpam-3763	72	8	)	)	PUNCT
ejpam-3763	72	9	=	=	SYM
ejpam-3763	72	10	n	n	X
ejpam-3763	72	11	≥	≥	NOUN
ejpam-3763	72	12	2	2	NUM
ejpam-3763	72	13	.	.	PUNCT
ejpam-3763	73	1	on	on	ADP
ejpam-3763	73	2	the	the	DET
ejpam-3763	73	3	other	other	ADJ
ejpam-3763	73	4	hand	hand	NOUN
ejpam-3763	73	5	,	,	PUNCT
ejpam-3763	73	6	if	if	SCONJ
ejpam-3763	73	7	v0	v0	NOUN
ejpam-3763	73	8	6=	6=	NOUN
ejpam-3763	73	9	∅	∅	NOUN
ejpam-3763	73	10	,	,	PUNCT
ejpam-3763	73	11	then	then	ADV
ejpam-3763	73	12	v2	v2	VERB
ejpam-3763	73	13	6=	6=	NOUN
ejpam-3763	73	14	∅	∅	NOUN
ejpam-3763	73	15	so	so	SCONJ
ejpam-3763	73	16	that	that	SCONJ
ejpam-3763	73	17	γpr(g	γpr(g	PROPN
ejpam-3763	73	18	)	)	PUNCT
ejpam-3763	73	19	≥	≥	NOUN
ejpam-3763	73	20	2|v2|	2|v2|	NUM
ejpam-3763	73	21	≥	≥	NOUN
ejpam-3763	73	22	2	2	NUM
ejpam-3763	73	23	.	.	PUNCT
ejpam-3763	73	24	by	by	ADP
ejpam-3763	73	25	theorem	theorem	ADJ
ejpam-3763	73	26	1.1(iii	1.1(iii	NUM
ejpam-3763	73	27	)	)	PUNCT
ejpam-3763	73	28	,	,	PUNCT
ejpam-3763	73	29	γpr(g	γpr(g	PROPN
ejpam-3763	73	30	)	)	PUNCT
ejpam-3763	73	31	≤	≤	NOUN
ejpam-3763	74	1	n	n	PRON
ejpam-3763	74	2	+	+	CCONJ
ejpam-3763	74	3	1	1	NUM
ejpam-3763	74	4	−∆(g	−∆(g	NOUN
ejpam-3763	74	5	)	)	PUNCT
ejpam-3763	74	6	.	.	PUNCT
ejpam-3763	75	1	now	now	ADV
ejpam-3763	75	2	,	,	PUNCT
ejpam-3763	75	3	let	let	VERB
ejpam-3763	75	4	s	s	PRON
ejpam-3763	75	5	⊆	⊆	NUM
ejpam-3763	75	6	v	v	NOUN
ejpam-3763	75	7	(	(	PUNCT
ejpam-3763	75	8	g	g	NOUN
ejpam-3763	75	9	)	)	PUNCT
ejpam-3763	75	10	be	be	AUX
ejpam-3763	75	11	a	a	DET
ejpam-3763	75	12	γp	γp	NOUN
ejpam-3763	75	13	-set	-set	PUNCT
ejpam-3763	75	14	of	of	ADP
ejpam-3763	75	15	g.	g.	PROPN
ejpam-3763	76	1	then	then	ADV
ejpam-3763	76	2	f	f	PROPN
ejpam-3763	76	3	=	=	SYM
ejpam-3763	76	4	(	(	PUNCT
ejpam-3763	76	5	v0	v0	PROPN
ejpam-3763	76	6	,	,	PUNCT
ejpam-3763	76	7	v1	v1	NOUN
ejpam-3763	76	8	,	,	PUNCT
ejpam-3763	76	9	v2	v2	NOUN
ejpam-3763	76	10	)	)	PUNCT
ejpam-3763	76	11	∈	∈	PROPN
ejpam-3763	76	12	prd(g	prd(g	PROPN
ejpam-3763	76	13	)	)	PUNCT
ejpam-3763	76	14	,	,	PUNCT
ejpam-3763	76	15	where	where	SCONJ
ejpam-3763	76	16	v0	v0	NOUN
ejpam-3763	76	17	=	=	SYM
ejpam-3763	76	18	v	v	PROPN
ejpam-3763	76	19	(	(	PUNCT
ejpam-3763	76	20	g	g	NOUN
ejpam-3763	76	21	)	)	PUNCT
ejpam-3763	76	22	\	\	PROPN
ejpam-3763	76	23	s	s	X
ejpam-3763	76	24	,	,	PUNCT
ejpam-3763	76	25	v1	v1	NOUN
ejpam-3763	76	26	=	=	SYM
ejpam-3763	76	27	∅	∅	NOUN
ejpam-3763	76	28	and	and	CCONJ
ejpam-3763	76	29	v2	v2	PROPN
ejpam-3763	76	30	=	=	SYM
ejpam-3763	76	31	s.	s.	PROPN
ejpam-3763	76	32	therefore	therefore	ADV
ejpam-3763	76	33	,	,	PUNCT
ejpam-3763	76	34	γpr(g	γpr(g	PROPN
ejpam-3763	76	35	)	)	PUNCT
ejpam-3763	76	36	≤	≤	NOUN
ejpam-3763	76	37	2|s|	2|s|	NUM
ejpam-3763	76	38	=	=	SYM
ejpam-3763	76	39	2γp	2γp	NOUN
ejpam-3763	76	40	(	(	PUNCT
ejpam-3763	76	41	g	g	NOUN
ejpam-3763	76	42	)	)	PUNCT
ejpam-3763	76	43	.	.	PUNCT
ejpam-3763	77	1	�	�	PROPN
ejpam-3763	77	2	observe	observe	VERB
ejpam-3763	77	3	that	that	SCONJ
ejpam-3763	77	4	γpr(ck	γpr(ck	PUNCT
ejpam-3763	77	5	)	)	PUNCT
ejpam-3763	77	6	=	=	SYM
ejpam-3763	77	7	4	4	NUM
ejpam-3763	77	8	=	=	SYM
ejpam-3763	77	9	k	k	PROPN
ejpam-3763	77	10	+	+	NOUN
ejpam-3763	77	11	1−∆(ck	1−∆(ck	NUM
ejpam-3763	77	12	)	)	PUNCT
ejpam-3763	77	13	<	<	X
ejpam-3763	77	14	2γp	2γp	ADJ
ejpam-3763	77	15	(	(	PUNCT
ejpam-3763	77	16	ck	ck	PROPN
ejpam-3763	77	17	)	)	PUNCT
ejpam-3763	77	18	for	for	ADP
ejpam-3763	77	19	k	k	PROPN
ejpam-3763	77	20	=	=	SYM
ejpam-3763	77	21	5	5	NUM
ejpam-3763	77	22	and	and	CCONJ
ejpam-3763	77	23	γpr(c3n	γpr(c3n	NUM
ejpam-3763	77	24	)	)	PUNCT
ejpam-3763	77	25	=	=	SYM
ejpam-3763	77	26	2n	2n	NUM
ejpam-3763	77	27	=	=	SYM
ejpam-3763	77	28	2γp	2γp	NOUN
ejpam-3763	77	29	(	(	PUNCT
ejpam-3763	77	30	c3n	c3n	PROPN
ejpam-3763	77	31	)	)	PUNCT
ejpam-3763	77	32	<	<	X
ejpam-3763	77	33	(	(	PUNCT
ejpam-3763	77	34	3n+	3n+	NUM
ejpam-3763	77	35	1)−∆(c3n	1)−∆(c3n	NUM
ejpam-3763	77	36	)	)	PUNCT
ejpam-3763	77	37	for	for	ADP
ejpam-3763	77	38	all	all	DET
ejpam-3763	77	39	n	n	PRON
ejpam-3763	77	40	≥	≥	NOUN
ejpam-3763	77	41	2	2	NUM
ejpam-3763	77	42	.	.	PUNCT
ejpam-3763	78	1	therefore	therefore	ADV
ejpam-3763	78	2	,	,	PUNCT
ejpam-3763	78	3	the	the	DET
ejpam-3763	78	4	upper	upper	ADJ
ejpam-3763	78	5	bound	bound	NOUN
ejpam-3763	78	6	of	of	ADP
ejpam-3763	78	7	the	the	DET
ejpam-3763	78	8	inequality	inequality	NOUN
ejpam-3763	78	9	in	in	ADP
ejpam-3763	78	10	proposition	proposition	NOUN
ejpam-3763	78	11	2.2	2.2	NUM
ejpam-3763	78	12	is	be	AUX
ejpam-3763	78	13	sharp	sharp	ADJ
ejpam-3763	78	14	and	and	CCONJ
ejpam-3763	78	15	may	may	AUX
ejpam-3763	78	16	be	be	AUX
ejpam-3763	78	17	determined	determine	VERB
ejpam-3763	78	18	by	by	ADP
ejpam-3763	78	19	exactly	exactly	ADV
ejpam-3763	78	20	one	one	NUM
ejpam-3763	78	21	of	of	ADP
ejpam-3763	78	22	n	n	PRON
ejpam-3763	78	23	+	+	CCONJ
ejpam-3763	78	24	1	1	NUM
ejpam-3763	78	25	−∆(g	−∆(g	NOUN
ejpam-3763	78	26	)	)	PUNCT
ejpam-3763	78	27	and	and	CCONJ
ejpam-3763	78	28	2γp	2γp	NOUN
ejpam-3763	78	29	(	(	PUNCT
ejpam-3763	78	30	g	g	NOUN
ejpam-3763	78	31	)	)	PUNCT
ejpam-3763	78	32	.	.	PUNCT
ejpam-3763	79	1	the	the	DET
ejpam-3763	79	2	inequality	inequality	NOUN
ejpam-3763	79	3	,	,	PUNCT
ejpam-3763	79	4	however	however	ADV
ejpam-3763	79	5	,	,	PUNCT
ejpam-3763	79	6	can	can	AUX
ejpam-3763	79	7	also	also	ADV
ejpam-3763	79	8	be	be	AUX
ejpam-3763	79	9	strict	strict	ADJ
ejpam-3763	79	10	.	.	PUNCT
ejpam-3763	80	1	to	to	PART
ejpam-3763	80	2	see	see	VERB
ejpam-3763	80	3	this	this	PRON
ejpam-3763	80	4	,	,	PUNCT
ejpam-3763	80	5	note	note	VERB
ejpam-3763	80	6	that	that	SCONJ
ejpam-3763	80	7	γpr(c7	γpr(c7	VERB
ejpam-3763	80	8	)	)	PUNCT
ejpam-3763	80	9	=	=	SYM
ejpam-3763	80	10	5	5	NUM
ejpam-3763	80	11	<	<	X
ejpam-3763	80	12	min{(7	min{(7	X
ejpam-3763	81	1	+	+	CCONJ
ejpam-3763	81	2	1)−∆(c7	1)−∆(c7	NUM
ejpam-3763	81	3	)	)	PUNCT
ejpam-3763	81	4	,	,	PUNCT
ejpam-3763	81	5	2γ	2γ	NOUN
ejpam-3763	81	6	p	p	X
ejpam-3763	81	7	(	(	PUNCT
ejpam-3763	81	8	c7	c7	PROPN
ejpam-3763	81	9	)	)	PUNCT
ejpam-3763	81	10	}	}	PUNCT
ejpam-3763	81	11	.	.	PUNCT
ejpam-3763	82	1	corollary	corollary	ADJ
ejpam-3763	82	2	2.3	2.3	NUM
ejpam-3763	82	3	.	.	PUNCT
ejpam-3763	83	1	let	let	VERB
ejpam-3763	83	2	g	g	PRON
ejpam-3763	83	3	be	be	AUX
ejpam-3763	83	4	a	a	DET
ejpam-3763	83	5	connected	connected	ADJ
ejpam-3763	83	6	graph	graph	NOUN
ejpam-3763	83	7	of	of	ADP
ejpam-3763	83	8	order	order	NOUN
ejpam-3763	83	9	n	n	PRON
ejpam-3763	83	10	≥	≥	NOUN
ejpam-3763	83	11	2	2	NUM
ejpam-3763	83	12	.	.	PUNCT
ejpam-3763	84	1	then	then	ADV
ejpam-3763	84	2	(	(	PUNCT
ejpam-3763	84	3	i	i	NOUN
ejpam-3763	84	4	)	)	PUNCT
ejpam-3763	85	1	[	[	X
ejpam-3763	85	2	19	19	NUM
ejpam-3763	85	3	]	]	PUNCT
ejpam-3763	85	4	γpr(g	γpr(g	PROPN
ejpam-3763	85	5	)	)	PUNCT
ejpam-3763	85	6	=	=	SYM
ejpam-3763	85	7	2	2	NUM
ejpam-3763	85	8	if	if	SCONJ
ejpam-3763	85	9	and	and	CCONJ
ejpam-3763	85	10	only	only	ADV
ejpam-3763	85	11	if	if	SCONJ
ejpam-3763	85	12	γ(g	γ(g	NOUN
ejpam-3763	85	13	)	)	PUNCT
ejpam-3763	85	14	=	=	SYM
ejpam-3763	86	1	1	1	X
ejpam-3763	86	2	.	.	PUNCT
ejpam-3763	86	3	l.	l.	PROPN
ejpam-3763	86	4	paleta	paleta	PROPN
ejpam-3763	86	5	,	,	PUNCT
ejpam-3763	86	6	f.	f.	PROPN
ejpam-3763	86	7	jamil	jamil	PROPN
ejpam-3763	86	8	/	/	SYM
ejpam-3763	86	9	eur	eur	PROPN
ejpam-3763	86	10	.	.	PUNCT
ejpam-3763	87	1	j.	j.	PROPN
ejpam-3763	87	2	pure	pure	PROPN
ejpam-3763	87	3	appl	appl	PROPN
ejpam-3763	87	4	.	.	PROPN
ejpam-3763	87	5	math	math	PROPN
ejpam-3763	87	6	,	,	PUNCT
ejpam-3763	87	7	13	13	NUM
ejpam-3763	87	8	(	(	PUNCT
ejpam-3763	87	9	3	3	NUM
ejpam-3763	87	10	)	)	PUNCT
ejpam-3763	87	11	(	(	PUNCT
ejpam-3763	87	12	2020	2020	NUM
ejpam-3763	87	13	)	)	PUNCT
ejpam-3763	87	14	,	,	PUNCT
ejpam-3763	87	15	529	529	NUM
ejpam-3763	87	16	-	-	SYM
ejpam-3763	87	17	548	548	NUM
ejpam-3763	87	18	532	532	NUM
ejpam-3763	87	19	(	(	PUNCT
ejpam-3763	87	20	ii	ii	NOUN
ejpam-3763	87	21	)	)	PUNCT
ejpam-3763	87	22	γpr(g	γpr(g	PROPN
ejpam-3763	87	23	)	)	PUNCT
ejpam-3763	88	1	=	=	SYM
ejpam-3763	88	2	n	n	NOUN
ejpam-3763	88	3	if	if	SCONJ
ejpam-3763	88	4	and	and	CCONJ
ejpam-3763	88	5	only	only	ADV
ejpam-3763	88	6	if	if	SCONJ
ejpam-3763	88	7	n	n	NOUN
ejpam-3763	88	8	=	=	SYM
ejpam-3763	88	9	2	2	X
ejpam-3763	88	10	.	.	PUNCT
ejpam-3763	88	11	(	(	PUNCT
ejpam-3763	88	12	iii	iii	X
ejpam-3763	88	13	)	)	PUNCT
ejpam-3763	88	14	[	[	X
ejpam-3763	88	15	19	19	NUM
ejpam-3763	88	16	]	]	PUNCT
ejpam-3763	88	17	γpr(g	γpr(g	PROPN
ejpam-3763	88	18	)	)	PUNCT
ejpam-3763	88	19	=	=	SYM
ejpam-3763	88	20	3	3	NUM
ejpam-3763	88	21	if	if	SCONJ
ejpam-3763	88	22	and	and	CCONJ
ejpam-3763	88	23	only	only	ADV
ejpam-3763	88	24	if	if	SCONJ
ejpam-3763	88	25	∆(g	∆(g	NOUN
ejpam-3763	88	26	)	)	PUNCT
ejpam-3763	88	27	=	=	SYM
ejpam-3763	89	1	n−	n−	NOUN
ejpam-3763	89	2	2	2	NUM
ejpam-3763	89	3	.	.	PUNCT
ejpam-3763	90	1	(	(	PUNCT
ejpam-3763	90	2	iv	iv	X
ejpam-3763	90	3	)	)	PUNCT
ejpam-3763	90	4	if	if	SCONJ
ejpam-3763	90	5	g	g	PROPN
ejpam-3763	90	6	is	be	AUX
ejpam-3763	90	7	the	the	DET
ejpam-3763	90	8	complete	complete	ADJ
ejpam-3763	90	9	multipartite	multipartite	ADJ
ejpam-3763	90	10	graph	graph	NOUN
ejpam-3763	90	11	kr1,r2,	kr1,r2,	PROPN
ejpam-3763	90	12	...	...	PUNCT
ejpam-3763	90	13	,rm	,rm	NOUN
ejpam-3763	90	14	,	,	PUNCT
ejpam-3763	90	15	where	where	SCONJ
ejpam-3763	90	16	2	2	NUM
ejpam-3763	90	17	≤	≤	NOUN
ejpam-3763	90	18	r1	r1	NOUN
ejpam-3763	90	19	≤	≤	NUM
ejpam-3763	90	20	r2	r2	PROPN
ejpam-3763	90	21	≤	≤	NUM
ejpam-3763	90	22	.	.	PUNCT
ejpam-3763	90	23	.	.	PUNCT
ejpam-3763	90	24	.	.	PUNCT
ejpam-3763	91	1	≤	≤	PROPN
ejpam-3763	91	2	rm	rm	PROPN
ejpam-3763	91	3	,	,	PUNCT
ejpam-3763	91	4	then	then	ADV
ejpam-3763	91	5	γpr(g	γpr(g	PROPN
ejpam-3763	91	6	)	)	PUNCT
ejpam-3763	91	7	=	=	PRON
ejpam-3763	91	8	{	{	PUNCT
ejpam-3763	91	9	min{r1	min{r1	NOUN
ejpam-3763	91	10	+	+	SYM
ejpam-3763	91	11	1	1	NUM
ejpam-3763	91	12	,	,	PUNCT
ejpam-3763	91	13	4	4	NUM
ejpam-3763	91	14	}	}	PUNCT
ejpam-3763	91	15	,	,	PUNCT
ejpam-3763	91	16	if	if	SCONJ
ejpam-3763	91	17	m	m	ADV
ejpam-3763	91	18	=	=	SYM
ejpam-3763	91	19	2	2	NUM
ejpam-3763	91	20	;	;	PUNCT
ejpam-3763	91	21	r1	r1	NOUN
ejpam-3763	91	22	+	+	CCONJ
ejpam-3763	91	23	1	1	NUM
ejpam-3763	91	24	,	,	PUNCT
ejpam-3763	91	25	if	if	SCONJ
ejpam-3763	91	26	m	m	PROPN
ejpam-3763	91	27	≥	≥	NOUN
ejpam-3763	91	28	3	3	NUM
ejpam-3763	91	29	.	.	PUNCT
ejpam-3763	92	1	proof	proof	NOUN
ejpam-3763	92	2	:	:	PUNCT
ejpam-3763	92	3	clearly	clearly	ADV
ejpam-3763	92	4	,	,	PUNCT
ejpam-3763	92	5	if	if	SCONJ
ejpam-3763	92	6	γ(g	γ(g	PROPN
ejpam-3763	92	7	)	)	PUNCT
ejpam-3763	92	8	=	=	SYM
ejpam-3763	93	1	1	1	NUM
ejpam-3763	93	2	,	,	PUNCT
ejpam-3763	93	3	then	then	ADV
ejpam-3763	93	4	γp	γp	PROPN
ejpam-3763	93	5	(	(	PUNCT
ejpam-3763	93	6	g	g	NOUN
ejpam-3763	93	7	)	)	PUNCT
ejpam-3763	93	8	=	=	SYM
ejpam-3763	93	9	1	1	NUM
ejpam-3763	93	10	and	and	CCONJ
ejpam-3763	93	11	the	the	DET
ejpam-3763	93	12	inequalities	inequality	NOUN
ejpam-3763	93	13	in	in	ADP
ejpam-3763	93	14	proposition	proposition	NOUN
ejpam-3763	93	15	2.2	2.2	NUM
ejpam-3763	93	16	imply	imply	NOUN
ejpam-3763	93	17	that	that	SCONJ
ejpam-3763	93	18	γpr(g	γpr(g	PRON
ejpam-3763	93	19	)	)	PUNCT
ejpam-3763	93	20	=	=	SYM
ejpam-3763	94	1	2	2	X
ejpam-3763	94	2	.	.	PUNCT
ejpam-3763	94	3	now	now	ADV
ejpam-3763	94	4	,	,	PUNCT
ejpam-3763	94	5	suppose	suppose	VERB
ejpam-3763	94	6	that	that	SCONJ
ejpam-3763	94	7	γpr(g	γpr(g	PROPN
ejpam-3763	94	8	)	)	PUNCT
ejpam-3763	94	9	=	=	SYM
ejpam-3763	94	10	2	2	NUM
ejpam-3763	94	11	,	,	PUNCT
ejpam-3763	94	12	and	and	CCONJ
ejpam-3763	94	13	let	let	VERB
ejpam-3763	94	14	f	f	PROPN
ejpam-3763	94	15	=	=	SYM
ejpam-3763	94	16	(	(	PUNCT
ejpam-3763	94	17	v0	v0	PROPN
ejpam-3763	94	18	,	,	PUNCT
ejpam-3763	94	19	v1	v1	NOUN
ejpam-3763	94	20	,	,	PUNCT
ejpam-3763	94	21	v2	v2	PROPN
ejpam-3763	94	22	)	)	PUNCT
ejpam-3763	94	23	be	be	AUX
ejpam-3763	94	24	a	a	DET
ejpam-3763	94	25	γpr	γpr	NOUN
ejpam-3763	94	26	-function	-function	NOUN
ejpam-3763	94	27	of	of	ADP
ejpam-3763	94	28	g.	g.	NOUN
ejpam-3763	94	29	if	if	SCONJ
ejpam-3763	94	30	v2	v2	NOUN
ejpam-3763	94	31	=	=	NOUN
ejpam-3763	94	32	∅	∅	NOUN
ejpam-3763	94	33	,	,	PUNCT
ejpam-3763	94	34	then	then	ADV
ejpam-3763	94	35	v	v	X
ejpam-3763	94	36	(	(	PUNCT
ejpam-3763	94	37	g	g	NOUN
ejpam-3763	94	38	)	)	PUNCT
ejpam-3763	94	39	=	=	SYM
ejpam-3763	94	40	v1	v1	NOUN
ejpam-3763	94	41	and	and	CCONJ
ejpam-3763	94	42	γpr(g	γpr(g	NUM
ejpam-3763	94	43	)	)	PUNCT
ejpam-3763	94	44	=	=	SYM
ejpam-3763	95	1	n	n	NOUN
ejpam-3763	95	2	=	=	SYM
ejpam-3763	95	3	2	2	X
ejpam-3763	95	4	.	.	PUNCT
ejpam-3763	95	5	since	since	SCONJ
ejpam-3763	95	6	g	g	PROPN
ejpam-3763	95	7	is	be	AUX
ejpam-3763	95	8	connected	connect	VERB
ejpam-3763	95	9	,	,	PUNCT
ejpam-3763	95	10	g	g	NOUN
ejpam-3763	95	11	=	=	PUNCT
ejpam-3763	95	12	p2	p2	PROPN
ejpam-3763	95	13	and	and	CCONJ
ejpam-3763	95	14	γ(g	γ(g	PROPN
ejpam-3763	95	15	)	)	PUNCT
ejpam-3763	95	16	=	=	PUNCT
ejpam-3763	96	1	1	1	X
ejpam-3763	96	2	.	.	X
ejpam-3763	97	1	if	if	SCONJ
ejpam-3763	97	2	v2	v2	PROPN
ejpam-3763	97	3	6=	6=	NOUN
ejpam-3763	97	4	∅	∅	NOUN
ejpam-3763	97	5	,	,	PUNCT
ejpam-3763	97	6	then	then	ADV
ejpam-3763	97	7	v1	v1	NOUN
ejpam-3763	97	8	=	=	SYM
ejpam-3763	97	9	∅	∅	NOUN
ejpam-3763	97	10	and	and	CCONJ
ejpam-3763	97	11	v2	v2	NOUN
ejpam-3763	97	12	=	=	SYM
ejpam-3763	97	13	{	{	PUNCT
ejpam-3763	97	14	v	v	NOUN
ejpam-3763	97	15	}	}	PUNCT
ejpam-3763	97	16	with	with	ADP
ejpam-3763	97	17	ng[v	ng[v	NOUN
ejpam-3763	97	18	]	]	X
ejpam-3763	97	19	=	=	SYM
ejpam-3763	97	20	v	v	X
ejpam-3763	97	21	(	(	PUNCT
ejpam-3763	97	22	g	g	NOUN
ejpam-3763	97	23	)	)	PUNCT
ejpam-3763	97	24	.	.	PUNCT
ejpam-3763	98	1	this	this	PRON
ejpam-3763	98	2	means	mean	VERB
ejpam-3763	98	3	that	that	SCONJ
ejpam-3763	98	4	γ(g	γ(g	PROPN
ejpam-3763	98	5	)	)	PUNCT
ejpam-3763	98	6	=	=	PUNCT
ejpam-3763	99	1	1	1	X
ejpam-3763	99	2	.	.	PUNCT
ejpam-3763	100	1	this	this	PRON
ejpam-3763	100	2	proves	prove	VERB
ejpam-3763	100	3	(	(	PUNCT
ejpam-3763	100	4	i	i	NOUN
ejpam-3763	100	5	)	)	PUNCT
ejpam-3763	100	6	.	.	PUNCT
ejpam-3763	101	1	if	if	SCONJ
ejpam-3763	101	2	n	n	NOUN
ejpam-3763	101	3	=	=	SYM
ejpam-3763	101	4	2	2	NUM
ejpam-3763	101	5	,	,	PUNCT
ejpam-3763	101	6	then	then	ADV
ejpam-3763	101	7	g	g	PROPN
ejpam-3763	101	8	=	=	PUNCT
ejpam-3763	101	9	p2	p2	PROPN
ejpam-3763	101	10	and	and	CCONJ
ejpam-3763	101	11	γpr(g	γpr(g	NUM
ejpam-3763	101	12	)	)	PUNCT
ejpam-3763	102	1	=	=	SYM
ejpam-3763	102	2	2	2	X
ejpam-3763	102	3	=	=	NOUN
ejpam-3763	102	4	n.	n.	NOUN
ejpam-3763	102	5	conversely	conversely	ADV
ejpam-3763	102	6	,	,	PUNCT
ejpam-3763	102	7	suppose	suppose	VERB
ejpam-3763	102	8	that	that	SCONJ
ejpam-3763	102	9	n	n	PROPN
ejpam-3763	102	10	≥	≥	NUM
ejpam-3763	102	11	3	3	NUM
ejpam-3763	102	12	.	.	PUNCT
ejpam-3763	102	13	pick	pick	VERB
ejpam-3763	102	14	v	v	NUM
ejpam-3763	102	15	∈	∈	PROPN
ejpam-3763	102	16	v	v	NOUN
ejpam-3763	102	17	(	(	PUNCT
ejpam-3763	102	18	g	g	NOUN
ejpam-3763	102	19	)	)	PUNCT
ejpam-3763	102	20	such	such	ADJ
ejpam-3763	102	21	that	that	PRON
ejpam-3763	102	22	degg(v	degg(v	PROPN
ejpam-3763	102	23	)	)	PUNCT
ejpam-3763	102	24	=	=	SYM
ejpam-3763	102	25	∆(g	∆(g	PROPN
ejpam-3763	102	26	)	)	PUNCT
ejpam-3763	102	27	≥	≥	NOUN
ejpam-3763	102	28	2	2	NUM
ejpam-3763	102	29	.	.	X
ejpam-3763	102	30	define	define	VERB
ejpam-3763	102	31	on	on	ADP
ejpam-3763	102	32	g	g	PROPN
ejpam-3763	102	33	f(x	f(x	PROPN
ejpam-3763	102	34	)	)	PUNCT
ejpam-3763	103	1	=	=	PUNCT
ejpam-3763	104	1			NOUN
ejpam-3763	104	2	2	2	NUM
ejpam-3763	104	3	,	,	PUNCT
ejpam-3763	104	4	if	if	SCONJ
ejpam-3763	104	5	x	x	X
ejpam-3763	104	6	=	=	SYM
ejpam-3763	104	7	v	v	NOUN
ejpam-3763	104	8	;	;	PUNCT
ejpam-3763	104	9	0	0	NUM
ejpam-3763	104	10	,	,	PUNCT
ejpam-3763	104	11	if	if	SCONJ
ejpam-3763	104	12	x	x	SYM
ejpam-3763	104	13	∈	∈	NOUN
ejpam-3763	104	14	ng(v	ng(v	NOUN
ejpam-3763	104	15	)	)	PUNCT
ejpam-3763	104	16	;	;	PUNCT
ejpam-3763	104	17	1	1	NUM
ejpam-3763	104	18	,	,	PUNCT
ejpam-3763	104	19	else	else	ADV
ejpam-3763	104	20	.	.	PUNCT
ejpam-3763	105	1	then	then	ADV
ejpam-3763	105	2	f	f	PROPN
ejpam-3763	105	3	∈	∈	PROPN
ejpam-3763	105	4	prd(g	prd(g	PROPN
ejpam-3763	105	5	)	)	PUNCT
ejpam-3763	105	6	and	and	CCONJ
ejpam-3763	105	7	ω(f	ω(f	NUM
ejpam-3763	105	8	)	)	PUNCT
ejpam-3763	106	1	=	=	SYM
ejpam-3763	106	2	n−	n−	NOUN
ejpam-3763	106	3	(	(	PUNCT
ejpam-3763	106	4	∆(g)−	∆(g)−	X
ejpam-3763	106	5	1	1	NUM
ejpam-3763	106	6	)	)	PUNCT
ejpam-3763	106	7	<	<	X
ejpam-3763	106	8	n	n	CCONJ
ejpam-3763	106	9	,	,	PUNCT
ejpam-3763	106	10	a	a	DET
ejpam-3763	106	11	contradiction	contradiction	NOUN
ejpam-3763	106	12	.	.	PUNCT
ejpam-3763	107	1	thus	thus	ADV
ejpam-3763	107	2	,	,	PUNCT
ejpam-3763	107	3	if	if	SCONJ
ejpam-3763	107	4	γpr(g	γpr(g	PROPN
ejpam-3763	107	5	)	)	PUNCT
ejpam-3763	107	6	=	=	SYM
ejpam-3763	108	1	n	n	CCONJ
ejpam-3763	108	2	,	,	PUNCT
ejpam-3763	108	3	then	then	ADV
ejpam-3763	108	4	n	n	NOUN
ejpam-3763	108	5	=	=	SYM
ejpam-3763	108	6	2	2	X
ejpam-3763	108	7	.	.	X
ejpam-3763	109	1	we	we	PRON
ejpam-3763	109	2	have	have	AUX
ejpam-3763	109	3	proved	prove	VERB
ejpam-3763	109	4	(	(	PUNCT
ejpam-3763	109	5	ii	ii	NOUN
ejpam-3763	109	6	)	)	PUNCT
ejpam-3763	109	7	.	.	PUNCT
ejpam-3763	110	1	if	if	SCONJ
ejpam-3763	110	2	∆(g	∆(g	NOUN
ejpam-3763	110	3	)	)	PUNCT
ejpam-3763	110	4	=	=	SYM
ejpam-3763	111	1	n	n	CCONJ
ejpam-3763	112	1	−	−	PROPN
ejpam-3763	112	2	2	2	NUM
ejpam-3763	112	3	,	,	PUNCT
ejpam-3763	112	4	then	then	ADV
ejpam-3763	112	5	proposition	proposition	VERB
ejpam-3763	112	6	2.2	2.2	NUM
ejpam-3763	112	7	implies	imply	VERB
ejpam-3763	112	8	that	that	SCONJ
ejpam-3763	112	9	2	2	NUM
ejpam-3763	112	10	≤	≤	NUM
ejpam-3763	112	11	γpr(g	γpr(g	PROPN
ejpam-3763	112	12	)	)	PUNCT
ejpam-3763	112	13	≤	≤	NOUN
ejpam-3763	112	14	3	3	NUM
ejpam-3763	112	15	.	.	PUNCT
ejpam-3763	113	1	since	since	SCONJ
ejpam-3763	113	2	γ(g	γ(g	PROPN
ejpam-3763	113	3	)	)	PUNCT
ejpam-3763	113	4	≥	≥	NOUN
ejpam-3763	113	5	2	2	NUM
ejpam-3763	113	6	,	,	PUNCT
ejpam-3763	113	7	γpr(g	γpr(g	PROPN
ejpam-3763	113	8	)	)	PUNCT
ejpam-3763	113	9	=	=	SYM
ejpam-3763	113	10	3	3	X
ejpam-3763	113	11	by	by	ADP
ejpam-3763	113	12	(	(	PUNCT
ejpam-3763	113	13	i	i	NOUN
ejpam-3763	113	14	)	)	PUNCT
ejpam-3763	113	15	.	.	PUNCT
ejpam-3763	114	1	conversely	conversely	ADV
ejpam-3763	114	2	,	,	PUNCT
ejpam-3763	114	3	suppose	suppose	VERB
ejpam-3763	114	4	that	that	SCONJ
ejpam-3763	114	5	γpr(g	γpr(g	PROPN
ejpam-3763	114	6	)	)	PUNCT
ejpam-3763	114	7	=	=	SYM
ejpam-3763	115	1	3	3	X
ejpam-3763	115	2	.	.	PUNCT
ejpam-3763	116	1	by	by	ADP
ejpam-3763	116	2	(	(	PUNCT
ejpam-3763	116	3	i	i	NOUN
ejpam-3763	116	4	)	)	PUNCT
ejpam-3763	116	5	,	,	PUNCT
ejpam-3763	116	6	γ(g	γ(g	PROPN
ejpam-3763	116	7	)	)	PUNCT
ejpam-3763	116	8	≥	≥	NOUN
ejpam-3763	116	9	2	2	NUM
ejpam-3763	116	10	so	so	SCONJ
ejpam-3763	116	11	that	that	PRON
ejpam-3763	116	12	∆(g	∆(g	NOUN
ejpam-3763	116	13	)	)	PUNCT
ejpam-3763	116	14	≤	≤	NOUN
ejpam-3763	116	15	n	n	CCONJ
ejpam-3763	116	16	−	−	PROPN
ejpam-3763	116	17	2	2	NUM
ejpam-3763	116	18	,	,	PUNCT
ejpam-3763	116	19	and	and	CCONJ
ejpam-3763	116	20	by	by	ADP
ejpam-3763	116	21	(	(	PUNCT
ejpam-3763	116	22	ii	ii	NOUN
ejpam-3763	116	23	)	)	PUNCT
ejpam-3763	116	24	,	,	PUNCT
ejpam-3763	116	25	n	n	X
ejpam-3763	116	26	≥	≥	NOUN
ejpam-3763	116	27	4	4	NUM
ejpam-3763	116	28	.	.	PUNCT
ejpam-3763	117	1	let	let	VERB
ejpam-3763	117	2	f	f	PROPN
ejpam-3763	117	3	=	=	SYM
ejpam-3763	117	4	(	(	PUNCT
ejpam-3763	117	5	v0	v0	PROPN
ejpam-3763	117	6	,	,	PUNCT
ejpam-3763	117	7	v1	v1	NOUN
ejpam-3763	117	8	,	,	PUNCT
ejpam-3763	117	9	v2	v2	PROPN
ejpam-3763	117	10	)	)	PUNCT
ejpam-3763	117	11	be	be	AUX
ejpam-3763	117	12	a	a	DET
ejpam-3763	117	13	γpr	γpr	NOUN
ejpam-3763	117	14	-function	-function	NOUN
ejpam-3763	117	15	on	on	ADP
ejpam-3763	117	16	g.	g.	NOUN
ejpam-3763	118	1	if	if	SCONJ
ejpam-3763	118	2	v2	v2	NOUN
ejpam-3763	118	3	=	=	NOUN
ejpam-3763	118	4	∅	∅	NOUN
ejpam-3763	118	5	,	,	PUNCT
ejpam-3763	118	6	then	then	ADV
ejpam-3763	118	7	v1	v1	VERB
ejpam-3763	118	8	=	=	SYM
ejpam-3763	118	9	v	v	PROPN
ejpam-3763	118	10	(	(	PUNCT
ejpam-3763	118	11	g	g	NOUN
ejpam-3763	118	12	)	)	PUNCT
ejpam-3763	118	13	and	and	CCONJ
ejpam-3763	118	14	γpr(g	γpr(g	NUM
ejpam-3763	118	15	)	)	PUNCT
ejpam-3763	119	1	=	=	SYM
ejpam-3763	119	2	n	n	X
ejpam-3763	119	3	≥	≥	NOUN
ejpam-3763	119	4	4	4	NUM
ejpam-3763	119	5	,	,	PUNCT
ejpam-3763	119	6	a	a	DET
ejpam-3763	119	7	contradiction	contradiction	NOUN
ejpam-3763	119	8	.	.	PUNCT
ejpam-3763	120	1	thus	thus	ADV
ejpam-3763	120	2	,	,	PUNCT
ejpam-3763	120	3	|v2|	|v2|	NOUN
ejpam-3763	120	4	=	=	NOUN
ejpam-3763	120	5	|v1|	|v1|	NOUN
ejpam-3763	120	6	=	=	SYM
ejpam-3763	120	7	1	1	NUM
ejpam-3763	120	8	,	,	PUNCT
ejpam-3763	120	9	say	say	VERB
ejpam-3763	120	10	v1	v1	NOUN
ejpam-3763	120	11	=	=	SYM
ejpam-3763	120	12	{	{	PUNCT
ejpam-3763	120	13	u	u	NOUN
ejpam-3763	120	14	}	}	PUNCT
ejpam-3763	120	15	and	and	CCONJ
ejpam-3763	120	16	v2	v2	NOUN
ejpam-3763	120	17	=	=	SYM
ejpam-3763	120	18	{	{	PUNCT
ejpam-3763	120	19	v	v	NOUN
ejpam-3763	120	20	}	}	PUNCT
ejpam-3763	120	21	.	.	PUNCT
ejpam-3763	121	1	this	this	PRON
ejpam-3763	121	2	means	mean	VERB
ejpam-3763	121	3	that	that	SCONJ
ejpam-3763	121	4	v	v	X
ejpam-3763	121	5	(	(	PUNCT
ejpam-3763	121	6	g)\{u	g)\{u	PROPN
ejpam-3763	121	7	,	,	PUNCT
ejpam-3763	121	8	v	v	NOUN
ejpam-3763	121	9	}	}	PUNCT
ejpam-3763	121	10	⊆	⊆	NUM
ejpam-3763	121	11	v0	v0	NOUN
ejpam-3763	121	12	.	.	PUNCT
ejpam-3763	121	13	further	far	ADV
ejpam-3763	121	14	,	,	PUNCT
ejpam-3763	121	15	by	by	ADP
ejpam-3763	121	16	proposition	proposition	NOUN
ejpam-3763	121	17	2.1	2.1	NUM
ejpam-3763	121	18	,	,	PUNCT
ejpam-3763	121	19	uv	uv	NOUN
ejpam-3763	121	20	/∈	/∈	PUNCT
ejpam-3763	121	21	e(g	e(g	PROPN
ejpam-3763	121	22	)	)	PUNCT
ejpam-3763	121	23	.	.	PUNCT
ejpam-3763	122	1	accordingly	accordingly	ADV
ejpam-3763	122	2	,	,	PUNCT
ejpam-3763	122	3	degg(v	degg(v	PROPN
ejpam-3763	122	4	)	)	PUNCT
ejpam-3763	122	5	=	=	PUNCT
ejpam-3763	122	6	n−	n−	NOUN
ejpam-3763	122	7	2	2	NUM
ejpam-3763	122	8	.	.	PUNCT
ejpam-3763	123	1	therefore	therefore	ADV
ejpam-3763	123	2	,	,	PUNCT
ejpam-3763	123	3	∆(g	∆(g	PROPN
ejpam-3763	123	4	)	)	PUNCT
ejpam-3763	123	5	≥	≥	NOUN
ejpam-3763	123	6	n−	n−	NOUN
ejpam-3763	123	7	2	2	NUM
ejpam-3763	123	8	.	.	PUNCT
ejpam-3763	124	1	this	this	PRON
ejpam-3763	124	2	proves	prove	VERB
ejpam-3763	124	3	(	(	PUNCT
ejpam-3763	124	4	iii	iii	NOUN
ejpam-3763	124	5	)	)	PUNCT
ejpam-3763	124	6	.	.	PUNCT
ejpam-3763	125	1	suppose	suppose	VERB
ejpam-3763	125	2	that	that	SCONJ
ejpam-3763	125	3	g	g	PROPN
ejpam-3763	125	4	is	be	AUX
ejpam-3763	125	5	the	the	DET
ejpam-3763	125	6	complete	complete	ADJ
ejpam-3763	125	7	multipartite	multipartite	ADJ
ejpam-3763	125	8	graph	graph	NOUN
ejpam-3763	125	9	described	describe	VERB
ejpam-3763	125	10	in	in	ADP
ejpam-3763	125	11	(	(	PUNCT
ejpam-3763	125	12	iv	iv	NOUN
ejpam-3763	125	13	)	)	PUNCT
ejpam-3763	125	14	.	.	PUNCT
ejpam-3763	126	1	then	then	ADV
ejpam-3763	126	2	∆(g	∆(g	PROPN
ejpam-3763	126	3	)	)	PUNCT
ejpam-3763	126	4	=	=	SYM
ejpam-3763	126	5	n	n	NUM
ejpam-3763	126	6	−	−	PROPN
ejpam-3763	126	7	r1	r1	PROPN
ejpam-3763	126	8	.	.	PUNCT
ejpam-3763	126	9	suppose	suppose	VERB
ejpam-3763	126	10	first	first	ADV
ejpam-3763	126	11	that	that	SCONJ
ejpam-3763	126	12	m	m	VERB
ejpam-3763	126	13	=	=	ADJ
ejpam-3763	126	14	2	2	X
ejpam-3763	126	15	.	.	PUNCT
ejpam-3763	126	16	then	then	ADV
ejpam-3763	126	17	γ(g	γ(g	PROPN
ejpam-3763	126	18	)	)	PUNCT
ejpam-3763	127	1	=	=	SYM
ejpam-3763	127	2	γp	γp	PROPN
ejpam-3763	127	3	(	(	PUNCT
ejpam-3763	127	4	g	g	NOUN
ejpam-3763	127	5	)	)	PUNCT
ejpam-3763	127	6	=	=	SYM
ejpam-3763	127	7	2	2	X
ejpam-3763	127	8	.	.	PUNCT
ejpam-3763	127	9	by	by	ADP
ejpam-3763	127	10	proposition	proposition	NOUN
ejpam-3763	127	11	2.2	2.2	NUM
ejpam-3763	127	12	,	,	PUNCT
ejpam-3763	127	13	γpr(g	γpr(g	PROPN
ejpam-3763	127	14	)	)	PUNCT
ejpam-3763	127	15	≤	≤	NOUN
ejpam-3763	127	16	min{r1	min{r1	X
ejpam-3763	127	17	+	+	SYM
ejpam-3763	127	18	1	1	NUM
ejpam-3763	127	19	,	,	PUNCT
ejpam-3763	127	20	4	4	NUM
ejpam-3763	127	21	}	}	PUNCT
ejpam-3763	127	22	.	.	PUNCT
ejpam-3763	128	1	also	also	ADV
ejpam-3763	128	2	,	,	PUNCT
ejpam-3763	128	3	by	by	ADP
ejpam-3763	128	4	(	(	PUNCT
ejpam-3763	128	5	i	i	NOUN
ejpam-3763	128	6	)	)	PUNCT
ejpam-3763	128	7	,	,	PUNCT
ejpam-3763	128	8	γpr(g	γpr(g	PROPN
ejpam-3763	128	9	)	)	PUNCT
ejpam-3763	128	10	≥	≥	NOUN
ejpam-3763	128	11	3	3	NUM
ejpam-3763	128	12	.	.	PUNCT
ejpam-3763	129	1	if	if	SCONJ
ejpam-3763	129	2	r1	r1	PROPN
ejpam-3763	129	3	=	=	SYM
ejpam-3763	129	4	2	2	NUM
ejpam-3763	129	5	,	,	PUNCT
ejpam-3763	129	6	then	then	ADV
ejpam-3763	129	7	γpr(g	γpr(g	PROPN
ejpam-3763	129	8	)	)	PUNCT
ejpam-3763	129	9	=	=	SYM
ejpam-3763	129	10	3	3	X
ejpam-3763	129	11	=	=	X
ejpam-3763	129	12	r1	r1	PROPN
ejpam-3763	129	13	+	+	CCONJ
ejpam-3763	129	14	1	1	X
ejpam-3763	129	15	.	.	PUNCT
ejpam-3763	130	1	on	on	ADP
ejpam-3763	130	2	the	the	DET
ejpam-3763	130	3	other	other	ADJ
ejpam-3763	130	4	hand	hand	NOUN
ejpam-3763	130	5	,	,	PUNCT
ejpam-3763	130	6	if	if	SCONJ
ejpam-3763	130	7	r1	r1	PROPN
ejpam-3763	130	8	≥	≥	PRON
ejpam-3763	130	9	3	3	NUM
ejpam-3763	130	10	,	,	PUNCT
ejpam-3763	130	11	then	then	ADV
ejpam-3763	130	12	γpr(g	γpr(g	PRON
ejpam-3763	130	13	)	)	PUNCT
ejpam-3763	130	14	=	=	SYM
ejpam-3763	130	15	4	4	NUM
ejpam-3763	130	16	≥	≥	NOUN
ejpam-3763	130	17	r1	r1	NOUN
ejpam-3763	130	18	+	+	CCONJ
ejpam-3763	130	19	1	1	X
ejpam-3763	130	20	.	.	PUNCT
ejpam-3763	131	1	now	now	ADV
ejpam-3763	131	2	,	,	PUNCT
ejpam-3763	131	3	assume	assume	VERB
ejpam-3763	131	4	that	that	SCONJ
ejpam-3763	131	5	m	m	PROPN
ejpam-3763	131	6	≥	≥	NOUN
ejpam-3763	131	7	3	3	NUM
ejpam-3763	131	8	.	.	PUNCT
ejpam-3763	132	1	by	by	ADP
ejpam-3763	132	2	(	(	PUNCT
ejpam-3763	132	3	ii	ii	NOUN
ejpam-3763	132	4	)	)	PUNCT
ejpam-3763	132	5	,	,	PUNCT
ejpam-3763	132	6	γpr(g	γpr(g	PROPN
ejpam-3763	132	7	)	)	PUNCT
ejpam-3763	132	8	<	<	X
ejpam-3763	132	9	n.	n.	PROPN
ejpam-3763	132	10	let	let	VERB
ejpam-3763	132	11	f	f	PROPN
ejpam-3763	132	12	=	=	SYM
ejpam-3763	132	13	(	(	PUNCT
ejpam-3763	132	14	v0	v0	PROPN
ejpam-3763	132	15	,	,	PUNCT
ejpam-3763	132	16	v1	v1	NOUN
ejpam-3763	132	17	,	,	PUNCT
ejpam-3763	132	18	v2	v2	PROPN
ejpam-3763	132	19	)	)	PUNCT
ejpam-3763	132	20	be	be	AUX
ejpam-3763	132	21	a	a	DET
ejpam-3763	132	22	γpr	γpr	NOUN
ejpam-3763	132	23	-function	-function	NOUN
ejpam-3763	132	24	on	on	ADP
ejpam-3763	132	25	g.	g.	PROPN
ejpam-3763	132	26	then	then	ADV
ejpam-3763	132	27	|v2|	|v2|	ADV
ejpam-3763	132	28	=	=	SYM
ejpam-3763	133	1	1	1	X
ejpam-3763	133	2	,	,	PUNCT
ejpam-3763	133	3	say	say	VERB
ejpam-3763	133	4	v2	v2	NOUN
ejpam-3763	133	5	=	=	SYM
ejpam-3763	133	6	{	{	PUNCT
ejpam-3763	133	7	v	v	NOUN
ejpam-3763	133	8	}	}	PUNCT
ejpam-3763	133	9	.	.	PUNCT
ejpam-3763	134	1	since	since	SCONJ
ejpam-3763	134	2	f	f	PROPN
ejpam-3763	134	3	is	be	AUX
ejpam-3763	134	4	a	a	DET
ejpam-3763	134	5	γpr	γpr	NOUN
ejpam-3763	134	6	-function	-function	NOUN
ejpam-3763	134	7	,	,	PUNCT
ejpam-3763	134	8	v	v	NOUN
ejpam-3763	134	9	∈	∈	PROPN
ejpam-3763	134	10	u	u	NOUN
ejpam-3763	134	11	,	,	PUNCT
ejpam-3763	134	12	where	where	SCONJ
ejpam-3763	134	13	u	u	NOUN
ejpam-3763	134	14	is	be	AUX
ejpam-3763	134	15	the	the	DET
ejpam-3763	134	16	partite	partite	ADJ
ejpam-3763	134	17	set	set	NOUN
ejpam-3763	134	18	of	of	ADP
ejpam-3763	134	19	g	g	NOUN
ejpam-3763	134	20	with	with	ADP
ejpam-3763	134	21	|u	|u	ADJ
ejpam-3763	134	22	|	|	NOUN
ejpam-3763	134	23	=	=	SYM
ejpam-3763	134	24	r1	r1	PROPN
ejpam-3763	134	25	.	.	PUNCT
ejpam-3763	135	1	more	more	ADV
ejpam-3763	135	2	precisely	precisely	ADV
ejpam-3763	135	3	,	,	PUNCT
ejpam-3763	135	4	f(v	f(v	PROPN
ejpam-3763	135	5	)	)	PUNCT
ejpam-3763	135	6	=	=	SYM
ejpam-3763	135	7	2	2	NUM
ejpam-3763	135	8	,	,	PUNCT
ejpam-3763	135	9	f(x	f(x	PROPN
ejpam-3763	135	10	)	)	PUNCT
ejpam-3763	135	11	=	=	SYM
ejpam-3763	135	12	1	1	NUM
ejpam-3763	135	13	for	for	ADP
ejpam-3763	135	14	all	all	DET
ejpam-3763	135	15	x	x	SYM
ejpam-3763	135	16	∈	∈	PROPN
ejpam-3763	135	17	u	u	NOUN
ejpam-3763	135	18	\	\	PROPN
ejpam-3763	135	19	{	{	PUNCT
ejpam-3763	135	20	v	v	NOUN
ejpam-3763	135	21	}	}	PUNCT
ejpam-3763	135	22	and	and	CCONJ
ejpam-3763	135	23	f(x	f(x	PROPN
ejpam-3763	135	24	)	)	PUNCT
ejpam-3763	136	1	=	=	SYM
ejpam-3763	136	2	0	0	NUM
ejpam-3763	137	1	for	for	ADP
ejpam-3763	137	2	all	all	PRON
ejpam-3763	137	3	x	x	SYM
ejpam-3763	137	4	∈	∈	PROPN
ejpam-3763	137	5	v	v	NOUN
ejpam-3763	137	6	(	(	PUNCT
ejpam-3763	137	7	g	g	NOUN
ejpam-3763	137	8	)	)	PUNCT
ejpam-3763	137	9	\	\	PROPN
ejpam-3763	137	10	u	u	NOUN
ejpam-3763	137	11	.	.	PUNCT
ejpam-3763	138	1	thus	thus	ADV
ejpam-3763	138	2	,	,	PUNCT
ejpam-3763	138	3	γpr(g	γpr(g	PROPN
ejpam-3763	138	4	)	)	PUNCT
ejpam-3763	138	5	=	=	SYM
ejpam-3763	138	6	ωg(f	ωg(f	X
ejpam-3763	138	7	)	)	PUNCT
ejpam-3763	138	8	=	=	VERB
ejpam-3763	138	9	r1	r1	NOUN
ejpam-3763	138	10	+	+	CCONJ
ejpam-3763	138	11	1	1	X
ejpam-3763	138	12	.	.	PUNCT
ejpam-3763	139	1	this	this	PRON
ejpam-3763	139	2	proves	prove	VERB
ejpam-3763	139	3	(	(	PUNCT
ejpam-3763	139	4	iv	iv	NUM
ejpam-3763	139	5	)	)	PUNCT
ejpam-3763	139	6	.	.	PUNCT
ejpam-3763	140	1	�	�	PROPN
ejpam-3763	140	2	proposition	proposition	VERB
ejpam-3763	140	3	2.4	2.4	NUM
ejpam-3763	140	4	.	.	PUNCT
ejpam-3763	141	1	[	[	X
ejpam-3763	141	2	19	19	NUM
ejpam-3763	141	3	]	]	PUNCT
ejpam-3763	141	4	let	let	VERB
ejpam-3763	141	5	g1	g1	PROPN
ejpam-3763	141	6	,	,	PUNCT
ejpam-3763	141	7	g2	g2	PROPN
ejpam-3763	141	8	,	,	PUNCT
ejpam-3763	141	9	.	.	PUNCT
ejpam-3763	141	10	.	.	PUNCT
ejpam-3763	142	1	.	.	PUNCT
ejpam-3763	143	1	,	,	PUNCT
ejpam-3763	143	2	gk	gk	PROPN
ejpam-3763	143	3	be	be	AUX
ejpam-3763	143	4	the	the	DET
ejpam-3763	143	5	components	component	NOUN
ejpam-3763	143	6	of	of	ADP
ejpam-3763	143	7	g.	g.	PROPN
ejpam-3763	143	8	then	then	ADV
ejpam-3763	143	9	γpr(g	γpr(g	PRON
ejpam-3763	143	10	)	)	PUNCT
ejpam-3763	144	1	=	=	SYM
ejpam-3763	144	2	∑k	∑k	PROPN
ejpam-3763	144	3	j=1	j=1	PROPN
ejpam-3763	144	4	γ	γ	PROPN
ejpam-3763	144	5	p	p	PROPN
ejpam-3763	144	6	r(gj	r(gj	PROPN
ejpam-3763	144	7	)	)	PUNCT
ejpam-3763	144	8	.	.	PUNCT
ejpam-3763	145	1	proposition	proposition	NOUN
ejpam-3763	145	2	2.4	2.4	NUM
ejpam-3763	145	3	and	and	CCONJ
ejpam-3763	145	4	corollary	corollary	ADJ
ejpam-3763	145	5	2.3(ii	2.3(ii	NUM
ejpam-3763	145	6	)	)	PUNCT
ejpam-3763	145	7	yield	yield	VERB
ejpam-3763	145	8	the	the	DET
ejpam-3763	145	9	following	follow	VERB
ejpam-3763	145	10	corollary	corollary	NOUN
ejpam-3763	145	11	.	.	PUNCT
ejpam-3763	146	1	l.	l.	PROPN
ejpam-3763	146	2	paleta	paleta	PROPN
ejpam-3763	146	3	,	,	PUNCT
ejpam-3763	146	4	f.	f.	PROPN
ejpam-3763	146	5	jamil	jamil	PROPN
ejpam-3763	146	6	/	/	SYM
ejpam-3763	146	7	eur	eur	PROPN
ejpam-3763	146	8	.	.	PUNCT
ejpam-3763	147	1	j.	j.	PROPN
ejpam-3763	147	2	pure	pure	PROPN
ejpam-3763	147	3	appl	appl	PROPN
ejpam-3763	147	4	.	.	PROPN
ejpam-3763	147	5	math	math	PROPN
ejpam-3763	147	6	,	,	PUNCT
ejpam-3763	147	7	13	13	NUM
ejpam-3763	147	8	(	(	PUNCT
ejpam-3763	147	9	3	3	NUM
ejpam-3763	147	10	)	)	PUNCT
ejpam-3763	147	11	(	(	PUNCT
ejpam-3763	147	12	2020	2020	NUM
ejpam-3763	147	13	)	)	PUNCT
ejpam-3763	147	14	,	,	PUNCT
ejpam-3763	147	15	529	529	NUM
ejpam-3763	147	16	-	-	SYM
ejpam-3763	147	17	548	548	NUM
ejpam-3763	147	18	533	533	NUM
ejpam-3763	147	19	corollary	corollary	NOUN
ejpam-3763	147	20	2.5	2.5	NUM
ejpam-3763	147	21	.	.	PUNCT
ejpam-3763	148	1	let	let	VERB
ejpam-3763	148	2	g	g	PRON
ejpam-3763	148	3	be	be	AUX
ejpam-3763	148	4	a	a	DET
ejpam-3763	148	5	graph	graph	NOUN
ejpam-3763	148	6	of	of	ADP
ejpam-3763	148	7	order	order	NOUN
ejpam-3763	148	8	n.	n.	NOUN
ejpam-3763	148	9	then	then	ADV
ejpam-3763	148	10	γpr(g	γpr(g	PROPN
ejpam-3763	148	11	)	)	PUNCT
ejpam-3763	149	1	=	=	SYM
ejpam-3763	149	2	n	n	NOUN
ejpam-3763	149	3	if	if	SCONJ
ejpam-3763	149	4	and	and	CCONJ
ejpam-3763	149	5	only	only	ADV
ejpam-3763	149	6	if	if	SCONJ
ejpam-3763	149	7	g	g	PROPN
ejpam-3763	149	8	=	=	SYM
ejpam-3763	149	9	∪kj=1gj	∪kj=1gj	NOUN
ejpam-3763	149	10	,	,	PUNCT
ejpam-3763	149	11	where	where	SCONJ
ejpam-3763	149	12	gj	gj	PROPN
ejpam-3763	149	13	∈	∈	PROPN
ejpam-3763	149	14	{	{	PUNCT
ejpam-3763	149	15	k1,k2	k1,k2	PROPN
ejpam-3763	149	16	}	}	PUNCT
ejpam-3763	149	17	for	for	ADP
ejpam-3763	149	18	all	all	DET
ejpam-3763	149	19	j	j	NOUN
ejpam-3763	149	20	=	=	SYM
ejpam-3763	149	21	1	1	NUM
ejpam-3763	149	22	,	,	PUNCT
ejpam-3763	149	23	2	2	NUM
ejpam-3763	149	24	,	,	PUNCT
ejpam-3763	149	25	.	.	PUNCT
ejpam-3763	149	26	.	.	PUNCT
ejpam-3763	149	27	.	.	PUNCT
ejpam-3763	150	1	,	,	PUNCT
ejpam-3763	150	2	k.	k.	PROPN
ejpam-3763	150	3	corollary	corollary	PROPN
ejpam-3763	150	4	2.6	2.6	NUM
ejpam-3763	150	5	.	.	PUNCT
ejpam-3763	151	1	let	let	VERB
ejpam-3763	151	2	g	g	PRON
ejpam-3763	151	3	be	be	AUX
ejpam-3763	151	4	a	a	DET
ejpam-3763	151	5	graph	graph	NOUN
ejpam-3763	151	6	of	of	ADP
ejpam-3763	151	7	order	order	NOUN
ejpam-3763	151	8	n.	n.	NOUN
ejpam-3763	151	9	then	then	ADV
ejpam-3763	151	10	γ(g	γ(g	PROPN
ejpam-3763	151	11	)	)	PUNCT
ejpam-3763	152	1	=	=	SYM
ejpam-3763	152	2	γpr(g	γpr(g	PROPN
ejpam-3763	152	3	)	)	PUNCT
ejpam-3763	153	1	if	if	SCONJ
ejpam-3763	153	2	and	and	CCONJ
ejpam-3763	153	3	only	only	ADV
ejpam-3763	153	4	if	if	SCONJ
ejpam-3763	153	5	g	g	PROPN
ejpam-3763	153	6	=	=	PROPN
ejpam-3763	153	7	kn	kn	PROPN
ejpam-3763	153	8	.	.	PUNCT
ejpam-3763	153	9	proof	proof	NOUN
ejpam-3763	153	10	:	:	PUNCT
ejpam-3763	153	11	if	if	SCONJ
ejpam-3763	153	12	g	g	PROPN
ejpam-3763	153	13	=	=	SYM
ejpam-3763	153	14	kn	kn	PROPN
ejpam-3763	153	15	,	,	PUNCT
ejpam-3763	153	16	then	then	ADV
ejpam-3763	153	17	γ(g	γ(g	PROPN
ejpam-3763	153	18	)	)	PUNCT
ejpam-3763	153	19	=	=	SYM
ejpam-3763	153	20	n	n	NOUN
ejpam-3763	153	21	and	and	CCONJ
ejpam-3763	153	22	by	by	ADP
ejpam-3763	153	23	corollary	corollary	ADJ
ejpam-3763	153	24	2.5	2.5	NUM
ejpam-3763	153	25	,	,	PUNCT
ejpam-3763	153	26	γpr(g	γpr(g	PROPN
ejpam-3763	153	27	)	)	PUNCT
ejpam-3763	153	28	=	=	VERB
ejpam-3763	154	1	n.	n.	NOUN
ejpam-3763	154	2	conversely	conversely	ADV
ejpam-3763	154	3	,	,	PUNCT
ejpam-3763	154	4	suppose	suppose	VERB
ejpam-3763	154	5	that	that	SCONJ
ejpam-3763	154	6	γ(g	γ(g	PROPN
ejpam-3763	154	7	)	)	PUNCT
ejpam-3763	154	8	=	=	SYM
ejpam-3763	154	9	γpr(g	γpr(g	PROPN
ejpam-3763	154	10	)	)	PUNCT
ejpam-3763	154	11	,	,	PUNCT
ejpam-3763	154	12	and	and	CCONJ
ejpam-3763	154	13	let	let	VERB
ejpam-3763	154	14	f	f	PROPN
ejpam-3763	154	15	=	=	SYM
ejpam-3763	154	16	(	(	PUNCT
ejpam-3763	154	17	v0	v0	PROPN
ejpam-3763	154	18	,	,	PUNCT
ejpam-3763	154	19	v1	v1	NOUN
ejpam-3763	154	20	,	,	PUNCT
ejpam-3763	154	21	v2	v2	PROPN
ejpam-3763	154	22	)	)	PUNCT
ejpam-3763	154	23	be	be	AUX
ejpam-3763	154	24	a	a	DET
ejpam-3763	154	25	γpr	γpr	NOUN
ejpam-3763	154	26	-function	-function	NOUN
ejpam-3763	154	27	of	of	ADP
ejpam-3763	154	28	g.	g.	PROPN
ejpam-3763	154	29	note	note	VERB
ejpam-3763	154	30	that	that	SCONJ
ejpam-3763	154	31	if	if	SCONJ
ejpam-3763	154	32	v2	v2	PROPN
ejpam-3763	154	33	6=	6=	NOUN
ejpam-3763	154	34	∅	∅	NOUN
ejpam-3763	154	35	,	,	PUNCT
ejpam-3763	154	36	then	then	ADV
ejpam-3763	154	37	γ(g	γ(g	PROPN
ejpam-3763	154	38	)	)	PUNCT
ejpam-3763	154	39	≤	≤	NUM
ejpam-3763	154	40	|v1|	|v1|	NOUN
ejpam-3763	154	41	+	+	X
ejpam-3763	154	42	|v2|	|v2|	X
ejpam-3763	154	43	<	<	X
ejpam-3763	154	44	γpr(g	γpr(g	PROPN
ejpam-3763	154	45	)	)	PUNCT
ejpam-3763	154	46	,	,	PUNCT
ejpam-3763	154	47	a	a	DET
ejpam-3763	154	48	contradiction	contradiction	NOUN
ejpam-3763	154	49	.	.	PUNCT
ejpam-3763	155	1	thus	thus	ADV
ejpam-3763	155	2	,	,	PUNCT
ejpam-3763	155	3	v2	v2	PROPN
ejpam-3763	155	4	=	=	SYM
ejpam-3763	155	5	v0	v0	NOUN
ejpam-3763	155	6	=	=	SYM
ejpam-3763	155	7	∅	∅	NOUN
ejpam-3763	155	8	and	and	CCONJ
ejpam-3763	155	9	γpr(g	γpr(g	PRON
ejpam-3763	155	10	)	)	PUNCT
ejpam-3763	155	11	=	=	VERB
ejpam-3763	155	12	n.	n.	NOUN
ejpam-3763	155	13	this	this	PRON
ejpam-3763	155	14	means	mean	VERB
ejpam-3763	155	15	that	that	SCONJ
ejpam-3763	155	16	γ(g	γ(g	PROPN
ejpam-3763	155	17	)	)	PUNCT
ejpam-3763	155	18	=	=	SYM
ejpam-3763	156	1	n	n	PROPN
ejpam-3763	156	2	and	and	CCONJ
ejpam-3763	156	3	,	,	PUNCT
ejpam-3763	156	4	thus	thus	ADV
ejpam-3763	156	5	,	,	PUNCT
ejpam-3763	156	6	g	g	PROPN
ejpam-3763	156	7	=	=	SYM
ejpam-3763	156	8	kn	kn	PROPN
ejpam-3763	156	9	.	.	PUNCT
ejpam-3763	156	10	�	�	PROPN
ejpam-3763	156	11	2.1	2.1	NUM
ejpam-3763	156	12	.	.	PUNCT
ejpam-3763	157	1	on	on	ADP
ejpam-3763	157	2	the	the	DET
ejpam-3763	157	3	join	join	NOUN
ejpam-3763	157	4	of	of	ADP
ejpam-3763	157	5	graphs	graph	NOUN
ejpam-3763	157	6	by	by	ADP
ejpam-3763	157	7	corollary	corollary	ADJ
ejpam-3763	157	8	2.3(i	2.3(i	NUM
ejpam-3763	157	9	)	)	PUNCT
ejpam-3763	157	10	,	,	PUNCT
ejpam-3763	157	11	γpr(g+kn	γpr(g+kn	NOUN
ejpam-3763	157	12	)	)	PUNCT
ejpam-3763	157	13	=	=	SYM
ejpam-3763	157	14	2	2	NUM
ejpam-3763	157	15	for	for	ADP
ejpam-3763	157	16	all	all	DET
ejpam-3763	157	17	graphs	graph	NOUN
ejpam-3763	157	18	g	g	NOUN
ejpam-3763	157	19	and	and	CCONJ
ejpam-3763	157	20	for	for	ADP
ejpam-3763	157	21	all	all	DET
ejpam-3763	157	22	n	n	PRON
ejpam-3763	157	23	≥	≥	NOUN
ejpam-3763	157	24	1	1	NUM
ejpam-3763	157	25	.	.	PUNCT
ejpam-3763	158	1	the	the	DET
ejpam-3763	158	2	following	follow	VERB
ejpam-3763	158	3	theorem	theorem	NOUN
ejpam-3763	158	4	characterizes	characterize	VERB
ejpam-3763	158	5	all	all	DET
ejpam-3763	158	6	prd	prd	NOUN
ejpam-3763	158	7	-	-	PUNCT
ejpam-3763	158	8	functions	function	NOUN
ejpam-3763	158	9	on	on	ADP
ejpam-3763	158	10	the	the	DET
ejpam-3763	158	11	join	join	NOUN
ejpam-3763	158	12	of	of	ADP
ejpam-3763	158	13	nontrivial	nontrivial	ADJ
ejpam-3763	158	14	connected	connect	VERB
ejpam-3763	158	15	graphs	graph	NOUN
ejpam-3763	158	16	.	.	PUNCT
ejpam-3763	159	1	theorem	theorem	ADJ
ejpam-3763	159	2	2.7	2.7	NUM
ejpam-3763	159	3	.	.	PUNCT
ejpam-3763	160	1	let	let	VERB
ejpam-3763	160	2	g	g	NOUN
ejpam-3763	160	3	and	and	CCONJ
ejpam-3763	160	4	h	h	NOUN
ejpam-3763	160	5	be	be	VERB
ejpam-3763	160	6	any	any	DET
ejpam-3763	160	7	nontrivial	nontrivial	ADJ
ejpam-3763	160	8	connected	connect	VERB
ejpam-3763	160	9	graphs	graph	NOUN
ejpam-3763	160	10	and	and	CCONJ
ejpam-3763	160	11	f	f	NOUN
ejpam-3763	160	12	=	=	SYM
ejpam-3763	160	13	(	(	PUNCT
ejpam-3763	160	14	v0	v0	PROPN
ejpam-3763	160	15	,	,	PUNCT
ejpam-3763	160	16	v1	v1	NOUN
ejpam-3763	160	17	,	,	PUNCT
ejpam-3763	160	18	v2	v2	PROPN
ejpam-3763	160	19	)	)	PUNCT
ejpam-3763	160	20	.	.	PUNCT
ejpam-3763	161	1	then	then	ADV
ejpam-3763	161	2	f	f	PROPN
ejpam-3763	161	3	∈	∈	PROPN
ejpam-3763	161	4	prd(g+h	prd(g+h	NOUN
ejpam-3763	161	5	)	)	PUNCT
ejpam-3763	161	6	if	if	SCONJ
ejpam-3763	161	7	and	and	CCONJ
ejpam-3763	161	8	only	only	ADV
ejpam-3763	161	9	if	if	SCONJ
ejpam-3763	161	10	one	one	NUM
ejpam-3763	161	11	of	of	ADP
ejpam-3763	161	12	the	the	DET
ejpam-3763	161	13	following	follow	VERB
ejpam-3763	161	14	holds	hold	VERB
ejpam-3763	161	15	:	:	PUNCT
ejpam-3763	161	16	(	(	PUNCT
ejpam-3763	161	17	i	i	NOUN
ejpam-3763	161	18	)	)	PUNCT
ejpam-3763	161	19	v2	v2	VERB
ejpam-3763	161	20	⊆	⊆	NUM
ejpam-3763	161	21	v	v	NOUN
ejpam-3763	161	22	(	(	PUNCT
ejpam-3763	161	23	g	g	NOUN
ejpam-3763	161	24	)	)	PUNCT
ejpam-3763	161	25	and	and	CCONJ
ejpam-3763	161	26	one	one	NUM
ejpam-3763	161	27	of	of	ADP
ejpam-3763	161	28	the	the	DET
ejpam-3763	161	29	following	following	NOUN
ejpam-3763	161	30	holds	hold	VERB
ejpam-3763	161	31	:	:	PUNCT
ejpam-3763	161	32	(	(	PUNCT
ejpam-3763	161	33	a	a	X
ejpam-3763	161	34	)	)	PUNCT
ejpam-3763	161	35	v0	v0	NOUN
ejpam-3763	161	36	⊆	⊆	NUM
ejpam-3763	161	37	v	v	NOUN
ejpam-3763	161	38	(	(	PUNCT
ejpam-3763	161	39	g	g	NOUN
ejpam-3763	161	40	)	)	PUNCT
ejpam-3763	161	41	,	,	PUNCT
ejpam-3763	161	42	v	v	X
ejpam-3763	161	43	(	(	PUNCT
ejpam-3763	161	44	h	h	NOUN
ejpam-3763	161	45	)	)	PUNCT
ejpam-3763	161	46	⊆	⊆	NUM
ejpam-3763	161	47	v1	v1	NOUN
ejpam-3763	161	48	and	and	CCONJ
ejpam-3763	161	49	(	(	PUNCT
ejpam-3763	161	50	v0	v0	NOUN
ejpam-3763	161	51	,	,	PUNCT
ejpam-3763	161	52	v1	v1	NOUN
ejpam-3763	161	53	∩	∩	ADJ
ejpam-3763	161	54	v	v	NOUN
ejpam-3763	161	55	(	(	PUNCT
ejpam-3763	161	56	g	g	NOUN
ejpam-3763	161	57	)	)	PUNCT
ejpam-3763	161	58	,	,	PUNCT
ejpam-3763	161	59	v2	v2	PROPN
ejpam-3763	161	60	)	)	PUNCT
ejpam-3763	161	61	∈	∈	PROPN
ejpam-3763	161	62	prd(g	prd(g	PROPN
ejpam-3763	161	63	)	)	PUNCT
ejpam-3763	161	64	;	;	PUNCT
ejpam-3763	161	65	(	(	PUNCT
ejpam-3763	161	66	b	b	X
ejpam-3763	161	67	)	)	PUNCT
ejpam-3763	161	68	v0	v0	NOUN
ejpam-3763	161	69	∩	∩	ADJ
ejpam-3763	161	70	v	v	X
ejpam-3763	161	71	(	(	PUNCT
ejpam-3763	161	72	h	h	NOUN
ejpam-3763	161	73	)	)	PUNCT
ejpam-3763	161	74	6=	6=	NOUN
ejpam-3763	161	75	∅	∅	NOUN
ejpam-3763	161	76	and	and	CCONJ
ejpam-3763	161	77	v2	v2	NOUN
ejpam-3763	161	78	=	=	SYM
ejpam-3763	161	79	{	{	PUNCT
ejpam-3763	161	80	v	v	NOUN
ejpam-3763	161	81	}	}	PUNCT
ejpam-3763	161	82	for	for	ADP
ejpam-3763	161	83	which	which	PRON
ejpam-3763	161	84	v0	v0	NOUN
ejpam-3763	161	85	∩	∩	NOUN
ejpam-3763	161	86	v	v	X
ejpam-3763	161	87	(	(	PUNCT
ejpam-3763	161	88	g	g	NOUN
ejpam-3763	161	89	)	)	PUNCT
ejpam-3763	161	90	⊆	⊆	NUM
ejpam-3763	161	91	ng(v	ng(v	NUM
ejpam-3763	161	92	)	)	PUNCT
ejpam-3763	161	93	.	.	PUNCT
ejpam-3763	162	1	(	(	PUNCT
ejpam-3763	162	2	ii	ii	X
ejpam-3763	162	3	)	)	PUNCT
ejpam-3763	162	4	v2	v2	PROPN
ejpam-3763	162	5	⊆	⊆	NUM
ejpam-3763	162	6	v	v	NOUN
ejpam-3763	162	7	(	(	PUNCT
ejpam-3763	162	8	h	h	NOUN
ejpam-3763	162	9	)	)	PUNCT
ejpam-3763	162	10	and	and	CCONJ
ejpam-3763	162	11	one	one	NUM
ejpam-3763	162	12	of	of	ADP
ejpam-3763	162	13	the	the	DET
ejpam-3763	162	14	following	following	NOUN
ejpam-3763	162	15	holds	hold	VERB
ejpam-3763	162	16	:	:	PUNCT
ejpam-3763	162	17	(	(	PUNCT
ejpam-3763	162	18	a	a	X
ejpam-3763	162	19	)	)	PUNCT
ejpam-3763	162	20	v0	v0	NOUN
ejpam-3763	162	21	⊆	⊆	NUM
ejpam-3763	162	22	v	v	NOUN
ejpam-3763	162	23	(	(	PUNCT
ejpam-3763	162	24	h	h	NOUN
ejpam-3763	162	25	)	)	PUNCT
ejpam-3763	162	26	,	,	PUNCT
ejpam-3763	162	27	v	v	X
ejpam-3763	162	28	(	(	PUNCT
ejpam-3763	162	29	g	g	NOUN
ejpam-3763	162	30	)	)	PUNCT
ejpam-3763	162	31	⊆	⊆	NUM
ejpam-3763	162	32	v1	v1	NOUN
ejpam-3763	162	33	and	and	CCONJ
ejpam-3763	162	34	(	(	PUNCT
ejpam-3763	162	35	v0	v0	NOUN
ejpam-3763	162	36	,	,	PUNCT
ejpam-3763	162	37	v1	v1	NOUN
ejpam-3763	162	38	∩	∩	ADJ
ejpam-3763	162	39	v	v	NOUN
ejpam-3763	162	40	(	(	PUNCT
ejpam-3763	162	41	h	h	NOUN
ejpam-3763	162	42	)	)	PUNCT
ejpam-3763	162	43	,	,	PUNCT
ejpam-3763	162	44	v2	v2	PROPN
ejpam-3763	162	45	)	)	PUNCT
ejpam-3763	162	46	∈	∈	PROPN
ejpam-3763	162	47	prd(h	prd(h	PROPN
ejpam-3763	162	48	)	)	PUNCT
ejpam-3763	162	49	;	;	PUNCT
ejpam-3763	162	50	(	(	PUNCT
ejpam-3763	162	51	b	b	X
ejpam-3763	162	52	)	)	PUNCT
ejpam-3763	162	53	v0	v0	NOUN
ejpam-3763	162	54	∩	∩	X
ejpam-3763	162	55	v	v	X
ejpam-3763	162	56	(	(	PUNCT
ejpam-3763	162	57	g	g	NOUN
ejpam-3763	162	58	)	)	PUNCT
ejpam-3763	162	59	6=	6=	ADP
ejpam-3763	162	60	∅	∅	NOUN
ejpam-3763	162	61	and	and	CCONJ
ejpam-3763	162	62	v2	v2	NOUN
ejpam-3763	162	63	=	=	SYM
ejpam-3763	162	64	{	{	PUNCT
ejpam-3763	162	65	v	v	NOUN
ejpam-3763	162	66	}	}	PUNCT
ejpam-3763	162	67	for	for	ADP
ejpam-3763	162	68	which	which	PRON
ejpam-3763	162	69	v0	v0	NOUN
ejpam-3763	162	70	∩	∩	NOUN
ejpam-3763	162	71	v	v	X
ejpam-3763	162	72	(	(	PUNCT
ejpam-3763	162	73	h	h	NOUN
ejpam-3763	162	74	)	)	PUNCT
ejpam-3763	162	75	⊆	⊆	NUM
ejpam-3763	162	76	nh(v	nh(v	NOUN
ejpam-3763	162	77	)	)	PUNCT
ejpam-3763	162	78	.	.	PUNCT
ejpam-3763	163	1	(	(	PUNCT
ejpam-3763	163	2	iii	iii	X
ejpam-3763	163	3	)	)	PUNCT
ejpam-3763	163	4	a1	a1	NOUN
ejpam-3763	163	5	=	=	SYM
ejpam-3763	163	6	v2	v2	PROPN
ejpam-3763	163	7	∩	∩	NOUN
ejpam-3763	163	8	v	v	NOUN
ejpam-3763	163	9	(	(	PUNCT
ejpam-3763	163	10	g	g	NOUN
ejpam-3763	163	11	)	)	PUNCT
ejpam-3763	163	12	6=	6=	ADP
ejpam-3763	163	13	∅	∅	NOUN
ejpam-3763	163	14	and	and	CCONJ
ejpam-3763	163	15	a2	a2	PROPN
ejpam-3763	163	16	=	=	SYM
ejpam-3763	163	17	v2	v2	PROPN
ejpam-3763	163	18	∩	∩	NOUN
ejpam-3763	163	19	v	v	NOUN
ejpam-3763	163	20	(	(	PUNCT
ejpam-3763	163	21	h	h	NOUN
ejpam-3763	163	22	)	)	PUNCT
ejpam-3763	163	23	6=	6=	ADP
ejpam-3763	163	24	∅	∅	NOUN
ejpam-3763	163	25	and	and	CCONJ
ejpam-3763	163	26	the	the	DET
ejpam-3763	163	27	following	follow	VERB
ejpam-3763	163	28	holds	hold	VERB
ejpam-3763	163	29	:	:	PUNCT
ejpam-3763	163	30	(	(	PUNCT
ejpam-3763	163	31	a	a	X
ejpam-3763	163	32	)	)	PUNCT
ejpam-3763	163	33	if	if	SCONJ
ejpam-3763	163	34	v0	v0	NOUN
ejpam-3763	163	35	∩	∩	NOUN
ejpam-3763	163	36	v	v	X
ejpam-3763	163	37	(	(	PUNCT
ejpam-3763	163	38	g	g	NOUN
ejpam-3763	163	39	)	)	PUNCT
ejpam-3763	163	40	6=	6=	ADP
ejpam-3763	163	41	∅	∅	NOUN
ejpam-3763	163	42	,	,	PUNCT
ejpam-3763	163	43	then	then	ADV
ejpam-3763	163	44	|a2|	|a2|	NOUN
ejpam-3763	163	45	=	=	SYM
ejpam-3763	163	46	1	1	NUM
ejpam-3763	163	47	and	and	CCONJ
ejpam-3763	163	48	(	(	PUNCT
ejpam-3763	163	49	v0	v0	NOUN
ejpam-3763	163	50	∩	∩	NOUN
ejpam-3763	163	51	v	v	X
ejpam-3763	163	52	(	(	PUNCT
ejpam-3763	163	53	g	g	NOUN
ejpam-3763	163	54	)	)	PUNCT
ejpam-3763	163	55	)	)	PUNCT
ejpam-3763	164	1	∩ng(a1	∩ng(a1	ADP
ejpam-3763	164	2	)	)	PUNCT
ejpam-3763	164	3	=	=	SYM
ejpam-3763	164	4	∅	∅	NOUN
ejpam-3763	164	5	;	;	PUNCT
ejpam-3763	164	6	(	(	PUNCT
ejpam-3763	164	7	b	b	X
ejpam-3763	164	8	)	)	PUNCT
ejpam-3763	164	9	if	if	SCONJ
ejpam-3763	164	10	v0	v0	NOUN
ejpam-3763	164	11	∩	∩	NOUN
ejpam-3763	164	12	v	v	X
ejpam-3763	164	13	(	(	PUNCT
ejpam-3763	164	14	h	h	NOUN
ejpam-3763	164	15	)	)	PUNCT
ejpam-3763	164	16	6=	6=	NOUN
ejpam-3763	164	17	∅	∅	NOUN
ejpam-3763	164	18	,	,	PUNCT
ejpam-3763	164	19	then	then	ADV
ejpam-3763	164	20	|a1|	|a1|	X
ejpam-3763	164	21	=	=	SYM
ejpam-3763	164	22	1	1	NUM
ejpam-3763	164	23	and	and	CCONJ
ejpam-3763	164	24	(	(	PUNCT
ejpam-3763	164	25	v0	v0	NOUN
ejpam-3763	164	26	∩	∩	NOUN
ejpam-3763	164	27	v	v	X
ejpam-3763	164	28	(	(	PUNCT
ejpam-3763	164	29	h	h	NOUN
ejpam-3763	164	30	)	)	PUNCT
ejpam-3763	164	31	)	)	PUNCT
ejpam-3763	164	32	∩nh(a2	∩nh(a2	NOUN
ejpam-3763	164	33	)	)	PUNCT
ejpam-3763	165	1	=	=	PUNCT
ejpam-3763	165	2	∅.	∅.	PRON
ejpam-3763	165	3	proof	proof	NOUN
ejpam-3763	165	4	:	:	PUNCT
ejpam-3763	165	5	assume	assume	VERB
ejpam-3763	165	6	that	that	SCONJ
ejpam-3763	165	7	f	f	PROPN
ejpam-3763	165	8	is	be	AUX
ejpam-3763	165	9	a	a	DET
ejpam-3763	165	10	perfect	perfect	ADJ
ejpam-3763	165	11	roman	roman	ADJ
ejpam-3763	165	12	dominating	dominating	NOUN
ejpam-3763	165	13	function	function	NOUN
ejpam-3763	165	14	on	on	ADP
ejpam-3763	165	15	g	g	PROPN
ejpam-3763	165	16	+	+	CCONJ
ejpam-3763	165	17	h.	h.	NOUN
ejpam-3763	165	18	we	we	PRON
ejpam-3763	165	19	consider	consider	VERB
ejpam-3763	165	20	three	three	NUM
ejpam-3763	165	21	cases	case	NOUN
ejpam-3763	165	22	:	:	PUNCT
ejpam-3763	165	23	case	case	NOUN
ejpam-3763	165	24	1	1	NUM
ejpam-3763	165	25	:	:	PUNCT
ejpam-3763	165	26	suppose	suppose	VERB
ejpam-3763	165	27	that	that	SCONJ
ejpam-3763	165	28	v2	v2	VERB
ejpam-3763	165	29	⊆	⊆	NUM
ejpam-3763	165	30	v	v	NOUN
ejpam-3763	165	31	(	(	PUNCT
ejpam-3763	165	32	g	g	NOUN
ejpam-3763	165	33	)	)	PUNCT
ejpam-3763	165	34	.	.	PUNCT
ejpam-3763	166	1	if	if	SCONJ
ejpam-3763	166	2	v0	v0	NOUN
ejpam-3763	166	3	⊆	⊆	NUM
ejpam-3763	166	4	v	v	NOUN
ejpam-3763	166	5	(	(	PUNCT
ejpam-3763	166	6	g	g	NOUN
ejpam-3763	166	7	)	)	PUNCT
ejpam-3763	166	8	,	,	PUNCT
ejpam-3763	166	9	then	then	ADV
ejpam-3763	166	10	v	v	X
ejpam-3763	166	11	(	(	PUNCT
ejpam-3763	166	12	h	h	NOUN
ejpam-3763	166	13	)	)	PUNCT
ejpam-3763	166	14	⊆	⊆	NUM
ejpam-3763	166	15	v1	v1	NOUN
ejpam-3763	166	16	and	and	CCONJ
ejpam-3763	166	17	the	the	DET
ejpam-3763	166	18	restriction	restriction	NOUN
ejpam-3763	166	19	f	f	PROPN
ejpam-3763	166	20	|v	|v	PROPN
ejpam-3763	166	21	(	(	PUNCT
ejpam-3763	166	22	g	g	NOUN
ejpam-3763	166	23	)	)	PUNCT
ejpam-3763	166	24	=	=	SYM
ejpam-3763	166	25	(	(	PUNCT
ejpam-3763	166	26	v0	v0	NOUN
ejpam-3763	166	27	,	,	PUNCT
ejpam-3763	166	28	v1	v1	NOUN
ejpam-3763	166	29	∩	∩	ADJ
ejpam-3763	166	30	v	v	NOUN
ejpam-3763	166	31	(	(	PUNCT
ejpam-3763	166	32	g	g	NOUN
ejpam-3763	166	33	)	)	PUNCT
ejpam-3763	166	34	,	,	PUNCT
ejpam-3763	166	35	v2	v2	PROPN
ejpam-3763	166	36	)	)	PUNCT
ejpam-3763	166	37	of	of	ADP
ejpam-3763	166	38	f	f	PROPN
ejpam-3763	166	39	on	on	ADP
ejpam-3763	166	40	g	g	PROPN
ejpam-3763	166	41	is	be	AUX
ejpam-3763	166	42	a	a	DET
ejpam-3763	166	43	perfect	perfect	ADJ
ejpam-3763	166	44	dominating	dominating	NOUN
ejpam-3763	166	45	function	function	NOUN
ejpam-3763	166	46	on	on	ADP
ejpam-3763	166	47	g.	g.	PROPN
ejpam-3763	166	48	suppose	suppose	VERB
ejpam-3763	166	49	that	that	SCONJ
ejpam-3763	166	50	v0	v0	NOUN
ejpam-3763	166	51	∩	∩	NOUN
ejpam-3763	166	52	v	v	X
ejpam-3763	166	53	(	(	PUNCT
ejpam-3763	166	54	h	h	NOUN
ejpam-3763	166	55	)	)	PUNCT
ejpam-3763	166	56	6=	6=	ADP
ejpam-3763	166	57	∅.	∅.	ADP
ejpam-3763	166	58	then	then	ADV
ejpam-3763	166	59	,	,	PUNCT
ejpam-3763	166	60	|v2|	|v2|	NOUN
ejpam-3763	166	61	=	=	SYM
ejpam-3763	166	62	1	1	X
ejpam-3763	166	63	,	,	PUNCT
ejpam-3763	166	64	say	say	VERB
ejpam-3763	166	65	v2	v2	NOUN
ejpam-3763	166	66	=	=	SYM
ejpam-3763	166	67	{	{	PUNCT
ejpam-3763	166	68	v	v	NOUN
ejpam-3763	166	69	}	}	PUNCT
ejpam-3763	166	70	.	.	PUNCT
ejpam-3763	167	1	necessarily	necessarily	ADV
ejpam-3763	167	2	,	,	PUNCT
ejpam-3763	167	3	v0	v0	PROPN
ejpam-3763	167	4	∩	∩	ADJ
ejpam-3763	167	5	v	v	X
ejpam-3763	167	6	(	(	PUNCT
ejpam-3763	167	7	g	g	NOUN
ejpam-3763	167	8	)	)	PUNCT
ejpam-3763	167	9	⊆	⊆	NUM
ejpam-3763	167	10	ng(v	ng(v	NUM
ejpam-3763	167	11	)	)	PUNCT
ejpam-3763	167	12	.	.	PUNCT
ejpam-3763	168	1	case	case	NOUN
ejpam-3763	168	2	2	2	NUM
ejpam-3763	168	3	:	:	PUNCT
ejpam-3763	168	4	similarly	similarly	ADV
ejpam-3763	168	5	,	,	PUNCT
ejpam-3763	168	6	if	if	SCONJ
ejpam-3763	168	7	v2	v2	PROPN
ejpam-3763	168	8	⊆	⊆	NUM
ejpam-3763	168	9	v	v	NOUN
ejpam-3763	168	10	(	(	PUNCT
ejpam-3763	168	11	h	h	NOUN
ejpam-3763	168	12	)	)	PUNCT
ejpam-3763	168	13	,	,	PUNCT
ejpam-3763	168	14	then	then	ADV
ejpam-3763	168	15	either	either	CCONJ
ejpam-3763	168	16	(	(	PUNCT
ejpam-3763	168	17	ii)(a	ii)(a	PROPN
ejpam-3763	168	18	)	)	PUNCT
ejpam-3763	168	19	or	or	CCONJ
ejpam-3763	168	20	(	(	PUNCT
ejpam-3763	168	21	ii)(b	ii)(b	ADJ
ejpam-3763	168	22	)	)	PUNCT
ejpam-3763	168	23	holds	hold	VERB
ejpam-3763	168	24	.	.	PUNCT
ejpam-3763	169	1	case	case	NOUN
ejpam-3763	169	2	3	3	X
ejpam-3763	169	3	:	:	PUNCT
ejpam-3763	169	4	assume	assume	VERB
ejpam-3763	169	5	that	that	SCONJ
ejpam-3763	169	6	v2	v2	NOUN
ejpam-3763	169	7	intersects	intersect	NOUN
ejpam-3763	169	8	both	both	PRON
ejpam-3763	169	9	v	v	NOUN
ejpam-3763	169	10	(	(	PUNCT
ejpam-3763	169	11	g	g	NOUN
ejpam-3763	169	12	)	)	PUNCT
ejpam-3763	169	13	and	and	CCONJ
ejpam-3763	169	14	v	v	NOUN
ejpam-3763	169	15	(	(	PUNCT
ejpam-3763	169	16	h	h	NOUN
ejpam-3763	169	17	)	)	PUNCT
ejpam-3763	169	18	,	,	PUNCT
ejpam-3763	169	19	and	and	CCONJ
ejpam-3763	169	20	a1	a1	NOUN
ejpam-3763	169	21	=	=	SYM
ejpam-3763	169	22	v2	v2	PROPN
ejpam-3763	169	23	∩	∩	NOUN
ejpam-3763	169	24	v	v	NOUN
ejpam-3763	169	25	(	(	PUNCT
ejpam-3763	169	26	g	g	NOUN
ejpam-3763	169	27	)	)	PUNCT
ejpam-3763	169	28	and	and	CCONJ
ejpam-3763	169	29	a2	a2	PROPN
ejpam-3763	169	30	=	=	SYM
ejpam-3763	169	31	v2∩v	v2∩v	PROPN
ejpam-3763	169	32	(	(	PUNCT
ejpam-3763	169	33	h	h	NOUN
ejpam-3763	169	34	)	)	PUNCT
ejpam-3763	169	35	.	.	PUNCT
ejpam-3763	170	1	suppose	suppose	VERB
ejpam-3763	170	2	that	that	SCONJ
ejpam-3763	170	3	v0∩v	v0∩v	PROPN
ejpam-3763	170	4	(	(	PUNCT
ejpam-3763	170	5	g	g	NOUN
ejpam-3763	170	6	)	)	PUNCT
ejpam-3763	170	7	6=	6=	ADP
ejpam-3763	170	8	∅	∅	NOUN
ejpam-3763	170	9	,	,	PUNCT
ejpam-3763	170	10	and	and	CCONJ
ejpam-3763	170	11	let	let	VERB
ejpam-3763	170	12	v	v	NUM
ejpam-3763	170	13	∈	∈	NOUN
ejpam-3763	170	14	v0∩v	v0∩v	ADP
ejpam-3763	170	15	(	(	PUNCT
ejpam-3763	170	16	g	g	NOUN
ejpam-3763	170	17	)	)	PUNCT
ejpam-3763	170	18	.	.	PUNCT
ejpam-3763	171	1	since	since	SCONJ
ejpam-3763	171	2	a2	a2	PROPN
ejpam-3763	171	3	⊆	⊆	NUM
ejpam-3763	171	4	ng+h(v	ng+h(v	NOUN
ejpam-3763	171	5	)	)	PUNCT
ejpam-3763	171	6	,	,	PUNCT
ejpam-3763	171	7	|a2|	|a2|	NOUN
ejpam-3763	171	8	=	=	SYM
ejpam-3763	171	9	1	1	NUM
ejpam-3763	171	10	and	and	CCONJ
ejpam-3763	171	11	v	v	NOUN
ejpam-3763	171	12	/∈	/∈	PUNCT
ejpam-3763	171	13	ng(a1	ng(a1	NOUN
ejpam-3763	171	14	)	)	PUNCT
ejpam-3763	171	15	.	.	PUNCT
ejpam-3763	172	1	since	since	SCONJ
ejpam-3763	172	2	v	v	NOUN
ejpam-3763	172	3	is	be	AUX
ejpam-3763	172	4	arbitrary	arbitrary	ADJ
ejpam-3763	172	5	,	,	PUNCT
ejpam-3763	172	6	(	(	PUNCT
ejpam-3763	172	7	iii)(a	iii)(a	NOUN
ejpam-3763	172	8	)	)	PUNCT
ejpam-3763	172	9	holds	hold	VERB
ejpam-3763	172	10	.	.	PUNCT
ejpam-3763	173	1	similarly	similarly	ADV
ejpam-3763	173	2	,	,	PUNCT
ejpam-3763	173	3	(	(	PUNCT
ejpam-3763	173	4	iii)(b	iii)(b	ADJ
ejpam-3763	173	5	)	)	PUNCT
ejpam-3763	173	6	holds	hold	VERB
ejpam-3763	173	7	.	.	PUNCT
ejpam-3763	174	1	conversely	conversely	ADV
ejpam-3763	174	2	,	,	PUNCT
ejpam-3763	174	3	suppose	suppose	VERB
ejpam-3763	174	4	that	that	SCONJ
ejpam-3763	174	5	(	(	PUNCT
ejpam-3763	174	6	i)(a	i)(a	NOUN
ejpam-3763	174	7	)	)	PUNCT
ejpam-3763	174	8	holds	hold	VERB
ejpam-3763	174	9	for	for	ADP
ejpam-3763	174	10	f	f	PROPN
ejpam-3763	174	11	,	,	PUNCT
ejpam-3763	174	12	and	and	CCONJ
ejpam-3763	174	13	let	let	VERB
ejpam-3763	174	14	w	w	PROPN
ejpam-3763	174	15	∈	∈	PROPN
ejpam-3763	174	16	v0	v0	NOUN
ejpam-3763	174	17	.	.	PUNCT
ejpam-3763	175	1	then	then	ADV
ejpam-3763	175	2	w	w	PROPN
ejpam-3763	175	3	∈	∈	PROPN
ejpam-3763	175	4	v	v	ADP
ejpam-3763	175	5	(	(	PUNCT
ejpam-3763	175	6	g	g	NOUN
ejpam-3763	175	7	)	)	PUNCT
ejpam-3763	175	8	and	and	CCONJ
ejpam-3763	175	9	there	there	PRON
ejpam-3763	175	10	exists	exist	VERB
ejpam-3763	175	11	a	a	DET
ejpam-3763	175	12	unique	unique	ADJ
ejpam-3763	175	13	u	u	NOUN
ejpam-3763	175	14	∈	∈	NOUN
ejpam-3763	175	15	v2	v2	NOUN
ejpam-3763	175	16	for	for	ADP
ejpam-3763	175	17	which	which	PRON
ejpam-3763	175	18	uw	uw	PROPN
ejpam-3763	175	19	∈	∈	PROPN
ejpam-3763	175	20	e(g	e(g	PROPN
ejpam-3763	175	21	)	)	PUNCT
ejpam-3763	175	22	.	.	PUNCT
ejpam-3763	176	1	since	since	SCONJ
ejpam-3763	176	2	v	v	NOUN
ejpam-3763	176	3	(	(	PUNCT
ejpam-3763	176	4	h	h	NOUN
ejpam-3763	176	5	)	)	PUNCT
ejpam-3763	176	6	⊆	⊆	NUM
ejpam-3763	176	7	v1	v1	NOUN
ejpam-3763	176	8	,	,	PUNCT
ejpam-3763	176	9	u	u	NOUN
ejpam-3763	176	10	is	be	AUX
ejpam-3763	176	11	unique	unique	ADJ
ejpam-3763	176	12	in	in	ADP
ejpam-3763	176	13	v	v	NOUN
ejpam-3763	176	14	(	(	PUNCT
ejpam-3763	176	15	g+h	g+h	NOUN
ejpam-3763	176	16	)	)	PUNCT
ejpam-3763	176	17	for	for	ADP
ejpam-3763	176	18	l.	l.	PROPN
ejpam-3763	176	19	paleta	paleta	PROPN
ejpam-3763	176	20	,	,	PUNCT
ejpam-3763	176	21	f.	f.	PROPN
ejpam-3763	176	22	jamil	jamil	PROPN
ejpam-3763	176	23	/	/	SYM
ejpam-3763	176	24	eur	eur	PROPN
ejpam-3763	176	25	.	.	PUNCT
ejpam-3763	177	1	j.	j.	PROPN
ejpam-3763	177	2	pure	pure	PROPN
ejpam-3763	177	3	appl	appl	PROPN
ejpam-3763	177	4	.	.	PROPN
ejpam-3763	177	5	math	math	PROPN
ejpam-3763	177	6	,	,	PUNCT
ejpam-3763	177	7	13	13	NUM
ejpam-3763	177	8	(	(	PUNCT
ejpam-3763	177	9	3	3	NUM
ejpam-3763	177	10	)	)	PUNCT
ejpam-3763	177	11	(	(	PUNCT
ejpam-3763	177	12	2020	2020	NUM
ejpam-3763	177	13	)	)	PUNCT
ejpam-3763	177	14	,	,	PUNCT
ejpam-3763	177	15	529	529	NUM
ejpam-3763	177	16	-	-	SYM
ejpam-3763	177	17	548	548	NUM
ejpam-3763	177	18	534	534	NUM
ejpam-3763	177	19	which	which	PRON
ejpam-3763	177	20	uw	uw	PROPN
ejpam-3763	177	21	∈	∈	PROPN
ejpam-3763	177	22	e(g+h	e(g+h	NUM
ejpam-3763	177	23	)	)	PUNCT
ejpam-3763	177	24	.	.	PUNCT
ejpam-3763	178	1	this	this	PRON
ejpam-3763	178	2	means	mean	VERB
ejpam-3763	178	3	that	that	SCONJ
ejpam-3763	178	4	f	f	PROPN
ejpam-3763	178	5	∈	∈	PROPN
ejpam-3763	178	6	prd(g+h	prd(g+h	NOUN
ejpam-3763	178	7	)	)	PUNCT
ejpam-3763	178	8	.	.	PUNCT
ejpam-3763	179	1	suppose	suppose	VERB
ejpam-3763	179	2	that	that	SCONJ
ejpam-3763	179	3	(	(	PUNCT
ejpam-3763	179	4	i)(b	i)(b	NUM
ejpam-3763	179	5	)	)	PUNCT
ejpam-3763	179	6	holds	hold	VERB
ejpam-3763	179	7	for	for	ADP
ejpam-3763	179	8	f	f	PROPN
ejpam-3763	179	9	,	,	PUNCT
ejpam-3763	179	10	and	and	CCONJ
ejpam-3763	179	11	let	let	VERB
ejpam-3763	179	12	w	w	PROPN
ejpam-3763	179	13	∈	∈	PROPN
ejpam-3763	179	14	v0	v0	NOUN
ejpam-3763	179	15	.	.	PUNCT
ejpam-3763	180	1	whether	whether	SCONJ
ejpam-3763	180	2	w	w	PROPN
ejpam-3763	180	3	∈	∈	PROPN
ejpam-3763	180	4	v	v	ADP
ejpam-3763	180	5	(	(	PUNCT
ejpam-3763	180	6	g	g	NOUN
ejpam-3763	180	7	)	)	PUNCT
ejpam-3763	180	8	or	or	CCONJ
ejpam-3763	180	9	w	w	PROPN
ejpam-3763	180	10	∈	∈	PROPN
ejpam-3763	180	11	v	v	ADP
ejpam-3763	180	12	(	(	PUNCT
ejpam-3763	180	13	h	h	NOUN
ejpam-3763	180	14	)	)	PUNCT
ejpam-3763	180	15	,	,	PUNCT
ejpam-3763	180	16	v	v	NOUN
ejpam-3763	180	17	is	be	AUX
ejpam-3763	180	18	a	a	DET
ejpam-3763	180	19	unique	unique	ADJ
ejpam-3763	180	20	element	element	NOUN
ejpam-3763	180	21	in	in	ADP
ejpam-3763	180	22	v2	v2	PROPN
ejpam-3763	180	23	for	for	ADP
ejpam-3763	180	24	which	which	PRON
ejpam-3763	180	25	wv	wv	PROPN
ejpam-3763	180	26	∈	∈	PROPN
ejpam-3763	180	27	e(g	e(g	PROPN
ejpam-3763	180	28	+	+	CCONJ
ejpam-3763	180	29	h	h	NOUN
ejpam-3763	180	30	)	)	PUNCT
ejpam-3763	180	31	.	.	PUNCT
ejpam-3763	181	1	thus	thus	ADV
ejpam-3763	181	2	,	,	PUNCT
ejpam-3763	181	3	f	f	PROPN
ejpam-3763	181	4	∈	∈	PROPN
ejpam-3763	181	5	prd(g	prd(g	PROPN
ejpam-3763	181	6	+	+	CCONJ
ejpam-3763	181	7	h	h	NOUN
ejpam-3763	181	8	)	)	PUNCT
ejpam-3763	181	9	.	.	PUNCT
ejpam-3763	182	1	similarly	similarly	ADV
ejpam-3763	182	2	,	,	PUNCT
ejpam-3763	182	3	if	if	SCONJ
ejpam-3763	182	4	(	(	PUNCT
ejpam-3763	182	5	ii	ii	NOUN
ejpam-3763	182	6	)	)	PUNCT
ejpam-3763	182	7	holds	hold	VERB
ejpam-3763	182	8	,	,	PUNCT
ejpam-3763	182	9	the	the	DET
ejpam-3763	182	10	same	same	ADJ
