id	sid	tid	token	lemma	pos
ejpam-6851	1	1	european	european	PROPN
ejpam-6851	1	2	journal	journal	PROPN
ejpam-6851	1	3	of	of	ADP
ejpam-6851	1	4	pure	pure	ADJ
ejpam-6851	1	5	and	and	CCONJ
ejpam-6851	1	6	applied	applied	ADJ
ejpam-6851	1	7	mathematics	mathematic	NOUN
ejpam-6851	1	8	2025	2025	NUM
ejpam-6851	1	9	,	,	PUNCT
ejpam-6851	1	10	vol	vol	NOUN
ejpam-6851	1	11	.	.	PROPN
ejpam-6851	1	12	18	18	NUM
ejpam-6851	1	13	,	,	PUNCT
ejpam-6851	1	14	issue	issue	NOUN
ejpam-6851	1	15	4	4	NUM
ejpam-6851	1	16	,	,	PUNCT
ejpam-6851	1	17	article	article	NOUN
ejpam-6851	1	18	number	number	NOUN
ejpam-6851	1	19	6851	6851	NUM
ejpam-6851	1	20	issn	issn	VERB
ejpam-6851	1	21	1307	1307	NUM
ejpam-6851	1	22	-	-	SYM
ejpam-6851	1	23	5543	5543	NUM
ejpam-6851	1	24	–	–	PUNCT
ejpam-6851	1	25	ejpam.com	ejpam.com	X
ejpam-6851	1	26	published	publish	VERB
ejpam-6851	1	27	by	by	ADP
ejpam-6851	1	28	new	new	PROPN
ejpam-6851	1	29	york	york	PROPN
ejpam-6851	1	30	business	business	PROPN
ejpam-6851	1	31	global	global	ADJ
ejpam-6851	1	32	strong	strong	ADJ
ejpam-6851	1	33	and	and	CCONJ
ejpam-6851	1	34	weak	weak	ADJ
ejpam-6851	1	35	dominating	dominating	NOUN
ejpam-6851	1	36	sets	set	NOUN
ejpam-6851	1	37	of	of	ADP
ejpam-6851	1	38	graphs	graph	NOUN
ejpam-6851	1	39	under	under	ADP
ejpam-6851	1	40	some	some	DET
ejpam-6851	1	41	binary	binary	ADJ
ejpam-6851	1	42	operations	operation	NOUN
ejpam-6851	1	43	jerra	jerra	PROPN
ejpam-6851	1	44	mae	mae	PROPN
ejpam-6851	1	45	c.	c.	PROPN
ejpam-6851	1	46	molles1	molles1	PROPN
ejpam-6851	1	47	,	,	PUNCT
ejpam-6851	2	1	ferdinand	ferdinand	PROPN
ejpam-6851	2	2	p.	p.	PROPN
ejpam-6851	3	1	jamil1,2	jamil1,2	PROPN
ejpam-6851	3	2	,	,	PUNCT
ejpam-6851	3	3	sergio	sergio	PROPN
ejpam-6851	3	4	r.	r.	PROPN
ejpam-6851	3	5	canoy	canoy	PROPN
ejpam-6851	3	6	,	,	PUNCT
ejpam-6851	3	7	jr.1,2,∗	jr.1,2,∗	PROPN
ejpam-6851	3	8	1	1	NUM
ejpam-6851	3	9	department	department	NOUN
ejpam-6851	3	10	of	of	ADP
ejpam-6851	3	11	mathematics	mathematic	NOUN
ejpam-6851	3	12	and	and	CCONJ
ejpam-6851	3	13	statistics	statistic	NOUN
ejpam-6851	3	14	,	,	PUNCT
ejpam-6851	3	15	college	college	NOUN
ejpam-6851	3	16	of	of	ADP
ejpam-6851	3	17	science	science	NOUN
ejpam-6851	3	18	and	and	CCONJ
ejpam-6851	3	19	mathematics	mathematic	NOUN
ejpam-6851	3	20	,	,	PUNCT
ejpam-6851	3	21	msu	msu	PROPN
ejpam-6851	3	22	-	-	PUNCT
ejpam-6851	3	23	iligan	iligan	PROPN
ejpam-6851	3	24	institute	institute	PROPN
ejpam-6851	3	25	of	of	ADP
ejpam-6851	3	26	technology	technology	PROPN
ejpam-6851	3	27	,	,	PUNCT
ejpam-6851	3	28	iligan	iligan	PROPN
ejpam-6851	3	29	city	city	PROPN
ejpam-6851	3	30	,	,	PUNCT
ejpam-6851	3	31	philippines	philippine	NOUN
ejpam-6851	3	32	2	2	NUM
ejpam-6851	3	33	center	center	NOUN
ejpam-6851	3	34	of	of	ADP
ejpam-6851	3	35	mathematical	mathematical	ADJ
ejpam-6851	3	36	and	and	CCONJ
ejpam-6851	3	37	theoretical	theoretical	ADJ
ejpam-6851	3	38	physical	physical	ADJ
ejpam-6851	3	39	sciences	science	NOUN
ejpam-6851	3	40	prism	prism	NOUN
ejpam-6851	3	41	,	,	PUNCT
ejpam-6851	3	42	msu	msu	PROPN
ejpam-6851	3	43	-	-	PUNCT
ejpam-6851	3	44	iligan	iligan	PROPN
ejpam-6851	3	45	institute	institute	PROPN
ejpam-6851	3	46	of	of	ADP
ejpam-6851	3	47	technology	technology	PROPN
ejpam-6851	3	48	,	,	PUNCT
ejpam-6851	3	49	iligan	iligan	PROPN
ejpam-6851	3	50	city	city	PROPN
ejpam-6851	3	51	,	,	PUNCT
ejpam-6851	3	52	philippines	philippine	NOUN
ejpam-6851	3	53	abstract	abstract	ADJ
ejpam-6851	3	54	.	.	PUNCT
ejpam-6851	4	1	a	a	DET
ejpam-6851	4	2	set	set	NOUN
ejpam-6851	4	3	s	s	NOUN
ejpam-6851	4	4	of	of	ADP
ejpam-6851	4	5	vertices	vertex	NOUN
ejpam-6851	4	6	of	of	ADP
ejpam-6851	4	7	a	a	DET
ejpam-6851	4	8	graph	graph	NOUN
ejpam-6851	4	9	g	g	NOUN
ejpam-6851	4	10	is	be	AUX
ejpam-6851	4	11	a	a	DET
ejpam-6851	4	12	strong	strong	ADJ
ejpam-6851	4	13	(	(	PUNCT
ejpam-6851	4	14	resp	resp	NOUN
ejpam-6851	4	15	.	.	PUNCT
ejpam-6851	5	1	weak	weak	ADJ
ejpam-6851	5	2	)	)	PUNCT
ejpam-6851	5	3	dominating	dominating	NOUN
ejpam-6851	5	4	set	set	NOUN
ejpam-6851	5	5	of	of	ADP
ejpam-6851	5	6	g	g	PROPN
ejpam-6851	5	7	if	if	SCONJ
ejpam-6851	5	8	for	for	ADP
ejpam-6851	5	9	every	every	DET
ejpam-6851	5	10	vertex	vertex	NOUN
ejpam-6851	5	11	v	v	NOUN
ejpam-6851	5	12	of	of	ADP
ejpam-6851	5	13	g	g	NOUN
ejpam-6851	5	14	outside	outside	ADP
ejpam-6851	5	15	of	of	ADP
ejpam-6851	5	16	s	s	PROPN
ejpam-6851	5	17	,	,	PUNCT
ejpam-6851	5	18	there	there	PRON
ejpam-6851	5	19	is	be	VERB
ejpam-6851	5	20	a	a	DET
ejpam-6851	5	21	vertex	vertex	NOUN
ejpam-6851	5	22	u	u	NOUN
ejpam-6851	5	23	inside	inside	ADP
ejpam-6851	5	24	of	of	ADP
ejpam-6851	5	25	s	s	PRON
ejpam-6851	5	26	such	such	ADJ
ejpam-6851	5	27	that	that	PRON
ejpam-6851	5	28	u	u	NOUN
ejpam-6851	5	29	and	and	CCONJ
ejpam-6851	5	30	v	v	NOUN
ejpam-6851	5	31	are	be	AUX
ejpam-6851	5	32	adjacent	adjacent	ADJ
ejpam-6851	5	33	and	and	CCONJ
ejpam-6851	5	34	degg(v	degg(v	PROPN
ejpam-6851	5	35	)	)	PUNCT
ejpam-6851	5	36	≤	≤	NOUN
ejpam-6851	5	37	degg(u	degg(u	PROPN
ejpam-6851	5	38	)	)	PUNCT
ejpam-6851	5	39	(	(	PUNCT
ejpam-6851	6	1	resp	resp	NOUN
ejpam-6851	6	2	.	.	PUNCT
ejpam-6851	7	1	degg(v	degg(v	PROPN
ejpam-6851	7	2	)	)	PUNCT
ejpam-6851	7	3	≥	≥	NOUN
ejpam-6851	7	4	degg(u	degg(u	PROPN
ejpam-6851	7	5	)	)	PUNCT
ejpam-6851	7	6	)	)	PUNCT
ejpam-6851	7	7	.	.	PUNCT
ejpam-6851	8	1	the	the	DET
ejpam-6851	8	2	minimum	minimum	ADJ
ejpam-6851	8	3	cardinality	cardinality	NOUN
ejpam-6851	8	4	of	of	ADP
ejpam-6851	8	5	a	a	DET
ejpam-6851	8	6	strong	strong	ADJ
ejpam-6851	8	7	(	(	PUNCT
ejpam-6851	8	8	resp	resp	NOUN
ejpam-6851	8	9	.	.	PUNCT
ejpam-6851	9	1	weak	weak	ADJ
ejpam-6851	9	2	)	)	PUNCT
ejpam-6851	9	3	dominating	dominating	NOUN
ejpam-6851	9	4	set	set	NOUN
ejpam-6851	9	5	is	be	AUX
ejpam-6851	9	6	called	call	VERB
ejpam-6851	9	7	the	the	DET
ejpam-6851	9	8	strong	strong	ADJ
ejpam-6851	9	9	(	(	PUNCT
ejpam-6851	9	10	resp	resp	NOUN
ejpam-6851	9	11	.	.	PUNCT
ejpam-6851	10	1	weak	weak	ADJ
ejpam-6851	10	2	)	)	PUNCT
ejpam-6851	10	3	domination	domination	NOUN
ejpam-6851	10	4	number	number	NOUN
ejpam-6851	10	5	of	of	ADP
ejpam-6851	10	6	g	g	NOUN
ejpam-6851	10	7	,	,	PUNCT
ejpam-6851	10	8	and	and	CCONJ
ejpam-6851	10	9	is	be	AUX
ejpam-6851	10	10	denoted	denote	VERB
ejpam-6851	10	11	by	by	ADP
ejpam-6851	10	12	γs(g	γs(g	NOUN
ejpam-6851	10	13	)	)	PUNCT
ejpam-6851	10	14	(	(	PUNCT
ejpam-6851	10	15	resp	resp	NOUN
ejpam-6851	10	16	.	.	PUNCT
ejpam-6851	10	17	γw(g	γw(g	PUNCT
ejpam-6851	10	18	)	)	PUNCT
ejpam-6851	10	19	)	)	PUNCT
ejpam-6851	10	20	.	.	PUNCT
ejpam-6851	11	1	in	in	ADP
ejpam-6851	11	2	this	this	DET
ejpam-6851	11	3	paper	paper	NOUN
ejpam-6851	11	4	,	,	PUNCT
ejpam-6851	11	5	we	we	PRON
ejpam-6851	11	6	characterize	characterize	VERB
ejpam-6851	11	7	the	the	DET
ejpam-6851	11	8	strong	strong	ADJ
ejpam-6851	11	9	and	and	CCONJ
ejpam-6851	11	10	weak	weak	ADJ
ejpam-6851	11	11	dominating	dominating	NOUN
ejpam-6851	11	12	sets	set	NOUN
ejpam-6851	11	13	of	of	ADP
ejpam-6851	11	14	graphs	graph	NOUN
ejpam-6851	11	15	under	under	ADP
ejpam-6851	11	16	some	some	DET
ejpam-6851	11	17	binary	binary	ADJ
ejpam-6851	11	18	operations	operation	NOUN
ejpam-6851	11	19	.	.	PUNCT
ejpam-6851	12	1	as	as	ADP
ejpam-6851	12	2	a	a	DET
ejpam-6851	12	3	result	result	NOUN
ejpam-6851	12	4	,	,	PUNCT
ejpam-6851	12	5	we	we	PRON
ejpam-6851	12	6	also	also	ADV
ejpam-6851	12	7	determine	determine	VERB
ejpam-6851	12	8	the	the	DET
ejpam-6851	12	9	exact	exact	ADJ
ejpam-6851	12	10	values	value	NOUN
ejpam-6851	12	11	of	of	ADP
ejpam-6851	12	12	or	or	CCONJ
ejpam-6851	12	13	sharp	sharp	ADJ
ejpam-6851	12	14	bounds	bound	NOUN
ejpam-6851	12	15	for	for	ADP
ejpam-6851	12	16	the	the	DET
ejpam-6851	12	17	corresponding	corresponding	ADJ
ejpam-6851	12	18	strong	strong	ADJ
ejpam-6851	12	19	and	and	CCONJ
ejpam-6851	12	20	weak	weak	ADJ
ejpam-6851	12	21	domination	domination	NOUN
ejpam-6851	12	22	numbers	number	NOUN
ejpam-6851	12	23	.	.	PUNCT
ejpam-6851	13	1	2020	2020	NUM
ejpam-6851	13	2	mathematics	mathematic	NOUN
ejpam-6851	13	3	subject	subject	NOUN
ejpam-6851	13	4	classifications	classification	NOUN
ejpam-6851	13	5	:	:	PUNCT
ejpam-6851	13	6	05c69	05c69	X
ejpam-6851	13	7	key	key	ADJ
ejpam-6851	13	8	words	word	NOUN
ejpam-6851	13	9	and	and	CCONJ
ejpam-6851	13	10	phrases	phrase	NOUN
ejpam-6851	13	11	:	:	PUNCT
ejpam-6851	13	12	strong	strong	ADJ
ejpam-6851	13	13	dominating	dominating	NOUN
ejpam-6851	13	14	,	,	PUNCT
ejpam-6851	13	15	weak	weak	ADJ
ejpam-6851	13	16	dominating	dominating	NOUN
ejpam-6851	13	17	,	,	PUNCT
ejpam-6851	13	18	shadow	shadow	NOUN
ejpam-6851	13	19	,	,	PUNCT
ejpam-6851	13	20	join	join	NOUN
ejpam-6851	13	21	,	,	PUNCT
ejpam-6851	13	22	corona	corona	PROPN
ejpam-6851	13	23	,	,	PUNCT
ejpam-6851	13	24	edge	edge	NOUN
ejpam-6851	13	25	corona	corona	NOUN
ejpam-6851	13	26	,	,	PUNCT
ejpam-6851	13	27	lexicographic	lexicographic	ADJ
ejpam-6851	13	28	product	product	NOUN
ejpam-6851	13	29	1	1	NUM
ejpam-6851	13	30	.	.	PUNCT
ejpam-6851	13	31	introduction	introduction	NOUN
ejpam-6851	13	32	all	all	ADV
ejpam-6851	13	33	throughout	throughout	ADP
ejpam-6851	13	34	this	this	DET
ejpam-6851	13	35	paper	paper	NOUN
ejpam-6851	13	36	,	,	PUNCT
ejpam-6851	13	37	we	we	PRON
ejpam-6851	13	38	consider	consider	VERB
ejpam-6851	13	39	only	only	ADV
ejpam-6851	13	40	graphs	graph	NOUN
ejpam-6851	13	41	which	which	PRON
ejpam-6851	13	42	are	be	AUX
ejpam-6851	13	43	simple	simple	ADJ
ejpam-6851	13	44	,	,	PUNCT
ejpam-6851	13	45	finite	finite	ADJ
ejpam-6851	13	46	and	and	CCONJ
ejpam-6851	13	47	undirected	undirected	ADJ
ejpam-6851	13	48	.	.	PUNCT
ejpam-6851	14	1	given	give	VERB
ejpam-6851	14	2	a	a	DET
ejpam-6851	14	3	graph	graph	NOUN
ejpam-6851	14	4	g	g	NOUN
ejpam-6851	14	5	=	=	PUNCT
ejpam-6851	14	6	(	(	PUNCT
ejpam-6851	14	7	v	v	NOUN
ejpam-6851	14	8	(	(	PUNCT
ejpam-6851	14	9	g	g	NOUN
ejpam-6851	14	10	)	)	PUNCT
ejpam-6851	14	11	,	,	PUNCT
ejpam-6851	14	12	e(g	e(g	PROPN
ejpam-6851	14	13	)	)	PUNCT
ejpam-6851	14	14	)	)	PUNCT
ejpam-6851	14	15	,	,	PUNCT
ejpam-6851	14	16	we	we	PRON
ejpam-6851	14	17	call	call	VERB
ejpam-6851	14	18	v	v	ADP
ejpam-6851	14	19	(	(	PUNCT
ejpam-6851	14	20	g	g	NOUN
ejpam-6851	14	21	)	)	PUNCT
ejpam-6851	14	22	the	the	DET
ejpam-6851	14	23	vertex	vertex	NOUN
ejpam-6851	14	24	set	set	NOUN
ejpam-6851	14	25	of	of	ADP
ejpam-6851	14	26	g	g	PROPN
ejpam-6851	14	27	and	and	CCONJ
ejpam-6851	14	28	e(g	e(g	PROPN
ejpam-6851	14	29	)	)	PUNCT
ejpam-6851	14	30	its	its	PRON
ejpam-6851	14	31	edge	edge	NOUN
ejpam-6851	14	32	set	set	NOUN
ejpam-6851	14	33	.	.	PUNCT
ejpam-6851	15	1	the	the	DET
ejpam-6851	15	2	cardinality	cardinality	PROPN
ejpam-6851	15	3	|v	|v	PROPN
ejpam-6851	15	4	(	(	PUNCT
ejpam-6851	15	5	g)|	g)|	NOUN
ejpam-6851	15	6	of	of	ADP
ejpam-6851	15	7	v	v	NOUN
ejpam-6851	15	8	(	(	PUNCT
ejpam-6851	15	9	g	g	NOUN
ejpam-6851	15	10	)	)	PUNCT
ejpam-6851	15	11	is	be	AUX
ejpam-6851	15	12	the	the	DET
ejpam-6851	15	13	order	order	NOUN
ejpam-6851	15	14	of	of	ADP
ejpam-6851	15	15	g.	g.	PROPN
ejpam-6851	15	16	all	all	DET
ejpam-6851	15	17	terminologies	terminology	NOUN
ejpam-6851	15	18	used	use	VERB
ejpam-6851	15	19	here	here	ADV
ejpam-6851	15	20	which	which	PRON
ejpam-6851	15	21	are	be	AUX
ejpam-6851	15	22	not	not	PART
ejpam-6851	15	23	being	be	AUX
ejpam-6851	15	24	defined	define	VERB
ejpam-6851	15	25	are	be	AUX
ejpam-6851	15	26	adapted	adapt	VERB
ejpam-6851	15	27	from	from	ADP
ejpam-6851	15	28	[	[	X
ejpam-6851	15	29	1	1	NUM
ejpam-6851	15	30	]	]	PUNCT
ejpam-6851	15	31	.	.	PUNCT
ejpam-6851	16	1	let	let	VERB
ejpam-6851	16	2	g	g	NOUN
ejpam-6851	16	3	and	and	CCONJ
ejpam-6851	16	4	h	h	NOUN
ejpam-6851	16	5	be	be	AUX
ejpam-6851	16	6	disjoint	disjoint	NOUN
ejpam-6851	16	7	graphs	graph	NOUN
ejpam-6851	16	8	.	.	PUNCT
ejpam-6851	17	1	by	by	ADP
ejpam-6851	17	2	g	g	PROPN
ejpam-6851	17	3	∪	∪	PROPN
ejpam-6851	17	4	h	h	NOUN
ejpam-6851	17	5	,	,	PUNCT
ejpam-6851	17	6	we	we	PRON
ejpam-6851	17	7	mean	mean	VERB
ejpam-6851	17	8	the	the	DET
ejpam-6851	17	9	graph	graph	NOUN
ejpam-6851	17	10	with	with	ADP
ejpam-6851	17	11	v	v	NOUN
ejpam-6851	17	12	(	(	PUNCT
ejpam-6851	17	13	g	g	PROPN
ejpam-6851	17	14	∪	∪	ADJ
ejpam-6851	17	15	h	h	NOUN
ejpam-6851	17	16	)	)	PUNCT
ejpam-6851	17	17	=	=	NOUN
ejpam-6851	17	18	v	v	NOUN
ejpam-6851	17	19	(	(	PUNCT
ejpam-6851	17	20	g)∪v	g)∪v	NOUN
ejpam-6851	17	21	(	(	PUNCT
ejpam-6851	17	22	h	h	NOUN
ejpam-6851	17	23	)	)	PUNCT
ejpam-6851	17	24	and	and	CCONJ
ejpam-6851	17	25	e(g∪h	e(g∪h	NOUN
ejpam-6851	17	26	)	)	PUNCT
ejpam-6851	17	27	=	=	PUNCT
ejpam-6851	18	1	e(g)∪e(h	e(g)∪e(h	PROPN
ejpam-6851	18	2	)	)	PUNCT
ejpam-6851	18	3	.	.	PUNCT
ejpam-6851	19	1	the	the	DET
ejpam-6851	19	2	complementary	complementary	ADJ
ejpam-6851	19	3	prism	prism	NOUN
ejpam-6851	19	4	gg	gg	PROPN
ejpam-6851	19	5	is	be	AUX
ejpam-6851	19	6	formed	form	VERB
ejpam-6851	19	7	from	from	ADP
ejpam-6851	19	8	g	g	PROPN
ejpam-6851	19	9	and	and	CCONJ
ejpam-6851	19	10	its	its	PRON
ejpam-6851	19	11	complement	complement	NOUN
ejpam-6851	19	12	g	g	NOUN
ejpam-6851	19	13	by	by	ADP
ejpam-6851	19	14	adding	add	VERB
ejpam-6851	19	15	a	a	DET
ejpam-6851	19	16	perfect	perfect	ADJ
ejpam-6851	19	17	matching	matching	NOUN
ejpam-6851	19	18	between	between	ADP
ejpam-6851	19	19	corresponding	corresponding	ADJ
ejpam-6851	19	20	vertices	vertex	NOUN
ejpam-6851	19	21	of	of	ADP
ejpam-6851	19	22	g	g	PROPN
ejpam-6851	19	23	and	and	CCONJ
ejpam-6851	19	24	g.	g.	PROPN
ejpam-6851	19	25	if	if	SCONJ
ejpam-6851	19	26	for	for	ADP
ejpam-6851	19	27	each	each	DET
ejpam-6851	19	28	v	v	NUM
ejpam-6851	19	29	∈	∈	PROPN
ejpam-6851	19	30	v	v	NOUN
ejpam-6851	19	31	(	(	PUNCT
ejpam-6851	19	32	g	g	NOUN
ejpam-6851	19	33	)	)	PUNCT
ejpam-6851	19	34	,	,	PUNCT
ejpam-6851	19	35	v	v	NOUN
ejpam-6851	19	36	is	be	AUX
ejpam-6851	19	37	the	the	DET
ejpam-6851	19	38	vertex	vertex	NOUN
ejpam-6851	19	39	in	in	ADP
ejpam-6851	19	40	g	g	PROPN
ejpam-6851	19	41	corresponding	correspond	VERB
ejpam-6851	19	42	to	to	ADP
ejpam-6851	19	43	v	v	NOUN
ejpam-6851	19	44	,	,	PUNCT
ejpam-6851	19	45	then	then	ADV
ejpam-6851	19	46	gg	gg	PROPN
ejpam-6851	19	47	is	be	AUX
ejpam-6851	19	48	formed	form	VERB
ejpam-6851	19	49	by	by	ADP
ejpam-6851	19	50	adding	add	VERB
ejpam-6851	19	51	the	the	DET
ejpam-6851	19	52	edge	edge	NOUN
ejpam-6851	19	53	vv	vv	NOUN
ejpam-6851	19	54	for	for	ADP
ejpam-6851	19	55	every	every	DET
ejpam-6851	19	56	v	v	NUM
ejpam-6851	19	57	∈	∈	NOUN
ejpam-6851	19	58	v	v	NOUN
ejpam-6851	19	59	(	(	PUNCT
ejpam-6851	19	60	g	g	NOUN
ejpam-6851	19	61	)	)	PUNCT
ejpam-6851	19	62	.	.	PUNCT
ejpam-6851	20	1	the	the	DET
ejpam-6851	20	2	join	join	NOUN
ejpam-6851	20	3	of	of	ADP
ejpam-6851	20	4	g	g	PROPN
ejpam-6851	20	5	and	and	CCONJ
ejpam-6851	20	6	h	h	NOUN
ejpam-6851	20	7	is	be	AUX
ejpam-6851	20	8	the	the	DET
ejpam-6851	20	9	graph	graph	NOUN
ejpam-6851	20	10	g	g	NOUN
ejpam-6851	20	11	+	+	CCONJ
ejpam-6851	20	12	h	h	NOUN
ejpam-6851	20	13	with	with	ADP
ejpam-6851	20	14	vertex	vertex	NOUN
ejpam-6851	20	15	set	set	VERB
ejpam-6851	20	16	v	v	NOUN
ejpam-6851	20	17	(	(	PUNCT
ejpam-6851	20	18	g	g	NOUN
ejpam-6851	20	19	)	)	PUNCT
ejpam-6851	20	20	∪	∪	NOUN
ejpam-6851	20	21	v	v	NOUN
ejpam-6851	20	22	(	(	PUNCT
ejpam-6851	20	23	h	h	NOUN
ejpam-6851	20	24	)	)	PUNCT
ejpam-6851	20	25	and	and	CCONJ
ejpam-6851	20	26	edge	edge	VERB
ejpam-6851	20	27	set	set	VERB
ejpam-6851	20	28	e(g	e(g	NOUN
ejpam-6851	20	29	)	)	PUNCT
ejpam-6851	20	30	∪	∪	ADP
ejpam-6851	20	31	e(h	e(h	PROPN
ejpam-6851	20	32	)	)	PUNCT
ejpam-6851	20	33	∪	∪	NOUN
ejpam-6851	20	34	{	{	PUNCT
ejpam-6851	20	35	uv	uv	NOUN
ejpam-6851	20	36	:	:	PUNCT
ejpam-6851	20	37	u	u	PROPN
ejpam-6851	20	38	∈	∈	PROPN
ejpam-6851	20	39	v	v	ADP
ejpam-6851	20	40	(	(	PUNCT
ejpam-6851	20	41	g	g	NOUN
ejpam-6851	20	42	)	)	PUNCT
ejpam-6851	20	43	,	,	PUNCT
ejpam-6851	20	44	v	v	X
ejpam-6851	20	45	∈	∈	PROPN
ejpam-6851	20	46	v	v	NOUN
ejpam-6851	20	47	(	(	PUNCT
ejpam-6851	20	48	h	h	NOUN
ejpam-6851	20	49	)	)	PUNCT
ejpam-6851	20	50	}	}	PUNCT
ejpam-6851	20	51	.	.	PUNCT
ejpam-6851	21	1	∗corresponding	∗corresponde	VERB
ejpam-6851	21	2	author	author	NOUN
ejpam-6851	21	3	.	.	PUNCT
ejpam-6851	22	1	doi	doi	NOUN
ejpam-6851	22	2	:	:	PUNCT
ejpam-6851	22	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6851	https://doi.org/10.29020/nybg.ejpam.v18i4.6851	NOUN
ejpam-6851	22	4	email	email	NOUN
ejpam-6851	22	5	addresses	address	NOUN
ejpam-6851	22	6	:	:	PUNCT
ejpam-6851	23	1	jerramae.molles@g.msuiit.edu.ph	jerramae.molles@g.msuiit.edu.ph	PROPN
ejpam-6851	23	2	(	(	PUNCT
ejpam-6851	23	3	j.	j.	PROPN
ejpam-6851	23	4	m.	m.	PROPN
ejpam-6851	23	5	molles	molles	PROPN
ejpam-6851	23	6	)	)	PUNCT
ejpam-6851	23	7	,	,	PUNCT
ejpam-6851	23	8	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-6851	23	9	(	(	PUNCT
ejpam-6851	23	10	f.	f.	PROPN
ejpam-6851	23	11	p.	p.	PROPN
ejpam-6851	23	12	jamil	jamil	PROPN
ejpam-6851	23	13	)	)	PUNCT
ejpam-6851	23	14	,	,	PUNCT
ejpam-6851	23	15	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-6851	23	16	(	(	PUNCT
ejpam-6851	23	17	s.	s.	PROPN
ejpam-6851	23	18	r.	r.	PROPN
ejpam-6851	23	19	canoy	canoy	PROPN
ejpam-6851	23	20	jr	jr	PROPN
ejpam-6851	23	21	.	.	PUNCT
ejpam-6851	23	22	)	)	PUNCT
ejpam-6851	23	23	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6851	24	1	1	1	NUM
ejpam-6851	24	2	copyright	copyright	NOUN
ejpam-6851	24	3	:	:	PUNCT
ejpam-6851	24	4	©	©	PROPN
ejpam-6851	24	5	2025	2025	NUM
ejpam-6851	24	6	the	the	DET
ejpam-6851	24	7	author(s	author(s	NOUN
ejpam-6851	24	8	)	)	PUNCT
ejpam-6851	24	9	.	.	PUNCT
ejpam-6851	25	1	(	(	PUNCT
ejpam-6851	25	2	cc	cc	NOUN
ejpam-6851	25	3	by	by	ADP
ejpam-6851	25	4	-	-	PUNCT
ejpam-6851	25	5	nc	nc	PROPN
ejpam-6851	25	6	4.0	4.0	NUM
ejpam-6851	25	7	)	)	PUNCT
ejpam-6851	25	8	j.	j.	PROPN
ejpam-6851	25	9	m.	m.	PROPN
ejpam-6851	25	10	molles	molles	PROPN
ejpam-6851	25	11	,	,	PUNCT
ejpam-6851	25	12	f.	f.	PROPN
ejpam-6851	25	13	p.	p.	PROPN
ejpam-6851	25	14	jamil	jamil	PROPN
ejpam-6851	25	15	,	,	PUNCT
ejpam-6851	25	16	s.	s.	PROPN
ejpam-6851	25	17	r.	r.	PROPN
ejpam-6851	25	18	canoy	canoy	PROPN
ejpam-6851	25	19	/	/	SYM
ejpam-6851	25	20	eur	eur	PROPN
ejpam-6851	25	21	.	.	PUNCT
ejpam-6851	26	1	j.	j.	PROPN
ejpam-6851	26	2	pure	pure	PROPN
ejpam-6851	26	3	appl	appl	PROPN
ejpam-6851	26	4	.	.	PROPN
ejpam-6851	26	5	math	math	PROPN
ejpam-6851	26	6	,	,	PUNCT
ejpam-6851	26	7	18	18	NUM
ejpam-6851	26	8	(	(	PUNCT
ejpam-6851	26	9	4	4	NUM
ejpam-6851	26	10	)	)	PUNCT
ejpam-6851	26	11	(	(	PUNCT
ejpam-6851	26	12	2025	2025	NUM
ejpam-6851	26	13	)	)	PUNCT
ejpam-6851	26	14	,	,	PUNCT
ejpam-6851	26	15	6851	6851	NUM
ejpam-6851	26	16	2	2	NUM
ejpam-6851	26	17	of	of	ADP
ejpam-6851	26	18	18	18	NUM
ejpam-6851	26	19	the	the	DET
ejpam-6851	26	20	corona	corona	NOUN
ejpam-6851	26	21	of	of	ADP
ejpam-6851	26	22	g	g	PROPN
ejpam-6851	26	23	and	and	CCONJ
ejpam-6851	26	24	h	h	NOUN
ejpam-6851	26	25	is	be	AUX
ejpam-6851	26	26	the	the	DET
ejpam-6851	26	27	graph	graph	NOUN
ejpam-6851	26	28	g	g	PROPN
ejpam-6851	26	29	◦	◦	NOUN
ejpam-6851	26	30	h	h	NOUN
ejpam-6851	26	31	obtained	obtain	VERB
ejpam-6851	26	32	by	by	ADP
ejpam-6851	26	33	taking	take	VERB
ejpam-6851	26	34	one	one	NUM
ejpam-6851	26	35	copy	copy	NOUN
ejpam-6851	26	36	of	of	ADP
ejpam-6851	26	37	g	g	PROPN
ejpam-6851	26	38	and	and	CCONJ
ejpam-6851	26	39	|v	|v	PROPN
ejpam-6851	26	40	(	(	PUNCT
ejpam-6851	26	41	g)|	g)|	NOUN
ejpam-6851	26	42	copies	copy	NOUN
ejpam-6851	26	43	of	of	ADP
ejpam-6851	26	44	h	h	NOUN
ejpam-6851	26	45	,	,	PUNCT
ejpam-6851	26	46	and	and	CCONJ
ejpam-6851	26	47	then	then	ADV
ejpam-6851	26	48	joining	join	VERB
ejpam-6851	26	49	the	the	DET
ejpam-6851	26	50	ith	ith	PROPN
ejpam-6851	26	51	vertex	vertex	NOUN
ejpam-6851	26	52	of	of	ADP
ejpam-6851	26	53	g	g	NOUN
ejpam-6851	26	54	to	to	ADP
ejpam-6851	26	55	every	every	DET
ejpam-6851	26	56	vertex	vertex	NOUN
ejpam-6851	26	57	in	in	ADP
ejpam-6851	26	58	the	the	DET
ejpam-6851	26	59	ith	ith	PROPN
ejpam-6851	26	60	copy	copy	NOUN
ejpam-6851	26	61	of	of	ADP
ejpam-6851	26	62	h.	h.	PROPN
ejpam-6851	26	63	the	the	DET
ejpam-6851	26	64	edge	edge	NOUN
ejpam-6851	26	65	corona	corona	NOUN
ejpam-6851	26	66	of	of	ADP
ejpam-6851	26	67	g	g	PROPN
ejpam-6851	26	68	and	and	CCONJ
ejpam-6851	26	69	h	h	NOUN
ejpam-6851	26	70	is	be	AUX
ejpam-6851	26	71	the	the	DET
ejpam-6851	26	72	graph	graph	NOUN
ejpam-6851	26	73	g	g	PROPN
ejpam-6851	26	74	⋄	⋄	PROPN
ejpam-6851	26	75	h	h	NOUN
ejpam-6851	26	76	obtained	obtain	VERB
ejpam-6851	26	77	by	by	ADP
ejpam-6851	26	78	taking	take	VERB
ejpam-6851	26	79	one	one	NUM
ejpam-6851	26	80	copy	copy	NOUN
ejpam-6851	26	81	of	of	ADP
ejpam-6851	26	82	g	g	PROPN
ejpam-6851	26	83	and	and	CCONJ
ejpam-6851	26	84	|e(g)|	|e(g)|	ADJ
ejpam-6851	26	85	copies	copy	NOUN
ejpam-6851	26	86	of	of	ADP
ejpam-6851	26	87	h	h	NOUN
ejpam-6851	26	88	and	and	CCONJ
ejpam-6851	26	89	joining	join	VERB
ejpam-6851	26	90	each	each	PRON
ejpam-6851	26	91	of	of	ADP
ejpam-6851	26	92	the	the	DET
ejpam-6851	26	93	end	end	NOUN
ejpam-6851	26	94	vertices	vertice	VERB
ejpam-6851	26	95	u	u	NOUN
ejpam-6851	26	96	and	and	CCONJ
ejpam-6851	26	97	v	v	NOUN
ejpam-6851	26	98	of	of	ADP
ejpam-6851	26	99	each	each	DET
ejpam-6851	26	100	edge	edge	NOUN
ejpam-6851	26	101	uv	uv	NOUN
ejpam-6851	26	102	of	of	ADP
ejpam-6851	26	103	g	g	NOUN
ejpam-6851	26	104	to	to	ADP
ejpam-6851	26	105	every	every	DET
ejpam-6851	26	106	vertex	vertex	NOUN
ejpam-6851	26	107	of	of	ADP
ejpam-6851	26	108	the	the	DET
ejpam-6851	26	109	copy	copy	NOUN
ejpam-6851	26	110	huv	huv	PROPN
ejpam-6851	26	111	of	of	ADP
ejpam-6851	26	112	h.	h.	PROPN
ejpam-6851	26	113	the	the	DET
ejpam-6851	26	114	lexicographic	lexicographic	ADJ
ejpam-6851	26	115	product	product	NOUN
ejpam-6851	26	116	of	of	ADP
ejpam-6851	26	117	g	g	PROPN
ejpam-6851	26	118	and	and	CCONJ
ejpam-6851	26	119	h	h	NOUN
ejpam-6851	26	120	is	be	AUX
ejpam-6851	26	121	the	the	DET
ejpam-6851	26	122	graph	graph	NOUN
ejpam-6851	26	123	g[h	g[h	PROPN
ejpam-6851	26	124	]	]	PUNCT
ejpam-6851	26	125	with	with	ADP
ejpam-6851	26	126	v	v	NOUN
ejpam-6851	26	127	(	(	PUNCT
ejpam-6851	26	128	g[h	g[h	PROPN
ejpam-6851	26	129	]	]	PUNCT
ejpam-6851	26	130	)	)	PUNCT
ejpam-6851	26	131	=	=	SYM
ejpam-6851	26	132	v	v	X
ejpam-6851	26	133	(	(	PUNCT
ejpam-6851	26	134	g	g	NOUN
ejpam-6851	26	135	)	)	PUNCT
ejpam-6851	26	136	×	×	NOUN
ejpam-6851	26	137	v	v	NOUN
ejpam-6851	26	138	(	(	PUNCT
ejpam-6851	26	139	h	h	NOUN
ejpam-6851	26	140	)	)	PUNCT
ejpam-6851	26	141	and	and	CCONJ
ejpam-6851	26	142	(	(	PUNCT
ejpam-6851	26	143	u	u	NOUN
ejpam-6851	26	144	,	,	PUNCT
ejpam-6851	26	145	v)(u′	v)(u′	NOUN
ejpam-6851	26	146	,	,	PUNCT
ejpam-6851	26	147	v′	v′	NOUN
ejpam-6851	26	148	)	)	PUNCT
ejpam-6851	26	149	∈	∈	NOUN
ejpam-6851	26	150	e(g[h	e(g[h	NOUN
ejpam-6851	26	151	]	]	PUNCT
ejpam-6851	26	152	)	)	PUNCT
ejpam-6851	26	153	if	if	SCONJ
ejpam-6851	26	154	and	and	CCONJ
ejpam-6851	26	155	only	only	ADV
ejpam-6851	26	156	if	if	SCONJ
ejpam-6851	26	157	either	either	CCONJ
ejpam-6851	26	158	uu′	uu′	PROPN
ejpam-6851	26	159	∈	∈	PROPN
ejpam-6851	26	160	e(g	e(g	PROPN
ejpam-6851	26	161	)	)	PUNCT
ejpam-6851	26	162	or	or	CCONJ
ejpam-6851	26	163	u	u	X
ejpam-6851	26	164	=	=	PUNCT
ejpam-6851	26	165	u′	u′	PROPN
ejpam-6851	26	166	and	and	CCONJ
ejpam-6851	26	167	vv′	vv′	NOUN
ejpam-6851	26	168	∈	∈	PROPN
ejpam-6851	26	169	e(h	e(h	PROPN
ejpam-6851	26	170	)	)	PUNCT
ejpam-6851	26	171	.	.	PUNCT
ejpam-6851	27	1	in	in	ADP
ejpam-6851	27	2	any	any	PRON
ejpam-6851	27	3	of	of	ADP
ejpam-6851	27	4	these	these	DET
ejpam-6851	27	5	graphs	graph	NOUN
ejpam-6851	27	6	,	,	PUNCT
ejpam-6851	27	7	g	g	PROPN
ejpam-6851	27	8	and	and	CCONJ
ejpam-6851	27	9	h	h	NOUN
ejpam-6851	27	10	are	be	AUX
ejpam-6851	27	11	referred	refer	VERB
ejpam-6851	27	12	to	to	ADP
ejpam-6851	27	13	as	as	ADP
ejpam-6851	27	14	their	their	PRON
ejpam-6851	27	15	basic	basic	ADJ
ejpam-6851	27	16	component	component	NOUN
ejpam-6851	27	17	graphs	graph	NOUN
ejpam-6851	27	18	.	.	PUNCT
ejpam-6851	28	1	vertices	vertice	VERB
ejpam-6851	28	2	u	u	NOUN
ejpam-6851	28	3	and	and	CCONJ
ejpam-6851	28	4	v	v	NOUN
ejpam-6851	28	5	of	of	ADP
ejpam-6851	28	6	a	a	DET
ejpam-6851	28	7	graph	graph	NOUN
ejpam-6851	28	8	g	g	NOUN
ejpam-6851	28	9	are	be	AUX
ejpam-6851	28	10	neighbors	neighbor	NOUN
ejpam-6851	28	11	if	if	SCONJ
ejpam-6851	28	12	uv	uv	PROPN
ejpam-6851	28	13	∈	∈	PROPN
ejpam-6851	28	14	e(g	e(g	PROPN
ejpam-6851	28	15	)	)	PUNCT
ejpam-6851	28	16	.	.	PUNCT
ejpam-6851	29	1	the	the	DET
ejpam-6851	29	2	open	open	ADJ
ejpam-6851	29	3	neighborhood	neighborhood	NOUN
ejpam-6851	29	4	of	of	ADP
ejpam-6851	29	5	v	v	NOUN
ejpam-6851	29	6	refers	refer	VERB
ejpam-6851	29	7	to	to	ADP
ejpam-6851	29	8	the	the	DET
ejpam-6851	29	9	set	set	NOUN
ejpam-6851	29	10	ng(v	ng(v	PUNCT
ejpam-6851	29	11	)	)	PUNCT
ejpam-6851	29	12	consisting	consist	VERB
ejpam-6851	29	13	of	of	ADP
ejpam-6851	29	14	all	all	DET
ejpam-6851	29	15	neighbors	neighbor	NOUN
ejpam-6851	29	16	of	of	ADP
ejpam-6851	29	17	v.	v.	ADP
ejpam-6851	29	18	the	the	DET
ejpam-6851	29	19	degree	degree	NOUN
ejpam-6851	29	20	of	of	ADP
ejpam-6851	29	21	v	v	NOUN
ejpam-6851	29	22	refers	refer	VERB
ejpam-6851	29	23	to	to	ADP
ejpam-6851	29	24	the	the	DET
ejpam-6851	29	25	cardinality	cardinality	NOUN
ejpam-6851	29	26	|ng(v)|	|ng(v)|	NOUN
ejpam-6851	29	27	of	of	ADP
ejpam-6851	29	28	the	the	DET
ejpam-6851	29	29	open	open	ADJ
ejpam-6851	29	30	neighborhood	neighborhood	NOUN
ejpam-6851	29	31	of	of	ADP
ejpam-6851	29	32	v	v	NOUN
ejpam-6851	29	33	,	,	PUNCT
ejpam-6851	29	34	∆(g	∆(g	NOUN
ejpam-6851	29	35	)	)	PUNCT
ejpam-6851	29	36	is	be	AUX
ejpam-6851	29	37	the	the	DET
ejpam-6851	29	38	maximum	maximum	ADJ
ejpam-6851	29	39	degree	degree	NOUN
ejpam-6851	29	40	of	of	ADP
ejpam-6851	29	41	a	a	DET
ejpam-6851	29	42	vertex	vertex	NOUN
ejpam-6851	29	43	of	of	ADP
ejpam-6851	29	44	g	g	NOUN
ejpam-6851	29	45	and	and	CCONJ
ejpam-6851	29	46	δ(g	δ(g	PUNCT
ejpam-6851	29	47	)	)	PUNCT
ejpam-6851	29	48	is	be	AUX
ejpam-6851	29	49	the	the	DET
ejpam-6851	29	50	minimum	minimum	ADJ
ejpam-6851	29	51	degree	degree	NOUN
ejpam-6851	29	52	of	of	ADP
ejpam-6851	29	53	a	a	DET
ejpam-6851	29	54	vertex	vertex	NOUN
ejpam-6851	29	55	of	of	ADP
ejpam-6851	29	56	g.	g.	PROPN
ejpam-6851	29	57	if	if	SCONJ
ejpam-6851	29	58	|ng(v)|	|ng(v)|	PROPN
ejpam-6851	29	59	=	=	SYM
ejpam-6851	29	60	1	1	NUM
ejpam-6851	29	61	,	,	PUNCT
ejpam-6851	29	62	then	then	ADV
ejpam-6851	29	63	v	v	NOUN
ejpam-6851	29	64	is	be	AUX
ejpam-6851	29	65	an	an	DET
ejpam-6851	29	66	endvertex	endvertex	NOUN
ejpam-6851	29	67	,	,	PUNCT
ejpam-6851	29	68	and	and	CCONJ
ejpam-6851	29	69	,	,	PUNCT
ejpam-6851	29	70	in	in	ADP
ejpam-6851	29	71	this	this	DET
ejpam-6851	29	72	case	case	NOUN
ejpam-6851	29	73	,	,	PUNCT
ejpam-6851	29	74	if	if	SCONJ
ejpam-6851	29	75	u	u	PROPN
ejpam-6851	29	76	∈	∈	PROPN
ejpam-6851	29	77	ng(v	ng(v	NOUN
ejpam-6851	29	78	)	)	PUNCT
ejpam-6851	29	79	,	,	PUNCT
ejpam-6851	29	80	then	then	ADV
ejpam-6851	29	81	u	u	NOUN
ejpam-6851	29	82	is	be	AUX
ejpam-6851	29	83	the	the	DET
ejpam-6851	29	84	support	support	NOUN
ejpam-6851	29	85	vertex	vertex	NOUN
ejpam-6851	29	86	of	of	ADP
ejpam-6851	29	87	v.	v.	ADP
ejpam-6851	29	88	the	the	DET
ejpam-6851	29	89	symbols	symbol	NOUN
ejpam-6851	29	90	end(g	end(g	PROPN
ejpam-6851	29	91	)	)	PUNCT
ejpam-6851	29	92	and	and	CCONJ
ejpam-6851	29	93	supp(g	supp(g	NOUN
ejpam-6851	29	94	)	)	PUNCT
ejpam-6851	29	95	denote	denote	VERB
ejpam-6851	29	96	the	the	DET
ejpam-6851	29	97	set	set	NOUN
ejpam-6851	29	98	of	of	ADP
ejpam-6851	29	99	all	all	DET
ejpam-6851	29	100	endvertices	endvertice	NOUN
ejpam-6851	29	101	and	and	CCONJ
ejpam-6851	29	102	the	the	DET
ejpam-6851	29	103	set	set	NOUN
ejpam-6851	29	104	of	of	ADP
ejpam-6851	29	105	all	all	DET
ejpam-6851	29	106	support	support	NOUN
ejpam-6851	29	107	vertices	vertex	NOUN
ejpam-6851	29	108	of	of	ADP
ejpam-6851	29	109	g	g	NOUN
ejpam-6851	29	110	,	,	PUNCT
ejpam-6851	29	111	respectively	respectively	ADV
ejpam-6851	29	112	.	.	PUNCT
ejpam-6851	30	1	the	the	DET
ejpam-6851	30	2	closed	closed	ADJ
ejpam-6851	30	3	neighborhood	neighborhood	NOUN
ejpam-6851	30	4	of	of	ADP
ejpam-6851	30	5	v	v	NOUN
ejpam-6851	30	6	is	be	AUX
ejpam-6851	30	7	the	the	DET
ejpam-6851	30	8	set	set	NOUN
ejpam-6851	30	9	ng[v	ng[v	NOUN
ejpam-6851	30	10	]	]	X
ejpam-6851	30	11	=	=	SYM
ejpam-6851	30	12	ng(v	ng(v	X
ejpam-6851	30	13	)	)	PUNCT
ejpam-6851	30	14	∪	∪	ADP
ejpam-6851	30	15	{	{	PUNCT
ejpam-6851	30	16	v	v	NOUN
ejpam-6851	30	17	}	}	PUNCT
ejpam-6851	30	18	.	.	PUNCT
ejpam-6851	31	1	customarily	customarily	ADV
ejpam-6851	31	2	,	,	PUNCT
ejpam-6851	31	3	for	for	ADP
ejpam-6851	31	4	s	s	PROPN
ejpam-6851	31	5	⊆	⊆	NUM
ejpam-6851	31	6	v	v	NOUN
ejpam-6851	31	7	(	(	PUNCT
ejpam-6851	31	8	g	g	NOUN
ejpam-6851	31	9	)	)	PUNCT
ejpam-6851	31	10	,	,	PUNCT
ejpam-6851	31	11	ng(s	ng(s	NUM
ejpam-6851	31	12	)	)	PUNCT
ejpam-6851	31	13	=	=	SYM
ejpam-6851	31	14	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-6851	31	15	)	)	PUNCT
ejpam-6851	31	16	and	and	CCONJ
ejpam-6851	31	17	ng[s	ng[s	PROPN
ejpam-6851	31	18	]	]	PUNCT
ejpam-6851	31	19	=	=	SYM
ejpam-6851	31	20	∪v∈sng[v	∪v∈sng[v	X
ejpam-6851	31	21	]	]	PUNCT
ejpam-6851	31	22	.	.	PUNCT
ejpam-6851	32	1	a	a	DET
ejpam-6851	32	2	subset	subset	NOUN
ejpam-6851	32	3	s	s	VERB
ejpam-6851	32	4	⊆	⊆	NUM
ejpam-6851	32	5	v	v	NOUN
ejpam-6851	32	6	(	(	PUNCT
ejpam-6851	32	7	g	g	NOUN
ejpam-6851	32	8	)	)	PUNCT
ejpam-6851	32	9	is	be	AUX
ejpam-6851	32	10	a	a	DET
ejpam-6851	32	11	dominating	dominating	NOUN
ejpam-6851	32	12	set	set	NOUN
ejpam-6851	32	13	of	of	ADP
ejpam-6851	32	14	g	g	PROPN
ejpam-6851	32	15	if	if	SCONJ
ejpam-6851	32	16	ng[s	ng[	NOUN
ejpam-6851	32	17	]	]	PUNCT
ejpam-6851	32	18	=	=	SYM
ejpam-6851	32	19	v	v	NOUN
ejpam-6851	32	20	(	(	PUNCT
ejpam-6851	32	21	g	g	NOUN
ejpam-6851	32	22	)	)	PUNCT
ejpam-6851	32	23	.	.	PUNCT
ejpam-6851	33	1	in	in	ADP
ejpam-6851	33	2	case	case	NOUN
ejpam-6851	33	3	ng(s	ng(s	NUM
ejpam-6851	33	4	)	)	PUNCT
ejpam-6851	33	5	=	=	SYM
ejpam-6851	33	6	v	v	X
ejpam-6851	33	7	(	(	PUNCT
ejpam-6851	33	8	g	g	NOUN
ejpam-6851	33	9	)	)	PUNCT
ejpam-6851	33	10	,	,	PUNCT
ejpam-6851	33	11	then	then	ADV
ejpam-6851	33	12	s	s	VERB
ejpam-6851	33	13	is	be	AUX
ejpam-6851	33	14	a	a	DET
ejpam-6851	33	15	total	total	ADJ
ejpam-6851	33	16	dominating	dominating	NOUN
ejpam-6851	33	17	set	set	NOUN
ejpam-6851	33	18	of	of	ADP
ejpam-6851	33	19	g.	g.	PROPN
ejpam-6851	33	20	the	the	DET
ejpam-6851	33	21	minimum	minimum	PROPN
ejpam-6851	33	22	cardinality	cardinality	PROPN
ejpam-6851	33	23	γ(g	γ(g	PROPN
ejpam-6851	33	24	)	)	PUNCT
ejpam-6851	33	25	of	of	ADP
ejpam-6851	33	26	a	a	DET
ejpam-6851	33	27	dominating	dominating	NOUN
ejpam-6851	33	28	set	set	NOUN
ejpam-6851	33	29	of	of	ADP
ejpam-6851	33	30	g	g	PROPN
ejpam-6851	33	31	is	be	AUX
ejpam-6851	33	32	the	the	DET
ejpam-6851	33	33	domination	domination	NOUN
ejpam-6851	33	34	number	number	NOUN
ejpam-6851	33	35	of	of	ADP
ejpam-6851	33	36	g	g	NOUN
ejpam-6851	33	37	,	,	PUNCT
ejpam-6851	33	38	and	and	CCONJ
ejpam-6851	33	39	the	the	DET
ejpam-6851	33	40	minimum	minimum	ADJ
ejpam-6851	33	41	cardinality	cardinality	NOUN
ejpam-6851	33	42	γt(g	γt(g	PUNCT
ejpam-6851	33	43	)	)	PUNCT
ejpam-6851	33	44	of	of	ADP
ejpam-6851	33	45	a	a	DET
ejpam-6851	33	46	total	total	ADJ
ejpam-6851	33	47	dominating	dominating	NOUN
ejpam-6851	33	48	set	set	NOUN
ejpam-6851	33	49	is	be	AUX
ejpam-6851	33	50	the	the	DET
ejpam-6851	33	51	total	total	ADJ
ejpam-6851	33	52	domination	domination	NOUN
ejpam-6851	33	53	number	number	NOUN
ejpam-6851	33	54	of	of	ADP
ejpam-6851	33	55	g.	g.	PROPN
ejpam-6851	33	56	a	a	DET
ejpam-6851	33	57	dominating	dominating	NOUN
ejpam-6851	33	58	set	set	NOUN
ejpam-6851	33	59	of	of	ADP
ejpam-6851	33	60	cardinality	cardinality	PROPN
ejpam-6851	33	61	γ(g	γ(g	PROPN
ejpam-6851	33	62	)	)	PUNCT
ejpam-6851	33	63	is	be	AUX
ejpam-6851	33	64	called	call	VERB
ejpam-6851	33	65	a	a	DET
ejpam-6851	33	66	γ	γ	NOUN
ejpam-6851	33	67	-	-	PUNCT
ejpam-6851	33	68	set	set	NOUN
ejpam-6851	33	69	of	of	ADP
ejpam-6851	33	70	g.	g.	PROPN
ejpam-6851	33	71	similarly	similarly	ADV
ejpam-6851	33	72	,	,	PUNCT
ejpam-6851	33	73	a	a	DET
ejpam-6851	33	74	γt	γt	NOUN
ejpam-6851	33	75	-	-	ADJ
ejpam-6851	33	76	set	set	ADJ
ejpam-6851	33	77	is	be	AUX
ejpam-6851	33	78	a	a	DET
ejpam-6851	33	79	total	total	ADJ
ejpam-6851	33	80	dominating	dominating	NOUN
ejpam-6851	33	81	set	set	NOUN
ejpam-6851	33	82	of	of	ADP
ejpam-6851	33	83	cardinality	cardinality	NOUN
ejpam-6851	33	84	γt(g	γt(g	NUM
ejpam-6851	33	85	)	)	PUNCT
ejpam-6851	33	86	.	.	PUNCT
ejpam-6851	34	1	the	the	DET
ejpam-6851	34	2	reader	reader	NOUN
ejpam-6851	34	3	is	be	AUX
ejpam-6851	34	4	referred	refer	VERB
ejpam-6851	34	5	to	to	ADP
ejpam-6851	34	6	[	[	X
ejpam-6851	34	7	2–7	2–7	X
ejpam-6851	34	8	]	]	X
ejpam-6851	34	9	for	for	ADP
ejpam-6851	34	10	the	the	DET
ejpam-6851	34	11	history	history	NOUN
ejpam-6851	34	12	,	,	PUNCT
ejpam-6851	34	13	fundamental	fundamental	ADJ
ejpam-6851	34	14	concepts	concept	NOUN
ejpam-6851	34	15	and	and	CCONJ
ejpam-6851	34	16	recent	recent	ADJ
ejpam-6851	34	17	developments	development	NOUN
ejpam-6851	34	18	of	of	ADP
ejpam-6851	34	19	domination	domination	NOUN
ejpam-6851	34	20	in	in	ADP
ejpam-6851	34	21	graphs	graph	NOUN
ejpam-6851	34	22	as	as	ADV
ejpam-6851	34	23	well	well	ADV
ejpam-6851	34	24	as	as	ADP
ejpam-6851	34	25	its	its	PRON
ejpam-6851	34	26	various	various	ADJ
ejpam-6851	34	27	applications	application	NOUN
ejpam-6851	34	28	.	.	PUNCT
ejpam-6851	35	1	for	for	ADP
ejpam-6851	35	2	two	two	NUM
ejpam-6851	35	3	vertices	vertex	NOUN
ejpam-6851	35	4	u	u	NOUN
ejpam-6851	35	5	,	,	PUNCT
ejpam-6851	35	6	v	v	NOUN
ejpam-6851	35	7	∈	∈	PROPN
ejpam-6851	35	8	v	v	NOUN
ejpam-6851	35	9	(	(	PUNCT
ejpam-6851	35	10	g	g	NOUN
ejpam-6851	35	11	)	)	PUNCT
ejpam-6851	35	12	,	,	PUNCT
ejpam-6851	35	13	v	v	NOUN
ejpam-6851	35	14	is	be	AUX
ejpam-6851	35	15	said	say	VERB
ejpam-6851	35	16	to	to	PART
ejpam-6851	35	17	strongly	strongly	ADV
ejpam-6851	35	18	dominate	dominate	VERB
ejpam-6851	35	19	u	u	NOUN
ejpam-6851	35	20	in	in	ADP
ejpam-6851	35	21	g	g	PROPN
ejpam-6851	35	22	if	if	SCONJ
ejpam-6851	35	23	uv	uv	PROPN
ejpam-6851	35	24	∈	∈	PROPN
ejpam-6851	35	25	e(g	e(g	PROPN
ejpam-6851	35	26	)	)	PUNCT
ejpam-6851	35	27	and	and	CCONJ
ejpam-6851	35	28	degg(v	degg(v	PROPN
ejpam-6851	35	29	)	)	PUNCT
ejpam-6851	35	30	≥	≥	NOUN
ejpam-6851	35	31	degg(u	degg(u	PROPN
ejpam-6851	35	32	)	)	PUNCT
ejpam-6851	35	33	.	.	PUNCT
ejpam-6851	36	1	in	in	ADP
ejpam-6851	36	2	this	this	DET
ejpam-6851	36	3	case	case	NOUN
ejpam-6851	36	4	,	,	PUNCT
ejpam-6851	36	5	we	we	PRON
ejpam-6851	36	6	also	also	ADV
ejpam-6851	36	7	say	say	VERB
ejpam-6851	36	8	that	that	SCONJ
ejpam-6851	36	9	u	u	PRON
ejpam-6851	36	10	weakly	weakly	ADV
ejpam-6851	36	11	dominates	dominate	VERB
ejpam-6851	36	12	v.	v.	CCONJ
ejpam-6851	36	13	we	we	PRON
ejpam-6851	36	14	write	write	VERB
ejpam-6851	36	15	v	v	ADP
ejpam-6851	36	16	≽g	≽g	PROPN
ejpam-6851	36	17	u	u	NOUN
ejpam-6851	36	18	or	or	CCONJ
ejpam-6851	36	19	u	u	NOUN
ejpam-6851	36	20	≼g	≼g	PROPN
ejpam-6851	36	21	v	v	NOUN
ejpam-6851	36	22	to	to	PART
ejpam-6851	36	23	mean	mean	VERB
ejpam-6851	36	24	that	that	SCONJ
ejpam-6851	36	25	v	v	NOUN
ejpam-6851	36	26	strongly	strongly	ADV
ejpam-6851	36	27	dominates	dominate	VERB
ejpam-6851	36	28	u	u	NOUN
ejpam-6851	36	29	or	or	CCONJ
ejpam-6851	36	30	,	,	PUNCT
ejpam-6851	36	31	equivalently	equivalently	ADV
ejpam-6851	36	32	,	,	PUNCT
ejpam-6851	36	33	u	u	PROPN
ejpam-6851	36	34	weakly	weakly	ADV
ejpam-6851	36	35	dominates	dominate	VERB
ejpam-6851	36	36	v.	v.	ADP
ejpam-6851	36	37	a	a	DET
ejpam-6851	36	38	subset	subset	NOUN
ejpam-6851	36	39	s	s	VERB
ejpam-6851	36	40	⊆	⊆	NUM
ejpam-6851	36	41	v	v	NOUN
ejpam-6851	36	42	(	(	PUNCT
ejpam-6851	36	43	g	g	NOUN
ejpam-6851	36	44	)	)	PUNCT
ejpam-6851	36	45	is	be	AUX
ejpam-6851	36	46	said	say	VERB
ejpam-6851	36	47	to	to	PART
ejpam-6851	36	48	strongly	strongly	ADV
ejpam-6851	36	49	dominate	dominate	VERB
ejpam-6851	36	50	(	(	PUNCT
ejpam-6851	36	51	resp	resp	NOUN
ejpam-6851	36	52	.	.	PUNCT
ejpam-6851	37	1	weakly	weakly	ADJ
ejpam-6851	37	2	dominate	dominate	VERB
ejpam-6851	37	3	)	)	PUNCT
ejpam-6851	37	4	u	u	NOUN
ejpam-6851	37	5	∈	∈	PROPN
ejpam-6851	37	6	v	v	ADP
ejpam-6851	37	7	(	(	PUNCT
ejpam-6851	37	8	g	g	NOUN
ejpam-6851	37	9	)	)	PUNCT
ejpam-6851	37	10	\	\	PROPN
ejpam-6851	38	1	s	s	PART
ejpam-6851	38	2	in	in	ADP
ejpam-6851	38	3	g	g	PROPN
ejpam-6851	38	4	if	if	SCONJ
ejpam-6851	38	5	there	there	PRON
ejpam-6851	38	6	exists	exist	VERB
ejpam-6851	38	7	v	v	ADP
ejpam-6851	38	8	∈	∈	PROPN
ejpam-6851	38	9	s	s	NOUN
ejpam-6851	38	10	for	for	ADP
ejpam-6851	38	11	which	which	PRON
ejpam-6851	38	12	v	v	ADP
ejpam-6851	38	13	≽g	≽g	PROPN
ejpam-6851	38	14	u	u	NOUN
ejpam-6851	38	15	(	(	PUNCT
ejpam-6851	38	16	resp	resp	NOUN
ejpam-6851	38	17	.	.	PUNCT
ejpam-6851	39	1	u	u	PRON
ejpam-6851	39	2	≽g	≽g	PROPN
ejpam-6851	39	3	v	v	NOUN
ejpam-6851	39	4	)	)	PUNCT
ejpam-6851	39	5	in	in	ADP
ejpam-6851	39	6	g.	g.	PROPN
ejpam-6851	39	7	in	in	ADP
ejpam-6851	39	8	this	this	DET
ejpam-6851	39	9	case	case	NOUN
ejpam-6851	39	10	we	we	PRON
ejpam-6851	39	11	write	write	VERB
ejpam-6851	39	12	u	u	PROPN
ejpam-6851	39	13	≼g	≼g	PROPN
ejpam-6851	39	14	s	s	X
ejpam-6851	39	15	(	(	PUNCT
ejpam-6851	39	16	resp	resp	NOUN
ejpam-6851	39	17	.	.	PUNCT
ejpam-6851	40	1	u	u	PRON
ejpam-6851	40	2	≽g	≽g	PROPN
ejpam-6851	40	3	s	s	PART
ejpam-6851	40	4	)	)	PUNCT
ejpam-6851	40	5	.	.	PUNCT
ejpam-6851	41	1	for	for	ADP
ejpam-6851	41	2	s	s	PROPN
ejpam-6851	41	3	,	,	PUNCT
ejpam-6851	41	4	d	d	PROPN
ejpam-6851	41	5	⊆	⊆	NUM
ejpam-6851	41	6	v	v	ADP
ejpam-6851	41	7	(	(	PUNCT
ejpam-6851	41	8	g	g	NOUN
ejpam-6851	41	9	)	)	PUNCT
ejpam-6851	41	10	,	,	PUNCT
ejpam-6851	41	11	s	s	VERB
ejpam-6851	41	12	is	be	AUX
ejpam-6851	41	13	said	say	VERB
ejpam-6851	41	14	to	to	PART
ejpam-6851	41	15	strongly	strongly	ADV
ejpam-6851	41	16	dominate	dominate	VERB
ejpam-6851	41	17	(	(	PUNCT
ejpam-6851	41	18	resp	resp	NOUN
ejpam-6851	41	19	.	.	PUNCT
ejpam-6851	42	1	weakly	weakly	ADJ
ejpam-6851	42	2	dominate	dominate	VERB
ejpam-6851	42	3	)	)	PUNCT
ejpam-6851	43	1	d	d	NOUN
ejpam-6851	43	2	if	if	SCONJ
ejpam-6851	43	3	s	s	PRON
ejpam-6851	43	4	strongly	strongly	ADV
ejpam-6851	43	5	dominates	dominate	VERB
ejpam-6851	43	6	(	(	PUNCT
ejpam-6851	43	7	resp	resp	NOUN
ejpam-6851	43	8	.	.	PUNCT
ejpam-6851	44	1	weakly	weakly	ADJ
ejpam-6851	44	2	dominates	dominate	VERB
ejpam-6851	44	3	)	)	PUNCT
ejpam-6851	44	4	every	every	DET
ejpam-6851	44	5	vertex	vertex	NOUN
ejpam-6851	44	6	v	v	ADP
ejpam-6851	44	7	∈	∈	PROPN
ejpam-6851	44	8	d	d	X
ejpam-6851	44	9	\	\	PROPN
ejpam-6851	44	10	s.	s.	PROPN
ejpam-6851	45	1	we	we	PRON
ejpam-6851	45	2	say	say	VERB
ejpam-6851	45	3	s	s	PRON
ejpam-6851	45	4	is	be	AUX
ejpam-6851	45	5	a	a	DET
ejpam-6851	45	6	strong	strong	ADJ
ejpam-6851	45	7	dominating	dominating	NOUN
ejpam-6851	45	8	set	set	NOUN
ejpam-6851	45	9	(	(	PUNCT
ejpam-6851	45	10	resp	resp	NOUN
ejpam-6851	45	11	.	.	PUNCT
ejpam-6851	46	1	weak	weak	ADJ
ejpam-6851	46	2	dominating	dominating	NOUN
ejpam-6851	46	3	set	set	NOUN
ejpam-6851	46	4	)	)	PUNCT
ejpam-6851	46	5	of	of	ADP
ejpam-6851	46	6	g	g	PROPN
ejpam-6851	46	7	if	if	SCONJ
ejpam-6851	46	8	s	s	PRON
ejpam-6851	46	9	strongly	strongly	ADV
ejpam-6851	46	10	dominates	dominate	VERB
ejpam-6851	46	11	(	(	PUNCT
ejpam-6851	46	12	resp	resp	NOUN
ejpam-6851	46	13	.	.	PUNCT
ejpam-6851	47	1	weakly	weakly	ADJ
ejpam-6851	47	2	dominates	dominate	VERB
ejpam-6851	47	3	)	)	PUNCT
ejpam-6851	47	4	v	v	NOUN
ejpam-6851	47	5	(	(	PUNCT
ejpam-6851	47	6	g	g	NOUN
ejpam-6851	47	7	)	)	PUNCT
ejpam-6851	47	8	,	,	PUNCT
ejpam-6851	47	9	i.e.	i.e.	X
ejpam-6851	47	10	,	,	PUNCT
ejpam-6851	47	11	for	for	ADP
ejpam-6851	47	12	each	each	DET
ejpam-6851	47	13	u	u	PROPN
ejpam-6851	47	14	∈	∈	PROPN
ejpam-6851	47	15	v	v	ADP
ejpam-6851	47	16	(	(	PUNCT
ejpam-6851	47	17	g	g	NOUN
ejpam-6851	47	18	)	)	PUNCT
ejpam-6851	47	19	\	\	PROPN
ejpam-6851	48	1	s	s	X
ejpam-6851	48	2	,	,	PUNCT
ejpam-6851	48	3	u	u	PROPN
ejpam-6851	48	4	≼g	≼g	PROPN
ejpam-6851	48	5	s	s	X
ejpam-6851	48	6	(	(	PUNCT
ejpam-6851	48	7	resp	resp	NOUN
ejpam-6851	48	8	.	.	PUNCT
ejpam-6851	49	1	u	u	PRON
ejpam-6851	49	2	≽g	≽g	PROPN
ejpam-6851	49	3	s	s	PART
ejpam-6851	49	4	)	)	PUNCT
ejpam-6851	49	5	in	in	ADP
ejpam-6851	49	6	g.	g.	PROPN
ejpam-6851	49	7	the	the	DET
ejpam-6851	49	8	minimum	minimum	ADJ
ejpam-6851	49	9	cardinality	cardinality	NOUN
ejpam-6851	49	10	of	of	ADP
ejpam-6851	49	11	a	a	DET
ejpam-6851	49	12	strong	strong	ADJ
ejpam-6851	49	13	dominating	dominating	NOUN
ejpam-6851	49	14	set	set	NOUN
ejpam-6851	49	15	(	(	PUNCT
ejpam-6851	49	16	resp	resp	NOUN
ejpam-6851	49	17	.	.	PUNCT
ejpam-6851	50	1	weak	weak	ADJ
ejpam-6851	50	2	dominating	dominating	NOUN
ejpam-6851	50	3	set	set	NOUN
ejpam-6851	50	4	)	)	PUNCT
ejpam-6851	50	5	of	of	ADP
ejpam-6851	50	6	g	g	PROPN
ejpam-6851	50	7	is	be	AUX
ejpam-6851	50	8	the	the	DET
ejpam-6851	50	9	strong	strong	ADJ
ejpam-6851	50	10	domination	domination	NOUN
ejpam-6851	50	11	number	number	NOUN
ejpam-6851	50	12	(	(	PUNCT
ejpam-6851	50	13	resp	resp	NOUN
ejpam-6851	50	14	.	.	PUNCT
ejpam-6851	51	1	weak	weak	ADJ
ejpam-6851	51	2	domination	domination	NOUN
ejpam-6851	51	3	number	number	NOUN
ejpam-6851	51	4	)	)	PUNCT
ejpam-6851	51	5	of	of	ADP
ejpam-6851	51	6	g	g	NOUN
ejpam-6851	51	7	,	,	PUNCT
ejpam-6851	51	8	which	which	PRON
ejpam-6851	51	9	is	be	AUX
ejpam-6851	51	10	denoted	denote	VERB
ejpam-6851	51	11	by	by	ADP
ejpam-6851	51	12	γs(g	γs(g	NOUN
ejpam-6851	51	13	)	)	PUNCT
ejpam-6851	51	14	(	(	PUNCT
ejpam-6851	51	15	resp	resp	NOUN
ejpam-6851	51	16	.	.	PUNCT
ejpam-6851	51	17	γw(g	γw(g	PUNCT
ejpam-6851	51	18	)	)	PUNCT
ejpam-6851	51	19	)	)	PUNCT
ejpam-6851	51	20	.	.	PUNCT
ejpam-6851	52	1	any	any	DET
ejpam-6851	52	2	strong	strong	ADJ
ejpam-6851	52	3	dominating	dominating	NOUN
ejpam-6851	52	4	set	set	NOUN
ejpam-6851	52	5	(	(	PUNCT
ejpam-6851	52	6	resp	resp	NOUN
ejpam-6851	52	7	.	.	PUNCT
ejpam-6851	53	1	weak	weak	ADJ
ejpam-6851	53	2	dominating	dominating	NOUN
ejpam-6851	53	3	set	set	NOUN
ejpam-6851	53	4	)	)	PUNCT
ejpam-6851	53	5	of	of	ADP
ejpam-6851	53	6	g	g	NOUN
ejpam-6851	53	7	of	of	ADP
ejpam-6851	53	8	cardinality	cardinality	NOUN
ejpam-6851	53	9	γs(g	γs(g	PUNCT
ejpam-6851	53	10	)	)	PUNCT
ejpam-6851	53	11	(	(	PUNCT
ejpam-6851	53	12	resp	resp	NOUN
ejpam-6851	53	13	.	.	PUNCT
ejpam-6851	53	14	γw(g	γw(g	PUNCT
ejpam-6851	53	15	)	)	PUNCT
ejpam-6851	53	16	)	)	PUNCT
ejpam-6851	53	17	is	be	AUX
ejpam-6851	53	18	called	call	VERB
ejpam-6851	53	19	a	a	DET
ejpam-6851	53	20	γs	γs	NOUN
ejpam-6851	53	21	-	-	PUNCT
ejpam-6851	53	22	set	set	VERB
ejpam-6851	53	23	(	(	PUNCT
ejpam-6851	53	24	resp	resp	NOUN
ejpam-6851	53	25	.	.	PUNCT
ejpam-6851	54	1	γw	γw	NOUN
ejpam-6851	54	2	-	-	PUNCT
ejpam-6851	54	3	set	set	NOUN
ejpam-6851	54	4	)	)	PUNCT
ejpam-6851	54	5	of	of	ADP
ejpam-6851	54	6	g.	g.	PROPN
ejpam-6851	54	7	the	the	DET
ejpam-6851	54	8	concepts	concept	NOUN
ejpam-6851	54	9	of	of	ADP
ejpam-6851	54	10	strong	strong	ADJ
ejpam-6851	54	11	and	and	CCONJ
ejpam-6851	54	12	weak	weak	ADJ
ejpam-6851	54	13	domination	domination	NOUN
ejpam-6851	54	14	were	be	AUX
ejpam-6851	54	15	first	first	ADV
ejpam-6851	54	16	introduced	introduce	VERB
ejpam-6851	54	17	by	by	ADP
ejpam-6851	54	18	e.	e.	PROPN
ejpam-6851	54	19	sampathkumar	sampathkumar	PROPN
ejpam-6851	54	20	and	and	CCONJ
ejpam-6851	54	21	l.	l.	PROPN
ejpam-6851	54	22	pushpa	pushpa	PROPN
ejpam-6851	54	23	latha	latha	PROPN
ejpam-6851	55	1	[	[	X
ejpam-6851	55	2	8	8	NUM
ejpam-6851	55	3	]	]	PUNCT
ejpam-6851	55	4	in	in	ADP
ejpam-6851	55	5	1996	1996	NUM
ejpam-6851	55	6	.	.	PUNCT
ejpam-6851	56	1	thereafter	thereafter	ADV
ejpam-6851	56	2	,	,	PUNCT
ejpam-6851	56	3	several	several	ADJ
ejpam-6851	56	4	further	further	ADJ
ejpam-6851	56	5	studies	study	NOUN
ejpam-6851	56	6	have	have	AUX
ejpam-6851	56	7	been	be	AUX
ejpam-6851	56	8	done	do	VERB
ejpam-6851	56	9	on	on	ADP
ejpam-6851	56	10	these	these	DET
ejpam-6851	56	11	two	two	NUM
ejpam-6851	56	12	concepts	concept	NOUN
ejpam-6851	56	13	(	(	PUNCT
ejpam-6851	56	14	see	see	VERB
ejpam-6851	56	15	[	[	X
ejpam-6851	56	16	9	9	NUM
ejpam-6851	56	17	,	,	PUNCT
ejpam-6851	56	18	10	10	NUM
ejpam-6851	56	19	]	]	PUNCT
ejpam-6851	56	20	,	,	PUNCT
ejpam-6851	57	1	[	[	X
ejpam-6851	57	2	11][12	11][12	X
ejpam-6851	57	3	]	]	X
ejpam-6851	57	4	,	,	PUNCT
ejpam-6851	57	5	[	[	X
ejpam-6851	57	6	13	13	NUM
ejpam-6851	57	7	,	,	PUNCT
ejpam-6851	57	8	14	14	NUM
ejpam-6851	57	9	]	]	PUNCT
ejpam-6851	57	10	,	,	PUNCT
ejpam-6851	58	1	[	[	X
ejpam-6851	58	2	15]-[16	15]-[16	NUM
ejpam-6851	58	3	]	]	X
ejpam-6851	58	4	)	)	PUNCT
ejpam-6851	58	5	.	.	PUNCT
ejpam-6851	59	1	in	in	ADP
ejpam-6851	59	2	particular	particular	ADJ
ejpam-6851	59	3	,	,	PUNCT
ejpam-6851	59	4	properties	property	NOUN
ejpam-6851	59	5	and	and	CCONJ
ejpam-6851	59	6	characteristics	characteristic	NOUN
ejpam-6851	59	7	of	of	ADP
ejpam-6851	59	8	strong	strong	ADJ
ejpam-6851	59	9	and	and	CCONJ
ejpam-6851	59	10	weak	weak	ADJ
ejpam-6851	59	11	dominating	dominating	NOUN
ejpam-6851	59	12	sets	set	NOUN
ejpam-6851	59	13	are	be	AUX
ejpam-6851	59	14	explored	explore	VERB
ejpam-6851	59	15	in	in	ADP
ejpam-6851	59	16	[	[	X
ejpam-6851	59	17	12	12	NUM
ejpam-6851	59	18	,	,	PUNCT
ejpam-6851	59	19	17	17	NUM
ejpam-6851	59	20	]	]	PUNCT
ejpam-6851	59	21	.	.	PUNCT
ejpam-6851	60	1	bounds	bound	NOUN
ejpam-6851	60	2	on	on	ADP
ejpam-6851	60	3	j.	j.	PROPN
ejpam-6851	60	4	m.	m.	PROPN
ejpam-6851	60	5	molles	molles	PROPN
ejpam-6851	60	6	,	,	PUNCT
ejpam-6851	60	7	f.	f.	PROPN
ejpam-6851	60	8	p.	p.	PROPN
ejpam-6851	60	9	jamil	jamil	PROPN
ejpam-6851	60	10	,	,	PUNCT
ejpam-6851	60	11	s.	s.	PROPN
ejpam-6851	60	12	r.	r.	PROPN
ejpam-6851	60	13	canoy	canoy	PROPN
ejpam-6851	60	14	/	/	SYM
