id	sid	tid	token	lemma	pos
ejpam-4356	1	1	european	european	PROPN
ejpam-4356	1	2	journal	journal	PROPN
ejpam-4356	1	3	of	of	ADP
ejpam-4356	1	4	pure	pure	ADJ
ejpam-4356	1	5	and	and	CCONJ
ejpam-4356	1	6	applied	apply	VERB
ejpam-4356	1	7	mathematics	mathematic	NOUN
ejpam-4356	1	8	vol	vol	NOUN
ejpam-4356	1	9	.	.	PROPN
ejpam-4356	2	1	15	15	NUM
ejpam-4356	2	2	,	,	PUNCT
ejpam-4356	2	3	no	no	INTJ
ejpam-4356	2	4	.	.	NOUN
ejpam-4356	2	5	2	2	NUM
ejpam-4356	2	6	,	,	PUNCT
ejpam-4356	2	7	2022	2022	NUM
ejpam-4356	2	8	,	,	PUNCT
ejpam-4356	2	9	736	736	NUM
ejpam-4356	2	10	-	-	SYM
ejpam-4356	2	11	752	752	NUM
ejpam-4356	2	12	issn	issn	PROPN
ejpam-4356	2	13	1307	1307	NUM
ejpam-4356	2	14	-	-	SYM
ejpam-4356	2	15	5543	5543	NUM
ejpam-4356	2	16	–	–	PUNCT
ejpam-4356	2	17	ejpam.com	ejpam.com	X
ejpam-4356	2	18	published	publish	VERB
ejpam-4356	2	19	by	by	ADP
ejpam-4356	2	20	new	new	PROPN
ejpam-4356	2	21	york	york	PROPN
ejpam-4356	2	22	business	business	PROPN
ejpam-4356	2	23	global	global	PROPN
ejpam-4356	2	24	on	on	ADP
ejpam-4356	2	25	weakly	weakly	ADJ
ejpam-4356	2	26	connected	connected	ADJ
ejpam-4356	2	27	closed	close	VERB
ejpam-4356	2	28	geodetic	geodetic	ADJ
ejpam-4356	2	29	domination	domination	NOUN
ejpam-4356	2	30	in	in	ADP
ejpam-4356	2	31	graphs	graph	NOUN
ejpam-4356	2	32	under	under	ADP
ejpam-4356	2	33	some	some	DET
ejpam-4356	2	34	binary	binary	ADJ
ejpam-4356	2	35	operations	operation	NOUN
ejpam-4356	2	36	jamil	jamil	PROPN
ejpam-4356	2	37	j.	j.	PROPN
ejpam-4356	2	38	hamja1,∗	hamja1,∗	PROPN
ejpam-4356	2	39	,	,	PUNCT
ejpam-4356	2	40	imelda	imelda	PROPN
ejpam-4356	2	41	s.	s.	PROPN
ejpam-4356	2	42	aniversario2	aniversario2	PROPN
ejpam-4356	2	43	,	,	PUNCT
ejpam-4356	3	1	helen	helen	PROPN
ejpam-4356	3	2	m.	m.	PROPN
ejpam-4356	3	3	rara2	rara2	PROPN
ejpam-4356	3	4	1	1	NUM
ejpam-4356	3	5	office	office	NOUN
ejpam-4356	3	6	of	of	ADP
ejpam-4356	3	7	the	the	DET
ejpam-4356	3	8	vice	vice	NOUN
ejpam-4356	3	9	chancellor	chancellor	NOUN
ejpam-4356	3	10	for	for	ADP
ejpam-4356	3	11	academic	academic	ADJ
ejpam-4356	3	12	affairs	affair	NOUN
ejpam-4356	3	13	,	,	PUNCT
ejpam-4356	3	14	msu	msu	PROPN
ejpam-4356	3	15	-	-	PUNCT
ejpam-4356	3	16	tawi	tawi	NOUN
ejpam-4356	3	17	-	-	PUNCT
ejpam-4356	3	18	tawi	tawi	NOUN
ejpam-4356	3	19	college	college	PROPN
ejpam-4356	3	20	of	of	ADP
ejpam-4356	3	21	technology	technology	NOUN
ejpam-4356	3	22	and	and	CCONJ
ejpam-4356	3	23	oceanography	oceanography	NOUN
ejpam-4356	3	24	,	,	PUNCT
ejpam-4356	3	25	7500	7500	NUM
ejpam-4356	3	26	tawi	tawi	NOUN
ejpam-4356	3	27	-	-	PUNCT
ejpam-4356	3	28	tawi	tawi	NOUN
ejpam-4356	3	29	,	,	PUNCT
ejpam-4356	3	30	philippines	philippines	PROPN
ejpam-4356	3	31	2	2	NUM
ejpam-4356	3	32	department	department	NOUN
ejpam-4356	3	33	of	of	ADP
ejpam-4356	3	34	mathematics	mathematic	NOUN
ejpam-4356	3	35	and	and	CCONJ
ejpam-4356	3	36	statistics	statistic	NOUN
ejpam-4356	3	37	,	,	PUNCT
ejpam-4356	3	38	college	college	NOUN
ejpam-4356	3	39	of	of	ADP
ejpam-4356	3	40	science	science	NOUN
ejpam-4356	3	41	in	in	ADP
ejpam-4356	3	42	mathematics	mathematic	NOUN
ejpam-4356	3	43	,	,	PUNCT
ejpam-4356	3	44	msu	msu	PROPN
ejpam-4356	3	45	-	-	PUNCT
ejpam-4356	3	46	iligan	iligan	PROPN
ejpam-4356	3	47	institute	institute	PROPN
ejpam-4356	3	48	of	of	ADP
ejpam-4356	3	49	technology	technology	PROPN
ejpam-4356	3	50	,	,	PUNCT
ejpam-4356	3	51	9200	9200	NUM
ejpam-4356	3	52	iligan	iligan	ADJ
ejpam-4356	3	53	city	city	NOUN
ejpam-4356	3	54	,	,	PUNCT
ejpam-4356	3	55	philippines	philippine	NOUN
ejpam-4356	3	56	abstract	abstract	ADJ
ejpam-4356	3	57	.	.	PUNCT
ejpam-4356	4	1	let	let	VERB
ejpam-4356	4	2	g	g	PRON
ejpam-4356	4	3	be	be	AUX
ejpam-4356	4	4	a	a	DET
ejpam-4356	4	5	simple	simple	ADJ
ejpam-4356	4	6	connected	connected	ADJ
ejpam-4356	4	7	graph	graph	NOUN
ejpam-4356	4	8	.	.	PUNCT
ejpam-4356	5	1	for	for	ADP
ejpam-4356	5	2	s	s	PROPN
ejpam-4356	5	3	⊆	⊆	NUM
ejpam-4356	5	4	v	v	NOUN
ejpam-4356	5	5	(	(	PUNCT
ejpam-4356	5	6	g	g	NOUN
ejpam-4356	5	7	)	)	PUNCT
ejpam-4356	5	8	,	,	PUNCT
ejpam-4356	5	9	the	the	DET
ejpam-4356	5	10	weakly	weakly	ADV
ejpam-4356	5	11	connected	connected	ADJ
ejpam-4356	5	12	closed	closed	ADJ
ejpam-4356	5	13	geodetic	geodetic	ADJ
ejpam-4356	5	14	dominating	dominating	NOUN
ejpam-4356	5	15	set	set	NOUN
ejpam-4356	5	16	s	s	NOUN
ejpam-4356	5	17	of	of	ADP
ejpam-4356	5	18	g	g	PROPN
ejpam-4356	5	19	is	be	AUX
ejpam-4356	5	20	a	a	DET
ejpam-4356	5	21	geodetic	geodetic	ADJ
ejpam-4356	5	22	closure	closure	NOUN
ejpam-4356	5	23	ig[s	ig[	NOUN
ejpam-4356	5	24	]	]	PUNCT
ejpam-4356	5	25	which	which	PRON
ejpam-4356	5	26	is	be	AUX
ejpam-4356	5	27	between	between	ADP
ejpam-4356	5	28	s	s	PRON
ejpam-4356	5	29	and	and	CCONJ
ejpam-4356	5	30	is	be	AUX
ejpam-4356	5	31	the	the	DET
ejpam-4356	5	32	set	set	NOUN
ejpam-4356	5	33	of	of	ADP
ejpam-4356	5	34	all	all	DET
ejpam-4356	5	35	vertices	vertex	NOUN
ejpam-4356	5	36	on	on	ADP
ejpam-4356	5	37	geodesics	geodesic	NOUN
ejpam-4356	5	38	(	(	PUNCT
ejpam-4356	5	39	shortest	short	ADJ
ejpam-4356	5	40	path	path	NOUN
ejpam-4356	5	41	)	)	PUNCT
ejpam-4356	5	42	between	between	ADP
ejpam-4356	5	43	two	two	NUM
ejpam-4356	5	44	vertices	vertex	NOUN
ejpam-4356	5	45	of	of	ADP
ejpam-4356	5	46	s.	s.	PROPN
ejpam-4356	5	47	we	we	PRON
ejpam-4356	5	48	select	select	VERB
ejpam-4356	5	49	vertices	vertex	NOUN
ejpam-4356	5	50	of	of	ADP
ejpam-4356	5	51	g	g	PROPN
ejpam-4356	5	52	sequentially	sequentially	ADV
ejpam-4356	5	53	as	as	SCONJ
ejpam-4356	5	54	follows	follow	VERB
ejpam-4356	5	55	:	:	PUNCT
ejpam-4356	5	56	select	select	VERB
ejpam-4356	5	57	a	a	DET
ejpam-4356	5	58	vertex	vertex	NOUN
ejpam-4356	5	59	v1	v1	NOUN
ejpam-4356	5	60	and	and	CCONJ
ejpam-4356	5	61	let	let	VERB
ejpam-4356	5	62	s1	s1	PROPN
ejpam-4356	5	63	=	=	SYM
ejpam-4356	5	64	{	{	PUNCT
ejpam-4356	5	65	v1	v1	NOUN
ejpam-4356	5	66	}	}	PUNCT
ejpam-4356	5	67	.	.	PUNCT
ejpam-4356	6	1	select	select	VERB
ejpam-4356	6	2	a	a	DET
ejpam-4356	6	3	vertex	vertex	NOUN
ejpam-4356	6	4	v2	v2	NOUN
ejpam-4356	6	5	̸=	̸=	PROPN
ejpam-4356	6	6	v1	v1	NOUN
ejpam-4356	6	7	and	and	CCONJ
ejpam-4356	6	8	let	let	VERB
ejpam-4356	6	9	s2	s2	VERB
ejpam-4356	6	10	=	=	SYM
ejpam-4356	6	11	{	{	PUNCT
ejpam-4356	6	12	v1	v1	PROPN
ejpam-4356	6	13	,	,	PUNCT
ejpam-4356	6	14	v2	v2	PROPN
ejpam-4356	6	15	}	}	PUNCT
ejpam-4356	6	16	.	.	PUNCT
ejpam-4356	7	1	then	then	ADV
ejpam-4356	7	2	successively	successively	ADV
ejpam-4356	7	3	select	select	VERB
ejpam-4356	7	4	vertex	vertex	NOUN
ejpam-4356	7	5	vi	vi	PROPN
ejpam-4356	7	6	/∈	/∈	NOUN
ejpam-4356	7	7	ig[si−1	ig[si−1	PROPN
ejpam-4356	7	8	]	]	PUNCT
ejpam-4356	7	9	and	and	CCONJ
ejpam-4356	7	10	let	let	VERB
ejpam-4356	7	11	si	si	X
ejpam-4356	7	12	=	=	ADJ
ejpam-4356	7	13	{	{	PUNCT
ejpam-4356	7	14	v1	v1	PROPN
ejpam-4356	7	15	,	,	PUNCT
ejpam-4356	7	16	v2	v2	PROPN
ejpam-4356	7	17	,	,	PUNCT
ejpam-4356	7	18	...	...	PUNCT
ejpam-4356	7	19	,	,	PUNCT
ejpam-4356	7	20	vi	vi	X
ejpam-4356	7	21	}	}	PUNCT
ejpam-4356	7	22	for	for	ADP
ejpam-4356	7	23	i	i	PROPN
ejpam-4356	7	24	=	=	NOUN
ejpam-4356	7	25	1	1	NUM
ejpam-4356	7	26	,	,	PUNCT
ejpam-4356	7	27	2	2	NUM
ejpam-4356	7	28	,	,	PUNCT
ejpam-4356	7	29	...	...	PUNCT
ejpam-4356	7	30	,	,	PUNCT
ejpam-4356	7	31	k	k	PROPN
ejpam-4356	7	32	until	until	SCONJ
ejpam-4356	7	33	we	we	PRON
ejpam-4356	7	34	select	select	VERB
ejpam-4356	7	35	a	a	DET
ejpam-4356	7	36	vertex	vertex	NOUN
ejpam-4356	7	37	vk	vk	NOUN
ejpam-4356	7	38	in	in	ADP
ejpam-4356	7	39	the	the	DET
ejpam-4356	7	40	given	give	VERB
ejpam-4356	7	41	manner	manner	NOUN
ejpam-4356	7	42	that	that	PRON
ejpam-4356	7	43	yields	yield	VERB
ejpam-4356	7	44	ig[sk	ig[sk	X
ejpam-4356	7	45	]	]	X
ejpam-4356	7	46	=	=	SYM
ejpam-4356	7	47	v	v	X
ejpam-4356	7	48	(	(	PUNCT
ejpam-4356	7	49	g	g	NOUN
ejpam-4356	7	50	)	)	PUNCT
ejpam-4356	7	51	.	.	PUNCT
ejpam-4356	8	1	also	also	ADV
ejpam-4356	8	2	,	,	PUNCT
ejpam-4356	8	3	the	the	DET
ejpam-4356	8	4	subgraph	subgraph	NOUN
ejpam-4356	8	5	weakly	weakly	ADV
ejpam-4356	8	6	induced	induced	ADJ
ejpam-4356	8	7	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	8	8	by	by	ADP
ejpam-4356	8	9	s	s	PRON
ejpam-4356	8	10	is	be	AUX
ejpam-4356	8	11	connected	connect	VERB
ejpam-4356	8	12	where	where	SCONJ
ejpam-4356	8	13	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	8	14	=	=	PUNCT
ejpam-4356	8	15	⟨n	⟨n	NUM
ejpam-4356	9	1	[	[	X
ejpam-4356	9	2	s	s	X
ejpam-4356	9	3	]	]	X
ejpam-4356	9	4	,	,	PUNCT
ejpam-4356	9	5	ew⟩	ew⟩	PUNCT
ejpam-4356	9	6	with	with	ADP
ejpam-4356	9	7	ew	ew	PROPN
ejpam-4356	9	8	=	=	SYM
ejpam-4356	9	9	{	{	PUNCT
ejpam-4356	9	10	u	u	NOUN
ejpam-4356	9	11	,	,	PUNCT
ejpam-4356	9	12	v	v	PROPN
ejpam-4356	9	13	∈	∈	PROPN
ejpam-4356	9	14	e(g	e(g	PROPN
ejpam-4356	9	15	)	)	PUNCT
ejpam-4356	9	16	:	:	PUNCT
ejpam-4356	9	17	u	u	PROPN
ejpam-4356	9	18	∈	∈	PROPN
ejpam-4356	9	19	s	s	X
ejpam-4356	9	20	or	or	CCONJ
ejpam-4356	9	21	v	v	ADP
ejpam-4356	9	22	∈	∈	NOUN
ejpam-4356	9	23	s	s	PART
ejpam-4356	9	24	}	}	PUNCT
ejpam-4356	9	25	and	and	CCONJ
ejpam-4356	9	26	s	s	VERB
ejpam-4356	9	27	is	be	AUX
ejpam-4356	9	28	a	a	DET
ejpam-4356	9	29	dominating	dominating	NOUN
ejpam-4356	9	30	set	set	NOUN
ejpam-4356	9	31	of	of	ADP
ejpam-4356	9	32	g.	g.	PROPN
ejpam-4356	9	33	the	the	DET
ejpam-4356	9	34	minimum	minimum	ADJ
ejpam-4356	9	35	cardinality	cardinality	NOUN
ejpam-4356	9	36	of	of	ADP
ejpam-4356	9	37	weakly	weakly	ADJ
ejpam-4356	9	38	connected	connected	ADJ
ejpam-4356	9	39	closed	closed	ADJ
ejpam-4356	9	40	geodetic	geodetic	ADJ
ejpam-4356	9	41	dominating	dominating	NOUN
ejpam-4356	9	42	set	set	NOUN
ejpam-4356	9	43	of	of	ADP
ejpam-4356	9	44	g	g	PROPN
ejpam-4356	9	45	is	be	AUX
ejpam-4356	9	46	denoted	denote	VERB
ejpam-4356	9	47	by	by	ADP
ejpam-4356	9	48	γwcg(g	γwcg(g	NOUN
ejpam-4356	9	49	)	)	PUNCT
ejpam-4356	9	50	.	.	PUNCT
ejpam-4356	10	1	in	in	ADP
ejpam-4356	10	2	this	this	DET
ejpam-4356	10	3	paper	paper	NOUN
ejpam-4356	10	4	,	,	PUNCT
ejpam-4356	10	5	the	the	DET
ejpam-4356	10	6	authors	author	NOUN
ejpam-4356	10	7	show	show	VERB
ejpam-4356	10	8	and	and	CCONJ
ejpam-4356	10	9	investigate	investigate	VERB
ejpam-4356	10	10	the	the	DET
ejpam-4356	10	11	concept	concept	NOUN
ejpam-4356	10	12	weakly	weakly	ADV
ejpam-4356	10	13	connected	connected	ADJ
ejpam-4356	10	14	closed	closed	ADJ
ejpam-4356	10	15	geodetic	geodetic	ADJ
ejpam-4356	10	16	dominating	dominating	NOUN
ejpam-4356	10	17	sets	set	NOUN
ejpam-4356	10	18	of	of	ADP
ejpam-4356	10	19	some	some	DET
ejpam-4356	10	20	graphs	graph	NOUN
ejpam-4356	10	21	and	and	CCONJ
ejpam-4356	10	22	the	the	DET
ejpam-4356	10	23	join	join	NOUN
ejpam-4356	10	24	,	,	PUNCT
ejpam-4356	10	25	corona	corona	PROPN
ejpam-4356	10	26	,	,	PUNCT
ejpam-4356	10	27	and	and	CCONJ
ejpam-4356	10	28	cartesian	cartesian	ADJ
ejpam-4356	10	29	product	product	NOUN
ejpam-4356	10	30	of	of	ADP
ejpam-4356	10	31	two	two	NUM
ejpam-4356	10	32	graphs	graph	NOUN
ejpam-4356	10	33	are	be	AUX
ejpam-4356	10	34	characterized	characterize	VERB
ejpam-4356	10	35	.	.	PUNCT
ejpam-4356	11	1	the	the	DET
ejpam-4356	11	2	weakly	weakly	ADJ
ejpam-4356	11	3	connected	connected	ADJ
ejpam-4356	11	4	closed	close	VERB
ejpam-4356	11	5	geodetic	geodetic	ADJ
ejpam-4356	11	6	domination	domination	NOUN
ejpam-4356	11	7	numbers	number	NOUN
ejpam-4356	11	8	of	of	ADP
ejpam-4356	11	9	these	these	DET
ejpam-4356	11	10	graphs	graph	NOUN
ejpam-4356	11	11	are	be	AUX
ejpam-4356	11	12	determined	determine	VERB
ejpam-4356	11	13	.	.	PUNCT
ejpam-4356	12	1	also	also	ADV
ejpam-4356	12	2	,	,	PUNCT
ejpam-4356	12	3	some	some	DET
ejpam-4356	12	4	relationships	relationship	NOUN
ejpam-4356	12	5	between	between	ADP
ejpam-4356	12	6	weakly	weakly	ADV
ejpam-4356	12	7	connected	connected	ADJ
ejpam-4356	12	8	closed	closed	ADJ
ejpam-4356	12	9	geodetic	geodetic	ADJ
ejpam-4356	12	10	dominating	dominating	NOUN
ejpam-4356	12	11	set	set	NOUN
ejpam-4356	12	12	,	,	PUNCT
ejpam-4356	12	13	weakly	weakly	ADV
ejpam-4356	12	14	connected	connected	ADJ
ejpam-4356	12	15	closed	closed	ADJ
ejpam-4356	12	16	geodetic	geodetic	ADJ
ejpam-4356	12	17	set	set	NOUN
ejpam-4356	12	18	,	,	PUNCT
ejpam-4356	12	19	geodetic	geodetic	ADJ
ejpam-4356	12	20	dominating	dominating	NOUN
ejpam-4356	12	21	set	set	NOUN
ejpam-4356	12	22	,	,	PUNCT
ejpam-4356	12	23	and	and	CCONJ
ejpam-4356	12	24	geodetic	geodetic	ADJ
ejpam-4356	12	25	connected	connected	ADJ
ejpam-4356	12	26	dominating	dominating	NOUN
ejpam-4356	12	27	set	set	NOUN
ejpam-4356	12	28	are	be	AUX
ejpam-4356	12	29	established	establish	VERB
ejpam-4356	12	30	.	.	PUNCT
ejpam-4356	13	1	2020	2020	NUM
ejpam-4356	13	2	mathematics	mathematics	PROPN
ejpam-4356	13	3	subject	subject	NOUN
ejpam-4356	13	4	classifications	classification	NOUN
ejpam-4356	13	5	:	:	PUNCT
ejpam-4356	13	6	05c69	05c69	X
ejpam-4356	13	7	key	key	ADJ
ejpam-4356	13	8	words	word	NOUN
ejpam-4356	13	9	and	and	CCONJ
ejpam-4356	13	10	phrases	phrase	NOUN
ejpam-4356	13	11	:	:	PUNCT
ejpam-4356	13	12	weakly	weakly	ADJ
ejpam-4356	13	13	connected	connected	ADJ
ejpam-4356	13	14	closed	closed	ADJ
ejpam-4356	13	15	geodetic	geodetic	ADJ
ejpam-4356	13	16	dominating	dominating	NOUN
ejpam-4356	13	17	set	set	NOUN
ejpam-4356	13	18	,	,	PUNCT
ejpam-4356	13	19	and	and	CCONJ
ejpam-4356	13	20	weakly	weakly	ADV
ejpam-4356	13	21	connected	connected	ADJ
ejpam-4356	13	22	closed	close	VERB
ejpam-4356	13	23	geodetic	geodetic	ADJ
ejpam-4356	13	24	domination	domination	NOUN
ejpam-4356	13	25	number	number	NOUN
ejpam-4356	13	26	.	.	PUNCT
ejpam-4356	14	1	1	1	X
ejpam-4356	14	2	.	.	X
ejpam-4356	14	3	introduction	introduction	NOUN
ejpam-4356	14	4	in	in	ADP
ejpam-4356	14	5	this	this	DET
ejpam-4356	14	6	paper	paper	NOUN
ejpam-4356	14	7	we	we	PRON
ejpam-4356	14	8	explore	explore	VERB
ejpam-4356	14	9	a	a	DET
ejpam-4356	14	10	parameter	parameter	NOUN
ejpam-4356	14	11	that	that	PRON
ejpam-4356	14	12	is	be	AUX
ejpam-4356	14	13	,	,	PUNCT
ejpam-4356	14	14	defined	define	VERB
ejpam-4356	14	15	in	in	ADP
ejpam-4356	14	16	the	the	DET
ejpam-4356	14	17	same	same	ADJ
ejpam-4356	14	18	manner	manner	NOUN
ejpam-4356	14	19	that	that	SCONJ
ejpam-4356	14	20	the	the	DET
ejpam-4356	14	21	wellknown	wellknown	ADJ
ejpam-4356	14	22	weakly	weakly	ADJ
ejpam-4356	14	23	connected	connected	ADJ
ejpam-4356	14	24	closed	close	VERB
ejpam-4356	14	25	geodetic	geodetic	ADJ
ejpam-4356	14	26	number	number	NOUN
ejpam-4356	14	27	of	of	ADP
ejpam-4356	14	28	a	a	DET
ejpam-4356	14	29	graph	graph	NOUN
ejpam-4356	14	30	g	g	NOUN
ejpam-4356	14	31	is	be	AUX
ejpam-4356	14	32	.	.	PUNCT
ejpam-4356	15	1	indeed	indeed	ADV
ejpam-4356	15	2	,	,	PUNCT
ejpam-4356	15	3	while	while	SCONJ
ejpam-4356	15	4	a	a	DET
ejpam-4356	15	5	weakly	weakly	ADV
ejpam-4356	15	6	connected	connected	ADJ
ejpam-4356	15	7	closed	closed	ADJ
ejpam-4356	15	8	geodetic	geodetic	ADJ
ejpam-4356	15	9	set	set	NOUN
ejpam-4356	15	10	of	of	ADP
ejpam-4356	15	11	a	a	DET
ejpam-4356	15	12	graph	graph	NOUN
ejpam-4356	15	13	g	g	NOUN
ejpam-4356	15	14	necessitates	necessitate	VERB
ejpam-4356	15	15	a	a	DET
ejpam-4356	15	16	geodetic	geodetic	ADJ
ejpam-4356	15	17	closure	closure	NOUN
ejpam-4356	15	18	ig[s	ig[	NOUN
ejpam-4356	15	19	]	]	PUNCT
ejpam-4356	15	20	which	which	PRON
ejpam-4356	15	21	is	be	AUX
ejpam-4356	15	22	between	between	ADP
ejpam-4356	15	23	s	s	PRON
ejpam-4356	15	24	and	and	CCONJ
ejpam-4356	15	25	is	be	AUX
ejpam-4356	15	26	the	the	DET
ejpam-4356	15	27	set	set	NOUN
ejpam-4356	15	28	of	of	ADP
ejpam-4356	15	29	all	all	DET
ejpam-4356	15	30	vertices	vertex	NOUN
ejpam-4356	15	31	on	on	ADP
ejpam-4356	15	32	geodesics	geodesic	NOUN
ejpam-4356	15	33	(	(	PUNCT
ejpam-4356	15	34	shortest	short	ADJ
ejpam-4356	15	35	path	path	NOUN
ejpam-4356	15	36	)	)	PUNCT
ejpam-4356	15	37	between	between	ADP
ejpam-4356	15	38	two	two	NUM
ejpam-4356	15	39	vertices	vertex	NOUN
ejpam-4356	15	40	of	of	ADP
ejpam-4356	15	41	s	s	PRON
ejpam-4356	15	42	and	and	CCONJ
ejpam-4356	15	43	the	the	DET
ejpam-4356	15	44	subgraph	subgraph	NOUN
ejpam-4356	15	45	weakly	weakly	ADV
ejpam-4356	15	46	induced	induced	ADJ
ejpam-4356	15	47	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	15	48	by	by	ADP
ejpam-4356	15	49	s	s	PRON
ejpam-4356	15	50	is	be	AUX
ejpam-4356	15	51	connected	connect	VERB
ejpam-4356	15	52	where	where	SCONJ
ejpam-4356	15	53	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	15	54	=	=	PUNCT
ejpam-4356	15	55	⟨n	⟨n	NUM
ejpam-4356	16	1	[	[	X
ejpam-4356	16	2	s	s	X
ejpam-4356	16	3	]	]	X
ejpam-4356	16	4	,	,	PUNCT
ejpam-4356	16	5	ew⟩	ew⟩	VERB
ejpam-4356	16	6	with	with	ADP
ejpam-4356	16	7	∗corresponding	∗corresponde	VERB
ejpam-4356	16	8	author	author	NOUN
ejpam-4356	16	9	.	.	PUNCT
ejpam-4356	17	1	doi	doi	NOUN
ejpam-4356	17	2	:	:	PUNCT
ejpam-4356	17	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4356	https://doi.org/10.29020/nybg.ejpam.v15i2.4356	NOUN
ejpam-4356	17	4	email	email	NOUN
ejpam-4356	17	5	addresses	address	NOUN
ejpam-4356	17	6	:	:	PUNCT
ejpam-4356	17	7	jamil.hamja@g.msuiit.edu.ph	jamil.hamja@g.msuiit.edu.ph	PROPN
ejpam-4356	17	8	(	(	PUNCT
ejpam-4356	17	9	j.	j.	PROPN
ejpam-4356	17	10	hamja	hamja	PROPN
ejpam-4356	17	11	)	)	PUNCT
ejpam-4356	17	12	,	,	PUNCT
ejpam-4356	17	13	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-4356	17	14	(	(	PUNCT
ejpam-4356	17	15	i.	i.	PROPN
ejpam-4356	17	16	aniversario	aniversario	PROPN
ejpam-4356	17	17	)	)	PUNCT
ejpam-4356	17	18	,	,	PUNCT
ejpam-4356	17	19	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4356	17	20	(	(	PUNCT
ejpam-4356	17	21	h.	h.	PROPN
ejpam-4356	17	22	rara	rara	PROPN
ejpam-4356	17	23	)	)	PUNCT
ejpam-4356	17	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4356	18	1	736	736	NUM
ejpam-4356	19	1	©	©	ADP
ejpam-4356	19	2	2022	2022	NUM
ejpam-4356	19	3	ejpam	ejpam	VERB
ejpam-4356	19	4	all	all	DET
ejpam-4356	19	5	rights	right	NOUN
ejpam-4356	19	6	reserved	reserve	VERB
ejpam-4356	19	7	.	.	PUNCT
ejpam-4356	20	1	j.	j.	PROPN
ejpam-4356	20	2	hamja	hamja	PROPN
ejpam-4356	20	3	,	,	PUNCT
ejpam-4356	20	4	i.	i.	PROPN
ejpam-4356	20	5	aniversario	aniversario	PROPN
ejpam-4356	20	6	,	,	PUNCT
ejpam-4356	20	7	h.	h.	PROPN
ejpam-4356	20	8	rara	rara	PROPN
ejpam-4356	20	9	/	/	SYM
ejpam-4356	20	10	eur	eur	PROPN
ejpam-4356	20	11	.	.	PUNCT
ejpam-4356	21	1	j.	j.	PROPN
ejpam-4356	21	2	pure	pure	PROPN
ejpam-4356	21	3	appl	appl	PROPN
ejpam-4356	21	4	.	.	PROPN
ejpam-4356	21	5	math	math	PROPN
ejpam-4356	21	6	,	,	PUNCT
ejpam-4356	21	7	15	15	NUM
ejpam-4356	21	8	(	(	PUNCT
ejpam-4356	21	9	2	2	NUM
ejpam-4356	21	10	)	)	PUNCT
ejpam-4356	21	11	(	(	PUNCT
ejpam-4356	21	12	2022	2022	NUM
ejpam-4356	21	13	)	)	PUNCT
ejpam-4356	21	14	,	,	PUNCT
ejpam-4356	21	15	736	736	NUM
ejpam-4356	21	16	-	-	SYM
ejpam-4356	21	17	752	752	NUM
ejpam-4356	21	18	737	737	NUM
ejpam-4356	21	19	ew	ew	NOUN
ejpam-4356	21	20	=	=	PUNCT
ejpam-4356	21	21	{	{	PUNCT
ejpam-4356	21	22	u	u	NOUN
ejpam-4356	21	23	,	,	PUNCT
ejpam-4356	21	24	v	v	PROPN
ejpam-4356	21	25	∈	∈	PROPN
ejpam-4356	21	26	e(g	e(g	PROPN
ejpam-4356	21	27	)	)	PUNCT
ejpam-4356	21	28	:	:	PUNCT
ejpam-4356	22	1	u	u	PROPN
ejpam-4356	22	2	∈	∈	PROPN
ejpam-4356	22	3	s	s	X
ejpam-4356	22	4	or	or	CCONJ
ejpam-4356	22	5	v	v	ADP
ejpam-4356	22	6	∈	∈	NOUN
ejpam-4356	22	7	s	s	PART
ejpam-4356	22	8	}	}	PUNCT
ejpam-4356	22	9	.	.	PUNCT
ejpam-4356	23	1	the	the	DET
ejpam-4356	23	2	motivation	motivation	NOUN
ejpam-4356	23	3	of	of	ADP
ejpam-4356	23	4	introducing	introduce	VERB
ejpam-4356	23	5	the	the	DET
ejpam-4356	23	6	concept	concept	NOUN
ejpam-4356	23	7	is	be	AUX
ejpam-4356	23	8	to	to	PART
ejpam-4356	23	9	give	give	VERB
ejpam-4356	23	10	a	a	DET
ejpam-4356	23	11	further	further	ADJ
ejpam-4356	23	12	investgation	investgation	NOUN
ejpam-4356	23	13	on	on	ADP
ejpam-4356	23	14	weakly	weakly	ADJ
ejpam-4356	23	15	connected	connected	ADJ
ejpam-4356	23	16	domination	domination	NOUN
ejpam-4356	23	17	,	,	PUNCT
ejpam-4356	23	18	closed	close	VERB
ejpam-4356	23	19	geodetic	geodetic	ADJ
ejpam-4356	23	20	domination	domination	NOUN
ejpam-4356	23	21	and	and	CCONJ
ejpam-4356	23	22	some	some	PRON
ejpam-4356	23	23	of	of	ADP
ejpam-4356	23	24	its	its	PRON
ejpam-4356	23	25	variations	variation	NOUN
ejpam-4356	23	26	.	.	PUNCT
ejpam-4356	24	1	in	in	ADP
ejpam-4356	24	2	fact	fact	NOUN
ejpam-4356	24	3	,	,	PUNCT
ejpam-4356	24	4	it	it	PRON
ejpam-4356	24	5	can	can	AUX
ejpam-4356	24	6	be	be	AUX
ejpam-4356	24	7	shown	show	VERB
ejpam-4356	24	8	that	that	SCONJ
ejpam-4356	24	9	every	every	DET
ejpam-4356	24	10	weakly	weakly	ADV
ejpam-4356	24	11	connected	connected	ADJ
ejpam-4356	24	12	closed	closed	ADJ
ejpam-4356	24	13	geodetic	geodetic	ADJ
ejpam-4356	24	14	dominating	dominating	NOUN
ejpam-4356	24	15	set	set	NOUN
ejpam-4356	24	16	is	be	AUX
ejpam-4356	24	17	a	a	DET
ejpam-4356	24	18	weakly	weakly	ADV
ejpam-4356	24	19	connected	connected	ADJ
ejpam-4356	24	20	closed	closed	ADJ
ejpam-4356	24	21	geodetic	geodetic	ADJ
ejpam-4356	24	22	set	set	NOUN
ejpam-4356	24	23	of	of	ADP
ejpam-4356	24	24	a	a	DET
ejpam-4356	24	25	graph	graph	NOUN
ejpam-4356	24	26	g.	g.	NOUN
ejpam-4356	24	27	thereupon	thereupon	ADV
ejpam-4356	24	28	,	,	PUNCT
ejpam-4356	24	29	the	the	DET
ejpam-4356	24	30	weakly	weakly	ADV
ejpam-4356	24	31	connected	connected	ADJ
ejpam-4356	24	32	closed	closed	ADJ
ejpam-4356	24	33	geodetic	geodetic	ADJ
ejpam-4356	24	34	number	number	NOUN
ejpam-4356	24	35	of	of	ADP
ejpam-4356	24	36	a	a	DET
ejpam-4356	24	37	graph	graph	NOUN
ejpam-4356	24	38	g	g	NOUN
ejpam-4356	24	39	is	be	AUX
ejpam-4356	24	40	at	at	ADP
ejpam-4356	24	41	most	most	ADV
ejpam-4356	24	42	equal	equal	ADJ
ejpam-4356	24	43	to	to	ADP
ejpam-4356	24	44	the	the	DET
ejpam-4356	24	45	weakly	weakly	ADV
ejpam-4356	24	46	connected	connected	ADJ
ejpam-4356	24	47	closed	close	VERB
ejpam-4356	24	48	geodetic	geodetic	ADJ
ejpam-4356	24	49	domination	domination	NOUN
ejpam-4356	24	50	number	number	NOUN
ejpam-4356	24	51	of	of	ADP
ejpam-4356	24	52	a	a	DET
ejpam-4356	24	53	graph	graph	NOUN
ejpam-4356	24	54	g.	g.	NOUN
ejpam-4356	24	55	the	the	DET
ejpam-4356	24	56	concept	concept	NOUN
ejpam-4356	24	57	of	of	ADP
ejpam-4356	24	58	weakly	weakly	ADJ
ejpam-4356	24	59	connected	connected	ADJ
ejpam-4356	24	60	closed	closed	ADJ
ejpam-4356	24	61	geodetic	geodetic	ADJ
ejpam-4356	24	62	nmbers	nmber	NOUN
ejpam-4356	24	63	was	be	AUX
ejpam-4356	24	64	introduce	introduce	ADJ
ejpam-4356	24	65	and	and	CCONJ
ejpam-4356	24	66	studied	study	VERB
ejpam-4356	24	67	by	by	ADP
ejpam-4356	24	68	patangan	patangan	NOUN
ejpam-4356	24	69	,	,	PUNCT
ejpam-4356	24	70	et	et	NOUN
ejpam-4356	24	71	.	.	PUNCT
ejpam-4356	25	1	al	al	PROPN
ejpam-4356	26	1	[	[	X
ejpam-4356	26	2	12	12	NUM
ejpam-4356	26	3	]	]	PUNCT
ejpam-4356	26	4	.	.	PUNCT
ejpam-4356	27	1	some	some	DET
ejpam-4356	27	2	concept	concept	NOUN
ejpam-4356	27	3	and	and	CCONJ
ejpam-4356	27	4	its	its	PRON
ejpam-4356	27	5	number	number	NOUN
ejpam-4356	27	6	are	be	AUX
ejpam-4356	27	7	also	also	ADV
ejpam-4356	27	8	introduced	introduce	VERB
ejpam-4356	27	9	by	by	ADP
ejpam-4356	27	10	aniversario	aniversario	NOUN
ejpam-4356	27	11	,	,	PUNCT
ejpam-4356	27	12	et.al	et.al	VERB
ejpam-4356	27	13	[	[	X
ejpam-4356	27	14	1	1	NUM
ejpam-4356	27	15	]	]	PUNCT
ejpam-4356	27	16	,	,	PUNCT
ejpam-4356	27	17	chellathurai	chellathurai	PROPN
ejpam-4356	27	18	,	,	PUNCT
ejpam-4356	27	19	et	et	NOUN
ejpam-4356	27	20	.	.	PUNCT
ejpam-4356	28	1	al	al	PROPN
ejpam-4356	29	1	[	[	X
ejpam-4356	29	2	6	6	NUM
ejpam-4356	29	3	]	]	PUNCT
ejpam-4356	29	4	,	,	PUNCT
ejpam-4356	29	5	dunbar	dunbar	NOUN
ejpam-4356	29	6	,	,	PUNCT
ejpam-4356	29	7	et.al	et.al	PROPN
ejpam-4356	29	8	[	[	X
ejpam-4356	29	9	7	7	NUM
ejpam-4356	29	10	]	]	PUNCT
ejpam-4356	29	11	,	,	PUNCT
ejpam-4356	29	12	jamil	jamil	PROPN
ejpam-4356	29	13	,	,	PUNCT
ejpam-4356	29	14	et.al	et.al	VERB
ejpam-4356	30	1	[	[	X
ejpam-4356	30	2	11	11	NUM
ejpam-4356	30	3	]	]	PUNCT
ejpam-4356	30	4	,	,	PUNCT
ejpam-4356	30	5	and	and	CCONJ
ejpam-4356	30	6	sandueta	sandueta	ADJ
ejpam-4356	30	7	,	,	PUNCT
ejpam-4356	30	8	et.al	et.al	VERB
ejpam-4356	30	9	[	[	PUNCT
ejpam-4356	30	10	13	13	NUM
ejpam-4356	30	11	]	]	PUNCT
ejpam-4356	30	12	.	.	PUNCT
ejpam-4356	31	1	furthermore	furthermore	ADV
ejpam-4356	31	2	,	,	PUNCT
ejpam-4356	31	3	the	the	DET
ejpam-4356	31	4	weakly	weakly	ADV
ejpam-4356	31	5	connected	connected	ADJ
ejpam-4356	31	6	closed	closed	ADJ
ejpam-4356	31	7	geodetic	geodetic	ADJ
ejpam-4356	31	8	number	number	NOUN
ejpam-4356	31	9	of	of	ADP
ejpam-4356	31	10	a	a	DET
ejpam-4356	31	11	graph	graph	NOUN
ejpam-4356	31	12	may	may	AUX
ejpam-4356	31	13	be	be	AUX
ejpam-4356	31	14	used	use	VERB
ejpam-4356	31	15	to	to	PART
ejpam-4356	31	16	give	give	VERB
ejpam-4356	31	17	bounds	bound	NOUN
ejpam-4356	31	18	on	on	ADP
ejpam-4356	31	19	some	some	DET
ejpam-4356	31	20	weakly	weakly	ADV
ejpam-4356	31	21	connected	connected	ADJ
ejpam-4356	31	22	closed	close	VERB
ejpam-4356	31	23	geodetic	geodetic	ADJ
ejpam-4356	31	24	domination	domination	NOUN
ejpam-4356	31	25	related	relate	VERB
ejpam-4356	31	26	parameters	parameter	NOUN
ejpam-4356	31	27	.	.	PUNCT
ejpam-4356	32	1	moreover	moreover	ADV
ejpam-4356	32	2	,	,	PUNCT
ejpam-4356	32	3	this	this	DET
ejpam-4356	32	4	newly	newly	ADV
ejpam-4356	32	5	concept	concept	NOUN
ejpam-4356	32	6	may	may	AUX
ejpam-4356	32	7	be	be	AUX
ejpam-4356	32	8	applied	apply	VERB
ejpam-4356	32	9	to	to	PART
ejpam-4356	32	10	introduce	introduce	VERB
ejpam-4356	32	11	some	some	DET
ejpam-4356	32	12	concepts	concept	NOUN
ejpam-4356	32	13	(	(	PUNCT
ejpam-4356	32	14	say	say	INTJ
ejpam-4356	32	15	,	,	PUNCT
ejpam-4356	32	16	a	a	DET
ejpam-4356	32	17	variant	variant	NOUN
ejpam-4356	32	18	of	of	ADP
ejpam-4356	32	19	weakly	weakly	ADJ
ejpam-4356	32	20	connected	connected	ADJ
ejpam-4356	32	21	closed	close	VERB
ejpam-4356	32	22	geodetic	geodetic	ADJ
ejpam-4356	32	23	domination	domination	NOUN
ejpam-4356	32	24	)	)	PUNCT
ejpam-4356	32	25	in	in	ADP
ejpam-4356	32	26	the	the	DET
ejpam-4356	32	27	future	future	NOUN
ejpam-4356	32	28	.	.	PUNCT
ejpam-4356	33	1	2	2	X
ejpam-4356	33	2	.	.	X
ejpam-4356	33	3	terminology	terminology	NOUN
ejpam-4356	33	4	and	and	CCONJ
ejpam-4356	33	5	notation	notation	NOUN
ejpam-4356	33	6	a	a	DET
ejpam-4356	33	7	set	set	NOUN
ejpam-4356	33	8	is	be	AUX
ejpam-4356	33	9	a	a	DET
ejpam-4356	33	10	dominating	dominating	NOUN
ejpam-4356	33	11	set	set	NOUN
ejpam-4356	33	12	of	of	ADP
ejpam-4356	33	13	g	g	PROPN
ejpam-4356	33	14	if	if	SCONJ
ejpam-4356	33	15	ng[s	ng[	NOUN
ejpam-4356	33	16	]	]	PUNCT
ejpam-4356	33	17	=	=	SYM
ejpam-4356	33	18	v	v	NOUN
ejpam-4356	33	19	(	(	PUNCT
ejpam-4356	33	20	g	g	NOUN
ejpam-4356	33	21	)	)	PUNCT
ejpam-4356	33	22	.	.	PUNCT
ejpam-4356	34	1	the	the	DET
ejpam-4356	34	2	domination	domination	NOUN
ejpam-4356	34	3	number	number	NOUN
ejpam-4356	34	4	of	of	ADP
ejpam-4356	34	5	g	g	NOUN
ejpam-4356	34	6	,	,	PUNCT
ejpam-4356	34	7	denoted	denote	VERB
ejpam-4356	34	8	by	by	ADP
ejpam-4356	34	9	γ(g	γ(g	PROPN
ejpam-4356	34	10	)	)	PUNCT
ejpam-4356	34	11	,	,	PUNCT
ejpam-4356	34	12	is	be	AUX
ejpam-4356	34	13	the	the	DET
ejpam-4356	34	14	minimum	minimum	ADJ
ejpam-4356	34	15	cardinality	cardinality	NOUN
ejpam-4356	34	16	among	among	ADP
ejpam-4356	34	17	the	the	DET
ejpam-4356	34	18	dominating	dominating	NOUN
ejpam-4356	34	19	sets	set	NOUN
ejpam-4356	34	20	of	of	ADP
ejpam-4356	34	21	g.	g.	PROPN
ejpam-4356	34	22	a	a	DET
ejpam-4356	34	23	dominating	dominating	NOUN
ejpam-4356	34	24	set	set	NOUN
ejpam-4356	34	25	s	s	NOUN
ejpam-4356	34	26	with	with	ADP
ejpam-4356	34	27	|s|	|s|	PROPN
ejpam-4356	34	28	=	=	SYM
ejpam-4356	34	29	γ(g	γ(g	PROPN
ejpam-4356	34	30	)	)	PUNCT
ejpam-4356	34	31	is	be	AUX
ejpam-4356	34	32	said	say	VERB
ejpam-4356	34	33	to	to	PART
ejpam-4356	34	34	be	be	AUX
ejpam-4356	34	35	γ	γ	X
ejpam-4356	34	36	-	-	PUNCT
ejpam-4356	34	37	set	set	NOUN
ejpam-4356	34	38	of	of	ADP
ejpam-4356	34	39	g.	g.	PROPN
ejpam-4356	34	40	a	a	DET
ejpam-4356	34	41	connected	connect	VERB
ejpam-4356	34	42	dominating	dominating	NOUN
ejpam-4356	34	43	set	set	NOUN
ejpam-4356	34	44	s	s	PROPN
ejpam-4356	34	45	of	of	ADP
ejpam-4356	34	46	a	a	DET
ejpam-4356	34	47	graph	graph	NOUN
ejpam-4356	34	48	g	g	NOUN
ejpam-4356	34	49	is	be	AUX
ejpam-4356	34	50	a	a	DET
ejpam-4356	34	51	dominating	dominating	NOUN
ejpam-4356	34	52	set	set	NOUN
ejpam-4356	34	53	such	such	ADJ
ejpam-4356	34	54	that	that	SCONJ
ejpam-4356	34	55	the	the	DET
ejpam-4356	34	56	subgraph	subgraph	NOUN
ejpam-4356	34	57	⟨s⟩	⟨s⟩	PROPN
ejpam-4356	34	58	induced	induce	VERB
ejpam-4356	34	59	by	by	ADP
ejpam-4356	34	60	s	s	PROPN
ejpam-4356	34	61	in	in	ADP
ejpam-4356	34	62	g	g	PROPN
ejpam-4356	34	63	is	be	AUX
ejpam-4356	34	64	connected	connect	VERB
ejpam-4356	34	65	.	.	PUNCT
ejpam-4356	35	1	the	the	DET
ejpam-4356	35	2	minimum	minimum	ADJ
ejpam-4356	35	3	cardinality	cardinality	NOUN
ejpam-4356	35	4	of	of	ADP
ejpam-4356	35	5	a	a	DET
ejpam-4356	35	6	connected	connect	VERB
ejpam-4356	35	7	dominating	dominating	NOUN
ejpam-4356	35	8	set	set	NOUN
ejpam-4356	35	9	of	of	ADP
ejpam-4356	35	10	g	g	PROPN
ejpam-4356	35	11	is	be	AUX
ejpam-4356	35	12	called	call	VERB
ejpam-4356	35	13	the	the	DET
ejpam-4356	35	14	connected	connected	ADJ
ejpam-4356	35	15	domination	domination	NOUN
ejpam-4356	35	16	number	number	NOUN
ejpam-4356	35	17	of	of	ADP
ejpam-4356	35	18	g	g	NOUN
ejpam-4356	35	19	,	,	PUNCT
ejpam-4356	35	20	denoted	denote	VERB
ejpam-4356	35	21	by	by	ADP
ejpam-4356	35	22	γc(g	γc(g	NOUN
ejpam-4356	35	23	)	)	PUNCT
ejpam-4356	35	24	.	.	PUNCT
ejpam-4356	36	1	a	a	DET
ejpam-4356	36	2	connected	connect	VERB
ejpam-4356	36	3	dominating	dominating	NOUN
ejpam-4356	36	4	set	set	NOUN
ejpam-4356	36	5	s	s	NOUN
ejpam-4356	36	6	with	with	ADP
ejpam-4356	36	7	|s|	|s|	NOUN
ejpam-4356	36	8	=	=	SYM
ejpam-4356	36	9	γc(g	γc(g	X
ejpam-4356	36	10	)	)	PUNCT
ejpam-4356	36	11	is	be	AUX
ejpam-4356	36	12	called	call	VERB
ejpam-4356	36	13	γc	γc	NOUN
ejpam-4356	36	14	-	-	PUNCT
ejpam-4356	36	15	set	set	NOUN
ejpam-4356	36	16	of	of	ADP
ejpam-4356	36	17	g	g	PROPN
ejpam-4356	36	18	tarr	tarr	NOUN
ejpam-4356	36	19	,	,	PUNCT
ejpam-4356	36	20	et.al	et.al	VERB
ejpam-4356	36	21	[	[	X
ejpam-4356	36	22	14	14	NUM
ejpam-4356	36	23	]	]	PUNCT
ejpam-4356	36	24	,	,	PUNCT
ejpam-4356	36	25	and	and	CCONJ
ejpam-4356	36	26	duckworth	duckworth	NOUN
ejpam-4356	36	27	,	,	PUNCT
ejpam-4356	36	28	et.al	et.al	VERB
ejpam-4356	36	29	[	[	X
ejpam-4356	36	30	8	8	NUM
ejpam-4356	36	31	]	]	PUNCT
ejpam-4356	36	32	.	.	PUNCT
ejpam-4356	37	1	let	let	VERB
ejpam-4356	37	2	s	s	PRON
ejpam-4356	37	3	⊆	⊆	NUM
ejpam-4356	37	4	v	v	NOUN
ejpam-4356	37	5	(	(	PUNCT
ejpam-4356	37	6	g	g	NOUN
ejpam-4356	37	7	)	)	PUNCT
ejpam-4356	37	8	.	.	PUNCT
ejpam-4356	38	1	the	the	DET
ejpam-4356	38	2	subgraph	subgraph	NOUN
ejpam-4356	38	3	weakly	weakly	ADV
ejpam-4356	38	4	induced	induce	VERB
ejpam-4356	38	5	by	by	ADP
ejpam-4356	38	6	s	s	PROPN
ejpam-4356	38	7	is	be	AUX
ejpam-4356	38	8	the	the	DET
ejpam-4356	38	9	graph	graph	NOUN
ejpam-4356	38	10	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	38	11	=	=	PUNCT
ejpam-4356	38	12	(	(	PUNCT
ejpam-4356	38	13	ng[s	ng[s	PROPN
ejpam-4356	38	14	]	]	PUNCT
ejpam-4356	38	15	,	,	PUNCT
ejpam-4356	38	16	ew	ew	PROPN
ejpam-4356	38	17	)	)	PUNCT
ejpam-4356	38	18	,	,	PUNCT
ejpam-4356	38	19	where	where	SCONJ
ejpam-4356	38	20	ew	ew	AUX
ejpam-4356	38	21	=	=	PRON
ejpam-4356	38	22	{	{	PUNCT
ejpam-4356	38	23	uv	uv	PROPN
ejpam-4356	38	24	∈	∈	PROPN
ejpam-4356	38	25	e(g	e(g	PROPN
ejpam-4356	38	26	)	)	PUNCT
ejpam-4356	38	27	:	:	PUNCT
ejpam-4356	39	1	u	u	PROPN
ejpam-4356	39	2	∈	∈	PROPN
ejpam-4356	39	3	s	s	X
ejpam-4356	39	4	or	or	CCONJ
ejpam-4356	39	5	v	v	ADP
ejpam-4356	39	6	∈	∈	NOUN
ejpam-4356	39	7	s	s	PART
ejpam-4356	39	8	}	}	PUNCT
ejpam-4356	39	9	.	.	PUNCT
ejpam-4356	40	1	the	the	DET
ejpam-4356	40	2	symbol	symbol	NOUN
ejpam-4356	40	3	ew(s	ew(s	PRON
ejpam-4356	40	4	)	)	PUNCT
ejpam-4356	40	5	means	mean	VERB
ejpam-4356	40	6	ew	ew	INTJ
ejpam-4356	40	7	,	,	PUNCT
ejpam-4356	40	8	patangan	patangan	NOUN
ejpam-4356	40	9	,	,	PUNCT
ejpam-4356	40	10	et.al	et.al	VERB
ejpam-4356	40	11	[	[	X
ejpam-4356	40	12	12	12	NUM
ejpam-4356	40	13	]	]	PUNCT
ejpam-4356	40	14	.	.	PUNCT
ejpam-4356	41	1	a	a	DET
ejpam-4356	41	2	dominating	dominating	NOUN
ejpam-4356	41	3	set	set	NOUN
ejpam-4356	41	4	s	s	PROPN
ejpam-4356	41	5	⊆	⊆	NUM
ejpam-4356	41	6	v	v	NOUN
ejpam-4356	41	7	(	(	PUNCT
ejpam-4356	41	8	g	g	NOUN
ejpam-4356	41	9	)	)	PUNCT
ejpam-4356	41	10	is	be	AUX
ejpam-4356	41	11	a	a	DET
ejpam-4356	41	12	weakly	weakly	ADV
ejpam-4356	41	13	connected	connected	ADJ
ejpam-4356	41	14	dominating	dominating	NOUN
ejpam-4356	41	15	set	set	VERB
ejpam-4356	41	16	in	in	ADP
ejpam-4356	41	17	g	g	PROPN
ejpam-4356	41	18	if	if	SCONJ
ejpam-4356	41	19	the	the	DET
ejpam-4356	41	20	subgraph	subgraph	PROPN
ejpam-4356	41	21	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	41	22	weakly	weakly	ADV
ejpam-4356	41	23	induced	induce	VERB
ejpam-4356	41	24	by	by	ADP
ejpam-4356	41	25	s	s	PRON
ejpam-4356	41	26	is	be	AUX
ejpam-4356	41	27	connected	connect	VERB
ejpam-4356	41	28	.	.	PUNCT
ejpam-4356	42	1	the	the	DET
ejpam-4356	42	2	weakly	weakly	ADJ
ejpam-4356	42	3	connected	connected	ADJ
ejpam-4356	42	4	domination	domination	NOUN
ejpam-4356	42	5	number	number	NOUN
ejpam-4356	42	6	γw(g	γw(g	PUNCT
ejpam-4356	42	7	)	)	PUNCT
ejpam-4356	42	8	of	of	ADP
ejpam-4356	42	9	g	g	PROPN
ejpam-4356	42	10	is	be	AUX
ejpam-4356	42	11	the	the	DET
ejpam-4356	42	12	minimum	minimum	ADJ
ejpam-4356	42	13	cardinality	cardinality	NOUN
ejpam-4356	42	14	among	among	ADP
ejpam-4356	42	15	all	all	DET
ejpam-4356	42	16	weakly	weakly	ADV
ejpam-4356	42	17	connected	connected	ADJ
ejpam-4356	42	18	dominating	dominating	NOUN
ejpam-4356	42	19	sets	set	NOUN
ejpam-4356	42	20	of	of	ADP
ejpam-4356	42	21	g.	g.	PROPN
ejpam-4356	42	22	a	a	DET
ejpam-4356	42	23	weakly	weakly	ADV
ejpam-4356	42	24	connected	connected	ADJ
ejpam-4356	42	25	dominating	dominating	NOUN
ejpam-4356	42	26	set	set	NOUN
ejpam-4356	42	27	s	s	NOUN
ejpam-4356	42	28	with	with	ADP
ejpam-4356	42	29	|s|	|s|	NOUN
ejpam-4356	42	30	=	=	NOUN
ejpam-4356	42	31	γw(g	γw(g	X
ejpam-4356	42	32	)	)	PUNCT
ejpam-4356	42	33	is	be	AUX
ejpam-4356	42	34	said	say	VERB
ejpam-4356	42	35	to	to	PART
ejpam-4356	42	36	be	be	AUX
ejpam-4356	42	37	γw	γw	NOUN
ejpam-4356	42	38	-	-	PUNCT
ejpam-4356	42	39	set	set	NOUN
ejpam-4356	42	40	of	of	ADP
ejpam-4356	42	41	g	g	PROPN
ejpam-4356	42	42	,	,	PUNCT
ejpam-4356	42	43	sandueta	sandueta	ADJ
ejpam-4356	42	44	,	,	PUNCT
ejpam-4356	42	45	et.al	et.al	VERB
ejpam-4356	42	46	[	[	X
ejpam-4356	42	47	13	13	NUM
ejpam-4356	42	48	]	]	PUNCT
ejpam-4356	42	49	.	.	PUNCT
ejpam-4356	43	1	let	let	VERB
ejpam-4356	43	2	u	u	NOUN
ejpam-4356	43	3	,	,	PUNCT
ejpam-4356	43	4	v	v	PROPN
ejpam-4356	43	5	∈	∈	PROPN
ejpam-4356	43	6	v	v	NOUN
ejpam-4356	43	7	(	(	PUNCT
ejpam-4356	43	8	g	g	NOUN
ejpam-4356	43	9	)	)	PUNCT
ejpam-4356	43	10	.	.	PUNCT
ejpam-4356	44	1	a	a	DET
ejpam-4356	44	2	shortest	short	ADJ
ejpam-4356	44	3	path	path	NOUN
ejpam-4356	44	4	from	from	ADP
ejpam-4356	44	5	u	u	NOUN
ejpam-4356	44	6	to	to	ADP
ejpam-4356	44	7	v	v	NOUN
ejpam-4356	44	8	in	in	ADP
ejpam-4356	44	9	g	g	PROPN
ejpam-4356	44	10	is	be	AUX
ejpam-4356	44	11	called	call	VERB
ejpam-4356	44	12	a	a	DET
ejpam-4356	44	13	u	u	NOUN
ejpam-4356	44	14	-	-	NOUN
ejpam-4356	44	15	v	v	ADJ
ejpam-4356	44	16	geodesic	geodesic	NOUN
ejpam-4356	44	17	of	of	ADP
ejpam-4356	44	18	g.	g.	PROPN
ejpam-4356	44	19	the	the	DET
ejpam-4356	44	20	set	set	NOUN
ejpam-4356	44	21	ig[u	ig[u	PROPN
ejpam-4356	44	22	,	,	PUNCT
ejpam-4356	44	23	v	v	NOUN
ejpam-4356	44	24	]	]	PUNCT
ejpam-4356	44	25	consists	consist	VERB
ejpam-4356	44	26	of	of	ADP
ejpam-4356	44	27	u	u	NOUN
ejpam-4356	44	28	,	,	PUNCT
ejpam-4356	44	29	v	v	NOUN
ejpam-4356	44	30	,	,	PUNCT
ejpam-4356	44	31	and	and	CCONJ
ejpam-4356	44	32	all	all	DET
ejpam-4356	44	33	vertices	vertex	NOUN
ejpam-4356	44	34	lying	lie	VERB
ejpam-4356	44	35	in	in	ADP
ejpam-4356	44	36	some	some	DET
ejpam-4356	44	37	u	u	NOUN
ejpam-4356	44	38	-	-	NOUN
ejpam-4356	44	39	v	v	ADJ
ejpam-4356	44	40	geodesic	geodesic	NOUN
ejpam-4356	44	41	of	of	ADP
ejpam-4356	44	42	g.	g.	PROPN
ejpam-4356	44	43	for	for	ADP
ejpam-4356	44	44	a	a	DET
ejpam-4356	44	45	nonempty	nonempty	ADJ
ejpam-4356	44	46	subset	subset	NOUN
ejpam-4356	44	47	s	s	NOUN
ejpam-4356	44	48	of	of	ADP
ejpam-4356	44	49	v	v	NOUN
ejpam-4356	44	50	(	(	PUNCT
ejpam-4356	44	51	g	g	NOUN
ejpam-4356	44	52	)	)	PUNCT
ejpam-4356	44	53	,	,	PUNCT
ejpam-4356	44	54	ig[s	ig[s	PROPN
ejpam-4356	44	55	]	]	PUNCT
ejpam-4356	45	1	=	=	SYM
ejpam-4356	45	2	⋃	⋃	NOUN
ejpam-4356	45	3	u	u	NOUN
ejpam-4356	45	4	,	,	PUNCT
ejpam-4356	45	5	v∈s	v∈s	NOUN
ejpam-4356	45	6	i[u	i[u	NOUN
ejpam-4356	45	7	,	,	PUNCT
ejpam-4356	45	8	v	v	NOUN
ejpam-4356	45	9	]	]	X
ejpam-4356	45	10	,	,	PUNCT
ejpam-4356	45	11	chartrand	chartrand	PROPN
ejpam-4356	45	12	,	,	PUNCT
ejpam-4356	45	13	et.al	et.al	VERB
ejpam-4356	45	14	[	[	X
ejpam-4356	45	15	4	4	NUM
ejpam-4356	45	16	]	]	PUNCT
ejpam-4356	45	17	.	.	PUNCT
ejpam-4356	46	1	let	let	VERB
ejpam-4356	46	2	g	g	PRON
ejpam-4356	46	3	be	be	AUX
ejpam-4356	46	4	a	a	DET
ejpam-4356	46	5	connected	connected	ADJ
ejpam-4356	46	6	graph	graph	NOUN
ejpam-4356	46	7	,	,	PUNCT
ejpam-4356	46	8	then	then	ADV
ejpam-4356	46	9	set	set	VERB
ejpam-4356	46	10	s	s	PRON
ejpam-4356	46	11	⊆	⊆	NUM
ejpam-4356	46	12	v	v	NOUN
ejpam-4356	46	13	(	(	PUNCT
ejpam-4356	46	14	g	g	NOUN
ejpam-4356	46	15	)	)	PUNCT
ejpam-4356	46	16	is	be	AUX
ejpam-4356	46	17	a	a	DET
ejpam-4356	46	18	geodetic	geodetic	ADJ
ejpam-4356	46	19	set	set	NOUN
ejpam-4356	46	20	of	of	ADP
ejpam-4356	46	21	g	g	PROPN
ejpam-4356	46	22	if	if	SCONJ
ejpam-4356	46	23	ig[s	ig[	NOUN
ejpam-4356	46	24	]	]	X
ejpam-4356	46	25	=	=	SYM
ejpam-4356	46	26	v	v	X
ejpam-4356	46	27	(	(	PUNCT
ejpam-4356	46	28	g	g	NOUN
ejpam-4356	46	29	)	)	PUNCT
ejpam-4356	46	30	.	.	PUNCT
ejpam-4356	47	1	the	the	DET
ejpam-4356	47	2	set	set	NOUN
ejpam-4356	47	3	ig[s	ig[s	PROPN
ejpam-4356	47	4	]	]	PUNCT
ejpam-4356	47	5	is	be	AUX
ejpam-4356	47	6	called	call	VERB
ejpam-4356	47	7	the	the	DET
ejpam-4356	47	8	geodetic	geodetic	ADJ
ejpam-4356	47	9	closure	closure	NOUN
ejpam-4356	47	10	of	of	ADP
ejpam-4356	47	11	g.	g.	PROPN
ejpam-4356	47	12	the	the	DET
ejpam-4356	47	13	minimum	minimum	ADJ
ejpam-4356	47	14	cardinality	cardinality	NOUN
ejpam-4356	47	15	of	of	ADP
ejpam-4356	47	16	a	a	DET
ejpam-4356	47	17	geodetic	geodetic	ADJ
ejpam-4356	47	18	set	set	NOUN
ejpam-4356	47	19	is	be	AUX
ejpam-4356	47	20	the	the	DET
ejpam-4356	47	21	geodetic	geodetic	ADJ
ejpam-4356	47	22	number	number	NOUN
ejpam-4356	47	23	of	of	ADP
ejpam-4356	47	24	g	g	NOUN
ejpam-4356	47	25	,	,	PUNCT
ejpam-4356	47	26	and	and	CCONJ
ejpam-4356	47	27	is	be	AUX
ejpam-4356	47	28	denoted	denote	VERB
ejpam-4356	47	29	by	by	ADP
ejpam-4356	47	30	g(g	g(g	PROPN
ejpam-4356	47	31	)	)	PUNCT
ejpam-4356	47	32	.	.	PUNCT
ejpam-4356	48	1	the	the	DET
ejpam-4356	48	2	geodetic	geodetic	ADJ
ejpam-4356	48	3	number	number	NOUN
ejpam-4356	48	4	of	of	ADP
ejpam-4356	48	5	a	a	DET
ejpam-4356	48	6	disconnected	disconnected	ADJ
ejpam-4356	48	7	graph	graph	NOUN
ejpam-4356	48	8	is	be	AUX
ejpam-4356	48	9	the	the	DET
ejpam-4356	48	10	sum	sum	NOUN
ejpam-4356	48	11	of	of	ADP
ejpam-4356	48	12	the	the	DET
ejpam-4356	48	13	geodetic	geodetic	ADJ
ejpam-4356	48	14	numbers	number	NOUN
ejpam-4356	48	15	of	of	ADP
ejpam-4356	48	16	its	its	PRON
ejpam-4356	48	17	components	component	NOUN
ejpam-4356	48	18	.	.	PUNCT
ejpam-4356	49	1	a	a	DET
ejpam-4356	49	2	geodetic	geodetic	ADJ
ejpam-4356	49	3	set	set	NOUN
ejpam-4356	49	4	of	of	ADP
ejpam-4356	49	5	cardinality	cardinality	PROPN
ejpam-4356	49	6	g(g	g(g	PROPN
ejpam-4356	49	7	)	)	PUNCT
ejpam-4356	49	8	is	be	AUX
ejpam-4356	49	9	called	call	VERB
ejpam-4356	49	10	a	a	DET
ejpam-4356	49	11	g	g	NOUN
ejpam-4356	49	12	-	-	PUNCT
ejpam-4356	49	13	set	set	NOUN
ejpam-4356	49	14	.	.	PUNCT
ejpam-4356	50	1	henceforth	henceforth	ADV
ejpam-4356	50	2	,	,	PUNCT
ejpam-4356	50	3	the	the	DET
ejpam-4356	50	4	set	set	NOUN
ejpam-4356	50	5	ig(u	ig(u	NOUN
ejpam-4356	50	6	,	,	PUNCT
ejpam-4356	50	7	v	v	NOUN
ejpam-4356	50	8	)	)	PUNCT
ejpam-4356	50	9	denotes	denote	VERB
ejpam-4356	50	10	the	the	DET
ejpam-4356	50	11	set	set	NOUN
ejpam-4356	50	12	ig[u	ig[u	PROPN
ejpam-4356	50	13	,	,	PUNCT
ejpam-4356	50	14	v	v	NOUN
ejpam-4356	50	15	]	]	PUNCT
ejpam-4356	50	16	\	\	PUNCT
ejpam-4356	50	17	{	{	PUNCT
ejpam-4356	50	18	u	u	NOUN
ejpam-4356	50	19	,	,	PUNCT
ejpam-4356	50	20	v	v	NOUN
ejpam-4356	50	21	}	}	PUNCT
ejpam-4356	50	22	.	.	PUNCT
ejpam-4356	51	1	a	a	DET
ejpam-4356	51	2	set	set	NOUN
ejpam-4356	51	3	s	s	NOUN
ejpam-4356	51	4	⊆	⊆	NUM
ejpam-4356	51	5	v	v	NOUN
ejpam-4356	51	6	(	(	PUNCT
ejpam-4356	51	7	g	g	NOUN
ejpam-4356	51	8	)	)	PUNCT
ejpam-4356	51	9	is	be	AUX
ejpam-4356	51	10	called	call	VERB
ejpam-4356	51	11	a	a	DET
ejpam-4356	51	12	geodetic	geodetic	ADJ
ejpam-4356	51	13	dominating	dominating	NOUN
ejpam-4356	51	14	set	set	NOUN
ejpam-4356	51	15	of	of	ADP
ejpam-4356	51	16	g	g	PROPN