ejpam-3763	182	11	conclusion	conclusion	NOUN
ejpam-3763	182	12	is	be	AUX
ejpam-3763	182	13	attained	attain	VERB
ejpam-3763	182	14	for	for	ADP
ejpam-3763	182	15	f	f	PROPN
ejpam-3763	182	16	.	.	PUNCT
ejpam-3763	183	1	suppose	suppose	VERB
ejpam-3763	183	2	now	now	ADV
ejpam-3763	183	3	that	that	SCONJ
ejpam-3763	183	4	(	(	PUNCT
ejpam-3763	183	5	iii	iii	NOUN
ejpam-3763	183	6	)	)	PUNCT
ejpam-3763	183	7	holds	hold	VERB
ejpam-3763	183	8	for	for	ADP
ejpam-3763	183	9	f	f	PROPN
ejpam-3763	183	10	.	.	PUNCT
ejpam-3763	184	1	let	let	VERB
ejpam-3763	184	2	v	v	NUM
ejpam-3763	184	3	∈	∈	PROPN
ejpam-3763	184	4	v0	v0	NOUN
ejpam-3763	184	5	.	.	PUNCT
ejpam-3763	185	1	if	if	SCONJ
ejpam-3763	185	2	v	v	NUM
ejpam-3763	185	3	∈	∈	PROPN
ejpam-3763	185	4	v	v	NOUN
ejpam-3763	185	5	(	(	PUNCT
ejpam-3763	185	6	g	g	NOUN
ejpam-3763	185	7	)	)	PUNCT
ejpam-3763	185	8	,	,	PUNCT
ejpam-3763	185	9	then	then	ADV
ejpam-3763	185	10	by	by	ADP
ejpam-3763	185	11	condition	condition	NOUN
ejpam-3763	185	12	(	(	PUNCT
ejpam-3763	185	13	a	a	NOUN
ejpam-3763	185	14	)	)	PUNCT
ejpam-3763	185	15	,	,	PUNCT
ejpam-3763	185	16	a2	a2	PROPN
ejpam-3763	185	17	=	=	SYM
ejpam-3763	185	18	{	{	PUNCT
ejpam-3763	185	19	u	u	NOUN
ejpam-3763	185	20	}	}	PUNCT
ejpam-3763	185	21	for	for	ADP
ejpam-3763	185	22	some	some	DET
ejpam-3763	185	23	u	u	PROPN
ejpam-3763	185	24	∈	∈	PROPN
ejpam-3763	185	25	v	v	ADP
ejpam-3763	185	26	(	(	PUNCT
ejpam-3763	185	27	h	h	NOUN
ejpam-3763	185	28	)	)	PUNCT
ejpam-3763	185	29	and	and	CCONJ
ejpam-3763	185	30	ng+h(v	ng+h(v	NUM
ejpam-3763	185	31	)	)	PUNCT
ejpam-3763	185	32	=	=	PRON
ejpam-3763	185	33	{	{	PUNCT
ejpam-3763	185	34	u	u	NOUN
ejpam-3763	185	35	}	}	PUNCT
ejpam-3763	185	36	.	.	PUNCT
ejpam-3763	186	1	similarly	similarly	ADV
ejpam-3763	186	2	,	,	PUNCT
ejpam-3763	186	3	if	if	SCONJ
ejpam-3763	186	4	v	v	NUM
ejpam-3763	186	5	∈	∈	PROPN
ejpam-3763	186	6	v	v	NOUN
ejpam-3763	186	7	(	(	PUNCT
ejpam-3763	186	8	h	h	NOUN
ejpam-3763	186	9	)	)	PUNCT
ejpam-3763	186	10	,	,	PUNCT
ejpam-3763	186	11	then	then	ADV
ejpam-3763	186	12	a1	a1	NOUN
ejpam-3763	186	13	=	=	SYM
ejpam-3763	186	14	{	{	PUNCT
ejpam-3763	186	15	u	u	NOUN
ejpam-3763	186	16	}	}	PUNCT
ejpam-3763	186	17	for	for	ADP
ejpam-3763	186	18	some	some	DET
ejpam-3763	186	19	u	u	NOUN
ejpam-3763	186	20	∈	∈	PROPN
ejpam-3763	186	21	v	v	ADP
ejpam-3763	186	22	(	(	PUNCT
ejpam-3763	186	23	g	g	NOUN
ejpam-3763	186	24	)	)	PUNCT
ejpam-3763	186	25	and	and	CCONJ
ejpam-3763	186	26	ng+h(v	ng+h(v	NUM
ejpam-3763	186	27	)	)	PUNCT
ejpam-3763	186	28	=	=	PRON
ejpam-3763	186	29	{	{	PUNCT
ejpam-3763	186	30	u	u	NOUN
ejpam-3763	186	31	}	}	PUNCT
ejpam-3763	186	32	.	.	PUNCT
ejpam-3763	187	1	accordingly	accordingly	ADV
ejpam-3763	187	2	,	,	PUNCT
ejpam-3763	187	3	f	f	PROPN
ejpam-3763	187	4	∈	∈	PROPN
ejpam-3763	187	5	prd(g+h	prd(g+h	NOUN
ejpam-3763	187	6	)	)	PUNCT
ejpam-3763	187	7	.	.	PUNCT
ejpam-3763	188	1	�	�	PROPN
ejpam-3763	188	2	we	we	PRON
ejpam-3763	188	3	now	now	ADV
ejpam-3763	188	4	use	use	VERB
ejpam-3763	188	5	theorem	theorem	ADJ
ejpam-3763	188	6	2.7	2.7	NUM
ejpam-3763	188	7	to	to	PART
ejpam-3763	188	8	prove	prove	VERB
ejpam-3763	188	9	the	the	DET
ejpam-3763	188	10	following	following	ADJ
ejpam-3763	188	11	result	result	NOUN
ejpam-3763	188	12	which	which	PRON
ejpam-3763	188	13	is	be	AUX
ejpam-3763	188	14	also	also	ADV
ejpam-3763	188	15	provided	provide	VERB
ejpam-3763	188	16	in	in	ADP
ejpam-3763	188	17	[	[	X
ejpam-3763	188	18	19	19	NUM
ejpam-3763	188	19	]	]	PUNCT
ejpam-3763	188	20	.	.	PUNCT
ejpam-3763	189	1	corollary	corollary	ADJ
ejpam-3763	189	2	2.8	2.8	NUM
ejpam-3763	189	3	.	.	PUNCT
ejpam-3763	190	1	[	[	X
ejpam-3763	190	2	19	19	NUM
ejpam-3763	190	3	]	]	PUNCT
ejpam-3763	190	4	let	let	VERB
ejpam-3763	190	5	gand	gand	PROPN
ejpam-3763	190	6	h	h	PROPN
ejpam-3763	190	7	be	be	AUX
ejpam-3763	190	8	nontrivial	nontrivial	ADJ
ejpam-3763	190	9	connected	connect	VERB
ejpam-3763	190	10	graphs	graph	NOUN
ejpam-3763	190	11	of	of	ADP
ejpam-3763	190	12	orders	order	NOUN
ejpam-3763	190	13	m	m	VERB
ejpam-3763	190	14	and	and	CCONJ
ejpam-3763	190	15	n	n	CCONJ
ejpam-3763	190	16	,	,	PUNCT
ejpam-3763	190	17	respectively	respectively	ADV
ejpam-3763	190	18	.	.	PUNCT
ejpam-3763	191	1	then	then	ADV
ejpam-3763	191	2	γpr(g+h	γpr(g+h	PUNCT
ejpam-3763	191	3	)	)	PUNCT
ejpam-3763	191	4	=	=	SYM
ejpam-3763	191	5	min{4	min{4	X
ejpam-3763	191	6	+	+	PUNCT
ejpam-3763	191	7	δ(g	δ(g	PROPN
ejpam-3763	191	8	)	)	PUNCT
ejpam-3763	192	1	+	+	NUM
ejpam-3763	192	2	δ(h),m+	δ(h),m+	PROPN
ejpam-3763	192	3	1−∆(g	1−∆(g	NUM
ejpam-3763	192	4	)	)	PUNCT
ejpam-3763	192	5	,	,	PUNCT
ejpam-3763	192	6	n+	n+	PUNCT
ejpam-3763	192	7	1−∆(h	1−∆(h	NUM
ejpam-3763	192	8	)	)	PUNCT
ejpam-3763	192	9	}	}	PUNCT
ejpam-3763	192	10	.	.	PUNCT
ejpam-3763	193	1	proof	proof	NOUN
ejpam-3763	193	2	:	:	PUNCT
ejpam-3763	193	3	let	let	VERB
ejpam-3763	193	4	α	α	NOUN
ejpam-3763	193	5	=	=	PUNCT
ejpam-3763	193	6	min{4	min{4	NOUN
ejpam-3763	193	7	+	+	PUNCT
ejpam-3763	193	8	δ(g	δ(g	ADV
ejpam-3763	193	9	)	)	PUNCT
ejpam-3763	193	10	+	+	CCONJ
ejpam-3763	193	11	δ(h),m	δ(h),m	ADJ
ejpam-3763	193	12	+	+	CCONJ
ejpam-3763	193	13	1	1	NUM
ejpam-3763	193	14	−∆(g	−∆(g	NOUN
ejpam-3763	193	15	)	)	PUNCT
ejpam-3763	193	16	,	,	PUNCT
ejpam-3763	193	17	n	n	PROPN
ejpam-3763	193	18	+	+	CCONJ
ejpam-3763	193	19	1	1	NUM
ejpam-3763	193	20	−∆(h	−∆(h	NOUN
ejpam-3763	193	21	)	)	PUNCT
ejpam-3763	193	22	}	}	PUNCT
ejpam-3763	193	23	.	.	PUNCT
ejpam-3763	194	1	let	let	VERB
ejpam-3763	194	2	v	v	NUM
ejpam-3763	194	3	∈	∈	PROPN
ejpam-3763	194	4	v	v	NOUN
ejpam-3763	194	5	(	(	PUNCT
ejpam-3763	194	6	g	g	NOUN
ejpam-3763	194	7	)	)	PUNCT
ejpam-3763	194	8	for	for	ADP
ejpam-3763	194	9	which	which	PRON
ejpam-3763	194	10	degg(v	degg(v	PROPN
ejpam-3763	194	11	)	)	PUNCT
ejpam-3763	194	12	=	=	SYM
ejpam-3763	194	13	∆(g	∆(g	PROPN
ejpam-3763	194	14	)	)	PUNCT
ejpam-3763	194	15	.	.	PUNCT
ejpam-3763	195	1	define	define	VERB
ejpam-3763	195	2	f	f	PROPN
ejpam-3763	195	3	=	=	SYM
ejpam-3763	195	4	(	(	PUNCT
ejpam-3763	195	5	v0	v0	PROPN
ejpam-3763	195	6	,	,	PUNCT
ejpam-3763	195	7	v1	v1	NOUN
ejpam-3763	195	8	,	,	PUNCT
ejpam-3763	195	9	v2	v2	PROPN
ejpam-3763	195	10	)	)	PUNCT
ejpam-3763	195	11	on	on	ADP
ejpam-3763	195	12	g+h	g+h	PROPN
ejpam-3763	195	13	by	by	ADP
ejpam-3763	195	14	f(x	f(x	PROPN
ejpam-3763	195	15	)	)	PUNCT
ejpam-3763	196	1	=	=	PUNCT
ejpam-3763	197	1			NOUN
ejpam-3763	197	2	2	2	NUM
ejpam-3763	197	3	,	,	PUNCT
ejpam-3763	197	4	if	if	SCONJ
ejpam-3763	197	5	x	x	X
ejpam-3763	197	6	=	=	SYM
ejpam-3763	197	7	v	v	NOUN
ejpam-3763	197	8	;	;	PUNCT
ejpam-3763	197	9	0	0	NUM
ejpam-3763	197	10	,	,	PUNCT
ejpam-3763	197	11	if	if	SCONJ
ejpam-3763	197	12	x	x	PROPN
ejpam-3763	197	13	∈	∈	PROPN
ejpam-3763	197	14	v	v	ADP
ejpam-3763	197	15	(	(	PUNCT
ejpam-3763	197	16	h	h	NOUN
ejpam-3763	197	17	)	)	PUNCT
ejpam-3763	197	18	∪ng(v	∪ng(v	NOUN
ejpam-3763	197	19	)	)	PUNCT
ejpam-3763	197	20	;	;	PUNCT
ejpam-3763	197	21	1	1	NUM
ejpam-3763	197	22	,	,	PUNCT
ejpam-3763	197	23	else	else	ADV
ejpam-3763	197	24	.	.	PUNCT
ejpam-3763	198	1	since	since	SCONJ
ejpam-3763	198	2	f	f	PROPN
ejpam-3763	198	3	satisfies	satisfy	VERB
ejpam-3763	198	4	condition	condition	NOUN
ejpam-3763	198	5	(	(	PUNCT
ejpam-3763	198	6	i)(b	i)(b	NUM
ejpam-3763	198	7	)	)	PUNCT
ejpam-3763	198	8	of	of	ADP
ejpam-3763	198	9	proposition	proposition	NOUN
ejpam-3763	198	10	2.7	2.7	NUM
ejpam-3763	198	11	,	,	PUNCT
ejpam-3763	198	12	f	f	X
ejpam-3763	198	13	=	=	SYM
ejpam-3763	198	14	(	(	PUNCT
ejpam-3763	198	15	v0	v0	PROPN
ejpam-3763	198	16	,	,	PUNCT
ejpam-3763	198	17	v1	v1	NOUN
ejpam-3763	198	18	,	,	PUNCT
ejpam-3763	198	19	v2	v2	NOUN
ejpam-3763	198	20	)	)	PUNCT
ejpam-3763	198	21	∈	∈	PROPN
ejpam-3763	198	22	prd(g+h	prd(g+h	NOUN
ejpam-3763	198	23	)	)	PUNCT
ejpam-3763	198	24	with	with	ADP
ejpam-3763	198	25	v2	v2	NOUN
ejpam-3763	198	26	=	=	SYM
ejpam-3763	198	27	{	{	PUNCT
ejpam-3763	198	28	v	v	NOUN
ejpam-3763	198	29	}	}	PUNCT
ejpam-3763	198	30	and	and	CCONJ
ejpam-3763	198	31	v1	v1	PROPN
ejpam-3763	198	32	=	=	SYM
ejpam-3763	198	33	v	v	NOUN
ejpam-3763	198	34	(	(	PUNCT
ejpam-3763	198	35	g	g	NOUN
ejpam-3763	198	36	)	)	PUNCT
ejpam-3763	198	37	\ng[v	\ng[v	NOUN
ejpam-3763	198	38	]	]	PUNCT
ejpam-3763	198	39	.	.	PUNCT
ejpam-3763	199	1	thus	thus	ADV
ejpam-3763	199	2	,	,	PUNCT
ejpam-3763	199	3	γpr(g+h	γpr(g+h	NOUN
ejpam-3763	199	4	)	)	PUNCT
ejpam-3763	199	5	≤	≤	NUM
ejpam-3763	199	6	ωg+h(f	ωg+h(f	PROPN
ejpam-3763	199	7	)	)	PUNCT
ejpam-3763	199	8	=	=	SYM
ejpam-3763	199	9	|v	|v	X
ejpam-3763	199	10	(	(	PUNCT
ejpam-3763	199	11	g	g	NOUN
ejpam-3763	199	12	)	)	PUNCT
ejpam-3763	199	13	\ng[v]|+	\ng[v]|+	PROPN
ejpam-3763	199	14	2	2	NUM
ejpam-3763	199	15	=	=	SYM
ejpam-3763	199	16	m+	m+	NUM
ejpam-3763	199	17	1−∆(g	1−∆(g	NUM
ejpam-3763	199	18	)	)	PUNCT
ejpam-3763	199	19	.	.	PUNCT
ejpam-3763	200	1	similarly	similarly	ADV
ejpam-3763	200	2	,	,	PUNCT
ejpam-3763	200	3	γpr(g+h	γpr(g+h	NOUN
ejpam-3763	200	4	)	)	PUNCT
ejpam-3763	200	5	≤	≤	NUM
ejpam-3763	200	6	n+	n+	PUNCT
ejpam-3763	200	7	1−∆(h	1−∆(h	NUM
ejpam-3763	200	8	)	)	PUNCT
ejpam-3763	200	9	.	.	PUNCT
ejpam-3763	201	1	now	now	ADV
ejpam-3763	201	2	,	,	PUNCT
ejpam-3763	201	3	pick	pick	VERB
ejpam-3763	201	4	u	u	PRON
ejpam-3763	201	5	∈	∈	PROPN
ejpam-3763	201	6	v	v	ADP
ejpam-3763	201	7	(	(	PUNCT
ejpam-3763	201	8	g	g	NOUN
ejpam-3763	201	9	)	)	PUNCT
ejpam-3763	201	10	and	and	CCONJ
ejpam-3763	201	11	v	v	ADP
ejpam-3763	201	12	∈	∈	PROPN
ejpam-3763	201	13	v	v	NOUN
ejpam-3763	201	14	(	(	PUNCT
ejpam-3763	201	15	h	h	NOUN
ejpam-3763	201	16	)	)	PUNCT
ejpam-3763	201	17	such	such	ADJ
ejpam-3763	201	18	that	that	DET
ejpam-3763	201	19	degg(u	degg(u	NOUN
ejpam-3763	201	20	)	)	PUNCT
ejpam-3763	201	21	=	=	PUNCT
ejpam-3763	201	22	δ(g	δ(g	X
ejpam-3763	201	23	)	)	PUNCT
ejpam-3763	201	24	and	and	CCONJ
ejpam-3763	201	25	degh(v	degh(v	PROPN
ejpam-3763	201	26	)	)	PUNCT
ejpam-3763	201	27	=	=	SYM
ejpam-3763	201	28	δ(h	δ(h	PROPN
ejpam-3763	201	29	)	)	PUNCT
ejpam-3763	201	30	,	,	PUNCT
ejpam-3763	201	31	and	and	CCONJ
ejpam-3763	201	32	define	define	VERB
ejpam-3763	201	33	f	f	PROPN
ejpam-3763	201	34	=	=	SYM
ejpam-3763	201	35	(	(	PUNCT
ejpam-3763	201	36	v0	v0	PROPN
ejpam-3763	201	37	,	,	PUNCT
ejpam-3763	201	38	v1	v1	NOUN
ejpam-3763	201	39	,	,	PUNCT
ejpam-3763	201	40	v2	v2	PROPN
ejpam-3763	201	41	)	)	PUNCT
ejpam-3763	201	42	on	on	ADP
ejpam-3763	201	43	g+h	g+h	PROPN
ejpam-3763	201	44	by	by	ADP
ejpam-3763	201	45	f(x	f(x	PROPN
ejpam-3763	201	46	)	)	PUNCT
ejpam-3763	202	1	=	=	PUNCT
ejpam-3763	203	1			NOUN
ejpam-3763	203	2	2	2	NUM
ejpam-3763	203	3	,	,	PUNCT
ejpam-3763	203	4	if	if	SCONJ
ejpam-3763	203	5	x	x	ADP
ejpam-3763	203	6	=	=	SYM
ejpam-3763	203	7	u	u	NOUN
ejpam-3763	203	8	,	,	PUNCT
ejpam-3763	203	9	v	v	NOUN
ejpam-3763	203	10	;	;	PUNCT
ejpam-3763	203	11	1	1	NUM
ejpam-3763	203	12	,	,	PUNCT
ejpam-3763	203	13	if	if	SCONJ
ejpam-3763	203	14	x	x	PROPN
ejpam-3763	203	15	∈	∈	PROPN
ejpam-3763	203	16	ng(u	ng(u	NOUN
ejpam-3763	203	17	)	)	PUNCT
ejpam-3763	203	18	∪nh(v	∪nh(v	PROPN
ejpam-3763	203	19	)	)	PUNCT
ejpam-3763	203	20	;	;	PUNCT
ejpam-3763	203	21	0	0	NUM
ejpam-3763	203	22	,	,	PUNCT
ejpam-3763	203	23	else	else	ADV
ejpam-3763	203	24	.	.	PUNCT
ejpam-3763	204	1	since	since	SCONJ
ejpam-3763	204	2	f	f	PROPN
ejpam-3763	204	3	satisfies	satisfie	NOUN
ejpam-3763	204	4	proposition	proposition	VERB
ejpam-3763	204	5	2.7	2.7	NUM
ejpam-3763	204	6	(	(	PUNCT
ejpam-3763	204	7	iii	iii	NOUN
ejpam-3763	204	8	)	)	PUNCT
ejpam-3763	204	9	,	,	PUNCT
ejpam-3763	204	10	f	f	PROPN
ejpam-3763	204	11	∈	∈	PROPN
ejpam-3763	204	12	prd(g	prd(g	PROPN
ejpam-3763	204	13	+	+	CCONJ
ejpam-3763	204	14	h	h	NOUN
ejpam-3763	204	15	)	)	PUNCT
ejpam-3763	204	16	.	.	PUNCT
ejpam-3763	205	1	since	since	SCONJ
ejpam-3763	205	2	v2	v2	PROPN
ejpam-3763	205	3	=	=	SYM
ejpam-3763	205	4	{	{	PUNCT
ejpam-3763	205	5	u	u	NOUN
ejpam-3763	205	6	,	,	PUNCT
ejpam-3763	205	7	v	v	NOUN
ejpam-3763	205	8	}	}	PUNCT
ejpam-3763	205	9	and	and	CCONJ
ejpam-3763	205	10	v1	v1	PROPN
ejpam-3763	205	11	=	=	SYM
ejpam-3763	205	12	ng(u	ng(u	X
ejpam-3763	205	13	)	)	PUNCT
ejpam-3763	205	14	∪nh(v	∪nh(v	NOUN
ejpam-3763	205	15	)	)	PUNCT
ejpam-3763	205	16	,	,	PUNCT
ejpam-3763	205	17	γpr(g+h	γpr(g+h	NOUN
ejpam-3763	205	18	)	)	PUNCT
ejpam-3763	205	19	≤	≤	NUM
ejpam-3763	205	20	ωg+h(f	ωg+h(f	PROPN
ejpam-3763	205	21	)	)	PUNCT
ejpam-3763	205	22	=	=	SYM
ejpam-3763	205	23	|ng(u	|ng(u	X
ejpam-3763	205	24	)	)	PUNCT
ejpam-3763	205	25	∪nh(v)|+	∪nh(v)|+	VERB
ejpam-3763	205	26	4	4	NUM
ejpam-3763	205	27	=	=	SYM
ejpam-3763	205	28	4	4	NUM
ejpam-3763	205	29	+	+	NUM
ejpam-3763	205	30	δ(g	δ(g	X
ejpam-3763	205	31	)	)	PUNCT
ejpam-3763	205	32	+	+	CCONJ
ejpam-3763	205	33	δ(h	δ(h	NOUN
ejpam-3763	205	34	)	)	PUNCT
ejpam-3763	205	35	.	.	PUNCT
ejpam-3763	206	1	all	all	PRON
ejpam-3763	206	2	of	of	ADP
ejpam-3763	206	3	the	the	DET
ejpam-3763	206	4	above	above	ADJ
ejpam-3763	206	5	show	show	VERB
ejpam-3763	206	6	that	that	SCONJ
ejpam-3763	206	7	γpr(g+h	γpr(g+h	NOUN
ejpam-3763	206	8	)	)	PUNCT
ejpam-3763	206	9	≤	≤	NUM
ejpam-3763	207	1	α	α	X
ejpam-3763	207	2	.	.	PUNCT
ejpam-3763	208	1	now	now	ADV
ejpam-3763	208	2	,	,	PUNCT
ejpam-3763	208	3	let	let	VERB
ejpam-3763	208	4	f	f	PROPN
ejpam-3763	208	5	=	=	SYM
ejpam-3763	208	6	(	(	PUNCT
ejpam-3763	208	7	v0	v0	PROPN
ejpam-3763	208	8	,	,	PUNCT
ejpam-3763	208	9	v1	v1	NOUN
ejpam-3763	208	10	,	,	PUNCT
ejpam-3763	208	11	v2	v2	PROPN
ejpam-3763	208	12	)	)	PUNCT
ejpam-3763	208	13	be	be	AUX
ejpam-3763	208	14	a	a	DET
ejpam-3763	208	15	γpr	γpr	NOUN
ejpam-3763	208	16	-function	-function	NOUN
ejpam-3763	208	17	of	of	ADP
ejpam-3763	208	18	g	g	PROPN
ejpam-3763	208	19	+	+	CCONJ
ejpam-3763	208	20	h.	h.	NOUN
ejpam-3763	208	21	by	by	ADP
ejpam-3763	208	22	corollary	corollary	ADJ
ejpam-3763	208	23	2.3(ii	2.3(ii	NUM
ejpam-3763	208	24	)	)	PUNCT
ejpam-3763	208	25	,	,	PUNCT
ejpam-3763	208	26	since	since	SCONJ
ejpam-3763	208	27	m+	m+	NUM
ejpam-3763	208	28	n	n	CCONJ
ejpam-3763	208	29	≥	≥	NOUN
ejpam-3763	208	30	4	4	NUM
ejpam-3763	208	31	,	,	PUNCT
ejpam-3763	208	32	v2	v2	PROPN
ejpam-3763	208	33	6=	6=	ADP
ejpam-3763	208	34	∅.	∅.	PRON
ejpam-3763	208	35	assume	assume	VERB
ejpam-3763	208	36	a1	a1	NOUN
ejpam-3763	208	37	=	=	SYM
ejpam-3763	208	38	v2	v2	PROPN
ejpam-3763	208	39	∩	∩	NOUN
ejpam-3763	208	40	v	v	NOUN
ejpam-3763	208	41	(	(	PUNCT
ejpam-3763	208	42	g	g	NOUN
ejpam-3763	208	43	)	)	PUNCT
ejpam-3763	208	44	6=	6=	ADP
ejpam-3763	208	45	∅.	∅.	PROPN
ejpam-3763	208	46	we	we	PRON
ejpam-3763	208	47	consider	consider	VERB
ejpam-3763	208	48	two	two	NUM
ejpam-3763	208	49	cases	case	NOUN
ejpam-3763	208	50	:	:	PUNCT
ejpam-3763	208	51	l.	l.	PROPN
ejpam-3763	208	52	paleta	paleta	PROPN
ejpam-3763	208	53	,	,	PUNCT
ejpam-3763	208	54	f.	f.	PROPN
ejpam-3763	208	55	jamil	jamil	PROPN
ejpam-3763	208	56	/	/	SYM
ejpam-3763	208	57	eur	eur	PROPN
ejpam-3763	208	58	.	.	PUNCT
ejpam-3763	209	1	j.	j.	PROPN
ejpam-3763	209	2	pure	pure	PROPN
ejpam-3763	209	3	appl	appl	PROPN
ejpam-3763	209	4	.	.	PROPN
ejpam-3763	209	5	math	math	PROPN
ejpam-3763	209	6	,	,	PUNCT
ejpam-3763	209	7	13	13	NUM
ejpam-3763	209	8	(	(	PUNCT
ejpam-3763	209	9	3	3	NUM
ejpam-3763	209	10	)	)	PUNCT
ejpam-3763	209	11	(	(	PUNCT
ejpam-3763	209	12	2020	2020	NUM
ejpam-3763	209	13	)	)	PUNCT
ejpam-3763	209	14	,	,	PUNCT
ejpam-3763	209	15	529	529	NUM
ejpam-3763	209	16	-	-	SYM
ejpam-3763	209	17	548	548	NUM
ejpam-3763	209	18	535	535	NUM
ejpam-3763	209	19	case	case	NOUN
ejpam-3763	209	20	1	1	NUM
ejpam-3763	209	21	:	:	PUNCT
ejpam-3763	209	22	suppose	suppose	VERB
ejpam-3763	209	23	that	that	SCONJ
ejpam-3763	209	24	a2	a2	PROPN
ejpam-3763	209	25	=	=	SYM
ejpam-3763	209	26	v2	v2	PROPN
ejpam-3763	209	27	∩	∩	NOUN
ejpam-3763	209	28	v	v	NOUN
ejpam-3763	209	29	(	(	PUNCT
ejpam-3763	209	30	h	h	NOUN
ejpam-3763	209	31	)	)	PUNCT
ejpam-3763	209	32	=	=	PUNCT
ejpam-3763	209	33	∅.	∅.	NOUN
ejpam-3763	209	34	if	if	SCONJ
ejpam-3763	209	35	proposition	proposition	NOUN
ejpam-3763	209	36	2.7(i)(a	2.7(i)(a	NUM
ejpam-3763	209	37	)	)	PUNCT
ejpam-3763	209	38	holds	hold	VERB
ejpam-3763	209	39	for	for	ADP
ejpam-3763	209	40	f	f	PROPN
ejpam-3763	209	41	,	,	PUNCT
ejpam-3763	209	42	then	then	ADV
ejpam-3763	209	43	ωg+h(f	ωg+h(f	PROPN
ejpam-3763	209	44	)	)	PUNCT
ejpam-3763	209	45	≥	≥	NUM
ejpam-3763	209	46	n+	n+	NUM
ejpam-3763	209	47	γpr(g	γpr(g	PROPN
ejpam-3763	209	48	)	)	PUNCT
ejpam-3763	209	49	>	>	X
ejpam-3763	210	1	n	n	PRON
ejpam-3763	210	2	≥	≥	NUM
ejpam-3763	210	3	n+	n+	NUM
ejpam-3763	210	4	1−∆(h	1−∆(h	NUM
ejpam-3763	210	5	)	)	PUNCT
ejpam-3763	210	6	≥	≥	NOUN
ejpam-3763	210	7	α	α	NOUN
ejpam-3763	210	8	.	.	PUNCT
ejpam-3763	211	1	on	on	ADP
ejpam-3763	211	2	the	the	DET
ejpam-3763	211	3	other	other	ADJ
ejpam-3763	211	4	hand	hand	NOUN
ejpam-3763	211	5	,	,	PUNCT
ejpam-3763	211	6	if	if	SCONJ
ejpam-3763	211	7	proposition	proposition	NOUN
ejpam-3763	211	8	2.7(i)(b	2.7(i)(b	NUM
ejpam-3763	211	9	)	)	PUNCT
ejpam-3763	211	10	holds	hold	VERB
ejpam-3763	211	11	for	for	ADP
ejpam-3763	211	12	f	f	PROPN
ejpam-3763	211	13	,	,	PUNCT
ejpam-3763	211	14	then	then	ADV
ejpam-3763	211	15	ωg+h(f	ωg+h(f	VERB
ejpam-3763	211	16	)	)	PUNCT
ejpam-3763	211	17	≥	≥	NOUN
ejpam-3763	211	18	2	2	NUM
ejpam-3763	211	19	+	+	CCONJ
ejpam-3763	212	1	|v	|v	X
ejpam-3763	212	2	(	(	PUNCT
ejpam-3763	212	3	g	g	NOUN
ejpam-3763	212	4	)	)	PUNCT
ejpam-3763	212	5	\ng[v]|	\ng[v]|	NUM
ejpam-3763	212	6	≥	≥	NOUN
ejpam-3763	212	7	m+	m+	NUM
ejpam-3763	212	8	1−∆(g	1−∆(g	NUM
ejpam-3763	212	9	)	)	PUNCT
ejpam-3763	212	10	≥	≥	PROPN
ejpam-3763	212	11	α	α	NOUN
ejpam-3763	212	12	.	.	PUNCT
ejpam-3763	212	13	case	case	NOUN
ejpam-3763	212	14	2	2	NUM
ejpam-3763	212	15	:	:	PUNCT
ejpam-3763	212	16	suppose	suppose	VERB
ejpam-3763	212	17	that	that	SCONJ
ejpam-3763	212	18	a2	a2	PROPN
ejpam-3763	212	19	=	=	SYM
ejpam-3763	212	20	v2	v2	PROPN
ejpam-3763	212	21	∩	∩	NOUN
ejpam-3763	212	22	v	v	NOUN
ejpam-3763	212	23	(	(	PUNCT
ejpam-3763	212	24	h	h	NOUN
ejpam-3763	212	25	)	)	PUNCT
ejpam-3763	212	26	6=	6=	ADP
ejpam-3763	212	27	∅.	∅.	ADP
ejpam-3763	212	28	if	if	SCONJ
ejpam-3763	212	29	|a1|	|a1|	X
ejpam-3763	212	30	≥	≥	X
ejpam-3763	212	31	2	2	NUM
ejpam-3763	212	32	and	and	CCONJ
ejpam-3763	212	33	|a2|	|a2|	VERB
ejpam-3763	212	34	≥	≥	NOUN
ejpam-3763	212	35	2	2	NUM
ejpam-3763	212	36	,	,	PUNCT
ejpam-3763	212	37	then	then	ADV
ejpam-3763	212	38	v0	v0	NOUN
ejpam-3763	212	39	=	=	SYM
ejpam-3763	212	40	∅	∅	NOUN
ejpam-3763	212	41	and	and	CCONJ
ejpam-3763	212	42	γpr(g	γpr(g	PRON
ejpam-3763	212	43	+	+	CCONJ
ejpam-3763	212	44	h	h	X
ejpam-3763	212	45	)	)	PUNCT
ejpam-3763	212	46	>	>	X
ejpam-3763	212	47	m	m	PROPN
ejpam-3763	212	48	+	+	SYM
ejpam-3763	212	49	n	n	CCONJ
ejpam-3763	212	50	,	,	PUNCT
ejpam-3763	212	51	which	which	PRON
ejpam-3763	212	52	is	be	AUX
ejpam-3763	212	53	impossible	impossible	ADJ
ejpam-3763	212	54	.	.	PUNCT
ejpam-3763	213	1	assume	assume	VERB
ejpam-3763	213	2	that	that	SCONJ
ejpam-3763	213	3	|a2|	|a2|	NOUN
ejpam-3763	213	4	=	=	SYM
ejpam-3763	213	5	1	1	X
ejpam-3763	213	6	.	.	X
ejpam-3763	213	7	we	we	PRON
ejpam-3763	213	8	consider	consider	VERB
ejpam-3763	213	9	two	two	NUM
ejpam-3763	213	10	subcases	subcase	NOUN
ejpam-3763	213	11	.	.	PUNCT
ejpam-3763	214	1	first	first	ADV
ejpam-3763	214	2	,	,	PUNCT
ejpam-3763	214	3	suppose	suppose	VERB
ejpam-3763	214	4	that	that	SCONJ
ejpam-3763	214	5	|a1|	|a1|	NOUN
ejpam-3763	214	6	≥	≥	PROPN
ejpam-3763	214	7	2	2	NUM
ejpam-3763	214	8	.	.	PUNCT
ejpam-3763	214	9	then	then	ADV
ejpam-3763	214	10	v0∩v	v0∩v	PROPN
ejpam-3763	214	11	(	(	PUNCT
ejpam-3763	214	12	h	h	NOUN
ejpam-3763	214	13	)	)	PUNCT
ejpam-3763	214	14	=	=	NOUN
ejpam-3763	214	15	∅	∅	NOUN
ejpam-3763	214	16	,	,	PUNCT
ejpam-3763	214	17	and	and	CCONJ
ejpam-3763	214	18	since	since	SCONJ
ejpam-3763	214	19	f	f	PROPN
ejpam-3763	214	20	is	be	AUX
ejpam-3763	214	21	a	a	DET
ejpam-3763	214	22	γpr	γpr	ADJ
ejpam-3763	214	23	-function	-function	NOUN
ejpam-3763	214	24	of	of	ADP
ejpam-3763	214	25	g	g	NOUN
ejpam-3763	214	26	+	+	CCONJ
ejpam-3763	214	27	h	h	NOUN
ejpam-3763	214	28	,	,	PUNCT
ejpam-3763	214	29	v	v	ADJ
ejpam-3763	214	30	(	(	PUNCT
ejpam-3763	214	31	g	g	NOUN
ejpam-3763	214	32	)	)	PUNCT
ejpam-3763	214	33	\ng[a1	\ng[a1	X
ejpam-3763	214	34	]	]	PUNCT
ejpam-3763	214	35	⊆	⊆	NUM
ejpam-3763	214	36	v0	v0	NOUN
ejpam-3763	214	37	(	(	PUNCT
ejpam-3763	214	38	by	by	ADP
ejpam-3763	214	39	proposition	proposition	NOUN
ejpam-3763	214	40	2.1	2.1	NUM
ejpam-3763	214	41	)	)	PUNCT
ejpam-3763	214	42	and	and	CCONJ
ejpam-3763	214	43	ng(a1	ng(a1	NOUN
ejpam-3763	214	44	)	)	PUNCT
ejpam-3763	214	45	\	\	NOUN
ejpam-3763	214	46	a1	a1	NOUN
ejpam-3763	214	47	⊆	⊆	NUM
ejpam-3763	214	48	v1	v1	NOUN
ejpam-3763	214	49	.	.	PUNCT
ejpam-3763	215	1	this	this	PRON
ejpam-3763	215	2	means	mean	VERB
ejpam-3763	215	3	that	that	SCONJ
ejpam-3763	215	4	|v1|	|v1|	PROPN
ejpam-3763	215	5	≥	≥	X
ejpam-3763	215	6	|v	|v	PROPN
ejpam-3763	215	7	(	(	PUNCT
ejpam-3763	215	8	h	h	NOUN
ejpam-3763	215	9	)	)	PUNCT
ejpam-3763	215	10	\	\	PROPN
ejpam-3763	215	11	v2|+	v2|+	PROPN
ejpam-3763	215	12	|ng(a1	|ng(a1	NOUN
ejpam-3763	215	13	)	)	PUNCT
ejpam-3763	215	14	\a1|	\a1|	NOUN
ejpam-3763	215	15	so	so	SCONJ
ejpam-3763	215	16	that	that	PRON
ejpam-3763	215	17	ωg+h(f	ωg+h(f	X
ejpam-3763	215	18	)	)	PUNCT
ejpam-3763	215	19	=	=	SYM
ejpam-3763	215	20	(	(	PUNCT
ejpam-3763	215	21	n−	n−	NOUN
ejpam-3763	215	22	1	1	NUM
ejpam-3763	215	23	)	)	PUNCT
ejpam-3763	216	1	+	+	CCONJ
ejpam-3763	216	2	|ng(a1	|ng(a1	NOUN
ejpam-3763	216	3	)	)	PUNCT
ejpam-3763	216	4	\a1|+	\a1|+	NOUN
ejpam-3763	216	5	2|v2|	2|v2|	NUM
ejpam-3763	216	6	≥	≥	NOUN
ejpam-3763	216	7	n+	n+	ADP
ejpam-3763	216	8	5	5	NUM
ejpam-3763	216	9	>	>	PUNCT
ejpam-3763	216	10	n+	n+	NUM
ejpam-3763	216	11	1−∆(h	1−∆(h	NUM
ejpam-3763	216	12	)	)	PUNCT
ejpam-3763	216	13	.	.	PUNCT
ejpam-3763	217	1	finally	finally	ADV
ejpam-3763	217	2	,	,	PUNCT
ejpam-3763	217	3	suppose	suppose	VERB
ejpam-3763	217	4	that	that	SCONJ
ejpam-3763	217	5	|a1|	|a1|	X
ejpam-3763	217	6	=	=	SYM
ejpam-3763	217	7	1	1	X
ejpam-3763	217	8	.	.	PUNCT
ejpam-3763	218	1	let	let	VERB
ejpam-3763	218	2	a1	a1	NOUN
ejpam-3763	218	3	=	=	SYM
ejpam-3763	218	4	{	{	PUNCT
ejpam-3763	218	5	u	u	NOUN
ejpam-3763	218	6	}	}	PUNCT
ejpam-3763	218	7	and	and	CCONJ
ejpam-3763	218	8	a2	a2	PROPN
ejpam-3763	218	9	=	=	SYM
ejpam-3763	218	10	{	{	PUNCT
ejpam-3763	218	11	v	v	NOUN
ejpam-3763	218	12	}	}	PUNCT
ejpam-3763	218	13	for	for	ADP
ejpam-3763	218	14	some	some	DET
ejpam-3763	218	15	u	u	NOUN
ejpam-3763	218	16	∈	∈	PROPN
ejpam-3763	218	17	v	v	ADP
ejpam-3763	218	18	(	(	PUNCT
ejpam-3763	218	19	g	g	NOUN
ejpam-3763	218	20	)	)	PUNCT
ejpam-3763	218	21	and	and	CCONJ
ejpam-3763	218	22	v	v	ADP
ejpam-3763	218	23	∈	∈	PROPN
ejpam-3763	218	24	v	v	NOUN
ejpam-3763	218	25	(	(	PUNCT
ejpam-3763	218	26	h	h	NOUN
ejpam-3763	218	27	)	)	PUNCT
ejpam-3763	218	28	.	.	PUNCT
ejpam-3763	219	1	by	by	ADP
ejpam-3763	219	2	proposition	proposition	NOUN
ejpam-3763	219	3	2.1	2.1	NUM
ejpam-3763	219	4	,	,	PUNCT
ejpam-3763	219	5	f(x	f(x	PROPN
ejpam-3763	219	6	)	)	PUNCT
ejpam-3763	219	7	=	=	SYM
ejpam-3763	219	8	0	0	NUM
ejpam-3763	220	1	for	for	ADP
ejpam-3763	220	2	all	all	PRON
ejpam-3763	220	3	x	x	SYM
ejpam-3763	220	4	∈	∈	PROPN
ejpam-3763	220	5	v	v	NOUN
ejpam-3763	220	6	(	(	PUNCT
ejpam-3763	220	7	g+h	g+h	NOUN
ejpam-3763	220	8	)	)	PUNCT
ejpam-3763	220	9	\	\	PUNCT
ejpam-3763	221	1	(	(	PUNCT
ejpam-3763	221	2	ng[u	ng[u	PROPN
ejpam-3763	221	3	]	]	PUNCT
ejpam-3763	221	4	∪nh	∪nh	PROPN
ejpam-3763	222	1	[	[	X
ejpam-3763	222	2	v	v	X
ejpam-3763	222	3	]	]	X
ejpam-3763	222	4	)	)	PUNCT
ejpam-3763	222	5	.	.	PUNCT
ejpam-3763	223	1	thus	thus	ADV
ejpam-3763	223	2	,	,	PUNCT
ejpam-3763	223	3	ωg+h(f	ωg+h(f	PROPN
ejpam-3763	223	4	)	)	PUNCT
ejpam-3763	223	5	≥	≥	PROPN
ejpam-3763	223	6	2|a1	2|a1	NUM
ejpam-3763	223	7	∪a2|+	∪a2|+	PROPN
ejpam-3763	223	8	|ng(u	|ng(u	PROPN
ejpam-3763	223	9	)	)	PUNCT
ejpam-3763	223	10	∪nh(v)|	∪nh(v)|	NOUN
ejpam-3763	223	11	≥	≥	NOUN
ejpam-3763	223	12	4	4	NUM
ejpam-3763	223	13	+	+	PUNCT
ejpam-3763	223	14	δ(g	δ(g	PROPN
ejpam-3763	223	15	)	)	PUNCT
ejpam-3763	224	1	+	+	CCONJ
ejpam-3763	224	2	δ(h	δ(h	PROPN
ejpam-3763	224	3	)	)	PUNCT
ejpam-3763	224	4	≥	≥	NOUN
ejpam-3763	224	5	α	α	NOUN
ejpam-3763	224	6	.	.	PUNCT
ejpam-3763	225	1	all	all	DET
ejpam-3763	225	2	cases	case	NOUN
ejpam-3763	225	3	above	above	ADV
ejpam-3763	225	4	imply	imply	VERB
ejpam-3763	225	5	that	that	DET
ejpam-3763	225	6	γpr(g+h	γpr(g+h	NOUN
ejpam-3763	225	7	)	)	PUNCT
ejpam-3763	225	8	≥	≥	PROPN
ejpam-3763	225	9	α	α	X
ejpam-3763	225	10	.	.	PUNCT
ejpam-3763	225	11	�	�	PROPN
ejpam-3763	225	12	in	in	ADP
ejpam-3763	225	13	particular	particular	ADJ
ejpam-3763	225	14	,	,	PUNCT
ejpam-3763	225	15	if	if	SCONJ
ejpam-3763	225	16	m	m	PROPN
ejpam-3763	225	17	≥	≥	NOUN
ejpam-3763	225	18	n	n	CCONJ
ejpam-3763	225	19	,	,	PUNCT
ejpam-3763	225	20	then	then	ADV
ejpam-3763	225	21	γpr(pm	γpr(pm	NOUN
ejpam-3763	225	22	+	+	CCONJ
ejpam-3763	225	23	pn	pn	X
ejpam-3763	225	24	)	)	PUNCT
ejpam-3763	225	25	=	=	PRON
ejpam-3763	225	26	{	{	PUNCT
ejpam-3763	225	27	n−	n−	NOUN
ejpam-3763	225	28	1	1	NUM
ejpam-3763	225	29	,	,	PUNCT
ejpam-3763	225	30	if	if	SCONJ
ejpam-3763	225	31	n	n	PRON
ejpam-3763	225	32	≤	≤	ADV
ejpam-3763	225	33	6	6	NUM
ejpam-3763	225	34	;	;	PUNCT
ejpam-3763	225	35	6	6	NUM
ejpam-3763	225	36	,	,	PUNCT
ejpam-3763	225	37	if	if	SCONJ
ejpam-3763	225	38	n	n	PRON
ejpam-3763	225	39	≥	≥	NOUN
ejpam-3763	225	40	7	7	NUM
ejpam-3763	225	41	.	.	PUNCT
ejpam-3763	226	1	and	and	CCONJ
ejpam-3763	226	2	γpr(cm	γpr(cm	PRON
ejpam-3763	226	3	+	+	CCONJ
ejpam-3763	226	4	pn	pn	X
ejpam-3763	226	5	)	)	PUNCT
ejpam-3763	226	6	=	=	PRON
ejpam-3763	226	7	{	{	PUNCT
ejpam-3763	226	8	n−	n−	NOUN
ejpam-3763	226	9	1	1	NUM
ejpam-3763	226	10	,	,	PUNCT
ejpam-3763	226	11	if	if	SCONJ
ejpam-3763	226	12	n	n	PRON
ejpam-3763	226	13	≤	≤	ADV
ejpam-3763	226	14	7	7	NUM
ejpam-3763	226	15	;	;	PUNCT
ejpam-3763	226	16	7	7	NUM
ejpam-3763	226	17	,	,	PUNCT
ejpam-3763	226	18	if	if	SCONJ
ejpam-3763	226	19	n	n	PRON
ejpam-3763	226	20	≥	≥	NOUN
ejpam-3763	226	21	8	8	NUM
ejpam-3763	226	22	.	.	PUNCT
ejpam-3763	226	23	2.2	2.2	NUM
ejpam-3763	226	24	.	.	PUNCT
ejpam-3763	227	1	on	on	ADP
ejpam-3763	227	2	the	the	DET
ejpam-3763	227	3	corona	corona	NOUN
ejpam-3763	227	4	of	of	ADP
ejpam-3763	227	5	graphs	graph	NOUN
ejpam-3763	227	6	let	let	VERB
ejpam-3763	227	7	g	g	NOUN
ejpam-3763	227	8	and	and	CCONJ
ejpam-3763	227	9	h	h	NOUN
ejpam-3763	227	10	be	be	AUX
ejpam-3763	227	11	connected	connect	VERB
ejpam-3763	227	12	graphs	graph	NOUN
ejpam-3763	227	13	.	.	PUNCT
ejpam-3763	228	1	adapting	adapt	VERB
ejpam-3763	228	2	the	the	DET
ejpam-3763	228	3	notation	notation	NOUN
ejpam-3763	228	4	used	use	VERB
ejpam-3763	228	5	in	in	ADP
ejpam-3763	228	6	[	[	X
ejpam-3763	228	7	6	6	NUM
ejpam-3763	228	8	]	]	PUNCT
ejpam-3763	228	9	,	,	PUNCT
ejpam-3763	228	10	for	for	ADP
ejpam-3763	228	11	each	each	DET
ejpam-3763	228	12	v	v	NUM
ejpam-3763	228	13	∈	∈	PROPN
ejpam-3763	228	14	v	v	NOUN
ejpam-3763	228	15	(	(	PUNCT
ejpam-3763	228	16	g	g	NOUN
ejpam-3763	228	17	)	)	PUNCT
ejpam-3763	228	18	,	,	PUNCT
ejpam-3763	228	19	hv	hv	PROPN
ejpam-3763	228	20	denotes	denote	VERB
ejpam-3763	228	21	that	that	PRON
ejpam-3763	228	22	copy	copy	VERB
ejpam-3763	228	23	of	of	ADP
ejpam-3763	228	24	h	h	PRON
ejpam-3763	228	25	which	which	PRON
ejpam-3763	228	26	is	be	AUX
ejpam-3763	228	27	joined	join	VERB
ejpam-3763	228	28	with	with	ADP
ejpam-3763	228	29	v	v	NOUN
ejpam-3763	228	30	in	in	ADP
ejpam-3763	228	31	g	g	PROPN
ejpam-3763	228	32	◦	◦	NOUN
ejpam-3763	228	33	h.	h.	NOUN
ejpam-3763	228	34	in	in	ADP
ejpam-3763	228	35	case	case	NOUN
ejpam-3763	228	36	h	h	NOUN
ejpam-3763	228	37	=	=	PRON
ejpam-3763	228	38	{	{	PUNCT
ejpam-3763	228	39	x	x	NOUN
ejpam-3763	228	40	}	}	PUNCT
ejpam-3763	228	41	,	,	PUNCT
ejpam-3763	228	42	we	we	PRON
ejpam-3763	228	43	write	write	VERB
ejpam-3763	228	44	v	v	PROPN
ejpam-3763	228	45	(	(	PUNCT
ejpam-3763	228	46	hv	hv	NOUN
ejpam-3763	228	47	)	)	PUNCT
ejpam-3763	228	48	=	=	PRON
ejpam-3763	228	49	{	{	PUNCT
ejpam-3763	228	50	xv	xv	PROPN
ejpam-3763	228	51	}	}	PUNCT
ejpam-3763	228	52	.	.	PUNCT
ejpam-3763	229	1	then	then	ADV
ejpam-3763	229	2	v	v	X
ejpam-3763	229	3	(	(	PUNCT
ejpam-3763	229	4	g+h	g+h	NOUN
ejpam-3763	229	5	)	)	PUNCT
ejpam-3763	229	6	=	=	SYM
ejpam-3763	230	1	∪v∈v	∪v∈v	X
ejpam-3763	230	2	(	(	PUNCT
ejpam-3763	230	3	g)v	g)v	X
ejpam-3763	230	4	(	(	PUNCT
ejpam-3763	230	5	hv	hv	PROPN
ejpam-3763	230	6	+	+	PROPN
ejpam-3763	230	7	v	v	NOUN
ejpam-3763	230	8	)	)	PUNCT
ejpam-3763	230	9	,	,	PUNCT
ejpam-3763	230	10	where	where	SCONJ
ejpam-3763	230	11	hv	hv	PROPN
ejpam-3763	230	12	+	+	NOUN
ejpam-3763	230	13	v	v	NOUN
ejpam-3763	230	14	=	=	SYM
ejpam-3763	230	15	hv	hv	PROPN
ejpam-3763	230	16	+	+	PROPN
ejpam-3763	230	17	〈	〈	PROPN
ejpam-3763	230	18	v	v	NOUN
ejpam-3763	230	19	〉	〉	NOUN
ejpam-3763	230	20	.	.	PUNCT
ejpam-3763	231	1	it	it	PRON
ejpam-3763	231	2	is	be	AUX
ejpam-3763	231	3	worth	worth	ADJ
ejpam-3763	231	4	noting	note	VERB
ejpam-3763	231	5	that	that	SCONJ
ejpam-3763	231	6	k1	k1	NOUN
ejpam-3763	231	7	◦	◦	NOUN
ejpam-3763	231	8	h	h	NOUN
ejpam-3763	231	9	=	=	SYM
ejpam-3763	231	10	h	h	PROPN
ejpam-3763	232	1	+	+	NOUN
ejpam-3763	232	2	k1	k1	NOUN
ejpam-3763	232	3	for	for	ADP
ejpam-3763	232	4	any	any	DET
ejpam-3763	232	5	graph	graph	NOUN
ejpam-3763	232	6	h.	h.	NOUN
ejpam-3763	232	7	theorem	theorem	VERB
ejpam-3763	232	8	2.9	2.9	NUM
ejpam-3763	232	9	.	.	PUNCT
ejpam-3763	233	1	for	for	ADP
ejpam-3763	233	2	nontrivial	nontrivial	ADJ
ejpam-3763	233	3	connected	connect	VERB
ejpam-3763	233	4	graphs	graph	NOUN
ejpam-3763	233	5	g	g	ADP
ejpam-3763	233	6	of	of	ADP
ejpam-3763	233	7	order	order	NOUN
ejpam-3763	233	8	n	n	CCONJ
ejpam-3763	233	9	,	,	PUNCT
ejpam-3763	233	10	γpr(g	γpr(g	PROPN
ejpam-3763	233	11	◦	◦	NOUN
ejpam-3763	233	12	k1	k1	NOUN
ejpam-3763	233	13	)	)	PUNCT
ejpam-3763	233	14	=	=	SYM
ejpam-3763	233	15	min{ωg(f	min{ωg(f	NOUN
ejpam-3763	233	16	)	)	PUNCT
ejpam-3763	234	1	+	+	NUM
ejpam-3763	234	2	n−	n−	NOUN
ejpam-3763	234	3	|v2|	|v2|	ADV
ejpam-3763	234	4	:	:	PUNCT
ejpam-3763	235	1	f	f	X
ejpam-3763	235	2	=	=	SYM
ejpam-3763	235	3	(	(	PUNCT
ejpam-3763	235	4	v0	v0	PROPN
ejpam-3763	235	5	,	,	PUNCT
ejpam-3763	235	6	v1	v1	NOUN
ejpam-3763	235	7	,	,	PUNCT
ejpam-3763	235	8	v2	v2	NOUN
ejpam-3763	235	9	)	)	PUNCT
ejpam-3763	235	10	∈	∈	PROPN
ejpam-3763	235	11	prd(g	prd(g	PROPN
ejpam-3763	235	12	)	)	PUNCT
ejpam-3763	235	13	}	}	PUNCT
ejpam-3763	235	14	.	.	PUNCT
ejpam-3763	236	1	in	in	ADP
ejpam-3763	236	2	particular	particular	ADJ
ejpam-3763	236	3	,	,	PUNCT
ejpam-3763	236	4	γpr(kn	γpr(kn	NOUN
ejpam-3763	236	5	◦	◦	NOUN
ejpam-3763	236	6	k1	k1	NOUN
ejpam-3763	236	7	)	)	PUNCT
ejpam-3763	236	8	=	=	PUNCT
ejpam-3763	237	1	n+	n+	PUNCT
ejpam-3763	237	2	1	1	X
ejpam-3763	237	3	.	.	X
ejpam-3763	237	4	proof	proof	NOUN
ejpam-3763	237	5	:	:	PUNCT
ejpam-3763	237	6	write	write	VERB
ejpam-3763	237	7	h	h	NOUN
ejpam-3763	237	8	=	=	SYM
ejpam-3763	237	9	{	{	PUNCT
ejpam-3763	237	10	x	x	NOUN
ejpam-3763	237	11	}	}	PUNCT
ejpam-3763	237	12	,	,	PUNCT
ejpam-3763	237	13	and	and	CCONJ
ejpam-3763	237	14	put	put	VERB
ejpam-3763	237	15	α	α	NOUN
ejpam-3763	237	16	=	=	SYM
ejpam-3763	237	17	min{ωg(f	min{ωg(f	NOUN
ejpam-3763	237	18	)	)	PUNCT
ejpam-3763	238	1	+	+	NUM
ejpam-3763	238	2	n−	n−	NOUN
ejpam-3763	238	3	|v2|	|v2|	ADV
ejpam-3763	238	4	:	:	PUNCT
ejpam-3763	239	1	f	f	X
ejpam-3763	239	2	=	=	SYM
ejpam-3763	239	3	(	(	PUNCT
ejpam-3763	239	4	v0	v0	PROPN
ejpam-3763	239	5	,	,	PUNCT
ejpam-3763	239	6	v1	v1	NOUN
ejpam-3763	239	7	,	,	PUNCT
ejpam-3763	239	8	v2	v2	NOUN
ejpam-3763	239	9	)	)	PUNCT
ejpam-3763	239	10	∈	∈	PROPN
ejpam-3763	239	11	prd(g	prd(g	PROPN
ejpam-3763	239	12	)	)	PUNCT
ejpam-3763	239	13	}	}	PUNCT
ejpam-3763	239	14	.	.	PUNCT
ejpam-3763	240	1	let	let	VERB
ejpam-3763	240	2	f	f	PROPN
ejpam-3763	240	3	=	=	SYM
ejpam-3763	240	4	(	(	PUNCT
ejpam-3763	240	5	v0	v0	PROPN
ejpam-3763	240	6	,	,	PUNCT
ejpam-3763	240	7	v1	v1	NOUN
ejpam-3763	240	8	,	,	PUNCT
ejpam-3763	240	9	v2	v2	NOUN
ejpam-3763	240	10	)	)	PUNCT
ejpam-3763	240	11	∈	∈	PROPN
ejpam-3763	240	12	prd(g	prd(g	PROPN
ejpam-3763	240	13	)	)	PUNCT
ejpam-3763	240	14	.	.	PUNCT
ejpam-3763	241	1	define	define	VERB
ejpam-3763	241	2	f∗	f∗	NOUN
ejpam-3763	241	3	=	=	SYM
ejpam-3763	241	4	(	(	PUNCT
ejpam-3763	241	5	v	v	NOUN
ejpam-3763	241	6	∗0	∗0	PROPN
ejpam-3763	241	7	,	,	PUNCT
ejpam-3763	241	8	v	v	NOUN
ejpam-3763	241	9	∗	∗	NOUN
ejpam-3763	241	10	1	1	NUM
ejpam-3763	241	11	,	,	PUNCT
ejpam-3763	241	12	v	v	NOUN
ejpam-3763	241	13	∗	∗	NOUN
ejpam-3763	241	14	2	2	NUM
ejpam-3763	241	15	)	)	PUNCT
ejpam-3763	241	16	on	on	ADP
ejpam-3763	241	17	g	g	PROPN
ejpam-3763	241	18	◦	◦	NOUN
ejpam-3763	241	19	k1	k1	NOUN
ejpam-3763	241	20	by	by	ADP
ejpam-3763	241	21	f∗(z	f∗(z	NOUN
ejpam-3763	241	22	)	)	PUNCT
ejpam-3763	241	23	=	=	PUNCT
ejpam-3763	242	1			PROPN
ejpam-3763	242	2	f(z	f(z	PROPN
ejpam-3763	242	3	)	)	PUNCT
ejpam-3763	242	4	,	,	PUNCT
ejpam-3763	242	5	if	if	SCONJ
ejpam-3763	242	6	z	z	PROPN
ejpam-3763	242	7	∈	∈	PROPN
ejpam-3763	242	8	v	v	ADP
ejpam-3763	242	9	(	(	PUNCT
ejpam-3763	242	10	g	g	NOUN
ejpam-3763	242	11	)	)	PUNCT
ejpam-3763	242	12	;	;	PUNCT
ejpam-3763	242	13	1	1	X
ejpam-3763	242	14	,	,	PUNCT
ejpam-3763	242	15	if	if	SCONJ
ejpam-3763	242	16	z	z	NOUN
ejpam-3763	242	17	=	=	SYM
ejpam-3763	242	18	xv	xv	PROPN
ejpam-3763	242	19	for	for	ADP
ejpam-3763	242	20	some	some	DET
ejpam-3763	242	21	v	v	ADP
ejpam-3763	242	22	∈	∈	PROPN
ejpam-3763	242	23	v0	v0	NOUN
ejpam-3763	242	24	∪	∪	NOUN
ejpam-3763	242	25	v1	v1	NOUN
ejpam-3763	242	26	;	;	PUNCT
ejpam-3763	242	27	0	0	NUM
ejpam-3763	242	28	,	,	PUNCT
ejpam-3763	242	29	if	if	SCONJ
ejpam-3763	242	30	z	z	NOUN
ejpam-3763	242	31	=	=	SYM
ejpam-3763	242	32	xv	xv	PROPN
ejpam-3763	242	33	for	for	ADP
ejpam-3763	242	34	some	some	DET
ejpam-3763	242	35	v	v	ADP
ejpam-3763	242	36	∈	∈	PROPN
ejpam-3763	242	37	v2	v2	NOUN
ejpam-3763	242	38	.	.	PUNCT
ejpam-3763	242	39	l.	l.	PROPN
ejpam-3763	242	40	paleta	paleta	PROPN
ejpam-3763	242	41	,	,	PUNCT
ejpam-3763	242	42	f.	f.	PROPN
ejpam-3763	242	43	jamil	jamil	PROPN
ejpam-3763	242	44	/	/	SYM
ejpam-3763	242	45	eur	eur	PROPN
ejpam-3763	242	46	.	.	PUNCT
ejpam-3763	243	1	j.	j.	PROPN
ejpam-3763	243	2	pure	pure	PROPN
ejpam-3763	243	3	appl	appl	PROPN
ejpam-3763	243	4	.	.	PROPN
ejpam-3763	243	5	math	math	PROPN
ejpam-3763	243	6	,	,	PUNCT
ejpam-3763	243	7	13	13	NUM
ejpam-3763	243	8	(	(	PUNCT
ejpam-3763	243	9	3	3	NUM
ejpam-3763	243	10	)	)	PUNCT
ejpam-3763	243	11	(	(	PUNCT
ejpam-3763	243	12	2020	2020	NUM
ejpam-3763	243	13	)	)	PUNCT
ejpam-3763	243	14	,	,	PUNCT
ejpam-3763	243	15	529	529	NUM
ejpam-3763	243	16	-	-	SYM
ejpam-3763	243	17	548	548	NUM
ejpam-3763	243	18	536	536	NUM
ejpam-3763	243	19	then	then	ADV
ejpam-3763	243	20	f∗	f∗	PROPN
ejpam-3763	243	21	∈	∈	PROPN
ejpam-3763	243	22	prd(g	prd(g	PROPN
ejpam-3763	243	23	◦	◦	NOUN
ejpam-3763	243	24	k1	k1	NOUN
ejpam-3763	243	25	)	)	PUNCT
ejpam-3763	243	26	with	with	ADP
ejpam-3763	243	27	v	v	NUM
ejpam-3763	243	28	∗0	∗0	NOUN
ejpam-3763	243	29	=	=	SYM
ejpam-3763	243	30	v0	v0	NOUN
ejpam-3763	243	31	∪	∪	NOUN
ejpam-3763	243	32	{	{	PUNCT
ejpam-3763	243	33	xv	xv	NOUN
ejpam-3763	243	34	:	:	PUNCT
ejpam-3763	243	35	v	v	NUM
ejpam-3763	243	36	∈	∈	PROPN
ejpam-3763	243	37	v2	v2	PROPN
ejpam-3763	243	38	}	}	PUNCT
ejpam-3763	243	39	,	,	PUNCT
ejpam-3763	243	40	v	v	ADP
ejpam-3763	243	41	∗1	∗1	PROPN
ejpam-3763	243	42	=	=	SYM
ejpam-3763	243	43	v1	v1	NOUN
ejpam-3763	243	44	∪	∪	X
ejpam-3763	243	45	{	{	PUNCT
ejpam-3763	243	46	xv	xv	NOUN
ejpam-3763	243	47	:	:	PUNCT
ejpam-3763	243	48	v	v	NUM
ejpam-3763	243	49	∈	∈	PROPN
ejpam-3763	243	50	v0	v0	NOUN
ejpam-3763	243	51	∪	∪	X
ejpam-3763	243	52	v1	v1	PROPN
ejpam-3763	243	53	}	}	PUNCT
ejpam-3763	243	54	and	and	CCONJ
ejpam-3763	243	55	v	v	ADP
ejpam-3763	243	56	∗2	∗2	PROPN
ejpam-3763	243	57	=	=	SYM
ejpam-3763	243	58	v2	v2	PROPN
ejpam-3763	243	59	.	.	PUNCT
ejpam-3763	244	1	moreover	moreover	ADV
ejpam-3763	244	2	,	,	PUNCT
ejpam-3763	244	3	ωg	ωg	NOUN
ejpam-3763	244	4	◦	◦	NOUN
ejpam-3763	244	5	k1(f∗	k1(f∗	NOUN
ejpam-3763	244	6	)	)	PUNCT
ejpam-3763	244	7	=	=	PUNCT
ejpam-3763	245	1	ωg(f	ωg(f	X
ejpam-3763	245	2	)	)	PUNCT
ejpam-3763	246	1	+	+	CCONJ
ejpam-3763	246	2	n−	n−	NOUN
ejpam-3763	246	3	|v2|	|v2|	ADV
ejpam-3763	246	4	.	.	PUNCT
ejpam-3763	247	1	thus	thus	ADV
ejpam-3763	247	2	,	,	PUNCT
ejpam-3763	247	3	γpr(g	γpr(g	PROPN
ejpam-3763	247	4	◦	◦	NOUN
ejpam-3763	247	5	k1	k1	NOUN
ejpam-3763	247	6	)	)	PUNCT
ejpam-3763	247	7	≤	≤	NOUN
ejpam-3763	247	8	α	α	X
ejpam-3763	247	9	.	.	PUNCT
ejpam-3763	248	1	let	let	VERB
ejpam-3763	248	2	f	f	PROPN
ejpam-3763	248	3	=	=	SYM
ejpam-3763	248	4	(	(	PUNCT
ejpam-3763	248	5	v0	v0	PROPN
ejpam-3763	248	6	,	,	PUNCT
ejpam-3763	248	7	v1	v1	NOUN
ejpam-3763	248	8	,	,	PUNCT
ejpam-3763	248	9	v2	v2	PROPN
ejpam-3763	248	10	)	)	PUNCT
ejpam-3763	248	11	be	be	AUX
ejpam-3763	248	12	a	a	DET
ejpam-3763	248	13	γpr	γpr	NOUN
ejpam-3763	248	14	-function	-function	NOUN
ejpam-3763	248	15	on	on	ADP
ejpam-3763	248	16	g	g	PROPN
ejpam-3763	248	17	◦	◦	NOUN
ejpam-3763	248	18	k1	k1	NOUN
ejpam-3763	248	19	,	,	PUNCT
ejpam-3763	248	20	and	and	CCONJ
ejpam-3763	248	21	let	let	VERB
ejpam-3763	248	22	a	a	DET
ejpam-3763	248	23	denote	denote	NOUN
ejpam-3763	248	24	the	the	DET
ejpam-3763	248	25	set	set	NOUN
ejpam-3763	248	26	of	of	ADP
ejpam-3763	248	27	all	all	DET
ejpam-3763	248	28	u	u	PROPN
ejpam-3763	248	29	∈	∈	PROPN
ejpam-3763	248	30	v0	v0	NOUN
ejpam-3763	248	31	∩	∩	X
ejpam-3763	248	32	v	v	X
ejpam-3763	248	33	(	(	PUNCT
ejpam-3763	248	34	g	g	NOUN
ejpam-3763	248	35	)	)	PUNCT
ejpam-3763	248	36	for	for	ADP
ejpam-3763	248	37	which	which	PRON
ejpam-3763	248	38	uv	uv	NOUN
ejpam-3763	248	39	/∈	/∈	PROPN
ejpam-3763	248	40	e(g	e(g	PROPN
ejpam-3763	248	41	)	)	PUNCT
ejpam-3763	248	42	for	for	ADP
ejpam-3763	248	43	all	all	DET
ejpam-3763	248	44	v	v	NOUN
ejpam-3763	248	45	∈	∈	PROPN
ejpam-3763	248	46	v2	v2	NOUN
ejpam-3763	248	47	∩	∩	ADJ
ejpam-3763	248	48	v	v	NOUN
ejpam-3763	248	49	(	(	PUNCT
ejpam-3763	248	50	g	g	NOUN
ejpam-3763	248	51	)	)	PUNCT
ejpam-3763	248	52	.	.	PUNCT
ejpam-3763	249	1	then	then	ADV
ejpam-3763	249	2	for	for	ADP
ejpam-3763	249	3	each	each	DET
ejpam-3763	249	4	u	u	PROPN
ejpam-3763	249	5	∈	∈	PROPN
ejpam-3763	249	6	a	a	PRON
ejpam-3763	249	7	,	,	PUNCT
ejpam-3763	249	8	v2	v2	PROPN
ejpam-3763	249	9	∩ng	∩ng	PROPN
ejpam-3763	249	10	◦	◦	NOUN
ejpam-3763	249	11	k1(u	k1(u	NOUN
ejpam-3763	249	12	)	)	PUNCT
ejpam-3763	249	13	=	=	PRON
ejpam-3763	249	14	{	{	PUNCT
ejpam-3763	249	15	xu	xu	INTJ
ejpam-3763	249	16	}	}	PUNCT
ejpam-3763	249	17	.	.	PUNCT
ejpam-3763	250	1	define	define	VERB
ejpam-3763	250	2	f∗	f∗	NOUN
ejpam-3763	250	3	=	=	SYM
ejpam-3763	250	4	(	(	PUNCT
ejpam-3763	250	5	v	v	NOUN
ejpam-3763	250	6	∗0	∗0	PROPN
ejpam-3763	250	7	,	,	PUNCT
ejpam-3763	250	8	v	v	NOUN
ejpam-3763	250	9	∗	∗	NOUN
ejpam-3763	250	10	1	1	NUM
ejpam-3763	250	11	,	,	PUNCT
ejpam-3763	250	12	v	v	NOUN
ejpam-3763	250	13	∗	∗	NOUN
ejpam-3763	250	14	2	2	NUM
ejpam-3763	250	15	)	)	PUNCT
ejpam-3763	250	16	on	on	ADP
ejpam-3763	250	17	g	g	PROPN
ejpam-3763	250	18	◦	◦	NOUN
ejpam-3763	250	19	k1	k1	NOUN
ejpam-3763	250	20	by	by	ADP
ejpam-3763	250	21	f∗(z	f∗(z	NOUN
ejpam-3763	250	22	)	)	PUNCT
ejpam-3763	250	23	=	=	PUNCT
ejpam-3763	251	1			PROPN
ejpam-3763	251	2	f(z	f(z	PROPN
ejpam-3763	251	3	)	)	PUNCT
ejpam-3763	251	4	,	,	PUNCT
ejpam-3763	251	5	if	if	SCONJ
ejpam-3763	251	6	z	z	PROPN
ejpam-3763	251	7	∈	∈	PROPN
ejpam-3763	251	8	v	v	ADP
ejpam-3763	251	9	(	(	PUNCT
ejpam-3763	251	10	g	g	NOUN
ejpam-3763	251	11	)	)	PUNCT
ejpam-3763	251	12	\a	\a	ADJ
ejpam-3763	251	13	;	;	PUNCT
ejpam-3763	251	14	1	1	X
ejpam-3763	251	15	,	,	PUNCT
ejpam-3763	251	16	if	if	SCONJ
ejpam-3763	251	17	z	z	NOUN
ejpam-3763	251	18	∈	∈	VERB
ejpam-3763	251	19	a	a	DET
ejpam-3763	251	20	∪	∪	X
ejpam-3763	251	21	{	{	PUNCT
ejpam-3763	251	22	xu	xu	NOUN
ejpam-3763	251	23	:	:	PUNCT
ejpam-3763	251	24	u	u	PROPN
ejpam-3763	251	25	∈	∈	PROPN
ejpam-3763	251	26	(	(	PUNCT
ejpam-3763	251	27	v0	v0	NOUN
ejpam-3763	251	28	∪	∪	X
ejpam-3763	251	29	v1	v1	NOUN
ejpam-3763	251	30	)	)	PUNCT
ejpam-3763	251	31	∩	∩	ADJ
ejpam-3763	251	32	v	v	X
ejpam-3763	251	33	(	(	PUNCT
ejpam-3763	251	34	g	g	NOUN
ejpam-3763	251	35	)	)	PUNCT
ejpam-3763	251	36	}	}	PUNCT
ejpam-3763	251	37	;	;	PUNCT
ejpam-3763	251	38	0	0	X
ejpam-3763	251	39	,	,	PUNCT
ejpam-3763	251	40	if	if	SCONJ
ejpam-3763	251	41	z	z	PROPN
ejpam-3763	251	42	∈	∈	PROPN
ejpam-3763	251	43	{	{	PUNCT
ejpam-3763	251	44	xv	xv	NOUN
ejpam-3763	251	45	:	:	PUNCT
ejpam-3763	251	46	v	v	NUM
ejpam-3763	251	47	∈	∈	PROPN
ejpam-3763	251	48	v2	v2	PROPN
ejpam-3763	251	49	∩	∩	ADJ
ejpam-3763	251	50	v	v	NOUN
ejpam-3763	251	51	(	(	PUNCT
ejpam-3763	251	52	g	g	NOUN
ejpam-3763	251	53	)	)	PUNCT
ejpam-3763	251	54	}	}	PUNCT
ejpam-3763	251	55	.	.	PUNCT
ejpam-3763	252	1	then	then	ADV
ejpam-3763	252	2	f∗	f∗	PROPN
ejpam-3763	252	3	∈	∈	PROPN
ejpam-3763	252	4	prd(g	prd(g	PROPN
ejpam-3763	252	5	◦	◦	NOUN
ejpam-3763	252	6	k1	k1	PROPN
ejpam-3763	252	7	)	)	PUNCT
ejpam-3763	252	8	with	with	ADP
ejpam-3763	252	9	v	v	NUM
ejpam-3763	252	10	∗0	∗0	NOUN
ejpam-3763	252	11	=	=	SYM
ejpam-3763	252	12	(	(	PUNCT
ejpam-3763	252	13	(	(	PUNCT
ejpam-3763	252	14	v0	v0	NOUN
ejpam-3763	252	15	∩	∩	NOUN
ejpam-3763	252	16	v	v	X
ejpam-3763	252	17	(	(	PUNCT
ejpam-3763	252	18	g	g	NOUN
ejpam-3763	252	19	)	)	PUNCT
ejpam-3763	252	20	)	)	PUNCT
ejpam-3763	252	21	\a	\a	NUM
ejpam-3763	252	22	)	)	PUNCT
ejpam-3763	252	23	∪	∪	ADP
ejpam-3763	252	24	{	{	PUNCT
ejpam-3763	252	25	xu	xu	INTJ
ejpam-3763	252	26	:	:	PUNCT
ejpam-3763	252	27	u	u	PROPN
ejpam-3763	252	28	∈	∈	PROPN
ejpam-3763	252	29	v2	v2	PROPN
ejpam-3763	252	30	∩	∩	ADJ
ejpam-3763	252	31	v	v	NOUN
ejpam-3763	252	32	(	(	PUNCT
ejpam-3763	252	33	g	g	NOUN
ejpam-3763	252	34	)	)	PUNCT
ejpam-3763	252	35	}	}	PUNCT
ejpam-3763	252	36	,	,	PUNCT
ejpam-3763	252	37	v	v	ADP
ejpam-3763	252	38	∗1	∗1	PROPN
ejpam-3763	252	39	=	=	PUNCT
ejpam-3763	252	40	a	a	DET
ejpam-3763	252	41	∪	∪	ADJ
ejpam-3763	252	42	(	(	PUNCT
ejpam-3763	252	43	v1	v1	NOUN
ejpam-3763	252	44	∩	∩	ADJ
ejpam-3763	252	45	v	v	NOUN
ejpam-3763	252	46	(	(	PUNCT
ejpam-3763	252	47	g	g	NOUN
ejpam-3763	252	48	)	)	PUNCT
ejpam-3763	252	49	)	)	PUNCT
ejpam-3763	252	50	∪	∪	ADP
ejpam-3763	252	51	{	{	PUNCT
ejpam-3763	252	52	xu	xu	INTJ
ejpam-3763	252	53	:	:	PUNCT
ejpam-3763	252	54	u	u	PROPN
ejpam-3763	252	55	∈	∈	PROPN
ejpam-3763	252	56	(	(	PUNCT
ejpam-3763	252	57	v0	v0	NOUN
ejpam-3763	252	58	∪	∪	X
ejpam-3763	252	59	v1	v1	NOUN
ejpam-3763	252	60	)	)	PUNCT
ejpam-3763	252	61	∩	∩	ADJ
ejpam-3763	252	62	v	v	X
ejpam-3763	252	63	(	(	PUNCT
ejpam-3763	252	64	g	g	NOUN
ejpam-3763	252	65	)	)	PUNCT
ejpam-3763	252	66	}	}	PUNCT
ejpam-3763	252	67	and	and	CCONJ
ejpam-3763	252	68	v	v	ADP
ejpam-3763	252	69	∗2	∗2	PROPN
ejpam-3763	252	70	=	=	SYM
ejpam-3763	252	71	v2	v2	PROPN
ejpam-3763	252	72	∩	∩	NOUN
ejpam-3763	252	73	v	v	NOUN
ejpam-3763	252	74	(	(	PUNCT
ejpam-3763	252	75	g	g	NOUN
ejpam-3763	252	76	)	)	PUNCT
ejpam-3763	252	77	.	.	PUNCT
ejpam-3763	253	1	observe	observe	VERB
ejpam-3763	253	2	that	that	SCONJ
ejpam-3763	253	3	f(u	f(u	PROPN
ejpam-3763	253	4	)	)	PUNCT
ejpam-3763	253	5	+	+	NUM
ejpam-3763	254	1	f(xu	f(xu	NUM
ejpam-3763	254	2	)	)	PUNCT
ejpam-3763	254	3	=	=	SYM
ejpam-3763	254	4	2	2	NUM
ejpam-3763	254	5	=	=	SYM
ejpam-3763	254	6	f∗(u	f∗(u	PROPN
ejpam-3763	254	7	)	)	PUNCT
ejpam-3763	254	8	+	+	X
ejpam-3763	254	9	f∗(xu	f∗(xu	NOUN
ejpam-3763	254	10	)	)	PUNCT
ejpam-3763	254	11	for	for	ADP
ejpam-3763	254	12	each	each	DET
ejpam-3763	254	13	u	u	PROPN
ejpam-3763	254	14	∈	∈	PROPN
ejpam-3763	254	15	a	a	PRON
ejpam-3763	254	16	,	,	PUNCT
ejpam-3763	254	17	and	and	CCONJ
ejpam-3763	254	18	f(u	f(u	PROPN
ejpam-3763	254	19	)	)	PUNCT
ejpam-3763	254	20	+	+	NUM
ejpam-3763	254	21	f(xu	f(xu	NUM
ejpam-3763	254	22	)	)	PUNCT
ejpam-3763	254	23	≥	≥	NOUN
ejpam-3763	254	24	f∗(u	f∗(u	NUM
ejpam-3763	254	25	)	)	PUNCT
ejpam-3763	255	1	+	+	X
ejpam-3763	255	2	f∗(xu	f∗(xu	NOUN
ejpam-3763	255	3	)	)	PUNCT
ejpam-3763	255	4	for	for	ADP
ejpam-3763	255	5	each	each	DET
ejpam-3763	255	6	u	u	PROPN
ejpam-3763	255	7	∈	∈	PROPN
ejpam-3763	255	8	v	v	ADP
ejpam-3763	255	9	(	(	PUNCT
ejpam-3763	255	10	g	g	NOUN
ejpam-3763	255	11	)	)	PUNCT
ejpam-3763	255	12	\a	\a	ADJ
ejpam-3763	255	13	.	.	PUNCT
ejpam-3763	256	1	thus	thus	ADV
ejpam-3763	256	2	,	,	PUNCT
ejpam-3763	256	3	ωg	ωg	NOUN
ejpam-3763	256	4	◦	◦	NOUN
ejpam-3763	256	5	k1(f	k1(f	NOUN
ejpam-3763	256	6	)	)	PUNCT
ejpam-3763	256	7	=	=	SYM
ejpam-3763	256	8	∑	∑	PUNCT
ejpam-3763	257	1	u∈a	u∈a	PROPN
ejpam-3763	257	2	(	(	PUNCT
ejpam-3763	257	3	f(u	f(u	PROPN
ejpam-3763	257	4	)	)	PUNCT
ejpam-3763	257	5	+	+	NUM
ejpam-3763	257	6	f(xu	f(xu	NUM
ejpam-3763	257	7	)	)	PUNCT
ejpam-3763	257	8	)	)	PUNCT
ejpam-3763	258	1	+	+	CCONJ
ejpam-3763	258	2	∑	∑	PUNCT
ejpam-3763	258	3	v∈v	v∈v	NOUN
ejpam-3763	258	4	(	(	PUNCT
ejpam-3763	258	5	g)\a	g)\a	NOUN
ejpam-3763	258	6	(	(	PUNCT
ejpam-3763	258	7	f(u	f(u	PROPN
ejpam-3763	258	8	)	)	PUNCT
ejpam-3763	258	9	+	+	NUM
ejpam-3763	258	10	f(xu	f(xu	NUM
ejpam-3763	258	11	)	)	PUNCT
ejpam-3763	258	12	)	)	PUNCT
ejpam-3763	258	13	≥	≥	X
ejpam-3763	258	14	∑	∑	ADV
ejpam-3763	258	15	u∈a	u∈a	PROPN
ejpam-3763	258	16	(	(	PUNCT
ejpam-3763	258	17	f∗(u	f∗(u	NOUN
ejpam-3763	258	18	)	)	PUNCT
ejpam-3763	258	19	+	+	X
ejpam-3763	258	20	f∗(xu	f∗(xu	NOUN
ejpam-3763	258	21	)	)	PUNCT
ejpam-3763	258	22	)	)	PUNCT
ejpam-3763	259	1	+	+	CCONJ
ejpam-3763	259	2	∑	∑	PUNCT
ejpam-3763	259	3	u∈v	u∈v	NOUN
ejpam-3763	259	4	(	(	PUNCT
ejpam-3763	259	5	g)\a	g)\a	NOUN
ejpam-3763	259	6	(	(	PUNCT
ejpam-3763	259	7	f∗(u	f∗(u	NOUN
ejpam-3763	259	8	)	)	PUNCT
ejpam-3763	259	9	+	+	X
ejpam-3763	259	10	f∗(xu	f∗(xu	NOUN
ejpam-3763	259	11	)	)	PUNCT
ejpam-3763	259	12	)	)	PUNCT
ejpam-3763	260	1	=	=	PUNCT
ejpam-3763	260	2	ωg	ωg	NOUN
ejpam-3763	260	3	◦	◦	NOUN
ejpam-3763	260	4	k1(f∗	k1(f∗	NOUN
ejpam-3763	260	5	)	)	PUNCT
ejpam-3763	260	6	.	.	PUNCT
ejpam-3763	261	1	since	since	SCONJ
ejpam-3763	261	2	f	f	PROPN
ejpam-3763	261	3	is	be	AUX
ejpam-3763	261	4	a	a	DET
ejpam-3763	261	5	γpr	γpr	NOUN
ejpam-3763	261	6	-function	-function	NOUN
ejpam-3763	261	7	,	,	PUNCT
ejpam-3763	261	8	ωg	ωg	NOUN
ejpam-3763	261	9	◦	◦	NOUN
ejpam-3763	261	10	k1(f	k1(f	NOUN
ejpam-3763	261	11	)	)	PUNCT
ejpam-3763	261	12	=	=	SYM
ejpam-3763	261	13	ωg	ωg	NOUN
ejpam-3763	261	14	◦	◦	NOUN
ejpam-3763	261	15	k1(f∗	k1(f∗	NOUN
ejpam-3763	261	16	)	)	PUNCT
ejpam-3763	261	17	.	.	PUNCT
ejpam-3763	262	1	moreover	moreover	ADV
ejpam-3763	262	2	,	,	PUNCT
ejpam-3763	262	3	for	for	ADP
ejpam-3763	262	4	each	each	DET
ejpam-3763	262	5	u	u	PROPN
ejpam-3763	262	6	∈	∈	PROPN
ejpam-3763	262	7	v	v	ADP
ejpam-3763	262	8	∗0	∗0	PROPN
ejpam-3763	262	9	∩	∩	ADJ
ejpam-3763	262	10	v	v	ADP
ejpam-3763	262	11	(	(	PUNCT
ejpam-3763	262	12	g	g	NOUN
ejpam-3763	262	13	)	)	PUNCT
ejpam-3763	262	14	,	,	PUNCT
ejpam-3763	262	15	u	u	PROPN
ejpam-3763	262	16	∈	∈	PROPN
ejpam-3763	262	17	(	(	PUNCT
ejpam-3763	262	18	v0	v0	NOUN
ejpam-3763	262	19	∩	∩	NOUN
ejpam-3763	262	20	v	v	NOUN
ejpam-3763	262	21	(	(	PUNCT
ejpam-3763	262	22	g))\a	g))\a	PUNCT
ejpam-3763	262	23	so	so	SCONJ
ejpam-3763	262	24	that	that	SCONJ
ejpam-3763	262	25	there	there	PRON
ejpam-3763	262	26	exists	exist	VERB
ejpam-3763	262	27	a	a	DET
ejpam-3763	262	28	unique	unique	ADJ
ejpam-3763	262	29	v	v	ADP
ejpam-3763	262	30	∈	∈	NOUN
ejpam-3763	262	31	v2∩v	v2∩v	NOUN
ejpam-3763	262	32	(	(	PUNCT
ejpam-3763	262	33	g	g	NOUN
ejpam-3763	262	34	)	)	PUNCT
ejpam-3763	262	35	=	=	SYM
ejpam-3763	262	36	v	v	ADP
ejpam-3763	262	37	∗2	∗2	NOUN
ejpam-3763	262	38	such	such	ADJ
ejpam-3763	262	39	that	that	SCONJ
ejpam-3763	262	40	uv	uv	PROPN
ejpam-3763	262	41	∈	∈	PROPN
ejpam-3763	262	42	e(g	e(g	PROPN
ejpam-3763	262	43	)	)	PUNCT
ejpam-3763	262	44	.	.	PUNCT
ejpam-3763	263	1	this	this	PRON
ejpam-3763	263	2	means	mean	VERB
ejpam-3763	263	3	that	that	SCONJ
ejpam-3763	263	4	the	the	DET
ejpam-3763	263	5	restriction	restriction	NOUN
ejpam-3763	263	6	f∗|g	f∗|g	NOUN
ejpam-3763	263	7	of	of	ADP
ejpam-3763	263	8	f∗	f∗	NOUN
ejpam-3763	263	9	to	to	ADP
ejpam-3763	263	10	g	g	PROPN
ejpam-3763	263	11	is	be	AUX
ejpam-3763	263	12	a	a	DET
ejpam-3763	263	13	perfect	perfect	ADJ
ejpam-3763	263	14	roman	roman	ADJ
ejpam-3763	263	15	dominating	dominating	NOUN
ejpam-3763	263	16	function	function	NOUN
ejpam-3763	263	17	on	on	ADP
ejpam-3763	263	18	g.	g.	PROPN
ejpam-3763	263	19	thus	thus	ADV
ejpam-3763	263	20	,	,	PUNCT
ejpam-3763	263	21	γpr(g	γpr(g	PROPN
ejpam-3763	263	22	◦	◦	NOUN
ejpam-3763	263	23	k1	k1	NOUN
ejpam-3763	263	24	)	)	PUNCT
ejpam-3763	263	25	=	=	SYM
ejpam-3763	263	26	ωg	ωg	NOUN
ejpam-3763	263	27	◦	◦	NOUN
ejpam-3763	263	28	k1(f∗	k1(f∗	NOUN
ejpam-3763	263	29	)	)	PUNCT
ejpam-3763	263	30	=	=	SYM
ejpam-3763	263	31	ωg(f∗|g	ωg(f∗|g	PROPN
ejpam-3763	263	32	)	)	PUNCT
ejpam-3763	263	33	+	+	CCONJ
ejpam-3763	263	34	∑	∑	PUNCT
ejpam-3763	263	35	v∈v	v∈v	NOUN
ejpam-3763	263	36	(	(	PUNCT
ejpam-3763	263	37	g	g	NOUN
ejpam-3763	263	38	)	)	PUNCT
ejpam-3763	263	39	f∗(xv	f∗(xv	PROPN
ejpam-3763	263	40	)	)	PUNCT
ejpam-3763	263	41	=	=	SYM
ejpam-3763	263	42	ωg(f∗|g	ωg(f∗|g	PROPN
ejpam-3763	263	43	)	)	PUNCT
ejpam-3763	263	44	+	+	CCONJ
ejpam-3763	263	45	|	|	ADV
ejpam-3763	263	46	(	(	PUNCT
ejpam-3763	263	47	v0	v0	NOUN
ejpam-3763	263	48	∪	∪	X
ejpam-3763	263	49	v1	v1	NOUN
ejpam-3763	263	50	)	)	PUNCT
ejpam-3763	263	51	∩	∩	ADJ
ejpam-3763	263	52	v	v	X
ejpam-3763	263	53	(	(	PUNCT
ejpam-3763	263	54	g)|	g)|	NOUN
ejpam-3763	263	55	=	=	PUNCT
ejpam-3763	263	56	ωg(f∗|g	ωg(f∗|g	PROPN
ejpam-3763	263	57	)	)	PUNCT
ejpam-3763	263	58	+	+	NUM
ejpam-3763	263	59	n−	n−	NOUN
ejpam-3763	263	60	|v	|v	NOUN
ejpam-3763	263	61	∗2	∗2	PROPN
ejpam-3763	263	62	∩	∩	NOUN
ejpam-3763	263	63	v	v	X
ejpam-3763	263	64	(	(	PUNCT
ejpam-3763	263	65	g)|	g)|	PROPN
ejpam-3763	263	66	≥	≥	NUM
ejpam-3763	263	67	α	α	NOUN
ejpam-3763	263	68	.	.	PUNCT
ejpam-3763	263	69	�	�	PROPN
ejpam-3763	264	1	it	it	PRON
ejpam-3763	264	2	follows	follow	VERB
ejpam-3763	264	3	from	from	ADP
ejpam-3763	264	4	theorem	theorem	ADJ
ejpam-3763	264	5	2.9	2.9	NUM
ejpam-3763	264	6	that	that	PRON
ejpam-3763	264	7	for	for	ADP
ejpam-3763	264	8	all	all	DET
ejpam-3763	264	9	connected	connected	ADJ
ejpam-3763	264	10	graphs	graph	NOUN
ejpam-3763	264	11	g	g	ADP
ejpam-3763	264	12	of	of	ADP
ejpam-3763	264	13	order	order	NOUN
ejpam-3763	264	14	n	n	PRON
ejpam-3763	264	15	≥	≥	NOUN
ejpam-3763	264	16	2	2	NUM
ejpam-3763	264	17	,	,	PUNCT
ejpam-3763	264	18	γpr(g	γpr(g	PROPN
ejpam-3763	264	19	◦	◦	NOUN
ejpam-3763	264	20	k1	k1	NOUN
ejpam-3763	264	21	)	)	PUNCT
ejpam-3763	264	22	≤	≤	PUNCT
ejpam-3763	264	23	γpr(g	γpr(g	PROPN
ejpam-3763	264	24	)	)	PUNCT
ejpam-3763	265	1	+	+	CCONJ
ejpam-3763	265	2	n−	n−	NOUN
ejpam-3763	265	3	λ	λ	PROPN
ejpam-3763	265	4	,	,	PUNCT
ejpam-3763	265	5	where	where	SCONJ
ejpam-3763	265	6	λ	λ	X
ejpam-3763	265	7	=	=	SYM
ejpam-3763	265	8	max{|v2|	max{|v2|	PROPN
ejpam-3763	265	9	:	:	PUNCT
ejpam-3763	265	10	(	(	PUNCT
ejpam-3763	265	11	v0	v0	NOUN
ejpam-3763	265	12	,	,	PUNCT
ejpam-3763	265	13	v1	v1	NOUN
ejpam-3763	265	14	,	,	PUNCT
ejpam-3763	265	15	v2	v2	PROPN
ejpam-3763	265	16	)	)	PUNCT
ejpam-3763	265	17	is	be	AUX
ejpam-3763	265	18	a	a	DET
ejpam-3763	265	19	γpr	γpr	NOUN
ejpam-3763	265	20	-function	-function	NOUN
ejpam-3763	265	21	on	on	ADP
ejpam-3763	265	22	g	g	NOUN
ejpam-3763	265	23	}	}	PUNCT
ejpam-3763	265	24	,	,	PUNCT
ejpam-3763	265	25	and	and	CCONJ
ejpam-3763	265	26	this	this	DET
ejpam-3763	265	27	bound	bind	VERB
ejpam-3763	265	28	is	be	AUX
ejpam-3763	265	29	sharp	sharp	ADJ
ejpam-3763	265	30	.	.	PUNCT
ejpam-3763	266	1	verify	verify	VERB
ejpam-3763	266	2	that	that	PRON
ejpam-3763	266	3	equality	equality	NOUN
ejpam-3763	266	4	is	be	AUX
ejpam-3763	266	5	attained	attain	VERB
ejpam-3763	266	6	if	if	SCONJ
ejpam-3763	266	7	g	g	PROPN
ejpam-3763	266	8	is	be	AUX
ejpam-3763	266	9	a	a	DET
ejpam-3763	266	10	cycle	cycle	NOUN
ejpam-3763	266	11	cn	cn	NOUN
ejpam-3763	266	12	(	(	PUNCT
ejpam-3763	266	13	n	n	CCONJ
ejpam-3763	266	14	≥	≥	NOUN
ejpam-3763	266	15	3	3	NUM
ejpam-3763	266	16	)	)	PUNCT
ejpam-3763	266	17	,	,	PUNCT
ejpam-3763	266	18	a	a	DET
ejpam-3763	266	19	path	path	NOUN
ejpam-3763	266	20	pn	pn	PROPN
ejpam-3763	266	21	(	(	PUNCT
ejpam-3763	266	22	n	n	CCONJ
ejpam-3763	266	23	≥	≥	NOUN
ejpam-3763	266	24	2	2	NUM
ejpam-3763	266	25	)	)	PUNCT
ejpam-3763	266	26	,	,	PUNCT
ejpam-3763	266	27	or	or	CCONJ
ejpam-3763	266	28	any	any	DET
ejpam-3763	266	29	graph	graph	NOUN
ejpam-3763	266	30	with	with	ADP
ejpam-3763	266	31	γ(g	γ(g	PROPN
ejpam-3763	266	32	)	)	PUNCT
ejpam-3763	266	33	=	=	PUNCT
ejpam-3763	267	1	1	1	X
ejpam-3763	267	2	.	.	PUNCT
ejpam-3763	268	1	our	our	PRON
ejpam-3763	268	2	desired	desire	VERB
ejpam-3763	268	3	result	result	NOUN
ejpam-3763	268	4	for	for	ADP
ejpam-3763	268	5	more	more	ADJ
ejpam-3763	268	6	general	general	ADJ
ejpam-3763	268	7	graphs	graph	NOUN
ejpam-3763	268	8	g	g	NOUN
ejpam-3763	268	9	and	and	CCONJ
ejpam-3763	268	10	h	h	NOUN
ejpam-3763	268	11	will	will	AUX
ejpam-3763	268	12	follow	follow	VERB
ejpam-3763	268	13	from	from	ADP
ejpam-3763	268	14	the	the	DET
ejpam-3763	268	15	following	follow	VERB
ejpam-3763	268	16	characterization	characterization	NOUN
ejpam-3763	268	17	.	.	PUNCT
ejpam-3763	269	1	l.	l.	PROPN
ejpam-3763	269	2	paleta	paleta	PROPN
ejpam-3763	269	3	,	,	PUNCT
ejpam-3763	269	4	f.	f.	PROPN
ejpam-3763	269	5	jamil	jamil	PROPN
ejpam-3763	269	6	/	/	SYM
ejpam-3763	269	7	eur	eur	PROPN
ejpam-3763	269	8	.	.	PUNCT
ejpam-3763	270	1	j.	j.	PROPN
ejpam-3763	270	2	pure	pure	PROPN
ejpam-3763	270	3	appl	appl	PROPN
ejpam-3763	270	4	.	.	PROPN
ejpam-3763	270	5	math	math	PROPN
ejpam-3763	270	6	,	,	PUNCT
ejpam-3763	270	7	13	13	NUM
ejpam-3763	270	8	(	(	PUNCT
ejpam-3763	270	9	3	3	NUM
ejpam-3763	270	10	)	)	PUNCT
ejpam-3763	270	11	(	(	PUNCT
ejpam-3763	270	12	2020	2020	NUM
ejpam-3763	270	13	)	)	PUNCT
ejpam-3763	270	14	,	,	PUNCT
ejpam-3763	270	15	529	529	NUM
ejpam-3763	270	16	-	-	SYM
ejpam-3763	270	17	548	548	NUM
ejpam-3763	270	18	537	537	NUM
ejpam-3763	270	19	theorem	theorem	VERB
ejpam-3763	270	20	2.10	2.10	NUM
ejpam-3763	270	21	.	.	PUNCT
ejpam-3763	271	1	let	let	VERB
ejpam-3763	271	2	g	g	NOUN
ejpam-3763	271	3	and	and	CCONJ
ejpam-3763	271	4	h	h	NOUN
ejpam-3763	271	5	be	be	AUX
ejpam-3763	271	6	nontrivial	nontrivial	ADJ
ejpam-3763	271	7	graphs	graph	NOUN
ejpam-3763	271	8	with	with	ADP
ejpam-3763	271	9	g	g	NOUN
ejpam-3763	271	10	connected	connect	VERB
ejpam-3763	271	11	,	,	PUNCT
ejpam-3763	271	12	and	and	CCONJ
ejpam-3763	271	13	f	f	PROPN
ejpam-3763	271	14	=	=	SYM
ejpam-3763	271	15	(	(	PUNCT
ejpam-3763	271	16	v0	v0	PROPN
ejpam-3763	271	17	,	,	PUNCT
ejpam-3763	271	18	v1	v1	NOUN
ejpam-3763	271	19	,	,	PUNCT
ejpam-3763	271	20	v2	v2	PROPN
ejpam-3763	271	21	)	)	PUNCT
ejpam-3763	271	22	.	.	PUNCT
ejpam-3763	272	1	then	then	ADV
ejpam-3763	272	2	f	f	PROPN
ejpam-3763	272	3	∈	∈	PROPN
ejpam-3763	272	4	prd(g	prd(g	PROPN
ejpam-3763	272	5	◦	◦	NOUN
ejpam-3763	272	6	h	h	NOUN
ejpam-3763	272	7	)	)	PUNCT
ejpam-3763	272	8	if	if	SCONJ
ejpam-3763	272	9	and	and	CCONJ
ejpam-3763	272	10	only	only	ADV
ejpam-3763	272	11	if	if	SCONJ
ejpam-3763	272	12	the	the	DET
ejpam-3763	272	13	following	follow	VERB
ejpam-3763	272	14	holds	hold	VERB
ejpam-3763	272	15	:	:	PUNCT
ejpam-3763	272	16	(	(	PUNCT
ejpam-3763	272	17	i	i	NOUN
ejpam-3763	272	18	)	)	PUNCT
ejpam-3763	272	19	for	for	ADP
ejpam-3763	272	20	all	all	DET
ejpam-3763	272	21	v	v	PROPN
ejpam-3763	272	22	∈	∈	PROPN
ejpam-3763	272	23	v0	v0	NOUN
ejpam-3763	272	24	∩	∩	X
ejpam-3763	272	25	v	v	X
ejpam-3763	272	26	(	(	PUNCT
ejpam-3763	272	27	g	g	NOUN
ejpam-3763	272	28	)	)	PUNCT
ejpam-3763	272	29	either	either	CCONJ
ejpam-3763	272	30	(	(	PUNCT
ejpam-3763	272	31	a	a	X
ejpam-3763	272	32	)	)	PUNCT
ejpam-3763	272	33	v2∩ng(v	v2∩ng(v	PROPN
ejpam-3763	272	34	)	)	PUNCT
ejpam-3763	273	1	=	=	NOUN
ejpam-3763	273	2	∅	∅	NOUN
ejpam-3763	273	3	and	and	CCONJ
ejpam-3763	273	4	v2∩v	v2∩v	PROPN
ejpam-3763	273	5	(	(	PUNCT
ejpam-3763	273	6	hv	hv	PROPN
ejpam-3763	273	7	)	)	PUNCT
ejpam-3763	273	8	=	=	PRON
ejpam-3763	273	9	{	{	PUNCT
ejpam-3763	273	10	u	u	NOUN
ejpam-3763	273	11	}	}	PUNCT
ejpam-3763	273	12	with	with	ADP
ejpam-3763	273	13	u	u	NOUN
ejpam-3763	273	14	satisfying	satisfy	VERB
ejpam-3763	273	15	v0∩v	v0∩v	PROPN
ejpam-3763	273	16	(	(	PUNCT
ejpam-3763	273	17	hv	hv	PROPN
ejpam-3763	273	18	)	)	PUNCT
ejpam-3763	273	19	⊆	⊆	NUM
ejpam-3763	273	20	nhv(u	nhv(u	PROPN
ejpam-3763	273	21	)	)	PUNCT
ejpam-3763	273	22	;	;	PUNCT
ejpam-3763	273	23	or	or	CCONJ
ejpam-3763	273	24	(	(	PUNCT
ejpam-3763	273	25	b	b	NOUN
ejpam-3763	273	26	)	)	PUNCT
ejpam-3763	273	27	|v2	|v2	NOUN
ejpam-3763	274	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-3763	275	1	=	=	SYM
ejpam-3763	275	2	1	1	NUM
ejpam-3763	275	3	and	and	CCONJ
ejpam-3763	275	4	v	v	NOUN
ejpam-3763	275	5	(	(	PUNCT
ejpam-3763	275	6	hv	hv	PROPN
ejpam-3763	275	7	)	)	PUNCT
ejpam-3763	275	8	⊆	⊆	NUM
ejpam-3763	275	9	v1	v1	NOUN
ejpam-3763	275	10	;	;	PUNCT
ejpam-3763	275	11	(	(	PUNCT
ejpam-3763	275	12	ii	ii	NOUN
ejpam-3763	275	13	)	)	PUNCT
ejpam-3763	275	14	for	for	ADP
ejpam-3763	275	15	all	all	DET
ejpam-3763	275	16	v	v	ADP
ejpam-3763	275	17	∈	∈	NOUN
ejpam-3763	275	18	v1∩v	v1∩v	NOUN
ejpam-3763	275	19	(	(	PUNCT
ejpam-3763	275	20	g	g	NOUN
ejpam-3763	275	21	)	)	PUNCT
ejpam-3763	275	22	,	,	PUNCT
ejpam-3763	275	23	the	the	DET
ejpam-3763	275	24	restriction	restriction	NOUN
ejpam-3763	275	25	f	f	PROPN
ejpam-3763	275	26	|hv	|hv	NUM
ejpam-3763	275	27	of	of	ADP
ejpam-3763	275	28	f	f	PROPN
ejpam-3763	275	29	to	to	ADP
ejpam-3763	275	30	hv	hv	PROPN
ejpam-3763	275	31	is	be	AUX
ejpam-3763	275	32	a	a	DET
ejpam-3763	275	33	perfect	perfect	ADJ
ejpam-3763	275	34	roman	roman	ADJ
ejpam-3763	275	35	dominating	dominating	NOUN
ejpam-3763	275	36	function	function	NOUN