ejpam-6851	60	15	eur	eur	PROPN
ejpam-6851	60	16	.	.	PUNCT
ejpam-6851	61	1	j.	j.	PROPN
ejpam-6851	61	2	pure	pure	PROPN
ejpam-6851	61	3	appl	appl	PROPN
ejpam-6851	61	4	.	.	PROPN
ejpam-6851	61	5	math	math	PROPN
ejpam-6851	61	6	,	,	PUNCT
ejpam-6851	61	7	18	18	NUM
ejpam-6851	61	8	(	(	PUNCT
ejpam-6851	61	9	4	4	NUM
ejpam-6851	61	10	)	)	PUNCT
ejpam-6851	61	11	(	(	PUNCT
ejpam-6851	61	12	2025	2025	NUM
ejpam-6851	61	13	)	)	PUNCT
ejpam-6851	61	14	,	,	PUNCT
ejpam-6851	61	15	6851	6851	NUM
ejpam-6851	61	16	3	3	NUM
ejpam-6851	61	17	of	of	ADP
ejpam-6851	61	18	18	18	NUM
ejpam-6851	61	19	γs(g	γs(g	NUM
ejpam-6851	61	20	)	)	PUNCT
ejpam-6851	61	21	and	and	CCONJ
ejpam-6851	61	22	γw(g	γw(g	NUM
ejpam-6851	61	23	)	)	PUNCT
ejpam-6851	61	24	are	be	AUX
ejpam-6851	61	25	studied	study	VERB
ejpam-6851	61	26	in	in	ADP
ejpam-6851	61	27	[	[	X
ejpam-6851	61	28	18–21	18–21	NUM
ejpam-6851	61	29	]	]	PUNCT
ejpam-6851	61	30	,	,	PUNCT
ejpam-6851	61	31	and	and	CCONJ
ejpam-6851	61	32	investigation	investigation	NOUN
ejpam-6851	61	33	of	of	ADP
ejpam-6851	61	34	strong	strong	ADJ
ejpam-6851	61	35	and	and	CCONJ
ejpam-6851	61	36	weak	weak	ADJ
ejpam-6851	61	37	domination	domination	NOUN
ejpam-6851	61	38	in	in	ADP
ejpam-6851	61	39	families	family	NOUN
ejpam-6851	61	40	of	of	ADP
ejpam-6851	61	41	graphs	graph	NOUN
ejpam-6851	61	42	are	be	AUX
ejpam-6851	61	43	done	do	VERB
ejpam-6851	61	44	in	in	ADP
ejpam-6851	61	45	[	[	X
ejpam-6851	61	46	22–25	22–25	NUM
ejpam-6851	61	47	]	]	PUNCT
ejpam-6851	61	48	.	.	PUNCT
ejpam-6851	62	1	in	in	ADP
ejpam-6851	62	2	this	this	DET
ejpam-6851	62	3	present	present	ADJ
ejpam-6851	62	4	study	study	NOUN
ejpam-6851	62	5	,	,	PUNCT
ejpam-6851	62	6	we	we	PRON
ejpam-6851	62	7	continue	continue	VERB
ejpam-6851	62	8	the	the	DET
ejpam-6851	62	9	investigation	investigation	NOUN
ejpam-6851	62	10	of	of	ADP
ejpam-6851	62	11	these	these	DET
ejpam-6851	62	12	two	two	NUM
ejpam-6851	62	13	concepts	concept	NOUN
ejpam-6851	62	14	,	,	PUNCT
ejpam-6851	62	15	particularly	particularly	ADV
ejpam-6851	62	16	on	on	ADP
ejpam-6851	62	17	characterizing	characterize	VERB
ejpam-6851	62	18	the	the	DET
ejpam-6851	62	19	strong	strong	ADJ
ejpam-6851	62	20	and	and	CCONJ
ejpam-6851	62	21	weak	weak	ADJ
ejpam-6851	62	22	dominating	dominating	NOUN
ejpam-6851	62	23	sets	set	NOUN
ejpam-6851	62	24	in	in	ADP
ejpam-6851	62	25	families	family	NOUN
ejpam-6851	62	26	of	of	ADP
ejpam-6851	62	27	graphs	graph	NOUN
ejpam-6851	62	28	involving	involve	VERB
ejpam-6851	62	29	the	the	DET
ejpam-6851	62	30	complementary	complementary	ADJ
ejpam-6851	62	31	prism	prism	NOUN
ejpam-6851	62	32	of	of	ADP
ejpam-6851	62	33	graphs	graph	NOUN
ejpam-6851	62	34	,	,	PUNCT
ejpam-6851	62	35	join	join	NOUN
ejpam-6851	62	36	,	,	PUNCT
ejpam-6851	62	37	corona	corona	PROPN
ejpam-6851	62	38	,	,	PUNCT
ejpam-6851	62	39	edge	edge	NOUN
ejpam-6851	62	40	corona	corona	NOUN
ejpam-6851	62	41	and	and	CCONJ
ejpam-6851	62	42	lexicographic	lexicographic	ADJ
ejpam-6851	62	43	product	product	NOUN
ejpam-6851	62	44	of	of	ADP
ejpam-6851	62	45	graphs	graph	NOUN
ejpam-6851	62	46	.	.	PUNCT
ejpam-6851	63	1	for	for	ADP
ejpam-6851	63	2	v	v	NUM
ejpam-6851	63	3	∈	∈	PROPN
ejpam-6851	63	4	v	v	NOUN
ejpam-6851	63	5	(	(	PUNCT
ejpam-6851	63	6	g	g	NOUN
ejpam-6851	63	7	)	)	PUNCT
ejpam-6851	63	8	,	,	PUNCT
ejpam-6851	63	9	write	write	VERB
ejpam-6851	63	10	ng(v	ng(v	X
ejpam-6851	63	11	≽	≽	PROPN
ejpam-6851	63	12	)	)	PUNCT
ejpam-6851	63	13	=	=	PRON
ejpam-6851	64	1	{	{	PUNCT
ejpam-6851	64	2	u	u	NOUN
ejpam-6851	64	3	∈	∈	PROPN
ejpam-6851	64	4	v	v	NOUN
ejpam-6851	64	5	(	(	PUNCT
ejpam-6851	64	6	g	g	NOUN
ejpam-6851	64	7	)	)	PUNCT
ejpam-6851	64	8	:	:	PUNCT
ejpam-6851	65	1	u	u	NOUN
ejpam-6851	65	2	≼	≼	ADJ
ejpam-6851	65	3	v	v	ADP
ejpam-6851	65	4	}	}	PUNCT
ejpam-6851	65	5	,	,	PUNCT
ejpam-6851	65	6	ng(v	ng(v	PUNCT
ejpam-6851	65	7	≼	≼	ADJ
ejpam-6851	65	8	)	)	PUNCT
ejpam-6851	65	9	=	=	SYM
ejpam-6851	65	10	{	{	PUNCT
ejpam-6851	65	11	u	u	NOUN
ejpam-6851	65	12	∈	∈	PROPN
ejpam-6851	65	13	v	v	NOUN
ejpam-6851	65	14	(	(	PUNCT
ejpam-6851	65	15	g	g	NOUN
ejpam-6851	65	16	)	)	PUNCT
ejpam-6851	65	17	:	:	PUNCT
ejpam-6851	65	18	u	u	NOUN
ejpam-6851	65	19	≽	≽	PROPN
ejpam-6851	65	20	v	v	NOUN
ejpam-6851	65	21	}	}	PUNCT
ejpam-6851	65	22	,	,	PUNCT
ejpam-6851	65	23	ng[v	ng[v	X
ejpam-6851	65	24	≽	≽	PROPN
ejpam-6851	65	25	]	]	X
ejpam-6851	65	26	=	=	SYM
ejpam-6851	65	27	ng(v	ng(v	X
ejpam-6851	65	28	≽	≽	PROPN
ejpam-6851	65	29	)	)	PUNCT
ejpam-6851	65	30	∪	∪	ADP
ejpam-6851	65	31	{	{	PUNCT
ejpam-6851	65	32	v	v	NOUN
ejpam-6851	65	33	}	}	PUNCT
ejpam-6851	65	34	and	and	CCONJ
ejpam-6851	65	35	ng[v	ng[v	X
ejpam-6851	65	36	≼	≼	ADJ
ejpam-6851	65	37	]	]	X
ejpam-6851	65	38	=	=	SYM
ejpam-6851	65	39	ng(v	ng(v	X
ejpam-6851	65	40	≼	≼	ADJ
ejpam-6851	65	41	)	)	PUNCT
ejpam-6851	65	42	∪	∪	ADP
ejpam-6851	65	43	{	{	PUNCT
ejpam-6851	65	44	v	v	NOUN
ejpam-6851	65	45	}	}	PUNCT
ejpam-6851	65	46	.	.	PUNCT
ejpam-6851	66	1	for	for	ADP
ejpam-6851	66	2	s	s	PROPN
ejpam-6851	66	3	⊆	⊆	NUM
ejpam-6851	66	4	v	v	NOUN
ejpam-6851	66	5	(	(	PUNCT
ejpam-6851	66	6	g	g	NOUN
ejpam-6851	66	7	)	)	PUNCT
ejpam-6851	66	8	,	,	PUNCT
ejpam-6851	66	9	ng(s	ng(s	X
ejpam-6851	66	10	≽	≽	PROPN
ejpam-6851	66	11	)	)	PUNCT
ejpam-6851	66	12	=	=	SYM
ejpam-6851	66	13	∪v∈sng(v	∪v∈sng(v	DET
ejpam-6851	66	14	≽	≽	PROPN
ejpam-6851	66	15	)	)	PUNCT
ejpam-6851	66	16	and	and	CCONJ
ejpam-6851	66	17	ng(s	ng(s	X
ejpam-6851	66	18	≼	≼	ADJ
ejpam-6851	66	19	)	)	PUNCT
ejpam-6851	67	1	=	=	PUNCT
ejpam-6851	67	2	∪v∈sng(v	∪v∈sng(v	PRON
ejpam-6851	67	3	≼	≼	NOUN
ejpam-6851	67	4	)	)	PUNCT
ejpam-6851	67	5	.	.	PUNCT
ejpam-6851	68	1	we	we	PRON
ejpam-6851	68	2	also	also	ADV
ejpam-6851	68	3	write	write	VERB
ejpam-6851	68	4	ng[s	ng[s	PROPN
ejpam-6851	68	5	≽	≽	PROPN
ejpam-6851	68	6	]	]	X
ejpam-6851	68	7	=	=	X
ejpam-6851	68	8	ng(s	ng(s	NUM
ejpam-6851	68	9	≽)∪	≽)∪	PROPN
ejpam-6851	68	10	s	s	PROPN
ejpam-6851	68	11	and	and	CCONJ
ejpam-6851	68	12	ng[s	ng[s	PROPN
ejpam-6851	68	13	≼	≼	ADJ
ejpam-6851	68	14	]	]	X
ejpam-6851	68	15	=	=	SYM
ejpam-6851	68	16	ng(s	ng(s	NUM
ejpam-6851	68	17	≼)∪	≼)∪	ADJ
ejpam-6851	68	18	s.	s.	PROPN
ejpam-6851	68	19	hence	hence	ADV
ejpam-6851	68	20	,	,	PUNCT
ejpam-6851	68	21	s	s	VERB
ejpam-6851	68	22	is	be	AUX
ejpam-6851	68	23	a	a	DET
ejpam-6851	68	24	strong	strong	ADJ
ejpam-6851	68	25	(	(	PUNCT
ejpam-6851	68	26	resp	resp	NOUN
ejpam-6851	68	27	.	.	PUNCT
ejpam-6851	69	1	weak	weak	ADJ
ejpam-6851	69	2	)	)	PUNCT
ejpam-6851	69	3	dominating	dominating	NOUN
ejpam-6851	69	4	set	set	NOUN
ejpam-6851	69	5	of	of	ADP
ejpam-6851	69	6	g	g	PROPN
ejpam-6851	69	7	if	if	SCONJ
ejpam-6851	70	1	and	and	CCONJ
ejpam-6851	70	2	only	only	ADV
ejpam-6851	70	3	if	if	SCONJ
ejpam-6851	70	4	ng[s	ng[s	PROPN
ejpam-6851	70	5	≽	≽	PROPN
ejpam-6851	70	6	]	]	X
ejpam-6851	70	7	=	=	SYM
ejpam-6851	70	8	v	v	X
ejpam-6851	70	9	(	(	PUNCT
ejpam-6851	70	10	g	g	NOUN
ejpam-6851	70	11	)	)	PUNCT
ejpam-6851	70	12	(	(	PUNCT
ejpam-6851	70	13	resp	resp	NOUN
ejpam-6851	70	14	.	.	PUNCT
ejpam-6851	71	1	ng[s	ng[s	PROPN
ejpam-6851	71	2	≼	≼	ADJ
ejpam-6851	71	3	]	]	X
ejpam-6851	71	4	=	=	SYM
ejpam-6851	71	5	v	v	X
ejpam-6851	71	6	(	(	PUNCT
ejpam-6851	71	7	g	g	NOUN
ejpam-6851	71	8	)	)	PUNCT
ejpam-6851	71	9	)	)	PUNCT
ejpam-6851	71	10	.	.	PUNCT
ejpam-6851	72	1	the	the	DET
ejpam-6851	72	2	symbol	symbol	NOUN
ejpam-6851	72	3	γs(g	γs(g	PUNCT
ejpam-6851	72	4	)	)	PUNCT
ejpam-6851	72	5	(	(	PUNCT
ejpam-6851	72	6	resp	resp	NOUN
ejpam-6851	72	7	.	.	PUNCT
ejpam-6851	72	8	γw(g	γw(g	PUNCT
ejpam-6851	72	9	)	)	PUNCT
ejpam-6851	72	10	)	)	PUNCT
ejpam-6851	72	11	denotes	denote	VERB
ejpam-6851	72	12	the	the	DET
ejpam-6851	72	13	family	family	NOUN
ejpam-6851	72	14	of	of	ADP
ejpam-6851	72	15	all	all	PRON
ejpam-6851	72	16	strong	strong	ADJ
ejpam-6851	72	17	(	(	PUNCT
ejpam-6851	72	18	resp	resp	NOUN
ejpam-6851	72	19	.	.	PUNCT
ejpam-6851	73	1	weak	weak	ADJ
ejpam-6851	73	2	)	)	PUNCT
ejpam-6851	73	3	dominating	dominating	NOUN
ejpam-6851	73	4	sets	set	NOUN
ejpam-6851	73	5	of	of	ADP
ejpam-6851	73	6	g.	g.	PROPN
ejpam-6851	73	7	thus	thus	ADV
ejpam-6851	73	8	,	,	PUNCT
ejpam-6851	73	9	γs(g	γs(g	PUNCT
ejpam-6851	73	10	)	)	PUNCT
ejpam-6851	74	1	=	=	NOUN
ejpam-6851	74	2	min{|s|	min{|s|	NOUN
ejpam-6851	74	3	:	:	PUNCT
ejpam-6851	74	4	s	s	X
ejpam-6851	74	5	∈	∈	NOUN
ejpam-6851	74	6	γs(g	γs(g	PUNCT
ejpam-6851	74	7	)	)	PUNCT
ejpam-6851	74	8	}	}	PUNCT
ejpam-6851	74	9	and	and	CCONJ
ejpam-6851	74	10	γw(g	γw(g	NUM
ejpam-6851	74	11	)	)	PUNCT
ejpam-6851	75	1	=	=	SYM
ejpam-6851	75	2	min{|s|	min{|s|	NOUN
ejpam-6851	75	3	:	:	PUNCT
ejpam-6851	75	4	s	s	VERB
ejpam-6851	75	5	∈	∈	NOUN
ejpam-6851	75	6	γw(g	γw(g	PUNCT
ejpam-6851	75	7	)	)	PUNCT
ejpam-6851	75	8	}	}	PUNCT
ejpam-6851	75	9	.	.	PUNCT
ejpam-6851	76	1	2	2	X
ejpam-6851	76	2	.	.	X
ejpam-6851	76	3	preliminary	preliminary	ADJ
ejpam-6851	76	4	results	result	NOUN
ejpam-6851	76	5	it	it	PRON
ejpam-6851	76	6	is	be	AUX
ejpam-6851	76	7	worth	worth	ADJ
ejpam-6851	76	8	noting	note	VERB
ejpam-6851	76	9	that	that	SCONJ
ejpam-6851	76	10	strong	strong	ADJ
ejpam-6851	76	11	and	and	CCONJ
ejpam-6851	76	12	weak	weak	ADJ
ejpam-6851	76	13	dominating	dominating	NOUN
ejpam-6851	76	14	sets	set	NOUN
ejpam-6851	76	15	are	be	AUX
ejpam-6851	76	16	necessarily	necessarily	ADV
ejpam-6851	76	17	dominating	dominate	VERB
ejpam-6851	76	18	sets	set	NOUN
ejpam-6851	76	19	.	.	PUNCT
ejpam-6851	77	1	hence	hence	ADV
ejpam-6851	77	2	,	,	PUNCT
ejpam-6851	77	3	for	for	ADP
ejpam-6851	77	4	a	a	DET
ejpam-6851	77	5	graph	graph	NOUN
ejpam-6851	77	6	of	of	ADP
ejpam-6851	77	7	order	order	NOUN
ejpam-6851	77	8	n	n	CCONJ
ejpam-6851	77	9	,	,	PUNCT
ejpam-6851	77	10	γ(g	γ(g	PROPN
ejpam-6851	77	11	)	)	PUNCT
ejpam-6851	77	12	≤	≤	NOUN
ejpam-6851	77	13	γs(g	γs(g	PUNCT
ejpam-6851	77	14	)	)	PUNCT
ejpam-6851	77	15	≤	≤	NUM
ejpam-6851	77	16	n−∆(g	n−∆(g	PROPN
ejpam-6851	77	17	)	)	PUNCT
ejpam-6851	77	18	and	and	CCONJ
ejpam-6851	77	19	γ(g	γ(g	PROPN
ejpam-6851	77	20	)	)	PUNCT
ejpam-6851	77	21	≤	≤	NOUN
ejpam-6851	77	22	γw(g	γw(g	PUNCT
ejpam-6851	77	23	)	)	PUNCT
ejpam-6851	77	24	≤	≤	NUM
ejpam-6851	77	25	n−	n−	NOUN
ejpam-6851	77	26	δ(g	δ(g	ADV
ejpam-6851	77	27	)	)	PUNCT
ejpam-6851	78	1	[	[	X
ejpam-6851	78	2	26	26	NUM
ejpam-6851	78	3	]	]	PUNCT
ejpam-6851	78	4	.	.	PUNCT
ejpam-6851	79	1	the	the	DET
ejpam-6851	79	2	following	follow	VERB
ejpam-6851	79	3	are	be	AUX
ejpam-6851	79	4	immediate	immediate	ADJ
ejpam-6851	79	5	observations	observation	NOUN
ejpam-6851	79	6	.	.	PUNCT
ejpam-6851	80	1	remark	remark	PROPN
ejpam-6851	80	2	1	1	NUM
ejpam-6851	80	3	.	.	PUNCT
ejpam-6851	81	1	let	let	VERB
ejpam-6851	81	2	g	g	NOUN
ejpam-6851	81	3	be	be	AUX
ejpam-6851	81	4	any	any	DET
ejpam-6851	81	5	graph	graph	NOUN
ejpam-6851	81	6	of	of	ADP
ejpam-6851	81	7	order	order	NOUN
ejpam-6851	81	8	n.	n.	NOUN
ejpam-6851	81	9	then	then	ADV
ejpam-6851	81	10	(	(	PUNCT
ejpam-6851	81	11	i	i	NOUN
ejpam-6851	81	12	)	)	PUNCT
ejpam-6851	81	13	γs(g	γs(g	PUNCT
ejpam-6851	81	14	)	)	PUNCT
ejpam-6851	81	15	=	=	SYM
ejpam-6851	81	16	1	1	NUM
ejpam-6851	81	17	if	if	SCONJ
ejpam-6851	81	18	and	and	CCONJ
ejpam-6851	81	19	only	only	ADV
ejpam-6851	81	20	if	if	SCONJ
ejpam-6851	81	21	γ(g	γ(g	NOUN
ejpam-6851	81	22	)	)	PUNCT
ejpam-6851	81	23	=	=	SYM
ejpam-6851	81	24	1	1	NUM
ejpam-6851	81	25	;	;	PUNCT
ejpam-6851	81	26	(	(	PUNCT
ejpam-6851	81	27	ii	ii	NOUN
ejpam-6851	81	28	)	)	PUNCT
ejpam-6851	81	29	γw(g	γw(g	PUNCT
ejpam-6851	81	30	)	)	PUNCT
ejpam-6851	82	1	=	=	SYM
ejpam-6851	82	2	1	1	NUM
ejpam-6851	82	3	if	if	SCONJ
ejpam-6851	82	4	and	and	CCONJ
ejpam-6851	82	5	only	only	ADV
ejpam-6851	82	6	if	if	SCONJ
ejpam-6851	82	7	g	g	PROPN
ejpam-6851	82	8	=	=	PROPN
ejpam-6851	82	9	kn	kn	PROPN
ejpam-6851	82	10	;	;	PUNCT
ejpam-6851	82	11	(	(	PUNCT
ejpam-6851	82	12	iii	iii	NOUN
ejpam-6851	82	13	)	)	PUNCT
ejpam-6851	82	14	γs(g	γs(g	PUNCT
ejpam-6851	82	15	)	)	PUNCT
ejpam-6851	82	16	=	=	SYM
ejpam-6851	82	17	n	n	PROPN
ejpam-6851	82	18	(	(	PUNCT
ejpam-6851	82	19	resp	resp	NOUN
ejpam-6851	82	20	.	.	PUNCT
ejpam-6851	82	21	γw(g	γw(g	PUNCT
ejpam-6851	82	22	)	)	PUNCT
ejpam-6851	82	23	=	=	SYM
ejpam-6851	82	24	n	n	CCONJ
ejpam-6851	82	25	)	)	PUNCT
ejpam-6851	82	26	if	if	SCONJ
ejpam-6851	82	27	and	and	CCONJ
ejpam-6851	82	28	only	only	ADV
ejpam-6851	82	29	if	if	SCONJ
ejpam-6851	82	30	g	g	PROPN
ejpam-6851	82	31	=	=	PROPN
ejpam-6851	82	32	kn	kn	PROPN
ejpam-6851	82	33	;	;	PUNCT
ejpam-6851	82	34	(	(	PUNCT
ejpam-6851	82	35	iv	iv	X
ejpam-6851	82	36	)	)	PUNCT
ejpam-6851	82	37	γs(g	γs(g	PUNCT
ejpam-6851	82	38	)	)	PUNCT
ejpam-6851	82	39	=	=	PUNCT
ejpam-6851	82	40	n−	n−	NOUN
ejpam-6851	82	41	1	1	NUM
ejpam-6851	82	42	if	if	SCONJ
ejpam-6851	83	1	and	and	CCONJ
ejpam-6851	83	2	only	only	ADV
ejpam-6851	83	3	if	if	SCONJ
ejpam-6851	83	4	g	g	PROPN
ejpam-6851	83	5	=	=	SYM
ejpam-6851	83	6	k2	k2	PROPN
ejpam-6851	83	7	or	or	CCONJ
ejpam-6851	83	8	g	g	PROPN
ejpam-6851	83	9	=	=	PROPN
ejpam-6851	83	10	k2	k2	PROPN
ejpam-6851	83	11	∪kn−2	∪kn−2	PROPN
ejpam-6851	83	12	;	;	PUNCT
ejpam-6851	83	13	and	and	CCONJ
ejpam-6851	83	14	(	(	PUNCT
ejpam-6851	83	15	v	v	NOUN
ejpam-6851	83	16	)	)	PUNCT
ejpam-6851	83	17	γw(g	γw(g	PUNCT
ejpam-6851	83	18	)	)	PUNCT
ejpam-6851	84	1	=	=	PUNCT
ejpam-6851	84	2	n−	n−	NOUN
ejpam-6851	84	3	1	1	NUM
ejpam-6851	84	4	if	if	SCONJ
ejpam-6851	84	5	and	and	CCONJ
ejpam-6851	84	6	only	only	ADV
ejpam-6851	84	7	if	if	SCONJ
ejpam-6851	84	8	g	g	NOUN
ejpam-6851	84	9	=	=	PUNCT
ejpam-6851	84	10	k1,n−1	k1,n−1	ADJ
ejpam-6851	84	11	or	or	CCONJ
ejpam-6851	84	12	g	g	PROPN
ejpam-6851	84	13	=	=	SYM
ejpam-6851	84	14	k1,(n−k−1	k1,(n−k−1	NOUN
ejpam-6851	84	15	)	)	PUNCT
ejpam-6851	84	16	∪kk	∪kk	PROPN
ejpam-6851	84	17	.	.	PUNCT
ejpam-6851	85	1	remark	remark	PROPN
ejpam-6851	85	2	2	2	NUM
ejpam-6851	85	3	.	.	PUNCT
ejpam-6851	86	1	let	let	VERB
ejpam-6851	86	2	g	g	PRON
ejpam-6851	86	3	be	be	AUX
ejpam-6851	86	4	a	a	DET
ejpam-6851	86	5	connected	connected	ADJ
ejpam-6851	86	6	graph	graph	NOUN
ejpam-6851	86	7	.	.	PUNCT
ejpam-6851	87	1	then	then	ADV
ejpam-6851	87	2	γs(g	γs(g	PUNCT
ejpam-6851	87	3	)	)	PUNCT
ejpam-6851	87	4	=	=	SYM
ejpam-6851	87	5	2	2	NUM
ejpam-6851	87	6	(	(	PUNCT
ejpam-6851	87	7	resp	resp	NOUN
ejpam-6851	87	8	.	.	PUNCT
ejpam-6851	87	9	γw(g	γw(g	PUNCT
ejpam-6851	87	10	)	)	PUNCT
ejpam-6851	88	1	=	=	SYM
ejpam-6851	88	2	2	2	X
ejpam-6851	88	3	)	)	PUNCT
ejpam-6851	88	4	if	if	SCONJ
ejpam-6851	88	5	and	and	CCONJ
ejpam-6851	88	6	only	only	ADV
ejpam-6851	88	7	if	if	SCONJ
ejpam-6851	88	8	γ(g	γ(g	NOUN
ejpam-6851	88	9	)	)	PUNCT
ejpam-6851	88	10	=	=	SYM
ejpam-6851	88	11	2	2	NUM
ejpam-6851	88	12	and	and	CCONJ
ejpam-6851	88	13	g	g	PROPN
ejpam-6851	88	14	has	have	VERB
ejpam-6851	88	15	a	a	DET
ejpam-6851	88	16	γ	γ	X
ejpam-6851	88	17	-	-	PUNCT
ejpam-6851	88	18	set	set	VERB
ejpam-6851	88	19	s	s	PART
ejpam-6851	88	20	=	=	PUNCT
ejpam-6851	88	21	{	{	PUNCT
ejpam-6851	88	22	u	u	NOUN
ejpam-6851	88	23	,	,	PUNCT
ejpam-6851	88	24	v	v	NOUN
ejpam-6851	88	25	}	}	PUNCT
ejpam-6851	88	26	for	for	ADP
ejpam-6851	88	27	which	which	PRON
ejpam-6851	88	28	x	x	PUNCT
ejpam-6851	88	29	≼	≼	ADJ
ejpam-6851	88	30	u	u	NOUN
ejpam-6851	88	31	(	(	PUNCT
ejpam-6851	88	32	resp	resp	NOUN
ejpam-6851	88	33	.	.	PUNCT
ejpam-6851	89	1	x	x	X
ejpam-6851	90	1	≽	≽	PROPN
ejpam-6851	90	2	u	u	NOUN
ejpam-6851	90	3	)	)	PUNCT
ejpam-6851	90	4	or	or	CCONJ
ejpam-6851	90	5	x	x	ADJ
ejpam-6851	90	6	≼	≼	NOUN
ejpam-6851	90	7	v	v	NOUN
ejpam-6851	90	8	(	(	PUNCT
ejpam-6851	90	9	resp	resp	NOUN
ejpam-6851	90	10	.	.	PUNCT
ejpam-6851	91	1	x	x	X
ejpam-6851	92	1	≽	≽	NOUN
ejpam-6851	92	2	v	v	NOUN
ejpam-6851	92	3	)	)	PUNCT
ejpam-6851	92	4	for	for	ADP
ejpam-6851	92	5	each	each	DET
ejpam-6851	92	6	x	x	SYM
ejpam-6851	92	7	∈	∈	PROPN
ejpam-6851	92	8	v	v	ADP
ejpam-6851	92	9	(	(	PUNCT
ejpam-6851	92	10	g	g	NOUN
ejpam-6851	92	11	)	)	PUNCT
ejpam-6851	92	12	\	\	PUNCT
ejpam-6851	93	1	s.	s.	PROPN
ejpam-6851	93	2	j.	j.	PROPN
ejpam-6851	93	3	m.	m.	PROPN
ejpam-6851	93	4	molles	molles	PROPN
ejpam-6851	93	5	,	,	PUNCT
ejpam-6851	93	6	f.	f.	PROPN
ejpam-6851	93	7	p.	p.	PROPN
ejpam-6851	93	8	jamil	jamil	PROPN
ejpam-6851	93	9	,	,	PUNCT
ejpam-6851	93	10	s.	s.	PROPN
ejpam-6851	93	11	r.	r.	PROPN
ejpam-6851	93	12	canoy	canoy	PROPN
ejpam-6851	93	13	/	/	SYM
ejpam-6851	93	14	eur	eur	PROPN
ejpam-6851	93	15	.	.	PUNCT
ejpam-6851	94	1	j.	j.	PROPN
ejpam-6851	94	2	pure	pure	PROPN
ejpam-6851	94	3	appl	appl	PROPN
ejpam-6851	94	4	.	.	PROPN
ejpam-6851	94	5	math	math	PROPN
ejpam-6851	94	6	,	,	PUNCT
ejpam-6851	94	7	18	18	NUM
ejpam-6851	94	8	(	(	PUNCT
ejpam-6851	94	9	4	4	NUM
ejpam-6851	94	10	)	)	PUNCT
ejpam-6851	94	11	(	(	PUNCT
ejpam-6851	94	12	2025	2025	NUM
ejpam-6851	94	13	)	)	PUNCT
ejpam-6851	94	14	,	,	PUNCT
ejpam-6851	94	15	6851	6851	NUM
ejpam-6851	94	16	4	4	NUM
ejpam-6851	94	17	of	of	ADP
ejpam-6851	94	18	18	18	NUM
ejpam-6851	94	19	lemma	lemma	PROPN
ejpam-6851	94	20	1	1	NUM
ejpam-6851	94	21	.	.	PUNCT
ejpam-6851	95	1	if	if	SCONJ
ejpam-6851	95	2	g	g	PROPN
ejpam-6851	95	3	is	be	AUX
ejpam-6851	95	4	connected	connect	VERB
ejpam-6851	95	5	of	of	ADP
ejpam-6851	95	6	order	order	NOUN
ejpam-6851	95	7	n	n	PRON
ejpam-6851	95	8	≥	≥	NOUN
ejpam-6851	95	9	3	3	NUM
ejpam-6851	95	10	,	,	PUNCT
ejpam-6851	95	11	then	then	ADV
ejpam-6851	95	12	for	for	ADP
ejpam-6851	95	13	each	each	DET
ejpam-6851	95	14	s	s	PROPN
ejpam-6851	95	15	∈	∈	NOUN
ejpam-6851	95	16	γs(g	γs(g	PUNCT
ejpam-6851	95	17	)	)	PUNCT
ejpam-6851	95	18	there	there	PRON
ejpam-6851	95	19	exists	exist	VERB
ejpam-6851	95	20	s∗	s∗	PROPN
ejpam-6851	95	21	∈	∈	PROPN
ejpam-6851	95	22	γs(g	γs(g	PUNCT
ejpam-6851	95	23	)	)	PUNCT
ejpam-6851	95	24	for	for	ADP
ejpam-6851	95	25	which	which	PRON
ejpam-6851	95	26	s∗	s∗	PROPN
ejpam-6851	95	27	∩	∩	X
ejpam-6851	95	28	end(g	end(g	PROPN
ejpam-6851	95	29	)	)	PUNCT
ejpam-6851	95	30	=	=	NOUN
ejpam-6851	95	31	∅	∅	NOUN
ejpam-6851	95	32	and	and	CCONJ
ejpam-6851	95	33	|s∗|	|s∗|	NUM
ejpam-6851	95	34	≤	≤	NUM
ejpam-6851	95	35	|s|	|s|	PROPN
ejpam-6851	95	36	.	.	PUNCT
ejpam-6851	96	1	consequently	consequently	ADV
ejpam-6851	96	2	,	,	PUNCT
ejpam-6851	96	3	g	g	PROPN
ejpam-6851	96	4	has	have	VERB
ejpam-6851	96	5	a	a	DET
ejpam-6851	96	6	γs	γs	NOUN
ejpam-6851	96	7	-	-	PUNCT
ejpam-6851	96	8	set	set	VERB
ejpam-6851	96	9	s	s	NOUN
ejpam-6851	96	10	for	for	ADP
ejpam-6851	96	11	which	which	PRON
ejpam-6851	96	12	s	s	VERB
ejpam-6851	96	13	∩	∩	X
ejpam-6851	96	14	end(g	end(g	PROPN
ejpam-6851	96	15	)	)	PUNCT
ejpam-6851	96	16	=	=	PUNCT
ejpam-6851	96	17	∅.	∅.	NOUN
ejpam-6851	96	18	proof	proof	NOUN
ejpam-6851	96	19	.	.	PUNCT
ejpam-6851	97	1	let	let	VERB
ejpam-6851	97	2	s	s	PRON
ejpam-6851	97	3	∈	∈	NOUN
ejpam-6851	97	4	γs(g	γs(g	PUNCT
ejpam-6851	97	5	)	)	PUNCT
ejpam-6851	97	6	.	.	PUNCT
ejpam-6851	98	1	if	if	SCONJ
ejpam-6851	98	2	s∩end(g	s∩end(g	NUM
ejpam-6851	98	3	)	)	PUNCT
ejpam-6851	98	4	=	=	NOUN
ejpam-6851	98	5	∅	∅	NOUN
ejpam-6851	98	6	,	,	PUNCT
ejpam-6851	98	7	then	then	ADV
ejpam-6851	98	8	let	let	VERB
ejpam-6851	98	9	s∗	s∗	PROPN
ejpam-6851	98	10	=	=	PUNCT
ejpam-6851	98	11	s.	s.	PROPN
ejpam-6851	98	12	suppose	suppose	VERB
ejpam-6851	98	13	that	that	SCONJ
ejpam-6851	98	14	s∩end(g	s∩end(g	X
ejpam-6851	98	15	)	)	PUNCT
ejpam-6851	98	16	̸=	̸=	PROPN
ejpam-6851	98	17	∅.	∅.	VERB
ejpam-6851	98	18	for	for	ADP
ejpam-6851	98	19	each	each	DET
ejpam-6851	98	20	v	v	NUM
ejpam-6851	98	21	∈	∈	NOUN
ejpam-6851	98	22	s	s	NOUN
ejpam-6851	98	23	∩	∩	ADJ
ejpam-6851	98	24	end(g	end(g	PROPN
ejpam-6851	98	25	)	)	PUNCT
ejpam-6851	98	26	,	,	PUNCT
ejpam-6851	98	27	let	let	VERB
ejpam-6851	98	28	xv	xv	PRON
ejpam-6851	98	29	be	be	AUX
ejpam-6851	98	30	the	the	DET
ejpam-6851	98	31	support	support	NOUN
ejpam-6851	98	32	vertex	vertex	NOUN
ejpam-6851	98	33	v.	v.	ADP
ejpam-6851	98	34	then	then	ADV
ejpam-6851	98	35	|{xv	|{xv	PUNCT
ejpam-6851	98	36	/∈	/∈	PUNCT
ejpam-6851	99	1	s	s	PART
ejpam-6851	99	2	:	:	PUNCT
ejpam-6851	99	3	v	v	NUM
ejpam-6851	99	4	∈	∈	PROPN
ejpam-6851	99	5	s	s	NOUN
ejpam-6851	99	6	∩	∩	ADJ
ejpam-6851	99	7	end(g)}|	end(g)}|	NOUN
ejpam-6851	99	8	≤	≤	NOUN
ejpam-6851	99	9	|s	|s	PROPN
ejpam-6851	99	10	∩	∩	ADJ
ejpam-6851	99	11	end(g)|	end(g)|	PROPN
ejpam-6851	99	12	.	.	PROPN
ejpam-6851	99	13	put	put	VERB
ejpam-6851	99	14	s∗	s∗	PROPN
ejpam-6851	99	15	=	=	SYM
ejpam-6851	99	16	(	(	PUNCT
ejpam-6851	99	17	s	s	NOUN
ejpam-6851	99	18	\	\	PROPN
ejpam-6851	99	19	end(g	end(g	PROPN
ejpam-6851	99	20	)	)	PUNCT
ejpam-6851	99	21	)	)	PUNCT
ejpam-6851	99	22	∪	∪	ADP
ejpam-6851	99	23	{	{	PUNCT
ejpam-6851	99	24	xv	xv	PROPN
ejpam-6851	99	25	/∈	/∈	PROPN
ejpam-6851	99	26	s	s	PART
ejpam-6851	99	27	:	:	PUNCT
ejpam-6851	99	28	v	v	NUM
ejpam-6851	99	29	∈	∈	PROPN
ejpam-6851	99	30	s	s	PART
ejpam-6851	99	31	∩	∩	ADJ
ejpam-6851	99	32	end(g	end(g	PROPN
ejpam-6851	99	33	)	)	PUNCT
ejpam-6851	99	34	}	}	PUNCT
ejpam-6851	99	35	.	.	PUNCT
ejpam-6851	100	1	then	then	ADV
ejpam-6851	100	2	s∗	s∗	PROPN
ejpam-6851	100	3	∈	∈	PROPN
ejpam-6851	100	4	γs(g	γs(g	PUNCT
ejpam-6851	100	5	)	)	PUNCT
ejpam-6851	100	6	and	and	CCONJ
ejpam-6851	100	7	|s∗|	|s∗|	NUM
ejpam-6851	100	8	=	=	SYM
ejpam-6851	100	9	|s	|s	PROPN
ejpam-6851	100	10	\	\	PROPN
ejpam-6851	101	1	end(g)|+	end(g)|+	PROPN
ejpam-6851	101	2	|{xv	|{xv	PUNCT
ejpam-6851	101	3	/∈	/∈	PROPN
ejpam-6851	102	1	s	s	PART
ejpam-6851	102	2	:	:	PUNCT
ejpam-6851	102	3	v	v	NUM
ejpam-6851	102	4	∈	∈	PROPN
ejpam-6851	102	5	s	s	PART
ejpam-6851	103	1	∩	∩	ADJ
ejpam-6851	103	2	end(g)}|	end(g)}|	NOUN
ejpam-6851	103	3	≤	≤	NUM
ejpam-6851	103	4	|s|	|s|	PROPN
ejpam-6851	103	5	.	.	PUNCT
ejpam-6851	104	1	lemma	lemma	PROPN
ejpam-6851	104	2	2	2	X
ejpam-6851	104	3	.	.	PUNCT
ejpam-6851	105	1	let	let	VERB
ejpam-6851	105	2	g	g	PRON
ejpam-6851	105	3	be	be	AUX
ejpam-6851	105	4	a	a	DET
ejpam-6851	105	5	connected	connected	ADJ
ejpam-6851	105	6	graph	graph	NOUN
ejpam-6851	105	7	.	.	PUNCT
ejpam-6851	106	1	then	then	ADV
ejpam-6851	106	2	for	for	ADP
ejpam-6851	106	3	each	each	DET
ejpam-6851	106	4	s	s	PROPN
ejpam-6851	106	5	∈	∈	NOUN
ejpam-6851	106	6	γs(g	γs(g	PUNCT
ejpam-6851	106	7	)	)	PUNCT
ejpam-6851	106	8	(	(	PUNCT
ejpam-6851	106	9	resp	resp	NOUN
ejpam-6851	106	10	.	.	PUNCT
ejpam-6851	107	1	s	s	PART
ejpam-6851	107	2	∈	∈	NOUN
ejpam-6851	107	3	γw(g	γw(g	PUNCT
ejpam-6851	107	4	)	)	PUNCT
ejpam-6851	107	5	)	)	PUNCT
ejpam-6851	108	1	,	,	PUNCT
ejpam-6851	108	2	s	s	PROPN
ejpam-6851	108	3	contains	contain	VERB
ejpam-6851	108	4	a	a	DET
ejpam-6851	108	5	vertex	vertex	NOUN
ejpam-6851	108	6	v	v	NOUN
ejpam-6851	108	7	for	for	ADP
ejpam-6851	108	8	which	which	PRON
ejpam-6851	108	9	degg(v	degg(v	PROPN
ejpam-6851	108	10	)	)	PUNCT
ejpam-6851	108	11	=	=	SYM
ejpam-6851	108	12	∆(g	∆(g	PROPN
ejpam-6851	108	13	)	)	PUNCT
ejpam-6851	108	14	(	(	PUNCT
ejpam-6851	108	15	resp	resp	NOUN
ejpam-6851	108	16	.	.	PUNCT
ejpam-6851	109	1	degg(v	degg(v	PROPN
ejpam-6851	109	2	)	)	PUNCT
ejpam-6851	109	3	=	=	PUNCT
ejpam-6851	109	4	δ(g	δ(g	X
ejpam-6851	109	5	)	)	PUNCT
ejpam-6851	109	6	)	)	PUNCT
ejpam-6851	109	7	.	.	PUNCT
ejpam-6851	110	1	proof	proof	NOUN
ejpam-6851	110	2	.	.	PUNCT
ejpam-6851	111	1	let	let	VERB
ejpam-6851	111	2	s	s	PRON
ejpam-6851	111	3	⊆	⊆	NUM
ejpam-6851	111	4	v	v	NOUN
ejpam-6851	111	5	(	(	PUNCT
ejpam-6851	111	6	g	g	NOUN
ejpam-6851	111	7	)	)	PUNCT
ejpam-6851	111	8	be	be	AUX
ejpam-6851	111	9	a	a	DET
ejpam-6851	111	10	strong	strong	ADJ
ejpam-6851	111	11	dominating	dominating	NOUN
ejpam-6851	111	12	set	set	NOUN
ejpam-6851	111	13	of	of	ADP
ejpam-6851	111	14	g.	g.	PROPN
ejpam-6851	111	15	let	let	VERB
ejpam-6851	111	16	v	v	NUM
ejpam-6851	111	17	∈	∈	PROPN
ejpam-6851	111	18	v	v	NOUN
ejpam-6851	111	19	(	(	PUNCT
ejpam-6851	111	20	g	g	NOUN
ejpam-6851	111	21	)	)	PUNCT
ejpam-6851	111	22	for	for	ADP
ejpam-6851	111	23	which	which	PRON
ejpam-6851	111	24	degg(v	degg(v	PROPN
ejpam-6851	111	25	)	)	PUNCT
ejpam-6851	111	26	=	=	SYM
ejpam-6851	111	27	∆(g	∆(g	PROPN
ejpam-6851	111	28	)	)	PUNCT
ejpam-6851	111	29	.	.	PUNCT
ejpam-6851	112	1	if	if	SCONJ
ejpam-6851	112	2	v	v	NUM
ejpam-6851	112	3	∈	∈	PROPN
ejpam-6851	112	4	s	s	NOUN
ejpam-6851	112	5	,	,	PUNCT
ejpam-6851	112	6	then	then	ADV
ejpam-6851	112	7	we	we	PRON
ejpam-6851	112	8	are	be	AUX
ejpam-6851	112	9	done	do	VERB
ejpam-6851	112	10	.	.	PUNCT
ejpam-6851	113	1	suppose	suppose	VERB
ejpam-6851	113	2	v	v	X
ejpam-6851	113	3	/∈	/∈	PUNCT
ejpam-6851	113	4	s.	s.	PROPN
ejpam-6851	113	5	since	since	SCONJ
ejpam-6851	113	6	s	s	PROPN
ejpam-6851	113	7	∈	∈	PROPN
ejpam-6851	113	8	γs(g	γs(g	PUNCT
ejpam-6851	113	9	)	)	PUNCT
ejpam-6851	113	10	,	,	PUNCT
ejpam-6851	113	11	there	there	PRON
ejpam-6851	113	12	exists	exist	VERB
ejpam-6851	113	13	u	u	PROPN
ejpam-6851	113	14	∈	∈	PROPN
ejpam-6851	113	15	s	s	X
ejpam-6851	113	16	for	for	ADP
ejpam-6851	113	17	which	which	PRON
ejpam-6851	113	18	v	v	ADP
ejpam-6851	113	19	≼	≼	ADV
ejpam-6851	113	20	u.	u.	PROPN
ejpam-6851	113	21	necessarily	necessarily	ADV
ejpam-6851	113	22	,	,	PUNCT
ejpam-6851	113	23	degg(u	degg(u	PROPN
ejpam-6851	113	24	)	)	PUNCT
ejpam-6851	113	25	=	=	SYM
ejpam-6851	113	26	∆(g	∆(g	NOUN
ejpam-6851	113	27	)	)	PUNCT
ejpam-6851	113	28	.	.	PUNCT
ejpam-6851	114	1	parallel	parallel	ADJ
ejpam-6851	114	2	arguments	argument	NOUN
ejpam-6851	114	3	will	will	AUX
ejpam-6851	114	4	prove	prove	VERB
ejpam-6851	114	5	the	the	DET
ejpam-6851	114	6	case	case	NOUN
ejpam-6851	114	7	of	of	ADP
ejpam-6851	114	8	the	the	DET
ejpam-6851	114	9	weak	weak	ADJ
ejpam-6851	114	10	domination	domination	NOUN
ejpam-6851	114	11	.	.	PUNCT
ejpam-6851	115	1	remark	remark	PROPN
ejpam-6851	115	2	3	3	NUM
ejpam-6851	115	3	.	.	PUNCT
ejpam-6851	116	1	[	[	X
ejpam-6851	116	2	27	27	NUM
ejpam-6851	116	3	]	]	PUNCT
ejpam-6851	116	4	(	(	PUNCT
ejpam-6851	116	5	i	i	NOUN
ejpam-6851	116	6	)	)	PUNCT
ejpam-6851	116	7	for	for	ADP
ejpam-6851	116	8	a	a	DET
ejpam-6851	116	9	cycle	cycle	NOUN
ejpam-6851	116	10	cn	cn	PROPN
ejpam-6851	116	11	,	,	PUNCT
ejpam-6851	116	12	γs(cn	γs(cn	NOUN
ejpam-6851	116	13	)	)	PUNCT
ejpam-6851	116	14	=	=	SYM
ejpam-6851	116	15	γw(cn	γw(cn	PROPN
ejpam-6851	116	16	)	)	PUNCT
ejpam-6851	116	17	=	=	PRON
ejpam-6851	117	1	⌈n3	⌈n3	VERB
ejpam-6851	117	2	⌉.	⌉.	ADV
ejpam-6851	117	3	(	(	PUNCT
ejpam-6851	117	4	ii	ii	NOUN
ejpam-6851	117	5	)	)	PUNCT
ejpam-6851	117	6	for	for	ADP
ejpam-6851	117	7	a	a	DET
ejpam-6851	117	8	path	path	NOUN
ejpam-6851	117	9	pn	pn	PROPN
ejpam-6851	117	10	,	,	PUNCT
ejpam-6851	117	11	γs(pn	γs(pn	PROPN
ejpam-6851	117	12	)	)	PUNCT
ejpam-6851	117	13	=	=	PUNCT
ejpam-6851	117	14	⌈n	⌈n	NOUN
ejpam-6851	117	15	3	3	NUM
ejpam-6851	117	16	⌉	⌉	NOUN
ejpam-6851	117	17	and	and	CCONJ
ejpam-6851	117	18	γw(pn	γw(pn	NUM
ejpam-6851	117	19	)	)	PUNCT
ejpam-6851	117	20	=	=	PRON
ejpam-6851	117	21	{	{	PUNCT
ejpam-6851	117	22	⌈n3	⌈n3	X
ejpam-6851	117	23	⌉	⌉	X
ejpam-6851	117	24	,	,	PUNCT
ejpam-6851	117	25	if	if	SCONJ
ejpam-6851	117	26	n	n	PROPN
ejpam-6851	117	27	=	=	SYM
ejpam-6851	117	28	1(mod	1(mod	NUM
ejpam-6851	117	29	3	3	NUM
ejpam-6851	117	30	)	)	PUNCT
ejpam-6851	117	31	,	,	PUNCT
ejpam-6851	117	32	1	1	NUM
ejpam-6851	117	33	+	+	CCONJ
ejpam-6851	117	34	⌈n3	⌈n3	ADJ
ejpam-6851	117	35	⌉	⌉	X
ejpam-6851	117	36	,	,	PUNCT
ejpam-6851	117	37	else	else	ADV
ejpam-6851	117	38	.	.	PUNCT
ejpam-6851	118	1	in	in	ADP
ejpam-6851	118	2	what	what	PRON
ejpam-6851	118	3	follows	follow	VERB
ejpam-6851	118	4	,	,	PUNCT
ejpam-6851	118	5	for	for	ADP
ejpam-6851	118	6	the	the	DET
ejpam-6851	118	7	purpose	purpose	NOUN
ejpam-6851	118	8	of	of	ADP
ejpam-6851	118	9	emphasis	emphasis	NOUN
ejpam-6851	118	10	,	,	PUNCT
ejpam-6851	118	11	we	we	PRON
ejpam-6851	118	12	write	write	VERB
ejpam-6851	118	13	x	x	PUNCT
ejpam-6851	118	14	≼g	≼g	PROPN
ejpam-6851	118	15	y	y	PROPN
ejpam-6851	118	16	to	to	PART
ejpam-6851	118	17	mean	mean	VERB
ejpam-6851	118	18	x	x	PUNCT
ejpam-6851	118	19	≼	≼	PROPN
ejpam-6851	118	20	y	y	PROPN
ejpam-6851	118	21	in	in	ADP
ejpam-6851	118	22	g.	g.	PROPN
ejpam-6851	118	23	3	3	NUM
ejpam-6851	118	24	.	.	PUNCT
ejpam-6851	119	1	in	in	ADP
ejpam-6851	119	2	the	the	DET
ejpam-6851	119	3	complementary	complementary	ADJ
ejpam-6851	119	4	prism	prism	NOUN
ejpam-6851	119	5	of	of	ADP
ejpam-6851	119	6	graphs	graph	NOUN
ejpam-6851	119	7	proposition	proposition	NOUN
ejpam-6851	119	8	1	1	NUM
ejpam-6851	119	9	.	.	PUNCT
ejpam-6851	120	1	let	let	VERB
ejpam-6851	120	2	g	g	NOUN
ejpam-6851	120	3	be	be	AUX
ejpam-6851	120	4	any	any	DET
ejpam-6851	120	5	graph	graph	NOUN
ejpam-6851	120	6	.	.	PUNCT
ejpam-6851	121	1	then	then	ADV
ejpam-6851	121	2	(	(	PUNCT
ejpam-6851	121	3	i	i	NOUN
ejpam-6851	121	4	)	)	PUNCT
ejpam-6851	121	5	γs(gg	γs(gg	PROPN
ejpam-6851	121	6	)	)	PUNCT
ejpam-6851	121	7	=	=	SYM
ejpam-6851	121	8	1	1	NUM
ejpam-6851	121	9	(	(	PUNCT
ejpam-6851	121	10	resp	resp	NOUN
ejpam-6851	121	11	.	.	PUNCT
ejpam-6851	122	1	γw(gg	γw(gg	NOUN
ejpam-6851	122	2	)	)	PUNCT
ejpam-6851	123	1	=	=	SYM
ejpam-6851	123	2	1	1	X
ejpam-6851	123	3	)	)	PUNCT
ejpam-6851	123	4	if	if	SCONJ
ejpam-6851	123	5	and	and	CCONJ
ejpam-6851	123	6	only	only	ADV
ejpam-6851	123	7	if	if	SCONJ
ejpam-6851	123	8	g	g	PROPN
ejpam-6851	123	9	=	=	SYM
ejpam-6851	123	10	k1	k1	PROPN
ejpam-6851	123	11	;	;	PUNCT
ejpam-6851	123	12	(	(	PUNCT
ejpam-6851	123	13	ii	ii	NOUN
ejpam-6851	123	14	)	)	PUNCT
ejpam-6851	123	15	γs(gg	γs(gg	PROPN
ejpam-6851	123	16	)	)	PUNCT
ejpam-6851	123	17	=	=	SYM
ejpam-6851	123	18	2	2	NUM
ejpam-6851	124	1	if	if	SCONJ
ejpam-6851	124	2	and	and	CCONJ
ejpam-6851	124	3	only	only	ADV
ejpam-6851	124	4	if	if	SCONJ
ejpam-6851	124	5	exactly	exactly	ADV
ejpam-6851	124	6	one	one	NUM
ejpam-6851	124	7	of	of	ADP
ejpam-6851	124	8	the	the	DET
ejpam-6851	124	9	following	following	NOUN
ejpam-6851	124	10	holds	hold	VERB
ejpam-6851	124	11	:	:	PUNCT
ejpam-6851	124	12	(	(	PUNCT
ejpam-6851	124	13	a	a	X
ejpam-6851	124	14	)	)	PUNCT
ejpam-6851	124	15	g	g	NOUN
ejpam-6851	124	16	has	have	VERB
ejpam-6851	124	17	an	an	DET
ejpam-6851	124	18	isolated	isolated	ADJ
ejpam-6851	124	19	vertex	vertex	NOUN
ejpam-6851	124	20	x	x	PUNCT
ejpam-6851	124	21	for	for	ADP
ejpam-6851	124	22	which	which	PRON
ejpam-6851	124	23	γ(g−	γ(g−	NOUN
ejpam-6851	124	24	x	x	NOUN
ejpam-6851	124	25	)	)	PUNCT
ejpam-6851	124	26	=	=	SYM
ejpam-6851	125	1	1	1	X
ejpam-6851	125	2	.	.	PUNCT
ejpam-6851	125	3	(	(	PUNCT
ejpam-6851	125	4	b	b	X
ejpam-6851	125	5	)	)	PUNCT
ejpam-6851	125	6	g	g	NOUN
ejpam-6851	125	7	has	have	VERB
ejpam-6851	125	8	an	an	DET
ejpam-6851	125	9	isolated	isolated	ADJ
ejpam-6851	125	10	vertex	vertex	NOUN
ejpam-6851	125	11	x	x	PUNCT
ejpam-6851	125	12	for	for	ADP
ejpam-6851	125	13	which	which	PRON
ejpam-6851	125	14	γ(g−	γ(g−	NOUN
ejpam-6851	125	15	x	x	NOUN
ejpam-6851	125	16	)	)	PUNCT
ejpam-6851	125	17	=	=	SYM
ejpam-6851	125	18	1	1	X
ejpam-6851	125	19	.	.	PUNCT
ejpam-6851	125	20	(	(	PUNCT
ejpam-6851	125	21	iii	iii	X
ejpam-6851	125	22	)	)	PUNCT
ejpam-6851	125	23	γw(gg	γw(gg	PROPN
ejpam-6851	125	24	)	)	PUNCT
ejpam-6851	125	25	=	=	SYM
ejpam-6851	125	26	2	2	NUM
ejpam-6851	125	27	if	if	SCONJ
ejpam-6851	125	28	and	and	CCONJ
ejpam-6851	125	29	only	only	ADV
ejpam-6851	125	30	if	if	SCONJ
ejpam-6851	125	31	g	g	PROPN
ejpam-6851	125	32	∈	∈	PROPN
ejpam-6851	125	33	{	{	PUNCT
ejpam-6851	125	34	k2,k2	k2,k2	PROPN
ejpam-6851	125	35	}	}	PUNCT
ejpam-6851	125	36	.	.	PUNCT
ejpam-6851	126	1	j.	j.	PROPN
ejpam-6851	126	2	m.	m.	PROPN
ejpam-6851	126	3	molles	molles	PROPN
ejpam-6851	126	4	,	,	PUNCT
ejpam-6851	126	5	f.	f.	PROPN
ejpam-6851	126	6	p.	p.	PROPN
ejpam-6851	126	7	jamil	jamil	PROPN
ejpam-6851	126	8	,	,	PUNCT
ejpam-6851	126	9	s.	s.	PROPN
ejpam-6851	126	10	r.	r.	PROPN
ejpam-6851	126	11	canoy	canoy	PROPN
ejpam-6851	126	12	/	/	SYM
ejpam-6851	126	13	eur	eur	PROPN
ejpam-6851	126	14	.	.	PUNCT
ejpam-6851	127	1	j.	j.	PROPN
ejpam-6851	127	2	pure	pure	PROPN
ejpam-6851	127	3	appl	appl	PROPN
ejpam-6851	127	4	.	.	PROPN
ejpam-6851	127	5	math	math	PROPN
ejpam-6851	127	6	,	,	PUNCT
ejpam-6851	127	7	18	18	NUM
ejpam-6851	127	8	(	(	PUNCT
ejpam-6851	127	9	4	4	NUM
ejpam-6851	127	10	)	)	PUNCT
ejpam-6851	127	11	(	(	PUNCT
ejpam-6851	127	12	2025	2025	NUM
ejpam-6851	127	13	)	)	PUNCT
ejpam-6851	127	14	,	,	PUNCT
ejpam-6851	127	15	6851	6851	NUM
ejpam-6851	127	16	5	5	NUM
ejpam-6851	127	17	of	of	ADP
ejpam-6851	127	18	18	18	NUM
ejpam-6851	127	19	proof	proof	NOUN
ejpam-6851	127	20	.	.	PUNCT
ejpam-6851	128	1	statement	statement	NOUN
ejpam-6851	128	2	(	(	PUNCT
ejpam-6851	128	3	i	i	NOUN
ejpam-6851	128	4	)	)	PUNCT
ejpam-6851	128	5	immediately	immediately	ADV
ejpam-6851	128	6	follows	follow	VERB
ejpam-6851	128	7	from	from	ADP
ejpam-6851	128	8	observation	observation	NOUN
ejpam-6851	128	9	1(i	1(i	NUM
ejpam-6851	128	10	)	)	PUNCT
ejpam-6851	128	11	.	.	PUNCT
ejpam-6851	129	1	we	we	PRON
ejpam-6851	129	2	prove	prove	VERB
ejpam-6851	129	3	(	(	PUNCT
ejpam-6851	129	4	ii	ii	NOUN
ejpam-6851	129	5	)	)	PUNCT
ejpam-6851	129	6	.	.	PUNCT
ejpam-6851	130	1	suppose	suppose	VERB
ejpam-6851	130	2	that	that	SCONJ
ejpam-6851	130	3	γs(gg	γs(gg	PROPN
ejpam-6851	130	4	)	)	PUNCT
ejpam-6851	131	1	=	=	SYM
ejpam-6851	131	2	2	2	X
ejpam-6851	131	3	.	.	PUNCT
ejpam-6851	131	4	by	by	ADP
ejpam-6851	131	5	(	(	PUNCT
ejpam-6851	131	6	i	i	NOUN
ejpam-6851	131	7	)	)	PUNCT
ejpam-6851	131	8	,	,	PUNCT
ejpam-6851	131	9	g	g	PROPN
ejpam-6851	131	10	̸=	̸=	PROPN
ejpam-6851	131	11	k1	k1	NOUN
ejpam-6851	131	12	.	.	PUNCT
ejpam-6851	132	1	by	by	ADP
ejpam-6851	132	2	observation	observation	NOUN
ejpam-6851	132	3	2	2	NUM
ejpam-6851	132	4	,	,	PUNCT
ejpam-6851	132	5	there	there	PRON
ejpam-6851	132	6	exists	exist	VERB
ejpam-6851	132	7	a	a	DET
ejpam-6851	132	8	γ	γ	NOUN
ejpam-6851	132	9	-	-	PUNCT
ejpam-6851	132	10	set	set	VERB
ejpam-6851	132	11	s	s	PART
ejpam-6851	132	12	=	=	PUNCT
ejpam-6851	132	13	{	{	PUNCT
ejpam-6851	132	14	u	u	NOUN
ejpam-6851	132	15	,	,	PUNCT
ejpam-6851	132	16	v	v	NOUN
ejpam-6851	132	17	}	}	PUNCT
ejpam-6851	132	18	of	of	ADP
ejpam-6851	132	19	gg	gg	NOUN
ejpam-6851	132	20	for	for	ADP
ejpam-6851	132	21	which	which	PRON
ejpam-6851	132	22	x	x	SYM
ejpam-6851	132	23	≼gg	≼gg	NOUN
ejpam-6851	132	24	u	u	NOUN
ejpam-6851	132	25	or	or	CCONJ
ejpam-6851	132	26	x	x	PUNCT
ejpam-6851	132	27	≼gg	≼gg	NOUN
ejpam-6851	132	28	v	v	NOUN
ejpam-6851	132	29	for	for	ADP
ejpam-6851	132	30	each	each	DET
ejpam-6851	132	31	x	x	SYM
ejpam-6851	132	32	∈	∈	PROPN
ejpam-6851	132	33	v	v	NOUN
ejpam-6851	132	34	(	(	PUNCT
ejpam-6851	132	35	gg	gg	NOUN
ejpam-6851	132	36	)	)	PUNCT
ejpam-6851	132	37	\	\	PROPN
ejpam-6851	133	1	s.	s.	PROPN
ejpam-6851	133	2	if	if	SCONJ
ejpam-6851	133	3	u	u	PROPN
ejpam-6851	133	4	,	,	PUNCT
ejpam-6851	133	5	v	v	PROPN
ejpam-6851	133	6	∈	∈	PROPN
ejpam-6851	133	7	v	v	NOUN
ejpam-6851	133	8	(	(	PUNCT
ejpam-6851	133	9	g	g	NOUN
ejpam-6851	133	10	)	)	PUNCT
ejpam-6851	133	11	(	(	PUNCT
ejpam-6851	133	12	resp	resp	NOUN
ejpam-6851	133	13	.	.	PUNCT
ejpam-6851	134	1	u	u	NOUN
ejpam-6851	134	2	,	,	PUNCT
ejpam-6851	134	3	v	v	PROPN
ejpam-6851	134	4	∈	∈	PROPN
ejpam-6851	134	5	v	v	NOUN
ejpam-6851	134	6	(	(	PUNCT
ejpam-6851	134	7	g	g	NOUN
ejpam-6851	134	8	)	)	PUNCT
ejpam-6851	134	9	)	)	PUNCT
ejpam-6851	134	10	,	,	PUNCT
ejpam-6851	134	11	then	then	ADV
ejpam-6851	134	12	g	g	PROPN
ejpam-6851	134	13	=	=	PROPN
ejpam-6851	134	14	k2	k2	PROPN
ejpam-6851	134	15	(	(	PUNCT
ejpam-6851	134	16	resp	resp	NOUN
ejpam-6851	134	17	.	.	PUNCT
ejpam-6851	135	1	g	g	PROPN
ejpam-6851	135	2	=	=	SYM
ejpam-6851	135	3	k2	k2	PROPN
ejpam-6851	135	4	)	)	PUNCT
ejpam-6851	135	5	and	and	CCONJ
ejpam-6851	135	6	(	(	PUNCT
ejpam-6851	135	7	b	b	NOUN
ejpam-6851	135	8	)	)	PUNCT
ejpam-6851	135	9	holds	hold	NOUN
ejpam-6851	135	10	(	(	PUNCT
ejpam-6851	135	11	resp	resp	NOUN
ejpam-6851	135	12	.	.	PUNCT
ejpam-6851	136	1	(	(	PUNCT
ejpam-6851	136	2	a	a	X
ejpam-6851	136	3	)	)	PUNCT
ejpam-6851	136	4	holds	hold	NOUN
ejpam-6851	136	5	)	)	PUNCT
ejpam-6851	136	6	.	.	PUNCT
ejpam-6851	137	1	assume	assume	VERB
ejpam-6851	137	2	wlog	wlog	NOUN
ejpam-6851	137	3	that	that	SCONJ
ejpam-6851	137	4	u	u	PROPN
ejpam-6851	137	5	∈	∈	PROPN
ejpam-6851	137	6	v	v	ADP
ejpam-6851	137	7	(	(	PUNCT
ejpam-6851	137	8	g	g	NOUN
ejpam-6851	137	9	)	)	PUNCT
ejpam-6851	137	10	and	and	CCONJ
ejpam-6851	137	11	v	v	ADP
ejpam-6851	137	12	∈	∈	NOUN
ejpam-6851	137	13	v	v	NOUN
ejpam-6851	137	14	(	(	PUNCT
ejpam-6851	137	15	g	g	NOUN
ejpam-6851	137	16	)	)	PUNCT
ejpam-6851	137	17	.	.	PUNCT
ejpam-6851	138	1	suppose	suppose	VERB
ejpam-6851	138	2	further	far	ADV
ejpam-6851	138	3	that	that	SCONJ
ejpam-6851	138	4	uv	uv	PROPN
ejpam-6851	138	5	∈	∈	PROPN
ejpam-6851	138	6	e(gg	e(gg	PROPN
ejpam-6851	138	7	)	)	PUNCT
ejpam-6851	138	8	and	and	CCONJ
ejpam-6851	138	9	g	g	PROPN
ejpam-6851	138	10	̸=	̸=	PROPN
ejpam-6851	138	11	k2	k2	NOUN
ejpam-6851	138	12	.	.	PUNCT
ejpam-6851	139	1	necessarily	necessarily	ADV
ejpam-6851	139	2	,	,	PUNCT
ejpam-6851	139	3	u	u	NOUN
ejpam-6851	139	4	≽g	≽g	PROPN
ejpam-6851	139	5	v	v	X
ejpam-6851	139	6	(	(	PUNCT
ejpam-6851	139	7	g	g	NOUN
ejpam-6851	139	8	)	)	PUNCT
ejpam-6851	139	9	\	\	NOUN
ejpam-6851	139	10	{	{	PUNCT
ejpam-6851	139	11	u	u	NOUN
ejpam-6851	139	12	}	}	PUNCT
ejpam-6851	139	13	and	and	CCONJ
ejpam-6851	139	14	v	v	ADP
ejpam-6851	139	15	≽g	≽g	PROPN
ejpam-6851	139	16	v	v	NOUN
ejpam-6851	139	17	(	(	PUNCT
ejpam-6851	139	18	g	g	NOUN
ejpam-6851	139	19	)	)	PUNCT
ejpam-6851	139	20	\	\	NOUN
ejpam-6851	139	21	{	{	PUNCT
ejpam-6851	139	22	u	u	NOUN
ejpam-6851	139	23	,	,	PUNCT
ejpam-6851	139	24	v	v	NOUN
ejpam-6851	139	25	}	}	PUNCT
ejpam-6851	139	26	̸=	̸=	PROPN
ejpam-6851	139	27	∅.	∅.	ADP
ejpam-6851	139	28	the	the	DET
ejpam-6851	139	29	former	former	ADJ
ejpam-6851	139	30	implies	imply	VERB
ejpam-6851	139	31	that	that	SCONJ
ejpam-6851	139	32	ng[u	ng[u	PROPN
ejpam-6851	139	33	]	]	X
ejpam-6851	139	34	=	=	SYM
ejpam-6851	139	35	v	v	X
ejpam-6851	139	36	(	(	PUNCT
ejpam-6851	139	37	g	g	NOUN
ejpam-6851	139	38	)	)	PUNCT
ejpam-6851	139	39	and	and	CCONJ
ejpam-6851	139	40	consequently	consequently	ADV
ejpam-6851	139	41	,	,	PUNCT
ejpam-6851	139	42	u	u	NOUN
ejpam-6851	139	43	is	be	AUX
ejpam-6851	139	44	a	a	DET
ejpam-6851	139	45	(	(	PUNCT
ejpam-6851	139	46	unique	unique	ADJ
ejpam-6851	139	47	)	)	PUNCT
ejpam-6851	139	48	isolated	isolated	ADJ
ejpam-6851	139	49	vertex	vertex	NOUN
ejpam-6851	139	50	of	of	ADP
ejpam-6851	139	51	g.	g.	PROPN
ejpam-6851	139	52	the	the	DET
ejpam-6851	139	53	latter	latter	ADJ
ejpam-6851	139	54	implies	imply	VERB
ejpam-6851	139	55	that	that	SCONJ
ejpam-6851	139	56	ng−u[v	ng−u[v	PROPN
ejpam-6851	139	57	]	]	X
ejpam-6851	139	58	=	=	SYM
ejpam-6851	139	59	v	v	X
ejpam-6851	139	60	(	(	PUNCT
ejpam-6851	139	61	g−u	g−u	NOUN
ejpam-6851	139	62	)	)	PUNCT
ejpam-6851	139	63	.	.	PUNCT
ejpam-6851	140	1	this	this	PRON
ejpam-6851	140	2	shows	show	VERB
ejpam-6851	140	3	that	that	SCONJ
ejpam-6851	140	4	(	(	PUNCT
ejpam-6851	140	5	b	b	X
ejpam-6851	140	6	)	)	PUNCT
ejpam-6851	140	7	holds	hold	NOUN
ejpam-6851	140	8	.	.	PUNCT
ejpam-6851	141	1	similarly	similarly	ADV
ejpam-6851	141	2	,	,	PUNCT
ejpam-6851	141	3	if	if	SCONJ
ejpam-6851	141	4	uv	uv	PROPN
ejpam-6851	141	5	∈	∈	PROPN
ejpam-6851	141	6	e(g	e(g	PROPN
ejpam-6851	141	7	)	)	PUNCT
ejpam-6851	141	8	and	and	CCONJ
ejpam-6851	141	9	g	g	PROPN
ejpam-6851	141	10	̸=	̸=	PROPN
ejpam-6851	141	11	k2	k2	NOUN
ejpam-6851	141	12	,	,	PUNCT
ejpam-6851	141	13	then	then	ADV
ejpam-6851	141	14	u	u	NOUN
ejpam-6851	141	15	is	be	AUX
ejpam-6851	141	16	an	an	DET
ejpam-6851	141	17	isolated	isolated	ADJ
ejpam-6851	141	18	vertex	vertex	NOUN
ejpam-6851	141	19	of	of	ADP
ejpam-6851	141	20	g	g	PROPN
ejpam-6851	141	21	and	and	CCONJ
ejpam-6851	141	22	γ(g−	γ(g−	PROPN
ejpam-6851	141	23	u	u	NOUN
ejpam-6851	141	24	)	)	PUNCT
ejpam-6851	141	25	=	=	SYM
ejpam-6851	141	26	1	1	NUM
ejpam-6851	141	27	,	,	PUNCT
ejpam-6851	141	28	showing	show	VERB
ejpam-6851	141	29	that	that	SCONJ
ejpam-6851	141	30	(	(	PUNCT
ejpam-6851	141	31	a	a	X
ejpam-6851	141	32	)	)	PUNCT
ejpam-6851	141	33	holds	hold	NOUN
ejpam-6851	141	34	.	.	PUNCT
ejpam-6851	142	1	conversely	conversely	ADV
ejpam-6851	142	2	,	,	PUNCT
ejpam-6851	142	3	suppose	suppose	VERB
ejpam-6851	142	4	that	that	SCONJ
ejpam-6851	142	5	(	(	PUNCT
ejpam-6851	142	6	a	a	X
ejpam-6851	142	7	)	)	PUNCT
ejpam-6851	142	8	holds	hold	VERB
ejpam-6851	142	9	for	for	ADP
ejpam-6851	142	10	g.	g.	PROPN
ejpam-6851	142	11	let	let	VERB
ejpam-6851	142	12	x	x	PRON
ejpam-6851	142	13	be	be	AUX
ejpam-6851	142	14	an	an	DET
ejpam-6851	142	15	isolated	isolated	ADJ
ejpam-6851	142	16	vertex	vertex	NOUN
ejpam-6851	142	17	of	of	ADP
ejpam-6851	142	18	g	g	NOUN
ejpam-6851	142	19	and	and	CCONJ
ejpam-6851	142	20	let	let	VERB
ejpam-6851	142	21	z	z	NOUN
ejpam-6851	142	22	∈	∈	PROPN
ejpam-6851	142	23	v	v	NOUN
ejpam-6851	142	24	(	(	PUNCT
ejpam-6851	142	25	g	g	PROPN
ejpam-6851	142	26	−	−	PROPN
ejpam-6851	142	27	x	x	NOUN
ejpam-6851	142	28	)	)	PUNCT
ejpam-6851	142	29	such	such	ADJ
ejpam-6851	142	30	that	that	PRON
ejpam-6851	142	31	ng−x[z	ng−x[z	PROPN
ejpam-6851	142	32	]	]	X
ejpam-6851	142	33	=	=	SYM
ejpam-6851	142	34	v	v	X
ejpam-6851	142	35	(	(	PUNCT
ejpam-6851	142	36	g	g	PROPN
ejpam-6851	142	37	−	−	PROPN
ejpam-6851	142	38	x	x	NOUN
ejpam-6851	142	39	)	)	PUNCT
ejpam-6851	142	40	.	.	PUNCT
ejpam-6851	143	1	clearly	clearly	ADV
ejpam-6851	143	2	,	,	PUNCT
ejpam-6851	143	3	g	g	PROPN
ejpam-6851	143	4	̸=	̸=	PROPN
ejpam-6851	143	5	k1	k1	NOUN
ejpam-6851	143	6	so	so	SCONJ
ejpam-6851	143	7	that	that	DET
ejpam-6851	143	8	γs(gg	γs(gg	NOUN
ejpam-6851	143	9	)	)	PUNCT
ejpam-6851	143	10	≥	≥	NOUN
ejpam-6851	143	11	2	2	NUM
ejpam-6851	143	12	.	.	PUNCT
ejpam-6851	143	13	put	put	VERB
ejpam-6851	143	14	s	s	PART
ejpam-6851	143	15	=	=	PUNCT
ejpam-6851	143	16	{	{	PUNCT
ejpam-6851	143	17	x	x	NOUN
ejpam-6851	143	18	,	,	PUNCT
ejpam-6851	143	19	z	z	NOUN
ejpam-6851	143	20	}	}	PUNCT
ejpam-6851	143	21	.	.	PUNCT
ejpam-6851	144	1	since	since	SCONJ
ejpam-6851	144	2	ng[x	ng[x	PROPN
ejpam-6851	144	3	]	]	X
ejpam-6851	144	4	=	=	SYM
ejpam-6851	144	5	v	v	X
ejpam-6851	144	6	(	(	PUNCT
ejpam-6851	144	7	g	g	NOUN
ejpam-6851	144	8	)	)	PUNCT
ejpam-6851	144	9	,	,	PUNCT
ejpam-6851	144	10	x	x	X
ejpam-6851	144	11	≽gg	≽gg	VERB
ejpam-6851	144	12	v	v	X
ejpam-6851	144	13	(	(	PUNCT
ejpam-6851	144	14	g	g	NOUN
ejpam-6851	144	15	)	)	PUNCT
ejpam-6851	144	16	∪	∪	NOUN
ejpam-6851	144	17	{	{	PUNCT
ejpam-6851	144	18	x	x	NOUN
ejpam-6851	144	19	}	}	PUNCT
ejpam-6851	144	20	\	\	NOUN
ejpam-6851	144	21	{	{	PUNCT
ejpam-6851	144	22	x	x	NOUN
ejpam-6851	144	23	}	}	PUNCT
ejpam-6851	144	24	.	.	PUNCT
ejpam-6851	145	1	on	on	ADP
ejpam-6851	145	2	the	the	DET
ejpam-6851	145	3	other	other	ADJ
ejpam-6851	145	4	hand	hand	NOUN
ejpam-6851	145	5	,	,	PUNCT
ejpam-6851	145	6	z	z	NOUN
ejpam-6851	145	7	≽g	≽g	PROPN
ejpam-6851	145	8	v	v	NOUN
ejpam-6851	145	9	(	(	PUNCT
ejpam-6851	145	10	g	g	NOUN
ejpam-6851	145	11	)	)	PUNCT
ejpam-6851	145	12	\	\	NOUN
ejpam-6851	145	13	{	{	PUNCT
ejpam-6851	145	14	x	x	X
ejpam-6851	145	15	,	,	PUNCT
ejpam-6851	145	16	z	z	NOUN
ejpam-6851	145	17	}	}	PUNCT
ejpam-6851	145	18	.	.	PUNCT
ejpam-6851	146	1	by	by	ADP
ejpam-6851	146	2	observation	observation	NOUN
ejpam-6851	146	3	2	2	NUM
ejpam-6851	146	4	,	,	PUNCT
ejpam-6851	146	5	s	s	PROPN
ejpam-6851	146	6	∈	∈	PROPN
ejpam-6851	146	7	γs(gg	γs(gg	PROPN
ejpam-6851	146	8	)	)	PUNCT
ejpam-6851	146	9	.	.	PUNCT
ejpam-6851	147	1	thus	thus	ADV
ejpam-6851	147	2	,	,	PUNCT
ejpam-6851	147	3	γs(gg	γs(gg	PROPN
ejpam-6851	147	4	)	)	PUNCT
ejpam-6851	147	5	≤	≤	NUM
ejpam-6851	147	6	2	2	NUM
ejpam-6851	147	7	.	.	PUNCT
ejpam-6851	148	1	similarly	similarly	ADV
ejpam-6851	148	2	,	,	PUNCT
ejpam-6851	148	3	if	if	SCONJ
ejpam-6851	148	4	(	(	PUNCT
ejpam-6851	148	5	b	b	NOUN
ejpam-6851	148	6	)	)	PUNCT
ejpam-6851	148	7	holds	hold	NOUN
ejpam-6851	148	8	,	,	PUNCT
ejpam-6851	148	9	then	then	ADV
ejpam-6851	148	10	γs(gg	γs(gg	PROPN
ejpam-6851	148	11	)	)	PUNCT
ejpam-6851	149	1	=	=	SYM
ejpam-6851	149	2	2	2	X
ejpam-6851	149	3	.	.	PUNCT
ejpam-6851	150	1	this	this	PRON
ejpam-6851	150	2	proves	prove	VERB
ejpam-6851	150	3	(	(	PUNCT
ejpam-6851	150	4	ii	ii	NOUN
ejpam-6851	150	5	)	)	PUNCT
ejpam-6851	150	6	.	.	PUNCT
ejpam-6851	151	1	now	now	ADV
ejpam-6851	151	2	suppose	suppose	VERB
ejpam-6851	151	3	that	that	SCONJ
ejpam-6851	151	4	γw(gg	γw(gg	PROPN
ejpam-6851	151	5	)	)	PUNCT
ejpam-6851	151	6	=	=	SYM
ejpam-6851	151	7	2	2	NUM
ejpam-6851	151	8	,	,	PUNCT
ejpam-6851	151	9	and	and	CCONJ
ejpam-6851	151	10	let	let	VERB
ejpam-6851	151	11	s	s	PRON
ejpam-6851	151	12	=	=	PUNCT
ejpam-6851	151	13	{	{	PUNCT
ejpam-6851	151	14	u	u	NOUN
ejpam-6851	151	15	,	,	PUNCT
ejpam-6851	151	16	v	v	NOUN
ejpam-6851	151	17	}	}	PUNCT
ejpam-6851	151	18	be	be	AUX
ejpam-6851	151	19	a	a	DET
ejpam-6851	151	20	γ	γ	NOUN
ejpam-6851	151	21	-	-	PUNCT
ejpam-6851	151	22	set	set	NOUN
ejpam-6851	151	23	of	of	ADP
ejpam-6851	151	24	gg	gg	NOUN
ejpam-6851	151	25	such	such	ADJ
ejpam-6851	151	26	that	that	SCONJ
ejpam-6851	151	27	u	u	PROPN
ejpam-6851	151	28	≼gg	≼gg	VERB
ejpam-6851	151	29	x	x	SYM
ejpam-6851	151	30	or	or	CCONJ
ejpam-6851	151	31	v	v	ADP
ejpam-6851	151	32	≼gg	≼gg	VERB
ejpam-6851	151	33	x	x	PUNCT
ejpam-6851	151	34	for	for	ADP
ejpam-6851	151	35	each	each	DET
ejpam-6851	151	36	x	x	SYM
ejpam-6851	151	37	∈	∈	PROPN
ejpam-6851	151	38	v	v	NOUN
ejpam-6851	151	39	(	(	PUNCT
ejpam-6851	151	40	gg	gg	NOUN
ejpam-6851	151	41	)	)	PUNCT
ejpam-6851	151	42	\	\	PUNCT
ejpam-6851	151	43	s.	s.	PROPN
ejpam-6851	151	44	suppose	suppose	VERB
ejpam-6851	151	45	that	that	SCONJ
ejpam-6851	151	46	u	u	PROPN
ejpam-6851	151	47	∈	∈	PROPN
ejpam-6851	151	48	v	v	ADP
ejpam-6851	151	49	(	(	PUNCT
ejpam-6851	151	50	g	g	NOUN
ejpam-6851	151	51	)	)	PUNCT
ejpam-6851	151	52	and	and	CCONJ
ejpam-6851	151	53	v	v	ADP
ejpam-6851	151	54	∈	∈	NOUN
ejpam-6851	151	55	v	v	NOUN
ejpam-6851	151	56	(	(	PUNCT
ejpam-6851	151	57	g	g	NOUN
ejpam-6851	151	58	)	)	PUNCT
ejpam-6851	151	59	.	.	PUNCT
ejpam-6851	152	1	assume	assume	VERB
ejpam-6851	152	2	uv	uv	PROPN
ejpam-6851	152	3	∈	∈	PROPN
