id	sid	tid	token	lemma	pos
ejpam-5602	1	1	european	european	PROPN
ejpam-5602	1	2	journal	journal	PROPN
ejpam-5602	1	3	of	of	ADP
ejpam-5602	1	4	pure	pure	ADJ
ejpam-5602	1	5	and	and	CCONJ
ejpam-5602	1	6	applied	applied	ADJ
ejpam-5602	1	7	mathematics	mathematic	NOUN
ejpam-5602	1	8	2025	2025	NUM
ejpam-5602	1	9	,	,	PUNCT
ejpam-5602	1	10	vol	vol	NOUN
ejpam-5602	1	11	.	.	PROPN
ejpam-5602	1	12	18	18	NUM
ejpam-5602	1	13	,	,	PUNCT
ejpam-5602	1	14	issue	issue	NOUN
ejpam-5602	1	15	1	1	NUM
ejpam-5602	1	16	,	,	PUNCT
ejpam-5602	1	17	article	article	NOUN
ejpam-5602	1	18	number	number	NOUN
ejpam-5602	1	19	5602	5602	NUM
ejpam-5602	1	20	issn	issn	VERB
ejpam-5602	1	21	1307	1307	NUM
ejpam-5602	1	22	-	-	SYM
ejpam-5602	1	23	5543	5543	NUM
ejpam-5602	1	24	–	–	PUNCT
ejpam-5602	1	25	ejpam.com	ejpam.com	X
ejpam-5602	1	26	published	publish	VERB
ejpam-5602	1	27	by	by	ADP
ejpam-5602	1	28	new	new	PROPN
ejpam-5602	1	29	york	york	PROPN
ejpam-5602	1	30	business	business	PROPN
ejpam-5602	1	31	global	global	PROPN
ejpam-5602	1	32	on	on	ADP
ejpam-5602	1	33	total	total	ADJ
ejpam-5602	1	34	double	double	ADJ
ejpam-5602	1	35	italian	italian	ADJ
ejpam-5602	1	36	domination	domination	NOUN
ejpam-5602	1	37	in	in	ADP
ejpam-5602	1	38	graphs	graphs	PROPN
ejpam-5602	1	39	sheryl	sheryl	PROPN
ejpam-5602	1	40	jane	jane	PROPN
ejpam-5602	1	41	l.	l.	PROPN
ejpam-5602	1	42	sumbalan1,2,∗	sumbalan1,2,∗	PROPN
ejpam-5602	1	43	,	,	PUNCT
ejpam-5602	2	1	sheila	sheila	PROPN
ejpam-5602	2	2	m.	m.	PROPN
ejpam-5602	2	3	menchavez1,2	menchavez1,2	PROPN
ejpam-5602	2	4	,	,	PUNCT
ejpam-5602	2	5	ferdinand	ferdinand	PROPN
ejpam-5602	3	1	p.	p.	PROPN
ejpam-5602	4	1	jamil1,2	jamil1,2	PROPN
ejpam-5602	4	2	1	1	NUM
ejpam-5602	4	3	department	department	NOUN
ejpam-5602	4	4	of	of	ADP
ejpam-5602	4	5	mathematics	mathematic	NOUN
ejpam-5602	4	6	and	and	CCONJ
ejpam-5602	4	7	statistics	statistic	NOUN
ejpam-5602	4	8	,	,	PUNCT
ejpam-5602	4	9	college	college	NOUN
ejpam-5602	4	10	of	of	ADP
ejpam-5602	4	11	science	science	NOUN
ejpam-5602	4	12	and	and	CCONJ
ejpam-5602	4	13	mathematics	mathematic	NOUN
ejpam-5602	4	14	,	,	PUNCT
ejpam-5602	4	15	mindanao	mindanao	PROPN
ejpam-5602	4	16	state	state	PROPN
ejpam-5602	4	17	university	university	PROPN
ejpam-5602	4	18	-	-	PUNCT
ejpam-5602	4	19	iligan	iligan	PROPN
ejpam-5602	4	20	institute	institute	PROPN
ejpam-5602	4	21	of	of	ADP
ejpam-5602	4	22	technology	technology	PROPN
ejpam-5602	4	23	,	,	PUNCT
ejpam-5602	4	24	9200	9200	NUM
ejpam-5602	4	25	iligan	iligan	ADJ
ejpam-5602	4	26	city	city	NOUN
ejpam-5602	4	27	,	,	PUNCT
ejpam-5602	4	28	philippines	philippine	NOUN
ejpam-5602	4	29	2	2	NUM
ejpam-5602	4	30	center	center	NOUN
ejpam-5602	4	31	for	for	ADP
ejpam-5602	4	32	mathematical	mathematical	ADJ
ejpam-5602	4	33	and	and	CCONJ
ejpam-5602	4	34	theoretical	theoretical	ADJ
ejpam-5602	4	35	physical	physical	ADJ
ejpam-5602	4	36	sciences	science	NOUN
ejpam-5602	4	37	(	(	PUNCT
ejpam-5602	4	38	cmtps	cmtps	PROPN
ejpam-5602	4	39	)	)	PUNCT
ejpam-5602	4	40	,	,	PUNCT
ejpam-5602	4	41	premier	premier	PROPN
ejpam-5602	4	42	research	research	PROPN
ejpam-5602	4	43	institute	institute	PROPN
ejpam-5602	4	44	of	of	ADP
ejpam-5602	4	45	science	science	NOUN
ejpam-5602	4	46	and	and	CCONJ
ejpam-5602	4	47	mathematics	mathematics	PROPN
ejpam-5602	4	48	(	(	PUNCT
ejpam-5602	4	49	prism	prism	NOUN
ejpam-5602	4	50	)	)	PUNCT
ejpam-5602	4	51	,	,	PUNCT
ejpam-5602	4	52	mindanao	mindanao	PROPN
ejpam-5602	4	53	state	state	PROPN
ejpam-5602	4	54	university	university	PROPN
ejpam-5602	4	55	iligan	iligan	PROPN
ejpam-5602	4	56	institute	institute	PROPN
ejpam-5602	4	57	of	of	ADP
ejpam-5602	4	58	technology	technology	PROPN
ejpam-5602	4	59	,	,	PUNCT
ejpam-5602	4	60	9200	9200	NUM
ejpam-5602	4	61	iligan	iligan	ADJ
ejpam-5602	4	62	city	city	NOUN
ejpam-5602	4	63	,	,	PUNCT
ejpam-5602	4	64	philippines	philippine	NOUN
ejpam-5602	4	65	abstract	abstract	ADJ
ejpam-5602	4	66	.	.	PUNCT
ejpam-5602	5	1	for	for	ADP
ejpam-5602	5	2	a	a	DET
ejpam-5602	5	3	simple	simple	ADJ
ejpam-5602	5	4	graph	graph	NOUN
ejpam-5602	5	5	g	g	PROPN
ejpam-5602	5	6	=	=	PUNCT
ejpam-5602	5	7	(	(	PUNCT
ejpam-5602	5	8	v	v	NOUN
ejpam-5602	5	9	(	(	PUNCT
ejpam-5602	5	10	g	g	NOUN
ejpam-5602	5	11	)	)	PUNCT
ejpam-5602	5	12	,	,	PUNCT
ejpam-5602	5	13	e	e	X
ejpam-5602	5	14	(	(	PUNCT
ejpam-5602	5	15	g	g	NOUN
ejpam-5602	5	16	)	)	PUNCT
ejpam-5602	5	17	)	)	PUNCT
ejpam-5602	5	18	,	,	PUNCT
ejpam-5602	5	19	a	a	DET
ejpam-5602	5	20	total	total	ADJ
ejpam-5602	5	21	double	double	ADJ
ejpam-5602	5	22	italian	italian	ADJ
ejpam-5602	5	23	dominating	dominating	NOUN
ejpam-5602	5	24	function	function	NOUN
ejpam-5602	5	25	is	be	AUX
ejpam-5602	5	26	a	a	DET
ejpam-5602	5	27	function	function	NOUN
ejpam-5602	5	28	f	f	NOUN
ejpam-5602	5	29	:	:	PUNCT
ejpam-5602	5	30	v	v	X
ejpam-5602	5	31	(	(	PUNCT
ejpam-5602	5	32	g	g	NOUN
ejpam-5602	5	33	)	)	PUNCT
ejpam-5602	5	34	→	→	SYM
ejpam-5602	5	35	{	{	PUNCT
ejpam-5602	5	36	0	0	NUM
ejpam-5602	5	37	,	,	PUNCT
ejpam-5602	5	38	1	1	NUM
ejpam-5602	5	39	,	,	PUNCT
ejpam-5602	5	40	2	2	NUM
ejpam-5602	5	41	,	,	PUNCT
ejpam-5602	5	42	3	3	NUM
ejpam-5602	5	43	}	}	PUNCT
ejpam-5602	5	44	with	with	ADP
ejpam-5602	5	45	properties	property	NOUN
ejpam-5602	5	46	that	that	PRON
ejpam-5602	5	47	every	every	DET
ejpam-5602	5	48	vertex	vertex	NOUN
ejpam-5602	5	49	v	v	ADP
ejpam-5602	5	50	∈	∈	PROPN
ejpam-5602	5	51	v	v	NOUN
ejpam-5602	5	52	(	(	PUNCT
ejpam-5602	5	53	g	g	NOUN
ejpam-5602	5	54	)	)	PUNCT
ejpam-5602	5	55	with	with	ADP
ejpam-5602	5	56	f	f	PROPN
ejpam-5602	5	57	(	(	PUNCT
ejpam-5602	5	58	v	v	NOUN
ejpam-5602	5	59	)	)	PUNCT
ejpam-5602	5	60	∈	∈	NOUN
ejpam-5602	5	61	{	{	PUNCT
ejpam-5602	5	62	0	0	NUM
ejpam-5602	5	63	,	,	PUNCT
ejpam-5602	5	64	1},∑	1},∑	PROPN
ejpam-5602	5	65	u∈n	u∈n	NOUN
ejpam-5602	6	1	[	[	X
ejpam-5602	6	2	v	v	X
ejpam-5602	6	3	]	]	X
ejpam-5602	6	4	f	f	X
ejpam-5602	6	5	(	(	PUNCT
ejpam-5602	6	6	u	u	NOUN
ejpam-5602	6	7	)	)	PUNCT
ejpam-5602	6	8	≥	≥	NOUN
ejpam-5602	6	9	3	3	NUM
ejpam-5602	6	10	and	and	CCONJ
ejpam-5602	6	11	every	every	DET
ejpam-5602	6	12	vertex	vertex	NOUN
ejpam-5602	6	13	v	v	ADP
ejpam-5602	6	14	∈	∈	PROPN
ejpam-5602	6	15	v	v	NOUN
ejpam-5602	6	16	(	(	PUNCT
ejpam-5602	6	17	g	g	NOUN
ejpam-5602	6	18	)	)	PUNCT
ejpam-5602	6	19	with	with	ADP
ejpam-5602	6	20	f(v	f(v	NOUN
ejpam-5602	6	21	)	)	PUNCT
ejpam-5602	6	22	̸=	̸=	PROPN
ejpam-5602	6	23	0	0	NUM
ejpam-5602	6	24	has	have	VERB
ejpam-5602	6	25	a	a	DET
ejpam-5602	6	26	neighbor	neighbor	NOUN
ejpam-5602	6	27	u	u	NOUN
ejpam-5602	6	28	with	with	ADP
ejpam-5602	6	29	f(u	f(u	PROPN
ejpam-5602	6	30	)	)	PUNCT
ejpam-5602	6	31	̸=	̸=	PROPN
ejpam-5602	6	32	0	0	NUM
ejpam-5602	6	33	.	.	PUNCT
ejpam-5602	7	1	the	the	DET
ejpam-5602	7	2	weight	weight	NOUN
ejpam-5602	7	3	of	of	ADP
ejpam-5602	7	4	a	a	DET
ejpam-5602	7	5	total	total	ADJ
ejpam-5602	7	6	double	double	ADJ
ejpam-5602	7	7	italian	italian	ADJ
ejpam-5602	7	8	dominating	dominating	NOUN
ejpam-5602	7	9	function	function	NOUN
ejpam-5602	7	10	is	be	AUX
ejpam-5602	7	11	the	the	DET
ejpam-5602	7	12	sum	sum	NOUN
ejpam-5602	7	13	ωg	ωg	PROPN
ejpam-5602	7	14	(	(	PUNCT
ejpam-5602	7	15	f	f	X
ejpam-5602	7	16	)	)	PUNCT
ejpam-5602	7	17	=	=	SYM
ejpam-5602	7	18	∑	∑	PUNCT
ejpam-5602	7	19	v∈v	v∈v	NOUN
ejpam-5602	7	20	(	(	PUNCT
ejpam-5602	7	21	g	g	NOUN
ejpam-5602	7	22	)	)	PUNCT
ejpam-5602	7	23	f	f	NOUN
ejpam-5602	7	24	(	(	PUNCT
ejpam-5602	7	25	v	v	NOUN
ejpam-5602	7	26	)	)	PUNCT
ejpam-5602	7	27	≥	≥	NOUN
ejpam-5602	7	28	3	3	NUM
ejpam-5602	7	29	and	and	CCONJ
ejpam-5602	7	30	the	the	DET
ejpam-5602	7	31	minimum	minimum	ADJ
ejpam-5602	7	32	weight	weight	NOUN
ejpam-5602	7	33	of	of	ADP
ejpam-5602	7	34	all	all	DET
ejpam-5602	7	35	the	the	DET
ejpam-5602	7	36	total	total	ADJ
ejpam-5602	7	37	double	double	ADJ
ejpam-5602	7	38	italian	italian	ADJ
ejpam-5602	7	39	dominating	dominating	NOUN
ejpam-5602	7	40	functions	function	NOUN
ejpam-5602	7	41	on	on	ADP
ejpam-5602	7	42	a	a	DET
ejpam-5602	7	43	graph	graph	NOUN
ejpam-5602	7	44	g	g	NOUN
ejpam-5602	7	45	is	be	AUX
ejpam-5602	7	46	the	the	DET
ejpam-5602	7	47	total	total	ADJ
ejpam-5602	7	48	double	double	ADJ
ejpam-5602	7	49	italian	italian	ADJ
ejpam-5602	7	50	domination	domination	NOUN
ejpam-5602	7	51	number	number	NOUN
ejpam-5602	7	52	,	,	PUNCT
ejpam-5602	7	53	denoted	denote	VERB
ejpam-5602	7	54	by	by	ADP
ejpam-5602	7	55	γtdi	γtdi	PROPN
ejpam-5602	7	56	(	(	PUNCT
ejpam-5602	7	57	g	g	NOUN
ejpam-5602	7	58	)	)	PUNCT
ejpam-5602	7	59	.	.	PUNCT
ejpam-5602	8	1	in	in	ADP
ejpam-5602	8	2	this	this	DET
ejpam-5602	8	3	paper	paper	NOUN
ejpam-5602	8	4	we	we	PRON
ejpam-5602	8	5	explore	explore	VERB
ejpam-5602	8	6	further	far	ADV
ejpam-5602	8	7	the	the	DET
ejpam-5602	8	8	concept	concept	NOUN
ejpam-5602	8	9	of	of	ADP
ejpam-5602	8	10	total	total	ADJ
ejpam-5602	8	11	double	double	ADJ
ejpam-5602	8	12	italian	italian	ADJ
ejpam-5602	8	13	domination	domination	NOUN
ejpam-5602	8	14	.	.	PUNCT
ejpam-5602	9	1	we	we	PRON
ejpam-5602	9	2	characterize	characterize	VERB
ejpam-5602	9	3	graphs	graph	NOUN
ejpam-5602	9	4	g	g	NOUN
ejpam-5602	9	5	with	with	ADP
ejpam-5602	9	6	smaller	small	ADJ
ejpam-5602	9	7	values	value	NOUN
ejpam-5602	9	8	for	for	ADP
ejpam-5602	9	9	γtdi(g	γtdi(g	NOUN
ejpam-5602	9	10	)	)	PUNCT
ejpam-5602	9	11	.	.	PUNCT
ejpam-5602	10	1	also	also	ADV
ejpam-5602	10	2	,	,	PUNCT
ejpam-5602	10	3	we	we	PRON
ejpam-5602	10	4	characterize	characterize	VERB
ejpam-5602	10	5	the	the	DET
ejpam-5602	10	6	total	total	ADJ
ejpam-5602	10	7	double	double	ADJ
ejpam-5602	10	8	italian	italian	ADJ
ejpam-5602	10	9	dominating	dominating	NOUN
ejpam-5602	10	10	function	function	NOUN
ejpam-5602	10	11	on	on	ADP
ejpam-5602	10	12	the	the	DET
ejpam-5602	10	13	join	join	NOUN
ejpam-5602	10	14	,	,	PUNCT
ejpam-5602	10	15	corona	corona	PROPN
ejpam-5602	10	16	,	,	PUNCT
ejpam-5602	10	17	edge	edge	NOUN
ejpam-5602	10	18	corona	corona	NOUN
ejpam-5602	10	19	,	,	PUNCT
ejpam-5602	10	20	and	and	CCONJ
ejpam-5602	10	21	complementary	complementary	ADJ
ejpam-5602	10	22	prism	prism	NOUN
ejpam-5602	10	23	of	of	ADP
ejpam-5602	10	24	graphs	graph	NOUN
ejpam-5602	10	25	.	.	PUNCT
ejpam-5602	11	1	exact	exact	ADJ
ejpam-5602	11	2	values	value	NOUN
ejpam-5602	11	3	or	or	CCONJ
ejpam-5602	11	4	bounds	bound	NOUN
ejpam-5602	11	5	are	be	AUX
ejpam-5602	11	6	also	also	ADV
ejpam-5602	11	7	determined	determined	ADJ
ejpam-5602	11	8	for	for	ADP
ejpam-5602	11	9	their	their	PRON
ejpam-5602	11	10	respective	respective	ADJ
ejpam-5602	11	11	total	total	ADJ
ejpam-5602	11	12	double	double	ADJ
ejpam-5602	11	13	italian	italian	ADJ
ejpam-5602	11	14	domination	domination	NOUN
ejpam-5602	11	15	number	number	NOUN
ejpam-5602	11	16	.	.	PUNCT
ejpam-5602	12	1	2020	2020	NUM
ejpam-5602	12	2	mathematics	mathematic	NOUN
ejpam-5602	12	3	subject	subject	NOUN
ejpam-5602	12	4	classifications	classification	NOUN
ejpam-5602	12	5	:	:	PUNCT
ejpam-5602	12	6	05c69	05c69	X
ejpam-5602	12	7	key	key	ADJ
ejpam-5602	12	8	words	word	NOUN
ejpam-5602	12	9	and	and	CCONJ
ejpam-5602	12	10	phrases	phrase	NOUN
ejpam-5602	12	11	:	:	PUNCT
ejpam-5602	12	12	total	total	ADJ
ejpam-5602	12	13	double	double	ADJ
ejpam-5602	12	14	italian	italian	ADJ
ejpam-5602	12	15	dominating	dominating	NOUN
ejpam-5602	12	16	function	function	NOUN
ejpam-5602	12	17	,	,	PUNCT
ejpam-5602	12	18	total	total	ADJ
ejpam-5602	12	19	double	double	ADJ
ejpam-5602	12	20	italian	italian	ADJ
ejpam-5602	12	21	domination	domination	NOUN
ejpam-5602	12	22	number	number	NOUN
ejpam-5602	12	23	.	.	PUNCT
ejpam-5602	13	1	1	1	X
ejpam-5602	13	2	.	.	X
ejpam-5602	13	3	introduction	introduction	NOUN
ejpam-5602	13	4	since	since	SCONJ
ejpam-5602	13	5	its	its	PRON
ejpam-5602	13	6	introduction	introduction	NOUN
ejpam-5602	13	7	in	in	ADP
ejpam-5602	13	8	2004	2004	NUM
ejpam-5602	13	9	by	by	ADP
ejpam-5602	13	10	cockayne	cockayne	PROPN
ejpam-5602	13	11	et	et	PROPN
ejpam-5602	13	12	al	al	PROPN
ejpam-5602	13	13	.	.	PUNCT
ejpam-5602	14	1	[	[	X
ejpam-5602	14	2	12	12	NUM
ejpam-5602	14	3	]	]	PUNCT
ejpam-5602	14	4	,	,	PUNCT
ejpam-5602	14	5	roman	roman	ADJ
ejpam-5602	14	6	domination	domination	NOUN
ejpam-5602	14	7	is	be	AUX
ejpam-5602	14	8	one	one	NUM
ejpam-5602	14	9	of	of	ADP
ejpam-5602	14	10	the	the	DET
ejpam-5602	14	11	most	most	ADV
ejpam-5602	14	12	well	well	ADV
ejpam-5602	14	13	-	-	PUNCT
ejpam-5602	14	14	studied	study	VERB
ejpam-5602	14	15	concepts	concept	NOUN
ejpam-5602	14	16	in	in	ADP
ejpam-5602	14	17	graph	graph	NOUN
ejpam-5602	14	18	theory	theory	NOUN
ejpam-5602	14	19	.	.	PUNCT
ejpam-5602	15	1	for	for	ADP
ejpam-5602	15	2	a	a	DET
ejpam-5602	15	3	comprehensive	comprehensive	ADJ
ejpam-5602	15	4	understanding	understanding	NOUN
ejpam-5602	15	5	of	of	ADP
ejpam-5602	15	6	its	its	PRON
ejpam-5602	15	7	origins	origin	NOUN
ejpam-5602	15	8	,	,	PUNCT
ejpam-5602	15	9	historical	historical	ADJ
ejpam-5602	15	10	development	development	NOUN
ejpam-5602	15	11	,	,	PUNCT
ejpam-5602	15	12	and	and	CCONJ
ejpam-5602	15	13	significance	significance	NOUN
ejpam-5602	15	14	in	in	ADP
ejpam-5602	15	15	the	the	DET
ejpam-5602	15	16	field	field	NOUN
ejpam-5602	15	17	along	along	ADP
ejpam-5602	15	18	with	with	ADP
ejpam-5602	15	19	recent	recent	ADJ
ejpam-5602	15	20	advances	advance	NOUN
ejpam-5602	15	21	,	,	PUNCT
ejpam-5602	15	22	we	we	PRON
ejpam-5602	15	23	refer	refer	VERB
ejpam-5602	15	24	to	to	ADP
ejpam-5602	15	25	[	[	X
ejpam-5602	15	26	1	1	NUM
ejpam-5602	15	27	,	,	PUNCT
ejpam-5602	15	28	2	2	NUM
ejpam-5602	15	29	,	,	PUNCT
ejpam-5602	15	30	10	10	NUM
ejpam-5602	15	31	,	,	PUNCT
ejpam-5602	15	32	13	13	NUM
ejpam-5602	15	33	,	,	PUNCT
ejpam-5602	15	34	16–19	16–19	NUM
ejpam-5602	15	35	,	,	PUNCT
ejpam-5602	15	36	21	21	NUM
ejpam-5602	15	37	,	,	PUNCT
ejpam-5602	15	38	22	22	NUM
ejpam-5602	15	39	,	,	PUNCT
ejpam-5602	15	40	24	24	NUM
ejpam-5602	15	41	,	,	PUNCT
ejpam-5602	15	42	25	25	NUM
ejpam-5602	15	43	]	]	PUNCT
ejpam-5602	15	44	.	.	PUNCT
ejpam-5602	16	1	building	build	VERB
ejpam-5602	16	2	on	on	ADP
ejpam-5602	16	3	the	the	DET
ejpam-5602	16	4	foundations	foundation	NOUN
ejpam-5602	16	5	of	of	ADP
ejpam-5602	16	6	roman	roman	ADJ
ejpam-5602	16	7	domination	domination	NOUN
ejpam-5602	16	8	,	,	PUNCT
ejpam-5602	16	9	chellali	chellali	PROPN
ejpam-5602	16	10	et	et	PROPN
ejpam-5602	16	11	al	al	PROPN
ejpam-5602	16	12	.	.	PUNCT
ejpam-5602	17	1	[	[	X
ejpam-5602	17	2	13	13	NUM
ejpam-5602	17	3	]	]	PUNCT
ejpam-5602	17	4	introduced	introduce	VERB
ejpam-5602	17	5	a	a	DET
ejpam-5602	17	6	broader	broad	ADJ
ejpam-5602	17	7	concept	concept	NOUN
ejpam-5602	17	8	known	know	VERB
ejpam-5602	17	9	as	as	ADP
ejpam-5602	17	10	italian	italian	ADJ
ejpam-5602	17	11	domination	domination	NOUN
ejpam-5602	17	12	(	(	PUNCT
ejpam-5602	17	13	also	also	ADV
ejpam-5602	17	14	referred	refer	VERB
ejpam-5602	17	15	as	as	ADP
ejpam-5602	17	16	roman-{2	roman-{2	NOUN
ejpam-5602	17	17	}	}	PUNCT
ejpam-5602	17	18	domination	domination	NOUN
ejpam-5602	17	19	)	)	PUNCT
ejpam-5602	17	20	.	.	PUNCT
ejpam-5602	18	1	meanwhile	meanwhile	ADV
ejpam-5602	18	2	,	,	PUNCT
ejpam-5602	18	3	beeler	beeler	PROPN
ejpam-5602	18	4	et	et	PROPN
ejpam-5602	18	5	al	al	PROPN
ejpam-5602	18	6	.	.	PUNCT
ejpam-5602	19	1	[	[	X
ejpam-5602	19	2	10	10	NUM
ejpam-5602	19	3	]	]	PUNCT
ejpam-5602	19	4	extended	extend	VERB
ejpam-5602	19	5	the	the	DET
ejpam-5602	19	6	idea	idea	NOUN
ejpam-5602	19	7	even	even	ADV
ejpam-5602	19	8	further	far	ADV
ejpam-5602	19	9	by	by	ADP
ejpam-5602	19	10	developing	develop	VERB
ejpam-5602	19	11	the	the	DET
ejpam-5602	19	12	notion	notion	NOUN
ejpam-5602	19	13	of	of	ADP
ejpam-5602	19	14	double	double	ADJ
ejpam-5602	19	15	roman	roman	ADJ
ejpam-5602	19	16	domination	domination	NOUN
ejpam-5602	19	17	,	,	PUNCT
ejpam-5602	19	18	a	a	DET
ejpam-5602	19	19	stronger	strong	ADJ
ejpam-5602	19	20	variant	variant	NOUN
ejpam-5602	19	21	that	that	PRON
ejpam-5602	19	22	inspires	inspire	VERB
ejpam-5602	19	23	new	new	ADJ
ejpam-5602	19	24	research	research	NOUN
ejpam-5602	19	25	in	in	ADP
ejpam-5602	19	26	the	the	DET
ejpam-5602	19	27	field	field	NOUN
ejpam-5602	19	28	.	.	PUNCT
ejpam-5602	20	1	∗corresponding	∗corresponde	VERB
ejpam-5602	20	2	author	author	NOUN
ejpam-5602	20	3	.	.	PUNCT
ejpam-5602	21	1	doi	doi	NOUN
ejpam-5602	21	2	:	:	PUNCT
ejpam-5602	21	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5602	https://doi.org/10.29020/nybg.ejpam.v18i1.5602	NUM
ejpam-5602	21	4	email	email	NOUN
ejpam-5602	21	5	addresses	address	NOUN
ejpam-5602	21	6	:	:	PUNCT
ejpam-5602	21	7	sheryljane.sumbalan@g.msuiit.edu.ph	sheryljane.sumbalan@g.msuiit.edu.ph	PROPN
ejpam-5602	21	8	(	(	PUNCT
ejpam-5602	21	9	s.j	s.j	PROPN
ejpam-5602	21	10	.	.	PROPN
ejpam-5602	21	11	sumbalan	sumbalan	PROPN
ejpam-5602	21	12	)	)	PUNCT
ejpam-5602	21	13	,	,	PUNCT
ejpam-5602	21	14	sheila.menchavez@g.msu.iit.edu.ph	sheila.menchavez@g.msu.iit.edu.ph	PROPN
ejpam-5602	21	15	(	(	PUNCT
ejpam-5602	21	16	s.	s.	PROPN
ejpam-5602	21	17	menchavez	menchavez	PROPN
ejpam-5602	21	18	)	)	PUNCT
ejpam-5602	21	19	,	,	PUNCT
ejpam-5602	21	20	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-5602	21	21	(	(	PUNCT
ejpam-5602	21	22	f.	f.	PROPN
ejpam-5602	21	23	jamil	jamil	PROPN
ejpam-5602	21	24	)	)	PUNCT
ejpam-5602	21	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5602	22	1	1	1	NUM
ejpam-5602	22	2	copyright	copyright	NOUN
ejpam-5602	22	3	:	:	PUNCT
ejpam-5602	22	4	©	©	PROPN
ejpam-5602	22	5	2025	2025	NUM
ejpam-5602	22	6	the	the	DET
ejpam-5602	22	7	author(s	author(s	NOUN
ejpam-5602	22	8	)	)	PUNCT
ejpam-5602	22	9	.	.	PUNCT
ejpam-5602	23	1	(	(	PUNCT
ejpam-5602	23	2	cc	cc	NOUN
ejpam-5602	23	3	by	by	ADP
ejpam-5602	23	4	-	-	PUNCT
ejpam-5602	23	5	nc	nc	PROPN
ejpam-5602	23	6	4.0	4.0	NUM
ejpam-5602	23	7	)	)	PUNCT
ejpam-5602	23	8	s.j.l	s.j.l	NOUN
ejpam-5602	23	9	.	.	PUNCT
ejpam-5602	23	10	sumbalan	sumbalan	PROPN
ejpam-5602	23	11	,	,	PUNCT
ejpam-5602	23	12	s.m	s.m	PROPN
ejpam-5602	23	13	.	.	PROPN
ejpam-5602	23	14	menchavez	menchavez	PROPN
ejpam-5602	23	15	,	,	PUNCT
ejpam-5602	23	16	f.p	f.p	PROPN
ejpam-5602	23	17	.	.	PROPN
ejpam-5602	23	18	jamil	jamil	PROPN
ejpam-5602	23	19	/	/	SYM
ejpam-5602	23	20	eur	eur	PROPN
ejpam-5602	23	21	.	.	PUNCT
ejpam-5602	24	1	j.	j.	PROPN
ejpam-5602	24	2	pure	pure	PROPN
ejpam-5602	24	3	appl	appl	PROPN
ejpam-5602	24	4	.	.	PROPN
ejpam-5602	24	5	math	math	PROPN
ejpam-5602	24	6	,	,	PUNCT
ejpam-5602	24	7	18	18	NUM
ejpam-5602	24	8	(	(	PUNCT
ejpam-5602	24	9	1	1	NUM
ejpam-5602	24	10	)	)	PUNCT
ejpam-5602	24	11	(	(	PUNCT
ejpam-5602	24	12	2025	2025	NUM
ejpam-5602	24	13	)	)	PUNCT
ejpam-5602	24	14	,	,	PUNCT
ejpam-5602	24	15	5602	5602	NUM
ejpam-5602	24	16	2	2	NUM
ejpam-5602	24	17	of	of	ADP
ejpam-5602	24	18	18	18	NUM
ejpam-5602	24	19	in	in	ADP
ejpam-5602	24	20	2020	2020	NUM
ejpam-5602	24	21	,	,	PUNCT
ejpam-5602	24	22	mojdeh	mojdeh	PROPN
ejpam-5602	24	23	et	et	PROPN
ejpam-5602	24	24	al	al	PROPN
ejpam-5602	24	25	.	.	PUNCT
ejpam-5602	25	1	[	[	X
ejpam-5602	25	2	19	19	NUM
ejpam-5602	25	3	]	]	PUNCT
ejpam-5602	25	4	introduced	introduce	VERB
ejpam-5602	25	5	the	the	DET
ejpam-5602	25	6	concept	concept	NOUN
ejpam-5602	25	7	of	of	ADP
ejpam-5602	25	8	double	double	ADJ
ejpam-5602	25	9	italian	italian	ADJ
ejpam-5602	25	10	domination	domination	NOUN
ejpam-5602	25	11	(	(	PUNCT
ejpam-5602	25	12	or	or	CCONJ
ejpam-5602	25	13	roman	roman	ADJ
ejpam-5602	25	14	{	{	PUNCT
ejpam-5602	25	15	3}-domination	3}-domination	NUM
ejpam-5602	25	16	)	)	PUNCT
ejpam-5602	25	17	which	which	PRON
ejpam-5602	25	18	is	be	AUX
ejpam-5602	25	19	an	an	DET
ejpam-5602	25	20	optimization	optimization	NOUN
ejpam-5602	25	21	of	of	ADP
ejpam-5602	25	22	the	the	DET
ejpam-5602	25	23	double	double	ADJ
ejpam-5602	25	24	roman	roman	ADJ
ejpam-5602	25	25	domination	domination	NOUN
ejpam-5602	25	26	.	.	PUNCT
ejpam-5602	26	1	in	in	ADP
ejpam-5602	26	2	the	the	DET
ejpam-5602	26	3	same	same	ADJ
ejpam-5602	26	4	year	year	NOUN
ejpam-5602	26	5	,	,	PUNCT
ejpam-5602	26	6	shao	shao	PROPN
ejpam-5602	26	7	et	et	PROPN
ejpam-5602	26	8	al	al	PROPN
ejpam-5602	26	9	.	.	PUNCT
ejpam-5602	27	1	[	[	X
ejpam-5602	27	2	26	26	NUM
ejpam-5602	27	3	]	]	PUNCT
ejpam-5602	27	4	initiated	initiate	VERB
ejpam-5602	27	5	the	the	DET
ejpam-5602	27	6	study	study	NOUN
ejpam-5602	27	7	of	of	ADP
ejpam-5602	27	8	total	total	ADJ
ejpam-5602	27	9	double	double	ADJ
ejpam-5602	27	10	italian	italian	ADJ
ejpam-5602	27	11	domination	domination	NOUN
ejpam-5602	27	12	and	and	CCONJ
ejpam-5602	27	13	have	have	AUX
ejpam-5602	27	14	shown	show	VERB
ejpam-5602	27	15	its	its	PRON
ejpam-5602	27	16	relationship	relationship	NOUN
ejpam-5602	27	17	to	to	ADP
ejpam-5602	27	18	other	other	ADJ
ejpam-5602	27	19	domination	domination	NOUN
ejpam-5602	27	20	parameters	parameter	NOUN
ejpam-5602	27	21	.	.	PUNCT
ejpam-5602	28	1	this	this	DET
ejpam-5602	28	2	present	present	ADJ
ejpam-5602	28	3	paper	paper	NOUN
ejpam-5602	28	4	investigates	investigate	VERB
ejpam-5602	28	5	further	far	ADV
ejpam-5602	28	6	the	the	DET
ejpam-5602	28	7	total	total	ADJ
ejpam-5602	28	8	double	double	ADJ
ejpam-5602	28	9	italian	italian	ADJ
ejpam-5602	28	10	domination	domination	NOUN
ejpam-5602	28	11	,	,	PUNCT
ejpam-5602	28	12	particularly	particularly	ADV
ejpam-5602	28	13	in	in	ADP
ejpam-5602	28	14	graphs	graph	NOUN
ejpam-5602	28	15	under	under	ADP
ejpam-5602	28	16	the	the	DET
ejpam-5602	28	17	join	join	NOUN
ejpam-5602	28	18	,	,	PUNCT
ejpam-5602	28	19	corona	corona	PROPN
ejpam-5602	28	20	,	,	PUNCT
ejpam-5602	28	21	edge	edge	NOUN
ejpam-5602	28	22	corona	corona	NOUN
ejpam-5602	28	23	and	and	CCONJ
ejpam-5602	28	24	complementary	complementary	ADJ
ejpam-5602	28	25	prism	prism	NOUN
ejpam-5602	28	26	of	of	ADP
ejpam-5602	28	27	graphs	graph	NOUN
ejpam-5602	28	28	.	.	PUNCT
ejpam-5602	29	1	throughout	throughout	ADP
ejpam-5602	29	2	this	this	DET
ejpam-5602	29	3	paper	paper	NOUN
ejpam-5602	29	4	,	,	PUNCT
ejpam-5602	29	5	all	all	DET
ejpam-5602	29	6	graphs	graph	NOUN
ejpam-5602	29	7	considered	consider	VERB
ejpam-5602	29	8	are	be	AUX
ejpam-5602	29	9	undirected	undirected	ADJ
ejpam-5602	29	10	,	,	PUNCT
ejpam-5602	29	11	finite	finite	ADJ
ejpam-5602	29	12	and	and	CCONJ
ejpam-5602	29	13	simple	simple	ADJ
ejpam-5602	29	14	.	.	PUNCT
ejpam-5602	30	1	see	see	VERB
ejpam-5602	31	1	[	[	X
ejpam-5602	31	2	3	3	NUM
ejpam-5602	31	3	,	,	PUNCT
ejpam-5602	31	4	4	4	NUM
ejpam-5602	31	5	,	,	PUNCT
ejpam-5602	31	6	9	9	NUM
ejpam-5602	31	7	]	]	PUNCT
ejpam-5602	31	8	for	for	ADP
ejpam-5602	31	9	all	all	DET
ejpam-5602	31	10	the	the	DET
ejpam-5602	31	11	basic	basic	ADJ
ejpam-5602	31	12	graph	graph	NOUN
ejpam-5602	31	13	terminologies	terminology	NOUN
ejpam-5602	31	14	that	that	PRON
ejpam-5602	31	15	are	be	AUX
ejpam-5602	31	16	not	not	PART
ejpam-5602	31	17	defined	define	VERB
ejpam-5602	31	18	but	but	CCONJ
ejpam-5602	31	19	used	use	VERB
ejpam-5602	31	20	in	in	ADP
ejpam-5602	31	21	this	this	DET
ejpam-5602	31	22	paper	paper	NOUN
ejpam-5602	31	23	.	.	PUNCT
ejpam-5602	32	1	for	for	ADP
ejpam-5602	32	2	a	a	DET
ejpam-5602	32	3	graph	graph	NOUN
ejpam-5602	32	4	g	g	NOUN
ejpam-5602	32	5	=	=	PUNCT
ejpam-5602	32	6	(	(	PUNCT
ejpam-5602	32	7	v	v	NOUN
ejpam-5602	32	8	(	(	PUNCT
ejpam-5602	32	9	g	g	NOUN
ejpam-5602	32	10	)	)	PUNCT
ejpam-5602	32	11	,	,	PUNCT
ejpam-5602	32	12	e(g	e(g	PROPN
ejpam-5602	32	13	)	)	PUNCT
ejpam-5602	32	14	)	)	PUNCT
ejpam-5602	32	15	,	,	PUNCT
ejpam-5602	32	16	the	the	DET
ejpam-5602	32	17	open	open	ADJ
ejpam-5602	32	18	neighborhood	neighborhood	NOUN
ejpam-5602	32	19	of	of	ADP
ejpam-5602	32	20	a	a	DET
ejpam-5602	32	21	vertex	vertex	NOUN
ejpam-5602	32	22	v	v	ADP
ejpam-5602	32	23	∈	∈	NOUN
ejpam-5602	32	24	v	v	NOUN
ejpam-5602	32	25	(	(	PUNCT
ejpam-5602	32	26	g	g	NOUN
ejpam-5602	32	27	)	)	PUNCT
ejpam-5602	32	28	,	,	PUNCT
ejpam-5602	32	29	denoted	denote	VERB
ejpam-5602	32	30	by	by	ADP
ejpam-5602	32	31	ng(v	ng(v	NOUN
ejpam-5602	32	32	)	)	PUNCT
ejpam-5602	32	33	,	,	PUNCT
ejpam-5602	32	34	consists	consist	VERB
ejpam-5602	32	35	of	of	ADP
ejpam-5602	32	36	all	all	DET
ejpam-5602	32	37	the	the	DET
ejpam-5602	32	38	vertices	vertex	NOUN
ejpam-5602	32	39	adjacent	adjacent	ADJ
ejpam-5602	32	40	to	to	ADP
ejpam-5602	32	41	v	v	NOUN
ejpam-5602	32	42	and	and	CCONJ
ejpam-5602	32	43	its	its	PRON
ejpam-5602	32	44	closed	closed	ADJ
ejpam-5602	32	45	neighborhood	neighborhood	NOUN
ejpam-5602	32	46	,	,	PUNCT
ejpam-5602	32	47	denoted	denote	VERB
ejpam-5602	32	48	by	by	ADP
ejpam-5602	32	49	ng[v	ng[v	NOUN
ejpam-5602	32	50	]	]	PUNCT
ejpam-5602	32	51	,	,	PUNCT
ejpam-5602	32	52	is	be	AUX
ejpam-5602	32	53	the	the	DET
ejpam-5602	32	54	open	open	ADJ
ejpam-5602	32	55	neighborhood	neighborhood	NOUN
ejpam-5602	32	56	of	of	ADP
ejpam-5602	32	57	v	v	NOUN
ejpam-5602	32	58	together	together	ADV
ejpam-5602	32	59	with	with	ADP
ejpam-5602	32	60	vertex	vertex	NOUN
ejpam-5602	32	61	v.	v.	ADP
ejpam-5602	32	62	the	the	DET
ejpam-5602	32	63	degree	degree	NOUN
ejpam-5602	32	64	of	of	ADP
ejpam-5602	32	65	v	v	NOUN
ejpam-5602	32	66	,	,	PUNCT
ejpam-5602	32	67	denoted	denote	VERB
ejpam-5602	32	68	by	by	ADP
ejpam-5602	32	69	degg(v	degg(v	PROPN
ejpam-5602	32	70	)	)	PUNCT
ejpam-5602	32	71	,	,	PUNCT
ejpam-5602	32	72	degg(v	degg(v	PROPN
ejpam-5602	32	73	)	)	PUNCT
ejpam-5602	32	74	=	=	SYM
ejpam-5602	32	75	|ng(v)|	|ng(v)|	NOUN
ejpam-5602	32	76	.	.	PUNCT
ejpam-5602	33	1	the	the	DET
ejpam-5602	33	2	minimum	minimum	NOUN
ejpam-5602	33	3	degree	degree	NOUN
ejpam-5602	33	4	,	,	PUNCT
ejpam-5602	33	5	δ(g	δ(g	PROPN
ejpam-5602	33	6	)	)	PUNCT
ejpam-5602	33	7	of	of	ADP
ejpam-5602	33	8	g	g	PROPN
ejpam-5602	33	9	is	be	AUX
ejpam-5602	33	10	the	the	DET
ejpam-5602	33	11	minimum	minimum	ADJ
ejpam-5602	33	12	degree	degree	NOUN
ejpam-5602	33	13	among	among	ADP
ejpam-5602	33	14	the	the	DET
ejpam-5602	33	15	vertices	vertex	NOUN
ejpam-5602	33	16	of	of	ADP
ejpam-5602	33	17	g.	g.	PROPN
ejpam-5602	33	18	the	the	DET
ejpam-5602	33	19	maximum	maximum	ADJ
ejpam-5602	33	20	degree	degree	NOUN
ejpam-5602	33	21	of	of	ADP
ejpam-5602	33	22	g	g	NOUN
ejpam-5602	33	23	,	,	PUNCT
ejpam-5602	33	24	denoted	denote	VERB
ejpam-5602	33	25	by	by	ADP
ejpam-5602	33	26	∆(g	∆(g	PROPN
ejpam-5602	33	27	)	)	PUNCT
ejpam-5602	33	28	,	,	PUNCT
ejpam-5602	33	29	is	be	AUX
ejpam-5602	33	30	the	the	DET
ejpam-5602	33	31	maximum	maximum	ADJ
ejpam-5602	33	32	degree	degree	NOUN
ejpam-5602	33	33	among	among	ADP
ejpam-5602	33	34	the	the	DET
ejpam-5602	33	35	vertices	vertex	NOUN
ejpam-5602	33	36	of	of	ADP
ejpam-5602	33	37	g.	g.	NOUN
ejpam-5602	33	38	for	for	ADP
ejpam-5602	33	39	s	s	PROPN
ejpam-5602	33	40	⊆	⊆	NUM
ejpam-5602	33	41	v	v	NOUN
ejpam-5602	33	42	(	(	PUNCT
ejpam-5602	33	43	g	g	NOUN
ejpam-5602	33	44	)	)	PUNCT
ejpam-5602	33	45	,	,	PUNCT
ejpam-5602	33	46	ng(s	ng(s	NUM
ejpam-5602	33	47	)	)	PUNCT
ejpam-5602	33	48	=	=	SYM
ejpam-5602	33	49	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-5602	33	50	)	)	PUNCT
ejpam-5602	33	51	and	and	CCONJ
ejpam-5602	33	52	ng[s	ng[s	PROPN
ejpam-5602	33	53	]	]	PUNCT
ejpam-5602	34	1	=	=	SYM
ejpam-5602	34	2	s	s	NOUN
ejpam-5602	34	3	∪ng(s	∪ng(s	NOUN
ejpam-5602	34	4	)	)	PUNCT
ejpam-5602	34	5	.	.	PUNCT
ejpam-5602	35	1	let	let	VERB
ejpam-5602	35	2	g	g	NOUN
ejpam-5602	35	3	and	and	CCONJ
ejpam-5602	35	4	h	h	NOUN
ejpam-5602	35	5	be	be	AUX
ejpam-5602	35	6	graphs	graph	NOUN
ejpam-5602	35	7	with	with	ADP
ejpam-5602	35	8	disjoint	disjoint	ADJ
ejpam-5602	35	9	vertex	vertex	NOUN
ejpam-5602	35	10	sets	set	NOUN
ejpam-5602	35	11	.	.	PUNCT
ejpam-5602	36	1	the	the	DET
ejpam-5602	36	2	join	join	NOUN
ejpam-5602	36	3	of	of	ADP
ejpam-5602	36	4	graphs	graph	NOUN
ejpam-5602	36	5	g	g	NOUN
ejpam-5602	36	6	and	and	CCONJ
ejpam-5602	36	7	h	h	NOUN
ejpam-5602	36	8	is	be	AUX
ejpam-5602	36	9	the	the	DET
ejpam-5602	36	10	graph	graph	NOUN
ejpam-5602	36	11	g	g	PROPN
ejpam-5602	36	12	+	+	NOUN
ejpam-5602	36	13	h	h	NOUN
ejpam-5602	36	14	with	with	ADP
ejpam-5602	36	15	vertex	vertex	NOUN
ejpam-5602	36	16	set	set	VERB
ejpam-5602	36	17	v	v	NOUN
ejpam-5602	36	18	(	(	PUNCT
ejpam-5602	36	19	g	g	PROPN
ejpam-5602	36	20	+	+	NOUN
ejpam-5602	36	21	h	h	NOUN
ejpam-5602	36	22	)	)	PUNCT
ejpam-5602	36	23	=	=	NOUN
ejpam-5602	36	24	v	v	X
ejpam-5602	36	25	(	(	PUNCT
ejpam-5602	36	26	g	g	NOUN
ejpam-5602	36	27	)	)	PUNCT
ejpam-5602	36	28	∪	∪	NOUN
ejpam-5602	36	29	v	v	NOUN
ejpam-5602	36	30	(	(	PUNCT
ejpam-5602	36	31	h	h	NOUN
ejpam-5602	36	32	)	)	PUNCT
ejpam-5602	36	33	and	and	CCONJ
ejpam-5602	36	34	edge	edge	NOUN
ejpam-5602	36	35	set	set	VERB
ejpam-5602	36	36	e(g	e(g	PROPN
ejpam-5602	36	37	+	+	PROPN
ejpam-5602	36	38	h	h	NOUN
ejpam-5602	36	39	)	)	PUNCT
ejpam-5602	36	40	=	=	SYM
ejpam-5602	36	41	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	X
ejpam-5602	36	42	:	:	PUNCT
ejpam-5602	36	43	u	u	PROPN
ejpam-5602	36	44	∈	∈	PROPN
ejpam-5602	36	45	v	v	NOUN
ejpam-5602	36	46	(	(	PUNCT
ejpam-5602	36	47	g)∧	g)∧	PROPN
ejpam-5602	36	48	v	v	ADP
ejpam-5602	36	49	∈	∈	PROPN
ejpam-5602	36	50	v	v	NOUN
ejpam-5602	36	51	(	(	PUNCT
ejpam-5602	36	52	h	h	NOUN
ejpam-5602	36	53	)	)	PUNCT
ejpam-5602	36	54	}	}	PUNCT
ejpam-5602	36	55	.	.	PUNCT
ejpam-5602	37	1	the	the	DET
ejpam-5602	37	2	corona	corona	NOUN
ejpam-5602	37	3	of	of	ADP
ejpam-5602	37	4	g	g	PROPN
ejpam-5602	37	5	and	and	CCONJ
ejpam-5602	37	6	h	h	NOUN
ejpam-5602	37	7	,	,	PUNCT
ejpam-5602	37	8	g	g	PROPN
ejpam-5602	37	9	◦	◦	NOUN
ejpam-5602	37	10	h	h	NOUN
ejpam-5602	37	11	,	,	PUNCT
ejpam-5602	37	12	is	be	AUX
ejpam-5602	37	13	the	the	DET
ejpam-5602	37	14	graph	graph	NOUN
ejpam-5602	37	15	obtained	obtain	VERB
ejpam-5602	37	16	by	by	ADP
ejpam-5602	37	17	taking	take	VERB
ejpam-5602	37	18	one	one	NUM
ejpam-5602	37	19	copy	copy	NOUN
ejpam-5602	37	20	of	of	ADP
ejpam-5602	37	21	g	g	PROPN
ejpam-5602	37	22	and	and	CCONJ
ejpam-5602	37	23	|v	|v	PROPN
ejpam-5602	37	24	(	(	PUNCT
ejpam-5602	37	25	g)|	g)|	NOUN
ejpam-5602	37	26	copies	copy	NOUN
ejpam-5602	37	27	of	of	ADP
ejpam-5602	37	28	h	h	NOUN
ejpam-5602	37	29	and	and	CCONJ
ejpam-5602	37	30	then	then	ADV
ejpam-5602	37	31	joining	join	VERB
ejpam-5602	37	32	the	the	DET
ejpam-5602	37	33	ith	ith	PROPN
ejpam-5602	37	34	vertex	vertex	NOUN
ejpam-5602	37	35	of	of	ADP
ejpam-5602	37	36	g	g	NOUN
ejpam-5602	37	37	to	to	ADP
ejpam-5602	37	38	every	every	DET
ejpam-5602	37	39	vertex	vertex	NOUN
ejpam-5602	37	40	of	of	ADP
ejpam-5602	37	41	the	the	DET
ejpam-5602	37	42	ith	ith	PROPN
ejpam-5602	37	43	copy	copy	NOUN
ejpam-5602	37	44	of	of	ADP
ejpam-5602	37	45	h.	h.	PROPN
ejpam-5602	37	46	the	the	DET
ejpam-5602	37	47	edge	edge	NOUN
ejpam-5602	37	48	corona	corona	PROPN
ejpam-5602	37	49	,	,	PUNCT
ejpam-5602	37	50	denoted	denote	VERB
ejpam-5602	37	51	by	by	ADP
ejpam-5602	37	52	g	g	PROPN
ejpam-5602	37	53	⋄h	⋄h	PROPN
ejpam-5602	37	54	,	,	PUNCT
ejpam-5602	37	55	of	of	ADP
ejpam-5602	37	56	g	g	PROPN
ejpam-5602	37	57	and	and	CCONJ
ejpam-5602	37	58	h	h	NOUN
ejpam-5602	37	59	is	be	AUX
ejpam-5602	37	60	a	a	DET
ejpam-5602	37	61	graph	graph	NOUN
ejpam-5602	37	62	obtained	obtain	VERB
ejpam-5602	37	63	by	by	ADP
ejpam-5602	37	64	taking	take	VERB
ejpam-5602	37	65	one	one	NUM
ejpam-5602	37	66	copy	copy	NOUN
ejpam-5602	37	67	of	of	ADP
ejpam-5602	37	68	g	g	PROPN
ejpam-5602	37	69	and	and	CCONJ
ejpam-5602	37	70	|e(g)|	|e(g)|	ADJ
ejpam-5602	37	71	copies	copy	NOUN
ejpam-5602	37	72	of	of	ADP
ejpam-5602	37	73	h	h	NOUN
ejpam-5602	37	74	and	and	CCONJ
ejpam-5602	37	75	joining	join	VERB
ejpam-5602	37	76	each	each	PRON
ejpam-5602	37	77	of	of	ADP
ejpam-5602	37	78	the	the	DET
ejpam-5602	37	79	end	end	NOUN
ejpam-5602	37	80	vertices	vertice	VERB
ejpam-5602	37	81	u	u	NOUN
ejpam-5602	37	82	and	and	CCONJ
ejpam-5602	37	83	v	v	NOUN
ejpam-5602	37	84	of	of	ADP
ejpam-5602	37	85	each	each	DET
ejpam-5602	37	86	edge	edge	NOUN
ejpam-5602	37	87	uv	uv	NOUN
ejpam-5602	37	88	of	of	ADP
ejpam-5602	37	89	g	g	NOUN
ejpam-5602	37	90	to	to	ADP
ejpam-5602	37	91	every	every	DET
ejpam-5602	37	92	vertex	vertex	NOUN
ejpam-5602	37	93	of	of	ADP
ejpam-5602	37	94	the	the	DET
ejpam-5602	37	95	copy	copy	NOUN
ejpam-5602	37	96	huv	huv	PROPN
ejpam-5602	37	97	of	of	ADP
ejpam-5602	37	98	h.	h.	PROPN
ejpam-5602	37	99	the	the	DET
ejpam-5602	37	100	complementary	complementary	ADJ
ejpam-5602	37	101	prism	prism	NOUN
ejpam-5602	37	102	,	,	PUNCT
ejpam-5602	37	103	denoted	denote	VERB
ejpam-5602	37	104	gg	gg	NOUN
ejpam-5602	37	105	,	,	PUNCT
ejpam-5602	37	106	is	be	AUX
ejpam-5602	37	107	formed	form	VERB
ejpam-5602	37	108	from	from	ADP
ejpam-5602	37	109	the	the	DET
ejpam-5602	37	110	disjoint	disjoint	PROPN
ejpam-5602	37	111	union	union	NOUN
ejpam-5602	37	112	of	of	ADP
ejpam-5602	37	113	g	g	PROPN
ejpam-5602	37	114	and	and	CCONJ
ejpam-5602	37	115	its	its	PRON
ejpam-5602	37	116	complement	complement	NOUN
ejpam-5602	37	117	g	g	NOUN
ejpam-5602	37	118	by	by	ADP
ejpam-5602	37	119	adding	add	VERB
ejpam-5602	37	120	a	a	DET
ejpam-5602	37	121	perfect	perfect	ADJ
ejpam-5602	37	122	matching	matching	NOUN
ejpam-5602	37	123	between	between	ADP
ejpam-5602	37	124	corresponding	corresponding	ADJ
ejpam-5602	37	125	vertices	vertex	NOUN
ejpam-5602	37	126	of	of	ADP
ejpam-5602	37	127	g	g	PROPN
ejpam-5602	37	128	and	and	CCONJ
ejpam-5602	37	129	g.	g.	VERB
ejpam-5602	37	130	the	the	DET
ejpam-5602	37	131	gluing	gluing	NOUN
ejpam-5602	37	132	of	of	ADP
ejpam-5602	37	133	g	g	PROPN
ejpam-5602	37	134	and	and	CCONJ
ejpam-5602	37	135	h	h	NOUN
ejpam-5602	37	136	along	along	ADP
ejpam-5602	37	137	a	a	DET
ejpam-5602	37	138	common	common	ADJ
ejpam-5602	37	139	subgraph	subgraph	NOUN
ejpam-5602	37	140	k	k	PROPN
ejpam-5602	37	141	is	be	AUX
ejpam-5602	37	142	the	the	DET
ejpam-5602	37	143	graph	graph	NOUN
ejpam-5602	37	144	g	g	PROPN
ejpam-5602	37	145	⊔k	⊔k	NUM
ejpam-5602	37	146	h	h	NOUN
ejpam-5602	37	147	by	by	ADP
ejpam-5602	37	148	combining	combine	VERB
ejpam-5602	37	149	g	g	NOUN
ejpam-5602	37	150	and	and	CCONJ
ejpam-5602	37	151	h	h	NOUN
ejpam-5602	37	152	through	through	ADP
ejpam-5602	37	153	k.	k.	PROPN
ejpam-5602	37	154	graphs	graphs	PROPN
ejpam-5602	37	155	c4	c4	VERB
ejpam-5602	37	156	⊔p3	⊔p3	NUM
ejpam-5602	37	157	c4	c4	NOUN
ejpam-5602	37	158	and	and	CCONJ
ejpam-5602	37	159	c4	c4	NOUN
ejpam-5602	37	160	⊔k2	⊔k2	ADP
ejpam-5602	37	161	k3	k3	NOUN
ejpam-5602	37	162	are	be	AUX
ejpam-5602	37	163	given	give	VERB
ejpam-5602	37	164	in	in	ADP
ejpam-5602	37	165	figure	figure	NOUN
ejpam-5602	37	166	1	1	NUM
ejpam-5602	37	167	.	.	PUNCT
ejpam-5602	38	1	we	we	PRON
ejpam-5602	38	2	refer	refer	VERB
ejpam-5602	38	3	to	to	ADP
ejpam-5602	38	4	[	[	X
ejpam-5602	38	5	5	5	NUM
ejpam-5602	38	6	]	]	PUNCT
ejpam-5602	38	7	for	for	ADP
ejpam-5602	38	8	a	a	DET
ejpam-5602	38	9	detailed	detailed	ADJ
ejpam-5602	38	10	information	information	NOUN
ejpam-5602	38	11	on	on	ADP
ejpam-5602	38	12	the	the	DET
ejpam-5602	38	13	gluing	gluing	NOUN
ejpam-5602	38	14	of	of	ADP
ejpam-5602	38	15	graphs	graph	NOUN
ejpam-5602	38	16	.	.	PUNCT
ejpam-5602	39	1	a	a	DET
ejpam-5602	39	2	set	set	NOUN
ejpam-5602	39	3	s	s	NOUN
ejpam-5602	39	4	⊆	⊆	NUM
ejpam-5602	39	5	v	v	NOUN
ejpam-5602	39	6	(	(	PUNCT
ejpam-5602	39	7	g	g	NOUN
ejpam-5602	39	8	)	)	PUNCT
ejpam-5602	39	9	is	be	AUX
ejpam-5602	39	10	a	a	DET
ejpam-5602	39	11	dominating	dominating	NOUN
ejpam-5602	39	12	set	set	NOUN
ejpam-5602	39	13	of	of	ADP
ejpam-5602	39	14	g	g	PROPN
ejpam-5602	39	15	if	if	SCONJ
ejpam-5602	39	16	ng[s	ng[	NOUN
ejpam-5602	39	17	]	]	PUNCT
ejpam-5602	39	18	=	=	SYM
ejpam-5602	39	19	v	v	NOUN
ejpam-5602	39	20	(	(	PUNCT
ejpam-5602	39	21	g	g	NOUN
ejpam-5602	39	22	)	)	PUNCT
ejpam-5602	39	23	.	.	PUNCT
ejpam-5602	40	1	the	the	DET
ejpam-5602	40	2	domination	domination	NOUN
ejpam-5602	40	3	number	number	NOUN
ejpam-5602	40	4	of	of	ADP
ejpam-5602	40	5	g	g	NOUN
ejpam-5602	40	6	,	,	PUNCT
ejpam-5602	40	7	denoted	denote	VERB
ejpam-5602	40	8	by	by	ADP
ejpam-5602	40	9	γ(g	γ(g	PROPN
ejpam-5602	40	10	)	)	PUNCT
ejpam-5602	40	11	,	,	PUNCT
ejpam-5602	40	12	is	be	AUX
ejpam-5602	40	13	the	the	DET
ejpam-5602	40	14	smallest	small	ADJ
ejpam-5602	40	15	cardinality	cardinality	NOUN
ejpam-5602	40	16	of	of	ADP
ejpam-5602	40	17	a	a	DET
ejpam-5602	40	18	dominating	dominating	NOUN
ejpam-5602	40	19	set	set	NOUN
ejpam-5602	40	20	of	of	ADP
ejpam-5602	40	21	g.	g.	PROPN
ejpam-5602	40	22	a	a	DET
ejpam-5602	40	23	set	set	NOUN
ejpam-5602	40	24	s	s	NOUN
ejpam-5602	40	25	of	of	ADP
ejpam-5602	40	26	vertices	vertex	NOUN
ejpam-5602	40	27	in	in	ADP
ejpam-5602	40	28	a	a	DET
ejpam-5602	40	29	graph	graph	NOUN
ejpam-5602	40	30	g	g	NOUN
ejpam-5602	40	31	is	be	AUX
ejpam-5602	40	32	called	call	VERB
ejpam-5602	40	33	a	a	DET
ejpam-5602	40	34	total	total	ADJ
ejpam-5602	40	35	dominating	dominating	NOUN
ejpam-5602	40	36	set	set	NOUN
ejpam-5602	40	37	if	if	SCONJ
ejpam-5602	40	38	ng(s	ng(s	NUM
ejpam-5602	40	39	)	)	PUNCT
ejpam-5602	40	40	=	=	SYM
ejpam-5602	40	41	v	v	X
ejpam-5602	40	42	(	(	PUNCT
ejpam-5602	40	43	g	g	NOUN
ejpam-5602	40	44	)	)	PUNCT
ejpam-5602	40	45	.	.	PUNCT
ejpam-5602	41	1	the	the	DET
ejpam-5602	41	2	total	total	ADJ
ejpam-5602	41	3	domination	domination	NOUN
ejpam-5602	41	4	number	number	NOUN
ejpam-5602	41	5	γt(g	γt(g	PUNCT
ejpam-5602	41	6	)	)	PUNCT
ejpam-5602	41	7	of	of	ADP
ejpam-5602	41	8	g	g	PROPN
ejpam-5602	41	9	is	be	AUX
ejpam-5602	41	10	the	the	DET
ejpam-5602	41	11	minimum	minimum	ADJ
ejpam-5602	41	12	cardinality	cardinality	NOUN
ejpam-5602	41	13	of	of	ADP
ejpam-5602	41	14	a	a	DET
ejpam-5602	41	15	total	total	ADJ
ejpam-5602	41	16	dominating	dominating	NOUN
ejpam-5602	41	17	set	set	NOUN
ejpam-5602	41	18	of	of	ADP
ejpam-5602	41	19	vertices	vertex	NOUN
ejpam-5602	41	20	in	in	ADP
ejpam-5602	41	21	g.	g.	PROPN
ejpam-5602	41	22	a	a	DET
ejpam-5602	41	23	dominating	dominating	NOUN
ejpam-5602	41	24	set	set	NOUN
ejpam-5602	41	25	of	of	ADP
ejpam-5602	41	26	g	g	PROPN
ejpam-5602	41	27	of	of	ADP
ejpam-5602	41	28	cardinality	cardinality	PROPN
ejpam-5602	41	29	γ(g	γ(g	PROPN
ejpam-5602	41	30	)	)	PUNCT
ejpam-5602	41	31	is	be	AUX
ejpam-5602	41	32	referred	refer	VERB
ejpam-5602	41	33	to	to	ADP
ejpam-5602	41	34	as	as	ADP
ejpam-5602	41	35	γ	γ	NOUN
ejpam-5602	41	36	-	-	PUNCT
ejpam-5602	41	37	set	set	NOUN
ejpam-5602	41	38	of	of	ADP
ejpam-5602	41	39	g.	g.	PROPN
ejpam-5602	41	40	a	a	DET
ejpam-5602	41	41	total	total	ADJ
ejpam-5602	41	42	dominating	dominating	NOUN
ejpam-5602	41	43	set	set	VERB
ejpam-5602	41	44	ofg	ofg	PROPN
ejpam-5602	41	45	of	of	ADP
ejpam-5602	41	46	cardinality	cardinality	PROPN
ejpam-5602	41	47	γt(g	γt(g	PUNCT
ejpam-5602	41	48	)	)	PUNCT
ejpam-5602	41	49	is	be	AUX
ejpam-5602	41	50	called	call	VERB
ejpam-5602	41	51	a	a	DET
ejpam-5602	41	52	γt	γt	NOUN
ejpam-5602	41	53	-	-	ADJ
ejpam-5602	41	54	set	set	VERB
ejpam-5602	41	55	ofg	ofg	NOUN
ejpam-5602	41	56	.	.	PUNCT
ejpam-5602	42	1	we	we	PRON
ejpam-5602	42	2	refer	refer	VERB
ejpam-5602	42	3	to	to	ADP
ejpam-5602	42	4	[	[	X
ejpam-5602	42	5	6	6	NUM
ejpam-5602	42	6	,	,	PUNCT
ejpam-5602	42	7	11	11	NUM
ejpam-5602	42	8	,	,	PUNCT
ejpam-5602	42	9	14	14	NUM
ejpam-5602	42	10	,	,	PUNCT
ejpam-5602	42	11	15	15	NUM
ejpam-5602	42	12	,	,	PUNCT
ejpam-5602	42	13	20	20	NUM
ejpam-5602	42	14	]	]	PUNCT
ejpam-5602	42	15	for	for	ADP
ejpam-5602	42	16	the	the	DET
ejpam-5602	42	17	fundamental	fundamental	ADJ
ejpam-5602	42	18	concepts	concept	NOUN
ejpam-5602	42	19	,	,	PUNCT
ejpam-5602	42	20	some	some	DET
ejpam-5602	42	21	recent	recent	ADJ
ejpam-5602	42	22	developments	development	NOUN
ejpam-5602	42	23	and	and	CCONJ
ejpam-5602	42	24	applications	application	NOUN
ejpam-5602	42	25	of	of	ADP
ejpam-5602	42	26	domination	domination	NOUN
ejpam-5602	42	27	and	and	CCONJ
ejpam-5602	42	28	total	total	ADJ
ejpam-5602	42	29	domination	domination	NOUN
ejpam-5602	42	30	in	in	ADP
ejpam-5602	42	31	graphs	graph	NOUN
ejpam-5602	42	32	.	.	PUNCT
ejpam-5602	43	1	for	for	ADP
ejpam-5602	43	2	a	a	DET
ejpam-5602	43	3	positive	positive	ADJ
ejpam-5602	43	4	integer	integer	NOUN
ejpam-5602	43	5	k	k	PROPN
ejpam-5602	43	6	,	,	PUNCT
ejpam-5602	43	7	a	a	DET
ejpam-5602	43	8	set	set	NOUN
ejpam-5602	43	9	d	d	NOUN
ejpam-5602	43	10	⊆	⊆	NUM
ejpam-5602	43	11	v	v	ADP
ejpam-5602	43	12	(	(	PUNCT
ejpam-5602	43	13	g	g	NOUN
ejpam-5602	43	14	)	)	PUNCT
ejpam-5602	43	15	is	be	AUX
ejpam-5602	43	16	called	call	VERB
ejpam-5602	43	17	a	a	DET
ejpam-5602	43	18	k	k	ADJ
ejpam-5602	43	19	-	-	PUNCT
ejpam-5602	43	20	dominating	dominating	NOUN
ejpam-5602	43	21	set	set	NOUN
ejpam-5602	43	22	if	if	SCONJ
ejpam-5602	43	23	each	each	DET
ejpam-5602	43	24	v	v	ADP
ejpam-5602	43	25	∈	∈	NOUN
ejpam-5602	43	26	v	v	NOUN
ejpam-5602	43	27	(	(	PUNCT
ejpam-5602	43	28	g	g	NOUN
ejpam-5602	43	29	)	)	PUNCT
ejpam-5602	43	30	\d	\d	NOUN
ejpam-5602	43	31	is	be	AUX
ejpam-5602	43	32	adjacent	adjacent	ADJ
ejpam-5602	43	33	to	to	ADP
ejpam-5602	43	34	at	at	ADP
ejpam-5602	43	35	least	least	ADJ
ejpam-5602	43	36	k	k	X
ejpam-5602	43	37	vertices	vertice	VERB
ejpam-5602	43	38	in	in	ADP
ejpam-5602	43	39	d.	d.	PROPN
ejpam-5602	43	40	the	the	DET
ejpam-5602	43	41	k	k	ADJ
ejpam-5602	43	42	-	-	PUNCT
ejpam-5602	43	43	domination	domination	NOUN
ejpam-5602	43	44	number	number	NOUN
ejpam-5602	43	45	γk(g	γk(g	PUNCT
ejpam-5602	43	46	)	)	PUNCT
ejpam-5602	43	47	is	be	AUX
ejpam-5602	43	48	then	then	ADV
ejpam-5602	43	49	defined	define	VERB
ejpam-5602	43	50	to	to	PART
ejpam-5602	43	51	be	be	AUX
ejpam-5602	43	52	the	the	DET
ejpam-5602	43	53	smallest	small	ADJ
ejpam-5602	43	54	cardinality	cardinality	NOUN
ejpam-5602	43	55	of	of	ADP
ejpam-5602	43	56	a	a	DET
ejpam-5602	43	57	k	k	ADV
ejpam-5602	43	58	-	-	PUNCT
ejpam-5602	43	59	dominating	dominating	ADJ
ejpam-5602	43	60	set	set	NOUN
ejpam-5602	43	61	of	of	ADP
ejpam-5602	43	62	g.	g.	PROPN
ejpam-5602	43	63	m.	m.	PROPN
ejpam-5602	43	64	chellali	chellali	PROPN
ejpam-5602	43	65	et	et	PROPN
ejpam-5602	43	66	al	al	PROPN
ejpam-5602	43	67	.	.	PUNCT
ejpam-5602	44	1	in	in	ADP
ejpam-5602	44	2	[	[	X
ejpam-5602	44	3	8	8	NUM
ejpam-5602	44	4	]	]	PUNCT
ejpam-5602	44	5	presented	present	VERB
ejpam-5602	44	6	an	an	DET
ejpam-5602	44	7	outstanding	outstanding	ADJ
ejpam-5602	44	8	survey	survey	NOUN
ejpam-5602	44	9	of	of	ADP
ejpam-5602	44	10	results	result	NOUN
ejpam-5602	44	11	in	in	ADP
ejpam-5602	44	12	k	k	NOUN
ejpam-5602	44	13	-	-	NOUN
ejpam-5602	44	14	domination	domination	NOUN
ejpam-5602	44	15	in	in	ADP
ejpam-5602	44	16	graphs	graph	NOUN
ejpam-5602	44	17	.	.	PUNCT
ejpam-5602	45	1	a	a	DET
ejpam-5602	45	2	subset	subset	NOUN
ejpam-5602	45	3	s	s	VERB
ejpam-5602	45	4	⊆	⊆	NUM
ejpam-5602	45	5	v	v	NOUN
ejpam-5602	45	6	(	(	PUNCT
ejpam-5602	45	7	g	g	NOUN
ejpam-5602	45	8	)	)	PUNCT
ejpam-5602	45	9	is	be	AUX
ejpam-5602	45	10	a	a	DET
ejpam-5602	45	11	vertex	vertex	NOUN
ejpam-5602	45	12	cover	cover	NOUN
ejpam-5602	45	13	of	of	ADP
ejpam-5602	45	14	g	g	PROPN
ejpam-5602	45	15	if	if	SCONJ
ejpam-5602	45	16	for	for	ADP
ejpam-5602	45	17	every	every	DET
ejpam-5602	45	18	edge	edge	NOUN
ejpam-5602	45	19	uv	uv	PROPN
ejpam-5602	45	20	∈	∈	PROPN
ejpam-5602	45	21	e(g	e(g	PROPN
ejpam-5602	45	22	)	)	PUNCT
ejpam-5602	45	23	,	,	PUNCT
ejpam-5602	46	1	u	u	PROPN
ejpam-5602	46	2	∈	∈	PROPN
ejpam-5602	46	3	s	s	X
ejpam-5602	46	4	or	or	CCONJ
ejpam-5602	46	5	v	v	ADP
ejpam-5602	46	6	∈	∈	PROPN
ejpam-5602	46	7	s.	s.	PROPN
ejpam-5602	46	8	s.j.l	s.j.l	PROPN
ejpam-5602	46	9	.	.	PUNCT
ejpam-5602	46	10	sumbalan	sumbalan	PROPN
ejpam-5602	46	11	,	,	PUNCT
ejpam-5602	46	12	s.m	s.m	PROPN
ejpam-5602	46	13	.	.	PROPN
ejpam-5602	46	14	menchavez	menchavez	PROPN
ejpam-5602	46	15	,	,	PUNCT
ejpam-5602	46	16	f.p	f.p	PROPN
ejpam-5602	46	17	.	.	PROPN
ejpam-5602	46	18	jamil	jamil	PROPN
ejpam-5602	46	19	/	/	SYM
ejpam-5602	46	20	eur	eur	PROPN
ejpam-5602	46	21	.	.	PUNCT
ejpam-5602	47	1	j.	j.	PROPN
ejpam-5602	47	2	pure	pure	PROPN
ejpam-5602	47	3	appl	appl	PROPN
ejpam-5602	47	4	.	.	PROPN
ejpam-5602	47	5	math	math	PROPN
ejpam-5602	47	6	,	,	PUNCT
ejpam-5602	47	7	18	18	NUM
ejpam-5602	47	8	(	(	PUNCT
ejpam-5602	47	9	1	1	NUM
ejpam-5602	47	10	)	)	PUNCT
ejpam-5602	47	11	(	(	PUNCT
ejpam-5602	47	12	2025	2025	NUM
ejpam-5602	47	13	)	)	PUNCT
ejpam-5602	47	14	,	,	PUNCT
ejpam-5602	47	15	5602	5602	NUM
ejpam-5602	47	16	3	3	NUM
ejpam-5602	47	17	of	of	ADP
ejpam-5602	47	18	18	18	NUM
ejpam-5602	47	19	the	the	DET
ejpam-5602	47	20	smallest	small	ADJ
ejpam-5602	47	21	cardinality	cardinality	NOUN
ejpam-5602	47	22	of	of	ADP
ejpam-5602	47	23	a	a	DET
ejpam-5602	47	24	vertex	vertex	NOUN
ejpam-5602	47	25	cover	cover	NOUN
ejpam-5602	47	26	is	be	AUX
ejpam-5602	47	27	the	the	DET
ejpam-5602	47	28	vertex	vertex	NOUN
ejpam-5602	47	29	cover	cover	NOUN
ejpam-5602	47	30	number	number	NOUN
ejpam-5602	47	31	of	of	ADP
ejpam-5602	47	32	g	g	NOUN
ejpam-5602	47	33	,	,	PUNCT
ejpam-5602	47	34	and	and	CCONJ
ejpam-5602	47	35	is	be	AUX
ejpam-5602	47	36	denoted	denote	VERB
ejpam-5602	47	37	by	by	ADP
ejpam-5602	47	38	β(g	β(g	PROPN
ejpam-5602	47	39	)	)	PUNCT
ejpam-5602	47	40	.	.	PUNCT
ejpam-5602	48	1	excellent	excellent	ADJ
ejpam-5602	48	2	references	reference	NOUN
ejpam-5602	48	3	for	for	ADP
ejpam-5602	48	4	vertex	vertex	NOUN
ejpam-5602	48	5	cover	cover	NOUN
ejpam-5602	48	6	include	include	VERB
ejpam-5602	48	7	[	[	X
ejpam-5602	48	8	7	7	NUM
ejpam-5602	48	9	,	,	PUNCT
ejpam-5602	48	10	23	23	NUM
ejpam-5602	48	11	]	]	PUNCT
ejpam-5602	48	12	.	.	PUNCT
ejpam-5602	49	1	a	a	DET
ejpam-5602	49	2	double	double	ADJ
ejpam-5602	49	3	italian	italian	ADJ
ejpam-5602	49	4	dominating	dominating	NOUN
ejpam-5602	49	5	function	function	NOUN
ejpam-5602	49	6	(	(	PUNCT
ejpam-5602	49	7	or	or	CCONJ
ejpam-5602	49	8	didf	didf	NOUN
ejpam-5602	49	9	)	)	PUNCT
ejpam-5602	49	10	of	of	ADP
ejpam-5602	49	11	g	g	PROPN
ejpam-5602	49	12	is	be	AUX
ejpam-5602	49	13	a	a	DET
ejpam-5602	49	14	function	function	NOUN
ejpam-5602	49	15	f	f	NOUN
ejpam-5602	49	16	:	:	PUNCT
ejpam-5602	49	17	v	v	X
ejpam-5602	49	18	(	(	PUNCT
ejpam-5602	49	19	g	g	NOUN
ejpam-5602	49	20	)	)	PUNCT
ejpam-5602	49	21	→	→	SYM
ejpam-5602	49	22	{	{	PUNCT
ejpam-5602	49	23	0	0	NUM
ejpam-5602	49	24	,	,	PUNCT
ejpam-5602	49	25	1	1	NUM
ejpam-5602	49	26	,	,	PUNCT
ejpam-5602	49	27	2	2	NUM
ejpam-5602	49	28	,	,	PUNCT
ejpam-5602	49	29	3	3	NUM
ejpam-5602	49	30	}	}	PUNCT
ejpam-5602	49	31	having	have	VERB
ejpam-5602	49	32	the	the	DET
ejpam-5602	49	33	property	property	NOUN
ejpam-5602	49	34	that	that	PRON
ejpam-5602	49	35	for	for	ADP
ejpam-5602	49	36	every	every	DET
ejpam-5602	49	37	vertex	vertex	NOUN
ejpam-5602	49	38	v	v	ADP
ejpam-5602	49	39	∈	∈	NOUN
ejpam-5602	49	40	v	v	NOUN
ejpam-5602	49	41	(	(	PUNCT
ejpam-5602	49	42	g	g	NOUN
ejpam-5602	49	43	)	)	PUNCT
ejpam-5602	49	44	,	,	PUNCT
ejpam-5602	49	45	if	if	SCONJ
ejpam-5602	49	46	f(v	f(v	NOUN
ejpam-5602	49	47	)	)	PUNCT
ejpam-5602	49	48	∈	∈	PROPN
ejpam-5602	49	49	{	{	PUNCT
ejpam-5602	49	50	0	0	NUM
ejpam-5602	49	51	,	,	PUNCT
ejpam-5602	49	52	1	1	NUM
ejpam-5602	49	53	}	}	PUNCT
ejpam-5602	49	54	,	,	PUNCT
ejpam-5602	49	55	then	then	ADV
ejpam-5602	49	56	∑	∑	PUNCT
ejpam-5602	49	57	u∈n	u∈n	X
ejpam-5602	49	58	[	[	X
ejpam-5602	49	59	v	v	X
ejpam-5602	49	60	]	]	X
ejpam-5602	49	61	f(u	f(u	PROPN
ejpam-5602	49	62	)	)	PUNCT
ejpam-5602	49	63	≥	≥	NOUN
ejpam-5602	49	64	3	3	NUM
ejpam-5602	49	65	.	.	PUNCT
ejpam-5602	50	1	the	the	DET
ejpam-5602	50	2	weight	weight	NOUN
ejpam-5602	50	3	of	of	ADP
ejpam-5602	50	4	a	a	DET
ejpam-5602	50	5	didf	didf	NOUN
ejpam-5602	50	6	is	be	AUX
ejpam-5602	50	7	the	the	DET
ejpam-5602	50	8	sum	sum	NOUN
ejpam-5602	50	9	ωg(f	ωg(f	PUNCT
ejpam-5602	50	10	)	)	PUNCT
ejpam-5602	50	11	=	=	SYM
ejpam-5602	50	12	∑	∑	PUNCT
ejpam-5602	50	13	v∈v	v∈v	PROPN
ejpam-5602	50	14	(	(	PUNCT
ejpam-5602	50	15	g	g	NOUN
ejpam-5602	50	16	)	)	PUNCT
ejpam-5602	50	17	f(v	f(v	NOUN
ejpam-5602	50	18	)	)	PUNCT
ejpam-5602	50	19	,	,	PUNCT
ejpam-5602	50	20	and	and	CCONJ
ejpam-5602	50	21	the	the	DET
ejpam-5602	50	22	minimum	minimum	ADJ
ejpam-5602	50	23	weight	weight	NOUN
ejpam-5602	50	24	of	of	ADP
ejpam-5602	50	25	a	a	DET
ejpam-5602	50	26	didf	didf	PROPN
ejpam-5602	50	27	f	f	PROPN
ejpam-5602	50	28	is	be	AUX
ejpam-5602	50	29	the	the	DET
ejpam-5602	50	30	double	double	ADJ
ejpam-5602	50	31	italian	italian	ADJ
ejpam-5602	50	32	domination	domination	NOUN
ejpam-5602	50	33	number	number	NOUN
ejpam-5602	50	34	,	,	PUNCT
ejpam-5602	50	35	denoted	denote	VERB
ejpam-5602	50	36	by	by	ADP
ejpam-5602	50	37	γdi(g	γdi(g	PROPN
ejpam-5602	50	38	)	)	PUNCT
ejpam-5602	50	39	.	.	PUNCT
ejpam-5602	51	1	a	a	DET
ejpam-5602	51	2	didf	didf	PROPN
ejpam-5602	51	3	function	function	VERB
ejpam-5602	51	4	f	f	PROPN
ejpam-5602	51	5	:	:	PUNCT
ejpam-5602	51	6	v	v	X
ejpam-5602	51	7	(	(	PUNCT
ejpam-5602	51	8	g	g	NOUN
ejpam-5602	51	9	)	)	PUNCT
ejpam-5602	51	10	→	→	SYM
ejpam-5602	51	11	{	{	PUNCT
ejpam-5602	51	12	0	0	NUM
ejpam-5602	51	13	,	,	PUNCT
ejpam-5602	51	14	1	1	NUM
ejpam-5602	51	15	,	,	PUNCT