ejpam-4356	51	17	if	if	SCONJ
ejpam-4356	51	18	s	s	VERB
ejpam-4356	51	19	is	be	AUX
ejpam-4356	51	20	both	both	PRON
ejpam-4356	51	21	a	a	DET
ejpam-4356	51	22	geodetic	geodetic	ADJ
ejpam-4356	51	23	set	set	NOUN
ejpam-4356	51	24	and	and	CCONJ
ejpam-4356	51	25	a	a	DET
ejpam-4356	51	26	dominating	dominating	NOUN
ejpam-4356	51	27	set	set	NOUN
ejpam-4356	51	28	.	.	PUNCT
ejpam-4356	52	1	the	the	DET
ejpam-4356	52	2	minimum	minimum	ADJ
ejpam-4356	52	3	cardinality	cardinality	NOUN
ejpam-4356	52	4	of	of	ADP
ejpam-4356	52	5	a	a	DET
ejpam-4356	52	6	geodetic	geodetic	ADJ
ejpam-4356	52	7	dominating	dominating	NOUN
ejpam-4356	52	8	set	set	NOUN
ejpam-4356	52	9	of	of	ADP
ejpam-4356	52	10	g	g	PROPN
ejpam-4356	52	11	is	be	AUX
ejpam-4356	52	12	the	the	DET
ejpam-4356	52	13	geodetic	geodetic	ADJ
ejpam-4356	52	14	domination	domination	NOUN
ejpam-4356	52	15	number	number	NOUN
ejpam-4356	52	16	of	of	ADP
ejpam-4356	52	17	g	g	NOUN
ejpam-4356	52	18	,	,	PUNCT
ejpam-4356	52	19	and	and	CCONJ
ejpam-4356	52	20	is	be	AUX
ejpam-4356	52	21	denoted	denote	VERB
ejpam-4356	52	22	by	by	ADP
ejpam-4356	52	23	γg(g	γg(g	NOUN
ejpam-4356	52	24	)	)	PUNCT
ejpam-4356	52	25	.	.	PUNCT
ejpam-4356	53	1	a	a	DET
ejpam-4356	53	2	geodetic	geodetic	ADJ
ejpam-4356	53	3	dominating	dominating	NOUN
ejpam-4356	53	4	set	set	NOUN
ejpam-4356	53	5	s	s	NOUN
ejpam-4356	53	6	with	with	ADP
ejpam-4356	53	7	|s|	|s|	PROPN
ejpam-4356	53	8	=	=	SYM
ejpam-4356	53	9	γg(g	γg(g	X
ejpam-4356	53	10	)	)	PUNCT
ejpam-4356	53	11	is	be	AUX
ejpam-4356	53	12	said	say	VERB
ejpam-4356	53	13	to	to	PART
ejpam-4356	53	14	be	be	AUX
ejpam-4356	53	15	a	a	DET
ejpam-4356	53	16	γg	γg	ADV
ejpam-4356	53	17	-	-	PUNCT
ejpam-4356	53	18	set	set	VERB
ejpam-4356	53	19	g.a	g.a	NOUN
ejpam-4356	53	20	set	set	NOUN
ejpam-4356	53	21	of	of	ADP
ejpam-4356	53	22	vertices	vertex	NOUN
ejpam-4356	53	23	in	in	ADP
ejpam-4356	53	24	s	s	PRON
ejpam-4356	53	25	in	in	ADP
ejpam-4356	53	26	a	a	DET
ejpam-4356	53	27	graph	graph	NOUN
ejpam-4356	53	28	g	g	NOUN
ejpam-4356	53	29	is	be	AUX
ejpam-4356	53	30	said	say	VERB
ejpam-4356	53	31	to	to	PART
ejpam-4356	53	32	be	be	AUX
ejpam-4356	53	33	geodetic	geodetic	ADJ
ejpam-4356	53	34	connected	connected	ADJ
ejpam-4356	53	35	dominating	dominating	NOUN
ejpam-4356	53	36	set	set	NOUN
ejpam-4356	53	37	j.	j.	PROPN
ejpam-4356	53	38	hamja	hamja	PROPN
ejpam-4356	53	39	,	,	PUNCT
ejpam-4356	53	40	i.	i.	PROPN
ejpam-4356	53	41	aniversario	aniversario	PROPN
ejpam-4356	53	42	,	,	PUNCT
ejpam-4356	53	43	h.	h.	PROPN
ejpam-4356	53	44	rara	rara	PROPN
ejpam-4356	53	45	/	/	SYM
ejpam-4356	53	46	eur	eur	PROPN
ejpam-4356	53	47	.	.	PUNCT
ejpam-4356	54	1	j.	j.	PROPN
ejpam-4356	54	2	pure	pure	PROPN
ejpam-4356	54	3	appl	appl	PROPN
ejpam-4356	54	4	.	.	PROPN
ejpam-4356	54	5	math	math	PROPN
ejpam-4356	54	6	,	,	PUNCT
ejpam-4356	54	7	15	15	NUM
ejpam-4356	54	8	(	(	PUNCT
ejpam-4356	54	9	2	2	NUM
ejpam-4356	54	10	)	)	PUNCT
ejpam-4356	54	11	(	(	PUNCT
ejpam-4356	54	12	2022	2022	NUM
ejpam-4356	54	13	)	)	PUNCT
ejpam-4356	54	14	,	,	PUNCT
ejpam-4356	54	15	736	736	NUM
ejpam-4356	54	16	-	-	SYM
ejpam-4356	54	17	752	752	NUM
ejpam-4356	54	18	738	738	NUM
ejpam-4356	54	19	of	of	ADP
ejpam-4356	54	20	g	g	NOUN
ejpam-4356	54	21	if	if	SCONJ
ejpam-4356	54	22	s	s	VERB
ejpam-4356	54	23	is	be	AUX
ejpam-4356	54	24	both	both	PRON
ejpam-4356	54	25	a	a	DET
ejpam-4356	54	26	geodetic	geodetic	ADJ
ejpam-4356	54	27	set	set	NOUN
ejpam-4356	54	28	and	and	CCONJ
ejpam-4356	54	29	connected	connected	ADJ
ejpam-4356	54	30	dominating	dominating	NOUN
ejpam-4356	54	31	set	set	NOUN
ejpam-4356	54	32	.	.	PUNCT
ejpam-4356	55	1	the	the	DET
ejpam-4356	55	2	minimum	minimum	ADJ
ejpam-4356	55	3	cardinality	cardinality	NOUN
ejpam-4356	55	4	of	of	ADP
ejpam-4356	55	5	a	a	DET
ejpam-4356	55	6	geodetic	geodetic	ADJ
ejpam-4356	55	7	connected	connected	ADJ
ejpam-4356	55	8	dominating	dominating	NOUN
ejpam-4356	55	9	set	set	NOUN
ejpam-4356	55	10	of	of	ADP
ejpam-4356	55	11	g	g	PROPN
ejpam-4356	55	12	is	be	AUX
ejpam-4356	55	13	called	call	VERB
ejpam-4356	55	14	a	a	DET
ejpam-4356	55	15	geodetic	geodetic	ADJ
ejpam-4356	55	16	connected	connect	VERB
ejpam-4356	55	17	domination	domination	NOUN
ejpam-4356	55	18	number	number	NOUN
ejpam-4356	55	19	of	of	ADP
ejpam-4356	55	20	g	g	NOUN
ejpam-4356	55	21	,	,	PUNCT
ejpam-4356	55	22	denoted	denote	VERB
ejpam-4356	55	23	by	by	ADP
ejpam-4356	55	24	γgc(g	γgc(g	PROPN
ejpam-4356	55	25	)	)	PUNCT
ejpam-4356	55	26	.	.	PUNCT
ejpam-4356	56	1	a	a	DET
ejpam-4356	56	2	geodetic	geodetic	ADJ
ejpam-4356	56	3	connected	connected	ADJ
ejpam-4356	56	4	dominating	dominating	NOUN
ejpam-4356	56	5	set	set	NOUN
ejpam-4356	56	6	s	s	NOUN
ejpam-4356	56	7	with	with	ADP
ejpam-4356	56	8	|s|	|s|	PROPN
ejpam-4356	56	9	=	=	PUNCT
ejpam-4356	56	10	γgc(g	γgc(g	PROPN
ejpam-4356	56	11	)	)	PUNCT
ejpam-4356	56	12	is	be	AUX
ejpam-4356	56	13	said	say	VERB
ejpam-4356	56	14	to	to	PART
ejpam-4356	56	15	be	be	AUX
ejpam-4356	56	16	a	a	DET
ejpam-4356	56	17	γgc	γgc	NOUN
ejpam-4356	56	18	-	-	PUNCT
ejpam-4356	56	19	set	set	NOUN
ejpam-4356	56	20	of	of	ADP
ejpam-4356	56	21	g.	g.	PROPN
ejpam-4356	56	22	the	the	DET
ejpam-4356	56	23	geoodesic	geoodesic	PROPN
ejpam-4356	56	24	set	set	NOUN
ejpam-4356	56	25	,	,	PUNCT
ejpam-4356	56	26	geodetic	geodetic	ADJ
ejpam-4356	56	27	dominating	dominating	NOUN
ejpam-4356	56	28	set	set	NOUN
ejpam-4356	56	29	and	and	CCONJ
ejpam-4356	56	30	geodetic	geodetic	ADJ
ejpam-4356	56	31	connected	connected	ADJ
ejpam-4356	56	32	dominating	dominating	NOUN
ejpam-4356	56	33	set	set	NOUN
ejpam-4356	56	34	are	be	AUX
ejpam-4356	56	35	studied	study	VERB
ejpam-4356	56	36	by	by	ADP
ejpam-4356	56	37	escuadro	escuadro	NOUN
ejpam-4356	56	38	,	,	PUNCT
ejpam-4356	56	39	et.al	et.al	VERB
ejpam-4356	56	40	[	[	X
ejpam-4356	56	41	9	9	NUM
ejpam-4356	56	42	]	]	PUNCT
ejpam-4356	56	43	,	,	PUNCT
ejpam-4356	56	44	patangan	patangan	ADP
ejpam-4356	56	45	et.al	et.al	NOUN
ejpam-4356	56	46	,	,	PUNCT
ejpam-4356	56	47	[	[	X
ejpam-4356	56	48	12	12	NUM
ejpam-4356	56	49	]	]	PUNCT
ejpam-4356	56	50	,	,	PUNCT
ejpam-4356	56	51	and	and	CCONJ
ejpam-4356	56	52	tejaswini	tejaswini	NOUN
ejpam-4356	56	53	,	,	PUNCT
ejpam-4356	56	54	et.al	et.al	VERB
ejpam-4356	56	55	[	[	X
ejpam-4356	56	56	15	15	NUM
ejpam-4356	56	57	]	]	PUNCT
ejpam-4356	56	58	.	.	PUNCT
ejpam-4356	57	1	the	the	DET
ejpam-4356	57	2	set	set	NOUN
ejpam-4356	57	3	s	s	PART
ejpam-4356	57	4	is	be	AUX
ejpam-4356	57	5	a	a	DET
ejpam-4356	57	6	closed	closed	ADJ
ejpam-4356	57	7	geodetic	geodetic	ADJ
ejpam-4356	57	8	cover	cover	NOUN
ejpam-4356	57	9	of	of	ADP
ejpam-4356	57	10	a	a	DET
ejpam-4356	57	11	graph	graph	NOUN
ejpam-4356	57	12	g	g	NOUN
ejpam-4356	57	13	if	if	SCONJ
ejpam-4356	57	14	s	s	VERB
ejpam-4356	57	15	=	=	NOUN
ejpam-4356	57	16	{	{	PUNCT
ejpam-4356	57	17	v1	v1	PROPN
ejpam-4356	57	18	,	,	PUNCT
ejpam-4356	57	19	v2	v2	PROPN
ejpam-4356	57	20	,	,	PUNCT
ejpam-4356	57	21	...	...	PUNCT
ejpam-4356	57	22	,	,	PUNCT
ejpam-4356	57	23	vk	vk	ADP
ejpam-4356	57	24	}	}	PUNCT
ejpam-4356	57	25	and	and	CCONJ
ejpam-4356	57	26	is	be	AUX
ejpam-4356	57	27	obtained	obtain	VERB
ejpam-4356	57	28	by	by	ADP
ejpam-4356	57	29	choosing	choose	VERB
ejpam-4356	57	30	the	the	DET
ejpam-4356	57	31	vertices	vertex	NOUN
ejpam-4356	57	32	v1	v1	NOUN
ejpam-4356	57	33	,	,	PUNCT
ejpam-4356	57	34	v2	v2	PROPN
ejpam-4356	57	35	,	,	PUNCT
ejpam-4356	57	36	...	...	PUNCT
ejpam-4356	57	37	,	,	PUNCT
ejpam-4356	57	38	vk	vk	VERB
ejpam-4356	57	39	such	such	ADJ
ejpam-4356	57	40	that	that	SCONJ
ejpam-4356	57	41	the	the	DET
ejpam-4356	57	42	following	follow	VERB
ejpam-4356	57	43	hold	hold	NOUN
ejpam-4356	57	44	:	:	PUNCT
ejpam-4356	57	45	(	(	PUNCT
ejpam-4356	57	46	i	i	NOUN
ejpam-4356	57	47	)	)	PUNCT
ejpam-4356	57	48	v1	v1	PROPN
ejpam-4356	57	49	̸=	̸=	PROPN
ejpam-4356	57	50	v2	v2	PROPN
ejpam-4356	57	51	;	;	PUNCT
ejpam-4356	57	52	(	(	PUNCT
ejpam-4356	57	53	ii	ii	NOUN
ejpam-4356	57	54	)	)	PUNCT
ejpam-4356	57	55	vi	vi	PROPN
ejpam-4356	57	56	/∈	/∈	NOUN
ejpam-4356	57	57	ig[si−1	ig[si−1	PROPN
ejpam-4356	57	58	]	]	PUNCT
ejpam-4356	57	59	for	for	ADP
ejpam-4356	57	60	3	3	NUM
ejpam-4356	57	61	≤	≤	NOUN
ejpam-4356	58	1	i	i	NOUN
ejpam-4356	58	2	≤	≤	PROPN
ejpam-4356	59	1	k	k	NOUN
ejpam-4356	59	2	;	;	PUNCT
ejpam-4356	59	3	and	and	CCONJ
ejpam-4356	59	4	(	(	PUNCT
ejpam-4356	59	5	ii	ii	NOUN
ejpam-4356	59	6	)	)	PUNCT
ejpam-4356	59	7	ig[sk	ig[sk	NOUN
ejpam-4356	59	8	]	]	X
ejpam-4356	59	9	=	=	SYM
ejpam-4356	59	10	v	v	X
ejpam-4356	59	11	(	(	PUNCT
ejpam-4356	59	12	g	g	NOUN
ejpam-4356	59	13	)	)	PUNCT
ejpam-4356	59	14	,	,	PUNCT
ejpam-4356	59	15	where	where	SCONJ
ejpam-4356	59	16	si	si	PROPN
ejpam-4356	59	17	=	=	ADJ
ejpam-4356	59	18	{	{	PUNCT
ejpam-4356	59	19	v1	v1	PROPN
ejpam-4356	59	20	,	,	PUNCT
ejpam-4356	59	21	v2	v2	PROPN
ejpam-4356	59	22	,	,	PUNCT
ejpam-4356	59	23	...	...	PUNCT
ejpam-4356	59	24	,	,	PUNCT
ejpam-4356	59	25	vi	vi	X
ejpam-4356	59	26	}	}	PUNCT
ejpam-4356	59	27	for	for	ADP
ejpam-4356	59	28	all	all	DET
ejpam-4356	59	29	i	i	PRON
ejpam-4356	59	30	=	=	NOUN
ejpam-4356	59	31	1	1	NUM
ejpam-4356	59	32	,	,	PUNCT
ejpam-4356	59	33	2	2	NUM
ejpam-4356	59	34	,	,	PUNCT
ejpam-4356	59	35	...	...	PUNCT
ejpam-4356	59	36	,	,	PUNCT
ejpam-4356	59	37	k	k	X
ejpam-4356	59	38	if	if	SCONJ
ejpam-4356	59	39	s	s	VERB
ejpam-4356	59	40	⊆	⊆	NUM
ejpam-4356	59	41	v	v	NOUN
ejpam-4356	59	42	(	(	PUNCT
ejpam-4356	59	43	g	g	NOUN
ejpam-4356	59	44	)	)	PUNCT
ejpam-4356	59	45	satisfies	satisfie	NOUN
ejpam-4356	59	46	(	(	PUNCT
ejpam-4356	59	47	i	i	NOUN
ejpam-4356	59	48	)	)	PUNCT
ejpam-4356	59	49	and	and	CCONJ
ejpam-4356	59	50	(	(	PUNCT
ejpam-4356	59	51	ii	ii	NOUN
ejpam-4356	59	52	)	)	PUNCT
ejpam-4356	59	53	of	of	ADP
ejpam-4356	59	54	the	the	DET
ejpam-4356	59	55	definition	definition	NOUN
ejpam-4356	59	56	above	above	ADV
ejpam-4356	59	57	,	,	PUNCT
ejpam-4356	59	58	then	then	ADV
ejpam-4356	59	59	s	s	VERB
ejpam-4356	59	60	is	be	AUX
ejpam-4356	59	61	a	a	DET
ejpam-4356	59	62	closed	closed	ADJ
ejpam-4356	59	63	geodetic	geodetic	ADJ
ejpam-4356	59	64	subset	subset	NOUN
ejpam-4356	59	65	of	of	ADP
ejpam-4356	59	66	v	v	NOUN
ejpam-4356	59	67	(	(	PUNCT
ejpam-4356	59	68	g	g	NOUN
ejpam-4356	59	69	)	)	PUNCT
ejpam-4356	59	70	.	.	PUNCT
ejpam-4356	60	1	the	the	DET
ejpam-4356	60	2	collection	collection	NOUN
ejpam-4356	60	3	of	of	ADP
ejpam-4356	60	4	all	all	DET
ejpam-4356	60	5	closed	closed	ADJ
ejpam-4356	60	6	geodetic	geodetic	ADJ
ejpam-4356	60	7	covers	cover	NOUN
ejpam-4356	60	8	of	of	ADP
ejpam-4356	60	9	g	g	PROPN
ejpam-4356	60	10	is	be	AUX
ejpam-4356	60	11	denoted	denote	VERB
ejpam-4356	60	12	by	by	ADP
ejpam-4356	60	13	c∗(g	c∗(g	PROPN
ejpam-4356	60	14	)	)	PUNCT
ejpam-4356	60	15	.	.	PUNCT
ejpam-4356	61	1	the	the	DET
ejpam-4356	61	2	closed	closed	ADJ
ejpam-4356	61	3	geodetic	geodetic	ADJ
ejpam-4356	61	4	number	number	NOUN
ejpam-4356	61	5	of	of	ADP
ejpam-4356	61	6	g	g	NOUN
ejpam-4356	61	7	,	,	PUNCT
ejpam-4356	61	8	is	be	AUX
ejpam-4356	61	9	given	give	VERB
ejpam-4356	61	10	by	by	ADP
ejpam-4356	61	11	cgn(g	cgn(g	PROPN
ejpam-4356	61	12	)	)	PUNCT
ejpam-4356	62	1	=	=	NOUN
ejpam-4356	62	2	min{|s|	min{|s|	NOUN
ejpam-4356	62	3	:	:	PUNCT
ejpam-4356	62	4	s	s	X
ejpam-4356	62	5	∈	∈	PROPN
ejpam-4356	62	6	c∗(g	c∗(g	PROPN
ejpam-4356	62	7	)	)	PUNCT
ejpam-4356	62	8	}	}	PUNCT
ejpam-4356	62	9	.	.	PUNCT
ejpam-4356	63	1	a	a	DET
ejpam-4356	63	2	set	set	NOUN
ejpam-4356	63	3	s	s	NOUN
ejpam-4356	63	4	∈	∈	PROPN
ejpam-4356	63	5	c∗(g	c∗(g	PROPN
ejpam-4356	63	6	)	)	PUNCT
ejpam-4356	63	7	with	with	ADP
ejpam-4356	63	8	|s|	|s|	PROPN
ejpam-4356	63	9	=	=	SYM
ejpam-4356	63	10	cgn(g	cgn(g	PROPN
ejpam-4356	63	11	)	)	PUNCT
ejpam-4356	63	12	is	be	AUX
ejpam-4356	63	13	called	call	VERB
ejpam-4356	63	14	the	the	DET
ejpam-4356	63	15	closed	closed	ADJ
ejpam-4356	63	16	geodetic	geodetic	ADJ
ejpam-4356	63	17	basis	basis	NOUN
ejpam-4356	63	18	of	of	ADP
ejpam-4356	63	19	g	g	NOUN
ejpam-4356	63	20	and	and	CCONJ
ejpam-4356	63	21	is	be	AUX
ejpam-4356	63	22	denoted	denote	VERB
ejpam-4356	63	23	by	by	ADP
ejpam-4356	63	24	cgb(g	cgb(g	NOUN
ejpam-4356	63	25	)	)	PUNCT
ejpam-4356	63	26	aniversario	aniversario	NOUN
ejpam-4356	63	27	,	,	PUNCT
ejpam-4356	63	28	et.al	et.al	VERB
ejpam-4356	63	29	[	[	X
ejpam-4356	63	30	1	1	NUM
ejpam-4356	63	31	]	]	PUNCT
ejpam-4356	63	32	,	,	PUNCT
ejpam-4356	63	33	and	and	CCONJ
ejpam-4356	63	34	patangan	patangan	VERB
ejpam-4356	63	35	,	,	PUNCT
ejpam-4356	63	36	et.al	et.al	VERB
ejpam-4356	63	37	[	[	X
ejpam-4356	63	38	12	12	NUM
ejpam-4356	63	39	]	]	PUNCT
ejpam-4356	63	40	.	.	PUNCT
ejpam-4356	64	1	a	a	DET
ejpam-4356	64	2	vertex	vertex	NOUN
ejpam-4356	64	3	v	v	NOUN
ejpam-4356	64	4	in	in	ADP
ejpam-4356	64	5	a	a	DET
ejpam-4356	64	6	connected	connected	ADJ
ejpam-4356	64	7	g	g	NOUN
ejpam-4356	64	8	is	be	AUX
ejpam-4356	64	9	an	an	DET
ejpam-4356	64	10	extreme	extreme	ADJ
ejpam-4356	64	11	vertex	vertex	NOUN
ejpam-4356	64	12	if	if	SCONJ
ejpam-4356	64	13	the	the	DET
ejpam-4356	64	14	neighborhood	neighborhood	NOUN
ejpam-4356	64	15	n(v	n(v	PROPN
ejpam-4356	64	16	)	)	PUNCT
ejpam-4356	64	17	of	of	ADP
ejpam-4356	64	18	v	v	NUM
ejpam-4356	64	19	induces	induce	VERB
ejpam-4356	64	20	a	a	DET
ejpam-4356	64	21	complete	complete	ADJ
ejpam-4356	64	22	subgraph	subgraph	NOUN
ejpam-4356	64	23	of	of	ADP
ejpam-4356	64	24	g.	g.	PROPN
ejpam-4356	64	25	the	the	DET
ejpam-4356	64	26	set	set	NOUN
ejpam-4356	64	27	of	of	ADP
ejpam-4356	64	28	all	all	DET
ejpam-4356	64	29	extreme	extreme	ADJ
ejpam-4356	64	30	vertices	vertex	NOUN
ejpam-4356	64	31	in	in	ADP
ejpam-4356	64	32	g	g	PROPN
ejpam-4356	64	33	is	be	AUX
ejpam-4356	64	34	denoted	denote	VERB
ejpam-4356	64	35	by	by	ADP
ejpam-4356	64	36	ext(g	ext(g	PROPN
ejpam-4356	64	37	)	)	PUNCT
ejpam-4356	64	38	.	.	PUNCT
ejpam-4356	65	1	by	by	ADP
ejpam-4356	65	2	a	a	DET
ejpam-4356	65	3	neighborhood	neighborhood	NOUN
ejpam-4356	65	4	n(v	n(v	PROPN
ejpam-4356	65	5	)	)	PUNCT
ejpam-4356	65	6	of	of	ADP
ejpam-4356	65	7	a	a	DET
ejpam-4356	65	8	vertex	vertex	NOUN
ejpam-4356	65	9	v	v	NOUN
ejpam-4356	65	10	in	in	ADP
ejpam-4356	65	11	g	g	PROPN
ejpam-4356	65	12	is	be	AUX
ejpam-4356	65	13	the	the	DET
ejpam-4356	65	14	set	set	NOUN
ejpam-4356	65	15	of	of	ADP
ejpam-4356	65	16	all	all	DET
ejpam-4356	65	17	vertices	vertex	NOUN
ejpam-4356	65	18	x	x	VERB
ejpam-4356	65	19	in	in	ADP
ejpam-4356	65	20	g	g	PROPN
ejpam-4356	65	21	suh	suh	PROPN
ejpam-4356	65	22	that	that	PRON
ejpam-4356	65	23	dg(v	dg(v	VERB
ejpam-4356	65	24	,	,	PUNCT
ejpam-4356	65	25	x	x	NOUN
ejpam-4356	65	26	)	)	PUNCT
ejpam-4356	65	27	≤	≤	NUM
ejpam-4356	65	28	1	1	NUM
ejpam-4356	65	29	.	.	PUNCT
ejpam-4356	66	1	a	a	DET
ejpam-4356	66	2	set	set	NOUN
ejpam-4356	66	3	s	s	NOUN
ejpam-4356	66	4	⊆	⊆	NUM
ejpam-4356	66	5	v	v	NOUN
ejpam-4356	66	6	(	(	PUNCT
ejpam-4356	66	7	g	g	NOUN
ejpam-4356	66	8	)	)	PUNCT
ejpam-4356	66	9	is	be	AUX
ejpam-4356	66	10	said	say	VERB
ejpam-4356	66	11	to	to	PART
ejpam-4356	66	12	be	be	AUX
ejpam-4356	66	13	a	a	DET
ejpam-4356	66	14	closure	closure	NOUN
ejpam-4356	66	15	absorbing	absorb	VERB
ejpam-4356	66	16	set	set	NOUN
ejpam-4356	66	17	in	in	ADP
ejpam-4356	66	18	g	g	PROPN
ejpam-4356	66	19	if	if	SCONJ
ejpam-4356	66	20	for	for	ADP
ejpam-4356	66	21	every	every	PRON
ejpam-4356	66	22	v	v	NUM
ejpam-4356	66	23	∈	∈	NOUN
ejpam-4356	66	24	v	v	NOUN
ejpam-4356	66	25	(	(	PUNCT
ejpam-4356	66	26	g	g	NOUN
ejpam-4356	66	27	)	)	PUNCT
ejpam-4356	66	28	\	\	PROPN
ejpam-4356	67	1	s	s	X
ejpam-4356	67	2	,	,	PUNCT
ejpam-4356	67	3	there	there	PRON
ejpam-4356	67	4	exist	exist	VERB
ejpam-4356	67	5	u	u	NOUN
ejpam-4356	67	6	,	,	PUNCT
ejpam-4356	67	7	w	w	PROPN
ejpam-4356	67	8	∈	∈	PROPN
ejpam-4356	67	9	n(v	n(v	PROPN
ejpam-4356	67	10	)	)	PUNCT
ejpam-4356	67	11	∩	∩	PROPN
ejpam-4356	67	12	s	s	PART
ejpam-4356	67	13	with	with	ADP
ejpam-4356	67	14	dg(u	dg(u	ADJ
ejpam-4356	67	15	,	,	PUNCT
ejpam-4356	67	16	w	w	NOUN
ejpam-4356	67	17	)	)	PUNCT
ejpam-4356	67	18	=	=	SYM
ejpam-4356	67	19	2	2	NUM
ejpam-4356	67	20	,	,	PUNCT
ejpam-4356	67	21	cagaanan	cagaanan	NOUN
ejpam-4356	67	22	[	[	X
ejpam-4356	67	23	3	3	NUM
ejpam-4356	67	24	]	]	PUNCT
ejpam-4356	67	25	,	,	PUNCT
ejpam-4356	67	26	and	and	CCONJ
ejpam-4356	67	27	aniversario	aniversario	NOUN
ejpam-4356	67	28	,	,	PUNCT
ejpam-4356	67	29	et.al	et.al	VERB
ejpam-4356	67	30	[	[	X
ejpam-4356	67	31	1	1	NUM
ejpam-4356	67	32	]	]	PUNCT
ejpam-4356	67	33	.	.	PUNCT
ejpam-4356	68	1	let	let	VERB
ejpam-4356	68	2	g	g	NOUN
ejpam-4356	68	3	be	be	AUX
ejpam-4356	68	4	the	the	DET
ejpam-4356	68	5	connected	connected	ADJ
ejpam-4356	68	6	graph	graph	NOUN
ejpam-4356	68	7	and	and	CCONJ
ejpam-4356	68	8	s	s	VERB
ejpam-4356	68	9	⊆	⊆	NUM
ejpam-4356	68	10	v	v	NOUN
ejpam-4356	68	11	(	(	PUNCT
ejpam-4356	68	12	g	g	NOUN
ejpam-4356	68	13	)	)	PUNCT
ejpam-4356	68	14	.	.	PUNCT
ejpam-4356	69	1	the	the	DET
ejpam-4356	69	2	2	2	NUM
ejpam-4356	69	3	path	path	NOUN
ejpam-4356	69	4	closure	closure	NOUN
ejpam-4356	69	5	p2[s]g	p2[s]g	PROPN
ejpam-4356	69	6	of	of	ADP
ejpam-4356	69	7	s	s	PRON
ejpam-4356	69	8	is	be	AUX
ejpam-4356	69	9	that	that	PRON
ejpam-4356	69	10	set	set	VERB
ejpam-4356	69	11	p2[s]g	p2[s]g	PROPN
ejpam-4356	69	12	=	=	SYM
ejpam-4356	69	13	s	s	X
ejpam-4356	69	14	∪	∪	X
ejpam-4356	69	15	{	{	PUNCT
ejpam-4356	69	16	w	w	NOUN
ejpam-4356	69	17	∈	∈	PROPN
ejpam-4356	69	18	v	v	ADP
ejpam-4356	69	19	(	(	PUNCT
ejpam-4356	69	20	g	g	NOUN
ejpam-4356	69	21	)	)	PUNCT
ejpam-4356	69	22	:	:	PUNCT
ejpam-4356	69	23	w	w	X
ejpam-4356	69	24	∈	∈	PROPN
ejpam-4356	69	25	ig[u	ig[u	PROPN
ejpam-4356	69	26	,	,	PUNCT
ejpam-4356	69	27	v	v	NOUN
ejpam-4356	69	28	]	]	PUNCT
ejpam-4356	69	29	for	for	ADP
ejpam-4356	69	30	some	some	DET
ejpam-4356	69	31	u	u	NOUN
ejpam-4356	69	32	,	,	PUNCT
ejpam-4356	69	33	v	v	PROPN
ejpam-4356	69	34	∈	∈	NOUN
ejpam-4356	69	35	s	s	PART
ejpam-4356	69	36	with	with	ADP
ejpam-4356	69	37	dg(u	dg(u	ADJ
ejpam-4356	69	38	,	,	PUNCT
ejpam-4356	69	39	v	v	NOUN
ejpam-4356	69	40	)	)	PUNCT
ejpam-4356	69	41	=	=	SYM
ejpam-4356	69	42	2	2	NUM
ejpam-4356	69	43	}	}	PUNCT
ejpam-4356	69	44	.	.	PUNCT
ejpam-4356	70	1	the	the	DET
ejpam-4356	70	2	set	set	NOUN
ejpam-4356	70	3	s	s	PART
ejpam-4356	70	4	is	be	AUX
ejpam-4356	70	5	called	call	VERB
ejpam-4356	70	6	2	2	NUM
ejpam-4356	70	7	path	path	NOUN
ejpam-4356	70	8	closure	closure	NOUN
ejpam-4356	70	9	absorbing	absorb	VERB
ejpam-4356	70	10	set	set	VERB
ejpam-4356	70	11	if	if	SCONJ
ejpam-4356	70	12	p2[s]g	p2[s]g	PROPN
ejpam-4356	70	13	=	=	SYM
ejpam-4356	70	14	v	v	PROPN
ejpam-4356	70	15	(	(	PUNCT
ejpam-4356	70	16	g	g	NOUN
ejpam-4356	70	17	)	)	PUNCT
ejpam-4356	70	18	,	,	PUNCT
ejpam-4356	70	19	canoy	canoy	NOUN
ejpam-4356	70	20	,	,	PUNCT
ejpam-4356	70	21	et.al	et.al	VERB
ejpam-4356	70	22	[	[	X
ejpam-4356	70	23	5	5	NUM
ejpam-4356	70	24	]	]	PUNCT
ejpam-4356	70	25	,	,	PUNCT
ejpam-4356	70	26	and	and	CCONJ
ejpam-4356	70	27	aniversario	aniversario	NOUN
ejpam-4356	70	28	,	,	PUNCT
ejpam-4356	70	29	et.al	et.al	VERB
ejpam-4356	70	30	[	[	X
ejpam-4356	70	31	1	1	NUM
ejpam-4356	70	32	]	]	PUNCT
ejpam-4356	70	33	.	.	PUNCT
ejpam-4356	71	1	a	a	DET
ejpam-4356	71	2	set	set	NOUN
ejpam-4356	71	3	s	s	PART
ejpam-4356	71	4	is	be	AUX
ejpam-4356	71	5	called	call	VERB
ejpam-4356	71	6	a	a	DET
ejpam-4356	71	7	weakly	weakly	ADV
ejpam-4356	71	8	connected	connected	ADJ
ejpam-4356	71	9	closed	closed	ADJ
ejpam-4356	71	10	geodetic	geodetic	ADJ
ejpam-4356	71	11	set	set	NOUN
ejpam-4356	71	12	of	of	ADP
ejpam-4356	71	13	g	g	NOUN
ejpam-4356	71	14	,	,	PUNCT
ejpam-4356	71	15	if	if	SCONJ
ejpam-4356	71	16	it	it	PRON
ejpam-4356	71	17	satisfies	satisfy	VERB
ejpam-4356	71	18	the	the	DET
ejpam-4356	71	19	following	follow	VERB
ejpam-4356	71	20	properties	property	NOUN
ejpam-4356	71	21	:	:	PUNCT
ejpam-4356	71	22	(	(	PUNCT
ejpam-4356	71	23	i	i	NOUN
ejpam-4356	71	24	)	)	PUNCT
ejpam-4356	71	25	s	s	PART
ejpam-4356	71	26	∈	∈	PROPN
ejpam-4356	71	27	c∗(g	c∗(g	PROPN
ejpam-4356	71	28	)	)	PUNCT
ejpam-4356	71	29	;	;	PUNCT
ejpam-4356	71	30	and	and	CCONJ
ejpam-4356	71	31	(	(	PUNCT
ejpam-4356	71	32	ii	ii	NOUN
ejpam-4356	71	33	)	)	PUNCT
ejpam-4356	71	34	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4356	71	35	is	be	AUX
ejpam-4356	71	36	connected	connect	VERB
ejpam-4356	71	37	.	.	PUNCT
ejpam-4356	72	1	the	the	DET
ejpam-4356	72	2	minimum	minimum	ADJ
ejpam-4356	72	3	cardinality	cardinality	NOUN
ejpam-4356	72	4	of	of	ADP
ejpam-4356	72	5	a	a	DET
ejpam-4356	72	6	weakly	weakly	ADV
ejpam-4356	72	7	connected	connected	ADJ
ejpam-4356	72	8	closed	closed	ADJ
ejpam-4356	72	9	geodetic	geodetic	ADJ
ejpam-4356	72	10	set	set	NOUN
ejpam-4356	72	11	is	be	AUX
ejpam-4356	72	12	called	call	VERB
ejpam-4356	72	13	the	the	DET
ejpam-4356	72	14	weakly	weakly	ADV
ejpam-4356	72	15	connected	connected	ADJ
ejpam-4356	72	16	closed	close	VERB
ejpam-4356	72	17	geodetic	geodetic	ADJ
ejpam-4356	72	18	number	number	NOUN
ejpam-4356	72	19	of	of	ADP
ejpam-4356	72	20	g	g	NOUN
ejpam-4356	72	21	,	,	PUNCT
ejpam-4356	72	22	denoted	denote	VERB
ejpam-4356	72	23	by	by	ADP
ejpam-4356	72	24	wcgn(g	wcgn(g	NOUN
ejpam-4356	72	25	)	)	PUNCT
ejpam-4356	72	26	.	.	PUNCT
ejpam-4356	73	1	in	in	ADP
ejpam-4356	73	2	a	a	DET
ejpam-4356	73	3	weakly	weakly	ADV
ejpam-4356	73	4	connected	connected	ADJ
ejpam-4356	73	5	closed	closed	ADJ
ejpam-4356	73	6	geodetic	geodetic	ADJ
ejpam-4356	73	7	set	set	NOUN
ejpam-4356	73	8	s	s	PROPN
ejpam-4356	73	9	,	,	PUNCT
ejpam-4356	73	10	for	for	ADP
ejpam-4356	73	11	every	every	DET
ejpam-4356	73	12	v	v	NUM
ejpam-4356	73	13	∈	∈	PROPN
ejpam-4356	73	14	s	s	NOUN
ejpam-4356	73	15	,	,	PUNCT
ejpam-4356	73	16	there	there	PRON
ejpam-4356	73	17	exists	exist	VERB
ejpam-4356	73	18	u	u	PROPN
ejpam-4356	73	19	∈	∈	PROPN
ejpam-4356	73	20	s	s	VERB
ejpam-4356	73	21	such	such	ADJ
ejpam-4356	73	22	that	that	PRON
ejpam-4356	73	23	dg(u	dg(u	ADJ
ejpam-4356	73	24	,	,	PUNCT
ejpam-4356	73	25	v	v	NOUN
ejpam-4356	73	26	)	)	PUNCT
ejpam-4356	73	27	≤	≤	NOUN
ejpam-4356	73	28	2	2	NUM
ejpam-4356	73	29	.	.	PUNCT
ejpam-4356	74	1	moreover	moreover	ADV
ejpam-4356	74	2	,	,	PUNCT
ejpam-4356	74	3	if	if	SCONJ
ejpam-4356	74	4	{	{	PUNCT
ejpam-4356	74	5	s1	s1	NOUN
ejpam-4356	74	6	,	,	PUNCT
ejpam-4356	74	7	s2	s2	PROPN
ejpam-4356	74	8	,	,	PUNCT
ejpam-4356	74	9	...	...	PUNCT
ejpam-4356	74	10	,	,	PUNCT
ejpam-4356	74	11	sk	sk	VERB
ejpam-4356	74	12	}	}	PUNCT
ejpam-4356	74	13	is	be	AUX
ejpam-4356	74	14	the	the	DET
ejpam-4356	74	15	sequence	sequence	NOUN
ejpam-4356	74	16	corresponding	correspond	VERB
ejpam-4356	74	17	to	to	ADP
ejpam-4356	74	18	the	the	DET
ejpam-4356	74	19	weakly	weakly	ADV
ejpam-4356	74	20	connected	connected	ADJ
ejpam-4356	74	21	geodetic	geodetic	ADJ
ejpam-4356	74	22	set	set	NOUN
ejpam-4356	74	23	s	s	PART
ejpam-4356	74	24	,	,	PUNCT
ejpam-4356	74	25	⟨si⟩w	⟨si⟩w	VERB
ejpam-4356	74	26	is	be	AUX
ejpam-4356	74	27	connected	connect	VERB
ejpam-4356	74	28	for	for	ADP
ejpam-4356	74	29	each	each	DET
ejpam-4356	74	30	i	i	NOUN
ejpam-4356	74	31	=	=	NOUN
ejpam-4356	74	32	1	1	NUM
ejpam-4356	74	33	,	,	PUNCT
ejpam-4356	74	34	2	2	NUM
ejpam-4356	74	35	,	,	PUNCT
ejpam-4356	74	36	...	...	PUNCT
ejpam-4356	74	37	,	,	PUNCT
ejpam-4356	74	38	k	k	NOUN
ejpam-4356	74	39	,	,	PUNCT
ejpam-4356	74	40	patangan	patangan	NOUN
ejpam-4356	74	41	,	,	PUNCT
ejpam-4356	74	42	et.al	et.al	VERB
ejpam-4356	74	43	[	[	X
ejpam-4356	74	44	12	12	NUM
ejpam-4356	74	45	]	]	PUNCT
ejpam-4356	74	46	.	.	PUNCT
ejpam-4356	75	1	3	3	X
ejpam-4356	75	2	.	.	X
ejpam-4356	75	3	results	result	VERB
ejpam-4356	75	4	definition	definition	NOUN
ejpam-4356	75	5	1	1	NUM
ejpam-4356	75	6	.	.	PUNCT
ejpam-4356	76	1	a	a	DET
ejpam-4356	76	2	weakly	weakly	ADV
ejpam-4356	76	3	connected	connected	ADJ
ejpam-4356	76	4	closed	closed	ADJ
ejpam-4356	76	5	geodetic	geodetic	ADJ
ejpam-4356	76	6	set	set	NOUN
ejpam-4356	76	7	of	of	ADP
ejpam-4356	76	8	g	g	NOUN
ejpam-4356	76	9	which	which	PRON
ejpam-4356	76	10	is	be	AUX
ejpam-4356	76	11	dominating	dominate	VERB
ejpam-4356	76	12	is	be	AUX
ejpam-4356	76	13	called	call	VERB
ejpam-4356	76	14	a	a	DET
ejpam-4356	76	15	weakly	weakly	ADV
ejpam-4356	76	16	connected	connected	ADJ
ejpam-4356	76	17	closed	closed	ADJ
ejpam-4356	76	18	geodetic	geodetic	ADJ
ejpam-4356	76	19	dominating	dominating	NOUN
ejpam-4356	76	20	set	set	NOUN
ejpam-4356	76	21	of	of	ADP
ejpam-4356	76	22	g.	g.	PROPN
ejpam-4356	76	23	the	the	DET
ejpam-4356	76	24	minimum	minimum	ADJ
ejpam-4356	76	25	cardinality	cardinality	NOUN
ejpam-4356	76	26	of	of	ADP
ejpam-4356	76	27	a	a	DET
ejpam-4356	76	28	weakly	weakly	ADJ
ejpam-4356	76	29	j.	j.	PROPN
ejpam-4356	76	30	hamja	hamja	PROPN
ejpam-4356	76	31	,	,	PUNCT
ejpam-4356	76	32	i.	i.	PROPN
ejpam-4356	76	33	aniversario	aniversario	PROPN
ejpam-4356	76	34	,	,	PUNCT
ejpam-4356	76	35	h.	h.	PROPN
ejpam-4356	76	36	rara	rara	PROPN
ejpam-4356	76	37	/	/	SYM
ejpam-4356	76	38	eur	eur	PROPN
ejpam-4356	76	39	.	.	PUNCT
ejpam-4356	77	1	j.	j.	PROPN
ejpam-4356	77	2	pure	pure	PROPN
ejpam-4356	77	3	appl	appl	PROPN
ejpam-4356	77	4	.	.	PROPN
ejpam-4356	77	5	math	math	PROPN
ejpam-4356	77	6	,	,	PUNCT
ejpam-4356	77	7	15	15	NUM
ejpam-4356	77	8	(	(	PUNCT
ejpam-4356	77	9	2	2	NUM
ejpam-4356	77	10	)	)	PUNCT
ejpam-4356	77	11	(	(	PUNCT
ejpam-4356	77	12	2022	2022	NUM
ejpam-4356	77	13	)	)	PUNCT
ejpam-4356	77	14	,	,	PUNCT
ejpam-4356	77	15	736	736	NUM
ejpam-4356	77	16	-	-	SYM
ejpam-4356	77	17	752	752	NUM
ejpam-4356	77	18	739	739	NUM
ejpam-4356	77	19	connected	connect	VERB
ejpam-4356	77	20	closed	closed	ADJ
ejpam-4356	77	21	geodetic	geodetic	ADJ
ejpam-4356	77	22	dominating	dominating	NOUN
ejpam-4356	77	23	set	set	NOUN
ejpam-4356	77	24	is	be	AUX
ejpam-4356	77	25	called	call	VERB
ejpam-4356	77	26	weakly	weakly	ADV
ejpam-4356	77	27	connected	connected	ADJ
ejpam-4356	77	28	closed	close	VERB
ejpam-4356	77	29	geodetic	geodetic	ADJ
ejpam-4356	77	30	domination	domination	NOUN
ejpam-4356	77	31	number	number	NOUN
ejpam-4356	77	32	of	of	ADP
ejpam-4356	77	33	g	g	NOUN
ejpam-4356	77	34	,	,	PUNCT
ejpam-4356	77	35	denoted	denote	VERB
ejpam-4356	77	36	by	by	ADP
ejpam-4356	77	37	γwcg(g	γwcg(g	PROPN
ejpam-4356	77	38	)	)	PUNCT
ejpam-4356	77	39	.	.	PUNCT
ejpam-4356	78	1	a	a	DET
ejpam-4356	78	2	weakly	weakly	ADV
ejpam-4356	78	3	connected	connected	ADJ
ejpam-4356	78	4	closed	closed	ADJ
ejpam-4356	78	5	geodetic	geodetic	ADJ
ejpam-4356	78	6	dominating	dominating	NOUN
ejpam-4356	78	7	set	set	NOUN
ejpam-4356	78	8	s	s	NOUN
ejpam-4356	78	9	with	with	ADP
ejpam-4356	78	10	|s|	|s|	PROPN
ejpam-4356	78	11	=	=	PUNCT
ejpam-4356	78	12	γwcg(g	γwcg(g	NOUN
ejpam-4356	78	13	)	)	PUNCT
ejpam-4356	78	14	is	be	AUX
ejpam-4356	78	15	said	say	VERB
ejpam-4356	78	16	to	to	PART
ejpam-4356	78	17	be	be	AUX
ejpam-4356	78	18	a	a	DET
ejpam-4356	78	19	γwcg	γwcg	NOUN
ejpam-4356	78	20	-	-	PUNCT
ejpam-4356	78	21	set	set	NOUN
ejpam-4356	78	22	of	of	ADP
ejpam-4356	78	23	g.	g.	PROPN
ejpam-4356	78	24	example	example	NOUN
ejpam-4356	79	1	1	1	X
ejpam-4356	79	2	.	.	PUNCT
ejpam-4356	80	1	let	let	VERB
ejpam-4356	80	2	g	g	NOUN
ejpam-4356	80	3	be	be	AUX
ejpam-4356	80	4	the	the	DET
ejpam-4356	80	5	graph	graph	NOUN
ejpam-4356	80	6	in	in	ADP
ejpam-4356	80	7	figure	figure	NOUN
ejpam-4356	80	8	1	1	NUM
ejpam-4356	80	9	and	and	CCONJ
ejpam-4356	80	10	s	s	NOUN
ejpam-4356	80	11	=	=	PUNCT
ejpam-4356	80	12	{	{	PUNCT
ejpam-4356	80	13	u2	u2	PROPN
ejpam-4356	80	14	,	,	PUNCT
ejpam-4356	80	15	u4	u4	PROPN
ejpam-4356	80	16	,	,	PUNCT
ejpam-4356	80	17	u6	u6	PROPN
ejpam-4356	80	18	}	}	PUNCT
ejpam-4356	80	19	.	.	PUNCT
ejpam-4356	81	1	then	then	ADV
ejpam-4356	81	2	u2	u2	PROPN
ejpam-4356	81	3	̸=	̸=	PROPN
ejpam-4356	81	4	u4	u4	PROPN
ejpam-4356	81	5	with	with	ADP
ejpam-4356	81	6	u6	u6	PROPN
ejpam-4356	81	7	/∈	/∈	PUNCT
ejpam-4356	82	1	ig[u2	ig[u2	PROPN
ejpam-4356	82	2	,	,	PUNCT
ejpam-4356	82	3	u4	u4	PROPN
ejpam-4356	82	4	]	]	PUNCT
ejpam-4356	82	5	and	and	CCONJ
ejpam-4356	82	6	ig[u2	ig[u2	PROPN
ejpam-4356	82	7	,	,	PUNCT
ejpam-4356	82	8	u4	u4	NOUN
ejpam-4356	82	9	]	]	X
ejpam-4356	82	10	=	=	X
ejpam-4356	82	11	{	{	PUNCT
ejpam-4356	82	12	u2	u2	PROPN
ejpam-4356	82	13	,	,	PUNCT
ejpam-4356	82	14	u4	u4	PROPN
ejpam-4356	82	15	}	}	PUNCT
ejpam-4356	82	16	,	,	PUNCT
ejpam-4356	82	17	ig[u2	ig[u2	PROPN
ejpam-4356	82	18	,	,	PUNCT
ejpam-4356	82	19	u6	u6	NOUN
ejpam-4356	82	20	]	]	PUNCT
ejpam-4356	82	21	=	=	SYM
ejpam-4356	82	22	{	{	PUNCT
ejpam-4356	82	23	u2	u2	PROPN
ejpam-4356	82	24	,	,	PUNCT
ejpam-4356	82	25	u1	u1	NOUN
ejpam-4356	82	26	,	,	PUNCT
ejpam-4356	82	27	u6	u6	NOUN
ejpam-4356	82	28	}	}	PUNCT
ejpam-4356	82	29	∪	∪	NOUN
ejpam-4356	82	30	{	{	PUNCT
ejpam-4356	82	31	u2	u2	PROPN
ejpam-4356	82	32	,	,	PUNCT
ejpam-4356	82	33	u5	u5	PROPN
ejpam-4356	82	34	,	,	PUNCT
ejpam-4356	82	35	u6	u6	NOUN
ejpam-4356	82	36	}	}	PUNCT
ejpam-4356	82	37	=	=	SYM
ejpam-4356	82	38	{	{	PUNCT
ejpam-4356	82	39	u1	u1	NOUN
ejpam-4356	82	40	,	,	PUNCT
ejpam-4356	82	41	u2	u2	PROPN
ejpam-4356	82	42	,	,	PUNCT
ejpam-4356	82	43	u5	u5	PROPN
ejpam-4356	82	44	,	,	PUNCT
ejpam-4356	82	45	u6	u6	NOUN
ejpam-4356	82	46	}	}	PUNCT
ejpam-4356	82	47	and	and	CCONJ
ejpam-4356	82	48	ig[u4	ig[u4	PROPN
ejpam-4356	82	49	,	,	PUNCT
ejpam-4356	82	50	u6	u6	NOUN
ejpam-4356	82	51	]	]	PUNCT
ejpam-4356	82	52	=	=	SYM
ejpam-4356	82	53	{	{	PUNCT
ejpam-4356	82	54	u4	u4	PROPN
ejpam-4356	82	55	,	,	PUNCT
ejpam-4356	82	56	u5	u5	PROPN
ejpam-4356	82	57	,	,	PUNCT
ejpam-4356	82	58	u6	u6	NOUN
ejpam-4356	82	59	}	}	PUNCT
ejpam-4356	82	60	∪	∪	NOUN
ejpam-4356	82	61	{	{	PUNCT
ejpam-4356	82	62	u4	u4	PROPN
ejpam-4356	82	63	,	,	PUNCT
ejpam-4356	82	64	u3	u3	NOUN
ejpam-4356	82	65	,	,	PUNCT
ejpam-4356	82	66	u6	u6	NOUN
ejpam-4356	82	67	}	}	PUNCT
ejpam-4356	82	68	=	=	SYM
ejpam-4356	82	69	{	{	PUNCT
ejpam-4356	82	70	u3	u3	PROPN
ejpam-4356	82	71	,	,	PUNCT
ejpam-4356	82	72	u4	u4	PROPN
ejpam-4356	82	73	,	,	PUNCT
ejpam-4356	82	74	u5	u5	PROPN
ejpam-4356	82	75	,	,	PUNCT
ejpam-4356	82	76	u6	u6	NOUN
ejpam-4356	82	77	}	}	PUNCT
ejpam-4356	82	78	.	.	PUNCT
ejpam-4356	83	1	thus	thus	ADV
ejpam-4356	83	2	,	,	PUNCT
ejpam-4356	83	3	ig[s	ig[s	PROPN
ejpam-4356	83	4	]	]	PUNCT
ejpam-4356	83	5	=	=	PRON
ejpam-4356	83	6	{	{	PUNCT
ejpam-4356	83	7	u1	u1	NOUN
ejpam-4356	83	8	,	,	PUNCT
ejpam-4356	83	9	u2	u2	NOUN
ejpam-4356	83	10	,	,	PUNCT
ejpam-4356	83	11	u3	u3	PROPN
ejpam-4356	83	12	,	,	PUNCT
ejpam-4356	83	13	u4	u4	PROPN
ejpam-4356	83	14	,	,	PUNCT
ejpam-4356	83	15	u5	u5	PROPN
ejpam-4356	83	16	,	,	PUNCT
ejpam-4356	83	17	u6	u6	NOUN
ejpam-4356	83	18	}	}	PUNCT
ejpam-4356	83	19	=	=	SYM
ejpam-4356	83	20	v	v	NOUN
ejpam-4356	83	21	(	(	PUNCT
ejpam-4356	83	22	g	g	NOUN
ejpam-4356	83	23	)	)	PUNCT
ejpam-4356	83	24	.	.	PUNCT
ejpam-4356	84	1	since	since	SCONJ
ejpam-4356	84	2	u6	u6	PROPN
ejpam-4356	84	3	/∈	/∈	PUNCT
ejpam-4356	85	1	ig[u2	ig[u2	PROPN
ejpam-4356	85	2	,	,	PUNCT
ejpam-4356	85	3	u4	u4	PROPN
ejpam-4356	85	4	]	]	X
ejpam-4356	85	5	,	,	PUNCT
ejpam-4356	85	6	ig[s	ig[s	PROPN
ejpam-4356	85	7	]	]	PUNCT
ejpam-4356	85	8	is	be	AUX
ejpam-4356	85	9	a	a	DET
ejpam-4356	85	10	geodetic	geodetic	ADJ
ejpam-4356	85	11	closure	closure	NOUN
ejpam-4356	85	12	of	of	ADP
ejpam-4356	85	13	s.	s.	PROPN
ejpam-4356	85	14	also	also	ADV
ejpam-4356	85	15	,	,	PUNCT
ejpam-4356	85	16	ng[s	ng[s	PROPN
ejpam-4356	85	17	]	]	PUNCT
ejpam-4356	85	18	=	=	SYM
ejpam-4356	85	19	v	v	X
ejpam-4356	85	20	(	(	PUNCT
ejpam-4356	85	21	g	g	NOUN
ejpam-4356	85	22	)	)	PUNCT
ejpam-4356	85	23	,	,	PUNCT
ejpam-4356	85	24	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4356	85	25	is	be	AUX
ejpam-4356	85	26	connected	connect	VERB
ejpam-4356	85	27	.	.	PUNCT
ejpam-4356	86	1	in	in	ADP
ejpam-4356	86	2	fact	fact	NOUN
ejpam-4356	86	3	,	,	PUNCT
ejpam-4356	86	4	it	it	PRON
ejpam-4356	86	5	can	can	AUX
ejpam-4356	86	6	be	be	AUX
ejpam-4356	86	7	verified	verify	VERB
ejpam-4356	86	8	that	that	SCONJ
ejpam-4356	86	9	there	there	PRON
ejpam-4356	86	10	is	be	VERB
ejpam-4356	86	11	no	no	DET
ejpam-4356	86	12	set	set	NOUN
ejpam-4356	86	13	of	of	ADP
ejpam-4356	86	14	lesser	less	ADJ
ejpam-4356	86	15	cardinality	cardinality	NOUN
ejpam-4356	86	16	than	than	ADP
ejpam-4356	86	17	s	s	PRON
ejpam-4356	86	18	that	that	PRON
ejpam-4356	86	19	is	be	AUX
ejpam-4356	86	20	a	a	DET
ejpam-4356	86	21	weakly	weakly	ADV
ejpam-4356	86	22	connected	connect	VERB
ejpam-4356	86	23	.	.	PUNCT
ejpam-4356	87	1	note	note	VERB
ejpam-4356	87	2	that	that	DET
ejpam-4356	87	3	u6	u6	PROPN
ejpam-4356	87	4	/∈	/∈	PUNCT
ejpam-4356	88	1	ig[u2	ig[u2	PROPN
ejpam-4356	88	2	,	,	PUNCT
ejpam-4356	88	3	u4	u4	PROPN
ejpam-4356	88	4	]	]	X
ejpam-4356	88	5	.	.	PUNCT
ejpam-4356	89	1	thus	thus	ADV
ejpam-4356	89	2	,	,	PUNCT
ejpam-4356	89	3	s	s	VERB
ejpam-4356	89	4	=	=	PUNCT
ejpam-4356	89	5	{	{	PUNCT
ejpam-4356	89	6	u2	u2	PROPN
ejpam-4356	89	7	,	,	PUNCT
ejpam-4356	89	8	u4	u4	PROPN
ejpam-4356	89	9	,	,	PUNCT
ejpam-4356	89	10	u6	u6	PROPN
ejpam-4356	89	11	}	}	PUNCT
ejpam-4356	89	12	is	be	AUX
ejpam-4356	89	13	a	a	DET
ejpam-4356	89	14	weakly	weakly	ADV
ejpam-4356	89	15	connected	connected	ADJ
ejpam-4356	89	16	closed	closed	ADJ
ejpam-4356	89	17	geodetic	geodetic	ADJ
ejpam-4356	89	18	set	set	NOUN
ejpam-4356	89	19	and	and	CCONJ
ejpam-4356	89	20	dominating	dominating	NOUN
ejpam-4356	89	21	.	.	PUNCT
ejpam-4356	90	1	u1	u1	PROPN
ejpam-4356	90	2	u2	u2	PROPN
ejpam-4356	90	3	u3	u3	PROPN
ejpam-4356	90	4	u4u5	u4u5	PROPN
ejpam-4356	90	5	u6	u6	NOUN
ejpam-4356	90	6	g	g	PROPN
ejpam-4356	90	7	:	:	PUNCT
ejpam-4356	90	8	u1	u1	PROPN
ejpam-4356	90	9	u2	u2	PROPN
ejpam-4356	90	10	u3	u3	PROPN
ejpam-4356	90	11	u4u5	u4u5	PROPN
ejpam-4356	90	12	u6	u6	PROPN
ejpam-4356	90	13	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	90	14	:	:	PUNCT
ejpam-4356	90	15	figure	figure	NOUN
ejpam-4356	90	16	1	1	NUM
ejpam-4356	90	17	:	:	PUNCT
ejpam-4356	90	18	graph	graph	VERB
ejpam-4356	90	19	g	g	NOUN
ejpam-4356	90	20	with	with	ADP
ejpam-4356	90	21	γwcg(g	γwcg(g	NOUN
ejpam-4356	90	22	)	)	PUNCT
ejpam-4356	90	23	=	=	SYM
ejpam-4356	90	24	3	3	NUM
ejpam-4356	90	25	remark	remark	NOUN
ejpam-4356	90	26	1	1	NUM
ejpam-4356	90	27	.	.	PUNCT
ejpam-4356	91	1	every	every	DET
ejpam-4356	91	2	weakly	weakly	ADV
ejpam-4356	91	3	connected	connected	ADJ
ejpam-4356	91	4	closed	closed	ADJ
ejpam-4356	91	5	geodetic	geodetic	ADJ
ejpam-4356	91	6	dominating	dominating	NOUN
ejpam-4356	91	7	set	set	NOUN
ejpam-4356	91	8	of	of	ADP
ejpam-4356	91	9	a	a	DET
ejpam-4356	91	10	graph	graph	NOUN
ejpam-4356	91	11	g	g	NOUN
ejpam-4356	91	12	is	be	AUX
ejpam-4356	91	13	weakly	weakly	ADV
ejpam-4356	91	14	connected	connected	ADJ
ejpam-4356	91	15	closed	closed	ADJ
ejpam-4356	91	16	geodetic	geodetic	ADJ
ejpam-4356	91	17	set	set	NOUN
ejpam-4356	91	18	.	.	PUNCT
ejpam-4356	92	1	so	so	ADV
ejpam-4356	92	2	,	,	PUNCT
ejpam-4356	92	3	wcgn(g	wcgn(g	NOUN
ejpam-4356	92	4	)	)	PUNCT
ejpam-4356	92	5	≤	≤	NUM
ejpam-4356	92	6	γwcg(g	γwcg(g	NOUN
ejpam-4356	92	7	)	)	PUNCT
ejpam-4356	92	8	.	.	PUNCT
ejpam-4356	93	1	remark	remark	PROPN
ejpam-4356	93	2	2	2	NUM
ejpam-4356	93	3	.	.	PUNCT
ejpam-4356	94	1	for	for	ADP
ejpam-4356	94	2	any	any	DET
ejpam-4356	94	3	nontrivial	nontrivial	ADJ
ejpam-4356	94	4	connected	connect	VERB
ejpam-4356	94	5	graph	graph	NOUN
ejpam-4356	94	6	g	g	NOUN
ejpam-4356	94	7	of	of	ADP
ejpam-4356	94	8	order	order	NOUN
ejpam-4356	94	9	n	n	CCONJ
ejpam-4356	94	10	,	,	PUNCT
ejpam-4356	94	11	2	2	NUM
ejpam-4356	94	12	≤	≤	NUM
ejpam-4356	94	13	max{γ(g	max{γ(g	PROPN
ejpam-4356	94	14	)	)	PUNCT
ejpam-4356	94	15	,	,	PUNCT
ejpam-4356	94	16	wcg(g	wcg(g	PROPN
ejpam-4356	94	17	)	)	PUNCT
ejpam-4356	94	18	}	}	PUNCT
ejpam-4356	94	19	≤	≤	NUM
ejpam-4356	94	20	γwcg(g	γwcg(g	NOUN
ejpam-4356	94	21	)	)	PUNCT
ejpam-4356	94	22	≤	≤	NOUN
ejpam-4356	94	23	n.	n.	NOUN
ejpam-4356	94	24	remark	remark	NOUN
ejpam-4356	94	25	3	3	NUM
ejpam-4356	94	26	.	.	PUNCT
ejpam-4356	95	1	every	every	DET
ejpam-4356	95	2	superset	superset	NOUN
ejpam-4356	95	3	of	of	ADP
ejpam-4356	95	4	a	a	DET
ejpam-4356	95	5	weakly	weakly	ADV
ejpam-4356	95	6	connected	connected	ADJ
ejpam-4356	95	7	closed	closed	ADJ
ejpam-4356	95	8	geodetic	geodetic	ADJ
ejpam-4356	95	9	dominating	dominating	NOUN
ejpam-4356	95	10	set	set	NOUN
ejpam-4356	95	11	is	be	AUX
ejpam-4356	95	12	weakly	weakly	ADV
ejpam-4356	95	13	connected	connected	ADJ
ejpam-4356	95	14	closed	closed	ADJ
ejpam-4356	95	15	geodetic	geodetic	ADJ
ejpam-4356	95	16	dominating	dominating	NOUN
ejpam-4356	95	17	set	set	NOUN
ejpam-4356	95	18	.	.	PUNCT
ejpam-4356	96	1	lemma	lemma	PROPN
ejpam-4356	96	2	1	1	NUM
ejpam-4356	96	3	.	.	PUNCT
ejpam-4356	96	4	aniversario	aniversario	PROPN
ejpam-4356	96	5	,	,	PUNCT
ejpam-4356	96	6	et	et	PROPN
ejpam-4356	96	7	al	al	PROPN
ejpam-4356	97	1	[	[	X
ejpam-4356	97	2	1	1	X
ejpam-4356	97	3	]	]	PUNCT
ejpam-4356	97	4	every	every	DET
ejpam-4356	97	5	geodetic	geodetic	ADJ
ejpam-4356	97	6	cover	cover	NOUN
ejpam-4356	97	7	of	of	ADP
ejpam-4356	97	8	a	a	DET
ejpam-4356	97	9	connected	connected	ADJ
ejpam-4356	97	10	graph	graph	NOUN
ejpam-4356	97	11	g	g	NOUN
ejpam-4356	97	12	contains	contain	VERB
ejpam-4356	97	13	all	all	DET
ejpam-4356	97	14	its	its	PRON
ejpam-4356	97	15	extreme	extreme	ADJ
ejpam-4356	97	16	vertices	vertex	NOUN
ejpam-4356	97	17	.	.	PUNCT
ejpam-4356	98	1	theorem	theorem	NOUN
ejpam-4356	98	2	1	1	NUM
ejpam-4356	98	3	.	.	PUNCT
ejpam-4356	99	1	let	let	VERB
ejpam-4356	99	2	g	g	PRON
ejpam-4356	99	3	be	be	AUX
ejpam-4356	99	4	a	a	DET
ejpam-4356	99	5	connected	connected	ADJ
ejpam-4356	99	6	graph	graph	NOUN
ejpam-4356	99	7	of	of	ADP
ejpam-4356	99	8	order	order	NOUN
ejpam-4356	99	9	n.	n.	NOUN
ejpam-4356	100	1	then	then	ADV
ejpam-4356	100	2	(	(	PUNCT
ejpam-4356	100	3	i	i	NOUN
ejpam-4356	100	4	)	)	PUNCT
ejpam-4356	100	5	every	every	DET
ejpam-4356	100	6	weakly	weakly	ADV
ejpam-4356	100	7	connected	connected	ADJ
ejpam-4356	100	8	closed	closed	ADJ
ejpam-4356	100	9	geodetic	geodetic	ADJ
ejpam-4356	100	10	dominating	dominating	NOUN
ejpam-4356	100	11	set	set	NOUN
ejpam-4356	100	12	of	of	ADP
ejpam-4356	100	13	g	g	PROPN
ejpam-4356	100	14	contains	contain	VERB
ejpam-4356	100	15	its	its	PRON
ejpam-4356	100	16	extreme	extreme	ADJ
ejpam-4356	100	17	vertices	vertex	NOUN
ejpam-4356	100	18	.	.	PUNCT
ejpam-4356	101	1	j.	j.	PROPN
ejpam-4356	101	2	hamja	hamja	PROPN
ejpam-4356	101	3	,	,	PUNCT
ejpam-4356	101	4	i.	i.	PROPN
ejpam-4356	101	5	aniversario	aniversario	PROPN
ejpam-4356	101	6	,	,	PUNCT
ejpam-4356	101	7	h.	h.	PROPN
ejpam-4356	101	8	rara	rara	PROPN
ejpam-4356	101	9	/	/	SYM
ejpam-4356	101	10	eur	eur	PROPN
ejpam-4356	101	11	.	.	PUNCT
ejpam-4356	102	1	j.	j.	PROPN
ejpam-4356	102	2	pure	pure	PROPN
ejpam-4356	102	3	appl	appl	PROPN
ejpam-4356	102	4	.	.	PROPN
ejpam-4356	102	5	math	math	PROPN
ejpam-4356	102	6	,	,	PUNCT
ejpam-4356	102	7	15	15	NUM
ejpam-4356	102	8	(	(	PUNCT
ejpam-4356	102	9	2	2	NUM
ejpam-4356	102	10	)	)	PUNCT
ejpam-4356	102	11	(	(	PUNCT
ejpam-4356	102	12	2022	2022	NUM
ejpam-4356	102	13	)	)	PUNCT
ejpam-4356	102	14	,	,	PUNCT
ejpam-4356	102	15	736	736	NUM
ejpam-4356	102	16	-	-	SYM
ejpam-4356	102	17	752	752	NUM
ejpam-4356	102	18	740	740	NUM
ejpam-4356	102	19	(	(	PUNCT
ejpam-4356	102	20	ii	ii	NOUN
ejpam-4356	102	21	)	)	PUNCT
ejpam-4356	102	22	if	if	SCONJ
ejpam-4356	102	23	the	the	DET
ejpam-4356	102	24	set	set	NOUN
ejpam-4356	102	25	s	s	X
ejpam-4356	102	26	of	of	ADP
ejpam-4356	102	27	extreme	extreme	ADJ
ejpam-4356	102	28	vertices	vertex	NOUN
ejpam-4356	102	29	of	of	ADP
ejpam-4356	102	30	g	g	PROPN
ejpam-4356	102	31	is	be	AUX
ejpam-4356	102	32	a	a	DET
ejpam-4356	102	33	weakly	weakly	ADV
ejpam-4356	102	34	connected	connected	ADJ
ejpam-4356	102	35	closed	closed	ADJ
ejpam-4356	102	36	geodetic	geodetic	ADJ
ejpam-4356	102	37	dominating	dominating	NOUN
ejpam-4356	102	38	set	set	NOUN
ejpam-4356	102	39	of	of	ADP
ejpam-4356	102	40	g.	g.	PROPN
ejpam-4356	103	1	then	then	ADV
ejpam-4356	103	2	s	s	VERB
ejpam-4356	103	3	is	be	AUX
ejpam-4356	103	4	a	a	DET
ejpam-4356	103	5	unique	unique	ADJ
ejpam-4356	103	6	minimum	minimum	ADJ
ejpam-4356	103	7	weakly	weakly	ADJ
ejpam-4356	103	8	connected	connect	VERB
ejpam-4356	103	9	closed	closed	ADJ
ejpam-4356	103	10	geodetic	geodetic	ADJ
ejpam-4356	103	11	dominating	dominating	NOUN
ejpam-4356	103	12	set	set	NOUN
ejpam-4356	103	13	of	of	ADP
ejpam-4356	103	14	g	g	PROPN
ejpam-4356	103	15	and	and	CCONJ
ejpam-4356	103	16	γwcg(g	γwcg(g	NOUN
ejpam-4356	103	17	)	)	PUNCT
ejpam-4356	103	18	=	=	SYM
ejpam-4356	103	19	|s|	|s|	PROPN
ejpam-4356	103	20	.	.	PUNCT
ejpam-4356	103	21	proof	proof	NOUN
ejpam-4356	103	22	.	.	PUNCT
ejpam-4356	104	1	(	(	PUNCT
ejpam-4356	104	2	i	i	NOUN
ejpam-4356	104	3	)	)	PUNCT
ejpam-4356	104	4	let	let	VERB
ejpam-4356	104	5	s	s	PRON
ejpam-4356	104	6	be	be	AUX
ejpam-4356	104	7	a	a	DET
ejpam-4356	104	8	weakly	weakly	ADV
ejpam-4356	104	9	connected	connected	ADJ
ejpam-4356	104	10	closed	closed	ADJ
ejpam-4356	104	11	geodetic	geodetic	ADJ
ejpam-4356	104	12	dominating	dominating	NOUN
ejpam-4356	104	13	set	set	NOUN
ejpam-4356	104	14	and	and	CCONJ
ejpam-4356	104	15	let	let	VERB
ejpam-4356	104	16	v	v	PART
ejpam-4356	104	17	be	be	AUX
ejpam-4356	104	18	an	an	DET
ejpam-4356	104	19	extreme	extreme	ADJ
ejpam-4356	104	20	vertex	vertex	NOUN