ejpam-6851	152	4	e(g	e(g	PROPN
ejpam-6851	152	5	)	)	PUNCT
ejpam-6851	152	6	.	.	PUNCT
ejpam-6851	153	1	since	since	SCONJ
ejpam-6851	153	2	u	u	PRON
ejpam-6851	153	3	≼gg	≼gg	SYM
ejpam-6851	153	4	u	u	NOUN
ejpam-6851	153	5	,	,	PUNCT
ejpam-6851	153	6	there	there	PRON
ejpam-6851	153	7	exists	exist	VERB
ejpam-6851	153	8	w	w	PROPN
ejpam-6851	153	9	∈	∈	PROPN
ejpam-6851	153	10	v	v	ADP
ejpam-6851	153	11	(	(	PUNCT
ejpam-6851	153	12	g	g	NOUN
ejpam-6851	153	13	)	)	PUNCT
ejpam-6851	153	14	such	such	ADJ
ejpam-6851	153	15	that	that	SCONJ
ejpam-6851	153	16	u	u	PROPN
ejpam-6851	153	17	w	w	PROPN
ejpam-6851	153	18	∈	∈	PROPN
ejpam-6851	153	19	e(g	e(g	PROPN
ejpam-6851	153	20	)	)	PUNCT
ejpam-6851	153	21	.	.	PUNCT
ejpam-6851	154	1	because	because	SCONJ
ejpam-6851	154	2	uw	uw	PROPN
ejpam-6851	154	3	/∈	/∈	PROPN
ejpam-6851	154	4	e(g	e(g	PROPN
ejpam-6851	154	5	)	)	PUNCT
ejpam-6851	154	6	,	,	PUNCT
ejpam-6851	154	7	wv	wv	PROPN
ejpam-6851	154	8	∈	∈	PROPN
ejpam-6851	154	9	e(gg	e(gg	PROPN
ejpam-6851	154	10	)	)	PUNCT
ejpam-6851	154	11	,	,	PUNCT
ejpam-6851	154	12	which	which	PRON
ejpam-6851	154	13	is	be	AUX
ejpam-6851	154	14	impossible	impossible	ADJ
ejpam-6851	154	15	.	.	PUNCT
ejpam-6851	155	1	thus	thus	ADV
ejpam-6851	155	2	,	,	PUNCT
ejpam-6851	155	3	u	u	NOUN
ejpam-6851	155	4	,	,	PUNCT
ejpam-6851	155	5	v	v	NOUN
ejpam-6851	155	6	∈	∈	PROPN
ejpam-6851	155	7	v	v	NOUN
ejpam-6851	155	8	(	(	PUNCT
ejpam-6851	155	9	g	g	NOUN
ejpam-6851	155	10	)	)	PUNCT
ejpam-6851	155	11	or	or	CCONJ
ejpam-6851	155	12	u	u	NOUN
ejpam-6851	155	13	,	,	PUNCT
ejpam-6851	155	14	v	v	NOUN
ejpam-6851	155	15	∈	∈	PROPN
ejpam-6851	155	16	v	v	NOUN
ejpam-6851	155	17	(	(	PUNCT
ejpam-6851	155	18	g	g	NOUN
ejpam-6851	155	19	)	)	PUNCT
ejpam-6851	155	20	.	.	PUNCT
ejpam-6851	156	1	this	this	PRON
ejpam-6851	156	2	implies	imply	VERB
ejpam-6851	156	3	that	that	SCONJ
ejpam-6851	156	4	g	g	PROPN
ejpam-6851	156	5	=	=	SYM
ejpam-6851	156	6	k2	k2	PROPN
ejpam-6851	156	7	or	or	CCONJ
ejpam-6851	156	8	g	g	NOUN
ejpam-6851	156	9	=	=	SYM
ejpam-6851	156	10	k2	k2	PROPN
ejpam-6851	156	11	.	.	PUNCT
ejpam-6851	157	1	the	the	DET
ejpam-6851	157	2	converse	converse	NOUN
ejpam-6851	157	3	is	be	AUX
ejpam-6851	157	4	easy	easy	ADJ
ejpam-6851	157	5	.	.	PUNCT
ejpam-6851	158	1	this	this	PRON
ejpam-6851	158	2	proves	prove	VERB
ejpam-6851	158	3	(	(	PUNCT
ejpam-6851	158	4	iii	iii	NOUN
ejpam-6851	158	5	)	)	PUNCT
ejpam-6851	158	6	.	.	PUNCT
ejpam-6851	159	1	remark	remark	PROPN
ejpam-6851	159	2	4	4	NUM
ejpam-6851	159	3	.	.	PUNCT
ejpam-6851	160	1	let	let	VERB
ejpam-6851	160	2	g	g	NOUN
ejpam-6851	160	3	be	be	AUX
ejpam-6851	160	4	any	any	DET
ejpam-6851	160	5	graph	graph	NOUN
ejpam-6851	160	6	.	.	PUNCT
ejpam-6851	161	1	then	then	ADV
ejpam-6851	161	2	s	s	VERB
ejpam-6851	161	3	⊆	⊆	NUM
ejpam-6851	161	4	v	v	NOUN
ejpam-6851	161	5	(	(	PUNCT
ejpam-6851	161	6	gg	gg	NOUN
ejpam-6851	161	7	)	)	PUNCT
ejpam-6851	161	8	is	be	AUX
ejpam-6851	161	9	a	a	DET
ejpam-6851	161	10	strong	strong	ADJ
ejpam-6851	161	11	dominating	dominating	NOUN
ejpam-6851	161	12	set	set	NOUN
ejpam-6851	161	13	of	of	ADP
ejpam-6851	161	14	gg	gg	PROPN
ejpam-6851	161	15	if	if	SCONJ
ejpam-6851	161	16	and	and	CCONJ
ejpam-6851	161	17	only	only	ADV
ejpam-6851	161	18	if	if	SCONJ
ejpam-6851	161	19	s	s	NOUN
ejpam-6851	161	20	=	=	PUNCT
ejpam-6851	161	21	sg	sg	PART
ejpam-6851	161	22	∪sg	∪sg	VERB
ejpam-6851	161	23	with	with	ADP
ejpam-6851	161	24	sg	sg	ADP
ejpam-6851	161	25	⊆	⊆	NUM
ejpam-6851	161	26	v	v	NOUN
ejpam-6851	161	27	(	(	PUNCT
ejpam-6851	161	28	g	g	NOUN
ejpam-6851	161	29	)	)	PUNCT
ejpam-6851	161	30	and	and	CCONJ
ejpam-6851	161	31	sg	sg	ADP
ejpam-6851	161	32	such	such	ADJ
ejpam-6851	161	33	that	that	PRON
ejpam-6851	161	34	for	for	ADP
ejpam-6851	161	35	each	each	DET
ejpam-6851	161	36	x	x	SYM
ejpam-6851	161	37	∈	∈	PROPN
ejpam-6851	161	38	v	v	ADP
ejpam-6851	161	39	(	(	PUNCT
ejpam-6851	161	40	g	g	NOUN
ejpam-6851	161	41	)	)	PUNCT
ejpam-6851	161	42	\sg	\sg	PROPN
ejpam-6851	161	43	(	(	PUNCT
ejpam-6851	161	44	resp	resp	NOUN
ejpam-6851	161	45	.	.	PUNCT
ejpam-6851	162	1	x	x	PUNCT
ejpam-6851	162	2	∈	∈	NOUN
ejpam-6851	162	3	v	v	ADP
ejpam-6851	162	4	(	(	PUNCT
ejpam-6851	162	5	g	g	NOUN
ejpam-6851	162	6	)	)	PUNCT
ejpam-6851	162	7	\	\	PROPN
ejpam-6851	162	8	sg	sg	PROPN
ejpam-6851	162	9	)	)	PUNCT
ejpam-6851	162	10	,	,	PUNCT
ejpam-6851	162	11	x	x	PROPN
ejpam-6851	162	12	≼g	≼g	NOUN
ejpam-6851	162	13	sg	sg	PROPN
ejpam-6851	162	14	(	(	PUNCT
ejpam-6851	162	15	resp	resp	NOUN
ejpam-6851	162	16	.	.	PUNCT
ejpam-6851	163	1	x	x	PUNCT
ejpam-6851	163	2	≼g	≼g	NOUN
ejpam-6851	163	3	sg	sg	NOUN
ejpam-6851	163	4	)	)	PUNCT
ejpam-6851	163	5	or	or	CCONJ
ejpam-6851	163	6	x	x	SYM
ejpam-6851	163	7	∈	∈	PROPN
ejpam-6851	163	8	sg	sg	PROPN
ejpam-6851	163	9	(	(	PUNCT
ejpam-6851	163	10	resp	resp	PROPN
ejpam-6851	163	11	.	.	PUNCT
ejpam-6851	164	1	x	x	X
ejpam-6851	164	2	∈	∈	PROPN
ejpam-6851	164	3	sg	sg	PROPN
ejpam-6851	164	4	)	)	PUNCT
ejpam-6851	164	5	and	and	CCONJ
ejpam-6851	164	6	x	x	PUNCT
ejpam-6851	164	7	≼gg	≼gg	ADJ
ejpam-6851	164	8	x.	x.	NOUN
ejpam-6851	164	9	let	let	VERB
ejpam-6851	164	10	g	g	PRON
ejpam-6851	164	11	be	be	AUX
ejpam-6851	164	12	of	of	ADP
ejpam-6851	164	13	order	order	NOUN
ejpam-6851	164	14	n.	n.	NOUN
ejpam-6851	164	15	put	put	VERB
ejpam-6851	164	16	sg	sg	NOUN
ejpam-6851	164	17	=	=	PUNCT
ejpam-6851	164	18	{	{	PUNCT
ejpam-6851	164	19	x	x	PUNCT
ejpam-6851	164	20	∈	∈	PROPN
ejpam-6851	164	21	v	v	NOUN
ejpam-6851	164	22	(	(	PUNCT
ejpam-6851	164	23	g	g	NOUN
ejpam-6851	164	24	)	)	PUNCT
ejpam-6851	164	25	:	:	PUNCT
ejpam-6851	164	26	x	x	X
ejpam-6851	164	27	≼gg	≼gg	ADJ
ejpam-6851	164	28	x	x	NOUN
ejpam-6851	164	29	}	}	PUNCT
ejpam-6851	164	30	and	and	CCONJ
ejpam-6851	164	31	sg	sg	ADV
ejpam-6851	164	32	=	=	PUNCT
ejpam-6851	164	33	{	{	PUNCT
ejpam-6851	164	34	x	x	X
ejpam-6851	164	35	:	:	PUNCT
ejpam-6851	164	36	x	x	SYM
ejpam-6851	164	37	∈	∈	NOUN
ejpam-6851	164	38	v	v	ADP
ejpam-6851	164	39	(	(	PUNCT
ejpam-6851	164	40	g	g	NOUN
ejpam-6851	164	41	)	)	PUNCT
ejpam-6851	164	42	\	\	NOUN
ejpam-6851	164	43	sg	sg	PROPN
ejpam-6851	164	44	}	}	PUNCT
ejpam-6851	164	45	.	.	PUNCT
ejpam-6851	165	1	by	by	ADP
ejpam-6851	165	2	observation	observation	NOUN
ejpam-6851	165	3	4	4	NUM
ejpam-6851	165	4	,	,	PUNCT
ejpam-6851	165	5	s	s	PART
ejpam-6851	165	6	=	=	PUNCT
ejpam-6851	165	7	sg	sg	X
ejpam-6851	165	8	∪	∪	ADJ
ejpam-6851	165	9	sg	sg	ADP
ejpam-6851	165	10	∈	∈	PROPN
ejpam-6851	165	11	γs(gg	γs(gg	PROPN
ejpam-6851	165	12	)	)	PUNCT
ejpam-6851	165	13	,	,	PUNCT
ejpam-6851	165	14	showing	show	VERB
ejpam-6851	165	15	γs(gg	γs(gg	PROPN
ejpam-6851	165	16	)	)	PUNCT
ejpam-6851	165	17	≤	≤	NUM
ejpam-6851	165	18	|s|	|s|	PROPN
ejpam-6851	165	19	=	=	SYM
ejpam-6851	165	20	n.	n.	NOUN
ejpam-6851	165	21	if	if	SCONJ
ejpam-6851	165	22	γ(g	γ(g	PROPN
ejpam-6851	165	23	)	)	PUNCT
ejpam-6851	166	1	=	=	SYM
ejpam-6851	166	2	1	1	NUM
ejpam-6851	166	3	or	or	CCONJ
ejpam-6851	166	4	g	g	PROPN
ejpam-6851	166	5	has	have	VERB
ejpam-6851	166	6	an	an	DET
ejpam-6851	166	7	isolated	isolated	ADJ
ejpam-6851	166	8	vertex	vertex	NOUN
ejpam-6851	166	9	,	,	PUNCT
ejpam-6851	166	10	this	this	PRON
ejpam-6851	166	11	bound	bind	VERB
ejpam-6851	166	12	coincides	coincide	NOUN
ejpam-6851	166	13	with	with	ADP
ejpam-6851	166	14	the	the	DET
ejpam-6851	166	15	bound	bind	VERB
ejpam-6851	166	16	given	give	VERB
ejpam-6851	166	17	in	in	ADP
ejpam-6851	166	18	equation	equation	NOUN
ejpam-6851	166	19	(	(	PUNCT
ejpam-6851	166	20	1	1	NUM
ejpam-6851	166	21	)	)	PUNCT
ejpam-6851	166	22	for	for	ADP
ejpam-6851	166	23	γs(gg	γs(gg	PROPN
ejpam-6851	166	24	)	)	PUNCT
ejpam-6851	166	25	.	.	PUNCT
ejpam-6851	167	1	replacing	replace	VERB
ejpam-6851	167	2	“	"	PUNCT
ejpam-6851	167	3	≼gg	≼gg	NOUN
ejpam-6851	167	4	”	"	PUNCT
ejpam-6851	167	5	with	with	ADP
ejpam-6851	167	6	“	"	PUNCT
ejpam-6851	167	7	≽gg	≽gg	VERB
ejpam-6851	167	8	”	"	PUNCT
ejpam-6851	167	9	in	in	ADP
ejpam-6851	167	10	the	the	DET
ejpam-6851	167	11	definition	definition	NOUN
ejpam-6851	167	12	of	of	ADP
ejpam-6851	167	13	sg	sg	PROPN
ejpam-6851	167	14	will	will	AUX
ejpam-6851	167	15	show	show	VERB
ejpam-6851	167	16	that	that	SCONJ
ejpam-6851	167	17	γw(gg	γw(gg	PROPN
ejpam-6851	167	18	)	)	PUNCT
ejpam-6851	167	19	≤	≤	PROPN
ejpam-6851	167	20	n.	n.	NOUN
ejpam-6851	167	21	in	in	ADP
ejpam-6851	167	22	particular	particular	ADJ
ejpam-6851	167	23	,	,	PUNCT
ejpam-6851	167	24	if	if	SCONJ
ejpam-6851	167	25	g	g	PROPN
ejpam-6851	167	26	∈	∈	PROPN
ejpam-6851	167	27	{	{	PUNCT
ejpam-6851	167	28	kn	kn	PROPN
ejpam-6851	167	29	,	,	PUNCT
ejpam-6851	167	30	kn	kn	PROPN
ejpam-6851	167	31	}	}	PUNCT
ejpam-6851	167	32	,	,	PUNCT
ejpam-6851	167	33	then	then	ADV
ejpam-6851	167	34	γs(gg	γs(gg	PROPN
ejpam-6851	167	35	)	)	PUNCT
ejpam-6851	167	36	=	=	SYM
ejpam-6851	167	37	n	n	PROPN
ejpam-6851	167	38	=	=	SYM
ejpam-6851	167	39	γw(gg	γw(gg	PROPN
ejpam-6851	167	40	)	)	PUNCT
ejpam-6851	167	41	.	.	PUNCT
ejpam-6851	168	1	proposition	proposition	NOUN
ejpam-6851	168	2	2	2	NUM
ejpam-6851	168	3	.	.	PUNCT
ejpam-6851	168	4	(	(	PUNCT
ejpam-6851	168	5	i	i	NOUN
ejpam-6851	168	6	)	)	PUNCT
ejpam-6851	168	7	for	for	ADP
ejpam-6851	168	8	all	all	DET
ejpam-6851	168	9	n	n	PRON
ejpam-6851	168	10	≥	≥	NOUN
ejpam-6851	168	11	3	3	NUM
ejpam-6851	168	12	,	,	PUNCT
ejpam-6851	168	13	γs(pnpn	γs(pnpn	NOUN
ejpam-6851	168	14	)	)	PUNCT
ejpam-6851	168	15	=	=	PRON
ejpam-6851	168	16	{	{	PUNCT
ejpam-6851	168	17	1	1	NUM
ejpam-6851	168	18	+	+	CCONJ
ejpam-6851	168	19	⌈n3	⌈n3	ADJ
ejpam-6851	168	20	⌉	⌉	NOUN
ejpam-6851	168	21	,	,	PUNCT
ejpam-6851	168	22	if	if	SCONJ
ejpam-6851	168	23	3	3	NUM
ejpam-6851	168	24	≤	≤	NUM
ejpam-6851	168	25	n	n	PRON
ejpam-6851	168	26	≤	≤	NOUN
ejpam-6851	168	27	5	5	NUM
ejpam-6851	168	28	;	;	PUNCT
ejpam-6851	168	29	2	2	NUM
ejpam-6851	168	30	+	+	CCONJ
ejpam-6851	168	31	⌈n−2	⌈n−2	ADJ
ejpam-6851	168	32	3	3	NUM
ejpam-6851	168	33	⌉	⌉	NOUN
ejpam-6851	168	34	,	,	PUNCT
ejpam-6851	168	35	if	if	SCONJ
ejpam-6851	168	36	n	n	PRON
ejpam-6851	168	37	≥	≥	NOUN
ejpam-6851	168	38	6	6	NUM
ejpam-6851	168	39	,	,	PUNCT
ejpam-6851	168	40	and	and	CCONJ
ejpam-6851	168	41	γw(pnpn	γw(pnpn	NOUN
ejpam-6851	168	42	)	)	PUNCT
ejpam-6851	169	1	=	=	SYM
ejpam-6851	169	2			NOUN
ejpam-6851	169	3	3	3	NUM
ejpam-6851	169	4	,	,	PUNCT
ejpam-6851	169	5	if	if	SCONJ
ejpam-6851	169	6	n	n	NOUN
ejpam-6851	169	7	=	=	SYM
ejpam-6851	169	8	3	3	NUM
ejpam-6851	169	9	,	,	PUNCT
ejpam-6851	169	10	4	4	NUM
ejpam-6851	169	11	,	,	PUNCT
ejpam-6851	169	12	if	if	SCONJ
ejpam-6851	169	13	4	4	NUM
ejpam-6851	169	14	≤	≤	NUM
ejpam-6851	169	15	n	n	PRON
ejpam-6851	169	16	≤	≤	NOUN
ejpam-6851	169	17	6	6	NUM
ejpam-6851	169	18	;	;	PUNCT
ejpam-6851	169	19	2	2	NUM
ejpam-6851	169	20	+	+	CCONJ
ejpam-6851	169	21	⌈n3	⌈n3	ADJ
ejpam-6851	169	22	⌉	⌉	NOUN
ejpam-6851	169	23	,	,	PUNCT
ejpam-6851	169	24	if	if	SCONJ
ejpam-6851	169	25	n	n	PRON
ejpam-6851	169	26	≥	≥	NOUN
ejpam-6851	169	27	7	7	NUM
ejpam-6851	169	28	,	,	PUNCT
ejpam-6851	169	29	(	(	PUNCT
ejpam-6851	169	30	ii	ii	NOUN
ejpam-6851	169	31	)	)	PUNCT
ejpam-6851	169	32	for	for	ADP
ejpam-6851	169	33	n	n	X
ejpam-6851	169	34	≥	≥	NUM
ejpam-6851	169	35	4	4	NUM
ejpam-6851	169	36	,	,	PUNCT
ejpam-6851	169	37	γs(cncn	γs(cncn	NUM
ejpam-6851	169	38	)	)	PUNCT
ejpam-6851	169	39	=	=	SYM
ejpam-6851	169	40	γw(cncn	γw(cncn	NUM
ejpam-6851	169	41	)	)	PUNCT
ejpam-6851	169	42	=	=	PRON
ejpam-6851	169	43	{	{	PUNCT
ejpam-6851	169	44	3	3	NUM
ejpam-6851	169	45	,	,	PUNCT
ejpam-6851	169	46	if	if	SCONJ
ejpam-6851	169	47	n	n	NOUN
ejpam-6851	169	48	=	=	SYM
ejpam-6851	169	49	5	5	NUM
ejpam-6851	169	50	;	;	PUNCT
ejpam-6851	169	51	2	2	NUM
ejpam-6851	169	52	+	+	CCONJ
ejpam-6851	169	53	⌈n3	⌈n3	ADJ
ejpam-6851	169	54	⌉	⌉	X
ejpam-6851	169	55	,	,	PUNCT
ejpam-6851	169	56	else	else	ADV
ejpam-6851	169	57	.	.	PUNCT
ejpam-6851	170	1	j.	j.	PROPN
ejpam-6851	170	2	m.	m.	PROPN
ejpam-6851	170	3	molles	molles	PROPN
ejpam-6851	170	4	,	,	PUNCT
ejpam-6851	170	5	f.	f.	PROPN
ejpam-6851	170	6	p.	p.	PROPN
ejpam-6851	170	7	jamil	jamil	PROPN
ejpam-6851	170	8	,	,	PUNCT
ejpam-6851	170	9	s.	s.	PROPN
ejpam-6851	170	10	r.	r.	PROPN
ejpam-6851	170	11	canoy	canoy	PROPN
ejpam-6851	170	12	/	/	SYM
ejpam-6851	170	13	eur	eur	PROPN
ejpam-6851	170	14	.	.	PUNCT
ejpam-6851	171	1	j.	j.	PROPN
ejpam-6851	171	2	pure	pure	PROPN
ejpam-6851	171	3	appl	appl	PROPN
ejpam-6851	171	4	.	.	PROPN
ejpam-6851	171	5	math	math	PROPN
ejpam-6851	171	6	,	,	PUNCT
ejpam-6851	171	7	18	18	NUM
ejpam-6851	171	8	(	(	PUNCT
ejpam-6851	171	9	4	4	NUM
ejpam-6851	171	10	)	)	PUNCT
ejpam-6851	171	11	(	(	PUNCT
ejpam-6851	171	12	2025	2025	NUM
ejpam-6851	171	13	)	)	PUNCT
ejpam-6851	171	14	,	,	PUNCT
ejpam-6851	171	15	6851	6851	NUM
ejpam-6851	171	16	6	6	NUM
ejpam-6851	171	17	of	of	ADP
ejpam-6851	171	18	18	18	NUM
ejpam-6851	171	19	proof	proof	NOUN
ejpam-6851	171	20	.	.	PUNCT
ejpam-6851	172	1	for	for	ADP
ejpam-6851	172	2	(	(	PUNCT
ejpam-6851	172	3	i	i	NOUN
ejpam-6851	172	4	)	)	PUNCT
ejpam-6851	172	5	,	,	PUNCT
ejpam-6851	172	6	put	put	VERB
ejpam-6851	172	7	g	g	NOUN
ejpam-6851	172	8	=	=	PUNCT
ejpam-6851	172	9	pn	pn	PROPN
ejpam-6851	172	10	=	=	PUNCT
ejpam-6851	173	1	[	[	X
ejpam-6851	173	2	x1	x1	PROPN
ejpam-6851	173	3	,	,	PUNCT
ejpam-6851	173	4	x2	x2	PROPN
ejpam-6851	173	5	,	,	PUNCT
ejpam-6851	173	6	.	.	PUNCT
ejpam-6851	173	7	.	.	PUNCT
ejpam-6851	174	1	.	.	PUNCT
ejpam-6851	175	1	,	,	PUNCT
ejpam-6851	176	1	xn	xn	X
ejpam-6851	176	2	]	]	PUNCT
ejpam-6851	176	3	and	and	CCONJ
ejpam-6851	176	4	for	for	ADP
ejpam-6851	176	5	any	any	DET
ejpam-6851	176	6	s	s	NOUN
ejpam-6851	176	7	⊆	⊆	NUM
ejpam-6851	176	8	v	v	NOUN
ejpam-6851	176	9	(	(	PUNCT
ejpam-6851	176	10	gg	gg	PROPN
ejpam-6851	176	11	)	)	PUNCT
ejpam-6851	176	12	,	,	PUNCT
ejpam-6851	176	13	define	define	VERB
ejpam-6851	176	14	sg	sg	ADP
ejpam-6851	176	15	=	=	PUNCT
ejpam-6851	176	16	s∩v	s∩v	PROPN
ejpam-6851	176	17	(	(	PUNCT
ejpam-6851	176	18	g	g	NOUN
ejpam-6851	176	19	)	)	PUNCT
ejpam-6851	176	20	and	and	CCONJ
ejpam-6851	176	21	sg	sg	X
ejpam-6851	176	22	=	=	PUNCT
ejpam-6851	176	23	s∩v	s∩v	PROPN
ejpam-6851	176	24	(	(	PUNCT
ejpam-6851	176	25	g	g	NOUN
ejpam-6851	176	26	)	)	PUNCT
ejpam-6851	176	27	.	.	PUNCT
ejpam-6851	177	1	the	the	DET
ejpam-6851	177	2	value	value	NOUN
ejpam-6851	177	3	of	of	ADP
ejpam-6851	177	4	γs(gg	γs(gg	PROPN
ejpam-6851	177	5	)	)	PUNCT
ejpam-6851	177	6	can	can	AUX
ejpam-6851	177	7	readily	readily	ADV
ejpam-6851	177	8	be	be	AUX
ejpam-6851	177	9	checked	check	VERB
ejpam-6851	177	10	when	when	SCONJ
ejpam-6851	177	11	3	3	NUM
ejpam-6851	177	12	≤	≤	NOUN
ejpam-6851	177	13	n	n	PRON
ejpam-6851	177	14	≤	≤	NOUN
ejpam-6851	177	15	5	5	NUM
ejpam-6851	177	16	.	.	PUNCT
ejpam-6851	178	1	let	let	VERB
ejpam-6851	178	2	n	n	PRON
ejpam-6851	178	3	≥	≥	NUM
ejpam-6851	178	4	6	6	NUM
ejpam-6851	178	5	.	.	PUNCT
ejpam-6851	179	1	let	let	VERB
ejpam-6851	179	2	a	a	DET
ejpam-6851	179	3	⊆	⊆	NUM
ejpam-6851	179	4	{	{	PUNCT
ejpam-6851	179	5	x2	x2	PROPN
ejpam-6851	179	6	,	,	PUNCT
ejpam-6851	179	7	x4	x4	PROPN
ejpam-6851	179	8	,	,	PUNCT
ejpam-6851	179	9	.	.	PUNCT
ejpam-6851	179	10	.	.	PUNCT
ejpam-6851	180	1	.	.	PUNCT
ejpam-6851	181	1	,	,	PUNCT
ejpam-6851	181	2	xn−1	xn−1	PROPN
ejpam-6851	181	3	}	}	PUNCT
ejpam-6851	181	4	be	be	VERB
ejpam-6851	181	5	a	a	DET
ejpam-6851	181	6	γ	γ	NOUN
ejpam-6851	181	7	-	-	PUNCT
ejpam-6851	181	8	set	set	NOUN
ejpam-6851	181	9	of	of	ADP
ejpam-6851	181	10	the	the	DET
ejpam-6851	181	11	path	path	NOUN
ejpam-6851	181	12	p	p	NOUN
ejpam-6851	182	1	=	=	PUNCT
ejpam-6851	183	1	[	[	X
ejpam-6851	183	2	x2	x2	PROPN
ejpam-6851	183	3	,	,	PUNCT
ejpam-6851	183	4	x4	x4	PROPN
ejpam-6851	183	5	,	,	PUNCT
ejpam-6851	183	6	.	.	PUNCT
ejpam-6851	183	7	.	.	PUNCT
ejpam-6851	184	1	.	.	PUNCT
ejpam-6851	185	1	,	,	PUNCT
ejpam-6851	185	2	xn−1	xn−1	PROPN
ejpam-6851	185	3	]	]	PUNCT
ejpam-6851	185	4	.	.	PUNCT
ejpam-6851	186	1	then	then	ADV
ejpam-6851	186	2	by	by	ADP
ejpam-6851	186	3	observation	observation	NOUN
ejpam-6851	186	4	4	4	NUM
ejpam-6851	186	5	,	,	PUNCT
ejpam-6851	186	6	s	s	VERB
ejpam-6851	186	7	=	=	PUNCT
ejpam-6851	186	8	a	a	DET
ejpam-6851	186	9	∪	∪	X
ejpam-6851	186	10	{	{	PUNCT
ejpam-6851	186	11	x1	x1	PROPN
ejpam-6851	186	12	,	,	PUNCT
ejpam-6851	186	13	xn	xn	PROPN
ejpam-6851	186	14	}	}	PUNCT
ejpam-6851	186	15	∈	∈	PROPN
ejpam-6851	186	16	γs(gg	γs(gg	PROPN
ejpam-6851	186	17	)	)	PUNCT
ejpam-6851	186	18	.	.	PUNCT
ejpam-6851	187	1	hence	hence	ADV
ejpam-6851	187	2	,	,	PUNCT
ejpam-6851	187	3	γs(gg	γs(gg	PROPN
ejpam-6851	187	4	)	)	PUNCT
ejpam-6851	187	5	≤	≤	NUM
ejpam-6851	187	6	|s|	|s|	PROPN
ejpam-6851	187	7	=	=	SYM
ejpam-6851	187	8	2	2	NUM
ejpam-6851	187	9	+	+	NOUN
ejpam-6851	187	10	γ(pn−2	γ(pn−2	NOUN
ejpam-6851	187	11	)	)	PUNCT
ejpam-6851	187	12	=	=	SYM
ejpam-6851	187	13	2	2	NUM
ejpam-6851	187	14	+	+	CCONJ
ejpam-6851	187	15	⌈n−2	⌈n−2	ADJ
ejpam-6851	187	16	3	3	NUM
ejpam-6851	187	17	⌉.	⌉.	ADV
ejpam-6851	187	18	to	to	PART
ejpam-6851	187	19	get	get	VERB
ejpam-6851	187	20	the	the	DET
ejpam-6851	187	21	other	other	ADJ
ejpam-6851	187	22	inequality	inequality	NOUN
ejpam-6851	187	23	,	,	PUNCT
ejpam-6851	187	24	let	let	VERB
ejpam-6851	187	25	s	s	PRON
ejpam-6851	187	26	⊆	⊆	NUM
ejpam-6851	187	27	v	v	NOUN
ejpam-6851	187	28	(	(	PUNCT
ejpam-6851	187	29	gg	gg	NOUN
ejpam-6851	187	30	)	)	PUNCT
ejpam-6851	187	31	be	be	AUX
ejpam-6851	187	32	a	a	DET
ejpam-6851	187	33	γs	γs	NOUN
ejpam-6851	187	34	-	-	PUNCT
ejpam-6851	187	35	set	set	NOUN
ejpam-6851	187	36	of	of	ADP
ejpam-6851	187	37	gg	gg	PROPN
ejpam-6851	187	38	.	.	PUNCT
ejpam-6851	188	1	since	since	SCONJ
ejpam-6851	188	2	degg(x	degg(x	NUM
ejpam-6851	188	3	)	)	PUNCT
ejpam-6851	188	4	<	<	X
ejpam-6851	188	5	degg(x	degg(x	NOUN
ejpam-6851	188	6	)	)	PUNCT
ejpam-6851	188	7	for	for	ADP
ejpam-6851	188	8	all	all	PRON
ejpam-6851	188	9	x	x	SYM
ejpam-6851	188	10	∈	∈	PROPN
ejpam-6851	188	11	v	v	NOUN
ejpam-6851	188	12	(	(	PUNCT
ejpam-6851	188	13	g	g	NOUN
ejpam-6851	188	14	)	)	PUNCT
ejpam-6851	188	15	,	,	PUNCT
ejpam-6851	188	16	observation	observation	NOUN
ejpam-6851	188	17	4	4	NUM
ejpam-6851	188	18	implies	imply	VERB
ejpam-6851	188	19	that	that	SCONJ
ejpam-6851	188	20	sg	sg	PROPN
ejpam-6851	188	21	∈	∈	PROPN
ejpam-6851	188	22	γs(g	γs(g	PUNCT
ejpam-6851	188	23	)	)	PUNCT
ejpam-6851	188	24	.	.	PUNCT
ejpam-6851	189	1	in	in	ADP
ejpam-6851	189	2	view	view	NOUN
ejpam-6851	189	3	of	of	ADP
ejpam-6851	189	4	lemma	lemma	PROPN
ejpam-6851	189	5	2	2	NUM
ejpam-6851	189	6	,	,	PUNCT
ejpam-6851	189	7	we	we	PRON
ejpam-6851	189	8	may	may	AUX
ejpam-6851	189	9	assume	assume	VERB
ejpam-6851	189	10	x1	x1	PROPN
ejpam-6851	189	11	∈	∈	PROPN
ejpam-6851	189	12	sg	sg	PROPN
ejpam-6851	189	13	.	.	PUNCT
ejpam-6851	190	1	since	since	SCONJ
ejpam-6851	190	2	v	v	NOUN
ejpam-6851	190	3	(	(	PUNCT
ejpam-6851	190	4	g	g	NOUN
ejpam-6851	190	5	)	)	PUNCT
ejpam-6851	190	6	\	\	NOUN
ejpam-6851	190	7	{	{	PUNCT
ejpam-6851	190	8	x2	x2	NOUN
ejpam-6851	190	9	}	}	PUNCT
ejpam-6851	190	10	≼g	≼g	PROPN
ejpam-6851	190	11	x1	x1	PROPN
ejpam-6851	190	12	,	,	PUNCT
ejpam-6851	190	13	|sg|	|sg|	PROPN
ejpam-6851	190	14	≥	≥	NOUN
ejpam-6851	190	15	2	2	NUM
ejpam-6851	190	16	.	.	PUNCT
ejpam-6851	191	1	in	in	ADP
ejpam-6851	191	2	case	case	NOUN
ejpam-6851	191	3	x2	x2	PROPN
ejpam-6851	191	4	∈	∈	PROPN
ejpam-6851	191	5	sg	sg	PROPN
ejpam-6851	191	6	,	,	PUNCT
ejpam-6851	191	7	choose	choose	VERB
ejpam-6851	191	8	x	x	X
ejpam-6851	191	9	=	=	SYM
ejpam-6851	191	10	x2	x2	PROPN
ejpam-6851	191	11	.	.	PUNCT
ejpam-6851	192	1	otherwise	otherwise	ADV
ejpam-6851	192	2	,	,	PUNCT
ejpam-6851	192	3	choose	choose	VERB
ejpam-6851	192	4	x	x	PUNCT
ejpam-6851	192	5	∈	∈	PROPN
ejpam-6851	192	6	v	v	ADP
ejpam-6851	192	7	(	(	PUNCT
ejpam-6851	192	8	g	g	NOUN
ejpam-6851	192	9	)	)	PUNCT
ejpam-6851	192	10	such	such	ADJ
ejpam-6851	192	11	that	that	SCONJ
ejpam-6851	192	12	x	x	SYM
ejpam-6851	192	13	∈	∈	NOUN
ejpam-6851	192	14	sg	sg	ADP
ejpam-6851	192	15	\	\	PROPN
ejpam-6851	192	16	{	{	PUNCT
ejpam-6851	192	17	x1	x1	PROPN
ejpam-6851	192	18	}	}	PUNCT
ejpam-6851	192	19	and	and	CCONJ
ejpam-6851	192	20	x2	x2	PROPN
ejpam-6851	193	1	≼	≼	ADJ
ejpam-6851	193	2	x.	x.	NOUN
ejpam-6851	194	1	if	if	SCONJ
ejpam-6851	194	2	x	x	PROPN
ejpam-6851	194	3	/∈	/∈	PUNCT
ejpam-6851	194	4	sg	sg	PROPN
ejpam-6851	194	5	,	,	PUNCT
ejpam-6851	194	6	then	then	ADV
ejpam-6851	194	7	s∗	s∗	PROPN
ejpam-6851	194	8	=	=	SYM
ejpam-6851	194	9	s	s	PART
ejpam-6851	194	10	\	\	X
ejpam-6851	194	11	{	{	PUNCT
ejpam-6851	194	12	x	x	NOUN
ejpam-6851	194	13	,	,	PUNCT
ejpam-6851	194	14	x1	x1	ADJ
ejpam-6851	194	15	}	}	PUNCT
ejpam-6851	194	16	strongly	strongly	ADV
ejpam-6851	194	17	dominates	dominate	VERB
ejpam-6851	194	18	v	v	NOUN
ejpam-6851	194	19	(	(	PUNCT
ejpam-6851	194	20	g	g	NOUN
ejpam-6851	194	21	)	)	PUNCT
ejpam-6851	194	22	\	\	NOUN
ejpam-6851	194	23	{	{	PUNCT
ejpam-6851	194	24	x	x	NOUN
ejpam-6851	194	25	,	,	PUNCT
ejpam-6851	194	26	x1	x1	PROPN
ejpam-6851	194	27	}	}	PUNCT
ejpam-6851	194	28	.	.	PUNCT
ejpam-6851	195	1	in	in	ADP
ejpam-6851	195	2	this	this	DET
ejpam-6851	195	3	case	case	NOUN
ejpam-6851	195	4	,	,	PUNCT
ejpam-6851	195	5	|s|	|s|	X
ejpam-6851	195	6	≥	≥	NOUN
ejpam-6851	195	7	2	2	NUM
ejpam-6851	195	8	+	+	CCONJ
ejpam-6851	195	9	γs(pn−2	γs(pn−2	PROPN
ejpam-6851	195	10	)	)	PUNCT
ejpam-6851	195	11	.	.	PUNCT
ejpam-6851	196	1	if	if	SCONJ
ejpam-6851	196	2	x	x	SYM
ejpam-6851	196	3	∈	∈	PROPN
ejpam-6851	196	4	sg	sg	PROPN
ejpam-6851	196	5	,	,	PUNCT
ejpam-6851	196	6	then	then	ADV
ejpam-6851	196	7	s	s	VERB
ejpam-6851	196	8	\	\	X
ejpam-6851	196	9	{	{	PUNCT
ejpam-6851	196	10	x	x	NOUN
ejpam-6851	196	11	,	,	PUNCT
ejpam-6851	196	12	x1	x1	ADJ
ejpam-6851	196	13	}	}	PUNCT
ejpam-6851	196	14	strongly	strongly	ADV
ejpam-6851	196	15	dominates	dominate	VERB
ejpam-6851	196	16	v	v	NOUN
ejpam-6851	196	17	(	(	PUNCT
ejpam-6851	196	18	g	g	NOUN
ejpam-6851	196	19	)	)	PUNCT
ejpam-6851	196	20	\	\	NOUN
ejpam-6851	196	21	{	{	PUNCT
ejpam-6851	196	22	x1	x1	PROPN
ejpam-6851	196	23	}	}	PUNCT
ejpam-6851	196	24	so	so	SCONJ
ejpam-6851	196	25	that	that	SCONJ
ejpam-6851	196	26	|s|	|s|	VERB
ejpam-6851	196	27	≥	≥	NOUN
ejpam-6851	196	28	2	2	NUM
ejpam-6851	196	29	+	+	CCONJ
ejpam-6851	196	30	γs(pn−1	γs(pn−1	NOUN
ejpam-6851	196	31	)	)	PUNCT
ejpam-6851	196	32	≥	≥	NOUN
ejpam-6851	196	33	2	2	NUM
ejpam-6851	196	34	+	+	CCONJ
ejpam-6851	196	35	γs(pn−2	γs(pn−2	PROPN
ejpam-6851	196	36	)	)	PUNCT
ejpam-6851	196	37	.	.	PUNCT
ejpam-6851	197	1	in	in	ADP
ejpam-6851	197	2	any	any	DET
ejpam-6851	197	3	case	case	NOUN
ejpam-6851	197	4	,	,	PUNCT
ejpam-6851	197	5	γs(gg	γs(gg	PROPN
ejpam-6851	197	6	)	)	PUNCT
ejpam-6851	197	7	≥	≥	NOUN
ejpam-6851	197	8	2	2	NUM
ejpam-6851	197	9	+	+	CCONJ
ejpam-6851	197	10	γs(pn−2	γs(pn−2	PROPN
ejpam-6851	197	11	)	)	PUNCT
ejpam-6851	197	12	=	=	SYM
ejpam-6851	198	1	2	2	NUM
ejpam-6851	198	2	+	+	CCONJ
ejpam-6851	198	3	⌈n−2	⌈n−2	ADJ
ejpam-6851	198	4	3	3	NUM
ejpam-6851	198	5	⌉.	⌉.	ADV
ejpam-6851	198	6	for	for	ADP
ejpam-6851	198	7	γw(gg	γw(gg	PROPN
ejpam-6851	198	8	)	)	PUNCT
ejpam-6851	198	9	,	,	PUNCT
ejpam-6851	198	10	the	the	DET
ejpam-6851	198	11	case	case	NOUN
ejpam-6851	198	12	where	where	SCONJ
ejpam-6851	198	13	3	3	NUM
ejpam-6851	198	14	≤	≤	NOUN
ejpam-6851	198	15	n	n	PRON
ejpam-6851	198	16	≤	≤	NUM
ejpam-6851	198	17	6	6	NUM
ejpam-6851	198	18	can	can	AUX
ejpam-6851	198	19	be	be	AUX
ejpam-6851	198	20	readily	readily	ADV
ejpam-6851	198	21	verified	verify	VERB
ejpam-6851	198	22	.	.	PUNCT
ejpam-6851	199	1	let	let	VERB
ejpam-6851	199	2	n	n	PRON
ejpam-6851	199	3	≥	≥	NOUN
ejpam-6851	199	4	7	7	NUM
ejpam-6851	199	5	.	.	PUNCT
ejpam-6851	200	1	put	put	VERB
ejpam-6851	200	2	s	s	PART
ejpam-6851	200	3	=	=	PUNCT
ejpam-6851	200	4	{	{	PUNCT
ejpam-6851	200	5	x1	x1	PROPN
ejpam-6851	200	6	,	,	PUNCT
ejpam-6851	200	7	x2	x2	PROPN
ejpam-6851	200	8	,	,	PUNCT
ejpam-6851	200	9	x3	x3	ADJ
ejpam-6851	200	10	,	,	PUNCT
ejpam-6851	200	11	x6	x6	PROPN
ejpam-6851	200	12	,	,	PUNCT
ejpam-6851	200	13	.	.	PUNCT
ejpam-6851	200	14	.	.	PUNCT
ejpam-6851	200	15	.	.	PUNCT
ejpam-6851	201	1	,	,	PUNCT
ejpam-6851	201	2	x3k	x3k	PROPN
ejpam-6851	201	3	}	}	PUNCT
ejpam-6851	201	4	whenever	whenever	SCONJ
ejpam-6851	201	5	n	n	PROPN
ejpam-6851	201	6	=	=	SYM
ejpam-6851	201	7	3k	3k	NUM
ejpam-6851	201	8	;	;	PUNCT
ejpam-6851	201	9	otherwise	otherwise	ADV
ejpam-6851	201	10	write	write	VERB
ejpam-6851	201	11	s	s	NOUN
ejpam-6851	201	12	=	=	PUNCT
ejpam-6851	201	13	{	{	PUNCT
ejpam-6851	201	14	x1	x1	PROPN
ejpam-6851	201	15	,	,	PUNCT
ejpam-6851	201	16	x2	x2	PROPN
ejpam-6851	201	17	,	,	PUNCT
ejpam-6851	201	18	x3	x3	ADJ
ejpam-6851	201	19	,	,	PUNCT
ejpam-6851	201	20	x6	x6	PROPN
ejpam-6851	201	21	,	,	PUNCT
ejpam-6851	201	22	.	.	PUNCT
ejpam-6851	201	23	.	.	PUNCT
ejpam-6851	202	1	.	.	PUNCT
ejpam-6851	203	1	,	,	PUNCT
ejpam-6851	203	2	x3⌊n	x3⌊n	PROPN
ejpam-6851	203	3	3	3	NUM
ejpam-6851	203	4	⌋	⌋	NOUN
ejpam-6851	203	5	,	,	PUNCT
ejpam-6851	203	6	xn	xn	NUM
ejpam-6851	203	7	}	}	PUNCT
ejpam-6851	203	8	.	.	PUNCT
ejpam-6851	204	1	by	by	ADP
ejpam-6851	204	2	observation	observation	NOUN
ejpam-6851	204	3	4	4	NUM
ejpam-6851	204	4	,	,	PUNCT
ejpam-6851	204	5	s	s	VERB
ejpam-6851	204	6	is	be	AUX
ejpam-6851	204	7	a	a	DET
ejpam-6851	204	8	weak	weak	ADJ
ejpam-6851	204	9	dominating	dominating	NOUN
ejpam-6851	204	10	set	set	NOUN
ejpam-6851	204	11	of	of	ADP
ejpam-6851	204	12	gg	gg	PROPN
ejpam-6851	204	13	.	.	PUNCT
ejpam-6851	205	1	thus	thus	ADV
ejpam-6851	205	2	,	,	PUNCT
ejpam-6851	205	3	γw(gg	γw(gg	PROPN
ejpam-6851	205	4	)	)	PUNCT
ejpam-6851	205	5	≤	≤	NUM
ejpam-6851	205	6	|s|	|s|	PROPN
ejpam-6851	205	7	=	=	SYM
ejpam-6851	205	8	2	2	NUM
ejpam-6851	205	9	+	+	CCONJ
ejpam-6851	205	10	⌈n3	⌈n3	X
ejpam-6851	205	11	⌉.	⌉.	ADV
ejpam-6851	205	12	now	now	ADV
ejpam-6851	205	13	,	,	PUNCT
ejpam-6851	205	14	let	let	VERB
ejpam-6851	205	15	s	s	PRON
ejpam-6851	205	16	⊆	⊆	NUM
ejpam-6851	205	17	v	v	NOUN
ejpam-6851	205	18	(	(	PUNCT
ejpam-6851	205	19	gg	gg	NOUN
ejpam-6851	205	20	)	)	PUNCT
ejpam-6851	205	21	be	be	AUX
ejpam-6851	205	22	a	a	DET
ejpam-6851	205	23	γw	γw	NOUN
ejpam-6851	205	24	-	-	PUNCT
ejpam-6851	205	25	set	set	NOUN
ejpam-6851	205	26	of	of	ADP
ejpam-6851	205	27	gg	gg	PROPN
ejpam-6851	205	28	.	.	PUNCT
ejpam-6851	206	1	because	because	SCONJ
ejpam-6851	206	2	degg(x	degg(x	NOUN
ejpam-6851	206	3	)	)	PUNCT
ejpam-6851	206	4	<	<	X
ejpam-6851	206	5	degg(x	degg(x	NOUN
ejpam-6851	206	6	)	)	PUNCT
ejpam-6851	206	7	for	for	ADP
ejpam-6851	206	8	all	all	PRON
ejpam-6851	206	9	x	x	SYM
ejpam-6851	206	10	∈	∈	PROPN
ejpam-6851	206	11	v	v	NOUN
ejpam-6851	206	12	(	(	PUNCT
ejpam-6851	206	13	g	g	NOUN
ejpam-6851	206	14	)	)	PUNCT
ejpam-6851	206	15	,	,	PUNCT
ejpam-6851	206	16	sg	sg	ADP
ejpam-6851	206	17	∈	∈	PROPN
ejpam-6851	206	18	γw(g	γw(g	PUNCT
ejpam-6851	206	19	)	)	PUNCT
ejpam-6851	206	20	.	.	PUNCT
ejpam-6851	207	1	hence	hence	ADV
ejpam-6851	207	2	,	,	PUNCT
ejpam-6851	207	3	γw(gg	γw(gg	PROPN
ejpam-6851	207	4	)	)	PUNCT
ejpam-6851	207	5	=	=	SYM
ejpam-6851	207	6	|s|	|s|	NOUN
ejpam-6851	207	7	≥	≥	NOUN
ejpam-6851	207	8	|sg|	|sg|	PROPN
ejpam-6851	207	9	+	+	CCONJ
ejpam-6851	207	10	γw(g	γw(g	NUM
ejpam-6851	207	11	)	)	PUNCT
ejpam-6851	207	12	.	.	PUNCT
ejpam-6851	208	1	moreover	moreover	ADV
ejpam-6851	208	2	,	,	PUNCT
ejpam-6851	208	3	since	since	SCONJ
ejpam-6851	208	4	n	n	PROPN
ejpam-6851	208	5	≥	≥	X
ejpam-6851	208	6	7	7	NUM
ejpam-6851	208	7	,	,	PUNCT
ejpam-6851	208	8	|s|	|s|	VERB
ejpam-6851	208	9	≤	≤	ADV
ejpam-6851	208	10	2	2	NUM
ejpam-6851	208	11	+	+	CCONJ
ejpam-6851	208	12	⌈n3	⌈n3	X
ejpam-6851	208	13	⌉	⌉	ADP
ejpam-6851	208	14	≤	≤	NOUN
ejpam-6851	208	15	n	n	CCONJ
ejpam-6851	208	16	−	−	PROPN
ejpam-6851	208	17	2	2	NUM
ejpam-6851	208	18	,	,	PUNCT
ejpam-6851	208	19	and	and	CCONJ
ejpam-6851	208	20	consequently	consequently	ADV
ejpam-6851	208	21	,	,	PUNCT
ejpam-6851	208	22	sg	sg	ADP
ejpam-6851	208	23	̸=	̸=	PROPN
ejpam-6851	208	24	∅.	∅.	ADV
ejpam-6851	208	25	if	if	SCONJ
ejpam-6851	208	26	n	n	PROPN
ejpam-6851	208	27	=	=	SYM
ejpam-6851	208	28	1(mod	1(mod	NUM
ejpam-6851	208	29	3	3	NUM
ejpam-6851	208	30	)	)	PUNCT
ejpam-6851	208	31	,	,	PUNCT
ejpam-6851	208	32	then	then	ADV
ejpam-6851	208	33	|sg|	|sg|	NOUN
ejpam-6851	208	34	≥	≥	NOUN
ejpam-6851	208	35	2	2	NUM
ejpam-6851	208	36	.	.	PUNCT
ejpam-6851	209	1	in	in	ADP
ejpam-6851	209	2	view	view	NOUN
ejpam-6851	209	3	of	of	ADP
ejpam-6851	209	4	observation	observation	NOUN
ejpam-6851	209	5	3	3	NUM
ejpam-6851	209	6	,	,	PUNCT
ejpam-6851	209	7	in	in	ADP
ejpam-6851	209	8	any	any	DET
ejpam-6851	209	9	case	case	NOUN
ejpam-6851	209	10	,	,	PUNCT
ejpam-6851	209	11	γw(gg	γw(gg	PROPN
ejpam-6851	209	12	)	)	PUNCT
ejpam-6851	209	13	=	=	PUNCT
ejpam-6851	209	14	|s|	|s|	PROPN
ejpam-6851	209	15	≥	≥	NOUN
ejpam-6851	209	16	2	2	NUM
ejpam-6851	209	17	+	+	CCONJ
ejpam-6851	209	18	⌈n3	⌈n3	X
ejpam-6851	209	19	⌉.	⌉.	ADV
ejpam-6851	209	20	for	for	ADP
ejpam-6851	209	21	(	(	PUNCT
ejpam-6851	209	22	ii	ii	NOUN
ejpam-6851	209	23	)	)	PUNCT
ejpam-6851	209	24	,	,	PUNCT
ejpam-6851	209	25	the	the	DET
ejpam-6851	209	26	case	case	NOUN
ejpam-6851	209	27	where	where	SCONJ
ejpam-6851	209	28	4	4	NUM
ejpam-6851	209	29	≤	≤	NOUN
ejpam-6851	209	30	n	n	PRON
ejpam-6851	209	31	≤	≤	NUM
ejpam-6851	209	32	5	5	NUM
ejpam-6851	209	33	can	can	AUX
ejpam-6851	209	34	be	be	AUX
ejpam-6851	209	35	readily	readily	ADV
ejpam-6851	209	36	verified	verify	VERB
ejpam-6851	209	37	.	.	PUNCT
ejpam-6851	210	1	similar	similar	ADJ
ejpam-6851	210	2	arguments	argument	NOUN
ejpam-6851	210	3	used	use	VERB
ejpam-6851	210	4	in	in	ADP
ejpam-6851	210	5	the	the	DET
ejpam-6851	210	6	proof	proof	NOUN
ejpam-6851	210	7	of	of	ADP
ejpam-6851	210	8	statement	statement	NOUN
ejpam-6851	210	9	(	(	PUNCT
ejpam-6851	210	10	i	i	NOUN
ejpam-6851	210	11	)	)	PUNCT
ejpam-6851	210	12	will	will	AUX
ejpam-6851	210	13	prove	prove	VERB
ejpam-6851	210	14	the	the	DET
ejpam-6851	210	15	case	case	NOUN
ejpam-6851	210	16	where	where	SCONJ
ejpam-6851	210	17	n	n	NUM
ejpam-6851	210	18	≥	≥	NOUN
ejpam-6851	210	19	6	6	NUM
ejpam-6851	210	20	.	.	NOUN
ejpam-6851	210	21	4	4	NUM
ejpam-6851	210	22	.	.	X
ejpam-6851	211	1	in	in	ADP
ejpam-6851	211	2	the	the	DET
ejpam-6851	211	3	join	join	NOUN
ejpam-6851	211	4	of	of	ADP
ejpam-6851	211	5	graphs	graph	NOUN
ejpam-6851	211	6	remark	remark	VERB
ejpam-6851	211	7	5	5	NUM
ejpam-6851	211	8	.	.	PUNCT
ejpam-6851	212	1	let	let	VERB
ejpam-6851	212	2	g	g	NOUN
ejpam-6851	212	3	and	and	CCONJ
ejpam-6851	212	4	h	h	NOUN
ejpam-6851	212	5	be	be	AUX
ejpam-6851	212	6	connected	connect	VERB
ejpam-6851	212	7	graphs	graph	NOUN
ejpam-6851	212	8	of	of	ADP
ejpam-6851	212	9	orders	order	NOUN
ejpam-6851	212	10	m	m	VERB
ejpam-6851	212	11	and	and	CCONJ
ejpam-6851	212	12	n	n	CCONJ
ejpam-6851	212	13	,	,	PUNCT
ejpam-6851	212	14	respectively	respectively	ADV
ejpam-6851	212	15	.	.	PUNCT
ejpam-6851	213	1	then	then	ADV
ejpam-6851	213	2	(	(	PUNCT
ejpam-6851	213	3	i	i	NOUN
ejpam-6851	213	4	)	)	PUNCT
ejpam-6851	213	5	for	for	ADP
ejpam-6851	213	6	u	u	NOUN
ejpam-6851	213	7	,	,	PUNCT
ejpam-6851	213	8	v	v	PROPN
ejpam-6851	213	9	∈	∈	PROPN
ejpam-6851	213	10	v	v	NOUN
ejpam-6851	213	11	(	(	PUNCT
ejpam-6851	213	12	g	g	NOUN
ejpam-6851	213	13	)	)	PUNCT
ejpam-6851	213	14	,	,	PUNCT
ejpam-6851	213	15	u	u	PRON
ejpam-6851	213	16	≼g+h	≼g+h	VERB
ejpam-6851	213	17	v	v	INTJ
ejpam-6851	213	18	if	if	SCONJ
ejpam-6851	214	1	and	and	CCONJ
ejpam-6851	214	2	only	only	ADV
ejpam-6851	214	3	if	if	SCONJ
ejpam-6851	214	4	u	u	PROPN
ejpam-6851	214	5	≼g	≼g	PROPN
ejpam-6851	214	6	v.	v.	ADP
ejpam-6851	214	7	(	(	PUNCT
ejpam-6851	214	8	ii	ii	NOUN
ejpam-6851	214	9	)	)	PUNCT
ejpam-6851	214	10	for	for	ADP
ejpam-6851	214	11	v	v	NUM
ejpam-6851	214	12	∈	∈	PROPN
ejpam-6851	214	13	v	v	NOUN
ejpam-6851	214	14	(	(	PUNCT
ejpam-6851	214	15	g	g	NOUN
ejpam-6851	214	16	)	)	PUNCT
ejpam-6851	214	17	and	and	CCONJ
ejpam-6851	214	18	u	u	PROPN
ejpam-6851	214	19	∈	∈	PROPN
ejpam-6851	214	20	v	v	ADP
ejpam-6851	214	21	(	(	PUNCT
ejpam-6851	214	22	h	h	NOUN
ejpam-6851	214	23	)	)	PUNCT
ejpam-6851	214	24	,	,	PUNCT
ejpam-6851	214	25	u	u	PRON
ejpam-6851	214	26	≼g+h	≼g+h	VERB
ejpam-6851	214	27	v	v	INTJ
ejpam-6851	214	28	if	if	SCONJ
ejpam-6851	215	1	and	and	CCONJ
ejpam-6851	215	2	only	only	ADV
ejpam-6851	215	3	if	if	SCONJ
ejpam-6851	215	4	degg(v	degg(v	PROPN
ejpam-6851	215	5	)	)	PUNCT
ejpam-6851	215	6	+	+	NUM
ejpam-6851	215	7	n	n	CCONJ
ejpam-6851	215	8	≥	≥	NOUN
ejpam-6851	215	9	degh(u	degh(u	PROPN
ejpam-6851	215	10	)	)	PUNCT
ejpam-6851	215	11	+	+	NOUN
ejpam-6851	215	12	m.	m.	NOUN
ejpam-6851	215	13	theorem	theorem	VERB
ejpam-6851	215	14	1	1	X
ejpam-6851	215	15	.	.	PUNCT
ejpam-6851	216	1	let	let	VERB
ejpam-6851	216	2	g	g	NOUN
ejpam-6851	216	3	,	,	PUNCT
ejpam-6851	216	4	h	h	NOUN
ejpam-6851	216	5	be	be	AUX
ejpam-6851	216	6	connected	connect	VERB
ejpam-6851	216	7	graphs	graph	NOUN
ejpam-6851	216	8	of	of	ADP
ejpam-6851	216	9	orders	order	NOUN
ejpam-6851	216	10	m	m	VERB
ejpam-6851	216	11	and	and	CCONJ
ejpam-6851	216	12	n	n	CCONJ
ejpam-6851	216	13	,	,	PUNCT
ejpam-6851	216	14	respectively	respectively	ADV
ejpam-6851	216	15	.	.	PUNCT
ejpam-6851	217	1	let	let	VERB
ejpam-6851	217	2	s	s	PRON
ejpam-6851	217	3	⊆	⊆	NUM
ejpam-6851	217	4	v	v	NOUN
ejpam-6851	217	5	(	(	PUNCT
ejpam-6851	217	6	g+h	g+h	PROPN
ejpam-6851	217	7	)	)	PUNCT
ejpam-6851	217	8	.	.	PUNCT
ejpam-6851	218	1	then	then	ADV
ejpam-6851	218	2	s	s	VERB
ejpam-6851	218	3	∈	∈	PROPN
ejpam-6851	218	4	γs(g+h	γs(g+h	PROPN
ejpam-6851	218	5	)	)	PUNCT
ejpam-6851	219	1	if	if	SCONJ
ejpam-6851	219	2	and	and	CCONJ
ejpam-6851	219	3	only	only	ADV
ejpam-6851	219	4	if	if	SCONJ
ejpam-6851	219	5	one	one	NUM
ejpam-6851	219	6	of	of	ADP
ejpam-6851	219	7	the	the	DET
ejpam-6851	219	8	following	follow	VERB
ejpam-6851	219	9	holds	hold	VERB
ejpam-6851	219	10	:	:	PUNCT
ejpam-6851	219	11	(	(	PUNCT
ejpam-6851	219	12	i	i	NOUN
ejpam-6851	219	13	)	)	PUNCT
ejpam-6851	219	14	s	s	VERB
ejpam-6851	219	15	⊆	⊆	NUM
ejpam-6851	219	16	v	v	NOUN
ejpam-6851	219	17	(	(	PUNCT
ejpam-6851	219	18	g	g	NOUN
ejpam-6851	219	19	)	)	PUNCT
ejpam-6851	219	20	such	such	ADJ
ejpam-6851	219	21	that	that	DET
ejpam-6851	219	22	s	s	X
ejpam-6851	219	23	∈	∈	NOUN
ejpam-6851	219	24	γs(g	γs(g	PUNCT
ejpam-6851	219	25	)	)	PUNCT
ejpam-6851	219	26	and	and	CCONJ
ejpam-6851	219	27	s	s	VERB
ejpam-6851	219	28	contains	contain	VERB
ejpam-6851	219	29	a	a	DET
ejpam-6851	219	30	vertex	vertex	NOUN
ejpam-6851	219	31	v	v	NOUN
ejpam-6851	219	32	for	for	ADP
ejpam-6851	219	33	which	which	PRON
ejpam-6851	219	34	degg(v	degg(v	PROPN
ejpam-6851	219	35	)	)	PUNCT
ejpam-6851	219	36	≥	≥	NOUN
ejpam-6851	219	37	∆(h	∆(h	NOUN
ejpam-6851	219	38	)	)	PUNCT
ejpam-6851	219	39	+	+	PROPN
ejpam-6851	219	40	m−	m−	PROPN
ejpam-6851	219	41	n.	n.	PROPN
ejpam-6851	219	42	(	(	PUNCT
ejpam-6851	219	43	ii	ii	PROPN
ejpam-6851	219	44	)	)	PUNCT
ejpam-6851	219	45	s	s	PART
ejpam-6851	219	46	⊆	⊆	NUM
ejpam-6851	219	47	v	v	NOUN
ejpam-6851	219	48	(	(	PUNCT
ejpam-6851	219	49	h	h	NOUN
ejpam-6851	219	50	)	)	PUNCT
ejpam-6851	219	51	such	such	ADJ
ejpam-6851	219	52	that	that	PRON
ejpam-6851	219	53	s	s	VERB
ejpam-6851	219	54	∈	∈	NOUN
ejpam-6851	219	55	γs(h	γs(h	NUM
ejpam-6851	219	56	)	)	PUNCT
ejpam-6851	219	57	and	and	CCONJ
ejpam-6851	219	58	s	s	VERB
ejpam-6851	219	59	contains	contain	VERB
ejpam-6851	219	60	a	a	DET
ejpam-6851	219	61	vertex	vertex	NOUN
ejpam-6851	219	62	v	v	NOUN
ejpam-6851	219	63	for	for	ADP
ejpam-6851	219	64	which	which	PRON
ejpam-6851	219	65	degh(v	degh(v	NOUN
ejpam-6851	219	66	)	)	PUNCT
ejpam-6851	219	67	≥	≥	NOUN
ejpam-6851	219	68	∆(g	∆(g	NOUN
ejpam-6851	219	69	)	)	PUNCT
ejpam-6851	219	70	+	+	NUM
ejpam-6851	219	71	n−m	n−m	PROPN
ejpam-6851	219	72	.	.	PUNCT
ejpam-6851	220	1	(	(	PUNCT
ejpam-6851	220	2	iii	iii	X
ejpam-6851	220	3	)	)	PUNCT
ejpam-6851	220	4	sg	sg	ADP
ejpam-6851	220	5	=	=	SYM
ejpam-6851	220	6	s	s	PROPN
ejpam-6851	220	7	∩	∩	ADJ
ejpam-6851	220	8	v	v	X
ejpam-6851	220	9	(	(	PUNCT
ejpam-6851	220	10	g	g	NOUN
ejpam-6851	220	11	)	)	PUNCT
ejpam-6851	220	12	̸=	̸=	PROPN
ejpam-6851	220	13	∅	∅	NOUN
ejpam-6851	220	14	and	and	CCONJ
ejpam-6851	220	15	sh	sh	INTJ
ejpam-6851	220	16	=	=	SYM
ejpam-6851	220	17	s	s	PROPN
ejpam-6851	220	18	∩	∩	ADJ
ejpam-6851	220	19	v	v	ADJ
ejpam-6851	220	20	(	(	PUNCT
ejpam-6851	220	21	h	h	NOUN
ejpam-6851	220	22	)	)	PUNCT
ejpam-6851	220	23	̸=	̸=	PROPN
ejpam-6851	220	24	∅	∅	NOUN
ejpam-6851	220	25	and	and	CCONJ
ejpam-6851	220	26	one	one	NUM
ejpam-6851	220	27	of	of	ADP
ejpam-6851	220	28	the	the	DET
ejpam-6851	220	29	following	following	NOUN
ejpam-6851	220	30	holds	hold	VERB
ejpam-6851	220	31	for	for	ADP
ejpam-6851	220	32	each	each	DET
ejpam-6851	220	33	u	u	PROPN
ejpam-6851	220	34	∈	∈	PROPN
ejpam-6851	220	35	v	v	NOUN
ejpam-6851	220	36	(	(	PUNCT
ejpam-6851	220	37	g+h	g+h	NOUN
ejpam-6851	220	38	)	)	PUNCT
ejpam-6851	220	39	\	\	PUNCT
ejpam-6851	221	1	s	s	PART
ejpam-6851	221	2	:	:	PUNCT
ejpam-6851	221	3	(	(	PUNCT
ejpam-6851	221	4	a	a	X
ejpam-6851	221	5	)	)	PUNCT
ejpam-6851	221	6	u	u	NOUN
ejpam-6851	221	7	∈	∈	PROPN
ejpam-6851	221	8	v	v	NOUN
ejpam-6851	221	9	(	(	PUNCT
ejpam-6851	221	10	g	g	NOUN
ejpam-6851	221	11	)	)	PUNCT
ejpam-6851	221	12	and	and	CCONJ
ejpam-6851	221	13	u	u	PROPN
ejpam-6851	221	14	≼g	≼g	PROPN
ejpam-6851	221	15	sg	sg	NOUN
ejpam-6851	221	16	or	or	CCONJ
ejpam-6851	221	17	there	there	PRON
ejpam-6851	221	18	exists	exist	VERB
ejpam-6851	221	19	v	v	ADP
ejpam-6851	221	20	∈	∈	NOUN
ejpam-6851	221	21	sh	sh	INTJ
ejpam-6851	221	22	for	for	ADP
ejpam-6851	221	23	which	which	PRON
ejpam-6851	221	24	degh(v	degh(v	NOUN
ejpam-6851	221	25	)	)	PUNCT
ejpam-6851	221	26	≥	≥	NOUN
ejpam-6851	221	27	degg(u	degg(u	PROPN
ejpam-6851	221	28	)	)	PUNCT
ejpam-6851	222	1	+	+	CCONJ
ejpam-6851	222	2	n−m	n−m	PROPN
ejpam-6851	222	3	;	;	PUNCT
ejpam-6851	222	4	j.	j.	PROPN
ejpam-6851	222	5	m.	m.	PROPN
ejpam-6851	222	6	molles	molles	PROPN
ejpam-6851	222	7	,	,	PUNCT
ejpam-6851	222	8	f.	f.	PROPN
ejpam-6851	222	9	p.	p.	PROPN
ejpam-6851	222	10	jamil	jamil	PROPN
ejpam-6851	222	11	,	,	PUNCT
ejpam-6851	222	12	s.	s.	PROPN
ejpam-6851	222	13	r.	r.	PROPN
ejpam-6851	222	14	canoy	canoy	PROPN
ejpam-6851	222	15	/	/	SYM
ejpam-6851	222	16	eur	eur	PROPN
ejpam-6851	222	17	.	.	PUNCT
ejpam-6851	223	1	j.	j.	PROPN
ejpam-6851	223	2	pure	pure	PROPN
ejpam-6851	223	3	appl	appl	PROPN
ejpam-6851	223	4	.	.	PROPN
ejpam-6851	223	5	math	math	PROPN
ejpam-6851	223	6	,	,	PUNCT
ejpam-6851	223	7	18	18	NUM
ejpam-6851	223	8	(	(	PUNCT
ejpam-6851	223	9	4	4	NUM
ejpam-6851	223	10	)	)	PUNCT
ejpam-6851	223	11	(	(	PUNCT
ejpam-6851	223	12	2025	2025	NUM
ejpam-6851	223	13	)	)	PUNCT
ejpam-6851	223	14	,	,	PUNCT
ejpam-6851	223	15	6851	6851	NUM
ejpam-6851	223	16	7	7	NUM
ejpam-6851	223	17	of	of	ADP
ejpam-6851	223	18	18	18	NUM
ejpam-6851	223	19	(	(	PUNCT
ejpam-6851	223	20	b	b	NOUN
ejpam-6851	223	21	)	)	PUNCT
ejpam-6851	223	22	u	u	NOUN
ejpam-6851	223	23	∈	∈	PROPN
ejpam-6851	223	24	v	v	ADP
ejpam-6851	223	25	(	(	PUNCT
ejpam-6851	223	26	h	h	NOUN
ejpam-6851	223	27	)	)	PUNCT
ejpam-6851	223	28	and	and	CCONJ
ejpam-6851	223	29	u	u	X
ejpam-6851	224	1	≼h	≼h	PROPN
ejpam-6851	224	2	sh	sh	INTJ
ejpam-6851	224	3	or	or	CCONJ
ejpam-6851	224	4	there	there	PRON
ejpam-6851	224	5	exists	exist	VERB
ejpam-6851	224	6	v	v	ADP
ejpam-6851	224	7	∈	∈	PROPN
ejpam-6851	224	8	sg	sg	NOUN
ejpam-6851	224	9	for	for	ADP
ejpam-6851	224	10	which	which	PRON
ejpam-6851	224	11	degg(v	degg(v	PROPN
ejpam-6851	224	12	)	)	PUNCT
ejpam-6851	224	13	≥	≥	NOUN
ejpam-6851	224	14	degh(u)+	degh(u)+	NOUN
ejpam-6851	224	15	m−	m−	PROPN
ejpam-6851	224	16	n.	n.	PROPN
ejpam-6851	224	17	proof	proof	NOUN
ejpam-6851	224	18	.	.	PUNCT
ejpam-6851	225	1	assume	assume	VERB
ejpam-6851	225	2	that	that	SCONJ
ejpam-6851	225	3	s	s	VERB
ejpam-6851	225	4	∈	∈	NOUN
ejpam-6851	225	5	γs(g	γs(g	PUNCT
ejpam-6851	225	6	+	+	NOUN
ejpam-6851	225	7	h	h	NOUN
ejpam-6851	225	8	)	)	PUNCT
ejpam-6851	225	9	.	.	PUNCT
ejpam-6851	226	1	suppose	suppose	VERB
ejpam-6851	226	2	that	that	SCONJ
ejpam-6851	226	3	s	s	VERB
ejpam-6851	226	4	⊆	⊆	NUM
ejpam-6851	226	5	v	v	NOUN
ejpam-6851	226	6	(	(	PUNCT
ejpam-6851	226	7	g	g	NOUN
ejpam-6851	226	8	)	)	PUNCT
ejpam-6851	226	9	.	.	PUNCT
ejpam-6851	227	1	by	by	ADP
ejpam-6851	227	2	observation	observation	NOUN
ejpam-6851	227	3	5(i	5(i	NUM
ejpam-6851	227	4	)	)	PUNCT
ejpam-6851	227	5	,	,	PUNCT
ejpam-6851	227	6	s	s	PROPN
ejpam-6851	227	7	∈	∈	NOUN
ejpam-6851	227	8	γs(g	γs(g	PUNCT
ejpam-6851	227	9	)	)	PUNCT
ejpam-6851	227	10	.	.	PUNCT
ejpam-6851	228	1	pick	pick	VERB
ejpam-6851	228	2	u	u	PRON
ejpam-6851	228	3	∈	∈	PROPN
ejpam-6851	228	4	v	v	ADP
ejpam-6851	228	5	(	(	PUNCT
ejpam-6851	228	6	h	h	NOUN
ejpam-6851	228	7	)	)	PUNCT
ejpam-6851	228	8	for	for	ADP
ejpam-6851	228	9	which	which	PRON
ejpam-6851	228	10	degh(u	degh(u	NOUN
ejpam-6851	228	11	)	)	PUNCT
ejpam-6851	228	12	=	=	SYM
ejpam-6851	228	13	∆(h	∆(h	NOUN
ejpam-6851	228	14	)	)	PUNCT
ejpam-6851	228	15	.	.	PUNCT
ejpam-6851	229	1	since	since	SCONJ
ejpam-6851	229	2	s	s	PROPN
ejpam-6851	229	3	∈	∈	PROPN
ejpam-6851	229	4	γs(g	γs(g	PUNCT
ejpam-6851	229	5	+	+	SYM
ejpam-6851	229	6	h	h	X
ejpam-6851	229	7	)	)	PUNCT
ejpam-6851	229	8	there	there	PRON
ejpam-6851	229	9	exists	exist	VERB
ejpam-6851	229	10	v	v	ADP
ejpam-6851	229	11	∈	∈	PROPN
ejpam-6851	229	12	s	s	NOUN
ejpam-6851	229	13	for	for	ADP
ejpam-6851	229	14	which	which	PRON
ejpam-6851	229	15	u	u	PRON
ejpam-6851	229	16	≼g+h	≼g+h	NOUN
ejpam-6851	229	17	v.	v.	INTJ
ejpam-6851	229	18	by	by	ADP
ejpam-6851	229	19	observation	observation	NOUN
ejpam-6851	229	20	5(ii	5(ii	NUM
ejpam-6851	229	21	)	)	PUNCT
ejpam-6851	229	22	,	,	PUNCT
ejpam-6851	229	23	degg(v	degg(v	PROPN
ejpam-6851	229	24	)	)	PUNCT
ejpam-6851	229	25	+	+	NUM
ejpam-6851	229	26	n	n	CCONJ
ejpam-6851	229	27	≥	≥	NOUN
ejpam-6851	229	28	∆(h	∆(h	NOUN
ejpam-6851	229	29	)	)	PUNCT
ejpam-6851	229	30	+	+	NOUN
ejpam-6851	229	31	m	m	VERB
ejpam-6851	229	32	or	or	CCONJ
ejpam-6851	229	33	,	,	PUNCT
ejpam-6851	229	34	equivalently	equivalently	ADV
ejpam-6851	229	35	,	,	PUNCT
ejpam-6851	229	36	degg(v	degg(v	PROPN
ejpam-6851	229	37	)	)	PUNCT
ejpam-6851	229	38	≥	≥	NOUN
ejpam-6851	229	39	∆(h	∆(h	NOUN
ejpam-6851	229	40	)	)	PUNCT
ejpam-6851	229	41	+	+	NUM
ejpam-6851	229	42	m	m	VERB
ejpam-6851	229	43	−	−	PROPN
ejpam-6851	229	44	n.	n.	NOUN
ejpam-6851	229	45	similarly	similarly	ADV
ejpam-6851	229	46	,	,	PUNCT
ejpam-6851	229	47	if	if	SCONJ
ejpam-6851	229	48	s	s	VERB
ejpam-6851	229	49	⊆	⊆	NUM
ejpam-6851	229	50	v	v	NOUN
ejpam-6851	229	51	(	(	PUNCT
ejpam-6851	229	52	h	h	NOUN
ejpam-6851	229	53	)	)	PUNCT
ejpam-6851	229	54	,	,	PUNCT
ejpam-6851	229	55	then	then	ADV
ejpam-6851	229	56	(	(	PUNCT
ejpam-6851	229	57	ii	ii	NOUN
ejpam-6851	229	58	)	)	PUNCT
ejpam-6851	229	59	holds	hold	VERB
ejpam-6851	229	60	.	.	PUNCT
ejpam-6851	230	1	next	next	ADV
ejpam-6851	230	2	,	,	PUNCT
ejpam-6851	230	3	suppose	suppose	VERB
ejpam-6851	230	4	that	that	SCONJ
ejpam-6851	230	5	s	s	VERB
ejpam-6851	230	6	intersects	intersect	NOUN
ejpam-6851	230	7	both	both	PRON
ejpam-6851	230	8	v	v	NOUN
ejpam-6851	230	9	(	(	PUNCT
ejpam-6851	230	10	g	g	NOUN
ejpam-6851	230	11	)	)	PUNCT
ejpam-6851	230	12	and	and	CCONJ
ejpam-6851	230	13	v	v	NOUN
ejpam-6851	230	14	(	(	PUNCT
ejpam-6851	230	15	h	h	NOUN
ejpam-6851	230	16	)	)	PUNCT
ejpam-6851	230	17	.	.	PUNCT
ejpam-6851	231	1	let	let	VERB
ejpam-6851	231	2	u	u	PRON
ejpam-6851	231	3	∈	∈	PROPN
ejpam-6851	231	4	v	v	X
ejpam-6851	231	5	(	(	PUNCT
ejpam-6851	231	6	g+h	g+h	NOUN
ejpam-6851	231	7	)	)	PUNCT
ejpam-6851	231	8	\s	\s	NOUN
ejpam-6851	231	9	,	,	PUNCT
ejpam-6851	231	10	and	and	CCONJ
ejpam-6851	231	11	suppose	suppose	VERB
ejpam-6851	231	12	that	that	SCONJ
ejpam-6851	231	13	u	u	PROPN
ejpam-6851	231	14	∈	∈	PROPN
ejpam-6851	231	15	v	v	ADP
ejpam-6851	231	16	(	(	PUNCT
ejpam-6851	231	17	g	g	NOUN
ejpam-6851	231	18	)	)	PUNCT
ejpam-6851	231	19	.	.	PUNCT
ejpam-6851	232	1	then	then	ADV
ejpam-6851	232	2	there	there	PRON
ejpam-6851	232	3	exists	exist	VERB
ejpam-6851	232	4	v	v	ADP
ejpam-6851	232	5	∈	∈	PROPN
ejpam-6851	232	6	s	s	NOUN
ejpam-6851	232	7	for	for	ADP
ejpam-6851	232	8	which	which	PRON
ejpam-6851	232	9	u	u	PRON
ejpam-6851	232	10	≼g+h	≼g+h	NOUN
ejpam-6851	232	11	v.	v.	INTJ
ejpam-6851	232	12	if	if	SCONJ
ejpam-6851	232	13	v	v	NUM
ejpam-6851	232	14	∈	∈	PROPN
ejpam-6851	232	15	v	v	NOUN
ejpam-6851	232	16	(	(	PUNCT
ejpam-6851	232	17	g	g	NOUN
ejpam-6851	232	18	)	)	PUNCT
ejpam-6851	232	19	,	,	PUNCT
ejpam-6851	232	20	then	then	ADV
ejpam-6851	232	21	u	u	PROPN
ejpam-6851	232	22	≼g	≼g	PROPN
ejpam-6851	232	23	v.	v.	ADP
ejpam-6851	232	24	this	this	PRON
ejpam-6851	232	25	means	mean	VERB
ejpam-6851	232	26	that	that	SCONJ
ejpam-6851	232	27	u	u	PROPN
ejpam-6851	232	28	≼g	≼g	PROPN
ejpam-6851	232	29	sg	sg	NOUN
ejpam-6851	232	30	.	.	PUNCT
ejpam-6851	233	1	if	if	SCONJ
ejpam-6851	233	2	v	v	NUM
ejpam-6851	233	3	∈	∈	PROPN
ejpam-6851	233	4	v	v	NOUN
ejpam-6851	233	5	(	(	PUNCT
ejpam-6851	233	6	h	h	NOUN
ejpam-6851	233	7	)	)	PUNCT
ejpam-6851	233	8	,	,	PUNCT
ejpam-6851	233	9	then	then	ADV
ejpam-6851	233	10	by	by	ADP
ejpam-6851	233	11	observation	observation	NOUN
ejpam-6851	233	12	5(ii	5(ii	NUM
ejpam-6851	233	13	)	)	PUNCT
ejpam-6851	233	14	,	,	PUNCT
ejpam-6851	233	15	degh(v	degh(v	PROPN
ejpam-6851	233	16	)	)	PUNCT
ejpam-6851	233	17	≥	≥	NOUN
ejpam-6851	233	18	degg(u)+n−m	degg(u)+n−m	PROPN
ejpam-6851	233	19	,	,	PUNCT
ejpam-6851	233	20	and	and	CCONJ
ejpam-6851	233	21	(	(	PUNCT
ejpam-6851	233	22	a	a	X
ejpam-6851	233	23	)	)	PUNCT
ejpam-6851	233	24	holds	hold	NOUN
ejpam-6851	233	25	.	.	PUNCT
ejpam-6851	234	1	similarly	similarly	ADV
ejpam-6851	234	2	,	,	PUNCT
ejpam-6851	234	3	if	if	SCONJ
ejpam-6851	234	4	u	u	PROPN
ejpam-6851	234	5	∈	∈	PROPN
ejpam-6851	234	6	v	v	ADP
ejpam-6851	234	7	(	(	PUNCT
ejpam-6851	234	8	h	h	NOUN
ejpam-6851	234	9	)	)	PUNCT
ejpam-6851	234	10	,	,	PUNCT
ejpam-6851	234	11	then	then	ADV
ejpam-6851	234	12	(	(	PUNCT
ejpam-6851	234	13	b	b	X
ejpam-6851	234	14	)	)	PUNCT