ejpam-5602	51	16	2	2	NUM
ejpam-5602	51	17	,	,	PUNCT
ejpam-5602	51	18	3	3	NUM
ejpam-5602	51	19	}	}	PUNCT
ejpam-5602	51	20	is	be	AUX
ejpam-5602	51	21	a	a	DET
ejpam-5602	51	22	total	total	ADJ
ejpam-5602	51	23	double	double	ADJ
ejpam-5602	51	24	italian	italian	ADJ
ejpam-5602	51	25	dominating	dominating	NOUN
ejpam-5602	51	26	function	function	NOUN
ejpam-5602	51	27	(	(	PUNCT
ejpam-5602	51	28	or	or	CCONJ
ejpam-5602	51	29	tdidf	tdidf	NOUN
ejpam-5602	51	30	)	)	PUNCT
ejpam-5602	51	31	of	of	ADP
ejpam-5602	51	32	g	g	PROPN
ejpam-5602	51	33	if	if	SCONJ
ejpam-5602	51	34	for	for	ADP
ejpam-5602	51	35	each	each	DET
ejpam-5602	51	36	v	v	NUM
ejpam-5602	51	37	∈	∈	PROPN
ejpam-5602	51	38	v	v	NOUN
ejpam-5602	51	39	(	(	PUNCT
ejpam-5602	51	40	g	g	NOUN
ejpam-5602	51	41	)	)	PUNCT
ejpam-5602	51	42	with	with	ADP
ejpam-5602	51	43	f(v	f(v	NOUN
ejpam-5602	51	44	)	)	PUNCT
ejpam-5602	51	45	̸=	̸=	PROPN
ejpam-5602	51	46	0	0	NUM
ejpam-5602	51	47	,	,	PUNCT
ejpam-5602	51	48	there	there	PRON
ejpam-5602	51	49	exists	exist	VERB
ejpam-5602	51	50	u	u	PROPN
ejpam-5602	51	51	∈	∈	PROPN
ejpam-5602	51	52	v	v	ADP
ejpam-5602	51	53	(	(	PUNCT
ejpam-5602	51	54	g	g	NOUN
ejpam-5602	51	55	)	)	PUNCT
ejpam-5602	51	56	such	such	ADJ
ejpam-5602	51	57	that	that	DET
ejpam-5602	51	58	f(u	f(u	PROPN
ejpam-5602	51	59	)	)	PUNCT
ejpam-5602	51	60	̸=	̸=	PROPN
ejpam-5602	51	61	0	0	NUM
ejpam-5602	52	1	and	and	CCONJ
ejpam-5602	52	2	uv	uv	PROPN
ejpam-5602	52	3	∈	∈	PROPN
ejpam-5602	52	4	e(g	e(g	PROPN
ejpam-5602	52	5	)	)	PUNCT
ejpam-5602	52	6	.	.	PUNCT
ejpam-5602	53	1	the	the	DET
ejpam-5602	53	2	minimum	minimum	ADJ
ejpam-5602	53	3	weight	weight	NOUN
ejpam-5602	53	4	of	of	ADP
ejpam-5602	53	5	a	a	DET
ejpam-5602	53	6	tdidf	tdidf	NOUN
ejpam-5602	53	7	of	of	ADP
ejpam-5602	53	8	g	g	PROPN
ejpam-5602	53	9	is	be	AUX
ejpam-5602	53	10	the	the	DET
ejpam-5602	53	11	total	total	ADJ
ejpam-5602	53	12	double	double	ADJ
ejpam-5602	53	13	italian	italian	ADJ
ejpam-5602	53	14	domination	domination	NOUN
ejpam-5602	53	15	number	number	NOUN
ejpam-5602	53	16	of	of	ADP
ejpam-5602	53	17	g	g	NOUN
ejpam-5602	53	18	,	,	PUNCT
ejpam-5602	53	19	and	and	CCONJ
ejpam-5602	53	20	is	be	AUX
ejpam-5602	53	21	denoted	denote	VERB
ejpam-5602	53	22	by	by	ADP
ejpam-5602	53	23	γtdi(g	γtdi(g	PROPN
ejpam-5602	53	24	)	)	PUNCT
ejpam-5602	53	25	.	.	PUNCT
ejpam-5602	54	1	we	we	PRON
ejpam-5602	54	2	write	write	VERB
ejpam-5602	54	3	f	f	PROPN
ejpam-5602	54	4	∈	∈	PROPN
ejpam-5602	54	5	tdidf	tdidf	NOUN
ejpam-5602	54	6	(	(	PUNCT
ejpam-5602	54	7	g	g	NOUN
ejpam-5602	54	8	)	)	PUNCT
ejpam-5602	54	9	to	to	PART
ejpam-5602	54	10	mean	mean	VERB
ejpam-5602	54	11	that	that	SCONJ
ejpam-5602	54	12	f	f	PROPN
ejpam-5602	54	13	is	be	AUX
ejpam-5602	54	14	tdidf	tdidf	NOUN
ejpam-5602	54	15	of	of	ADP
ejpam-5602	54	16	g.	g.	PROPN
ejpam-5602	54	17	any	any	DET
ejpam-5602	54	18	tdidf	tdidf	NOUN
ejpam-5602	54	19	f	f	PROPN
ejpam-5602	54	20	of	of	ADP
ejpam-5602	54	21	g	g	PROPN
ejpam-5602	54	22	with	with	ADP
ejpam-5602	54	23	weight	weight	NOUN
ejpam-5602	54	24	γtdi(g	γtdi(g	PROPN
ejpam-5602	54	25	)	)	PUNCT
ejpam-5602	54	26	is	be	AUX
ejpam-5602	54	27	referred	refer	VERB
ejpam-5602	54	28	to	to	ADP
ejpam-5602	54	29	as	as	ADP
ejpam-5602	54	30	γtdi	γtdi	PROPN
ejpam-5602	54	31	-function	-function	NOUN
ejpam-5602	54	32	of	of	ADP
ejpam-5602	54	33	g.	g.	NOUN
ejpam-5602	54	34	for	for	ADP
ejpam-5602	54	35	a	a	DET
ejpam-5602	54	36	function	function	NOUN
ejpam-5602	55	1	f	f	NOUN
ejpam-5602	55	2	:	:	PUNCT
ejpam-5602	55	3	v	v	X
ejpam-5602	55	4	(	(	PUNCT
ejpam-5602	55	5	g	g	NOUN
ejpam-5602	55	6	)	)	PUNCT
ejpam-5602	55	7	→	→	SYM
ejpam-5602	55	8	{	{	PUNCT
ejpam-5602	55	9	0	0	NUM
ejpam-5602	55	10	,	,	PUNCT
ejpam-5602	55	11	1	1	NUM
ejpam-5602	55	12	,	,	PUNCT
ejpam-5602	55	13	2	2	NUM
ejpam-5602	55	14	,	,	PUNCT
ejpam-5602	55	15	3	3	NUM
ejpam-5602	55	16	}	}	PUNCT
ejpam-5602	55	17	,	,	PUNCT
ejpam-5602	55	18	let	let	VERB
ejpam-5602	55	19	(	(	PUNCT
ejpam-5602	55	20	v0	v0	NOUN
ejpam-5602	55	21	,	,	PUNCT
ejpam-5602	55	22	v1	v1	NOUN
ejpam-5602	55	23	,	,	PUNCT
ejpam-5602	55	24	v2	v2	PROPN
ejpam-5602	55	25	,	,	PUNCT
ejpam-5602	55	26	v3	v3	PROPN
ejpam-5602	55	27	)	)	PUNCT
ejpam-5602	55	28	be	be	VERB
ejpam-5602	55	29	the	the	DET
ejpam-5602	55	30	ordered	order	VERB
ejpam-5602	55	31	partition	partition	NOUN
ejpam-5602	55	32	induced	induce	VERB
ejpam-5602	55	33	by	by	ADP
ejpam-5602	55	34	f	f	PROPN
ejpam-5602	55	35	,	,	PUNCT
ejpam-5602	55	36	where	where	SCONJ
ejpam-5602	55	37	vi	vi	VERB
ejpam-5602	55	38	=	=	PRON
ejpam-5602	55	39	{	{	PUNCT
ejpam-5602	55	40	v	v	NUM
ejpam-5602	55	41	∈	∈	NOUN
ejpam-5602	55	42	v	v	NOUN
ejpam-5602	55	43	(	(	PUNCT
ejpam-5602	55	44	g	g	NOUN
ejpam-5602	55	45	)	)	PUNCT
ejpam-5602	55	46	:	:	PUNCT
ejpam-5602	55	47	f(v	f(v	NOUN
ejpam-5602	55	48	)	)	PUNCT
ejpam-5602	56	1	=	=	PUNCT
ejpam-5602	56	2	i	i	PROPN
ejpam-5602	56	3	}	}	PUNCT
ejpam-5602	56	4	for	for	ADP
ejpam-5602	56	5	i	i	PROPN
ejpam-5602	56	6	∈	∈	PROPN
ejpam-5602	56	7	{	{	PUNCT
ejpam-5602	56	8	0	0	NUM
ejpam-5602	56	9	,	,	PUNCT
ejpam-5602	56	10	1	1	NUM
ejpam-5602	56	11	,	,	PUNCT
ejpam-5602	56	12	2	2	NUM
ejpam-5602	56	13	,	,	PUNCT
ejpam-5602	56	14	3	3	NUM
ejpam-5602	56	15	}	}	PUNCT
ejpam-5602	56	16	.	.	PUNCT
ejpam-5602	57	1	then	then	ADV
ejpam-5602	57	2	we	we	PRON
ejpam-5602	57	3	can	can	AUX
ejpam-5602	57	4	write	write	VERB
ejpam-5602	57	5	f	f	PROPN
ejpam-5602	57	6	=	=	SYM
ejpam-5602	57	7	(	(	PUNCT
ejpam-5602	57	8	v0	v0	PROPN
ejpam-5602	57	9	,	,	PUNCT
ejpam-5602	57	10	v1	v1	NOUN
ejpam-5602	57	11	,	,	PUNCT
ejpam-5602	57	12	v2	v2	PROPN
ejpam-5602	57	13	,	,	PUNCT
ejpam-5602	57	14	v3	v3	PROPN
ejpam-5602	57	15	)	)	PUNCT
ejpam-5602	57	16	.	.	PUNCT
ejpam-5602	58	1	the	the	DET
ejpam-5602	58	2	weight	weight	NOUN
ejpam-5602	58	3	of	of	ADP
ejpam-5602	58	4	f	f	PROPN
ejpam-5602	58	5	is	be	AUX
ejpam-5602	58	6	defined	define	VERB
ejpam-5602	58	7	by	by	ADP
ejpam-5602	58	8	ωg(f	ωg(f	NOUN
ejpam-5602	58	9	)	)	PUNCT
ejpam-5602	58	10	=	=	PUNCT
ejpam-5602	58	11	|v1|+	|v1|+	ADP
ejpam-5602	58	12	2|v2|+	2|v2|+	NUM
ejpam-5602	58	13	3|v3|	3|v3|	NUM
ejpam-5602	58	14	.	.	PUNCT
ejpam-5602	59	1	more	more	ADV
ejpam-5602	59	2	precisely	precisely	ADV
ejpam-5602	59	3	,	,	PUNCT
ejpam-5602	59	4	f	f	PROPN
ejpam-5602	59	5	=	=	SYM
ejpam-5602	59	6	(	(	PUNCT
ejpam-5602	59	7	v0	v0	PROPN
ejpam-5602	59	8	,	,	PUNCT
ejpam-5602	59	9	v1	v1	NOUN
ejpam-5602	59	10	,	,	PUNCT
ejpam-5602	59	11	v2	v2	PROPN
ejpam-5602	59	12	,	,	PUNCT
ejpam-5602	59	13	v3	v3	PROPN
ejpam-5602	59	14	)	)	PUNCT
ejpam-5602	59	15	∈	∈	PROPN
ejpam-5602	59	16	tdidf	tdidf	NOUN
ejpam-5602	59	17	(	(	PUNCT
ejpam-5602	59	18	g	g	NOUN
ejpam-5602	59	19	)	)	PUNCT
ejpam-5602	59	20	if	if	SCONJ
ejpam-5602	59	21	each	each	PRON
ejpam-5602	59	22	of	of	ADP
ejpam-5602	59	23	the	the	DET
ejpam-5602	59	24	following	follow	VERB
ejpam-5602	59	25	holds	hold	VERB
ejpam-5602	59	26	:	:	PUNCT
ejpam-5602	59	27	(	(	PUNCT
ejpam-5602	59	28	i	i	NOUN
ejpam-5602	59	29	)	)	PUNCT
ejpam-5602	59	30	for	for	ADP
ejpam-5602	59	31	each	each	DET
ejpam-5602	59	32	v	v	ADP
ejpam-5602	59	33	∈	∈	PROPN
ejpam-5602	59	34	v0	v0	NOUN
ejpam-5602	59	35	,	,	PUNCT
ejpam-5602	59	36	at	at	ADP
ejpam-5602	59	37	least	least	ADJ
ejpam-5602	59	38	one	one	NUM
ejpam-5602	59	39	of	of	ADP
ejpam-5602	59	40	the	the	DET
ejpam-5602	59	41	following	following	NOUN
ejpam-5602	59	42	holds	hold	VERB
ejpam-5602	59	43	:	:	PUNCT
ejpam-5602	59	44	(	(	PUNCT
ejpam-5602	59	45	a	a	X
ejpam-5602	59	46	)	)	PUNCT
ejpam-5602	59	47	|v1	|v1	PROPN
ejpam-5602	60	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-5602	60	2	≥	≥	NUM
ejpam-5602	60	3	3	3	NUM
ejpam-5602	60	4	;	;	PUNCT
ejpam-5602	60	5	(	(	PUNCT
ejpam-5602	60	6	b	b	X
ejpam-5602	60	7	)	)	PUNCT
ejpam-5602	60	8	|v1	|v1	VERB
ejpam-5602	61	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-5602	61	2	≥	≥	NUM
ejpam-5602	61	3	1	1	NUM
ejpam-5602	61	4	and	and	CCONJ
ejpam-5602	61	5	|v2	|v2	VERB
ejpam-5602	61	6	∩ng(v)|	∩ng(v)|	PROPN
ejpam-5602	61	7	≥	≥	NUM
ejpam-5602	61	8	1	1	NUM
ejpam-5602	61	9	;	;	PUNCT
ejpam-5602	61	10	(	(	PUNCT
ejpam-5602	61	11	c	c	X
ejpam-5602	61	12	)	)	PUNCT
ejpam-5602	61	13	|v2	|v2	NOUN
ejpam-5602	62	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-5602	62	2	≥	≥	NOUN
ejpam-5602	62	3	2	2	NUM
ejpam-5602	62	4	;	;	PUNCT
ejpam-5602	62	5	(	(	PUNCT
ejpam-5602	62	6	d	d	X
ejpam-5602	62	7	)	)	PUNCT
ejpam-5602	62	8	|v3	|v3	NOUN
ejpam-5602	62	9	∩ng(v)|	∩ng(v)|	PROPN
ejpam-5602	62	10	≥	≥	NUM
ejpam-5602	62	11	1	1	NUM
ejpam-5602	62	12	.	.	PUNCT
ejpam-5602	62	13	(	(	PUNCT
ejpam-5602	62	14	ii	ii	NOUN
ejpam-5602	62	15	)	)	PUNCT
ejpam-5602	62	16	for	for	ADP
ejpam-5602	62	17	each	each	DET
ejpam-5602	62	18	v	v	X
ejpam-5602	62	19	∈	∈	PROPN
ejpam-5602	62	20	v1	v1	NOUN
ejpam-5602	62	21	,	,	PUNCT
ejpam-5602	62	22	at	at	ADP
ejpam-5602	62	23	least	least	ADJ
ejpam-5602	62	24	one	one	NUM
ejpam-5602	62	25	of	of	ADP
ejpam-5602	62	26	the	the	DET
ejpam-5602	62	27	following	following	NOUN
ejpam-5602	62	28	holds	hold	VERB
ejpam-5602	62	29	:	:	PUNCT
ejpam-5602	62	30	(	(	PUNCT
ejpam-5602	62	31	a	a	X
ejpam-5602	62	32	)	)	PUNCT
ejpam-5602	62	33	|v1	|v1	PROPN
ejpam-5602	63	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-5602	63	2	≥	≥	NUM
ejpam-5602	63	3	2	2	NUM
ejpam-5602	63	4	;	;	PUNCT
ejpam-5602	63	5	(	(	PUNCT
ejpam-5602	63	6	b	b	X
ejpam-5602	63	7	)	)	PUNCT
ejpam-5602	63	8	|(v2	|(v2	NOUN
ejpam-5602	63	9	∪	∪	PROPN
ejpam-5602	63	10	v3	v3	PROPN
ejpam-5602	63	11	)	)	PUNCT
ejpam-5602	63	12	∩ng(v)|	∩ng(v)|	PROPN
ejpam-5602	63	13	≥	≥	NUM
ejpam-5602	63	14	1	1	NUM
ejpam-5602	63	15	.	.	PUNCT
ejpam-5602	63	16	(	(	PUNCT
ejpam-5602	63	17	iii	iii	NOUN
ejpam-5602	63	18	)	)	PUNCT
ejpam-5602	63	19	for	for	ADP
ejpam-5602	63	20	each	each	DET
ejpam-5602	63	21	v	v	NUM
ejpam-5602	63	22	∈	∈	PROPN
ejpam-5602	63	23	v1	v1	NOUN
ejpam-5602	63	24	∪	∪	NOUN
ejpam-5602	63	25	v2	v2	PROPN
ejpam-5602	63	26	∪	∪	X
ejpam-5602	63	27	v3	v3	PROPN
ejpam-5602	63	28	,	,	PUNCT
ejpam-5602	63	29	|(v1	|(v1	VERB
ejpam-5602	63	30	∪	∪	ADP
ejpam-5602	63	31	v2	v2	PROPN
ejpam-5602	63	32	∪	∪	X
ejpam-5602	63	33	v3	v3	PROPN
ejpam-5602	63	34	)	)	PUNCT
ejpam-5602	64	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-5602	64	2	≥	≥	NUM
ejpam-5602	64	3	1	1	NUM
ejpam-5602	64	4	.	.	NOUN
ejpam-5602	64	5	2	2	NUM
ejpam-5602	64	6	.	.	X
ejpam-5602	64	7	preliminary	preliminary	ADJ
ejpam-5602	64	8	results	result	NOUN
ejpam-5602	64	9	proposition	proposition	VERB
ejpam-5602	64	10	1	1	NUM
ejpam-5602	64	11	.	.	PUNCT
ejpam-5602	65	1	[	[	X
ejpam-5602	65	2	26	26	NUM
ejpam-5602	65	3	]	]	X
ejpam-5602	65	4	if	if	SCONJ
ejpam-5602	65	5	g	g	PROPN
ejpam-5602	65	6	is	be	AUX
ejpam-5602	65	7	a	a	DET
ejpam-5602	65	8	connected	connected	ADJ
ejpam-5602	65	9	graph	graph	NOUN
ejpam-5602	65	10	of	of	ADP
ejpam-5602	65	11	order	order	NOUN
ejpam-5602	65	12	n	n	PRON
ejpam-5602	65	13	≥	≥	NOUN
ejpam-5602	65	14	2	2	NUM
ejpam-5602	65	15	,	,	PUNCT
ejpam-5602	65	16	then	then	ADV
ejpam-5602	65	17	γtdi(g	γtdi(g	PROPN
ejpam-5602	65	18	)	)	PUNCT
ejpam-5602	65	19	≥	≥	NOUN
ejpam-5602	65	20	3	3	NUM
ejpam-5602	65	21	and	and	CCONJ
ejpam-5602	65	22	γtdi(g	γtdi(g	PROPN
ejpam-5602	65	23	)	)	PUNCT
ejpam-5602	66	1	=	=	SYM
ejpam-5602	66	2	3	3	NUM
ejpam-5602	66	3	if	if	SCONJ
ejpam-5602	66	4	and	and	CCONJ
ejpam-5602	66	5	only	only	ADV
ejpam-5602	66	6	if	if	SCONJ
ejpam-5602	66	7	g	g	PROPN
ejpam-5602	66	8	has	have	VERB
ejpam-5602	66	9	at	at	ADV
ejpam-5602	66	10	least	least	ADV
ejpam-5602	66	11	two	two	NUM
ejpam-5602	66	12	vertices	vertex	NOUN
ejpam-5602	66	13	of	of	ADP
ejpam-5602	66	14	degree	degree	NOUN
ejpam-5602	66	15	∆(g	∆(g	NOUN
ejpam-5602	66	16	)	)	PUNCT
ejpam-5602	67	1	=	=	PUNCT
ejpam-5602	67	2	n−	n−	NOUN
ejpam-5602	67	3	1	1	NUM
ejpam-5602	67	4	.	.	PUNCT
ejpam-5602	67	5	proposition	proposition	NOUN
ejpam-5602	67	6	2	2	NUM
ejpam-5602	67	7	.	.	PUNCT
ejpam-5602	68	1	[	[	X
ejpam-5602	68	2	26	26	NUM
ejpam-5602	68	3	]	]	X
ejpam-5602	68	4	if	if	SCONJ
ejpam-5602	68	5	g	g	PROPN
ejpam-5602	68	6	has	have	VERB
ejpam-5602	68	7	only	only	ADV
ejpam-5602	68	8	one	one	NUM
ejpam-5602	68	9	vertex	vertex	NOUN
ejpam-5602	68	10	of	of	ADP
ejpam-5602	68	11	degree	degree	NOUN
ejpam-5602	68	12	∆(g	∆(g	NOUN
ejpam-5602	68	13	)	)	PUNCT
ejpam-5602	69	1	=	=	PUNCT
ejpam-5602	69	2	n−	n−	NOUN
ejpam-5602	69	3	1	1	NUM
ejpam-5602	69	4	,	,	PUNCT
ejpam-5602	69	5	then	then	ADV
ejpam-5602	69	6	γtdi(g	γtdi(g	ADP
ejpam-5602	69	7	)	)	PUNCT
ejpam-5602	69	8	=	=	SYM
ejpam-5602	69	9	4	4	X
ejpam-5602	69	10	.	.	PUNCT
ejpam-5602	69	11	theorem	theorem	NOUN
ejpam-5602	69	12	1	1	NUM
ejpam-5602	69	13	.	.	PUNCT
ejpam-5602	70	1	[	[	X
ejpam-5602	70	2	26	26	NUM
ejpam-5602	70	3	]	]	X
ejpam-5602	70	4	if	if	SCONJ
ejpam-5602	70	5	g	g	PROPN
ejpam-5602	70	6	is	be	AUX
ejpam-5602	70	7	a	a	DET
ejpam-5602	70	8	graph	graph	NOUN
ejpam-5602	70	9	with	with	ADP
ejpam-5602	70	10	δ(g	δ(g	PROPN
ejpam-5602	70	11	)	)	PUNCT
ejpam-5602	70	12	=	=	SYM
ejpam-5602	70	13	δ	δ	PROPN
ejpam-5602	70	14	≥	≥	NUM
ejpam-5602	70	15	2	2	NUM
ejpam-5602	70	16	,	,	PUNCT
ejpam-5602	70	17	then	then	ADV
ejpam-5602	70	18	γtdi(g	γtdi(g	PROPN
ejpam-5602	70	19	)	)	PUNCT
ejpam-5602	70	20	≤	≤	PUNCT
ejpam-5602	70	21	|v	|v	X
ejpam-5602	70	22	(	(	PUNCT
ejpam-5602	70	23	g)|+	g)|+	PROPN
ejpam-5602	70	24	2−	2−	NUM
ejpam-5602	70	25	δ	δ	PROPN
ejpam-5602	70	26	,	,	PUNCT
ejpam-5602	70	27	and	and	CCONJ
ejpam-5602	70	28	this	this	DET
ejpam-5602	70	29	bound	bind	VERB
ejpam-5602	70	30	is	be	AUX
ejpam-5602	70	31	sharp	sharp	ADJ
ejpam-5602	70	32	.	.	PUNCT
ejpam-5602	71	1	proposition	proposition	NOUN
ejpam-5602	71	2	3	3	X
ejpam-5602	71	3	.	.	PUNCT
ejpam-5602	72	1	let	let	VERB
ejpam-5602	72	2	g	g	PRON
ejpam-5602	72	3	be	be	AUX
ejpam-5602	72	4	a	a	DET
ejpam-5602	72	5	nontrivial	nontrivial	ADJ
ejpam-5602	72	6	connected	connect	VERB
ejpam-5602	72	7	graph	graph	NOUN
ejpam-5602	72	8	of	of	ADP
ejpam-5602	72	9	order	order	NOUN
ejpam-5602	72	10	n	n	PRON
ejpam-5602	72	11	≥	≥	NOUN
ejpam-5602	72	12	4	4	NUM
ejpam-5602	72	13	.	.	PUNCT
ejpam-5602	73	1	then	then	ADV
ejpam-5602	73	2	γtdi(g	γtdi(g	PROPN
ejpam-5602	73	3	)	)	PUNCT
ejpam-5602	73	4	=	=	SYM
ejpam-5602	74	1	4	4	NUM
ejpam-5602	74	2	if	if	SCONJ
ejpam-5602	74	3	and	and	CCONJ
ejpam-5602	74	4	only	only	ADV
ejpam-5602	74	5	if	if	SCONJ
ejpam-5602	74	6	one	one	NUM
ejpam-5602	74	7	of	of	ADP
ejpam-5602	74	8	the	the	DET
ejpam-5602	74	9	following	follow	VERB
ejpam-5602	74	10	holds	hold	NOUN
ejpam-5602	74	11	:	:	PUNCT
ejpam-5602	74	12	s.j.l	s.j.l	NOUN
ejpam-5602	74	13	.	.	PUNCT
ejpam-5602	74	14	sumbalan	sumbalan	PROPN
ejpam-5602	74	15	,	,	PUNCT
ejpam-5602	74	16	s.m	s.m	PROPN
ejpam-5602	74	17	.	.	PROPN
ejpam-5602	74	18	menchavez	menchavez	PROPN
ejpam-5602	74	19	,	,	PUNCT
ejpam-5602	74	20	f.p	f.p	PROPN
ejpam-5602	74	21	.	.	PROPN
ejpam-5602	74	22	jamil	jamil	PROPN
ejpam-5602	74	23	/	/	SYM
ejpam-5602	74	24	eur	eur	PROPN
ejpam-5602	74	25	.	.	PUNCT
ejpam-5602	75	1	j.	j.	PROPN
ejpam-5602	75	2	pure	pure	PROPN
ejpam-5602	75	3	appl	appl	PROPN
ejpam-5602	75	4	.	.	PROPN
ejpam-5602	75	5	math	math	PROPN
ejpam-5602	75	6	,	,	PUNCT
ejpam-5602	75	7	18	18	NUM
ejpam-5602	75	8	(	(	PUNCT
ejpam-5602	75	9	1	1	NUM
ejpam-5602	75	10	)	)	PUNCT
ejpam-5602	75	11	(	(	PUNCT
ejpam-5602	75	12	2025	2025	NUM
ejpam-5602	75	13	)	)	PUNCT
ejpam-5602	75	14	,	,	PUNCT
ejpam-5602	75	15	5602	5602	NUM
ejpam-5602	75	16	4	4	NUM
ejpam-5602	75	17	of	of	ADP
ejpam-5602	75	18	18	18	NUM
ejpam-5602	75	19	(	(	PUNCT
ejpam-5602	75	20	i	i	NOUN
ejpam-5602	75	21	)	)	PUNCT
ejpam-5602	75	22	g	g	PROPN
ejpam-5602	75	23	has	have	VERB
ejpam-5602	75	24	exactly	exactly	ADV
ejpam-5602	75	25	one	one	NUM
ejpam-5602	75	26	vertex	vertex	NOUN
ejpam-5602	75	27	of	of	ADP
ejpam-5602	75	28	degree	degree	NOUN
ejpam-5602	75	29	∆(g	∆(g	NOUN
ejpam-5602	75	30	)	)	PUNCT
ejpam-5602	75	31	=	=	PUNCT
ejpam-5602	75	32	n−	n−	NOUN
ejpam-5602	75	33	1	1	NUM
ejpam-5602	75	34	;	;	PUNCT
ejpam-5602	75	35	(	(	PUNCT
ejpam-5602	75	36	ii	ii	NOUN
ejpam-5602	75	37	)	)	PUNCT
ejpam-5602	75	38	γ(g	γ(g	PROPN
ejpam-5602	75	39	)	)	PUNCT
ejpam-5602	75	40	≥	≥	NOUN
ejpam-5602	75	41	2	2	NUM
ejpam-5602	75	42	and	and	CCONJ
ejpam-5602	75	43	g	g	PROPN
ejpam-5602	75	44	has	have	VERB
ejpam-5602	75	45	a	a	DET
ejpam-5602	75	46	3	3	NUM
ejpam-5602	75	47	-	-	PUNCT
ejpam-5602	75	48	dominating	dominating	NOUN
ejpam-5602	75	49	set	set	NOUN
ejpam-5602	75	50	d	d	NOUN
ejpam-5602	75	51	with	with	ADP
ejpam-5602	75	52	|d|	|d|	PROPN
ejpam-5602	75	53	=	=	SYM
ejpam-5602	75	54	4	4	NUM
ejpam-5602	75	55	and	and	CCONJ
ejpam-5602	75	56	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	75	57	)	)	PUNCT
ejpam-5602	75	58	≥	≥	NOUN
ejpam-5602	75	59	2	2	NUM
ejpam-5602	75	60	.	.	PUNCT
ejpam-5602	76	1	proof	proof	NOUN
ejpam-5602	76	2	:	:	PUNCT
ejpam-5602	76	3	suppose	suppose	VERB
ejpam-5602	76	4	that	that	SCONJ
ejpam-5602	76	5	γtdi(g	γtdi(g	PROPN
ejpam-5602	76	6	)	)	PUNCT
ejpam-5602	76	7	=	=	SYM
ejpam-5602	77	1	4	4	X
ejpam-5602	77	2	.	.	X
ejpam-5602	78	1	if	if	SCONJ
ejpam-5602	78	2	γ(g	γ(g	PROPN
ejpam-5602	78	3	)	)	PUNCT
ejpam-5602	78	4	=	=	SYM
ejpam-5602	78	5	1	1	NUM
ejpam-5602	78	6	,	,	PUNCT
ejpam-5602	78	7	then	then	ADV
ejpam-5602	78	8	by	by	ADP
ejpam-5602	78	9	proposition	proposition	NOUN
ejpam-5602	78	10	1	1	NUM
ejpam-5602	78	11	and	and	CCONJ
ejpam-5602	78	12	proposition	proposition	NOUN
ejpam-5602	78	13	2	2	NUM
ejpam-5602	78	14	,	,	PUNCT
ejpam-5602	78	15	g	g	PROPN
ejpam-5602	78	16	contains	contain	VERB
ejpam-5602	78	17	exactly	exactly	ADV
ejpam-5602	78	18	one	one	NUM
ejpam-5602	78	19	vertex	vertex	NOUN
ejpam-5602	78	20	of	of	ADP
ejpam-5602	78	21	degree	degree	NOUN
ejpam-5602	78	22	n	n	CCONJ
ejpam-5602	78	23	−	−	PROPN
ejpam-5602	78	24	1	1	NUM
ejpam-5602	78	25	,	,	PUNCT
ejpam-5602	78	26	and	and	CCONJ
ejpam-5602	78	27	(	(	PUNCT
ejpam-5602	78	28	i	i	NOUN
ejpam-5602	78	29	)	)	PUNCT
ejpam-5602	78	30	holds	hold	VERB
ejpam-5602	78	31	.	.	PUNCT
ejpam-5602	78	32	suppose	suppose	VERB
ejpam-5602	78	33	that	that	SCONJ
ejpam-5602	78	34	γ(g	γ(g	PROPN
ejpam-5602	78	35	)	)	PUNCT
ejpam-5602	78	36	≥	≥	NOUN
ejpam-5602	78	37	2	2	NUM
ejpam-5602	78	38	.	.	PUNCT
ejpam-5602	78	39	let	let	VERB
ejpam-5602	78	40	f	f	PROPN
ejpam-5602	78	41	=	=	SYM
ejpam-5602	78	42	(	(	PUNCT
ejpam-5602	78	43	v0	v0	PROPN
ejpam-5602	78	44	,	,	PUNCT
ejpam-5602	78	45	v1	v1	NOUN
ejpam-5602	78	46	,	,	PUNCT
ejpam-5602	78	47	v2	v2	PROPN
ejpam-5602	78	48	,	,	PUNCT
ejpam-5602	78	49	v3	v3	PROPN
ejpam-5602	78	50	)	)	PUNCT
ejpam-5602	78	51	be	be	VERB
ejpam-5602	78	52	a	a	DET
ejpam-5602	78	53	γtdi	γtdi	NOUN
ejpam-5602	78	54	-function	-function	NOUN
ejpam-5602	78	55	of	of	ADP
ejpam-5602	78	56	g.	g.	PROPN
ejpam-5602	78	57	since	since	SCONJ
ejpam-5602	78	58	γ(g	γ(g	PROPN
ejpam-5602	78	59	)	)	PUNCT
ejpam-5602	78	60	̸=	̸=	PROPN
ejpam-5602	78	61	1	1	NUM
ejpam-5602	78	62	,	,	PUNCT
ejpam-5602	78	63	v2	v2	PROPN
ejpam-5602	78	64	=	=	SYM
ejpam-5602	78	65	v3	v3	PROPN
ejpam-5602	78	66	=	=	PUNCT
ejpam-5602	78	67	∅	∅	NOUN
ejpam-5602	78	68	and	and	CCONJ
ejpam-5602	78	69	|v1|	|v1|	NOUN
ejpam-5602	78	70	=	=	SYM
ejpam-5602	78	71	4	4	X
ejpam-5602	78	72	.	.	PUNCT
ejpam-5602	78	73	put	put	VERB
ejpam-5602	78	74	d	d	NOUN
ejpam-5602	78	75	=	=	SYM
ejpam-5602	78	76	v1	v1	PROPN
ejpam-5602	78	77	.	.	PUNCT
ejpam-5602	79	1	then	then	ADV
ejpam-5602	79	2	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	79	3	)	)	PUNCT
ejpam-5602	79	4	≥	≥	NOUN
ejpam-5602	79	5	2	2	NUM
ejpam-5602	79	6	.	.	PUNCT
ejpam-5602	80	1	if	if	SCONJ
ejpam-5602	80	2	v0	v0	NOUN
ejpam-5602	80	3	=	=	SYM
ejpam-5602	80	4	∅	∅	NOUN
ejpam-5602	80	5	,	,	PUNCT
ejpam-5602	80	6	then	then	ADV
ejpam-5602	80	7	g	g	PROPN
ejpam-5602	80	8	=	=	PROPN
ejpam-5602	80	9	c4	c4	NOUN
ejpam-5602	80	10	.	.	PUNCT
ejpam-5602	81	1	if	if	SCONJ
ejpam-5602	81	2	v0	v0	NOUN
ejpam-5602	81	3	̸=	̸=	PROPN
ejpam-5602	81	4	∅	∅	NOUN
ejpam-5602	81	5	,	,	PUNCT
ejpam-5602	81	6	then	then	ADV
ejpam-5602	81	7	3	3	NUM
ejpam-5602	81	8	≤	≤	NUM
ejpam-5602	81	9	|ng(v	|ng(v	NOUN
ejpam-5602	81	10	)	)	PUNCT
ejpam-5602	81	11	∩	∩	NOUN
ejpam-5602	81	12	v1|	v1|	ADJ
ejpam-5602	81	13	≤	≤	ADV
ejpam-5602	81	14	4	4	NUM
ejpam-5602	81	15	for	for	ADP
ejpam-5602	81	16	every	every	DET
ejpam-5602	81	17	v	v	PROPN
ejpam-5602	81	18	∈	∈	PROPN
ejpam-5602	81	19	v0	v0	NOUN
ejpam-5602	81	20	.	.	PUNCT
ejpam-5602	82	1	in	in	ADP
ejpam-5602	82	2	any	any	DET
ejpam-5602	82	3	case	case	NOUN
ejpam-5602	82	4	,	,	PUNCT
ejpam-5602	82	5	d	d	PRON
ejpam-5602	82	6	is	be	AUX
ejpam-5602	82	7	a	a	DET
ejpam-5602	82	8	3	3	NUM
ejpam-5602	82	9	-	-	PUNCT
ejpam-5602	82	10	dominating	dominate	VERB
ejpam-5602	82	11	set	set	NOUN
ejpam-5602	82	12	of	of	ADP
ejpam-5602	82	13	g.	g.	PROPN
ejpam-5602	82	14	thus	thus	ADV
ejpam-5602	82	15	,	,	PUNCT
ejpam-5602	82	16	(	(	PUNCT
ejpam-5602	82	17	ii	ii	NOUN
ejpam-5602	82	18	)	)	PUNCT
ejpam-5602	82	19	holds	hold	VERB
ejpam-5602	82	20	.	.	PUNCT
ejpam-5602	83	1	conversely	conversely	ADV
ejpam-5602	83	2	,	,	PUNCT
ejpam-5602	83	3	if	if	SCONJ
ejpam-5602	83	4	(	(	PUNCT
ejpam-5602	83	5	i	i	NOUN
ejpam-5602	83	6	)	)	PUNCT
ejpam-5602	83	7	holds	hold	VERB
ejpam-5602	83	8	,	,	PUNCT
ejpam-5602	83	9	then	then	ADV
ejpam-5602	83	10	the	the	DET
ejpam-5602	83	11	desired	desire	VERB
ejpam-5602	83	12	result	result	NOUN
ejpam-5602	83	13	follows	follow	VERB
ejpam-5602	83	14	from	from	ADP
ejpam-5602	83	15	proposition	proposition	NOUN
ejpam-5602	83	16	2	2	NUM
ejpam-5602	83	17	.	.	PUNCT
ejpam-5602	84	1	suppose	suppose	VERB
ejpam-5602	84	2	(	(	PUNCT
ejpam-5602	84	3	ii	ii	NOUN
ejpam-5602	84	4	)	)	PUNCT
ejpam-5602	84	5	holds	hold	VERB
ejpam-5602	84	6	.	.	PUNCT
ejpam-5602	85	1	by	by	ADP
ejpam-5602	85	2	proposition	proposition	NOUN
ejpam-5602	85	3	1	1	NUM
ejpam-5602	85	4	and	and	CCONJ
ejpam-5602	85	5	proposition	proposition	NOUN
ejpam-5602	85	6	2	2	NUM
ejpam-5602	85	7	,	,	PUNCT
ejpam-5602	85	8	γtdi(g	γtdi(g	PROPN
ejpam-5602	85	9	)	)	PUNCT
ejpam-5602	85	10	≥	≥	NOUN
ejpam-5602	85	11	4	4	NUM
ejpam-5602	85	12	.	.	PUNCT
ejpam-5602	86	1	on	on	ADP
ejpam-5602	86	2	the	the	DET
ejpam-5602	86	3	other	other	ADJ
ejpam-5602	86	4	hand	hand	NOUN
ejpam-5602	86	5	,	,	PUNCT
ejpam-5602	86	6	since	since	SCONJ
ejpam-5602	86	7	f	f	PROPN
ejpam-5602	86	8	=	=	PUNCT
ejpam-5602	86	9	(	(	PUNCT
ejpam-5602	86	10	v	v	NOUN
ejpam-5602	86	11	(	(	PUNCT
ejpam-5602	86	12	g	g	NOUN
ejpam-5602	86	13	)	)	PUNCT
ejpam-5602	86	14	\	\	PUNCT
ejpam-5602	86	15	d	d	X
ejpam-5602	86	16	,	,	PUNCT
ejpam-5602	86	17	d,∅,∅	d,∅,∅	PROPN
ejpam-5602	86	18	)	)	PUNCT
ejpam-5602	86	19	is	be	AUX
ejpam-5602	86	20	a	a	DET
ejpam-5602	86	21	total	total	ADJ
ejpam-5602	86	22	double	double	ADJ
ejpam-5602	86	23	italian	italian	ADJ
ejpam-5602	86	24	dominating	dominating	NOUN
ejpam-5602	86	25	function	function	NOUN
ejpam-5602	86	26	on	on	ADP
ejpam-5602	86	27	g	g	PROPN
ejpam-5602	86	28	,	,	PUNCT
ejpam-5602	86	29	γtdi(g	γtdi(g	PROPN
ejpam-5602	86	30	)	)	PUNCT
ejpam-5602	86	31	≤	≤	NOUN
ejpam-5602	86	32	|d|	|d|	PROPN
ejpam-5602	86	33	=	=	SYM
ejpam-5602	86	34	4	4	NUM
ejpam-5602	86	35	.	.	PUNCT
ejpam-5602	87	1	therefore	therefore	ADV
ejpam-5602	87	2	,	,	PUNCT
ejpam-5602	87	3	γtdi(g	γtdi(g	ADV
ejpam-5602	87	4	)	)	PUNCT
ejpam-5602	87	5	=	=	PUNCT
ejpam-5602	88	1	4	4	X
ejpam-5602	88	2	.	.	X
ejpam-5602	88	3	■	■	PUNCT
ejpam-5602	88	4	in	in	ADP
ejpam-5602	88	5	statement	statement	NOUN
ejpam-5602	88	6	(	(	PUNCT
ejpam-5602	88	7	ii	ii	NOUN
ejpam-5602	88	8	)	)	PUNCT
ejpam-5602	88	9	of	of	ADP
ejpam-5602	88	10	proposition	proposition	NOUN
ejpam-5602	88	11	3	3	NUM
ejpam-5602	88	12	,	,	PUNCT
ejpam-5602	88	13	it	it	PRON
ejpam-5602	88	14	is	be	AUX
ejpam-5602	88	15	not	not	PART
ejpam-5602	88	16	necessary	necessary	ADJ
ejpam-5602	88	17	that	that	SCONJ
ejpam-5602	88	18	γ3(g	γ3(g	NUM
ejpam-5602	88	19	)	)	PUNCT
ejpam-5602	88	20	=	=	SYM
ejpam-5602	88	21	4	4	X
ejpam-5602	88	22	.	.	PUNCT
ejpam-5602	88	23	to	to	PART
ejpam-5602	88	24	see	see	VERB
ejpam-5602	88	25	this	this	PRON
ejpam-5602	88	26	,	,	PUNCT
ejpam-5602	88	27	note	note	VERB
ejpam-5602	88	28	that	that	SCONJ
ejpam-5602	88	29	if	if	SCONJ
ejpam-5602	88	30	g	g	PROPN
ejpam-5602	88	31	=	=	SYM
ejpam-5602	88	32	c4	c4	NOUN
ejpam-5602	88	33	+	+	CCONJ
ejpam-5602	88	34	k3	k3	ADJ
ejpam-5602	88	35	,	,	PUNCT
ejpam-5602	88	36	then	then	ADV
ejpam-5602	88	37	γtdi(g	γtdi(g	ADV
ejpam-5602	88	38	)	)	PUNCT
ejpam-5602	88	39	=	=	SYM
ejpam-5602	88	40	4	4	NUM
ejpam-5602	88	41	while	while	NOUN
ejpam-5602	88	42	γ3(g	γ3(g	NUM
ejpam-5602	88	43	)	)	PUNCT
ejpam-5602	88	44	=	=	SYM
ejpam-5602	89	1	3	3	X
ejpam-5602	89	2	.	.	X
ejpam-5602	89	3	it	it	PRON
ejpam-5602	89	4	can	can	AUX
ejpam-5602	89	5	be	be	AUX
ejpam-5602	89	6	verified	verify	VERB
ejpam-5602	89	7	that	that	SCONJ
ejpam-5602	89	8	if	if	SCONJ
ejpam-5602	89	9	g	g	PROPN
ejpam-5602	89	10	is	be	AUX
ejpam-5602	89	11	connected	connect	VERB
ejpam-5602	89	12	of	of	ADP
ejpam-5602	89	13	order	order	NOUN
ejpam-5602	89	14	n	n	NOUN
ejpam-5602	89	15	=	=	SYM
ejpam-5602	89	16	4	4	NUM
ejpam-5602	89	17	,	,	PUNCT
ejpam-5602	89	18	then	then	ADV
ejpam-5602	89	19	γtdi(g	γtdi(g	PROPN
ejpam-5602	89	20	)	)	PUNCT
ejpam-5602	89	21	̸=	̸=	PROPN
ejpam-5602	89	22	5	5	NUM
ejpam-5602	89	23	.	.	PUNCT
ejpam-5602	90	1	proposition	proposition	NOUN
ejpam-5602	90	2	4	4	NUM
ejpam-5602	90	3	.	.	PUNCT
ejpam-5602	91	1	let	let	VERB
ejpam-5602	91	2	g	g	PRON
ejpam-5602	91	3	be	be	AUX
ejpam-5602	91	4	a	a	DET
ejpam-5602	91	5	nontrivial	nontrivial	ADJ
ejpam-5602	91	6	connected	connect	VERB
ejpam-5602	91	7	graph	graph	NOUN
ejpam-5602	91	8	of	of	ADP
ejpam-5602	91	9	order	order	NOUN
ejpam-5602	91	10	n	n	PRON
ejpam-5602	91	11	≥	≥	NUM
ejpam-5602	91	12	5	5	NUM
ejpam-5602	91	13	.	.	PUNCT
ejpam-5602	92	1	then	then	ADV
ejpam-5602	92	2	γtdi(g	γtdi(g	PROPN
ejpam-5602	92	3	)	)	PUNCT
ejpam-5602	92	4	=	=	SYM
ejpam-5602	92	5	5	5	NUM
ejpam-5602	92	6	if	if	SCONJ
ejpam-5602	92	7	and	and	CCONJ
ejpam-5602	92	8	only	only	ADV
ejpam-5602	92	9	if	if	SCONJ
ejpam-5602	92	10	one	one	NUM
ejpam-5602	92	11	of	of	ADP
ejpam-5602	92	12	the	the	DET
ejpam-5602	92	13	following	follow	VERB
ejpam-5602	92	14	holds	hold	VERB
ejpam-5602	92	15	:	:	PUNCT
ejpam-5602	92	16	(	(	PUNCT
ejpam-5602	92	17	i	i	NOUN
ejpam-5602	92	18	)	)	PUNCT
ejpam-5602	92	19	g	g	PROPN
ejpam-5602	92	20	∈	∈	PROPN
ejpam-5602	92	21	{	{	PUNCT
ejpam-5602	92	22	c5,k2,3,k3	c5,k2,3,k3	NOUN
ejpam-5602	92	23	⊔k2	⊔k2	ADP
ejpam-5602	92	24	c4,k2	c4,k2	PROPN
ejpam-5602	92	25	+	+	CCONJ
ejpam-5602	92	26	(	(	PUNCT
ejpam-5602	92	27	k1	k1	PROPN
ejpam-5602	92	28	∪k2	∪k2	X
ejpam-5602	92	29	)	)	PUNCT
ejpam-5602	92	30	}	}	PUNCT
ejpam-5602	92	31	(	(	PUNCT
ejpam-5602	92	32	see	see	VERB
ejpam-5602	92	33	figure	figure	NOUN
ejpam-5602	92	34	1	1	NUM
ejpam-5602	92	35	)	)	PUNCT
ejpam-5602	92	36	;	;	PUNCT
ejpam-5602	92	37	(	(	PUNCT
ejpam-5602	92	38	ii	ii	NOUN
ejpam-5602	92	39	)	)	PUNCT
ejpam-5602	92	40	n	n	CCONJ
ejpam-5602	92	41	>	>	SYM
ejpam-5602	92	42	5	5	NUM
ejpam-5602	92	43	,	,	PUNCT
ejpam-5602	92	44	γ(g	γ(g	PROPN
ejpam-5602	92	45	)	)	PUNCT
ejpam-5602	92	46	≥	≥	NOUN
ejpam-5602	92	47	2	2	NUM
ejpam-5602	92	48	,	,	PUNCT
ejpam-5602	92	49	g	g	PROPN
ejpam-5602	92	50	does	do	AUX
ejpam-5602	92	51	not	not	PART
ejpam-5602	92	52	contain	contain	VERB
ejpam-5602	92	53	a	a	DET
ejpam-5602	92	54	3	3	NUM
ejpam-5602	92	55	-	-	PUNCT
ejpam-5602	92	56	dominating	dominating	NOUN
ejpam-5602	92	57	set	set	NOUN
ejpam-5602	92	58	d	d	NOUN
ejpam-5602	92	59	with	with	ADP
ejpam-5602	92	60	|d|	|d|	PROPN
ejpam-5602	92	61	=	=	SYM
ejpam-5602	92	62	4	4	NUM
ejpam-5602	92	63	and	and	CCONJ
ejpam-5602	92	64	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	92	65	)	)	PUNCT
ejpam-5602	92	66	≥	≥	NOUN
ejpam-5602	92	67	2	2	NUM
ejpam-5602	92	68	,	,	PUNCT
ejpam-5602	92	69	and	and	CCONJ
ejpam-5602	92	70	one	one	NUM
ejpam-5602	92	71	of	of	ADP
ejpam-5602	92	72	the	the	DET
ejpam-5602	92	73	following	following	NOUN
ejpam-5602	92	74	holds	hold	VERB
ejpam-5602	92	75	:	:	PUNCT
ejpam-5602	92	76	(	(	PUNCT
ejpam-5602	92	77	a	a	X
ejpam-5602	92	78	)	)	PUNCT
ejpam-5602	92	79	g	g	NOUN
ejpam-5602	92	80	contains	contain	VERB
ejpam-5602	92	81	a	a	DET
ejpam-5602	92	82	3	3	NUM
ejpam-5602	92	83	-	-	PUNCT
ejpam-5602	92	84	dominating	dominating	NOUN
ejpam-5602	92	85	set	set	NOUN
ejpam-5602	92	86	d	d	NOUN
ejpam-5602	92	87	with	with	ADP
ejpam-5602	92	88	|d|	|d|	PROPN
ejpam-5602	92	89	=	=	SYM
ejpam-5602	92	90	5	5	NUM
ejpam-5602	92	91	and	and	CCONJ
ejpam-5602	92	92	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	92	93	)	)	PUNCT
ejpam-5602	92	94	≥	≥	NOUN
ejpam-5602	92	95	2	2	NUM
ejpam-5602	92	96	;	;	PUNCT
ejpam-5602	92	97	(	(	PUNCT
ejpam-5602	92	98	b	b	X
ejpam-5602	92	99	)	)	PUNCT
ejpam-5602	92	100	g	g	NOUN
ejpam-5602	92	101	contains	contain	VERB
ejpam-5602	92	102	a	a	DET
ejpam-5602	92	103	2	2	NUM
ejpam-5602	92	104	-	-	PUNCT
ejpam-5602	92	105	dominating	dominating	NOUN
ejpam-5602	92	106	set	set	NOUN
ejpam-5602	92	107	d	d	NOUN
ejpam-5602	92	108	with	with	ADP
ejpam-5602	92	109	|d|	|d|	PROPN
ejpam-5602	92	110	=	=	SYM
ejpam-5602	92	111	3	3	NUM
ejpam-5602	92	112	and	and	CCONJ
ejpam-5602	92	113	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	92	114	is	be	AUX
ejpam-5602	92	115	connected	connect	VERB
ejpam-5602	92	116	.	.	PUNCT
ejpam-5602	93	1	(	(	PUNCT
ejpam-5602	93	2	c	c	X
ejpam-5602	93	3	)	)	PUNCT
ejpam-5602	93	4	g	g	NOUN
ejpam-5602	93	5	contains	contain	VERB
ejpam-5602	93	6	a	a	DET
ejpam-5602	93	7	2	2	NUM
ejpam-5602	93	8	-	-	PUNCT
ejpam-5602	93	9	dominating	dominating	NOUN
ejpam-5602	93	10	set	set	NOUN
ejpam-5602	93	11	d	d	NOUN
ejpam-5602	93	12	with	with	ADP
ejpam-5602	93	13	|d|	|d|	PROPN
ejpam-5602	93	14	=	=	PROPN
ejpam-5602	93	15	4	4	NUM
ejpam-5602	93	16	such	such	ADJ
ejpam-5602	93	17	that	that	SCONJ
ejpam-5602	93	18	there	there	PRON
ejpam-5602	93	19	exists	exist	VERB
ejpam-5602	93	20	v	v	ADP
ejpam-5602	93	21	∈	∈	PROPN
ejpam-5602	93	22	d	d	NOUN
ejpam-5602	93	23	for	for	ADP
ejpam-5602	93	24	which	which	PRON
ejpam-5602	93	25	uv	uv	NOUN
ejpam-5602	93	26	∈	∈	PROPN
ejpam-5602	93	27	e(g	e(g	PROPN
ejpam-5602	93	28	)	)	PUNCT
ejpam-5602	93	29	for	for	ADP
ejpam-5602	93	30	all	all	DET
ejpam-5602	93	31	u	u	PROPN
ejpam-5602	93	32	∈	∈	PROPN
ejpam-5602	93	33	v	v	NOUN
ejpam-5602	93	34	(	(	PUNCT
ejpam-5602	93	35	g	g	NOUN
ejpam-5602	93	36	)	)	PUNCT
ejpam-5602	93	37	\d	\d	NOUN
ejpam-5602	93	38	with	with	ADP
ejpam-5602	93	39	|ng(u)∩d|	|ng(u)∩d|	PROPN
ejpam-5602	93	40	=	=	SYM
ejpam-5602	93	41	2	2	X
ejpam-5602	93	42	.	.	PUNCT
ejpam-5602	94	1	moreover	moreover	ADV
ejpam-5602	94	2	,	,	PUNCT
ejpam-5602	94	3	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	94	4	is	be	AUX
ejpam-5602	94	5	connected	connect	VERB
ejpam-5602	94	6	and	and	CCONJ
ejpam-5602	94	7	xv	xv	PROPN
ejpam-5602	94	8	∈	∈	PROPN
ejpam-5602	94	9	e(g	e(g	PROPN
ejpam-5602	94	10	)	)	PUNCT
ejpam-5602	94	11	for	for	ADP
ejpam-5602	94	12	every	every	DET
ejpam-5602	94	13	x	x	SYM
ejpam-5602	94	14	∈	∈	PROPN
ejpam-5602	94	15	d	d	X
ejpam-5602	94	16	\	\	PROPN
ejpam-5602	94	17	{	{	PUNCT
ejpam-5602	94	18	v	v	NOUN
ejpam-5602	94	19	}	}	PUNCT
ejpam-5602	94	20	with	with	ADP
ejpam-5602	94	21	|ng(x	|ng(x	NOUN
ejpam-5602	94	22	)	)	PUNCT
ejpam-5602	94	23	∩d|	∩d|	PUNCT
ejpam-5602	95	1	=	=	PUNCT
ejpam-5602	95	2	1	1	X
ejpam-5602	95	3	.	.	X
ejpam-5602	95	4	proof	proof	NOUN
ejpam-5602	95	5	:	:	PUNCT
ejpam-5602	95	6	suppose	suppose	VERB
ejpam-5602	95	7	that	that	SCONJ
ejpam-5602	95	8	γtdi(g	γtdi(g	PROPN
ejpam-5602	95	9	)	)	PUNCT
ejpam-5602	95	10	=	=	SYM
ejpam-5602	95	11	5	5	X
ejpam-5602	95	12	.	.	PUNCT
ejpam-5602	95	13	by	by	ADP
ejpam-5602	95	14	proposition	proposition	NOUN
ejpam-5602	95	15	1	1	NUM
ejpam-5602	95	16	and	and	CCONJ
ejpam-5602	95	17	proposition	proposition	NOUN
ejpam-5602	95	18	3	3	NUM
ejpam-5602	95	19	,	,	PUNCT
ejpam-5602	95	20	γ(g	γ(g	PROPN
ejpam-5602	95	21	)	)	PUNCT
ejpam-5602	95	22	≥	≥	NOUN
ejpam-5602	95	23	2	2	NUM
ejpam-5602	95	24	and	and	CCONJ
ejpam-5602	95	25	g	g	NOUN
ejpam-5602	95	26	does	do	AUX
ejpam-5602	95	27	not	not	PART
ejpam-5602	95	28	contain	contain	VERB
ejpam-5602	95	29	a	a	DET
ejpam-5602	95	30	3	3	NUM
ejpam-5602	95	31	-	-	PUNCT
ejpam-5602	95	32	dominating	dominating	NOUN
ejpam-5602	95	33	set	set	NOUN
ejpam-5602	95	34	d	d	NOUN
ejpam-5602	95	35	with	with	ADP
ejpam-5602	95	36	|d|	|d|	PROPN
ejpam-5602	95	37	=	=	SYM
ejpam-5602	95	38	4	4	NUM
ejpam-5602	95	39	and	and	CCONJ
ejpam-5602	95	40	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	95	41	)	)	PUNCT
ejpam-5602	95	42	≥	≥	NOUN
ejpam-5602	96	1	2	2	NUM
ejpam-5602	96	2	.	.	PUNCT
ejpam-5602	97	1	if	if	SCONJ
ejpam-5602	97	2	n	n	NOUN
ejpam-5602	97	3	=	=	SYM
ejpam-5602	97	4	5	5	NUM
ejpam-5602	97	5	,	,	PUNCT
ejpam-5602	97	6	then	then	ADV
ejpam-5602	97	7	g	g	PROPN
ejpam-5602	97	8	∈	∈	PROPN
ejpam-5602	97	9	{	{	PUNCT
ejpam-5602	97	10	c5,k2,3,k3⊔k2c4,k2+(k1	c5,k2,3,k3⊔k2c4,k2+(k1	PROPN
ejpam-5602	97	11	∪k2	∪k2	X
ejpam-5602	97	12	)	)	PUNCT
ejpam-5602	97	13	}	}	PUNCT
ejpam-5602	97	14	.	.	PUNCT
ejpam-5602	98	1	assume	assume	VERB
ejpam-5602	98	2	that	that	SCONJ
ejpam-5602	98	3	n	n	X
ejpam-5602	98	4	>	>	X
ejpam-5602	98	5	5	5	X
ejpam-5602	98	6	.	.	PUNCT
ejpam-5602	99	1	let	let	VERB
ejpam-5602	99	2	f	f	PROPN
ejpam-5602	99	3	=	=	SYM
ejpam-5602	99	4	(	(	PUNCT
ejpam-5602	99	5	v0	v0	PROPN
ejpam-5602	99	6	,	,	PUNCT
ejpam-5602	99	7	v1	v1	NOUN
ejpam-5602	99	8	,	,	PUNCT
ejpam-5602	99	9	v2	v2	PROPN
ejpam-5602	99	10	,	,	PUNCT
ejpam-5602	99	11	v3	v3	PROPN
ejpam-5602	99	12	)	)	PUNCT
ejpam-5602	99	13	be	be	VERB
ejpam-5602	99	14	a	a	DET
ejpam-5602	99	15	γtdi	γtdi	PROPN
ejpam-5602	99	16	function	function	NOUN
ejpam-5602	99	17	of	of	ADP
ejpam-5602	99	18	g.	g.	PROPN
ejpam-5602	99	19	by	by	ADP
ejpam-5602	99	20	proposition	proposition	NOUN
ejpam-5602	99	21	1	1	NUM
ejpam-5602	99	22	and	and	CCONJ
ejpam-5602	99	23	proposition	proposition	NOUN
ejpam-5602	99	24	3	3	NUM
ejpam-5602	99	25	,	,	PUNCT
ejpam-5602	99	26	v3	v3	PROPN
ejpam-5602	99	27	=	=	PUNCT
ejpam-5602	99	28	∅.	∅.	AUX
ejpam-5602	99	29	consider	consider	VERB
ejpam-5602	99	30	the	the	DET
ejpam-5602	99	31	following	follow	VERB
ejpam-5602	99	32	cases	case	NOUN
ejpam-5602	99	33	:	:	PUNCT
ejpam-5602	99	34	case	case	NOUN
ejpam-5602	99	35	1	1	NUM
ejpam-5602	99	36	:	:	PUNCT
ejpam-5602	99	37	suppose	suppose	VERB
ejpam-5602	99	38	that	that	SCONJ
ejpam-5602	99	39	|v1|	|v1|	NOUN
ejpam-5602	99	40	=	=	SYM
ejpam-5602	99	41	5	5	NUM
ejpam-5602	99	42	and	and	CCONJ
ejpam-5602	99	43	|v2|	|v2|	NOUN
ejpam-5602	99	44	=	=	SYM
ejpam-5602	99	45	0	0	X
ejpam-5602	99	46	.	.	PUNCT
ejpam-5602	100	1	since	since	SCONJ
ejpam-5602	100	2	n	n	PROPN
ejpam-5602	100	3	>	>	SYM
ejpam-5602	100	4	5	5	NUM
ejpam-5602	100	5	,	,	PUNCT
ejpam-5602	100	6	v0	v0	PROPN
ejpam-5602	100	7	̸=	̸=	PROPN
ejpam-5602	100	8	∅.	∅.	NOUN
ejpam-5602	100	9	then	then	ADV
ejpam-5602	100	10	3	3	NUM
ejpam-5602	100	11	≤	≤	NOUN
ejpam-5602	100	12	|ng(u	|ng(u	NOUN
ejpam-5602	100	13	)	)	PUNCT
ejpam-5602	100	14	∩	∩	NOUN
ejpam-5602	100	15	v1|	v1|	ADJ
ejpam-5602	100	16	≤	≤	ADJ
ejpam-5602	100	17	5	5	NUM
ejpam-5602	100	18	for	for	ADP
ejpam-5602	100	19	every	every	DET
ejpam-5602	100	20	u	u	PROPN
ejpam-5602	100	21	∈	∈	PROPN
ejpam-5602	100	22	v0	v0	NOUN
ejpam-5602	100	23	.	.	PUNCT
ejpam-5602	101	1	hence	hence	ADV
ejpam-5602	101	2	,	,	PUNCT
ejpam-5602	101	3	d	d	PROPN
ejpam-5602	101	4	=	=	SYM
ejpam-5602	101	5	v1	v1	NOUN
ejpam-5602	101	6	is	be	AUX
ejpam-5602	101	7	a	a	DET
ejpam-5602	101	8	3	3	NUM
ejpam-5602	101	9	-	-	PUNCT
ejpam-5602	101	10	dominating	dominating	NOUN
ejpam-5602	101	11	set	set	NOUN
ejpam-5602	101	12	on	on	ADP
ejpam-5602	101	13	g.	g.	PROPN
ejpam-5602	101	14	since	since	SCONJ
ejpam-5602	101	15	|ng(v	|ng(v	NOUN
ejpam-5602	101	16	)	)	PUNCT
ejpam-5602	101	17	∩	∩	NOUN
ejpam-5602	101	18	v1|	v1|	NOUN
ejpam-5602	101	19	≥	≥	NUM
ejpam-5602	101	20	2	2	NUM
ejpam-5602	101	21	for	for	ADP
ejpam-5602	101	22	every	every	DET
ejpam-5602	101	23	v	v	NUM
ejpam-5602	101	24	∈	∈	PROPN
ejpam-5602	101	25	v1	v1	NOUN
ejpam-5602	101	26	,	,	PUNCT
ejpam-5602	101	27	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	101	28	)	)	PUNCT
ejpam-5602	101	29	≥	≥	NOUN
ejpam-5602	101	30	2	2	NUM
ejpam-5602	101	31	and	and	CCONJ
ejpam-5602	101	32	(	(	PUNCT
ejpam-5602	101	33	ii)(a	ii)(a	PROPN
ejpam-5602	101	34	)	)	PUNCT
ejpam-5602	101	35	holds	hold	VERB
ejpam-5602	101	36	.	.	PUNCT
ejpam-5602	102	1	case	case	NOUN
ejpam-5602	102	2	2	2	NUM
ejpam-5602	102	3	:	:	PUNCT
ejpam-5602	102	4	suppose	suppose	VERB
ejpam-5602	102	5	that	that	SCONJ
ejpam-5602	102	6	|v1|	|v1|	NOUN
ejpam-5602	102	7	=	=	SYM
ejpam-5602	102	8	1	1	NUM
ejpam-5602	102	9	and	and	CCONJ
ejpam-5602	102	10	|v2|	|v2|	NOUN
ejpam-5602	102	11	=	=	SYM
ejpam-5602	102	12	2	2	X
ejpam-5602	102	13	.	.	PUNCT
ejpam-5602	102	14	since	since	SCONJ
ejpam-5602	102	15	n	n	PROPN
ejpam-5602	102	16	>	>	SYM
ejpam-5602	102	17	5	5	NUM
ejpam-5602	102	18	,	,	PUNCT
ejpam-5602	102	19	v0	v0	PROPN
ejpam-5602	102	20	̸=	̸=	PROPN
ejpam-5602	102	21	∅.	∅.	VERB
ejpam-5602	102	22	thus	thus	ADV
ejpam-5602	102	23	d	d	NOUN
ejpam-5602	102	24	=	=	SYM
ejpam-5602	102	25	v1	v1	NOUN
ejpam-5602	102	26	∪	∪	NOUN
ejpam-5602	102	27	v2	v2	NOUN
ejpam-5602	102	28	is	be	AUX
ejpam-5602	102	29	a	a	DET
ejpam-5602	102	30	2	2	NUM
ejpam-5602	102	31	-	-	PUNCT
ejpam-5602	102	32	dominating	dominating	NOUN
ejpam-5602	102	33	set	set	NOUN
ejpam-5602	102	34	of	of	ADP
ejpam-5602	102	35	g.	g.	PROPN
ejpam-5602	102	36	moreover	moreover	ADV
ejpam-5602	102	37	,	,	PUNCT
ejpam-5602	102	38	since	since	SCONJ
ejpam-5602	102	39	f	f	PROPN
ejpam-5602	102	40	∈	∈	PROPN
ejpam-5602	102	41	tidf	tidf	PROPN
ejpam-5602	102	42	(	(	PUNCT
ejpam-5602	102	43	g	g	NOUN
ejpam-5602	102	44	)	)	PUNCT
ejpam-5602	102	45	,	,	PUNCT
ejpam-5602	102	46	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	102	47	is	be	AUX
ejpam-5602	102	48	connected	connect	VERB
ejpam-5602	102	49	.	.	PUNCT
ejpam-5602	103	1	therefore	therefore	ADV
ejpam-5602	103	2	,	,	PUNCT
ejpam-5602	103	3	(	(	PUNCT
ejpam-5602	103	4	ii)(b	ii)(b	ADJ
ejpam-5602	103	5	)	)	PUNCT
ejpam-5602	103	6	holds	hold	VERB
ejpam-5602	103	7	.	.	PUNCT
ejpam-5602	104	1	s.j.l	s.j.l	PROPN
ejpam-5602	104	2	.	.	PUNCT
ejpam-5602	104	3	sumbalan	sumbalan	PROPN
ejpam-5602	104	4	,	,	PUNCT
ejpam-5602	104	5	s.m	s.m	PROPN
ejpam-5602	104	6	.	.	PROPN
ejpam-5602	104	7	menchavez	menchavez	PROPN
ejpam-5602	104	8	,	,	PUNCT
ejpam-5602	104	9	f.p	f.p	PROPN
ejpam-5602	104	10	.	.	PROPN
ejpam-5602	104	11	jamil	jamil	PROPN
ejpam-5602	104	12	/	/	SYM
ejpam-5602	104	13	eur	eur	PROPN
ejpam-5602	104	14	.	.	PUNCT
ejpam-5602	105	1	j.	j.	PROPN
ejpam-5602	105	2	pure	pure	PROPN
ejpam-5602	105	3	appl	appl	PROPN
ejpam-5602	105	4	.	.	PROPN
ejpam-5602	105	5	math	math	PROPN
ejpam-5602	105	6	,	,	PUNCT
ejpam-5602	105	7	18	18	NUM
ejpam-5602	105	8	(	(	PUNCT
ejpam-5602	105	9	1	1	NUM
ejpam-5602	105	10	)	)	PUNCT
ejpam-5602	105	11	(	(	PUNCT
ejpam-5602	105	12	2025	2025	NUM
ejpam-5602	105	13	)	)	PUNCT
ejpam-5602	105	14	,	,	PUNCT
ejpam-5602	105	15	5602	5602	NUM
ejpam-5602	105	16	5	5	NUM
ejpam-5602	105	17	of	of	ADP
ejpam-5602	105	18	18	18	NUM
ejpam-5602	105	19	case	case	NOUN
ejpam-5602	105	20	3	3	NUM
ejpam-5602	105	21	:	:	PUNCT
ejpam-5602	105	22	suppose	suppose	VERB
ejpam-5602	105	23	that	that	SCONJ
ejpam-5602	105	24	|v1|	|v1|	NOUN
ejpam-5602	105	25	=	=	SYM
ejpam-5602	105	26	3	3	NUM
ejpam-5602	105	27	and	and	CCONJ
ejpam-5602	105	28	|v2|	|v2|	NOUN
ejpam-5602	105	29	=	=	NOUN
ejpam-5602	105	30	1	1	X
ejpam-5602	105	31	.	.	PUNCT
ejpam-5602	105	32	put	put	VERB
ejpam-5602	105	33	v2	v2	NOUN
ejpam-5602	105	34	=	=	PUNCT
ejpam-5602	105	35	{	{	PUNCT
ejpam-5602	105	36	v	v	NOUN
ejpam-5602	105	37	}	}	PUNCT
ejpam-5602	105	38	.	.	PUNCT
ejpam-5602	106	1	then	then	ADV
ejpam-5602	106	2	for	for	ADP
ejpam-5602	106	3	each	each	DET
ejpam-5602	106	4	u	u	PROPN
ejpam-5602	106	5	∈	∈	PROPN
ejpam-5602	106	6	v0	v0	NOUN
ejpam-5602	106	7	,	,	PUNCT
ejpam-5602	106	8	either	either	CCONJ
ejpam-5602	106	9	|n(u	|n(u	PROPN
ejpam-5602	106	10	)	)	PUNCT
ejpam-5602	106	11	∩	∩	ADJ
ejpam-5602	106	12	v1|	v1|	NOUN
ejpam-5602	106	13	=	=	SYM
ejpam-5602	106	14	3	3	NUM
ejpam-5602	106	15	or	or	CCONJ
ejpam-5602	106	16	1	1	NUM
ejpam-5602	106	17	≤	≤	PROPN
ejpam-5602	106	18	|n(u	|n(u	PROPN
ejpam-5602	106	19	)	)	PUNCT
ejpam-5602	106	20	∩	∩	PROPN
ejpam-5602	106	21	v1|	v1|	ADJ
ejpam-5602	106	22	≤	≤	ADJ
ejpam-5602	106	23	2	2	NUM
ejpam-5602	106	24	and	and	CCONJ
ejpam-5602	106	25	uv	uv	NOUN
ejpam-5602	106	26	∈	∈	PROPN
ejpam-5602	106	27	e(g	e(g	PROPN
ejpam-5602	106	28	)	)	PUNCT
ejpam-5602	106	29	.	.	PUNCT
ejpam-5602	107	1	hence	hence	ADV
ejpam-5602	107	2	,	,	PUNCT
ejpam-5602	107	3	|n(u	|n(u	PROPN
ejpam-5602	107	4	)	)	PUNCT
ejpam-5602	107	5	∩	∩	NOUN
ejpam-5602	107	6	(	(	PUNCT
ejpam-5602	107	7	v1	v1	PROPN
ejpam-5602	107	8	∪	∪	ADJ
ejpam-5602	107	9	v2)|	v2)|	PROPN
ejpam-5602	107	10	≥	≥	NUM
ejpam-5602	107	11	2	2	NUM
ejpam-5602	107	12	.	.	PUNCT
ejpam-5602	108	1	thus	thus	ADV
ejpam-5602	108	2	,	,	PUNCT
ejpam-5602	108	3	d	d	X
ejpam-5602	108	4	=	=	SYM
ejpam-5602	108	5	v1	v1	NOUN
ejpam-5602	108	6	∪	∪	NOUN
ejpam-5602	108	7	v2	v2	NOUN
ejpam-5602	108	8	is	be	AUX
ejpam-5602	108	9	a	a	DET
ejpam-5602	108	10	2	2	NUM
ejpam-5602	108	11	-	-	PUNCT
ejpam-5602	108	12	dominating	dominating	NOUN
ejpam-5602	108	13	set	set	NOUN
ejpam-5602	108	14	of	of	ADP
ejpam-5602	108	15	g.	g.	PROPN
ejpam-5602	108	16	observe	observe	VERB
ejpam-5602	108	17	that	that	SCONJ
ejpam-5602	108	18	,	,	PUNCT
ejpam-5602	108	19	if	if	SCONJ
ejpam-5602	108	20	|n(u	|n(u	NOUN
ejpam-5602	108	21	)	)	PUNCT
ejpam-5602	108	22	∩	∩	NOUN
ejpam-5602	108	23	(	(	PUNCT
ejpam-5602	108	24	v1	v1	NOUN
ejpam-5602	108	25	∪	∪	ADJ
ejpam-5602	108	26	v2)|	v2)|	PROPN
ejpam-5602	108	27	=	=	SYM
ejpam-5602	108	28	2	2	NUM
ejpam-5602	108	29	,	,	PUNCT
ejpam-5602	108	30	then	then	ADV
ejpam-5602	108	31	uv	uv	PROPN
ejpam-5602	108	32	∈	∈	PROPN
ejpam-5602	108	33	e(g	e(g	PROPN
ejpam-5602	108	34	)	)	PUNCT
ejpam-5602	108	35	.	.	PUNCT
ejpam-5602	109	1	by	by	ADP
ejpam-5602	109	2	the	the	DET
ejpam-5602	109	3	definition	definition	NOUN
ejpam-5602	109	4	of	of	ADP
ejpam-5602	109	5	f	f	PROPN
ejpam-5602	109	6	,	,	PUNCT
ejpam-5602	109	7	⟨v1	⟨v1	PROPN
ejpam-5602	109	8	∪	∪	ADP
ejpam-5602	109	9	v2⟩	v2⟩	PROPN
ejpam-5602	109	10	has	have	VERB
ejpam-5602	109	11	no	no	DET
ejpam-5602	109	12	isolated	isolated	ADJ
ejpam-5602	109	13	vertex	vertex	NOUN
ejpam-5602	109	14	.	.	PUNCT
ejpam-5602	110	1	if	if	SCONJ
ejpam-5602	110	2	u′	u′	PROPN
ejpam-5602	110	3	∈	∈	NOUN
ejpam-5602	110	4	v1	v1	NOUN
ejpam-5602	110	5	such	such	ADJ
ejpam-5602	110	6	that	that	PRON
ejpam-5602	110	7	d⟨s⟩(u	d⟨s⟩(u	PROPN
ejpam-5602	110	8	′	′	NOUN
ejpam-5602	110	9	)	)	PUNCT
ejpam-5602	110	10	=	=	SYM
ejpam-5602	110	11	1	1	NUM
ejpam-5602	110	12	,	,	PUNCT
ejpam-5602	110	13	then	then	ADV
ejpam-5602	110	14	u′v	u′v	PROPN
ejpam-5602	110	15	∈	∈	PROPN
ejpam-5602	110	16	e(g	e(g	PROPN
ejpam-5602	110	17	)	)	PUNCT
ejpam-5602	110	18	.	.	PUNCT
ejpam-5602	111	1	thus	thus	ADV
ejpam-5602	111	2	,	,	PUNCT
ejpam-5602	111	3	(	(	PUNCT
ejpam-5602	111	4	ii)(c	ii)(c	PROPN
ejpam-5602	111	5	)	)	PUNCT
ejpam-5602	111	6	holds	hold	VERB
ejpam-5602	111	7	.	.	PUNCT
ejpam-5602	112	1	conversely	conversely	ADV
ejpam-5602	112	2	,	,	PUNCT
ejpam-5602	112	3	if	if	SCONJ
ejpam-5602	112	4	g	g	PROPN
ejpam-5602	112	5	∈	∈	PROPN
ejpam-5602	112	6	{	{	PUNCT
ejpam-5602	112	7	c5,k2,3,k3	c5,k2,3,k3	NOUN
ejpam-5602	112	8	⊔k2	⊔k2	ADP
ejpam-5602	112	9	c4,k2	c4,k2	PROPN
ejpam-5602	112	10	+	+	CCONJ
ejpam-5602	112	11	(	(	PUNCT
ejpam-5602	112	12	k1	k1	PROPN
ejpam-5602	112	13	∪k2	∪k2	X
ejpam-5602	112	14	)	)	PUNCT
ejpam-5602	112	15	}	}	PUNCT
ejpam-5602	112	16	,	,	PUNCT
ejpam-5602	112	17	then	then	ADV
ejpam-5602	112	18	γtdi(g	γtdi(g	ADV
ejpam-5602	112	19	)	)	PUNCT
ejpam-5602	112	20	=	=	SYM
ejpam-5602	113	1	5	5	X
ejpam-5602	113	2	.	.	PUNCT
ejpam-5602	113	3	now	now	ADV
ejpam-5602	113	4	,	,	PUNCT
ejpam-5602	113	5	suppose	suppose	VERB
ejpam-5602	113	6	that	that	SCONJ
ejpam-5602	113	7	n	n	PROPN
ejpam-5602	113	8	>	>	X
ejpam-5602	113	9	5	5	NUM
ejpam-5602	113	10	,	,	PUNCT
ejpam-5602	113	11	γ(g	γ(g	PROPN
ejpam-5602	113	12	)	)	PUNCT
ejpam-5602	113	13	≥	≥	NOUN
ejpam-5602	113	14	2	2	NUM
ejpam-5602	113	15	,	,	PUNCT
ejpam-5602	113	16	g	g	PROPN
ejpam-5602	113	17	does	do	AUX
ejpam-5602	113	18	not	not	PART
ejpam-5602	113	19	contain	contain	VERB
ejpam-5602	113	20	a	a	DET
ejpam-5602	113	21	3	3	NUM
ejpam-5602	113	22	-	-	PUNCT
ejpam-5602	113	23	dominating	dominate	VERB
ejpam-5602	113	24	set	set	NOUN
ejpam-5602	113	25	d	d	NOUN
ejpam-5602	113	26	for	for	ADP
ejpam-5602	113	27	which	which	PRON
ejpam-5602	113	28	|d|	|d|	PROPN
ejpam-5602	113	29	=	=	SYM
ejpam-5602	113	30	4	4	NUM
ejpam-5602	113	31	and	and	CCONJ
ejpam-5602	113	32	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	113	33	)	)	PUNCT
ejpam-5602	113	34	≥	≥	NOUN
ejpam-5602	114	1	2	2	NUM
ejpam-5602	114	2	.	.	PUNCT
ejpam-5602	114	3	then	then	ADV
ejpam-5602	114	4	by	by	ADP
ejpam-5602	114	5	proposition	proposition	NOUN
ejpam-5602	114	6	3	3	NUM
ejpam-5602	114	7	,	,	PUNCT
ejpam-5602	114	8	γtdi(g	γtdi(g	PROPN
ejpam-5602	114	9	)	)	PUNCT
ejpam-5602	114	10	≥	≥	NOUN
ejpam-5602	114	11	5	5	NUM
ejpam-5602	114	12	.	.	PUNCT
ejpam-5602	114	13	assume	assume	VERB
ejpam-5602	114	14	that	that	SCONJ
ejpam-5602	114	15	(	(	PUNCT
ejpam-5602	114	16	ii)(a	ii)(a	NOUN
ejpam-5602	114	17	)	)	PUNCT
ejpam-5602	114	18	holds	hold	VERB
ejpam-5602	114	19	.	.	PUNCT
ejpam-5602	115	1	let	let	VERB
ejpam-5602	115	2	v0	v0	NOUN
ejpam-5602	115	3	=	=	SYM
ejpam-5602	115	4	v	v	PROPN
ejpam-5602	115	5	(	(	PUNCT
ejpam-5602	115	6	g	g	NOUN
ejpam-5602	115	7	)	)	PUNCT
ejpam-5602	115	8	\	\	PUNCT
ejpam-5602	116	1	d	d	X
ejpam-5602	116	2	,	,	PUNCT
ejpam-5602	116	3	v1	v1	NOUN
ejpam-5602	116	4	=	=	SYM
ejpam-5602	116	5	d	d	PROPN
ejpam-5602	116	6	,	,	PUNCT
ejpam-5602	116	7	v2	v2	NOUN
ejpam-5602	116	8	=	=	SYM
ejpam-5602	116	9	∅	∅	NOUN
ejpam-5602	116	10	,	,	PUNCT
ejpam-5602	116	11	and	and	CCONJ
ejpam-5602	116	12	v3	v3	PROPN
ejpam-5602	116	13	=	=	PUNCT
ejpam-5602	116	14	∅.	∅.	PROPN
ejpam-5602	116	15	then	then	ADV
ejpam-5602	116	16	f	f	PROPN
ejpam-5602	116	17	=	=	SYM
ejpam-5602	116	18	(	(	PUNCT
ejpam-5602	116	19	v0	v0	PROPN
ejpam-5602	116	20	,	,	PUNCT
ejpam-5602	116	21	v1	v1	NOUN
ejpam-5602	116	22	,	,	PUNCT
ejpam-5602	116	23	v2	v2	PROPN
ejpam-5602	116	24	,	,	PUNCT
ejpam-5602	116	25	v3	v3	PROPN
ejpam-5602	116	26	)	)	PUNCT
ejpam-5602	116	27	is	be	AUX
ejpam-5602	116	28	a	a	DET
ejpam-5602	116	29	tdidf	tdidf	NOUN
ejpam-5602	116	30	on	on	ADP
ejpam-5602	116	31	g	g	NOUN
ejpam-5602	116	32	with	with	ADP
ejpam-5602	116	33	ωg(f	ωg(f	NOUN
ejpam-5602	116	34	)	)	PUNCT
ejpam-5602	116	35	=	=	SYM
ejpam-5602	116	36	5	5	X
ejpam-5602	116	37	.	.	PUNCT
ejpam-5602	117	1	this	this	PRON
ejpam-5602	117	2	means	mean	VERB
ejpam-5602	117	3	that	that	SCONJ
ejpam-5602	117	4	γtdi(g	γtdi(g	NOUN
ejpam-5602	117	5	)	)	PUNCT
ejpam-5602	117	6	=	=	SYM
ejpam-5602	117	7	5	5	X
ejpam-5602	117	8	.	.	X
ejpam-5602	117	9	assume	assume	VERB
ejpam-5602	117	10	(	(	PUNCT
ejpam-5602	117	11	ii)(b	ii)(b	ADJ
ejpam-5602	117	12	)	)	PUNCT
ejpam-5602	117	13	holds	hold	VERB
ejpam-5602	117	14	.	.	PUNCT
ejpam-5602	118	1	take	take	VERB
ejpam-5602	118	2	x	x	SYM
ejpam-5602	118	3	∈	∈	PROPN
ejpam-5602	118	4	d.	d.	NOUN
ejpam-5602	118	5	let	let	VERB
ejpam-5602	118	6	v0	v0	PROPN
ejpam-5602	118	7	=	=	SYM
ejpam-5602	118	8	v	v	PROPN
ejpam-5602	118	9	(	(	PUNCT
ejpam-5602	118	10	g	g	NOUN
ejpam-5602	118	11	)	)	PUNCT
ejpam-5602	118	12	\d	\d	NOUN
ejpam-5602	118	13	,	,	PUNCT
ejpam-5602	118	14	v1	v1	NOUN
ejpam-5602	118	15	=	=	SYM
ejpam-5602	118	16	{	{	PUNCT
ejpam-5602	118	17	x	x	NOUN
ejpam-5602	118	18	}	}	PUNCT
ejpam-5602	118	19	,	,	PUNCT
ejpam-5602	118	20	v2	v2	PROPN
ejpam-5602	118	21	=	=	SYM
ejpam-5602	118	22	d	d	NOUN
ejpam-5602	118	23	\	\	X
ejpam-5602	118	24	{	{	PUNCT
ejpam-5602	118	25	x	x	NOUN
ejpam-5602	118	26	}	}	PUNCT
ejpam-5602	118	27	,	,	PUNCT
ejpam-5602	118	28	and	and	CCONJ
ejpam-5602	118	29	v3	v3	PROPN
ejpam-5602	118	30	=	=	PUNCT
ejpam-5602	118	31	∅.	∅.	PROPN
ejpam-5602	118	32	then	then	ADV
ejpam-5602	118	33	f	f	PROPN
ejpam-5602	118	34	=	=	SYM
ejpam-5602	118	35	(	(	PUNCT
ejpam-5602	118	36	v0	v0	PROPN
ejpam-5602	118	37	,	,	PUNCT
ejpam-5602	118	38	v1	v1	NOUN
ejpam-5602	118	39	,	,	PUNCT
ejpam-5602	118	40	v2	v2	PROPN
ejpam-5602	118	41	,	,	PUNCT
ejpam-5602	118	42	v3	v3	PROPN
ejpam-5602	118	43	)	)	PUNCT
ejpam-5602	118	44	is	be	AUX
ejpam-5602	118	45	a	a	DET
ejpam-5602	118	46	tdidf	tdidf	NOUN
ejpam-5602	118	47	on	on	ADP
ejpam-5602	118	48	g	g	NOUN
ejpam-5602	118	49	with	with	ADP
ejpam-5602	118	50	ωg(f	ωg(f	NOUN