ejpam-4356	104	21	of	of	ADP
ejpam-4356	104	22	g.	g.	PROPN
ejpam-4356	104	23	assume	assume	VERB
ejpam-4356	104	24	that	that	SCONJ
ejpam-4356	104	25	v	v	X
ejpam-4356	104	26	/∈	/∈	PUNCT
ejpam-4356	105	1	s.	s.	PROPN
ejpam-4356	105	2	then	then	ADV
ejpam-4356	105	3	by	by	ADP
ejpam-4356	105	4	lemma	lemma	PROPN
ejpam-4356	105	5	1	1	NUM
ejpam-4356	105	6	,	,	PUNCT
ejpam-4356	105	7	s	s	VERB
ejpam-4356	105	8	is	be	AUX
ejpam-4356	105	9	not	not	PART
ejpam-4356	105	10	a	a	DET
ejpam-4356	105	11	geodetic	geodetic	ADJ
ejpam-4356	105	12	cover	cover	NOUN
ejpam-4356	105	13	of	of	ADP
ejpam-4356	105	14	g.	g.	PROPN
ejpam-4356	105	15	thus	thus	ADV
ejpam-4356	105	16	,	,	PUNCT
ejpam-4356	105	17	s	s	VERB
ejpam-4356	105	18	is	be	AUX
ejpam-4356	105	19	not	not	PART
ejpam-4356	105	20	a	a	DET
ejpam-4356	105	21	closed	closed	ADJ
ejpam-4356	105	22	geodetic	geodetic	ADJ
ejpam-4356	105	23	dominating	dominating	NOUN
ejpam-4356	105	24	set	set	NOUN
ejpam-4356	105	25	of	of	ADP
ejpam-4356	105	26	g.	g.	PROPN
ejpam-4356	105	27	hence	hence	ADV
ejpam-4356	105	28	,	,	PUNCT
ejpam-4356	105	29	s	s	VERB
ejpam-4356	105	30	is	be	AUX
ejpam-4356	105	31	not	not	PART
ejpam-4356	105	32	weakly	weakly	ADV
ejpam-4356	105	33	connected	connected	ADJ
ejpam-4356	105	34	closed	closed	ADJ
ejpam-4356	105	35	geodetic	geodetic	ADJ
ejpam-4356	105	36	dominating	dominating	NOUN
ejpam-4356	105	37	set	set	NOUN
ejpam-4356	105	38	of	of	ADP
ejpam-4356	105	39	g	g	NOUN
ejpam-4356	105	40	,	,	PUNCT
ejpam-4356	105	41	which	which	PRON
ejpam-4356	105	42	is	be	AUX
ejpam-4356	105	43	a	a	DET
ejpam-4356	105	44	contradiction	contradiction	NOUN
ejpam-4356	105	45	.	.	PUNCT
ejpam-4356	106	1	therefore	therefore	ADV
ejpam-4356	106	2	,	,	PUNCT
ejpam-4356	106	3	each	each	DET
ejpam-4356	106	4	extreme	extreme	ADJ
ejpam-4356	106	5	vertex	vertex	NOUN
ejpam-4356	106	6	of	of	ADP
ejpam-4356	106	7	g	g	PROPN
ejpam-4356	106	8	belongs	belong	VERB
ejpam-4356	106	9	to	to	ADP
ejpam-4356	106	10	every	every	DET
ejpam-4356	106	11	weakly	weakly	ADV
ejpam-4356	106	12	connected	connect	VERB
ejpam-4356	106	13	closed	closed	ADJ
ejpam-4356	106	14	geodetic	geodetic	ADJ
ejpam-4356	106	15	dominating	dominating	NOUN
ejpam-4356	106	16	set	set	NOUN
ejpam-4356	106	17	of	of	ADP
ejpam-4356	106	18	g.	g.	PROPN
ejpam-4356	106	19	(	(	PUNCT
ejpam-4356	106	20	ii	ii	PROPN
ejpam-4356	106	21	)	)	PUNCT
ejpam-4356	106	22	let	let	VERB
ejpam-4356	106	23	s	s	PRON
ejpam-4356	106	24	be	be	AUX
ejpam-4356	106	25	a	a	DET
ejpam-4356	106	26	set	set	NOUN
ejpam-4356	106	27	of	of	ADP
ejpam-4356	106	28	extreme	extreme	ADJ
ejpam-4356	106	29	vertices	vertex	NOUN
ejpam-4356	106	30	of	of	ADP
ejpam-4356	106	31	g.	g.	PROPN
ejpam-4356	106	32	suppose	suppose	VERB
ejpam-4356	106	33	s	s	VERB
ejpam-4356	106	34	is	be	AUX
ejpam-4356	106	35	a	a	DET
ejpam-4356	106	36	weakly	weakly	ADV
ejpam-4356	106	37	connected	connected	ADJ
ejpam-4356	106	38	closed	closed	ADJ
ejpam-4356	106	39	geodetic	geodetic	ADJ
ejpam-4356	106	40	dominating	dominating	NOUN
ejpam-4356	106	41	set	set	NOUN
ejpam-4356	106	42	of	of	ADP
ejpam-4356	106	43	g	g	PROPN
ejpam-4356	106	44	and	and	CCONJ
ejpam-4356	106	45	let	let	VERB
ejpam-4356	106	46	v	v	PART
ejpam-4356	106	47	be	be	AUX
ejpam-4356	106	48	an	an	DET
ejpam-4356	106	49	extreme	extreme	ADJ
ejpam-4356	106	50	vertex	vertex	NOUN
ejpam-4356	106	51	of	of	ADP
ejpam-4356	106	52	g.	g.	PROPN
ejpam-4356	106	53	claim	claim	VERB
ejpam-4356	106	54	1	1	NUM
ejpam-4356	106	55	:	:	PUNCT
ejpam-4356	106	56	s	s	VERB
ejpam-4356	106	57	is	be	AUX
ejpam-4356	106	58	a	a	DET
ejpam-4356	106	59	minimum	minimum	ADJ
ejpam-4356	106	60	weakly	weakly	ADJ
ejpam-4356	106	61	connected	connect	VERB
ejpam-4356	106	62	closed	closed	ADJ
ejpam-4356	106	63	geodetic	geodetic	ADJ
ejpam-4356	106	64	dominating	dominating	NOUN
ejpam-4356	106	65	set	set	NOUN
ejpam-4356	106	66	of	of	ADP
ejpam-4356	106	67	g.	g.	PROPN
ejpam-4356	106	68	suppose	suppose	VERB
ejpam-4356	106	69	s	s	NOUN
ejpam-4356	106	70	is	be	AUX
ejpam-4356	106	71	not	not	PART
ejpam-4356	106	72	γwcg	γwcg	NOUN
ejpam-4356	106	73	-	-	PUNCT
ejpam-4356	106	74	set	set	NOUN
ejpam-4356	106	75	of	of	ADP
ejpam-4356	106	76	g.	g.	PROPN
ejpam-4356	106	77	then	then	ADV
ejpam-4356	106	78	there	there	PRON
ejpam-4356	106	79	exists	exist	VERB
ejpam-4356	106	80	v	v	ADP
ejpam-4356	106	81	∈	∈	PROPN
ejpam-4356	106	82	s	s	VERB
ejpam-4356	106	83	such	such	ADJ
ejpam-4356	106	84	that	that	DET
ejpam-4356	106	85	s	s	VERB
ejpam-4356	106	86	\{v	\{v	ADV
ejpam-4356	106	87	}	}	PUNCT
ejpam-4356	106	88	is	be	AUX
ejpam-4356	106	89	a	a	DET
ejpam-4356	106	90	weakly	weakly	ADV
ejpam-4356	106	91	connected	connected	ADJ
ejpam-4356	106	92	closed	closed	ADJ
ejpam-4356	106	93	geodetic	geodetic	ADJ
ejpam-4356	106	94	dominating	dominating	NOUN
ejpam-4356	106	95	set	set	NOUN
ejpam-4356	106	96	of	of	ADP
ejpam-4356	106	97	g.	g.	PROPN
ejpam-4356	107	1	so	so	ADV
ejpam-4356	107	2	,	,	PUNCT
ejpam-4356	107	3	v	v	INTJ
ejpam-4356	107	4	/∈	/∈	PUNCT
ejpam-4356	108	1	ig[u	ig[u	PROPN
ejpam-4356	108	2	,	,	PUNCT
ejpam-4356	108	3	w	w	NOUN
ejpam-4356	108	4	]	]	PUNCT
ejpam-4356	108	5	for	for	ADP
ejpam-4356	108	6	some	some	DET
ejpam-4356	108	7	u	u	NOUN
ejpam-4356	108	8	,	,	PUNCT
ejpam-4356	108	9	w	w	PROPN
ejpam-4356	108	10	∈	∈	PROPN
ejpam-4356	108	11	s	s	X
ejpam-4356	108	12	and	and	CCONJ
ejpam-4356	108	13	v	v	ADP
ejpam-4356	108	14	̸=	̸=	PROPN
ejpam-4356	108	15	x	x	NUM
ejpam-4356	108	16	,	,	PUNCT
ejpam-4356	108	17	y	y	PROPN
ejpam-4356	108	18	for	for	ADP
ejpam-4356	108	19	all	all	DET
ejpam-4356	108	20	x	x	NOUN
ejpam-4356	108	21	,	,	PUNCT
ejpam-4356	108	22	y	y	PROPN
ejpam-4356	108	23	∈	∈	PROPN
ejpam-4356	108	24	v	v	ADP
ejpam-4356	108	25	(	(	PUNCT
ejpam-4356	108	26	g	g	NOUN
ejpam-4356	108	27	)	)	PUNCT
ejpam-4356	108	28	since	since	SCONJ
ejpam-4356	108	29	v	v	NOUN
ejpam-4356	108	30	is	be	AUX
ejpam-4356	108	31	an	an	DET
ejpam-4356	108	32	extreme	extreme	ADJ
ejpam-4356	108	33	vertex	vertex	NOUN
ejpam-4356	108	34	of	of	ADP
ejpam-4356	108	35	g.	g.	PROPN
ejpam-4356	109	1	then	then	ADV
ejpam-4356	109	2	v	v	ADP
ejpam-4356	109	3	/∈	/∈	NOUN
ejpam-4356	110	1	v	v	NOUN
ejpam-4356	110	2	(	(	PUNCT
ejpam-4356	110	3	g	g	NOUN
ejpam-4356	110	4	)	)	PUNCT
ejpam-4356	110	5	,	,	PUNCT
ejpam-4356	110	6	which	which	PRON
ejpam-4356	110	7	is	be	AUX
ejpam-4356	110	8	a	a	DET
ejpam-4356	110	9	contradiction	contradiction	NOUN
ejpam-4356	110	10	.	.	PUNCT
ejpam-4356	111	1	consequently	consequently	ADV
ejpam-4356	111	2	,	,	PUNCT
ejpam-4356	111	3	s	s	VERB
ejpam-4356	111	4	is	be	AUX
ejpam-4356	111	5	a	a	DET
ejpam-4356	111	6	minimum	minimum	ADJ
ejpam-4356	111	7	weakly	weakly	ADJ
ejpam-4356	111	8	connected	connect	VERB
ejpam-4356	111	9	closed	closed	ADJ
ejpam-4356	111	10	geodetic	geodetic	ADJ
ejpam-4356	111	11	dominating	dominating	NOUN
ejpam-4356	111	12	set	set	NOUN
ejpam-4356	111	13	of	of	ADP
ejpam-4356	111	14	g.	g.	PROPN
ejpam-4356	111	15	claim	claim	VERB
ejpam-4356	111	16	2	2	NUM
ejpam-4356	111	17	:	:	PUNCT
ejpam-4356	111	18	s	s	VERB
ejpam-4356	111	19	is	be	AUX
ejpam-4356	111	20	unque	unque	ADJ
ejpam-4356	111	21	minimum	minimum	ADJ
ejpam-4356	111	22	weakly	weakly	ADV
ejpam-4356	111	23	connected	connect	VERB
ejpam-4356	111	24	closed	closed	ADJ
ejpam-4356	111	25	geodetic	geodetic	ADJ
ejpam-4356	111	26	dominating	dominating	NOUN
ejpam-4356	111	27	set	set	NOUN
ejpam-4356	111	28	of	of	ADP
ejpam-4356	111	29	g.	g.	PROPN
ejpam-4356	111	30	let	let	VERB
ejpam-4356	111	31	s	s	PRON
ejpam-4356	111	32	be	be	AUX
ejpam-4356	111	33	a	a	DET
ejpam-4356	111	34	unique	unique	ADJ
ejpam-4356	111	35	weakly	weakly	ADJ
ejpam-4356	111	36	connected	connected	ADJ
ejpam-4356	111	37	closed	closed	ADJ
ejpam-4356	111	38	geodetic	geodetic	ADJ
ejpam-4356	111	39	dominating	dominating	NOUN
ejpam-4356	111	40	set	set	NOUN
ejpam-4356	111	41	of	of	ADP
ejpam-4356	111	42	g.	g.	PROPN
ejpam-4356	111	43	then	then	ADV
ejpam-4356	111	44	since	since	SCONJ
ejpam-4356	111	45	s	s	NOUN
ejpam-4356	111	46	contains	contain	VERB
ejpam-4356	111	47	its	its	PRON
ejpam-4356	111	48	extreme	extreme	ADJ
ejpam-4356	111	49	vertices	vertex	NOUN
ejpam-4356	111	50	and	and	CCONJ
ejpam-4356	111	51	is	be	AUX
ejpam-4356	111	52	a	a	DET
ejpam-4356	111	53	minimum	minimum	ADJ
ejpam-4356	111	54	weakly	weakly	ADJ
ejpam-4356	111	55	connected	connect	VERB
ejpam-4356	111	56	closed	closed	ADJ
ejpam-4356	111	57	geodetic	geodetic	ADJ
ejpam-4356	111	58	dominating	dominating	NOUN
ejpam-4356	111	59	set	set	NOUN
ejpam-4356	111	60	of	of	ADP
ejpam-4356	111	61	g.	g.	PROPN
ejpam-4356	111	62	therefore	therefore	ADV
ejpam-4356	111	63	,	,	PUNCT
ejpam-4356	111	64	s	s	VERB
ejpam-4356	111	65	is	be	AUX
ejpam-4356	111	66	unque	unque	ADJ
ejpam-4356	111	67	minimum	minimum	ADJ
ejpam-4356	111	68	weakly	weakly	ADV
ejpam-4356	111	69	connected	connect	VERB
ejpam-4356	111	70	closed	closed	ADJ
ejpam-4356	111	71	geodetic	geodetic	ADJ
ejpam-4356	111	72	dominating	dominating	NOUN
ejpam-4356	111	73	set	set	NOUN
ejpam-4356	111	74	of	of	ADP
ejpam-4356	111	75	g.	g.	PROPN
ejpam-4356	111	76	furthermore	furthermore	ADV
ejpam-4356	111	77	,	,	PUNCT
ejpam-4356	111	78	unique	unique	ADJ
ejpam-4356	111	79	.	.	PUNCT
ejpam-4356	112	1	the	the	DET
ejpam-4356	112	2	next	next	ADJ
ejpam-4356	112	3	result	result	NOUN
ejpam-4356	112	4	immediately	immediately	ADV
ejpam-4356	112	5	follows	follow	VERB
ejpam-4356	112	6	from	from	ADP
ejpam-4356	112	7	theorem	theorem	ADJ
ejpam-4356	112	8	1	1	NUM
ejpam-4356	112	9	.	.	PUNCT
ejpam-4356	112	10	corollary	corollary	ADJ
ejpam-4356	112	11	1	1	NUM
ejpam-4356	112	12	.	.	PUNCT
ejpam-4356	113	1	every	every	DET
ejpam-4356	113	2	weakly	weakly	ADV
ejpam-4356	113	3	connected	connected	ADJ
ejpam-4356	113	4	closed	closed	ADJ
ejpam-4356	113	5	geodetic	geodetic	ADJ
ejpam-4356	113	6	dominating	dominating	NOUN
ejpam-4356	113	7	set	set	NOUN
ejpam-4356	113	8	of	of	ADP
ejpam-4356	113	9	g	g	PROPN
ejpam-4356	113	10	contains	contain	VERB
ejpam-4356	113	11	its	its	PRON
ejpam-4356	113	12	extreme	extreme	ADJ
ejpam-4356	113	13	vertices	vertex	NOUN
ejpam-4356	113	14	,	,	PUNCT
ejpam-4356	113	15	then	then	ADV
ejpam-4356	113	16	(	(	PUNCT
ejpam-4356	113	17	i	i	NOUN
ejpam-4356	113	18	)	)	PUNCT
ejpam-4356	113	19	the	the	DET
ejpam-4356	113	20	complete	complete	ADJ
ejpam-4356	113	21	graph	graph	NOUN
ejpam-4356	113	22	kn	kn	PROPN
ejpam-4356	113	23	has	have	VERB
ejpam-4356	113	24	γwcg(kn	γwcg(kn	PROPN
ejpam-4356	113	25	)	)	PUNCT
ejpam-4356	113	26	=	=	SYM
ejpam-4356	113	27	n	n	PROPN
ejpam-4356	113	28	for	for	ADP
ejpam-4356	113	29	n	n	PRON
ejpam-4356	113	30	≥	≥	NUM
ejpam-4356	113	31	2	2	NUM
ejpam-4356	113	32	.	.	PUNCT
ejpam-4356	113	33	(	(	PUNCT
ejpam-4356	113	34	ii	ii	NOUN
ejpam-4356	113	35	)	)	PUNCT
ejpam-4356	114	1	the	the	DET
ejpam-4356	114	2	path	path	NOUN
ejpam-4356	114	3	pn	pn	NOUN
ejpam-4356	114	4	of	of	ADP
ejpam-4356	114	5	order	order	NOUN
ejpam-4356	114	6	n	n	PRON
ejpam-4356	114	7	has	have	AUX
ejpam-4356	114	8	γwcg(pn	γwcg(pn	VERB
ejpam-4356	114	9	)	)	PUNCT
ejpam-4356	114	10	=	=	PUNCT
ejpam-4356	114	11	⌈	⌈	SYM
ejpam-4356	114	12	n+1	n+1	PROPN
ejpam-4356	114	13	2	2	NUM
ejpam-4356	114	14	⌉	⌉	X
ejpam-4356	114	15	.	.	PUNCT
ejpam-4356	115	1	(	(	PUNCT
ejpam-4356	115	2	iii	iii	X
ejpam-4356	115	3	)	)	PUNCT
ejpam-4356	115	4	the	the	DET
ejpam-4356	115	5	cycle	cycle	NOUN
ejpam-4356	115	6	cn	cn	NOUN
ejpam-4356	115	7	of	of	ADP
ejpam-4356	115	8	order	order	NOUN
ejpam-4356	115	9	n	n	PRON
ejpam-4356	115	10	has	have	VERB
ejpam-4356	115	11	γwcg(cn	γwcg(cn	NOUN
ejpam-4356	115	12	)	)	PUNCT
ejpam-4356	115	13	=	=	PUNCT
ejpam-4356	116	1	⌈	⌈	PROPN
ejpam-4356	116	2	n	n	PRON
ejpam-4356	116	3	2	2	NUM
ejpam-4356	116	4	⌉	⌉	X
ejpam-4356	116	5	for	for	ADP
ejpam-4356	116	6	n	n	PRON
ejpam-4356	116	7	≥	≥	NOUN
ejpam-4356	116	8	4	4	NUM
ejpam-4356	116	9	.	.	PUNCT
ejpam-4356	116	10	(	(	PUNCT
ejpam-4356	116	11	iv	iv	X
ejpam-4356	116	12	)	)	PUNCT
ejpam-4356	116	13	the	the	DET
ejpam-4356	116	14	complement	complement	NOUN
ejpam-4356	116	15	of	of	ADP
ejpam-4356	116	16	a	a	DET
ejpam-4356	116	17	cycle	cycle	NOUN
ejpam-4356	116	18	cn	cn	NOUN
ejpam-4356	116	19	of	of	ADP
ejpam-4356	116	20	order	order	NOUN
ejpam-4356	116	21	n	n	PRON
ejpam-4356	116	22	has	have	VERB
ejpam-4356	116	23	γwcg(cn	γwcg(cn	NOUN
ejpam-4356	116	24	)	)	PUNCT
ejpam-4356	116	25	=	=	SYM
ejpam-4356	116	26	3	3	NUM
ejpam-4356	116	27	for	for	ADP
ejpam-4356	116	28	n	n	X
ejpam-4356	116	29	≥	≥	NUM
ejpam-4356	116	30	5	5	NUM
ejpam-4356	116	31	.	.	PUNCT
ejpam-4356	117	1	(	(	PUNCT
ejpam-4356	117	2	v	v	NOUN
ejpam-4356	117	3	)	)	PUNCT
ejpam-4356	117	4	the	the	DET
ejpam-4356	117	5	fan	fan	NOUN
ejpam-4356	117	6	fn	fn	NOUN
ejpam-4356	117	7	of	of	ADP
ejpam-4356	117	8	order	order	NOUN
ejpam-4356	118	1	n	n	PRON
ejpam-4356	118	2	has	have	AUX
ejpam-4356	118	3	γwcg(fn	γwcg(fn	VERB
ejpam-4356	118	4	)	)	PUNCT
ejpam-4356	118	5	=	=	PUNCT
ejpam-4356	118	6	⌈	⌈	PROPN
ejpam-4356	118	7	n	n	PRON
ejpam-4356	118	8	2	2	NUM
ejpam-4356	118	9	⌉	⌉	X
ejpam-4356	118	10	for	for	ADP
ejpam-4356	118	11	n	n	PRON
ejpam-4356	118	12	≥	≥	NOUN
ejpam-4356	118	13	4	4	NUM
ejpam-4356	118	14	.	.	PUNCT
ejpam-4356	118	15	(	(	PUNCT
ejpam-4356	118	16	vi	vi	X
ejpam-4356	118	17	)	)	PUNCT
ejpam-4356	118	18	the	the	DET
ejpam-4356	118	19	wheel	wheel	NOUN
ejpam-4356	118	20	wn	wn	NOUN
ejpam-4356	118	21	of	of	ADP
ejpam-4356	118	22	order	order	NOUN
ejpam-4356	118	23	n	n	PRON
ejpam-4356	118	24	has	have	VERB
ejpam-4356	118	25	γwcg(wn	γwcg(wn	X
ejpam-4356	118	26	)	)	PUNCT
ejpam-4356	118	27	=	=	PUNCT
ejpam-4356	119	1	⌈	⌈	SYM
ejpam-4356	119	2	n−1	n−1	PROPN
ejpam-4356	119	3	2	2	NUM
ejpam-4356	119	4	⌉	⌉	X
ejpam-4356	119	5	for	for	ADP
ejpam-4356	119	6	n	n	PRON
ejpam-4356	119	7	≥	≥	NUM
ejpam-4356	119	8	5	5	NUM
ejpam-4356	119	9	.	.	PUNCT
ejpam-4356	119	10	(	(	PUNCT
ejpam-4356	119	11	vii	vii	PROPN
ejpam-4356	119	12	)	)	PUNCT
ejpam-4356	119	13	the	the	DET
ejpam-4356	119	14	petersen	petersen	PROPN
ejpam-4356	119	15	graph	graph	NOUN
ejpam-4356	119	16	g	g	PROPN
ejpam-4356	119	17	has	have	VERB
ejpam-4356	119	18	γwcg(g	γwcg(g	NOUN
ejpam-4356	119	19	)	)	PUNCT
ejpam-4356	119	20	=	=	SYM
ejpam-4356	119	21	4	4	X
ejpam-4356	119	22	.	.	PUNCT
ejpam-4356	119	23	j.	j.	PROPN
ejpam-4356	119	24	hamja	hamja	PROPN
ejpam-4356	119	25	,	,	PUNCT
ejpam-4356	119	26	i.	i.	PROPN
ejpam-4356	119	27	aniversario	aniversario	PROPN
ejpam-4356	119	28	,	,	PUNCT
ejpam-4356	119	29	h.	h.	PROPN
ejpam-4356	119	30	rara	rara	PROPN
ejpam-4356	119	31	/	/	SYM
ejpam-4356	119	32	eur	eur	PROPN
ejpam-4356	119	33	.	.	PUNCT
ejpam-4356	120	1	j.	j.	PROPN
ejpam-4356	120	2	pure	pure	PROPN
ejpam-4356	120	3	appl	appl	PROPN
ejpam-4356	120	4	.	.	PROPN
ejpam-4356	120	5	math	math	PROPN
ejpam-4356	120	6	,	,	PUNCT
ejpam-4356	120	7	15	15	NUM
ejpam-4356	120	8	(	(	PUNCT
ejpam-4356	120	9	2	2	NUM
ejpam-4356	120	10	)	)	PUNCT
ejpam-4356	120	11	(	(	PUNCT
ejpam-4356	120	12	2022	2022	NUM
ejpam-4356	120	13	)	)	PUNCT
ejpam-4356	120	14	,	,	PUNCT
ejpam-4356	120	15	736	736	NUM
ejpam-4356	120	16	-	-	SYM
ejpam-4356	120	17	752	752	NUM
ejpam-4356	120	18	741	741	NUM
ejpam-4356	120	19	theorem	theorem	NOUN
ejpam-4356	120	20	2	2	NUM
ejpam-4356	120	21	.	.	PUNCT
ejpam-4356	121	1	let	let	VERB
ejpam-4356	121	2	g	g	PRON
ejpam-4356	121	3	be	be	AUX
ejpam-4356	121	4	a	a	DET
ejpam-4356	121	5	connected	connected	ADJ
ejpam-4356	121	6	graph	graph	NOUN
ejpam-4356	121	7	of	of	ADP
ejpam-4356	121	8	order	order	NOUN
ejpam-4356	121	9	n.	n.	NOUN
ejpam-4356	121	10	then	then	ADV
ejpam-4356	121	11	γwcg(g	γwcg(g	PROPN
ejpam-4356	121	12	)	)	PUNCT
ejpam-4356	121	13	=	=	SYM
ejpam-4356	122	1	n	n	NOUN
ejpam-4356	122	2	if	if	SCONJ
ejpam-4356	122	3	and	and	CCONJ
ejpam-4356	122	4	only	only	ADV
ejpam-4356	122	5	if	if	SCONJ
ejpam-4356	122	6	g	g	PROPN
ejpam-4356	122	7	=	=	PROPN
ejpam-4356	122	8	kn	kn	PROPN
ejpam-4356	122	9	.	.	PUNCT
ejpam-4356	122	10	proof	proof	PROPN
ejpam-4356	122	11	.	.	PUNCT
ejpam-4356	123	1	suppose	suppose	VERB
ejpam-4356	123	2	that	that	SCONJ
ejpam-4356	123	3	γwcg(g	γwcg(g	NOUN
ejpam-4356	123	4	)	)	PUNCT
ejpam-4356	123	5	=	=	SYM
ejpam-4356	123	6	n.	n.	NOUN
ejpam-4356	123	7	assume	assume	VERB
ejpam-4356	123	8	that	that	SCONJ
ejpam-4356	123	9	g	g	PROPN
ejpam-4356	123	10	̸=	̸=	PROPN
ejpam-4356	123	11	kn	kn	PROPN
ejpam-4356	123	12	.	.	PUNCT
ejpam-4356	124	1	then	then	ADV
ejpam-4356	124	2	there	there	PRON
ejpam-4356	124	3	exist	exist	VERB
ejpam-4356	124	4	x	x	NOUN
ejpam-4356	124	5	,	,	PUNCT
ejpam-4356	124	6	y	y	PROPN
ejpam-4356	124	7	∈	∈	PROPN
ejpam-4356	124	8	v	v	ADP
ejpam-4356	124	9	(	(	PUNCT
ejpam-4356	124	10	g	g	NOUN
ejpam-4356	124	11	)	)	PUNCT
ejpam-4356	124	12	such	such	ADJ
ejpam-4356	124	13	that	that	DET
ejpam-4356	124	14	dg(x	dg(x	PROPN
ejpam-4356	124	15	,	,	PUNCT
ejpam-4356	124	16	y	y	NOUN
ejpam-4356	124	17	)	)	PUNCT
ejpam-4356	124	18	=	=	SYM
ejpam-4356	125	1	2	2	X
ejpam-4356	125	2	.	.	PUNCT
ejpam-4356	125	3	now	now	ADV
ejpam-4356	125	4	,	,	PUNCT
ejpam-4356	125	5	construct	construct	VERB
ejpam-4356	125	6	a	a	DET
ejpam-4356	125	7	set	set	NOUN
ejpam-4356	125	8	s	s	PART
ejpam-4356	125	9	=	=	PUNCT
ejpam-4356	125	10	{	{	PUNCT
ejpam-4356	125	11	v1	v1	PROPN
ejpam-4356	125	12	,	,	PUNCT
ejpam-4356	125	13	v2	v2	PROPN
ejpam-4356	125	14	,	,	PUNCT
ejpam-4356	125	15	...	...	PUNCT
ejpam-4356	125	16	,	,	PUNCT
ejpam-4356	125	17	vk	vk	ADP
ejpam-4356	125	18	}	}	PUNCT
ejpam-4356	125	19	where	where	SCONJ
ejpam-4356	125	20	s	s	VERB
ejpam-4356	125	21	∈	∈	PROPN
ejpam-4356	125	22	c∗(g	c∗(g	PROPN
ejpam-4356	125	23	)	)	PUNCT
ejpam-4356	125	24	and	and	CCONJ
ejpam-4356	125	25	x	x	X
ejpam-4356	125	26	=	=	SYM
ejpam-4356	125	27	v1	v1	PROPN
ejpam-4356	125	28	and	and	CCONJ
ejpam-4356	125	29	y	y	NOUN
ejpam-4356	125	30	=	=	SYM
ejpam-4356	125	31	v2	v2	PROPN
ejpam-4356	125	32	.	.	PUNCT
ejpam-4356	126	1	since	since	SCONJ
ejpam-4356	126	2	ig[v1	ig[v1	PROPN
ejpam-4356	126	3	,	,	PUNCT
ejpam-4356	126	4	v2	v2	PROPN
ejpam-4356	126	5	]	]	PUNCT
ejpam-4356	126	6	̸=	̸=	PROPN
ejpam-4356	126	7	{	{	PUNCT
ejpam-4356	126	8	v1	v1	PROPN
ejpam-4356	126	9	,	,	PUNCT
ejpam-4356	126	10	v2	v2	NOUN
ejpam-4356	126	11	}	}	PUNCT
ejpam-4356	126	12	and	and	CCONJ
ejpam-4356	126	13	vi	vi	NOUN
ejpam-4356	126	14	∈	∈	NOUN
ejpam-4356	126	15	ig[si−1	ig[si−1	NOUN
ejpam-4356	126	16	]	]	PUNCT
ejpam-4356	126	17	for	for	ADP
ejpam-4356	126	18	all	all	DET
ejpam-4356	126	19	i	i	PRON
ejpam-4356	126	20	=	=	NOUN
ejpam-4356	126	21	3	3	NUM
ejpam-4356	126	22	,	,	PUNCT
ejpam-4356	126	23	2	2	NUM
ejpam-4356	126	24	,	,	PUNCT
ejpam-4356	126	25	4	4	NUM
ejpam-4356	126	26	,	,	PUNCT
ejpam-4356	126	27	...	...	PUNCT
ejpam-4356	126	28	,	,	PUNCT
ejpam-4356	126	29	k	k	X
ejpam-4356	126	30	,	,	PUNCT
ejpam-4356	126	31	we	we	PRON
ejpam-4356	126	32	have	have	VERB
ejpam-4356	126	33	ig[s	ig[	NOUN
ejpam-4356	126	34	]	]	PUNCT
ejpam-4356	126	35	̸=	̸=	PROPN
ejpam-4356	126	36	s.	s.	PROPN
ejpam-4356	126	37	in	in	ADP
ejpam-4356	126	38	fact	fact	NOUN
ejpam-4356	126	39	,	,	PUNCT
ejpam-4356	126	40	ig[s	ig[s	PROPN
ejpam-4356	126	41	]	]	X
ejpam-4356	126	42	=	=	SYM
ejpam-4356	126	43	v	v	X
ejpam-4356	126	44	(	(	PUNCT
ejpam-4356	126	45	g	g	NOUN
ejpam-4356	126	46	)	)	PUNCT
ejpam-4356	126	47	.	.	PUNCT
ejpam-4356	127	1	thus	thus	ADV
ejpam-4356	127	2	,	,	PUNCT
ejpam-4356	127	3	k	k	PROPN
ejpam-4356	127	4	<	<	X
ejpam-4356	127	5	n.	n.	PROPN
ejpam-4356	127	6	moreover	moreover	ADV
ejpam-4356	127	7	,	,	PUNCT
ejpam-4356	127	8	since	since	SCONJ
ejpam-4356	127	9	ng[s	ng[	NOUN
ejpam-4356	127	10	]	]	PUNCT
ejpam-4356	127	11	=	=	SYM
ejpam-4356	127	12	v	v	X
ejpam-4356	127	13	(	(	PUNCT
ejpam-4356	127	14	g	g	NOUN
ejpam-4356	127	15	)	)	PUNCT
ejpam-4356	127	16	and	and	CCONJ
ejpam-4356	127	17	ew(s	ew(s	NUM
ejpam-4356	127	18	)	)	PUNCT
ejpam-4356	127	19	of	of	ADP
ejpam-4356	127	20	g	g	PROPN
ejpam-4356	127	21	is	be	AUX
ejpam-4356	127	22	induces	induce	VERB
ejpam-4356	127	23	a	a	DET
ejpam-4356	127	24	connected	connected	ADJ
ejpam-4356	127	25	subgraph	subgraph	NOUN
ejpam-4356	127	26	,	,	PUNCT
ejpam-4356	127	27	it	it	PRON
ejpam-4356	127	28	follows	follow	VERB
ejpam-4356	127	29	that	that	SCONJ
ejpam-4356	127	30	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	127	31	is	be	AUX
ejpam-4356	127	32	also	also	ADV
ejpam-4356	127	33	connected	connect	VERB
ejpam-4356	127	34	,	,	PUNCT
ejpam-4356	127	35	furthermore	furthermore	ADV
ejpam-4356	127	36	,	,	PUNCT
ejpam-4356	127	37	since	since	SCONJ
ejpam-4356	127	38	ig[s	ig[s	PROPN
ejpam-4356	127	39	]	]	X
ejpam-4356	127	40	=	=	SYM
ejpam-4356	127	41	v	v	X
ejpam-4356	127	42	(	(	PUNCT
ejpam-4356	127	43	g	g	NOUN
ejpam-4356	127	44	)	)	PUNCT
ejpam-4356	127	45	,	,	PUNCT
ejpam-4356	127	46	it	it	PRON
ejpam-4356	127	47	follows	follow	VERB
ejpam-4356	127	48	that	that	SCONJ
ejpam-4356	127	49	s	s	VERB
ejpam-4356	127	50	is	be	AUX
ejpam-4356	127	51	a	a	DET
ejpam-4356	127	52	dominating	dominating	NOUN
ejpam-4356	127	53	set	set	NOUN
ejpam-4356	127	54	of	of	ADP
ejpam-4356	127	55	g.	g.	PROPN
ejpam-4356	127	56	therefore	therefore	ADV
ejpam-4356	127	57	.	.	PUNCT
ejpam-4356	128	1	γwcg(g	γwcg(g	NOUN
ejpam-4356	128	2	)	)	PUNCT
ejpam-4356	128	3	=	=	SYM
ejpam-4356	129	1	n	n	PROPN
ejpam-4356	129	2	which	which	PRON
ejpam-4356	129	3	is	be	AUX
ejpam-4356	129	4	a	a	DET
ejpam-4356	129	5	contradiction	contradiction	NOUN
ejpam-4356	129	6	to	to	ADP
ejpam-4356	129	7	the	the	DET
ejpam-4356	129	8	assumption	assumption	NOUN
ejpam-4356	129	9	.	.	PUNCT
ejpam-4356	130	1	consequently	consequently	ADV
ejpam-4356	130	2	,	,	PUNCT
ejpam-4356	130	3	g	g	PROPN
ejpam-4356	130	4	=	=	SYM
ejpam-4356	130	5	kn	kn	PROPN
ejpam-4356	130	6	.	.	PUNCT
ejpam-4356	131	1	the	the	DET
ejpam-4356	131	2	converse	converse	NOUN
ejpam-4356	131	3	follows	follow	VERB
ejpam-4356	131	4	from	from	ADP
ejpam-4356	131	5	corollary	corollary	ADJ
ejpam-4356	131	6	1	1	NUM
ejpam-4356	131	7	(	(	PUNCT
ejpam-4356	131	8	i	i	NOUN
ejpam-4356	131	9	)	)	PUNCT
ejpam-4356	131	10	.	.	PUNCT
ejpam-4356	132	1	lemma	lemma	PROPN
ejpam-4356	132	2	2	2	X
ejpam-4356	132	3	.	.	PUNCT
ejpam-4356	133	1	let	let	VERB
ejpam-4356	133	2	m	m	PRON
ejpam-4356	133	3	,	,	PUNCT
ejpam-4356	133	4	n	n	PRON
ejpam-4356	133	5	≥	≥	NOUN
ejpam-4356	133	6	2	2	NUM
ejpam-4356	133	7	and	and	CCONJ
ejpam-4356	133	8	let	let	VERB
ejpam-4356	133	9	u	u	PRON
ejpam-4356	133	10	and	and	CCONJ
ejpam-4356	133	11	w	w	PROPN
ejpam-4356	133	12	be	be	AUX
ejpam-4356	133	13	the	the	DET
ejpam-4356	133	14	partite	partite	ADJ
ejpam-4356	133	15	sets	set	NOUN
ejpam-4356	133	16	of	of	ADP
ejpam-4356	133	17	km	km	PROPN
ejpam-4356	133	18	,	,	PUNCT
ejpam-4356	133	19	n.	n.	NOUN
ejpam-4356	133	20	a	a	DET
ejpam-4356	133	21	subset	subset	NOUN
ejpam-4356	133	22	s	s	NOUN
ejpam-4356	133	23	of	of	ADP
ejpam-4356	133	24	v	v	NOUN
ejpam-4356	133	25	(	(	PUNCT
ejpam-4356	133	26	km	km	PROPN
ejpam-4356	133	27	,	,	PUNCT
ejpam-4356	133	28	n	n	CCONJ
ejpam-4356	133	29	)	)	PUNCT
ejpam-4356	133	30	is	be	AUX
ejpam-4356	133	31	a	a	DET
ejpam-4356	133	32	weakly	weakly	ADV
ejpam-4356	133	33	connected	connected	ADJ
ejpam-4356	133	34	closed	closed	ADJ
ejpam-4356	133	35	geodetic	geodetic	ADJ
ejpam-4356	133	36	dominating	dominating	NOUN
ejpam-4356	133	37	set	set	NOUN
ejpam-4356	133	38	of	of	ADP
ejpam-4356	133	39	km	km	PROPN
ejpam-4356	133	40	,	,	PUNCT
ejpam-4356	133	41	n	n	CCONJ
ejpam-4356	133	42	if	if	SCONJ
ejpam-4356	133	43	and	and	CCONJ
ejpam-4356	133	44	only	only	ADV
ejpam-4356	133	45	if	if	SCONJ
ejpam-4356	133	46	s	s	NOUN
ejpam-4356	133	47	is	be	AUX
ejpam-4356	133	48	any	any	PRON
ejpam-4356	133	49	of	of	ADP
ejpam-4356	133	50	the	the	DET
ejpam-4356	133	51	following	following	NOUN
ejpam-4356	133	52	:	:	PUNCT
ejpam-4356	133	53	(	(	PUNCT
ejpam-4356	133	54	i	i	NOUN
ejpam-4356	133	55	)	)	PUNCT
ejpam-4356	133	56	s	s	PART
ejpam-4356	134	1	=	=	SYM
ejpam-4356	134	2	u	u	NOUN
ejpam-4356	134	3	;	;	PUNCT
ejpam-4356	134	4	(	(	PUNCT
ejpam-4356	134	5	ii	ii	NOUN
ejpam-4356	134	6	)	)	PUNCT
ejpam-4356	134	7	s	s	PART
ejpam-4356	135	1	=	=	SYM
ejpam-4356	135	2	w	w	PROPN
ejpam-4356	135	3	;	;	PUNCT
ejpam-4356	135	4	(	(	PUNCT
ejpam-4356	135	5	iii	iii	X
ejpam-4356	135	6	)	)	PUNCT
ejpam-4356	135	7	s	s	PART
ejpam-4356	135	8	=	=	SYM
ejpam-4356	135	9	u	u	NOUN
ejpam-4356	135	10	∪	∪	X
ejpam-4356	135	11	{	{	PUNCT
ejpam-4356	135	12	w	w	NOUN
ejpam-4356	135	13	}	}	PUNCT
ejpam-4356	135	14	for	for	ADP
ejpam-4356	135	15	some	some	DET
ejpam-4356	135	16	w	w	PROPN
ejpam-4356	135	17	∈	∈	PROPN
ejpam-4356	135	18	w	w	NOUN
ejpam-4356	135	19	;	;	PUNCT
ejpam-4356	135	20	(	(	PUNCT
ejpam-4356	135	21	iv	iv	X
ejpam-4356	135	22	)	)	PUNCT
ejpam-4356	135	23	s	s	PART
ejpam-4356	136	1	=	=	NOUN
ejpam-4356	136	2	w	w	NOUN
ejpam-4356	136	3	∪	∪	X
ejpam-4356	136	4	{	{	PUNCT
ejpam-4356	136	5	u	u	NOUN
ejpam-4356	136	6	}	}	PUNCT
ejpam-4356	136	7	for	for	ADP
ejpam-4356	136	8	some	some	DET
ejpam-4356	136	9	u	u	NOUN
ejpam-4356	136	10	∈	∈	PROPN
ejpam-4356	136	11	u	u	NOUN
ejpam-4356	136	12	.	.	PUNCT
ejpam-4356	137	1	theorem	theorem	NOUN
ejpam-4356	137	2	3	3	X
ejpam-4356	137	3	.	.	PUNCT
ejpam-4356	138	1	let	let	VERB
ejpam-4356	138	2	m	m	PRON
ejpam-4356	138	3	,	,	PUNCT
ejpam-4356	138	4	n	n	PRON
ejpam-4356	138	5	≥	≥	NOUN
ejpam-4356	138	6	2	2	NUM
ejpam-4356	138	7	and	and	CCONJ
ejpam-4356	138	8	let	let	VERB
ejpam-4356	138	9	u	u	PRON
ejpam-4356	138	10	and	and	CCONJ
ejpam-4356	138	11	w	w	PROPN
ejpam-4356	138	12	be	be	AUX
ejpam-4356	138	13	the	the	DET
ejpam-4356	138	14	partite	partite	ADJ
ejpam-4356	138	15	sets	set	NOUN
ejpam-4356	138	16	of	of	ADP
ejpam-4356	138	17	km	km	PROPN
ejpam-4356	138	18	,	,	PUNCT
ejpam-4356	138	19	n.	n.	PROPN
ejpam-4356	138	20	then	then	ADV
ejpam-4356	138	21	γwcg(km	γwcg(km	PROPN
ejpam-4356	138	22	,	,	PUNCT
ejpam-4356	138	23	n	n	CCONJ
ejpam-4356	138	24	)	)	PUNCT
ejpam-4356	139	1	=	=	NOUN
ejpam-4356	139	2	min{|s|	min{|s|	NOUN
ejpam-4356	139	3	:	:	PUNCT
ejpam-4356	139	4	s	s	X
ejpam-4356	139	5	∈	∈	PROPN
ejpam-4356	139	6	w(km	w(km	PROPN
ejpam-4356	139	7	,	,	PUNCT
ejpam-4356	139	8	n	n	CCONJ
ejpam-4356	139	9	)	)	PUNCT
ejpam-4356	139	10	}	}	PUNCT
ejpam-4356	139	11	.	.	PUNCT
ejpam-4356	140	1	proof	proof	NOUN
ejpam-4356	140	2	.	.	PUNCT
ejpam-4356	141	1	let	let	VERB
ejpam-4356	141	2	m	m	PRON
ejpam-4356	141	3	,	,	PUNCT
ejpam-4356	141	4	n	n	PRON
ejpam-4356	141	5	≥	≥	NOUN
ejpam-4356	141	6	2	2	NUM
ejpam-4356	141	7	and	and	CCONJ
ejpam-4356	141	8	let	let	VERB
ejpam-4356	141	9	u	u	PRON
ejpam-4356	141	10	and	and	CCONJ
ejpam-4356	141	11	w	w	PROPN
ejpam-4356	141	12	be	be	AUX
ejpam-4356	141	13	the	the	DET
ejpam-4356	141	14	partite	partite	ADJ
ejpam-4356	141	15	sets	set	NOUN
ejpam-4356	141	16	of	of	ADP
ejpam-4356	141	17	km	km	PROPN
ejpam-4356	141	18	,	,	PUNCT
ejpam-4356	141	19	n.	n.	NOUN
ejpam-4356	141	20	by	by	ADP
ejpam-4356	141	21	lemma	lemma	PROPN
ejpam-4356	141	22	2	2	NUM
ejpam-4356	141	23	,	,	PUNCT
ejpam-4356	141	24	γwcg(km	γwcg(km	NOUN
ejpam-4356	141	25	,	,	PUNCT
ejpam-4356	141	26	n	n	CCONJ
ejpam-4356	141	27	)	)	PUNCT
ejpam-4356	141	28	=	=	SYM
ejpam-4356	141	29	min{|u	min{|u	PROPN
ejpam-4356	141	30	|	|	ADV
ejpam-4356	141	31	,	,	PUNCT
ejpam-4356	141	32	|w	|w	ADJ
ejpam-4356	141	33	|	|	NOUN
ejpam-4356	141	34	,	,	PUNCT
ejpam-4356	141	35	|u	|u	ADJ
ejpam-4356	141	36	∪	∪	X
ejpam-4356	141	37	{	{	PUNCT
ejpam-4356	141	38	w}|	w}|	NOUN
ejpam-4356	141	39	for	for	ADP
ejpam-4356	141	40	some	some	DET
ejpam-4356	141	41	w	w	NOUN
ejpam-4356	141	42	∈	∈	PROPN
ejpam-4356	141	43	w	w	NOUN
ejpam-4356	141	44	and	and	CCONJ
ejpam-4356	141	45	|w	|w	ADJ
ejpam-4356	141	46	∪	∪	NOUN
ejpam-4356	141	47	{	{	PUNCT
ejpam-4356	141	48	u}|	u}|	NOUN
ejpam-4356	141	49	for	for	ADP
ejpam-4356	141	50	some	some	DET
ejpam-4356	141	51	u	u	NOUN
ejpam-4356	141	52	∈	∈	PROPN
ejpam-4356	141	53	u	u	NOUN
ejpam-4356	141	54	}	}	PUNCT
ejpam-4356	141	55	.	.	PUNCT
ejpam-4356	142	1	corollary	corollary	ADJ
ejpam-4356	142	2	2	2	NUM
ejpam-4356	142	3	.	.	PUNCT
ejpam-4356	143	1	let	let	VERB
ejpam-4356	143	2	m	m	PRON
ejpam-4356	143	3	,	,	PUNCT
ejpam-4356	143	4	n	n	PRON
ejpam-4356	143	5	≥	≥	NOUN
ejpam-4356	143	6	2	2	NUM
ejpam-4356	143	7	and	and	CCONJ
ejpam-4356	143	8	let	let	VERB
ejpam-4356	143	9	u	u	PRON
ejpam-4356	143	10	and	and	CCONJ
ejpam-4356	143	11	w	w	PROPN
ejpam-4356	143	12	be	be	AUX
ejpam-4356	143	13	the	the	DET
ejpam-4356	143	14	partite	partite	ADJ
ejpam-4356	143	15	sets	set	NOUN
ejpam-4356	143	16	of	of	ADP
ejpam-4356	143	17	km	km	PROPN
ejpam-4356	143	18	,	,	PUNCT
ejpam-4356	143	19	n.	n.	PROPN
ejpam-4356	143	20	then	then	ADV
ejpam-4356	143	21	γwcg(km	γwcg(km	PROPN
ejpam-4356	143	22	,	,	PUNCT
ejpam-4356	143	23	n	n	CCONJ
ejpam-4356	143	24	)	)	PUNCT
ejpam-4356	143	25	=	=	SYM
ejpam-4356	143	26	min{m	min{m	PROPN
ejpam-4356	143	27	,	,	PUNCT
ejpam-4356	143	28	n	n	CCONJ
ejpam-4356	143	29	}	}	PUNCT
ejpam-4356	143	30	.	.	PUNCT
ejpam-4356	144	1	theorem	theorem	ADJ
ejpam-4356	144	2	4	4	NUM
ejpam-4356	144	3	.	.	PUNCT
ejpam-4356	145	1	let	let	VERB
ejpam-4356	145	2	m	m	PRON
ejpam-4356	145	3	,	,	PUNCT
ejpam-4356	145	4	n	n	PRON
ejpam-4356	145	5	≥	≥	NOUN
ejpam-4356	145	6	2	2	NUM
ejpam-4356	145	7	and	and	CCONJ
ejpam-4356	145	8	s	s	VERB
ejpam-4356	145	9	⊆	⊆	NUM
ejpam-4356	145	10	v	v	NOUN
ejpam-4356	145	11	(	(	PUNCT
ejpam-4356	145	12	km	km	PROPN
ejpam-4356	145	13	,	,	PUNCT
ejpam-4356	145	14	n	n	CCONJ
ejpam-4356	145	15	)	)	PUNCT
ejpam-4356	145	16	.	.	PUNCT
ejpam-4356	146	1	then	then	ADV
ejpam-4356	146	2	s	s	VERB
ejpam-4356	146	3	is	be	AUX
ejpam-4356	146	4	a	a	DET
ejpam-4356	146	5	γwcg	γwcg	NOUN
ejpam-4356	146	6	-	-	PUNCT
ejpam-4356	146	7	set	set	NOUN
ejpam-4356	146	8	of	of	ADP
ejpam-4356	146	9	km	km	PROPN
ejpam-4356	146	10	,	,	PUNCT
ejpam-4356	146	11	n	n	CCONJ
ejpam-4356	146	12	if	if	SCONJ
ejpam-4356	146	13	and	and	CCONJ
ejpam-4356	146	14	only	only	ADV
ejpam-4356	146	15	if	if	SCONJ
ejpam-4356	146	16	s	s	NOUN
ejpam-4356	146	17	is	be	AUX
ejpam-4356	146	18	wcg	wcg	NOUN
ejpam-4356	146	19	-	-	PUNCT
ejpam-4356	146	20	set	set	NOUN
ejpam-4356	146	21	of	of	ADP
ejpam-4356	146	22	km	km	PROPN
ejpam-4356	146	23	,	,	PUNCT
ejpam-4356	146	24	n.	n.	PROPN
ejpam-4356	146	25	theorem	theorem	VERB
ejpam-4356	146	26	5	5	NUM
ejpam-4356	146	27	.	.	X
ejpam-4356	146	28	for	for	ADP
ejpam-4356	146	29	the	the	DET
ejpam-4356	146	30	complete	complete	ADJ
ejpam-4356	146	31	bipartite	bipartite	PROPN
ejpam-4356	146	32	km	km	PROPN
ejpam-4356	146	33	,	,	PUNCT
ejpam-4356	146	34	n	n	CCONJ
ejpam-4356	146	35	,	,	PUNCT
ejpam-4356	146	36	(	(	PUNCT
ejpam-4356	146	37	i	i	NOUN
ejpam-4356	146	38	)	)	PUNCT
ejpam-4356	146	39	γwcg(km	γwcg(km	PROPN
ejpam-4356	146	40	,	,	PUNCT
ejpam-4356	146	41	n	n	CCONJ
ejpam-4356	146	42	)	)	PUNCT
ejpam-4356	146	43	=	=	SYM
ejpam-4356	146	44	2	2	NUM
ejpam-4356	146	45	,	,	PUNCT
ejpam-4356	146	46	for	for	ADP
ejpam-4356	146	47	m	m	PROPN
ejpam-4356	146	48	=	=	SYM
ejpam-4356	146	49	n	n	PROPN
ejpam-4356	146	50	=	=	SYM
ejpam-4356	146	51	1	1	NUM
ejpam-4356	146	52	.	.	PUNCT
ejpam-4356	146	53	(	(	PUNCT
ejpam-4356	146	54	ii	ii	NOUN
ejpam-4356	146	55	)	)	PUNCT
ejpam-4356	146	56	γwcg(km	γwcg(km	PROPN
ejpam-4356	146	57	,	,	PUNCT
ejpam-4356	146	58	n	n	CCONJ
ejpam-4356	146	59	)	)	PUNCT
ejpam-4356	146	60	=	=	SYM
ejpam-4356	146	61	n	n	CCONJ
ejpam-4356	146	62	,	,	PUNCT
ejpam-4356	146	63	for	for	ADP
ejpam-4356	146	64	n	n	DET
ejpam-4356	146	65	≥	≥	NUM
ejpam-4356	146	66	2	2	NUM
ejpam-4356	146	67	,	,	PUNCT
ejpam-4356	146	68	m	m	VERB
ejpam-4356	146	69	=	=	NOUN
ejpam-4356	146	70	1	1	X
ejpam-4356	146	71	.	.	PUNCT
ejpam-4356	146	72	(	(	PUNCT
ejpam-4356	146	73	iii	iii	X
ejpam-4356	146	74	)	)	PUNCT
ejpam-4356	146	75	γwcg(km	γwcg(km	NOUN
ejpam-4356	146	76	,	,	PUNCT
ejpam-4356	146	77	n	n	CCONJ
ejpam-4356	146	78	)	)	PUNCT
ejpam-4356	146	79	=	=	SYM
ejpam-4356	146	80	m	m	PROPN
ejpam-4356	146	81	,	,	PUNCT
ejpam-4356	146	82	for	for	ADP
ejpam-4356	146	83	m	m	PROPN
ejpam-4356	146	84	≥	≥	NOUN
ejpam-4356	146	85	2	2	NUM
ejpam-4356	146	86	,	,	PUNCT
ejpam-4356	146	87	n	n	NOUN
ejpam-4356	146	88	=	=	SYM
ejpam-4356	146	89	1	1	X
ejpam-4356	146	90	.	.	PUNCT
ejpam-4356	146	91	corollary	corollary	ADJ
ejpam-4356	146	92	3	3	NUM
ejpam-4356	146	93	.	.	PUNCT
ejpam-4356	147	1	the	the	DET
ejpam-4356	147	2	star	star	NOUN
ejpam-4356	147	3	k1,n−1	k1,n−1	ADJ
ejpam-4356	147	4	of	of	ADP
ejpam-4356	147	5	order	order	NOUN
ejpam-4356	147	6	n	n	PRON
ejpam-4356	147	7	has	have	AUX
ejpam-4356	147	8	γwcg(k1,n−1	γwcg(k1,n−1	ADJ
ejpam-4356	147	9	)	)	PUNCT
ejpam-4356	148	1	=	=	PUNCT
ejpam-4356	148	2	n−	n−	NOUN
ejpam-4356	148	3	1	1	NUM
ejpam-4356	148	4	.	.	PUNCT
ejpam-4356	149	1	j.	j.	PROPN
ejpam-4356	149	2	hamja	hamja	PROPN
ejpam-4356	149	3	,	,	PUNCT
ejpam-4356	149	4	i.	i.	PROPN
ejpam-4356	149	5	aniversario	aniversario	PROPN
ejpam-4356	149	6	,	,	PUNCT
ejpam-4356	149	7	h.	h.	PROPN
ejpam-4356	149	8	rara	rara	PROPN
ejpam-4356	149	9	/	/	SYM
ejpam-4356	149	10	eur	eur	PROPN
ejpam-4356	149	11	.	.	PUNCT
ejpam-4356	150	1	j.	j.	PROPN
ejpam-4356	150	2	pure	pure	PROPN
ejpam-4356	150	3	appl	appl	PROPN
ejpam-4356	150	4	.	.	PROPN
ejpam-4356	150	5	math	math	PROPN
ejpam-4356	150	6	,	,	PUNCT
ejpam-4356	150	7	15	15	NUM
ejpam-4356	150	8	(	(	PUNCT
ejpam-4356	150	9	2	2	NUM
ejpam-4356	150	10	)	)	PUNCT
ejpam-4356	150	11	(	(	PUNCT
ejpam-4356	150	12	2022	2022	NUM
ejpam-4356	150	13	)	)	PUNCT
ejpam-4356	150	14	,	,	PUNCT
ejpam-4356	150	15	736	736	NUM
ejpam-4356	150	16	-	-	SYM
ejpam-4356	150	17	752	752	NUM
ejpam-4356	150	18	742	742	NUM
ejpam-4356	150	19	theorem	theorem	NOUN
ejpam-4356	150	20	6	6	NUM
ejpam-4356	150	21	.	.	PUNCT
ejpam-4356	150	22	for	for	ADP
ejpam-4356	150	23	a	a	DET
ejpam-4356	150	24	helm	helm	NOUN
ejpam-4356	150	25	hn	hn	NOUN
ejpam-4356	150	26	,	,	PUNCT
ejpam-4356	150	27	γwcg(hn	γwcg(hn	PROPN
ejpam-4356	150	28	)	)	PUNCT
ejpam-4356	150	29	=	=	PUNCT
ejpam-4356	150	30	n+	n+	ADP
ejpam-4356	150	31	1	1	NUM
ejpam-4356	150	32	for	for	ADP
ejpam-4356	150	33	n	n	X
ejpam-4356	150	34	≥	≥	NOUN
ejpam-4356	150	35	3	3	NUM
ejpam-4356	150	36	.	.	PUNCT
ejpam-4356	151	1	proof	proof	NOUN
ejpam-4356	151	2	.	.	PUNCT
ejpam-4356	152	1	let	let	VERB
ejpam-4356	152	2	ui	ui	PROPN
ejpam-4356	152	3	be	be	AUX
ejpam-4356	152	4	the	the	DET
ejpam-4356	152	5	vertices	vertex	NOUN
ejpam-4356	152	6	of	of	ADP
ejpam-4356	152	7	a	a	DET
ejpam-4356	152	8	cycle	cycle	NOUN
ejpam-4356	152	9	cn	cn	PROPN
ejpam-4356	152	10	where	where	SCONJ
ejpam-4356	152	11	n	n	NOUN
ejpam-4356	152	12	=	=	SYM
ejpam-4356	152	13	1	1	NUM
ejpam-4356	152	14	,	,	PUNCT
ejpam-4356	152	15	2	2	NUM
ejpam-4356	152	16	,	,	PUNCT
ejpam-4356	152	17	3	3	NUM
ejpam-4356	152	18	,	,	PUNCT
ejpam-4356	152	19	...	...	PUNCT
ejpam-4356	152	20	,	,	PUNCT
ejpam-4356	152	21	n	n	CCONJ
ejpam-4356	152	22	,	,	PUNCT
ejpam-4356	152	23	v	v	X
ejpam-4356	152	24	′	′	NOUN
ejpam-4356	152	25	be	be	AUX
ejpam-4356	152	26	the	the	DET
ejpam-4356	152	27	center	center	ADJ
ejpam-4356	152	28	vertex	vertex	NOUN
ejpam-4356	152	29	of	of	ADP
ejpam-4356	152	30	hn	hn	PROPN
ejpam-4356	152	31	and	and	CCONJ
ejpam-4356	152	32	vi	vi	PROPN
ejpam-4356	152	33	be	be	AUX
ejpam-4356	152	34	the	the	DET
ejpam-4356	152	35	pendant	pendant	ADJ
ejpam-4356	152	36	vertices	vertex	NOUN
ejpam-4356	152	37	of	of	ADP
ejpam-4356	152	38	hn	hn	PRON
ejpam-4356	152	39	where	where	SCONJ
ejpam-4356	152	40	n	n	NOUN
ejpam-4356	152	41	=	=	SYM
ejpam-4356	152	42	1	1	NUM
ejpam-4356	152	43	,	,	PUNCT
ejpam-4356	152	44	2	2	NUM
ejpam-4356	152	45	,	,	PUNCT
ejpam-4356	152	46	3	3	NUM
ejpam-4356	152	47	,	,	PUNCT
ejpam-4356	152	48	...	...	PUNCT
ejpam-4356	152	49	,	,	PUNCT
ejpam-4356	152	50	n.	n.	PROPN
ejpam-4356	152	51	then	then	ADV
ejpam-4356	152	52	every	every	DET
ejpam-4356	152	53	vi	vi	NOUN
ejpam-4356	152	54	is	be	AUX
ejpam-4356	152	55	connected	connect	VERB
ejpam-4356	152	56	to	to	ADP
ejpam-4356	152	57	each	each	DET
ejpam-4356	152	58	vertex	vertex	NOUN
ejpam-4356	153	1	ui	ui	PROPN
ejpam-4356	153	2	.	.	PUNCT
ejpam-4356	154	1	let	let	VERB
ejpam-4356	154	2	s1	s1	PROPN
ejpam-4356	154	3	=	=	SYM
ejpam-4356	154	4	{	{	PUNCT
ejpam-4356	154	5	v1	v1	NOUN
ejpam-4356	154	6	}	}	PUNCT
ejpam-4356	154	7	and	and	CCONJ
ejpam-4356	154	8	s2	s2	VERB
ejpam-4356	154	9	=	=	SYM
ejpam-4356	154	10	{	{	PUNCT
ejpam-4356	154	11	v1	v1	PROPN
ejpam-4356	154	12	,	,	PUNCT
ejpam-4356	154	13	v3	v3	PROPN
ejpam-4356	154	14	}	}	PUNCT
ejpam-4356	154	15	where	where	SCONJ
ejpam-4356	154	16	ihn	ihn	PROPN
ejpam-4356	154	17	[	[	X
ejpam-4356	154	18	s2	s2	X
ejpam-4356	154	19	]	]	X
ejpam-4356	154	20	=	=	SYM
ejpam-4356	154	21	{	{	PUNCT
ejpam-4356	154	22	v1	v1	PROPN
ejpam-4356	154	23	,	,	PUNCT
ejpam-4356	154	24	v2	v2	PROPN
ejpam-4356	154	25	,	,	PUNCT
ejpam-4356	154	26	v3	v3	PROPN
ejpam-4356	154	27	}	}	PUNCT
ejpam-4356	154	28	.	.	PUNCT
ejpam-4356	155	1	continuing	continue	VERB
ejpam-4356	155	2	this	this	DET
ejpam-4356	155	3	process	process	NOUN
ejpam-4356	155	4	we	we	PRON
ejpam-4356	155	5	obtain	obtain	VERB
ejpam-4356	155	6	a	a	DET
ejpam-4356	155	7	set	set	ADJ
ejpam-4356	155	8	sn	sn	PROPN
ejpam-4356	155	9	∈	∈	PROPN
ejpam-4356	155	10	c∗(g	c∗(g	PROPN
ejpam-4356	155	11	)	)	PUNCT
ejpam-4356	155	12	where	where	SCONJ
ejpam-4356	155	13	ihn	ihn	PROPN
ejpam-4356	155	14	[	[	X
ejpam-4356	155	15	sn	sn	X
ejpam-4356	155	16	]	]	X
ejpam-4356	155	17	=	=	SYM
ejpam-4356	155	18	v	v	X
ejpam-4356	155	19	(	(	PUNCT
ejpam-4356	155	20	hn	hn	PROPN
ejpam-4356	155	21	)	)	PUNCT
ejpam-4356	155	22	.	.	PUNCT
ejpam-4356	156	1	therefore	therefore	ADV
ejpam-4356	156	2	sn	sn	PROPN
ejpam-4356	156	3	is	be	AUX
ejpam-4356	156	4	a	a	DET
ejpam-4356	156	5	closed	closed	ADJ
ejpam-4356	156	6	geodetic	geodetic	ADJ
ejpam-4356	156	7	cover	cover	NOUN
ejpam-4356	156	8	of	of	ADP
ejpam-4356	156	9	hn	hn	PROPN
ejpam-4356	156	10	.	.	PUNCT
ejpam-4356	157	1	however	however	ADV
ejpam-4356	157	2	,	,	PUNCT
ejpam-4356	157	3	sn	sn	PROPN
ejpam-4356	157	4	is	be	AUX
ejpam-4356	157	5	not	not	PART
ejpam-4356	157	6	a	a	DET
ejpam-4356	157	7	dominating	dominating	NOUN
ejpam-4356	157	8	set	set	NOUN
ejpam-4356	157	9	of	of	ADP
ejpam-4356	157	10	hn	hn	PROPN
ejpam-4356	157	11	since	since	SCONJ
ejpam-4356	157	12	sn	sn	PROPN
ejpam-4356	157	13	does	do	AUX
ejpam-4356	157	14	not	not	PART
ejpam-4356	157	15	dominate	dominate	VERB
ejpam-4356	157	16	the	the	DET
ejpam-4356	157	17	vertex	vertex	NOUN
ejpam-4356	157	18	v	v	NOUN
ejpam-4356	157	19	′	′	NOUN
ejpam-4356	157	20	.	.	PUNCT
ejpam-4356	158	1	now	now	ADV
ejpam-4356	158	2	,	,	PUNCT
ejpam-4356	158	3	we	we	PRON
ejpam-4356	158	4	need	need	VERB
ejpam-4356	158	5	to	to	PART
ejpam-4356	158	6	pick	pick	VERB
ejpam-4356	158	7	v	v	NUM
ejpam-4356	158	8	′	′	NUM
ejpam-4356	158	9	/∈	/∈	PUNCT
ejpam-4356	159	1	sn	sn	PROPN
ejpam-4356	159	2	for	for	ADP
ejpam-4356	159	3	sn+1	sn+1	NOUN
ejpam-4356	159	4	=	=	SYM
ejpam-4356	159	5	{	{	PUNCT
ejpam-4356	159	6	v′	v′	PROPN
ejpam-4356	159	7	,	,	PUNCT
ejpam-4356	159	8	v1	v1	PROPN
ejpam-4356	159	9	,	,	PUNCT
ejpam-4356	159	10	...	...	PUNCT
ejpam-4356	159	11	,	,	PUNCT
ejpam-4356	159	12	vn	vn	PROPN
ejpam-4356	159	13	}	}	PUNCT
ejpam-4356	159	14	.	.	PUNCT
ejpam-4356	160	1	let	let	VERB
ejpam-4356	160	2	s1	s1	PROPN
ejpam-4356	160	3	=	=	PUNCT
ejpam-4356	160	4	{	{	PUNCT
ejpam-4356	160	5	v′	v′	PROPN
ejpam-4356	160	6	}	}	PUNCT
ejpam-4356	160	7	,	,	PUNCT
ejpam-4356	160	8	s2	s2	NOUN
ejpam-4356	160	9	=	=	SYM
ejpam-4356	160	10	{	{	PUNCT
ejpam-4356	160	11	v′	v′	PROPN
ejpam-4356	160	12	,	,	PUNCT
ejpam-4356	160	13	v2	v2	PROPN
ejpam-4356	160	14	}	}	PUNCT
ejpam-4356	160	15	where	where	SCONJ
ejpam-4356	160	16	ihn	ihn	PROPN
ejpam-4356	160	17	[	[	X
ejpam-4356	160	18	s2	s2	X
ejpam-4356	160	19	]	]	X
ejpam-4356	160	20	=	=	SYM
ejpam-4356	160	21	{	{	PUNCT
ejpam-4356	160	22	v′	v′	PROPN
ejpam-4356	160	23	,	,	PUNCT
ejpam-4356	160	24	v1	v1	NOUN
ejpam-4356	160	25	,	,	PUNCT
ejpam-4356	160	26	v2	v2	PROPN
ejpam-4356	160	27	}	}	PUNCT
ejpam-4356	160	28	.	.	PUNCT
ejpam-4356	161	1	continuing	continue	VERB
ejpam-4356	161	2	this	this	DET
ejpam-4356	161	3	process	process	NOUN
ejpam-4356	161	4	we	we	PRON
ejpam-4356	161	5	obtain	obtain	VERB
ejpam-4356	161	6	a	a	DET
ejpam-4356	161	7	set	set	VERB
ejpam-4356	161	8	sn+1	sn+1	NOUN
ejpam-4356	161	9	∈	∈	PROPN
ejpam-4356	161	10	c∗(g	c∗(g	PROPN
ejpam-4356	161	11	)	)	PUNCT
ejpam-4356	161	12	where	where	SCONJ
ejpam-4356	161	13	ih2	ih2	NOUN
ejpam-4356	161	14	[	[	X
ejpam-4356	161	15	sn+1	sn+1	X
ejpam-4356	161	16	]	]	X
ejpam-4356	161	17	=	=	SYM
ejpam-4356	161	18	v	v	X
ejpam-4356	161	19	(	(	PUNCT
ejpam-4356	161	20	hn	hn	PROPN
ejpam-4356	161	21	)	)	PUNCT
ejpam-4356	161	22	.	.	PUNCT
ejpam-4356	162	1	thus	thus	ADV
ejpam-4356	162	2	,	,	PUNCT
ejpam-4356	162	3	sn+1	sn+1	X
ejpam-4356	162	4	is	be	AUX
ejpam-4356	162	5	both	both	PRON
ejpam-4356	162	6	closed	close	VERB
ejpam-4356	162	7	geodetic	geodetic	ADJ
ejpam-4356	162	8	cover	cover	NOUN
ejpam-4356	162	9	and	and	CCONJ
ejpam-4356	162	10	dominating	dominate	VERB
ejpam-4356	162	11	set	set	NOUN
ejpam-4356	162	12	of	of	ADP
ejpam-4356	162	13	hn	hn	PROPN
ejpam-4356	162	14	.	.	PUNCT
ejpam-4356	163	1	clearly	clearly	ADV
ejpam-4356	163	2	,	,	PUNCT
