id	sid	tid	token	lemma	pos
ejpam-4963	1	1	european	european	PROPN
ejpam-4963	1	2	journal	journal	PROPN
ejpam-4963	1	3	of	of	ADP
ejpam-4963	1	4	pure	pure	ADJ
ejpam-4963	1	5	and	and	CCONJ
ejpam-4963	1	6	applied	apply	VERB
ejpam-4963	1	7	mathematics	mathematic	NOUN
ejpam-4963	1	8	vol	vol	NOUN
ejpam-4963	1	9	.	.	PROPN
ejpam-4963	2	1	17	17	NUM
ejpam-4963	2	2	,	,	PUNCT
ejpam-4963	2	3	no	no	INTJ
ejpam-4963	2	4	.	.	NOUN
ejpam-4963	2	5	2	2	NUM
ejpam-4963	2	6	,	,	PUNCT
ejpam-4963	2	7	2024	2024	NUM
ejpam-4963	2	8	,	,	PUNCT
ejpam-4963	2	9	969	969	NUM
ejpam-4963	2	10	-	-	SYM
ejpam-4963	2	11	978	978	NUM
ejpam-4963	2	12	issn	issn	PROPN
ejpam-4963	2	13	1307	1307	NUM
ejpam-4963	2	14	-	-	SYM
ejpam-4963	2	15	5543	5543	NUM
ejpam-4963	2	16	–	–	PUNCT
ejpam-4963	2	17	ejpam.com	ejpam.com	X
ejpam-4963	2	18	published	publish	VERB
ejpam-4963	2	19	by	by	ADP
ejpam-4963	2	20	new	new	PROPN
ejpam-4963	2	21	york	york	PROPN
ejpam-4963	2	22	business	business	PROPN
ejpam-4963	2	23	global	global	ADJ
ejpam-4963	2	24	perfect	perfect	ADJ
ejpam-4963	2	25	equitable	equitable	ADJ
ejpam-4963	2	26	isolate	isolate	NOUN
ejpam-4963	2	27	dominations	domination	NOUN
ejpam-4963	2	28	in	in	ADP
ejpam-4963	2	29	graphs	graph	NOUN
ejpam-4963	2	30	mark	mark	PROPN
ejpam-4963	2	31	l.	l.	PROPN
ejpam-4963	2	32	caay1,∗	caay1,∗	PROPN
ejpam-4963	2	33	,	,	PUNCT
ejpam-4963	2	34	andrew	andrew	PROPN
ejpam-4963	2	35	c.	c.	PROPN
ejpam-4963	2	36	hernandez1	hernandez1	PROPN
ejpam-4963	3	1	1	1	NUM
ejpam-4963	3	2	department	department	NOUN
ejpam-4963	3	3	of	of	ADP
ejpam-4963	3	4	mathematics	mathematic	NOUN
ejpam-4963	3	5	and	and	CCONJ
ejpam-4963	3	6	statistics	statistic	NOUN
ejpam-4963	3	7	,	,	PUNCT
ejpam-4963	3	8	college	college	NOUN
ejpam-4963	3	9	of	of	ADP
ejpam-4963	3	10	science	science	NOUN
ejpam-4963	3	11	,	,	PUNCT
ejpam-4963	3	12	polytechnic	polytechnic	ADJ
ejpam-4963	3	13	university	university	NOUN
ejpam-4963	3	14	of	of	ADP
ejpam-4963	3	15	the	the	DET
ejpam-4963	3	16	philippines	philippine	NOUN
ejpam-4963	3	17	,	,	PUNCT
ejpam-4963	3	18	sta	sta	PROPN
ejpam-4963	3	19	.	.	PUNCT
ejpam-4963	4	1	mesa	mesa	PROPN
ejpam-4963	4	2	,	,	PUNCT
ejpam-4963	4	3	manila	manila	PROPN
ejpam-4963	4	4	city	city	PROPN
ejpam-4963	4	5	,	,	PUNCT
ejpam-4963	4	6	1016	1016	NUM
ejpam-4963	4	7	metro	metro	PROPN
ejpam-4963	4	8	manila	manila	PROPN
ejpam-4963	4	9	,	,	PUNCT
ejpam-4963	4	10	philippines	philippine	NOUN
ejpam-4963	4	11	abstract	abstract	ADJ
ejpam-4963	4	12	.	.	PUNCT
ejpam-4963	5	1	a	a	DET
ejpam-4963	5	2	subset	subset	NOUN
ejpam-4963	5	3	s	s	VERB
ejpam-4963	5	4	⊆	⊆	NUM
ejpam-4963	5	5	v	v	NOUN
ejpam-4963	5	6	(	(	PUNCT
ejpam-4963	5	7	g	g	NOUN
ejpam-4963	5	8	)	)	PUNCT
ejpam-4963	5	9	is	be	AUX
ejpam-4963	5	10	said	say	VERB
ejpam-4963	5	11	to	to	PART
ejpam-4963	5	12	be	be	AUX
ejpam-4963	5	13	a	a	DET
ejpam-4963	5	14	perfect	perfect	ADJ
ejpam-4963	5	15	equitable	equitable	ADJ
ejpam-4963	5	16	isolate	isolate	NOUN
ejpam-4963	5	17	dominating	dominate	VERB
ejpam-4963	5	18	set	set	NOUN
ejpam-4963	5	19	of	of	ADP
ejpam-4963	5	20	a	a	DET
ejpam-4963	5	21	graph	graph	NOUN
ejpam-4963	5	22	g	g	NOUN
ejpam-4963	5	23	if	if	SCONJ
ejpam-4963	5	24	it	it	PRON
ejpam-4963	5	25	is	be	AUX
ejpam-4963	5	26	both	both	PRON
ejpam-4963	5	27	perfect	perfect	ADJ
ejpam-4963	5	28	equitable	equitable	ADJ
ejpam-4963	5	29	dominating	dominating	NOUN
ejpam-4963	5	30	set	set	NOUN
ejpam-4963	5	31	of	of	ADP
ejpam-4963	5	32	g	g	PROPN
ejpam-4963	5	33	and	and	CCONJ
ejpam-4963	5	34	isolate	isolate	VERB
ejpam-4963	5	35	dominating	dominating	NOUN
ejpam-4963	5	36	set	set	NOUN
ejpam-4963	5	37	of	of	ADP
ejpam-4963	5	38	g.	g.	PROPN
ejpam-4963	5	39	the	the	DET
ejpam-4963	5	40	minimum	minimum	ADJ
ejpam-4963	5	41	cardinality	cardinality	NOUN
ejpam-4963	5	42	of	of	ADP
ejpam-4963	5	43	a	a	DET
ejpam-4963	5	44	perfect	perfect	ADJ
ejpam-4963	5	45	equitable	equitable	ADJ
ejpam-4963	5	46	isolate	isolate	NOUN
ejpam-4963	5	47	dominating	dominating	NOUN
ejpam-4963	5	48	set	set	NOUN
ejpam-4963	5	49	is	be	AUX
ejpam-4963	5	50	called	call	VERB
ejpam-4963	5	51	perfect	perfect	ADJ
ejpam-4963	5	52	equitable	equitable	ADJ
ejpam-4963	5	53	isolate	isolate	NOUN
ejpam-4963	5	54	domination	domination	NOUN
ejpam-4963	5	55	number	number	NOUN
ejpam-4963	5	56	of	of	ADP
ejpam-4963	5	57	g	g	NOUN
ejpam-4963	5	58	and	and	CCONJ
ejpam-4963	5	59	is	be	AUX
ejpam-4963	5	60	denoted	denote	VERB
ejpam-4963	5	61	by	by	ADP
ejpam-4963	5	62	γpe0(g	γpe0(g	NOUN
ejpam-4963	5	63	)	)	PUNCT
ejpam-4963	5	64	.	.	PUNCT
ejpam-4963	6	1	a	a	DET
ejpam-4963	6	2	perfect	perfect	ADJ
ejpam-4963	6	3	equitable	equitable	ADJ
ejpam-4963	6	4	isolate	isolate	NOUN
ejpam-4963	6	5	dominating	dominate	VERB
ejpam-4963	6	6	set	set	NOUN
ejpam-4963	6	7	s	s	PROPN
ejpam-4963	6	8	of	of	ADP
ejpam-4963	6	9	g	g	PROPN
ejpam-4963	6	10	is	be	AUX
ejpam-4963	6	11	called	call	VERB
ejpam-4963	6	12	γpe0	γpe0	NOUN
ejpam-4963	6	13	-	-	PUNCT
ejpam-4963	6	14	set	set	NOUN
ejpam-4963	6	15	of	of	ADP
ejpam-4963	6	16	g.	g.	PROPN
ejpam-4963	6	17	in	in	ADP
ejpam-4963	6	18	this	this	DET
ejpam-4963	6	19	paper	paper	NOUN
ejpam-4963	6	20	,	,	PUNCT
ejpam-4963	6	21	the	the	DET
ejpam-4963	6	22	authors	author	NOUN
ejpam-4963	6	23	give	give	VERB
ejpam-4963	6	24	characterizations	characterization	NOUN
ejpam-4963	6	25	of	of	ADP
ejpam-4963	6	26	a	a	DET
ejpam-4963	6	27	perfect	perfect	ADJ
ejpam-4963	6	28	equitable	equitable	ADJ
ejpam-4963	6	29	isolate	isolate	NOUN
ejpam-4963	6	30	dominating	dominate	VERB
ejpam-4963	6	31	set	set	NOUN
ejpam-4963	6	32	of	of	ADP
ejpam-4963	6	33	some	some	DET
ejpam-4963	6	34	graphs	graph	NOUN
ejpam-4963	6	35	and	and	CCONJ
ejpam-4963	6	36	graphs	graph	NOUN
ejpam-4963	6	37	obtained	obtain	VERB
ejpam-4963	6	38	from	from	ADP
ejpam-4963	6	39	the	the	DET
ejpam-4963	6	40	join	join	NOUN
ejpam-4963	6	41	and	and	CCONJ
ejpam-4963	6	42	corona	corona	NOUN
ejpam-4963	6	43	of	of	ADP
ejpam-4963	6	44	two	two	NUM
ejpam-4963	6	45	graphs	graph	NOUN
ejpam-4963	6	46	.	.	PUNCT
ejpam-4963	7	1	furthermore	furthermore	ADV
ejpam-4963	7	2	,	,	PUNCT
ejpam-4963	7	3	the	the	DET
ejpam-4963	7	4	perfect	perfect	ADJ
ejpam-4963	7	5	equitable	equitable	ADJ
ejpam-4963	7	6	isolate	isolate	NOUN
ejpam-4963	7	7	domination	domination	NOUN
ejpam-4963	7	8	numbers	number	NOUN
ejpam-4963	7	9	of	of	ADP
ejpam-4963	7	10	these	these	DET
ejpam-4963	7	11	graphs	graph	NOUN
ejpam-4963	7	12	is	be	AUX
ejpam-4963	7	13	determined	determine	VERB
ejpam-4963	7	14	,	,	PUNCT
ejpam-4963	7	15	and	and	CCONJ
ejpam-4963	7	16	the	the	DET
ejpam-4963	7	17	graphs	graph	NOUN
ejpam-4963	7	18	with	with	ADP
ejpam-4963	7	19	no	no	DET
ejpam-4963	7	20	perfect	perfect	ADJ
ejpam-4963	7	21	equitable	equitable	ADJ
ejpam-4963	7	22	isolate	isolate	NOUN
ejpam-4963	7	23	dominating	dominating	NOUN
ejpam-4963	7	24	sets	set	NOUN
ejpam-4963	7	25	are	be	AUX
ejpam-4963	7	26	investigated	investigate	VERB
ejpam-4963	7	27	.	.	PUNCT
ejpam-4963	8	1	2020	2020	NUM
ejpam-4963	8	2	mathematics	mathematic	NOUN
ejpam-4963	8	3	subject	subject	NOUN
ejpam-4963	8	4	classifications	classification	NOUN
ejpam-4963	8	5	:	:	PUNCT
ejpam-4963	8	6	05c69	05c69	NUM
ejpam-4963	8	7	,	,	PUNCT
ejpam-4963	8	8	05c38	05c38	NUM
ejpam-4963	8	9	,	,	PUNCT
ejpam-4963	8	10	05c76	05c76	DET
ejpam-4963	8	11	key	key	ADJ
ejpam-4963	8	12	words	word	NOUN
ejpam-4963	8	13	and	and	CCONJ
ejpam-4963	8	14	phrases	phrase	NOUN
ejpam-4963	8	15	:	:	PUNCT
ejpam-4963	8	16	perfect	perfect	ADJ
ejpam-4963	8	17	domination	domination	NOUN
ejpam-4963	8	18	,	,	PUNCT
ejpam-4963	8	19	equitable	equitable	ADJ
ejpam-4963	8	20	domination	domination	NOUN
ejpam-4963	8	21	,	,	PUNCT
ejpam-4963	8	22	perfect	perfect	ADJ
ejpam-4963	8	23	equitable	equitable	ADJ
ejpam-4963	8	24	domination	domination	NOUN
ejpam-4963	8	25	,	,	PUNCT
ejpam-4963	8	26	isolate	isolate	VERB
ejpam-4963	8	27	domination	domination	NOUN
ejpam-4963	8	28	,	,	PUNCT
ejpam-4963	8	29	perfect	perfect	ADJ
ejpam-4963	8	30	equitable	equitable	ADJ
ejpam-4963	8	31	isolate	isolate	NOUN
ejpam-4963	8	32	domination	domination	NOUN
ejpam-4963	8	33	1	1	NUM
ejpam-4963	8	34	.	.	PUNCT
ejpam-4963	9	1	introduction	introduction	NOUN
ejpam-4963	9	2	recently	recently	ADV
ejpam-4963	9	3	,	,	PUNCT
ejpam-4963	9	4	there	there	PRON
ejpam-4963	9	5	has	have	AUX
ejpam-4963	9	6	been	be	AUX
ejpam-4963	9	7	a	a	DET
ejpam-4963	9	8	growing	grow	VERB
ejpam-4963	9	9	interest	interest	NOUN
ejpam-4963	9	10	in	in	ADP
ejpam-4963	9	11	the	the	DET
ejpam-4963	9	12	applications	application	NOUN
ejpam-4963	9	13	of	of	ADP
ejpam-4963	9	14	one	one	NUM
ejpam-4963	9	15	of	of	ADP
ejpam-4963	9	16	the	the	DET
ejpam-4963	9	17	widest	wide	ADJ
ejpam-4963	9	18	research	research	NOUN
ejpam-4963	9	19	topics	topic	NOUN
ejpam-4963	9	20	in	in	ADP
ejpam-4963	9	21	graph	graph	NOUN
ejpam-4963	9	22	theory	theory	NOUN
ejpam-4963	9	23	,	,	PUNCT
ejpam-4963	9	24	the	the	DET
ejpam-4963	9	25	study	study	NOUN
ejpam-4963	9	26	of	of	ADP
ejpam-4963	9	27	domination	domination	NOUN
ejpam-4963	9	28	in	in	ADP
ejpam-4963	9	29	graphs	graph	NOUN
ejpam-4963	9	30	,	,	PUNCT
ejpam-4963	9	31	which	which	PRON
ejpam-4963	9	32	was	be	AUX
ejpam-4963	9	33	developed	develop	VERB
ejpam-4963	9	34	by	by	ADP
ejpam-4963	9	35	claude	claude	PROPN
ejpam-4963	9	36	berge	berge	PROPN
ejpam-4963	9	37	in	in	ADP
ejpam-4963	9	38	1958	1958	NUM
ejpam-4963	9	39	when	when	SCONJ
ejpam-4963	9	40	he	he	PRON
ejpam-4963	9	41	introduced	introduce	VERB
ejpam-4963	9	42	the	the	DET
ejpam-4963	9	43	coefficient	coefficient	NOUN
ejpam-4963	9	44	of	of	ADP
ejpam-4963	9	45	external	external	ADJ
ejpam-4963	9	46	stability	stability	NOUN
ejpam-4963	9	47	known	know	VERB
ejpam-4963	9	48	today	today	NOUN
ejpam-4963	9	49	as	as	ADP
ejpam-4963	9	50	domination	domination	NOUN
ejpam-4963	9	51	[	[	X
ejpam-4963	9	52	2	2	NUM
ejpam-4963	9	53	]	]	PUNCT
ejpam-4963	9	54	.	.	PUNCT
ejpam-4963	10	1	due	due	ADP
ejpam-4963	10	2	to	to	ADP
ejpam-4963	10	3	the	the	DET
ejpam-4963	10	4	richness	richness	NOUN
ejpam-4963	10	5	of	of	ADP
ejpam-4963	10	6	the	the	DET
ejpam-4963	10	7	research	research	NOUN
ejpam-4963	10	8	and	and	CCONJ
ejpam-4963	10	9	applications	application	NOUN
ejpam-4963	10	10	to	to	PART
ejpam-4963	10	11	graphs	graph	NOUN
ejpam-4963	10	12	,	,	PUNCT
ejpam-4963	10	13	many	many	ADJ
ejpam-4963	10	14	variants	variant	NOUN
ejpam-4963	10	15	of	of	ADP
ejpam-4963	10	16	domination	domination	NOUN
ejpam-4963	10	17	started	start	VERB
ejpam-4963	10	18	to	to	PART
ejpam-4963	10	19	prosper	prosper	VERB
ejpam-4963	10	20	and	and	CCONJ
ejpam-4963	10	21	some	some	PRON
ejpam-4963	10	22	of	of	ADP
ejpam-4963	10	23	these	these	DET
ejpam-4963	10	24	variants	variant	NOUN
ejpam-4963	10	25	are	be	AUX
ejpam-4963	10	26	the	the	DET
ejpam-4963	10	27	isolate	isolate	ADJ
ejpam-4963	10	28	domination	domination	NOUN
ejpam-4963	10	29	and	and	CCONJ
ejpam-4963	10	30	perfect	perfect	ADJ
ejpam-4963	10	31	equitable	equitable	ADJ
ejpam-4963	10	32	domination	domination	NOUN
ejpam-4963	10	33	in	in	ADP
ejpam-4963	10	34	graph	graph	NOUN
ejpam-4963	10	35	.	.	PUNCT
ejpam-4963	11	1	the	the	DET
ejpam-4963	11	2	concept	concept	NOUN
ejpam-4963	11	3	of	of	ADP
ejpam-4963	11	4	perfect	perfect	ADJ
ejpam-4963	11	5	domination	domination	NOUN
ejpam-4963	11	6	was	be	AUX
ejpam-4963	11	7	first	first	ADV
ejpam-4963	11	8	introduced	introduce	VERB
ejpam-4963	11	9	by	by	ADP
ejpam-4963	11	10	livingston	livingston	PROPN
ejpam-4963	11	11	and	and	CCONJ
ejpam-4963	11	12	stout	stout	NOUN
ejpam-4963	12	1	[	[	X
ejpam-4963	12	2	16	16	NUM
ejpam-4963	12	3	]	]	PUNCT
ejpam-4963	12	4	as	as	ADP
ejpam-4963	12	5	an	an	DET
ejpam-4963	12	6	answer	answer	NOUN
ejpam-4963	12	7	to	to	ADP
ejpam-4963	12	8	the	the	DET
ejpam-4963	12	9	problem	problem	NOUN
ejpam-4963	12	10	of	of	ADP
ejpam-4963	12	11	the	the	DET
ejpam-4963	12	12	supplement	supplement	NOUN
ejpam-4963	12	13	study	study	NOUN
ejpam-4963	12	14	conducted	conduct	VERB
ejpam-4963	12	15	by	by	ADP
ejpam-4963	12	16	the	the	DET
ejpam-4963	12	17	same	same	ADJ
ejpam-4963	12	18	authors	author	NOUN
ejpam-4963	12	19	in	in	ADP
ejpam-4963	12	20	[	[	X
ejpam-4963	12	21	15	15	NUM
ejpam-4963	12	22	]	]	PUNCT
ejpam-4963	12	23	.	.	PUNCT
ejpam-4963	13	1	this	this	DET
ejpam-4963	13	2	notion	notion	NOUN
ejpam-4963	13	3	has	have	AUX
ejpam-4963	13	4	been	be	AUX
ejpam-4963	13	5	celebrated	celebrate	VERB
ejpam-4963	13	6	for	for	ADP
ejpam-4963	13	7	years	year	NOUN
ejpam-4963	13	8	,	,	PUNCT
ejpam-4963	13	9	and	and	CCONJ
ejpam-4963	13	10	many	many	ADJ
ejpam-4963	13	11	studies	study	NOUN
ejpam-4963	13	12	of	of	ADP
ejpam-4963	13	13	this	this	DET
ejpam-4963	13	14	kind	kind	NOUN
ejpam-4963	13	15	have	have	AUX
ejpam-4963	13	16	been	be	AUX
ejpam-4963	13	17	introduced	introduce	VERB
ejpam-4963	13	18	.	.	PUNCT
ejpam-4963	14	1	caay	caay	VERB
ejpam-4963	14	2	and	and	CCONJ
ejpam-4963	14	3	palahang	palahang	VERB
ejpam-4963	15	1	[	[	X
ejpam-4963	15	2	6	6	NUM
ejpam-4963	15	3	]	]	PUNCT
ejpam-4963	15	4	introduced	introduce	VERB
ejpam-4963	15	5	the	the	DET
ejpam-4963	15	6	notion	notion	NOUN
ejpam-4963	15	7	of	of	ADP
ejpam-4963	15	8	perfect	perfect	ADJ
ejpam-4963	15	9	independent	independent	ADJ
ejpam-4963	15	10	domination	domination	NOUN
ejpam-4963	15	11	of	of	ADP
ejpam-4963	15	12	graphs	graph	NOUN
ejpam-4963	15	13	where	where	SCONJ
ejpam-4963	15	14	they	they	PRON
ejpam-4963	15	15	joined	join	VERB
ejpam-4963	15	16	the	the	DET
ejpam-4963	15	17	notion	notion	NOUN
ejpam-4963	15	18	of	of	ADP
ejpam-4963	15	19	perfect	perfect	ADJ
ejpam-4963	15	20	domination	domination	NOUN
ejpam-4963	15	21	and	and	CCONJ
ejpam-4963	15	22	independent	independent	ADJ
ejpam-4963	15	23	domination	domination	NOUN
ejpam-4963	15	24	and	and	CCONJ
ejpam-4963	15	25	investigate	investigate	VERB
ejpam-4963	15	26	the	the	DET
ejpam-4963	15	27	existence	existence	NOUN
ejpam-4963	15	28	of	of	ADP
ejpam-4963	15	29	such	such	ADJ
ejpam-4963	15	30	variant	variant	NOUN
ejpam-4963	15	31	and	and	CCONJ
ejpam-4963	15	32	the	the	DET
ejpam-4963	15	33	corresponding	corresponding	ADJ
ejpam-4963	15	34	number	number	NOUN
ejpam-4963	15	35	to	to	AUX
ejpam-4963	15	36	graph	graph	NOUN
ejpam-4963	15	37	.	.	PUNCT
ejpam-4963	16	1	there	there	PRON
ejpam-4963	16	2	are	be	VERB
ejpam-4963	16	3	also	also	ADV
ejpam-4963	16	4	many	many	ADJ
ejpam-4963	16	5	variants	variant	NOUN
ejpam-4963	16	6	of	of	ADP
ejpam-4963	16	7	perfect	perfect	ADJ
ejpam-4963	16	8	dominations	domination	NOUN
ejpam-4963	16	9	of	of	ADP
ejpam-4963	16	10	graphs	graph	NOUN
ejpam-4963	16	11	which	which	PRON
ejpam-4963	16	12	are	be	AUX
ejpam-4963	16	13	found	find	VERB
ejpam-4963	16	14	∗corresponding	∗corresponde	VERB
ejpam-4963	16	15	author	author	NOUN
ejpam-4963	16	16	.	.	PUNCT
ejpam-4963	17	1	doi	doi	NOUN
ejpam-4963	17	2	:	:	PUNCT
ejpam-4963	17	3	https://doi.org/10.29020/nybg.ejpam.v17i2.4963	https://doi.org/10.29020/nybg.ejpam.v17i2.4963	PROPN
ejpam-4963	17	4	email	email	NOUN
ejpam-4963	17	5	addresses	address	NOUN
ejpam-4963	17	6	:	:	PUNCT
ejpam-4963	17	7	mark.caay@adamson.edu.ph	mark.caay@adamson.edu.ph	PROPN
ejpam-4963	17	8	(	(	PUNCT
ejpam-4963	17	9	m.	m.	NOUN
ejpam-4963	17	10	caay	caay	PROPN
ejpam-4963	17	11	)	)	PUNCT
ejpam-4963	17	12	,	,	PUNCT
ejpam-4963	17	13	andrew.hernndez@pup.edu.ph	andrew.hernndez@pup.edu.ph	PROPN
ejpam-4963	17	14	(	(	PUNCT
ejpam-4963	17	15	a.	a.	PROPN
ejpam-4963	17	16	hernandez	hernandez	PROPN
ejpam-4963	17	17	)	)	PUNCT
ejpam-4963	17	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4963	18	1	969	969	NUM
ejpam-4963	19	1	©	©	NOUN
ejpam-4963	19	2	2024	2024	NUM
ejpam-4963	19	3	ejpam	ejpam	NOUN
ejpam-4963	19	4	all	all	DET
ejpam-4963	19	5	rights	right	NOUN
ejpam-4963	19	6	reserved	reserve	VERB
ejpam-4963	19	7	.	.	PUNCT
ejpam-4963	20	1	m.	m.	NOUN
ejpam-4963	20	2	caay	caay	PROPN
ejpam-4963	20	3	,	,	PUNCT
ejpam-4963	20	4	a.	a.	PROPN
ejpam-4963	20	5	hernandez	hernandez	PROPN
ejpam-4963	20	6	/	/	SYM
ejpam-4963	20	7	eur	eur	PROPN
ejpam-4963	20	8	.	.	PUNCT
ejpam-4963	21	1	j.	j.	PROPN
ejpam-4963	21	2	pure	pure	PROPN
ejpam-4963	21	3	appl	appl	PROPN
ejpam-4963	21	4	.	.	PROPN
ejpam-4963	21	5	math	math	PROPN
ejpam-4963	21	6	,	,	PUNCT
ejpam-4963	21	7	17	17	NUM
ejpam-4963	21	8	(	(	PUNCT
ejpam-4963	21	9	2	2	NUM
ejpam-4963	21	10	)	)	PUNCT
ejpam-4963	21	11	(	(	PUNCT
ejpam-4963	21	12	2024	2024	NUM
ejpam-4963	21	13	)	)	PUNCT
ejpam-4963	21	14	,	,	PUNCT
ejpam-4963	21	15	969	969	NUM
ejpam-4963	21	16	-	-	SYM
ejpam-4963	21	17	978	978	NUM
ejpam-4963	21	18	970	970	NUM
ejpam-4963	21	19	in	in	ADP
ejpam-4963	21	20	the	the	DET
ejpam-4963	21	21	paper	paper	NOUN
ejpam-4963	21	22	of	of	ADP
ejpam-4963	21	23	[	[	X
ejpam-4963	21	24	16	16	NUM
ejpam-4963	21	25	]	]	PUNCT
ejpam-4963	21	26	,	,	PUNCT
ejpam-4963	21	27	[	[	X
ejpam-4963	21	28	10	10	NUM
ejpam-4963	21	29	]	]	PUNCT
ejpam-4963	21	30	and	and	CCONJ
ejpam-4963	22	1	[	[	X
ejpam-4963	22	2	11	11	NUM
ejpam-4963	22	3	]	]	PUNCT
ejpam-4963	22	4	.	.	PUNCT
ejpam-4963	23	1	another	another	DET
ejpam-4963	23	2	variant	variant	NOUN
ejpam-4963	23	3	of	of	ADP
ejpam-4963	23	4	domination	domination	NOUN
ejpam-4963	23	5	is	be	AUX
ejpam-4963	23	6	the	the	DET
ejpam-4963	23	7	equitable	equitable	ADJ
ejpam-4963	23	8	domination	domination	NOUN
ejpam-4963	23	9	graph	graph	NOUN
ejpam-4963	23	10	.	.	PUNCT
ejpam-4963	24	1	the	the	DET
ejpam-4963	24	2	concept	concept	NOUN
ejpam-4963	24	3	of	of	ADP
ejpam-4963	24	4	equitable	equitable	ADJ
ejpam-4963	24	5	domination	domination	NOUN
ejpam-4963	24	6	was	be	AUX
ejpam-4963	24	7	believed	believe	VERB
ejpam-4963	24	8	to	to	PART
ejpam-4963	24	9	have	have	AUX
ejpam-4963	24	10	been	be	AUX
ejpam-4963	24	11	introduced	introduce	VERB
ejpam-4963	24	12	by	by	ADP
ejpam-4963	24	13	a.	a.	PROPN
ejpam-4963	24	14	anitha	anitha	PROPN
ejpam-4963	24	15	,	,	PUNCT
ejpam-4963	24	16	et.al	et.al	PROPN
ejpam-4963	24	17	.	.	PUNCT
ejpam-4963	25	1	in	in	ADP
ejpam-4963	25	2	[	[	X
ejpam-4963	25	3	8	8	NUM
ejpam-4963	25	4	]	]	PUNCT
ejpam-4963	25	5	and	and	CCONJ
ejpam-4963	25	6	it	it	PRON
ejpam-4963	25	7	was	be	AUX
ejpam-4963	25	8	also	also	ADV
ejpam-4963	25	9	discussed	discuss	VERB
ejpam-4963	25	10	in	in	ADP
ejpam-4963	25	11	the	the	DET
ejpam-4963	25	12	paper	paper	NOUN
ejpam-4963	25	13	of	of	ADP
ejpam-4963	25	14	g.	g.	PROPN
ejpam-4963	25	15	deepak	deepak	PROPN
ejpam-4963	25	16	,	,	PUNCT
ejpam-4963	25	17	et.al	et.al	PROPN
ejpam-4963	25	18	.	.	PUNCT
ejpam-4963	26	1	in	in	ADP
ejpam-4963	26	2	[	[	X
ejpam-4963	26	3	9	9	NUM
ejpam-4963	26	4	]	]	PUNCT
ejpam-4963	26	5	.	.	PUNCT
ejpam-4963	27	1	this	this	DET
ejpam-4963	27	2	concept	concept	NOUN
ejpam-4963	27	3	has	have	AUX
ejpam-4963	27	4	extended	extend	VERB
ejpam-4963	27	5	further	far	ADV
ejpam-4963	27	6	and	and	CCONJ
ejpam-4963	27	7	so	so	ADV
ejpam-4963	27	8	caay	caay	VERB
ejpam-4963	27	9	and	and	CCONJ
ejpam-4963	27	10	durog	durog	NOUN
ejpam-4963	27	11	in	in	ADP
ejpam-4963	27	12	[	[	X
ejpam-4963	27	13	5	5	NUM
ejpam-4963	27	14	]	]	PUNCT
ejpam-4963	27	15	introduced	introduce	VERB
ejpam-4963	27	16	the	the	DET
ejpam-4963	27	17	notion	notion	NOUN
ejpam-4963	27	18	of	of	ADP
ejpam-4963	27	19	independent	independent	ADJ
ejpam-4963	27	20	equitable	equitable	ADJ
ejpam-4963	27	21	domination	domination	NOUN
ejpam-4963	27	22	in	in	ADP
ejpam-4963	27	23	graphs	graph	NOUN
ejpam-4963	27	24	.	.	PUNCT
ejpam-4963	28	1	furthermore	furthermore	ADV
ejpam-4963	28	2	,	,	PUNCT
ejpam-4963	28	3	this	this	DET
ejpam-4963	28	4	concept	concept	NOUN
ejpam-4963	28	5	has	have	AUX
ejpam-4963	28	6	also	also	ADV
ejpam-4963	28	7	been	be	AUX
ejpam-4963	28	8	developed	develop	VERB
ejpam-4963	28	9	by	by	ADP
ejpam-4963	28	10	caay	caay	NOUN
ejpam-4963	28	11	and	and	CCONJ
ejpam-4963	28	12	arugay	arugay	ADJ
ejpam-4963	28	13	when	when	SCONJ
ejpam-4963	28	14	they	they	PRON
ejpam-4963	28	15	introduced	introduce	VERB
ejpam-4963	28	16	the	the	DET
ejpam-4963	28	17	notion	notion	NOUN
ejpam-4963	28	18	of	of	ADP
ejpam-4963	28	19	perfect	perfect	ADJ