ejpam-5602	118	51	)	)	PUNCT
ejpam-5602	118	52	=	=	SYM
ejpam-5602	119	1	5	5	X
ejpam-5602	119	2	.	.	X
ejpam-5602	120	1	hence	hence	ADV
ejpam-5602	120	2	,	,	PUNCT
ejpam-5602	120	3	γtdi(g	γtdi(g	ADV
ejpam-5602	120	4	)	)	PUNCT
ejpam-5602	120	5	=	=	SYM
ejpam-5602	121	1	5	5	X
ejpam-5602	121	2	.	.	X
ejpam-5602	121	3	assume	assume	VERB
ejpam-5602	121	4	(	(	PUNCT
ejpam-5602	121	5	ii)(c	ii)(c	PROPN
ejpam-5602	121	6	)	)	PUNCT
ejpam-5602	121	7	holds	hold	VERB
ejpam-5602	121	8	.	.	PUNCT
ejpam-5602	122	1	let	let	VERB
ejpam-5602	122	2	v	v	X
ejpam-5602	122	3	∈	∈	PROPN
ejpam-5602	122	4	d.	d.	NOUN
ejpam-5602	122	5	then	then	ADV
ejpam-5602	122	6	f	f	PROPN
ejpam-5602	122	7	=	=	SYM
ejpam-5602	122	8	(	(	PUNCT
ejpam-5602	122	9	v0	v0	PROPN
ejpam-5602	122	10	,	,	PUNCT
ejpam-5602	122	11	v1	v1	NOUN
ejpam-5602	122	12	,	,	PUNCT
ejpam-5602	122	13	v2	v2	PROPN
ejpam-5602	122	14	,	,	PUNCT
ejpam-5602	122	15	v3	v3	PROPN
ejpam-5602	122	16	)	)	PUNCT
ejpam-5602	122	17	where	where	SCONJ
ejpam-5602	122	18	v0	v0	NOUN
ejpam-5602	122	19	=	=	SYM
ejpam-5602	122	20	v	v	PROPN
ejpam-5602	122	21	(	(	PUNCT
ejpam-5602	122	22	g	g	NOUN
ejpam-5602	122	23	)	)	PUNCT
ejpam-5602	122	24	\d	\d	NOUN
ejpam-5602	122	25	,	,	PUNCT
ejpam-5602	122	26	v1	v1	NOUN
ejpam-5602	122	27	=	=	SYM
ejpam-5602	122	28	d	d	SYM
ejpam-5602	122	29	\	\	PROPN
ejpam-5602	122	30	{	{	PUNCT
ejpam-5602	122	31	v	v	NOUN
ejpam-5602	122	32	}	}	PUNCT
ejpam-5602	122	33	,	,	PUNCT
ejpam-5602	122	34	v2	v2	PROPN
ejpam-5602	122	35	=	=	SYM
ejpam-5602	122	36	{	{	PUNCT
ejpam-5602	122	37	v	v	NOUN
ejpam-5602	122	38	}	}	PUNCT
ejpam-5602	122	39	,	,	PUNCT
ejpam-5602	122	40	and	and	CCONJ
ejpam-5602	122	41	v3	v3	PROPN
ejpam-5602	122	42	=	=	PUNCT
ejpam-5602	122	43	∅	∅	NOUN
ejpam-5602	122	44	is	be	AUX
ejpam-5602	122	45	a	a	DET
ejpam-5602	122	46	tdidf	tdidf	NOUN
ejpam-5602	122	47	on	on	ADP
ejpam-5602	122	48	g	g	NOUN
ejpam-5602	122	49	with	with	ADP
ejpam-5602	122	50	ωg(f	ωg(f	NOUN
ejpam-5602	122	51	)	)	PUNCT
ejpam-5602	123	1	=	=	SYM
ejpam-5602	123	2	5	5	X
ejpam-5602	123	3	.	.	PUNCT
ejpam-5602	123	4	thus	thus	ADV
ejpam-5602	123	5	,	,	PUNCT
ejpam-5602	123	6	γtdi(g	γtdi(g	ADV
ejpam-5602	123	7	)	)	PUNCT
ejpam-5602	123	8	=	=	SYM
ejpam-5602	123	9	5	5	X
ejpam-5602	123	10	.	.	X
ejpam-5602	123	11	■	■	PUNCT
ejpam-5602	123	12	c4	c4	VERB
ejpam-5602	123	13	⊔p3	⊔p3	NUM
ejpam-5602	123	14	c4	c4	NOUN
ejpam-5602	123	15	=	=	SYM
ejpam-5602	123	16	k3,2	k3,2	NOUN
ejpam-5602	123	17	k3	k3	VERB
ejpam-5602	123	18	⊔k2	⊔k2	ADP
ejpam-5602	123	19	c4	c4	NOUN
ejpam-5602	123	20	k2	k2	PROPN
ejpam-5602	123	21	+	+	CCONJ
ejpam-5602	123	22	(	(	PUNCT
ejpam-5602	123	23	k1	k1	PROPN
ejpam-5602	123	24	∪k2	∪k2	X
ejpam-5602	123	25	)	)	PUNCT
ejpam-5602	123	26	figure	figure	NOUN
ejpam-5602	123	27	1	1	NUM
ejpam-5602	123	28	:	:	PUNCT
ejpam-5602	123	29	examples	example	NOUN
ejpam-5602	123	30	of	of	ADP
ejpam-5602	123	31	graphs	graph	NOUN
ejpam-5602	123	32	g	g	NOUN
ejpam-5602	123	33	with	with	ADP
ejpam-5602	123	34	γtdi(g	γtdi(g	PROPN
ejpam-5602	123	35	)	)	PUNCT
ejpam-5602	123	36	=	=	PUNCT
ejpam-5602	123	37	5	5	NUM
ejpam-5602	123	38	3	3	NUM
ejpam-5602	123	39	.	.	PUNCT
ejpam-5602	124	1	on	on	ADP
ejpam-5602	124	2	the	the	DET
ejpam-5602	124	3	join	join	NOUN
ejpam-5602	124	4	of	of	ADP
ejpam-5602	124	5	graphs	graph	NOUN
ejpam-5602	124	6	in	in	ADP
ejpam-5602	124	7	this	this	DET
ejpam-5602	124	8	section	section	NOUN
ejpam-5602	124	9	,	,	PUNCT
ejpam-5602	124	10	we	we	PRON
ejpam-5602	124	11	denote	denote	VERB
ejpam-5602	124	12	by	by	ADP
ejpam-5602	124	13	f	f	PROPN
ejpam-5602	124	14	|g	|g	VERB
ejpam-5602	124	15	the	the	DET
ejpam-5602	124	16	restriction	restriction	NOUN
ejpam-5602	124	17	of	of	ADP
ejpam-5602	124	18	the	the	DET
ejpam-5602	124	19	function	function	NOUN
ejpam-5602	124	20	f	f	PROPN
ejpam-5602	124	21	on	on	ADP
ejpam-5602	124	22	the	the	DET
ejpam-5602	124	23	subgraph	subgraph	NOUN
ejpam-5602	124	24	g	g	NOUN
ejpam-5602	124	25	of	of	ADP
ejpam-5602	124	26	a	a	DET
ejpam-5602	124	27	graph	graph	NOUN
ejpam-5602	124	28	h.	h.	NOUN
ejpam-5602	124	29	the	the	DET
ejpam-5602	124	30	following	follow	VERB
ejpam-5602	124	31	proposition	proposition	NOUN
ejpam-5602	124	32	characterizes	characterize	VERB
ejpam-5602	124	33	all	all	DET
ejpam-5602	124	34	tdidf	tdidf	NOUN
ejpam-5602	124	35	on	on	ADP
ejpam-5602	124	36	the	the	DET
ejpam-5602	124	37	join	join	NOUN
ejpam-5602	124	38	of	of	ADP
ejpam-5602	124	39	two	two	NUM
ejpam-5602	124	40	nontrivial	nontrivial	ADJ
ejpam-5602	124	41	connected	connect	VERB
ejpam-5602	124	42	graphs	graph	NOUN
ejpam-5602	124	43	.	.	PUNCT
ejpam-5602	125	1	proposition	proposition	NOUN
ejpam-5602	125	2	5	5	NUM
ejpam-5602	125	3	.	.	PUNCT
ejpam-5602	126	1	let	let	VERB
ejpam-5602	126	2	g	g	NOUN
ejpam-5602	126	3	and	and	CCONJ
ejpam-5602	126	4	h	h	NOUN
ejpam-5602	126	5	be	be	AUX
ejpam-5602	126	6	nontrivial	nontrivial	ADJ
ejpam-5602	126	7	connected	connected	ADJ
ejpam-5602	126	8	graphs	graph	NOUN
ejpam-5602	126	9	.	.	PUNCT
ejpam-5602	127	1	then	then	ADV
ejpam-5602	127	2	f	f	X
ejpam-5602	127	3	=	=	SYM
ejpam-5602	127	4	(	(	PUNCT
ejpam-5602	127	5	v0	v0	PROPN
ejpam-5602	127	6	,	,	PUNCT
ejpam-5602	127	7	v1	v1	NOUN
ejpam-5602	127	8	,	,	PUNCT
ejpam-5602	127	9	v2	v2	PROPN
ejpam-5602	127	10	,	,	PUNCT
ejpam-5602	127	11	v3	v3	PROPN
ejpam-5602	127	12	)	)	PUNCT
ejpam-5602	127	13	is	be	AUX
ejpam-5602	127	14	a	a	DET
ejpam-5602	127	15	tdidf	tdidf	NOUN
ejpam-5602	127	16	on	on	ADP
ejpam-5602	127	17	(	(	PUNCT
ejpam-5602	127	18	g+h	g+h	NOUN
ejpam-5602	127	19	)	)	PUNCT
ejpam-5602	128	1	if	if	SCONJ
ejpam-5602	128	2	and	and	CCONJ
ejpam-5602	128	3	only	only	ADV
ejpam-5602	128	4	if	if	SCONJ
ejpam-5602	128	5	one	one	NUM
ejpam-5602	128	6	of	of	ADP
ejpam-5602	128	7	the	the	DET
ejpam-5602	128	8	following	follow	VERB
ejpam-5602	128	9	holds	hold	VERB
ejpam-5602	128	10	:	:	PUNCT
ejpam-5602	128	11	(	(	PUNCT
ejpam-5602	128	12	i	i	NOUN
ejpam-5602	128	13	)	)	PUNCT
ejpam-5602	128	14	f	f	PROPN
ejpam-5602	128	15	|g	|g	PROPN
ejpam-5602	128	16	∈	∈	PROPN
ejpam-5602	128	17	tdidf	tdidf	NOUN
ejpam-5602	128	18	(	(	PUNCT
ejpam-5602	128	19	g	g	NOUN
ejpam-5602	128	20	)	)	PUNCT
ejpam-5602	128	21	;	;	PUNCT
ejpam-5602	128	22	(	(	PUNCT
ejpam-5602	128	23	ii	ii	X
ejpam-5602	128	24	)	)	PUNCT
ejpam-5602	128	25	f	f	PROPN
ejpam-5602	128	26	|h	|h	PROPN
ejpam-5602	128	27	∈	∈	PROPN
ejpam-5602	128	28	tdidf	tdidf	PROPN
ejpam-5602	128	29	(	(	PUNCT
ejpam-5602	128	30	h	h	NOUN
ejpam-5602	128	31	)	)	PUNCT
ejpam-5602	128	32	;	;	PUNCT
ejpam-5602	128	33	(	(	PUNCT
ejpam-5602	128	34	iii	iii	X
ejpam-5602	128	35	)	)	PUNCT
ejpam-5602	128	36	f	f	PROPN
ejpam-5602	128	37	|g	|g	PROPN
ejpam-5602	128	38	/∈	/∈	PUNCT
ejpam-5602	128	39	tdidf	tdidf	NOUN
ejpam-5602	128	40	(	(	PUNCT
ejpam-5602	128	41	g	g	NOUN
ejpam-5602	128	42	)	)	PUNCT
ejpam-5602	128	43	,	,	PUNCT
ejpam-5602	128	44	f	f	PROPN
ejpam-5602	128	45	|h	|h	PROPN
ejpam-5602	128	46	/∈	/∈	PUNCT
ejpam-5602	128	47	tdidf	tdidf	PROPN
ejpam-5602	128	48	(	(	PUNCT
ejpam-5602	128	49	h	h	NOUN
ejpam-5602	128	50	)	)	PUNCT
ejpam-5602	128	51	,	,	PUNCT
ejpam-5602	128	52	and	and	CCONJ
ejpam-5602	128	53	each	each	PRON
ejpam-5602	128	54	of	of	ADP
ejpam-5602	128	55	the	the	DET
ejpam-5602	128	56	following	following	NOUN
ejpam-5602	128	57	holds	hold	VERB
ejpam-5602	128	58	:	:	PUNCT
ejpam-5602	128	59	(	(	PUNCT
ejpam-5602	128	60	a	a	X
ejpam-5602	128	61	)	)	PUNCT
ejpam-5602	128	62	for	for	ADP
ejpam-5602	128	63	every	every	DET
ejpam-5602	128	64	v	v	PROPN
ejpam-5602	128	65	∈	∈	PROPN
ejpam-5602	128	66	v0	v0	NOUN
ejpam-5602	128	67	∪	∪	X
ejpam-5602	128	68	v1	v1	PROPN
ejpam-5602	128	69	,	,	PUNCT
ejpam-5602	128	70	(	(	PUNCT
ejpam-5602	128	71	1	1	NUM
ejpam-5602	128	72	)	)	PUNCT
ejpam-5602	128	73	ωh(f	ωh(f	NUM
ejpam-5602	128	74	|h	|h	NOUN
ejpam-5602	128	75	)	)	PUNCT
ejpam-5602	128	76	≥	≥	NOUN
ejpam-5602	128	77	3−	3−	NUM
ejpam-5602	128	78	f	f	X
ejpam-5602	128	79	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	128	80	]	]	X
ejpam-5602	128	81	)	)	PUNCT
ejpam-5602	128	82	,	,	PUNCT
ejpam-5602	128	83	whenever	whenever	SCONJ
ejpam-5602	128	84	v	v	NUM
ejpam-5602	128	85	∈	∈	PROPN
ejpam-5602	128	86	v	v	NOUN
ejpam-5602	128	87	(	(	PUNCT
ejpam-5602	128	88	g	g	NOUN
ejpam-5602	128	89	)	)	PUNCT
ejpam-5602	128	90	and	and	CCONJ
ejpam-5602	128	91	f	f	PROPN
ejpam-5602	128	92	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	128	93	]	]	X
ejpam-5602	128	94	)	)	PUNCT
ejpam-5602	128	95	<	<	X
ejpam-5602	128	96	3	3	NUM
ejpam-5602	128	97	;	;	PUNCT
ejpam-5602	128	98	(	(	PUNCT
ejpam-5602	128	99	2	2	X
ejpam-5602	128	100	)	)	PUNCT
ejpam-5602	128	101	ωg(f	ωg(f	NUM
ejpam-5602	128	102	|g	|g	NOUN
ejpam-5602	128	103	)	)	PUNCT
ejpam-5602	128	104	≥	≥	NOUN
ejpam-5602	128	105	3−	3−	NUM
ejpam-5602	128	106	f	f	X
ejpam-5602	128	107	|h(nh	|h(nh	PROPN
ejpam-5602	129	1	[	[	X
ejpam-5602	129	2	v	v	NOUN
ejpam-5602	129	3	]	]	X
ejpam-5602	129	4	)	)	PUNCT
ejpam-5602	129	5	,	,	PUNCT
ejpam-5602	129	6	whenever	whenever	SCONJ
ejpam-5602	129	7	v	v	NUM
ejpam-5602	129	8	∈	∈	PROPN
ejpam-5602	129	9	v	v	NOUN
ejpam-5602	129	10	(	(	PUNCT
ejpam-5602	129	11	h	h	NOUN
ejpam-5602	129	12	)	)	PUNCT
ejpam-5602	129	13	and	and	CCONJ
ejpam-5602	129	14	f	f	X
ejpam-5602	129	15	|h(nh	|h(nh	PROPN
ejpam-5602	130	1	[	[	X
ejpam-5602	130	2	v	v	NOUN
ejpam-5602	130	3	]	]	X
ejpam-5602	130	4	)	)	PUNCT
ejpam-5602	130	5	<	<	X
ejpam-5602	130	6	3	3	X
ejpam-5602	130	7	.	.	PUNCT
ejpam-5602	130	8	(	(	PUNCT
ejpam-5602	130	9	b	b	NOUN
ejpam-5602	130	10	)	)	PUNCT
ejpam-5602	130	11	for	for	ADP
ejpam-5602	130	12	every	every	DET
ejpam-5602	130	13	v	v	NUM
ejpam-5602	130	14	∈	∈	PROPN
ejpam-5602	130	15	v1	v1	NOUN
ejpam-5602	130	16	∪	∪	NOUN
ejpam-5602	130	17	v2	v2	PROPN
ejpam-5602	130	18	∪	∪	NOUN
ejpam-5602	130	19	v3	v3	PROPN
ejpam-5602	130	20	,	,	PUNCT
ejpam-5602	131	1	s.j.l	s.j.l	NOUN
ejpam-5602	131	2	.	.	PUNCT
ejpam-5602	131	3	sumbalan	sumbalan	PROPN
ejpam-5602	131	4	,	,	PUNCT
ejpam-5602	131	5	s.m	s.m	PROPN
ejpam-5602	131	6	.	.	PROPN
ejpam-5602	131	7	menchavez	menchavez	PROPN
ejpam-5602	131	8	,	,	PUNCT
ejpam-5602	131	9	f.p	f.p	PROPN
ejpam-5602	131	10	.	.	PROPN
ejpam-5602	131	11	jamil	jamil	PROPN
ejpam-5602	131	12	/	/	SYM
ejpam-5602	131	13	eur	eur	PROPN
ejpam-5602	131	14	.	.	PUNCT
ejpam-5602	132	1	j.	j.	PROPN
ejpam-5602	132	2	pure	pure	PROPN
ejpam-5602	132	3	appl	appl	PROPN
ejpam-5602	132	4	.	.	PROPN
ejpam-5602	132	5	math	math	PROPN
ejpam-5602	132	6	,	,	PUNCT
ejpam-5602	132	7	18	18	NUM
ejpam-5602	132	8	(	(	PUNCT
ejpam-5602	132	9	1	1	NUM
ejpam-5602	132	10	)	)	PUNCT
ejpam-5602	132	11	(	(	PUNCT
ejpam-5602	132	12	2025	2025	NUM
ejpam-5602	132	13	)	)	PUNCT
ejpam-5602	132	14	,	,	PUNCT
ejpam-5602	132	15	5602	5602	NUM
ejpam-5602	132	16	6	6	NUM
ejpam-5602	132	17	of	of	ADP
ejpam-5602	132	18	18	18	NUM
ejpam-5602	132	19	(	(	PUNCT
ejpam-5602	132	20	1	1	NUM
ejpam-5602	132	21	)	)	PUNCT
ejpam-5602	132	22	(	(	PUNCT
ejpam-5602	132	23	v1	v1	VERB
ejpam-5602	132	24	∪	∪	ADP
ejpam-5602	132	25	v2	v2	PROPN
ejpam-5602	132	26	∪	∪	X
ejpam-5602	132	27	v3	v3	PROPN
ejpam-5602	132	28	)	)	PUNCT
ejpam-5602	132	29	∩	∩	PROPN
ejpam-5602	132	30	v	v	ADP
ejpam-5602	132	31	(	(	PUNCT
ejpam-5602	132	32	h	h	NOUN
ejpam-5602	132	33	)	)	PUNCT
ejpam-5602	132	34	̸=	̸=	NOUN
ejpam-5602	132	35	∅	∅	NOUN
ejpam-5602	132	36	,	,	PUNCT
ejpam-5602	132	37	whenever	whenever	SCONJ
ejpam-5602	132	38	v	v	NUM
ejpam-5602	132	39	∈	∈	PROPN
ejpam-5602	132	40	v	v	NOUN
ejpam-5602	132	41	(	(	PUNCT
ejpam-5602	132	42	g	g	NOUN
ejpam-5602	132	43	)	)	PUNCT
ejpam-5602	132	44	and	and	CCONJ
ejpam-5602	132	45	ng(v	ng(v	NUM
ejpam-5602	132	46	)	)	PUNCT
ejpam-5602	132	47	⊆	⊆	NUM
ejpam-5602	132	48	v0	v0	NOUN
ejpam-5602	132	49	;	;	PUNCT
ejpam-5602	132	50	(	(	PUNCT
ejpam-5602	132	51	2	2	X
ejpam-5602	132	52	)	)	PUNCT
ejpam-5602	132	53	(	(	PUNCT
ejpam-5602	132	54	v1	v1	VERB
ejpam-5602	132	55	∪	∪	ADP
ejpam-5602	132	56	v2	v2	PROPN
ejpam-5602	132	57	∪	∪	X
ejpam-5602	132	58	v3	v3	PROPN
ejpam-5602	132	59	)	)	PUNCT
ejpam-5602	132	60	∩	∩	PROPN
ejpam-5602	132	61	v	v	ADP
ejpam-5602	132	62	(	(	PUNCT
ejpam-5602	132	63	g	g	NOUN
ejpam-5602	132	64	)	)	PUNCT
ejpam-5602	132	65	̸=	̸=	NOUN
ejpam-5602	132	66	∅	∅	NOUN
ejpam-5602	132	67	,	,	PUNCT
ejpam-5602	132	68	whenever	whenever	SCONJ
ejpam-5602	132	69	v	v	NUM
ejpam-5602	132	70	∈	∈	PROPN
ejpam-5602	132	71	v	v	NOUN
ejpam-5602	132	72	(	(	PUNCT
ejpam-5602	132	73	h	h	NOUN
ejpam-5602	132	74	)	)	PUNCT
ejpam-5602	132	75	and	and	CCONJ
ejpam-5602	132	76	nh(v	nh(v	NOUN
ejpam-5602	132	77	)	)	PUNCT
ejpam-5602	132	78	⊆	⊆	NUM
ejpam-5602	132	79	v0	v0	NOUN
ejpam-5602	132	80	.	.	PUNCT
ejpam-5602	133	1	proof	proof	NOUN
ejpam-5602	133	2	:	:	PUNCT
ejpam-5602	133	3	let	let	VERB
ejpam-5602	133	4	f	f	PROPN
ejpam-5602	133	5	=	=	SYM
ejpam-5602	133	6	(	(	PUNCT
ejpam-5602	133	7	v0	v0	PROPN
ejpam-5602	133	8	,	,	PUNCT
ejpam-5602	133	9	v1	v1	NOUN
ejpam-5602	133	10	,	,	PUNCT
ejpam-5602	133	11	v2	v2	PROPN
ejpam-5602	133	12	,	,	PUNCT
ejpam-5602	133	13	v3	v3	PROPN
ejpam-5602	133	14	)	)	PUNCT
ejpam-5602	133	15	be	be	VERB
ejpam-5602	133	16	a	a	DET
ejpam-5602	133	17	function	function	NOUN
ejpam-5602	133	18	on	on	ADP
ejpam-5602	133	19	v	v	NOUN
ejpam-5602	133	20	(	(	PUNCT
ejpam-5602	133	21	g	g	PROPN
ejpam-5602	133	22	+	+	PROPN
ejpam-5602	133	23	h	h	NOUN
ejpam-5602	133	24	)	)	PUNCT
ejpam-5602	133	25	.	.	PUNCT
ejpam-5602	134	1	assume	assume	VERB
ejpam-5602	134	2	that	that	SCONJ
ejpam-5602	134	3	(	(	PUNCT
ejpam-5602	134	4	i	i	NOUN
ejpam-5602	134	5	)	)	PUNCT
ejpam-5602	134	6	holds	hold	VERB
ejpam-5602	134	7	for	for	ADP
ejpam-5602	134	8	f	f	PROPN
ejpam-5602	134	9	.	.	PUNCT
ejpam-5602	135	1	let	let	VERB
ejpam-5602	135	2	v	v	X
ejpam-5602	135	3	∈	∈	PROPN
ejpam-5602	135	4	(	(	PUNCT
ejpam-5602	135	5	v0	v0	NOUN
ejpam-5602	135	6	∪	∪	X
ejpam-5602	135	7	v1	v1	NOUN
ejpam-5602	135	8	)	)	PUNCT
ejpam-5602	135	9	∩	∩	ADJ
ejpam-5602	135	10	v	v	X
ejpam-5602	135	11	(	(	PUNCT
ejpam-5602	135	12	g+h	g+h	PROPN
ejpam-5602	135	13	)	)	PUNCT
ejpam-5602	135	14	.	.	PUNCT
ejpam-5602	136	1	if	if	SCONJ
ejpam-5602	136	2	v	v	NUM
ejpam-5602	136	3	∈	∈	PROPN
ejpam-5602	136	4	v	v	NOUN
ejpam-5602	136	5	(	(	PUNCT
ejpam-5602	136	6	g	g	NOUN
ejpam-5602	136	7	)	)	PUNCT
ejpam-5602	136	8	,	,	PUNCT
ejpam-5602	136	9	then	then	ADV
ejpam-5602	136	10	3	3	NUM
ejpam-5602	136	11	≤	≤	NOUN
ejpam-5602	136	12	f	f	X
ejpam-5602	136	13	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	136	14	]	]	X
ejpam-5602	136	15	)	)	PUNCT
ejpam-5602	136	16	=	=	SYM
ejpam-5602	136	17	∑	∑	PUNCT
ejpam-5602	136	18	x∈ng[v	x∈ng[v	PROPN
ejpam-5602	136	19	]	]	X
ejpam-5602	136	20	f(x	f(x	PROPN
ejpam-5602	136	21	)	)	PUNCT
ejpam-5602	136	22	≤	≤	PUNCT
ejpam-5602	136	23	∑	∑	PUNCT
ejpam-5602	136	24	x∈ng+h	x∈ng+h	PUNCT
ejpam-5602	137	1	[	[	X
ejpam-5602	137	2	v	v	X
ejpam-5602	137	3	]	]	X
ejpam-5602	137	4	f(x	f(x	PROPN
ejpam-5602	137	5	)	)	PUNCT
ejpam-5602	137	6	=	=	PUNCT
ejpam-5602	138	1	f(ng+h	f(ng+h	PROPN
ejpam-5602	138	2	[	[	X
ejpam-5602	138	3	v	v	NOUN
ejpam-5602	138	4	]	]	PUNCT
ejpam-5602	138	5	)	)	PUNCT
ejpam-5602	138	6	.	.	PUNCT
ejpam-5602	139	1	suppose	suppose	VERB
ejpam-5602	139	2	that	that	SCONJ
ejpam-5602	139	3	v	v	NUM
ejpam-5602	139	4	∈	∈	PROPN
ejpam-5602	139	5	v	v	NOUN
ejpam-5602	139	6	(	(	PUNCT
ejpam-5602	139	7	h	h	NOUN
ejpam-5602	139	8	)	)	PUNCT
ejpam-5602	139	9	.	.	PUNCT
ejpam-5602	140	1	since	since	SCONJ
ejpam-5602	140	2	f	f	PROPN
ejpam-5602	140	3	|g	|g	PROPN
ejpam-5602	140	4	is	be	AUX
ejpam-5602	140	5	a	a	DET
ejpam-5602	140	6	tdidf	tdidf	NOUN
ejpam-5602	140	7	on	on	ADP
ejpam-5602	140	8	g	g	NOUN
ejpam-5602	140	9	,	,	PUNCT
ejpam-5602	140	10	proposition	proposition	NOUN
ejpam-5602	140	11	1	1	NUM
ejpam-5602	140	12	implies	imply	VERB
ejpam-5602	140	13	that	that	SCONJ
ejpam-5602	140	14	ωg(f	ωg(f	NUM
ejpam-5602	140	15	|g	|g	NOUN
ejpam-5602	140	16	)	)	PUNCT
ejpam-5602	140	17	≥	≥	NOUN
ejpam-5602	140	18	3	3	NUM
ejpam-5602	140	19	.	.	PUNCT
ejpam-5602	141	1	hence	hence	ADV
ejpam-5602	141	2	,	,	PUNCT
ejpam-5602	141	3	f(ng+h	f(ng+h	PROPN
ejpam-5602	141	4	[	[	X
ejpam-5602	141	5	v	v	NOUN
ejpam-5602	141	6	]	]	X
ejpam-5602	141	7	)	)	PUNCT
ejpam-5602	141	8	=	=	PUNCT
ejpam-5602	142	1	∑	∑	PUNCT
ejpam-5602	142	2	x∈ng+h	x∈ng+h	PUNCT
ejpam-5602	143	1	[	[	X
ejpam-5602	143	2	v	v	X
ejpam-5602	143	3	]	]	X
ejpam-5602	143	4	f(x	f(x	PROPN
ejpam-5602	143	5	)	)	PUNCT
ejpam-5602	143	6	=	=	PUNCT
ejpam-5602	144	1	∑	∑	PUNCT
ejpam-5602	144	2	x∈ng+h	x∈ng+h	PUNCT
ejpam-5602	145	1	[	[	X
ejpam-5602	145	2	v]\v	v]\v	INTJ
ejpam-5602	145	3	(	(	PUNCT
ejpam-5602	145	4	g	g	NOUN
ejpam-5602	145	5	)	)	PUNCT
ejpam-5602	145	6	f(x	f(x	PROPN
ejpam-5602	145	7	)	)	PUNCT
ejpam-5602	146	1	+	+	CCONJ
ejpam-5602	146	2	∑	∑	PROPN
ejpam-5602	146	3	x∈v	x∈v	PROPN
ejpam-5602	146	4	(	(	PUNCT
ejpam-5602	146	5	g	g	NOUN
ejpam-5602	146	6	)	)	PUNCT
ejpam-5602	146	7	f(x	f(x	PROPN
ejpam-5602	146	8	)	)	PUNCT
ejpam-5602	146	9	≥	≥	NOUN
ejpam-5602	146	10	3	3	NUM
ejpam-5602	146	11	.	.	PUNCT
ejpam-5602	147	1	now	now	ADV
ejpam-5602	147	2	,	,	PUNCT
ejpam-5602	147	3	let	let	VERB
ejpam-5602	147	4	v	v	NUM
ejpam-5602	147	5	∈	∈	NOUN
ejpam-5602	147	6	v1	v1	NOUN
ejpam-5602	147	7	∪	∪	NOUN
ejpam-5602	147	8	v2	v2	PROPN
ejpam-5602	147	9	∪	∪	X
ejpam-5602	147	10	v3	v3	PROPN
ejpam-5602	147	11	.	.	PUNCT
ejpam-5602	148	1	if	if	SCONJ
ejpam-5602	148	2	v	v	NUM
ejpam-5602	148	3	∈	∈	PROPN
ejpam-5602	148	4	v	v	NOUN
ejpam-5602	148	5	(	(	PUNCT
ejpam-5602	148	6	g	g	NOUN
ejpam-5602	148	7	)	)	PUNCT
ejpam-5602	148	8	,	,	PUNCT
ejpam-5602	148	9	then	then	ADV
ejpam-5602	148	10	since	since	SCONJ
ejpam-5602	148	11	f	f	PROPN
ejpam-5602	148	12	|g	|g	PROPN
ejpam-5602	148	13	∈	∈	PROPN
ejpam-5602	148	14	tdidf	tdidf	NOUN
ejpam-5602	148	15	(	(	PUNCT
ejpam-5602	148	16	g	g	NOUN
ejpam-5602	148	17	)	)	PUNCT
ejpam-5602	148	18	,	,	PUNCT
ejpam-5602	148	19	there	there	PRON
ejpam-5602	148	20	exists	exist	VERB
ejpam-5602	148	21	u	u	PROPN
ejpam-5602	148	22	∈	∈	PROPN
ejpam-5602	148	23	(	(	PUNCT
ejpam-5602	148	24	(	(	PUNCT
ejpam-5602	148	25	v1	v1	VERB
ejpam-5602	148	26	∪	∪	NOUN
ejpam-5602	148	27	v2	v2	PROPN
ejpam-5602	148	28	∪	∪	X
ejpam-5602	148	29	v3	v3	PROPN
ejpam-5602	148	30	)	)	PUNCT
ejpam-5602	148	31	∩	∩	PROPN
ejpam-5602	148	32	v	v	X
ejpam-5602	148	33	(	(	PUNCT
ejpam-5602	148	34	g	g	NOUN
ejpam-5602	148	35	)	)	PUNCT
ejpam-5602	148	36	)	)	PUNCT
ejpam-5602	148	37	\	\	PROPN
ejpam-5602	148	38	{	{	PUNCT
ejpam-5602	148	39	v	v	NOUN
ejpam-5602	148	40	}	}	PUNCT
ejpam-5602	148	41	such	such	ADJ
ejpam-5602	148	42	that	that	SCONJ
ejpam-5602	148	43	vu	vu	PROPN
ejpam-5602	148	44	∈	∈	PROPN
ejpam-5602	148	45	e(g	e(g	PROPN
ejpam-5602	148	46	)	)	PUNCT
ejpam-5602	148	47	⊆	⊆	NUM
ejpam-5602	148	48	e(g	e(g	NOUN
ejpam-5602	148	49	+	+	PROPN
ejpam-5602	148	50	h	h	NOUN
ejpam-5602	148	51	)	)	PUNCT
ejpam-5602	148	52	.	.	PUNCT
ejpam-5602	149	1	if	if	SCONJ
ejpam-5602	149	2	v	v	NUM
ejpam-5602	149	3	∈	∈	PROPN
ejpam-5602	149	4	v	v	NOUN
ejpam-5602	149	5	(	(	PUNCT
ejpam-5602	149	6	h	h	NOUN
ejpam-5602	149	7	)	)	PUNCT
ejpam-5602	149	8	,	,	PUNCT
ejpam-5602	149	9	then	then	ADV
ejpam-5602	149	10	∅	∅	NOUN
ejpam-5602	149	11	̸=	̸=	PROPN
ejpam-5602	149	12	(	(	PUNCT
ejpam-5602	149	13	v1∪v2∪v3)∩v	v1∪v2∪v3)∩v	PROPN
ejpam-5602	149	14	(	(	PUNCT
ejpam-5602	149	15	g	g	NOUN
ejpam-5602	149	16	)	)	PUNCT
ejpam-5602	149	17	⊆	⊆	NUM
ejpam-5602	149	18	ng+h(v	ng+h(v	NOUN
ejpam-5602	149	19	)	)	PUNCT
ejpam-5602	149	20	.	.	PUNCT
ejpam-5602	150	1	thus	thus	ADV
ejpam-5602	150	2	,	,	PUNCT
ejpam-5602	150	3	f	f	PROPN
ejpam-5602	150	4	∈	∈	PROPN
ejpam-5602	150	5	tdidf	tdidf	NOUN
ejpam-5602	150	6	(	(	PUNCT
ejpam-5602	150	7	g+h	g+h	PROPN
ejpam-5602	150	8	)	)	PUNCT
ejpam-5602	150	9	.	.	PUNCT
ejpam-5602	151	1	similarly	similarly	ADV
ejpam-5602	151	2	,	,	PUNCT
ejpam-5602	151	3	if	if	SCONJ
ejpam-5602	151	4	condition	condition	NOUN
ejpam-5602	151	5	(	(	PUNCT
ejpam-5602	151	6	ii	ii	NOUN
ejpam-5602	151	7	)	)	PUNCT
ejpam-5602	151	8	holds	hold	VERB
ejpam-5602	151	9	for	for	ADP
ejpam-5602	151	10	f	f	PROPN
ejpam-5602	151	11	,	,	PUNCT
ejpam-5602	151	12	then	then	ADV
ejpam-5602	151	13	f	f	PROPN
ejpam-5602	151	14	∈	∈	PROPN
ejpam-5602	151	15	tdidf	tdidf	NOUN
ejpam-5602	151	16	(	(	PUNCT
ejpam-5602	151	17	g	g	NOUN
ejpam-5602	151	18	+	+	NOUN
ejpam-5602	151	19	h	h	NOUN
ejpam-5602	151	20	)	)	PUNCT
ejpam-5602	151	21	.	.	PUNCT
ejpam-5602	152	1	suppose	suppose	VERB
ejpam-5602	152	2	(	(	PUNCT
ejpam-5602	152	3	iii	iii	NOUN
ejpam-5602	152	4	)	)	PUNCT
ejpam-5602	152	5	holds	hold	VERB
ejpam-5602	152	6	.	.	PUNCT
ejpam-5602	153	1	let	let	VERB
ejpam-5602	153	2	v	v	NUM
ejpam-5602	153	3	∈	∈	PROPN
ejpam-5602	153	4	v0	v0	NOUN
ejpam-5602	153	5	∪	∪	X
ejpam-5602	153	6	v1	v1	NOUN
ejpam-5602	153	7	.	.	PUNCT
ejpam-5602	154	1	if	if	SCONJ
ejpam-5602	154	2	v	v	NUM
ejpam-5602	154	3	∈	∈	PROPN
ejpam-5602	154	4	v	v	NOUN
ejpam-5602	154	5	(	(	PUNCT
ejpam-5602	154	6	g	g	NOUN
ejpam-5602	154	7	)	)	PUNCT
ejpam-5602	154	8	such	such	ADJ
ejpam-5602	154	9	that	that	SCONJ
ejpam-5602	154	10	f	f	PROPN
ejpam-5602	154	11	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	154	12	]	]	X
ejpam-5602	154	13	)	)	PUNCT
ejpam-5602	154	14	<	<	X
ejpam-5602	155	1	3	3	NUM
ejpam-5602	155	2	,	,	PUNCT
ejpam-5602	155	3	then	then	ADV
ejpam-5602	155	4	by	by	ADP
ejpam-5602	155	5	(	(	PUNCT
ejpam-5602	155	6	iii)(a	iii)(a	PROPN
ejpam-5602	155	7	)	)	PUNCT
ejpam-5602	155	8	,	,	PUNCT
ejpam-5602	155	9	ωh(f	ωh(f	NUM
ejpam-5602	155	10	|h	|h	NOUN
ejpam-5602	155	11	)	)	PUNCT
ejpam-5602	155	12	≥	≥	NOUN
ejpam-5602	155	13	3	3	NUM
ejpam-5602	155	14	−	−	PROPN
ejpam-5602	155	15	f	f	PROPN
ejpam-5602	155	16	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	155	17	]	]	NUM
ejpam-5602	155	18	)	)	PUNCT
ejpam-5602	155	19	.	.	PUNCT
ejpam-5602	156	1	since	since	SCONJ
ejpam-5602	156	2	f(ng+h	f(ng+h	PROPN
ejpam-5602	156	3	[	[	X
ejpam-5602	156	4	v	v	NOUN
ejpam-5602	156	5	]	]	X
ejpam-5602	156	6	)	)	PUNCT
ejpam-5602	156	7	=	=	SYM
ejpam-5602	156	8	f	f	X
ejpam-5602	156	9	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	156	10	]	]	X
ejpam-5602	156	11	)	)	PUNCT
ejpam-5602	156	12	+	+	CCONJ
ejpam-5602	156	13	ωh(f	ωh(f	NUM
ejpam-5602	156	14	|h	|h	NOUN
ejpam-5602	156	15	)	)	PUNCT
ejpam-5602	156	16	,	,	PUNCT
ejpam-5602	156	17	f(ng+h	f(ng+h	PROPN
ejpam-5602	156	18	[	[	X
ejpam-5602	156	19	v	v	NOUN
ejpam-5602	156	20	]	]	PUNCT
ejpam-5602	156	21	)	)	PUNCT
ejpam-5602	156	22	≥	≥	NOUN
ejpam-5602	156	23	3	3	NUM
ejpam-5602	156	24	.	.	PUNCT
ejpam-5602	156	25	similarly	similarly	ADV
ejpam-5602	156	26	,	,	PUNCT
ejpam-5602	156	27	if	if	SCONJ
ejpam-5602	156	28	v	v	NUM
ejpam-5602	156	29	∈	∈	PROPN
ejpam-5602	156	30	v	v	NOUN
ejpam-5602	156	31	(	(	PUNCT
ejpam-5602	156	32	h	h	NOUN
ejpam-5602	156	33	)	)	PUNCT
ejpam-5602	156	34	with	with	ADP
ejpam-5602	156	35	f	f	PROPN
ejpam-5602	156	36	|h(nh	|h(nh	PROPN
ejpam-5602	156	37	[	[	X
ejpam-5602	156	38	v	v	NOUN
ejpam-5602	156	39	]	]	X
ejpam-5602	156	40	)	)	PUNCT
ejpam-5602	156	41	<	<	X
ejpam-5602	156	42	3	3	NUM
ejpam-5602	156	43	then	then	ADV
ejpam-5602	156	44	f(ng+h	f(ng+h	PROPN
ejpam-5602	156	45	[	[	X
ejpam-5602	156	46	v	v	NOUN
ejpam-5602	156	47	]	]	PUNCT
ejpam-5602	156	48	)	)	PUNCT
ejpam-5602	156	49	≥	≥	NOUN
ejpam-5602	157	1	3	3	NUM
ejpam-5602	157	2	.	.	PUNCT
ejpam-5602	158	1	since	since	SCONJ
ejpam-5602	158	2	v	v	NOUN
ejpam-5602	158	3	is	be	AUX
ejpam-5602	158	4	arbitrary	arbitrary	ADJ
ejpam-5602	158	5	,	,	PUNCT
ejpam-5602	158	6	f(ng+h	f(ng+h	PROPN
ejpam-5602	158	7	[	[	X
ejpam-5602	158	8	v	v	NOUN
ejpam-5602	158	9	]	]	PUNCT
ejpam-5602	158	10	)	)	PUNCT
ejpam-5602	158	11	≥	≥	NOUN
ejpam-5602	158	12	3	3	NUM
ejpam-5602	158	13	for	for	ADP
ejpam-5602	158	14	each	each	DET
ejpam-5602	158	15	v	v	ADP
ejpam-5602	158	16	∈	∈	PROPN
ejpam-5602	158	17	v0	v0	NOUN
ejpam-5602	158	18	∪	∪	X
ejpam-5602	158	19	v1	v1	NOUN
ejpam-5602	158	20	.	.	PUNCT
ejpam-5602	159	1	let	let	VERB
ejpam-5602	159	2	u	u	PRON
ejpam-5602	159	3	∈	∈	PROPN
ejpam-5602	159	4	v1	v1	NOUN
ejpam-5602	159	5	∪	∪	ADP
ejpam-5602	159	6	v2	v2	PROPN
ejpam-5602	159	7	∪	∪	X
ejpam-5602	159	8	v3	v3	PROPN
ejpam-5602	159	9	.	.	PUNCT
ejpam-5602	160	1	if	if	SCONJ
ejpam-5602	160	2	u	u	PROPN
ejpam-5602	160	3	∈	∈	PROPN
ejpam-5602	160	4	v	v	ADP
ejpam-5602	160	5	(	(	PUNCT
ejpam-5602	160	6	g	g	NOUN
ejpam-5602	160	7	)	)	PUNCT
ejpam-5602	160	8	with	with	ADP
ejpam-5602	160	9	ng(u	ng(u	NOUN
ejpam-5602	160	10	)	)	PUNCT
ejpam-5602	160	11	⊆	⊆	NUM
ejpam-5602	160	12	v0	v0	NOUN
ejpam-5602	160	13	,	,	PUNCT
ejpam-5602	160	14	then	then	ADV
ejpam-5602	160	15	by	by	ADP
ejpam-5602	160	16	(	(	PUNCT
ejpam-5602	160	17	iii)(b	iii)(b	NOUN
ejpam-5602	160	18	)	)	PUNCT
ejpam-5602	160	19	,	,	PUNCT
ejpam-5602	160	20	(	(	PUNCT
ejpam-5602	160	21	v1	v1	VERB
ejpam-5602	160	22	∪	∪	ADP
ejpam-5602	160	23	v2	v2	PROPN
ejpam-5602	160	24	∪	∪	X
ejpam-5602	160	25	v3	v3	PROPN
ejpam-5602	160	26	)	)	PUNCT
ejpam-5602	160	27	∩	∩	PROPN
ejpam-5602	160	28	v	v	ADP
ejpam-5602	160	29	(	(	PUNCT
ejpam-5602	160	30	h	h	NOUN
ejpam-5602	160	31	)	)	PUNCT
ejpam-5602	160	32	̸=	̸=	PROPN
ejpam-5602	160	33	∅.	∅.	ADP
ejpam-5602	160	34	this	this	PRON
ejpam-5602	160	35	means	mean	VERB
ejpam-5602	160	36	that	that	SCONJ
ejpam-5602	160	37	ng+h(u	ng+h(u	NOUN
ejpam-5602	160	38	)	)	PUNCT
ejpam-5602	160	39	∩	∩	NOUN
ejpam-5602	160	40	(	(	PUNCT
ejpam-5602	160	41	v1	v1	VERB
ejpam-5602	160	42	∪	∪	ADP
ejpam-5602	160	43	v2	v2	PROPN
ejpam-5602	160	44	∪	∪	X
ejpam-5602	160	45	v3	v3	NOUN
ejpam-5602	160	46	)	)	PUNCT
ejpam-5602	160	47	̸=	̸=	PROPN
ejpam-5602	160	48	∅.	∅.	PRON
ejpam-5602	160	49	similarly	similarly	ADV
ejpam-5602	160	50	,	,	PUNCT
ejpam-5602	160	51	ng+h(u	ng+h(u	PROPN
ejpam-5602	160	52	)	)	PUNCT
ejpam-5602	160	53	∩	∩	NOUN
ejpam-5602	160	54	(	(	PUNCT
ejpam-5602	160	55	v1	v1	VERB
ejpam-5602	160	56	∪	∪	ADP
ejpam-5602	160	57	v2	v2	PROPN
ejpam-5602	160	58	∪	∪	X
ejpam-5602	160	59	v3	v3	PROPN
ejpam-5602	160	60	)	)	PUNCT
ejpam-5602	160	61	̸=	̸=	PROPN
ejpam-5602	160	62	∅	∅	NOUN
ejpam-5602	160	63	for	for	ADP
ejpam-5602	160	64	each	each	PRON
ejpam-5602	160	65	u	u	PROPN
ejpam-5602	160	66	∈	∈	PROPN
ejpam-5602	160	67	v	v	ADP
ejpam-5602	160	68	(	(	PUNCT
ejpam-5602	160	69	h	h	NOUN
ejpam-5602	160	70	)	)	PUNCT
ejpam-5602	160	71	with	with	ADP
ejpam-5602	160	72	nh(u	nh(u	NOUN
ejpam-5602	160	73	)	)	PUNCT
ejpam-5602	160	74	⊆	⊆	NUM
ejpam-5602	160	75	v0	v0	NOUN
ejpam-5602	160	76	.	.	PUNCT
ejpam-5602	161	1	thus	thus	ADV
ejpam-5602	161	2	,	,	PUNCT
ejpam-5602	161	3	⟨v1	⟨v1	PROPN
ejpam-5602	161	4	∪	∪	ADP
ejpam-5602	161	5	v2	v2	PROPN
ejpam-5602	161	6	∪	∪	NOUN
ejpam-5602	161	7	v3⟩	v3⟩	PRON
ejpam-5602	161	8	has	have	VERB
ejpam-5602	161	9	no	no	DET
ejpam-5602	161	10	isolated	isolated	ADJ
ejpam-5602	161	11	vertex	vertex	NOUN
ejpam-5602	161	12	.	.	PUNCT
ejpam-5602	162	1	therefore	therefore	ADV
ejpam-5602	162	2	,	,	PUNCT
ejpam-5602	162	3	f	f	PROPN
ejpam-5602	162	4	∈	∈	PROPN
ejpam-5602	162	5	tdidf	tdidf	NOUN
ejpam-5602	162	6	(	(	PUNCT
ejpam-5602	162	7	g+h	g+h	PROPN
ejpam-5602	162	8	)	)	PUNCT
ejpam-5602	162	9	.	.	PUNCT
ejpam-5602	163	1	conversely	conversely	ADV
ejpam-5602	163	2	,	,	PUNCT
ejpam-5602	163	3	suppose	suppose	VERB
ejpam-5602	163	4	that	that	SCONJ
ejpam-5602	163	5	f	f	PROPN
ejpam-5602	163	6	∈	∈	PROPN
ejpam-5602	163	7	tdidf	tdidf	NOUN
ejpam-5602	163	8	(	(	PUNCT
ejpam-5602	163	9	g+h	g+h	PROPN
ejpam-5602	163	10	)	)	PUNCT
ejpam-5602	163	11	.	.	PUNCT
ejpam-5602	164	1	suppose	suppose	VERB
ejpam-5602	164	2	neither	neither	CCONJ
ejpam-5602	164	3	(	(	PUNCT
ejpam-5602	164	4	i	i	NOUN
ejpam-5602	164	5	)	)	PUNCT
ejpam-5602	164	6	nor	nor	CCONJ
ejpam-5602	164	7	(	(	PUNCT
ejpam-5602	164	8	ii	ii	NOUN
ejpam-5602	164	9	)	)	PUNCT
ejpam-5602	164	10	holds	hold	VERB
ejpam-5602	164	11	for	for	ADP
ejpam-5602	164	12	f	f	PROPN
ejpam-5602	164	13	,	,	PUNCT
ejpam-5602	165	1	i.e.	i.e.	X
ejpam-5602	165	2	,	,	PUNCT
ejpam-5602	165	3	f	f	PROPN
ejpam-5602	165	4	|g	|g	PROPN
ejpam-5602	165	5	/∈	/∈	PUNCT
ejpam-5602	165	6	tdidf	tdidf	PROPN
ejpam-5602	165	7	(	(	PUNCT
ejpam-5602	165	8	g+h	g+h	PROPN
ejpam-5602	165	9	)	)	PUNCT
ejpam-5602	165	10	and	and	CCONJ
ejpam-5602	165	11	f	f	PROPN
ejpam-5602	165	12	|h	|h	PROPN
ejpam-5602	165	13	/∈	/∈	PUNCT
ejpam-5602	165	14	tdidf	tdidf	PROPN
ejpam-5602	165	15	(	(	PUNCT
ejpam-5602	165	16	g+h	g+h	PROPN
ejpam-5602	165	17	)	)	PUNCT
ejpam-5602	165	18	.	.	PUNCT
ejpam-5602	166	1	since	since	SCONJ
ejpam-5602	166	2	f	f	PROPN
ejpam-5602	166	3	|g	|g	PROPN
ejpam-5602	166	4	/∈	/∈	PUNCT
ejpam-5602	166	5	tdidf	tdidf	PROPN
ejpam-5602	166	6	(	(	PUNCT
ejpam-5602	166	7	g+h	g+h	PROPN
ejpam-5602	166	8	)	)	PUNCT
ejpam-5602	166	9	,	,	PUNCT
ejpam-5602	166	10	either	either	CCONJ
ejpam-5602	166	11	there	there	PRON
ejpam-5602	166	12	exists	exist	VERB
ejpam-5602	166	13	v	v	ADP
ejpam-5602	166	14	∈	∈	PROPN
ejpam-5602	166	15	[	[	X
ejpam-5602	166	16	(	(	PUNCT
ejpam-5602	166	17	v0	v0	NOUN
ejpam-5602	166	18	∪	∪	X
ejpam-5602	166	19	v1	v1	NOUN
ejpam-5602	166	20	)	)	PUNCT
ejpam-5602	166	21	∩	∩	ADJ
ejpam-5602	166	22	v	v	X
ejpam-5602	166	23	(	(	PUNCT
ejpam-5602	166	24	g	g	NOUN
ejpam-5602	166	25	)	)	PUNCT
ejpam-5602	166	26	]	]	PUNCT
ejpam-5602	166	27	with	with	ADP
ejpam-5602	166	28	f	f	PROPN
ejpam-5602	166	29	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	166	30	]	]	X
ejpam-5602	166	31	)	)	PUNCT
ejpam-5602	166	32	<	<	X
ejpam-5602	166	33	3	3	NUM
ejpam-5602	166	34	or	or	CCONJ
ejpam-5602	166	35	⟨(v1	⟨(v1	VERB
ejpam-5602	166	36	∪	∪	VERB
ejpam-5602	166	37	v2	v2	PROPN
ejpam-5602	166	38	∪	∪	X
ejpam-5602	166	39	v3	v3	PROPN
ejpam-5602	166	40	)	)	PUNCT
ejpam-5602	166	41	∩	∩	ADJ
ejpam-5602	166	42	v	v	X
ejpam-5602	166	43	(	(	PUNCT
ejpam-5602	166	44	g)⟩	g)⟩	PROPN
ejpam-5602	166	45	has	have	VERB
ejpam-5602	166	46	an	an	DET
ejpam-5602	166	47	isolated	isolated	ADJ
ejpam-5602	166	48	vertex	vertex	NOUN
ejpam-5602	166	49	or	or	CCONJ
ejpam-5602	166	50	both	both	PRON
ejpam-5602	166	51	.	.	PUNCT
ejpam-5602	167	1	assume	assume	VERB
ejpam-5602	167	2	that	that	SCONJ
ejpam-5602	167	3	there	there	PRON
ejpam-5602	167	4	exists	exist	VERB
ejpam-5602	167	5	v	v	ADP
ejpam-5602	167	6	∈	∈	PROPN
ejpam-5602	167	7	[	[	X
ejpam-5602	167	8	(	(	PUNCT
ejpam-5602	167	9	v0	v0	NOUN
ejpam-5602	167	10	∪	∪	X
ejpam-5602	167	11	v1	v1	NOUN
ejpam-5602	167	12	)	)	PUNCT
ejpam-5602	167	13	∩	∩	ADJ
ejpam-5602	167	14	v	v	X
ejpam-5602	167	15	(	(	PUNCT
ejpam-5602	167	16	g	g	NOUN
ejpam-5602	167	17	)	)	PUNCT
ejpam-5602	167	18	]	]	PUNCT
ejpam-5602	167	19	with	with	ADP
ejpam-5602	167	20	f	f	PROPN
ejpam-5602	167	21	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	167	22	]	]	X
ejpam-5602	167	23	)	)	PUNCT
ejpam-5602	167	24	<	<	X
ejpam-5602	167	25	3	3	X
ejpam-5602	167	26	.	.	PUNCT
ejpam-5602	168	1	since	since	SCONJ
ejpam-5602	168	2	f	f	PROPN
ejpam-5602	168	3	∈	∈	PROPN
ejpam-5602	168	4	tdidf	tdidf	NOUN
ejpam-5602	168	5	(	(	PUNCT
ejpam-5602	168	6	g+h	g+h	PROPN
ejpam-5602	168	7	)	)	PUNCT
ejpam-5602	168	8	,	,	PUNCT
ejpam-5602	168	9	ωh(f	ωh(f	NUM
ejpam-5602	168	10	|h	|h	NOUN
ejpam-5602	168	11	)	)	PUNCT
ejpam-5602	168	12	≥	≥	NOUN
ejpam-5602	168	13	3−	3−	NUM
ejpam-5602	168	14	f	f	X
ejpam-5602	168	15	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	168	16	]	]	NUM
ejpam-5602	168	17	)	)	PUNCT
ejpam-5602	168	18	.	.	PUNCT
ejpam-5602	169	1	thus	thus	ADV
ejpam-5602	169	2	,	,	PUNCT
ejpam-5602	169	3	(	(	PUNCT
ejpam-5602	169	4	iii)(a(1	iii)(a(1	ADJ
ejpam-5602	169	5	)	)	PUNCT
ejpam-5602	169	6	)	)	PUNCT
ejpam-5602	169	7	holds	hold	VERB
ejpam-5602	169	8	.	.	PUNCT
ejpam-5602	170	1	similarly	similarly	ADV
ejpam-5602	170	2	,	,	PUNCT
ejpam-5602	170	3	(	(	PUNCT
ejpam-5602	170	4	iii)(a(2	iii)(a(2	PROPN
ejpam-5602	170	5	)	)	PUNCT
ejpam-5602	170	6	)	)	PUNCT
ejpam-5602	170	7	follows	follow	VERB
ejpam-5602	170	8	.	.	PUNCT
ejpam-5602	171	1	on	on	ADP
ejpam-5602	171	2	the	the	DET
ejpam-5602	171	3	other	other	ADJ
ejpam-5602	171	4	hand	hand	NOUN
ejpam-5602	171	5	,	,	PUNCT
ejpam-5602	171	6	assume	assume	VERB
ejpam-5602	171	7	that	that	SCONJ
ejpam-5602	171	8	⟨(v1∪v2∪v3)∩v	⟨(v1∪v2∪v3)∩v	PROPN
ejpam-5602	171	9	(	(	PUNCT
ejpam-5602	171	10	g)⟩	g)⟩	PROPN
ejpam-5602	171	11	has	have	VERB
ejpam-5602	171	12	an	an	DET
ejpam-5602	171	13	isolated	isolated	ADJ
ejpam-5602	171	14	vertex	vertex	NOUN
ejpam-5602	171	15	.	.	PUNCT
ejpam-5602	172	1	let	let	VERB
ejpam-5602	172	2	u	u	PRON
ejpam-5602	172	3	∈	∈	PROPN
ejpam-5602	172	4	[	[	X
ejpam-5602	172	5	(	(	PUNCT
ejpam-5602	172	6	v1	v1	VERB
ejpam-5602	172	7	∪	∪	NOUN
ejpam-5602	172	8	v2	v2	PROPN
ejpam-5602	172	9	∪	∪	X
ejpam-5602	172	10	v3	v3	PROPN
ejpam-5602	172	11	)	)	PUNCT
ejpam-5602	172	12	∩	∩	PROPN
ejpam-5602	172	13	v	v	X
ejpam-5602	172	14	(	(	PUNCT
ejpam-5602	172	15	g	g	NOUN
ejpam-5602	172	16	)	)	PUNCT
ejpam-5602	172	17	]	]	PUNCT
ejpam-5602	172	18	such	such	ADJ
ejpam-5602	172	19	that	that	SCONJ
ejpam-5602	172	20	ng(v	ng(v	NUM
ejpam-5602	172	21	)	)	PUNCT
ejpam-5602	172	22	⊆	⊆	NUM
ejpam-5602	172	23	v0	v0	NOUN
ejpam-5602	172	24	.	.	PUNCT
ejpam-5602	173	1	since	since	SCONJ
ejpam-5602	173	2	⟨v1	⟨v1	PROPN
ejpam-5602	173	3	∪	∪	ADP
ejpam-5602	173	4	v2	v2	PROPN
ejpam-5602	173	5	∪	∪	NOUN
ejpam-5602	173	6	v3⟩	v3⟩	PRON
ejpam-5602	173	7	is	be	AUX
ejpam-5602	173	8	isolated	isolate	VERB
ejpam-5602	173	9	vertex	vertex	NOUN
ejpam-5602	173	10	-	-	PUNCT
ejpam-5602	173	11	free	free	ADJ
ejpam-5602	173	12	,	,	PUNCT
ejpam-5602	173	13	(	(	PUNCT
ejpam-5602	173	14	v1	v1	VERB
ejpam-5602	173	15	∪	∪	NOUN
ejpam-5602	173	16	v2	v2	PROPN
ejpam-5602	173	17	∪	∪	X
ejpam-5602	173	18	v3	v3	PROPN
ejpam-5602	173	19	)	)	PUNCT
ejpam-5602	173	20	∩	∩	PROPN
ejpam-5602	173	21	v	v	ADP
ejpam-5602	173	22	(	(	PUNCT
ejpam-5602	173	23	h	h	NOUN
ejpam-5602	173	24	)	)	PUNCT
ejpam-5602	173	25	̸=	̸=	PROPN
ejpam-5602	173	26	∅.	∅.	ADV
ejpam-5602	173	27	thus	thus	ADV
ejpam-5602	173	28	,	,	PUNCT
ejpam-5602	173	29	(	(	PUNCT
ejpam-5602	173	30	iii)(b(1	iii)(b(1	PROPN
ejpam-5602	173	31	)	)	PUNCT
ejpam-5602	173	32	)	)	PUNCT
ejpam-5602	173	33	holds	hold	VERB
ejpam-5602	173	34	.	.	PUNCT
ejpam-5602	174	1	similarly	similarly	ADV
ejpam-5602	174	2	,	,	PUNCT
ejpam-5602	174	3	(	(	PUNCT
ejpam-5602	174	4	iii)(b(2	iii)(b(2	PROPN
ejpam-5602	174	5	)	)	PUNCT
ejpam-5602	174	6	)	)	PUNCT
ejpam-5602	174	7	follows	follow	VERB
ejpam-5602	174	8	.	.	PUNCT
ejpam-5602	175	1	■	■	PUNCT
ejpam-5602	175	2	corollary	corollary	ADJ
ejpam-5602	175	3	1	1	NUM
ejpam-5602	175	4	.	.	PUNCT
ejpam-5602	176	1	let	let	VERB
ejpam-5602	176	2	g	g	NOUN
ejpam-5602	176	3	and	and	CCONJ
ejpam-5602	176	4	h	h	NOUN
ejpam-5602	176	5	be	be	AUX
ejpam-5602	176	6	nontrivial	nontrivial	ADJ
ejpam-5602	176	7	connected	connected	ADJ
ejpam-5602	176	8	graphs	graph	NOUN
ejpam-5602	176	9	.	.	PUNCT
ejpam-5602	177	1	then	then	ADV
ejpam-5602	177	2	3	3	NUM
ejpam-5602	177	3	≤	≤	NUM
ejpam-5602	177	4	γtdi(g+h	γtdi(g+h	NOUN
ejpam-5602	177	5	)	)	PUNCT
ejpam-5602	177	6	≤	≤	NUM
ejpam-5602	177	7	min{6	min{6	NOUN
ejpam-5602	177	8	,	,	PUNCT
ejpam-5602	177	9	γtdi(g	γtdi(g	PROPN
ejpam-5602	177	10	)	)	PUNCT
ejpam-5602	177	11	,	,	PUNCT
ejpam-5602	177	12	γtdi(h	γtdi(h	PROPN
ejpam-5602	177	13	)	)	PUNCT
ejpam-5602	177	14	}	}	PUNCT
ejpam-5602	177	15	.	.	PUNCT
ejpam-5602	178	1	(	(	PUNCT
ejpam-5602	178	2	1	1	X
ejpam-5602	178	3	)	)	PUNCT
ejpam-5602	178	4	proof	proof	NOUN
ejpam-5602	178	5	:	:	PUNCT
ejpam-5602	178	6	the	the	DET
ejpam-5602	178	7	lower	low	ADJ
ejpam-5602	178	8	bound	bind	VERB
ejpam-5602	178	9	follows	follow	VERB
ejpam-5602	178	10	immediately	immediately	ADV
ejpam-5602	178	11	from	from	ADP
ejpam-5602	178	12	propositon	propositon	NOUN
ejpam-5602	178	13	1	1	NUM
ejpam-5602	178	14	.	.	PUNCT
ejpam-5602	178	15	to	to	PART
ejpam-5602	178	16	show	show	VERB
ejpam-5602	178	17	the	the	DET
ejpam-5602	178	18	upperbound	upperbound	NOUN
ejpam-5602	178	19	,	,	PUNCT
ejpam-5602	178	20	take	take	VERB
ejpam-5602	178	21	u	u	PRON
ejpam-5602	178	22	∈	∈	PROPN
ejpam-5602	178	23	v	v	NOUN
ejpam-5602	178	24	(	(	PUNCT
ejpam-5602	178	25	g	g	NOUN
ejpam-5602	178	26	)	)	PUNCT
ejpam-5602	178	27	and	and	CCONJ
ejpam-5602	178	28	v	v	ADP
ejpam-5602	178	29	∈	∈	PROPN
ejpam-5602	178	30	v	v	NOUN
ejpam-5602	178	31	(	(	PUNCT
ejpam-5602	178	32	h	h	NOUN
ejpam-5602	178	33	)	)	PUNCT
ejpam-5602	178	34	.	.	PUNCT
ejpam-5602	179	1	then	then	ADV
ejpam-5602	179	2	f	f	PROPN
ejpam-5602	179	3	=	=	PUNCT
ejpam-5602	179	4	(	(	PUNCT
ejpam-5602	179	5	v	v	NOUN
ejpam-5602	179	6	(	(	PUNCT
ejpam-5602	179	7	g	g	NOUN
ejpam-5602	179	8	)	)	PUNCT
ejpam-5602	179	9	\	\	NOUN
ejpam-5602	179	10	{	{	PUNCT
ejpam-5602	179	11	u	u	PROPN
ejpam-5602	179	12	,	,	PUNCT
ejpam-5602	179	13	v},∅,∅	v},∅,∅	NOUN
ejpam-5602	179	14	,	,	PUNCT
ejpam-5602	179	15	{	{	PUNCT
ejpam-5602	179	16	u	u	NOUN
ejpam-5602	179	17	,	,	PUNCT
ejpam-5602	179	18	v	v	NOUN
ejpam-5602	179	19	}	}	PUNCT
ejpam-5602	179	20	)	)	PUNCT
ejpam-5602	179	21	is	be	AUX
ejpam-5602	179	22	a	a	DET
ejpam-5602	179	23	tdidf	tdidf	NOUN
ejpam-5602	179	24	on	on	ADP
ejpam-5602	179	25	g	g	PROPN
ejpam-5602	179	26	+	+	CCONJ
ejpam-5602	179	27	h	h	NOUN
ejpam-5602	179	28	,	,	PUNCT
ejpam-5602	179	29	with	with	ADP
ejpam-5602	179	30	ωg+h(f	ωg+h(f	PRON
ejpam-5602	179	31	)	)	PUNCT
ejpam-5602	179	32	=	=	SYM
ejpam-5602	179	33	6	6	NUM
ejpam-5602	179	34	.	.	PUNCT
ejpam-5602	180	1	thus	thus	ADV
ejpam-5602	180	2	,	,	PUNCT
ejpam-5602	180	3	γtdi(g	γtdi(g	ADV
ejpam-5602	180	4	+	+	CCONJ
ejpam-5602	180	5	h	h	NOUN
ejpam-5602	180	6	)	)	PUNCT
ejpam-5602	180	7	≤	≤	NOUN
ejpam-5602	180	8	6	6	NUM
ejpam-5602	180	9	.	.	PUNCT
ejpam-5602	181	1	let	let	VERB
ejpam-5602	181	2	f	f	PROPN
ejpam-5602	181	3	=	=	SYM
ejpam-5602	181	4	(	(	PUNCT
ejpam-5602	181	5	v0	v0	PROPN
ejpam-5602	181	6	,	,	PUNCT
ejpam-5602	181	7	v1	v1	NOUN
ejpam-5602	181	8	,	,	PUNCT
ejpam-5602	181	9	v2	v2	PROPN
ejpam-5602	181	10	,	,	PUNCT
ejpam-5602	181	11	v3	v3	PROPN
ejpam-5602	181	12	)	)	PUNCT
ejpam-5602	181	13	be	be	VERB
ejpam-5602	181	14	a	a	DET
ejpam-5602	181	15	γtdi	γtdi	PROPN
ejpam-5602	181	16	function	function	NOUN
ejpam-5602	181	17	of	of	ADP
ejpam-5602	181	18	g.	g.	PROPN
ejpam-5602	181	19	by	by	ADP
ejpam-5602	181	20	proposition	proposition	NOUN
ejpam-5602	181	21	5	5	NUM
ejpam-5602	181	22	,	,	PUNCT
ejpam-5602	181	23	g	g	NOUN
ejpam-5602	181	24	=	=	SYM
ejpam-5602	181	25	(	(	PUNCT
ejpam-5602	181	26	v0	v0	PROPN
ejpam-5602	181	27	∪	∪	X
ejpam-5602	181	28	v	v	NOUN
ejpam-5602	181	29	(	(	PUNCT
ejpam-5602	181	30	h	h	NOUN
ejpam-5602	181	31	)	)	PUNCT
ejpam-5602	181	32	,	,	PUNCT
ejpam-5602	181	33	v1	v1	VERB
ejpam-5602	181	34	∪	∪	ADJ
ejpam-5602	181	35	v	v	NOUN
ejpam-5602	181	36	(	(	PUNCT
ejpam-5602	181	37	h	h	NOUN
ejpam-5602	181	38	)	)	PUNCT
ejpam-5602	181	39	,	,	PUNCT
ejpam-5602	181	40	v2	v2	PROPN
ejpam-5602	181	41	∪	∪	NOUN
ejpam-5602	181	42	v	v	NOUN
ejpam-5602	181	43	(	(	PUNCT
ejpam-5602	181	44	h	h	NOUN
ejpam-5602	181	45	)	)	PUNCT
ejpam-5602	181	46	,	,	PUNCT
ejpam-5602	181	47	v3	v3	PROPN
ejpam-5602	181	48	∪	∪	ADP
ejpam-5602	181	49	v	v	PROPN
ejpam-5602	181	50	(	(	PUNCT
ejpam-5602	181	51	h	h	NOUN
ejpam-5602	181	52	)	)	PUNCT
ejpam-5602	181	53	)	)	PUNCT
ejpam-5602	181	54	is	be	AUX
ejpam-5602	181	55	a	a	DET
ejpam-5602	181	56	tdidf	tdidf	NOUN
ejpam-5602	181	57	on	on	ADP
ejpam-5602	181	58	g	g	PROPN
ejpam-5602	181	59	with	with	ADP
ejpam-5602	181	60	ωg+h(f	ωg+h(f	PROPN
ejpam-5602	181	61	)	)	PUNCT
ejpam-5602	181	62	=	=	SYM
ejpam-5602	181	63	ωg(f	ωg(f	NUM
ejpam-5602	181	64	)	)	PUNCT
ejpam-5602	181	65	.	.	PUNCT
ejpam-5602	182	1	this	this	PRON
ejpam-5602	182	2	means	mean	VERB
ejpam-5602	182	3	that	that	SCONJ
ejpam-5602	182	4	γtdi(g+h	γtdi(g+h	NOUN
ejpam-5602	182	5	)	)	PUNCT
ejpam-5602	182	6	≤	≤	NUM
ejpam-5602	182	7	γtdi(g	γtdi(g	PROPN
ejpam-5602	182	8	)	)	PUNCT
ejpam-5602	182	9	.	.	PUNCT
ejpam-5602	183	1	similarly	similarly	ADV
ejpam-5602	183	2	,	,	PUNCT
ejpam-5602	183	3	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	183	4	)	)	PUNCT
ejpam-5602	183	5	≤	≤	NUM
ejpam-5602	183	6	γtdi(h	γtdi(h	PROPN
ejpam-5602	183	7	)	)	PUNCT
ejpam-5602	183	8	.	.	PUNCT
ejpam-5602	184	1	■	■	PUNCT
ejpam-5602	184	2	s.j.l	s.j.l	NOUN
ejpam-5602	184	3	.	.	PUNCT
ejpam-5602	184	4	sumbalan	sumbalan	PROPN
ejpam-5602	184	5	,	,	PUNCT
ejpam-5602	184	6	s.m	s.m	PROPN
ejpam-5602	184	7	.	.	PROPN
ejpam-5602	184	8	menchavez	menchavez	PROPN
ejpam-5602	184	9	,	,	PUNCT
ejpam-5602	184	10	f.p	f.p	PROPN
ejpam-5602	184	11	.	.	PROPN
ejpam-5602	184	12	jamil	jamil	PROPN
ejpam-5602	184	13	/	/	SYM
ejpam-5602	184	14	eur	eur	PROPN
ejpam-5602	184	15	.	.	PUNCT
ejpam-5602	185	1	j.	j.	PROPN
ejpam-5602	185	2	pure	pure	PROPN
ejpam-5602	185	3	appl	appl	PROPN
ejpam-5602	185	4	.	.	PROPN
ejpam-5602	185	5	math	math	PROPN
ejpam-5602	185	6	,	,	PUNCT
ejpam-5602	185	7	18	18	NUM
ejpam-5602	185	8	(	(	PUNCT
ejpam-5602	185	9	1	1	NUM
ejpam-5602	185	10	)	)	PUNCT
ejpam-5602	185	11	(	(	PUNCT
ejpam-5602	185	12	2025	2025	NUM
ejpam-5602	185	13	)	)	PUNCT
ejpam-5602	185	14	,	,	PUNCT
ejpam-5602	185	15	5602	5602	NUM
ejpam-5602	185	16	7	7	NUM
ejpam-5602	185	17	of	of	ADP
ejpam-5602	185	18	18	18	NUM
ejpam-5602	185	19	corollary	corollary	ADJ
ejpam-5602	185	20	2	2	NUM
ejpam-5602	185	21	.	.	PUNCT
ejpam-5602	186	1	let	let	VERB
ejpam-5602	186	2	g	g	NOUN
ejpam-5602	186	3	and	and	CCONJ
ejpam-5602	186	4	h	h	NOUN
ejpam-5602	186	5	be	be	AUX
ejpam-5602	186	6	nontrivial	nontrivial	ADJ
ejpam-5602	186	7	connected	connected	ADJ
ejpam-5602	186	8	graphs	graph	NOUN
ejpam-5602	186	9	.	.	PUNCT
ejpam-5602	187	1	if	if	SCONJ
ejpam-5602	187	2	there	there	PRON
ejpam-5602	187	3	exists	exist	VERB
ejpam-5602	187	4	a	a	DET
ejpam-5602	187	5	γtdi	γtdi	NOUN
ejpam-5602	187	6	-	-	PUNCT
ejpam-5602	187	7	function	function	NOUN
ejpam-5602	187	8	f	f	NOUN
ejpam-5602	187	9	=	=	SYM
ejpam-5602	187	10	(	(	PUNCT
ejpam-5602	187	11	v0	v0	PROPN
ejpam-5602	187	12	,	,	PUNCT
ejpam-5602	187	13	v1	v1	NOUN
ejpam-5602	187	14	,	,	PUNCT
ejpam-5602	187	15	v2	v2	PROPN
ejpam-5602	187	16	,	,	PUNCT
ejpam-5602	187	17	v3	v3	PROPN
ejpam-5602	187	18	)	)	PUNCT
ejpam-5602	187	19	of	of	ADP
ejpam-5602	187	20	g+h	g+h	PROPN
ejpam-5602	187	21	such	such	ADJ
ejpam-5602	187	22	that	that	SCONJ
ejpam-5602	187	23	either	either	CCONJ
ejpam-5602	187	24	f	f	PROPN
ejpam-5602	187	25	|g	|g	PROPN
ejpam-5602	187	26	is	be	AUX
ejpam-5602	187	27	a	a	DET
ejpam-5602	187	28	tdidf	tdidf	NOUN
ejpam-5602	187	29	on	on	ADP
ejpam-5602	187	30	g	g	PROPN
ejpam-5602	187	31	or	or	CCONJ
ejpam-5602	187	32	f	f	PROPN
ejpam-5602	187	33	|h	|h	NOUN
ejpam-5602	187	34	is	be	AUX
ejpam-5602	187	35	a	a	DET
ejpam-5602	187	36	tdidf	tdidf	NOUN
ejpam-5602	187	37	on	on	ADP
ejpam-5602	187	38	h	h	PROPN
ejpam-5602	187	39	then	then	ADV
ejpam-5602	187	40	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	187	41	)	)	PUNCT
ejpam-5602	188	1	=	=	SYM
ejpam-5602	188	2	min{γtdi(g	min{γtdi(g	PROPN
ejpam-5602	188	3	)	)	PUNCT
ejpam-5602	188	4	,	,	PUNCT
ejpam-5602	188	5	γtdi(h	γtdi(h	PROPN
ejpam-5602	188	6	)	)	PUNCT
ejpam-5602	188	7	}	}	PUNCT
ejpam-5602	188	8	.	.	PUNCT
ejpam-5602	189	1	proof	proof	NOUN
ejpam-5602	189	2	:	:	PUNCT
ejpam-5602	189	3	by	by	ADP
ejpam-5602	189	4	corollary	corollary	ADJ
ejpam-5602	189	5	1	1	NUM
ejpam-5602	189	6	,	,	PUNCT
ejpam-5602	189	7	γtdi(g	γtdi(g	NOUN
ejpam-5602	189	8	+	+	CCONJ
ejpam-5602	189	9	h	h	NOUN
ejpam-5602	189	10	)	)	PUNCT
ejpam-5602	189	11	≤	≤	NUM
ejpam-5602	189	12	min{γtdi(g	min{γtdi(g	NOUN
ejpam-5602	189	13	)	)	PUNCT
ejpam-5602	189	14	,	,	PUNCT
ejpam-5602	189	15	γtdi(h	γtdi(h	PROPN
ejpam-5602	189	16	)	)	PUNCT
ejpam-5602	189	17	}	}	PUNCT
ejpam-5602	189	18	.	.	PUNCT
ejpam-5602	190	1	assume	assume	VERB
ejpam-5602	190	2	,	,	PUNCT
ejpam-5602	190	3	wlog	wlog	PROPN
ejpam-5602	190	4	,	,	PUNCT
ejpam-5602	190	5	f	f	PROPN
ejpam-5602	190	6	|g	|g	X
ejpam-5602	190	7	=	=	SYM
ejpam-5602	190	8	(	(	PUNCT
ejpam-5602	190	9	v0	v0	NOUN
ejpam-5602	190	10	∩	∩	NOUN
ejpam-5602	190	11	v	v	X
ejpam-5602	190	12	(	(	PUNCT
ejpam-5602	190	13	g	g	NOUN
ejpam-5602	190	14	)	)	PUNCT
ejpam-5602	190	15	,	,	PUNCT
ejpam-5602	190	16	v1	v1	NOUN
ejpam-5602	190	17	∩	∩	ADJ
ejpam-5602	190	18	v	v	NOUN
ejpam-5602	190	19	(	(	PUNCT
ejpam-5602	190	20	g	g	NOUN
ejpam-5602	190	21	)	)	PUNCT
ejpam-5602	190	22	,	,	PUNCT
ejpam-5602	190	23	v2	v2	PROPN
ejpam-5602	190	24	∩	∩	ADJ
ejpam-5602	190	25	v	v	NOUN
ejpam-5602	190	26	(	(	PUNCT
ejpam-5602	190	27	g	g	NOUN
ejpam-5602	190	28	)	)	PUNCT
ejpam-5602	190	29	,	,	PUNCT
ejpam-5602	190	30	v3	v3	PROPN
ejpam-5602	190	31	∩	∩	PROPN
ejpam-5602	190	32	v	v	X
ejpam-5602	190	33	(	(	PUNCT
ejpam-5602	190	34	g	g	NOUN
ejpam-5602	190	35	)	)	PUNCT
ejpam-5602	190	36	)	)	PUNCT
ejpam-5602	190	37	is	be	AUX
ejpam-5602	190	38	a	a	DET
ejpam-5602	190	39	tdidf	tdidf	NOUN
ejpam-5602	190	40	on	on	ADP
ejpam-5602	190	41	g.	g.	PROPN
ejpam-5602	190	42	then	then	ADV
ejpam-5602	190	43	γtdi(g	γtdi(g	PROPN
ejpam-5602	190	44	)	)	PUNCT
ejpam-5602	190	45	≤	≤	NOUN
ejpam-5602	190	46	ωg(f	ωg(f	NUM
ejpam-5602	190	47	|g	|g	NOUN
ejpam-5602	190	48	)	)	PUNCT
ejpam-5602	190	49	≤	≤	NOUN
ejpam-5602	190	50	ωg+h(f	ωg+h(f	PROPN
ejpam-5602	190	51	)	)	PUNCT
ejpam-5602	190	52	.	.	PUNCT
ejpam-5602	191	1	this	this	PRON
ejpam-5602	191	2	implies	imply	VERB
ejpam-5602	191	3	that	that	SCONJ
ejpam-5602	191	4	γtdi(g	γtdi(g	PROPN
ejpam-5602	191	5	+	+	NOUN
ejpam-5602	191	6	h	h	NOUN
ejpam-5602	191	7	)	)	PUNCT
ejpam-5602	191	8	≥	≥	NOUN
ejpam-5602	191	9	min{γtdi(g	min{γtdi(g	NOUN
ejpam-5602	191	10	)	)	PUNCT
ejpam-5602	191	11	,	,	PUNCT
ejpam-5602	191	12	γtdi(h	γtdi(h	PROPN
ejpam-5602	191	13	)	)	PUNCT
ejpam-5602	191	14	}	}	PUNCT
ejpam-5602	191	15	.	.	PUNCT
ejpam-5602	192	1	therefore	therefore	ADV
ejpam-5602	192	2	,	,	PUNCT
ejpam-5602	192	3	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	192	4	)	)	PUNCT
ejpam-5602	192	5	=	=	SYM
ejpam-5602	192	6	min{γtdi(g	min{γtdi(g	PROPN
ejpam-5602	192	7	)	)	PUNCT
ejpam-5602	192	8	,	,	PUNCT
ejpam-5602	192	9	γtdi(h	γtdi(h	PROPN
ejpam-5602	192	10	)	)	PUNCT
ejpam-5602	192	11	}	}	PUNCT
ejpam-5602	192	12	.	.	PUNCT
ejpam-5602	193	1	■	■	PUNCT
ejpam-5602	193	2	proposition	proposition	NOUN
ejpam-5602	193	3	6	6	NUM
ejpam-5602	193	4	.	.	PUNCT
ejpam-5602	194	1	let	let	VERB
ejpam-5602	194	2	g	g	NOUN
ejpam-5602	194	3	and	and	CCONJ
ejpam-5602	194	4	h	h	NOUN
ejpam-5602	194	5	be	be	AUX
ejpam-5602	194	6	nontrivial	nontrivial	ADJ
ejpam-5602	194	7	connected	connect	VERB
ejpam-5602	194	8	graphs	graph	NOUN
ejpam-5602	194	9	of	of	ADP
ejpam-5602	194	10	orders	order	NOUN
ejpam-5602	194	11	n	n	PRON
ejpam-5602	194	12	and	and	CCONJ
ejpam-5602	194	13	m	m	PROPN
ejpam-5602	194	14	,	,	PUNCT
ejpam-5602	194	15	respectively	respectively	ADV
ejpam-5602	194	16	.	.	PUNCT
ejpam-5602	195	1	then	then	ADV
ejpam-5602	195	2	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	195	3	)	)	PUNCT
ejpam-5602	195	4	=	=	SYM
ejpam-5602	196	1	3	3	NUM
ejpam-5602	196	2	if	if	SCONJ
ejpam-5602	196	3	and	and	CCONJ
ejpam-5602	196	4	only	only	ADV
ejpam-5602	196	5	if	if	SCONJ
ejpam-5602	196	6	one	one	NUM
ejpam-5602	196	7	of	of	ADP
ejpam-5602	196	8	the	the	DET
ejpam-5602	196	9	following	follow	VERB
ejpam-5602	196	10	holds	hold	VERB
ejpam-5602	196	11	:	:	PUNCT
ejpam-5602	196	12	(	(	PUNCT
ejpam-5602	196	13	i	i	NOUN
ejpam-5602	196	14	)	)	PUNCT
ejpam-5602	196	15	γtdi(g	γtdi(g	PROPN
ejpam-5602	196	16	)	)	PUNCT
ejpam-5602	196	17	=	=	SYM
ejpam-5602	197	1	3	3	NUM
ejpam-5602	197	2	;	;	PUNCT
ejpam-5602	197	3	(	(	PUNCT
ejpam-5602	197	4	ii	ii	NOUN
ejpam-5602	197	5	)	)	PUNCT
ejpam-5602	197	6	γtdi(h	γtdi(h	PROPN
ejpam-5602	197	7	)	)	PUNCT
ejpam-5602	197	8	=	=	SYM
ejpam-5602	197	9	3	3	NUM
ejpam-5602	197	10	;	;	PUNCT
ejpam-5602	197	11	(	(	PUNCT
ejpam-5602	197	12	iii	iii	X
ejpam-5602	197	13	)	)	PUNCT
ejpam-5602	197	14	g	g	NOUN
ejpam-5602	197	15	and	and	CCONJ
ejpam-5602	197	16	h	h	NOUN
ejpam-5602	197	17	each	each	PRON
ejpam-5602	197	18	contains	contain	VERB
ejpam-5602	197	19	at	at	ADP
ejpam-5602	197	20	least	least	ADV
ejpam-5602	197	21	one	one	NUM
ejpam-5602	197	22	vertex	vertex	NOUN
ejpam-5602	197	23	of	of	ADP
ejpam-5602	197	24	degree	degree	NOUN
ejpam-5602	197	25	n−	n−	NOUN
ejpam-5602	197	26	1	1	NUM
ejpam-5602	197	27	and	and	CCONJ
ejpam-5602	197	28	m−	m−	PROPN
ejpam-5602	197	29	1	1	NUM
ejpam-5602	197	30	,	,	PUNCT
ejpam-5602	197	31	respectively	respectively	ADV
ejpam-5602	197	32	.	.	PUNCT
ejpam-5602	198	1	proof	proof	NOUN
ejpam-5602	198	2	:	:	PUNCT
ejpam-5602	198	3	suppose	suppose	VERB
ejpam-5602	198	4	that	that	SCONJ
ejpam-5602	198	5	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	198	6	)	)	PUNCT
ejpam-5602	198	7	=	=	SYM
ejpam-5602	199	1	3	3	X
ejpam-5602	199	2	.	.	PUNCT
ejpam-5602	199	3	by	by	ADP
ejpam-5602	199	4	proposition	proposition	NOUN
ejpam-5602	199	5	1	1	NUM
ejpam-5602	199	6	,	,	PUNCT
ejpam-5602	199	7	g+h	g+h	PROPN