ejpam-4356	163	3	ng[sn+1	ng[sn+1	ADV
ejpam-4356	163	4	]	]	X
ejpam-4356	163	5	=	=	SYM
ejpam-4356	163	6	v	v	X
ejpam-4356	163	7	(	(	PUNCT
ejpam-4356	163	8	hn	hn	PROPN
ejpam-4356	163	9	)	)	PUNCT
ejpam-4356	163	10	and	and	CCONJ
ejpam-4356	163	11	ew(s	ew(s	CCONJ
ejpam-4356	163	12	)	)	PUNCT
ejpam-4356	163	13	induces	induce	VERB
ejpam-4356	163	14	a	a	DET
ejpam-4356	163	15	connected	connected	ADJ
ejpam-4356	163	16	subgraph	subgraph	NOUN
ejpam-4356	163	17	.	.	PUNCT
ejpam-4356	164	1	it	it	PRON
ejpam-4356	164	2	follows	follow	VERB
ejpam-4356	164	3	that	that	PRON
ejpam-4356	164	4	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	164	5	is	be	AUX
ejpam-4356	164	6	connected	connect	VERB
ejpam-4356	164	7	.	.	PUNCT
ejpam-4356	165	1	therefore	therefore	ADV
ejpam-4356	165	2	,	,	PUNCT
ejpam-4356	165	3	sn+1	sn+1	X
ejpam-4356	165	4	is	be	AUX
ejpam-4356	165	5	weakly	weakly	ADV
ejpam-4356	165	6	connected	connected	ADJ
ejpam-4356	165	7	closed	closed	ADJ
ejpam-4356	165	8	geodetic	geodetic	ADJ
ejpam-4356	165	9	dominating	dominating	NOUN
ejpam-4356	165	10	set	set	NOUN
ejpam-4356	165	11	of	of	ADP
ejpam-4356	165	12	hn	hn	PROPN
ejpam-4356	165	13	.	.	PUNCT
ejpam-4356	166	1	furthermore	furthermore	ADV
ejpam-4356	166	2	,	,	PUNCT
ejpam-4356	166	3	γwcg(hn	γwcg(hn	PROPN
ejpam-4356	166	4	)	)	PUNCT
ejpam-4356	166	5	=	=	SYM
ejpam-4356	166	6	|sn+1|	|sn+1|	NOUN
ejpam-4356	166	7	=	=	PUNCT
ejpam-4356	166	8	n+	n+	PUNCT
ejpam-4356	167	1	1	1	X
ejpam-4356	167	2	.	.	PUNCT
ejpam-4356	168	1	the	the	DET
ejpam-4356	168	2	next	next	ADJ
ejpam-4356	168	3	results	result	NOUN
ejpam-4356	168	4	present	present	VERB
ejpam-4356	168	5	some	some	DET
ejpam-4356	168	6	relationships	relationship	NOUN
ejpam-4356	168	7	between	between	ADP
ejpam-4356	168	8	γwcg(g	γwcg(g	NOUN
ejpam-4356	168	9	)	)	PUNCT
ejpam-4356	168	10	,	,	PUNCT
ejpam-4356	168	11	wcgn(g	wcgn(g	NOUN
ejpam-4356	168	12	)	)	PUNCT
ejpam-4356	168	13	,	,	PUNCT
ejpam-4356	168	14	γw(g	γw(g	NUM
ejpam-4356	168	15	)	)	PUNCT
ejpam-4356	168	16	,	,	PUNCT
ejpam-4356	168	17	γg(g	γg(g	NOUN
ejpam-4356	168	18	)	)	PUNCT
ejpam-4356	168	19	,	,	PUNCT
ejpam-4356	168	20	γgc(g	γgc(g	PROPN
ejpam-4356	168	21	)	)	PUNCT
ejpam-4356	168	22	and	and	CCONJ
ejpam-4356	168	23	γ(g	γ(g	PROPN
ejpam-4356	168	24	)	)	PUNCT
ejpam-4356	168	25	.	.	PUNCT
ejpam-4356	169	1	theorem	theorem	VERB
ejpam-4356	169	2	7	7	NUM
ejpam-4356	169	3	.	.	PUNCT
ejpam-4356	170	1	let	let	VERB
ejpam-4356	170	2	g	g	NOUN
ejpam-4356	170	3	be	be	AUX
ejpam-4356	170	4	any	any	DET
ejpam-4356	170	5	connected	connected	ADJ
ejpam-4356	170	6	graph	graph	NOUN
ejpam-4356	170	7	of	of	ADP
ejpam-4356	170	8	order	order	NOUN
ejpam-4356	170	9	n	n	PRON
ejpam-4356	170	10	≥	≥	NOUN
ejpam-4356	170	11	2	2	NUM
ejpam-4356	170	12	.	.	PUNCT
ejpam-4356	170	13	then	then	ADV
ejpam-4356	170	14	γwcg(g	γwcg(g	NOUN
ejpam-4356	170	15	)	)	PUNCT
ejpam-4356	170	16	=	=	SYM
ejpam-4356	170	17	2	2	NUM
ejpam-4356	171	1	if	if	SCONJ
ejpam-4356	171	2	and	and	CCONJ
ejpam-4356	171	3	only	only	ADV
ejpam-4356	171	4	if	if	SCONJ
ejpam-4356	171	5	wcgn(g	wcgn(g	NUM
ejpam-4356	171	6	)	)	PUNCT
ejpam-4356	171	7	=	=	SYM
ejpam-4356	171	8	2	2	X
ejpam-4356	171	9	.	.	X
ejpam-4356	171	10	theorem	theorem	VERB
ejpam-4356	171	11	8	8	NUM
ejpam-4356	171	12	.	.	PUNCT
ejpam-4356	172	1	if	if	SCONJ
ejpam-4356	172	2	g	g	PROPN
ejpam-4356	172	3	is	be	AUX
ejpam-4356	172	4	a	a	DET
ejpam-4356	172	5	connected	connected	ADJ
ejpam-4356	172	6	graph	graph	NOUN
ejpam-4356	172	7	with	with	ADP
ejpam-4356	172	8	γ(g	γ(g	PROPN
ejpam-4356	172	9	)	)	PUNCT
ejpam-4356	172	10	=	=	SYM
ejpam-4356	172	11	1	1	NUM
ejpam-4356	172	12	,	,	PUNCT
ejpam-4356	172	13	then	then	ADV
ejpam-4356	172	14	γwcg(g	γwcg(g	NOUN
ejpam-4356	172	15	)	)	PUNCT
ejpam-4356	173	1	=	=	SYM
ejpam-4356	173	2	wcgn(g	wcgn(g	NOUN
ejpam-4356	173	3	)	)	PUNCT
ejpam-4356	173	4	.	.	PUNCT
ejpam-4356	174	1	proposition	proposition	NOUN
ejpam-4356	174	2	1	1	NUM
ejpam-4356	174	3	.	.	PUNCT
ejpam-4356	175	1	for	for	ADP
ejpam-4356	175	2	a	a	DET
ejpam-4356	175	3	complete	complete	ADJ
ejpam-4356	175	4	bipartite	bipartite	NOUN
ejpam-4356	175	5	graph	graph	NOUN
ejpam-4356	175	6	km	km	PROPN
ejpam-4356	175	7	,	,	PUNCT
ejpam-4356	175	8	n	n	CCONJ
ejpam-4356	175	9	with	with	ADP
ejpam-4356	175	10	integers	integer	NOUN
ejpam-4356	175	11	m	m	PRON
ejpam-4356	175	12	,	,	PUNCT
ejpam-4356	175	13	n	n	PRON
ejpam-4356	175	14	≥	≥	NOUN
ejpam-4356	175	15	2	2	NUM
ejpam-4356	175	16	,	,	PUNCT
ejpam-4356	175	17	γwcg(km	γwcg(km	NOUN
ejpam-4356	175	18	,	,	PUNCT
ejpam-4356	175	19	n	n	CCONJ
ejpam-4356	175	20	)	)	PUNCT
ejpam-4356	175	21	=	=	SYM
ejpam-4356	175	22	min{m	min{m	PROPN
ejpam-4356	175	23	,	,	PUNCT
ejpam-4356	175	24	n	n	CCONJ
ejpam-4356	175	25	}	}	PUNCT
ejpam-4356	175	26	=	=	SYM
ejpam-4356	175	27	wcgn(km	wcgn(km	ADJ
ejpam-4356	175	28	,	,	PUNCT
ejpam-4356	175	29	n	n	CCONJ
ejpam-4356	175	30	)	)	PUNCT
ejpam-4356	175	31	.	.	PUNCT
ejpam-4356	176	1	theorem	theorem	NOUN
ejpam-4356	176	2	9	9	NUM
ejpam-4356	176	3	.	.	PUNCT
ejpam-4356	177	1	let	let	VERB
ejpam-4356	177	2	g	g	PRON
ejpam-4356	177	3	be	be	AUX
ejpam-4356	177	4	a	a	DET
ejpam-4356	177	5	connected	connected	ADJ
ejpam-4356	177	6	graph	graph	NOUN
ejpam-4356	177	7	of	of	ADP
ejpam-4356	177	8	order	order	NOUN
ejpam-4356	177	9	n.	n.	NOUN
ejpam-4356	177	10	then	then	ADV
ejpam-4356	177	11	,	,	PUNCT
ejpam-4356	177	12	γg(g	γg(g	NOUN
ejpam-4356	177	13	)	)	PUNCT
ejpam-4356	177	14	≤	≤	NUM
ejpam-4356	177	15	γwcg(g	γwcg(g	NOUN
ejpam-4356	177	16	)	)	PUNCT
ejpam-4356	177	17	.	.	PUNCT
ejpam-4356	178	1	proof	proof	NOUN
ejpam-4356	178	2	.	.	PUNCT
ejpam-4356	179	1	let	let	VERB
ejpam-4356	179	2	g	g	PRON
ejpam-4356	179	3	be	be	AUX
ejpam-4356	179	4	a	a	DET
ejpam-4356	179	5	connected	connected	ADJ
ejpam-4356	179	6	graph	graph	NOUN
ejpam-4356	179	7	.	.	PUNCT
ejpam-4356	179	8	suppose	suppose	VERB
ejpam-4356	179	9	that	that	SCONJ
ejpam-4356	179	10	γwcg(g	γwcg(g	NOUN
ejpam-4356	179	11	)	)	PUNCT
ejpam-4356	179	12	<	<	X
ejpam-4356	179	13	γg(g	γg(g	NOUN
ejpam-4356	179	14	)	)	PUNCT
ejpam-4356	179	15	.	.	PUNCT
ejpam-4356	180	1	let	let	VERB
ejpam-4356	180	2	s	s	PRON
ejpam-4356	180	3	=	=	NOUN
ejpam-4356	180	4	{	{	PUNCT
ejpam-4356	180	5	v1	v1	PROPN
ejpam-4356	180	6	,	,	PUNCT
ejpam-4356	180	7	v2	v2	PROPN
ejpam-4356	180	8	,	,	PUNCT
ejpam-4356	180	9	v3	v3	PROPN
ejpam-4356	180	10	,	,	PUNCT
ejpam-4356	180	11	...	...	PUNCT
ejpam-4356	180	12	,	,	PUNCT
ejpam-4356	180	13	vi	vi	X
ejpam-4356	180	14	}	}	PUNCT
ejpam-4356	180	15	is	be	AUX
ejpam-4356	180	16	a	a	DET
ejpam-4356	180	17	γg	γg	ADV
ejpam-4356	180	18	-	-	PUNCT
ejpam-4356	180	19	set	set	NOUN
ejpam-4356	180	20	of	of	ADP
ejpam-4356	180	21	g.	g.	PROPN
ejpam-4356	180	22	then	then	ADV
ejpam-4356	180	23	γwcg(g	γwcg(g	PROPN
ejpam-4356	180	24	)	)	PUNCT
ejpam-4356	180	25	<	<	X
ejpam-4356	180	26	|s|	|s|	PROPN
ejpam-4356	180	27	=	=	SYM
ejpam-4356	180	28	γg(g	γg(g	NOUN
ejpam-4356	180	29	)	)	PUNCT
ejpam-4356	180	30	.	.	PUNCT
ejpam-4356	181	1	hence	hence	ADV
ejpam-4356	181	2	,	,	PUNCT
ejpam-4356	181	3	by	by	ADP
ejpam-4356	181	4	removing	remove	VERB
ejpam-4356	181	5	an	an	DET
ejpam-4356	181	6	element	element	NOUN
ejpam-4356	181	7	in	in	ADP
ejpam-4356	181	8	s	s	PROPN
ejpam-4356	181	9	,	,	PUNCT
ejpam-4356	181	10	say	say	VERB
ejpam-4356	181	11	v1	v1	VERB
ejpam-4356	181	12	we	we	PRON
ejpam-4356	181	13	have	have	VERB
ejpam-4356	181	14	γwcg(g	γwcg(g	NOUN
ejpam-4356	181	15	)	)	PUNCT
ejpam-4356	181	16	≤|s|	≤|s|	PROPN
ejpam-4356	181	17	.	.	PUNCT
ejpam-4356	182	1	if	if	SCONJ
ejpam-4356	182	2	|s	|s	PROPN
ejpam-4356	182	3	\	\	PROPN
ejpam-4356	182	4	{	{	PUNCT
ejpam-4356	182	5	u1}|	u1}|	PROPN
ejpam-4356	182	6	=	=	SYM
ejpam-4356	182	7	γwcg(g	γwcg(g	PROPN
ejpam-4356	182	8	)	)	PUNCT
ejpam-4356	182	9	,	,	PUNCT
ejpam-4356	182	10	then	then	ADV
ejpam-4356	182	11	s	s	VERB
ejpam-4356	182	12	\	\	PROPN
ejpam-4356	182	13	{	{	PUNCT
ejpam-4356	182	14	u1	u1	NOUN
ejpam-4356	182	15	}	}	PUNCT
ejpam-4356	182	16	is	be	AUX
ejpam-4356	182	17	a	a	DET
ejpam-4356	182	18	geodetic	geodetic	ADJ
ejpam-4356	182	19	dominating	dominating	NOUN
ejpam-4356	182	20	set	set	NOUN
ejpam-4356	182	21	of	of	ADP
ejpam-4356	182	22	g	g	PROPN
ejpam-4356	182	23	,	,	PUNCT
ejpam-4356	182	24	a	a	DET
ejpam-4356	182	25	contradiction	contradiction	NOUN
ejpam-4356	182	26	.	.	PUNCT
ejpam-4356	183	1	if	if	SCONJ
ejpam-4356	183	2	γwcg(g	γwcg(g	NOUN
ejpam-4356	183	3	)	)	PUNCT
ejpam-4356	183	4	<	<	X
ejpam-4356	183	5	|s	|s	PROPN
ejpam-4356	183	6	\	\	PROPN
ejpam-4356	183	7	{	{	PUNCT
ejpam-4356	183	8	u1}|	u1}|	PROPN
ejpam-4356	183	9	,	,	PUNCT
ejpam-4356	183	10	then	then	ADV
ejpam-4356	183	11	repeat	repeat	VERB
ejpam-4356	183	12	the	the	DET
ejpam-4356	183	13	process	process	NOUN
ejpam-4356	183	14	above	above	ADV
ejpam-4356	183	15	until	until	SCONJ
ejpam-4356	183	16	we	we	PRON
ejpam-4356	183	17	get	get	VERB
ejpam-4356	183	18	|s	|s	PROPN
ejpam-4356	183	19	\	\	PROPN
ejpam-4356	183	20	{	{	PUNCT
ejpam-4356	183	21	u′is}|	u′is}|	PROPN
ejpam-4356	183	22	=	=	SYM
ejpam-4356	183	23	γwcg(g	γwcg(g	PROPN
ejpam-4356	183	24	)	)	PUNCT
ejpam-4356	183	25	.	.	PUNCT
ejpam-4356	184	1	therefore	therefore	ADV
ejpam-4356	184	2	,	,	PUNCT
ejpam-4356	184	3	s	s	VERB
ejpam-4356	184	4	\	\	X
ejpam-4356	184	5	{	{	PUNCT
ejpam-4356	184	6	u′is	u′is	PROPN
ejpam-4356	184	7	}	}	PUNCT
ejpam-4356	184	8	is	be	AUX
ejpam-4356	184	9	a	a	DET
ejpam-4356	184	10	geodetic	geodetic	ADJ
ejpam-4356	184	11	dominating	dominating	NOUN
ejpam-4356	184	12	set	set	NOUN
ejpam-4356	184	13	of	of	ADP
ejpam-4356	184	14	g	g	NOUN
ejpam-4356	184	15	,	,	PUNCT
ejpam-4356	184	16	which	which	PRON
ejpam-4356	184	17	is	be	AUX
ejpam-4356	184	18	a	a	DET
ejpam-4356	184	19	contradiction	contradiction	NOUN
ejpam-4356	184	20	.	.	PUNCT
ejpam-4356	185	1	consequently	consequently	ADV
ejpam-4356	185	2	,	,	PUNCT
ejpam-4356	185	3	we	we	PRON
ejpam-4356	185	4	have	have	VERB
ejpam-4356	185	5	γg(g	γg(g	NOUN
ejpam-4356	185	6	)	)	PUNCT
ejpam-4356	185	7	≤	≤	NUM
ejpam-4356	185	8	γwcg(g	γwcg(g	NOUN
ejpam-4356	185	9	)	)	PUNCT
ejpam-4356	185	10	in	in	ADP
ejpam-4356	185	11	any	any	DET
ejpam-4356	185	12	case	case	NOUN
ejpam-4356	185	13	.	.	PUNCT
ejpam-4356	186	1	theorem	theorem	ADJ
ejpam-4356	186	2	10	10	NUM
ejpam-4356	186	3	.	.	PUNCT
ejpam-4356	187	1	let	let	VERB
ejpam-4356	187	2	g	g	PRON
ejpam-4356	187	3	be	be	AUX
ejpam-4356	187	4	a	a	DET
ejpam-4356	187	5	complete	complete	ADJ
ejpam-4356	187	6	graph	graph	NOUN
ejpam-4356	187	7	kn	kn	PROPN
ejpam-4356	187	8	for	for	ADP
ejpam-4356	187	9	n	n	X
ejpam-4356	187	10	≥	≥	NUM
ejpam-4356	187	11	2	2	NUM
ejpam-4356	187	12	,	,	PUNCT
ejpam-4356	188	1	if	if	SCONJ
ejpam-4356	188	2	g	g	PROPN
ejpam-4356	188	3	=	=	SYM
ejpam-4356	188	4	kn	kn	PROPN
ejpam-4356	188	5	,	,	PUNCT
ejpam-4356	188	6	then	then	ADV
ejpam-4356	188	7	γg(kn	γg(kn	NOUN
ejpam-4356	188	8	)	)	PUNCT
ejpam-4356	189	1	=	=	SYM
ejpam-4356	189	2	γwcg(kn	γwcg(kn	PROPN
ejpam-4356	189	3	)	)	PUNCT
ejpam-4356	189	4	.	.	PUNCT
ejpam-4356	190	1	corollary	corollary	ADJ
ejpam-4356	190	2	4	4	NUM
ejpam-4356	190	3	.	.	PUNCT
ejpam-4356	191	1	the	the	DET
ejpam-4356	191	2	γwcg(g	γwcg(g	NOUN
ejpam-4356	191	3	)	)	PUNCT
ejpam-4356	191	4	=	=	PUNCT
ejpam-4356	191	5	γw(g	γw(g	PUNCT
ejpam-4356	191	6	)	)	PUNCT
ejpam-4356	191	7	for	for	ADP
ejpam-4356	191	8	some	some	DET
ejpam-4356	191	9	special	special	ADJ
ejpam-4356	191	10	graphs	graph	NOUN
ejpam-4356	191	11	given	give	VERB
ejpam-4356	191	12	as	as	SCONJ
ejpam-4356	191	13	follows	follow	VERB
ejpam-4356	191	14	:	:	PUNCT
ejpam-4356	191	15	(	(	PUNCT
ejpam-4356	191	16	i	i	NOUN
ejpam-4356	191	17	)	)	PUNCT
ejpam-4356	191	18	the	the	DET
ejpam-4356	191	19	complement	complement	NOUN
ejpam-4356	191	20	of	of	ADP
ejpam-4356	191	21	a	a	DET
ejpam-4356	191	22	cycle	cycle	NOUN
ejpam-4356	191	23	cn	cn	NOUN
ejpam-4356	191	24	of	of	ADP
ejpam-4356	191	25	order	order	NOUN
ejpam-4356	191	26	n	n	PRON
ejpam-4356	191	27	has	have	VERB
ejpam-4356	191	28	γwcg(cn	γwcg(cn	NOUN
ejpam-4356	191	29	)	)	PUNCT
ejpam-4356	191	30	=	=	SYM
ejpam-4356	191	31	3	3	NUM
ejpam-4356	191	32	=	=	SYM
ejpam-4356	191	33	γg(cn	γg(cn	NOUN
ejpam-4356	191	34	)	)	PUNCT
ejpam-4356	191	35	for	for	ADP
ejpam-4356	191	36	n	n	X
ejpam-4356	191	37	≥	≥	NUM
ejpam-4356	191	38	5	5	NUM
ejpam-4356	191	39	.	.	PUNCT
ejpam-4356	192	1	j.	j.	PROPN
ejpam-4356	192	2	hamja	hamja	PROPN
ejpam-4356	192	3	,	,	PUNCT
ejpam-4356	192	4	i.	i.	PROPN
ejpam-4356	192	5	aniversario	aniversario	PROPN
ejpam-4356	192	6	,	,	PUNCT
ejpam-4356	192	7	h.	h.	PROPN
ejpam-4356	192	8	rara	rara	PROPN
ejpam-4356	192	9	/	/	SYM
ejpam-4356	192	10	eur	eur	PROPN
ejpam-4356	192	11	.	.	PUNCT
ejpam-4356	193	1	j.	j.	PROPN
ejpam-4356	193	2	pure	pure	PROPN
ejpam-4356	193	3	appl	appl	PROPN
ejpam-4356	193	4	.	.	PROPN
ejpam-4356	193	5	math	math	PROPN
ejpam-4356	193	6	,	,	PUNCT
ejpam-4356	193	7	15	15	NUM
ejpam-4356	193	8	(	(	PUNCT
ejpam-4356	193	9	2	2	NUM
ejpam-4356	193	10	)	)	PUNCT
ejpam-4356	193	11	(	(	PUNCT
ejpam-4356	193	12	2022	2022	NUM
ejpam-4356	193	13	)	)	PUNCT
ejpam-4356	193	14	,	,	PUNCT
ejpam-4356	193	15	736	736	NUM
ejpam-4356	193	16	-	-	SYM
ejpam-4356	193	17	752	752	NUM
ejpam-4356	193	18	743	743	NUM
ejpam-4356	193	19	(	(	PUNCT
ejpam-4356	193	20	ii	ii	NOUN
ejpam-4356	193	21	)	)	PUNCT
ejpam-4356	193	22	the	the	DET
ejpam-4356	193	23	star	star	NOUN
ejpam-4356	193	24	graph	graph	NOUN
ejpam-4356	193	25	k1,n−1	k1,n−1	ADJ
ejpam-4356	193	26	of	of	ADP
ejpam-4356	193	27	order	order	NOUN
ejpam-4356	193	28	n	n	PRON
ejpam-4356	193	29	has	have	AUX
ejpam-4356	193	30	γwcg(k1,n−1	γwcg(k1,n−1	ADJ
ejpam-4356	193	31	)	)	PUNCT
ejpam-4356	194	1	=	=	PUNCT
ejpam-4356	194	2	n−	n−	NOUN
ejpam-4356	194	3	1	1	NUM
ejpam-4356	194	4	=	=	SYM
ejpam-4356	194	5	γg(k1,n−1	γg(k1,n−1	PROPN
ejpam-4356	194	6	)	)	PUNCT
ejpam-4356	194	7	.	.	PUNCT
ejpam-4356	195	1	(	(	PUNCT
ejpam-4356	195	2	iii	iii	X
ejpam-4356	195	3	)	)	PUNCT
ejpam-4356	195	4	the	the	DET
ejpam-4356	195	5	wheel	wheel	NOUN
ejpam-4356	195	6	graph	graph	NOUN
ejpam-4356	196	1	wn	wn	PROPN
ejpam-4356	196	2	has	have	VERB
ejpam-4356	196	3	γwcg(wn	γwcg(wn	NOUN
ejpam-4356	196	4	)	)	PUNCT
ejpam-4356	196	5	=	=	PUNCT
ejpam-4356	197	1	⌈	⌈	SYM
ejpam-4356	197	2	n−1	n−1	PROPN
ejpam-4356	197	3	2	2	NUM
ejpam-4356	197	4	⌉	⌉	NOUN
ejpam-4356	197	5	=	=	SYM
ejpam-4356	197	6	γg(wn	γg(wn	PROPN
ejpam-4356	197	7	)	)	PUNCT
ejpam-4356	197	8	for	for	ADP
ejpam-4356	197	9	n	n	X
ejpam-4356	197	10	≥	≥	NUM
ejpam-4356	197	11	5	5	NUM
ejpam-4356	197	12	.	.	PUNCT
ejpam-4356	197	13	theorem	theorem	VERB
ejpam-4356	197	14	11	11	NUM
ejpam-4356	197	15	.	.	PUNCT
ejpam-4356	198	1	the	the	DET
ejpam-4356	198	2	complete	complete	ADJ
ejpam-4356	198	3	bipartite	bipartite	PROPN
ejpam-4356	198	4	km	km	PROPN
ejpam-4356	198	5	,	,	PUNCT
ejpam-4356	198	6	n	n	PRON
ejpam-4356	198	7	has	have	VERB
ejpam-4356	198	8	γg(km	γg(km	PROPN
ejpam-4356	198	9	,	,	PUNCT
ejpam-4356	198	10	n	n	CCONJ
ejpam-4356	198	11	)	)	PUNCT
ejpam-4356	198	12	≤	≤	NOUN
ejpam-4356	198	13	γwcg(km	γwcg(km	PROPN
ejpam-4356	198	14	,	,	PUNCT
ejpam-4356	198	15	n	n	CCONJ
ejpam-4356	198	16	)	)	PUNCT
ejpam-4356	198	17	,	,	PUNCT
ejpam-4356	198	18	for	for	ADP
ejpam-4356	198	19	m	m	PROPN
ejpam-4356	198	20	,	,	PUNCT
ejpam-4356	198	21	n	n	PRON
ejpam-4356	198	22	≥	≥	NOUN
ejpam-4356	198	23	2	2	NUM
ejpam-4356	198	24	.	.	X
ejpam-4356	198	25	proposition	proposition	NOUN
ejpam-4356	198	26	2	2	NUM
ejpam-4356	198	27	.	.	PUNCT
ejpam-4356	199	1	let	let	VERB
ejpam-4356	199	2	g	g	PRON
ejpam-4356	199	3	be	be	AUX
ejpam-4356	199	4	a	a	DET
ejpam-4356	199	5	complete	complete	ADJ
ejpam-4356	199	6	graph	graph	NOUN
ejpam-4356	199	7	kn	kn	PROPN
ejpam-4356	199	8	for	for	ADP
ejpam-4356	199	9	n	n	PROPN
ejpam-4356	199	10	≥	≥	NUM
ejpam-4356	199	11	2	2	NUM
ejpam-4356	199	12	vertices	vertex	NOUN
ejpam-4356	199	13	.	.	PUNCT
ejpam-4356	200	1	then	then	ADV
ejpam-4356	200	2	γwcg(kn	γwcg(kn	VERB
ejpam-4356	200	3	)	)	PUNCT
ejpam-4356	200	4	=	=	PUNCT
ejpam-4356	200	5	γgc(kn	γgc(kn	NOUN
ejpam-4356	200	6	)	)	PUNCT
ejpam-4356	200	7	.	.	PUNCT
ejpam-4356	201	1	proposition	proposition	NOUN
ejpam-4356	201	2	3	3	X
ejpam-4356	201	3	.	.	PUNCT
ejpam-4356	202	1	let	let	VERB
ejpam-4356	202	2	g	g	PRON
ejpam-4356	202	3	be	be	AUX
ejpam-4356	202	4	a	a	DET
ejpam-4356	202	5	path	path	NOUN
ejpam-4356	202	6	pn	pn	NOUN
ejpam-4356	202	7	,	,	PUNCT
ejpam-4356	202	8	then	then	ADV
ejpam-4356	202	9	γwcg(pn	γwcg(pn	ADJ
ejpam-4356	202	10	)	)	PUNCT
ejpam-4356	202	11	<	<	X
ejpam-4356	202	12	γgc(pn	γgc(pn	NUM
ejpam-4356	202	13	)	)	PUNCT
ejpam-4356	202	14	.	.	PUNCT
ejpam-4356	203	1	theorem	theorem	NOUN
ejpam-4356	203	2	12	12	NUM
ejpam-4356	203	3	.	.	PUNCT
ejpam-4356	204	1	let	let	VERB
ejpam-4356	204	2	g	g	PRON
ejpam-4356	204	3	be	be	AUX
ejpam-4356	204	4	a	a	DET
ejpam-4356	204	5	cycle	cycle	NOUN
ejpam-4356	204	6	cn	cn	PROPN
ejpam-4356	204	7	,	,	PUNCT
ejpam-4356	204	8	then	then	ADV
ejpam-4356	204	9	γwcg(cn	γwcg(cn	NOUN
ejpam-4356	204	10	)	)	PUNCT
ejpam-4356	204	11	≤	≤	NOUN
ejpam-4356	204	12	γgc(cn	γgc(cn	NOUN
ejpam-4356	204	13	)	)	PUNCT
ejpam-4356	204	14	for	for	ADP
ejpam-4356	204	15	n	n	X
ejpam-4356	204	16	≥	≥	NUM
ejpam-4356	204	17	4	4	NUM
ejpam-4356	204	18	.	.	PUNCT
ejpam-4356	204	19	theorem	theorem	VERB
ejpam-4356	204	20	13	13	NUM
ejpam-4356	204	21	.	.	PUNCT
ejpam-4356	205	1	let	let	VERB
ejpam-4356	205	2	g	g	PRON
ejpam-4356	205	3	be	be	AUX
ejpam-4356	205	4	a	a	DET
ejpam-4356	205	5	complete	complete	ADJ
ejpam-4356	205	6	bipartite	bipartite	ADJ
ejpam-4356	205	7	km	km	PROPN
ejpam-4356	205	8	,	,	PUNCT
ejpam-4356	205	9	n	n	NOUN
ejpam-4356	205	10	for	for	ADP
ejpam-4356	205	11	2	2	NUM
ejpam-4356	205	12	≤	≤	NUM
ejpam-4356	205	13	m	m	NOUN
ejpam-4356	205	14	,	,	PUNCT
ejpam-4356	205	15	n	n	ADV
ejpam-4356	205	16	≤	≤	NUM
ejpam-4356	205	17	4	4	NUM
ejpam-4356	205	18	.	.	PUNCT
ejpam-4356	206	1	then	then	ADV
ejpam-4356	206	2	γwcg(km	γwcg(km	PROPN
ejpam-4356	206	3	,	,	PUNCT
ejpam-4356	206	4	n	n	CCONJ
ejpam-4356	206	5	)	)	PUNCT
ejpam-4356	206	6	≤	≤	NOUN
ejpam-4356	206	7	γgc(km	γgc(km	NOUN
ejpam-4356	206	8	,	,	PUNCT
ejpam-4356	206	9	n	n	CCONJ
ejpam-4356	206	10	)	)	PUNCT
ejpam-4356	206	11	.	.	PUNCT
ejpam-4356	207	1	corollary	corollary	ADJ
ejpam-4356	207	2	5	5	NUM
ejpam-4356	207	3	.	.	PUNCT
ejpam-4356	208	1	if	if	SCONJ
ejpam-4356	208	2	g	g	PROPN
ejpam-4356	208	3	is	be	AUX
ejpam-4356	208	4	a	a	DET
ejpam-4356	208	5	complete	complete	ADJ
ejpam-4356	208	6	bipartite	bipartite	PROPN
ejpam-4356	208	7	km	km	PROPN
ejpam-4356	208	8	,	,	PUNCT
ejpam-4356	208	9	n	n	PROPN
ejpam-4356	208	10	for	for	ADP
ejpam-4356	208	11	m	m	PROPN
ejpam-4356	208	12	,	,	PUNCT
ejpam-4356	208	13	n	n	PRON
ejpam-4356	208	14	≥	≥	NOUN
ejpam-4356	208	15	5	5	NUM
ejpam-4356	208	16	.	.	PUNCT
ejpam-4356	208	17	then	then	ADV
ejpam-4356	208	18	γwcg(km	γwcg(km	PROPN
ejpam-4356	208	19	,	,	PUNCT
ejpam-4356	208	20	n	n	CCONJ
ejpam-4356	208	21	)	)	PUNCT
ejpam-4356	208	22	≥	≥	NOUN
ejpam-4356	208	23	γgc(km	γgc(km	NOUN
ejpam-4356	208	24	,	,	PUNCT
ejpam-4356	208	25	n	n	CCONJ
ejpam-4356	208	26	)	)	PUNCT
ejpam-4356	208	27	.	.	PUNCT
ejpam-4356	209	1	the	the	DET
ejpam-4356	209	2	join	join	NOUN
ejpam-4356	209	3	of	of	ADP
ejpam-4356	209	4	two	two	NUM
ejpam-4356	209	5	graphs	graph	NOUN
ejpam-4356	209	6	g	g	NOUN
ejpam-4356	209	7	and	and	CCONJ
ejpam-4356	209	8	h	h	NOUN
ejpam-4356	209	9	,	,	PUNCT
ejpam-4356	209	10	denoted	denote	VERB
ejpam-4356	209	11	by	by	ADP
ejpam-4356	209	12	g	g	PROPN
ejpam-4356	209	13	+	+	PROPN
ejpam-4356	209	14	h	h	NOUN
ejpam-4356	209	15	,	,	PUNCT
ejpam-4356	209	16	is	be	AUX
ejpam-4356	209	17	the	the	DET
ejpam-4356	209	18	graph	graph	NOUN
ejpam-4356	209	19	with	with	ADP
ejpam-4356	209	20	vertex	vertex	NOUN
ejpam-4356	209	21	-	-	PUNCT
ejpam-4356	209	22	set	set	VERB
ejpam-4356	209	23	v	v	NOUN
ejpam-4356	209	24	(	(	PUNCT
ejpam-4356	209	25	g+h	g+h	NOUN
ejpam-4356	209	26	)	)	PUNCT
ejpam-4356	209	27	=	=	SYM
ejpam-4356	209	28	v	v	X
ejpam-4356	209	29	(	(	PUNCT
ejpam-4356	209	30	g	g	NOUN
ejpam-4356	209	31	)	)	PUNCT
ejpam-4356	209	32	•	•	ADP
ejpam-4356	209	33	∪	∪	X
ejpam-4356	209	34	v	v	NOUN
ejpam-4356	209	35	(	(	PUNCT
ejpam-4356	209	36	h	h	NOUN
ejpam-4356	209	37	)	)	PUNCT
ejpam-4356	209	38	and	and	CCONJ
ejpam-4356	209	39	edge	edge	NOUN
ejpam-4356	209	40	-	-	PUNCT
ejpam-4356	209	41	set	set	VERB
ejpam-4356	209	42	e(g+h	e(g+h	NUM
ejpam-4356	209	43	)	)	PUNCT
ejpam-4356	209	44	=	=	SYM
ejpam-4356	209	45	e(g	e(g	PROPN
ejpam-4356	209	46	)	)	PUNCT
ejpam-4356	209	47	•	•	NOUN
ejpam-4356	209	48	∪e(h	∪e(h	NOUN
ejpam-4356	209	49	)	)	PUNCT
ejpam-4356	209	50	•	•	NOUN
ejpam-4356	209	51	∪	∪	X
ejpam-4356	209	52	{	{	PUNCT
ejpam-4356	209	53	uv	uv	NOUN
ejpam-4356	209	54	:	:	PUNCT
ejpam-4356	209	55	u	u	PROPN
ejpam-4356	209	56	∈	∈	PROPN
ejpam-4356	209	57	v	v	ADP
ejpam-4356	209	58	(	(	PUNCT
ejpam-4356	209	59	g	g	NOUN
ejpam-4356	209	60	)	)	PUNCT
ejpam-4356	209	61	,	,	PUNCT
ejpam-4356	209	62	v	v	X
ejpam-4356	209	63	∈	∈	PROPN
ejpam-4356	209	64	v	v	NOUN
ejpam-4356	209	65	(	(	PUNCT
ejpam-4356	209	66	h	h	NOUN
ejpam-4356	209	67	)	)	PUNCT
ejpam-4356	209	68	}	}	PUNCT
ejpam-4356	209	69	,	,	PUNCT
ejpam-4356	209	70	harary	harary	NOUN
ejpam-4356	210	1	[	[	X
ejpam-4356	210	2	2	2	NUM
ejpam-4356	210	3	]	]	PUNCT
ejpam-4356	210	4	.	.	PUNCT
ejpam-4356	211	1	lemma	lemma	PROPN
ejpam-4356	211	2	3	3	NUM
ejpam-4356	211	3	.	.	PROPN
ejpam-4356	211	4	aniversario	aniversario	PROPN
ejpam-4356	211	5	,	,	PUNCT
ejpam-4356	211	6	et.al	et.al	VERB
ejpam-4356	211	7	[	[	X
ejpam-4356	211	8	1	1	NUM
ejpam-4356	211	9	]	]	X
ejpam-4356	211	10	if	if	SCONJ
ejpam-4356	211	11	g	g	PROPN
ejpam-4356	211	12	is	be	AUX
ejpam-4356	211	13	a	a	DET
ejpam-4356	211	14	connected	connected	ADJ
ejpam-4356	211	15	graph	graph	NOUN
ejpam-4356	211	16	and	and	CCONJ
ejpam-4356	211	17	diam(g	diam(g	NOUN
ejpam-4356	211	18	)	)	PUNCT
ejpam-4356	212	1	=	=	SYM
ejpam-4356	212	2	2	2	NUM
ejpam-4356	212	3	,	,	PUNCT
ejpam-4356	212	4	then	then	ADV
ejpam-4356	212	5	every	every	DET
ejpam-4356	212	6	geodetic	geodetic	ADJ
ejpam-4356	212	7	cover	cover	NOUN
ejpam-4356	212	8	of	of	ADP
ejpam-4356	212	9	g	g	PROPN
ejpam-4356	212	10	is	be	AUX
ejpam-4356	212	11	a	a	DET
ejpam-4356	212	12	2	2	NUM
ejpam-4356	212	13	-	-	PUNCT
ejpam-4356	212	14	path	path	NOUN
ejpam-4356	212	15	closure	closure	NOUN
ejpam-4356	212	16	absorbing	absorb	VERB
ejpam-4356	212	17	set	set	VERB
ejpam-4356	212	18	in	in	ADP
ejpam-4356	212	19	g.	g.	PROPN
ejpam-4356	212	20	theorem	theorem	VERB
ejpam-4356	212	21	14	14	NUM
ejpam-4356	212	22	.	.	PUNCT
ejpam-4356	212	23	aniversario	aniversario	PROPN
ejpam-4356	212	24	,	,	PUNCT
ejpam-4356	212	25	et.al	et.al	PROPN
ejpam-4356	212	26	.	.	PUNCT
ejpam-4356	213	1	[	[	X
ejpam-4356	213	2	1	1	X
ejpam-4356	213	3	]	]	PUNCT
ejpam-4356	213	4	let	let	VERB
ejpam-4356	213	5	h	h	PRON
ejpam-4356	213	6	be	be	AUX
ejpam-4356	213	7	a	a	DET
ejpam-4356	213	8	connected	connected	ADJ
ejpam-4356	213	9	noncomplete	noncomplete	ADJ
ejpam-4356	213	10	graph	graph	NOUN
ejpam-4356	213	11	,	,	PUNCT
ejpam-4356	213	12	and	and	CCONJ
ejpam-4356	213	13	let	let	VERB
ejpam-4356	213	14	g	g	NOUN
ejpam-4356	213	15	=	=	PUNCT
ejpam-4356	213	16	h	h	PROPN
ejpam-4356	214	1	+	+	NOUN
ejpam-4356	215	1	kp	kp	INTJ
ejpam-4356	215	2	.	.	PUNCT
ejpam-4356	215	3	let	let	VERB
ejpam-4356	215	4	s	s	PRON
ejpam-4356	215	5	⊆	⊆	NUM
ejpam-4356	215	6	v	v	NOUN
ejpam-4356	215	7	(	(	PUNCT
ejpam-4356	215	8	h	h	NOUN
ejpam-4356	215	9	)	)	PUNCT
ejpam-4356	215	10	.	.	PUNCT
ejpam-4356	216	1	if	if	SCONJ
ejpam-4356	216	2	s	s	NOUN
ejpam-4356	216	3	is	be	AUX
ejpam-4356	216	4	a	a	DET
ejpam-4356	216	5	2	2	NUM
ejpam-4356	216	6	-	-	PUNCT
ejpam-4356	216	7	path	path	NOUN
ejpam-4356	216	8	closure	closure	NOUN
ejpam-4356	216	9	absorbing	absorb	VERB
ejpam-4356	216	10	set	set	NOUN
ejpam-4356	216	11	in	in	ADP
ejpam-4356	216	12	h	h	NOUN
ejpam-4356	216	13	and	and	CCONJ
ejpam-4356	216	14	s	s	PROPN
ejpam-4356	216	15	∈	∈	PROPN
ejpam-4356	216	16	c∗(h	c∗(h	PROPN
ejpam-4356	216	17	)	)	PUNCT
ejpam-4356	216	18	,	,	PUNCT
ejpam-4356	216	19	then	then	ADV
ejpam-4356	216	20	s	s	VERB
ejpam-4356	216	21	∈	∈	PROPN
ejpam-4356	216	22	c∗(g	c∗(g	PROPN
ejpam-4356	216	23	)	)	PUNCT
ejpam-4356	216	24	.	.	PUNCT
ejpam-4356	217	1	theorem	theorem	NOUN
ejpam-4356	217	2	15	15	NUM
ejpam-4356	217	3	.	.	PUNCT
ejpam-4356	218	1	let	let	VERB
ejpam-4356	218	2	h	h	PRON
ejpam-4356	218	3	be	be	AUX
ejpam-4356	218	4	a	a	DET
ejpam-4356	218	5	connected	connected	ADJ
ejpam-4356	218	6	noncomplete	noncomplete	ADJ
ejpam-4356	218	7	graph	graph	NOUN
ejpam-4356	218	8	and	and	CCONJ
ejpam-4356	218	9	let	let	VERB
ejpam-4356	218	10	g	g	NOUN
ejpam-4356	218	11	=	=	PUNCT
ejpam-4356	218	12	h	h	PROPN
ejpam-4356	219	1	+	+	CCONJ
ejpam-4356	220	1	kp	kp	PROPN
ejpam-4356	220	2	.	.	PUNCT
ejpam-4356	221	1	if	if	SCONJ
ejpam-4356	221	2	s	s	PROPN
ejpam-4356	221	3	is	be	AUX
ejpam-4356	221	4	a	a	DET
ejpam-4356	221	5	2	2	NUM
ejpam-4356	221	6	-	-	PUNCT
ejpam-4356	221	7	path	path	NOUN
ejpam-4356	221	8	closure	closure	NOUN
ejpam-4356	221	9	absorbing	absorb	VERB
ejpam-4356	221	10	in	in	ADP
ejpam-4356	221	11	h	h	PROPN
ejpam-4356	221	12	and	and	CCONJ
ejpam-4356	221	13	s	s	PROPN
ejpam-4356	221	14	∈	∈	PROPN
ejpam-4356	221	15	w(h	w(h	PROPN
ejpam-4356	221	16	)	)	PUNCT
ejpam-4356	221	17	,	,	PUNCT
ejpam-4356	221	18	then	then	ADV
ejpam-4356	221	19	s	s	VERB
ejpam-4356	221	20	∈	∈	PROPN
ejpam-4356	221	21	w(g	w(g	PROPN
ejpam-4356	221	22	)	)	PUNCT
ejpam-4356	221	23	.	.	PUNCT
ejpam-4356	222	1	proof	proof	NOUN
ejpam-4356	222	2	.	.	PUNCT
ejpam-4356	223	1	let	let	VERB
ejpam-4356	223	2	h	h	PRON
ejpam-4356	223	3	be	be	AUX
ejpam-4356	223	4	a	a	DET
ejpam-4356	223	5	connected	connected	ADJ
ejpam-4356	223	6	noncomplete	noncomplete	ADJ
ejpam-4356	223	7	graph	graph	NOUN
ejpam-4356	223	8	and	and	CCONJ
ejpam-4356	223	9	let	let	VERB
ejpam-4356	223	10	g	g	NOUN
ejpam-4356	223	11	=	=	PUNCT
ejpam-4356	223	12	h	h	PROPN
ejpam-4356	224	1	+	+	NOUN
ejpam-4356	224	2	kp	kp	AUX
ejpam-4356	224	3	.	.	PUNCT
ejpam-4356	224	4	suppose	suppose	VERB
ejpam-4356	224	5	that	that	SCONJ
ejpam-4356	224	6	s	s	VERB
ejpam-4356	224	7	is	be	AUX
ejpam-4356	224	8	a	a	DET
ejpam-4356	224	9	2	2	NUM
ejpam-4356	224	10	path	path	NOUN
ejpam-4356	224	11	closure	closure	NOUN
ejpam-4356	224	12	absorbing	absorb	VERB
ejpam-4356	224	13	in	in	ADP
ejpam-4356	224	14	h	h	PROPN
ejpam-4356	224	15	and	and	CCONJ
ejpam-4356	224	16	s	s	PROPN
ejpam-4356	224	17	∈	∈	PROPN
ejpam-4356	224	18	w(h	w(h	PROPN
ejpam-4356	224	19	)	)	PUNCT
ejpam-4356	224	20	.	.	PUNCT
ejpam-4356	225	1	then	then	ADV
ejpam-4356	225	2	by	by	ADP
ejpam-4356	225	3	theorem	theorem	NOUN
ejpam-4356	225	4	14	14	NUM
ejpam-4356	225	5	,	,	PUNCT
ejpam-4356	225	6	s	s	PART
ejpam-4356	225	7	∈	∈	PROPN
ejpam-4356	225	8	c∗(g	c∗(g	PROPN
ejpam-4356	225	9	)	)	PUNCT
ejpam-4356	225	10	.	.	PUNCT
ejpam-4356	226	1	to	to	PART
ejpam-4356	226	2	show	show	VERB
ejpam-4356	226	3	that	that	SCONJ
ejpam-4356	226	4	s	s	VERB
ejpam-4356	226	5	is	be	AUX
ejpam-4356	226	6	a	a	DET
ejpam-4356	226	7	weakly	weakly	ADV
ejpam-4356	226	8	connected	connected	ADJ
ejpam-4356	226	9	dominating	dominating	NOUN
ejpam-4356	226	10	set	set	NOUN
ejpam-4356	226	11	of	of	ADP
ejpam-4356	226	12	g.	g.	PROPN
ejpam-4356	226	13	since	since	SCONJ
ejpam-4356	226	14	g	g	PROPN
ejpam-4356	226	15	is	be	AUX
ejpam-4356	226	16	connected	connect	VERB
ejpam-4356	226	17	,	,	PUNCT
ejpam-4356	226	18	for	for	ADP
ejpam-4356	226	19	every	every	DET
ejpam-4356	226	20	u	u	NOUN
ejpam-4356	226	21	,	,	PUNCT
ejpam-4356	226	22	v	v	ADP
ejpam-4356	226	23	∈	∈	PROPN
ejpam-4356	226	24	s	s	NOUN
ejpam-4356	226	25	,	,	PUNCT
ejpam-4356	226	26	dg(u	dg(u	X
ejpam-4356	226	27	,	,	PUNCT
ejpam-4356	226	28	v	v	NOUN
ejpam-4356	226	29	)	)	PUNCT
ejpam-4356	226	30	=	=	SYM
ejpam-4356	226	31	2	2	NUM
ejpam-4356	226	32	and	and	CCONJ
ejpam-4356	226	33	for	for	ADP
ejpam-4356	226	34	all	all	DET
ejpam-4356	226	35	y	y	PROPN
ejpam-4356	226	36	∈	∈	PROPN
ejpam-4356	226	37	v	v	NOUN
ejpam-4356	226	38	(	(	PUNCT
ejpam-4356	226	39	kp	kp	PROPN
ejpam-4356	226	40	)	)	PUNCT
ejpam-4356	226	41	,	,	PUNCT
ejpam-4356	226	42	y	y	PROPN
ejpam-4356	226	43	is	be	AUX
ejpam-4356	226	44	in	in	ADP
ejpam-4356	226	45	u	u	NOUN
ejpam-4356	226	46	-	-	NOUN
ejpam-4356	226	47	v	v	ADJ
ejpam-4356	226	48	geodesic	geodesic	NOUN
ejpam-4356	226	49	.	.	PUNCT
ejpam-4356	227	1	thus	thus	ADV
ejpam-4356	227	2	,	,	PUNCT
ejpam-4356	227	3	v	v	X
ejpam-4356	227	4	(	(	PUNCT
ejpam-4356	227	5	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	227	6	)	)	PUNCT
ejpam-4356	227	7	=	=	SYM
ejpam-4356	227	8	v	v	X
ejpam-4356	227	9	(	(	PUNCT
ejpam-4356	227	10	g	g	NOUN
ejpam-4356	227	11	)	)	PUNCT
ejpam-4356	227	12	.	.	PUNCT
ejpam-4356	228	1	it	it	PRON
ejpam-4356	228	2	remains	remain	VERB
ejpam-4356	228	3	to	to	PART
ejpam-4356	228	4	show	show	VERB
ejpam-4356	228	5	that	that	SCONJ
ejpam-4356	228	6	for	for	ADP
ejpam-4356	228	7	every	every	DET
ejpam-4356	228	8	u	u	NOUN
ejpam-4356	228	9	,	,	PUNCT
ejpam-4356	228	10	v	v	ADP
ejpam-4356	228	11	∈	∈	NOUN
ejpam-4356	228	12	s	s	VERB
ejpam-4356	228	13	there	there	PRON
ejpam-4356	228	14	is	be	VERB
ejpam-4356	228	15	an	an	DET
ejpam-4356	228	16	edge	edge	NOUN
ejpam-4356	228	17	mu	mu	NOUN
ejpam-4356	228	18	or	or	CCONJ
ejpam-4356	228	19	nv	nv	PROPN
ejpam-4356	228	20	with	with	ADP
ejpam-4356	228	21	m	m	PROPN
ejpam-4356	228	22	,	,	PUNCT
ejpam-4356	228	23	n	n	PROPN
ejpam-4356	228	24	∈	∈	NOUN
ejpam-4356	228	25	v	v	NOUN
ejpam-4356	228	26	(	(	PUNCT
ejpam-4356	228	27	g	g	NOUN
ejpam-4356	228	28	)	)	PUNCT
ejpam-4356	228	29	\	\	PUNCT
ejpam-4356	229	1	s.	s.	PROPN
ejpam-4356	229	2	suppose	suppose	VERB
ejpam-4356	229	3	there	there	PRON
ejpam-4356	229	4	exists	exist	VERB
ejpam-4356	229	5	x	x	X
ejpam-4356	229	6	∈	∈	PROPN
ejpam-4356	229	7	s	s	VERB
ejpam-4356	229	8	such	such	ADJ
ejpam-4356	229	9	that	that	SCONJ
ejpam-4356	229	10	mx	mx	PROPN
ejpam-4356	229	11	,	,	PUNCT
ejpam-4356	229	12	nx	nx	PROPN
ejpam-4356	229	13	/∈	/∈	PUNCT
ejpam-4356	229	14	ew(s	ew(s	PROPN
ejpam-4356	229	15	)	)	PUNCT
ejpam-4356	229	16	for	for	ADP
ejpam-4356	229	17	any	any	DET
ejpam-4356	229	18	m	m	NOUN
ejpam-4356	229	19	,	,	PUNCT
ejpam-4356	229	20	n	n	PROPN
ejpam-4356	229	21	∈	∈	PROPN
ejpam-4356	229	22	v	v	NOUN
ejpam-4356	229	23	(	(	PUNCT
ejpam-4356	229	24	g	g	NOUN
ejpam-4356	229	25	)	)	PUNCT
ejpam-4356	229	26	\	\	PUNCT
ejpam-4356	230	1	s.	s.	PROPN
ejpam-4356	230	2	if	if	SCONJ
ejpam-4356	230	3	m	m	PROPN
ejpam-4356	230	4	,	,	PUNCT
ejpam-4356	230	5	n	n	PROPN
ejpam-4356	230	6	∈	∈	PROPN
ejpam-4356	230	7	v	v	NOUN
ejpam-4356	230	8	(	(	PUNCT
ejpam-4356	230	9	kp	kp	PROPN
ejpam-4356	230	10	)	)	PUNCT
ejpam-4356	230	11	,	,	PUNCT
ejpam-4356	230	12	then	then	ADV
ejpam-4356	230	13	mx	mx	PROPN
ejpam-4356	230	14	,	,	PUNCT
ejpam-4356	230	15	nx	nx	PROPN
ejpam-4356	230	16	∈	∈	PROPN
ejpam-4356	230	17	ew(s	ew(s	PRON
ejpam-4356	230	18	)	)	PUNCT
ejpam-4356	230	19	.	.	PUNCT
ejpam-4356	231	1	however	however	ADV
ejpam-4356	231	2	,	,	PUNCT
ejpam-4356	231	3	if	if	SCONJ
ejpam-4356	231	4	m	m	PROPN
ejpam-4356	231	5	,	,	PUNCT
ejpam-4356	231	6	n	n	PROPN
ejpam-4356	231	7	∈	∈	PROPN
ejpam-4356	231	8	v	v	NOUN
ejpam-4356	231	9	(	(	PUNCT
ejpam-4356	231	10	h	h	NOUN
ejpam-4356	231	11	)	)	PUNCT
ejpam-4356	231	12	\	\	PROPN
ejpam-4356	232	1	s	s	X
ejpam-4356	232	2	,	,	PUNCT
ejpam-4356	232	3	then	then	ADV
ejpam-4356	232	4	mx	mx	PROPN
ejpam-4356	232	5	,	,	PUNCT
ejpam-4356	232	6	nx	nx	PROPN
ejpam-4356	232	7	∈	∈	PROPN
ejpam-4356	232	8	ew(s	ew(s	PRON
ejpam-4356	232	9	)	)	PUNCT
ejpam-4356	232	10	.	.	PUNCT
ejpam-4356	233	1	further	far	ADV
ejpam-4356	233	2	,	,	PUNCT
ejpam-4356	233	3	if	if	SCONJ
ejpam-4356	233	4	without	without	ADP
ejpam-4356	233	5	loss	loss	NOUN
ejpam-4356	233	6	of	of	ADP
ejpam-4356	233	7	generality	generality	NOUN
ejpam-4356	233	8	,	,	PUNCT
ejpam-4356	233	9	m	m	PROPN
ejpam-4356	233	10	∈	∈	PROPN
ejpam-4356	233	11	v	v	NOUN
ejpam-4356	233	12	(	(	PUNCT
ejpam-4356	233	13	kp	kp	PROPN
ejpam-4356	233	14	)	)	PUNCT
ejpam-4356	233	15	and	and	CCONJ
ejpam-4356	233	16	n	n	PRON
ejpam-4356	233	17	∈	∈	NOUN
ejpam-4356	233	18	v	v	NOUN
ejpam-4356	233	19	(	(	PUNCT
ejpam-4356	233	20	h	h	NOUN
ejpam-4356	233	21	)	)	PUNCT
ejpam-4356	233	22	\	\	PROPN
ejpam-4356	233	23	s	s	PROPN
ejpam-4356	233	24	,	,	PUNCT
ejpam-4356	233	25	j.	j.	PROPN
ejpam-4356	233	26	hamja	hamja	PROPN
ejpam-4356	233	27	,	,	PUNCT
ejpam-4356	233	28	i.	i.	PROPN
ejpam-4356	233	29	aniversario	aniversario	PROPN
ejpam-4356	233	30	,	,	PUNCT
ejpam-4356	233	31	h.	h.	PROPN
ejpam-4356	233	32	rara	rara	PROPN
ejpam-4356	233	33	/	/	SYM
ejpam-4356	233	34	eur	eur	PROPN
ejpam-4356	233	35	.	.	PUNCT
ejpam-4356	234	1	j.	j.	PROPN
ejpam-4356	234	2	pure	pure	PROPN
ejpam-4356	234	3	appl	appl	PROPN
ejpam-4356	234	4	.	.	PROPN
ejpam-4356	234	5	math	math	PROPN
ejpam-4356	234	6	,	,	PUNCT
ejpam-4356	234	7	15	15	NUM
ejpam-4356	234	8	(	(	PUNCT
ejpam-4356	234	9	2	2	NUM
ejpam-4356	234	10	)	)	PUNCT
ejpam-4356	234	11	(	(	PUNCT
ejpam-4356	234	12	2022	2022	NUM
ejpam-4356	234	13	)	)	PUNCT
ejpam-4356	234	14	,	,	PUNCT
ejpam-4356	234	15	736	736	NUM
ejpam-4356	234	16	-	-	SYM
ejpam-4356	234	17	752	752	NUM
ejpam-4356	234	18	744	744	NUM
ejpam-4356	234	19	then	then	ADV
ejpam-4356	234	20	mx	mx	NOUN
ejpam-4356	234	21	,	,	PUNCT
ejpam-4356	234	22	nx	nx	PROPN
ejpam-4356	234	23	∈	∈	PROPN
ejpam-4356	234	24	ew(s	ew(s	PRON
ejpam-4356	234	25	)	)	PUNCT
ejpam-4356	234	26	.	.	PUNCT
ejpam-4356	235	1	in	in	ADP
ejpam-4356	235	2	either	either	DET
ejpam-4356	235	3	case	case	NOUN
ejpam-4356	235	4	,	,	PUNCT
ejpam-4356	235	5	mx	mx	PROPN
ejpam-4356	235	6	,	,	PUNCT
ejpam-4356	235	7	nx	nx	PROPN
ejpam-4356	235	8	∈	∈	PROPN
ejpam-4356	235	9	ew(s	ew(s	PRON
ejpam-4356	235	10	)	)	PUNCT
ejpam-4356	235	11	.	.	PUNCT
ejpam-4356	236	1	hence	hence	ADV
ejpam-4356	236	2	,	,	PUNCT
ejpam-4356	236	3	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4356	236	4	is	be	AUX
ejpam-4356	236	5	connected	connect	VERB
ejpam-4356	236	6	.	.	PUNCT
ejpam-4356	237	1	it	it	PRON
ejpam-4356	237	2	follows	follow	VERB
ejpam-4356	237	3	that	that	SCONJ
ejpam-4356	237	4	s	s	VERB
ejpam-4356	237	5	is	be	AUX
ejpam-4356	237	6	a	a	DET
ejpam-4356	237	7	weakly	weakly	ADV
ejpam-4356	237	8	connected	connected	ADJ
ejpam-4356	237	9	set	set	NOUN
ejpam-4356	237	10	of	of	ADP
ejpam-4356	237	11	g.	g.	PROPN
ejpam-4356	237	12	since	since	SCONJ
ejpam-4356	237	13	every	every	DET
ejpam-4356	237	14	vertex	vertex	NOUN
ejpam-4356	237	15	in	in	ADP
ejpam-4356	237	16	h	h	NOUN
ejpam-4356	237	17	is	be	AUX
ejpam-4356	237	18	adjacent	adjacent	ADJ
ejpam-4356	237	19	to	to	ADP
ejpam-4356	237	20	every	every	DET
ejpam-4356	237	21	vertex	vertex	NOUN
ejpam-4356	237	22	in	in	ADP
ejpam-4356	237	23	kp	kp	NOUN
ejpam-4356	237	24	,	,	PUNCT
ejpam-4356	237	25	there	there	PRON
ejpam-4356	237	26	exist	exist	VERB
ejpam-4356	237	27	u	u	NOUN
ejpam-4356	237	28	,	,	PUNCT
ejpam-4356	237	29	v	v	PROPN
ejpam-4356	237	30	∈	∈	NOUN
ejpam-4356	237	31	s	s	VERB
ejpam-4356	237	32	such	such	ADJ
ejpam-4356	237	33	that	that	DET
ejpam-4356	237	34	dh(u	dh(u	PROPN
ejpam-4356	237	35	,	,	PUNCT
ejpam-4356	237	36	v	v	NOUN
ejpam-4356	237	37	)	)	PUNCT
ejpam-4356	237	38	=	=	SYM
ejpam-4356	237	39	2	2	NUM
ejpam-4356	237	40	such	such	ADJ
ejpam-4356	237	41	that	that	SCONJ
ejpam-4356	237	42	every	every	DET
ejpam-4356	237	43	vertex	vertex	NOUN
ejpam-4356	237	44	in	in	ADP
ejpam-4356	237	45	kp	kp	PROPN
ejpam-4356	237	46	lies	lie	VERB
ejpam-4356	237	47	in	in	ADP
ejpam-4356	237	48	the	the	DET
ejpam-4356	237	49	u	u	NOUN
ejpam-4356	237	50	−	−	PROPN
ejpam-4356	237	51	v	v	ADP
ejpam-4356	237	52	geodesic	geodesic	NOUN
ejpam-4356	237	53	of	of	ADP
ejpam-4356	237	54	g	g	NOUN
ejpam-4356	237	55	and	and	CCONJ
ejpam-4356	237	56	dg(u	dg(u	X
ejpam-4356	237	57	,	,	PUNCT
ejpam-4356	237	58	v	v	NOUN
ejpam-4356	237	59	)	)	PUNCT
ejpam-4356	237	60	=	=	SYM
ejpam-4356	238	1	2	2	X
ejpam-4356	238	2	.	.	PUNCT
ejpam-4356	238	3	it	it	PRON
ejpam-4356	238	4	follows	follow	VERB
ejpam-4356	238	5	that	that	SCONJ
ejpam-4356	238	6	v	v	X
ejpam-4356	238	7	(	(	PUNCT
ejpam-4356	238	8	kp	kp	PROPN
ejpam-4356	238	9	)	)	PUNCT
ejpam-4356	238	10	⊆	⊆	NUM
ejpam-4356	238	11	n	n	PROPN
ejpam-4356	238	12	[	[	X
ejpam-4356	238	13	s	s	X
ejpam-4356	238	14	]	]	X
ejpam-4356	238	15	.	.	PUNCT
ejpam-4356	239	1	hence	hence	ADV
ejpam-4356	239	2	,	,	PUNCT
ejpam-4356	239	3	v	v	X
ejpam-4356	239	4	(	(	PUNCT
ejpam-4356	239	5	g	g	NOUN
ejpam-4356	239	6	)	)	PUNCT
ejpam-4356	239	7	=	=	NOUN
ejpam-4356	239	8	v	v	X
ejpam-4356	239	9	(	(	PUNCT
ejpam-4356	239	10	h	h	NOUN
ejpam-4356	239	11	)	)	PUNCT
ejpam-4356	239	12	∪	∪	NOUN
ejpam-4356	239	13	v	v	NOUN
ejpam-4356	239	14	(	(	PUNCT
ejpam-4356	239	15	kp	kp	PROPN
ejpam-4356	239	16	)	)	PUNCT
ejpam-4356	239	17	⊆	⊆	NUM
ejpam-4356	239	18	n	n	PROPN
ejpam-4356	239	19	[	[	X
ejpam-4356	239	20	s	s	X
ejpam-4356	239	21	]	]	X
ejpam-4356	239	22	.	.	PUNCT
ejpam-4356	240	1	hence	hence	ADV
ejpam-4356	240	2	,	,	PUNCT
ejpam-4356	240	3	s	s	VERB
ejpam-4356	240	4	is	be	AUX
ejpam-4356	240	5	a	a	DET
ejpam-4356	240	6	dominating	dominating	NOUN
ejpam-4356	240	7	set	set	NOUN
ejpam-4356	240	8	of	of	ADP
ejpam-4356	240	9	g.	g.	PROPN
ejpam-4356	240	10	thus	thus	ADV
ejpam-4356	240	11	,	,	PUNCT
ejpam-4356	240	12	s	s	VERB
ejpam-4356	240	13	is	be	AUX
ejpam-4356	240	14	a	a	DET
ejpam-4356	240	15	γwcg	γwcg	NOUN
ejpam-4356	240	16	set	set	NOUN
ejpam-4356	240	17	,	,	PUNCT
ejpam-4356	240	18	that	that	PRON
ejpam-4356	240	19	is	be	AUX
ejpam-4356	240	20	s	s	PROPN
ejpam-4356	240	21	∈	∈	NOUN
ejpam-4356	240	22	w(g	w(g	PROPN
ejpam-4356	240	23	)	)	PUNCT
ejpam-4356	240	24	.	.	PUNCT
ejpam-4356	241	1	theorem	theorem	VERB
ejpam-4356	241	2	16	16	NUM
ejpam-4356	241	3	.	.	PUNCT
ejpam-4356	242	1	let	let	VERB
ejpam-4356	242	2	h	h	PRON
ejpam-4356	242	3	be	be	AUX
ejpam-4356	242	4	a	a	DET
ejpam-4356	242	5	connected	connected	ADJ
ejpam-4356	242	6	noncomplete	noncomplete	ADJ
ejpam-4356	242	7	graph	graph	NOUN
ejpam-4356	242	8	and	and	CCONJ
ejpam-4356	242	9	g	g	PROPN
ejpam-4356	242	10	=	=	PROPN
ejpam-4356	242	11	h+kp	h+kp	PROPN
ejpam-4356	242	12	.	.	PUNCT
ejpam-4356	243	1	if	if	SCONJ
ejpam-4356	243	2	s	s	PROPN
ejpam-4356	243	3	is	be	AUX
ejpam-4356	243	4	a	a	DET
ejpam-4356	243	5	γwcg	γwcg	NOUN
ejpam-4356	243	6	-	-	PUNCT
ejpam-4356	243	7	set	set	NOUN
ejpam-4356	243	8	of	of	ADP
ejpam-4356	243	9	g	g	NOUN
ejpam-4356	243	10	,	,	PUNCT
ejpam-4356	243	11	then	then	ADV
ejpam-4356	243	12	s	s	VERB
ejpam-4356	243	13	⊆	⊆	NUM
ejpam-4356	243	14	v	v	NOUN
ejpam-4356	243	15	(	(	PUNCT
ejpam-4356	243	16	h	h	NOUN
ejpam-4356	243	17	)	)	PUNCT
ejpam-4356	243	18	and	and	CCONJ
ejpam-4356	243	19	s	s	VERB
ejpam-4356	243	20	is	be	AUX
ejpam-4356	243	21	a	a	DET
ejpam-4356	243	22	2	2	NUM
ejpam-4356	243	23	-	-	PUNCT
ejpam-4356	243	24	path	path	NOUN
ejpam-4356	243	25	closure	closure	NOUN
ejpam-4356	243	26	absorbing	absorb	VERB
ejpam-4356	243	27	set	set	NOUN
ejpam-4356	243	28	in	in	ADP
ejpam-4356	243	29	h.	h.	PROPN
ejpam-4356	243	30	corollary	corollary	PROPN
ejpam-4356	243	31	6	6	NUM
ejpam-4356	243	32	.	.	PUNCT
ejpam-4356	244	1	let	let	VERB
ejpam-4356	244	2	h	h	PRON
ejpam-4356	244	3	be	be	AUX
ejpam-4356	244	4	a	a	DET
ejpam-4356	244	5	connected	connected	ADJ
ejpam-4356	244	6	noncomplete	noncomplete	ADJ
ejpam-4356	244	7	graph	graph	NOUN
ejpam-4356	244	8	and	and	CCONJ
ejpam-4356	244	9	g	g	NOUN
ejpam-4356	244	10	=	=	PROPN
ejpam-4356	244	11	h	h	PROPN
ejpam-4356	245	1	+	+	NOUN
ejpam-4356	245	2	kp	kp	NOUN
ejpam-4356	245	3	,	,	PUNCT
ejpam-4356	245	4	then	then	ADV
ejpam-4356	245	5	γwcg(h	γwcg(h	PROPN
ejpam-4356	245	6	+	+	ADJ
ejpam-4356	245	7	kp	kp	INTJ
ejpam-4356	245	8	)	)	PUNCT
ejpam-4356	245	9	=	=	SYM
ejpam-4356	245	10	min{|s|	min{|s|	NOUN
ejpam-4356	245	11	:	:	PUNCT
ejpam-4356	245	12	s	s	VERB
ejpam-4356	245	13	⊆	⊆	NUM
ejpam-4356	245	14	v	v	NOUN
ejpam-4356	245	15	(	(	PUNCT
ejpam-4356	245	16	h	h	NOUN
ejpam-4356	245	17	)	)	PUNCT
ejpam-4356	245	18	,	,	PUNCT
ejpam-4356	245	19	s	s	PROPN
ejpam-4356	245	20	∈	∈	PROPN
ejpam-4356	245	21	w(g	w(g	PROPN
ejpam-4356	245	22	)	)	PUNCT
ejpam-4356	245	23	and	and	CCONJ
ejpam-4356	245	24	p2[s]h	p2[s]h	PROPN
ejpam-4356	245	25	=	=	PUNCT
ejpam-4356	245	26	v	v	PROPN
ejpam-4356	245	27	(	(	PUNCT
ejpam-4356	245	28	h	h	NOUN
ejpam-4356	245	29	)	)	PUNCT
ejpam-4356	245	30	}	}	PUNCT
ejpam-4356	245	31	.	.	PUNCT
ejpam-4356	246	1	proof	proof	NOUN
ejpam-4356	246	2	.	.	PUNCT
ejpam-4356	247	1	define	define	VERB
ejpam-4356	247	2	ω	ω	PROPN
ejpam-4356	247	3	=	=	SYM
ejpam-4356	247	4	min{[s	min{[s	PROPN
ejpam-4356	247	5	]	]	PUNCT
ejpam-4356	247	6	:	:	PUNCT
ejpam-4356	247	7	s	s	VERB
ejpam-4356	247	8	⊆	⊆	NUM
ejpam-4356	247	9	v	v	NOUN
ejpam-4356	247	10	(	(	PUNCT
ejpam-4356	247	11	h	h	NOUN
ejpam-4356	247	12	)	)	PUNCT
ejpam-4356	247	13	,	,	PUNCT
ejpam-4356	247	14	s	s	PROPN
ejpam-4356	247	15	∈	∈	PROPN
ejpam-4356	247	16	w(g	w(g	PROPN
ejpam-4356	247	17	)	)	PUNCT
ejpam-4356	247	18	and	and	CCONJ
ejpam-4356	247	19	p2[s]h	p2[s]h	PROPN
ejpam-4356	247	20	=	=	PUNCT
ejpam-4356	247	21	v	v	PROPN