ejpam-6851	234	15	holds	hold	VERB
ejpam-6851	234	16	.	.	PUNCT
ejpam-6851	235	1	conversely	conversely	ADV
ejpam-6851	235	2	,	,	PUNCT
ejpam-6851	235	3	suppose	suppose	VERB
ejpam-6851	235	4	that	that	SCONJ
ejpam-6851	235	5	(	(	PUNCT
ejpam-6851	235	6	i	i	NOUN
ejpam-6851	235	7	)	)	PUNCT
ejpam-6851	235	8	holds	hold	VERB
ejpam-6851	235	9	for	for	ADP
ejpam-6851	235	10	s.	s.	PROPN
ejpam-6851	235	11	let	let	VERB
ejpam-6851	235	12	u	u	PRON
ejpam-6851	235	13	∈	∈	PROPN
ejpam-6851	235	14	v	v	NOUN
ejpam-6851	235	15	(	(	PUNCT
ejpam-6851	235	16	g	g	PROPN
ejpam-6851	235	17	+	+	NOUN
ejpam-6851	235	18	h	h	NOUN
ejpam-6851	235	19	)	)	PUNCT
ejpam-6851	235	20	\	\	PUNCT
ejpam-6851	236	1	s.	s.	PROPN
ejpam-6851	236	2	if	if	SCONJ
ejpam-6851	236	3	u	u	PROPN
ejpam-6851	236	4	∈	∈	PROPN
ejpam-6851	236	5	v	v	X
ejpam-6851	236	6	(	(	PUNCT
ejpam-6851	236	7	g	g	NOUN
ejpam-6851	236	8	)	)	PUNCT
ejpam-6851	236	9	,	,	PUNCT
ejpam-6851	236	10	then	then	ADV
ejpam-6851	236	11	u	u	PROPN
ejpam-6851	236	12	≼g	≼g	PROPN
ejpam-6851	236	13	s	s	PART
ejpam-6851	236	14	,	,	PUNCT
ejpam-6851	236	15	and	and	CCONJ
ejpam-6851	236	16	hence	hence	ADV
ejpam-6851	236	17	u	u	NOUN
ejpam-6851	236	18	≼g+h	≼g+h	NOUN
ejpam-6851	236	19	s.	s.	PROPN
ejpam-6851	236	20	suppose	suppose	VERB
ejpam-6851	236	21	that	that	SCONJ
ejpam-6851	236	22	u	u	PROPN
ejpam-6851	236	23	∈	∈	PROPN
ejpam-6851	236	24	v	v	ADP
ejpam-6851	236	25	(	(	PUNCT
ejpam-6851	236	26	h	h	NOUN
ejpam-6851	236	27	)	)	PUNCT
ejpam-6851	236	28	.	.	PUNCT
ejpam-6851	237	1	there	there	PRON
ejpam-6851	237	2	exists	exist	VERB
ejpam-6851	237	3	v	v	ADP
ejpam-6851	237	4	∈	∈	PROPN
ejpam-6851	237	5	s	s	NOUN
ejpam-6851	237	6	for	for	ADP
ejpam-6851	237	7	which	which	PRON
ejpam-6851	237	8	degg(v	degg(v	PROPN
ejpam-6851	237	9	)	)	PUNCT
ejpam-6851	237	10	≥	≥	NOUN
ejpam-6851	237	11	∆(h	∆(h	NOUN
ejpam-6851	237	12	)	)	PUNCT
ejpam-6851	237	13	+	+	NOUN
ejpam-6851	237	14	m−	m−	PROPN
ejpam-6851	237	15	n.	n.	PROPN
ejpam-6851	237	16	this	this	PRON
ejpam-6851	237	17	means	mean	VERB
ejpam-6851	237	18	degg+h(u	degg+h(u	NOUN
ejpam-6851	237	19	)	)	PUNCT
ejpam-6851	238	1	=	=	SYM
ejpam-6851	238	2	degh(u	degh(u	PROPN
ejpam-6851	238	3	)	)	PUNCT
ejpam-6851	239	1	+	+	ADP
ejpam-6851	239	2	m	m	VERB
ejpam-6851	239	3	≤	≤	ADJ
ejpam-6851	239	4	∆(h	∆(h	NOUN
ejpam-6851	239	5	)	)	PUNCT
ejpam-6851	239	6	+	+	ADP
ejpam-6851	239	7	m	m	VERB
ejpam-6851	239	8	≤	≤	NUM
ejpam-6851	239	9	degg(v	degg(v	PROPN
ejpam-6851	239	10	)	)	PUNCT
ejpam-6851	239	11	+	+	NUM
ejpam-6851	239	12	n	n	PROPN
ejpam-6851	239	13	=	=	SYM
ejpam-6851	239	14	degg+h(v	degg+h(v	NOUN
ejpam-6851	239	15	)	)	PUNCT
ejpam-6851	239	16	.	.	PUNCT
ejpam-6851	240	1	thus	thus	ADV
ejpam-6851	240	2	,	,	PUNCT
ejpam-6851	240	3	u	u	PRON
ejpam-6851	240	4	≼g+h	≼g+h	NOUN
ejpam-6851	240	5	v	v	NOUN
ejpam-6851	240	6	,	,	PUNCT
ejpam-6851	240	7	and	and	CCONJ
ejpam-6851	240	8	consequently	consequently	ADV
ejpam-6851	240	9	,	,	PUNCT
ejpam-6851	240	10	u	u	PROPN
ejpam-6851	240	11	≼g+h	≼g+h	NOUN
ejpam-6851	240	12	s.	s.	PROPN
ejpam-6851	240	13	accordingly	accordingly	ADV
ejpam-6851	240	14	,	,	PUNCT
ejpam-6851	240	15	s	s	PROPN
ejpam-6851	240	16	∈	∈	PROPN
ejpam-6851	240	17	γs(g+h	γs(g+h	PROPN
ejpam-6851	240	18	)	)	PUNCT
ejpam-6851	240	19	.	.	PUNCT
ejpam-6851	241	1	similarly	similarly	ADV
ejpam-6851	241	2	,	,	PUNCT
ejpam-6851	241	3	if	if	SCONJ
ejpam-6851	241	4	(	(	PUNCT
ejpam-6851	241	5	ii	ii	NOUN
ejpam-6851	241	6	)	)	PUNCT
ejpam-6851	241	7	holds	hold	VERB
ejpam-6851	241	8	,	,	PUNCT
ejpam-6851	241	9	then	then	ADV
ejpam-6851	241	10	s	s	VERB
ejpam-6851	241	11	∈	∈	PROPN
ejpam-6851	241	12	γs(g+h	γs(g+h	PROPN
ejpam-6851	241	13	)	)	PUNCT
ejpam-6851	241	14	.	.	PUNCT
ejpam-6851	242	1	finally	finally	ADV
ejpam-6851	242	2	,	,	PUNCT
ejpam-6851	242	3	suppose	suppose	VERB
ejpam-6851	242	4	that	that	SCONJ
ejpam-6851	242	5	(	(	PUNCT
ejpam-6851	242	6	iii	iii	NOUN
ejpam-6851	242	7	)	)	PUNCT
ejpam-6851	242	8	holds	hold	VERB
ejpam-6851	242	9	for	for	ADP
ejpam-6851	242	10	s.	s.	PROPN
ejpam-6851	242	11	let	let	VERB
ejpam-6851	242	12	u	u	PRON
ejpam-6851	242	13	∈	∈	PROPN
ejpam-6851	242	14	v	v	ADP
ejpam-6851	242	15	(	(	PUNCT
ejpam-6851	242	16	g	g	NOUN
ejpam-6851	242	17	)	)	PUNCT
ejpam-6851	242	18	\s	\s	NOUN
ejpam-6851	242	19	.	.	PUNCT
ejpam-6851	243	1	if	if	SCONJ
ejpam-6851	243	2	u	u	PROPN
ejpam-6851	243	3	≼g	≼g	PROPN
ejpam-6851	243	4	sg	sg	PROPN
ejpam-6851	243	5	,	,	PUNCT
ejpam-6851	243	6	then	then	ADV
ejpam-6851	243	7	u	u	NOUN
ejpam-6851	243	8	≼g+h	≼g+h	NOUN
ejpam-6851	243	9	s.	s.	PROPN
ejpam-6851	243	10	suppose	suppose	VERB
ejpam-6851	243	11	that	that	SCONJ
ejpam-6851	243	12	sg	sg	PROPN
ejpam-6851	243	13	does	do	AUX
ejpam-6851	243	14	not	not	PART
ejpam-6851	243	15	strongly	strongly	ADV
ejpam-6851	243	16	dominate	dominate	VERB
ejpam-6851	243	17	u.	u.	NOUN
ejpam-6851	243	18	by	by	ADP
ejpam-6851	243	19	condition	condition	NOUN
ejpam-6851	243	20	(	(	PUNCT
ejpam-6851	243	21	a	a	X
ejpam-6851	243	22	)	)	PUNCT
ejpam-6851	243	23	,	,	PUNCT
ejpam-6851	243	24	there	there	PRON
ejpam-6851	243	25	exists	exist	VERB
ejpam-6851	243	26	v	v	ADP
ejpam-6851	243	27	∈	∈	NOUN
ejpam-6851	243	28	sh	sh	INTJ
ejpam-6851	243	29	for	for	ADP
ejpam-6851	243	30	which	which	PRON
ejpam-6851	243	31	degh(v)+m	degh(v)+m	PROPN
ejpam-6851	243	32	≥	≥	PRON
ejpam-6851	243	33	degg(u)+n	degg(u)+n	NOUN
ejpam-6851	243	34	.	.	PUNCT
ejpam-6851	244	1	this	this	PRON
ejpam-6851	244	2	means	mean	VERB
ejpam-6851	244	3	that	that	SCONJ
ejpam-6851	244	4	degg+h(v	degg+h(v	PROPN
ejpam-6851	244	5	)	)	PUNCT
ejpam-6851	244	6	≥	≥	NOUN
ejpam-6851	244	7	degg+h(u	degg+h(u	NOUN
ejpam-6851	244	8	)	)	PUNCT
ejpam-6851	244	9	and	and	CCONJ
ejpam-6851	244	10	u	u	NOUN
ejpam-6851	244	11	≼g+h	≼g+h	NOUN
ejpam-6851	244	12	v.	v.	CCONJ
ejpam-6851	244	13	thus	thus	ADV
ejpam-6851	244	14	,	,	PUNCT
ejpam-6851	244	15	u	u	PRON
ejpam-6851	244	16	≼g+h	≼g+h	NOUN
ejpam-6851	244	17	s.	s.	PROPN
ejpam-6851	244	18	similarly	similarly	ADV
ejpam-6851	244	19	,	,	PUNCT
ejpam-6851	244	20	if	if	SCONJ
ejpam-6851	244	21	u	u	PROPN
ejpam-6851	244	22	∈	∈	PROPN
ejpam-6851	244	23	v	v	ADP
ejpam-6851	244	24	(	(	PUNCT
ejpam-6851	244	25	h	h	NOUN
ejpam-6851	244	26	)	)	PUNCT
ejpam-6851	244	27	\	\	PROPN
ejpam-6851	244	28	s	s	PART
ejpam-6851	244	29	and	and	CCONJ
ejpam-6851	244	30	sh	sh	PROPN
ejpam-6851	244	31	does	do	AUX
ejpam-6851	244	32	not	not	PART
ejpam-6851	244	33	strongly	strongly	ADV
ejpam-6851	244	34	dominate	dominate	VERB
ejpam-6851	244	35	u	u	NOUN
ejpam-6851	244	36	,	,	PUNCT
ejpam-6851	244	37	then	then	ADV
ejpam-6851	244	38	there	there	PRON
ejpam-6851	244	39	exists	exist	VERB
ejpam-6851	244	40	v	v	ADP
ejpam-6851	244	41	∈	∈	PROPN
ejpam-6851	244	42	sg	sg	NOUN
ejpam-6851	244	43	for	for	ADP
ejpam-6851	244	44	which	which	PRON
ejpam-6851	244	45	u	u	PRON
ejpam-6851	244	46	≼g+h	≼g+h	NOUN
ejpam-6851	244	47	v	v	ADP
ejpam-6851	244	48	,	,	PUNCT
ejpam-6851	244	49	and	and	CCONJ
ejpam-6851	244	50	therefore	therefore	ADV
ejpam-6851	244	51	u	u	PRON
ejpam-6851	244	52	≼g+h	≼g+h	NOUN
ejpam-6851	244	53	s.	s.	PROPN
ejpam-6851	244	54	therefore	therefore	ADV
ejpam-6851	244	55	,	,	PUNCT
ejpam-6851	244	56	s	s	PROPN
ejpam-6851	244	57	∈	∈	PROPN
ejpam-6851	244	58	γs(g+h	γs(g+h	PROPN
ejpam-6851	244	59	)	)	PUNCT
ejpam-6851	244	60	.	.	PUNCT
ejpam-6851	245	1	corollary	corollary	ADJ
ejpam-6851	245	2	1	1	NUM
ejpam-6851	245	3	.	.	PUNCT
ejpam-6851	246	1	let	let	VERB
ejpam-6851	246	2	g	g	NOUN
ejpam-6851	246	3	and	and	CCONJ
ejpam-6851	246	4	h	h	NOUN
ejpam-6851	246	5	be	be	AUX
ejpam-6851	246	6	connected	connect	VERB
ejpam-6851	246	7	graphs	graph	NOUN
ejpam-6851	246	8	of	of	ADP
ejpam-6851	246	9	orders	order	NOUN
ejpam-6851	246	10	m	m	VERB
ejpam-6851	246	11	and	and	CCONJ
ejpam-6851	246	12	n	n	CCONJ
ejpam-6851	246	13	,	,	PUNCT
ejpam-6851	246	14	respectively	respectively	ADV
ejpam-6851	246	15	.	.	PUNCT
ejpam-6851	247	1	(	(	PUNCT
ejpam-6851	247	2	i	i	NOUN
ejpam-6851	247	3	)	)	PUNCT
ejpam-6851	247	4	γs(g+h	γs(g+h	PROPN
ejpam-6851	247	5	)	)	PUNCT
ejpam-6851	247	6	=	=	SYM
ejpam-6851	247	7	1	1	NUM
ejpam-6851	247	8	if	if	SCONJ
ejpam-6851	247	9	and	and	CCONJ
ejpam-6851	247	10	only	only	ADV
ejpam-6851	247	11	if	if	SCONJ
ejpam-6851	247	12	γ(g	γ(g	PROPN
ejpam-6851	247	13	)	)	PUNCT
ejpam-6851	247	14	=	=	SYM
ejpam-6851	247	15	1	1	NUM
ejpam-6851	247	16	or	or	CCONJ
ejpam-6851	247	17	γ(h	γ(h	NOUN
ejpam-6851	247	18	)	)	PUNCT
ejpam-6851	247	19	=	=	SYM
ejpam-6851	248	1	1	1	X
ejpam-6851	248	2	.	.	PUNCT
ejpam-6851	248	3	(	(	PUNCT
ejpam-6851	248	4	ii	ii	NOUN
ejpam-6851	248	5	)	)	PUNCT
ejpam-6851	248	6	assume	assume	VERB
ejpam-6851	248	7	γ(g	γ(g	PROPN
ejpam-6851	248	8	)	)	PUNCT
ejpam-6851	248	9	≥	≥	NOUN
ejpam-6851	248	10	2	2	NUM
ejpam-6851	248	11	and	and	CCONJ
ejpam-6851	248	12	γ(h	γ(h	NOUN
ejpam-6851	248	13	)	)	PUNCT
ejpam-6851	248	14	≥	≥	NOUN
ejpam-6851	248	15	2	2	NUM
ejpam-6851	248	16	.	.	PUNCT
ejpam-6851	249	1	(	(	PUNCT
ejpam-6851	249	2	a	a	X
ejpam-6851	249	3	)	)	PUNCT
ejpam-6851	249	4	if	if	SCONJ
ejpam-6851	249	5	∆(g	∆(g	NOUN
ejpam-6851	249	6	)	)	PUNCT
ejpam-6851	249	7	+	+	NUM
ejpam-6851	249	8	n	n	NOUN
ejpam-6851	249	9	=	=	SYM
ejpam-6851	249	10	∆(h	∆(h	NOUN
ejpam-6851	249	11	)	)	PUNCT
ejpam-6851	249	12	+	+	NOUN
ejpam-6851	249	13	m	m	NOUN
ejpam-6851	249	14	,	,	PUNCT
ejpam-6851	249	15	then	then	ADV
ejpam-6851	249	16	γs(g+h	γs(g+h	PROPN
ejpam-6851	249	17	)	)	PUNCT
ejpam-6851	249	18	=	=	SYM
ejpam-6851	250	1	2	2	X
ejpam-6851	250	2	.	.	PUNCT
ejpam-6851	250	3	(	(	PUNCT
ejpam-6851	250	4	b	b	X
ejpam-6851	250	5	)	)	PUNCT
ejpam-6851	250	6	if	if	SCONJ
ejpam-6851	250	7	∆(g	∆(g	NOUN
ejpam-6851	250	8	)	)	PUNCT
ejpam-6851	250	9	+	+	NUM
ejpam-6851	250	10	n	n	CCONJ
ejpam-6851	250	11	>	>	X
ejpam-6851	250	12	∆(h	∆(h	NOUN
ejpam-6851	250	13	)	)	PUNCT
ejpam-6851	251	1	+	+	NOUN
ejpam-6851	251	2	m	m	NOUN
ejpam-6851	251	3	,	,	PUNCT
ejpam-6851	251	4	then	then	ADV
ejpam-6851	251	5	γs(g+h	γs(g+h	PROPN
ejpam-6851	251	6	)	)	PUNCT
ejpam-6851	251	7	=	=	SYM
ejpam-6851	251	8	min{γs(g	min{γs(g	PROPN
ejpam-6851	251	9	)	)	PUNCT
ejpam-6851	251	10	,	,	PUNCT
ejpam-6851	251	11	1	1	NUM
ejpam-6851	251	12	+	+	ADJ
ejpam-6851	251	13	γs(k	γs(k	NOUN
ejpam-6851	251	14	)	)	PUNCT
ejpam-6851	251	15	}	}	PUNCT
ejpam-6851	251	16	,	,	PUNCT
ejpam-6851	252	1	where	where	SCONJ
ejpam-6851	252	2	k	k	PROPN
ejpam-6851	252	3	=	=	PUNCT
ejpam-6851	252	4	⟨v	⟨v	PROPN
ejpam-6851	252	5	(	(	PUNCT
ejpam-6851	252	6	g	g	NOUN
ejpam-6851	252	7	)	)	PUNCT
ejpam-6851	252	8	\ng+h	\ng+h	NOUN
ejpam-6851	252	9	[	[	X
ejpam-6851	252	10	u	u	X
ejpam-6851	252	11	≽]⟩	≽]⟩	NOUN
ejpam-6851	252	12	and	and	CCONJ
ejpam-6851	252	13	u	u	PROPN
ejpam-6851	252	14	∈	∈	PROPN
ejpam-6851	252	15	v	v	ADP
ejpam-6851	252	16	(	(	PUNCT
ejpam-6851	252	17	h	h	NOUN
ejpam-6851	252	18	)	)	PUNCT
ejpam-6851	252	19	for	for	ADP
ejpam-6851	252	20	which	which	PRON
ejpam-6851	252	21	degh(u	degh(u	NOUN
ejpam-6851	252	22	)	)	PUNCT
ejpam-6851	252	23	=	=	SYM
ejpam-6851	252	24	∆(h	∆(h	NOUN
ejpam-6851	252	25	)	)	PUNCT
ejpam-6851	252	26	.	.	PUNCT
ejpam-6851	253	1	proof	proof	NOUN
ejpam-6851	253	2	.	.	PUNCT
ejpam-6851	254	1	statement	statement	NOUN
ejpam-6851	254	2	(	(	PUNCT
ejpam-6851	254	3	i	i	NOUN
ejpam-6851	254	4	)	)	PUNCT
ejpam-6851	254	5	follows	follow	VERB
ejpam-6851	254	6	immediately	immediately	ADV
ejpam-6851	254	7	from	from	ADP
ejpam-6851	254	8	theorem	theorem	ADJ
ejpam-6851	254	9	1(i	1(i	NUM
ejpam-6851	254	10	)	)	PUNCT
ejpam-6851	254	11	.	.	PUNCT
ejpam-6851	255	1	assume	assume	VERB
ejpam-6851	255	2	that	that	SCONJ
ejpam-6851	255	3	γ(g	γ(g	PROPN
ejpam-6851	255	4	)	)	PUNCT
ejpam-6851	255	5	≥	≥	NOUN
ejpam-6851	255	6	2	2	NUM
ejpam-6851	255	7	and	and	CCONJ
ejpam-6851	255	8	γ(h	γ(h	NOUN
ejpam-6851	255	9	)	)	PUNCT
ejpam-6851	255	10	≥	≥	NOUN
ejpam-6851	255	11	2	2	NUM
ejpam-6851	255	12	.	.	PUNCT
ejpam-6851	255	13	suppose	suppose	VERB
ejpam-6851	255	14	that	that	SCONJ
ejpam-6851	255	15	∆(g	∆(g	PROPN
ejpam-6851	255	16	)	)	PUNCT
ejpam-6851	255	17	+	+	NUM
ejpam-6851	255	18	n	n	NOUN
ejpam-6851	255	19	=	=	SYM
ejpam-6851	255	20	∆(h	∆(h	NOUN
ejpam-6851	255	21	)	)	PUNCT
ejpam-6851	255	22	+	+	NOUN
ejpam-6851	255	23	m.	m.	NOUN
ejpam-6851	255	24	pick	pick	VERB
ejpam-6851	255	25	u	u	PROPN
ejpam-6851	255	26	∈	∈	PROPN
ejpam-6851	255	27	v	v	ADP
ejpam-6851	255	28	(	(	PUNCT
ejpam-6851	255	29	g	g	NOUN
ejpam-6851	255	30	)	)	PUNCT
ejpam-6851	255	31	and	and	CCONJ
ejpam-6851	255	32	v	v	ADP
ejpam-6851	255	33	∈	∈	PROPN
ejpam-6851	255	34	v	v	NOUN
ejpam-6851	255	35	(	(	PUNCT
ejpam-6851	255	36	h	h	NOUN
ejpam-6851	255	37	)	)	PUNCT
ejpam-6851	255	38	such	such	ADJ
ejpam-6851	255	39	that	that	DET
ejpam-6851	255	40	degg(u	degg(u	NOUN
ejpam-6851	255	41	)	)	PUNCT
ejpam-6851	255	42	=	=	SYM
ejpam-6851	255	43	∆(g	∆(g	PROPN
ejpam-6851	255	44	)	)	PUNCT
ejpam-6851	255	45	and	and	CCONJ
ejpam-6851	255	46	degh(v	degh(v	PROPN
ejpam-6851	255	47	)	)	PUNCT
ejpam-6851	255	48	=	=	SYM
ejpam-6851	255	49	∆(h	∆(h	NOUN
ejpam-6851	255	50	)	)	PUNCT
ejpam-6851	255	51	.	.	PUNCT
ejpam-6851	256	1	since	since	SCONJ
ejpam-6851	256	2	s	s	PART
ejpam-6851	256	3	=	=	SYM
ejpam-6851	256	4	{	{	PUNCT
ejpam-6851	256	5	u	u	NOUN
ejpam-6851	256	6	,	,	PUNCT
ejpam-6851	256	7	v	v	NOUN
ejpam-6851	256	8	}	}	PUNCT
ejpam-6851	256	9	satisfies	satisfie	NOUN
ejpam-6851	256	10	condition	condition	NOUN
ejpam-6851	256	11	(	(	PUNCT
ejpam-6851	256	12	iii	iii	NOUN
ejpam-6851	256	13	)	)	PUNCT
ejpam-6851	256	14	of	of	ADP
ejpam-6851	256	15	theorem	theorem	NOUN
ejpam-6851	256	16	1	1	NUM
ejpam-6851	256	17	,	,	PUNCT
ejpam-6851	256	18	s	s	PROPN
ejpam-6851	256	19	∈	∈	PROPN
ejpam-6851	256	20	γs(g+h	γs(g+h	PROPN
ejpam-6851	256	21	)	)	PUNCT
ejpam-6851	256	22	.	.	PUNCT
ejpam-6851	257	1	in	in	ADP
ejpam-6851	257	2	this	this	DET
ejpam-6851	257	3	case	case	NOUN
ejpam-6851	257	4	,	,	PUNCT
ejpam-6851	257	5	γs(g+h	γs(g+h	NOUN
ejpam-6851	257	6	)	)	PUNCT
ejpam-6851	257	7	=	=	SYM
ejpam-6851	257	8	|s|	|s|	NOUN
ejpam-6851	257	9	=	=	SYM
ejpam-6851	257	10	2	2	NUM
ejpam-6851	257	11	and	and	CCONJ
ejpam-6851	257	12	(	(	PUNCT
ejpam-6851	257	13	ii)(a	ii)(a	PROPN
ejpam-6851	257	14	)	)	PUNCT
ejpam-6851	257	15	holds	hold	VERB
ejpam-6851	257	16	.	.	PUNCT
ejpam-6851	258	1	to	to	PART
ejpam-6851	258	2	prove	prove	VERB
ejpam-6851	258	3	(	(	PUNCT
ejpam-6851	258	4	ii)(b	ii)(b	PROPN
ejpam-6851	258	5	)	)	PUNCT
ejpam-6851	258	6	,	,	PUNCT
ejpam-6851	258	7	suppose	suppose	VERB
ejpam-6851	258	8	that	that	SCONJ
ejpam-6851	258	9	∆(g	∆(g	PROPN
ejpam-6851	258	10	)	)	PUNCT
ejpam-6851	258	11	+	+	NUM
ejpam-6851	258	12	n	n	CCONJ
ejpam-6851	258	13	>	>	X
ejpam-6851	258	14	∆(h	∆(h	NOUN
ejpam-6851	258	15	)	)	PUNCT
ejpam-6851	258	16	+	+	NUM
ejpam-6851	258	17	m.	m.	NOUN
ejpam-6851	258	18	first	first	ADV
ejpam-6851	258	19	,	,	PUNCT
ejpam-6851	258	20	let	let	VERB
ejpam-6851	258	21	s	s	PRON
ejpam-6851	258	22	⊆	⊆	NUM
ejpam-6851	258	23	v	v	NOUN
ejpam-6851	258	24	(	(	PUNCT
ejpam-6851	258	25	g	g	NOUN
ejpam-6851	258	26	)	)	PUNCT
ejpam-6851	258	27	be	be	AUX
ejpam-6851	258	28	a	a	DET
ejpam-6851	258	29	γs	γs	NOUN
ejpam-6851	258	30	-	-	PUNCT
ejpam-6851	258	31	set	set	NOUN
ejpam-6851	258	32	of	of	ADP
ejpam-6851	258	33	g.	g.	PROPN
ejpam-6851	258	34	by	by	ADP
ejpam-6851	258	35	j.	j.	PROPN
ejpam-6851	258	36	m.	m.	PROPN
ejpam-6851	258	37	molles	molles	PROPN
ejpam-6851	258	38	,	,	PUNCT
ejpam-6851	258	39	f.	f.	PROPN
ejpam-6851	258	40	p.	p.	PROPN
ejpam-6851	258	41	jamil	jamil	PROPN
ejpam-6851	258	42	,	,	PUNCT
ejpam-6851	258	43	s.	s.	PROPN
ejpam-6851	258	44	r.	r.	PROPN
ejpam-6851	258	45	canoy	canoy	PROPN
ejpam-6851	258	46	/	/	SYM
ejpam-6851	258	47	eur	eur	PROPN
ejpam-6851	258	48	.	.	PUNCT
ejpam-6851	259	1	j.	j.	PROPN
ejpam-6851	259	2	pure	pure	PROPN
ejpam-6851	259	3	appl	appl	PROPN
ejpam-6851	259	4	.	.	PROPN
ejpam-6851	259	5	math	math	PROPN
ejpam-6851	259	6	,	,	PUNCT
ejpam-6851	259	7	18	18	NUM
ejpam-6851	259	8	(	(	PUNCT
ejpam-6851	259	9	4	4	NUM
ejpam-6851	259	10	)	)	PUNCT
ejpam-6851	259	11	(	(	PUNCT
ejpam-6851	259	12	2025	2025	NUM
ejpam-6851	259	13	)	)	PUNCT
ejpam-6851	259	14	,	,	PUNCT
ejpam-6851	259	15	6851	6851	NUM
ejpam-6851	259	16	8	8	NUM
ejpam-6851	259	17	of	of	ADP
ejpam-6851	259	18	18	18	NUM
ejpam-6851	259	19	lemma	lemma	PROPN
ejpam-6851	259	20	2	2	NUM
ejpam-6851	259	21	,	,	PUNCT
ejpam-6851	259	22	there	there	PRON
ejpam-6851	259	23	exists	exist	VERB
ejpam-6851	259	24	v	v	ADP
ejpam-6851	259	25	∈	∈	PROPN
ejpam-6851	259	26	s	s	VERB
ejpam-6851	259	27	such	such	ADJ
ejpam-6851	259	28	that	that	PRON
ejpam-6851	259	29	degg(v	degg(v	PROPN
ejpam-6851	259	30	)	)	PUNCT
ejpam-6851	259	31	=	=	SYM
ejpam-6851	259	32	∆(g	∆(g	PROPN
ejpam-6851	259	33	)	)	PUNCT
ejpam-6851	259	34	.	.	PUNCT
ejpam-6851	260	1	then	then	ADV
ejpam-6851	260	2	degg(v	degg(v	PROPN
ejpam-6851	260	3	)	)	PUNCT
ejpam-6851	260	4	+	+	NUM
ejpam-6851	260	5	n	n	CCONJ
ejpam-6851	260	6	>	>	X
ejpam-6851	260	7	∆(h	∆(h	NOUN
ejpam-6851	260	8	)	)	PUNCT
ejpam-6851	261	1	+	+	NOUN
ejpam-6851	261	2	m.	m.	NOUN
ejpam-6851	261	3	by	by	ADP
ejpam-6851	261	4	theorem	theorem	NOUN
ejpam-6851	261	5	1	1	NUM
ejpam-6851	261	6	,	,	PUNCT
ejpam-6851	261	7	s	s	PROPN
ejpam-6851	261	8	∈	∈	PROPN
ejpam-6851	261	9	γs(g+h	γs(g+h	PROPN
ejpam-6851	261	10	)	)	PUNCT
ejpam-6851	261	11	.	.	PUNCT
ejpam-6851	262	1	thus	thus	ADV
ejpam-6851	262	2	,	,	PUNCT
ejpam-6851	262	3	γs(g+h	γs(g+h	NOUN
ejpam-6851	262	4	)	)	PUNCT
ejpam-6851	262	5	≤	≤	NUM
ejpam-6851	262	6	|s|	|s|	PROPN
ejpam-6851	262	7	=	=	NOUN
ejpam-6851	262	8	γs(g	γs(g	NUM
ejpam-6851	262	9	)	)	PUNCT
ejpam-6851	262	10	.	.	PUNCT
ejpam-6851	263	1	next	next	ADV
ejpam-6851	263	2	,	,	PUNCT
ejpam-6851	263	3	pick	pick	VERB
ejpam-6851	263	4	u	u	PRON
ejpam-6851	263	5	∈	∈	PROPN
ejpam-6851	263	6	v	v	ADP
ejpam-6851	263	7	(	(	PUNCT
ejpam-6851	263	8	h	h	NOUN
ejpam-6851	263	9	)	)	PUNCT
ejpam-6851	263	10	for	for	ADP
ejpam-6851	263	11	which	which	PRON
ejpam-6851	263	12	degh(u	degh(u	NOUN
ejpam-6851	263	13	)	)	PUNCT
ejpam-6851	263	14	=	=	SYM
ejpam-6851	263	15	∆(h	∆(h	NOUN
ejpam-6851	263	16	)	)	PUNCT
ejpam-6851	263	17	.	.	PUNCT
ejpam-6851	264	1	since	since	SCONJ
ejpam-6851	264	2	∆(g	∆(g	PROPN
ejpam-6851	264	3	)	)	PUNCT
ejpam-6851	264	4	+	+	NUM
ejpam-6851	264	5	n	n	CCONJ
ejpam-6851	264	6	>	>	X
ejpam-6851	264	7	∆(h	∆(h	NOUN
ejpam-6851	264	8	)	)	PUNCT
ejpam-6851	264	9	+	+	PROPN
ejpam-6851	264	10	m	m	PROPN
ejpam-6851	264	11	,	,	PUNCT
ejpam-6851	264	12	v	v	X
ejpam-6851	264	13	(	(	PUNCT
ejpam-6851	264	14	g	g	NOUN
ejpam-6851	264	15	)	)	PUNCT
ejpam-6851	264	16	\	\	X
ejpam-6851	265	1	ng+h	ng+h	PROPN
ejpam-6851	266	1	[	[	X
ejpam-6851	266	2	u	u	X
ejpam-6851	266	3	≽	≽	PROPN
ejpam-6851	266	4	]	]	X
ejpam-6851	266	5	̸=	̸=	PROPN
ejpam-6851	266	6	∅.	∅.	ADV
ejpam-6851	266	7	let	let	VERB
ejpam-6851	266	8	k	k	PROPN
ejpam-6851	266	9	=	=	PUNCT
ejpam-6851	266	10	⟨v	⟨v	PROPN
ejpam-6851	266	11	(	(	PUNCT
ejpam-6851	266	12	g	g	NOUN
ejpam-6851	266	13	)	)	PUNCT
ejpam-6851	266	14	\	\	X
ejpam-6851	267	1	ng+h	ng+h	PROPN
ejpam-6851	268	1	[	[	X
ejpam-6851	268	2	u	u	X
ejpam-6851	268	3	≽]⟩.	≽]⟩.	ADJ
ejpam-6851	268	4	choose	choose	VERB
ejpam-6851	268	5	a	a	DET
ejpam-6851	268	6	γs	γs	NOUN
ejpam-6851	268	7	-	-	PUNCT
ejpam-6851	268	8	set	set	ADJ
ejpam-6851	268	9	s∗	s∗	PROPN
ejpam-6851	268	10	of	of	ADP
ejpam-6851	268	11	k.	k.	PROPN
ejpam-6851	268	12	put	put	PROPN
ejpam-6851	268	13	s	s	PART
ejpam-6851	268	14	=	=	PUNCT
ejpam-6851	268	15	s∗	s∗	PROPN
ejpam-6851	268	16	∪	∪	X
ejpam-6851	268	17	{	{	PUNCT
ejpam-6851	268	18	u	u	NOUN
ejpam-6851	268	19	}	}	PUNCT
ejpam-6851	268	20	.	.	PUNCT
ejpam-6851	269	1	since	since	SCONJ
ejpam-6851	269	2	s	s	PART
ejpam-6851	269	3	satisfies	satisfie	NOUN
ejpam-6851	269	4	theorem	theorem	VERB
ejpam-6851	269	5	1(iii	1(iii	NUM
ejpam-6851	269	6	)	)	PUNCT
ejpam-6851	269	7	,	,	PUNCT
ejpam-6851	269	8	s	s	PROPN
ejpam-6851	269	9	∈	∈	PROPN
ejpam-6851	269	10	γs(g+h	γs(g+h	PROPN
ejpam-6851	269	11	)	)	PUNCT
ejpam-6851	269	12	.	.	PUNCT
ejpam-6851	270	1	thus	thus	ADV
ejpam-6851	270	2	,	,	PUNCT
ejpam-6851	270	3	γs(g+h	γs(g+h	NOUN
ejpam-6851	270	4	)	)	PUNCT
ejpam-6851	270	5	≤	≤	NUM
ejpam-6851	270	6	|s|	|s|	PROPN
ejpam-6851	270	7	=	=	SYM
ejpam-6851	270	8	1	1	NUM
ejpam-6851	270	9	+	+	NUM
ejpam-6851	270	10	γs(k	γs(k	NOUN
ejpam-6851	270	11	)	)	PUNCT
ejpam-6851	270	12	.	.	PUNCT
ejpam-6851	271	1	therefore	therefore	ADV
ejpam-6851	271	2	,	,	PUNCT
ejpam-6851	271	3	γs(g	γs(g	PUNCT
ejpam-6851	271	4	+	+	CCONJ
ejpam-6851	271	5	h	h	X
ejpam-6851	271	6	)	)	PUNCT
ejpam-6851	271	7	≤	≤	NOUN
ejpam-6851	271	8	min{γs(g	min{γs(g	PROPN
ejpam-6851	271	9	)	)	PUNCT
ejpam-6851	271	10	,	,	PUNCT
ejpam-6851	271	11	1	1	NUM
ejpam-6851	271	12	+	+	ADJ
ejpam-6851	271	13	γs(k	γs(k	NOUN
ejpam-6851	271	14	)	)	PUNCT
ejpam-6851	271	15	}	}	PUNCT
ejpam-6851	271	16	.	.	PUNCT
ejpam-6851	272	1	now	now	ADV
ejpam-6851	272	2	,	,	PUNCT
ejpam-6851	272	3	let	let	VERB
ejpam-6851	272	4	s	s	PRON
ejpam-6851	272	5	⊆	⊆	NUM
ejpam-6851	272	6	v	v	NOUN
ejpam-6851	272	7	(	(	PUNCT
ejpam-6851	272	8	g	g	PROPN
ejpam-6851	272	9	+	+	NOUN
ejpam-6851	272	10	h	h	NOUN
ejpam-6851	272	11	)	)	PUNCT
ejpam-6851	272	12	be	be	VERB
ejpam-6851	272	13	a	a	DET
ejpam-6851	272	14	γs	γs	NOUN
ejpam-6851	272	15	-	-	PUNCT
ejpam-6851	272	16	set	set	NOUN
ejpam-6851	272	17	of	of	ADP
ejpam-6851	272	18	g+h	g+h	PROPN
ejpam-6851	272	19	.	.	PUNCT
ejpam-6851	273	1	by	by	ADP
ejpam-6851	273	2	lemma	lemma	PROPN
ejpam-6851	273	3	2	2	NUM
ejpam-6851	273	4	,	,	PUNCT
ejpam-6851	273	5	s	s	VERB
ejpam-6851	273	6	⊈	⊈	PROPN
ejpam-6851	273	7	v	v	NOUN
ejpam-6851	273	8	(	(	PUNCT
ejpam-6851	273	9	h	h	NOUN
ejpam-6851	273	10	)	)	PUNCT
ejpam-6851	273	11	.	.	PUNCT
ejpam-6851	274	1	if	if	SCONJ
ejpam-6851	274	2	s	s	VERB
ejpam-6851	274	3	⊆	⊆	NUM
ejpam-6851	274	4	v	v	NOUN
ejpam-6851	274	5	(	(	PUNCT
ejpam-6851	274	6	g	g	NOUN
ejpam-6851	274	7	)	)	PUNCT
ejpam-6851	274	8	,	,	PUNCT
ejpam-6851	274	9	then	then	ADV
ejpam-6851	274	10	by	by	ADP
ejpam-6851	274	11	theorem	theorem	NOUN
ejpam-6851	274	12	1	1	NUM
ejpam-6851	274	13	,	,	PUNCT
ejpam-6851	274	14	s	s	NOUN
ejpam-6851	274	15	∈	∈	NOUN
ejpam-6851	274	16	γs(g	γs(g	PUNCT
ejpam-6851	274	17	)	)	PUNCT
ejpam-6851	274	18	,	,	PUNCT
ejpam-6851	274	19	showing	show	VERB
ejpam-6851	274	20	γs(g	γs(g	PUNCT
ejpam-6851	274	21	)	)	PUNCT
ejpam-6851	274	22	≤	≤	NUM
ejpam-6851	274	23	|s|	|s|	PROPN
ejpam-6851	274	24	=	=	PROPN
ejpam-6851	274	25	γs(g	γs(g	X
ejpam-6851	274	26	+	+	NOUN
ejpam-6851	274	27	h	h	NOUN
ejpam-6851	274	28	)	)	PUNCT
ejpam-6851	274	29	.	.	PUNCT
ejpam-6851	274	30	suppose	suppose	VERB
ejpam-6851	274	31	that	that	SCONJ
ejpam-6851	274	32	sg	sg	VERB
ejpam-6851	274	33	=	=	SYM
ejpam-6851	274	34	s	s	PROPN
ejpam-6851	274	35	∩	∩	ADJ
ejpam-6851	274	36	v	v	X
ejpam-6851	274	37	(	(	PUNCT
ejpam-6851	274	38	g	g	NOUN
ejpam-6851	274	39	)	)	PUNCT
ejpam-6851	274	40	̸=	̸=	PROPN
ejpam-6851	274	41	∅	∅	NOUN
ejpam-6851	274	42	and	and	CCONJ
ejpam-6851	274	43	sh	sh	INTJ
ejpam-6851	274	44	=	=	SYM
ejpam-6851	274	45	s	s	PROPN
ejpam-6851	274	46	∩	∩	ADJ
ejpam-6851	274	47	v	v	ADJ
ejpam-6851	274	48	(	(	PUNCT
ejpam-6851	274	49	h	h	NOUN
ejpam-6851	274	50	)	)	PUNCT
ejpam-6851	274	51	̸=	̸=	PROPN
ejpam-6851	274	52	∅.	∅.	ADV
ejpam-6851	274	53	since	since	SCONJ
ejpam-6851	274	54	∆(g)+n	∆(g)+n	PROPN
ejpam-6851	274	55	>	>	X
ejpam-6851	274	56	∆(h)+m	∆(h)+m	PROPN
ejpam-6851	274	57	,	,	PUNCT
ejpam-6851	274	58	v	v	X
ejpam-6851	274	59	(	(	PUNCT
ejpam-6851	274	60	g	g	NOUN
ejpam-6851	274	61	)	)	PUNCT
ejpam-6851	275	1	\ng+h	\ng+h	PRON
ejpam-6851	276	1	[	[	X
ejpam-6851	276	2	sh	sh	PROPN
ejpam-6851	276	3	≽	≽	PROPN
ejpam-6851	276	4	]	]	X
ejpam-6851	276	5	̸=	̸=	PROPN
ejpam-6851	276	6	∅.	∅.	ADV
ejpam-6851	276	7	put	put	VERB
ejpam-6851	276	8	k	k	PROPN
ejpam-6851	276	9	=	=	PUNCT
ejpam-6851	276	10	⟨v	⟨v	NUM
ejpam-6851	276	11	(	(	PUNCT
ejpam-6851	276	12	g	g	NOUN
ejpam-6851	276	13	)	)	PUNCT
ejpam-6851	277	1	\ng+h	\ng+h	PRON
ejpam-6851	278	1	[	[	X
ejpam-6851	278	2	sh	sh	INTJ
ejpam-6851	278	3	≽]⟩.	≽]⟩.	VERB
ejpam-6851	278	4	we	we	PRON
ejpam-6851	278	5	claim	claim	VERB
ejpam-6851	278	6	that	that	SCONJ
ejpam-6851	278	7	sg	sg	PROPN
ejpam-6851	278	8	is	be	AUX
ejpam-6851	278	9	a	a	DET
ejpam-6851	278	10	strong	strong	ADJ
ejpam-6851	278	11	dominating	dominating	NOUN
ejpam-6851	278	12	set	set	NOUN
ejpam-6851	278	13	of	of	ADP
ejpam-6851	278	14	k.	k.	PROPN
ejpam-6851	278	15	let	let	VERB
ejpam-6851	278	16	u	u	PRON
ejpam-6851	278	17	∈	∈	PROPN
ejpam-6851	278	18	v	v	X
ejpam-6851	278	19	(	(	PUNCT
ejpam-6851	278	20	k)\sg	k)\sg	PROPN
ejpam-6851	278	21	.	.	PUNCT
ejpam-6851	279	1	since	since	SCONJ
ejpam-6851	279	2	u	u	PROPN
ejpam-6851	279	3	∈	∈	PROPN
ejpam-6851	279	4	v	v	NOUN
ejpam-6851	279	5	(	(	PUNCT
ejpam-6851	279	6	g)\s	g)\s	NOUN
ejpam-6851	279	7	,	,	PUNCT
ejpam-6851	279	8	there	there	PRON
ejpam-6851	279	9	exist	exist	VERB
ejpam-6851	279	10	v	v	ADP
ejpam-6851	279	11	∈	∈	NOUN
ejpam-6851	279	12	s	s	NOUN
ejpam-6851	279	13	for	for	ADP
ejpam-6851	279	14	which	which	PRON
ejpam-6851	279	15	uv	uv	NOUN
ejpam-6851	279	16	∈	∈	PROPN
ejpam-6851	279	17	e(g	e(g	NOUN
ejpam-6851	279	18	+	+	CCONJ
ejpam-6851	279	19	k	k	NOUN
ejpam-6851	279	20	)	)	PUNCT
ejpam-6851	279	21	and	and	CCONJ
ejpam-6851	280	1	u	u	NOUN
ejpam-6851	280	2	≼g+k	≼g+k	PROPN
ejpam-6851	280	3	v.	v.	CCONJ
ejpam-6851	280	4	because	because	SCONJ
ejpam-6851	280	5	u	u	NOUN
ejpam-6851	280	6	is	be	AUX
ejpam-6851	280	7	not	not	PART
ejpam-6851	280	8	strongly	strongly	ADV
ejpam-6851	280	9	dominated	dominate	VERB
ejpam-6851	280	10	by	by	ADP
ejpam-6851	280	11	sh	sh	NOUN
ejpam-6851	280	12	in	in	ADP
ejpam-6851	280	13	g	g	PROPN
ejpam-6851	280	14	+	+	PROPN
ejpam-6851	280	15	h	h	NOUN
ejpam-6851	280	16	,	,	PUNCT
ejpam-6851	280	17	v	v	NOUN
ejpam-6851	280	18	∈	∈	PROPN
ejpam-6851	280	19	sg	sg	NOUN
ejpam-6851	280	20	.	.	PUNCT
ejpam-6851	281	1	since	since	SCONJ
ejpam-6851	281	2	u	u	NOUN
ejpam-6851	281	3	is	be	AUX
ejpam-6851	281	4	arbitrary	arbitrary	ADJ
ejpam-6851	281	5	,	,	PUNCT
ejpam-6851	281	6	sg	sg	PROPN
ejpam-6851	281	7	is	be	AUX
ejpam-6851	281	8	a	a	DET
ejpam-6851	281	9	strong	strong	ADJ
ejpam-6851	281	10	dominating	dominating	NOUN
ejpam-6851	281	11	set	set	NOUN
ejpam-6851	281	12	of	of	ADP
ejpam-6851	281	13	k.	k.	PROPN
ejpam-6851	281	14	thus	thus	ADV
ejpam-6851	281	15	,	,	PUNCT
ejpam-6851	281	16	γs(k	γs(k	NOUN
ejpam-6851	281	17	)	)	PUNCT
ejpam-6851	281	18	≤	≤	NUM
ejpam-6851	281	19	|sg|	|sg|	NOUN
ejpam-6851	281	20	.	.	PUNCT
ejpam-6851	282	1	since	since	SCONJ
ejpam-6851	282	2	|sh	|sh	ADP
ejpam-6851	282	3	|	|	ADV
ejpam-6851	282	4	≥	≥	NOUN
ejpam-6851	282	5	1	1	NUM
ejpam-6851	282	6	,	,	PUNCT
ejpam-6851	282	7	γs(g	γs(g	PUNCT
ejpam-6851	282	8	+	+	NOUN
ejpam-6851	282	9	h	h	NOUN
ejpam-6851	282	10	)	)	PUNCT
ejpam-6851	282	11	=	=	SYM
ejpam-6851	282	12	|sg|	|sg|	NOUN
ejpam-6851	282	13	+	+	CCONJ
ejpam-6851	282	14	|sh	|sh	VERB
ejpam-6851	282	15	|	|	ADV
ejpam-6851	282	16	≥	≥	NOUN
ejpam-6851	282	17	1	1	NUM
ejpam-6851	282	18	+	+	CCONJ
ejpam-6851	282	19	γs(k	γs(k	NOUN
ejpam-6851	282	20	)	)	PUNCT
ejpam-6851	282	21	.	.	PUNCT
ejpam-6851	283	1	the	the	DET
ejpam-6851	283	2	above	above	ADJ
ejpam-6851	283	3	results	result	NOUN
ejpam-6851	283	4	imply	imply	VERB
ejpam-6851	283	5	that	that	PRON
ejpam-6851	283	6	γs(g+h	γs(g+h	PUNCT
ejpam-6851	283	7	)	)	PUNCT
ejpam-6851	283	8	=	=	SYM
ejpam-6851	283	9	min{γs(g	min{γs(g	PROPN
ejpam-6851	283	10	)	)	PUNCT
ejpam-6851	283	11	,	,	PUNCT
ejpam-6851	283	12	1	1	NUM
ejpam-6851	283	13	+	+	ADJ
ejpam-6851	283	14	γs(k	γs(k	NOUN
ejpam-6851	283	15	)	)	PUNCT
ejpam-6851	283	16	}	}	PUNCT
ejpam-6851	283	17	.	.	PUNCT
ejpam-6851	284	1	verify	verify	VERB
ejpam-6851	284	2	that	that	SCONJ
ejpam-6851	284	3	γs(p4	γs(p4	NOUN
ejpam-6851	284	4	+	+	CCONJ
ejpam-6851	284	5	p6	p6	ADJ
ejpam-6851	284	6	)	)	PUNCT
ejpam-6851	284	7	=	=	SYM
ejpam-6851	284	8	γs(p4	γs(p4	NOUN
ejpam-6851	284	9	)	)	PUNCT
ejpam-6851	284	10	=	=	SYM
ejpam-6851	284	11	2	2	X
ejpam-6851	284	12	.	.	X
ejpam-6851	285	1	on	on	ADP
ejpam-6851	285	2	the	the	DET
ejpam-6851	285	3	other	other	ADJ
ejpam-6851	285	4	hand	hand	NOUN
ejpam-6851	285	5	,	,	PUNCT
ejpam-6851	285	6	if	if	SCONJ
ejpam-6851	285	7	g	g	PROPN
ejpam-6851	285	8	is	be	AUX
ejpam-6851	285	9	as	as	ADP
ejpam-6851	285	10	in	in	ADP
ejpam-6851	285	11	figure	figure	NOUN
ejpam-6851	285	12	1	1	NUM
ejpam-6851	285	13	,	,	PUNCT
ejpam-6851	285	14	then	then	ADV
ejpam-6851	285	15	γs(g	γs(g	PUNCT
ejpam-6851	285	16	+	+	CCONJ
ejpam-6851	285	17	p8	p8	ADJ
ejpam-6851	285	18	)	)	PUNCT
ejpam-6851	285	19	=	=	SYM
ejpam-6851	286	1	1	1	NUM
ejpam-6851	286	2	+	+	NUM
ejpam-6851	286	3	γs(k	γs(k	NOUN
ejpam-6851	286	4	)	)	PUNCT
ejpam-6851	286	5	=	=	SYM
ejpam-6851	287	1	2	2	NUM
ejpam-6851	287	2	,	,	PUNCT
ejpam-6851	287	3	where	where	SCONJ
ejpam-6851	287	4	k	k	PROPN
ejpam-6851	287	5	=	=	PUNCT
ejpam-6851	287	6	⟨v	⟨v	PROPN
ejpam-6851	287	7	(	(	PUNCT
ejpam-6851	287	8	g	g	NOUN
ejpam-6851	287	9	)	)	PUNCT
ejpam-6851	287	10	\	\	NOUN
ejpam-6851	288	1	ng+p8	ng+p8	PROPN
ejpam-6851	289	1	[	[	X
ejpam-6851	289	2	u	u	X
ejpam-6851	289	3	≽]⟩	≽]⟩	NOUN
ejpam-6851	289	4	=	=	PUNCT
ejpam-6851	289	5	⟨{v}⟩	⟨{v}⟩	NOUN
ejpam-6851	289	6	and	and	CCONJ
ejpam-6851	289	7	u	u	PROPN
ejpam-6851	289	8	∈	∈	PROPN
ejpam-6851	289	9	v	v	X
ejpam-6851	289	10	(	(	PUNCT
ejpam-6851	289	11	p8	p8	PROPN
ejpam-6851	289	12	)	)	PUNCT
ejpam-6851	289	13	with	with	ADP
ejpam-6851	289	14	degp8(u	degp8(u	NOUN
ejpam-6851	289	15	)	)	PUNCT
ejpam-6851	289	16	=	=	SYM
ejpam-6851	289	17	2	2	X
ejpam-6851	289	18	.	.	PUNCT
ejpam-6851	289	19	..................................................................................................	..................................................................................................	PUNCT
ejpam-6851	290	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-6851	290	2	..................................................................................................	..................................................................................................	PUNCT
ejpam-6851	291	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-6851	291	2	..................................................................................................	..................................................................................................	PUNCT
ejpam-6851	292	1	....................................	....................................	PUNCT
ejpam-6851	292	2	....................................	....................................	PUNCT
ejpam-6851	293	1	....................................	....................................	PUNCT
ejpam-6851	293	2	....................................	....................................	PUNCT
ejpam-6851	294	1	....................................	....................................	PUNCT
ejpam-6851	294	2	............	............	PUNCT
ejpam-6851	294	3	...........	...........	PUNCT
ejpam-6851	294	4	...........	...........	PUNCT
ejpam-6851	294	5	.......	.......	PUNCT
ejpam-6851	294	6	.........................................	.........................................	PUNCT
ejpam-6851	294	7	.........................................	.........................................	PUNCT
ejpam-6851	294	8	............	............	PUNCT
ejpam-6851	294	9	...........	...........	PUNCT
ejpam-6851	294	10	...........	...........	PUNCT
ejpam-6851	294	11	.......	.......	PUNCT
ejpam-6851	295	1	g	g	NOUN
ejpam-6851	295	2	:	:	PUNCT
ejpam-6851	295	3	v	v	NUM
ejpam-6851	295	4	•	•	NUM
ejpam-6851	295	5	figure	figure	NOUN
ejpam-6851	295	6	1	1	NUM
ejpam-6851	295	7	:	:	PUNCT
ejpam-6851	295	8	graph	graph	VERB
ejpam-6851	295	9	g	g	ADP
ejpam-6851	295	10	the	the	DET
ejpam-6851	295	11	following	follow	VERB
ejpam-6851	295	12	versions	version	NOUN
ejpam-6851	295	13	for	for	ADP
ejpam-6851	295	14	weak	weak	ADJ
ejpam-6851	295	15	domination	domination	NOUN
ejpam-6851	295	16	follow	follow	VERB
ejpam-6851	295	17	similar	similar	ADJ
ejpam-6851	295	18	proofs	proof	NOUN
ejpam-6851	295	19	.	.	PUNCT
ejpam-6851	296	1	theorem	theorem	NOUN
ejpam-6851	296	2	2	2	NUM
ejpam-6851	296	3	.	.	PUNCT
ejpam-6851	297	1	let	let	VERB
ejpam-6851	297	2	g	g	NOUN
ejpam-6851	297	3	,	,	PUNCT
ejpam-6851	297	4	h	h	NOUN
ejpam-6851	297	5	be	be	AUX
ejpam-6851	297	6	connected	connect	VERB
ejpam-6851	297	7	graphs	graph	NOUN
ejpam-6851	297	8	of	of	ADP
ejpam-6851	297	9	orders	order	NOUN
ejpam-6851	297	10	m	m	VERB
ejpam-6851	297	11	and	and	CCONJ
ejpam-6851	297	12	n	n	CCONJ
ejpam-6851	297	13	,	,	PUNCT
ejpam-6851	297	14	respectively	respectively	ADV
ejpam-6851	297	15	.	.	PUNCT
ejpam-6851	298	1	let	let	VERB
ejpam-6851	298	2	s	s	PRON
ejpam-6851	298	3	⊆	⊆	NUM
ejpam-6851	298	4	v	v	NOUN
ejpam-6851	298	5	(	(	PUNCT
ejpam-6851	298	6	g+h	g+h	PROPN
ejpam-6851	298	7	)	)	PUNCT
ejpam-6851	298	8	.	.	PUNCT
ejpam-6851	299	1	then	then	ADV
ejpam-6851	299	2	s	s	VERB
ejpam-6851	299	3	∈	∈	PROPN
ejpam-6851	299	4	γw(g+h	γw(g+h	PROPN
ejpam-6851	299	5	)	)	PUNCT
ejpam-6851	300	1	if	if	SCONJ
ejpam-6851	300	2	and	and	CCONJ
ejpam-6851	300	3	only	only	ADV
ejpam-6851	300	4	if	if	SCONJ
ejpam-6851	300	5	one	one	NUM
ejpam-6851	300	6	of	of	ADP
ejpam-6851	300	7	the	the	DET
ejpam-6851	300	8	following	follow	VERB
ejpam-6851	300	9	holds	hold	VERB
ejpam-6851	300	10	:	:	PUNCT
ejpam-6851	300	11	(	(	PUNCT
ejpam-6851	300	12	i	i	NOUN
ejpam-6851	300	13	)	)	PUNCT
ejpam-6851	300	14	s	s	VERB
ejpam-6851	300	15	⊆	⊆	NUM
ejpam-6851	300	16	v	v	NOUN
ejpam-6851	300	17	(	(	PUNCT
ejpam-6851	300	18	g	g	NOUN
ejpam-6851	300	19	)	)	PUNCT
ejpam-6851	300	20	such	such	ADJ
ejpam-6851	300	21	that	that	PRON
ejpam-6851	300	22	s	s	VERB
ejpam-6851	300	23	∈	∈	NOUN
ejpam-6851	300	24	γw(g	γw(g	PUNCT
ejpam-6851	300	25	)	)	PUNCT
ejpam-6851	300	26	and	and	CCONJ
ejpam-6851	300	27	s	s	VERB
ejpam-6851	300	28	contains	contain	VERB
ejpam-6851	300	29	a	a	DET
ejpam-6851	300	30	vertex	vertex	NOUN
ejpam-6851	300	31	v	v	NOUN
ejpam-6851	300	32	for	for	ADP
ejpam-6851	300	33	which	which	PRON
ejpam-6851	300	34	degg(v	degg(v	PROPN
ejpam-6851	300	35	)	)	PUNCT
ejpam-6851	300	36	≤	≤	NOUN
ejpam-6851	300	37	δ(h	δ(h	PROPN
ejpam-6851	300	38	)	)	PUNCT
ejpam-6851	301	1	+	+	ADP
ejpam-6851	301	2	m−	m−	PROPN
ejpam-6851	301	3	n.	n.	PROPN
ejpam-6851	301	4	(	(	PUNCT
ejpam-6851	301	5	ii	ii	PROPN
ejpam-6851	301	6	)	)	PUNCT
ejpam-6851	301	7	s	s	PART
ejpam-6851	301	8	⊆	⊆	NUM
ejpam-6851	301	9	v	v	NOUN
ejpam-6851	301	10	(	(	PUNCT
ejpam-6851	301	11	h	h	NOUN
ejpam-6851	301	12	)	)	PUNCT
ejpam-6851	301	13	such	such	ADJ
ejpam-6851	301	14	that	that	PRON
ejpam-6851	301	15	s	s	VERB
ejpam-6851	301	16	∈	∈	PROPN
ejpam-6851	301	17	γw(h	γw(h	NOUN
ejpam-6851	301	18	)	)	PUNCT
ejpam-6851	301	19	and	and	CCONJ
ejpam-6851	301	20	s	s	VERB
ejpam-6851	301	21	contains	contain	VERB
ejpam-6851	301	22	a	a	DET
ejpam-6851	301	23	vertex	vertex	NOUN
ejpam-6851	301	24	v	v	NOUN
ejpam-6851	301	25	for	for	ADP
ejpam-6851	301	26	which	which	PRON
ejpam-6851	301	27	degh(v	degh(v	NOUN
ejpam-6851	301	28	)	)	PUNCT
ejpam-6851	301	29	≤	≤	NOUN
ejpam-6851	301	30	δ(g	δ(g	PUNCT
ejpam-6851	301	31	)	)	PUNCT
ejpam-6851	301	32	+	+	NUM
ejpam-6851	301	33	n−m	n−m	PROPN
ejpam-6851	301	34	.	.	PUNCT
ejpam-6851	302	1	(	(	PUNCT
ejpam-6851	302	2	iii	iii	X
ejpam-6851	302	3	)	)	PUNCT
ejpam-6851	302	4	sg	sg	ADP
ejpam-6851	302	5	=	=	SYM
ejpam-6851	302	6	s	s	PROPN
ejpam-6851	302	7	∩	∩	ADJ
ejpam-6851	302	8	v	v	X
ejpam-6851	302	9	(	(	PUNCT
ejpam-6851	302	10	g	g	NOUN
ejpam-6851	302	11	)	)	PUNCT
ejpam-6851	302	12	̸=	̸=	PROPN
ejpam-6851	302	13	∅	∅	NOUN
ejpam-6851	302	14	and	and	CCONJ
ejpam-6851	302	15	sh	sh	INTJ
ejpam-6851	302	16	=	=	SYM
ejpam-6851	302	17	s	s	PROPN
ejpam-6851	302	18	∩	∩	ADJ
ejpam-6851	302	19	v	v	ADJ
ejpam-6851	302	20	(	(	PUNCT
ejpam-6851	302	21	h	h	NOUN
ejpam-6851	302	22	)	)	PUNCT
ejpam-6851	302	23	̸=	̸=	PROPN
ejpam-6851	302	24	∅	∅	NOUN
ejpam-6851	302	25	and	and	CCONJ
ejpam-6851	302	26	one	one	NUM
ejpam-6851	302	27	of	of	ADP
ejpam-6851	302	28	the	the	DET
ejpam-6851	302	29	following	following	NOUN
ejpam-6851	302	30	holds	hold	VERB
ejpam-6851	302	31	for	for	ADP
ejpam-6851	302	32	each	each	DET
ejpam-6851	302	33	u	u	PROPN
ejpam-6851	302	34	∈	∈	PROPN
ejpam-6851	302	35	v	v	NOUN
ejpam-6851	302	36	(	(	PUNCT
ejpam-6851	302	37	g+h	g+h	NOUN
ejpam-6851	302	38	)	)	PUNCT
ejpam-6851	302	39	\	\	PUNCT
ejpam-6851	303	1	s	s	PART
ejpam-6851	303	2	:	:	PUNCT
ejpam-6851	303	3	(	(	PUNCT
ejpam-6851	303	4	a	a	X
ejpam-6851	303	5	)	)	PUNCT
ejpam-6851	303	6	u	u	NOUN
ejpam-6851	303	7	∈	∈	PROPN
ejpam-6851	303	8	v	v	NOUN
ejpam-6851	303	9	(	(	PUNCT
ejpam-6851	303	10	g	g	NOUN
ejpam-6851	303	11	)	)	PUNCT
ejpam-6851	303	12	and	and	CCONJ
ejpam-6851	303	13	u	u	X
ejpam-6851	303	14	≽g	≽g	PROPN
ejpam-6851	303	15	sg	sg	NOUN
ejpam-6851	303	16	or	or	CCONJ
ejpam-6851	303	17	there	there	PRON
ejpam-6851	303	18	exists	exist	VERB
ejpam-6851	303	19	v	v	ADP
ejpam-6851	303	20	∈	∈	NOUN
ejpam-6851	303	21	sh	sh	INTJ
ejpam-6851	303	22	for	for	ADP
ejpam-6851	303	23	which	which	PRON
ejpam-6851	303	24	degh(v	degh(v	NOUN
ejpam-6851	303	25	)	)	PUNCT
ejpam-6851	303	26	≤	≤	NOUN
ejpam-6851	303	27	degg(u	degg(u	PROPN
ejpam-6851	303	28	)	)	PUNCT
ejpam-6851	303	29	+	+	CCONJ
ejpam-6851	303	30	n−m	n−m	PROPN
ejpam-6851	303	31	;	;	PUNCT
ejpam-6851	303	32	j.	j.	PROPN
ejpam-6851	303	33	m.	m.	PROPN
ejpam-6851	303	34	molles	molles	PROPN
ejpam-6851	303	35	,	,	PUNCT
ejpam-6851	303	36	f.	f.	PROPN
ejpam-6851	303	37	p.	p.	PROPN
ejpam-6851	303	38	jamil	jamil	PROPN
ejpam-6851	303	39	,	,	PUNCT
ejpam-6851	303	40	s.	s.	PROPN
ejpam-6851	303	41	r.	r.	PROPN
ejpam-6851	303	42	canoy	canoy	PROPN
ejpam-6851	303	43	/	/	SYM
ejpam-6851	303	44	eur	eur	PROPN
ejpam-6851	303	45	.	.	PUNCT
ejpam-6851	304	1	j.	j.	PROPN
ejpam-6851	304	2	pure	pure	PROPN
ejpam-6851	304	3	appl	appl	PROPN
ejpam-6851	304	4	.	.	PROPN
ejpam-6851	304	5	math	math	PROPN
ejpam-6851	304	6	,	,	PUNCT
ejpam-6851	304	7	18	18	NUM
ejpam-6851	304	8	(	(	PUNCT
ejpam-6851	304	9	4	4	NUM
ejpam-6851	304	10	)	)	PUNCT
ejpam-6851	304	11	(	(	PUNCT
ejpam-6851	304	12	2025	2025	NUM
ejpam-6851	304	13	)	)	PUNCT
ejpam-6851	304	14	,	,	PUNCT
ejpam-6851	304	15	6851	6851	NUM
ejpam-6851	304	16	9	9	NUM
ejpam-6851	304	17	of	of	ADP
ejpam-6851	304	18	18	18	NUM
ejpam-6851	304	19	(	(	PUNCT
ejpam-6851	304	20	b	b	NOUN
ejpam-6851	304	21	)	)	PUNCT
ejpam-6851	304	22	u	u	NOUN
ejpam-6851	304	23	∈	∈	PROPN
ejpam-6851	304	24	v	v	ADP
ejpam-6851	304	25	(	(	PUNCT
ejpam-6851	304	26	h	h	NOUN
ejpam-6851	304	27	)	)	PUNCT
ejpam-6851	304	28	and	and	CCONJ
ejpam-6851	304	29	u	u	NOUN
ejpam-6851	304	30	≽h	≽h	ADV
ejpam-6851	304	31	sh	sh	INTJ
ejpam-6851	305	1	or	or	CCONJ
ejpam-6851	305	2	there	there	ADV
ejpam-6851	305	3	exists	exist	VERB
ejpam-6851	305	4	v	v	ADP
ejpam-6851	305	5	∈	∈	PROPN
ejpam-6851	305	6	sg	sg	NOUN
ejpam-6851	305	7	for	for	ADP
ejpam-6851	305	8	which	which	PRON
ejpam-6851	305	9	degg(v	degg(v	PROPN
ejpam-6851	305	10	)	)	PUNCT
ejpam-6851	305	11	≤	≤	NOUN
ejpam-6851	305	12	degh(u)+	degh(u)+	NOUN
ejpam-6851	305	13	m−	m−	PROPN
ejpam-6851	305	14	n.	n.	PROPN
ejpam-6851	305	15	corollary	corollary	NOUN
ejpam-6851	305	16	2	2	NUM
ejpam-6851	305	17	.	.	PUNCT
ejpam-6851	306	1	let	let	VERB
ejpam-6851	306	2	g	g	NOUN
ejpam-6851	306	3	and	and	CCONJ
ejpam-6851	306	4	h	h	NOUN
ejpam-6851	306	5	be	be	AUX
ejpam-6851	306	6	connected	connect	VERB
ejpam-6851	306	7	graphs	graph	NOUN
ejpam-6851	306	8	of	of	ADP
ejpam-6851	306	9	orders	order	NOUN
ejpam-6851	306	10	m	m	VERB
ejpam-6851	306	11	and	and	CCONJ
ejpam-6851	306	12	n	n	CCONJ
ejpam-6851	306	13	,	,	PUNCT
ejpam-6851	306	14	respectively	respectively	ADV
ejpam-6851	306	15	.	.	PUNCT
ejpam-6851	307	1	assume	assume	VERB
ejpam-6851	307	2	γ(g	γ(g	PROPN
ejpam-6851	307	3	)	)	PUNCT
ejpam-6851	307	4	≥	≥	NOUN
ejpam-6851	307	5	2	2	NUM
ejpam-6851	307	6	and	and	CCONJ
ejpam-6851	307	7	γ(h	γ(h	NOUN
ejpam-6851	307	8	)	)	PUNCT
ejpam-6851	307	9	≥	≥	NOUN
ejpam-6851	308	1	2	2	NUM
ejpam-6851	308	2	.	.	PUNCT
ejpam-6851	308	3	then	then	ADV
ejpam-6851	308	4	the	the	DET
ejpam-6851	308	5	following	follow	VERB
ejpam-6851	308	6	holds	hold	VERB
ejpam-6851	308	7	:	:	PUNCT
ejpam-6851	308	8	(	(	PUNCT
ejpam-6851	308	9	a	a	X
ejpam-6851	308	10	)	)	PUNCT
ejpam-6851	308	11	if	if	SCONJ
ejpam-6851	308	12	δ(g	δ(g	VERB
ejpam-6851	308	13	)	)	PUNCT
ejpam-6851	308	14	+	+	NUM
ejpam-6851	308	15	n	n	NOUN
ejpam-6851	308	16	=	=	SYM
ejpam-6851	308	17	δ(h	δ(h	PROPN
ejpam-6851	308	18	)	)	PUNCT
ejpam-6851	309	1	+	+	NOUN
ejpam-6851	309	2	m	m	PROPN
ejpam-6851	309	3	,	,	PUNCT
ejpam-6851	309	4	then	then	ADV
ejpam-6851	309	5	γw(g+h	γw(g+h	PROPN
ejpam-6851	309	6	)	)	PUNCT
ejpam-6851	309	7	=	=	SYM
ejpam-6851	309	8	2	2	X
ejpam-6851	309	9	.	.	PUNCT
ejpam-6851	309	10	(	(	PUNCT
ejpam-6851	309	11	b	b	X
ejpam-6851	309	12	)	)	PUNCT
ejpam-6851	309	13	if	if	SCONJ
ejpam-6851	309	14	δ(g	δ(g	VERB
ejpam-6851	309	15	)	)	PUNCT
ejpam-6851	309	16	+	+	CCONJ
ejpam-6851	309	17	n	n	CCONJ
ejpam-6851	309	18	<	<	X
ejpam-6851	309	19	δ(h	δ(h	PROPN
ejpam-6851	309	20	)	)	PUNCT
ejpam-6851	310	1	+	+	NOUN
ejpam-6851	310	2	m	m	PROPN
ejpam-6851	310	3	,	,	PUNCT
ejpam-6851	310	4	then	then	ADV
ejpam-6851	310	5	γw(g+h	γw(g+h	PROPN
ejpam-6851	310	6	)	)	PUNCT
ejpam-6851	310	7	=	=	PUNCT
ejpam-6851	310	8	min{γw(g	min{γw(g	NUM
ejpam-6851	310	9	)	)	PUNCT
ejpam-6851	310	10	,	,	PUNCT
ejpam-6851	310	11	1	1	NUM
ejpam-6851	310	12	+	+	CCONJ
ejpam-6851	310	13	γw(k	γw(k	NOUN
ejpam-6851	310	14	)	)	PUNCT
ejpam-6851	310	15	}	}	PUNCT
ejpam-6851	310	16	,	,	PUNCT
ejpam-6851	310	17	where	where	SCONJ
ejpam-6851	310	18	k	k	PROPN
ejpam-6851	310	19	=	=	PUNCT
ejpam-6851	310	20	⟨v	⟨v	PROPN
ejpam-6851	310	21	(	(	PUNCT
ejpam-6851	310	22	g	g	NOUN
ejpam-6851	310	23	)	)	PUNCT
ejpam-6851	310	24	\ng+h	\ng+h	PROPN
ejpam-6851	310	25	[	[	X
ejpam-6851	310	26	u	u	X
ejpam-6851	310	27	≼]⟩	≼]⟩	NOUN
ejpam-6851	310	28	and	and	CCONJ
ejpam-6851	310	29	u	u	NOUN
ejpam-6851	310	30	∈	∈	PROPN
ejpam-6851	310	31	v	v	ADP
ejpam-6851	310	32	(	(	PUNCT
ejpam-6851	310	33	h	h	NOUN
ejpam-6851	310	34	)	)	PUNCT
ejpam-6851	310	35	for	for	ADP
ejpam-6851	310	36	which	which	PRON
ejpam-6851	310	37	degh(u	degh(u	NOUN
ejpam-6851	310	38	)	)	PUNCT
ejpam-6851	310	39	=	=	SYM
ejpam-6851	310	40	δ(h	δ(h	PROPN
ejpam-6851	310	41	)	)	PUNCT
ejpam-6851	310	42	.	.	PUNCT
ejpam-6851	311	1	example	example	NOUN
ejpam-6851	312	1	1	1	NUM
ejpam-6851	312	2	.	.	X
ejpam-6851	313	1	for	for	ADP
ejpam-6851	313	2	m	m	PROPN
ejpam-6851	313	3	,	,	PUNCT
ejpam-6851	313	4	n	n	PRON
ejpam-6851	313	5	≥	≥	NOUN
ejpam-6851	313	6	4	4	NUM
ejpam-6851	313	7	,	,	PUNCT
ejpam-6851	313	8	(	(	PUNCT
ejpam-6851	313	9	1	1	X
ejpam-6851	313	10	)	)	PUNCT
ejpam-6851	313	11	γs(pm	γs(pm	NOUN
ejpam-6851	313	12	+	+	CCONJ
ejpam-6851	313	13	pn	pn	NOUN
ejpam-6851	313	14	)	)	PUNCT
ejpam-6851	313	15	=	=	NOUN
ejpam-6851	313	16	{	{	PUNCT
ejpam-6851	313	17	2	2	NUM
ejpam-6851	313	18	,	,	PUNCT
ejpam-6851	313	19	if	if	SCONJ
ejpam-6851	313	20	m	m	PROPN
ejpam-6851	313	21	=	=	SYM
ejpam-6851	313	22	n	n	CCONJ
ejpam-6851	313	23	;	;	PUNCT
ejpam-6851	313	24	⌈m3	⌈m3	ADJ
ejpam-6851	313	25	⌉	⌉	NOUN
ejpam-6851	313	26	,	,	PUNCT
ejpam-6851	313	27	if	if	SCONJ
ejpam-6851	313	28	m	m	VERB
ejpam-6851	313	29	<	<	X
ejpam-6851	313	30	n	n	CCONJ
ejpam-6851	313	31	,	,	PUNCT
ejpam-6851	313	32	(	(	PUNCT
ejpam-6851	313	33	2	2	X
ejpam-6851	313	34	)	)	PUNCT
ejpam-6851	313	35	γw(pm	γw(pm	NOUN
ejpam-6851	313	36	+	+	CCONJ
ejpam-6851	313	37	pn	pn	NOUN
ejpam-6851	313	38	)	)	PUNCT
ejpam-6851	313	39	=	=	PUNCT
ejpam-6851	313	40			NOUN
ejpam-6851	313	41	2	2	NUM
ejpam-6851	313	42	,	,	PUNCT
ejpam-6851	313	43	if	if	SCONJ
ejpam-6851	313	44	m	m	PROPN
ejpam-6851	313	45	=	=	SYM
ejpam-6851	313	46	n	n	CCONJ
ejpam-6851	313	47	;	;	PUNCT
ejpam-6851	313	48	3	3	X
ejpam-6851	313	49	,	,	PUNCT
ejpam-6851	313	50	if	if	SCONJ
ejpam-6851	313	51	m	m	ADV
ejpam-6851	313	52	=	=	SYM
ejpam-6851	313	53	n+	n+	ADP
ejpam-6851	313	54	1	1	NUM
ejpam-6851	313	55	;	;	PUNCT
ejpam-6851	313	56	⌈m3	⌈m3	ADJ
ejpam-6851	313	57	⌉	⌉	NOUN
ejpam-6851	313	58	,	,	PUNCT
ejpam-6851	313	59	if	if	SCONJ
ejpam-6851	313	60	m	m	PROPN
ejpam-6851	313	61	≥	≥	NOUN
ejpam-6851	313	62	n+	n+	NUM
ejpam-6851	313	63	2;m	2;m	NUM
ejpam-6851	313	64	≡	≡	PROPN
ejpam-6851	313	65	1	1	NUM
ejpam-6851	313	66	(	(	PUNCT
ejpam-6851	313	67	mod	mod	NOUN
ejpam-6851	313	68	3	3	NUM
ejpam-6851	313	69	)	)	PUNCT
ejpam-6851	313	70	;	;	PUNCT
ejpam-6851	313	71	⌈m3	⌈m3	ADJ
ejpam-6851	313	72	⌉+	⌉+	NOUN
ejpam-6851	313	73	1	1	NUM
ejpam-6851	313	74	,	,	PUNCT
ejpam-6851	313	75	if	if	SCONJ
ejpam-6851	313	76	m	m	ADJ
ejpam-6851	313	77	≥	≥	NOUN
ejpam-6851	313	78	n+	n+	NUM
ejpam-6851	313	79	2;m	2;m	NUM
ejpam-6851	313	80	≡	≡	PROPN
ejpam-6851	313	81	0	0	NUM
ejpam-6851	313	82	,	,	PUNCT
ejpam-6851	313	83	2	2	NUM
ejpam-6851	313	84	(	(	PUNCT
ejpam-6851	313	85	mod	mod	NOUN
ejpam-6851	313	86	3	3	NUM
ejpam-6851	313	87	)	)	PUNCT
ejpam-6851	313	88	,	,	PUNCT
ejpam-6851	313	89	(	(	PUNCT
ejpam-6851	313	90	3	3	X
ejpam-6851	313	91	)	)	PUNCT
ejpam-6851	313	92	γs(cm	γs(cm	PROPN
ejpam-6851	314	1	+	+	CCONJ
ejpam-6851	314	2	cn	cn	PROPN
ejpam-6851	314	3	)	)	PUNCT
ejpam-6851	314	4	=	=	NOUN
ejpam-6851	314	5	{	{	PUNCT
ejpam-6851	314	6	2	2	NUM
ejpam-6851	314	7	,	,	PUNCT
ejpam-6851	314	8	if	if	SCONJ
ejpam-6851	314	9	m	m	PROPN
ejpam-6851	314	10	=	=	SYM
ejpam-6851	314	11	n	n	CCONJ
ejpam-6851	314	12	;	;	PUNCT
ejpam-6851	314	13	⌈m3	⌈m3	ADJ
ejpam-6851	314	14	⌉	⌉	NOUN
ejpam-6851	314	15	,	,	PUNCT
ejpam-6851	314	16	if	if	SCONJ
ejpam-6851	314	17	m	m	VERB
ejpam-6851	314	18	<	<	X
ejpam-6851	314	19	n	n	CCONJ
ejpam-6851	314	20	,	,	PUNCT
ejpam-6851	314	21	γw(cm	γw(cm	NOUN
ejpam-6851	314	22	+	+	PUNCT
ejpam-6851	315	1	cn	cn	X
ejpam-6851	315	2	)	)	PUNCT
ejpam-6851	315	3	=	=	NOUN
ejpam-6851	315	4	{	{	PUNCT
ejpam-6851	315	5	2	2	NUM
ejpam-6851	315	6	,	,	PUNCT