ejpam-5602	199	8	has	have	VERB
ejpam-5602	199	9	at	at	ADV
ejpam-5602	199	10	least	least	ADV
ejpam-5602	199	11	two	two	NUM
ejpam-5602	199	12	vertices	vertex	NOUN
ejpam-5602	199	13	of	of	ADP
ejpam-5602	199	14	degree	degree	NOUN
ejpam-5602	199	15	n	n	PROPN
ejpam-5602	199	16	+	+	CCONJ
ejpam-5602	199	17	m	m	NOUN
ejpam-5602	199	18	−	−	NOUN
ejpam-5602	200	1	1	1	NUM
ejpam-5602	200	2	.	.	PUNCT
ejpam-5602	201	1	take	take	VERB
ejpam-5602	201	2	u	u	NOUN
ejpam-5602	201	3	,	,	PUNCT
ejpam-5602	201	4	v	v	PROPN
ejpam-5602	201	5	∈	∈	PROPN
ejpam-5602	201	6	v	v	NOUN
ejpam-5602	201	7	(	(	PUNCT
ejpam-5602	201	8	g	g	PROPN
ejpam-5602	201	9	+	+	NOUN
ejpam-5602	201	10	h	h	NOUN
ejpam-5602	201	11	)	)	PUNCT
ejpam-5602	201	12	for	for	ADP
ejpam-5602	201	13	which	which	PRON
ejpam-5602	201	14	dg+h(u	dg+h(u	NOUN
ejpam-5602	201	15	)	)	PUNCT
ejpam-5602	201	16	=	=	SYM
ejpam-5602	201	17	n	n	PROPN
ejpam-5602	201	18	+	+	NOUN
ejpam-5602	201	19	m	m	VERB
ejpam-5602	201	20	−	−	NUM
ejpam-5602	201	21	1	1	NUM
ejpam-5602	201	22	and	and	CCONJ
ejpam-5602	201	23	dg+h(v	dg+h(v	ADJ
ejpam-5602	201	24	)	)	PUNCT
ejpam-5602	201	25	=	=	SYM
ejpam-5602	201	26	n	n	PROPN
ejpam-5602	201	27	+	+	NOUN
ejpam-5602	201	28	m	m	VERB
ejpam-5602	201	29	−	−	NOUN
ejpam-5602	202	1	1	1	NUM
ejpam-5602	202	2	.	.	PUNCT
ejpam-5602	203	1	if	if	SCONJ
ejpam-5602	203	2	u	u	NOUN
ejpam-5602	203	3	,	,	PUNCT
ejpam-5602	203	4	v	v	PROPN
ejpam-5602	203	5	∈	∈	PROPN
ejpam-5602	203	6	v	v	NOUN
ejpam-5602	203	7	(	(	PUNCT
ejpam-5602	203	8	g	g	NOUN
ejpam-5602	203	9	)	)	PUNCT
ejpam-5602	203	10	,	,	PUNCT
ejpam-5602	203	11	then	then	ADV
ejpam-5602	203	12	both	both	DET
ejpam-5602	203	13	u	u	NOUN
ejpam-5602	203	14	and	and	CCONJ
ejpam-5602	203	15	v	v	NOUN
ejpam-5602	203	16	have	have	VERB
ejpam-5602	203	17	degree	degree	NOUN
ejpam-5602	203	18	n	n	CCONJ
ejpam-5602	203	19	−	−	PROPN
ejpam-5602	203	20	1	1	NUM
ejpam-5602	203	21	.	.	PUNCT
ejpam-5602	204	1	by	by	ADP
ejpam-5602	204	2	proposition	proposition	NOUN
ejpam-5602	204	3	1	1	NUM
ejpam-5602	204	4	,	,	PUNCT
ejpam-5602	204	5	(	(	PUNCT
ejpam-5602	204	6	i	i	NOUN
ejpam-5602	204	7	)	)	PUNCT
ejpam-5602	204	8	holds	hold	VERB
ejpam-5602	204	9	.	.	PUNCT
ejpam-5602	205	1	similarly	similarly	ADV
ejpam-5602	205	2	,	,	PUNCT
ejpam-5602	205	3	if	if	SCONJ
ejpam-5602	205	4	u	u	NOUN
ejpam-5602	205	5	,	,	PUNCT
ejpam-5602	205	6	v	v	PROPN
ejpam-5602	205	7	∈	∈	PROPN
ejpam-5602	205	8	v	v	NOUN
ejpam-5602	205	9	(	(	PUNCT
ejpam-5602	205	10	h	h	NOUN
ejpam-5602	205	11	)	)	PUNCT
ejpam-5602	205	12	,	,	PUNCT
ejpam-5602	205	13	then	then	ADV
ejpam-5602	205	14	(	(	PUNCT
ejpam-5602	205	15	ii	ii	NOUN
ejpam-5602	205	16	)	)	PUNCT
ejpam-5602	205	17	holds	hold	VERB
ejpam-5602	205	18	.	.	PUNCT
ejpam-5602	206	1	if	if	SCONJ
ejpam-5602	206	2	u	u	PROPN
ejpam-5602	206	3	∈	∈	PROPN
ejpam-5602	206	4	v	v	ADP
ejpam-5602	206	5	(	(	PUNCT
ejpam-5602	206	6	g	g	NOUN
ejpam-5602	206	7	)	)	PUNCT
ejpam-5602	206	8	and	and	CCONJ
ejpam-5602	206	9	v	v	ADP
ejpam-5602	206	10	∈	∈	PROPN
ejpam-5602	206	11	v	v	NOUN
ejpam-5602	206	12	(	(	PUNCT
ejpam-5602	206	13	h	h	NOUN
ejpam-5602	206	14	)	)	PUNCT
ejpam-5602	206	15	,	,	PUNCT
ejpam-5602	206	16	then	then	ADV
ejpam-5602	206	17	(	(	PUNCT
ejpam-5602	206	18	iii	iii	NOUN
ejpam-5602	206	19	)	)	PUNCT
ejpam-5602	206	20	holds	hold	VERB
ejpam-5602	206	21	.	.	PUNCT
ejpam-5602	207	1	conversely	conversely	ADV
ejpam-5602	207	2	,	,	PUNCT
ejpam-5602	207	3	if	if	SCONJ
ejpam-5602	207	4	(	(	PUNCT
ejpam-5602	207	5	i	i	NOUN
ejpam-5602	207	6	)	)	PUNCT
ejpam-5602	207	7	or	or	CCONJ
ejpam-5602	207	8	(	(	PUNCT
ejpam-5602	207	9	ii	ii	NOUN
ejpam-5602	207	10	)	)	PUNCT
ejpam-5602	207	11	holds	hold	VERB
ejpam-5602	207	12	,	,	PUNCT
ejpam-5602	207	13	then	then	ADV
ejpam-5602	207	14	equation	equation	NOUN
ejpam-5602	207	15	(	(	PUNCT
ejpam-5602	207	16	1	1	NUM
ejpam-5602	207	17	)	)	PUNCT
ejpam-5602	207	18	in	in	ADP
ejpam-5602	207	19	corollary	corollary	ADJ
ejpam-5602	207	20	1	1	NUM
ejpam-5602	207	21	yields	yield	NOUN
ejpam-5602	207	22	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	207	23	)	)	PUNCT
ejpam-5602	208	1	=	=	SYM
ejpam-5602	208	2	3	3	X
ejpam-5602	208	3	.	.	X
ejpam-5602	208	4	suppose	suppose	VERB
ejpam-5602	208	5	(	(	PUNCT
ejpam-5602	208	6	iii	iii	NOUN
ejpam-5602	208	7	)	)	PUNCT
ejpam-5602	208	8	holds	hold	VERB
ejpam-5602	208	9	.	.	PUNCT
ejpam-5602	209	1	then	then	ADV
ejpam-5602	209	2	g	g	PROPN
ejpam-5602	209	3	+	+	PROPN
ejpam-5602	209	4	h	h	NOUN
ejpam-5602	209	5	contains	contain	VERB
ejpam-5602	209	6	at	at	ADV
ejpam-5602	209	7	least	least	ADV
ejpam-5602	209	8	two	two	NUM
ejpam-5602	209	9	vertices	vertex	NOUN
ejpam-5602	209	10	of	of	ADP
ejpam-5602	209	11	maximum	maximum	ADJ
ejpam-5602	209	12	degree	degree	NOUN
ejpam-5602	209	13	∆(g+h	∆(g+h	NOUN
ejpam-5602	209	14	)	)	PUNCT
ejpam-5602	210	1	=	=	SYM
ejpam-5602	210	2	(	(	PUNCT
ejpam-5602	210	3	m+	m+	NUM
ejpam-5602	210	4	n)−	n)−	PROPN
ejpam-5602	210	5	1	1	NUM
ejpam-5602	210	6	.	.	PUNCT
ejpam-5602	211	1	by	by	ADP
ejpam-5602	211	2	proposition	proposition	NOUN
ejpam-5602	211	3	1	1	NUM
ejpam-5602	211	4	,	,	PUNCT
ejpam-5602	211	5	γtdi(g+h	γtdi(g+h	NOUN
ejpam-5602	211	6	)	)	PUNCT
ejpam-5602	211	7	=	=	SYM
ejpam-5602	211	8	3	3	X
ejpam-5602	211	9	.	.	X
ejpam-5602	211	10	■	■	PUNCT
ejpam-5602	211	11	proposition	proposition	NOUN
ejpam-5602	211	12	7	7	NUM
ejpam-5602	211	13	.	.	PUNCT
ejpam-5602	211	14	let	let	VERB
ejpam-5602	211	15	g	g	NOUN
ejpam-5602	211	16	and	and	CCONJ
ejpam-5602	211	17	h	h	NOUN
ejpam-5602	211	18	be	be	AUX
ejpam-5602	211	19	nontrivial	nontrivial	ADJ
ejpam-5602	211	20	connected	connect	VERB
ejpam-5602	211	21	graphs	graph	NOUN
ejpam-5602	211	22	of	of	ADP
ejpam-5602	211	23	orders	order	NOUN
ejpam-5602	211	24	n	n	PRON
ejpam-5602	211	25	and	and	CCONJ
ejpam-5602	211	26	m	m	PROPN
ejpam-5602	211	27	,	,	PUNCT
ejpam-5602	211	28	respectively	respectively	ADV
ejpam-5602	211	29	.	.	PUNCT
ejpam-5602	212	1	then	then	ADV
ejpam-5602	212	2	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	212	3	)	)	PUNCT
ejpam-5602	212	4	=	=	SYM
ejpam-5602	212	5	4	4	NUM
ejpam-5602	212	6	if	if	SCONJ
ejpam-5602	212	7	and	and	CCONJ
ejpam-5602	212	8	only	only	ADV
ejpam-5602	212	9	if	if	SCONJ
ejpam-5602	212	10	one	one	NUM
ejpam-5602	212	11	of	of	ADP
ejpam-5602	212	12	the	the	DET
ejpam-5602	212	13	following	follow	VERB
ejpam-5602	212	14	holds	hold	VERB
ejpam-5602	212	15	:	:	PUNCT
ejpam-5602	212	16	(	(	PUNCT
ejpam-5602	212	17	i	i	NOUN
ejpam-5602	212	18	)	)	PUNCT
ejpam-5602	212	19	∆(h	∆(h	NOUN
ejpam-5602	212	20	)	)	PUNCT
ejpam-5602	212	21	≤	≤	NOUN
ejpam-5602	212	22	m−	m−	PROPN
ejpam-5602	212	23	2	2	NUM
ejpam-5602	212	24	and	and	CCONJ
ejpam-5602	212	25	g	g	PROPN
ejpam-5602	212	26	has	have	VERB
ejpam-5602	212	27	exactly	exactly	ADV
ejpam-5602	212	28	one	one	NUM
ejpam-5602	212	29	vertex	vertex	NOUN
ejpam-5602	212	30	of	of	ADP
ejpam-5602	212	31	degree	degree	NOUN
ejpam-5602	212	32	n−	n−	NOUN
ejpam-5602	212	33	1	1	NUM
ejpam-5602	212	34	;	;	PUNCT
ejpam-5602	212	35	(	(	PUNCT
ejpam-5602	212	36	ii	ii	NOUN
ejpam-5602	212	37	)	)	PUNCT
ejpam-5602	212	38	∆(g	∆(g	NOUN
ejpam-5602	212	39	)	)	PUNCT
ejpam-5602	212	40	≤	≤	NUM
ejpam-5602	212	41	n−	n−	NOUN
ejpam-5602	212	42	2	2	NUM
ejpam-5602	212	43	and	and	CCONJ
ejpam-5602	212	44	h	h	NOUN
ejpam-5602	212	45	has	have	VERB
ejpam-5602	212	46	exactly	exactly	ADV
ejpam-5602	212	47	one	one	NUM
ejpam-5602	212	48	vertex	vertex	NOUN
ejpam-5602	212	49	of	of	ADP
ejpam-5602	212	50	degree	degree	NOUN
ejpam-5602	212	51	m−	m−	PROPN
ejpam-5602	212	52	1	1	NUM
ejpam-5602	212	53	;	;	PUNCT
ejpam-5602	212	54	(	(	PUNCT
ejpam-5602	212	55	iii	iii	X
ejpam-5602	212	56	)	)	PUNCT
ejpam-5602	212	57	γ(g	γ(g	PROPN
ejpam-5602	212	58	)	)	PUNCT
ejpam-5602	212	59	=	=	SYM
ejpam-5602	212	60	2	2	NUM
ejpam-5602	212	61	and	and	CCONJ
ejpam-5602	212	62	γ(h	γ(h	NOUN
ejpam-5602	212	63	)	)	PUNCT
ejpam-5602	212	64	=	=	SYM
ejpam-5602	212	65	2	2	X
ejpam-5602	212	66	.	.	PUNCT
ejpam-5602	212	67	(	(	PUNCT
ejpam-5602	212	68	iv	iv	X
ejpam-5602	212	69	)	)	PUNCT
ejpam-5602	212	70	γ(g	γ(g	PROPN
ejpam-5602	212	71	)	)	PUNCT
ejpam-5602	212	72	≥	≥	NOUN
ejpam-5602	212	73	2	2	NUM
ejpam-5602	212	74	and	and	CCONJ
ejpam-5602	212	75	γ(h	γ(h	NOUN
ejpam-5602	212	76	)	)	PUNCT
ejpam-5602	212	77	≥	≥	NOUN
ejpam-5602	212	78	2	2	NUM
ejpam-5602	212	79	and	and	CCONJ
ejpam-5602	212	80	one	one	NUM
ejpam-5602	212	81	of	of	ADP
ejpam-5602	212	82	the	the	DET
ejpam-5602	212	83	following	following	NOUN
ejpam-5602	212	84	holds	hold	VERB
ejpam-5602	212	85	:	:	PUNCT
ejpam-5602	212	86	(	(	PUNCT
ejpam-5602	212	87	a	a	X
ejpam-5602	212	88	)	)	PUNCT
ejpam-5602	212	89	g	g	NOUN
ejpam-5602	212	90	or	or	CCONJ
ejpam-5602	212	91	h	h	NOUN
ejpam-5602	212	92	has	have	VERB
ejpam-5602	212	93	a	a	DET
ejpam-5602	212	94	3	3	NUM
ejpam-5602	212	95	-	-	PUNCT
ejpam-5602	212	96	dominating	dominating	NOUN
ejpam-5602	212	97	set	set	NOUN
ejpam-5602	212	98	d	d	NOUN
ejpam-5602	212	99	with	with	ADP
ejpam-5602	212	100	|d|	|d|	PROPN
ejpam-5602	212	101	=	=	SYM
ejpam-5602	212	102	4	4	NUM
ejpam-5602	212	103	and	and	CCONJ
ejpam-5602	212	104	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	212	105	)	)	PUNCT
ejpam-5602	212	106	≥	≥	NOUN
ejpam-5602	212	107	2	2	NUM
ejpam-5602	212	108	;	;	PUNCT
ejpam-5602	212	109	(	(	PUNCT
ejpam-5602	212	110	b	b	X
ejpam-5602	212	111	)	)	PUNCT
ejpam-5602	212	112	g	g	NOUN
ejpam-5602	212	113	or	or	CCONJ
ejpam-5602	212	114	h	h	NOUN
ejpam-5602	212	115	has	have	VERB
ejpam-5602	212	116	a	a	DET
ejpam-5602	212	117	2	2	NUM
ejpam-5602	212	118	-	-	PUNCT
ejpam-5602	212	119	dominating	dominating	NOUN
ejpam-5602	212	120	set	set	NOUN
ejpam-5602	212	121	d	d	ADP
ejpam-5602	212	122	such	such	ADJ
ejpam-5602	212	123	that	that	DET
ejpam-5602	212	124	|d|	|d|	PROPN
ejpam-5602	212	125	=	=	SYM
ejpam-5602	212	126	3	3	NUM
ejpam-5602	212	127	and	and	CCONJ
ejpam-5602	212	128	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	212	129	is	be	AUX
ejpam-5602	212	130	connected	connect	VERB
ejpam-5602	212	131	;	;	PUNCT
ejpam-5602	212	132	proof	proof	NOUN
ejpam-5602	212	133	:	:	PUNCT
ejpam-5602	212	134	assume	assume	VERB
ejpam-5602	212	135	that	that	SCONJ
ejpam-5602	212	136	γtdi(g	γtdi(g	PROPN
ejpam-5602	212	137	+	+	CCONJ
ejpam-5602	212	138	h	h	NOUN
ejpam-5602	212	139	)	)	PUNCT
ejpam-5602	212	140	=	=	PUNCT
ejpam-5602	213	1	4	4	X
ejpam-5602	213	2	.	.	PUNCT
ejpam-5602	214	1	if	if	SCONJ
ejpam-5602	214	2	g	g	PROPN
ejpam-5602	214	3	+	+	NOUN
ejpam-5602	214	4	h	h	NOUN
ejpam-5602	214	5	has	have	VERB
ejpam-5602	214	6	exactly	exactly	ADV
ejpam-5602	214	7	one	one	NUM
ejpam-5602	214	8	vertex	vertex	NOUN
ejpam-5602	214	9	v	v	NOUN
ejpam-5602	214	10	for	for	ADP
ejpam-5602	214	11	which	which	PRON
ejpam-5602	214	12	degg+h(v	degg+h(v	NOUN
ejpam-5602	214	13	)	)	PUNCT
ejpam-5602	215	1	=	=	PUNCT
ejpam-5602	216	1	m	m	AUX
ejpam-5602	216	2	+	+	NOUN
ejpam-5602	216	3	n	n	CCONJ
ejpam-5602	216	4	−	−	PROPN
ejpam-5602	216	5	1	1	NUM
ejpam-5602	216	6	,	,	PUNCT
ejpam-5602	216	7	then	then	ADV
ejpam-5602	216	8	(	(	PUNCT
ejpam-5602	216	9	i	i	NOUN
ejpam-5602	216	10	)	)	PUNCT
ejpam-5602	216	11	or	or	CCONJ
ejpam-5602	216	12	(	(	PUNCT
ejpam-5602	216	13	ii	ii	NOUN
ejpam-5602	216	14	)	)	PUNCT
ejpam-5602	216	15	holds	hold	VERB
ejpam-5602	216	16	.	.	PUNCT
ejpam-5602	217	1	otherwise	otherwise	ADV
ejpam-5602	217	2	,	,	PUNCT
ejpam-5602	217	3	by	by	ADP
ejpam-5602	217	4	proposition	proposition	NOUN
ejpam-5602	217	5	3	3	NUM
ejpam-5602	217	6	,	,	PUNCT
ejpam-5602	217	7	γ(g	γ(g	PROPN
ejpam-5602	217	8	)	)	PUNCT
ejpam-5602	217	9	≥	≥	NOUN
ejpam-5602	217	10	2	2	NUM
ejpam-5602	217	11	,	,	PUNCT
ejpam-5602	217	12	γ(h	γ(h	NOUN
ejpam-5602	217	13	)	)	PUNCT
ejpam-5602	217	14	≥	≥	NOUN
ejpam-5602	217	15	2	2	NUM
ejpam-5602	217	16	and	and	CCONJ
ejpam-5602	217	17	g	g	PROPN
ejpam-5602	217	18	+	+	CCONJ
ejpam-5602	218	1	h	h	NOUN
ejpam-5602	219	1	has	have	VERB
ejpam-5602	219	2	a	a	DET
ejpam-5602	219	3	3	3	NUM
ejpam-5602	219	4	-	-	PUNCT
ejpam-5602	219	5	dominating	dominating	NOUN
ejpam-5602	219	6	set	set	NOUN
ejpam-5602	219	7	d	d	NOUN
ejpam-5602	219	8	with	with	ADP
ejpam-5602	219	9	|d|	|d|	PROPN
ejpam-5602	219	10	=	=	SYM
ejpam-5602	219	11	4	4	NUM
ejpam-5602	219	12	and	and	CCONJ
ejpam-5602	219	13	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	219	14	)	)	PUNCT
ejpam-5602	219	15	≥	≥	NOUN
ejpam-5602	220	1	2	2	NUM
ejpam-5602	220	2	.	.	PUNCT
ejpam-5602	220	3	let	let	VERB
ejpam-5602	220	4	dg	dg	VERB
ejpam-5602	220	5	=	=	SYM
ejpam-5602	220	6	d	d	PROPN
ejpam-5602	220	7	∩	∩	ADJ
ejpam-5602	220	8	v	v	X
ejpam-5602	220	9	(	(	PUNCT
ejpam-5602	220	10	g	g	NOUN
ejpam-5602	220	11	)	)	PUNCT
ejpam-5602	220	12	and	and	CCONJ
ejpam-5602	220	13	dh	dh	NOUN
ejpam-5602	220	14	=	=	SYM
ejpam-5602	220	15	d	d	PROPN
ejpam-5602	220	16	∩	∩	ADJ
ejpam-5602	220	17	v	v	X
ejpam-5602	220	18	(	(	PUNCT
ejpam-5602	220	19	h	h	NOUN
ejpam-5602	220	20	)	)	PUNCT
ejpam-5602	220	21	.	.	PUNCT
ejpam-5602	221	1	suppose	suppose	VERB
ejpam-5602	221	2	first	first	ADV
ejpam-5602	221	3	that	that	SCONJ
ejpam-5602	221	4	|dg|	|dg|	NOUN
ejpam-5602	221	5	=	=	SYM
ejpam-5602	221	6	2	2	NUM
ejpam-5602	221	7	=	=	SYM
ejpam-5602	221	8	|dh	|dh	NOUN
ejpam-5602	221	9	|	|	NOUN
ejpam-5602	221	10	.	.	PUNCT
ejpam-5602	222	1	for	for	ADP
ejpam-5602	222	2	each	each	DET
ejpam-5602	222	3	x	x	SYM
ejpam-5602	222	4	∈	∈	PROPN
ejpam-5602	222	5	v	v	ADP
ejpam-5602	222	6	(	(	PUNCT
ejpam-5602	222	7	g	g	NOUN
ejpam-5602	222	8	)	)	PUNCT
ejpam-5602	222	9	\	\	PROPN
ejpam-5602	222	10	dg	dg	PROPN
ejpam-5602	222	11	,	,	PUNCT
ejpam-5602	222	12	since	since	SCONJ
ejpam-5602	222	13	d	d	NOUN
ejpam-5602	222	14	is	be	AUX
ejpam-5602	222	15	a	a	DET
ejpam-5602	222	16	3	3	NUM
ejpam-5602	222	17	-	-	PUNCT
ejpam-5602	222	18	dominating	dominate	VERB
ejpam-5602	222	19	set	set	NOUN
ejpam-5602	222	20	of	of	ADP
ejpam-5602	222	21	g	g	PROPN
ejpam-5602	223	1	+	+	CCONJ
ejpam-5602	223	2	h	h	NOUN
ejpam-5602	223	3	,	,	PUNCT
ejpam-5602	223	4	there	there	PRON
ejpam-5602	223	5	exists	exist	VERB
ejpam-5602	223	6	u	u	PROPN
ejpam-5602	223	7	∈	∈	NOUN
ejpam-5602	223	8	dg	dg	VERB
ejpam-5602	223	9	for	for	ADP
ejpam-5602	223	10	which	which	PRON
ejpam-5602	223	11	ux	ux	PROPN
ejpam-5602	223	12	∈	∈	PROPN
ejpam-5602	223	13	e(g	e(g	PROPN
ejpam-5602	223	14	)	)	PUNCT
ejpam-5602	223	15	.	.	PUNCT
ejpam-5602	224	1	thus	thus	ADV
ejpam-5602	224	2	,	,	PUNCT
ejpam-5602	224	3	dg	dg	PROPN
ejpam-5602	224	4	is	be	AUX
ejpam-5602	224	5	a	a	DET
ejpam-5602	224	6	dominating	dominating	NOUN
ejpam-5602	224	7	set	set	NOUN
ejpam-5602	224	8	of	of	ADP
ejpam-5602	224	9	g.	g.	PROPN
ejpam-5602	224	10	since	since	SCONJ
ejpam-5602	224	11	γ(g	γ(g	PROPN
ejpam-5602	224	12	)	)	PUNCT
ejpam-5602	224	13	≥	≥	NOUN
ejpam-5602	224	14	2	2	NUM
ejpam-5602	224	15	,	,	PUNCT
ejpam-5602	224	16	γ(g	γ(g	PROPN
ejpam-5602	224	17	)	)	PUNCT
ejpam-5602	225	1	=	=	SYM
ejpam-5602	225	2	|dg|	|dg|	PROPN
ejpam-5602	225	3	=	=	SYM
ejpam-5602	225	4	2	2	NUM
ejpam-5602	225	5	s.j.l	s.j.l	NOUN
ejpam-5602	225	6	.	.	PUNCT
ejpam-5602	225	7	sumbalan	sumbalan	PROPN
ejpam-5602	225	8	,	,	PUNCT
ejpam-5602	225	9	s.m	s.m	PROPN
ejpam-5602	225	10	.	.	PROPN
ejpam-5602	225	11	menchavez	menchavez	PROPN
ejpam-5602	225	12	,	,	PUNCT
ejpam-5602	225	13	f.p	f.p	PROPN
ejpam-5602	225	14	.	.	PROPN
ejpam-5602	225	15	jamil	jamil	PROPN
ejpam-5602	225	16	/	/	SYM
ejpam-5602	225	17	eur	eur	PROPN
ejpam-5602	225	18	.	.	PUNCT
ejpam-5602	226	1	j.	j.	PROPN
ejpam-5602	226	2	pure	pure	PROPN
ejpam-5602	226	3	appl	appl	PROPN
ejpam-5602	226	4	.	.	PROPN
ejpam-5602	226	5	math	math	PROPN
ejpam-5602	226	6	,	,	PUNCT
ejpam-5602	226	7	18	18	NUM
ejpam-5602	226	8	(	(	PUNCT
ejpam-5602	226	9	1	1	NUM
ejpam-5602	226	10	)	)	PUNCT
ejpam-5602	226	11	(	(	PUNCT
ejpam-5602	226	12	2025	2025	NUM
ejpam-5602	226	13	)	)	PUNCT
ejpam-5602	226	14	,	,	PUNCT
ejpam-5602	226	15	5602	5602	NUM
ejpam-5602	226	16	8	8	NUM
ejpam-5602	226	17	of	of	ADP
ejpam-5602	226	18	18	18	NUM
ejpam-5602	226	19	similarly	similarly	ADV
ejpam-5602	226	20	,	,	PUNCT
ejpam-5602	226	21	γ(h	γ(h	NOUN
ejpam-5602	226	22	)	)	PUNCT
ejpam-5602	226	23	=	=	SYM
ejpam-5602	227	1	2	2	X
ejpam-5602	227	2	.	.	PUNCT
ejpam-5602	227	3	thus	thus	ADV
ejpam-5602	227	4	,	,	PUNCT
ejpam-5602	227	5	(	(	PUNCT
ejpam-5602	227	6	iii	iii	NOUN
ejpam-5602	227	7	)	)	PUNCT
ejpam-5602	227	8	holds	hold	VERB
ejpam-5602	227	9	.	.	PUNCT
ejpam-5602	228	1	next	next	ADV
ejpam-5602	228	2	,	,	PUNCT
ejpam-5602	228	3	if	if	SCONJ
ejpam-5602	228	4	d	d	PROPN
ejpam-5602	228	5	⊆	⊆	NUM
ejpam-5602	228	6	v	v	ADP
ejpam-5602	228	7	(	(	PUNCT
ejpam-5602	228	8	g	g	NOUN
ejpam-5602	228	9	)	)	PUNCT
ejpam-5602	228	10	or	or	CCONJ
ejpam-5602	228	11	d	d	PROPN
ejpam-5602	228	12	⊆	⊆	NUM
ejpam-5602	228	13	v	v	ADP
ejpam-5602	228	14	(	(	PUNCT
ejpam-5602	228	15	h	h	NOUN
ejpam-5602	228	16	)	)	PUNCT
ejpam-5602	228	17	,	,	PUNCT
ejpam-5602	228	18	then	then	ADV
ejpam-5602	228	19	(	(	PUNCT
ejpam-5602	228	20	iv)(a	iv)(a	NOUN
ejpam-5602	228	21	)	)	PUNCT
ejpam-5602	228	22	holds	hold	VERB
ejpam-5602	228	23	.	.	PUNCT
ejpam-5602	229	1	finally	finally	ADV
ejpam-5602	229	2	,	,	PUNCT
ejpam-5602	229	3	wlog	wlog	PROPN
ejpam-5602	229	4	suppose	suppose	VERB
ejpam-5602	229	5	that	that	SCONJ
ejpam-5602	229	6	|dg|	|dg|	PROPN
ejpam-5602	229	7	=	=	NUM
ejpam-5602	229	8	3	3	NUM
ejpam-5602	229	9	and	and	CCONJ
ejpam-5602	229	10	|dh	|dh	NOUN
ejpam-5602	229	11	|	|	ADV
ejpam-5602	229	12	=	=	SYM
ejpam-5602	229	13	1	1	X
ejpam-5602	229	14	.	.	PUNCT
ejpam-5602	229	15	clearly	clearly	ADV
ejpam-5602	229	16	,	,	PUNCT
ejpam-5602	229	17	dg	dg	PROPN
ejpam-5602	229	18	is	be	AUX
ejpam-5602	229	19	a	a	DET
ejpam-5602	229	20	2	2	NUM
ejpam-5602	229	21	-	-	PUNCT
ejpam-5602	229	22	dominating	dominating	NOUN
ejpam-5602	229	23	set	set	NOUN
ejpam-5602	229	24	of	of	ADP
ejpam-5602	229	25	g.	g.	PROPN
ejpam-5602	229	26	since	since	SCONJ
ejpam-5602	229	27	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	229	28	)	)	PUNCT
ejpam-5602	229	29	≥	≥	NOUN
ejpam-5602	229	30	2	2	NUM
ejpam-5602	229	31	,	,	PUNCT
ejpam-5602	229	32	⟨dg⟩	⟨dg⟩	PROPN
ejpam-5602	229	33	is	be	AUX
ejpam-5602	229	34	connected	connect	VERB
ejpam-5602	229	35	and	and	CCONJ
ejpam-5602	229	36	(	(	PUNCT
ejpam-5602	229	37	iv)(b	iv)(b	ADJ
ejpam-5602	229	38	)	)	PUNCT
ejpam-5602	229	39	holds	hold	VERB
ejpam-5602	229	40	.	.	PUNCT
ejpam-5602	230	1	conversely	conversely	ADV
ejpam-5602	230	2	,	,	PUNCT
ejpam-5602	230	3	note	note	VERB
ejpam-5602	230	4	that	that	SCONJ
ejpam-5602	230	5	each	each	PRON
ejpam-5602	230	6	of	of	ADP
ejpam-5602	230	7	the	the	DET
ejpam-5602	230	8	conditions	condition	NOUN
ejpam-5602	230	9	implies	imply	VERB
ejpam-5602	230	10	that	that	SCONJ
ejpam-5602	230	11	one	one	NUM
ejpam-5602	230	12	of	of	ADP
ejpam-5602	230	13	the	the	DET
ejpam-5602	230	14	conditions	condition	NOUN
ejpam-5602	230	15	in	in	ADP
ejpam-5602	230	16	proposition	proposition	NOUN
ejpam-5602	230	17	3	3	NUM
ejpam-5602	230	18	is	be	AUX
ejpam-5602	230	19	satisfied	satisfied	ADJ
ejpam-5602	230	20	for	for	ADP
ejpam-5602	230	21	g+h	g+h	PROPN
ejpam-5602	230	22	.	.	PUNCT
ejpam-5602	231	1	thus	thus	ADV
ejpam-5602	231	2	,	,	PUNCT
ejpam-5602	231	3	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	231	4	)	)	PUNCT
ejpam-5602	231	5	=	=	PUNCT
ejpam-5602	232	1	4	4	X
ejpam-5602	232	2	.	.	X
ejpam-5602	232	3	■	■	PUNCT
ejpam-5602	232	4	in	in	ADP
ejpam-5602	232	5	view	view	NOUN
ejpam-5602	232	6	of	of	ADP
ejpam-5602	232	7	proposition	proposition	NOUN
ejpam-5602	232	8	4	4	NUM
ejpam-5602	232	9	,	,	PUNCT
ejpam-5602	232	10	if	if	SCONJ
ejpam-5602	232	11	g	g	PROPN
ejpam-5602	232	12	and	and	CCONJ
ejpam-5602	232	13	h	h	NOUN
ejpam-5602	232	14	are	be	AUX
ejpam-5602	232	15	nontrivial	nontrivial	ADJ
ejpam-5602	232	16	graphs	graph	NOUN
ejpam-5602	232	17	of	of	ADP
ejpam-5602	232	18	orders	order	NOUN
ejpam-5602	232	19	n	n	PRON
ejpam-5602	232	20	and	and	CCONJ
ejpam-5602	232	21	m	m	PROPN
ejpam-5602	232	22	,	,	PUNCT
ejpam-5602	232	23	respectively	respectively	ADV
ejpam-5602	232	24	with	with	ADP
ejpam-5602	232	25	n+m	n+m	PROPN
ejpam-5602	232	26	=	=	SYM
ejpam-5602	232	27	5	5	NUM
ejpam-5602	232	28	,	,	PUNCT
ejpam-5602	232	29	then	then	ADV
ejpam-5602	232	30	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	232	31	)	)	PUNCT
ejpam-5602	233	1	=	=	PUNCT
ejpam-5602	233	2	5	5	NUM
ejpam-5602	233	3	if	if	SCONJ
ejpam-5602	233	4	and	and	CCONJ
ejpam-5602	233	5	only	only	ADV
ejpam-5602	233	6	if	if	SCONJ
ejpam-5602	233	7	g+h	g+h	PROPN
ejpam-5602	233	8	∈	∈	PROPN
ejpam-5602	233	9	{	{	PUNCT
ejpam-5602	233	10	k2,3,k2+(k1	k2,3,k2+(k1	PROPN
ejpam-5602	233	11	∪k2	∪k2	X
ejpam-5602	233	12	)	)	PUNCT
ejpam-5602	233	13	}	}	PUNCT
ejpam-5602	233	14	.	.	PUNCT
ejpam-5602	234	1	proposition	proposition	NOUN
ejpam-5602	234	2	8	8	NUM
ejpam-5602	234	3	.	.	PUNCT
ejpam-5602	235	1	let	let	VERB
ejpam-5602	235	2	g	g	NOUN
ejpam-5602	235	3	and	and	CCONJ
ejpam-5602	235	4	h	h	NOUN
ejpam-5602	235	5	be	be	AUX
ejpam-5602	235	6	nontrivial	nontrivial	ADJ
ejpam-5602	235	7	graphs	graph	NOUN
ejpam-5602	235	8	of	of	ADP
ejpam-5602	235	9	orders	order	NOUN
ejpam-5602	235	10	n	n	PRON
ejpam-5602	235	11	and	and	CCONJ
ejpam-5602	235	12	m	m	PROPN
ejpam-5602	235	13	,	,	PUNCT
ejpam-5602	235	14	respectively	respectively	ADV
ejpam-5602	235	15	,	,	PUNCT
ejpam-5602	235	16	such	such	ADJ
ejpam-5602	235	17	that	that	DET
ejpam-5602	235	18	m+	m+	NOUN
ejpam-5602	235	19	n	n	CCONJ
ejpam-5602	235	20	>	>	X
ejpam-5602	235	21	5	5	NUM
ejpam-5602	235	22	.	.	PUNCT
ejpam-5602	235	23	then	then	ADV
ejpam-5602	235	24	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	235	25	)	)	PUNCT
ejpam-5602	236	1	=	=	PUNCT
ejpam-5602	236	2	5	5	NUM
ejpam-5602	236	3	if	if	SCONJ
ejpam-5602	236	4	and	and	CCONJ
ejpam-5602	236	5	only	only	ADV
ejpam-5602	236	6	if	if	SCONJ
ejpam-5602	236	7	each	each	PRON
ejpam-5602	236	8	of	of	ADP
ejpam-5602	236	9	the	the	DET
ejpam-5602	236	10	following	follow	VERB
ejpam-5602	236	11	holds	hold	VERB
ejpam-5602	236	12	:	:	PUNCT
ejpam-5602	236	13	(	(	PUNCT
ejpam-5602	236	14	i	i	NOUN
ejpam-5602	236	15	)	)	PUNCT
ejpam-5602	236	16	γ(g	γ(g	PROPN
ejpam-5602	236	17	)	)	PUNCT
ejpam-5602	236	18	≥	≥	NOUN
ejpam-5602	236	19	2	2	NUM
ejpam-5602	236	20	and	and	CCONJ
ejpam-5602	236	21	γ(h	γ(h	NOUN
ejpam-5602	236	22	)	)	PUNCT
ejpam-5602	236	23	≥	≥	NOUN
ejpam-5602	236	24	2	2	NUM
ejpam-5602	236	25	,	,	PUNCT
ejpam-5602	236	26	but	but	CCONJ
ejpam-5602	236	27	γ(g	γ(g	PROPN
ejpam-5602	236	28	)	)	PUNCT
ejpam-5602	236	29	and	and	CCONJ
ejpam-5602	236	30	γ(h	γ(h	NOUN
ejpam-5602	236	31	)	)	PUNCT
ejpam-5602	236	32	can	can	AUX
ejpam-5602	236	33	not	not	PART
ejpam-5602	236	34	be	be	AUX
ejpam-5602	236	35	both	both	ADV
ejpam-5602	236	36	equal	equal	ADJ
ejpam-5602	236	37	to	to	ADP
ejpam-5602	236	38	2	2	NUM
ejpam-5602	236	39	;	;	PUNCT
ejpam-5602	236	40	(	(	PUNCT
ejpam-5602	236	41	ii	ii	NOUN
ejpam-5602	236	42	)	)	PUNCT
ejpam-5602	236	43	neither	neither	CCONJ
ejpam-5602	236	44	g	g	PROPN
ejpam-5602	236	45	nor	nor	CCONJ
ejpam-5602	236	46	h	h	NOUN
ejpam-5602	236	47	contains	contain	VERB
ejpam-5602	236	48	a	a	DET
ejpam-5602	236	49	2	2	NUM
ejpam-5602	236	50	-	-	PUNCT
ejpam-5602	236	51	dominating	dominating	NOUN
ejpam-5602	236	52	set	set	NOUN
ejpam-5602	236	53	d	d	NOUN
ejpam-5602	236	54	for	for	ADP
ejpam-5602	236	55	which	which	PRON
ejpam-5602	236	56	|d|	|d|	PROPN
ejpam-5602	236	57	=	=	SYM
ejpam-5602	236	58	3	3	NUM
ejpam-5602	236	59	and	and	CCONJ
ejpam-5602	236	60	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	236	61	is	be	AUX
ejpam-5602	236	62	connected	connect	VERB
ejpam-5602	236	63	;	;	PUNCT
ejpam-5602	236	64	(	(	PUNCT
ejpam-5602	236	65	iii	iii	X
ejpam-5602	236	66	)	)	PUNCT
ejpam-5602	236	67	neither	neither	CCONJ
ejpam-5602	236	68	g	g	PROPN
ejpam-5602	236	69	nor	nor	CCONJ
ejpam-5602	236	70	h	h	NOUN
ejpam-5602	236	71	has	have	VERB
ejpam-5602	236	72	a	a	DET
ejpam-5602	236	73	3	3	NUM
ejpam-5602	236	74	-	-	PUNCT
ejpam-5602	236	75	dominating	dominating	NOUN
ejpam-5602	236	76	set	set	NOUN
ejpam-5602	236	77	d	d	NOUN
ejpam-5602	236	78	with	with	ADP
ejpam-5602	236	79	|d|	|d|	PROPN
ejpam-5602	236	80	=	=	SYM
ejpam-5602	236	81	4	4	NUM
ejpam-5602	236	82	and	and	CCONJ
ejpam-5602	236	83	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	236	84	)	)	PUNCT
ejpam-5602	236	85	≥	≥	NOUN
ejpam-5602	236	86	2	2	NUM
ejpam-5602	236	87	;	;	PUNCT
ejpam-5602	236	88	(	(	PUNCT
ejpam-5602	236	89	iv	iv	X
ejpam-5602	236	90	)	)	PUNCT
ejpam-5602	236	91	one	one	NUM
ejpam-5602	236	92	of	of	ADP
ejpam-5602	236	93	the	the	DET
ejpam-5602	236	94	following	following	NOUN
ejpam-5602	236	95	holds	hold	VERB
ejpam-5602	236	96	:	:	PUNCT
ejpam-5602	236	97	(	(	PUNCT
ejpam-5602	236	98	a	a	X
ejpam-5602	236	99	)	)	PUNCT
ejpam-5602	236	100	min{γtdi(g	min{γtdi(g	NOUN
ejpam-5602	236	101	)	)	PUNCT
ejpam-5602	236	102	,	,	PUNCT
ejpam-5602	236	103	γtdi(h	γtdi(h	PROPN
ejpam-5602	236	104	)	)	PUNCT
ejpam-5602	236	105	}	}	PUNCT
ejpam-5602	236	106	=	=	SYM
ejpam-5602	236	107	5	5	NUM
ejpam-5602	236	108	;	;	PUNCT
ejpam-5602	236	109	(	(	PUNCT
ejpam-5602	236	110	b	b	X
ejpam-5602	236	111	)	)	PUNCT
ejpam-5602	236	112	g	g	NOUN
ejpam-5602	236	113	or	or	CCONJ
ejpam-5602	236	114	h	h	NOUN
ejpam-5602	236	115	has	have	VERB
ejpam-5602	236	116	a	a	DET
ejpam-5602	236	117	2	2	NUM
ejpam-5602	236	118	-	-	PUNCT
ejpam-5602	236	119	dominating	dominating	NOUN
ejpam-5602	236	120	set	set	NOUN
ejpam-5602	236	121	d	d	NOUN
ejpam-5602	236	122	for	for	ADP
ejpam-5602	236	123	which	which	PRON
ejpam-5602	236	124	|d|	|d|	PROPN
ejpam-5602	236	125	=	=	SYM
ejpam-5602	236	126	4	4	NUM
ejpam-5602	236	127	and	and	CCONJ
ejpam-5602	236	128	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	236	129	is	be	AUX
ejpam-5602	236	130	connected	connect	VERB
ejpam-5602	236	131	;	;	PUNCT
ejpam-5602	236	132	(	(	PUNCT
ejpam-5602	236	133	c	c	X
ejpam-5602	236	134	)	)	PUNCT
ejpam-5602	236	135	g	g	NOUN
ejpam-5602	236	136	or	or	CCONJ
ejpam-5602	236	137	h	h	NOUN
ejpam-5602	236	138	has	have	VERB
ejpam-5602	236	139	a	a	DET
ejpam-5602	236	140	dominating	dominating	NOUN
ejpam-5602	236	141	set	set	NOUN
ejpam-5602	236	142	d	d	NOUN
ejpam-5602	236	143	with	with	ADP
ejpam-5602	236	144	|d|	|d|	PROPN
ejpam-5602	236	145	=	=	SYM
ejpam-5602	236	146	3	3	NUM
ejpam-5602	236	147	;	;	PUNCT
ejpam-5602	236	148	(	(	PUNCT
ejpam-5602	236	149	d	d	X
ejpam-5602	236	150	)	)	PUNCT
ejpam-5602	236	151	γ(g	γ(g	PROPN
ejpam-5602	236	152	)	)	PUNCT
ejpam-5602	237	1	=	=	SYM
ejpam-5602	237	2	2	2	NUM
ejpam-5602	237	3	and	and	CCONJ
ejpam-5602	237	4	γ(h	γ(h	NOUN
ejpam-5602	237	5	)	)	PUNCT
ejpam-5602	237	6	≥	≥	NOUN
ejpam-5602	237	7	3	3	NUM
ejpam-5602	237	8	;	;	PUNCT
ejpam-5602	237	9	(	(	PUNCT
ejpam-5602	237	10	e	e	NOUN
ejpam-5602	237	11	)	)	PUNCT
ejpam-5602	237	12	γ(h	γ(h	NOUN
ejpam-5602	237	13	)	)	PUNCT
ejpam-5602	238	1	=	=	SYM
ejpam-5602	238	2	2	2	NUM
ejpam-5602	238	3	and	and	CCONJ
ejpam-5602	238	4	γ(g	γ(g	PROPN
ejpam-5602	238	5	)	)	PUNCT
ejpam-5602	238	6	≥	≥	NOUN
ejpam-5602	238	7	3	3	NUM
ejpam-5602	238	8	.	.	PUNCT
ejpam-5602	238	9	proof	proof	NOUN
ejpam-5602	238	10	:	:	PUNCT
ejpam-5602	238	11	suppose	suppose	VERB
ejpam-5602	238	12	that	that	SCONJ
ejpam-5602	238	13	γtdi(g	γtdi(g	PROPN
ejpam-5602	238	14	+	+	CCONJ
ejpam-5602	238	15	h	h	NOUN
ejpam-5602	238	16	)	)	PUNCT
ejpam-5602	238	17	=	=	SYM
ejpam-5602	238	18	5	5	X
ejpam-5602	238	19	.	.	PUNCT
ejpam-5602	238	20	by	by	ADP
ejpam-5602	238	21	proposition	proposition	NOUN
ejpam-5602	238	22	6	6	NUM
ejpam-5602	238	23	,	,	PUNCT
ejpam-5602	238	24	γ(g	γ(g	PROPN
ejpam-5602	238	25	)	)	PUNCT
ejpam-5602	238	26	≥	≥	NOUN
ejpam-5602	238	27	2	2	NUM
ejpam-5602	238	28	and	and	CCONJ
ejpam-5602	238	29	γ(h	γ(h	NOUN
ejpam-5602	238	30	)	)	PUNCT
ejpam-5602	238	31	≥	≥	NOUN
ejpam-5602	238	32	2	2	NUM
ejpam-5602	238	33	.	.	PUNCT
ejpam-5602	239	1	moreover	moreover	ADV
ejpam-5602	239	2	,	,	PUNCT
ejpam-5602	239	3	by	by	ADP
ejpam-5602	239	4	proposition	proposition	NOUN
ejpam-5602	239	5	7	7	NUM
ejpam-5602	239	6	,	,	PUNCT
ejpam-5602	239	7	γ(g	γ(g	PROPN
ejpam-5602	239	8	)	)	PUNCT
ejpam-5602	239	9	and	and	CCONJ
ejpam-5602	239	10	γ(h	γ(h	NOUN
ejpam-5602	239	11	)	)	PUNCT
ejpam-5602	239	12	can	can	AUX
ejpam-5602	239	13	not	not	PART
ejpam-5602	239	14	be	be	AUX
ejpam-5602	239	15	both	both	ADV
ejpam-5602	239	16	equal	equal	ADJ
ejpam-5602	239	17	to	to	ADP
ejpam-5602	239	18	2	2	NUM
ejpam-5602	239	19	;	;	PUNCT
ejpam-5602	239	20	neither	neither	CCONJ
ejpam-5602	239	21	g	g	NOUN
ejpam-5602	239	22	nor	nor	CCONJ
ejpam-5602	239	23	h	h	NOUN
ejpam-5602	239	24	contains	contain	VERB
ejpam-5602	239	25	a	a	DET
ejpam-5602	239	26	2	2	NUM
ejpam-5602	239	27	-	-	PUNCT
ejpam-5602	239	28	dominating	dominating	NOUN
ejpam-5602	239	29	set	set	NOUN
ejpam-5602	239	30	d	d	NOUN
ejpam-5602	239	31	for	for	ADP
ejpam-5602	239	32	which	which	PRON
ejpam-5602	239	33	|d|	|d|	PROPN
ejpam-5602	239	34	=	=	SYM
ejpam-5602	239	35	3	3	NUM
ejpam-5602	239	36	and	and	CCONJ
ejpam-5602	239	37	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	239	38	is	be	AUX
ejpam-5602	239	39	connected	connect	VERB
ejpam-5602	239	40	;	;	PUNCT
ejpam-5602	239	41	and	and	CCONJ
ejpam-5602	239	42	neither	neither	CCONJ
ejpam-5602	239	43	g	g	NOUN
ejpam-5602	239	44	nor	nor	CCONJ
ejpam-5602	239	45	h	h	NOUN
ejpam-5602	239	46	has	have	VERB
ejpam-5602	239	47	a	a	DET
ejpam-5602	239	48	3	3	NUM
ejpam-5602	239	49	-	-	PUNCT
ejpam-5602	239	50	dominating	dominating	NOUN
ejpam-5602	239	51	set	set	NOUN
ejpam-5602	239	52	d	d	NOUN
ejpam-5602	239	53	with	with	ADP
ejpam-5602	239	54	|d|	|d|	PROPN
ejpam-5602	239	55	=	=	SYM
ejpam-5602	239	56	4	4	NUM
ejpam-5602	239	57	and	and	CCONJ
ejpam-5602	239	58	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	239	59	)	)	PUNCT
ejpam-5602	239	60	≥	≥	NOUN
ejpam-5602	240	1	2	2	NUM
ejpam-5602	240	2	.	.	PUNCT
ejpam-5602	241	1	now	now	ADV
ejpam-5602	241	2	we	we	PRON
ejpam-5602	241	3	claim	claim	VERB
ejpam-5602	241	4	that	that	SCONJ
ejpam-5602	241	5	α	α	PRON
ejpam-5602	241	6	=	=	PUNCT
ejpam-5602	241	7	min{γtdi(g	min{γtdi(g	PROPN
ejpam-5602	241	8	)	)	PUNCT
ejpam-5602	241	9	,	,	PUNCT
ejpam-5602	241	10	γtdi(h	γtdi(h	PROPN
ejpam-5602	241	11	)	)	PUNCT
ejpam-5602	241	12	}	}	PUNCT
ejpam-5602	241	13	≥	≥	NOUN
ejpam-5602	241	14	5	5	NUM
ejpam-5602	241	15	.	.	PUNCT
ejpam-5602	241	16	suppose	suppose	VERB
ejpam-5602	241	17	not	not	PART
ejpam-5602	241	18	.	.	PUNCT
ejpam-5602	242	1	then	then	ADV
ejpam-5602	242	2	α	α	X
ejpam-5602	242	3	=	=	SYM
ejpam-5602	242	4	4	4	NUM
ejpam-5602	242	5	.	.	NOUN
ejpam-5602	242	6	wlog	wlog	NOUN
ejpam-5602	242	7	,	,	PUNCT
ejpam-5602	242	8	assume	assume	VERB
ejpam-5602	242	9	γtdi(g	γtdi(g	PROPN
ejpam-5602	242	10	)	)	PUNCT
ejpam-5602	242	11	=	=	SYM
ejpam-5602	243	1	4	4	X
ejpam-5602	243	2	.	.	PUNCT
ejpam-5602	243	3	by	by	ADP
ejpam-5602	243	4	proposition	proposition	NOUN
ejpam-5602	243	5	3	3	NUM
ejpam-5602	243	6	,	,	PUNCT
ejpam-5602	243	7	g	g	PROPN
ejpam-5602	243	8	has	have	VERB
ejpam-5602	243	9	a	a	DET
ejpam-5602	243	10	3	3	NUM
ejpam-5602	243	11	-	-	PUNCT
ejpam-5602	243	12	dominating	dominating	NOUN
ejpam-5602	243	13	set	set	NOUN
ejpam-5602	243	14	d	d	NOUN
ejpam-5602	243	15	with	with	ADP
ejpam-5602	243	16	|d|	|d|	PROPN
ejpam-5602	243	17	=	=	SYM
ejpam-5602	243	18	4	4	NUM
ejpam-5602	243	19	and	and	CCONJ
ejpam-5602	243	20	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	243	21	)	)	PUNCT
ejpam-5602	243	22	≥	≥	NOUN
ejpam-5602	243	23	2	2	NUM
ejpam-5602	243	24	,	,	PUNCT
ejpam-5602	243	25	a	a	DET
ejpam-5602	243	26	contradiction	contradiction	NOUN
ejpam-5602	243	27	.	.	PUNCT
ejpam-5602	244	1	this	this	PRON
ejpam-5602	244	2	establishes	establish	VERB
ejpam-5602	244	3	our	our	PRON
ejpam-5602	244	4	claim	claim	NOUN
ejpam-5602	244	5	.	.	PUNCT
ejpam-5602	245	1	if	if	SCONJ
ejpam-5602	245	2	α	α	PRON
ejpam-5602	245	3	=	=	SYM
ejpam-5602	245	4	5	5	NUM
ejpam-5602	245	5	,	,	PUNCT
ejpam-5602	245	6	then	then	ADV
ejpam-5602	245	7	(	(	PUNCT
ejpam-5602	245	8	iv)(a	iv)(a	NOUN
ejpam-5602	245	9	)	)	PUNCT
ejpam-5602	245	10	holds	hold	VERB
ejpam-5602	245	11	.	.	PUNCT
ejpam-5602	246	1	suppose	suppose	VERB
ejpam-5602	246	2	that	that	SCONJ
ejpam-5602	246	3	α	α	PRON
ejpam-5602	246	4	>	>	X
ejpam-5602	246	5	5	5	NUM
ejpam-5602	246	6	.	.	PUNCT
ejpam-5602	247	1	in	in	ADP
ejpam-5602	247	2	view	view	NOUN
ejpam-5602	247	3	of	of	ADP
ejpam-5602	247	4	proposition	proposition	NOUN
ejpam-5602	247	5	4	4	NUM
ejpam-5602	247	6	,	,	PUNCT
ejpam-5602	247	7	one	one	NUM
ejpam-5602	247	8	of	of	ADP
ejpam-5602	247	9	the	the	DET
ejpam-5602	247	10	following	follow	VERB
ejpam-5602	247	11	cases	case	NOUN
ejpam-5602	247	12	holds	hold	VERB
ejpam-5602	247	13	:	:	PUNCT
ejpam-5602	247	14	case	case	NOUN
ejpam-5602	247	15	1	1	NUM
ejpam-5602	247	16	:	:	PUNCT
ejpam-5602	247	17	g	g	NOUN
ejpam-5602	247	18	+	+	PROPN
ejpam-5602	247	19	h	h	NOUN
ejpam-5602	247	20	contains	contain	VERB
ejpam-5602	247	21	a	a	DET
ejpam-5602	247	22	3	3	NUM
ejpam-5602	247	23	-	-	PUNCT
ejpam-5602	247	24	dominating	dominating	NOUN
ejpam-5602	247	25	set	set	NOUN
ejpam-5602	247	26	d	d	NOUN
ejpam-5602	247	27	with	with	ADP
ejpam-5602	247	28	|d|	|d|	PROPN
ejpam-5602	247	29	=	=	SYM
ejpam-5602	247	30	5	5	NUM
ejpam-5602	247	31	and	and	CCONJ
ejpam-5602	247	32	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	247	33	)	)	PUNCT
ejpam-5602	247	34	≥	≥	NOUN
ejpam-5602	248	1	2	2	NUM
ejpam-5602	248	2	.	.	PUNCT
ejpam-5602	248	3	let	let	VERB
ejpam-5602	248	4	dg	dg	VERB
ejpam-5602	248	5	=	=	SYM
ejpam-5602	248	6	d	d	PROPN
ejpam-5602	248	7	∩	∩	ADJ
ejpam-5602	248	8	v	v	X
ejpam-5602	248	9	(	(	PUNCT
ejpam-5602	248	10	g	g	NOUN
ejpam-5602	248	11	)	)	PUNCT
ejpam-5602	248	12	and	and	CCONJ
ejpam-5602	248	13	dh	dh	NOUN
ejpam-5602	248	14	=	=	SYM
ejpam-5602	248	15	d	d	PROPN
ejpam-5602	248	16	∩	∩	ADJ
ejpam-5602	248	17	v	v	X
ejpam-5602	248	18	(	(	PUNCT
ejpam-5602	248	19	h	h	NOUN
ejpam-5602	248	20	)	)	PUNCT
ejpam-5602	248	21	.	.	PUNCT
ejpam-5602	249	1	since	since	SCONJ
ejpam-5602	249	2	α	α	PROPN
ejpam-5602	249	3	>	>	X
ejpam-5602	249	4	5	5	NUM
ejpam-5602	249	5	,	,	PUNCT
ejpam-5602	249	6	1	1	NUM
ejpam-5602	249	7	≤	≤	NUM
ejpam-5602	249	8	|dg|	|dg|	PROPN
ejpam-5602	249	9	≤	≤	NUM
ejpam-5602	249	10	4	4	NUM
ejpam-5602	249	11	and	and	CCONJ
ejpam-5602	249	12	1	1	NUM
ejpam-5602	249	13	≤	≤	NOUN
ejpam-5602	249	14	|dh	|dh	NUM
ejpam-5602	249	15	|	|	ADV
ejpam-5602	249	16	≤	≤	ADJ
ejpam-5602	249	17	4	4	NUM
ejpam-5602	249	18	.	.	PUNCT
ejpam-5602	250	1	if	if	SCONJ
ejpam-5602	250	2	either	either	PRON
ejpam-5602	250	3	|dg|	|dg|	PROPN
ejpam-5602	250	4	=	=	SYM
ejpam-5602	250	5	4	4	NUM
ejpam-5602	250	6	or	or	CCONJ
ejpam-5602	250	7	|dh	|dh	NOUN
ejpam-5602	250	8	|	|	ADV
ejpam-5602	250	9	=	=	SYM
ejpam-5602	250	10	4	4	NUM
ejpam-5602	250	11	,	,	PUNCT
ejpam-5602	250	12	then	then	ADV
ejpam-5602	250	13	(	(	PUNCT
ejpam-5602	250	14	iv)(b	iv)(b	ADJ
ejpam-5602	250	15	)	)	PUNCT
ejpam-5602	250	16	holds	hold	VERB
ejpam-5602	250	17	.	.	PUNCT
ejpam-5602	251	1	if	if	SCONJ
ejpam-5602	251	2	either	either	DET
ejpam-5602	251	3	|dg|	|dg|	PROPN
ejpam-5602	251	4	=	=	SYM
ejpam-5602	251	5	3	3	NUM
ejpam-5602	251	6	or	or	CCONJ
ejpam-5602	251	7	|dh	|dh	VERB
ejpam-5602	251	8	|	|	ADV
ejpam-5602	251	9	=	=	SYM
ejpam-5602	251	10	3	3	NUM
ejpam-5602	251	11	,	,	PUNCT
ejpam-5602	251	12	then	then	ADV
ejpam-5602	251	13	(	(	PUNCT
ejpam-5602	251	14	iv)(c	iv)(c	PROPN
ejpam-5602	251	15	)	)	PUNCT
ejpam-5602	251	16	holds	hold	VERB
ejpam-5602	251	17	.	.	PUNCT
ejpam-5602	252	1	case	case	NOUN
ejpam-5602	252	2	2	2	NUM
ejpam-5602	252	3	:	:	PUNCT
ejpam-5602	252	4	g	g	NOUN
ejpam-5602	252	5	+	+	PROPN
ejpam-5602	252	6	h	h	NOUN
ejpam-5602	252	7	contains	contain	VERB
ejpam-5602	252	8	a	a	DET
ejpam-5602	252	9	2	2	NUM
ejpam-5602	252	10	-	-	PUNCT
ejpam-5602	252	11	dominating	dominating	NOUN
ejpam-5602	252	12	set	set	NOUN
ejpam-5602	252	13	d	d	NOUN
ejpam-5602	252	14	with	with	ADP
ejpam-5602	252	15	|d|	|d|	PROPN
ejpam-5602	252	16	=	=	SYM
ejpam-5602	252	17	3	3	NUM
ejpam-5602	252	18	and	and	CCONJ
ejpam-5602	252	19	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	252	20	is	be	AUX
ejpam-5602	252	21	connected	connect	VERB
ejpam-5602	252	22	.	.	PUNCT
ejpam-5602	253	1	if	if	SCONJ
ejpam-5602	253	2	dg	dg	NOUN
ejpam-5602	253	3	=	=	SYM
ejpam-5602	253	4	d	d	PROPN
ejpam-5602	253	5	∩	∩	ADJ
ejpam-5602	253	6	v	v	X
ejpam-5602	253	7	(	(	PUNCT
ejpam-5602	253	8	g	g	NOUN
ejpam-5602	253	9	)	)	PUNCT
ejpam-5602	253	10	and	and	CCONJ
ejpam-5602	253	11	dh	dh	NOUN
ejpam-5602	254	1	=	=	SYM
ejpam-5602	254	2	d	d	PROPN
ejpam-5602	254	3	∩	∩	ADJ
ejpam-5602	254	4	v	v	X
ejpam-5602	254	5	(	(	PUNCT
ejpam-5602	254	6	h	h	NOUN
ejpam-5602	254	7	)	)	PUNCT
ejpam-5602	254	8	,	,	PUNCT
ejpam-5602	254	9	then	then	ADV
ejpam-5602	254	10	1	1	NUM
ejpam-5602	254	11	≤	≤	NUM
ejpam-5602	254	12	|dg|	|dg|	PROPN
ejpam-5602	254	13	≤	≤	NUM
ejpam-5602	254	14	2	2	NUM
ejpam-5602	254	15	and	and	CCONJ
ejpam-5602	254	16	1	1	NUM
ejpam-5602	254	17	≤	≤	NOUN
ejpam-5602	254	18	|dh	|dh	NUM
ejpam-5602	254	19	|	|	ADV
ejpam-5602	254	20	≤	≤	ADJ
ejpam-5602	254	21	2	2	NUM
ejpam-5602	254	22	.	.	PUNCT
ejpam-5602	255	1	if	if	SCONJ
ejpam-5602	255	2	|dg|	|dg|	PROPN
ejpam-5602	255	3	=	=	SYM
ejpam-5602	255	4	2	2	NUM
ejpam-5602	255	5	and	and	CCONJ
ejpam-5602	255	6	|dh	|dh	NOUN
ejpam-5602	255	7	|	|	NOUN
ejpam-5602	255	8	=	=	SYM
ejpam-5602	255	9	1	1	NUM
ejpam-5602	255	10	,	,	PUNCT
ejpam-5602	255	11	then	then	ADV
ejpam-5602	255	12	dg	dg	PROPN
ejpam-5602	255	13	is	be	AUX
ejpam-5602	255	14	a	a	DET
ejpam-5602	255	15	dominating	dominating	NOUN
ejpam-5602	255	16	set	set	NOUN
ejpam-5602	255	17	of	of	ADP
ejpam-5602	255	18	g	g	PROPN
ejpam-5602	255	19	and	and	CCONJ
ejpam-5602	255	20	γ(g	γ(g	PROPN
ejpam-5602	255	21	)	)	PUNCT
ejpam-5602	256	1	=	=	SYM
ejpam-5602	256	2	2	2	X
ejpam-5602	256	3	.	.	PUNCT
ejpam-5602	256	4	by	by	ADP
ejpam-5602	256	5	(	(	PUNCT
ejpam-5602	256	6	i	i	NOUN
ejpam-5602	256	7	)	)	PUNCT
ejpam-5602	256	8	,	,	PUNCT
ejpam-5602	256	9	γ(h	γ(h	PROPN
ejpam-5602	256	10	)	)	PUNCT
ejpam-5602	256	11	≥	≥	NOUN
ejpam-5602	256	12	3	3	NUM
ejpam-5602	256	13	,	,	PUNCT
ejpam-5602	256	14	and	and	CCONJ
ejpam-5602	256	15	(	(	PUNCT
ejpam-5602	256	16	iv)(d	iv)(d	PROPN
ejpam-5602	256	17	)	)	PUNCT
ejpam-5602	256	18	holds	hold	VERB
ejpam-5602	256	19	.	.	PUNCT
ejpam-5602	257	1	similarly	similarly	ADV
ejpam-5602	257	2	,	,	PUNCT
ejpam-5602	257	3	if	if	SCONJ
ejpam-5602	257	4	|dg|	|dg|	PROPN
ejpam-5602	257	5	=	=	SYM
ejpam-5602	257	6	1	1	NUM
ejpam-5602	257	7	and	and	CCONJ
ejpam-5602	257	8	|dh	|dh	VERB
ejpam-5602	257	9	|	|	ADV
ejpam-5602	257	10	=	=	SYM
ejpam-5602	257	11	2	2	NUM
ejpam-5602	257	12	,	,	PUNCT
ejpam-5602	257	13	then	then	ADV
ejpam-5602	257	14	(	(	PUNCT
ejpam-5602	257	15	iv)(e	iv)(e	PROPN
ejpam-5602	257	16	)	)	PUNCT
ejpam-5602	257	17	holds	hold	VERB
ejpam-5602	257	18	.	.	PUNCT
ejpam-5602	258	1	s.j.l	s.j.l	PROPN
ejpam-5602	258	2	.	.	PUNCT
ejpam-5602	258	3	sumbalan	sumbalan	PROPN
ejpam-5602	258	4	,	,	PUNCT
ejpam-5602	258	5	s.m	s.m	PROPN
ejpam-5602	258	6	.	.	PROPN
ejpam-5602	258	7	menchavez	menchavez	PROPN
ejpam-5602	258	8	,	,	PUNCT
ejpam-5602	258	9	f.p	f.p	PROPN
ejpam-5602	258	10	.	.	PROPN
ejpam-5602	258	11	jamil	jamil	PROPN
ejpam-5602	258	12	/	/	SYM
ejpam-5602	258	13	eur	eur	PROPN
ejpam-5602	258	14	.	.	PUNCT
ejpam-5602	259	1	j.	j.	PROPN
ejpam-5602	259	2	pure	pure	PROPN
ejpam-5602	259	3	appl	appl	PROPN
ejpam-5602	259	4	.	.	PROPN
ejpam-5602	259	5	math	math	PROPN
ejpam-5602	259	6	,	,	PUNCT
ejpam-5602	259	7	18	18	NUM
ejpam-5602	259	8	(	(	PUNCT
ejpam-5602	259	9	1	1	NUM
ejpam-5602	259	10	)	)	PUNCT
ejpam-5602	259	11	(	(	PUNCT
ejpam-5602	259	12	2025	2025	NUM
ejpam-5602	259	13	)	)	PUNCT
ejpam-5602	259	14	,	,	PUNCT
ejpam-5602	259	15	5602	5602	NUM
ejpam-5602	259	16	9	9	NUM
ejpam-5602	259	17	of	of	ADP
ejpam-5602	259	18	18	18	NUM
ejpam-5602	259	19	case	case	NOUN
ejpam-5602	259	20	3	3	NUM
ejpam-5602	259	21	:	:	PUNCT
ejpam-5602	259	22	g+h	g+h	PROPN
ejpam-5602	259	23	contains	contain	VERB
ejpam-5602	259	24	a	a	DET
ejpam-5602	259	25	2	2	NUM
ejpam-5602	259	26	-	-	PUNCT
ejpam-5602	259	27	dominating	dominating	NOUN
ejpam-5602	259	28	set	set	NOUN
ejpam-5602	259	29	d	d	NOUN
ejpam-5602	259	30	with	with	ADP
ejpam-5602	259	31	|d|	|d|	PROPN
ejpam-5602	259	32	=	=	PROPN
ejpam-5602	259	33	4	4	NUM
ejpam-5602	259	34	such	such	ADJ
ejpam-5602	259	35	that	that	SCONJ
ejpam-5602	259	36	there	there	PRON
ejpam-5602	259	37	exists	exist	VERB
ejpam-5602	259	38	v	v	ADP
ejpam-5602	259	39	∈	∈	PROPN
ejpam-5602	259	40	d	d	NOUN
ejpam-5602	259	41	for	for	ADP
ejpam-5602	259	42	which	which	PRON
ejpam-5602	259	43	uv	uv	NOUN
ejpam-5602	259	44	∈	∈	PROPN
ejpam-5602	259	45	e(g+h	e(g+h	NUM
ejpam-5602	259	46	)	)	PUNCT
ejpam-5602	259	47	for	for	ADP
ejpam-5602	259	48	all	all	PRON
ejpam-5602	259	49	u	u	PROPN
ejpam-5602	259	50	∈	∈	PROPN
ejpam-5602	259	51	v	v	NOUN
ejpam-5602	259	52	(	(	PUNCT
ejpam-5602	259	53	g+h	g+h	NOUN
ejpam-5602	259	54	)	)	PUNCT
ejpam-5602	259	55	\d	\d	NOUN
ejpam-5602	259	56	with	with	ADP
ejpam-5602	259	57	|ng+h(u	|ng+h(u	X
ejpam-5602	259	58	)	)	PUNCT
ejpam-5602	259	59	∩d|	∩d|	PUNCT
ejpam-5602	260	1	=	=	PUNCT
ejpam-5602	260	2	2	2	X
ejpam-5602	260	3	.	.	PUNCT
ejpam-5602	261	1	moreover	moreover	ADV
ejpam-5602	261	2	,	,	PUNCT
ejpam-5602	261	3	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	261	4	is	be	AUX
ejpam-5602	261	5	connected	connect	VERB
ejpam-5602	261	6	and	and	CCONJ
ejpam-5602	261	7	xv	xv	PROPN
ejpam-5602	261	8	∈	∈	PROPN
ejpam-5602	261	9	e(g	e(g	PROPN
ejpam-5602	262	1	+	+	CCONJ
ejpam-5602	262	2	h	h	NOUN
ejpam-5602	262	3	)	)	PUNCT
ejpam-5602	262	4	for	for	ADP
ejpam-5602	262	5	every	every	DET
ejpam-5602	262	6	x	x	SYM
ejpam-5602	262	7	∈	∈	PROPN
ejpam-5602	262	8	d	d	X
ejpam-5602	262	9	\	\	PROPN
ejpam-5602	262	10	{	{	PUNCT
ejpam-5602	262	11	v	v	NOUN
ejpam-5602	262	12	}	}	PUNCT
ejpam-5602	262	13	with	with	ADP
ejpam-5602	262	14	|ng+h(x	|ng+h(x	NOUN
ejpam-5602	262	15	)	)	PUNCT
ejpam-5602	262	16	∩	∩	NOUN
ejpam-5602	262	17	d|	d|	PROPN
ejpam-5602	262	18	=	=	SYM
ejpam-5602	263	1	1	1	X
ejpam-5602	263	2	.	.	PUNCT
ejpam-5602	264	1	if	if	SCONJ
ejpam-5602	264	2	dg	dg	NOUN
ejpam-5602	264	3	=	=	SYM
ejpam-5602	264	4	d	d	PROPN
ejpam-5602	264	5	∩	∩	ADJ
ejpam-5602	264	6	v	v	X
ejpam-5602	264	7	(	(	PUNCT
ejpam-5602	264	8	g	g	NOUN
ejpam-5602	264	9	)	)	PUNCT
ejpam-5602	264	10	and	and	CCONJ
ejpam-5602	264	11	dh	dh	NOUN
ejpam-5602	265	1	=	=	SYM
ejpam-5602	265	2	d	d	PROPN
ejpam-5602	265	3	∩	∩	ADJ
ejpam-5602	265	4	v	v	X
ejpam-5602	265	5	(	(	PUNCT
ejpam-5602	265	6	h	h	NOUN
ejpam-5602	265	7	)	)	PUNCT
ejpam-5602	265	8	,	,	PUNCT
ejpam-5602	265	9	then	then	ADV
ejpam-5602	265	10	1	1	NUM
ejpam-5602	265	11	≤	≤	NUM
ejpam-5602	265	12	|dg|	|dg|	PROPN
ejpam-5602	265	13	≤	≤	NUM
ejpam-5602	265	14	3	3	NUM
ejpam-5602	265	15	and	and	CCONJ
ejpam-5602	265	16	1	1	NUM
ejpam-5602	265	17	≤	≤	NOUN
ejpam-5602	265	18	|dh	|dh	NUM
ejpam-5602	265	19	|	|	ADV
ejpam-5602	265	20	≤	≤	ADJ
ejpam-5602	265	21	3	3	NUM
ejpam-5602	265	22	.	.	PUNCT
ejpam-5602	266	1	if	if	SCONJ
ejpam-5602	266	2	|dg|	|dg|	PROPN
ejpam-5602	266	3	=	=	SYM
ejpam-5602	266	4	3	3	NUM
ejpam-5602	266	5	and	and	CCONJ
ejpam-5602	266	6	|dh	|dh	NOUN
ejpam-5602	266	7	|	|	NOUN
ejpam-5602	266	8	=	=	SYM
ejpam-5602	266	9	1	1	NUM
ejpam-5602	266	10	,	,	PUNCT
ejpam-5602	266	11	then	then	ADV
ejpam-5602	266	12	whether	whether	SCONJ
ejpam-5602	266	13	v	v	NUM
ejpam-5602	266	14	∈	∈	NOUN
ejpam-5602	266	15	v	v	NOUN
ejpam-5602	266	16	(	(	PUNCT
ejpam-5602	266	17	g	g	NOUN
ejpam-5602	266	18	)	)	PUNCT
ejpam-5602	266	19	or	or	CCONJ
ejpam-5602	266	20	v	v	ADP
ejpam-5602	266	21	∈	∈	PROPN
ejpam-5602	266	22	v	v	NOUN
ejpam-5602	266	23	(	(	PUNCT
ejpam-5602	266	24	h	h	NOUN
ejpam-5602	266	25	)	)	PUNCT
ejpam-5602	266	26	,	,	PUNCT
ejpam-5602	266	27	dg	dg	PROPN
ejpam-5602	266	28	is	be	AUX
ejpam-5602	266	29	a	a	DET
ejpam-5602	266	30	dominating	dominating	NOUN
ejpam-5602	266	31	set	set	NOUN
ejpam-5602	266	32	of	of	ADP
ejpam-5602	266	33	g.	g.	PROPN
ejpam-5602	266	34	similarly	similarly	ADV
ejpam-5602	266	35	,	,	PUNCT
ejpam-5602	266	36	if	if	SCONJ
ejpam-5602	266	37	|dh	|dh	NUM
ejpam-5602	266	38	|	|	ADV
ejpam-5602	266	39	=	=	SYM
ejpam-5602	266	40	3	3	NUM
ejpam-5602	266	41	and	and	CCONJ
ejpam-5602	266	42	|dg|	|dg|	PROPN
ejpam-5602	266	43	=	=	SYM
ejpam-5602	266	44	1	1	NUM
ejpam-5602	266	45	,	,	PUNCT
ejpam-5602	266	46	then	then	ADV
ejpam-5602	266	47	dh	dh	PROPN
ejpam-5602	266	48	is	be	AUX
ejpam-5602	266	49	a	a	DET
ejpam-5602	266	50	dominating	dominating	NOUN
ejpam-5602	266	51	set	set	NOUN
ejpam-5602	266	52	of	of	ADP
ejpam-5602	266	53	h.	h.	PROPN
ejpam-5602	266	54	this	this	PRON
ejpam-5602	266	55	implies	imply	VERB
ejpam-5602	266	56	(	(	PUNCT
ejpam-5602	266	57	ii)(c	ii)(c	PROPN
ejpam-5602	266	58	)	)	PUNCT
ejpam-5602	266	59	.	.	PUNCT
ejpam-5602	267	1	suppose	suppose	VERB
ejpam-5602	267	2	that	that	SCONJ
ejpam-5602	267	3	|dg|	|dg|	PROPN
ejpam-5602	267	4	=	=	SYM
ejpam-5602	267	5	2	2	NUM
ejpam-5602	267	6	=	=	SYM
ejpam-5602	267	7	|dh	|dh	PROPN
ejpam-5602	267	8	|	|	ADV
ejpam-5602	267	9	.	.	PUNCT
ejpam-5602	268	1	then	then	ADV
ejpam-5602	268	2	either	either	CCONJ
ejpam-5602	268	3	γ(g	γ(g	PROPN
ejpam-5602	268	4	)	)	PUNCT
ejpam-5602	268	5	=	=	SYM
ejpam-5602	268	6	2	2	NUM
ejpam-5602	268	7	and	and	CCONJ
ejpam-5602	268	8	γ(h	γ(h	NOUN
ejpam-5602	268	9	)	)	PUNCT
ejpam-5602	268	10	≥	≥	NOUN
ejpam-5602	268	11	3	3	NUM
ejpam-5602	268	12	or	or	CCONJ
ejpam-5602	268	13	γ(h	γ(h	NOUN
ejpam-5602	268	14	)	)	PUNCT
ejpam-5602	269	1	=	=	SYM
ejpam-5602	269	2	2	2	NUM
ejpam-5602	269	3	and	and	CCONJ
ejpam-5602	269	4	γ(g	γ(g	PROPN
ejpam-5602	269	5	)	)	PUNCT
ejpam-5602	269	6	≥	≥	NOUN
ejpam-5602	269	7	3	3	NUM
ejpam-5602	269	8	.	.	PUNCT
ejpam-5602	270	1	conversely	conversely	ADV
ejpam-5602	270	2	,	,	PUNCT
ejpam-5602	270	3	assume	assume	VERB
ejpam-5602	270	4	that	that	SCONJ
ejpam-5602	270	5	statements	statement	NOUN
ejpam-5602	270	6	(	(	PUNCT
ejpam-5602	270	7	i)-(iii	i)-(iii	NOUN
ejpam-5602	270	8	)	)	PUNCT
ejpam-5602	270	9	hold	hold	NOUN
ejpam-5602	270	10	.	.	PUNCT
ejpam-5602	270	11	suppose	suppose	VERB
ejpam-5602	270	12	that	that	SCONJ
ejpam-5602	270	13	(	(	PUNCT
ejpam-5602	270	14	iv)(a	iv)(a	NOUN
ejpam-5602	270	15	)	)	PUNCT
ejpam-5602	270	16	holds	hold	VERB
ejpam-5602	270	17	.	.	PUNCT
ejpam-5602	270	18	wlog	wlog	PROPN
ejpam-5602	270	19	,	,	PUNCT
ejpam-5602	270	20	assume	assume	VERB
ejpam-5602	270	21	γtdi(g	γtdi(g	PROPN
ejpam-5602	270	22	)	)	PUNCT
ejpam-5602	270	23	=	=	SYM
ejpam-5602	271	1	5	5	X
ejpam-5602	271	2	.	.	X
ejpam-5602	272	1	in	in	ADP
ejpam-5602	272	2	view	view	NOUN
ejpam-5602	272	3	of	of	ADP
ejpam-5602	272	4	proposition	proposition	NOUN
ejpam-5602	272	5	5	5	NUM
ejpam-5602	272	6	,	,	PUNCT
ejpam-5602	272	7	γtdi(g+h	γtdi(g+h	NOUN
ejpam-5602	272	8	)	)	PUNCT
ejpam-5602	272	9	≤	≤	NUM
ejpam-5602	272	10	γtdi(g	γtdi(g	NOUN
ejpam-5602	272	11	)	)	PUNCT
ejpam-5602	272	12	=	=	SYM
ejpam-5602	273	1	5	5	X
ejpam-5602	273	2	.	.	PUNCT
ejpam-5602	273	3	since	since	SCONJ
ejpam-5602	273	4	statements	statement	NOUN
ejpam-5602	273	5	(	(	PUNCT
ejpam-5602	273	6	i)-(iii	i)-(iii	NOUN
ejpam-5602	273	7	)	)	PUNCT
ejpam-5602	273	8	hold	hold	NOUN
ejpam-5602	273	9	,	,	PUNCT
ejpam-5602	273	10	proposition	proposition	NOUN
ejpam-5602	273	11	6	6	NUM
ejpam-5602	273	12	and	and	CCONJ
ejpam-5602	273	13	proposition	proposition	NOUN
ejpam-5602	273	14	7	7	NUM
ejpam-5602	273	15	imply	imply	VERB
ejpam-5602	273	16	that	that	SCONJ
ejpam-5602	273	17	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	273	18	)	)	PUNCT
ejpam-5602	273	19	≥	≥	NOUN
ejpam-5602	273	20	5	5	NUM
ejpam-5602	273	21	.	.	PUNCT
ejpam-5602	273	22	suppose	suppose	VERB
ejpam-5602	273	23	that	that	SCONJ
ejpam-5602	273	24	(	(	PUNCT
ejpam-5602	273	25	iv)(b	iv)(b	ADJ
ejpam-5602	273	26	)	)	PUNCT
ejpam-5602	273	27	holds	hold	VERB
ejpam-5602	273	28	,	,	PUNCT
ejpam-5602	273	29	say	say	VERB
ejpam-5602	273	30	g	g	PROPN
ejpam-5602	273	31	has	have	VERB
ejpam-5602	273	32	a	a	DET
ejpam-5602	273	33	2	2	NUM
ejpam-5602	273	34	-	-	PUNCT
ejpam-5602	273	35	dominating	dominating	NOUN
ejpam-5602	273	36	set	set	NOUN
ejpam-5602	273	37	d	d	NOUN
ejpam-5602	273	38	for	for	ADP
ejpam-5602	273	39	which	which	PRON
ejpam-5602	273	40	|d|	|d|	PROPN
ejpam-5602	273	41	=	=	SYM
ejpam-5602	273	42	4	4	NUM
ejpam-5602	273	43	and	and	CCONJ
ejpam-5602	273	44	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	273	45	is	be	AUX
ejpam-5602	273	46	connected	connect	VERB
ejpam-5602	273	47	.	.	PUNCT
ejpam-5602	274	1	pick	pick	VERB
ejpam-5602	274	2	v	v	NUM
ejpam-5602	274	3	∈	∈	PROPN
ejpam-5602	274	4	v	v	NOUN
ejpam-5602	274	5	(	(	PUNCT
ejpam-5602	274	6	h	h	NOUN