ejpam-4356	247	22	(	(	PUNCT
ejpam-4356	247	23	h	h	NOUN
ejpam-4356	247	24	)	)	PUNCT
ejpam-4356	247	25	}	}	PUNCT
ejpam-4356	247	26	.	.	PUNCT
ejpam-4356	248	1	case	case	NOUN
ejpam-4356	248	2	1	1	X
ejpam-4356	248	3	.	.	PUNCT
ejpam-4356	248	4	suppose	suppose	VERB
ejpam-4356	248	5	that	that	SCONJ
ejpam-4356	248	6	h	h	NOUN
ejpam-4356	248	7	is	be	AUX
ejpam-4356	248	8	a	a	DET
ejpam-4356	248	9	connected	connected	ADJ
ejpam-4356	248	10	noncomplete	noncomplete	ADJ
ejpam-4356	248	11	graph	graph	NOUN
ejpam-4356	248	12	and	and	CCONJ
ejpam-4356	248	13	g	g	NOUN
ejpam-4356	248	14	=	=	PROPN
ejpam-4356	248	15	h	h	PROPN
ejpam-4356	249	1	+	+	CCONJ
ejpam-4356	249	2	kp	kp	PROPN
ejpam-4356	249	3	,	,	PUNCT
ejpam-4356	249	4	then	then	ADV
ejpam-4356	249	5	γwcg(g	γwcg(g	NOUN
ejpam-4356	249	6	)	)	PUNCT
ejpam-4356	249	7	≤	≤	PROPN
ejpam-4356	249	8	ω	ω	PROPN
ejpam-4356	249	9	.	.	PUNCT
ejpam-4356	249	10	case	case	NOUN
ejpam-4356	249	11	2	2	NUM
ejpam-4356	249	12	.	.	PUNCT
ejpam-4356	249	13	suppose	suppose	VERB
ejpam-4356	249	14	that	that	SCONJ
ejpam-4356	249	15	s	s	VERB
ejpam-4356	249	16	∈	∈	NOUN
ejpam-4356	249	17	w(g	w(g	PROPN
ejpam-4356	249	18	)	)	PUNCT
ejpam-4356	249	19	.	.	PUNCT
ejpam-4356	250	1	let	let	VERB
ejpam-4356	250	2	s	s	PRON
ejpam-4356	250	3	⊆	⊆	NUM
ejpam-4356	250	4	v	v	NOUN
ejpam-4356	250	5	(	(	PUNCT
ejpam-4356	250	6	g	g	NOUN
ejpam-4356	250	7	)	)	PUNCT
ejpam-4356	250	8	be	be	AUX
ejpam-4356	250	9	a	a	DET
ejpam-4356	250	10	γwcg	γwcg	NOUN
ejpam-4356	250	11	-	-	PUNCT
ejpam-4356	250	12	set	set	NOUN
ejpam-4356	250	13	of	of	ADP
ejpam-4356	250	14	g.	g.	PROPN
ejpam-4356	250	15	then	then	ADV
ejpam-4356	250	16	by	by	ADP
ejpam-4356	250	17	theorem	theorem	NOUN
ejpam-4356	250	18	16	16	NUM
ejpam-4356	250	19	,	,	PUNCT
ejpam-4356	250	20	s	s	VERB
ejpam-4356	250	21	⊆	⊆	NUM
ejpam-4356	250	22	v	v	NOUN
ejpam-4356	250	23	(	(	PUNCT
ejpam-4356	250	24	h	h	NOUN
ejpam-4356	250	25	)	)	PUNCT
ejpam-4356	250	26	and	and	CCONJ
ejpam-4356	250	27	s	s	VERB
ejpam-4356	250	28	is	be	AUX
ejpam-4356	250	29	a	a	DET
ejpam-4356	250	30	2	2	NUM
ejpam-4356	250	31	-	-	PUNCT
ejpam-4356	250	32	path	path	NOUN
ejpam-4356	250	33	closure	closure	NOUN
ejpam-4356	250	34	absorbing	absorb	VERB
ejpam-4356	250	35	set	set	NOUN
ejpam-4356	250	36	in	in	ADP
ejpam-4356	250	37	h.	h.	PROPN
ejpam-4356	250	38	hence	hence	ADV
ejpam-4356	250	39	γwcg(g	γwcg(g	PROPN
ejpam-4356	250	40	)	)	PUNCT
ejpam-4356	251	1	=	=	PROPN
ejpam-4356	251	2	|s|≥	|s|≥	PROPN
ejpam-4356	251	3	ω	ω	NOUN
ejpam-4356	251	4	.	.	PUNCT
ejpam-4356	252	1	consequently	consequently	ADV
ejpam-4356	252	2	,	,	PUNCT
ejpam-4356	252	3	by	by	ADP
ejpam-4356	252	4	combining	combine	VERB
ejpam-4356	252	5	these	these	DET
ejpam-4356	252	6	two	two	NUM
ejpam-4356	252	7	inequalities	inequality	NOUN
ejpam-4356	252	8	the	the	DET
ejpam-4356	252	9	conclusion	conclusion	NOUN
ejpam-4356	252	10	follows	follow	VERB
ejpam-4356	252	11	.	.	PUNCT
ejpam-4356	253	1	corollary	corollary	ADJ
ejpam-4356	253	2	7	7	NUM
ejpam-4356	253	3	.	.	PUNCT
ejpam-4356	254	1	let	let	VERB
ejpam-4356	254	2	h	h	PRON
ejpam-4356	254	3	be	be	AUX
ejpam-4356	254	4	a	a	DET
ejpam-4356	254	5	connected	connected	ADJ
ejpam-4356	254	6	noncomplete	noncomplete	ADJ
ejpam-4356	254	7	graph	graph	NOUN
ejpam-4356	254	8	and	and	CCONJ
ejpam-4356	254	9	let	let	VERB
ejpam-4356	254	10	g	g	PROPN
ejpam-4356	254	11	=	=	PROPN
ejpam-4356	254	12	h+kp	h+kp	PROPN
ejpam-4356	254	13	.	.	PUNCT
ejpam-4356	255	1	if	if	SCONJ
ejpam-4356	255	2	diam(h	diam(h	NOUN
ejpam-4356	255	3	)	)	PUNCT
ejpam-4356	255	4	=	=	SYM
ejpam-4356	255	5	2	2	NUM
ejpam-4356	255	6	,	,	PUNCT
ejpam-4356	255	7	then	then	ADV
ejpam-4356	255	8	γwcg(g	γwcg(g	NOUN
ejpam-4356	255	9	)	)	PUNCT
ejpam-4356	256	1	=	=	SYM
ejpam-4356	256	2	γwcg(h	γwcg(h	PROPN
ejpam-4356	256	3	)	)	PUNCT
ejpam-4356	256	4	.	.	PUNCT
ejpam-4356	257	1	proof	proof	NOUN
ejpam-4356	257	2	.	.	PUNCT
ejpam-4356	258	1	suppose	suppose	VERB
ejpam-4356	258	2	that	that	SCONJ
ejpam-4356	258	3	g	g	NOUN
ejpam-4356	258	4	=	=	PUNCT
ejpam-4356	258	5	h	h	PROPN
ejpam-4356	259	1	+	+	NOUN
ejpam-4356	259	2	kp	kp	X
ejpam-4356	259	3	where	where	SCONJ
ejpam-4356	259	4	h	h	NOUN
ejpam-4356	259	5	is	be	AUX
ejpam-4356	259	6	a	a	DET
ejpam-4356	259	7	noncomplete	noncomplete	ADJ
ejpam-4356	259	8	graph	graph	NOUN
ejpam-4356	259	9	with	with	ADP
ejpam-4356	259	10	diam(h	diam(h	NOUN
ejpam-4356	259	11	)	)	PUNCT
ejpam-4356	259	12	=	=	SYM
ejpam-4356	259	13	2	2	X
ejpam-4356	259	14	.	.	X
ejpam-4356	259	15	case	case	NOUN
ejpam-4356	259	16	1	1	X
ejpam-4356	259	17	.	.	PUNCT
ejpam-4356	260	1	let	let	VERB
ejpam-4356	260	2	s	s	PRON
ejpam-4356	260	3	⊆	⊆	NUM
ejpam-4356	260	4	v	v	NOUN
ejpam-4356	260	5	(	(	PUNCT
ejpam-4356	260	6	h	h	NOUN
ejpam-4356	260	7	)	)	PUNCT
ejpam-4356	260	8	such	such	ADJ
ejpam-4356	260	9	that	that	DET
ejpam-4356	260	10	s	s	VERB
ejpam-4356	260	11	∈	∈	NOUN
ejpam-4356	260	12	w(g	w(g	PROPN
ejpam-4356	260	13	)	)	PUNCT
ejpam-4356	260	14	.	.	PUNCT
ejpam-4356	261	1	then	then	ADV
ejpam-4356	261	2	by	by	ADP
ejpam-4356	261	3	corollary	corollary	ADJ
ejpam-4356	261	4	6	6	NUM
ejpam-4356	261	5	,	,	PUNCT
ejpam-4356	261	6	γwcg(g	γwcg(g	NOUN
ejpam-4356	261	7	)	)	PUNCT
ejpam-4356	261	8	=	=	NOUN
ejpam-4356	261	9	|s|≥	|s|≥	PROPN
ejpam-4356	261	10	γwcg(h	γwcg(h	NOUN
ejpam-4356	261	11	)	)	PUNCT
ejpam-4356	261	12	.	.	PUNCT
ejpam-4356	262	1	case	case	NOUN
ejpam-4356	262	2	2	2	X
ejpam-4356	262	3	.	.	PUNCT
ejpam-4356	263	1	let	let	VERB
ejpam-4356	263	2	s	s	PRON
ejpam-4356	263	3	be	be	AUX
ejpam-4356	263	4	a	a	DET
ejpam-4356	263	5	γwcg(g)-set	γwcg(g)-set	NOUN
ejpam-4356	263	6	of	of	ADP
ejpam-4356	263	7	g.	g.	PROPN
ejpam-4356	263	8	then	then	ADV
ejpam-4356	263	9	by	by	ADP
ejpam-4356	263	10	theorem	theorem	NOUN
ejpam-4356	263	11	16	16	NUM
ejpam-4356	263	12	,	,	PUNCT
ejpam-4356	263	13	s	s	VERB
ejpam-4356	263	14	⊆	⊆	NUM
ejpam-4356	263	15	v	v	NOUN
ejpam-4356	263	16	(	(	PUNCT
ejpam-4356	263	17	h	h	NOUN
ejpam-4356	263	18	)	)	PUNCT
ejpam-4356	263	19	and	and	CCONJ
ejpam-4356	263	20	s	s	VERB
ejpam-4356	263	21	is	be	AUX
ejpam-4356	263	22	a	a	DET
ejpam-4356	263	23	2	2	NUM
ejpam-4356	263	24	-	-	PUNCT
ejpam-4356	263	25	path	path	NOUN
ejpam-4356	263	26	closure	closure	NOUN
ejpam-4356	263	27	absorbing	absorb	VERB
ejpam-4356	263	28	set	set	NOUN
ejpam-4356	263	29	in	in	ADP
ejpam-4356	263	30	h.	h.	PROPN
ejpam-4356	263	31	thus	thus	ADV
ejpam-4356	263	32	,	,	PUNCT
ejpam-4356	263	33	by	by	ADP
ejpam-4356	263	34	theorem	theorem	NOUN
ejpam-4356	263	35	15	15	NUM
ejpam-4356	263	36	,	,	PUNCT
ejpam-4356	263	37	s	s	NOUN
ejpam-4356	263	38	∈	∈	NOUN
ejpam-4356	263	39	w(g	w(g	PROPN
ejpam-4356	263	40	)	)	PUNCT
ejpam-4356	263	41	.	.	PUNCT
ejpam-4356	264	1	hence	hence	ADV
ejpam-4356	264	2	,	,	PUNCT
ejpam-4356	264	3	by	by	ADP
ejpam-4356	264	4	corollary	corollary	ADJ
ejpam-4356	264	5	6	6	NUM
ejpam-4356	264	6	,	,	PUNCT
ejpam-4356	264	7	γwcg(g	γwcg(g	NOUN
ejpam-4356	264	8	)	)	PUNCT
ejpam-4356	265	1	=	=	NOUN
ejpam-4356	265	2	|s|≤	|s|≤	NOUN
ejpam-4356	265	3	γwcg(h	γwcg(h	NOUN
ejpam-4356	265	4	)	)	PUNCT
ejpam-4356	265	5	.	.	PUNCT
ejpam-4356	266	1	consequently	consequently	ADV
ejpam-4356	266	2	,	,	PUNCT
ejpam-4356	266	3	combining	combine	VERB
ejpam-4356	266	4	these	these	DET
ejpam-4356	266	5	two	two	NUM
ejpam-4356	266	6	inequalities	inequality	NOUN
ejpam-4356	266	7	the	the	DET
ejpam-4356	266	8	conclusion	conclusion	NOUN
ejpam-4356	266	9	follows	follow	VERB
ejpam-4356	266	10	.	.	PUNCT
ejpam-4356	267	1	theorem	theorem	NOUN
ejpam-4356	267	2	17	17	NUM
ejpam-4356	267	3	.	.	PUNCT
ejpam-4356	268	1	let	let	VERB
ejpam-4356	268	2	g	g	NOUN
ejpam-4356	268	3	=	=	PUNCT
ejpam-4356	268	4	h	h	PROPN
ejpam-4356	269	1	+	+	PROPN
ejpam-4356	269	2	k	k	PROPN
ejpam-4356	269	3	where	where	SCONJ
ejpam-4356	269	4	h	h	NOUN
ejpam-4356	269	5	and	and	CCONJ
ejpam-4356	269	6	k	k	PROPN
ejpam-4356	269	7	are	be	AUX
ejpam-4356	269	8	connected	connect	VERB
ejpam-4356	269	9	noncomplete	noncomplete	ADJ
ejpam-4356	269	10	graphs	graph	NOUN
ejpam-4356	269	11	.	.	PUNCT
ejpam-4356	270	1	if	if	SCONJ
ejpam-4356	270	2	s	s	PROPN
ejpam-4356	270	3	is	be	AUX
ejpam-4356	270	4	a	a	DET
ejpam-4356	270	5	γwcg	γwcg	NOUN
ejpam-4356	270	6	-	-	PUNCT
ejpam-4356	270	7	set	set	NOUN
ejpam-4356	270	8	of	of	ADP
ejpam-4356	270	9	g	g	NOUN
ejpam-4356	270	10	,	,	PUNCT
ejpam-4356	270	11	then	then	ADV
ejpam-4356	270	12	either	either	CCONJ
ejpam-4356	270	13	(	(	PUNCT
ejpam-4356	270	14	i.	i.	PROPN
ejpam-4356	270	15	)	)	PUNCT
ejpam-4356	270	16	s	s	PART
ejpam-4356	270	17	⊆	⊆	NUM
ejpam-4356	270	18	v	v	NOUN
ejpam-4356	270	19	(	(	PUNCT
ejpam-4356	270	20	h	h	NOUN
ejpam-4356	270	21	)	)	PUNCT
ejpam-4356	270	22	,	,	PUNCT
ejpam-4356	270	23	where	where	SCONJ
ejpam-4356	270	24	s	s	NOUN
ejpam-4356	270	25	is	be	AUX
ejpam-4356	270	26	a	a	DET
ejpam-4356	270	27	2	2	NUM
ejpam-4356	270	28	-	-	PUNCT
ejpam-4356	270	29	path	path	NOUN
ejpam-4356	270	30	closure	closure	NOUN
ejpam-4356	270	31	absorbing	absorb	VERB
ejpam-4356	270	32	set	set	NOUN
ejpam-4356	270	33	in	in	ADP
ejpam-4356	270	34	h	h	NOUN
ejpam-4356	270	35	,	,	PUNCT
ejpam-4356	270	36	or	or	CCONJ
ejpam-4356	270	37	(	(	PUNCT
ejpam-4356	270	38	ii	ii	NOUN
ejpam-4356	270	39	.	.	PUNCT
ejpam-4356	270	40	)	)	PUNCT
ejpam-4356	270	41	s	s	PART
ejpam-4356	270	42	⊆	⊆	NUM
ejpam-4356	270	43	v	v	NOUN
ejpam-4356	270	44	(	(	PUNCT
ejpam-4356	270	45	k	k	NOUN
ejpam-4356	270	46	)	)	PUNCT
ejpam-4356	270	47	,	,	PUNCT
ejpam-4356	270	48	where	where	SCONJ
ejpam-4356	270	49	s	s	NOUN
ejpam-4356	270	50	is	be	AUX
ejpam-4356	270	51	a	a	DET
ejpam-4356	270	52	2	2	NUM
ejpam-4356	270	53	-	-	PUNCT
ejpam-4356	270	54	path	path	NOUN
ejpam-4356	270	55	closure	closure	NOUN
ejpam-4356	270	56	absorbing	absorb	VERB
ejpam-4356	270	57	set	set	NOUN
ejpam-4356	270	58	in	in	ADP
ejpam-4356	270	59	k.	k.	PROPN
ejpam-4356	270	60	proof	proof	PROPN
ejpam-4356	270	61	.	.	PUNCT
ejpam-4356	271	1	let	let	VERB
ejpam-4356	271	2	g	g	NOUN
ejpam-4356	271	3	=	=	PUNCT
ejpam-4356	271	4	h	h	PROPN
ejpam-4356	272	1	+	+	PROPN
ejpam-4356	272	2	k	k	PROPN
ejpam-4356	272	3	where	where	SCONJ
ejpam-4356	272	4	h	h	NOUN
ejpam-4356	272	5	and	and	CCONJ
ejpam-4356	272	6	k	k	PROPN
ejpam-4356	272	7	are	be	AUX
ejpam-4356	272	8	connected	connect	VERB
ejpam-4356	272	9	noncomplete	noncomplete	ADJ
ejpam-4356	272	10	graphs	graph	NOUN
ejpam-4356	272	11	.	.	PUNCT
ejpam-4356	273	1	suppose	suppose	VERB
ejpam-4356	273	2	γwcg(g	γwcg(g	NOUN
ejpam-4356	273	3	)	)	PUNCT
ejpam-4356	273	4	=	=	SYM
ejpam-4356	274	1	k	k	PROPN
ejpam-4356	275	1	and	and	CCONJ
ejpam-4356	275	2	let	let	VERB
ejpam-4356	275	3	s	s	PRON
ejpam-4356	275	4	=	=	PUNCT
ejpam-4356	275	5	{	{	PUNCT
ejpam-4356	275	6	y1	y1	PROPN
ejpam-4356	275	7	,	,	PUNCT
ejpam-4356	275	8	y2	y2	PROPN
ejpam-4356	275	9	,	,	PUNCT
ejpam-4356	275	10	...	...	PUNCT
ejpam-4356	275	11	,	,	PUNCT
ejpam-4356	275	12	yk	yk	PROPN
ejpam-4356	275	13	}	}	PUNCT
ejpam-4356	275	14	∈	∈	PROPN
ejpam-4356	275	15	w(g	w(g	PROPN
ejpam-4356	275	16	)	)	PUNCT
ejpam-4356	275	17	.	.	PUNCT
ejpam-4356	276	1	if	if	SCONJ
ejpam-4356	276	2	⟨s⟩	⟨s⟩	PROPN
ejpam-4356	276	3	is	be	AUX
ejpam-4356	276	4	a	a	DET
ejpam-4356	276	5	complete	complete	ADJ
ejpam-4356	276	6	subgraph	subgraph	NOUN
ejpam-4356	276	7	of	of	ADP
ejpam-4356	276	8	g	g	PROPN
ejpam-4356	276	9	and	and	CCONJ
ejpam-4356	276	10	ig[s	ig[s	PROPN
ejpam-4356	276	11	]	]	X
ejpam-4356	276	12	=	=	SYM
ejpam-4356	276	13	v	v	X
ejpam-4356	276	14	(	(	PUNCT
ejpam-4356	276	15	g	g	NOUN
ejpam-4356	276	16	)	)	PUNCT
ejpam-4356	276	17	,	,	PUNCT
ejpam-4356	276	18	then	then	ADV
ejpam-4356	276	19	ng[s	ng[s	PROPN
ejpam-4356	276	20	]	]	PUNCT
ejpam-4356	276	21	=	=	SYM
ejpam-4356	276	22	v	v	X
ejpam-4356	276	23	(	(	PUNCT
ejpam-4356	276	24	g	g	NOUN
ejpam-4356	276	25	)	)	PUNCT
ejpam-4356	276	26	and	and	CCONJ
ejpam-4356	276	27	ew(s	ew(s	X
ejpam-4356	276	28	)	)	PUNCT
ejpam-4356	276	29	is	be	AUX
ejpam-4356	276	30	connected	connect	VERB
ejpam-4356	276	31	which	which	PRON
ejpam-4356	276	32	implies	imply	VERB
ejpam-4356	276	33	that	that	SCONJ
ejpam-4356	276	34	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	276	35	is	be	AUX
ejpam-4356	276	36	connected	connect	VERB
ejpam-4356	276	37	.	.	PUNCT
ejpam-4356	277	1	hence	hence	ADV
ejpam-4356	277	2	,	,	PUNCT
ejpam-4356	277	3	v	v	PROPN
ejpam-4356	277	4	(	(	PUNCT
ejpam-4356	277	5	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	277	6	)	)	PUNCT
ejpam-4356	277	7	=	=	SYM
ejpam-4356	277	8	v	v	X
ejpam-4356	277	9	(	(	PUNCT
ejpam-4356	277	10	g	g	NOUN
ejpam-4356	277	11	)	)	PUNCT
ejpam-4356	277	12	,	,	PUNCT
ejpam-4356	277	13	a	a	DET
ejpam-4356	277	14	contradiction	contradiction	NOUN
ejpam-4356	277	15	.	.	PUNCT
ejpam-4356	278	1	thus	thus	ADV
ejpam-4356	278	2	,	,	PUNCT
ejpam-4356	278	3	there	there	PRON
ejpam-4356	278	4	exist	exist	VERB
ejpam-4356	278	5	integers	integer	NOUN
ejpam-4356	278	6	i	i	PRON
ejpam-4356	278	7	,	,	PUNCT
ejpam-4356	278	8	j	j	PROPN
ejpam-4356	278	9	,	,	PUNCT
ejpam-4356	278	10	j.	j.	PROPN
ejpam-4356	278	11	hamja	hamja	PROPN
ejpam-4356	278	12	,	,	PUNCT
ejpam-4356	278	13	i.	i.	PROPN
ejpam-4356	278	14	aniversario	aniversario	PROPN
ejpam-4356	278	15	,	,	PUNCT
ejpam-4356	278	16	h.	h.	PROPN
ejpam-4356	278	17	rara	rara	PROPN
ejpam-4356	278	18	/	/	SYM
ejpam-4356	278	19	eur	eur	PROPN
ejpam-4356	278	20	.	.	PUNCT
ejpam-4356	279	1	j.	j.	PROPN
ejpam-4356	279	2	pure	pure	PROPN
ejpam-4356	279	3	appl	appl	PROPN
ejpam-4356	279	4	.	.	PROPN
ejpam-4356	279	5	math	math	PROPN
ejpam-4356	279	6	,	,	PUNCT
ejpam-4356	279	7	15	15	NUM
ejpam-4356	279	8	(	(	PUNCT
ejpam-4356	279	9	2	2	NUM
ejpam-4356	279	10	)	)	PUNCT
ejpam-4356	279	11	(	(	PUNCT
ejpam-4356	279	12	2022	2022	NUM
ejpam-4356	279	13	)	)	PUNCT
ejpam-4356	279	14	,	,	PUNCT
ejpam-4356	279	15	736	736	NUM
ejpam-4356	279	16	-	-	SYM
ejpam-4356	279	17	752	752	NUM
ejpam-4356	279	18	745	745	NUM
ejpam-4356	279	19	1	1	NUM
ejpam-4356	279	20	≤	≤	NUM
ejpam-4356	280	1	i	i	PRON
ejpam-4356	280	2	<	<	X
ejpam-4356	280	3	j	j	PROPN
ejpam-4356	280	4	≤	≤	PROPN
ejpam-4356	281	1	k	k	PRON
ejpam-4356	281	2	such	such	ADJ
ejpam-4356	281	3	that	that	SCONJ
ejpam-4356	281	4	dg(yi	dg(yi	PROPN
ejpam-4356	281	5	,	,	PUNCT
ejpam-4356	281	6	yj	yj	PROPN
ejpam-4356	281	7	)	)	PUNCT
ejpam-4356	281	8	=	=	SYM
ejpam-4356	282	1	2	2	X
ejpam-4356	282	2	.	.	X
ejpam-4356	282	3	either	either	CCONJ
ejpam-4356	282	4	yi	yi	PROPN
ejpam-4356	282	5	,	,	PUNCT
ejpam-4356	282	6	yj	yj	PROPN
ejpam-4356	282	7	∈	∈	PROPN
ejpam-4356	282	8	v	v	ADP
ejpam-4356	282	9	(	(	PUNCT
ejpam-4356	282	10	h	h	NOUN
ejpam-4356	282	11	)	)	PUNCT
ejpam-4356	282	12	or	or	CCONJ
ejpam-4356	282	13	yi	yi	PROPN
ejpam-4356	282	14	,	,	PUNCT
ejpam-4356	282	15	yj	yj	PROPN
ejpam-4356	282	16	∈	∈	PROPN
ejpam-4356	282	17	v	v	ADP
ejpam-4356	282	18	(	(	PUNCT
ejpam-4356	282	19	k	k	NOUN
ejpam-4356	282	20	)	)	PUNCT
ejpam-4356	282	21	.	.	PUNCT
ejpam-4356	283	1	suppose	suppose	VERB
ejpam-4356	283	2	yi	yi	PROPN
ejpam-4356	283	3	,	,	PUNCT
ejpam-4356	283	4	yj	yj	PROPN
ejpam-4356	283	5	∈	∈	PROPN
ejpam-4356	283	6	v	v	ADP
ejpam-4356	283	7	(	(	PUNCT
ejpam-4356	283	8	h	h	NOUN
ejpam-4356	283	9	)	)	PUNCT
ejpam-4356	283	10	.	.	PUNCT
ejpam-4356	284	1	we	we	PRON
ejpam-4356	284	2	claim	claim	VERB
ejpam-4356	284	3	that	that	SCONJ
ejpam-4356	284	4	s	s	VERB
ejpam-4356	284	5	∩	∩	ADJ
ejpam-4356	284	6	v	v	X
ejpam-4356	284	7	(	(	PUNCT
ejpam-4356	284	8	k	k	NOUN
ejpam-4356	284	9	)	)	PUNCT
ejpam-4356	284	10	=	=	PUNCT
ejpam-4356	284	11	∅.	∅.	VERB
ejpam-4356	284	12	clearly	clearly	ADV
ejpam-4356	284	13	,	,	PUNCT
ejpam-4356	284	14	v	v	X
ejpam-4356	284	15	(	(	PUNCT
ejpam-4356	284	16	k	k	NOUN
ejpam-4356	284	17	)	)	PUNCT
ejpam-4356	284	18	⊆	⊆	NUM
ejpam-4356	284	19	ig[yi	ig[yi	PROPN
ejpam-4356	284	20	,	,	PUNCT
ejpam-4356	284	21	yj	yj	PROPN
ejpam-4356	284	22	]	]	PUNCT
ejpam-4356	284	23	.	.	PUNCT
ejpam-4356	284	24	suppose	suppose	VERB
ejpam-4356	284	25	that	that	SCONJ
ejpam-4356	284	26	s	s	VERB
ejpam-4356	284	27	∩	∩	ADJ
ejpam-4356	284	28	v	v	X
ejpam-4356	284	29	(	(	PUNCT
ejpam-4356	284	30	k	k	NOUN
ejpam-4356	284	31	)	)	PUNCT
ejpam-4356	284	32	=	=	SYM
ejpam-4356	284	33	{	{	PUNCT
ejpam-4356	284	34	z	z	NOUN
ejpam-4356	284	35	}	}	PUNCT
ejpam-4356	284	36	and	and	CCONJ
ejpam-4356	284	37	let	let	VERB
ejpam-4356	284	38	z	z	NOUN
ejpam-4356	284	39	=	=	SYM
ejpam-4356	284	40	yl	yl	NOUN
ejpam-4356	284	41	.	.	PUNCT
ejpam-4356	285	1	then	then	ADV
ejpam-4356	285	2	l	l	X
ejpam-4356	285	3	<	<	X
ejpam-4356	285	4	j.	j.	PROPN
ejpam-4356	285	5	we	we	PRON
ejpam-4356	285	6	consider	consider	VERB
ejpam-4356	285	7	the	the	DET
ejpam-4356	285	8	set	set	NOUN
ejpam-4356	285	9	s∗	s∗	PROPN
ejpam-4356	285	10	=	=	SYM
ejpam-4356	285	11	{	{	PUNCT
ejpam-4356	285	12	xi	xi	PROPN
ejpam-4356	285	13	,	,	PUNCT
ejpam-4356	285	14	x2	x2	PROPN
ejpam-4356	285	15	,	,	PUNCT
ejpam-4356	285	16	...	...	PUNCT
ejpam-4356	285	17	,	,	PUNCT
ejpam-4356	285	18	xk−1	xk−1	PROPN
ejpam-4356	285	19	}	}	PUNCT
ejpam-4356	285	20	where	where	SCONJ
ejpam-4356	285	21	xn	xn	PROPN
ejpam-4356	286	1	=	=	PRON
ejpam-4356	287	1	{	{	PUNCT
ejpam-4356	288	1	yn	yn	INTJ
ejpam-4356	288	2	,	,	PUNCT
ejpam-4356	288	3	if	if	SCONJ
ejpam-4356	288	4	1	1	NUM
ejpam-4356	288	5	≤	≤	NUM
ejpam-4356	288	6	n	n	PRON
ejpam-4356	288	7	≤	≤	NOUN
ejpam-4356	288	8	l	l	NOUN
ejpam-4356	288	9	−	−	PROPN
ejpam-4356	288	10	1	1	NUM
ejpam-4356	288	11	yn+1	yn+1	NOUN
ejpam-4356	288	12	,	,	PUNCT
ejpam-4356	288	13	if	if	SCONJ
ejpam-4356	288	14	l	l	NOUN
ejpam-4356	288	15	≤	≤	NOUN
ejpam-4356	288	16	n	n	PRON
ejpam-4356	288	17	≤	≤	NOUN
ejpam-4356	289	1	k	k	NOUN
ejpam-4356	289	2	−	−	NOUN
ejpam-4356	289	3	1	1	NUM
ejpam-4356	289	4	.	.	PUNCT
ejpam-4356	290	1	since	since	SCONJ
ejpam-4356	290	2	dg(yl	dg(yl	NOUN
ejpam-4356	290	3	,	,	PUNCT
ejpam-4356	290	4	yn	yn	PROPN
ejpam-4356	290	5	)	)	PUNCT
ejpam-4356	290	6	=	=	SYM
ejpam-4356	290	7	1	1	NUM
ejpam-4356	290	8	for	for	ADP
ejpam-4356	290	9	all	all	PRON
ejpam-4356	290	10	n	n	NOUN
ejpam-4356	290	11	=	=	SYM
ejpam-4356	290	12	1	1	NUM
ejpam-4356	290	13	,	,	PUNCT
ejpam-4356	290	14	2	2	NUM
ejpam-4356	290	15	,	,	PUNCT
ejpam-4356	290	16	...	...	PUNCT
ejpam-4356	290	17	,	,	PUNCT
ejpam-4356	291	1	l	l	PROPN
ejpam-4356	291	2	−	−	NOUN
ejpam-4356	291	3	1	1	NUM
ejpam-4356	291	4	,	,	PUNCT
ejpam-4356	291	5	l	l	PROPN
ejpam-4356	291	6	+	+	NOUN
ejpam-4356	291	7	1	1	NUM
ejpam-4356	291	8	,	,	PUNCT
ejpam-4356	291	9	...	...	PUNCT
ejpam-4356	291	10	,	,	PUNCT
ejpam-4356	291	11	k	k	X
ejpam-4356	291	12	,	,	PUNCT
ejpam-4356	291	13	ig[s	ig[s	PROPN
ejpam-4356	291	14	∗	∗	NOUN
ejpam-4356	291	15	]	]	PUNCT
ejpam-4356	291	16	=	=	SYM
ejpam-4356	291	17	v	v	NOUN
ejpam-4356	291	18	(	(	PUNCT
ejpam-4356	291	19	g	g	NOUN
ejpam-4356	291	20	)	)	PUNCT
ejpam-4356	291	21	.	.	PUNCT
ejpam-4356	292	1	this	this	PRON
ejpam-4356	292	2	implies	imply	VERB
ejpam-4356	292	3	that	that	PRON
ejpam-4356	292	4	s∗	s∗	PROPN
ejpam-4356	292	5	∈	∈	PROPN
ejpam-4356	292	6	c∗(g	c∗(g	PROPN
ejpam-4356	292	7	)	)	PUNCT
ejpam-4356	292	8	.	.	PUNCT
ejpam-4356	293	1	since	since	SCONJ
ejpam-4356	293	2	g	g	PROPN
ejpam-4356	293	3	is	be	AUX
ejpam-4356	293	4	connected	connect	VERB
ejpam-4356	293	5	,	,	PUNCT
ejpam-4356	293	6	for	for	ADP
ejpam-4356	293	7	every	every	DET
ejpam-4356	293	8	xi	xi	PROPN
ejpam-4356	293	9	,	,	PUNCT
ejpam-4356	293	10	xj	xj	PROPN
ejpam-4356	293	11	∈	∈	PROPN
ejpam-4356	293	12	s∗	s∗	PROPN
ejpam-4356	293	13	,	,	PUNCT
ejpam-4356	293	14	dg(xi	dg(xi	PROPN
ejpam-4356	293	15	,	,	PUNCT
ejpam-4356	293	16	xj	xj	PROPN
ejpam-4356	293	17	)	)	PUNCT
ejpam-4356	293	18	=	=	SYM
ejpam-4356	294	1	2	2	X
ejpam-4356	294	2	.	.	PUNCT
ejpam-4356	294	3	then	then	ADV
ejpam-4356	294	4	there	there	PRON
ejpam-4356	294	5	exists	exist	VERB
ejpam-4356	294	6	z	z	PROPN
ejpam-4356	294	7	∈	∈	PROPN
ejpam-4356	294	8	v	v	ADP
ejpam-4356	294	9	(	(	PUNCT
ejpam-4356	294	10	g	g	NOUN
ejpam-4356	294	11	)	)	PUNCT
ejpam-4356	294	12	\	\	PUNCT
ejpam-4356	295	1	s	s	VERB
ejpam-4356	295	2	such	such	ADJ
ejpam-4356	295	3	that	that	SCONJ
ejpam-4356	295	4	z	z	NOUN
ejpam-4356	295	5	lies	lie	VERB
ejpam-4356	295	6	in	in	ADP
ejpam-4356	295	7	xi	xi	PROPN
ejpam-4356	295	8	-	-	PUNCT
ejpam-4356	295	9	xj	xj	PROPN
ejpam-4356	295	10	geodesic	geodesic	NOUN
ejpam-4356	295	11	.	.	PUNCT
ejpam-4356	296	1	thus	thus	ADV
ejpam-4356	296	2	,	,	PUNCT
ejpam-4356	296	3	for	for	ADP
ejpam-4356	296	4	ng[s	ng[s	PROPN
ejpam-4356	296	5	∗	∗	NOUN
ejpam-4356	296	6	]	]	PUNCT
ejpam-4356	296	7	=	=	SYM
ejpam-4356	296	8	v	v	X
ejpam-4356	296	9	(	(	PUNCT
ejpam-4356	296	10	g	g	NOUN
ejpam-4356	296	11	)	)	PUNCT
ejpam-4356	296	12	and	and	CCONJ
ejpam-4356	296	13	xi	xi	PROPN
ejpam-4356	296	14	,	,	PUNCT
ejpam-4356	296	15	xj	xj	PROPN
ejpam-4356	296	16	∈	∈	PROPN
ejpam-4356	296	17	ew(s	ew(s	PRON
ejpam-4356	296	18	)	)	PUNCT
ejpam-4356	296	19	for	for	ADP
ejpam-4356	296	20	all	all	DET
ejpam-4356	296	21	z	z	NOUN
ejpam-4356	296	22	∈	∈	PROPN
ejpam-4356	296	23	v	v	NOUN
ejpam-4356	296	24	(	(	PUNCT
ejpam-4356	296	25	g)\s	g)\s	NOUN
ejpam-4356	296	26	.	.	PUNCT
ejpam-4356	297	1	this	this	PRON
ejpam-4356	297	2	implies	imply	VERB
ejpam-4356	297	3	that	that	SCONJ
ejpam-4356	297	4	s∗	s∗	PROPN
ejpam-4356	297	5	∈	∈	PROPN
ejpam-4356	297	6	w(g	w(g	PROPN
ejpam-4356	297	7	)	)	PUNCT
ejpam-4356	297	8	,	,	PUNCT
ejpam-4356	297	9	contrary	contrary	ADV
ejpam-4356	297	10	to	to	ADP
ejpam-4356	297	11	the	the	DET
ejpam-4356	297	12	assumption	assumption	NOUN
ejpam-4356	297	13	that	that	SCONJ
ejpam-4356	297	14	γwcg(g	γwcg(g	NOUN
ejpam-4356	297	15	)	)	PUNCT
ejpam-4356	297	16	=	=	PUNCT
ejpam-4356	298	1	k.	k.	PROPN
ejpam-4356	298	2	suppose	suppose	VERB
ejpam-4356	298	3	that	that	SCONJ
ejpam-4356	298	4	|s	|s	PROPN
ejpam-4356	298	5	∩	∩	PROPN
ejpam-4356	298	6	v	v	X
ejpam-4356	298	7	(	(	PUNCT
ejpam-4356	298	8	k)|	k)|	NOUN
ejpam-4356	298	9	≥	≥	NOUN
ejpam-4356	298	10	2	2	NUM
ejpam-4356	298	11	.	.	PUNCT
ejpam-4356	298	12	in	in	ADP
ejpam-4356	298	13	here	here	ADV
ejpam-4356	298	14	,	,	PUNCT
ejpam-4356	298	15	we	we	PRON
ejpam-4356	298	16	consider	consider	VERB
ejpam-4356	298	17	two	two	NUM
ejpam-4356	298	18	subcases	subcase	NOUN
ejpam-4356	298	19	,	,	PUNCT
ejpam-4356	298	20	subcase	subcase	NOUN
ejpam-4356	298	21	1	1	NUM
ejpam-4356	298	22	.	.	PUNCT
ejpam-4356	298	23	when	when	SCONJ
ejpam-4356	298	24	dg(x	dg(x	NUM
ejpam-4356	298	25	,	,	PUNCT
ejpam-4356	298	26	y	y	NOUN
ejpam-4356	298	27	)	)	PUNCT
ejpam-4356	298	28	=	=	SYM
ejpam-4356	298	29	1	1	NUM
ejpam-4356	298	30	for	for	ADP
ejpam-4356	298	31	all	all	DET
ejpam-4356	298	32	x	x	NOUN
ejpam-4356	298	33	,	,	PUNCT
ejpam-4356	298	34	y	y	PROPN
ejpam-4356	298	35	∈	∈	PROPN
ejpam-4356	298	36	s	s	PART
ejpam-4356	298	37	∩	∩	ADJ
ejpam-4356	298	38	v	v	X
ejpam-4356	298	39	(	(	PUNCT
ejpam-4356	298	40	k	k	NOUN
ejpam-4356	298	41	)	)	PUNCT
ejpam-4356	298	42	;	;	PUNCT
ejpam-4356	298	43	and	and	CCONJ
ejpam-4356	298	44	subcase	subcase	NOUN
ejpam-4356	298	45	2	2	NUM
ejpam-4356	298	46	.	.	PUNCT
ejpam-4356	298	47	when	when	SCONJ
ejpam-4356	298	48	for	for	ADP
ejpam-4356	298	49	some	some	DET
ejpam-4356	298	50	x	x	NOUN
ejpam-4356	298	51	,	,	PUNCT
ejpam-4356	298	52	y	y	PROPN
ejpam-4356	298	53	∈	∈	PROPN
ejpam-4356	298	54	s	s	VERB
ejpam-4356	298	55	⋂	⋂	PROPN
ejpam-4356	298	56	v	v	X
ejpam-4356	298	57	(	(	PUNCT
ejpam-4356	298	58	k	k	NOUN
ejpam-4356	298	59	)	)	PUNCT
ejpam-4356	298	60	,	,	PUNCT
ejpam-4356	298	61	dg(x	dg(x	X
ejpam-4356	298	62	,	,	PUNCT
ejpam-4356	298	63	y	y	NOUN
ejpam-4356	298	64	)	)	PUNCT
ejpam-4356	298	65	=	=	SYM
ejpam-4356	298	66	2	2	X
ejpam-4356	298	67	.	.	PUNCT
ejpam-4356	298	68	suppose	suppose	VERB
ejpam-4356	298	69	that	that	SCONJ
ejpam-4356	298	70	dg(x	dg(x	PROPN
ejpam-4356	298	71	,	,	PUNCT
ejpam-4356	298	72	y	y	NOUN
ejpam-4356	298	73	)	)	PUNCT
ejpam-4356	298	74	=	=	SYM
ejpam-4356	298	75	1	1	NUM
ejpam-4356	298	76	for	for	ADP
ejpam-4356	298	77	all	all	DET
ejpam-4356	298	78	x	x	NOUN
ejpam-4356	298	79	,	,	PUNCT
ejpam-4356	299	1	y	y	PROPN
ejpam-4356	299	2	∈	∈	PROPN
ejpam-4356	299	3	s	s	PART
ejpam-4356	299	4	∩	∩	ADJ
ejpam-4356	299	5	v	v	X
ejpam-4356	299	6	(	(	PUNCT
ejpam-4356	299	7	k	k	NOUN
ejpam-4356	299	8	)	)	PUNCT
ejpam-4356	299	9	=	=	SYM
ejpam-4356	299	10	{	{	PUNCT
ejpam-4356	299	11	yr1	yr1	PROPN
ejpam-4356	299	12	,	,	PUNCT
ejpam-4356	299	13	yr2	yr2	PROPN
ejpam-4356	299	14	,	,	PUNCT
ejpam-4356	299	15	...	...	PUNCT
ejpam-4356	299	16	,	,	PUNCT
ejpam-4356	299	17	yrl	yrl	PROPN
ejpam-4356	299	18	}	}	PUNCT
ejpam-4356	299	19	.	.	PUNCT
ejpam-4356	300	1	then	then	ADV
ejpam-4356	300	2	rn	rn	PROPN
ejpam-4356	300	3	<	<	X
ejpam-4356	300	4	j	j	PROPN
ejpam-4356	300	5	for	for	ADP
ejpam-4356	300	6	all	all	DET
ejpam-4356	300	7	n	n	NOUN
ejpam-4356	300	8	=	=	SYM
ejpam-4356	300	9	1	1	NUM
ejpam-4356	300	10	,	,	PUNCT
ejpam-4356	300	11	2	2	NUM
ejpam-4356	300	12	,	,	PUNCT
ejpam-4356	300	13	...	...	PUNCT
ejpam-4356	300	14	,	,	PUNCT
ejpam-4356	300	15	l.	l.	PROPN
ejpam-4356	300	16	we	we	PRON
ejpam-4356	300	17	consider	consider	VERB
ejpam-4356	300	18	the	the	DET
ejpam-4356	300	19	set	set	NOUN
ejpam-4356	300	20	s∗	s∗	PROPN
ejpam-4356	300	21	=	=	SYM
ejpam-4356	300	22	s	s	PROPN
ejpam-4356	300	23	∩	∩	ADJ
ejpam-4356	300	24	v	v	ADJ
ejpam-4356	300	25	(	(	PUNCT
ejpam-4356	300	26	h	h	NOUN
ejpam-4356	300	27	)	)	PUNCT
ejpam-4356	300	28	.	.	PUNCT
ejpam-4356	301	1	write	write	VERB
ejpam-4356	301	2	s∗	s∗	PROPN
ejpam-4356	301	3	=	=	SYM
ejpam-4356	301	4	{	{	PUNCT
ejpam-4356	301	5	x1	x1	PROPN
ejpam-4356	301	6	,	,	PUNCT
ejpam-4356	301	7	x2	x2	PROPN
ejpam-4356	301	8	,	,	PUNCT
ejpam-4356	301	9	...	...	PUNCT
ejpam-4356	301	10	,	,	PUNCT
ejpam-4356	301	11	xk−l	xk−l	PROPN
ejpam-4356	301	12	}	}	PUNCT
ejpam-4356	301	13	such	such	ADJ
ejpam-4356	301	14	that	that	SCONJ
ejpam-4356	301	15	if	if	SCONJ
ejpam-4356	301	16	xn	xn	NOUN
ejpam-4356	301	17	=	=	SYM
ejpam-4356	301	18	yp	yp	PROPN
ejpam-4356	301	19	and	and	CCONJ
ejpam-4356	301	20	xm	xm	PROPN
ejpam-4356	301	21	=	=	SYM
ejpam-4356	301	22	yq	yq	PROPN
ejpam-4356	301	23	,	,	PUNCT
ejpam-4356	301	24	then	then	ADV
ejpam-4356	301	25	n	n	CCONJ
ejpam-4356	301	26	<	<	X
ejpam-4356	301	27	m	m	NOUN
ejpam-4356	301	28	if	if	SCONJ
ejpam-4356	301	29	and	and	CCONJ
ejpam-4356	301	30	only	only	ADV
ejpam-4356	301	31	if	if	SCONJ
ejpam-4356	301	32	p	p	X
ejpam-4356	301	33	<	<	X
ejpam-4356	301	34	q.	q.	PROPN
ejpam-4356	301	35	since	since	SCONJ
ejpam-4356	301	36	yi	yi	PROPN
ejpam-4356	301	37	,	,	PUNCT
ejpam-4356	301	38	yj	yj	PROPN
ejpam-4356	301	39	∈	∈	PROPN
ejpam-4356	301	40	s∗	s∗	PROPN
ejpam-4356	301	41	,	,	PUNCT
ejpam-4356	301	42	we	we	PRON
ejpam-4356	301	43	have	have	VERB
ejpam-4356	301	44	for	for	ADP
ejpam-4356	301	45	every	every	DET
ejpam-4356	301	46	n	n	NOUN
ejpam-4356	301	47	=	=	SYM
ejpam-4356	301	48	1	1	NUM
ejpam-4356	301	49	,	,	PUNCT
ejpam-4356	301	50	2	2	NUM
ejpam-4356	301	51	,	,	PUNCT
ejpam-4356	301	52	...	...	PUNCT
ejpam-4356	301	53	,	,	PUNCT
ejpam-4356	301	54	l	l	NOUN
ejpam-4356	301	55	,	,	PUNCT
ejpam-4356	301	56	ig[x	ig[x	PROPN
ejpam-4356	301	57	,	,	PUNCT
ejpam-4356	301	58	yrn	yrn	X
ejpam-4356	301	59	]	]	X
ejpam-4356	301	60	=	=	PUNCT
ejpam-4356	301	61	{	{	PUNCT
ejpam-4356	301	62	x	x	NOUN
ejpam-4356	301	63	,	,	PUNCT
ejpam-4356	301	64	yrn	yrn	INTJ
ejpam-4356	301	65	}	}	PUNCT
ejpam-4356	301	66	⊆	⊆	NUM
ejpam-4356	301	67	ig[s	ig[s	PROPN
ejpam-4356	301	68	∗	∗	NOUN
ejpam-4356	301	69	]	]	PUNCT
ejpam-4356	301	70	for	for	ADP
ejpam-4356	301	71	all	all	DET
ejpam-4356	301	72	x	x	PROPN
ejpam-4356	301	73	∈	∈	PROPN
ejpam-4356	301	74	s.	s.	PROPN
ejpam-4356	301	75	thus	thus	ADV
ejpam-4356	301	76	,	,	PUNCT
ejpam-4356	301	77	ig[s	ig[s	PROPN
ejpam-4356	301	78	∗	∗	NOUN
ejpam-4356	301	79	]	]	PUNCT
ejpam-4356	302	1	=	=	SYM
ejpam-4356	302	2	ig[s	ig[s	PROPN
ejpam-4356	302	3	]	]	X
ejpam-4356	302	4	=	=	SYM
ejpam-4356	302	5	v	v	X
ejpam-4356	302	6	(	(	PUNCT
ejpam-4356	302	7	g	g	NOUN
ejpam-4356	302	8	)	)	PUNCT
ejpam-4356	302	9	.	.	PUNCT
ejpam-4356	303	1	hence	hence	ADV
ejpam-4356	303	2	,	,	PUNCT
ejpam-4356	303	3	there	there	PRON
ejpam-4356	303	4	exists	exist	VERB
ejpam-4356	303	5	z	z	PROPN
ejpam-4356	303	6	∈	∈	PROPN
ejpam-4356	303	7	v	v	ADP
ejpam-4356	303	8	(	(	PUNCT
ejpam-4356	303	9	g	g	NOUN
ejpam-4356	303	10	)	)	PUNCT
ejpam-4356	303	11	\	\	NOUN
ejpam-4356	303	12	s∗	s∗	VERB
ejpam-4356	303	13	such	such	ADJ
ejpam-4356	303	14	that	that	SCONJ
ejpam-4356	303	15	z	z	NOUN
ejpam-4356	303	16	lies	lie	VERB
ejpam-4356	303	17	in	in	ADP
ejpam-4356	303	18	x	x	ADJ
ejpam-4356	303	19	-	-	NOUN
ejpam-4356	303	20	yrn	yrn	PRON
ejpam-4356	303	21	geodesic	geodesic	NOUN
ejpam-4356	303	22	.	.	PUNCT
ejpam-4356	304	1	thus	thus	ADV
ejpam-4356	304	2	,	,	PUNCT
ejpam-4356	304	3	ng[s	ng[s	PROPN
ejpam-4356	304	4	∗	∗	NOUN
ejpam-4356	304	5	]	]	X
ejpam-4356	304	6	=	=	SYM
ejpam-4356	304	7	ng[s	ng[s	PROPN
ejpam-4356	304	8	]	]	X
ejpam-4356	304	9	=	=	SYM
ejpam-4356	304	10	v	v	X
ejpam-4356	304	11	(	(	PUNCT
ejpam-4356	304	12	g	g	NOUN
ejpam-4356	304	13	)	)	PUNCT
ejpam-4356	304	14	and	and	CCONJ
ejpam-4356	304	15	xz	xz	PROPN
ejpam-4356	304	16	,	,	PUNCT
ejpam-4356	304	17	yz	yz	PROPN
ejpam-4356	304	18	∈	∈	PROPN
ejpam-4356	304	19	e(⟨s⟩w	e(⟨s⟩w	PROPN
ejpam-4356	304	20	)	)	PUNCT
ejpam-4356	304	21	for	for	ADP
ejpam-4356	304	22	all	all	DET
ejpam-4356	304	23	z	z	NOUN
ejpam-4356	304	24	∈	∈	PROPN
ejpam-4356	304	25	v	v	ADP
ejpam-4356	304	26	(	(	PUNCT
ejpam-4356	304	27	g	g	NOUN
ejpam-4356	304	28	)	)	PUNCT
ejpam-4356	304	29	\	\	VERB
ejpam-4356	305	1	s∗.	s∗.	ADJ
ejpam-4356	305	2	this	this	PRON
ejpam-4356	305	3	means	mean	VERB
ejpam-4356	305	4	that	that	SCONJ
ejpam-4356	305	5	s∗	s∗	PROPN
ejpam-4356	305	6	∈	∈	PROPN
ejpam-4356	305	7	w(g	w(g	PROPN
ejpam-4356	305	8	)	)	PUNCT
ejpam-4356	305	9	.	.	PUNCT
ejpam-4356	306	1	the	the	DET
ejpam-4356	306	2	fact	fact	NOUN
ejpam-4356	306	3	that	that	SCONJ
ejpam-4356	306	4	k	k	X
ejpam-4356	306	5	-	-	PUNCT
ejpam-4356	306	6	l	l	NOUN
ejpam-4356	306	7	<	<	X
ejpam-4356	306	8	k	k	X
ejpam-4356	306	9	,	,	PUNCT
ejpam-4356	306	10	a	a	DET
ejpam-4356	306	11	contradiction	contradiction	NOUN
ejpam-4356	306	12	.	.	PUNCT
ejpam-4356	307	1	lastly	lastly	ADV
ejpam-4356	307	2	,	,	PUNCT
ejpam-4356	307	3	suppose	suppose	VERB
ejpam-4356	307	4	that	that	SCONJ
ejpam-4356	307	5	dg(ym	dg(ym	PROPN
ejpam-4356	307	6	,	,	PUNCT
ejpam-4356	307	7	yn	yn	PROPN
ejpam-4356	307	8	)	)	PUNCT
ejpam-4356	307	9	=	=	SYM
ejpam-4356	307	10	2	2	NUM
ejpam-4356	307	11	for	for	ADP
ejpam-4356	307	12	some	some	DET
ejpam-4356	307	13	ym	ym	NOUN
ejpam-4356	307	14	,	,	PUNCT
ejpam-4356	307	15	yn	yn	PROPN
ejpam-4356	307	16	∈	∈	PROPN
ejpam-4356	307	17	s	s	PART
ejpam-4356	307	18	∩	∩	ADJ
ejpam-4356	307	19	v	v	X
ejpam-4356	307	20	(	(	PUNCT
ejpam-4356	307	21	k	k	NOUN
ejpam-4356	307	22	)	)	PUNCT
ejpam-4356	307	23	with	with	ADP
ejpam-4356	307	24	m	m	PROPN
ejpam-4356	307	25	<	<	X
ejpam-4356	307	26	n.	n.	NOUN
ejpam-4356	307	27	again	again	ADV
ejpam-4356	307	28	,	,	PUNCT
ejpam-4356	307	29	we	we	PRON
ejpam-4356	307	30	must	must	AUX
ejpam-4356	307	31	have	have	VERB
ejpam-4356	307	32	n	n	PROPN
ejpam-4356	307	33	<	<	X
ejpam-4356	307	34	j.	j.	PROPN
ejpam-4356	308	1	but	but	CCONJ
ejpam-4356	308	2	,	,	PUNCT
ejpam-4356	308	3	if	if	SCONJ
ejpam-4356	308	4	dg(ym	dg(ym	PROPN
ejpam-4356	308	5	,	,	PUNCT
ejpam-4356	308	6	yn	yn	PROPN
ejpam-4356	308	7	)	)	PUNCT
ejpam-4356	308	8	=	=	SYM
ejpam-4356	308	9	2	2	NUM
ejpam-4356	308	10	,	,	PUNCT
ejpam-4356	308	11	then	then	ADV
ejpam-4356	308	12	v	v	X
ejpam-4356	308	13	(	(	PUNCT
ejpam-4356	308	14	h	h	NOUN
ejpam-4356	308	15	)	)	PUNCT
ejpam-4356	308	16	⊆	⊆	NUM
ejpam-4356	308	17	ig[ym	ig[ym	NOUN
ejpam-4356	308	18	,	,	PUNCT
ejpam-4356	308	19	yn	yn	X
ejpam-4356	308	20	]	]	X
ejpam-4356	308	21	,	,	PUNCT
ejpam-4356	308	22	and	and	CCONJ
ejpam-4356	308	23	in	in	ADP
ejpam-4356	308	24	particular	particular	ADJ
ejpam-4356	308	25	,	,	PUNCT
ejpam-4356	308	26	yj	yj	PROPN
ejpam-4356	308	27	∈	∈	PROPN
ejpam-4356	308	28	ig[ym	ig[ym	PROPN
ejpam-4356	308	29	,	,	PUNCT
ejpam-4356	308	30	yn	yn	X
ejpam-4356	308	31	]	]	PUNCT
ejpam-4356	308	32	.	.	PUNCT
ejpam-4356	309	1	but	but	CCONJ
ejpam-4356	309	2	by	by	ADP
ejpam-4356	309	3	definition	definition	NOUN
ejpam-4356	309	4	of	of	ADP
ejpam-4356	309	5	s	s	PROPN
ejpam-4356	309	6	,	,	PUNCT
ejpam-4356	309	7	yj	yj	PROPN
ejpam-4356	309	8	/∈	/∈	PUNCT
ejpam-4356	309	9	ig[sn	ig[sn	NOUN
ejpam-4356	309	10	]	]	PUNCT
ejpam-4356	309	11	.	.	PUNCT
ejpam-4356	310	1	it	it	PRON
ejpam-4356	310	2	follows	follow	VERB
ejpam-4356	310	3	that	that	SCONJ
ejpam-4356	310	4	yj	yj	PROPN
ejpam-4356	310	5	/∈	/∈	PUNCT
ejpam-4356	310	6	ng[sn	ng[sn	ADV
ejpam-4356	310	7	]	]	PUNCT
ejpam-4356	310	8	.	.	PUNCT
ejpam-4356	311	1	hence	hence	ADV
ejpam-4356	311	2	,	,	PUNCT
ejpam-4356	311	3	ng[sn	ng[sn	ADV
ejpam-4356	311	4	]	]	PUNCT
ejpam-4356	311	5	̸=	̸=	PROPN
ejpam-4356	311	6	v	v	NOUN
ejpam-4356	311	7	(	(	PUNCT
ejpam-4356	311	8	g	g	NOUN
ejpam-4356	311	9	)	)	PUNCT
ejpam-4356	311	10	.	.	PUNCT
ejpam-4356	312	1	thus	thus	ADV
ejpam-4356	312	2	,	,	PUNCT
ejpam-4356	312	3	sn	sn	PROPN
ejpam-4356	312	4	/∈	/∈	PUNCT
ejpam-4356	312	5	w(g	w(g	PROPN
ejpam-4356	312	6	)	)	PUNCT
ejpam-4356	312	7	,	,	PUNCT
ejpam-4356	312	8	a	a	DET
ejpam-4356	312	9	contradiction	contradiction	NOUN
ejpam-4356	312	10	.	.	PUNCT
ejpam-4356	313	1	now	now	ADV
ejpam-4356	313	2	,	,	PUNCT
ejpam-4356	313	3	we	we	PRON
ejpam-4356	313	4	are	be	AUX
ejpam-4356	313	5	left	leave	VERB
ejpam-4356	313	6	to	to	PART
ejpam-4356	313	7	show	show	VERB
ejpam-4356	313	8	that	that	SCONJ
ejpam-4356	313	9	s	s	VERB
ejpam-4356	313	10	is	be	AUX
ejpam-4356	313	11	a	a	DET
ejpam-4356	313	12	2	2	NUM
ejpam-4356	313	13	-	-	PUNCT
ejpam-4356	313	14	path	path	NOUN
ejpam-4356	313	15	closure	closure	NOUN
ejpam-4356	313	16	absorbing	absorb	VERB
ejpam-4356	313	17	in	in	ADP
ejpam-4356	313	18	h.	h.	PROPN
ejpam-4356	313	19	suppose	suppose	VERB
ejpam-4356	313	20	that	that	SCONJ
ejpam-4356	313	21	s	s	VERB
ejpam-4356	313	22	⊆	⊆	NUM
ejpam-4356	313	23	v	v	NOUN
ejpam-4356	313	24	(	(	PUNCT
ejpam-4356	313	25	h	h	NOUN
ejpam-4356	313	26	)	)	PUNCT
ejpam-4356	313	27	.	.	PUNCT
ejpam-4356	314	1	by	by	ADP
ejpam-4356	314	2	theorem	theorem	NOUN
ejpam-4356	314	3	16	16	NUM
ejpam-4356	314	4	and	and	CCONJ
ejpam-4356	314	5	lemma	lemma	PROPN
ejpam-4356	314	6	3	3	NUM
ejpam-4356	314	7	,	,	PUNCT
ejpam-4356	314	8	p2[s]g	p2[s]g	PROPN
ejpam-4356	314	9	=	=	SYM
ejpam-4356	314	10	v	v	PROPN
ejpam-4356	314	11	(	(	PUNCT
ejpam-4356	314	12	g	g	NOUN
ejpam-4356	314	13	)	)	PUNCT
ejpam-4356	314	14	.	.	PUNCT
ejpam-4356	315	1	let	let	VERB
ejpam-4356	315	2	z	z	NOUN
ejpam-4356	315	3	∈	∈	PROPN
ejpam-4356	315	4	v	v	ADP
ejpam-4356	315	5	(	(	PUNCT
ejpam-4356	315	6	h	h	NOUN
ejpam-4356	315	7	)	)	PUNCT
ejpam-4356	315	8	\	\	PUNCT
ejpam-4356	316	1	s.	s.	PROPN
ejpam-4356	316	2	then	then	ADV
ejpam-4356	316	3	z	z	PROPN
ejpam-4356	316	4	∈	∈	PROPN
ejpam-4356	316	5	v	v	ADP
ejpam-4356	316	6	(	(	PUNCT
ejpam-4356	316	7	g	g	NOUN
ejpam-4356	316	8	)	)	PUNCT
ejpam-4356	316	9	\	\	PROPN
ejpam-4356	317	1	s	s	X
ejpam-4356	317	2	,	,	PUNCT
ejpam-4356	317	3	and	and	CCONJ
ejpam-4356	317	4	there	there	PRON
ejpam-4356	317	5	exist	exist	VERB
ejpam-4356	317	6	x	x	NOUN
ejpam-4356	317	7	,	,	PUNCT
ejpam-4356	317	8	y	y	PROPN
ejpam-4356	317	9	∈	∈	PROPN
ejpam-4356	317	10	s	s	VERB
ejpam-4356	317	11	such	such	ADJ
ejpam-4356	317	12	that	that	SCONJ
ejpam-4356	317	13	z	z	PROPN
ejpam-4356	317	14	∈	∈	PROPN
ejpam-4356	317	15	ig[x	ig[x	PROPN
ejpam-4356	317	16	,	,	PUNCT
ejpam-4356	317	17	y	y	PROPN
ejpam-4356	317	18	]	]	PUNCT
ejpam-4356	317	19	and	and	CCONJ
ejpam-4356	317	20	dg(x	dg(x	NUM
ejpam-4356	317	21	,	,	PUNCT
ejpam-4356	317	22	y	y	NOUN
ejpam-4356	317	23	)	)	PUNCT
ejpam-4356	317	24	=	=	SYM
ejpam-4356	318	1	2	2	X
ejpam-4356	318	2	.	.	PUNCT
ejpam-4356	318	3	this	this	PRON
ejpam-4356	318	4	implies	imply	VERB
ejpam-4356	318	5	that	that	SCONJ
ejpam-4356	318	6	[	[	X
ejpam-4356	318	7	x	x	X
ejpam-4356	318	8	,	,	PUNCT
ejpam-4356	318	9	z	z	PROPN
ejpam-4356	318	10	,	,	PUNCT
ejpam-4356	318	11	y	y	PROPN
ejpam-4356	318	12	]	]	X
ejpam-4356	318	13	is	be	AUX
ejpam-4356	318	14	a	a	DET
ejpam-4356	318	15	x	x	NOUN
ejpam-4356	318	16	-	-	NOUN
ejpam-4356	318	17	y	y	ADJ
ejpam-4356	318	18	geodesic	geodesic	NOUN
ejpam-4356	318	19	in	in	ADP
ejpam-4356	318	20	h.	h.	PROPN
ejpam-4356	318	21	thus	thus	ADV
ejpam-4356	318	22	,	,	PUNCT
ejpam-4356	318	23	z	z	PROPN
ejpam-4356	318	24	∈	∈	PROPN
ejpam-4356	318	25	ih	ih	X
ejpam-4356	319	1	[	[	X
ejpam-4356	319	2	x	x	X
ejpam-4356	319	3	,	,	PUNCT
ejpam-4356	319	4	y	y	PROPN
ejpam-4356	319	5	]	]	X
ejpam-4356	319	6	and	and	CCONJ
ejpam-4356	319	7	dh(x	dh(x	PROPN
ejpam-4356	319	8	,	,	PUNCT
ejpam-4356	319	9	y	y	NOUN
ejpam-4356	319	10	)	)	PUNCT
ejpam-4356	319	11	=	=	SYM
ejpam-4356	319	12	2	2	X
ejpam-4356	319	13	.	.	PUNCT
ejpam-4356	319	14	this	this	PRON
ejpam-4356	319	15	means	mean	VERB
ejpam-4356	319	16	that	that	SCONJ
ejpam-4356	319	17	p2[s]h	p2[s]h	PRON
ejpam-4356	319	18	=	=	PUNCT
ejpam-4356	319	19	v	v	PROPN
ejpam-4356	319	20	(	(	PUNCT
ejpam-4356	319	21	h	h	NOUN
ejpam-4356	319	22	)	)	PUNCT
ejpam-4356	319	23	,	,	PUNCT
ejpam-4356	319	24	and	and	CCONJ
ejpam-4356	319	25	so	so	ADV
ejpam-4356	319	26	s	s	VERB
ejpam-4356	319	27	is	be	AUX
ejpam-4356	319	28	a	a	DET
ejpam-4356	319	29	2	2	NUM
ejpam-4356	319	30	-	-	PUNCT
ejpam-4356	319	31	path	path	NOUN
ejpam-4356	319	32	closure	closure	NOUN
ejpam-4356	319	33	absorbing	absorb	VERB
ejpam-4356	319	34	in	in	ADP
ejpam-4356	319	35	h.	h.	PROPN
ejpam-4356	319	36	similarly	similarly	ADV
ejpam-4356	319	37	,	,	PUNCT
ejpam-4356	319	38	if	if	SCONJ
ejpam-4356	319	39	yi	yi	PROPN
ejpam-4356	319	40	,	,	PUNCT
ejpam-4356	319	41	yj	yj	PROPN
ejpam-4356	319	42	∈	∈	PROPN
ejpam-4356	319	43	v	v	ADP
ejpam-4356	319	44	(	(	PUNCT
ejpam-4356	319	45	k	k	NOUN
ejpam-4356	319	46	)	)	PUNCT
ejpam-4356	319	47	,	,	PUNCT
ejpam-4356	319	48	then	then	ADV
ejpam-4356	319	49	s	s	VERB
ejpam-4356	319	50	⊆	⊆	NUM
ejpam-4356	319	51	v	v	NOUN
ejpam-4356	319	52	(	(	PUNCT
ejpam-4356	319	53	k	k	NOUN
ejpam-4356	319	54	)	)	PUNCT
ejpam-4356	319	55	.	.	PUNCT
ejpam-4356	320	1	moreover	moreover	ADV
ejpam-4356	320	2	,	,	PUNCT
ejpam-4356	320	3	if	if	SCONJ
ejpam-4356	320	4	s	s	VERB
ejpam-4356	320	5	⊆	⊆	NUM
ejpam-4356	320	6	v	v	NOUN
ejpam-4356	320	7	(	(	PUNCT
ejpam-4356	320	8	k	k	NOUN
ejpam-4356	320	9	)	)	PUNCT
ejpam-4356	320	10	,	,	PUNCT
ejpam-4356	320	11	then	then	ADV
ejpam-4356	320	12	s	s	VERB
ejpam-4356	320	13	is	be	AUX
ejpam-4356	320	14	a	a	DET
ejpam-4356	320	15	2	2	NUM
ejpam-4356	320	16	-	-	PUNCT
ejpam-4356	320	17	path	path	NOUN
ejpam-4356	320	18	closure	closure	NOUN
ejpam-4356	320	19	absorbing	absorb	VERB
ejpam-4356	320	20	in	in	ADP
ejpam-4356	320	21	k.	k.	PROPN
ejpam-4356	320	22	theorem	theorem	PROPN
ejpam-4356	320	23	18	18	NUM
ejpam-4356	320	24	.	.	PUNCT
ejpam-4356	321	1	let	let	VERB
ejpam-4356	321	2	g	g	NOUN
ejpam-4356	321	3	=	=	PUNCT
ejpam-4356	321	4	h	h	PROPN
ejpam-4356	322	1	+	+	CCONJ
ejpam-4356	322	2	k	k	ADJ
ejpam-4356	322	3	,	,	PUNCT
ejpam-4356	323	1	where	where	SCONJ
ejpam-4356	323	2	h	h	NOUN
ejpam-4356	323	3	and	and	CCONJ
ejpam-4356	323	4	k	k	PROPN
ejpam-4356	323	5	are	be	AUX
ejpam-4356	323	6	connected	connect	VERB
ejpam-4356	323	7	noncomplete	noncomplete	ADJ
ejpam-4356	323	8	graphs	graph	NOUN
ejpam-4356	323	9	.	.	PUNCT
ejpam-4356	324	1	if	if	SCONJ
ejpam-4356	324	2	either	either	PRON
ejpam-4356	324	3	(	(	PUNCT
ejpam-4356	324	4	i.	i.	NOUN
ejpam-4356	324	5	)	)	PUNCT
ejpam-4356	324	6	s	s	PART
ejpam-4356	324	7	⊆	⊆	NUM
ejpam-4356	324	8	v	v	NOUN
ejpam-4356	324	9	(	(	PUNCT
ejpam-4356	324	10	h	h	NOUN
ejpam-4356	324	11	)	)	PUNCT
ejpam-4356	324	12	,	,	PUNCT
ejpam-4356	324	13	where	where	SCONJ
ejpam-4356	324	14	s	s	NOUN
ejpam-4356	324	15	is	be	AUX
ejpam-4356	324	16	a	a	DET
ejpam-4356	324	17	2	2	NUM
ejpam-4356	324	18	-	-	PUNCT
ejpam-4356	324	19	path	path	NOUN
ejpam-4356	324	20	closure	closure	NOUN
ejpam-4356	324	21	absorbing	absorb	VERB
ejpam-4356	324	22	set	set	NOUN
ejpam-4356	324	23	in	in	ADP
ejpam-4356	324	24	h	h	NOUN
ejpam-4356	324	25	and	and	CCONJ
ejpam-4356	324	26	s	s	PROPN
ejpam-4356	324	27	∈	∈	PROPN
ejpam-4356	324	28	w(h	w(h	PROPN
ejpam-4356	324	29	)	)	PUNCT
ejpam-4356	324	30	or	or	CCONJ
ejpam-4356	324	31	(	(	PUNCT
ejpam-4356	324	32	ii	ii	NOUN
ejpam-4356	324	33	.	.	PUNCT
ejpam-4356	324	34	)	)	PUNCT
ejpam-4356	324	35	s	s	PART
ejpam-4356	324	36	⊆	⊆	NUM
ejpam-4356	324	37	v	v	NOUN
ejpam-4356	324	38	(	(	PUNCT
ejpam-4356	324	39	k	k	NOUN
ejpam-4356	324	40	)	)	PUNCT
ejpam-4356	324	41	,	,	PUNCT
ejpam-4356	324	42	where	where	SCONJ
ejpam-4356	324	43	s	s	NOUN
ejpam-4356	324	44	is	be	AUX
ejpam-4356	324	45	a	a	DET
ejpam-4356	324	46	2	2	NUM
ejpam-4356	324	47	-	-	PUNCT
ejpam-4356	324	48	path	path	NOUN
ejpam-4356	324	49	closure	closure	NOUN
ejpam-4356	324	50	absorbing	absorb	VERB
ejpam-4356	324	51	set	set	NOUN
ejpam-4356	324	52	in	in	ADP
ejpam-4356	324	53	k	k	PROPN
ejpam-4356	324	54	and	and	CCONJ
ejpam-4356	324	55	s	s	PROPN
ejpam-4356	324	56	∈	∈	PROPN
ejpam-4356	324	57	w(k	w(k	PROPN
ejpam-4356	324	58	)	)	PUNCT
ejpam-4356	324	59	,	,	PUNCT