ejpam-6851	315	7	if	if	SCONJ
ejpam-6851	315	8	m	m	PROPN
ejpam-6851	315	9	=	=	SYM
ejpam-6851	315	10	n	n	CCONJ
ejpam-6851	315	11	;	;	PUNCT
ejpam-6851	315	12	⌈n3	⌈n3	X
ejpam-6851	315	13	⌉	⌉	X
ejpam-6851	315	14	,	,	PUNCT
ejpam-6851	315	15	if	if	SCONJ
ejpam-6851	315	16	m	m	VERB
ejpam-6851	315	17	<	<	X
ejpam-6851	315	18	n	n	CCONJ
ejpam-6851	315	19	;	;	PUNCT
ejpam-6851	315	20	5	5	X
ejpam-6851	315	21	.	.	X
ejpam-6851	315	22	in	in	ADP
ejpam-6851	315	23	the	the	DET
ejpam-6851	315	24	corona	corona	NOUN
ejpam-6851	315	25	of	of	ADP
ejpam-6851	315	26	graphs	graph	NOUN
ejpam-6851	315	27	proposition	proposition	NOUN
ejpam-6851	315	28	3	3	X
ejpam-6851	315	29	.	.	PUNCT
ejpam-6851	316	1	let	let	VERB
ejpam-6851	316	2	g	g	PRON
ejpam-6851	316	3	be	be	AUX
ejpam-6851	316	4	a	a	DET
ejpam-6851	316	5	nontrivial	nontrivial	ADJ
ejpam-6851	316	6	connected	connect	VERB
ejpam-6851	316	7	graph	graph	NOUN
ejpam-6851	316	8	and	and	CCONJ
ejpam-6851	316	9	h	h	NOUN
ejpam-6851	316	10	any	any	DET
ejpam-6851	316	11	graph	graph	NOUN
ejpam-6851	316	12	,	,	PUNCT
ejpam-6851	316	13	and	and	CCONJ
ejpam-6851	316	14	let	let	VERB
ejpam-6851	316	15	s	s	PRON
ejpam-6851	316	16	⊆	⊆	NUM
ejpam-6851	316	17	v	v	NOUN
ejpam-6851	316	18	(	(	PUNCT
ejpam-6851	316	19	g	g	PROPN
ejpam-6851	316	20	◦	◦	NOUN
ejpam-6851	316	21	h	h	NOUN
ejpam-6851	316	22	)	)	PUNCT
ejpam-6851	316	23	.	.	PUNCT
ejpam-6851	317	1	then	then	ADV
ejpam-6851	317	2	s	s	VERB
ejpam-6851	317	3	∈	∈	NOUN
ejpam-6851	317	4	γs(g	γs(g	PUNCT
ejpam-6851	317	5	◦	◦	NOUN
ejpam-6851	317	6	h	h	NOUN
ejpam-6851	317	7	)	)	PUNCT
ejpam-6851	317	8	if	if	SCONJ
ejpam-6851	317	9	and	and	CCONJ
ejpam-6851	317	10	only	only	ADV
ejpam-6851	317	11	if	if	SCONJ
ejpam-6851	317	12	s	s	VERB
ejpam-6851	317	13	=	=	NOUN
ejpam-6851	317	14	a	a	DET
ejpam-6851	317	15	∪	∪	X
ejpam-6851	317	16	(	(	PUNCT
ejpam-6851	317	17	∪v∈v	∪v∈v	X
ejpam-6851	317	18	(	(	PUNCT
ejpam-6851	317	19	g)sv	g)sv	PROPN
ejpam-6851	317	20	)	)	PUNCT
ejpam-6851	317	21	,	,	PUNCT
ejpam-6851	317	22	(	(	PUNCT
ejpam-6851	317	23	1	1	X
ejpam-6851	317	24	)	)	PUNCT
ejpam-6851	317	25	where	where	SCONJ
ejpam-6851	317	26	a	a	DET
ejpam-6851	317	27	⊆	⊆	NUM
ejpam-6851	317	28	v	v	NOUN
ejpam-6851	317	29	(	(	PUNCT
ejpam-6851	317	30	g	g	NOUN
ejpam-6851	317	31	)	)	PUNCT
ejpam-6851	317	32	and	and	CCONJ
ejpam-6851	317	33	sv	sv	X
ejpam-6851	317	34	⊆	⊆	NUM
ejpam-6851	317	35	v	v	X
ejpam-6851	317	36	(	(	PUNCT
ejpam-6851	317	37	hv	hv	NOUN
ejpam-6851	317	38	)	)	PUNCT
ejpam-6851	317	39	such	such	ADJ
ejpam-6851	317	40	that	that	SCONJ
ejpam-6851	317	41	the	the	DET
ejpam-6851	317	42	following	follow	VERB
ejpam-6851	317	43	hold	hold	NOUN
ejpam-6851	317	44	:	:	PUNCT
ejpam-6851	317	45	(	(	PUNCT
ejpam-6851	317	46	i	i	NOUN
ejpam-6851	317	47	)	)	PUNCT
ejpam-6851	317	48	a	a	DET
ejpam-6851	317	49	∈	∈	NOUN
ejpam-6851	317	50	γs(g	γs(g	NUM
ejpam-6851	317	51	)	)	PUNCT
ejpam-6851	317	52	;	;	PUNCT
ejpam-6851	317	53	and	and	CCONJ
ejpam-6851	317	54	(	(	PUNCT
ejpam-6851	317	55	ii	ii	NOUN
ejpam-6851	317	56	)	)	PUNCT
ejpam-6851	317	57	for	for	ADP
ejpam-6851	317	58	each	each	DET
ejpam-6851	317	59	v	v	NUM
ejpam-6851	317	60	∈	∈	PROPN
ejpam-6851	317	61	v	v	NOUN
ejpam-6851	317	62	(	(	PUNCT
ejpam-6851	317	63	g	g	NOUN
ejpam-6851	317	64	)	)	PUNCT
ejpam-6851	317	65	\a	\a	ADJ
ejpam-6851	317	66	,	,	PUNCT
ejpam-6851	317	67	sv	sv	PROPN
ejpam-6851	317	68	∈	∈	PROPN
ejpam-6851	317	69	γs(h	γs(h	PUNCT
ejpam-6851	317	70	v	v	NOUN
ejpam-6851	317	71	)	)	PUNCT
ejpam-6851	317	72	.	.	PUNCT
ejpam-6851	318	1	proof	proof	NOUN
ejpam-6851	318	2	.	.	PUNCT
ejpam-6851	319	1	assume	assume	VERB
ejpam-6851	319	2	that	that	SCONJ
ejpam-6851	319	3	s	s	VERB
ejpam-6851	319	4	∈	∈	NOUN
ejpam-6851	319	5	γs(g	γs(g	PUNCT
ejpam-6851	319	6	◦	◦	NOUN
ejpam-6851	319	7	h	h	NOUN
ejpam-6851	319	8	)	)	PUNCT
ejpam-6851	319	9	.	.	PUNCT
ejpam-6851	320	1	put	put	VERB
ejpam-6851	320	2	a	a	DET
ejpam-6851	320	3	=	=	SYM
ejpam-6851	320	4	s	s	NOUN
ejpam-6851	320	5	∩	∩	ADJ
ejpam-6851	320	6	v	v	X
ejpam-6851	320	7	(	(	PUNCT
ejpam-6851	320	8	g	g	NOUN
ejpam-6851	320	9	)	)	PUNCT
ejpam-6851	320	10	and	and	CCONJ
ejpam-6851	320	11	sv	sv	X
ejpam-6851	320	12	=	=	PUNCT
ejpam-6851	320	13	a	a	DET
ejpam-6851	320	14	∩	∩	ADJ
ejpam-6851	320	15	v	v	NOUN
ejpam-6851	320	16	(	(	PUNCT
ejpam-6851	320	17	hv	hv	PROPN
ejpam-6851	320	18	)	)	PUNCT
ejpam-6851	320	19	for	for	ADP
ejpam-6851	320	20	all	all	PRON
ejpam-6851	320	21	v	v	ADP
ejpam-6851	320	22	∈	∈	NOUN
ejpam-6851	320	23	v	v	NOUN
ejpam-6851	320	24	(	(	PUNCT
ejpam-6851	320	25	g	g	NOUN
ejpam-6851	320	26	)	)	PUNCT
ejpam-6851	320	27	.	.	PUNCT
ejpam-6851	321	1	then	then	ADV
ejpam-6851	321	2	equation	equation	NOUN
ejpam-6851	321	3	1	1	NUM
ejpam-6851	321	4	holds	hold	VERB
ejpam-6851	321	5	.	.	PUNCT
ejpam-6851	322	1	to	to	PART
ejpam-6851	322	2	prove	prove	VERB
ejpam-6851	322	3	(	(	PUNCT
ejpam-6851	322	4	i	i	NOUN
ejpam-6851	322	5	)	)	PUNCT
ejpam-6851	322	6	,	,	PUNCT
ejpam-6851	322	7	let	let	VERB
ejpam-6851	322	8	v	v	NUM
ejpam-6851	322	9	∈	∈	PROPN
ejpam-6851	322	10	v	v	NOUN
ejpam-6851	322	11	(	(	PUNCT
ejpam-6851	322	12	g	g	NOUN
ejpam-6851	322	13	)	)	PUNCT
ejpam-6851	322	14	\a	\a	ADJ
ejpam-6851	322	15	.	.	PUNCT
ejpam-6851	323	1	there	there	PRON
ejpam-6851	323	2	exists	exist	VERB
ejpam-6851	323	3	u	u	PROPN
ejpam-6851	323	4	∈	∈	PROPN
ejpam-6851	323	5	s	s	X
ejpam-6851	323	6	for	for	ADP
ejpam-6851	323	7	which	which	PRON
ejpam-6851	323	8	v	v	ADP
ejpam-6851	323	9	≼g	≼g	PROPN
ejpam-6851	323	10	◦	◦	NOUN
ejpam-6851	323	11	h	h	NOUN
ejpam-6851	323	12	u.	u.	NOUN
ejpam-6851	323	13	since	since	SCONJ
ejpam-6851	323	14	degg	degg	NOUN
ejpam-6851	323	15	◦	◦	NOUN
ejpam-6851	323	16	h(v	h(v	PROPN
ejpam-6851	323	17	)	)	PUNCT
ejpam-6851	323	18	>	>	X
ejpam-6851	323	19	degg	degg	NOUN
ejpam-6851	323	20	◦	◦	PROPN
ejpam-6851	323	21	h(w	h(w	PROPN
ejpam-6851	323	22	)	)	PUNCT
ejpam-6851	323	23	for	for	ADP
ejpam-6851	323	24	all	all	DET
ejpam-6851	323	25	w	w	PROPN
ejpam-6851	323	26	∈	∈	PROPN
ejpam-6851	323	27	v	v	ADP
ejpam-6851	323	28	(	(	PUNCT
ejpam-6851	323	29	hv	hv	PROPN
ejpam-6851	323	30	)	)	PUNCT
ejpam-6851	323	31	,	,	PUNCT
ejpam-6851	323	32	u	u	PROPN
ejpam-6851	323	33	/∈	/∈	PUNCT
ejpam-6851	323	34	sv	sv	INTJ
ejpam-6851	323	35	.	.	PUNCT
ejpam-6851	324	1	hence	hence	ADV
ejpam-6851	324	2	,	,	PUNCT
ejpam-6851	324	3	u	u	PROPN
ejpam-6851	324	4	∈	∈	PROPN
ejpam-6851	324	5	a.	a.	NOUN
ejpam-6851	324	6	this	this	PRON
ejpam-6851	324	7	means	mean	VERB
ejpam-6851	324	8	that	that	SCONJ
ejpam-6851	324	9	v	v	X
ejpam-6851	324	10	≼g	≼g	PROPN
ejpam-6851	324	11	a.	a.	NOUN
ejpam-6851	324	12	thus	thus	ADV
ejpam-6851	324	13	,	,	PUNCT
ejpam-6851	324	14	a	a	DET
ejpam-6851	324	15	∈	∈	NOUN
ejpam-6851	324	16	γs(g	γs(g	NUM
ejpam-6851	324	17	)	)	PUNCT
ejpam-6851	324	18	,	,	PUNCT
ejpam-6851	324	19	and	and	CCONJ
ejpam-6851	324	20	(	(	PUNCT
ejpam-6851	324	21	i	i	NOUN
ejpam-6851	324	22	)	)	PUNCT
ejpam-6851	324	23	holds	hold	VERB
ejpam-6851	324	24	.	.	PUNCT
ejpam-6851	325	1	to	to	PART
ejpam-6851	325	2	prove	prove	VERB
ejpam-6851	325	3	(	(	PUNCT
ejpam-6851	325	4	ii	ii	NOUN
ejpam-6851	325	5	)	)	PUNCT
ejpam-6851	325	6	,	,	PUNCT
ejpam-6851	325	7	let	let	VERB
ejpam-6851	325	8	v	v	NUM
ejpam-6851	325	9	∈	∈	PROPN
ejpam-6851	325	10	v	v	NOUN
ejpam-6851	325	11	(	(	PUNCT
ejpam-6851	325	12	g	g	NOUN
ejpam-6851	325	13	)	)	PUNCT
ejpam-6851	325	14	\a	\a	VERB
ejpam-6851	325	15	j.	j.	PROPN
ejpam-6851	325	16	m.	m.	PROPN
ejpam-6851	325	17	molles	molles	PROPN
ejpam-6851	325	18	,	,	PUNCT
ejpam-6851	325	19	f.	f.	PROPN
ejpam-6851	325	20	p.	p.	PROPN
ejpam-6851	325	21	jamil	jamil	PROPN
ejpam-6851	325	22	,	,	PUNCT
ejpam-6851	325	23	s.	s.	PROPN
ejpam-6851	325	24	r.	r.	PROPN
ejpam-6851	325	25	canoy	canoy	PROPN
ejpam-6851	325	26	/	/	SYM
ejpam-6851	325	27	eur	eur	PROPN
ejpam-6851	325	28	.	.	PUNCT
ejpam-6851	326	1	j.	j.	PROPN
ejpam-6851	326	2	pure	pure	PROPN
ejpam-6851	326	3	appl	appl	PROPN
ejpam-6851	326	4	.	.	PROPN
ejpam-6851	326	5	math	math	PROPN
ejpam-6851	326	6	,	,	PUNCT
ejpam-6851	326	7	18	18	NUM
ejpam-6851	326	8	(	(	PUNCT
ejpam-6851	326	9	4	4	NUM
ejpam-6851	326	10	)	)	PUNCT
ejpam-6851	326	11	(	(	PUNCT
ejpam-6851	326	12	2025	2025	NUM
ejpam-6851	326	13	)	)	PUNCT
ejpam-6851	326	14	,	,	PUNCT
ejpam-6851	326	15	6851	6851	NUM
ejpam-6851	326	16	10	10	NUM
ejpam-6851	326	17	of	of	ADP
ejpam-6851	326	18	18	18	NUM
ejpam-6851	327	1	and	and	CCONJ
ejpam-6851	327	2	let	let	VERB
ejpam-6851	327	3	u	u	PRON
ejpam-6851	327	4	∈	∈	PROPN
ejpam-6851	327	5	v	v	X
ejpam-6851	327	6	(	(	PUNCT
ejpam-6851	327	7	hv	hv	PROPN
ejpam-6851	327	8	)	)	PUNCT
ejpam-6851	327	9	\	\	PROPN
ejpam-6851	328	1	sv	sv	PROPN
ejpam-6851	328	2	.	.	PUNCT
ejpam-6851	329	1	there	there	PRON
ejpam-6851	329	2	exists	exist	VERB
ejpam-6851	329	3	w	w	PROPN
ejpam-6851	329	4	∈	∈	PROPN
ejpam-6851	329	5	s	s	NOUN
ejpam-6851	329	6	for	for	ADP
ejpam-6851	329	7	which	which	PRON
ejpam-6851	329	8	u	u	PROPN
ejpam-6851	329	9	≼g	≼g	PROPN
ejpam-6851	329	10	◦	◦	NOUN
ejpam-6851	329	11	h	h	PROPN
ejpam-6851	329	12	w.	w.	NOUN
ejpam-6851	329	13	since	since	SCONJ
ejpam-6851	329	14	w	w	PROPN
ejpam-6851	329	15	̸=	̸=	PROPN
ejpam-6851	329	16	v	v	NOUN
ejpam-6851	329	17	,	,	PUNCT
ejpam-6851	329	18	w	w	PROPN
ejpam-6851	329	19	∈	∈	PROPN
ejpam-6851	329	20	sv	sv	PROPN
ejpam-6851	329	21	.	.	PUNCT
ejpam-6851	330	1	thus	thus	ADV
ejpam-6851	330	2	,	,	PUNCT
ejpam-6851	330	3	u	u	PROPN
ejpam-6851	330	4	≼hv	≼hv	X
ejpam-6851	330	5	sv	sv	PROPN
ejpam-6851	330	6	.	.	PUNCT
ejpam-6851	331	1	therefore	therefore	ADV
ejpam-6851	331	2	,	,	PUNCT
ejpam-6851	331	3	sv	sv	PROPN
ejpam-6851	331	4	∈	∈	PROPN
ejpam-6851	331	5	γs(h	γs(h	PUNCT
ejpam-6851	331	6	v	v	NOUN
ejpam-6851	331	7	)	)	PUNCT
ejpam-6851	331	8	,	,	PUNCT
ejpam-6851	331	9	and	and	CCONJ
ejpam-6851	331	10	(	(	PUNCT
ejpam-6851	331	11	ii	ii	NOUN
ejpam-6851	331	12	)	)	PUNCT
ejpam-6851	331	13	holds	hold	VERB
ejpam-6851	331	14	.	.	PUNCT
ejpam-6851	332	1	conversely	conversely	ADV
ejpam-6851	332	2	,	,	PUNCT
ejpam-6851	332	3	suppose	suppose	VERB
ejpam-6851	332	4	that	that	SCONJ
ejpam-6851	332	5	equation	equation	NOUN
ejpam-6851	332	6	1	1	NUM
ejpam-6851	332	7	holds	hold	VERB
ejpam-6851	332	8	for	for	ADP
ejpam-6851	332	9	s	s	PRON
ejpam-6851	332	10	together	together	ADV
ejpam-6851	332	11	with	with	ADP
ejpam-6851	332	12	conditions	condition	NOUN
ejpam-6851	332	13	(	(	PUNCT
ejpam-6851	332	14	i	i	NOUN
ejpam-6851	332	15	)	)	PUNCT
ejpam-6851	332	16	and	and	CCONJ
ejpam-6851	332	17	(	(	PUNCT
ejpam-6851	332	18	ii	ii	NOUN
ejpam-6851	332	19	)	)	PUNCT
ejpam-6851	332	20	.	.	PUNCT
ejpam-6851	333	1	let	let	VERB
ejpam-6851	333	2	w	w	NOUN
ejpam-6851	333	3	∈	∈	PROPN
ejpam-6851	333	4	v	v	NOUN
ejpam-6851	333	5	(	(	PUNCT
ejpam-6851	333	6	g	g	PROPN
ejpam-6851	333	7	◦	◦	NOUN
ejpam-6851	333	8	h	h	NOUN
ejpam-6851	333	9	)	)	PUNCT
ejpam-6851	333	10	\	\	PROPN
ejpam-6851	334	1	s	s	PROPN
ejpam-6851	334	2	,	,	PUNCT
ejpam-6851	334	3	and	and	CCONJ
ejpam-6851	334	4	let	let	VERB
ejpam-6851	334	5	v	v	NUM
ejpam-6851	334	6	∈	∈	PROPN
ejpam-6851	334	7	v	v	NOUN
ejpam-6851	334	8	(	(	PUNCT
ejpam-6851	334	9	g	g	NOUN
ejpam-6851	334	10	)	)	PUNCT
ejpam-6851	334	11	for	for	ADP
ejpam-6851	334	12	which	which	PRON
ejpam-6851	334	13	w	w	PROPN
ejpam-6851	334	14	∈	∈	PROPN
ejpam-6851	334	15	v	v	X
ejpam-6851	334	16	(	(	PUNCT
ejpam-6851	334	17	hv	hv	PROPN
ejpam-6851	334	18	+	+	PROPN
ejpam-6851	334	19	v	v	NOUN
ejpam-6851	334	20	)	)	PUNCT
ejpam-6851	334	21	.	.	PUNCT
ejpam-6851	335	1	if	if	SCONJ
ejpam-6851	335	2	w	w	PROPN
ejpam-6851	335	3	∈	∈	PROPN
ejpam-6851	335	4	v	v	ADP
ejpam-6851	335	5	(	(	PUNCT
ejpam-6851	335	6	hv	hv	NOUN
ejpam-6851	335	7	)	)	PUNCT
ejpam-6851	335	8	and	and	CCONJ
ejpam-6851	335	9	v	v	ADP
ejpam-6851	335	10	∈	∈	PROPN
ejpam-6851	335	11	a	a	PRON
ejpam-6851	335	12	,	,	PUNCT
ejpam-6851	335	13	then	then	ADV
ejpam-6851	335	14	w	w	PROPN
ejpam-6851	335	15	≼g	≼g	PROPN
ejpam-6851	335	16	◦	◦	NOUN
ejpam-6851	335	17	h	h	NOUN
ejpam-6851	335	18	s.	s.	PROPN
ejpam-6851	335	19	on	on	ADP
ejpam-6851	335	20	the	the	DET
ejpam-6851	335	21	other	other	ADJ
ejpam-6851	335	22	hand	hand	NOUN
ejpam-6851	335	23	,	,	PUNCT
ejpam-6851	335	24	if	if	SCONJ
ejpam-6851	335	25	w	w	PROPN
ejpam-6851	335	26	∈	∈	PROPN
ejpam-6851	335	27	v	v	ADP
ejpam-6851	335	28	(	(	PUNCT
ejpam-6851	335	29	hv	hv	PROPN
ejpam-6851	335	30	)	)	PUNCT
ejpam-6851	335	31	and	and	CCONJ
ejpam-6851	335	32	v	v	ADP
ejpam-6851	335	33	/∈	/∈	PROPN
ejpam-6851	335	34	a	a	PRON
ejpam-6851	335	35	,	,	PUNCT
ejpam-6851	335	36	then	then	ADV
ejpam-6851	335	37	w	w	PROPN
ejpam-6851	335	38	≼hv	≼hv	NOUN
ejpam-6851	335	39	sv	sv	INTJ
ejpam-6851	335	40	by	by	ADP
ejpam-6851	335	41	(	(	PUNCT
ejpam-6851	335	42	ii	ii	NOUN
ejpam-6851	335	43	)	)	PUNCT
ejpam-6851	335	44	so	so	SCONJ
ejpam-6851	335	45	that	that	SCONJ
ejpam-6851	335	46	w	w	PROPN
ejpam-6851	335	47	≼g	≼g	PROPN
ejpam-6851	335	48	◦	◦	NOUN
ejpam-6851	335	49	h	h	NOUN
ejpam-6851	335	50	s.	s.	PROPN
ejpam-6851	335	51	suppose	suppose	VERB
ejpam-6851	335	52	that	that	SCONJ
ejpam-6851	335	53	w	w	PROPN
ejpam-6851	335	54	=	=	PUNCT
ejpam-6851	335	55	v.	v.	PROPN
ejpam-6851	335	56	by	by	ADP
ejpam-6851	335	57	(	(	PUNCT
ejpam-6851	335	58	i	i	NOUN
ejpam-6851	335	59	)	)	PUNCT
ejpam-6851	335	60	,	,	PUNCT
ejpam-6851	335	61	w	w	PROPN
ejpam-6851	335	62	≼g	≼g	PROPN
ejpam-6851	335	63	a	a	PRON
ejpam-6851	335	64	and	and	CCONJ
ejpam-6851	335	65	,	,	PUNCT
ejpam-6851	335	66	consequently	consequently	ADV
ejpam-6851	335	67	,	,	PUNCT
ejpam-6851	335	68	w	w	PROPN
ejpam-6851	335	69	≼g	≼g	PROPN
ejpam-6851	335	70	◦	◦	NOUN
ejpam-6851	335	71	h	h	NOUN
ejpam-6851	335	72	a.	a.	NOUN
ejpam-6851	335	73	thus	thus	ADV
ejpam-6851	335	74	,	,	PUNCT
ejpam-6851	335	75	w	w	PROPN
ejpam-6851	335	76	≼g	≼g	PROPN
ejpam-6851	335	77	◦	◦	NOUN
ejpam-6851	335	78	h	h	NOUN
ejpam-6851	335	79	s.	s.	PROPN
ejpam-6851	335	80	accordingly	accordingly	ADV
ejpam-6851	335	81	,	,	PUNCT
ejpam-6851	335	82	s	s	PROPN
ejpam-6851	335	83	∈	∈	NOUN
ejpam-6851	335	84	γs(g	γs(g	PUNCT
ejpam-6851	335	85	◦	◦	NOUN
ejpam-6851	335	86	h	h	NOUN
ejpam-6851	335	87	)	)	PUNCT
ejpam-6851	335	88	.	.	PUNCT
ejpam-6851	336	1	proposition	proposition	NOUN
ejpam-6851	336	2	4	4	NUM
ejpam-6851	336	3	.	.	PUNCT
ejpam-6851	337	1	let	let	VERB
ejpam-6851	337	2	g	g	PRON
ejpam-6851	337	3	be	be	AUX
ejpam-6851	337	4	a	a	DET
ejpam-6851	337	5	nontrivial	nontrivial	ADJ
ejpam-6851	337	6	connected	connect	VERB
ejpam-6851	337	7	graph	graph	NOUN
ejpam-6851	337	8	and	and	CCONJ
ejpam-6851	337	9	h	h	NOUN
ejpam-6851	337	10	any	any	DET
ejpam-6851	337	11	graph	graph	NOUN
ejpam-6851	337	12	,	,	PUNCT
ejpam-6851	337	13	and	and	CCONJ
ejpam-6851	337	14	let	let	VERB
ejpam-6851	337	15	s	s	PRON
ejpam-6851	337	16	⊆	⊆	NUM
ejpam-6851	337	17	v	v	NOUN
ejpam-6851	337	18	(	(	PUNCT
ejpam-6851	337	19	g	g	PROPN
ejpam-6851	337	20	◦	◦	NOUN
ejpam-6851	337	21	h	h	NOUN
ejpam-6851	337	22	)	)	PUNCT
ejpam-6851	337	23	.	.	PUNCT
ejpam-6851	338	1	then	then	ADV
ejpam-6851	338	2	s	s	VERB
ejpam-6851	338	3	∈	∈	NOUN
ejpam-6851	338	4	γw(g	γw(g	PUNCT
ejpam-6851	338	5	◦	◦	NOUN
ejpam-6851	338	6	h	h	NOUN
ejpam-6851	338	7	)	)	PUNCT
ejpam-6851	338	8	if	if	SCONJ
ejpam-6851	338	9	and	and	CCONJ
ejpam-6851	338	10	only	only	ADV
ejpam-6851	338	11	if	if	SCONJ
ejpam-6851	338	12	s	s	VERB
ejpam-6851	338	13	=	=	NOUN
ejpam-6851	338	14	a	a	DET
ejpam-6851	338	15	∪	∪	X
ejpam-6851	338	16	(	(	PUNCT
ejpam-6851	338	17	∪v∈v	∪v∈v	X
ejpam-6851	338	18	(	(	PUNCT
ejpam-6851	338	19	g)sv	g)sv	PROPN
ejpam-6851	338	20	)	)	PUNCT
ejpam-6851	338	21	,	,	PUNCT
ejpam-6851	338	22	where	where	SCONJ
ejpam-6851	338	23	a	a	DET
ejpam-6851	338	24	⊆	⊆	NUM
ejpam-6851	338	25	v	v	NOUN
ejpam-6851	338	26	(	(	PUNCT
ejpam-6851	338	27	g	g	NOUN
ejpam-6851	338	28	)	)	PUNCT
ejpam-6851	338	29	and	and	CCONJ
ejpam-6851	338	30	sv	sv	ADP
ejpam-6851	338	31	∈	∈	PROPN
ejpam-6851	338	32	γw(h	γw(h	PUNCT
ejpam-6851	338	33	v	v	NOUN
ejpam-6851	338	34	)	)	PUNCT
ejpam-6851	338	35	for	for	ADP
ejpam-6851	338	36	each	each	DET
ejpam-6851	338	37	v	v	NUM
ejpam-6851	338	38	∈	∈	PROPN
ejpam-6851	338	39	v	v	NOUN
ejpam-6851	338	40	(	(	PUNCT
ejpam-6851	338	41	g	g	NOUN
ejpam-6851	338	42	)	)	PUNCT
ejpam-6851	338	43	.	.	PUNCT
ejpam-6851	339	1	proof	proof	NOUN
ejpam-6851	339	2	.	.	PUNCT
ejpam-6851	340	1	suppose	suppose	VERB
ejpam-6851	340	2	that	that	SCONJ
ejpam-6851	340	3	s	s	VERB
ejpam-6851	340	4	∈	∈	NOUN
ejpam-6851	340	5	γw(g	γw(g	PUNCT
ejpam-6851	340	6	◦	◦	NOUN
ejpam-6851	340	7	h	h	NOUN
ejpam-6851	340	8	)	)	PUNCT
ejpam-6851	340	9	.	.	PUNCT
ejpam-6851	341	1	then	then	ADV
ejpam-6851	341	2	s	s	VERB
ejpam-6851	341	3	=	=	SYM
ejpam-6851	341	4	a∪	a∪	PROPN
ejpam-6851	341	5	(	(	PUNCT
ejpam-6851	341	6	∪v∈v	∪v∈v	X
ejpam-6851	341	7	(	(	PUNCT
ejpam-6851	341	8	g)sv	g)sv	PROPN
ejpam-6851	341	9	)	)	PUNCT
ejpam-6851	341	10	,	,	PUNCT
ejpam-6851	341	11	where	where	SCONJ
ejpam-6851	341	12	a	a	DET
ejpam-6851	341	13	=	=	SYM
ejpam-6851	341	14	s	s	NOUN
ejpam-6851	341	15	∩v	∩v	NOUN
ejpam-6851	341	16	(	(	PUNCT
ejpam-6851	341	17	g	g	NOUN
ejpam-6851	341	18	)	)	PUNCT
ejpam-6851	341	19	and	and	CCONJ
ejpam-6851	341	20	sv	sv	X
ejpam-6851	341	21	=	=	SYM
ejpam-6851	341	22	s	s	PROPN
ejpam-6851	341	23	∩	∩	ADJ
ejpam-6851	341	24	v	v	X
ejpam-6851	341	25	(	(	PUNCT
ejpam-6851	341	26	hv	hv	PROPN
ejpam-6851	341	27	)	)	PUNCT
ejpam-6851	341	28	for	for	ADP
ejpam-6851	341	29	each	each	DET
ejpam-6851	341	30	v	v	NUM
ejpam-6851	341	31	∈	∈	PROPN
ejpam-6851	341	32	v	v	NOUN
ejpam-6851	341	33	(	(	PUNCT
ejpam-6851	341	34	g	g	NOUN
ejpam-6851	341	35	)	)	PUNCT
ejpam-6851	341	36	.	.	PUNCT
ejpam-6851	342	1	let	let	VERB
ejpam-6851	342	2	v	v	NUM
ejpam-6851	342	3	∈	∈	PROPN
ejpam-6851	342	4	v	v	NOUN
ejpam-6851	342	5	(	(	PUNCT
ejpam-6851	342	6	g	g	NOUN
ejpam-6851	342	7	)	)	PUNCT
ejpam-6851	342	8	,	,	PUNCT
ejpam-6851	342	9	and	and	CCONJ
ejpam-6851	342	10	let	let	VERB
ejpam-6851	342	11	x	x	SYM
ejpam-6851	342	12	∈	∈	PROPN
ejpam-6851	342	13	v	v	ADP
ejpam-6851	342	14	(	(	PUNCT
ejpam-6851	342	15	hv	hv	PROPN
ejpam-6851	342	16	)	)	PUNCT
ejpam-6851	342	17	\	\	PROPN
ejpam-6851	343	1	sv	sv	PROPN
ejpam-6851	343	2	.	.	PUNCT
ejpam-6851	344	1	there	there	PRON
ejpam-6851	344	2	exists	exist	VERB
ejpam-6851	344	3	y	y	PROPN
ejpam-6851	344	4	∈	∈	PROPN
ejpam-6851	344	5	s	s	X
ejpam-6851	344	6	for	for	ADP
ejpam-6851	344	7	which	which	PRON
ejpam-6851	344	8	x	x	PUNCT
ejpam-6851	344	9	≽g	≽g	NOUN
ejpam-6851	344	10	◦	◦	NOUN
ejpam-6851	344	11	h	h	NOUN
ejpam-6851	344	12	y.	y.	NOUN
ejpam-6851	344	13	since	since	SCONJ
ejpam-6851	344	14	degg	degg	NOUN
ejpam-6851	344	15	◦	◦	NOUN
ejpam-6851	344	16	h(x	h(x	PROPN
ejpam-6851	344	17	)	)	PUNCT
ejpam-6851	344	18	<	<	X
ejpam-6851	344	19	degg	degg	NOUN
ejpam-6851	344	20	◦	◦	NOUN
ejpam-6851	344	21	h(v	h(v	PROPN
ejpam-6851	344	22	)	)	PUNCT
ejpam-6851	344	23	,	,	PUNCT
ejpam-6851	344	24	y	y	PROPN
ejpam-6851	344	25	∈	∈	PROPN
ejpam-6851	344	26	sv	sv	INTJ
ejpam-6851	344	27	and	and	CCONJ
ejpam-6851	344	28	x	x	ADP
ejpam-6851	344	29	≽hv	≽hv	PROPN
ejpam-6851	344	30	y.	y.	PROPN
ejpam-6851	344	31	thus	thus	ADV
ejpam-6851	344	32	,	,	PUNCT
ejpam-6851	344	33	sv	sv	PROPN
ejpam-6851	344	34	∈	∈	PROPN
ejpam-6851	344	35	γw(h	γw(h	PUNCT
ejpam-6851	344	36	v	v	NOUN
ejpam-6851	344	37	)	)	PUNCT
ejpam-6851	344	38	.	.	PUNCT
ejpam-6851	345	1	conversely	conversely	ADV
ejpam-6851	345	2	,	,	PUNCT
ejpam-6851	345	3	suppose	suppose	VERB
ejpam-6851	345	4	that	that	SCONJ
ejpam-6851	345	5	s	s	VERB
ejpam-6851	345	6	=	=	PUNCT
ejpam-6851	345	7	a	a	DET
ejpam-6851	345	8	∪	∪	X
ejpam-6851	345	9	(	(	PUNCT
ejpam-6851	345	10	∪v∈v	∪v∈v	X
ejpam-6851	345	11	(	(	PUNCT
ejpam-6851	345	12	g)sv	g)sv	PROPN
ejpam-6851	345	13	)	)	PUNCT
ejpam-6851	345	14	,	,	PUNCT
ejpam-6851	345	15	where	where	SCONJ
ejpam-6851	345	16	a	a	DET
ejpam-6851	345	17	⊆	⊆	NUM
ejpam-6851	345	18	v	v	NOUN
ejpam-6851	345	19	(	(	PUNCT
ejpam-6851	345	20	g	g	NOUN
ejpam-6851	345	21	)	)	PUNCT
ejpam-6851	345	22	and	and	CCONJ
ejpam-6851	345	23	sv	sv	ADP
ejpam-6851	345	24	∈	∈	PROPN
ejpam-6851	345	25	γw(h	γw(h	PUNCT
ejpam-6851	345	26	v	v	NOUN
ejpam-6851	345	27	)	)	PUNCT
ejpam-6851	345	28	for	for	ADP
ejpam-6851	345	29	each	each	DET
ejpam-6851	345	30	v	v	NUM
ejpam-6851	345	31	∈	∈	PROPN
ejpam-6851	345	32	v	v	NOUN
ejpam-6851	345	33	(	(	PUNCT
ejpam-6851	345	34	g	g	NOUN
ejpam-6851	345	35	)	)	PUNCT
ejpam-6851	345	36	.	.	PUNCT
ejpam-6851	346	1	let	let	VERB
ejpam-6851	346	2	x	x	SYM
ejpam-6851	346	3	∈	∈	PROPN
ejpam-6851	346	4	v	v	X
ejpam-6851	346	5	(	(	PUNCT
ejpam-6851	346	6	g	g	PROPN
ejpam-6851	346	7	◦	◦	NOUN
ejpam-6851	346	8	h	h	NOUN
ejpam-6851	346	9	)	)	PUNCT
ejpam-6851	346	10	\	\	PROPN
ejpam-6851	347	1	s	s	PROPN
ejpam-6851	347	2	,	,	PUNCT
ejpam-6851	347	3	and	and	CCONJ
ejpam-6851	347	4	let	let	VERB
ejpam-6851	347	5	v	v	NUM
ejpam-6851	347	6	∈	∈	PROPN
ejpam-6851	347	7	v	v	NOUN
ejpam-6851	347	8	(	(	PUNCT
ejpam-6851	347	9	g	g	NOUN
ejpam-6851	347	10	)	)	PUNCT
ejpam-6851	347	11	such	such	ADJ
ejpam-6851	347	12	that	that	SCONJ
ejpam-6851	347	13	x	x	SYM
ejpam-6851	347	14	∈	∈	NOUN
ejpam-6851	347	15	v	v	X
ejpam-6851	347	16	(	(	PUNCT
ejpam-6851	347	17	hv	hv	PROPN
ejpam-6851	347	18	+	+	PROPN
ejpam-6851	347	19	v	v	NOUN
ejpam-6851	347	20	)	)	PUNCT
ejpam-6851	347	21	.	.	PUNCT
ejpam-6851	348	1	note	note	VERB
ejpam-6851	348	2	that	that	SCONJ
ejpam-6851	348	3	sv	sv	PROPN
ejpam-6851	348	4	̸=	̸=	PROPN
ejpam-6851	348	5	∅.	∅.	VERB
ejpam-6851	348	6	if	if	SCONJ
ejpam-6851	348	7	x	x	PROPN
ejpam-6851	348	8	=	=	SYM
ejpam-6851	348	9	v	v	NOUN
ejpam-6851	348	10	,	,	PUNCT
ejpam-6851	348	11	then	then	ADV
ejpam-6851	348	12	pick	pick	VERB
ejpam-6851	348	13	any	any	DET
ejpam-6851	348	14	w	w	PROPN
ejpam-6851	348	15	∈	∈	PROPN
ejpam-6851	348	16	sv	sv	PROPN
ejpam-6851	348	17	.	.	PUNCT
ejpam-6851	349	1	then	then	ADV
ejpam-6851	349	2	x	x	PUNCT
ejpam-6851	349	3	≽g	≽g	PROPN
ejpam-6851	349	4	◦	◦	NOUN
ejpam-6851	349	5	h	h	NOUN
ejpam-6851	349	6	w.	w.	NOUN
ejpam-6851	349	7	if	if	SCONJ
ejpam-6851	349	8	x	x	PROPN
ejpam-6851	349	9	̸=	̸=	PROPN
ejpam-6851	349	10	v	v	NOUN
ejpam-6851	349	11	,	,	PUNCT
ejpam-6851	349	12	then	then	ADV
ejpam-6851	349	13	x	x	SYM
ejpam-6851	349	14	∈	∈	PROPN
ejpam-6851	349	15	v	v	ADP
ejpam-6851	349	16	(	(	PUNCT
ejpam-6851	349	17	hv	hv	PROPN
ejpam-6851	349	18	)	)	PUNCT
ejpam-6851	349	19	\	\	PROPN
ejpam-6851	350	1	sv	sv	PROPN
ejpam-6851	350	2	,	,	PUNCT
ejpam-6851	350	3	and	and	CCONJ
ejpam-6851	350	4	there	there	PRON
ejpam-6851	350	5	exists	exist	VERB
ejpam-6851	350	6	y	y	PROPN
ejpam-6851	350	7	∈	∈	PROPN
ejpam-6851	350	8	sv	sv	INTJ
ejpam-6851	350	9	such	such	ADJ
ejpam-6851	350	10	that	that	SCONJ
ejpam-6851	350	11	x	x	PRON
ejpam-6851	350	12	≽hv	≽hv	VERB
ejpam-6851	350	13	y.	y.	NOUN
ejpam-6851	350	14	this	this	PRON
ejpam-6851	350	15	means	mean	VERB
ejpam-6851	350	16	x	x	PUNCT
ejpam-6851	350	17	≽g	≽g	PROPN
ejpam-6851	350	18	◦	◦	NOUN
ejpam-6851	350	19	h	h	NOUN
ejpam-6851	350	20	y.	y.	NOUN
ejpam-6851	350	21	therefore	therefore	ADV
ejpam-6851	350	22	,	,	PUNCT
ejpam-6851	350	23	s	s	PROPN
ejpam-6851	350	24	∈	∈	NOUN
ejpam-6851	350	25	γw(g	γw(g	PUNCT
ejpam-6851	350	26	◦	◦	NOUN
ejpam-6851	350	27	h	h	NOUN
ejpam-6851	350	28	)	)	PUNCT
ejpam-6851	350	29	.	.	PUNCT
ejpam-6851	351	1	corollary	corollary	ADJ
ejpam-6851	351	2	3	3	X
ejpam-6851	351	3	.	.	PUNCT
ejpam-6851	352	1	if	if	SCONJ
ejpam-6851	352	2	g	g	PROPN
ejpam-6851	352	3	is	be	AUX
ejpam-6851	352	4	a	a	DET
ejpam-6851	352	5	connected	connected	ADJ
ejpam-6851	352	6	graph	graph	NOUN
ejpam-6851	352	7	of	of	ADP
ejpam-6851	352	8	order	order	NOUN
ejpam-6851	352	9	n	n	PRON
ejpam-6851	352	10	≥	≥	NOUN
ejpam-6851	352	11	2	2	NUM
ejpam-6851	352	12	.	.	PUNCT
ejpam-6851	353	1	then	then	ADV
ejpam-6851	353	2	(	(	PUNCT
ejpam-6851	353	3	i	i	NOUN
ejpam-6851	353	4	)	)	PUNCT
ejpam-6851	354	1	[	[	X
ejpam-6851	354	2	25	25	NUM
ejpam-6851	354	3	]	]	PUNCT
ejpam-6851	354	4	γs(g	γs(g	PUNCT
ejpam-6851	354	5	◦	◦	NOUN
ejpam-6851	354	6	h	h	NOUN
ejpam-6851	354	7	)	)	PUNCT
ejpam-6851	354	8	=	=	SYM
ejpam-6851	354	9	n	n	PROPN
ejpam-6851	354	10	for	for	ADP
ejpam-6851	354	11	any	any	DET
ejpam-6851	354	12	graph	graph	NOUN
ejpam-6851	354	13	h.	h.	PROPN
ejpam-6851	354	14	(	(	PUNCT
ejpam-6851	354	15	ii	ii	PROPN
ejpam-6851	354	16	)	)	PUNCT
ejpam-6851	354	17	γw(g	γw(g	PUNCT
ejpam-6851	354	18	◦	◦	NOUN
ejpam-6851	354	19	h	h	NOUN
ejpam-6851	354	20	)	)	PUNCT
ejpam-6851	354	21	=	=	SYM
ejpam-6851	354	22	nγw(h	nγw(h	PROPN
ejpam-6851	354	23	)	)	PUNCT
ejpam-6851	354	24	for	for	ADP
ejpam-6851	354	25	any	any	DET
ejpam-6851	354	26	graph	graph	NOUN
ejpam-6851	354	27	h.	h.	NOUN
ejpam-6851	354	28	proof	proof	NOUN
ejpam-6851	354	29	.	.	PUNCT
ejpam-6851	355	1	by	by	ADP
ejpam-6851	355	2	proposition	proposition	NOUN
ejpam-6851	355	3	3	3	NUM
ejpam-6851	355	4	,	,	PUNCT
ejpam-6851	355	5	v	v	NOUN
ejpam-6851	355	6	(	(	PUNCT
ejpam-6851	355	7	g	g	NOUN
ejpam-6851	355	8	)	)	PUNCT
ejpam-6851	355	9	is	be	AUX
ejpam-6851	355	10	a	a	DET
ejpam-6851	355	11	strong	strong	ADJ
ejpam-6851	355	12	dominating	dominating	NOUN
ejpam-6851	355	13	set	set	NOUN
ejpam-6851	355	14	of	of	ADP
ejpam-6851	355	15	g	g	PROPN
ejpam-6851	355	16	◦	◦	NOUN
ejpam-6851	355	17	h.	h.	NOUN
ejpam-6851	355	18	thus	thus	ADV
ejpam-6851	355	19	,	,	PUNCT
ejpam-6851	355	20	γs(g	γs(g	PUNCT
ejpam-6851	355	21	◦	◦	NOUN
ejpam-6851	355	22	h	h	NOUN
ejpam-6851	355	23	)	)	PUNCT
ejpam-6851	355	24	≤	≤	NOUN
ejpam-6851	355	25	n.	n.	NOUN
ejpam-6851	355	26	now	now	ADV
ejpam-6851	355	27	,	,	PUNCT
ejpam-6851	355	28	let	let	VERB
ejpam-6851	355	29	s	s	PRON
ejpam-6851	355	30	⊆	⊆	NUM
ejpam-6851	355	31	v	v	NOUN
ejpam-6851	355	32	(	(	PUNCT
ejpam-6851	355	33	g	g	PROPN
ejpam-6851	355	34	◦	◦	NOUN
ejpam-6851	355	35	h	h	NOUN
ejpam-6851	355	36	)	)	PUNCT
ejpam-6851	355	37	be	be	VERB
ejpam-6851	355	38	a	a	DET
ejpam-6851	355	39	strong	strong	ADJ
ejpam-6851	355	40	dominating	dominating	NOUN
ejpam-6851	355	41	set	set	NOUN
ejpam-6851	355	42	of	of	ADP
ejpam-6851	355	43	g	g	PROPN
ejpam-6851	355	44	◦	◦	NOUN
ejpam-6851	355	45	h	h	NOUN
ejpam-6851	355	46	,	,	PUNCT
ejpam-6851	355	47	and	and	CCONJ
ejpam-6851	355	48	let	let	VERB
ejpam-6851	355	49	a	a	DET
ejpam-6851	355	50	⊆	⊆	NUM
ejpam-6851	355	51	v	v	NOUN
ejpam-6851	355	52	(	(	PUNCT
ejpam-6851	355	53	g	g	NOUN
ejpam-6851	355	54	)	)	PUNCT
ejpam-6851	355	55	and	and	CCONJ
ejpam-6851	355	56	sv	sv	X
ejpam-6851	355	57	⊆	⊆	NUM
ejpam-6851	355	58	v	v	ADP
ejpam-6851	355	59	(	(	PUNCT
ejpam-6851	355	60	hv	hv	NOUN
ejpam-6851	355	61	)	)	PUNCT
ejpam-6851	355	62	be	be	VERB
ejpam-6851	355	63	as	as	SCONJ
ejpam-6851	355	64	provided	provide	VERB
ejpam-6851	355	65	in	in	ADP
ejpam-6851	355	66	proposition	proposition	NOUN
ejpam-6851	355	67	3	3	NUM
ejpam-6851	355	68	such	such	ADJ
ejpam-6851	355	69	that	that	DET
ejpam-6851	355	70	s	s	PART
ejpam-6851	355	71	=	=	PUNCT
ejpam-6851	355	72	a	a	DET
ejpam-6851	355	73	∪	∪	X
ejpam-6851	355	74	(	(	PUNCT
ejpam-6851	355	75	∪v∈v	∪v∈v	X
ejpam-6851	355	76	(	(	PUNCT
ejpam-6851	355	77	g)sv	g)sv	PROPN
ejpam-6851	355	78	)	)	PUNCT
ejpam-6851	355	79	.	.	PUNCT
ejpam-6851	356	1	by	by	ADP
ejpam-6851	356	2	proposition	proposition	NOUN
ejpam-6851	356	3	3(ii	3(ii	NUM
ejpam-6851	356	4	)	)	PUNCT
ejpam-6851	356	5	,	,	PUNCT
ejpam-6851	356	6	|sv|	|sv|	PROPN
ejpam-6851	356	7	≥	≥	NUM
ejpam-6851	356	8	1	1	NUM
ejpam-6851	356	9	for	for	ADP
ejpam-6851	356	10	all	all	PRON
ejpam-6851	356	11	v	v	ADP
ejpam-6851	356	12	∈	∈	NUM
ejpam-6851	356	13	v	v	NOUN
ejpam-6851	356	14	(	(	PUNCT
ejpam-6851	356	15	g	g	NOUN
ejpam-6851	356	16	)	)	PUNCT
ejpam-6851	356	17	\	\	NOUN
ejpam-6851	356	18	a.	a.	NOUN
ejpam-6851	356	19	thus	thus	ADV
ejpam-6851	356	20	,	,	PUNCT
ejpam-6851	356	21	|s|	|s|	PRON
ejpam-6851	356	22	≥	≥	PRON
ejpam-6851	356	23	|a|+	|a|+	NOUN
ejpam-6851	356	24	|v	|v	X
ejpam-6851	356	25	(	(	PUNCT
ejpam-6851	356	26	g	g	NOUN
ejpam-6851	356	27	)	)	PUNCT
ejpam-6851	356	28	\	\	PUNCT
ejpam-6851	357	1	a|	a|	PROPN
ejpam-6851	357	2	=	=	PUNCT
ejpam-6851	357	3	n.	n.	NOUN
ejpam-6851	357	4	since	since	SCONJ
ejpam-6851	357	5	s	s	NOUN
ejpam-6851	357	6	is	be	AUX
ejpam-6851	357	7	arbitrary	arbitrary	ADJ
ejpam-6851	357	8	,	,	PUNCT
ejpam-6851	357	9	γs(g	γs(g	PUNCT
ejpam-6851	357	10	◦	◦	NOUN
ejpam-6851	357	11	h	h	NOUN
ejpam-6851	357	12	)	)	PUNCT
ejpam-6851	357	13	≥	≥	NOUN
ejpam-6851	357	14	n.	n.	NOUN
ejpam-6851	357	15	statement	statement	PROPN
ejpam-6851	357	16	(	(	PUNCT
ejpam-6851	357	17	ii	ii	NOUN
ejpam-6851	357	18	)	)	PUNCT
ejpam-6851	357	19	is	be	AUX
ejpam-6851	357	20	easy	easy	ADJ
ejpam-6851	357	21	.	.	PUNCT
ejpam-6851	358	1	5.1	5.1	NUM
ejpam-6851	358	2	.	.	PUNCT
ejpam-6851	359	1	in	in	ADP
ejpam-6851	359	2	the	the	DET
ejpam-6851	359	3	edge	edge	NOUN
ejpam-6851	359	4	corona	corona	NOUN
ejpam-6851	359	5	of	of	ADP
ejpam-6851	359	6	graphs	graph	NOUN
ejpam-6851	359	7	given	give	VERB
ejpam-6851	359	8	graphs	graph	NOUN
ejpam-6851	359	9	g	g	NOUN
ejpam-6851	359	10	and	and	CCONJ
ejpam-6851	359	11	h	h	NOUN
ejpam-6851	359	12	,	,	PUNCT
ejpam-6851	359	13	we	we	PRON
ejpam-6851	359	14	write	write	VERB
ejpam-6851	359	15	huv	huv	PROPN
ejpam-6851	359	16	to	to	PART
ejpam-6851	359	17	denote	denote	VERB
ejpam-6851	359	18	that	that	DET
ejpam-6851	359	19	copy	copy	NOUN
ejpam-6851	359	20	of	of	ADP
ejpam-6851	359	21	h	h	NOUN
ejpam-6851	359	22	that	that	PRON
ejpam-6851	359	23	is	be	AUX
ejpam-6851	359	24	being	be	AUX
ejpam-6851	359	25	joined	join	VERB
ejpam-6851	359	26	with	with	ADP
ejpam-6851	359	27	the	the	DET
ejpam-6851	359	28	endvertices	endvertice	NOUN
ejpam-6851	359	29	of	of	ADP
ejpam-6851	359	30	the	the	DET
ejpam-6851	359	31	edge	edge	NOUN
ejpam-6851	359	32	uv	uv	PROPN
ejpam-6851	359	33	∈	∈	PROPN
ejpam-6851	359	34	e(g	e(g	PROPN
ejpam-6851	359	35	)	)	PUNCT
ejpam-6851	359	36	in	in	ADP
ejpam-6851	359	37	the	the	DET
ejpam-6851	359	38	edge	edge	NOUN
ejpam-6851	359	39	corona	corona	PROPN
ejpam-6851	359	40	g	g	PROPN
ejpam-6851	359	41	⋄	⋄	PROPN
ejpam-6851	359	42	h.	h.	PROPN
ejpam-6851	359	43	for	for	ADP
ejpam-6851	359	44	uv	uv	PROPN
ejpam-6851	359	45	∈	∈	PROPN
ejpam-6851	359	46	e(g	e(g	PROPN
ejpam-6851	359	47	)	)	PUNCT
ejpam-6851	359	48	,	,	PUNCT
ejpam-6851	359	49	we	we	PRON
ejpam-6851	359	50	write	write	VERB
ejpam-6851	359	51	huv	huv	PROPN
ejpam-6851	360	1	+	+	CCONJ
ejpam-6851	360	2	uv	uv	PROPN
ejpam-6851	360	3	=	=	PUNCT
ejpam-6851	360	4	huv	huv	PROPN
ejpam-6851	360	5	+	+	NUM
ejpam-6851	360	6	⟨{u	⟨{u	PROPN
ejpam-6851	360	7	,	,	PUNCT
ejpam-6851	360	8	v}⟩.	v}⟩.	VERB
ejpam-6851	360	9	if	if	SCONJ
ejpam-6851	360	10	x	x	PROPN
ejpam-6851	360	11	∈	∈	PROPN
ejpam-6851	360	12	v	v	ADP
ejpam-6851	360	13	(	(	PUNCT
ejpam-6851	360	14	h	h	NOUN
ejpam-6851	360	15	)	)	PUNCT
ejpam-6851	360	16	,	,	PUNCT
ejpam-6851	360	17	then	then	ADV
ejpam-6851	360	18	we	we	PRON
ejpam-6851	360	19	write	write	VERB
ejpam-6851	360	20	xuv	xuv	PROPN
ejpam-6851	360	21	to	to	PART
ejpam-6851	360	22	denote	denote	VERB
ejpam-6851	360	23	the	the	DET
ejpam-6851	360	24	corresponding	corresponding	ADJ
ejpam-6851	360	25	vertex	vertex	NOUN
ejpam-6851	360	26	in	in	ADP
ejpam-6851	360	27	huv	huv	PROPN
ejpam-6851	360	28	.	.	PUNCT
ejpam-6851	361	1	j.	j.	PROPN
ejpam-6851	361	2	m.	m.	PROPN
ejpam-6851	361	3	molles	molles	PROPN
ejpam-6851	361	4	,	,	PUNCT
ejpam-6851	361	5	f.	f.	PROPN
ejpam-6851	361	6	p.	p.	PROPN
ejpam-6851	361	7	jamil	jamil	PROPN
ejpam-6851	361	8	,	,	PUNCT
ejpam-6851	361	9	s.	s.	PROPN
ejpam-6851	361	10	r.	r.	PROPN
ejpam-6851	361	11	canoy	canoy	PROPN
ejpam-6851	361	12	/	/	SYM
ejpam-6851	361	13	eur	eur	PROPN
ejpam-6851	361	14	.	.	PUNCT
ejpam-6851	362	1	j.	j.	PROPN
ejpam-6851	362	2	pure	pure	PROPN
ejpam-6851	362	3	appl	appl	PROPN
ejpam-6851	362	4	.	.	PROPN
ejpam-6851	362	5	math	math	PROPN
ejpam-6851	362	6	,	,	PUNCT
ejpam-6851	362	7	18	18	NUM
ejpam-6851	362	8	(	(	PUNCT
ejpam-6851	362	9	4	4	NUM
ejpam-6851	362	10	)	)	PUNCT
ejpam-6851	362	11	(	(	PUNCT
ejpam-6851	362	12	2025	2025	NUM
ejpam-6851	362	13	)	)	PUNCT
ejpam-6851	362	14	,	,	PUNCT
ejpam-6851	362	15	6851	6851	NUM
ejpam-6851	362	16	11	11	NUM
ejpam-6851	362	17	of	of	ADP
ejpam-6851	362	18	18	18	NUM
ejpam-6851	362	19	proposition	proposition	NOUN
ejpam-6851	362	20	5	5	NUM
ejpam-6851	362	21	.	.	PUNCT
ejpam-6851	363	1	let	let	VERB
ejpam-6851	363	2	g	g	NOUN
ejpam-6851	363	3	and	and	CCONJ
ejpam-6851	363	4	h	h	NOUN
ejpam-6851	363	5	be	be	VERB
ejpam-6851	363	6	a	a	DET
ejpam-6851	363	7	nontrivial	nontrivial	ADJ
ejpam-6851	363	8	connected	connect	VERB
ejpam-6851	363	9	graphs	graph	NOUN
ejpam-6851	363	10	with	with	ADP
ejpam-6851	363	11	δ(g	δ(g	PROPN
ejpam-6851	363	12	)	)	PUNCT
ejpam-6851	363	13	≥	≥	NOUN
ejpam-6851	363	14	2	2	NUM
ejpam-6851	363	15	or	or	CCONJ
ejpam-6851	363	16	γ(h	γ(h	NOUN
ejpam-6851	363	17	)	)	PUNCT
ejpam-6851	363	18	≥	≥	NOUN
ejpam-6851	363	19	2	2	NUM
ejpam-6851	363	20	,	,	PUNCT
ejpam-6851	363	21	and	and	CCONJ
ejpam-6851	363	22	let	let	VERB
ejpam-6851	363	23	s	s	PRON
ejpam-6851	363	24	⊆	⊆	NUM
ejpam-6851	363	25	v	v	NOUN
ejpam-6851	363	26	(	(	PUNCT
ejpam-6851	363	27	g	g	PROPN
ejpam-6851	363	28	⋄h	⋄h	PROPN
ejpam-6851	363	29	)	)	PUNCT
ejpam-6851	363	30	.	.	PUNCT
ejpam-6851	364	1	then	then	ADV
ejpam-6851	364	2	s	s	VERB
ejpam-6851	364	3	∈	∈	PROPN
ejpam-6851	364	4	γs(g	γs(g	PUNCT
ejpam-6851	364	5	⋄h	⋄h	PROPN
ejpam-6851	364	6	)	)	PUNCT
ejpam-6851	364	7	if	if	SCONJ
ejpam-6851	364	8	and	and	CCONJ
ejpam-6851	364	9	only	only	ADV
ejpam-6851	364	10	if	if	SCONJ
ejpam-6851	364	11	s	s	VERB
ejpam-6851	364	12	=	=	NOUN
ejpam-6851	364	13	a	a	DET
ejpam-6851	364	14	∪	∪	X
ejpam-6851	364	15	(	(	PUNCT
ejpam-6851	364	16	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-6851	364	17	)	)	PUNCT
ejpam-6851	364	18	,	,	PUNCT
ejpam-6851	364	19	(	(	PUNCT
ejpam-6851	364	20	2	2	X
ejpam-6851	364	21	)	)	PUNCT
ejpam-6851	364	22	where	where	SCONJ
ejpam-6851	364	23	a	a	DET
ejpam-6851	364	24	⊆	⊆	NUM
ejpam-6851	364	25	v	v	NOUN
ejpam-6851	364	26	(	(	PUNCT
ejpam-6851	364	27	g	g	NOUN
ejpam-6851	364	28	)	)	PUNCT
ejpam-6851	364	29	and	and	CCONJ
ejpam-6851	364	30	suv	suv	PROPN
ejpam-6851	364	31	⊆	⊆	NUM
ejpam-6851	364	32	v	v	NOUN
ejpam-6851	364	33	(	(	PUNCT
ejpam-6851	364	34	huv	huv	PROPN
ejpam-6851	364	35	satisfying	satisfy	VERB
ejpam-6851	364	36	the	the	DET
ejpam-6851	364	37	following	following	NOUN
ejpam-6851	364	38	:	:	PUNCT
ejpam-6851	364	39	(	(	PUNCT
ejpam-6851	364	40	i	i	NOUN
ejpam-6851	364	41	)	)	PUNCT
ejpam-6851	364	42	a	a	DET
ejpam-6851	364	43	∈	∈	NOUN
ejpam-6851	364	44	γs(g	γs(g	NUM
ejpam-6851	364	45	)	)	PUNCT
ejpam-6851	364	46	;	;	PUNCT
ejpam-6851	364	47	and	and	CCONJ
ejpam-6851	364	48	(	(	PUNCT
ejpam-6851	364	49	ii	ii	NOUN
ejpam-6851	364	50	)	)	PUNCT
ejpam-6851	364	51	for	for	ADP
ejpam-6851	364	52	each	each	DET
ejpam-6851	364	53	uv	uv	PROPN
ejpam-6851	364	54	∈	∈	PROPN
ejpam-6851	364	55	e(g	e(g	PROPN
ejpam-6851	364	56	)	)	PUNCT
ejpam-6851	364	57	for	for	ADP
ejpam-6851	364	58	which	which	PRON
ejpam-6851	364	59	{	{	PUNCT
ejpam-6851	364	60	u	u	NOUN
ejpam-6851	364	61	,	,	PUNCT
ejpam-6851	364	62	v	v	NOUN
ejpam-6851	364	63	}	}	PUNCT
ejpam-6851	364	64	∩a	∩a	NOUN
ejpam-6851	364	65	=	=	NOUN
ejpam-6851	364	66	∅	∅	NOUN
ejpam-6851	364	67	,	,	PUNCT
ejpam-6851	364	68	suv	suv	PROPN
ejpam-6851	364	69	∈	∈	PROPN
ejpam-6851	364	70	γs(h	γs(h	X
ejpam-6851	364	71	uv	uv	NOUN
ejpam-6851	364	72	)	)	PUNCT
ejpam-6851	364	73	.	.	PUNCT
ejpam-6851	365	1	proof	proof	NOUN
ejpam-6851	365	2	.	.	PUNCT
ejpam-6851	366	1	assume	assume	VERB
ejpam-6851	366	2	that	that	SCONJ
ejpam-6851	366	3	s	s	VERB
ejpam-6851	366	4	is	be	AUX
ejpam-6851	366	5	strong	strong	ADJ
ejpam-6851	366	6	dominating	dominating	NOUN
ejpam-6851	366	7	set	set	NOUN
ejpam-6851	366	8	of	of	ADP
ejpam-6851	366	9	g	g	PROPN
ejpam-6851	366	10	◦	◦	PROPN
ejpam-6851	366	11	h.	h.	PROPN
ejpam-6851	366	12	put	put	VERB
ejpam-6851	366	13	a	a	DET
ejpam-6851	366	14	=	=	SYM
ejpam-6851	366	15	s	s	NOUN
ejpam-6851	366	16	∩	∩	ADJ
ejpam-6851	366	17	v	v	X
ejpam-6851	366	18	(	(	PUNCT
ejpam-6851	366	19	g	g	NOUN
ejpam-6851	366	20	)	)	PUNCT
ejpam-6851	366	21	and	and	CCONJ
ejpam-6851	366	22	suv	suv	PROPN
ejpam-6851	366	23	=	=	PROPN
ejpam-6851	366	24	s	s	PROPN
ejpam-6851	366	25	∩	∩	ADJ
ejpam-6851	366	26	v	v	X
ejpam-6851	366	27	(	(	PUNCT
ejpam-6851	366	28	huv	huv	PROPN
ejpam-6851	366	29	)	)	PUNCT
ejpam-6851	366	30	for	for	ADP
ejpam-6851	366	31	each	each	DET
ejpam-6851	366	32	uv	uv	PROPN
ejpam-6851	366	33	∈	∈	PROPN
ejpam-6851	366	34	e(g	e(g	PROPN
ejpam-6851	366	35	)	)	PUNCT
ejpam-6851	366	36	.	.	PUNCT
ejpam-6851	367	1	then	then	ADV
ejpam-6851	367	2	equation	equation	NOUN
ejpam-6851	367	3	2	2	NUM
ejpam-6851	367	4	holds	hold	VERB
ejpam-6851	367	5	.	.	PUNCT
ejpam-6851	368	1	let	let	VERB
ejpam-6851	368	2	v	v	NUM
ejpam-6851	368	3	∈	∈	PROPN
ejpam-6851	368	4	v	v	NOUN
ejpam-6851	368	5	(	(	PUNCT
ejpam-6851	368	6	g	g	NOUN
ejpam-6851	368	7	)	)	PUNCT
ejpam-6851	368	8	\a	\a	ADJ
ejpam-6851	368	9	.	.	PUNCT
ejpam-6851	369	1	there	there	PRON
ejpam-6851	369	2	exists	exist	VERB
ejpam-6851	369	3	u	u	PROPN
ejpam-6851	369	4	∈	∈	PROPN
ejpam-6851	369	5	s	s	X
ejpam-6851	369	6	for	for	ADP
ejpam-6851	369	7	which	which	PRON
ejpam-6851	369	8	v	v	ADP
ejpam-6851	369	9	≼g⋄h	≼g⋄h	PROPN
ejpam-6851	369	10	u.	u.	VERB
ejpam-6851	369	11	if	if	SCONJ
ejpam-6851	369	12	δ(g	δ(g	PROPN
ejpam-6851	369	13	)	)	PUNCT
ejpam-6851	369	14	≥	≥	NOUN
ejpam-6851	369	15	2	2	NUM
ejpam-6851	369	16	or	or	CCONJ
ejpam-6851	369	17	γ(h	γ(h	NOUN
ejpam-6851	369	18	)	)	PUNCT
ejpam-6851	369	19	≥	≥	NOUN
ejpam-6851	369	20	2	2	NUM
ejpam-6851	369	21	,	,	PUNCT
ejpam-6851	369	22	then	then	ADV
ejpam-6851	369	23	degg⋄h(w	degg⋄h(w	PROPN
ejpam-6851	369	24	)	)	PUNCT
ejpam-6851	369	25	<	<	X
ejpam-6851	369	26	degg⋄h(v	degg⋄h(v	PROPN
ejpam-6851	369	27	)	)	PUNCT
ejpam-6851	369	28	for	for	ADP
ejpam-6851	369	29	all	all	DET
ejpam-6851	369	30	w	w	PROPN
ejpam-6851	369	31	∈	∈	PROPN
ejpam-6851	369	32	v	v	ADP
ejpam-6851	369	33	(	(	PUNCT
ejpam-6851	369	34	hxv	hxv	PROPN
ejpam-6851	369	35	)	)	PUNCT
ejpam-6851	369	36	,	,	PUNCT
ejpam-6851	369	37	for	for	ADP
ejpam-6851	369	38	all	all	DET
ejpam-6851	369	39	x	x	SYM
ejpam-6851	369	40	∈	∈	NOUN
ejpam-6851	369	41	ng(v	ng(v	NOUN
ejpam-6851	369	42	)	)	PUNCT
ejpam-6851	369	43	.	.	PUNCT
ejpam-6851	370	1	thus	thus	ADV
ejpam-6851	370	2	,	,	PUNCT
ejpam-6851	370	3	u	u	PROPN
ejpam-6851	370	4	∈	∈	PROPN
ejpam-6851	370	5	a.	a.	NOUN
ejpam-6851	370	6	hence	hence	ADV
ejpam-6851	370	7	,	,	PUNCT
ejpam-6851	370	8	u	u	PROPN
ejpam-6851	370	9	≼g	≼g	PROPN
ejpam-6851	370	10	a	a	PRON
ejpam-6851	370	11	and	and	CCONJ
ejpam-6851	370	12	a	a	DET
ejpam-6851	370	13	∈	∈	NOUN
ejpam-6851	370	14	γs(g	γs(g	NUM
ejpam-6851	370	15	)	)	PUNCT
ejpam-6851	370	16	.	.	PUNCT
ejpam-6851	371	1	this	this	PRON
ejpam-6851	371	2	proves	prove	VERB
ejpam-6851	371	3	(	(	PUNCT
ejpam-6851	371	4	i	i	NOUN
ejpam-6851	371	5	)	)	PUNCT
ejpam-6851	371	6	.	.	PUNCT
ejpam-6851	372	1	now	now	ADV
ejpam-6851	372	2	,	,	PUNCT
ejpam-6851	372	3	let	let	VERB
ejpam-6851	372	4	uv	uv	PRON
ejpam-6851	372	5	∈	∈	PROPN
ejpam-6851	372	6	e(g	e(g	PROPN
ejpam-6851	372	7	)	)	PUNCT
ejpam-6851	372	8	with	with	ADP
ejpam-6851	372	9	u	u	PROPN
ejpam-6851	372	10	/∈	/∈	PROPN
ejpam-6851	372	11	a	a	PRON
ejpam-6851	372	12	and	and	CCONJ
ejpam-6851	372	13	v	v	NOUN
ejpam-6851	372	14	/∈	/∈	PROPN
ejpam-6851	372	15	a	a	PRON
ejpam-6851	372	16	,	,	PUNCT
ejpam-6851	372	17	and	and	CCONJ
ejpam-6851	372	18	let	let	VERB
ejpam-6851	372	19	w	w	PROPN
ejpam-6851	372	20	∈	∈	PROPN
ejpam-6851	372	21	v	v	X
ejpam-6851	372	22	(	(	PUNCT
ejpam-6851	372	23	huv	huv	PROPN
ejpam-6851	372	24	)	)	PUNCT
ejpam-6851	372	25	\	\	PROPN
ejpam-6851	372	26	suv	suv	PROPN
ejpam-6851	372	27	.	.	PUNCT
ejpam-6851	373	1	there	there	PRON
ejpam-6851	373	2	exists	exist	VERB
ejpam-6851	373	3	z	z	PROPN
ejpam-6851	373	4	∈	∈	PROPN
ejpam-6851	373	5	s	s	X
ejpam-6851	373	6	for	for	ADP
ejpam-6851	373	7	which	which	PRON
ejpam-6851	373	8	w	w	PROPN
ejpam-6851	373	9	≼g⋄h	≼g⋄h	PROPN
ejpam-6851	373	10	z.	z.	PROPN
ejpam-6851	373	11	clearly	clearly	ADV
ejpam-6851	373	12	,	,	PUNCT
ejpam-6851	373	13	z	z	PROPN
ejpam-6851	373	14	∈	∈	PROPN
ejpam-6851	373	15	suv	suv	NOUN
ejpam-6851	373	16	so	so	SCONJ
ejpam-6851	373	17	that	that	SCONJ
ejpam-6851	373	18	w	w	PROPN
ejpam-6851	373	19	≼	≼	PROPN
ejpam-6851	373	20	suv	suv	PROPN
ejpam-6851	373	21	.	.	PUNCT
ejpam-6851	374	1	therefore	therefore	ADV
ejpam-6851	374	2	,	,	PUNCT
ejpam-6851	374	3	suv	suv	PROPN
ejpam-6851	374	4	is	be	AUX
ejpam-6851	374	5	a	a	DET
ejpam-6851	374	6	strong	strong	ADJ
ejpam-6851	374	7	dominating	dominating	NOUN
ejpam-6851	374	8	set	set	NOUN
ejpam-6851	374	9	of	of	ADP
ejpam-6851	374	10	huv	huv	PROPN
ejpam-6851	374	11	.	.	PUNCT
ejpam-6851	375	1	conversely	conversely	ADV
ejpam-6851	375	2	,	,	PUNCT
ejpam-6851	375	3	assume	assume	VERB
ejpam-6851	375	4	that	that	SCONJ
ejpam-6851	375	5	(	(	PUNCT
ejpam-6851	375	6	i	i	NOUN
ejpam-6851	375	7	)	)	PUNCT
ejpam-6851	375	8	and	and	CCONJ
ejpam-6851	375	9	(	(	PUNCT
ejpam-6851	375	10	ii	ii	NOUN
ejpam-6851	375	11	)	)	PUNCT
ejpam-6851	375	12	hold	hold	VERB
ejpam-6851	375	13	for	for	ADP
ejpam-6851	375	14	s.	s.	PROPN
ejpam-6851	375	15	let	let	VERB
ejpam-6851	375	16	v	v	ADP
ejpam-6851	375	17	∈	∈	PROPN
ejpam-6851	375	18	v	v	NOUN
ejpam-6851	375	19	(	(	PUNCT
ejpam-6851	375	20	g	g	PROPN
ejpam-6851	375	21	⋄h	⋄h	PROPN
ejpam-6851	375	22	)	)	PUNCT
ejpam-6851	375	23	\	\	PUNCT
ejpam-6851	376	1	s.	s.	PROPN
ejpam-6851	376	2	there	there	PRON
ejpam-6851	376	3	exists	exist	VERB
ejpam-6851	376	4	xy	xy	PROPN
ejpam-6851	376	5	∈	∈	PROPN
ejpam-6851	376	6	e(g	e(g	PROPN
ejpam-6851	376	7	)	)	PUNCT
ejpam-6851	376	8	such	such	ADJ
ejpam-6851	376	9	that	that	PRON
ejpam-6851	376	10	v	v	NUM
ejpam-6851	376	11	∈	∈	PROPN
ejpam-6851	376	12	v	v	NOUN
ejpam-6851	376	13	(	(	PUNCT
ejpam-6851	376	14	hxy	hxy	NOUN
ejpam-6851	376	15	+	+	X
ejpam-6851	376	16	xy	xy	PROPN
ejpam-6851	376	17	)	)	PUNCT
ejpam-6851	376	18	.	.	PUNCT
ejpam-6851	377	1	first	first	ADV
ejpam-6851	377	2	,	,	PUNCT
ejpam-6851	377	3	suppose	suppose	VERB
ejpam-6851	377	4	that	that	SCONJ
ejpam-6851	377	5	v	v	ADP
ejpam-6851	377	6	∈	∈	PROPN
ejpam-6851	377	7	v	v	NOUN
ejpam-6851	377	8	(	(	PUNCT
ejpam-6851	377	9	hxy	hxy	NOUN
ejpam-6851	377	10	)	)	PUNCT
ejpam-6851	377	11	.	.	PUNCT
ejpam-6851	378	1	if	if	SCONJ
ejpam-6851	378	2	x	x	SYM
ejpam-6851	378	3	∈	∈	PROPN
ejpam-6851	378	4	a	a	DET
ejpam-6851	378	5	,	,	PUNCT
ejpam-6851	378	6	then	then	ADV
ejpam-6851	378	7	v	v	ADP
ejpam-6851	378	8	≼	≼	PROPN
ejpam-6851	378	9	x.	x.	NOUN
ejpam-6851	378	10	similarly	similarly	ADV
ejpam-6851	378	11	,	,	PUNCT
ejpam-6851	378	12	if	if	SCONJ
ejpam-6851	378	13	y	y	PROPN
ejpam-6851	378	14	∈	∈	PROPN
ejpam-6851	378	15	a	a	PRON
ejpam-6851	378	16	,	,	PUNCT
ejpam-6851	378	17	then	then	ADV
ejpam-6851	378	18	v	v	ADP
ejpam-6851	378	19	≼	≼	PROPN
ejpam-6851	378	20	y.	y.	NOUN
ejpam-6851	378	21	in	in	ADP
ejpam-6851	378	22	any	any	DET
ejpam-6851	378	23	case	case	NOUN
ejpam-6851	378	24	,	,	PUNCT
ejpam-6851	378	25	v	v	ADP
ejpam-6851	378	26	≼	≼	PROPN
ejpam-6851	378	27	s.	s.	PROPN
ejpam-6851	378	28	suppose	suppose	VERB
ejpam-6851	378	29	that	that	SCONJ
ejpam-6851	378	30	x	x	PROPN
ejpam-6851	378	31	,	,	PUNCT
ejpam-6851	378	32	y	y	PROPN
ejpam-6851	378	33	/∈	/∈	PUNCT
ejpam-6851	378	34	a.	a.	NOUN
ejpam-6851	378	35	by	by	ADP
ejpam-6851	378	36	(	(	PUNCT
ejpam-6851	378	37	ii	ii	NOUN
ejpam-6851	378	38	)	)	PUNCT
ejpam-6851	378	39	,	,	PUNCT
ejpam-6851	378	40	v	v	ADP
ejpam-6851	378	41	≼	≼	PROPN
ejpam-6851	378	42	sxy	sxy	PROPN
ejpam-6851	378	43	.	.	PUNCT
ejpam-6851	379	1	thus	thus	ADV
ejpam-6851	379	2	v	v	ADP
ejpam-6851	379	3	≼	≼	PROPN
ejpam-6851	379	4	s.	s.	PROPN
ejpam-6851	379	5	next	next	ADV
ejpam-6851	379	6	,	,	PUNCT
ejpam-6851	379	7	suppose	suppose	VERB
ejpam-6851	379	8	that	that	SCONJ
ejpam-6851	379	9	v	v	AUX
ejpam-6851	379	10	=	=	SYM
ejpam-6851	379	11	x	x	X
ejpam-6851	379	12	or	or	CCONJ
ejpam-6851	379	13	v	v	X
ejpam-6851	379	14	=	=	X
ejpam-6851	379	15	y.	y.	NOUN
ejpam-6851	379	16	by	by	ADP
ejpam-6851	379	17	(	(	PUNCT
ejpam-6851	379	18	i	i	NOUN
ejpam-6851	379	19	)	)	PUNCT
ejpam-6851	379	20	,	,	PUNCT
ejpam-6851	379	21	there	there	PRON
ejpam-6851	379	22	exists	exist	VERB
ejpam-6851	379	23	w	w	PROPN
ejpam-6851	379	24	∈	∈	PROPN
ejpam-6851	379	25	a	a	DET
ejpam-6851	379	26	for	for	ADP
ejpam-6851	379	27	which	which	PRON
ejpam-6851	379	28	v	v	ADP
ejpam-6851	379	29	≼	≼	PROPN
ejpam-6851	379	30	w.	w.	PROPN
ejpam-6851	379	31	therefore	therefore	ADV
ejpam-6851	379	32	,	,	PUNCT
ejpam-6851	379	33	v	v	ADP
ejpam-6851	379	34	≼	≼	PROPN
ejpam-6851	379	35	s.	s.	PROPN
ejpam-6851	379	36	accordingly	accordingly	ADV
ejpam-6851	379	37	,	,	PUNCT
ejpam-6851	379	38	s	s	VERB
ejpam-6851	379	39	is	be	AUX
ejpam-6851	379	40	a	a	DET
ejpam-6851	379	41	strong	strong	ADJ
ejpam-6851	379	42	dominating	dominating	NOUN
ejpam-6851	379	43	set	set	NOUN
ejpam-6851	379	44	of	of	ADP
ejpam-6851	379	45	g	g	PROPN
ejpam-6851	379	46	⋄h	⋄h	PROPN
ejpam-6851	379	47	.	.	PUNCT
ejpam-6851	380	1	the	the	DET
ejpam-6851	380	2	set	set	NOUN
ejpam-6851	380	3	a	a	PRON
ejpam-6851	380	4	in	in	ADP
ejpam-6851	380	5	proposition	proposition	NOUN
ejpam-6851	380	6	5	5	NUM
ejpam-6851	380	7	need	need	AUX
ejpam-6851	380	8	not	not	PART
ejpam-6851	380	9	be	be	AUX
ejpam-6851	380	10	a	a	DET
ejpam-6851	380	11	strong	strong	ADJ
ejpam-6851	380	12	dominating	dominating	NOUN
ejpam-6851	380	13	set	set	NOUN
ejpam-6851	380	14	of	of	ADP
ejpam-6851	380	15	g	g	NOUN
ejpam-6851	380	16	whenever	whenever	SCONJ
ejpam-6851	380	17	δ(g	δ(g	X
ejpam-6851	380	18	)	)	PUNCT
ejpam-6851	380	19	=	=	SYM
ejpam-6851	380	20	1	1	NUM
ejpam-6851	380	21	=	=	SYM
ejpam-6851	380	22	γ(h	γ(h	NOUN
ejpam-6851	380	23	)	)	PUNCT
ejpam-6851	380	24	.	.	PUNCT
ejpam-6851	381	1	consider	consider	VERB
ejpam-6851	381	2	the	the	DET
ejpam-6851	381	3	edge	edge	NOUN
ejpam-6851	381	4	corona	corona	NOUN
ejpam-6851	381	5	p5	p5	PROPN