ejpam-5602	274	7	)	)	PUNCT
ejpam-5602	274	8	.	.	PUNCT
ejpam-5602	275	1	then	then	ADV
ejpam-5602	275	2	d	d	X
ejpam-5602	275	3	∪	∪	X
ejpam-5602	275	4	{	{	PUNCT
ejpam-5602	275	5	v	v	NOUN
ejpam-5602	275	6	}	}	PUNCT
ejpam-5602	275	7	is	be	AUX
ejpam-5602	275	8	a	a	DET
ejpam-5602	275	9	3	3	NUM
ejpam-5602	275	10	-	-	PUNCT
ejpam-5602	275	11	dominating	dominate	VERB
ejpam-5602	275	12	set	set	NOUN
ejpam-5602	275	13	of	of	ADP
ejpam-5602	275	14	g+h	g+h	PROPN
ejpam-5602	275	15	with	with	ADP
ejpam-5602	275	16	δ(⟨d	δ(⟨d	NOUN
ejpam-5602	275	17	∪	∪	X
ejpam-5602	275	18	{	{	PUNCT
ejpam-5602	275	19	v}⟩	v}⟩	NOUN
ejpam-5602	275	20	)	)	PUNCT
ejpam-5602	275	21	≥	≥	NOUN
ejpam-5602	275	22	2	2	NUM
ejpam-5602	275	23	.	.	PUNCT
ejpam-5602	276	1	by	by	ADP
ejpam-5602	276	2	proposition	proposition	NOUN
ejpam-5602	276	3	4	4	NUM
ejpam-5602	276	4	,	,	PUNCT
ejpam-5602	276	5	γtdi(g	γtdi(g	NOUN
ejpam-5602	277	1	+	+	NOUN
ejpam-5602	277	2	h	h	NOUN
ejpam-5602	277	3	)	)	PUNCT
ejpam-5602	277	4	=	=	SYM
ejpam-5602	277	5	5	5	X
ejpam-5602	277	6	.	.	PUNCT
ejpam-5602	277	7	suppose	suppose	VERB
ejpam-5602	277	8	that	that	SCONJ
ejpam-5602	277	9	(	(	PUNCT
ejpam-5602	277	10	iv)(c	iv)(c	PROPN
ejpam-5602	277	11	)	)	PUNCT
ejpam-5602	277	12	holds	hold	NOUN
ejpam-5602	277	13	,	,	PUNCT
ejpam-5602	277	14	say	say	VERB
ejpam-5602	277	15	g	g	PROPN
ejpam-5602	277	16	has	have	VERB
ejpam-5602	277	17	a	a	DET
ejpam-5602	277	18	dominating	dominating	NOUN
ejpam-5602	277	19	set	set	NOUN
ejpam-5602	277	20	d	d	NOUN
ejpam-5602	277	21	with	with	ADP
ejpam-5602	277	22	|d|	|d|	PROPN
ejpam-5602	277	23	=	=	SYM
ejpam-5602	277	24	3	3	X
ejpam-5602	277	25	.	.	X
ejpam-5602	277	26	choose	choose	VERB
ejpam-5602	277	27	v	v	NUM
ejpam-5602	277	28	∈	∈	PROPN
ejpam-5602	277	29	v	v	NOUN
ejpam-5602	277	30	(	(	PUNCT
ejpam-5602	277	31	h	h	NOUN
ejpam-5602	277	32	)	)	PUNCT
ejpam-5602	277	33	.	.	PUNCT
ejpam-5602	278	1	then	then	ADV
ejpam-5602	278	2	d	d	X
ejpam-5602	278	3	∪	∪	X
ejpam-5602	278	4	{	{	PUNCT
ejpam-5602	278	5	v	v	NOUN
ejpam-5602	278	6	}	}	PUNCT
ejpam-5602	278	7	satisfies	satisfie	NOUN
ejpam-5602	278	8	proposition	proposition	NOUN
ejpam-5602	278	9	4(ii)(c	4(ii)(c	NUM
ejpam-5602	278	10	)	)	PUNCT
ejpam-5602	278	11	.	.	PUNCT
ejpam-5602	279	1	thus	thus	ADV
ejpam-5602	279	2	,	,	PUNCT
ejpam-5602	279	3	γtdi(g	γtdi(g	ADV
ejpam-5602	279	4	+	+	CCONJ
ejpam-5602	279	5	h	h	NOUN
ejpam-5602	279	6	)	)	PUNCT
ejpam-5602	279	7	=	=	SYM
ejpam-5602	279	8	5	5	X
ejpam-5602	279	9	.	.	PUNCT
ejpam-5602	279	10	suppose	suppose	VERB
ejpam-5602	279	11	that	that	SCONJ
ejpam-5602	279	12	(	(	PUNCT
ejpam-5602	279	13	iv)(d	iv)(d	PROPN
ejpam-5602	279	14	)	)	PUNCT
ejpam-5602	279	15	holds	hold	VERB
ejpam-5602	279	16	.	.	PUNCT
ejpam-5602	280	1	then	then	ADV
ejpam-5602	280	2	d	d	X
ejpam-5602	280	3	∪	∪	X
ejpam-5602	280	4	{	{	PUNCT
ejpam-5602	280	5	v	v	NOUN
ejpam-5602	280	6	}	}	PUNCT
ejpam-5602	280	7	is	be	AUX
ejpam-5602	280	8	a	a	DET
ejpam-5602	280	9	2	2	NUM
ejpam-5602	280	10	-	-	PUNCT
ejpam-5602	280	11	dominating	dominate	VERB
ejpam-5602	280	12	set	set	NOUN
ejpam-5602	280	13	of	of	ADP
ejpam-5602	280	14	cardinality	cardinality	PROPN
ejpam-5602	280	15	3	3	NUM
ejpam-5602	280	16	and	and	CCONJ
ejpam-5602	280	17	⟨d	⟨d	PROPN
ejpam-5602	280	18	∪	∪	X
ejpam-5602	280	19	{	{	PUNCT
ejpam-5602	280	20	v}⟩	v}⟩	NOUN
ejpam-5602	280	21	is	be	AUX
ejpam-5602	280	22	connected	connect	VERB
ejpam-5602	280	23	.	.	PUNCT
ejpam-5602	281	1	thus	thus	ADV
ejpam-5602	281	2	,	,	PUNCT
ejpam-5602	281	3	γtdi(g	γtdi(g	ADV
ejpam-5602	281	4	+	+	CCONJ
ejpam-5602	281	5	h	h	NOUN
ejpam-5602	281	6	)	)	PUNCT
ejpam-5602	281	7	=	=	SYM
ejpam-5602	281	8	5	5	X
ejpam-5602	281	9	.	.	X
ejpam-5602	281	10	similarly	similarly	ADV
ejpam-5602	281	11	,	,	PUNCT
ejpam-5602	281	12	if	if	SCONJ
ejpam-5602	281	13	(	(	PUNCT
ejpam-5602	281	14	iv)(e	iv)(e	PROPN
ejpam-5602	281	15	)	)	PUNCT
ejpam-5602	281	16	holds	hold	VERB
ejpam-5602	281	17	,	,	PUNCT
ejpam-5602	281	18	then	then	ADV
ejpam-5602	281	19	γtdi(g+h	γtdi(g+h	PROPN
ejpam-5602	281	20	)	)	PUNCT
ejpam-5602	281	21	=	=	SYM
ejpam-5602	282	1	5	5	X
ejpam-5602	282	2	.	.	X
ejpam-5602	282	3	■	■	PUNCT
ejpam-5602	282	4	in	in	ADP
ejpam-5602	282	5	view	view	NOUN
ejpam-5602	282	6	of	of	ADP
ejpam-5602	282	7	the	the	DET
ejpam-5602	282	8	above	above	ADJ
ejpam-5602	282	9	results	result	NOUN
ejpam-5602	282	10	,	,	PUNCT
ejpam-5602	282	11	in	in	ADP
ejpam-5602	282	12	particular	particular	ADJ
ejpam-5602	282	13	,	,	PUNCT
ejpam-5602	282	14	if	if	SCONJ
ejpam-5602	282	15	γ(g	γ(g	PROPN
ejpam-5602	282	16	)	)	PUNCT
ejpam-5602	282	17	≥	≥	NOUN
ejpam-5602	282	18	5	5	NUM
ejpam-5602	282	19	and	and	CCONJ
ejpam-5602	282	20	γ(h	γ(h	NOUN
ejpam-5602	282	21	)	)	PUNCT
ejpam-5602	282	22	≥	≥	NOUN
ejpam-5602	282	23	5	5	NUM
ejpam-5602	282	24	,	,	PUNCT
ejpam-5602	282	25	then	then	ADV
ejpam-5602	282	26	γtdi(g	γtdi(g	NOUN
ejpam-5602	282	27	+	+	CCONJ
ejpam-5602	282	28	h	h	X
ejpam-5602	282	29	)	)	PUNCT
ejpam-5602	282	30	=	=	NOUN
ejpam-5602	282	31	6	6	NUM
ejpam-5602	282	32	.	.	NOUN
ejpam-5602	282	33	4	4	NUM
ejpam-5602	282	34	.	.	X
ejpam-5602	282	35	on	on	ADP
ejpam-5602	282	36	the	the	DET
ejpam-5602	282	37	corona	corona	NOUN
ejpam-5602	282	38	of	of	ADP
ejpam-5602	282	39	graphs	graph	NOUN
ejpam-5602	282	40	let	let	VERB
ejpam-5602	282	41	g	g	NOUN
ejpam-5602	282	42	and	and	CCONJ
ejpam-5602	282	43	h	h	NOUN
ejpam-5602	282	44	be	be	AUX
ejpam-5602	282	45	connected	connect	VERB
ejpam-5602	282	46	graphs	graph	NOUN
ejpam-5602	282	47	.	.	PUNCT
ejpam-5602	283	1	we	we	PRON
ejpam-5602	283	2	adapt	adapt	VERB
ejpam-5602	283	3	the	the	DET
ejpam-5602	283	4	notation	notation	NOUN
ejpam-5602	283	5	hv	hv	PROPN
ejpam-5602	283	6	used	use	VERB
ejpam-5602	283	7	in	in	ADP
ejpam-5602	283	8	[	[	X
ejpam-5602	283	9	16	16	NUM
ejpam-5602	283	10	]	]	PUNCT
ejpam-5602	283	11	to	to	PART
ejpam-5602	283	12	denote	denote	VERB
ejpam-5602	283	13	the	the	DET
ejpam-5602	283	14	copy	copy	NOUN
ejpam-5602	283	15	of	of	ADP
ejpam-5602	283	16	h	h	NOUN
ejpam-5602	283	17	whose	whose	DET
ejpam-5602	283	18	vertices	vertex	NOUN
ejpam-5602	283	19	is	be	AUX
ejpam-5602	283	20	joined	join	VERB
ejpam-5602	283	21	to	to	ADP
ejpam-5602	283	22	v	v	ADP
ejpam-5602	283	23	∈	∈	PROPN
ejpam-5602	283	24	v	v	NOUN
ejpam-5602	283	25	(	(	PUNCT
ejpam-5602	283	26	g	g	NOUN
ejpam-5602	283	27	)	)	PUNCT
ejpam-5602	283	28	.	.	PUNCT
ejpam-5602	284	1	proposition	proposition	NOUN
ejpam-5602	284	2	9	9	NUM
ejpam-5602	284	3	.	.	PUNCT
ejpam-5602	285	1	let	let	VERB
ejpam-5602	285	2	g	g	PRON
ejpam-5602	285	3	be	be	AUX
ejpam-5602	285	4	a	a	DET
ejpam-5602	285	5	nontrivial	nontrivial	ADJ
ejpam-5602	285	6	connected	connect	VERB
ejpam-5602	285	7	graph	graph	NOUN
ejpam-5602	285	8	and	and	CCONJ
ejpam-5602	285	9	h	h	NOUN
ejpam-5602	285	10	be	be	AUX
ejpam-5602	285	11	any	any	DET
ejpam-5602	285	12	graph	graph	NOUN
ejpam-5602	285	13	without	without	ADP
ejpam-5602	285	14	isolated	isolated	ADJ
ejpam-5602	285	15	vertices	vertex	NOUN
ejpam-5602	285	16	,	,	PUNCT
ejpam-5602	285	17	and	and	CCONJ
ejpam-5602	285	18	let	let	VERB
ejpam-5602	285	19	f	f	PROPN
ejpam-5602	285	20	=	=	SYM
ejpam-5602	285	21	(	(	PUNCT
ejpam-5602	285	22	v0	v0	PROPN
ejpam-5602	285	23	,	,	PUNCT
ejpam-5602	285	24	v1	v1	NOUN
ejpam-5602	285	25	,	,	PUNCT
ejpam-5602	285	26	v2	v2	PROPN
ejpam-5602	285	27	,	,	PUNCT
ejpam-5602	285	28	v3	v3	PROPN
ejpam-5602	285	29	)	)	PUNCT
ejpam-5602	285	30	be	be	VERB
ejpam-5602	285	31	a	a	DET
ejpam-5602	285	32	function	function	NOUN
ejpam-5602	285	33	on	on	ADP
ejpam-5602	285	34	v	v	NOUN
ejpam-5602	285	35	(	(	PUNCT
ejpam-5602	285	36	g	g	PROPN
ejpam-5602	285	37	◦	◦	NOUN
ejpam-5602	285	38	h	h	NOUN
ejpam-5602	285	39	)	)	PUNCT
ejpam-5602	285	40	.	.	PUNCT
ejpam-5602	286	1	then	then	ADV
ejpam-5602	286	2	f	f	PROPN
ejpam-5602	286	3	∈	∈	PROPN
ejpam-5602	286	4	tdidf	tdidf	NOUN
ejpam-5602	286	5	(	(	PUNCT
ejpam-5602	286	6	g	g	PROPN
ejpam-5602	286	7	◦	◦	NOUN
ejpam-5602	286	8	h	h	NOUN
ejpam-5602	286	9	)	)	PUNCT
ejpam-5602	286	10	if	if	SCONJ
ejpam-5602	286	11	and	and	CCONJ
ejpam-5602	286	12	only	only	ADV
ejpam-5602	286	13	if	if	SCONJ
ejpam-5602	286	14	each	each	PRON
ejpam-5602	286	15	of	of	ADP
ejpam-5602	286	16	the	the	DET
ejpam-5602	286	17	following	follow	VERB
ejpam-5602	286	18	holds	hold	VERB
ejpam-5602	286	19	:	:	PUNCT
ejpam-5602	286	20	(	(	PUNCT
ejpam-5602	286	21	i	i	NOUN
ejpam-5602	286	22	)	)	PUNCT
ejpam-5602	286	23	for	for	ADP
ejpam-5602	286	24	each	each	PRON
ejpam-5602	286	25	v	v	ADP
ejpam-5602	286	26	∈	∈	PROPN
ejpam-5602	286	27	v0	v0	NOUN
ejpam-5602	286	28	∩	∩	X
ejpam-5602	286	29	v	v	X
ejpam-5602	286	30	(	(	PUNCT
ejpam-5602	286	31	g	g	NOUN
ejpam-5602	286	32	)	)	PUNCT
ejpam-5602	286	33	,	,	PUNCT
ejpam-5602	286	34	f	f	PROPN
ejpam-5602	286	35	|hv	|hv	PROPN
ejpam-5602	286	36	∈	∈	PROPN
ejpam-5602	286	37	tdidf	tdidf	NOUN
ejpam-5602	286	38	(	(	PUNCT
ejpam-5602	286	39	hv	hv	PROPN
ejpam-5602	286	40	)	)	PUNCT
ejpam-5602	286	41	;	;	PUNCT
ejpam-5602	286	42	(	(	PUNCT
ejpam-5602	286	43	ii	ii	NOUN
ejpam-5602	286	44	)	)	PUNCT
ejpam-5602	286	45	for	for	ADP
ejpam-5602	286	46	each	each	DET
ejpam-5602	286	47	v	v	NUM
ejpam-5602	286	48	∈	∈	PROPN
ejpam-5602	286	49	v1	v1	NOUN
ejpam-5602	286	50	∩	∩	ADJ
ejpam-5602	286	51	v	v	NOUN
ejpam-5602	286	52	(	(	PUNCT
ejpam-5602	286	53	g	g	NOUN
ejpam-5602	286	54	)	)	PUNCT
ejpam-5602	286	55	,	,	PUNCT
ejpam-5602	286	56	f(nhv	f(nhv	PUNCT
ejpam-5602	287	1	[	[	X
ejpam-5602	287	2	u	u	X
ejpam-5602	287	3	]	]	X
ejpam-5602	287	4	)	)	PUNCT
ejpam-5602	287	5	≥	≥	NOUN
ejpam-5602	287	6	2	2	NUM
ejpam-5602	287	7	for	for	ADP
ejpam-5602	287	8	all	all	DET
ejpam-5602	287	9	u	u	PROPN
ejpam-5602	287	10	∈	∈	PROPN
ejpam-5602	287	11	(	(	PUNCT
ejpam-5602	287	12	v0	v0	NOUN
ejpam-5602	287	13	∪	∪	X
ejpam-5602	287	14	v1	v1	NOUN
ejpam-5602	287	15	)	)	PUNCT
ejpam-5602	287	16	∩	∩	ADJ
ejpam-5602	287	17	v	v	X
ejpam-5602	287	18	(	(	PUNCT
ejpam-5602	287	19	hv	hv	PROPN
ejpam-5602	287	20	)	)	PUNCT
ejpam-5602	287	21	;	;	PUNCT
ejpam-5602	287	22	(	(	PUNCT
ejpam-5602	287	23	iii	iii	X
ejpam-5602	287	24	)	)	PUNCT
ejpam-5602	287	25	for	for	ADP
ejpam-5602	287	26	each	each	DET
ejpam-5602	287	27	v	v	NUM
ejpam-5602	287	28	∈	∈	PROPN
ejpam-5602	287	29	v2	v2	NOUN
ejpam-5602	287	30	∩	∩	ADJ
ejpam-5602	287	31	v	v	NOUN
ejpam-5602	287	32	(	(	PUNCT
ejpam-5602	287	33	g	g	NOUN
ejpam-5602	287	34	)	)	PUNCT
ejpam-5602	287	35	,	,	PUNCT
ejpam-5602	287	36	f(nhv(u	f(nhv(u	NOUN
ejpam-5602	287	37	)	)	PUNCT
ejpam-5602	287	38	)	)	PUNCT
ejpam-5602	287	39	≥	≥	NOUN
ejpam-5602	287	40	1	1	NUM
ejpam-5602	287	41	for	for	ADP
ejpam-5602	287	42	all	all	DET
ejpam-5602	287	43	u	u	PROPN
ejpam-5602	287	44	∈	∈	PROPN
ejpam-5602	287	45	v0	v0	NOUN
ejpam-5602	287	46	∩	∩	X
ejpam-5602	287	47	v	v	X
ejpam-5602	287	48	(	(	PUNCT
ejpam-5602	287	49	hv	hv	PROPN
ejpam-5602	287	50	)	)	PUNCT
ejpam-5602	287	51	;	;	PUNCT
ejpam-5602	287	52	(	(	PUNCT
ejpam-5602	287	53	iv	iv	X
ejpam-5602	287	54	)	)	PUNCT
ejpam-5602	287	55	for	for	ADP
ejpam-5602	287	56	each	each	DET
ejpam-5602	287	57	v	v	PROPN
ejpam-5602	287	58	∈	∈	PROPN
ejpam-5602	287	59	v3	v3	PROPN
ejpam-5602	287	60	∩	∩	PROPN
ejpam-5602	287	61	v	v	X
ejpam-5602	287	62	(	(	PUNCT
ejpam-5602	287	63	g	g	NOUN
ejpam-5602	287	64	)	)	PUNCT
ejpam-5602	287	65	for	for	ADP
ejpam-5602	287	66	which	which	PRON
ejpam-5602	287	67	ng(v	ng(v	PUNCT
ejpam-5602	287	68	)	)	PUNCT
ejpam-5602	287	69	⊆	⊆	NUM
ejpam-5602	287	70	v0	v0	NOUN
ejpam-5602	287	71	,	,	PUNCT
ejpam-5602	287	72	f(v	f(v	PROPN
ejpam-5602	287	73	(	(	PUNCT
ejpam-5602	287	74	hv	hv	NOUN
ejpam-5602	287	75	)	)	PUNCT
ejpam-5602	287	76	)	)	PUNCT
ejpam-5602	287	77	≥	≥	NOUN
ejpam-5602	288	1	1	1	X
ejpam-5602	288	2	.	.	PUNCT
ejpam-5602	288	3	proof	proof	NOUN
ejpam-5602	288	4	:	:	PUNCT
ejpam-5602	288	5	note	note	VERB
ejpam-5602	288	6	first	first	ADV
ejpam-5602	288	7	that	that	SCONJ
ejpam-5602	288	8	hv	hv	PROPN
ejpam-5602	288	9	admits	admit	VERB
ejpam-5602	288	10	a	a	DET
ejpam-5602	288	11	tdidf	tdidf	NOUN
ejpam-5602	288	12	for	for	ADP
ejpam-5602	288	13	every	every	DET
ejpam-5602	288	14	v	v	NUM
ejpam-5602	288	15	∈	∈	NOUN
ejpam-5602	288	16	v	v	NOUN
ejpam-5602	288	17	(	(	PUNCT
ejpam-5602	288	18	g	g	NOUN
ejpam-5602	288	19	)	)	PUNCT
ejpam-5602	288	20	.	.	PUNCT
ejpam-5602	289	1	assume	assume	VERB
ejpam-5602	289	2	f	f	PROPN
ejpam-5602	289	3	∈	∈	PROPN
ejpam-5602	289	4	tdidf	tdidf	NOUN
ejpam-5602	289	5	(	(	PUNCT
ejpam-5602	289	6	g	g	ADP
ejpam-5602	289	7	◦	◦	NOUN
ejpam-5602	289	8	h	h	NOUN
ejpam-5602	289	9	)	)	PUNCT
ejpam-5602	289	10	.	.	PUNCT
ejpam-5602	290	1	for	for	ADP
ejpam-5602	290	2	each	each	PRON
ejpam-5602	290	3	v	v	NUM
ejpam-5602	290	4	∈	∈	PROPN
ejpam-5602	290	5	v	v	NOUN
ejpam-5602	290	6	(	(	PUNCT
ejpam-5602	290	7	g	g	NOUN
ejpam-5602	290	8	)	)	PUNCT
ejpam-5602	290	9	,	,	PUNCT
ejpam-5602	290	10	ng	ng	PROPN
ejpam-5602	290	11	◦	◦	NOUN
ejpam-5602	290	12	h	h	NOUN
ejpam-5602	290	13	[	[	X
ejpam-5602	290	14	u	u	X
ejpam-5602	290	15	]	]	X
ejpam-5602	290	16	=	=	SYM
ejpam-5602	290	17	{	{	PUNCT
ejpam-5602	290	18	v	v	NOUN
ejpam-5602	290	19	}	}	PUNCT
ejpam-5602	290	20	∪nhv	∪nhv	NOUN
ejpam-5602	290	21	[	[	X
ejpam-5602	290	22	u	u	X
ejpam-5602	290	23	]	]	X
ejpam-5602	290	24	(	(	PUNCT
ejpam-5602	290	25	2	2	NUM
ejpam-5602	290	26	)	)	PUNCT
ejpam-5602	291	1	so	so	SCONJ
ejpam-5602	291	2	that	that	SCONJ
ejpam-5602	291	3	f(ng	f(ng	PROPN
ejpam-5602	291	4	◦	◦	NOUN
ejpam-5602	291	5	h	h	NOUN
ejpam-5602	291	6	[	[	X
ejpam-5602	291	7	u	u	X
ejpam-5602	291	8	]	]	X
ejpam-5602	291	9	)	)	PUNCT
ejpam-5602	291	10	=	=	SYM
ejpam-5602	291	11	f(v	f(v	NOUN
ejpam-5602	291	12	)	)	PUNCT
ejpam-5602	292	1	+	+	CCONJ
ejpam-5602	292	2	f(nhv	f(nhv	X
ejpam-5602	293	1	[	[	X
ejpam-5602	293	2	u	u	X
ejpam-5602	293	3	]	]	X
ejpam-5602	293	4	)	)	PUNCT
ejpam-5602	293	5	(	(	PUNCT
ejpam-5602	293	6	3	3	X
ejpam-5602	293	7	)	)	PUNCT
ejpam-5602	293	8	s.j.l	s.j.l	NOUN
ejpam-5602	293	9	.	.	PUNCT
ejpam-5602	294	1	sumbalan	sumbalan	PROPN
ejpam-5602	294	2	,	,	PUNCT
ejpam-5602	294	3	s.m	s.m	PROPN
ejpam-5602	294	4	.	.	PROPN
ejpam-5602	294	5	menchavez	menchavez	PROPN
ejpam-5602	294	6	,	,	PUNCT
ejpam-5602	294	7	f.p	f.p	PROPN
ejpam-5602	294	8	.	.	PROPN
ejpam-5602	294	9	jamil	jamil	PROPN
ejpam-5602	294	10	/	/	SYM
ejpam-5602	294	11	eur	eur	PROPN
ejpam-5602	294	12	.	.	PUNCT
ejpam-5602	295	1	j.	j.	PROPN
ejpam-5602	295	2	pure	pure	PROPN
ejpam-5602	295	3	appl	appl	PROPN
ejpam-5602	295	4	.	.	PROPN
ejpam-5602	295	5	math	math	PROPN
ejpam-5602	295	6	,	,	PUNCT
ejpam-5602	295	7	18	18	NUM
ejpam-5602	295	8	(	(	PUNCT
ejpam-5602	295	9	1	1	NUM
ejpam-5602	295	10	)	)	PUNCT
ejpam-5602	295	11	(	(	PUNCT
ejpam-5602	295	12	2025	2025	NUM
ejpam-5602	295	13	)	)	PUNCT
ejpam-5602	295	14	,	,	PUNCT
ejpam-5602	295	15	5602	5602	NUM
ejpam-5602	295	16	10	10	NUM
ejpam-5602	295	17	of	of	ADP
ejpam-5602	295	18	18	18	NUM
ejpam-5602	295	19	for	for	ADP
ejpam-5602	295	20	all	all	DET
ejpam-5602	295	21	u	u	PROPN
ejpam-5602	295	22	∈	∈	PROPN
ejpam-5602	295	23	v	v	NOUN
ejpam-5602	295	24	(	(	PUNCT
ejpam-5602	295	25	hv	hv	PROPN
ejpam-5602	295	26	)	)	PUNCT
ejpam-5602	295	27	.	.	PUNCT
ejpam-5602	296	1	it	it	PRON
ejpam-5602	296	2	follows	follow	VERB
ejpam-5602	296	3	from	from	ADP
ejpam-5602	296	4	equation	equation	NOUN
ejpam-5602	296	5	(	(	PUNCT
ejpam-5602	296	6	2	2	NUM
ejpam-5602	296	7	)	)	PUNCT
ejpam-5602	296	8	and	and	CCONJ
ejpam-5602	296	9	equation	equation	NOUN
ejpam-5602	296	10	(	(	PUNCT
ejpam-5602	296	11	3	3	NUM
ejpam-5602	296	12	)	)	PUNCT
ejpam-5602	296	13	that	that	SCONJ
ejpam-5602	296	14	if	if	SCONJ
ejpam-5602	296	15	v	v	PROPN
ejpam-5602	296	16	∈	∈	PROPN
ejpam-5602	296	17	v0	v0	NOUN
ejpam-5602	296	18	,	,	PUNCT
ejpam-5602	296	19	then	then	ADV
ejpam-5602	296	20	f	f	PROPN
ejpam-5602	296	21	|hv(nhv	|hv(nhv	PROPN
ejpam-5602	297	1	[	[	X
ejpam-5602	297	2	u	u	X
ejpam-5602	297	3	]	]	X
ejpam-5602	297	4	)	)	PUNCT
ejpam-5602	297	5	=	=	SYM
ejpam-5602	298	1	f(ng	f(ng	NUM
ejpam-5602	298	2	◦	◦	NOUN
ejpam-5602	298	3	h	h	NOUN
ejpam-5602	298	4	[	[	X
ejpam-5602	298	5	u	u	X
ejpam-5602	298	6	]	]	X
ejpam-5602	298	7	)	)	PUNCT
ejpam-5602	298	8	≥	≥	NOUN
ejpam-5602	298	9	3	3	NUM
ejpam-5602	298	10	for	for	ADP
ejpam-5602	298	11	all	all	DET
ejpam-5602	298	12	u	u	PROPN
ejpam-5602	298	13	∈	∈	PROPN
ejpam-5602	298	14	(	(	PUNCT
ejpam-5602	298	15	v0	v0	NOUN
ejpam-5602	298	16	∪	∪	X
ejpam-5602	298	17	v1	v1	NOUN
ejpam-5602	298	18	)	)	PUNCT
ejpam-5602	298	19	∩	∩	ADJ
ejpam-5602	298	20	v	v	X
ejpam-5602	298	21	(	(	PUNCT
ejpam-5602	298	22	hv	hv	PROPN
ejpam-5602	298	23	)	)	PUNCT
ejpam-5602	298	24	and	and	CCONJ
ejpam-5602	298	25	ng	ng	PROPN
ejpam-5602	298	26	◦	◦	PROPN
ejpam-5602	298	27	h(u	h(u	PROPN
ejpam-5602	298	28	)	)	PUNCT
ejpam-5602	298	29	∩	∩	NOUN
ejpam-5602	298	30	[	[	X
ejpam-5602	298	31	v1	v1	NOUN
ejpam-5602	298	32	∪	∪	VERB
ejpam-5602	298	33	v2	v2	PROPN
ejpam-5602	298	34	∪	∪	X
ejpam-5602	298	35	v3	v3	PROPN
ejpam-5602	298	36	]	]	X
ejpam-5602	298	37	=	=	SYM
ejpam-5602	298	38	nhv(u	nhv(u	PROPN
ejpam-5602	298	39	)	)	PUNCT
ejpam-5602	298	40	∩	∩	NOUN
ejpam-5602	298	41	[	[	X
ejpam-5602	298	42	(	(	PUNCT
ejpam-5602	298	43	v1	v1	VERB
ejpam-5602	298	44	∪	∪	NOUN
ejpam-5602	298	45	v2	v2	PROPN
ejpam-5602	298	46	∪	∪	X
ejpam-5602	298	47	v3	v3	PROPN
ejpam-5602	298	48	)	)	PUNCT
ejpam-5602	298	49	∩	∩	PROPN
ejpam-5602	298	50	v	v	X
ejpam-5602	298	51	(	(	PUNCT
ejpam-5602	298	52	hv	hv	PROPN
ejpam-5602	298	53	)	)	PUNCT
ejpam-5602	298	54	]	]	PUNCT
ejpam-5602	298	55	for	for	ADP
ejpam-5602	298	56	all	all	DET
ejpam-5602	298	57	u	u	PROPN
ejpam-5602	298	58	∈	∈	PROPN
ejpam-5602	298	59	(	(	PUNCT
ejpam-5602	298	60	v1	v1	NOUN
ejpam-5602	298	61	∪	∪	NOUN
ejpam-5602	298	62	v2	v2	PROPN
ejpam-5602	298	63	∪	∪	X
ejpam-5602	298	64	v3	v3	PROPN
ejpam-5602	298	65	)	)	PUNCT
ejpam-5602	298	66	∩	∩	PROPN
ejpam-5602	298	67	v	v	X
ejpam-5602	298	68	(	(	PUNCT
ejpam-5602	298	69	hv	hv	PROPN
ejpam-5602	298	70	)	)	PUNCT
ejpam-5602	298	71	.	.	PUNCT
ejpam-5602	299	1	thus	thus	ADV
ejpam-5602	299	2	,	,	PUNCT
ejpam-5602	299	3	f	f	PROPN
ejpam-5602	299	4	|hv	|hv	PROPN
ejpam-5602	299	5	∈	∈	PROPN
ejpam-5602	299	6	tdidf	tdidf	NOUN
ejpam-5602	299	7	(	(	PUNCT
ejpam-5602	299	8	hv	hv	PROPN
ejpam-5602	299	9	)	)	PUNCT
ejpam-5602	299	10	and	and	CCONJ
ejpam-5602	299	11	(	(	PUNCT
ejpam-5602	299	12	i	i	NOUN
ejpam-5602	299	13	)	)	PUNCT
ejpam-5602	299	14	holds	hold	VERB
ejpam-5602	299	15	.	.	PUNCT
ejpam-5602	300	1	similarly	similarly	ADV
ejpam-5602	300	2	,	,	PUNCT
ejpam-5602	300	3	(	(	PUNCT
ejpam-5602	300	4	ii	ii	NOUN
ejpam-5602	300	5	)	)	PUNCT
ejpam-5602	300	6	and	and	CCONJ
ejpam-5602	300	7	(	(	PUNCT
ejpam-5602	300	8	iii	iii	X
ejpam-5602	300	9	)	)	PUNCT
ejpam-5602	300	10	follow	follow	VERB
ejpam-5602	300	11	immediately	immediately	ADV
ejpam-5602	300	12	from	from	ADP
ejpam-5602	300	13	equation	equation	NOUN
ejpam-5602	300	14	(	(	PUNCT
ejpam-5602	300	15	3	3	NUM
ejpam-5602	300	16	)	)	PUNCT
ejpam-5602	300	17	.	.	PUNCT
ejpam-5602	301	1	statement	statement	NOUN
ejpam-5602	301	2	(	(	PUNCT
ejpam-5602	301	3	iv	iv	X
ejpam-5602	301	4	)	)	PUNCT
ejpam-5602	301	5	follows	follow	VERB
ejpam-5602	301	6	from	from	ADP
ejpam-5602	301	7	the	the	DET
ejpam-5602	301	8	fact	fact	NOUN
ejpam-5602	301	9	that	that	SCONJ
ejpam-5602	301	10	⟨v1∪v2∪v3⟩	⟨v1∪v2∪v3⟩	NOUN
ejpam-5602	301	11	has	have	AUX
ejpam-5602	301	12	no	no	DET
ejpam-5602	301	13	isolated	isolated	ADJ
ejpam-5602	301	14	vertex	vertex	NOUN
ejpam-5602	301	15	.	.	PUNCT
ejpam-5602	302	1	conversely	conversely	ADV
ejpam-5602	302	2	,	,	PUNCT
ejpam-5602	302	3	suppose	suppose	VERB
ejpam-5602	302	4	conditions	condition	NOUN
ejpam-5602	302	5	(	(	PUNCT
ejpam-5602	302	6	i	i	NOUN
ejpam-5602	302	7	)	)	PUNCT
ejpam-5602	302	8	(	(	PUNCT
ejpam-5602	302	9	iv	iv	X
ejpam-5602	302	10	)	)	PUNCT
ejpam-5602	302	11	hold	hold	NOUN
ejpam-5602	302	12	for	for	ADP
ejpam-5602	302	13	f	f	PROPN
ejpam-5602	302	14	.	.	PUNCT
ejpam-5602	303	1	first	first	ADV
ejpam-5602	303	2	,	,	PUNCT
ejpam-5602	303	3	let	let	VERB
ejpam-5602	303	4	u	u	PRON
ejpam-5602	303	5	∈	∈	PROPN
ejpam-5602	303	6	v0	v0	NOUN
ejpam-5602	303	7	,	,	PUNCT
ejpam-5602	303	8	and	and	CCONJ
ejpam-5602	303	9	let	let	VERB
ejpam-5602	303	10	v	v	NUM
ejpam-5602	303	11	∈	∈	PROPN
ejpam-5602	303	12	v	v	NOUN
ejpam-5602	303	13	(	(	PUNCT
ejpam-5602	303	14	g	g	NOUN
ejpam-5602	303	15	)	)	PUNCT
ejpam-5602	303	16	for	for	ADP
ejpam-5602	303	17	which	which	PRON
ejpam-5602	303	18	u	u	PROPN
ejpam-5602	303	19	∈	∈	PROPN
ejpam-5602	303	20	v	v	NOUN
ejpam-5602	303	21	(	(	PUNCT
ejpam-5602	303	22	hv	hv	PROPN
ejpam-5602	303	23	+	+	PROPN
ejpam-5602	303	24	v	v	NOUN
ejpam-5602	303	25	)	)	PUNCT
ejpam-5602	303	26	.	.	PUNCT
ejpam-5602	304	1	suppose	suppose	VERB
ejpam-5602	304	2	that	that	SCONJ
ejpam-5602	304	3	v	v	PROPN
ejpam-5602	304	4	∈	∈	PROPN
ejpam-5602	304	5	v0	v0	NOUN
ejpam-5602	304	6	.	.	PUNCT
ejpam-5602	305	1	if	if	SCONJ
ejpam-5602	305	2	u	u	PROPN
ejpam-5602	305	3	̸=	̸=	PROPN
ejpam-5602	305	4	v	v	NOUN
ejpam-5602	305	5	,	,	PUNCT
ejpam-5602	305	6	then	then	ADV
ejpam-5602	305	7	by	by	ADP
ejpam-5602	305	8	(	(	PUNCT
ejpam-5602	305	9	i	i	NOUN
ejpam-5602	305	10	)	)	PUNCT
ejpam-5602	305	11	,	,	PUNCT
ejpam-5602	305	12	f(ng	f(ng	PROPN
ejpam-5602	305	13	◦	◦	NOUN
ejpam-5602	305	14	h	h	NOUN
ejpam-5602	306	1	[	[	X
ejpam-5602	306	2	u	u	X
ejpam-5602	306	3	]	]	X
ejpam-5602	306	4	)	)	PUNCT
ejpam-5602	307	1	=	=	SYM
ejpam-5602	307	2	f	f	PROPN
ejpam-5602	307	3	|hv(nhv	|hv(nhv	PROPN
ejpam-5602	308	1	[	[	X
ejpam-5602	308	2	u	u	X
ejpam-5602	308	3	]	]	X
ejpam-5602	308	4	)	)	PUNCT
ejpam-5602	308	5	≥	≥	NOUN
ejpam-5602	308	6	3	3	X
ejpam-5602	308	7	.	.	PUNCT
ejpam-5602	308	8	suppose	suppose	VERB
ejpam-5602	308	9	that	that	SCONJ
ejpam-5602	308	10	u	u	PROPN
ejpam-5602	308	11	=	=	PUNCT
ejpam-5602	308	12	v.	v.	ADP
ejpam-5602	308	13	statement	statement	NOUN
ejpam-5602	308	14	(	(	PUNCT
ejpam-5602	308	15	i	i	NOUN
ejpam-5602	308	16	)	)	PUNCT
ejpam-5602	308	17	implies	imply	VERB
ejpam-5602	308	18	that	that	SCONJ
ejpam-5602	308	19	f(ng	f(ng	PROPN
ejpam-5602	308	20	◦	◦	NOUN
ejpam-5602	308	21	h	h	NOUN
ejpam-5602	308	22	[	[	X
ejpam-5602	308	23	u	u	X
ejpam-5602	308	24	]	]	X
ejpam-5602	308	25	)	)	PUNCT
ejpam-5602	308	26	≥	≥	PROPN
ejpam-5602	308	27	f	f	X
ejpam-5602	308	28	|hv(v	|hv(v	PROPN
ejpam-5602	308	29	(	(	PUNCT
ejpam-5602	308	30	hv	hv	NOUN
ejpam-5602	308	31	)	)	PUNCT
ejpam-5602	308	32	)	)	PUNCT
ejpam-5602	308	33	≥	≥	NOUN
ejpam-5602	308	34	3	3	X
ejpam-5602	308	35	.	.	PUNCT
ejpam-5602	308	36	suppose	suppose	VERB
ejpam-5602	308	37	that	that	SCONJ
ejpam-5602	308	38	v	v	ADP
ejpam-5602	308	39	∈	∈	PROPN
ejpam-5602	308	40	v	v	NOUN
ejpam-5602	308	41	(	(	PUNCT
ejpam-5602	308	42	g	g	NOUN
ejpam-5602	308	43	)	)	PUNCT
ejpam-5602	308	44	\	\	PROPN
ejpam-5602	308	45	v0	v0	NOUN
ejpam-5602	308	46	.	.	PUNCT
ejpam-5602	309	1	then	then	ADV
ejpam-5602	309	2	u	u	PROPN
ejpam-5602	309	3	∈	∈	PROPN
ejpam-5602	309	4	v0	v0	NOUN
ejpam-5602	309	5	∩	∩	X
ejpam-5602	309	6	v	v	X
ejpam-5602	309	7	(	(	PUNCT
ejpam-5602	309	8	hv	hv	PROPN
ejpam-5602	309	9	)	)	PUNCT
ejpam-5602	309	10	and	and	CCONJ
ejpam-5602	309	11	v	v	ADP
ejpam-5602	309	12	∈	∈	PROPN
ejpam-5602	309	13	ng	ng	PROPN
ejpam-5602	309	14	◦	◦	NOUN
ejpam-5602	309	15	h	h	NOUN
ejpam-5602	310	1	[	[	X
ejpam-5602	310	2	u	u	X
ejpam-5602	310	3	]	]	X
ejpam-5602	310	4	.	.	PUNCT
ejpam-5602	311	1	if	if	SCONJ
ejpam-5602	311	2	v	v	PROPN
ejpam-5602	311	3	∈	∈	PROPN
ejpam-5602	311	4	v3	v3	PROPN
ejpam-5602	311	5	,	,	PUNCT
ejpam-5602	311	6	then	then	ADV
ejpam-5602	311	7	f(ng	f(ng	PROPN
ejpam-5602	311	8	◦	◦	NOUN
ejpam-5602	311	9	h	h	NOUN
ejpam-5602	312	1	[	[	X
ejpam-5602	312	2	u	u	X
ejpam-5602	312	3	]	]	X
ejpam-5602	312	4	)	)	PUNCT
ejpam-5602	312	5	≥	≥	NOUN
ejpam-5602	312	6	f(v	f(v	NOUN
ejpam-5602	312	7	)	)	PUNCT
ejpam-5602	312	8	=	=	SYM
ejpam-5602	313	1	3	3	X
ejpam-5602	313	2	.	.	X
ejpam-5602	314	1	if	if	SCONJ
ejpam-5602	314	2	v	v	NUM
ejpam-5602	314	3	∈	∈	PROPN
ejpam-5602	314	4	v1	v1	NOUN
ejpam-5602	314	5	∪	∪	NOUN
ejpam-5602	314	6	v2	v2	NOUN
ejpam-5602	314	7	,	,	PUNCT
ejpam-5602	314	8	then	then	ADV
ejpam-5602	314	9	by	by	ADP
ejpam-5602	314	10	(	(	PUNCT
ejpam-5602	314	11	ii	ii	NOUN
ejpam-5602	314	12	)	)	PUNCT
ejpam-5602	314	13	and	and	CCONJ
ejpam-5602	314	14	(	(	PUNCT
ejpam-5602	314	15	iii	iii	NOUN
ejpam-5602	314	16	)	)	PUNCT
ejpam-5602	314	17	,	,	PUNCT
ejpam-5602	314	18	f(ng	f(ng	PROPN
ejpam-5602	314	19	◦	◦	NOUN
ejpam-5602	314	20	h	h	NOUN
ejpam-5602	315	1	[	[	X
ejpam-5602	315	2	u	u	X
ejpam-5602	315	3	]	]	X
ejpam-5602	315	4	)	)	PUNCT
ejpam-5602	315	5	=	=	SYM
ejpam-5602	315	6	f(v	f(v	NOUN
ejpam-5602	315	7	)	)	PUNCT
ejpam-5602	316	1	+	+	CCONJ
ejpam-5602	316	2	f(nhv	f(nhv	X
ejpam-5602	317	1	[	[	X
ejpam-5602	317	2	u	u	X
ejpam-5602	317	3	]	]	X
ejpam-5602	317	4	)	)	PUNCT
ejpam-5602	317	5	≥	≥	NOUN
ejpam-5602	317	6	3	3	NUM
ejpam-5602	317	7	.	.	PUNCT
ejpam-5602	317	8	similar	similar	ADJ
ejpam-5602	317	9	arguments	argument	NOUN
ejpam-5602	317	10	show	show	VERB
ejpam-5602	317	11	that	that	SCONJ
ejpam-5602	317	12	if	if	SCONJ
ejpam-5602	317	13	u	u	PROPN
ejpam-5602	317	14	∈	∈	PROPN
ejpam-5602	317	15	v1	v1	NOUN
ejpam-5602	317	16	,	,	PUNCT
ejpam-5602	317	17	then	then	ADV
ejpam-5602	317	18	f(ng	f(ng	PROPN
ejpam-5602	317	19	◦	◦	NOUN
ejpam-5602	317	20	h	h	NOUN
ejpam-5602	318	1	[	[	X
ejpam-5602	318	2	u	u	X
ejpam-5602	318	3	]	]	X
ejpam-5602	318	4	)	)	PUNCT
ejpam-5602	318	5	≥	≥	NOUN
ejpam-5602	318	6	3	3	NUM
ejpam-5602	318	7	.	.	PUNCT
ejpam-5602	319	1	now	now	ADV
ejpam-5602	319	2	,	,	PUNCT
ejpam-5602	319	3	let	let	VERB
ejpam-5602	319	4	v	v	NUM
ejpam-5602	319	5	∈	∈	NOUN
ejpam-5602	319	6	v1	v1	NOUN
ejpam-5602	319	7	∪	∪	NOUN
ejpam-5602	319	8	v2	v2	PROPN
ejpam-5602	319	9	∪	∪	X
ejpam-5602	319	10	v3	v3	PROPN
ejpam-5602	319	11	.	.	PUNCT
ejpam-5602	320	1	consider	consider	VERB
ejpam-5602	320	2	the	the	DET
ejpam-5602	320	3	following	follow	VERB
ejpam-5602	320	4	cases	case	NOUN
ejpam-5602	320	5	:	:	PUNCT
ejpam-5602	320	6	case	case	NOUN
ejpam-5602	320	7	1	1	NUM
ejpam-5602	320	8	:	:	PUNCT
ejpam-5602	320	9	suppose	suppose	VERB
ejpam-5602	320	10	v	v	NUM
ejpam-5602	320	11	∈	∈	PROPN
ejpam-5602	320	12	v	v	NOUN
ejpam-5602	320	13	(	(	PUNCT
ejpam-5602	320	14	g	g	NOUN
ejpam-5602	320	15	)	)	PUNCT
ejpam-5602	320	16	.	.	PUNCT
ejpam-5602	321	1	if	if	SCONJ
ejpam-5602	321	2	v0∩v	v0∩v	PROPN
ejpam-5602	321	3	(	(	PUNCT
ejpam-5602	321	4	hv	hv	NOUN
ejpam-5602	321	5	)	)	PUNCT
ejpam-5602	321	6	=	=	NOUN
ejpam-5602	321	7	∅	∅	NOUN
ejpam-5602	321	8	,	,	PUNCT
ejpam-5602	321	9	then	then	ADV
ejpam-5602	321	10	for	for	ADP
ejpam-5602	321	11	each	each	DET
ejpam-5602	321	12	u	u	PROPN
ejpam-5602	321	13	∈	∈	PROPN
ejpam-5602	321	14	v	v	PROPN
ejpam-5602	321	15	(	(	PUNCT
ejpam-5602	321	16	hv	hv	PROPN
ejpam-5602	321	17	)	)	PUNCT
ejpam-5602	321	18	,	,	PUNCT
ejpam-5602	321	19	u	u	PROPN
ejpam-5602	321	20	∈	∈	PRON
ejpam-5602	321	21	v1∪v2∪v3	v1∪v2∪v3	NOUN
ejpam-5602	321	22	and	and	CCONJ
ejpam-5602	321	23	uv	uv	NOUN
ejpam-5602	321	24	∈	∈	PROPN
ejpam-5602	321	25	e(g	e(g	PROPN
ejpam-5602	321	26	◦	◦	NOUN
ejpam-5602	321	27	h	h	NOUN
ejpam-5602	321	28	)	)	PUNCT
ejpam-5602	321	29	.	.	PUNCT
ejpam-5602	321	30	suppose	suppose	VERB
ejpam-5602	321	31	that	that	SCONJ
ejpam-5602	321	32	v0	v0	NOUN
ejpam-5602	321	33	∩	∩	NOUN
ejpam-5602	321	34	v	v	X
ejpam-5602	321	35	(	(	PUNCT
ejpam-5602	321	36	hv	hv	NOUN
ejpam-5602	321	37	)	)	PUNCT
ejpam-5602	321	38	̸=	̸=	PROPN
ejpam-5602	321	39	∅	∅	NOUN
ejpam-5602	321	40	,	,	PUNCT
ejpam-5602	321	41	say	say	VERB
ejpam-5602	321	42	w	w	PROPN
ejpam-5602	321	43	∈	∈	PROPN
ejpam-5602	321	44	v0	v0	NOUN
ejpam-5602	321	45	∩	∩	X
ejpam-5602	321	46	v	v	X
ejpam-5602	321	47	(	(	PUNCT
ejpam-5602	321	48	hv	hv	PROPN
ejpam-5602	321	49	)	)	PUNCT
ejpam-5602	321	50	.	.	PUNCT
ejpam-5602	322	1	if	if	SCONJ
ejpam-5602	322	2	v	v	NUM
ejpam-5602	322	3	∈	∈	PROPN
ejpam-5602	322	4	v1	v1	NOUN
ejpam-5602	322	5	∪	∪	NOUN
ejpam-5602	322	6	v2	v2	NOUN
ejpam-5602	322	7	,	,	PUNCT
ejpam-5602	322	8	then	then	ADV
ejpam-5602	322	9	by	by	ADP
ejpam-5602	322	10	conditions	condition	NOUN
ejpam-5602	322	11	(	(	PUNCT
ejpam-5602	322	12	ii	ii	NOUN
ejpam-5602	322	13	)	)	PUNCT
ejpam-5602	322	14	and	and	CCONJ
ejpam-5602	322	15	(	(	PUNCT
ejpam-5602	322	16	iii	iii	NOUN
ejpam-5602	322	17	)	)	PUNCT
ejpam-5602	322	18	,	,	PUNCT
ejpam-5602	322	19	there	there	PRON
ejpam-5602	322	20	exists	exist	VERB
ejpam-5602	322	21	u	u	PROPN
ejpam-5602	322	22	∈	∈	PROPN
ejpam-5602	322	23	[	[	X
ejpam-5602	322	24	(	(	PUNCT
ejpam-5602	322	25	v1	v1	VERB
ejpam-5602	322	26	∪	∪	NOUN
ejpam-5602	322	27	v2	v2	PROPN
ejpam-5602	322	28	∪	∪	X
ejpam-5602	322	29	v3	v3	PROPN
ejpam-5602	322	30	)	)	PUNCT
ejpam-5602	322	31	∩	∩	PROPN
ejpam-5602	322	32	v	v	X
ejpam-5602	322	33	(	(	PUNCT
ejpam-5602	322	34	hv	hv	PROPN
ejpam-5602	322	35	)	)	PUNCT
ejpam-5602	322	36	]	]	PUNCT
ejpam-5602	322	37	for	for	ADP
ejpam-5602	322	38	which	which	PRON
ejpam-5602	322	39	uw	uw	PROPN
ejpam-5602	322	40	∈	∈	PROPN
ejpam-5602	322	41	e(hv	e(hv	PROPN
ejpam-5602	322	42	)	)	PUNCT
ejpam-5602	322	43	.	.	PUNCT
ejpam-5602	323	1	incidentally	incidentally	ADV
ejpam-5602	323	2	,	,	PUNCT
ejpam-5602	323	3	uv	uv	PROPN
ejpam-5602	323	4	∈	∈	PROPN
ejpam-5602	323	5	e(g	e(g	PROPN
ejpam-5602	323	6	◦	◦	NOUN
ejpam-5602	323	7	h	h	NOUN
ejpam-5602	323	8	)	)	PUNCT
ejpam-5602	323	9	.	.	PUNCT
ejpam-5602	324	1	suppose	suppose	VERB
ejpam-5602	324	2	that	that	SCONJ
ejpam-5602	324	3	v	v	PROPN
ejpam-5602	324	4	∈	∈	PROPN
ejpam-5602	324	5	v3	v3	PROPN
ejpam-5602	324	6	.	.	PUNCT
ejpam-5602	325	1	then	then	ADV
ejpam-5602	325	2	either	either	CCONJ
ejpam-5602	325	3	there	there	PRON
ejpam-5602	325	4	exists	exist	VERB
ejpam-5602	325	5	u	u	PROPN
ejpam-5602	325	6	∈	∈	PROPN
ejpam-5602	325	7	[	[	X
ejpam-5602	325	8	(	(	PUNCT
ejpam-5602	325	9	v1	v1	NOUN
ejpam-5602	325	10	∪v2	∪v2	NOUN
ejpam-5602	325	11	∪v3)∩ng(v	∪v3)∩ng(v	PROPN
ejpam-5602	325	12	)	)	PUNCT
ejpam-5602	325	13	]	]	PUNCT
ejpam-5602	325	14	or	or	CCONJ
ejpam-5602	325	15	,	,	PUNCT
ejpam-5602	325	16	by	by	ADP
ejpam-5602	325	17	condition	condition	NOUN
ejpam-5602	325	18	(	(	PUNCT
ejpam-5602	325	19	iv	iv	NUM
ejpam-5602	325	20	)	)	PUNCT
ejpam-5602	325	21	,	,	PUNCT
ejpam-5602	325	22	there	there	PRON
ejpam-5602	325	23	exists	exist	VERB
ejpam-5602	325	24	u	u	PROPN
ejpam-5602	325	25	∈	∈	PROPN
ejpam-5602	325	26	v	v	ADP
ejpam-5602	325	27	(	(	PUNCT
ejpam-5602	325	28	hv	hv	PROPN
ejpam-5602	325	29	)	)	PUNCT
ejpam-5602	325	30	for	for	ADP
ejpam-5602	325	31	which	which	PRON
ejpam-5602	325	32	f(u	f(u	PROPN
ejpam-5602	325	33	)	)	PUNCT
ejpam-5602	325	34	≥	≥	NOUN
ejpam-5602	325	35	1	1	NUM
ejpam-5602	325	36	.	.	PUNCT
ejpam-5602	326	1	in	in	ADP
ejpam-5602	326	2	this	this	DET
ejpam-5602	326	3	case	case	NOUN
ejpam-5602	326	4	,	,	PUNCT
ejpam-5602	326	5	uv	uv	PROPN
ejpam-5602	326	6	∈	∈	PROPN
ejpam-5602	326	7	e(g	e(g	PROPN
ejpam-5602	326	8	◦	◦	NOUN
ejpam-5602	326	9	h	h	NOUN
ejpam-5602	326	10	)	)	PUNCT
ejpam-5602	326	11	.	.	PUNCT
ejpam-5602	327	1	case	case	NOUN
ejpam-5602	327	2	2	2	NUM
ejpam-5602	327	3	:	:	PUNCT
ejpam-5602	327	4	suppose	suppose	VERB
ejpam-5602	327	5	v	v	NUM
ejpam-5602	327	6	∈	∈	PROPN
ejpam-5602	327	7	v	v	NOUN
ejpam-5602	327	8	(	(	PUNCT
ejpam-5602	327	9	hx	hx	PROPN
ejpam-5602	327	10	)	)	PUNCT
ejpam-5602	327	11	for	for	ADP
ejpam-5602	327	12	some	some	DET
ejpam-5602	327	13	x	x	SYM
ejpam-5602	327	14	∈	∈	PROPN
ejpam-5602	327	15	v	v	NOUN
ejpam-5602	327	16	(	(	PUNCT
ejpam-5602	327	17	g	g	NOUN
ejpam-5602	327	18	)	)	PUNCT
ejpam-5602	327	19	.	.	PUNCT
ejpam-5602	328	1	if	if	SCONJ
ejpam-5602	328	2	x	x	SYM
ejpam-5602	328	3	∈	∈	PROPN
ejpam-5602	328	4	v1	v1	NOUN
ejpam-5602	328	5	∪v2	∪v2	PROPN
ejpam-5602	328	6	∪v3	∪v3	NOUN
ejpam-5602	328	7	,	,	PUNCT
ejpam-5602	328	8	then	then	ADV
ejpam-5602	328	9	we	we	PRON
ejpam-5602	328	10	are	be	AUX
ejpam-5602	328	11	done	do	VERB
ejpam-5602	328	12	.	.	PUNCT
ejpam-5602	329	1	if	if	SCONJ
ejpam-5602	329	2	x	x	PROPN
ejpam-5602	329	3	∈	∈	PROPN
ejpam-5602	329	4	v0	v0	NOUN
ejpam-5602	329	5	,	,	PUNCT
ejpam-5602	329	6	then	then	ADV
ejpam-5602	329	7	since	since	SCONJ
ejpam-5602	329	8	f	f	PROPN
ejpam-5602	329	9	|hx	|hx	PROPN
ejpam-5602	329	10	∈	∈	PROPN
ejpam-5602	329	11	tdidf	tdidf	NOUN
ejpam-5602	329	12	(	(	PUNCT
ejpam-5602	329	13	hx	hx	PROPN
ejpam-5602	329	14	)	)	PUNCT
ejpam-5602	329	15	(	(	PUNCT
ejpam-5602	329	16	condition	condition	NOUN
ejpam-5602	329	17	(	(	PUNCT
ejpam-5602	329	18	i	i	NOUN
ejpam-5602	329	19	)	)	PUNCT
ejpam-5602	329	20	)	)	PUNCT
ejpam-5602	329	21	,	,	PUNCT
ejpam-5602	329	22	there	there	PRON
ejpam-5602	329	23	exists	exist	VERB
ejpam-5602	329	24	u	u	PROPN
ejpam-5602	329	25	∈	∈	PROPN
ejpam-5602	329	26	[	[	X
ejpam-5602	329	27	(	(	PUNCT
ejpam-5602	329	28	v1	v1	VERB
ejpam-5602	329	29	∪	∪	NOUN
ejpam-5602	329	30	v2	v2	PROPN
ejpam-5602	329	31	∪	∪	X
ejpam-5602	329	32	v3	v3	PROPN
ejpam-5602	329	33	)	)	PUNCT
ejpam-5602	329	34	∩	∩	PROPN
ejpam-5602	329	35	v	v	X
ejpam-5602	329	36	(	(	PUNCT
ejpam-5602	329	37	hv	hv	PROPN
ejpam-5602	329	38	)	)	PUNCT
ejpam-5602	329	39	]	]	PUNCT
ejpam-5602	329	40	for	for	ADP
ejpam-5602	329	41	which	which	PRON
ejpam-5602	329	42	uv	uv	PROPN
ejpam-5602	329	43	∈	∈	PROPN
ejpam-5602	329	44	e(hx	e(hx	PROPN
ejpam-5602	329	45	)	)	PUNCT
ejpam-5602	329	46	,	,	PUNCT
ejpam-5602	329	47	which	which	PRON
ejpam-5602	329	48	means	mean	VERB
ejpam-5602	329	49	uv	uv	PROPN
ejpam-5602	329	50	∈	∈	PROPN
ejpam-5602	329	51	e(g	e(g	PROPN
ejpam-5602	329	52	◦	◦	NOUN
ejpam-5602	329	53	h	h	NOUN
ejpam-5602	329	54	)	)	PUNCT
ejpam-5602	329	55	.	.	PUNCT
ejpam-5602	330	1	■	■	PUNCT
ejpam-5602	330	2	corollary	corollary	ADJ
ejpam-5602	330	3	3	3	X
ejpam-5602	330	4	.	.	PUNCT
ejpam-5602	331	1	let	let	VERB
ejpam-5602	331	2	g	g	PRON
ejpam-5602	331	3	be	be	AUX
ejpam-5602	331	4	a	a	DET
ejpam-5602	331	5	nontrivial	nontrivial	ADJ
ejpam-5602	331	6	connected	connect	VERB
ejpam-5602	331	7	graph	graph	NOUN
ejpam-5602	331	8	of	of	ADP
ejpam-5602	331	9	order	order	NOUN
ejpam-5602	331	10	n	n	CCONJ
ejpam-5602	331	11	,	,	PUNCT
ejpam-5602	331	12	and	and	CCONJ
ejpam-5602	331	13	let	let	VERB
ejpam-5602	331	14	h	h	NOUN
ejpam-5602	331	15	be	be	AUX
ejpam-5602	331	16	any	any	DET
ejpam-5602	331	17	graph	graph	NOUN
ejpam-5602	331	18	.	.	PUNCT
ejpam-5602	332	1	then	then	ADV
ejpam-5602	332	2	γtdi(g	γtdi(g	PROPN
ejpam-5602	332	3	◦	◦	NOUN
ejpam-5602	332	4	h	h	NOUN
ejpam-5602	332	5	)	)	PUNCT
ejpam-5602	333	1	=	=	SYM
ejpam-5602	333	2	3n	3n	NOUN
ejpam-5602	333	3	.	.	PUNCT
ejpam-5602	334	1	proof	proof	NOUN
ejpam-5602	334	2	:	:	PUNCT
ejpam-5602	334	3	since	since	SCONJ
ejpam-5602	334	4	f	f	PROPN
ejpam-5602	334	5	=	=	SYM
ejpam-5602	334	6	(	(	PUNCT
ejpam-5602	334	7	∪x∈v	∪x∈v	X
ejpam-5602	334	8	(	(	PUNCT
ejpam-5602	334	9	g)v	g)v	X
ejpam-5602	334	10	(	(	PUNCT
ejpam-5602	334	11	hx),∅,∅	hx),∅,∅	NOUN
ejpam-5602	334	12	,	,	PUNCT
ejpam-5602	334	13	v	v	NOUN
ejpam-5602	334	14	(	(	PUNCT
ejpam-5602	334	15	g	g	NOUN
ejpam-5602	334	16	)	)	PUNCT
ejpam-5602	334	17	)	)	PUNCT
ejpam-5602	335	1	∈	∈	PROPN
ejpam-5602	335	2	tdidf	tdidf	NOUN
ejpam-5602	335	3	(	(	PUNCT
ejpam-5602	335	4	g	g	PROPN
ejpam-5602	335	5	◦	◦	NOUN
ejpam-5602	335	6	h	h	NOUN
ejpam-5602	335	7	)	)	PUNCT
ejpam-5602	335	8	,	,	PUNCT
ejpam-5602	335	9	γtdi(g	γtdi(g	ADP
ejpam-5602	335	10	◦	◦	NOUN
ejpam-5602	335	11	h	h	NOUN
ejpam-5602	335	12	)	)	PUNCT
ejpam-5602	335	13	≤	≤	NUM
ejpam-5602	335	14	3n	3n	NUM
ejpam-5602	335	15	.	.	PUNCT
ejpam-5602	336	1	to	to	PART
ejpam-5602	336	2	get	get	VERB
ejpam-5602	336	3	the	the	DET
ejpam-5602	336	4	other	other	ADJ
ejpam-5602	336	5	inequality	inequality	NOUN
ejpam-5602	336	6	,	,	PUNCT
ejpam-5602	336	7	first	first	ADV
ejpam-5602	336	8	,	,	PUNCT
ejpam-5602	336	9	suppose	suppose	VERB
ejpam-5602	336	10	that	that	SCONJ
ejpam-5602	336	11	h	h	NOUN
ejpam-5602	336	12	has	have	VERB
ejpam-5602	336	13	an	an	DET
ejpam-5602	336	14	isolated	isolated	ADJ
ejpam-5602	336	15	vertex	vertex	NOUN
ejpam-5602	336	16	,	,	PUNCT
ejpam-5602	336	17	say	say	VERB
ejpam-5602	336	18	x.	x.	NOUN
ejpam-5602	336	19	for	for	ADP
ejpam-5602	336	20	each	each	DET
ejpam-5602	336	21	v	v	NUM
ejpam-5602	336	22	∈	∈	PROPN
ejpam-5602	336	23	v	v	NOUN
ejpam-5602	336	24	(	(	PUNCT
ejpam-5602	336	25	g	g	NOUN
ejpam-5602	336	26	)	)	PUNCT
ejpam-5602	336	27	,	,	PUNCT
ejpam-5602	336	28	let	let	VERB
ejpam-5602	336	29	xv	xv	PRON
ejpam-5602	336	30	denote	denote	VERB
ejpam-5602	336	31	the	the	DET
ejpam-5602	336	32	isolated	isolated	ADJ
ejpam-5602	336	33	vertex	vertex	NOUN
ejpam-5602	336	34	of	of	ADP
ejpam-5602	336	35	hv	hv	PROPN
ejpam-5602	336	36	being	be	AUX
ejpam-5602	336	37	identified	identify	VERB
ejpam-5602	336	38	with	with	ADP
ejpam-5602	336	39	x.	x.	NOUN
ejpam-5602	336	40	let	let	VERB
ejpam-5602	336	41	f	f	PROPN
ejpam-5602	336	42	=	=	SYM
ejpam-5602	336	43	(	(	PUNCT
ejpam-5602	336	44	v0	v0	PROPN
ejpam-5602	336	45	,	,	PUNCT
ejpam-5602	336	46	v1	v1	NOUN
ejpam-5602	336	47	,	,	PUNCT
ejpam-5602	336	48	v2	v2	PROPN
ejpam-5602	336	49	,	,	PUNCT
ejpam-5602	336	50	v3	v3	PROPN
ejpam-5602	336	51	)	)	PUNCT
ejpam-5602	336	52	be	be	VERB
ejpam-5602	336	53	a	a	DET
ejpam-5602	336	54	γtdi	γtdi	NOUN
ejpam-5602	336	55	-function	-function	NOUN
ejpam-5602	336	56	of	of	ADP
ejpam-5602	336	57	g	g	PROPN
ejpam-5602	336	58	◦	◦	NOUN
ejpam-5602	336	59	h.	h.	PROPN
ejpam-5602	336	60	since	since	SCONJ
ejpam-5602	336	61	xv	xv	PROPN
ejpam-5602	336	62	is	be	AUX
ejpam-5602	336	63	an	an	DET
ejpam-5602	336	64	endvertex	endvertex	NOUN
ejpam-5602	336	65	in	in	ADP
ejpam-5602	336	66	hv	hv	PROPN
ejpam-5602	337	1	+	+	SYM
ejpam-5602	337	2	v	v	NOUN
ejpam-5602	337	3	,	,	PUNCT
ejpam-5602	337	4	f(v	f(v	PROPN
ejpam-5602	337	5	(	(	PUNCT
ejpam-5602	337	6	hv	hv	NOUN
ejpam-5602	337	7	+	+	PROPN
ejpam-5602	337	8	v	v	NOUN
ejpam-5602	337	9	)	)	PUNCT
ejpam-5602	337	10	)	)	PUNCT
ejpam-5602	337	11	≥	≥	NOUN
ejpam-5602	337	12	f(v	f(v	NOUN
ejpam-5602	337	13	)	)	PUNCT
ejpam-5602	337	14	+	+	SYM
ejpam-5602	337	15	f(xv	f(xv	NOUN
ejpam-5602	337	16	)	)	PUNCT
ejpam-5602	337	17	≥	≥	NOUN
ejpam-5602	337	18	3	3	NUM
ejpam-5602	337	19	for	for	ADP
ejpam-5602	337	20	all	all	DET
ejpam-5602	337	21	v	v	ADP
ejpam-5602	337	22	∈	∈	NOUN
ejpam-5602	337	23	v	v	NOUN
ejpam-5602	337	24	(	(	PUNCT
ejpam-5602	337	25	g	g	NOUN
ejpam-5602	337	26	)	)	PUNCT
ejpam-5602	337	27	.	.	PUNCT
ejpam-5602	338	1	this	this	DET
ejpam-5602	338	2	yields	yield	NOUN
ejpam-5602	338	3	γtdi(g	γtdi(g	ADP
ejpam-5602	338	4	◦	◦	NOUN
ejpam-5602	338	5	h	h	NOUN
ejpam-5602	338	6	)	)	PUNCT
ejpam-5602	338	7	≥	≥	PROPN
ejpam-5602	338	8	∑	∑	PUNCT
ejpam-5602	338	9	v∈v	v∈v	PROPN
ejpam-5602	338	10	(	(	PUNCT
ejpam-5602	338	11	g	g	NOUN
ejpam-5602	338	12	)	)	PUNCT
ejpam-5602	338	13	f(v	f(v	PROPN
ejpam-5602	338	14	(	(	PUNCT
ejpam-5602	338	15	hv	hv	NOUN
ejpam-5602	338	16	+	+	PROPN
ejpam-5602	338	17	v	v	NOUN
ejpam-5602	338	18	)	)	PUNCT
ejpam-5602	338	19	≥	≥	NOUN
ejpam-5602	338	20	3n	3n	NUM
ejpam-5602	338	21	.	.	PUNCT
ejpam-5602	339	1	next	next	ADV
ejpam-5602	339	2	,	,	PUNCT
ejpam-5602	339	3	suppose	suppose	VERB
ejpam-5602	339	4	that	that	SCONJ
ejpam-5602	339	5	h	h	NOUN
ejpam-5602	339	6	has	have	VERB
ejpam-5602	339	7	no	no	DET
ejpam-5602	339	8	isolated	isolated	ADJ
ejpam-5602	339	9	vertices	vertex	NOUN
ejpam-5602	339	10	,	,	PUNCT
ejpam-5602	339	11	and	and	CCONJ
ejpam-5602	339	12	let	let	VERB
ejpam-5602	339	13	f	f	PROPN
ejpam-5602	339	14	=	=	SYM
ejpam-5602	339	15	(	(	PUNCT
ejpam-5602	339	16	v0	v0	PROPN
ejpam-5602	339	17	,	,	PUNCT
ejpam-5602	339	18	v1	v1	NOUN
ejpam-5602	339	19	,	,	PUNCT
ejpam-5602	339	20	v2	v2	PROPN
ejpam-5602	339	21	,	,	PUNCT
ejpam-5602	339	22	v3	v3	PROPN
ejpam-5602	339	23	)	)	PUNCT
ejpam-5602	339	24	be	be	VERB
ejpam-5602	339	25	a	a	DET
ejpam-5602	339	26	γtdi	γtdi	NOUN
ejpam-5602	339	27	function	function	NOUN
ejpam-5602	339	28	of	of	ADP
ejpam-5602	339	29	g	g	PROPN
ejpam-5602	339	30	◦	◦	NOUN
ejpam-5602	339	31	h.	h.	NOUN
ejpam-5602	339	32	let	let	VERB
ejpam-5602	339	33	v	v	NUM
ejpam-5602	339	34	∈	∈	PROPN
ejpam-5602	339	35	v	v	NOUN
ejpam-5602	339	36	(	(	PUNCT
ejpam-5602	339	37	g	g	NOUN
ejpam-5602	339	38	)	)	PUNCT
ejpam-5602	339	39	.	.	PUNCT
ejpam-5602	340	1	clearly	clearly	ADV
ejpam-5602	340	2	,	,	PUNCT
ejpam-5602	340	3	if	if	SCONJ
ejpam-5602	340	4	v	v	PROPN
ejpam-5602	340	5	∈	∈	PROPN
ejpam-5602	340	6	v3	v3	PROPN
ejpam-5602	340	7	,	,	PUNCT
ejpam-5602	340	8	then	then	ADV
ejpam-5602	340	9	f(v	f(v	PROPN
ejpam-5602	340	10	(	(	PUNCT
ejpam-5602	340	11	hv	hv	NOUN
ejpam-5602	340	12	+	+	PROPN
ejpam-5602	340	13	v	v	NOUN
ejpam-5602	340	14	)	)	PUNCT
ejpam-5602	340	15	)	)	PUNCT
ejpam-5602	340	16	≥	≥	NOUN
ejpam-5602	341	1	3	3	X
ejpam-5602	341	2	.	.	PUNCT
ejpam-5602	342	1	if	if	SCONJ
ejpam-5602	342	2	v	v	NUM
ejpam-5602	342	3	∈	∈	PROPN
ejpam-5602	342	4	v0	v0	NOUN
ejpam-5602	342	5	,	,	PUNCT
ejpam-5602	342	6	then	then	ADV
ejpam-5602	342	7	f	f	PROPN
ejpam-5602	342	8	|hv	|hv	PROPN
ejpam-5602	342	9	∈	∈	PROPN
ejpam-5602	342	10	tdidf	tdidf	NOUN
ejpam-5602	342	11	(	(	PUNCT
ejpam-5602	342	12	hv	hv	NOUN
ejpam-5602	342	13	)	)	PUNCT
ejpam-5602	342	14	by	by	ADP
ejpam-5602	342	15	proposition	proposition	NOUN
ejpam-5602	342	16	9	9	NUM
ejpam-5602	342	17	(	(	PUNCT
ejpam-5602	342	18	i	i	NOUN
ejpam-5602	342	19	)	)	PUNCT
ejpam-5602	342	20	.	.	PUNCT
ejpam-5602	343	1	thus	thus	ADV
ejpam-5602	343	2	,	,	PUNCT
ejpam-5602	343	3	f(v	f(v	PROPN
ejpam-5602	343	4	(	(	PUNCT
ejpam-5602	343	5	hv	hv	NOUN
ejpam-5602	343	6	+	+	PROPN
ejpam-5602	343	7	v	v	NOUN
ejpam-5602	343	8	)	)	PUNCT
ejpam-5602	343	9	)	)	PUNCT
ejpam-5602	344	1	=	=	PUNCT
ejpam-5602	345	1	f	f	X
ejpam-5602	345	2	|hv(v	|hv(v	PROPN
ejpam-5602	345	3	(	(	PUNCT
ejpam-5602	345	4	hv	hv	NOUN
ejpam-5602	345	5	)	)	PUNCT
ejpam-5602	345	6	)	)	PUNCT
ejpam-5602	345	7	≥	≥	NOUN
ejpam-5602	345	8	3	3	X
ejpam-5602	345	9	.	.	PUNCT
ejpam-5602	345	10	suppose	suppose	VERB
ejpam-5602	345	11	that	that	SCONJ
ejpam-5602	345	12	v	v	NUM
ejpam-5602	345	13	∈	∈	PROPN
ejpam-5602	345	14	v1	v1	NOUN
ejpam-5602	345	15	∪	∪	NOUN
ejpam-5602	345	16	v2	v2	NOUN
ejpam-5602	345	17	.	.	PUNCT
ejpam-5602	346	1	if	if	SCONJ
ejpam-5602	346	2	v0	v0	NOUN
ejpam-5602	346	3	∩	∩	NOUN
ejpam-5602	346	4	v	v	X
ejpam-5602	346	5	(	(	PUNCT
ejpam-5602	346	6	hv	hv	NOUN
ejpam-5602	346	7	)	)	PUNCT
ejpam-5602	346	8	=	=	NOUN
ejpam-5602	346	9	∅	∅	NOUN
ejpam-5602	346	10	,	,	PUNCT
ejpam-5602	346	11	then	then	ADV
ejpam-5602	346	12	since	since	SCONJ
ejpam-5602	346	13	|v	|v	PROPN
ejpam-5602	346	14	(	(	PUNCT
ejpam-5602	346	15	hv)|	hv)|	X
ejpam-5602	346	16	≥	≥	NOUN
ejpam-5602	346	17	2	2	NUM
ejpam-5602	346	18	,	,	PUNCT
ejpam-5602	346	19	f(v	f(v	PROPN
ejpam-5602	346	20	(	(	PUNCT
ejpam-5602	346	21	hv	hv	NOUN
ejpam-5602	346	22	)	)	PUNCT
ejpam-5602	346	23	)	)	PUNCT
ejpam-5602	346	24	≥	≥	NOUN
ejpam-5602	347	1	2	2	NUM
ejpam-5602	347	2	so	so	ADV
ejpam-5602	347	3	s.j.l	s.j.l	NOUN
ejpam-5602	347	4	.	.	PUNCT
ejpam-5602	348	1	sumbalan	sumbalan	PROPN
ejpam-5602	348	2	,	,	PUNCT
ejpam-5602	348	3	s.m	s.m	PROPN
ejpam-5602	348	4	.	.	PROPN
ejpam-5602	348	5	menchavez	menchavez	PROPN
ejpam-5602	348	6	,	,	PUNCT
ejpam-5602	348	7	f.p	f.p	PROPN
ejpam-5602	348	8	.	.	PROPN
ejpam-5602	348	9	jamil	jamil	PROPN
ejpam-5602	348	10	/	/	SYM
ejpam-5602	348	11	eur	eur	PROPN
ejpam-5602	348	12	.	.	PUNCT
ejpam-5602	349	1	j.	j.	PROPN
ejpam-5602	349	2	pure	pure	PROPN
ejpam-5602	349	3	appl	appl	PROPN
ejpam-5602	349	4	.	.	PROPN
ejpam-5602	349	5	math	math	PROPN
ejpam-5602	349	6	,	,	PUNCT
ejpam-5602	349	7	18	18	NUM
ejpam-5602	349	8	(	(	PUNCT
ejpam-5602	349	9	1	1	NUM
ejpam-5602	349	10	)	)	PUNCT
ejpam-5602	349	11	(	(	PUNCT
ejpam-5602	349	12	2025	2025	NUM
ejpam-5602	349	13	)	)	PUNCT
ejpam-5602	349	14	,	,	PUNCT
ejpam-5602	349	15	5602	5602	NUM
ejpam-5602	349	16	11	11	NUM
ejpam-5602	349	17	of	of	ADP
ejpam-5602	349	18	18	18	NUM
ejpam-5602	350	1	that	that	PRON
ejpam-5602	350	2	f(v	f(v	PROPN
ejpam-5602	350	3	(	(	PUNCT
ejpam-5602	350	4	hv	hv	NOUN
ejpam-5602	350	5	+	+	PROPN
ejpam-5602	350	6	v	v	NOUN
ejpam-5602	350	7	)	)	PUNCT
ejpam-5602	350	8	)	)	PUNCT
ejpam-5602	350	9	=	=	SYM
ejpam-5602	350	10	f(v	f(v	NOUN
ejpam-5602	350	11	)	)	PUNCT
ejpam-5602	351	1	+	+	NUM
ejpam-5602	351	2	f(v	f(v	PROPN
ejpam-5602	351	3	(	(	PUNCT
ejpam-5602	351	4	hv	hv	NOUN
ejpam-5602	351	5	)	)	PUNCT
ejpam-5602	351	6	)	)	PUNCT
ejpam-5602	351	7	≥	≥	NOUN
ejpam-5602	351	8	3	3	NUM
ejpam-5602	351	9	.	.	PUNCT
ejpam-5602	351	10	on	on	ADP
ejpam-5602	351	11	the	the	DET
ejpam-5602	351	12	other	other	ADJ
ejpam-5602	351	13	hand	hand	NOUN
ejpam-5602	351	14	,	,	PUNCT
ejpam-5602	351	15	if	if	SCONJ
ejpam-5602	351	16	v0	v0	NOUN
ejpam-5602	351	17	∩	∩	NOUN
ejpam-5602	351	18	v	v	X
ejpam-5602	351	19	(	(	PUNCT
ejpam-5602	351	20	hv	hv	NOUN
ejpam-5602	351	21	)	)	PUNCT
ejpam-5602	351	22	̸=	̸=	PROPN
ejpam-5602	351	23	∅	∅	NOUN
ejpam-5602	351	24	,	,	PUNCT
ejpam-5602	351	25	say	say	VERB
ejpam-5602	351	26	u	u	PROPN
ejpam-5602	351	27	∈	∈	PROPN
ejpam-5602	351	28	v0	v0	NOUN
ejpam-5602	351	29	∩	∩	X
ejpam-5602	351	30	v	v	X
ejpam-5602	351	31	(	(	PUNCT
ejpam-5602	351	32	hv	hv	PROPN
ejpam-5602	351	33	)	)	PUNCT
ejpam-5602	351	34	,	,	PUNCT
ejpam-5602	351	35	then	then	ADV
ejpam-5602	351	36	proposition	proposition	NOUN
ejpam-5602	351	37	9(ii	9(ii	NUM
ejpam-5602	351	38	)	)	PUNCT
ejpam-5602	351	39	and	and	CCONJ
ejpam-5602	351	40	proposition	proposition	NOUN
ejpam-5602	351	41	9(iii	9(iii	NUM
ejpam-5602	351	42	)	)	PUNCT
ejpam-5602	351	43	yield	yield	NOUN
ejpam-5602	351	44	f(v	f(v	PROPN
ejpam-5602	351	45	(	(	PUNCT
ejpam-5602	351	46	hv	hv	NOUN
ejpam-5602	351	47	+	+	PROPN
ejpam-5602	351	48	v	v	NOUN
ejpam-5602	351	49	)	)	PUNCT
ejpam-5602	351	50	)	)	PUNCT
ejpam-5602	351	51	≥	≥	NOUN
ejpam-5602	351	52	f(v	f(v	NOUN
ejpam-5602	351	53	)	)	PUNCT
ejpam-5602	352	1	+	+	CCONJ
ejpam-5602	352	2	f(nhv	f(nhv	X
ejpam-5602	353	1	[	[	X
ejpam-5602	353	2	u	u	X
ejpam-5602	353	3	]	]	X
ejpam-5602	353	4	)	)	PUNCT
ejpam-5602	353	5	≥	≥	NOUN
ejpam-5602	353	6	3	3	NUM
ejpam-5602	353	7	.	.	PUNCT
ejpam-5602	354	1	therefore	therefore	ADV
ejpam-5602	354	2	,	,	PUNCT
ejpam-5602	354	3	γtdi(g	γtdi(g	PROPN
ejpam-5602	354	4	◦	◦	NOUN
ejpam-5602	354	5	h	h	NOUN
ejpam-5602	354	6	)	)	PUNCT
ejpam-5602	354	7	=	=	SYM
ejpam-5602	355	1	ωg	ωg	PART
ejpam-5602	355	2	◦	◦	NOUN
ejpam-5602	355	3	h(f	h(f	NOUN
ejpam-5602	355	4	)	)	PUNCT
ejpam-5602	356	1	=	=	PUNCT
ejpam-5602	356	2	∑	∑	PUNCT
ejpam-5602	356	3	v∈v	v∈v	PROPN
ejpam-5602	356	4	(	(	PUNCT
ejpam-5602	356	5	g	g	NOUN
ejpam-5602	356	6	)	)	PUNCT
ejpam-5602	356	7	f(v	f(v	PROPN
ejpam-5602	356	8	(	(	PUNCT
ejpam-5602	356	9	hv	hv	NOUN
ejpam-5602	356	10	+	+	PROPN
ejpam-5602	356	11	v	v	NOUN
ejpam-5602	356	12	)	)	PUNCT
ejpam-5602	356	13	)	)	PUNCT
ejpam-5602	356	14	≥	≥	NOUN
ejpam-5602	356	15	3n	3n	NUM
ejpam-5602	356	16	.	.	PUNCT
ejpam-5602	357	1	■	■	PUNCT
ejpam-5602	357	2	5	5	X
ejpam-5602	357	3	.	.	PUNCT
ejpam-5602	357	4	on	on	ADP
ejpam-5602	357	5	the	the	DET
ejpam-5602	357	6	edge	edge	NOUN
ejpam-5602	357	7	corona	corona	NOUN
ejpam-5602	357	8	of	of	ADP
ejpam-5602	357	9	graphs	graph	NOUN
ejpam-5602	357	10	we	we	PRON
ejpam-5602	357	11	adapt	adapt	VERB
ejpam-5602	357	12	the	the	DET
ejpam-5602	357	13	following	follow	VERB
ejpam-5602	357	14	notations	notation	NOUN
ejpam-5602	357	15	from	from	ADP
ejpam-5602	357	16	[	[	X
ejpam-5602	357	17	21	21	NUM
ejpam-5602	357	18	]	]	PUNCT
ejpam-5602	357	19	.	.	PUNCT
ejpam-5602	358	1	given	give	VERB
ejpam-5602	358	2	graphs	graph	NOUN
ejpam-5602	358	3	g	g	NOUN
ejpam-5602	358	4	and	and	CCONJ
ejpam-5602	358	5	h	h	NOUN
ejpam-5602	358	6	,	,	PUNCT
ejpam-5602	358	7	we	we	PRON
ejpam-5602	358	8	write	write	VERB
ejpam-5602	358	9	huv	huv	PROPN
ejpam-5602	358	10	to	to	PART
ejpam-5602	358	11	denote	denote	VERB
ejpam-5602	358	12	the	the	DET
ejpam-5602	358	13	copy	copy	NOUN
ejpam-5602	358	14	of	of	ADP
ejpam-5602	358	15	h	h	NOUN
ejpam-5602	358	16	that	that	PRON
ejpam-5602	358	17	is	be	AUX
ejpam-5602	358	18	being	be	AUX
ejpam-5602	358	19	joined	join	VERB
ejpam-5602	358	20	with	with	ADP
ejpam-5602	358	21	the	the	DET
ejpam-5602	358	22	end	end	NOUN
ejpam-5602	358	23	vertices	vertex	NOUN
ejpam-5602	358	24	of	of	ADP
ejpam-5602	358	25	the	the	DET
ejpam-5602	358	26	edge	edge	NOUN
ejpam-5602	358	27	uv	uv	PROPN
ejpam-5602	358	28	∈	∈	PROPN
ejpam-5602	358	29	e(g	e(g	PROPN
ejpam-5602	358	30	)	)	PUNCT
ejpam-5602	358	31	in	in	ADP
ejpam-5602	358	32	the	the	DET
ejpam-5602	358	33	edge	edge	NOUN
ejpam-5602	358	34	corona	corona	PROPN
ejpam-5602	358	35	g	g	PROPN
ejpam-5602	358	36	⋄	⋄	PROPN
ejpam-5602	358	37	h.	h.	PROPN
ejpam-5602	359	1	moreover	moreover	ADV
ejpam-5602	359	2	,	,	PUNCT
ejpam-5602	359	3	we	we	PRON
ejpam-5602	359	4	denote	denote	VERB
ejpam-5602	359	5	by	by	ADP
ejpam-5602	359	6	huv	huv	PROPN
ejpam-5602	360	1	+	+	CCONJ