ejpam-4963	28	20	equitable	equitable	ADJ
ejpam-4963	28	21	domination	domination	NOUN
ejpam-4963	28	22	in	in	ADP
ejpam-4963	28	23	[	[	X
ejpam-4963	28	24	4	4	NUM
ejpam-4963	28	25	]	]	PUNCT
ejpam-4963	28	26	which	which	PRON
ejpam-4963	28	27	studied	study	VERB
ejpam-4963	28	28	about	about	ADP
ejpam-4963	28	29	the	the	DET
ejpam-4963	28	30	domination	domination	NOUN
ejpam-4963	28	31	that	that	PRON
ejpam-4963	28	32	is	be	AUX
ejpam-4963	28	33	perfect	perfect	ADJ
ejpam-4963	28	34	and	and	CCONJ
ejpam-4963	28	35	equitable	equitable	ADJ
ejpam-4963	28	36	at	at	ADP
ejpam-4963	28	37	the	the	DET
ejpam-4963	28	38	same	same	ADJ
ejpam-4963	28	39	time	time	NOUN
ejpam-4963	28	40	.	.	PUNCT
ejpam-4963	29	1	furthermore	furthermore	ADV
ejpam-4963	29	2	,	,	PUNCT
ejpam-4963	29	3	in	in	ADP
ejpam-4963	29	4	2024	2024	NUM
ejpam-4963	29	5	,	,	PUNCT
ejpam-4963	29	6	caay	caay	VERB
ejpam-4963	29	7	in	in	ADP
ejpam-4963	29	8	[	[	X
ejpam-4963	29	9	3	3	NUM
ejpam-4963	29	10	]	]	PUNCT
ejpam-4963	29	11	introduced	introduce	VERB
ejpam-4963	29	12	the	the	DET
ejpam-4963	29	13	notion	notion	NOUN
ejpam-4963	29	14	of	of	ADP
ejpam-4963	29	15	equitable	equitable	ADJ
ejpam-4963	29	16	rings	ring	NOUN
ejpam-4963	29	17	domination	domination	NOUN
ejpam-4963	29	18	in	in	ADP
ejpam-4963	29	19	graphs	graph	NOUN
ejpam-4963	29	20	.	.	PUNCT
ejpam-4963	30	1	in	in	ADP
ejpam-4963	30	2	2013	2013	NUM
ejpam-4963	30	3	,	,	PUNCT
ejpam-4963	30	4	the	the	DET
ejpam-4963	30	5	concept	concept	NOUN
ejpam-4963	30	6	of	of	ADP
ejpam-4963	30	7	isolate	isolate	ADJ
ejpam-4963	30	8	domination	domination	NOUN
ejpam-4963	30	9	in	in	ADP
ejpam-4963	30	10	graphs	graph	NOUN
ejpam-4963	30	11	was	be	AUX
ejpam-4963	30	12	studied	study	VERB
ejpam-4963	30	13	by	by	ADP
ejpam-4963	30	14	hamid	hamid	PROPN
ejpam-4963	30	15	and	and	CCONJ
ejpam-4963	30	16	balamurugan	balamurugan	VERB
ejpam-4963	30	17	[	[	X
ejpam-4963	30	18	13	13	NUM
ejpam-4963	30	19	]	]	PUNCT
ejpam-4963	30	20	.	.	PUNCT
ejpam-4963	31	1	because	because	SCONJ
ejpam-4963	31	2	this	this	DET
ejpam-4963	31	3	study	study	NOUN
ejpam-4963	31	4	gives	give	VERB
ejpam-4963	31	5	a	a	DET
ejpam-4963	31	6	lot	lot	NOUN
ejpam-4963	31	7	of	of	ADP
ejpam-4963	31	8	opportunity	opportunity	NOUN
ejpam-4963	31	9	to	to	PART
ejpam-4963	31	10	see	see	VERB
ejpam-4963	31	11	many	many	ADJ
ejpam-4963	31	12	research	research	NOUN
ejpam-4963	31	13	topics	topic	NOUN
ejpam-4963	31	14	,	,	PUNCT
ejpam-4963	31	15	a	a	DET
ejpam-4963	31	16	lot	lot	NOUN
ejpam-4963	31	17	of	of	ADP
ejpam-4963	31	18	mathematician	mathematician	NOUN
ejpam-4963	31	19	studied	study	VERB
ejpam-4963	31	20	many	many	ADJ
ejpam-4963	31	21	variants	variant	NOUN
ejpam-4963	31	22	of	of	ADP
ejpam-4963	31	23	this	this	PRON
ejpam-4963	31	24	.	.	PUNCT
ejpam-4963	32	1	armada	armada	PROPN
ejpam-4963	32	2	and	and	CCONJ
ejpam-4963	32	3	hamja	hamja	VERB
ejpam-4963	32	4	in	in	ADP
ejpam-4963	32	5	[	[	X
ejpam-4963	32	6	1	1	X
ejpam-4963	32	7	]	]	PUNCT
ejpam-4963	32	8	studied	study	VERB
ejpam-4963	32	9	the	the	DET
ejpam-4963	32	10	perfect	perfect	ADJ
ejpam-4963	32	11	isolate	isolate	NOUN
ejpam-4963	32	12	domination	domination	NOUN
ejpam-4963	32	13	in	in	ADP
ejpam-4963	32	14	graphs	graph	NOUN
ejpam-4963	32	15	where	where	SCONJ
ejpam-4963	32	16	they	they	PRON
ejpam-4963	32	17	defined	define	VERB
ejpam-4963	32	18	a	a	DET
ejpam-4963	32	19	domination	domination	NOUN
ejpam-4963	32	20	to	to	PART
ejpam-4963	32	21	be	be	AUX
ejpam-4963	32	22	perfect	perfect	ADJ
ejpam-4963	32	23	and	and	CCONJ
ejpam-4963	32	24	isolate	isolate	VERB
ejpam-4963	32	25	at	at	ADP
ejpam-4963	32	26	the	the	DET
ejpam-4963	32	27	same	same	ADJ
ejpam-4963	32	28	time	time	NOUN
ejpam-4963	32	29	.	.	PUNCT
ejpam-4963	33	1	many	many	ADJ
ejpam-4963	33	2	authors	author	NOUN
ejpam-4963	33	3	also	also	ADV
ejpam-4963	33	4	have	have	AUX
ejpam-4963	33	5	made	make	VERB
ejpam-4963	33	6	a	a	DET
ejpam-4963	33	7	lot	lot	NOUN
ejpam-4963	33	8	of	of	ADP
ejpam-4963	33	9	studies	study	NOUN
ejpam-4963	33	10	on	on	ADP
ejpam-4963	33	11	this	this	DET
ejpam-4963	33	12	different	different	ADJ
ejpam-4963	33	13	variants	variant	NOUN
ejpam-4963	33	14	and	and	CCONJ
ejpam-4963	33	15	can	can	AUX
ejpam-4963	33	16	be	be	AUX
ejpam-4963	33	17	found	find	VERB
ejpam-4963	33	18	in	in	ADP
ejpam-4963	33	19	[	[	X
ejpam-4963	33	20	17	17	NUM
ejpam-4963	33	21	]	]	PUNCT
ejpam-4963	33	22	.	.	PUNCT
ejpam-4963	34	1	in	in	ADP
ejpam-4963	34	2	this	this	DET
ejpam-4963	34	3	paper	paper	NOUN
ejpam-4963	34	4	,	,	PUNCT
ejpam-4963	34	5	we	we	PRON
ejpam-4963	34	6	study	study	VERB
ejpam-4963	34	7	the	the	DET
ejpam-4963	34	8	perfect	perfect	ADJ
ejpam-4963	34	9	equitable	equitable	ADJ
ejpam-4963	34	10	isolate	isolate	NOUN
ejpam-4963	34	11	domination	domination	NOUN
ejpam-4963	34	12	in	in	ADP
ejpam-4963	34	13	graphs	graph	NOUN
ejpam-4963	34	14	.	.	PUNCT
ejpam-4963	35	1	a	a	DET
ejpam-4963	35	2	subset	subset	NOUN
ejpam-4963	35	3	s	s	VERB
ejpam-4963	35	4	⊆	⊆	NUM
ejpam-4963	35	5	v	v	NOUN
ejpam-4963	35	6	(	(	PUNCT
ejpam-4963	35	7	g	g	NOUN
ejpam-4963	35	8	)	)	PUNCT
ejpam-4963	35	9	is	be	AUX
ejpam-4963	35	10	said	say	VERB
ejpam-4963	35	11	to	to	PART
ejpam-4963	35	12	be	be	AUX
ejpam-4963	35	13	a	a	DET
ejpam-4963	35	14	perfect	perfect	ADJ
ejpam-4963	35	15	equitable	equitable	ADJ
ejpam-4963	35	16	isolate	isolate	NOUN
ejpam-4963	35	17	dominating	dominating	NOUN
ejpam-4963	35	18	set	set	NOUN
ejpam-4963	35	19	if	if	SCONJ
ejpam-4963	35	20	it	it	PRON
ejpam-4963	35	21	is	be	AUX
ejpam-4963	35	22	a	a	DET
ejpam-4963	35	23	isolate	isolate	ADJ
ejpam-4963	35	24	dominating	dominating	NOUN
ejpam-4963	35	25	set	set	NOUN
ejpam-4963	35	26	and	and	CCONJ
ejpam-4963	35	27	if	if	SCONJ
ejpam-4963	35	28	it	it	PRON
ejpam-4963	35	29	is	be	AUX
ejpam-4963	35	30	perfect	perfect	ADJ
ejpam-4963	35	31	equitable	equitable	ADJ
ejpam-4963	35	32	dominating	dominating	NOUN
ejpam-4963	35	33	set	set	NOUN
ejpam-4963	35	34	.	.	PUNCT
ejpam-4963	36	1	to	to	PART
ejpam-4963	36	2	give	give	VERB
ejpam-4963	36	3	clarity	clarity	NOUN
ejpam-4963	36	4	,	,	PUNCT
ejpam-4963	36	5	the	the	DET
ejpam-4963	36	6	flow	flow	NOUN
ejpam-4963	36	7	of	of	ADP
ejpam-4963	36	8	our	our	PRON
ejpam-4963	36	9	paper	paper	NOUN
ejpam-4963	36	10	is	be	AUX
ejpam-4963	36	11	as	as	SCONJ
ejpam-4963	36	12	follows	follow	VERB
ejpam-4963	36	13	:	:	PUNCT
ejpam-4963	36	14	in	in	ADP
ejpam-4963	36	15	section	section	NOUN
ejpam-4963	36	16	2	2	NUM
ejpam-4963	36	17	,	,	PUNCT
ejpam-4963	36	18	we	we	PRON
ejpam-4963	36	19	introduce	introduce	VERB
ejpam-4963	36	20	the	the	DET
ejpam-4963	36	21	necessary	necessary	ADJ
ejpam-4963	36	22	notations	notation	NOUN
ejpam-4963	36	23	and	and	CCONJ
ejpam-4963	36	24	basic	basic	ADJ
ejpam-4963	36	25	concepts	concept	NOUN
ejpam-4963	36	26	that	that	PRON
ejpam-4963	36	27	are	be	AUX
ejpam-4963	36	28	used	use	VERB
ejpam-4963	36	29	in	in	ADP
ejpam-4963	36	30	this	this	DET
ejpam-4963	36	31	study	study	NOUN
ejpam-4963	36	32	.	.	PUNCT
ejpam-4963	37	1	we	we	PRON
ejpam-4963	37	2	also	also	ADV
ejpam-4963	37	3	introduce	introduce	VERB
ejpam-4963	37	4	the	the	DET
ejpam-4963	37	5	isolate	isolate	ADJ
ejpam-4963	37	6	domination	domination	NOUN
ejpam-4963	37	7	and	and	CCONJ
ejpam-4963	37	8	perfect	perfect	ADJ
ejpam-4963	37	9	equitable	equitable	ADJ
ejpam-4963	37	10	dominations	domination	NOUN
ejpam-4963	37	11	,	,	PUNCT
ejpam-4963	37	12	and	and	CCONJ
ejpam-4963	37	13	some	some	PRON
ejpam-4963	37	14	of	of	ADP
ejpam-4963	37	15	their	their	PRON
ejpam-4963	37	16	results	result	NOUN
ejpam-4963	37	17	from	from	ADP
ejpam-4963	37	18	the	the	DET
ejpam-4963	37	19	references	reference	NOUN
ejpam-4963	37	20	that	that	PRON
ejpam-4963	37	21	are	be	AUX
ejpam-4963	37	22	used	use	VERB
ejpam-4963	37	23	in	in	ADP
ejpam-4963	37	24	the	the	DET
ejpam-4963	37	25	discussion	discussion	NOUN
ejpam-4963	37	26	of	of	ADP
ejpam-4963	37	27	the	the	DET
ejpam-4963	37	28	study	study	NOUN
ejpam-4963	37	29	.	.	PUNCT
ejpam-4963	38	1	we	we	PRON
ejpam-4963	38	2	also	also	ADV
ejpam-4963	38	3	established	establish	VERB
ejpam-4963	38	4	the	the	DET
ejpam-4963	38	5	case	case	NOUN
ejpam-4963	38	6	when	when	SCONJ
ejpam-4963	38	7	these	these	DET
ejpam-4963	38	8	two	two	NUM
ejpam-4963	38	9	dominations	domination	NOUN
ejpam-4963	38	10	imply	imply	VERB
ejpam-4963	38	11	each	each	DET
ejpam-4963	38	12	other	other	ADJ
ejpam-4963	38	13	and	and	CCONJ
ejpam-4963	38	14	so	so	ADV
ejpam-4963	38	15	we	we	PRON
ejpam-4963	38	16	come	come	VERB
ejpam-4963	38	17	up	up	ADP
ejpam-4963	38	18	with	with	ADP
ejpam-4963	38	19	our	our	PRON
ejpam-4963	38	20	formal	formal	ADJ
ejpam-4963	38	21	working	working	NOUN
ejpam-4963	38	22	definition	definition	NOUN
ejpam-4963	38	23	.	.	PUNCT
ejpam-4963	39	1	in	in	ADP
ejpam-4963	39	2	section	section	NOUN
ejpam-4963	39	3	3	3	NUM
ejpam-4963	39	4	,	,	PUNCT
ejpam-4963	39	5	we	we	PRON
ejpam-4963	39	6	show	show	VERB
ejpam-4963	39	7	our	our	PRON
ejpam-4963	39	8	results	result	NOUN
ejpam-4963	39	9	of	of	ADP
ejpam-4963	39	10	our	our	PRON
ejpam-4963	39	11	study	study	NOUN
ejpam-4963	39	12	.	.	PUNCT
ejpam-4963	40	1	2	2	X
ejpam-4963	40	2	.	.	NUM
ejpam-4963	40	3	preliminaries	preliminary	NOUN
ejpam-4963	40	4	and	and	CCONJ
ejpam-4963	40	5	the	the	DET
ejpam-4963	40	6	working	work	VERB
ejpam-4963	40	7	definitions	definition	NOUN
ejpam-4963	40	8	throughout	throughout	ADP
ejpam-4963	40	9	this	this	DET
ejpam-4963	40	10	paper	paper	NOUN
ejpam-4963	40	11	,	,	PUNCT
ejpam-4963	40	12	the	the	DET
ejpam-4963	40	13	graph	graph	NOUN
ejpam-4963	40	14	we	we	PRON
ejpam-4963	40	15	consider	consider	VERB
ejpam-4963	40	16	here	here	ADV
ejpam-4963	40	17	is	be	AUX
ejpam-4963	40	18	a	a	DET
ejpam-4963	40	19	connected	connected	ADJ
ejpam-4963	40	20	simple	simple	ADJ
ejpam-4963	40	21	graph	graph	NOUN
ejpam-4963	40	22	.	.	PUNCT
ejpam-4963	41	1	that	that	PRON
ejpam-4963	41	2	means	mean	VERB
ejpam-4963	41	3	,	,	PUNCT
ejpam-4963	41	4	there	there	PRON
ejpam-4963	41	5	are	be	VERB
ejpam-4963	41	6	no	no	DET
ejpam-4963	41	7	loops	loop	NOUN
ejpam-4963	41	8	and	and	CCONJ
ejpam-4963	41	9	multiple	multiple	ADJ
ejpam-4963	41	10	edges	edge	NOUN
ejpam-4963	41	11	.	.	PUNCT
ejpam-4963	42	1	a	a	DET
ejpam-4963	42	2	pair	pair	NOUN
ejpam-4963	42	3	g	g	NOUN
ejpam-4963	42	4	=	=	SYM
ejpam-4963	42	5	(	(	PUNCT
ejpam-4963	42	6	v	v	NOUN
ejpam-4963	42	7	(	(	PUNCT
ejpam-4963	42	8	g	g	NOUN
ejpam-4963	42	9	)	)	PUNCT
ejpam-4963	42	10	,	,	PUNCT
ejpam-4963	42	11	e(g	e(g	PROPN
ejpam-4963	42	12	)	)	PUNCT
ejpam-4963	42	13	)	)	PUNCT
ejpam-4963	42	14	is	be	AUX
ejpam-4963	42	15	called	call	VERB
ejpam-4963	42	16	a	a	DET
ejpam-4963	42	17	graph	graph	NOUN
ejpam-4963	42	18	(	(	PUNCT
ejpam-4963	42	19	on	on	ADP
ejpam-4963	42	20	v	v	NOUN
ejpam-4963	42	21	)	)	PUNCT
ejpam-4963	42	22	.	.	PUNCT
ejpam-4963	43	1	the	the	DET
ejpam-4963	43	2	elements	element	NOUN
ejpam-4963	43	3	of	of	ADP
ejpam-4963	43	4	v	v	NOUN
ejpam-4963	43	5	(	(	PUNCT
ejpam-4963	43	6	g	g	NOUN
ejpam-4963	43	7	)	)	PUNCT
ejpam-4963	43	8	are	be	AUX
ejpam-4963	43	9	called	call	VERB
ejpam-4963	43	10	the	the	DET
ejpam-4963	43	11	vertices	vertex	NOUN
ejpam-4963	43	12	of	of	ADP
ejpam-4963	43	13	g	g	NOUN
ejpam-4963	43	14	and	and	CCONJ
ejpam-4963	43	15	the	the	DET
ejpam-4963	43	16	elements	element	NOUN
ejpam-4963	43	17	of	of	ADP
ejpam-4963	43	18	e(g	e(g	PROPN
ejpam-4963	43	19	)	)	PUNCT
ejpam-4963	43	20	are	be	AUX
ejpam-4963	43	21	called	call	VERB
ejpam-4963	43	22	the	the	DET
ejpam-4963	43	23	edges	edge	NOUN
ejpam-4963	43	24	of	of	ADP
ejpam-4963	43	25	g.	g.	PROPN
ejpam-4963	43	26	if	if	SCONJ
ejpam-4963	43	27	no	no	DET
ejpam-4963	43	28	confusion	confusion	NOUN
ejpam-4963	43	29	arises	arise	VERB
ejpam-4963	43	30	,	,	PUNCT
ejpam-4963	43	31	we	we	PRON
ejpam-4963	43	32	can	can	AUX
ejpam-4963	43	33	use	use	VERB
ejpam-4963	43	34	v	v	NOUN
ejpam-4963	43	35	and	and	CCONJ
ejpam-4963	43	36	e	e	NOUN
ejpam-4963	43	37	to	to	PART
ejpam-4963	43	38	denote	denote	VERB
ejpam-4963	43	39	the	the	DET
ejpam-4963	43	40	set	set	NOUN
ejpam-4963	43	41	of	of	ADP
ejpam-4963	43	42	vertices	vertex	NOUN
ejpam-4963	43	43	and	and	CCONJ
ejpam-4963	43	44	set	set	NOUN
ejpam-4963	43	45	of	of	ADP
ejpam-4963	43	46	edges	edge	NOUN
ejpam-4963	43	47	of	of	ADP
ejpam-4963	43	48	g	g	NOUN
ejpam-4963	43	49	,	,	PUNCT
ejpam-4963	43	50	respectively	respectively	ADV
ejpam-4963	43	51	.	.	PUNCT
ejpam-4963	44	1	suppose	suppose	VERB
ejpam-4963	44	2	v	v	ADP
ejpam-4963	44	3	∈	∈	PROPN
ejpam-4963	44	4	v	v	NOUN
ejpam-4963	44	5	,	,	PUNCT
ejpam-4963	44	6	the	the	DET
ejpam-4963	44	7	neighborhood	neighborhood	NOUN
ejpam-4963	44	8	of	of	ADP
ejpam-4963	44	9	v	v	NOUN
ejpam-4963	44	10	is	be	AUX
ejpam-4963	44	11	the	the	DET
ejpam-4963	44	12	set	set	NOUN
ejpam-4963	44	13	ng(v	ng(v	PUNCT
ejpam-4963	44	14	)	)	PUNCT
ejpam-4963	44	15	=	=	SYM
ejpam-4963	45	1	{	{	PUNCT
ejpam-4963	45	2	u	u	NOUN
ejpam-4963	45	3	∈	∈	PROPN
ejpam-4963	45	4	v	v	NOUN
ejpam-4963	45	5	:	:	PUNCT
ejpam-4963	45	6	uv	uv	PROPN
ejpam-4963	45	7	∈	∈	PROPN
ejpam-4963	45	8	e.	e.	PROPN
ejpam-4963	45	9	}	}	PUNCT
ejpam-4963	45	10	.	.	PUNCT
ejpam-4963	46	1	given	give	VERB
ejpam-4963	46	2	d	d	PROPN
ejpam-4963	46	3	⊆	⊆	NUM
ejpam-4963	46	4	v	v	NOUN
ejpam-4963	46	5	,	,	PUNCT
ejpam-4963	46	6	the	the	DET
ejpam-4963	46	7	set	set	NOUN
ejpam-4963	46	8	ng(d	ng(d	PUNCT
ejpam-4963	46	9	)	)	PUNCT
ejpam-4963	46	10	=	=	SYM
ejpam-4963	46	11	n(d	n(d	NOUN
ejpam-4963	46	12	)	)	PUNCT
ejpam-4963	46	13	=	=	SYM
ejpam-4963	47	1	⋃	⋃	NOUN
ejpam-4963	47	2	v∈d	v∈d	NOUN
ejpam-4963	47	3	ng(v	ng(v	NUM
ejpam-4963	47	4	)	)	PUNCT
ejpam-4963	47	5	and	and	CCONJ
ejpam-4963	47	6	the	the	DET
ejpam-4963	47	7	set	set	NOUN
ejpam-4963	47	8	ng[d	ng[d	PROPN
ejpam-4963	47	9	]	]	PUNCT
ejpam-4963	47	10	=	=	SYM
ejpam-4963	48	1	n	n	PROPN
ejpam-4963	49	1	[	[	X
ejpam-4963	49	2	d	d	X
ejpam-4963	49	3	]	]	X
ejpam-4963	49	4	=	=	SYM
ejpam-4963	49	5	d	d	X
ejpam-4963	49	6	⋃	⋃	PROPN
ejpam-4963	49	7	n(d	n(d	NOUN
ejpam-4963	49	8	)	)	PUNCT
ejpam-4963	49	9	are	be	AUX
ejpam-4963	49	10	the	the	DET
ejpam-4963	49	11	open	open	ADJ
ejpam-4963	49	12	neighborhood	neighborhood	NOUN
ejpam-4963	49	13	and	and	CCONJ
ejpam-4963	49	14	the	the	DET
ejpam-4963	49	15	closed	closed	ADJ
ejpam-4963	49	16	neighborhood	neighborhood	NOUN
ejpam-4963	49	17	of	of	ADP
ejpam-4963	49	18	d	d	NOUN
ejpam-4963	49	19	respectively	respectively	ADV
ejpam-4963	49	20	.	.	PUNCT
ejpam-4963	50	1	in	in	ADP
ejpam-4963	50	2	this	this	DET
ejpam-4963	50	3	paper	paper	NOUN
ejpam-4963	50	4	,	,	PUNCT
ejpam-4963	50	5	we	we	PRON
ejpam-4963	50	6	denote	denote	VERB
ejpam-4963	50	7	∆(g	∆(g	PROPN
ejpam-4963	50	8	)	)	PUNCT
ejpam-4963	50	9	and	and	CCONJ
ejpam-4963	50	10	δ(g	δ(g	PROPN
ejpam-4963	50	11	)	)	PUNCT
ejpam-4963	50	12	to	to	PART
ejpam-4963	50	13	be	be	AUX
ejpam-4963	50	14	the	the	DET
ejpam-4963	50	15	minimum	minimum	ADJ
ejpam-4963	50	16	and	and	CCONJ
ejpam-4963	50	17	maximum	maximum	ADJ
ejpam-4963	50	18	degree	degree	NOUN
ejpam-4963	50	19	of	of	ADP
ejpam-4963	50	20	g	g	NOUN
ejpam-4963	50	21	,	,	PUNCT
ejpam-4963	50	22	respectively	respectively	ADV
ejpam-4963	50	23	.	.	PUNCT
ejpam-4963	51	1	we	we	PRON
ejpam-4963	51	2	denote	denote	VERB
ejpam-4963	51	3	pn	pn	PROPN
ejpam-4963	51	4	,	,	PUNCT
ejpam-4963	51	5	cn	cn	PROPN
ejpam-4963	51	6	,	,	PUNCT
ejpam-4963	51	7	kn	kn	PROPN
ejpam-4963	51	8	,	,	PUNCT
ejpam-4963	51	9	tn	tn	PROPN
ejpam-4963	51	10	for	for	ADP
ejpam-4963	51	11	the	the	DET
ejpam-4963	51	12	path	path	NOUN
ejpam-4963	51	13	graph	graph	NOUN
ejpam-4963	51	14	,	,	PUNCT
ejpam-4963	51	15	cycle	cycle	NOUN
ejpam-4963	51	16	graph	graph	NOUN
ejpam-4963	51	17	,	,	PUNCT
ejpam-4963	51	18	complete	complete	ADJ
ejpam-4963	51	19	graph	graph	NOUN
ejpam-4963	51	20	and	and	CCONJ
ejpam-4963	51	21	trees	tree	NOUN
ejpam-4963	51	22	of	of	ADP
ejpam-4963	51	23	order	order	NOUN
ejpam-4963	51	24	n	n	CCONJ
ejpam-4963	51	25	,	,	PUNCT
ejpam-4963	51	26	respectively	respectively	ADV
ejpam-4963	51	27	.	.	PUNCT
ejpam-4963	52	1	theorem	theorem	NOUN
ejpam-4963	52	2	1	1	NUM
ejpam-4963	52	3	.	.	PUNCT
ejpam-4963	53	1	[	[	X
ejpam-4963	53	2	7	7	X
ejpam-4963	53	3	]	]	X
ejpam-4963	53	4	a	a	DET
ejpam-4963	53	5	graph	graph	NOUN
ejpam-4963	53	6	g	g	NOUN
ejpam-4963	53	7	is	be	AUX
ejpam-4963	53	8	a	a	DET
ejpam-4963	53	9	cycle	cycle	NOUN
ejpam-4963	53	10	graph	graph	NOUN
ejpam-4963	53	11	if	if	SCONJ
ejpam-4963	53	12	and	and	CCONJ
ejpam-4963	53	13	only	only	ADV
ejpam-4963	53	14	if	if	SCONJ
ejpam-4963	53	15	every	every	DET
ejpam-4963	53	16	vertex	vertex	NOUN
ejpam-4963	53	17	of	of	ADP
ejpam-4963	53	18	g	g	PROPN
ejpam-4963	53	19	is	be	AUX
ejpam-4963	53	20	adjacent	adjacent	ADJ
ejpam-4963	53	21	to	to	ADP
ejpam-4963	53	22	two	two	NUM
ejpam-4963	53	23	other	other	ADJ
ejpam-4963	53	24	vertices	vertex	NOUN
ejpam-4963	53	25	.	.	PUNCT
ejpam-4963	54	1	m.	m.	NOUN
ejpam-4963	54	2	caay	caay	PROPN
ejpam-4963	54	3	,	,	PUNCT
ejpam-4963	54	4	a.	a.	PROPN
ejpam-4963	54	5	hernandez	hernandez	PROPN
ejpam-4963	54	6	/	/	SYM
ejpam-4963	54	7	eur	eur	PROPN
ejpam-4963	54	8	.	.	PUNCT
ejpam-4963	55	1	j.	j.	PROPN
ejpam-4963	55	2	pure	pure	PROPN
ejpam-4963	55	3	appl	appl	PROPN
ejpam-4963	55	4	.	.	PROPN
ejpam-4963	55	5	math	math	PROPN
ejpam-4963	55	6	,	,	PUNCT
ejpam-4963	55	7	17	17	NUM
ejpam-4963	55	8	(	(	PUNCT
ejpam-4963	55	9	2	2	NUM
ejpam-4963	55	10	)	)	PUNCT
ejpam-4963	55	11	(	(	PUNCT
ejpam-4963	55	12	2024	2024	NUM
ejpam-4963	55	13	)	)	PUNCT
ejpam-4963	55	14	,	,	PUNCT
ejpam-4963	55	15	969	969	NUM
ejpam-4963	55	16	-	-	SYM
ejpam-4963	55	17	978	978	NUM
ejpam-4963	55	18	971	971	NUM
ejpam-4963	55	19	definition	definition	NOUN
ejpam-4963	55	20	1	1	NUM
ejpam-4963	55	21	.	.	PUNCT
ejpam-4963	56	1	[	[	X
ejpam-4963	56	2	7	7	X
ejpam-4963	56	3	]	]	X
ejpam-4963	56	4	a	a	DET
ejpam-4963	56	5	spanning	span	VERB
ejpam-4963	56	6	subgraph	subgraph	NOUN
ejpam-4963	56	7	of	of	ADP
ejpam-4963	56	8	a	a	DET
ejpam-4963	56	9	graph	graph	NOUN
ejpam-4963	56	10	g	g	NOUN
ejpam-4963	56	11	is	be	AUX
ejpam-4963	56	12	a	a	DET
ejpam-4963	56	13	subgraph	subgraph	NOUN
ejpam-4963	56	14	obtained	obtain	VERB
ejpam-4963	56	15	by	by	ADP
ejpam-4963	56	16	deleting	delete	VERB
ejpam-4963	56	17	some	some	DET
ejpam-4963	56	18	edges	edge	NOUN
ejpam-4963	56	19	of	of	ADP
ejpam-4963	56	20	g	g	NOUN
ejpam-4963	56	21	with	with	ADP
ejpam-4963	56	22	the	the	DET
ejpam-4963	56	23	same	same	ADJ
ejpam-4963	56	24	vertex	vertex	NOUN
ejpam-4963	56	25	set	set	NOUN
ejpam-4963	56	26	.	.	PUNCT
ejpam-4963	56	27	example	example	NOUN
ejpam-4963	57	1	1	1	NUM
ejpam-4963	57	2	.	.	PUNCT
ejpam-4963	57	3	a	a	DET
ejpam-4963	57	4	cycle	cycle	NOUN
ejpam-4963	57	5	cn	cn	PROPN
ejpam-4963	57	6	is	be	AUX
ejpam-4963	57	7	a	a	DET
ejpam-4963	57	8	spanning	span	VERB
ejpam-4963	57	9	subgraph	subgraph	NOUN
ejpam-4963	57	10	of	of	ADP
ejpam-4963	57	11	a	a	DET
ejpam-4963	57	12	complete	complete	ADJ
ejpam-4963	57	13	graph	graph	NOUN
ejpam-4963	57	14	kn	kn	PROPN
ejpam-4963	57	15	.	.	PUNCT
ejpam-4963	58	1	the	the	DET
ejpam-4963	58	2	following	follow	VERB
ejpam-4963	58	3	are	be	AUX
ejpam-4963	58	4	the	the	DET
ejpam-4963	58	5	definitions	definition	NOUN
ejpam-4963	58	6	of	of	ADP
ejpam-4963	58	7	the	the	DET
ejpam-4963	58	8	binary	binary	ADJ
ejpam-4963	58	9	operations	operation	NOUN
ejpam-4963	58	10	in	in	ADP
ejpam-4963	58	11	graphs	graph	NOUN
ejpam-4963	58	12	used	use	VERB
ejpam-4963	58	13	in	in	ADP
ejpam-4963	58	14	this	this	DET
ejpam-4963	58	15	study	study	NOUN
ejpam-4963	58	16	:	:	PUNCT
ejpam-4963	58	17	join	join	VERB
ejpam-4963	58	18	,	,	PUNCT
ejpam-4963	58	19	corona	corona	NOUN
ejpam-4963	58	20	and	and	CCONJ
ejpam-4963	58	21	cartesian	cartesian	ADJ
ejpam-4963	58	22	product	product	NOUN
ejpam-4963	58	23	.	.	PUNCT
ejpam-4963	59	1	definition	definition	NOUN
ejpam-4963	59	2	2	2	NUM
ejpam-4963	59	3	.	.	PUNCT
ejpam-4963	60	1	[	[	X
ejpam-4963	60	2	14	14	NUM
ejpam-4963	60	3	]	]	PUNCT
ejpam-4963	60	4	the	the	DET
ejpam-4963	60	5	join	join	NOUN
ejpam-4963	60	6	g+h	g+h	PROPN
ejpam-4963	60	7	of	of	ADP
ejpam-4963	60	8	the	the	DET