ejpam-4356	324	60	then	then	ADV
ejpam-4356	324	61	s	s	VERB
ejpam-4356	324	62	∈	∈	PROPN
ejpam-4356	324	63	w(g	w(g	PROPN
ejpam-4356	324	64	)	)	PUNCT
ejpam-4356	324	65	.	.	PUNCT
ejpam-4356	325	1	j.	j.	PROPN
ejpam-4356	325	2	hamja	hamja	PROPN
ejpam-4356	325	3	,	,	PUNCT
ejpam-4356	325	4	i.	i.	PROPN
ejpam-4356	325	5	aniversario	aniversario	PROPN
ejpam-4356	325	6	,	,	PUNCT
ejpam-4356	325	7	h.	h.	PROPN
ejpam-4356	325	8	rara	rara	PROPN
ejpam-4356	325	9	/	/	SYM
ejpam-4356	325	10	eur	eur	PROPN
ejpam-4356	325	11	.	.	PUNCT
ejpam-4356	326	1	j.	j.	PROPN
ejpam-4356	326	2	pure	pure	PROPN
ejpam-4356	326	3	appl	appl	PROPN
ejpam-4356	326	4	.	.	PROPN
ejpam-4356	326	5	math	math	PROPN
ejpam-4356	326	6	,	,	PUNCT
ejpam-4356	326	7	15	15	NUM
ejpam-4356	326	8	(	(	PUNCT
ejpam-4356	326	9	2	2	NUM
ejpam-4356	326	10	)	)	PUNCT
ejpam-4356	326	11	(	(	PUNCT
ejpam-4356	326	12	2022	2022	NUM
ejpam-4356	326	13	)	)	PUNCT
ejpam-4356	326	14	,	,	PUNCT
ejpam-4356	326	15	736	736	NUM
ejpam-4356	326	16	-	-	SYM
ejpam-4356	326	17	752	752	NUM
ejpam-4356	326	18	746	746	NUM
ejpam-4356	326	19	theorem	theorem	NOUN
ejpam-4356	326	20	19	19	NUM
ejpam-4356	326	21	.	.	PUNCT
ejpam-4356	327	1	let	let	VERB
ejpam-4356	327	2	g	g	NOUN
ejpam-4356	327	3	=	=	PUNCT
ejpam-4356	327	4	h	h	PROPN
ejpam-4356	328	1	+	+	CCONJ
ejpam-4356	328	2	k	k	ADJ
ejpam-4356	328	3	,	,	PUNCT
ejpam-4356	329	1	where	where	SCONJ
ejpam-4356	329	2	h	h	NOUN
ejpam-4356	329	3	and	and	CCONJ
ejpam-4356	329	4	k	k	PROPN
ejpam-4356	329	5	are	be	AUX
ejpam-4356	329	6	connected	connect	VERB
ejpam-4356	329	7	noncomplete	noncomplete	ADJ
ejpam-4356	329	8	graphs	graph	NOUN
ejpam-4356	329	9	.	.	PUNCT
ejpam-4356	330	1	then	then	ADV
ejpam-4356	330	2	γwcg(g	γwcg(g	NOUN
ejpam-4356	330	3	)	)	PUNCT
ejpam-4356	330	4	=	=	SYM
ejpam-4356	330	5	min{γ(h),γ(k	min{γ(h),γ(k	PROPN
ejpam-4356	330	6	)	)	PUNCT
ejpam-4356	330	7	}	}	PUNCT
ejpam-4356	330	8	,	,	PUNCT
ejpam-4356	330	9	where	where	SCONJ
ejpam-4356	330	10	γ(h	γ(h	NOUN
ejpam-4356	330	11	)	)	PUNCT
ejpam-4356	330	12	=	=	SYM
ejpam-4356	330	13	min{|s|	min{|s|	NOUN
ejpam-4356	330	14	:	:	PUNCT
ejpam-4356	330	15	s	s	VERB
ejpam-4356	330	16	⊆	⊆	NUM
ejpam-4356	330	17	v	v	NOUN
ejpam-4356	330	18	(	(	PUNCT
ejpam-4356	330	19	h	h	NOUN
ejpam-4356	330	20	)	)	PUNCT
ejpam-4356	330	21	,	,	PUNCT
ejpam-4356	330	22	s	s	PROPN
ejpam-4356	330	23	∈	∈	PROPN
ejpam-4356	330	24	w(g	w(g	PROPN
ejpam-4356	330	25	)	)	PUNCT
ejpam-4356	330	26	and	and	CCONJ
ejpam-4356	330	27	p2[s]h	p2[s]h	PROPN
ejpam-4356	330	28	=	=	PUNCT
ejpam-4356	330	29	v	v	PROPN
ejpam-4356	330	30	(	(	PUNCT
ejpam-4356	330	31	h	h	NOUN
ejpam-4356	330	32	)	)	PUNCT
ejpam-4356	330	33	}	}	PUNCT
ejpam-4356	330	34	and	and	CCONJ
ejpam-4356	330	35	γ(k	γ(k	PROPN
ejpam-4356	330	36	)	)	PUNCT
ejpam-4356	331	1	=	=	SYM
ejpam-4356	331	2	min{|s|	min{|s|	NOUN
ejpam-4356	331	3	:	:	PUNCT
ejpam-4356	331	4	s	s	VERB
ejpam-4356	331	5	⊆	⊆	NUM
ejpam-4356	331	6	v	v	NOUN
ejpam-4356	331	7	(	(	PUNCT
ejpam-4356	331	8	k	k	NOUN
ejpam-4356	331	9	)	)	PUNCT
ejpam-4356	331	10	,	,	PUNCT
ejpam-4356	331	11	s	s	PROPN
ejpam-4356	331	12	∈	∈	NOUN
ejpam-4356	331	13	w(g	w(g	PROPN
ejpam-4356	331	14	)	)	PUNCT
ejpam-4356	331	15	and	and	CCONJ
ejpam-4356	331	16	p2[s]k	p2[s]k	PROPN
ejpam-4356	331	17	=	=	SYM
ejpam-4356	331	18	v	v	PROPN
ejpam-4356	331	19	(	(	PUNCT
ejpam-4356	331	20	k	k	NOUN
ejpam-4356	331	21	)	)	PUNCT
ejpam-4356	331	22	}	}	PUNCT
ejpam-4356	331	23	.	.	PUNCT
ejpam-4356	332	1	proof	proof	NOUN
ejpam-4356	332	2	.	.	PUNCT
ejpam-4356	333	1	let	let	VERB
ejpam-4356	333	2	g	g	PRON
ejpam-4356	333	3	be	be	AUX
ejpam-4356	333	4	a	a	DET
ejpam-4356	333	5	connected	connected	ADJ
ejpam-4356	333	6	graph	graph	NOUN
ejpam-4356	333	7	and	and	CCONJ
ejpam-4356	333	8	let	let	VERB
ejpam-4356	333	9	g	g	NOUN
ejpam-4356	333	10	=	=	PUNCT
ejpam-4356	333	11	h	h	PROPN
ejpam-4356	334	1	+	+	PROPN
ejpam-4356	334	2	k	k	PROPN
ejpam-4356	334	3	where	where	SCONJ
ejpam-4356	334	4	h	h	NOUN
ejpam-4356	334	5	and	and	CCONJ
ejpam-4356	334	6	k	k	PROPN
ejpam-4356	334	7	are	be	AUX
ejpam-4356	334	8	connected	connect	VERB
ejpam-4356	334	9	noncomplete	noncomplete	ADJ
ejpam-4356	334	10	graphs	graph	NOUN
ejpam-4356	334	11	.	.	PUNCT
ejpam-4356	335	1	assume	assume	VERB
ejpam-4356	335	2	that	that	SCONJ
ejpam-4356	335	3	s	s	VERB
ejpam-4356	335	4	⊆	⊆	NUM
ejpam-4356	335	5	v	v	NOUN
ejpam-4356	335	6	(	(	PUNCT
ejpam-4356	335	7	g	g	NOUN
ejpam-4356	335	8	)	)	PUNCT
ejpam-4356	335	9	is	be	AUX
ejpam-4356	335	10	a	a	DET
ejpam-4356	335	11	γwcg	γwcg	NOUN
ejpam-4356	335	12	-	-	PUNCT
ejpam-4356	335	13	set	set	NOUN
ejpam-4356	335	14	of	of	ADP
ejpam-4356	335	15	g.	g.	PROPN
ejpam-4356	335	16	then	then	ADV
ejpam-4356	335	17	by	by	ADP
ejpam-4356	335	18	theorem	theorem	NOUN
ejpam-4356	335	19	17	17	NUM
ejpam-4356	335	20	,	,	PUNCT
ejpam-4356	335	21	we	we	PRON
ejpam-4356	335	22	have	have	VERB
ejpam-4356	335	23	s	s	VERB
ejpam-4356	335	24	⊆	⊆	NUM
ejpam-4356	335	25	v	v	NOUN
ejpam-4356	335	26	(	(	PUNCT
ejpam-4356	335	27	h	h	NOUN
ejpam-4356	335	28	)	)	PUNCT
ejpam-4356	335	29	and	and	CCONJ
ejpam-4356	335	30	s	s	VERB
ejpam-4356	335	31	is	be	AUX
ejpam-4356	335	32	a	a	DET
ejpam-4356	335	33	2	2	NUM
ejpam-4356	335	34	-	-	PUNCT
ejpam-4356	335	35	path	path	NOUN
ejpam-4356	335	36	closure	closure	NOUN
ejpam-4356	335	37	absorbing	absorb	VERB
ejpam-4356	335	38	set	set	NOUN
ejpam-4356	335	39	in	in	ADP
ejpam-4356	335	40	h	h	NOUN
ejpam-4356	335	41	or	or	CCONJ
ejpam-4356	335	42	s	s	PROPN
ejpam-4356	335	43	⊆	⊆	NUM
ejpam-4356	335	44	v	v	NOUN
ejpam-4356	335	45	(	(	PUNCT
ejpam-4356	335	46	k	k	NOUN
ejpam-4356	335	47	)	)	PUNCT
ejpam-4356	335	48	and	and	CCONJ
ejpam-4356	335	49	s	s	VERB
ejpam-4356	335	50	is	be	AUX
ejpam-4356	335	51	a	a	DET
ejpam-4356	335	52	2	2	NUM
ejpam-4356	335	53	-	-	PUNCT
ejpam-4356	335	54	path	path	NOUN
ejpam-4356	335	55	closure	closure	NOUN
ejpam-4356	335	56	absorbing	absorb	VERB
ejpam-4356	335	57	set	set	NOUN
ejpam-4356	335	58	in	in	ADP
ejpam-4356	335	59	k.	k.	PROPN
ejpam-4356	335	60	hence	hence	ADV
ejpam-4356	335	61	,	,	PUNCT
ejpam-4356	335	62	γwcg(g	γwcg(g	PROPN
ejpam-4356	335	63	)	)	PUNCT
ejpam-4356	335	64	≥	≥	NOUN
ejpam-4356	335	65	min{γ(h),γ(k	min{γ(h),γ(k	PROPN
ejpam-4356	335	66	)	)	PUNCT
ejpam-4356	335	67	}	}	PUNCT
ejpam-4356	335	68	,	,	PUNCT
ejpam-4356	335	69	where	where	SCONJ
ejpam-4356	335	70	γ(h	γ(h	NOUN
ejpam-4356	335	71	)	)	PUNCT
ejpam-4356	335	72	=	=	SYM
ejpam-4356	335	73	min{|s|	min{|s|	NOUN
ejpam-4356	335	74	:	:	PUNCT
ejpam-4356	335	75	s	s	VERB
ejpam-4356	335	76	⊆	⊆	NUM
ejpam-4356	335	77	v	v	NOUN
ejpam-4356	335	78	(	(	PUNCT
ejpam-4356	335	79	h	h	NOUN
ejpam-4356	335	80	)	)	PUNCT
ejpam-4356	335	81	,	,	PUNCT
ejpam-4356	335	82	s	s	PROPN
ejpam-4356	335	83	∈	∈	PROPN
ejpam-4356	335	84	w(g	w(g	PROPN
ejpam-4356	335	85	)	)	PUNCT
ejpam-4356	335	86	and	and	CCONJ
ejpam-4356	335	87	p2[s]h	p2[s]h	PROPN
ejpam-4356	335	88	=	=	PUNCT
ejpam-4356	335	89	v	v	PROPN
ejpam-4356	335	90	(	(	PUNCT
ejpam-4356	335	91	h	h	NOUN
ejpam-4356	335	92	)	)	PUNCT
ejpam-4356	335	93	}	}	PUNCT
ejpam-4356	335	94	and	and	CCONJ
ejpam-4356	335	95	γ(k	γ(k	PROPN
ejpam-4356	335	96	)	)	PUNCT
ejpam-4356	336	1	=	=	SYM
ejpam-4356	336	2	min{|s|	min{|s|	NOUN
ejpam-4356	336	3	:	:	PUNCT
ejpam-4356	336	4	s	s	VERB
ejpam-4356	336	5	⊆	⊆	NUM
ejpam-4356	336	6	v	v	NOUN
ejpam-4356	336	7	(	(	PUNCT
ejpam-4356	336	8	k	k	NOUN
ejpam-4356	336	9	)	)	PUNCT
ejpam-4356	336	10	,	,	PUNCT
ejpam-4356	336	11	s	s	PROPN
ejpam-4356	336	12	∈	∈	NOUN
ejpam-4356	336	13	w(g	w(g	PROPN
ejpam-4356	336	14	)	)	PUNCT
ejpam-4356	336	15	and	and	CCONJ
ejpam-4356	336	16	p2[s]k	p2[s]k	PROPN
ejpam-4356	336	17	=	=	SYM
ejpam-4356	336	18	v	v	PROPN
ejpam-4356	336	19	(	(	PUNCT
ejpam-4356	336	20	k	k	NOUN
ejpam-4356	336	21	)	)	PUNCT
ejpam-4356	336	22	}	}	PUNCT
ejpam-4356	336	23	.	.	PUNCT
ejpam-4356	337	1	by	by	ADP
ejpam-4356	337	2	theorem	theorem	ADJ
ejpam-4356	337	3	18	18	NUM
ejpam-4356	337	4	,	,	PUNCT
ejpam-4356	337	5	γwcg(g	γwcg(g	NOUN
ejpam-4356	337	6	)	)	PUNCT
ejpam-4356	337	7	≤	≤	NOUN
ejpam-4356	337	8	min{γ(h),γ(k	min{γ(h),γ(k	PROPN
ejpam-4356	337	9	)	)	PUNCT
ejpam-4356	337	10	}	}	PUNCT
ejpam-4356	337	11	.	.	PUNCT
ejpam-4356	338	1	consequently	consequently	ADV
ejpam-4356	338	2	,	,	PUNCT
ejpam-4356	338	3	γwcg(g	γwcg(g	PROPN
ejpam-4356	338	4	)	)	PUNCT
ejpam-4356	338	5	=	=	SYM
ejpam-4356	338	6	min{γ(h),γ(k	min{γ(h),γ(k	PROPN
ejpam-4356	338	7	)	)	PUNCT
ejpam-4356	338	8	}	}	PUNCT
ejpam-4356	338	9	.	.	PUNCT
ejpam-4356	339	1	corollary	corollary	ADJ
ejpam-4356	339	2	8	8	NUM
ejpam-4356	339	3	.	.	PUNCT
ejpam-4356	340	1	the	the	DET
ejpam-4356	340	2	weakly	weakly	ADV
ejpam-4356	340	3	connected	connected	ADJ
ejpam-4356	340	4	closed	close	VERB
ejpam-4356	340	5	geodetic	geodetic	ADJ
ejpam-4356	340	6	domination	domination	NOUN
ejpam-4356	340	7	number	number	NOUN
ejpam-4356	340	8	of	of	ADP
ejpam-4356	340	9	the	the	DET
ejpam-4356	340	10	join	join	NOUN
ejpam-4356	340	11	graph	graph	NOUN
ejpam-4356	340	12	of	of	ADP
ejpam-4356	340	13	the	the	DET
ejpam-4356	340	14	path	path	NOUN
ejpam-4356	340	15	graph	graph	NOUN
ejpam-4356	340	16	pn	pn	PROPN
ejpam-4356	340	17	,	,	PUNCT
ejpam-4356	340	18	cycle	cycle	NOUN
ejpam-4356	340	19	graph	graph	NOUN
ejpam-4356	340	20	cn	cn	PROPN
ejpam-4356	340	21	,	,	PUNCT
ejpam-4356	340	22	and	and	CCONJ
ejpam-4356	340	23	complete	complete	ADJ
ejpam-4356	340	24	bipartite	bipartite	PROPN
ejpam-4356	340	25	graph	graph	NOUN
ejpam-4356	340	26	km	km	PROPN
ejpam-4356	340	27	,	,	PUNCT
ejpam-4356	340	28	n	n	PRON
ejpam-4356	340	29	are	be	AUX
ejpam-4356	340	30	given	give	VERB
ejpam-4356	340	31	as	as	SCONJ
ejpam-4356	340	32	follows	follow	VERB
ejpam-4356	340	33	.	.	PUNCT
ejpam-4356	341	1	(	(	PUNCT
ejpam-4356	341	2	i.	i.	NOUN
ejpam-4356	341	3	)	)	PUNCT
ejpam-4356	341	4	γwcg(pm	γwcg(pm	VERB
ejpam-4356	341	5	+	+	CCONJ
ejpam-4356	341	6	pn	pn	NOUN
ejpam-4356	341	7	)	)	PUNCT
ejpam-4356	341	8	=	=	SYM
ejpam-4356	342	1	min{⌈m+1	min{⌈m+1	NOUN
ejpam-4356	342	2	2	2	NUM
ejpam-4356	342	3	⌉	⌉	NOUN
ejpam-4356	342	4	,	,	PUNCT
ejpam-4356	342	5	⌈n+1	⌈n+1	PROPN
ejpam-4356	342	6	2	2	NUM
ejpam-4356	342	7	⌉	⌉	NOUN
ejpam-4356	342	8	}	}	PUNCT
ejpam-4356	342	9	,	,	PUNCT
ejpam-4356	342	10	for	for	ADP
ejpam-4356	342	11	m	m	PROPN
ejpam-4356	342	12	,	,	PUNCT
ejpam-4356	342	13	n	n	PROPN
ejpam-4356	342	14	>	>	X
ejpam-4356	342	15	2	2	NUM
ejpam-4356	342	16	.	.	PUNCT
ejpam-4356	342	17	(	(	PUNCT
ejpam-4356	342	18	ii	ii	NOUN
ejpam-4356	342	19	.	.	PUNCT
ejpam-4356	342	20	)	)	PUNCT
ejpam-4356	343	1	γwcg(cm	γwcg(cm	PROPN
ejpam-4356	343	2	+	+	CCONJ
ejpam-4356	343	3	cn	cn	ADJ
ejpam-4356	343	4	)	)	PUNCT
ejpam-4356	343	5	=	=	SYM
ejpam-4356	343	6	min{⌈m2	min{⌈m2	PROPN
ejpam-4356	343	7	⌉	⌉	NOUN
ejpam-4356	343	8	,	,	PUNCT
ejpam-4356	343	9	⌈	⌈	NOUN
ejpam-4356	343	10	n	n	PRON
ejpam-4356	343	11	2	2	NUM
ejpam-4356	343	12	⌉	⌉	NOUN
ejpam-4356	343	13	}	}	PUNCT
ejpam-4356	343	14	,	,	PUNCT
ejpam-4356	343	15	for	for	ADP
ejpam-4356	343	16	m	m	PROPN
ejpam-4356	343	17	,	,	PUNCT
ejpam-4356	343	18	n	n	PROPN
ejpam-4356	343	19	>	>	X
ejpam-4356	343	20	3	3	X
ejpam-4356	343	21	.	.	PUNCT
ejpam-4356	343	22	(	(	PUNCT
ejpam-4356	343	23	iii	iii	NOUN
ejpam-4356	343	24	.	.	PUNCT
ejpam-4356	343	25	)	)	PUNCT
ejpam-4356	344	1	γwcg(km	γwcg(km	PROPN
ejpam-4356	344	2	,	,	PUNCT
ejpam-4356	344	3	n	n	PROPN
ejpam-4356	344	4	+	+	NOUN
ejpam-4356	344	5	kp	kp	INTJ
ejpam-4356	344	6	)	)	PUNCT
ejpam-4356	344	7	=	=	SYM
ejpam-4356	344	8	min{m	min{m	PROPN
ejpam-4356	344	9	,	,	PUNCT
ejpam-4356	344	10	n	n	CCONJ
ejpam-4356	344	11	}	}	PUNCT
ejpam-4356	344	12	,	,	PUNCT
ejpam-4356	344	13	for	for	ADP
ejpam-4356	344	14	m	m	PROPN
ejpam-4356	344	15	,	,	PUNCT
ejpam-4356	344	16	n	n	PROPN
ejpam-4356	344	17	>	>	X
ejpam-4356	344	18	2	2	X
ejpam-4356	344	19	.	.	PUNCT
ejpam-4356	344	20	(	(	PUNCT
ejpam-4356	344	21	iv	iv	PROPN
ejpam-4356	344	22	.	.	PUNCT
ejpam-4356	344	23	)	)	PUNCT
ejpam-4356	345	1	γwcg(km	γwcg(km	PROPN
ejpam-4356	345	2	,	,	PUNCT
ejpam-4356	345	3	n	n	PROPN
ejpam-4356	345	4	+	+	ADJ
ejpam-4356	345	5	kp	kp	PROPN
ejpam-4356	345	6	,	,	PUNCT
ejpam-4356	345	7	q	q	NOUN
ejpam-4356	345	8	)	)	PUNCT
ejpam-4356	345	9	=	=	SYM
ejpam-4356	345	10	min{m	min{m	PROPN
ejpam-4356	345	11	,	,	PUNCT
ejpam-4356	345	12	n	n	CCONJ
ejpam-4356	345	13	,	,	PUNCT
ejpam-4356	345	14	p	p	X
ejpam-4356	345	15	,	,	PUNCT
ejpam-4356	345	16	q	q	NOUN
ejpam-4356	345	17	}	}	PUNCT
ejpam-4356	345	18	,	,	PUNCT
ejpam-4356	345	19	for	for	ADP
ejpam-4356	345	20	m	m	PROPN
ejpam-4356	345	21	,	,	PUNCT
ejpam-4356	345	22	n	n	CCONJ
ejpam-4356	345	23	,	,	PUNCT
ejpam-4356	345	24	p	p	X
ejpam-4356	345	25	,	,	PUNCT
ejpam-4356	345	26	q	q	X
ejpam-4356	345	27	≥	≥	NOUN
ejpam-4356	345	28	2	2	NUM
ejpam-4356	345	29	.	.	PUNCT
ejpam-4356	345	30	corollary	corollary	ADJ
ejpam-4356	345	31	9	9	NUM
ejpam-4356	345	32	.	.	PUNCT
ejpam-4356	346	1	let	let	VERB
ejpam-4356	346	2	h	h	NOUN
ejpam-4356	346	3	and	and	CCONJ
ejpam-4356	346	4	k	k	PROPN
ejpam-4356	346	5	are	be	AUX
ejpam-4356	346	6	connected	connect	VERB
ejpam-4356	346	7	noncomplete	noncomplete	ADJ
ejpam-4356	346	8	graphs	graph	NOUN
ejpam-4356	346	9	and	and	CCONJ
ejpam-4356	346	10	g	g	NOUN
ejpam-4356	346	11	=	=	NOUN
ejpam-4356	346	12	h	h	PROPN
ejpam-4356	347	1	+	+	CCONJ
ejpam-4356	347	2	k.	k.	NOUN
ejpam-4356	348	1	if	if	SCONJ
ejpam-4356	348	2	diam(h	diam(h	PROPN
ejpam-4356	348	3	)	)	PUNCT
ejpam-4356	348	4	=	=	SYM
ejpam-4356	348	5	diam(k	diam(k	NOUN
ejpam-4356	348	6	)	)	PUNCT
ejpam-4356	348	7	=	=	SYM
ejpam-4356	348	8	2	2	NUM
ejpam-4356	348	9	,	,	PUNCT
ejpam-4356	348	10	then	then	ADV
ejpam-4356	348	11	γwcg(g	γwcg(g	NOUN
ejpam-4356	348	12	)	)	PUNCT
ejpam-4356	348	13	=	=	PUNCT
ejpam-4356	349	1	min{γwcg(h	min{γwcg(h	PROPN
ejpam-4356	349	2	)	)	PUNCT
ejpam-4356	349	3	,	,	PUNCT
ejpam-4356	349	4	γwcg(k	γwcg(k	NOUN
ejpam-4356	349	5	)	)	PUNCT
ejpam-4356	349	6	}	}	PUNCT
ejpam-4356	349	7	.	.	PUNCT
ejpam-4356	350	1	the	the	DET
ejpam-4356	350	2	corona	corona	NOUN
ejpam-4356	350	3	of	of	ADP
ejpam-4356	350	4	graphs	graph	NOUN
ejpam-4356	350	5	g	g	PROPN
ejpam-4356	350	6	and	and	CCONJ
ejpam-4356	350	7	h	h	NOUN
ejpam-4356	350	8	,	,	PUNCT
ejpam-4356	350	9	g	g	PROPN
ejpam-4356	350	10	◦	◦	NOUN
ejpam-4356	350	11	h	h	NOUN
ejpam-4356	350	12	,	,	PUNCT
ejpam-4356	350	13	is	be	AUX
ejpam-4356	350	14	the	the	DET
ejpam-4356	350	15	graph	graph	NOUN
ejpam-4356	350	16	obtained	obtain	VERB
ejpam-4356	350	17	by	by	ADP
ejpam-4356	350	18	taking	take	VERB
ejpam-4356	350	19	one	one	NUM
ejpam-4356	350	20	copy	copy	NOUN
ejpam-4356	350	21	of	of	ADP
ejpam-4356	350	22	g	g	PROPN
ejpam-4356	350	23	and	and	CCONJ
ejpam-4356	350	24	|v	|v	PROPN
ejpam-4356	350	25	(	(	PUNCT
ejpam-4356	350	26	g)|	g)|	NOUN
ejpam-4356	350	27	copies	copy	NOUN
ejpam-4356	350	28	of	of	ADP
ejpam-4356	350	29	h	h	NOUN
ejpam-4356	350	30	,	,	PUNCT
ejpam-4356	350	31	and	and	CCONJ
ejpam-4356	350	32	then	then	ADV
ejpam-4356	350	33	joining	join	VERB
ejpam-4356	350	34	the	the	DET
ejpam-4356	350	35	ith	ith	PROPN
ejpam-4356	350	36	vertex	vertex	NOUN
ejpam-4356	350	37	of	of	ADP
ejpam-4356	350	38	g	g	NOUN
ejpam-4356	350	39	to	to	ADP
ejpam-4356	350	40	every	every	DET
ejpam-4356	350	41	vertex	vertex	NOUN
ejpam-4356	350	42	of	of	ADP
ejpam-4356	350	43	the	the	DET
ejpam-4356	350	44	ith	ith	PROPN
ejpam-4356	350	45	copy	copy	NOUN
ejpam-4356	350	46	of	of	ADP
ejpam-4356	350	47	h.	h.	PROPN
ejpam-4356	350	48	for	for	ADP
ejpam-4356	350	49	every	every	DET
ejpam-4356	350	50	v	v	NUM
ejpam-4356	350	51	∈	∈	PROPN
ejpam-4356	350	52	v	v	NOUN
ejpam-4356	350	53	(	(	PUNCT
ejpam-4356	350	54	g	g	NOUN
ejpam-4356	350	55	)	)	PUNCT
ejpam-4356	350	56	,	,	PUNCT
ejpam-4356	350	57	denote	denote	VERB
ejpam-4356	350	58	by	by	ADP
ejpam-4356	350	59	hv	hv	PROPN
ejpam-4356	350	60	the	the	DET
ejpam-4356	350	61	copy	copy	NOUN
ejpam-4356	350	62	of	of	ADP
ejpam-4356	350	63	h	h	NOUN
ejpam-4356	350	64	whose	whose	DET
ejpam-4356	350	65	vertices	vertex	NOUN
ejpam-4356	350	66	are	be	AUX
ejpam-4356	350	67	attached	attach	VERB
ejpam-4356	350	68	one	one	NUM
ejpam-4356	350	69	by	by	ADP
ejpam-4356	350	70	one	one	NUM
ejpam-4356	350	71	to	to	ADP
ejpam-4356	350	72	the	the	DET
ejpam-4356	350	73	vertex	vertex	NOUN
ejpam-4356	350	74	v.	v.	ADP
ejpam-4356	350	75	subsequently	subsequently	ADV
ejpam-4356	350	76	,	,	PUNCT
ejpam-4356	350	77	denote	denote	VERB
ejpam-4356	350	78	by	by	ADP
ejpam-4356	350	79	v	v	PRON
ejpam-4356	350	80	+	+	CCONJ
ejpam-4356	350	81	hv	hv	NOUN
ejpam-4356	350	82	the	the	DET
ejpam-4356	350	83	subgraph	subgraph	NOUN
ejpam-4356	350	84	of	of	ADP
ejpam-4356	350	85	the	the	DET
ejpam-4356	350	86	corona	corona	NOUN
ejpam-4356	350	87	g	g	PROPN
ejpam-4356	350	88	◦	◦	NOUN
ejpam-4356	350	89	h	h	NOUN
ejpam-4356	350	90	corresponding	correspond	VERB
ejpam-4356	350	91	to	to	ADP
ejpam-4356	350	92	the	the	DET
ejpam-4356	350	93	join	join	NOUN
ejpam-4356	350	94	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4356	350	95	,	,	PUNCT
ejpam-4356	350	96	v	v	PROPN
ejpam-4356	350	97	∈	∈	PROPN
ejpam-4356	350	98	v	v	NOUN
ejpam-4356	350	99	(	(	PUNCT
ejpam-4356	350	100	g	g	NOUN
ejpam-4356	350	101	)	)	PUNCT
ejpam-4356	350	102	,	,	PUNCT
ejpam-4356	350	103	harary	harary	NOUN
ejpam-4356	351	1	[	[	X
ejpam-4356	351	2	2	2	NUM
ejpam-4356	351	3	]	]	PUNCT
ejpam-4356	351	4	.	.	PUNCT
ejpam-4356	352	1	theorem	theorem	ADJ
ejpam-4356	352	2	20	20	NUM
ejpam-4356	352	3	.	.	PUNCT
ejpam-4356	353	1	jamil	jamil	PROPN
ejpam-4356	353	2	,	,	PUNCT
ejpam-4356	353	3	et.al	et.al	VERB
ejpam-4356	353	4	[	[	X
ejpam-4356	353	5	11	11	NUM
ejpam-4356	353	6	]	]	PUNCT
ejpam-4356	353	7	let	let	VERB
ejpam-4356	353	8	g	g	NOUN
ejpam-4356	353	9	=	=	PUNCT
ejpam-4356	353	10	h	h	PROPN
ejpam-4356	353	11	◦	◦	NOUN
ejpam-4356	353	12	k	k	NOUN
ejpam-4356	353	13	,	,	PUNCT
ejpam-4356	353	14	where	where	SCONJ
ejpam-4356	353	15	h	h	NOUN
ejpam-4356	353	16	is	be	AUX
ejpam-4356	353	17	a	a	DET
ejpam-4356	353	18	nontrivial	nontrivial	ADJ
ejpam-4356	353	19	connected	connect	VERB
ejpam-4356	353	20	graph	graph	NOUN
ejpam-4356	353	21	and	and	CCONJ
ejpam-4356	353	22	k	k	PROPN
ejpam-4356	353	23	a	a	DET
ejpam-4356	353	24	noncomplete	noncomplete	ADJ
ejpam-4356	353	25	graph	graph	NOUN
ejpam-4356	353	26	,	,	PUNCT
ejpam-4356	353	27	and	and	CCONJ
ejpam-4356	353	28	let	let	VERB
ejpam-4356	353	29	s	s	PRON
ejpam-4356	353	30	⊆	⊆	NUM
ejpam-4356	353	31	v	v	NOUN
ejpam-4356	353	32	(	(	PUNCT
ejpam-4356	353	33	g	g	NOUN
ejpam-4356	353	34	)	)	PUNCT
ejpam-4356	353	35	.	.	PUNCT
ejpam-4356	354	1	then	then	ADV
ejpam-4356	354	2	s	s	VERB
ejpam-4356	354	3	∈	∈	PROPN
ejpam-4356	354	4	c∗(g	c∗(g	PROPN
ejpam-4356	354	5	)	)	PUNCT
ejpam-4356	354	6	if	if	SCONJ
ejpam-4356	354	7	and	and	CCONJ
ejpam-4356	354	8	only	only	ADV
ejpam-4356	354	9	if	if	SCONJ
ejpam-4356	354	10	s	s	VERB
ejpam-4356	354	11	=	=	X
ejpam-4356	354	12	(	(	PUNCT
ejpam-4356	354	13	⋃	⋃	ADJ
ejpam-4356	354	14	v∈v	v∈v	NOUN
ejpam-4356	354	15	(	(	PUNCT
ejpam-4356	354	16	h	h	NOUN
ejpam-4356	354	17	)	)	PUNCT
ejpam-4356	354	18	sv	sv	NOUN
ejpam-4356	354	19	)	)	PUNCT
ejpam-4356	354	20	∪	∪	NOUN
ejpam-4356	354	21	s0	s0	PROPN
ejpam-4356	354	22	,	,	PUNCT
ejpam-4356	354	23	where	where	SCONJ
ejpam-4356	354	24	sv	sv	PROPN
ejpam-4356	354	25	⊆	⊆	NUM
ejpam-4356	354	26	v	v	PROPN
ejpam-4356	354	27	(	(	PUNCT
ejpam-4356	354	28	kv	kv	PROPN
ejpam-4356	354	29	)	)	PUNCT
ejpam-4356	354	30	and	and	CCONJ
ejpam-4356	354	31	sv	sv	ADP
ejpam-4356	354	32	∈	∈	PROPN
ejpam-4356	354	33	c∗(v	c∗(v	PROPN
ejpam-4356	354	34	+	+	CCONJ
ejpam-4356	354	35	kv	kv	PROPN
ejpam-4356	354	36	)	)	PUNCT
ejpam-4356	354	37	,	,	PUNCT
ejpam-4356	354	38	and	and	CCONJ
ejpam-4356	354	39	s0	s0	NOUN
ejpam-4356	354	40	is	be	AUX
ejpam-4356	354	41	a	a	DET
ejpam-4356	354	42	closed	closed	ADJ
ejpam-4356	354	43	geodetic	geodetic	ADJ
ejpam-4356	354	44	subset	subset	NOUN
ejpam-4356	354	45	of	of	ADP
ejpam-4356	354	46	v	v	PROPN
ejpam-4356	354	47	(	(	PUNCT
ejpam-4356	354	48	h	h	NOUN
ejpam-4356	354	49	)	)	PUNCT
ejpam-4356	354	50	.	.	PUNCT
ejpam-4356	355	1	lemma	lemma	PROPN
ejpam-4356	355	2	4	4	X
ejpam-4356	355	3	.	.	PUNCT
ejpam-4356	356	1	let	let	VERB
ejpam-4356	356	2	g	g	NOUN
ejpam-4356	356	3	=	=	PUNCT
ejpam-4356	356	4	h	h	PROPN
ejpam-4356	356	5	◦	◦	NOUN
ejpam-4356	356	6	k	k	NOUN
ejpam-4356	356	7	,	,	PUNCT
ejpam-4356	356	8	where	where	SCONJ
ejpam-4356	356	9	h	h	NOUN
ejpam-4356	356	10	is	be	AUX
ejpam-4356	356	11	a	a	DET
ejpam-4356	356	12	nontrivial	nontrivial	ADJ
ejpam-4356	356	13	connected	connect	VERB
ejpam-4356	356	14	graph	graph	NOUN
ejpam-4356	356	15	,	,	PUNCT
ejpam-4356	356	16	and	and	CCONJ
ejpam-4356	356	17	k	k	X
ejpam-4356	356	18	a	a	DET
ejpam-4356	356	19	noncomplete	noncomplete	ADJ
ejpam-4356	356	20	graph	graph	NOUN
ejpam-4356	356	21	.	.	PUNCT
ejpam-4356	357	1	if	if	SCONJ
ejpam-4356	357	2	s	s	X
ejpam-4356	357	3	∈	∈	PROPN
ejpam-4356	357	4	w(g	w(g	PROPN
ejpam-4356	357	5	)	)	PUNCT
ejpam-4356	357	6	,	,	PUNCT
ejpam-4356	357	7	then	then	ADV
ejpam-4356	357	8	s	s	VERB
ejpam-4356	357	9	∩	∩	ADJ
ejpam-4356	357	10	v	v	X
ejpam-4356	357	11	(	(	PUNCT
ejpam-4356	357	12	kv	kv	PROPN
ejpam-4356	357	13	)	)	PUNCT
ejpam-4356	357	14	∈	∈	PROPN
ejpam-4356	357	15	w(v	w(v	PROPN
ejpam-4356	357	16	+	+	PROPN
ejpam-4356	357	17	kv	kv	PROPN
ejpam-4356	357	18	)	)	PUNCT
ejpam-4356	357	19	for	for	ADP
ejpam-4356	357	20	all	all	DET
ejpam-4356	357	21	v	v	ADP
ejpam-4356	357	22	∈	∈	NOUN
ejpam-4356	357	23	v	v	NOUN
ejpam-4356	357	24	(	(	PUNCT
ejpam-4356	357	25	h	h	NOUN
ejpam-4356	357	26	)	)	PUNCT
ejpam-4356	357	27	.	.	PUNCT
ejpam-4356	358	1	lemma	lemma	PROPN
ejpam-4356	358	2	5	5	X
ejpam-4356	358	3	.	.	PUNCT
ejpam-4356	359	1	let	let	VERB
ejpam-4356	359	2	g	g	NOUN
ejpam-4356	359	3	=	=	PUNCT
ejpam-4356	359	4	h	h	PROPN
ejpam-4356	359	5	◦	◦	NOUN
ejpam-4356	359	6	k	k	NOUN
ejpam-4356	359	7	,	,	PUNCT
ejpam-4356	359	8	where	where	SCONJ
ejpam-4356	359	9	h	h	NOUN
ejpam-4356	359	10	is	be	AUX
ejpam-4356	359	11	a	a	DET
ejpam-4356	359	12	nontrivial	nontrivial	ADJ
ejpam-4356	359	13	connected	connect	VERB
ejpam-4356	359	14	graph	graph	NOUN
ejpam-4356	359	15	of	of	ADP
ejpam-4356	359	16	order	order	NOUN
ejpam-4356	359	17	m	m	VERB
ejpam-4356	359	18	and	and	CCONJ
ejpam-4356	359	19	k	k	X
ejpam-4356	359	20	a	a	DET
ejpam-4356	359	21	noncomplete	noncomplete	ADJ
ejpam-4356	359	22	graph	graph	NOUN
ejpam-4356	359	23	.	.	PUNCT
ejpam-4356	360	1	let	let	VERB
ejpam-4356	360	2	sv	sv	PROPN
ejpam-4356	360	3	⊆	⊆	NUM
ejpam-4356	360	4	v	v	PROPN
ejpam-4356	360	5	(	(	PUNCT
ejpam-4356	360	6	kv	kv	PROPN
ejpam-4356	360	7	)	)	PUNCT
ejpam-4356	360	8	for	for	ADP
ejpam-4356	360	9	all	all	DET
ejpam-4356	360	10	v	v	ADP
ejpam-4356	360	11	∈	∈	NOUN
ejpam-4356	360	12	v	v	NOUN
ejpam-4356	360	13	(	(	PUNCT
ejpam-4356	360	14	h	h	NOUN
ejpam-4356	360	15	)	)	PUNCT
ejpam-4356	360	16	.	.	PUNCT
ejpam-4356	361	1	if	if	SCONJ
ejpam-4356	361	2	sv	sv	PROPN
ejpam-4356	361	3	∈	∈	PROPN
ejpam-4356	361	4	w(v	w(v	PROPN
ejpam-4356	361	5	+	+	CCONJ
ejpam-4356	361	6	kv	kv	PROPN
ejpam-4356	361	7	)	)	PUNCT
ejpam-4356	361	8	for	for	ADP
ejpam-4356	361	9	each	each	DET
ejpam-4356	361	10	v	v	NUM
ejpam-4356	361	11	∈	∈	PROPN
ejpam-4356	361	12	v	v	NOUN
ejpam-4356	361	13	(	(	PUNCT
ejpam-4356	361	14	h	h	NOUN
ejpam-4356	361	15	)	)	PUNCT
ejpam-4356	361	16	,	,	PUNCT
ejpam-4356	361	17	then	then	ADV
ejpam-4356	361	18	s	s	VERB
ejpam-4356	361	19	=	=	PUNCT
ejpam-4356	361	20	⋃	⋃	NOUN
ejpam-4356	361	21	v∈v	v∈v	NOUN
ejpam-4356	361	22	(	(	PUNCT
ejpam-4356	361	23	h	h	NOUN
ejpam-4356	361	24	)	)	PUNCT
ejpam-4356	361	25	sv	sv	PROPN
ejpam-4356	361	26	∈	∈	PROPN
ejpam-4356	361	27	w(g	w(g	PROPN
ejpam-4356	361	28	)	)	PUNCT
ejpam-4356	361	29	.	.	PUNCT
ejpam-4356	362	1	j.	j.	PROPN
ejpam-4356	362	2	hamja	hamja	PROPN
ejpam-4356	362	3	,	,	PUNCT
ejpam-4356	362	4	i.	i.	PROPN
ejpam-4356	362	5	aniversario	aniversario	PROPN
ejpam-4356	362	6	,	,	PUNCT
ejpam-4356	362	7	h.	h.	PROPN
ejpam-4356	362	8	rara	rara	PROPN
ejpam-4356	362	9	/	/	SYM
ejpam-4356	362	10	eur	eur	PROPN
ejpam-4356	362	11	.	.	PUNCT
ejpam-4356	363	1	j.	j.	PROPN
ejpam-4356	363	2	pure	pure	PROPN
ejpam-4356	363	3	appl	appl	PROPN
ejpam-4356	363	4	.	.	PROPN
ejpam-4356	363	5	math	math	PROPN
ejpam-4356	363	6	,	,	PUNCT
ejpam-4356	363	7	15	15	NUM
ejpam-4356	363	8	(	(	PUNCT
ejpam-4356	363	9	2	2	NUM
ejpam-4356	363	10	)	)	PUNCT
ejpam-4356	363	11	(	(	PUNCT
ejpam-4356	363	12	2022	2022	NUM
ejpam-4356	363	13	)	)	PUNCT
ejpam-4356	363	14	,	,	PUNCT
ejpam-4356	363	15	736	736	NUM
ejpam-4356	363	16	-	-	SYM
ejpam-4356	363	17	752	752	NUM
ejpam-4356	363	18	747	747	NUM
ejpam-4356	363	19	theorem	theorem	NOUN
ejpam-4356	363	20	21	21	NUM
ejpam-4356	363	21	.	.	PUNCT
ejpam-4356	364	1	let	let	VERB
ejpam-4356	364	2	g	g	NOUN
ejpam-4356	364	3	=	=	PUNCT
ejpam-4356	364	4	h	h	PROPN
ejpam-4356	364	5	◦	◦	NOUN
ejpam-4356	364	6	k	k	NOUN
ejpam-4356	364	7	,	,	PUNCT
ejpam-4356	364	8	where	where	SCONJ
ejpam-4356	364	9	h	h	NOUN
ejpam-4356	364	10	is	be	AUX
ejpam-4356	364	11	a	a	DET
ejpam-4356	364	12	nontrivial	nontrivial	ADJ
ejpam-4356	364	13	connected	connect	VERB
ejpam-4356	364	14	graph	graph	NOUN
ejpam-4356	364	15	and	and	CCONJ
ejpam-4356	364	16	k	k	PROPN
ejpam-4356	364	17	a	a	DET
ejpam-4356	364	18	noncomplete	noncomplete	ADJ
ejpam-4356	364	19	graph	graph	NOUN
ejpam-4356	364	20	,	,	PUNCT
ejpam-4356	364	21	and	and	CCONJ
ejpam-4356	364	22	let	let	VERB
ejpam-4356	364	23	sv	sv	PROPN
ejpam-4356	364	24	⊆	⊆	NUM
ejpam-4356	364	25	v	v	NOUN
ejpam-4356	364	26	(	(	PUNCT
ejpam-4356	364	27	g	g	NOUN
ejpam-4356	364	28	)	)	PUNCT
ejpam-4356	364	29	.	.	PUNCT
ejpam-4356	365	1	then	then	ADV
ejpam-4356	365	2	s	s	VERB
ejpam-4356	365	3	∈	∈	PROPN
ejpam-4356	365	4	w(g	w(g	PROPN
ejpam-4356	365	5	)	)	PUNCT
ejpam-4356	365	6	if	if	SCONJ
ejpam-4356	365	7	and	and	CCONJ
ejpam-4356	365	8	only	only	ADV
ejpam-4356	365	9	if	if	SCONJ
ejpam-4356	365	10	s	s	VERB
ejpam-4356	365	11	=	=	X
ejpam-4356	365	12	(	(	PUNCT
ejpam-4356	365	13	⋃	⋃	ADJ
ejpam-4356	365	14	v∈v	v∈v	NOUN
ejpam-4356	365	15	(	(	PUNCT
ejpam-4356	365	16	h	h	NOUN
ejpam-4356	365	17	)	)	PUNCT
ejpam-4356	365	18	sv)∪s0	sv)∪s0	NOUN
ejpam-4356	365	19	,	,	PUNCT
ejpam-4356	365	20	where	where	SCONJ
ejpam-4356	365	21	sv	sv	PROPN
ejpam-4356	365	22	⊆	⊆	NUM
ejpam-4356	365	23	v	v	PROPN
ejpam-4356	365	24	(	(	PUNCT
ejpam-4356	365	25	kv	kv	PROPN
ejpam-4356	365	26	)	)	PUNCT
ejpam-4356	365	27	and	and	CCONJ
ejpam-4356	365	28	sv	sv	ADP
ejpam-4356	365	29	∈	∈	PROPN
ejpam-4356	365	30	w(v	w(v	PROPN
ejpam-4356	365	31	+	+	PROPN
ejpam-4356	365	32	kv	kv	PROPN
ejpam-4356	365	33	)	)	PUNCT
ejpam-4356	365	34	,	,	PUNCT
ejpam-4356	365	35	and	and	CCONJ
ejpam-4356	365	36	s0	s0	NOUN
ejpam-4356	365	37	is	be	AUX
ejpam-4356	365	38	a	a	DET
ejpam-4356	365	39	weakly	weakly	ADV
ejpam-4356	365	40	connected	connected	ADJ
ejpam-4356	365	41	closed	closed	ADJ
ejpam-4356	365	42	geodetic	geodetic	ADJ
ejpam-4356	365	43	subset	subset	NOUN
ejpam-4356	365	44	of	of	ADP
ejpam-4356	365	45	v	v	PROPN
ejpam-4356	365	46	(	(	PUNCT
ejpam-4356	365	47	h	h	NOUN
ejpam-4356	365	48	)	)	PUNCT
ejpam-4356	365	49	.	.	PUNCT
ejpam-4356	366	1	proof	proof	NOUN
ejpam-4356	366	2	.	.	PUNCT
ejpam-4356	367	1	suppose	suppose	VERB
ejpam-4356	367	2	that	that	SCONJ
ejpam-4356	367	3	s	s	VERB
ejpam-4356	367	4	∈	∈	NOUN
ejpam-4356	367	5	w(g	w(g	PROPN
ejpam-4356	367	6	)	)	PUNCT
ejpam-4356	367	7	.	.	PUNCT
ejpam-4356	368	1	then	then	ADV
ejpam-4356	368	2	s	s	VERB
ejpam-4356	368	3	∈	∈	PROPN
ejpam-4356	368	4	c∗(g	c∗(g	PROPN
ejpam-4356	368	5	)	)	PUNCT
ejpam-4356	368	6	.	.	PUNCT
ejpam-4356	369	1	by	by	ADP
ejpam-4356	369	2	theorem	theorem	NOUN
ejpam-4356	369	3	20	20	NUM
ejpam-4356	369	4	,	,	PUNCT
ejpam-4356	369	5	s	s	AUX
ejpam-4356	369	6	=	=	PUNCT
ejpam-4356	369	7	(	(	PUNCT
ejpam-4356	369	8	⋃	⋃	ADJ
ejpam-4356	369	9	v∈v	v∈v	NOUN
ejpam-4356	369	10	(	(	PUNCT
ejpam-4356	369	11	h	h	NOUN
ejpam-4356	369	12	)	)	PUNCT
ejpam-4356	369	13	sv	sv	NOUN
ejpam-4356	369	14	)	)	PUNCT
ejpam-4356	369	15	∪	∪	NOUN
ejpam-4356	369	16	s0	s0	PROPN
ejpam-4356	369	17	.	.	PUNCT
ejpam-4356	370	1	where	where	SCONJ
ejpam-4356	370	2	sv	sv	PROPN
ejpam-4356	370	3	⊆	⊆	NUM
ejpam-4356	370	4	v	v	X
ejpam-4356	370	5	(	(	PUNCT
ejpam-4356	370	6	k	k	NOUN
ejpam-4356	370	7	)	)	PUNCT
ejpam-4356	370	8	and	and	CCONJ
ejpam-4356	370	9	sv	sv	ADP
ejpam-4356	370	10	∈	∈	PROPN
ejpam-4356	370	11	c∗(v	c∗(v	PROPN
ejpam-4356	370	12	+	+	CCONJ
ejpam-4356	370	13	kv	kv	PROPN
ejpam-4356	370	14	)	)	PUNCT
ejpam-4356	370	15	and	and	CCONJ
ejpam-4356	370	16	s0	s0	PROPN
ejpam-4356	370	17	is	be	AUX
ejpam-4356	370	18	a	a	DET
ejpam-4356	370	19	closed	closed	ADJ
ejpam-4356	370	20	geodetic	geodetic	ADJ
ejpam-4356	370	21	subset	subset	NOUN
ejpam-4356	370	22	.	.	PUNCT
ejpam-4356	371	1	by	by	ADP
ejpam-4356	371	2	lemma	lemma	PROPN
ejpam-4356	371	3	4	4	NUM
ejpam-4356	371	4	,	,	PUNCT
ejpam-4356	371	5	s	s	VERB
ejpam-4356	371	6	∩	∩	ADJ
ejpam-4356	371	7	v	v	X
ejpam-4356	371	8	(	(	PUNCT
ejpam-4356	371	9	kv	kv	PROPN
ejpam-4356	371	10	)	)	PUNCT
ejpam-4356	371	11	∈	∈	PROPN
ejpam-4356	371	12	w(v+kv	w(v+kv	NOUN
ejpam-4356	371	13	)	)	PUNCT
ejpam-4356	371	14	for	for	ADP
ejpam-4356	371	15	all	all	DET
ejpam-4356	371	16	v	v	ADP
ejpam-4356	371	17	∈	∈	NOUN
ejpam-4356	371	18	v	v	NOUN
ejpam-4356	371	19	(	(	PUNCT
ejpam-4356	371	20	h	h	NOUN
ejpam-4356	371	21	)	)	PUNCT
ejpam-4356	371	22	.	.	PUNCT
ejpam-4356	372	1	thus	thus	ADV
ejpam-4356	372	2	,	,	PUNCT
ejpam-4356	372	3	s0	s0	PROPN
ejpam-4356	372	4	=	=	SYM
ejpam-4356	372	5	s	s	PART
ejpam-4356	372	6	\	\	NOUN
ejpam-4356	372	7	⋃	⋃	NOUN
ejpam-4356	372	8	v∈v	v∈v	NOUN
ejpam-4356	372	9	(	(	PUNCT
ejpam-4356	372	10	h	h	NOUN
ejpam-4356	372	11	)	)	PUNCT
ejpam-4356	372	12	sv	sv	PROPN
ejpam-4356	372	13	is	be	AUX
ejpam-4356	372	14	a	a	DET
ejpam-4356	372	15	closed	closed	ADJ
ejpam-4356	372	16	geodetic	geodetic	ADJ
ejpam-4356	372	17	subset	subset	NOUN
ejpam-4356	372	18	is	be	AUX
ejpam-4356	372	19	also	also	ADV
ejpam-4356	372	20	a	a	DET
ejpam-4356	372	21	weakly	weakly	ADV
ejpam-4356	372	22	connected	connected	ADJ
ejpam-4356	372	23	closed	closed	ADJ
ejpam-4356	372	24	geodetic	geodetic	ADJ
ejpam-4356	372	25	subset	subset	NOUN
ejpam-4356	372	26	of	of	ADP
ejpam-4356	372	27	v(h	v(h	NOUN
ejpam-4356	372	28	)	)	PUNCT
ejpam-4356	372	29	.	.	PUNCT
ejpam-4356	373	1	it	it	PRON
ejpam-4356	373	2	remeains	remeain	VERB
ejpam-4356	373	3	to	to	PART
ejpam-4356	373	4	show	show	VERB
ejpam-4356	373	5	that	that	SCONJ
ejpam-4356	373	6	sv	sv	PROPN
ejpam-4356	373	7	∈	∈	PROPN
ejpam-4356	373	8	w(v	w(v	PROPN
ejpam-4356	373	9	+	+	PROPN
ejpam-4356	373	10	kv	kv	PROPN
ejpam-4356	373	11	)	)	PUNCT
ejpam-4356	373	12	.	.	PUNCT
ejpam-4356	374	1	that	that	PRON
ejpam-4356	374	2	is	be	AUX
ejpam-4356	374	3	,	,	PUNCT
ejpam-4356	374	4	sv	sv	PROPN
ejpam-4356	374	5	is	be	AUX
ejpam-4356	374	6	a	a	DET
ejpam-4356	374	7	weakly	weakly	ADV
ejpam-4356	374	8	connected	connected	ADJ
ejpam-4356	374	9	closed	closed	ADJ
ejpam-4356	374	10	geodetic	geodetic	ADJ
ejpam-4356	374	11	dominating	dominating	NOUN
ejpam-4356	374	12	set	set	NOUN
ejpam-4356	374	13	of	of	ADP
ejpam-4356	374	14	v	v	DET
ejpam-4356	374	15	+	+	PROPN
ejpam-4356	374	16	kv	kv	PROPN
ejpam-4356	374	17	.	.	PUNCT
ejpam-4356	375	1	now	now	ADV
ejpam-4356	375	2	for	for	ADP
ejpam-4356	375	3	any	any	DET
ejpam-4356	375	4	x	x	NOUN
ejpam-4356	375	5	,	,	PUNCT
ejpam-4356	375	6	y	y	PROPN
ejpam-4356	375	7	∈	∈	PROPN
ejpam-4356	375	8	sv	sv	VERB
ejpam-4356	375	9	there	there	PRON
ejpam-4356	375	10	exists	exist	VERB
ejpam-4356	375	11	z	z	PROPN
ejpam-4356	375	12	∈	∈	PROPN
ejpam-4356	375	13	sv	sv	INTJ
ejpam-4356	375	14	such	such	ADJ
ejpam-4356	375	15	that	that	SCONJ
ejpam-4356	375	16	xz	xz	PROPN
ejpam-4356	375	17	,	,	PUNCT
ejpam-4356	375	18	yz	yz	PROPN
ejpam-4356	375	19	∈	∈	PROPN
ejpam-4356	375	20	e(v+kv	e(v+kv	NUM
ejpam-4356	375	21	)	)	PUNCT
ejpam-4356	375	22	.	.	PUNCT
ejpam-4356	376	1	thus	thus	ADV
ejpam-4356	376	2	,	,	PUNCT
ejpam-4356	376	3	ew(sv	ew(sv	PROPN
ejpam-4356	376	4	)	)	PUNCT
ejpam-4356	376	5	will	will	AUX
ejpam-4356	376	6	induce	induce	VERB
ejpam-4356	376	7	a	a	DET
ejpam-4356	376	8	connected	connected	ADJ
ejpam-4356	376	9	subgraph	subgraph	NOUN
ejpam-4356	376	10	since	since	SCONJ
ejpam-4356	376	11	n	n	PROPN
ejpam-4356	376	12	[	[	X
ejpam-4356	376	13	sv	sv	X
ejpam-4356	376	14	]	]	X
ejpam-4356	376	15	=	=	SYM
ejpam-4356	376	16	v	v	X
ejpam-4356	376	17	(	(	PUNCT
ejpam-4356	376	18	v	v	PROPN
ejpam-4356	376	19	+	+	PROPN
ejpam-4356	376	20	kv	kv	PROPN
ejpam-4356	376	21	)	)	PUNCT
ejpam-4356	376	22	,	,	PUNCT
ejpam-4356	376	23	we	we	PRON
ejpam-4356	376	24	have	have	VERB
ejpam-4356	376	25	sv	sv	PROPN
ejpam-4356	376	26	∈	∈	PROPN
ejpam-4356	376	27	w(v	w(v	PROPN
ejpam-4356	376	28	+	+	PROPN
ejpam-4356	376	29	kv	kv	PROPN
ejpam-4356	376	30	)	)	PUNCT
ejpam-4356	376	31	.	.	PUNCT
ejpam-4356	377	1	conversely	conversely	ADV
ejpam-4356	377	2	,	,	PUNCT
ejpam-4356	377	3	suppose	suppose	VERB
ejpam-4356	377	4	that	that	SCONJ
ejpam-4356	377	5	s	s	VERB
ejpam-4356	377	6	=	=	X
ejpam-4356	377	7	(	(	PUNCT
ejpam-4356	377	8	⋃	⋃	ADJ
ejpam-4356	377	9	v∈v	v∈v	NOUN
ejpam-4356	377	10	(	(	PUNCT
ejpam-4356	377	11	h	h	NOUN
ejpam-4356	377	12	)	)	PUNCT
ejpam-4356	377	13	sv)∪s0	sv)∪s0	NOUN
ejpam-4356	377	14	.	.	PUNCT
ejpam-4356	378	1	where	where	SCONJ
ejpam-4356	378	2	sv	sv	PROPN
ejpam-4356	378	3	⊆	⊆	NUM
ejpam-4356	378	4	v	v	X
ejpam-4356	378	5	(	(	PUNCT
ejpam-4356	378	6	k	k	NOUN
ejpam-4356	378	7	)	)	PUNCT
ejpam-4356	378	8	and	and	CCONJ
ejpam-4356	378	9	sv	sv	PROPN
ejpam-4356	378	10	∈	∈	PROPN
ejpam-4356	378	11	w(v+kv	w(v+kv	PROPN
ejpam-4356	378	12	)	)	PUNCT
ejpam-4356	378	13	and	and	CCONJ
ejpam-4356	378	14	s0	s0	PROPN
ejpam-4356	378	15	is	be	AUX
ejpam-4356	378	16	a	a	DET
ejpam-4356	378	17	weakly	weakly	ADV
ejpam-4356	378	18	connected	connected	ADJ
ejpam-4356	378	19	closed	closed	ADJ
ejpam-4356	378	20	geodetic	geodetic	ADJ
ejpam-4356	378	21	subset	subset	NOUN
ejpam-4356	378	22	of	of	ADP
ejpam-4356	378	23	v	v	PROPN
ejpam-4356	378	24	(	(	PUNCT
ejpam-4356	378	25	h	h	NOUN
ejpam-4356	378	26	)	)	PUNCT
ejpam-4356	378	27	.	.	PUNCT
ejpam-4356	379	1	by	by	ADP
ejpam-4356	379	2	lemma	lemma	PROPN
ejpam-4356	379	3	5	5	NUM
ejpam-4356	379	4	,	,	PUNCT
ejpam-4356	379	5	⋃	⋃	ADJ
ejpam-4356	379	6	v∈v	v∈v	NOUN
ejpam-4356	379	7	(	(	PUNCT
ejpam-4356	379	8	h	h	NOUN
ejpam-4356	379	9	)	)	PUNCT
ejpam-4356	379	10	sv	sv	PROPN
ejpam-4356	379	11	∈	∈	PROPN
ejpam-4356	379	12	w(g	w(g	PROPN
ejpam-4356	379	13	)	)	PUNCT
ejpam-4356	379	14	.	.	PUNCT
ejpam-4356	380	1	if	if	SCONJ
ejpam-4356	380	2	s0	s0	PROPN
ejpam-4356	380	3	=	=	PUNCT
ejpam-4356	380	4	∅	∅	NOUN
ejpam-4356	380	5	,	,	PUNCT
ejpam-4356	380	6	then	then	ADV
ejpam-4356	380	7	we	we	PRON
ejpam-4356	380	8	are	be	AUX
ejpam-4356	380	9	done	do	VERB
ejpam-4356	380	10	.	.	PUNCT
ejpam-4356	381	1	suppose	suppose	VERB
ejpam-4356	381	2	that	that	SCONJ
ejpam-4356	381	3	s0	s0	PROPN
ejpam-4356	381	4	̸=	̸=	PROPN
ejpam-4356	381	5	∅.	∅.	ADV
ejpam-4356	381	6	by	by	ADP
ejpam-4356	381	7	theorem	theorem	ADJ
ejpam-4356	381	8	20	20	NUM
ejpam-4356	381	9	and	and	CCONJ
ejpam-4356	381	10	and	and	CCONJ
ejpam-4356	381	11	lemma	lemma	PROPN
ejpam-4356	381	12	3	3	NUM
ejpam-4356	381	13	,	,	PUNCT
ejpam-4356	381	14	s	s	PART
ejpam-4356	381	15	=	=	PUNCT
ejpam-4356	381	16	(	(	PUNCT
ejpam-4356	381	17	⋃	⋃	ADJ
ejpam-4356	381	18	v∈v	v∈v	NOUN
ejpam-4356	381	19	(	(	PUNCT
ejpam-4356	381	20	h	h	NOUN
ejpam-4356	381	21	)	)	PUNCT
ejpam-4356	381	22	sv	sv	NOUN
ejpam-4356	381	23	)	)	PUNCT
ejpam-4356	381	24	∪	∪	NOUN
ejpam-4356	381	25	s0	s0	PROPN
ejpam-4356	381	26	gives	give	VERB
ejpam-4356	381	27	s0	s0	PROPN
ejpam-4356	381	28	=	=	PUNCT
ejpam-4356	381	29	s	s	PART
ejpam-4356	381	30	\	\	NOUN
ejpam-4356	381	31	⋃	⋃	NOUN
ejpam-4356	381	32	v∈v	v∈v	NOUN
ejpam-4356	381	33	(	(	PUNCT
ejpam-4356	381	34	h	h	NOUN
ejpam-4356	381	35	)	)	PUNCT
ejpam-4356	381	36	,	,	PUNCT
ejpam-4356	381	37	where	where	SCONJ
ejpam-4356	381	38	s	s	VERB
ejpam-4356	381	39	∈	∈	PROPN
ejpam-4356	381	40	c∗(g	c∗(g	PROPN
ejpam-4356	381	41	)	)	PUNCT
ejpam-4356	381	42	and	and	CCONJ
ejpam-4356	381	43	⋃	⋃	ADJ
ejpam-4356	381	44	v∈v	v∈v	NOUN
ejpam-4356	381	45	(	(	PUNCT
ejpam-4356	381	46	h	h	NOUN
ejpam-4356	381	47	)	)	PUNCT
ejpam-4356	381	48	∈	∈	PROPN
ejpam-4356	381	49	c∗(g	c∗(g	PROPN
ejpam-4356	381	50	)	)	PUNCT
ejpam-4356	381	51	and	and	CCONJ
ejpam-4356	381	52	s0	s0	PROPN
ejpam-4356	381	53	is	be	AUX
ejpam-4356	381	54	a	a	DET
ejpam-4356	381	55	weakly	weakly	ADV
ejpam-4356	381	56	connected	connected	ADJ
ejpam-4356	381	57	closed	closed	ADJ
ejpam-4356	381	58	geodetic	geodetic	ADJ
ejpam-4356	381	59	subset	subset	NOUN
ejpam-4356	381	60	of	of	ADP
ejpam-4356	381	61	v(h	v(h	NOUN
ejpam-4356	381	62	)	)	PUNCT
ejpam-4356	381	63	.	.	PUNCT
ejpam-4356	382	1	thus	thus	ADV
ejpam-4356	382	2	,	,	PUNCT
ejpam-4356	382	3	for	for	ADP
ejpam-4356	382	4	any	any	DET
ejpam-4356	382	5	x	x	NOUN
ejpam-4356	382	6	,	,	PUNCT
ejpam-4356	382	7	y	y	PROPN
ejpam-4356	382	8	∈	∈	PROPN
ejpam-4356	382	9	v	v	ADP
ejpam-4356	382	10	(	(	PUNCT
ejpam-4356	382	11	g	g	NOUN
ejpam-4356	382	12	)	)	PUNCT
ejpam-4356	382	13	\	\	PROPN
ejpam-4356	383	1	s	s	VERB
ejpam-4356	383	2	there	there	PRON
ejpam-4356	383	3	exists	exist	VERB
ejpam-4356	383	4	s	s	X
ejpam-4356	383	5	∈	∈	PROPN
ejpam-4356	383	6	s	s	VERB
ejpam-4356	383	7	such	such	ADJ
ejpam-4356	383	8	that	that	DET
ejpam-4356	383	9	xs	xs	PROPN
ejpam-4356	383	10	,	,	PUNCT
ejpam-4356	383	11	ys	ys	PROPN
ejpam-4356	383	12	∈	∈	PROPN
ejpam-4356	383	13	e(g	e(g	PROPN
ejpam-4356	383	14	)	)	PUNCT
ejpam-4356	383	15	.	.	PUNCT
ejpam-4356	384	1	hence	hence	ADV
ejpam-4356	384	2	,	,	PUNCT
ejpam-4356	384	3	ew(s	ew(s	X
ejpam-4356	384	4	)	)	PUNCT
ejpam-4356	384	5	will	will	AUX
ejpam-4356	384	6	induce	induce	VERB
ejpam-4356	384	7	a	a	DET
ejpam-4356	384	8	weakly	weakly	ADV
ejpam-4356	384	9	connected	connected	ADJ
ejpam-4356	384	10	subgraph	subgraph	NOUN
ejpam-4356	384	11	of	of	ADP
ejpam-4356	384	12	g.	g.	PROPN
ejpam-4356	384	13	therefore	therefore	ADV
ejpam-4356	384	14	,	,	PUNCT
ejpam-4356	384	15	s	s	VERB
ejpam-4356	384	16	=	=	PUNCT
ejpam-4356	384	17	(	(	PUNCT
ejpam-4356	384	18	⋃	⋃	ADJ
ejpam-4356	384	19	v∈v	v∈v	NOUN
ejpam-4356	384	20	(	(	PUNCT
ejpam-4356	384	21	h	h	NOUN
ejpam-4356	384	22	)	)	PUNCT
ejpam-4356	384	23	sv	sv	NOUN
ejpam-4356	384	24	)	)	PUNCT
ejpam-4356	384	25	∪	∪	VERB
ejpam-4356	384	26	s0	s0	PROPN
ejpam-4356	384	27	∈	∈	PROPN
ejpam-4356	384	28	w(g	w(g	PROPN
ejpam-4356	384	29	)	)	PUNCT
ejpam-4356	384	30	.	.	PUNCT
ejpam-4356	385	1	corollary	corollary	ADJ
ejpam-4356	385	2	10	10	NUM
ejpam-4356	385	3	.	.	PUNCT
ejpam-4356	386	1	let	let	VERB
ejpam-4356	386	2	g	g	NOUN
ejpam-4356	386	3	=	=	PUNCT
ejpam-4356	386	4	h	h	PROPN
ejpam-4356	386	5	◦	◦	NOUN
ejpam-4356	386	6	k	k	NOUN
ejpam-4356	386	7	,	,	PUNCT
ejpam-4356	386	8	where	where	SCONJ
ejpam-4356	386	9	h	h	NOUN
ejpam-4356	386	10	is	be	AUX
ejpam-4356	386	11	a	a	DET
ejpam-4356	386	12	connected	connected	ADJ
ejpam-4356	386	13	graph	graph	NOUN
ejpam-4356	386	14	and	and	CCONJ
ejpam-4356	386	15	k	k	PROPN
ejpam-4356	386	16	a	a	DET
ejpam-4356	386	17	noncomplete	noncomplete	ADJ
ejpam-4356	386	18	graph	graph	NOUN
ejpam-4356	386	19	.	.	PUNCT
ejpam-4356	387	1	then	then	ADV
ejpam-4356	387	2	s	s	VERB
ejpam-4356	387	3	is	be	AUX
ejpam-4356	387	4	γwcg	γwcg	NOUN
ejpam-4356	387	5	-	-	PUNCT
ejpam-4356	387	6	set	set	NOUN
ejpam-4356	387	7	of	of	ADP
ejpam-4356	387	8	g	g	PROPN
ejpam-4356	387	9	if	if	SCONJ
ejpam-4356	387	10	and	and	CCONJ
ejpam-4356	387	11	only	only	ADV
ejpam-4356	387	12	if	if	SCONJ
ejpam-4356	387	13	s	s	X
ejpam-4356	387	14	=	=	PUNCT
ejpam-4356	387	15	⋃	⋃	NOUN
ejpam-4356	387	16	v∈v	v∈v	NOUN
ejpam-4356	387	17	(	(	PUNCT
ejpam-4356	387	18	h	h	NOUN
ejpam-4356	387	19	)	)	PUNCT
ejpam-4356	387	20	sv	sv	NOUN
ejpam-4356	387	21	,	,	PUNCT
ejpam-4356	387	22	where	where	SCONJ
ejpam-4356	387	23	each	each	PRON
ejpam-4356	387	24	sv	sv	PROPN
ejpam-4356	388	1	⊆	⊆	NUM
ejpam-4356	388	2	v	v	ADP
ejpam-4356	388	3	(	(	PUNCT
ejpam-4356	388	4	v	v	NOUN
ejpam-4356	388	5	+	+	CCONJ
ejpam-4356	388	6	kv	kv	NOUN
ejpam-4356	388	7	)	)	PUNCT
ejpam-4356	388	8	is	be	AUX
ejpam-4356	388	9	γwcg	γwcg	NOUN
ejpam-4356	388	10	-	-	PUNCT
ejpam-4356	388	11	set	set	NOUN
ejpam-4356	388	12	of	of	ADP
ejpam-4356	388	13	v	v	DET
ejpam-4356	388	14	+	+	PROPN
ejpam-4356	388	15	kv	kv	PROPN
ejpam-4356	388	16	.	.	PUNCT
ejpam-4356	389	1	corollary	corollary	ADJ
ejpam-4356	389	2	11	11	NUM
ejpam-4356	389	3	.	.	PUNCT
ejpam-4356	390	1	let	let	VERB
ejpam-4356	390	2	g	g	NOUN
ejpam-4356	390	3	=	=	PUNCT
ejpam-4356	390	4	h	h	PROPN
ejpam-4356	391	1	◦	◦	NOUN
ejpam-4356	391	2	k	k	NOUN
ejpam-4356	391	3	,	,	PUNCT
ejpam-4356	391	4	where	where	SCONJ
ejpam-4356	391	5	h	h	NOUN
ejpam-4356	391	6	is	be	AUX
ejpam-4356	391	7	a	a	DET
ejpam-4356	391	8	connected	connected	ADJ
ejpam-4356	391	9	graph	graph	NOUN
ejpam-4356	391	10	of	of	ADP
ejpam-4356	391	11	order	order	NOUN
ejpam-4356	391	12	m	m	VERB
ejpam-4356	391	13	and	and	CCONJ
ejpam-4356	391	14	k	k	X
ejpam-4356	391	15	a	a	DET
ejpam-4356	391	16	noncomplete	noncomplete	ADJ