ejpam-5602	360	2	uv	uv	ADP
ejpam-5602	360	3	the	the	DET
ejpam-5602	360	4	subgraph	subgraph	NOUN
ejpam-5602	360	5	of	of	ADP
ejpam-5602	360	6	g	g	PROPN
ejpam-5602	360	7	⋄	⋄	PROPN
ejpam-5602	360	8	h	h	NOUN
ejpam-5602	360	9	corresponding	correspond	VERB
ejpam-5602	360	10	to	to	ADP
ejpam-5602	360	11	the	the	DET
ejpam-5602	360	12	join	join	NOUN
ejpam-5602	360	13	huv	huv	PROPN
ejpam-5602	360	14	+	+	CCONJ
ejpam-5602	360	15	⟨u	⟨u	NOUN
ejpam-5602	360	16	,	,	PUNCT
ejpam-5602	360	17	v⟩	v⟩	NOUN
ejpam-5602	360	18	,	,	PUNCT
ejpam-5602	360	19	u	u	NOUN
ejpam-5602	360	20	,	,	PUNCT
ejpam-5602	360	21	v	v	NOUN
ejpam-5602	360	22	∈	∈	PROPN
ejpam-5602	360	23	v	v	NOUN
ejpam-5602	360	24	(	(	PUNCT
ejpam-5602	360	25	g	g	NOUN
ejpam-5602	360	26	)	)	PUNCT
ejpam-5602	360	27	.	.	PUNCT
ejpam-5602	361	1	for	for	ADP
ejpam-5602	361	2	f	f	PROPN
ejpam-5602	361	3	=	=	SYM
ejpam-5602	361	4	(	(	PUNCT
ejpam-5602	361	5	v0	v0	PROPN
ejpam-5602	361	6	,	,	PUNCT
ejpam-5602	361	7	v1	v1	NOUN
ejpam-5602	361	8	,	,	PUNCT
ejpam-5602	361	9	v2	v2	PROPN
ejpam-5602	361	10	,	,	PUNCT
ejpam-5602	361	11	v3	v3	PROPN
ejpam-5602	361	12	)	)	PUNCT
ejpam-5602	361	13	on	on	ADP
ejpam-5602	361	14	v	v	NUM
ejpam-5602	361	15	(	(	PUNCT
ejpam-5602	361	16	g	g	PROPN
ejpam-5602	361	17	⋄h	⋄h	PROPN
ejpam-5602	361	18	)	)	PUNCT
ejpam-5602	361	19	,	,	PUNCT
ejpam-5602	361	20	we	we	PRON
ejpam-5602	361	21	write	write	VERB
ejpam-5602	361	22	for	for	ADP
ejpam-5602	361	23	each	each	DET
ejpam-5602	361	24	i	i	PRON
ejpam-5602	361	25	,	,	PUNCT
ejpam-5602	361	26	j	j	PROPN
ejpam-5602	361	27	∈	∈	PROPN
ejpam-5602	361	28	{	{	PUNCT
ejpam-5602	361	29	0	0	NUM
ejpam-5602	361	30	,	,	PUNCT
ejpam-5602	361	31	1	1	NUM
ejpam-5602	361	32	,	,	PUNCT
ejpam-5602	361	33	2	2	NUM
ejpam-5602	361	34	,	,	PUNCT
ejpam-5602	361	35	3	3	NUM
ejpam-5602	361	36	}	}	PUNCT
ejpam-5602	361	37	,	,	PUNCT
ejpam-5602	361	38	eij	eij	PROPN
ejpam-5602	361	39	=	=	PUNCT
ejpam-5602	361	40	{	{	PUNCT
ejpam-5602	361	41	uv	uv	PROPN
ejpam-5602	361	42	∈	∈	PROPN
ejpam-5602	361	43	e(g	e(g	PROPN
ejpam-5602	361	44	)	)	PUNCT
ejpam-5602	361	45	:	:	PUNCT
ejpam-5602	361	46	either	either	CCONJ
ejpam-5602	361	47	u	u	PROPN
ejpam-5602	361	48	∈	∈	PROPN
ejpam-5602	361	49	vi	vi	PROPN
ejpam-5602	361	50	and	and	CCONJ
ejpam-5602	361	51	v	v	NOUN
ejpam-5602	361	52	∈	∈	PROPN
ejpam-5602	361	53	vj	vj	NOUN
ejpam-5602	361	54	or	or	CCONJ
ejpam-5602	361	55	u	u	PROPN
ejpam-5602	361	56	∈	∈	PROPN
ejpam-5602	361	57	vj	vj	NOUN
ejpam-5602	361	58	and	and	CCONJ
ejpam-5602	361	59	v	v	ADP
ejpam-5602	361	60	∈	∈	PROPN
ejpam-5602	361	61	vi	vi	NOUN
ejpam-5602	361	62	}	}	PUNCT
ejpam-5602	361	63	.	.	PUNCT
ejpam-5602	362	1	proposition	proposition	NOUN
ejpam-5602	362	2	10	10	NUM
ejpam-5602	362	3	.	.	PUNCT
ejpam-5602	363	1	let	let	VERB
ejpam-5602	363	2	g	g	PRON
ejpam-5602	363	3	be	be	AUX
ejpam-5602	363	4	nontrivial	nontrivial	ADJ
ejpam-5602	363	5	connected	connect	VERB
ejpam-5602	363	6	graph	graph	NOUN
ejpam-5602	363	7	and	and	CCONJ
ejpam-5602	363	8	h	h	NOUN
ejpam-5602	363	9	be	be	AUX
ejpam-5602	363	10	any	any	DET
ejpam-5602	363	11	graph	graph	NOUN
ejpam-5602	363	12	without	without	ADP
ejpam-5602	363	13	isolated	isolated	ADJ
ejpam-5602	363	14	vertices	vertex	NOUN
ejpam-5602	363	15	.	.	PUNCT
ejpam-5602	364	1	let	let	VERB
ejpam-5602	364	2	f	f	PROPN
ejpam-5602	364	3	=	=	SYM
ejpam-5602	364	4	(	(	PUNCT
ejpam-5602	364	5	v0	v0	PROPN
ejpam-5602	364	6	,	,	PUNCT
ejpam-5602	364	7	v1	v1	NOUN
ejpam-5602	364	8	,	,	PUNCT
ejpam-5602	364	9	v2	v2	PROPN
ejpam-5602	364	10	,	,	PUNCT
ejpam-5602	364	11	v3	v3	PROPN
ejpam-5602	364	12	)	)	PUNCT
ejpam-5602	364	13	be	be	VERB
ejpam-5602	364	14	a	a	DET
ejpam-5602	364	15	function	function	NOUN
ejpam-5602	364	16	on	on	ADP
ejpam-5602	364	17	v	v	ADP
ejpam-5602	364	18	(	(	PUNCT
ejpam-5602	364	19	g	g	NOUN
ejpam-5602	364	20	)	)	PUNCT
ejpam-5602	364	21	.	.	PUNCT
ejpam-5602	365	1	then	then	ADV
ejpam-5602	365	2	f	f	PROPN
ejpam-5602	365	3	∈	∈	PROPN
ejpam-5602	365	4	tdidf	tdidf	NOUN
ejpam-5602	365	5	(	(	PUNCT
ejpam-5602	365	6	g	g	PROPN
ejpam-5602	365	7	⋄h	⋄h	PROPN
ejpam-5602	365	8	)	)	PUNCT
ejpam-5602	366	1	if	if	SCONJ
ejpam-5602	366	2	and	and	CCONJ
ejpam-5602	366	3	only	only	ADV
ejpam-5602	366	4	if	if	SCONJ
ejpam-5602	366	5	each	each	PRON
ejpam-5602	366	6	of	of	ADP
ejpam-5602	366	7	the	the	DET
ejpam-5602	366	8	following	follow	VERB
ejpam-5602	366	9	holds	hold	VERB
ejpam-5602	366	10	:	:	PUNCT
ejpam-5602	366	11	(	(	PUNCT
ejpam-5602	366	12	i	i	NOUN
ejpam-5602	366	13	)	)	PUNCT
ejpam-5602	366	14	for	for	ADP
ejpam-5602	366	15	each	each	DET
ejpam-5602	366	16	uv	uv	PROPN
ejpam-5602	366	17	∈	∈	PROPN
ejpam-5602	366	18	e00	e00	PROPN
ejpam-5602	366	19	,	,	PUNCT
ejpam-5602	366	20	f	f	X
ejpam-5602	366	21	|huv	|huv	PROPN
ejpam-5602	366	22	∈	∈	PROPN
ejpam-5602	366	23	tdidf	tdidf	NOUN
ejpam-5602	366	24	(	(	PUNCT
ejpam-5602	366	25	huv	huv	PROPN
ejpam-5602	366	26	)	)	PUNCT
ejpam-5602	366	27	;	;	PUNCT
ejpam-5602	366	28	(	(	PUNCT
ejpam-5602	366	29	ii	ii	NOUN
ejpam-5602	366	30	)	)	PUNCT
ejpam-5602	366	31	for	for	ADP
ejpam-5602	366	32	each	each	DET
ejpam-5602	366	33	uv	uv	NOUN
ejpam-5602	366	34	∈	∈	PROPN
ejpam-5602	366	35	e01	e01	NOUN
ejpam-5602	366	36	,	,	PUNCT
ejpam-5602	366	37	f(nhuv	f(nhuv	NOUN
ejpam-5602	367	1	[	[	X
ejpam-5602	367	2	w	w	NOUN
ejpam-5602	367	3	]	]	X
ejpam-5602	367	4	)	)	PUNCT
ejpam-5602	367	5	≥	≥	NOUN
ejpam-5602	367	6	2	2	NUM
ejpam-5602	367	7	for	for	ADP
ejpam-5602	367	8	all	all	DET
ejpam-5602	367	9	w	w	PROPN
ejpam-5602	367	10	∈	∈	NOUN
ejpam-5602	367	11	(	(	PUNCT
ejpam-5602	367	12	v0	v0	NOUN
ejpam-5602	367	13	∪	∪	X
ejpam-5602	367	14	v1	v1	NOUN
ejpam-5602	367	15	)	)	PUNCT
ejpam-5602	367	16	∩	∩	ADJ
ejpam-5602	367	17	v	v	X
ejpam-5602	367	18	(	(	PUNCT
ejpam-5602	367	19	huv	huv	PROPN
ejpam-5602	367	20	)	)	PUNCT
ejpam-5602	367	21	;	;	PUNCT
ejpam-5602	367	22	(	(	PUNCT
ejpam-5602	367	23	iii	iii	X
ejpam-5602	367	24	)	)	PUNCT
ejpam-5602	367	25	for	for	ADP
ejpam-5602	367	26	each	each	DET
ejpam-5602	367	27	uv	uv	NOUN
ejpam-5602	367	28	∈	∈	NOUN
ejpam-5602	367	29	e11	e11	X
ejpam-5602	367	30	∪	∪	X
ejpam-5602	367	31	e02	e02	NOUN
ejpam-5602	367	32	,	,	PUNCT
ejpam-5602	367	33	f(nhuv	f(nhuv	NOUN
ejpam-5602	368	1	[	[	X
ejpam-5602	368	2	w	w	NOUN
ejpam-5602	368	3	]	]	X
ejpam-5602	368	4	)	)	PUNCT
ejpam-5602	368	5	≥	≥	NOUN
ejpam-5602	368	6	1	1	NUM
ejpam-5602	368	7	for	for	ADP
ejpam-5602	368	8	all	all	DET
ejpam-5602	368	9	w	w	PROPN
ejpam-5602	368	10	∈	∈	PROPN
ejpam-5602	368	11	v0	v0	NOUN
ejpam-5602	368	12	∩	∩	X
ejpam-5602	368	13	v	v	X
ejpam-5602	368	14	(	(	PUNCT
ejpam-5602	368	15	huv	huv	PROPN
ejpam-5602	368	16	)	)	PUNCT
ejpam-5602	368	17	;	;	PUNCT
ejpam-5602	368	18	(	(	PUNCT
ejpam-5602	368	19	iv	iv	X
ejpam-5602	368	20	)	)	PUNCT
ejpam-5602	368	21	for	for	ADP
ejpam-5602	368	22	each	each	DET
ejpam-5602	368	23	uv	uv	NOUN
ejpam-5602	368	24	∈	∈	PROPN
ejpam-5602	368	25	e03	e03	NOUN
ejpam-5602	368	26	with	with	ADP
ejpam-5602	368	27	v	v	PROPN
ejpam-5602	368	28	∈	∈	PROPN
ejpam-5602	368	29	v3	v3	PROPN
ejpam-5602	368	30	and	and	CCONJ
ejpam-5602	368	31	ng(v	ng(v	NUM
ejpam-5602	368	32	)	)	PUNCT
ejpam-5602	368	33	⊆	⊆	NUM
ejpam-5602	368	34	v0	v0	NOUN
ejpam-5602	368	35	,	,	PUNCT
ejpam-5602	368	36	we	we	PRON
ejpam-5602	368	37	have	have	VERB
ejpam-5602	368	38	v	v	NUM
ejpam-5602	368	39	(	(	PUNCT
ejpam-5602	368	40	huv	huv	PROPN
ejpam-5602	368	41	)	)	PUNCT
ejpam-5602	368	42	\	\	PROPN
ejpam-5602	368	43	v0	v0	PROPN
ejpam-5602	368	44	̸=	̸=	PROPN
ejpam-5602	368	45	∅.	∅.	PRON
ejpam-5602	368	46	proof	proof	NOUN
ejpam-5602	368	47	:	:	PUNCT
ejpam-5602	368	48	since	since	SCONJ
ejpam-5602	368	49	h	h	NOUN
ejpam-5602	368	50	has	have	VERB
ejpam-5602	368	51	no	no	DET
ejpam-5602	368	52	isolated	isolated	ADJ
ejpam-5602	368	53	vertices	vertex	NOUN
ejpam-5602	368	54	,	,	PUNCT
ejpam-5602	368	55	huv	huv	PROPN
ejpam-5602	368	56	admits	admit	VERB
ejpam-5602	368	57	a	a	DET
ejpam-5602	368	58	tdidf	tdidf	NOUN
ejpam-5602	368	59	for	for	ADP
ejpam-5602	368	60	each	each	DET
ejpam-5602	368	61	uv	uv	PROPN
ejpam-5602	368	62	∈	∈	PROPN
ejpam-5602	368	63	e(g	e(g	PROPN
ejpam-5602	368	64	)	)	PUNCT
ejpam-5602	368	65	.	.	PUNCT
ejpam-5602	369	1	if	if	SCONJ
ejpam-5602	369	2	f	f	PROPN
ejpam-5602	369	3	∈	∈	PROPN
ejpam-5602	369	4	tdidf	tdidf	NOUN
ejpam-5602	369	5	(	(	PUNCT
ejpam-5602	369	6	g	g	PROPN
ejpam-5602	369	7	⋄	⋄	PROPN
ejpam-5602	369	8	h	h	NOUN
ejpam-5602	369	9	)	)	PUNCT
ejpam-5602	369	10	,	,	PUNCT
ejpam-5602	369	11	then	then	ADV
ejpam-5602	369	12	properties	property	NOUN
ejpam-5602	369	13	(	(	PUNCT
ejpam-5602	369	14	i)-(iii	i)-(iii	NOUN
ejpam-5602	369	15	)	)	PUNCT
ejpam-5602	369	16	follow	follow	VERB
ejpam-5602	369	17	immediately	immediately	ADV
ejpam-5602	369	18	from	from	ADP
ejpam-5602	369	19	the	the	DET
ejpam-5602	369	20	fact	fact	NOUN
ejpam-5602	369	21	that	that	SCONJ
ejpam-5602	369	22	for	for	ADP
ejpam-5602	369	23	each	each	DET
ejpam-5602	369	24	uv	uv	PROPN
ejpam-5602	369	25	∈	∈	PROPN
ejpam-5602	369	26	e(g	e(g	PROPN
ejpam-5602	369	27	)	)	PUNCT
ejpam-5602	369	28	,	,	PUNCT
ejpam-5602	369	29	f(ng⋄h	f(ng⋄h	VERB
ejpam-5602	370	1	[	[	X
ejpam-5602	370	2	w	w	X
ejpam-5602	370	3	]	]	X
ejpam-5602	370	4	)	)	PUNCT
ejpam-5602	370	5	=	=	SYM
ejpam-5602	370	6	f(u	f(u	PROPN
ejpam-5602	370	7	)	)	PUNCT
ejpam-5602	370	8	+	+	NUM
ejpam-5602	370	9	f(v	f(v	NOUN
ejpam-5602	370	10	)	)	PUNCT
ejpam-5602	371	1	+	+	CCONJ
ejpam-5602	371	2	f(nhuv	f(nhuv	ADJ
ejpam-5602	372	1	[	[	X
ejpam-5602	372	2	w	w	NOUN
ejpam-5602	372	3	]	]	X
ejpam-5602	372	4	)	)	PUNCT
ejpam-5602	372	5	for	for	ADP
ejpam-5602	372	6	all	all	DET
ejpam-5602	372	7	w	w	PROPN
ejpam-5602	372	8	∈	∈	PROPN
ejpam-5602	372	9	v	v	NOUN
ejpam-5602	372	10	(	(	PUNCT
ejpam-5602	372	11	huv	huv	PROPN
ejpam-5602	372	12	)	)	PUNCT
ejpam-5602	372	13	.	.	PUNCT
ejpam-5602	373	1	while	while	SCONJ
ejpam-5602	373	2	property	property	NOUN
ejpam-5602	373	3	(	(	PUNCT
ejpam-5602	373	4	iv	iv	X
ejpam-5602	373	5	)	)	PUNCT
ejpam-5602	373	6	is	be	AUX
ejpam-5602	373	7	clear	clear	ADJ
ejpam-5602	373	8	from	from	ADP
ejpam-5602	373	9	the	the	DET
ejpam-5602	373	10	definition	definition	NOUN
ejpam-5602	373	11	of	of	ADP
ejpam-5602	373	12	f	f	PROPN
ejpam-5602	373	13	.	.	PUNCT
ejpam-5602	374	1	conversely	conversely	ADV
ejpam-5602	374	2	,	,	PUNCT
ejpam-5602	374	3	suppose	suppose	VERB
ejpam-5602	374	4	that	that	SCONJ
ejpam-5602	374	5	conditions	condition	NOUN
ejpam-5602	374	6	(	(	PUNCT
ejpam-5602	374	7	i)-(iv	i)-(iv	X
ejpam-5602	374	8	)	)	PUNCT
ejpam-5602	374	9	hold	hold	VERB
ejpam-5602	374	10	for	for	ADP
ejpam-5602	374	11	f	f	PROPN
ejpam-5602	374	12	.	.	PUNCT
ejpam-5602	375	1	let	let	VERB
ejpam-5602	375	2	w	w	PROPN
ejpam-5602	375	3	∈	∈	PROPN
ejpam-5602	375	4	v0	v0	NOUN
ejpam-5602	375	5	and	and	CCONJ
ejpam-5602	375	6	uv	uv	NOUN
ejpam-5602	375	7	∈	∈	PROPN
ejpam-5602	375	8	e(g	e(g	PROPN
ejpam-5602	375	9	)	)	PUNCT
ejpam-5602	375	10	for	for	ADP
ejpam-5602	375	11	which	which	PRON
ejpam-5602	375	12	w	w	PROPN
ejpam-5602	375	13	∈	∈	PROPN
ejpam-5602	375	14	v	v	X
ejpam-5602	375	15	(	(	PUNCT
ejpam-5602	375	16	huv	huv	PROPN
ejpam-5602	375	17	+	+	NUM
ejpam-5602	375	18	uv	uv	NOUN
ejpam-5602	375	19	)	)	PUNCT
ejpam-5602	375	20	.	.	PUNCT
ejpam-5602	376	1	clearly	clearly	ADV
ejpam-5602	376	2	,	,	PUNCT
ejpam-5602	376	3	if	if	SCONJ
ejpam-5602	376	4	uv	uv	NOUN
ejpam-5602	376	5	∈	∈	PROPN
ejpam-5602	376	6	[	[	X
ejpam-5602	376	7	e03	e03	NOUN
ejpam-5602	376	8	∪	∪	ADP
ejpam-5602	376	9	e12	e12	NOUN
ejpam-5602	376	10	∪	∪	ADJ
ejpam-5602	376	11	e13	e13	PROPN
ejpam-5602	376	12	∪	∪	ADP
ejpam-5602	376	13	e22	e22	PROPN
ejpam-5602	376	14	∪	∪	X
ejpam-5602	376	15	e23	e23	PROPN
ejpam-5602	376	16	∪	∪	X
ejpam-5602	376	17	e33	e33	PROPN
ejpam-5602	376	18	]	]	PUNCT
ejpam-5602	376	19	,	,	PUNCT
ejpam-5602	376	20	then	then	ADV
ejpam-5602	376	21	f(ng⋄h	f(ng⋄h	PROPN
ejpam-5602	377	1	[	[	X
ejpam-5602	377	2	w	w	X
ejpam-5602	377	3	]	]	X
ejpam-5602	377	4	)	)	PUNCT
ejpam-5602	377	5	≥	≥	NOUN
ejpam-5602	378	1	3	3	X
ejpam-5602	378	2	.	.	PUNCT
ejpam-5602	379	1	we	we	PRON
ejpam-5602	379	2	proceed	proceed	VERB
ejpam-5602	379	3	with	with	ADP
ejpam-5602	379	4	the	the	DET
ejpam-5602	379	5	following	follow	VERB
ejpam-5602	379	6	cases	case	NOUN
ejpam-5602	379	7	:	:	PUNCT
ejpam-5602	379	8	case	case	NOUN
ejpam-5602	379	9	1	1	NUM
ejpam-5602	379	10	:	:	PUNCT
ejpam-5602	379	11	suppose	suppose	VERB
ejpam-5602	379	12	that	that	SCONJ
ejpam-5602	379	13	uv	uv	PROPN
ejpam-5602	379	14	∈	∈	PROPN
ejpam-5602	379	15	e00	e00	PROPN
ejpam-5602	379	16	.	.	PUNCT
ejpam-5602	380	1	then	then	ADV
ejpam-5602	380	2	f	f	X
ejpam-5602	380	3	|huv	|huv	PROPN
ejpam-5602	380	4	∈	∈	PROPN
ejpam-5602	380	5	didf	didf	PROPN
ejpam-5602	380	6	(	(	PUNCT
ejpam-5602	380	7	huv	huv	PROPN
ejpam-5602	380	8	)	)	PUNCT
ejpam-5602	380	9	by	by	ADP
ejpam-5602	380	10	(	(	PUNCT
ejpam-5602	380	11	i	i	NOUN
ejpam-5602	380	12	)	)	PUNCT
ejpam-5602	380	13	.	.	PUNCT
ejpam-5602	381	1	if	if	SCONJ
ejpam-5602	381	2	w	w	NOUN
ejpam-5602	381	3	=	=	VERB
ejpam-5602	381	4	u	u	NOUN
ejpam-5602	381	5	or	or	CCONJ
ejpam-5602	381	6	w	w	PROPN
ejpam-5602	381	7	=	=	PUNCT
ejpam-5602	381	8	v	v	NOUN
ejpam-5602	381	9	,	,	PUNCT
ejpam-5602	381	10	then	then	ADV
ejpam-5602	381	11	f(ng⋄h	f(ng⋄h	PROPN
ejpam-5602	382	1	[	[	X
ejpam-5602	382	2	w	w	X
ejpam-5602	382	3	]	]	X
ejpam-5602	382	4	)	)	PUNCT
ejpam-5602	382	5	≥	≥	PROPN
ejpam-5602	382	6	f	f	PROPN
ejpam-5602	382	7	|huv(v	|huv(v	PROPN
ejpam-5602	382	8	(	(	PUNCT
ejpam-5602	382	9	huv	huv	PROPN
ejpam-5602	382	10	)	)	PUNCT
ejpam-5602	382	11	)	)	PUNCT
ejpam-5602	382	12	≥	≥	NOUN
ejpam-5602	383	1	3	3	NUM
ejpam-5602	383	2	.	.	PUNCT
ejpam-5602	384	1	if	if	SCONJ
ejpam-5602	384	2	u	u	PROPN
ejpam-5602	384	3	̸=	̸=	PROPN
ejpam-5602	384	4	w	w	ADP
ejpam-5602	384	5	̸=	̸=	PROPN
ejpam-5602	384	6	v	v	NOUN
ejpam-5602	384	7	,	,	PUNCT
ejpam-5602	384	8	then	then	ADV
ejpam-5602	384	9	f(ng⋄h	f(ng⋄h	PROPN
ejpam-5602	385	1	[	[	X
ejpam-5602	385	2	w	w	X
ejpam-5602	385	3	]	]	X
ejpam-5602	385	4	)	)	PUNCT
ejpam-5602	386	1	=	=	SYM
ejpam-5602	386	2	f	f	PROPN
ejpam-5602	386	3	|huv(nhuv	|huv(nhuv	X
ejpam-5602	387	1	[	[	X
ejpam-5602	387	2	w	w	NOUN
ejpam-5602	387	3	]	]	X
ejpam-5602	387	4	)	)	PUNCT
ejpam-5602	387	5	≥	≥	NOUN
ejpam-5602	387	6	3	3	X
ejpam-5602	387	7	.	.	PUNCT
ejpam-5602	387	8	s.j.l	s.j.l	PROPN
ejpam-5602	387	9	.	.	PUNCT
ejpam-5602	387	10	sumbalan	sumbalan	PROPN
ejpam-5602	387	11	,	,	PUNCT
ejpam-5602	387	12	s.m	s.m	PROPN
ejpam-5602	387	13	.	.	PROPN
ejpam-5602	387	14	menchavez	menchavez	PROPN
ejpam-5602	387	15	,	,	PUNCT
ejpam-5602	387	16	f.p	f.p	PROPN
ejpam-5602	387	17	.	.	PROPN
ejpam-5602	387	18	jamil	jamil	PROPN
ejpam-5602	387	19	/	/	SYM
ejpam-5602	387	20	eur	eur	PROPN
ejpam-5602	387	21	.	.	PUNCT
ejpam-5602	388	1	j.	j.	PROPN
ejpam-5602	388	2	pure	pure	PROPN
ejpam-5602	388	3	appl	appl	PROPN
ejpam-5602	388	4	.	.	PROPN
ejpam-5602	388	5	math	math	PROPN
ejpam-5602	388	6	,	,	PUNCT
ejpam-5602	388	7	18	18	NUM
ejpam-5602	388	8	(	(	PUNCT
ejpam-5602	388	9	1	1	NUM
ejpam-5602	388	10	)	)	PUNCT
ejpam-5602	388	11	(	(	PUNCT
ejpam-5602	388	12	2025	2025	NUM
ejpam-5602	388	13	)	)	PUNCT
ejpam-5602	388	14	,	,	PUNCT
ejpam-5602	388	15	5602	5602	NUM
ejpam-5602	388	16	12	12	NUM
ejpam-5602	388	17	of	of	ADP
ejpam-5602	388	18	18	18	NUM
ejpam-5602	388	19	case	case	NOUN
ejpam-5602	388	20	2	2	NUM
ejpam-5602	388	21	:	:	PUNCT
ejpam-5602	388	22	suppose	suppose	VERB
ejpam-5602	388	23	that	that	SCONJ
ejpam-5602	388	24	uv	uv	PROPN
ejpam-5602	388	25	∈	∈	PROPN
ejpam-5602	388	26	e01	e01	PROPN
ejpam-5602	388	27	∪	∪	X
ejpam-5602	388	28	e02	e02	NOUN
ejpam-5602	388	29	,	,	PUNCT
ejpam-5602	388	30	and	and	CCONJ
ejpam-5602	388	31	assume	assume	VERB
ejpam-5602	388	32	u	u	PROPN
ejpam-5602	388	33	∈	∈	PROPN
ejpam-5602	388	34	v0	v0	NOUN
ejpam-5602	388	35	.	.	PUNCT
ejpam-5602	389	1	if	if	SCONJ
ejpam-5602	389	2	v0	v0	NOUN
ejpam-5602	389	3	∩	∩	NOUN
ejpam-5602	389	4	v	v	X
ejpam-5602	389	5	(	(	PUNCT
ejpam-5602	389	6	huv	huv	PROPN
ejpam-5602	389	7	)	)	PUNCT
ejpam-5602	389	8	=	=	NOUN
ejpam-5602	389	9	∅	∅	NOUN
ejpam-5602	389	10	,	,	PUNCT
ejpam-5602	389	11	then	then	ADV
ejpam-5602	389	12	w	w	PROPN
ejpam-5602	389	13	=	=	SYM
ejpam-5602	389	14	u	u	PROPN
ejpam-5602	389	15	and	and	CCONJ
ejpam-5602	389	16	since	since	SCONJ
ejpam-5602	389	17	huv	huv	PROPN
ejpam-5602	389	18	has	have	VERB
ejpam-5602	389	19	no	no	DET
ejpam-5602	389	20	isolated	isolated	ADJ
ejpam-5602	389	21	vertices	vertex	NOUN
ejpam-5602	389	22	,	,	PUNCT
ejpam-5602	389	23	f(v	f(v	PROPN
ejpam-5602	389	24	(	(	PUNCT
ejpam-5602	389	25	huv	huv	PROPN
ejpam-5602	389	26	)	)	PUNCT
ejpam-5602	389	27	≥	≥	NOUN
ejpam-5602	389	28	2	2	NUM
ejpam-5602	389	29	.	.	PUNCT
ejpam-5602	389	30	thus	thus	ADV
ejpam-5602	389	31	,	,	PUNCT
ejpam-5602	389	32	f(ng⋄h	f(ng⋄h	NOUN
ejpam-5602	390	1	[	[	X
ejpam-5602	390	2	w	w	NOUN
ejpam-5602	390	3	]	]	X
ejpam-5602	390	4	)	)	PUNCT
ejpam-5602	390	5	≥	≥	NOUN
ejpam-5602	390	6	f(v	f(v	NOUN
ejpam-5602	390	7	)	)	PUNCT
ejpam-5602	391	1	+	+	NUM
ejpam-5602	391	2	f(v	f(v	PROPN
ejpam-5602	391	3	(	(	PUNCT
ejpam-5602	391	4	huv	huv	PROPN
ejpam-5602	391	5	)	)	PUNCT
ejpam-5602	391	6	)	)	PUNCT
ejpam-5602	391	7	≥	≥	NOUN
ejpam-5602	391	8	3	3	X
ejpam-5602	391	9	.	.	PUNCT
ejpam-5602	391	10	suppose	suppose	VERB
ejpam-5602	391	11	that	that	SCONJ
ejpam-5602	391	12	v0	v0	NOUN
ejpam-5602	391	13	∩	∩	NOUN
ejpam-5602	391	14	v	v	X
ejpam-5602	391	15	(	(	PUNCT
ejpam-5602	391	16	huv	huv	PROPN
ejpam-5602	391	17	)	)	PUNCT
ejpam-5602	391	18	̸=	̸=	PROPN
ejpam-5602	391	19	∅	∅	NOUN
ejpam-5602	391	20	,	,	PUNCT
ejpam-5602	391	21	say	say	VERB
ejpam-5602	391	22	z	z	NOUN
ejpam-5602	391	23	∈	∈	PROPN
ejpam-5602	391	24	v0	v0	NOUN
ejpam-5602	391	25	∩	∩	X
ejpam-5602	391	26	v	v	X
ejpam-5602	391	27	(	(	PUNCT
ejpam-5602	391	28	huv	huv	PROPN
ejpam-5602	391	29	)	)	PUNCT
ejpam-5602	391	30	.	.	PUNCT
ejpam-5602	392	1	if	if	SCONJ
ejpam-5602	392	2	w	w	PROPN
ejpam-5602	392	3	=	=	SYM
ejpam-5602	392	4	u	u	NOUN
ejpam-5602	392	5	,	,	PUNCT
ejpam-5602	392	6	then	then	ADV
ejpam-5602	392	7	by	by	ADP
ejpam-5602	392	8	(	(	PUNCT
ejpam-5602	392	9	ii	ii	NOUN
ejpam-5602	392	10	)	)	PUNCT
ejpam-5602	392	11	and	and	CCONJ
ejpam-5602	392	12	(	(	PUNCT
ejpam-5602	392	13	iii	iii	NOUN
ejpam-5602	392	14	)	)	PUNCT
ejpam-5602	392	15	,	,	PUNCT
ejpam-5602	392	16	f(ng⋄h	f(ng⋄h	VERB
ejpam-5602	393	1	[	[	X
ejpam-5602	393	2	w	w	NOUN
ejpam-5602	393	3	]	]	X
ejpam-5602	393	4	)	)	PUNCT
ejpam-5602	393	5	≥	≥	NOUN
ejpam-5602	393	6	f(v	f(v	NOUN
ejpam-5602	393	7	)	)	PUNCT
ejpam-5602	394	1	+	+	NUM
ejpam-5602	394	2	f(nhuv	f(nhuv	ADJ
ejpam-5602	395	1	[	[	X
ejpam-5602	395	2	z	z	NOUN
ejpam-5602	395	3	]	]	X
ejpam-5602	395	4	)	)	PUNCT
ejpam-5602	395	5	≥	≥	NOUN
ejpam-5602	396	1	3	3	NUM
ejpam-5602	396	2	.	.	PUNCT
ejpam-5602	397	1	if	if	SCONJ
ejpam-5602	397	2	w	w	PROPN
ejpam-5602	397	3	∈	∈	PROPN
ejpam-5602	397	4	v	v	X
ejpam-5602	397	5	(	(	PUNCT
ejpam-5602	397	6	huv	huv	PROPN
ejpam-5602	397	7	)	)	PUNCT
ejpam-5602	397	8	,	,	PUNCT
ejpam-5602	397	9	then	then	ADV
ejpam-5602	397	10	f(ng⋄h	f(ng⋄h	PROPN
ejpam-5602	398	1	[	[	X
ejpam-5602	398	2	w	w	NOUN
ejpam-5602	398	3	]	]	X
ejpam-5602	398	4	)	)	PUNCT
ejpam-5602	398	5	≥	≥	NOUN
ejpam-5602	398	6	f(v	f(v	NOUN
ejpam-5602	398	7	)	)	PUNCT
ejpam-5602	399	1	+	+	CCONJ
ejpam-5602	399	2	f(nhuv	f(nhuv	ADJ
ejpam-5602	400	1	[	[	X
ejpam-5602	400	2	w	w	NOUN
ejpam-5602	400	3	]	]	X
ejpam-5602	400	4	)	)	PUNCT
ejpam-5602	400	5	≥	≥	NOUN
ejpam-5602	400	6	3	3	NUM
ejpam-5602	400	7	.	.	PUNCT
ejpam-5602	400	8	case	case	NOUN
ejpam-5602	400	9	3	3	X
ejpam-5602	400	10	:	:	PUNCT
ejpam-5602	400	11	suppose	suppose	VERB
ejpam-5602	400	12	that	that	SCONJ
ejpam-5602	400	13	uv	uv	PROPN
ejpam-5602	400	14	∈	∈	PROPN
ejpam-5602	400	15	e11	e11	NOUN
ejpam-5602	400	16	.	.	PUNCT
ejpam-5602	401	1	then	then	ADV
ejpam-5602	401	2	w	w	PROPN
ejpam-5602	401	3	∈	∈	PROPN
ejpam-5602	401	4	v	v	ADP
ejpam-5602	401	5	(	(	PUNCT
ejpam-5602	401	6	huv	huv	PROPN
ejpam-5602	401	7	)	)	PUNCT
ejpam-5602	401	8	and	and	CCONJ
ejpam-5602	401	9	by	by	ADP
ejpam-5602	401	10	(	(	PUNCT
ejpam-5602	401	11	iii	iii	NOUN
ejpam-5602	401	12	)	)	PUNCT
ejpam-5602	401	13	,	,	PUNCT
ejpam-5602	401	14	f(ng⋄h	f(ng⋄h	VERB
ejpam-5602	402	1	[	[	X
ejpam-5602	402	2	w	w	X
ejpam-5602	402	3	]	]	X
ejpam-5602	402	4	)	)	PUNCT
ejpam-5602	402	5	≥	≥	NOUN
ejpam-5602	402	6	f(u	f(u	PROPN
ejpam-5602	402	7	)	)	PUNCT
ejpam-5602	402	8	+	+	NUM
ejpam-5602	402	9	f(v	f(v	NOUN
ejpam-5602	402	10	)	)	PUNCT
ejpam-5602	403	1	+	+	NUM
ejpam-5602	403	2	f(nhuv)[w	f(nhuv)[w	NOUN
ejpam-5602	403	3	]	]	PUNCT
ejpam-5602	403	4	)	)	PUNCT
ejpam-5602	403	5	≥	≥	NOUN
ejpam-5602	403	6	3	3	NUM
ejpam-5602	403	7	.	.	PUNCT
ejpam-5602	403	8	following	follow	VERB
ejpam-5602	403	9	similar	similar	ADJ
ejpam-5602	403	10	arguments	argument	NOUN
ejpam-5602	403	11	,	,	PUNCT
ejpam-5602	403	12	f(ng⋄h	f(ng⋄h	NOUN
ejpam-5602	404	1	[	[	X
ejpam-5602	404	2	w	w	X
ejpam-5602	404	3	]	]	X
ejpam-5602	404	4	)	)	PUNCT
ejpam-5602	404	5	≥	≥	NOUN
ejpam-5602	404	6	3	3	NUM
ejpam-5602	404	7	for	for	ADP
ejpam-5602	404	8	all	all	DET
ejpam-5602	404	9	w	w	PROPN
ejpam-5602	404	10	∈	∈	PROPN
ejpam-5602	404	11	v1	v1	NOUN
ejpam-5602	404	12	.	.	PUNCT
ejpam-5602	405	1	finally	finally	ADV
ejpam-5602	405	2	,	,	PUNCT
ejpam-5602	405	3	let	let	VERB
ejpam-5602	405	4	v	v	NUM
ejpam-5602	405	5	∈	∈	NOUN
ejpam-5602	405	6	v1	v1	NOUN
ejpam-5602	405	7	∪	∪	NOUN
ejpam-5602	405	8	v2	v2	PROPN
ejpam-5602	405	9	∪	∪	X
ejpam-5602	405	10	v3	v3	PROPN
ejpam-5602	405	11	.	.	PUNCT
ejpam-5602	406	1	first	first	ADV
ejpam-5602	406	2	,	,	PUNCT
ejpam-5602	406	3	suppose	suppose	VERB
ejpam-5602	406	4	that	that	SCONJ
ejpam-5602	406	5	v	v	ADP
ejpam-5602	406	6	∈	∈	PROPN
ejpam-5602	406	7	v	v	NOUN
ejpam-5602	406	8	(	(	PUNCT
ejpam-5602	406	9	g	g	NOUN
ejpam-5602	406	10	)	)	PUNCT
ejpam-5602	406	11	.	.	PUNCT
ejpam-5602	407	1	if	if	SCONJ
ejpam-5602	407	2	ng(v	ng(v	NOUN
ejpam-5602	407	3	)	)	PUNCT
ejpam-5602	407	4	⊈	⊈	PROPN
ejpam-5602	407	5	v0	v0	NOUN
ejpam-5602	407	6	,	,	PUNCT
ejpam-5602	407	7	then	then	ADV
ejpam-5602	407	8	there	there	PRON
ejpam-5602	407	9	exists	exist	VERB
ejpam-5602	407	10	x	x	X
ejpam-5602	407	11	∈	∈	NOUN
ejpam-5602	407	12	v1	v1	NOUN
ejpam-5602	407	13	∪	∪	NOUN
ejpam-5602	407	14	v2	v2	PROPN
ejpam-5602	407	15	∪	∪	X
ejpam-5602	407	16	v3	v3	PROPN
ejpam-5602	407	17	such	such	ADJ
ejpam-5602	407	18	that	that	SCONJ
ejpam-5602	407	19	xv	xv	PROPN
ejpam-5602	407	20	∈	∈	PROPN
ejpam-5602	407	21	e(g	e(g	PROPN
ejpam-5602	407	22	⋄	⋄	PROPN
ejpam-5602	407	23	h	h	NOUN
ejpam-5602	407	24	)	)	PUNCT
ejpam-5602	407	25	.	.	PUNCT
ejpam-5602	408	1	suppose	suppose	VERB
ejpam-5602	408	2	that	that	SCONJ
ejpam-5602	408	3	ng(v	ng(v	NOUN
ejpam-5602	408	4	)	)	PUNCT
ejpam-5602	408	5	⊆	⊆	NUM
ejpam-5602	408	6	v0	v0	NOUN
ejpam-5602	408	7	,	,	PUNCT
ejpam-5602	408	8	and	and	CCONJ
ejpam-5602	408	9	let	let	VERB
ejpam-5602	408	10	u	u	PRON
ejpam-5602	408	11	∈	∈	PROPN
ejpam-5602	408	12	ng(v	ng(v	PUNCT
ejpam-5602	408	13	)	)	PUNCT
ejpam-5602	408	14	.	.	PUNCT
ejpam-5602	409	1	then	then	ADV
ejpam-5602	409	2	uv	uv	PROPN
ejpam-5602	409	3	∈	∈	PROPN
ejpam-5602	409	4	e01	e01	PROPN
ejpam-5602	409	5	∪	∪	X
ejpam-5602	409	6	e02	e02	X
ejpam-5602	409	7	∪	∪	X
ejpam-5602	409	8	e03	e03	NOUN
ejpam-5602	409	9	.	.	PUNCT
ejpam-5602	410	1	in	in	ADP
ejpam-5602	410	2	view	view	NOUN
ejpam-5602	410	3	of	of	ADP
ejpam-5602	410	4	conditions	condition	NOUN
ejpam-5602	410	5	(	(	PUNCT
ejpam-5602	410	6	ii)-(iv	ii)-(iv	NOUN
ejpam-5602	410	7	)	)	PUNCT
ejpam-5602	410	8	,	,	PUNCT
ejpam-5602	410	9	f(v	f(v	PROPN
ejpam-5602	410	10	(	(	PUNCT
ejpam-5602	410	11	huv	huv	PROPN
ejpam-5602	410	12	)	)	PUNCT
ejpam-5602	410	13	≥	≥	NOUN
ejpam-5602	410	14	1	1	NUM
ejpam-5602	410	15	.	.	PUNCT
ejpam-5602	411	1	thus	thus	ADV
ejpam-5602	411	2	,	,	PUNCT
ejpam-5602	411	3	there	there	PRON
ejpam-5602	411	4	exists	exist	VERB
ejpam-5602	411	5	u	u	PROPN
ejpam-5602	411	6	∈	∈	PROPN
ejpam-5602	411	7	[	[	X
ejpam-5602	411	8	(	(	PUNCT
ejpam-5602	411	9	v1	v1	VERB
ejpam-5602	411	10	∪	∪	NOUN
ejpam-5602	411	11	v2	v2	PROPN
ejpam-5602	411	12	∪	∪	X
ejpam-5602	411	13	v3	v3	PROPN
ejpam-5602	411	14	)	)	PUNCT
ejpam-5602	411	15	∩	∩	PROPN
ejpam-5602	411	16	v	v	X
ejpam-5602	411	17	(	(	PUNCT
ejpam-5602	411	18	huv	huv	PROPN
ejpam-5602	411	19	)	)	PUNCT
ejpam-5602	411	20	]	]	PUNCT
ejpam-5602	411	21	for	for	ADP
ejpam-5602	411	22	which	which	PRON
ejpam-5602	411	23	uv	uv	NOUN
ejpam-5602	411	24	∈	∈	PROPN
ejpam-5602	411	25	e(g	e(g	PROPN
ejpam-5602	411	26	⋄h	⋄h	PROPN
ejpam-5602	411	27	)	)	PUNCT
ejpam-5602	411	28	.	.	PUNCT
ejpam-5602	412	1	next	next	ADV
ejpam-5602	412	2	,	,	PUNCT
ejpam-5602	412	3	suppose	suppose	VERB
ejpam-5602	412	4	that	that	SCONJ
ejpam-5602	412	5	v	v	ADP
ejpam-5602	412	6	∈	∈	PROPN
ejpam-5602	412	7	v	v	NOUN
ejpam-5602	412	8	(	(	PUNCT
ejpam-5602	412	9	hxy	hxy	NOUN
ejpam-5602	412	10	)	)	PUNCT
ejpam-5602	412	11	for	for	ADP
ejpam-5602	412	12	some	some	DET
ejpam-5602	412	13	xy	xy	PROPN
ejpam-5602	412	14	∈	∈	PROPN
ejpam-5602	412	15	e(g	e(g	PROPN
ejpam-5602	412	16	)	)	PUNCT
ejpam-5602	412	17	.	.	PUNCT
ejpam-5602	413	1	if	if	SCONJ
ejpam-5602	413	2	x	x	PROPN
ejpam-5602	413	3	/∈	/∈	PROPN
ejpam-5602	413	4	v0	v0	PROPN
ejpam-5602	413	5	,	,	PUNCT
ejpam-5602	413	6	then	then	ADV
ejpam-5602	413	7	x	x	PART
ejpam-5602	413	8	∈	∈	NOUN
ejpam-5602	413	9	v1	v1	NOUN
ejpam-5602	413	10	∪	∪	NOUN
ejpam-5602	413	11	v2	v2	PROPN
ejpam-5602	413	12	∪	∪	X
ejpam-5602	413	13	v3	v3	PROPN
ejpam-5602	413	14	with	with	ADP
ejpam-5602	413	15	xv	xv	PROPN
ejpam-5602	413	16	∈	∈	PROPN
ejpam-5602	413	17	e(g	e(g	PROPN
ejpam-5602	413	18	⋄	⋄	PROPN
ejpam-5602	413	19	h	h	NOUN
ejpam-5602	413	20	)	)	PUNCT
ejpam-5602	413	21	.	.	PUNCT
ejpam-5602	414	1	similarly	similarly	ADV
ejpam-5602	414	2	,	,	PUNCT
ejpam-5602	414	3	if	if	SCONJ
ejpam-5602	414	4	y	y	PROPN
ejpam-5602	414	5	/∈	/∈	PUNCT
ejpam-5602	414	6	v0	v0	PROPN
ejpam-5602	414	7	,	,	PUNCT
ejpam-5602	414	8	then	then	ADV
ejpam-5602	414	9	y	y	PROPN
ejpam-5602	414	10	∈	∈	PROPN
ejpam-5602	414	11	v1	v1	PROPN
ejpam-5602	414	12	∪	∪	ADP
ejpam-5602	414	13	v2	v2	PROPN
ejpam-5602	414	14	∪	∪	X
ejpam-5602	414	15	v3	v3	PROPN
ejpam-5602	414	16	with	with	ADP
ejpam-5602	414	17	yv	yv	PROPN
ejpam-5602	414	18	∈	∈	PROPN
ejpam-5602	414	19	e(g	e(g	PROPN
ejpam-5602	414	20	⋄	⋄	PROPN
ejpam-5602	414	21	h	h	NOUN
ejpam-5602	414	22	)	)	PUNCT
ejpam-5602	414	23	.	.	PUNCT
ejpam-5602	415	1	suppose	suppose	VERB
ejpam-5602	415	2	that	that	SCONJ
ejpam-5602	415	3	xy	xy	PROPN
ejpam-5602	415	4	∈	∈	PROPN
ejpam-5602	415	5	e00	e00	PROPN
ejpam-5602	415	6	.	.	PUNCT
ejpam-5602	416	1	by	by	ADP
ejpam-5602	416	2	(	(	PUNCT
ejpam-5602	416	3	i	i	NOUN
ejpam-5602	416	4	)	)	PUNCT
ejpam-5602	416	5	,	,	PUNCT
ejpam-5602	416	6	f	f	PROPN
ejpam-5602	416	7	|hxy	|hxy	PROPN
ejpam-5602	416	8	∈	∈	PROPN
ejpam-5602	416	9	tdidf	tdidf	NOUN
ejpam-5602	416	10	(	(	PUNCT
ejpam-5602	416	11	huv	huv	PROPN
ejpam-5602	416	12	)	)	PUNCT
ejpam-5602	416	13	so	so	SCONJ
ejpam-5602	416	14	that	that	SCONJ
ejpam-5602	416	15	there	there	PRON
ejpam-5602	416	16	exists	exist	VERB
ejpam-5602	416	17	u	u	PROPN
ejpam-5602	416	18	∈	∈	PROPN
ejpam-5602	416	19	v	v	PROPN
ejpam-5602	416	20	(	(	PUNCT
ejpam-5602	416	21	hxy	hxy	NOUN
ejpam-5602	416	22	)	)	PUNCT
ejpam-5602	416	23	for	for	ADP
ejpam-5602	416	24	which	which	PRON
ejpam-5602	416	25	f(u	f(u	PROPN
ejpam-5602	416	26	)	)	PUNCT
ejpam-5602	416	27	=	=	SYM
ejpam-5602	416	28	f	f	PROPN
ejpam-5602	416	29	|hxy(u	|hxy(u	PROPN
ejpam-5602	416	30	)	)	PUNCT
ejpam-5602	416	31	>	>	X
ejpam-5602	416	32	0	0	PUNCT
ejpam-5602	417	1	and	and	CCONJ
ejpam-5602	417	2	uv	uv	PROPN
ejpam-5602	417	3	∈	∈	PROPN
ejpam-5602	417	4	e(g	e(g	PROPN
ejpam-5602	417	5	⋄h	⋄h	PROPN
ejpam-5602	417	6	)	)	PUNCT
ejpam-5602	417	7	.	.	PUNCT
ejpam-5602	418	1	the	the	DET
ejpam-5602	418	2	argument	argument	NOUN
ejpam-5602	418	3	above	above	ADV
ejpam-5602	418	4	implies	imply	VERB
ejpam-5602	418	5	that	that	SCONJ
ejpam-5602	418	6	f	f	PROPN
ejpam-5602	418	7	∈	∈	PROPN
ejpam-5602	418	8	tdidf	tdidf	NOUN
ejpam-5602	418	9	(	(	PUNCT
ejpam-5602	418	10	g	g	PROPN
ejpam-5602	418	11	⋄h	⋄h	PROPN
ejpam-5602	418	12	)	)	PUNCT
ejpam-5602	418	13	.	.	PUNCT
ejpam-5602	419	1	■	■	PUNCT
ejpam-5602	419	2	for	for	ADP
ejpam-5602	419	3	the	the	DET
ejpam-5602	419	4	purpose	purpose	NOUN
ejpam-5602	419	5	of	of	ADP
ejpam-5602	419	6	the	the	DET
ejpam-5602	419	7	next	next	ADJ
ejpam-5602	419	8	result	result	NOUN
ejpam-5602	419	9	,	,	PUNCT
ejpam-5602	419	10	we	we	PRON
ejpam-5602	419	11	define	define	VERB
ejpam-5602	419	12	for	for	ADP
ejpam-5602	419	13	any	any	PRON
ejpam-5602	419	14	d	d	PROPN
ejpam-5602	419	15	⊆	⊆	NUM
ejpam-5602	419	16	v	v	NOUN
ejpam-5602	419	17	(	(	PUNCT
ejpam-5602	419	18	g	g	NOUN
ejpam-5602	419	19	)	)	PUNCT
ejpam-5602	419	20	,	,	PUNCT
ejpam-5602	419	21	e(g	e(g	PROPN
ejpam-5602	419	22	,	,	PUNCT
ejpam-5602	419	23	d	d	NOUN
ejpam-5602	419	24	)	)	PUNCT
ejpam-5602	419	25	=	=	NOUN
ejpam-5602	419	26	{	{	PUNCT
ejpam-5602	419	27	uv	uv	NOUN
ejpam-5602	419	28	∈	∈	PROPN
ejpam-5602	419	29	e(g	e(g	PROPN
ejpam-5602	419	30	)	)	PUNCT
ejpam-5602	419	31	:	:	PUNCT
ejpam-5602	419	32	both	both	DET
ejpam-5602	419	33	u	u	NOUN
ejpam-5602	419	34	,	,	PUNCT
ejpam-5602	419	35	v	v	NOUN
ejpam-5602	419	36	/∈	/∈	PUNCT
ejpam-5602	419	37	d	d	NOUN
ejpam-5602	419	38	}	}	PUNCT
ejpam-5602	419	39	.	.	PUNCT
ejpam-5602	420	1	let	let	VERB
ejpam-5602	420	2	g	g	NOUN
ejpam-5602	420	3	=	=	SYM
ejpam-5602	420	4	p5	p5	PROPN
ejpam-5602	420	5	=	=	PUNCT
ejpam-5602	421	1	[	[	X
ejpam-5602	421	2	v1	v1	NOUN
ejpam-5602	421	3	,	,	PUNCT
ejpam-5602	421	4	v2	v2	PROPN
ejpam-5602	421	5	,	,	PUNCT
ejpam-5602	421	6	v3	v3	PROPN
ejpam-5602	421	7	,	,	PUNCT
ejpam-5602	421	8	v4	v4	PROPN
ejpam-5602	421	9	,	,	PUNCT
ejpam-5602	421	10	v5	v5	PROPN
ejpam-5602	421	11	]	]	X
ejpam-5602	421	12	.	.	PUNCT
ejpam-5602	422	1	if	if	SCONJ
ejpam-5602	422	2	s1	s1	PROPN
ejpam-5602	422	3	=	=	PUNCT
ejpam-5602	422	4	{	{	PUNCT
ejpam-5602	422	5	v1	v1	PROPN
ejpam-5602	422	6	,	,	PUNCT
ejpam-5602	422	7	v4	v4	NOUN
ejpam-5602	422	8	}	}	PUNCT
ejpam-5602	422	9	and	and	CCONJ
ejpam-5602	422	10	s2	s2	VERB
ejpam-5602	422	11	=	=	SYM
ejpam-5602	422	12	{	{	PUNCT
ejpam-5602	422	13	v1	v1	PROPN
ejpam-5602	422	14	,	,	PUNCT
ejpam-5602	422	15	v2	v2	PROPN
ejpam-5602	422	16	}	}	PUNCT
ejpam-5602	422	17	,	,	PUNCT
ejpam-5602	422	18	then	then	ADV
ejpam-5602	422	19	e(g	e(g	PROPN
ejpam-5602	422	20	,	,	PUNCT
ejpam-5602	422	21	s1	s1	NOUN
ejpam-5602	422	22	)	)	PUNCT
ejpam-5602	422	23	=	=	NOUN
ejpam-5602	422	24	∅	∅	NOUN
ejpam-5602	422	25	and	and	CCONJ
ejpam-5602	422	26	e(g	e(g	PROPN
ejpam-5602	422	27	,	,	PUNCT
ejpam-5602	422	28	s2	s2	PROPN
ejpam-5602	422	29	)	)	PUNCT
ejpam-5602	422	30	=	=	PRON
ejpam-5602	422	31	{	{	PUNCT
ejpam-5602	422	32	v3v4	v3v4	PROPN
ejpam-5602	422	33	,	,	PUNCT
ejpam-5602	422	34	v4v5	v4v5	NOUN
ejpam-5602	422	35	}	}	PUNCT
ejpam-5602	422	36	.	.	PUNCT
ejpam-5602	423	1	corollary	corollary	ADJ
ejpam-5602	423	2	4	4	NUM
ejpam-5602	423	3	.	.	PUNCT
ejpam-5602	424	1	let	let	VERB
ejpam-5602	424	2	g	g	PRON
ejpam-5602	424	3	be	be	AUX
ejpam-5602	424	4	a	a	DET
ejpam-5602	424	5	nontrivial	nontrivial	ADJ
ejpam-5602	424	6	connected	connect	VERB
ejpam-5602	424	7	graph	graph	NOUN
ejpam-5602	424	8	of	of	ADP
ejpam-5602	424	9	order	order	NOUN
ejpam-5602	424	10	n.	n.	NOUN
ejpam-5602	424	11	then	then	ADV
ejpam-5602	424	12	for	for	ADP
ejpam-5602	424	13	any	any	DET
ejpam-5602	424	14	graph	graph	NOUN
ejpam-5602	424	15	h	h	NOUN
ejpam-5602	424	16	,	,	PUNCT
ejpam-5602	424	17	3	3	NUM
ejpam-5602	424	18	≤	≤	NUM
ejpam-5602	424	19	γtdi(g	γtdi(g	NOUN
ejpam-5602	424	20	⋄h	⋄h	NOUN
ejpam-5602	424	21	)	)	PUNCT
ejpam-5602	424	22	≤	≤	NOUN
ejpam-5602	424	23	n+	n+	NUM
ejpam-5602	424	24	β(g	β(g	PROPN
ejpam-5602	424	25	)	)	PUNCT
ejpam-5602	424	26	.	.	PUNCT
ejpam-5602	425	1	moreover	moreover	ADV
ejpam-5602	425	2	,	,	PUNCT
ejpam-5602	425	3	if	if	SCONJ
ejpam-5602	425	4	h	h	NOUN
ejpam-5602	425	5	has	have	VERB
ejpam-5602	425	6	no	no	DET
ejpam-5602	425	7	isolated	isolated	ADJ
ejpam-5602	425	8	vertices	vertex	NOUN
ejpam-5602	425	9	,	,	PUNCT
ejpam-5602	425	10	then	then	ADV
ejpam-5602	425	11	3	3	NUM
ejpam-5602	425	12	≤	≤	NUM
ejpam-5602	425	13	γtdi(g	γtdi(g	NOUN
ejpam-5602	425	14	⋄h	⋄h	NOUN
ejpam-5602	425	15	)	)	PUNCT
ejpam-5602	425	16	≤	≤	NUM
ejpam-5602	425	17	min{n+	min{n+	VERB
ejpam-5602	425	18	β(g	β(g	PROPN
ejpam-5602	425	19	)	)	PUNCT
ejpam-5602	425	20	,	,	PUNCT
ejpam-5602	425	21	θ(g	θ(g	PROPN
ejpam-5602	425	22	⋄h	⋄h	NOUN
ejpam-5602	425	23	)	)	PUNCT
ejpam-5602	425	24	}	}	PUNCT
ejpam-5602	425	25	where	where	SCONJ
ejpam-5602	425	26	θ(g	θ(g	PROPN
ejpam-5602	425	27	⋄h	⋄h	NOUN
ejpam-5602	425	28	)	)	PUNCT
ejpam-5602	425	29	=	=	SYM
ejpam-5602	426	1	3γt(g	3γt(g	NUM
ejpam-5602	426	2	)	)	PUNCT
ejpam-5602	426	3	+	+	CCONJ
ejpam-5602	426	4	γtdi(h)min{|e(g	γtdi(h)min{|e(g	NOUN
ejpam-5602	426	5	,	,	PUNCT
ejpam-5602	426	6	s)|	s)|	NOUN
ejpam-5602	426	7	:	:	PUNCT
ejpam-5602	426	8	s	s	VERB
ejpam-5602	426	9	is	be	AUX
ejpam-5602	426	10	a	a	DET
ejpam-5602	426	11	γt	γt	NOUN
ejpam-5602	426	12	-	-	NOUN
ejpam-5602	426	13	set	set	NOUN
ejpam-5602	426	14	of	of	ADP
ejpam-5602	426	15	g	g	NOUN
ejpam-5602	426	16	}	}	PUNCT
ejpam-5602	426	17	,	,	PUNCT
ejpam-5602	426	18	and	and	CCONJ
ejpam-5602	426	19	these	these	DET
ejpam-5602	426	20	bounds	bound	NOUN
ejpam-5602	426	21	are	be	AUX
ejpam-5602	426	22	sharp	sharp	ADJ
ejpam-5602	426	23	.	.	PUNCT
ejpam-5602	427	1	s.j.l	s.j.l	PROPN
ejpam-5602	427	2	.	.	PUNCT
ejpam-5602	427	3	sumbalan	sumbalan	PROPN
ejpam-5602	427	4	,	,	PUNCT
ejpam-5602	427	5	s.m	s.m	PROPN
ejpam-5602	427	6	.	.	PROPN
ejpam-5602	427	7	menchavez	menchavez	PROPN
ejpam-5602	427	8	,	,	PUNCT
ejpam-5602	427	9	f.p	f.p	PROPN
ejpam-5602	427	10	.	.	PROPN
ejpam-5602	427	11	jamil	jamil	PROPN
ejpam-5602	427	12	/	/	SYM
ejpam-5602	427	13	eur	eur	PROPN
ejpam-5602	427	14	.	.	PUNCT
ejpam-5602	428	1	j.	j.	PROPN
ejpam-5602	428	2	pure	pure	PROPN
ejpam-5602	428	3	appl	appl	PROPN
ejpam-5602	428	4	.	.	PROPN
ejpam-5602	428	5	math	math	PROPN
ejpam-5602	428	6	,	,	PUNCT
ejpam-5602	428	7	18	18	NUM
ejpam-5602	428	8	(	(	PUNCT
ejpam-5602	428	9	1	1	NUM
ejpam-5602	428	10	)	)	PUNCT
ejpam-5602	428	11	(	(	PUNCT
ejpam-5602	428	12	2025	2025	NUM
ejpam-5602	428	13	)	)	PUNCT
ejpam-5602	428	14	,	,	PUNCT
ejpam-5602	428	15	5602	5602	NUM
ejpam-5602	428	16	13	13	NUM
ejpam-5602	428	17	of	of	ADP
ejpam-5602	428	18	18	18	NUM
ejpam-5602	428	19	proof	proof	NOUN
ejpam-5602	428	20	:	:	PUNCT
ejpam-5602	428	21	the	the	DET
ejpam-5602	428	22	lower	low	ADJ
ejpam-5602	428	23	bound	bind	VERB
ejpam-5602	428	24	follows	follow	VERB
ejpam-5602	428	25	immediately	immediately	ADV
ejpam-5602	428	26	from	from	ADP
ejpam-5602	428	27	proposition	proposition	NOUN
ejpam-5602	428	28	1	1	NUM
ejpam-5602	428	29	.	.	PUNCT
ejpam-5602	429	1	let	let	VERB
ejpam-5602	429	2	s	s	PRON
ejpam-5602	429	3	⊆	⊆	NUM
ejpam-5602	429	4	v	v	NOUN
ejpam-5602	429	5	(	(	PUNCT
ejpam-5602	429	6	g	g	NOUN
ejpam-5602	429	7	)	)	PUNCT
ejpam-5602	429	8	be	be	AUX
ejpam-5602	429	9	a	a	DET
ejpam-5602	429	10	β	β	NOUN
ejpam-5602	429	11	-	-	NOUN
ejpam-5602	429	12	set	set	NOUN
ejpam-5602	429	13	of	of	ADP
ejpam-5602	429	14	g.	g.	PROPN
ejpam-5602	430	1	then	then	ADV
ejpam-5602	430	2	f	f	PROPN
ejpam-5602	430	3	=	=	SYM
ejpam-5602	430	4	(	(	PUNCT
ejpam-5602	430	5	v0	v0	PROPN
ejpam-5602	430	6	,	,	PUNCT
ejpam-5602	430	7	v1	v1	NOUN
ejpam-5602	430	8	,	,	PUNCT
ejpam-5602	430	9	v2	v2	PROPN
ejpam-5602	430	10	,	,	PUNCT
ejpam-5602	430	11	v3	v3	PROPN
ejpam-5602	430	12	)	)	PUNCT
ejpam-5602	430	13	∈	∈	PROPN
ejpam-5602	430	14	tdidf	tdidf	NOUN
ejpam-5602	430	15	(	(	PUNCT
ejpam-5602	430	16	g	g	PROPN
ejpam-5602	430	17	⋄	⋄	PROPN
ejpam-5602	430	18	h	h	NOUN
ejpam-5602	430	19	)	)	PUNCT
ejpam-5602	430	20	,	,	PUNCT
ejpam-5602	430	21	where	where	SCONJ
ejpam-5602	430	22	v0	v0	NOUN
ejpam-5602	430	23	=	=	SYM
ejpam-5602	430	24	∪uv∈e(g)v	∪uv∈e(g)v	PROPN
ejpam-5602	430	25	(	(	PUNCT
ejpam-5602	430	26	huv	huv	PROPN
ejpam-5602	430	27	)	)	PUNCT
ejpam-5602	430	28	,	,	PUNCT
ejpam-5602	430	29	v1	v1	NOUN
ejpam-5602	430	30	=	=	SYM
ejpam-5602	430	31	v	v	NOUN
ejpam-5602	430	32	(	(	PUNCT
ejpam-5602	430	33	g	g	NOUN
ejpam-5602	430	34	)	)	PUNCT
ejpam-5602	430	35	\	\	PROPN
ejpam-5602	430	36	s	s	X
ejpam-5602	430	37	,	,	PUNCT
ejpam-5602	430	38	v2	v2	PROPN
ejpam-5602	430	39	=	=	SYM
ejpam-5602	430	40	s	s	PROPN
ejpam-5602	430	41	and	and	CCONJ
ejpam-5602	430	42	v3	v3	PROPN
ejpam-5602	430	43	=	=	PUNCT
ejpam-5602	430	44	∅.	∅.	ADV
ejpam-5602	430	45	thus	thus	ADV
ejpam-5602	430	46	,	,	PUNCT
ejpam-5602	430	47	γtdi(g	γtdi(g	PROPN
ejpam-5602	430	48	⋄h	⋄h	NOUN
ejpam-5602	430	49	)	)	PUNCT
ejpam-5602	430	50	≤	≤	NOUN
ejpam-5602	431	1	2|s|+	2|s|+	NUM
ejpam-5602	431	2	n−	n−	NOUN
ejpam-5602	431	3	|s|	|s|	NOUN
ejpam-5602	431	4	=	=	PUNCT
ejpam-5602	431	5	n+	n+	NUM
ejpam-5602	431	6	β(g	β(g	PROPN
ejpam-5602	431	7	)	)	PUNCT
ejpam-5602	431	8	.	.	PUNCT
ejpam-5602	432	1	assume	assume	VERB
ejpam-5602	432	2	thath	thath	PROPN
ejpam-5602	432	3	has	have	VERB
ejpam-5602	432	4	no	no	DET
ejpam-5602	432	5	isolated	isolated	ADJ
ejpam-5602	432	6	vertices	vertex	NOUN
ejpam-5602	432	7	.	.	PUNCT
ejpam-5602	433	1	thenhuv	thenhuv	NOUN
ejpam-5602	433	2	admits	admit	VERB
ejpam-5602	433	3	a	a	DET
ejpam-5602	433	4	tdidf	tdidf	NOUN
ejpam-5602	433	5	.	.	PUNCT
ejpam-5602	434	1	let	let	VERB
ejpam-5602	434	2	s	s	PRON
ejpam-5602	434	3	be	be	AUX
ejpam-5602	434	4	a	a	DET
ejpam-5602	434	5	γt	γt	NOUN
ejpam-5602	434	6	-	-	NOUN
ejpam-5602	434	7	set	set	NOUN
ejpam-5602	434	8	of	of	ADP
ejpam-5602	434	9	g.	g.	PROPN
ejpam-5602	434	10	suppose	suppose	VERB
ejpam-5602	434	11	fuv	fuv	ADV
ejpam-5602	434	12	=	=	SYM
ejpam-5602	434	13	(	(	PUNCT
ejpam-5602	434	14	v	v	NOUN
ejpam-5602	434	15	uv	uv	NOUN
ejpam-5602	434	16	0	0	NUM
ejpam-5602	434	17	,	,	PUNCT
ejpam-5602	434	18	v	v	NOUN
ejpam-5602	434	19	uv	uv	NOUN
ejpam-5602	434	20	1	1	NUM
ejpam-5602	434	21	,	,	PUNCT
ejpam-5602	434	22	v	v	NOUN
ejpam-5602	434	23	uv	uv	NOUN
ejpam-5602	434	24	2	2	NUM
ejpam-5602	434	25	,	,	PUNCT
ejpam-5602	434	26	v	v	NOUN
ejpam-5602	434	27	uv	uv	NOUN
ejpam-5602	434	28	3	3	NUM
ejpam-5602	434	29	)	)	PUNCT
ejpam-5602	434	30	is	be	AUX
ejpam-5602	434	31	a	a	DET
ejpam-5602	434	32	γtdi	γtdi	NOUN
ejpam-5602	434	33	-function	-function	NOUN
ejpam-5602	434	34	of	of	ADP
ejpam-5602	434	35	huv	huv	PROPN
ejpam-5602	434	36	for	for	ADP
ejpam-5602	434	37	each	each	DET
ejpam-5602	434	38	uv	uv	PROPN
ejpam-5602	434	39	∈	∈	PROPN
ejpam-5602	434	40	e(g	e(g	PROPN
ejpam-5602	434	41	,	,	PUNCT
ejpam-5602	434	42	s	s	PROPN
ejpam-5602	434	43	)	)	PUNCT
ejpam-5602	434	44	.	.	PUNCT
ejpam-5602	435	1	define	define	VERB
ejpam-5602	435	2	f	f	PROPN
ejpam-5602	435	3	=	=	SYM
ejpam-5602	435	4	(	(	PUNCT
ejpam-5602	435	5	v0	v0	PROPN
ejpam-5602	435	6	,	,	PUNCT
ejpam-5602	435	7	v1	v1	NOUN
ejpam-5602	435	8	,	,	PUNCT
ejpam-5602	435	9	v2	v2	PROPN
ejpam-5602	435	10	,	,	PUNCT
ejpam-5602	435	11	v3	v3	PROPN
ejpam-5602	435	12	)	)	PUNCT
ejpam-5602	435	13	on	on	ADP
ejpam-5602	435	14	g	g	PROPN
ejpam-5602	435	15	⋄h	⋄h	PROPN
ejpam-5602	435	16	,	,	PUNCT
ejpam-5602	435	17	where	where	SCONJ
ejpam-5602	435	18	v0	v0	NOUN
ejpam-5602	435	19	=	=	SYM
ejpam-5602	435	20	(	(	PUNCT
ejpam-5602	435	21	v	v	NOUN
ejpam-5602	435	22	(	(	PUNCT
ejpam-5602	435	23	g	g	NOUN
ejpam-5602	435	24	)	)	PUNCT
ejpam-5602	435	25	\	\	PROPN
ejpam-5602	436	1	s	s	X
ejpam-5602	436	2	)	)	PUNCT
ejpam-5602	436	3	∪	∪	NOUN
ejpam-5602	436	4	(	(	PUNCT
ejpam-5602	436	5	∪uv∈e(g	∪uv∈e(g	NOUN
ejpam-5602	436	6	,	,	PUNCT
ejpam-5602	436	7	s)v	s)v	NOUN
ejpam-5602	436	8	uv	uv	NOUN
ejpam-5602	436	9	0	0	NUM
ejpam-5602	436	10	)	)	PUNCT
ejpam-5602	436	11	∪	∪	NOUN
ejpam-5602	436	12	(	(	PUNCT
ejpam-5602	436	13	∪uv∈e(g)\e(g	∪uv∈e(g)\e(g	NOUN
ejpam-5602	436	14	,	,	PUNCT
ejpam-5602	436	15	s)v	s)v	X
ejpam-5602	436	16	(	(	PUNCT
ejpam-5602	436	17	huv	huv	PROPN
ejpam-5602	436	18	)	)	PUNCT
ejpam-5602	436	19	)	)	PUNCT
ejpam-5602	436	20	,	,	PUNCT
ejpam-5602	436	21	v1	v1	NOUN
ejpam-5602	436	22	=	=	SYM
ejpam-5602	436	23	∪uv∈e(g	∪uv∈e(g	NOUN
ejpam-5602	436	24	,	,	PUNCT
ejpam-5602	436	25	s)v	s)v	PRON
ejpam-5602	436	26	uv	uv	NOUN
ejpam-5602	436	27	1	1	NUM
ejpam-5602	436	28	,	,	PUNCT
ejpam-5602	436	29	v2	v2	PROPN
ejpam-5602	436	30	=	=	SYM
ejpam-5602	436	31	∪uv∈e(g	∪uv∈e(g	NOUN
ejpam-5602	436	32	,	,	PUNCT
ejpam-5602	436	33	s)v	s)v	NOUN
ejpam-5602	436	34	uv	uv	NOUN
ejpam-5602	436	35	2	2	NUM
ejpam-5602	436	36	,	,	PUNCT
ejpam-5602	436	37	and	and	CCONJ
ejpam-5602	436	38	v3	v3	PROPN
ejpam-5602	436	39	=	=	SYM
ejpam-5602	436	40	s	s	PART
ejpam-5602	436	41	∪	∪	X
ejpam-5602	436	42	(	(	PUNCT
ejpam-5602	436	43	∪uv∈e(g	∪uv∈e(g	NOUN
ejpam-5602	436	44	,	,	PUNCT
ejpam-5602	436	45	s)v	s)v	NOUN
ejpam-5602	436	46	uv	uv	NOUN
ejpam-5602	436	47	3	3	NUM
ejpam-5602	436	48	)	)	PUNCT
ejpam-5602	436	49	.	.	PUNCT
ejpam-5602	437	1	note	note	VERB
ejpam-5602	437	2	that	that	SCONJ
ejpam-5602	437	3	e01	e01	NOUN
ejpam-5602	437	4	=	=	SYM
ejpam-5602	437	5	e02	e02	NOUN
ejpam-5602	437	6	=	=	SYM
ejpam-5602	437	7	e11	e11	NOUN
ejpam-5602	437	8	=	=	NOUN
ejpam-5602	437	9	∅	∅	NOUN
ejpam-5602	437	10	and	and	CCONJ
ejpam-5602	437	11	(	(	PUNCT
ejpam-5602	437	12	v1	v1	VERB
ejpam-5602	437	13	∪	∪	NOUN
ejpam-5602	437	14	v2	v2	NOUN
ejpam-5602	437	15	)	)	PUNCT
ejpam-5602	437	16	∩	∩	ADJ
ejpam-5602	437	17	v	v	X
ejpam-5602	437	18	(	(	PUNCT
ejpam-5602	437	19	g	g	NOUN
ejpam-5602	437	20	)	)	PUNCT
ejpam-5602	437	21	=	=	NOUN
ejpam-5602	437	22	∅.	∅.	VERB
ejpam-5602	437	23	moreover	moreover	ADV
ejpam-5602	437	24	,	,	PUNCT
ejpam-5602	437	25	v3	v3	PROPN
ejpam-5602	437	26	∩	∩	PROPN
ejpam-5602	437	27	v	v	X
ejpam-5602	437	28	(	(	PUNCT
ejpam-5602	437	29	g	g	NOUN
ejpam-5602	437	30	)	)	PUNCT
ejpam-5602	438	1	=	=	SYM
ejpam-5602	438	2	s	s	VERB
ejpam-5602	438	3	is	be	AUX
ejpam-5602	438	4	a	a	DET
ejpam-5602	438	5	γt	γt	NOUN
ejpam-5602	438	6	-	-	NOUN
ejpam-5602	438	7	set	set	NOUN
ejpam-5602	438	8	of	of	ADP
ejpam-5602	438	9	g	g	NOUN
ejpam-5602	438	10	so	so	SCONJ
ejpam-5602	438	11	that	that	SCONJ
ejpam-5602	438	12	ng(x	ng(x	NUM
ejpam-5602	438	13	)	)	PUNCT
ejpam-5602	438	14	⊈	⊈	PROPN
ejpam-5602	438	15	v0	v0	NOUN
ejpam-5602	438	16	for	for	ADP
ejpam-5602	438	17	each	each	DET
ejpam-5602	438	18	x	x	PROPN
ejpam-5602	438	19	∈	∈	PROPN
ejpam-5602	438	20	v3	v3	PROPN
ejpam-5602	438	21	∩	∩	PROPN
ejpam-5602	438	22	v	v	X
ejpam-5602	438	23	(	(	PUNCT
ejpam-5602	438	24	g	g	NOUN
ejpam-5602	438	25	)	)	PUNCT
ejpam-5602	438	26	.	.	PUNCT
ejpam-5602	439	1	hence	hence	ADV
ejpam-5602	439	2	,	,	PUNCT
ejpam-5602	439	3	we	we	PRON
ejpam-5602	439	4	only	only	ADV
ejpam-5602	439	5	need	need	VERB
ejpam-5602	439	6	to	to	PART
ejpam-5602	439	7	satisfy	satisfy	VERB
ejpam-5602	439	8	condition	condition	NOUN
ejpam-5602	439	9	(	(	PUNCT
ejpam-5602	439	10	i	i	NOUN
ejpam-5602	439	11	)	)	PUNCT
ejpam-5602	439	12	in	in	ADP
ejpam-5602	439	13	proposition	proposition	NOUN
ejpam-5602	439	14	10	10	NUM
ejpam-5602	439	15	.	.	PUNCT
ejpam-5602	440	1	let	let	VERB
ejpam-5602	440	2	uv	uv	PRON
ejpam-5602	440	3	∈	∈	PROPN
ejpam-5602	440	4	e00	e00	PROPN
ejpam-5602	440	5	.	.	PUNCT
ejpam-5602	441	1	then	then	ADV
ejpam-5602	441	2	f	f	X
ejpam-5602	441	3	|huv	|huv	X
ejpam-5602	441	4	=	=	PUNCT
ejpam-5602	441	5	fuv	fuv	PROPN
ejpam-5602	441	6	∈	∈	PROPN
ejpam-5602	441	7	tdidf	tdidf	NOUN
ejpam-5602	441	8	(	(	PUNCT
ejpam-5602	441	9	huv	huv	PROPN
ejpam-5602	441	10	)	)	PUNCT
ejpam-5602	441	11	.	.	PUNCT
ejpam-5602	442	1	thus	thus	ADV
ejpam-5602	442	2	,	,	PUNCT
ejpam-5602	442	3	f	f	PROPN
ejpam-5602	442	4	∈	∈	PROPN
ejpam-5602	442	5	tdidf	tdidf	NOUN
ejpam-5602	442	6	(	(	PUNCT
ejpam-5602	442	7	g	g	PROPN
ejpam-5602	442	8	⋄	⋄	PROPN
ejpam-5602	442	9	h	h	NOUN
ejpam-5602	442	10	)	)	PUNCT
ejpam-5602	442	11	with	with	ADP
ejpam-5602	442	12	ωg⋄h(g	ωg⋄h(g	NOUN
ejpam-5602	442	13	)	)	PUNCT
ejpam-5602	442	14	=	=	SYM
ejpam-5602	442	15	3γ(g	3γ(g	NUM
ejpam-5602	442	16	)	)	PUNCT
ejpam-5602	443	1	+	+	CCONJ
ejpam-5602	443	2	γtdi(h)|e(g	γtdi(h)|e(g	PROPN
ejpam-5602	443	3	,	,	PUNCT
ejpam-5602	443	4	s)|	s)|	NOUN
ejpam-5602	443	5	.	.	PUNCT
ejpam-5602	444	1	it	it	PRON
ejpam-5602	444	2	follows	follow	VERB
ejpam-5602	444	3	that	that	SCONJ
ejpam-5602	444	4	,	,	PUNCT
ejpam-5602	444	5	γtdi(g	γtdi(g	PROPN
ejpam-5602	444	6	⋄h	⋄h	NOUN
ejpam-5602	444	7	)	)	PUNCT
ejpam-5602	444	8	≤	≤	NOUN
ejpam-5602	445	1	θ(g	θ(g	NUM
ejpam-5602	445	2	⋄h	⋄h	NOUN
ejpam-5602	445	3	)	)	PUNCT
ejpam-5602	445	4	.	.	PUNCT
ejpam-5602	446	1	for	for	ADP
ejpam-5602	446	2	the	the	DET
ejpam-5602	446	3	sharpness	sharpness	NOUN
ejpam-5602	446	4	,	,	PUNCT
ejpam-5602	446	5	note	note	VERB
ejpam-5602	446	6	first	first	ADV
ejpam-5602	446	7	that	that	SCONJ
ejpam-5602	446	8	for	for	ADP
ejpam-5602	446	9	the	the	DET
ejpam-5602	446	10	left	left	ADJ
ejpam-5602	446	11	-	-	PUNCT
ejpam-5602	446	12	hand	hand	NOUN
ejpam-5602	446	13	side	side	NOUN
ejpam-5602	446	14	,	,	PUNCT
ejpam-5602	446	15	γtdi(p2	γtdi(p2	ADJ
ejpam-5602	446	16	⋄	⋄	PROPN
ejpam-5602	446	17	h	h	NOUN
ejpam-5602	446	18	)	)	PUNCT
ejpam-5602	446	19	=	=	SYM
ejpam-5602	446	20	3	3	NUM
ejpam-5602	446	21	for	for	ADP
ejpam-5602	446	22	any	any	DET
ejpam-5602	446	23	h.	h.	NOUN
ejpam-5602	446	24	for	for	ADP
ejpam-5602	446	25	the	the	DET
ejpam-5602	446	26	right	right	ADJ
ejpam-5602	446	27	-	-	PUNCT
ejpam-5602	446	28	hand	hand	NOUN
ejpam-5602	446	29	side	side	NOUN
ejpam-5602	446	30	,	,	PUNCT
ejpam-5602	446	31	consider	consider	VERB
ejpam-5602	446	32	the	the	DET
ejpam-5602	446	33	following	follow	VERB
ejpam-5602	446	34	graphs	graph	NOUN
ejpam-5602	446	35	.	.	PUNCT
ejpam-5602	447	1	if	if	SCONJ
ejpam-5602	447	2	g	g	PROPN
ejpam-5602	447	3	=	=	SYM
ejpam-5602	447	4	c4	c4	NOUN
ejpam-5602	447	5	of	of	ADP
ejpam-5602	447	6	order	order	NOUN
ejpam-5602	447	7	n	n	NOUN
ejpam-5602	447	8	=	=	SYM
ejpam-5602	447	9	4	4	NUM
ejpam-5602	447	10	,	,	PUNCT
ejpam-5602	447	11	then	then	ADV
ejpam-5602	447	12	for	for	ADP
ejpam-5602	447	13	any	any	DET
ejpam-5602	447	14	h	h	NOUN
ejpam-5602	447	15	,	,	PUNCT
ejpam-5602	447	16	γtdi(g	γtdi(g	PROPN
ejpam-5602	447	17	⋄	⋄	PROPN
ejpam-5602	447	18	h	h	NOUN
ejpam-5602	447	19	)	)	PUNCT
ejpam-5602	447	20	=	=	SYM
ejpam-5602	448	1	6	6	NUM
ejpam-5602	448	2	=	=	SYM
ejpam-5602	448	3	n	n	NOUN
ejpam-5602	448	4	+	+	NUM
ejpam-5602	448	5	β(g	β(g	PROPN
ejpam-5602	448	6	)	)	PUNCT
ejpam-5602	448	7	.	.	PUNCT
ejpam-5602	449	1	on	on	ADP
ejpam-5602	449	2	the	the	DET
ejpam-5602	449	3	other	other	ADJ
ejpam-5602	449	4	hand	hand	NOUN
ejpam-5602	449	5	,	,	PUNCT
ejpam-5602	449	6	if	if	SCONJ
ejpam-5602	449	7	g	g	PROPN
ejpam-5602	449	8	is	be	AUX
ejpam-5602	449	9	the	the	DET
ejpam-5602	449	10	graph	graph	NOUN
ejpam-5602	449	11	in	in	ADP
ejpam-5602	449	12	figure	figure	NOUN
ejpam-5602	449	13	2	2	NUM
ejpam-5602	449	14	,	,	PUNCT
ejpam-5602	449	15	then	then	ADV
ejpam-5602	449	16	for	for	ADP
ejpam-5602	449	17	any	any	DET
ejpam-5602	449	18	h	h	NOUN
ejpam-5602	449	19	with	with	ADP
ejpam-5602	449	20	γtdi(h	γtdi(h	PROPN
ejpam-5602	449	21	)	)	PUNCT
ejpam-5602	449	22	=	=	SYM
ejpam-5602	449	23	3	3	NUM
ejpam-5602	449	24	,	,	PUNCT
ejpam-5602	449	25	γtdi(g	γtdi(g	PROPN
ejpam-5602	449	26	⋄h	⋄h	PROPN
ejpam-5602	449	27	)	)	PUNCT
ejpam-5602	449	28	=	=	SYM
ejpam-5602	449	29	15	15	NUM
ejpam-5602	449	30	=	=	SYM
ejpam-5602	449	31	θ(g	θ(g	NUM
ejpam-5602	449	32	⋄h	⋄h	NOUN
ejpam-5602	449	33	)	)	PUNCT
ejpam-5602	449	34	.	.	PUNCT
ejpam-5602	450	1	■	■	PUNCT
ejpam-5602	450	2	figure	figure	NOUN
ejpam-5602	450	3	2	2	NUM
ejpam-5602	450	4	:	:	PUNCT
ejpam-5602	450	5	example	example	NOUN
ejpam-5602	450	6	of	of	ADP
ejpam-5602	450	7	a	a	DET
ejpam-5602	450	8	graph	graph	NOUN
ejpam-5602	450	9	g	g	NOUN
ejpam-5602	450	10	for	for	ADP
ejpam-5602	450	11	which	which	PRON
ejpam-5602	450	12	γtdi(g	γtdi(g	DET
ejpam-5602	450	13	⋄h	⋄h	NOUN
ejpam-5602	450	14	)	)	PUNCT
ejpam-5602	450	15	=	=	PUNCT
ejpam-5602	451	1	θ(g	θ(g	NUM
ejpam-5602	451	2	⋄h	⋄h	PROPN
ejpam-5602	451	3	)	)	PUNCT
ejpam-5602	451	4	strict	strict	ADJ
ejpam-5602	451	5	inequality	inequality	NOUN
ejpam-5602	451	6	in	in	ADP
ejpam-5602	451	7	corollary	corollary	ADJ
ejpam-5602	451	8	4	4	NUM
ejpam-5602	451	9	may	may	AUX
ejpam-5602	451	10	also	also	ADV
ejpam-5602	451	11	be	be	AUX
ejpam-5602	451	12	attained	attain	VERB
ejpam-5602	451	13	.	.	PUNCT
ejpam-5602	452	1	consider	consider	VERB
ejpam-5602	452	2	,	,	PUNCT
ejpam-5602	452	3	for	for	ADP
ejpam-5602	452	4	example	example	NOUN
ejpam-5602	452	5	,	,	PUNCT
ejpam-5602	452	6	the	the	DET
ejpam-5602	452	7	star	star	NOUN
ejpam-5602	452	8	graph	graph	NOUN
ejpam-5602	452	9	g	g	PROPN
ejpam-5602	452	10	=	=	PROPN
ejpam-5602	452	11	k1,7	k1,7	PROPN
ejpam-5602	452	12	.	.	PUNCT
ejpam-5602	453	1	for	for	ADP