ejpam-4963	60	9	two	two	NUM
ejpam-4963	60	10	graphs	graph	NOUN
ejpam-4963	60	11	g	g	NOUN
ejpam-4963	60	12	and	and	CCONJ
ejpam-4963	60	13	h	h	NOUN
ejpam-4963	60	14	is	be	AUX
ejpam-4963	60	15	the	the	DET
ejpam-4963	60	16	graph	graph	NOUN
ejpam-4963	60	17	with	with	ADP
ejpam-4963	60	18	vertex	vertex	NOUN
ejpam-4963	60	19	set	set	VERB
ejpam-4963	60	20	v	v	NOUN
ejpam-4963	60	21	(	(	PUNCT
ejpam-4963	60	22	g+h	g+h	NOUN
ejpam-4963	60	23	)	)	PUNCT
ejpam-4963	60	24	=	=	SYM
ejpam-4963	60	25	v	v	X
ejpam-4963	60	26	(	(	PUNCT
ejpam-4963	60	27	g	g	NOUN
ejpam-4963	60	28	)	)	PUNCT
ejpam-4963	61	1	+	+	X
ejpam-4963	61	2	v	v	X
ejpam-4963	61	3	(	(	PUNCT
ejpam-4963	61	4	h	h	NOUN
ejpam-4963	61	5	)	)	PUNCT
ejpam-4963	61	6	and	and	CCONJ
ejpam-4963	61	7	the	the	DET
ejpam-4963	61	8	edge	edge	NOUN
ejpam-4963	61	9	set	set	VERB
ejpam-4963	61	10	e(g+h	e(g+h	PRON
ejpam-4963	61	11	)	)	PUNCT
ejpam-4963	61	12	=	=	SYM
ejpam-4963	61	13	e(g	e(g	NOUN
ejpam-4963	61	14	)	)	PUNCT
ejpam-4963	61	15	∪	∪	ADP
ejpam-4963	61	16	e(h	e(h	PROPN
ejpam-4963	61	17	)	)	PUNCT
ejpam-4963	61	18	∪	∪	NOUN
ejpam-4963	61	19	{	{	PUNCT
ejpam-4963	61	20	uv	uv	NOUN
ejpam-4963	61	21	:	:	PUNCT
ejpam-4963	61	22	u	u	PROPN
ejpam-4963	61	23	∈	∈	PROPN
ejpam-4963	61	24	v	v	ADP
ejpam-4963	61	25	(	(	PUNCT
ejpam-4963	61	26	g	g	NOUN
ejpam-4963	61	27	)	)	PUNCT
ejpam-4963	61	28	,	,	PUNCT
ejpam-4963	61	29	v	v	X
ejpam-4963	61	30	∈	∈	PROPN
ejpam-4963	61	31	v	v	NOUN
ejpam-4963	61	32	(	(	PUNCT
ejpam-4963	61	33	h	h	NOUN
ejpam-4963	61	34	)	)	PUNCT
ejpam-4963	61	35	}	}	PUNCT
ejpam-4963	61	36	.	.	PUNCT
ejpam-4963	62	1	definition	definition	NOUN
ejpam-4963	62	2	3	3	NUM
ejpam-4963	62	3	.	.	PUNCT
ejpam-4963	63	1	[	[	X
ejpam-4963	63	2	12	12	NUM
ejpam-4963	63	3	]	]	PUNCT
ejpam-4963	63	4	the	the	DET
ejpam-4963	63	5	corona	corona	NOUN
ejpam-4963	63	6	g	g	PROPN
ejpam-4963	63	7	◦	◦	NOUN
ejpam-4963	63	8	h	h	NOUN
ejpam-4963	63	9	of	of	ADP
ejpam-4963	63	10	two	two	NUM
ejpam-4963	63	11	graphs	graph	NOUN
ejpam-4963	63	12	g	g	NOUN
ejpam-4963	63	13	and	and	CCONJ
ejpam-4963	63	14	h	h	NOUN
ejpam-4963	63	15	is	be	AUX
ejpam-4963	63	16	the	the	DET
ejpam-4963	63	17	graph	graph	NOUN
ejpam-4963	63	18	obtained	obtain	VERB
ejpam-4963	63	19	by	by	ADP
ejpam-4963	63	20	taking	take	VERB
ejpam-4963	63	21	one	one	NUM
ejpam-4963	63	22	copy	copy	NOUN
ejpam-4963	63	23	of	of	ADP
ejpam-4963	63	24	g	g	NOUN
ejpam-4963	63	25	of	of	ADP
ejpam-4963	63	26	order	order	NOUN
ejpam-4963	63	27	n	n	NOUN
ejpam-4963	63	28	and	and	CCONJ
ejpam-4963	63	29	n	n	PRON
ejpam-4963	63	30	copies	copy	NOUN
ejpam-4963	63	31	of	of	ADP
ejpam-4963	63	32	h	h	NOUN
ejpam-4963	63	33	,	,	PUNCT
ejpam-4963	63	34	and	and	CCONJ
ejpam-4963	63	35	then	then	ADV
ejpam-4963	63	36	joining	join	VERB
ejpam-4963	63	37	the	the	DET
ejpam-4963	63	38	ith	ith	PROPN
ejpam-4963	63	39	vertex	vertex	NOUN
ejpam-4963	63	40	of	of	ADP
ejpam-4963	63	41	g	g	NOUN
ejpam-4963	63	42	to	to	ADP
ejpam-4963	63	43	every	every	DET
ejpam-4963	63	44	vertex	vertex	NOUN
ejpam-4963	63	45	in	in	ADP
ejpam-4963	63	46	the	the	DET
ejpam-4963	63	47	ith	ith	PROPN
ejpam-4963	63	48	copy	copy	NOUN
ejpam-4963	63	49	of	of	ADP
ejpam-4963	63	50	h.	h.	PROPN
ejpam-4963	63	51	in	in	ADP
ejpam-4963	63	52	[	[	X
ejpam-4963	63	53	2	2	NUM
ejpam-4963	63	54	]	]	PUNCT
ejpam-4963	63	55	,	,	PUNCT
ejpam-4963	63	56	a	a	DET
ejpam-4963	63	57	subset	subset	NOUN
ejpam-4963	63	58	s	s	X
ejpam-4963	63	59	of	of	ADP
ejpam-4963	63	60	v	v	NOUN
ejpam-4963	63	61	(	(	PUNCT
ejpam-4963	63	62	g	g	NOUN
ejpam-4963	63	63	)	)	PUNCT
ejpam-4963	63	64	is	be	AUX
ejpam-4963	63	65	a	a	DET
ejpam-4963	63	66	dominating	dominating	NOUN
ejpam-4963	63	67	set	set	NOUN
ejpam-4963	63	68	of	of	ADP
ejpam-4963	63	69	g	g	PROPN
ejpam-4963	63	70	if	if	SCONJ
ejpam-4963	63	71	for	for	ADP
ejpam-4963	63	72	every	every	DET
ejpam-4963	63	73	v	v	NUM
ejpam-4963	63	74	∈	∈	NOUN
ejpam-4963	63	75	v	v	NOUN
ejpam-4963	63	76	(	(	PUNCT
ejpam-4963	63	77	g)\s	g)\s	NOUN
ejpam-4963	63	78	,	,	PUNCT
ejpam-4963	63	79	there	there	PRON
ejpam-4963	63	80	exists	exist	VERB
ejpam-4963	63	81	u	u	PROPN
ejpam-4963	63	82	∈	∈	PROPN
ejpam-4963	63	83	s	s	VERB
ejpam-4963	63	84	such	such	ADJ
ejpam-4963	63	85	that	that	DET
ejpam-4963	63	86	uv	uv	PROPN
ejpam-4963	63	87	∈	∈	PROPN
ejpam-4963	63	88	e(g	e(g	PROPN
ejpam-4963	63	89	)	)	PUNCT
ejpam-4963	63	90	.	.	PUNCT
ejpam-4963	64	1	that	that	PRON
ejpam-4963	64	2	is	be	AUX
ejpam-4963	64	3	,	,	PUNCT
ejpam-4963	64	4	n	n	X
ejpam-4963	64	5	[	[	X
ejpam-4963	64	6	s	s	X
ejpam-4963	64	7	]	]	X
ejpam-4963	64	8	=	=	SYM
ejpam-4963	64	9	v	v	NOUN
ejpam-4963	64	10	(	(	PUNCT
ejpam-4963	64	11	g	g	NOUN
ejpam-4963	64	12	)	)	PUNCT
ejpam-4963	64	13	.	.	PUNCT
ejpam-4963	65	1	the	the	DET
ejpam-4963	65	2	minimum	minimum	ADJ
ejpam-4963	65	3	cardinality	cardinality	NOUN
ejpam-4963	65	4	of	of	ADP
ejpam-4963	65	5	the	the	DET
ejpam-4963	65	6	dominating	dominating	NOUN
ejpam-4963	65	7	set	set	NOUN
ejpam-4963	65	8	s	s	PROPN
ejpam-4963	65	9	of	of	ADP
ejpam-4963	65	10	g	g	PROPN
ejpam-4963	65	11	is	be	AUX
ejpam-4963	65	12	called	call	VERB
ejpam-4963	65	13	a	a	DET
ejpam-4963	65	14	domination	domination	NOUN
ejpam-4963	65	15	number	number	NOUN
ejpam-4963	65	16	of	of	ADP
ejpam-4963	65	17	g	g	NOUN
ejpam-4963	65	18	and	and	CCONJ
ejpam-4963	65	19	is	be	AUX
ejpam-4963	65	20	denoted	denote	VERB
ejpam-4963	65	21	by	by	ADP
ejpam-4963	65	22	γ(g	γ(g	PROPN
ejpam-4963	65	23	)	)	PUNCT
ejpam-4963	65	24	.	.	PUNCT
ejpam-4963	66	1	in	in	ADP
ejpam-4963	66	2	this	this	DET
ejpam-4963	66	3	case	case	NOUN
ejpam-4963	66	4	,	,	PUNCT
ejpam-4963	66	5	s	s	VERB
ejpam-4963	66	6	is	be	AUX
ejpam-4963	66	7	called	call	VERB
ejpam-4963	66	8	γ	γ	NOUN
ejpam-4963	66	9	-	-	PUNCT
ejpam-4963	66	10	set	set	NOUN
ejpam-4963	66	11	of	of	ADP
ejpam-4963	66	12	g.	g.	PROPN
ejpam-4963	66	13	in	in	ADP
ejpam-4963	66	14	[	[	X
ejpam-4963	66	15	16	16	NUM
ejpam-4963	66	16	]	]	X
ejpam-4963	66	17	,	,	PUNCT
ejpam-4963	66	18	a	a	DET
ejpam-4963	66	19	dominating	dominating	NOUN
ejpam-4963	66	20	set	set	NOUN
ejpam-4963	66	21	s	s	NOUN
ejpam-4963	66	22	of	of	ADP
ejpam-4963	66	23	g	g	PROPN
ejpam-4963	66	24	is	be	AUX
ejpam-4963	66	25	said	say	VERB
ejpam-4963	66	26	to	to	PART
ejpam-4963	66	27	be	be	AUX
ejpam-4963	66	28	a	a	DET
ejpam-4963	66	29	perfect	perfect	ADJ
ejpam-4963	66	30	dominating	dominating	NOUN
ejpam-4963	66	31	set	set	NOUN
ejpam-4963	66	32	of	of	ADP
ejpam-4963	66	33	g	g	PROPN
ejpam-4963	66	34	if	if	SCONJ
ejpam-4963	66	35	every	every	DET
ejpam-4963	66	36	vertex	vertex	NOUN
ejpam-4963	66	37	v	v	ADP
ejpam-4963	66	38	∈	∈	PROPN
ejpam-4963	66	39	v	v	NOUN
ejpam-4963	66	40	(	(	PUNCT
ejpam-4963	66	41	g	g	NOUN
ejpam-4963	66	42	)	)	PUNCT
ejpam-4963	66	43	\	\	PROPN
ejpam-4963	67	1	s	s	PART
ejpam-4963	67	2	is	be	AUX
ejpam-4963	67	3	dominated	dominate	VERB
ejpam-4963	67	4	by	by	ADP
ejpam-4963	67	5	exactly	exactly	ADV
ejpam-4963	67	6	one	one	NUM
ejpam-4963	67	7	vertex	vertex	NOUN
ejpam-4963	67	8	u	u	NOUN
ejpam-4963	67	9	∈	∈	PROPN
ejpam-4963	67	10	s.	s.	PROPN
ejpam-4963	67	11	the	the	DET
ejpam-4963	67	12	minimum	minimum	ADJ
ejpam-4963	67	13	cardinality	cardinality	NOUN
ejpam-4963	67	14	of	of	ADP
ejpam-4963	67	15	a	a	DET
ejpam-4963	67	16	perfect	perfect	ADJ
ejpam-4963	67	17	dominating	dominating	NOUN
ejpam-4963	67	18	set	set	NOUN
ejpam-4963	67	19	s	s	NOUN
ejpam-4963	67	20	of	of	ADP
ejpam-4963	67	21	g	g	PROPN
ejpam-4963	67	22	is	be	AUX
ejpam-4963	67	23	called	call	VERB
ejpam-4963	67	24	a	a	DET
ejpam-4963	67	25	perfect	perfect	ADJ
ejpam-4963	67	26	domination	domination	NOUN
ejpam-4963	67	27	number	number	NOUN
ejpam-4963	67	28	of	of	ADP
ejpam-4963	67	29	g	g	NOUN
ejpam-4963	67	30	and	and	CCONJ
ejpam-4963	67	31	is	be	AUX
ejpam-4963	67	32	denoted	denote	VERB
ejpam-4963	67	33	by	by	ADP
ejpam-4963	67	34	γp(g	γp(g	NOUN
ejpam-4963	67	35	)	)	PUNCT
ejpam-4963	67	36	.	.	PUNCT
ejpam-4963	68	1	in	in	ADP
ejpam-4963	68	2	this	this	DET
ejpam-4963	68	3	case	case	NOUN
ejpam-4963	68	4	,	,	PUNCT
ejpam-4963	68	5	we	we	PRON
ejpam-4963	68	6	say	say	VERB
ejpam-4963	68	7	s	s	PRON
ejpam-4963	68	8	a	a	DET
ejpam-4963	68	9	γp	γp	NOUN
ejpam-4963	68	10	-	-	PUNCT
ejpam-4963	68	11	set	set	NOUN
ejpam-4963	68	12	of	of	ADP
ejpam-4963	68	13	g.	g.	PROPN
ejpam-4963	68	14	in	in	ADP
ejpam-4963	68	15	[	[	X
ejpam-4963	68	16	8	8	NUM
ejpam-4963	68	17	]	]	PUNCT
ejpam-4963	68	18	and	and	CCONJ
ejpam-4963	68	19	[	[	X
ejpam-4963	68	20	9	9	NUM
ejpam-4963	68	21	]	]	PUNCT
ejpam-4963	68	22	,	,	PUNCT
ejpam-4963	68	23	a	a	DET
ejpam-4963	68	24	dominating	dominating	NOUN
ejpam-4963	68	25	set	set	NOUN
ejpam-4963	68	26	s	s	NOUN
ejpam-4963	68	27	of	of	ADP
ejpam-4963	68	28	g	g	PROPN
ejpam-4963	68	29	is	be	AUX
ejpam-4963	68	30	said	say	VERB
ejpam-4963	68	31	to	to	PART
ejpam-4963	68	32	be	be	AUX
ejpam-4963	68	33	an	an	DET
ejpam-4963	68	34	equitable	equitable	ADJ
ejpam-4963	68	35	dominating	dominating	NOUN
ejpam-4963	68	36	set	set	NOUN
ejpam-4963	68	37	of	of	ADP
ejpam-4963	68	38	g	g	PROPN
ejpam-4963	68	39	if	if	SCONJ
ejpam-4963	68	40	for	for	ADP
ejpam-4963	68	41	every	every	DET
ejpam-4963	68	42	v	v	NUM
ejpam-4963	68	43	∈	∈	NOUN
ejpam-4963	68	44	v	v	NOUN
ejpam-4963	68	45	(	(	PUNCT
ejpam-4963	68	46	g)\s	g)\s	NOUN
ejpam-4963	68	47	,	,	PUNCT
ejpam-4963	68	48	there	there	PRON
ejpam-4963	68	49	exists	exist	VERB
ejpam-4963	68	50	u	u	PROPN
ejpam-4963	68	51	∈	∈	PROPN
ejpam-4963	68	52	s	s	PART
ejpam-4963	68	53	with	with	ADP
ejpam-4963	68	54	uv	uv	PROPN
ejpam-4963	68	55	∈	∈	PROPN
ejpam-4963	68	56	e(g	e(g	PROPN
ejpam-4963	68	57	)	)	PUNCT
ejpam-4963	68	58	such	such	ADJ
ejpam-4963	68	59	that	that	SCONJ
ejpam-4963	68	60	|deg(u)−	|deg(u)−	PROPN
ejpam-4963	68	61	deg(v)|	deg(v)|	PROPN
ejpam-4963	68	62	≤	≤	PROPN
ejpam-4963	68	63	1	1	NUM
ejpam-4963	68	64	.	.	PUNCT
ejpam-4963	69	1	the	the	DET
ejpam-4963	69	2	minimum	minimum	ADJ
ejpam-4963	69	3	cardinality	cardinality	NOUN
ejpam-4963	69	4	of	of	ADP
ejpam-4963	69	5	an	an	DET
ejpam-4963	69	6	equitable	equitable	ADJ
ejpam-4963	69	7	dominating	dominating	NOUN
ejpam-4963	69	8	set	set	NOUN
ejpam-4963	69	9	s	s	PROPN
ejpam-4963	69	10	of	of	ADP
ejpam-4963	69	11	g	g	PROPN
ejpam-4963	69	12	is	be	AUX
ejpam-4963	69	13	called	call	VERB
ejpam-4963	69	14	an	an	DET
ejpam-4963	69	15	equitable	equitable	ADJ
ejpam-4963	69	16	domination	domination	NOUN
ejpam-4963	69	17	number	number	NOUN
ejpam-4963	69	18	of	of	ADP
ejpam-4963	69	19	g	g	NOUN
ejpam-4963	69	20	and	and	CCONJ
ejpam-4963	69	21	is	be	AUX
ejpam-4963	69	22	denoted	denote	VERB
ejpam-4963	69	23	by	by	ADP
ejpam-4963	69	24	γe(g	γe(g	NUM
ejpam-4963	69	25	)	)	PUNCT
ejpam-4963	69	26	.	.	PUNCT
ejpam-4963	70	1	in	in	ADP
ejpam-4963	70	2	this	this	DET
ejpam-4963	70	3	case	case	NOUN
ejpam-4963	70	4	,	,	PUNCT
ejpam-4963	70	5	we	we	PRON
ejpam-4963	70	6	say	say	VERB
ejpam-4963	70	7	s	s	PRON
ejpam-4963	70	8	a	a	DET
ejpam-4963	70	9	γe	γe	NOUN
ejpam-4963	70	10	-	-	PUNCT
ejpam-4963	70	11	set	set	NOUN
ejpam-4963	70	12	of	of	ADP
ejpam-4963	70	13	g.	g.	PROPN
ejpam-4963	70	14	caay	caay	PROPN
ejpam-4963	70	15	and	and	CCONJ
ejpam-4963	70	16	arugay	arugay	ADJ
ejpam-4963	70	17	in	in	ADP
ejpam-4963	70	18	[	[	X
ejpam-4963	70	19	4	4	NUM
ejpam-4963	70	20	]	]	PUNCT
ejpam-4963	70	21	introduced	introduce	VERB
ejpam-4963	70	22	the	the	DET
ejpam-4963	70	23	notion	notion	NOUN
ejpam-4963	70	24	of	of	ADP
ejpam-4963	70	25	perfect	perfect	ADJ
ejpam-4963	70	26	equitable	equitable	ADJ
ejpam-4963	70	27	domination	domination	NOUN
ejpam-4963	70	28	.	.	PUNCT
ejpam-4963	71	1	a	a	DET
ejpam-4963	71	2	dominating	dominating	NOUN
ejpam-4963	71	3	set	set	NOUN
ejpam-4963	71	4	s	s	NOUN
ejpam-4963	71	5	of	of	ADP
ejpam-4963	71	6	g	g	PROPN
ejpam-4963	71	7	is	be	AUX
ejpam-4963	71	8	said	say	VERB
ejpam-4963	71	9	to	to	PART
ejpam-4963	71	10	be	be	AUX
ejpam-4963	71	11	a	a	DET
ejpam-4963	71	12	perfect	perfect	ADJ
ejpam-4963	71	13	equitable	equitable	ADJ
ejpam-4963	71	14	dominating	dominating	NOUN
ejpam-4963	71	15	set	set	NOUN
ejpam-4963	71	16	of	of	ADP
ejpam-4963	71	17	g	g	PROPN
ejpam-4963	71	18	if	if	SCONJ
ejpam-4963	71	19	for	for	SCONJ
ejpam-4963	71	20	it	it	PRON
ejpam-4963	71	21	is	be	AUX
ejpam-4963	71	22	both	both	CCONJ
ejpam-4963	71	23	perfect	perfect	ADJ
ejpam-4963	71	24	and	and	CCONJ
ejpam-4963	71	25	equitable	equitable	ADJ
ejpam-4963	71	26	dominating	dominating	NOUN
ejpam-4963	71	27	set	set	NOUN
ejpam-4963	71	28	.	.	PUNCT
ejpam-4963	72	1	the	the	DET
ejpam-4963	72	2	minimum	minimum	ADJ
ejpam-4963	72	3	cardinality	cardinality	NOUN
ejpam-4963	72	4	of	of	ADP
ejpam-4963	72	5	a	a	DET
ejpam-4963	72	6	perfect	perfect	ADJ
ejpam-4963	72	7	equitable	equitable	ADJ
ejpam-4963	72	8	dominating	dominating	NOUN
ejpam-4963	72	9	set	set	NOUN
ejpam-4963	72	10	s	s	PROPN
ejpam-4963	72	11	of	of	ADP
ejpam-4963	72	12	g	g	PROPN
ejpam-4963	72	13	is	be	AUX
ejpam-4963	72	14	called	call	VERB
ejpam-4963	72	15	a	a	DET
ejpam-4963	72	16	perfect	perfect	ADJ
ejpam-4963	72	17	equitable	equitable	ADJ
ejpam-4963	72	18	domination	domination	NOUN
ejpam-4963	72	19	number	number	NOUN
ejpam-4963	72	20	of	of	ADP
ejpam-4963	72	21	g	g	NOUN
ejpam-4963	72	22	and	and	CCONJ
ejpam-4963	72	23	is	be	AUX
ejpam-4963	72	24	denoted	denote	VERB
ejpam-4963	72	25	by	by	ADP
ejpam-4963	72	26	γpe(g	γpe(g	PROPN
ejpam-4963	72	27	)	)	PUNCT
ejpam-4963	72	28	.	.	PUNCT
ejpam-4963	73	1	in	in	ADP
ejpam-4963	73	2	this	this	DET
ejpam-4963	73	3	case	case	NOUN
ejpam-4963	73	4	,	,	PUNCT
ejpam-4963	73	5	we	we	PRON
ejpam-4963	73	6	say	say	VERB
ejpam-4963	73	7	s	s	PRON
ejpam-4963	73	8	a	a	DET
ejpam-4963	73	9	γpe	γpe	NOUN
ejpam-4963	73	10	-	-	PUNCT
ejpam-4963	73	11	set	set	NOUN
ejpam-4963	73	12	of	of	ADP
ejpam-4963	73	13	g.	g.	PROPN
ejpam-4963	73	14	finally	finally	ADV
ejpam-4963	73	15	,	,	PUNCT
ejpam-4963	73	16	in	in	ADP
ejpam-4963	73	17	[	[	X
ejpam-4963	73	18	13	13	NUM
ejpam-4963	73	19	]	]	PUNCT
ejpam-4963	73	20	,	,	PUNCT
ejpam-4963	73	21	a	a	DET
ejpam-4963	73	22	dominating	dominating	NOUN
ejpam-4963	73	23	set	set	NOUN
ejpam-4963	73	24	s	s	PROPN
ejpam-4963	73	25	⊆	⊆	NUM
ejpam-4963	73	26	v	v	NOUN
ejpam-4963	73	27	(	(	PUNCT
ejpam-4963	73	28	g	g	NOUN
ejpam-4963	73	29	)	)	PUNCT
ejpam-4963	73	30	is	be	AUX
ejpam-4963	73	31	said	say	VERB
ejpam-4963	73	32	to	to	PART
ejpam-4963	73	33	be	be	AUX
ejpam-4963	73	34	an	an	DET
ejpam-4963	73	35	isolate	isolate	NOUN
ejpam-4963	73	36	dominating	dominating	NOUN
ejpam-4963	73	37	set	set	NOUN
ejpam-4963	73	38	of	of	ADP
ejpam-4963	73	39	g	g	PROPN
ejpam-4963	73	40	if	if	SCONJ
ejpam-4963	73	41	there	there	PRON
ejpam-4963	73	42	exists	exist	VERB
ejpam-4963	73	43	u	u	PROPN
ejpam-4963	73	44	∈	∈	PROPN
ejpam-4963	73	45	s	s	VERB
ejpam-4963	73	46	such	such	ADJ
ejpam-4963	73	47	that	that	PRON
ejpam-4963	73	48	uv	uv	NOUN
ejpam-4963	73	49	/∈	/∈	PUNCT
ejpam-4963	73	50	e(g	e(g	PROPN
ejpam-4963	73	51	)	)	PUNCT
ejpam-4963	73	52	for	for	ADP
ejpam-4963	73	53	all	all	DET
ejpam-4963	73	54	v	v	NOUN
ejpam-4963	73	55	∈	∈	PROPN
ejpam-4963	73	56	s.	s.	PROPN
ejpam-4963	73	57	the	the	DET
ejpam-4963	73	58	minimum	minimum	ADJ
ejpam-4963	73	59	cardinality	cardinality	NOUN
ejpam-4963	73	60	of	of	ADP
ejpam-4963	73	61	an	an	DET
ejpam-4963	73	62	equitable	equitable	ADJ
ejpam-4963	73	63	dominating	dominating	NOUN
ejpam-4963	73	64	set	set	NOUN
ejpam-4963	73	65	s	s	PROPN
ejpam-4963	73	66	of	of	ADP
ejpam-4963	73	67	g	g	PROPN
ejpam-4963	73	68	is	be	AUX
ejpam-4963	73	69	called	call	VERB
ejpam-4963	73	70	an	an	DET
ejpam-4963	73	71	isolate	isolate	ADJ
ejpam-4963	73	72	domination	domination	NOUN
ejpam-4963	73	73	number	number	NOUN
ejpam-4963	73	74	of	of	ADP
ejpam-4963	73	75	g	g	NOUN
ejpam-4963	73	76	and	and	CCONJ
ejpam-4963	73	77	is	be	AUX
ejpam-4963	73	78	denoted	denote	VERB
ejpam-4963	73	79	by	by	ADP
ejpam-4963	73	80	γ0(g	γ0(g	NOUN
ejpam-4963	73	81	)	)	PUNCT
ejpam-4963	73	82	.	.	PUNCT
ejpam-4963	74	1	in	in	ADP
ejpam-4963	74	2	this	this	DET
ejpam-4963	74	3	case	case	NOUN
ejpam-4963	74	4	,	,	PUNCT
ejpam-4963	74	5	we	we	PRON
ejpam-4963	74	6	say	say	VERB
ejpam-4963	74	7	s	s	PRON
ejpam-4963	74	8	a	a	DET
ejpam-4963	74	9	γ0	γ0	NOUN
ejpam-4963	74	10	-	-	PUNCT
ejpam-4963	74	11	set	set	NOUN
ejpam-4963	74	12	of	of	ADP
ejpam-4963	74	13	g.	g.	PROPN
ejpam-4963	74	14	m.	m.	PROPN
ejpam-4963	74	15	caay	caay	PROPN
ejpam-4963	74	16	,	,	PUNCT
ejpam-4963	74	17	a.	a.	PROPN
ejpam-4963	74	18	hernandez	hernandez	PROPN
ejpam-4963	74	19	/	/	SYM
ejpam-4963	74	20	eur	eur	PROPN
ejpam-4963	74	21	.	.	PUNCT
ejpam-4963	75	1	j.	j.	PROPN
ejpam-4963	75	2	pure	pure	PROPN
ejpam-4963	75	3	appl	appl	PROPN
ejpam-4963	75	4	.	.	PROPN
ejpam-4963	75	5	math	math	PROPN
ejpam-4963	75	6	,	,	PUNCT
ejpam-4963	75	7	17	17	NUM
ejpam-4963	75	8	(	(	PUNCT
ejpam-4963	75	9	2	2	NUM
ejpam-4963	75	10	)	)	PUNCT
ejpam-4963	75	11	(	(	PUNCT
ejpam-4963	75	12	2024	2024	NUM
ejpam-4963	75	13	)	)	PUNCT
ejpam-4963	75	14	,	,	PUNCT
ejpam-4963	75	15	969	969	NUM
ejpam-4963	75	16	-	-	SYM
ejpam-4963	75	17	978	978	NUM
ejpam-4963	75	18	972	972	NUM
ejpam-4963	75	19	theorem	theorem	NOUN
ejpam-4963	75	20	2	2	NUM
ejpam-4963	75	21	.	.	PUNCT
ejpam-4963	76	1	[	[	X
ejpam-4963	76	2	13	13	NUM
ejpam-4963	76	3	]	]	PUNCT
ejpam-4963	76	4	a	a	DET
ejpam-4963	76	5	dominating	dominating	NOUN
ejpam-4963	76	6	set	set	NOUN
ejpam-4963	76	7	s	s	NOUN
ejpam-4963	76	8	of	of	ADP
ejpam-4963	76	9	g	g	PROPN
ejpam-4963	76	10	is	be	AUX
ejpam-4963	76	11	a	a	DET
ejpam-4963	76	12	minimal	minimal	ADJ
ejpam-4963	76	13	dominating	dominating	NOUN
ejpam-4963	76	14	set	set	VERB
ejpam-4963	76	15	if	if	SCONJ
ejpam-4963	76	16	and	and	CCONJ
ejpam-4963	76	17	only	only	ADV
ejpam-4963	76	18	if	if	SCONJ
ejpam-4963	76	19	for	for	ADP
ejpam-4963	76	20	every	every	DET
ejpam-4963	76	21	u	u	PROPN
ejpam-4963	76	22	∈	∈	PROPN
ejpam-4963	76	23	s	s	PROPN
ejpam-4963	76	24	,	,	PUNCT
ejpam-4963	76	25	u	u	NOUN
ejpam-4963	76	26	is	be	AUX
ejpam-4963	76	27	an	an	DET
ejpam-4963	76	28	isolate	isolate	NOUN
ejpam-4963	76	29	of	of	ADP
ejpam-4963	76	30	⟨s⟩.	⟨s⟩.	PROPN
ejpam-4963	76	31	in	in	ADP
ejpam-4963	76	32	particular	particular	ADJ
ejpam-4963	76	33	,	,	PUNCT
ejpam-4963	76	34	s	s	PART
ejpam-4963	76	35	=	=	PUNCT
ejpam-4963	76	36	{	{	PUNCT
ejpam-4963	76	37	u	u	NOUN
ejpam-4963	76	38	}	}	PUNCT
ejpam-4963	76	39	is	be	AUX
ejpam-4963	76	40	a	a	DET
ejpam-4963	76	41	γ	γ	NOUN
ejpam-4963	76	42	-	-	PUNCT
ejpam-4963	76	43	set	set	NOUN
ejpam-4963	76	44	of	of	ADP
ejpam-4963	76	45	g	g	PROPN
ejpam-4963	76	46	if	if	SCONJ
ejpam-4963	77	1	and	and	CCONJ
ejpam-4963	77	2	only	only	ADV
ejpam-4963	77	3	if	if	SCONJ
ejpam-4963	77	4	s	s	NOUN
ejpam-4963	77	5	is	be	AUX
ejpam-4963	77	6	a	a	DET
ejpam-4963	77	7	γ0	γ0	NOUN
ejpam-4963	77	8	-	-	PUNCT
ejpam-4963	77	9	set	set	NOUN
ejpam-4963	77	10	of	of	ADP
ejpam-4963	77	11	g.	g.	PROPN
ejpam-4963	77	12	theorem	theorem	VERB
ejpam-4963	77	13	3	3	NUM
ejpam-4963	77	14	.	.	PUNCT
ejpam-4963	78	1	[	[	X
ejpam-4963	78	2	16	16	NUM
ejpam-4963	78	3	]	]	PUNCT
ejpam-4963	78	4	if	if	SCONJ
ejpam-4963	78	5	∆(g	∆(g	NOUN
ejpam-4963	78	6	)	)	PUNCT
ejpam-4963	78	7	=	=	PUNCT
ejpam-4963	78	8	n−	n−	NOUN
ejpam-4963	78	9	1	1	NUM
ejpam-4963	78	10	for	for	ADP
ejpam-4963	78	11	any	any	DET
ejpam-4963	78	12	graph	graph	NOUN
ejpam-4963	78	13	g	g	NOUN
ejpam-4963	78	14	of	of	ADP
ejpam-4963	78	15	order	order	NOUN
ejpam-4963	78	16	n	n	CCONJ
ejpam-4963	78	17	,	,	PUNCT
ejpam-4963	78	18	then	then	ADV
ejpam-4963	78	19	γp(g	γp(g	PUNCT
ejpam-4963	78	20	)	)	PUNCT
ejpam-4963	78	21	=	=	SYM
ejpam-4963	79	1	1	1	X
ejpam-4963	79	2	.	.	PUNCT
ejpam-4963	79	3	in	in	ADP
ejpam-4963	79	4	other	other	ADJ
ejpam-4963	79	5	words	word	NOUN
ejpam-4963	79	6	,	,	PUNCT
ejpam-4963	79	7	s	s	PART
ejpam-4963	79	8	=	=	PUNCT
ejpam-4963	79	9	{	{	PUNCT
ejpam-4963	79	10	u	u	NOUN
ejpam-4963	79	11	}	}	PUNCT
ejpam-4963	79	12	is	be	AUX
ejpam-4963	79	13	a	a	DET
ejpam-4963	79	14	γ	γ	NOUN
ejpam-4963	79	15	-	-	PUNCT
ejpam-4963	79	16	set	set	NOUN
ejpam-4963	79	17	of	of	ADP
ejpam-4963	79	18	g	g	PROPN
ejpam-4963	79	19	if	if	SCONJ
ejpam-4963	80	1	and	and	CCONJ