ejpam-4356	391	17	graph	graph	NOUN
ejpam-4356	391	18	.	.	PUNCT
ejpam-4356	392	1	then	then	ADV
ejpam-4356	392	2	γwcg(g	γwcg(g	NOUN
ejpam-4356	392	3	)	)	PUNCT
ejpam-4356	392	4	=	=	PUNCT
ejpam-4356	392	5	m	m	PRON
ejpam-4356	392	6	·	·	PUNCT
ejpam-4356	392	7	γwcg(k1	γwcg(k1	NOUN
ejpam-4356	392	8	◦	◦	NOUN
ejpam-4356	392	9	k	k	NOUN
ejpam-4356	392	10	)	)	PUNCT
ejpam-4356	392	11	.	.	PUNCT
ejpam-4356	393	1	theorem	theorem	NOUN
ejpam-4356	393	2	22	22	NUM
ejpam-4356	393	3	.	.	PUNCT
ejpam-4356	394	1	let	let	VERB
ejpam-4356	394	2	g	g	NOUN
ejpam-4356	394	3	=	=	PUNCT
ejpam-4356	394	4	h	h	PROPN
ejpam-4356	394	5	◦	◦	NOUN
ejpam-4356	394	6	k	k	NOUN
ejpam-4356	394	7	,	,	PUNCT
ejpam-4356	394	8	where	where	SCONJ
ejpam-4356	394	9	h	h	NOUN
ejpam-4356	394	10	is	be	AUX
ejpam-4356	394	11	a	a	DET
ejpam-4356	394	12	connected	connected	ADJ
ejpam-4356	394	13	graph	graph	NOUN
ejpam-4356	394	14	of	of	ADP
ejpam-4356	394	15	order	order	NOUN
ejpam-4356	394	16	m.	m.	NOUN
ejpam-4356	394	17	if	if	SCONJ
ejpam-4356	394	18	n	n	PRON
ejpam-4356	394	19	≥	≥	NOUN
ejpam-4356	394	20	3	3	NUM
ejpam-4356	394	21	,	,	PUNCT
ejpam-4356	394	22	then	then	ADV
ejpam-4356	394	23	γwcg(h	γwcg(h	INTJ
ejpam-4356	394	24	◦	◦	NOUN
ejpam-4356	394	25	cn	cn	NUM
ejpam-4356	394	26	)	)	PUNCT
ejpam-4356	394	27	=	=	SYM
ejpam-4356	394	28	m	m	PROPN
ejpam-4356	394	29	·	·	PUNCT
ejpam-4356	394	30	⌈n2	⌈n2	VERB
ejpam-4356	394	31	⌉.	⌉.	ADV
ejpam-4356	394	32	proof	proof	NOUN
ejpam-4356	394	33	.	.	PUNCT
ejpam-4356	395	1	let	let	VERB
ejpam-4356	395	2	g	g	NOUN
ejpam-4356	395	3	=	=	PUNCT
ejpam-4356	395	4	h	h	PROPN
ejpam-4356	396	1	◦	◦	NOUN
ejpam-4356	396	2	k	k	NOUN
ejpam-4356	396	3	,	,	PUNCT
ejpam-4356	396	4	where	where	SCONJ
ejpam-4356	396	5	h	h	NOUN
ejpam-4356	396	6	is	be	AUX
ejpam-4356	396	7	a	a	DET
ejpam-4356	396	8	connected	connected	ADJ
ejpam-4356	396	9	graph	graph	NOUN
ejpam-4356	396	10	of	of	ADP
ejpam-4356	396	11	order	order	NOUN
ejpam-4356	396	12	m	m	VERB
ejpam-4356	396	13	and	and	CCONJ
ejpam-4356	396	14	k	k	PROPN
ejpam-4356	396	15	=	=	X
ejpam-4356	396	16	cn	cn	PROPN
ejpam-4356	396	17	be	be	AUX
ejpam-4356	396	18	a	a	DET
ejpam-4356	396	19	noncomplete	noncomplete	ADJ
ejpam-4356	396	20	graph	graph	NOUN
ejpam-4356	396	21	.	.	PUNCT
ejpam-4356	397	1	then	then	ADV
ejpam-4356	397	2	,	,	PUNCT
ejpam-4356	397	3	we	we	PRON
ejpam-4356	397	4	have	have	VERB
ejpam-4356	397	5	γwcg(h	γwcg(h	NUM
ejpam-4356	397	6	◦	◦	NOUN
ejpam-4356	397	7	cn	cn	ADJ
ejpam-4356	397	8	)	)	PUNCT
ejpam-4356	397	9	=	=	PUNCT
ejpam-4356	397	10	m	m	NOUN
ejpam-4356	397	11	·	·	PUNCT
ejpam-4356	397	12	γwcg(k1	γwcg(k1	ADJ
ejpam-4356	397	13	◦	◦	NOUN
ejpam-4356	397	14	cn	cn	PROPN
ejpam-4356	397	15	)	)	PUNCT
ejpam-4356	397	16	,	,	PUNCT
ejpam-4356	397	17	by	by	ADP
ejpam-4356	397	18	corollary	corollary	ADJ
ejpam-4356	397	19	11	11	NUM
ejpam-4356	397	20	j.	j.	PROPN
ejpam-4356	397	21	hamja	hamja	PROPN
ejpam-4356	397	22	,	,	PUNCT
ejpam-4356	397	23	i.	i.	PROPN
ejpam-4356	397	24	aniversario	aniversario	PROPN
ejpam-4356	397	25	,	,	PUNCT
ejpam-4356	397	26	h.	h.	PROPN
ejpam-4356	397	27	rara	rara	PROPN
ejpam-4356	397	28	/	/	SYM
ejpam-4356	397	29	eur	eur	PROPN
ejpam-4356	397	30	.	.	PUNCT
ejpam-4356	398	1	j.	j.	PROPN
ejpam-4356	398	2	pure	pure	PROPN
ejpam-4356	398	3	appl	appl	PROPN
ejpam-4356	398	4	.	.	PROPN
ejpam-4356	398	5	math	math	PROPN
ejpam-4356	398	6	,	,	PUNCT
ejpam-4356	398	7	15	15	NUM
ejpam-4356	398	8	(	(	PUNCT
ejpam-4356	398	9	2	2	NUM
ejpam-4356	398	10	)	)	PUNCT
ejpam-4356	398	11	(	(	PUNCT
ejpam-4356	398	12	2022	2022	NUM
ejpam-4356	398	13	)	)	PUNCT
ejpam-4356	398	14	,	,	PUNCT
ejpam-4356	398	15	736	736	NUM
ejpam-4356	398	16	-	-	SYM
ejpam-4356	398	17	752	752	NUM
ejpam-4356	398	18	748	748	NUM
ejpam-4356	398	19	=	=	SYM
ejpam-4356	398	20	m	m	PROPN
ejpam-4356	398	21	·	·	PUNCT
ejpam-4356	398	22	γwcg(wn+1	γwcg(wn+1	NUM
ejpam-4356	398	23	)	)	PUNCT
ejpam-4356	399	1	=	=	SYM
ejpam-4356	399	2	m	m	NOUN
ejpam-4356	399	3	·	·	PUNCT
ejpam-4356	399	4	⌈n+	⌈n+	NOUN
ejpam-4356	399	5	1−	1−	NUM
ejpam-4356	399	6	1	1	NUM
ejpam-4356	399	7	2	2	NUM
ejpam-4356	399	8	⌉	⌉	NOUN
ejpam-4356	399	9	,	,	PUNCT
ejpam-4356	399	10	by	by	ADP
ejpam-4356	399	11	corolary	corolary	ADJ
ejpam-4356	399	12	1	1	NUM
ejpam-4356	399	13	(	(	PUNCT
ejpam-4356	399	14	vi	vi	NOUN
ejpam-4356	399	15	)	)	PUNCT
ejpam-4356	399	16	=	=	PRON
ejpam-4356	399	17	m	m	AUX
ejpam-4356	399	18	·	·	PUNCT
ejpam-4356	399	19	⌈n	⌈n	VERB
ejpam-4356	399	20	2	2	NUM
ejpam-4356	399	21	⌉	⌉	NOUN
ejpam-4356	399	22	corollary	corollary	ADJ
ejpam-4356	399	23	12	12	NUM
ejpam-4356	399	24	.	.	PUNCT
ejpam-4356	400	1	if	if	SCONJ
ejpam-4356	400	2	g	g	NOUN
ejpam-4356	400	3	=	=	NOUN
ejpam-4356	400	4	pm	pm	NOUN
ejpam-4356	400	5	◦	◦	NOUN
ejpam-4356	400	6	cn	cn	PROPN
ejpam-4356	400	7	.	.	PUNCT
ejpam-4356	401	1	then	then	ADV
ejpam-4356	401	2	γwcg(g	γwcg(g	PROPN
ejpam-4356	401	3	)	)	PUNCT
ejpam-4356	401	4	=	=	PUNCT
ejpam-4356	402	1	m	m	PROPN
ejpam-4356	402	2	·	·	PUNCT
ejpam-4356	402	3	⌈	⌈	NOUN
ejpam-4356	402	4	n	n	CCONJ
ejpam-4356	402	5	2	2	NUM
ejpam-4356	402	6	⌉	⌉	X
ejpam-4356	402	7	for	for	ADP
ejpam-4356	402	8	n	n	PRON
ejpam-4356	402	9	≥	≥	NUM
ejpam-4356	402	10	3	3	NUM
ejpam-4356	402	11	.	.	PUNCT
ejpam-4356	402	12	theorem	theorem	VERB
ejpam-4356	402	13	23	23	NUM
ejpam-4356	402	14	.	.	PUNCT
ejpam-4356	403	1	let	let	VERB
ejpam-4356	403	2	g	g	NOUN
ejpam-4356	403	3	=	=	PUNCT
ejpam-4356	403	4	h	h	PROPN
ejpam-4356	403	5	◦	◦	NOUN
ejpam-4356	403	6	k	k	NOUN
ejpam-4356	403	7	,	,	PUNCT
ejpam-4356	403	8	where	where	SCONJ
ejpam-4356	403	9	h	h	NOUN
ejpam-4356	403	10	is	be	AUX
ejpam-4356	403	11	a	a	DET
ejpam-4356	403	12	connected	connected	ADJ
ejpam-4356	403	13	graph	graph	NOUN
ejpam-4356	403	14	of	of	ADP
ejpam-4356	403	15	order	order	NOUN
ejpam-4356	403	16	m.	m.	NOUN
ejpam-4356	403	17	if	if	SCONJ
ejpam-4356	403	18	n	n	PRON
ejpam-4356	403	19	≥	≥	NOUN
ejpam-4356	403	20	3	3	NUM
ejpam-4356	403	21	,	,	PUNCT
ejpam-4356	403	22	then	then	ADV
ejpam-4356	403	23	γwcg(h	γwcg(h	INTJ
ejpam-4356	403	24	◦	◦	NOUN
ejpam-4356	403	25	pn	pn	NOUN
ejpam-4356	403	26	)	)	PUNCT
ejpam-4356	403	27	=	=	PUNCT
ejpam-4356	403	28	m	m	PROPN
ejpam-4356	403	29	·	·	PUNCT
ejpam-4356	403	30	⌊n+2	⌊n+2	AUX
ejpam-4356	403	31	2	2	NUM
ejpam-4356	403	32	⌋.	⌋.	NOUN
ejpam-4356	403	33	proof	proof	NOUN
ejpam-4356	403	34	.	.	PUNCT
ejpam-4356	404	1	let	let	VERB
ejpam-4356	404	2	g	g	NOUN
ejpam-4356	404	3	=	=	PUNCT
ejpam-4356	404	4	h	h	PROPN
ejpam-4356	405	1	◦	◦	NOUN
ejpam-4356	405	2	k	k	NOUN
ejpam-4356	405	3	,	,	PUNCT
ejpam-4356	405	4	where	where	SCONJ
ejpam-4356	405	5	h	h	NOUN
ejpam-4356	405	6	is	be	AUX
ejpam-4356	405	7	a	a	DET
ejpam-4356	405	8	connected	connected	ADJ
ejpam-4356	405	9	graph	graph	NOUN
ejpam-4356	405	10	of	of	ADP
ejpam-4356	405	11	order	order	NOUN
ejpam-4356	405	12	m	m	VERB
ejpam-4356	405	13	and	and	CCONJ
ejpam-4356	405	14	k	k	PROPN
ejpam-4356	405	15	=	=	NOUN
ejpam-4356	405	16	pn	pn	AUX
ejpam-4356	405	17	be	be	AUX
ejpam-4356	405	18	a	a	DET
ejpam-4356	405	19	noncomplete	noncomplete	ADJ
ejpam-4356	405	20	graph	graph	NOUN
ejpam-4356	405	21	.	.	PUNCT
ejpam-4356	406	1	then	then	ADV
ejpam-4356	406	2	,	,	PUNCT
ejpam-4356	406	3	we	we	PRON
ejpam-4356	406	4	have	have	VERB
ejpam-4356	406	5	γwcg(h	γwcg(h	NUM
ejpam-4356	406	6	◦	◦	NOUN
ejpam-4356	406	7	pn	pn	PROPN
ejpam-4356	406	8	)	)	PUNCT
ejpam-4356	406	9	=	=	PUNCT
ejpam-4356	406	10	m	m	NOUN
ejpam-4356	406	11	·	·	PUNCT
ejpam-4356	406	12	γwcg(k1	γwcg(k1	ADJ
ejpam-4356	406	13	◦	◦	NOUN
ejpam-4356	406	14	pn	pn	NOUN
ejpam-4356	406	15	)	)	PUNCT
ejpam-4356	406	16	,	,	PUNCT
ejpam-4356	406	17	by	by	ADP
ejpam-4356	406	18	corollary	corollary	ADJ
ejpam-4356	406	19	11	11	NUM
ejpam-4356	406	20	=	=	SYM
ejpam-4356	406	21	m	m	PROPN
ejpam-4356	406	22	·	·	PUNCT
ejpam-4356	406	23	γwcg(fn+1	γwcg(fn+1	PROPN
ejpam-4356	406	24	)	)	PUNCT
ejpam-4356	407	1	=	=	SYM
ejpam-4356	408	1	m	m	NOUN
ejpam-4356	408	2	·	·	PUNCT
ejpam-4356	408	3	⌈n+	⌈n+	NOUN
ejpam-4356	408	4	1	1	NUM
ejpam-4356	408	5	2	2	NUM
ejpam-4356	408	6	⌉	⌉	NOUN
ejpam-4356	408	7	,	,	PUNCT
ejpam-4356	408	8	by	by	ADP
ejpam-4356	408	9	corolary	corolary	ADJ
ejpam-4356	408	10	1	1	NUM
ejpam-4356	408	11	(	(	PUNCT
ejpam-4356	408	12	v	v	NOUN
ejpam-4356	408	13	)	)	PUNCT
ejpam-4356	408	14	corollary	corollary	ADJ
ejpam-4356	408	15	13	13	NUM
ejpam-4356	408	16	.	.	PUNCT
ejpam-4356	409	1	if	if	SCONJ
ejpam-4356	409	2	g	g	NOUN
ejpam-4356	409	3	=	=	SYM
ejpam-4356	409	4	cm	cm	NOUN
ejpam-4356	409	5	◦	◦	NOUN
ejpam-4356	409	6	pn	pn	PROPN
ejpam-4356	409	7	.	.	PUNCT
ejpam-4356	409	8	then	then	ADV
ejpam-4356	409	9	γwcg(g	γwcg(g	PROPN
ejpam-4356	409	10	)	)	PUNCT
ejpam-4356	409	11	=	=	PUNCT
ejpam-4356	409	12	m	m	PROPN
ejpam-4356	409	13	·	·	PUNCT
ejpam-4356	409	14	⌈	⌈	SYM
ejpam-4356	409	15	n+1	n+1	PROPN
ejpam-4356	409	16	2	2	NUM
ejpam-4356	409	17	⌉	⌉	NOUN
ejpam-4356	409	18	,	,	PUNCT
ejpam-4356	409	19	n	n	X
ejpam-4356	409	20	≥	≥	NOUN
ejpam-4356	409	21	3	3	NUM
ejpam-4356	409	22	.	.	PUNCT
ejpam-4356	409	23	theorem	theorem	NOUN
ejpam-4356	409	24	24	24	NUM
ejpam-4356	409	25	.	.	PUNCT
ejpam-4356	410	1	let	let	VERB
ejpam-4356	410	2	h	h	PRON
ejpam-4356	410	3	be	be	AUX
ejpam-4356	410	4	a	a	DET
ejpam-4356	410	5	nontrivial	nontrivial	ADJ
ejpam-4356	410	6	connected	connect	VERB
ejpam-4356	410	7	graph	graph	NOUN
ejpam-4356	410	8	of	of	ADP
ejpam-4356	410	9	order	order	NOUN
ejpam-4356	410	10	n	n	NOUN
ejpam-4356	410	11	and	and	CCONJ
ejpam-4356	410	12	k	k	PROPN
ejpam-4356	410	13	=	=	SYM
ejpam-4356	410	14	kn	kn	PROPN
ejpam-4356	410	15	.	.	PUNCT
ejpam-4356	411	1	then	then	ADV
ejpam-4356	411	2	s	s	VERB
ejpam-4356	411	3	=	=	PUNCT
ejpam-4356	411	4	⋃	⋃	NOUN
ejpam-4356	411	5	v∈v	v∈v	NOUN
ejpam-4356	411	6	(	(	PUNCT
ejpam-4356	411	7	h	h	NOUN
ejpam-4356	411	8	)	)	PUNCT
ejpam-4356	411	9	v	v	NOUN
ejpam-4356	411	10	(	(	PUNCT
ejpam-4356	411	11	v	v	PROPN
ejpam-4356	411	12	+	+	PROPN
ejpam-4356	411	13	kv	kv	NOUN
ejpam-4356	411	14	)	)	PUNCT
ejpam-4356	411	15	is	be	AUX
ejpam-4356	411	16	a	a	DET
ejpam-4356	411	17	γwcg	γwcg	NOUN
ejpam-4356	411	18	-	-	PUNCT
ejpam-4356	411	19	set	set	NOUN
ejpam-4356	411	20	of	of	ADP
ejpam-4356	411	21	h	h	PROPN
ejpam-4356	411	22	◦	◦	PROPN
ejpam-4356	411	23	kn	kn	PROPN
ejpam-4356	411	24	.	.	PUNCT
ejpam-4356	412	1	proof	proof	NOUN
ejpam-4356	412	2	.	.	PUNCT
ejpam-4356	413	1	let	let	VERB
ejpam-4356	413	2	h	h	PRON
ejpam-4356	413	3	be	be	AUX
ejpam-4356	413	4	a	a	DET
ejpam-4356	413	5	nontrivial	nontrivial	ADJ
ejpam-4356	413	6	connected	connect	VERB
ejpam-4356	413	7	graph	graph	NOUN
ejpam-4356	413	8	of	of	ADP
ejpam-4356	413	9	order	order	NOUN
ejpam-4356	413	10	n	n	NOUN
ejpam-4356	413	11	and	and	CCONJ
ejpam-4356	413	12	k	k	PROPN
ejpam-4356	413	13	=	=	SYM
ejpam-4356	413	14	kn	kn	PROPN
ejpam-4356	413	15	.	.	PROPN
ejpam-4356	413	16	suppose	suppose	VERB
ejpam-4356	413	17	that	that	SCONJ
ejpam-4356	413	18	s	s	VERB
ejpam-4356	413	19	=	=	PUNCT
ejpam-4356	413	20	⋃	⋃	NOUN
ejpam-4356	413	21	v∈v	v∈v	NOUN
ejpam-4356	413	22	(	(	PUNCT
ejpam-4356	413	23	h	h	NOUN
ejpam-4356	413	24	)	)	PUNCT
ejpam-4356	413	25	sv	sv	PROPN
ejpam-4356	413	26	,	,	PUNCT
ejpam-4356	413	27	sv	sv	PROPN
ejpam-4356	413	28	=	=	SYM
ejpam-4356	413	29	v	v	PROPN
ejpam-4356	413	30	(	(	PUNCT
ejpam-4356	413	31	v	v	NOUN
ejpam-4356	413	32	+	+	CCONJ
ejpam-4356	413	33	kv	kv	PROPN
ejpam-4356	413	34	)	)	PUNCT
ejpam-4356	413	35	.	.	PUNCT
ejpam-4356	414	1	by	by	ADP
ejpam-4356	414	2	lemma	lemma	PROPN
ejpam-4356	414	3	5	5	NUM
ejpam-4356	414	4	,	,	PUNCT
ejpam-4356	414	5	s	s	PART
ejpam-4356	414	6	=	=	PUNCT
ejpam-4356	414	7	⋃	⋃	NOUN
ejpam-4356	414	8	v∈v	v∈v	NOUN
ejpam-4356	414	9	(	(	PUNCT
ejpam-4356	414	10	h	h	NOUN
ejpam-4356	414	11	)	)	PUNCT
ejpam-4356	414	12	sv	sv	PROPN
ejpam-4356	415	1	∈	∈	PROPN
ejpam-4356	415	2	w(h	w(h	PROPN
ejpam-4356	415	3	◦	◦	PROPN
ejpam-4356	415	4	kn	kn	PROPN
ejpam-4356	415	5	)	)	PUNCT
ejpam-4356	415	6	.	.	PUNCT
ejpam-4356	416	1	then	then	ADV
ejpam-4356	416	2	,	,	PUNCT
ejpam-4356	416	3	by	by	ADP
ejpam-4356	416	4	corollary	corollary	ADJ
ejpam-4356	416	5	10	10	NUM
ejpam-4356	416	6	,	,	PUNCT
ejpam-4356	416	7	s	s	PART
ejpam-4356	416	8	=	=	PUNCT
ejpam-4356	416	9	⋃	⋃	NOUN
ejpam-4356	416	10	v∈v	v∈v	NOUN
ejpam-4356	416	11	(	(	PUNCT
ejpam-4356	416	12	h	h	NOUN
ejpam-4356	416	13	)	)	PUNCT
ejpam-4356	416	14	v	v	NOUN
ejpam-4356	416	15	(	(	PUNCT
ejpam-4356	416	16	v	v	PROPN
ejpam-4356	416	17	+	+	PROPN
ejpam-4356	416	18	kv	kv	NOUN
ejpam-4356	416	19	)	)	PUNCT
ejpam-4356	416	20	is	be	AUX
ejpam-4356	416	21	a	a	DET
ejpam-4356	416	22	γwcg	γwcg	NOUN
ejpam-4356	416	23	-	-	PUNCT
ejpam-4356	416	24	set	set	NOUN
ejpam-4356	416	25	of	of	ADP
ejpam-4356	416	26	h	h	PROPN
ejpam-4356	416	27	◦	◦	PROPN
ejpam-4356	416	28	kn	kn	PROPN
ejpam-4356	416	29	.	.	PUNCT
ejpam-4356	416	30	corollary	corollary	ADJ
ejpam-4356	416	31	14	14	NUM
ejpam-4356	416	32	.	.	PUNCT
ejpam-4356	417	1	let	let	VERB
ejpam-4356	417	2	g	g	NOUN
ejpam-4356	417	3	=	=	PUNCT
ejpam-4356	417	4	h	h	PROPN
ejpam-4356	417	5	◦	◦	NOUN
ejpam-4356	417	6	k	k	NOUN
ejpam-4356	417	7	,	,	PUNCT
ejpam-4356	417	8	where	where	SCONJ
ejpam-4356	417	9	h	h	NOUN
ejpam-4356	417	10	is	be	AUX
ejpam-4356	417	11	a	a	DET
ejpam-4356	417	12	nontrivial	nontrivial	ADJ
ejpam-4356	417	13	connected	connect	VERB
ejpam-4356	417	14	graph	graph	NOUN
ejpam-4356	417	15	of	of	ADP
ejpam-4356	417	16	order	order	NOUN
ejpam-4356	417	17	m	m	VERB
ejpam-4356	417	18	and	and	CCONJ
ejpam-4356	417	19	k	k	PROPN
ejpam-4356	417	20	=	=	SYM
ejpam-4356	417	21	kn	kn	PROPN
ejpam-4356	417	22	with	with	ADP
ejpam-4356	417	23	n	n	PRON
ejpam-4356	417	24	≥	≥	NUM
ejpam-4356	417	25	4	4	NUM
ejpam-4356	417	26	.	.	PUNCT
ejpam-4356	417	27	then	then	ADV
ejpam-4356	417	28	γwcg(g	γwcg(g	NOUN
ejpam-4356	417	29	)	)	PUNCT
ejpam-4356	417	30	=	=	PUNCT
ejpam-4356	417	31	m	m	PROPN
ejpam-4356	417	32	·	·	PUNCT
ejpam-4356	417	33	(	(	PUNCT
ejpam-4356	417	34	n+	n+	NOUN
ejpam-4356	417	35	1	1	NUM
ejpam-4356	417	36	)	)	PUNCT
ejpam-4356	417	37	.	.	PUNCT
ejpam-4356	418	1	the	the	DET
ejpam-4356	418	2	cartesian	cartesian	ADJ
ejpam-4356	418	3	product	product	NOUN
ejpam-4356	418	4	of	of	ADP
ejpam-4356	418	5	two	two	NUM
ejpam-4356	418	6	graphs	graph	NOUN
ejpam-4356	418	7	g	g	NOUN
ejpam-4356	418	8	and	and	CCONJ
ejpam-4356	418	9	h	h	NOUN
ejpam-4356	418	10	,	,	PUNCT
ejpam-4356	418	11	denoted	denote	VERB
ejpam-4356	418	12	by	by	ADP
ejpam-4356	418	13	g	g	PROPN
ejpam-4356	418	14	□	□	PROPN
ejpam-4356	418	15	h	h	NOUN
ejpam-4356	418	16	is	be	AUX
ejpam-4356	418	17	the	the	DET
ejpam-4356	418	18	graph	graph	NOUN
ejpam-4356	418	19	with	with	ADP
ejpam-4356	418	20	v	v	NOUN
ejpam-4356	418	21	(	(	PUNCT
ejpam-4356	418	22	g	g	NOUN
ejpam-4356	418	23	□	□	NOUN
ejpam-4356	418	24	h	h	NOUN
ejpam-4356	418	25	)	)	PUNCT
ejpam-4356	418	26	=	=	NOUN
ejpam-4356	418	27	v	v	X
ejpam-4356	418	28	(	(	PUNCT
ejpam-4356	418	29	g)×	g)×	NOUN
ejpam-4356	418	30	v	v	NOUN
ejpam-4356	418	31	(	(	PUNCT
ejpam-4356	418	32	h	h	NOUN
ejpam-4356	418	33	)	)	PUNCT
ejpam-4356	418	34	and	and	CCONJ
ejpam-4356	418	35	edge	edge	VERB
ejpam-4356	418	36	set	set	VERB
ejpam-4356	418	37	e(g	e(g	PROPN
ejpam-4356	418	38	□	□	SYM
ejpam-4356	418	39	h	h	NOUN
ejpam-4356	418	40	)	)	PUNCT
ejpam-4356	418	41	satisfying	satisfy	VERB
ejpam-4356	418	42	the	the	DET
ejpam-4356	418	43	following	follow	VERB
ejpam-4356	418	44	conditions	condition	NOUN
ejpam-4356	418	45	:	:	PUNCT
ejpam-4356	418	46	(	(	PUNCT
ejpam-4356	418	47	u1	u1	PROPN
ejpam-4356	418	48	,	,	PUNCT
ejpam-4356	418	49	v1)(u2	v1)(u2	PROPN
ejpam-4356	418	50	,	,	PUNCT
ejpam-4356	418	51	v2	v2	PROPN
ejpam-4356	418	52	)	)	PUNCT
ejpam-4356	418	53	∈	∈	PROPN
ejpam-4356	418	54	e(g	e(g	PROPN
ejpam-4356	418	55	□	□	SYM
ejpam-4356	418	56	h	h	NOUN
ejpam-4356	418	57	)	)	PUNCT
ejpam-4356	418	58	if	if	SCONJ
ejpam-4356	418	59	and	and	CCONJ
ejpam-4356	418	60	only	only	ADV
ejpam-4356	418	61	if	if	SCONJ
ejpam-4356	418	62	either	either	PRON
ejpam-4356	418	63	u1u2	u1u2	PROPN
ejpam-4356	418	64	∈	∈	PROPN
ejpam-4356	418	65	e(g	e(g	PROPN
ejpam-4356	418	66	)	)	PUNCT
ejpam-4356	418	67	and	and	CCONJ
ejpam-4356	418	68	v1	v1	NOUN
ejpam-4356	418	69	=	=	SYM
ejpam-4356	418	70	v2	v2	NOUN
ejpam-4356	418	71	or	or	CCONJ
ejpam-4356	418	72	u1	u1	NOUN
ejpam-4356	418	73	=	=	SYM
ejpam-4356	418	74	u2	u2	PROPN
ejpam-4356	418	75	and	and	CCONJ
ejpam-4356	418	76	v1v2	v1v2	PUNCT
ejpam-4356	418	77	∈	∈	PROPN
ejpam-4356	418	78	e(h	e(h	PROPN
ejpam-4356	418	79	)	)	PUNCT
ejpam-4356	418	80	,	,	PUNCT
ejpam-4356	418	81	harary	harary	NOUN
ejpam-4356	419	1	[	[	X
ejpam-4356	419	2	2	2	NUM
ejpam-4356	419	3	]	]	PUNCT
ejpam-4356	419	4	.	.	PUNCT
ejpam-4356	420	1	j.	j.	PROPN
ejpam-4356	420	2	hamja	hamja	PROPN
ejpam-4356	420	3	,	,	PUNCT
ejpam-4356	420	4	i.	i.	PROPN
ejpam-4356	420	5	aniversario	aniversario	PROPN
ejpam-4356	420	6	,	,	PUNCT
ejpam-4356	420	7	h.	h.	PROPN
ejpam-4356	420	8	rara	rara	PROPN
ejpam-4356	420	9	/	/	SYM
ejpam-4356	420	10	eur	eur	PROPN
ejpam-4356	420	11	.	.	PUNCT
ejpam-4356	421	1	j.	j.	PROPN
ejpam-4356	421	2	pure	pure	PROPN
ejpam-4356	421	3	appl	appl	PROPN
ejpam-4356	421	4	.	.	PROPN
ejpam-4356	421	5	math	math	PROPN
ejpam-4356	421	6	,	,	PUNCT
ejpam-4356	421	7	15	15	NUM
ejpam-4356	421	8	(	(	PUNCT
ejpam-4356	421	9	2	2	NUM
ejpam-4356	421	10	)	)	PUNCT
ejpam-4356	421	11	(	(	PUNCT
ejpam-4356	421	12	2022	2022	NUM
ejpam-4356	421	13	)	)	PUNCT
ejpam-4356	421	14	,	,	PUNCT
ejpam-4356	421	15	736	736	NUM
ejpam-4356	421	16	-	-	SYM
ejpam-4356	421	17	752	752	NUM
ejpam-4356	421	18	749	749	NUM
ejpam-4356	421	19	lemma	lemma	PROPN
ejpam-4356	421	20	6	6	NUM
ejpam-4356	421	21	.	.	PUNCT
ejpam-4356	421	22	chellathurai	chellathurai	NOUN
ejpam-4356	421	23	,	,	PUNCT
ejpam-4356	421	24	et.al	et.al	VERB
ejpam-4356	421	25	[	[	X
ejpam-4356	421	26	6	6	NUM
ejpam-4356	421	27	]	]	PUNCT
ejpam-4356	421	28	let	let	VERB
ejpam-4356	421	29	g	g	NOUN
ejpam-4356	421	30	=	=	SYM
ejpam-4356	421	31	(	(	PUNCT
ejpam-4356	421	32	v	v	NOUN
ejpam-4356	421	33	,	,	PUNCT
ejpam-4356	421	34	e	e	NOUN
ejpam-4356	421	35	)	)	PUNCT
ejpam-4356	421	36	be	be	VERB
ejpam-4356	421	37	the	the	DET
ejpam-4356	421	38	cartesian	cartesian	ADJ
ejpam-4356	421	39	product	product	NOUN
ejpam-4356	421	40	h	h	NOUN
ejpam-4356	421	41	□	□	PROPN
ejpam-4356	421	42	k	k	X
ejpam-4356	421	43	of	of	ADP
ejpam-4356	421	44	connected	connected	ADJ
ejpam-4356	421	45	graphs	graph	NOUN
ejpam-4356	421	46	h	h	NOUN
ejpam-4356	421	47	=	=	SYM
ejpam-4356	421	48	(	(	PUNCT
ejpam-4356	421	49	v1	v1	NOUN
ejpam-4356	421	50	,	,	PUNCT
ejpam-4356	421	51	e1	e1	NOUN
ejpam-4356	421	52	)	)	PUNCT
ejpam-4356	421	53	and	and	CCONJ
ejpam-4356	421	54	k	k	NOUN
ejpam-4356	421	55	=	=	PRON
ejpam-4356	421	56	(	(	PUNCT
ejpam-4356	421	57	v2	v2	PROPN
ejpam-4356	421	58	,	,	PUNCT
ejpam-4356	421	59	e2	e2	PROPN
ejpam-4356	421	60	)	)	PUNCT
ejpam-4356	421	61	.	.	PUNCT
ejpam-4356	422	1	if	if	SCONJ
ejpam-4356	422	2	s	s	VERB
ejpam-4356	422	3	⊆	⊆	NUM
ejpam-4356	422	4	v	v	NOUN
ejpam-4356	422	5	,	,	PUNCT
ejpam-4356	422	6	then	then	ADV
ejpam-4356	422	7	ig[s	ig[s	PROPN
ejpam-4356	422	8	]	]	PUNCT
ejpam-4356	422	9	⊆	⊆	NUM
ejpam-4356	422	10	ig[s1]	ig[s1]	NOUN
ejpam-4356	422	11	□	□	SYM
ejpam-4356	422	12	ig[s2	ig[s2	PROPN
ejpam-4356	422	13	]	]	PUNCT
ejpam-4356	422	14	.	.	PUNCT
ejpam-4356	423	1	lemma	lemma	PROPN
ejpam-4356	423	2	7	7	NUM
ejpam-4356	423	3	.	.	PUNCT
ejpam-4356	423	4	chellathurai	chellathurai	NOUN
ejpam-4356	423	5	,	,	PUNCT
ejpam-4356	423	6	et.al	et.al	VERB
ejpam-4356	423	7	[	[	X
ejpam-4356	423	8	6	6	NUM
ejpam-4356	423	9	]	]	PUNCT
ejpam-4356	423	10	let	let	VERB
ejpam-4356	423	11	g	g	NOUN
ejpam-4356	423	12	=	=	SYM
ejpam-4356	423	13	(	(	PUNCT
ejpam-4356	423	14	v	v	NOUN
ejpam-4356	423	15	,	,	PUNCT
ejpam-4356	423	16	e	e	NOUN
ejpam-4356	423	17	)	)	PUNCT
ejpam-4356	423	18	be	be	VERB
ejpam-4356	423	19	the	the	DET
ejpam-4356	423	20	cartesian	cartesian	ADJ
ejpam-4356	423	21	product	product	NOUN
ejpam-4356	423	22	h	h	NOUN
ejpam-4356	423	23	□	□	PROPN
ejpam-4356	423	24	k	k	X
ejpam-4356	423	25	of	of	ADP
ejpam-4356	423	26	connected	connected	ADJ
ejpam-4356	423	27	graphs	graph	NOUN
ejpam-4356	423	28	h	h	NOUN
ejpam-4356	423	29	=	=	SYM
ejpam-4356	423	30	(	(	PUNCT
ejpam-4356	423	31	v1	v1	NOUN
ejpam-4356	423	32	,	,	PUNCT
ejpam-4356	423	33	e1	e1	NOUN
ejpam-4356	423	34	)	)	PUNCT
ejpam-4356	423	35	and	and	CCONJ
ejpam-4356	423	36	k	k	NOUN
ejpam-4356	423	37	=	=	PRON
ejpam-4356	423	38	(	(	PUNCT
ejpam-4356	423	39	v2	v2	PROPN
ejpam-4356	423	40	,	,	PUNCT
ejpam-4356	423	41	e2	e2	PROPN
ejpam-4356	423	42	)	)	PUNCT
ejpam-4356	423	43	.	.	PUNCT
ejpam-4356	424	1	if	if	SCONJ
ejpam-4356	424	2	s	s	VERB
ejpam-4356	424	3	⊆	⊆	NUM
ejpam-4356	424	4	v	v	NOUN
ejpam-4356	424	5	,	,	PUNCT
ejpam-4356	424	6	then	then	ADV
ejpam-4356	424	7	ng[s	ng[s	PROPN
ejpam-4356	424	8	]	]	PUNCT
ejpam-4356	424	9	⊆	⊆	NUM
ejpam-4356	424	10	ng[s1]	ng[s1]	NOUN
ejpam-4356	424	11	□	□	SYM
ejpam-4356	424	12	ng[s2	ng[s2	PROPN
ejpam-4356	424	13	]	]	X
ejpam-4356	424	14	lemma	lemma	PROPN
ejpam-4356	424	15	8	8	NUM
ejpam-4356	424	16	.	.	PUNCT
ejpam-4356	425	1	let	let	VERB
ejpam-4356	425	2	h	h	NOUN
ejpam-4356	425	3	and	and	CCONJ
ejpam-4356	425	4	j	j	PROPN
ejpam-4356	425	5	be	be	AUX
ejpam-4356	425	6	graphs	graph	NOUN
ejpam-4356	425	7	of	of	ADP
ejpam-4356	425	8	order	order	NOUN
ejpam-4356	425	9	m	m	VERB
ejpam-4356	425	10	and	and	CCONJ
ejpam-4356	425	11	n	n	PRON
ejpam-4356	425	12	respectively	respectively	ADV
ejpam-4356	425	13	,	,	PUNCT
ejpam-4356	425	14	and	and	CCONJ
ejpam-4356	425	15	let	let	VERB
ejpam-4356	425	16	g	g	PROPN
ejpam-4356	425	17	=	=	NOUN
ejpam-4356	425	18	h	h	PROPN
ejpam-4356	425	19	□	□	PROPN
ejpam-4356	425	20	j	j	PROPN
ejpam-4356	425	21	be	be	VERB
ejpam-4356	425	22	the	the	DET
ejpam-4356	425	23	cartesian	cartesian	ADJ
ejpam-4356	425	24	product	product	NOUN
ejpam-4356	425	25	of	of	ADP
ejpam-4356	425	26	graphs	graph	NOUN
ejpam-4356	425	27	h	h	NOUN
ejpam-4356	425	28	and	and	CCONJ
ejpam-4356	425	29	j	j	PROPN
ejpam-4356	425	30	.	.	PUNCT
ejpam-4356	426	1	(	(	PUNCT
ejpam-4356	426	2	i.	i.	PROPN
ejpam-4356	426	3	)	)	PUNCT
ejpam-4356	427	1	if	if	SCONJ
ejpam-4356	427	2	s	s	VERB
ejpam-4356	427	3	⊆	⊆	NUM
ejpam-4356	427	4	v	v	NOUN
ejpam-4356	427	5	(	(	PUNCT
ejpam-4356	427	6	h	h	NOUN
ejpam-4356	427	7	)	)	PUNCT
ejpam-4356	427	8	(	(	PUNCT
ejpam-4356	427	9	or	or	CCONJ
ejpam-4356	427	10	s	s	PRON
ejpam-4356	427	11	⊆	⊆	NUM
ejpam-4356	427	12	v	v	NOUN
ejpam-4356	427	13	(	(	PUNCT
ejpam-4356	427	14	j	j	NOUN
ejpam-4356	427	15	)	)	PUNCT
ejpam-4356	427	16	)	)	PUNCT
ejpam-4356	427	17	,	,	PUNCT
ejpam-4356	427	18	then	then	ADV
ejpam-4356	427	19	v	v	X
ejpam-4356	427	20	[	[	X
ejpam-4356	427	21	s×{vi	s×{vi	NOUN
ejpam-4356	427	22	}	}	PUNCT
ejpam-4356	427	23	]	]	PUNCT
ejpam-4356	428	1	⊆	⊆	NUM
ejpam-4356	428	2	v	v	X
ejpam-4356	428	3	(	(	PUNCT
ejpam-4356	428	4	hi)(orv	hi)(orv	X
ejpam-4356	428	5	(	(	PUNCT
ejpam-4356	428	6	ji	ji	NOUN
ejpam-4356	428	7	)	)	PUNCT
ejpam-4356	428	8	)	)	PUNCT
ejpam-4356	428	9	for	for	ADP
ejpam-4356	428	10	v	v	NUM
ejpam-4356	428	11	∈	∈	PROPN
ejpam-4356	428	12	ji	ji	X
ejpam-4356	428	13	(	(	PUNCT
ejpam-4356	428	14	or	or	CCONJ
ejpam-4356	428	15	hi	hi	INTJ
ejpam-4356	428	16	)	)	PUNCT
ejpam-4356	428	17	.	.	PUNCT
ejpam-4356	429	1	(	(	PUNCT
ejpam-4356	429	2	ii	ii	X
ejpam-4356	429	3	.	.	PUNCT
ejpam-4356	429	4	)	)	PUNCT
ejpam-4356	430	1	if	if	SCONJ
ejpam-4356	430	2	s	s	VERB
ejpam-4356	430	3	⊆	⊆	NUM
ejpam-4356	430	4	v	v	NOUN
ejpam-4356	430	5	(	(	PUNCT
ejpam-4356	430	6	h	h	NOUN
ejpam-4356	430	7	)	)	PUNCT
ejpam-4356	430	8	(	(	PUNCT
ejpam-4356	430	9	or	or	CCONJ
ejpam-4356	430	10	s	s	PRON
ejpam-4356	430	11	⊆	⊆	NUM
ejpam-4356	430	12	v	v	NOUN
ejpam-4356	430	13	(	(	PUNCT
ejpam-4356	430	14	j	j	NOUN
ejpam-4356	430	15	)	)	PUNCT
ejpam-4356	430	16	)	)	PUNCT
ejpam-4356	430	17	is	be	AUX
ejpam-4356	430	18	a	a	DET
ejpam-4356	430	19	γwcg	γwcg	NOUN
ejpam-4356	430	20	-	-	PUNCT
ejpam-4356	430	21	set	set	NOUN
ejpam-4356	430	22	of	of	ADP
ejpam-4356	430	23	a	a	DET
ejpam-4356	430	24	graph	graph	NOUN
ejpam-4356	430	25	h	h	NOUN
ejpam-4356	430	26	(	(	PUNCT
ejpam-4356	430	27	or	or	CCONJ
ejpam-4356	430	28	j	j	NOUN
ejpam-4356	430	29	)	)	PUNCT
ejpam-4356	430	30	,	,	PUNCT
ejpam-4356	430	31	then	then	ADV
ejpam-4356	430	32	v	v	ADP
ejpam-4356	430	33	[	[	X
ejpam-4356	430	34	s	s	X
ejpam-4356	430	35	×	×	NOUN
ejpam-4356	430	36	{	{	PUNCT
ejpam-4356	430	37	vi	vi	NOUN
ejpam-4356	430	38	}	}	PUNCT
ejpam-4356	430	39	]	]	PUNCT
ejpam-4356	430	40	is	be	AUX
ejpam-4356	430	41	a	a	DET
ejpam-4356	430	42	γwcg	γwcg	NOUN
ejpam-4356	430	43	-	-	PUNCT
ejpam-4356	430	44	set	set	NOUN
ejpam-4356	430	45	of	of	ADP
ejpam-4356	430	46	graph	graph	NOUN
ejpam-4356	430	47	hi	hi	INTJ
ejpam-4356	430	48	(	(	PUNCT
ejpam-4356	430	49	or	or	CCONJ
ejpam-4356	430	50	ji	ji	PROPN
ejpam-4356	430	51	)	)	PUNCT
ejpam-4356	430	52	.	.	PUNCT
ejpam-4356	431	1	but	but	CCONJ
ejpam-4356	431	2	,	,	PUNCT
ejpam-4356	431	3	v	v	X
ejpam-4356	431	4	[	[	X
ejpam-4356	431	5	s	s	X
ejpam-4356	431	6	×	×	NOUN
ejpam-4356	431	7	{	{	PUNCT
ejpam-4356	431	8	vi	vi	NOUN
ejpam-4356	431	9	}	}	PUNCT
ejpam-4356	431	10	]	]	PUNCT
ejpam-4356	431	11	is	be	AUX
ejpam-4356	431	12	not	not	PART
ejpam-4356	431	13	a	a	DET
ejpam-4356	431	14	γwcg	γwcg	NOUN
ejpam-4356	431	15	-	-	PUNCT
ejpam-4356	431	16	set	set	NOUN
ejpam-4356	431	17	of	of	ADP
ejpam-4356	431	18	g.	g.	PROPN
ejpam-4356	431	19	remark	remark	PROPN
ejpam-4356	431	20	4	4	NUM
ejpam-4356	431	21	.	.	PUNCT
ejpam-4356	432	1	let	let	VERB
ejpam-4356	432	2	h	h	NOUN
ejpam-4356	432	3	and	and	CCONJ
ejpam-4356	432	4	j	j	PROPN
ejpam-4356	432	5	be	be	AUX
ejpam-4356	432	6	graphs	graph	NOUN
ejpam-4356	432	7	of	of	ADP
ejpam-4356	432	8	order	order	NOUN
ejpam-4356	432	9	m	m	VERB
ejpam-4356	432	10	and	and	CCONJ
ejpam-4356	432	11	n	n	PRON
ejpam-4356	432	12	respectively	respectively	ADV
ejpam-4356	432	13	,	,	PUNCT
ejpam-4356	432	14	and	and	CCONJ
ejpam-4356	432	15	let	let	VERB
ejpam-4356	432	16	h	h	PRON
ejpam-4356	432	17	□	□	VERB
ejpam-4356	432	18	j	j	PROPN
ejpam-4356	432	19	be	be	VERB
ejpam-4356	432	20	the	the	DET
ejpam-4356	432	21	cartesian	cartesian	ADJ
ejpam-4356	432	22	product	product	NOUN
ejpam-4356	432	23	of	of	ADP
ejpam-4356	432	24	graphs	graph	NOUN
ejpam-4356	432	25	h	h	NOUN
ejpam-4356	432	26	and	and	CCONJ
ejpam-4356	432	27	j	j	PROPN
ejpam-4356	432	28	.	.	PUNCT
ejpam-4356	433	1	if	if	SCONJ
ejpam-4356	433	2	s	s	VERB
ejpam-4356	433	3	⊆	⊆	NUM
ejpam-4356	433	4	v	v	NOUN
ejpam-4356	433	5	(	(	PUNCT
ejpam-4356	433	6	h	h	NOUN
ejpam-4356	433	7	)	)	PUNCT
ejpam-4356	433	8	(	(	PUNCT
ejpam-4356	433	9	or	or	CCONJ
ejpam-4356	433	10	s	s	PRON
ejpam-4356	433	11	⊆	⊆	NUM
ejpam-4356	433	12	v	v	NOUN
ejpam-4356	433	13	(	(	PUNCT
ejpam-4356	433	14	j	j	NOUN
ejpam-4356	433	15	)	)	PUNCT
ejpam-4356	433	16	)	)	PUNCT
ejpam-4356	433	17	is	be	AUX
ejpam-4356	433	18	a	a	DET
ejpam-4356	433	19	γwcg	γwcg	NOUN
ejpam-4356	433	20	-	-	PUNCT
ejpam-4356	433	21	set	set	NOUN
ejpam-4356	433	22	of	of	ADP
ejpam-4356	433	23	graphs	graph	NOUN
ejpam-4356	433	24	h	h	NOUN
ejpam-4356	433	25	(	(	PUNCT
ejpam-4356	433	26	or	or	CCONJ
ejpam-4356	433	27	j	j	NOUN
ejpam-4356	433	28	)	)	PUNCT
ejpam-4356	433	29	,	,	PUNCT
ejpam-4356	433	30	then	then	ADV
ejpam-4356	433	31	s	s	AUX
ejpam-4356	433	32	×	×	PROPN
ejpam-4356	433	33	{	{	PUNCT
ejpam-4356	433	34	vi	vi	NOUN
ejpam-4356	433	35	}	}	PUNCT
ejpam-4356	433	36	is	be	AUX
ejpam-4356	433	37	a	a	DET
ejpam-4356	433	38	γwcg	γwcg	NOUN
ejpam-4356	433	39	-	-	PUNCT
ejpam-4356	433	40	set	set	NOUN
ejpam-4356	433	41	of	of	ADP
ejpam-4356	433	42	graph	graph	NOUN
ejpam-4356	433	43	hi	hi	INTJ
ejpam-4356	433	44	(	(	PUNCT
ejpam-4356	433	45	or	or	CCONJ
ejpam-4356	433	46	ji	ji	PROPN
ejpam-4356	433	47	)	)	PUNCT
ejpam-4356	433	48	.	.	PUNCT
ejpam-4356	434	1	theorem	theorem	VERB
ejpam-4356	434	2	25	25	NUM
ejpam-4356	434	3	.	.	PUNCT
ejpam-4356	435	1	let	let	VERB
ejpam-4356	435	2	h	h	NOUN
ejpam-4356	435	3	and	and	CCONJ
ejpam-4356	435	4	j	j	PROPN
ejpam-4356	435	5	be	be	AUX
ejpam-4356	435	6	connected	connect	VERB
ejpam-4356	435	7	graphs	graph	NOUN
ejpam-4356	435	8	.	.	PUNCT
ejpam-4356	436	1	then	then	ADV
ejpam-4356	436	2	γwcg(h	γwcg(h	PROPN
ejpam-4356	436	3	□	□	PROPN
ejpam-4356	436	4	j	j	NOUN
ejpam-4356	436	5	)	)	PUNCT
ejpam-4356	436	6	≥	≥	NOUN
ejpam-4356	436	7	max{γwcg(h	max{γwcg(h	PROPN
ejpam-4356	436	8	)	)	PUNCT
ejpam-4356	436	9	,	,	PUNCT
ejpam-4356	436	10	γwcg(j	γwcg(j	NOUN
ejpam-4356	436	11	)	)	PUNCT
ejpam-4356	436	12	}	}	PUNCT
ejpam-4356	436	13	.	.	PUNCT
ejpam-4356	437	1	equality	equality	NOUN
ejpam-4356	437	2	holds	hold	VERB
ejpam-4356	437	3	if	if	SCONJ
ejpam-4356	437	4	h	h	PROPN
ejpam-4356	437	5	and	and	CCONJ
ejpam-4356	437	6	j	j	PROPN
ejpam-4356	437	7	are	be	AUX
ejpam-4356	437	8	complete	complete	ADJ
ejpam-4356	437	9	graphs	graph	NOUN
ejpam-4356	437	10	.	.	PUNCT
ejpam-4356	438	1	proof	proof	NOUN
ejpam-4356	438	2	.	.	PUNCT
ejpam-4356	439	1	let	let	VERB
ejpam-4356	439	2	s	s	PRON
ejpam-4356	439	3	⊆	⊆	NUM
ejpam-4356	439	4	v	v	NOUN
ejpam-4356	439	5	(	(	PUNCT
ejpam-4356	439	6	h	h	NOUN
ejpam-4356	439	7	□	□	PROPN
ejpam-4356	439	8	j	j	NOUN
ejpam-4356	439	9	)	)	PUNCT
ejpam-4356	439	10	be	be	VERB
ejpam-4356	439	11	a	a	DET
ejpam-4356	439	12	γwcg	γwcg	NOUN
ejpam-4356	439	13	-	-	PUNCT
ejpam-4356	439	14	set	set	NOUN
ejpam-4356	439	15	of	of	ADP
ejpam-4356	439	16	h	h	NOUN
ejpam-4356	439	17	□	□	PROPN
ejpam-4356	439	18	j	j	PROPN
ejpam-4356	439	19	.	.	PUNCT
ejpam-4356	440	1	then	then	ADV
ejpam-4356	440	2	by	by	ADP
ejpam-4356	440	3	lemma	lemma	PROPN
ejpam-4356	440	4	6	6	NUM
ejpam-4356	440	5	and	and	CCONJ
ejpam-4356	440	6	7	7	NUM
ejpam-4356	440	7	,	,	PUNCT
ejpam-4356	440	8	v	v	NOUN
ejpam-4356	440	9	(	(	PUNCT
ejpam-4356	440	10	h	h	NOUN
ejpam-4356	440	11	□	□	PROPN
ejpam-4356	440	12	j	j	NOUN
ejpam-4356	440	13	)	)	PUNCT
ejpam-4356	440	14	=	=	SYM
ejpam-4356	440	15	ig[s	ig[s	PROPN
ejpam-4356	440	16	]	]	X
ejpam-4356	440	17	⊆	⊆	NUM
ejpam-4356	440	18	ig[s1]	ig[s1]	NOUN
ejpam-4356	440	19	□	□	SYM
ejpam-4356	440	20	ig[s2	ig[s2	PROPN
ejpam-4356	440	21	]	]	PUNCT
ejpam-4356	440	22	and	and	CCONJ
ejpam-4356	440	23	v	v	NOUN
ejpam-4356	440	24	(	(	PUNCT
ejpam-4356	440	25	h	h	NOUN
ejpam-4356	440	26	□	□	PROPN
ejpam-4356	440	27	j	j	NOUN
ejpam-4356	440	28	)	)	PUNCT
ejpam-4356	440	29	=	=	SYM
ejpam-4356	440	30	ng[s	ng[s	PROPN
ejpam-4356	440	31	]	]	PUNCT
ejpam-4356	440	32	⊆	⊆	NUM
ejpam-4356	440	33	ng[s1]	ng[s1]	NOUN
ejpam-4356	440	34	□	□	SYM
ejpam-4356	440	35	ng[s2	ng[s2	PROPN
ejpam-4356	440	36	]	]	X
ejpam-4356	440	37	.	.	PUNCT
ejpam-4356	441	1	since	since	SCONJ
ejpam-4356	441	2	g	g	PROPN
ejpam-4356	441	3	is	be	AUX
ejpam-4356	441	4	connected	connect	VERB
ejpam-4356	441	5	and	and	CCONJ
ejpam-4356	441	6	ng[s	ng[	NOUN
ejpam-4356	441	7	]	]	PUNCT
ejpam-4356	441	8	=	=	SYM
ejpam-4356	441	9	v	v	X
ejpam-4356	441	10	(	(	PUNCT
ejpam-4356	441	11	h	h	NOUN
ejpam-4356	441	12	□	□	PROPN
ejpam-4356	441	13	j	j	NOUN
ejpam-4356	441	14	)	)	PUNCT
ejpam-4356	441	15	,	,	PUNCT
ejpam-4356	441	16	there	there	PRON
ejpam-4356	441	17	exists	exist	VERB
ejpam-4356	441	18	xv	xv	PROPN
ejpam-4356	441	19	,	,	PUNCT
ejpam-4356	441	20	vy	vy	NOUN
ejpam-4356	441	21	∈	∈	PROPN
ejpam-4356	441	22	e(h	e(h	PROPN
ejpam-4356	441	23	□	□	SYM
ejpam-4356	441	24	j	j	NOUN
ejpam-4356	441	25	)	)	PUNCT
ejpam-4356	441	26	such	such	ADJ
ejpam-4356	441	27	that	that	SCONJ
ejpam-4356	441	28	x	x	SYM
ejpam-4356	441	29	∈	∈	NOUN
ejpam-4356	441	30	s	s	X
ejpam-4356	441	31	or	or	CCONJ
ejpam-4356	441	32	y	y	PROPN
ejpam-4356	441	33	∈	∈	PROPN
ejpam-4356	441	34	s	s	VERB
ejpam-4356	441	35	for	for	ADP
ejpam-4356	441	36	some	some	DET
ejpam-4356	441	37	v	v	ADP
ejpam-4356	441	38	∈	∈	PROPN
ejpam-4356	441	39	v	v	NOUN
ejpam-4356	441	40	(	(	PUNCT
ejpam-4356	441	41	h	h	NOUN
ejpam-4356	441	42	□	□	PROPN
ejpam-4356	441	43	j	j	NOUN
ejpam-4356	441	44	)	)	PUNCT
ejpam-4356	441	45	.	.	PUNCT
ejpam-4356	442	1	hence	hence	ADV
ejpam-4356	442	2	,	,	PUNCT
ejpam-4356	442	3	⟨s⟩w	⟨s⟩w	VERB
ejpam-4356	442	4	⊆	⊆	NUM
ejpam-4356	442	5	⟨s1⟩w	⟨s1⟩w	NOUN
ejpam-4356	442	6	□	□	SYM
ejpam-4356	442	7	⟨s2⟩w	⟨s2⟩w	PROPN
ejpam-4356	442	8	is	be	AUX
ejpam-4356	442	9	also	also	ADV
ejpam-4356	442	10	connected	connect	VERB
ejpam-4356	442	11	.	.	PUNCT
ejpam-4356	443	1	thus	thus	ADV
ejpam-4356	443	2	,	,	PUNCT
ejpam-4356	443	3	s1	s1	NOUN
ejpam-4356	443	4	and	and	CCONJ
ejpam-4356	443	5	s2	s2	PROPN
ejpam-4356	443	6	are	be	AUX
ejpam-4356	443	7	γwcg	γwcg	NOUN
ejpam-4356	443	8	-	-	PUNCT
ejpam-4356	443	9	sets	set	NOUN
ejpam-4356	443	10	of	of	ADP
ejpam-4356	443	11	h	h	NOUN
ejpam-4356	443	12	and	and	CCONJ
ejpam-4356	443	13	j	j	PROPN
ejpam-4356	443	14	respectively	respectively	ADV
ejpam-4356	443	15	,	,	PUNCT
ejpam-4356	443	16	with	with	ADP
ejpam-4356	443	17	γwcg(h	γwcg(h	NOUN
ejpam-4356	443	18	)	)	PUNCT
ejpam-4356	443	19	≤	≤	NOUN
ejpam-4356	443	20	|s1|	|s1|	NOUN
ejpam-4356	443	21	and	and	CCONJ
ejpam-4356	443	22	γwcg(j	γwcg(j	NOUN
ejpam-4356	443	23	)	)	PUNCT
ejpam-4356	443	24	≤	≤	NUM
ejpam-4356	443	25	|s2|	|s2|	NOUN
ejpam-4356	443	26	.	.	PUNCT
ejpam-4356	444	1	therefore	therefore	ADV
ejpam-4356	444	2	,	,	PUNCT
ejpam-4356	444	3	γwcg(h	γwcg(h	PROPN
ejpam-4356	444	4	□	□	PROPN
ejpam-4356	444	5	j	j	NOUN
ejpam-4356	444	6	)	)	PUNCT
ejpam-4356	444	7	=	=	SYM
ejpam-4356	444	8	|s|	|s|	PROPN
ejpam-4356	444	9	≥	≥	PROPN
ejpam-4356	444	10	max{|s1|	max{|s1|	PROPN
ejpam-4356	444	11	|s2|	|s2|	PROPN
ejpam-4356	444	12	}	}	PUNCT
ejpam-4356	444	13	≥	≥	NOUN
ejpam-4356	444	14	max{γwcg(h	max{γwcg(h	NOUN
ejpam-4356	444	15	)	)	PUNCT
ejpam-4356	444	16	,	,	PUNCT
ejpam-4356	444	17	γwcg(k	γwcg(k	NOUN
ejpam-4356	444	18	)	)	PUNCT
ejpam-4356	444	19	}	}	PUNCT
ejpam-4356	444	20	.	.	PUNCT
ejpam-4356	445	1	so	so	ADV
ejpam-4356	445	2	,	,	PUNCT
ejpam-4356	445	3	equality	equality	NOUN
ejpam-4356	445	4	holds	hold	VERB
ejpam-4356	445	5	.	.	PUNCT
ejpam-4356	446	1	corollary	corollary	ADJ
ejpam-4356	446	2	15	15	NUM
ejpam-4356	446	3	.	.	PUNCT
ejpam-4356	447	1	for	for	ADP
ejpam-4356	447	2	every	every	DET
ejpam-4356	447	3	nontrivial	nontrivial	ADJ
ejpam-4356	447	4	connected	connect	VERB
ejpam-4356	447	5	graph	graph	NOUN
ejpam-4356	447	6	h	h	PROPN
ejpam-4356	447	7	,	,	PUNCT
ejpam-4356	447	8	γwcg(h	γwcg(h	NOUN
ejpam-4356	447	9	)	)	PUNCT
ejpam-4356	447	10	≤	≤	NUM
ejpam-4356	447	11	γwcg(h	γwcg(h	PROPN
ejpam-4356	447	12	□	□	PROPN
ejpam-4356	447	13	kn	kn	PROPN
ejpam-4356	447	14	)	)	PUNCT
ejpam-4356	447	15	.	.	PUNCT
ejpam-4356	448	1	theorem	theorem	NOUN
ejpam-4356	448	2	26	26	NUM
ejpam-4356	448	3	.	.	PUNCT
ejpam-4356	449	1	let	let	VERB
ejpam-4356	449	2	h	h	PRON
ejpam-4356	449	3	be	be	AUX
ejpam-4356	449	4	a	a	DET
ejpam-4356	449	5	connected	connected	ADJ
ejpam-4356	449	6	graph	graph	NOUN
ejpam-4356	449	7	of	of	ADP
ejpam-4356	449	8	order	order	NOUN
ejpam-4356	449	9	at	at	ADV
ejpam-4356	449	10	least	least	ADV
ejpam-4356	449	11	3	3	NUM
ejpam-4356	449	12	and	and	CCONJ
ejpam-4356	449	13	diameter	diameter	NOUN
ejpam-4356	449	14	at	at	ADP
ejpam-4356	449	15	most	most	ADV
ejpam-4356	449	16	2	2	NUM
ejpam-4356	449	17	.	.	PUNCT
ejpam-4356	450	1	then	then	ADV
ejpam-4356	450	2	h	h	PROPN
ejpam-4356	450	3	has	have	VERB
ejpam-4356	450	4	γwcg	γwcg	NOUN
ejpam-4356	450	5	-	-	PUNCT
ejpam-4356	450	6	set	set	VERB
ejpam-4356	450	7	s	s	NOUN
ejpam-4356	450	8	with	with	ADP
ejpam-4356	450	9	a	a	DET
ejpam-4356	450	10	vertex	vertex	NOUN
ejpam-4356	450	11	x	x	NOUN
ejpam-4356	450	12	such	such	ADJ
ejpam-4356	450	13	that	that	SCONJ
ejpam-4356	450	14	every	every	DET
ejpam-4356	450	15	vertex	vertex	NOUN
ejpam-4356	450	16	of	of	ADP
ejpam-4356	450	17	h	h	NOUN
ejpam-4356	450	18	lies	lie	VERB
ejpam-4356	450	19	on	on	ADP
ejpam-4356	450	20	some	some	DET
ejpam-4356	450	21	uv	uv	NOUN
ejpam-4356	450	22	geodesic	geodesic	NOUN
ejpam-4356	450	23	in	in	ADP
ejpam-4356	450	24	h	h	NOUN
ejpam-4356	450	25	for	for	ADP
ejpam-4356	450	26	some	some	DET
ejpam-4356	450	27	w	w	PROPN
ejpam-4356	450	28	∈	∈	PROPN
ejpam-4356	450	29	s	s	PART
ejpam-4356	450	30	and	and	CCONJ
ejpam-4356	450	31	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	450	32	=	=	PUNCT
ejpam-4356	451	1	⟨nh	⟨nh	PUNCT
ejpam-4356	452	1	[	[	X
ejpam-4356	452	2	s	s	X
ejpam-4356	452	3	]	]	X
ejpam-4356	452	4	,	,	PUNCT
ejpam-4356	452	5	ew⟩	ew⟩	PROPN
ejpam-4356	452	6	is	be	AUX
ejpam-4356	452	7	connected	connect	VERB
ejpam-4356	452	8	if	if	SCONJ
ejpam-4356	452	9	and	and	CCONJ
ejpam-4356	452	10	only	only	ADV
ejpam-4356	452	11	if	if	SCONJ
ejpam-4356	452	12	γwcg(h	γwcg(h	NOUN
ejpam-4356	452	13	)	)	PUNCT
ejpam-4356	453	1	=	=	SYM
ejpam-4356	453	2	γwcg(h	γwcg(h	PROPN
ejpam-4356	453	3	□	□	PROPN
ejpam-4356	453	4	k2	k2	NOUN
ejpam-4356	453	5	)	)	PUNCT
ejpam-4356	453	6	.	.	PUNCT
ejpam-4356	454	1	proof	proof	NOUN
ejpam-4356	454	2	.	.	PUNCT
ejpam-4356	455	1	let	let	VERB
ejpam-4356	455	2	h	h	PRON
ejpam-4356	455	3	□	□	ADJ
ejpam-4356	455	4	k2	k2	X
ejpam-4356	455	5	be	be	AUX
ejpam-4356	455	6	formed	form	VERB
ejpam-4356	455	7	from	from	ADP
ejpam-4356	455	8	two	two	NUM
ejpam-4356	455	9	copies	copy	NOUN
ejpam-4356	455	10	h1	h1	NOUN
ejpam-4356	455	11	and	and	CCONJ
ejpam-4356	455	12	h2	h2	PROPN
ejpam-4356	455	13	of	of	ADP
ejpam-4356	455	14	h	h	PROPN
ejpam-4356	455	15	and	and	CCONJ
ejpam-4356	455	16	s	s	AUX
ejpam-4356	455	17	be	be	AUX
ejpam-4356	455	18	a	a	DET
ejpam-4356	455	19	minimum	minimum	ADJ
ejpam-4356	455	20	weakly	weakly	ADJ
ejpam-4356	455	21	connected	connect	VERB
ejpam-4356	455	22	closed	closed	ADJ
ejpam-4356	455	23	geodetic	geodetic	ADJ
ejpam-4356	455	24	dominating	dominating	NOUN
ejpam-4356	455	25	set	set	NOUN
ejpam-4356	455	26	of	of	ADP
ejpam-4356	455	27	h1	h1	NOUN
ejpam-4356	455	28	such	such	ADJ
ejpam-4356	455	29	that	that	SCONJ
ejpam-4356	455	30	s	s	NOUN
ejpam-4356	455	31	contains	contain	VERB
ejpam-4356	455	32	a	a	DET
ejpam-4356	455	33	vertex	vertex	NOUN
ejpam-4356	455	34	v	v	NOUN
ejpam-4356	455	35	with	with	ADP
ejpam-4356	455	36	the	the	DET
ejpam-4356	455	37	property	property	NOUN
ejpam-4356	455	38	that	that	PRON
ejpam-4356	455	39	every	every	DET
ejpam-4356	455	40	vertex	vertex	NOUN
ejpam-4356	455	41	of	of	ADP
ejpam-4356	455	42	h1	h1	PROPN
ejpam-4356	455	43	lies	lie	VERB
ejpam-4356	455	44	on	on	ADP
ejpam-4356	455	45	some	some	DET
ejpam-4356	455	46	u−v	u−v	PUNCT
ejpam-4356	455	47	geodesic	geodesic	NOUN
ejpam-4356	455	48	in	in	ADP
ejpam-4356	455	49	h1	h1	NOUN
ejpam-4356	455	50	for	for	ADP
ejpam-4356	455	51	some	some	DET
ejpam-4356	455	52	v	v	NOUN
ejpam-4356	455	53	∈	∈	NOUN
ejpam-4356	455	54	s.	s.	PROPN
ejpam-4356	455	55	let	let	VERB
ejpam-4356	455	56	d	d	NOUN
ejpam-4356	455	57	consists	consist	VERB
ejpam-4356	455	58	of	of	ADP
ejpam-4356	455	59	vertex	vertex	NOUN
ejpam-4356	455	60	x	x	PUNCT
ejpam-4356	455	61	together	together	ADV
ejpam-4356	455	62	with	with	ADP
ejpam-4356	455	63	those	those	DET
ejpam-4356	455	64	vertices	vertex	NOUN
ejpam-4356	455	65	of	of	ADP
ejpam-4356	455	66	h2	h2	NOUN
ejpam-4356	455	67	corresponding	correspond	VERB
ejpam-4356	455	68	to	to	ADP
ejpam-4356	455	69	those	those	DET
ejpam-4356	455	70	vertices	vertex	NOUN
ejpam-4356	455	71	in	in	ADP
ejpam-4356	455	72	s	s	PRON
ejpam-4356	455	73	−{u	−{u	NOUN
ejpam-4356	455	74	}	}	PUNCT
ejpam-4356	455	75	.	.	PUNCT
ejpam-4356	456	1	hence	hence	ADV
ejpam-4356	456	2	,	,	PUNCT
ejpam-4356	456	3	|d|	|d|	PROPN
ejpam-4356	456	4	=	=	SYM
ejpam-4356	456	5	|s|	|s|	PROPN
ejpam-4356	456	6	.	.	PUNCT
ejpam-4356	457	1	we	we	PRON
ejpam-4356	457	2	show	show	VERB
ejpam-4356	457	3	that	that	SCONJ
ejpam-4356	457	4	d	d	NOUN
ejpam-4356	457	5	is	be	AUX
ejpam-4356	457	6	weakly	weakly	ADV
ejpam-4356	457	7	connceted	conncete	VERB
ejpam-4356	457	8	closed	closed	ADJ
ejpam-4356	457	9	geodetic	geodetic	ADJ
ejpam-4356	457	10	dominating	dominating	NOUN
ejpam-4356	457	11	set	set	NOUN
ejpam-4356	457	12	of	of	ADP
ejpam-4356	457	13	h	h	NOUN
ejpam-4356	457	14	□	□	PROPN
ejpam-4356	457	15	k2	k2	NOUN
ejpam-4356	457	16	.	.	PUNCT
ejpam-4356	458	1	let	let	VERB
ejpam-4356	458	2	x	x	PUNCT
ejpam-4356	458	3	/∈	/∈	PUNCT
ejpam-4356	459	1	d	d	NOUN
ejpam-4356	459	2	be	be	AUX
ejpam-4356	459	3	a	a	DET
ejpam-4356	459	4	vertex	vertex	NOUN
ejpam-4356	459	5	of	of	ADP
ejpam-4356	459	6	h	h	NOUN
ejpam-4356	459	7	□	□	PROPN
ejpam-4356	459	8	k2	k2	NOUN
ejpam-4356	459	9	.	.	PUNCT
ejpam-4356	460	1	first	first	ADV
ejpam-4356	460	2	,	,	PUNCT
ejpam-4356	460	3	suppose	suppose	VERB
ejpam-4356	460	4	that	that	SCONJ
ejpam-4356	460	5	x	x	SYM
ejpam-4356	460	6	∈	∈	NOUN
ejpam-4356	460	7	v	v	X
ejpam-4356	460	8	(	(	PUNCT
ejpam-4356	460	9	h1	h1	PROPN
ejpam-4356	460	10	)	)	PUNCT
ejpam-4356	460	11	.	.	PUNCT
ejpam-4356	461	1	since	since	SCONJ
ejpam-4356	461	2	,	,	PUNCT
ejpam-4356	461	3	ih	ih	X
ejpam-4356	461	4	[	[	X
ejpam-4356	461	5	s	s	X
ejpam-4356	461	6	]	]	X
ejpam-4356	461	7	=	=	SYM
ejpam-4356	461	8	v	v	X
ejpam-4356	461	9	(	(	PUNCT
ejpam-4356	461	10	h1	h1	PROPN
ejpam-4356	461	11	)	)	PUNCT
ejpam-4356	461	12	and	and	CCONJ
ejpam-4356	461	13	diam(h1	diam(h1	NOUN
ejpam-4356	461	14	)	)	PUNCT
ejpam-4356	461	15	≤	≤	NOUN
ejpam-4356	461	16	2	2	NUM
ejpam-4356	461	17	,	,	PUNCT