ejpam-5602	453	2	any	any	DET
ejpam-5602	453	3	graph	graph	NOUN
ejpam-5602	453	4	h	h	NOUN
ejpam-5602	453	5	without	without	ADP
ejpam-5602	453	6	isolated	isolated	ADJ
ejpam-5602	453	7	vertices	vertex	NOUN
ejpam-5602	453	8	,	,	PUNCT
ejpam-5602	453	9	γtdi(g	γtdi(g	PROPN
ejpam-5602	453	10	⋄h	⋄h	NOUN
ejpam-5602	453	11	)	)	PUNCT
ejpam-5602	453	12	=	=	PUNCT
ejpam-5602	453	13	4	4	NUM
ejpam-5602	453	14	<	<	SYM
ejpam-5602	453	15	6	6	NUM
ejpam-5602	453	16	=	=	SYM
ejpam-5602	453	17	min{n+	min{n+	NOUN
ejpam-5602	453	18	β(g	β(g	PROPN
ejpam-5602	453	19	)	)	PUNCT
ejpam-5602	453	20	,	,	PUNCT
ejpam-5602	453	21	θ(g	θ(g	PROPN
ejpam-5602	453	22	⋄h	⋄h	NOUN
ejpam-5602	453	23	)	)	PUNCT
ejpam-5602	453	24	}	}	PUNCT
ejpam-5602	453	25	.	.	PUNCT
ejpam-5602	454	1	6	6	X
ejpam-5602	454	2	.	.	X
ejpam-5602	454	3	on	on	ADP
ejpam-5602	454	4	the	the	DET
ejpam-5602	454	5	complementary	complementary	ADJ
ejpam-5602	454	6	prism	prism	NOUN
ejpam-5602	454	7	of	of	ADP
ejpam-5602	454	8	graphs	graph	NOUN
ejpam-5602	454	9	proposition	proposition	NOUN
ejpam-5602	454	10	11	11	NUM
ejpam-5602	454	11	.	.	PUNCT
ejpam-5602	455	1	let	let	VERB
ejpam-5602	455	2	g	g	NOUN
ejpam-5602	455	3	be	be	AUX
ejpam-5602	455	4	any	any	DET
ejpam-5602	455	5	graph	graph	NOUN
ejpam-5602	455	6	.	.	PUNCT
ejpam-5602	456	1	then	then	ADV
ejpam-5602	456	2	s.j.l	s.j.l	VERB
ejpam-5602	456	3	.	.	PUNCT
ejpam-5602	456	4	sumbalan	sumbalan	PROPN
ejpam-5602	456	5	,	,	PUNCT
ejpam-5602	456	6	s.m	s.m	PROPN
ejpam-5602	456	7	.	.	PROPN
ejpam-5602	456	8	menchavez	menchavez	PROPN
ejpam-5602	456	9	,	,	PUNCT
ejpam-5602	456	10	f.p	f.p	PROPN
ejpam-5602	456	11	.	.	PROPN
ejpam-5602	456	12	jamil	jamil	PROPN
ejpam-5602	456	13	/	/	SYM
ejpam-5602	456	14	eur	eur	PROPN
ejpam-5602	456	15	.	.	PUNCT
ejpam-5602	457	1	j.	j.	PROPN
ejpam-5602	457	2	pure	pure	PROPN
ejpam-5602	457	3	appl	appl	PROPN
ejpam-5602	457	4	.	.	PROPN
ejpam-5602	457	5	math	math	PROPN
ejpam-5602	457	6	,	,	PUNCT
ejpam-5602	457	7	18	18	NUM
ejpam-5602	457	8	(	(	PUNCT
ejpam-5602	457	9	1	1	NUM
ejpam-5602	457	10	)	)	PUNCT
ejpam-5602	457	11	(	(	PUNCT
ejpam-5602	457	12	2025	2025	NUM
ejpam-5602	457	13	)	)	PUNCT
ejpam-5602	457	14	,	,	PUNCT
ejpam-5602	457	15	5602	5602	NUM
ejpam-5602	457	16	14	14	NUM
ejpam-5602	457	17	of	of	ADP
ejpam-5602	457	18	18	18	NUM
ejpam-5602	457	19	(	(	PUNCT
ejpam-5602	457	20	i	i	NOUN
ejpam-5602	457	21	)	)	PUNCT
ejpam-5602	457	22	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	457	23	)	)	PUNCT
ejpam-5602	457	24	=	=	SYM
ejpam-5602	457	25	3	3	NUM
ejpam-5602	458	1	if	if	SCONJ
ejpam-5602	458	2	and	and	CCONJ
ejpam-5602	458	3	only	only	ADV
ejpam-5602	458	4	if	if	SCONJ
ejpam-5602	458	5	g	g	PROPN
ejpam-5602	458	6	=	=	SYM
ejpam-5602	458	7	k1	k1	PROPN
ejpam-5602	458	8	;	;	PUNCT
ejpam-5602	458	9	(	(	PUNCT
ejpam-5602	458	10	ii	ii	NOUN
ejpam-5602	458	11	)	)	PUNCT
ejpam-5602	458	12	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	458	13	)	)	PUNCT
ejpam-5602	458	14	≥	≥	NOUN
ejpam-5602	458	15	6	6	NUM
ejpam-5602	458	16	whenever	whenever	SCONJ
ejpam-5602	458	17	g	g	PROPN
ejpam-5602	458	18	is	be	AUX
ejpam-5602	458	19	nontrivial	nontrivial	ADJ
ejpam-5602	458	20	,	,	PUNCT
ejpam-5602	458	21	and	and	CCONJ
ejpam-5602	458	22	this	this	DET
ejpam-5602	458	23	lower	lower	ADV
ejpam-5602	458	24	bound	bind	VERB
ejpam-5602	458	25	is	be	AUX
ejpam-5602	458	26	sharp	sharp	ADJ
ejpam-5602	458	27	.	.	PUNCT
ejpam-5602	459	1	proof	proof	NOUN
ejpam-5602	459	2	:	:	PUNCT
ejpam-5602	459	3	statement	statement	NOUN
ejpam-5602	459	4	(	(	PUNCT
ejpam-5602	459	5	i	i	NOUN
ejpam-5602	459	6	)	)	PUNCT
ejpam-5602	459	7	follows	follow	VERB
ejpam-5602	459	8	immediately	immediately	ADV
ejpam-5602	459	9	from	from	ADP
ejpam-5602	459	10	proposition	proposition	NOUN
ejpam-5602	459	11	1	1	NUM
ejpam-5602	459	12	.	.	PUNCT
ejpam-5602	460	1	assume	assume	VERB
ejpam-5602	460	2	g	g	PROPN
ejpam-5602	460	3	is	be	AUX
ejpam-5602	460	4	nontrivial	nontrivial	ADJ
ejpam-5602	460	5	.	.	PUNCT
ejpam-5602	461	1	suppose	suppose	VERB
ejpam-5602	461	2	that	that	SCONJ
ejpam-5602	461	3	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	461	4	)	)	PUNCT
ejpam-5602	461	5	=	=	SYM
ejpam-5602	462	1	4	4	X
ejpam-5602	462	2	.	.	PUNCT
ejpam-5602	462	3	then	then	ADV
ejpam-5602	462	4	γ(gg	γ(gg	X
ejpam-5602	462	5	)	)	PUNCT
ejpam-5602	462	6	̸=	̸=	PROPN
ejpam-5602	462	7	1	1	NUM
ejpam-5602	462	8	.	.	PUNCT
ejpam-5602	463	1	by	by	ADP
ejpam-5602	463	2	proposition	proposition	NOUN
ejpam-5602	463	3	3	3	NUM
ejpam-5602	463	4	,	,	PUNCT
ejpam-5602	463	5	γ(gg	γ(gg	NUM
ejpam-5602	463	6	)	)	PUNCT
ejpam-5602	463	7	≥	≥	NOUN
ejpam-5602	463	8	2	2	NUM
ejpam-5602	463	9	and	and	CCONJ
ejpam-5602	463	10	gg	gg	PROPN
ejpam-5602	463	11	has	have	VERB
ejpam-5602	463	12	a	a	DET
ejpam-5602	463	13	3	3	NUM
ejpam-5602	463	14	-	-	PUNCT
ejpam-5602	463	15	dominating	dominating	NOUN
ejpam-5602	463	16	set	set	NOUN
ejpam-5602	463	17	d	d	NOUN
ejpam-5602	463	18	with	with	ADP
ejpam-5602	463	19	|d|	|d|	PROPN
ejpam-5602	463	20	=	=	SYM
ejpam-5602	463	21	4	4	NUM
ejpam-5602	463	22	and	and	CCONJ
ejpam-5602	463	23	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	463	24	)	)	PUNCT
ejpam-5602	463	25	≥	≥	NOUN
ejpam-5602	464	1	2	2	NUM
ejpam-5602	464	2	.	.	PUNCT
ejpam-5602	465	1	if	if	SCONJ
ejpam-5602	465	2	|d	|d	NOUN
ejpam-5602	465	3	∩	∩	ADJ
ejpam-5602	465	4	v	v	X
ejpam-5602	465	5	(	(	PUNCT
ejpam-5602	465	6	g)|	g)|	VERB
ejpam-5602	465	7	≥	≥	NOUN
ejpam-5602	465	8	3	3	NUM
ejpam-5602	465	9	,	,	PUNCT
ejpam-5602	465	10	then	then	ADV
ejpam-5602	465	11	there	there	PRON
ejpam-5602	465	12	exists	exist	VERB
ejpam-5602	465	13	u	u	PROPN
ejpam-5602	465	14	∈	∈	PROPN
ejpam-5602	465	15	d	d	PROPN
ejpam-5602	465	16	∩	∩	ADJ
ejpam-5602	465	17	v	v	X
ejpam-5602	465	18	(	(	PUNCT
ejpam-5602	465	19	g	g	NOUN
ejpam-5602	465	20	)	)	PUNCT
ejpam-5602	465	21	for	for	ADP
ejpam-5602	465	22	which	which	PRON
ejpam-5602	465	23	u	u	PROPN
ejpam-5602	465	24	/∈	/∈	PROPN
ejpam-5602	465	25	d.	d.	PROPN
ejpam-5602	465	26	for	for	ADP
ejpam-5602	465	27	this	this	DET
ejpam-5602	465	28	u	u	NOUN
ejpam-5602	465	29	,	,	PUNCT
ejpam-5602	465	30	|d	|d	NOUN
ejpam-5602	465	31	∩ngg(u)|	∩ngg(u)|	NOUN
ejpam-5602	465	32	≤	≤	NUM
ejpam-5602	465	33	2	2	NUM
ejpam-5602	465	34	,	,	PUNCT
ejpam-5602	465	35	a	a	DET
ejpam-5602	465	36	contradiction	contradiction	NOUN
ejpam-5602	465	37	.	.	PUNCT
ejpam-5602	466	1	a	a	DET
ejpam-5602	466	2	similar	similar	ADJ
ejpam-5602	466	3	contradiction	contradiction	NOUN
ejpam-5602	466	4	is	be	AUX
ejpam-5602	466	5	attained	attain	VERB
ejpam-5602	466	6	if	if	SCONJ
ejpam-5602	466	7	|d	|d	NOUN
ejpam-5602	466	8	∩	∩	ADJ
ejpam-5602	466	9	v	v	X
ejpam-5602	466	10	(	(	PUNCT
ejpam-5602	466	11	g)|	g)|	VERB
ejpam-5602	466	12	≥	≥	NOUN
ejpam-5602	466	13	3	3	NUM
ejpam-5602	466	14	.	.	PUNCT
ejpam-5602	466	15	suppose	suppose	VERB
ejpam-5602	466	16	that	that	SCONJ
ejpam-5602	466	17	|d	|d	NOUN
ejpam-5602	466	18	∩	∩	ADJ
ejpam-5602	466	19	v	v	NOUN
ejpam-5602	466	20	(	(	PUNCT
ejpam-5602	466	21	g)|	g)|	NOUN
ejpam-5602	466	22	=	=	SYM
ejpam-5602	466	23	2	2	NUM
ejpam-5602	466	24	=	=	NOUN
ejpam-5602	466	25	|d	|d	NOUN
ejpam-5602	466	26	∩	∩	ADJ
ejpam-5602	466	27	v	v	X
ejpam-5602	466	28	(	(	PUNCT
ejpam-5602	466	29	g)|	g)|	NOUN
ejpam-5602	466	30	.	.	PUNCT
ejpam-5602	467	1	since	since	SCONJ
ejpam-5602	467	2	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	467	3	)	)	PUNCT
ejpam-5602	467	4	≥	≥	NOUN
ejpam-5602	467	5	2	2	NUM
ejpam-5602	467	6	,	,	PUNCT
ejpam-5602	467	7	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	467	8	=	=	SYM
ejpam-5602	467	9	c4	c4	NOUN
ejpam-5602	467	10	,	,	PUNCT
ejpam-5602	467	11	which	which	PRON
ejpam-5602	467	12	is	be	AUX
ejpam-5602	467	13	impossible	impossible	ADJ
ejpam-5602	467	14	.	.	PUNCT
ejpam-5602	468	1	thus	thus	ADV
ejpam-5602	468	2	,	,	PUNCT
ejpam-5602	468	3	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	468	4	)	)	PUNCT
ejpam-5602	468	5	̸=	̸=	PROPN
ejpam-5602	468	6	4	4	NUM
ejpam-5602	468	7	.	.	PUNCT
ejpam-5602	468	8	suppose	suppose	VERB
ejpam-5602	468	9	that	that	SCONJ
ejpam-5602	468	10	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	468	11	)	)	PUNCT
ejpam-5602	468	12	=	=	SYM
ejpam-5602	468	13	5	5	X
ejpam-5602	468	14	.	.	X
ejpam-5602	468	15	in	in	ADP
ejpam-5602	468	16	view	view	NOUN
ejpam-5602	468	17	of	of	ADP
ejpam-5602	468	18	proposition	proposition	NOUN
ejpam-5602	468	19	4	4	NUM
ejpam-5602	468	20	,	,	PUNCT
ejpam-5602	468	21	it	it	PRON
ejpam-5602	468	22	suffices	suffice	VERB
ejpam-5602	468	23	to	to	PART
ejpam-5602	468	24	consider	consider	VERB
ejpam-5602	468	25	the	the	DET
ejpam-5602	468	26	following	follow	VERB
ejpam-5602	468	27	cases	case	NOUN
ejpam-5602	468	28	:	:	PUNCT
ejpam-5602	468	29	case	case	NOUN
ejpam-5602	468	30	1	1	NUM
ejpam-5602	468	31	:	:	PUNCT
ejpam-5602	468	32	gg	gg	NOUN
ejpam-5602	468	33	has	have	AUX
ejpam-5602	468	34	a	a	DET
ejpam-5602	468	35	3	3	NUM
ejpam-5602	468	36	-	-	PUNCT
ejpam-5602	468	37	dominating	dominating	NOUN
ejpam-5602	468	38	set	set	NOUN
ejpam-5602	468	39	d	d	NOUN
ejpam-5602	468	40	with	with	ADP
ejpam-5602	468	41	|d|	|d|	PROPN
ejpam-5602	468	42	=	=	SYM
ejpam-5602	468	43	5	5	NUM
ejpam-5602	468	44	and	and	CCONJ
ejpam-5602	468	45	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	468	46	)	)	PUNCT
ejpam-5602	468	47	≥	≥	NOUN
ejpam-5602	469	1	2	2	NUM
ejpam-5602	469	2	.	.	PUNCT
ejpam-5602	470	1	if	if	SCONJ
ejpam-5602	470	2	d	d	PROPN
ejpam-5602	470	3	⊆	⊆	NUM
ejpam-5602	470	4	v	v	ADP
ejpam-5602	470	5	(	(	PUNCT
ejpam-5602	470	6	g	g	NOUN
ejpam-5602	470	7	)	)	PUNCT
ejpam-5602	470	8	and	and	CCONJ
ejpam-5602	470	9	u	u	PROPN
ejpam-5602	470	10	∈	∈	PROPN
ejpam-5602	470	11	d	d	NOUN
ejpam-5602	470	12	,	,	PUNCT
ejpam-5602	470	13	then	then	ADV
ejpam-5602	470	14	|d	|d	VERB
ejpam-5602	470	15	∩	∩	PROPN
ejpam-5602	470	16	ngg(u)|	ngg(u)|	PROPN
ejpam-5602	470	17	≤	≤	NOUN
ejpam-5602	470	18	1	1	NUM
ejpam-5602	470	19	,	,	PUNCT
ejpam-5602	470	20	a	a	DET
ejpam-5602	470	21	contradiction	contradiction	NOUN
ejpam-5602	470	22	.	.	PUNCT
ejpam-5602	471	1	similarly	similarly	ADV
ejpam-5602	471	2	,	,	PUNCT
ejpam-5602	471	3	a	a	DET
ejpam-5602	471	4	contradiction	contradiction	NOUN
ejpam-5602	471	5	is	be	AUX
ejpam-5602	471	6	attained	attain	VERB
ejpam-5602	471	7	if	if	SCONJ
ejpam-5602	471	8	d	d	PROPN
ejpam-5602	471	9	⊆	⊆	NUM
ejpam-5602	471	10	v	v	ADP
ejpam-5602	471	11	(	(	PUNCT
ejpam-5602	471	12	g	g	NOUN
ejpam-5602	471	13	)	)	PUNCT
ejpam-5602	471	14	.	.	PUNCT
ejpam-5602	472	1	since	since	SCONJ
ejpam-5602	472	2	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	472	3	)	)	PUNCT
ejpam-5602	472	4	≥	≥	NOUN
ejpam-5602	472	5	2	2	NUM
ejpam-5602	472	6	,	,	PUNCT
ejpam-5602	472	7	|d	|d	NOUN
ejpam-5602	472	8	∩v	∩v	NOUN
ejpam-5602	472	9	(	(	PUNCT
ejpam-5602	472	10	g)|	g)|	NOUN
ejpam-5602	472	11	=	=	NOUN
ejpam-5602	472	12	̸	̸	NUM
ejpam-5602	472	13	4	4	NUM
ejpam-5602	472	14	and	and	CCONJ
ejpam-5602	472	15	|d	|d	NOUN
ejpam-5602	472	16	∩v	∩v	NOUN
ejpam-5602	472	17	(	(	PUNCT
ejpam-5602	472	18	g)|	g)|	NOUN
ejpam-5602	472	19	=	=	NOUN
ejpam-5602	472	20	̸	̸	NUM
ejpam-5602	472	21	4	4	NUM
ejpam-5602	472	22	.	.	X
ejpam-5602	472	23	assume	assume	VERB
ejpam-5602	472	24	,	,	PUNCT
ejpam-5602	472	25	wlog	wlog	NOUN
ejpam-5602	472	26	,	,	PUNCT
ejpam-5602	472	27	that	that	PRON
ejpam-5602	472	28	|d	|d	VERB
ejpam-5602	472	29	∩	∩	ADJ
ejpam-5602	472	30	v	v	NOUN
ejpam-5602	472	31	(	(	PUNCT
ejpam-5602	472	32	g)|	g)|	NOUN
ejpam-5602	472	33	=	=	SYM
ejpam-5602	472	34	3	3	NUM
ejpam-5602	472	35	and	and	CCONJ
ejpam-5602	472	36	|d	|d	NOUN
ejpam-5602	472	37	∩	∩	ADJ
ejpam-5602	472	38	v	v	NOUN
ejpam-5602	472	39	(	(	PUNCT
ejpam-5602	472	40	g)|	g)|	NOUN
ejpam-5602	472	41	=	=	SYM
ejpam-5602	472	42	2	2	NUM
ejpam-5602	472	43	.	.	PUNCT
ejpam-5602	472	44	since	since	SCONJ
ejpam-5602	472	45	δ(⟨d⟩	δ(⟨d⟩	PROPN
ejpam-5602	472	46	)	)	PUNCT
ejpam-5602	472	47	≥	≥	NOUN
ejpam-5602	472	48	2	2	NUM
ejpam-5602	472	49	,	,	PUNCT
ejpam-5602	472	50	there	there	PRON
ejpam-5602	472	51	exist	exist	VERB
ejpam-5602	472	52	u	u	NOUN
ejpam-5602	472	53	,	,	PUNCT
ejpam-5602	473	1	v	v	NOUN
ejpam-5602	473	2	∈	∈	PROPN
ejpam-5602	473	3	d	d	NOUN
ejpam-5602	473	4	∩	∩	ADJ
ejpam-5602	473	5	v	v	X
ejpam-5602	473	6	(	(	PUNCT
ejpam-5602	473	7	g	g	NOUN
ejpam-5602	473	8	)	)	PUNCT
ejpam-5602	473	9	such	such	ADJ
ejpam-5602	473	10	that	that	SCONJ
ejpam-5602	473	11	d	d	PROPN
ejpam-5602	473	12	∩	∩	ADJ
ejpam-5602	473	13	v	v	X
ejpam-5602	473	14	(	(	PUNCT
ejpam-5602	473	15	g	g	NOUN
ejpam-5602	473	16	)	)	PUNCT
ejpam-5602	473	17	=	=	SYM
ejpam-5602	473	18	{	{	PUNCT
ejpam-5602	473	19	u	u	NOUN
ejpam-5602	473	20	,	,	PUNCT
ejpam-5602	473	21	v	v	NOUN
ejpam-5602	473	22	}	}	PUNCT
ejpam-5602	473	23	and	and	CCONJ
ejpam-5602	473	24	u	u	NOUN
ejpam-5602	473	25	v	v	ADP
ejpam-5602	473	26	∈	∈	PROPN
ejpam-5602	473	27	e(g	e(g	PROPN
ejpam-5602	473	28	)	)	PUNCT
ejpam-5602	473	29	.	.	PUNCT
ejpam-5602	474	1	if	if	SCONJ
ejpam-5602	474	2	w	w	PROPN
ejpam-5602	474	3	∈	∈	PROPN
ejpam-5602	474	4	(	(	PUNCT
ejpam-5602	474	5	d	d	X
ejpam-5602	474	6	∩	∩	ADJ
ejpam-5602	474	7	v	v	X
ejpam-5602	474	8	(	(	PUNCT
ejpam-5602	474	9	g	g	NOUN
ejpam-5602	474	10	)	)	PUNCT
ejpam-5602	474	11	)	)	PUNCT
ejpam-5602	474	12	\	\	NOUN
ejpam-5602	474	13	{	{	PUNCT
ejpam-5602	474	14	u	u	NOUN
ejpam-5602	474	15	,	,	PUNCT
ejpam-5602	474	16	v	v	NOUN
ejpam-5602	474	17	}	}	PUNCT
ejpam-5602	474	18	,	,	PUNCT
ejpam-5602	474	19	then	then	ADV
ejpam-5602	474	20	w	w	ADP
ejpam-5602	474	21	/∈	/∈	PUNCT
ejpam-5602	475	1	d	d	NOUN
ejpam-5602	475	2	and	and	CCONJ
ejpam-5602	475	3	|d	|d	NOUN
ejpam-5602	475	4	∩ngg(w)|	∩ngg(w)|	PUNCT
ejpam-5602	475	5	=	=	SYM
ejpam-5602	475	6	1	1	NUM
ejpam-5602	475	7	,	,	PUNCT
ejpam-5602	475	8	a	a	DET
ejpam-5602	475	9	contradiction	contradiction	NOUN
ejpam-5602	475	10	.	.	PUNCT
ejpam-5602	476	1	case	case	NOUN
ejpam-5602	476	2	2	2	NUM
ejpam-5602	476	3	:	:	PUNCT
ejpam-5602	476	4	gg	gg	NOUN
ejpam-5602	476	5	has	have	VERB
ejpam-5602	476	6	a	a	DET
ejpam-5602	476	7	2	2	NUM
ejpam-5602	476	8	-	-	PUNCT
ejpam-5602	476	9	dominating	dominating	NOUN
ejpam-5602	476	10	set	set	NOUN
ejpam-5602	476	11	d	d	NOUN
ejpam-5602	476	12	with	with	ADP
ejpam-5602	476	13	|d|	|d|	PROPN
ejpam-5602	476	14	=	=	SYM
ejpam-5602	476	15	3	3	NUM
ejpam-5602	476	16	and	and	CCONJ
ejpam-5602	476	17	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	476	18	is	be	AUX
ejpam-5602	476	19	connected	connect	VERB
ejpam-5602	476	20	.	.	PUNCT
ejpam-5602	477	1	following	follow	VERB
ejpam-5602	477	2	a	a	DET
ejpam-5602	477	3	similar	similar	ADJ
ejpam-5602	477	4	argument	argument	NOUN
ejpam-5602	477	5	,	,	PUNCT
ejpam-5602	477	6	d	d	ADP
ejpam-5602	477	7	∩	∩	ADJ
ejpam-5602	477	8	v	v	X
ejpam-5602	477	9	(	(	PUNCT
ejpam-5602	477	10	g	g	NOUN
ejpam-5602	477	11	)	)	PUNCT
ejpam-5602	477	12	̸=	̸=	PROPN
ejpam-5602	477	13	∅	∅	NOUN
ejpam-5602	477	14	and	and	CCONJ
ejpam-5602	477	15	d	d	PROPN
ejpam-5602	477	16	∩	∩	ADJ
ejpam-5602	477	17	v	v	X
ejpam-5602	477	18	(	(	PUNCT
ejpam-5602	477	19	g	g	NOUN
ejpam-5602	477	20	)	)	PUNCT
ejpam-5602	477	21	̸=	̸=	PROPN
ejpam-5602	477	22	∅.	∅.	ADP
ejpam-5602	477	23	assume	assume	VERB
ejpam-5602	477	24	|d	|d	NOUN
ejpam-5602	477	25	∩	∩	ADJ
ejpam-5602	477	26	v	v	NOUN
ejpam-5602	477	27	(	(	PUNCT
ejpam-5602	477	28	g)|	g)|	NOUN
ejpam-5602	477	29	=	=	SYM
ejpam-5602	477	30	2	2	NUM
ejpam-5602	477	31	and	and	CCONJ
ejpam-5602	477	32	|d	|d	NOUN
ejpam-5602	477	33	∩	∩	ADJ
ejpam-5602	477	34	v	v	NOUN
ejpam-5602	477	35	(	(	PUNCT
ejpam-5602	477	36	g)|	g)|	NOUN
ejpam-5602	477	37	=	=	SYM
ejpam-5602	477	38	1	1	NUM
ejpam-5602	477	39	,	,	PUNCT
ejpam-5602	477	40	say	say	VERB
ejpam-5602	477	41	d	d	ADP
ejpam-5602	477	42	∩	∩	ADJ
ejpam-5602	477	43	v	v	X
ejpam-5602	477	44	(	(	PUNCT
ejpam-5602	477	45	g	g	NOUN
ejpam-5602	477	46	)	)	PUNCT
ejpam-5602	477	47	=	=	SYM
ejpam-5602	477	48	{	{	PUNCT
ejpam-5602	477	49	u	u	NOUN
ejpam-5602	477	50	,	,	PUNCT
ejpam-5602	477	51	v	v	NOUN
ejpam-5602	477	52	}	}	PUNCT
ejpam-5602	477	53	and	and	CCONJ
ejpam-5602	477	54	d	d	PROPN
ejpam-5602	477	55	∩	∩	ADJ
ejpam-5602	477	56	v	v	X
ejpam-5602	477	57	(	(	PUNCT
ejpam-5602	477	58	g	g	NOUN
ejpam-5602	477	59	)	)	PUNCT
ejpam-5602	477	60	=	=	PRON
ejpam-5602	477	61	{	{	PUNCT
ejpam-5602	477	62	w	w	NOUN
ejpam-5602	477	63	}	}	PUNCT
ejpam-5602	477	64	.	.	PUNCT
ejpam-5602	478	1	since	since	SCONJ
ejpam-5602	478	2	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	478	3	is	be	AUX
ejpam-5602	478	4	connected	connect	VERB
ejpam-5602	478	5	,	,	PUNCT
ejpam-5602	478	6	either	either	CCONJ
ejpam-5602	478	7	u	u	PROPN
ejpam-5602	478	8	=	=	PROPN
ejpam-5602	478	9	w	w	PROPN
ejpam-5602	478	10	and	and	CCONJ
ejpam-5602	478	11	d∩ngg(v	d∩ngg(v	PROPN
ejpam-5602	478	12	)	)	PUNCT
ejpam-5602	479	1	=	=	PRON
ejpam-5602	479	2	{	{	PUNCT
ejpam-5602	479	3	v	v	NOUN
ejpam-5602	479	4	}	}	PUNCT
ejpam-5602	479	5	or	or	CCONJ
ejpam-5602	479	6	v	v	ADP
ejpam-5602	479	7	=	=	SYM
ejpam-5602	479	8	w	w	PROPN
ejpam-5602	479	9	and	and	CCONJ
ejpam-5602	479	10	d∩ngg(u	d∩ngg(u	PROPN
ejpam-5602	479	11	)	)	PUNCT
ejpam-5602	479	12	=	=	SYM
ejpam-5602	479	13	{	{	PUNCT
ejpam-5602	479	14	u	u	NOUN
ejpam-5602	479	15	}	}	PUNCT
ejpam-5602	479	16	,	,	PUNCT
ejpam-5602	479	17	which	which	PRON
ejpam-5602	479	18	is	be	AUX
ejpam-5602	479	19	impossible	impossible	ADJ
ejpam-5602	479	20	.	.	PUNCT
ejpam-5602	480	1	case	case	NOUN
ejpam-5602	480	2	3	3	X
ejpam-5602	480	3	:	:	PUNCT
ejpam-5602	480	4	gg	gg	NOUN
ejpam-5602	480	5	contains	contain	VERB
ejpam-5602	480	6	a	a	DET
ejpam-5602	480	7	2	2	NUM
ejpam-5602	480	8	-	-	PUNCT
ejpam-5602	480	9	dominating	dominating	NOUN
ejpam-5602	480	10	set	set	NOUN
ejpam-5602	480	11	d	d	NOUN
ejpam-5602	480	12	with	with	ADP
ejpam-5602	480	13	|d|	|d|	PROPN
ejpam-5602	480	14	=	=	PROPN
ejpam-5602	480	15	4	4	NUM
ejpam-5602	480	16	such	such	ADJ
ejpam-5602	480	17	that	that	SCONJ
ejpam-5602	480	18	there	there	PRON
ejpam-5602	480	19	exists	exist	VERB
ejpam-5602	480	20	v	v	ADP
ejpam-5602	480	21	∈	∈	PROPN
ejpam-5602	480	22	d	d	NOUN
ejpam-5602	480	23	for	for	ADP
ejpam-5602	480	24	which	which	PRON
ejpam-5602	480	25	uv	uv	NOUN
ejpam-5602	480	26	∈	∈	PROPN
ejpam-5602	480	27	e(gg	e(gg	PROPN
ejpam-5602	480	28	)	)	PUNCT
ejpam-5602	480	29	for	for	ADP
ejpam-5602	480	30	all	all	DET
ejpam-5602	480	31	u	u	PROPN
ejpam-5602	480	32	∈	∈	PROPN
ejpam-5602	480	33	v	v	NOUN
ejpam-5602	480	34	(	(	PUNCT
ejpam-5602	480	35	gg	gg	NOUN
ejpam-5602	480	36	)	)	PUNCT
ejpam-5602	480	37	\	\	PUNCT
ejpam-5602	481	1	d	d	NOUN
ejpam-5602	481	2	with	with	ADP
ejpam-5602	481	3	|ngg(u	|ngg(u	NOUN
ejpam-5602	481	4	)	)	PUNCT
ejpam-5602	481	5	∩	∩	NOUN
ejpam-5602	481	6	d|	d|	PROPN
ejpam-5602	481	7	=	=	SYM
ejpam-5602	481	8	2	2	X
ejpam-5602	481	9	.	.	PUNCT
ejpam-5602	482	1	moreover	moreover	ADV
ejpam-5602	482	2	,	,	PUNCT
ejpam-5602	482	3	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	482	4	is	be	AUX
ejpam-5602	482	5	connected	connect	VERB
ejpam-5602	482	6	and	and	CCONJ
ejpam-5602	482	7	xv	xv	X
ejpam-5602	482	8	∈	∈	PROPN
ejpam-5602	482	9	e(gg	e(gg	PROPN
ejpam-5602	482	10	)	)	PUNCT
ejpam-5602	482	11	for	for	ADP
ejpam-5602	482	12	every	every	DET
ejpam-5602	482	13	x	x	SYM
ejpam-5602	482	14	∈	∈	PROPN
ejpam-5602	482	15	d	d	X
ejpam-5602	482	16	\	\	PROPN
ejpam-5602	482	17	{	{	PUNCT
ejpam-5602	482	18	v	v	NOUN
ejpam-5602	482	19	}	}	PUNCT
ejpam-5602	482	20	with	with	ADP
ejpam-5602	482	21	|ngg(x	|ngg(x	NOUN
ejpam-5602	482	22	)	)	PUNCT
ejpam-5602	482	23	∩	∩	NOUN
ejpam-5602	482	24	d|	d|	PROPN
ejpam-5602	483	1	=	=	SYM
ejpam-5602	483	2	1	1	X
ejpam-5602	483	3	.	.	PUNCT
ejpam-5602	484	1	if	if	SCONJ
ejpam-5602	484	2	|d	|d	NOUN
ejpam-5602	484	3	∩	∩	ADJ
ejpam-5602	484	4	v	v	X
ejpam-5602	484	5	(	(	PUNCT
ejpam-5602	484	6	g)|	g)|	VERB
ejpam-5602	484	7	≥	≥	NOUN
ejpam-5602	484	8	3	3	NUM
ejpam-5602	484	9	,	,	PUNCT
ejpam-5602	484	10	then	then	ADV
ejpam-5602	484	11	since	since	SCONJ
ejpam-5602	484	12	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	484	13	is	be	AUX
ejpam-5602	484	14	connected	connect	VERB
ejpam-5602	484	15	,	,	PUNCT
ejpam-5602	484	16	there	there	PRON
ejpam-5602	484	17	exists	exist	VERB
ejpam-5602	484	18	u	u	PROPN
ejpam-5602	484	19	∈	∈	PROPN
ejpam-5602	484	20	d	d	PROPN
ejpam-5602	484	21	∩	∩	ADJ
ejpam-5602	484	22	v	v	X
ejpam-5602	484	23	(	(	PUNCT
ejpam-5602	484	24	g	g	NOUN
ejpam-5602	484	25	)	)	PUNCT
ejpam-5602	484	26	such	such	ADJ
ejpam-5602	484	27	that	that	PRON
ejpam-5602	484	28	u	u	NOUN
ejpam-5602	484	29	/∈	/∈	PROPN
ejpam-5602	485	1	d	d	NOUN
ejpam-5602	485	2	and	and	CCONJ
ejpam-5602	485	3	|ngg(u	|ngg(u	PROPN
ejpam-5602	485	4	)	)	PUNCT
ejpam-5602	485	5	∩	∩	NOUN
ejpam-5602	485	6	d|	d|	PROPN
ejpam-5602	485	7	=	=	SYM
ejpam-5602	485	8	1	1	NUM
ejpam-5602	485	9	,	,	PUNCT
ejpam-5602	485	10	a	a	DET
ejpam-5602	485	11	contradiction	contradiction	NOUN
ejpam-5602	485	12	.	.	PUNCT
ejpam-5602	486	1	thus	thus	ADV
ejpam-5602	486	2	,	,	PUNCT
ejpam-5602	486	3	|d	|d	NOUN
ejpam-5602	486	4	∩	∩	ADJ
ejpam-5602	486	5	v	v	NOUN
ejpam-5602	486	6	(	(	PUNCT
ejpam-5602	486	7	g)|	g)|	NOUN
ejpam-5602	486	8	=	=	SYM
ejpam-5602	486	9	2	2	NUM
ejpam-5602	486	10	and	and	CCONJ
ejpam-5602	486	11	|d	|d	NOUN
ejpam-5602	486	12	∩	∩	ADJ
ejpam-5602	486	13	v	v	NOUN
ejpam-5602	486	14	(	(	PUNCT
ejpam-5602	486	15	g)|	g)|	NOUN
ejpam-5602	486	16	=	=	SYM
ejpam-5602	486	17	2	2	X
ejpam-5602	486	18	.	.	X
ejpam-5602	486	19	assume	assume	VERB
ejpam-5602	486	20	,	,	PUNCT
ejpam-5602	486	21	v	v	NOUN
ejpam-5602	486	22	∈	∈	PROPN
ejpam-5602	486	23	d	d	NOUN
ejpam-5602	486	24	∩	∩	ADJ
ejpam-5602	486	25	v	v	X
ejpam-5602	486	26	(	(	PUNCT
ejpam-5602	486	27	g	g	NOUN
ejpam-5602	486	28	)	)	PUNCT
ejpam-5602	486	29	.	.	PUNCT
ejpam-5602	487	1	let	let	VERB
ejpam-5602	487	2	d	d	NOUN
ejpam-5602	487	3	∩	∩	ADJ
ejpam-5602	487	4	v	v	X
ejpam-5602	487	5	(	(	PUNCT
ejpam-5602	487	6	g	g	NOUN
ejpam-5602	487	7	)	)	PUNCT
ejpam-5602	487	8	=	=	SYM
ejpam-5602	487	9	{	{	PUNCT
ejpam-5602	487	10	x	x	NOUN
ejpam-5602	487	11	,	,	PUNCT
ejpam-5602	487	12	v	v	NOUN
ejpam-5602	487	13	}	}	PUNCT
ejpam-5602	487	14	.	.	PUNCT
ejpam-5602	488	1	since	since	SCONJ
ejpam-5602	488	2	⟨d⟩	⟨d⟩	PROPN
ejpam-5602	488	3	is	be	AUX
ejpam-5602	488	4	connected	connect	VERB
ejpam-5602	488	5	,	,	PUNCT
ejpam-5602	488	6	d	d	X
ejpam-5602	488	7	=	=	PRON
ejpam-5602	488	8	{	{	PUNCT
ejpam-5602	488	9	x	x	NOUN
ejpam-5602	488	10	,	,	PUNCT
ejpam-5602	488	11	v	v	NOUN
ejpam-5602	488	12	,	,	PUNCT
ejpam-5602	488	13	x	x	NOUN
ejpam-5602	488	14	,	,	PUNCT
ejpam-5602	488	15	v	v	NOUN
ejpam-5602	488	16	}	}	PUNCT
ejpam-5602	488	17	,	,	PUNCT
ejpam-5602	488	18	xv	xv	PROPN
ejpam-5602	488	19	/∈	/∈	PUNCT
ejpam-5602	488	20	e(gg	e(gg	NUM
ejpam-5602	488	21	)	)	PUNCT
ejpam-5602	488	22	,	,	PUNCT
ejpam-5602	488	23	and	and	CCONJ
ejpam-5602	488	24	ngg(x	ngg(x	X
ejpam-5602	488	25	)	)	PUNCT
ejpam-5602	488	26	∩d	∩d	VERB
ejpam-5602	489	1	=	=	PUNCT
ejpam-5602	489	2	{	{	PUNCT
ejpam-5602	489	3	x	x	NOUN
ejpam-5602	489	4	}	}	PUNCT
ejpam-5602	489	5	.	.	PUNCT
ejpam-5602	490	1	this	this	PRON
ejpam-5602	490	2	is	be	AUX
ejpam-5602	490	3	a	a	DET
ejpam-5602	490	4	contradiction	contradiction	NOUN
ejpam-5602	490	5	.	.	PUNCT
ejpam-5602	491	1	the	the	DET
ejpam-5602	491	2	above	above	ADJ
ejpam-5602	491	3	contradictions	contradiction	NOUN
ejpam-5602	491	4	imply	imply	VERB
ejpam-5602	491	5	that	that	SCONJ
ejpam-5602	491	6	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	491	7	)	)	PUNCT
ejpam-5602	491	8	̸=	̸=	PROPN
ejpam-5602	491	9	5	5	NUM
ejpam-5602	491	10	.	.	PUNCT
ejpam-5602	492	1	finally	finally	ADV
ejpam-5602	492	2	,	,	PUNCT
ejpam-5602	492	3	observe	observe	VERB
ejpam-5602	492	4	that	that	SCONJ
ejpam-5602	492	5	if	if	SCONJ
ejpam-5602	492	6	g	g	NOUN
ejpam-5602	492	7	=	=	NOUN
ejpam-5602	492	8	p2	p2	NOUN
ejpam-5602	492	9	,	,	PUNCT
ejpam-5602	492	10	then	then	ADV
ejpam-5602	492	11	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	492	12	)	)	PUNCT
ejpam-5602	492	13	=	=	SYM
ejpam-5602	492	14	γtdi(p4	γtdi(p4	NOUN
ejpam-5602	492	15	)	)	PUNCT
ejpam-5602	492	16	=	=	SYM
ejpam-5602	492	17	6	6	NUM
ejpam-5602	492	18	,	,	PUNCT
ejpam-5602	492	19	showing	show	VERB
ejpam-5602	492	20	that	that	SCONJ
ejpam-5602	492	21	the	the	DET
ejpam-5602	492	22	bound	bind	VERB
ejpam-5602	492	23	provided	provide	VERB
ejpam-5602	492	24	in	in	ADP
ejpam-5602	492	25	(	(	PUNCT
ejpam-5602	492	26	ii	ii	NOUN
ejpam-5602	492	27	)	)	PUNCT
ejpam-5602	492	28	is	be	AUX
ejpam-5602	492	29	sharp	sharp	ADJ
ejpam-5602	492	30	.	.	PUNCT
ejpam-5602	493	1	■	■	PUNCT
ejpam-5602	493	2	the	the	DET
ejpam-5602	493	3	following	follow	VERB
ejpam-5602	493	4	proposition	proposition	NOUN
ejpam-5602	493	5	is	be	AUX
ejpam-5602	493	6	clear	clear	ADJ
ejpam-5602	493	7	.	.	PUNCT
ejpam-5602	494	1	proposition	proposition	NOUN
ejpam-5602	494	2	12	12	NUM
ejpam-5602	494	3	.	.	PUNCT
ejpam-5602	495	1	let	let	VERB
ejpam-5602	495	2	g	g	PRON
ejpam-5602	495	3	be	be	AUX
ejpam-5602	495	4	a	a	DET
ejpam-5602	495	5	nontrivial	nontrivial	ADJ
ejpam-5602	495	6	connected	connect	VERB
ejpam-5602	495	7	graph	graph	NOUN
ejpam-5602	495	8	.	.	PUNCT
ejpam-5602	496	1	then	then	ADV
ejpam-5602	496	2	f	f	PROPN
ejpam-5602	496	3	=	=	SYM
ejpam-5602	496	4	(	(	PUNCT
ejpam-5602	496	5	v0	v0	PROPN
ejpam-5602	496	6	,	,	PUNCT
ejpam-5602	496	7	v1	v1	NOUN
ejpam-5602	496	8	,	,	PUNCT
ejpam-5602	496	9	v2	v2	PROPN
ejpam-5602	496	10	,	,	PUNCT
ejpam-5602	496	11	v3	v3	PROPN
ejpam-5602	496	12	)	)	PUNCT
ejpam-5602	496	13	is	be	AUX
ejpam-5602	496	14	a	a	DET
ejpam-5602	496	15	tdidf	tdidf	NOUN
ejpam-5602	496	16	on	on	ADP
ejpam-5602	496	17	gg	gg	PROPN
ejpam-5602	496	18	if	if	SCONJ
ejpam-5602	497	1	and	and	CCONJ
ejpam-5602	497	2	only	only	ADV
ejpam-5602	497	3	if	if	SCONJ
ejpam-5602	497	4	each	each	PRON
ejpam-5602	497	5	of	of	ADP
ejpam-5602	497	6	the	the	DET
ejpam-5602	497	7	following	follow	VERB
ejpam-5602	497	8	holds	hold	VERB
ejpam-5602	497	9	:	:	PUNCT
ejpam-5602	497	10	(	(	PUNCT
ejpam-5602	497	11	i	i	NOUN
ejpam-5602	497	12	)	)	PUNCT
ejpam-5602	497	13	for	for	ADP
ejpam-5602	497	14	each	each	PRON
ejpam-5602	497	15	v	v	X
ejpam-5602	497	16	∈	∈	PROPN
ejpam-5602	497	17	(	(	PUNCT
ejpam-5602	497	18	v0	v0	NOUN
ejpam-5602	497	19	∪	∪	X
ejpam-5602	497	20	v1	v1	NOUN
ejpam-5602	497	21	)	)	PUNCT
ejpam-5602	497	22	∩	∩	ADJ
ejpam-5602	497	23	v	v	X
ejpam-5602	497	24	(	(	PUNCT
ejpam-5602	497	25	g	g	NOUN
ejpam-5602	497	26	)	)	PUNCT
ejpam-5602	497	27	,	,	PUNCT
ejpam-5602	497	28	either	either	CCONJ
ejpam-5602	497	29	f	f	PROPN
ejpam-5602	497	30	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	497	31	]	]	X
ejpam-5602	497	32	)	)	PUNCT
ejpam-5602	497	33	≥	≥	NOUN
ejpam-5602	497	34	3	3	NUM
ejpam-5602	497	35	or	or	CCONJ
ejpam-5602	497	36	f	f	PROPN
ejpam-5602	497	37	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	497	38	]	]	X
ejpam-5602	497	39	)	)	PUNCT
ejpam-5602	497	40	<	<	X
ejpam-5602	497	41	3	3	NUM
ejpam-5602	497	42	and	and	CCONJ
ejpam-5602	497	43	3−	3−	NUM
ejpam-5602	497	44	f	f	X
ejpam-5602	497	45	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	497	46	]	]	X
ejpam-5602	497	47	)	)	PUNCT
ejpam-5602	497	48	≤	≤	NUM
ejpam-5602	497	49	f(v	f(v	NOUN
ejpam-5602	497	50	)	)	PUNCT
ejpam-5602	497	51	;	;	PUNCT
ejpam-5602	497	52	(	(	PUNCT
ejpam-5602	497	53	ii	ii	NOUN
ejpam-5602	497	54	)	)	PUNCT
ejpam-5602	497	55	for	for	ADP
ejpam-5602	497	56	each	each	PRON
ejpam-5602	497	57	v	v	X
ejpam-5602	497	58	∈	∈	PROPN
ejpam-5602	497	59	(	(	PUNCT
ejpam-5602	497	60	v0	v0	NOUN
ejpam-5602	497	61	∪	∪	X
ejpam-5602	497	62	v1	v1	NOUN
ejpam-5602	497	63	)	)	PUNCT
ejpam-5602	497	64	∩	∩	ADJ
ejpam-5602	497	65	v	v	X
ejpam-5602	497	66	(	(	PUNCT
ejpam-5602	497	67	g	g	NOUN
ejpam-5602	497	68	)	)	PUNCT
ejpam-5602	497	69	,	,	PUNCT
ejpam-5602	497	70	either	either	CCONJ
ejpam-5602	497	71	f	f	PROPN
ejpam-5602	497	72	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	497	73	]	]	X
ejpam-5602	497	74	)	)	PUNCT
ejpam-5602	497	75	≥	≥	NOUN
ejpam-5602	497	76	3	3	NUM
ejpam-5602	497	77	or	or	CCONJ
ejpam-5602	497	78	f	f	PROPN
ejpam-5602	497	79	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	497	80	]	]	X
ejpam-5602	497	81	)	)	PUNCT
ejpam-5602	497	82	<	<	X
ejpam-5602	497	83	3	3	NUM
ejpam-5602	497	84	and	and	CCONJ
ejpam-5602	497	85	3−	3−	NUM
ejpam-5602	497	86	f	f	X
ejpam-5602	497	87	|g(ng[v	|g(ng[v	PROPN
ejpam-5602	497	88	]	]	X
ejpam-5602	497	89	)	)	PUNCT
ejpam-5602	497	90	≤	≤	NUM
ejpam-5602	497	91	f(v	f(v	NOUN
ejpam-5602	497	92	)	)	PUNCT
ejpam-5602	497	93	;	;	PUNCT
ejpam-5602	497	94	(	(	PUNCT
ejpam-5602	497	95	iii	iii	X
ejpam-5602	497	96	)	)	PUNCT
ejpam-5602	497	97	for	for	ADP
ejpam-5602	497	98	each	each	DET
ejpam-5602	497	99	v	v	NUM
ejpam-5602	497	100	∈	∈	PROPN
ejpam-5602	497	101	v	v	NOUN
ejpam-5602	497	102	(	(	PUNCT
ejpam-5602	497	103	g	g	NOUN
ejpam-5602	497	104	)	)	PUNCT
ejpam-5602	497	105	∩	∩	NOUN
ejpam-5602	497	106	(	(	PUNCT
ejpam-5602	497	107	v1	v1	VERB
ejpam-5602	497	108	∪	∪	ADP
ejpam-5602	497	109	v2	v2	PROPN
ejpam-5602	497	110	∪	∪	X
ejpam-5602	497	111	v3	v3	PROPN
ejpam-5602	497	112	)	)	PUNCT
ejpam-5602	497	113	,	,	PUNCT
ejpam-5602	497	114	v	v	X
ejpam-5602	497	115	/∈	/∈	PROPN
ejpam-5602	497	116	v0	v0	NOUN
ejpam-5602	497	117	whenever	whenever	SCONJ
ejpam-5602	497	118	ng(v	ng(v	NOUN
ejpam-5602	497	119	)	)	PUNCT
ejpam-5602	497	120	⊆	⊆	NUM
ejpam-5602	497	121	v0	v0	NOUN
ejpam-5602	497	122	;	;	PUNCT
ejpam-5602	497	123	s.j.l	s.j.l	NOUN
ejpam-5602	497	124	.	.	PUNCT
ejpam-5602	497	125	sumbalan	sumbalan	PROPN
ejpam-5602	497	126	,	,	PUNCT
ejpam-5602	497	127	s.m	s.m	PROPN
ejpam-5602	497	128	.	.	PROPN
ejpam-5602	497	129	menchavez	menchavez	PROPN
ejpam-5602	497	130	,	,	PUNCT
ejpam-5602	497	131	f.p	f.p	PROPN
ejpam-5602	497	132	.	.	PROPN
ejpam-5602	497	133	jamil	jamil	PROPN
ejpam-5602	497	134	/	/	SYM
ejpam-5602	497	135	eur	eur	PROPN
ejpam-5602	497	136	.	.	PUNCT
ejpam-5602	498	1	j.	j.	PROPN
ejpam-5602	498	2	pure	pure	PROPN
ejpam-5602	498	3	appl	appl	PROPN
ejpam-5602	498	4	.	.	PROPN
ejpam-5602	498	5	math	math	PROPN
ejpam-5602	498	6	,	,	PUNCT
ejpam-5602	498	7	18	18	NUM
ejpam-5602	498	8	(	(	PUNCT
ejpam-5602	498	9	1	1	NUM
ejpam-5602	498	10	)	)	PUNCT
ejpam-5602	498	11	(	(	PUNCT
ejpam-5602	498	12	2025	2025	NUM
ejpam-5602	498	13	)	)	PUNCT
ejpam-5602	498	14	,	,	PUNCT
ejpam-5602	498	15	5602	5602	NUM
ejpam-5602	498	16	15	15	NUM
ejpam-5602	498	17	of	of	ADP
ejpam-5602	498	18	18	18	NUM
ejpam-5602	498	19	(	(	PUNCT
ejpam-5602	498	20	iv	iv	NOUN
ejpam-5602	498	21	)	)	PUNCT
ejpam-5602	498	22	for	for	ADP
ejpam-5602	498	23	each	each	DET
ejpam-5602	498	24	v	v	NUM
ejpam-5602	498	25	∈	∈	PROPN
ejpam-5602	498	26	v	v	NOUN
ejpam-5602	498	27	(	(	PUNCT
ejpam-5602	498	28	g	g	NOUN
ejpam-5602	498	29	)	)	PUNCT
ejpam-5602	498	30	∩	∩	NOUN
ejpam-5602	498	31	(	(	PUNCT
ejpam-5602	498	32	v1	v1	VERB
ejpam-5602	498	33	∪	∪	ADP
ejpam-5602	498	34	v2	v2	PROPN
ejpam-5602	498	35	∪	∪	X
ejpam-5602	498	36	v3	v3	PROPN
ejpam-5602	498	37	)	)	PUNCT
ejpam-5602	498	38	,	,	PUNCT
ejpam-5602	498	39	v	v	X
ejpam-5602	498	40	/∈	/∈	PROPN
ejpam-5602	498	41	v0	v0	NOUN
ejpam-5602	499	1	whenever	whenever	SCONJ
ejpam-5602	499	2	ng(v	ng(v	NOUN
ejpam-5602	499	3	)	)	PUNCT
ejpam-5602	499	4	⊆	⊆	NUM
ejpam-5602	499	5	v0	v0	NOUN
ejpam-5602	499	6	.	.	NOUN
ejpam-5602	499	7	2	2	NUM
ejpam-5602	499	8	v4	v4	NOUN
ejpam-5602	499	9	1	1	NUM
ejpam-5602	499	10	v1	v1	NOUN
ejpam-5602	499	11	1	1	NUM
ejpam-5602	499	12	v2	v2	PROPN
ejpam-5602	499	13	1	1	NUM
ejpam-5602	499	14	v3	v3	PROPN
ejpam-5602	499	15	1	1	NUM
ejpam-5602	499	16	v1	v1	PROPN
ejpam-5602	499	17	1	1	NUM
ejpam-5602	499	18	v3	v3	PROPN
ejpam-5602	499	19	1	1	NUM
ejpam-5602	499	20	u1	u1	NOUN
ejpam-5602	499	21	1	1	NUM
ejpam-5602	499	22	u2	u2	PROPN
ejpam-5602	499	23	1	1	NUM
ejpam-5602	499	24	u3	u3	NOUN
ejpam-5602	499	25	1	1	NUM
ejpam-5602	499	26	u4	u4	PROPN
ejpam-5602	499	27	1	1	NUM
ejpam-5602	499	28	u2	u2	PROPN
ejpam-5602	499	29	1	1	NUM
ejpam-5602	499	30	u1	u1	NOUN
ejpam-5602	499	31	1	1	NUM
ejpam-5602	499	32	u4	u4	PROPN
ejpam-5602	499	33	1	1	NUM
ejpam-5602	499	34	u3	u3	NOUN
ejpam-5602	499	35	0v2	0v2	NUM
ejpam-5602	499	36	0	0	NUM
ejpam-5602	499	37	v4	v4	NOUN
ejpam-5602	499	38	figure	figure	NOUN
ejpam-5602	499	39	3	3	NUM
ejpam-5602	499	40	:	:	PUNCT
ejpam-5602	499	41	the	the	DET
ejpam-5602	499	42	complementary	complementary	ADJ
ejpam-5602	499	43	prisms	prism	NOUN
ejpam-5602	499	44	p4p	p4p	PROPN
ejpam-5602	499	45	4	4	NUM
ejpam-5602	499	46	and	and	CCONJ
ejpam-5602	499	47	c4c4	c4c4	ADJ
ejpam-5602	499	48	proposition	proposition	NOUN
ejpam-5602	499	49	13	13	NUM
ejpam-5602	499	50	.	.	PUNCT
ejpam-5602	500	1	let	let	VERB
ejpam-5602	500	2	g	g	PRON
ejpam-5602	500	3	be	be	AUX
ejpam-5602	500	4	a	a	DET
ejpam-5602	500	5	nontrivial	nontrivial	ADJ
ejpam-5602	500	6	connected	connect	VERB
ejpam-5602	500	7	graph	graph	NOUN
ejpam-5602	500	8	of	of	ADP
ejpam-5602	500	9	order	order	NOUN
ejpam-5602	500	10	n.	n.	NOUN
ejpam-5602	500	11	then	then	ADV
ejpam-5602	500	12	6	6	NUM
ejpam-5602	500	13	≤	≤	ADV
ejpam-5602	500	14	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	500	15	)	)	PUNCT
ejpam-5602	500	16	≤	≤	NUM
ejpam-5602	500	17	3n	3n	NUM
ejpam-5602	500	18	.	.	PUNCT
ejpam-5602	501	1	(	(	PUNCT
ejpam-5602	501	2	4	4	X
ejpam-5602	501	3	)	)	PUNCT
ejpam-5602	501	4	moreover	moreover	ADV
ejpam-5602	501	5	,	,	PUNCT
ejpam-5602	501	6	if	if	SCONJ
ejpam-5602	501	7	γ(g	γ(g	PROPN
ejpam-5602	501	8	)	)	PUNCT
ejpam-5602	501	9	̸=	̸=	PROPN
ejpam-5602	501	10	1	1	NUM
ejpam-5602	501	11	and	and	CCONJ
ejpam-5602	501	12	γ(g	γ(g	PROPN
ejpam-5602	501	13	)	)	PUNCT
ejpam-5602	501	14	̸=	̸=	PROPN
ejpam-5602	501	15	1	1	NUM
ejpam-5602	501	16	,	,	PUNCT
ejpam-5602	501	17	then	then	ADV
ejpam-5602	501	18	1	1	NUM
ejpam-5602	501	19	+	+	NUM
ejpam-5602	501	20	max{γtdi(g	max{γtdi(g	NOUN
ejpam-5602	501	21	)	)	PUNCT
ejpam-5602	501	22	,	,	PUNCT
ejpam-5602	501	23	γtdi(g	γtdi(g	PROPN
ejpam-5602	501	24	)	)	PUNCT
ejpam-5602	501	25	}	}	PUNCT
ejpam-5602	501	26	≤	≤	NUM
ejpam-5602	501	27	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	501	28	)	)	PUNCT
ejpam-5602	501	29	≤	≤	NUM
ejpam-5602	501	30	2n	2n	NUM
ejpam-5602	501	31	.	.	PUNCT
ejpam-5602	502	1	(	(	PUNCT
ejpam-5602	502	2	5	5	X
ejpam-5602	502	3	)	)	PUNCT
ejpam-5602	502	4	these	these	DET
ejpam-5602	502	5	bounds	bound	NOUN
ejpam-5602	502	6	are	be	AUX
ejpam-5602	502	7	sharp	sharp	ADJ
ejpam-5602	502	8	.	.	PUNCT
ejpam-5602	503	1	proof	proof	NOUN
ejpam-5602	503	2	:	:	PUNCT
ejpam-5602	503	3	the	the	DET
ejpam-5602	503	4	left	left	ADJ
ejpam-5602	503	5	-	-	PUNCT
ejpam-5602	503	6	hand	hand	NOUN
ejpam-5602	503	7	inequality	inequality	NOUN
ejpam-5602	503	8	in	in	ADP
ejpam-5602	503	9	inequality	inequality	NOUN
ejpam-5602	503	10	4	4	NUM
ejpam-5602	503	11	is	be	AUX
ejpam-5602	503	12	a	a	DET
ejpam-5602	503	13	reiteration	reiteration	NOUN
ejpam-5602	503	14	of	of	ADP
ejpam-5602	503	15	proposition	proposition	NOUN
ejpam-5602	503	16	11	11	NUM
ejpam-5602	503	17	.	.	PUNCT
ejpam-5602	504	1	by	by	ADP
ejpam-5602	504	2	proposition	proposition	NOUN
ejpam-5602	504	3	12	12	NUM
ejpam-5602	504	4	,	,	PUNCT
ejpam-5602	504	5	the	the	DET
ejpam-5602	504	6	function	function	NOUN
ejpam-5602	504	7	f	f	PROPN
ejpam-5602	504	8	=	=	SYM
ejpam-5602	504	9	(	(	PUNCT
ejpam-5602	504	10	v	v	NOUN
ejpam-5602	504	11	(	(	PUNCT
ejpam-5602	504	12	g),∅,∅	g),∅,∅	PROPN
ejpam-5602	504	13	,	,	PUNCT
ejpam-5602	504	14	v	v	NOUN
ejpam-5602	504	15	(	(	PUNCT
ejpam-5602	504	16	g	g	NOUN
ejpam-5602	504	17	)	)	PUNCT
ejpam-5602	504	18	)	)	PUNCT
ejpam-5602	505	1	∈	∈	PROPN
ejpam-5602	505	2	tdidf	tdidf	NOUN
ejpam-5602	505	3	(	(	PUNCT
ejpam-5602	505	4	gg	gg	NOUN
ejpam-5602	505	5	)	)	PUNCT
ejpam-5602	505	6	.	.	PUNCT
ejpam-5602	506	1	thus	thus	ADV
ejpam-5602	506	2	,	,	PUNCT
ejpam-5602	506	3	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	506	4	)	)	PUNCT
ejpam-5602	506	5	≤	≤	NOUN
ejpam-5602	506	6	3|v3|	3|v3|	NUM
ejpam-5602	506	7	=	=	SYM
ejpam-5602	506	8	3n	3n	NOUN
ejpam-5602	506	9	and	and	CCONJ
ejpam-5602	506	10	the	the	DET
ejpam-5602	506	11	inequality	inequality	NOUN
ejpam-5602	506	12	4	4	NUM
ejpam-5602	506	13	holds	hold	VERB
ejpam-5602	506	14	.	.	PUNCT
ejpam-5602	507	1	now	now	ADV
ejpam-5602	507	2	,	,	PUNCT
ejpam-5602	507	3	suppose	suppose	VERB
ejpam-5602	507	4	that	that	SCONJ
ejpam-5602	507	5	γ(g	γ(g	PROPN
ejpam-5602	507	6	)	)	PUNCT
ejpam-5602	507	7	̸=	̸=	PROPN
ejpam-5602	507	8	1	1	NUM
ejpam-5602	507	9	and	and	CCONJ
ejpam-5602	507	10	γ(g	γ(g	PROPN
ejpam-5602	507	11	)	)	PUNCT
ejpam-5602	507	12	̸=	̸=	PROPN
ejpam-5602	507	13	1	1	NUM
ejpam-5602	507	14	.	.	PUNCT
ejpam-5602	508	1	let	let	VERB
ejpam-5602	508	2	v0	v0	NOUN
ejpam-5602	508	3	=	=	SYM
ejpam-5602	508	4	∅	∅	NOUN
ejpam-5602	508	5	=	=	SYM
ejpam-5602	508	6	v2	v2	PROPN
ejpam-5602	508	7	=	=	SYM
ejpam-5602	508	8	v3	v3	PROPN
ejpam-5602	508	9	and	and	CCONJ
ejpam-5602	508	10	v1	v1	PROPN
ejpam-5602	508	11	=	=	SYM
ejpam-5602	508	12	v	v	NOUN
ejpam-5602	508	13	(	(	PUNCT
ejpam-5602	508	14	g	g	NOUN
ejpam-5602	508	15	)	)	PUNCT
ejpam-5602	508	16	∪	∪	NOUN
ejpam-5602	508	17	v	v	NOUN
ejpam-5602	508	18	(	(	PUNCT
ejpam-5602	508	19	g	g	NOUN
ejpam-5602	508	20	)	)	PUNCT
ejpam-5602	508	21	,	,	PUNCT
ejpam-5602	508	22	and	and	CCONJ
ejpam-5602	508	23	let	let	VERB
ejpam-5602	508	24	f	f	PROPN
ejpam-5602	508	25	=	=	SYM
ejpam-5602	508	26	(	(	PUNCT
ejpam-5602	508	27	v0	v0	PROPN
ejpam-5602	508	28	,	,	PUNCT
ejpam-5602	508	29	v1	v1	NOUN
ejpam-5602	508	30	,	,	PUNCT
ejpam-5602	508	31	v2	v2	PROPN
ejpam-5602	508	32	,	,	PUNCT
ejpam-5602	508	33	v3	v3	PROPN
ejpam-5602	508	34	)	)	PUNCT
ejpam-5602	508	35	.	.	PUNCT
ejpam-5602	509	1	for	for	ADP
ejpam-5602	509	2	each	each	DET
ejpam-5602	509	3	v	v	NUM
ejpam-5602	509	4	∈	∈	PROPN
ejpam-5602	509	5	v	v	NOUN
ejpam-5602	509	6	(	(	PUNCT
ejpam-5602	509	7	g	g	NOUN
ejpam-5602	509	8	)	)	PUNCT
ejpam-5602	509	9	,	,	PUNCT
ejpam-5602	509	10	since	since	SCONJ
ejpam-5602	509	11	v	v	NOUN
ejpam-5602	509	12	is	be	AUX
ejpam-5602	509	13	not	not	PART
ejpam-5602	509	14	an	an	DET
ejpam-5602	509	15	isolated	isolated	ADJ
ejpam-5602	509	16	vertex	vertex	NOUN
ejpam-5602	509	17	,	,	PUNCT
ejpam-5602	509	18	there	there	PRON
ejpam-5602	509	19	exists	exist	VERB
ejpam-5602	509	20	u	u	PROPN
ejpam-5602	509	21	∈	∈	PROPN
ejpam-5602	509	22	v	v	ADP
ejpam-5602	509	23	(	(	PUNCT
ejpam-5602	509	24	g	g	NOUN
ejpam-5602	509	25	)	)	PUNCT
ejpam-5602	509	26	for	for	ADP
ejpam-5602	509	27	which	which	PRON
ejpam-5602	509	28	uv	uv	NOUN
ejpam-5602	509	29	∈	∈	PROPN
ejpam-5602	509	30	e(g	e(g	PROPN
ejpam-5602	509	31	)	)	PUNCT
ejpam-5602	509	32	.	.	PUNCT
ejpam-5602	510	1	thus	thus	ADV
ejpam-5602	510	2	,	,	PUNCT
ejpam-5602	510	3	{	{	PUNCT
ejpam-5602	510	4	v	v	NOUN
ejpam-5602	510	5	,	,	PUNCT
ejpam-5602	510	6	u	u	NOUN
ejpam-5602	510	7	}	}	PUNCT
ejpam-5602	510	8	⊆	⊆	NUM
ejpam-5602	510	9	ng[v	ng[v	NOUN
ejpam-5602	510	10	]	]	PUNCT
ejpam-5602	510	11	so	so	SCONJ
ejpam-5602	510	12	that	that	SCONJ
ejpam-5602	510	13	f(ng[v	f(ng[v	PROPN
ejpam-5602	510	14	]	]	PUNCT
ejpam-5602	510	15	)	)	PUNCT
ejpam-5602	510	16	≥	≥	NOUN
ejpam-5602	511	1	2	2	NUM
ejpam-5602	511	2	.	.	PUNCT
ejpam-5602	512	1	if	if	SCONJ
ejpam-5602	512	2	f(ng[v	f(ng[v	PROPN
ejpam-5602	512	3	]	]	PUNCT
ejpam-5602	512	4	)	)	PUNCT
ejpam-5602	512	5	=	=	SYM
ejpam-5602	512	6	2	2	NUM
ejpam-5602	512	7	,	,	PUNCT
ejpam-5602	512	8	then	then	ADV
ejpam-5602	512	9	3	3	NUM
ejpam-5602	512	10	−	−	PROPN
ejpam-5602	512	11	f(ng[v	f(ng[v	PROPN
ejpam-5602	512	12	]	]	PUNCT
ejpam-5602	512	13	)	)	PUNCT
ejpam-5602	512	14	=	=	SYM
ejpam-5602	512	15	1	1	NUM
ejpam-5602	512	16	≤	≤	NUM
ejpam-5602	512	17	f(v	f(v	NOUN
ejpam-5602	512	18	)	)	PUNCT
ejpam-5602	512	19	.	.	PUNCT
ejpam-5602	513	1	thus	thus	ADV
ejpam-5602	513	2	,	,	PUNCT
ejpam-5602	513	3	condition	condition	NOUN
ejpam-5602	513	4	(	(	PUNCT
ejpam-5602	513	5	i	i	NOUN
ejpam-5602	513	6	)	)	PUNCT
ejpam-5602	513	7	in	in	ADP
ejpam-5602	513	8	proposition	proposition	NOUN
ejpam-5602	513	9	12	12	NUM
ejpam-5602	513	10	holds	hold	NOUN
ejpam-5602	513	11	.	.	PUNCT
ejpam-5602	514	1	similarly	similarly	ADV
ejpam-5602	514	2	,	,	PUNCT
ejpam-5602	514	3	since	since	SCONJ
ejpam-5602	514	4	g	g	PROPN
ejpam-5602	514	5	has	have	VERB
ejpam-5602	514	6	no	no	DET
ejpam-5602	514	7	isolated	isolated	ADJ
ejpam-5602	514	8	vertex	vertex	NOUN
ejpam-5602	514	9	,	,	PUNCT
ejpam-5602	514	10	proposition	proposition	NOUN
ejpam-5602	514	11	12(ii	12(ii	NUM
ejpam-5602	514	12	)	)	PUNCT
ejpam-5602	514	13	holds	hold	VERB
ejpam-5602	514	14	.	.	PUNCT
ejpam-5602	515	1	since	since	SCONJ
ejpam-5602	515	2	v0	v0	NOUN
ejpam-5602	515	3	=	=	SYM
ejpam-5602	515	4	∅	∅	NOUN
ejpam-5602	515	5	,	,	PUNCT
ejpam-5602	515	6	conditions	condition	NOUN
ejpam-5602	515	7	(	(	PUNCT
ejpam-5602	515	8	iii	iii	NOUN
ejpam-5602	515	9	)	)	PUNCT
ejpam-5602	515	10	and	and	CCONJ
ejpam-5602	515	11	(	(	PUNCT
ejpam-5602	515	12	iv	iv	X
ejpam-5602	515	13	)	)	PUNCT
ejpam-5602	515	14	of	of	ADP
ejpam-5602	515	15	proposition	proposition	NOUN
ejpam-5602	515	16	12	12	NUM
ejpam-5602	515	17	also	also	ADV
ejpam-5602	515	18	hold	hold	VERB
ejpam-5602	515	19	.	.	PUNCT
ejpam-5602	516	1	thus	thus	ADV
ejpam-5602	516	2	,	,	PUNCT
ejpam-5602	516	3	f	f	PROPN
ejpam-5602	516	4	∈	∈	PROPN
ejpam-5602	516	5	tdidf	tdidf	NOUN
ejpam-5602	516	6	(	(	PUNCT
ejpam-5602	516	7	gg	gg	PROPN
ejpam-5602	516	8	)	)	PUNCT
ejpam-5602	516	9	.	.	PUNCT
ejpam-5602	517	1	therefore	therefore	ADV
ejpam-5602	517	2	,	,	PUNCT
ejpam-5602	517	3	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	517	4	)	)	PUNCT
ejpam-5602	517	5	≤	≤	NOUN
ejpam-5602	517	6	2n	2n	NUM
ejpam-5602	517	7	.	.	PUNCT
ejpam-5602	518	1	wlog	wlog	PROPN
ejpam-5602	518	2	assume	assume	VERB
ejpam-5602	518	3	that	that	SCONJ
ejpam-5602	518	4	γtdi(g	γtdi(g	PROPN
ejpam-5602	518	5	)	)	PUNCT
ejpam-5602	518	6	≥	≥	NOUN
ejpam-5602	518	7	γtdi(g	γtdi(g	PROPN
ejpam-5602	518	8	)	)	PUNCT
ejpam-5602	518	9	.	.	PUNCT
ejpam-5602	519	1	let	let	VERB
ejpam-5602	519	2	f	f	PRON
ejpam-5602	519	3	be	be	AUX
ejpam-5602	519	4	a	a	DET
ejpam-5602	519	5	γtdi	γtdi	NOUN
ejpam-5602	519	6	-function	-function	NOUN
ejpam-5602	519	7	of	of	ADP
ejpam-5602	519	8	gg	gg	NOUN
ejpam-5602	519	9	.	.	PUNCT
ejpam-5602	520	1	if	if	SCONJ
ejpam-5602	520	2	v	v	INTJ
ejpam-5602	520	3	(	(	PUNCT
ejpam-5602	520	4	g	g	NOUN
ejpam-5602	520	5	)	)	PUNCT
ejpam-5602	520	6	⊆	⊆	NUM
ejpam-5602	520	7	v0	v0	NOUN
ejpam-5602	520	8	,	,	PUNCT
ejpam-5602	520	9	then	then	ADV
ejpam-5602	520	10	v	v	X
ejpam-5602	520	11	(	(	PUNCT
ejpam-5602	520	12	g	g	NOUN
ejpam-5602	520	13	)	)	PUNCT
ejpam-5602	520	14	⊆	⊆	NUM
ejpam-5602	520	15	v3	v3	PROPN
ejpam-5602	520	16	and	and	CCONJ
ejpam-5602	520	17	ωgg(f	ωgg(f	NUM
ejpam-5602	520	18	)	)	PUNCT
ejpam-5602	520	19	=	=	SYM
ejpam-5602	521	1	3|v	3|v	NUM
ejpam-5602	521	2	(	(	PUNCT
ejpam-5602	521	3	g)|	g)|	PROPN
ejpam-5602	521	4	.	.	PUNCT
ejpam-5602	522	1	however	however	ADV
ejpam-5602	522	2	,	,	PUNCT
ejpam-5602	522	3	by	by	ADP
ejpam-5602	522	4	theorem	theorem	NOUN
ejpam-5602	522	5	1	1	NUM
ejpam-5602	522	6	,	,	PUNCT
ejpam-5602	522	7	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	522	8	)	)	PUNCT
ejpam-5602	522	9	≤	≤	NOUN
ejpam-5602	522	10	|v	|v	X
ejpam-5602	522	11	(	(	PUNCT
ejpam-5602	522	12	gg)|+	gg)|+	PROPN
ejpam-5602	522	13	2−	2−	NUM
ejpam-5602	522	14	δ(gg	δ(gg	NUM
ejpam-5602	522	15	)	)	PUNCT
ejpam-5602	522	16	.	.	PUNCT
ejpam-5602	523	1	since	since	SCONJ
ejpam-5602	523	2	g	g	PROPN
ejpam-5602	523	3	and	and	CCONJ
ejpam-5602	523	4	g	g	PROPN
ejpam-5602	523	5	have	have	VERB
ejpam-5602	523	6	no	no	DET
ejpam-5602	523	7	isolated	isolated	ADJ
ejpam-5602	523	8	vertices	vertex	NOUN
ejpam-5602	523	9	,	,	PUNCT
ejpam-5602	523	10	the	the	DET
ejpam-5602	523	11	least	least	ADV
ejpam-5602	523	12	possible	possible	ADJ
ejpam-5602	523	13	value	value	NOUN
ejpam-5602	523	14	of	of	ADP
ejpam-5602	523	15	δ(gg	δ(gg	ADJ
ejpam-5602	523	16	)	)	PUNCT
ejpam-5602	523	17	is	be	AUX
ejpam-5602	523	18	2	2	NUM
ejpam-5602	523	19	.	.	PUNCT
ejpam-5602	524	1	hence	hence	ADV
ejpam-5602	524	2	,	,	PUNCT
ejpam-5602	524	3	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	524	4	)	)	PUNCT
ejpam-5602	524	5	≤	≤	NOUN
ejpam-5602	524	6	2|v	2|v	PROPN
ejpam-5602	524	7	(	(	PUNCT
ejpam-5602	524	8	g)|	g)|	VERB
ejpam-5602	524	9	<	<	X
ejpam-5602	524	10	3|v	3|v	NUM
ejpam-5602	524	11	(	(	PUNCT
ejpam-5602	524	12	g)|	g)|	PROPN
ejpam-5602	524	13	,	,	PUNCT
ejpam-5602	524	14	a	a	DET
ejpam-5602	524	15	contradiction	contradiction	NOUN
ejpam-5602	524	16	.	.	PUNCT
ejpam-5602	525	1	suppose	suppose	VERB
ejpam-5602	525	2	f	f	PROPN
ejpam-5602	525	3	|g	|g	PROPN
ejpam-5602	525	4	is	be	AUX
ejpam-5602	525	5	a	a	DET
ejpam-5602	525	6	tdidf	tdidf	NOUN
ejpam-5602	525	7	ong	ong	PROPN
ejpam-5602	525	8	.	.	PUNCT
ejpam-5602	526	1	since	since	SCONJ
ejpam-5602	526	2	v	v	NOUN
ejpam-5602	526	3	(	(	PUNCT
ejpam-5602	526	4	g	g	NOUN
ejpam-5602	526	5	)	)	PUNCT
ejpam-5602	526	6	⊈	⊈	PROPN
ejpam-5602	526	7	v0	v0	NOUN
ejpam-5602	526	8	,	,	PUNCT
ejpam-5602	526	9	(	(	PUNCT
ejpam-5602	526	10	v1	v1	VERB
ejpam-5602	526	11	∪	∪	NOUN
ejpam-5602	526	12	v2	v2	PROPN
ejpam-5602	526	13	∪	∪	X
ejpam-5602	526	14	v3	v3	PROPN
ejpam-5602	526	15	)	)	PUNCT
ejpam-5602	526	16	∩	∩	PROPN
ejpam-5602	526	17	v	v	ADP
ejpam-5602	526	18	(	(	PUNCT
ejpam-5602	526	19	g	g	NOUN
ejpam-5602	526	20	)	)	PUNCT
ejpam-5602	526	21	̸=	̸=	PROPN
ejpam-5602	526	22	∅	∅	NOUN
ejpam-5602	526	23	and	and	CCONJ
ejpam-5602	526	24	ω(f	ω(f	PROPN
ejpam-5602	526	25	|g	|g	NOUN
ejpam-5602	526	26	)	)	PUNCT
ejpam-5602	526	27	≥	≥	NOUN
ejpam-5602	526	28	1	1	NUM
ejpam-5602	526	29	.	.	PUNCT
ejpam-5602	527	1	thus	thus	ADV
ejpam-5602	527	2	,	,	PUNCT
ejpam-5602	527	3	ω(f	ω(f	PROPN
ejpam-5602	527	4	|g	|g	NOUN
ejpam-5602	527	5	)	)	PUNCT
ejpam-5602	527	6	+	+	CCONJ
ejpam-5602	527	7	1	1	NUM
ejpam-5602	527	8	≤	≤	NUM
ejpam-5602	527	9	ω(f	ω(f	PUNCT
ejpam-5602	527	10	|g	|g	NOUN
ejpam-5602	527	11	)	)	PUNCT
ejpam-5602	527	12	+	+	CCONJ
ejpam-5602	527	13	ω(f	ω(f	PROPN
ejpam-5602	527	14	|g	|g	NOUN
ejpam-5602	527	15	)	)	PUNCT
ejpam-5602	527	16	=	=	SYM
ejpam-5602	527	17	ωgg(f	ωgg(f	PROPN
ejpam-5602	527	18	)	)	PUNCT
ejpam-5602	527	19	s.j.l	s.j.l	NOUN
ejpam-5602	527	20	.	.	PUNCT
ejpam-5602	528	1	sumbalan	sumbalan	PROPN
ejpam-5602	528	2	,	,	PUNCT
ejpam-5602	528	3	s.m	s.m	PROPN
ejpam-5602	528	4	.	.	PROPN
ejpam-5602	528	5	menchavez	menchavez	PROPN
ejpam-5602	528	6	,	,	PUNCT
ejpam-5602	528	7	f.p	f.p	PROPN
ejpam-5602	528	8	.	.	PROPN
ejpam-5602	528	9	jamil	jamil	PROPN
ejpam-5602	528	10	/	/	SYM
ejpam-5602	528	11	eur	eur	PROPN
ejpam-5602	528	12	.	.	PUNCT
ejpam-5602	529	1	j.	j.	PROPN
ejpam-5602	529	2	pure	pure	PROPN
ejpam-5602	529	3	appl	appl	PROPN
ejpam-5602	529	4	.	.	PROPN
ejpam-5602	529	5	math	math	PROPN
ejpam-5602	529	6	,	,	PUNCT
ejpam-5602	529	7	18	18	NUM
ejpam-5602	529	8	(	(	PUNCT
ejpam-5602	529	9	1	1	NUM
ejpam-5602	529	10	)	)	PUNCT
ejpam-5602	529	11	(	(	PUNCT
ejpam-5602	529	12	2025	2025	NUM
ejpam-5602	529	13	)	)	PUNCT
ejpam-5602	529	14	,	,	PUNCT
ejpam-5602	529	15	5602	5602	NUM
ejpam-5602	529	16	16	16	NUM
ejpam-5602	529	17	of	of	ADP
ejpam-5602	529	18	18	18	NUM
ejpam-5602	529	19	suppose	suppose	VERB
ejpam-5602	529	20	f	f	PROPN
ejpam-5602	529	21	|g	|g	PROPN
ejpam-5602	529	22	is	be	AUX
ejpam-5602	529	23	not	not	PART
ejpam-5602	529	24	a	a	DET
ejpam-5602	529	25	tdidf	tdidf	NOUN
ejpam-5602	529	26	on	on	ADP
ejpam-5602	529	27	g.	g.	PROPN
ejpam-5602	529	28	let	let	VERB
ejpam-5602	529	29	a	a	DET
ejpam-5602	529	30	=	=	X
ejpam-5602	529	31	{	{	PUNCT
ejpam-5602	529	32	v	v	NOUN
ejpam-5602	529	33	∈	∈	PROPN
ejpam-5602	529	34	v0	v0	NOUN
ejpam-5602	529	35	∩	∩	X
ejpam-5602	529	36	v	v	X
ejpam-5602	529	37	(	(	PUNCT
ejpam-5602	529	38	g	g	NOUN
ejpam-5602	529	39	)	)	PUNCT
ejpam-5602	529	40	:	:	PUNCT
ejpam-5602	529	41	0	0	NUM
ejpam-5602	529	42	≤	≤	NUM
ejpam-5602	529	43	f(ng(v	f(ng(v	NOUN
ejpam-5602	529	44	)	)	PUNCT
ejpam-5602	529	45	)	)	PUNCT
ejpam-5602	529	46	≤	≤	NUM
ejpam-5602	529	47	1	1	NUM
ejpam-5602	529	48	}	}	PUNCT
ejpam-5602	529	49	,	,	PUNCT
ejpam-5602	529	50	b	b	X
ejpam-5602	529	51	=	=	PRON
ejpam-5602	529	52	{	{	PUNCT
ejpam-5602	529	53	v	v	NUM
ejpam-5602	529	54	∈	∈	NOUN
ejpam-5602	529	55	v	v	NOUN
ejpam-5602	529	56	(	(	PUNCT
ejpam-5602	529	57	g	g	NOUN
ejpam-5602	529	58	)	)	PUNCT
ejpam-5602	529	59	∩	∩	ADJ
ejpam-5602	529	60	v0	v0	NOUN
ejpam-5602	529	61	:	:	PUNCT
ejpam-5602	529	62	f(ng(v	f(ng(v	X
ejpam-5602	529	63	)	)	PUNCT
ejpam-5602	529	64	)	)	PUNCT
ejpam-5602	530	1	=	=	SYM
ejpam-5602	530	2	2	2	X
ejpam-5602	530	3	}	}	PUNCT
ejpam-5602	530	4	,	,	PUNCT
ejpam-5602	530	5	c	c	X
ejpam-5602	530	6	=	=	PRON
ejpam-5602	530	7	{	{	PUNCT
ejpam-5602	530	8	v	v	NUM
ejpam-5602	530	9	∈	∈	NOUN
ejpam-5602	530	10	v	v	NOUN