ejpam-4963	80	2	only	only	ADV
ejpam-4963	80	3	if	if	SCONJ
ejpam-4963	80	4	s	s	NOUN
ejpam-4963	80	5	is	be	AUX
ejpam-4963	80	6	a	a	DET
ejpam-4963	80	7	γp	γp	NOUN
ejpam-4963	80	8	-	-	PUNCT
ejpam-4963	80	9	set	set	NOUN
ejpam-4963	80	10	of	of	ADP
ejpam-4963	80	11	g.	g.	PROPN
ejpam-4963	80	12	theorem	theorem	VERB
ejpam-4963	80	13	4	4	NUM
ejpam-4963	80	14	.	.	PUNCT
ejpam-4963	81	1	[	[	X
ejpam-4963	81	2	4	4	NUM
ejpam-4963	81	3	]	]	PUNCT
ejpam-4963	81	4	given	give	VERB
ejpam-4963	81	5	a	a	DET
ejpam-4963	81	6	path	path	NOUN
ejpam-4963	81	7	pn	pn	NOUN
ejpam-4963	81	8	and	and	CCONJ
ejpam-4963	81	9	cycle	cycle	NOUN
ejpam-4963	81	10	cn	cn	PROPN
ejpam-4963	81	11	,	,	PUNCT
ejpam-4963	81	12	n	n	PRON
ejpam-4963	81	13	≥	≥	NOUN
ejpam-4963	81	14	3	3	NUM
ejpam-4963	81	15	,	,	PUNCT
ejpam-4963	81	16	γpe(pn	γpe(pn	NOUN
ejpam-4963	81	17	)	)	PUNCT
ejpam-4963	81	18	=	=	SYM
ejpam-4963	81	19	γpe(cn	γpe(cn	NOUN
ejpam-4963	81	20	)	)	PUNCT
ejpam-4963	81	21	=	=	PUNCT
ejpam-4963	81	22	⌈n	⌈n	NOUN
ejpam-4963	81	23	3	3	NUM
ejpam-4963	81	24	⌉	⌉	X
ejpam-4963	81	25	.	.	PUNCT
ejpam-4963	82	1	moreover	moreover	ADV
ejpam-4963	82	2	,	,	PUNCT
ejpam-4963	82	3	in	in	ADP
ejpam-4963	82	4	path	path	NOUN
ejpam-4963	82	5	pn	pn	NOUN
ejpam-4963	82	6	and	and	CCONJ
ejpam-4963	82	7	cycle	cycle	NOUN
ejpam-4963	82	8	cn	cn	PROPN
ejpam-4963	82	9	,	,	PUNCT
ejpam-4963	82	10	consecutive	consecutive	ADJ
ejpam-4963	82	11	vertices	vertex	NOUN
ejpam-4963	82	12	of	of	ADP
ejpam-4963	82	13	γpe	γpe	NOUN
ejpam-4963	82	14	-	-	PUNCT
ejpam-4963	82	15	sets	set	NOUN
ejpam-4963	82	16	are	be	AUX
ejpam-4963	82	17	either	either	CCONJ
ejpam-4963	82	18	adjacent	adjacent	ADJ
ejpam-4963	82	19	or	or	CCONJ
ejpam-4963	82	20	at	at	ADP
ejpam-4963	82	21	a	a	DET
ejpam-4963	82	22	distance	distance	NOUN
ejpam-4963	82	23	3	3	NUM
ejpam-4963	82	24	apart	apart	ADV
ejpam-4963	82	25	it	it	PRON
ejpam-4963	82	26	is	be	AUX
ejpam-4963	82	27	natural	natural	ADJ
ejpam-4963	82	28	to	to	PART
ejpam-4963	82	29	ask	ask	VERB
ejpam-4963	82	30	if	if	SCONJ
ejpam-4963	82	31	what	what	PRON
ejpam-4963	82	32	is	be	AUX
ejpam-4963	82	33	the	the	DET
ejpam-4963	82	34	relationship	relationship	NOUN
ejpam-4963	82	35	of	of	ADP
ejpam-4963	82	36	the	the	DET
ejpam-4963	82	37	perfect	perfect	ADJ
ejpam-4963	82	38	equitable	equitable	ADJ
ejpam-4963	82	39	domination	domination	NOUN
ejpam-4963	82	40	and	and	CCONJ
ejpam-4963	82	41	the	the	DET
ejpam-4963	82	42	isolate	isolate	ADJ
ejpam-4963	82	43	domination	domination	NOUN
ejpam-4963	82	44	in	in	ADP
ejpam-4963	82	45	graphs	graph	NOUN
ejpam-4963	82	46	in	in	ADP
ejpam-4963	82	47	terms	term	NOUN
ejpam-4963	82	48	of	of	ADP
ejpam-4963	82	49	cardinality	cardinality	NOUN
ejpam-4963	82	50	.	.	PUNCT
ejpam-4963	83	1	the	the	DET
ejpam-4963	83	2	result	result	NOUN
ejpam-4963	83	3	is	be	AUX
ejpam-4963	83	4	negative	negative	ADJ
ejpam-4963	83	5	in	in	ADP
ejpam-4963	83	6	general	general	ADJ
ejpam-4963	83	7	.	.	PUNCT
ejpam-4963	84	1	there	there	PRON
ejpam-4963	84	2	is	be	VERB
ejpam-4963	84	3	no	no	DET
ejpam-4963	84	4	general	general	ADJ
ejpam-4963	84	5	way	way	NOUN
ejpam-4963	84	6	to	to	PART
ejpam-4963	84	7	determine	determine	VERB
ejpam-4963	84	8	which	which	DET
ejpam-4963	84	9	one	one	NOUN
ejpam-4963	84	10	is	be	AUX
ejpam-4963	84	11	larger	large	ADJ
ejpam-4963	84	12	.	.	PUNCT
ejpam-4963	85	1	however	however	ADV
ejpam-4963	85	2	,	,	PUNCT
ejpam-4963	85	3	the	the	DET
ejpam-4963	85	4	following	follow	VERB
ejpam-4963	85	5	results	result	NOUN
ejpam-4963	85	6	will	will	AUX
ejpam-4963	85	7	tell	tell	VERB
ejpam-4963	85	8	about	about	ADP
ejpam-4963	85	9	the	the	DET
ejpam-4963	85	10	idea	idea	NOUN
ejpam-4963	85	11	between	between	ADP
ejpam-4963	85	12	the	the	DET
ejpam-4963	85	13	perfect	perfect	ADJ
ejpam-4963	85	14	equitable	equitable	ADJ
ejpam-4963	85	15	versus	versus	ADP
ejpam-4963	85	16	the	the	DET
ejpam-4963	85	17	perfect	perfect	ADJ
ejpam-4963	85	18	equitable	equitable	ADJ
ejpam-4963	85	19	isolate	isolate	NOUN
ejpam-4963	85	20	and	and	CCONJ
ejpam-4963	85	21	the	the	DET
ejpam-4963	85	22	isolate	isolate	NOUN
ejpam-4963	85	23	versus	versus	ADP
ejpam-4963	85	24	perfect	perfect	ADJ
ejpam-4963	85	25	equitable	equitable	ADJ
ejpam-4963	85	26	isolate	isolate	NOUN
ejpam-4963	85	27	.	.	PUNCT
ejpam-4963	86	1	following	follow	VERB
ejpam-4963	86	2	the	the	DET
ejpam-4963	86	3	above	above	ADJ
ejpam-4963	86	4	definitions	definition	NOUN
ejpam-4963	86	5	,	,	PUNCT
ejpam-4963	86	6	we	we	PRON
ejpam-4963	86	7	have	have	VERB
ejpam-4963	86	8	the	the	DET
ejpam-4963	86	9	following	follow	VERB
ejpam-4963	86	10	results	result	NOUN
ejpam-4963	86	11	which	which	PRON
ejpam-4963	86	12	are	be	AUX
ejpam-4963	86	13	very	very	ADV
ejpam-4963	86	14	obvious	obvious	ADJ
ejpam-4963	86	15	.	.	PUNCT
ejpam-4963	87	1	theorem	theorem	NOUN
ejpam-4963	87	2	5	5	NUM
ejpam-4963	87	3	.	.	PUNCT
ejpam-4963	88	1	if	if	SCONJ
ejpam-4963	88	2	γpe(g	γpe(g	PROPN
ejpam-4963	88	3	)	)	PUNCT
ejpam-4963	89	1	=	=	SYM
ejpam-4963	89	2	k	k	PROPN
ejpam-4963	89	3	for	for	ADP
ejpam-4963	89	4	some	some	DET
ejpam-4963	89	5	positive	positive	ADJ
ejpam-4963	89	6	integer	integer	NOUN
ejpam-4963	89	7	k	k	PROPN
ejpam-4963	89	8	and	and	CCONJ
ejpam-4963	89	9	s	s	PROPN
ejpam-4963	89	10	is	be	AUX
ejpam-4963	89	11	a	a	DET
ejpam-4963	89	12	γpe	γpe	NOUN
ejpam-4963	89	13	-	-	PUNCT
ejpam-4963	89	14	set	set	NOUN
ejpam-4963	89	15	of	of	ADP
ejpam-4963	89	16	g	g	NOUN
ejpam-4963	89	17	such	such	ADJ
ejpam-4963	89	18	that	that	SCONJ
ejpam-4963	89	19	⟨s⟩	⟨s⟩	PROPN
ejpam-4963	89	20	has	have	VERB
ejpam-4963	89	21	an	an	DET
ejpam-4963	89	22	isolated	isolated	ADJ
ejpam-4963	89	23	vertex	vertex	NOUN
ejpam-4963	89	24	,	,	PUNCT
ejpam-4963	89	25	then	then	ADV
ejpam-4963	89	26	γpe0(g	γpe0(g	NOUN
ejpam-4963	89	27	)	)	PUNCT
ejpam-4963	89	28	=	=	SYM
ejpam-4963	89	29	k.	k.	PROPN
ejpam-4963	89	30	theorem	theorem	VERB
ejpam-4963	89	31	6	6	NUM
ejpam-4963	89	32	.	.	PUNCT
ejpam-4963	90	1	if	if	SCONJ
ejpam-4963	90	2	γ0(g	γ0(g	NOUN
ejpam-4963	90	3	)	)	PUNCT
ejpam-4963	90	4	=	=	SYM
ejpam-4963	90	5	k	k	PROPN
ejpam-4963	90	6	for	for	ADP
ejpam-4963	90	7	some	some	DET
ejpam-4963	90	8	positive	positive	ADJ
ejpam-4963	90	9	integer	integer	NOUN
ejpam-4963	90	10	k	k	PROPN
ejpam-4963	90	11	and	and	CCONJ
ejpam-4963	90	12	s	s	PROPN
ejpam-4963	90	13	is	be	AUX
ejpam-4963	90	14	a	a	DET
ejpam-4963	90	15	γ0	γ0	NOUN
ejpam-4963	90	16	-	-	PUNCT
ejpam-4963	90	17	set	set	NOUN
ejpam-4963	90	18	of	of	ADP
ejpam-4963	90	19	g	g	NOUN
ejpam-4963	90	20	such	such	ADJ
ejpam-4963	90	21	that	that	SCONJ
ejpam-4963	90	22	every	every	DET
ejpam-4963	90	23	vertex	vertex	NOUN
ejpam-4963	90	24	v	v	ADP
ejpam-4963	90	25	∈	∈	PROPN
ejpam-4963	90	26	v	v	NOUN
ejpam-4963	90	27	(	(	PUNCT
ejpam-4963	90	28	g	g	NOUN
ejpam-4963	90	29	)	)	PUNCT
ejpam-4963	90	30	\s	\s	NOUN
ejpam-4963	90	31	is	be	AUX
ejpam-4963	90	32	dominated	dominate	VERB
ejpam-4963	90	33	by	by	ADP
ejpam-4963	90	34	exactly	exactly	ADV
ejpam-4963	90	35	one	one	NUM
ejpam-4963	90	36	vertex	vertex	NOUN
ejpam-4963	90	37	in	in	ADP
ejpam-4963	90	38	s	s	PROPN
ejpam-4963	90	39	,	,	PUNCT
ejpam-4963	90	40	and	and	CCONJ
ejpam-4963	90	41	u	u	PROPN
ejpam-4963	90	42	∈	∈	PROPN
ejpam-4963	90	43	s	s	X
ejpam-4963	90	44	,	,	PUNCT
ejpam-4963	90	45	there	there	PRON
ejpam-4963	90	46	exists	exist	VERB
ejpam-4963	90	47	v	v	ADP
ejpam-4963	90	48	∈	∈	PROPN
ejpam-4963	90	49	v	v	NOUN
ejpam-4963	90	50	(	(	PUNCT
ejpam-4963	90	51	g	g	NOUN
ejpam-4963	90	52	)	)	PUNCT
ejpam-4963	90	53	\	\	PROPN
ejpam-4963	91	1	s	s	PART
ejpam-4963	91	2	with	with	ADP
ejpam-4963	91	3	uv	uv	PROPN
ejpam-4963	91	4	∈	∈	PROPN
ejpam-4963	91	5	e(g	e(g	PROPN
ejpam-4963	91	6	)	)	PUNCT
ejpam-4963	92	1	such	such	ADJ
ejpam-4963	92	2	that	that	SCONJ
ejpam-4963	92	3	|deg(u)−	|deg(u)−	PROPN
ejpam-4963	92	4	deg(v)|	deg(v)|	PROPN
ejpam-4963	92	5	≤	≤	PROPN
ejpam-4963	92	6	1	1	NUM
ejpam-4963	92	7	,	,	PUNCT
ejpam-4963	92	8	then	then	ADV
ejpam-4963	92	9	γpe0(g	γpe0(g	NOUN
ejpam-4963	92	10	)	)	PUNCT
ejpam-4963	92	11	=	=	PUNCT
ejpam-4963	93	1	k.	k.	PROPN
ejpam-4963	93	2	theorems	theorem	VERB
ejpam-4963	93	3	5	5	NUM
ejpam-4963	93	4	and	and	CCONJ
ejpam-4963	93	5	6	6	NUM
ejpam-4963	93	6	give	give	VERB
ejpam-4963	93	7	rise	rise	NOUN
ejpam-4963	93	8	to	to	ADP
ejpam-4963	93	9	the	the	DET
ejpam-4963	93	10	definition	definition	NOUN
ejpam-4963	93	11	of	of	ADP
ejpam-4963	93	12	the	the	DET
ejpam-4963	93	13	our	our	PRON
ejpam-4963	93	14	working	working	NOUN
ejpam-4963	93	15	definition	definition	NOUN
ejpam-4963	93	16	.	.	PUNCT
ejpam-4963	94	1	they	they	PRON
ejpam-4963	94	2	simply	simply	ADV
ejpam-4963	94	3	tell	tell	VERB
ejpam-4963	94	4	that	that	SCONJ
ejpam-4963	94	5	a	a	DET
ejpam-4963	94	6	dominating	dominating	NOUN
ejpam-4963	94	7	set	set	NOUN
ejpam-4963	94	8	that	that	PRON
ejpam-4963	94	9	is	be	AUX
ejpam-4963	94	10	a	a	DET
ejpam-4963	94	11	perfect	perfect	ADJ
ejpam-4963	94	12	equitable	equitable	ADJ
ejpam-4963	94	13	dominating	dominating	NOUN
ejpam-4963	94	14	set	set	NOUN
ejpam-4963	94	15	and	and	CCONJ
ejpam-4963	94	16	an	an	DET
ejpam-4963	94	17	isolate	isolate	NOUN
ejpam-4963	94	18	dominating	dominating	NOUN
ejpam-4963	94	19	set	set	NOUN
ejpam-4963	94	20	,	,	PUNCT
ejpam-4963	94	21	then	then	ADV
ejpam-4963	94	22	it	it	PRON
ejpam-4963	94	23	is	be	AUX
ejpam-4963	94	24	a	a	DET
ejpam-4963	94	25	perfect	perfect	ADJ
ejpam-4963	94	26	equitable	equitable	ADJ
ejpam-4963	94	27	isolate	isolate	NOUN
ejpam-4963	94	28	dominating	dominating	NOUN
ejpam-4963	94	29	set	set	NOUN
ejpam-4963	94	30	.	.	PUNCT
ejpam-4963	95	1	definition	definition	NOUN
ejpam-4963	95	2	4	4	NUM
ejpam-4963	95	3	.	.	PUNCT
ejpam-4963	96	1	a	a	DET
ejpam-4963	96	2	dominating	dominating	NOUN
ejpam-4963	96	3	set	set	NOUN
ejpam-4963	96	4	s	s	PROPN
ejpam-4963	96	5	⊆	⊆	NUM
ejpam-4963	96	6	v	v	NOUN
ejpam-4963	96	7	(	(	PUNCT
ejpam-4963	96	8	g	g	NOUN
ejpam-4963	96	9	)	)	PUNCT
ejpam-4963	96	10	is	be	AUX
ejpam-4963	96	11	said	say	VERB
ejpam-4963	96	12	to	to	PART
ejpam-4963	96	13	be	be	AUX
ejpam-4963	96	14	a	a	DET
ejpam-4963	96	15	perfect	perfect	ADJ
ejpam-4963	96	16	equitable	equitable	ADJ
ejpam-4963	96	17	isolate	isolate	NOUN
ejpam-4963	96	18	dominating	dominating	NOUN
ejpam-4963	96	19	set	set	NOUN
ejpam-4963	96	20	(	(	PUNCT
ejpam-4963	96	21	peid	peid	NOUN
ejpam-4963	96	22	)	)	PUNCT
ejpam-4963	96	23	of	of	ADP
ejpam-4963	96	24	g	g	PROPN
ejpam-4963	96	25	if	if	SCONJ
ejpam-4963	96	26	it	it	PRON
ejpam-4963	96	27	is	be	AUX
ejpam-4963	96	28	both	both	PRON
ejpam-4963	96	29	perfect	perfect	ADJ
ejpam-4963	96	30	equitable	equitable	ADJ
ejpam-4963	96	31	isolate	isolate	NOUN
ejpam-4963	96	32	dominating	dominating	NOUN
ejpam-4963	96	33	set	set	NOUN
ejpam-4963	96	34	.	.	PUNCT
ejpam-4963	97	1	the	the	DET
ejpam-4963	97	2	minimum	minimum	ADJ
ejpam-4963	97	3	cardinality	cardinality	NOUN
ejpam-4963	97	4	of	of	ADP
ejpam-4963	97	5	a	a	DET
ejpam-4963	97	6	perfect	perfect	ADJ
ejpam-4963	97	7	equitable	equitable	ADJ
ejpam-4963	97	8	isolate	isolate	NOUN
ejpam-4963	97	9	dominating	dominate	VERB
ejpam-4963	97	10	set	set	NOUN
ejpam-4963	97	11	s	s	PROPN
ejpam-4963	97	12	of	of	ADP
ejpam-4963	97	13	g	g	PROPN
ejpam-4963	97	14	is	be	AUX
ejpam-4963	97	15	called	call	VERB
ejpam-4963	97	16	a	a	DET
ejpam-4963	97	17	perfect	perfect	ADJ
ejpam-4963	97	18	equitable	equitable	ADJ
ejpam-4963	97	19	isolate	isolate	NOUN
ejpam-4963	97	20	domination	domination	NOUN
ejpam-4963	97	21	number	number	NOUN
ejpam-4963	97	22	of	of	ADP
ejpam-4963	97	23	g	g	NOUN
ejpam-4963	97	24	and	and	CCONJ
ejpam-4963	97	25	is	be	AUX
ejpam-4963	97	26	denoted	denote	VERB
ejpam-4963	97	27	by	by	ADP
ejpam-4963	97	28	γpe0(g	γpe0(g	NOUN
ejpam-4963	97	29	)	)	PUNCT
ejpam-4963	97	30	.	.	PUNCT
ejpam-4963	98	1	in	in	ADP
ejpam-4963	98	2	this	this	DET
ejpam-4963	98	3	case	case	NOUN
ejpam-4963	98	4	,	,	PUNCT
ejpam-4963	98	5	we	we	PRON
ejpam-4963	98	6	say	say	VERB
ejpam-4963	98	7	s	s	PRON
ejpam-4963	98	8	a	a	DET
ejpam-4963	98	9	γpe0	γpe0	NOUN
ejpam-4963	98	10	-	-	PUNCT
ejpam-4963	98	11	set	set	NOUN
ejpam-4963	98	12	of	of	ADP
ejpam-4963	98	13	g.	g.	PROPN
ejpam-4963	98	14	also	also	ADV
ejpam-4963	98	15	,	,	PUNCT
ejpam-4963	98	16	if	if	SCONJ
ejpam-4963	98	17	u	u	PROPN
ejpam-4963	98	18	∈	∈	PROPN
ejpam-4963	98	19	s	s	VERB
ejpam-4963	98	20	such	such	ADJ
ejpam-4963	98	21	that	that	SCONJ
ejpam-4963	98	22	uv	uv	PROPN
ejpam-4963	98	23	∈	∈	PROPN
ejpam-4963	98	24	e(g	e(g	PROPN
ejpam-4963	98	25	)	)	PUNCT
ejpam-4963	98	26	for	for	ADP
ejpam-4963	98	27	some	some	DET
ejpam-4963	98	28	v	v	ADP
ejpam-4963	98	29	∈	∈	PROPN
ejpam-4963	98	30	v	v	NOUN
ejpam-4963	98	31	(	(	PUNCT
ejpam-4963	98	32	g	g	NOUN
ejpam-4963	98	33	)	)	PUNCT
ejpam-4963	98	34	\	\	PROPN
ejpam-4963	99	1	s	s	X
ejpam-4963	99	2	,	,	PUNCT
ejpam-4963	99	3	then	then	ADV
ejpam-4963	99	4	either	either	CCONJ
ejpam-4963	99	5	u	u	NOUN
ejpam-4963	99	6	is	be	AUX
ejpam-4963	99	7	said	say	VERB
ejpam-4963	99	8	to	to	ADP
ejpam-4963	99	9	peidly	peidly	ADV
ejpam-4963	99	10	-	-	PUNCT
ejpam-4963	99	11	dominate	dominate	VERB
ejpam-4963	99	12	v	v	NOUN
ejpam-4963	99	13	,	,	PUNCT
ejpam-4963	99	14	or	or	CCONJ
ejpam-4963	99	15	v	v	NOUN
ejpam-4963	99	16	is	be	AUX
ejpam-4963	99	17	peidly	peidly	ADV
ejpam-4963	99	18	-	-	PUNCT
ejpam-4963	99	19	dominated	dominate	VERB
ejpam-4963	99	20	by	by	ADP
ejpam-4963	99	21	u.	u.	PROPN
ejpam-4963	99	22	example	example	NOUN
ejpam-4963	99	23	2	2	X
ejpam-4963	99	24	.	.	X
ejpam-4963	99	25	consider	consider	VERB
ejpam-4963	99	26	the	the	DET
ejpam-4963	99	27	graph	graph	NOUN
ejpam-4963	99	28	in	in	ADP
ejpam-4963	99	29	figure	figure	NOUN
ejpam-4963	99	30	1	1	NUM
ejpam-4963	99	31	.	.	PUNCT
ejpam-4963	99	32	note	note	VERB
ejpam-4963	99	33	that	that	SCONJ
ejpam-4963	99	34	the	the	DET
ejpam-4963	99	35	set	set	NOUN
ejpam-4963	99	36	{	{	PUNCT
ejpam-4963	99	37	u1	u1	NOUN
ejpam-4963	99	38	,	,	PUNCT
ejpam-4963	99	39	u5	u5	PROPN
ejpam-4963	99	40	}	}	PUNCT
ejpam-4963	99	41	and	and	CCONJ
ejpam-4963	99	42	{	{	PUNCT
ejpam-4963	99	43	u1	u1	NOUN
ejpam-4963	99	44	,	,	PUNCT
ejpam-4963	99	45	u8	u8	PROPN
ejpam-4963	99	46	}	}	PUNCT
ejpam-4963	99	47	are	be	AUX
ejpam-4963	99	48	γ	γ	NOUN
ejpam-4963	99	49	-	-	PUNCT
ejpam-4963	99	50	sets	set	NOUN
ejpam-4963	99	51	.	.	PUNCT
ejpam-4963	100	1	for	for	ADP
ejpam-4963	100	2	{	{	PUNCT
ejpam-4963	100	3	u4	u4	PROPN
ejpam-4963	100	4	,	,	PUNCT
ejpam-4963	100	5	u5	u5	PROPN
ejpam-4963	100	6	}	}	PUNCT
ejpam-4963	100	7	,	,	PUNCT
ejpam-4963	100	8	note	note	VERB
ejpam-4963	100	9	that	that	SCONJ
ejpam-4963	100	10	ng(u4	ng(u4	ADP
ejpam-4963	100	11	)	)	PUNCT
ejpam-4963	100	12	=	=	PRON
ejpam-4963	100	13	{	{	PUNCT
ejpam-4963	100	14	u1	u1	NOUN
ejpam-4963	100	15	,	,	PUNCT
ejpam-4963	100	16	u2	u2	NOUN
ejpam-4963	100	17	,	,	PUNCT
ejpam-4963	100	18	u3	u3	NOUN
ejpam-4963	100	19	,	,	PUNCT
ejpam-4963	100	20	u5	u5	PROPN
ejpam-4963	100	21	}	}	PUNCT
ejpam-4963	100	22	and	and	CCONJ
ejpam-4963	100	23	ng(u5	ng(u5	ADJ
ejpam-4963	100	24	)	)	PUNCT
ejpam-4963	100	25	=	=	SYM
ejpam-4963	100	26	{	{	PUNCT
ejpam-4963	100	27	u4	u4	PROPN
ejpam-4963	100	28	,	,	PUNCT
ejpam-4963	100	29	u6	u6	PROPN
ejpam-4963	100	30	,	,	PUNCT
ejpam-4963	100	31	u7	u7	PROPN
ejpam-4963	100	32	,	,	PUNCT
ejpam-4963	100	33	u8	u8	PROPN
ejpam-4963	100	34	}	}	PUNCT
ejpam-4963	100	35	.	.	PUNCT
ejpam-4963	101	1	thus	thus	ADV
ejpam-4963	101	2	,	,	PUNCT
ejpam-4963	101	3	ng(u4	ng(u4	NOUN
ejpam-4963	101	4	)	)	PUNCT
ejpam-4963	101	5	∩ng(u5	∩ng(u5	PROPN
ejpam-4963	101	6	)	)	PUNCT
ejpam-4963	102	1	=	=	PUNCT
ejpam-4963	102	2	∅.	∅.	ADP
ejpam-4963	102	3	thus	thus	ADV
ejpam-4963	102	4	,	,	PUNCT
ejpam-4963	102	5	{	{	PUNCT
ejpam-4963	102	6	u4	u4	PROPN
ejpam-4963	102	7	,	,	PUNCT
ejpam-4963	102	8	u5	u5	PROPN
ejpam-4963	102	9	}	}	PUNCT
ejpam-4963	102	10	is	be	AUX
ejpam-4963	102	11	a	a	DET
ejpam-4963	102	12	γp	γp	NOUN
ejpam-4963	102	13	-	-	PUNCT
ejpam-4963	102	14	set	set	NOUN
ejpam-4963	102	15	.	.	PUNCT
ejpam-4963	103	1	also	also	ADV
ejpam-4963	103	2	,	,	PUNCT
ejpam-4963	103	3	observe	observe	VERB
ejpam-4963	103	4	that	that	SCONJ
ejpam-4963	103	5	|deg(u4)−	|deg(u4)−	VERB
ejpam-4963	103	6	deg(u1)|	deg(u1)|	DET
ejpam-4963	103	7	≤	≤	ADJ
ejpam-4963	103	8	1	1	NUM
ejpam-4963	103	9	|deg(u4)−	|deg(u4)−	NOUN
ejpam-4963	103	10	deg(u2)|	deg(u2)|	X
ejpam-4963	103	11	≤	≤	ADJ
ejpam-4963	103	12	1	1	NUM
ejpam-4963	103	13	|deg(u4)−	|deg(u4)−	NOUN
ejpam-4963	103	14	deg(u3)|	deg(u3)|	ADV
ejpam-4963	103	15	≤	≤	NUM
ejpam-4963	103	16	1	1	NUM
ejpam-4963	103	17	|deg(u5)−	|deg(u5)−	ADV
ejpam-4963	103	18	deg(u6)|	deg(u6)|	ADJ
ejpam-4963	103	19	≤	≤	NUM
ejpam-4963	103	20	1	1	NUM
ejpam-4963	103	21	m.	m.	NOUN
ejpam-4963	103	22	caay	caay	PROPN
ejpam-4963	103	23	,	,	PUNCT
ejpam-4963	103	24	a.	a.	PROPN
ejpam-4963	103	25	hernandez	hernandez	PROPN
ejpam-4963	103	26	/	/	SYM
ejpam-4963	103	27	eur	eur	PROPN
ejpam-4963	103	28	.	.	PUNCT
ejpam-4963	104	1	j.	j.	PROPN
ejpam-4963	104	2	pure	pure	PROPN
ejpam-4963	104	3	appl	appl	PROPN
ejpam-4963	104	4	.	.	PROPN
ejpam-4963	104	5	math	math	PROPN
ejpam-4963	104	6	,	,	PUNCT
ejpam-4963	104	7	17	17	NUM
ejpam-4963	104	8	(	(	PUNCT
ejpam-4963	104	9	2	2	NUM
ejpam-4963	104	10	)	)	PUNCT
ejpam-4963	104	11	(	(	PUNCT
ejpam-4963	104	12	2024	2024	NUM
ejpam-4963	104	13	)	)	PUNCT
ejpam-4963	104	14	,	,	PUNCT
ejpam-4963	104	15	969	969	NUM
ejpam-4963	104	16	-	-	SYM
ejpam-4963	104	17	978	978	NUM
ejpam-4963	104	18	973	973	NUM
ejpam-4963	104	19	|deg(u5)−	|deg(u5)−	NOUN
ejpam-4963	104	20	deg(u7)|	deg(u7)|	ADJ
ejpam-4963	104	21	≤	≤	NUM
ejpam-4963	104	22	1	1	NUM
ejpam-4963	104	23	|deg(u5)−	|deg(u5)−	ADV
ejpam-4963	104	24	deg(u8)|	deg(u8)|	VERB
ejpam-4963	104	25	≤	≤	NUM
ejpam-4963	104	26	1	1	NUM
ejpam-4963	104	27	.	.	PUNCT
ejpam-4963	105	1	thus	thus	ADV
ejpam-4963	105	2	,	,	PUNCT
ejpam-4963	105	3	{	{	PUNCT
ejpam-4963	105	4	u4	u4	PROPN
ejpam-4963	105	5	,	,	PUNCT
ejpam-4963	105	6	u5	u5	PROPN
ejpam-4963	105	7	}	}	PUNCT
ejpam-4963	105	8	is	be	AUX
ejpam-4963	105	9	γe	γe	VERB
ejpam-4963	105	10	-	-	PUNCT
ejpam-4963	105	11	set	set	ADJ
ejpam-4963	105	12	implying	imply	VERB
ejpam-4963	105	13	that	that	SCONJ
ejpam-4963	105	14	it	it	PRON
ejpam-4963	105	15	is	be	AUX
ejpam-4963	105	16	a	a	DET
ejpam-4963	105	17	γpe	γpe	NOUN
ejpam-4963	105	18	-	-	PUNCT
ejpam-4963	105	19	set	set	NOUN
ejpam-4963	105	20	.	.	PUNCT
ejpam-4963	106	1	however	however	ADV
ejpam-4963	106	2	,	,	PUNCT
ejpam-4963	106	3	u4u5	u4u5	PROPN
ejpam-4963	106	4	∈	∈	PROPN
ejpam-4963	106	5	e(g	e(g	PROPN
ejpam-4963	106	6	)	)	PUNCT
ejpam-4963	106	7	.	.	PUNCT
ejpam-4963	107	1	this	this	PRON
ejpam-4963	107	2	means	mean	VERB
ejpam-4963	107	3	that	that	SCONJ
ejpam-4963	107	4	{	{	PUNCT
ejpam-4963	107	5	u4	u4	PROPN
ejpam-4963	107	6	,	,	PUNCT
ejpam-4963	107	7	u5	u5	PROPN
ejpam-4963	107	8	}	}	PUNCT
ejpam-4963	107	9	is	be	AUX
ejpam-4963	107	10	not	not	PART
ejpam-4963	107	11	a	a	DET
ejpam-4963	107	12	γ0	γ0	NOUN
ejpam-4963	107	13	,	,	PUNCT
ejpam-4963	107	14	and	and	CCONJ
ejpam-4963	107	15	so	so	ADV
ejpam-4963	107	16	it	it	PRON
ejpam-4963	107	17	is	be	AUX
ejpam-4963	107	18	not	not	PART
ejpam-4963	107	19	a	a	DET
ejpam-4963	107	20	γpe0	γpe0	NOUN
ejpam-4963	107	21	-	-	PUNCT
ejpam-4963	107	22	set	set	NOUN
ejpam-4963	107	23	.	.	PUNCT
ejpam-4963	108	1	now	now	ADV
ejpam-4963	108	2	for	for	ADP
ejpam-4963	108	3	the	the	DET
ejpam-4963	108	4	γ	γ	X
ejpam-4963	108	5	-	-	PUNCT
ejpam-4963	108	6	set	set	VERB
ejpam-4963	108	7	{	{	PUNCT
ejpam-4963	108	8	u1	u1	NOUN
ejpam-4963	108	9	,	,	PUNCT
ejpam-4963	108	10	u8	u8	PROPN
ejpam-4963	108	11	}	}	PUNCT
ejpam-4963	108	12	,	,	PUNCT
ejpam-4963	108	13	ng(u1	ng(u1	NOUN
ejpam-4963	108	14	)	)	PUNCT
ejpam-4963	108	15	=	=	SYM
ejpam-4963	108	16	{	{	PUNCT
ejpam-4963	108	17	u2	u2	PROPN
ejpam-4963	108	18	,	,	PUNCT
ejpam-4963	108	19	u3	u3	NOUN
ejpam-4963	108	20	,	,	PUNCT
ejpam-4963	108	21	u4	u4	PROPN
ejpam-4963	108	22	}	}	PUNCT
ejpam-4963	108	23	and	and	CCONJ
ejpam-4963	108	24	ng(u8	ng(u8	ADJ
ejpam-4963	108	25	)	)	PUNCT
ejpam-4963	108	26	=	=	SYM
ejpam-4963	108	27	{	{	PUNCT