ejpam-6851	381	6	⋄	⋄	PROPN
ejpam-6851	381	7	p3	p3	PROPN
ejpam-6851	381	8	in	in	ADP
ejpam-6851	381	9	figure	figure	NOUN
ejpam-6851	381	10	2	2	NUM
ejpam-6851	381	11	.	.	PUNCT
ejpam-6851	382	1	the	the	DET
ejpam-6851	382	2	set	set	NOUN
ejpam-6851	382	3	s	s	PRON
ejpam-6851	382	4	of	of	ADP
ejpam-6851	382	5	darkened	darken	VERB
ejpam-6851	382	6	vertices	vertex	NOUN
ejpam-6851	382	7	is	be	AUX
ejpam-6851	382	8	a	a	DET
ejpam-6851	382	9	strong	strong	ADJ
ejpam-6851	382	10	dominating	dominating	NOUN
ejpam-6851	382	11	set	set	NOUN
ejpam-6851	382	12	of	of	ADP
ejpam-6851	382	13	p5	p5	PROPN
ejpam-6851	382	14	⋄	⋄	PROPN
ejpam-6851	382	15	p3	p3	PROPN
ejpam-6851	382	16	.	.	PUNCT
ejpam-6851	383	1	however	however	ADV
ejpam-6851	383	2	a	a	PRON
ejpam-6851	383	3	=	=	X
ejpam-6851	383	4	s	s	NOUN
ejpam-6851	383	5	∩	∩	ADJ
ejpam-6851	383	6	v	v	NOUN
ejpam-6851	383	7	(	(	PUNCT
ejpam-6851	383	8	p5	p5	ADJ
ejpam-6851	383	9	)	)	PUNCT
ejpam-6851	383	10	is	be	AUX
ejpam-6851	383	11	not	not	PART
ejpam-6851	383	12	a	a	DET
ejpam-6851	383	13	strong	strong	ADJ
ejpam-6851	383	14	dominating	dominating	NOUN
ejpam-6851	383	15	set	set	NOUN
ejpam-6851	383	16	of	of	ADP
ejpam-6851	383	17	p5	p5	PROPN
ejpam-6851	383	18	.	.	PUNCT
ejpam-6851	384	1	.................................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................................	PUNCT
ejpam-6851	384	2	.................................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................................	PUNCT
ejpam-6851	384	3	.................................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................................	PUNCT
ejpam-6851	384	4	.................................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................................	PUNCT
ejpam-6851	384	5	....................................	....................................	PUNCT
ejpam-6851	385	1	..............................................................	..............................................................	PUNCT
ejpam-6851	385	2	..............................................................	..............................................................	PUNCT
ejpam-6851	386	1	....................................	....................................	PUNCT
ejpam-6851	386	2	..........	..........	PUNCT
ejpam-6851	387	1	.........	.........	PUNCT
ejpam-6851	387	2	.........	.........	PUNCT
ejpam-6851	388	1	.........	.........	PUNCT
ejpam-6851	388	2	.........	.........	PUNCT
ejpam-6851	389	1	.........	.........	PUNCT
ejpam-6851	389	2	.........	.........	PUNCT
ejpam-6851	390	1	.........	.........	PUNCT
ejpam-6851	390	2	.........	.........	PUNCT
ejpam-6851	391	1	.........	.........	PUNCT
ejpam-6851	391	2	.........	.........	PUNCT
ejpam-6851	392	1	.........	.........	PUNCT
ejpam-6851	392	2	.........	.........	PUNCT
ejpam-6851	393	1	.........	.........	PUNCT
ejpam-6851	393	2	.........	.........	PUNCT
ejpam-6851	394	1	.........	.........	PUNCT
ejpam-6851	394	2	.....	.....	PUNCT
ejpam-6851	394	3	...........	...........	PUNCT
ejpam-6851	394	4	..........	..........	PUNCT
ejpam-6851	395	1	..........	..........	PUNCT
ejpam-6851	395	2	..........	..........	PUNCT
ejpam-6851	396	1	..........	..........	PUNCT
ejpam-6851	396	2	..........	..........	PUNCT
ejpam-6851	397	1	..........	..........	PUNCT
ejpam-6851	397	2	..........	..........	PUNCT
ejpam-6851	398	1	..........	..........	PUNCT
ejpam-6851	398	2	..........	..........	PUNCT
ejpam-6851	399	1	..........	..........	PUNCT
ejpam-6851	399	2	..........	..........	PUNCT
ejpam-6851	400	1	..........	..........	PUNCT
ejpam-6851	400	2	..........	..........	PUNCT
ejpam-6851	401	1	..........	..........	PUNCT
ejpam-6851	401	2	..........	..........	PUNCT
ejpam-6851	402	1	........	........	PUNCT
ejpam-6851	402	2	............	............	PUNCT
ejpam-6851	402	3	...........	...........	PUNCT
ejpam-6851	402	4	...........	...........	PUNCT
ejpam-6851	402	5	...........	...........	PUNCT
ejpam-6851	402	6	...........	...........	PUNCT
ejpam-6851	402	7	...........	...........	PUNCT
ejpam-6851	402	8	...........	...........	PUNCT
ejpam-6851	402	9	...........	...........	PUNCT
ejpam-6851	402	10	...........	...........	PUNCT
ejpam-6851	402	11	...........	...........	PUNCT
ejpam-6851	402	12	...........	...........	PUNCT
ejpam-6851	402	13	...........	...........	PUNCT
ejpam-6851	402	14	...........	...........	PUNCT
ejpam-6851	402	15	...........	...........	PUNCT
ejpam-6851	402	16	...........	...........	PUNCT
ejpam-6851	402	17	...........	...........	PUNCT
ejpam-6851	402	18	...........	...........	PUNCT
ejpam-6851	402	19	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-6851	402	20	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-6851	403	1	......................................................................................................................................................	......................................................................................................................................................	NUM
ejpam-6851	403	2	..............................................................	..............................................................	PUNCT
ejpam-6851	403	3	..............................................................	..............................................................	PUNCT
ejpam-6851	403	4	....................................	....................................	PUNCT
ejpam-6851	404	1	..........	..........	PUNCT
ejpam-6851	404	2	.........	.........	PUNCT
ejpam-6851	405	1	.........	.........	PUNCT
ejpam-6851	405	2	.........	.........	PUNCT
ejpam-6851	406	1	.........	.........	PUNCT
ejpam-6851	406	2	.........	.........	PUNCT
ejpam-6851	407	1	.........	.........	PUNCT
ejpam-6851	407	2	.........	.........	PUNCT
ejpam-6851	408	1	.........	.........	PUNCT
ejpam-6851	408	2	.........	.........	PUNCT
ejpam-6851	409	1	.........	.........	PUNCT
ejpam-6851	409	2	.........	.........	PUNCT
ejpam-6851	410	1	.........	.........	PUNCT
ejpam-6851	410	2	.........	.........	PUNCT
ejpam-6851	411	1	.........	.........	PUNCT
ejpam-6851	411	2	.........	.........	PUNCT
ejpam-6851	412	1	.....	.....	PUNCT
ejpam-6851	412	2	...........	...........	PUNCT
ejpam-6851	412	3	..........	..........	PUNCT
ejpam-6851	413	1	..........	..........	PUNCT
ejpam-6851	413	2	..........	..........	PUNCT
ejpam-6851	414	1	..........	..........	PUNCT
ejpam-6851	414	2	..........	..........	PUNCT
ejpam-6851	415	1	..........	..........	PUNCT
ejpam-6851	415	2	..........	..........	PUNCT
ejpam-6851	416	1	..........	..........	PUNCT
ejpam-6851	416	2	..........	..........	PUNCT
ejpam-6851	417	1	..........	..........	PUNCT
ejpam-6851	417	2	..........	..........	PUNCT
ejpam-6851	418	1	..........	..........	PUNCT
ejpam-6851	418	2	..........	..........	PUNCT
ejpam-6851	419	1	..........	..........	PUNCT
ejpam-6851	419	2	..........	..........	PUNCT
ejpam-6851	420	1	........	........	PUNCT
ejpam-6851	420	2	............	............	PUNCT
ejpam-6851	420	3	...........	...........	PUNCT
ejpam-6851	420	4	...........	...........	PUNCT
ejpam-6851	420	5	...........	...........	PUNCT
ejpam-6851	420	6	...........	...........	PUNCT
ejpam-6851	420	7	...........	...........	PUNCT
ejpam-6851	420	8	...........	...........	PUNCT
ejpam-6851	420	9	...........	...........	PUNCT
ejpam-6851	420	10	...........	...........	PUNCT
ejpam-6851	420	11	...........	...........	PUNCT
ejpam-6851	420	12	...........	...........	PUNCT
ejpam-6851	420	13	...........	...........	PUNCT
ejpam-6851	420	14	...........	...........	PUNCT
ejpam-6851	420	15	...........	...........	PUNCT
ejpam-6851	420	16	...........	...........	PUNCT
ejpam-6851	420	17	...........	...........	PUNCT
ejpam-6851	420	18	...........	...........	PUNCT
ejpam-6851	420	19	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-6851	420	20	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-6851	421	1	......................................................................................................................................................	......................................................................................................................................................	NUM
ejpam-6851	421	2	..............................................................	..............................................................	PUNCT
ejpam-6851	421	3	..............................................................	..............................................................	PUNCT
ejpam-6851	422	1	.....................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................	INTJ
ejpam-6851	422	2	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-6851	422	3	................................................................................................................................................................	................................................................................................................................................................	PUNCT
ejpam-6851	422	4	.........	.........	PUNCT
ejpam-6851	423	1	.........	.........	PUNCT
ejpam-6851	423	2	.........	.........	PUNCT
ejpam-6851	424	1	.........	.........	PUNCT
ejpam-6851	424	2	.........	.........	PUNCT
ejpam-6851	425	1	.........	.........	PUNCT
ejpam-6851	425	2	.........	.........	PUNCT
ejpam-6851	426	1	.........	.........	PUNCT
ejpam-6851	426	2	.........	.........	PUNCT
ejpam-6851	427	1	.........	.........	PUNCT
ejpam-6851	427	2	.........	.........	PUNCT
ejpam-6851	428	1	.........	.........	PUNCT
ejpam-6851	428	2	.........	.........	PUNCT
ejpam-6851	429	1	.........	.........	PUNCT
ejpam-6851	429	2	.........	.........	PUNCT
ejpam-6851	430	1	.....	.....	PUNCT
ejpam-6851	430	2	...........	...........	PUNCT
ejpam-6851	430	3	..........	..........	PUNCT
ejpam-6851	431	1	..........	..........	PUNCT
ejpam-6851	431	2	..........	..........	PUNCT
ejpam-6851	432	1	..........	..........	PUNCT
ejpam-6851	432	2	..........	..........	PUNCT
ejpam-6851	433	1	..........	..........	PUNCT
ejpam-6851	433	2	..........	..........	PUNCT
ejpam-6851	434	1	..........	..........	PUNCT
ejpam-6851	434	2	..........	..........	PUNCT
ejpam-6851	435	1	..........	..........	PUNCT
ejpam-6851	435	2	..........	..........	PUNCT
ejpam-6851	436	1	..........	..........	PUNCT
ejpam-6851	436	2	..........	..........	PUNCT
ejpam-6851	437	1	..........	..........	PUNCT
ejpam-6851	437	2	..........	..........	PUNCT
ejpam-6851	438	1	........	........	PUNCT
ejpam-6851	438	2	............	............	PUNCT
ejpam-6851	438	3	...........	...........	PUNCT
ejpam-6851	438	4	...........	...........	PUNCT
ejpam-6851	438	5	...........	...........	PUNCT
ejpam-6851	438	6	...........	...........	PUNCT
ejpam-6851	438	7	...........	...........	PUNCT
ejpam-6851	438	8	...........	...........	PUNCT
ejpam-6851	438	9	...........	...........	PUNCT
ejpam-6851	438	10	...........	...........	PUNCT
ejpam-6851	438	11	...........	...........	PUNCT
ejpam-6851	438	12	...........	...........	PUNCT
ejpam-6851	438	13	...........	...........	PUNCT
ejpam-6851	438	14	...........	...........	PUNCT
ejpam-6851	438	15	...........	...........	PUNCT
ejpam-6851	438	16	...........	...........	PUNCT
ejpam-6851	438	17	...........	...........	PUNCT
ejpam-6851	438	18	...........	...........	PUNCT
ejpam-6851	438	19	.....	.....	PUNCT
ejpam-6851	438	20	..............................................................	..............................................................	PUNCT
ejpam-6851	438	21	..............................................................	..............................................................	PUNCT
ejpam-6851	438	22	....................................	....................................	PUNCT
ejpam-6851	439	1	..........	..........	PUNCT
ejpam-6851	439	2	.........	.........	PUNCT
ejpam-6851	440	1	.........	.........	PUNCT
ejpam-6851	440	2	.........	.........	PUNCT
ejpam-6851	441	1	.........	.........	PUNCT
ejpam-6851	441	2	.........	.........	PUNCT
ejpam-6851	442	1	.........	.........	PUNCT
ejpam-6851	442	2	.........	.........	PUNCT
ejpam-6851	443	1	.........	.........	PUNCT
ejpam-6851	443	2	.........	.........	PUNCT
ejpam-6851	444	1	.........	.........	PUNCT
ejpam-6851	444	2	.........	.........	PUNCT
ejpam-6851	445	1	.........	.........	PUNCT
ejpam-6851	445	2	.........	.........	PUNCT
ejpam-6851	446	1	.........	.........	PUNCT
ejpam-6851	446	2	.........	.........	PUNCT
ejpam-6851	447	1	.....	.....	PUNCT
ejpam-6851	447	2	...........	...........	PUNCT
ejpam-6851	447	3	..........	..........	PUNCT
ejpam-6851	448	1	..........	..........	PUNCT
ejpam-6851	448	2	..........	..........	PUNCT
ejpam-6851	449	1	..........	..........	PUNCT
ejpam-6851	449	2	..........	..........	PUNCT
ejpam-6851	450	1	..........	..........	PUNCT
ejpam-6851	450	2	..........	..........	PUNCT
ejpam-6851	451	1	..........	..........	PUNCT
ejpam-6851	451	2	..........	..........	PUNCT
ejpam-6851	452	1	..........	..........	PUNCT
ejpam-6851	452	2	..........	..........	PUNCT
ejpam-6851	453	1	..........	..........	PUNCT
ejpam-6851	453	2	..........	..........	PUNCT
ejpam-6851	454	1	..........	..........	PUNCT
ejpam-6851	454	2	..........	..........	PUNCT
ejpam-6851	455	1	........	........	PUNCT
ejpam-6851	455	2	............	............	PUNCT
ejpam-6851	455	3	...........	...........	PUNCT
ejpam-6851	455	4	...........	...........	PUNCT
ejpam-6851	455	5	...........	...........	PUNCT
ejpam-6851	455	6	...........	...........	PUNCT
ejpam-6851	455	7	...........	...........	PUNCT
ejpam-6851	455	8	...........	...........	PUNCT
ejpam-6851	455	9	...........	...........	PUNCT
ejpam-6851	455	10	...........	...........	PUNCT
ejpam-6851	455	11	...........	...........	PUNCT
ejpam-6851	455	12	...........	...........	PUNCT
ejpam-6851	455	13	...........	...........	PUNCT
ejpam-6851	455	14	...........	...........	PUNCT
ejpam-6851	455	15	...........	...........	PUNCT
ejpam-6851	455	16	...........	...........	PUNCT
ejpam-6851	455	17	...........	...........	PUNCT
ejpam-6851	455	18	...........	...........	PUNCT
ejpam-6851	456	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-6851	456	2	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-6851	457	1	......................................................................................................................................................	......................................................................................................................................................	NUM
ejpam-6851	458	1	•	•	NUM
ejpam-6851	458	2	•	•	NOUN
ejpam-6851	458	3	•	•	NUM
ejpam-6851	458	4	figure	figure	NOUN
ejpam-6851	458	5	2	2	NUM
ejpam-6851	458	6	:	:	PUNCT
ejpam-6851	458	7	graph	graph	VERB
ejpam-6851	458	8	p5	p5	PROPN
ejpam-6851	458	9	⋄	⋄	PROPN
ejpam-6851	458	10	p3	p3	PROPN
ejpam-6851	458	11	proposition	proposition	NOUN
ejpam-6851	458	12	6	6	NUM
ejpam-6851	458	13	.	.	PUNCT
ejpam-6851	459	1	let	let	VERB
ejpam-6851	459	2	g	g	NOUN
ejpam-6851	460	1	and	and	CCONJ
ejpam-6851	460	2	h	h	NOUN
ejpam-6851	460	3	be	be	VERB
ejpam-6851	460	4	a	a	DET
ejpam-6851	460	5	nontrivial	nontrivial	ADJ
ejpam-6851	460	6	connected	connect	VERB
ejpam-6851	460	7	graphs	graph	NOUN
ejpam-6851	460	8	where	where	SCONJ
ejpam-6851	460	9	γ(h	γ(h	NOUN
ejpam-6851	460	10	)	)	PUNCT
ejpam-6851	460	11	̸=	̸=	PROPN
ejpam-6851	460	12	1	1	NUM
ejpam-6851	460	13	,	,	PUNCT
ejpam-6851	460	14	and	and	CCONJ
ejpam-6851	460	15	let	let	VERB
ejpam-6851	460	16	s	s	PRON
ejpam-6851	460	17	⊆	⊆	NUM
ejpam-6851	460	18	v	v	NOUN
ejpam-6851	460	19	(	(	PUNCT
ejpam-6851	460	20	g	g	PROPN
ejpam-6851	460	21	⋄h	⋄h	PROPN
ejpam-6851	460	22	)	)	PUNCT
ejpam-6851	460	23	.	.	PUNCT
ejpam-6851	461	1	then	then	ADV
ejpam-6851	461	2	s	s	VERB
ejpam-6851	461	3	∈	∈	PROPN
ejpam-6851	461	4	γw(g	γw(g	PUNCT
ejpam-6851	461	5	⋄h	⋄h	X
ejpam-6851	461	6	)	)	PUNCT
ejpam-6851	461	7	if	if	SCONJ
ejpam-6851	461	8	and	and	CCONJ
ejpam-6851	461	9	only	only	ADV
ejpam-6851	461	10	if	if	SCONJ
ejpam-6851	461	11	s	s	VERB
ejpam-6851	461	12	=	=	NOUN
ejpam-6851	461	13	a	a	DET
ejpam-6851	461	14	∪	∪	X
ejpam-6851	461	15	(	(	PUNCT
ejpam-6851	461	16	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-6851	461	17	)	)	PUNCT
ejpam-6851	461	18	,	,	PUNCT
ejpam-6851	461	19	where	where	SCONJ
ejpam-6851	461	20	a	a	DET
ejpam-6851	461	21	⊆	⊆	NUM
ejpam-6851	461	22	v	v	NOUN
ejpam-6851	461	23	(	(	PUNCT
ejpam-6851	461	24	g	g	NOUN
ejpam-6851	461	25	)	)	PUNCT
ejpam-6851	461	26	and	and	CCONJ
ejpam-6851	461	27	suv	suv	PROPN
ejpam-6851	461	28	∈	∈	PROPN
ejpam-6851	461	29	γw(h	γw(h	PUNCT
ejpam-6851	461	30	uv	uv	NOUN
ejpam-6851	461	31	)	)	PUNCT
ejpam-6851	461	32	for	for	ADP
ejpam-6851	461	33	each	each	DET
ejpam-6851	461	34	uv	uv	PROPN
ejpam-6851	461	35	∈	∈	PROPN
ejpam-6851	461	36	e(g	e(g	PROPN
ejpam-6851	461	37	)	)	PUNCT
ejpam-6851	461	38	.	.	PUNCT
ejpam-6851	462	1	proof	proof	NOUN
ejpam-6851	462	2	.	.	PUNCT
ejpam-6851	463	1	assume	assume	VERB
ejpam-6851	463	2	that	that	SCONJ
ejpam-6851	463	3	s	s	VERB
ejpam-6851	463	4	∈	∈	X
ejpam-6851	463	5	γw(g	γw(g	PUNCT
ejpam-6851	463	6	⋄	⋄	PROPN
ejpam-6851	463	7	h	h	NOUN
ejpam-6851	463	8	)	)	PUNCT
ejpam-6851	463	9	.	.	PUNCT
ejpam-6851	464	1	let	let	VERB
ejpam-6851	464	2	a	a	DET
ejpam-6851	464	3	=	=	X
ejpam-6851	464	4	s	s	NOUN
ejpam-6851	464	5	∩	∩	ADJ
ejpam-6851	464	6	v	v	X
ejpam-6851	464	7	(	(	PUNCT
ejpam-6851	464	8	g	g	NOUN
ejpam-6851	464	9	)	)	PUNCT
ejpam-6851	464	10	and	and	CCONJ
ejpam-6851	464	11	suv	suv	PROPN
ejpam-6851	464	12	=	=	PROPN
ejpam-6851	464	13	s	s	PROPN
ejpam-6851	464	14	∩	∩	ADJ
ejpam-6851	464	15	v	v	X
ejpam-6851	464	16	(	(	PUNCT
ejpam-6851	464	17	huv	huv	PROPN
ejpam-6851	464	18	)	)	PUNCT
ejpam-6851	464	19	for	for	ADP
ejpam-6851	464	20	each	each	DET
ejpam-6851	464	21	uv	uv	PROPN
ejpam-6851	464	22	∈	∈	PROPN
ejpam-6851	464	23	e(g	e(g	PROPN
ejpam-6851	464	24	)	)	PUNCT
ejpam-6851	464	25	.	.	PUNCT
ejpam-6851	465	1	then	then	ADV
ejpam-6851	465	2	s	s	VERB
ejpam-6851	465	3	=	=	SYM
ejpam-6851	465	4	a∪	a∪	PROPN
ejpam-6851	465	5	(	(	PUNCT
ejpam-6851	465	6	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-6851	465	7	)	)	PUNCT
ejpam-6851	465	8	.	.	PUNCT
ejpam-6851	466	1	let	let	VERB
ejpam-6851	466	2	uv	uv	PRON
ejpam-6851	466	3	∈	∈	PROPN
ejpam-6851	466	4	e(g	e(g	PROPN
ejpam-6851	466	5	)	)	PUNCT
ejpam-6851	466	6	and	and	CCONJ
ejpam-6851	466	7	let	let	VERB
ejpam-6851	466	8	x	x	SYM
ejpam-6851	466	9	∈	∈	PROPN
ejpam-6851	466	10	v	v	X
ejpam-6851	466	11	(	(	PUNCT
ejpam-6851	466	12	huv	huv	PROPN
ejpam-6851	466	13	)	)	PUNCT
ejpam-6851	466	14	\suv	\suv	PROPN
ejpam-6851	466	15	.	.	PUNCT
ejpam-6851	467	1	j.	j.	PROPN
ejpam-6851	467	2	m.	m.	PROPN
ejpam-6851	467	3	molles	molles	PROPN
ejpam-6851	467	4	,	,	PUNCT
ejpam-6851	467	5	f.	f.	PROPN
ejpam-6851	467	6	p.	p.	PROPN
ejpam-6851	467	7	jamil	jamil	PROPN
ejpam-6851	467	8	,	,	PUNCT
ejpam-6851	467	9	s.	s.	PROPN
ejpam-6851	467	10	r.	r.	PROPN
ejpam-6851	467	11	canoy	canoy	PROPN
ejpam-6851	467	12	/	/	SYM
ejpam-6851	467	13	eur	eur	PROPN
ejpam-6851	467	14	.	.	PUNCT
ejpam-6851	468	1	j.	j.	PROPN
ejpam-6851	468	2	pure	pure	PROPN
ejpam-6851	468	3	appl	appl	PROPN
ejpam-6851	468	4	.	.	PROPN
ejpam-6851	468	5	math	math	PROPN
ejpam-6851	468	6	,	,	PUNCT
ejpam-6851	468	7	18	18	NUM
ejpam-6851	468	8	(	(	PUNCT
ejpam-6851	468	9	4	4	NUM
ejpam-6851	468	10	)	)	PUNCT
ejpam-6851	468	11	(	(	PUNCT
ejpam-6851	468	12	2025	2025	NUM
ejpam-6851	468	13	)	)	PUNCT
ejpam-6851	468	14	,	,	PUNCT
ejpam-6851	468	15	6851	6851	NUM
ejpam-6851	468	16	12	12	NUM
ejpam-6851	468	17	of	of	ADP
ejpam-6851	468	18	18	18	NUM
ejpam-6851	468	19	there	there	ADV
ejpam-6851	468	20	exists	exist	VERB
ejpam-6851	468	21	y	y	PROPN
ejpam-6851	468	22	∈	∈	PROPN
ejpam-6851	468	23	s	s	VERB
ejpam-6851	468	24	such	such	ADJ
ejpam-6851	468	25	that	that	SCONJ
ejpam-6851	468	26	x	x	X
ejpam-6851	468	27	≽g⋄h	≽g⋄h	PROPN
ejpam-6851	468	28	y.	y.	NOUN
ejpam-6851	468	29	since	since	SCONJ
ejpam-6851	468	30	min{degg⋄h(u	min{degg⋄h(u	PROPN
ejpam-6851	468	31	)	)	PUNCT
ejpam-6851	468	32	,	,	PUNCT
ejpam-6851	468	33	degg⋄h(v	degg⋄h(v	PROPN
ejpam-6851	468	34	)	)	PUNCT
ejpam-6851	468	35	}	}	PUNCT
ejpam-6851	468	36	>	>	X
ejpam-6851	469	1	degg⋄h(x	degg⋄h(x	PROPN
ejpam-6851	469	2	)	)	PUNCT
ejpam-6851	469	3	,	,	PUNCT
ejpam-6851	469	4	y	y	PROPN
ejpam-6851	469	5	/∈	/∈	PUNCT
ejpam-6851	469	6	{	{	PUNCT
ejpam-6851	469	7	u	u	NOUN
ejpam-6851	469	8	,	,	PUNCT
ejpam-6851	469	9	v	v	NOUN
ejpam-6851	469	10	}	}	PUNCT
ejpam-6851	469	11	.	.	PUNCT
ejpam-6851	470	1	thus	thus	ADV
ejpam-6851	470	2	,	,	PUNCT
ejpam-6851	470	3	y	y	PROPN
ejpam-6851	470	4	∈	∈	PROPN
ejpam-6851	470	5	suv	suv	PROPN
ejpam-6851	470	6	and	and	CCONJ
ejpam-6851	470	7	y	y	PROPN
ejpam-6851	470	8	≽huv	≽huv	PROPN
ejpam-6851	470	9	suv	suv	PROPN
ejpam-6851	470	10	.	.	PUNCT
ejpam-6851	471	1	this	this	PRON
ejpam-6851	471	2	shows	show	VERB
ejpam-6851	471	3	that	that	SCONJ
ejpam-6851	471	4	suv	suv	PROPN
ejpam-6851	471	5	∈	∈	PROPN
ejpam-6851	471	6	γw(h	γw(h	PUNCT
ejpam-6851	471	7	uv	uv	NOUN
ejpam-6851	471	8	)	)	PUNCT
ejpam-6851	471	9	.	.	PUNCT
ejpam-6851	472	1	conversely	conversely	ADV
ejpam-6851	472	2	,	,	PUNCT
ejpam-6851	472	3	let	let	VERB
ejpam-6851	472	4	x	x	PUNCT
ejpam-6851	472	5	∈	∈	PROPN
ejpam-6851	472	6	v	v	NOUN
ejpam-6851	472	7	(	(	PUNCT
ejpam-6851	472	8	g	g	PROPN
ejpam-6851	472	9	⋄h	⋄h	PROPN
ejpam-6851	472	10	)	)	PUNCT
ejpam-6851	472	11	\	\	PROPN
ejpam-6851	473	1	s.	s.	PROPN
ejpam-6851	473	2	let	let	VERB
ejpam-6851	473	3	uv	uv	PRON
ejpam-6851	473	4	∈	∈	PROPN
ejpam-6851	473	5	e(g	e(g	PROPN
ejpam-6851	473	6	)	)	PUNCT
ejpam-6851	473	7	such	such	ADJ
ejpam-6851	473	8	that	that	SCONJ
ejpam-6851	473	9	x	x	SYM
ejpam-6851	473	10	∈	∈	NOUN
ejpam-6851	473	11	v	v	X
ejpam-6851	473	12	(	(	PUNCT
ejpam-6851	473	13	huv	huv	PROPN
ejpam-6851	473	14	+	+	NUM
ejpam-6851	473	15	uv	uv	NOUN
ejpam-6851	473	16	)	)	PUNCT
ejpam-6851	473	17	.	.	PUNCT
ejpam-6851	474	1	since	since	SCONJ
ejpam-6851	474	2	suv	suv	PROPN
ejpam-6851	474	3	∈	∈	PROPN
ejpam-6851	474	4	γw(h	γw(h	PUNCT
ejpam-6851	474	5	uv	uv	NOUN
ejpam-6851	474	6	)	)	PUNCT
ejpam-6851	474	7	,	,	PUNCT
ejpam-6851	474	8	suv	suv	PROPN
ejpam-6851	474	9	̸=	̸=	PROPN
ejpam-6851	474	10	∅.	∅.	VERB
ejpam-6851	474	11	if	if	SCONJ
ejpam-6851	474	12	x	x	SYM
ejpam-6851	474	13	∈	∈	PROPN
ejpam-6851	474	14	{	{	PUNCT
ejpam-6851	474	15	u	u	NOUN
ejpam-6851	474	16	,	,	PUNCT
ejpam-6851	474	17	v	v	NOUN
ejpam-6851	474	18	}	}	PUNCT
ejpam-6851	474	19	,	,	PUNCT
ejpam-6851	474	20	then	then	ADV
ejpam-6851	474	21	x	x	PUNCT
ejpam-6851	474	22	≽g⋄h	≽g⋄h	NOUN
ejpam-6851	474	23	w	w	VERB
ejpam-6851	474	24	for	for	ADP
ejpam-6851	474	25	each	each	DET
ejpam-6851	474	26	w	w	PROPN
ejpam-6851	474	27	∈	∈	PROPN
ejpam-6851	474	28	suv	suv	NOUN
ejpam-6851	474	29	.	.	PUNCT
ejpam-6851	475	1	also	also	ADV
ejpam-6851	475	2	,	,	PUNCT
ejpam-6851	475	3	if	if	SCONJ
ejpam-6851	475	4	x	x	SYM
ejpam-6851	475	5	∈	∈	PROPN
ejpam-6851	475	6	v	v	NOUN
ejpam-6851	475	7	(	(	PUNCT
ejpam-6851	475	8	huv	huv	PROPN
ejpam-6851	475	9	)	)	PUNCT
ejpam-6851	475	10	\	\	PROPN
ejpam-6851	475	11	suv	suv	PROPN
ejpam-6851	475	12	,	,	PUNCT
ejpam-6851	475	13	then	then	ADV
ejpam-6851	475	14	there	there	PRON
ejpam-6851	475	15	exists	exist	VERB
ejpam-6851	475	16	w	w	PROPN
ejpam-6851	475	17	∈	∈	PROPN
ejpam-6851	475	18	suv	suv	NOUN
ejpam-6851	475	19	for	for	ADP
ejpam-6851	475	20	which	which	PRON
ejpam-6851	475	21	x	x	SYM
ejpam-6851	475	22	≽huv	≽huv	PROPN
ejpam-6851	475	23	w.	w.	PROPN
ejpam-6851	475	24	this	this	PRON
ejpam-6851	475	25	means	mean	VERB
ejpam-6851	475	26	x	x	PUNCT
ejpam-6851	475	27	≽g⋄h	≽g⋄h	PROPN
ejpam-6851	475	28	w.	w.	NOUN
ejpam-6851	475	29	therefore	therefore	ADV
ejpam-6851	475	30	,	,	PUNCT
ejpam-6851	475	31	s	s	PROPN
ejpam-6851	475	32	∈	∈	NOUN
ejpam-6851	475	33	γw(g	γw(g	PUNCT
ejpam-6851	475	34	⋄h	⋄h	PROPN
ejpam-6851	475	35	)	)	PUNCT
ejpam-6851	475	36	.	.	PUNCT
ejpam-6851	476	1	for	for	ADP
ejpam-6851	476	2	a	a	DET
ejpam-6851	476	3	nonempty	nonempty	NOUN
ejpam-6851	476	4	a	a	DET
ejpam-6851	476	5	⊆	⊆	NUM
ejpam-6851	476	6	v	v	NOUN
ejpam-6851	476	7	(	(	PUNCT
ejpam-6851	476	8	g	g	NOUN
ejpam-6851	476	9	)	)	PUNCT
ejpam-6851	476	10	,	,	PUNCT
ejpam-6851	476	11	define	define	VERB
ejpam-6851	476	12	ae	ae	PROPN
ejpam-6851	476	13	=	=	PUNCT
ejpam-6851	476	14	{	{	PUNCT
ejpam-6851	476	15	uv	uv	PROPN
ejpam-6851	476	16	∈	∈	PROPN
ejpam-6851	476	17	e(g	e(g	PROPN
ejpam-6851	476	18	)	)	PUNCT
ejpam-6851	476	19	:	:	PUNCT
ejpam-6851	476	20	u	u	NOUN
ejpam-6851	476	21	/∈	/∈	VERB
ejpam-6851	476	22	a	a	PRON
ejpam-6851	476	23	and	and	CCONJ
ejpam-6851	476	24	v	v	NOUN
ejpam-6851	476	25	/∈	/∈	PUNCT
ejpam-6851	476	26	a	a	PRON
ejpam-6851	476	27	}	}	PUNCT
ejpam-6851	476	28	.	.	PUNCT
ejpam-6851	477	1	corollary	corollary	ADJ
ejpam-6851	477	2	4	4	NUM
ejpam-6851	477	3	.	.	PUNCT
ejpam-6851	478	1	let	let	VERB
ejpam-6851	478	2	g	g	NOUN
ejpam-6851	478	3	and	and	CCONJ
ejpam-6851	478	4	h	h	NOUN
ejpam-6851	478	5	be	be	AUX
ejpam-6851	478	6	connected	connect	VERB
ejpam-6851	478	7	graphs	graph	NOUN
ejpam-6851	478	8	where	where	SCONJ
ejpam-6851	478	9	g	g	PROPN
ejpam-6851	478	10	is	be	AUX
ejpam-6851	478	11	nontrivial	nontrivial	ADJ
ejpam-6851	478	12	.	.	PUNCT
ejpam-6851	479	1	then	then	ADV
ejpam-6851	479	2	(	(	PUNCT
ejpam-6851	479	3	i	i	NOUN
ejpam-6851	479	4	)	)	PUNCT
ejpam-6851	479	5	γs(g	γs(g	PUNCT
ejpam-6851	479	6	⋄h	⋄h	X
ejpam-6851	479	7	)	)	PUNCT
ejpam-6851	479	8	=	=	PUNCT
ejpam-6851	480	1	min{|a|+	min{|a|+	PROPN
ejpam-6851	480	2	|ae|	|ae|	X
ejpam-6851	480	3	:	:	PUNCT
ejpam-6851	480	4	a	a	DET
ejpam-6851	480	5	∈	∈	NOUN
ejpam-6851	480	6	γs(g	γs(g	PUNCT
ejpam-6851	480	7	)	)	PUNCT
ejpam-6851	480	8	}	}	PUNCT
ejpam-6851	480	9	.	.	PUNCT
ejpam-6851	481	1	(	(	PUNCT
ejpam-6851	481	2	ii	ii	NOUN
ejpam-6851	481	3	)	)	PUNCT
ejpam-6851	481	4	γw(g	γw(g	PUNCT
ejpam-6851	482	1	⋄h	⋄h	PROPN
ejpam-6851	482	2	)	)	PUNCT
ejpam-6851	482	3	=	=	SYM
ejpam-6851	482	4	|e(g)|γw(h	|e(g)|γw(h	PROPN
ejpam-6851	482	5	)	)	PUNCT
ejpam-6851	482	6	.	.	PUNCT
ejpam-6851	483	1	proof	proof	NOUN
ejpam-6851	483	2	.	.	PUNCT
ejpam-6851	484	1	to	to	PART
ejpam-6851	484	2	prove	prove	VERB
ejpam-6851	484	3	(	(	PUNCT
ejpam-6851	484	4	i	i	NOUN
ejpam-6851	484	5	)	)	PUNCT
ejpam-6851	484	6	,	,	PUNCT
ejpam-6851	484	7	put	put	VERB
ejpam-6851	484	8	α	α	X
ejpam-6851	485	1	=	=	PUNCT
ejpam-6851	485	2	min{|a|+	min{|a|+	PROPN
ejpam-6851	485	3	|ae|	|ae|	PROPN
ejpam-6851	485	4	:	:	PUNCT
ejpam-6851	485	5	a	a	DET
ejpam-6851	485	6	∈	∈	NOUN
ejpam-6851	485	7	γs(g	γs(g	PUNCT
ejpam-6851	485	8	)	)	PUNCT
ejpam-6851	485	9	}	}	PUNCT
ejpam-6851	485	10	.	.	PUNCT
ejpam-6851	486	1	let	let	VERB
ejpam-6851	486	2	n	n	NOUN
ejpam-6851	486	3	=	=	PRON
ejpam-6851	486	4	|v	|v	PROPN
ejpam-6851	486	5	(	(	PUNCT
ejpam-6851	486	6	g)|	g)|	NOUN
ejpam-6851	486	7	.	.	PUNCT
ejpam-6851	487	1	if	if	SCONJ
ejpam-6851	487	2	n	n	NOUN
ejpam-6851	487	3	=	=	SYM
ejpam-6851	487	4	2	2	NUM
ejpam-6851	487	5	,	,	PUNCT
ejpam-6851	487	6	then	then	ADV
ejpam-6851	487	7	γs(g	γs(g	PUNCT
ejpam-6851	487	8	⋄h	⋄h	PROPN
ejpam-6851	487	9	)	)	PUNCT
ejpam-6851	487	10	=	=	SYM
ejpam-6851	488	1	1	1	NUM
ejpam-6851	488	2	=	=	SYM
ejpam-6851	488	3	α	α	X
ejpam-6851	488	4	.	.	PUNCT
ejpam-6851	488	5	assume	assume	VERB
ejpam-6851	488	6	that	that	SCONJ
ejpam-6851	488	7	n	n	NUM
ejpam-6851	488	8	≥	≥	NUM
ejpam-6851	488	9	3	3	X
ejpam-6851	488	10	.	.	PUNCT
ejpam-6851	489	1	we	we	PRON
ejpam-6851	489	2	consider	consider	VERB
ejpam-6851	489	3	the	the	DET
ejpam-6851	489	4	following	follow	VERB
ejpam-6851	489	5	cases	case	NOUN
ejpam-6851	489	6	:	:	PUNCT
ejpam-6851	489	7	case	case	NOUN
ejpam-6851	489	8	1	1	NUM
ejpam-6851	489	9	:	:	PUNCT
ejpam-6851	489	10	suppose	suppose	VERB
ejpam-6851	489	11	that	that	SCONJ
ejpam-6851	489	12	δ(g	δ(g	PROPN
ejpam-6851	489	13	)	)	PUNCT
ejpam-6851	489	14	≥	≥	NOUN
ejpam-6851	489	15	2	2	NUM
ejpam-6851	489	16	or	or	CCONJ
ejpam-6851	489	17	γ(h	γ(h	NOUN
ejpam-6851	489	18	)	)	PUNCT
ejpam-6851	489	19	≥	≥	NOUN
ejpam-6851	489	20	2	2	NUM
ejpam-6851	489	21	.	.	PUNCT
ejpam-6851	489	22	let	let	VERB
ejpam-6851	489	23	a	a	DET
ejpam-6851	489	24	∈	∈	NOUN
ejpam-6851	489	25	γs(g	γs(g	NUM
ejpam-6851	489	26	)	)	PUNCT
ejpam-6851	489	27	.	.	PUNCT
ejpam-6851	490	1	for	for	ADP
ejpam-6851	490	2	each	each	DET
ejpam-6851	490	3	uv	uv	PROPN
ejpam-6851	490	4	∈	∈	PROPN
ejpam-6851	490	5	ae	ae	PROPN
ejpam-6851	490	6	,	,	PUNCT
ejpam-6851	490	7	denote	denote	VERB
ejpam-6851	490	8	by	by	ADP
ejpam-6851	490	9	wuv	wuv	NOUN
ejpam-6851	490	10	exactly	exactly	ADV
ejpam-6851	490	11	one	one	NUM
ejpam-6851	490	12	of	of	ADP
ejpam-6851	490	13	u	u	NOUN
ejpam-6851	490	14	and	and	CCONJ
ejpam-6851	490	15	v.	v.	CCONJ
ejpam-6851	490	16	then	then	ADV
ejpam-6851	490	17	wuv	wuv	INTJ
ejpam-6851	490	18	strongly	strongly	ADV
ejpam-6851	490	19	dominates	dominate	VERB
ejpam-6851	490	20	v	v	NUM
ejpam-6851	490	21	(	(	PUNCT
ejpam-6851	490	22	huv	huv	PROPN
ejpam-6851	490	23	)	)	PUNCT
ejpam-6851	490	24	.	.	PUNCT
ejpam-6851	491	1	define	define	VERB
ejpam-6851	491	2	a∗	a∗	PROPN
ejpam-6851	491	3	=	=	PUNCT
ejpam-6851	491	4	a	a	DET
ejpam-6851	491	5	∪	∪	X
ejpam-6851	491	6	{	{	PUNCT
ejpam-6851	491	7	wuv	wuv	NOUN
ejpam-6851	491	8	:	:	PUNCT
ejpam-6851	491	9	uv	uv	PROPN
ejpam-6851	491	10	∈	∈	PROPN
ejpam-6851	491	11	ae	ae	PROPN
ejpam-6851	491	12	}	}	PUNCT
ejpam-6851	491	13	.	.	PUNCT
ejpam-6851	492	1	then	then	ADV
ejpam-6851	492	2	a∗	a∗	PROPN
ejpam-6851	492	3	∈	∈	PROPN
ejpam-6851	492	4	γs(g	γs(g	PUNCT
ejpam-6851	492	5	)	)	PUNCT
ejpam-6851	492	6	with	with	ADP
ejpam-6851	492	7	(	(	PUNCT
ejpam-6851	492	8	a∗)e	a∗)e	ADJ
ejpam-6851	492	9	=	=	SYM
ejpam-6851	492	10	∅	∅	NOUN
ejpam-6851	492	11	and	and	CCONJ
ejpam-6851	492	12	|{wuv	|{wuv	NOUN
ejpam-6851	492	13	:	:	PUNCT
ejpam-6851	492	14	uv	uv	NOUN
ejpam-6851	492	15	∈	∈	PROPN
ejpam-6851	492	16	ae}|	ae}|	X
ejpam-6851	492	17	≤	≤	NUM
ejpam-6851	492	18	|ae|	|ae|	PROPN
ejpam-6851	492	19	.	.	PUNCT
ejpam-6851	493	1	by	by	ADP
ejpam-6851	493	2	proposition	proposition	NOUN
ejpam-6851	493	3	5	5	NUM
ejpam-6851	493	4	,	,	PUNCT
ejpam-6851	493	5	a∗	a∗	PROPN
ejpam-6851	493	6	∈	∈	PROPN
ejpam-6851	493	7	γs(g	γs(g	PUNCT
ejpam-6851	493	8	⋄	⋄	PROPN
ejpam-6851	493	9	h	h	NOUN
ejpam-6851	493	10	)	)	PUNCT
ejpam-6851	493	11	so	so	SCONJ
ejpam-6851	493	12	that	that	SCONJ
ejpam-6851	493	13	γs(g	γs(g	PUNCT
ejpam-6851	493	14	⋄h	⋄h	PROPN
ejpam-6851	493	15	)	)	PUNCT
ejpam-6851	493	16	≤	≤	NOUN
ejpam-6851	493	17	|a∗|	|a∗|	PUNCT
ejpam-6851	493	18	≤	≤	NUM
ejpam-6851	493	19	|a|+	|a|+	NOUN
ejpam-6851	493	20	|ae|	|ae|	PROPN
ejpam-6851	493	21	.	.	PUNCT
ejpam-6851	494	1	since	since	SCONJ
ejpam-6851	494	2	a	a	PRON
ejpam-6851	494	3	is	be	AUX
ejpam-6851	494	4	arbitrary	arbitrary	ADJ
ejpam-6851	494	5	,	,	PUNCT
ejpam-6851	494	6	γs(g	γs(g	PUNCT
ejpam-6851	494	7	⋄h	⋄h	PROPN
ejpam-6851	494	8	)	)	PUNCT
ejpam-6851	494	9	≤	≤	NOUN
ejpam-6851	495	1	α	α	X
ejpam-6851	495	2	.	.	PUNCT
ejpam-6851	496	1	to	to	PART
ejpam-6851	496	2	get	get	VERB
ejpam-6851	496	3	the	the	DET
ejpam-6851	496	4	other	other	ADJ
ejpam-6851	496	5	inequality	inequality	NOUN
ejpam-6851	496	6	,	,	PUNCT
ejpam-6851	496	7	let	let	VERB
ejpam-6851	496	8	s	s	PRON
ejpam-6851	496	9	⊆	⊆	NUM
ejpam-6851	496	10	v	v	NOUN
ejpam-6851	496	11	(	(	PUNCT
ejpam-6851	496	12	g	g	PROPN
ejpam-6851	496	13	⋄h	⋄h	PROPN
ejpam-6851	496	14	)	)	PUNCT
ejpam-6851	496	15	be	be	AUX
ejpam-6851	496	16	a	a	DET
ejpam-6851	496	17	γs	γs	NOUN
ejpam-6851	496	18	-	-	PUNCT
ejpam-6851	496	19	set	set	NOUN
ejpam-6851	496	20	of	of	ADP
ejpam-6851	496	21	g	g	PROPN
ejpam-6851	496	22	⋄h	⋄h	PROPN
ejpam-6851	496	23	.	.	PUNCT
ejpam-6851	497	1	by	by	ADP
ejpam-6851	497	2	proposition	proposition	NOUN
ejpam-6851	497	3	5	5	NUM
ejpam-6851	497	4	,	,	PUNCT
ejpam-6851	497	5	there	there	PRON
ejpam-6851	497	6	exists	exist	VERB
ejpam-6851	497	7	a	a	DET
ejpam-6851	497	8	∈	∈	NOUN
ejpam-6851	497	9	γs(g	γs(g	PUNCT
ejpam-6851	497	10	)	)	PUNCT
ejpam-6851	497	11	such	such	ADJ
ejpam-6851	497	12	that	that	PRON
ejpam-6851	497	13	s	s	VERB
ejpam-6851	497	14	=	=	PUNCT
ejpam-6851	497	15	a	a	DET
ejpam-6851	497	16	∪	∪	X
ejpam-6851	497	17	(	(	PUNCT
ejpam-6851	497	18	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-6851	497	19	)	)	PUNCT
ejpam-6851	497	20	,	,	PUNCT
ejpam-6851	497	21	where	where	SCONJ
ejpam-6851	497	22	suv	suv	PROPN
ejpam-6851	497	23	∈	∈	PROPN
ejpam-6851	497	24	γs(h	γs(h	SYM
ejpam-6851	497	25	uv	uv	NOUN
ejpam-6851	497	26	)	)	PUNCT
ejpam-6851	497	27	for	for	ADP
ejpam-6851	497	28	each	each	DET
ejpam-6851	497	29	uv	uv	PROPN
ejpam-6851	497	30	∈	∈	PROPN
ejpam-6851	497	31	ae	ae	PROPN
ejpam-6851	497	32	.	.	PUNCT
ejpam-6851	498	1	we	we	PRON
ejpam-6851	498	2	have	have	VERB
ejpam-6851	498	3	γs(g	γs(g	PUNCT
ejpam-6851	498	4	⋄h	⋄h	PROPN
ejpam-6851	498	5	)	)	PUNCT
ejpam-6851	498	6	=	=	PUNCT
ejpam-6851	498	7	|s|	|s|	NOUN
ejpam-6851	498	8	≥	≥	PRON
ejpam-6851	498	9	|a|+	|a|+	VERB
ejpam-6851	498	10	∑	∑	PUNCT
ejpam-6851	498	11	uv∈ae	uv∈ae	PUNCT
ejpam-6851	498	12	|suv|	|suv|	PROPN
ejpam-6851	498	13	≥	≥	PRON
ejpam-6851	498	14	|a|+	|a|+	VERB
ejpam-6851	498	15	|ae|γs(h	|ae|γs(h	PROPN
ejpam-6851	498	16	)	)	PUNCT
ejpam-6851	498	17	≥	≥	NOUN
ejpam-6851	498	18	α	α	NOUN
ejpam-6851	498	19	.	.	PUNCT
ejpam-6851	498	20	case	case	NOUN
ejpam-6851	498	21	2	2	NUM
ejpam-6851	498	22	:	:	PUNCT
ejpam-6851	498	23	suppose	suppose	VERB
ejpam-6851	498	24	that	that	SCONJ
ejpam-6851	498	25	δ(g	δ(g	PROPN
ejpam-6851	498	26	)	)	PUNCT
ejpam-6851	498	27	=	=	SYM
ejpam-6851	498	28	1	1	NUM
ejpam-6851	498	29	=	=	SYM
ejpam-6851	498	30	γ(h	γ(h	NOUN
ejpam-6851	498	31	)	)	PUNCT
ejpam-6851	498	32	.	.	PUNCT
ejpam-6851	499	1	for	for	ADP
ejpam-6851	499	2	each	each	DET
ejpam-6851	499	3	uv	uv	PROPN
ejpam-6851	499	4	∈	∈	PROPN
ejpam-6851	499	5	e(g	e(g	PROPN
ejpam-6851	499	6	)	)	PUNCT
ejpam-6851	499	7	,	,	PUNCT
ejpam-6851	499	8	let	let	VERB
ejpam-6851	499	9	xuv	xuv	PRON
ejpam-6851	499	10	∈	∈	PROPN
ejpam-6851	499	11	v	v	X
ejpam-6851	499	12	(	(	PUNCT
ejpam-6851	499	13	huv	huv	PROPN
ejpam-6851	499	14	)	)	PUNCT
ejpam-6851	499	15	such	such	ADJ
ejpam-6851	499	16	that	that	DET
ejpam-6851	499	17	nhuv	nhuv	PROPN
ejpam-6851	500	1	[	[	X
ejpam-6851	500	2	xuv	xuv	X
ejpam-6851	500	3	]	]	X
ejpam-6851	500	4	=	=	SYM
ejpam-6851	500	5	v	v	X
ejpam-6851	500	6	(	(	PUNCT
ejpam-6851	500	7	huv	huv	PROPN
ejpam-6851	500	8	)	)	PUNCT
ejpam-6851	500	9	.	.	PUNCT
ejpam-6851	501	1	it	it	PRON
ejpam-6851	501	2	is	be	AUX
ejpam-6851	501	3	worth	worth	ADJ
ejpam-6851	501	4	noting	note	VERB
ejpam-6851	501	5	that	that	SCONJ
ejpam-6851	501	6	if	if	SCONJ
ejpam-6851	501	7	u	u	PROPN
ejpam-6851	501	8	∈	∈	PROPN
ejpam-6851	501	9	end(g	end(g	PROPN
ejpam-6851	501	10	)	)	PUNCT
ejpam-6851	501	11	or	or	CCONJ
ejpam-6851	501	12	v	v	ADP
ejpam-6851	501	13	∈	∈	PROPN
ejpam-6851	501	14	end(g	end(g	PROPN
ejpam-6851	501	15	)	)	PUNCT
ejpam-6851	501	16	,	,	PUNCT
ejpam-6851	501	17	say	say	VERB
ejpam-6851	501	18	u	u	PROPN
ejpam-6851	501	19	∈	∈	PROPN
ejpam-6851	501	20	end(g	end(g	PROPN
ejpam-6851	501	21	)	)	PUNCT
ejpam-6851	501	22	,	,	PUNCT
ejpam-6851	501	23	then	then	ADV
ejpam-6851	501	24	degg⋄h(xuv	degg⋄h(xuv	PROPN
ejpam-6851	501	25	)	)	PUNCT
ejpam-6851	502	1	=	=	SYM
ejpam-6851	502	2	degg⋄h(u	degg⋄h(u	PROPN
ejpam-6851	502	3	)	)	PUNCT
ejpam-6851	502	4	.	.	PUNCT
ejpam-6851	503	1	also	also	ADV
ejpam-6851	503	2	,	,	PUNCT
ejpam-6851	503	3	degg⋄h(xuv	degg⋄h(xuv	PROPN
ejpam-6851	503	4	)	)	PUNCT
ejpam-6851	503	5	<	<	X
ejpam-6851	504	1	degg⋄h(y	degg⋄h(y	PROPN
ejpam-6851	504	2	)	)	PUNCT
ejpam-6851	505	1	for	for	ADP
ejpam-6851	505	2	all	all	DET
ejpam-6851	505	3	y	y	PROPN
ejpam-6851	505	4	∈	∈	PROPN
ejpam-6851	505	5	{	{	PUNCT
ejpam-6851	505	6	u	u	NOUN
ejpam-6851	505	7	,	,	PUNCT
ejpam-6851	505	8	v	v	NOUN
ejpam-6851	505	9	}	}	PUNCT
ejpam-6851	505	10	\	\	PROPN
ejpam-6851	505	11	end(g	end(g	PROPN
ejpam-6851	505	12	)	)	PUNCT
ejpam-6851	505	13	and	and	CCONJ
ejpam-6851	505	14	that	that	SCONJ
ejpam-6851	505	15	{	{	PUNCT
ejpam-6851	505	16	xuv	xuv	NOUN
ejpam-6851	505	17	}	}	PUNCT
ejpam-6851	505	18	∈	∈	PROPN
ejpam-6851	505	19	γs(h	γs(h	X
ejpam-6851	505	20	uv	uv	NOUN
ejpam-6851	505	21	)	)	PUNCT
ejpam-6851	505	22	.	.	PUNCT
ejpam-6851	506	1	choose	choose	VERB
ejpam-6851	506	2	a	a	DET
ejpam-6851	506	3	∈	∈	NOUN
ejpam-6851	506	4	γs(g	γs(g	PUNCT
ejpam-6851	506	5	)	)	PUNCT
ejpam-6851	506	6	such	such	ADJ
ejpam-6851	506	7	that	that	SCONJ
ejpam-6851	506	8	|a|+	|a|+	VERB
ejpam-6851	506	9	|ae|	|ae|	X
ejpam-6851	506	10	=	=	SYM
ejpam-6851	506	11	α	α	X
ejpam-6851	506	12	.	.	PUNCT
ejpam-6851	506	13	construct	construct	VERB
ejpam-6851	506	14	an	an	DET
ejpam-6851	506	15	a∗	a∗	PROPN
ejpam-6851	506	16	∈	∈	NOUN
ejpam-6851	506	17	γs(g	γs(g	PUNCT
ejpam-6851	506	18	)	)	PUNCT
ejpam-6851	506	19	as	as	ADP
ejpam-6851	506	20	in	in	ADP
ejpam-6851	506	21	the	the	DET
ejpam-6851	506	22	proof	proof	NOUN
ejpam-6851	506	23	of	of	ADP
ejpam-6851	506	24	lemma	lemma	PROPN
ejpam-6851	506	25	1	1	NUM
ejpam-6851	507	1	such	such	ADJ
ejpam-6851	507	2	that	that	SCONJ
ejpam-6851	507	3	|a∗|	|a∗|	ADV
ejpam-6851	507	4	≤	≤	NUM
ejpam-6851	507	5	|a|	|a|	NOUN
ejpam-6851	507	6	and	and	CCONJ
ejpam-6851	507	7	a∗∩end(g	a∗∩end(g	NUM
ejpam-6851	507	8	)	)	PUNCT
ejpam-6851	508	1	=	=	PUNCT
ejpam-6851	508	2	∅.	∅.	PRON
ejpam-6851	508	3	more	more	ADV
ejpam-6851	508	4	precisely	precisely	ADV
ejpam-6851	508	5	,	,	PUNCT
ejpam-6851	508	6	a∗	a∗	NOUN
ejpam-6851	508	7	=	=	SYM
ejpam-6851	508	8	(	(	PUNCT
ejpam-6851	508	9	a\end(g))∪	a\end(g))∪	PROPN
ejpam-6851	508	10	{	{	PUNCT
ejpam-6851	508	11	xv	xv	PROPN
ejpam-6851	508	12	/∈	/∈	VERB
ejpam-6851	509	1	a	a	DET
ejpam-6851	509	2	:	:	PUNCT
ejpam-6851	509	3	v	v	NUM
ejpam-6851	509	4	∈	∈	PROPN
ejpam-6851	509	5	a	a	DET
ejpam-6851	509	6	∩	∩	ADJ
ejpam-6851	509	7	end(g	end(g	PROPN
ejpam-6851	509	8	)	)	PUNCT
ejpam-6851	509	9	}	}	PUNCT
ejpam-6851	509	10	.	.	PUNCT
ejpam-6851	510	1	define	define	VERB
ejpam-6851	510	2	s∗	s∗	PROPN
ejpam-6851	510	3	=	=	SYM
ejpam-6851	510	4	a∗	a∗	PROPN
ejpam-6851	510	5	∪	∪	X
ejpam-6851	510	6	(	(	PUNCT
ejpam-6851	510	7	∪uv∈ae{xuv	∪uv∈ae{xuv	NOUN
ejpam-6851	510	8	}	}	PUNCT
ejpam-6851	510	9	)	)	PUNCT
ejpam-6851	510	10	.	.	PUNCT
ejpam-6851	511	1	then	then	ADV
ejpam-6851	511	2	s∗	s∗	PROPN
ejpam-6851	511	3	∈	∈	PROPN
ejpam-6851	511	4	γs(g	γs(g	PUNCT
ejpam-6851	511	5	⋄	⋄	PROPN
ejpam-6851	511	6	h	h	NOUN
ejpam-6851	511	7	)	)	PUNCT
ejpam-6851	511	8	.	.	PUNCT
ejpam-6851	512	1	thus	thus	ADV
ejpam-6851	512	2	,	,	PUNCT
ejpam-6851	512	3	γs(g	γs(g	PUNCT
ejpam-6851	512	4	⋄h	⋄h	PROPN
ejpam-6851	512	5	)	)	PUNCT
ejpam-6851	512	6	≤	≤	NOUN
ejpam-6851	512	7	|s∗|	|s∗|	NUM
ejpam-6851	512	8	≤	≤	NUM
ejpam-6851	512	9	|a|+	|a|+	NOUN
ejpam-6851	512	10	|ae|	|ae|	PUNCT
ejpam-6851	512	11	=	=	SYM
ejpam-6851	512	12	α	α	X
ejpam-6851	512	13	.	.	PUNCT
ejpam-6851	513	1	j.	j.	PROPN
ejpam-6851	513	2	m.	m.	PROPN
ejpam-6851	513	3	molles	molles	PROPN
ejpam-6851	513	4	,	,	PUNCT
ejpam-6851	513	5	f.	f.	PROPN
ejpam-6851	513	6	p.	p.	PROPN
ejpam-6851	513	7	jamil	jamil	PROPN
ejpam-6851	513	8	,	,	PUNCT
ejpam-6851	513	9	s.	s.	PROPN
ejpam-6851	513	10	r.	r.	PROPN
ejpam-6851	513	11	canoy	canoy	PROPN
ejpam-6851	513	12	/	/	SYM
ejpam-6851	513	13	eur	eur	PROPN
ejpam-6851	513	14	.	.	PUNCT
ejpam-6851	514	1	j.	j.	PROPN
ejpam-6851	514	2	pure	pure	PROPN
ejpam-6851	514	3	appl	appl	PROPN
ejpam-6851	514	4	.	.	PROPN
ejpam-6851	514	5	math	math	PROPN
ejpam-6851	514	6	,	,	PUNCT
ejpam-6851	514	7	18	18	NUM
ejpam-6851	514	8	(	(	PUNCT
ejpam-6851	514	9	4	4	NUM
ejpam-6851	514	10	)	)	PUNCT
ejpam-6851	514	11	(	(	PUNCT
ejpam-6851	514	12	2025	2025	NUM
ejpam-6851	514	13	)	)	PUNCT
ejpam-6851	514	14	,	,	PUNCT
ejpam-6851	514	15	6851	6851	NUM
ejpam-6851	514	16	13	13	NUM
ejpam-6851	514	17	of	of	ADP
ejpam-6851	514	18	18	18	NUM
ejpam-6851	514	19	to	to	PART
ejpam-6851	514	20	get	get	VERB
ejpam-6851	514	21	the	the	DET
ejpam-6851	514	22	other	other	ADJ
ejpam-6851	514	23	inequality	inequality	NOUN
ejpam-6851	514	24	,	,	PUNCT
ejpam-6851	514	25	let	let	VERB
ejpam-6851	514	26	s	s	PRON
ejpam-6851	514	27	⊆	⊆	NUM
ejpam-6851	514	28	v	v	NOUN
ejpam-6851	514	29	(	(	PUNCT
ejpam-6851	514	30	g	g	PROPN
ejpam-6851	514	31	⋄h	⋄h	PROPN
ejpam-6851	514	32	)	)	PUNCT
ejpam-6851	514	33	be	be	AUX
ejpam-6851	514	34	a	a	DET
ejpam-6851	514	35	γs	γs	NOUN
ejpam-6851	514	36	-	-	PUNCT
ejpam-6851	514	37	set	set	NOUN
ejpam-6851	514	38	of	of	ADP
ejpam-6851	514	39	g	g	PROPN
ejpam-6851	514	40	⋄h	⋄h	PROPN
ejpam-6851	514	41	.	.	PUNCT
ejpam-6851	515	1	put	put	VERB
ejpam-6851	515	2	a	a	DET
ejpam-6851	515	3	=	=	X
ejpam-6851	515	4	s	s	NOUN
ejpam-6851	515	5	∩v	∩v	NOUN
ejpam-6851	515	6	(	(	PUNCT
ejpam-6851	515	7	g	g	NOUN
ejpam-6851	515	8	)	)	PUNCT
ejpam-6851	515	9	and	and	CCONJ
ejpam-6851	515	10	suv	suv	PROPN
ejpam-6851	515	11	=	=	PROPN
ejpam-6851	515	12	s	s	PROPN
ejpam-6851	515	13	∩	∩	ADJ
ejpam-6851	515	14	v	v	X
ejpam-6851	515	15	(	(	PUNCT
ejpam-6851	515	16	huv	huv	PROPN
ejpam-6851	515	17	)	)	PUNCT
ejpam-6851	515	18	for	for	ADP
ejpam-6851	515	19	all	all	DET
ejpam-6851	515	20	uv	uv	PROPN
ejpam-6851	515	21	∈	∈	PROPN
ejpam-6851	515	22	e(g	e(g	PROPN
ejpam-6851	515	23	)	)	PUNCT
ejpam-6851	515	24	.	.	PUNCT
ejpam-6851	516	1	let	let	VERB
ejpam-6851	516	2	ae	ae	PROPN
ejpam-6851	516	3	=	=	PUNCT
ejpam-6851	516	4	{	{	PUNCT
ejpam-6851	516	5	uv	uv	PROPN
ejpam-6851	516	6	∈	∈	PROPN
ejpam-6851	516	7	e(g	e(g	PROPN
ejpam-6851	516	8	)	)	PUNCT
ejpam-6851	516	9	:	:	PUNCT
ejpam-6851	517	1	u	u	NOUN
ejpam-6851	517	2	,	,	PUNCT
ejpam-6851	517	3	v	v	NOUN
ejpam-6851	517	4	/∈	/∈	PROPN
ejpam-6851	517	5	a	a	PRON
ejpam-6851	517	6	}	}	PUNCT
ejpam-6851	517	7	.	.	PUNCT
ejpam-6851	518	1	if	if	SCONJ
ejpam-6851	518	2	uv	uv	PROPN
ejpam-6851	518	3	∈	∈	PROPN
ejpam-6851	518	4	ae	ae	PROPN
ejpam-6851	518	5	,	,	PUNCT
ejpam-6851	518	6	then	then	ADV
ejpam-6851	518	7	suv	suv	PROPN
ejpam-6851	518	8	is	be	AUX
ejpam-6851	518	9	a	a	DET
ejpam-6851	518	10	γs	γs	NOUN
ejpam-6851	518	11	-	-	PUNCT
ejpam-6851	518	12	set	set	NOUN
ejpam-6851	518	13	of	of	ADP
ejpam-6851	518	14	h	h	NOUN
ejpam-6851	518	15	uv	uv	NOUN
ejpam-6851	518	16	.	.	PUNCT
ejpam-6851	519	1	hence	hence	ADV
ejpam-6851	519	2	,	,	PUNCT
ejpam-6851	519	3	suv	suv	PROPN
ejpam-6851	519	4	=	=	SYM
ejpam-6851	519	5	{	{	PUNCT
ejpam-6851	519	6	xuv	xuv	PROPN
ejpam-6851	519	7	}	}	PUNCT
ejpam-6851	519	8	where	where	SCONJ
ejpam-6851	519	9	xuv	xuv	PROPN
ejpam-6851	519	10	∈	∈	PROPN
ejpam-6851	519	11	v	v	X
ejpam-6851	519	12	(	(	PUNCT
ejpam-6851	519	13	huv	huv	PROPN
ejpam-6851	519	14	)	)	PUNCT
ejpam-6851	519	15	such	such	ADJ
ejpam-6851	519	16	that	that	DET
ejpam-6851	519	17	nhuv	nhuv	PROPN
ejpam-6851	520	1	[	[	X
ejpam-6851	520	2	xuv	xuv	X
ejpam-6851	520	3	]	]	X
ejpam-6851	520	4	=	=	SYM
ejpam-6851	520	5	v	v	X
ejpam-6851	520	6	(	(	PUNCT
ejpam-6851	520	7	huv	huv	PROPN
ejpam-6851	520	8	)	)	PUNCT
ejpam-6851	520	9	.	.	PUNCT
ejpam-6851	521	1	thus	thus	ADV
ejpam-6851	521	2	,	,	PUNCT
ejpam-6851	521	3	γs(g	γs(g	PUNCT
ejpam-6851	521	4	⋄h	⋄h	PROPN
ejpam-6851	521	5	)	)	PUNCT
ejpam-6851	521	6	=	=	SYM
ejpam-6851	521	7	|s|	|s|	NOUN
ejpam-6851	521	8	=	=	PUNCT
ejpam-6851	521	9	|a|+	|a|+	NOUN
ejpam-6851	521	10	∑	∑	PUNCT
ejpam-6851	521	11	uv∈ae	uv∈ae	X
ejpam-6851	521	12	|suv|+	|suv|+	NOUN
ejpam-6851	521	13	∑	∑	ADP
ejpam-6851	521	14	uv∈e(g)\ae	uv∈e(g)\ae	PROPN
ejpam-6851	521	15	|suv|	|suv|	NOUN
ejpam-6851	521	16	=	=	PUNCT
ejpam-6851	521	17	|a|+	|a|+	NOUN
ejpam-6851	521	18	|ae|+	|ae|+	NOUN
ejpam-6851	521	19	∑	∑	ADP
ejpam-6851	521	20	uv∈e(g)\ae	uv∈e(g)\ae	PROPN
ejpam-6851	521	21	|suv|	|suv|	PROPN
ejpam-6851	521	22	≥	≥	PRON
ejpam-6851	521	23	|a|+	|a|+	VERB
ejpam-6851	521	24	|ae|	|ae|	PUNCT
ejpam-6851	521	25	=	=	SYM
ejpam-6851	521	26	α	α	X
ejpam-6851	521	27	.	.	PUNCT
ejpam-6851	522	1	to	to	PART
ejpam-6851	522	2	prove	prove	VERB
ejpam-6851	522	3	(	(	PUNCT
ejpam-6851	522	4	ii	ii	NOUN
ejpam-6851	522	5	)	)	PUNCT
ejpam-6851	522	6	,	,	PUNCT
ejpam-6851	522	7	note	note	VERB
ejpam-6851	522	8	that	that	SCONJ
ejpam-6851	522	9	if	if	SCONJ
ejpam-6851	522	10	γ(h	γ(h	NOUN
ejpam-6851	522	11	)	)	PUNCT
ejpam-6851	522	12	̸=	̸=	PROPN
ejpam-6851	522	13	1	1	NUM
ejpam-6851	522	14	,	,	PUNCT
ejpam-6851	522	15	then	then	ADV
ejpam-6851	522	16	it	it	PRON
ejpam-6851	522	17	follows	follow	VERB
ejpam-6851	522	18	from	from	ADP
ejpam-6851	522	19	proposition	proposition	NOUN
ejpam-6851	522	20	6	6	NUM
ejpam-6851	522	21	that	that	PRON
ejpam-6851	522	22	s	s	VERB
ejpam-6851	522	23	⊆	⊆	NUM
ejpam-6851	522	24	v	v	NOUN
ejpam-6851	522	25	(	(	PUNCT
ejpam-6851	522	26	g	g	PROPN
ejpam-6851	522	27	⋄	⋄	PROPN
ejpam-6851	522	28	h	h	NOUN
ejpam-6851	522	29	)	)	PUNCT
ejpam-6851	522	30	is	be	AUX
ejpam-6851	522	31	a	a	DET
ejpam-6851	522	32	γw	γw	NOUN
ejpam-6851	522	33	-	-	PUNCT
ejpam-6851	522	34	set	set	NOUN
ejpam-6851	522	35	of	of	ADP
ejpam-6851	522	36	g	g	PROPN
ejpam-6851	522	37	⋄	⋄	PROPN
ejpam-6851	522	38	h	h	NOUN
ejpam-6851	523	1	if	if	SCONJ
ejpam-6851	523	2	and	and	CCONJ
ejpam-6851	523	3	only	only	ADV
ejpam-6851	523	4	if	if	SCONJ
ejpam-6851	523	5	s	s	X
ejpam-6851	523	6	=	=	SYM
ejpam-6851	523	7	∪uv∈e(gsuv	∪uv∈e(gsuv	NOUN
ejpam-6851	523	8	,	,	PUNCT
ejpam-6851	523	9	where	where	SCONJ
ejpam-6851	523	10	suv	suv	PROPN
ejpam-6851	523	11	is	be	AUX
ejpam-6851	523	12	a	a	DET
ejpam-6851	523	13	γw	γw	NOUN
ejpam-6851	523	14	-	-	PUNCT
ejpam-6851	523	15	set	set	NOUN
ejpam-6851	523	16	of	of	ADP
ejpam-6851	523	17	huv	huv	PROPN
ejpam-6851	523	18	for	for	ADP
ejpam-6851	523	19	each	each	DET
ejpam-6851	523	20	uv	uv	PROPN