ejpam-3763	275	37	on	on	ADP
ejpam-3763	275	38	hv	hv	PROPN
ejpam-3763	275	39	;	;	PUNCT
ejpam-3763	275	40	(	(	PUNCT
ejpam-3763	275	41	iii	iii	NOUN
ejpam-3763	275	42	)	)	PUNCT
ejpam-3763	275	43	for	for	ADP
ejpam-3763	275	44	all	all	DET
ejpam-3763	275	45	v	v	NOUN
ejpam-3763	275	46	∈	∈	PROPN
ejpam-3763	275	47	v2	v2	NOUN
ejpam-3763	275	48	∩	∩	ADJ
ejpam-3763	275	49	v	v	NOUN
ejpam-3763	275	50	(	(	PUNCT
ejpam-3763	275	51	g	g	NOUN
ejpam-3763	275	52	)	)	PUNCT
ejpam-3763	275	53	for	for	ADP
ejpam-3763	275	54	which	which	PRON
ejpam-3763	275	55	v0	v0	NOUN
ejpam-3763	275	56	∩	∩	NOUN
ejpam-3763	275	57	v	v	X
ejpam-3763	275	58	(	(	PUNCT
ejpam-3763	275	59	hv	hv	PROPN
ejpam-3763	275	60	)	)	PUNCT
ejpam-3763	275	61	6=	6=	NOUN
ejpam-3763	275	62	∅	∅	NOUN
ejpam-3763	275	63	,	,	PUNCT
ejpam-3763	275	64	v0	v0	PROPN
ejpam-3763	275	65	∩nhv(v2	∩nhv(v2	PROPN
ejpam-3763	275	66	∩	∩	PROPN
ejpam-3763	275	67	v	v	PROPN
ejpam-3763	275	68	(	(	PUNCT
ejpam-3763	275	69	hv	hv	NOUN
ejpam-3763	275	70	)	)	PUNCT
ejpam-3763	275	71	)	)	PUNCT
ejpam-3763	276	1	=	=	PUNCT
ejpam-3763	276	2	∅.	∅.	PRON
ejpam-3763	276	3	proof	proof	NOUN
ejpam-3763	276	4	:	:	PUNCT
ejpam-3763	276	5	assume	assume	VERB
ejpam-3763	276	6	that	that	SCONJ
ejpam-3763	276	7	f	f	PROPN
ejpam-3763	276	8	∈	∈	PROPN
ejpam-3763	276	9	prd(g	prd(g	ADP
ejpam-3763	276	10	◦	◦	NOUN
ejpam-3763	276	11	h	h	NOUN
ejpam-3763	276	12	)	)	PUNCT
ejpam-3763	276	13	.	.	PUNCT
ejpam-3763	277	1	let	let	VERB
ejpam-3763	277	2	v	v	NUM
ejpam-3763	277	3	∈	∈	PROPN
ejpam-3763	277	4	v0	v0	NOUN
ejpam-3763	277	5	∩	∩	X
ejpam-3763	277	6	v	v	X
ejpam-3763	277	7	(	(	PUNCT
ejpam-3763	277	8	g	g	NOUN
ejpam-3763	277	9	)	)	PUNCT
ejpam-3763	277	10	.	.	PUNCT
ejpam-3763	278	1	then	then	ADV
ejpam-3763	278	2	there	there	PRON
ejpam-3763	278	3	exists	exist	VERB
ejpam-3763	278	4	a	a	DET
ejpam-3763	278	5	unique	unique	ADJ
ejpam-3763	278	6	u	u	NOUN
ejpam-3763	278	7	∈	∈	NOUN
ejpam-3763	278	8	v2	v2	NOUN
ejpam-3763	278	9	for	for	ADP
ejpam-3763	278	10	which	which	PRON
ejpam-3763	278	11	u	u	PROPN
ejpam-3763	278	12	∈	∈	PROPN
ejpam-3763	278	13	ng	ng	PROPN
ejpam-3763	278	14	◦	◦	NOUN
ejpam-3763	278	15	h(v	h(v	NOUN
ejpam-3763	278	16	)	)	PUNCT
ejpam-3763	279	1	=	=	SYM
ejpam-3763	279	2	v	v	X
ejpam-3763	279	3	(	(	PUNCT
ejpam-3763	279	4	hv)∪ng(v	hv)∪ng(v	PROPN
ejpam-3763	279	5	)	)	PUNCT
ejpam-3763	279	6	.	.	PUNCT
ejpam-3763	280	1	if	if	SCONJ
ejpam-3763	280	2	v2∩ng(v	v2∩ng(v	NOUN
ejpam-3763	280	3	)	)	PUNCT
ejpam-3763	281	1	=	=	NOUN
ejpam-3763	281	2	∅	∅	NOUN
ejpam-3763	281	3	,	,	PUNCT
ejpam-3763	281	4	then	then	ADV
ejpam-3763	281	5	v2∩v	v2∩v	PROPN
ejpam-3763	281	6	(	(	PUNCT
ejpam-3763	281	7	hv	hv	PROPN
ejpam-3763	281	8	)	)	PUNCT
ejpam-3763	281	9	=	=	PRON
ejpam-3763	281	10	{	{	PUNCT
ejpam-3763	281	11	u	u	NOUN
ejpam-3763	281	12	}	}	PUNCT
ejpam-3763	281	13	and	and	CCONJ
ejpam-3763	281	14	v0	v0	PROPN
ejpam-3763	281	15	∩	∩	ADJ
ejpam-3763	281	16	v	v	X
ejpam-3763	281	17	(	(	PUNCT
ejpam-3763	281	18	hv	hv	PROPN
ejpam-3763	281	19	)	)	PUNCT
ejpam-3763	281	20	⊆	⊆	NUM
ejpam-3763	281	21	nhv(u	nhv(u	PROPN
ejpam-3763	281	22	)	)	PUNCT
ejpam-3763	281	23	.	.	PUNCT
ejpam-3763	282	1	suppose	suppose	VERB
ejpam-3763	282	2	that	that	SCONJ
ejpam-3763	282	3	v2	v2	PROPN
ejpam-3763	282	4	∩	∩	NOUN
ejpam-3763	282	5	ng(v	ng(v	NUM
ejpam-3763	282	6	)	)	PUNCT
ejpam-3763	282	7	6=	6=	ADP
ejpam-3763	282	8	∅.	∅.	VERB
ejpam-3763	282	9	then	then	ADV
ejpam-3763	282	10	|v2	|v2	NOUN
ejpam-3763	282	11	∩	∩	PROPN
ejpam-3763	282	12	ng(v)|	ng(v)|	AUX
ejpam-3763	282	13	=	=	SYM
ejpam-3763	282	14	1	1	NUM
ejpam-3763	282	15	and	and	CCONJ
ejpam-3763	282	16	v2	v2	PROPN
ejpam-3763	282	17	∩v	∩v	NOUN
ejpam-3763	282	18	(	(	PUNCT
ejpam-3763	282	19	hv	hv	PROPN
ejpam-3763	282	20	)	)	PUNCT
ejpam-3763	282	21	=	=	NOUN
ejpam-3763	282	22	∅.	∅.	PRON
ejpam-3763	282	23	moreover	moreover	ADV
ejpam-3763	282	24	,	,	PUNCT
ejpam-3763	282	25	if	if	SCONJ
ejpam-3763	282	26	w	w	PROPN
ejpam-3763	282	27	∈	∈	PROPN
ejpam-3763	282	28	v0	v0	NOUN
ejpam-3763	282	29	∩v	∩v	NOUN
ejpam-3763	282	30	(	(	PUNCT
ejpam-3763	282	31	hv	hv	PROPN
ejpam-3763	282	32	)	)	PUNCT
ejpam-3763	282	33	,	,	PUNCT
ejpam-3763	282	34	then	then	ADV
ejpam-3763	282	35	there	there	PRON
ejpam-3763	282	36	exists	exist	VERB
ejpam-3763	282	37	a	a	DET
ejpam-3763	282	38	unique	unique	ADJ
ejpam-3763	282	39	z	z	NOUN
ejpam-3763	282	40	∈	∈	NOUN
ejpam-3763	282	41	v2	v2	PROPN
ejpam-3763	282	42	∩v	∩v	NOUN
ejpam-3763	282	43	(	(	PUNCT
ejpam-3763	282	44	hv	hv	X
ejpam-3763	282	45	)	)	PUNCT
ejpam-3763	282	46	such	such	ADJ
ejpam-3763	282	47	that	that	SCONJ
ejpam-3763	282	48	wz	wz	ADP
ejpam-3763	282	49	∈	∈	PROPN
ejpam-3763	282	50	e(hv	e(hv	PROPN
ejpam-3763	282	51	)	)	PUNCT
ejpam-3763	282	52	.	.	PUNCT
ejpam-3763	283	1	since	since	SCONJ
ejpam-3763	283	2	vz	vz	PROPN
ejpam-3763	283	3	∈	∈	PROPN
ejpam-3763	283	4	e(g	e(g	PROPN
ejpam-3763	283	5	◦	◦	PROPN
ejpam-3763	283	6	h	h	NOUN
ejpam-3763	283	7	)	)	PUNCT
ejpam-3763	283	8	,	,	PUNCT
ejpam-3763	283	9	this	this	PRON
ejpam-3763	283	10	is	be	AUX
ejpam-3763	283	11	impossible	impossible	ADJ
ejpam-3763	283	12	.	.	PUNCT
ejpam-3763	284	1	thus	thus	ADV
ejpam-3763	284	2	,	,	PUNCT
ejpam-3763	284	3	v	v	INTJ
ejpam-3763	284	4	(	(	PUNCT
ejpam-3763	284	5	hv	hv	PROPN
ejpam-3763	284	6	)	)	PUNCT
ejpam-3763	284	7	⊆	⊆	NUM
ejpam-3763	284	8	v1	v1	NOUN
ejpam-3763	284	9	.	.	PUNCT
ejpam-3763	285	1	this	this	PRON
ejpam-3763	285	2	proves	prove	VERB
ejpam-3763	285	3	(	(	PUNCT
ejpam-3763	285	4	i	i	NOUN
ejpam-3763	285	5	)	)	PUNCT
ejpam-3763	285	6	.	.	PUNCT
ejpam-3763	286	1	next	next	ADV
ejpam-3763	286	2	,	,	PUNCT
ejpam-3763	286	3	let	let	VERB
ejpam-3763	286	4	v	v	NUM
ejpam-3763	286	5	∈	∈	NOUN
ejpam-3763	286	6	v1	v1	NOUN
ejpam-3763	286	7	∩	∩	ADJ
ejpam-3763	286	8	v	v	NOUN
ejpam-3763	286	9	(	(	PUNCT
ejpam-3763	286	10	g	g	NOUN
ejpam-3763	286	11	)	)	PUNCT
ejpam-3763	286	12	,	,	PUNCT
ejpam-3763	286	13	and	and	CCONJ
ejpam-3763	286	14	let	let	VERB
ejpam-3763	286	15	w	w	PROPN
ejpam-3763	286	16	∈	∈	PROPN
ejpam-3763	286	17	v0	v0	NOUN
ejpam-3763	286	18	∩	∩	X
ejpam-3763	286	19	v	v	X
ejpam-3763	286	20	(	(	PUNCT
ejpam-3763	286	21	hv	hv	PROPN
ejpam-3763	286	22	)	)	PUNCT
ejpam-3763	286	23	.	.	PUNCT
ejpam-3763	287	1	since	since	SCONJ
ejpam-3763	287	2	f	f	PROPN
ejpam-3763	287	3	is	be	AUX
ejpam-3763	287	4	a	a	DET
ejpam-3763	287	5	perfect	perfect	ADJ
ejpam-3763	287	6	roman	roman	ADJ
ejpam-3763	287	7	dominating	dominating	NOUN
ejpam-3763	287	8	function	function	NOUN
ejpam-3763	287	9	,	,	PUNCT
ejpam-3763	287	10	there	there	PRON
ejpam-3763	287	11	exists	exist	VERB
ejpam-3763	287	12	unique	unique	ADJ
ejpam-3763	287	13	u	u	NOUN
ejpam-3763	287	14	∈	∈	NOUN
ejpam-3763	287	15	v2	v2	NOUN
ejpam-3763	287	16	for	for	ADP
ejpam-3763	287	17	which	which	PRON
ejpam-3763	287	18	uw	uw	PROPN
ejpam-3763	287	19	∈	∈	PROPN
ejpam-3763	287	20	e(g	e(g	PROPN
ejpam-3763	287	21	◦	◦	NOUN
ejpam-3763	287	22	h	h	NOUN
ejpam-3763	287	23	)	)	PUNCT
ejpam-3763	287	24	.	.	PUNCT
ejpam-3763	288	1	since	since	SCONJ
ejpam-3763	288	2	v	v	NUM
ejpam-3763	288	3	∈	∈	PROPN
ejpam-3763	288	4	v1	v1	NOUN
ejpam-3763	288	5	,	,	PUNCT
ejpam-3763	288	6	u	u	PROPN
ejpam-3763	288	7	∈	∈	PROPN
ejpam-3763	288	8	v2	v2	PROPN
ejpam-3763	288	9	∩v	∩v	NOUN
ejpam-3763	288	10	(	(	PUNCT
ejpam-3763	288	11	hv	hv	PROPN
ejpam-3763	288	12	)	)	PUNCT
ejpam-3763	288	13	and	and	CCONJ
ejpam-3763	288	14	uw	uw	PROPN
ejpam-3763	288	15	∈	∈	PROPN
ejpam-3763	288	16	e(hv	e(hv	PROPN
ejpam-3763	288	17	)	)	PUNCT
ejpam-3763	288	18	.	.	PUNCT
ejpam-3763	289	1	thus	thus	ADV
ejpam-3763	289	2	,	,	PUNCT
ejpam-3763	289	3	f	f	PROPN
ejpam-3763	289	4	|hv	|hv	PROPN
ejpam-3763	289	5	is	be	AUX
ejpam-3763	289	6	a	a	DET
ejpam-3763	289	7	perfect	perfect	ADJ
ejpam-3763	289	8	roman	roman	ADJ
ejpam-3763	289	9	dominating	dominating	NOUN
ejpam-3763	289	10	function	function	NOUN
ejpam-3763	289	11	on	on	ADP
ejpam-3763	289	12	hv	hv	PROPN
ejpam-3763	289	13	,	,	PUNCT
ejpam-3763	289	14	and	and	CCONJ
ejpam-3763	289	15	(	(	PUNCT
ejpam-3763	289	16	ii	ii	NOUN
ejpam-3763	289	17	)	)	PUNCT
ejpam-3763	289	18	holds	hold	VERB
ejpam-3763	289	19	.	.	PUNCT
ejpam-3763	290	1	statement	statement	NOUN
ejpam-3763	290	2	(	(	PUNCT
ejpam-3763	290	3	iii	iii	NOUN
ejpam-3763	290	4	)	)	PUNCT
ejpam-3763	290	5	is	be	AUX
ejpam-3763	290	6	clear	clear	ADJ
ejpam-3763	290	7	.	.	PUNCT
ejpam-3763	291	1	conversely	conversely	ADV
ejpam-3763	291	2	,	,	PUNCT
ejpam-3763	291	3	suppose	suppose	VERB
ejpam-3763	291	4	that	that	SCONJ
ejpam-3763	291	5	conditions	condition	NOUN
ejpam-3763	291	6	(	(	PUNCT
ejpam-3763	291	7	i	i	NOUN
ejpam-3763	291	8	)	)	PUNCT
ejpam-3763	291	9	,	,	PUNCT
ejpam-3763	291	10	(	(	PUNCT
ejpam-3763	291	11	ii	ii	NOUN
ejpam-3763	291	12	)	)	PUNCT
ejpam-3763	291	13	and	and	CCONJ
ejpam-3763	291	14	(	(	PUNCT
ejpam-3763	291	15	iii	iii	X
ejpam-3763	291	16	)	)	PUNCT
ejpam-3763	291	17	hold	hold	VERB
ejpam-3763	291	18	for	for	ADP
ejpam-3763	291	19	f	f	PROPN
ejpam-3763	291	20	,	,	PUNCT
ejpam-3763	291	21	and	and	CCONJ
ejpam-3763	291	22	let	let	VERB
ejpam-3763	291	23	w	w	PROPN
ejpam-3763	291	24	∈	∈	PROPN
ejpam-3763	291	25	v0	v0	NOUN
ejpam-3763	291	26	.	.	PUNCT
ejpam-3763	292	1	then	then	ADV
ejpam-3763	292	2	w	w	PROPN
ejpam-3763	292	3	∈	∈	PROPN
ejpam-3763	292	4	v	v	ADP
ejpam-3763	292	5	(	(	PUNCT
ejpam-3763	292	6	hv+v	hv+v	PROPN
ejpam-3763	292	7	)	)	PUNCT
ejpam-3763	292	8	for	for	ADP
ejpam-3763	292	9	some	some	DET
ejpam-3763	292	10	v	v	ADP
ejpam-3763	292	11	∈	∈	PROPN
ejpam-3763	292	12	v	v	NOUN
ejpam-3763	292	13	(	(	PUNCT
ejpam-3763	292	14	g	g	NOUN
ejpam-3763	292	15	)	)	PUNCT
ejpam-3763	292	16	.	.	PUNCT
ejpam-3763	293	1	if	if	SCONJ
ejpam-3763	293	2	w	w	PROPN
ejpam-3763	293	3	=	=	SYM
ejpam-3763	293	4	v	v	NOUN
ejpam-3763	293	5	,	,	PUNCT
ejpam-3763	293	6	then	then	ADV
ejpam-3763	293	7	by	by	ADP
ejpam-3763	293	8	condition	condition	NOUN
ejpam-3763	293	9	(	(	PUNCT
ejpam-3763	293	10	i	i	NOUN
ejpam-3763	293	11	)	)	PUNCT
ejpam-3763	293	12	,	,	PUNCT
ejpam-3763	293	13	v2∩(v	v2∩(v	PROPN
ejpam-3763	293	14	(	(	PUNCT
ejpam-3763	293	15	hv	hv	NOUN
ejpam-3763	293	16	)	)	PUNCT
ejpam-3763	293	17	∪ng(w	∪ng(w	NOUN
ejpam-3763	293	18	)	)	PUNCT
ejpam-3763	293	19	)	)	PUNCT
ejpam-3763	294	1	=	=	PRON
ejpam-3763	294	2	{	{	PUNCT
ejpam-3763	294	3	u	u	NOUN
ejpam-3763	294	4	}	}	PUNCT
ejpam-3763	294	5	for	for	ADP
ejpam-3763	294	6	some	some	DET
ejpam-3763	294	7	u	u	PROPN
ejpam-3763	294	8	∈	∈	PROPN
ejpam-3763	294	9	v	v	NOUN
ejpam-3763	294	10	(	(	PUNCT
ejpam-3763	294	11	g	g	PROPN
ejpam-3763	294	12	◦	◦	NOUN
ejpam-3763	294	13	h	h	NOUN
ejpam-3763	294	14	)	)	PUNCT
ejpam-3763	294	15	.	.	PUNCT
ejpam-3763	295	1	this	this	PRON
ejpam-3763	295	2	means	mean	VERB
ejpam-3763	295	3	that	that	SCONJ
ejpam-3763	295	4	v2	v2	PROPN
ejpam-3763	295	5	∩	∩	NOUN
ejpam-3763	295	6	ng	ng	PROPN
ejpam-3763	295	7	◦	◦	NOUN
ejpam-3763	295	8	h(w	h(w	NOUN
ejpam-3763	295	9	)	)	PUNCT
ejpam-3763	296	1	=	=	PRON
ejpam-3763	296	2	{	{	PUNCT
ejpam-3763	296	3	u	u	NOUN
ejpam-3763	296	4	}	}	PUNCT
ejpam-3763	296	5	.	.	PUNCT
ejpam-3763	297	1	suppose	suppose	VERB
ejpam-3763	297	2	that	that	SCONJ
ejpam-3763	297	3	w	w	PROPN
ejpam-3763	297	4	∈	∈	PROPN
ejpam-3763	297	5	v	v	ADP
ejpam-3763	297	6	(	(	PUNCT
ejpam-3763	297	7	hv	hv	PROPN
ejpam-3763	297	8	)	)	PUNCT
ejpam-3763	297	9	.	.	PUNCT
ejpam-3763	298	1	we	we	PRON
ejpam-3763	298	2	consider	consider	VERB
ejpam-3763	298	3	three	three	NUM
ejpam-3763	298	4	cases	case	NOUN
ejpam-3763	298	5	:	:	PUNCT
ejpam-3763	298	6	case	case	NOUN
ejpam-3763	298	7	1	1	NUM
ejpam-3763	298	8	:	:	PUNCT
ejpam-3763	298	9	suppose	suppose	VERB
ejpam-3763	298	10	that	that	SCONJ
ejpam-3763	298	11	v	v	PROPN
ejpam-3763	298	12	∈	∈	PROPN
ejpam-3763	298	13	v0	v0	NOUN
ejpam-3763	298	14	.	.	PUNCT
ejpam-3763	299	1	since	since	SCONJ
ejpam-3763	299	2	w	w	PROPN
ejpam-3763	299	3	∈	∈	PROPN
ejpam-3763	299	4	v0	v0	NOUN
ejpam-3763	299	5	∩	∩	X
ejpam-3763	299	6	v	v	X
ejpam-3763	299	7	(	(	PUNCT
ejpam-3763	299	8	hv	hv	PROPN
ejpam-3763	299	9	)	)	PUNCT
ejpam-3763	299	10	,	,	PUNCT
ejpam-3763	299	11	v	v	PROPN
ejpam-3763	299	12	(	(	PUNCT
ejpam-3763	299	13	hv	hv	NOUN
ejpam-3763	299	14	)	)	PUNCT
ejpam-3763	299	15	*	*	PUNCT
ejpam-3763	299	16	v1	v1	PROPN
ejpam-3763	299	17	.	.	PUNCT
ejpam-3763	300	1	thus	thus	ADV
ejpam-3763	300	2	,	,	PUNCT
ejpam-3763	300	3	by	by	ADP
ejpam-3763	300	4	condition	condition	NOUN
ejpam-3763	300	5	(	(	PUNCT
ejpam-3763	300	6	i	i	NOUN
ejpam-3763	300	7	)	)	PUNCT
ejpam-3763	300	8	there	there	PRON
ejpam-3763	300	9	exists	exist	VERB
ejpam-3763	300	10	u	u	PROPN
ejpam-3763	300	11	∈	∈	PROPN
ejpam-3763	300	12	v	v	ADP
ejpam-3763	300	13	(	(	PUNCT
ejpam-3763	300	14	hv	hv	PROPN
ejpam-3763	300	15	)	)	PUNCT
ejpam-3763	300	16	for	for	ADP
ejpam-3763	300	17	which	which	PRON
ejpam-3763	300	18	v2	v2	NOUN
ejpam-3763	300	19	∩	∩	NOUN
ejpam-3763	300	20	v	v	NOUN
ejpam-3763	300	21	(	(	PUNCT
ejpam-3763	300	22	hv	hv	NOUN
ejpam-3763	300	23	)	)	PUNCT
ejpam-3763	300	24	=	=	PRON
ejpam-3763	300	25	{	{	PUNCT
ejpam-3763	300	26	u	u	NOUN
ejpam-3763	300	27	}	}	PUNCT
ejpam-3763	300	28	and	and	CCONJ
ejpam-3763	300	29	v0	v0	PROPN
ejpam-3763	300	30	∩	∩	ADJ
ejpam-3763	300	31	v	v	X
ejpam-3763	300	32	(	(	PUNCT
ejpam-3763	300	33	hv	hv	PROPN
ejpam-3763	300	34	)	)	PUNCT
ejpam-3763	300	35	⊆	⊆	NUM
ejpam-3763	300	36	nhv(u	nhv(u	PROPN
ejpam-3763	300	37	)	)	PUNCT
ejpam-3763	300	38	.	.	PUNCT
ejpam-3763	301	1	this	this	PRON
ejpam-3763	301	2	means	mean	VERB
ejpam-3763	301	3	that	that	SCONJ
ejpam-3763	301	4	v2	v2	VERB
ejpam-3763	301	5	∩ng	∩ng	VERB
ejpam-3763	301	6	◦	◦	NOUN
ejpam-3763	301	7	h(w	h(w	NOUN
ejpam-3763	301	8	)	)	PUNCT
ejpam-3763	302	1	=	=	PRON
ejpam-3763	302	2	{	{	PUNCT
ejpam-3763	302	3	u	u	NOUN
ejpam-3763	302	4	}	}	PUNCT
ejpam-3763	302	5	.	.	PUNCT
ejpam-3763	303	1	case	case	NOUN
ejpam-3763	303	2	2	2	NUM
ejpam-3763	303	3	:	:	PUNCT
ejpam-3763	303	4	suppose	suppose	VERB
ejpam-3763	303	5	that	that	SCONJ
ejpam-3763	303	6	v	v	NUM
ejpam-3763	303	7	∈	∈	PROPN
ejpam-3763	303	8	v1	v1	NOUN
ejpam-3763	303	9	.	.	PUNCT
ejpam-3763	304	1	by	by	ADP
ejpam-3763	304	2	condition	condition	NOUN
ejpam-3763	304	3	(	(	PUNCT
ejpam-3763	304	4	ii	ii	NOUN
ejpam-3763	304	5	)	)	PUNCT
ejpam-3763	304	6	,	,	PUNCT
ejpam-3763	304	7	there	there	PRON
ejpam-3763	304	8	exists	exist	VERB
ejpam-3763	304	9	a	a	DET
ejpam-3763	304	10	unique	unique	ADJ
ejpam-3763	304	11	u	u	NOUN
ejpam-3763	304	12	∈	∈	PROPN
ejpam-3763	304	13	v2	v2	PROPN
ejpam-3763	304	14	∩	∩	ADJ
ejpam-3763	304	15	v	v	X
ejpam-3763	304	16	(	(	PUNCT
ejpam-3763	304	17	hv	hv	PROPN
ejpam-3763	304	18	)	)	PUNCT
ejpam-3763	304	19	such	such	ADJ
ejpam-3763	304	20	that	that	SCONJ
ejpam-3763	304	21	uw	uw	PROPN
ejpam-3763	304	22	∈	∈	PROPN
ejpam-3763	304	23	e(hv	e(hv	PROPN
ejpam-3763	304	24	)	)	PUNCT
ejpam-3763	304	25	⊆	⊆	NUM
ejpam-3763	304	26	e(g	e(g	NOUN
ejpam-3763	304	27	◦	◦	NOUN
ejpam-3763	304	28	h	h	NOUN
ejpam-3763	304	29	)	)	PUNCT
ejpam-3763	304	30	.	.	PUNCT
ejpam-3763	305	1	this	this	PRON
ejpam-3763	305	2	implies	imply	VERB
ejpam-3763	305	3	that	that	SCONJ
ejpam-3763	305	4	v2	v2	PROPN
ejpam-3763	305	5	∩ng	∩ng	NOUN
ejpam-3763	305	6	◦	◦	NOUN
ejpam-3763	305	7	h(w	h(w	NOUN
ejpam-3763	305	8	)	)	PUNCT
ejpam-3763	306	1	=	=	PRON
ejpam-3763	306	2	{	{	PUNCT
ejpam-3763	306	3	u	u	NOUN
ejpam-3763	306	4	}	}	PUNCT
ejpam-3763	306	5	.	.	PUNCT
ejpam-3763	307	1	case	case	NOUN
ejpam-3763	307	2	3	3	X
ejpam-3763	307	3	:	:	PUNCT
ejpam-3763	307	4	suppose	suppose	VERB
ejpam-3763	307	5	that	that	SCONJ
ejpam-3763	307	6	v	v	X
ejpam-3763	307	7	∈	∈	PROPN
ejpam-3763	307	8	v2	v2	NOUN
ejpam-3763	307	9	.	.	PUNCT
ejpam-3763	308	1	since	since	SCONJ
ejpam-3763	308	2	w	w	PROPN
ejpam-3763	308	3	∈	∈	PROPN
ejpam-3763	308	4	v0	v0	NOUN
ejpam-3763	308	5	∩	∩	X
ejpam-3763	308	6	v	v	X
ejpam-3763	308	7	(	(	PUNCT
ejpam-3763	308	8	hv	hv	PROPN
ejpam-3763	308	9	)	)	PUNCT
ejpam-3763	308	10	,	,	PUNCT
ejpam-3763	308	11	condition	condition	NOUN
ejpam-3763	308	12	(	(	PUNCT
ejpam-3763	308	13	iii	iii	NOUN
ejpam-3763	308	14	)	)	PUNCT
ejpam-3763	308	15	implies	imply	VERB
ejpam-3763	308	16	that	that	SCONJ
ejpam-3763	308	17	w	w	PROPN
ejpam-3763	308	18	/∈	/∈	PROPN
ejpam-3763	308	19	nhv(v2	nhv(v2	PROPN
ejpam-3763	308	20	∩	∩	PROPN
ejpam-3763	308	21	v	v	PROPN
ejpam-3763	308	22	(	(	PUNCT
ejpam-3763	308	23	hv	hv	PROPN
ejpam-3763	308	24	)	)	PUNCT
ejpam-3763	308	25	.	.	PUNCT
ejpam-3763	309	1	thus	thus	ADV
ejpam-3763	309	2	,	,	PUNCT
ejpam-3763	309	3	v2	v2	PROPN
ejpam-3763	309	4	∩ng	∩ng	NOUN
ejpam-3763	309	5	◦	◦	NOUN
ejpam-3763	309	6	h(w	h(w	NOUN
ejpam-3763	309	7	)	)	PUNCT
ejpam-3763	310	1	=	=	PRON
ejpam-3763	310	2	{	{	PUNCT
ejpam-3763	310	3	v	v	NOUN
ejpam-3763	310	4	}	}	PUNCT
ejpam-3763	310	5	.	.	PUNCT
ejpam-3763	311	1	therefore	therefore	ADV
ejpam-3763	311	2	,	,	PUNCT
ejpam-3763	311	3	f	f	PROPN
ejpam-3763	311	4	is	be	AUX
ejpam-3763	311	5	a	a	DET
ejpam-3763	311	6	perfect	perfect	ADJ
ejpam-3763	311	7	roman	roman	ADJ
ejpam-3763	311	8	dominating	dominating	NOUN
ejpam-3763	311	9	function	function	NOUN
ejpam-3763	311	10	on	on	ADP
ejpam-3763	311	11	v	v	PROPN
ejpam-3763	311	12	(	(	PUNCT
ejpam-3763	311	13	g	g	PROPN
ejpam-3763	311	14	◦	◦	NOUN
ejpam-3763	311	15	h	h	NOUN
ejpam-3763	311	16	)	)	PUNCT
ejpam-3763	311	17	.	.	PUNCT
ejpam-3763	312	1	�	�	PROPN
ejpam-3763	312	2	corollary	corollary	NOUN
ejpam-3763	312	3	2.11	2.11	NUM
ejpam-3763	312	4	.	.	PUNCT
ejpam-3763	313	1	let	let	VERB
ejpam-3763	313	2	g	g	NOUN
ejpam-3763	313	3	and	and	CCONJ
ejpam-3763	313	4	h	h	NOUN
ejpam-3763	313	5	be	be	AUX
ejpam-3763	313	6	nontrivial	nontrivial	ADJ
ejpam-3763	313	7	graphs	graph	NOUN
ejpam-3763	313	8	with	with	ADP
ejpam-3763	313	9	g	g	NOUN
ejpam-3763	313	10	connected	connect	VERB
ejpam-3763	313	11	of	of	ADP
ejpam-3763	313	12	order	order	NOUN
ejpam-3763	314	1	n.	n.	NOUN
ejpam-3763	314	2	then	then	ADV
ejpam-3763	314	3	γpr(g	γpr(g	PROPN
ejpam-3763	314	4	◦	◦	NOUN
ejpam-3763	314	5	h	h	NOUN
ejpam-3763	314	6	)	)	PUNCT
ejpam-3763	314	7	=	=	SYM
ejpam-3763	314	8	2n	2n	NUM
ejpam-3763	314	9	.	.	PUNCT
ejpam-3763	315	1	proof	proof	NOUN
ejpam-3763	315	2	:	:	PUNCT
ejpam-3763	315	3	by	by	ADP
ejpam-3763	315	4	theorem	theorem	NOUN
ejpam-3763	315	5	2.7	2.7	NUM
ejpam-3763	315	6	,	,	PUNCT
ejpam-3763	315	7	the	the	DET
ejpam-3763	315	8	function	function	NOUN
ejpam-3763	315	9	f	f	X
ejpam-3763	315	10	=	=	SYM
ejpam-3763	315	11	(	(	PUNCT
ejpam-3763	315	12	v0	v0	PROPN
ejpam-3763	315	13	,	,	PUNCT
ejpam-3763	315	14	v1	v1	NOUN
ejpam-3763	315	15	,	,	PUNCT
ejpam-3763	315	16	v2	v2	NOUN
ejpam-3763	315	17	)	)	PUNCT
ejpam-3763	315	18	defined	define	VERB
ejpam-3763	315	19	by	by	ADP
ejpam-3763	315	20	f(x	f(x	PROPN
ejpam-3763	315	21	)	)	PUNCT
ejpam-3763	315	22	=	=	SYM
ejpam-3763	315	23	2	2	NUM
ejpam-3763	315	24	for	for	ADP
ejpam-3763	315	25	all	all	PRON
ejpam-3763	315	26	v	v	ADP
ejpam-3763	315	27	∈	∈	NOUN
ejpam-3763	315	28	v	v	NOUN
ejpam-3763	315	29	(	(	PUNCT
ejpam-3763	315	30	g	g	NOUN
ejpam-3763	315	31	)	)	PUNCT
ejpam-3763	315	32	,	,	PUNCT
ejpam-3763	315	33	and	and	CCONJ
ejpam-3763	315	34	f(x	f(x	PROPN
ejpam-3763	315	35	)	)	PUNCT
ejpam-3763	316	1	=	=	PUNCT
ejpam-3763	317	1	0	0	NUM
ejpam-3763	318	1	else	else	ADV
ejpam-3763	318	2	,	,	PUNCT
ejpam-3763	318	3	is	be	AUX
ejpam-3763	318	4	a	a	DET
ejpam-3763	318	5	perfect	perfect	ADJ
ejpam-3763	318	6	roman	roman	ADJ
ejpam-3763	318	7	dominating	dominating	NOUN
ejpam-3763	318	8	function	function	NOUN
ejpam-3763	318	9	ong	ong	PROPN
ejpam-3763	318	10	◦	◦	PROPN
ejpam-3763	318	11	h.	h.	PROPN
ejpam-3763	318	12	thus	thus	ADV
ejpam-3763	318	13	,	,	PUNCT
ejpam-3763	318	14	γpr(g	γpr(g	PROPN
ejpam-3763	318	15	◦	◦	NOUN
ejpam-3763	318	16	h	h	NOUN
ejpam-3763	318	17	)	)	PUNCT
ejpam-3763	318	18	≤	≤	NUM
ejpam-3763	318	19	2n	2n	NUM
ejpam-3763	318	20	.	.	PUNCT
ejpam-3763	319	1	now	now	ADV
ejpam-3763	319	2	,	,	PUNCT
ejpam-3763	319	3	let	let	VERB
ejpam-3763	319	4	f	f	PROPN
ejpam-3763	319	5	=	=	SYM
ejpam-3763	319	6	(	(	PUNCT
ejpam-3763	319	7	v0	v0	PROPN
ejpam-3763	319	8	,	,	PUNCT
ejpam-3763	319	9	v1	v1	NOUN
ejpam-3763	319	10	,	,	PUNCT
ejpam-3763	319	11	v2	v2	PROPN
ejpam-3763	319	12	)	)	PUNCT
ejpam-3763	319	13	be	be	AUX
ejpam-3763	319	14	a	a	DET
ejpam-3763	319	15	γpr	γpr	NOUN
ejpam-3763	319	16	-function	-function	NOUN
ejpam-3763	319	17	on	on	ADP
ejpam-3763	319	18	v	v	NOUN
ejpam-3763	319	19	(	(	PUNCT
ejpam-3763	319	20	g	g	PROPN
ejpam-3763	319	21	◦	◦	NOUN
ejpam-3763	319	22	h	h	NOUN
ejpam-3763	319	23	)	)	PUNCT
ejpam-3763	319	24	.	.	PUNCT
ejpam-3763	320	1	let	let	VERB
ejpam-3763	320	2	v	v	NUM
ejpam-3763	320	3	∈	∈	PROPN
ejpam-3763	320	4	v	v	NOUN
ejpam-3763	320	5	(	(	PUNCT
ejpam-3763	320	6	g	g	NOUN
ejpam-3763	320	7	)	)	PUNCT
ejpam-3763	320	8	.	.	PUNCT
ejpam-3763	321	1	clearly	clearly	ADV
ejpam-3763	321	2	,	,	PUNCT
ejpam-3763	321	3	if	if	SCONJ
ejpam-3763	321	4	v	v	NUM
ejpam-3763	321	5	∈	∈	PROPN
ejpam-3763	321	6	v2	v2	NOUN
ejpam-3763	321	7	,	,	PUNCT
ejpam-3763	321	8	then	then	ADV
ejpam-3763	321	9	∑	∑	PUNCT
ejpam-3763	321	10	x∈v	x∈v	PROPN
ejpam-3763	321	11	(	(	PUNCT
ejpam-3763	321	12	hv+v	hv+v	PROPN
ejpam-3763	321	13	)	)	PUNCT
ejpam-3763	321	14	f(x	f(x	PROPN
ejpam-3763	321	15	)	)	PUNCT
ejpam-3763	321	16	≥	≥	NOUN
ejpam-3763	322	1	2	2	NUM
ejpam-3763	322	2	.	.	PUNCT
ejpam-3763	323	1	if	if	SCONJ
ejpam-3763	323	2	v	v	NUM
ejpam-3763	323	3	∈	∈	PROPN
ejpam-3763	323	4	v0	v0	NOUN
ejpam-3763	323	5	,	,	PUNCT
ejpam-3763	323	6	then	then	ADV
ejpam-3763	323	7	by	by	ADP
ejpam-3763	323	8	proposition	proposition	NOUN
ejpam-3763	323	9	2.10(i	2.10(i	NUM
ejpam-3763	323	10	)	)	PUNCT
ejpam-3763	323	11	and	and	CCONJ
ejpam-3763	323	12	since	since	SCONJ
ejpam-3763	323	13	l.	l.	PROPN
ejpam-3763	323	14	paleta	paleta	PROPN
ejpam-3763	323	15	,	,	PUNCT
ejpam-3763	323	16	f.	f.	PROPN
ejpam-3763	323	17	jamil	jamil	PROPN
ejpam-3763	323	18	/	/	SYM
ejpam-3763	323	19	eur	eur	PROPN
ejpam-3763	323	20	.	.	PUNCT
ejpam-3763	324	1	j.	j.	PROPN
ejpam-3763	324	2	pure	pure	PROPN
ejpam-3763	324	3	appl	appl	PROPN
ejpam-3763	324	4	.	.	PROPN
ejpam-3763	324	5	math	math	PROPN
ejpam-3763	324	6	,	,	PUNCT
ejpam-3763	324	7	13	13	NUM
ejpam-3763	324	8	(	(	PUNCT
ejpam-3763	324	9	3	3	NUM
ejpam-3763	324	10	)	)	PUNCT
ejpam-3763	324	11	(	(	PUNCT
ejpam-3763	324	12	2020	2020	NUM
ejpam-3763	324	13	)	)	PUNCT
ejpam-3763	324	14	,	,	PUNCT
ejpam-3763	324	15	529	529	NUM
ejpam-3763	324	16	-	-	SYM
ejpam-3763	324	17	548	548	NUM
ejpam-3763	324	18	538	538	NUM
ejpam-3763	324	19	|v	|v	X
ejpam-3763	324	20	(	(	PUNCT
ejpam-3763	324	21	hv|	hv|	NOUN
ejpam-3763	324	22	≥	≥	NOUN
ejpam-3763	324	23	2	2	NUM
ejpam-3763	324	24	,	,	PUNCT
ejpam-3763	324	25	∑	∑	ADV
ejpam-3763	324	26	x∈v	x∈v	PROPN
ejpam-3763	324	27	(	(	PUNCT
ejpam-3763	324	28	hv+v	hv+v	PROPN
ejpam-3763	324	29	)	)	PUNCT
ejpam-3763	324	30	f(x	f(x	PROPN
ejpam-3763	324	31	)	)	PUNCT
ejpam-3763	324	32	≥	≥	NOUN
ejpam-3763	324	33	2	2	NUM
ejpam-3763	324	34	.	.	PUNCT
ejpam-3763	325	1	finally	finally	ADV
ejpam-3763	325	2	,	,	PUNCT
ejpam-3763	325	3	if	if	SCONJ
ejpam-3763	325	4	v	v	NUM
ejpam-3763	325	5	∈	∈	PROPN
ejpam-3763	325	6	v1	v1	NOUN
ejpam-3763	325	7	,	,	PUNCT
ejpam-3763	325	8	then	then	ADV
ejpam-3763	325	9	by	by	ADP
ejpam-3763	325	10	proposition	proposition	NOUN
ejpam-3763	325	11	2.10(ii),∑	2.10(ii),∑	NUM
ejpam-3763	325	12	x∈v	x∈v	PROPN
ejpam-3763	325	13	(	(	PUNCT
ejpam-3763	325	14	hv+v	hv+v	PROPN
ejpam-3763	325	15	)	)	PUNCT
ejpam-3763	325	16	f(x	f(x	PROPN
ejpam-3763	325	17	)	)	PUNCT
ejpam-3763	325	18	>	>	X
ejpam-3763	326	1	2	2	X
ejpam-3763	326	2	.	.	PUNCT
ejpam-3763	326	3	therefore	therefore	ADV
ejpam-3763	326	4	,	,	PUNCT
ejpam-3763	326	5	γpr(g	γpr(g	PROPN
ejpam-3763	326	6	◦	◦	NOUN
ejpam-3763	326	7	h	h	NOUN
ejpam-3763	326	8	)	)	PUNCT
ejpam-3763	327	1	=	=	SYM
ejpam-3763	327	2	ωg	ωg	PART
ejpam-3763	327	3	◦	◦	NOUN
ejpam-3763	327	4	h(f	h(f	NOUN
ejpam-3763	327	5	)	)	PUNCT
ejpam-3763	328	1	=	=	PUNCT
ejpam-3763	328	2	∑	∑	PUNCT
ejpam-3763	328	3	v∈v	v∈v	NOUN
ejpam-3763	328	4	(	(	PUNCT
ejpam-3763	328	5	g	g	NOUN
ejpam-3763	328	6	)	)	PUNCT
ejpam-3763	328	7			PROPN
ejpam-3763	328	8	∑	∑	PROPN
ejpam-3763	328	9	x∈v	x∈v	PROPN
ejpam-3763	328	10	(	(	PUNCT
ejpam-3763	328	11	hv+v	hv+v	PROPN
ejpam-3763	328	12	)	)	PUNCT
ejpam-3763	328	13	f(x	f(x	PROPN
ejpam-3763	328	14	)	)	PUNCT
ejpam-3763	329	1			PROPN
ejpam-3763	329	2	≥	≥	NUM
ejpam-3763	329	3	2n	2n	NUM
ejpam-3763	329	4	.	.	PUNCT
ejpam-3763	330	1	�	�	PROPN
ejpam-3763	330	2	2.3	2.3	NUM
ejpam-3763	330	3	.	.	PUNCT
ejpam-3763	331	1	on	on	ADP
ejpam-3763	331	2	the	the	DET
ejpam-3763	331	3	complementary	complementary	ADJ
ejpam-3763	331	4	prisms	prism	NOUN
ejpam-3763	331	5	let	let	VERB
ejpam-3763	331	6	f	f	PROPN
ejpam-3763	331	7	=	=	SYM
ejpam-3763	331	8	(	(	PUNCT
ejpam-3763	331	9	v0	v0	PROPN
ejpam-3763	331	10	,	,	PUNCT
ejpam-3763	331	11	v1	v1	NOUN
ejpam-3763	331	12	,	,	PUNCT
ejpam-3763	331	13	v2	v2	NOUN
ejpam-3763	331	14	)	)	PUNCT
ejpam-3763	331	15	∈	∈	NOUN
ejpam-3763	331	16	prd(gg	prd(gg	NOUN
ejpam-3763	331	17	)	)	PUNCT
ejpam-3763	331	18	.	.	PUNCT
ejpam-3763	332	1	suppose	suppose	VERB
ejpam-3763	332	2	that	that	SCONJ
ejpam-3763	332	3	for	for	ADP
ejpam-3763	332	4	the	the	DET
ejpam-3763	332	5	restriction	restriction	NOUN
ejpam-3763	332	6	f	f	PROPN
ejpam-3763	332	7	|g	|g	PROPN
ejpam-3763	332	8	/∈	/∈	PUNCT
ejpam-3763	333	1	prd(g	prd(g	NUM
ejpam-3763	333	2	)	)	PUNCT
ejpam-3763	333	3	.	.	PUNCT
ejpam-3763	334	1	then	then	ADV
ejpam-3763	334	2	there	there	PRON
ejpam-3763	334	3	exists	exist	VERB
ejpam-3763	334	4	v	v	ADP
ejpam-3763	334	5	∈	∈	PROPN
ejpam-3763	334	6	v	v	NOUN
ejpam-3763	334	7	(	(	PUNCT
ejpam-3763	334	8	g	g	NOUN
ejpam-3763	334	9	)	)	PUNCT
ejpam-3763	334	10	such	such	ADJ
ejpam-3763	334	11	that	that	DET
ejpam-3763	334	12	v	v	NUM
ejpam-3763	334	13	∈	∈	PROPN
ejpam-3763	334	14	v0	v0	NOUN
ejpam-3763	334	15	and	and	CCONJ
ejpam-3763	334	16	v2	v2	PROPN
ejpam-3763	334	17	∩ngg(v	∩ngg(v	PUNCT
ejpam-3763	334	18	)	)	PUNCT
ejpam-3763	334	19	=	=	PRON
ejpam-3763	334	20	{	{	PUNCT
ejpam-3763	334	21	v	v	NOUN
ejpam-3763	334	22	}	}	PUNCT
ejpam-3763	334	23	.	.	PUNCT
ejpam-3763	335	1	let	let	VERB
ejpam-3763	335	2	u	u	PRON
ejpam-3763	335	3	∈	∈	PROPN
ejpam-3763	335	4	v0	v0	NOUN
ejpam-3763	335	5	∩	∩	X
ejpam-3763	335	6	v	v	X
ejpam-3763	335	7	(	(	PUNCT
ejpam-3763	335	8	g	g	NOUN
ejpam-3763	335	9	)	)	PUNCT
ejpam-3763	335	10	.	.	PUNCT
ejpam-3763	336	1	there	there	PRON
ejpam-3763	336	2	exists	exist	VERB
ejpam-3763	336	3	w	w	PROPN
ejpam-3763	336	4	∈	∈	PROPN
ejpam-3763	336	5	v	v	ADP
ejpam-3763	336	6	(	(	PUNCT
ejpam-3763	336	7	gg	gg	NOUN
ejpam-3763	336	8	)	)	PUNCT
ejpam-3763	336	9	such	such	ADJ
ejpam-3763	336	10	that	that	SCONJ
ejpam-3763	336	11	v2	v2	PROPN
ejpam-3763	336	12	∩	∩	NOUN
ejpam-3763	336	13	ngg(u	ngg(u	PROPN
ejpam-3763	336	14	)	)	PUNCT
ejpam-3763	336	15	=	=	PRON
ejpam-3763	336	16	{	{	PUNCT
ejpam-3763	336	17	w	w	NOUN
ejpam-3763	336	18	}	}	PUNCT
ejpam-3763	336	19	.	.	PUNCT
ejpam-3763	337	1	if	if	SCONJ
ejpam-3763	337	2	w	w	PROPN
ejpam-3763	337	3	=	=	SYM
ejpam-3763	337	4	u	u	NOUN
ejpam-3763	337	5	,	,	PUNCT
ejpam-3763	337	6	then	then	ADV
ejpam-3763	337	7	uv	uv	PROPN
ejpam-3763	337	8	/∈	/∈	PUNCT
ejpam-3763	337	9	e(g	e(g	PROPN
ejpam-3763	337	10	,	,	PUNCT
ejpam-3763	337	11	and	and	CCONJ
ejpam-3763	337	12	consequently	consequently	ADV
ejpam-3763	337	13	,	,	PUNCT
ejpam-3763	337	14	uv	uv	PROPN
ejpam-3763	337	15	∈	∈	PROPN
ejpam-3763	337	16	e(g	e(g	PROPN
ejpam-3763	337	17	)	)	PUNCT
ejpam-3763	337	18	,	,	PUNCT
ejpam-3763	337	19	a	a	DET
ejpam-3763	337	20	contradiction	contradiction	NOUN
ejpam-3763	337	21	.	.	PUNCT
ejpam-3763	338	1	thus	thus	ADV
ejpam-3763	338	2	,	,	PUNCT
ejpam-3763	338	3	w	w	PROPN
ejpam-3763	338	4	∈	∈	PROPN
ejpam-3763	338	5	v2∩v	v2∩v	NOUN
ejpam-3763	338	6	(	(	PUNCT
ejpam-3763	338	7	g	g	NOUN
ejpam-3763	338	8	)	)	PUNCT
ejpam-3763	338	9	.	.	PUNCT
ejpam-3763	339	1	this	this	PRON
ejpam-3763	339	2	proves	prove	VERB
ejpam-3763	339	3	the	the	DET
ejpam-3763	339	4	following	follow	VERB
ejpam-3763	339	5	lemma	lemma	PROPN
ejpam-3763	339	6	.	.	PUNCT
ejpam-3763	340	1	lemma	lemma	PROPN
ejpam-3763	340	2	2.12	2.12	NUM
ejpam-3763	340	3	.	.	PUNCT
ejpam-3763	341	1	let	let	VERB
ejpam-3763	341	2	g	g	NOUN
ejpam-3763	341	3	be	be	AUX
ejpam-3763	341	4	any	any	DET
ejpam-3763	341	5	graph	graph	NOUN
ejpam-3763	341	6	.	.	PUNCT
ejpam-3763	342	1	if	if	SCONJ
ejpam-3763	342	2	f	f	PROPN
ejpam-3763	342	3	∈	∈	PROPN
ejpam-3763	342	4	prd(gg	prd(gg	NOUN
ejpam-3763	342	5	)	)	PUNCT
ejpam-3763	342	6	,	,	PUNCT
ejpam-3763	342	7	then	then	ADV
ejpam-3763	342	8	f	f	PROPN
ejpam-3763	342	9	|g	|g	PROPN
ejpam-3763	342	10	∈	∈	PROPN
ejpam-3763	342	11	prd(g	prd(g	PROPN
ejpam-3763	342	12	)	)	PUNCT
ejpam-3763	342	13	or	or	CCONJ
ejpam-3763	342	14	f	f	PROPN
ejpam-3763	342	15	|g	|g	PROPN
ejpam-3763	342	16	∈	∈	PROPN
ejpam-3763	342	17	prd(g	prd(g	PROPN
ejpam-3763	342	18	)	)	PUNCT
ejpam-3763	342	19	.	.	PUNCT
ejpam-3763	343	1	proposition	proposition	NOUN
ejpam-3763	343	2	2.13	2.13	NUM
ejpam-3763	343	3	.	.	PUNCT
ejpam-3763	344	1	let	let	VERB
ejpam-3763	344	2	g	g	PRON
ejpam-3763	344	3	be	be	AUX
ejpam-3763	344	4	a	a	DET
ejpam-3763	344	5	graph	graph	NOUN
ejpam-3763	344	6	of	of	ADP
ejpam-3763	344	7	order	order	NOUN
ejpam-3763	344	8	n.	n.	NOUN
ejpam-3763	344	9	then	then	ADV
ejpam-3763	344	10	(	(	PUNCT
ejpam-3763	344	11	i	i	NOUN
ejpam-3763	344	12	)	)	PUNCT
ejpam-3763	345	1	γ(gg	γ(gg	NUM
ejpam-3763	345	2	)	)	PUNCT
ejpam-3763	346	1	<	<	X
ejpam-3763	346	2	γpr(gg	γpr(gg	NOUN
ejpam-3763	346	3	)	)	PUNCT
ejpam-3763	346	4	;	;	PUNCT
ejpam-3763	346	5	(	(	PUNCT
ejpam-3763	346	6	ii	ii	NOUN
ejpam-3763	346	7	)	)	PUNCT
ejpam-3763	346	8	γpr(gg	γpr(gg	NOUN
ejpam-3763	346	9	)	)	PUNCT
ejpam-3763	346	10	=	=	SYM
ejpam-3763	346	11	2	2	NUM
ejpam-3763	346	12	if	if	SCONJ
ejpam-3763	346	13	and	and	CCONJ
ejpam-3763	346	14	only	only	ADV
ejpam-3763	346	15	if	if	SCONJ
ejpam-3763	346	16	n	n	PROPN
ejpam-3763	346	17	=	=	SYM
ejpam-3763	346	18	1	1	NUM
ejpam-3763	346	19	;	;	PUNCT
ejpam-3763	346	20	(	(	PUNCT
ejpam-3763	346	21	iii	iii	NOUN
ejpam-3763	346	22	)	)	PUNCT
ejpam-3763	346	23	γpr(gg	γpr(gg	NOUN
ejpam-3763	346	24	)	)	PUNCT
ejpam-3763	346	25	=	=	SYM
ejpam-3763	346	26	3	3	NUM
ejpam-3763	347	1	if	if	SCONJ
ejpam-3763	347	2	and	and	CCONJ
ejpam-3763	347	3	only	only	ADV
ejpam-3763	347	4	if	if	SCONJ
ejpam-3763	347	5	g	g	PROPN
ejpam-3763	347	6	∈	∈	PROPN
ejpam-3763	347	7	{	{	PUNCT
ejpam-3763	347	8	k2,k2	k2,k2	PROPN
ejpam-3763	347	9	}	}	PUNCT
ejpam-3763	347	10	;	;	PUNCT
ejpam-3763	347	11	(	(	PUNCT
ejpam-3763	347	12	iv	iv	X
ejpam-3763	347	13	)	)	PUNCT
ejpam-3763	347	14	if	if	SCONJ
ejpam-3763	347	15	γ(g	γ(g	PROPN
ejpam-3763	347	16	)	)	PUNCT
ejpam-3763	347	17	=	=	SYM
ejpam-3763	347	18	1	1	NUM
ejpam-3763	347	19	,	,	PUNCT
ejpam-3763	347	20	then	then	ADV
ejpam-3763	347	21	γpr(gg	γpr(gg	X
ejpam-3763	347	22	)	)	PUNCT
ejpam-3763	347	23	≤	≤	NOUN
ejpam-3763	347	24	n	n	CCONJ
ejpam-3763	347	25	+	+	CCONJ
ejpam-3763	347	26	1	1	NUM
ejpam-3763	347	27	and	and	CCONJ
ejpam-3763	347	28	equality	equality	NOUN
ejpam-3763	347	29	is	be	AUX
ejpam-3763	347	30	attained	attain	VERB
ejpam-3763	347	31	if	if	SCONJ
ejpam-3763	347	32	degg(v	degg(v	VERB
ejpam-3763	347	33	)	)	PUNCT
ejpam-3763	347	34	≤	≤	NOUN
ejpam-3763	347	35	3	3	NUM
ejpam-3763	347	36	for	for	ADP
ejpam-3763	347	37	all	all	DET
ejpam-3763	347	38	v	v	NOUN
ejpam-3763	347	39	/∈	/∈	PUNCT
ejpam-3763	348	1	dom(g	dom(g	NOUN
ejpam-3763	348	2	)	)	PUNCT
ejpam-3763	348	3	or	or	CCONJ
ejpam-3763	348	4	g	g	PROPN
ejpam-3763	348	5	is	be	AUX
ejpam-3763	348	6	the	the	DET
ejpam-3763	348	7	disjoint	disjoint	PROPN
ejpam-3763	348	8	union	union	NOUN
ejpam-3763	348	9	of	of	ADP
ejpam-3763	348	10	kj	kj	PROPN
ejpam-3763	348	11	∈	∈	PROPN
ejpam-3763	348	12	{	{	PUNCT
ejpam-3763	348	13	k1,k2	k1,k2	PROPN
ejpam-3763	348	14	}	}	PUNCT
ejpam-3763	348	15	.	.	PUNCT
ejpam-3763	349	1	proof	proof	NOUN
ejpam-3763	349	2	:	:	PUNCT
ejpam-3763	349	3	since	since	SCONJ
ejpam-3763	349	4	gg	gg	PROPN
ejpam-3763	349	5	is	be	AUX
ejpam-3763	349	6	connected	connect	VERB
ejpam-3763	349	7	,	,	PUNCT
ejpam-3763	349	8	(	(	PUNCT
ejpam-3763	349	9	i	i	NOUN
ejpam-3763	349	10	)	)	PUNCT
ejpam-3763	349	11	follows	follow	VERB
ejpam-3763	349	12	from	from	ADP
ejpam-3763	349	13	corollary	corollary	ADJ
ejpam-3763	349	14	2.6	2.6	NUM
ejpam-3763	349	15	.	.	PUNCT
ejpam-3763	350	1	if	if	SCONJ
ejpam-3763	350	2	n	n	NOUN
ejpam-3763	350	3	=	=	SYM
ejpam-3763	350	4	1	1	NUM
ejpam-3763	350	5	,	,	PUNCT
ejpam-3763	350	6	then	then	ADV
ejpam-3763	350	7	gg	gg	PROPN
ejpam-3763	350	8	=	=	SYM
ejpam-3763	350	9	k2	k2	PROPN
ejpam-3763	350	10	and	and	CCONJ
ejpam-3763	350	11	γpr(gg	γpr(gg	NUM
ejpam-3763	350	12	)	)	PUNCT
ejpam-3763	351	1	=	=	SYM
ejpam-3763	351	2	2	2	X
ejpam-3763	351	3	.	.	PUNCT
ejpam-3763	351	4	suppose	suppose	VERB
ejpam-3763	351	5	that	that	SCONJ
ejpam-3763	351	6	γpr(gg	γpr(gg	NOUN
ejpam-3763	351	7	)	)	PUNCT
ejpam-3763	351	8	=	=	SYM
ejpam-3763	351	9	2	2	NUM
ejpam-3763	351	10	,	,	PUNCT
ejpam-3763	351	11	and	and	CCONJ
ejpam-3763	351	12	let	let	VERB
ejpam-3763	351	13	f	f	PRON
ejpam-3763	351	14	be	be	AUX
ejpam-3763	351	15	a	a	DET
ejpam-3763	351	16	γpr	γpr	NOUN
ejpam-3763	351	17	-function	-function	NOUN
ejpam-3763	351	18	of	of	ADP
ejpam-3763	351	19	gg	gg	NOUN
ejpam-3763	351	20	.	.	PUNCT
ejpam-3763	352	1	by	by	ADP
ejpam-3763	352	2	lemma	lemma	PROPN
ejpam-3763	352	3	2.12	2.12	NUM
ejpam-3763	352	4	,	,	PUNCT
ejpam-3763	352	5	we	we	PRON
ejpam-3763	352	6	may	may	AUX
ejpam-3763	352	7	assume	assume	VERB
ejpam-3763	352	8	that	that	SCONJ
ejpam-3763	352	9	f	f	PROPN
ejpam-3763	352	10	|g	|g	PROPN
ejpam-3763	352	11	∈	∈	PROPN
ejpam-3763	352	12	prd(g	prd(g	PROPN
ejpam-3763	352	13	)	)	PUNCT
ejpam-3763	352	14	.	.	PUNCT
ejpam-3763	353	1	if	if	SCONJ
ejpam-3763	353	2	ωg(f	ωg(f	NUM
ejpam-3763	353	3	|g	|g	NOUN
ejpam-3763	353	4	)	)	PUNCT
ejpam-3763	353	5	=	=	SYM
ejpam-3763	353	6	1	1	NUM
ejpam-3763	353	7	,	,	PUNCT
ejpam-3763	353	8	then	then	ADV
ejpam-3763	353	9	n	n	NOUN
ejpam-3763	353	10	=	=	SYM
ejpam-3763	353	11	1	1	X
ejpam-3763	353	12	.	.	PUNCT
ejpam-3763	354	1	if	if	SCONJ
ejpam-3763	354	2	ωg(f	ωg(f	NUM
ejpam-3763	354	3	|g	|g	NOUN
ejpam-3763	354	4	)	)	PUNCT
ejpam-3763	354	5	=	=	SYM
ejpam-3763	354	6	2	2	NUM
ejpam-3763	354	7	,	,	PUNCT
ejpam-3763	354	8	then	then	ADV
ejpam-3763	354	9	g	g	PROPN
ejpam-3763	354	10	=	=	PUNCT
ejpam-3763	354	11	{	{	PUNCT
ejpam-3763	354	12	v	v	NOUN
ejpam-3763	354	13	}	}	PUNCT
ejpam-3763	354	14	with	with	ADP
ejpam-3763	354	15	f(v	f(v	NOUN
ejpam-3763	354	16	)	)	PUNCT
ejpam-3763	354	17	=	=	SYM
ejpam-3763	354	18	f	f	X
ejpam-3763	354	19	|g(v	|g(v	PROPN
ejpam-3763	354	20	)	)	PUNCT
ejpam-3763	354	21	=	=	SYM
ejpam-3763	354	22	2	2	NUM
ejpam-3763	354	23	and	and	CCONJ
ejpam-3763	354	24	f(v	f(v	NOUN
ejpam-3763	354	25	)	)	PUNCT
ejpam-3763	354	26	=	=	SYM
ejpam-3763	355	1	0	0	X
ejpam-3763	355	2	.	.	PUNCT
ejpam-3763	356	1	if	if	SCONJ
ejpam-3763	356	2	g	g	PROPN
ejpam-3763	356	3	∈	∈	PROPN
ejpam-3763	356	4	{	{	PUNCT
ejpam-3763	356	5	k2,k2	k2,k2	PROPN
ejpam-3763	356	6	}	}	PUNCT
ejpam-3763	356	7	,	,	PUNCT
ejpam-3763	356	8	then	then	ADV
ejpam-3763	356	9	gg	gg	PROPN
ejpam-3763	356	10	is	be	AUX
ejpam-3763	356	11	isomorphic	isomorphic	ADJ
ejpam-3763	356	12	to	to	ADP
ejpam-3763	356	13	p4	p4	ADJ
ejpam-3763	356	14	.	.	PUNCT
ejpam-3763	357	1	thus	thus	ADV
ejpam-3763	357	2	,	,	PUNCT
ejpam-3763	357	3	γpr(gg	γpr(gg	X
ejpam-3763	357	4	)	)	PUNCT
ejpam-3763	357	5	=	=	SYM
ejpam-3763	357	6	3	3	X
ejpam-3763	357	7	.	.	PUNCT
ejpam-3763	357	8	conversely	conversely	ADV
ejpam-3763	357	9	,	,	PUNCT
ejpam-3763	357	10	suppose	suppose	VERB
ejpam-3763	357	11	that	that	SCONJ
ejpam-3763	357	12	γpr(gg	γpr(gg	NOUN
ejpam-3763	357	13	)	)	PUNCT
ejpam-3763	357	14	=	=	SYM
ejpam-3763	358	1	3	3	X
ejpam-3763	358	2	.	.	PUNCT
ejpam-3763	358	3	by	by	ADP
ejpam-3763	358	4	proposition	proposition	NOUN
ejpam-3763	358	5	2.3(iii	2.3(iii	NUM
ejpam-3763	358	6	)	)	PUNCT
ejpam-3763	358	7	,	,	PUNCT
ejpam-3763	358	8	∆(gg	∆(gg	NOUN
ejpam-3763	358	9	)	)	PUNCT
ejpam-3763	358	10	=	=	PUNCT
ejpam-3763	359	1	2n−	2n−	NUM
ejpam-3763	359	2	2	2	NUM
ejpam-3763	359	3	.	.	PUNCT
ejpam-3763	360	1	let	let	VERB
ejpam-3763	360	2	v	v	NUM
ejpam-3763	360	3	∈	∈	PROPN
ejpam-3763	360	4	v	v	NOUN
ejpam-3763	360	5	(	(	PUNCT
ejpam-3763	360	6	gg	gg	NOUN
ejpam-3763	360	7	)	)	PUNCT
ejpam-3763	360	8	be	be	AUX
ejpam-3763	360	9	such	such	ADJ
ejpam-3763	360	10	that	that	DET
ejpam-3763	360	11	deggg(v	deggg(v	NOUN
ejpam-3763	360	12	)	)	PUNCT
ejpam-3763	360	13	=	=	SYM
ejpam-3763	360	14	2n	2n	NUM
ejpam-3763	361	1	−	−	NOUN
ejpam-3763	361	2	2	2	X
ejpam-3763	361	3	.	.	NOUN
ejpam-3763	361	4	without	without	ADP
ejpam-3763	361	5	loss	loss	NOUN
ejpam-3763	361	6	of	of	ADP
ejpam-3763	361	7	generality	generality	NOUN
ejpam-3763	361	8	,	,	PUNCT
ejpam-3763	361	9	assume	assume	VERB
ejpam-3763	361	10	that	that	SCONJ
ejpam-3763	361	11	v	v	X
ejpam-3763	361	12	∈	∈	PROPN
ejpam-3763	361	13	v	v	NOUN
ejpam-3763	361	14	(	(	PUNCT
ejpam-3763	361	15	g	g	NOUN
ejpam-3763	361	16	)	)	PUNCT
ejpam-3763	361	17	.	.	PUNCT
ejpam-3763	362	1	since	since	SCONJ
ejpam-3763	362	2	ngg(v	ngg(v	PROPN
ejpam-3763	362	3	)	)	PUNCT
ejpam-3763	362	4	∩	∩	NOUN
ejpam-3763	362	5	v	v	X
ejpam-3763	362	6	(	(	PUNCT
ejpam-3763	362	7	g	g	NOUN
ejpam-3763	362	8	)	)	PUNCT
ejpam-3763	362	9	=	=	SYM
ejpam-3763	362	10	{	{	PUNCT
ejpam-3763	362	11	v	v	NOUN
ejpam-3763	362	12	}	}	PUNCT
ejpam-3763	362	13	,	,	PUNCT
ejpam-3763	362	14	degg(v	degg(v	PROPN
ejpam-3763	362	15	)	)	PUNCT
ejpam-3763	362	16	=	=	PUNCT
ejpam-3763	363	1	2n−	2n−	NUM
ejpam-3763	363	2	3	3	NUM
ejpam-3763	363	3	≤	≤	NUM
ejpam-3763	363	4	n−	n−	NOUN
ejpam-3763	363	5	1	1	NUM
ejpam-3763	363	6	.	.	PUNCT
ejpam-3763	364	1	necessarily	necessarily	ADV
ejpam-3763	364	2	,	,	PUNCT
ejpam-3763	364	3	n	n	PRON
ejpam-3763	364	4	≤	≤	NOUN
ejpam-3763	364	5	2	2	NUM
ejpam-3763	364	6	.	.	PUNCT
ejpam-3763	365	1	by	by	ADP
ejpam-3763	365	2	(	(	PUNCT
ejpam-3763	365	3	ii	ii	NOUN
ejpam-3763	365	4	)	)	PUNCT
ejpam-3763	365	5	,	,	PUNCT
ejpam-3763	365	6	n	n	NOUN
ejpam-3763	365	7	=	=	SYM
ejpam-3763	365	8	2	2	NUM
ejpam-3763	365	9	and	and	CCONJ
ejpam-3763	365	10	g	g	NOUN
ejpam-3763	365	11	=	=	PROPN
ejpam-3763	365	12	k2	k2	PROPN
ejpam-3763	365	13	.	.	PUNCT
ejpam-3763	366	1	if	if	SCONJ
ejpam-3763	366	2	γ(g	γ(g	PROPN
ejpam-3763	366	3	)	)	PUNCT
ejpam-3763	366	4	=	=	SYM
ejpam-3763	366	5	1	1	NUM
ejpam-3763	366	6	,	,	PUNCT
ejpam-3763	366	7	then	then	ADV
ejpam-3763	366	8	by	by	ADP
ejpam-3763	366	9	proposition	proposition	NOUN
ejpam-3763	366	10	2.2	2.2	NUM
ejpam-3763	366	11	,	,	PUNCT
ejpam-3763	366	12	γpr(gg	γpr(gg	NUM
ejpam-3763	366	13	)	)	PUNCT
ejpam-3763	366	14	≤	≤	NUM
ejpam-3763	366	15	n+1	n+1	PROPN
ejpam-3763	366	16	.	.	PUNCT
ejpam-3763	367	1	first	first	ADV
ejpam-3763	367	2	,	,	PUNCT
ejpam-3763	367	3	suppose	suppose	VERB
ejpam-3763	367	4	that	that	SCONJ
ejpam-3763	367	5	degg(v	degg(v	PROPN
ejpam-3763	367	6	)	)	PUNCT
ejpam-3763	367	7	≤	≤	NOUN
ejpam-3763	367	8	3	3	NUM
ejpam-3763	367	9	for	for	ADP
ejpam-3763	367	10	all	all	DET
ejpam-3763	367	11	v	v	NOUN
ejpam-3763	367	12	/∈	/∈	PUNCT
ejpam-3763	367	13	dom(g	dom(g	NOUN
ejpam-3763	367	14	)	)	PUNCT
ejpam-3763	367	15	.	.	PUNCT
ejpam-3763	368	1	let	let	VERB
ejpam-3763	368	2	f	f	PROPN
ejpam-3763	368	3	=	=	SYM
ejpam-3763	368	4	(	(	PUNCT
ejpam-3763	368	5	v0	v0	PROPN
ejpam-3763	368	6	,	,	PUNCT
ejpam-3763	368	7	v1	v1	NOUN
ejpam-3763	368	8	,	,	PUNCT
ejpam-3763	368	9	v2	v2	PROPN
ejpam-3763	368	10	)	)	PUNCT
ejpam-3763	368	11	be	be	AUX
ejpam-3763	368	12	a	a	DET
ejpam-3763	368	13	γpr	γpr	NOUN
ejpam-3763	368	14	-function	-function	NOUN
ejpam-3763	368	15	of	of	ADP
ejpam-3763	368	16	gg	gg	NOUN
ejpam-3763	368	17	.	.	PUNCT
ejpam-3763	369	1	since	since	SCONJ
ejpam-3763	369	2	ωgg(f	ωgg(f	NUM
ejpam-3763	369	3	)	)	PUNCT
ejpam-3763	369	4	≤	≤	NOUN
ejpam-3763	369	5	n+	n+	PUNCT
ejpam-3763	369	6	1	1	NUM
ejpam-3763	369	7	,	,	PUNCT
ejpam-3763	369	8	v2	v2	PROPN
ejpam-3763	369	9	6=	6=	ADP
ejpam-3763	369	10	∅.	∅.	NOUN
ejpam-3763	369	11	we	we	PRON
ejpam-3763	369	12	consider	consider	VERB
ejpam-3763	369	13	two	two	NUM
ejpam-3763	369	14	cases	case	NOUN
ejpam-3763	369	15	:	:	PUNCT
ejpam-3763	369	16	l.	l.	PROPN
ejpam-3763	369	17	paleta	paleta	PROPN
ejpam-3763	369	18	,	,	PUNCT
ejpam-3763	369	19	f.	f.	PROPN
ejpam-3763	369	20	jamil	jamil	PROPN
ejpam-3763	369	21	/	/	SYM
ejpam-3763	369	22	eur	eur	PROPN
ejpam-3763	369	23	.	.	PUNCT
ejpam-3763	370	1	j.	j.	PROPN
ejpam-3763	370	2	pure	pure	PROPN
ejpam-3763	370	3	appl	appl	PROPN
ejpam-3763	370	4	.	.	PROPN
ejpam-3763	370	5	math	math	PROPN
ejpam-3763	370	6	,	,	PUNCT
ejpam-3763	370	7	13	13	NUM
ejpam-3763	370	8	(	(	PUNCT
ejpam-3763	370	9	3	3	NUM
ejpam-3763	370	10	)	)	PUNCT
ejpam-3763	370	11	(	(	PUNCT
ejpam-3763	370	12	2020	2020	NUM
ejpam-3763	370	13	)	)	PUNCT
ejpam-3763	370	14	,	,	PUNCT
ejpam-3763	370	15	529	529	NUM
ejpam-3763	370	16	-	-	SYM
ejpam-3763	370	17	548	548	NUM
ejpam-3763	370	18	539	539	NUM
ejpam-3763	370	19	case	case	NOUN
ejpam-3763	370	20	1	1	NUM
ejpam-3763	370	21	:	:	PUNCT
ejpam-3763	370	22	suppose	suppose	VERB
ejpam-3763	370	23	that	that	SCONJ
ejpam-3763	370	24	v2	v2	PROPN
ejpam-3763	370	25	∩	∩	NOUN
ejpam-3763	370	26	v	v	NOUN
ejpam-3763	370	27	(	(	PUNCT
ejpam-3763	370	28	g	g	NOUN
ejpam-3763	370	29	)	)	PUNCT
ejpam-3763	370	30	=	=	PUNCT
ejpam-3763	370	31	∅.	∅.	NOUN
ejpam-3763	370	32	if	if	SCONJ
ejpam-3763	370	33	v	v	X
ejpam-3763	370	34	(	(	PUNCT
ejpam-3763	370	35	g	g	NOUN
ejpam-3763	370	36	)	)	PUNCT
ejpam-3763	370	37	⊆	⊆	NUM
ejpam-3763	370	38	v1	v1	NOUN
ejpam-3763	370	39	,	,	PUNCT
ejpam-3763	370	40	then	then	ADV
ejpam-3763	370	41	v	v	X
ejpam-3763	370	42	(	(	PUNCT
ejpam-3763	370	43	g	g	NOUN
ejpam-3763	370	44	)	)	PUNCT
ejpam-3763	370	45	*	*	PUNCT
ejpam-3763	370	46	v0	v0	NOUN
ejpam-3763	370	47	so	so	SCONJ
ejpam-3763	370	48	that	that	SCONJ
ejpam-3763	370	49	ωgg(f	ωgg(f	NUM
ejpam-3763	370	50	)	)	PUNCT
ejpam-3763	370	51	≥	≥	NUM
ejpam-3763	370	52	n+	n+	PUNCT
ejpam-3763	370	53	1	1	X
ejpam-3763	370	54	.	.	PUNCT
ejpam-3763	370	55	suppose	suppose	VERB
ejpam-3763	370	56	that	that	SCONJ
ejpam-3763	370	57	v	v	INTJ
ejpam-3763	370	58	(	(	PUNCT
ejpam-3763	370	59	g	g	NOUN
ejpam-3763	370	60	)	)	PUNCT
ejpam-3763	370	61	∩	∩	NOUN
ejpam-3763	370	62	v0	v0	NOUN
ejpam-3763	370	63	6=	6=	X
ejpam-3763	370	64	∅.	∅.	ADP
ejpam-3763	370	65	then	then	ADV
ejpam-3763	370	66	ωgg(f	ωgg(f	NUM
ejpam-3763	370	67	)	)	PUNCT
ejpam-3763	370	68	=	=	SYM
ejpam-3763	370	69	∑	∑	SYM
ejpam-3763	370	70	w∈v0∩v	w∈v0∩v	PROPN
ejpam-3763	370	71	(	(	PUNCT
ejpam-3763	370	72	g	g	NOUN
ejpam-3763	370	73	)	)	PUNCT
ejpam-3763	370	74	f(w	f(w	PROPN
ejpam-3763	370	75	)	)	PUNCT
ejpam-3763	371	1	+	+	CCONJ
ejpam-3763	371	2	∑	∑	PUNCT
ejpam-3763	371	3	w∈v1∩v	w∈v1∩v	NOUN
ejpam-3763	371	4	(	(	PUNCT
ejpam-3763	371	5	g	g	NOUN
ejpam-3763	371	6	)	)	PUNCT
ejpam-3763	371	7	(	(	PUNCT
ejpam-3763	371	8	f(w	f(w	NOUN
ejpam-3763	371	9	)	)	PUNCT
ejpam-3763	371	10	+	+	NUM
ejpam-3763	371	11	f(w	f(w	NOUN
ejpam-3763	371	12	)	)	PUNCT
ejpam-3763	371	13	)	)	PUNCT
ejpam-3763	371	14	≥	≥	X
ejpam-3763	371	15	n+	n+	PUNCT
ejpam-3763	371	16	1	1	X
ejpam-3763	371	17	.	.	X
ejpam-3763	371	18	case	case	NOUN
ejpam-3763	371	19	2	2	NUM
ejpam-3763	371	20	:	:	PUNCT
ejpam-3763	371	21	assume	assume	VERB
ejpam-3763	371	22	that	that	SCONJ
ejpam-3763	371	23	v2	v2	PROPN
ejpam-3763	371	24	∩	∩	NOUN
ejpam-3763	371	25	v	v	NOUN
ejpam-3763	371	26	(	(	PUNCT
ejpam-3763	371	27	g	g	NOUN
ejpam-3763	371	28	)	)	PUNCT
ejpam-3763	371	29	6=	6=	ADP
ejpam-3763	371	30	∅.	∅.	NOUN
ejpam-3763	371	31	we	we	PRON
ejpam-3763	371	32	consider	consider	VERB
ejpam-3763	371	33	two	two	NUM
ejpam-3763	371	34	subcases	subcase	NOUN
ejpam-3763	371	35	:	:	PUNCT
ejpam-3763	371	36	subcase	subcase	NOUN
ejpam-3763	371	37	2.1	2.1	NUM
ejpam-3763	371	38	:	:	PUNCT
ejpam-3763	371	39	suppose	suppose	VERB
ejpam-3763	371	40	that	that	SCONJ
ejpam-3763	371	41	v2	v2	PROPN
ejpam-3763	371	42	contains	contain	VERB
ejpam-3763	371	43	a	a	DET
ejpam-3763	371	44	dominating	dominating	NOUN
ejpam-3763	371	45	vertex	vertex	NOUN
ejpam-3763	371	46	v	v	NOUN
ejpam-3763	371	47	of	of	ADP
ejpam-3763	371	48	g.	g.	PROPN
ejpam-3763	371	49	since	since	SCONJ
ejpam-3763	371	50	f	f	PROPN
ejpam-3763	371	51	is	be	AUX
ejpam-3763	371	52	a	a	DET
ejpam-3763	371	53	γpr	γpr	NOUN
ejpam-3763	371	54	-function	-function	NOUN
ejpam-3763	371	55	,	,	PUNCT
ejpam-3763	371	56	ng(v	ng(v	PUNCT
ejpam-3763	371	57	)	)	PUNCT
ejpam-3763	371	58	∪	∪	ADP
ejpam-3763	371	59	{	{	PUNCT
ejpam-3763	371	60	v	v	NOUN
ejpam-3763	371	61	}	}	PUNCT
ejpam-3763	371	62	⊆	⊆	NUM
ejpam-3763	371	63	v0	v0	NOUN
ejpam-3763	371	64	.	.	PUNCT
ejpam-3763	372	1	let	let	VERB
ejpam-3763	372	2	w	w	NOUN
ejpam-3763	372	3	∈	∈	PROPN
ejpam-3763	372	4	v	v	ADP
ejpam-3763	372	5	(	(	PUNCT
ejpam-3763	372	6	g	g	NOUN
ejpam-3763	372	7	)	)	PUNCT
ejpam-3763	372	8	\	\	NOUN
ejpam-3763	372	9	{	{	PUNCT
ejpam-3763	372	10	v	v	NOUN
ejpam-3763	372	11	}	}	PUNCT
ejpam-3763	372	12	.	.	PUNCT
ejpam-3763	373	1	suppose	suppose	VERB
ejpam-3763	373	2	that	that	SCONJ
ejpam-3763	373	3	w	w	PROPN
ejpam-3763	373	4	∈	∈	PROPN
ejpam-3763	373	5	v0	v0	NOUN
ejpam-3763	373	6	.	.	PUNCT
ejpam-3763	374	1	there	there	PRON
ejpam-3763	374	2	exists	exist	VERB
ejpam-3763	374	3	u	u	PROPN
ejpam-3763	374	4	∈	∈	PROPN
ejpam-3763	374	5	v	v	ADP
ejpam-3763	374	6	(	(	PUNCT
ejpam-3763	374	7	g	g	NOUN
ejpam-3763	374	8	)	)	PUNCT
ejpam-3763	374	9	such	such	ADJ
ejpam-3763	374	10	that	that	SCONJ
ejpam-3763	374	11	ng(w	ng(w	NOUN
ejpam-3763	374	12	)	)	PUNCT
ejpam-3763	374	13	∩	∩	ADJ
ejpam-3763	374	14	v2	v2	NOUN
ejpam-3763	374	15	=	=	SYM
ejpam-3763	374	16	{	{	PUNCT
ejpam-3763	374	17	u	u	NOUN
ejpam-3763	374	18	}	}	PUNCT
ejpam-3763	374	19	.	.	PUNCT
ejpam-3763	375	1	since	since	SCONJ
ejpam-3763	375	2	wv	wv	PROPN
ejpam-3763	375	3	/∈	/∈	PUNCT
ejpam-3763	375	4	e(g	e(g	PROPN
ejpam-3763	375	5	)	)	PUNCT
ejpam-3763	375	6	,	,	PUNCT
ejpam-3763	375	7	u	u	PROPN
ejpam-3763	375	8	6=	6=	PROPN
ejpam-3763	375	9	v.	v.	ADP
ejpam-3763	375	10	thus	thus	ADV
ejpam-3763	375	11	,	,	PUNCT
ejpam-3763	375	12	u	u	PROPN
ejpam-3763	375	13	∈	∈	PROPN
ejpam-3763	375	14	v0	v0	NOUN
ejpam-3763	375	15	and	and	CCONJ
ejpam-3763	375	16	v	v	NOUN
ejpam-3763	375	17	,	,	PUNCT
ejpam-3763	375	18	u	u	PROPN
ejpam-3763	375	19	∈	∈	PROPN
ejpam-3763	375	20	ngg(u	ngg(u	PROPN
ejpam-3763	375	21	)	)	PUNCT
ejpam-3763	375	22	∩	∩	ADJ
ejpam-3763	375	23	v2	v2	PROPN
ejpam-3763	375	24	,	,	PUNCT
ejpam-3763	375	25	a	a	DET
ejpam-3763	375	26	contradiction	contradiction	NOUN
ejpam-3763	375	27	.	.	PUNCT
ejpam-3763	376	1	this	this	PRON
ejpam-3763	376	2	means	mean	VERB
ejpam-3763	376	3	that	that	SCONJ
ejpam-3763	376	4	f(w	f(w	PROPN
ejpam-3763	376	5	)	)	PUNCT
ejpam-3763	376	6	≥	≥	NOUN
ejpam-3763	376	7	1	1	NUM
ejpam-3763	376	8	.	.	PUNCT
ejpam-3763	377	1	therefore	therefore	ADV
ejpam-3763	377	2	,	,	PUNCT
ejpam-3763	377	3	ωgg(f	ωgg(f	PROPN
ejpam-3763	377	4	)	)	PUNCT
ejpam-3763	377	5	=	=	SYM
ejpam-3763	377	6	2	2	NUM
ejpam-3763	377	7	+	+	CCONJ
ejpam-3763	377	8	∑	∑	PROPN
ejpam-3763	377	9	w∈v	w∈v	PROPN
ejpam-3763	377	10	(	(	PUNCT
ejpam-3763	377	11	g)\{v	g)\{v	PROPN
ejpam-3763	377	12	}	}	PUNCT
ejpam-3763	377	13	f(w	f(w	PROPN
ejpam-3763	377	14	)	)	PUNCT
ejpam-3763	377	15	≥	≥	NOUN
ejpam-3763	377	16	2	2	NUM
ejpam-3763	377	17	+	+	NUM
ejpam-3763	377	18	n−	n−	NOUN
ejpam-3763	377	19	1	1	NUM
ejpam-3763	377	20	=	=	SYM
ejpam-3763	377	21	n+	n+	PUNCT
ejpam-3763	377	22	1	1	X
ejpam-3763	377	23	.	.	X
ejpam-3763	377	24	subcase	subcase	PROPN
ejpam-3763	377	25	2.2	2.2	NUM
ejpam-3763	377	26	:	:	PUNCT
ejpam-3763	377	27	suppose	suppose	VERB
ejpam-3763	377	28	that	that	SCONJ
ejpam-3763	377	29	v2	v2	PROPN
ejpam-3763	377	30	∩dom(g	∩dom(g	NOUN
ejpam-3763	377	31	)	)	PUNCT
ejpam-3763	377	32	=	=	PUNCT
ejpam-3763	377	33	∅.	∅.	PROPN
ejpam-3763	377	34	choos	choos	X
ejpam-3763	377	35	v	v	ADP
ejpam-3763	377	36	∈	∈	PROPN
ejpam-3763	377	37	dom(g	dom(g	NOUN
ejpam-3763	377	38	)	)	PUNCT
ejpam-3763	377	39	.	.	PUNCT
ejpam-3763	378	1	put	put	VERB
ejpam-3763	378	2	a	a	PRON
ejpam-3763	378	3	=	=	X
ejpam-3763	378	4	{	{	PUNCT
ejpam-3763	378	5	w	w	PROPN
ejpam-3763	378	6	∈	∈	PROPN
ejpam-3763	378	7	v	v	ADP
ejpam-3763	378	8	(	(	PUNCT
ejpam-3763	378	9	g	g	NOUN
ejpam-3763	378	10	)	)	PUNCT
ejpam-3763	378	11	:	:	PUNCT
ejpam-3763	378	12	f(w	f(w	X
ejpam-3763	378	13	)	)	PUNCT
ejpam-3763	378	14	=	=	PUNCT
ejpam-3763	378	15	f(w	f(w	PROPN
ejpam-3763	378	16	)	)	PUNCT
ejpam-3763	378	17	=	=	PUNCT
ejpam-3763	378	18	0	0	NUM
ejpam-3763	378	19	}	}	PUNCT
ejpam-3763	378	20	.	.	PUNCT
ejpam-3763	379	1	if	if	SCONJ
ejpam-3763	379	2	a	a	DET
ejpam-3763	379	3	=	=	NOUN
ejpam-3763	379	4	∅	∅	NOUN
ejpam-3763	379	5	,	,	PUNCT
ejpam-3763	379	6	then	then	ADV
ejpam-3763	379	7	f(w	f(w	PROPN
ejpam-3763	379	8	)	)	PUNCT
ejpam-3763	379	9	+	+	NUM
ejpam-3763	379	10	f(w	f(w	PROPN
ejpam-3763	379	11	)	)	PUNCT
ejpam-3763	379	12	≥	≥	NOUN
ejpam-3763	379	13	1	1	NUM
ejpam-3763	379	14	for	for	ADP
ejpam-3763	379	15	all	all	DET
ejpam-3763	379	16	w	w	PROPN
ejpam-3763	379	17	∈	∈	PROPN
ejpam-3763	379	18	v	v	ADP
ejpam-3763	379	19	(	(	PUNCT
ejpam-3763	379	20	g	g	NOUN
ejpam-3763	379	21	)	)	PUNCT
ejpam-3763	379	22	and	and	CCONJ
ejpam-3763	379	23	since	since	SCONJ
ejpam-3763	379	24	v2	v2	PROPN
ejpam-3763	379	25	∩	∩	NOUN
ejpam-3763	379	26	v	v	NOUN
ejpam-3763	379	27	(	(	PUNCT
ejpam-3763	379	28	g	g	NOUN
ejpam-3763	379	29	)	)	PUNCT
ejpam-3763	379	30	6=	6=	ADP
ejpam-3763	379	31	∅	∅	NOUN
ejpam-3763	379	32	,	,	PUNCT
ejpam-3763	379	33	we	we	PRON
ejpam-3763	379	34	have	have	VERB
ejpam-3763	379	35	ωgg(f	ωgg(f	NUM
ejpam-3763	379	36	)	)	PUNCT
ejpam-3763	379	37	≥	≥	NOUN
ejpam-3763	379	38	n	n	NOUN
ejpam-3763	379	39	+	+	NUM
ejpam-3763	379	40	1	1	X
ejpam-3763	379	41	.	.	PUNCT
ejpam-3763	379	42	suppose	suppose	VERB
ejpam-3763	379	43	that	that	SCONJ
ejpam-3763	379	44	a	a	DET
ejpam-3763	379	45	6=	6=	NUM
ejpam-3763	379	46	∅.	∅.	ADP
ejpam-3763	379	47	here	here	ADV
ejpam-3763	379	48	,	,	PUNCT
ejpam-3763	379	49	we	we	PRON
ejpam-3763	379	50	work	work	VERB
ejpam-3763	379	51	on	on	ADP
ejpam-3763	379	52	two	two	NUM
ejpam-3763	379	53	subcases	subcase	NOUN
ejpam-3763	379	54	:	:	PUNCT
ejpam-3763	379	55	subcase	subcase	NOUN
ejpam-3763	379	56	2.2.1	2.2.1	NUM
ejpam-3763	379	57	:	:	PUNCT
ejpam-3763	379	58	suppose	suppose	VERB
ejpam-3763	379	59	that	that	SCONJ
ejpam-3763	379	60	v	v	PROPN
ejpam-3763	379	61	∈	∈	PROPN
ejpam-3763	379	62	v0	v0	NOUN
ejpam-3763	379	63	.	.	PUNCT
ejpam-3763	380	1	if	if	SCONJ
ejpam-3763	380	2	f(v	f(v	NOUN
ejpam-3763	380	3	)	)	PUNCT
ejpam-3763	380	4	=	=	SYM
ejpam-3763	380	5	2	2	NUM
ejpam-3763	380	6	,	,	PUNCT
ejpam-3763	380	7	then	then	ADV
ejpam-3763	380	8	v	v	NOUN
ejpam-3763	380	9	(	(	PUNCT
ejpam-3763	380	10	g	g	NOUN
ejpam-3763	380	11	)	)	PUNCT
ejpam-3763	380	12	∩	∩	ADJ
ejpam-3763	380	13	v2	v2	NOUN
ejpam-3763	380	14	=	=	PUNCT
ejpam-3763	380	15	∅	∅	NOUN
ejpam-3763	380	16	and	and	CCONJ
ejpam-3763	380	17	so	so	ADV
ejpam-3763	380	18	f(u	f(u	PROPN
ejpam-3763	380	19	)	)	PUNCT
ejpam-3763	380	20	=	=	SYM
ejpam-3763	380	21	2	2	NUM
ejpam-3763	380	22	for	for	ADP
ejpam-3763	380	23	each	each	DET
ejpam-3763	380	24	u	u	PROPN
ejpam-3763	380	25	∈	∈	PROPN
ejpam-3763	380	26	v0	v0	NOUN
ejpam-3763	380	27	∩	∩	X
ejpam-3763	380	28	v	v	X
ejpam-3763	380	29	(	(	PUNCT
ejpam-3763	380	30	g	g	NOUN
ejpam-3763	380	31	)	)	PUNCT
ejpam-3763	380	32	.	.	PUNCT
ejpam-3763	381	1	this	this	PRON
ejpam-3763	381	2	implies	imply	VERB
ejpam-3763	381	3	that	that	SCONJ
ejpam-3763	381	4	ωgg(f	ωgg(f	PROPN
ejpam-3763	381	5	)	)	PUNCT
ejpam-3763	381	6	≥	≥	NOUN
ejpam-3763	381	7	n	n	NOUN
ejpam-3763	381	8	+	+	NUM
ejpam-3763	381	9	1	1	X
ejpam-3763	381	10	.	.	PUNCT
ejpam-3763	381	11	suppose	suppose	VERB
ejpam-3763	381	12	that	that	SCONJ
ejpam-3763	381	13	f(v	f(v	NOUN
ejpam-3763	381	14	)	)	PUNCT
ejpam-3763	381	15	=	=	SYM
ejpam-3763	382	1	1	1	X
ejpam-3763	382	2	.	.	PUNCT
ejpam-3763	382	3	then	then	ADV
ejpam-3763	382	4	there	there	PRON
ejpam-3763	382	5	exists	exist	VERB
ejpam-3763	382	6	u	u	PROPN
ejpam-3763	382	7	∈	∈	PROPN
ejpam-3763	382	8	v	v	ADP
ejpam-3763	382	9	(	(	PUNCT
ejpam-3763	382	10	g	g	NOUN
ejpam-3763	382	11	)	)	PUNCT
ejpam-3763	382	12	such	such	ADJ
ejpam-3763	382	13	that	that	SCONJ
ejpam-3763	382	14	v2	v2	PROPN
ejpam-3763	382	15	∩	∩	NOUN
ejpam-3763	382	16	v	v	NOUN
ejpam-3763	382	17	(	(	PUNCT
ejpam-3763	382	18	g	g	NOUN
ejpam-3763	382	19	)	)	PUNCT
ejpam-3763	382	20	=	=	PRON
ejpam-3763	382	21	{	{	PUNCT
ejpam-3763	382	22	u	u	NOUN
ejpam-3763	382	23	}	}	PUNCT
ejpam-3763	382	24	.	.	PUNCT
ejpam-3763	383	1	moreover	moreover	ADV
ejpam-3763	383	2	,	,	PUNCT
ejpam-3763	383	3	for	for	ADP
ejpam-3763	383	4	each	each	DET
ejpam-3763	383	5	w	w	PROPN
ejpam-3763	383	6	∈	∈	PROPN
ejpam-3763	383	7	a	a	PRON
ejpam-3763	383	8	,	,	PUNCT
ejpam-3763	383	9	wu	wu	PROPN
ejpam-3763	383	10	∈	∈	PROPN
ejpam-3763	383	11	e(g	e(g	PROPN
ejpam-3763	383	12	)	)	PUNCT
ejpam-3763	383	13	.	.	PUNCT
ejpam-3763	384	1	since	since	SCONJ
ejpam-3763	384	2	degg(u	degg(u	PROPN
ejpam-3763	384	3	)	)	PUNCT
ejpam-3763	384	4	≤	≤	NOUN
ejpam-3763	384	5	3	3	NUM
ejpam-3763	384	6	and	and	CCONJ
ejpam-3763	384	7	uv	uv	PROPN
ejpam-3763	384	8	∈	∈	PROPN
ejpam-3763	384	9	e(g	e(g	PROPN
ejpam-3763	384	10	)	)	PUNCT
ejpam-3763	384	11	,	,	PUNCT
ejpam-3763	384	12	|a|	|a|	NOUN
ejpam-3763	384	13	≤	≤	ADV
ejpam-3763	384	14	2	2	NUM
ejpam-3763	384	15	.	.	PUNCT
ejpam-3763	384	16	suppose	suppose	VERB
ejpam-3763	384	17	that	that	SCONJ
ejpam-3763	384	18	a	a	DET
ejpam-3763	384	19	=	=	X
ejpam-3763	384	20	{	{	PUNCT
ejpam-3763	384	21	w	w	NOUN
ejpam-3763	384	22	}	}	PUNCT
ejpam-3763	384	23	.	.	PUNCT
ejpam-3763	385	1	there	there	PRON
ejpam-3763	385	2	exists	exist	VERB
ejpam-3763	385	3	a	a	DET
ejpam-3763	385	4	∈	∈	PROPN
ejpam-3763	385	5	v	v	NOUN
ejpam-3763	385	6	(	(	PUNCT
ejpam-3763	385	7	g	g	NOUN
ejpam-3763	385	8	)	)	PUNCT
ejpam-3763	385	9	such	such	ADJ
ejpam-3763	385	10	that	that	DET
ejpam-3763	385	11	u	u	PROPN
ejpam-3763	385	12	6=	6=	ADP
ejpam-3763	385	13	a	a	PRON
ejpam-3763	385	14	and	and	CCONJ
ejpam-3763	385	15	ng(w	ng(w	NOUN
ejpam-3763	385	16	)	)	PUNCT
ejpam-3763	385	17	∩	∩	ADJ
ejpam-3763	385	18	v2	v2	NOUN
ejpam-3763	385	19	=	=	SYM
ejpam-3763	385	20	{	{	PUNCT
ejpam-3763	385	21	a	a	NOUN
ejpam-3763	385	22	}	}	PUNCT
ejpam-3763	385	23	.	.	PUNCT
ejpam-3763	386	1	since	since	SCONJ
ejpam-3763	386	2	α	α	NOUN
ejpam-3763	386	3	=	=	SYM
ejpam-3763	386	4	(	(	PUNCT
ejpam-3763	386	5	f(u	f(u	PROPN
ejpam-3763	386	6	)	)	PUNCT
ejpam-3763	386	7	+	+	CCONJ
ejpam-3763	386	8	f(u	f(u	NOUN
ejpam-3763	386	9	)	)	PUNCT
ejpam-3763	386	10	)	)	PUNCT
ejpam-3763	387	1	+	+	CCONJ
ejpam-3763	387	2	(	(	PUNCT
ejpam-3763	387	3	f(w	f(w	NOUN
ejpam-3763	387	4	)	)	PUNCT
ejpam-3763	387	5	+	+	NUM
ejpam-3763	387	6	f(w	f(w	NOUN
ejpam-3763	387	7	)	)	PUNCT
ejpam-3763	387	8	)	)	PUNCT
ejpam-3763	388	1	+	+	CCONJ
ejpam-3763	388	2	(	(	PUNCT
ejpam-3763	388	3	f(a	f(a	NOUN
ejpam-3763	388	4	)	)	PUNCT
ejpam-3763	388	5	+	+	NUM
ejpam-3763	388	6	f(a	f(a	NOUN
ejpam-3763	388	7	)	)	PUNCT
ejpam-3763	388	8	)	)	PUNCT
ejpam-3763	388	9	≥	≥	NOUN
ejpam-3763	388	10	4	4	NUM
ejpam-3763	388	11	,	,	PUNCT
ejpam-3763	388	12	ωgg(f	ωgg(f	NUM
ejpam-3763	388	13	)	)	PUNCT
ejpam-3763	388	14	=	=	SYM
ejpam-3763	388	15	α+	α+	X
ejpam-3763	388	16	∑	∑	PUNCT
ejpam-3763	388	17	x∈v	x∈v	PROPN
ejpam-3763	388	18	(	(	PUNCT
ejpam-3763	388	19	g)\{u	g)\{u	PROPN
ejpam-3763	388	20	,	,	PUNCT
ejpam-3763	388	21	w	w	PROPN
ejpam-3763	388	22	,	,	PUNCT
ejpam-3763	388	23	a	a	PRON
ejpam-3763	388	24	}	}	PUNCT
ejpam-3763	388	25	(	(	PUNCT
ejpam-3763	388	26	f(x	f(x	PROPN
ejpam-3763	388	27	)	)	PUNCT
ejpam-3763	388	28	+	+	CCONJ
ejpam-3763	388	29	f(x	f(x	PROPN
ejpam-3763	388	30	)	)	PUNCT
ejpam-3763	388	31	)	)	PUNCT
ejpam-3763	388	32	≥	≥	NOUN
ejpam-3763	388	33	4	4	NUM
ejpam-3763	388	34	+	+	CCONJ
ejpam-3763	388	35	(	(	PUNCT
ejpam-3763	388	36	n−	n−	NOUN
ejpam-3763	388	37	4	4	NUM
ejpam-3763	388	38	)	)	PUNCT
ejpam-3763	388	39	+	+	CCONJ
ejpam-3763	388	40	1	1	NUM
ejpam-3763	388	41	=	=	SYM
ejpam-3763	388	42	n+	n+	PRON
ejpam-3763	388	43	1	1	X
ejpam-3763	388	44	.	.	PUNCT
ejpam-3763	389	1	now	now	ADV
ejpam-3763	389	2	,	,	PUNCT
ejpam-3763	389	3	suppose	suppose	VERB
ejpam-3763	389	4	that	that	SCONJ
ejpam-3763	389	5	a	a	PRON
ejpam-3763	389	6	=	=	X
ejpam-3763	389	7	{	{	PUNCT
ejpam-3763	389	8	w	w	PROPN
ejpam-3763	389	9	,	,	PUNCT
ejpam-3763	389	10	z	z	NOUN
ejpam-3763	389	11	}	}	PUNCT
ejpam-3763	389	12	.	.	PUNCT
ejpam-3763	390	1	there	there	PRON
ejpam-3763	390	2	exist	exist	VERB
ejpam-3763	390	3	a	a	DET
ejpam-3763	390	4	,	,	PUNCT
ejpam-3763	390	5	b	b	PROPN
ejpam-3763	390	6	∈	∈	PROPN
ejpam-3763	390	7	v	v	NOUN
ejpam-3763	390	8	(	(	PUNCT
ejpam-3763	390	9	g	g	NOUN
ejpam-3763	390	10	)	)	PUNCT
ejpam-3763	390	11	such	such	ADJ
ejpam-3763	390	12	that	that	SCONJ
ejpam-3763	390	13	a	a	DET
ejpam-3763	390	14	,	,	PUNCT
ejpam-3763	390	15	b	b	PROPN
ejpam-3763	390	16	∈	∈	PROPN
ejpam-3763	390	17	v2	v2	PROPN
ejpam-3763	390	18	,	,	PUNCT
ejpam-3763	390	19	wa	wa	ADJ
ejpam-3763	390	20	,	,	PUNCT
ejpam-3763	390	21	zb	zb	PROPN
ejpam-3763	390	22	∈	∈	PROPN
ejpam-3763	390	23	e(g	e(g	PROPN
ejpam-3763	390	24	)	)	PUNCT
ejpam-3763	390	25	and	and	CCONJ
ejpam-3763	390	26	a	a	DET
ejpam-3763	390	27	,	,	PUNCT
ejpam-3763	390	28	b	b	PROPN
ejpam-3763	390	29	∈	∈	PROPN
ejpam-3763	390	30	ng(u	ng(u	NOUN
ejpam-3763	390	31	)	)	PUNCT
ejpam-3763	390	32	.	.	PUNCT
ejpam-3763	391	1	thus	thus	ADV
ejpam-3763	391	2	,	,	PUNCT
ejpam-3763	391	3	f(u	f(u	PROPN
ejpam-3763	391	4	)	)	PUNCT
ejpam-3763	391	5	=	=	SYM
ejpam-3763	391	6	f(a	f(a	PROPN
ejpam-3763	391	7	)	)	PUNCT
ejpam-3763	391	8	=	=	SYM
ejpam-3763	391	9	f(b	f(b	X
ejpam-3763	391	10	)	)	PUNCT
ejpam-3763	391	11	=	=	SYM
ejpam-3763	391	12	1	1	NUM
ejpam-3763	391	13	and	and	CCONJ
ejpam-3763	391	14	whether	whether	SCONJ
ejpam-3763	391	15	a	a	DET
ejpam-3763	391	16	=	=	SYM