ejpam-4963	108	28	u5	u5	PROPN
ejpam-4963	108	29	,	,	PUNCT
ejpam-4963	108	30	u6	u6	PROPN
ejpam-4963	108	31	,	,	PUNCT
ejpam-4963	108	32	u7	u7	PROPN
ejpam-4963	108	33	}	}	PUNCT
ejpam-4963	108	34	.	.	PUNCT
ejpam-4963	109	1	thus	thus	ADV
ejpam-4963	109	2	,	,	PUNCT
ejpam-4963	109	3	ng(u1	ng(u1	NOUN
ejpam-4963	109	4	)	)	PUNCT
ejpam-4963	109	5	∩ng(u8	∩ng(u8	NUM
ejpam-4963	109	6	)	)	PUNCT
ejpam-4963	110	1	=	=	PUNCT
ejpam-4963	110	2	∅.	∅.	ADP
ejpam-4963	110	3	this	this	PRON
ejpam-4963	110	4	means	mean	VERB
ejpam-4963	110	5	that	that	SCONJ
ejpam-4963	110	6	{	{	PUNCT
ejpam-4963	110	7	u1	u1	NOUN
ejpam-4963	110	8	,	,	PUNCT
ejpam-4963	110	9	u8	u8	PROPN
ejpam-4963	110	10	}	}	PUNCT
ejpam-4963	110	11	is	be	AUX
ejpam-4963	110	12	a	a	DET
ejpam-4963	110	13	γp	γp	NOUN
ejpam-4963	110	14	-	-	PUNCT
ejpam-4963	110	15	set	set	NOUN
ejpam-4963	110	16	.	.	PUNCT
ejpam-4963	111	1	also	also	ADV
ejpam-4963	111	2	,	,	PUNCT
ejpam-4963	111	3	observe	observe	VERB
ejpam-4963	111	4	that	that	DET
ejpam-4963	111	5	|deg(u1)−	|deg(u1)−	NOUN
ejpam-4963	111	6	deg(u2)|	deg(u2)|	NOUN
ejpam-4963	111	7	≤	≤	ADJ
ejpam-4963	111	8	1	1	NUM
ejpam-4963	111	9	|deg(u1)−	|deg(u1)−	NOUN
ejpam-4963	111	10	deg(u3)|	deg(u3)|	CCONJ
ejpam-4963	111	11	≤	≤	ADV
ejpam-4963	111	12	1	1	NUM
ejpam-4963	111	13	|deg(u1)−	|deg(u1)−	NOUN
ejpam-4963	111	14	deg(u4)|	deg(u4)|	NOUN
ejpam-4963	111	15	≤	≤	NUM
ejpam-4963	111	16	1	1	NUM
ejpam-4963	111	17	|deg(u8)−	|deg(u8)−	NOUN
ejpam-4963	111	18	deg(u5)|	deg(u5)|	ADV
ejpam-4963	111	19	≤	≤	ADV
ejpam-4963	111	20	1	1	NUM
ejpam-4963	111	21	|deg(u8)−	|deg(u8)−	NOUN
ejpam-4963	111	22	deg(u6)|	deg(u6)|	ADV
ejpam-4963	111	23	≤	≤	NUM
ejpam-4963	111	24	1	1	NUM
ejpam-4963	111	25	|deg(u8)−	|deg(u8)−	NOUN
ejpam-4963	111	26	deg(u7)|	deg(u7)|	ADJ
ejpam-4963	111	27	≤	≤	ADJ
ejpam-4963	111	28	1	1	NUM
ejpam-4963	111	29	.	.	PUNCT
ejpam-4963	112	1	thus	thus	ADV
ejpam-4963	112	2	,	,	PUNCT
ejpam-4963	112	3	{	{	PUNCT
ejpam-4963	112	4	u1	u1	NOUN
ejpam-4963	112	5	,	,	PUNCT
ejpam-4963	112	6	u8	u8	PROPN
ejpam-4963	112	7	}	}	PUNCT
ejpam-4963	112	8	is	be	AUX
ejpam-4963	112	9	γe	γe	VERB
ejpam-4963	112	10	-	-	PUNCT
ejpam-4963	112	11	set	set	ADJ
ejpam-4963	112	12	implying	imply	VERB
ejpam-4963	112	13	that	that	SCONJ
ejpam-4963	112	14	it	it	PRON
ejpam-4963	112	15	is	be	AUX
ejpam-4963	112	16	a	a	DET
ejpam-4963	112	17	γpe	γpe	NOUN
ejpam-4963	112	18	-	-	PUNCT
ejpam-4963	112	19	set	set	NOUN
ejpam-4963	112	20	.	.	PUNCT
ejpam-4963	113	1	also	also	ADV
ejpam-4963	113	2	,	,	PUNCT
ejpam-4963	113	3	u1u8	u1u8	INTJ
ejpam-4963	113	4	/∈	/∈	PUNCT
ejpam-4963	113	5	e(g	e(g	PROPN
ejpam-4963	113	6	)	)	PUNCT
ejpam-4963	114	1	and	and	CCONJ
ejpam-4963	114	2	so	so	ADV
ejpam-4963	114	3	{	{	PUNCT
ejpam-4963	114	4	u1	u1	NOUN
ejpam-4963	114	5	,	,	PUNCT
ejpam-4963	114	6	u8	u8	PROPN
ejpam-4963	114	7	}	}	PUNCT
ejpam-4963	114	8	is	be	AUX
ejpam-4963	114	9	γ0	γ0	NOUN
ejpam-4963	114	10	-	-	PUNCT
ejpam-4963	114	11	set	set	NOUN
ejpam-4963	114	12	.	.	PUNCT
ejpam-4963	115	1	therefore	therefore	ADV
ejpam-4963	115	2	,	,	PUNCT
ejpam-4963	115	3	{	{	PUNCT
ejpam-4963	115	4	u1	u1	NOUN
ejpam-4963	115	5	,	,	PUNCT
ejpam-4963	115	6	u8	u8	PROPN
ejpam-4963	115	7	}	}	PUNCT
ejpam-4963	115	8	is	be	AUX
ejpam-4963	115	9	a	a	DET
ejpam-4963	115	10	γpe0	γpe0	NOUN
ejpam-4963	115	11	-	-	PUNCT
ejpam-4963	115	12	set	set	NOUN
ejpam-4963	115	13	.	.	PUNCT
ejpam-4963	116	1	consequently	consequently	ADV
ejpam-4963	116	2	,	,	PUNCT
ejpam-4963	116	3	γpe0(g	γpe0(g	NOUN
ejpam-4963	116	4	)	)	PUNCT
ejpam-4963	116	5	=	=	SYM
ejpam-4963	116	6	2	2	X
ejpam-4963	116	7	.	.	X
ejpam-4963	116	8	figure	figure	NOUN
ejpam-4963	116	9	1	1	NUM
ejpam-4963	116	10	:	:	PUNCT
ejpam-4963	116	11	example	example	NOUN
ejpam-4963	116	12	of	of	ADP
ejpam-4963	116	13	γpe0	γpe0	NOUN
ejpam-4963	116	14	-	-	PUNCT
ejpam-4963	116	15	set	set	NOUN
ejpam-4963	116	16	in	in	ADP
ejpam-4963	116	17	a	a	DET
ejpam-4963	116	18	graph	graph	NOUN
ejpam-4963	116	19	g.	g.	NOUN
ejpam-4963	117	1	the	the	DET
ejpam-4963	117	2	following	follow	VERB
ejpam-4963	117	3	propositions	proposition	NOUN
ejpam-4963	117	4	follow	follow	VERB
ejpam-4963	117	5	directly	directly	ADV
ejpam-4963	117	6	from	from	ADP
ejpam-4963	117	7	definition	definition	NOUN
ejpam-4963	117	8	4	4	NUM
ejpam-4963	117	9	.	.	PUNCT
ejpam-4963	117	10	proposition	proposition	NOUN
ejpam-4963	117	11	1	1	NUM
ejpam-4963	117	12	.	.	PUNCT
ejpam-4963	118	1	let	let	VERB
ejpam-4963	118	2	s	s	PRON
ejpam-4963	118	3	be	be	AUX
ejpam-4963	118	4	a	a	DET
ejpam-4963	118	5	γ0	γ0	NOUN
ejpam-4963	118	6	-	-	PUNCT
ejpam-4963	118	7	set	set	NOUN
ejpam-4963	118	8	of	of	ADP
ejpam-4963	118	9	g.	g.	PROPN
ejpam-4963	119	1	then	then	ADV
ejpam-4963	119	2	s	s	VERB
ejpam-4963	119	3	is	be	AUX
ejpam-4963	119	4	a	a	DET
ejpam-4963	119	5	γpe0	γpe0	NOUN
ejpam-4963	119	6	-	-	PUNCT
ejpam-4963	119	7	set	set	VERB
ejpam-4963	119	8	if	if	SCONJ
ejpam-4963	119	9	and	and	CCONJ
ejpam-4963	119	10	only	only	ADV
ejpam-4963	119	11	if	if	SCONJ
ejpam-4963	119	12	for	for	ADP
ejpam-4963	119	13	every	every	PRON
ejpam-4963	119	14	v	v	NUM
ejpam-4963	119	15	∈	∈	NOUN
ejpam-4963	119	16	v	v	NOUN
ejpam-4963	119	17	(	(	PUNCT
ejpam-4963	119	18	g	g	NOUN
ejpam-4963	119	19	)	)	PUNCT
ejpam-4963	119	20	\	\	PROPN
ejpam-4963	119	21	s	s	PROPN
ejpam-4963	119	22	,	,	PUNCT
ejpam-4963	119	23	ng(v	ng(v	PUNCT
ejpam-4963	119	24	)	)	PUNCT
ejpam-4963	119	25	∩	∩	NOUN
ejpam-4963	119	26	s	s	PART
ejpam-4963	119	27	=	=	SYM
ejpam-4963	119	28	{	{	PUNCT
ejpam-4963	119	29	u	u	NOUN
ejpam-4963	119	30	}	}	PUNCT
ejpam-4963	119	31	for	for	ADP
ejpam-4963	119	32	some	some	DET
ejpam-4963	119	33	u	u	NOUN
ejpam-4963	119	34	∈	∈	PROPN
ejpam-4963	119	35	s	s	X
ejpam-4963	119	36	and	and	CCONJ
ejpam-4963	119	37	for	for	ADP
ejpam-4963	119	38	every	every	PRON
ejpam-4963	119	39	v	v	NUM
ejpam-4963	119	40	∈	∈	PROPN
ejpam-4963	119	41	v	v	NOUN
ejpam-4963	119	42	(	(	PUNCT
ejpam-4963	119	43	g	g	NOUN
ejpam-4963	119	44	)	)	PUNCT
ejpam-4963	119	45	\	\	PROPN
ejpam-4963	120	1	s	s	X
ejpam-4963	120	2	,	,	PUNCT
ejpam-4963	120	3	there	there	PRON
ejpam-4963	120	4	exists	exist	VERB
ejpam-4963	120	5	u	u	PROPN
ejpam-4963	120	6	∈	∈	PROPN
ejpam-4963	120	7	s	s	PART
ejpam-4963	120	8	with	with	ADP
ejpam-4963	120	9	uv	uv	PROPN
ejpam-4963	120	10	∈	∈	PROPN
ejpam-4963	120	11	e(g	e(g	PROPN
ejpam-4963	120	12	)	)	PUNCT
ejpam-4963	120	13	such	such	ADJ
ejpam-4963	120	14	that	that	SCONJ
ejpam-4963	120	15	|deg(u)−	|deg(u)−	ADP
ejpam-4963	120	16	deg(v)|	deg(v)|	PROPN
ejpam-4963	120	17	≤	≤	ADJ
ejpam-4963	120	18	1	1	NUM
ejpam-4963	120	19	proposition	proposition	NOUN
ejpam-4963	120	20	2	2	NUM
ejpam-4963	120	21	.	.	PUNCT
ejpam-4963	121	1	if	if	SCONJ
ejpam-4963	121	2	s	s	PROPN
ejpam-4963	121	3	is	be	AUX
ejpam-4963	121	4	γ	γ	NOUN
ejpam-4963	121	5	-	-	PUNCT
ejpam-4963	121	6	set	set	ADJ
ejpam-4963	121	7	,	,	PUNCT
ejpam-4963	121	8	or	or	CCONJ
ejpam-4963	121	9	a	a	DET
ejpam-4963	121	10	γpe	γpe	NOUN
ejpam-4963	121	11	-	-	PUNCT
ejpam-4963	121	12	set	set	NOUN
ejpam-4963	121	13	,	,	PUNCT
ejpam-4963	121	14	or	or	CCONJ
ejpam-4963	121	15	a	a	DET
ejpam-4963	121	16	γ0	γ0	NOUN
ejpam-4963	121	17	-	-	PUNCT
ejpam-4963	121	18	set	set	NOUN
ejpam-4963	121	19	of	of	ADP
ejpam-4963	121	20	g	g	NOUN
ejpam-4963	121	21	with	with	ADP
ejpam-4963	121	22	|s|	|s|	NOUN
ejpam-4963	121	23	=	=	SYM
ejpam-4963	121	24	1	1	NUM
ejpam-4963	121	25	,	,	PUNCT
ejpam-4963	121	26	then	then	ADV
ejpam-4963	121	27	s	s	VERB
ejpam-4963	121	28	is	be	AUX
ejpam-4963	121	29	γpe0	γpe0	NOUN
ejpam-4963	121	30	-	-	PUNCT
ejpam-4963	121	31	set	set	NOUN
ejpam-4963	121	32	of	of	ADP
ejpam-4963	121	33	g.	g.	PROPN
ejpam-4963	121	34	in	in	ADP
ejpam-4963	121	35	particular	particular	ADJ
ejpam-4963	121	36	,	,	PUNCT
ejpam-4963	121	37	γ(g	γ(g	PROPN
ejpam-4963	121	38	)	)	PUNCT
ejpam-4963	121	39	=	=	SYM
ejpam-4963	121	40	γpe(g	γpe(g	PROPN
ejpam-4963	121	41	)	)	PUNCT
ejpam-4963	121	42	=	=	PUNCT
ejpam-4963	122	1	γ0(g	γ0(g	X
ejpam-4963	122	2	)	)	PUNCT
ejpam-4963	122	3	=	=	SYM
ejpam-4963	122	4	1	1	NUM
ejpam-4963	122	5	if	if	SCONJ
ejpam-4963	122	6	and	and	CCONJ
ejpam-4963	122	7	only	only	ADV
ejpam-4963	122	8	if	if	SCONJ
ejpam-4963	122	9	γpe0(g	γpe0(g	NOUN
ejpam-4963	122	10	)	)	PUNCT
ejpam-4963	122	11	=	=	SYM
ejpam-4963	123	1	1	1	NUM
ejpam-4963	123	2	.	.	NOUN
ejpam-4963	123	3	3	3	X
ejpam-4963	123	4	.	.	X
ejpam-4963	123	5	peid	peid	VERB
ejpam-4963	123	6	in	in	ADP
ejpam-4963	123	7	some	some	DET
ejpam-4963	123	8	graphs	graph	NOUN
ejpam-4963	123	9	in	in	ADP
ejpam-4963	123	10	this	this	DET
ejpam-4963	123	11	section	section	NOUN
ejpam-4963	123	12	,	,	PUNCT
ejpam-4963	123	13	we	we	PRON
ejpam-4963	123	14	present	present	VERB
ejpam-4963	123	15	the	the	DET
ejpam-4963	123	16	results	result	NOUN
ejpam-4963	123	17	for	for	ADP
ejpam-4963	123	18	equitable	equitable	ADJ
ejpam-4963	123	19	isolate	isolate	NOUN
ejpam-4963	123	20	dominations	domination	NOUN
ejpam-4963	123	21	in	in	ADP
ejpam-4963	123	22	graphs	graph	NOUN
ejpam-4963	123	23	.	.	PUNCT
ejpam-4963	124	1	the	the	DET
ejpam-4963	124	2	minimality	minimality	NOUN
ejpam-4963	124	3	of	of	ADP
ejpam-4963	124	4	a	a	DET
ejpam-4963	124	5	perfect	perfect	ADJ
ejpam-4963	124	6	equitable	equitable	ADJ
ejpam-4963	124	7	isolate	isolate	NOUN
ejpam-4963	124	8	dominating	dominate	VERB
ejpam-4963	124	9	set	set	NOUN
ejpam-4963	124	10	s	s	PRON
ejpam-4963	124	11	follows	follow	VERB
ejpam-4963	124	12	from	from	ADP
ejpam-4963	124	13	the	the	DET
ejpam-4963	124	14	paper	paper	NOUN
ejpam-4963	124	15	of	of	ADP
ejpam-4963	124	16	[	[	X
ejpam-4963	124	17	8	8	NUM
ejpam-4963	124	18	]	]	PUNCT
ejpam-4963	124	19	,	,	PUNCT
ejpam-4963	124	20	m.	m.	NOUN
ejpam-4963	124	21	caay	caay	PROPN
ejpam-4963	124	22	,	,	PUNCT
ejpam-4963	124	23	a.	a.	PROPN
ejpam-4963	124	24	hernandez	hernandez	PROPN
ejpam-4963	124	25	/	/	SYM
ejpam-4963	124	26	eur	eur	PROPN
ejpam-4963	124	27	.	.	PUNCT
ejpam-4963	125	1	j.	j.	PROPN
ejpam-4963	125	2	pure	pure	PROPN
ejpam-4963	125	3	appl	appl	PROPN
ejpam-4963	125	4	.	.	PROPN
ejpam-4963	125	5	math	math	PROPN
ejpam-4963	125	6	,	,	PUNCT
ejpam-4963	125	7	17	17	NUM
ejpam-4963	125	8	(	(	PUNCT
ejpam-4963	125	9	2	2	NUM
ejpam-4963	125	10	)	)	PUNCT
ejpam-4963	125	11	(	(	PUNCT
ejpam-4963	125	12	2024	2024	NUM
ejpam-4963	125	13	)	)	PUNCT
ejpam-4963	125	14	,	,	PUNCT
ejpam-4963	125	15	969	969	NUM
ejpam-4963	125	16	-	-	SYM
ejpam-4963	125	17	978	978	NUM
ejpam-4963	125	18	974	974	NUM
ejpam-4963	126	1	[	[	SYM
ejpam-4963	126	2	4	4	NUM
ejpam-4963	126	3	]	]	PUNCT
ejpam-4963	126	4	and	and	CCONJ
ejpam-4963	126	5	[	[	X
ejpam-4963	126	6	16	16	NUM
ejpam-4963	126	7	]	]	PUNCT
ejpam-4963	126	8	,	,	PUNCT
ejpam-4963	126	9	with	with	ADP
ejpam-4963	126	10	the	the	DET
ejpam-4963	126	11	additional	additional	ADJ
ejpam-4963	126	12	property	property	NOUN
ejpam-4963	126	13	that	that	PRON
ejpam-4963	126	14	it	it	PRON
ejpam-4963	126	15	acquires	acquire	VERB
ejpam-4963	126	16	at	at	ADP
ejpam-4963	126	17	least	least	ADV
ejpam-4963	126	18	one	one	NUM
ejpam-4963	126	19	vertex	vertex	NOUN
ejpam-4963	126	20	in	in	ADP
ejpam-4963	126	21	s	s	PRON
ejpam-4963	126	22	that	that	PRON
ejpam-4963	126	23	is	be	AUX
ejpam-4963	126	24	not	not	PART
ejpam-4963	126	25	adjacent	adjacent	ADJ
ejpam-4963	126	26	to	to	ADP
ejpam-4963	126	27	the	the	DET
ejpam-4963	126	28	other	other	ADJ
ejpam-4963	126	29	vertices	vertex	NOUN
ejpam-4963	126	30	in	in	ADP
ejpam-4963	126	31	s	s	PRON
ejpam-4963	126	32	[	[	X
ejpam-4963	126	33	13	13	NUM
ejpam-4963	126	34	]	]	PUNCT
ejpam-4963	126	35	.	.	PUNCT
ejpam-4963	127	1	proposition	proposition	NOUN
ejpam-4963	127	2	3	3	NUM
ejpam-4963	127	3	.	.	PUNCT
ejpam-4963	127	4	given	give	VERB
ejpam-4963	127	5	a	a	DET
ejpam-4963	127	6	path	path	NOUN
ejpam-4963	127	7	pn	pn	NOUN
ejpam-4963	127	8	and	and	CCONJ
ejpam-4963	127	9	cycle	cycle	NOUN
ejpam-4963	127	10	cn	cn	PROPN
ejpam-4963	127	11	,	,	PUNCT
ejpam-4963	127	12	n	n	PRON
ejpam-4963	127	13	≥	≥	NOUN
ejpam-4963	127	14	6	6	NUM
ejpam-4963	127	15	,	,	PUNCT
ejpam-4963	127	16	γpe0(pn	γpe0(pn	ADJ
ejpam-4963	127	17	)	)	PUNCT
ejpam-4963	127	18	=	=	SYM
ejpam-4963	127	19	γpe0(cn	γpe0(cn	PROPN
ejpam-4963	127	20	)	)	PUNCT
ejpam-4963	127	21	=	=	PUNCT
ejpam-4963	127	22	⌈n	⌈n	NOUN
ejpam-4963	127	23	3	3	NUM
ejpam-4963	127	24	⌉	⌉	X
ejpam-4963	127	25	.	.	PUNCT
ejpam-4963	128	1	proof	proof	NOUN
ejpam-4963	128	2	.	.	PUNCT
ejpam-4963	129	1	the	the	DET
ejpam-4963	129	2	proof	proof	NOUN
ejpam-4963	129	3	follows	follow	VERB
ejpam-4963	129	4	from	from	ADP
ejpam-4963	129	5	theorem	theorem	ADJ
ejpam-4963	129	6	4	4	NUM
ejpam-4963	129	7	.	.	PUNCT
ejpam-4963	129	8	corollary	corollary	ADJ
ejpam-4963	129	9	1	1	NUM
ejpam-4963	129	10	.	.	PUNCT
ejpam-4963	130	1	there	there	PRON
ejpam-4963	130	2	does	do	AUX
ejpam-4963	130	3	not	not	PART
ejpam-4963	130	4	exist	exist	VERB
ejpam-4963	130	5	γpe0	γpe0	NOUN
ejpam-4963	130	6	-	-	PUNCT
ejpam-4963	130	7	set	set	NOUN
ejpam-4963	130	8	of	of	ADP
ejpam-4963	130	9	c4	c4	NOUN
ejpam-4963	130	10	and	and	CCONJ
ejpam-4963	130	11	c5	c5	PROPN
ejpam-4963	130	12	.	.	PUNCT
ejpam-4963	131	1	theorem	theorem	VERB
ejpam-4963	131	2	7	7	NUM
ejpam-4963	131	3	.	.	PUNCT
ejpam-4963	132	1	let	let	VERB
ejpam-4963	132	2	g	g	NOUN
ejpam-4963	132	3	be	be	AUX
ejpam-4963	132	4	any	any	DET
ejpam-4963	132	5	connected	connected	ADJ
ejpam-4963	132	6	graph	graph	NOUN
ejpam-4963	132	7	of	of	ADP
ejpam-4963	132	8	order	order	NOUN
ejpam-4963	132	9	n	n	PRON
ejpam-4963	132	10	≥	≥	NOUN
ejpam-4963	132	11	2	2	NUM
ejpam-4963	132	12	.	.	PUNCT
ejpam-4963	133	1	if	if	SCONJ
ejpam-4963	133	2	γpe0(g	γpe0(g	NOUN
ejpam-4963	133	3	)	)	PUNCT
ejpam-4963	133	4	=	=	SYM
ejpam-4963	133	5	1	1	NUM
ejpam-4963	133	6	,	,	PUNCT
ejpam-4963	133	7	then	then	ADV
ejpam-4963	133	8	∆(g	∆(g	NOUN
ejpam-4963	133	9	)	)	PUNCT
ejpam-4963	133	10	=	=	PUNCT
ejpam-4963	134	1	n−	n−	NOUN
ejpam-4963	134	2	1	1	NUM
ejpam-4963	134	3	.	.	PUNCT
ejpam-4963	135	1	conversely	conversely	ADV
ejpam-4963	135	2	,	,	PUNCT
ejpam-4963	135	3	if	if	SCONJ
ejpam-4963	135	4	∆(g	∆(g	NOUN
ejpam-4963	135	5	)	)	PUNCT
ejpam-4963	135	6	=	=	SYM
ejpam-4963	135	7	n−	n−	NOUN
ejpam-4963	135	8	1	1	NUM
ejpam-4963	135	9	and	and	CCONJ
ejpam-4963	135	10	δ(g	δ(g	PROPN
ejpam-4963	135	11	)	)	PUNCT
ejpam-4963	135	12	≥	≥	NOUN
ejpam-4963	135	13	n−	n−	NOUN
ejpam-4963	135	14	2	2	NUM
ejpam-4963	135	15	,	,	PUNCT
ejpam-4963	135	16	then	then	ADV
ejpam-4963	135	17	γpe0(g	γpe0(g	NOUN
ejpam-4963	135	18	)	)	PUNCT
ejpam-4963	135	19	=	=	SYM
ejpam-4963	136	1	1	1	X
ejpam-4963	136	2	.	.	PUNCT
ejpam-4963	136	3	proof	proof	NOUN
ejpam-4963	136	4	.	.	PUNCT
ejpam-4963	136	5	suppose	suppose	VERB
ejpam-4963	136	6	that	that	SCONJ
ejpam-4963	136	7	γpe0(g	γpe0(g	NOUN
ejpam-4963	136	8	)	)	PUNCT
ejpam-4963	136	9	=	=	SYM
ejpam-4963	137	1	1	1	X
ejpam-4963	137	2	.	.	PUNCT
ejpam-4963	137	3	let	let	VERB
ejpam-4963	137	4	s	s	AUX
ejpam-4963	137	5	=	=	PUNCT
ejpam-4963	137	6	{	{	PUNCT
ejpam-4963	137	7	u	u	NOUN
ejpam-4963	137	8	}	}	PUNCT
ejpam-4963	137	9	be	be	VERB
ejpam-4963	137	10	the	the	DET
ejpam-4963	137	11	γpe0	γpe0	NOUN
ejpam-4963	137	12	−	−	NOUN
ejpam-4963	137	13	set	set	NOUN
ejpam-4963	137	14	of	of	ADP
ejpam-4963	137	15	g.	g.	PROPN
ejpam-4963	137	16	if	if	SCONJ
ejpam-4963	137	17	g	g	PROPN
ejpam-4963	137	18	is	be	AUX
ejpam-4963	137	19	trivial	trivial	ADJ
ejpam-4963	137	20	,	,	PUNCT
ejpam-4963	137	21	then	then	ADV
ejpam-4963	137	22	we	we	PRON
ejpam-4963	137	23	are	be	AUX
ejpam-4963	137	24	done	do	VERB
ejpam-4963	137	25	.	.	PUNCT
ejpam-4963	138	1	assume	assume	VERB
ejpam-4963	138	2	g	g	PROPN
ejpam-4963	138	3	is	be	AUX
ejpam-4963	138	4	nontrivial	nontrivial	ADJ
ejpam-4963	138	5	.	.	PUNCT
ejpam-4963	139	1	then	then	ADV
ejpam-4963	139	2	every	every	DET
ejpam-4963	139	3	vertex	vertex	NOUN
ejpam-4963	139	4	v	v	ADP
ejpam-4963	139	5	∈	∈	PROPN
ejpam-4963	139	6	v	v	NOUN
ejpam-4963	139	7	(	(	PUNCT
ejpam-4963	139	8	g	g	NOUN
ejpam-4963	139	9	)	)	PUNCT
ejpam-4963	139	10	\	\	PROPN
ejpam-4963	140	1	s	s	PART
ejpam-4963	140	2	is	be	AUX
ejpam-4963	140	3	adjacent	adjacent	ADJ
ejpam-4963	140	4	to	to	ADP
ejpam-4963	140	5	u	u	PROPN
ejpam-4963	140	6	∈	∈	PROPN
ejpam-4963	140	7	s.	s.	PROPN
ejpam-4963	140	8	hence	hence	ADV
ejpam-4963	140	9	,	,	PUNCT
ejpam-4963	140	10	deg(u	deg(u	PROPN
ejpam-4963	140	11	)	)	PUNCT
ejpam-4963	140	12	=	=	SYM
ejpam-4963	141	1	n	n	CCONJ
ejpam-4963	141	2	−	−	NOUN
ejpam-4963	142	1	1	1	X
ejpam-4963	142	2	.	.	PUNCT
ejpam-4963	143	1	this	this	PRON
ejpam-4963	143	2	means	mean	VERB
ejpam-4963	143	3	that	that	SCONJ
ejpam-4963	143	4	∆(g	∆(g	NOUN
ejpam-4963	143	5	)	)	PUNCT
ejpam-4963	143	6	=	=	SYM
ejpam-4963	144	1	n	n	CCONJ
ejpam-4963	145	1	−	−	NOUN
ejpam-4963	145	2	1	1	NUM
ejpam-4963	145	3	.	.	PUNCT
ejpam-4963	146	1	conversely	conversely	ADV
ejpam-4963	146	2	,	,	PUNCT
ejpam-4963	146	3	suppose	suppose	VERB
ejpam-4963	146	4	∆(g	∆(g	NOUN
ejpam-4963	146	5	)	)	PUNCT
ejpam-4963	146	6	=	=	SYM
ejpam-4963	147	1	n	n	CCONJ
ejpam-4963	147	2	−	−	PROPN
ejpam-4963	147	3	1	1	NUM
ejpam-4963	147	4	and	and	CCONJ
ejpam-4963	147	5	δ(g	δ(g	PROPN
ejpam-4963	147	6	)	)	PUNCT
ejpam-4963	147	7	≥	≥	NOUN
ejpam-4963	147	8	n	n	CCONJ
ejpam-4963	147	9	−	−	PROPN
ejpam-4963	147	10	2	2	NUM
ejpam-4963	147	11	.	.	PUNCT
ejpam-4963	148	1	then	then	ADV
ejpam-4963	148	2	the	the	DET
ejpam-4963	148	3	vertices	vertex	NOUN
ejpam-4963	148	4	of	of	ADP
ejpam-4963	148	5	g	g	NOUN
ejpam-4963	148	6	are	be	AUX
ejpam-4963	148	7	either	either	PRON
ejpam-4963	148	8	of	of	ADP
ejpam-4963	148	9	degree	degree	NOUN
ejpam-4963	148	10	n	n	CCONJ
ejpam-4963	148	11	−	−	PROPN
ejpam-4963	148	12	1	1	NUM
ejpam-4963	148	13	or	or	CCONJ
ejpam-4963	148	14	n	n	CCONJ
ejpam-4963	148	15	−	−	PROPN
ejpam-4963	148	16	2	2	NUM
ejpam-4963	148	17	.	.	NOUN
ejpam-4963	148	18	without	without	ADP
ejpam-4963	148	19	loss	loss	NOUN
ejpam-4963	148	20	of	of	ADP
ejpam-4963	148	21	generality	generality	NOUN
ejpam-4963	148	22	,	,	PUNCT
ejpam-4963	148	23	take	take	VERB
ejpam-4963	148	24	a	a	DET
ejpam-4963	148	25	vertex	vertex	NOUN
ejpam-4963	148	26	of	of	ADP
ejpam-4963	148	27	degree	degree	NOUN
ejpam-4963	148	28	n	n	CCONJ
ejpam-4963	148	29	−	−	PROPN
ejpam-4963	148	30	1	1	NUM
ejpam-4963	148	31	,	,	PUNCT
ejpam-4963	148	32	say	say	VERB
ejpam-4963	148	33	u	u	PROPN
ejpam-4963	148	34	∈	∈	PROPN
ejpam-4963	148	35	v	v	ADP
ejpam-4963	148	36	(	(	PUNCT
ejpam-4963	148	37	g	g	NOUN
ejpam-4963	148	38	)	)	PUNCT
ejpam-4963	148	39	.	.	PUNCT
ejpam-4963	149	1	then	then	ADV
ejpam-4963	149	2	u	u	PRON
ejpam-4963	149	3	dominates	dominate	VERB
ejpam-4963	149	4	all	all	DET
ejpam-4963	149	5	other	other	ADJ
ejpam-4963	149	6	vertices	vertex	NOUN
ejpam-4963	149	7	of	of	ADP
ejpam-4963	149	8	g.	g.	PROPN
ejpam-4963	149	9	since	since	SCONJ
ejpam-4963	149	10	other	other	ADJ
ejpam-4963	149	11	vertices	vertex	NOUN
ejpam-4963	149	12	of	of	ADP
ejpam-4963	149	13	g	g	NOUN
ejpam-4963	149	14	are	be	AUX
ejpam-4963	149	15	either	either	PRON
ejpam-4963	149	16	of	of	ADP
ejpam-4963	149	17	degree	degree	NOUN
ejpam-4963	149	18	n	n	CCONJ
ejpam-4963	149	19	−	−	PROPN
ejpam-4963	149	20	1	1	NUM
ejpam-4963	149	21	or	or	CCONJ
ejpam-4963	149	22	n−	n−	NOUN
ejpam-4963	149	23	2	2	NUM
ejpam-4963	149	24	,	,	PUNCT
ejpam-4963	149	25	it	it	PRON
ejpam-4963	149	26	follows	follow	VERB
ejpam-4963	149	27	that	that	SCONJ
ejpam-4963	149	28	for	for	ADP
ejpam-4963	149	29	every	every	DET
ejpam-4963	149	30	v	v	NUM
ejpam-4963	149	31	∈	∈	PROPN
ejpam-4963	149	32	v	v	NOUN
ejpam-4963	149	33	(	(	PUNCT
ejpam-4963	149	34	g){u	g){u	X
ejpam-4963	149	35	}	}	PUNCT
ejpam-4963	149	36	,	,	PUNCT
ejpam-4963	149	37	|	|	ADV
ejpam-4963	149	38	deg(v)−	deg(v)−	VERB
ejpam-4963	149	39	deg(u)|	deg(u)|	PROPN
ejpam-4963	149	40	≤	≤	ADJ
ejpam-4963	149	41	1	1	NUM
ejpam-4963	149	42	.	.	PUNCT
ejpam-4963	150	1	take	take	VERB
ejpam-4963	150	2	s	s	PART
ejpam-4963	150	3	=	=	PUNCT
ejpam-4963	150	4	{	{	PUNCT
ejpam-4963	150	5	u	u	NOUN
ejpam-4963	150	6	}	}	PUNCT
ejpam-4963	150	7	and	and	CCONJ
ejpam-4963	150	8	so	so	ADV
ejpam-4963	150	9	it	it	PRON