ejpam-6851	523	21	∈	∈	PROPN
ejpam-6851	523	22	e(g	e(g	PROPN
ejpam-6851	523	23	)	)	PUNCT
ejpam-6851	523	24	.	.	PUNCT
ejpam-6851	524	1	in	in	ADP
ejpam-6851	524	2	this	this	DET
ejpam-6851	524	3	case	case	NOUN
ejpam-6851	524	4	,	,	PUNCT
ejpam-6851	524	5	γw(g	γw(g	PUNCT
ejpam-6851	524	6	⋄	⋄	PROPN
ejpam-6851	524	7	h	h	NOUN
ejpam-6851	524	8	)	)	PUNCT
ejpam-6851	524	9	=	=	SYM
ejpam-6851	524	10	|e(g)|γw(h	|e(g)|γw(h	NUM
ejpam-6851	524	11	)	)	PUNCT
ejpam-6851	524	12	.	.	PUNCT
ejpam-6851	525	1	now	now	ADV
ejpam-6851	525	2	suppose	suppose	VERB
ejpam-6851	525	3	that	that	SCONJ
ejpam-6851	525	4	γ(h	γ(h	NOUN
ejpam-6851	525	5	)	)	PUNCT
ejpam-6851	525	6	=	=	PUNCT
ejpam-6851	526	1	1	1	X
ejpam-6851	526	2	.	.	X
ejpam-6851	527	1	if	if	SCONJ
ejpam-6851	527	2	h	h	NOUN
ejpam-6851	527	3	is	be	AUX
ejpam-6851	527	4	complete	complete	ADJ
ejpam-6851	527	5	,	,	PUNCT
ejpam-6851	527	6	then	then	ADV
ejpam-6851	527	7	γw(g	γw(g	PUNCT
ejpam-6851	527	8	⋄h	⋄h	PROPN
ejpam-6851	527	9	)	)	PUNCT
ejpam-6851	528	1	=	=	PUNCT
ejpam-6851	528	2	|e(g)|	|e(g)|	NOUN
ejpam-6851	528	3	=	=	SYM
ejpam-6851	528	4	|e(g)|γw(h	|e(g)|γw(h	NUM
ejpam-6851	528	5	)	)	PUNCT
ejpam-6851	528	6	.	.	PUNCT
ejpam-6851	529	1	assume	assume	VERB
ejpam-6851	529	2	h	h	NOUN
ejpam-6851	529	3	is	be	AUX
ejpam-6851	529	4	not	not	PART
ejpam-6851	529	5	complete	complete	ADJ
ejpam-6851	529	6	.	.	PUNCT
ejpam-6851	530	1	in	in	ADP
ejpam-6851	530	2	view	view	NOUN
ejpam-6851	530	3	of	of	ADP
ejpam-6851	530	4	lemma	lemma	PROPN
ejpam-6851	530	5	2	2	NUM
ejpam-6851	530	6	,	,	PUNCT
ejpam-6851	530	7	s	s	NOUN
ejpam-6851	530	8	contains	contain	VERB
ejpam-6851	530	9	xuv	xuv	NOUN
ejpam-6851	530	10	for	for	ADP
ejpam-6851	530	11	which	which	PRON
ejpam-6851	530	12	δ(huv	δ(huv	PRON
ejpam-6851	530	13	)	)	PUNCT
ejpam-6851	531	1	=	=	SYM
ejpam-6851	531	2	deghuv(xuv	deghuv(xuv	PROPN
ejpam-6851	531	3	)	)	PUNCT
ejpam-6851	531	4	for	for	ADP
ejpam-6851	531	5	each	each	DET
ejpam-6851	531	6	uv	uv	PROPN
ejpam-6851	531	7	∈	∈	PROPN
ejpam-6851	531	8	e(g	e(g	PROPN
ejpam-6851	531	9	)	)	PUNCT
ejpam-6851	531	10	.	.	PUNCT
ejpam-6851	532	1	since	since	SCONJ
ejpam-6851	532	2	s	s	PROPN
ejpam-6851	532	3	is	be	AUX
ejpam-6851	532	4	a	a	DET
ejpam-6851	532	5	γw	γw	NOUN
ejpam-6851	532	6	-	-	PUNCT
ejpam-6851	532	7	set	set	VERB
ejpam-6851	532	8	and	and	CCONJ
ejpam-6851	532	9	u	u	NOUN
ejpam-6851	532	10	≽g⋄h	≽g⋄h	PROPN
ejpam-6851	532	11	xuv	xuv	NOUN
ejpam-6851	532	12	and	and	CCONJ
ejpam-6851	532	13	v	v	ADP
ejpam-6851	532	14	≽g⋄h	≽g⋄h	PROPN
ejpam-6851	532	15	xuv	xuv	PROPN
ejpam-6851	532	16	,	,	PUNCT
ejpam-6851	532	17	{	{	PUNCT
ejpam-6851	532	18	u	u	NOUN
ejpam-6851	532	19	,	,	PUNCT
ejpam-6851	532	20	v	v	NOUN
ejpam-6851	532	21	}	}	PUNCT
ejpam-6851	532	22	∩	∩	ADJ
ejpam-6851	532	23	suv	suv	NOUN
ejpam-6851	532	24	=	=	NOUN
ejpam-6851	532	25	∅	∅	NOUN
ejpam-6851	532	26	for	for	ADP
ejpam-6851	532	27	all	all	DET
ejpam-6851	532	28	uv	uv	PROPN
ejpam-6851	532	29	∈	∈	PROPN
ejpam-6851	532	30	e(g	e(g	PROPN
ejpam-6851	532	31	)	)	PUNCT
ejpam-6851	532	32	.	.	PUNCT
ejpam-6851	533	1	consequently	consequently	ADV
ejpam-6851	533	2	,	,	PUNCT
ejpam-6851	533	3	s	s	PART
ejpam-6851	533	4	=	=	VERB
ejpam-6851	533	5	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-6851	533	6	where	where	SCONJ
ejpam-6851	533	7	suv	suv	PROPN
ejpam-6851	533	8	is	be	AUX
ejpam-6851	533	9	a	a	DET
ejpam-6851	533	10	γs	γs	NOUN
ejpam-6851	533	11	-	-	PUNCT
ejpam-6851	533	12	set	set	NOUN
ejpam-6851	533	13	of	of	ADP
ejpam-6851	533	14	h	h	NOUN
ejpam-6851	533	15	uv	uv	NOUN
ejpam-6851	533	16	.	.	PUNCT
ejpam-6851	534	1	therefore	therefore	ADV
ejpam-6851	534	2	,	,	PUNCT
ejpam-6851	534	3	γs(g	γs(g	PUNCT
ejpam-6851	534	4	⋄h	⋄h	PROPN
ejpam-6851	534	5	)	)	PUNCT
ejpam-6851	534	6	=	=	SYM
ejpam-6851	534	7	|s|	|s|	PROPN
ejpam-6851	534	8	=	=	PUNCT
ejpam-6851	534	9	|e(g)|γw(h	|e(g)|γw(h	NUM
ejpam-6851	534	10	)	)	PUNCT
ejpam-6851	534	11	.	.	PUNCT
ejpam-6851	535	1	the	the	DET
ejpam-6851	535	2	value	value	NOUN
ejpam-6851	535	3	of	of	ADP
ejpam-6851	535	4	γs(g	γs(g	PUNCT
ejpam-6851	535	5	⋄h	⋄h	PROPN
ejpam-6851	535	6	)	)	PUNCT
ejpam-6851	535	7	in	in	ADP
ejpam-6851	535	8	corollary	corollary	ADJ
ejpam-6851	535	9	4	4	NUM
ejpam-6851	535	10	is	be	AUX
ejpam-6851	535	11	not	not	PART
ejpam-6851	535	12	necessarily	necessarily	ADV
ejpam-6851	535	13	determined	determine	VERB
ejpam-6851	535	14	by	by	ADP
ejpam-6851	535	15	a	a	DET
ejpam-6851	535	16	γs	γs	NOUN
ejpam-6851	535	17	-	-	PUNCT
ejpam-6851	535	18	set	set	VERB
ejpam-6851	535	19	a	a	PRON
ejpam-6851	535	20	of	of	ADP
ejpam-6851	535	21	g.	g.	NOUN
ejpam-6851	535	22	observe	observe	VERB
ejpam-6851	535	23	that	that	SCONJ
ejpam-6851	535	24	γs(c6	γs(c6	ADP
ejpam-6851	535	25	⋄	⋄	PROPN
ejpam-6851	535	26	h	h	NOUN
ejpam-6851	535	27	)	)	PUNCT
ejpam-6851	535	28	=	=	SYM
ejpam-6851	535	29	3	3	NUM
ejpam-6851	535	30	for	for	ADP
ejpam-6851	535	31	any	any	DET
ejpam-6851	535	32	connected	connected	ADJ
ejpam-6851	535	33	graph	graph	NOUN
ejpam-6851	535	34	h	h	NOUN
ejpam-6851	535	35	,	,	PUNCT
ejpam-6851	535	36	and	and	CCONJ
ejpam-6851	535	37	is	be	AUX
ejpam-6851	535	38	not	not	PART
ejpam-6851	535	39	determined	determine	VERB
ejpam-6851	535	40	by	by	ADP
ejpam-6851	535	41	any	any	DET
ejpam-6851	535	42	γs	γs	NOUN
ejpam-6851	535	43	-	-	PUNCT
ejpam-6851	535	44	set	set	NOUN
ejpam-6851	535	45	of	of	ADP
ejpam-6851	535	46	c6	c6	PROPN
ejpam-6851	535	47	.	.	PUNCT
ejpam-6851	536	1	example	example	NOUN
ejpam-6851	537	1	2	2	NUM
ejpam-6851	537	2	.	.	PUNCT
ejpam-6851	537	3	let	let	VERB
ejpam-6851	537	4	g	g	NOUN
ejpam-6851	537	5	be	be	AUX
ejpam-6851	537	6	any	any	DET
ejpam-6851	537	7	graph	graph	NOUN
ejpam-6851	537	8	.	.	PUNCT
ejpam-6851	538	1	for	for	ADP
ejpam-6851	538	2	positive	positive	ADJ
ejpam-6851	538	3	integers	integer	NOUN
ejpam-6851	538	4	n	n	PRON
ejpam-6851	538	5	≥	≥	NOUN
ejpam-6851	538	6	2	2	NUM
ejpam-6851	538	7	and	and	CCONJ
ejpam-6851	538	8	m	m	PROPN
ejpam-6851	538	9	≥	≥	NOUN
ejpam-6851	538	10	3	3	NUM
ejpam-6851	538	11	,	,	PUNCT
ejpam-6851	538	12	(	(	PUNCT
ejpam-6851	538	13	i	i	NOUN
ejpam-6851	538	14	)	)	PUNCT
ejpam-6851	539	1	[	[	X
ejpam-6851	539	2	25	25	NUM
ejpam-6851	539	3	]	]	X
ejpam-6851	539	4	γs(pn	γs(pn	NOUN
ejpam-6851	539	5	⋄g	⋄g	NOUN
ejpam-6851	539	6	)	)	PUNCT
ejpam-6851	539	7	=	=	SYM
ejpam-6851	539	8	⌊n2	⌊n2	X
ejpam-6851	539	9	⌋	⌋	NOUN
ejpam-6851	539	10	and	and	CCONJ
ejpam-6851	539	11	γs(cm	γs(cm	NOUN
ejpam-6851	539	12	⋄g	⋄g	ADP
ejpam-6851	539	13	)	)	PUNCT
ejpam-6851	540	1	=	=	PRON
ejpam-6851	540	2	⌈m2	⌈m2	PROPN
ejpam-6851	540	3	⌉	⌉	X
ejpam-6851	540	4	;	;	PUNCT
ejpam-6851	540	5	(	(	PUNCT
ejpam-6851	540	6	ii	ii	NOUN
ejpam-6851	540	7	)	)	PUNCT
ejpam-6851	540	8	γw(pn	γw(pn	NOUN
ejpam-6851	540	9	⋄g	⋄g	NOUN
ejpam-6851	540	10	)	)	PUNCT
ejpam-6851	540	11	=	=	PUNCT
ejpam-6851	540	12	(	(	PUNCT
ejpam-6851	540	13	n+	n+	NUM
ejpam-6851	540	14	1)γs(g	1)γs(g	NUM
ejpam-6851	540	15	)	)	PUNCT
ejpam-6851	540	16	and	and	CCONJ
ejpam-6851	540	17	γw(cm	γw(cm	NOUN
ejpam-6851	540	18	⋄g	⋄g	X
ejpam-6851	540	19	)	)	PUNCT
ejpam-6851	540	20	=	=	PUNCT
ejpam-6851	540	21	mγw(g	mγw(g	PROPN
ejpam-6851	540	22	)	)	PUNCT
ejpam-6851	540	23	.	.	PUNCT
ejpam-6851	541	1	6	6	X
ejpam-6851	541	2	.	.	X
ejpam-6851	541	3	in	in	ADP
ejpam-6851	541	4	the	the	DET
ejpam-6851	541	5	lexicographic	lexicographic	ADJ
ejpam-6851	541	6	product	product	NOUN
ejpam-6851	541	7	of	of	ADP
ejpam-6851	541	8	graphs	graph	NOUN
ejpam-6851	541	9	here	here	ADV
ejpam-6851	541	10	we	we	PRON
ejpam-6851	541	11	note	note	VERB
ejpam-6851	541	12	that	that	SCONJ
ejpam-6851	541	13	for	for	ADP
ejpam-6851	541	14	(	(	PUNCT
ejpam-6851	541	15	u	u	NOUN
ejpam-6851	541	16	,	,	PUNCT
ejpam-6851	541	17	v	v	NOUN
ejpam-6851	541	18	)	)	PUNCT
ejpam-6851	541	19	∈	∈	NOUN
ejpam-6851	541	20	v	v	NOUN
ejpam-6851	541	21	(	(	PUNCT
ejpam-6851	541	22	g[h	g[h	PROPN
ejpam-6851	541	23	]	]	PUNCT
ejpam-6851	541	24	)	)	PUNCT
ejpam-6851	541	25	,	,	PUNCT
ejpam-6851	541	26	degg[h]((u	degg[h]((u	PROPN
ejpam-6851	541	27	,	,	PUNCT
ejpam-6851	541	28	v	v	NOUN
ejpam-6851	541	29	)	)	PUNCT
ejpam-6851	541	30	)	)	PUNCT
ejpam-6851	542	1	=	=	SYM
ejpam-6851	542	2	|v	|v	PROPN
ejpam-6851	542	3	(	(	PUNCT
ejpam-6851	542	4	h)|degg(u	h)|degg(u	NOUN
ejpam-6851	542	5	)	)	PUNCT
ejpam-6851	542	6	+	+	NUM
ejpam-6851	542	7	degh(v	degh(v	NOUN
ejpam-6851	542	8	)	)	PUNCT
ejpam-6851	542	9	.	.	PUNCT
ejpam-6851	543	1	for	for	ADP
ejpam-6851	543	2	s	s	PROPN
ejpam-6851	543	3	⊆	⊆	NUM
ejpam-6851	543	4	v	v	NOUN
ejpam-6851	543	5	(	(	PUNCT
ejpam-6851	543	6	g[h	g[h	PROPN
ejpam-6851	543	7	]	]	PUNCT
ejpam-6851	543	8	)	)	PUNCT
ejpam-6851	543	9	,	,	PUNCT
ejpam-6851	543	10	the	the	DET
ejpam-6851	543	11	projection	projection	NOUN
ejpam-6851	543	12	of	of	ADP
ejpam-6851	543	13	s	s	NOUN
ejpam-6851	543	14	with	with	ADP
ejpam-6851	543	15	respect	respect	NOUN
ejpam-6851	543	16	to	to	ADP
ejpam-6851	543	17	g	g	PROPN
ejpam-6851	543	18	refers	refer	VERB
ejpam-6851	543	19	to	to	ADP
ejpam-6851	543	20	the	the	DET
ejpam-6851	543	21	set	set	NOUN
ejpam-6851	543	22	sg	sg	X
ejpam-6851	543	23	=	=	PUNCT
ejpam-6851	543	24	{	{	PUNCT
ejpam-6851	543	25	x	x	PUNCT
ejpam-6851	543	26	∈	∈	PROPN
ejpam-6851	543	27	v	v	NOUN
ejpam-6851	543	28	(	(	PUNCT
ejpam-6851	543	29	g	g	NOUN
ejpam-6851	543	30	)	)	PUNCT
ejpam-6851	543	31	:	:	PUNCT
ejpam-6851	543	32	∃y	∃y	PROPN
ejpam-6851	543	33	∈	∈	PROPN
ejpam-6851	543	34	v	v	PROPN
ejpam-6851	543	35	(	(	PUNCT
ejpam-6851	543	36	h	h	NOUN
ejpam-6851	543	37	)	)	PUNCT
ejpam-6851	543	38	for	for	ADP
ejpam-6851	543	39	which	which	PRON
ejpam-6851	543	40	(	(	PUNCT
ejpam-6851	543	41	x	x	NOUN
ejpam-6851	543	42	,	,	PUNCT
ejpam-6851	543	43	y	y	PROPN
ejpam-6851	543	44	)	)	PUNCT
ejpam-6851	543	45	∈	∈	PROPN
ejpam-6851	543	46	s	s	PART
ejpam-6851	543	47	}	}	PUNCT
ejpam-6851	543	48	.	.	PUNCT
ejpam-6851	544	1	if	if	SCONJ
ejpam-6851	544	2	s1	s1	PROPN
ejpam-6851	544	3	∈	∈	PROPN
ejpam-6851	544	4	γs(g	γs(g	PUNCT
ejpam-6851	544	5	)	)	PUNCT
ejpam-6851	544	6	(	(	PUNCT
ejpam-6851	544	7	resp	resp	NOUN
ejpam-6851	544	8	.	.	PUNCT
ejpam-6851	545	1	s1	s1	PROPN
ejpam-6851	545	2	∈	∈	PROPN
ejpam-6851	545	3	γw(g	γw(g	PUNCT
ejpam-6851	545	4	)	)	PUNCT
ejpam-6851	545	5	)	)	PUNCT
ejpam-6851	545	6	and	and	CCONJ
ejpam-6851	545	7	s2	s2	VERB
ejpam-6851	545	8	∈	∈	PROPN
ejpam-6851	545	9	γs(h	γs(h	NUM
ejpam-6851	545	10	)	)	PUNCT
ejpam-6851	545	11	(	(	PUNCT
ejpam-6851	545	12	resp	resp	NOUN
ejpam-6851	545	13	.	.	PUNCT
ejpam-6851	546	1	s2	s2	PROPN
ejpam-6851	546	2	∈	∈	PROPN
ejpam-6851	546	3	γw(h	γw(h	NOUN
ejpam-6851	546	4	)	)	PUNCT
ejpam-6851	546	5	)	)	PUNCT
ejpam-6851	547	1	,	,	PUNCT
ejpam-6851	547	2	then	then	ADV
ejpam-6851	547	3	s1	s1	PROPN
ejpam-6851	547	4	×	×	PROPN
ejpam-6851	547	5	s2	s2	NOUN
ejpam-6851	547	6	∈	∈	PROPN
ejpam-6851	547	7	γs(g[h	γs(g[h	NOUN
ejpam-6851	547	8	]	]	X
ejpam-6851	547	9	)	)	PUNCT
ejpam-6851	547	10	(	(	PUNCT
ejpam-6851	547	11	resp	resp	NOUN
ejpam-6851	547	12	.	.	PUNCT
ejpam-6851	548	1	s1	s1	NOUN
ejpam-6851	548	2	×	×	PROPN
ejpam-6851	548	3	s2	s2	PROPN
ejpam-6851	548	4	∈	∈	PROPN
ejpam-6851	548	5	γw(g[h	γw(g[h	NOUN
ejpam-6851	548	6	]	]	PUNCT
ejpam-6851	548	7	)	)	PUNCT
ejpam-6851	548	8	)	)	PUNCT
ejpam-6851	548	9	.	.	PUNCT
ejpam-6851	549	1	consequently	consequently	ADV
ejpam-6851	549	2	,	,	PUNCT
ejpam-6851	549	3	γs(g[h	γs(g[h	NOUN
ejpam-6851	549	4	]	]	X
ejpam-6851	549	5	)	)	PUNCT
ejpam-6851	549	6	≤	≤	NUM
ejpam-6851	549	7	γs(g)γs(h	γs(g)γs(h	NOUN
ejpam-6851	549	8	)	)	PUNCT
ejpam-6851	549	9	(	(	PUNCT
ejpam-6851	549	10	resp	resp	NOUN
ejpam-6851	549	11	.	.	PUNCT
ejpam-6851	550	1	γw(g[h	γw(g[h	NOUN
ejpam-6851	550	2	]	]	PUNCT
ejpam-6851	550	3	)	)	PUNCT
ejpam-6851	550	4	≥	≥	PROPN
ejpam-6851	550	5	γw(g)γw(h	γw(g)γw(h	NOUN
ejpam-6851	550	6	)	)	PUNCT
ejpam-6851	550	7	)	)	PUNCT
ejpam-6851	550	8	.	.	PUNCT
ejpam-6851	551	1	j.	j.	PROPN
ejpam-6851	551	2	m.	m.	PROPN
ejpam-6851	551	3	molles	molles	PROPN
ejpam-6851	551	4	,	,	PUNCT
ejpam-6851	551	5	f.	f.	PROPN
ejpam-6851	551	6	p.	p.	PROPN
ejpam-6851	551	7	jamil	jamil	PROPN
ejpam-6851	551	8	,	,	PUNCT
ejpam-6851	551	9	s.	s.	PROPN
ejpam-6851	551	10	r.	r.	PROPN
ejpam-6851	551	11	canoy	canoy	PROPN
ejpam-6851	551	12	/	/	SYM
ejpam-6851	551	13	eur	eur	PROPN
ejpam-6851	551	14	.	.	PUNCT
ejpam-6851	552	1	j.	j.	PROPN
ejpam-6851	552	2	pure	pure	PROPN
ejpam-6851	552	3	appl	appl	PROPN
ejpam-6851	552	4	.	.	PROPN
ejpam-6851	552	5	math	math	PROPN
ejpam-6851	552	6	,	,	PUNCT
ejpam-6851	552	7	18	18	NUM
ejpam-6851	552	8	(	(	PUNCT
ejpam-6851	552	9	4	4	NUM
ejpam-6851	552	10	)	)	PUNCT
ejpam-6851	552	11	(	(	PUNCT
ejpam-6851	552	12	2025	2025	NUM
ejpam-6851	552	13	)	)	PUNCT
ejpam-6851	552	14	,	,	PUNCT
ejpam-6851	552	15	6851	6851	NUM
ejpam-6851	552	16	14	14	NUM
ejpam-6851	552	17	of	of	ADP
ejpam-6851	552	18	18	18	NUM
ejpam-6851	552	19	proposition	proposition	NOUN
ejpam-6851	552	20	7	7	NUM
ejpam-6851	552	21	.	.	PUNCT
ejpam-6851	553	1	let	let	VERB
ejpam-6851	553	2	g	g	NOUN
ejpam-6851	553	3	and	and	CCONJ
ejpam-6851	553	4	h	h	NOUN
ejpam-6851	553	5	be	be	AUX
ejpam-6851	553	6	nontrivial	nontrivial	ADJ
ejpam-6851	553	7	connected	connected	ADJ
ejpam-6851	553	8	graphs	graph	NOUN
ejpam-6851	553	9	,	,	PUNCT
ejpam-6851	553	10	and	and	CCONJ
ejpam-6851	553	11	let	let	VERB
ejpam-6851	553	12	s	s	PRON
ejpam-6851	553	13	∈	∈	PROPN
ejpam-6851	553	14	γs(g[h	γs(g[h	NOUN
ejpam-6851	553	15	]	]	PUNCT
ejpam-6851	553	16	)	)	PUNCT
ejpam-6851	553	17	.	.	PUNCT
ejpam-6851	554	1	then	then	ADV
ejpam-6851	554	2	s	s	AUX
ejpam-6851	554	3	=	=	PUNCT
ejpam-6851	554	4	∪x∈a	∪x∈a	PROPN
ejpam-6851	554	5	(	(	PUNCT
ejpam-6851	554	6	{	{	PUNCT
ejpam-6851	554	7	x	x	NOUN
ejpam-6851	554	8	}	}	PUNCT
ejpam-6851	554	9	×	×	PROPN
ejpam-6851	554	10	tx	tx	PROPN
ejpam-6851	554	11	)	)	PUNCT
ejpam-6851	554	12	,	,	PUNCT
ejpam-6851	554	13	where	where	SCONJ
ejpam-6851	554	14	a	a	DET
ejpam-6851	554	15	⊆	⊆	NUM
ejpam-6851	554	16	v	v	NOUN
ejpam-6851	554	17	(	(	PUNCT
ejpam-6851	554	18	g	g	NOUN
ejpam-6851	554	19	)	)	PUNCT
ejpam-6851	554	20	and	and	CCONJ
ejpam-6851	554	21	tx	tx	VERB
ejpam-6851	554	22	⊆	⊆	NUM
ejpam-6851	554	23	v	v	NOUN
ejpam-6851	554	24	(	(	PUNCT
ejpam-6851	554	25	h	h	NOUN
ejpam-6851	554	26	)	)	PUNCT
ejpam-6851	554	27	satisfying	satisfy	VERB
ejpam-6851	554	28	the	the	DET
ejpam-6851	554	29	following	following	NOUN
ejpam-6851	554	30	.	.	PUNCT
ejpam-6851	555	1	(	(	PUNCT
ejpam-6851	555	2	i	i	NOUN
ejpam-6851	555	3	)	)	PUNCT
ejpam-6851	555	4	a	a	DET
ejpam-6851	555	5	∈	∈	NOUN
ejpam-6851	555	6	γs(g	γs(g	PUNCT
ejpam-6851	555	7	;	;	PUNCT
ejpam-6851	555	8	and	and	CCONJ
ejpam-6851	555	9	(	(	PUNCT
ejpam-6851	555	10	ii	ii	NOUN
ejpam-6851	555	11	)	)	PUNCT
ejpam-6851	555	12	for	for	ADP
ejpam-6851	555	13	each	each	DET
ejpam-6851	555	14	x	x	SYM
ejpam-6851	555	15	∈	∈	PROPN
ejpam-6851	555	16	a	a	DET
ejpam-6851	555	17	\ng(a	\ng(a	PROPN
ejpam-6851	555	18	≽	≽	PROPN
ejpam-6851	555	19	)	)	PUNCT
ejpam-6851	555	20	,	,	PUNCT
ejpam-6851	555	21	tx	tx	PROPN
ejpam-6851	555	22	∈	∈	PROPN
ejpam-6851	555	23	γs(h	γs(h	NUM
ejpam-6851	555	24	)	)	PUNCT
ejpam-6851	555	25	.	.	PUNCT
ejpam-6851	556	1	proof	proof	NOUN
ejpam-6851	556	2	.	.	PUNCT
ejpam-6851	557	1	put	put	VERB
ejpam-6851	557	2	a	a	DET
ejpam-6851	557	3	=	=	PUNCT
ejpam-6851	557	4	sg	sg	PROPN
ejpam-6851	557	5	,	,	PUNCT
ejpam-6851	557	6	the	the	DET
ejpam-6851	557	7	projection	projection	NOUN
ejpam-6851	557	8	of	of	ADP
ejpam-6851	557	9	s	s	NOUN
ejpam-6851	557	10	under	under	ADP
ejpam-6851	557	11	g.	g.	NOUN
ejpam-6851	557	12	for	for	ADP
ejpam-6851	557	13	each	each	DET
ejpam-6851	557	14	x	x	PROPN
ejpam-6851	557	15	∈	∈	PROPN
ejpam-6851	557	16	a	a	PRON
ejpam-6851	557	17	,	,	PUNCT
ejpam-6851	557	18	define	define	VERB
ejpam-6851	557	19	tx	tx	PROPN
ejpam-6851	558	1	=	=	PUNCT
ejpam-6851	558	2	{	{	PUNCT
ejpam-6851	558	3	y	y	PROPN
ejpam-6851	558	4	∈	∈	PROPN
ejpam-6851	558	5	v	v	PROPN
ejpam-6851	558	6	(	(	PUNCT
ejpam-6851	558	7	h	h	NOUN
ejpam-6851	558	8	)	)	PUNCT
ejpam-6851	558	9	:	:	PUNCT
ejpam-6851	558	10	(	(	PUNCT
ejpam-6851	558	11	x	x	X
ejpam-6851	558	12	,	,	PUNCT
ejpam-6851	558	13	y	y	PROPN
ejpam-6851	558	14	)	)	PUNCT
ejpam-6851	558	15	∈	∈	PROPN
ejpam-6851	558	16	s	s	PART
ejpam-6851	558	17	}	}	PUNCT
ejpam-6851	558	18	.	.	PUNCT
ejpam-6851	559	1	then	then	ADV
ejpam-6851	559	2	s	s	AUX
ejpam-6851	559	3	=	=	PUNCT
ejpam-6851	559	4	∪x∈a	∪x∈a	PROPN
ejpam-6851	559	5	(	(	PUNCT
ejpam-6851	559	6	{	{	PUNCT
ejpam-6851	559	7	x	x	NOUN
ejpam-6851	559	8	}	}	PUNCT
ejpam-6851	559	9	×	×	PROPN
ejpam-6851	559	10	tx	tx	PROPN
ejpam-6851	559	11	)	)	PUNCT
ejpam-6851	559	12	.	.	PUNCT
ejpam-6851	560	1	let	let	VERB
ejpam-6851	560	2	x	x	SYM
ejpam-6851	560	3	∈	∈	PROPN
ejpam-6851	560	4	v	v	X
ejpam-6851	560	5	(	(	PUNCT
ejpam-6851	560	6	g	g	NOUN
ejpam-6851	560	7	)	)	PUNCT
ejpam-6851	560	8	\	\	PROPN
ejpam-6851	560	9	a	a	PRON
ejpam-6851	560	10	,	,	PUNCT
ejpam-6851	560	11	and	and	CCONJ
ejpam-6851	560	12	pick	pick	VERB
ejpam-6851	560	13	z	z	PROPN
ejpam-6851	560	14	∈	∈	PROPN
ejpam-6851	560	15	v	v	ADP
ejpam-6851	560	16	(	(	PUNCT
ejpam-6851	560	17	h	h	NOUN
ejpam-6851	560	18	)	)	PUNCT
ejpam-6851	560	19	such	such	ADJ
ejpam-6851	560	20	that	that	PRON
ejpam-6851	560	21	degh(z	degh(z	NOUN
ejpam-6851	560	22	)	)	PUNCT
ejpam-6851	560	23	=	=	SYM
ejpam-6851	560	24	∆(h	∆(h	NOUN
ejpam-6851	560	25	)	)	PUNCT
ejpam-6851	560	26	.	.	PUNCT
ejpam-6851	561	1	since	since	SCONJ
ejpam-6851	561	2	(	(	PUNCT
ejpam-6851	561	3	x	x	X
ejpam-6851	561	4	,	,	PUNCT
ejpam-6851	561	5	z	z	NOUN
ejpam-6851	561	6	)	)	PUNCT
ejpam-6851	561	7	/∈	/∈	PUNCT
ejpam-6851	561	8	s	s	X
ejpam-6851	561	9	,	,	PUNCT
ejpam-6851	561	10	there	there	PRON
ejpam-6851	561	11	exists	exist	VERB
ejpam-6851	561	12	(	(	PUNCT
ejpam-6851	561	13	u	u	NOUN
ejpam-6851	561	14	,	,	PUNCT
ejpam-6851	561	15	v	v	NOUN
ejpam-6851	561	16	)	)	PUNCT
ejpam-6851	561	17	∈	∈	PROPN
ejpam-6851	561	18	s	s	NOUN
ejpam-6851	561	19	for	for	ADP
ejpam-6851	561	20	which	which	PRON
ejpam-6851	561	21	(	(	PUNCT
ejpam-6851	561	22	x	x	X
ejpam-6851	561	23	,	,	PUNCT
ejpam-6851	561	24	z	z	NOUN
ejpam-6851	561	25	)	)	PUNCT
ejpam-6851	561	26	≼g[h	≼g[h	PROPN
ejpam-6851	561	27	]	]	PUNCT
ejpam-6851	561	28	(	(	PUNCT
ejpam-6851	561	29	u	u	NOUN
ejpam-6851	561	30	,	,	PUNCT
ejpam-6851	561	31	v	v	NOUN
ejpam-6851	561	32	)	)	PUNCT
ejpam-6851	561	33	.	.	PUNCT
ejpam-6851	562	1	since	since	SCONJ
ejpam-6851	562	2	x	x	PROPN
ejpam-6851	562	3	̸=	̸=	PROPN
ejpam-6851	562	4	u	u	NOUN
ejpam-6851	562	5	,	,	PUNCT
ejpam-6851	562	6	u	u	PROPN
ejpam-6851	562	7	∈	∈	PROPN
ejpam-6851	562	8	a	a	DET
ejpam-6851	562	9	∩	∩	NOUN
ejpam-6851	562	10	ng(x	ng(x	NUM
ejpam-6851	562	11	)	)	PUNCT
ejpam-6851	562	12	.	.	PUNCT
ejpam-6851	563	1	moreover	moreover	ADV
ejpam-6851	563	2	,	,	PUNCT
ejpam-6851	563	3	since	since	SCONJ
ejpam-6851	563	4	(	(	PUNCT
ejpam-6851	563	5	x	x	X
ejpam-6851	563	6	,	,	PUNCT
ejpam-6851	563	7	z	z	NOUN
ejpam-6851	563	8	)	)	PUNCT
ejpam-6851	563	9	≼g[h	≼g[h	PROPN
ejpam-6851	563	10	]	]	PUNCT
ejpam-6851	563	11	(	(	PUNCT
ejpam-6851	563	12	u	u	NOUN
ejpam-6851	563	13	,	,	PUNCT
ejpam-6851	563	14	v	v	NOUN
ejpam-6851	563	15	)	)	PUNCT
ejpam-6851	563	16	and	and	CCONJ
ejpam-6851	563	17	degh(z	degh(z	NOUN
ejpam-6851	563	18	)	)	PUNCT
ejpam-6851	563	19	≥	≥	PROPN
ejpam-6851	563	20	degh(v	degh(v	PROPN
ejpam-6851	563	21	)	)	PUNCT
ejpam-6851	563	22	,	,	PUNCT
ejpam-6851	563	23	degg(x	degg(x	NOUN
ejpam-6851	563	24	)	)	PUNCT
ejpam-6851	563	25	≤	≤	NOUN
ejpam-6851	563	26	degg(u	degg(u	PROPN
ejpam-6851	563	27	)	)	PUNCT
ejpam-6851	563	28	,	,	PUNCT
ejpam-6851	563	29	i.e.	i.e.	X
ejpam-6851	563	30	,	,	PUNCT
ejpam-6851	563	31	x	x	PROPN
ejpam-6851	563	32	≼g	≼g	PROPN
ejpam-6851	563	33	u.	u.	PROPN
ejpam-6851	563	34	thus	thus	ADV
ejpam-6851	563	35	,	,	PUNCT
ejpam-6851	563	36	a	a	DET
ejpam-6851	563	37	∈	∈	NOUN
ejpam-6851	563	38	γs(g	γs(g	NUM
ejpam-6851	563	39	)	)	PUNCT
ejpam-6851	563	40	,	,	PUNCT
ejpam-6851	563	41	and	and	CCONJ
ejpam-6851	563	42	(	(	PUNCT
ejpam-6851	563	43	i	i	NOUN
ejpam-6851	563	44	)	)	PUNCT
ejpam-6851	563	45	holds	hold	VERB
ejpam-6851	563	46	.	.	PUNCT
ejpam-6851	564	1	to	to	PART
ejpam-6851	564	2	show	show	VERB
ejpam-6851	564	3	(	(	PUNCT
ejpam-6851	564	4	ii	ii	NOUN
ejpam-6851	564	5	)	)	PUNCT
ejpam-6851	564	6	,	,	PUNCT
ejpam-6851	564	7	put	put	VERB
ejpam-6851	564	8	n	n	NOUN
ejpam-6851	564	9	=	=	SYM
ejpam-6851	564	10	|v	|v	X
ejpam-6851	564	11	(	(	PUNCT
ejpam-6851	564	12	h)|	h)|	NOUN
ejpam-6851	564	13	and	and	CCONJ
ejpam-6851	564	14	let	let	VERB
ejpam-6851	564	15	x	x	SYM
ejpam-6851	564	16	∈	∈	VERB
ejpam-6851	564	17	a	a	DET
ejpam-6851	564	18	\	\	PROPN
ejpam-6851	564	19	ng(a	ng(a	SYM
ejpam-6851	564	20	≽	≽	PROPN
ejpam-6851	564	21	)	)	PUNCT
ejpam-6851	564	22	.	.	PUNCT
ejpam-6851	565	1	we	we	PRON
ejpam-6851	565	2	claim	claim	VERB
ejpam-6851	565	3	that	that	SCONJ
ejpam-6851	565	4	tx	tx	PROPN
ejpam-6851	565	5	∈	∈	PROPN
ejpam-6851	565	6	γs(h	γs(h	NUM
ejpam-6851	565	7	)	)	PUNCT
ejpam-6851	565	8	.	.	PUNCT
ejpam-6851	566	1	to	to	ADP
ejpam-6851	566	2	this	this	DET
ejpam-6851	566	3	end	end	NOUN
ejpam-6851	566	4	,	,	PUNCT
ejpam-6851	566	5	let	let	VERB
ejpam-6851	566	6	y	y	PROPN
ejpam-6851	566	7	∈	∈	PROPN
ejpam-6851	566	8	v	v	ADP
ejpam-6851	566	9	(	(	PUNCT
ejpam-6851	566	10	h	h	NOUN
ejpam-6851	566	11	)	)	PUNCT
ejpam-6851	566	12	\	\	PROPN
ejpam-6851	567	1	tx	tx	PROPN
ejpam-6851	567	2	.	.	PUNCT
ejpam-6851	568	1	since	since	SCONJ
ejpam-6851	568	2	(	(	PUNCT
ejpam-6851	568	3	x	x	NOUN
ejpam-6851	568	4	,	,	PUNCT
ejpam-6851	568	5	y	y	PROPN
ejpam-6851	568	6	)	)	PUNCT
ejpam-6851	568	7	/∈	/∈	PUNCT
ejpam-6851	569	1	s	s	X
ejpam-6851	569	2	,	,	PUNCT
ejpam-6851	569	3	there	there	PRON
ejpam-6851	569	4	exists	exist	VERB
ejpam-6851	569	5	(	(	PUNCT
ejpam-6851	569	6	u	u	NOUN
ejpam-6851	569	7	,	,	PUNCT
ejpam-6851	569	8	v	v	NOUN
ejpam-6851	569	9	)	)	PUNCT
ejpam-6851	569	10	∈	∈	PROPN
ejpam-6851	569	11	s	s	NOUN
ejpam-6851	569	12	for	for	ADP
ejpam-6851	569	13	which	which	PRON
ejpam-6851	569	14	(	(	PUNCT
ejpam-6851	569	15	x	x	NOUN
ejpam-6851	569	16	,	,	PUNCT
ejpam-6851	569	17	y	y	NOUN
ejpam-6851	569	18	)	)	PUNCT
ejpam-6851	569	19	≼g[h	≼g[h	PROPN
ejpam-6851	569	20	]	]	PUNCT
ejpam-6851	569	21	(	(	PUNCT
ejpam-6851	569	22	u	u	NOUN
ejpam-6851	569	23	,	,	PUNCT
ejpam-6851	569	24	v	v	NOUN
ejpam-6851	569	25	)	)	PUNCT
ejpam-6851	569	26	.	.	PUNCT
ejpam-6851	570	1	if	if	SCONJ
ejpam-6851	570	2	x	x	X
ejpam-6851	570	3	̸=	̸=	PROPN
ejpam-6851	570	4	u	u	NOUN
ejpam-6851	570	5	,	,	PUNCT
ejpam-6851	570	6	then	then	ADV
ejpam-6851	570	7	since	since	SCONJ
ejpam-6851	570	8	x	x	PROPN
ejpam-6851	570	9	/∈	/∈	PROPN
ejpam-6851	570	10	ng(a	ng(a	NUM
ejpam-6851	570	11	≽	≽	NOUN
ejpam-6851	570	12	)	)	PUNCT
ejpam-6851	570	13	,	,	PUNCT
ejpam-6851	570	14	degg(u	degg(u	PROPN
ejpam-6851	570	15	)	)	PUNCT
ejpam-6851	570	16	<	<	X
ejpam-6851	570	17	degg(x	degg(x	NOUN
ejpam-6851	570	18	)	)	PUNCT
ejpam-6851	570	19	.	.	PUNCT
ejpam-6851	571	1	thus	thus	ADV
ejpam-6851	571	2	,	,	PUNCT
ejpam-6851	571	3	n	n	PRON
ejpam-6851	571	4	≤	≤	NOUN
ejpam-6851	571	5	n[degg(x)−	n[degg(x)−	PROPN
ejpam-6851	571	6	degg(u	degg(u	PROPN
ejpam-6851	571	7	)	)	PUNCT
ejpam-6851	571	8	]	]	PUNCT
ejpam-6851	572	1	≤	≤	PROPN
ejpam-6851	572	2	degh(v)−	degh(v)−	PROPN
ejpam-6851	572	3	degh(y	degh(y	PROPN
ejpam-6851	572	4	)	)	PUNCT
ejpam-6851	572	5	,	,	PUNCT
ejpam-6851	572	6	which	which	PRON
ejpam-6851	572	7	is	be	AUX
ejpam-6851	572	8	impossible	impossible	ADJ
ejpam-6851	572	9	.	.	PUNCT
ejpam-6851	573	1	thus	thus	ADV
ejpam-6851	573	2	,	,	PUNCT
ejpam-6851	573	3	x	x	SYM
ejpam-6851	573	4	=	=	PUNCT
ejpam-6851	573	5	u	u	NOUN
ejpam-6851	573	6	so	so	SCONJ
ejpam-6851	573	7	that	that	SCONJ
ejpam-6851	573	8	v	v	NUM
ejpam-6851	573	9	∈	∈	PROPN
ejpam-6851	573	10	tx	tx	ADP
ejpam-6851	573	11	∩nh(y	∩nh(y	NOUN
ejpam-6851	573	12	)	)	PUNCT
ejpam-6851	573	13	,	,	PUNCT
ejpam-6851	573	14	and	and	CCONJ
ejpam-6851	573	15	necessarily	necessarily	ADV
ejpam-6851	573	16	,	,	PUNCT
ejpam-6851	573	17	y	y	PROPN
ejpam-6851	573	18	≼h	≼h	PROPN
ejpam-6851	573	19	v.	v.	CCONJ
ejpam-6851	573	20	accordingly	accordingly	ADV
ejpam-6851	573	21	,	,	PUNCT
ejpam-6851	573	22	tx	tx	PROPN
ejpam-6851	573	23	∈	∈	PROPN
ejpam-6851	573	24	γs(h	γs(h	NOUN
ejpam-6851	573	25	)	)	PUNCT
ejpam-6851	573	26	.	.	PUNCT
ejpam-6851	574	1	proposition	proposition	NOUN
ejpam-6851	574	2	8	8	NUM
ejpam-6851	574	3	.	.	PUNCT
ejpam-6851	575	1	let	let	VERB
ejpam-6851	575	2	g	g	NOUN
ejpam-6851	575	3	and	and	CCONJ
ejpam-6851	575	4	h	h	NOUN
ejpam-6851	575	5	be	be	AUX
ejpam-6851	575	6	connected	connect	VERB
ejpam-6851	575	7	nontrivial	nontrivial	ADJ
ejpam-6851	575	8	graphs	graph	NOUN
ejpam-6851	575	9	,	,	PUNCT
ejpam-6851	575	10	and	and	CCONJ
ejpam-6851	575	11	s	s	X
ejpam-6851	575	12	=	=	PUNCT
ejpam-6851	575	13	∪x∈a	∪x∈a	PROPN
ejpam-6851	575	14	(	(	PUNCT
ejpam-6851	575	15	{	{	PUNCT
ejpam-6851	575	16	x	x	NOUN
ejpam-6851	575	17	}	}	PUNCT
ejpam-6851	575	18	×	×	PROPN
ejpam-6851	575	19	tx	tx	PROPN
ejpam-6851	575	20	)	)	PUNCT
ejpam-6851	575	21	,	,	PUNCT
ejpam-6851	575	22	where	where	SCONJ
ejpam-6851	575	23	a	a	DET
ejpam-6851	575	24	⊆	⊆	NUM
ejpam-6851	575	25	v	v	NOUN
ejpam-6851	575	26	(	(	PUNCT
ejpam-6851	575	27	g	g	NOUN
ejpam-6851	575	28	)	)	PUNCT
ejpam-6851	575	29	and	and	CCONJ
ejpam-6851	575	30	tx	tx	VERB
ejpam-6851	575	31	=	=	PUNCT
ejpam-6851	575	32	{	{	PUNCT
ejpam-6851	575	33	y	y	PROPN
ejpam-6851	575	34	∈	∈	PROPN
ejpam-6851	575	35	v	v	PROPN
ejpam-6851	575	36	(	(	PUNCT
ejpam-6851	575	37	h	h	NOUN
ejpam-6851	575	38	)	)	PUNCT
ejpam-6851	575	39	:	:	PUNCT
ejpam-6851	575	40	(	(	PUNCT
ejpam-6851	575	41	x	x	X
ejpam-6851	575	42	,	,	PUNCT
ejpam-6851	575	43	y	y	PROPN
ejpam-6851	575	44	)	)	PUNCT
ejpam-6851	575	45	∈	∈	PROPN
ejpam-6851	575	46	s	s	PART
ejpam-6851	575	47	}	}	PUNCT
ejpam-6851	575	48	.	.	PUNCT
ejpam-6851	576	1	suppose	suppose	VERB
ejpam-6851	576	2	that	that	SCONJ
ejpam-6851	576	3	each	each	PRON
ejpam-6851	576	4	of	of	ADP
ejpam-6851	576	5	the	the	DET
ejpam-6851	576	6	following	following	NOUN
ejpam-6851	576	7	holds	hold	VERB
ejpam-6851	576	8	for	for	ADP
ejpam-6851	576	9	a	a	DET
ejpam-6851	576	10	:	:	PUNCT
ejpam-6851	576	11	(	(	PUNCT
ejpam-6851	576	12	i	i	NOUN
ejpam-6851	576	13	)	)	PUNCT
ejpam-6851	576	14	a	a	DET
ejpam-6851	576	15	∈	∈	NOUN
ejpam-6851	576	16	γs(g	γs(g	PUNCT
ejpam-6851	576	17	)	)	PUNCT
ejpam-6851	576	18	;	;	PUNCT
ejpam-6851	576	19	(	(	PUNCT
ejpam-6851	576	20	ii	ii	NOUN
ejpam-6851	576	21	)	)	PUNCT
ejpam-6851	576	22	for	for	ADP
ejpam-6851	576	23	each	each	DET
ejpam-6851	576	24	x	x	SYM
ejpam-6851	576	25	∈	∈	PROPN
ejpam-6851	576	26	a	a	DET
ejpam-6851	576	27	∩ng(a	∩ng(a	PROPN
ejpam-6851	576	28	≽	≽	PROPN
ejpam-6851	576	29	)	)	PUNCT
ejpam-6851	576	30	,	,	PUNCT
ejpam-6851	576	31	there	there	PRON
ejpam-6851	576	32	exists	exist	VERB
ejpam-6851	576	33	y	y	PROPN
ejpam-6851	576	34	∈	∈	PROPN
ejpam-6851	576	35	tx	tx	VERB
ejpam-6851	576	36	such	such	ADJ
ejpam-6851	576	37	that	that	PRON
ejpam-6851	576	38	degh(y	degh(y	ADJ
ejpam-6851	576	39	)	)	PUNCT
ejpam-6851	576	40	=	=	SYM
ejpam-6851	576	41	∆(h	∆(h	NOUN
ejpam-6851	576	42	)	)	PUNCT
ejpam-6851	576	43	;	;	PUNCT
ejpam-6851	576	44	and	and	CCONJ
ejpam-6851	576	45	(	(	PUNCT
ejpam-6851	576	46	iii	iii	NOUN
ejpam-6851	576	47	)	)	PUNCT
ejpam-6851	576	48	for	for	ADP
ejpam-6851	576	49	each	each	DET
ejpam-6851	576	50	x	x	SYM
ejpam-6851	576	51	∈	∈	PROPN
ejpam-6851	576	52	a	a	DET
ejpam-6851	576	53	\ng(a	\ng(a	PROPN
ejpam-6851	576	54	≽	≽	PROPN
ejpam-6851	576	55	)	)	PUNCT
ejpam-6851	576	56	,	,	PUNCT
ejpam-6851	576	57	tx	tx	PROPN
ejpam-6851	576	58	∈	∈	PROPN
ejpam-6851	576	59	γs(h	γs(h	NUM
ejpam-6851	576	60	)	)	PUNCT
ejpam-6851	576	61	.	.	PUNCT
ejpam-6851	577	1	then	then	ADV
ejpam-6851	577	2	s	s	VERB
ejpam-6851	577	3	∈	∈	PROPN
ejpam-6851	577	4	γs(g[h	γs(g[h	NOUN
ejpam-6851	577	5	]	]	X
ejpam-6851	577	6	)	)	PUNCT
ejpam-6851	577	7	.	.	PUNCT
ejpam-6851	578	1	proof	proof	NOUN
ejpam-6851	578	2	.	.	PUNCT
ejpam-6851	579	1	let	let	VERB
ejpam-6851	579	2	(	(	PUNCT
ejpam-6851	579	3	x	x	NOUN
ejpam-6851	579	4	,	,	PUNCT
ejpam-6851	579	5	y	y	NOUN
ejpam-6851	579	6	)	)	PUNCT
ejpam-6851	579	7	∈	∈	PROPN
ejpam-6851	579	8	v	v	NOUN
ejpam-6851	579	9	(	(	PUNCT
ejpam-6851	579	10	g[h	g[h	PROPN
ejpam-6851	579	11	]	]	PUNCT
ejpam-6851	579	12	)	)	PUNCT
ejpam-6851	579	13	\	\	PUNCT
ejpam-6851	580	1	s.	s.	PROPN
ejpam-6851	580	2	we	we	PRON
ejpam-6851	580	3	consider	consider	VERB
ejpam-6851	580	4	the	the	DET
ejpam-6851	580	5	following	follow	VERB
ejpam-6851	580	6	cases	case	NOUN
ejpam-6851	580	7	:	:	PUNCT
ejpam-6851	580	8	case	case	NOUN
ejpam-6851	580	9	1	1	NUM
ejpam-6851	580	10	:	:	PUNCT
ejpam-6851	580	11	x	x	X
ejpam-6851	580	12	/∈	/∈	PUNCT
ejpam-6851	581	1	a	a	INTJ
ejpam-6851	581	2	if	if	NOUN
ejpam-6851	581	3	x	x	PROPN
ejpam-6851	581	4	/∈	/∈	NOUN
ejpam-6851	582	1	a	a	INTJ
ejpam-6851	582	2	,	,	PUNCT
ejpam-6851	582	3	then	then	ADV
ejpam-6851	582	4	by	by	ADP
ejpam-6851	582	5	(	(	PUNCT
ejpam-6851	582	6	i	i	NOUN
ejpam-6851	582	7	)	)	PUNCT
ejpam-6851	582	8	,	,	PUNCT
ejpam-6851	582	9	there	there	PRON
ejpam-6851	582	10	exists	exist	VERB
ejpam-6851	582	11	u	u	PROPN
ejpam-6851	582	12	∈	∈	PROPN
ejpam-6851	582	13	a	a	DET
ejpam-6851	582	14	such	such	ADJ
ejpam-6851	582	15	that	that	SCONJ
ejpam-6851	582	16	x	x	X
ejpam-6851	582	17	≼g	≼g	NOUN
ejpam-6851	582	18	u.	u.	VERB
ejpam-6851	582	19	if	if	SCONJ
ejpam-6851	582	20	u	u	PROPN
ejpam-6851	582	21	/∈	/∈	PROPN
ejpam-6851	582	22	ng(a	ng(a	PUNCT
ejpam-6851	583	1	≽	≽	PROPN
ejpam-6851	583	2	)	)	PUNCT
ejpam-6851	583	3	,	,	PUNCT
ejpam-6851	583	4	then	then	ADV
ejpam-6851	583	5	by	by	ADP
ejpam-6851	583	6	(	(	PUNCT
ejpam-6851	583	7	iii	iii	NOUN
ejpam-6851	583	8	)	)	PUNCT
ejpam-6851	583	9	,	,	PUNCT
ejpam-6851	583	10	tu	tu	PROPN
ejpam-6851	583	11	∈	∈	PROPN
ejpam-6851	583	12	γs(h	γs(h	NUM
ejpam-6851	583	13	)	)	PUNCT
ejpam-6851	583	14	so	so	SCONJ
ejpam-6851	583	15	that	that	SCONJ
ejpam-6851	583	16	,	,	PUNCT
ejpam-6851	583	17	by	by	ADP
ejpam-6851	583	18	lemma	lemma	PROPN
ejpam-6851	583	19	2	2	NUM
ejpam-6851	583	20	,	,	PUNCT
ejpam-6851	583	21	tu	tu	PROPN
ejpam-6851	583	22	contains	contain	VERB
ejpam-6851	583	23	a	a	DET
ejpam-6851	583	24	vertex	vertex	NOUN
ejpam-6851	583	25	w	w	NOUN
ejpam-6851	583	26	for	for	ADP
ejpam-6851	583	27	which	which	PRON
ejpam-6851	583	28	degh(w	degh(w	PROPN
ejpam-6851	583	29	)	)	PUNCT
ejpam-6851	583	30	=	=	SYM
ejpam-6851	583	31	∆(h	∆(h	NOUN
ejpam-6851	583	32	)	)	PUNCT
ejpam-6851	583	33	.	.	PUNCT
ejpam-6851	584	1	here	here	ADV
ejpam-6851	584	2	we	we	PRON
ejpam-6851	584	3	have	have	VERB
ejpam-6851	584	4	(	(	PUNCT
ejpam-6851	584	5	u	u	NOUN
ejpam-6851	584	6	,	,	PUNCT
ejpam-6851	584	7	w	w	NOUN
ejpam-6851	584	8	)	)	PUNCT
ejpam-6851	584	9	∈	∈	PROPN
ejpam-6851	584	10	s	s	PART
ejpam-6851	584	11	∩	∩	NOUN
ejpam-6851	584	12	ng[h]((x	ng[h]((x	NOUN
ejpam-6851	584	13	,	,	PUNCT
ejpam-6851	584	14	y	y	NOUN
ejpam-6851	584	15	)	)	PUNCT
ejpam-6851	584	16	)	)	PUNCT
ejpam-6851	585	1	and	and	CCONJ
ejpam-6851	585	2	(	(	PUNCT
ejpam-6851	585	3	x	x	NOUN
ejpam-6851	585	4	,	,	PUNCT
ejpam-6851	585	5	y	y	NOUN
ejpam-6851	585	6	)	)	PUNCT
ejpam-6851	585	7	≼g[h	≼g[h	PROPN
ejpam-6851	585	8	]	]	PUNCT
ejpam-6851	585	9	(	(	PUNCT
ejpam-6851	585	10	u	u	NOUN
ejpam-6851	585	11	,	,	PUNCT
ejpam-6851	585	12	w	w	NOUN
ejpam-6851	585	13	)	)	PUNCT
ejpam-6851	585	14	.	.	PUNCT
ejpam-6851	585	15	suppose	suppose	VERB
ejpam-6851	585	16	that	that	SCONJ
ejpam-6851	585	17	u	u	PROPN
ejpam-6851	585	18	∈	∈	PROPN
ejpam-6851	585	19	ng(a	ng(a	CCONJ
ejpam-6851	585	20	≽	≽	NOUN
ejpam-6851	585	21	)	)	PUNCT
ejpam-6851	585	22	.	.	PUNCT
ejpam-6851	586	1	then	then	ADV
ejpam-6851	586	2	by	by	ADP
ejpam-6851	586	3	(	(	PUNCT
ejpam-6851	586	4	ii	ii	NOUN
ejpam-6851	586	5	)	)	PUNCT
ejpam-6851	586	6	,	,	PUNCT
ejpam-6851	586	7	there	there	PRON
ejpam-6851	586	8	exists	exist	VERB
ejpam-6851	586	9	v	v	ADP
ejpam-6851	586	10	∈	∈	PROPN
ejpam-6851	586	11	tu	tu	PROPN
ejpam-6851	586	12	for	for	ADP
ejpam-6851	586	13	which	which	PRON
ejpam-6851	586	14	degh(v	degh(v	NOUN
ejpam-6851	586	15	)	)	PUNCT
ejpam-6851	586	16	=	=	SYM
ejpam-6851	586	17	∆(h	∆(h	NOUN
ejpam-6851	586	18	)	)	PUNCT
ejpam-6851	586	19	.	.	PUNCT
ejpam-6851	587	1	it	it	PRON
ejpam-6851	587	2	means	mean	VERB
ejpam-6851	587	3	(	(	PUNCT
ejpam-6851	587	4	u	u	NOUN
ejpam-6851	587	5	,	,	PUNCT
ejpam-6851	587	6	v	v	NOUN
ejpam-6851	587	7	)	)	PUNCT
ejpam-6851	587	8	∈	∈	PROPN
ejpam-6851	587	9	s	s	PART
ejpam-6851	587	10	∩ng[h]((x	∩ng[h]((x	NOUN
ejpam-6851	587	11	,	,	PUNCT
ejpam-6851	587	12	y	y	NOUN
ejpam-6851	587	13	)	)	PUNCT
ejpam-6851	587	14	)	)	PUNCT
ejpam-6851	588	1	and	and	CCONJ
ejpam-6851	588	2	(	(	PUNCT
ejpam-6851	588	3	x	x	NOUN
ejpam-6851	588	4	,	,	PUNCT
ejpam-6851	588	5	y	y	NOUN
ejpam-6851	588	6	)	)	PUNCT
ejpam-6851	588	7	≼g[h	≼g[h	PROPN
ejpam-6851	588	8	]	]	PUNCT
ejpam-6851	588	9	(	(	PUNCT
ejpam-6851	588	10	u	u	NOUN
ejpam-6851	588	11	,	,	PUNCT
ejpam-6851	588	12	v	v	NOUN
ejpam-6851	588	13	)	)	PUNCT
ejpam-6851	588	14	.	.	PUNCT
ejpam-6851	589	1	case	case	NOUN
ejpam-6851	589	2	2	2	NUM
ejpam-6851	589	3	:	:	PUNCT
ejpam-6851	589	4	x	x	SYM
ejpam-6851	589	5	∈	∈	VERB
ejpam-6851	589	6	a	a	DET
ejpam-6851	589	7	∩ng(a	∩ng(a	PROPN
ejpam-6851	589	8	≽	≽	PROPN
ejpam-6851	589	9	)	)	PUNCT
ejpam-6851	589	10	if	if	SCONJ
ejpam-6851	589	11	x	x	SYM
ejpam-6851	589	12	∈	∈	PROPN
ejpam-6851	589	13	a	a	DET
ejpam-6851	589	14	∩	∩	X
ejpam-6851	589	15	ng(a	ng(a	PRON
ejpam-6851	589	16	≽	≽	NOUN
ejpam-6851	589	17	)	)	PUNCT
ejpam-6851	589	18	and	and	CCONJ
ejpam-6851	589	19	u	u	PROPN
ejpam-6851	589	20	∈	∈	PROPN
ejpam-6851	589	21	a	a	DET
ejpam-6851	589	22	such	such	ADJ
ejpam-6851	589	23	that	that	SCONJ
ejpam-6851	589	24	x	x	X
ejpam-6851	589	25	≼g	≼g	NOUN
ejpam-6851	589	26	u	u	NOUN
ejpam-6851	589	27	,	,	PUNCT
ejpam-6851	589	28	then	then	ADV
ejpam-6851	589	29	by	by	ADP
ejpam-6851	589	30	(	(	PUNCT
ejpam-6851	589	31	ii	ii	NOUN
ejpam-6851	589	32	)	)	PUNCT
ejpam-6851	589	33	,	,	PUNCT
ejpam-6851	589	34	there	there	PRON
ejpam-6851	589	35	exists	exist	VERB
ejpam-6851	589	36	v	v	ADP
ejpam-6851	589	37	∈	∈	PROPN
ejpam-6851	589	38	tu	tu	PROPN
ejpam-6851	589	39	such	such	ADJ
ejpam-6851	589	40	that	that	DET
ejpam-6851	589	41	degh(v	degh(v	NOUN
ejpam-6851	589	42	)	)	PUNCT
ejpam-6851	589	43	=	=	SYM
ejpam-6851	589	44	∆(h	∆(h	NOUN
ejpam-6851	589	45	)	)	PUNCT
ejpam-6851	589	46	.	.	PUNCT
ejpam-6851	590	1	thus	thus	ADV
ejpam-6851	590	2	,	,	PUNCT
ejpam-6851	590	3	(	(	PUNCT
ejpam-6851	590	4	u	u	NOUN
ejpam-6851	590	5	,	,	PUNCT
ejpam-6851	590	6	v	v	NOUN
ejpam-6851	590	7	)	)	PUNCT
ejpam-6851	590	8	∈	∈	PROPN
ejpam-6851	590	9	s	s	PART
ejpam-6851	590	10	∩ng[h]((x	∩ng[h]((x	NOUN
ejpam-6851	590	11	,	,	PUNCT
ejpam-6851	590	12	y	y	NOUN
ejpam-6851	590	13	)	)	PUNCT
ejpam-6851	590	14	)	)	PUNCT
ejpam-6851	591	1	and	and	CCONJ
ejpam-6851	591	2	(	(	PUNCT
ejpam-6851	591	3	x	x	NOUN
ejpam-6851	591	4	,	,	PUNCT
ejpam-6851	591	5	y	y	NOUN
ejpam-6851	591	6	)	)	PUNCT
ejpam-6851	591	7	≼g[h	≼g[h	PROPN
ejpam-6851	591	8	]	]	PUNCT
ejpam-6851	591	9	(	(	PUNCT
ejpam-6851	591	10	u	u	NOUN
ejpam-6851	591	11	,	,	PUNCT
ejpam-6851	591	12	v	v	NOUN
ejpam-6851	591	13	)	)	PUNCT
ejpam-6851	591	14	.	.	PUNCT
ejpam-6851	592	1	case	case	NOUN
ejpam-6851	592	2	3	3	NUM
ejpam-6851	592	3	:	:	PUNCT
ejpam-6851	592	4	x	x	SYM
ejpam-6851	592	5	∈	∈	PROPN
ejpam-6851	592	6	a	a	DET
ejpam-6851	592	7	\ng(a	\ng(a	PROPN
ejpam-6851	592	8	≽	≽	NOUN
ejpam-6851	592	9	)	)	PUNCT
ejpam-6851	592	10	suppose	suppose	VERB
ejpam-6851	592	11	that	that	SCONJ
ejpam-6851	592	12	x	x	SYM
ejpam-6851	592	13	∈	∈	PROPN
ejpam-6851	592	14	a	a	DET
ejpam-6851	592	15	\	\	PROPN
ejpam-6851	592	16	ng(a	ng(a	SYM
ejpam-6851	592	17	≽	≽	PROPN
ejpam-6851	592	18	)	)	PUNCT
ejpam-6851	592	19	.	.	PUNCT
ejpam-6851	593	1	then	then	ADV
ejpam-6851	593	2	tx	tx	PROPN
ejpam-6851	593	3	∈	∈	PROPN
ejpam-6851	593	4	γs(h	γs(h	NUM
ejpam-6851	593	5	)	)	PUNCT
ejpam-6851	593	6	.	.	PUNCT
ejpam-6851	594	1	thus	thus	ADV
ejpam-6851	594	2	,	,	PUNCT
ejpam-6851	594	3	there	there	PRON
ejpam-6851	594	4	exists	exist	VERB
ejpam-6851	594	5	w	w	PROPN
ejpam-6851	594	6	∈	∈	PROPN
ejpam-6851	594	7	tx	tx	NOUN
ejpam-6851	594	8	for	for	ADP
ejpam-6851	594	9	which	which	PRON
ejpam-6851	594	10	y	y	PROPN
ejpam-6851	594	11	≼h	≼h	PROPN
ejpam-6851	594	12	w.	w.	NOUN
ejpam-6851	594	13	here	here	ADV
ejpam-6851	594	14	we	we	PRON
ejpam-6851	594	15	have	have	VERB
ejpam-6851	594	16	(	(	PUNCT
ejpam-6851	594	17	x	x	NOUN
ejpam-6851	594	18	,	,	PUNCT
ejpam-6851	594	19	w	w	NOUN
ejpam-6851	594	20	)	)	PUNCT
ejpam-6851	594	21	∈	∈	PROPN
ejpam-6851	594	22	s	s	PART
ejpam-6851	594	23	∩ng[h]((x	∩ng[h]((x	NOUN
ejpam-6851	594	24	,	,	PUNCT
ejpam-6851	594	25	y	y	NOUN
ejpam-6851	594	26	)	)	PUNCT
ejpam-6851	594	27	)	)	PUNCT
ejpam-6851	595	1	and	and	CCONJ
ejpam-6851	595	2	(	(	PUNCT
ejpam-6851	595	3	x	x	NOUN
ejpam-6851	595	4	,	,	PUNCT
ejpam-6851	595	5	y	y	NOUN
ejpam-6851	595	6	)	)	PUNCT
ejpam-6851	595	7	≼g[h	≼g[h	PROPN
ejpam-6851	595	8	]	]	PUNCT
ejpam-6851	595	9	(	(	PUNCT
ejpam-6851	595	10	x	x	X
ejpam-6851	595	11	,	,	PUNCT
ejpam-6851	595	12	w	w	NOUN
ejpam-6851	595	13	)	)	PUNCT
ejpam-6851	595	14	.	.	PUNCT
ejpam-6851	596	1	all	all	DET
ejpam-6851	596	2	3	3	NUM
ejpam-6851	596	3	cases	case	NOUN
ejpam-6851	596	4	above	above	ADV
ejpam-6851	596	5	imply	imply	VERB
ejpam-6851	596	6	that	that	PRON
ejpam-6851	596	7	s	s	VERB
ejpam-6851	596	8	∈	∈	PROPN
ejpam-6851	596	9	γs(g[h	γs(g[h	NOUN
ejpam-6851	596	10	]	]	X
ejpam-6851	596	11	)	)	PUNCT
ejpam-6851	596	12	.	.	PUNCT
ejpam-6851	597	1	similar	similar	ADJ
ejpam-6851	597	2	arguments	argument	NOUN
ejpam-6851	597	3	will	will	AUX
ejpam-6851	597	4	also	also	ADV
ejpam-6851	597	5	prove	prove	VERB
ejpam-6851	597	6	the	the	DET
ejpam-6851	597	7	following	follow	VERB
ejpam-6851	597	8	two	two	NUM
ejpam-6851	597	9	propositions	proposition	NOUN
ejpam-6851	597	10	for	for	ADP
ejpam-6851	597	11	weak	weak	ADJ
ejpam-6851	597	12	domination	domination	NOUN
ejpam-6851	597	13	:	:	PUNCT
ejpam-6851	597	14	j.	j.	PROPN
ejpam-6851	597	15	m.	m.	PROPN
ejpam-6851	597	16	molles	molles	PROPN
ejpam-6851	597	17	,	,	PUNCT
ejpam-6851	597	18	f.	f.	PROPN
ejpam-6851	597	19	p.	p.	PROPN
ejpam-6851	597	20	jamil	jamil	PROPN
ejpam-6851	597	21	,	,	PUNCT
ejpam-6851	597	22	s.	s.	PROPN
ejpam-6851	597	23	r.	r.	PROPN
ejpam-6851	597	24	canoy	canoy	PROPN
ejpam-6851	597	25	/	/	SYM
ejpam-6851	597	26	eur	eur	PROPN
ejpam-6851	597	27	.	.	PUNCT
ejpam-6851	598	1	j.	j.	PROPN
ejpam-6851	598	2	pure	pure	PROPN
ejpam-6851	598	3	appl	appl	PROPN
ejpam-6851	598	4	.	.	PROPN
ejpam-6851	598	5	math	math	PROPN
ejpam-6851	598	6	,	,	PUNCT
ejpam-6851	598	7	18	18	NUM
ejpam-6851	598	8	(	(	PUNCT
ejpam-6851	598	9	4	4	NUM
ejpam-6851	598	10	)	)	PUNCT
ejpam-6851	598	11	(	(	PUNCT
ejpam-6851	598	12	2025	2025	NUM
ejpam-6851	598	13	)	)	PUNCT
ejpam-6851	598	14	,	,	PUNCT
ejpam-6851	598	15	6851	6851	NUM
ejpam-6851	598	16	15	15	NUM
ejpam-6851	598	17	of	of	ADP
ejpam-6851	598	18	18	18	NUM
ejpam-6851	598	19	proposition	proposition	NOUN
ejpam-6851	598	20	9	9	NUM
ejpam-6851	598	21	.	.	PUNCT
ejpam-6851	599	1	let	let	VERB
ejpam-6851	599	2	g	g	NOUN
ejpam-6851	599	3	and	and	CCONJ
ejpam-6851	599	4	h	h	NOUN
ejpam-6851	599	5	be	be	AUX
ejpam-6851	599	6	nontrivial	nontrivial	ADJ
ejpam-6851	599	7	connected	connected	ADJ
ejpam-6851	599	8	graphs	graph	NOUN
ejpam-6851	599	9	,	,	PUNCT
ejpam-6851	599	10	and	and	CCONJ
ejpam-6851	599	11	let	let	VERB
ejpam-6851	599	12	s	s	PRON
ejpam-6851	599	13	∈	∈	NOUN
ejpam-6851	599	14	γw(g[h	γw(g[h	NOUN
ejpam-6851	599	15	]	]	PUNCT
ejpam-6851	599	16	)	)	PUNCT
ejpam-6851	599	17	)	)	PUNCT
ejpam-6851	599	18	.	.	PUNCT
ejpam-6851	600	1	then	then	ADV
ejpam-6851	600	2	s	s	AUX
ejpam-6851	600	3	=	=	PUNCT
ejpam-6851	600	4	∪x∈a	∪x∈a	PROPN
ejpam-6851	600	5	(	(	PUNCT
ejpam-6851	600	6	{	{	PUNCT
ejpam-6851	600	7	x	x	NOUN
ejpam-6851	600	8	}	}	PUNCT
ejpam-6851	600	9	×	×	PROPN
ejpam-6851	600	10	tx	tx	PROPN
ejpam-6851	600	11	)	)	PUNCT
ejpam-6851	600	12	,	,	PUNCT
ejpam-6851	600	13	where	where	SCONJ
ejpam-6851	600	14	a	a	DET
ejpam-6851	600	15	⊆	⊆	NUM
ejpam-6851	600	16	v	v	NOUN
ejpam-6851	600	17	(	(	PUNCT
ejpam-6851	600	18	g	g	NOUN
ejpam-6851	600	19	)	)	PUNCT
ejpam-6851	600	20	and	and	CCONJ
ejpam-6851	600	21	tx	tx	VERB
ejpam-6851	600	22	⊆	⊆	NUM
ejpam-6851	600	23	v	v	NOUN
ejpam-6851	600	24	(	(	PUNCT
ejpam-6851	600	25	h	h	NOUN
ejpam-6851	600	26	)	)	PUNCT
ejpam-6851	600	27	satisfying	satisfy	VERB
ejpam-6851	600	28	the	the	DET
ejpam-6851	600	29	following	following	NOUN
ejpam-6851	600	30	.	.	PUNCT
ejpam-6851	601	1	(	(	PUNCT
ejpam-6851	601	2	i	i	NOUN
ejpam-6851	601	3	)	)	PUNCT
ejpam-6851	601	4	a	a	DET
ejpam-6851	601	5	∈	∈	NOUN
ejpam-6851	601	6	γw(g	γw(g	PUNCT
ejpam-6851	601	7	)	)	PUNCT
ejpam-6851	601	8	;	;	PUNCT
ejpam-6851	601	9	and	and	CCONJ
ejpam-6851	601	10	(	(	PUNCT
ejpam-6851	601	11	ii	ii	NOUN
ejpam-6851	601	12	)	)	PUNCT
ejpam-6851	601	13	for	for	ADP
ejpam-6851	601	14	each	each	DET
ejpam-6851	601	15	x	x	SYM
ejpam-6851	601	16	∈	∈	PROPN
ejpam-6851	601	17	a	a	DET
ejpam-6851	601	18	\ng(a	\ng(a	PROPN
ejpam-6851	601	19	≼	≼	NOUN
ejpam-6851	601	20	)	)	PUNCT
ejpam-6851	601	21	,	,	PUNCT
ejpam-6851	601	22	tx	tx	PROPN
ejpam-6851	601	23	∈	∈	PROPN
ejpam-6851	601	24	γw(h	γw(h	PROPN
ejpam-6851	601	25	)	)	PUNCT
ejpam-6851	601	26	.	.	PUNCT
ejpam-6851	602	1	proposition	proposition	NOUN
ejpam-6851	602	2	10	10	NUM
ejpam-6851	602	3	.	.	PUNCT
ejpam-6851	603	1	let	let	VERB
ejpam-6851	603	2	g	g	NOUN
ejpam-6851	603	3	and	and	CCONJ
ejpam-6851	603	4	h	h	NOUN
ejpam-6851	603	5	be	be	AUX
ejpam-6851	603	6	connected	connect	VERB
ejpam-6851	603	7	nontrivial	nontrivial	ADJ
ejpam-6851	603	8	graphs	graph	NOUN
ejpam-6851	603	9	,	,	PUNCT
ejpam-6851	603	10	and	and	CCONJ
ejpam-6851	603	11	s	s	X
ejpam-6851	603	12	=	=	PUNCT
ejpam-6851	603	13	∪x∈a	∪x∈a	PROPN
ejpam-6851	603	14	(	(	PUNCT
ejpam-6851	603	15	{	{	PUNCT
ejpam-6851	603	16	x	x	NOUN
ejpam-6851	603	17	}	}	PUNCT
ejpam-6851	603	18	×	×	PROPN
ejpam-6851	603	19	tx	tx	PROPN
ejpam-6851	603	20	)	)	PUNCT
ejpam-6851	603	21	,	,	PUNCT
ejpam-6851	603	22	where	where	SCONJ
ejpam-6851	603	23	a	a	DET
ejpam-6851	603	24	⊆	⊆	NUM
ejpam-6851	603	25	v	v	NOUN
ejpam-6851	603	26	(	(	PUNCT
ejpam-6851	603	27	g	g	NOUN
ejpam-6851	603	28	)	)	PUNCT
ejpam-6851	603	29	and	and	CCONJ
ejpam-6851	603	30	tx	tx	VERB
ejpam-6851	603	31	=	=	PUNCT
ejpam-6851	603	32	{	{	PUNCT
ejpam-6851	603	33	y	y	PROPN
ejpam-6851	603	34	∈	∈	PROPN
ejpam-6851	603	35	v	v	PROPN
ejpam-6851	603	36	(	(	PUNCT
ejpam-6851	603	37	h	h	NOUN
ejpam-6851	603	38	)	)	PUNCT
ejpam-6851	603	39	:	:	PUNCT
ejpam-6851	603	40	(	(	PUNCT
ejpam-6851	603	41	x	x	X
ejpam-6851	603	42	,	,	PUNCT
ejpam-6851	603	43	y	y	PROPN
ejpam-6851	603	44	)	)	PUNCT
ejpam-6851	603	45	∈	∈	PROPN
ejpam-6851	603	46	s	s	PART
ejpam-6851	603	47	}	}	PUNCT
ejpam-6851	603	48	.	.	PUNCT
ejpam-6851	604	1	suppose	suppose	VERB
ejpam-6851	604	2	that	that	SCONJ
ejpam-6851	604	3	each	each	PRON
ejpam-6851	604	4	of	of	ADP
ejpam-6851	604	5	the	the	DET
ejpam-6851	604	6	following	following	NOUN
ejpam-6851	604	7	holds	hold	VERB
ejpam-6851	604	8	for	for	ADP
ejpam-6851	604	9	a	a	DET
ejpam-6851	604	10	:	:	PUNCT
ejpam-6851	604	11	(	(	PUNCT
ejpam-6851	604	12	i	i	NOUN
ejpam-6851	604	13	)	)	PUNCT
ejpam-6851	604	14	a	a	DET
ejpam-6851	604	15	∈	∈	NOUN
ejpam-6851	604	16	γw(g	γw(g	PUNCT
ejpam-6851	604	17	)	)	PUNCT
ejpam-6851	604	18	;	;	PUNCT
ejpam-6851	604	19	(	(	PUNCT
ejpam-6851	604	20	ii	ii	NOUN
ejpam-6851	604	21	)	)	PUNCT
ejpam-6851	604	22	for	for	ADP
ejpam-6851	604	23	each	each	DET
ejpam-6851	604	24	x	x	SYM
ejpam-6851	604	25	∈	∈	PROPN
ejpam-6851	604	26	a	a	DET
ejpam-6851	604	27	∩ng(a	∩ng(a	NOUN
ejpam-6851	604	28	≼	≼	ADJ
ejpam-6851	604	29	)	)	PUNCT
ejpam-6851	604	30	,	,	PUNCT
ejpam-6851	604	31	there	there	PRON
ejpam-6851	604	32	exists	exist	VERB
ejpam-6851	604	33	y	y	PROPN
ejpam-6851	604	34	∈	∈	PROPN
ejpam-6851	604	35	tx	tx	VERB
ejpam-6851	604	36	such	such	ADJ
ejpam-6851	604	37	that	that	PRON
ejpam-6851	604	38	degh(y	degh(y	PROPN
ejpam-6851	604	39	)	)	PUNCT
ejpam-6851	604	40	=	=	SYM
ejpam-6851	604	41	δ(h	δ(h	PROPN
ejpam-6851	604	42	)	)	PUNCT
ejpam-6851	604	43	;	;	PUNCT
ejpam-6851	604	44	and	and	CCONJ
ejpam-6851	604	45	(	(	PUNCT
ejpam-6851	604	46	iii	iii	NOUN
ejpam-6851	604	47	)	)	PUNCT
ejpam-6851	604	48	for	for	ADP
ejpam-6851	604	49	each	each	DET
ejpam-6851	604	50	x	x	SYM
ejpam-6851	604	51	∈	∈	PROPN
ejpam-6851	604	52	a	a	DET
ejpam-6851	604	53	\ng(a	\ng(a	PROPN
ejpam-6851	604	54	≼	≼	NOUN
ejpam-6851	604	55	)	)	PUNCT
ejpam-6851	604	56	,	,	PUNCT
ejpam-6851	604	57	tx	tx	PROPN
ejpam-6851	604	58	∈	∈	PROPN
ejpam-6851	604	59	γw(h	γw(h	NOUN
ejpam-6851	604	60	)	)	PUNCT
ejpam-6851	604	61	.	.	PUNCT
ejpam-6851	605	1	then	then	ADV
ejpam-6851	605	2	s	s	VERB
ejpam-6851	605	3	∈	∈	PROPN
ejpam-6851	605	4	γw(g[h	γw(g[h	NOUN
ejpam-6851	605	5	]	]	PUNCT
ejpam-6851	605	6	)	)	PUNCT
ejpam-6851	605	7	.	.	PUNCT
ejpam-6851	606	1	proposition	proposition	NOUN
ejpam-6851	606	2	11	11	NUM
ejpam-6851	606	3	.	.	PUNCT
ejpam-6851	607	1	let	let	VERB
ejpam-6851	607	2	g	g	NOUN
ejpam-6851	607	3	and	and	CCONJ
ejpam-6851	607	4	h	h	NOUN
ejpam-6851	607	5	be	be	AUX
ejpam-6851	607	6	nontrivial	nontrivial	ADJ
ejpam-6851	607	7	connected	connected	ADJ
ejpam-6851	607	8	graphs	graph	NOUN
ejpam-6851	607	9	.	.	PUNCT
ejpam-6851	608	1	then	then	ADV
ejpam-6851	608	2	for	for	SCONJ
ejpam-6851	608	3	each	each	DET
ejpam-6851	608	4	s∗	s∗	PROPN
ejpam-6851	608	5	∈	∈	PROPN
ejpam-6851	608	6	γs(g[h	γs(g[h	NOUN
ejpam-6851	608	7	]	]	PUNCT
ejpam-6851	608	8	)	)	PUNCT
ejpam-6851	608	9	,	,	PUNCT
ejpam-6851	608	10	there	there	PRON
ejpam-6851	608	11	exists	exist	VERB
ejpam-6851	608	12	s	s	PART
ejpam-6851	608	13	=	=	PUNCT
ejpam-6851	608	14	∪x∈a	∪x∈a	X
ejpam-6851	608	15	(	(	PUNCT
ejpam-6851	608	16	{	{	PUNCT
ejpam-6851	608	17	x	x	NOUN