ejpam-3763	391	17	b	b	NOUN
ejpam-3763	391	18	or	or	CCONJ
ejpam-3763	391	19	a	a	DET
ejpam-3763	391	20	6=	6=	PROPN
ejpam-3763	391	21	b	b	PROPN
ejpam-3763	391	22	,	,	PUNCT
ejpam-3763	391	23	α	α	NOUN
ejpam-3763	391	24	=	=	X
ejpam-3763	391	25	(	(	PUNCT
ejpam-3763	391	26	f(u	f(u	PROPN
ejpam-3763	391	27	)	)	PUNCT
ejpam-3763	391	28	+	+	CCONJ
ejpam-3763	391	29	f(u	f(u	NOUN
ejpam-3763	391	30	)	)	PUNCT
ejpam-3763	391	31	)	)	PUNCT
ejpam-3763	392	1	+	+	CCONJ
ejpam-3763	392	2	(	(	PUNCT
ejpam-3763	392	3	f(w	f(w	NOUN
ejpam-3763	392	4	)	)	PUNCT
ejpam-3763	392	5	+	+	NUM
ejpam-3763	392	6	f(w	f(w	NOUN
ejpam-3763	392	7	)	)	PUNCT
ejpam-3763	392	8	)	)	PUNCT
ejpam-3763	393	1	+	+	CCONJ
ejpam-3763	393	2	(	(	PUNCT
ejpam-3763	393	3	f(z	f(z	PROPN
ejpam-3763	393	4	)	)	PUNCT
ejpam-3763	393	5	+	+	CCONJ
ejpam-3763	393	6	f(z	f(z	NOUN
ejpam-3763	393	7	)	)	PUNCT
ejpam-3763	393	8	)	)	PUNCT
ejpam-3763	394	1	+	+	CCONJ
ejpam-3763	394	2	(	(	PUNCT
ejpam-3763	394	3	f(a	f(a	NOUN
ejpam-3763	394	4	)	)	PUNCT
ejpam-3763	394	5	+	+	NUM
ejpam-3763	394	6	f(a	f(a	NOUN
ejpam-3763	394	7	)	)	PUNCT
ejpam-3763	394	8	)	)	PUNCT
ejpam-3763	395	1	+	+	CCONJ
ejpam-3763	395	2	(	(	PUNCT
ejpam-3763	395	3	f(b	f(b	PROPN
ejpam-3763	395	4	)	)	PUNCT
ejpam-3763	395	5	+	+	SYM
ejpam-3763	395	6	f(b	f(b	X
ejpam-3763	395	7	)	)	PUNCT
ejpam-3763	395	8	)	)	PUNCT
ejpam-3763	395	9	≥	≥	NOUN
ejpam-3763	395	10	6	6	NUM
ejpam-3763	395	11	.	.	PUNCT
ejpam-3763	395	12	thus	thus	ADV
ejpam-3763	395	13	,	,	PUNCT
ejpam-3763	395	14	ωgg(f	ωgg(f	PROPN
ejpam-3763	395	15	)	)	PUNCT
ejpam-3763	395	16	=	=	SYM
ejpam-3763	395	17	α+	α+	X
ejpam-3763	395	18	∑	∑	PUNCT
ejpam-3763	395	19	x∈v	x∈v	PROPN
ejpam-3763	395	20	(	(	PUNCT
ejpam-3763	395	21	g)\{u	g)\{u	PROPN
ejpam-3763	395	22	,	,	PUNCT
ejpam-3763	395	23	w	w	PROPN
ejpam-3763	395	24	,	,	PUNCT
ejpam-3763	395	25	z	z	PROPN
ejpam-3763	395	26	,	,	PUNCT
ejpam-3763	395	27	a	a	PRON
ejpam-3763	395	28	,	,	PUNCT
ejpam-3763	395	29	b	b	NOUN
ejpam-3763	395	30	}	}	PUNCT
ejpam-3763	395	31	(	(	PUNCT
ejpam-3763	395	32	f(x	f(x	PROPN
ejpam-3763	395	33	)	)	PUNCT
ejpam-3763	395	34	+	+	CCONJ
ejpam-3763	395	35	f(x	f(x	PROPN
ejpam-3763	395	36	)	)	PUNCT
ejpam-3763	395	37	)	)	PUNCT
ejpam-3763	395	38	≥	≥	NOUN
ejpam-3763	395	39	6	6	NUM
ejpam-3763	396	1	+	+	CCONJ
ejpam-3763	396	2	(	(	PUNCT
ejpam-3763	396	3	n−	n−	NOUN
ejpam-3763	396	4	6	6	NUM
ejpam-3763	396	5	)	)	PUNCT
ejpam-3763	396	6	+	+	CCONJ
ejpam-3763	396	7	1	1	NUM
ejpam-3763	396	8	=	=	SYM
ejpam-3763	396	9	n+	n+	PUNCT
ejpam-3763	396	10	1	1	X
ejpam-3763	396	11	.	.	X
ejpam-3763	396	12	subcase	subcase	PROPN
ejpam-3763	396	13	2.2.2	2.2.2	NUM
ejpam-3763	396	14	:	:	PUNCT
ejpam-3763	396	15	suppose	suppose	VERB
ejpam-3763	396	16	that	that	SCONJ
ejpam-3763	396	17	v	v	NOUN
ejpam-3763	396	18	,	,	PUNCT
ejpam-3763	396	19	v	v	NOUN
ejpam-3763	396	20	∈	∈	PROPN
ejpam-3763	396	21	v1	v1	NOUN
ejpam-3763	396	22	.	.	PUNCT
ejpam-3763	397	1	for	for	ADP
ejpam-3763	397	2	each	each	DET
ejpam-3763	397	3	w	w	PROPN
ejpam-3763	397	4	∈	∈	PROPN
ejpam-3763	397	5	a	a	PRON
ejpam-3763	397	6	,	,	PUNCT
ejpam-3763	397	7	there	there	PRON
ejpam-3763	397	8	exist	exist	VERB
ejpam-3763	397	9	distinct	distinct	ADJ
ejpam-3763	397	10	vertices	vertex	NOUN
ejpam-3763	397	11	u	u	NOUN
ejpam-3763	397	12	,	,	PUNCT
ejpam-3763	397	13	z	z	PROPN
ejpam-3763	397	14	∈	∈	PROPN
ejpam-3763	397	15	v	v	ADP
ejpam-3763	397	16	(	(	PUNCT
ejpam-3763	397	17	g	g	NOUN
ejpam-3763	397	18	)	)	PUNCT
ejpam-3763	397	19	such	such	ADJ
ejpam-3763	397	20	that	that	SCONJ
ejpam-3763	397	21	u	u	NOUN
ejpam-3763	397	22	,	,	PUNCT
ejpam-3763	397	23	z	z	PROPN
ejpam-3763	397	24	∈	∈	PROPN
ejpam-3763	397	25	v2	v2	PROPN
ejpam-3763	397	26	,	,	PUNCT
ejpam-3763	397	27	uw	uw	PROPN
ejpam-3763	397	28	∈	∈	PROPN
ejpam-3763	397	29	e(g	e(g	PROPN
ejpam-3763	397	30	)	)	PUNCT
ejpam-3763	397	31	and	and	CCONJ
ejpam-3763	397	32	wz	wz	ADP
ejpam-3763	397	33	∈	∈	PROPN
ejpam-3763	397	34	e(g	e(g	PROPN
ejpam-3763	397	35	)	)	PUNCT
ejpam-3763	397	36	.	.	PUNCT
ejpam-3763	398	1	again	again	ADV
ejpam-3763	398	2	,	,	PUNCT
ejpam-3763	398	3	for	for	ADP
ejpam-3763	398	4	each	each	DET
ejpam-3763	398	5	u	u	PROPN
ejpam-3763	398	6	∈	∈	PROPN
ejpam-3763	398	7	v2	v2	PROPN
ejpam-3763	398	8	∩	∩	ADJ
ejpam-3763	398	9	v	v	NOUN
ejpam-3763	398	10	(	(	PUNCT
ejpam-3763	398	11	g	g	NOUN
ejpam-3763	398	12	)	)	PUNCT
ejpam-3763	398	13	,	,	PUNCT
ejpam-3763	398	14	since	since	SCONJ
ejpam-3763	398	15	degg(u	degg(u	PROPN
ejpam-3763	398	16	)	)	PUNCT
ejpam-3763	398	17	≤	≤	NOUN
ejpam-3763	398	18	3	3	NUM
ejpam-3763	398	19	,	,	PUNCT
ejpam-3763	398	20	there	there	PRON
ejpam-3763	398	21	can	can	AUX
ejpam-3763	398	22	only	only	ADV
ejpam-3763	398	23	be	be	AUX
ejpam-3763	398	24	at	at	ADP
ejpam-3763	398	25	most	most	ADV
ejpam-3763	398	26	two	two	NUM
ejpam-3763	398	27	vertices	vertex	NOUN
ejpam-3763	398	28	a	a	DET
ejpam-3763	398	29	,	,	PUNCT
ejpam-3763	398	30	b	b	PROPN
ejpam-3763	398	31	∈	∈	PROPN
ejpam-3763	398	32	a	a	PRON
ejpam-3763	398	33	for	for	ADP
ejpam-3763	398	34	which	which	PRON
ejpam-3763	398	35	ua	ua	PROPN
ejpam-3763	398	36	,	,	PUNCT
ejpam-3763	398	37	ub	ub	PROPN
ejpam-3763	398	38	∈	∈	PROPN
ejpam-3763	398	39	e(g	e(g	PROPN
ejpam-3763	398	40	)	)	PUNCT
ejpam-3763	398	41	.	.	PUNCT
ejpam-3763	399	1	using	use	VERB
ejpam-3763	399	2	similar	similar	ADJ
ejpam-3763	399	3	arguments	argument	NOUN
ejpam-3763	399	4	,	,	PUNCT
ejpam-3763	399	5	if	if	SCONJ
ejpam-3763	399	6	|a|	|a|	NUM
ejpam-3763	399	7	≤	≤	ADV
ejpam-3763	399	8	2	2	NUM
ejpam-3763	399	9	,	,	PUNCT
ejpam-3763	399	10	then	then	ADV
ejpam-3763	399	11	ωgg(f	ωgg(f	NUM
ejpam-3763	399	12	)	)	PUNCT
ejpam-3763	399	13	≥	≥	NOUN
ejpam-3763	399	14	n	n	NOUN
ejpam-3763	399	15	+	+	NUM
ejpam-3763	399	16	1	1	X
ejpam-3763	399	17	.	.	PUNCT
ejpam-3763	399	18	to	to	PART
ejpam-3763	399	19	proceed	proceed	VERB
ejpam-3763	399	20	,	,	PUNCT
ejpam-3763	399	21	we	we	PRON
ejpam-3763	399	22	only	only	ADV
ejpam-3763	399	23	have	have	VERB
ejpam-3763	399	24	to	to	PART
ejpam-3763	399	25	consider	consider	VERB
ejpam-3763	399	26	the	the	DET
ejpam-3763	399	27	case	case	NOUN
ejpam-3763	399	28	where	where	SCONJ
ejpam-3763	399	29	3	3	NUM
ejpam-3763	399	30	≤	≤	NUM
ejpam-3763	399	31	|a|	|a|	NOUN
ejpam-3763	399	32	≤	≤	NOUN
ejpam-3763	399	33	4	4	NUM
ejpam-3763	399	34	.	.	PUNCT
ejpam-3763	400	1	other	other	ADJ
ejpam-3763	400	2	cases	case	NOUN
ejpam-3763	400	3	follow	follow	VERB
ejpam-3763	400	4	inductively	inductively	ADV
ejpam-3763	400	5	.	.	PUNCT
ejpam-3763	401	1	l.	l.	PROPN
ejpam-3763	401	2	paleta	paleta	PROPN
ejpam-3763	401	3	,	,	PUNCT
ejpam-3763	401	4	f.	f.	PROPN
ejpam-3763	401	5	jamil	jamil	PROPN
ejpam-3763	401	6	/	/	SYM
ejpam-3763	401	7	eur	eur	PROPN
ejpam-3763	401	8	.	.	PUNCT
ejpam-3763	402	1	j.	j.	PROPN
ejpam-3763	402	2	pure	pure	PROPN
ejpam-3763	402	3	appl	appl	PROPN
ejpam-3763	402	4	.	.	PROPN
ejpam-3763	402	5	math	math	PROPN
ejpam-3763	402	6	,	,	PUNCT
ejpam-3763	402	7	13	13	NUM
ejpam-3763	402	8	(	(	PUNCT
ejpam-3763	402	9	3	3	NUM
ejpam-3763	402	10	)	)	PUNCT
ejpam-3763	402	11	(	(	PUNCT
ejpam-3763	402	12	2020	2020	NUM
ejpam-3763	402	13	)	)	PUNCT
ejpam-3763	402	14	,	,	PUNCT
ejpam-3763	402	15	529	529	NUM
ejpam-3763	402	16	-	-	SYM
ejpam-3763	402	17	548	548	NUM
ejpam-3763	402	18	540	540	NUM
ejpam-3763	402	19	suppose	suppose	VERB
ejpam-3763	402	20	that	that	SCONJ
ejpam-3763	402	21	a	a	PRON
ejpam-3763	402	22	=	=	SYM
ejpam-3763	402	23	{	{	PUNCT
ejpam-3763	402	24	x	x	PROPN
ejpam-3763	402	25	,	,	PUNCT
ejpam-3763	402	26	y	y	PROPN
ejpam-3763	402	27	,	,	PUNCT
ejpam-3763	402	28	w	w	PROPN
ejpam-3763	402	29	}	}	PUNCT
ejpam-3763	402	30	.	.	PUNCT
ejpam-3763	403	1	the	the	DET
ejpam-3763	403	2	only	only	ADJ
ejpam-3763	403	3	nontrivial	nontrivial	ADJ
ejpam-3763	403	4	scenario	scenario	NOUN
ejpam-3763	403	5	is	be	AUX
ejpam-3763	403	6	the	the	DET
ejpam-3763	403	7	following	following	NOUN
ejpam-3763	403	8	:	:	PUNCT
ejpam-3763	403	9	there	there	PRON
ejpam-3763	403	10	exist	exist	VERB
ejpam-3763	403	11	a	a	PRON
ejpam-3763	403	12	,	,	PUNCT
ejpam-3763	403	13	c	c	PROPN
ejpam-3763	403	14	∈	∈	PROPN
ejpam-3763	403	15	v2	v2	PROPN
ejpam-3763	403	16	∩	∩	ADJ
ejpam-3763	403	17	v	v	NOUN
ejpam-3763	403	18	(	(	PUNCT
ejpam-3763	403	19	g	g	NOUN
ejpam-3763	403	20	)	)	PUNCT
ejpam-3763	403	21	and	and	CCONJ
ejpam-3763	403	22	b	b	X
ejpam-3763	403	23	∈	∈	NOUN
ejpam-3763	403	24	v	v	ADP
ejpam-3763	403	25	(	(	PUNCT
ejpam-3763	403	26	g	g	NOUN
ejpam-3763	403	27	)	)	PUNCT
ejpam-3763	403	28	such	such	ADJ
ejpam-3763	403	29	that	that	DET
ejpam-3763	403	30	b	b	PROPN
ejpam-3763	403	31	∈	∈	PROPN
ejpam-3763	403	32	v2	v2	PROPN
ejpam-3763	403	33	,	,	PUNCT
ejpam-3763	403	34	ac	ac	PROPN
ejpam-3763	403	35	/∈	/∈	PUNCT
ejpam-3763	403	36	e(g	e(g	PROPN
ejpam-3763	403	37	)	)	PUNCT
ejpam-3763	403	38	,	,	PUNCT
ejpam-3763	403	39	wc	wc	PROPN
ejpam-3763	403	40	∈	∈	PROPN
ejpam-3763	403	41	e(g	e(g	PROPN
ejpam-3763	403	42	)	)	PUNCT
ejpam-3763	403	43	,	,	PUNCT
ejpam-3763	403	44	{	{	PUNCT
ejpam-3763	403	45	x	x	NOUN
ejpam-3763	403	46	,	,	PUNCT
ejpam-3763	403	47	y	y	PROPN
ejpam-3763	403	48	}	}	PUNCT
ejpam-3763	403	49	⊆	⊆	NUM
ejpam-3763	403	50	ng(a	ng(a	NOUN
ejpam-3763	403	51	)	)	PUNCT
ejpam-3763	403	52	,	,	PUNCT
ejpam-3763	403	53	and	and	CCONJ
ejpam-3763	403	54	{	{	PUNCT
ejpam-3763	403	55	x	x	NOUN
ejpam-3763	403	56	,	,	PUNCT
ejpam-3763	403	57	y	y	PROPN
ejpam-3763	403	58	,	,	PUNCT
ejpam-3763	403	59	w	w	PROPN
ejpam-3763	403	60	}	}	PUNCT
ejpam-3763	403	61	⊆	⊆	NUM
ejpam-3763	403	62	ng(b	ng(b	NOUN
ejpam-3763	403	63	)	)	PUNCT
ejpam-3763	403	64	.	.	PUNCT
ejpam-3763	404	1	since	since	SCONJ
ejpam-3763	404	2	ab	ab	PROPN
ejpam-3763	404	3	∈	∈	PROPN
ejpam-3763	404	4	e(g	e(g	PROPN
ejpam-3763	404	5	)	)	PUNCT
ejpam-3763	404	6	,	,	PUNCT
ejpam-3763	404	7	f(a	f(a	NOUN
ejpam-3763	404	8	)	)	PUNCT
ejpam-3763	404	9	=	=	SYM
ejpam-3763	405	1	1	1	X
ejpam-3763	405	2	.	.	PUNCT
ejpam-3763	405	3	thus	thus	ADV
ejpam-3763	405	4	,	,	PUNCT
ejpam-3763	405	5	ωgg(f	ωgg(f	PROPN
ejpam-3763	405	6	)	)	PUNCT
ejpam-3763	405	7	=	=	PUNCT
ejpam-3763	405	8	∑	∑	PUNCT
ejpam-3763	405	9	u∈{a	u∈{a	ADJ
ejpam-3763	405	10	,	,	PUNCT
ejpam-3763	405	11	x	x	NOUN
ejpam-3763	405	12	,	,	PUNCT
ejpam-3763	405	13	y	y	PROPN
ejpam-3763	405	14	,	,	PUNCT
ejpam-3763	405	15	b	b	PROPN
ejpam-3763	405	16	,	,	PUNCT
ejpam-3763	405	17	w	w	PROPN
ejpam-3763	405	18	,	,	PUNCT
ejpam-3763	405	19	c	c	NOUN
ejpam-3763	405	20	}	}	PUNCT
ejpam-3763	405	21	(	(	PUNCT
ejpam-3763	405	22	f(u	f(u	PROPN
ejpam-3763	405	23	)	)	PUNCT
ejpam-3763	405	24	+	+	CCONJ
ejpam-3763	405	25	f(u	f(u	NOUN
ejpam-3763	405	26	)	)	PUNCT
ejpam-3763	405	27	)	)	PUNCT
ejpam-3763	406	1	+	+	CCONJ
ejpam-3763	406	2	∑	∑	ADP
ejpam-3763	406	3	u∈v	u∈v	NOUN
ejpam-3763	406	4	(	(	PUNCT
ejpam-3763	406	5	g)\{a	g)\{a	PROPN
ejpam-3763	406	6	,	,	PUNCT
ejpam-3763	406	7	b	b	NOUN
ejpam-3763	406	8	,	,	PUNCT
ejpam-3763	406	9	c	c	NOUN
ejpam-3763	406	10	,	,	PUNCT
ejpam-3763	406	11	x	x	NOUN
ejpam-3763	406	12	,	,	PUNCT
ejpam-3763	406	13	y	y	PROPN
ejpam-3763	406	14	,	,	PUNCT
ejpam-3763	406	15	w	w	NOUN
ejpam-3763	406	16	}	}	PUNCT
ejpam-3763	406	17	(	(	PUNCT
ejpam-3763	406	18	f(u	f(u	PROPN
ejpam-3763	406	19	)	)	PUNCT
ejpam-3763	406	20	+	+	CCONJ
ejpam-3763	406	21	f(u	f(u	NOUN
ejpam-3763	406	22	)	)	PUNCT
ejpam-3763	406	23	)	)	PUNCT
ejpam-3763	406	24	≥	≥	NOUN
ejpam-3763	406	25	7	7	NUM
ejpam-3763	407	1	+	+	CCONJ
ejpam-3763	407	2	(	(	PUNCT
ejpam-3763	407	3	n−	n−	NOUN
ejpam-3763	407	4	7	7	NUM
ejpam-3763	407	5	)	)	PUNCT
ejpam-3763	407	6	+	+	CCONJ
ejpam-3763	407	7	2	2	NUM
ejpam-3763	407	8	>	>	SYM
ejpam-3763	407	9	n+	n+	PUNCT
ejpam-3763	407	10	1	1	X
ejpam-3763	407	11	.	.	PUNCT
ejpam-3763	408	1	finally	finally	ADV
ejpam-3763	408	2	,	,	PUNCT
ejpam-3763	408	3	suppose	suppose	VERB
ejpam-3763	408	4	that	that	SCONJ
ejpam-3763	408	5	a	a	DET
ejpam-3763	408	6	=	=	SYM
ejpam-3763	408	7	{	{	PUNCT
ejpam-3763	408	8	x	x	PROPN
ejpam-3763	408	9	,	,	PUNCT
ejpam-3763	408	10	y	y	PROPN
ejpam-3763	408	11	,	,	PUNCT
ejpam-3763	408	12	z	z	PROPN
ejpam-3763	408	13	,	,	PUNCT
ejpam-3763	408	14	w	w	NOUN
ejpam-3763	408	15	}	}	PUNCT
ejpam-3763	408	16	.	.	PUNCT
ejpam-3763	409	1	it	it	PRON
ejpam-3763	409	2	is	be	AUX
ejpam-3763	409	3	enough	enough	ADJ
ejpam-3763	409	4	to	to	PART
ejpam-3763	409	5	consider	consider	VERB
ejpam-3763	409	6	only	only	ADV
ejpam-3763	409	7	the	the	DET
ejpam-3763	409	8	following	follow	VERB
ejpam-3763	409	9	nontrivial	nontrivial	ADJ
ejpam-3763	409	10	case	case	NOUN
ejpam-3763	409	11	:	:	PUNCT
ejpam-3763	409	12	there	there	PRON
ejpam-3763	409	13	exist	exist	VERB
ejpam-3763	409	14	a	a	PRON
ejpam-3763	409	15	,	,	PUNCT
ejpam-3763	409	16	c	c	PROPN
ejpam-3763	409	17	∈	∈	PROPN
ejpam-3763	409	18	v2	v2	PROPN
ejpam-3763	409	19	∩	∩	ADJ
ejpam-3763	409	20	v	v	NOUN
ejpam-3763	409	21	(	(	PUNCT
ejpam-3763	409	22	g	g	NOUN
ejpam-3763	409	23	)	)	PUNCT
ejpam-3763	409	24	and	and	CCONJ
ejpam-3763	409	25	b	b	X
ejpam-3763	409	26	∈	∈	NOUN
ejpam-3763	409	27	v	v	ADP
ejpam-3763	409	28	(	(	PUNCT
ejpam-3763	409	29	g	g	NOUN
ejpam-3763	409	30	)	)	PUNCT
ejpam-3763	409	31	such	such	ADJ
ejpam-3763	409	32	that	that	DET
ejpam-3763	409	33	b	b	PROPN
ejpam-3763	409	34	∈	∈	PROPN
ejpam-3763	409	35	v2	v2	PROPN
ejpam-3763	409	36	,	,	PUNCT
ejpam-3763	409	37	ac	ac	PROPN
ejpam-3763	409	38	/∈	/∈	PUNCT
ejpam-3763	409	39	e(g	e(g	PROPN
ejpam-3763	409	40	)	)	PUNCT
ejpam-3763	409	41	,	,	PUNCT
ejpam-3763	409	42	{	{	PUNCT
ejpam-3763	409	43	x	x	NOUN
ejpam-3763	409	44	,	,	PUNCT
ejpam-3763	409	45	y	y	PROPN
ejpam-3763	409	46	}	}	PUNCT
ejpam-3763	409	47	⊆	⊆	NUM
ejpam-3763	409	48	ng(a	ng(a	NOUN
ejpam-3763	409	49	)	)	PUNCT
ejpam-3763	409	50	,	,	PUNCT
ejpam-3763	409	51	{	{	PUNCT
ejpam-3763	409	52	w	w	NOUN
ejpam-3763	409	53	,	,	PUNCT
ejpam-3763	409	54	z	z	NOUN
ejpam-3763	409	55	}	}	PUNCT
ejpam-3763	409	56	⊆	⊆	NUM
ejpam-3763	409	57	ng(c	ng(c	NUM
ejpam-3763	409	58	)	)	PUNCT
ejpam-3763	409	59	,	,	PUNCT
ejpam-3763	409	60	and	and	CCONJ
ejpam-3763	409	61	{	{	PUNCT
ejpam-3763	409	62	x	x	NOUN
ejpam-3763	409	63	,	,	PUNCT
ejpam-3763	409	64	y	y	PROPN
ejpam-3763	409	65	,	,	PUNCT
ejpam-3763	409	66	z	z	PROPN
ejpam-3763	409	67	,	,	PUNCT
ejpam-3763	409	68	w	w	NOUN
ejpam-3763	409	69	}	}	PUNCT
ejpam-3763	409	70	⊆	⊆	NUM
ejpam-3763	409	71	ng(b	ng(b	NOUN
ejpam-3763	409	72	)	)	PUNCT
ejpam-3763	409	73	.	.	PUNCT
ejpam-3763	410	1	since	since	SCONJ
ejpam-3763	410	2	ab	ab	PROPN
ejpam-3763	410	3	,	,	PUNCT
ejpam-3763	410	4	cb	cb	PROPN
ejpam-3763	410	5	∈	∈	PROPN
ejpam-3763	410	6	e(g	e(g	PROPN
ejpam-3763	410	7	)	)	PUNCT
ejpam-3763	410	8	,	,	PUNCT
ejpam-3763	410	9	f(a	f(a	NOUN
ejpam-3763	410	10	)	)	PUNCT
ejpam-3763	410	11	=	=	SYM
ejpam-3763	410	12	f(c	f(c	PROPN
ejpam-3763	410	13	)	)	PUNCT
ejpam-3763	410	14	=	=	SYM
ejpam-3763	411	1	1	1	X
ejpam-3763	411	2	.	.	PUNCT
ejpam-3763	411	3	hence	hence	ADV
ejpam-3763	411	4	,	,	PUNCT
ejpam-3763	411	5	ωgg(f	ωgg(f	PROPN
ejpam-3763	411	6	)	)	PUNCT
ejpam-3763	411	7	=	=	PUNCT
ejpam-3763	411	8	∑	∑	PUNCT
ejpam-3763	411	9	u∈{a	u∈{a	ADJ
ejpam-3763	411	10	,	,	PUNCT
ejpam-3763	411	11	b	b	NOUN
ejpam-3763	411	12	,	,	PUNCT
ejpam-3763	411	13	c	c	NOUN
ejpam-3763	411	14	,	,	PUNCT
ejpam-3763	411	15	x	x	NOUN
ejpam-3763	411	16	,	,	PUNCT
ejpam-3763	411	17	y	y	PROPN
ejpam-3763	411	18	,	,	PUNCT
ejpam-3763	411	19	w	w	PROPN
ejpam-3763	411	20	,	,	PUNCT
ejpam-3763	411	21	z	z	NOUN
ejpam-3763	411	22	}	}	PUNCT
ejpam-3763	411	23	(	(	PUNCT
ejpam-3763	411	24	f(u	f(u	PROPN
ejpam-3763	411	25	)	)	PUNCT
ejpam-3763	411	26	+	+	CCONJ
ejpam-3763	411	27	f(u	f(u	NOUN
ejpam-3763	411	28	)	)	PUNCT
ejpam-3763	411	29	)	)	PUNCT
ejpam-3763	412	1	+	+	CCONJ
ejpam-3763	412	2	∑	∑	ADP
ejpam-3763	412	3	u∈v	u∈v	NOUN
ejpam-3763	412	4	(	(	PUNCT
ejpam-3763	412	5	g)\{a	g)\{a	PROPN
ejpam-3763	412	6	,	,	PUNCT
ejpam-3763	412	7	b	b	NOUN
ejpam-3763	412	8	,	,	PUNCT
ejpam-3763	412	9	c	c	NOUN
ejpam-3763	412	10	,	,	PUNCT
ejpam-3763	412	11	x	x	NOUN
ejpam-3763	412	12	,	,	PUNCT
ejpam-3763	412	13	y	y	PROPN
ejpam-3763	412	14	,	,	PUNCT
ejpam-3763	412	15	w	w	PROPN
ejpam-3763	412	16	,	,	PUNCT
ejpam-3763	412	17	z	z	NOUN
ejpam-3763	412	18	}	}	PUNCT
ejpam-3763	412	19	(	(	PUNCT
ejpam-3763	412	20	f(u	f(u	PROPN
ejpam-3763	412	21	)	)	PUNCT
ejpam-3763	412	22	+	+	CCONJ
ejpam-3763	412	23	f(u	f(u	NOUN
ejpam-3763	412	24	)	)	PUNCT
ejpam-3763	412	25	)	)	PUNCT
ejpam-3763	412	26	≥	≥	NOUN
ejpam-3763	412	27	8	8	NUM
ejpam-3763	412	28	+	+	CCONJ
ejpam-3763	412	29	(	(	PUNCT
ejpam-3763	412	30	n−	n−	NOUN
ejpam-3763	412	31	8)	8)	NUM
ejpam-3763	412	32	+	+	CCONJ
ejpam-3763	412	33	2	2	NUM
ejpam-3763	412	34	>	>	SYM
ejpam-3763	412	35	n+	n+	PUNCT
ejpam-3763	412	36	1	1	X
ejpam-3763	412	37	.	.	X
ejpam-3763	413	1	all	all	PRON
ejpam-3763	413	2	of	of	ADP
ejpam-3763	413	3	the	the	DET
ejpam-3763	413	4	above	above	ADJ
ejpam-3763	413	5	cases	case	NOUN
ejpam-3763	413	6	show	show	VERB
ejpam-3763	413	7	that	that	SCONJ
ejpam-3763	413	8	γpr(g	γpr(g	PRON
ejpam-3763	413	9	)	)	PUNCT
ejpam-3763	413	10	=	=	SYM
ejpam-3763	413	11	ωgg(f	ωgg(f	PROPN
ejpam-3763	413	12	)	)	PUNCT
ejpam-3763	413	13	≥	≥	NUM
ejpam-3763	413	14	n+	n+	PUNCT
ejpam-3763	414	1	1	1	X
ejpam-3763	414	2	.	.	PUNCT
ejpam-3763	415	1	next	next	ADV
ejpam-3763	415	2	,	,	PUNCT
ejpam-3763	415	3	suppose	suppose	VERB
ejpam-3763	415	4	that	that	SCONJ
ejpam-3763	415	5	g	g	PROPN
ejpam-3763	415	6	is	be	AUX
ejpam-3763	415	7	the	the	DET
ejpam-3763	415	8	union	union	NOUN
ejpam-3763	415	9	of	of	ADP
ejpam-3763	415	10	kj	kj	PROPN
ejpam-3763	415	11	∈	∈	PROPN
ejpam-3763	415	12	{	{	PUNCT
ejpam-3763	415	13	k1,k2	k1,k2	PROPN
ejpam-3763	415	14	}	}	PUNCT
ejpam-3763	415	15	,	,	PUNCT
ejpam-3763	415	16	and	and	CCONJ
ejpam-3763	415	17	let	let	VERB
ejpam-3763	415	18	f	f	PROPN
ejpam-3763	415	19	=	=	SYM
ejpam-3763	415	20	(	(	PUNCT
ejpam-3763	415	21	v0	v0	PROPN
ejpam-3763	415	22	,	,	PUNCT
ejpam-3763	415	23	v1	v1	NOUN
ejpam-3763	415	24	,	,	PUNCT
ejpam-3763	415	25	v2	v2	PROPN
ejpam-3763	415	26	)	)	PUNCT
ejpam-3763	415	27	be	be	AUX
ejpam-3763	415	28	a	a	DET
ejpam-3763	415	29	γpr	γpr	NOUN
ejpam-3763	415	30	-function	-function	NOUN
ejpam-3763	415	31	of	of	ADP
ejpam-3763	415	32	gg	gg	NOUN
ejpam-3763	415	33	.	.	PUNCT
ejpam-3763	416	1	as	as	SCONJ
ejpam-3763	416	2	shown	show	VERB
ejpam-3763	416	3	previously	previously	ADV
ejpam-3763	416	4	,	,	PUNCT
ejpam-3763	416	5	we	we	PRON
ejpam-3763	416	6	may	may	AUX
ejpam-3763	416	7	assume	assume	VERB
ejpam-3763	416	8	that	that	SCONJ
ejpam-3763	416	9	v2	v2	PROPN
ejpam-3763	416	10	∩	∩	NOUN
ejpam-3763	416	11	v	v	NOUN
ejpam-3763	416	12	(	(	PUNCT
ejpam-3763	416	13	g	g	NOUN
ejpam-3763	416	14	)	)	PUNCT
ejpam-3763	416	15	6=	6=	ADP
ejpam-3763	416	16	∅	∅	NOUN
ejpam-3763	416	17	,	,	PUNCT
ejpam-3763	416	18	and	and	CCONJ
ejpam-3763	416	19	if	if	SCONJ
ejpam-3763	416	20	v2	v2	PROPN
ejpam-3763	416	21	contains	contain	VERB
ejpam-3763	416	22	a	a	DET
ejpam-3763	416	23	dominating	dominating	NOUN
ejpam-3763	416	24	vertex	vertex	NOUN
ejpam-3763	416	25	of	of	ADP
ejpam-3763	416	26	g	g	NOUN
ejpam-3763	416	27	,	,	PUNCT
ejpam-3763	416	28	then	then	ADV
ejpam-3763	416	29	ωgg(f	ωgg(f	NUM
ejpam-3763	416	30	)	)	PUNCT
ejpam-3763	416	31	≥	≥	NOUN
ejpam-3763	416	32	n	n	NOUN
ejpam-3763	416	33	+	+	NUM
ejpam-3763	416	34	1	1	NUM
ejpam-3763	416	35	.	.	PUNCT
ejpam-3763	417	1	henceforth	henceforth	ADV
ejpam-3763	417	2	,	,	PUNCT
ejpam-3763	417	3	we	we	PRON
ejpam-3763	417	4	assume	assume	VERB
ejpam-3763	417	5	that	that	SCONJ
ejpam-3763	417	6	v2∩dom(g	v2∩dom(g	NOUN
ejpam-3763	417	7	)	)	PUNCT
ejpam-3763	417	8	=	=	VERB
ejpam-3763	417	9	∅.	∅.	AUX
ejpam-3763	417	10	pick	pick	VERB
ejpam-3763	417	11	v	v	NUM
ejpam-3763	417	12	∈	∈	NOUN
ejpam-3763	417	13	dom(g	dom(g	NOUN
ejpam-3763	417	14	)	)	PUNCT
ejpam-3763	417	15	.	.	PUNCT
ejpam-3763	418	1	then	then	ADV
ejpam-3763	418	2	v	v	X
ejpam-3763	418	3	∈	∈	NOUN
ejpam-3763	418	4	iso(g	iso(g	NOUN
ejpam-3763	418	5	)	)	PUNCT
ejpam-3763	418	6	.	.	PUNCT
ejpam-3763	419	1	note	note	VERB
ejpam-3763	419	2	that	that	SCONJ
ejpam-3763	419	3	for	for	ADP
ejpam-3763	419	4	all	all	DET
ejpam-3763	419	5	x	x	SYM
ejpam-3763	419	6	∈	∈	NOUN
ejpam-3763	419	7	iso(g	iso(g	NOUN
ejpam-3763	419	8	)	)	PUNCT
ejpam-3763	419	9	,	,	PUNCT
ejpam-3763	419	10	x	x	PUNCT
ejpam-3763	419	11	/∈	/∈	PUNCT
ejpam-3763	420	1	a	a	PRON
ejpam-3763	420	2	=	=	X
ejpam-3763	420	3	{	{	PUNCT
ejpam-3763	420	4	w	w	PROPN
ejpam-3763	420	5	∈	∈	PROPN
ejpam-3763	420	6	v	v	ADP
ejpam-3763	420	7	(	(	PUNCT
ejpam-3763	420	8	g	g	NOUN
ejpam-3763	420	9	)	)	PUNCT
ejpam-3763	420	10	:	:	PUNCT
ejpam-3763	420	11	f(w	f(w	X
ejpam-3763	420	12	)	)	PUNCT
ejpam-3763	420	13	=	=	PUNCT
ejpam-3763	420	14	f(w	f(w	PROPN
ejpam-3763	420	15	)	)	PUNCT
ejpam-3763	420	16	=	=	SYM
ejpam-3763	421	1	0	0	X
ejpam-3763	421	2	}	}	PUNCT
ejpam-3763	422	1	so	so	SCONJ
ejpam-3763	422	2	that	that	SCONJ
ejpam-3763	422	3	(	(	PUNCT
ejpam-3763	422	4	f(x	f(x	PROPN
ejpam-3763	422	5	)	)	PUNCT
ejpam-3763	422	6	+	+	CCONJ
ejpam-3763	422	7	f(x	f(x	PROPN
ejpam-3763	422	8	)	)	PUNCT
ejpam-3763	422	9	)	)	PUNCT
ejpam-3763	422	10	≥	≥	NOUN
ejpam-3763	422	11	1	1	NUM
ejpam-3763	422	12	.	.	PUNCT
ejpam-3763	422	13	also	also	ADV
ejpam-3763	422	14	,	,	PUNCT
ejpam-3763	422	15	for	for	ADP
ejpam-3763	422	16	all	all	DET
ejpam-3763	422	17	x	x	NOUN
ejpam-3763	422	18	,	,	PUNCT
ejpam-3763	422	19	y	y	PROPN
ejpam-3763	422	20	∈	∈	PROPN
ejpam-3763	422	21	v	v	ADP
ejpam-3763	422	22	(	(	PUNCT
ejpam-3763	422	23	g	g	NOUN
ejpam-3763	422	24	)	)	PUNCT
ejpam-3763	422	25	for	for	ADP
ejpam-3763	422	26	which	which	PRON
ejpam-3763	422	27	xy	xy	PROPN
ejpam-3763	422	28	∈	∈	PROPN
ejpam-3763	422	29	e(g	e(g	PROPN
ejpam-3763	422	30	)	)	PUNCT
ejpam-3763	422	31	,	,	PUNCT
ejpam-3763	422	32	if	if	SCONJ
ejpam-3763	422	33	x	x	PROPN
ejpam-3763	422	34	∈	∈	PROPN
ejpam-3763	422	35	a	a	PRON
ejpam-3763	422	36	,	,	PUNCT
ejpam-3763	422	37	then	then	ADV
ejpam-3763	422	38	y	y	PROPN
ejpam-3763	422	39	∈	∈	PROPN
ejpam-3763	422	40	v2	v2	PROPN
ejpam-3763	422	41	and	and	CCONJ
ejpam-3763	422	42	so	so	ADV
ejpam-3763	422	43	(	(	PUNCT
ejpam-3763	422	44	f(x	f(x	PROPN
ejpam-3763	422	45	)	)	PUNCT
ejpam-3763	422	46	+	+	CCONJ
ejpam-3763	422	47	f(x	f(x	PROPN
ejpam-3763	422	48	)	)	PUNCT
ejpam-3763	422	49	)	)	PUNCT
ejpam-3763	423	1	+	+	CCONJ
ejpam-3763	423	2	(	(	PUNCT
ejpam-3763	423	3	f(y	f(y	NOUN
ejpam-3763	423	4	)	)	PUNCT
ejpam-3763	423	5	+	+	SYM
ejpam-3763	423	6	f(y	f(y	NOUN
ejpam-3763	423	7	)	)	PUNCT
ejpam-3763	423	8	)	)	PUNCT
ejpam-3763	423	9	≥	≥	NOUN
ejpam-3763	424	1	2	2	NUM
ejpam-3763	424	2	.	.	PUNCT
ejpam-3763	425	1	thus	thus	ADV
ejpam-3763	425	2	,	,	PUNCT
ejpam-3763	425	3	if	if	SCONJ
ejpam-3763	425	4	v	v	NUM
ejpam-3763	425	5	∈	∈	PROPN
ejpam-3763	425	6	v0	v0	NOUN
ejpam-3763	425	7	and	and	CCONJ
ejpam-3763	425	8	u	u	NOUN
ejpam-3763	425	9	∈	∈	PROPN
ejpam-3763	425	10	v	v	ADP
ejpam-3763	425	11	(	(	PUNCT
ejpam-3763	425	12	g	g	NOUN
ejpam-3763	425	13	)	)	PUNCT
ejpam-3763	425	14	such	such	ADJ
ejpam-3763	425	15	that	that	SCONJ
ejpam-3763	425	16	v2	v2	PROPN
ejpam-3763	425	17	∩	∩	NOUN
ejpam-3763	425	18	v	v	NOUN
ejpam-3763	425	19	(	(	PUNCT
ejpam-3763	425	20	g	g	NOUN
ejpam-3763	425	21	)	)	PUNCT
ejpam-3763	425	22	=	=	PRON
ejpam-3763	425	23	{	{	PUNCT
ejpam-3763	425	24	u	u	NOUN
ejpam-3763	425	25	}	}	PUNCT
ejpam-3763	425	26	,	,	PUNCT
ejpam-3763	425	27	then	then	ADV
ejpam-3763	425	28	ωgg(f	ωgg(f	NUM
ejpam-3763	425	29	)	)	PUNCT
ejpam-3763	425	30	=	=	PUNCT
ejpam-3763	425	31	(	(	PUNCT
ejpam-3763	425	32	f(u	f(u	PROPN
ejpam-3763	425	33	)	)	PUNCT
ejpam-3763	425	34	+	+	CCONJ
ejpam-3763	425	35	f(u	f(u	NOUN
ejpam-3763	425	36	)	)	PUNCT
ejpam-3763	425	37	)	)	PUNCT
ejpam-3763	426	1	+	+	CCONJ
ejpam-3763	426	2	∑	∑	ADV
ejpam-3763	426	3	x∈iso(g	x∈iso(g	PROPN
ejpam-3763	426	4	)	)	PUNCT
ejpam-3763	426	5	(	(	PUNCT
ejpam-3763	426	6	f(x	f(x	PROPN
ejpam-3763	426	7	)	)	PUNCT
ejpam-3763	426	8	+	+	CCONJ
ejpam-3763	426	9	f(x	f(x	PROPN
ejpam-3763	426	10	)	)	PUNCT
ejpam-3763	426	11	)	)	PUNCT
ejpam-3763	427	1	+	+	CCONJ
ejpam-3763	427	2	∑	∑	PUNCT
ejpam-3763	427	3	xy∈e(g	xy∈e(g	NUM
ejpam-3763	427	4	)	)	PUNCT
ejpam-3763	427	5	(	(	PUNCT
ejpam-3763	427	6	(	(	PUNCT
ejpam-3763	427	7	f(x	f(x	PROPN
ejpam-3763	427	8	)	)	PUNCT
ejpam-3763	427	9	+	+	CCONJ
ejpam-3763	427	10	f(x	f(x	PROPN
ejpam-3763	427	11	)	)	PUNCT
ejpam-3763	427	12	)	)	PUNCT
ejpam-3763	428	1	+	+	CCONJ
ejpam-3763	428	2	(	(	PUNCT
ejpam-3763	428	3	f(y	f(y	NOUN
ejpam-3763	428	4	)	)	PUNCT
ejpam-3763	428	5	+	+	SYM
ejpam-3763	428	6	f(y	f(y	NOUN
ejpam-3763	428	7	)	)	PUNCT
ejpam-3763	428	8	)	)	PUNCT
ejpam-3763	428	9	)	)	PUNCT
ejpam-3763	429	1	≥	≥	X
ejpam-3763	429	2	n+	n+	PUNCT
ejpam-3763	430	1	1	1	X
ejpam-3763	430	2	.	.	PUNCT
ejpam-3763	431	1	on	on	ADP
ejpam-3763	431	2	the	the	DET
ejpam-3763	431	3	other	other	ADJ
ejpam-3763	431	4	hand	hand	NOUN
ejpam-3763	431	5	,	,	PUNCT
ejpam-3763	431	6	if	if	SCONJ
ejpam-3763	431	7	v	v	NUM
ejpam-3763	431	8	∈	∈	PROPN
ejpam-3763	431	9	v1	v1	NOUN
ejpam-3763	431	10	,	,	PUNCT
ejpam-3763	431	11	then	then	ADV
ejpam-3763	431	12	f(v	f(v	NOUN
ejpam-3763	431	13	)	)	PUNCT
ejpam-3763	432	1	=	=	SYM
ejpam-3763	432	2	1	1	NUM
ejpam-3763	432	3	and	and	CCONJ
ejpam-3763	432	4	ωgg(f	ωgg(f	NUM
ejpam-3763	432	5	)	)	PUNCT
ejpam-3763	432	6	=	=	SYM
ejpam-3763	432	7	(	(	PUNCT
ejpam-3763	432	8	f(v	f(v	PROPN
ejpam-3763	432	9	)	)	PUNCT
ejpam-3763	432	10	+	+	NUM
ejpam-3763	432	11	f(v	f(v	NOUN
ejpam-3763	432	12	)	)	PUNCT
ejpam-3763	432	13	)	)	PUNCT
ejpam-3763	433	1	+	+	CCONJ
ejpam-3763	433	2	∑	∑	PROPN
ejpam-3763	433	3	x∈iso(g)\{v	x∈iso(g)\{v	PUNCT
ejpam-3763	433	4	}	}	PUNCT
ejpam-3763	433	5	(	(	PUNCT
ejpam-3763	433	6	f(x	f(x	PROPN
ejpam-3763	433	7	)	)	PUNCT
ejpam-3763	433	8	+	+	CCONJ
ejpam-3763	433	9	f(x	f(x	PROPN
ejpam-3763	433	10	)	)	PUNCT
ejpam-3763	433	11	)	)	PUNCT
ejpam-3763	434	1	+	+	CCONJ
ejpam-3763	434	2	∑	∑	PUNCT
ejpam-3763	434	3	xy∈e(g	xy∈e(g	NUM
ejpam-3763	434	4	)	)	PUNCT
ejpam-3763	434	5	(	(	PUNCT
ejpam-3763	434	6	(	(	PUNCT
ejpam-3763	434	7	f(x	f(x	PROPN
ejpam-3763	434	8	)	)	PUNCT
ejpam-3763	434	9	+	+	CCONJ
ejpam-3763	434	10	f(x	f(x	PROPN
ejpam-3763	434	11	)	)	PUNCT
ejpam-3763	434	12	)	)	PUNCT
ejpam-3763	435	1	+	+	CCONJ
ejpam-3763	435	2	(	(	PUNCT
ejpam-3763	435	3	f(y	f(y	NOUN
ejpam-3763	435	4	)	)	PUNCT
ejpam-3763	435	5	+	+	SYM
ejpam-3763	435	6	f(y	f(y	NOUN
ejpam-3763	435	7	)	)	PUNCT
ejpam-3763	435	8	)	)	PUNCT
ejpam-3763	435	9	)	)	PUNCT
ejpam-3763	436	1	≥	≥	X
ejpam-3763	436	2	n+	n+	PUNCT
ejpam-3763	436	3	1	1	X
ejpam-3763	436	4	.	.	PUNCT
ejpam-3763	436	5	therefore	therefore	ADV
ejpam-3763	436	6	,	,	PUNCT
ejpam-3763	436	7	γpr(gg	γpr(gg	PROPN
ejpam-3763	436	8	)	)	PUNCT
ejpam-3763	436	9	≥	≥	X
ejpam-3763	436	10	n+	n+	PUNCT
ejpam-3763	436	11	1	1	X
ejpam-3763	436	12	.	.	X
ejpam-3763	436	13	�	�	PROPN
ejpam-3763	436	14	l.	l.	PROPN
ejpam-3763	436	15	paleta	paleta	PROPN
ejpam-3763	436	16	,	,	PUNCT
ejpam-3763	436	17	f.	f.	PROPN
ejpam-3763	436	18	jamil	jamil	PROPN
ejpam-3763	436	19	/	/	SYM
ejpam-3763	436	20	eur	eur	PROPN
ejpam-3763	436	21	.	.	PUNCT
ejpam-3763	437	1	j.	j.	PROPN
ejpam-3763	437	2	pure	pure	PROPN
ejpam-3763	437	3	appl	appl	PROPN
ejpam-3763	437	4	.	.	PROPN
ejpam-3763	437	5	math	math	PROPN
ejpam-3763	437	6	,	,	PUNCT
ejpam-3763	437	7	13	13	NUM
ejpam-3763	437	8	(	(	PUNCT
ejpam-3763	437	9	3	3	NUM
ejpam-3763	437	10	)	)	PUNCT
ejpam-3763	437	11	(	(	PUNCT
ejpam-3763	437	12	2020	2020	NUM
ejpam-3763	437	13	)	)	PUNCT
ejpam-3763	437	14	,	,	PUNCT
ejpam-3763	437	15	529	529	NUM
ejpam-3763	437	16	-	-	SYM
ejpam-3763	437	17	548	548	NUM
ejpam-3763	437	18	541	541	NUM
ejpam-3763	437	19	as	as	SCONJ
ejpam-3763	437	20	shown	show	VERB
ejpam-3763	437	21	by	by	ADP
ejpam-3763	437	22	the	the	DET
ejpam-3763	437	23	graph	graph	NOUN
ejpam-3763	437	24	g	g	PROPN
ejpam-3763	437	25	in	in	ADP
ejpam-3763	437	26	figure	figure	NOUN
ejpam-3763	437	27	1	1	NUM
ejpam-3763	437	28	,	,	PUNCT
ejpam-3763	437	29	strict	strict	ADJ
ejpam-3763	437	30	inequality	inequality	NOUN
ejpam-3763	437	31	may	may	AUX
ejpam-3763	437	32	be	be	AUX
ejpam-3763	437	33	attained	attain	VERB
ejpam-3763	437	34	in	in	ADP
ejpam-3763	437	35	proposition	proposition	NOUN
ejpam-3763	437	36	2.13(iv	2.13(iv	NUM
ejpam-3763	437	37	)	)	PUNCT
ejpam-3763	437	38	if	if	SCONJ
ejpam-3763	437	39	we	we	PRON
ejpam-3763	437	40	remove	remove	VERB
ejpam-3763	437	41	the	the	DET
ejpam-3763	437	42	condition	condition	NOUN
ejpam-3763	437	43	that	that	SCONJ
ejpam-3763	437	44	degg(v	degg(v	VERB
ejpam-3763	437	45	)	)	PUNCT
ejpam-3763	437	46	≤	≤	NOUN
ejpam-3763	437	47	3	3	NUM
ejpam-3763	437	48	for	for	ADP
ejpam-3763	437	49	all	all	DET
ejpam-3763	437	50	nondominating	nondominate	VERB
ejpam-3763	437	51	vertices	vertex	NOUN
ejpam-3763	437	52	v	v	ADP
ejpam-3763	437	53	of	of	ADP
ejpam-3763	437	54	g.	g.	NOUN
ejpam-3763	437	55	for	for	ADP
ejpam-3763	437	56	such	such	ADJ
ejpam-3763	437	57	g	g	NOUN
ejpam-3763	437	58	,	,	PUNCT
ejpam-3763	437	59	γpr(gg	γpr(gg	NUM
ejpam-3763	437	60	)	)	PUNCT
ejpam-3763	437	61	=	=	SYM
ejpam-3763	437	62	6	6	NUM
ejpam-3763	437	63	<	<	X
ejpam-3763	437	64	|v	|v	PROPN
ejpam-3763	437	65	(	(	PUNCT
ejpam-3763	437	66	g)|+	g)|+	NOUN
ejpam-3763	437	67	1	1	NUM
ejpam-3763	437	68	.	.	PUNCT
ejpam-3763	437	69	....................................	....................................	PUNCT
ejpam-3763	438	1	....................................	....................................	PUNCT
ejpam-3763	438	2	....................................	....................................	PUNCT
ejpam-3763	439	1	....................................	....................................	PUNCT
ejpam-3763	439	2	....................................	....................................	PUNCT
ejpam-3763	440	1	....................................	....................................	PUNCT
ejpam-3763	440	2	..........	..........	PUNCT
ejpam-3763	441	1	.........	.........	PUNCT
ejpam-3763	441	2	.........	.........	PUNCT
ejpam-3763	442	1	.........	.........	PUNCT
ejpam-3763	442	2	.........	.........	PUNCT
ejpam-3763	443	1	.........	.........	PUNCT
ejpam-3763	443	2	.........	.........	PUNCT
ejpam-3763	444	1	.........	.........	PUNCT
ejpam-3763	444	2	...	...	PUNCT
ejpam-3763	445	1	..........	..........	PUNCT
ejpam-3763	445	2	.........	.........	PUNCT
ejpam-3763	446	1	.........	.........	PUNCT
ejpam-3763	446	2	.........	.........	PUNCT
ejpam-3763	447	1	.........	.........	PUNCT
ejpam-3763	447	2	.........	.........	PUNCT
ejpam-3763	448	1	.........	.........	PUNCT
ejpam-3763	448	2	.........	.........	PUNCT
ejpam-3763	448	3	...	...	PUNCT
ejpam-3763	448	4	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-3763	448	5	...............................................................................................................................................................................	...............................................................................................................................................................................	PUNCT
ejpam-3763	448	6	............................................................................................................................................................................	............................................................................................................................................................................	PUNCT
ejpam-3763	449	1	.........	.........	PUNCT
ejpam-3763	450	1	..........	..........	PUNCT
ejpam-3763	450	2	..........	..........	PUNCT
ejpam-3763	451	1	..........	..........	PUNCT
ejpam-3763	451	2	..........	..........	PUNCT
ejpam-3763	452	1	..........	..........	PUNCT
ejpam-3763	452	2	..........	..........	PUNCT
ejpam-3763	453	1	..........	..........	PUNCT
ejpam-3763	453	2	..........	..........	PUNCT
ejpam-3763	454	1	..........	..........	PUNCT
ejpam-3763	454	2	..........	..........	PUNCT
ejpam-3763	455	1	..........	..........	PUNCT
ejpam-3763	455	2	..........	..........	PUNCT
ejpam-3763	456	1	..........	..........	PUNCT
ejpam-3763	456	2	..........	..........	PUNCT
ejpam-3763	457	1	..........	..........	PUNCT
ejpam-3763	457	2	.....	.....	PUNCT
ejpam-3763	458	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-3763	458	2	............................................................................................................................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-3763	459	1	g	g	NOUN
ejpam-3763	459	2	:	:	PUNCT
ejpam-3763	459	3	....................................	....................................	PUNCT
ejpam-3763	459	4	....................................	....................................	PUNCT
ejpam-3763	459	5	....................................	....................................	PUNCT
ejpam-3763	459	6	....................................	....................................	PUNCT
ejpam-3763	459	7	....................................	....................................	PUNCT
ejpam-3763	459	8	....................................	....................................	PUNCT
ejpam-3763	459	9	....................................	....................................	PUNCT
ejpam-3763	459	10	....................................	....................................	PUNCT
ejpam-3763	459	11	....................................	....................................	PUNCT
ejpam-3763	459	12	....................................	....................................	PUNCT
ejpam-3763	459	13	....................................	....................................	PUNCT
ejpam-3763	459	14	....................................	....................................	PUNCT
ejpam-3763	460	1	..........	..........	PUNCT
ejpam-3763	460	2	.........	.........	PUNCT
ejpam-3763	461	1	.........	.........	PUNCT
ejpam-3763	461	2	.........	.........	PUNCT
ejpam-3763	462	1	.........	.........	PUNCT
ejpam-3763	462	2	.........	.........	PUNCT
ejpam-3763	463	1	.........	.........	PUNCT
ejpam-3763	463	2	.........	.........	PUNCT
ejpam-3763	463	3	...	...	PUNCT
ejpam-3763	464	1	..........	..........	PUNCT
ejpam-3763	464	2	.........	.........	PUNCT
ejpam-3763	465	1	.........	.........	PUNCT
ejpam-3763	465	2	.........	.........	PUNCT
ejpam-3763	466	1	.........	.........	PUNCT
ejpam-3763	466	2	.........	.........	PUNCT
ejpam-3763	467	1	.........	.........	PUNCT
ejpam-3763	467	2	.........	.........	PUNCT
ejpam-3763	467	3	...	...	PUNCT
ejpam-3763	467	4	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-3763	467	5	...............................................................................................................................................................................	...............................................................................................................................................................................	PUNCT
ejpam-3763	467	6	............................................................................................................................................................................	............................................................................................................................................................................	PUNCT
ejpam-3763	468	1	.........	.........	PUNCT
ejpam-3763	469	1	..........	..........	PUNCT
ejpam-3763	469	2	..........	..........	PUNCT
ejpam-3763	470	1	..........	..........	PUNCT
ejpam-3763	470	2	..........	..........	PUNCT
ejpam-3763	471	1	..........	..........	PUNCT
ejpam-3763	471	2	..........	..........	PUNCT
ejpam-3763	472	1	..........	..........	PUNCT
ejpam-3763	472	2	..........	..........	PUNCT
ejpam-3763	473	1	..........	..........	PUNCT
ejpam-3763	473	2	..........	..........	PUNCT
ejpam-3763	474	1	..........	..........	PUNCT
ejpam-3763	474	2	..........	..........	PUNCT
ejpam-3763	475	1	..........	..........	PUNCT
ejpam-3763	475	2	..........	..........	PUNCT
ejpam-3763	476	1	..........	..........	PUNCT
ejpam-3763	476	2	.....	.....	PUNCT
ejpam-3763	477	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-3763	477	2	............................................................................................................................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-3763	477	3	........................................................................	........................................................................	PUNCT
ejpam-3763	477	4	.........	.........	PUNCT
ejpam-3763	477	5	........	........	PUNCT
ejpam-3763	477	6	........	........	PUNCT
ejpam-3763	477	7	........	........	PUNCT
ejpam-3763	477	8	........	........	PUNCT
ejpam-3763	477	9	........	........	PUNCT
ejpam-3763	477	10	........	........	PUNCT
ejpam-3763	477	11	........	........	PUNCT
ejpam-3763	478	1	................	................	PUNCT
ejpam-3763	478	2	........	........	PUNCT
ejpam-3763	478	3	........	........	PUNCT
ejpam-3763	478	4	........	........	PUNCT
ejpam-3763	478	5	........	........	PUNCT
ejpam-3763	478	6	........	........	PUNCT
ejpam-3763	478	7	........	........	PUNCT
ejpam-3763	478	8	........	........	PUNCT
ejpam-3763	478	9	........	........	PUNCT
ejpam-3763	478	10	........	........	PUNCT
ejpam-3763	478	11	........	........	PUNCT
ejpam-3763	478	12	........	........	PUNCT
ejpam-3763	478	13	..	..	PUNCT
ejpam-3763	478	14	.........	.........	PUNCT
ejpam-3763	478	15	........	........	PUNCT
ejpam-3763	478	16	........	........	PUNCT
ejpam-3763	478	17	........	........	PUNCT
ejpam-3763	478	18	........	........	PUNCT
ejpam-3763	478	19	........	........	PUNCT
ejpam-3763	478	20	........	........	PUNCT
ejpam-3763	478	21	........	........	PUNCT
ejpam-3763	478	22	........	........	PUNCT
ejpam-3763	478	23	........	........	PUNCT
ejpam-3763	478	24	........	........	PUNCT
ejpam-3763	478	25	........	........	PUNCT
ejpam-3763	478	26	........	........	PUNCT
ejpam-3763	478	27	........	........	PUNCT
ejpam-3763	478	28	.......	.......	PUNCT
ejpam-3763	478	29	.........	.........	PUNCT
ejpam-3763	478	30	........	........	PUNCT
ejpam-3763	478	31	........	........	PUNCT
ejpam-3763	478	32	........	........	PUNCT
ejpam-3763	478	33	........	........	PUNCT
ejpam-3763	478	34	........	........	PUNCT
ejpam-3763	478	35	........	........	PUNCT
ejpam-3763	478	36	........	........	PUNCT
ejpam-3763	478	37	........	........	PUNCT
ejpam-3763	478	38	........	........	PUNCT
ejpam-3763	478	39	........	........	PUNCT
ejpam-3763	478	40	........	........	PUNCT
ejpam-3763	478	41	..	..	PUNCT
ejpam-3763	478	42	.........	.........	PUNCT
ejpam-3763	478	43	........	........	PUNCT
ejpam-3763	478	44	........	........	PUNCT
ejpam-3763	478	45	........	........	PUNCT
ejpam-3763	478	46	........	........	PUNCT
ejpam-3763	478	47	........	........	PUNCT
ejpam-3763	478	48	........	........	PUNCT
ejpam-3763	478	49	........	........	PUNCT
ejpam-3763	478	50	.......	.......	PUNCT
ejpam-3763	479	1	...............................................................................................................................................................	...............................................................................................................................................................	PUNCT
ejpam-3763	479	2	.....................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................	PUNCT
ejpam-3763	480	1	...............................................................................	...............................................................................	PUNCT
ejpam-3763	480	2	..............................................................................	..............................................................................	PUNCT
ejpam-3763	481	1	..............................................................................	..............................................................................	PUNCT
ejpam-3763	481	2	.............................	.............................	PUNCT
ejpam-3763	481	3	...............	...............	PUNCT
ejpam-3763	482	1	..............	..............	PUNCT
ejpam-3763	482	2	..............	..............	PUNCT
ejpam-3763	483	1	..............	..............	PUNCT
ejpam-3763	483	2	..............	..............	PUNCT
ejpam-3763	484	1	..............	..............	PUNCT
ejpam-3763	484	2	...	...	PUNCT
ejpam-3763	485	1	.............................................................	.............................................................	PUNCT
ejpam-3763	485	2	................	................	PUNCT
ejpam-3763	485	3	...............	...............	PUNCT
ejpam-3763	485	4	...............	...............	PUNCT
ejpam-3763	485	5	...............	...............	PUNCT
ejpam-3763	485	6	...............	...............	PUNCT
ejpam-3763	485	7	...............	...............	PUNCT
ejpam-3763	485	8	...............	...............	PUNCT
ejpam-3763	485	9	..............	..............	PUNCT
ejpam-3763	486	1	..........	..........	PUNCT
ejpam-3763	486	2	.........	.........	PUNCT
ejpam-3763	487	1	.........	.........	PUNCT
ejpam-3763	487	2	.........	.........	PUNCT
ejpam-3763	488	1	.........	.........	PUNCT
ejpam-3763	488	2	.........	.........	PUNCT
ejpam-3763	489	1	.........	.........	PUNCT
ejpam-3763	489	2	.........	.........	PUNCT
ejpam-3763	490	1	..	..	PUNCT
ejpam-3763	490	2	0	0	NUM
ejpam-3763	491	1	00	00	NUM
ejpam-3763	491	2	0	0	NUM
ejpam-3763	491	3	0	0	NUM
ejpam-3763	491	4	0	0	NUM
ejpam-3763	491	5	0	0	NUM
ejpam-3763	491	6	0	0	NUM
ejpam-3763	491	7	2	2	NUM
ejpam-3763	491	8	2	2	NUM
ejpam-3763	491	9	1	1	NUM
ejpam-3763	491	10	1	1	NUM
ejpam-3763	491	11	gg	gg	NOUN
ejpam-3763	491	12	figure	figure	NOUN
ejpam-3763	491	13	1	1	NUM
ejpam-3763	491	14	:	:	PUNCT
ejpam-3763	491	15	graph	graph	VERB
ejpam-3763	491	16	g	g	NOUN
ejpam-3763	491	17	with	with	ADP
ejpam-3763	491	18	γ(g	γ(g	PROPN
ejpam-3763	491	19	)	)	PUNCT
ejpam-3763	491	20	=	=	SYM
ejpam-3763	492	1	1	1	NUM
ejpam-3763	492	2	and	and	CCONJ
ejpam-3763	492	3	γp	γp	NOUN
ejpam-3763	492	4	r	r	NOUN
ejpam-3763	492	5	(	(	PUNCT
ejpam-3763	492	6	gg	gg	NOUN
ejpam-3763	492	7	)	)	PUNCT
ejpam-3763	492	8	<	<	X
ejpam-3763	492	9	|v	|v	PROPN
ejpam-3763	492	10	(	(	PUNCT
ejpam-3763	492	11	g)|+	g)|+	PROPN
ejpam-3763	492	12	1	1	NUM
ejpam-3763	492	13	pick	pick	NOUN
ejpam-3763	492	14	g	g	PROPN
ejpam-3763	492	15	=	=	PROPN
ejpam-3763	492	16	kn	kn	PROPN
ejpam-3763	492	17	.	.	PUNCT
ejpam-3763	493	1	by	by	ADP
ejpam-3763	493	2	proposition	proposition	NOUN
ejpam-3763	493	3	2.13(iv	2.13(iv	NUM
ejpam-3763	493	4	)	)	PUNCT
ejpam-3763	493	5	and	and	CCONJ
ejpam-3763	493	6	corollary	corollary	ADJ
ejpam-3763	493	7	2.5	2.5	NUM
ejpam-3763	493	8	,	,	PUNCT
ejpam-3763	493	9	γpr(gg	γpr(gg	NUM
ejpam-3763	493	10	)	)	PUNCT
ejpam-3763	493	11	=	=	SYM
ejpam-3763	493	12	1	1	NUM
ejpam-3763	493	13	+	+	NUM
ejpam-3763	493	14	max{γpr(g	max{γpr(g	PROPN
ejpam-3763	493	15	)	)	PUNCT
ejpam-3763	493	16	,	,	PUNCT
ejpam-3763	493	17	γpr(g	γpr(g	PROPN
ejpam-3763	493	18	)	)	PUNCT
ejpam-3763	493	19	}	}	PUNCT
ejpam-3763	493	20	.	.	PUNCT
ejpam-3763	494	1	observe	observe	VERB
ejpam-3763	494	2	also	also	ADV
ejpam-3763	494	3	that	that	SCONJ
ejpam-3763	494	4	if	if	SCONJ
ejpam-3763	494	5	v	v	NUM
ejpam-3763	494	6	∈	∈	PROPN
ejpam-3763	494	7	v	v	NOUN
ejpam-3763	494	8	(	(	PUNCT
ejpam-3763	494	9	g	g	NOUN
ejpam-3763	494	10	)	)	PUNCT
ejpam-3763	494	11	,	,	PUNCT
ejpam-3763	494	12	then	then	ADV
ejpam-3763	494	13	f	f	PROPN
ejpam-3763	494	14	=	=	PUNCT
ejpam-3763	494	15	(	(	PUNCT
ejpam-3763	494	16	v	v	NOUN
ejpam-3763	494	17	(	(	PUNCT
ejpam-3763	494	18	g	g	NOUN
ejpam-3763	494	19	)	)	PUNCT
ejpam-3763	494	20	\	\	NOUN
ejpam-3763	494	21	{	{	PUNCT
ejpam-3763	494	22	v},∅	v},∅	PROPN
ejpam-3763	494	23	,	,	PUNCT
ejpam-3763	494	24	{	{	PUNCT
ejpam-3763	494	25	v	v	NOUN
ejpam-3763	494	26	}	}	PUNCT
ejpam-3763	494	27	)	)	PUNCT
ejpam-3763	494	28	∈	∈	PROPN
ejpam-3763	494	29	prd(g	prd(g	PROPN
ejpam-3763	494	30	)	)	PUNCT
ejpam-3763	494	31	and	and	CCONJ
ejpam-3763	494	32	γpr(gg	γpr(gg	NUM
ejpam-3763	494	33	)	)	PUNCT
ejpam-3763	494	34	=	=	SYM
ejpam-3763	495	1	ωg(f	ωg(f	X
ejpam-3763	495	2	)	)	PUNCT
ejpam-3763	496	1	+	+	CCONJ
ejpam-3763	496	2	n	n	CCONJ
ejpam-3763	496	3	−	−	NOUN
ejpam-3763	496	4	|v2|	|v2|	NOUN
ejpam-3763	496	5	.	.	PUNCT
ejpam-3763	497	1	the	the	DET
ejpam-3763	497	2	following	follow	VERB
ejpam-3763	497	3	result	result	NOUN
ejpam-3763	497	4	shows	show	VERB
ejpam-3763	497	5	that	that	SCONJ
ejpam-3763	497	6	these	these	DET
ejpam-3763	497	7	two	two	NUM
ejpam-3763	497	8	expressions	expression	NOUN
ejpam-3763	497	9	serve	serve	VERB
ejpam-3763	497	10	as	as	ADP
ejpam-3763	497	11	sharp	sharp	ADJ
ejpam-3763	497	12	lower	low	ADJ
ejpam-3763	497	13	and	and	CCONJ
ejpam-3763	497	14	upper	upper	ADJ
ejpam-3763	497	15	bounds	bound	NOUN
ejpam-3763	497	16	,	,	PUNCT
ejpam-3763	497	17	respectively	respectively	ADV
ejpam-3763	497	18	,	,	PUNCT
ejpam-3763	497	19	of	of	ADP
ejpam-3763	497	20	γpr(gg	γpr(gg	NOUN
ejpam-3763	497	21	)	)	PUNCT
ejpam-3763	497	22	for	for	ADP
ejpam-3763	497	23	a	a	DET
ejpam-3763	497	24	general	general	ADJ
ejpam-3763	497	25	graph	graph	NOUN
ejpam-3763	497	26	g.	g.	NOUN
ejpam-3763	497	27	theorem	theorem	VERB
ejpam-3763	497	28	2.14	2.14	NUM
ejpam-3763	497	29	.	.	PUNCT
ejpam-3763	498	1	for	for	ADP
ejpam-3763	498	2	any	any	DET
ejpam-3763	498	3	graph	graph	NOUN
ejpam-3763	498	4	g	g	NOUN
ejpam-3763	498	5	,	,	PUNCT
ejpam-3763	498	6	1	1	NUM
ejpam-3763	498	7	+	+	CCONJ
ejpam-3763	498	8	max{γpr(g	max{γpr(g	PROPN
ejpam-3763	498	9	)	)	PUNCT
ejpam-3763	498	10	,	,	PUNCT
ejpam-3763	498	11	γpr(g	γpr(g	PROPN
ejpam-3763	498	12	)	)	PUNCT
ejpam-3763	498	13	}	}	PUNCT
ejpam-3763	498	14	≤	≤	NUM
ejpam-3763	498	15	γpr(gg	γpr(gg	NOUN
ejpam-3763	498	16	)	)	PUNCT
ejpam-3763	498	17	≤	≤	NOUN
ejpam-3763	498	18	ρ	ρ	PROPN
ejpam-3763	498	19	,	,	PUNCT
ejpam-3763	498	20	where	where	SCONJ
ejpam-3763	498	21	ρ	ρ	PROPN
ejpam-3763	498	22	=	=	SYM
ejpam-3763	498	23	min{ωg(f	min{ωg(f	NOUN
ejpam-3763	498	24	)	)	PUNCT
ejpam-3763	499	1	+	+	NUM
ejpam-3763	499	2	n−	n−	NOUN
ejpam-3763	499	3	|v2|	|v2|	ADV
ejpam-3763	499	4	:	:	PUNCT
ejpam-3763	500	1	f	f	X
ejpam-3763	500	2	=	=	SYM
ejpam-3763	500	3	(	(	PUNCT
ejpam-3763	500	4	v0	v0	PROPN
ejpam-3763	500	5	,	,	PUNCT
ejpam-3763	500	6	v1	v1	NOUN
ejpam-3763	500	7	,	,	PUNCT
ejpam-3763	500	8	v2	v2	NOUN
ejpam-3763	500	9	)	)	PUNCT
ejpam-3763	500	10	∈	∈	PROPN
ejpam-3763	500	11	prd(g	prd(g	PROPN
ejpam-3763	500	12	)	)	PUNCT
ejpam-3763	500	13	∪	∪	ADP
ejpam-3763	500	14	prd(g	prd(g	NUM
ejpam-3763	500	15	)	)	PUNCT
ejpam-3763	500	16	}	}	PUNCT
ejpam-3763	500	17	.	.	PUNCT
ejpam-3763	501	1	proof	proof	NOUN
ejpam-3763	501	2	:	:	PUNCT
ejpam-3763	501	3	wlog	wlog	PROPN
ejpam-3763	501	4	assume	assume	VERB
ejpam-3763	501	5	that	that	SCONJ
ejpam-3763	501	6	for	for	ADP
ejpam-3763	501	7	some	some	DET
ejpam-3763	501	8	f	f	NOUN
ejpam-3763	501	9	=	=	SYM
ejpam-3763	501	10	(	(	PUNCT
ejpam-3763	501	11	v0	v0	PROPN
ejpam-3763	501	12	,	,	PUNCT
ejpam-3763	501	13	v1	v1	NOUN
ejpam-3763	501	14	,	,	PUNCT
ejpam-3763	501	15	v2	v2	PROPN
ejpam-3763	501	16	)	)	PUNCT
ejpam-3763	501	17	on	on	ADP
ejpam-3763	501	18	g	g	PROPN
ejpam-3763	501	19	,	,	PUNCT
ejpam-3763	501	20	ρ	ρ	NOUN
ejpam-3763	501	21	=	=	PUNCT
ejpam-3763	501	22	ωg(f	ωg(f	X
ejpam-3763	501	23	)	)	PUNCT
ejpam-3763	501	24	+	+	CCONJ
ejpam-3763	501	25	n−	n−	NOUN
ejpam-3763	501	26	|v2|	|v2|	ADV
ejpam-3763	501	27	.	.	PUNCT
ejpam-3763	502	1	extend	extend	VERB
ejpam-3763	502	2	f	f	PROPN
ejpam-3763	502	3	to	to	PART
ejpam-3763	502	4	gg	gg	VERB
ejpam-3763	502	5	by	by	ADP
ejpam-3763	502	6	defining	define	VERB
ejpam-3763	502	7	f(v	f(v	NOUN
ejpam-3763	502	8	)	)	PUNCT
ejpam-3763	503	1	=	=	SYM
ejpam-3763	503	2	0	0	NUM
ejpam-3763	504	1	for	for	ADP
ejpam-3763	504	2	all	all	PRON
ejpam-3763	504	3	v	v	ADP
ejpam-3763	504	4	∈	∈	NOUN
ejpam-3763	504	5	v2	v2	NOUN
ejpam-3763	504	6	and	and	CCONJ
ejpam-3763	504	7	f(v	f(v	NOUN
ejpam-3763	504	8	)	)	PUNCT
ejpam-3763	504	9	=	=	SYM
ejpam-3763	504	10	1	1	NUM
ejpam-3763	504	11	for	for	ADP
ejpam-3763	504	12	all	all	PRON
ejpam-3763	504	13	v	v	ADP
ejpam-3763	504	14	∈	∈	NUM
ejpam-3763	504	15	v	v	NOUN
ejpam-3763	504	16	(	(	PUNCT
ejpam-3763	504	17	g	g	NOUN
ejpam-3763	504	18	)	)	PUNCT
ejpam-3763	504	19	\	\	PROPN
ejpam-3763	505	1	v2	v2	PROPN
ejpam-3763	505	2	.	.	PUNCT
ejpam-3763	506	1	then	then	ADV
ejpam-3763	506	2	the	the	DET
ejpam-3763	506	3	extension	extension	NOUN
ejpam-3763	506	4	f	f	PROPN
ejpam-3763	506	5	∈	∈	PROPN
ejpam-3763	506	6	prd(gg	prd(gg	NOUN
ejpam-3763	506	7	)	)	PUNCT
ejpam-3763	506	8	and	and	CCONJ
ejpam-3763	506	9	γpr(gg	γpr(gg	X
ejpam-3763	506	10	)	)	PUNCT
ejpam-3763	506	11	≤	≤	NOUN
ejpam-3763	506	12	ωg(f	ωg(f	PUNCT
ejpam-3763	506	13	)	)	PUNCT
ejpam-3763	506	14	+	+	CCONJ
ejpam-3763	506	15	n−	n−	NOUN
ejpam-3763	506	16	|v2|	|v2|	ADV
ejpam-3763	506	17	.	.	PUNCT
ejpam-3763	507	1	thus	thus	ADV
ejpam-3763	507	2	,	,	PUNCT
ejpam-3763	507	3	γpr(gg	γpr(gg	X
ejpam-3763	507	4	)	)	PUNCT
ejpam-3763	507	5	≤	≤	NOUN
ejpam-3763	507	6	ρ	ρ	NOUN
ejpam-3763	507	7	.	.	PUNCT
ejpam-3763	508	1	in	in	ADP
ejpam-3763	508	2	view	view	NOUN
ejpam-3763	508	3	of	of	ADP
ejpam-3763	508	4	proposition	proposition	NOUN
ejpam-3763	508	5	2.13(iv	2.13(iv	NUM
ejpam-3763	508	6	)	)	PUNCT
ejpam-3763	508	7	,	,	PUNCT
ejpam-3763	508	8	we	we	PRON
ejpam-3763	508	9	assume	assume	VERB
ejpam-3763	508	10	that	that	SCONJ
ejpam-3763	508	11	neither	neither	CCONJ
ejpam-3763	508	12	g	g	PROPN
ejpam-3763	508	13	nor	nor	CCONJ
ejpam-3763	508	14	g	g	PROPN
ejpam-3763	508	15	is	be	AUX
ejpam-3763	508	16	a	a	DET
ejpam-3763	508	17	complete	complete	ADJ
ejpam-3763	508	18	graph	graph	NOUN
ejpam-3763	508	19	.	.	PUNCT
ejpam-3763	508	20	wlog	wlog	PROPN
ejpam-3763	508	21	,	,	PUNCT
ejpam-3763	508	22	assume	assume	VERB
ejpam-3763	508	23	that	that	SCONJ
ejpam-3763	508	24	γpr(g	γpr(g	PROPN
ejpam-3763	508	25	)	)	PUNCT
ejpam-3763	508	26	≥	≥	NOUN
ejpam-3763	508	27	γpr(g	γpr(g	PROPN
ejpam-3763	508	28	)	)	PUNCT
ejpam-3763	508	29	.	.	PUNCT
ejpam-3763	509	1	let	let	VERB
ejpam-3763	509	2	f	f	PROPN
ejpam-3763	509	3	=	=	SYM
ejpam-3763	509	4	(	(	PUNCT
ejpam-3763	509	5	v0	v0	PROPN
ejpam-3763	509	6	,	,	PUNCT
ejpam-3763	509	7	v1	v1	NOUN
ejpam-3763	509	8	,	,	PUNCT
ejpam-3763	509	9	v2	v2	PROPN
ejpam-3763	509	10	)	)	PUNCT
ejpam-3763	509	11	be	be	AUX
ejpam-3763	509	12	a	a	DET
ejpam-3763	509	13	γpr	γpr	NOUN
ejpam-3763	509	14	-function	-function	NOUN
ejpam-3763	509	15	on	on	ADP
ejpam-3763	509	16	gg	gg	NOUN
ejpam-3763	509	17	.	.	PUNCT
ejpam-3763	510	1	if	if	SCONJ
ejpam-3763	510	2	v	v	INTJ
ejpam-3763	510	3	(	(	PUNCT
ejpam-3763	510	4	g	g	NOUN
ejpam-3763	510	5	)	)	PUNCT
ejpam-3763	510	6	⊆	⊆	NUM
ejpam-3763	510	7	v0	v0	NOUN
ejpam-3763	510	8	,	,	PUNCT
ejpam-3763	510	9	then	then	ADV
ejpam-3763	510	10	v2	v2	VERB
ejpam-3763	510	11	=	=	SYM
ejpam-3763	510	12	v	v	NOUN
ejpam-3763	510	13	(	(	PUNCT
ejpam-3763	510	14	g	g	NOUN
ejpam-3763	510	15	)	)	PUNCT
ejpam-3763	511	1	so	so	SCONJ
ejpam-3763	511	2	that	that	SCONJ
ejpam-3763	511	3	γpr(gg	γpr(gg	NOUN
ejpam-3763	511	4	)	)	PUNCT
ejpam-3763	511	5	=	=	SYM
ejpam-3763	511	6	2|v2|	2|v2|	NUM
ejpam-3763	511	7	=	=	SYM
ejpam-3763	511	8	|v	|v	PROPN
ejpam-3763	511	9	(	(	PUNCT
ejpam-3763	511	10	gg)|	gg)|	PROPN
ejpam-3763	511	11	.	.	PUNCT
ejpam-3763	512	1	since	since	SCONJ
ejpam-3763	512	2	gg	gg	PROPN
ejpam-3763	512	3	is	be	AUX
ejpam-3763	512	4	connected	connect	VERB
ejpam-3763	512	5	,	,	PUNCT
ejpam-3763	512	6	n	n	NOUN
ejpam-3763	512	7	=	=	SYM
ejpam-3763	512	8	1	1	NUM
ejpam-3763	512	9	by	by	ADP
ejpam-3763	512	10	corollary	corollary	ADJ
ejpam-3763	512	11	2.5	2.5	NUM
ejpam-3763	512	12	and	and	CCONJ
ejpam-3763	512	13	corollary	corollary	ADJ
ejpam-3763	512	14	2.3(ii	2.3(ii	NUM
ejpam-3763	512	15	)	)	PUNCT
ejpam-3763	512	16	.	.	PUNCT
ejpam-3763	513	1	this	this	PRON
ejpam-3763	513	2	is	be	AUX
ejpam-3763	513	3	contradictory	contradictory	ADJ
ejpam-3763	513	4	to	to	ADP
ejpam-3763	513	5	our	our	PRON
ejpam-3763	513	6	assumption	assumption	NOUN
ejpam-3763	513	7	.	.	PUNCT
ejpam-3763	514	1	thus	thus	ADV
ejpam-3763	514	2	,	,	PUNCT
ejpam-3763	514	3	v	v	INTJ
ejpam-3763	514	4	(	(	PUNCT
ejpam-3763	514	5	g	g	NOUN
ejpam-3763	514	6	)	)	PUNCT
ejpam-3763	514	7	∩	∩	NOUN
ejpam-3763	514	8	(	(	PUNCT
ejpam-3763	514	9	v1	v1	NOUN
ejpam-3763	514	10	∪	∪	X
ejpam-3763	514	11	v2	v2	NOUN
ejpam-3763	514	12	)	)	PUNCT
ejpam-3763	514	13	6=	6=	ADP
ejpam-3763	514	14	∅.	∅.	ADP
ejpam-3763	514	15	if	if	SCONJ
ejpam-3763	514	16	v2	v2	PROPN
ejpam-3763	514	17	∩	∩	NOUN
ejpam-3763	514	18	v	v	NOUN
ejpam-3763	514	19	(	(	PUNCT
ejpam-3763	514	20	g	g	NOUN
ejpam-3763	514	21	)	)	PUNCT
ejpam-3763	514	22	=	=	NOUN
ejpam-3763	514	23	∅	∅	NOUN
ejpam-3763	514	24	,	,	PUNCT
ejpam-3763	514	25	then	then	ADV
ejpam-3763	514	26	g	g	PROPN
ejpam-3763	514	27	=	=	SYM
ejpam-3763	514	28	(	(	PUNCT
ejpam-3763	514	29	v0	v0	NOUN
ejpam-3763	514	30	∩	∩	NOUN
ejpam-3763	514	31	v	v	X
ejpam-3763	514	32	(	(	PUNCT
ejpam-3763	514	33	g	g	NOUN
ejpam-3763	514	34	)	)	PUNCT
ejpam-3763	514	35	,	,	PUNCT
ejpam-3763	514	36	v1	v1	NOUN
ejpam-3763	514	37	∩	∩	ADJ
ejpam-3763	514	38	v	v	NOUN
ejpam-3763	514	39	(	(	PUNCT
ejpam-3763	514	40	g	g	NOUN
ejpam-3763	514	41	)	)	PUNCT
ejpam-3763	514	42	,	,	PUNCT
ejpam-3763	514	43	v2	v2	PROPN
ejpam-3763	514	44	)	)	PUNCT
ejpam-3763	514	45	∈	∈	PROPN
ejpam-3763	514	46	prd(g	prd(g	PROPN
ejpam-3763	514	47	)	)	PUNCT
ejpam-3763	514	48	.	.	PUNCT
ejpam-3763	515	1	since	since	SCONJ
ejpam-3763	515	2	v	v	NOUN
ejpam-3763	515	3	(	(	PUNCT
ejpam-3763	515	4	g	g	NOUN
ejpam-3763	515	5	)	)	PUNCT
ejpam-3763	515	6	∩	∩	NOUN
ejpam-3763	515	7	v1	v1	NOUN
ejpam-3763	515	8	6=	6=	NOUN
ejpam-3763	515	9	∅	∅	NOUN
ejpam-3763	515	10	,	,	PUNCT
ejpam-3763	515	11	γpr(gg	γpr(gg	NUM
ejpam-3763	515	12	)	)	PUNCT
ejpam-3763	515	13	=	=	SYM
ejpam-3763	515	14	ωgg(f	ωgg(f	PROPN
ejpam-3763	515	15	)	)	PUNCT
ejpam-3763	515	16	≥	≥	NOUN
ejpam-3763	515	17	ωg(g	ωg(g	NUM
ejpam-3763	515	18	)	)	PUNCT
ejpam-3763	515	19	+	+	CCONJ
ejpam-3763	515	20	1	1	NUM
ejpam-3763	515	21	≥	≥	NOUN
ejpam-3763	515	22	γpr(g	γpr(g	PROPN
ejpam-3763	515	23	)	)	PUNCT
ejpam-3763	516	1	+	+	CCONJ
ejpam-3763	516	2	1	1	X
ejpam-3763	516	3	.	.	X
ejpam-3763	516	4	suppose	suppose	VERB
ejpam-3763	516	5	that	that	SCONJ
ejpam-3763	516	6	v2	v2	PROPN
ejpam-3763	516	7	∩	∩	NOUN
ejpam-3763	516	8	v	v	NOUN
ejpam-3763	516	9	(	(	PUNCT
ejpam-3763	516	10	g	g	NOUN
ejpam-3763	516	11	)	)	PUNCT
ejpam-3763	516	12	6=	6=	ADP
ejpam-3763	516	13	∅	∅	NOUN
ejpam-3763	516	14	,	,	PUNCT
ejpam-3763	516	15	and	and	CCONJ
ejpam-3763	516	16	let	let	VERB
ejpam-3763	516	17	a	a	DET
ejpam-3763	516	18	=	=	X
ejpam-3763	516	19	{	{	PUNCT
ejpam-3763	516	20	v	v	NOUN
ejpam-3763	516	21	∈	∈	PROPN
ejpam-3763	516	22	v0	v0	NOUN
ejpam-3763	516	23	:	:	PUNCT
ejpam-3763	516	24	v2	v2	VERB
ejpam-3763	516	25	∩	∩	ADJ
ejpam-3763	516	26	ngg(v	ngg(v	NOUN
ejpam-3763	516	27	)	)	PUNCT
ejpam-3763	516	28	=	=	PRON
ejpam-3763	516	29	{	{	PUNCT
ejpam-3763	516	30	v	v	NOUN
ejpam-3763	516	31	}	}	PUNCT
ejpam-3763	516	32	}	}	PUNCT
ejpam-3763	516	33	.	.	PUNCT
ejpam-3763	517	1	define	define	VERB
ejpam-3763	517	2	g	g	PROPN
ejpam-3763	517	3	=	=	SYM
ejpam-3763	517	4	(	(	PUNCT
ejpam-3763	517	5	v	v	NOUN
ejpam-3763	517	6	∗0	∗0	PROPN
ejpam-3763	517	7	,	,	PUNCT
ejpam-3763	517	8	v	v	NOUN
ejpam-3763	517	9	∗	∗	NOUN
ejpam-3763	517	10	1	1	NUM
ejpam-3763	517	11	,	,	PUNCT
ejpam-3763	517	12	v	v	NOUN
ejpam-3763	517	13	∗	∗	NOUN
ejpam-3763	517	14	2	2	NUM
ejpam-3763	517	15	)	)	PUNCT
ejpam-3763	517	16	on	on	ADP
ejpam-3763	517	17	g	g	PROPN
ejpam-3763	517	18	by	by	ADP
ejpam-3763	517	19	g(x	g(x	NOUN
ejpam-3763	517	20	)	)	PUNCT
ejpam-3763	518	1	=	=	PRON
ejpam-3763	518	2	{	{	PUNCT
ejpam-3763	518	3	f(x	f(x	PROPN
ejpam-3763	518	4	)	)	PUNCT
ejpam-3763	518	5	,	,	PUNCT
ejpam-3763	518	6	if	if	SCONJ
ejpam-3763	518	7	x	x	SYM
ejpam-3763	518	8	∈	∈	PROPN
ejpam-3763	518	9	v	v	ADP
ejpam-3763	518	10	(	(	PUNCT
ejpam-3763	518	11	g	g	NOUN
ejpam-3763	518	12	)	)	PUNCT
ejpam-3763	518	13	\a	\a	ADJ
ejpam-3763	518	14	;	;	PUNCT
ejpam-3763	518	15	1	1	NUM
ejpam-3763	518	16	,	,	PUNCT
ejpam-3763	518	17	if	if	SCONJ
ejpam-3763	518	18	x	x	PROPN
ejpam-3763	518	19	∈	∈	PROPN
ejpam-3763	518	20	a.	a.	NOUN
ejpam-3763	518	21	l.	l.	PROPN
ejpam-3763	518	22	paleta	paleta	PROPN
ejpam-3763	518	23	,	,	PUNCT
ejpam-3763	518	24	f.	f.	PROPN
ejpam-3763	518	25	jamil	jamil	PROPN
ejpam-3763	518	26	/	/	SYM
ejpam-3763	518	27	eur	eur	PROPN
ejpam-3763	518	28	.	.	PUNCT
ejpam-3763	519	1	j.	j.	PROPN
ejpam-3763	519	2	pure	pure	PROPN
ejpam-3763	519	3	appl	appl	PROPN
ejpam-3763	519	4	.	.	PROPN
ejpam-3763	519	5	math	math	PROPN
ejpam-3763	519	6	,	,	PUNCT
ejpam-3763	519	7	13	13	NUM
ejpam-3763	519	8	(	(	PUNCT
ejpam-3763	519	9	3	3	NUM
ejpam-3763	519	10	)	)	PUNCT
ejpam-3763	519	11	(	(	PUNCT
ejpam-3763	519	12	2020	2020	NUM
ejpam-3763	519	13	)	)	PUNCT
ejpam-3763	519	14	,	,	PUNCT
ejpam-3763	519	15	529	529	NUM
ejpam-3763	519	16	-	-	SYM
ejpam-3763	519	17	548	548	NUM
ejpam-3763	519	18	542	542	NUM
ejpam-3763	519	19	then	then	ADV
ejpam-3763	519	20	g	g	PROPN
ejpam-3763	519	21	∈	∈	PROPN
ejpam-3763	519	22	prd(g	prd(g	PROPN
ejpam-3763	519	23	)	)	PUNCT
ejpam-3763	519	24	with	with	ADP
ejpam-3763	519	25	v	v	NUM
ejpam-3763	519	26	∗0	∗0	NOUN
ejpam-3763	519	27	=	=	SYM
ejpam-3763	519	28	(	(	PUNCT
ejpam-3763	519	29	v0	v0	NOUN
ejpam-3763	519	30	\a)∩v	\a)∩v	PROPN
ejpam-3763	519	31	(	(	PUNCT
ejpam-3763	519	32	g	g	NOUN
ejpam-3763	519	33	)	)	PUNCT
ejpam-3763	519	34	,	,	PUNCT
ejpam-3763	519	35	v	v	ADP
ejpam-3763	519	36	∗1	∗1	PROPN
ejpam-3763	519	37	=	=	NOUN
ejpam-3763	519	38	a∪(v1	a∪(v1	NOUN
ejpam-3763	519	39	∩	∩	ADJ
ejpam-3763	519	40	v	v	NOUN
ejpam-3763	519	41	(	(	PUNCT
ejpam-3763	519	42	g	g	NOUN
ejpam-3763	519	43	)	)	PUNCT