ejpam-4356	461	18	it	it	PRON
ejpam-4356	461	19	follows	follow	VERB
ejpam-4356	461	20	that	that	SCONJ
ejpam-4356	461	21	,	,	PUNCT
ejpam-4356	461	22	x	x	PUNCT
ejpam-4356	461	23	∈	∈	NOUN
ejpam-4356	461	24	ih	ih	X
ejpam-4356	462	1	[	[	X
ejpam-4356	462	2	u	u	NOUN
ejpam-4356	462	3	,	,	PUNCT
ejpam-4356	462	4	v	v	NOUN
ejpam-4356	462	5	]	]	X
ejpam-4356	462	6	=	=	PUNCT
ejpam-4356	462	7	ih	ih	X
ejpam-4356	463	1	[	[	X
ejpam-4356	463	2	s	s	X
ejpam-4356	463	3	]	]	X
ejpam-4356	463	4	and	and	CCONJ
ejpam-4356	463	5	v	v	ADP
ejpam-4356	463	6	̸=	̸=	PROPN
ejpam-4356	463	7	x.	x.	NOUN
ejpam-4356	463	8	since	since	SCONJ
ejpam-4356	463	9	j.	j.	PROPN
ejpam-4356	463	10	hamja	hamja	PROPN
ejpam-4356	463	11	,	,	PUNCT
ejpam-4356	463	12	i.	i.	PROPN
ejpam-4356	463	13	aniversario	aniversario	PROPN
ejpam-4356	463	14	,	,	PUNCT
ejpam-4356	463	15	h.	h.	PROPN
ejpam-4356	463	16	rara	rara	PROPN
ejpam-4356	463	17	/	/	SYM
ejpam-4356	463	18	eur	eur	PROPN
ejpam-4356	463	19	.	.	PUNCT
ejpam-4356	464	1	j.	j.	PROPN
ejpam-4356	464	2	pure	pure	PROPN
ejpam-4356	464	3	appl	appl	PROPN
ejpam-4356	464	4	.	.	PROPN
ejpam-4356	464	5	math	math	PROPN
ejpam-4356	464	6	,	,	PUNCT
ejpam-4356	464	7	15	15	NUM
ejpam-4356	464	8	(	(	PUNCT
ejpam-4356	464	9	2	2	NUM
ejpam-4356	464	10	)	)	PUNCT
ejpam-4356	464	11	(	(	PUNCT
ejpam-4356	464	12	2022	2022	NUM
ejpam-4356	464	13	)	)	PUNCT
ejpam-4356	464	14	,	,	PUNCT
ejpam-4356	464	15	736	736	NUM
ejpam-4356	464	16	-	-	SYM
ejpam-4356	464	17	752	752	NUM
ejpam-4356	464	18	750	750	NUM
ejpam-4356	464	19	v	v	NOUN
ejpam-4356	464	20	′	′	NOUN
ejpam-4356	464	21	is	be	AUX
ejpam-4356	464	22	the	the	DET
ejpam-4356	464	23	corresponding	corresponding	ADJ
ejpam-4356	464	24	vertex	vertex	NOUN
ejpam-4356	464	25	of	of	ADP
ejpam-4356	464	26	v	v	NUM
ejpam-4356	464	27	∈	∈	PROPN
ejpam-4356	464	28	s	s	NOUN
ejpam-4356	464	29	,	,	PUNCT
ejpam-4356	465	1	v′	v′	NOUN
ejpam-4356	465	2	∈	∈	PROPN
ejpam-4356	465	3	d	d	NOUN
ejpam-4356	465	4	and	and	CCONJ
ejpam-4356	465	5	x	x	SYM
ejpam-4356	465	6	∈	∈	PROPN
ejpam-4356	465	7	n	n	CCONJ
ejpam-4356	466	1	[	[	X
ejpam-4356	466	2	d	d	X
ejpam-4356	466	3	]	]	X
ejpam-4356	466	4	where	where	SCONJ
ejpam-4356	466	5	v	v	ADP
ejpam-4356	466	6	̸=	̸=	PROPN
ejpam-4356	466	7	x.	x.	NOUN
ejpam-4356	466	8	also	also	ADV
ejpam-4356	466	9	,	,	PUNCT
ejpam-4356	466	10	since	since	SCONJ
ejpam-4356	466	11	nh	nh	PROPN
ejpam-4356	466	12	[	[	X
ejpam-4356	466	13	s	s	X
ejpam-4356	466	14	]	]	X
ejpam-4356	466	15	=	=	SYM
ejpam-4356	466	16	v	v	X
ejpam-4356	466	17	(	(	PUNCT
ejpam-4356	466	18	h1	h1	PROPN
ejpam-4356	466	19	)	)	PUNCT
ejpam-4356	466	20	and	and	CCONJ
ejpam-4356	466	21	ew	ew	INTJ
ejpam-4356	466	22	=	=	PUNCT
ejpam-4356	466	23	{	{	PUNCT
ejpam-4356	466	24	uv′	uv′	PROPN
ejpam-4356	466	25	∈	∈	PROPN
ejpam-4356	466	26	e(h1	e(h1	NOUN
ejpam-4356	466	27	)	)	PUNCT
ejpam-4356	466	28	:	:	PUNCT
ejpam-4356	467	1	u	u	PROPN
ejpam-4356	467	2	∈	∈	PROPN
ejpam-4356	467	3	s	s	PART
ejpam-4356	467	4	or	or	CCONJ
ejpam-4356	467	5	v′	v′	PROPN
ejpam-4356	467	6	∈	∈	PROPN
ejpam-4356	467	7	s	s	PART
ejpam-4356	467	8	}	}	PUNCT
ejpam-4356	467	9	which	which	PRON
ejpam-4356	467	10	implies	imply	VERB
ejpam-4356	467	11	that	that	SCONJ
ejpam-4356	467	12	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	467	13	is	be	AUX
ejpam-4356	467	14	connected	connect	VERB
ejpam-4356	467	15	,	,	PUNCT
ejpam-4356	467	16	and	and	CCONJ
ejpam-4356	467	17	diam(h1	diam(h1	NOUN
ejpam-4356	467	18	)	)	PUNCT
ejpam-4356	467	19	≤	≤	NOUN
ejpam-4356	467	20	2	2	NUM
ejpam-4356	467	21	,	,	PUNCT
ejpam-4356	467	22	x	x	SYM
ejpam-4356	467	23	∈	∈	NOUN
ejpam-4356	467	24	nh	nh	X
ejpam-4356	468	1	[	[	X
ejpam-4356	468	2	d	d	X
ejpam-4356	468	3	]	]	X
ejpam-4356	468	4	where	where	SCONJ
ejpam-4356	468	5	v	v	ADP
ejpam-4356	468	6	̸=	̸=	PROPN
ejpam-4356	468	7	x.	x.	NOUN
ejpam-4356	468	8	therefore	therefore	ADV
ejpam-4356	468	9	,	,	PUNCT
ejpam-4356	468	10	d	d	X
ejpam-4356	468	11	is	be	AUX
ejpam-4356	468	12	a	a	DET
ejpam-4356	468	13	weakly	weakly	ADV
ejpam-4356	468	14	connected	connected	ADJ
ejpam-4356	468	15	closed	closed	ADJ
ejpam-4356	468	16	geodetic	geodetic	ADJ
ejpam-4356	468	17	dominating	dominating	NOUN
ejpam-4356	468	18	set	set	NOUN
ejpam-4356	468	19	of	of	ADP
ejpam-4356	468	20	h	h	NOUN
ejpam-4356	468	21	□	□	PROPN
ejpam-4356	468	22	k2	k2	NOUN
ejpam-4356	468	23	.	.	PUNCT
ejpam-4356	469	1	next	next	ADV
ejpam-4356	469	2	,	,	PUNCT
ejpam-4356	469	3	suppose	suppose	VERB
ejpam-4356	469	4	that	that	SCONJ
ejpam-4356	469	5	x	x	SYM
ejpam-4356	469	6	∈	∈	NOUN
ejpam-4356	469	7	ih	ih	X
ejpam-4356	470	1	[	[	X
ejpam-4356	470	2	u	u	X
ejpam-4356	470	3	′	′	NOUN
ejpam-4356	470	4	,	,	PUNCT
ejpam-4356	470	5	v	v	NOUN
ejpam-4356	470	6	′	′	NUM
ejpam-4356	470	7	]	]	PUNCT
ejpam-4356	470	8	,	,	PUNCT
ejpam-4356	470	9	where	where	SCONJ
ejpam-4356	470	10	u′	u′	PROPN
ejpam-4356	470	11	is	be	AUX
ejpam-4356	470	12	the	the	DET
ejpam-4356	470	13	vertex	vertex	NOUN
ejpam-4356	470	14	in	in	ADP
ejpam-4356	470	15	v	v	PROPN
ejpam-4356	470	16	(	(	PUNCT
ejpam-4356	470	17	h2	h2	NOUN
ejpam-4356	470	18	)	)	PUNCT
ejpam-4356	470	19	corresponding	correspond	VERB
ejpam-4356	470	20	to	to	ADP
ejpam-4356	470	21	v	v	NOUN
ejpam-4356	470	22	and	and	CCONJ
ejpam-4356	470	23	v	v	NOUN
ejpam-4356	470	24	′	′	NUM
ejpam-4356	470	25	∈	∈	PROPN
ejpam-4356	470	26	d.	d.	NOUN
ejpam-4356	470	27	since	since	SCONJ
ejpam-4356	470	28	diam(h2	diam(h2	NOUN
ejpam-4356	470	29	)	)	PUNCT
ejpam-4356	470	30	≤	≤	NOUN
ejpam-4356	470	31	2	2	NUM
ejpam-4356	470	32	,	,	PUNCT
ejpam-4356	470	33	x	x	SYM
ejpam-4356	470	34	∈	∈	NOUN
ejpam-4356	470	35	ih	ih	NOUN
ejpam-4356	471	1	[	[	X
ejpam-4356	471	2	u	u	NOUN
ejpam-4356	471	3	,	,	PUNCT
ejpam-4356	471	4	v	v	NOUN
ejpam-4356	471	5	′	′	NUM
ejpam-4356	471	6	]	]	PUNCT
ejpam-4356	472	1	⊆	⊆	NUM
ejpam-4356	472	2	ih	ih	NOUN
ejpam-4356	473	1	[	[	X
ejpam-4356	473	2	d	d	X
ejpam-4356	473	3	]	]	X
ejpam-4356	473	4	and	and	CCONJ
ejpam-4356	473	5	x	x	SYM
ejpam-4356	473	6	∈	∈	PROPN
ejpam-4356	473	7	nh	nh	PROPN
ejpam-4356	474	1	[	[	X
ejpam-4356	474	2	v	v	X
ejpam-4356	474	3	′	′	NOUN
ejpam-4356	474	4	]	]	PUNCT
ejpam-4356	475	1	⊆	⊆	NUM
ejpam-4356	475	2	nh	nh	NOUN
ejpam-4356	476	1	[	[	X
ejpam-4356	476	2	d	d	X
ejpam-4356	476	3	]	]	X
ejpam-4356	476	4	,	,	PUNCT
ejpam-4356	476	5	and	and	CCONJ
ejpam-4356	476	6	nh	nh	PROPN
ejpam-4356	477	1	[	[	X
ejpam-4356	477	2	s	s	X
ejpam-4356	477	3	]	]	X
ejpam-4356	477	4	=	=	SYM
ejpam-4356	477	5	v	v	X
ejpam-4356	477	6	(	(	PUNCT
ejpam-4356	477	7	h1	h1	PROPN
ejpam-4356	477	8	)	)	PUNCT
ejpam-4356	477	9	and	and	CCONJ
ejpam-4356	477	10	ew	ew	INTJ
ejpam-4356	477	11	=	=	PUNCT
ejpam-4356	477	12	{	{	PUNCT
ejpam-4356	477	13	uv′	uv′	PROPN
ejpam-4356	477	14	∈	∈	PROPN
ejpam-4356	477	15	e(h1	e(h1	NOUN
ejpam-4356	477	16	)	)	PUNCT
ejpam-4356	477	17	:	:	PUNCT
ejpam-4356	477	18	u	u	PROPN
ejpam-4356	477	19	∈	∈	PROPN
ejpam-4356	477	20	s	s	PART
ejpam-4356	477	21	or	or	CCONJ
ejpam-4356	477	22	v′	v′	PROPN
ejpam-4356	477	23	∈	∈	PROPN
ejpam-4356	477	24	s	s	PART
ejpam-4356	477	25	}	}	PUNCT
ejpam-4356	477	26	which	which	PRON
ejpam-4356	477	27	implies	imply	VERB
ejpam-4356	477	28	that	that	SCONJ
ejpam-4356	477	29	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	477	30	is	be	AUX
ejpam-4356	477	31	connected	connect	VERB
ejpam-4356	477	32	.	.	PUNCT
ejpam-4356	478	1	therefore	therefore	ADV
ejpam-4356	478	2	d	d	X
ejpam-4356	478	3	is	be	AUX
ejpam-4356	478	4	a	a	DET
ejpam-4356	478	5	weakly	weakly	ADV
ejpam-4356	478	6	connected	connected	ADJ
ejpam-4356	478	7	closed	closed	ADJ
ejpam-4356	478	8	geodetic	geodetic	ADJ
ejpam-4356	478	9	dominating	dominating	NOUN
ejpam-4356	478	10	set	set	NOUN
ejpam-4356	478	11	of	of	ADP
ejpam-4356	478	12	h	h	NOUN
ejpam-4356	478	13	□	□	PROPN
ejpam-4356	478	14	k2	k2	NOUN
ejpam-4356	478	15	.	.	PUNCT
ejpam-4356	479	1	now	now	ADV
ejpam-4356	479	2	,	,	PUNCT
ejpam-4356	479	3	γwcg(h	γwcg(h	PROPN
ejpam-4356	479	4	□	□	SYM
ejpam-4356	479	5	k2	k2	ADJ
ejpam-4356	479	6	)	)	PUNCT
ejpam-4356	479	7	≤	≤	NOUN
ejpam-4356	479	8	|d|	|d|	PROPN
ejpam-4356	479	9	=	=	SYM
ejpam-4356	479	10	|s|	|s|	PROPN
ejpam-4356	479	11	=	=	PUNCT
ejpam-4356	479	12	γwcg(h	γwcg(h	PROPN
ejpam-4356	479	13	)	)	PUNCT
ejpam-4356	479	14	.	.	PUNCT
ejpam-4356	480	1	consequently	consequently	ADV
ejpam-4356	480	2	,	,	PUNCT
ejpam-4356	480	3	by	by	ADP
ejpam-4356	480	4	corollary	corollary	ADJ
ejpam-4356	480	5	15	15	NUM
ejpam-4356	480	6	,	,	PUNCT
ejpam-4356	480	7	γwcg(h	γwcg(h	NOUN
ejpam-4356	480	8	)	)	PUNCT
ejpam-4356	480	9	=	=	SYM
ejpam-4356	480	10	γwcg(h	γwcg(h	PROPN
ejpam-4356	480	11	□	□	PROPN
ejpam-4356	480	12	k2	k2	NOUN
ejpam-4356	480	13	)	)	PUNCT
ejpam-4356	480	14	.	.	PUNCT
ejpam-4356	481	1	conversely	conversely	ADV
ejpam-4356	481	2	,	,	PUNCT
ejpam-4356	481	3	suppose	suppose	VERB
ejpam-4356	481	4	that	that	SCONJ
ejpam-4356	481	5	γwcg(h	γwcg(h	AUX
ejpam-4356	481	6	)	)	PUNCT
ejpam-4356	481	7	=	=	SYM
ejpam-4356	481	8	γwcg(h	γwcg(h	PROPN
ejpam-4356	481	9	□	□	PROPN
ejpam-4356	481	10	k2	k2	NOUN
ejpam-4356	481	11	)	)	PUNCT
ejpam-4356	481	12	where	where	SCONJ
ejpam-4356	481	13	h	h	NOUN
ejpam-4356	481	14	□	□	SYM
ejpam-4356	481	15	k2	k2	PROPN
ejpam-4356	481	16	is	be	AUX
ejpam-4356	481	17	formed	form	VERB
ejpam-4356	481	18	from	from	ADP
ejpam-4356	481	19	two	two	NUM
ejpam-4356	481	20	copies	copy	NOUN
ejpam-4356	481	21	of	of	ADP
ejpam-4356	481	22	h1	h1	NOUN
ejpam-4356	481	23	and	and	CCONJ
ejpam-4356	481	24	h2	h2	PROPN
ejpam-4356	481	25	of	of	ADP
ejpam-4356	481	26	h.	h.	PROPN
ejpam-4356	481	27	let	let	VERB
ejpam-4356	481	28	d	d	PRON
ejpam-4356	481	29	be	be	AUX
ejpam-4356	481	30	a	a	DET
ejpam-4356	481	31	minimum	minimum	ADJ
ejpam-4356	481	32	weakly	weakly	ADJ
ejpam-4356	481	33	connected	connect	VERB
ejpam-4356	481	34	closed	closed	ADJ
ejpam-4356	481	35	geodetic	geodetic	ADJ
ejpam-4356	481	36	dominaing	dominaing	NOUN
ejpam-4356	481	37	set	set	NOUN
ejpam-4356	481	38	of	of	ADP
ejpam-4356	481	39	h	h	NOUN
ejpam-4356	481	40	□	□	PROPN
ejpam-4356	481	41	k2	k2	NOUN
ejpam-4356	481	42	.	.	PUNCT
ejpam-4356	482	1	clearly	clearly	ADV
ejpam-4356	482	2	,	,	PUNCT
ejpam-4356	482	3	d∩v	d∩v	PROPN
ejpam-4356	482	4	(	(	PUNCT
ejpam-4356	482	5	hi	hi	INTJ
ejpam-4356	482	6	)	)	PUNCT
ejpam-4356	482	7	̸=	̸=	NOUN
ejpam-4356	482	8	∅	∅	NOUN
ejpam-4356	482	9	,	,	PUNCT
ejpam-4356	482	10	i	i	NOUN
ejpam-4356	482	11	=	=	NOUN
ejpam-4356	482	12	1	1	NUM
ejpam-4356	482	13	,	,	PUNCT
ejpam-4356	482	14	2	2	NUM
ejpam-4356	482	15	.	.	X
ejpam-4356	482	16	let	let	VERB
ejpam-4356	482	17	x	x	X
ejpam-4356	482	18	∈	∈	PROPN
ejpam-4356	482	19	d∩v	d∩v	PROPN
ejpam-4356	482	20	(	(	PUNCT
ejpam-4356	482	21	h1	h1	PROPN
ejpam-4356	482	22	)	)	PUNCT
ejpam-4356	482	23	and	and	CCONJ
ejpam-4356	482	24	let	let	VERB
ejpam-4356	482	25	s	s	PRON
ejpam-4356	482	26	consist	consist	VERB
ejpam-4356	482	27	of	of	ADP
ejpam-4356	482	28	vertices	vertex	NOUN
ejpam-4356	482	29	of	of	ADP
ejpam-4356	482	30	d∩v	d∩v	PROPN
ejpam-4356	482	31	(	(	PUNCT
ejpam-4356	482	32	h1	h1	PROPN
ejpam-4356	482	33	)	)	PUNCT
ejpam-4356	482	34	together	together	ADV
ejpam-4356	482	35	with	with	ADP
ejpam-4356	482	36	those	those	DET
ejpam-4356	482	37	vertices	vertex	NOUN
ejpam-4356	482	38	in	in	ADP
ejpam-4356	482	39	d∩v	d∩v	PROPN
ejpam-4356	482	40	(	(	PUNCT
ejpam-4356	482	41	h2	h2	PROPN
ejpam-4356	482	42	)	)	PUNCT
ejpam-4356	482	43	.	.	PUNCT
ejpam-4356	483	1	clearly	clearly	ADV
ejpam-4356	483	2	,	,	PUNCT
ejpam-4356	483	3	s	s	VERB
ejpam-4356	483	4	is	be	AUX
ejpam-4356	483	5	a	a	DET
ejpam-4356	483	6	weakly	weakly	ADV
ejpam-4356	483	7	connected	connected	ADJ
ejpam-4356	483	8	closed	closed	ADJ
ejpam-4356	483	9	geodetic	geodetic	ADJ
ejpam-4356	483	10	dominating	dominating	NOUN
ejpam-4356	483	11	set	set	NOUN
ejpam-4356	483	12	of	of	ADP
ejpam-4356	483	13	h1	h1	PROPN
ejpam-4356	483	14	and	and	CCONJ
ejpam-4356	483	15	|s|	|s|	PROPN
ejpam-4356	483	16	=	=	SYM
ejpam-4356	483	17	|d|	|d|	PROPN
ejpam-4356	483	18	.	.	PUNCT
ejpam-4356	484	1	since	since	SCONJ
ejpam-4356	484	2	,	,	PUNCT
ejpam-4356	484	3	d	d	PROPN
ejpam-4356	484	4	is	be	AUX
ejpam-4356	484	5	a	a	DET
ejpam-4356	484	6	minimum	minimum	ADJ
ejpam-4356	484	7	weakly	weakly	ADJ
ejpam-4356	484	8	connected	connect	VERB
ejpam-4356	484	9	closed	closed	ADJ
ejpam-4356	484	10	geodetic	geodetic	ADJ
ejpam-4356	484	11	dominating	dominating	NOUN
ejpam-4356	484	12	set	set	NOUN
ejpam-4356	484	13	of	of	ADP
ejpam-4356	484	14	h1	h1	PROPN
ejpam-4356	484	15	.	.	PUNCT
ejpam-4356	485	1	we	we	PRON
ejpam-4356	485	2	show	show	VERB
ejpam-4356	485	3	that	that	SCONJ
ejpam-4356	485	4	every	every	DET
ejpam-4356	485	5	vertex	vertex	NOUN
ejpam-4356	485	6	of	of	ADP
ejpam-4356	485	7	h1	h1	PROPN
ejpam-4356	485	8	lies	lie	VERB
ejpam-4356	485	9	on	on	ADP
ejpam-4356	485	10	some	some	DET
ejpam-4356	485	11	u−	u−	PROPN
ejpam-4356	485	12	v	v	ADJ
ejpam-4356	485	13	geodesic	geodesic	NOUN
ejpam-4356	485	14	for	for	ADP
ejpam-4356	485	15	some	some	DET
ejpam-4356	485	16	v	v	NOUN
ejpam-4356	485	17	∈	∈	PROPN
ejpam-4356	485	18	s	s	PART
ejpam-4356	485	19	and	and	CCONJ
ejpam-4356	485	20	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4356	485	21	=	=	PUNCT
ejpam-4356	486	1	⟨nh	⟨nh	PUNCT
ejpam-4356	487	1	[	[	X
ejpam-4356	487	2	s	s	X
ejpam-4356	487	3	]	]	X
ejpam-4356	487	4	,	,	PUNCT
ejpam-4356	487	5	ew⟩	ew⟩	PROPN
ejpam-4356	487	6	is	be	AUX
ejpam-4356	487	7	connected	connect	VERB
ejpam-4356	487	8	.	.	PUNCT
ejpam-4356	488	1	suppose	suppose	VERB
ejpam-4356	488	2	that	that	SCONJ
ejpam-4356	488	3	there	there	PRON
ejpam-4356	488	4	exists	exist	VERB
ejpam-4356	488	5	a	a	DET
ejpam-4356	488	6	vertex	vertex	NOUN
ejpam-4356	488	7	x	x	SYM
ejpam-4356	488	8	∈	∈	NOUN
ejpam-4356	488	9	v	v	X
ejpam-4356	488	10	(	(	PUNCT
ejpam-4356	488	11	h1	h1	PROPN
ejpam-4356	488	12	)	)	PUNCT
ejpam-4356	488	13	such	such	ADJ
ejpam-4356	488	14	that	that	SCONJ
ejpam-4356	488	15	x	x	SYM
ejpam-4356	488	16	∈	∈	NOUN
ejpam-4356	488	17	ih	ih	X
ejpam-4356	489	1	[	[	X
ejpam-4356	489	2	u	u	NOUN
ejpam-4356	489	3	,	,	PUNCT
ejpam-4356	489	4	v	v	ADP
ejpam-4356	489	5	]	]	PUNCT
ejpam-4356	489	6	for	for	ADP
ejpam-4356	489	7	all	all	PRON
ejpam-4356	489	8	v	v	NOUN
ejpam-4356	489	9	∈	∈	NOUN
ejpam-4356	489	10	s.	s.	PROPN
ejpam-4356	489	11	then	then	ADV
ejpam-4356	489	12	x	x	PROPN
ejpam-4356	489	13	/∈	/∈	PUNCT
ejpam-4356	489	14	nh	nh	PROPN
ejpam-4356	490	1	[	[	X
ejpam-4356	490	2	u	u	X
ejpam-4356	490	3	]	]	X
ejpam-4356	490	4	and	and	CCONJ
ejpam-4356	490	5	d(u	d(u	PROPN
ejpam-4356	490	6	,	,	PUNCT
ejpam-4356	490	7	x	x	X
ejpam-4356	490	8	)	)	PUNCT
ejpam-4356	490	9	=	=	SYM
ejpam-4356	490	10	d(u	d(u	PROPN
ejpam-4356	490	11	,	,	PUNCT
ejpam-4356	490	12	v	v	NOUN
ejpam-4356	490	13	)	)	PUNCT
ejpam-4356	490	14	+	+	CCONJ
ejpam-4356	490	15	d(u	d(u	PROPN
ejpam-4356	490	16	,	,	PUNCT
ejpam-4356	490	17	x	x	X
ejpam-4356	490	18	)	)	PUNCT
ejpam-4356	490	19	>	>	X
ejpam-4356	490	20	2	2	NUM
ejpam-4356	490	21	,	,	PUNCT
ejpam-4356	490	22	a	a	DET
ejpam-4356	490	23	contradiction	contradiction	NOUN
ejpam-4356	490	24	,	,	PUNCT
ejpam-4356	490	25	consequently	consequently	ADV
ejpam-4356	490	26	,	,	PUNCT
ejpam-4356	490	27	diam(h1	diam(h1	NOUN
ejpam-4356	490	28	)	)	PUNCT
ejpam-4356	490	29	≤	≤	NUM
ejpam-4356	490	30	2	2	NUM
ejpam-4356	490	31	.	.	X
ejpam-4356	490	32	conlusion	conlusion	NOUN
ejpam-4356	490	33	:	:	PUNCT
ejpam-4356	490	34	the	the	DET
ejpam-4356	490	35	paper	paper	NOUN
ejpam-4356	490	36	has	have	AUX
ejpam-4356	490	37	introduced	introduce	VERB
ejpam-4356	490	38	the	the	DET
ejpam-4356	490	39	concept	concept	NOUN
ejpam-4356	490	40	of	of	ADP
ejpam-4356	490	41	weakly	weakly	ADJ
ejpam-4356	490	42	connected	connected	ADJ
ejpam-4356	490	43	closed	closed	ADJ
ejpam-4356	490	44	geodetic	geodetic	ADJ
ejpam-4356	490	45	dominating	dominating	NOUN
ejpam-4356	490	46	sets	set	NOUN
ejpam-4356	490	47	of	of	ADP
ejpam-4356	490	48	some	some	DET
ejpam-4356	490	49	graphs	graph	NOUN
ejpam-4356	490	50	and	and	CCONJ
ejpam-4356	490	51	the	the	DET
ejpam-4356	490	52	join	join	NOUN
ejpam-4356	490	53	,	,	PUNCT
ejpam-4356	490	54	corona	corona	PROPN
ejpam-4356	490	55	,	,	PUNCT
ejpam-4356	490	56	and	and	CCONJ
ejpam-4356	490	57	cartesian	cartesian	ADJ
ejpam-4356	490	58	product	product	NOUN
ejpam-4356	490	59	of	of	ADP
ejpam-4356	490	60	two	two	NUM
ejpam-4356	490	61	graphs	graph	NOUN
ejpam-4356	490	62	are	be	AUX
ejpam-4356	490	63	characterized	characterize	VERB
ejpam-4356	490	64	.	.	PUNCT
ejpam-4356	491	1	the	the	DET
ejpam-4356	491	2	weakly	weakly	ADJ
ejpam-4356	491	3	connected	connected	ADJ
ejpam-4356	491	4	closed	close	VERB
ejpam-4356	491	5	geodetic	geodetic	ADJ
ejpam-4356	491	6	domination	domination	NOUN
ejpam-4356	491	7	numbers	number	NOUN
ejpam-4356	491	8	of	of	ADP
ejpam-4356	491	9	these	these	DET
ejpam-4356	491	10	graphs	graph	NOUN
ejpam-4356	491	11	are	be	AUX
ejpam-4356	491	12	determined	determine	VERB
ejpam-4356	491	13	.	.	PUNCT
ejpam-4356	492	1	also	also	ADV
ejpam-4356	492	2	,	,	PUNCT
ejpam-4356	492	3	some	some	DET
ejpam-4356	492	4	relationships	relationship	NOUN
ejpam-4356	492	5	between	between	ADP
ejpam-4356	492	6	weakly	weakly	ADV
ejpam-4356	492	7	connected	connected	ADJ
ejpam-4356	492	8	closed	closed	ADJ
ejpam-4356	492	9	geodetic	geodetic	ADJ
ejpam-4356	492	10	dominating	dominating	NOUN
ejpam-4356	492	11	set	set	NOUN
ejpam-4356	492	12	,	,	PUNCT
ejpam-4356	492	13	weakly	weakly	ADV
ejpam-4356	492	14	connected	connected	ADJ
ejpam-4356	492	15	closed	closed	ADJ
ejpam-4356	492	16	geodetic	geodetic	ADJ
ejpam-4356	492	17	set	set	NOUN
ejpam-4356	492	18	,	,	PUNCT
ejpam-4356	492	19	geodetic	geodetic	ADJ
ejpam-4356	492	20	dominating	dominating	NOUN
ejpam-4356	492	21	set	set	NOUN
ejpam-4356	492	22	,	,	PUNCT
ejpam-4356	492	23	and	and	CCONJ
ejpam-4356	492	24	geodetic	geodetic	ADJ
ejpam-4356	492	25	connected	connected	ADJ
ejpam-4356	492	26	dominating	dominating	NOUN
ejpam-4356	492	27	set	set	NOUN
ejpam-4356	492	28	are	be	AUX
ejpam-4356	492	29	established	establish	VERB
ejpam-4356	492	30	.	.	PUNCT
ejpam-4356	493	1	a	a	DET
ejpam-4356	493	2	worthwhile	worthwhile	ADJ
ejpam-4356	493	3	direction	direction	NOUN
ejpam-4356	493	4	for	for	ADP
ejpam-4356	493	5	further	further	ADJ
ejpam-4356	493	6	investigate	investigate	VERB
ejpam-4356	493	7	is	be	AUX
ejpam-4356	493	8	to	to	PART
ejpam-4356	493	9	establish	establish	VERB
ejpam-4356	493	10	other	other	ADJ
ejpam-4356	493	11	variations	variation	NOUN
ejpam-4356	493	12	of	of	ADP
ejpam-4356	493	13	the	the	DET
ejpam-4356	493	14	concept	concept	NOUN
ejpam-4356	493	15	of	of	ADP
ejpam-4356	493	16	the	the	DET
ejpam-4356	493	17	weakly	weakly	ADV
ejpam-4356	493	18	connected	connected	ADJ
ejpam-4356	493	19	closed	closed	ADJ
ejpam-4356	493	20	geodetic	geodetic	ADJ
ejpam-4356	493	21	dominating	dominating	NOUN
ejpam-4356	493	22	sets	set	NOUN
ejpam-4356	493	23	,	,	PUNCT
ejpam-4356	493	24	the	the	DET
ejpam-4356	493	25	weakly	weakly	ADV
ejpam-4356	493	26	connected	connected	ADJ
ejpam-4356	493	27	closed	closed	ADJ
ejpam-4356	493	28	geodetic	geodetic	ADJ
ejpam-4356	493	29	sets	set	NOUN
ejpam-4356	493	30	,	,	PUNCT
ejpam-4356	493	31	geodetic	geodetic	ADJ
ejpam-4356	493	32	dominating	dominating	NOUN
ejpam-4356	493	33	sets	set	NOUN
ejpam-4356	493	34	,	,	PUNCT
ejpam-4356	493	35	and	and	CCONJ
ejpam-4356	493	36	geodetic	geodetic	ADJ
ejpam-4356	493	37	connected	connected	ADJ
ejpam-4356	493	38	dominating	dominating	NOUN
ejpam-4356	493	39	sets	set	NOUN
ejpam-4356	493	40	,	,	PUNCT
ejpam-4356	493	41	characterize	characterize	VERB
ejpam-4356	493	42	the	the	DET
ejpam-4356	493	43	weakly	weakly	ADV
ejpam-4356	493	44	connected	connected	ADJ
ejpam-4356	493	45	closed	closed	ADJ
ejpam-4356	493	46	geodetic	geodetic	ADJ
ejpam-4356	493	47	dominating	dominating	NOUN
ejpam-4356	493	48	sets	set	NOUN
ejpam-4356	493	49	in	in	ADP
ejpam-4356	493	50	the	the	DET
ejpam-4356	493	51	lexicographic	lexicographic	ADJ
ejpam-4356	493	52	and	and	CCONJ
ejpam-4356	493	53	composition	composition	NOUN
ejpam-4356	493	54	of	of	ADP
ejpam-4356	493	55	two	two	NUM
ejpam-4356	493	56	graphs	graph	NOUN
ejpam-4356	493	57	and	and	CCONJ
ejpam-4356	493	58	determine	determine	VERB
ejpam-4356	493	59	the	the	DET
ejpam-4356	493	60	exact	exact	ADJ
ejpam-4356	493	61	values	value	NOUN
ejpam-4356	493	62	of	of	ADP
ejpam-4356	493	63	the	the	DET
ejpam-4356	493	64	weakly	weakly	ADV
ejpam-4356	493	65	connected	connected	ADJ
ejpam-4356	493	66	closed	close	VERB
ejpam-4356	493	67	geodetic	geodetic	ADJ
ejpam-4356	493	68	domination	domination	NOUN
ejpam-4356	493	69	numbers	number	NOUN
ejpam-4356	493	70	of	of	ADP
ejpam-4356	493	71	graphs	graph	NOUN
ejpam-4356	493	72	associated	associate	VERB
ejpam-4356	493	73	with	with	ADP
ejpam-4356	493	74	the	the	DET
ejpam-4356	493	75	lexicographic	lexicographic	ADJ
ejpam-4356	493	76	and	and	CCONJ
ejpam-4356	493	77	composition	composition	NOUN
ejpam-4356	493	78	of	of	ADP
ejpam-4356	493	79	two	two	NUM
ejpam-4356	493	80	graphs	graph	NOUN
ejpam-4356	493	81	.	.	PUNCT
ejpam-4356	494	1	acknowledgements	acknowledgement	NOUN
ejpam-4356	494	2	the	the	DET
ejpam-4356	494	3	authors	author	NOUN
ejpam-4356	494	4	would	would	AUX
ejpam-4356	494	5	like	like	VERB
ejpam-4356	494	6	to	to	PART
ejpam-4356	494	7	thank	thank	VERB
ejpam-4356	494	8	the	the	DET
ejpam-4356	494	9	referees	referee	NOUN
ejpam-4356	494	10	for	for	ADP
ejpam-4356	494	11	the	the	DET
ejpam-4356	494	12	invaluable	invaluable	ADJ
ejpam-4356	494	13	guidance	guidance	NOUN
ejpam-4356	494	14	the	the	PRON
ejpam-4356	494	15	give	give	VERB
ejpam-4356	494	16	us	we	PRON
ejpam-4356	494	17	through	through	ADP
ejpam-4356	494	18	their	their	PRON
ejpam-4356	494	19	comments	comment	NOUN
ejpam-4356	494	20	and	and	CCONJ
ejpam-4356	494	21	suggestions	suggestion	NOUN
ejpam-4356	494	22	which	which	PRON
ejpam-4356	494	23	led	lead	VERB
ejpam-4356	494	24	to	to	ADP
ejpam-4356	494	25	betterment	betterment	NOUN
ejpam-4356	494	26	of	of	ADP
ejpam-4356	494	27	the	the	DET
ejpam-4356	494	28	paper	paper	NOUN
ejpam-4356	494	29	.	.	PUNCT
ejpam-4356	495	1	this	this	DET
ejpam-4356	495	2	study	study	NOUN
ejpam-4356	495	3	has	have	AUX
ejpam-4356	495	4	been	be	AUX
ejpam-4356	495	5	supported	support	VERB
ejpam-4356	495	6	by	by	ADP
ejpam-4356	495	7	the	the	DET
ejpam-4356	495	8	department	department	PROPN
ejpam-4356	495	9	of	of	ADP
ejpam-4356	495	10	science	science	NOUN
ejpam-4356	495	11	and	and	CCONJ
ejpam-4356	495	12	technology	technology	NOUN
ejpam-4356	495	13	-	-	PUNCT
ejpam-4356	495	14	accelerated	accelerate	VERB
ejpam-4356	495	15	science	science	NOUN
ejpam-4356	495	16	and	and	CCONJ
ejpam-4356	495	17	technology	technology	NOUN
ejpam-4356	495	18	human	human	ADJ
ejpam-4356	495	19	resource	resource	NOUN
ejpam-4356	495	20	development	development	NOUN
ejpam-4356	495	21	program	program	NOUN
ejpam-4356	495	22	(	(	PUNCT
ejpam-4356	495	23	dost	dost	NOUN
ejpam-4356	495	24	-	-	PUNCT
ejpam-4356	495	25	asthrdp	asthrdp	ADJ
ejpam-4356	495	26	)	)	PUNCT
ejpam-4356	495	27	.	.	PUNCT
ejpam-4356	496	1	references	reference	NOUN
ejpam-4356	496	2	751	751	NUM
ejpam-4356	496	3	references	reference	NOUN
ejpam-4356	496	4	[	[	X
ejpam-4356	496	5	1	1	NUM
ejpam-4356	496	6	]	]	X
ejpam-4356	496	7	i.	i.	NOUN
ejpam-4356	496	8	aniversario	aniversario	PROPN
ejpam-4356	496	9	,	,	PUNCT
ejpam-4356	496	10	f.	f.	PROPN
ejpam-4356	496	11	jamil	jamil	PROPN
ejpam-4356	496	12	,	,	PUNCT
ejpam-4356	496	13	jr	jr	PROPN
ejpam-4356	496	14	.	.	PROPN
ejpam-4356	496	15	s.	s.	PROPN
ejpam-4356	496	16	canoy	canoy	PROPN
ejpam-4356	496	17	,	,	PUNCT
ejpam-4356	496	18	the	the	DET
ejpam-4356	496	19	closed	closed	ADJ
ejpam-4356	496	20	geodetic	geodetic	ADJ
ejpam-4356	496	21	numbers	number	NOUN
ejpam-4356	496	22	of	of	ADP
ejpam-4356	496	23	graph	graph	NOUN
ejpam-4356	496	24	,	,	PUNCT
ejpam-4356	496	25	utilitas	utilitas	PROPN
ejpam-4356	496	26	mathematica	mathematica	PROPN
ejpam-4356	496	27	,	,	PUNCT
ejpam-4356	496	28	74	74	NUM
ejpam-4356	496	29	(	(	PUNCT
ejpam-4356	496	30	2007	2007	NUM
ejpam-4356	496	31	)	)	PUNCT
ejpam-4356	496	32	,	,	PUNCT
ejpam-4356	497	1	pp	pp	ADP
ejpam-4356	497	2	.	.	PUNCT
ejpam-4356	498	1	3	3	NUM
ejpam-4356	498	2	18	18	NUM
ejpam-4356	498	3	.	.	PUNCT
ejpam-4356	499	1	[	[	X
ejpam-4356	499	2	2	2	NUM
ejpam-4356	499	3	]	]	PUNCT
ejpam-4356	499	4	f.	f.	PROPN
ejpam-4356	499	5	harary	harary	PROPN
ejpam-4356	499	6	,	,	PUNCT
ejpam-4356	499	7	graph	graph	NOUN
ejpam-4356	499	8	theory	theory	NOUN
ejpam-4356	499	9	,	,	PUNCT
ejpam-4356	499	10	addison	addison	PROPN
ejpam-4356	499	11	-	-	PUNCT
ejpam-4356	499	12	wesley	wesley	PROPN
ejpam-4356	499	13	publishing	publishing	PROPN
ejpam-4356	499	14	company	company	PROPN
ejpam-4356	499	15	,	,	PUNCT
ejpam-4356	499	16	inc	inc	PROPN
ejpam-4356	499	17	.	.	PROPN
ejpam-4356	499	18	,	,	PUNCT
ejpam-4356	499	19	usa	usa	PROPN
ejpam-4356	499	20	,	,	PUNCT
ejpam-4356	499	21	1969	1969	NUM
ejpam-4356	499	22	.	.	PUNCT
ejpam-4356	500	1	[	[	X
ejpam-4356	500	2	3	3	X
ejpam-4356	500	3	]	]	X
ejpam-4356	500	4	g.	g.	PROPN
ejpam-4356	500	5	cagaanan	cagaanan	PROPN
ejpam-4356	500	6	.	.	PUNCT
ejpam-4356	500	7	,	,	PUNCT
ejpam-4356	500	8	on	on	ADP
ejpam-4356	500	9	geodetic	geodetic	ADJ
ejpam-4356	500	10	covexity	covexity	NOUN
ejpam-4356	500	11	in	in	ADP
ejpam-4356	500	12	graphs	graph	NOUN
ejpam-4356	500	13	.	.	PUNCT
ejpam-4356	501	1	disertation	disertation	NOUN
ejpam-4356	501	2	.	.	PUNCT
ejpam-4356	502	1	msu	msu	PROPN
ejpam-4356	502	2	-	-	PUNCT
ejpam-4356	502	3	iligan	iligan	PROPN
ejpam-4356	502	4	institute	institute	PROPN
ejpam-4356	502	5	of	of	ADP
ejpam-4356	502	6	technology	technology	PROPN
ejpam-4356	502	7	,	,	PUNCT
ejpam-4356	502	8	march	march	PROPN
ejpam-4356	502	9	2004	2004	NUM
ejpam-4356	502	10	.	.	PUNCT
ejpam-4356	503	1	[	[	X
ejpam-4356	503	2	4	4	X
ejpam-4356	503	3	]	]	X
ejpam-4356	503	4	g.	g.	PROPN
ejpam-4356	503	5	chartrand	chartrand	PROPN
ejpam-4356	503	6	,	,	PUNCT
ejpam-4356	503	7	f.	f.	PROPN
ejpam-4356	503	8	harary	harary	PROPN
ejpam-4356	503	9	,	,	PUNCT
ejpam-4356	503	10	p.	p.	PROPN
ejpam-4356	503	11	zhang	zhang	PROPN
ejpam-4356	503	12	,	,	PUNCT
ejpam-4356	503	13	geodetics	geodetic	NOUN
ejpam-4356	503	14	sets	set	VERB
ejpam-4356	503	15	in	in	ADP
ejpam-4356	503	16	graphs	graph	NOUN
ejpam-4356	503	17	,	,	PUNCT
ejpam-4356	503	18	discussiones	discussione	NOUN
ejpam-4356	503	19	mathematicae	mathematicae	PROPN
ejpam-4356	503	20	graph	graph	NOUN
ejpam-4356	503	21	theory	theory	NOUN
ejpam-4356	503	22	20	20	NUM
ejpam-4356	503	23	(	(	PUNCT
ejpam-4356	503	24	2000	2000	NUM
ejpam-4356	503	25	)	)	PUNCT
ejpam-4356	503	26	129	129	NUM
ejpam-4356	503	27	-	-	SYM
ejpam-4356	503	28	138	138	NUM
ejpam-4356	503	29	[	[	X
ejpam-4356	503	30	5	5	NUM
ejpam-4356	503	31	]	]	X
ejpam-4356	503	32	jr	jr	PROPN
ejpam-4356	503	33	.	.	PROPN
ejpam-4356	503	34	s.	s.	PROPN
ejpam-4356	503	35	canoy	canoy	PROPN
ejpam-4356	503	36	,	,	PUNCT
ejpam-4356	503	37	g.	g.	PROPN
ejpam-4356	503	38	cagaanan	cagaanan	PROPN
ejpam-4356	503	39	,	,	PUNCT
ejpam-4356	503	40	s.	s.	PROPN
ejpam-4356	503	41	gervacio	gervacio	PROPN
ejpam-4356	503	42	,	,	PUNCT
ejpam-4356	503	43	covexity	covexity	NOUN
ejpam-4356	503	44	,	,	PUNCT
ejpam-4356	503	45	geodetic	geodetic	ADJ
ejpam-4356	503	46	,	,	PUNCT
ejpam-4356	503	47	and	and	CCONJ
ejpam-4356	503	48	hull	hull	NOUN
ejpam-4356	503	49	numbers	number	NOUN
ejpam-4356	503	50	of	of	ADP
ejpam-4356	503	51	the	the	DET
ejpam-4356	503	52	join	join	NOUN
ejpam-4356	503	53	of	of	ADP
ejpam-4356	503	54	graphs	graph	NOUN
ejpam-4356	503	55	.	.	PUNCT
ejpam-4356	504	1	utilitas	utilitas	PROPN
ejpam-4356	504	2	mathematica	mathematica	PROPN
ejpam-4356	504	3	71	71	NUM
ejpam-4356	504	4	(	(	PUNCT
ejpam-4356	504	5	2006	2006	NUM
ejpam-4356	504	6	)	)	PUNCT
ejpam-4356	504	7	,	,	PUNCT
ejpam-4356	504	8	to	to	PART
ejpam-4356	504	9	appear	appear	VERB
ejpam-4356	504	10	.	.	PUNCT
ejpam-4356	505	1	[	[	X
ejpam-4356	505	2	6	6	NUM
ejpam-4356	505	3	]	]	PUNCT
ejpam-4356	505	4	r.	r.	NOUN
ejpam-4356	505	5	chellathurai	chellathurai	PROPN
ejpam-4356	505	6	,	,	PUNCT
ejpam-4356	505	7	s.	s.	PROPN
ejpam-4356	505	8	padma	padma	PROPN
ejpam-4356	505	9	vijaya	vijaya	PROPN
ejpam-4356	505	10	,	,	PUNCT
ejpam-4356	505	11	,	,	PUNCT
ejpam-4356	505	12	the	the	DET
ejpam-4356	505	13	geodetic	geodetic	ADJ
ejpam-4356	505	14	domination	domination	NOUN
ejpam-4356	505	15	number	number	NOUN
ejpam-4356	505	16	for	for	ADP
ejpam-4356	505	17	the	the	DET
ejpam-4356	505	18	product	product	NOUN
ejpam-4356	505	19	of	of	ADP
ejpam-4356	505	20	graphs	graph	NOUN
ejpam-4356	505	21	,	,	PUNCT
ejpam-4356	505	22	transactions	transaction	NOUN
ejpam-4356	505	23	on	on	ADP
ejpam-4356	505	24	combinatorics	combinatoric	NOUN
ejpam-4356	505	25	,	,	PUNCT
ejpam-4356	505	26	issn	issn	PROPN
ejpam-4356	505	27	(	(	PUNCT
ejpam-4356	505	28	print	print	NOUN
ejpam-4356	505	29	):	):	PUNCT
ejpam-4356	505	30	2251	2251	NUM
ejpam-4356	505	31	-	-	SYM
ejpam-4356	505	32	8657	8657	NUM
ejpam-4356	505	33	,	,	PUNCT
ejpam-4356	505	34	issn	issn	PROPN
ejpam-4356	505	35	(	(	PUNCT
ejpam-4356	505	36	on	on	ADP
ejpam-4356	505	37	-	-	PUNCT
ejpam-4356	505	38	line	line	NOUN
ejpam-4356	505	39	):	):	PUNCT
ejpam-4356	505	40	2251	2251	NUM
ejpam-4356	505	41	-	-	SYM
ejpam-4356	505	42	8665	8665	NUM
ejpam-4356	505	43	vol	vol	NOUN
ejpam-4356	505	44	.	.	PROPN
ejpam-4356	505	45	3	3	NUM
ejpam-4356	505	46	no	no	NOUN
ejpam-4356	505	47	.	.	NOUN
ejpam-4356	505	48	4	4	NUM
ejpam-4356	505	49	(	(	PUNCT
ejpam-4356	505	50	2014	2014	NUM
ejpam-4356	505	51	)	)	PUNCT
ejpam-4356	505	52	,	,	PUNCT
ejpam-4356	505	53	pp	pp	PROPN
ejpam-4356	505	54	.	.	PUNCT
ejpam-4356	506	1	19	19	NUM
ejpam-4356	506	2	-	-	SYM
ejpam-4356	506	3	30	30	NUM
ejpam-4356	506	4	.	.	PUNCT
ejpam-4356	507	1	[	[	X
ejpam-4356	507	2	7	7	X
ejpam-4356	507	3	]	]	X
ejpam-4356	507	4	j.	j.	PROPN
ejpam-4356	507	5	dunbar	dunbar	PROPN
ejpam-4356	507	6	,	,	PUNCT
ejpam-4356	507	7	j.	j.	PROPN
ejpam-4356	507	8	grossman	grossman	PROPN
ejpam-4356	507	9	,	,	PUNCT
ejpam-4356	507	10	j.	j.	PROPN
ejpam-4356	507	11	hattingh	hattingh	PROPN
ejpam-4356	507	12	,	,	PUNCT
ejpam-4356	507	13	s.	s.	PROPN
ejpam-4356	507	14	hedetniemi	hedetniemi	PROPN
ejpam-4356	507	15	,	,	PUNCT
ejpam-4356	507	16	a.	a.	PROPN
ejpam-4356	507	17	mcrae	mcrae	PROPN
ejpam-4356	507	18	,	,	PUNCT
ejpam-4356	507	19	on	on	ADP
ejpam-4356	507	20	weakly	weakly	ADJ
ejpam-4356	507	21	connected	connected	ADJ
ejpam-4356	507	22	domination	domination	NOUN
ejpam-4356	507	23	in	in	ADP
ejpam-4356	507	24	graphs	graph	NOUN
ejpam-4356	507	25	,	,	PUNCT
ejpam-4356	507	26	discrete	discrete	ADJ
ejpam-4356	507	27	mathematics	mathematic	NOUN
ejpam-4356	507	28	167/168	167/168	NUM
ejpam-4356	507	29	(	(	PUNCT
ejpam-4356	507	30	1997	1997	NUM
ejpam-4356	507	31	)	)	PUNCT
ejpam-4356	507	32	261	261	NUM
ejpam-4356	507	33	-269	-269	NOUN
ejpam-4356	507	34	[	[	X
ejpam-4356	507	35	8	8	NUM
ejpam-4356	507	36	]	]	PUNCT
ejpam-4356	507	37	w.	w.	PROPN
ejpam-4356	507	38	duckworth	duckworth	PROPN
ejpam-4356	507	39	,	,	PUNCT
ejpam-4356	507	40	b.	b.	PROPN
ejpam-4356	507	41	mans	mans	PROPN
ejpam-4356	507	42	,	,	PUNCT
ejpam-4356	507	43	connected	connected	ADJ
ejpam-4356	507	44	domination	domination	NOUN
ejpam-4356	507	45	of	of	ADP
ejpam-4356	507	46	regular	regular	ADJ
ejpam-4356	507	47	graphs	graph	NOUN
ejpam-4356	507	48	,	,	PUNCT
ejpam-4356	507	49	discrete	discrete	ADJ
ejpam-4356	507	50	mathematics	mathematic	NOUN
ejpam-4356	507	51	309	309	NUM
ejpam-4356	507	52	(	(	PUNCT
ejpam-4356	507	53	2009	2009	NUM
ejpam-4356	507	54	)	)	PUNCT
ejpam-4356	507	55	2305–2322	2305–2322	PROPN
ejpam-4356	508	1	[	[	X
ejpam-4356	508	2	9	9	NUM
ejpam-4356	508	3	]	]	X
ejpam-4356	508	4	h.	h.	PROPN
ejpam-4356	508	5	escuadro	escuadro	PROPN
ejpam-4356	508	6	,	,	PUNCT
ejpam-4356	508	7	r.	r.	PROPN
ejpam-4356	508	8	gera	gera	PROPN
ejpam-4356	508	9	,	,	PUNCT
ejpam-4356	508	10	a.	a.	NOUN
ejpam-4356	508	11	hansberg	hansberg	PROPN
ejpam-4356	508	12	,	,	PUNCT
ejpam-4356	508	13	n.	n.	PROPN
ejpam-4356	508	14	jafari	jafari	PROPN
ejpam-4356	508	15	rad	rad	PROPN
ejpam-4356	508	16	,	,	PUNCT
ejpam-4356	508	17	and	and	CCONJ
ejpam-4356	508	18	l.	l.	PROPN
ejpam-4356	508	19	volkmann	volkmann	PROPN
ejpam-4356	508	20	,	,	PUNCT
ejpam-4356	508	21	geodetic	geodetic	ADJ
ejpam-4356	508	22	domination	domination	NOUN
ejpam-4356	508	23	in	in	ADP
ejpam-4356	508	24	graphs	graph	NOUN
ejpam-4356	508	25	.	.	PUNCT
ejpam-4356	509	1	j.	j.	PROPN
ejpam-4356	509	2	combin	combin	PROPN
ejpam-4356	509	3	.	.	PUNCT
ejpam-4356	509	4	math	math	NOUN
ejpam-4356	509	5	.	.	PUNCT
ejpam-4356	510	1	combin	combin	NOUN
ejpam-4356	510	2	comput	comput	NOUN
ejpam-4356	510	3	77	77	NUM
ejpam-4356	510	4	(	(	PUNCT
ejpam-4356	510	5	2011	2011	NUM
ejpam-4356	510	6	)	)	PUNCT
ejpam-4356	510	7	,	,	PUNCT
ejpam-4356	510	8	89	89	NUM
ejpam-4356	510	9	-	-	SYM
ejpam-4356	510	10	101	101	NUM
ejpam-4356	510	11	[	[	X
ejpam-4356	510	12	10	10	NUM
ejpam-4356	510	13	]	]	PUNCT
ejpam-4356	510	14	a.	a.	NOUN
ejpam-4356	510	15	hansberg	hansberg	PROPN
ejpam-4356	510	16	,	,	PUNCT
ejpam-4356	510	17	l.	l.	PROPN
ejpam-4356	510	18	volkmann	volkmann	PROPN
ejpam-4356	510	19	,	,	PUNCT
ejpam-4356	510	20	on	on	ADP
ejpam-4356	510	21	the	the	DET
ejpam-4356	510	22	geodetic	geodetic	ADJ
ejpam-4356	510	23	and	and	CCONJ
ejpam-4356	510	24	geodetic	geodetic	ADJ
ejpam-4356	510	25	domination	domination	NOUN
ejpam-4356	510	26	numbers	number	NOUN
ejpam-4356	510	27	of	of	ADP
ejpam-4356	510	28	a	a	DET
ejpam-4356	510	29	graph	graph	NOUN
ejpam-4356	510	30	,	,	PUNCT
ejpam-4356	510	31	lehrstuhl	lehrstuhl	PROPN
ejpam-4356	510	32	ii	ii	PROPN
ejpam-4356	510	33	für	für	PROPN
ejpam-4356	510	34	mathematik	mathematik	PROPN
ejpam-4356	510	35	,	,	PUNCT
ejpam-4356	510	36	rwth	rwth	PROPN
ejpam-4356	510	37	aachen	aachen	PROPN
ejpam-4356	510	38	university	university	PROPN
ejpam-4356	510	39	,	,	PUNCT
ejpam-4356	510	40	52056	52056	NUM
ejpam-4356	510	41	aachen	aachen	PROPN
ejpam-4356	510	42	,	,	PUNCT
ejpam-4356	510	43	germany	germany	PROPN
ejpam-4356	510	44	,	,	PUNCT
ejpam-4356	510	45	discrete	discrete	ADJ
ejpam-4356	510	46	mathematics	mathematic	NOUN
ejpam-4356	510	47	310	310	NUM
ejpam-4356	510	48	(	(	PUNCT
ejpam-4356	510	49	2010	2010	NUM
ejpam-4356	510	50	)	)	PUNCT
ejpam-4356	510	51	2140–2146	2140–2146	NUM
ejpam-4356	511	1	[	[	X
ejpam-4356	511	2	11	11	NUM
ejpam-4356	511	3	]	]	X
ejpam-4356	511	4	f.	f.	PROPN
ejpam-4356	511	5	jamil	jamil	PROPN
ejpam-4356	511	6	,	,	PUNCT
ejpam-4356	511	7	i.	i.	PROPN
ejpam-4356	511	8	aniversario	aniversario	PROPN
ejpam-4356	511	9	,	,	PUNCT
ejpam-4356	511	10	jr	jr	PROPN
ejpam-4356	511	11	.	.	PROPN
ejpam-4356	511	12	s.	s.	PROPN
ejpam-4356	511	13	canoy	canoy	PROPN
ejpam-4356	511	14	,	,	PUNCT
ejpam-4356	511	15	the	the	DET
ejpam-4356	511	16	closed	closed	ADJ
ejpam-4356	511	17	geodetic	geodetic	ADJ
ejpam-4356	511	18	numbers	number	NOUN
ejpam-4356	511	19	of	of	ADP
ejpam-4356	511	20	the	the	DET
ejpam-4356	511	21	corona	corona	NOUN
ejpam-4356	511	22	and	and	CCONJ
ejpam-4356	511	23	composition	composition	NOUN
ejpam-4356	511	24	of	of	ADP
ejpam-4356	511	25	graphs	graph	NOUN
ejpam-4356	511	26	,	,	PUNCT
ejpam-4356	511	27	msu	msu	PROPN
ejpam-4356	511	28	iligan	iligan	PROPN
ejpam-4356	511	29	institute	institute	PROPN
ejpam-4356	511	30	of	of	ADP
ejpam-4356	511	31	technology	technology	PROPN
ejpam-4356	511	32	9200	9200	NUM
ejpam-4356	511	33	iligan	iligan	ADJ
ejpam-4356	511	34	city	city	NOUN
ejpam-4356	511	35	,	,	PUNCT
ejpam-4356	511	36	utilitas	utilitas	PROPN
ejpam-4356	511	37	mathematica	mathematica	PROPN
ejpam-4356	511	38	74(2007	74(2007	NUM
ejpam-4356	511	39	)	)	PUNCT
ejpam-4356	511	40	,	,	PUNCT
ejpam-4356	511	41	pp.3	pp.3	PROPN
ejpam-4356	511	42	-	-	SYM
ejpam-4356	511	43	18	18	NUM
ejpam-4356	512	1	[	[	X
ejpam-4356	512	2	12	12	NUM
ejpam-4356	512	3	]	]	PUNCT
ejpam-4356	512	4	r.	r.	PROPN
ejpam-4356	512	5	patangan	patangan	PROPN
ejpam-4356	512	6	,	,	PUNCT
ejpam-4356	512	7	i.	i.	PROPN
ejpam-4356	512	8	aniversario	aniversario	PROPN
ejpam-4356	512	9	,	,	PUNCT
ejpam-4356	512	10	and	and	CCONJ
ejpam-4356	512	11	jr	jr	PROPN
ejpam-4356	512	12	.	.	PUNCT
ejpam-4356	512	13	a.	a.	PROPN
ejpam-4356	512	14	rosalio	rosalio	PROPN
ejpam-4356	512	15	,	,	PUNCT
ejpam-4356	512	16	weakly	weakly	ADV
ejpam-4356	512	17	connected	connected	ADJ
ejpam-4356	512	18	closed	close	VERB
ejpam-4356	512	19	geodetic	geodetic	ADJ
ejpam-4356	512	20	numbers	number	NOUN
ejpam-4356	512	21	of	of	ADP
ejpam-4356	512	22	graphs	graph	NOUN
ejpam-4356	512	23	,	,	PUNCT
ejpam-4356	512	24	international	international	ADJ
ejpam-4356	512	25	journal	journal	NOUN
ejpam-4356	512	26	of	of	ADP
ejpam-4356	512	27	mathematical	mathematical	ADJ
ejpam-4356	512	28	analysis	analysis	NOUN
ejpam-4356	512	29	vol	vol	NOUN
ejpam-4356	512	30	.	.	PUNCT
ejpam-4356	512	31	10	10	NUM
ejpam-4356	512	32	,	,	PUNCT
ejpam-4356	512	33	2016	2016	NUM
ejpam-4356	512	34	,	,	PUNCT
ejpam-4356	512	35	no	no	INTJ
ejpam-4356	512	36	.	.	NOUN
ejpam-4356	512	37	6	6	NUM
ejpam-4356	512	38	,	,	PUNCT
ejpam-4356	512	39	257	257	NUM
ejpam-4356	512	40	270	270	NUM
ejpam-4356	513	1	[	[	X
ejpam-4356	513	2	13	13	NUM
ejpam-4356	513	3	]	]	X
ejpam-4356	513	4	e.	e.	PROPN
ejpam-4356	513	5	sandueta	sandueta	PROPN
ejpam-4356	513	6	,	,	PUNCT
ejpam-4356	513	7	jr	jr	PROPN
ejpam-4356	513	8	.	.	PROPN
ejpam-4356	513	9	s.	s.	PROPN
ejpam-4356	513	10	canoy	canoy	PROPN
ejpam-4356	513	11	,	,	PUNCT
ejpam-4356	513	12	weakly	weakly	ADV
ejpam-4356	513	13	connected	connected	ADJ
ejpam-4356	513	14	domination	domination	NOUN
ejpam-4356	513	15	in	in	ADP
ejpam-4356	513	16	graphs	graph	NOUN
ejpam-4356	513	17	resulting	result	VERB
ejpam-4356	513	18	from	from	ADP
ejpam-4356	513	19	some	some	DET
ejpam-4356	513	20	graph	graph	NOUN
ejpam-4356	513	21	operations	operation	NOUN
ejpam-4356	513	22	,	,	PUNCT
ejpam-4356	513	23	international	international	PROPN
ejpam-4356	513	24	mathematical	mathematical	ADJ
ejpam-4356	513	25	forum	forum	PROPN
ejpam-4356	513	26	,	,	PUNCT
ejpam-4356	513	27	vol	vol	NOUN
ejpam-4356	513	28	.	.	PROPN
ejpam-4356	513	29	6	6	NUM
ejpam-4356	513	30	,	,	PUNCT
ejpam-4356	513	31	2011	2011	NUM
ejpam-4356	513	32	,	,	PUNCT
ejpam-4356	513	33	no	no	INTJ
ejpam-4356	513	34	.	.	NOUN
ejpam-4356	513	35	21	21	NUM
ejpam-4356	513	36	,	,	PUNCT
ejpam-4356	513	37	1031	1031	NUM
ejpam-4356	513	38	1035	1035	NUM
ejpam-4356	514	1	[	[	X
ejpam-4356	514	2	14	14	NUM
ejpam-4356	514	3	]	]	X
ejpam-4356	514	4	j.	j.	PROPN
ejpam-4356	514	5	tarr	tarr	PROPN
ejpam-4356	514	6	,	,	PUNCT
ejpam-4356	514	7	s.	s.	PROPN
ejpam-4356	514	8	suen	suen	PROPN
ejpam-4356	514	9	,	,	PUNCT
ejpam-4356	514	10	domination	domination	NOUN
ejpam-4356	514	11	in	in	ADP
ejpam-4356	514	12	graphs	graph	NOUN
ejpam-4356	514	13	,	,	PUNCT
ejpam-4356	514	14	graduate	graduate	NOUN
ejpam-4356	514	15	theses	thesis	NOUN
ejpam-4356	514	16	and	and	CCONJ
ejpam-4356	514	17	dissertations	dissertation	NOUN
ejpam-4356	514	18	,	,	PUNCT
ejpam-4356	514	19	university	university	NOUN
ejpam-4356	514	20	of	of	ADP
ejpam-4356	514	21	south	south	PROPN
ejpam-4356	514	22	florida	florida	PROPN
ejpam-4356	514	23	,	,	PUNCT
ejpam-4356	514	24	scholar	scholar	NOUN
ejpam-4356	514	25	commons	common	NOUN
ejpam-4356	514	26	,	,	PUNCT
ejpam-4356	514	27	graduate	graduate	NOUN
ejpam-4356	514	28	theses	thesis	NOUN
ejpam-4356	514	29	and	and	CCONJ
ejpam-4356	514	30	dissertations	dissertation	NOUN
ejpam-4356	514	31	,	,	PUNCT
ejpam-4356	514	32	5	5	NUM
ejpam-4356	514	33	-	-	SYM
ejpam-4356	514	34	19	19	NUM
ejpam-4356	514	35	-	-	PUNCT
ejpam-4356	514	36	2010	2010	NUM
ejpam-4356	514	37	references	reference	NOUN
ejpam-4356	514	38	752	752	NUM
ejpam-4356	514	39	[	[	X
ejpam-4356	514	40	15	15	NUM
ejpam-4356	514	41	]	]	X
ejpam-4356	514	42	k.m	k.m	PROPN
ejpam-4356	514	43	.	.	PROPN
ejpam-4356	514	44	tejaswini	tejaswini	PROPN
ejpam-4356	514	45	,	,	PUNCT
ejpam-4356	514	46	venkanagouda	venkanagouda	NOUN
ejpam-4356	514	47	m.	m.	NOUN
ejpam-4356	514	48	goudar	goudar	PROPN
ejpam-4356	514	49	,	,	PUNCT
ejpam-4356	514	50	venkatesha	venkatesha	PROPN
ejpam-4356	514	51	,	,	PUNCT
ejpam-4356	514	52	geodetic	geodetic	ADJ
ejpam-4356	514	53	connected	connect	VERB
ejpam-4356	514	54	domination	domination	NOUN
ejpam-4356	514	55	number	number	NOUN
ejpam-4356	514	56	of	of	ADP
ejpam-4356	514	57	a	a	DET
ejpam-4356	514	58	graph	graph	NOUN
ejpam-4356	514	59	,	,	PUNCT
ejpam-4356	514	60	journal	journal	NOUN
ejpam-4356	514	61	of	of	ADP
ejpam-4356	514	62	advances	advance	NOUN
ejpam-4356	514	63	in	in	ADP
ejpam-4356	514	64	mathematics	mathematic	NOUN
ejpam-4356	514	65	,	,	PUNCT
ejpam-4356	514	66	vol	vol	NOUN
ejpam-4356	514	67	.	.	PROPN
ejpam-4356	515	1	9	9	NUM
ejpam-4356	515	2	,	,	PUNCT
ejpam-4356	515	3	no	no	INTJ
ejpam-4356	515	4	.	.	NOUN
ejpam-4356	515	5	7	7	NUM
ejpam-4356	515	6	,	,	PUNCT
ejpam-4356	515	7	2014	2014	NUM
ejpam-4356	515	8	,	,	PUNCT
ejpam-4356	515	9	2812	2812	NUM
ejpam-4356	515	10	-	-	SYM
ejpam-4356	515	11	2816	2816	NUM