ejpam-4963	150	10	follows	follow	VERB
ejpam-4963	150	11	that	that	SCONJ
ejpam-4963	150	12	{	{	PUNCT
ejpam-4963	150	13	u	u	NOUN
ejpam-4963	150	14	}	}	PUNCT
ejpam-4963	150	15	is	be	AUX
ejpam-4963	150	16	γpe0	γpe0	NOUN
ejpam-4963	150	17	-	-	PUNCT
ejpam-4963	150	18	set	set	NOUN
ejpam-4963	150	19	of	of	ADP
ejpam-4963	150	20	g.	g.	PROPN
ejpam-4963	150	21	this	this	PRON
ejpam-4963	150	22	proves	prove	VERB
ejpam-4963	150	23	the	the	DET
ejpam-4963	150	24	claim	claim	NOUN
ejpam-4963	150	25	.	.	PUNCT
ejpam-4963	151	1	corollary	corollary	ADJ
ejpam-4963	151	2	2	2	NUM
ejpam-4963	151	3	.	.	PUNCT
ejpam-4963	151	4	given	give	VERB
ejpam-4963	151	5	a	a	DET
ejpam-4963	151	6	complete	complete	ADJ
ejpam-4963	151	7	graph	graph	NOUN
ejpam-4963	151	8	kn	kn	PROPN
ejpam-4963	151	9	,	,	PUNCT
ejpam-4963	151	10	n	n	PRON
ejpam-4963	151	11	≥	≥	NOUN
ejpam-4963	151	12	3	3	NUM
ejpam-4963	151	13	,	,	PUNCT
ejpam-4963	151	14	γpe0(kn	γpe0(kn	PROPN
ejpam-4963	151	15	)	)	PUNCT
ejpam-4963	151	16	=	=	SYM
ejpam-4963	152	1	1	1	X
ejpam-4963	152	2	.	.	X
ejpam-4963	152	3	proposition	proposition	NOUN
ejpam-4963	152	4	4	4	NUM
ejpam-4963	152	5	.	.	PUNCT
ejpam-4963	153	1	let	let	VERB
ejpam-4963	153	2	gn	gn	PROPN
ejpam-4963	153	3	,	,	PUNCT
ejpam-4963	153	4	m	m	VERB
ejpam-4963	153	5	is	be	AUX
ejpam-4963	153	6	a	a	DET
ejpam-4963	153	7	complete	complete	ADJ
ejpam-4963	153	8	bipartite	bipartite	NOUN
ejpam-4963	153	9	graph	graph	NOUN
ejpam-4963	153	10	.	.	PUNCT
ejpam-4963	154	1	if	if	SCONJ
ejpam-4963	154	2	|n−m|	|n−m|	PUNCT
ejpam-4963	154	3	≤	≤	NUM
ejpam-4963	154	4	1	1	NUM
ejpam-4963	154	5	.	.	PUNCT
ejpam-4963	155	1	then	then	ADV
ejpam-4963	155	2	there	there	PRON
ejpam-4963	155	3	exists	exist	VERB
ejpam-4963	155	4	a	a	DET
ejpam-4963	155	5	γpe	γpe	NOUN
ejpam-4963	155	6	-	-	PUNCT
ejpam-4963	155	7	set	set	NOUN
ejpam-4963	155	8	of	of	ADP
ejpam-4963	155	9	g	g	NOUN
ejpam-4963	155	10	but	but	CCONJ
ejpam-4963	155	11	there	there	PRON
ejpam-4963	155	12	does	do	AUX
ejpam-4963	155	13	not	not	PART
ejpam-4963	155	14	exist	exist	VERB
ejpam-4963	155	15	γpe0	γpe0	NOUN
ejpam-4963	155	16	-	-	PUNCT
ejpam-4963	155	17	set	set	NOUN
ejpam-4963	155	18	of	of	ADP
ejpam-4963	155	19	g	g	NOUN
ejpam-4963	155	20	,	,	PUNCT
ejpam-4963	155	21	or	or	CCONJ
ejpam-4963	155	22	there	there	PRON
ejpam-4963	155	23	does	do	AUX
ejpam-4963	155	24	exists	exist	VERB
ejpam-4963	155	25	γe0	γe0	PROPN
ejpam-4963	155	26	-	-	PUNCT
ejpam-4963	155	27	set	set	NOUN
ejpam-4963	155	28	of	of	ADP
ejpam-4963	155	29	g	g	NOUN
ejpam-4963	155	30	,	,	PUNCT
ejpam-4963	155	31	but	but	CCONJ
ejpam-4963	155	32	there	there	PRON
ejpam-4963	155	33	does	do	AUX
ejpam-4963	155	34	not	not	PART
ejpam-4963	155	35	exist	exist	VERB
ejpam-4963	155	36	γpe0	γpe0	NOUN
ejpam-4963	155	37	-	-	PUNCT
ejpam-4963	155	38	set	set	NOUN
ejpam-4963	155	39	of	of	ADP
ejpam-4963	155	40	g.	g.	PROPN
ejpam-4963	155	41	moreover	moreover	ADV
ejpam-4963	155	42	,	,	PUNCT
ejpam-4963	155	43	γpe(gn	γpe(gn	NOUN
ejpam-4963	155	44	,	,	PUNCT
ejpam-4963	155	45	m	m	NOUN
ejpam-4963	155	46	)	)	PUNCT
ejpam-4963	155	47	=	=	SYM
ejpam-4963	155	48	2	2	NUM
ejpam-4963	155	49	or	or	CCONJ
ejpam-4963	155	50	γpe0(gn	γpe0(gn	NOUN
ejpam-4963	155	51	,	,	PUNCT
ejpam-4963	155	52	m	m	NOUN
ejpam-4963	155	53	)	)	PUNCT
ejpam-4963	155	54	=	=	SYM
ejpam-4963	155	55	min{n	min{n	NOUN
ejpam-4963	155	56	,	,	PUNCT
ejpam-4963	155	57	m	m	NOUN
ejpam-4963	155	58	}	}	PUNCT
ejpam-4963	155	59	.	.	PUNCT
ejpam-4963	156	1	proof	proof	NOUN
ejpam-4963	156	2	.	.	PUNCT
ejpam-4963	157	1	let	let	VERB
ejpam-4963	157	2	p1	p1	NOUN
ejpam-4963	157	3	and	and	CCONJ
ejpam-4963	157	4	p2	p2	PROPN
ejpam-4963	157	5	be	be	VERB
ejpam-4963	157	6	the	the	DET
ejpam-4963	157	7	vertex	vertex	NOUN
ejpam-4963	157	8	partitions	partition	NOUN
ejpam-4963	157	9	of	of	ADP
ejpam-4963	157	10	a	a	DET
ejpam-4963	157	11	complete	complete	ADJ
ejpam-4963	157	12	bipartite	bipartite	NOUN
ejpam-4963	157	13	graph	graph	NOUN
ejpam-4963	157	14	g	g	ADP
ejpam-4963	157	15	such	such	ADJ
ejpam-4963	157	16	that	that	DET
ejpam-4963	157	17	|p1|	|p1|	NOUN
ejpam-4963	157	18	=	=	SYM
ejpam-4963	157	19	n	n	PROPN
ejpam-4963	157	20	and	and	CCONJ
ejpam-4963	157	21	|p2|	|p2|	PROPN
ejpam-4963	157	22	=	=	SYM
ejpam-4963	157	23	m.	m.	NOUN
ejpam-4963	157	24	let	let	VERB
ejpam-4963	157	25	u1	u1	PROPN
ejpam-4963	157	26	∈	∈	PROPN
ejpam-4963	157	27	p1	p1	NOUN
ejpam-4963	157	28	,	,	PUNCT
ejpam-4963	157	29	i	i	NOUN
ejpam-4963	157	30	=	=	NOUN
ejpam-4963	157	31	1	1	NUM
ejpam-4963	157	32	,	,	PUNCT
ejpam-4963	157	33	·	·	PUNCT
ejpam-4963	157	34	·	·	PUNCT
ejpam-4963	158	1	·	·	PUNCT
ejpam-4963	158	2	,	,	PUNCT
ejpam-4963	158	3	n	n	PROPN
ejpam-4963	158	4	and	and	CCONJ
ejpam-4963	158	5	vj	vj	DET
ejpam-4963	158	6	∈	∈	PROPN
ejpam-4963	158	7	p2	p2	NOUN
ejpam-4963	158	8	,	,	PUNCT
ejpam-4963	158	9	j	j	NOUN
ejpam-4963	158	10	=	=	SYM
ejpam-4963	158	11	1	1	NUM
ejpam-4963	158	12	,	,	PUNCT
ejpam-4963	158	13	·	·	PUNCT
ejpam-4963	158	14	·	·	PUNCT
ejpam-4963	158	15	·	·	PUNCT
ejpam-4963	158	16	,	,	PUNCT
ejpam-4963	158	17	m.	m.	NOUN
ejpam-4963	158	18	note	note	VERB
ejpam-4963	158	19	that	that	SCONJ
ejpam-4963	158	20	ui	ui	PROPN
ejpam-4963	158	21	dominates	dominate	VERB
ejpam-4963	158	22	vj	vj	INTJ
ejpam-4963	158	23	for	for	ADP
ejpam-4963	158	24	all	all	DET
ejpam-4963	158	25	ui	ui	PROPN
ejpam-4963	158	26	∈	∈	PROPN
ejpam-4963	158	27	p1	p1	NOUN
ejpam-4963	158	28	and	and	CCONJ
ejpam-4963	158	29	for	for	ADP
ejpam-4963	158	30	all	all	PRON
ejpam-4963	158	31	vj	vj	DET
ejpam-4963	158	32	∈	∈	PROPN
ejpam-4963	158	33	p2	p2	NOUN
ejpam-4963	158	34	with	with	ADP
ejpam-4963	158	35	i	i	PROPN
ejpam-4963	158	36	=	=	SYM
ejpam-4963	158	37	1	1	NUM
ejpam-4963	158	38	,	,	PUNCT
ejpam-4963	158	39	·	·	PUNCT
ejpam-4963	158	40	·	·	PUNCT
ejpam-4963	158	41	·	·	PUNCT
ejpam-4963	158	42	,	,	PUNCT
ejpam-4963	158	43	n	n	PROPN
ejpam-4963	158	44	and	and	CCONJ
ejpam-4963	158	45	j	j	PROPN
ejpam-4963	158	46	=	=	SYM
ejpam-4963	158	47	1	1	NUM
ejpam-4963	158	48	,	,	PUNCT
ejpam-4963	158	49	·	·	PUNCT
ejpam-4963	158	50	·	·	PUNCT
ejpam-4963	158	51	·	·	PUNCT
ejpam-4963	158	52	,	,	PUNCT
ejpam-4963	158	53	m.	m.	NOUN
ejpam-4963	158	54	since	since	SCONJ
ejpam-4963	158	55	|n−m|	|n−m|	PUNCT
ejpam-4963	158	56	≤	≤	NUM
ejpam-4963	158	57	1	1	NUM
ejpam-4963	158	58	,	,	PUNCT
ejpam-4963	158	59	|deg(u1)−	|deg(u1)−	NOUN
ejpam-4963	158	60	deg(vj)|	deg(vj)|	NOUN
ejpam-4963	158	61	≤	≤	NUM
ejpam-4963	158	62	1	1	NUM
ejpam-4963	158	63	,	,	PUNCT
ejpam-4963	158	64	for	for	ADP
ejpam-4963	158	65	all	all	DET
ejpam-4963	158	66	ui	ui	PROPN
ejpam-4963	158	67	∈	∈	PROPN
ejpam-4963	158	68	p1	p1	NOUN
ejpam-4963	158	69	and	and	CCONJ
ejpam-4963	158	70	vj	vj	DET
ejpam-4963	158	71	∈	∈	PROPN
ejpam-4963	158	72	p2	p2	NOUN
ejpam-4963	158	73	.	.	PUNCT
ejpam-4963	159	1	note	note	VERB
ejpam-4963	159	2	that	that	DET
ejpam-4963	159	3	uiuj	uiuj	NOUN
ejpam-4963	159	4	/∈	/∈	PUNCT
ejpam-4963	160	1	e(g	e(g	NOUN
ejpam-4963	160	2	)	)	PUNCT
ejpam-4963	161	1	for	for	ADP
ejpam-4963	161	2	all	all	DET
ejpam-4963	161	3	i	i	PRON
ejpam-4963	161	4	̸=	̸=	PROPN
ejpam-4963	161	5	j	j	PROPN
ejpam-4963	161	6	and	and	CCONJ
ejpam-4963	161	7	ui	ui	PROPN
ejpam-4963	161	8	and	and	CCONJ
ejpam-4963	161	9	uj	uj	PROPN
ejpam-4963	161	10	are	be	AUX
ejpam-4963	161	11	in	in	ADP
ejpam-4963	161	12	p1	p1	PROPN
ejpam-4963	161	13	.	.	PUNCT
ejpam-4963	162	1	thus	thus	ADV
ejpam-4963	162	2	,	,	PUNCT
ejpam-4963	162	3	p1	p1	PROPN
ejpam-4963	162	4	is	be	AUX
ejpam-4963	162	5	a	a	DET
ejpam-4963	162	6	γe0	γe0	NOUN
ejpam-4963	162	7	-	-	PUNCT
ejpam-4963	162	8	set	set	NOUN
ejpam-4963	162	9	of	of	ADP
ejpam-4963	162	10	g.	g.	PROPN
ejpam-4963	162	11	however	however	ADV
ejpam-4963	162	12	,	,	PUNCT
ejpam-4963	162	13	every	every	DET
ejpam-4963	162	14	vj	vj	PROPN
ejpam-4963	162	15	∈	∈	PROPN
ejpam-4963	162	16	p2	p2	NOUN
ejpam-4963	162	17	,	,	PUNCT
ejpam-4963	162	18	j	j	NOUN
ejpam-4963	162	19	=	=	SYM
ejpam-4963	162	20	1	1	NUM
ejpam-4963	162	21	,	,	PUNCT
ejpam-4963	162	22	·	·	PUNCT
ejpam-4963	162	23	·	·	PUNCT
ejpam-4963	162	24	·	·	PUNCT
ejpam-4963	162	25	,	,	PUNCT
ejpam-4963	162	26	m	m	VERB
ejpam-4963	162	27	is	be	AUX
ejpam-4963	162	28	dominated	dominate	VERB
ejpam-4963	162	29	by	by	ADP
ejpam-4963	162	30	all	all	DET
ejpam-4963	162	31	vertices	vertex	NOUN
ejpam-4963	162	32	of	of	ADP
ejpam-4963	162	33	p1	p1	NOUN
ejpam-4963	162	34	,	,	PUNCT
ejpam-4963	162	35	it	it	PRON
ejpam-4963	162	36	follows	follow	VERB
ejpam-4963	162	37	that	that	SCONJ
ejpam-4963	162	38	p1	p1	NOUN
ejpam-4963	162	39	is	be	AUX
ejpam-4963	162	40	not	not	PART
ejpam-4963	162	41	γp	γp	NOUN
ejpam-4963	162	42	-	-	PUNCT
ejpam-4963	162	43	set	set	VERB
ejpam-4963	163	1	and	and	CCONJ
ejpam-4963	163	2	so	so	ADV
ejpam-4963	163	3	it	it	PRON
ejpam-4963	163	4	is	be	AUX
ejpam-4963	163	5	not	not	PART
ejpam-4963	163	6	a	a	DET
ejpam-4963	163	7	γpe0	γpe0	NOUN
ejpam-4963	163	8	-	-	PUNCT
ejpam-4963	163	9	set	set	NOUN
ejpam-4963	163	10	of	of	ADP
ejpam-4963	163	11	g.	g.	PROPN
ejpam-4963	163	12	moreover	moreover	ADV
ejpam-4963	163	13	,	,	PUNCT
ejpam-4963	163	14	γe0(g	γe0(g	NOUN
ejpam-4963	163	15	)	)	PUNCT
ejpam-4963	163	16	=	=	SYM
ejpam-4963	163	17	min{n	min{n	NOUN
ejpam-4963	163	18	,	,	PUNCT
ejpam-4963	163	19	m	m	NOUN
ejpam-4963	163	20	}	}	PUNCT
ejpam-4963	163	21	.	.	PUNCT
ejpam-4963	164	1	now	now	ADV
ejpam-4963	164	2	suppose	suppose	VERB
ejpam-4963	164	3	we	we	PRON
ejpam-4963	164	4	pick	pick	VERB
ejpam-4963	164	5	one	one	NUM
ejpam-4963	164	6	ui	ui	PROPN
ejpam-4963	164	7	∈	∈	PROPN
ejpam-4963	164	8	p1	p1	NOUN
ejpam-4963	164	9	and	and	CCONJ
ejpam-4963	164	10	one	one	NUM
ejpam-4963	164	11	vj	vj	PRON
ejpam-4963	164	12	∈	∈	PROPN
ejpam-4963	164	13	p2	p2	NOUN
ejpam-4963	164	14	.	.	PUNCT
ejpam-4963	165	1	then	then	ADV
ejpam-4963	165	2	every	every	DET
ejpam-4963	165	3	vertices	vertex	NOUN
ejpam-4963	165	4	in	in	ADP
ejpam-4963	165	5	p2	p2	PROPN
ejpam-4963	165	6	is	be	AUX
ejpam-4963	165	7	dominated	dominate	VERB
ejpam-4963	165	8	by	by	ADP
ejpam-4963	165	9	ui	ui	NOUN
ejpam-4963	165	10	for	for	ADP
ejpam-4963	165	11	some	some	DET
ejpam-4963	165	12	i	i	PRON
ejpam-4963	165	13	and	and	CCONJ
ejpam-4963	165	14	every	every	DET
ejpam-4963	165	15	vertices	vertex	NOUN
ejpam-4963	165	16	in	in	ADP
ejpam-4963	165	17	p1	p1	PROPN
ejpam-4963	165	18	is	be	AUX
ejpam-4963	165	19	dominated	dominate	VERB
ejpam-4963	165	20	by	by	ADP
ejpam-4963	165	21	vj	vj	NOUN
ejpam-4963	165	22	for	for	ADP
ejpam-4963	165	23	some	some	DET
ejpam-4963	165	24	j.	j.	PROPN
ejpam-4963	165	25	thus	thus	ADV
ejpam-4963	165	26	,	,	PUNCT
ejpam-4963	165	27	{	{	PUNCT
ejpam-4963	165	28	ui	ui	NOUN
ejpam-4963	165	29	,	,	PUNCT
ejpam-4963	165	30	vj	vj	PROPN
ejpam-4963	165	31	}	}	PUNCT
ejpam-4963	165	32	is	be	AUX
ejpam-4963	165	33	a	a	DET
ejpam-4963	165	34	γpe	γpe	NOUN
ejpam-4963	165	35	-	-	PUNCT
ejpam-4963	165	36	set	set	NOUN
ejpam-4963	165	37	for	for	ADP
ejpam-4963	165	38	some	some	DET
ejpam-4963	165	39	i	i	PROPN
ejpam-4963	165	40	and	and	CCONJ
ejpam-4963	165	41	j.	j.	PROPN
ejpam-4963	165	42	however	however	ADV
ejpam-4963	165	43	,	,	PUNCT
ejpam-4963	165	44	uivj	uivj	PROPN
ejpam-4963	165	45	∈	∈	PROPN
ejpam-4963	165	46	e(g	e(g	PROPN
ejpam-4963	165	47	)	)	PUNCT
ejpam-4963	165	48	and	and	CCONJ
ejpam-4963	165	49	so	so	ADV
ejpam-4963	165	50	{	{	PUNCT
ejpam-4963	165	51	ui	ui	PROPN
ejpam-4963	165	52	,	,	PUNCT
ejpam-4963	165	53	vj	vj	PROPN
ejpam-4963	165	54	}	}	PUNCT
ejpam-4963	165	55	is	be	AUX
ejpam-4963	165	56	not	not	PART
ejpam-4963	165	57	a	a	DET
ejpam-4963	165	58	γ0	γ0	NOUN
ejpam-4963	165	59	-	-	PUNCT
ejpam-4963	165	60	set	set	NOUN
ejpam-4963	165	61	.	.	PUNCT
ejpam-4963	166	1	hence	hence	ADV
ejpam-4963	166	2	,	,	PUNCT
ejpam-4963	166	3	{	{	PUNCT
ejpam-4963	166	4	ui	ui	NOUN
ejpam-4963	166	5	,	,	PUNCT
ejpam-4963	166	6	vj	vj	PROPN
ejpam-4963	166	7	}	}	PUNCT
ejpam-4963	166	8	is	be	AUX
ejpam-4963	166	9	not	not	PART
ejpam-4963	166	10	a	a	DET
ejpam-4963	166	11	γpe0	γpe0	NOUN
ejpam-4963	166	12	-	-	PUNCT
ejpam-4963	166	13	set	set	NOUN
ejpam-4963	166	14	.	.	PUNCT
ejpam-4963	167	1	moreover	moreover	ADV
ejpam-4963	167	2	,	,	PUNCT
ejpam-4963	167	3	γpe(g	γpe(g	PROPN
ejpam-4963	167	4	)	)	PUNCT
ejpam-4963	167	5	=	=	SYM
ejpam-4963	168	1	2	2	X
ejpam-4963	168	2	.	.	PUNCT
ejpam-4963	168	3	this	this	PRON
ejpam-4963	168	4	proves	prove	VERB
ejpam-4963	168	5	the	the	DET
ejpam-4963	168	6	claim	claim	NOUN
ejpam-4963	168	7	.	.	PUNCT
ejpam-4963	169	1	theorem	theorem	ADJ
ejpam-4963	169	2	8	8	NUM
ejpam-4963	169	3	.	.	PUNCT
ejpam-4963	170	1	let	let	VERB
ejpam-4963	170	2	g	g	PROPN
ejpam-4963	170	3	=	=	PUNCT
ejpam-4963	170	4	gp1	gp1	PROPN
ejpam-4963	170	5	,	,	PUNCT
ejpam-4963	170	6	·	·	PUNCT
ejpam-4963	170	7	·	·	PUNCT
ejpam-4963	170	8	·	·	PUNCT
ejpam-4963	170	9	,	,	PUNCT
ejpam-4963	170	10	pk	pk	NOUN
ejpam-4963	170	11	be	be	AUX
ejpam-4963	170	12	a	a	DET
ejpam-4963	170	13	k	k	ADJ
ejpam-4963	170	14	-	-	ADJ
ejpam-4963	170	15	partite	partite	ADJ
ejpam-4963	170	16	graph	graph	NOUN
ejpam-4963	170	17	.	.	PUNCT
ejpam-4963	171	1	then	then	ADV
ejpam-4963	171	2	g	g	PROPN
ejpam-4963	171	3	has	have	VERB
ejpam-4963	171	4	a	a	DET
ejpam-4963	171	5	γpe0	γpe0	NOUN
ejpam-4963	171	6	-	-	PUNCT
ejpam-4963	171	7	set	set	NOUN
ejpam-4963	171	8	if	if	SCONJ
ejpam-4963	171	9	there	there	PRON
ejpam-4963	171	10	exists	exist	VERB
ejpam-4963	171	11	a	a	DET
ejpam-4963	171	12	vertex	vertex	NOUN
ejpam-4963	171	13	partition	partition	NOUN
ejpam-4963	171	14	pj	pj	PROPN
ejpam-4963	171	15	with	with	ADP
ejpam-4963	171	16	|pj	|pj	NUM
ejpam-4963	171	17	|	|	NOUN
ejpam-4963	171	18	=	=	SYM
ejpam-4963	171	19	1	1	NUM
ejpam-4963	171	20	and	and	CCONJ
ejpam-4963	171	21	|pk|	|pk|	VERB
ejpam-4963	171	22	≤	≤	NUM
ejpam-4963	171	23	2	2	NUM
ejpam-4963	171	24	,	,	PUNCT
ejpam-4963	171	25	for	for	SCONJ
ejpam-4963	171	26	all	all	DET
ejpam-4963	171	27	i	i	PRON
ejpam-4963	171	28	̸=	̸=	PROPN
ejpam-4963	171	29	j.	j.	PROPN
ejpam-4963	171	30	moreover	moreover	ADV
ejpam-4963	171	31	,	,	PUNCT
ejpam-4963	171	32	γpe0(g	γpe0(g	NOUN
ejpam-4963	171	33	)	)	PUNCT
ejpam-4963	171	34	=	=	SYM
ejpam-4963	171	35	1	1	X
ejpam-4963	171	36	.	.	X
ejpam-4963	171	37	m.	m.	NOUN
ejpam-4963	171	38	caay	caay	PROPN
ejpam-4963	171	39	,	,	PUNCT
ejpam-4963	171	40	a.	a.	PROPN
ejpam-4963	171	41	hernandez	hernandez	PROPN
ejpam-4963	171	42	/	/	SYM
ejpam-4963	171	43	eur	eur	PROPN
ejpam-4963	171	44	.	.	PUNCT
ejpam-4963	172	1	j.	j.	PROPN
ejpam-4963	172	2	pure	pure	PROPN
ejpam-4963	172	3	appl	appl	PROPN
ejpam-4963	172	4	.	.	PROPN
ejpam-4963	172	5	math	math	PROPN
ejpam-4963	172	6	,	,	PUNCT
ejpam-4963	172	7	17	17	NUM
ejpam-4963	172	8	(	(	PUNCT
ejpam-4963	172	9	2	2	NUM
ejpam-4963	172	10	)	)	PUNCT
ejpam-4963	172	11	(	(	PUNCT
ejpam-4963	172	12	2024	2024	NUM
ejpam-4963	172	13	)	)	PUNCT
ejpam-4963	172	14	,	,	PUNCT
ejpam-4963	172	15	969	969	NUM
ejpam-4963	172	16	-	-	SYM
ejpam-4963	172	17	978	978	NUM
ejpam-4963	172	18	975	975	NUM
ejpam-4963	172	19	proof	proof	NOUN
ejpam-4963	172	20	.	.	PUNCT
ejpam-4963	173	1	without	without	ADP
ejpam-4963	173	2	loss	loss	NOUN
ejpam-4963	173	3	of	of	ADP
ejpam-4963	173	4	generality	generality	NOUN
ejpam-4963	173	5	,	,	PUNCT
ejpam-4963	173	6	let	let	VERB
ejpam-4963	173	7	p1	p1	PROPN
ejpam-4963	173	8	be	be	AUX
ejpam-4963	173	9	such	such	ADJ
ejpam-4963	173	10	partition	partition	NOUN
ejpam-4963	173	11	with	with	ADP
ejpam-4963	173	12	|p1|	|p1|	NOUN
ejpam-4963	173	13	=	=	ADJ
ejpam-4963	173	14	1	1	X
ejpam-4963	173	15	.	.	PUNCT
ejpam-4963	174	1	then	then	ADV
ejpam-4963	174	2	for	for	ADP
ejpam-4963	174	3	partitions	partition	NOUN
ejpam-4963	174	4	pi	pi	NOUN
ejpam-4963	174	5	with	with	ADP
ejpam-4963	174	6	i	i	PRON
ejpam-4963	174	7	̸=	̸=	PROPN
ejpam-4963	174	8	1	1	NUM
ejpam-4963	174	9	,	,	PUNCT
ejpam-4963	174	10	either	either	CCONJ
ejpam-4963	174	11	|pi|	|pi|	NUM
ejpam-4963	174	12	=	=	SYM
ejpam-4963	174	13	1	1	NUM
ejpam-4963	174	14	or	or	CCONJ
ejpam-4963	174	15	|pi|	|pi|	NUM
ejpam-4963	174	16	=	=	SYM
ejpam-4963	174	17	2	2	X
ejpam-4963	174	18	.	.	PUNCT
ejpam-4963	174	19	let	let	VERB
ejpam-4963	174	20	u	u	PRON
ejpam-4963	174	21	∈	∈	PROPN
ejpam-4963	174	22	p1	p1	NOUN
ejpam-4963	174	23	.	.	PUNCT
ejpam-4963	175	1	then	then	ADV
ejpam-4963	175	2	deg(u	deg(u	PROPN
ejpam-4963	175	3	)	)	PUNCT
ejpam-4963	175	4	≤	≤	NOUN
ejpam-4963	175	5	2k	2k	NUM
ejpam-4963	175	6	.	.	PUNCT
ejpam-4963	176	1	also	also	ADV
ejpam-4963	176	2	,	,	PUNCT
ejpam-4963	176	3	deg(v	deg(v	PROPN
ejpam-4963	176	4	)	)	PUNCT
ejpam-4963	176	5	≤	≤	NOUN
ejpam-4963	176	6	2k+1	2k+1	NOUN
ejpam-4963	176	7	for	for	ADP
ejpam-4963	176	8	all	all	PRON
ejpam-4963	176	9	v	v	ADP
ejpam-4963	176	10	̸=	̸=	PROPN
ejpam-4963	176	11	u.	u.	PROPN
ejpam-4963	176	12	thus	thus	ADV
ejpam-4963	176	13	,	,	PUNCT
ejpam-4963	176	14	|deg(v)−	|deg(v)−	PROPN
ejpam-4963	176	15	deg(u)|	deg(u)|	PROPN
ejpam-4963	176	16	≤	≤	NUM
ejpam-4963	176	17	1	1	NUM
ejpam-4963	176	18	.	.	PUNCT
ejpam-4963	177	1	this	this	PRON
ejpam-4963	177	2	means	mean	VERB
ejpam-4963	177	3	that	that	SCONJ
ejpam-4963	177	4	{	{	PUNCT
ejpam-4963	177	5	u	u	NOUN
ejpam-4963	177	6	}	}	PUNCT
ejpam-4963	177	7	is	be	AUX
ejpam-4963	177	8	a	a	DET
ejpam-4963	177	9	γ	γ	NOUN
ejpam-4963	177	10	-	-	PUNCT
ejpam-4963	177	11	set	set	NOUN
ejpam-4963	177	12	.	.	PUNCT
ejpam-4963	178	1	since	since	SCONJ
ejpam-4963	178	2	u	u	NOUN
ejpam-4963	178	3	dominates	dominate	VERB
ejpam-4963	178	4	all	all	DET
ejpam-4963	178	5	vertices	vertex	NOUN
ejpam-4963	178	6	of	of	ADP
ejpam-4963	178	7	g	g	NOUN
ejpam-4963	178	8	,	,	PUNCT
ejpam-4963	178	9	{	{	PUNCT
ejpam-4963	178	10	u	u	NOUN
ejpam-4963	178	11	}	}	PUNCT
ejpam-4963	178	12	is	be	AUX
ejpam-4963	178	13	also	also	ADV
ejpam-4963	178	14	a	a	DET
ejpam-4963	178	15	γp	γp	NOUN
ejpam-4963	178	16	-	-	PUNCT
ejpam-4963	178	17	set	set	VERB
ejpam-4963	178	18	and	and	CCONJ
ejpam-4963	178	19	so	so	ADV
ejpam-4963	178	20	it	it	PRON
ejpam-4963	178	21	is	be	AUX
ejpam-4963	178	22	a	a	DET
ejpam-4963	178	23	γpe	γpe	NOUN
ejpam-4963	178	24	-	-	PUNCT
ejpam-4963	178	25	set	set	NOUN
ejpam-4963	178	26	.	.	PUNCT
ejpam-4963	179	1	by	by	ADP
ejpam-4963	179	2	theorem	theorem	NOUN
ejpam-4963	179	3	2	2	NUM
ejpam-4963	179	4	,	,	PUNCT
ejpam-4963	179	5	{	{	PUNCT
ejpam-4963	179	6	u	u	NOUN
ejpam-4963	179	7	}	}	PUNCT
ejpam-4963	179	8	is	be	AUX
ejpam-4963	179	9	a	a	DET
ejpam-4963	179	10	γ0	γ0	NOUN
ejpam-4963	179	11	-	-	PUNCT
ejpam-4963	179	12	set	set	NOUN
ejpam-4963	179	13	of	of	ADP
ejpam-4963	179	14	g.	g.	PROPN
ejpam-4963	179	15	therefore	therefore	ADV
ejpam-4963	179	16	,	,	PUNCT
ejpam-4963	179	17	{	{	PUNCT
ejpam-4963	179	18	u	u	NOUN
ejpam-4963	179	19	}	}	PUNCT
ejpam-4963	179	20	is	be	AUX
ejpam-4963	179	21	a	a	DET
ejpam-4963	179	22	γpe0	γpe0	NOUN
ejpam-4963	179	23	-	-	PUNCT
ejpam-4963	179	24	set	set	NOUN
ejpam-4963	179	25	of	of	ADP
ejpam-4963	179	26	g.	g.	PROPN
ejpam-4963	179	27	consequently	consequently	ADV
ejpam-4963	179	28	,	,	PUNCT
ejpam-4963	179	29	γpe0(g	γpe0(g	NOUN
ejpam-4963	179	30	)	)	PUNCT
ejpam-4963	179	31	=	=	SYM
ejpam-4963	179	32	1	1	X
ejpam-4963	179	33	.	.	X
ejpam-4963	179	34	theorem	theorem	NOUN
ejpam-4963	179	35	9	9	NUM
ejpam-4963	179	36	.	.	PUNCT
ejpam-4963	180	1	there	there	PRON
ejpam-4963	180	2	does	do	AUX
ejpam-4963	180	3	not	not	PART
ejpam-4963	180	4	exist	exist	VERB
ejpam-4963	180	5	γpe0	γpe0	NOUN
ejpam-4963	180	6	-	-	PUNCT
ejpam-4963	180	7	set	set	NOUN
ejpam-4963	180	8	of	of	ADP
ejpam-4963	180	9	gp1,···pk	gp1,···pk	NOUN
ejpam-4963	180	10	for	for	ADP
ejpam-4963	180	11	any	any	DET
ejpam-4963	180	12	non	non	ADJ
ejpam-4963	180	13	-	-	ADJ
ejpam-4963	180	14	trivial	trivial	ADJ
ejpam-4963	180	15	partition	partition	NOUN
ejpam-4963	180	16	pi	pi	NOUN
ejpam-4963	180	17	,	,	PUNCT
ejpam-4963	180	18	i	i	PRON
ejpam-4963	180	19	=	=	NOUN
ejpam-4963	180	20	1	1	NUM
ejpam-4963	180	21	,	,	PUNCT
ejpam-4963	180	22	·	·	PUNCT
ejpam-4963	180	23	·	·	PUNCT
ejpam-4963	180	24	·	·	PUNCT
ejpam-4963	180	25	,	,	PUNCT
ejpam-4963	180	26	k.	k.	PROPN
ejpam-4963	180	27	proof	proof	PROPN
ejpam-4963	180	28	.	.	PUNCT