ejpam-3763	519	44	)	)	PUNCT
ejpam-3763	519	45	and	and	CCONJ
ejpam-3763	519	46	v	v	ADP
ejpam-3763	519	47	∗2	∗2	PROPN
ejpam-3763	519	48	=	=	SYM
ejpam-3763	519	49	v2∩v	v2∩v	PROPN
ejpam-3763	519	50	(	(	PUNCT
ejpam-3763	519	51	g	g	NOUN
ejpam-3763	519	52	)	)	PUNCT
ejpam-3763	519	53	.	.	PUNCT
ejpam-3763	520	1	since	since	SCONJ
ejpam-3763	520	2	{	{	PUNCT
ejpam-3763	520	3	v	v	NOUN
ejpam-3763	520	4	:	:	PUNCT
ejpam-3763	520	5	v	v	NUM
ejpam-3763	520	6	∈	∈	PROPN
ejpam-3763	520	7	a	a	DET
ejpam-3763	520	8	}	}	PUNCT
ejpam-3763	520	9	⊆	⊆	NUM
ejpam-3763	520	10	v2	v2	PROPN
ejpam-3763	520	11	∩	∩	ADJ
ejpam-3763	520	12	v	v	NOUN
ejpam-3763	520	13	(	(	PUNCT
ejpam-3763	520	14	g	g	NOUN
ejpam-3763	520	15	)	)	PUNCT
ejpam-3763	520	16	,	,	PUNCT
ejpam-3763	520	17	γpr(gg	γpr(gg	X
ejpam-3763	520	18	)	)	PUNCT
ejpam-3763	520	19	=	=	SYM
ejpam-3763	520	20	ωg(g	ωg(g	NUM
ejpam-3763	520	21	)	)	PUNCT
ejpam-3763	520	22	+	+	CCONJ
ejpam-3763	520	23	∑	∑	PROPN
ejpam-3763	520	24	x∈v	x∈v	PROPN
ejpam-3763	520	25	(	(	PUNCT
ejpam-3763	520	26	g	g	NOUN
ejpam-3763	520	27	)	)	PUNCT
ejpam-3763	520	28	f(x)−	f(x)−	PROPN
ejpam-3763	520	29	|a|	|a|	PROPN
ejpam-3763	520	30	≥	≥	NOUN
ejpam-3763	520	31	ωg(g	ωg(g	PUNCT
ejpam-3763	520	32	)	)	PUNCT
ejpam-3763	520	33	+	+	CCONJ
ejpam-3763	520	34	1	1	NUM
ejpam-3763	520	35	≥	≥	NOUN
ejpam-3763	520	36	γpr(g	γpr(g	PROPN
ejpam-3763	520	37	)	)	PUNCT
ejpam-3763	520	38	+	+	CCONJ
ejpam-3763	520	39	1	1	X
ejpam-3763	520	40	.	.	X
ejpam-3763	520	41	�	�	PROPN
ejpam-3763	520	42	if	if	SCONJ
ejpam-3763	520	43	g	g	PROPN
ejpam-3763	520	44	=	=	PROPN
ejpam-3763	520	45	c5	c5	PROPN
ejpam-3763	520	46	,	,	PUNCT
ejpam-3763	520	47	then	then	ADV
ejpam-3763	520	48	g	g	PROPN
ejpam-3763	520	49	and	and	CCONJ
ejpam-3763	520	50	g	g	PROPN
ejpam-3763	520	51	are	be	AUX
ejpam-3763	520	52	isomorphic	isomorphic	ADJ
ejpam-3763	520	53	and	and	CCONJ
ejpam-3763	520	54	gg	gg	PROPN
ejpam-3763	520	55	is	be	AUX
ejpam-3763	520	56	isomorphic	isomorphic	ADJ
ejpam-3763	520	57	to	to	ADP
ejpam-3763	520	58	the	the	DET
ejpam-3763	520	59	petersen	petersen	NOUN
ejpam-3763	520	60	graph	graph	NOUN
ejpam-3763	520	61	.	.	PUNCT
ejpam-3763	520	62	observe	observe	VERB
ejpam-3763	520	63	that	that	SCONJ
ejpam-3763	520	64	γpr(gg	γpr(gg	NOUN
ejpam-3763	520	65	)	)	PUNCT
ejpam-3763	520	66	=	=	SYM
ejpam-3763	520	67	7	7	NUM
ejpam-3763	520	68	,	,	PUNCT
ejpam-3763	520	69	γpr(g	γpr(g	PROPN
ejpam-3763	520	70	)	)	PUNCT
ejpam-3763	520	71	=	=	SYM
ejpam-3763	521	1	γpr(g	γpr(g	PROPN
ejpam-3763	521	2	)	)	PUNCT
ejpam-3763	521	3	=	=	SYM
ejpam-3763	521	4	4	4	NUM
ejpam-3763	521	5	and	and	CCONJ
ejpam-3763	521	6	ρ	ρ	NUM
ejpam-3763	521	7	=	=	SYM
ejpam-3763	521	8	8	8	NUM
ejpam-3763	521	9	so	so	SCONJ
ejpam-3763	521	10	that	that	SCONJ
ejpam-3763	521	11	1	1	NUM
ejpam-3763	521	12	+	+	NUM
ejpam-3763	521	13	max{γpr(g	max{γpr(g	PROPN
ejpam-3763	521	14	)	)	PUNCT
ejpam-3763	521	15	,	,	PUNCT
ejpam-3763	521	16	γpr(g	γpr(g	PROPN
ejpam-3763	521	17	)	)	PUNCT
ejpam-3763	521	18	}	}	PUNCT
ejpam-3763	521	19	<	<	X
ejpam-3763	521	20	γpr(gg	γpr(gg	NOUN
ejpam-3763	521	21	)	)	PUNCT
ejpam-3763	521	22	<	<	X
ejpam-3763	521	23	ρ	ρ	PROPN
ejpam-3763	521	24	.	.	PUNCT
ejpam-3763	522	1	this	this	PRON
ejpam-3763	522	2	shows	show	VERB
ejpam-3763	522	3	that	that	SCONJ
ejpam-3763	522	4	strict	strict	ADJ
ejpam-3763	522	5	inequality	inequality	NOUN
ejpam-3763	522	6	can	can	AUX
ejpam-3763	522	7	be	be	AUX
ejpam-3763	522	8	attained	attain	VERB
ejpam-3763	522	9	at	at	ADP
ejpam-3763	522	10	each	each	DET
ejpam-3763	522	11	side	side	NOUN
ejpam-3763	522	12	of	of	ADP
ejpam-3763	522	13	the	the	DET
ejpam-3763	522	14	inequalities	inequality	NOUN
ejpam-3763	522	15	in	in	ADP
ejpam-3763	522	16	theorem	theorem	NOUN
ejpam-3763	522	17	2.14	2.14	NUM
ejpam-3763	522	18	.	.	PUNCT
ejpam-3763	523	1	2.4	2.4	NUM
ejpam-3763	523	2	.	.	PUNCT
ejpam-3763	524	1	on	on	ADP
ejpam-3763	524	2	the	the	DET
ejpam-3763	524	3	edge	edge	NOUN
ejpam-3763	524	4	corona	corona	NOUN
ejpam-3763	524	5	of	of	ADP
ejpam-3763	524	6	graphs	graph	NOUN
ejpam-3763	524	7	given	give	VERB
ejpam-3763	524	8	graphs	graph	NOUN
ejpam-3763	524	9	g	g	NOUN
ejpam-3763	524	10	and	and	CCONJ
ejpam-3763	524	11	h	h	NOUN
ejpam-3763	524	12	,	,	PUNCT
ejpam-3763	524	13	we	we	PRON
ejpam-3763	524	14	write	write	VERB
ejpam-3763	524	15	huv	huv	PROPN
ejpam-3763	524	16	to	to	PART
ejpam-3763	524	17	denote	denote	VERB
ejpam-3763	524	18	that	that	DET
ejpam-3763	524	19	copy	copy	NOUN
ejpam-3763	524	20	of	of	ADP
ejpam-3763	524	21	h	h	NOUN
ejpam-3763	524	22	that	that	PRON
ejpam-3763	524	23	is	be	AUX
ejpam-3763	524	24	being	be	AUX
ejpam-3763	524	25	joined	join	VERB
ejpam-3763	524	26	with	with	ADP
ejpam-3763	524	27	the	the	DET
ejpam-3763	524	28	endvertices	endvertice	NOUN
ejpam-3763	524	29	of	of	ADP
ejpam-3763	524	30	the	the	DET
ejpam-3763	524	31	edge	edge	NOUN
ejpam-3763	524	32	uv	uv	PROPN
ejpam-3763	524	33	∈	∈	PROPN
ejpam-3763	524	34	e(g	e(g	PROPN
ejpam-3763	524	35	)	)	PUNCT
ejpam-3763	524	36	in	in	ADP
ejpam-3763	524	37	the	the	DET
ejpam-3763	524	38	edge	edge	NOUN
ejpam-3763	524	39	corona	corona	PROPN
ejpam-3763	524	40	g	g	PROPN
ejpam-3763	524	41	�	�	PROPN
ejpam-3763	524	42	h.	h.	PROPN
ejpam-3763	524	43	if	if	SCONJ
ejpam-3763	524	44	h	h	PRON
ejpam-3763	524	45	=	=	PRON
ejpam-3763	524	46	{	{	PUNCT
ejpam-3763	524	47	x	x	NOUN
ejpam-3763	524	48	}	}	PUNCT
ejpam-3763	524	49	,	,	PUNCT
ejpam-3763	524	50	then	then	ADV
ejpam-3763	524	51	we	we	PRON
ejpam-3763	524	52	write	write	VERB
ejpam-3763	524	53	v	v	NOUN
ejpam-3763	524	54	(	(	PUNCT
ejpam-3763	524	55	huv	huv	PROPN
ejpam-3763	524	56	)	)	PUNCT
ejpam-3763	524	57	=	=	PRON
ejpam-3763	524	58	{	{	PUNCT
ejpam-3763	524	59	xuv	xuv	NOUN
ejpam-3763	524	60	}	}	PUNCT
ejpam-3763	524	61	.	.	PUNCT
ejpam-3763	525	1	for	for	ADP
ejpam-3763	525	2	an	an	DET
ejpam-3763	525	3	f	f	PROPN
ejpam-3763	525	4	∈	∈	PROPN
ejpam-3763	525	5	prd(g	prd(g	PROPN
ejpam-3763	525	6	)	)	PUNCT
ejpam-3763	525	7	,	,	PUNCT
ejpam-3763	525	8	we	we	PRON
ejpam-3763	525	9	write	write	VERB
ejpam-3763	525	10	for	for	ADP
ejpam-3763	525	11	each	each	PRON
ejpam-3763	525	12	a	a	NOUN
ejpam-3763	525	13	,	,	PUNCT
ejpam-3763	525	14	b	b	X
ejpam-3763	525	15	∈	∈	PROPN
ejpam-3763	525	16	{	{	PUNCT
ejpam-3763	525	17	0	0	NUM
ejpam-3763	525	18	,	,	PUNCT
ejpam-3763	525	19	1	1	NUM
ejpam-3763	525	20	,	,	PUNCT
ejpam-3763	525	21	2	2	NUM
ejpam-3763	525	22	}	}	PUNCT
ejpam-3763	525	23	,	,	PUNCT
ejpam-3763	525	24	eab(f	eab(f	PROPN
ejpam-3763	525	25	;	;	PUNCT
ejpam-3763	525	26	g	g	NOUN
ejpam-3763	525	27	)	)	PUNCT
ejpam-3763	525	28	=	=	PRON
ejpam-3763	525	29	{	{	PUNCT
ejpam-3763	525	30	uv	uv	PROPN
ejpam-3763	525	31	∈	∈	PROPN
ejpam-3763	525	32	e(g	e(g	PROPN
ejpam-3763	525	33	)	)	PUNCT
ejpam-3763	525	34	:	:	PUNCT
ejpam-3763	525	35	(	(	PUNCT
ejpam-3763	525	36	f(u	f(u	PROPN
ejpam-3763	525	37	)	)	PUNCT
ejpam-3763	525	38	=	=	PUNCT
ejpam-3763	526	1	a	a	DET
ejpam-3763	526	2	∧	∧	PROPN
ejpam-3763	526	3	f(v	f(v	NOUN
ejpam-3763	526	4	)	)	PUNCT
ejpam-3763	526	5	=	=	SYM
ejpam-3763	526	6	b	b	X
ejpam-3763	526	7	)	)	PUNCT
ejpam-3763	526	8	∨	∨	NOUN
ejpam-3763	526	9	(	(	PUNCT
ejpam-3763	526	10	f(u	f(u	PROPN
ejpam-3763	526	11	)	)	PUNCT
ejpam-3763	526	12	=	=	SYM
ejpam-3763	527	1	b	b	X
ejpam-3763	527	2	∧	∧	PROPN
ejpam-3763	527	3	f(v	f(v	NOUN
ejpam-3763	527	4	)	)	PUNCT
ejpam-3763	527	5	=	=	SYM
ejpam-3763	527	6	a	a	X
ejpam-3763	527	7	)	)	PUNCT
ejpam-3763	527	8	}	}	PUNCT
ejpam-3763	527	9	,	,	PUNCT
ejpam-3763	527	10	where	where	SCONJ
ejpam-3763	527	11	“	"	PUNCT
ejpam-3763	527	12	∧	∧	PROPN
ejpam-3763	527	13	“	"	PUNCT
ejpam-3763	527	14	and	and	CCONJ
ejpam-3763	527	15	“	"	PUNCT
ejpam-3763	527	16	∨	∨	NOUN
ejpam-3763	527	17	“	"	PUNCT
ejpam-3763	527	18	denote	denote	NOUN
ejpam-3763	527	19	“	"	PUNCT
ejpam-3763	527	20	and	and	CCONJ
ejpam-3763	527	21	“	"	PUNCT
ejpam-3763	527	22	and	and	CCONJ
ejpam-3763	527	23	“	"	PUNCT
ejpam-3763	527	24	or	or	CCONJ
ejpam-3763	527	25	“	"	PUNCT
ejpam-3763	527	26	,	,	PUNCT
ejpam-3763	527	27	respectively	respectively	ADV
ejpam-3763	527	28	.	.	PUNCT
ejpam-3763	528	1	theorem	theorem	VERB
ejpam-3763	528	2	2.15	2.15	NUM
ejpam-3763	528	3	.	.	PUNCT
ejpam-3763	529	1	let	let	VERB
ejpam-3763	529	2	g	g	PRON
ejpam-3763	529	3	be	be	AUX
ejpam-3763	529	4	a	a	DET
ejpam-3763	529	5	nontrivial	nontrivial	ADJ
ejpam-3763	529	6	connected	connect	VERB
ejpam-3763	529	7	graph	graph	NOUN
ejpam-3763	529	8	and	and	CCONJ
ejpam-3763	529	9	h	h	NOUN
ejpam-3763	529	10	any	any	DET
ejpam-3763	529	11	graph	graph	NOUN
ejpam-3763	529	12	of	of	ADP
ejpam-3763	529	13	order	order	NOUN
ejpam-3763	529	14	n.	n.	NOUN
ejpam-3763	529	15	then	then	ADV
ejpam-3763	529	16	γpr(g	γpr(g	PROPN
ejpam-3763	529	17	�	�	PROPN
ejpam-3763	529	18	h	h	NOUN
ejpam-3763	529	19	)	)	PUNCT
ejpam-3763	529	20	≤	≤	NOUN
ejpam-3763	529	21	α	α	NOUN
ejpam-3763	529	22	,	,	PUNCT
ejpam-3763	529	23	where	where	SCONJ
ejpam-3763	529	24	α	α	PROPN
ejpam-3763	529	25	=	=	NOUN
ejpam-3763	529	26	min	min	NOUN
ejpam-3763	529	27	g∈prd(g	g∈prd(g	PROPN
ejpam-3763	529	28	)	)	PUNCT
ejpam-3763	529	29	(	(	PUNCT
ejpam-3763	529	30	ωg(g	ωg(g	NOUN
ejpam-3763	529	31	)	)	PUNCT
ejpam-3763	530	1	+	+	CCONJ
ejpam-3763	530	2	|e11(g;g)|γpr(h	|e11(g;g)|γpr(h	NOUN
ejpam-3763	530	3	)	)	PUNCT
ejpam-3763	531	1	+	+	NUM
ejpam-3763	531	2	n	n	X
ejpam-3763	531	3	(	(	PUNCT
ejpam-3763	531	4	|e01(g;g)|+	|e01(g;g)|+	PROPN
ejpam-3763	531	5	|e22(g;g)|+	|e22(g;g)|+	PROPN
ejpam-3763	531	6	e00(g;g)|	e00(g;g)|	PROPN
ejpam-3763	531	7	)	)	PUNCT
ejpam-3763	531	8	)	)	PUNCT
ejpam-3763	531	9	,	,	PUNCT
ejpam-3763	531	10	and	and	CCONJ
ejpam-3763	531	11	this	this	DET
ejpam-3763	531	12	upper	upper	ADJ
ejpam-3763	531	13	bound	bind	VERB
ejpam-3763	531	14	is	be	AUX
ejpam-3763	531	15	sharp	sharp	ADJ
ejpam-3763	531	16	.	.	PUNCT
ejpam-3763	532	1	proof	proof	NOUN
ejpam-3763	532	2	:	:	PUNCT
ejpam-3763	532	3	let	let	VERB
ejpam-3763	532	4	g	g	PROPN
ejpam-3763	532	5	∈	∈	PROPN
ejpam-3763	532	6	prd(g	prd(g	PROPN
ejpam-3763	532	7	)	)	PUNCT
ejpam-3763	532	8	.	.	PUNCT
ejpam-3763	533	1	if	if	SCONJ
ejpam-3763	533	2	no	no	DET
ejpam-3763	533	3	confusion	confusion	NOUN
ejpam-3763	533	4	arises	arise	VERB
ejpam-3763	533	5	,	,	PUNCT
ejpam-3763	533	6	we	we	PRON
ejpam-3763	533	7	write	write	VERB
ejpam-3763	533	8	eab	eab	NOUN
ejpam-3763	533	9	=	=	SYM
ejpam-3763	533	10	eab(g;g	eab(g;g	NUM
ejpam-3763	533	11	)	)	PUNCT
ejpam-3763	533	12	.	.	PUNCT
ejpam-3763	534	1	let	let	VERB
ejpam-3763	534	2	h	h	NOUN
ejpam-3763	534	3	∈	∈	PROPN
ejpam-3763	534	4	prd(h	prd(h	PROPN
ejpam-3763	534	5	)	)	PUNCT
ejpam-3763	534	6	.	.	PUNCT
ejpam-3763	535	1	for	for	ADP
ejpam-3763	535	2	each	each	DET
ejpam-3763	535	3	ab	ab	PROPN
ejpam-3763	535	4	∈	∈	PROPN
ejpam-3763	535	5	e(g	e(g	PROPN
ejpam-3763	535	6	)	)	PUNCT
ejpam-3763	535	7	,	,	PUNCT
ejpam-3763	535	8	we	we	PRON
ejpam-3763	535	9	define	define	VERB
ejpam-3763	535	10	a	a	DET
ejpam-3763	535	11	copy	copy	NOUN
ejpam-3763	535	12	hab	hab	NOUN
ejpam-3763	535	13	of	of	ADP
ejpam-3763	535	14	h	h	NOUN
ejpam-3763	535	15	on	on	ADP
ejpam-3763	535	16	hab	hab	PROPN
ejpam-3763	535	17	.	.	PUNCT
ejpam-3763	536	1	define	define	VERB
ejpam-3763	536	2	the	the	DET
ejpam-3763	536	3	function	function	NOUN
ejpam-3763	536	4	f	f	PROPN
ejpam-3763	536	5	=	=	SYM
ejpam-3763	536	6	(	(	PUNCT
ejpam-3763	536	7	v0	v0	PROPN
ejpam-3763	536	8	,	,	PUNCT
ejpam-3763	536	9	v1	v1	NOUN
ejpam-3763	536	10	,	,	PUNCT
ejpam-3763	536	11	v2	v2	PROPN
ejpam-3763	536	12	)	)	PUNCT
ejpam-3763	536	13	on	on	ADP
ejpam-3763	536	14	g	g	PROPN
ejpam-3763	536	15	�	�	PROPN
ejpam-3763	536	16	h	h	NOUN
ejpam-3763	536	17	by	by	ADP
ejpam-3763	536	18	f(x	f(x	PROPN
ejpam-3763	536	19	)	)	PUNCT
ejpam-3763	537	1	=	=	PUNCT
ejpam-3763	537	2			PROPN
ejpam-3763	537	3	g(x	g(x	NOUN
ejpam-3763	537	4	)	)	PUNCT
ejpam-3763	537	5	,	,	PUNCT
ejpam-3763	537	6	if	if	SCONJ
ejpam-3763	537	7	x	x	SYM
ejpam-3763	537	8	∈	∈	PROPN
ejpam-3763	537	9	v	v	X
ejpam-3763	537	10	(	(	PUNCT
ejpam-3763	537	11	g	g	NOUN
ejpam-3763	537	12	)	)	PUNCT
ejpam-3763	537	13	;	;	PUNCT
ejpam-3763	537	14	huv(x	huv(x	PROPN
ejpam-3763	537	15	)	)	PUNCT
ejpam-3763	537	16	,	,	PUNCT
ejpam-3763	537	17	if	if	SCONJ
ejpam-3763	537	18	x	x	SYM
ejpam-3763	537	19	∈	∈	PROPN
ejpam-3763	537	20	v	v	NOUN
ejpam-3763	537	21	(	(	PUNCT
ejpam-3763	537	22	huv	huv	PROPN
ejpam-3763	537	23	)	)	PUNCT
ejpam-3763	537	24	,	,	PUNCT
ejpam-3763	537	25	where	where	SCONJ
ejpam-3763	537	26	uv	uv	NOUN
ejpam-3763	537	27	∈	∈	NOUN
ejpam-3763	537	28	e11	e11	X
ejpam-3763	537	29	;	;	PUNCT
ejpam-3763	537	30	0	0	NUM
ejpam-3763	537	31	,	,	PUNCT
ejpam-3763	537	32	if	if	SCONJ
ejpam-3763	537	33	x	x	PROPN
ejpam-3763	537	34	∈	∈	PROPN
ejpam-3763	537	35	v	v	NOUN
ejpam-3763	537	36	(	(	PUNCT
ejpam-3763	537	37	huv	huv	PROPN
ejpam-3763	537	38	)	)	PUNCT
ejpam-3763	537	39	,	,	PUNCT
ejpam-3763	537	40	where	where	SCONJ
ejpam-3763	537	41	uv	uv	NOUN
ejpam-3763	537	42	∈	∈	PROPN
ejpam-3763	537	43	e02	e02	NOUN
ejpam-3763	537	44	∪	∪	NOUN
ejpam-3763	537	45	e12	e12	NOUN
ejpam-3763	537	46	;	;	PUNCT
ejpam-3763	537	47	1	1	NUM
ejpam-3763	537	48	,	,	PUNCT
ejpam-3763	537	49	if	if	SCONJ
ejpam-3763	537	50	x	x	PROPN
ejpam-3763	537	51	∈	∈	PROPN
ejpam-3763	537	52	v	v	NOUN
ejpam-3763	537	53	(	(	PUNCT
ejpam-3763	537	54	huv),where	huv),where	INTJ
ejpam-3763	537	55	uv	uv	PROPN
ejpam-3763	537	56	∈	∈	PROPN
ejpam-3763	537	57	e01	e01	NOUN
ejpam-3763	537	58	∪	∪	X
ejpam-3763	537	59	e00	e00	PROPN
ejpam-3763	537	60	∪	∪	X
ejpam-3763	537	61	e22	e22	PROPN
ejpam-3763	537	62	.	.	PUNCT
ejpam-3763	538	1	l.	l.	PROPN
ejpam-3763	538	2	paleta	paleta	PROPN
ejpam-3763	538	3	,	,	PUNCT
ejpam-3763	538	4	f.	f.	PROPN
ejpam-3763	538	5	jamil	jamil	PROPN
ejpam-3763	538	6	/	/	SYM
ejpam-3763	538	7	eur	eur	PROPN
ejpam-3763	538	8	.	.	PUNCT
ejpam-3763	539	1	j.	j.	PROPN
ejpam-3763	539	2	pure	pure	PROPN
ejpam-3763	539	3	appl	appl	PROPN
ejpam-3763	539	4	.	.	PROPN
ejpam-3763	539	5	math	math	PROPN
ejpam-3763	539	6	,	,	PUNCT
ejpam-3763	539	7	13	13	NUM
ejpam-3763	539	8	(	(	PUNCT
ejpam-3763	539	9	3	3	NUM
ejpam-3763	539	10	)	)	PUNCT
ejpam-3763	539	11	(	(	PUNCT
ejpam-3763	539	12	2020	2020	NUM
ejpam-3763	539	13	)	)	PUNCT
ejpam-3763	539	14	,	,	PUNCT
ejpam-3763	539	15	529	529	NUM
ejpam-3763	539	16	-	-	SYM
ejpam-3763	539	17	548	548	NUM
ejpam-3763	539	18	543	543	NUM
ejpam-3763	539	19	we	we	PRON
ejpam-3763	539	20	claim	claim	VERB
ejpam-3763	539	21	that	that	SCONJ
ejpam-3763	539	22	f	f	PROPN
ejpam-3763	539	23	∈	∈	PROPN
ejpam-3763	539	24	prd(g	prd(g	PROPN
ejpam-3763	539	25	�	�	PROPN
ejpam-3763	539	26	h	h	NOUN
ejpam-3763	539	27	)	)	PUNCT
ejpam-3763	539	28	.	.	PUNCT
ejpam-3763	540	1	first	first	ADV
ejpam-3763	540	2	,	,	PUNCT
ejpam-3763	540	3	note	note	VERB
ejpam-3763	540	4	that	that	SCONJ
ejpam-3763	540	5	f	f	PROPN
ejpam-3763	540	6	|g	|g	VERB
ejpam-3763	540	7	=	=	SYM
ejpam-3763	540	8	g	g	PROPN
ejpam-3763	540	9	=	=	SYM
ejpam-3763	540	10	(	(	PUNCT
ejpam-3763	540	11	v0	v0	NOUN
ejpam-3763	540	12	∩	∩	NOUN
ejpam-3763	540	13	v	v	X
ejpam-3763	540	14	(	(	PUNCT
ejpam-3763	540	15	g	g	NOUN
ejpam-3763	540	16	)	)	PUNCT
ejpam-3763	540	17	,	,	PUNCT
ejpam-3763	540	18	v1	v1	NOUN
ejpam-3763	540	19	∩	∩	ADJ
ejpam-3763	540	20	v	v	NOUN
ejpam-3763	540	21	(	(	PUNCT
ejpam-3763	540	22	g	g	NOUN
ejpam-3763	540	23	)	)	PUNCT
ejpam-3763	540	24	,	,	PUNCT
ejpam-3763	540	25	v2	v2	PROPN
ejpam-3763	540	26	∩	∩	ADJ
ejpam-3763	540	27	v	v	NOUN
ejpam-3763	540	28	(	(	PUNCT
ejpam-3763	540	29	g	g	NOUN
ejpam-3763	540	30	)	)	PUNCT
ejpam-3763	540	31	)	)	PUNCT
ejpam-3763	540	32	.	.	PUNCT
ejpam-3763	541	1	let	let	VERB
ejpam-3763	541	2	x	x	SYM
ejpam-3763	541	3	∈	∈	PROPN
ejpam-3763	541	4	v0	v0	NOUN
ejpam-3763	541	5	.	.	PUNCT
ejpam-3763	541	6	suppose	suppose	VERB
ejpam-3763	541	7	that	that	SCONJ
ejpam-3763	541	8	x	x	SYM
ejpam-3763	541	9	∈	∈	NOUN
ejpam-3763	541	10	v	v	X
ejpam-3763	541	11	(	(	PUNCT
ejpam-3763	541	12	g	g	NOUN
ejpam-3763	541	13	)	)	PUNCT
ejpam-3763	541	14	.	.	PUNCT
ejpam-3763	542	1	thenng	thenng	PROPN
ejpam-3763	542	2	�	�	PROPN
ejpam-3763	542	3	h(x	h(x	PROPN
ejpam-3763	542	4	)	)	PUNCT
ejpam-3763	542	5	=	=	SYM
ejpam-3763	542	6	ng(x)∪	ng(x)∪	NOUN
ejpam-3763	542	7	(	(	PUNCT
ejpam-3763	542	8	∪u∈ng(x)v	∪u∈ng(x)v	PROPN
ejpam-3763	542	9	(	(	PUNCT
ejpam-3763	542	10	hux	hux	PROPN
ejpam-3763	542	11	)	)	PUNCT
ejpam-3763	542	12	)	)	PUNCT
ejpam-3763	542	13	.	.	PUNCT
ejpam-3763	543	1	since	since	SCONJ
ejpam-3763	543	2	g	g	PROPN
ejpam-3763	543	3	∈	∈	PROPN
ejpam-3763	543	4	prd(g	prd(g	PROPN
ejpam-3763	543	5	)	)	PUNCT
ejpam-3763	543	6	,	,	PUNCT
ejpam-3763	543	7	|v2	|v2	NOUN
ejpam-3763	543	8	∩	∩	ADJ
ejpam-3763	543	9	ng(x)|	ng(x)|	NOUN
ejpam-3763	543	10	=	=	SYM
ejpam-3763	543	11	1	1	NUM
ejpam-3763	543	12	,	,	PUNCT
ejpam-3763	543	13	say	say	VERB
ejpam-3763	543	14	v2	v2	NOUN
ejpam-3763	543	15	∩	∩	NOUN
ejpam-3763	543	16	ng(x	ng(x	NUM
ejpam-3763	543	17	)	)	PUNCT
ejpam-3763	543	18	=	=	PRON
ejpam-3763	543	19	{	{	PUNCT
ejpam-3763	543	20	z	z	NOUN
ejpam-3763	543	21	}	}	PUNCT
ejpam-3763	543	22	.	.	PUNCT
ejpam-3763	544	1	let	let	VERB
ejpam-3763	544	2	u	u	PRON
ejpam-3763	544	3	∈	∈	PROPN
ejpam-3763	544	4	ng(x	ng(x	NUM
ejpam-3763	544	5	)	)	PUNCT
ejpam-3763	544	6	,	,	PUNCT
ejpam-3763	544	7	and	and	CCONJ
ejpam-3763	544	8	let	let	VERB
ejpam-3763	544	9	y	y	PROPN
ejpam-3763	544	10	∈	∈	PROPN
ejpam-3763	544	11	v	v	PROPN
ejpam-3763	544	12	(	(	PUNCT
ejpam-3763	544	13	hxu	hxu	NOUN
ejpam-3763	544	14	)	)	PUNCT
ejpam-3763	544	15	.	.	PUNCT
ejpam-3763	545	1	if	if	SCONJ
ejpam-3763	545	2	u	u	PROPN
ejpam-3763	545	3	∈	∈	PROPN
ejpam-3763	545	4	v0	v0	NOUN
ejpam-3763	545	5	∪	∪	X
ejpam-3763	545	6	v1	v1	PROPN
ejpam-3763	545	7	,	,	PUNCT
ejpam-3763	545	8	then	then	ADV
ejpam-3763	545	9	y	y	PROPN
ejpam-3763	545	10	∈	∈	PROPN
ejpam-3763	545	11	v1	v1	NOUN
ejpam-3763	545	12	.	.	PUNCT
ejpam-3763	546	1	on	on	ADP
ejpam-3763	546	2	the	the	DET
ejpam-3763	546	3	other	other	ADJ
ejpam-3763	546	4	hand	hand	NOUN
ejpam-3763	546	5	,	,	PUNCT
ejpam-3763	546	6	if	if	SCONJ
ejpam-3763	546	7	u	u	PROPN
ejpam-3763	546	8	∈	∈	PROPN
ejpam-3763	546	9	v2	v2	PROPN
ejpam-3763	546	10	,	,	PUNCT
ejpam-3763	546	11	then	then	ADV
ejpam-3763	546	12	y	y	PROPN
ejpam-3763	546	13	∈	∈	PROPN
ejpam-3763	546	14	v0	v0	NOUN
ejpam-3763	546	15	.	.	PUNCT
ejpam-3763	547	1	thus	thus	ADV
ejpam-3763	547	2	,	,	PUNCT
ejpam-3763	547	3	v2	v2	PROPN
ejpam-3763	547	4	∩	∩	ADJ
ejpam-3763	547	5	v	v	NOUN
ejpam-3763	547	6	(	(	PUNCT
ejpam-3763	547	7	hux	hux	PROPN
ejpam-3763	547	8	)	)	PUNCT
ejpam-3763	548	1	=	=	PUNCT
ejpam-3763	548	2	∅.	∅.	NOUN
ejpam-3763	548	3	since	since	SCONJ
ejpam-3763	548	4	u	u	NOUN
ejpam-3763	548	5	is	be	AUX
ejpam-3763	548	6	arbitrary	arbitrary	ADJ
ejpam-3763	548	7	,	,	PUNCT
ejpam-3763	548	8	v2	v2	PROPN
ejpam-3763	548	9	∩	∩	NOUN
ejpam-3763	548	10	(	(	PUNCT
ejpam-3763	548	11	∪u∈ng(x)v	∪u∈ng(x)v	PROPN
ejpam-3763	548	12	(	(	PUNCT
ejpam-3763	548	13	hux	hux	PROPN
ejpam-3763	548	14	)	)	PUNCT
ejpam-3763	548	15	)	)	PUNCT
ejpam-3763	549	1	=	=	NOUN
ejpam-3763	549	2	∅	∅	NOUN
ejpam-3763	550	1	and	and	CCONJ
ejpam-3763	550	2	so	so	ADV
ejpam-3763	550	3	v2	v2	PROPN
ejpam-3763	550	4	∩	∩	ADJ
ejpam-3763	550	5	ng	ng	PROPN
ejpam-3763	550	6	�	�	PROPN
ejpam-3763	550	7	h(x	h(x	PROPN
ejpam-3763	550	8	)	)	PUNCT
ejpam-3763	551	1	=	=	PRON
ejpam-3763	551	2	{	{	PUNCT
ejpam-3763	551	3	z	z	NOUN
ejpam-3763	551	4	}	}	PUNCT
ejpam-3763	551	5	.	.	PUNCT
ejpam-3763	552	1	suppose	suppose	VERB
ejpam-3763	552	2	that	that	SCONJ
ejpam-3763	552	3	x	x	SYM
ejpam-3763	552	4	∈	∈	NOUN
ejpam-3763	552	5	v	v	NOUN
ejpam-3763	552	6	(	(	PUNCT
ejpam-3763	552	7	huv	huv	PROPN
ejpam-3763	552	8	)	)	PUNCT
ejpam-3763	552	9	for	for	ADP
ejpam-3763	552	10	some	some	DET
ejpam-3763	552	11	uv	uv	PROPN
ejpam-3763	552	12	∈	∈	PROPN
ejpam-3763	552	13	e(g	e(g	PROPN
ejpam-3763	552	14	)	)	PUNCT
ejpam-3763	552	15	.	.	PUNCT
ejpam-3763	553	1	then	then	ADV
ejpam-3763	553	2	ng	ng	PROPN
ejpam-3763	553	3	�	�	PROPN
ejpam-3763	553	4	h(x	h(x	PROPN
ejpam-3763	553	5	)	)	PUNCT
ejpam-3763	554	1	=	=	PRON
ejpam-3763	554	2	{	{	PUNCT
ejpam-3763	554	3	u	u	NOUN
ejpam-3763	554	4	,	,	PUNCT
ejpam-3763	554	5	v	v	NOUN
ejpam-3763	554	6	}	}	PUNCT
ejpam-3763	554	7	∪	∪	VERB
ejpam-3763	554	8	nhuv(x	nhuv(x	NOUN
ejpam-3763	554	9	)	)	PUNCT
ejpam-3763	554	10	.	.	PUNCT
ejpam-3763	555	1	since	since	SCONJ
ejpam-3763	555	2	f(x	f(x	PROPN
ejpam-3763	555	3	)	)	PUNCT
ejpam-3763	555	4	=	=	SYM
ejpam-3763	556	1	0	0	NUM
ejpam-3763	556	2	,	,	PUNCT
ejpam-3763	556	3	uv	uv	NOUN
ejpam-3763	556	4	/∈	/∈	PUNCT
ejpam-3763	556	5	e00	e00	PROPN
ejpam-3763	556	6	∪	∪	ADP
ejpam-3763	556	7	e22	e22	NOUN
ejpam-3763	556	8	∪	∪	ADJ
ejpam-3763	556	9	e01	e01	NOUN
ejpam-3763	556	10	.	.	PUNCT
ejpam-3763	557	1	if	if	SCONJ
ejpam-3763	557	2	uv	uv	PROPN
ejpam-3763	557	3	∈	∈	PROPN
ejpam-3763	557	4	e11	e11	NOUN
ejpam-3763	557	5	,	,	PUNCT
ejpam-3763	557	6	then	then	ADV
ejpam-3763	557	7	huv(x	huv(x	NUM
ejpam-3763	557	8	)	)	PUNCT
ejpam-3763	557	9	=	=	SYM
ejpam-3763	557	10	0	0	PUNCT
ejpam-3763	557	11	and	and	CCONJ
ejpam-3763	557	12	there	there	PRON
ejpam-3763	557	13	exists	exist	VERB
ejpam-3763	557	14	exactly	exactly	ADV
ejpam-3763	557	15	one	one	NUM
ejpam-3763	557	16	y	y	PROPN
ejpam-3763	557	17	∈	∈	PROPN
ejpam-3763	557	18	v	v	PROPN
ejpam-3763	557	19	(	(	PUNCT
ejpam-3763	557	20	huv	huv	PROPN
ejpam-3763	557	21	)	)	PUNCT
ejpam-3763	557	22	such	such	ADJ
ejpam-3763	557	23	that	that	SCONJ
ejpam-3763	557	24	xy	xy	PROPN
ejpam-3763	557	25	∈	∈	PROPN
ejpam-3763	557	26	e(huv	e(huv	PROPN
ejpam-3763	557	27	)	)	PUNCT
ejpam-3763	557	28	and	and	CCONJ
ejpam-3763	557	29	f(y	f(y	NOUN
ejpam-3763	557	30	)	)	PUNCT
ejpam-3763	557	31	=	=	SYM
ejpam-3763	557	32	huv(y	huv(y	X
ejpam-3763	557	33	)	)	PUNCT
ejpam-3763	557	34	=	=	SYM
ejpam-3763	557	35	2	2	X
ejpam-3763	557	36	.	.	PUNCT
ejpam-3763	557	37	in	in	ADP
ejpam-3763	557	38	this	this	DET
ejpam-3763	557	39	case	case	NOUN
ejpam-3763	557	40	,	,	PUNCT
ejpam-3763	557	41	v2	v2	PROPN
ejpam-3763	557	42	∩	∩	PROPN
ejpam-3763	557	43	ng	ng	PROPN
ejpam-3763	557	44	�	�	PROPN
ejpam-3763	557	45	h(x	h(x	PROPN
ejpam-3763	557	46	)	)	PUNCT
ejpam-3763	557	47	=	=	SYM
ejpam-3763	557	48	v2	v2	PROPN
ejpam-3763	557	49	∩	∩	NOUN
ejpam-3763	557	50	nhuv(x	nhuv(x	NOUN
ejpam-3763	557	51	)	)	PUNCT
ejpam-3763	557	52	=	=	SYM
ejpam-3763	557	53	{	{	PUNCT
ejpam-3763	557	54	y	y	NOUN
ejpam-3763	557	55	}	}	PUNCT
ejpam-3763	557	56	.	.	PUNCT
ejpam-3763	558	1	suppose	suppose	VERB
ejpam-3763	558	2	that	that	SCONJ
ejpam-3763	558	3	uv	uv	PROPN
ejpam-3763	558	4	∈	∈	PROPN
ejpam-3763	558	5	e02	e02	NOUN
ejpam-3763	558	6	∪	∪	X
ejpam-3763	558	7	e12	e12	NOUN
ejpam-3763	558	8	.	.	PUNCT
ejpam-3763	559	1	since	since	SCONJ
ejpam-3763	559	2	v	v	X
ejpam-3763	559	3	(	(	PUNCT
ejpam-3763	559	4	huv	huv	PROPN
ejpam-3763	559	5	)	)	PUNCT
ejpam-3763	559	6	⊆	⊆	NUM
ejpam-3763	559	7	v0	v0	NOUN
ejpam-3763	559	8	,	,	PUNCT
ejpam-3763	559	9	either	either	CCONJ
ejpam-3763	559	10	v2	v2	PROPN
ejpam-3763	559	11	∩ng	∩ng	PROPN
ejpam-3763	559	12	�	�	PROPN
ejpam-3763	559	13	h(x	h(x	PROPN
ejpam-3763	559	14	)	)	PUNCT
ejpam-3763	559	15	=	=	PRON
ejpam-3763	559	16	{	{	PUNCT
ejpam-3763	559	17	u	u	NOUN
ejpam-3763	559	18	}	}	PUNCT
ejpam-3763	559	19	or	or	CCONJ
ejpam-3763	559	20	v2	v2	VERB
ejpam-3763	559	21	∩ng	∩ng	PROPN
ejpam-3763	559	22	�	�	PROPN
ejpam-3763	559	23	h(x	h(x	PROPN
ejpam-3763	559	24	)	)	PUNCT
ejpam-3763	559	25	=	=	PRON
ejpam-3763	559	26	{	{	PUNCT
ejpam-3763	559	27	v	v	NOUN
ejpam-3763	559	28	}	}	PUNCT
ejpam-3763	559	29	.	.	PUNCT
ejpam-3763	560	1	accordingly	accordingly	ADV
ejpam-3763	560	2	,	,	PUNCT
ejpam-3763	560	3	f	f	PROPN
ejpam-3763	560	4	∈	∈	PROPN
ejpam-3763	560	5	prd(g	prd(g	PROPN
ejpam-3763	560	6	�	�	PROPN
ejpam-3763	560	7	h	h	NOUN
ejpam-3763	560	8	)	)	PUNCT
ejpam-3763	560	9	.	.	PUNCT
ejpam-3763	561	1	therefore	therefore	ADV
ejpam-3763	561	2	,	,	PUNCT
ejpam-3763	561	3	γpr(g	γpr(g	PROPN
ejpam-3763	561	4	�	�	PROPN
ejpam-3763	561	5	h	h	NOUN
ejpam-3763	561	6	)	)	PUNCT
ejpam-3763	561	7	≤	≤	NOUN
ejpam-3763	561	8	ωg(g	ωg(g	NUM
ejpam-3763	561	9	)	)	PUNCT
ejpam-3763	562	1	+	+	CCONJ
ejpam-3763	562	2	|e11|ωh(h	|e11|ωh(h	NUM
ejpam-3763	562	3	)	)	PUNCT
ejpam-3763	563	1	+	+	CCONJ
ejpam-3763	563	2	∑	∑	PUNCT
ejpam-3763	563	3	x∈{v	x∈{v	PROPN
ejpam-3763	563	4	(	(	PUNCT
ejpam-3763	563	5	huv):uv∈e00∪e01∪e22	huv):uv∈e00∪e01∪e22	PROPN
ejpam-3763	563	6	}	}	PUNCT
ejpam-3763	563	7	f(x	f(x	PROPN
ejpam-3763	563	8	)	)	PUNCT
ejpam-3763	563	9	=	=	PUNCT
ejpam-3763	563	10	ωg(g	ωg(g	NUM
ejpam-3763	563	11	)	)	PUNCT
ejpam-3763	563	12	+	+	CCONJ
ejpam-3763	563	13	|e11|ωh(h	|e11|ωh(h	NUM
ejpam-3763	563	14	)	)	PUNCT
ejpam-3763	563	15	+	+	CCONJ
ejpam-3763	564	1	n	n	X
ejpam-3763	564	2	(	(	PUNCT
ejpam-3763	564	3	|e01|+	|e01|+	NUM
ejpam-3763	564	4	|e22|+	|e22|+	X
ejpam-3763	564	5	e00|	e00|	ADJ
ejpam-3763	564	6	)	)	PUNCT
ejpam-3763	564	7	.	.	PUNCT
ejpam-3763	565	1	since	since	SCONJ
ejpam-3763	565	2	h	h	NOUN
ejpam-3763	565	3	is	be	AUX
ejpam-3763	565	4	arbitrary	arbitrary	ADJ
ejpam-3763	565	5	,	,	PUNCT
ejpam-3763	565	6	the	the	DET
ejpam-3763	565	7	desired	desire	VERB
ejpam-3763	565	8	inequality	inequality	NOUN
ejpam-3763	565	9	holds	hold	VERB
ejpam-3763	565	10	.	.	PUNCT
ejpam-3763	566	1	consider	consider	VERB
ejpam-3763	566	2	the	the	DET
ejpam-3763	566	3	graph	graph	NOUN
ejpam-3763	566	4	g	g	PROPN
ejpam-3763	566	5	�	�	PROPN
ejpam-3763	566	6	p3	p3	PROPN
ejpam-3763	566	7	in	in	ADP
ejpam-3763	566	8	figure	figure	NOUN
ejpam-3763	566	9	2	2	NUM
ejpam-3763	566	10	,	,	PUNCT
ejpam-3763	566	11	where	where	SCONJ
ejpam-3763	566	12	g	g	PROPN
ejpam-3763	566	13	is	be	AUX
ejpam-3763	566	14	the	the	DET
ejpam-3763	566	15	caterpillar	caterpillar	ADJ
ejpam-3763	566	16	ca(2	ca(2	NOUN
ejpam-3763	566	17	,	,	PUNCT
ejpam-3763	566	18	0	0	NUM
ejpam-3763	566	19	,	,	PUNCT
ejpam-3763	566	20	2	2	NUM
ejpam-3763	566	21	)	)	PUNCT
ejpam-3763	566	22	with	with	ADP
ejpam-3763	566	23	the	the	DET
ejpam-3763	566	24	corresponding	corresponding	ADJ
ejpam-3763	566	25	vertex	vertex	NOUN
ejpam-3763	566	26	labelling	labelling	NOUN
ejpam-3763	566	27	.	.	PUNCT
ejpam-3763	567	1	the	the	DET
ejpam-3763	567	2	function	function	NOUN
ejpam-3763	567	3	g	g	NOUN
ejpam-3763	567	4	on	on	ADP
ejpam-3763	567	5	v	v	ADP
ejpam-3763	567	6	(	(	PUNCT
ejpam-3763	567	7	g	g	NOUN
ejpam-3763	567	8	)	)	PUNCT
ejpam-3763	567	9	given	give	VERB
ejpam-3763	567	10	by	by	ADP
ejpam-3763	567	11	g(x	g(x	NOUN
ejpam-3763	567	12	)	)	PUNCT
ejpam-3763	567	13	=	=	SYM
ejpam-3763	567	14	g(z	g(z	ADJ
ejpam-3763	567	15	)	)	PUNCT
ejpam-3763	567	16	=	=	SYM
ejpam-3763	567	17	2	2	NUM
ejpam-3763	567	18	,	,	PUNCT
ejpam-3763	567	19	g(y	g(y	NOUN
ejpam-3763	567	20	)	)	PUNCT
ejpam-3763	567	21	=	=	SYM
ejpam-3763	567	22	1	1	NUM
ejpam-3763	567	23	and	and	CCONJ
ejpam-3763	567	24	g(x	g(x	NOUN
ejpam-3763	567	25	)	)	PUNCT
ejpam-3763	568	1	=	=	SYM
ejpam-3763	568	2	0	0	PUNCT
ejpam-3763	568	3	else	else	ADV
ejpam-3763	568	4	is	be	AUX
ejpam-3763	568	5	in	in	ADP
ejpam-3763	568	6	prd(g	prd(g	NUM
ejpam-3763	568	7	)	)	PUNCT
ejpam-3763	568	8	.	.	PUNCT
ejpam-3763	569	1	since	since	SCONJ
ejpam-3763	569	2	e00	e00	NOUN
ejpam-3763	569	3	=	=	SYM
ejpam-3763	569	4	e01	e01	X
ejpam-3763	569	5	=	=	SYM
ejpam-3763	569	6	e22	e22	X
ejpam-3763	569	7	=	=	SYM
ejpam-3763	569	8	e00	e00	NOUN
ejpam-3763	569	9	=	=	NOUN
ejpam-3763	569	10	∅	∅	NOUN
ejpam-3763	569	11	,	,	PUNCT
ejpam-3763	569	12	α	α	NOUN
ejpam-3763	569	13	≤	≤	NOUN
ejpam-3763	569	14	ωg(g	ωg(g	X
ejpam-3763	569	15	)	)	PUNCT
ejpam-3763	569	16	=	=	SYM
ejpam-3763	569	17	5	5	NUM
ejpam-3763	570	1	so	so	SCONJ
ejpam-3763	570	2	that	that	SCONJ
ejpam-3763	570	3	γpr(g	γpr(g	PROPN
ejpam-3763	570	4	�	�	PROPN
ejpam-3763	570	5	p3	p3	PROPN
ejpam-3763	570	6	)	)	PUNCT
ejpam-3763	570	7	≤	≤	NUM
ejpam-3763	570	8	5	5	NUM
ejpam-3763	570	9	.	.	PUNCT
ejpam-3763	571	1	now	now	ADV
ejpam-3763	571	2	,	,	PUNCT
ejpam-3763	571	3	note	note	VERB
ejpam-3763	571	4	that	that	SCONJ
ejpam-3763	571	5	{	{	PUNCT
ejpam-3763	571	6	x	x	X
ejpam-3763	571	7	,	,	PUNCT
ejpam-3763	571	8	z	z	NOUN
ejpam-3763	571	9	}	}	PUNCT
ejpam-3763	571	10	is	be	AUX
ejpam-3763	571	11	the	the	DET
ejpam-3763	571	12	unique	unique	ADJ
ejpam-3763	571	13	γ	γ	NOUN
ejpam-3763	571	14	-	-	NOUN
ejpam-3763	571	15	set	set	NOUN
ejpam-3763	571	16	of	of	ADP
ejpam-3763	571	17	g	g	PROPN
ejpam-3763	571	18	�	�	PROPN
ejpam-3763	571	19	p3	p3	PROPN
ejpam-3763	571	20	.	.	PUNCT
ejpam-3763	572	1	however	however	ADV
ejpam-3763	572	2	,	,	PUNCT
ejpam-3763	572	3	{	{	PUNCT
ejpam-3763	572	4	x	x	NOUN
ejpam-3763	572	5	,	,	PUNCT
ejpam-3763	572	6	z	z	NOUN
ejpam-3763	572	7	}	}	PUNCT
ejpam-3763	572	8	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	572	9	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	572	10	....................................	....................................	PUNCT
ejpam-3763	572	11	.........	.........	PUNCT
ejpam-3763	572	12	........	........	PUNCT
ejpam-3763	572	13	........	........	PUNCT
ejpam-3763	572	14	........	........	PUNCT
ejpam-3763	572	15	........	........	PUNCT
ejpam-3763	572	16	........	........	PUNCT
ejpam-3763	572	17	........	........	PUNCT
ejpam-3763	572	18	........	........	PUNCT
ejpam-3763	572	19	........	........	PUNCT
ejpam-3763	572	20	........	........	PUNCT
ejpam-3763	572	21	........	........	PUNCT
ejpam-3763	573	1	........	........	PUNCT
ejpam-3763	573	2	..	..	PUNCT
ejpam-3763	573	3	.	.	PUNCT
ejpam-3763	574	1	...................................	...................................	PUNCT
ejpam-3763	574	2	.........	.........	PUNCT
ejpam-3763	575	1	........	........	PUNCT
ejpam-3763	575	2	........	........	PUNCT
ejpam-3763	575	3	........	........	PUNCT
ejpam-3763	575	4	........	........	PUNCT
ejpam-3763	575	5	........	........	PUNCT
ejpam-3763	575	6	........	........	PUNCT
ejpam-3763	575	7	........	........	PUNCT
ejpam-3763	575	8	........	........	PUNCT
ejpam-3763	575	9	........	........	PUNCT
ejpam-3763	575	10	........	........	PUNCT
ejpam-3763	576	1	........	........	PUNCT
ejpam-3763	576	2	..	..	PUNCT
ejpam-3763	576	3	.	.	PUNCT
ejpam-3763	577	1	...................................	...................................	PUNCT
ejpam-3763	577	2	....................................	....................................	PUNCT
ejpam-3763	578	1	.........	.........	PUNCT
ejpam-3763	578	2	........	........	PUNCT
ejpam-3763	578	3	........	........	PUNCT
ejpam-3763	578	4	........	........	PUNCT
ejpam-3763	578	5	........	........	PUNCT
ejpam-3763	578	6	........	........	PUNCT
ejpam-3763	578	7	........	........	PUNCT
ejpam-3763	578	8	........	........	PUNCT
ejpam-3763	578	9	........	........	PUNCT
ejpam-3763	578	10	........	........	PUNCT
ejpam-3763	578	11	........	........	PUNCT
ejpam-3763	579	1	........	........	PUNCT
ejpam-3763	579	2	..	..	PUNCT
ejpam-3763	579	3	.	.	PUNCT
ejpam-3763	580	1	...................................	...................................	PUNCT
ejpam-3763	580	2	.........	.........	PUNCT
ejpam-3763	581	1	........	........	PUNCT
ejpam-3763	581	2	........	........	PUNCT
ejpam-3763	581	3	........	........	PUNCT
ejpam-3763	581	4	........	........	PUNCT
ejpam-3763	581	5	........	........	PUNCT
ejpam-3763	581	6	........	........	PUNCT
ejpam-3763	581	7	........	........	PUNCT
ejpam-3763	581	8	........	........	PUNCT
ejpam-3763	581	9	........	........	PUNCT
ejpam-3763	581	10	........	........	PUNCT
ejpam-3763	582	1	........	........	PUNCT
ejpam-3763	582	2	..	..	PUNCT
ejpam-3763	582	3	.	.	PUNCT
ejpam-3763	583	1	...................................	...................................	PUNCT
ejpam-3763	583	2	....................................	....................................	PUNCT
ejpam-3763	584	1	g	g	NOUN
ejpam-3763	584	2	x	x	PUNCT
ejpam-3763	584	3	y	y	PROPN
ejpam-3763	584	4	z	z	PROPN
ejpam-3763	584	5	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	584	6	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	584	7	....................................	....................................	PUNCT
ejpam-3763	584	8	.........	.........	PUNCT
ejpam-3763	584	9	........	........	PUNCT
ejpam-3763	584	10	........	........	PUNCT
ejpam-3763	584	11	........	........	PUNCT
ejpam-3763	584	12	........	........	PUNCT
ejpam-3763	584	13	........	........	PUNCT
ejpam-3763	584	14	........	........	PUNCT
ejpam-3763	584	15	........	........	PUNCT
ejpam-3763	584	16	........	........	PUNCT
ejpam-3763	584	17	........	........	PUNCT
ejpam-3763	584	18	........	........	PUNCT
ejpam-3763	584	19	........	........	PUNCT
ejpam-3763	584	20	..	..	PUNCT
ejpam-3763	584	21	.	.	PUNCT
ejpam-3763	584	22	...................................	...................................	PUNCT
ejpam-3763	584	23	.........	.........	PUNCT
ejpam-3763	584	24	........	........	PUNCT
ejpam-3763	584	25	........	........	PUNCT
ejpam-3763	584	26	........	........	PUNCT
ejpam-3763	584	27	........	........	PUNCT
ejpam-3763	584	28	........	........	PUNCT
ejpam-3763	584	29	........	........	PUNCT
ejpam-3763	584	30	........	........	PUNCT
ejpam-3763	584	31	........	........	PUNCT
ejpam-3763	584	32	........	........	PUNCT
ejpam-3763	584	33	........	........	PUNCT
ejpam-3763	584	34	........	........	PUNCT
ejpam-3763	584	35	..	..	PUNCT
ejpam-3763	584	36	.	.	PUNCT
ejpam-3763	584	37	...................................	...................................	PUNCT
ejpam-3763	585	1	....................................	....................................	PUNCT
ejpam-3763	585	2	.........	.........	PUNCT
ejpam-3763	586	1	........	........	PUNCT
ejpam-3763	586	2	........	........	PUNCT
ejpam-3763	586	3	........	........	PUNCT
ejpam-3763	586	4	........	........	PUNCT
ejpam-3763	586	5	........	........	PUNCT
ejpam-3763	586	6	........	........	PUNCT
ejpam-3763	586	7	........	........	PUNCT
ejpam-3763	586	8	........	........	PUNCT
ejpam-3763	586	9	........	........	PUNCT
ejpam-3763	586	10	........	........	PUNCT
ejpam-3763	586	11	........	........	PUNCT
ejpam-3763	586	12	..	..	PUNCT
ejpam-3763	586	13	.	.	PUNCT
ejpam-3763	587	1	...................................	...................................	PUNCT
ejpam-3763	587	2	.........	.........	PUNCT
ejpam-3763	588	1	........	........	PUNCT
ejpam-3763	588	2	........	........	PUNCT
ejpam-3763	588	3	........	........	PUNCT
ejpam-3763	588	4	........	........	PUNCT
ejpam-3763	588	5	........	........	PUNCT
ejpam-3763	588	6	........	........	PUNCT
ejpam-3763	588	7	........	........	PUNCT
ejpam-3763	588	8	........	........	PUNCT
ejpam-3763	588	9	........	........	PUNCT
ejpam-3763	588	10	........	........	PUNCT
ejpam-3763	589	1	........	........	PUNCT
ejpam-3763	589	2	..	..	PUNCT
ejpam-3763	589	3	.	.	PUNCT
ejpam-3763	590	1	...................................	...................................	PUNCT
ejpam-3763	590	2	....................................	....................................	PUNCT
ejpam-3763	591	1	.........	.........	PUNCT
ejpam-3763	591	2	........	........	PUNCT
ejpam-3763	592	1	....................................	....................................	PUNCT
ejpam-3763	592	2	.........	.........	PUNCT
ejpam-3763	593	1	........	........	PUNCT
ejpam-3763	593	2	....................................	....................................	PUNCT
ejpam-3763	594	1	....................................	....................................	PUNCT
ejpam-3763	594	2	.........	.........	PUNCT
ejpam-3763	595	1	........	........	PUNCT
ejpam-3763	595	2	....................................	....................................	PUNCT
ejpam-3763	595	3	.........	.........	PUNCT
ejpam-3763	596	1	........	........	PUNCT
ejpam-3763	596	2	....................................	....................................	PUNCT
ejpam-3763	597	1	....................................	....................................	PUNCT
ejpam-3763	597	2	.........	.........	PUNCT
ejpam-3763	598	1	........	........	PUNCT
ejpam-3763	598	2	....................................	....................................	PUNCT
ejpam-3763	598	3	.........	.........	PUNCT
ejpam-3763	599	1	........	........	PUNCT
ejpam-3763	599	2	....................................	....................................	PUNCT
ejpam-3763	600	1	....................................	....................................	PUNCT
ejpam-3763	600	2	.........	.........	PUNCT
ejpam-3763	601	1	........	........	PUNCT
ejpam-3763	601	2	....................................	....................................	PUNCT
ejpam-3763	601	3	.........	.........	PUNCT
ejpam-3763	602	1	........	........	PUNCT
ejpam-3763	602	2	....................................	....................................	PUNCT
ejpam-3763	602	3	....................................	....................................	PUNCT
ejpam-3763	602	4	.....................................................	.....................................................	PUNCT
ejpam-3763	602	5	.....................................................	.....................................................	PUNCT
ejpam-3763	603	1	....................................	....................................	PUNCT
ejpam-3763	603	2	.................	.................	PUNCT
ejpam-3763	604	1	.....................................................	.....................................................	PUNCT
ejpam-3763	604	2	........................................................................	........................................................................	PUNCT
ejpam-3763	605	1	g	g	PROPN
ejpam-3763	605	2	�	�	PROPN
ejpam-3763	605	3	p3	p3	PROPN
ejpam-3763	605	4	x	x	PROPN
ejpam-3763	605	5	y	y	PROPN
ejpam-3763	605	6	z	z	PROPN
ejpam-3763	605	7	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-3763	605	8	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3763	605	9	......................................................................................................	......................................................................................................	PUNCT
ejpam-3763	605	10	.................................	.................................	PUNCT
ejpam-3763	605	11	................................	................................	PUNCT
ejpam-3763	605	12	................................	................................	PUNCT
ejpam-3763	605	13	.....	.....	PUNCT
ejpam-3763	605	14	...................	...................	PUNCT
ejpam-3763	605	15	..................	..................	PUNCT
ejpam-3763	605	16	..................	..................	PUNCT
ejpam-3763	605	17	..................	..................	PUNCT
ejpam-3763	605	18	..................	..................	PUNCT
ejpam-3763	605	19	..................	..................	PUNCT
ejpam-3763	605	20	..	..	PUNCT
ejpam-3763	605	21	..............	..............	PUNCT
ejpam-3763	605	22	.............	.............	PUNCT
ejpam-3763	605	23	.............	.............	PUNCT
ejpam-3763	605	24	.............	.............	PUNCT
ejpam-3763	605	25	.............	.............	PUNCT
ejpam-3763	605	26	.............	.............	PUNCT
ejpam-3763	605	27	.............	.............	PUNCT
ejpam-3763	605	28	.............	.............	PUNCT
ejpam-3763	605	29	.............	.............	PUNCT
ejpam-3763	605	30	........	........	PUNCT
ejpam-3763	605	31	...............	...............	PUNCT
ejpam-3763	605	32	..............	..............	PUNCT
ejpam-3763	605	33	..............	..............	PUNCT
ejpam-3763	605	34	..............	..............	PUNCT
ejpam-3763	605	35	..............	..............	PUNCT
ejpam-3763	605	36	..............	..............	PUNCT
ejpam-3763	605	37	..............	..............	PUNCT
ejpam-3763	605	38	..............	..............	PUNCT
ejpam-3763	605	39	..............	..............	PUNCT
ejpam-3763	605	40	........	........	PUNCT
ejpam-3763	605	41	....................	....................	PUNCT
ejpam-3763	605	42	...................	...................	PUNCT
ejpam-3763	605	43	...................	...................	PUNCT
ejpam-3763	605	44	...................	...................	PUNCT
ejpam-3763	605	45	...................	...................	PUNCT
ejpam-3763	605	46	...................	...................	PUNCT
ejpam-3763	605	47	......	......	PUNCT
ejpam-3763	605	48	....................................	....................................	PUNCT
ejpam-3763	605	49	...................................	...................................	PUNCT
ejpam-3763	605	50	...................................	...................................	PUNCT
ejpam-3763	605	51	.......	.......	PUNCT
ejpam-3763	605	52	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-3763	606	1	.........................................................................................................................	.........................................................................................................................	PUNCT
ejpam-3763	606	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	607	1	..............	..............	PUNCT
ejpam-3763	607	2	.............	.............	PUNCT
ejpam-3763	607	3	.............	.............	PUNCT
ejpam-3763	607	4	.............	.............	PUNCT
ejpam-3763	607	5	.............	.............	PUNCT
ejpam-3763	607	6	.............	.............	PUNCT
ejpam-3763	607	7	.............	.............	PUNCT
ejpam-3763	607	8	.............	.............	PUNCT
ejpam-3763	607	9	.............	.............	PUNCT
ejpam-3763	607	10	........	........	PUNCT
ejpam-3763	608	1	...................	...................	PUNCT
ejpam-3763	608	2	..................	..................	PUNCT
ejpam-3763	609	1	..................	..................	PUNCT
ejpam-3763	609	2	..................	..................	PUNCT
ejpam-3763	610	1	..................	..................	PUNCT
ejpam-3763	610	2	..................	..................	PUNCT
ejpam-3763	610	3	..	..	PUNCT
ejpam-3763	610	4	.................................	.................................	PUNCT
ejpam-3763	611	1	................................	................................	PUNCT
ejpam-3763	611	2	................................	................................	PUNCT
ejpam-3763	612	1	.....	.....	PUNCT
ejpam-3763	612	2	......................................................................................................	......................................................................................................	PUNCT
ejpam-3763	612	3	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3763	613	1	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-3763	613	2	..............................................................................................................................	..............................................................................................................................	PROPN
ejpam-3763	614	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3763	614	2	......................................................................................................	......................................................................................................	PUNCT
ejpam-3763	614	3	.................................	.................................	PUNCT
ejpam-3763	615	1	................................	................................	PUNCT
ejpam-3763	615	2	................................	................................	PUNCT
ejpam-3763	616	1	.....	.....	PUNCT
ejpam-3763	616	2	...................	...................	PUNCT
ejpam-3763	617	1	..................	..................	PUNCT
ejpam-3763	617	2	..................	..................	PUNCT
ejpam-3763	618	1	..................	..................	PUNCT
ejpam-3763	618	2	..................	..................	PUNCT
ejpam-3763	619	1	..................	..................	PUNCT
ejpam-3763	619	2	..	..	PUNCT
ejpam-3763	619	3	..............	..............	PUNCT
ejpam-3763	619	4	.............	.............	PUNCT
ejpam-3763	619	5	.............	.............	PUNCT
ejpam-3763	619	6	.............	.............	PUNCT
ejpam-3763	619	7	.............	.............	PUNCT
ejpam-3763	619	8	.............	.............	PUNCT
ejpam-3763	619	9	.............	.............	PUNCT
ejpam-3763	619	10	.............	.............	PUNCT
ejpam-3763	619	11	.............	.............	PUNCT
ejpam-3763	619	12	........	........	PUNCT
ejpam-3763	619	13	........................................................................................	........................................................................................	PUNCT
ejpam-3763	619	14	...................................................................	...................................................................	PUNCT
ejpam-3763	619	15	.............................................................	.............................................................	PUNCT
ejpam-3763	620	1	.........	.........	PUNCT
ejpam-3763	620	2	.........	.........	PUNCT
ejpam-3763	621	1	.........	.........	PUNCT
ejpam-3763	621	2	.........	.........	PUNCT
ejpam-3763	622	1	.....	.....	PUNCT
ejpam-3763	622	2	............	............	PUNCT
ejpam-3763	622	3	...........	...........	PUNCT
ejpam-3763	622	4	...........	...........	PUNCT
ejpam-3763	622	5	...........	...........	PUNCT
ejpam-3763	622	6	...........	...........	PUNCT
ejpam-3763	622	7	...........	...........	PUNCT
ejpam-3763	622	8	...............	...............	PUNCT
ejpam-3763	622	9	..............	..............	PUNCT
ejpam-3763	622	10	..............	..............	PUNCT
ejpam-3763	622	11	..............	..............	PUNCT
ejpam-3763	622	12	..............	..............	PUNCT
ejpam-3763	622	13	..............	..............	PUNCT
ejpam-3763	622	14	...	...	PUNCT
ejpam-3763	623	1	..........	..........	PUNCT
ejpam-3763	623	2	.........	.........	PUNCT
ejpam-3763	624	1	.........	.........	PUNCT
ejpam-3763	624	2	.........	.........	PUNCT
ejpam-3763	625	1	.........	.........	PUNCT
ejpam-3763	625	2	.....	.....	PUNCT
ejpam-3763	625	3	............	............	PUNCT
ejpam-3763	625	4	...........	...........	PUNCT
ejpam-3763	625	5	...........	...........	PUNCT
ejpam-3763	625	6	...........	...........	PUNCT
ejpam-3763	625	7	...........	...........	PUNCT
ejpam-3763	625	8	...........	...........	PUNCT
ejpam-3763	625	9	...............	...............	PUNCT
ejpam-3763	625	10	..............	..............	PUNCT
ejpam-3763	625	11	..............	..............	PUNCT
ejpam-3763	625	12	..............	..............	PUNCT
ejpam-3763	626	1	..............	..............	PUNCT
ejpam-3763	626	2	..............	..............	PUNCT
ejpam-3763	626	3	...........................................................................................	...........................................................................................	PUNCT
ejpam-3763	627	1	...................................................................	...................................................................	PUNCT
ejpam-3763	627	2	...................................................	...................................................	PUNCT
ejpam-3763	628	1	..........	..........	PUNCT
ejpam-3763	628	2	.........	.........	PUNCT
ejpam-3763	629	1	.........	.........	PUNCT
ejpam-3763	629	2	.........	.........	PUNCT
ejpam-3763	630	1	.........	.........	PUNCT
ejpam-3763	630	2	.....	.....	PUNCT
ejpam-3763	630	3	............	............	PUNCT
ejpam-3763	630	4	...........	...........	PUNCT
ejpam-3763	630	5	...........	...........	PUNCT
ejpam-3763	630	6	...........	...........	PUNCT
ejpam-3763	630	7	...........	...........	PUNCT
ejpam-3763	630	8	...........	...........	PUNCT
ejpam-3763	630	9	...............	...............	PUNCT
ejpam-3763	630	10	..............	..............	PUNCT
ejpam-3763	630	11	..............	..............	PUNCT
ejpam-3763	630	12	..............	..............	PUNCT
ejpam-3763	630	13	..............	..............	PUNCT
ejpam-3763	630	14	..............	..............	PUNCT
ejpam-3763	630	15	...	...	PUNCT
ejpam-3763	631	1	figure	figure	NOUN
ejpam-3763	631	2	2	2	NUM
ejpam-3763	631	3	:	:	PUNCT
ejpam-3763	631	4	the	the	DET
ejpam-3763	631	5	edge	edge	NOUN
ejpam-3763	631	6	corona	corona	PROPN
ejpam-3763	631	7	g	g	PROPN
ejpam-3763	631	8	�	�	PROPN
ejpam-3763	631	9	p3	p3	PROPN
ejpam-3763	631	10	with	with	ADP
ejpam-3763	631	11	γp	γp	PROPN
ejpam-3763	631	12	r	r	NOUN
ejpam-3763	631	13	(	(	PUNCT
ejpam-3763	631	14	g	g	PROPN
ejpam-3763	631	15	�	�	PROPN
ejpam-3763	631	16	p3	p3	PROPN
ejpam-3763	631	17	)	)	PUNCT
ejpam-3763	632	1	=	=	SYM
ejpam-3763	632	2	5	5	NUM
ejpam-3763	632	3	does	do	AUX
ejpam-3763	632	4	not	not	PART
ejpam-3763	632	5	form	form	VERB
ejpam-3763	632	6	the	the	DET
ejpam-3763	632	7	v1	v1	NOUN
ejpam-3763	632	8	∪	∪	NOUN
ejpam-3763	632	9	v2	v2	NOUN
ejpam-3763	632	10	for	for	ADP
ejpam-3763	632	11	any	any	DET
ejpam-3763	632	12	f	f	NOUN
ejpam-3763	632	13	=	=	SYM
ejpam-3763	632	14	(	(	PUNCT
ejpam-3763	632	15	v0	v0	PROPN
ejpam-3763	632	16	,	,	PUNCT
ejpam-3763	632	17	v1	v1	NOUN
ejpam-3763	632	18	,	,	PUNCT
ejpam-3763	632	19	v2	v2	NOUN
ejpam-3763	632	20	)	)	PUNCT
ejpam-3763	632	21	∈	∈	PROPN
ejpam-3763	632	22	prd(g	prd(g	PROPN
ejpam-3763	632	23	�	�	PROPN
ejpam-3763	632	24	p3	p3	PROPN
ejpam-3763	632	25	)	)	PUNCT
ejpam-3763	632	26	.	.	PUNCT
ejpam-3763	633	1	thus	thus	ADV
ejpam-3763	633	2	,	,	PUNCT
ejpam-3763	633	3	γpr(g	γpr(g	PROPN
ejpam-3763	633	4	�	�	PROPN
ejpam-3763	633	5	p3	p3	PROPN
ejpam-3763	633	6	)	)	PUNCT
ejpam-3763	633	7	≥	≥	NOUN
ejpam-3763	633	8	5	5	NUM
ejpam-3763	633	9	.	.	PUNCT
ejpam-3763	633	10	�	�	PROPN
ejpam-3763	633	11	the	the	DET
ejpam-3763	633	12	value	value	NOUN
ejpam-3763	633	13	of	of	ADP
ejpam-3763	633	14	α	α	NOUN
ejpam-3763	633	15	in	in	ADP
ejpam-3763	633	16	theorem	theorem	NOUN
ejpam-3763	633	17	2.15	2.15	NUM
ejpam-3763	633	18	is	be	AUX
ejpam-3763	633	19	not	not	PART
ejpam-3763	633	20	necessarily	necessarily	ADV
ejpam-3763	633	21	determined	determine	VERB
ejpam-3763	633	22	by	by	ADP
ejpam-3763	633	23	a	a	DET
ejpam-3763	633	24	γpr	γpr	NOUN
ejpam-3763	633	25	-function	-function	NOUN
ejpam-3763	633	26	on	on	ADP
ejpam-3763	633	27	g.	g.	NOUN
ejpam-3763	633	28	consider	consider	VERB
ejpam-3763	633	29	the	the	DET
ejpam-3763	633	30	two	two	NUM
ejpam-3763	633	31	copies	copy	NOUN
ejpam-3763	633	32	of	of	ADP
ejpam-3763	633	33	the	the	DET
ejpam-3763	633	34	edge	edge	NOUN
ejpam-3763	633	35	corona	corona	PROPN
ejpam-3763	633	36	p5	p5	PROPN
ejpam-3763	633	37	�	�	PROPN
ejpam-3763	633	38	c4	c4	NOUN
ejpam-3763	633	39	given	give	VERB
ejpam-3763	633	40	in	in	ADP
ejpam-3763	633	41	figure	figure	NOUN
ejpam-3763	633	42	3	3	NUM
ejpam-3763	633	43	with	with	ADP
ejpam-3763	633	44	the	the	DET
ejpam-3763	633	45	corresponding	corresponding	ADJ
ejpam-3763	633	46	assignment	assignment	NOUN
ejpam-3763	633	47	of	of	ADP
ejpam-3763	633	48	colours	colour	NOUN
ejpam-3763	633	49	to	to	ADP
ejpam-3763	633	50	the	the	DET
ejpam-3763	633	51	vertices	vertex	NOUN
ejpam-3763	633	52	.	.	PUNCT
ejpam-3763	634	1	here	here	ADV
ejpam-3763	634	2	,	,	PUNCT
ejpam-3763	634	3	we	we	PRON
ejpam-3763	634	4	write	write	VERB
ejpam-3763	634	5	p5	p5	PROPN
ejpam-3763	634	6	=	=	SYM
ejpam-3763	634	7	{	{	PUNCT
ejpam-3763	634	8	x1	x1	PROPN
ejpam-3763	634	9	,	,	PUNCT
ejpam-3763	634	10	x2	x2	PROPN
ejpam-3763	634	11	,	,	PUNCT
ejpam-3763	634	12	x3	x3	PROPN
ejpam-3763	634	13	,	,	PUNCT
ejpam-3763	634	14	x4	x4	PROPN
ejpam-3763	634	15	,	,	PUNCT
ejpam-3763	634	16	x5	x5	PROPN
ejpam-3763	634	17	}	}	PUNCT
ejpam-3763	634	18	.	.	PUNCT
ejpam-3763	635	1	observe	observe	VERB
ejpam-3763	635	2	that	that	SCONJ
ejpam-3763	635	3	f	f	PROPN
ejpam-3763	635	4	=	=	PRON
ejpam-3763	635	5	(	(	PUNCT
ejpam-3763	635	6	{	{	PUNCT
ejpam-3763	635	7	x1	x1	ADJ
ejpam-3763	635	8	,	,	PUNCT
ejpam-3763	635	9	x3	x3	ADJ
ejpam-3763	635	10	,	,	PUNCT
ejpam-3763	635	11	x4},∅	x4},∅	PROPN
ejpam-3763	635	12	,	,	PUNCT
ejpam-3763	635	13	{	{	PUNCT
ejpam-3763	635	14	x2	x2	PROPN
ejpam-3763	635	15	,	,	PUNCT
ejpam-3763	635	16	x5	x5	PROPN
ejpam-3763	635	17	}	}	PUNCT
ejpam-3763	635	18	)	)	PUNCT
ejpam-3763	635	19	is	be	AUX
ejpam-3763	635	20	a	a	DET
ejpam-3763	635	21	γpr	γpr	NOUN
ejpam-3763	635	22	-function	-function	NOUN
ejpam-3763	635	23	on	on	ADP
ejpam-3763	635	24	p5	p5	ADJ
ejpam-3763	635	25	(	(	PUNCT
ejpam-3763	635	26	see	see	VERB
ejpam-3763	635	27	right	right	ADJ
ejpam-3763	635	28	-	-	PUNCT
ejpam-3763	635	29	hand	hand	NOUN
ejpam-3763	635	30	side	side	NOUN
ejpam-3763	635	31	figure	figure	NOUN
ejpam-3763	635	32	)	)	PUNCT
ejpam-3763	635	33	,	,	PUNCT
ejpam-3763	635	34	while	while	SCONJ
ejpam-3763	635	35	g	g	PROPN
ejpam-3763	635	36	=	=	PUNCT
ejpam-3763	635	37	(	(	PUNCT
ejpam-3763	635	38	{	{	PUNCT
ejpam-3763	635	39	x1	x1	PROPN
ejpam-3763	635	40	,	,	PUNCT
ejpam-3763	635	41	x5	x5	PROPN
ejpam-3763	635	42	}	}	PUNCT
ejpam-3763	635	43	,	,	PUNCT
ejpam-3763	635	44	{	{	PUNCT
ejpam-3763	635	45	x3	x3	ADJ
ejpam-3763	635	46	}	}	PUNCT
ejpam-3763	635	47	,	,	PUNCT
ejpam-3763	635	48	{	{	PUNCT
ejpam-3763	635	49	x2	x2	PROPN
ejpam-3763	635	50	,	,	PUNCT
ejpam-3763	635	51	x4	x4	PROPN
ejpam-3763	635	52	}	}	PUNCT
ejpam-3763	635	53	)	)	PUNCT
ejpam-3763	635	54	∈	∈	PROPN
ejpam-3763	635	55	prd(p5	prd(p5	NOUN
ejpam-3763	635	56	)	)	PUNCT
ejpam-3763	635	57	but	but	CCONJ
ejpam-3763	635	58	not	not	PART
ejpam-3763	635	59	a	a	DET
ejpam-3763	635	60	γpr	γpr	NOUN
ejpam-3763	635	61	-function	-function	NOUN
ejpam-3763	635	62	on	on	ADP
ejpam-3763	635	63	p5	p5	ADJ
ejpam-3763	635	64	(	(	PUNCT
ejpam-3763	635	65	see	see	VERB
ejpam-3763	635	66	left	left	ADJ
ejpam-3763	635	67	-	-	PUNCT
ejpam-3763	635	68	hand	hand	NOUN
ejpam-3763	635	69	side	side	NOUN
ejpam-3763	635	70	figure	figure	NOUN
ejpam-3763	635	71	)	)	PUNCT
ejpam-3763	635	72	.	.	PUNCT
ejpam-3763	636	1	verify	verify	VERB
ejpam-3763	636	2	that	that	SCONJ
ejpam-3763	636	3	γpr(p5	γpr(p5	PROPN
ejpam-3763	636	4	�	�	PROPN
ejpam-3763	636	5	c4	c4	PROPN
ejpam-3763	636	6	)	)	PUNCT
ejpam-3763	636	7	=	=	SYM
ejpam-3763	636	8	5	5	NUM
ejpam-3763	636	9	and	and	CCONJ
ejpam-3763	636	10	is	be	AUX
ejpam-3763	636	11	determined	determine	VERB
ejpam-3763	636	12	by	by	ADP
ejpam-3763	636	13	the	the	DET
ejpam-3763	636	14	function	function	NOUN
ejpam-3763	636	15	g.	g.	NOUN
ejpam-3763	636	16	from	from	ADP
ejpam-3763	636	17	theorem	theorem	ADJ
ejpam-3763	636	18	2.15	2.15	NUM
ejpam-3763	636	19	and	and	CCONJ
ejpam-3763	636	20	as	as	SCONJ
ejpam-3763	636	21	illustrated	illustrate	VERB
ejpam-3763	636	22	in	in	ADP
ejpam-3763	636	23	the	the	DET
ejpam-3763	636	24	preceding	precede	VERB
ejpam-3763	636	25	example	example	NOUN
ejpam-3763	636	26	,	,	PUNCT
ejpam-3763	636	27	the	the	DET
ejpam-3763	636	28	value	value	NOUN
ejpam-3763	636	29	of	of	ADP
ejpam-3763	636	30	α	α	NOUN
ejpam-3763	636	31	in	in	ADP
ejpam-3763	636	32	theorem	theorem	NOUN
ejpam-3763	636	33	2.15	2.15	NUM
ejpam-3763	636	34	is	be	AUX
ejpam-3763	636	35	determined	determine	VERB
ejpam-3763	636	36	by	by	ADP
ejpam-3763	636	37	the	the	DET
ejpam-3763	636	38	functions	function	NOUN
ejpam-3763	636	39	g	g	PROPN
ejpam-3763	636	40	∈	∈	PROPN
ejpam-3763	636	41	prd(g	prd(g	PROPN
ejpam-3763	636	42	)	)	PUNCT
ejpam-3763	636	43	for	for	ADP
ejpam-3763	636	44	which	which	PRON
ejpam-3763	636	45	most	most	ADJ
ejpam-3763	636	46	of	of	ADP
ejpam-3763	636	47	the	the	DET
ejpam-3763	636	48	sets	set	NOUN
ejpam-3763	636	49	l.	l.	PROPN
ejpam-3763	636	50	paleta	paleta	PROPN
ejpam-3763	636	51	,	,	PUNCT
ejpam-3763	636	52	f.	f.	PROPN
ejpam-3763	636	53	jamil	jamil	PROPN
ejpam-3763	636	54	/	/	SYM
ejpam-3763	636	55	eur	eur	PROPN
ejpam-3763	636	56	.	.	PUNCT
ejpam-3763	637	1	j.	j.	PROPN
ejpam-3763	637	2	pure	pure	PROPN
ejpam-3763	637	3	appl	appl	PROPN
ejpam-3763	637	4	.	.	PROPN
ejpam-3763	637	5	math	math	PROPN
ejpam-3763	637	6	,	,	PUNCT
ejpam-3763	637	7	13	13	NUM
ejpam-3763	637	8	(	(	PUNCT
ejpam-3763	637	9	3	3	NUM
ejpam-3763	637	10	)	)	PUNCT
ejpam-3763	637	11	(	(	PUNCT
ejpam-3763	637	12	2020	2020	NUM
ejpam-3763	637	13	)	)	PUNCT
ejpam-3763	637	14	,	,	PUNCT
ejpam-3763	637	15	529	529	NUM
ejpam-3763	637	16	-	-	SYM
ejpam-3763	637	17	548	548	NUM
ejpam-3763	637	18	544	544	NUM
ejpam-3763	637	19	.......................................................................................................................................	.......................................................................................................................................	NUM
ejpam-3763	637	20	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	637	21	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	637	22	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	637	23	....................................	....................................	PUNCT
ejpam-3763	637	24	............	............	PUNCT
ejpam-3763	637	25	...........	...........	PUNCT
ejpam-3763	638	1	.....	.....	PUNCT
ejpam-3763	638	2	....................................	....................................	PUNCT
ejpam-3763	639	1	................................................................................	................................................................................	PUNCT
ejpam-3763	639	2	..............	..............	PUNCT
ejpam-3763	640	1	.............	.............	PUNCT
ejpam-3763	640	2	.....	.....	PUNCT
ejpam-3763	640	3	.	.	PUNCT
ejpam-3763	640	4	...................................	...................................	PUNCT
ejpam-3763	641	1	.......................................	.......................................	PUNCT
ejpam-3763	641	2	........................................................................	........................................................................	PUNCT