ejpam-6851	608	18	}	}	PUNCT
ejpam-6851	608	19	×	×	PROPN
ejpam-6851	608	20	tx	tx	PROPN
ejpam-6851	608	21	)	)	PUNCT
ejpam-6851	608	22	∈	∈	PROPN
ejpam-6851	608	23	γs(g[h	γs(g[h	NOUN
ejpam-6851	608	24	]	]	X
ejpam-6851	608	25	)	)	PUNCT
ejpam-6851	608	26	satisfying	satisfy	VERB
ejpam-6851	608	27	the	the	DET
ejpam-6851	608	28	following	following	NOUN
ejpam-6851	608	29	:	:	PUNCT
ejpam-6851	608	30	(	(	PUNCT
ejpam-6851	608	31	i	i	NOUN
ejpam-6851	608	32	)	)	PUNCT
ejpam-6851	608	33	|s|	|s|	NOUN
ejpam-6851	608	34	=	=	SYM
ejpam-6851	608	35	|s∗|	|s∗|	NUM
ejpam-6851	608	36	;	;	PUNCT
ejpam-6851	608	37	(	(	PUNCT
ejpam-6851	608	38	ii	ii	NOUN
ejpam-6851	608	39	)	)	PUNCT
ejpam-6851	608	40	for	for	ADP
ejpam-6851	608	41	each	each	DET
ejpam-6851	608	42	x	x	SYM
ejpam-6851	608	43	∈	∈	PROPN
ejpam-6851	608	44	a	a	DET
ejpam-6851	608	45	∩ng(a	∩ng(a	PROPN
ejpam-6851	608	46	≽	≽	PROPN
ejpam-6851	608	47	)	)	PUNCT
ejpam-6851	608	48	,	,	PUNCT
ejpam-6851	608	49	there	there	PRON
ejpam-6851	608	50	exists	exist	VERB
ejpam-6851	608	51	y	y	PROPN
ejpam-6851	608	52	∈	∈	PROPN
ejpam-6851	608	53	tx	tx	PROPN
ejpam-6851	608	54	for	for	ADP
ejpam-6851	608	55	which	which	PRON
ejpam-6851	608	56	degh(y	degh(y	X
ejpam-6851	608	57	)	)	PUNCT
ejpam-6851	608	58	=	=	SYM
ejpam-6851	608	59	∆(h	∆(h	NOUN
ejpam-6851	608	60	)	)	PUNCT
ejpam-6851	608	61	.	.	PUNCT
ejpam-6851	609	1	proof	proof	NOUN
ejpam-6851	609	2	.	.	PUNCT
ejpam-6851	610	1	let	let	VERB
ejpam-6851	610	2	v	v	NUM
ejpam-6851	610	3	∈	∈	PROPN
ejpam-6851	610	4	v	v	NOUN
ejpam-6851	610	5	(	(	PUNCT
ejpam-6851	610	6	h	h	NOUN
ejpam-6851	610	7	)	)	PUNCT
ejpam-6851	610	8	such	such	ADJ
ejpam-6851	610	9	that	that	DET
ejpam-6851	610	10	degh(v	degh(v	NOUN
ejpam-6851	610	11	)	)	PUNCT
ejpam-6851	610	12	=	=	SYM
ejpam-6851	610	13	∆(h	∆(h	NOUN
ejpam-6851	610	14	)	)	PUNCT
ejpam-6851	610	15	.	.	PUNCT
ejpam-6851	611	1	write	write	VERB
ejpam-6851	611	2	s∗	s∗	PROPN
ejpam-6851	611	3	=	=	SYM
ejpam-6851	611	4	∪x∈a∗	∪x∈a∗	PROPN
ejpam-6851	611	5	(	(	PUNCT
ejpam-6851	611	6	{	{	PUNCT
ejpam-6851	611	7	x	x	NOUN
ejpam-6851	611	8	}	}	PUNCT
ejpam-6851	611	9	×	×	PROPN
ejpam-6851	611	10	t	t	NOUN
ejpam-6851	611	11	∗	∗	NOUN
ejpam-6851	611	12	x	x	PUNCT
ejpam-6851	611	13	)	)	PUNCT
ejpam-6851	611	14	,	,	PUNCT
ejpam-6851	611	15	where	where	SCONJ
ejpam-6851	611	16	a∗	a∗	PROPN
ejpam-6851	611	17	∈	∈	PROPN
ejpam-6851	611	18	γs(g	γs(g	PUNCT
ejpam-6851	611	19	)	)	PUNCT
ejpam-6851	611	20	and	and	CCONJ
ejpam-6851	611	21	t	t	PROPN
ejpam-6851	611	22	∗	∗	NOUN
ejpam-6851	611	23	x	x	PUNCT
ejpam-6851	611	24	∈	∈	NOUN
ejpam-6851	611	25	γs(h	γs(h	NOUN
ejpam-6851	611	26	)	)	PUNCT
ejpam-6851	611	27	for	for	ADP
ejpam-6851	611	28	each	each	DET
ejpam-6851	611	29	x	x	SYM
ejpam-6851	611	30	∈	∈	PROPN
ejpam-6851	611	31	a∗	a∗	NOUN
ejpam-6851	611	32	\ng(a	\ng(a	PROPN
ejpam-6851	611	33	∗	∗	NOUN
ejpam-6851	611	34	≽	≽	PROPN
ejpam-6851	611	35	)	)	PUNCT
ejpam-6851	611	36	.	.	PUNCT
ejpam-6851	612	1	for	for	ADP
ejpam-6851	612	2	each	each	DET
ejpam-6851	612	3	x	x	SYM
ejpam-6851	612	4	∈	∈	PROPN
ejpam-6851	612	5	a∗	a∗	PROPN
ejpam-6851	612	6	∩ng(a	∩ng(a	PROPN
ejpam-6851	612	7	∗	∗	PROPN
ejpam-6851	612	8	≽	≽	PROPN
ejpam-6851	612	9	)	)	PUNCT
ejpam-6851	612	10	,	,	PUNCT
ejpam-6851	612	11	let	let	VERB
ejpam-6851	612	12	yx	yx	PROPN
ejpam-6851	612	13	∈	∈	PROPN
ejpam-6851	612	14	tx	tx	PROPN
ejpam-6851	612	15	.	.	PUNCT
ejpam-6851	612	16	define	define	VERB
ejpam-6851	612	17	the	the	DET
ejpam-6851	612	18	following	following	NOUN
ejpam-6851	612	19	:	:	PUNCT
ejpam-6851	612	20	•	•	NUM
ejpam-6851	612	21	a	a	DET
ejpam-6851	612	22	=	=	SYM
ejpam-6851	612	23	a∗	a∗	NOUN
ejpam-6851	612	24	;	;	PUNCT
ejpam-6851	612	25	•	•	NUM
ejpam-6851	612	26	tx	tx	PROPN
ejpam-6851	612	27	=	=	SYM
ejpam-6851	612	28	t	t	PROPN
ejpam-6851	612	29	∗	∗	NOUN
ejpam-6851	612	30	x	x	PUNCT
ejpam-6851	612	31	for	for	ADP
ejpam-6851	612	32	each	each	DET
ejpam-6851	612	33	x	x	SYM
ejpam-6851	612	34	∈	∈	PROPN
ejpam-6851	612	35	a∗	a∗	NOUN
ejpam-6851	612	36	\ng(a	\ng(a	PROPN
ejpam-6851	612	37	∗	∗	NOUN
ejpam-6851	612	38	≽	≽	PROPN
ejpam-6851	612	39	)	)	PUNCT
ejpam-6851	612	40	;	;	PUNCT
ejpam-6851	612	41	and	and	CCONJ
ejpam-6851	612	42	•	•	NUM
ejpam-6851	612	43	tx	tx	NOUN
ejpam-6851	612	44	=	=	SYM
ejpam-6851	612	45	(	(	PUNCT
ejpam-6851	612	46	t	t	NOUN
ejpam-6851	612	47	∗	∗	X
ejpam-6851	612	48	x	x	X
ejpam-6851	612	49	\	\	PROPN
ejpam-6851	612	50	{	{	PUNCT
ejpam-6851	612	51	yx	yx	NOUN
ejpam-6851	612	52	}	}	PUNCT
ejpam-6851	612	53	)	)	PUNCT
ejpam-6851	612	54	∪	∪	ADP
ejpam-6851	612	55	{	{	PUNCT
ejpam-6851	612	56	v	v	NOUN
ejpam-6851	612	57	}	}	PUNCT
ejpam-6851	612	58	for	for	ADP
ejpam-6851	612	59	each	each	DET
ejpam-6851	612	60	x	x	SYM
ejpam-6851	612	61	∈	∈	PROPN
ejpam-6851	612	62	a∗	a∗	PROPN
ejpam-6851	612	63	∩ng(a	∩ng(a	PROPN
ejpam-6851	612	64	∗	∗	NOUN
ejpam-6851	612	65	≽	≽	PROPN
ejpam-6851	612	66	)	)	PUNCT
ejpam-6851	612	67	.	.	PUNCT
ejpam-6851	613	1	by	by	ADP
ejpam-6851	613	2	proposition	proposition	NOUN
ejpam-6851	613	3	8	8	NUM
ejpam-6851	613	4	,	,	PUNCT
ejpam-6851	613	5	s	s	X
ejpam-6851	613	6	=	=	PUNCT
ejpam-6851	613	7	∪x∈a	∪x∈a	X
ejpam-6851	613	8	(	(	PUNCT
ejpam-6851	613	9	{	{	PUNCT
ejpam-6851	613	10	x	x	NOUN
ejpam-6851	613	11	}	}	PUNCT
ejpam-6851	613	12	×	×	PROPN
ejpam-6851	613	13	tx	tx	PROPN
ejpam-6851	613	14	)	)	PUNCT
ejpam-6851	613	15	∈	∈	PROPN
ejpam-6851	613	16	γs(g[h	γs(g[h	NOUN
ejpam-6851	613	17	]	]	X
ejpam-6851	613	18	)	)	PUNCT
ejpam-6851	613	19	.	.	PUNCT
ejpam-6851	614	1	moreover	moreover	ADV
ejpam-6851	614	2	,	,	PUNCT
ejpam-6851	614	3	by	by	ADP
ejpam-6851	614	4	the	the	DET
ejpam-6851	614	5	construction	construction	NOUN
ejpam-6851	614	6	of	of	ADP
ejpam-6851	614	7	s	s	PROPN
ejpam-6851	614	8	,	,	PUNCT
ejpam-6851	614	9	|s|	|s|	NOUN
ejpam-6851	614	10	=	=	SYM
ejpam-6851	614	11	|s∗|	|s∗|	NUM
ejpam-6851	614	12	.	.	PUNCT
ejpam-6851	615	1	corollary	corollary	ADJ
ejpam-6851	615	2	5	5	NUM
ejpam-6851	615	3	.	.	PUNCT
ejpam-6851	616	1	let	let	VERB
ejpam-6851	616	2	g	g	NOUN
ejpam-6851	616	3	and	and	CCONJ
ejpam-6851	616	4	h	h	NOUN
ejpam-6851	616	5	be	be	AUX
ejpam-6851	616	6	nontrivial	nontrivial	ADJ
ejpam-6851	616	7	connected	connected	ADJ
ejpam-6851	616	8	graphs	graph	NOUN
ejpam-6851	616	9	.	.	PUNCT
ejpam-6851	617	1	then	then	ADV
ejpam-6851	617	2	γs(g[h	γs(g[h	VERB
ejpam-6851	617	3	]	]	X
ejpam-6851	617	4	)	)	PUNCT
ejpam-6851	618	1	=	=	PUNCT
ejpam-6851	618	2	min{|a	min{|a	NOUN
ejpam-6851	618	3	∩ng(a	∩ng(a	PROPN
ejpam-6851	618	4	≽)|+	≽)|+	NOUN
ejpam-6851	618	5	γs(h)|a	γs(h)|a	VERB
ejpam-6851	618	6	\ng(a	\ng(a	X
ejpam-6851	618	7	≽)|	≽)|	NOUN
ejpam-6851	618	8	:	:	PUNCT
ejpam-6851	618	9	a	a	DET
ejpam-6851	618	10	∈	∈	NOUN
ejpam-6851	618	11	γs(g	γs(g	PUNCT
ejpam-6851	618	12	)	)	PUNCT
ejpam-6851	618	13	}	}	PUNCT
ejpam-6851	618	14	,	,	PUNCT
ejpam-6851	618	15	and	and	CCONJ
ejpam-6851	618	16	γw(g[h	γw(g[h	NOUN
ejpam-6851	618	17	]	]	X
ejpam-6851	618	18	)	)	PUNCT
ejpam-6851	619	1	=	=	PUNCT
ejpam-6851	619	2	min{|a	min{|a	NOUN
ejpam-6851	619	3	∩ng(a	∩ng(a	PROPN
ejpam-6851	619	4	≼)|+	≼)|+	NOUN
ejpam-6851	619	5	γw(h)|a	γw(h)|a	ADJ
ejpam-6851	620	1	\ng(a	\ng(a	PRON
ejpam-6851	620	2	≼)|	≼)|	PROPN
ejpam-6851	620	3	:	:	PUNCT
ejpam-6851	620	4	a	a	DET
ejpam-6851	620	5	∈	∈	NOUN
ejpam-6851	620	6	γw(g	γw(g	PUNCT
ejpam-6851	620	7	)	)	PUNCT
ejpam-6851	620	8	}	}	PUNCT
ejpam-6851	620	9	.	.	PUNCT
ejpam-6851	621	1	j.	j.	PROPN
ejpam-6851	621	2	m.	m.	PROPN
ejpam-6851	621	3	molles	molles	PROPN
ejpam-6851	621	4	,	,	PUNCT
ejpam-6851	621	5	f.	f.	PROPN
ejpam-6851	621	6	p.	p.	PROPN
ejpam-6851	621	7	jamil	jamil	PROPN
ejpam-6851	621	8	,	,	PUNCT
ejpam-6851	621	9	s.	s.	PROPN
ejpam-6851	621	10	r.	r.	PROPN
ejpam-6851	621	11	canoy	canoy	PROPN
ejpam-6851	621	12	/	/	SYM
ejpam-6851	621	13	eur	eur	PROPN
ejpam-6851	621	14	.	.	PUNCT
ejpam-6851	622	1	j.	j.	PROPN
ejpam-6851	622	2	pure	pure	PROPN
ejpam-6851	622	3	appl	appl	PROPN
ejpam-6851	622	4	.	.	PROPN
ejpam-6851	622	5	math	math	PROPN
ejpam-6851	622	6	,	,	PUNCT
ejpam-6851	622	7	18	18	NUM
ejpam-6851	622	8	(	(	PUNCT
ejpam-6851	622	9	4	4	NUM
ejpam-6851	622	10	)	)	PUNCT
ejpam-6851	622	11	(	(	PUNCT
ejpam-6851	622	12	2025	2025	NUM
ejpam-6851	622	13	)	)	PUNCT
ejpam-6851	622	14	,	,	PUNCT
ejpam-6851	622	15	6851	6851	NUM
ejpam-6851	622	16	16	16	NUM
ejpam-6851	622	17	of	of	ADP
ejpam-6851	622	18	18	18	NUM
ejpam-6851	622	19	proof	proof	NOUN
ejpam-6851	622	20	.	.	PUNCT
ejpam-6851	623	1	put	put	VERB
ejpam-6851	623	2	α	α	NOUN
ejpam-6851	623	3	=	=	PUNCT
ejpam-6851	623	4	min{|a∩ng(a	min{|a∩ng(a	NUM
ejpam-6851	623	5	≽)|+γs(h)|a\ng(a	≽)|+γs(h)|a\ng(a	PROPN
ejpam-6851	624	1	≽)|	≽)|	NOUN
ejpam-6851	624	2	:	:	PUNCT
ejpam-6851	624	3	a	a	DET
ejpam-6851	624	4	∈	∈	NOUN
ejpam-6851	624	5	γs(g	γs(g	PUNCT
ejpam-6851	624	6	)	)	PUNCT
ejpam-6851	624	7	}	}	PUNCT
ejpam-6851	624	8	.	.	PUNCT
ejpam-6851	625	1	let	let	VERB
ejpam-6851	625	2	v	v	NUM
ejpam-6851	625	3	∈	∈	PROPN
ejpam-6851	625	4	v	v	NOUN
ejpam-6851	625	5	(	(	PUNCT
ejpam-6851	625	6	h	h	NOUN
ejpam-6851	625	7	)	)	PUNCT
ejpam-6851	625	8	such	such	ADJ
ejpam-6851	625	9	that	that	DET
ejpam-6851	625	10	degh(v	degh(v	NOUN
ejpam-6851	625	11	)	)	PUNCT
ejpam-6851	625	12	=	=	SYM
ejpam-6851	625	13	∆(h	∆(h	NOUN
ejpam-6851	625	14	)	)	PUNCT
ejpam-6851	625	15	,	,	PUNCT
ejpam-6851	625	16	and	and	CCONJ
ejpam-6851	625	17	let	let	VERB
ejpam-6851	625	18	a	a	DET
ejpam-6851	625	19	∈	∈	NOUN
ejpam-6851	625	20	γs(g	γs(g	PUNCT
ejpam-6851	625	21	)	)	PUNCT
ejpam-6851	625	22	such	such	ADJ
ejpam-6851	625	23	that	that	SCONJ
ejpam-6851	625	24	α	α	NOUN
ejpam-6851	625	25	=	=	X
ejpam-6851	625	26	|a|+	|a|+	NOUN
ejpam-6851	625	27	γs(h)|a	γs(h)|a	ADJ
ejpam-6851	625	28	\ng(a	\ng(a	ADP
ejpam-6851	625	29	≽)|	≽)|	NOUN
ejpam-6851	625	30	.	.	NOUN
ejpam-6851	625	31	for	for	ADP
ejpam-6851	625	32	each	each	DET
ejpam-6851	625	33	x	x	SYM
ejpam-6851	625	34	∈	∈	PROPN
ejpam-6851	625	35	a	a	DET
ejpam-6851	625	36	∩ng(a	∩ng(a	PROPN
ejpam-6851	625	37	≽	≽	PROPN
ejpam-6851	625	38	)	)	PUNCT
ejpam-6851	625	39	,	,	PUNCT
ejpam-6851	625	40	let	let	VERB
ejpam-6851	625	41	tx	tx	VERB
ejpam-6851	625	42	=	=	PUNCT
ejpam-6851	625	43	{	{	PUNCT
ejpam-6851	625	44	v	v	NOUN
ejpam-6851	625	45	}	}	PUNCT
ejpam-6851	625	46	and	and	CCONJ
ejpam-6851	625	47	for	for	ADP
ejpam-6851	625	48	each	each	DET
ejpam-6851	625	49	x	x	SYM
ejpam-6851	625	50	∈	∈	PROPN
ejpam-6851	625	51	a	a	DET
ejpam-6851	625	52	\ng(a	\ng(a	PROPN
ejpam-6851	625	53	≽	≽	PROPN
ejpam-6851	625	54	)	)	PUNCT
ejpam-6851	625	55	,	,	PUNCT
ejpam-6851	625	56	let	let	VERB
ejpam-6851	625	57	tx	tx	VERB
ejpam-6851	625	58	⊆	⊆	NUM
ejpam-6851	625	59	v	v	NOUN
ejpam-6851	625	60	(	(	PUNCT
ejpam-6851	625	61	h	h	NOUN
ejpam-6851	625	62	)	)	PUNCT
ejpam-6851	625	63	be	be	VERB
ejpam-6851	625	64	a	a	DET
ejpam-6851	625	65	γs	γs	NOUN
ejpam-6851	625	66	-	-	PUNCT
ejpam-6851	625	67	set	set	NOUN
ejpam-6851	625	68	of	of	ADP
ejpam-6851	625	69	h.	h.	NOUN
ejpam-6851	625	70	by	by	ADP
ejpam-6851	625	71	proposition	proposition	NOUN
ejpam-6851	625	72	8	8	NUM
ejpam-6851	625	73	,	,	PUNCT
ejpam-6851	625	74	s	s	X
ejpam-6851	625	75	=	=	PUNCT
ejpam-6851	625	76	∪x∈a	∪x∈a	X
ejpam-6851	625	77	(	(	PUNCT
ejpam-6851	625	78	{	{	PUNCT
ejpam-6851	625	79	x	x	NOUN
ejpam-6851	625	80	}	}	PUNCT
ejpam-6851	625	81	×	×	PROPN
ejpam-6851	625	82	tx	tx	PROPN
ejpam-6851	625	83	)	)	PUNCT
ejpam-6851	625	84	∈	∈	PROPN
ejpam-6851	625	85	γs(g[h	γs(g[h	NOUN
ejpam-6851	625	86	]	]	X
ejpam-6851	625	87	)	)	PUNCT
ejpam-6851	625	88	.	.	PUNCT
ejpam-6851	626	1	thus	thus	ADV
ejpam-6851	626	2	,	,	PUNCT
ejpam-6851	626	3	γs(g[h	γs(g[h	NOUN
ejpam-6851	626	4	]	]	X
ejpam-6851	626	5	)	)	PUNCT
ejpam-6851	626	6	≤	≤	NUM
ejpam-6851	626	7	|s|	|s|	PROPN
ejpam-6851	626	8	=	=	PROPN
ejpam-6851	626	9	|a	|a	VERB
ejpam-6851	626	10	∩ng(a	∩ng(a	PROPN
ejpam-6851	626	11	≽)|+	≽)|+	NOUN
ejpam-6851	626	12	γs(h)|a	γs(h)|a	VERB
ejpam-6851	626	13	\ng(a	\ng(a	PROPN
ejpam-6851	626	14	≽	≽	PROPN
ejpam-6851	626	15	)	)	PUNCT
ejpam-6851	626	16	=	=	SYM
ejpam-6851	627	1	α	α	X
ejpam-6851	627	2	.	.	PUNCT
ejpam-6851	628	1	let	let	AUX
ejpam-6851	628	2	s	s	PRON
ejpam-6851	628	3	=	=	PUNCT
ejpam-6851	628	4	∪x∈a	∪x∈a	VERB
ejpam-6851	628	5	(	(	PUNCT
ejpam-6851	628	6	{	{	PUNCT
ejpam-6851	628	7	x	x	NOUN
ejpam-6851	628	8	}	}	PUNCT
ejpam-6851	628	9	×	×	PROPN
ejpam-6851	628	10	tx	tx	PROPN
ejpam-6851	628	11	)	)	PUNCT
ejpam-6851	628	12	be	be	AUX
ejpam-6851	628	13	a	a	DET
ejpam-6851	628	14	γs	γs	NOUN
ejpam-6851	628	15	-	-	PUNCT
ejpam-6851	628	16	set	set	NOUN
ejpam-6851	628	17	of	of	ADP
ejpam-6851	628	18	g[h	g[h	NOUN
ejpam-6851	628	19	]	]	PUNCT
ejpam-6851	628	20	.	.	PUNCT
ejpam-6851	629	1	in	in	ADP
ejpam-6851	629	2	view	view	NOUN
ejpam-6851	629	3	of	of	ADP
ejpam-6851	629	4	proposition	proposition	NOUN
ejpam-6851	629	5	11	11	NUM
ejpam-6851	629	6	,	,	PUNCT
ejpam-6851	629	7	s	s	X
ejpam-6851	629	8	=	=	PUNCT
ejpam-6851	629	9	∪x∈a	∪x∈a	PROPN
ejpam-6851	629	10	(	(	PUNCT
ejpam-6851	629	11	{	{	PUNCT
ejpam-6851	629	12	x	x	NOUN
ejpam-6851	629	13	}	}	PUNCT
ejpam-6851	629	14	×	×	PROPN
ejpam-6851	629	15	tx	tx	PROPN
ejpam-6851	629	16	)	)	PUNCT
ejpam-6851	629	17	with	with	ADP
ejpam-6851	629	18	a	a	DET
ejpam-6851	629	19	⊆	⊆	NUM
ejpam-6851	629	20	v	v	NOUN
ejpam-6851	629	21	(	(	PUNCT
ejpam-6851	629	22	g	g	NOUN
ejpam-6851	629	23	)	)	PUNCT
ejpam-6851	629	24	and	and	CCONJ
ejpam-6851	629	25	tx	tx	VERB
ejpam-6851	629	26	⊆	⊆	NUM
ejpam-6851	629	27	v	v	NOUN
ejpam-6851	629	28	(	(	PUNCT
ejpam-6851	629	29	h	h	NOUN
ejpam-6851	629	30	)	)	PUNCT
ejpam-6851	629	31	,	,	PUNCT
ejpam-6851	629	32	where	where	SCONJ
ejpam-6851	629	33	a	a	DET
ejpam-6851	629	34	∈	∈	NOUN
ejpam-6851	629	35	γs(g	γs(g	NUM
ejpam-6851	629	36	)	)	PUNCT
ejpam-6851	629	37	,	,	PUNCT
ejpam-6851	629	38	tx	tx	ADP
ejpam-6851	629	39	̸=	̸=	PROPN
ejpam-6851	629	40	∅	∅	NOUN
ejpam-6851	629	41	for	for	ADP
ejpam-6851	629	42	each	each	DET
ejpam-6851	629	43	x	x	SYM
ejpam-6851	629	44	∈	∈	PROPN
ejpam-6851	629	45	a	a	DET
ejpam-6851	629	46	∩ng(a	∩ng(a	PROPN
ejpam-6851	629	47	≽	≽	PROPN
ejpam-6851	629	48	)	)	PUNCT
ejpam-6851	629	49	,	,	PUNCT
ejpam-6851	629	50	and	and	CCONJ
ejpam-6851	629	51	tx	tx	ADP
ejpam-6851	629	52	∈	∈	PROPN
ejpam-6851	629	53	γs(h	γs(h	NUM
ejpam-6851	629	54	)	)	PUNCT
ejpam-6851	629	55	for	for	ADP
ejpam-6851	629	56	each	each	DET
ejpam-6851	629	57	x	x	SYM
ejpam-6851	629	58	∈	∈	PROPN
ejpam-6851	629	59	a	a	DET
ejpam-6851	629	60	\ng(a	\ng(a	PROPN
ejpam-6851	629	61	≽	≽	PROPN
ejpam-6851	629	62	)	)	PUNCT
ejpam-6851	629	63	.	.	PUNCT
ejpam-6851	630	1	thus	thus	ADV
ejpam-6851	630	2	,	,	PUNCT
ejpam-6851	630	3	γs(g[h	γs(g[h	NOUN
ejpam-6851	630	4	]	]	X
ejpam-6851	630	5	)	)	PUNCT
ejpam-6851	630	6	=	=	SYM
ejpam-6851	630	7	|s|	|s|	PROPN
ejpam-6851	630	8	≥	≥	NOUN
ejpam-6851	630	9	|a	|a	X
ejpam-6851	630	10	∩ng(a	∩ng(a	PROPN
ejpam-6851	630	11	≽)|+	≽)|+	NOUN
ejpam-6851	630	12	γs(h)|a	γs(h)|a	VERB
ejpam-6851	630	13	\ng(a	\ng(a	ADP
ejpam-6851	630	14	≽)|	≽)|	NOUN
ejpam-6851	630	15	≥	≥	NOUN
ejpam-6851	630	16	α	α	NOUN
ejpam-6851	630	17	.	.	PUNCT
ejpam-6851	631	1	proof	proof	NOUN
ejpam-6851	631	2	for	for	ADP
ejpam-6851	631	3	the	the	DET
ejpam-6851	631	4	weak	weak	ADJ
ejpam-6851	631	5	domination	domination	NOUN
ejpam-6851	631	6	case	case	NOUN
ejpam-6851	631	7	is	be	AUX
ejpam-6851	631	8	similar	similar	ADJ
ejpam-6851	631	9	.	.	PUNCT
ejpam-6851	632	1	corollary	corollary	ADJ
ejpam-6851	632	2	6	6	NUM
ejpam-6851	632	3	.	.	PUNCT
ejpam-6851	633	1	the	the	DET
ejpam-6851	633	2	following	follow	VERB
ejpam-6851	633	3	hold	hold	NOUN
ejpam-6851	633	4	for	for	ADP
ejpam-6851	633	5	nontrivial	nontrivial	ADJ
ejpam-6851	633	6	connected	connect	VERB
ejpam-6851	633	7	graphs	graph	NOUN
ejpam-6851	633	8	g	g	NOUN
ejpam-6851	633	9	and	and	CCONJ
ejpam-6851	633	10	h	h	NOUN
ejpam-6851	633	11	:	:	PUNCT
ejpam-6851	633	12	(	(	PUNCT
ejpam-6851	633	13	i	i	NOUN
ejpam-6851	633	14	)	)	PUNCT
ejpam-6851	633	15	if	if	SCONJ
ejpam-6851	633	16	γ(h	γ(h	NOUN
ejpam-6851	633	17	)	)	PUNCT
ejpam-6851	633	18	=	=	SYM
ejpam-6851	633	19	1	1	NUM
ejpam-6851	633	20	,	,	PUNCT
ejpam-6851	633	21	then	then	ADV
ejpam-6851	633	22	γs(g[h	γs(g[h	VERB
ejpam-6851	633	23	]	]	X
ejpam-6851	633	24	)	)	PUNCT
ejpam-6851	633	25	=	=	SYM
ejpam-6851	633	26	γs(g	γs(g	NUM
ejpam-6851	633	27	)	)	PUNCT
ejpam-6851	633	28	.	.	PUNCT
ejpam-6851	634	1	(	(	PUNCT
ejpam-6851	634	2	ii	ii	NOUN
ejpam-6851	634	3	)	)	PUNCT
ejpam-6851	634	4	if	if	SCONJ
ejpam-6851	634	5	h	h	NOUN
ejpam-6851	634	6	is	be	AUX
ejpam-6851	634	7	a	a	DET
ejpam-6851	634	8	regular	regular	ADJ
ejpam-6851	634	9	graph	graph	NOUN
ejpam-6851	634	10	,	,	PUNCT
ejpam-6851	634	11	then	then	ADV
ejpam-6851	634	12	γs(g[h	γs(g[h	NOUN
ejpam-6851	634	13	]	]	X
ejpam-6851	634	14	)	)	PUNCT
ejpam-6851	634	15	=	=	PUNCT
ejpam-6851	634	16	min{|a	min{|a	NOUN
ejpam-6851	634	17	∩ng(a	∩ng(a	PROPN
ejpam-6851	634	18	≽)|+	≽)|+	NOUN
ejpam-6851	634	19	γ(h)|a	γ(h)|a	NOUN
ejpam-6851	634	20	\ng(a	\ng(a	X
ejpam-6851	634	21	≽)|	≽)|	NOUN
ejpam-6851	634	22	:	:	PUNCT
ejpam-6851	634	23	a	a	DET
ejpam-6851	634	24	∈	∈	NOUN
ejpam-6851	634	25	γs(g	γs(g	PUNCT
ejpam-6851	634	26	)	)	PUNCT
ejpam-6851	634	27	}	}	PUNCT
ejpam-6851	634	28	and	and	CCONJ
ejpam-6851	634	29	γw(g[h	γw(g[h	ADJ
ejpam-6851	634	30	]	]	X
ejpam-6851	634	31	)	)	PUNCT
ejpam-6851	635	1	=	=	PUNCT
ejpam-6851	635	2	min{|a	min{|a	NOUN
ejpam-6851	635	3	∩ng(a	∩ng(a	PROPN
ejpam-6851	635	4	≼)|+	≼)|+	NOUN
ejpam-6851	635	5	γ(h)|a	γ(h)|a	PROPN
ejpam-6851	635	6	\ng(a	\ng(a	PRON
ejpam-6851	635	7	≼)|	≼)|	PROPN
ejpam-6851	635	8	:	:	PUNCT
ejpam-6851	635	9	a	a	DET
ejpam-6851	635	10	∈	∈	NOUN
ejpam-6851	635	11	γw(g	γw(g	PUNCT
ejpam-6851	635	12	)	)	PUNCT
ejpam-6851	635	13	}	}	PUNCT
ejpam-6851	635	14	.	.	PUNCT
ejpam-6851	636	1	acknowledgements	acknowledgement	NOUN
ejpam-6851	636	2	this	this	DET
ejpam-6851	636	3	project	project	NOUN
ejpam-6851	636	4	is	be	AUX
ejpam-6851	636	5	fully	fully	ADV
ejpam-6851	636	6	supported	support	VERB
ejpam-6851	636	7	by	by	ADP
ejpam-6851	636	8	the	the	DET
ejpam-6851	636	9	dost	dost	NOUN
ejpam-6851	636	10	-	-	PUNCT
ejpam-6851	636	11	asthrd	asthrd	NOUN
ejpam-6851	636	12	of	of	ADP
ejpam-6851	636	13	the	the	DET
ejpam-6851	636	14	philippines	philippine	NOUN
ejpam-6851	636	15	and	and	CCONJ
ejpam-6851	636	16	the	the	DET
ejpam-6851	636	17	ovcre	ovcre	NOUN
ejpam-6851	636	18	of	of	ADP
ejpam-6851	636	19	msu	msu	PROPN
ejpam-6851	636	20	-	-	PUNCT
ejpam-6851	636	21	iligan	iligan	PROPN
ejpam-6851	636	22	institute	institute	PROPN
ejpam-6851	636	23	of	of	ADP
ejpam-6851	636	24	technology	technology	PROPN
ejpam-6851	636	25	.	.	PUNCT
ejpam-6851	637	1	references	reference	NOUN
ejpam-6851	637	2	[	[	X
ejpam-6851	637	3	1	1	NUM
ejpam-6851	637	4	]	]	X
ejpam-6851	637	5	f.	f.	PROPN
ejpam-6851	637	6	buckley	buckley	PROPN
ejpam-6851	637	7	and	and	CCONJ
ejpam-6851	637	8	f.	f.	PROPN
ejpam-6851	637	9	harary	harary	PROPN
ejpam-6851	637	10	.	.	PUNCT
ejpam-6851	638	1	distance	distance	NOUN
ejpam-6851	638	2	in	in	ADP
ejpam-6851	638	3	graphs	graph	NOUN
ejpam-6851	638	4	.	.	PUNCT
ejpam-6851	639	1	addison	addison	PROPN
ejpam-6851	639	2	-	-	PUNCT
ejpam-6851	639	3	wesley	wesley	PROPN
ejpam-6851	639	4	,	,	PUNCT
ejpam-6851	639	5	redwood	redwood	NOUN
ejpam-6851	639	6	city	city	NOUN
ejpam-6851	639	7	,	,	PUNCT
ejpam-6851	639	8	ca	ca	NOUN
ejpam-6851	639	9	,	,	PUNCT
ejpam-6851	639	10	1990	1990	NUM
ejpam-6851	639	11	.	.	PUNCT
ejpam-6851	640	1	[	[	X
ejpam-6851	640	2	2	2	NUM
ejpam-6851	640	3	]	]	PUNCT
ejpam-6851	640	4	claude	claude	PROPN
ejpam-6851	640	5	berge	berge	PROPN
ejpam-6851	640	6	.	.	PUNCT
ejpam-6851	641	1	théorie	théorie	PROPN
ejpam-6851	641	2	des	des	PROPN
ejpam-6851	641	3	graphes	graphes	PROPN
ejpam-6851	641	4	et	et	PROPN
ejpam-6851	641	5	ses	ses	PROPN
ejpam-6851	641	6	applications	application	NOUN
ejpam-6851	641	7	.	.	PUNCT
ejpam-6851	642	1	dunod	dunod	PROPN
ejpam-6851	642	2	,	,	PUNCT
ejpam-6851	642	3	paris	paris	PROPN
ejpam-6851	642	4	,	,	PUNCT
ejpam-6851	642	5	1958	1958	NUM
ejpam-6851	642	6	.	.	PUNCT
ejpam-6851	643	1	english	english	ADJ
ejpam-6851	643	2	translation	translation	NOUN
ejpam-6851	643	3	:	:	PUNCT
ejpam-6851	643	4	the	the	DET
ejpam-6851	643	5	theory	theory	NOUN
ejpam-6851	643	6	of	of	ADP
ejpam-6851	643	7	graphs	graph	NOUN
ejpam-6851	643	8	and	and	CCONJ
ejpam-6851	643	9	its	its	PRON
ejpam-6851	643	10	applications	application	NOUN
ejpam-6851	643	11	,	,	PUNCT
ejpam-6851	643	12	methuen	methuen	PROPN
ejpam-6851	643	13	(	(	PUNCT
ejpam-6851	643	14	london	london	PROPN
ejpam-6851	643	15	)	)	PUNCT
ejpam-6851	643	16	andwiley	andwiley	PROPN
ejpam-6851	643	17	(	(	PUNCT
ejpam-6851	643	18	new	new	PROPN
ejpam-6851	643	19	york	york	PROPN
ejpam-6851	643	20	)	)	PUNCT
ejpam-6851	643	21	,	,	PUNCT
ejpam-6851	643	22	1962	1962	NUM
ejpam-6851	643	23	.	.	PUNCT
ejpam-6851	644	1	[	[	X
ejpam-6851	644	2	3	3	X
ejpam-6851	644	3	]	]	X
ejpam-6851	644	4	e.	e.	PROPN
ejpam-6851	644	5	cockayne	cockayne	PROPN
ejpam-6851	644	6	and	and	CCONJ
ejpam-6851	644	7	s.	s.	PROPN
ejpam-6851	644	8	hedetniemi	hedetniemi	PROPN
ejpam-6851	644	9	.	.	PUNCT
ejpam-6851	645	1	towards	towards	ADP
ejpam-6851	645	2	a	a	DET
ejpam-6851	645	3	theory	theory	NOUN
ejpam-6851	645	4	of	of	ADP
ejpam-6851	645	5	domination	domination	NOUN
ejpam-6851	645	6	in	in	ADP
ejpam-6851	645	7	graphs	graph	NOUN
ejpam-6851	645	8	.	.	PUNCT
ejpam-6851	646	1	networks	network	NOUN
ejpam-6851	646	2	,	,	PUNCT
ejpam-6851	646	3	7(3):247–261	7(3):247–261	NUM
ejpam-6851	646	4	,	,	PUNCT
ejpam-6851	646	5	1977	1977	NUM
ejpam-6851	646	6	.	.	PUNCT
ejpam-6851	647	1	[	[	X
ejpam-6851	647	2	4	4	X
ejpam-6851	647	3	]	]	X
ejpam-6851	647	4	teresa	teresa	PROPN
ejpam-6851	647	5	w.	w.	PROPN
ejpam-6851	647	6	haynes	haynes	PROPN
ejpam-6851	647	7	,	,	PUNCT
ejpam-6851	647	8	stephen	stephen	PROPN
ejpam-6851	647	9	t.	t.	PROPN
ejpam-6851	647	10	hedetniemi	hedetniemi	PROPN
ejpam-6851	647	11	,	,	PUNCT
ejpam-6851	647	12	and	and	CCONJ
ejpam-6851	647	13	peter	peter	PROPN
ejpam-6851	647	14	j.	j.	PROPN
ejpam-6851	647	15	slater	slater	PROPN
ejpam-6851	647	16	.	.	PUNCT
ejpam-6851	648	1	fundamentals	fundamental	NOUN
ejpam-6851	648	2	of	of	ADP
ejpam-6851	648	3	domination	domination	NOUN
ejpam-6851	648	4	in	in	ADP
ejpam-6851	648	5	graphs	graph	NOUN
ejpam-6851	648	6	.	.	PUNCT
ejpam-6851	649	1	marcel	marcel	PROPN
ejpam-6851	649	2	dekker	dekker	PROPN
ejpam-6851	649	3	,	,	PUNCT
ejpam-6851	649	4	inc	inc	PROPN
ejpam-6851	649	5	.	.	PROPN
ejpam-6851	649	6	,	,	PUNCT
ejpam-6851	649	7	new	new	PROPN
ejpam-6851	649	8	york	york	PROPN
ejpam-6851	649	9	,	,	PUNCT
ejpam-6851	649	10	1998	1998	NUM
ejpam-6851	649	11	.	.	PUNCT
ejpam-6851	650	1	[	[	X
ejpam-6851	650	2	5	5	X
ejpam-6851	650	3	]	]	PUNCT
ejpam-6851	650	4	f.	f.	PROPN
ejpam-6851	650	5	p.	p.	PROPN
ejpam-6851	650	6	jamil	jamil	PROPN
ejpam-6851	650	7	and	and	CCONJ
ejpam-6851	650	8	r.	r.	PROPN
ejpam-6851	650	9	p.	p.	PROPN
ejpam-6851	650	10	malalay	malalay	PROPN
ejpam-6851	650	11	.	.	PUNCT
ejpam-6851	651	1	on	on	ADP
ejpam-6851	651	2	disjunctive	disjunctive	ADJ
ejpam-6851	651	3	domination	domination	NOUN
ejpam-6851	651	4	in	in	ADP
ejpam-6851	651	5	graphs	graph	NOUN
ejpam-6851	651	6	.	.	PUNCT
ejpam-6851	652	1	quaestiones	quaestione	NOUN
ejpam-6851	652	2	mathematicae	mathematicae	PROPN
ejpam-6851	652	3	,	,	PUNCT
ejpam-6851	652	4	43(2):149–168	43(2):149–168	PROPN
ejpam-6851	652	5	,	,	PUNCT
ejpam-6851	652	6	2020	2020	NUM
ejpam-6851	652	7	.	.	PUNCT
ejpam-6851	653	1	j.	j.	PROPN
ejpam-6851	653	2	m.	m.	PROPN
ejpam-6851	653	3	molles	molles	PROPN
ejpam-6851	653	4	,	,	PUNCT
ejpam-6851	653	5	f.	f.	PROPN
ejpam-6851	653	6	p.	p.	PROPN
ejpam-6851	653	7	jamil	jamil	PROPN
ejpam-6851	653	8	,	,	PUNCT
ejpam-6851	653	9	s.	s.	PROPN
ejpam-6851	653	10	r.	r.	PROPN
ejpam-6851	653	11	canoy	canoy	PROPN
ejpam-6851	653	12	/	/	SYM
ejpam-6851	653	13	eur	eur	PROPN
ejpam-6851	653	14	.	.	PUNCT
ejpam-6851	654	1	j.	j.	PROPN
ejpam-6851	654	2	pure	pure	PROPN
ejpam-6851	654	3	appl	appl	PROPN
ejpam-6851	654	4	.	.	PROPN
ejpam-6851	654	5	math	math	PROPN
ejpam-6851	654	6	,	,	PUNCT
ejpam-6851	654	7	18	18	NUM
ejpam-6851	654	8	(	(	PUNCT
ejpam-6851	654	9	4	4	NUM
ejpam-6851	654	10	)	)	PUNCT
ejpam-6851	654	11	(	(	PUNCT
ejpam-6851	654	12	2025	2025	NUM
ejpam-6851	654	13	)	)	PUNCT
ejpam-6851	654	14	,	,	PUNCT
ejpam-6851	654	15	6851	6851	NUM
ejpam-6851	654	16	17	17	NUM
ejpam-6851	654	17	of	of	ADP
ejpam-6851	654	18	18	18	NUM
ejpam-6851	654	19	[	[	SYM
ejpam-6851	654	20	6	6	NUM
ejpam-6851	654	21	]	]	PUNCT
ejpam-6851	654	22	h.	h.	PROPN
ejpam-6851	654	23	m.	m.	PROPN
ejpam-6851	654	24	nuenay	nuenay	PROPN
ejpam-6851	654	25	and	and	CCONJ
ejpam-6851	654	26	f.	f.	PROPN
ejpam-6851	654	27	p.	p.	PROPN
ejpam-6851	654	28	jamil	jamil	PROPN
ejpam-6851	654	29	.	.	PUNCT
ejpam-6851	655	1	on	on	ADP
ejpam-6851	655	2	minimal	minimal	ADJ
ejpam-6851	655	3	geodetic	geodetic	ADJ
ejpam-6851	655	4	domination	domination	NOUN
ejpam-6851	655	5	in	in	ADP
ejpam-6851	655	6	graphs	graph	NOUN
ejpam-6851	655	7	.	.	PUNCT
ejpam-6851	656	1	discussiones	discussione	NOUN
ejpam-6851	656	2	mathematicae	mathematicae	PROPN
ejpam-6851	656	3	graph	graph	NOUN
ejpam-6851	656	4	theory	theory	NOUN
ejpam-6851	656	5	,	,	PUNCT
ejpam-6851	656	6	35(3):403–418	35(3):403–418	PROPN
ejpam-6851	656	7	,	,	PUNCT
ejpam-6851	656	8	2015	2015	NUM
ejpam-6851	656	9	.	.	PUNCT
ejpam-6851	657	1	[	[	X
ejpam-6851	657	2	7	7	X
ejpam-6851	657	3	]	]	X
ejpam-6851	657	4	oystein	oystein	PROPN
ejpam-6851	657	5	ore	ore	PROPN
ejpam-6851	657	6	.	.	PUNCT
ejpam-6851	658	1	theory	theory	NOUN
ejpam-6851	658	2	of	of	ADP
ejpam-6851	658	3	graphs	graph	NOUN
ejpam-6851	658	4	,	,	PUNCT
ejpam-6851	658	5	volume	volume	NOUN
ejpam-6851	658	6	38	38	NUM
ejpam-6851	658	7	of	of	ADP
ejpam-6851	658	8	colloquium	colloquium	NOUN
ejpam-6851	658	9	publications	publication	NOUN
ejpam-6851	658	10	.	.	PUNCT
ejpam-6851	659	1	american	american	PROPN
ejpam-6851	659	2	mathematical	mathematical	PROPN
ejpam-6851	659	3	society	society	NOUN
ejpam-6851	659	4	,	,	PUNCT
ejpam-6851	659	5	providence	providence	NOUN
ejpam-6851	659	6	,	,	PUNCT
ejpam-6851	659	7	ri	ri	NOUN
ejpam-6851	659	8	,	,	PUNCT
ejpam-6851	659	9	1962	1962	NUM
ejpam-6851	659	10	.	.	PUNCT
ejpam-6851	660	1	[	[	X
ejpam-6851	660	2	8	8	X
ejpam-6851	660	3	]	]	X
ejpam-6851	660	4	e.	e.	PROPN
ejpam-6851	660	5	sampathkumar	sampathkumar	PROPN
ejpam-6851	660	6	and	and	CCONJ
ejpam-6851	660	7	l.	l.	PROPN
ejpam-6851	660	8	pushpa	pushpa	PROPN
ejpam-6851	660	9	latha	latha	PROPN
ejpam-6851	660	10	.	.	PUNCT
ejpam-6851	661	1	strong	strong	ADJ
ejpam-6851	661	2	,	,	PUNCT
ejpam-6851	661	3	weak	weak	ADJ
ejpam-6851	661	4	domination	domination	NOUN
ejpam-6851	661	5	and	and	CCONJ
ejpam-6851	661	6	domination	domination	NOUN
ejpam-6851	661	7	balance	balance	NOUN
ejpam-6851	661	8	in	in	ADP
ejpam-6851	661	9	graphs	graph	NOUN
ejpam-6851	661	10	.	.	PUNCT
ejpam-6851	662	1	discrete	discrete	ADJ
ejpam-6851	662	2	mathematics	mathematic	NOUN
ejpam-6851	662	3	,	,	PUNCT
ejpam-6851	662	4	161:235–242	161:235–242	NUM
ejpam-6851	662	5	,	,	PUNCT
ejpam-6851	662	6	1996	1996	NUM
ejpam-6851	662	7	.	.	PUNCT
ejpam-6851	663	1	[	[	X
ejpam-6851	663	2	9	9	NUM
ejpam-6851	663	3	]	]	PUNCT
ejpam-6851	663	4	r.	r.	PROPN
ejpam-6851	663	5	s.	s.	PROPN
ejpam-6851	663	6	bhat	bhat	PROPN
ejpam-6851	663	7	,	,	PUNCT
ejpam-6851	663	8	s.	s.	PROPN
ejpam-6851	663	9	s.	s.	PROPN
ejpam-6851	663	10	kamath	kamath	PROPN
ejpam-6851	663	11	,	,	PUNCT
ejpam-6851	663	12	and	and	CCONJ
ejpam-6851	663	13	s.	s.	PROPN
ejpam-6851	663	14	r.	r.	PROPN
ejpam-6851	663	15	bhat	bhat	PROPN
ejpam-6851	663	16	.	.	PUNCT
ejpam-6851	664	1	a	a	DET
ejpam-6851	664	2	bound	bind	VERB
ejpam-6851	664	3	on	on	ADP
ejpam-6851	664	4	weak	weak	ADJ
ejpam-6851	664	5	domination	domination	NOUN
ejpam-6851	664	6	number	number	NOUN
ejpam-6851	664	7	using	use	VERB
ejpam-6851	664	8	strong	strong	ADJ
ejpam-6851	664	9	(	(	PUNCT
ejpam-6851	664	10	weak	weak	ADJ
ejpam-6851	664	11	)	)	PUNCT
ejpam-6851	664	12	degree	degree	NOUN
ejpam-6851	664	13	concepts	concept	NOUN
ejpam-6851	664	14	of	of	ADP
ejpam-6851	664	15	graphs	graph	NOUN
ejpam-6851	664	16	.	.	PUNCT
ejpam-6851	665	1	opuscula	opuscula	PROPN
ejpam-6851	665	2	mathematica	mathematica	PROPN
ejpam-6851	665	3	,	,	PUNCT
ejpam-6851	665	4	32:235–238	32:235–238	PROPN
ejpam-6851	665	5	,	,	PUNCT
ejpam-6851	665	6	2012	2012	NUM
ejpam-6851	665	7	.	.	PUNCT
ejpam-6851	666	1	[	[	X
ejpam-6851	666	2	10	10	NUM
ejpam-6851	666	3	]	]	X
ejpam-6851	666	4	r.	r.	PROPN
ejpam-6851	666	5	boutrig	boutrig	PROPN
ejpam-6851	666	6	and	and	CCONJ
ejpam-6851	666	7	m.	m.	NOUN
ejpam-6851	666	8	chellali	chellali	PROPN
ejpam-6851	666	9	.	.	PUNCT
ejpam-6851	667	1	a	a	DET
ejpam-6851	667	2	note	note	NOUN
ejpam-6851	667	3	on	on	ADP
ejpam-6851	667	4	a	a	DET
ejpam-6851	667	5	relation	relation	NOUN
ejpam-6851	667	6	between	between	ADP
ejpam-6851	667	7	the	the	DET
ejpam-6851	667	8	weak	weak	ADJ
ejpam-6851	667	9	and	and	CCONJ
ejpam-6851	667	10	strong	strong	ADJ
ejpam-6851	667	11	domination	domination	NOUN
ejpam-6851	667	12	numbers	number	NOUN
ejpam-6851	667	13	of	of	ADP
ejpam-6851	667	14	a	a	DET
ejpam-6851	667	15	graph	graph	NOUN
ejpam-6851	667	16	.	.	PUNCT
ejpam-6851	668	1	opuscula	opuscula	PROPN
ejpam-6851	668	2	mathematica	mathematica	PROPN
ejpam-6851	668	3	,	,	PUNCT
ejpam-6851	668	4	32(2):235–238	32(2):235–238	PROPN
ejpam-6851	668	5	,	,	PUNCT
ejpam-6851	668	6	2012	2012	NUM
ejpam-6851	668	7	.	.	PUNCT
ejpam-6851	669	1	[	[	X
ejpam-6851	669	2	11	11	NUM
ejpam-6851	669	3	]	]	X
ejpam-6851	669	4	d.	d.	PROPN
ejpam-6851	669	5	derya	derya	PROPN
ejpam-6851	669	6	and	and	CCONJ
ejpam-6851	669	7	l.	l.	PROPN
ejpam-6851	669	8	berna	berna	PROPN
ejpam-6851	669	9	.	.	PUNCT
ejpam-6851	670	1	weak	weak	ADJ
ejpam-6851	670	2	and	and	CCONJ
ejpam-6851	670	3	strong	strong	ADJ
ejpam-6851	670	4	domination	domination	NOUN
ejpam-6851	670	5	on	on	ADP
ejpam-6851	670	6	some	some	DET
ejpam-6851	670	7	graphs	graph	NOUN
ejpam-6851	670	8	.	.	PUNCT
ejpam-6851	671	1	rairo	rairo	NOUN
ejpam-6851	671	2	operations	operation	NOUN
ejpam-6851	671	3	research	research	NOUN
ejpam-6851	671	4	,	,	PUNCT
ejpam-6851	671	5	56(4):2305–2314	56(4):2305–2314	NUM
ejpam-6851	671	6	,	,	PUNCT
ejpam-6851	671	7	2022	2022	NUM
ejpam-6851	671	8	.	.	PUNCT
ejpam-6851	672	1	[	[	X
ejpam-6851	672	2	12	12	NUM
ejpam-6851	672	3	]	]	PUNCT
ejpam-6851	672	4	j.	j.	PROPN
ejpam-6851	672	5	h.	h.	PROPN
ejpam-6851	672	6	hattingh	hattingh	PROPN
ejpam-6851	672	7	and	and	CCONJ
ejpam-6851	672	8	r.	r.	PROPN
ejpam-6851	672	9	laskar	laskar	PROPN
ejpam-6851	672	10	.	.	PUNCT
ejpam-6851	673	1	on	on	ADP
ejpam-6851	673	2	weak	weak	ADJ
ejpam-6851	673	3	domination	domination	NOUN
ejpam-6851	673	4	in	in	ADP
ejpam-6851	673	5	graphs	graph	NOUN
ejpam-6851	673	6	.	.	PUNCT
ejpam-6851	674	1	ars	ars	PROPN
ejpam-6851	674	2	combinatoria	combinatoria	PROPN
ejpam-6851	674	3	,	,	PUNCT
ejpam-6851	674	4	49:205–216	49:205–216	NUM
ejpam-6851	674	5	,	,	PUNCT
ejpam-6851	674	6	1998	1998	NUM
ejpam-6851	674	7	.	.	PUNCT
ejpam-6851	675	1	[	[	X
ejpam-6851	675	2	13	13	NUM
ejpam-6851	675	3	]	]	PUNCT
ejpam-6851	675	4	d.	d.	PROPN
ejpam-6851	675	5	rautenbach	rautenbach	PROPN
ejpam-6851	675	6	.	.	PUNCT
ejpam-6851	676	1	bounds	bound	VERB
ejpam-6851	676	2	on	on	ADP
ejpam-6851	676	3	the	the	DET
ejpam-6851	676	4	strong	strong	ADJ
ejpam-6851	676	5	domination	domination	NOUN
ejpam-6851	676	6	number	number	NOUN
ejpam-6851	676	7	.	.	PUNCT
ejpam-6851	677	1	discrete	discrete	ADJ
ejpam-6851	677	2	mathematics	mathematic	NOUN
ejpam-6851	677	3	,	,	PUNCT
ejpam-6851	677	4	215:201–212	215:201–212	NUM
ejpam-6851	677	5	,	,	PUNCT
ejpam-6851	677	6	2000	2000	NUM
ejpam-6851	677	7	.	.	PUNCT
ejpam-6851	678	1	[	[	X
ejpam-6851	678	2	14	14	NUM
ejpam-6851	678	3	]	]	X
ejpam-6851	678	4	d.	d.	PROPN
ejpam-6851	678	5	rautenbach	rautenbach	PROPN
ejpam-6851	678	6	.	.	PUNCT
ejpam-6851	679	1	bounds	bound	VERB
ejpam-6851	679	2	on	on	ADP
ejpam-6851	679	3	the	the	DET
ejpam-6851	679	4	weak	weak	ADJ
ejpam-6851	679	5	domination	domination	NOUN
ejpam-6851	679	6	number	number	NOUN
ejpam-6851	679	7	.	.	PUNCT
ejpam-6851	680	1	australian	australian	ADJ
ejpam-6851	680	2	journal	journal	NOUN
ejpam-6851	680	3	of	of	ADP
ejpam-6851	680	4	combinatorics	combinatorics	PROPN
ejpam-6851	680	5	,	,	PUNCT
ejpam-6851	680	6	18:245–251	18:245–251	PROPN
ejpam-6851	680	7	,	,	PUNCT
ejpam-6851	680	8	1998	1998	NUM
ejpam-6851	680	9	.	.	PUNCT
ejpam-6851	681	1	[	[	X
ejpam-6851	681	2	15	15	X
ejpam-6851	681	3	]	]	X
ejpam-6851	681	4	v.	v.	CCONJ
ejpam-6851	681	5	swaminathan	swaminathan	ADV
ejpam-6851	681	6	and	and	CCONJ
ejpam-6851	681	7	p.	p.	PROPN
ejpam-6851	681	8	thangaraju	thangaraju	PROPN
ejpam-6851	681	9	.	.	PUNCT
ejpam-6851	682	1	strong	strong	ADJ
ejpam-6851	682	2	and	and	CCONJ
ejpam-6851	682	3	weak	weak	ADJ
ejpam-6851	682	4	domination	domination	NOUN
ejpam-6851	682	5	in	in	ADP
ejpam-6851	682	6	graphs	graph	NOUN
ejpam-6851	682	7	.	.	PUNCT
ejpam-6851	683	1	electronic	electronic	ADJ
ejpam-6851	683	2	notes	note	NOUN
ejpam-6851	683	3	in	in	ADP
ejpam-6851	683	4	discrete	discrete	ADJ
ejpam-6851	683	5	mathematics	mathematic	NOUN
ejpam-6851	683	6	,	,	PUNCT
ejpam-6851	683	7	15:213–215	15:213–215	NUM
ejpam-6851	683	8	,	,	PUNCT
ejpam-6851	683	9	may	may	PROPN
ejpam-6851	683	10	2003	2003	NUM
ejpam-6851	683	11	.	.	PUNCT
ejpam-6851	684	1	[	[	X
ejpam-6851	684	2	16	16	NUM
ejpam-6851	684	3	]	]	X
ejpam-6851	684	4	h.	h.	PROPN
ejpam-6851	684	5	zaherifar	zaherifar	PROPN
ejpam-6851	684	6	,	,	PUNCT
ejpam-6851	684	7	s.	s.	PROPN
ejpam-6851	684	8	alikhani	alikhani	PROPN
ejpam-6851	684	9	,	,	PUNCT
ejpam-6851	684	10	and	and	CCONJ
ejpam-6851	684	11	n.	n.	PROPN
ejpam-6851	684	12	ghanbari	ghanbari	NOUN
ejpam-6851	684	13	.	.	PUNCT
ejpam-6851	685	1	on	on	ADP
ejpam-6851	685	2	the	the	DET
ejpam-6851	685	3	strong	strong	ADJ
ejpam-6851	685	4	dominating	dominating	NOUN
ejpam-6851	685	5	sets	set	NOUN
ejpam-6851	685	6	of	of	ADP
ejpam-6851	685	7	graphs	graph	NOUN
ejpam-6851	685	8	.	.	PUNCT
ejpam-6851	686	1	journal	journal	NOUN
ejpam-6851	686	2	of	of	ADP
ejpam-6851	686	3	algebraic	algebraic	PROPN
ejpam-6851	686	4	systems	system	NOUN
ejpam-6851	686	5	,	,	PUNCT
ejpam-6851	686	6	1:65–76	1:65–76	NUM
ejpam-6851	686	7	,	,	PUNCT
ejpam-6851	686	8	2023	2023	NUM
ejpam-6851	686	9	.	.	PUNCT
ejpam-6851	687	1	[	[	X
ejpam-6851	687	2	17	17	NUM
ejpam-6851	687	3	]	]	PUNCT
ejpam-6851	687	4	j.	j.	PROPN
ejpam-6851	687	5	h.	h.	PROPN
ejpam-6851	687	6	hattingh	hattingh	PROPN
ejpam-6851	687	7	and	and	CCONJ
ejpam-6851	687	8	m.	m.	NOUN
ejpam-6851	687	9	a.	a.	PROPN
ejpam-6851	687	10	henning	henning	PROPN
ejpam-6851	687	11	.	.	PUNCT
ejpam-6851	688	1	on	on	ADP
ejpam-6851	688	2	strong	strong	ADJ
ejpam-6851	688	3	domination	domination	NOUN
ejpam-6851	688	4	in	in	ADP
ejpam-6851	688	5	graphs	graph	NOUN
ejpam-6851	688	6	.	.	PUNCT
ejpam-6851	689	1	journal	journal	NOUN
ejpam-6851	689	2	of	of	ADP
ejpam-6851	689	3	combinatorial	combinatorial	ADJ
ejpam-6851	689	4	mathematics	mathematic	NOUN
ejpam-6851	689	5	and	and	CCONJ
ejpam-6851	689	6	combinatorial	combinatorial	ADJ
ejpam-6851	689	7	computing	computing	NOUN
ejpam-6851	689	8	,	,	PUNCT
ejpam-6851	689	9	26:73–92	26:73–92	NUM
ejpam-6851	689	10	,	,	PUNCT
ejpam-6851	689	11	1998	1998	NUM
ejpam-6851	689	12	.	.	PUNCT
ejpam-6851	690	1	[	[	X
ejpam-6851	690	2	18	18	NUM
ejpam-6851	690	3	]	]	X
ejpam-6851	690	4	r.s	r.s	PROPN
ejpam-6851	690	5	.	.	PROPN
ejpam-6851	690	6	bhat	bhat	PROPN
ejpam-6851	690	7	,	,	PUNCT
ejpam-6851	690	8	s.s	s.s	PROPN
ejpam-6851	690	9	.	.	PROPN
ejpam-6851	690	10	kamath	kamath	PROPN
ejpam-6851	690	11	,	,	PUNCT
ejpam-6851	690	12	and	and	CCONJ
ejpam-6851	690	13	s.r	s.r	PROPN
ejpam-6851	690	14	.	.	PROPN
ejpam-6851	690	15	bhat	bhat	PROPN
ejpam-6851	690	16	.	.	PUNCT
ejpam-6851	691	1	a	a	DET
ejpam-6851	691	2	bound	bind	VERB
ejpam-6851	691	3	on	on	ADP
ejpam-6851	691	4	weak	weak	ADJ
ejpam-6851	691	5	domination	domination	NOUN
ejpam-6851	691	6	number	number	NOUN
ejpam-6851	691	7	using	use	VERB
ejpam-6851	691	8	strong	strong	ADJ
ejpam-6851	691	9	(	(	PUNCT
ejpam-6851	691	10	weak	weak	ADJ
ejpam-6851	691	11	)	)	PUNCT
ejpam-6851	691	12	degree	degree	NOUN
ejpam-6851	691	13	concepts	concept	NOUN
ejpam-6851	691	14	of	of	ADP
ejpam-6851	691	15	graphs	graph	NOUN
ejpam-6851	691	16	.	.	PUNCT
ejpam-6851	692	1	opusc	opusc	PROPN
ejpam-6851	692	2	.	.	PUNCT
ejpam-6851	693	1	math	math	NOUN
ejpam-6851	693	2	.	.	PUNCT
ejpam-6851	693	3	,	,	PUNCT
ejpam-6851	694	1	32:235–238	32:235–238	PROPN
ejpam-6851	694	2	,	,	PUNCT
ejpam-6851	694	3	2012	2012	NUM
ejpam-6851	694	4	.	.	PUNCT
ejpam-6851	695	1	[	[	X
ejpam-6851	695	2	19	19	NUM
ejpam-6851	695	3	]	]	X
ejpam-6851	695	4	a.r	a.r	PROPN
ejpam-6851	695	5	.	.	PROPN
ejpam-6851	695	6	desal	desal	PROPN
ejpam-6851	695	7	and	and	CCONJ
ejpam-6851	695	8	d.b	d.b	PROPN
ejpam-6851	695	9	.	.	PROPN
ejpam-6851	695	10	gangadharappa	gangadharappa	PROPN
ejpam-6851	695	11	.	.	PUNCT
ejpam-6851	696	1	some	some	DET
ejpam-6851	696	2	bounds	bound	NOUN
ejpam-6851	696	3	on	on	ADP
ejpam-6851	696	4	strong	strong	ADJ
ejpam-6851	696	5	domination	domination	NOUN
ejpam-6851	696	6	number	number	NOUN
ejpam-6851	696	7	of	of	ADP
ejpam-6851	696	8	a	a	DET
ejpam-6851	696	9	graph	graph	NOUN
ejpam-6851	696	10	.	.	PUNCT
ejpam-6851	697	1	j.	j.	PROPN
ejpam-6851	697	2	com	com	PROPN
ejpam-6851	697	3	.	.	PUNCT
ejpam-6851	697	4	math	math	PROPN
ejpam-6851	697	5	.	.	PUNCT
ejpam-6851	698	1	sci	sci	PROPN
ejpam-6851	698	2	.	.	PROPN
ejpam-6851	698	3	,	,	PUNCT
ejpam-6851	698	4	2:399–580	2:399–580	PROPN
ejpam-6851	698	5	,	,	PUNCT
ejpam-6851	698	6	2011	2011	NUM
ejpam-6851	698	7	.	.	PUNCT
ejpam-6851	699	1	[	[	X
ejpam-6851	699	2	20	20	NUM
ejpam-6851	699	3	]	]	PUNCT
ejpam-6851	699	4	d.	d.	PROPN
ejpam-6851	699	5	rautenbach	rautenbach	PROPN
ejpam-6851	699	6	.	.	PUNCT
ejpam-6851	700	1	bounds	bound	VERB
ejpam-6851	700	2	on	on	ADP
ejpam-6851	700	3	the	the	DET
ejpam-6851	700	4	weak	weak	ADJ
ejpam-6851	700	5	domination	domination	NOUN
ejpam-6851	700	6	number	number	NOUN
ejpam-6851	700	7	.	.	PUNCT
ejpam-6851	701	1	australasian	australasian	ADJ
ejpam-6851	701	2	journal	journal	NOUN
ejpam-6851	701	3	of	of	ADP
ejpam-6851	701	4	combinatorics	combinatoric	NOUN
ejpam-6851	701	5	,	,	PUNCT
ejpam-6851	701	6	18:245–251	18:245–251	PROPN
ejpam-6851	701	7	,	,	PUNCT
ejpam-6851	701	8	1998	1998	NUM
ejpam-6851	701	9	.	.	PUNCT
ejpam-6851	702	1	[	[	X
ejpam-6851	702	2	21	21	NUM
ejpam-6851	702	3	]	]	X
ejpam-6851	702	4	d.	d.	PROPN
ejpam-6851	702	5	rautenbach	rautenbach	PROPN
ejpam-6851	702	6	.	.	PUNCT
ejpam-6851	703	1	bounds	bound	VERB
ejpam-6851	703	2	on	on	ADP
ejpam-6851	703	3	the	the	DET
ejpam-6851	703	4	strong	strong	ADJ
ejpam-6851	703	5	domination	domination	NOUN
ejpam-6851	703	6	number	number	NOUN
ejpam-6851	703	7	.	.	PUNCT
ejpam-6851	704	1	discrete	discrete	ADJ
ejpam-6851	704	2	mathematics	mathematic	NOUN
ejpam-6851	704	3	,	,	PUNCT
ejpam-6851	704	4	215:201–212	215:201–212	NUM
ejpam-6851	704	5	,	,	PUNCT
ejpam-6851	704	6	2000	2000	NUM
ejpam-6851	704	7	.	.	PUNCT
ejpam-6851	705	1	[	[	X
ejpam-6851	705	2	22	22	NUM
ejpam-6851	705	3	]	]	PUNCT
ejpam-6851	705	4	d.	d.	PROPN
ejpam-6851	705	5	dogan	dogan	PROPN
ejpam-6851	705	6	durgun	durgun	PROPN
ejpam-6851	705	7	and	and	CCONJ
ejpam-6851	705	8	b.	b.	PROPN
ejpam-6851	705	9	lokcu	lokcu	PROPN
ejpam-6851	705	10	.	.	PUNCT
ejpam-6851	706	1	strong	strong	ADJ
ejpam-6851	706	2	domination	domination	NOUN
ejpam-6851	706	3	number	number	NOUN
ejpam-6851	706	4	of	of	ADP
ejpam-6851	706	5	some	some	DET
ejpam-6851	706	6	graphs	graph	NOUN
ejpam-6851	706	7	.	.	PUNCT
ejpam-6851	707	1	celal	celal	PROPN
ejpam-6851	707	2	bayar	bayar	PROPN
ejpam-6851	707	3	univ	univ	PROPN
ejpam-6851	707	4	.	.	PUNCT
ejpam-6851	708	1	j.	j.	PROPN
ejpam-6851	708	2	sci	sci	PROPN
ejpam-6851	708	3	.	.	PROPN
ejpam-6851	708	4	,	,	PUNCT
ejpam-6851	708	5	11:89–91	11:89–91	NUM
ejpam-6851	708	6	,	,	PUNCT
ejpam-6851	708	7	2015	2015	NUM
ejpam-6851	708	8	.	.	PUNCT
ejpam-6851	709	1	[	[	X
ejpam-6851	709	2	23	23	NUM
ejpam-6851	709	3	]	]	PUNCT
ejpam-6851	709	4	d.	d.	PROPN
ejpam-6851	709	5	dogan	dogan	PROPN
ejpam-6851	709	6	durgun	durgun	PROPN
ejpam-6851	709	7	and	and	CCONJ
ejpam-6851	709	8	b.	b.	PROPN
ejpam-6851	709	9	lokcu	lokcu	PROPN
ejpam-6851	709	10	.	.	PUNCT
ejpam-6851	710	1	weak	weak	ADJ
ejpam-6851	710	2	and	and	CCONJ
ejpam-6851	710	3	strong	strong	ADJ
ejpam-6851	710	4	domination	domination	NOUN
ejpam-6851	710	5	in	in	ADP
ejpam-6851	710	6	thorn	thorn	NOUN
ejpam-6851	710	7	graphs	graph	NOUN
ejpam-6851	710	8	.	.	PUNCT
ejpam-6851	711	1	asian	asian	ADJ
ejpam-6851	711	2	-	-	PUNCT
ejpam-6851	711	3	european	european	ADJ
ejpam-6851	711	4	journal	journal	NOUN
ejpam-6851	711	5	of	of	ADP
ejpam-6851	711	6	mathematics	mathematic	NOUN
ejpam-6851	711	7	,	,	PUNCT
ejpam-6851	711	8	13:2050071	13:2050071	NUM
ejpam-6851	711	9	,	,	PUNCT
ejpam-6851	711	10	2020	2020	NUM
ejpam-6851	711	11	.	.	PUNCT
ejpam-6851	712	1	[	[	X
ejpam-6851	712	2	24	24	NUM
ejpam-6851	712	3	]	]	X
ejpam-6851	712	4	a.n	a.n	PROPN
ejpam-6851	712	5	.	.	PROPN
ejpam-6851	712	6	gani	gani	PROPN
ejpam-6851	712	7	and	and	CCONJ
ejpam-6851	712	8	m.b	m.b	PROPN
ejpam-6851	712	9	.	.	PROPN
ejpam-6851	712	10	ahamed	ahamed	PROPN
ejpam-6851	712	11	.	.	PUNCT
ejpam-6851	713	1	strong	strong	ADJ
ejpam-6851	713	2	and	and	CCONJ
ejpam-6851	713	3	weak	weak	ADJ
ejpam-6851	713	4	domination	domination	NOUN
ejpam-6851	713	5	in	in	ADP
ejpam-6851	713	6	fuzzy	fuzzy	ADJ
ejpam-6851	713	7	graphs	graph	NOUN
ejpam-6851	713	8	.	.	PUNCT
ejpam-6851	714	1	east	east	ADJ
ejpam-6851	714	2	asian	asian	PROPN
ejpam-6851	714	3	mathematical	mathematical	ADJ
ejpam-6851	714	4	journal	journal	NOUN
ejpam-6851	714	5	,	,	PUNCT
ejpam-6851	714	6	23:1–8	23:1–8	NUM
ejpam-6851	714	7	,	,	PUNCT
ejpam-6851	714	8	2007	2007	NUM
ejpam-6851	714	9	.	.	PUNCT
ejpam-6851	715	1	[	[	X
ejpam-6851	715	2	25	25	NUM
ejpam-6851	715	3	]	]	X
ejpam-6851	715	4	s.k	s.k	PROPN
ejpam-6851	715	5	.	.	PROPN
ejpam-6851	715	6	vaidya	vaidya	PROPN
ejpam-6851	715	7	and	and	CCONJ
ejpam-6851	715	8	s.h	s.h	PROPN
ejpam-6851	715	9	.	.	PROPN
ejpam-6851	715	10	karkar	karkar	PROPN
ejpam-6851	715	11	.	.	PUNCT
ejpam-6851	716	1	on	on	ADP
ejpam-6851	716	2	strong	strong	ADJ
ejpam-6851	716	3	domination	domination	NOUN
ejpam-6851	716	4	number	number	NOUN
ejpam-6851	716	5	of	of	ADP
ejpam-6851	716	6	corona	corona	NOUN
ejpam-6851	716	7	related	relate	VERB
ejpam-6851	716	8	graphs	graph	NOUN
ejpam-6851	716	9	.	.	PUNCT
ejpam-6851	717	1	malaya	malaya	PROPN
ejpam-6851	717	2	journal	journal	PROPN
ejpam-6851	717	3	of	of	ADP
ejpam-6851	717	4	matematik	matematik	PROPN
ejpam-6851	717	5	,	,	PUNCT
ejpam-6851	717	6	5(4):636–640	5(4):636–640	NUM
ejpam-6851	717	7	,	,	PUNCT
ejpam-6851	717	8	2017	2017	NUM
ejpam-6851	717	9	.	.	PUNCT
ejpam-6851	718	1	[	[	X
ejpam-6851	718	2	26	26	NUM
ejpam-6851	718	3	]	]	X
ejpam-6851	718	4	e.	e.	PROPN
ejpam-6851	718	5	sampathkumar	sampathkumar	PROPN
ejpam-6851	718	6	and	and	CCONJ
ejpam-6851	718	7	l.	l.	PROPN
ejpam-6851	718	8	pushpa	pushpa	PROPN
ejpam-6851	718	9	latha	latha	PROPN
ejpam-6851	718	10	.	.	PUNCT
ejpam-6851	719	1	strong	strong	ADJ
ejpam-6851	719	2	,	,	PUNCT
ejpam-6851	719	3	weak	weak	ADJ
ejpam-6851	719	4	domination	domination	NOUN
ejpam-6851	719	5	and	and	CCONJ
ejpam-6851	719	6	domination	domination	NOUN
ejpam-6851	719	7	balance	balance	NOUN
ejpam-6851	719	8	in	in	ADP
ejpam-6851	719	9	graphs	graph	NOUN
ejpam-6851	719	10	.	.	PUNCT
ejpam-6851	720	1	discrete	discrete	ADJ
ejpam-6851	720	2	mathematics	mathematic	NOUN
ejpam-6851	720	3	,	,	PUNCT
ejpam-6851	720	4	161:235–242	161:235–242	NUM
ejpam-6851	720	5	,	,	PUNCT
ejpam-6851	720	6	1996	1996	NUM
ejpam-6851	720	7	.	.	PUNCT
ejpam-6851	721	1	j.	j.	PROPN
ejpam-6851	721	2	m.	m.	PROPN
ejpam-6851	721	3	molles	molles	PROPN
ejpam-6851	721	4	,	,	PUNCT
ejpam-6851	721	5	f.	f.	PROPN
ejpam-6851	721	6	p.	p.	PROPN
ejpam-6851	721	7	jamil	jamil	PROPN
ejpam-6851	721	8	,	,	PUNCT
ejpam-6851	721	9	s.	s.	PROPN
ejpam-6851	721	10	r.	r.	PROPN
ejpam-6851	721	11	canoy	canoy	PROPN
ejpam-6851	721	12	/	/	SYM
ejpam-6851	721	13	eur	eur	PROPN
ejpam-6851	721	14	.	.	PUNCT
ejpam-6851	722	1	j.	j.	PROPN
ejpam-6851	722	2	pure	pure	PROPN
ejpam-6851	722	3	appl	appl	PROPN
ejpam-6851	722	4	.	.	PROPN
ejpam-6851	722	5	math	math	PROPN
ejpam-6851	722	6	,	,	PUNCT
ejpam-6851	722	7	18	18	NUM
ejpam-6851	722	8	(	(	PUNCT
ejpam-6851	722	9	4	4	NUM
ejpam-6851	722	10	)	)	PUNCT
ejpam-6851	722	11	(	(	PUNCT
ejpam-6851	722	12	2025	2025	NUM
ejpam-6851	722	13	)	)	PUNCT
ejpam-6851	722	14	,	,	PUNCT
ejpam-6851	722	15	6851	6851	NUM
ejpam-6851	722	16	18	18	NUM
ejpam-6851	722	17	of	of	ADP
ejpam-6851	722	18	18	18	NUM
ejpam-6851	722	19	[	[	SYM
ejpam-6851	722	20	27	27	NUM
ejpam-6851	722	21	]	]	X
ejpam-6851	722	22	r.	r.	PROPN
ejpam-6851	722	23	boutrig	boutrig	PROPN
ejpam-6851	722	24	and	and	CCONJ
ejpam-6851	722	25	m.	m.	NOUN
ejpam-6851	722	26	chellali	chellali	PROPN
ejpam-6851	722	27	.	.	PUNCT
ejpam-6851	723	1	a	a	DET
ejpam-6851	723	2	note	note	NOUN
ejpam-6851	723	3	on	on	ADP
ejpam-6851	723	4	a	a	DET
ejpam-6851	723	5	relation	relation	NOUN
ejpam-6851	723	6	between	between	ADP
ejpam-6851	723	7	the	the	DET
ejpam-6851	723	8	weak	weak	ADJ
ejpam-6851	723	9	and	and	CCONJ
ejpam-6851	723	10	strong	strong	ADJ
ejpam-6851	723	11	domination	domination	NOUN
ejpam-6851	723	12	numbers	number	NOUN
ejpam-6851	723	13	of	of	ADP
ejpam-6851	723	14	a	a	DET
ejpam-6851	723	15	graph	graph	NOUN
ejpam-6851	723	16	.	.	PUNCT
ejpam-6851	724	1	opuscula	opuscula	PROPN
ejpam-6851	724	2	mathematica	mathematica	PROPN
ejpam-6851	724	3	,	,	PUNCT
ejpam-6851	724	4	32(2):235–238	32(2):235–238	PROPN
ejpam-6851	724	5	,	,	PUNCT
ejpam-6851	724	6	2012	2012	NUM
ejpam-6851	724	7	.	.	PUNCT