ejpam-4963	181	1	suppose	suppose	VERB
ejpam-4963	181	2	on	on	ADP
ejpam-4963	181	3	the	the	DET
ejpam-4963	181	4	contrary	contrary	NOUN
ejpam-4963	181	5	that	that	SCONJ
ejpam-4963	181	6	there	there	PRON
ejpam-4963	181	7	exists	exist	VERB
ejpam-4963	181	8	a	a	DET
ejpam-4963	181	9	γpe0	γpe0	NOUN
ejpam-4963	181	10	-	-	PUNCT
ejpam-4963	181	11	set	set	NOUN
ejpam-4963	181	12	s	s	NOUN
ejpam-4963	181	13	of	of	ADP
ejpam-4963	181	14	g	g	PROPN
ejpam-4963	181	15	=	=	SYM
ejpam-4963	181	16	gp1	gp1	PROPN
ejpam-4963	181	17	,	,	PUNCT
ejpam-4963	181	18	·	·	PUNCT
ejpam-4963	181	19	·	·	PUNCT
ejpam-4963	181	20	·	·	PUNCT
ejpam-4963	181	21	,	,	PUNCT
ejpam-4963	181	22	pk	pk	NOUN
ejpam-4963	181	23	,	,	PUNCT
ejpam-4963	181	24	and	and	CCONJ
ejpam-4963	181	25	let	let	VERB
ejpam-4963	181	26	u	u	PRON
ejpam-4963	181	27	∈	∈	PROPN
ejpam-4963	181	28	s	s	VERB
ejpam-4963	181	29	such	such	ADJ
ejpam-4963	181	30	that	that	SCONJ
ejpam-4963	181	31	u	u	PROPN
ejpam-4963	181	32	∈	∈	PROPN
ejpam-4963	181	33	pk	pk	NOUN
ejpam-4963	181	34	for	for	ADP
ejpam-4963	181	35	some	some	DET
ejpam-4963	181	36	kth	kth	PROPN
ejpam-4963	181	37	vertex	vertex	NOUN
ejpam-4963	181	38	-	-	PUNCT
ejpam-4963	181	39	partition	partition	NOUN
ejpam-4963	181	40	of	of	ADP
ejpam-4963	181	41	g.	g.	PROPN
ejpam-4963	181	42	then	then	ADV
ejpam-4963	181	43	u	u	PROPN
ejpam-4963	181	44	dominates	dominate	VERB
ejpam-4963	181	45	vi	vi	INTJ
ejpam-4963	181	46	for	for	ADP
ejpam-4963	181	47	all	all	DET
ejpam-4963	181	48	vi	vi	PROPN
ejpam-4963	181	49	/∈	/∈	PUNCT
ejpam-4963	181	50	pk	pk	NOUN
ejpam-4963	181	51	.	.	NOUN
ejpam-4963	181	52	since	since	SCONJ
ejpam-4963	181	53	pk	pk	PROPN
ejpam-4963	181	54	is	be	AUX
ejpam-4963	181	55	non	non	ADJ
ejpam-4963	181	56	-	-	ADJ
ejpam-4963	181	57	trivial	trivial	ADJ
ejpam-4963	181	58	,	,	PUNCT
ejpam-4963	181	59	there	there	PRON
ejpam-4963	181	60	exists	exist	VERB
ejpam-4963	181	61	uj	uj	PROPN
ejpam-4963	181	62	∈	∈	PROPN
ejpam-4963	181	63	pk	pk	NOUN
ejpam-4963	181	64	with	with	ADP
ejpam-4963	181	65	uj	uj	PROPN
ejpam-4963	181	66	̸=	̸=	PROPN
ejpam-4963	181	67	u	u	NOUN
ejpam-4963	181	68	such	such	ADJ
ejpam-4963	181	69	that	that	SCONJ
ejpam-4963	181	70	u	u	NOUN
ejpam-4963	181	71	does	do	AUX
ejpam-4963	181	72	not	not	PART
ejpam-4963	181	73	dominate	dominate	VERB
ejpam-4963	181	74	uj	uj	PROPN
ejpam-4963	181	75	.	.	PUNCT
ejpam-4963	182	1	thus	thus	ADV
ejpam-4963	182	2	,	,	PUNCT
ejpam-4963	182	3	either	either	CCONJ
ejpam-4963	182	4	uj	uj	PROPN
ejpam-4963	182	5	∈	∈	PROPN
ejpam-4963	182	6	s	s	PART
ejpam-4963	182	7	or	or	CCONJ
ejpam-4963	182	8	uj	uj	PROPN
ejpam-4963	182	9	/∈	/∈	PUNCT
ejpam-4963	182	10	s.	s.	PROPN
ejpam-4963	182	11	if	if	SCONJ
ejpam-4963	182	12	uj	uj	PROPN
ejpam-4963	182	13	∈	∈	PROPN
ejpam-4963	182	14	s	s	PROPN
ejpam-4963	182	15	,	,	PUNCT
ejpam-4963	182	16	then	then	ADV
ejpam-4963	182	17	uj	uj	PROPN
ejpam-4963	182	18	must	must	AUX
ejpam-4963	182	19	dominate	dominate	VERB
ejpam-4963	182	20	vj	vj	NOUN
ejpam-4963	182	21	for	for	ADP
ejpam-4963	182	22	all	all	DET
ejpam-4963	182	23	vj	vj	PROPN
ejpam-4963	182	24	/∈	/∈	PROPN
ejpam-4963	182	25	pk	pk	PROPN
ejpam-4963	182	26	.	.	PUNCT
ejpam-4963	183	1	this	this	PRON
ejpam-4963	183	2	is	be	AUX
ejpam-4963	183	3	a	a	DET
ejpam-4963	183	4	contradiction	contradiction	NOUN
ejpam-4963	183	5	to	to	ADP
ejpam-4963	183	6	being	be	AUX
ejpam-4963	183	7	γpe0	γpe0	NOUN
ejpam-4963	183	8	-	-	PUNCT
ejpam-4963	183	9	set	set	NOUN
ejpam-4963	183	10	since	since	SCONJ
ejpam-4963	183	11	vj	vj	PROPN
ejpam-4963	183	12	is	be	AUX
ejpam-4963	183	13	dominated	dominate	VERB
ejpam-4963	183	14	by	by	ADP
ejpam-4963	183	15	u	u	NOUN
ejpam-4963	183	16	,	,	PUNCT
ejpam-4963	183	17	for	for	ADP
ejpam-4963	183	18	all	all	DET
ejpam-4963	183	19	vj	vj	PROPN
ejpam-4963	183	20	/∈	/∈	PUNCT
ejpam-4963	183	21	pk	pk	PROPN
ejpam-4963	183	22	.	.	PUNCT
ejpam-4963	184	1	if	if	SCONJ
ejpam-4963	184	2	uj	uj	PROPN
ejpam-4963	184	3	/∈	/∈	PUNCT
ejpam-4963	184	4	s	s	PART
ejpam-4963	184	5	,	,	PUNCT
ejpam-4963	184	6	then	then	ADV
ejpam-4963	184	7	there	there	PRON
ejpam-4963	184	8	must	must	AUX
ejpam-4963	184	9	be	be	AUX
ejpam-4963	184	10	vs	vs	ADP
ejpam-4963	184	11	/∈	/∈	PROPN
ejpam-4963	184	12	pk	pk	NOUN
ejpam-4963	184	13	such	such	ADJ
ejpam-4963	184	14	that	that	SCONJ
ejpam-4963	184	15	ujvs	ujvs	PROPN
ejpam-4963	184	16	∈	∈	PROPN
ejpam-4963	184	17	e(g	e(g	PROPN
ejpam-4963	184	18	)	)	PUNCT
ejpam-4963	184	19	.	.	PUNCT
ejpam-4963	185	1	but	but	CCONJ
ejpam-4963	185	2	vs	vs	ADP
ejpam-4963	185	3	is	be	AUX
ejpam-4963	185	4	adjacent	adjacent	ADJ
ejpam-4963	185	5	to	to	ADP
ejpam-4963	185	6	some	some	DET
ejpam-4963	185	7	vt	vt	PROPN
ejpam-4963	185	8	/∈	/∈	PROPN
ejpam-4963	185	9	pk	pk	NOUN
ejpam-4963	185	10	which	which	PRON
ejpam-4963	185	11	are	be	AUX
ejpam-4963	185	12	also	also	ADV
ejpam-4963	185	13	dominated	dominate	VERB
ejpam-4963	185	14	by	by	ADP
ejpam-4963	185	15	u.	u.	NOUN
ejpam-4963	185	16	this	this	PRON
ejpam-4963	185	17	is	be	AUX
ejpam-4963	185	18	also	also	ADV
ejpam-4963	185	19	a	a	DET
ejpam-4963	185	20	contradiction	contradiction	NOUN
ejpam-4963	185	21	to	to	ADP
ejpam-4963	185	22	being	be	AUX
ejpam-4963	185	23	γpe0	γpe0	NOUN
ejpam-4963	185	24	-	-	PUNCT
ejpam-4963	185	25	set	set	NOUN
ejpam-4963	185	26	.	.	PUNCT
ejpam-4963	186	1	therefore	therefore	ADV
ejpam-4963	186	2	,	,	PUNCT
ejpam-4963	186	3	there	there	PRON
ejpam-4963	186	4	does	do	AUX
ejpam-4963	186	5	not	not	PART
ejpam-4963	186	6	exist	exist	VERB
ejpam-4963	186	7	γpe0	γpe0	NOUN
ejpam-4963	186	8	-	-	PUNCT
ejpam-4963	186	9	set	set	NOUN
ejpam-4963	186	10	of	of	ADP
ejpam-4963	186	11	gp1,···pk	gp1,···pk	NOUN
ejpam-4963	186	12	for	for	ADP
ejpam-4963	186	13	any	any	DET
ejpam-4963	186	14	non	non	ADJ
ejpam-4963	186	15	-	-	ADJ
ejpam-4963	186	16	trivial	trivial	ADJ
ejpam-4963	186	17	partition	partition	NOUN
ejpam-4963	186	18	pi	pi	NOUN
ejpam-4963	186	19	,	,	PUNCT
ejpam-4963	186	20	i	i	PRON
ejpam-4963	186	21	=	=	NOUN
ejpam-4963	186	22	1	1	NUM
ejpam-4963	186	23	,	,	PUNCT
ejpam-4963	186	24	·	·	PUNCT
ejpam-4963	186	25	·	·	PUNCT
ejpam-4963	186	26	·	·	PUNCT
ejpam-4963	186	27	,	,	PUNCT
ejpam-4963	186	28	k.	k.	PROPN
ejpam-4963	186	29	4	4	X
ejpam-4963	186	30	.	.	X
ejpam-4963	186	31	peid	peid	VERB
ejpam-4963	186	32	in	in	ADP
ejpam-4963	186	33	the	the	DET
ejpam-4963	186	34	join	join	NOUN
ejpam-4963	186	35	of	of	ADP
ejpam-4963	186	36	graphs	graph	NOUN
ejpam-4963	186	37	the	the	DET
ejpam-4963	186	38	following	follow	VERB
ejpam-4963	186	39	proposition	proposition	NOUN
ejpam-4963	186	40	is	be	AUX
ejpam-4963	186	41	an	an	DET
ejpam-4963	186	42	obvious	obvious	ADJ
ejpam-4963	186	43	result	result	NOUN
ejpam-4963	186	44	.	.	PUNCT
ejpam-4963	187	1	proposition	proposition	NOUN
ejpam-4963	187	2	5	5	NUM
ejpam-4963	187	3	.	.	PUNCT
ejpam-4963	188	1	there	there	PRON
ejpam-4963	188	2	does	do	AUX
ejpam-4963	188	3	not	not	PART
ejpam-4963	188	4	exist	exist	VERB
ejpam-4963	188	5	a	a	DET
ejpam-4963	188	6	γpe0	γpe0	NOUN
ejpam-4963	188	7	-	-	PUNCT
ejpam-4963	188	8	set	set	NOUN
ejpam-4963	188	9	of	of	ADP
ejpam-4963	188	10	the	the	DET
ejpam-4963	188	11	following	follow	VERB
ejpam-4963	188	12	graphs	graph	NOUN
ejpam-4963	188	13	below	below	ADP
ejpam-4963	188	14	:	:	PUNCT
ejpam-4963	188	15	i.	i.	NOUN
ejpam-4963	188	16	wheel	wheel	PROPN
ejpam-4963	188	17	graph	graph	NOUN
ejpam-4963	188	18	,	,	PUNCT
ejpam-4963	188	19	wn	wn	PROPN
ejpam-4963	188	20	=	=	PROPN
ejpam-4963	188	21	k1	k1	PROPN
ejpam-4963	188	22	+	+	CCONJ
ejpam-4963	188	23	cn−1	cn−1	PROPN
ejpam-4963	188	24	,	,	PUNCT
ejpam-4963	188	25	n	n	PRON
ejpam-4963	188	26	≥	≥	NUM
ejpam-4963	188	27	6	6	NUM
ejpam-4963	188	28	ii	ii	NOUN
ejpam-4963	188	29	.	.	PUNCT
ejpam-4963	189	1	star	star	NOUN
ejpam-4963	189	2	graph	graph	NOUN
ejpam-4963	189	3	,	,	PUNCT
ejpam-4963	189	4	sn	sn	NOUN
ejpam-4963	189	5	=	=	SYM
ejpam-4963	189	6	k1	k1	PROPN
ejpam-4963	189	7	+	+	PROPN
ejpam-4963	189	8	kn−1	kn−1	PROPN
ejpam-4963	189	9	,	,	PUNCT
ejpam-4963	189	10	n	n	X
ejpam-4963	189	11	≥	≥	NOUN
ejpam-4963	189	12	4	4	NUM
ejpam-4963	189	13	iii	iii	NOUN
ejpam-4963	189	14	.	.	PUNCT
ejpam-4963	189	15	fan	fan	NOUN
ejpam-4963	189	16	graph	graph	NOUN
ejpam-4963	189	17	,	,	PUNCT
ejpam-4963	189	18	fn	fn	NOUN
ejpam-4963	189	19	=	=	SYM
ejpam-4963	189	20	k1	k1	PROPN
ejpam-4963	189	21	+	+	CCONJ
ejpam-4963	189	22	pn−1	pn−1	PROPN
ejpam-4963	189	23	,	,	PUNCT
ejpam-4963	189	24	n	n	PRON
ejpam-4963	189	25	≥	≥	NUM
ejpam-4963	189	26	5	5	NUM
ejpam-4963	189	27	iv	iv	NUM
ejpam-4963	189	28	.	.	PUNCT
ejpam-4963	189	29	friendship	friendship	NOUN
ejpam-4963	189	30	graph	graph	NOUN
ejpam-4963	189	31	,	,	PUNCT
ejpam-4963	189	32	frn	frn	PROPN
ejpam-4963	189	33	=	=	SYM
ejpam-4963	189	34	k1	k1	PROPN
ejpam-4963	189	35	+	+	CCONJ
ejpam-4963	189	36	np2	np2	PROPN
ejpam-4963	189	37	,	,	PUNCT
ejpam-4963	189	38	n	n	PRON
ejpam-4963	189	39	≥	≥	NOUN
ejpam-4963	189	40	2	2	NUM
ejpam-4963	189	41	v.	v.	ADP
ejpam-4963	189	42	windmill	windmill	NOUN
ejpam-4963	189	43	graph	graph	NOUN
ejpam-4963	189	44	wn	wn	PROPN
ejpam-4963	189	45	m	m	NOUN
ejpam-4963	189	46	=	=	PROPN
ejpam-4963	189	47	k1	k1	PROPN
ejpam-4963	189	48	+	+	CCONJ
ejpam-4963	189	49	cn−1	cn−1	PROPN
ejpam-4963	189	50	,	,	PUNCT
ejpam-4963	189	51	n	n	PRON
ejpam-4963	189	52	≥	≥	NOUN
ejpam-4963	189	53	2,m	2,m	NUM
ejpam-4963	189	54	≥	≥	NUM
ejpam-4963	189	55	3	3	NUM
ejpam-4963	189	56	theorem	theorem	VERB
ejpam-4963	189	57	10	10	NUM
ejpam-4963	189	58	.	.	PUNCT
ejpam-4963	190	1	let	let	VERB
ejpam-4963	190	2	g	g	NOUN
ejpam-4963	191	1	and	and	CCONJ
ejpam-4963	191	2	h	h	NOUN
ejpam-4963	191	3	be	be	VERB
ejpam-4963	191	4	any	any	DET
ejpam-4963	191	5	graphs	graph	NOUN
ejpam-4963	191	6	of	of	ADP
ejpam-4963	191	7	order	order	NOUN
ejpam-4963	191	8	n	n	NOUN
ejpam-4963	191	9	and	and	CCONJ
ejpam-4963	191	10	m	m	PROPN
ejpam-4963	191	11	,	,	PUNCT
ejpam-4963	191	12	respectively	respectively	ADV
ejpam-4963	191	13	,	,	PUNCT
ejpam-4963	191	14	with	with	ADP
ejpam-4963	191	15	γpe(g	γpe(g	PROPN
ejpam-4963	191	16	)	)	PUNCT
ejpam-4963	192	1	=	=	SYM
ejpam-4963	192	2	1	1	NUM
ejpam-4963	192	3	or	or	CCONJ
ejpam-4963	192	4	γpe(h	γpe(h	NUM
ejpam-4963	192	5	)	)	PUNCT
ejpam-4963	192	6	=	=	SYM
ejpam-4963	192	7	1	1	X
ejpam-4963	192	8	.	.	PUNCT
ejpam-4963	192	9	then	then	ADV
ejpam-4963	192	10	γpe0(g	γpe0(g	X
ejpam-4963	192	11	+	+	CCONJ
ejpam-4963	192	12	h	h	X
ejpam-4963	192	13	)	)	PUNCT
ejpam-4963	192	14	=	=	SYM
ejpam-4963	192	15	1	1	NUM
ejpam-4963	193	1	if	if	SCONJ
ejpam-4963	193	2	and	and	CCONJ
ejpam-4963	193	3	only	only	ADV
ejpam-4963	193	4	if	if	SCONJ
ejpam-4963	193	5	either	either	CCONJ
ejpam-4963	193	6	s1	s1	PROPN
ejpam-4963	193	7	=	=	SYM
ejpam-4963	193	8	{	{	PUNCT
ejpam-4963	193	9	u	u	NOUN
ejpam-4963	193	10	}	}	PUNCT
ejpam-4963	193	11	is	be	AUX
ejpam-4963	193	12	a	a	DET
ejpam-4963	193	13	γpe0	γpe0	NOUN
ejpam-4963	193	14	-	-	PUNCT
ejpam-4963	193	15	set	set	NOUN
ejpam-4963	193	16	of	of	ADP
ejpam-4963	193	17	g	g	NOUN
ejpam-4963	193	18	and	and	CCONJ
ejpam-4963	193	19	deg(v	deg(v	PROPN
ejpam-4963	193	20	)	)	PUNCT
ejpam-4963	193	21	≥	≥	NOUN
ejpam-4963	193	22	m−	m−	PROPN
ejpam-4963	193	23	2	2	NUM
ejpam-4963	193	24	for	for	ADP
ejpam-4963	193	25	all	all	PRON
ejpam-4963	193	26	v	v	ADP
ejpam-4963	193	27	∈	∈	NOUN
ejpam-4963	193	28	v	v	NOUN
ejpam-4963	193	29	(	(	PUNCT
ejpam-4963	193	30	h	h	NOUN
ejpam-4963	193	31	)	)	PUNCT
ejpam-4963	193	32	,	,	PUNCT
ejpam-4963	193	33	or	or	CCONJ
ejpam-4963	193	34	s2	s2	VERB
ejpam-4963	193	35	=	=	SYM
ejpam-4963	193	36	{	{	PUNCT
ejpam-4963	193	37	x	x	NOUN
ejpam-4963	193	38	}	}	PUNCT
ejpam-4963	193	39	is	be	AUX
ejpam-4963	193	40	a	a	DET
ejpam-4963	193	41	γpe0	γpe0	NOUN
ejpam-4963	193	42	-	-	PUNCT
ejpam-4963	193	43	set	set	NOUN
ejpam-4963	193	44	of	of	ADP
ejpam-4963	193	45	h	h	NOUN
ejpam-4963	193	46	and	and	CCONJ
ejpam-4963	193	47	deg(y	deg(y	PROPN
ejpam-4963	193	48	)	)	PUNCT
ejpam-4963	193	49	≥	≥	NOUN
ejpam-4963	193	50	n−	n−	NOUN
ejpam-4963	193	51	2	2	NUM
ejpam-4963	193	52	for	for	ADP
ejpam-4963	193	53	all	all	DET
ejpam-4963	193	54	y	y	PROPN
ejpam-4963	193	55	∈	∈	PROPN
ejpam-4963	193	56	v	v	NOUN
ejpam-4963	193	57	(	(	PUNCT
ejpam-4963	193	58	g	g	NOUN
ejpam-4963	193	59	)	)	PUNCT
ejpam-4963	193	60	.	.	PUNCT
ejpam-4963	194	1	proof	proof	NOUN
ejpam-4963	194	2	.	.	PUNCT
ejpam-4963	195	1	let	let	VERB
ejpam-4963	195	2	γpe0(g	γpe0(g	NOUN
ejpam-4963	195	3	+	+	CCONJ
ejpam-4963	195	4	h	h	X
ejpam-4963	195	5	)	)	PUNCT
ejpam-4963	195	6	=	=	SYM
ejpam-4963	196	1	1	1	X
ejpam-4963	196	2	.	.	PUNCT
ejpam-4963	196	3	by	by	ADP
ejpam-4963	196	4	theorem	theorem	ADJ
ejpam-4963	196	5	7	7	NUM
ejpam-4963	196	6	,	,	PUNCT
ejpam-4963	196	7	∆(g+h	∆(g+h	NOUN
ejpam-4963	196	8	)	)	PUNCT
ejpam-4963	196	9	=	=	SYM
ejpam-4963	197	1	(	(	PUNCT
ejpam-4963	197	2	n+m)−	n+m)−	ADJ
ejpam-4963	197	3	1	1	X
ejpam-4963	197	4	.	.	PUNCT
ejpam-4963	197	5	suppose	suppose	VERB
ejpam-4963	197	6	s	s	VERB
ejpam-4963	197	7	=	=	SYM
ejpam-4963	197	8	{	{	PUNCT
ejpam-4963	197	9	u	u	NOUN
ejpam-4963	197	10	}	}	PUNCT
ejpam-4963	197	11	⊆	⊆	NUM
ejpam-4963	197	12	v	v	NOUN
ejpam-4963	197	13	(	(	PUNCT
ejpam-4963	197	14	g	g	NOUN
ejpam-4963	197	15	)	)	PUNCT
ejpam-4963	197	16	be	be	AUX
ejpam-4963	197	17	a	a	DET
ejpam-4963	197	18	γpe0	γpe0	NOUN
ejpam-4963	197	19	-	-	PUNCT
ejpam-4963	197	20	set	set	NOUN
ejpam-4963	197	21	of	of	ADP
ejpam-4963	197	22	g	g	PROPN
ejpam-4963	197	23	+	+	PROPN
ejpam-4963	197	24	h.	h.	PROPN
ejpam-4963	197	25	this	this	PRON
ejpam-4963	197	26	means	mean	VERB
ejpam-4963	197	27	that	that	SCONJ
ejpam-4963	197	28	for	for	ADP
ejpam-4963	197	29	every	every	DET
ejpam-4963	197	30	v	v	NUM
ejpam-4963	197	31	∈	∈	NOUN
ejpam-4963	197	32	v	v	NOUN
ejpam-4963	197	33	(	(	PUNCT
ejpam-4963	197	34	g	g	PROPN
ejpam-4963	197	35	+	+	PROPN
ejpam-4963	197	36	h	h	NOUN
ejpam-4963	197	37	)	)	PUNCT
ejpam-4963	197	38	with	with	ADP
ejpam-4963	197	39	v	v	ADP
ejpam-4963	197	40	̸=	̸=	PROPN
ejpam-4963	197	41	u	u	NOUN
ejpam-4963	197	42	,	,	PUNCT
ejpam-4963	197	43	we	we	PRON
ejpam-4963	197	44	have	have	VERB
ejpam-4963	197	45	1	1	NUM
ejpam-4963	197	46	≥	≥	NOUN
ejpam-4963	197	47	|deg(u)−	|deg(u)−	PROPN
ejpam-4963	198	1	deg(v)|	deg(v)|	PROPN
ejpam-4963	198	2	m.	m.	PROPN
ejpam-4963	198	3	caay	caay	PROPN
ejpam-4963	198	4	,	,	PUNCT
ejpam-4963	198	5	a.	a.	PROPN
ejpam-4963	198	6	hernandez	hernandez	PROPN
ejpam-4963	198	7	/	/	SYM
ejpam-4963	198	8	eur	eur	PROPN
ejpam-4963	198	9	.	.	PUNCT
ejpam-4963	199	1	j.	j.	PROPN
ejpam-4963	199	2	pure	pure	PROPN
ejpam-4963	199	3	appl	appl	PROPN
ejpam-4963	199	4	.	.	PROPN
ejpam-4963	199	5	math	math	PROPN
ejpam-4963	199	6	,	,	PUNCT
ejpam-4963	199	7	17	17	NUM
ejpam-4963	199	8	(	(	PUNCT
ejpam-4963	199	9	2	2	NUM
ejpam-4963	199	10	)	)	PUNCT
ejpam-4963	199	11	(	(	PUNCT
ejpam-4963	199	12	2024	2024	NUM
ejpam-4963	199	13	)	)	PUNCT
ejpam-4963	199	14	,	,	PUNCT
ejpam-4963	199	15	969	969	NUM
ejpam-4963	199	16	-	-	SYM
ejpam-4963	199	17	978	978	NUM
ejpam-4963	199	18	976	976	NUM
ejpam-4963	199	19	≥	≥	NUM
ejpam-4963	199	20	|(n+m)−	|(n+m)−	NOUN
ejpam-4963	199	21	1−	1−	NUM
ejpam-4963	199	22	deg(v)|	deg(v)|	PROPN
ejpam-4963	199	23	≥	≥	NUM
ejpam-4963	199	24	|n+m−	|n+m−	ADP
ejpam-4963	199	25	1|	1|	NUM
ejpam-4963	199	26	−	−	PROPN
ejpam-4963	200	1	|	|	INTJ
ejpam-4963	200	2	deg(v)|	deg(v)|	PROPN
ejpam-4963	200	3	.	.	PROPN
ejpam-4963	200	4	thus	thus	ADV
ejpam-4963	200	5	,	,	PUNCT
ejpam-4963	200	6	deg(v	deg(v	PROPN
ejpam-4963	200	7	)	)	PUNCT
ejpam-4963	200	8	≥	≥	NOUN
ejpam-4963	200	9	(	(	PUNCT
ejpam-4963	200	10	m+	m+	NUM
ejpam-4963	200	11	n)−	n)−	NOUN
ejpam-4963	200	12	1−	1−	NUM
ejpam-4963	200	13	1	1	NUM
ejpam-4963	200	14	=	=	SYM
ejpam-4963	200	15	(	(	PUNCT
ejpam-4963	200	16	m+	m+	NUM
ejpam-4963	200	17	n)−	n)−	PROPN
ejpam-4963	200	18	2	2	NUM
ejpam-4963	200	19	.	.	PUNCT
ejpam-4963	201	1	this	this	PRON
ejpam-4963	201	2	means	mean	VERB
ejpam-4963	201	3	that	that	SCONJ
ejpam-4963	201	4	deg(v	deg(v	PROPN
ejpam-4963	201	5	)	)	PUNCT
ejpam-4963	201	6	≥	≥	NOUN
ejpam-4963	201	7	m−2	m−2	NUM
ejpam-4963	201	8	on	on	ADP
ejpam-4963	201	9	h	h	NOUN
ejpam-4963	201	10	for	for	ADP
ejpam-4963	201	11	all	all	DET
ejpam-4963	201	12	v	v	ADP
ejpam-4963	201	13	∈	∈	NOUN
ejpam-4963	201	14	v	v	NOUN
ejpam-4963	201	15	(	(	PUNCT
ejpam-4963	201	16	h	h	NOUN
ejpam-4963	201	17	)	)	PUNCT
ejpam-4963	201	18	.	.	PUNCT
ejpam-4963	202	1	similarly	similarly	ADV
ejpam-4963	202	2	,	,	PUNCT
ejpam-4963	202	3	if	if	SCONJ
ejpam-4963	202	4	s	s	VERB
ejpam-4963	202	5	=	=	PRON
ejpam-4963	202	6	{	{	PUNCT
ejpam-4963	202	7	x	x	NOUN
ejpam-4963	202	8	}	}	PUNCT
ejpam-4963	202	9	⊆	⊆	NUM
ejpam-4963	202	10	v	v	NOUN
ejpam-4963	202	11	(	(	PUNCT
ejpam-4963	202	12	h	h	NOUN
ejpam-4963	202	13	)	)	PUNCT
ejpam-4963	202	14	is	be	AUX
ejpam-4963	202	15	a	a	DET
ejpam-4963	202	16	γpe0	γpe0	NOUN
ejpam-4963	202	17	-	-	PUNCT
ejpam-4963	202	18	set	set	NOUN
ejpam-4963	202	19	of	of	ADP
ejpam-4963	202	20	g	g	PROPN
ejpam-4963	202	21	+	+	PROPN
ejpam-4963	202	22	h	h	NOUN
ejpam-4963	202	23	,	,	PUNCT
ejpam-4963	202	24	then	then	ADV
ejpam-4963	202	25	deg(y	deg(y	PROPN
ejpam-4963	202	26	)	)	PUNCT
ejpam-4963	202	27	≥	≥	NOUN
ejpam-4963	202	28	n	n	CCONJ
ejpam-4963	202	29	−	−	PROPN
ejpam-4963	202	30	2	2	NUM
ejpam-4963	202	31	on	on	ADP
ejpam-4963	202	32	g	g	NOUN
ejpam-4963	202	33	for	for	ADP
ejpam-4963	202	34	all	all	DET
ejpam-4963	202	35	y	y	PROPN
ejpam-4963	202	36	∈	∈	PROPN
ejpam-4963	202	37	v	v	NOUN
ejpam-4963	202	38	(	(	PUNCT
ejpam-4963	202	39	g	g	NOUN
ejpam-4963	202	40	)	)	PUNCT
ejpam-4963	202	41	.	.	PUNCT
ejpam-4963	203	1	conversely	conversely	ADV
ejpam-4963	203	2	,	,	PUNCT
ejpam-4963	203	3	suppose	suppose	VERB
ejpam-4963	203	4	s1	s1	NOUN
ejpam-4963	203	5	=	=	SYM
ejpam-4963	203	6	{	{	PUNCT
ejpam-4963	203	7	u	u	NOUN
ejpam-4963	203	8	}	}	PUNCT
ejpam-4963	203	9	is	be	AUX
ejpam-4963	203	10	a	a	DET
ejpam-4963	203	11	γpe0	γpe0	NOUN
ejpam-4963	203	12	-	-	PUNCT
ejpam-4963	203	13	set	set	NOUN
ejpam-4963	203	14	of	of	ADP
ejpam-4963	203	15	g	g	NOUN
ejpam-4963	203	16	and	and	CCONJ
ejpam-4963	203	17	deg(v	deg(v	PROPN
ejpam-4963	203	18	)	)	PUNCT
ejpam-4963	203	19	≥	≥	NOUN
ejpam-4963	203	20	m−	m−	PROPN
ejpam-4963	203	21	2	2	NUM
ejpam-4963	203	22	for	for	ADP
ejpam-4963	203	23	all	all	DET
ejpam-4963	203	24	v	v	ADP
ejpam-4963	203	25	∈	∈	NOUN
ejpam-4963	203	26	v	v	NOUN
ejpam-4963	203	27	(	(	PUNCT
ejpam-4963	203	28	h	h	NOUN
ejpam-4963	203	29	)	)	PUNCT
ejpam-4963	203	30	.	.	PUNCT
ejpam-4963	204	1	since	since	SCONJ
ejpam-4963	204	2	s1	s1	PROPN
ejpam-4963	204	3	=	=	PUNCT
ejpam-4963	204	4	{	{	PUNCT
ejpam-4963	204	5	u	u	NOUN
ejpam-4963	204	6	}	}	PUNCT
ejpam-4963	204	7	is	be	AUX
ejpam-4963	204	8	a	a	DET
ejpam-4963	204	9	γpe0	γpe0	NOUN
ejpam-4963	204	10	-	-	PUNCT
ejpam-4963	204	11	set	set	NOUN
ejpam-4963	204	12	of	of	ADP
ejpam-4963	204	13	g	g	NOUN
ejpam-4963	204	14	,	,	PUNCT
ejpam-4963	204	15	by	by	ADP
ejpam-4963	204	16	theorem	theorem	VERB
ejpam-4963	204	17	7	7	NUM
ejpam-4963	204	18	,	,	PUNCT
ejpam-4963	204	19	∆(g	∆(g	NOUN
ejpam-4963	204	20	)	)	PUNCT
ejpam-4963	204	21	=	=	SYM
ejpam-4963	205	1	n	n	CCONJ
ejpam-4963	205	2	−	−	NOUN
ejpam-4963	206	1	1	1	X
ejpam-4963	206	2	.	.	PUNCT
ejpam-4963	207	1	this	this	PRON
ejpam-4963	207	2	means	mean	VERB
ejpam-4963	207	3	that	that	SCONJ
ejpam-4963	207	4	deg(u	deg(u	ADJ
ejpam-4963	207	5	)	)	PUNCT
ejpam-4963	207	6	=	=	SYM
ejpam-4963	207	7	n	n	CCONJ
ejpam-4963	207	8	−	−	NUM
ejpam-4963	207	9	1	1	NUM
ejpam-4963	207	10	+	+	NUM
ejpam-4963	207	11	m	m	VERB
ejpam-4963	207	12	in	in	ADP
ejpam-4963	207	13	g	g	PROPN
ejpam-4963	208	1	+	+	CCONJ
ejpam-4963	208	2	h.	h.	PROPN
ejpam-4963	208	3	also	also	ADV
ejpam-4963	208	4	,	,	PUNCT
ejpam-4963	208	5	deg(v	deg(v	PROPN
ejpam-4963	208	6	)	)	PUNCT
ejpam-4963	208	7	≥	≥	NOUN
ejpam-4963	208	8	m	m	VERB
ejpam-4963	208	9	−	−	NOUN
ejpam-4963	208	10	2	2	NUM
ejpam-4963	208	11	for	for	ADP
ejpam-4963	208	12	every	every	DET
ejpam-4963	208	13	v	v	NUM
ejpam-4963	208	14	∈	∈	PROPN
ejpam-4963	208	15	v	v	NOUN
ejpam-4963	208	16	(	(	PUNCT