ejpam-3763	641	3	............	............	PUNCT
ejpam-3763	641	4	...........	...........	PUNCT
ejpam-3763	642	1	.....	.....	PUNCT
ejpam-3763	642	2	....................................	....................................	PUNCT
ejpam-3763	643	1	................................................................................	................................................................................	PUNCT
ejpam-3763	643	2	..............	..............	PUNCT
ejpam-3763	644	1	.............	.............	PUNCT
ejpam-3763	644	2	.....	.....	PUNCT
ejpam-3763	644	3	.	.	PUNCT
ejpam-3763	644	4	...................................	...................................	PUNCT
ejpam-3763	645	1	.......................................	.......................................	PUNCT
ejpam-3763	645	2	........................................................................	........................................................................	PUNCT
ejpam-3763	645	3	............	............	PUNCT
ejpam-3763	645	4	...........	...........	PUNCT
ejpam-3763	646	1	.....	.....	PUNCT
ejpam-3763	646	2	....................................	....................................	PUNCT
ejpam-3763	647	1	................................................................................	................................................................................	PUNCT
ejpam-3763	647	2	..............	..............	PUNCT
ejpam-3763	648	1	.............	.............	PUNCT
ejpam-3763	648	2	.....	.....	PUNCT
ejpam-3763	648	3	.	.	PUNCT
ejpam-3763	648	4	...................................	...................................	PUNCT
ejpam-3763	649	1	.......................................	.......................................	PUNCT
ejpam-3763	649	2	........................................................................	........................................................................	PUNCT
ejpam-3763	649	3	............	............	PUNCT
ejpam-3763	649	4	...........	...........	PUNCT
ejpam-3763	650	1	.....	.....	PUNCT
ejpam-3763	650	2	....................................	....................................	PUNCT
ejpam-3763	651	1	................................................................................	................................................................................	PUNCT
ejpam-3763	651	2	..............	..............	PUNCT
ejpam-3763	652	1	.............	.............	PUNCT
ejpam-3763	652	2	.....	.....	PUNCT
ejpam-3763	652	3	.	.	PUNCT
ejpam-3763	652	4	...................................	...................................	PUNCT
ejpam-3763	653	1	.......................................	.......................................	PUNCT
ejpam-3763	653	2	........................................................................	........................................................................	PUNCT
ejpam-3763	654	1	.........	.........	PUNCT
ejpam-3763	654	2	........	........	PUNCT
ejpam-3763	654	3	........	........	PUNCT
ejpam-3763	654	4	........	........	PUNCT
ejpam-3763	654	5	........	........	PUNCT
ejpam-3763	654	6	........	........	PUNCT
ejpam-3763	654	7	........	........	PUNCT
ejpam-3763	654	8	........	........	PUNCT
ejpam-3763	654	9	........	........	PUNCT
ejpam-3763	654	10	........	........	PUNCT
ejpam-3763	654	11	........	........	PUNCT
ejpam-3763	655	1	........	........	PUNCT
ejpam-3763	655	2	.....	.....	PUNCT
ejpam-3763	656	1	..........	..........	PUNCT
ejpam-3763	656	2	.........	.........	PUNCT
ejpam-3763	657	1	.........	.........	PUNCT
ejpam-3763	657	2	.........	.........	PUNCT
ejpam-3763	658	1	.........	.........	PUNCT
ejpam-3763	658	2	.........	.........	PUNCT
ejpam-3763	659	1	.........	.........	PUNCT
ejpam-3763	659	2	.........	.........	PUNCT
ejpam-3763	660	1	.........	.........	PUNCT
ejpam-3763	660	2	.........	.........	PUNCT
ejpam-3763	661	1	.........	.........	PUNCT
ejpam-3763	661	2	.........	.........	PUNCT
ejpam-3763	662	1	.........	.........	PUNCT
ejpam-3763	662	2	.........	.........	PUNCT
ejpam-3763	663	1	.........	.........	PUNCT
ejpam-3763	663	2	...........	...........	PUNCT
ejpam-3763	663	3	..........	..........	PUNCT
ejpam-3763	664	1	..........	..........	PUNCT
ejpam-3763	664	2	..........	..........	PUNCT
ejpam-3763	665	1	..........	..........	PUNCT
ejpam-3763	665	2	..........	..........	PUNCT
ejpam-3763	666	1	..........	..........	PUNCT
ejpam-3763	666	2	..........	..........	PUNCT
ejpam-3763	667	1	..........	..........	PUNCT
ejpam-3763	667	2	..........	..........	PUNCT
ejpam-3763	668	1	..........	..........	PUNCT
ejpam-3763	668	2	..........	..........	PUNCT
ejpam-3763	669	1	..........	..........	PUNCT
ejpam-3763	669	2	..........	..........	PUNCT
ejpam-3763	670	1	..........	..........	PUNCT
ejpam-3763	670	2	..........	..........	PUNCT
ejpam-3763	670	3	...	...	PUNCT
ejpam-3763	670	4	...........	...........	PUNCT
ejpam-3763	671	1	..........	..........	PUNCT
ejpam-3763	671	2	..........	..........	PUNCT
ejpam-3763	672	1	..........	..........	PUNCT
ejpam-3763	672	2	..........	..........	PUNCT
ejpam-3763	673	1	..........	..........	PUNCT
ejpam-3763	673	2	..........	..........	PUNCT
ejpam-3763	674	1	..........	..........	PUNCT
ejpam-3763	674	2	..........	..........	PUNCT
ejpam-3763	675	1	..........	..........	PUNCT
ejpam-3763	675	2	..........	..........	PUNCT
ejpam-3763	676	1	..........	..........	PUNCT
ejpam-3763	676	2	................................................................................................................................	................................................................................................................................	PUNCT
ejpam-3763	677	1	.................................................................................................................................................	.................................................................................................................................................	PUNCT
ejpam-3763	677	2	........	........	PUNCT
ejpam-3763	677	3	........	........	PUNCT
ejpam-3763	677	4	........	........	PUNCT
ejpam-3763	677	5	........	........	PUNCT
ejpam-3763	677	6	........	........	PUNCT
ejpam-3763	677	7	........	........	PUNCT
ejpam-3763	677	8	........	........	PUNCT
ejpam-3763	677	9	........	........	PUNCT
ejpam-3763	677	10	........	........	PUNCT
ejpam-3763	677	11	........	........	PUNCT
ejpam-3763	677	12	........	........	PUNCT
ejpam-3763	677	13	........	........	PUNCT
ejpam-3763	677	14	........	........	PUNCT
ejpam-3763	677	15	........	........	PUNCT
ejpam-3763	678	1	.....	.....	PUNCT
ejpam-3763	678	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3763	678	3	........	........	PUNCT
ejpam-3763	678	4	........	........	PUNCT
ejpam-3763	678	5	........	........	PUNCT
ejpam-3763	678	6	........	........	PUNCT
ejpam-3763	678	7	........	........	PUNCT
ejpam-3763	678	8	........	........	PUNCT
ejpam-3763	678	9	........	........	PUNCT
ejpam-3763	678	10	........	........	PUNCT
ejpam-3763	678	11	........	........	PUNCT
ejpam-3763	678	12	........	........	PUNCT
ejpam-3763	678	13	........	........	PUNCT
ejpam-3763	679	1	.....	.....	PUNCT
ejpam-3763	679	2	..........	..........	PUNCT
ejpam-3763	680	1	.........	.........	PUNCT
ejpam-3763	680	2	.........	.........	PUNCT
ejpam-3763	681	1	.........	.........	PUNCT
ejpam-3763	681	2	.........	.........	PUNCT
ejpam-3763	682	1	.........	.........	PUNCT
ejpam-3763	682	2	.........	.........	PUNCT
ejpam-3763	683	1	.........	.........	PUNCT
ejpam-3763	683	2	.........	.........	PUNCT
ejpam-3763	684	1	.........	.........	PUNCT
ejpam-3763	684	2	.........	.........	PUNCT
ejpam-3763	685	1	.........	.........	PUNCT
ejpam-3763	685	2	.........	.........	PUNCT
ejpam-3763	686	1	.........	.........	PUNCT
ejpam-3763	686	2	.........	.........	PUNCT
ejpam-3763	686	3	...........	...........	PUNCT
ejpam-3763	686	4	..........	..........	PUNCT
ejpam-3763	687	1	..........	..........	PUNCT
ejpam-3763	687	2	..........	..........	PUNCT
ejpam-3763	688	1	..........	..........	PUNCT
ejpam-3763	688	2	..........	..........	PUNCT
ejpam-3763	689	1	..........	..........	PUNCT
ejpam-3763	689	2	..........	..........	PUNCT
ejpam-3763	690	1	..........	..........	PUNCT
ejpam-3763	690	2	..........	..........	PUNCT
ejpam-3763	691	1	..........	..........	PUNCT
ejpam-3763	691	2	..........	..........	PUNCT
ejpam-3763	692	1	..........	..........	PUNCT
ejpam-3763	692	2	..........	..........	PUNCT
ejpam-3763	693	1	..........	..........	PUNCT
ejpam-3763	693	2	..........	..........	PUNCT
ejpam-3763	693	3	...	...	PUNCT
ejpam-3763	693	4	...........	...........	PUNCT
ejpam-3763	694	1	..........	..........	PUNCT
ejpam-3763	694	2	..........	..........	PUNCT
ejpam-3763	695	1	..........	..........	PUNCT
ejpam-3763	695	2	..........	..........	PUNCT
ejpam-3763	696	1	..........	..........	PUNCT
ejpam-3763	696	2	..........	..........	PUNCT
ejpam-3763	697	1	..........	..........	PUNCT
ejpam-3763	697	2	..........	..........	PUNCT
ejpam-3763	698	1	..........	..........	PUNCT
ejpam-3763	698	2	..........	..........	PUNCT
ejpam-3763	699	1	..........	..........	PUNCT
ejpam-3763	699	2	................................................................................................................................	................................................................................................................................	PUNCT
ejpam-3763	700	1	.................................................................................................................................................	.................................................................................................................................................	PUNCT
ejpam-3763	700	2	........	........	PUNCT
ejpam-3763	700	3	........	........	PUNCT
ejpam-3763	700	4	........	........	PUNCT
ejpam-3763	700	5	........	........	PUNCT
ejpam-3763	700	6	........	........	PUNCT
ejpam-3763	700	7	........	........	PUNCT
ejpam-3763	700	8	........	........	PUNCT
ejpam-3763	700	9	........	........	PUNCT
ejpam-3763	700	10	........	........	PUNCT
ejpam-3763	700	11	........	........	PUNCT
ejpam-3763	700	12	........	........	PUNCT
ejpam-3763	700	13	........	........	PUNCT
ejpam-3763	700	14	........	........	PUNCT
ejpam-3763	700	15	........	........	PUNCT
ejpam-3763	701	1	.....	.....	PUNCT
ejpam-3763	701	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3763	701	3	........	........	PUNCT
ejpam-3763	701	4	........	........	PUNCT
ejpam-3763	701	5	........	........	PUNCT
ejpam-3763	701	6	........	........	PUNCT
ejpam-3763	701	7	........	........	PUNCT
ejpam-3763	701	8	........	........	PUNCT
ejpam-3763	701	9	........	........	PUNCT
ejpam-3763	701	10	........	........	PUNCT
ejpam-3763	701	11	........	........	PUNCT
ejpam-3763	701	12	........	........	PUNCT
ejpam-3763	701	13	........	........	PUNCT
ejpam-3763	702	1	.....	.....	PUNCT
ejpam-3763	702	2	..........	..........	PUNCT
ejpam-3763	703	1	.........	.........	PUNCT
ejpam-3763	703	2	.........	.........	PUNCT
ejpam-3763	704	1	.........	.........	PUNCT
ejpam-3763	704	2	.........	.........	PUNCT
ejpam-3763	705	1	.........	.........	PUNCT
ejpam-3763	705	2	.........	.........	PUNCT
ejpam-3763	706	1	.........	.........	PUNCT
ejpam-3763	706	2	.........	.........	PUNCT
ejpam-3763	707	1	.........	.........	PUNCT
ejpam-3763	707	2	.........	.........	PUNCT
ejpam-3763	708	1	.........	.........	PUNCT
ejpam-3763	708	2	.........	.........	PUNCT
ejpam-3763	709	1	.........	.........	PUNCT
ejpam-3763	709	2	.........	.........	PUNCT
ejpam-3763	709	3	...........	...........	PUNCT
ejpam-3763	709	4	..........	..........	PUNCT
ejpam-3763	710	1	..........	..........	PUNCT
ejpam-3763	710	2	..........	..........	PUNCT
ejpam-3763	711	1	..........	..........	PUNCT
ejpam-3763	711	2	..........	..........	PUNCT
ejpam-3763	712	1	..........	..........	PUNCT
ejpam-3763	712	2	..........	..........	PUNCT
ejpam-3763	713	1	..........	..........	PUNCT
ejpam-3763	713	2	..........	..........	PUNCT
ejpam-3763	714	1	..........	..........	PUNCT
ejpam-3763	714	2	..........	..........	PUNCT
ejpam-3763	715	1	..........	..........	PUNCT
ejpam-3763	715	2	..........	..........	PUNCT
ejpam-3763	716	1	..........	..........	PUNCT
ejpam-3763	716	2	..........	..........	PUNCT
ejpam-3763	716	3	...	...	PUNCT
ejpam-3763	716	4	...........	...........	PUNCT
ejpam-3763	717	1	..........	..........	PUNCT
ejpam-3763	717	2	..........	..........	PUNCT
ejpam-3763	718	1	..........	..........	PUNCT
ejpam-3763	718	2	..........	..........	PUNCT
ejpam-3763	719	1	..........	..........	PUNCT
ejpam-3763	719	2	..........	..........	PUNCT
ejpam-3763	720	1	..........	..........	PUNCT
ejpam-3763	720	2	..........	..........	PUNCT
ejpam-3763	721	1	..........	..........	PUNCT
ejpam-3763	721	2	..........	..........	PUNCT
ejpam-3763	722	1	..........	..........	PUNCT
ejpam-3763	722	2	................................................................................................................................	................................................................................................................................	PUNCT
ejpam-3763	723	1	.................................................................................................................................................	.................................................................................................................................................	PUNCT
ejpam-3763	723	2	........	........	PUNCT
ejpam-3763	723	3	........	........	PUNCT
ejpam-3763	723	4	........	........	PUNCT
ejpam-3763	723	5	........	........	PUNCT
ejpam-3763	723	6	........	........	PUNCT
ejpam-3763	723	7	........	........	PUNCT
ejpam-3763	723	8	........	........	PUNCT
ejpam-3763	723	9	........	........	PUNCT
ejpam-3763	723	10	........	........	PUNCT
ejpam-3763	723	11	........	........	PUNCT
ejpam-3763	723	12	........	........	PUNCT
ejpam-3763	723	13	........	........	PUNCT
ejpam-3763	723	14	........	........	PUNCT
ejpam-3763	723	15	........	........	PUNCT
ejpam-3763	724	1	.....	.....	PUNCT
ejpam-3763	724	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3763	724	3	........	........	PUNCT
ejpam-3763	724	4	........	........	PUNCT
ejpam-3763	724	5	........	........	PUNCT
ejpam-3763	724	6	........	........	PUNCT
ejpam-3763	724	7	........	........	PUNCT
ejpam-3763	724	8	........	........	PUNCT
ejpam-3763	724	9	........	........	PUNCT
ejpam-3763	724	10	........	........	PUNCT
ejpam-3763	724	11	........	........	PUNCT
ejpam-3763	724	12	........	........	PUNCT
ejpam-3763	724	13	........	........	PUNCT
ejpam-3763	725	1	.....	.....	PUNCT
ejpam-3763	725	2	..........	..........	PUNCT
ejpam-3763	726	1	.........	.........	PUNCT
ejpam-3763	726	2	.........	.........	PUNCT
ejpam-3763	727	1	.........	.........	PUNCT
ejpam-3763	727	2	.........	.........	PUNCT
ejpam-3763	728	1	.........	.........	PUNCT
ejpam-3763	728	2	.........	.........	PUNCT
ejpam-3763	729	1	.........	.........	PUNCT
ejpam-3763	729	2	.........	.........	PUNCT
ejpam-3763	730	1	.........	.........	PUNCT
ejpam-3763	730	2	.........	.........	PUNCT
ejpam-3763	731	1	.........	.........	PUNCT
ejpam-3763	731	2	.........	.........	PUNCT
ejpam-3763	732	1	.........	.........	PUNCT
ejpam-3763	732	2	.........	.........	PUNCT
ejpam-3763	732	3	...........	...........	PUNCT
ejpam-3763	732	4	..........	..........	PUNCT
ejpam-3763	733	1	..........	..........	PUNCT
ejpam-3763	733	2	..........	..........	PUNCT
ejpam-3763	734	1	..........	..........	PUNCT
ejpam-3763	734	2	..........	..........	PUNCT
ejpam-3763	735	1	..........	..........	PUNCT
ejpam-3763	735	2	..........	..........	PUNCT
ejpam-3763	736	1	..........	..........	PUNCT
ejpam-3763	736	2	..........	..........	PUNCT
ejpam-3763	737	1	..........	..........	PUNCT
ejpam-3763	737	2	..........	..........	PUNCT
ejpam-3763	738	1	..........	..........	PUNCT
ejpam-3763	738	2	..........	..........	PUNCT
ejpam-3763	739	1	..........	..........	PUNCT
ejpam-3763	739	2	..........	..........	PUNCT
ejpam-3763	739	3	...	...	PUNCT
ejpam-3763	739	4	...........	...........	PUNCT
ejpam-3763	740	1	..........	..........	PUNCT
ejpam-3763	740	2	..........	..........	PUNCT
ejpam-3763	741	1	..........	..........	PUNCT
ejpam-3763	741	2	..........	..........	PUNCT
ejpam-3763	742	1	..........	..........	PUNCT
ejpam-3763	742	2	..........	..........	PUNCT
ejpam-3763	743	1	..........	..........	PUNCT
ejpam-3763	743	2	..........	..........	PUNCT
ejpam-3763	744	1	..........	..........	PUNCT
ejpam-3763	744	2	..........	..........	PUNCT
ejpam-3763	745	1	..........	..........	PUNCT
ejpam-3763	745	2	................................................................................................................................	................................................................................................................................	PUNCT
ejpam-3763	746	1	.................................................................................................................................................	.................................................................................................................................................	PUNCT
ejpam-3763	746	2	........	........	PUNCT
ejpam-3763	746	3	........	........	PUNCT
ejpam-3763	746	4	........	........	PUNCT
ejpam-3763	746	5	........	........	PUNCT
ejpam-3763	746	6	........	........	PUNCT
ejpam-3763	746	7	........	........	PUNCT
ejpam-3763	746	8	........	........	PUNCT
ejpam-3763	746	9	........	........	PUNCT
ejpam-3763	746	10	........	........	PUNCT
ejpam-3763	746	11	........	........	PUNCT
ejpam-3763	746	12	........	........	PUNCT
ejpam-3763	746	13	........	........	PUNCT
ejpam-3763	746	14	........	........	PUNCT
ejpam-3763	746	15	........	........	PUNCT
ejpam-3763	747	1	.....	.....	PUNCT
ejpam-3763	747	2	.......................................................................................................	.......................................................................................................	PUNCT
ejpam-3763	748	1	x1	x1	NUM
ejpam-3763	748	2	x2	x2	NOUN
ejpam-3763	748	3	x3	x3	PROPN
ejpam-3763	748	4	x4	x4	PROPN
ejpam-3763	748	5	x5	x5	PROPN
ejpam-3763	748	6	2	2	NUM
ejpam-3763	748	7	20	20	NUM
ejpam-3763	748	8	0	0	NUM
ejpam-3763	748	9	0	0	NUM
ejpam-3763	748	10	0	0	NUM
ejpam-3763	748	11	0	0	NUM
ejpam-3763	748	12	0	0	NUM
ejpam-3763	748	13	0	0	NUM
ejpam-3763	748	14	0	0	NUM
ejpam-3763	748	15	0	0	NUM
ejpam-3763	748	16	0	0	NUM
ejpam-3763	748	17	0	0	NUM
ejpam-3763	748	18	0	0	NUM
ejpam-3763	748	19	0	0	NUM
ejpam-3763	748	20	00	00	NUM
ejpam-3763	748	21	0	0	NUM
ejpam-3763	748	22	0	0	NUM
ejpam-3763	748	23	0	0	NUM
ejpam-3763	748	24	1	1	NUM
ejpam-3763	748	25	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	748	26	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	748	27	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	748	28	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	748	29	....................................	....................................	PUNCT
ejpam-3763	748	30	............	............	PUNCT
ejpam-3763	748	31	...........	...........	PUNCT
ejpam-3763	748	32	.....	.....	PUNCT
ejpam-3763	748	33	....................................	....................................	PUNCT
ejpam-3763	748	34	................................................................................	................................................................................	PUNCT
ejpam-3763	748	35	..............	..............	PUNCT
ejpam-3763	748	36	.............	.............	PUNCT
ejpam-3763	749	1	.....	.....	PUNCT
ejpam-3763	749	2	.	.	PUNCT
ejpam-3763	749	3	...................................	...................................	PUNCT
ejpam-3763	749	4	.......................................	.......................................	PUNCT
ejpam-3763	749	5	........................................................................	........................................................................	PUNCT
ejpam-3763	749	6	............	............	PUNCT
ejpam-3763	749	7	...........	...........	PUNCT
ejpam-3763	749	8	.....	.....	PUNCT
ejpam-3763	749	9	....................................	....................................	PUNCT
ejpam-3763	749	10	................................................................................	................................................................................	PUNCT
ejpam-3763	750	1	..............	..............	PUNCT
ejpam-3763	750	2	.............	.............	PUNCT
ejpam-3763	750	3	.....	.....	PUNCT
ejpam-3763	750	4	.	.	PUNCT
ejpam-3763	750	5	...................................	...................................	PUNCT
ejpam-3763	751	1	.......................................	.......................................	PUNCT
ejpam-3763	751	2	........................................................................	........................................................................	PUNCT
ejpam-3763	751	3	............	............	PUNCT
ejpam-3763	751	4	...........	...........	PUNCT
ejpam-3763	752	1	.....	.....	PUNCT
ejpam-3763	752	2	....................................	....................................	PUNCT
ejpam-3763	753	1	................................................................................	................................................................................	PUNCT
ejpam-3763	753	2	..............	..............	PUNCT
ejpam-3763	754	1	.............	.............	PUNCT
ejpam-3763	754	2	.....	.....	PUNCT
ejpam-3763	754	3	.	.	PUNCT
ejpam-3763	754	4	...................................	...................................	PUNCT
ejpam-3763	755	1	.......................................	.......................................	PUNCT
ejpam-3763	755	2	........................................................................	........................................................................	PUNCT
ejpam-3763	755	3	............	............	PUNCT
ejpam-3763	755	4	...........	...........	PUNCT
ejpam-3763	756	1	.....	.....	PUNCT
ejpam-3763	756	2	....................................	....................................	PUNCT
ejpam-3763	757	1	................................................................................	................................................................................	PUNCT
ejpam-3763	757	2	..............	..............	PUNCT
ejpam-3763	758	1	.............	.............	PUNCT
ejpam-3763	758	2	.....	.....	PUNCT
ejpam-3763	758	3	.	.	PUNCT
ejpam-3763	758	4	...................................	...................................	PUNCT
ejpam-3763	759	1	.......................................	.......................................	PUNCT
ejpam-3763	759	2	........................................................................	........................................................................	PUNCT
ejpam-3763	760	1	.........	.........	PUNCT
ejpam-3763	760	2	........	........	PUNCT
ejpam-3763	760	3	........	........	PUNCT
ejpam-3763	760	4	........	........	PUNCT
ejpam-3763	760	5	........	........	PUNCT
ejpam-3763	760	6	........	........	PUNCT
ejpam-3763	760	7	........	........	PUNCT
ejpam-3763	760	8	........	........	PUNCT
ejpam-3763	760	9	........	........	PUNCT
ejpam-3763	760	10	........	........	PUNCT
ejpam-3763	760	11	........	........	PUNCT
ejpam-3763	761	1	........	........	PUNCT
ejpam-3763	761	2	.....	.....	PUNCT
ejpam-3763	762	1	..........	..........	PUNCT
ejpam-3763	762	2	.........	.........	PUNCT
ejpam-3763	763	1	.........	.........	PUNCT
ejpam-3763	763	2	.........	.........	PUNCT
ejpam-3763	764	1	.........	.........	PUNCT
ejpam-3763	764	2	.........	.........	PUNCT
ejpam-3763	765	1	.........	.........	PUNCT
ejpam-3763	765	2	.........	.........	PUNCT
ejpam-3763	766	1	.........	.........	PUNCT
ejpam-3763	766	2	.........	.........	PUNCT
ejpam-3763	767	1	.........	.........	PUNCT
ejpam-3763	767	2	.........	.........	PUNCT
ejpam-3763	768	1	.........	.........	PUNCT
ejpam-3763	768	2	.........	.........	PUNCT
ejpam-3763	769	1	.........	.........	PUNCT
ejpam-3763	769	2	...........	...........	PUNCT
ejpam-3763	769	3	..........	..........	PUNCT
ejpam-3763	770	1	..........	..........	PUNCT
ejpam-3763	770	2	..........	..........	PUNCT
ejpam-3763	771	1	..........	..........	PUNCT
ejpam-3763	771	2	..........	..........	PUNCT
ejpam-3763	772	1	..........	..........	PUNCT
ejpam-3763	772	2	..........	..........	PUNCT
ejpam-3763	773	1	..........	..........	PUNCT
ejpam-3763	773	2	..........	..........	PUNCT
ejpam-3763	774	1	..........	..........	PUNCT
ejpam-3763	774	2	..........	..........	PUNCT
ejpam-3763	775	1	..........	..........	PUNCT
ejpam-3763	775	2	..........	..........	PUNCT
ejpam-3763	776	1	..........	..........	PUNCT
ejpam-3763	776	2	..........	..........	PUNCT
ejpam-3763	776	3	...	...	PUNCT
ejpam-3763	776	4	...........	...........	PUNCT
ejpam-3763	777	1	..........	..........	PUNCT
ejpam-3763	777	2	..........	..........	PUNCT
ejpam-3763	778	1	..........	..........	PUNCT
ejpam-3763	778	2	..........	..........	PUNCT
ejpam-3763	779	1	..........	..........	PUNCT
ejpam-3763	779	2	..........	..........	PUNCT
ejpam-3763	780	1	..........	..........	PUNCT
ejpam-3763	780	2	..........	..........	PUNCT
ejpam-3763	781	1	..........	..........	PUNCT
ejpam-3763	781	2	..........	..........	PUNCT
ejpam-3763	782	1	..........	..........	PUNCT
ejpam-3763	782	2	................................................................................................................................	................................................................................................................................	PUNCT
ejpam-3763	783	1	.................................................................................................................................................	.................................................................................................................................................	PUNCT
ejpam-3763	783	2	........	........	PUNCT
ejpam-3763	783	3	........	........	PUNCT
ejpam-3763	783	4	........	........	PUNCT
ejpam-3763	783	5	........	........	PUNCT
ejpam-3763	783	6	........	........	PUNCT
ejpam-3763	783	7	........	........	PUNCT
ejpam-3763	783	8	........	........	PUNCT
ejpam-3763	783	9	........	........	PUNCT
ejpam-3763	783	10	........	........	PUNCT
ejpam-3763	783	11	........	........	PUNCT
ejpam-3763	783	12	........	........	PUNCT
ejpam-3763	783	13	........	........	PUNCT
ejpam-3763	783	14	........	........	PUNCT
ejpam-3763	783	15	........	........	PUNCT
ejpam-3763	784	1	.....	.....	PUNCT
ejpam-3763	784	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3763	784	3	........	........	PUNCT
ejpam-3763	784	4	........	........	PUNCT
ejpam-3763	784	5	........	........	PUNCT
ejpam-3763	784	6	........	........	PUNCT
ejpam-3763	784	7	........	........	PUNCT
ejpam-3763	784	8	........	........	PUNCT
ejpam-3763	784	9	........	........	PUNCT
ejpam-3763	784	10	........	........	PUNCT
ejpam-3763	784	11	........	........	PUNCT
ejpam-3763	784	12	........	........	PUNCT
ejpam-3763	784	13	........	........	PUNCT
ejpam-3763	785	1	.....	.....	PUNCT
ejpam-3763	785	2	..........	..........	PUNCT
ejpam-3763	786	1	.........	.........	PUNCT
ejpam-3763	786	2	.........	.........	PUNCT
ejpam-3763	787	1	.........	.........	PUNCT
ejpam-3763	787	2	.........	.........	PUNCT
ejpam-3763	788	1	.........	.........	PUNCT
ejpam-3763	788	2	.........	.........	PUNCT
ejpam-3763	789	1	.........	.........	PUNCT
ejpam-3763	789	2	.........	.........	PUNCT
ejpam-3763	790	1	.........	.........	PUNCT
ejpam-3763	790	2	.........	.........	PUNCT
ejpam-3763	791	1	.........	.........	PUNCT
ejpam-3763	791	2	.........	.........	PUNCT
ejpam-3763	792	1	.........	.........	PUNCT
ejpam-3763	792	2	.........	.........	PUNCT
ejpam-3763	792	3	...........	...........	PUNCT
ejpam-3763	792	4	..........	..........	PUNCT
ejpam-3763	793	1	..........	..........	PUNCT
ejpam-3763	793	2	..........	..........	PUNCT
ejpam-3763	794	1	..........	..........	PUNCT
ejpam-3763	794	2	..........	..........	PUNCT
ejpam-3763	795	1	..........	..........	PUNCT
ejpam-3763	795	2	..........	..........	PUNCT
ejpam-3763	796	1	..........	..........	PUNCT
ejpam-3763	796	2	..........	..........	PUNCT
ejpam-3763	797	1	..........	..........	PUNCT
ejpam-3763	797	2	..........	..........	PUNCT
ejpam-3763	798	1	..........	..........	PUNCT
ejpam-3763	798	2	..........	..........	PUNCT
ejpam-3763	799	1	..........	..........	PUNCT
ejpam-3763	799	2	..........	..........	PUNCT
ejpam-3763	799	3	...	...	PUNCT
ejpam-3763	799	4	...........	...........	PUNCT
ejpam-3763	800	1	..........	..........	PUNCT
ejpam-3763	800	2	..........	..........	PUNCT
ejpam-3763	801	1	..........	..........	PUNCT
ejpam-3763	801	2	..........	..........	PUNCT
ejpam-3763	802	1	..........	..........	PUNCT
ejpam-3763	802	2	..........	..........	PUNCT
ejpam-3763	803	1	..........	..........	PUNCT
ejpam-3763	803	2	..........	..........	PUNCT
ejpam-3763	804	1	..........	..........	PUNCT
ejpam-3763	804	2	..........	..........	PUNCT
ejpam-3763	805	1	..........	..........	PUNCT
ejpam-3763	805	2	................................................................................................................................	................................................................................................................................	PUNCT
ejpam-3763	806	1	.................................................................................................................................................	.................................................................................................................................................	PUNCT
ejpam-3763	806	2	........	........	PUNCT
ejpam-3763	806	3	........	........	PUNCT
ejpam-3763	806	4	........	........	PUNCT
ejpam-3763	806	5	........	........	PUNCT
ejpam-3763	806	6	........	........	PUNCT
ejpam-3763	806	7	........	........	PUNCT
ejpam-3763	806	8	........	........	PUNCT
ejpam-3763	806	9	........	........	PUNCT
ejpam-3763	806	10	........	........	PUNCT
ejpam-3763	806	11	........	........	PUNCT
ejpam-3763	806	12	........	........	PUNCT
ejpam-3763	806	13	........	........	PUNCT
ejpam-3763	806	14	........	........	PUNCT
ejpam-3763	806	15	........	........	PUNCT
ejpam-3763	807	1	.....	.....	PUNCT
ejpam-3763	807	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3763	807	3	........	........	PUNCT
ejpam-3763	807	4	........	........	PUNCT
ejpam-3763	807	5	........	........	PUNCT
ejpam-3763	807	6	........	........	PUNCT
ejpam-3763	807	7	........	........	PUNCT
ejpam-3763	807	8	........	........	PUNCT
ejpam-3763	807	9	........	........	PUNCT
ejpam-3763	807	10	........	........	PUNCT
ejpam-3763	807	11	........	........	PUNCT
ejpam-3763	807	12	........	........	PUNCT
ejpam-3763	807	13	........	........	PUNCT
ejpam-3763	808	1	.....	.....	PUNCT
ejpam-3763	808	2	..........	..........	PUNCT
ejpam-3763	809	1	.........	.........	PUNCT
ejpam-3763	809	2	.........	.........	PUNCT
ejpam-3763	810	1	.........	.........	PUNCT
ejpam-3763	810	2	.........	.........	PUNCT
ejpam-3763	811	1	.........	.........	PUNCT
ejpam-3763	811	2	.........	.........	PUNCT
ejpam-3763	812	1	.........	.........	PUNCT
ejpam-3763	812	2	.........	.........	PUNCT
ejpam-3763	813	1	.........	.........	PUNCT
ejpam-3763	813	2	.........	.........	PUNCT
ejpam-3763	814	1	.........	.........	PUNCT
ejpam-3763	814	2	.........	.........	PUNCT
ejpam-3763	815	1	.........	.........	PUNCT
ejpam-3763	815	2	.........	.........	PUNCT
ejpam-3763	815	3	...........	...........	PUNCT
ejpam-3763	815	4	..........	..........	PUNCT
ejpam-3763	816	1	..........	..........	PUNCT
ejpam-3763	816	2	..........	..........	PUNCT
ejpam-3763	817	1	..........	..........	PUNCT
ejpam-3763	817	2	..........	..........	PUNCT
ejpam-3763	818	1	..........	..........	PUNCT
ejpam-3763	818	2	..........	..........	PUNCT
ejpam-3763	819	1	..........	..........	PUNCT
ejpam-3763	819	2	..........	..........	PUNCT
ejpam-3763	820	1	..........	..........	PUNCT
ejpam-3763	820	2	..........	..........	PUNCT
ejpam-3763	821	1	..........	..........	PUNCT
ejpam-3763	821	2	..........	..........	PUNCT
ejpam-3763	822	1	..........	..........	PUNCT
ejpam-3763	822	2	..........	..........	PUNCT
ejpam-3763	822	3	...	...	PUNCT
ejpam-3763	822	4	...........	...........	PUNCT
ejpam-3763	823	1	..........	..........	PUNCT
ejpam-3763	823	2	..........	..........	PUNCT
ejpam-3763	824	1	..........	..........	PUNCT
ejpam-3763	824	2	..........	..........	PUNCT
ejpam-3763	825	1	..........	..........	PUNCT
ejpam-3763	825	2	..........	..........	PUNCT
ejpam-3763	826	1	..........	..........	PUNCT
ejpam-3763	826	2	..........	..........	PUNCT
ejpam-3763	827	1	..........	..........	PUNCT
ejpam-3763	827	2	..........	..........	PUNCT
ejpam-3763	828	1	..........	..........	PUNCT
ejpam-3763	828	2	................................................................................................................................	................................................................................................................................	PUNCT
ejpam-3763	829	1	.................................................................................................................................................	.................................................................................................................................................	PUNCT
ejpam-3763	829	2	........	........	PUNCT
ejpam-3763	829	3	........	........	PUNCT
ejpam-3763	829	4	........	........	PUNCT
ejpam-3763	829	5	........	........	PUNCT
ejpam-3763	829	6	........	........	PUNCT
ejpam-3763	829	7	........	........	PUNCT
ejpam-3763	829	8	........	........	PUNCT
ejpam-3763	829	9	........	........	PUNCT
ejpam-3763	829	10	........	........	PUNCT
ejpam-3763	829	11	........	........	PUNCT
ejpam-3763	829	12	........	........	PUNCT
ejpam-3763	829	13	........	........	PUNCT
ejpam-3763	829	14	........	........	PUNCT
ejpam-3763	829	15	........	........	PUNCT
ejpam-3763	830	1	.....	.....	PUNCT
ejpam-3763	830	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3763	830	3	........	........	PUNCT
ejpam-3763	830	4	........	........	PUNCT
ejpam-3763	830	5	........	........	PUNCT
ejpam-3763	830	6	........	........	PUNCT
ejpam-3763	830	7	........	........	PUNCT
ejpam-3763	830	8	........	........	PUNCT
ejpam-3763	830	9	........	........	PUNCT
ejpam-3763	830	10	........	........	PUNCT
ejpam-3763	830	11	........	........	PUNCT
ejpam-3763	830	12	........	........	PUNCT
ejpam-3763	830	13	........	........	PUNCT
ejpam-3763	831	1	.....	.....	PUNCT
ejpam-3763	831	2	..........	..........	PUNCT
ejpam-3763	832	1	.........	.........	PUNCT
ejpam-3763	832	2	.........	.........	PUNCT
ejpam-3763	833	1	.........	.........	PUNCT
ejpam-3763	833	2	.........	.........	PUNCT
ejpam-3763	834	1	.........	.........	PUNCT
ejpam-3763	834	2	.........	.........	PUNCT
ejpam-3763	835	1	.........	.........	PUNCT
ejpam-3763	835	2	.........	.........	PUNCT
ejpam-3763	836	1	.........	.........	PUNCT
ejpam-3763	836	2	.........	.........	PUNCT
ejpam-3763	837	1	.........	.........	PUNCT
ejpam-3763	837	2	.........	.........	PUNCT
ejpam-3763	838	1	.........	.........	PUNCT
ejpam-3763	838	2	.........	.........	PUNCT
ejpam-3763	838	3	...........	...........	PUNCT
ejpam-3763	838	4	..........	..........	PUNCT
ejpam-3763	839	1	..........	..........	PUNCT
ejpam-3763	839	2	..........	..........	PUNCT
ejpam-3763	840	1	..........	..........	PUNCT
ejpam-3763	840	2	..........	..........	PUNCT
ejpam-3763	841	1	..........	..........	PUNCT
ejpam-3763	841	2	..........	..........	PUNCT
ejpam-3763	842	1	..........	..........	PUNCT
ejpam-3763	842	2	..........	..........	PUNCT
ejpam-3763	843	1	..........	..........	PUNCT
ejpam-3763	843	2	..........	..........	PUNCT
ejpam-3763	844	1	..........	..........	PUNCT
ejpam-3763	844	2	..........	..........	PUNCT
ejpam-3763	845	1	..........	..........	PUNCT
ejpam-3763	845	2	..........	..........	PUNCT
ejpam-3763	845	3	...	...	PUNCT
ejpam-3763	845	4	...........	...........	PUNCT
ejpam-3763	846	1	..........	..........	PUNCT
ejpam-3763	846	2	..........	..........	PUNCT
ejpam-3763	847	1	..........	..........	PUNCT
ejpam-3763	847	2	..........	..........	PUNCT
ejpam-3763	848	1	..........	..........	PUNCT
ejpam-3763	848	2	..........	..........	PUNCT
ejpam-3763	849	1	..........	..........	PUNCT
ejpam-3763	849	2	..........	..........	PUNCT
ejpam-3763	850	1	..........	..........	PUNCT
ejpam-3763	850	2	..........	..........	PUNCT
ejpam-3763	851	1	..........	..........	PUNCT
ejpam-3763	851	2	................................................................................................................................	................................................................................................................................	PUNCT
ejpam-3763	852	1	.................................................................................................................................................	.................................................................................................................................................	PUNCT
ejpam-3763	852	2	........	........	PUNCT
ejpam-3763	852	3	........	........	PUNCT
ejpam-3763	852	4	........	........	PUNCT
ejpam-3763	852	5	........	........	PUNCT
ejpam-3763	852	6	........	........	PUNCT
ejpam-3763	852	7	........	........	PUNCT
ejpam-3763	852	8	........	........	PUNCT
ejpam-3763	852	9	........	........	PUNCT
ejpam-3763	852	10	........	........	PUNCT
ejpam-3763	852	11	........	........	PUNCT
ejpam-3763	852	12	........	........	PUNCT
ejpam-3763	852	13	........	........	PUNCT
ejpam-3763	852	14	........	........	PUNCT
ejpam-3763	852	15	........	........	PUNCT
ejpam-3763	853	1	.....	.....	PUNCT
ejpam-3763	853	2	.......................................................................................................	.......................................................................................................	PUNCT
ejpam-3763	854	1	x1	x1	NUM
ejpam-3763	854	2	x2	x2	NOUN
ejpam-3763	854	3	x3	x3	PROPN
ejpam-3763	854	4	x4	x4	PROPN
ejpam-3763	854	5	x5	x5	PROPN
ejpam-3763	854	6	0	0	NUM
ejpam-3763	854	7	0	0	NUM
ejpam-3763	854	8	0	0	NUM
ejpam-3763	854	9	0	0	NUM
ejpam-3763	854	10	0	0	NUM
ejpam-3763	854	11	0	0	NUM
ejpam-3763	854	12	0	0	NUM
ejpam-3763	854	13	0	0	NUM
ejpam-3763	854	14	0	0	NUM
ejpam-3763	854	15	0	0	NUM
ejpam-3763	854	16	0	0	NUM
ejpam-3763	854	17	0	0	NUM
ejpam-3763	854	18	0	0	NUM
ejpam-3763	854	19	0	0	NUM
ejpam-3763	854	20	0	0	NUM
ejpam-3763	854	21	2	2	NUM
ejpam-3763	854	22	2	2	NUM
ejpam-3763	854	23	1	1	NUM
ejpam-3763	854	24	1	1	NUM
ejpam-3763	854	25	1	1	NUM
ejpam-3763	854	26	1	1	NUM
ejpam-3763	854	27	figure	figure	NOUN
ejpam-3763	854	28	3	3	NUM
ejpam-3763	854	29	:	:	PUNCT
ejpam-3763	854	30	the	the	DET
ejpam-3763	854	31	edge	edge	NOUN
ejpam-3763	854	32	corona	corona	NOUN
ejpam-3763	854	33	p5	p5	PROPN
ejpam-3763	854	34	�	�	PROPN
ejpam-3763	854	35	c4	c4	PROPN
ejpam-3763	854	36	e00(g;g	e00(g;g	PROPN
ejpam-3763	854	37	)	)	PUNCT
ejpam-3763	854	38	,	,	PUNCT
ejpam-3763	854	39	e22(g;g	e22(g;g	NOUN
ejpam-3763	854	40	)	)	PUNCT
ejpam-3763	854	41	,	,	PUNCT
ejpam-3763	854	42	e11(g;g	e11(g;g	NOUN
ejpam-3763	854	43	)	)	PUNCT
ejpam-3763	854	44	and	and	CCONJ
ejpam-3763	854	45	e01(g;g	e01(g;g	NOUN
ejpam-3763	854	46	)	)	PUNCT
ejpam-3763	854	47	are	be	AUX
ejpam-3763	854	48	empty	empty	ADJ
ejpam-3763	854	49	.	.	PUNCT
ejpam-3763	855	1	in	in	ADP
ejpam-3763	855	2	view	view	NOUN
ejpam-3763	855	3	of	of	ADP
ejpam-3763	855	4	such	such	ADJ
ejpam-3763	855	5	,	,	PUNCT
ejpam-3763	855	6	the	the	DET
ejpam-3763	855	7	following	follow	VERB
ejpam-3763	855	8	observation	observation	NOUN
ejpam-3763	855	9	can	can	AUX
ejpam-3763	855	10	be	be	AUX
ejpam-3763	855	11	easily	easily	ADV
ejpam-3763	855	12	verified	verify	VERB
ejpam-3763	855	13	.	.	PUNCT
ejpam-3763	856	1	corollary	corollary	ADJ
ejpam-3763	856	2	2.16	2.16	NUM
ejpam-3763	856	3	.	.	PUNCT
ejpam-3763	857	1	let	let	VERB
ejpam-3763	857	2	h	h	NOUN
ejpam-3763	857	3	be	be	AUX
ejpam-3763	857	4	any	any	DET
ejpam-3763	857	5	nontrivial	nontrivial	ADJ
ejpam-3763	857	6	graph	graph	NOUN
ejpam-3763	857	7	of	of	ADP
ejpam-3763	857	8	order	order	NOUN
ejpam-3763	857	9	m.	m.	NOUN
ejpam-3763	857	10	then	then	ADV
ejpam-3763	857	11	(	(	PUNCT
ejpam-3763	857	12	i	i	NOUN
ejpam-3763	857	13	)	)	PUNCT
ejpam-3763	857	14	for	for	ADP
ejpam-3763	857	15	the	the	DET
ejpam-3763	857	16	path	path	NOUN
ejpam-3763	857	17	pn	pn	PROPN
ejpam-3763	857	18	on	on	ADP
ejpam-3763	857	19	n	n	PRON
ejpam-3763	857	20	≥	≥	NUM
ejpam-3763	857	21	2	2	NUM
ejpam-3763	857	22	vertices	vertex	NOUN
ejpam-3763	857	23	,	,	PUNCT
ejpam-3763	857	24	γpr(pn	γpr(pn	NOUN
ejpam-3763	857	25	�	�	NOUN
ejpam-3763	857	26	h	h	NOUN
ejpam-3763	857	27	)	)	PUNCT
ejpam-3763	857	28	=	=	NOUN
ejpam-3763	858	1	3bn−22	3bn−22	NOUN
ejpam-3763	858	2	c+	c+	VERB
ejpam-3763	858	3	2	2	NUM
ejpam-3763	858	4	.	.	PUNCT
ejpam-3763	858	5	(	(	PUNCT
ejpam-3763	858	6	ii	ii	NOUN
ejpam-3763	858	7	)	)	PUNCT
ejpam-3763	858	8	if	if	SCONJ
ejpam-3763	858	9	m	m	PROPN
ejpam-3763	858	10	≥	≥	NOUN
ejpam-3763	858	11	3	3	NUM
ejpam-3763	858	12	,	,	PUNCT
ejpam-3763	858	13	then	then	ADV
ejpam-3763	858	14	for	for	ADP
ejpam-3763	858	15	the	the	DET
ejpam-3763	858	16	cycle	cycle	NOUN
ejpam-3763	858	17	cn	cn	PROPN
ejpam-3763	858	18	on	on	ADP
ejpam-3763	858	19	n	n	NUM
ejpam-3763	858	20	≥	≥	NUM
ejpam-3763	858	21	3	3	NUM
ejpam-3763	858	22	vertices	vertex	NOUN
ejpam-3763	858	23	,	,	PUNCT
ejpam-3763	858	24	γpr(cn	γpr(cn	NOUN
ejpam-3763	858	25	�	�	PROPN
ejpam-3763	858	26	h	h	NOUN
ejpam-3763	858	27	)	)	PUNCT
ejpam-3763	858	28	=	=	PRON
ejpam-3763	858	29	{	{	PUNCT
ejpam-3763	858	30	3k	3k	X
ejpam-3763	858	31	,	,	PUNCT
ejpam-3763	858	32	if	if	SCONJ
ejpam-3763	858	33	n	n	NOUN
ejpam-3763	858	34	=	=	SYM
ejpam-3763	858	35	2k	2k	NUM
ejpam-3763	858	36	;	;	PUNCT
ejpam-3763	858	37	3k	3k	NUM
ejpam-3763	858	38	+	+	CCONJ
ejpam-3763	858	39	1	1	NUM
ejpam-3763	858	40	+	+	NUM
ejpam-3763	858	41	γpr(h	γpr(h	NOUN
ejpam-3763	858	42	)	)	PUNCT
ejpam-3763	858	43	,	,	PUNCT
ejpam-3763	858	44	if	if	SCONJ
ejpam-3763	858	45	n	n	NOUN
ejpam-3763	858	46	=	=	SYM
ejpam-3763	858	47	2k	2k	NUM
ejpam-3763	858	48	+	+	CCONJ
ejpam-3763	858	49	1	1	X
ejpam-3763	858	50	.	.	X
ejpam-3763	858	51	(	(	PUNCT
ejpam-3763	858	52	iii	iii	X
ejpam-3763	858	53	)	)	PUNCT
ejpam-3763	858	54	if	if	SCONJ
ejpam-3763	858	55	m	m	PROPN
ejpam-3763	858	56	≥	≥	NOUN
ejpam-3763	858	57	3	3	NUM
ejpam-3763	858	58	,	,	PUNCT
ejpam-3763	858	59	then	then	ADV
ejpam-3763	858	60	for	for	ADP
ejpam-3763	858	61	2	2	NUM
ejpam-3763	858	62	≤	≤	NOUN
ejpam-3763	858	63	n	n	PRON
ejpam-3763	858	64	≤	≤	NOUN
ejpam-3763	858	65	k	k	PROPN
ejpam-3763	858	66	,	,	PUNCT
ejpam-3763	858	67	γpr(kn	γpr(kn	PROPN
ejpam-3763	858	68	,	,	PUNCT
ejpam-3763	858	69	k	k	PROPN
ejpam-3763	858	70	�	�	PROPN
ejpam-3763	858	71	h	h	PROPN
ejpam-3763	858	72	)	)	PUNCT
ejpam-3763	859	1	=	=	SYM
ejpam-3763	859	2	2n+	2n+	PROPN
ejpam-3763	859	3	k.	k.	NOUN
ejpam-3763	859	4	theorem	theorem	VERB
ejpam-3763	859	5	2.17	2.17	NUM
ejpam-3763	859	6	.	.	PUNCT
ejpam-3763	860	1	let	let	VERB
ejpam-3763	860	2	g	g	PRON
ejpam-3763	860	3	be	be	AUX
ejpam-3763	860	4	a	a	DET
ejpam-3763	860	5	nontrivial	nontrivial	ADJ
ejpam-3763	860	6	connected	connect	VERB
ejpam-3763	860	7	graph	graph	NOUN
ejpam-3763	860	8	.	.	PUNCT
ejpam-3763	861	1	then	then	ADV
ejpam-3763	861	2	γpr(g	γpr(g	PROPN
ejpam-3763	861	3	�	�	PROPN
ejpam-3763	861	4	k1	k1	PROPN
ejpam-3763	861	5	)	)	PUNCT
ejpam-3763	861	6	=	=	SYM
ejpam-3763	861	7	min	min	NOUN
ejpam-3763	861	8	g∈prd(g	g∈prd(g	PROPN
ejpam-3763	861	9	)	)	PUNCT
ejpam-3763	861	10	(	(	PUNCT
ejpam-3763	861	11	ωg(g	ωg(g	NOUN
ejpam-3763	861	12	)	)	PUNCT
ejpam-3763	862	1	+	+	CCONJ
ejpam-3763	862	2	|e00(g;g)|+	|e00(g;g)|+	PUNCT
ejpam-3763	862	3	|e01(g;g)|+	|e01(g;g)|+	PROPN
ejpam-3763	862	4	|e11(g;g)|+	|e11(g;g)|+	PUNCT
ejpam-3763	862	5	|e22(g;g)|	|e22(g;g)|	NOUN
ejpam-3763	862	6	)	)	PUNCT
ejpam-3763	862	7	.	.	PUNCT
ejpam-3763	863	1	proof	proof	NOUN
ejpam-3763	863	2	:	:	PUNCT
ejpam-3763	863	3	put	put	VERB
ejpam-3763	863	4	α	α	NOUN
ejpam-3763	863	5	=	=	SYM
ejpam-3763	863	6	min{ωg(g	min{ωg(g	PROPN
ejpam-3763	863	7	)	)	PUNCT
ejpam-3763	864	1	+	+	CCONJ
ejpam-3763	864	2	|e00(g;g)|+	|e00(g;g)|+	PUNCT
ejpam-3763	864	3	|e01(g;g)|+	|e01(g;g)|+	PROPN
ejpam-3763	864	4	|e11(g;g)|+	|e11(g;g)|+	PUNCT
ejpam-3763	864	5	|e22(g;g)|	|e22(g;g)|	NOUN
ejpam-3763	864	6	:	:	PUNCT
ejpam-3763	864	7	g	g	PROPN
ejpam-3763	864	8	∈	∈	PROPN
ejpam-3763	864	9	prd(g	prd(g	PROPN
ejpam-3763	864	10	)	)	PUNCT
ejpam-3763	864	11	}	}	PUNCT
ejpam-3763	864	12	.	.	PUNCT
ejpam-3763	865	1	by	by	ADP
ejpam-3763	865	2	theorem	theorem	NOUN
ejpam-3763	865	3	2.15	2.15	NUM
ejpam-3763	865	4	,	,	PUNCT
ejpam-3763	865	5	γpr(g	γpr(g	PROPN
ejpam-3763	865	6	�	�	PROPN
ejpam-3763	865	7	k1	k1	PROPN
ejpam-3763	865	8	)	)	PUNCT
ejpam-3763	865	9	≤	≤	NOUN
ejpam-3763	865	10	α	α	X
ejpam-3763	865	11	.	.	PUNCT
ejpam-3763	866	1	let	let	VERB
ejpam-3763	866	2	f	f	PROPN
ejpam-3763	866	3	=	=	SYM
ejpam-3763	866	4	(	(	PUNCT
ejpam-3763	866	5	v0	v0	PROPN
ejpam-3763	866	6	,	,	PUNCT
ejpam-3763	866	7	v1	v1	NOUN
ejpam-3763	866	8	,	,	PUNCT
ejpam-3763	866	9	v2	v2	PROPN
ejpam-3763	866	10	)	)	PUNCT
ejpam-3763	866	11	be	be	AUX
ejpam-3763	866	12	a	a	DET
ejpam-3763	866	13	γpr	γpr	NOUN
ejpam-3763	866	14	-function	-function	NOUN
ejpam-3763	866	15	on	on	ADP
ejpam-3763	866	16	g	g	PROPN
ejpam-3763	866	17	�	�	PROPN
ejpam-3763	866	18	k1	k1	PROPN
ejpam-3763	866	19	.	.	PUNCT
ejpam-3763	867	1	suppose	suppose	VERB
ejpam-3763	867	2	that	that	SCONJ
ejpam-3763	867	3	the	the	DET
ejpam-3763	867	4	restriction	restriction	NOUN
ejpam-3763	867	5	f	f	PROPN
ejpam-3763	867	6	|g	|g	NOUN
ejpam-3763	867	7	of	of	ADP
ejpam-3763	867	8	f	f	PROPN
ejpam-3763	867	9	to	to	ADP
ejpam-3763	867	10	g	g	PROPN
ejpam-3763	867	11	is	be	AUX
ejpam-3763	867	12	not	not	PART
ejpam-3763	867	13	a	a	DET
ejpam-3763	867	14	perfect	perfect	ADJ
ejpam-3763	867	15	roman	roman	ADJ
ejpam-3763	867	16	dominating	dominating	NOUN
ejpam-3763	867	17	function	function	NOUN
ejpam-3763	867	18	on	on	ADP
ejpam-3763	867	19	g.	g.	PROPN
ejpam-3763	867	20	we	we	PRON
ejpam-3763	867	21	will	will	AUX
ejpam-3763	867	22	construct	construct	VERB
ejpam-3763	867	23	a	a	DET
ejpam-3763	867	24	γpr	γpr	NOUN
ejpam-3763	867	25	-function	-function	NOUN
ejpam-3763	867	26	g	g	NOUN
ejpam-3763	867	27	on	on	ADP
ejpam-3763	867	28	g	g	PROPN
ejpam-3763	867	29	�	�	PROPN
ejpam-3763	867	30	k1	k1	PROPN
ejpam-3763	867	31	such	such	ADJ
ejpam-3763	867	32	that	that	SCONJ
ejpam-3763	867	33	ωg	ωg	PROPN
ejpam-3763	867	34	�	�	PROPN
ejpam-3763	867	35	k1(g	k1(g	PROPN
ejpam-3763	867	36	)	)	PUNCT
ejpam-3763	867	37	=	=	SYM
ejpam-3763	867	38	ωg	ωg	PROPN
ejpam-3763	867	39	�	�	PROPN
ejpam-3763	867	40	k1(f	k1(f	PROPN
ejpam-3763	867	41	)	)	PUNCT
ejpam-3763	867	42	and	and	CCONJ
ejpam-3763	867	43	its	its	PRON
ejpam-3763	867	44	restriction	restriction	NOUN
ejpam-3763	867	45	g|g	g|g	NOUN
ejpam-3763	867	46	to	to	ADP
ejpam-3763	867	47	g	g	PROPN
ejpam-3763	867	48	is	be	AUX
ejpam-3763	867	49	a	a	DET
ejpam-3763	867	50	perfect	perfect	ADJ
ejpam-3763	867	51	roman	roman	ADJ
ejpam-3763	867	52	dominating	dominating	NOUN
ejpam-3763	867	53	function	function	NOUN
ejpam-3763	867	54	on	on	ADP
ejpam-3763	867	55	g.	g.	PROPN
ejpam-3763	867	56	there	there	PRON
ejpam-3763	867	57	exists	exist	VERB
ejpam-3763	867	58	u	u	PROPN
ejpam-3763	867	59	∈	∈	PROPN
ejpam-3763	867	60	v0	v0	NOUN
ejpam-3763	867	61	∩	∩	X
ejpam-3763	867	62	v	v	X
ejpam-3763	867	63	(	(	PUNCT
ejpam-3763	867	64	g	g	NOUN
ejpam-3763	867	65	)	)	PUNCT
ejpam-3763	867	66	such	such	ADJ
ejpam-3763	867	67	that	that	DET
ejpam-3763	867	68	uv	uv	NOUN
ejpam-3763	867	69	/∈	/∈	PUNCT
ejpam-3763	867	70	e(g	e(g	PROPN
ejpam-3763	867	71	)	)	PUNCT
ejpam-3763	867	72	for	for	ADP
ejpam-3763	867	73	all	all	DET
ejpam-3763	867	74	v	v	NOUN
ejpam-3763	867	75	∈	∈	NOUN
ejpam-3763	867	76	v2∩v	v2∩v	NOUN
ejpam-3763	867	77	(	(	PUNCT
ejpam-3763	867	78	g	g	NOUN
ejpam-3763	867	79	)	)	PUNCT
ejpam-3763	867	80	.	.	PUNCT
ejpam-3763	868	1	this	this	PRON
ejpam-3763	868	2	means	mean	VERB
ejpam-3763	868	3	that	that	SCONJ
ejpam-3763	868	4	there	there	PRON
ejpam-3763	868	5	exists	exist	VERB
ejpam-3763	868	6	v	v	ADP
ejpam-3763	868	7	∈	∈	PROPN
ejpam-3763	868	8	ng(u	ng(u	NOUN
ejpam-3763	868	9	)	)	PUNCT
ejpam-3763	868	10	such	such	ADJ
ejpam-3763	868	11	that	that	SCONJ
ejpam-3763	868	12	v2∩ng	v2∩ng	PROPN
ejpam-3763	868	13	�	�	PROPN
ejpam-3763	868	14	k1(u	k1(u	PROPN
ejpam-3763	868	15	)	)	PUNCT
ejpam-3763	868	16	=	=	PRON
ejpam-3763	868	17	{	{	PUNCT
ejpam-3763	868	18	xuv	xuv	NOUN
ejpam-3763	868	19	}	}	PUNCT
ejpam-3763	868	20	.	.	PUNCT
ejpam-3763	869	1	case	case	NOUN
ejpam-3763	869	2	1	1	NUM
ejpam-3763	869	3	:	:	PUNCT
ejpam-3763	869	4	suppose	suppose	VERB
ejpam-3763	869	5	that	that	SCONJ
ejpam-3763	869	6	v	v	X
ejpam-3763	869	7	/∈	/∈	PROPN
ejpam-3763	869	8	v0	v0	PROPN
ejpam-3763	869	9	.	.	PUNCT
ejpam-3763	870	1	define	define	VERB
ejpam-3763	870	2	f1	f1	PROPN
ejpam-3763	870	3	=	=	SYM
ejpam-3763	870	4	(	(	PUNCT
ejpam-3763	870	5	v	v	NOUN
ejpam-3763	870	6	1	1	NUM
ejpam-3763	870	7	0	0	NUM
ejpam-3763	870	8	,	,	PUNCT
ejpam-3763	870	9	v	v	NOUN
ejpam-3763	870	10	1	1	NUM
ejpam-3763	870	11	1	1	NUM
ejpam-3763	870	12	,	,	PUNCT
ejpam-3763	870	13	v	v	NOUN
ejpam-3763	870	14	1	1	NUM
ejpam-3763	870	15	2	2	NUM
ejpam-3763	870	16	)	)	PUNCT
ejpam-3763	870	17	on	on	ADP
ejpam-3763	870	18	g	g	PROPN
ejpam-3763	870	19	�	�	PROPN
ejpam-3763	870	20	k1	k1	NOUN
ejpam-3763	870	21	by	by	ADP
ejpam-3763	870	22	f1(u	f1(u	NOUN
ejpam-3763	870	23	)	)	PUNCT
ejpam-3763	870	24	=	=	SYM
ejpam-3763	870	25	f1(xuv	f1(xuv	X
ejpam-3763	870	26	)	)	PUNCT
ejpam-3763	870	27	=	=	SYM
ejpam-3763	870	28	1	1	NUM
ejpam-3763	870	29	and	and	CCONJ
ejpam-3763	870	30	f1(x	f1(x	NUM
ejpam-3763	870	31	)	)	PUNCT
ejpam-3763	870	32	=	=	SYM
ejpam-3763	870	33	f(x	f(x	PROPN
ejpam-3763	870	34	)	)	PUNCT
ejpam-3763	870	35	for	for	ADP
ejpam-3763	870	36	all	all	PRON
ejpam-3763	870	37	x	x	SYM
ejpam-3763	870	38	∈	∈	PROPN
ejpam-3763	870	39	v	v	NOUN
ejpam-3763	870	40	(	(	PUNCT
ejpam-3763	870	41	g	g	PROPN
ejpam-3763	870	42	�	�	PROPN
ejpam-3763	870	43	k1	k1	PROPN
ejpam-3763	870	44	)	)	PUNCT
ejpam-3763	870	45	\	\	NOUN
ejpam-3763	871	1	{	{	PUNCT
ejpam-3763	871	2	u	u	NOUN
ejpam-3763	871	3	,	,	PUNCT
ejpam-3763	871	4	xuv	xuv	PROPN
ejpam-3763	871	5	}	}	PUNCT
ejpam-3763	871	6	.	.	PUNCT
ejpam-3763	872	1	then	then	ADV
ejpam-3763	872	2	f1	f1	PROPN
ejpam-3763	872	3	∈	∈	PROPN
ejpam-3763	872	4	prd(g	prd(g	PROPN
ejpam-3763	872	5	�	�	PROPN
ejpam-3763	872	6	k1	k1	PROPN
ejpam-3763	872	7	)	)	PUNCT
ejpam-3763	872	8	with	with	ADP
ejpam-3763	872	9	ωg	ωg	PROPN
ejpam-3763	872	10	�	�	NOUN
ejpam-3763	872	11	k1(f1	k1(f1	NOUN
ejpam-3763	872	12	)	)	PUNCT
ejpam-3763	872	13	=	=	SYM
ejpam-3763	872	14	ωg	ωg	PROPN
ejpam-3763	872	15	�	�	PROPN
ejpam-3763	872	16	k1(f	k1(f	PROPN
ejpam-3763	872	17	)	)	PUNCT
ejpam-3763	872	18	.	.	PUNCT
ejpam-3763	873	1	case	case	NOUN
ejpam-3763	873	2	2	2	NUM
ejpam-3763	873	3	:	:	PUNCT
ejpam-3763	873	4	suppose	suppose	VERB
ejpam-3763	873	5	that	that	SCONJ
ejpam-3763	873	6	v	v	PROPN
ejpam-3763	873	7	∈	∈	PROPN
ejpam-3763	873	8	v0	v0	NOUN
ejpam-3763	873	9	.	.	PUNCT
ejpam-3763	874	1	if	if	SCONJ
ejpam-3763	874	2	(	(	PUNCT
ejpam-3763	874	3	ng(v	ng(v	NOUN
ejpam-3763	874	4	)	)	PUNCT
ejpam-3763	874	5	\	\	NOUN
ejpam-3763	874	6	{	{	PUNCT
ejpam-3763	874	7	u})∩	u})∩	PROPN
ejpam-3763	874	8	v0	v0	NOUN
ejpam-3763	874	9	=	=	SYM
ejpam-3763	874	10	∅	∅	NOUN
ejpam-3763	874	11	,	,	PUNCT
ejpam-3763	874	12	then	then	ADV
ejpam-3763	874	13	take	take	VERB
ejpam-3763	874	14	f1	f1	NOUN
ejpam-3763	874	15	=	=	SYM
ejpam-3763	874	16	(	(	PUNCT
ejpam-3763	874	17	v	v	NOUN
ejpam-3763	874	18	1	1	NUM
ejpam-3763	874	19	0	0	NUM
ejpam-3763	874	20	,	,	PUNCT
ejpam-3763	874	21	v	v	NOUN
ejpam-3763	874	22	1	1	NUM
ejpam-3763	874	23	1	1	NUM
ejpam-3763	874	24	,	,	PUNCT
ejpam-3763	874	25	v	v	NOUN
ejpam-3763	874	26	1	1	NUM
ejpam-3763	874	27	2	2	NUM
ejpam-3763	874	28	)	)	PUNCT
ejpam-3763	874	29	on	on	ADP
ejpam-3763	874	30	g	g	NOUN
ejpam-3763	874	31	given	give	VERB
ejpam-3763	874	32	by	by	ADP
ejpam-3763	874	33	f1(v	f1(v	PROPN
ejpam-3763	874	34	)	)	PUNCT
ejpam-3763	874	35	=	=	SYM
ejpam-3763	874	36	2	2	NUM
ejpam-3763	874	37	,	,	PUNCT
ejpam-3763	874	38	f1(xuv	f1(xuv	NUM
ejpam-3763	874	39	)	)	PUNCT
ejpam-3763	874	40	=	=	SYM
ejpam-3763	874	41	0	0	NUM
ejpam-3763	874	42	and	and	CCONJ
ejpam-3763	874	43	f1(x	f1(x	NUM
ejpam-3763	874	44	)	)	PUNCT
ejpam-3763	874	45	=	=	SYM
ejpam-3763	874	46	f(x	f(x	PROPN
ejpam-3763	874	47	)	)	PUNCT
ejpam-3763	874	48	for	for	ADP
ejpam-3763	874	49	all	all	DET
ejpam-3763	874	50	x	x	SYM
ejpam-3763	874	51	∈	∈	NOUN
ejpam-3763	874	52	v	v	NOUN
ejpam-3763	874	53	(	(	PUNCT
ejpam-3763	874	54	g	g	PROPN
ejpam-3763	874	55	�	�	PROPN
ejpam-3763	874	56	k1)\{v	k1)\{v	PROPN
ejpam-3763	874	57	,	,	PUNCT
ejpam-3763	874	58	xuv	xuv	PROPN
ejpam-3763	874	59	}	}	PUNCT
ejpam-3763	874	60	.	.	PUNCT
ejpam-3763	875	1	then	then	ADV
ejpam-3763	875	2	f1	f1	PROPN
ejpam-3763	875	3	∈	∈	PROPN
ejpam-3763	875	4	prd(g	prd(g	PROPN
ejpam-3763	875	5	�	�	NOUN
ejpam-3763	875	6	k1	k1	NOUN
ejpam-3763	875	7	)	)	PUNCT
ejpam-3763	875	8	and	and	CCONJ
ejpam-3763	875	9	ωg	ωg	PROPN
ejpam-3763	875	10	�	�	NOUN
ejpam-3763	875	11	k1(f1	k1(f1	NOUN
ejpam-3763	875	12	)	)	PUNCT
ejpam-3763	875	13	=	=	SYM
ejpam-3763	875	14	ωg	ωg	PROPN
ejpam-3763	875	15	�	�	PROPN
ejpam-3763	875	16	k1(f	k1(f	PROPN
ejpam-3763	875	17	)	)	PUNCT
ejpam-3763	875	18	.	.	PUNCT
ejpam-3763	875	19	suppose	suppose	VERB
ejpam-3763	875	20	that	that	SCONJ
ejpam-3763	875	21	b	b	X
ejpam-3763	875	22	=	=	SYM
ejpam-3763	875	23	(	(	PUNCT
ejpam-3763	875	24	ng(v	ng(v	PROPN
ejpam-3763	875	25	)	)	PUNCT
ejpam-3763	875	26	\	\	NOUN
ejpam-3763	875	27	{	{	PUNCT
ejpam-3763	875	28	u})∩v0	u})∩v0	PROPN
ejpam-3763	875	29	6=	6=	X
ejpam-3763	875	30	∅.	∅.	PROPN
ejpam-3763	875	31	l.	l.	PROPN
ejpam-3763	875	32	paleta	paleta	PROPN
ejpam-3763	875	33	,	,	PUNCT
ejpam-3763	875	34	f.	f.	PROPN
ejpam-3763	875	35	jamil	jamil	PROPN
ejpam-3763	875	36	/	/	SYM
ejpam-3763	875	37	eur	eur	PROPN
ejpam-3763	875	38	.	.	PUNCT
ejpam-3763	876	1	j.	j.	PROPN
ejpam-3763	876	2	pure	pure	PROPN
ejpam-3763	876	3	appl	appl	PROPN
ejpam-3763	876	4	.	.	PROPN
ejpam-3763	876	5	math	math	PROPN
ejpam-3763	876	6	,	,	PUNCT
ejpam-3763	876	7	13	13	NUM
ejpam-3763	876	8	(	(	PUNCT
ejpam-3763	876	9	3	3	NUM
ejpam-3763	876	10	)	)	PUNCT
ejpam-3763	876	11	(	(	PUNCT
ejpam-3763	876	12	2020	2020	NUM
ejpam-3763	876	13	)	)	PUNCT
ejpam-3763	876	14	,	,	PUNCT
ejpam-3763	876	15	529	529	NUM
ejpam-3763	876	16	-	-	SYM
ejpam-3763	876	17	548	548	NUM
ejpam-3763	876	18	545	545	NUM
ejpam-3763	876	19	necessarily	necessarily	ADV
ejpam-3763	876	20	,	,	PUNCT
ejpam-3763	876	21	xvw	xvw	PROPN
ejpam-3763	876	22	∈	∈	PROPN
ejpam-3763	876	23	v1	v1	NOUN
ejpam-3763	876	24	for	for	ADP
ejpam-3763	876	25	each	each	DET
ejpam-3763	876	26	w	w	PROPN
ejpam-3763	876	27	∈	∈	PROPN
ejpam-3763	876	28	b.	b.	NOUN
ejpam-3763	877	1	in	in	ADP
ejpam-3763	877	2	this	this	DET
ejpam-3763	877	3	case	case	NOUN
ejpam-3763	877	4	,	,	PUNCT
ejpam-3763	877	5	take	take	VERB
ejpam-3763	877	6	the	the	DET
ejpam-3763	877	7	function	function	NOUN
ejpam-3763	877	8	f1	f1	NOUN
ejpam-3763	877	9	=	=	SYM
ejpam-3763	877	10	(	(	PUNCT
ejpam-3763	877	11	v	v	NOUN
ejpam-3763	877	12	1	1	NUM
ejpam-3763	877	13	0	0	NUM
ejpam-3763	877	14	,	,	PUNCT
ejpam-3763	877	15	v	v	NOUN
ejpam-3763	877	16	1	1	NUM
ejpam-3763	877	17	1	1	NUM
ejpam-3763	877	18	,	,	PUNCT
ejpam-3763	877	19	v	v	NOUN
ejpam-3763	877	20	1	1	NUM
ejpam-3763	877	21	2	2	NUM
ejpam-3763	877	22	)	)	PUNCT
ejpam-3763	877	23	on	on	ADP
ejpam-3763	877	24	g	g	PROPN
ejpam-3763	877	25	�	�	PROPN
ejpam-3763	877	26	k1	k1	PROPN
ejpam-3763	877	27	given	give	VERB
ejpam-3763	877	28	by	by	ADP
ejpam-3763	877	29	f1(x	f1(x	NUM
ejpam-3763	877	30	)	)	PUNCT
ejpam-3763	877	31	=	=	PUNCT
ejpam-3763	877	32			NOUN
ejpam-3763	877	33	2	2	NUM
ejpam-3763	877	34	,	,	PUNCT
ejpam-3763	877	35	if	if	SCONJ
ejpam-3763	877	36	x	x	X
ejpam-3763	877	37	=	=	SYM
ejpam-3763	877	38	v	v	NOUN
ejpam-3763	877	39	;	;	PUNCT
ejpam-3763	877	40	0	0	NUM
ejpam-3763	877	41	,	,	PUNCT
ejpam-3763	877	42	if	if	SCONJ
ejpam-3763	877	43	x	x	SYM
ejpam-3763	877	44	∈	∈	PROPN
ejpam-3763	877	45	{	{	PUNCT
ejpam-3763	877	46	xuv	xuv	PROPN
ejpam-3763	877	47	,	,	PUNCT
ejpam-3763	877	48	xvw	xvw	NOUN
ejpam-3763	877	49	:	:	PUNCT
ejpam-3763	877	50	w	w	PROPN
ejpam-3763	877	51	∈	∈	PROPN
ejpam-3763	877	52	b	b	PROPN
ejpam-3763	877	53	}	}	PUNCT
ejpam-3763	877	54	;	;	PUNCT
ejpam-3763	877	55	1	1	NUM
ejpam-3763	877	56	,	,	PUNCT
ejpam-3763	877	57	if	if	SCONJ
ejpam-3763	877	58	x	x	PROPN
ejpam-3763	877	59	∈	∈	PROPN
ejpam-3763	877	60	b	b	NOUN
ejpam-3763	877	61	;	;	PUNCT