ejpam-5602	530	11	(	(	PUNCT
ejpam-5602	530	12	g	g	NOUN
ejpam-5602	530	13	)	)	PUNCT
ejpam-5602	530	14	∩	∩	NOUN
ejpam-5602	530	15	v1	v1	NOUN
ejpam-5602	530	16	:	:	PUNCT
ejpam-5602	530	17	0	0	NUM
ejpam-5602	530	18	≤	≤	NUM
ejpam-5602	530	19	f(ng(v	f(ng(v	NOUN
ejpam-5602	530	20	)	)	PUNCT
ejpam-5602	530	21	)	)	PUNCT
ejpam-5602	530	22	≤	≤	NUM
ejpam-5602	530	23	1	1	NUM
ejpam-5602	530	24	}	}	PUNCT
ejpam-5602	530	25	,	,	PUNCT
ejpam-5602	530	26	d	d	PROPN
ejpam-5602	530	27	=	=	PRON
ejpam-5602	530	28	{	{	PUNCT
ejpam-5602	530	29	v	v	NUM
ejpam-5602	530	30	∈	∈	NOUN
ejpam-5602	530	31	v	v	NOUN
ejpam-5602	530	32	(	(	PUNCT
ejpam-5602	530	33	g	g	NOUN
ejpam-5602	530	34	)	)	PUNCT
ejpam-5602	530	35	∩	∩	NOUN
ejpam-5602	530	36	(	(	PUNCT
ejpam-5602	530	37	v2	v2	PROPN
ejpam-5602	530	38	∪	∪	X
ejpam-5602	530	39	v3	v3	PROPN
ejpam-5602	530	40	)	)	PUNCT
ejpam-5602	530	41	:	:	PUNCT
ejpam-5602	530	42	ng(v	ng(v	X
ejpam-5602	530	43	)	)	PUNCT
ejpam-5602	530	44	⊆	⊆	NUM
ejpam-5602	530	45	v0	v0	NOUN
ejpam-5602	530	46	\b	\b	NOUN
ejpam-5602	530	47	}	}	PUNCT
ejpam-5602	530	48	.	.	PUNCT
ejpam-5602	531	1	now	now	ADV
ejpam-5602	531	2	,	,	PUNCT
ejpam-5602	531	3	let	let	VERB
ejpam-5602	531	4	x	x	PRON
ejpam-5602	531	5	⊆	⊆	NUM
ejpam-5602	531	6	ng(d	ng(d	NUM
ejpam-5602	531	7	)	)	PUNCT
ejpam-5602	531	8	∩	∩	NOUN
ejpam-5602	531	9	v0	v0	NOUN
ejpam-5602	531	10	be	be	AUX
ejpam-5602	531	11	the	the	DET
ejpam-5602	531	12	smallest	small	ADJ
ejpam-5602	531	13	set	set	NOUN
ejpam-5602	531	14	that	that	PRON
ejpam-5602	531	15	dominates	dominate	VERB
ejpam-5602	531	16	d.	d.	PROPN
ejpam-5602	531	17	then	then	ADV
ejpam-5602	531	18	|x|	|x|	PROPN
ejpam-5602	531	19	≤	≤	PROPN
ejpam-5602	531	20	|d|	|d|	PROPN
ejpam-5602	531	21	.	.	PUNCT
ejpam-5602	532	1	define	define	VERB
ejpam-5602	532	2	a	a	DET
ejpam-5602	532	3	function	function	NOUN
ejpam-5602	532	4	g	g	NOUN
ejpam-5602	532	5	on	on	ADP
ejpam-5602	532	6	v	v	ADP
ejpam-5602	532	7	(	(	PUNCT
ejpam-5602	532	8	g	g	NOUN
ejpam-5602	532	9	)	)	PUNCT
ejpam-5602	532	10	as	as	SCONJ
ejpam-5602	532	11	follows	follow	VERB
ejpam-5602	532	12	:	:	PUNCT
ejpam-5602	532	13	g(x	g(x	NOUN
ejpam-5602	532	14	)	)	PUNCT
ejpam-5602	532	15	=	=	PUNCT
ejpam-5602	532	16			NOUN
ejpam-5602	532	17	0	0	NUM
ejpam-5602	532	18	,	,	PUNCT
ejpam-5602	532	19	if	if	SCONJ
ejpam-5602	532	20	x	x	SYM
ejpam-5602	532	21	∈	∈	PROPN
ejpam-5602	532	22	(	(	PUNCT
ejpam-5602	532	23	v	v	NOUN
ejpam-5602	532	24	(	(	PUNCT
ejpam-5602	532	25	g	g	NOUN
ejpam-5602	532	26	)	)	PUNCT
ejpam-5602	532	27	∩	∩	ADJ
ejpam-5602	532	28	v0	v0	NOUN
ejpam-5602	532	29	)	)	PUNCT
ejpam-5602	532	30	\	\	PUNCT
ejpam-5602	532	31	(	(	PUNCT
ejpam-5602	532	32	a	a	DET
ejpam-5602	532	33	∪b	∪b	X
ejpam-5602	532	34	∪x	∪x	NUM
ejpam-5602	532	35	)	)	PUNCT
ejpam-5602	532	36	;	;	PUNCT
ejpam-5602	532	37	1	1	NUM
ejpam-5602	532	38	,	,	PUNCT
ejpam-5602	532	39	if	if	SCONJ
ejpam-5602	532	40	x	x	PUNCT
ejpam-5602	532	41	∈	∈	PROPN
ejpam-5602	532	42	[	[	X
ejpam-5602	532	43	(	(	PUNCT
ejpam-5602	532	44	v	v	NOUN
ejpam-5602	532	45	(	(	PUNCT
ejpam-5602	532	46	g	g	NOUN
ejpam-5602	532	47	)	)	PUNCT
ejpam-5602	532	48	∩	∩	ADJ
ejpam-5602	532	49	v1	v1	NOUN
ejpam-5602	532	50	)	)	PUNCT
ejpam-5602	532	51	\	\	PUNCT
ejpam-5602	533	1	c	c	X
ejpam-5602	533	2	]	]	X
ejpam-5602	533	3	∪b	∪b	X
ejpam-5602	533	4	∪x	∪x	NOUN
ejpam-5602	533	5	;	;	PUNCT
ejpam-5602	533	6	2	2	NUM
ejpam-5602	533	7	,	,	PUNCT
ejpam-5602	533	8	if	if	SCONJ
ejpam-5602	533	9	x	x	SYM
ejpam-5602	533	10	∈	∈	PROPN
ejpam-5602	533	11	(	(	PUNCT
ejpam-5602	533	12	v	v	NOUN
ejpam-5602	533	13	(	(	PUNCT
ejpam-5602	533	14	g	g	NOUN
ejpam-5602	533	15	)	)	PUNCT
ejpam-5602	533	16	∩	∩	ADJ
ejpam-5602	533	17	v2	v2	NOUN
ejpam-5602	533	18	)	)	PUNCT
ejpam-5602	533	19	∪a	∪a	X
ejpam-5602	533	20	∪	∪	ADP
ejpam-5602	533	21	c	c	NOUN
ejpam-5602	533	22	;	;	PUNCT
ejpam-5602	533	23	3	3	NUM
ejpam-5602	533	24	,	,	PUNCT
ejpam-5602	533	25	if	if	SCONJ
ejpam-5602	533	26	x	x	SYM
ejpam-5602	533	27	∈	∈	PROPN
ejpam-5602	533	28	(	(	PUNCT
ejpam-5602	533	29	v	v	NOUN
ejpam-5602	533	30	(	(	PUNCT
ejpam-5602	533	31	g	g	NOUN
ejpam-5602	533	32	)	)	PUNCT
ejpam-5602	533	33	∩	∩	NOUN
ejpam-5602	533	34	v3	v3	PROPN
ejpam-5602	533	35	)	)	PUNCT
ejpam-5602	533	36	,	,	PUNCT
ejpam-5602	533	37	then	then	ADV
ejpam-5602	533	38	g	g	PROPN
ejpam-5602	533	39	is	be	AUX
ejpam-5602	533	40	a	a	DET
ejpam-5602	533	41	tdidf	tdidf	NOUN
ejpam-5602	533	42	on	on	ADP
ejpam-5602	533	43	g	g	NOUN
ejpam-5602	533	44	with	with	ADP
ejpam-5602	533	45	ωg(g	ωg(g	NOUN
ejpam-5602	533	46	)	)	PUNCT
ejpam-5602	534	1	=	=	SYM
ejpam-5602	534	2	|v	|v	X
ejpam-5602	534	3	(	(	PUNCT
ejpam-5602	534	4	g	g	NOUN
ejpam-5602	534	5	)	)	PUNCT
ejpam-5602	534	6	∩	∩	ADJ
ejpam-5602	534	7	v1|	v1|	NOUN
ejpam-5602	534	8	−	−	PROPN
ejpam-5602	534	9	|c|+	|c|+	NOUN
ejpam-5602	534	10	|b	|b	ADJ
ejpam-5602	534	11	∪x|+	∪x|+	PROPN
ejpam-5602	534	12	2|v	2|v	PROPN
ejpam-5602	534	13	(	(	PUNCT
ejpam-5602	534	14	g	g	NOUN
ejpam-5602	534	15	)	)	PUNCT
ejpam-5602	534	16	∩	∩	PROPN
ejpam-5602	534	17	v2|+	v2|+	PROPN
ejpam-5602	534	18	2|a|+	2|a|+	NUM
ejpam-5602	534	19	2|c|	2|c|	NUM
ejpam-5602	534	20	+	+	NUM
ejpam-5602	534	21	3|v	3|v	NUM
ejpam-5602	534	22	(	(	PUNCT
ejpam-5602	534	23	g	g	NOUN
ejpam-5602	534	24	)	)	PUNCT
ejpam-5602	534	25	∩	∩	NOUN
ejpam-5602	534	26	v3|	v3|	PROPN
ejpam-5602	534	27	=	=	SYM
ejpam-5602	534	28	|v	|v	X
ejpam-5602	534	29	(	(	PUNCT
ejpam-5602	534	30	g	g	NOUN
ejpam-5602	534	31	)	)	PUNCT
ejpam-5602	534	32	∩	∩	ADJ
ejpam-5602	534	33	v1|+	v1|+	PROPN
ejpam-5602	534	34	2|v	2|v	PROPN
ejpam-5602	534	35	(	(	PUNCT
ejpam-5602	534	36	g	g	NOUN
ejpam-5602	534	37	)	)	PUNCT
ejpam-5602	534	38	∩	∩	NOUN
ejpam-5602	534	39	v2|+	v2|+	NOUN
ejpam-5602	534	40	3|v	3|v	NUM
ejpam-5602	534	41	(	(	PUNCT
ejpam-5602	534	42	g	g	NOUN
ejpam-5602	534	43	)	)	PUNCT
ejpam-5602	534	44	∩	∩	NOUN
ejpam-5602	534	45	v3|+	v3|+	PROPN
ejpam-5602	534	46	2|a|+	2|a|+	NUM
ejpam-5602	534	47	|c|+	|c|+	NOUN
ejpam-5602	534	48	|b	|b	ADJ
ejpam-5602	534	49	∪x|	∪x|	PROPN
ejpam-5602	534	50	=	=	PUNCT
ejpam-5602	534	51	ωg(f	ωg(f	NUM
ejpam-5602	534	52	|g	|g	NOUN
ejpam-5602	534	53	)	)	PUNCT
ejpam-5602	534	54	+	+	NUM
ejpam-5602	534	55	2|a|+	2|a|+	NUM
ejpam-5602	534	56	|c|+	|c|+	NOUN
ejpam-5602	534	57	|b	|b	ADJ
ejpam-5602	534	58	∪x|	∪x|	NOUN
ejpam-5602	534	59	.	.	PUNCT
ejpam-5602	535	1	we	we	PRON
ejpam-5602	535	2	claim	claim	VERB
ejpam-5602	535	3	that	that	SCONJ
ejpam-5602	535	4	ωg(f	ωg(f	NUM
ejpam-5602	535	5	|g	|g	NOUN
ejpam-5602	535	6	)	)	PUNCT
ejpam-5602	535	7	−	−	PROPN
ejpam-5602	535	8	1	1	NUM
ejpam-5602	535	9	≤	≤	NUM
ejpam-5602	535	10	ωgg(f	ωgg(f	NUM
ejpam-5602	535	11	)	)	PUNCT
ejpam-5602	535	12	.	.	PUNCT
ejpam-5602	536	1	put	put	VERB
ejpam-5602	536	2	a1	a1	NOUN
ejpam-5602	536	3	=	=	PUNCT
ejpam-5602	536	4	{	{	PUNCT
ejpam-5602	536	5	v	v	NOUN
ejpam-5602	536	6	∈	∈	PROPN
ejpam-5602	536	7	v0	v0	NOUN
ejpam-5602	536	8	∩	∩	X
ejpam-5602	536	9	v	v	X
ejpam-5602	536	10	(	(	PUNCT
ejpam-5602	536	11	g	g	NOUN
ejpam-5602	536	12	)	)	PUNCT
ejpam-5602	536	13	:	:	PUNCT
ejpam-5602	537	1	f(ng(v	f(ng(v	X
ejpam-5602	537	2	)	)	PUNCT
ejpam-5602	537	3	)	)	PUNCT
ejpam-5602	538	1	=	=	PUNCT
ejpam-5602	538	2	0	0	NUM
ejpam-5602	538	3	}	}	PUNCT
ejpam-5602	538	4	,	,	PUNCT
ejpam-5602	538	5	a2	a2	PROPN
ejpam-5602	538	6	=	=	PUNCT
ejpam-5602	538	7	{	{	PUNCT
ejpam-5602	538	8	v	v	NUM
ejpam-5602	538	9	∈	∈	PROPN
ejpam-5602	538	10	v0	v0	NOUN
ejpam-5602	538	11	∩	∩	X
ejpam-5602	538	12	v	v	X
ejpam-5602	538	13	(	(	PUNCT
ejpam-5602	538	14	g	g	NOUN
ejpam-5602	538	15	)	)	PUNCT
ejpam-5602	538	16	:	:	PUNCT
ejpam-5602	538	17	f(ng(v	f(ng(v	X
ejpam-5602	538	18	)	)	PUNCT
ejpam-5602	538	19	)	)	PUNCT
ejpam-5602	539	1	=	=	PUNCT
ejpam-5602	539	2	1	1	X
ejpam-5602	539	3	}	}	PUNCT
ejpam-5602	539	4	,	,	PUNCT
ejpam-5602	539	5	c1	c1	PROPN
ejpam-5602	539	6	=	=	PUNCT
ejpam-5602	539	7	{	{	PUNCT
ejpam-5602	539	8	v	v	NUM
ejpam-5602	539	9	∈	∈	NOUN
ejpam-5602	539	10	v	v	NOUN
ejpam-5602	539	11	(	(	PUNCT
ejpam-5602	539	12	g	g	NOUN
ejpam-5602	539	13	)	)	PUNCT
ejpam-5602	539	14	∩	∩	ADJ
ejpam-5602	539	15	v1	v1	NOUN
ejpam-5602	539	16	:	:	PUNCT
ejpam-5602	539	17	f(ng(v	f(ng(v	X
ejpam-5602	539	18	)	)	PUNCT
ejpam-5602	539	19	)	)	PUNCT
ejpam-5602	539	20	=	=	PUNCT
ejpam-5602	540	1	0	0	NUM
ejpam-5602	540	2	}	}	PUNCT
ejpam-5602	540	3	,	,	PUNCT
ejpam-5602	540	4	and	and	CCONJ
ejpam-5602	540	5	c2	c2	PROPN
ejpam-5602	540	6	=	=	PUNCT
ejpam-5602	540	7	{	{	PUNCT
ejpam-5602	540	8	v	v	NUM
ejpam-5602	540	9	∈	∈	NOUN
ejpam-5602	540	10	v	v	NOUN
ejpam-5602	540	11	(	(	PUNCT
ejpam-5602	540	12	g	g	NOUN
ejpam-5602	540	13	)	)	PUNCT
ejpam-5602	540	14	∩	∩	ADJ
ejpam-5602	540	15	v1	v1	NOUN
ejpam-5602	540	16	:	:	PUNCT
ejpam-5602	540	17	f(ng(v	f(ng(v	X
ejpam-5602	540	18	)	)	PUNCT
ejpam-5602	540	19	)	)	PUNCT
ejpam-5602	540	20	=	=	PUNCT
ejpam-5602	541	1	1	1	NUM
ejpam-5602	541	2	}	}	PUNCT
ejpam-5602	541	3	.	.	PUNCT
ejpam-5602	542	1	then	then	ADV
ejpam-5602	542	2	a1	a1	VERB
ejpam-5602	542	3	∪	∪	X
ejpam-5602	542	4	a2	a2	PROPN
ejpam-5602	542	5	=	=	PUNCT
ejpam-5602	542	6	a	a	PROPN
ejpam-5602	542	7	and	and	CCONJ
ejpam-5602	542	8	c1	c1	PROPN
ejpam-5602	542	9	∪	∪	PROPN
ejpam-5602	542	10	c2	c2	PROPN
ejpam-5602	542	11	=	=	SYM
ejpam-5602	542	12	c.	c.	PROPN
ejpam-5602	542	13	now	now	ADV
ejpam-5602	542	14	,	,	PUNCT
ejpam-5602	542	15	we	we	PRON
ejpam-5602	542	16	denote	denote	VERB
ejpam-5602	542	17	by	by	ADP
ejpam-5602	542	18	s	s	NOUN
ejpam-5602	542	19	=	=	PUNCT
ejpam-5602	542	20	{	{	PUNCT
ejpam-5602	542	21	v	v	NUM
ejpam-5602	542	22	∈	∈	NOUN
ejpam-5602	542	23	v	v	NOUN
ejpam-5602	542	24	(	(	PUNCT
ejpam-5602	542	25	g	g	NOUN
ejpam-5602	542	26	)	)	PUNCT
ejpam-5602	542	27	:	:	PUNCT
ejpam-5602	542	28	v	v	X
ejpam-5602	542	29	∈	∈	PROPN
ejpam-5602	542	30	s	s	PART
ejpam-5602	542	31	}	}	PUNCT
ejpam-5602	542	32	for	for	ADP
ejpam-5602	542	33	each	each	PRON
ejpam-5602	542	34	s	s	PROPN
ejpam-5602	542	35	⊆	⊆	NUM
ejpam-5602	542	36	v	v	NOUN
ejpam-5602	542	37	(	(	PUNCT
ejpam-5602	542	38	g	g	NOUN
ejpam-5602	542	39	)	)	PUNCT
ejpam-5602	542	40	.	.	PUNCT
ejpam-5602	543	1	note	note	VERB
ejpam-5602	543	2	that	that	SCONJ
ejpam-5602	543	3	,	,	PUNCT
ejpam-5602	543	4	a1	a1	VERB
ejpam-5602	543	5	⊆	⊆	NUM
ejpam-5602	543	6	v	v	NOUN
ejpam-5602	543	7	(	(	PUNCT
ejpam-5602	543	8	g	g	NOUN
ejpam-5602	543	9	)	)	PUNCT
ejpam-5602	543	10	∩	∩	PROPN
ejpam-5602	543	11	v3	v3	PROPN
ejpam-5602	543	12	,	,	PUNCT
ejpam-5602	543	13	a2	a2	PROPN
ejpam-5602	543	14	⊆	⊆	NUM
ejpam-5602	543	15	v	v	NOUN
ejpam-5602	543	16	(	(	PUNCT
ejpam-5602	543	17	g)∩(v2∪v3	g)∩(v2∪v3	NOUN
ejpam-5602	543	18	)	)	PUNCT
ejpam-5602	543	19	,	,	PUNCT
ejpam-5602	543	20	b	b	X
ejpam-5602	543	21	⊆	⊆	NUM
ejpam-5602	543	22	v	v	NOUN
ejpam-5602	543	23	(	(	PUNCT
ejpam-5602	543	24	g)∩(v1∪v2∪v3	g)∩(v1∪v2∪v3	PROPN
ejpam-5602	543	25	)	)	PUNCT
ejpam-5602	543	26	,	,	PUNCT
ejpam-5602	543	27	c1	c1	PROPN
ejpam-5602	543	28	⊆	⊆	NUM
ejpam-5602	543	29	v	v	NOUN
ejpam-5602	543	30	(	(	PUNCT
ejpam-5602	543	31	g)∩(v2∪v3	g)∩(v2∪v3	NOUN
ejpam-5602	543	32	)	)	PUNCT
ejpam-5602	543	33	,	,	PUNCT
ejpam-5602	543	34	c2	c2	PROPN
ejpam-5602	543	35	⊆	⊆	NUM
ejpam-5602	543	36	v	v	PROPN
ejpam-5602	543	37	(	(	PUNCT
ejpam-5602	543	38	g)∩(v1∪v2∪v3	g)∩(v1∪v2∪v3	PROPN
ejpam-5602	543	39	)	)	PUNCT
ejpam-5602	543	40	,	,	PUNCT
ejpam-5602	543	41	and	and	CCONJ
ejpam-5602	543	42	d	d	X
ejpam-5602	543	43	⊆	⊆	NUM
ejpam-5602	543	44	v	v	ADP
ejpam-5602	543	45	(	(	PUNCT
ejpam-5602	543	46	g	g	NOUN
ejpam-5602	543	47	)	)	PUNCT
ejpam-5602	543	48	∩	∩	NOUN
ejpam-5602	543	49	(	(	PUNCT
ejpam-5602	543	50	v1	v1	VERB
ejpam-5602	543	51	∪	∪	ADP
ejpam-5602	543	52	v2	v2	PROPN
ejpam-5602	543	53	∪	∪	X
ejpam-5602	543	54	v3	v3	PROPN
ejpam-5602	543	55	)	)	PUNCT
ejpam-5602	543	56	.	.	PUNCT
ejpam-5602	544	1	wlog	wlog	PROPN
ejpam-5602	544	2	,	,	PUNCT
ejpam-5602	544	3	assume	assume	VERB
ejpam-5602	544	4	that	that	SCONJ
ejpam-5602	544	5	a2	a2	PROPN
ejpam-5602	544	6	⊆	⊆	NUM
ejpam-5602	544	7	v	v	NOUN
ejpam-5602	544	8	(	(	PUNCT
ejpam-5602	544	9	g	g	NOUN
ejpam-5602	544	10	)	)	PUNCT
ejpam-5602	544	11	∩	∩	ADJ
ejpam-5602	544	12	v2	v2	PROPN
ejpam-5602	544	13	,	,	PUNCT
ejpam-5602	544	14	b	b	PROPN
ejpam-5602	544	15	⊆	⊆	NUM
ejpam-5602	544	16	v	v	NOUN
ejpam-5602	544	17	(	(	PUNCT
ejpam-5602	544	18	g	g	NOUN
ejpam-5602	544	19	)	)	PUNCT
ejpam-5602	544	20	∩	∩	ADJ
ejpam-5602	544	21	v1	v1	NOUN
ejpam-5602	544	22	,	,	PUNCT
ejpam-5602	544	23	c1	c1	PROPN
ejpam-5602	544	24	⊆	⊆	NUM
ejpam-5602	544	25	v	v	NOUN
ejpam-5602	544	26	(	(	PUNCT
ejpam-5602	544	27	g	g	NOUN
ejpam-5602	544	28	)	)	PUNCT
ejpam-5602	544	29	∩	∩	ADJ
ejpam-5602	544	30	v2	v2	PROPN
ejpam-5602	544	31	,	,	PUNCT
ejpam-5602	544	32	c2	c2	PROPN
ejpam-5602	544	33	⊆	⊆	NUM
ejpam-5602	544	34	v	v	NOUN
ejpam-5602	544	35	(	(	PUNCT
ejpam-5602	544	36	g	g	NOUN
ejpam-5602	544	37	)	)	PUNCT
ejpam-5602	544	38	∩	∩	NOUN
ejpam-5602	544	39	v1	v1	NOUN
ejpam-5602	544	40	,	,	PUNCT
ejpam-5602	544	41	and	and	CCONJ
ejpam-5602	544	42	d	d	X
ejpam-5602	544	43	⊆	⊆	NUM
ejpam-5602	544	44	v	v	ADP
ejpam-5602	544	45	(	(	PUNCT
ejpam-5602	544	46	g	g	NOUN
ejpam-5602	544	47	)	)	PUNCT
ejpam-5602	544	48	∩	∩	NOUN
ejpam-5602	544	49	v1	v1	NOUN
ejpam-5602	544	50	.	.	PUNCT
ejpam-5602	545	1	then	then	ADV
ejpam-5602	545	2	c2	c2	PROPN
ejpam-5602	545	3	∩d	∩d	VERB
ejpam-5602	545	4	=	=	NOUN
ejpam-5602	545	5	∅	∅	NOUN
ejpam-5602	545	6	,	,	PUNCT
ejpam-5602	545	7	c2	c2	PROPN
ejpam-5602	545	8	∩	∩	ADJ
ejpam-5602	545	9	b	b	X
ejpam-5602	545	10	=	=	SYM
ejpam-5602	545	11	∅	∅	NOUN
ejpam-5602	545	12	and	and	CCONJ
ejpam-5602	545	13	a2	a2	PROPN
ejpam-5602	545	14	∩	∩	PROPN
ejpam-5602	545	15	c1	c1	NOUN
ejpam-5602	545	16	=	=	PUNCT
ejpam-5602	545	17	∅.	∅.	VERB
ejpam-5602	545	18	thus	thus	ADV
ejpam-5602	545	19	,	,	PUNCT
ejpam-5602	545	20	ωg(f	ωg(f	NUM
ejpam-5602	545	21	|g	|g	NOUN
ejpam-5602	545	22	)	)	PUNCT
ejpam-5602	545	23	=	=	SYM
ejpam-5602	545	24	|v	|v	X
ejpam-5602	545	25	(	(	PUNCT
ejpam-5602	545	26	g	g	NOUN
ejpam-5602	545	27	)	)	PUNCT
ejpam-5602	545	28	∩	∩	ADJ
ejpam-5602	545	29	v1|+	v1|+	PROPN
ejpam-5602	545	30	2|v	2|v	PROPN
ejpam-5602	545	31	(	(	PUNCT
ejpam-5602	545	32	g	g	NOUN
ejpam-5602	545	33	)	)	PUNCT
ejpam-5602	545	34	∩	∩	NOUN
ejpam-5602	545	35	v2|+	v2|+	NOUN
ejpam-5602	545	36	3|v	3|v	NUM
ejpam-5602	545	37	(	(	PUNCT
ejpam-5602	545	38	g	g	NOUN
ejpam-5602	545	39	)	)	PUNCT
ejpam-5602	545	40	∩	∩	NOUN
ejpam-5602	545	41	v3|	v3|	NOUN
ejpam-5602	545	42	≥	≥	NUM
ejpam-5602	545	43	3|a1|+	3|a1|+	NUM
ejpam-5602	545	44	2|a2|++2|c1|+	2|a2|++2|c1|+	NUM
ejpam-5602	545	45	|c2|+	|c2|+	ADP
ejpam-5602	545	46	|b	|b	ADJ
ejpam-5602	545	47	∪d|	∪d|	NOUN
ejpam-5602	545	48	=	=	SYM
ejpam-5602	545	49	2|a|+	2|a|+	NUM
ejpam-5602	545	50	|c|+	|c|+	NOUN
ejpam-5602	545	51	|a1|+	|a1|+	PRON
ejpam-5602	545	52	|c1|+	|c1|+	X
ejpam-5602	545	53	|b	|b	ADJ
ejpam-5602	545	54	∪d|	∪d|	PROPN
ejpam-5602	545	55	.	.	PUNCT
ejpam-5602	546	1	since	since	SCONJ
ejpam-5602	546	2	|x|	|x|	PROPN
ejpam-5602	546	3	≤	≤	NUM
ejpam-5602	546	4	|d|	|d|	PROPN
ejpam-5602	546	5	,	,	PUNCT
ejpam-5602	546	6	ωg(f	ωg(f	NUM
ejpam-5602	546	7	|g	|g	NOUN
ejpam-5602	546	8	)	)	PUNCT
ejpam-5602	546	9	≥	≥	NOUN
ejpam-5602	546	10	2|a|+	2|a|+	NUM
ejpam-5602	546	11	|c|+	|c|+	NOUN
ejpam-5602	546	12	|b	|b	NOUN
ejpam-5602	546	13	∪x|+	∪x|+	NOUN
ejpam-5602	546	14	1	1	NUM
ejpam-5602	546	15	.	.	PUNCT
ejpam-5602	546	16	hence	hence	ADV
ejpam-5602	546	17	,	,	PUNCT
ejpam-5602	546	18	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	546	19	)	)	PUNCT
ejpam-5602	546	20	=	=	SYM
ejpam-5602	546	21	ωgg(f	ωgg(f	PROPN
ejpam-5602	546	22	)	)	PUNCT
ejpam-5602	546	23	=	=	PUNCT
ejpam-5602	546	24	ωg(f	ωg(f	NUM
ejpam-5602	546	25	|g	|g	NOUN
ejpam-5602	546	26	)	)	PUNCT
ejpam-5602	546	27	+	+	CCONJ
ejpam-5602	546	28	ωg(f	ωg(f	NUM
ejpam-5602	546	29	|g	|g	NOUN
ejpam-5602	546	30	)	)	PUNCT
ejpam-5602	546	31	≥	≥	NOUN
ejpam-5602	546	32	ωg(f	ωg(f	NUM
ejpam-5602	546	33	|g	|g	NOUN
ejpam-5602	546	34	)	)	PUNCT
ejpam-5602	546	35	+	+	NUM
ejpam-5602	546	36	2|a|+	2|a|+	NUM
ejpam-5602	546	37	|c|+	|c|+	NOUN
ejpam-5602	546	38	|b	|b	ADJ
ejpam-5602	546	39	∪x|+	∪x|+	NOUN
ejpam-5602	546	40	1	1	NUM
ejpam-5602	546	41	=	=	SYM
ejpam-5602	546	42	ωg(g	ωg(g	NUM
ejpam-5602	546	43	)	)	PUNCT
ejpam-5602	547	1	+	+	CCONJ
ejpam-5602	547	2	1	1	X
ejpam-5602	547	3	.	.	X
ejpam-5602	547	4	therefore	therefore	ADV
ejpam-5602	547	5	,	,	PUNCT
ejpam-5602	547	6	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	547	7	)	)	PUNCT
ejpam-5602	547	8	≥	≥	NOUN
ejpam-5602	547	9	γtdi(g	γtdi(g	PROPN
ejpam-5602	547	10	)	)	PUNCT
ejpam-5602	548	1	+	+	CCONJ
ejpam-5602	549	1	1	1	X
ejpam-5602	549	2	.	.	X
ejpam-5602	549	3	if	if	SCONJ
ejpam-5602	549	4	g	g	PROPN
ejpam-5602	549	5	=	=	SYM
ejpam-5602	549	6	kn	kn	PROPN
ejpam-5602	549	7	,	,	PUNCT
ejpam-5602	549	8	then	then	ADV
ejpam-5602	549	9	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	549	10	)	)	PUNCT
ejpam-5602	549	11	=	=	SYM
ejpam-5602	550	1	3n	3n	NOUN
ejpam-5602	550	2	.	.	PUNCT
ejpam-5602	551	1	if	if	SCONJ
ejpam-5602	551	2	g	g	NOUN
ejpam-5602	551	3	=	=	SYM
ejpam-5602	551	4	p4	p4	ADJ
ejpam-5602	551	5	,	,	PUNCT
ejpam-5602	551	6	then	then	ADV
ejpam-5602	551	7	g	g	PROPN
ejpam-5602	551	8	=	=	PUNCT
ejpam-5602	551	9	p4	p4	ADJ
ejpam-5602	551	10	and	and	CCONJ
ejpam-5602	551	11	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	551	12	)	)	PUNCT
ejpam-5602	551	13	=	=	SYM
ejpam-5602	551	14	1	1	NUM
ejpam-5602	551	15	+	+	NUM
ejpam-5602	551	16	max{γtdi(g	max{γtdi(g	NOUN
ejpam-5602	551	17	)	)	PUNCT
ejpam-5602	551	18	,	,	PUNCT
ejpam-5602	551	19	γtdi(g	γtdi(g	PROPN
ejpam-5602	551	20	)	)	PUNCT
ejpam-5602	551	21	}	}	PUNCT
ejpam-5602	551	22	.	.	PUNCT
ejpam-5602	552	1	and	and	CCONJ
ejpam-5602	552	2	if	if	SCONJ
ejpam-5602	552	3	g	g	PROPN
ejpam-5602	552	4	=	=	SYM
ejpam-5602	552	5	cn	cn	PROPN
ejpam-5602	552	6	on	on	ADP
ejpam-5602	552	7	n	n	NOUN
ejpam-5602	552	8	=	=	SYM
ejpam-5602	552	9	4	4	NUM
ejpam-5602	552	10	vertices	vertex	NOUN
ejpam-5602	552	11	,	,	PUNCT
ejpam-5602	552	12	then	then	ADV
ejpam-5602	552	13	γtdi(gg	γtdi(gg	ADJ
ejpam-5602	552	14	)	)	PUNCT
ejpam-5602	552	15	=	=	SYM
ejpam-5602	552	16	2n	2n	NUM
ejpam-5602	552	17	.	.	PUNCT
ejpam-5602	553	1	therefore	therefore	ADV
ejpam-5602	553	2	,	,	PUNCT
ejpam-5602	553	3	the	the	DET
ejpam-5602	553	4	inequalities	inequality	NOUN
ejpam-5602	553	5	in	in	ADP
ejpam-5602	553	6	inequality	inequality	NOUN
ejpam-5602	553	7	4	4	NUM
ejpam-5602	553	8	and	and	CCONJ
ejpam-5602	553	9	inequality	inequality	NOUN
ejpam-5602	553	10	5	5	NUM
ejpam-5602	553	11	are	be	AUX
ejpam-5602	553	12	sharp	sharp	ADJ
ejpam-5602	553	13	.	.	PUNCT
ejpam-5602	554	1	■	■	PUNCT
ejpam-5602	554	2	s.j.l	s.j.l	NOUN
ejpam-5602	554	3	.	.	PUNCT
ejpam-5602	554	4	sumbalan	sumbalan	PROPN
ejpam-5602	554	5	,	,	PUNCT
ejpam-5602	554	6	s.m	s.m	PROPN
ejpam-5602	554	7	.	.	PROPN
ejpam-5602	554	8	menchavez	menchavez	PROPN
ejpam-5602	554	9	,	,	PUNCT
ejpam-5602	554	10	f.p	f.p	PROPN
ejpam-5602	554	11	.	.	PROPN
ejpam-5602	554	12	jamil	jamil	PROPN
ejpam-5602	554	13	/	/	SYM
ejpam-5602	554	14	eur	eur	PROPN
ejpam-5602	554	15	.	.	PUNCT
ejpam-5602	555	1	j.	j.	PROPN
ejpam-5602	555	2	pure	pure	PROPN
ejpam-5602	555	3	appl	appl	PROPN
ejpam-5602	555	4	.	.	PROPN
ejpam-5602	555	5	math	math	PROPN
ejpam-5602	555	6	,	,	PUNCT
ejpam-5602	555	7	18	18	NUM
ejpam-5602	555	8	(	(	PUNCT
ejpam-5602	555	9	1	1	NUM
ejpam-5602	555	10	)	)	PUNCT
ejpam-5602	555	11	(	(	PUNCT
ejpam-5602	555	12	2025	2025	NUM
ejpam-5602	555	13	)	)	PUNCT
ejpam-5602	555	14	,	,	PUNCT
ejpam-5602	555	15	5602	5602	NUM
ejpam-5602	555	16	17	17	NUM
ejpam-5602	555	17	of	of	ADP
ejpam-5602	555	18	18	18	NUM
ejpam-5602	555	19	acknowledgements	acknowledgement	NOUN
ejpam-5602	555	20	this	this	DET
ejpam-5602	555	21	research	research	NOUN
ejpam-5602	555	22	is	be	AUX
ejpam-5602	555	23	fully	fully	ADV
ejpam-5602	555	24	funded	fund	VERB
ejpam-5602	555	25	by	by	ADP
ejpam-5602	555	26	the	the	DET
ejpam-5602	555	27	department	department	PROPN
ejpam-5602	555	28	of	of	ADP
ejpam-5602	555	29	science	science	NOUN
ejpam-5602	555	30	and	and	CCONJ
ejpam-5602	555	31	technology	technology	NOUN
ejpam-5602	555	32	(	(	PUNCT
ejpam-5602	555	33	dost	dost	NOUN
ejpam-5602	555	34	)	)	PUNCT
ejpam-5602	555	35	under	under	ADP
ejpam-5602	555	36	the	the	DET
ejpam-5602	555	37	accelerated	accelerate	VERB
ejpam-5602	555	38	science	science	NOUN
ejpam-5602	555	39	and	and	CCONJ
ejpam-5602	555	40	technology	technology	NOUN
ejpam-5602	555	41	human	human	ADJ
ejpam-5602	555	42	resource	resource	NOUN
ejpam-5602	555	43	development	development	NOUN
ejpam-5602	555	44	program	program	NOUN
ejpam-5602	555	45	(	(	PUNCT
ejpam-5602	555	46	asthrdp	asthrdp	PROPN
ejpam-5602	555	47	)	)	PUNCT
ejpam-5602	555	48	and	and	CCONJ
ejpam-5602	555	49	the	the	DET
ejpam-5602	555	50	office	office	NOUN
ejpam-5602	555	51	of	of	ADP
ejpam-5602	555	52	the	the	DET
ejpam-5602	555	53	vice	vice	NOUN
ejpam-5602	555	54	chancellor	chancellor	NOUN
ejpam-5602	555	55	for	for	ADP
ejpam-5602	555	56	research	research	NOUN
ejpam-5602	555	57	and	and	CCONJ
ejpam-5602	555	58	enterprise	enterprise	NOUN
ejpam-5602	555	59	(	(	PUNCT
ejpam-5602	555	60	ovcre	ovcre	NOUN
ejpam-5602	555	61	)	)	PUNCT
ejpam-5602	555	62	,	,	PUNCT
ejpam-5602	555	63	msu	msu	PROPN
ejpam-5602	555	64	-	-	PUNCT
ejpam-5602	555	65	iigan	iigan	PROPN
ejpam-5602	555	66	institute	institute	PROPN
ejpam-5602	555	67	of	of	ADP
ejpam-5602	555	68	technology	technology	PROPN
ejpam-5602	555	69	,	,	PUNCT
ejpam-5602	555	70	philippines	philippine	NOUN
ejpam-5602	555	71	,	,	PUNCT
ejpam-5602	555	72	through	through	ADP
ejpam-5602	555	73	the	the	DET
ejpam-5602	555	74	premier	premier	PROPN
ejpam-5602	555	75	research	research	PROPN
ejpam-5602	555	76	institute	institute	PROPN
ejpam-5602	555	77	of	of	ADP
ejpam-5602	555	78	science	science	NOUN
ejpam-5602	555	79	and	and	CCONJ
ejpam-5602	555	80	mathematics	mathematics	PROPN
ejpam-5602	555	81	(	(	PUNCT
ejpam-5602	555	82	prism	prism	NOUN
ejpam-5602	555	83	)	)	PUNCT
ejpam-5602	555	84	.	.	PUNCT
ejpam-5602	556	1	references	reference	NOUN
ejpam-5602	556	2	[	[	X
ejpam-5602	556	3	1	1	NUM
ejpam-5602	556	4	]	]	PUNCT
ejpam-5602	556	5	r.	r.	PROPN
ejpam-5602	556	6	j.	j.	PROPN
ejpam-5602	556	7	fortosa	fortosa	PROPN
ejpam-5602	556	8	,	,	PUNCT
ejpam-5602	556	9	s.	s.	PROPN
ejpam-5602	556	10	r.	r.	PROPN
ejpam-5602	556	11	canoy	canoy	PROPN
ejpam-5602	556	12	,	,	PUNCT
ejpam-5602	556	13	and	and	CCONJ
ejpam-5602	556	14	f.	f.	PROPN
ejpam-5602	556	15	p.	p.	PROPN
ejpam-5602	556	16	jamil	jamil	PROPN
ejpam-5602	556	17	.	.	PUNCT
ejpam-5602	557	1	convex	convex	VERB
ejpam-5602	557	2	roman	roman	ADJ
ejpam-5602	557	3	dominating	dominating	NOUN
ejpam-5602	557	4	functions	function	NOUN
ejpam-5602	557	5	on	on	ADP
ejpam-5602	557	6	graphs	graph	NOUN
ejpam-5602	557	7	under	under	ADP
ejpam-5602	557	8	some	some	DET
ejpam-5602	557	9	binary	binary	ADJ
ejpam-5602	557	10	operations	operation	NOUN
ejpam-5602	557	11	.	.	PUNCT
ejpam-5602	558	1	european	european	ADJ
ejpam-5602	558	2	journal	journal	PROPN
ejpam-5602	558	3	of	of	ADP
ejpam-5602	558	4	pure	pure	ADJ
ejpam-5602	558	5	and	and	CCONJ
ejpam-5602	558	6	applied	applied	ADJ
ejpam-5602	558	7	mathematics	mathematic	NOUN
ejpam-5602	558	8	,	,	PUNCT
ejpam-5602	558	9	17(2):1335–1351	17(2):1335–1351	NUM
ejpam-5602	558	10	,	,	PUNCT
ejpam-5602	558	11	2024	2024	NUM
ejpam-5602	558	12	.	.	PUNCT
ejpam-5602	559	1	[	[	X
ejpam-5602	559	2	2	2	X
ejpam-5602	559	3	]	]	PUNCT
ejpam-5602	559	4	j.	j.	PROPN
ejpam-5602	559	5	b.	b.	PROPN
ejpam-5602	559	6	cariaga	cariaga	PROPN
ejpam-5602	559	7	and	and	CCONJ
ejpam-5602	559	8	f.	f.	PROPN
ejpam-5602	559	9	p.	p.	PROPN
ejpam-5602	559	10	jamil	jamil	PROPN
ejpam-5602	559	11	.	.	PUNCT
ejpam-5602	560	1	on	on	ADP
ejpam-5602	560	2	double	double	ADJ
ejpam-5602	560	3	roman	roman	ADJ
ejpam-5602	560	4	dominating	dominating	NOUN
ejpam-5602	560	5	functions	function	NOUN
ejpam-5602	560	6	in	in	ADP
ejpam-5602	560	7	graphs	graph	NOUN
ejpam-5602	560	8	.	.	PUNCT
ejpam-5602	561	1	european	european	ADJ
ejpam-5602	561	2	journal	journal	PROPN
ejpam-5602	561	3	of	of	ADP
ejpam-5602	561	4	pure	pure	ADJ
ejpam-5602	561	5	and	and	CCONJ
ejpam-5602	561	6	applied	applied	ADJ
ejpam-5602	561	7	mathematics	mathematic	NOUN
ejpam-5602	561	8	,	,	PUNCT
ejpam-5602	561	9	16(2):847–863	16(2):847–863	NOUN
ejpam-5602	561	10	,	,	PUNCT
ejpam-5602	561	11	2023	2023	NUM
ejpam-5602	561	12	.	.	PUNCT
ejpam-5602	562	1	[	[	X
ejpam-5602	562	2	3	3	X
ejpam-5602	562	3	]	]	X
ejpam-5602	562	4	g.	g.	PROPN
ejpam-5602	562	5	chartrand	chartrand	PROPN
ejpam-5602	562	6	and	and	CCONJ
ejpam-5602	562	7	l.	l.	PROPN
ejpam-5602	562	8	lesniak	lesniak	PROPN
ejpam-5602	562	9	.	.	PUNCT
ejpam-5602	563	1	graphs	graph	NOUN
ejpam-5602	563	2	and	and	CCONJ
ejpam-5602	563	3	digraphs	digraph	NOUN
ejpam-5602	563	4	:	:	PUNCT
ejpam-5602	563	5	third	third	ADJ
ejpam-5602	563	6	edition	edition	NOUN
ejpam-5602	563	7	.	.	PUNCT
ejpam-5602	564	1	chapman	chapman	PROPN
ejpam-5602	564	2	and	and	CCONJ
ejpam-5602	564	3	hall	hall	PROPN
ejpam-5602	564	4	,	,	PUNCT
ejpam-5602	564	5	london	london	PROPN
ejpam-5602	564	6	,	,	PUNCT
ejpam-5602	564	7	1996	1996	NUM
ejpam-5602	564	8	.	.	PUNCT
ejpam-5602	565	1	[	[	X
ejpam-5602	565	2	4	4	X
ejpam-5602	565	3	]	]	X
ejpam-5602	565	4	g.	g.	PROPN
ejpam-5602	565	5	chartrand	chartrand	PROPN
ejpam-5602	565	6	and	and	CCONJ
ejpam-5602	565	7	o.	o.	PROPN
ejpam-5602	565	8	r.	r.	PROPN
ejpam-5602	565	9	oellermann	oellermann	PROPN
ejpam-5602	565	10	.	.	PUNCT
ejpam-5602	566	1	applied	apply	VERB
ejpam-5602	566	2	and	and	CCONJ
ejpam-5602	566	3	algorithmic	algorithmic	ADJ
ejpam-5602	566	4	graph	graph	NOUN
ejpam-5602	566	5	theory	theory	NOUN
ejpam-5602	566	6	.	.	PUNCT
ejpam-5602	567	1	mcgraw	mcgraw	PROPN
ejpam-5602	567	2	-	-	PUNCT
ejpam-5602	567	3	hill	hill	PROPN
ejpam-5602	567	4	,	,	PUNCT
ejpam-5602	567	5	london	london	PROPN
ejpam-5602	567	6	,	,	PUNCT
ejpam-5602	567	7	1996	1996	NUM
ejpam-5602	567	8	.	.	PUNCT
ejpam-5602	568	1	[	[	X
ejpam-5602	568	2	5	5	NUM
ejpam-5602	568	3	]	]	PUNCT
ejpam-5602	568	4	a.	a.	NOUN
ejpam-5602	568	5	chilelli	chilelli	PROPN
ejpam-5602	568	6	and	and	CCONJ
ejpam-5602	568	7	j.	j.	PROPN
ejpam-5602	568	8	jun	jun	PROPN
ejpam-5602	568	9	.	.	PUNCT
ejpam-5602	569	1	gluing	gluing	NOUN
ejpam-5602	569	2	of	of	ADP
ejpam-5602	569	3	graphs	graph	NOUN
ejpam-5602	569	4	and	and	CCONJ
ejpam-5602	569	5	their	their	PRON
ejpam-5602	569	6	jacobians	jacobian	NOUN
ejpam-5602	569	7	.	.	PUNCT
ejpam-5602	570	1	involve	involve	NOUN
ejpam-5602	570	2	,	,	PUNCT
ejpam-5602	570	3	16(3):389–407	16(3):389–407	PROPN
ejpam-5602	570	4	,	,	PUNCT
ejpam-5602	570	5	2023	2023	NUM
ejpam-5602	570	6	.	.	PUNCT
ejpam-5602	571	1	[	[	X
ejpam-5602	571	2	6	6	NUM
ejpam-5602	571	3	]	]	PUNCT
ejpam-5602	571	4	e.	e.	PROPN
ejpam-5602	571	5	cockayne	cockayne	PROPN
ejpam-5602	571	6	and	and	CCONJ
ejpam-5602	571	7	s.	s.	PROPN
ejpam-5602	571	8	hedetniemi	hedetniemi	PROPN
ejpam-5602	571	9	.	.	PUNCT
ejpam-5602	572	1	towards	towards	ADP
ejpam-5602	572	2	a	a	DET
ejpam-5602	572	3	theory	theory	NOUN
ejpam-5602	572	4	of	of	ADP
ejpam-5602	572	5	domination	domination	NOUN
ejpam-5602	572	6	in	in	ADP
ejpam-5602	572	7	graphs	graph	NOUN
ejpam-5602	572	8	.	.	PUNCT
ejpam-5602	573	1	networks	network	NOUN
ejpam-5602	573	2	,	,	PUNCT
ejpam-5602	573	3	7(3):247–261	7(3):247–261	NUM
ejpam-5602	573	4	,	,	PUNCT
ejpam-5602	573	5	1977	1977	NUM
ejpam-5602	573	6	.	.	PUNCT
ejpam-5602	574	1	[	[	X
ejpam-5602	574	2	7	7	X
ejpam-5602	574	3	]	]	X
ejpam-5602	574	4	b.	b.	PROPN
ejpam-5602	574	5	escoffier	escoffier	PROPN
ejpam-5602	574	6	,	,	PUNCT
ejpam-5602	574	7	l.	l.	PROPN
ejpam-5602	574	8	gourves	gourves	PROPN
ejpam-5602	574	9	,	,	PUNCT
ejpam-5602	574	10	and	and	CCONJ
ejpam-5602	574	11	j.	j.	PROPN
ejpam-5602	574	12	monnot	monnot	PROPN
ejpam-5602	574	13	.	.	PUNCT
ejpam-5602	575	1	complexity	complexity	NOUN
ejpam-5602	575	2	and	and	CCONJ
ejpam-5602	575	3	approximation	approximation	NOUN
ejpam-5602	575	4	results	result	NOUN
ejpam-5602	575	5	for	for	ADP
ejpam-5602	575	6	the	the	DET
ejpam-5602	575	7	connected	connect	VERB
ejpam-5602	575	8	vertex	vertex	NOUN
ejpam-5602	575	9	cover	cover	NOUN
ejpam-5602	575	10	problem	problem	NOUN
ejpam-5602	575	11	in	in	ADP
ejpam-5602	575	12	graphs	graph	NOUN
ejpam-5602	575	13	and	and	CCONJ
ejpam-5602	575	14	hypergraphs	hypergraph	NOUN
ejpam-5602	575	15	.	.	PUNCT
ejpam-5602	576	1	journal	journal	NOUN
ejpam-5602	576	2	of	of	ADP
ejpam-5602	576	3	discrete	discrete	ADJ
ejpam-5602	576	4	algorithms	algorithm	NOUN
ejpam-5602	576	5	,	,	PUNCT
ejpam-5602	576	6	8(1):36–49	8(1):36–49	NUM
ejpam-5602	576	7	,	,	PUNCT
ejpam-5602	576	8	2010	2010	NUM
ejpam-5602	576	9	.	.	PUNCT
ejpam-5602	577	1	[	[	X
ejpam-5602	577	2	8	8	NUM
ejpam-5602	577	3	]	]	X
ejpam-5602	577	4	m.	m.	NOUN
ejpam-5602	577	5	chellali	chellali	PROPN
ejpam-5602	577	6	,	,	PUNCT
ejpam-5602	577	7	o.	o.	PROPN
ejpam-5602	577	8	favaron	favaron	PROPN
ejpam-5602	577	9	,	,	PUNCT
ejpam-5602	577	10	a.	a.	NOUN
ejpam-5602	577	11	hansberg	hansberg	PROPN
ejpam-5602	577	12	,	,	PUNCT
ejpam-5602	577	13	and	and	CCONJ
ejpam-5602	577	14	l.	l.	PROPN
ejpam-5602	577	15	volkmann	volkmann	PROPN
ejpam-5602	577	16	.	.	PUNCT
ejpam-5602	578	1	k	k	X
ejpam-5602	578	2	-	-	PUNCT
ejpam-5602	578	3	domination	domination	NOUN
ejpam-5602	578	4	and	and	CCONJ
ejpam-5602	578	5	kindependence	kindependence	NOUN
ejpam-5602	578	6	in	in	ADP
ejpam-5602	578	7	graphs	graph	NOUN
ejpam-5602	578	8	:	:	PUNCT
ejpam-5602	578	9	a	a	DET
ejpam-5602	578	10	survey	survey	NOUN
ejpam-5602	578	11	.	.	PUNCT
ejpam-5602	579	1	graphs	graph	NOUN
ejpam-5602	579	2	and	and	CCONJ
ejpam-5602	579	3	combinatorics	combinatoric	NOUN
ejpam-5602	579	4	,	,	PUNCT
ejpam-5602	579	5	28:1–55	28:1–55	NUM
ejpam-5602	579	6	,	,	PUNCT
ejpam-5602	579	7	2012	2012	NUM
ejpam-5602	579	8	.	.	PUNCT
ejpam-5602	580	1	[	[	X
ejpam-5602	580	2	9	9	NUM
ejpam-5602	580	3	]	]	PUNCT
ejpam-5602	580	4	f.	f.	PROPN
ejpam-5602	580	5	harary	harary	PROPN
ejpam-5602	580	6	.	.	PUNCT
ejpam-5602	581	1	graph	graph	NOUN
ejpam-5602	581	2	theory	theory	NOUN
ejpam-5602	581	3	.	.	PUNCT
ejpam-5602	582	1	massachusetts	massachusetts	PROPN
ejpam-5602	582	2	:	:	PUNCT
ejpam-5602	582	3	addison	addison	PROPN
ejpam-5602	582	4	-	-	PUNCT
ejpam-5602	582	5	wesley	wesley	PROPN
ejpam-5602	582	6	publication	publication	PROPN
ejpam-5602	582	7	company	company	PROPN
ejpam-5602	582	8	,	,	PUNCT
ejpam-5602	582	9	usa	usa	PROPN
ejpam-5602	582	10	,	,	PUNCT
ejpam-5602	582	11	1969	1969	NUM
ejpam-5602	582	12	.	.	PUNCT
ejpam-5602	583	1	[	[	X
ejpam-5602	583	2	10	10	NUM
ejpam-5602	583	3	]	]	X
ejpam-5602	583	4	r.	r.	PROPN
ejpam-5602	583	5	a.	a.	PROPN
ejpam-5602	583	6	beeler	beeler	PROPN
ejpam-5602	583	7	,	,	PUNCT
ejpam-5602	583	8	t.	t.	PROPN
ejpam-5602	583	9	w.	w.	PROPN
ejpam-5602	583	10	haynes	haynes	PROPN
ejpam-5602	583	11	,	,	PUNCT
ejpam-5602	583	12	and	and	CCONJ
ejpam-5602	583	13	s.	s.	PROPN
ejpam-5602	583	14	t.	t.	PROPN
ejpam-5602	583	15	hedetniemi	hedetniemi	PROPN
ejpam-5602	583	16	.	.	PUNCT
ejpam-5602	584	1	double	double	ADJ
ejpam-5602	584	2	roman	roman	ADJ
ejpam-5602	584	3	domination	domination	NOUN
ejpam-5602	584	4	.	.	PUNCT
ejpam-5602	585	1	discrete	discrete	ADJ
ejpam-5602	585	2	applied	apply	VERB
ejpam-5602	585	3	mathematics	mathematic	NOUN
ejpam-5602	585	4	,	,	PUNCT
ejpam-5602	585	5	211:23–29	211:23–29	NUM
ejpam-5602	585	6	,	,	PUNCT
ejpam-5602	585	7	2016	2016	NUM
ejpam-5602	585	8	.	.	PUNCT
ejpam-5602	586	1	[	[	X
ejpam-5602	586	2	11	11	NUM
ejpam-5602	586	3	]	]	PUNCT
ejpam-5602	586	4	w.	w.	PROPN
ejpam-5602	586	5	j.	j.	PROPN
ejpam-5602	586	6	desormeaux	desormeaux	PROPN
ejpam-5602	586	7	,	,	PUNCT
ejpam-5602	586	8	t.	t.	PROPN
ejpam-5602	586	9	w.	w.	PROPN
ejpam-5602	586	10	haynes	haynes	PROPN
ejpam-5602	586	11	,	,	PUNCT
ejpam-5602	586	12	and	and	CCONJ
ejpam-5602	586	13	m.	m.	PROPN
ejpam-5602	586	14	a.	a.	PROPN
ejpam-5602	586	15	henning	henning	PROPN
ejpam-5602	586	16	.	.	PUNCT
ejpam-5602	587	1	an	an	DET
ejpam-5602	587	2	extremal	extremal	ADJ
ejpam-5602	587	3	problem	problem	NOUN
ejpam-5602	587	4	for	for	ADP
ejpam-5602	587	5	total	total	ADJ
ejpam-5602	587	6	domination	domination	NOUN
ejpam-5602	587	7	stable	stable	ADJ
ejpam-5602	587	8	graphs	graph	NOUN
ejpam-5602	587	9	upon	upon	SCONJ
ejpam-5602	587	10	edge	edge	NOUN
ejpam-5602	587	11	removal	removal	NOUN
ejpam-5602	587	12	.	.	PUNCT
ejpam-5602	588	1	discrete	discrete	ADJ
ejpam-5602	588	2	applied	applied	ADJ
ejpam-5602	588	3	mathematics	mathematic	NOUN
ejpam-5602	588	4	,	,	PUNCT
ejpam-5602	588	5	159:1048–1052	159:1048–1052	NUM
ejpam-5602	588	6	,	,	PUNCT
ejpam-5602	588	7	2011	2011	NUM
ejpam-5602	588	8	.	.	PUNCT
ejpam-5602	589	1	[	[	X
ejpam-5602	589	2	12	12	NUM
ejpam-5602	589	3	]	]	PUNCT
ejpam-5602	589	4	e.	e.	PROPN
ejpam-5602	589	5	j.	j.	PROPN
ejpam-5602	589	6	cockayne	cockayne	PROPN
ejpam-5602	589	7	,	,	PUNCT
ejpam-5602	589	8	p.	p.	NOUN
ejpam-5602	589	9	a.	a.	NOUN
ejpam-5602	589	10	dreyer	dreyer	PROPN
ejpam-5602	589	11	,	,	PUNCT
ejpam-5602	589	12	s.	s.	PROPN
ejpam-5602	589	13	m.	m.	PROPN
ejpam-5602	589	14	hedetniemi	hedetniemi	ADV
ejpam-5602	589	15	,	,	PUNCT
ejpam-5602	589	16	and	and	CCONJ
ejpam-5602	589	17	s.	s.	PROPN
ejpam-5602	589	18	t.	t.	PROPN
ejpam-5602	589	19	hedetniemi	hedetniemi	PROPN
ejpam-5602	589	20	.	.	PUNCT
ejpam-5602	590	1	roman	roman	ADJ
ejpam-5602	590	2	domination	domination	NOUN
ejpam-5602	590	3	in	in	ADP
ejpam-5602	590	4	graphs	graph	NOUN
ejpam-5602	590	5	.	.	PUNCT
ejpam-5602	591	1	discrete	discrete	ADJ
ejpam-5602	591	2	mathematics	mathematic	NOUN
ejpam-5602	591	3	,	,	PUNCT
ejpam-5602	591	4	278:11–22	278:11–22	NUM
ejpam-5602	591	5	,	,	PUNCT
ejpam-5602	591	6	2004	2004	NUM
ejpam-5602	591	7	.	.	PUNCT
ejpam-5602	592	1	[	[	X
ejpam-5602	592	2	13	13	NUM
ejpam-5602	592	3	]	]	PUNCT
ejpam-5602	592	4	m.	m.	NOUN
ejpam-5602	592	5	chellali	chellali	PROPN
ejpam-5602	592	6	,	,	PUNCT
ejpam-5602	592	7	t.	t.	PROPN
ejpam-5602	592	8	w.	w.	PROPN
ejpam-5602	592	9	haynes	haynes	PROPN
ejpam-5602	592	10	,	,	PUNCT
ejpam-5602	592	11	s.	s.	PROPN
ejpam-5602	592	12	t.	t.	PROPN
ejpam-5602	592	13	hedetniemi	hedetniemi	PROPN
ejpam-5602	592	14	,	,	PUNCT
ejpam-5602	592	15	and	and	CCONJ
ejpam-5602	592	16	a.	a.	NOUN
ejpam-5602	592	17	a.	a.	PROPN
ejpam-5602	592	18	mcrae	mcrae	PROPN
ejpam-5602	592	19	.	.	PUNCT
ejpam-5602	593	1	roman	roman	PROPN
ejpam-5602	593	2	{	{	PUNCT
ejpam-5602	593	3	2}domination	2}domination	NOUN
ejpam-5602	593	4	.	.	PUNCT
ejpam-5602	594	1	discrete	discrete	ADJ
ejpam-5602	594	2	applied	apply	VERB
ejpam-5602	594	3	mathematics	mathematic	NOUN
ejpam-5602	594	4	,	,	PUNCT
ejpam-5602	594	5	211:22–28	211:22–28	PROPN
ejpam-5602	594	6	,	,	PUNCT
ejpam-5602	594	7	2016	2016	NUM
ejpam-5602	594	8	.	.	PUNCT
ejpam-5602	595	1	[	[	X
ejpam-5602	595	2	14	14	NUM
ejpam-5602	595	3	]	]	PUNCT
ejpam-5602	595	4	t.	t.	PROPN
ejpam-5602	595	5	w.	w.	PROPN
ejpam-5602	595	6	haynes	haynes	PROPN
ejpam-5602	595	7	,	,	PUNCT
ejpam-5602	595	8	s.	s.	PROPN
ejpam-5602	595	9	t.	t.	PROPN
ejpam-5602	595	10	hedetniemi	hedetniemi	PROPN
ejpam-5602	595	11	,	,	PUNCT
ejpam-5602	595	12	and	and	CCONJ
ejpam-5602	595	13	p.	p.	PROPN
ejpam-5602	595	14	j.	j.	PROPN
ejpam-5602	595	15	slater	slater	PROPN
ejpam-5602	595	16	.	.	PUNCT
ejpam-5602	596	1	fundamentals	fundamental	NOUN
ejpam-5602	596	2	of	of	ADP
ejpam-5602	596	3	domination	domination	NOUN
ejpam-5602	596	4	in	in	ADP
ejpam-5602	596	5	graphs	graph	NOUN
ejpam-5602	596	6	.	.	PUNCT
ejpam-5602	597	1	marcel	marcel	PROPN
ejpam-5602	597	2	dekker	dekker	PROPN
ejpam-5602	597	3	,	,	PUNCT
ejpam-5602	597	4	inc	inc	PROPN
ejpam-5602	597	5	.	.	PROPN
ejpam-5602	597	6	,	,	PUNCT
ejpam-5602	597	7	new	new	PROPN
ejpam-5602	597	8	york	york	PROPN
ejpam-5602	597	9	,	,	PUNCT
ejpam-5602	597	10	1998	1998	NUM
ejpam-5602	597	11	.	.	PUNCT
ejpam-5602	598	1	[	[	X
ejpam-5602	598	2	15	15	NUM
ejpam-5602	598	3	]	]	X
ejpam-5602	598	4	m.	m.	NOUN
ejpam-5602	598	5	henning	henning	PROPN
ejpam-5602	598	6	and	and	CCONJ
ejpam-5602	598	7	a.	a.	PROPN
ejpam-5602	598	8	yeo	yeo	PROPN
ejpam-5602	598	9	.	.	PROPN
ejpam-5602	599	1	total	total	ADJ
ejpam-5602	599	2	domination	domination	NOUN
ejpam-5602	599	3	in	in	ADP
ejpam-5602	599	4	graphs	graph	NOUN
ejpam-5602	599	5	.	.	PUNCT
ejpam-5602	600	1	springer	springer	NOUN
ejpam-5602	600	2	,	,	PUNCT
ejpam-5602	600	3	2013	2013	NUM
ejpam-5602	600	4	.	.	PUNCT
ejpam-5602	601	1	s.j.l	s.j.l	PROPN
ejpam-5602	601	2	.	.	PUNCT
ejpam-5602	601	3	sumbalan	sumbalan	PROPN
ejpam-5602	601	4	,	,	PUNCT
ejpam-5602	601	5	s.m	s.m	PROPN
ejpam-5602	601	6	.	.	PROPN
ejpam-5602	601	7	menchavez	menchavez	PROPN
ejpam-5602	601	8	,	,	PUNCT
ejpam-5602	601	9	f.p	f.p	PROPN
ejpam-5602	601	10	.	.	PROPN
ejpam-5602	601	11	jamil	jamil	PROPN
ejpam-5602	601	12	/	/	SYM
ejpam-5602	601	13	eur	eur	PROPN
ejpam-5602	601	14	.	.	PUNCT
ejpam-5602	602	1	j.	j.	PROPN
ejpam-5602	602	2	pure	pure	PROPN
ejpam-5602	602	3	appl	appl	PROPN
ejpam-5602	602	4	.	.	PROPN
ejpam-5602	602	5	math	math	PROPN
ejpam-5602	602	6	,	,	PUNCT
ejpam-5602	602	7	18	18	NUM
ejpam-5602	602	8	(	(	PUNCT
ejpam-5602	602	9	1	1	NUM
ejpam-5602	602	10	)	)	PUNCT
ejpam-5602	602	11	(	(	PUNCT
ejpam-5602	602	12	2025	2025	NUM
ejpam-5602	602	13	)	)	PUNCT
ejpam-5602	602	14	,	,	PUNCT
ejpam-5602	602	15	5602	5602	NUM
ejpam-5602	602	16	18	18	NUM
ejpam-5602	602	17	of	of	ADP
ejpam-5602	602	18	18	18	NUM
ejpam-5602	602	19	[	[	SYM
ejpam-5602	602	20	16	16	NUM
ejpam-5602	602	21	]	]	PUNCT
ejpam-5602	602	22	s.	s.	PROPN
ejpam-5602	602	23	r.	r.	PROPN
ejpam-5602	602	24	canoy	canoy	PROPN
ejpam-5602	602	25	,	,	PUNCT
ejpam-5602	602	26	f.	f.	PROPN
ejpam-5602	602	27	p.	p.	PROPN
ejpam-5602	602	28	jamil	jamil	PROPN
ejpam-5602	602	29	,	,	PUNCT
ejpam-5602	602	30	and	and	CCONJ
ejpam-5602	602	31	s.	s.	PROPN
ejpam-5602	602	32	m.	m.	PROPN
ejpam-5602	602	33	menchavez	menchavez	PROPN
ejpam-5602	602	34	.	.	PUNCT
ejpam-5602	603	1	hop	hop	PROPN
ejpam-5602	603	2	italian	italian	ADJ
ejpam-5602	603	3	domination	domination	NOUN
ejpam-5602	603	4	in	in	ADP
ejpam-5602	603	5	graphs	graph	NOUN
ejpam-5602	603	6	.	.	PUNCT
ejpam-5602	604	1	european	european	ADJ
ejpam-5602	604	2	journal	journal	PROPN
ejpam-5602	604	3	of	of	ADP
ejpam-5602	604	4	pure	pure	ADJ
ejpam-5602	604	5	and	and	CCONJ
ejpam-5602	604	6	applied	applied	ADJ
ejpam-5602	604	7	mathematics	mathematic	NOUN
ejpam-5602	604	8	,	,	PUNCT
ejpam-5602	604	9	16(4):2431–2449	16(4):2431–2449	NUM
ejpam-5602	604	10	,	,	PUNCT
ejpam-5602	604	11	2023	2023	NUM
ejpam-5602	604	12	.	.	PUNCT
ejpam-5602	605	1	[	[	X
ejpam-5602	605	2	17	17	NUM
ejpam-5602	605	3	]	]	PUNCT
ejpam-5602	605	4	a.	a.	NOUN
ejpam-5602	605	5	mohannad	mohannad	PROPN
ejpam-5602	605	6	and	and	CCONJ
ejpam-5602	605	7	d.	d.	PROPN
ejpam-5602	605	8	a.	a.	NOUN
ejpam-5602	605	9	mojdeh	mojdeh	PROPN
ejpam-5602	605	10	.	.	PUNCT
ejpam-5602	606	1	on	on	ADP
ejpam-5602	606	2	the	the	DET
ejpam-5602	606	3	total	total	ADJ
ejpam-5602	606	4	restrained	restrained	ADJ
ejpam-5602	606	5	double	double	ADJ
ejpam-5602	606	6	italian	italian	ADJ
ejpam-5602	606	7	domination	domination	NOUN
ejpam-5602	606	8	.	.	PUNCT
ejpam-5602	607	1	journal	journal	NOUN
ejpam-5602	607	2	of	of	ADP
ejpam-5602	607	3	algebra	algebra	PROPN
ejpam-5602	607	4	and	and	CCONJ
ejpam-5602	607	5	related	related	ADJ
ejpam-5602	607	6	topics	topic	NOUN
ejpam-5602	607	7	,	,	PUNCT
ejpam-5602	607	8	12(1):105–126	12(1):105–126	NOUN
ejpam-5602	607	9	,	,	PUNCT
ejpam-5602	607	10	2024	2024	NUM
ejpam-5602	607	11	.	.	PUNCT
ejpam-5602	608	1	[	[	X
ejpam-5602	608	2	18	18	NUM
ejpam-5602	608	3	]	]	PUNCT
ejpam-5602	608	4	a.	a.	NOUN
ejpam-5602	608	5	mohannad	mohannad	PROPN
ejpam-5602	608	6	and	and	CCONJ
ejpam-5602	608	7	d.	d.	PROPN
ejpam-5602	608	8	a.	a.	NOUN
ejpam-5602	608	9	mojdeh	mojdeh	PROPN
ejpam-5602	608	10	.	.	PUNCT
ejpam-5602	609	1	on	on	ADP
ejpam-5602	609	2	the	the	DET
ejpam-5602	609	3	(	(	PUNCT
ejpam-5602	609	4	total	total	NOUN
ejpam-5602	609	5	)	)	PUNCT
ejpam-5602	609	6	restrained	restrained	ADJ
ejpam-5602	609	7	double	double	ADJ
ejpam-5602	609	8	italian	italian	ADJ
ejpam-5602	609	9	domination	domination	NOUN
ejpam-5602	609	10	of	of	ADP
ejpam-5602	609	11	central	central	ADJ
ejpam-5602	609	12	of	of	ADP
ejpam-5602	609	13	graphs	graph	NOUN
ejpam-5602	609	14	.	.	PUNCT
ejpam-5602	610	1	discrete	discrete	ADJ
ejpam-5602	610	2	mathematics	mathematic	NOUN
ejpam-5602	610	3	,	,	PUNCT
ejpam-5602	610	4	algorithms	algorithm	NOUN
ejpam-5602	610	5	and	and	CCONJ
ejpam-5602	610	6	applications	application	NOUN
ejpam-5602	610	7	,	,	PUNCT
ejpam-5602	610	8	16(8):2350102	16(8):2350102	NUM
ejpam-5602	610	9	,	,	PUNCT
ejpam-5602	610	10	2024	2024	NUM
ejpam-5602	610	11	.	.	PUNCT
ejpam-5602	611	1	[	[	X
ejpam-5602	611	2	19	19	NUM
ejpam-5602	611	3	]	]	X
ejpam-5602	611	4	d.	d.	PROPN
ejpam-5602	611	5	a.	a.	NOUN
ejpam-5602	611	6	mojdeh	mojdeh	PROPN
ejpam-5602	611	7	and	and	CCONJ
ejpam-5602	611	8	l.	l.	PROPN
ejpam-5602	611	9	volkmann	volkmann	PROPN
ejpam-5602	611	10	.	.	PUNCT
ejpam-5602	612	1	roman	roman	PROPN
ejpam-5602	612	2	{	{	PUNCT
ejpam-5602	612	3	3}-domination	3}-domination	NUM
ejpam-5602	612	4	(	(	PUNCT
ejpam-5602	612	5	double	double	ADJ
ejpam-5602	612	6	italian	italian	ADJ
ejpam-5602	612	7	domination	domination	NOUN
ejpam-5602	612	8	)	)	PUNCT
ejpam-5602	612	9	.	.	PUNCT
ejpam-5602	613	1	discrete	discrete	ADJ
ejpam-5602	613	2	applied	applied	ADJ
ejpam-5602	613	3	mathematics	mathematic	NOUN
ejpam-5602	613	4	,	,	PUNCT
ejpam-5602	613	5	283:555–564	283:555–564	NUM
ejpam-5602	613	6	,	,	PUNCT
ejpam-5602	613	7	2020	2020	NUM
ejpam-5602	613	8	.	.	PUNCT
ejpam-5602	614	1	[	[	X
ejpam-5602	614	2	20	20	NUM
ejpam-5602	614	3	]	]	PUNCT
ejpam-5602	614	4	p.	p.	NOUN
ejpam-5602	614	5	dankelmann	dankelmann	PROPN
ejpam-5602	614	6	,	,	PUNCT
ejpam-5602	614	7	d.	d.	PROPN
ejpam-5602	614	8	day	day	PROPN
ejpam-5602	614	9	,	,	PUNCT
ejpam-5602	614	10	d.	d.	PROPN
ejpam-5602	614	11	erwin	erwin	PROPN
ejpam-5602	614	12	,	,	PUNCT
ejpam-5602	614	13	s.	s.	PROPN
ejpam-5602	614	14	mukwembi	mukwembi	PROPN
ejpam-5602	614	15	,	,	PUNCT
ejpam-5602	614	16	and	and	CCONJ
ejpam-5602	614	17	h.	h.	PROPN
ejpam-5602	614	18	swart	swart	PROPN
ejpam-5602	614	19	.	.	PUNCT
ejpam-5602	615	1	domination	domination	NOUN
ejpam-5602	615	2	with	with	ADP
ejpam-5602	615	3	exponential	exponential	ADJ
ejpam-5602	615	4	decay	decay	NOUN
ejpam-5602	615	5	.	.	PUNCT
ejpam-5602	616	1	discrete	discrete	ADJ
ejpam-5602	616	2	mathematics	mathematic	NOUN
ejpam-5602	616	3	,	,	PUNCT
ejpam-5602	616	4	309:5877	309:5877	NUM
ejpam-5602	616	5	–	–	PUNCT
ejpam-5602	616	6	5883	5883	NUM
ejpam-5602	616	7	,	,	PUNCT
ejpam-5602	616	8	2009	2009	NUM
ejpam-5602	616	9	.	.	PUNCT
ejpam-5602	617	1	[	[	X
ejpam-5602	617	2	21	21	NUM
ejpam-5602	617	3	]	]	X
ejpam-5602	617	4	l.	l.	PROPN
ejpam-5602	617	5	paleta	paleta	PROPN
ejpam-5602	617	6	and	and	CCONJ
ejpam-5602	617	7	f.	f.	PROPN
ejpam-5602	617	8	jamil	jamil	PROPN
ejpam-5602	617	9	.	.	PUNCT
ejpam-5602	618	1	more	more	ADJ
ejpam-5602	618	2	on	on	ADP
ejpam-5602	618	3	perfect	perfect	ADJ
ejpam-5602	618	4	roman	roman	ADJ
ejpam-5602	618	5	domination	domination	NOUN
ejpam-5602	618	6	in	in	ADP
ejpam-5602	618	7	graphs	graph	NOUN
ejpam-5602	618	8	.	.	PUNCT
ejpam-5602	619	1	european	european	ADJ
ejpam-5602	619	2	journal	journal	PROPN
ejpam-5602	619	3	of	of	ADP
ejpam-5602	619	4	pure	pure	ADJ
ejpam-5602	619	5	and	and	CCONJ
ejpam-5602	619	6	applied	applied	ADJ
ejpam-5602	619	7	mathematics	mathematic	NOUN
ejpam-5602	619	8	,	,	PUNCT
ejpam-5602	619	9	13(3):529–548	13(3):529–548	NOUN
ejpam-5602	619	10	,	,	PUNCT
ejpam-5602	619	11	2020	2020	NUM
ejpam-5602	619	12	.	.	PUNCT
ejpam-5602	620	1	[	[	X
ejpam-5602	620	2	22	22	NUM
ejpam-5602	620	3	]	]	X
ejpam-5602	620	4	l.	l.	PROPN
ejpam-5602	620	5	paleta	paleta	PROPN
ejpam-5602	620	6	and	and	CCONJ
ejpam-5602	620	7	f.	f.	PROPN
ejpam-5602	620	8	jamil	jamil	PROPN
ejpam-5602	620	9	.	.	PUNCT
ejpam-5602	621	1	on	on	ADP
ejpam-5602	621	2	perfect	perfect	ADJ
ejpam-5602	621	3	italian	italian	ADJ
ejpam-5602	621	4	domination	domination	NOUN
ejpam-5602	621	5	in	in	ADP
ejpam-5602	621	6	graphs	graph	NOUN
ejpam-5602	621	7	.	.	PUNCT
ejpam-5602	622	1	discrete	discrete	ADJ
ejpam-5602	622	2	mathematics	mathematic	NOUN
ejpam-5602	622	3	,	,	PUNCT
ejpam-5602	622	4	algorithms	algorithm	NOUN
ejpam-5602	622	5	and	and	CCONJ
ejpam-5602	622	6	applications	application	NOUN
ejpam-5602	622	7	,	,	PUNCT
ejpam-5602	622	8	16	16	NUM
ejpam-5602	622	9	,	,	PUNCT
ejpam-5602	622	10	2023	2023	NUM
ejpam-5602	622	11	.	.	PUNCT
ejpam-5602	623	1	[	[	X
ejpam-5602	623	2	23	23	NUM
ejpam-5602	623	3	]	]	X
ejpam-5602	623	4	p.	p.	PROPN
ejpam-5602	623	5	roushini	roushini	PROPN
ejpam-5602	623	6	leely	leely	ADV
ejpam-5602	623	7	pushpam	pushpam	VERB
ejpam-5602	623	8	and	and	CCONJ
ejpam-5602	623	9	c.	c.	PROPN
ejpam-5602	623	10	suseendran	suseendran	PROPN
ejpam-5602	623	11	.	.	PUNCT
ejpam-5602	624	1	secure	secure	ADJ
ejpam-5602	624	2	vertex	vertex	NOUN
ejpam-5602	624	3	cover	cover	NOUN
ejpam-5602	624	4	of	of	ADP
ejpam-5602	624	5	a	a	DET
ejpam-5602	624	6	graph	graph	NOUN
ejpam-5602	624	7	.	.	PUNCT
ejpam-5602	625	1	discrete	discrete	ADJ
ejpam-5602	625	2	mathematics	mathematic	NOUN
ejpam-5602	625	3	,	,	PUNCT
ejpam-5602	625	4	algorithms	algorithm	NOUN
ejpam-5602	625	5	and	and	CCONJ
ejpam-5602	625	6	applications	application	NOUN
ejpam-5602	625	7	,	,	PUNCT
ejpam-5602	625	8	9(2):1750026	9(2):1750026	NUM
ejpam-5602	625	9	,	,	PUNCT
ejpam-5602	625	10	2017	2017	NUM
ejpam-5602	625	11	.	.	PUNCT
ejpam-5602	626	1	[	[	X
ejpam-5602	626	2	24	24	NUM
ejpam-5602	626	3	]	]	X
ejpam-5602	626	4	j.	j.	PROPN
ejpam-5602	626	5	m.	m.	PROPN
ejpam-5602	626	6	rivera	rivera	PROPN
ejpam-5602	626	7	and	and	CCONJ
ejpam-5602	626	8	f.	f.	PROPN
ejpam-5602	626	9	jamil	jamil	PROPN
ejpam-5602	626	10	.	.	PUNCT
ejpam-5602	627	1	total	total	ADJ
ejpam-5602	627	2	roman	roman	ADJ
ejpam-5602	627	3	domination	domination	NOUN
ejpam-5602	627	4	in	in	ADP
ejpam-5602	627	5	the	the	DET
ejpam-5602	627	6	join	join	NOUN
ejpam-5602	627	7	,	,	PUNCT
ejpam-5602	627	8	corona	corona	NOUN
ejpam-5602	627	9	and	and	CCONJ
ejpam-5602	627	10	complementary	complementary	ADJ
ejpam-5602	627	11	prism	prism	NOUN
ejpam-5602	627	12	of	of	ADP
ejpam-5602	627	13	graphs	graph	NOUN
ejpam-5602	627	14	.	.	PUNCT
ejpam-5602	628	1	asia	asia	ADJ
ejpam-5602	628	2	-	-	PUNCT
ejpam-5602	628	3	pacific	pacific	PROPN
ejpam-5602	628	4	journal	journal	PROPN
ejpam-5602	628	5	of	of	ADP
ejpam-5602	628	6	science	science	NOUN
ejpam-5602	628	7	,	,	PUNCT
ejpam-5602	628	8	mathematics	mathematic	NOUN
ejpam-5602	628	9	and	and	CCONJ
ejpam-5602	628	10	engineering	engineering	NOUN
ejpam-5602	628	11	,	,	PUNCT
ejpam-5602	628	12	7(2):37–48	7(2):37–48	NUM
ejpam-5602	628	13	,	,	PUNCT
ejpam-5602	628	14	2021	2021	NUM
ejpam-5602	628	15	.	.	PUNCT
ejpam-5602	629	1	[	[	X
ejpam-5602	629	2	25	25	NUM
ejpam-5602	629	3	]	]	PUNCT
ejpam-5602	629	4	a.	a.	NOUN
ejpam-5602	629	5	khodkar	khodkar	PROPN
ejpam-5602	629	6	,	,	PUNCT
ejpam-5602	629	7	d.	d.	PROPN
ejpam-5602	629	8	a.	a.	NOUN
ejpam-5602	629	9	mojdeh	mojdeh	PROPN
ejpam-5602	629	10	,	,	PUNCT
ejpam-5602	629	11	b.	b.	PROPN
ejpam-5602	629	12	samadi	samadi	PROPN
ejpam-5602	629	13	,	,	PUNCT
ejpam-5602	629	14	and	and	CCONJ
ejpam-5602	629	15	i.	i.	PROPN
ejpam-5602	629	16	g.	g.	PROPN
ejpam-5602	629	17	yero	yero	PROPN
ejpam-5602	629	18	.	.	PUNCT
ejpam-5602	629	19	covering	cover	VERB
ejpam-5602	629	20	italian	italian	ADJ
ejpam-5602	629	21	domination	domination	NOUN
ejpam-5602	629	22	in	in	ADP
ejpam-5602	629	23	graphs	graph	NOUN
ejpam-5602	629	24	.	.	PUNCT
ejpam-5602	630	1	discrete	discrete	ADJ
ejpam-5602	630	2	applied	apply	VERB
ejpam-5602	630	3	mathematics	mathematic	NOUN
ejpam-5602	630	4	,	,	PUNCT
ejpam-5602	630	5	304:324–331	304:324–331	NUM
ejpam-5602	630	6	,	,	PUNCT
ejpam-5602	630	7	2021	2021	NUM
ejpam-5602	630	8	.	.	PUNCT
ejpam-5602	631	1	[	[	X
ejpam-5602	631	2	26	26	NUM
ejpam-5602	631	3	]	]	X
ejpam-5602	631	4	d.	d.	PROPN
ejpam-5602	631	5	a.	a.	NOUN
ejpam-5602	631	6	mojdeh	mojdeh	PROPN
ejpam-5602	631	7	z.	z.	PROPN
ejpam-5602	631	8	shao	shao	PROPN
ejpam-5602	631	9	.	.	PUNCT
ejpam-5602	632	1	total	total	ADJ
ejpam-5602	632	2	roman	roman	ADJ
ejpam-5602	632	3	3	3	NUM
ejpam-5602	632	4	-	-	PUNCT
ejpam-5602	632	5	domination	domination	NOUN
ejpam-5602	632	6	in	in	ADP
ejpam-5602	632	7	graphs	graph	NOUN
ejpam-5602	632	8	.	.	PUNCT
ejpam-5602	633	1	symmetry	symmetry	NOUN
ejpam-5602	633	2	,	,	PUNCT
ejpam-5602	633	3	12(2):268	12(2):268	NUM
ejpam-5602	633	4	,	,	PUNCT
ejpam-5602	633	5	2020	2020	NUM
ejpam-5602	633	6	.	.	PUNCT