ejpam-3763	877	62	f(x	f(x	PROPN
ejpam-3763	877	63	)	)	PUNCT
ejpam-3763	877	64	,	,	PUNCT
ejpam-3763	877	65	if	if	SCONJ
ejpam-3763	877	66	x	x	SYM
ejpam-3763	877	67	∈	∈	PROPN
ejpam-3763	877	68	v	v	NOUN
ejpam-3763	877	69	(	(	PUNCT
ejpam-3763	877	70	g	g	PROPN
ejpam-3763	877	71	�	�	PROPN
ejpam-3763	877	72	k1	k1	NOUN
ejpam-3763	877	73	)	)	PUNCT
ejpam-3763	877	74	\	\	PUNCT
ejpam-3763	878	1	(	(	PUNCT
ejpam-3763	878	2	b	b	NOUN
ejpam-3763	878	3	∪	∪	X
ejpam-3763	878	4	{	{	PUNCT
ejpam-3763	878	5	xvw	xvw	NOUN
ejpam-3763	878	6	:	:	PUNCT
ejpam-3763	878	7	w	w	PROPN
ejpam-3763	878	8	∈	∈	PROPN
ejpam-3763	878	9	b	b	NOUN
ejpam-3763	878	10	}	}	PUNCT
ejpam-3763	878	11	)	)	PUNCT
ejpam-3763	878	12	.	.	PUNCT
ejpam-3763	879	1	then	then	ADV
ejpam-3763	879	2	f1	f1	PROPN
ejpam-3763	879	3	∈	∈	PROPN
ejpam-3763	879	4	prd(g	prd(g	PROPN
ejpam-3763	879	5	�	�	PROPN
ejpam-3763	879	6	k1	k1	PROPN
ejpam-3763	879	7	)	)	PUNCT
ejpam-3763	879	8	with	with	ADP
ejpam-3763	879	9	v	v	NUM
ejpam-3763	879	10	1	1	NUM
ejpam-3763	879	11	0	0	NUM
ejpam-3763	879	12	=	=	SYM
ejpam-3763	879	13	(	(	PUNCT
ejpam-3763	879	14	v0	v0	PROPN
ejpam-3763	879	15	\	\	PROPN
ejpam-3763	879	16	{	{	PUNCT
ejpam-3763	879	17	v	v	NOUN
ejpam-3763	879	18	}	}	PUNCT
ejpam-3763	879	19	)	)	PUNCT
ejpam-3763	879	20	∪	∪	ADP
ejpam-3763	879	21	{	{	PUNCT
ejpam-3763	879	22	xuv	xuv	PROPN
ejpam-3763	879	23	,	,	PUNCT
ejpam-3763	879	24	xvw	xvw	NOUN
ejpam-3763	879	25	:	:	PUNCT
ejpam-3763	879	26	w	w	PROPN
ejpam-3763	879	27	∈	∈	PROPN
ejpam-3763	879	28	b	b	PROPN
ejpam-3763	879	29	}	}	PUNCT
ejpam-3763	879	30	,	,	PUNCT
ejpam-3763	879	31	v	v	NOUN
ejpam-3763	879	32	1	1	NUM
ejpam-3763	879	33	1	1	NUM
ejpam-3763	879	34	=	=	SYM
ejpam-3763	879	35	(	(	PUNCT
ejpam-3763	879	36	v1	v1	PROPN
ejpam-3763	879	37	\	\	PUNCT
ejpam-3763	879	38	{	{	PUNCT
ejpam-3763	879	39	xvw	xvw	NOUN
ejpam-3763	879	40	:	:	PUNCT
ejpam-3763	879	41	w	w	PROPN
ejpam-3763	879	42	∈	∈	PROPN
ejpam-3763	879	43	b	b	NOUN
ejpam-3763	879	44	}	}	PUNCT
ejpam-3763	879	45	)	)	PUNCT
ejpam-3763	879	46	∪	∪	PROPN
ejpam-3763	879	47	b	b	NOUN
ejpam-3763	879	48	and	and	CCONJ
ejpam-3763	879	49	v	v	NUM
ejpam-3763	879	50	1	1	NUM
ejpam-3763	879	51	2	2	NUM
ejpam-3763	879	52	=	=	SYM
ejpam-3763	879	53	(	(	PUNCT
ejpam-3763	879	54	v2	v2	PROPN
ejpam-3763	879	55	\	\	PROPN
ejpam-3763	879	56	{	{	PUNCT
ejpam-3763	879	57	xuv	xuv	NOUN
ejpam-3763	879	58	}	}	PUNCT
ejpam-3763	879	59	)	)	PUNCT
ejpam-3763	879	60	∪	∪	ADP
ejpam-3763	879	61	{	{	PUNCT
ejpam-3763	879	62	v	v	NOUN
ejpam-3763	879	63	}	}	PUNCT
ejpam-3763	879	64	.	.	PUNCT
ejpam-3763	880	1	it	it	PRON
ejpam-3763	880	2	is	be	AUX
ejpam-3763	880	3	easy	easy	ADJ
ejpam-3763	880	4	to	to	PART
ejpam-3763	880	5	verify	verify	VERB
ejpam-3763	880	6	that	that	DET
ejpam-3763	880	7	f1	f1	PROPN
ejpam-3763	880	8	∈	∈	PROPN
ejpam-3763	880	9	prd(g	prd(g	PROPN
ejpam-3763	880	10	�	�	PROPN
ejpam-3763	880	11	k1	k1	NOUN
ejpam-3763	880	12	)	)	PUNCT
ejpam-3763	880	13	and	and	CCONJ
ejpam-3763	880	14	ωg	ωg	PROPN
ejpam-3763	880	15	�	�	NOUN
ejpam-3763	880	16	k1(f1	k1(f1	NOUN
ejpam-3763	880	17	)	)	PUNCT
ejpam-3763	880	18	=	=	SYM
ejpam-3763	880	19	ωg	ωg	PROPN
ejpam-3763	880	20	�	�	PROPN
ejpam-3763	880	21	k1(f	k1(f	PROPN
ejpam-3763	880	22	)	)	PUNCT
ejpam-3763	880	23	.	.	PUNCT
ejpam-3763	881	1	if	if	SCONJ
ejpam-3763	881	2	f1|g	f1|g	NUM
ejpam-3763	881	3	/∈	/∈	PUNCT
ejpam-3763	881	4	prd(g	prd(g	NUM
ejpam-3763	881	5	)	)	PUNCT
ejpam-3763	881	6	,	,	PUNCT
ejpam-3763	881	7	then	then	ADV
ejpam-3763	881	8	we	we	PRON
ejpam-3763	881	9	follow	follow	VERB
ejpam-3763	881	10	the	the	DET
ejpam-3763	881	11	same	same	ADJ
ejpam-3763	881	12	process	process	NOUN
ejpam-3763	881	13	and	and	CCONJ
ejpam-3763	881	14	obtain	obtain	VERB
ejpam-3763	881	15	f2	f2	PROPN
ejpam-3763	881	16	∈	∈	PROPN
ejpam-3763	881	17	prd(g	prd(g	PROPN
ejpam-3763	881	18	�	�	NOUN
ejpam-3763	881	19	k1	k1	NOUN
ejpam-3763	881	20	)	)	PUNCT
ejpam-3763	881	21	with	with	ADP
ejpam-3763	881	22	ωg	ωg	PROPN
ejpam-3763	881	23	�	�	PROPN
ejpam-3763	881	24	k1(f2	k1(f2	NOUN
ejpam-3763	881	25	)	)	PUNCT
ejpam-3763	882	1	=	=	SYM
ejpam-3763	882	2	ωg	ωg	NOUN
ejpam-3763	882	3	�	�	PROPN
ejpam-3763	882	4	k1(f1	k1(f1	NOUN
ejpam-3763	882	5	)	)	PUNCT
ejpam-3763	882	6	=	=	SYM
ejpam-3763	882	7	ωg	ωg	PROPN
ejpam-3763	882	8	�	�	PROPN
ejpam-3763	882	9	k1(f	k1(f	PROPN
ejpam-3763	882	10	)	)	PUNCT
ejpam-3763	882	11	.	.	PUNCT
ejpam-3763	883	1	if	if	SCONJ
ejpam-3763	883	2	necessary	necessary	ADJ
ejpam-3763	883	3	,	,	PUNCT
ejpam-3763	883	4	we	we	PRON
ejpam-3763	883	5	do	do	VERB
ejpam-3763	883	6	a	a	DET
ejpam-3763	883	7	finitely	finitely	ADV
ejpam-3763	883	8	many	many	ADJ
ejpam-3763	883	9	repetitions	repetition	NOUN
ejpam-3763	883	10	of	of	ADP
ejpam-3763	883	11	the	the	DET
ejpam-3763	883	12	process	process	NOUN
ejpam-3763	883	13	until	until	SCONJ
ejpam-3763	883	14	we	we	PRON
ejpam-3763	883	15	obtain	obtain	VERB
ejpam-3763	883	16	a	a	DET
ejpam-3763	883	17	function	function	NOUN
ejpam-3763	883	18	g	g	NOUN
ejpam-3763	883	19	=	=	NOUN
ejpam-3763	883	20	fk	fk	INTJ
ejpam-3763	883	21	∈	∈	PROPN
ejpam-3763	883	22	prd(g	prd(g	PROPN
ejpam-3763	883	23	�	�	PROPN
ejpam-3763	883	24	k1	k1	NOUN
ejpam-3763	883	25	)	)	PUNCT
ejpam-3763	883	26	for	for	ADP
ejpam-3763	883	27	which	which	PRON
ejpam-3763	883	28	ωg	ωg	PROPN
ejpam-3763	883	29	�	�	PROPN
ejpam-3763	883	30	k1(g	k1(g	NUM
ejpam-3763	883	31	)	)	PUNCT
ejpam-3763	884	1	=	=	SYM
ejpam-3763	884	2	ωg	ωg	PROPN
ejpam-3763	884	3	�	�	PROPN
ejpam-3763	884	4	k1(f	k1(f	PROPN
ejpam-3763	884	5	)	)	PUNCT
ejpam-3763	884	6	and	and	CCONJ
ejpam-3763	884	7	g|g	g|g	NOUN
ejpam-3763	884	8	∈	∈	PROPN
ejpam-3763	884	9	prd(g	prd(g	PROPN
ejpam-3763	884	10	)	)	PUNCT
ejpam-3763	884	11	.	.	PUNCT
ejpam-3763	885	1	by	by	ADP
ejpam-3763	885	2	the	the	DET
ejpam-3763	885	3	definition	definition	NOUN
ejpam-3763	885	4	of	of	ADP
ejpam-3763	885	5	α	α	PROPN
ejpam-3763	885	6	,	,	PUNCT
ejpam-3763	885	7	γpr(g	γpr(g	PROPN
ejpam-3763	885	8	�	�	NOUN
ejpam-3763	885	9	k1	k1	PROPN
ejpam-3763	885	10	)	)	PUNCT
ejpam-3763	885	11	=	=	SYM
ejpam-3763	885	12	ωg	ωg	PROPN
ejpam-3763	885	13	�	�	PROPN
ejpam-3763	885	14	k1(g	k1(g	PROPN
ejpam-3763	885	15	)	)	PUNCT
ejpam-3763	885	16	≥	≥	NOUN
ejpam-3763	885	17	α	α	NOUN
ejpam-3763	885	18	.	.	PUNCT
ejpam-3763	885	19	�	�	PROPN
ejpam-3763	885	20	the	the	DET
ejpam-3763	885	21	value	value	NOUN
ejpam-3763	885	22	of	of	ADP
ejpam-3763	885	23	γpr(g	γpr(g	PROPN
ejpam-3763	885	24	�	�	PROPN
ejpam-3763	885	25	k1	k1	PROPN
ejpam-3763	885	26	)	)	PUNCT
ejpam-3763	885	27	in	in	ADP
ejpam-3763	885	28	theorem	theorem	NOUN
ejpam-3763	885	29	2.17	2.17	NUM
ejpam-3763	885	30	is	be	AUX
ejpam-3763	885	31	determined	determine	VERB
ejpam-3763	885	32	by	by	ADP
ejpam-3763	885	33	the	the	DET
ejpam-3763	885	34	functions	function	NOUN
ejpam-3763	885	35	g	g	PROPN
ejpam-3763	885	36	∈	∈	PROPN
ejpam-3763	885	37	prd(g	prd(g	PROPN
ejpam-3763	885	38	)	)	PUNCT
ejpam-3763	885	39	for	for	ADP
ejpam-3763	885	40	which	which	PRON
ejpam-3763	885	41	the	the	DET
ejpam-3763	885	42	sets	set	NOUN
ejpam-3763	885	43	e22	e22	NOUN
ejpam-3763	885	44	and	and	CCONJ
ejpam-3763	885	45	e11	e11	NOUN
ejpam-3763	885	46	are	be	AUX
ejpam-3763	885	47	empty	empty	ADJ
ejpam-3763	885	48	.	.	PUNCT
ejpam-3763	886	1	with	with	ADP
ejpam-3763	886	2	this	this	DET
ejpam-3763	886	3	observation	observation	NOUN
ejpam-3763	886	4	,	,	PUNCT
ejpam-3763	886	5	it	it	PRON
ejpam-3763	886	6	can	can	AUX
ejpam-3763	886	7	readily	readily	ADV
ejpam-3763	886	8	be	be	AUX
ejpam-3763	886	9	verified	verify	VERB
ejpam-3763	886	10	that	that	SCONJ
ejpam-3763	886	11	for	for	ADP
ejpam-3763	886	12	n	n	PRON
ejpam-3763	886	13	≥	≥	NOUN
ejpam-3763	886	14	1	1	NUM
ejpam-3763	886	15	and	and	CCONJ
ejpam-3763	886	16	m	m	PROPN
ejpam-3763	886	17	≥	≥	NOUN
ejpam-3763	886	18	3	3	NUM
ejpam-3763	886	19	,	,	PUNCT
ejpam-3763	886	20	γpr(pn	γpr(pn	NOUN
ejpam-3763	886	21	�	�	NOUN
ejpam-3763	886	22	k1	k1	NOUN
ejpam-3763	886	23	)	)	PUNCT
ejpam-3763	886	24	=	=	PUNCT
ejpam-3763	886	25	bn−	bn−	PUNCT
ejpam-3763	886	26	1	1	NUM
ejpam-3763	886	27	3	3	NUM
ejpam-3763	886	28	c+	c+	X
ejpam-3763	886	29	γpr(pn	γpr(pn	NOUN
ejpam-3763	886	30	)	)	PUNCT
ejpam-3763	886	31	and	and	CCONJ
ejpam-3763	886	32	γpr(cm	γpr(cm	NOUN
ejpam-3763	886	33	�	�	NOUN
ejpam-3763	886	34	k1	k1	PROPN
ejpam-3763	886	35	)	)	PUNCT
ejpam-3763	886	36	=	=	SYM
ejpam-3763	887	1	dn	dn	NOUN
ejpam-3763	887	2	3	3	NUM
ejpam-3763	887	3	e+	e+	X
ejpam-3763	887	4	γpr(cm	γpr(cm	NUM
ejpam-3763	887	5	)	)	PUNCT
ejpam-3763	887	6	.	.	PUNCT
ejpam-3763	888	1	2.5	2.5	NUM
ejpam-3763	888	2	.	.	PUNCT
ejpam-3763	889	1	on	on	ADP
ejpam-3763	889	2	the	the	DET
ejpam-3763	889	3	composition	composition	NOUN
ejpam-3763	889	4	of	of	ADP
ejpam-3763	889	5	graphs	graph	NOUN
ejpam-3763	889	6	given	give	VERB
ejpam-3763	889	7	s	s	PRON
ejpam-3763	889	8	⊆	⊆	NUM
ejpam-3763	889	9	v	v	NOUN
ejpam-3763	889	10	(	(	PUNCT
ejpam-3763	889	11	g[h	g[h	PROPN
ejpam-3763	889	12	]	]	PUNCT
ejpam-3763	889	13	)	)	PUNCT
ejpam-3763	889	14	,	,	PUNCT
ejpam-3763	889	15	we	we	PRON
ejpam-3763	889	16	write	write	VERB
ejpam-3763	889	17	sg	sg	X
ejpam-3763	889	18	=	=	PUNCT
ejpam-3763	889	19	{	{	PUNCT
ejpam-3763	889	20	x	x	PUNCT
ejpam-3763	889	21	∈	∈	PROPN
ejpam-3763	889	22	v	v	NOUN
ejpam-3763	889	23	(	(	PUNCT
ejpam-3763	889	24	g	g	NOUN
ejpam-3763	889	25	)	)	PUNCT
ejpam-3763	889	26	:	:	PUNCT
ejpam-3763	889	27	(	(	PUNCT
ejpam-3763	889	28	x	x	X
ejpam-3763	889	29	,	,	PUNCT
ejpam-3763	889	30	y	y	PROPN
ejpam-3763	889	31	)	)	PUNCT
ejpam-3763	889	32	∈	∈	PROPN
ejpam-3763	889	33	s	s	PART
ejpam-3763	889	34	for	for	ADP
ejpam-3763	889	35	some	some	DET
ejpam-3763	889	36	y	y	PROPN
ejpam-3763	889	37	∈	∈	PROPN
ejpam-3763	889	38	v	v	ADP
ejpam-3763	889	39	(	(	PUNCT
ejpam-3763	889	40	h	h	NOUN
ejpam-3763	889	41	)	)	PUNCT
ejpam-3763	889	42	}	}	PUNCT
ejpam-3763	889	43	,	,	PUNCT
ejpam-3763	889	44	which	which	PRON
ejpam-3763	889	45	is	be	AUX
ejpam-3763	889	46	called	call	VERB
ejpam-3763	889	47	the	the	DET
ejpam-3763	889	48	projection	projection	NOUN
ejpam-3763	889	49	of	of	ADP
ejpam-3763	889	50	g	g	NOUN
ejpam-3763	889	51	on	on	ADP
ejpam-3763	889	52	g[h	g[h	NOUN
ejpam-3763	889	53	]	]	PUNCT
ejpam-3763	889	54	.	.	PUNCT
ejpam-3763	890	1	proposition	proposition	NOUN
ejpam-3763	890	2	2.18	2.18	NUM
ejpam-3763	890	3	.	.	PUNCT
ejpam-3763	891	1	let	let	VERB
ejpam-3763	891	2	g	g	NOUN
ejpam-3763	891	3	and	and	CCONJ
ejpam-3763	891	4	h	h	NOUN
ejpam-3763	891	5	be	be	AUX
ejpam-3763	891	6	connected	connect	VERB
ejpam-3763	891	7	graphs	graph	NOUN
ejpam-3763	891	8	,	,	PUNCT
ejpam-3763	891	9	g	g	NOUN
ejpam-3763	891	10	noncomplete	noncomplete	NOUN
ejpam-3763	891	11	and	and	CCONJ
ejpam-3763	891	12	h	h	NOUN
ejpam-3763	891	13	of	of	ADP
ejpam-3763	891	14	order	order	NOUN
ejpam-3763	891	15	n	n	PRON
ejpam-3763	891	16	with	with	ADP
ejpam-3763	891	17	γ(h	γ(h	NOUN
ejpam-3763	891	18	)	)	PUNCT
ejpam-3763	891	19	=	=	SYM
ejpam-3763	892	1	1	1	X
ejpam-3763	892	2	.	.	PUNCT
ejpam-3763	893	1	then	then	ADV
ejpam-3763	893	2	γpr(g[h	γpr(g[h	NUM
ejpam-3763	893	3	]	]	PUNCT
ejpam-3763	893	4	)	)	PUNCT
ejpam-3763	893	5	≤	≤	NOUN
ejpam-3763	893	6	α	α	X
ejpam-3763	893	7	,	,	PUNCT
ejpam-3763	893	8	where	where	SCONJ
ejpam-3763	893	9	α	α	NOUN
ejpam-3763	893	10	=	=	SYM
ejpam-3763	893	11	min{(n−	min{(n−	PROPN
ejpam-3763	893	12	1	1	NUM
ejpam-3763	893	13	)	)	PUNCT
ejpam-3763	893	14	(	(	PUNCT
ejpam-3763	893	15	|v1|+	|v1|+	ADP
ejpam-3763	893	16	|v2	|v2	NOUN
ejpam-3763	893	17	∩ng(v2)|	∩ng(v2)|	NOUN
ejpam-3763	893	18	)	)	PUNCT
ejpam-3763	893	19	+	+	CCONJ
ejpam-3763	893	20	ωg(f	ωg(f	NOUN
ejpam-3763	893	21	)	)	PUNCT
ejpam-3763	893	22	:	:	PUNCT
ejpam-3763	894	1	f	f	X
ejpam-3763	894	2	=	=	SYM
ejpam-3763	894	3	(	(	PUNCT
ejpam-3763	894	4	v0	v0	PROPN
ejpam-3763	894	5	,	,	PUNCT
ejpam-3763	894	6	v1	v1	NOUN
ejpam-3763	894	7	,	,	PUNCT
ejpam-3763	894	8	v2	v2	NOUN
ejpam-3763	894	9	)	)	PUNCT
ejpam-3763	894	10	∈	∈	PROPN
ejpam-3763	894	11	prd(g	prd(g	PROPN
ejpam-3763	894	12	)	)	PUNCT
ejpam-3763	894	13	}	}	PUNCT
ejpam-3763	894	14	.	.	PUNCT
ejpam-3763	895	1	proof	proof	NOUN
ejpam-3763	895	2	:	:	PUNCT
ejpam-3763	895	3	let	let	VERB
ejpam-3763	895	4	v	v	NUM
ejpam-3763	895	5	∈	∈	PROPN
ejpam-3763	895	6	v	v	NOUN
ejpam-3763	895	7	(	(	PUNCT
ejpam-3763	895	8	h	h	NOUN
ejpam-3763	895	9	)	)	PUNCT
ejpam-3763	895	10	for	for	ADP
ejpam-3763	895	11	which	which	PRON
ejpam-3763	895	12	nh	nh	NOUN
ejpam-3763	896	1	[	[	X
ejpam-3763	896	2	v	v	X
ejpam-3763	896	3	]	]	X
ejpam-3763	896	4	=	=	SYM
ejpam-3763	896	5	v	v	ADJ
ejpam-3763	896	6	(	(	PUNCT
ejpam-3763	896	7	h	h	NOUN
ejpam-3763	896	8	)	)	PUNCT
ejpam-3763	896	9	.	.	PUNCT
ejpam-3763	897	1	let	let	VERB
ejpam-3763	897	2	f	f	PROPN
ejpam-3763	897	3	=	=	SYM
ejpam-3763	897	4	(	(	PUNCT
ejpam-3763	897	5	v0	v0	PROPN
ejpam-3763	897	6	,	,	PUNCT
ejpam-3763	897	7	v1	v1	NOUN
ejpam-3763	897	8	,	,	PUNCT
ejpam-3763	897	9	v2	v2	NOUN
ejpam-3763	897	10	)	)	PUNCT
ejpam-3763	897	11	∈	∈	PROPN
ejpam-3763	897	12	prd(g	prd(g	PROPN
ejpam-3763	897	13	)	)	PUNCT
ejpam-3763	897	14	such	such	ADJ
ejpam-3763	897	15	that	that	DET
ejpam-3763	897	16	v2	v2	PROPN
ejpam-3763	897	17	6=	6=	ADP
ejpam-3763	897	18	∅.	∅.	AUX
ejpam-3763	897	19	define	define	VERB
ejpam-3763	897	20	g	g	PROPN
ejpam-3763	897	21	=	=	SYM
ejpam-3763	897	22	(	(	PUNCT
ejpam-3763	897	23	v	v	NOUN
ejpam-3763	897	24	∗0	∗0	PROPN
ejpam-3763	897	25	,	,	PUNCT
ejpam-3763	897	26	v	v	NOUN
ejpam-3763	897	27	∗	∗	NOUN
ejpam-3763	897	28	1	1	NUM
ejpam-3763	897	29	,	,	PUNCT
ejpam-3763	897	30	v	v	NOUN
ejpam-3763	897	31	∗	∗	NOUN
ejpam-3763	897	32	2	2	NUM
ejpam-3763	897	33	)	)	PUNCT
ejpam-3763	897	34	on	on	ADP
ejpam-3763	897	35	g[h	g[h	NOUN
ejpam-3763	897	36	]	]	PUNCT
ejpam-3763	897	37	by	by	ADP
ejpam-3763	897	38	g((x	g((x	PROPN
ejpam-3763	897	39	,	,	PUNCT
ejpam-3763	897	40	y	y	PROPN
ejpam-3763	897	41	)	)	PUNCT
ejpam-3763	897	42	)	)	PUNCT
ejpam-3763	898	1	=	=	PUNCT
ejpam-3763	899	1			NOUN
ejpam-3763	899	2	0	0	NUM
ejpam-3763	899	3	,	,	PUNCT
ejpam-3763	899	4	if	if	SCONJ
ejpam-3763	899	5	(	(	PUNCT
ejpam-3763	899	6	x	x	SYM
ejpam-3763	899	7	∈	∈	PROPN
ejpam-3763	899	8	v2	v2	PROPN
ejpam-3763	899	9	\ng(v2	\ng(v2	PROPN
ejpam-3763	899	10	)	)	PUNCT
ejpam-3763	899	11	∧	∧	PROPN
ejpam-3763	899	12	y	y	PROPN
ejpam-3763	899	13	6=	6=	PROPN
ejpam-3763	899	14	v	v	NOUN
ejpam-3763	899	15	)	)	PUNCT
ejpam-3763	899	16	∨	∨	NOUN
ejpam-3763	899	17	(	(	PUNCT
ejpam-3763	899	18	x	x	SYM
ejpam-3763	899	19	∈	∈	PROPN
ejpam-3763	899	20	v0	v0	NOUN
ejpam-3763	899	21	)	)	PUNCT
ejpam-3763	899	22	;	;	PUNCT
ejpam-3763	899	23	1	1	X
ejpam-3763	899	24	,	,	PUNCT
ejpam-3763	899	25	if	if	SCONJ
ejpam-3763	899	26	(	(	PUNCT
ejpam-3763	899	27	x	x	SYM
ejpam-3763	899	28	∈	∈	NOUN
ejpam-3763	899	29	v2	v2	PROPN
ejpam-3763	899	30	∩ng(v2	∩ng(v2	NOUN
ejpam-3763	899	31	)	)	PUNCT
ejpam-3763	899	32	∧	∧	PROPN
ejpam-3763	899	33	y	y	PROPN
ejpam-3763	899	34	6=	6=	PROPN
ejpam-3763	899	35	v	v	NOUN
ejpam-3763	899	36	)	)	PUNCT
ejpam-3763	899	37	∨	∨	NOUN
ejpam-3763	899	38	(	(	PUNCT
ejpam-3763	899	39	x	x	SYM
ejpam-3763	899	40	∈	∈	PROPN
ejpam-3763	899	41	v1	v1	NOUN
ejpam-3763	899	42	)	)	PUNCT
ejpam-3763	899	43	;	;	PUNCT
ejpam-3763	899	44	2	2	X
ejpam-3763	899	45	,	,	PUNCT
ejpam-3763	899	46	if	if	SCONJ
ejpam-3763	899	47	x	x	PUNCT
ejpam-3763	899	48	∈	∈	PROPN
ejpam-3763	899	49	v2	v2	NOUN
ejpam-3763	899	50	and	and	CCONJ
ejpam-3763	899	51	y	y	PROPN
ejpam-3763	899	52	=	=	PROPN
ejpam-3763	899	53	v.	v.	NOUN
ejpam-3763	899	54	with	with	ADP
ejpam-3763	899	55	v	v	NUM
ejpam-3763	899	56	∗0	∗0	NOUN
ejpam-3763	899	57	=	=	SYM
ejpam-3763	899	58	(	(	PUNCT
ejpam-3763	899	59	(	(	PUNCT
ejpam-3763	899	60	v2	v2	PROPN
ejpam-3763	899	61	\ng(v2))×	\ng(v2))×	PROPN
ejpam-3763	899	62	(	(	PUNCT
ejpam-3763	899	63	v	v	NOUN
ejpam-3763	899	64	(	(	PUNCT
ejpam-3763	899	65	h	h	NOUN
ejpam-3763	899	66	)	)	PUNCT
ejpam-3763	899	67	\	\	NOUN
ejpam-3763	899	68	{	{	PUNCT
ejpam-3763	899	69	v	v	NOUN
ejpam-3763	899	70	}	}	PUNCT
ejpam-3763	899	71	)	)	PUNCT
ejpam-3763	899	72	)	)	PUNCT
ejpam-3763	899	73	∪	∪	NOUN
ejpam-3763	899	74	(	(	PUNCT
ejpam-3763	899	75	v0	v0	NOUN
ejpam-3763	899	76	×	×	NOUN
ejpam-3763	899	77	v	v	NOUN
ejpam-3763	899	78	(	(	PUNCT
ejpam-3763	899	79	h	h	NOUN
ejpam-3763	899	80	)	)	PUNCT
ejpam-3763	899	81	)	)	PUNCT
ejpam-3763	899	82	,	,	PUNCT
ejpam-3763	899	83	v	v	ADP
ejpam-3763	899	84	∗2	∗2	PROPN
ejpam-3763	899	85	=	=	SYM
ejpam-3763	900	1	v2	v2	VERB
ejpam-3763	900	2	×	×	NOUN
ejpam-3763	900	3	{	{	PUNCT
ejpam-3763	900	4	v	v	NOUN
ejpam-3763	900	5	}	}	PUNCT
ejpam-3763	900	6	and	and	CCONJ
ejpam-3763	900	7	v	v	X
ejpam-3763	900	8	∗1	∗1	NOUN
ejpam-3763	900	9	=	=	PUNCT
ejpam-3763	900	10	(	(	PUNCT
ejpam-3763	900	11	v1	v1	VERB
ejpam-3763	900	12	∪	∪	ADJ
ejpam-3763	900	13	v	v	NOUN
ejpam-3763	900	14	(	(	PUNCT
ejpam-3763	900	15	h	h	NOUN
ejpam-3763	900	16	)	)	PUNCT
ejpam-3763	900	17	)	)	PUNCT
ejpam-3763	900	18	∪	∪	X
ejpam-3763	900	19	(	(	PUNCT
ejpam-3763	900	20	(	(	PUNCT
ejpam-3763	900	21	v2	v2	INTJ
ejpam-3763	900	22	∩ng(v2))×	∩ng(v2))×	X
ejpam-3763	900	23	(	(	PUNCT
ejpam-3763	900	24	v	v	NOUN
ejpam-3763	900	25	(	(	PUNCT
ejpam-3763	900	26	h	h	NOUN
ejpam-3763	900	27	)	)	PUNCT
ejpam-3763	900	28	\	\	NOUN
ejpam-3763	900	29	{	{	PUNCT
ejpam-3763	900	30	v	v	NOUN
ejpam-3763	900	31	}	}	PUNCT
ejpam-3763	900	32	)	)	PUNCT
ejpam-3763	900	33	)	)	PUNCT
ejpam-3763	900	34	.	.	PUNCT
ejpam-3763	901	1	let	let	VERB
ejpam-3763	901	2	(	(	PUNCT
ejpam-3763	901	3	x	x	NOUN
ejpam-3763	901	4	,	,	PUNCT
ejpam-3763	901	5	y	y	NOUN
ejpam-3763	901	6	)	)	PUNCT
ejpam-3763	901	7	∈	∈	PROPN
ejpam-3763	901	8	v	v	ADP
ejpam-3763	901	9	∗0	∗0	PROPN
ejpam-3763	901	10	.	.	PUNCT
ejpam-3763	902	1	if	if	SCONJ
ejpam-3763	902	2	x	x	SYM
ejpam-3763	902	3	∈	∈	PROPN
ejpam-3763	902	4	v2	v2	PROPN
ejpam-3763	902	5	,	,	PUNCT
ejpam-3763	902	6	then	then	ADV
ejpam-3763	902	7	x	x	SYM
ejpam-3763	902	8	/∈	/∈	PUNCT
ejpam-3763	902	9	ng(v2	ng(v2	NOUN
ejpam-3763	902	10	)	)	PUNCT
ejpam-3763	902	11	so	so	SCONJ
ejpam-3763	902	12	that	that	SCONJ
ejpam-3763	902	13	ng[h]((x	ng[h]((x	NOUN
ejpam-3763	902	14	,	,	PUNCT
ejpam-3763	902	15	y	y	NOUN
ejpam-3763	902	16	)	)	PUNCT
ejpam-3763	902	17	)	)	PUNCT
ejpam-3763	902	18	∩	∩	PROPN
ejpam-3763	902	19	v	v	ADP
ejpam-3763	902	20	∗2	∗2	PROPN
ejpam-3763	902	21	=	=	PRON
ejpam-3763	902	22	{	{	PUNCT
ejpam-3763	902	23	(	(	PUNCT
ejpam-3763	902	24	x	x	NOUN
ejpam-3763	902	25	,	,	PUNCT
ejpam-3763	902	26	v	v	NOUN
ejpam-3763	902	27	)	)	PUNCT
ejpam-3763	902	28	}	}	PUNCT
ejpam-3763	902	29	.	.	PUNCT
ejpam-3763	903	1	if	if	SCONJ
ejpam-3763	903	2	x	x	PROPN
ejpam-3763	903	3	∈	∈	PROPN
ejpam-3763	903	4	v0	v0	NOUN
ejpam-3763	903	5	,	,	PUNCT
ejpam-3763	903	6	then	then	ADV
ejpam-3763	903	7	there	there	PRON
ejpam-3763	903	8	exists	exist	VERB
ejpam-3763	903	9	u	u	PROPN
ejpam-3763	903	10	∈	∈	PROPN
ejpam-3763	903	11	v2	v2	NOUN
ejpam-3763	904	1	such	such	ADJ
ejpam-3763	904	2	that	that	PRON
ejpam-3763	904	3	ng(x	ng(x	NUM
ejpam-3763	904	4	)	)	PUNCT
ejpam-3763	904	5	∩	∩	NOUN
ejpam-3763	904	6	v2	v2	NOUN
ejpam-3763	904	7	=	=	SYM
ejpam-3763	904	8	{	{	PUNCT
ejpam-3763	904	9	u	u	NOUN
ejpam-3763	904	10	}	}	PUNCT
ejpam-3763	904	11	,	,	PUNCT
ejpam-3763	904	12	which	which	PRON
ejpam-3763	904	13	implies	imply	VERB
ejpam-3763	904	14	that	that	SCONJ
ejpam-3763	904	15	ng[h]((x	ng[h]((x	NOUN
ejpam-3763	904	16	,	,	PUNCT
ejpam-3763	904	17	y	y	NOUN
ejpam-3763	904	18	)	)	PUNCT
ejpam-3763	904	19	)	)	PUNCT
ejpam-3763	904	20	∩	∩	PROPN
ejpam-3763	904	21	v	v	ADP
ejpam-3763	904	22	∗2	∗2	PROPN
ejpam-3763	904	23	=	=	PRON
ejpam-3763	904	24	{	{	PUNCT
ejpam-3763	904	25	(	(	PUNCT
ejpam-3763	904	26	u	u	NOUN
ejpam-3763	904	27	,	,	PUNCT
ejpam-3763	904	28	v	v	NOUN
ejpam-3763	904	29	)	)	PUNCT
ejpam-3763	904	30	}	}	PUNCT
ejpam-3763	904	31	.	.	PUNCT
ejpam-3763	905	1	thus	thus	ADV
ejpam-3763	905	2	,	,	PUNCT
ejpam-3763	905	3	g	g	PROPN
ejpam-3763	905	4	∈	∈	PROPN
ejpam-3763	905	5	prd(g[h	prd(g[h	NUM
ejpam-3763	905	6	]	]	PUNCT
ejpam-3763	905	7	)	)	PUNCT
ejpam-3763	905	8	.	.	PUNCT
ejpam-3763	906	1	therefore	therefore	ADV
ejpam-3763	906	2	,	,	PUNCT
ejpam-3763	906	3	γpr(g[h	γpr(g[h	NUM
ejpam-3763	906	4	]	]	PUNCT
ejpam-3763	906	5	)	)	PUNCT
ejpam-3763	906	6	≤	≤	NOUN
ejpam-3763	906	7	|v	|v	VERB
ejpam-3763	906	8	∗1	∗1	PROPN
ejpam-3763	906	9	|+2|v	|+2|v	NOUN
ejpam-3763	906	10	∗2	∗2	PROPN
ejpam-3763	906	11	|	|	ADV
ejpam-3763	906	12	=	=	SYM
ejpam-3763	906	13	(	(	PUNCT
ejpam-3763	906	14	n−1	n−1	PROPN
ejpam-3763	906	15	)	)	PUNCT
ejpam-3763	906	16	(	(	PUNCT
ejpam-3763	906	17	|v1|+	|v1|+	ADP
ejpam-3763	906	18	|v2	|v2	NOUN
ejpam-3763	906	19	∩ng(v2)|)+ωg(f	∩ng(v2)|)+ωg(f	NOUN
ejpam-3763	906	20	)	)	PUNCT
ejpam-3763	906	21	.	.	PUNCT
ejpam-3763	907	1	since	since	SCONJ
ejpam-3763	907	2	f	f	PROPN
ejpam-3763	907	3	is	be	AUX
ejpam-3763	907	4	arbitrary	arbitrary	ADJ
ejpam-3763	907	5	,	,	PUNCT
ejpam-3763	907	6	the	the	DET
ejpam-3763	907	7	desired	desire	VERB
ejpam-3763	907	8	inequality	inequality	NOUN
ejpam-3763	907	9	is	be	AUX
ejpam-3763	907	10	established	establish	VERB
ejpam-3763	907	11	.	.	PUNCT
ejpam-3763	908	1	�	�	PROPN
ejpam-3763	908	2	l.	l.	PROPN
ejpam-3763	908	3	paleta	paleta	PROPN
ejpam-3763	908	4	,	,	PUNCT
ejpam-3763	908	5	f.	f.	PROPN
ejpam-3763	908	6	jamil	jamil	PROPN
ejpam-3763	908	7	/	/	SYM
ejpam-3763	908	8	eur	eur	PROPN
ejpam-3763	908	9	.	.	PUNCT
ejpam-3763	909	1	j.	j.	PROPN
ejpam-3763	909	2	pure	pure	PROPN
ejpam-3763	909	3	appl	appl	PROPN
ejpam-3763	909	4	.	.	PROPN
ejpam-3763	909	5	math	math	PROPN
ejpam-3763	909	6	,	,	PUNCT
ejpam-3763	909	7	13	13	NUM
ejpam-3763	909	8	(	(	PUNCT
ejpam-3763	909	9	3	3	NUM
ejpam-3763	909	10	)	)	PUNCT
ejpam-3763	909	11	(	(	PUNCT
ejpam-3763	909	12	2020	2020	NUM
ejpam-3763	909	13	)	)	PUNCT
ejpam-3763	909	14	,	,	PUNCT
ejpam-3763	909	15	529	529	NUM
ejpam-3763	909	16	-	-	SYM
ejpam-3763	909	17	548	548	NUM
ejpam-3763	909	18	546	546	NUM
ejpam-3763	909	19	proposition	proposition	NOUN
ejpam-3763	909	20	2.19	2.19	NUM
ejpam-3763	909	21	.	.	PUNCT
ejpam-3763	910	1	let	let	VERB
ejpam-3763	910	2	g	g	PRON
ejpam-3763	910	3	be	be	AUX
ejpam-3763	910	4	a	a	DET
ejpam-3763	910	5	nontrivial	nontrivial	ADJ
ejpam-3763	910	6	connected	connect	VERB
ejpam-3763	910	7	graph	graph	NOUN
ejpam-3763	910	8	and	and	CCONJ
ejpam-3763	910	9	p	p	PRON
ejpam-3763	910	10	≥	≥	NUM
ejpam-3763	910	11	2	2	NUM
ejpam-3763	910	12	.	.	PUNCT
ejpam-3763	911	1	then	then	ADV
ejpam-3763	911	2	γpr(g[kp	γpr(g[kp	PROPN
ejpam-3763	911	3	]	]	PUNCT
ejpam-3763	911	4	)	)	PUNCT
ejpam-3763	911	5	=	=	SYM
ejpam-3763	911	6	α	α	X
ejpam-3763	911	7	,	,	PUNCT
ejpam-3763	911	8	where	where	SCONJ
ejpam-3763	911	9	α	α	NOUN
ejpam-3763	911	10	=	=	SYM
ejpam-3763	911	11	min{(n−	min{(n−	PROPN
ejpam-3763	911	12	1	1	NUM
ejpam-3763	911	13	)	)	PUNCT
ejpam-3763	911	14	(	(	PUNCT
ejpam-3763	911	15	|v1|+	|v1|+	ADP
ejpam-3763	911	16	|v2	|v2	NOUN
ejpam-3763	911	17	∩ng(v2)|	∩ng(v2)|	NOUN
ejpam-3763	911	18	)	)	PUNCT
ejpam-3763	912	1	+	+	CCONJ
ejpam-3763	912	2	ωg(f	ωg(f	NOUN
ejpam-3763	912	3	)	)	PUNCT
ejpam-3763	912	4	:	:	PUNCT
ejpam-3763	913	1	f	f	X
ejpam-3763	913	2	=	=	SYM
ejpam-3763	913	3	(	(	PUNCT
ejpam-3763	913	4	v0	v0	PROPN
ejpam-3763	913	5	,	,	PUNCT
ejpam-3763	913	6	v1	v1	NOUN
ejpam-3763	913	7	,	,	PUNCT
ejpam-3763	913	8	v2	v2	NOUN
ejpam-3763	913	9	)	)	PUNCT
ejpam-3763	913	10	∈	∈	PROPN
ejpam-3763	913	11	prd(g	prd(g	PROPN
ejpam-3763	913	12	)	)	PUNCT
ejpam-3763	913	13	}	}	PUNCT
ejpam-3763	913	14	.	.	PUNCT
ejpam-3763	914	1	proof	proof	NOUN
ejpam-3763	914	2	:	:	PUNCT
ejpam-3763	914	3	let	let	VERB
ejpam-3763	914	4	f	f	PROPN
ejpam-3763	914	5	=	=	SYM
ejpam-3763	914	6	(	(	PUNCT
ejpam-3763	914	7	v0	v0	PROPN
ejpam-3763	914	8	,	,	PUNCT
ejpam-3763	914	9	v1	v1	NOUN
ejpam-3763	914	10	,	,	PUNCT
ejpam-3763	914	11	v2	v2	PROPN
ejpam-3763	914	12	)	)	PUNCT
ejpam-3763	914	13	be	be	AUX
ejpam-3763	914	14	a	a	DET
ejpam-3763	914	15	γrp	γrp	VERB
ejpam-3763	914	16	-function	-function	NOUN
ejpam-3763	914	17	on	on	ADP
ejpam-3763	914	18	v	v	NOUN
ejpam-3763	914	19	(	(	PUNCT
ejpam-3763	914	20	g[h	g[h	PROPN
ejpam-3763	914	21	]	]	PUNCT
ejpam-3763	914	22	)	)	PUNCT
ejpam-3763	914	23	.	.	PUNCT
ejpam-3763	915	1	then	then	ADV
ejpam-3763	915	2	v2	v2	VERB
ejpam-3763	915	3	6=	6=	NOUN
ejpam-3763	915	4	∅	∅	NOUN
ejpam-3763	915	5	and	and	CCONJ
ejpam-3763	915	6	v0	v0	NOUN
ejpam-3763	915	7	6=	6=	X
ejpam-3763	915	8	∅.	∅.	ADP
ejpam-3763	915	9	first	first	ADV
ejpam-3763	915	10	,	,	PUNCT
ejpam-3763	915	11	we	we	PRON
ejpam-3763	915	12	claim	claim	VERB
ejpam-3763	915	13	that	that	SCONJ
ejpam-3763	915	14	(	(	PUNCT
ejpam-3763	915	15	v0)g	v0)g	PROPN
ejpam-3763	915	16	∩	∩	NOUN
ejpam-3763	915	17	(	(	PUNCT
ejpam-3763	915	18	v1)g	v1)g	NOUN
ejpam-3763	915	19	=	=	PUNCT
ejpam-3763	915	20	∅.	∅.	NOUN
ejpam-3763	915	21	suppose	suppose	VERB
ejpam-3763	915	22	not	not	PART
ejpam-3763	915	23	,	,	PUNCT
ejpam-3763	915	24	and	and	CCONJ
ejpam-3763	915	25	let	let	VERB
ejpam-3763	915	26	(	(	PUNCT
ejpam-3763	915	27	x	x	NOUN
ejpam-3763	915	28	,	,	PUNCT
ejpam-3763	915	29	y	y	NOUN
ejpam-3763	915	30	)	)	PUNCT
ejpam-3763	915	31	∈	∈	NOUN
ejpam-3763	915	32	v1	v1	NOUN
ejpam-3763	915	33	be	be	VERB
ejpam-3763	915	34	such	such	ADJ
ejpam-3763	915	35	that	that	SCONJ
ejpam-3763	915	36	(	(	PUNCT
ejpam-3763	915	37	x	x	X
ejpam-3763	915	38	,	,	PUNCT
ejpam-3763	915	39	z	z	NOUN
ejpam-3763	915	40	)	)	PUNCT
ejpam-3763	915	41	∈	∈	PROPN
ejpam-3763	915	42	v0	v0	NOUN
ejpam-3763	915	43	for	for	ADP
ejpam-3763	915	44	some	some	DET
ejpam-3763	915	45	z	z	NOUN
ejpam-3763	915	46	6=	6=	PUNCT
ejpam-3763	916	1	y.	y.	NOUN
ejpam-3763	916	2	there	there	PRON
ejpam-3763	916	3	exists	exist	VERB
ejpam-3763	916	4	unique	unique	ADJ
ejpam-3763	916	5	(	(	PUNCT
ejpam-3763	916	6	u	u	NOUN
ejpam-3763	916	7	,	,	PUNCT
ejpam-3763	916	8	v	v	NOUN
ejpam-3763	916	9	)	)	PUNCT
ejpam-3763	916	10	∈	∈	NOUN
ejpam-3763	916	11	v2	v2	NOUN
ejpam-3763	916	12	for	for	ADP
ejpam-3763	916	13	which	which	PRON
ejpam-3763	916	14	(	(	PUNCT
ejpam-3763	916	15	x	x	X
ejpam-3763	916	16	,	,	PUNCT
ejpam-3763	916	17	z)(u	z)(u	NUM
ejpam-3763	916	18	,	,	PUNCT
ejpam-3763	916	19	v	v	NOUN
ejpam-3763	916	20	)	)	PUNCT
ejpam-3763	916	21	∈	∈	NOUN
ejpam-3763	916	22	e(g[kp	e(g[kp	NOUN
ejpam-3763	916	23	]	]	X
ejpam-3763	916	24	.	.	PUNCT
ejpam-3763	917	1	if	if	SCONJ
ejpam-3763	917	2	u	u	PRON
ejpam-3763	917	3	=	=	SYM
ejpam-3763	917	4	x	x	NOUN
ejpam-3763	917	5	,	,	PUNCT
ejpam-3763	917	6	then	then	ADV
ejpam-3763	917	7	since	since	SCONJ
ejpam-3763	917	8	y	y	PROPN
ejpam-3763	917	9	6=	6=	PROPN
ejpam-3763	917	10	v	v	PROPN
ejpam-3763	917	11	,	,	PUNCT
ejpam-3763	917	12	(	(	PUNCT
ejpam-3763	917	13	x	x	X
ejpam-3763	917	14	,	,	PUNCT
ejpam-3763	917	15	y)(u	y)(u	ADJ
ejpam-3763	917	16	,	,	PUNCT
ejpam-3763	917	17	v	v	NOUN
ejpam-3763	917	18	)	)	PUNCT
ejpam-3763	917	19	∈	∈	NOUN
ejpam-3763	917	20	e(g[kp	e(g[kp	NOUN
ejpam-3763	917	21	]	]	PUNCT
ejpam-3763	917	22	)	)	PUNCT
ejpam-3763	917	23	.	.	PUNCT
ejpam-3763	918	1	thus	thus	ADV
ejpam-3763	918	2	,	,	PUNCT
ejpam-3763	918	3	whether	whether	SCONJ
ejpam-3763	918	4	u	u	PRON
ejpam-3763	918	5	=	=	NOUN
ejpam-3763	918	6	x	x	X
ejpam-3763	918	7	or	or	CCONJ
ejpam-3763	918	8	x	x	SYM
ejpam-3763	918	9	6=	6=	ADP
ejpam-3763	918	10	u	u	PROPN
ejpam-3763	918	11	,	,	PUNCT
ejpam-3763	918	12	(	(	PUNCT
ejpam-3763	918	13	x	x	X
ejpam-3763	918	14	,	,	PUNCT
ejpam-3763	918	15	y)(u	y)(u	ADJ
ejpam-3763	918	16	,	,	PUNCT
ejpam-3763	918	17	v	v	NOUN
ejpam-3763	918	18	)	)	PUNCT
ejpam-3763	918	19	∈	∈	NOUN
ejpam-3763	918	20	e(g[kp	e(g[kp	NOUN
ejpam-3763	918	21	]	]	PUNCT
ejpam-3763	918	22	)	)	PUNCT
ejpam-3763	918	23	.	.	PUNCT
ejpam-3763	919	1	by	by	ADP
ejpam-3763	919	2	proposition	proposition	NOUN
ejpam-3763	919	3	2.1	2.1	NUM
ejpam-3763	919	4	,	,	PUNCT
ejpam-3763	919	5	there	there	PRON
ejpam-3763	919	6	exists	exist	VERB
ejpam-3763	919	7	(	(	PUNCT
ejpam-3763	919	8	a	a	DET
ejpam-3763	919	9	,	,	PUNCT
ejpam-3763	919	10	b	b	NOUN
ejpam-3763	919	11	)	)	PUNCT
ejpam-3763	919	12	∈	∈	PROPN
ejpam-3763	919	13	v2	v2	NOUN
ejpam-3763	919	14	\	\	PROPN
ejpam-3763	919	15	{	{	PUNCT
ejpam-3763	919	16	(	(	PUNCT
ejpam-3763	919	17	u	u	NOUN
ejpam-3763	919	18	,	,	PUNCT
ejpam-3763	919	19	v	v	NOUN
ejpam-3763	919	20	)	)	PUNCT
ejpam-3763	919	21	}	}	PUNCT
ejpam-3763	919	22	such	such	ADJ
ejpam-3763	919	23	that	that	SCONJ
ejpam-3763	919	24	(	(	PUNCT
ejpam-3763	919	25	x	x	NOUN
ejpam-3763	919	26	,	,	PUNCT
ejpam-3763	919	27	y)(a	y)(a	PROPN
ejpam-3763	919	28	,	,	PUNCT
ejpam-3763	919	29	b	b	X
ejpam-3763	919	30	)	)	PUNCT
ejpam-3763	919	31	∈	∈	PROPN
ejpam-3763	919	32	e(g[kp	e(g[kp	NOUN
ejpam-3763	919	33	]	]	PUNCT
ejpam-3763	919	34	)	)	PUNCT
ejpam-3763	919	35	.	.	PUNCT
ejpam-3763	920	1	using	use	VERB
ejpam-3763	920	2	the	the	DET
ejpam-3763	920	3	same	same	ADJ
ejpam-3763	920	4	argument	argument	NOUN
ejpam-3763	920	5	,	,	PUNCT
ejpam-3763	920	6	whether	whether	SCONJ
ejpam-3763	920	7	x	x	X
ejpam-3763	920	8	=	=	PUNCT
ejpam-3763	920	9	a	a	DET
ejpam-3763	920	10	or	or	CCONJ
ejpam-3763	920	11	x	x	SYM
ejpam-3763	920	12	6=	6=	ADP
ejpam-3763	920	13	b	b	PROPN
ejpam-3763	920	14	,	,	PUNCT
ejpam-3763	920	15	(	(	PUNCT
ejpam-3763	920	16	x	x	NOUN
ejpam-3763	920	17	,	,	PUNCT
ejpam-3763	920	18	z)(a	z)(a	NUM
ejpam-3763	920	19	,	,	PUNCT
ejpam-3763	920	20	b	b	X
ejpam-3763	920	21	)	)	PUNCT
ejpam-3763	920	22	∈	∈	PROPN
ejpam-3763	920	23	e(g[kp	e(g[kp	NOUN
ejpam-3763	920	24	]	]	PUNCT
ejpam-3763	920	25	)	)	PUNCT
ejpam-3763	920	26	.	.	PUNCT
ejpam-3763	921	1	this	this	PRON
ejpam-3763	921	2	is	be	AUX
ejpam-3763	921	3	a	a	DET
ejpam-3763	921	4	contradiction	contradiction	NOUN
ejpam-3763	921	5	since	since	SCONJ
ejpam-3763	921	6	(	(	PUNCT
ejpam-3763	921	7	x	x	X
ejpam-3763	921	8	,	,	PUNCT
ejpam-3763	921	9	z	z	NOUN
ejpam-3763	921	10	)	)	PUNCT
ejpam-3763	921	11	∈	∈	PROPN
ejpam-3763	921	12	v0	v0	NOUN
ejpam-3763	921	13	.	.	PUNCT
ejpam-3763	922	1	fix	fix	VERB
ejpam-3763	922	2	v	v	ADP
ejpam-3763	922	3	∈	∈	NOUN
ejpam-3763	922	4	v	v	NOUN
ejpam-3763	922	5	(	(	PUNCT
ejpam-3763	922	6	kp	kp	PROPN
ejpam-3763	922	7	)	)	PUNCT
ejpam-3763	922	8	.	.	PUNCT
ejpam-3763	923	1	define	define	VERB
ejpam-3763	923	2	a	a	PRON
ejpam-3763	923	3	=	=	X
ejpam-3763	923	4	{	{	PUNCT
ejpam-3763	923	5	(	(	PUNCT
ejpam-3763	923	6	x	x	NOUN
ejpam-3763	923	7	,	,	PUNCT
ejpam-3763	923	8	v	v	NOUN
ejpam-3763	923	9	)	)	PUNCT
ejpam-3763	923	10	:	:	PUNCT
ejpam-3763	923	11	x	x	X
ejpam-3763	923	12	∈	∈	PROPN
ejpam-3763	923	13	(	(	PUNCT
ejpam-3763	923	14	v0)g	v0)g	NOUN
ejpam-3763	923	15	∩	∩	X
ejpam-3763	923	16	(	(	PUNCT
ejpam-3763	923	17	v2)g	v2)g	PROPN
ejpam-3763	923	18	}	}	PUNCT
ejpam-3763	923	19	,	,	PUNCT
ejpam-3763	923	20	b	b	X
ejpam-3763	923	21	=	=	PRON
ejpam-3763	923	22	{	{	PUNCT
ejpam-3763	923	23	(	(	PUNCT
ejpam-3763	923	24	x	x	NOUN
ejpam-3763	923	25	,	,	PUNCT
ejpam-3763	923	26	y	y	NOUN
ejpam-3763	923	27	)	)	PUNCT
ejpam-3763	923	28	∈	∈	NOUN
ejpam-3763	923	29	v2	v2	NOUN
ejpam-3763	923	30	:	:	PUNCT
ejpam-3763	924	1	x	x	X
ejpam-3763	924	2	/∈	/∈	INTJ
ejpam-3763	924	3	(	(	PUNCT
ejpam-3763	924	4	v0)g	v0)g	NOUN
ejpam-3763	924	5	}	}	PUNCT
ejpam-3763	924	6	and	and	CCONJ
ejpam-3763	924	7	c	c	X
ejpam-3763	924	8	=	=	SYM
ejpam-3763	924	9	{	{	PUNCT
ejpam-3763	924	10	(	(	PUNCT
ejpam-3763	924	11	x	x	NOUN
ejpam-3763	924	12	,	,	PUNCT
ejpam-3763	924	13	y	y	NOUN
ejpam-3763	924	14	)	)	PUNCT
ejpam-3763	924	15	∈	∈	NOUN
ejpam-3763	924	16	v2	v2	NOUN
ejpam-3763	924	17	:	:	PUNCT
ejpam-3763	924	18	x	x	SYM
ejpam-3763	924	19	∈	∈	PROPN
ejpam-3763	924	20	(	(	PUNCT
ejpam-3763	924	21	v0)g	v0)g	NOUN
ejpam-3763	924	22	,	,	PUNCT
ejpam-3763	924	23	y	y	PROPN
ejpam-3763	924	24	6=	6=	PROPN
ejpam-3763	924	25	v	v	NOUN
ejpam-3763	924	26	}	}	PUNCT
ejpam-3763	924	27	.	.	PUNCT
ejpam-3763	925	1	put	put	VERB
ejpam-3763	925	2	v	v	PRON
ejpam-3763	925	3	∗0	∗0	NOUN
ejpam-3763	925	4	=	=	SYM
ejpam-3763	925	5	(	(	PUNCT
ejpam-3763	925	6	v0	v0	NOUN
ejpam-3763	925	7	\a	\a	NUM
ejpam-3763	925	8	)	)	PUNCT
ejpam-3763	925	9	∪	∪	ADP
ejpam-3763	925	10	c	c	NOUN
ejpam-3763	925	11	,	,	PUNCT
ejpam-3763	925	12	v	v	NOUN
ejpam-3763	925	13	∗1	∗1	PROPN
ejpam-3763	925	14	=	=	SYM
ejpam-3763	925	15	v1	v1	PROPN
ejpam-3763	925	16	,	,	PUNCT
ejpam-3763	925	17	and	and	CCONJ
ejpam-3763	925	18	v	v	ADP
ejpam-3763	925	19	∗2	∗2	PROPN
ejpam-3763	925	20	=	=	PRON
ejpam-3763	925	21	a	a	DET
ejpam-3763	925	22	∪b	∪b	NOUN
ejpam-3763	925	23	.	.	PUNCT
ejpam-3763	926	1	then	then	ADV
ejpam-3763	926	2	{	{	PUNCT
ejpam-3763	926	3	v	v	NOUN
ejpam-3763	926	4	∗0	∗0	PROPN
ejpam-3763	926	5	,	,	PUNCT
ejpam-3763	926	6	v	v	ADP
ejpam-3763	926	7	∗1	∗1	PROPN
ejpam-3763	926	8	,	,	PUNCT
ejpam-3763	926	9	v	v	NOUN
ejpam-3763	926	10	∗2	∗2	PROPN
ejpam-3763	926	11	}	}	PUNCT
ejpam-3763	926	12	forms	form	VERB
ejpam-3763	926	13	a	a	DET
ejpam-3763	926	14	partition	partition	NOUN
ejpam-3763	926	15	of	of	ADP
ejpam-3763	926	16	v	v	NOUN
ejpam-3763	926	17	(	(	PUNCT
ejpam-3763	926	18	g[kp	g[kp	NOUN
ejpam-3763	926	19	]	]	PUNCT
ejpam-3763	926	20	)	)	PUNCT
ejpam-3763	926	21	.	.	PUNCT
ejpam-3763	927	1	note	note	VERB
ejpam-3763	927	2	here	here	ADV
ejpam-3763	927	3	that	that	SCONJ
ejpam-3763	927	4	,	,	PUNCT
ejpam-3763	927	5	in	in	ADP
ejpam-3763	927	6	particular	particular	ADJ
ejpam-3763	927	7	,	,	PUNCT
ejpam-3763	927	8	since	since	SCONJ
ejpam-3763	927	9	(	(	PUNCT
ejpam-3763	927	10	v0)g	v0)g	PROPN
ejpam-3763	927	11	∩	∩	NOUN
ejpam-3763	927	12	(	(	PUNCT
ejpam-3763	927	13	v1)g	v1)g	NOUN
ejpam-3763	927	14	=	=	SYM
ejpam-3763	927	15	∅	∅	NOUN
ejpam-3763	927	16	and	and	CCONJ
ejpam-3763	927	17	v1	v1	VERB
ejpam-3763	927	18	∩	∩	ADJ
ejpam-3763	927	19	v2	v2	NOUN
ejpam-3763	927	20	=	=	PUNCT
ejpam-3763	927	21	∅.	∅.	NOUN
ejpam-3763	927	22	now	now	ADV
ejpam-3763	927	23	,	,	PUNCT
ejpam-3763	927	24	let	let	VERB
ejpam-3763	927	25	(	(	PUNCT
ejpam-3763	927	26	x	x	NOUN
ejpam-3763	927	27	,	,	PUNCT
ejpam-3763	927	28	y	y	NOUN
ejpam-3763	927	29	)	)	PUNCT
ejpam-3763	927	30	∈	∈	PROPN
ejpam-3763	927	31	v	v	ADP
ejpam-3763	927	32	∗0	∗0	PROPN
ejpam-3763	927	33	.	.	PUNCT
ejpam-3763	928	1	case	case	NOUN
ejpam-3763	928	2	1	1	NUM
ejpam-3763	928	3	:	:	PUNCT
ejpam-3763	928	4	suppose	suppose	VERB
ejpam-3763	928	5	that	that	SCONJ
ejpam-3763	928	6	(	(	PUNCT
ejpam-3763	928	7	x	x	X
ejpam-3763	928	8	,	,	PUNCT
ejpam-3763	928	9	y	y	NOUN
ejpam-3763	928	10	)	)	PUNCT
ejpam-3763	928	11	∈	∈	PROPN
ejpam-3763	928	12	v0	v0	NOUN
ejpam-3763	928	13	\a	\a	VERB
ejpam-3763	928	14	.	.	PUNCT
ejpam-3763	929	1	there	there	PRON
ejpam-3763	929	2	exists	exist	VERB
ejpam-3763	929	3	(	(	PUNCT
ejpam-3763	929	4	u	u	NOUN
ejpam-3763	929	5	,	,	PUNCT
ejpam-3763	929	6	w	w	NOUN
ejpam-3763	929	7	)	)	PUNCT
ejpam-3763	929	8	∈	∈	NOUN
ejpam-3763	929	9	v2	v2	NOUN
ejpam-3763	929	10	such	such	ADJ
ejpam-3763	929	11	that	that	DET
ejpam-3763	929	12	ng[kp]((x	ng[kp]((x	NOUN
ejpam-3763	929	13	,	,	PUNCT
ejpam-3763	929	14	y))∩	y))∩	NOUN
ejpam-3763	929	15	v2	v2	PROPN
ejpam-3763	929	16	=	=	SYM
ejpam-3763	929	17	{	{	PUNCT
ejpam-3763	929	18	(	(	PUNCT
ejpam-3763	929	19	u	u	NOUN
ejpam-3763	929	20	,	,	PUNCT
ejpam-3763	929	21	w	w	NOUN
ejpam-3763	929	22	)	)	PUNCT
ejpam-3763	929	23	}	}	PUNCT
ejpam-3763	929	24	.	.	PUNCT
ejpam-3763	930	1	if	if	SCONJ
ejpam-3763	930	2	u	u	PROPN
ejpam-3763	930	3	/∈	/∈	PROPN
ejpam-3763	930	4	(	(	PUNCT
ejpam-3763	930	5	v0)g	v0)g	NOUN
ejpam-3763	930	6	,	,	PUNCT
ejpam-3763	930	7	then	then	ADV
ejpam-3763	930	8	(	(	PUNCT
ejpam-3763	930	9	u	u	NOUN
ejpam-3763	930	10	,	,	PUNCT
ejpam-3763	930	11	w	w	NOUN
ejpam-3763	930	12	)	)	PUNCT
ejpam-3763	930	13	∈	∈	PROPN
ejpam-3763	930	14	b	b	PROPN
ejpam-3763	930	15	and	and	CCONJ
ejpam-3763	930	16	ng[kp]((x	ng[kp]((x	NUM
ejpam-3763	930	17	,	,	PUNCT
ejpam-3763	930	18	y	y	NOUN
ejpam-3763	930	19	)	)	PUNCT
ejpam-3763	930	20	)	)	PUNCT
ejpam-3763	930	21	∩	∩	PROPN
ejpam-3763	930	22	v	v	ADP
ejpam-3763	930	23	∗2	∗2	PROPN
ejpam-3763	930	24	=	=	PRON
ejpam-3763	930	25	{	{	PUNCT
ejpam-3763	930	26	(	(	PUNCT
ejpam-3763	930	27	u	u	NOUN
ejpam-3763	930	28	,	,	PUNCT
ejpam-3763	930	29	w	w	NOUN
ejpam-3763	930	30	)	)	PUNCT
ejpam-3763	930	31	}	}	PUNCT
ejpam-3763	930	32	.	.	PUNCT
ejpam-3763	931	1	on	on	ADP
ejpam-3763	931	2	the	the	DET
ejpam-3763	931	3	other	other	ADJ
ejpam-3763	931	4	hand	hand	NOUN
ejpam-3763	931	5	,	,	PUNCT
ejpam-3763	931	6	if	if	SCONJ
ejpam-3763	931	7	u	u	PROPN
ejpam-3763	931	8	∈	∈	PROPN
ejpam-3763	931	9	(	(	PUNCT
ejpam-3763	931	10	v0)g	v0)g	NOUN
ejpam-3763	931	11	,	,	PUNCT
ejpam-3763	931	12	then	then	ADV
ejpam-3763	931	13	(	(	PUNCT
ejpam-3763	931	14	u	u	NOUN
ejpam-3763	931	15	,	,	PUNCT
ejpam-3763	931	16	v	v	NOUN
ejpam-3763	931	17	)	)	PUNCT
ejpam-3763	931	18	∈	∈	PROPN
ejpam-3763	931	19	a	a	PRON
ejpam-3763	931	20	and	and	CCONJ
ejpam-3763	931	21	ng[kp]((x	ng[kp]((x	NUM
ejpam-3763	931	22	,	,	PUNCT
ejpam-3763	931	23	y	y	NOUN
ejpam-3763	931	24	)	)	PUNCT
ejpam-3763	931	25	)	)	PUNCT
ejpam-3763	931	26	∩	∩	PROPN
ejpam-3763	931	27	v	v	ADP
ejpam-3763	931	28	∗2	∗2	PROPN
ejpam-3763	931	29	=	=	PRON
ejpam-3763	931	30	{	{	PUNCT
ejpam-3763	931	31	(	(	PUNCT
ejpam-3763	931	32	u	u	NOUN
ejpam-3763	931	33	,	,	PUNCT
ejpam-3763	931	34	v	v	NOUN
ejpam-3763	931	35	)	)	PUNCT
ejpam-3763	931	36	}	}	PUNCT
ejpam-3763	931	37	.	.	PUNCT
ejpam-3763	932	1	case	case	NOUN
ejpam-3763	932	2	2	2	NUM
ejpam-3763	932	3	:	:	PUNCT
ejpam-3763	932	4	suppose	suppose	VERB
ejpam-3763	932	5	that	that	SCONJ
ejpam-3763	932	6	(	(	PUNCT
ejpam-3763	932	7	x	x	X
ejpam-3763	932	8	,	,	PUNCT
ejpam-3763	932	9	y	y	NOUN
ejpam-3763	932	10	)	)	PUNCT
ejpam-3763	932	11	∈	∈	PROPN
ejpam-3763	932	12	c	c	NOUN
ejpam-3763	932	13	and	and	CCONJ
ejpam-3763	932	14	let	let	VERB
ejpam-3763	932	15	z	z	NOUN
ejpam-3763	932	16	∈	∈	PROPN
ejpam-3763	932	17	v	v	PROPN
ejpam-3763	932	18	(	(	PUNCT
ejpam-3763	932	19	kp	kp	PROPN
ejpam-3763	932	20	)	)	PUNCT
ejpam-3763	932	21	\	\	NOUN
ejpam-3763	932	22	{	{	PUNCT
ejpam-3763	932	23	y	y	NOUN
ejpam-3763	932	24	}	}	PUNCT
ejpam-3763	932	25	for	for	ADP
ejpam-3763	932	26	which	which	PRON
ejpam-3763	932	27	(	(	PUNCT
ejpam-3763	932	28	x	x	X
ejpam-3763	932	29	,	,	PUNCT
ejpam-3763	932	30	z	z	NOUN
ejpam-3763	932	31	)	)	PUNCT
ejpam-3763	932	32	∈	∈	PROPN
ejpam-3763	932	33	v0	v0	NOUN
ejpam-3763	932	34	.	.	PUNCT
ejpam-3763	933	1	since	since	SCONJ
ejpam-3763	933	2	(	(	PUNCT
ejpam-3763	933	3	x	x	X
ejpam-3763	933	4	,	,	PUNCT
ejpam-3763	933	5	y)(x	y)(x	PROPN
ejpam-3763	933	6	,	,	PUNCT
ejpam-3763	933	7	z	z	NOUN
ejpam-3763	933	8	)	)	PUNCT
ejpam-3763	933	9	∈	∈	PROPN
ejpam-3763	933	10	e(g[kp	e(g[kp	NOUN
ejpam-3763	933	11	]	]	PUNCT
ejpam-3763	933	12	)	)	PUNCT
ejpam-3763	933	13	and	and	CCONJ
ejpam-3763	933	14	(	(	PUNCT
ejpam-3763	933	15	x	x	NOUN
ejpam-3763	933	16	,	,	PUNCT
ejpam-3763	933	17	y	y	NOUN
ejpam-3763	933	18	)	)	PUNCT
ejpam-3763	933	19	∈	∈	PROPN
ejpam-3763	933	20	v2	v2	PROPN
ejpam-3763	933	21	,	,	PUNCT
ejpam-3763	933	22	ng[kp]((x	ng[kp]((x	NUM
ejpam-3763	933	23	,	,	PUNCT
ejpam-3763	933	24	z	z	NOUN
ejpam-3763	933	25	)	)	PUNCT
ejpam-3763	933	26	)	)	PUNCT
ejpam-3763	933	27	∩	∩	NOUN
ejpam-3763	933	28	v2	v2	NOUN
ejpam-3763	933	29	=	=	SYM
ejpam-3763	933	30	{	{	PUNCT
ejpam-3763	933	31	(	(	PUNCT
ejpam-3763	933	32	x	x	NOUN
ejpam-3763	933	33	,	,	PUNCT
ejpam-3763	933	34	y	y	NOUN
ejpam-3763	933	35	)	)	PUNCT
ejpam-3763	933	36	}	}	PUNCT
ejpam-3763	933	37	.	.	PUNCT
ejpam-3763	934	1	this	this	PRON
ejpam-3763	934	2	means	mean	VERB
ejpam-3763	934	3	that	that	SCONJ
ejpam-3763	934	4	(	(	PUNCT
ejpam-3763	934	5	x	x	NOUN
ejpam-3763	934	6	,	,	PUNCT
ejpam-3763	934	7	w	w	NOUN
ejpam-3763	934	8	)	)	PUNCT
ejpam-3763	934	9	/∈	/∈	PUNCT
ejpam-3763	935	1	v2	v2	PROPN
ejpam-3763	935	2	for	for	ADP
ejpam-3763	935	3	all	all	DET
ejpam-3763	935	4	w	w	PROPN
ejpam-3763	935	5	∈	∈	PROPN
ejpam-3763	935	6	v	v	NOUN
ejpam-3763	935	7	(	(	PUNCT
ejpam-3763	935	8	kp)\{y	kp)\{y	VERB
ejpam-3763	935	9	}	}	PUNCT
ejpam-3763	935	10	and	and	CCONJ
ejpam-3763	935	11	(	(	PUNCT
ejpam-3763	935	12	u	u	NOUN
ejpam-3763	935	13	,	,	PUNCT
ejpam-3763	935	14	w	w	NOUN
ejpam-3763	935	15	)	)	PUNCT
ejpam-3763	935	16	/∈	/∈	PUNCT
ejpam-3763	936	1	v2	v2	PROPN
ejpam-3763	936	2	for	for	ADP
ejpam-3763	936	3	all	all	DET
ejpam-3763	936	4	u	u	PROPN
ejpam-3763	936	5	∈	∈	PROPN
ejpam-3763	936	6	ng(x	ng(x	NUM
ejpam-3763	936	7	)	)	PUNCT
ejpam-3763	936	8	and	and	CCONJ
ejpam-3763	936	9	for	for	ADP
ejpam-3763	936	10	all	all	DET
ejpam-3763	936	11	w	w	PROPN
ejpam-3763	936	12	∈	∈	PROPN
ejpam-3763	936	13	v	v	NOUN
ejpam-3763	936	14	(	(	PUNCT
ejpam-3763	936	15	kp	kp	PROPN
ejpam-3763	936	16	)	)	PUNCT
ejpam-3763	936	17	.	.	PUNCT
ejpam-3763	937	1	thus	thus	ADV
ejpam-3763	937	2	,	,	PUNCT
ejpam-3763	937	3	ng[kp]((x	ng[kp]((x	NUM
ejpam-3763	937	4	,	,	PUNCT
ejpam-3763	937	5	y	y	NOUN
ejpam-3763	937	6	)	)	PUNCT
ejpam-3763	937	7	)	)	PUNCT
ejpam-3763	937	8	∩	∩	PROPN
ejpam-3763	937	9	v	v	ADP
ejpam-3763	937	10	∗2	∗2	PROPN
ejpam-3763	937	11	=	=	SYM
ejpam-3763	937	12	ng[kp]((x	ng[kp]((x	PROPN
ejpam-3763	937	13	,	,	PUNCT
ejpam-3763	937	14	y	y	NOUN
ejpam-3763	937	15	)	)	PUNCT
ejpam-3763	937	16	)	)	PUNCT
ejpam-3763	938	1	∩a	∩a	PROPN
ejpam-3763	938	2	=	=	PUNCT
ejpam-3763	939	1	{	{	PUNCT
ejpam-3763	939	2	(	(	PUNCT
ejpam-3763	939	3	x	x	NOUN
ejpam-3763	939	4	,	,	PUNCT
ejpam-3763	939	5	v	v	NOUN
ejpam-3763	939	6	)	)	PUNCT
ejpam-3763	939	7	}	}	PUNCT
ejpam-3763	939	8	.	.	PUNCT
ejpam-3763	940	1	accordingly	accordingly	ADV
ejpam-3763	940	2	,	,	PUNCT
ejpam-3763	940	3	the	the	DET
ejpam-3763	940	4	function	function	NOUN
ejpam-3763	940	5	g	g	NOUN
ejpam-3763	940	6	=	=	SYM
ejpam-3763	940	7	(	(	PUNCT
ejpam-3763	940	8	v	v	NOUN
ejpam-3763	940	9	∗0	∗0	PROPN
ejpam-3763	940	10	,	,	PUNCT
ejpam-3763	940	11	v	v	NOUN
ejpam-3763	940	12	∗	∗	NOUN
ejpam-3763	940	13	1	1	NUM
ejpam-3763	940	14	,	,	PUNCT
ejpam-3763	940	15	v	v	NOUN
ejpam-3763	940	16	∗	∗	X
ejpam-3763	940	17	2	2	NUM
ejpam-3763	940	18	)	)	PUNCT
ejpam-3763	940	19	∈	∈	PROPN
ejpam-3763	940	20	prd(g[kp	prd(g[kp	NOUN
ejpam-3763	940	21	]	]	PUNCT
ejpam-3763	940	22	)	)	PUNCT
ejpam-3763	940	23	.	.	PUNCT
ejpam-3763	941	1	since	since	SCONJ
ejpam-3763	941	2	v	v	NUM
ejpam-3763	941	3	∗1	∗1	NOUN
ejpam-3763	941	4	=	=	SYM
ejpam-3763	941	5	v1	v1	PROPN
ejpam-3763	941	6	and	and	CCONJ
ejpam-3763	941	7	|v	|v	PROPN
ejpam-3763	941	8	∗2	∗2	PROPN
ejpam-3763	941	9	|	|	ADV
ejpam-3763	941	10	≤	≤	NUM
ejpam-3763	941	11	|v2|	|v2|	NOUN
ejpam-3763	941	12	,	,	PUNCT
ejpam-3763	941	13	ωg[kp](f	ωg[kp](f	NOUN
ejpam-3763	941	14	)	)	PUNCT
ejpam-3763	941	15	≥	≥	NOUN
ejpam-3763	941	16	ωg[kp](g	ωg[kp](g	NOUN
ejpam-3763	941	17	)	)	PUNCT
ejpam-3763	941	18	.	.	PUNCT
ejpam-3763	942	1	because	because	SCONJ
ejpam-3763	942	2	f	f	PROPN
ejpam-3763	942	3	is	be	AUX
ejpam-3763	942	4	a	a	DET
ejpam-3763	942	5	γpr	γpr	ADJ
ejpam-3763	942	6	-function	-function	NOUN
ejpam-3763	942	7	of	of	ADP
ejpam-3763	942	8	g[kp	g[kp	NOUN
ejpam-3763	942	9	]	]	PUNCT
ejpam-3763	942	10	,	,	PUNCT
ejpam-3763	942	11	ωg[kp](f	ωg[kp](f	NOUN
ejpam-3763	942	12	)	)	PUNCT
ejpam-3763	942	13	=	=	SYM
ejpam-3763	942	14	ωg[kp](g	ωg[kp](g	NOUN
ejpam-3763	942	15	)	)	PUNCT
ejpam-3763	942	16	and	and	CCONJ
ejpam-3763	942	17	g	g	PROPN
ejpam-3763	942	18	is	be	AUX
ejpam-3763	942	19	a	a	DET
ejpam-3763	942	20	γpr	γpr	ADJ
ejpam-3763	942	21	-function	-function	NOUN
ejpam-3763	942	22	of	of	ADP
ejpam-3763	942	23	g[kp	g[kp	NOUN
ejpam-3763	942	24	]	]	PUNCT
ejpam-3763	942	25	.	.	PUNCT
ejpam-3763	943	1	define	define	VERB
ejpam-3763	943	2	the	the	DET
ejpam-3763	943	3	function	function	NOUN
ejpam-3763	943	4	h	h	NOUN
ejpam-3763	943	5	=	=	SYM
ejpam-3763	943	6	(	(	PUNCT
ejpam-3763	943	7	v	v	NUM
ejpam-3763	943	8	h	h	NOUN
ejpam-3763	943	9	0	0	NUM
ejpam-3763	943	10	,	,	PUNCT
ejpam-3763	943	11	v	v	NOUN
ejpam-3763	943	12	h	h	NOUN
ejpam-3763	943	13	1	1	NUM
ejpam-3763	943	14	,	,	PUNCT
ejpam-3763	943	15	v	v	NOUN
ejpam-3763	943	16	h	h	NOUN
ejpam-3763	943	17	2	2	NUM
ejpam-3763	943	18	)	)	PUNCT
ejpam-3763	943	19	on	on	ADP
ejpam-3763	943	20	g	g	PROPN
ejpam-3763	943	21	by	by	ADP
ejpam-3763	943	22	h(x	h(x	PROPN
ejpam-3763	943	23	)	)	PUNCT
ejpam-3763	944	1	=	=	PUNCT
ejpam-3763	945	1			NOUN
ejpam-3763	945	2	2	2	NUM
ejpam-3763	945	3	,	,	PUNCT
ejpam-3763	945	4	if	if	SCONJ
ejpam-3763	945	5	x	x	SYM
ejpam-3763	945	6	∈	∈	PROPN
ejpam-3763	945	7	(	(	PUNCT
ejpam-3763	945	8	v	v	NOUN
ejpam-3763	945	9	∗2	∗2	NOUN
ejpam-3763	945	10	)	)	PUNCT
ejpam-3763	945	11	g	g	NOUN
ejpam-3763	945	12	;	;	PUNCT
ejpam-3763	945	13	1	1	NUM
ejpam-3763	945	14	,	,	PUNCT
ejpam-3763	945	15	if	if	SCONJ
ejpam-3763	945	16	x	x	SYM
ejpam-3763	945	17	∈	∈	PROPN
ejpam-3763	945	18	(	(	PUNCT
ejpam-3763	945	19	v	v	NOUN
ejpam-3763	945	20	∗1	∗1	PROPN
ejpam-3763	945	21	)	)	PUNCT
ejpam-3763	945	22	g	g	NOUN
ejpam-3763	945	23	\	\	PROPN
ejpam-3763	945	24	(	(	PUNCT
ejpam-3763	945	25	v	v	NOUN
ejpam-3763	945	26	∗2	∗2	NOUN
ejpam-3763	945	27	)	)	PUNCT
ejpam-3763	945	28	g	g	NOUN
ejpam-3763	945	29	;	;	PUNCT
ejpam-3763	945	30	0	0	NUM
ejpam-3763	945	31	,	,	PUNCT
ejpam-3763	945	32	else	else	ADV
ejpam-3763	945	33	.	.	PUNCT
ejpam-3763	946	1	let	let	VERB
ejpam-3763	946	2	x	x	SYM
ejpam-3763	946	3	∈	∈	PROPN
ejpam-3763	946	4	v	v	ADP
ejpam-3763	946	5	h	h	NOUN
ejpam-3763	946	6	0	0	PROPN
ejpam-3763	946	7	.	.	PUNCT
ejpam-3763	947	1	then	then	ADV
ejpam-3763	947	2	(	(	PUNCT
ejpam-3763	947	3	x	x	X
ejpam-3763	947	4	,	,	PUNCT
ejpam-3763	947	5	y	y	NOUN
ejpam-3763	947	6	)	)	PUNCT
ejpam-3763	947	7	∈	∈	NOUN
ejpam-3763	947	8	v	v	ADP
ejpam-3763	947	9	∗0	∗0	PROPN
ejpam-3763	947	10	for	for	ADP
ejpam-3763	947	11	all	all	PRON
ejpam-3763	947	12	y	y	PROPN
ejpam-3763	947	13	∈	∈	PROPN
ejpam-3763	947	14	v	v	NOUN
ejpam-3763	947	15	(	(	PUNCT
ejpam-3763	947	16	kp	kp	PROPN
ejpam-3763	947	17	)	)	PUNCT
ejpam-3763	947	18	.	.	PUNCT
ejpam-3763	948	1	pick	pick	VERB
ejpam-3763	948	2	y	y	PROPN
ejpam-3763	948	3	∈	∈	PROPN
ejpam-3763	948	4	v	v	PROPN
ejpam-3763	948	5	(	(	PUNCT
ejpam-3763	948	6	kp	kp	PROPN
ejpam-3763	948	7	)	)	PUNCT
ejpam-3763	948	8	.	.	PUNCT
ejpam-3763	949	1	there	there	PRON
ejpam-3763	949	2	exists	exist	VERB
ejpam-3763	949	3	a	a	DET
ejpam-3763	949	4	unique	unique	ADJ
ejpam-3763	949	5	(	(	PUNCT
ejpam-3763	949	6	u	u	NOUN
ejpam-3763	949	7	,	,	PUNCT
ejpam-3763	949	8	v	v	NOUN
ejpam-3763	949	9	)	)	PUNCT
ejpam-3763	949	10	∈	∈	PROPN
ejpam-3763	949	11	v	v	ADP
ejpam-3763	949	12	∗2	∗2	PROPN
ejpam-3763	949	13	for	for	ADP
ejpam-3763	949	14	which	which	PRON
ejpam-3763	949	15	(	(	PUNCT
ejpam-3763	949	16	x	x	X
ejpam-3763	949	17	,	,	PUNCT
ejpam-3763	949	18	y)(u	y)(u	ADJ
ejpam-3763	949	19	,	,	PUNCT
ejpam-3763	949	20	v	v	NOUN
ejpam-3763	949	21	)	)	PUNCT
ejpam-3763	949	22	∈	∈	NOUN
ejpam-3763	949	23	e(g[kp	e(g[kp	NOUN
ejpam-3763	949	24	]	]	PUNCT
ejpam-3763	949	25	)	)	PUNCT
ejpam-3763	949	26	.	.	PUNCT
ejpam-3763	950	1	it	it	PRON
ejpam-3763	950	2	follows	follow	VERB
ejpam-3763	950	3	that	that	SCONJ
ejpam-3763	950	4	u	u	PROPN
ejpam-3763	950	5	∈	∈	PROPN
ejpam-3763	950	6	v	v	ADP
ejpam-3763	950	7	h	h	NOUN
ejpam-3763	950	8	2	2	NUM
ejpam-3763	950	9	and	and	CCONJ
ejpam-3763	950	10	ux	ux	NOUN
ejpam-3763	950	11	∈	∈	PROPN
ejpam-3763	950	12	e(g	e(g	PROPN
ejpam-3763	950	13	)	)	PUNCT
ejpam-3763	950	14	.	.	PUNCT
ejpam-3763	951	1	moreover	moreover	ADV
ejpam-3763	951	2	,	,	PUNCT
ejpam-3763	951	3	u	u	NOUN
ejpam-3763	951	4	is	be	AUX
ejpam-3763	951	5	unique	unique	ADJ
ejpam-3763	951	6	in	in	ADP
ejpam-3763	951	7	this	this	DET
ejpam-3763	951	8	sense	sense	NOUN
ejpam-3763	951	9	as	as	SCONJ
ejpam-3763	951	10	(	(	PUNCT
ejpam-3763	951	11	u	u	NOUN
ejpam-3763	951	12	,	,	PUNCT
ejpam-3763	951	13	v	v	NOUN
ejpam-3763	951	14	)	)	PUNCT
ejpam-3763	951	15	is	be	AUX
ejpam-3763	951	16	for	for	ADP
ejpam-3763	951	17	(	(	PUNCT
ejpam-3763	951	18	x	x	NOUN
ejpam-3763	951	19	,	,	PUNCT
ejpam-3763	951	20	y	y	PROPN
ejpam-3763	951	21	)	)	PUNCT
ejpam-3763	951	22	.	.	PUNCT
ejpam-3763	952	1	thus	thus	ADV
ejpam-3763	952	2	,	,	PUNCT
ejpam-3763	952	3	h	h	PROPN
ejpam-3763	952	4	∈	∈	PROPN
ejpam-3763	952	5	prd(g	prd(g	PROPN
ejpam-3763	952	6	)	)	PUNCT
ejpam-3763	952	7	.	.	PUNCT
ejpam-3763	953	1	finally	finally	ADV
ejpam-3763	953	2	,	,	PUNCT
ejpam-3763	953	3	let	let	VERB
ejpam-3763	953	4	x	x	PRON
ejpam-3763	953	5	,	,	PUNCT
ejpam-3763	953	6	u	u	PROPN
ejpam-3763	953	7	∈	∈	PROPN
ejpam-3763	953	8	v	v	ADP
ejpam-3763	953	9	h	h	NOUN
ejpam-3763	953	10	2	2	NUM
ejpam-3763	953	11	for	for	ADP
ejpam-3763	953	12	which	which	PRON
ejpam-3763	953	13	xu	xu	PROPN
ejpam-3763	953	14	∈	∈	PROPN
ejpam-3763	953	15	e(g	e(g	PROPN
ejpam-3763	953	16	)	)	PUNCT
ejpam-3763	953	17	.	.	PUNCT
ejpam-3763	954	1	let	let	VERB
ejpam-3763	954	2	y	y	PRON
ejpam-3763	954	3	,	,	PUNCT
ejpam-3763	954	4	v	v	PROPN
ejpam-3763	954	5	∈	∈	PROPN
ejpam-3763	954	6	v	v	NOUN
ejpam-3763	954	7	(	(	PUNCT
ejpam-3763	954	8	kp	kp	NOUN
ejpam-3763	954	9	)	)	PUNCT
ejpam-3763	954	10	such	such	ADJ
ejpam-3763	954	11	that	that	SCONJ
ejpam-3763	954	12	(	(	PUNCT
ejpam-3763	954	13	x	x	NOUN
ejpam-3763	954	14	,	,	PUNCT
ejpam-3763	954	15	y	y	PROPN
ejpam-3763	954	16	)	)	PUNCT
ejpam-3763	954	17	,	,	PUNCT
ejpam-3763	954	18	(	(	PUNCT
ejpam-3763	954	19	u	u	NOUN
ejpam-3763	954	20	,	,	PUNCT
ejpam-3763	954	21	v	v	NOUN
ejpam-3763	954	22	)	)	PUNCT
ejpam-3763	954	23	∈	∈	PROPN
ejpam-3763	954	24	v	v	ADP
ejpam-3763	954	25	∗2	∗2	PROPN
ejpam-3763	954	26	.	.	PUNCT
ejpam-3763	955	1	since	since	SCONJ
ejpam-3763	955	2	g	g	PROPN
ejpam-3763	955	3	is	be	AUX
ejpam-3763	955	4	a	a	DET
ejpam-3763	955	5	γpr	γpr	ADJ
ejpam-3763	955	6	-function	-function	NOUN
ejpam-3763	955	7	of	of	ADP
ejpam-3763	955	8	g[kp	g[kp	NOUN
ejpam-3763	955	9	]	]	PUNCT
ejpam-3763	955	10	,	,	PUNCT
ejpam-3763	955	11	(	(	PUNCT
ejpam-3763	955	12	x	x	NOUN
ejpam-3763	955	13	,	,	PUNCT
ejpam-3763	955	14	a	a	PRON
ejpam-3763	955	15	)	)	PUNCT
ejpam-3763	955	16	,	,	PUNCT
ejpam-3763	955	17	(	(	PUNCT
ejpam-3763	955	18	u	u	NOUN
ejpam-3763	955	19	,	,	PUNCT
ejpam-3763	955	20	b	b	NOUN
ejpam-3763	955	21	)	)	PUNCT
ejpam-3763	955	22	∈	∈	NOUN
ejpam-3763	955	23	v	v	ADP
ejpam-3763	955	24	∗1	∗1	PROPN
ejpam-3763	955	25	for	for	ADP
ejpam-3763	955	26	all	all	DET
ejpam-3763	955	27	a	a	DET
ejpam-3763	955	28	∈	∈	PROPN
ejpam-3763	955	29	v	v	NOUN
ejpam-3763	955	30	(	(	PUNCT
ejpam-3763	955	31	kp)\{y	kp)\{y	VERB
ejpam-3763	955	32	}	}	PUNCT
ejpam-3763	955	33	and	and	CCONJ
ejpam-3763	955	34	for	for	ADP
ejpam-3763	955	35	all	all	DET
ejpam-3763	955	36	references	reference	NOUN
ejpam-3763	955	37	547	547	NUM
ejpam-3763	955	38	b	b	NOUN
ejpam-3763	955	39	∈	∈	NOUN
ejpam-3763	955	40	v	v	NOUN
ejpam-3763	955	41	(	(	PUNCT
ejpam-3763	955	42	kp	kp	PROPN
ejpam-3763	955	43	)	)	PUNCT
ejpam-3763	955	44	\	\	PROPN
ejpam-3763	955	45	{	{	PUNCT
ejpam-3763	955	46	v	v	NOUN
ejpam-3763	955	47	}	}	PUNCT
ejpam-3763	955	48	.	.	PUNCT
ejpam-3763	956	1	on	on	ADP
ejpam-3763	956	2	the	the	DET
ejpam-3763	956	3	other	other	ADJ
ejpam-3763	956	4	hand	hand	NOUN
ejpam-3763	956	5	,	,	PUNCT
ejpam-3763	956	6	by	by	ADP
ejpam-3763	956	7	the	the	DET
ejpam-3763	956	8	definition	definition	NOUN
ejpam-3763	956	9	of	of	ADP
ejpam-3763	956	10	h	h	NOUN
ejpam-3763	956	11	,	,	PUNCT
ejpam-3763	956	12	for	for	ADP
ejpam-3763	956	13	each	each	DET
ejpam-3763	956	14	x	x	SYM
ejpam-3763	956	15	∈	∈	PROPN
ejpam-3763	956	16	v	v	NUM
ejpam-3763	956	17	h	h	NOUN
ejpam-3763	956	18	1	1	NUM
ejpam-3763	956	19	,	,	PUNCT
ejpam-3763	956	20	(	(	PUNCT
ejpam-3763	956	21	x	x	NOUN
ejpam-3763	956	22	,	,	PUNCT
ejpam-3763	956	23	y	y	NOUN
ejpam-3763	956	24	)	)	PUNCT
ejpam-3763	956	25	∈	∈	NOUN
ejpam-3763	956	26	v	v	ADP
ejpam-3763	956	27	∗1	∗1	PROPN
ejpam-3763	956	28	for	for	ADP
ejpam-3763	956	29	all	all	DET
ejpam-3763	956	30	y	y	PROPN
ejpam-3763	956	31	∈	∈	PROPN
ejpam-3763	956	32	v	v	NOUN
ejpam-3763	956	33	(	(	PUNCT
ejpam-3763	956	34	kp	kp	PROPN
ejpam-3763	956	35	)	)	PUNCT
ejpam-3763	956	36	.	.	PUNCT
ejpam-3763	957	1	thus	thus	ADV
ejpam-3763	957	2	,	,	PUNCT
ejpam-3763	957	3	|v	|v	PROPN
ejpam-3763	957	4	∗1	∗1	PROPN
ejpam-3763	957	5	|	|	ADV
ejpam-3763	957	6	≥	≥	NOUN
ejpam-3763	957	7	p|v	p|v	NOUN
ejpam-3763	957	8	h	h	NOUN
ejpam-3763	957	9	1	1	NUM
ejpam-3763	957	10	|+	|+	NOUN
ejpam-3763	957	11	(	(	PUNCT
ejpam-3763	957	12	p−	p−	NOUN
ejpam-3763	957	13	1)|v	1)|v	NUM
ejpam-3763	957	14	h	h	NOUN
ejpam-3763	957	15	2	2	NUM
ejpam-3763	957	16	∩ng(v	∩ng(v	PROPN
ejpam-3763	957	17	h	h	NOUN
ejpam-3763	957	18	2	2	X
ejpam-3763	957	19	)	)	PUNCT
ejpam-3763	957	20	|	|	ADV
ejpam-3763	957	21	.	.	PUNCT
ejpam-3763	958	1	therefore	therefore	ADV
ejpam-3763	958	2	,	,	PUNCT
ejpam-3763	958	3	γpr(g[kp	γpr(g[kp	NOUN
ejpam-3763	958	4	]	]	PUNCT
ejpam-3763	958	5	)	)	PUNCT
ejpam-3763	958	6	=	=	SYM
ejpam-3763	958	7	ωg[kp](g	ωg[kp](g	NOUN
ejpam-3763	958	8	)	)	PUNCT
ejpam-3763	958	9	=	=	PUNCT
ejpam-3763	959	1	|v	|v	PROPN
ejpam-3763	960	1	∗1	∗1	DET
ejpam-3763	960	2	|+	|+	NOUN
ejpam-3763	960	3	2|v	2|v	NUM
ejpam-3763	960	4	∗2	∗2	NOUN
ejpam-3763	960	5	|	|	ADV
ejpam-3763	960	6	≥	≥	NOUN
ejpam-3763	960	7	p|v	p|v	NOUN
ejpam-3763	960	8	h	h	NOUN
ejpam-3763	960	9	1	1	NUM
ejpam-3763	960	10	|+	|+	NOUN
ejpam-3763	960	11	(	(	PUNCT
ejpam-3763	960	12	p−	p−	NOUN
ejpam-3763	960	13	1)|v	1)|v	NUM
ejpam-3763	960	14	h	h	NOUN
ejpam-3763	960	15	2	2	NUM
ejpam-3763	960	16	∩ng(v	∩ng(v	PROPN
ejpam-3763	960	17	h	h	NOUN
ejpam-3763	960	18	2	2	NUM
ejpam-3763	960	19	)	)	PUNCT
ejpam-3763	960	20	|+	|+	NOUN
ejpam-3763	961	1	2|v	2|v	NUM
ejpam-3763	961	2	h	h	NOUN
ejpam-3763	961	3	2	2	NUM
ejpam-3763	961	4	|	|	NOUN
ejpam-3763	961	5	=	=	PUNCT
ejpam-3763	961	6	(	(	PUNCT
ejpam-3763	961	7	p−	p−	NOUN
ejpam-3763	961	8	1	1	NUM
ejpam-3763	961	9	)	)	PUNCT
ejpam-3763	961	10	(	(	PUNCT
ejpam-3763	961	11	|v	|v	PROPN
ejpam-3763	961	12	h	h	NOUN
ejpam-3763	961	13	1	1	NUM
ejpam-3763	961	14	|+	|+	NOUN
ejpam-3763	961	15	|v	|v	PROPN
ejpam-3763	961	16	h	h	NOUN
ejpam-3763	961	17	2	2	NUM
ejpam-3763	961	18	∩ng(v	∩ng(v	PROPN
ejpam-3763	961	19	h	h	NOUN
ejpam-3763	961	20	2	2	NUM
ejpam-3763	961	21	)	)	PUNCT
ejpam-3763	961	22	|	|	ADV
ejpam-3763	961	23	)	)	PUNCT
ejpam-3763	962	1	+	+	CCONJ
ejpam-3763	962	2	ωg(h	ωg(h	NOUN
ejpam-3763	962	3	)	)	PUNCT
ejpam-3763	962	4	≥	≥	PROPN
ejpam-3763	962	5	α	α	NOUN
ejpam-3763	962	6	.	.	PUNCT
ejpam-3763	963	1	the	the	DET
ejpam-3763	963	2	desired	desire	VERB
ejpam-3763	963	3	equality	equality	NOUN
ejpam-3763	963	4	is	be	AUX
ejpam-3763	963	5	completed	complete	VERB
ejpam-3763	963	6	by	by	ADP
ejpam-3763	963	7	proposition	proposition	NOUN
ejpam-3763	963	8	2.18	2.18	NUM
ejpam-3763	963	9	�	�	PROPN
ejpam-3763	963	10	equality	equality	NOUN
ejpam-3763	963	11	in	in	ADP
ejpam-3763	963	12	proposition	proposition	NOUN
ejpam-3763	963	13	2.18	2.18	NUM
ejpam-3763	963	14	is	be	AUX
ejpam-3763	963	15	possible	possible	ADJ
ejpam-3763	963	16	even	even	ADV
ejpam-3763	963	17	if	if	SCONJ
ejpam-3763	963	18	h	h	NOUN
ejpam-3763	963	19	is	be	AUX
ejpam-3763	963	20	not	not	PART
ejpam-3763	963	21	complete	complete	ADJ
ejpam-3763	963	22	.	.	PUNCT
ejpam-3763	964	1	consider	consider	VERB
ejpam-3763	964	2	the	the	DET
ejpam-3763	964	3	graph	graph	NOUN
ejpam-3763	964	4	g[p3	g[p3	NOUN
ejpam-3763	964	5	]	]	PUNCT
ejpam-3763	964	6	in	in	ADP
ejpam-3763	964	7	figure	figure	NOUN
ejpam-3763	964	8	4	4	NUM
ejpam-3763	964	9	,	,	PUNCT
ejpam-3763	964	10	with	with	ADP
ejpam-3763	964	11	g	g	NOUN
ejpam-3763	964	12	being	be	AUX
ejpam-3763	964	13	the	the	DET
ejpam-3763	964	14	caterpillar	caterpillar	ADJ
ejpam-3763	964	15	graph	graph	NOUN
ejpam-3763	964	16	ca(0	ca(0	NOUN
ejpam-3763	964	17	,	,	PUNCT
ejpam-3763	964	18	2	2	NUM
ejpam-3763	964	19	,	,	PUNCT
ejpam-3763	964	20	0	0	NUM
ejpam-3763	964	21	,	,	PUNCT
ejpam-3763	964	22	2	2	NUM
ejpam-3763	964	23	,	,	PUNCT
ejpam-3763	964	24	0	0	NUM
ejpam-3763	964	25	)	)	PUNCT
ejpam-3763	964	26	.	.	PUNCT
ejpam-3763	965	1	observe	observe	VERB
ejpam-3763	965	2	that	that	SCONJ
ejpam-3763	965	3	α	α	NOUN
ejpam-3763	965	4	=	=	VERB
ejpam-3763	965	5	7	7	X
ejpam-3763	965	6	.	.	PUNCT
ejpam-3763	965	7	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	965	8	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	966	1	....................................	....................................	PUNCT
ejpam-3763	966	2	...................................................	...................................................	PUNCT
ejpam-3763	967	1	....................................	....................................	PUNCT
ejpam-3763	967	2	...........................................................................................................................................................................	...........................................................................................................................................................................	PUNCT
ejpam-3763	967	3	....................................	....................................	PUNCT
ejpam-3763	967	4	..........................	..........................	PUNCT
ejpam-3763	968	1	.........................	.........................	PUNCT
ejpam-3763	968	2	.........................	.........................	PUNCT
ejpam-3763	969	1	....................................	....................................	PUNCT
ejpam-3763	969	2	....................................	....................................	PUNCT
ejpam-3763	970	1	...................	...................	PUNCT
ejpam-3763	970	2	..................	..................	PUNCT
ejpam-3763	971	1	..............	..............	PUNCT
ejpam-3763	971	2	....................................	....................................	PUNCT
ejpam-3763	972	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	972	2	....................................................................................................................................................	....................................................................................................................................................	PUNCT
ejpam-3763	973	1	....................................	....................................	PUNCT
ejpam-3763	974	1	....................................	....................................	PUNCT
ejpam-3763	975	1	g	g	X
ejpam-3763	975	2	....................................	....................................	PUNCT
ejpam-3763	975	3	....................................	....................................	PUNCT
ejpam-3763	975	4	....................................	....................................	PUNCT
ejpam-3763	975	5	....................................	....................................	PUNCT
ejpam-3763	975	6	....................................	....................................	PUNCT
ejpam-3763	975	7	....................................	....................................	PUNCT
ejpam-3763	975	8	....................................	....................................	PUNCT
ejpam-3763	975	9	....................................	....................................	PUNCT
ejpam-3763	975	10	....................................	....................................	PUNCT
ejpam-3763	975	11	....................................	....................................	PUNCT
ejpam-3763	975	12	....................................	....................................	PUNCT
ejpam-3763	975	13	....................................	....................................	PUNCT
ejpam-3763	975	14	....................................	....................................	PUNCT
ejpam-3763	975	15	....................................	....................................	PUNCT
ejpam-3763	975	16	....................................	....................................	PUNCT
ejpam-3763	975	17	....................................	....................................	PUNCT
ejpam-3763	975	18	....................................	....................................	PUNCT
ejpam-3763	975	19	....................................	....................................	PUNCT
ejpam-3763	975	20	....................................	....................................	PUNCT
ejpam-3763	975	21	....................................	....................................	PUNCT
ejpam-3763	975	22	....................................	....................................	PUNCT
ejpam-3763	975	23	....................................	....................................	PUNCT
ejpam-3763	975	24	....................................	....................................	PUNCT
ejpam-3763	975	25	....................................	....................................	PUNCT
ejpam-3763	975	26	....................................	....................................	PUNCT
ejpam-3763	975	27	....................................	....................................	PUNCT
ejpam-3763	975	28	....................................	....................................	PUNCT
ejpam-3763	976	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	976	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	977	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	977	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	978	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	978	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	979	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	979	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	980	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3763	980	2	.........	.........	PUNCT
ejpam-3763	980	3	........	........	PUNCT
ejpam-3763	980	4	........	........	PUNCT
ejpam-3763	980	5	........	........	PUNCT
ejpam-3763	980	6	........	........	PUNCT
ejpam-3763	980	7	........	........	PUNCT
ejpam-3763	980	8	........	........	PUNCT
ejpam-3763	980	9	........	........	PUNCT
ejpam-3763	980	10	.......	.......	PUNCT
ejpam-3763	981	1	....................................	....................................	PUNCT
ejpam-3763	981	2	.........	.........	PUNCT
ejpam-3763	982	1	........	........	PUNCT
ejpam-3763	982	2	........	........	PUNCT
ejpam-3763	982	3	........	........	PUNCT
ejpam-3763	982	4	........	........	PUNCT
ejpam-3763	982	5	........	........	PUNCT
ejpam-3763	982	6	........	........	PUNCT
ejpam-3763	982	7	........	........	PUNCT
ejpam-3763	982	8	.......	.......	PUNCT
ejpam-3763	982	9	....................................	....................................	PUNCT
ejpam-3763	983	1	....................................	....................................	PUNCT
ejpam-3763	983	2	.........	.........	PUNCT
ejpam-3763	983	3	........	........	PUNCT
ejpam-3763	983	4	........	........	PUNCT
ejpam-3763	983	5	........	........	PUNCT
ejpam-3763	983	6	........	........	PUNCT
ejpam-3763	983	7	........	........	PUNCT
ejpam-3763	983	8	........	........	PUNCT
ejpam-3763	983	9	........	........	PUNCT
ejpam-3763	983	10	.......	.......	PUNCT
ejpam-3763	984	1	....................................	....................................	PUNCT
ejpam-3763	984	2	.........	.........	PUNCT
ejpam-3763	985	1	........	........	PUNCT
ejpam-3763	985	2	........	........	PUNCT
ejpam-3763	985	3	........	........	PUNCT
ejpam-3763	985	4	........	........	PUNCT
ejpam-3763	985	5	........	........	PUNCT
ejpam-3763	985	6	........	........	PUNCT
ejpam-3763	985	7	........	........	PUNCT
ejpam-3763	985	8	.......	.......	PUNCT
ejpam-3763	985	9	....................................	....................................	PUNCT
ejpam-3763	986	1	....................................	....................................	PUNCT
ejpam-3763	986	2	.........	.........	PUNCT
ejpam-3763	986	3	........	........	PUNCT
ejpam-3763	986	4	........	........	PUNCT
ejpam-3763	986	5	........	........	PUNCT
ejpam-3763	986	6	........	........	PUNCT
ejpam-3763	986	7	........	........	PUNCT
ejpam-3763	986	8	........	........	PUNCT
ejpam-3763	986	9	........	........	PUNCT
ejpam-3763	986	10	.......	.......	PUNCT
ejpam-3763	987	1	....................................	....................................	PUNCT
ejpam-3763	987	2	.........	.........	PUNCT
ejpam-3763	988	1	........	........	PUNCT
ejpam-3763	988	2	........	........	PUNCT
ejpam-3763	988	3	........	........	PUNCT
ejpam-3763	988	4	........	........	PUNCT
ejpam-3763	988	5	........	........	PUNCT
ejpam-3763	988	6	........	........	PUNCT
ejpam-3763	988	7	........	........	PUNCT
ejpam-3763	988	8	.......	.......	PUNCT
ejpam-3763	988	9	....................................	....................................	PUNCT
ejpam-3763	988	10	....................................	....................................	PUNCT
ejpam-3763	989	1	.................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................	PUNCT
ejpam-3763	989	2	...........................................................................................................................................................................................	...........................................................................................................................................................................................	PUNCT
ejpam-3763	990	1	..............	..............	PUNCT
ejpam-3763	990	2	.............	.............	PUNCT
ejpam-3763	990	3	.............	.............	PUNCT
ejpam-3763	990	4	.............	.............	PUNCT
ejpam-3763	990	5	.............	.............	PUNCT
ejpam-3763	990	6	.............	.............	PUNCT
ejpam-3763	990	7	.............	.............	PUNCT
ejpam-3763	990	8	.............	.............	PUNCT
ejpam-3763	990	9	.............	.............	PUNCT
ejpam-3763	991	1	........	........	PUNCT
ejpam-3763	991	2	............................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................	PUNCT
ejpam-3763	992	1	..........	..........	PUNCT
ejpam-3763	992	2	..........	..........	PUNCT
ejpam-3763	993	1	..........	..........	PUNCT
ejpam-3763	993	2	..........	..........	PUNCT
ejpam-3763	994	1	..........	..........	PUNCT
ejpam-3763	994	2	..........	..........	PUNCT
ejpam-3763	995	1	..........	..........	PUNCT
ejpam-3763	995	2	..........	..........	PUNCT
ejpam-3763	996	1	..........	..........	PUNCT
ejpam-3763	996	2	..........	..........	PUNCT
ejpam-3763	997	1	..........	..........	PUNCT
ejpam-3763	997	2	..........	..........	PUNCT
ejpam-3763	998	1	..........	..........	PUNCT
ejpam-3763	998	2	..........	..........	PUNCT
ejpam-3763	999	1	..........	..........	PUNCT
ejpam-3763	999	2	..........	..........	PUNCT
ejpam-3763	1000	1	..........	..........	PUNCT
ejpam-3763	1000	2	......	......	PUNCT
ejpam-3763	1001	1	..............	..............	PUNCT
ejpam-3763	1001	2	.............	.............	PUNCT
ejpam-3763	1001	3	.............	.............	PUNCT
ejpam-3763	1001	4	.............	.............	PUNCT
ejpam-3763	1001	5	.............	.............	PUNCT
ejpam-3763	1001	6	.............	.............	PUNCT
ejpam-3763	1001	7	.............	.............	PUNCT
ejpam-3763	1001	8	.............	.............	PUNCT
ejpam-3763	1002	1	.............	.............	PUNCT
ejpam-3763	1002	2	........	........	PUNCT
ejpam-3763	1002	3	...................................................................................................	...................................................................................................	PUNCT
ejpam-3763	1002	4	...................................................................................................	...................................................................................................	PUNCT
ejpam-3763	1003	1	..............	..............	PUNCT
ejpam-3763	1003	2	.............	.............	PUNCT
ejpam-3763	1003	3	.............	.............	PUNCT
ejpam-3763	1003	4	.............	.............	PUNCT
ejpam-3763	1003	5	.............	.............	PUNCT
ejpam-3763	1003	6	.............	.............	PUNCT
ejpam-3763	1003	7	.............	.............	PUNCT
ejpam-3763	1003	8	.............	.............	PUNCT
ejpam-3763	1003	9	.............	.............	PUNCT
ejpam-3763	1003	10	........	........	PUNCT
ejpam-3763	1003	11	...........	...........	PUNCT
ejpam-3763	1003	12	..........	..........	PUNCT
ejpam-3763	1004	1	..........	..........	PUNCT
ejpam-3763	1004	2	..........	..........	PUNCT
ejpam-3763	1005	1	..........	..........	PUNCT
ejpam-3763	1005	2	..........	..........	PUNCT
ejpam-3763	1006	1	..........	..........	PUNCT
ejpam-3763	1006	2	..........	..........	PUNCT
ejpam-3763	1007	1	..........	..........	PUNCT
ejpam-3763	1007	2	..........	..........	PUNCT
ejpam-3763	1008	1	..........	..........	PUNCT
ejpam-3763	1008	2	..........	..........	PUNCT
ejpam-3763	1009	1	..........	..........	PUNCT
ejpam-3763	1009	2	..........	..........	PUNCT
ejpam-3763	1010	1	..........	..........	PUNCT
ejpam-3763	1010	2	..........	..........	PUNCT
ejpam-3763	1011	1	..........	..........	PUNCT
ejpam-3763	1011	2	..........	..........	PUNCT
ejpam-3763	1012	1	.......................................................................................................................................................................................................................................	.......................................................................................................................................................................................................................................	PUNCT
ejpam-3763	1012	2	..............	..............	PUNCT
ejpam-3763	1012	3	.............	.............	PUNCT
ejpam-3763	1012	4	.............	.............	PUNCT
ejpam-3763	1012	5	.............	.............	PUNCT
ejpam-3763	1012	6	.............	.............	PUNCT
ejpam-3763	1012	7	.............	.............	PUNCT
ejpam-3763	1012	8	.............	.............	PUNCT
ejpam-3763	1012	9	.............	.............	PUNCT
ejpam-3763	1012	10	.............	.............	PUNCT
ejpam-3763	1013	1	........	........	PUNCT
ejpam-3763	1013	2	...........................................................................................................................................................................................	...........................................................................................................................................................................................	PUNCT
ejpam-3763	1013	3	.................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................	PUNCT
ejpam-3763	1014	1	.........	.........	PUNCT
ejpam-3763	1014	2	........	........	PUNCT
ejpam-3763	1014	3	........	........	PUNCT
ejpam-3763	1014	4	........	........	PUNCT
ejpam-3763	1014	5	........	........	PUNCT
ejpam-3763	1014	6	........	........	PUNCT
ejpam-3763	1014	7	........	........	PUNCT
ejpam-3763	1014	8	........	........	PUNCT
ejpam-3763	1014	9	.......	.......	PUNCT
ejpam-3763	1014	10	.........	.........	PUNCT
ejpam-3763	1015	1	........	........	PUNCT
ejpam-3763	1015	2	........	........	PUNCT
ejpam-3763	1015	3	........	........	PUNCT
ejpam-3763	1015	4	........	........	PUNCT
ejpam-3763	1015	5	........	........	PUNCT
ejpam-3763	1015	6	........	........	PUNCT
ejpam-3763	1015	7	........	........	PUNCT
ejpam-3763	1015	8	.......	.......	PUNCT
ejpam-3763	1016	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3763	1016	2	............	............	PUNCT
ejpam-3763	1016	3	...........	...........	PUNCT
ejpam-3763	1016	4	...........	...........	PUNCT
ejpam-3763	1016	5	...........	...........	PUNCT
ejpam-3763	1016	6	...........	...........	PUNCT
ejpam-3763	1016	7	...........	...........	PUNCT
ejpam-3763	1016	8	............	............	PUNCT
ejpam-3763	1016	9	...........	...........	PUNCT
ejpam-3763	1016	10	...........	...........	PUNCT
ejpam-3763	1016	11	...........	...........	PUNCT
ejpam-3763	1016	12	...........	...........	PUNCT
ejpam-3763	1016	13	...........	...........	PUNCT
ejpam-3763	1016	14	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3763	1017	1	...................................................	...................................................	PUNCT
ejpam-3763	1017	2	...................................................	...................................................	PUNCT
ejpam-3763	1018	1	...................................................	...................................................	PUNCT
ejpam-3763	1018	2	............................................................................................................................................................................................	............................................................................................................................................................................................	PUNCT
ejpam-3763	1019	1	..........	..........	PUNCT
ejpam-3763	1019	2	.........	.........	PUNCT
ejpam-3763	1020	1	.........	.........	PUNCT
ejpam-3763	1020	2	.........	.........	PUNCT
ejpam-3763	1021	1	.........	.........	PUNCT
ejpam-3763	1021	2	.........	.........	PUNCT
ejpam-3763	1022	1	.........	.........	PUNCT
ejpam-3763	1022	2	.........	.........	PUNCT
ejpam-3763	1023	1	.........	.........	PUNCT
ejpam-3763	1023	2	.........	.........	PUNCT
ejpam-3763	1024	1	.........	.........	PUNCT
ejpam-3763	1024	2	.........	.........	PUNCT
ejpam-3763	1025	1	.........	.........	PUNCT
ejpam-3763	1025	2	.........	.........	PUNCT
ejpam-3763	1026	1	.........	.........	PUNCT
ejpam-3763	1026	2	.........	.........	PUNCT
ejpam-3763	1026	3	........	........	PUNCT
ejpam-3763	1026	4	........	........	PUNCT
ejpam-3763	1026	5	........	........	PUNCT
ejpam-3763	1026	6	........	........	PUNCT
ejpam-3763	1026	7	........	........	PUNCT
ejpam-3763	1026	8	........	........	PUNCT
ejpam-3763	1026	9	........	........	PUNCT
ejpam-3763	1026	10	.......	.......	PUNCT
ejpam-3763	1026	11	.........	.........	PUNCT
ejpam-3763	1026	12	........	........	PUNCT
ejpam-3763	1026	13	........	........	PUNCT
ejpam-3763	1026	14	........	........	PUNCT
ejpam-3763	1026	15	........	........	PUNCT
ejpam-3763	1026	16	........	........	PUNCT
ejpam-3763	1026	17	........	........	PUNCT
ejpam-3763	1026	18	........	........	PUNCT
ejpam-3763	1026	19	.......	.......	PUNCT
ejpam-3763	1026	20	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-3763	1027	1	..............	..............	PUNCT
ejpam-3763	1027	2	.............	.............	PUNCT
ejpam-3763	1027	3	.............	.............	PUNCT
ejpam-3763	1027	4	.............	.............	PUNCT
ejpam-3763	1027	5	.............	.............	PUNCT
ejpam-3763	1028	1	.............	.............	PUNCT
ejpam-3763	1028	2	.............	.............	PUNCT
ejpam-3763	1028	3	.............	.............	PUNCT
ejpam-3763	1028	4	.............	.............	PUNCT
ejpam-3763	1028	5	........	........	PUNCT
ejpam-3763	1028	6	..............	..............	PUNCT
ejpam-3763	1028	7	.............	.............	PUNCT
ejpam-3763	1028	8	.............	.............	PUNCT
ejpam-3763	1028	9	.............	.............	PUNCT
ejpam-3763	1028	10	.............	.............	PUNCT
ejpam-3763	1028	11	.............	.............	PUNCT
ejpam-3763	1028	12	.............	.............	PUNCT
ejpam-3763	1028	13	.............	.............	PUNCT
ejpam-3763	1028	14	.............	.............	PUNCT
ejpam-3763	1029	1	........	........	PUNCT
ejpam-3763	1029	2	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-3763	1030	1	...................................................................................................	...................................................................................................	PUNCT
ejpam-3763	1031	1	...................................................................................................	...................................................................................................	PUNCT
ejpam-3763	1032	1	...................................................................................................	...................................................................................................	PUNCT
ejpam-3763	1033	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-3763	1034	1	..........	..........	PUNCT
ejpam-3763	1035	1	..........	..........	PUNCT
ejpam-3763	1036	1	..........	..........	PUNCT
ejpam-3763	1037	1	..........	..........	PUNCT
ejpam-3763	1038	1	..........	..........	PUNCT
ejpam-3763	1039	1	..........	..........	PUNCT
ejpam-3763	1040	1	..........	..........	PUNCT
ejpam-3763	1041	1	..........	..........	PUNCT
ejpam-3763	1042	1	..........	..........	PUNCT
ejpam-3763	1043	1	..........	..........	PUNCT
ejpam-3763	1044	1	..........	..........	PUNCT
ejpam-3763	1045	1	..........	..........	PUNCT
ejpam-3763	1046	1	..........	..........	PUNCT
ejpam-3763	1047	1	..........	..........	PUNCT
ejpam-3763	1048	1	..........	..........	PUNCT
ejpam-3763	1049	1	..........	..........	PUNCT
ejpam-3763	1050	1	..........	..........	PUNCT
ejpam-3763	1051	1	......	......	PUNCT
ejpam-3763	1052	1	.........	.........	PUNCT
ejpam-3763	1053	1	........	........	PUNCT
ejpam-3763	1054	1	........	........	PUNCT
ejpam-3763	1055	1	........	........	PUNCT
ejpam-3763	1056	1	........	........	PUNCT
ejpam-3763	1057	1	........	........	PUNCT
ejpam-3763	1058	1	........	........	PUNCT
ejpam-3763	1059	1	........	........	PUNCT
ejpam-3763	1060	1	.......	.......	PUNCT
ejpam-3763	1061	1	.........	.........	PUNCT
ejpam-3763	1062	1	........	........	PUNCT
ejpam-3763	1063	1	........	........	PUNCT
ejpam-3763	1064	1	........	........	PUNCT
ejpam-3763	1065	1	........	........	PUNCT
ejpam-3763	1066	1	........	........	PUNCT
ejpam-3763	1067	1	........	........	PUNCT
ejpam-3763	1068	1	........	........	PUNCT
ejpam-3763	1069	1	.......	.......	PUNCT
ejpam-3763	1070	1	.............................	.............................	PUNCT
ejpam-3763	1071	1	............................	............................	PUNCT
ejpam-3763	1071	2	............................	............................	PUNCT
ejpam-3763	1071	3	.	.	PUNCT
ejpam-3763	1072	1	.................................................................................................	.................................................................................................	PUNCT
ejpam-3763	1072	2	...............................................................................................................................................................	...............................................................................................................................................................	PUNCT
ejpam-3763	1072	3	............	............	PUNCT
ejpam-3763	1073	1	...........	...........	PUNCT
ejpam-3763	1073	2	...........	...........	PUNCT
ejpam-3763	1073	3	...........	...........	PUNCT
ejpam-3763	1073	4	...........	...........	PUNCT
ejpam-3763	1073	5	...........	...........	PUNCT
ejpam-3763	1073	6	...........	...........	PUNCT
ejpam-3763	1073	7	...........	...........	PUNCT
ejpam-3763	1073	8	...........	...........	PUNCT
ejpam-3763	1073	9	...........	...........	PUNCT
ejpam-3763	1073	10	...........	...........	PUNCT
ejpam-3763	1073	11	...........	...........	PUNCT
ejpam-3763	1073	12	.............................	.............................	PUNCT
ejpam-3763	1073	13	............................	............................	PUNCT
ejpam-3763	1073	14	............................	............................	PUNCT
ejpam-3763	1073	15	.	.	PUNCT
ejpam-3763	1074	1	....................................................................................................	....................................................................................................	PUNCT
ejpam-3763	1074	2	..........	..........	PUNCT
ejpam-3763	1075	1	.........	.........	PUNCT
ejpam-3763	1075	2	.........	.........	PUNCT
ejpam-3763	1076	1	.........	.........	PUNCT
ejpam-3763	1076	2	.........	.........	PUNCT
ejpam-3763	1077	1	.........	.........	PUNCT
ejpam-3763	1077	2	.........	.........	PUNCT
ejpam-3763	1078	1	.........	.........	PUNCT
ejpam-3763	1078	2	.........	.........	PUNCT
ejpam-3763	1079	1	.........	.........	PUNCT
ejpam-3763	1079	2	.........	.........	PUNCT
ejpam-3763	1080	1	.........	.........	PUNCT
ejpam-3763	1080	2	.........	.........	PUNCT
ejpam-3763	1081	1	.........	.........	PUNCT
ejpam-3763	1081	2	.........	.........	PUNCT
ejpam-3763	1082	1	.........	.........	PUNCT
ejpam-3763	1082	2	.........	.........	PUNCT
ejpam-3763	1083	1	.........	.........	PUNCT
ejpam-3763	1083	2	.........	.........	PUNCT
ejpam-3763	1084	1	.........	.........	PUNCT
ejpam-3763	1084	2	.........	.........	PUNCT
ejpam-3763	1085	1	.........	.........	PUNCT
ejpam-3763	1085	2	..	..	PUNCT
ejpam-3763	1085	3	............	............	PUNCT
ejpam-3763	1085	4	...........	...........	PUNCT
ejpam-3763	1085	5	...........	...........	PUNCT
ejpam-3763	1085	6	...........	...........	PUNCT
ejpam-3763	1085	7	...........	...........	PUNCT
ejpam-3763	1085	8	...........	...........	PUNCT
ejpam-3763	1085	9	...........	...........	PUNCT
ejpam-3763	1085	10	...........	...........	PUNCT
ejpam-3763	1085	11	...........	...........	PUNCT
ejpam-3763	1085	12	...........	...........	PUNCT
ejpam-3763	1085	13	...........	...........	PUNCT
ejpam-3763	1085	14	...........	...........	PUNCT
ejpam-3763	1085	15	...................................	...................................	PUNCT
ejpam-3763	1085	16	..................................	..................................	PUNCT
ejpam-3763	1086	1	................	................	PUNCT
ejpam-3763	1086	2	.........	.........	PUNCT
ejpam-3763	1086	3	........	........	PUNCT
ejpam-3763	1086	4	........	........	PUNCT
ejpam-3763	1086	5	........	........	PUNCT
ejpam-3763	1086	6	........	........	PUNCT
ejpam-3763	1086	7	........	........	PUNCT
ejpam-3763	1086	8	........	........	PUNCT
ejpam-3763	1086	9	........	........	PUNCT
ejpam-3763	1086	10	.......	.......	PUNCT
ejpam-3763	1086	11	.........	.........	PUNCT
ejpam-3763	1086	12	........	........	PUNCT
ejpam-3763	1086	13	........	........	PUNCT
ejpam-3763	1086	14	........	........	PUNCT
ejpam-3763	1086	15	........	........	PUNCT
ejpam-3763	1086	16	........	........	PUNCT
ejpam-3763	1086	17	........	........	PUNCT
ejpam-3763	1086	18	........	........	PUNCT
ejpam-3763	1086	19	.......	.......	PUNCT
ejpam-3763	1087	1	..........	..........	PUNCT
ejpam-3763	1087	2	.........	.........	PUNCT
ejpam-3763	1088	1	.........	.........	PUNCT
ejpam-3763	1088	2	.........	.........	PUNCT
ejpam-3763	1089	1	.........	.........	PUNCT
ejpam-3763	1089	2	.........	.........	PUNCT
ejpam-3763	1090	1	.........	.........	PUNCT
ejpam-3763	1090	2	.........	.........	PUNCT
ejpam-3763	1091	1	.........	.........	PUNCT
ejpam-3763	1091	2	.........	.........	PUNCT
ejpam-3763	1092	1	.........	.........	PUNCT
ejpam-3763	1092	2	.........	.........	PUNCT
ejpam-3763	1093	1	..	..	PUNCT
ejpam-3763	1093	2	...................................................................	...................................................................	PUNCT
ejpam-3763	1093	3	...................................................................	...................................................................	PUNCT
ejpam-3763	1094	1	..........	..........	PUNCT
ejpam-3763	1094	2	.........	.........	PUNCT
ejpam-3763	1095	1	.........	.........	PUNCT
ejpam-3763	1095	2	.........	.........	PUNCT
ejpam-3763	1096	1	.........	.........	PUNCT
ejpam-3763	1096	2	.........	.........	PUNCT
ejpam-3763	1097	1	.........	.........	PUNCT
ejpam-3763	1097	2	.........	.........	PUNCT
ejpam-3763	1098	1	.........	.........	PUNCT
ejpam-3763	1098	2	.........	.........	PUNCT
ejpam-3763	1099	1	.........	.........	PUNCT
ejpam-3763	1099	2	.........	.........	PUNCT
ejpam-3763	1099	3	..	..	PUNCT
ejpam-3763	1099	4	...................	...................	PUNCT
ejpam-3763	1099	5	..................	..................	PUNCT
ejpam-3763	1100	1	..............	..............	PUNCT
ejpam-3763	1100	2	...................	...................	PUNCT
ejpam-3763	1101	1	..................	..................	PUNCT
ejpam-3763	1101	2	..............	..............	PUNCT
ejpam-3763	1102	1	...................	...................	PUNCT
ejpam-3763	1102	2	..................	..................	PUNCT
ejpam-3763	1103	1	..............	..............	PUNCT
ejpam-3763	1103	2	..........	..........	PUNCT
ejpam-3763	1104	1	.........	.........	PUNCT
ejpam-3763	1104	2	.........	.........	PUNCT
ejpam-3763	1105	1	.........	.........	PUNCT
ejpam-3763	1105	2	.........	.........	PUNCT
ejpam-3763	1106	1	.........	.........	PUNCT
ejpam-3763	1106	2	.........	.........	PUNCT
ejpam-3763	1107	1	.........	.........	PUNCT
ejpam-3763	1107	2	.........	.........	PUNCT
ejpam-3763	1108	1	.........	.........	PUNCT
ejpam-3763	1108	2	.........	.........	PUNCT
ejpam-3763	1109	1	.........	.........	PUNCT
ejpam-3763	1109	2	.........	.........	PUNCT
ejpam-3763	1110	1	.........	.........	PUNCT
ejpam-3763	1110	2	.........	.........	PUNCT
ejpam-3763	1111	1	.........	.........	PUNCT
ejpam-3763	1111	2	.........	.........	PUNCT
ejpam-3763	1112	1	.........	.........	PUNCT
ejpam-3763	1112	2	.........	.........	PUNCT
ejpam-3763	1113	1	.........	.........	PUNCT
ejpam-3763	1113	2	.......	.......	PUNCT
ejpam-3763	1114	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-3763	1114	2	.........	.........	PUNCT
ejpam-3763	1114	3	........	........	PUNCT
ejpam-3763	1114	4	........	........	PUNCT
ejpam-3763	1114	5	........	........	PUNCT
ejpam-3763	1114	6	........	........	PUNCT
ejpam-3763	1114	7	........	........	PUNCT
ejpam-3763	1114	8	........	........	PUNCT
ejpam-3763	1114	9	........	........	PUNCT
ejpam-3763	1114	10	.......	.......	PUNCT
ejpam-3763	1114	11	.........	.........	PUNCT
ejpam-3763	1114	12	........	........	PUNCT
ejpam-3763	1114	13	........	........	PUNCT
ejpam-3763	1114	14	........	........	PUNCT
ejpam-3763	1114	15	........	........	PUNCT
ejpam-3763	1114	16	........	........	PUNCT
ejpam-3763	1114	17	........	........	PUNCT
ejpam-3763	1114	18	........	........	PUNCT
ejpam-3763	1114	19	.......	.......	PUNCT
ejpam-3763	1115	1	..............	..............	PUNCT
ejpam-3763	1115	2	.............	.............	PUNCT
ejpam-3763	1115	3	.............	.............	PUNCT
ejpam-3763	1115	4	.............	.............	PUNCT
ejpam-3763	1115	5	.............	.............	PUNCT
ejpam-3763	1115	6	.............	.............	PUNCT
ejpam-3763	1115	7	.............	.............	PUNCT
ejpam-3763	1115	8	.............	.............	PUNCT
ejpam-3763	1115	9	.............	.............	PUNCT
ejpam-3763	1116	1	........	........	PUNCT
ejpam-3763	1116	2	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-3763	1116	3	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-3763	1117	1	..............	..............	PUNCT
ejpam-3763	1117	2	.............	.............	PUNCT
ejpam-3763	1117	3	.............	.............	PUNCT
ejpam-3763	1117	4	.............	.............	PUNCT
ejpam-3763	1117	5	.............	.............	PUNCT
ejpam-3763	1117	6	.............	.............	PUNCT
ejpam-3763	1117	7	.............	.............	PUNCT
ejpam-3763	1117	8	.............	.............	PUNCT
ejpam-3763	1117	9	.............	.............	PUNCT
ejpam-3763	1117	10	........	........	PUNCT
ejpam-3763	1117	11	...................................................................................................	...................................................................................................	PUNCT
ejpam-3763	1117	12	...................................................................................................	...................................................................................................	PUNCT
ejpam-3763	1118	1	..............................................................................................................	..............................................................................................................	PUNCT
ejpam-3763	1118	2	..........	..........	PUNCT
ejpam-3763	1119	1	..........	..........	PUNCT
ejpam-3763	1119	2	..........	..........	PUNCT
ejpam-3763	1120	1	..........	..........	PUNCT
ejpam-3763	1120	2	..........	..........	PUNCT
ejpam-3763	1121	1	..........	..........	PUNCT
ejpam-3763	1121	2	..........	..........	PUNCT
ejpam-3763	1122	1	..........	..........	PUNCT
ejpam-3763	1122	2	..........	..........	PUNCT
ejpam-3763	1123	1	..........	..........	PUNCT
ejpam-3763	1123	2	..........	..........	PUNCT
ejpam-3763	1124	1	..........	..........	PUNCT
ejpam-3763	1124	2	..........	..........	PUNCT
ejpam-3763	1125	1	..........	..........	PUNCT
ejpam-3763	1125	2	..........	..........	PUNCT
ejpam-3763	1126	1	..........	..........	PUNCT
ejpam-3763	1126	2	..........	..........	PUNCT
ejpam-3763	1127	1	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-3763	1127	2	.........	.........	PUNCT
ejpam-3763	1128	1	........	........	PUNCT
ejpam-3763	1128	2	........	........	PUNCT
ejpam-3763	1128	3	........	........	PUNCT
ejpam-3763	1128	4	........	........	PUNCT
ejpam-3763	1128	5	........	........	PUNCT
ejpam-3763	1128	6	........	........	PUNCT
ejpam-3763	1128	7	........	........	PUNCT
ejpam-3763	1128	8	.......	.......	PUNCT
ejpam-3763	1128	9	.........	.........	PUNCT
ejpam-3763	1128	10	........	........	PUNCT
ejpam-3763	1128	11	........	........	PUNCT
ejpam-3763	1128	12	........	........	PUNCT
ejpam-3763	1128	13	........	........	PUNCT
ejpam-3763	1128	14	........	........	PUNCT
ejpam-3763	1128	15	........	........	PUNCT
ejpam-3763	1128	16	........	........	PUNCT
ejpam-3763	1128	17	.......	.......	PUNCT
ejpam-3763	1128	18	......................................................................................	......................................................................................	PUNCT
ejpam-3763	1129	1	.................	.................	PUNCT
ejpam-3763	1130	1	................	................	PUNCT
ejpam-3763	1131	1	................	................	PUNCT
ejpam-3763	1132	1	................	................	PUNCT
ejpam-3763	1133	1	................	................	PUNCT
ejpam-3763	1134	1	................	................	PUNCT
ejpam-3763	1135	1	...........	...........	PUNCT
ejpam-3763	1136	1	..........	..........	PUNCT
ejpam-3763	1137	1	..........	..........	PUNCT
ejpam-3763	1138	1	..........	..........	PUNCT
ejpam-3763	1139	1	..........	..........	PUNCT
ejpam-3763	1140	1	..........	..........	PUNCT
ejpam-3763	1141	1	..........	..........	PUNCT
ejpam-3763	1142	1	..........	..........	PUNCT
ejpam-3763	1143	1	..........	..........	PUNCT
ejpam-3763	1144	1	..........	..........	PUNCT
ejpam-3763	1145	1	..........	..........	PUNCT
ejpam-3763	1146	1	..........	..........	PUNCT
ejpam-3763	1147	1	..........	..........	PUNCT
ejpam-3763	1148	1	..........	..........	PUNCT
ejpam-3763	1149	1	..........	..........	PUNCT
ejpam-3763	1150	1	........	........	PUNCT
ejpam-3763	1151	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-3763	1152	1	......................................................................................	......................................................................................	PUNCT
ejpam-3763	1153	1	................	................	PUNCT
ejpam-3763	1153	2	...............	...............	PUNCT
ejpam-3763	1153	3	...............	...............	PUNCT
ejpam-3763	1153	4	...............	...............	PUNCT
ejpam-3763	1153	5	...............	...............	PUNCT
ejpam-3763	1153	6	...............	...............	PUNCT
ejpam-3763	1153	7	.........	.........	PUNCT
ejpam-3763	1154	1	.........................................................................................................................................................................................................	.........................................................................................................................................................................................................	PUNCT
ejpam-3763	1154	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-3763	1155	1	.....................................................................................	.....................................................................................	PUNCT
ejpam-3763	1156	1	•	•	NUM
ejpam-3763	1156	2	•	•	NUM
ejpam-3763	1156	3	•	•	NUM
ejpam-3763	1156	4	•	•	NOUN
ejpam-3763	1156	5	•	•	NOUN
ejpam-3763	1156	6	g[p3	g[p3	NOUN
ejpam-3763	1156	7	]	]	PUNCT
ejpam-3763	1156	8	figure	figure	NOUN
ejpam-3763	1156	9	4	4	NUM
ejpam-3763	1156	10	:	:	PUNCT
ejpam-3763	1156	11	graph	graph	VERB
ejpam-3763	1156	12	g	g	NOUN
ejpam-3763	1156	13	with	with	ADP
ejpam-3763	1156	14	γp	γp	NOUN
ejpam-3763	1156	15	r	r	NOUN
ejpam-3763	1156	16	(	(	PUNCT
ejpam-3763	1156	17	g[p3	g[p3	NOUN
ejpam-3763	1156	18	]	]	X
ejpam-3763	1156	19	)	)	PUNCT
ejpam-3763	1157	1	=	=	SYM
ejpam-3763	1157	2	7	7	NUM
ejpam-3763	1157	3	on	on	ADP
ejpam-3763	1157	4	the	the	DET
ejpam-3763	1157	5	other	other	ADJ
ejpam-3763	1157	6	hand	hand	NOUN
ejpam-3763	1157	7	,	,	PUNCT
ejpam-3763	1157	8	γpr(g[p3	γpr(g[p3	NOUN
ejpam-3763	1157	9	]	]	X
ejpam-3763	1157	10	)	)	PUNCT
ejpam-3763	1157	11	=	=	SYM
ejpam-3763	1158	1	7	7	NUM
ejpam-3763	1158	2	,	,	PUNCT
ejpam-3763	1158	3	which	which	PRON
ejpam-3763	1158	4	is	be	AUX
ejpam-3763	1158	5	determined	determine	VERB
ejpam-3763	1158	6	by	by	ADP
ejpam-3763	1158	7	(	(	PUNCT
ejpam-3763	1158	8	v0	v0	NOUN
ejpam-3763	1158	9	,	,	PUNCT
ejpam-3763	1158	10	v1	v1	NOUN
ejpam-3763	1158	11	,	,	PUNCT
ejpam-3763	1158	12	v2	v2	NOUN
ejpam-3763	1158	13	)	)	PUNCT
ejpam-3763	1158	14	∈	∈	PROPN
ejpam-3763	1158	15	prd(g[p3	prd(g[p3	NOUN
ejpam-3763	1158	16	]	]	X
ejpam-3763	1158	17	)	)	PUNCT
ejpam-3763	1158	18	,	,	PUNCT
ejpam-3763	1158	19	where	where	SCONJ
ejpam-3763	1158	20	v1	v1	NOUN
ejpam-3763	1158	21	and	and	CCONJ
ejpam-3763	1158	22	v2	v2	NOUN
ejpam-3763	1158	23	are	be	AUX
ejpam-3763	1158	24	the	the	DET
ejpam-3763	1158	25	sets	set	NOUN
ejpam-3763	1158	26	of	of	ADP
ejpam-3763	1158	27	all	all	DET
ejpam-3763	1158	28	red	red	ADJ
ejpam-3763	1158	29	and	and	CCONJ
ejpam-3763	1158	30	all	all	DET
ejpam-3763	1158	31	black	black	ADJ
ejpam-3763	1158	32	vertices	vertex	NOUN
ejpam-3763	1158	33	,	,	PUNCT
ejpam-3763	1158	34	respectively	respectively	ADV
ejpam-3763	1158	35	,	,	PUNCT
ejpam-3763	1158	36	in	in	ADP
ejpam-3763	1158	37	g[p3	g[p3	NOUN
ejpam-3763	1158	38	]	]	PUNCT
ejpam-3763	1158	39	and	and	CCONJ
ejpam-3763	1158	40	v0	v0	PROPN
ejpam-3763	1158	41	=	=	SYM
ejpam-3763	1158	42	v	v	PROPN
ejpam-3763	1158	43	(	(	PUNCT
ejpam-3763	1158	44	g[p3	g[p3	NOUN
ejpam-3763	1158	45	]	]	X
ejpam-3763	1158	46	)	)	PUNCT
ejpam-3763	1158	47	\	\	PUNCT
ejpam-3763	1159	1	(	(	PUNCT
ejpam-3763	1159	2	v1	v1	VERB
ejpam-3763	1159	3	∪	∪	NOUN
ejpam-3763	1159	4	v2	v2	NOUN
ejpam-3763	1159	5	)	)	PUNCT
ejpam-3763	1159	6	.	.	PUNCT
ejpam-3763	1160	1	acknowledgements	acknowledgement	NOUN
ejpam-3763	1160	2	this	this	DET
ejpam-3763	1160	3	research	research	NOUN
ejpam-3763	1160	4	is	be	AUX
ejpam-3763	1160	5	fully	fully	ADV
ejpam-3763	1160	6	funded	fund	VERB
ejpam-3763	1160	7	by	by	ADP
ejpam-3763	1160	8	the	the	DET
ejpam-3763	1160	9	commission	commission	NOUN
ejpam-3763	1160	10	on	on	ADP
ejpam-3763	1160	11	higher	high	ADJ
ejpam-3763	1160	12	education	education	NOUN
ejpam-3763	1160	13	(	(	PUNCT
ejpam-3763	1160	14	ched	ched	ADJ
ejpam-3763	1160	15	)	)	PUNCT
ejpam-3763	1160	16	philippines	philippine	NOUN
ejpam-3763	1160	17	under	under	ADP
ejpam-3763	1160	18	the	the	DET
ejpam-3763	1160	19	ched	che	VERB
ejpam-3763	1160	20	k-12	k-12	PROPN
ejpam-3763	1160	21	transition	transition	NOUN
ejpam-3763	1160	22	program	program	NOUN
ejpam-3763	1160	23	and	and	CCONJ
ejpam-3763	1160	24	university	university	NOUN
ejpam-3763	1160	25	of	of	ADP
ejpam-3763	1160	26	southern	southern	ADJ
ejpam-3763	1160	27	mindanao	mindanao	PROPN
ejpam-3763	1160	28	research	research	NOUN
ejpam-3763	1160	29	and	and	CCONJ
ejpam-3763	1160	30	faculty	faculty	NOUN
ejpam-3763	1160	31	development	development	NOUN
ejpam-3763	1160	32	program	program	NOUN
ejpam-3763	1160	33	.	.	PUNCT
ejpam-3763	1161	1	references	reference	NOUN
ejpam-3763	1161	2	[	[	X
ejpam-3763	1161	3	1	1	NUM
ejpam-3763	1161	4	]	]	PUNCT
ejpam-3763	1161	5	h.	h.	NOUN
ejpam-3763	1161	6	abdollhzadeh	abdollhzadeh	PROPN
ejpam-3763	1161	7	ahangar	ahangar	NOUN
ejpam-3763	1161	8	.	.	PUNCT
ejpam-3763	1162	1	m.	m.	NOUN
ejpam-3763	1162	2	chellali	chellali	PROPN
ejpam-3763	1162	3	and	and	CCONJ
ejpam-3763	1162	4	s.m	s.m	PROPN
ejpam-3763	1162	5	.	.	PROPN
ejpam-3763	1162	6	sheikholeslami	sheikholeslami	PROPN
ejpam-3763	1162	7	,	,	PUNCT
ejpam-3763	1162	8	outer	outer	ADJ
ejpam-3763	1162	9	independent	independent	ADJ
ejpam-3763	1162	10	double	double	ADJ
ejpam-3763	1162	11	roman	roman	ADJ
ejpam-3763	1162	12	domination	domination	NOUN
ejpam-3763	1162	13	.	.	PUNCT
ejpam-3763	1163	1	appl	appl	PROPN
ejpam-3763	1163	2	.	.	PROPN
ejpam-3763	1163	3	math	math	PROPN
ejpam-3763	1163	4	.	.	PUNCT
ejpam-3763	1164	1	comput	comput	NOUN
ejpam-3763	1164	2	.	.	PUNCT
ejpam-3763	1164	3	,	,	PUNCT
ejpam-3763	1164	4	364(124617	364(124617	NUM
ejpam-3763	1164	5	)	)	PUNCT
ejpam-3763	1164	6	,	,	PUNCT
ejpam-3763	1164	7	2020	2020	NUM
ejpam-3763	1164	8	.	.	PUNCT
ejpam-3763	1165	1	[	[	X
ejpam-3763	1165	2	2	2	NUM
ejpam-3763	1165	3	]	]	PUNCT
ejpam-3763	1165	4	a.	a.	NOUN
ejpam-3763	1165	5	alhashim	alhashim	NOUN
ejpam-3763	1165	6	.	.	PUNCT
ejpam-3763	1166	1	w.	w.	PROPN
ejpam-3763	1166	2	desormeaux	desormeaux	PROPN
ejpam-3763	1166	3	and	and	CCONJ
ejpam-3763	1166	4	t.	t.	PROPN
ejpam-3763	1166	5	haynes	hayne	NOUN
ejpam-3763	1166	6	.	.	PUNCT
ejpam-3763	1167	1	roman	roman	ADJ
ejpam-3763	1167	2	domination	domination	NOUN
ejpam-3763	1167	3	in	in	ADP
ejpam-3763	1167	4	complementary	complementary	ADJ
ejpam-3763	1167	5	prisms	prism	NOUN
ejpam-3763	1167	6	.	.	PUNCT
ejpam-3763	1168	1	australian	australian	ADJ
ejpam-3763	1168	2	journal	journal	NOUN
ejpam-3763	1168	3	of	of	ADP
ejpam-3763	1168	4	combinatorics	combinatoric	NOUN
ejpam-3763	1168	5	,	,	PUNCT
ejpam-3763	1168	6	68(2):218–228	68(2):218–228	NUM
ejpam-3763	1168	7	,	,	PUNCT
ejpam-3763	1168	8	2017	2017	NUM
ejpam-3763	1168	9	.	.	PUNCT
ejpam-3763	1169	1	[	[	X
ejpam-3763	1169	2	3	3	X
ejpam-3763	1169	3	]	]	X
ejpam-3763	1169	4	j.	j.	PROPN
ejpam-3763	1169	5	arquilla	arquilla	PROPN
ejpam-3763	1169	6	and	and	CCONJ
ejpam-3763	1169	7	h.	h.	PROPN
ejpam-3763	1169	8	fredricksen	fredricksen	PROPN
ejpam-3763	1169	9	.	.	PUNCT
ejpam-3763	1170	1	“	"	PUNCT
ejpam-3763	1170	2	graphing	graph	VERB
ejpam-3763	1170	3	“	"	PUNCT
ejpam-3763	1170	4	an	an	DET
ejpam-3763	1170	5	optimal	optimal	ADJ
ejpam-3763	1170	6	grand	grand	ADJ
ejpam-3763	1170	7	strategy	strategy	NOUN
ejpam-3763	1170	8	.	.	PUNCT
ejpam-3763	1171	1	military	military	ADJ
ejpam-3763	1171	2	operations	operation	NOUN
ejpam-3763	1171	3	research	research	NOUN
ejpam-3763	1171	4	,	,	PUNCT
ejpam-3763	1171	5	1:3–19	1:3–19	NUM
ejpam-3763	1171	6	,	,	PUNCT
ejpam-3763	1171	7	1995	1995	NUM
ejpam-3763	1171	8	.	.	PUNCT
ejpam-3763	1172	1	[	[	X
ejpam-3763	1172	2	4	4	NUM
ejpam-3763	1172	3	]	]	X
ejpam-3763	1172	4	c.	c.	PROPN
ejpam-3763	1172	5	berge	berge	PROPN
ejpam-3763	1172	6	.	.	PUNCT
ejpam-3763	1173	1	the	the	DET
ejpam-3763	1173	2	theory	theory	NOUN
ejpam-3763	1173	3	of	of	ADP
ejpam-3763	1173	4	graphs	graph	NOUN
ejpam-3763	1173	5	and	and	CCONJ
ejpam-3763	1173	6	its	its	PRON
ejpam-3763	1173	7	applications	application	NOUN
ejpam-3763	1173	8	.	.	PUNCT
ejpam-3763	1174	1	wiley	wiley	PROPN
ejpam-3763	1174	2	,	,	PUNCT
ejpam-3763	1174	3	new	new	PROPN
ejpam-3763	1174	4	york	york	PROPN
ejpam-3763	1174	5	,	,	PUNCT
ejpam-3763	1174	6	1962	1962	NUM
ejpam-3763	1174	7	.	.	PUNCT
ejpam-3763	1175	1	references	reference	NOUN
ejpam-3763	1175	2	548	548	NUM
ejpam-3763	1175	3	[	[	X
ejpam-3763	1175	4	5	5	NUM
ejpam-3763	1175	5	]	]	X
ejpam-3763	1175	6	f.	f.	PROPN
ejpam-3763	1175	7	buckley	buckley	PROPN
ejpam-3763	1175	8	and	and	CCONJ
ejpam-3763	1175	9	f.	f.	PROPN
ejpam-3763	1175	10	harary	harary	PROPN
ejpam-3763	1175	11	.	.	PUNCT
ejpam-3763	1176	1	distance	distance	NOUN
ejpam-3763	1176	2	in	in	ADP
ejpam-3763	1176	3	graphs	graph	NOUN
ejpam-3763	1176	4	.	.	PUNCT
ejpam-3763	1177	1	addison	addison	PROPN
ejpam-3763	1177	2	-	-	PUNCT
ejpam-3763	1177	3	wesley	wesley	PROPN
ejpam-3763	1177	4	,	,	PUNCT
ejpam-3763	1177	5	redwood	redwood	NOUN
ejpam-3763	1177	6	city	city	NOUN
ejpam-3763	1177	7	,	,	PUNCT
ejpam-3763	1177	8	ca	ca	NOUN
ejpam-3763	1177	9	,	,	PUNCT
ejpam-3763	1177	10	1990	1990	NUM
ejpam-3763	1177	11	.	.	PUNCT
ejpam-3763	1178	1	[	[	X
ejpam-3763	1178	2	6	6	NUM
ejpam-3763	1178	3	]	]	PUNCT
ejpam-3763	1178	4	s.	s.	PROPN
ejpam-3763	1178	5	canoy	canoy	PROPN
ejpam-3763	1178	6	.	.	PUNCT
ejpam-3763	1179	1	r.	r.	PROPN
ejpam-3763	1179	2	mollejon	mollejon	NOUN
ejpam-3763	1179	3	and	and	CCONJ
ejpam-3763	1179	4	j.g	j.g	PROPN
ejpam-3763	1179	5	.	.	PROPN
ejpam-3763	1179	6	canoy	canoy	PROPN
ejpam-3763	1179	7	.	.	PUNCT
ejpam-3763	1180	1	hop	hop	PROPN
ejpam-3763	1180	2	dominating	dominating	NOUN
ejpam-3763	1180	3	sets	set	NOUN
ejpam-3763	1180	4	in	in	ADP
ejpam-3763	1180	5	graphs	graph	NOUN
ejpam-3763	1180	6	under	under	ADP
ejpam-3763	1180	7	binary	binary	ADJ
ejpam-3763	1180	8	operations	operation	NOUN
ejpam-3763	1180	9	.	.	PUNCT
ejpam-3763	1181	1	european	european	ADJ
ejpam-3763	1181	2	journal	journal	PROPN
ejpam-3763	1181	3	of	of	ADP
ejpam-3763	1181	4	pure	pure	ADJ
ejpam-3763	1181	5	and	and	CCONJ
ejpam-3763	1181	6	applied	applied	ADJ
ejpam-3763	1181	7	mathematics	mathematic	NOUN
ejpam-3763	1181	8	,	,	PUNCT
ejpam-3763	1181	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-3763	1181	10	,	,	PUNCT
ejpam-3763	1181	11	2019	2019	NUM
ejpam-3763	1181	12	.	.	PUNCT
ejpam-3763	1182	1	[	[	X
ejpam-3763	1182	2	7	7	X
ejpam-3763	1182	3	]	]	X
ejpam-3763	1182	4	b.	b.	PROPN
ejpam-3763	1182	5	chaluvaraju	chaluvaraju	PROPN
ejpam-3763	1182	6	and	and	CCONJ
ejpam-3763	1182	7	v.	v.	ADP
ejpam-3763	1182	8	chaitra	chaitra	PROPN
ejpam-3763	1182	9	.	.	PUNCT
ejpam-3763	1183	1	roman	roman	ADJ
ejpam-3763	1183	2	domination	domination	NOUN
ejpam-3763	1183	3	in	in	ADP
ejpam-3763	1183	4	complimentary	complimentary	ADJ
ejpam-3763	1183	5	prism	prism	NOUN
ejpam-3763	1183	6	.	.	PUNCT
ejpam-3763	1184	1	international	international	ADJ
ejpam-3763	1184	2	j.math	j.math	PROPN
ejpam-3763	1184	3	.	.	PUNCT
ejpam-3763	1185	1	combi	combi	PROPN
ejpam-3763	1185	2	.	.	PROPN
ejpam-3763	1185	3	,	,	PUNCT
ejpam-3763	1185	4	2:24–31	2:24–31	NUM
ejpam-3763	1185	5	,	,	PUNCT
ejpam-3763	1185	6	2012	2012	NUM
ejpam-3763	1185	7	.	.	PUNCT
ejpam-3763	1186	1	[	[	X
ejpam-3763	1186	2	8	8	NUM
ejpam-3763	1186	3	]	]	X
ejpam-3763	1186	4	e.	e.	PROPN
ejpam-3763	1186	5	cockayne	cockayne	PROPN
ejpam-3763	1186	6	.	.	PUNCT
ejpam-3763	1187	1	p.	p.	NOUN
ejpam-3763	1187	2	dreyer	dreyer	PROPN
ejpam-3763	1188	1	jr	jr	PROPN
ejpam-3763	1188	2	.	.	PROPN
ejpam-3763	1188	3	,	,	PUNCT
ejpam-3763	1188	4	s.m	s.m	PROPN
ejpam-3763	1188	5	.	.	PROPN
ejpam-3763	1188	6	hedetniemi	hedetniemi	PROPN
ejpam-3763	1188	7	and	and	CCONJ
ejpam-3763	1188	8	s.t	s.t	PROPN
ejpam-3763	1188	9	.	.	PROPN
ejpam-3763	1188	10	hedetniemi	hedetniemi	PROPN
ejpam-3763	1188	11	.	.	PUNCT
ejpam-3763	1189	1	roman	roman	ADJ
ejpam-3763	1189	2	domination	domination	NOUN
ejpam-3763	1189	3	in	in	ADP
ejpam-3763	1189	4	graphs	graph	NOUN
ejpam-3763	1189	5	.	.	PUNCT
ejpam-3763	1190	1	discrete	discrete	ADJ
ejpam-3763	1190	2	mathematics	mathematic	NOUN
ejpam-3763	1190	3	,	,	PUNCT
ejpam-3763	1190	4	278:11–22	278:11–22	NUM
ejpam-3763	1190	5	,	,	PUNCT
ejpam-3763	1190	6	2004	2004	NUM
ejpam-3763	1190	7	.	.	PUNCT
ejpam-3763	1191	1	[	[	X
ejpam-3763	1191	2	9	9	NUM
ejpam-3763	1191	3	]	]	X
ejpam-3763	1191	4	e.	e.	PROPN
ejpam-3763	1191	5	cockayne	cockayne	PROPN
ejpam-3763	1191	6	and	and	CCONJ
ejpam-3763	1191	7	s.	s.	PROPN
ejpam-3763	1191	8	hedetniemi	hedetniemi	PROPN
ejpam-3763	1191	9	.	.	PUNCT
ejpam-3763	1192	1	towards	towards	ADP
ejpam-3763	1192	2	a	a	DET
ejpam-3763	1192	3	theory	theory	NOUN
ejpam-3763	1192	4	of	of	ADP
ejpam-3763	1192	5	domination	domination	NOUN
ejpam-3763	1192	6	in	in	ADP
ejpam-3763	1192	7	graphs	graph	NOUN
ejpam-3763	1192	8	.	.	PUNCT
ejpam-3763	1193	1	networks	network	NOUN
ejpam-3763	1193	2	,	,	PUNCT
ejpam-3763	1193	3	7(3):1977	7(3):1977	NUM
ejpam-3763	1193	4	,	,	PUNCT
ejpam-3763	1193	5	1977	1977	NUM
ejpam-3763	1193	6	.	.	PUNCT
ejpam-3763	1194	1	[	[	X
ejpam-3763	1194	2	10	10	NUM
ejpam-3763	1194	3	]	]	PUNCT
ejpam-3763	1194	4	p.	p.	NOUN
ejpam-3763	1194	5	dankelmann	dankelmann	PROPN
ejpam-3763	1194	6	,	,	PUNCT
ejpam-3763	1194	7	d.	d.	PROPN
ejpam-3763	1194	8	day	day	PROPN
ejpam-3763	1194	9	,	,	PUNCT
ejpam-3763	1194	10	d.	d.	PROPN
ejpam-3763	1194	11	erwin	erwin	PROPN
ejpam-3763	1194	12	,	,	PUNCT
ejpam-3763	1194	13	s.	s.	PROPN
ejpam-3763	1194	14	mukwembi	mukwembi	PROPN
ejpam-3763	1194	15	,	,	PUNCT
ejpam-3763	1194	16	and	and	CCONJ
ejpam-3763	1194	17	h.	h.	PROPN
ejpam-3763	1194	18	swart	swart	PROPN
ejpam-3763	1194	19	.	.	PUNCT
ejpam-3763	1195	1	domination	domination	NOUN
ejpam-3763	1195	2	with	with	ADP
ejpam-3763	1195	3	exponential	exponential	ADJ
ejpam-3763	1195	4	decay	decay	NOUN
ejpam-3763	1195	5	.	.	PUNCT
ejpam-3763	1196	1	discrete	discrete	ADJ
ejpam-3763	1196	2	mathematics	mathematic	NOUN
ejpam-3763	1196	3	,	,	PUNCT
ejpam-3763	1196	4	309:5877–5883	309:5877–5883	NUM
ejpam-3763	1196	5	,	,	PUNCT
ejpam-3763	1196	6	2009	2009	NUM
ejpam-3763	1196	7	.	.	PUNCT
ejpam-3763	1197	1	[	[	X
ejpam-3763	1197	2	11	11	NUM
ejpam-3763	1197	3	]	]	PUNCT
ejpam-3763	1197	4	w.	w.	PROPN
ejpam-3763	1197	5	desormeaux	desormeaux	PROPN
ejpam-3763	1197	6	.	.	PUNCT
ejpam-3763	1198	1	t.w	t.w	PROPN
ejpam-3763	1198	2	.	.	PROPN
ejpam-3763	1198	3	haynes	haynes	PROPN
ejpam-3763	1198	4	and	and	CCONJ
ejpam-3763	1198	5	m.a	m.a	PROPN
ejpam-3763	1198	6	.	.	PROPN
ejpam-3763	1198	7	henning	henning	PROPN
ejpam-3763	1198	8	.	.	PUNCT
ejpam-3763	1199	1	an	an	DET
ejpam-3763	1199	2	extremal	extremal	ADJ
ejpam-3763	1199	3	problem	problem	NOUN
ejpam-3763	1199	4	for	for	ADP
ejpam-3763	1199	5	total	total	ADJ
ejpam-3763	1199	6	domination	domination	NOUN
ejpam-3763	1199	7	stable	stable	ADJ
ejpam-3763	1199	8	graphs	graph	NOUN
ejpam-3763	1199	9	upon	upon	SCONJ
ejpam-3763	1199	10	edge	edge	NOUN
ejpam-3763	1199	11	removal	removal	NOUN
ejpam-3763	1199	12	.	.	PUNCT
ejpam-3763	1200	1	discrete	discrete	ADJ
ejpam-3763	1200	2	applied	applied	ADJ
ejpam-3763	1200	3	mathematics	mathematic	NOUN
ejpam-3763	1200	4	,	,	PUNCT
ejpam-3763	1200	5	159:1048–1052	159:1048–1052	NUM
ejpam-3763	1200	6	,	,	PUNCT
ejpam-3763	1200	7	2011	2011	NUM
ejpam-3763	1200	8	.	.	PUNCT
ejpam-3763	1201	1	[	[	X
ejpam-3763	1201	2	12	12	NUM
ejpam-3763	1201	3	]	]	X
ejpam-3763	1201	4	o.	o.	PROPN
ejpam-3763	1201	5	favaron	favaron	PROPN
ejpam-3763	1201	6	.	.	PUNCT
ejpam-3763	1201	7	,	,	PUNCT
ejpam-3763	1201	8	h.	h.	PROPN
ejpam-3763	1201	9	karami	karami	PROPN
ejpam-3763	1201	10	and	and	CCONJ
ejpam-3763	1201	11	r.	r.	PROPN
ejpam-3763	1201	12	khoeilar	khoeilar	PROPN
ejpam-3763	1201	13	and	and	CCONJ
ejpam-3763	1201	14	s.m	s.m	PROPN
ejpam-3763	1201	15	.	.	PROPN
ejpam-3763	1201	16	sheikholeslami	sheikholeslami	PROPN
ejpam-3763	1201	17	.	.	PUNCT
ejpam-3763	1202	1	on	on	ADP
ejpam-3763	1202	2	the	the	DET
ejpam-3763	1202	3	roman	roman	ADJ
ejpam-3763	1202	4	domination	domination	NOUN
ejpam-3763	1202	5	number	number	NOUN
ejpam-3763	1202	6	of	of	ADP
ejpam-3763	1202	7	a	a	DET
ejpam-3763	1202	8	graph	graph	NOUN
ejpam-3763	1202	9	.	.	PUNCT
ejpam-3763	1202	10	discrete	discrete	ADJ
ejpam-3763	1202	11	mathematics	mathematic	NOUN
ejpam-3763	1202	12	,	,	PUNCT
ejpam-3763	1202	13	309:3447–3451	309:3447–3451	NUM
ejpam-3763	1202	14	,	,	PUNCT
ejpam-3763	1202	15	2009	2009	NUM
ejpam-3763	1202	16	.	.	PUNCT
ejpam-3763	1203	1	[	[	X
ejpam-3763	1203	2	13	13	NUM
ejpam-3763	1203	3	]	]	PUNCT
ejpam-3763	1203	4	t.	t.	PROPN
ejpam-3763	1203	5	haynes	haynes	PROPN
ejpam-3763	1203	6	,	,	PUNCT
ejpam-3763	1203	7	s.t	s.t	PROPN
ejpam-3763	1203	8	.	.	PROPN
ejpam-3763	1203	9	hedetniemi	hedetniemi	PROPN
ejpam-3763	1203	10	,	,	PUNCT
ejpam-3763	1203	11	and	and	CCONJ
ejpam-3763	1203	12	p.j	p.j	PROPN
ejpam-3763	1203	13	.	.	PROPN
ejpam-3763	1203	14	slater	slater	PROPN
ejpam-3763	1203	15	.	.	PUNCT
ejpam-3763	1204	1	fundamentals	fundamental	NOUN
ejpam-3763	1204	2	of	of	ADP
ejpam-3763	1204	3	domination	domination	NOUN
ejpam-3763	1204	4	in	in	ADP
ejpam-3763	1204	5	graphs	graph	NOUN
ejpam-3763	1204	6	.	.	PUNCT
ejpam-3763	1205	1	marcel	marcel	PROPN
ejpam-3763	1205	2	dekker	dekker	PROPN
ejpam-3763	1205	3	,	,	PUNCT
ejpam-3763	1205	4	inc	inc	PROPN
ejpam-3763	1205	5	.	.	PROPN
ejpam-3763	1205	6	,	,	PUNCT
ejpam-3763	1205	7	new	new	PROPN
ejpam-3763	1205	8	york	york	PROPN
ejpam-3763	1205	9	,	,	PUNCT
ejpam-3763	1205	10	1998	1998	NUM
ejpam-3763	1205	11	.	.	PUNCT
ejpam-3763	1206	1	[	[	X
ejpam-3763	1206	2	14	14	NUM
ejpam-3763	1206	3	]	]	PUNCT
ejpam-3763	1206	4	m.	m.	NOUN
ejpam-3763	1206	5	henning	henning	PROPN
ejpam-3763	1206	6	.	.	PUNCT
ejpam-3763	1207	1	w.	w.	PROPN
ejpam-3763	1207	2	klostermeyer	klostermeyer	PROPN
ejpam-3763	1207	3	and	and	CCONJ
ejpam-3763	1207	4	g.	g.	PROPN
ejpam-3763	1207	5	macgillivray	macgillivray	PROPN
ejpam-3763	1207	6	.	.	PUNCT
ejpam-3763	1208	1	perfect	perfect	ADJ
ejpam-3763	1208	2	roman	roman	ADJ
ejpam-3763	1208	3	domination	domination	NOUN
ejpam-3763	1208	4	in	in	ADP
ejpam-3763	1208	5	trees	tree	NOUN
ejpam-3763	1208	6	.	.	PUNCT
ejpam-3763	1209	1	discrete	discrete	ADJ
ejpam-3763	1209	2	applied	apply	VERB
ejpam-3763	1209	3	mathematics	mathematic	NOUN
ejpam-3763	1209	4	,	,	PUNCT
ejpam-3763	1209	5	236:235–245	236:235–245	NUM
ejpam-3763	1209	6	,	,	PUNCT
ejpam-3763	1209	7	2018	2018	NUM
ejpam-3763	1209	8	.	.	PUNCT
ejpam-3763	1210	1	[	[	X
ejpam-3763	1210	2	15	15	NUM
ejpam-3763	1210	3	]	]	X
ejpam-3763	1210	4	m.	m.	NOUN
ejpam-3763	1210	5	henning	henning	PROPN
ejpam-3763	1210	6	and	and	CCONJ
ejpam-3763	1210	7	w.	w.	PROPN
ejpam-3763	1210	8	klostermeyer	klostermeyer	PROPN
ejpam-3763	1210	9	.	.	PUNCT
ejpam-3763	1211	1	perfect	perfect	ADJ
ejpam-3763	1211	2	roman	roman	ADJ
ejpam-3763	1211	3	domination	domination	NOUN
ejpam-3763	1211	4	in	in	ADP
ejpam-3763	1211	5	regular	regular	ADJ
ejpam-3763	1211	6	grahs	grah	NOUN
ejpam-3763	1211	7	.	.	PUNCT
ejpam-3763	1212	1	applicable	applicable	ADJ
ejpam-3763	1212	2	analysis	analysis	NOUN
ejpam-3763	1212	3	and	and	CCONJ
ejpam-3763	1212	4	discrete	discrete	ADJ
ejpam-3763	1212	5	mathematics	mathematic	NOUN
ejpam-3763	1212	6	,	,	PUNCT
ejpam-3763	1212	7	12(1):143–152	12(1):143–152	NUM
ejpam-3763	1212	8	,	,	PUNCT
ejpam-3763	1212	9	2018	2018	NUM
ejpam-3763	1212	10	.	.	PUNCT
ejpam-3763	1213	1	[	[	X
ejpam-3763	1213	2	16	16	X
ejpam-3763	1213	3	]	]	X
ejpam-3763	1213	4	y.	y.	PROPN
ejpam-3763	1213	5	kwon	kwon	PROPN
ejpam-3763	1213	6	and	and	CCONJ
ejpam-3763	1213	7	j.	j.	PROPN
ejpam-3763	1213	8	lee	lee	PROPN
ejpam-3763	1213	9	.	.	PROPN
ejpam-3763	1213	10	perfect	perfect	ADJ
ejpam-3763	1213	11	dominating	dominating	NOUN
ejpam-3763	1213	12	sets	set	NOUN
ejpam-3763	1213	13	in	in	ADP
ejpam-3763	1213	14	cayley	cayley	ADJ
ejpam-3763	1213	15	graphs	graph	NOUN
ejpam-3763	1213	16	.	.	PUNCT
ejpam-3763	1214	1	discrete	discrete	ADJ
ejpam-3763	1214	2	applied	apply	VERB
ejpam-3763	1214	3	mathematics	mathematic	NOUN
ejpam-3763	1214	4	,	,	PUNCT
ejpam-3763	1214	5	162:259–263	162:259–263	NUM
ejpam-3763	1214	6	,	,	PUNCT
ejpam-3763	1214	7	2014	2014	NUM
ejpam-3763	1214	8	.	.	PUNCT
ejpam-3763	1215	1	[	[	X
ejpam-3763	1215	2	17	17	NUM
ejpam-3763	1215	3	]	]	X
ejpam-3763	1215	4	c.s	c.s	PROPN
ejpam-3763	1215	5	.	.	PROPN
ejpam-3763	1215	6	revelle	revelle	PROPN
ejpam-3763	1215	7	and	and	CCONJ
ejpam-3763	1215	8	k.e	k.e	PROPN
ejpam-3763	1215	9	.	.	PUNCT
ejpam-3763	1216	1	rosing	rosing	PROPN
ejpam-3763	1216	2	.	.	PUNCT
ejpam-3763	1217	1	defendens	defenden	VERB
ejpam-3763	1217	2	imperium	imperium	NOUN
ejpam-3763	1217	3	romanum	romanum	NOUN
ejpam-3763	1217	4	:	:	PUNCT
ejpam-3763	1217	5	a	a	DET
ejpam-3763	1217	6	classical	classical	ADJ
ejpam-3763	1217	7	problem	problem	NOUN
ejpam-3763	1217	8	in	in	ADP
ejpam-3763	1217	9	military	military	ADJ
ejpam-3763	1217	10	strategy	strategy	NOUN
ejpam-3763	1217	11	.	.	PUNCT
ejpam-3763	1218	1	amer	amer	PROPN
ejpam-3763	1218	2	.	.	PUNCT
ejpam-3763	1218	3	math	math	PROPN
ejpam-3763	1218	4	.	.	PUNCT
ejpam-3763	1219	1	monthly	monthly	ADJ
ejpam-3763	1219	2	,	,	PUNCT
ejpam-3763	1219	3	107(7):585–594	107(7):585–594	PROPN
ejpam-3763	1219	4	,	,	PUNCT
ejpam-3763	1219	5	2000	2000	NUM
ejpam-3763	1219	6	.	.	PUNCT
ejpam-3763	1220	1	[	[	X
ejpam-3763	1220	2	18	18	NUM
ejpam-3763	1220	3	]	]	X
ejpam-3763	1220	4	i.	i.	PROPN
ejpam-3763	1220	5	stewart	stewart	PROPN
ejpam-3763	1220	6	.	.	PUNCT
ejpam-3763	1221	1	defend	defend	VERB
ejpam-3763	1221	2	the	the	DET
ejpam-3763	1221	3	roman	roman	ADJ
ejpam-3763	1221	4	empire	empire	NOUN
ejpam-3763	1221	5	.	.	PUNCT
ejpam-3763	1222	1	sci	sci	PROPN
ejpam-3763	1222	2	.	.	PROPN
ejpam-3763	1222	3	amer	amer	PROPN
ejpam-3763	1222	4	.	.	PROPN
ejpam-3763	1222	5	,	,	PUNCT
ejpam-3763	1222	6	281(6):136–139	281(6):136–139	NUM
ejpam-3763	1222	7	,	,	PUNCT
ejpam-3763	1222	8	1999	1999	NUM
ejpam-3763	1222	9	.	.	PUNCT
ejpam-3763	1223	1	[	[	X
ejpam-3763	1223	2	19	19	NUM
ejpam-3763	1223	3	]	]	PUNCT
ejpam-3763	1223	4	j.	j.	PROPN
ejpam-3763	1223	5	yue	yue	PROPN
ejpam-3763	1223	6	and	and	CCONJ
ejpam-3763	1223	7	j.	j.	PROPN
ejpam-3763	1223	8	song	song	PROPN
ejpam-3763	1223	9	.	.	PUNCT
ejpam-3763	1224	1	note	note	NOUN
ejpam-3763	1224	2	on	on	ADP
ejpam-3763	1224	3	the	the	DET
ejpam-3763	1224	4	perfect	perfect	ADJ
ejpam-3763	1224	5	roman	roman	ADJ
ejpam-3763	1224	6	domination	domination	NOUN
ejpam-3763	1224	7	number	number	NOUN
ejpam-3763	1224	8	of	of	ADP
ejpam-3763	1224	9	graphs	graph	NOUN
ejpam-3763	1224	10	.	.	PUNCT
ejpam-3763	1225	1	applied	apply	VERB
ejpam-3763	1225	2	mathematics	mathematic	NOUN
ejpam-3763	1225	3	and	and	CCONJ
ejpam-3763	1225	4	computation	computation	NOUN
ejpam-3763	1225	5	,	,	PUNCT
ejpam-3763	1225	6	364:1–5	364:1–5	NUM
ejpam-3763	1225	7	,	,	PUNCT
ejpam-3763	1225	8	2020	2020	NUM
ejpam-3763	1225	9	.	.	PUNCT
ejpam-3763	1226	1	[	[	X
ejpam-3763	1226	2	20	20	NUM
ejpam-3763	1226	3	]	]	PUNCT
ejpam-3763	1226	4	j.	j.	PROPN
ejpam-3763	1226	5	yue	yue	PROPN
ejpam-3763	1226	6	,	,	PUNCT
ejpam-3763	1226	7	m.	m.	PROPN
ejpam-3763	1226	8	wei	wei	PROPN
ejpam-3763	1226	9	,	,	PUNCT
ejpam-3763	1226	10	m.	m.	PROPN
ejpam-3763	1226	11	li	li	PROPN
ejpam-3763	1226	12	,	,	PUNCT
ejpam-3763	1226	13	and	and	CCONJ
ejpam-3763	1226	14	g.	g.	PROPN
ejpam-3763	1226	15	liu	liu	PROPN
ejpam-3763	1226	16	.	.	PUNCT
ejpam-3763	1227	1	on	on	ADP
ejpam-3763	1227	2	the	the	DET
ejpam-3763	1227	3	double	double	ADJ
ejpam-3763	1227	4	roman	roman	ADJ
ejpam-3763	1227	5	domination	domination	NOUN
ejpam-3763	1227	6	of	of	ADP
ejpam-3763	1227	7	graphs	graph	NOUN
ejpam-3763	1227	8	.	.	PUNCT
ejpam-3763	1228	1	applied	apply	VERB
ejpam-3763	1228	2	mathematics	mathematic	NOUN
ejpam-3763	1228	3	and	and	CCONJ
ejpam-3763	1228	4	computation	computation	NOUN
ejpam-3763	1228	5	,	,	PUNCT
ejpam-3763	1228	6	338:669–675	338:669–675	NUM
ejpam-3763	1228	7	,	,	PUNCT
ejpam-3763	1228	8	2018	2018	NUM
ejpam-3763	1228	9	.	.	PUNCT