ejpam-4963	208	17	h	h	NOUN
ejpam-4963	208	18	)	)	PUNCT
ejpam-4963	208	19	implies	imply	VERB
ejpam-4963	208	20	that	that	SCONJ
ejpam-4963	208	21	deg(v	deg(v	PROPN
ejpam-4963	208	22	)	)	PUNCT
ejpam-4963	208	23	≥	≥	NOUN
ejpam-4963	208	24	m−	m−	PROPN
ejpam-4963	208	25	2	2	NUM
ejpam-4963	208	26	+	+	CCONJ
ejpam-4963	208	27	n	n	CCONJ
ejpam-4963	208	28	in	in	ADP
ejpam-4963	208	29	g+h	g+h	PROPN
ejpam-4963	208	30	.	.	PUNCT
ejpam-4963	209	1	thus	thus	ADV
ejpam-4963	209	2	,	,	PUNCT
ejpam-4963	209	3	|deg(u)−	|deg(u)−	PROPN
ejpam-4963	209	4	deg(v)|	deg(v)|	PROPN
ejpam-4963	209	5	≤	≤	PROPN
ejpam-4963	209	6	|(n−	|(n−	NOUN
ejpam-4963	209	7	1	1	NUM
ejpam-4963	210	1	+	+	PROPN
ejpam-4963	210	2	m)−	m)−	PROPN
ejpam-4963	210	3	(	(	PUNCT
ejpam-4963	210	4	m−	m−	PROPN
ejpam-4963	210	5	2−	2−	NUM
ejpam-4963	210	6	n)|	n)|	NOUN
ejpam-4963	210	7	=	=	SYM
ejpam-4963	210	8	1	1	X
ejpam-4963	210	9	.	.	PUNCT
ejpam-4963	210	10	hence	hence	ADV
ejpam-4963	210	11	,	,	PUNCT
ejpam-4963	210	12	s	s	PART
ejpam-4963	210	13	=	=	PUNCT
ejpam-4963	210	14	{	{	PUNCT
ejpam-4963	210	15	u	u	NOUN
ejpam-4963	210	16	}	}	PUNCT
ejpam-4963	210	17	is	be	AUX
ejpam-4963	210	18	a	a	DET
ejpam-4963	210	19	γpe0	γpe0	NOUN
ejpam-4963	210	20	-	-	PUNCT
ejpam-4963	210	21	set	set	NOUN
ejpam-4963	210	22	of	of	ADP
ejpam-4963	210	23	g	g	PROPN
ejpam-4963	210	24	+	+	CCONJ
ejpam-4963	210	25	h	h	NOUN
ejpam-4963	210	26	implying	imply	VERB
ejpam-4963	210	27	γpe0(g	γpe0(g	NOUN
ejpam-4963	210	28	+	+	CCONJ
ejpam-4963	210	29	h	h	X
ejpam-4963	210	30	)	)	PUNCT
ejpam-4963	210	31	=	=	SYM
ejpam-4963	211	1	1	1	X
ejpam-4963	211	2	.	.	PUNCT
ejpam-4963	211	3	the	the	DET
ejpam-4963	211	4	same	same	ADJ
ejpam-4963	211	5	argument	argument	NOUN
ejpam-4963	211	6	with	with	ADP
ejpam-4963	211	7	the	the	DET
ejpam-4963	211	8	other	other	ADJ
ejpam-4963	211	9	case	case	NOUN
ejpam-4963	211	10	.	.	PUNCT
ejpam-4963	212	1	the	the	DET
ejpam-4963	212	2	next	next	ADJ
ejpam-4963	212	3	corollary	corollary	NOUN
ejpam-4963	212	4	is	be	AUX
ejpam-4963	212	5	a	a	DET
ejpam-4963	212	6	very	very	ADV
ejpam-4963	212	7	obvious	obvious	ADJ
ejpam-4963	212	8	result	result	NOUN
ejpam-4963	212	9	as	as	ADP
ejpam-4963	212	10	a	a	DET
ejpam-4963	212	11	consequence	consequence	NOUN
ejpam-4963	212	12	of	of	ADP
ejpam-4963	212	13	theorem	theorem	ADJ
ejpam-4963	212	14	10	10	NUM
ejpam-4963	212	15	.	.	PUNCT
ejpam-4963	212	16	corollary	corollary	ADJ
ejpam-4963	212	17	3	3	X
ejpam-4963	212	18	.	.	PUNCT
ejpam-4963	213	1	let	let	VERB
ejpam-4963	213	2	g	g	NOUN
ejpam-4963	214	1	and	and	CCONJ
ejpam-4963	214	2	h	h	NOUN
ejpam-4963	214	3	be	be	VERB
ejpam-4963	214	4	any	any	DET
ejpam-4963	214	5	graphs	graph	NOUN
ejpam-4963	214	6	of	of	ADP
ejpam-4963	214	7	degree	degree	NOUN
ejpam-4963	214	8	n	n	PROPN
ejpam-4963	214	9	and	and	CCONJ
ejpam-4963	214	10	m	m	PROPN
ejpam-4963	214	11	,	,	PUNCT
ejpam-4963	214	12	respectively	respectively	ADV
ejpam-4963	214	13	.	.	PUNCT
ejpam-4963	215	1	if	if	SCONJ
ejpam-4963	215	2	∆(g	∆(g	NOUN
ejpam-4963	215	3	)	)	PUNCT
ejpam-4963	215	4	=	=	SYM
ejpam-4963	215	5	n−1	n−1	PROPN
ejpam-4963	215	6	and	and	CCONJ
ejpam-4963	215	7	δ(g	δ(g	PROPN
ejpam-4963	215	8	)	)	PUNCT
ejpam-4963	215	9	≥	≥	NOUN
ejpam-4963	215	10	n−	n−	NOUN
ejpam-4963	215	11	2	2	NUM
ejpam-4963	215	12	,	,	PUNCT
ejpam-4963	215	13	and	and	CCONJ
ejpam-4963	215	14	deg(u	deg(u	PROPN
ejpam-4963	215	15	)	)	PUNCT
ejpam-4963	215	16	≥	≥	NOUN
ejpam-4963	215	17	m−	m−	PROPN
ejpam-4963	215	18	2	2	NUM
ejpam-4963	215	19	for	for	ADP
ejpam-4963	215	20	all	all	PRON
ejpam-4963	215	21	u	u	NOUN
ejpam-4963	215	22	∈	∈	PROPN
ejpam-4963	215	23	v	v	NOUN
ejpam-4963	215	24	(	(	PUNCT
ejpam-4963	215	25	h	h	NOUN
ejpam-4963	215	26	)	)	PUNCT
ejpam-4963	215	27	.	.	PUNCT
ejpam-4963	216	1	then	then	ADV
ejpam-4963	216	2	γpe0(g+h	γpe0(g+h	X
ejpam-4963	216	3	)	)	PUNCT
ejpam-4963	216	4	=	=	SYM
ejpam-4963	216	5	1	1	X
ejpam-4963	216	6	.	.	PUNCT
ejpam-4963	216	7	theorem	theorem	VERB
ejpam-4963	216	8	11	11	NUM
ejpam-4963	216	9	.	.	PUNCT
ejpam-4963	217	1	let	let	VERB
ejpam-4963	217	2	s1	s1	NOUN
ejpam-4963	217	3	and	and	CCONJ
ejpam-4963	217	4	s2	s2	NOUN
ejpam-4963	217	5	be	be	AUX
ejpam-4963	217	6	the	the	DET
ejpam-4963	217	7	minimal	minimal	ADJ
ejpam-4963	217	8	nontrivial	nontrivial	ADJ
ejpam-4963	217	9	γpe0	γpe0	NOUN
ejpam-4963	217	10	-	-	PUNCT
ejpam-4963	217	11	sets	set	NOUN
ejpam-4963	217	12	of	of	ADP
ejpam-4963	217	13	g	g	PROPN
ejpam-4963	217	14	and	and	CCONJ
ejpam-4963	217	15	h	h	NOUN
ejpam-4963	217	16	,	,	PUNCT
ejpam-4963	217	17	respectively	respectively	ADV
ejpam-4963	217	18	.	.	PUNCT
ejpam-4963	218	1	that	that	PRON
ejpam-4963	218	2	is	be	AUX
ejpam-4963	218	3	,	,	PUNCT
ejpam-4963	218	4	|s1|	|s1|	NOUN
ejpam-4963	218	5	=	=	SYM
ejpam-4963	218	6	̸	̸	NUM
ejpam-4963	218	7	1	1	NUM
ejpam-4963	218	8	and	and	CCONJ
ejpam-4963	218	9	|s2|	|s2|	NOUN
ejpam-4963	218	10	̸=	̸=	PROPN
ejpam-4963	218	11	1	1	NUM
ejpam-4963	218	12	.	.	PUNCT
ejpam-4963	219	1	then	then	ADV
ejpam-4963	219	2	s1	s1	PROPN
ejpam-4963	219	3	∪	∪	PROPN
ejpam-4963	219	4	s2	s2	PROPN
ejpam-4963	219	5	is	be	AUX
ejpam-4963	219	6	a	a	DET
ejpam-4963	219	7	not	not	PART
ejpam-4963	219	8	a	a	DET
ejpam-4963	219	9	γpe0	γpe0	NOUN
ejpam-4963	219	10	-	-	PUNCT
ejpam-4963	219	11	set	set	NOUN
ejpam-4963	219	12	of	of	ADP
ejpam-4963	219	13	g+h	g+h	PROPN
ejpam-4963	219	14	but	but	CCONJ
ejpam-4963	219	15	a	a	DET
ejpam-4963	219	16	γe	γe	NOUN
ejpam-4963	219	17	-	-	PUNCT
ejpam-4963	219	18	set	set	NOUN
ejpam-4963	219	19	of	of	ADP
ejpam-4963	219	20	g+h	g+h	PROPN
ejpam-4963	219	21	.	.	PUNCT
ejpam-4963	220	1	proof	proof	NOUN
ejpam-4963	220	2	.	.	PUNCT
ejpam-4963	221	1	let	let	VERB
ejpam-4963	221	2	s1	s1	NOUN
ejpam-4963	221	3	and	and	CCONJ
ejpam-4963	221	4	s2	s2	NOUN
ejpam-4963	221	5	be	be	AUX
ejpam-4963	221	6	the	the	DET
ejpam-4963	221	7	minimal	minimal	ADJ
ejpam-4963	221	8	nontrivial	nontrivial	ADJ
ejpam-4963	221	9	γpe0	γpe0	NOUN
ejpam-4963	221	10	-	-	PUNCT
ejpam-4963	221	11	sets	set	NOUN
ejpam-4963	221	12	of	of	ADP
ejpam-4963	221	13	g	g	PROPN
ejpam-4963	221	14	and	and	CCONJ
ejpam-4963	221	15	h	h	NOUN
ejpam-4963	221	16	,	,	PUNCT
ejpam-4963	221	17	respectively	respectively	ADV
ejpam-4963	221	18	.	.	PUNCT
ejpam-4963	222	1	then	then	ADV
ejpam-4963	222	2	for	for	ADP
ejpam-4963	222	3	every	every	DET
ejpam-4963	222	4	u	u	PROPN
ejpam-4963	222	5	∈	∈	PROPN
ejpam-4963	222	6	v	v	ADP
ejpam-4963	222	7	(	(	PUNCT
ejpam-4963	222	8	g	g	NOUN
ejpam-4963	222	9	)	)	PUNCT
ejpam-4963	222	10	\	\	NOUN
ejpam-4963	222	11	s1	s1	NOUN
ejpam-4963	222	12	,	,	PUNCT
ejpam-4963	222	13	there	there	PRON
ejpam-4963	222	14	exists	exist	VERB
ejpam-4963	222	15	exactly	exactly	ADV
ejpam-4963	222	16	v	v	ADP
ejpam-4963	222	17	∈	∈	NOUN
ejpam-4963	222	18	s1	s1	NOUN
ejpam-4963	222	19	such	such	ADJ
ejpam-4963	222	20	that	that	SCONJ
ejpam-4963	222	21	uv	uv	PROPN
ejpam-4963	222	22	∈	∈	PROPN
ejpam-4963	222	23	e(g	e(g	PROPN
ejpam-4963	222	24	)	)	PUNCT
ejpam-4963	222	25	and	and	CCONJ
ejpam-4963	222	26	|deg(u)−	|deg(u)−	VERB
ejpam-4963	222	27	deg(v)|	deg(v)|	PROPN
ejpam-4963	222	28	≤	≤	PROPN
ejpam-4963	222	29	1	1	NUM
ejpam-4963	222	30	,	,	PUNCT
ejpam-4963	222	31	and	and	CCONJ
ejpam-4963	222	32	there	there	PRON
ejpam-4963	222	33	exists	exist	VERB
ejpam-4963	222	34	vi	vi	PROPN
ejpam-4963	222	35	∈	∈	PROPN
ejpam-4963	222	36	s1	s1	NOUN
ejpam-4963	222	37	such	such	ADJ
ejpam-4963	222	38	that	that	DET
ejpam-4963	222	39	viv	viv	PROPN
ejpam-4963	222	40	/∈	/∈	PUNCT
ejpam-4963	222	41	e(g	e(g	PROPN
ejpam-4963	222	42	)	)	PUNCT
ejpam-4963	222	43	for	for	ADP
ejpam-4963	222	44	some	some	DET
ejpam-4963	222	45	v	v	ADP
ejpam-4963	222	46	∈	∈	PROPN
ejpam-4963	222	47	s1	s1	NOUN
ejpam-4963	222	48	.	.	PUNCT
ejpam-4963	223	1	similarly	similarly	ADV
ejpam-4963	223	2	,	,	PUNCT
ejpam-4963	223	3	for	for	ADP
ejpam-4963	223	4	every	every	DET
ejpam-4963	223	5	x	x	SYM
ejpam-4963	223	6	∈	∈	PROPN
ejpam-4963	223	7	v	v	ADP
ejpam-4963	223	8	(	(	PUNCT
ejpam-4963	223	9	h	h	NOUN
ejpam-4963	223	10	)	)	PUNCT
ejpam-4963	223	11	\	\	NOUN
ejpam-4963	223	12	s2	s2	PROPN
ejpam-4963	223	13	,	,	PUNCT
ejpam-4963	223	14	there	there	PRON
ejpam-4963	223	15	exists	exist	VERB
ejpam-4963	223	16	exactly	exactly	ADV
ejpam-4963	223	17	y	y	PROPN
ejpam-4963	223	18	∈	∈	PROPN
ejpam-4963	223	19	s2	s2	NOUN
ejpam-4963	223	20	such	such	ADJ
ejpam-4963	223	21	that	that	SCONJ
ejpam-4963	223	22	xy	xy	PROPN
ejpam-4963	223	23	∈	∈	PROPN
ejpam-4963	223	24	e(g	e(g	PROPN
ejpam-4963	223	25	)	)	PUNCT
ejpam-4963	223	26	and	and	CCONJ
ejpam-4963	223	27	|deg(x)−	|deg(x)−	PROPN
ejpam-4963	223	28	deg(y)|	deg(y)|	PROPN
ejpam-4963	223	29	≤	≤	PROPN
ejpam-4963	223	30	1	1	NUM
ejpam-4963	223	31	,	,	PUNCT
ejpam-4963	223	32	and	and	CCONJ
ejpam-4963	223	33	there	there	PRON
ejpam-4963	223	34	exists	exist	VERB
ejpam-4963	223	35	yj	yj	PROPN
ejpam-4963	223	36	∈	∈	PROPN
ejpam-4963	223	37	s2	s2	NOUN
ejpam-4963	223	38	such	such	ADJ
ejpam-4963	223	39	that	that	DET
ejpam-4963	223	40	yjy	yjy	PROPN
ejpam-4963	223	41	/∈	/∈	PUNCT
ejpam-4963	223	42	e(g	e(g	PROPN
ejpam-4963	223	43	)	)	PUNCT
ejpam-4963	223	44	for	for	ADP
ejpam-4963	223	45	some	some	DET
ejpam-4963	223	46	y	y	PROPN
ejpam-4963	223	47	∈	∈	PROPN
ejpam-4963	223	48	s1	s1	PROPN
ejpam-4963	223	49	.	.	PUNCT
ejpam-4963	224	1	then	then	ADV
ejpam-4963	224	2	s1	s1	PROPN
ejpam-4963	224	3	∪	∪	PROPN
ejpam-4963	224	4	s2	s2	NOUN
ejpam-4963	224	5	:	:	PUNCT
ejpam-4963	224	6	=	=	SYM
ejpam-4963	224	7	{	{	PUNCT
ejpam-4963	224	8	vi	vi	PROPN
ejpam-4963	224	9	,	,	PUNCT
ejpam-4963	224	10	yj	yj	PROPN
ejpam-4963	224	11	,	,	PUNCT
ejpam-4963	224	12	vi	vi	PROPN
ejpam-4963	224	13	∈	∈	PROPN
ejpam-4963	224	14	s1	s1	NOUN
ejpam-4963	224	15	,	,	PUNCT
ejpam-4963	224	16	yj	yj	PROPN
ejpam-4963	224	17	∈	∈	PROPN
ejpam-4963	224	18	s2	s2	PROPN
ejpam-4963	224	19	,	,	PUNCT
ejpam-4963	224	20	for	for	ADP
ejpam-4963	224	21	some	some	DET
ejpam-4963	224	22	i	i	PROPN
ejpam-4963	224	23	,	,	PUNCT
ejpam-4963	224	24	j	j	PROPN
ejpam-4963	224	25	}	}	PUNCT
ejpam-4963	224	26	⊆	⊆	NUM
ejpam-4963	224	27	v	v	NOUN
ejpam-4963	224	28	(	(	PUNCT
ejpam-4963	224	29	g	g	PROPN
ejpam-4963	224	30	+	+	NOUN
ejpam-4963	224	31	h	h	NOUN
ejpam-4963	224	32	)	)	PUNCT
ejpam-4963	224	33	.	.	PUNCT
ejpam-4963	225	1	thus	thus	ADV
ejpam-4963	225	2	,	,	PUNCT
ejpam-4963	225	3	for	for	ADP
ejpam-4963	225	4	all	all	DET
ejpam-4963	225	5	w	w	PROPN
ejpam-4963	225	6	∈	∈	PROPN
ejpam-4963	225	7	v	v	NOUN
ejpam-4963	225	8	(	(	PUNCT
ejpam-4963	225	9	g+h	g+h	NOUN
ejpam-4963	225	10	)	)	PUNCT
ejpam-4963	225	11	\	\	PUNCT
ejpam-4963	226	1	(	(	PUNCT
ejpam-4963	226	2	s1	s1	PROPN
ejpam-4963	226	3	∪	∪	X
ejpam-4963	226	4	s2	s2	PROPN
ejpam-4963	226	5	)	)	PUNCT
ejpam-4963	226	6	,	,	PUNCT
ejpam-4963	226	7	there	there	PRON
ejpam-4963	226	8	exists	exist	VERB
ejpam-4963	226	9	z	z	NOUN
ejpam-4963	226	10	∈	∈	PROPN
ejpam-4963	226	11	s1	s1	NOUN
ejpam-4963	226	12	∪	∪	ADP
ejpam-4963	226	13	s2	s2	NOUN
ejpam-4963	226	14	such	such	ADJ
ejpam-4963	226	15	that	that	SCONJ
ejpam-4963	226	16	wz	wz	ADP
ejpam-4963	226	17	∈	∈	PRON
ejpam-4963	226	18	e(g+h	e(g+h	NUM
ejpam-4963	226	19	)	)	PUNCT
ejpam-4963	226	20	and	and	CCONJ
ejpam-4963	226	21	|deg(w)−	|deg(w)−	PROPN
ejpam-4963	226	22	deg(z)|	deg(z)|	PROPN
ejpam-4963	226	23	≤	≤	ADJ
ejpam-4963	226	24	1	1	NUM
ejpam-4963	226	25	.	.	PUNCT
ejpam-4963	227	1	hence	hence	ADV
ejpam-4963	227	2	,	,	PUNCT
ejpam-4963	227	3	s1	s1	PROPN
ejpam-4963	227	4	∪	∪	NOUN
ejpam-4963	227	5	s2	s2	NOUN
ejpam-4963	227	6	is	be	AUX
ejpam-4963	227	7	a	a	DET
ejpam-4963	227	8	γe	γe	NOUN
ejpam-4963	227	9	-	-	PUNCT
ejpam-4963	227	10	set	set	NOUN
ejpam-4963	227	11	of	of	ADP
ejpam-4963	227	12	g+h	g+h	PROPN
ejpam-4963	227	13	.	.	PUNCT
ejpam-4963	228	1	now	now	ADV
ejpam-4963	228	2	if	if	SCONJ
ejpam-4963	228	3	vi	vi	PROPN
ejpam-4963	228	4	∈	∈	PROPN
ejpam-4963	228	5	s1	s1	NOUN
ejpam-4963	228	6	is	be	AUX
ejpam-4963	228	7	an	an	DET
ejpam-4963	228	8	isolated	isolated	ADJ
ejpam-4963	228	9	vertex	vertex	NOUN
ejpam-4963	228	10	of	of	ADP
ejpam-4963	228	11	s1	s1	NOUN
ejpam-4963	228	12	,	,	PUNCT
ejpam-4963	228	13	then	then	ADV
ejpam-4963	228	14	viuj	viuj	ADJ
ejpam-4963	228	15	∈	∈	PROPN
ejpam-4963	228	16	e(g	e(g	PROPN
ejpam-4963	229	1	+	+	NOUN
ejpam-4963	229	2	h	h	NOUN
ejpam-4963	229	3	)	)	PUNCT
ejpam-4963	229	4	for	for	ADP
ejpam-4963	229	5	all	all	DET
ejpam-4963	229	6	uj	uj	PROPN
ejpam-4963	229	7	∈	∈	PROPN
ejpam-4963	229	8	s2	s2	PROPN
ejpam-4963	229	9	,	,	PUNCT
ejpam-4963	229	10	and	and	CCONJ
ejpam-4963	229	11	vkuj	vkuj	PROPN
ejpam-4963	229	12	∈	∈	PROPN
ejpam-4963	230	1	e(g	e(g	PROPN
ejpam-4963	231	1	+	+	NOUN
ejpam-4963	231	2	h	h	NOUN
ejpam-4963	231	3	)	)	PUNCT
ejpam-4963	231	4	,	,	PUNCT
ejpam-4963	231	5	for	for	ADP
ejpam-4963	231	6	all	all	DET
ejpam-4963	231	7	vk	vk	ADP
ejpam-4963	231	8	∈	∈	PROPN
ejpam-4963	231	9	s1	s1	NOUN
ejpam-4963	231	10	with	with	ADP
ejpam-4963	231	11	vi	vi	PROPN
ejpam-4963	231	12	̸=	̸=	PROPN
ejpam-4963	231	13	vk	vk	NOUN
ejpam-4963	231	14	.	.	PUNCT
ejpam-4963	232	1	this	this	PRON
ejpam-4963	232	2	means	mean	VERB
ejpam-4963	232	3	that	that	SCONJ
ejpam-4963	232	4	vi	vi	PROPN
ejpam-4963	232	5	is	be	AUX
ejpam-4963	232	6	no	no	ADV
ejpam-4963	232	7	longer	long	ADV
ejpam-4963	232	8	isolated	isolate	VERB
ejpam-4963	232	9	.	.	PUNCT
ejpam-4963	233	1	since	since	SCONJ
ejpam-4963	233	2	vi	vi	PROPN
ejpam-4963	233	3	is	be	AUX
ejpam-4963	233	4	arbitrary	arbitrary	ADJ
ejpam-4963	233	5	,	,	PUNCT
ejpam-4963	233	6	this	this	PRON
ejpam-4963	233	7	holds	hold	VERB
ejpam-4963	233	8	for	for	ADP
ejpam-4963	233	9	all	all	DET
ejpam-4963	233	10	isolated	isolated	ADJ
ejpam-4963	233	11	dominating	dominating	NOUN
ejpam-4963	233	12	vertices	vertex	NOUN
ejpam-4963	233	13	.	.	PUNCT
ejpam-4963	234	1	hence	hence	ADV
ejpam-4963	234	2	,	,	PUNCT
ejpam-4963	234	3	s1	s1	PROPN
ejpam-4963	234	4	∪	∪	NOUN
ejpam-4963	234	5	s2	s2	NOUN
ejpam-4963	234	6	is	be	AUX
ejpam-4963	234	7	not	not	PART
ejpam-4963	234	8	γe0	γe0	NOUN
ejpam-4963	234	9	-	-	PUNCT
ejpam-4963	234	10	set	set	NOUN
ejpam-4963	234	11	of	of	ADP
ejpam-4963	234	12	g+h	g+h	PROPN
ejpam-4963	234	13	.	.	PUNCT
ejpam-4963	235	1	moreover	moreover	ADV
ejpam-4963	235	2	,	,	PUNCT
ejpam-4963	235	3	for	for	ADP
ejpam-4963	235	4	every	every	DET
ejpam-4963	235	5	u	u	PROPN
ejpam-4963	235	6	∈	∈	PROPN
ejpam-4963	235	7	v	v	ADP
ejpam-4963	235	8	(	(	PUNCT
ejpam-4963	235	9	g	g	NOUN
ejpam-4963	235	10	)	)	PUNCT
ejpam-4963	235	11	\	\	NOUN
ejpam-4963	235	12	s1	s1	NOUN
ejpam-4963	235	13	,	,	PUNCT
ejpam-4963	235	14	there	there	PRON
ejpam-4963	235	15	exists	exist	VERB
ejpam-4963	235	16	exactly	exactly	ADV
ejpam-4963	235	17	one	one	NUM
ejpam-4963	235	18	v	v	NOUN
ejpam-4963	235	19	∈	∈	NOUN
ejpam-4963	235	20	s1	s1	NOUN
ejpam-4963	235	21	such	such	ADJ
ejpam-4963	235	22	that	that	SCONJ
ejpam-4963	235	23	uv1	uv1	PROPN
ejpam-4963	235	24	∈	∈	PROPN
ejpam-4963	235	25	e(g	e(g	PROPN
ejpam-4963	235	26	)	)	PUNCT
ejpam-4963	235	27	however	however	ADV
ejpam-4963	235	28	,	,	PUNCT
ejpam-4963	235	29	u	u	NOUN
ejpam-4963	235	30	is	be	AUX
ejpam-4963	235	31	adjacent	adjacent	ADJ
ejpam-4963	235	32	to	to	ADP
ejpam-4963	235	33	vertices	vertex	NOUN
ejpam-4963	235	34	of	of	ADP
ejpam-4963	235	35	h.	h.	PROPN
ejpam-4963	235	36	this	this	PRON
ejpam-4963	235	37	means	mean	VERB
ejpam-4963	235	38	that	that	SCONJ
ejpam-4963	235	39	u	u	PRON
ejpam-4963	235	40	is	be	AUX
ejpam-4963	235	41	adjacent	adjacent	ADJ
ejpam-4963	235	42	to	to	ADP
ejpam-4963	235	43	some	some	DET
ejpam-4963	235	44	wj	wj	PROPN
ejpam-4963	235	45	∈	∈	PROPN
ejpam-4963	235	46	s2	s2	PROPN
ejpam-4963	235	47	.	.	PUNCT
ejpam-4963	236	1	hence	hence	ADV
ejpam-4963	236	2	,	,	PUNCT
ejpam-4963	236	3	s1	s1	PROPN
ejpam-4963	236	4	∪	∪	NOUN
ejpam-4963	236	5	s2	s2	NOUN
ejpam-4963	236	6	is	be	AUX
ejpam-4963	236	7	not	not	PART
ejpam-4963	236	8	γp0	γp0	NOUN
ejpam-4963	236	9	-	-	PUNCT
ejpam-4963	236	10	set	set	NOUN
ejpam-4963	236	11	of	of	ADP
ejpam-4963	236	12	g+h	g+h	PROPN
ejpam-4963	236	13	.	.	PUNCT
ejpam-4963	237	1	this	this	PRON
ejpam-4963	237	2	proves	prove	VERB
ejpam-4963	237	3	the	the	DET
ejpam-4963	237	4	claim	claim	NOUN
ejpam-4963	237	5	.	.	PUNCT
ejpam-4963	238	1	remark	remark	NOUN
ejpam-4963	238	2	1	1	NUM
ejpam-4963	238	3	.	.	PUNCT
ejpam-4963	239	1	s1	s1	NOUN
ejpam-4963	239	2	∪	∪	PROPN
ejpam-4963	239	3	s2	s2	PROPN
ejpam-4963	239	4	is	be	AUX
ejpam-4963	239	5	a	a	DET
ejpam-4963	239	6	γe	γe	NOUN
ejpam-4963	239	7	-	-	PUNCT
ejpam-4963	239	8	set	set	NOUN
ejpam-4963	239	9	of	of	ADP
ejpam-4963	239	10	g+h	g+h	PROPN
ejpam-4963	239	11	of	of	ADP
ejpam-4963	239	12	theorem	theorem	NOUN
ejpam-4963	239	13	11	11	NUM
ejpam-4963	239	14	is	be	AUX
ejpam-4963	239	15	not	not	PART
ejpam-4963	239	16	necessarily	necessarily	ADV
ejpam-4963	239	17	minimal	minimal	ADJ
ejpam-4963	239	18	.	.	PUNCT
ejpam-4963	240	1	references	reference	NOUN
ejpam-4963	240	2	977	977	NUM
ejpam-4963	240	3	5	5	NUM
ejpam-4963	240	4	.	.	PUNCT
ejpam-4963	241	1	peid	peid	VERB
ejpam-4963	241	2	in	in	ADP
ejpam-4963	241	3	the	the	DET
ejpam-4963	241	4	corona	corona	NOUN
ejpam-4963	241	5	of	of	ADP
ejpam-4963	241	6	graphs	graph	NOUN
ejpam-4963	241	7	theorem	theorem	VERB
ejpam-4963	241	8	12	12	NUM
ejpam-4963	241	9	.	.	PUNCT
ejpam-4963	242	1	there	there	PRON
ejpam-4963	242	2	does	do	AUX
ejpam-4963	242	3	not	not	PART
ejpam-4963	242	4	exist	exist	VERB
ejpam-4963	242	5	a	a	DET
ejpam-4963	242	6	γpe0	γpe0	NOUN
ejpam-4963	242	7	-	-	PUNCT
ejpam-4963	242	8	set	set	NOUN
ejpam-4963	242	9	of	of	ADP
ejpam-4963	242	10	g	g	PROPN
ejpam-4963	242	11	◦	◦	NOUN
ejpam-4963	242	12	h	h	NOUN
ejpam-4963	242	13	for	for	ADP
ejpam-4963	242	14	any	any	DET
ejpam-4963	242	15	non	non	ADJ
ejpam-4963	242	16	-	-	ADJ
ejpam-4963	242	17	trivial	trivial	ADJ
ejpam-4963	242	18	graphs	graph	NOUN
ejpam-4963	242	19	g	g	NOUN
ejpam-4963	242	20	and	and	CCONJ
ejpam-4963	242	21	h.	h.	PROPN
ejpam-4963	242	22	proof	proof	NOUN
ejpam-4963	242	23	.	.	PUNCT
ejpam-4963	243	1	suppose	suppose	VERB
ejpam-4963	243	2	on	on	ADP
ejpam-4963	243	3	the	the	DET
ejpam-4963	243	4	contrary	contrary	NOUN
ejpam-4963	243	5	that	that	SCONJ
ejpam-4963	243	6	there	there	PRON
ejpam-4963	243	7	exists	exist	VERB
ejpam-4963	243	8	a	a	DET
ejpam-4963	243	9	γpe0	γpe0	NOUN
ejpam-4963	243	10	-	-	PUNCT
ejpam-4963	243	11	set	set	NOUN
ejpam-4963	243	12	s	s	NOUN
ejpam-4963	243	13	of	of	ADP
ejpam-4963	243	14	g	g	PROPN
ejpam-4963	243	15	◦	◦	NOUN
ejpam-4963	243	16	h.	h.	NOUN
ejpam-4963	243	17	then	then	ADV
ejpam-4963	243	18	either	either	CCONJ
ejpam-4963	243	19	s	s	VERB
ejpam-4963	243	20	⊆	⊆	NUM
ejpam-4963	243	21	v	v	NOUN
ejpam-4963	243	22	(	(	PUNCT
ejpam-4963	243	23	g	g	NOUN
ejpam-4963	243	24	)	)	PUNCT
ejpam-4963	243	25	or	or	CCONJ
ejpam-4963	243	26	s	s	PRON
ejpam-4963	243	27	⊆	⊆	NUM
ejpam-4963	243	28	v	v	NOUN
ejpam-4963	243	29	(	(	PUNCT
ejpam-4963	243	30	h	h	NOUN
ejpam-4963	243	31	)	)	PUNCT
ejpam-4963	243	32	or	or	CCONJ
ejpam-4963	243	33	s	s	PRON
ejpam-4963	243	34	⊆	⊆	NUM
ejpam-4963	243	35	v	v	NOUN
ejpam-4963	243	36	(	(	PUNCT
ejpam-4963	243	37	g	g	PROPN
ejpam-4963	243	38	+	+	NOUN
ejpam-4963	243	39	h	h	NOUN
ejpam-4963	243	40	)	)	PUNCT
ejpam-4963	243	41	.	.	PUNCT
ejpam-4963	244	1	suppose	suppose	VERB
ejpam-4963	244	2	s	s	VERB
ejpam-4963	244	3	⊆	⊆	NUM
ejpam-4963	244	4	v	v	NOUN
ejpam-4963	244	5	(	(	PUNCT
ejpam-4963	244	6	g	g	NOUN
ejpam-4963	244	7	)	)	PUNCT
ejpam-4963	244	8	and	and	CCONJ
ejpam-4963	244	9	let	let	VERB
ejpam-4963	244	10	u	u	PRON
ejpam-4963	244	11	∈	∈	PROPN
ejpam-4963	244	12	s.	s.	PROPN
ejpam-4963	244	13	then	then	ADV
ejpam-4963	244	14	u	u	PROPN
ejpam-4963	244	15	∈	∈	PROPN
ejpam-4963	244	16	v	v	NOUN
ejpam-4963	244	17	(	(	PUNCT
ejpam-4963	244	18	g	g	NOUN
ejpam-4963	244	19	)	)	PUNCT
ejpam-4963	244	20	.	.	PUNCT
ejpam-4963	245	1	this	this	PRON
ejpam-4963	245	2	means	mean	VERB
ejpam-4963	245	3	that	that	SCONJ
ejpam-4963	245	4	the	the	DET
ejpam-4963	245	5	degree	degree	NOUN
ejpam-4963	245	6	of	of	ADP
ejpam-4963	245	7	u	u	NOUN
ejpam-4963	245	8	in	in	ADP
ejpam-4963	245	9	g	g	PROPN
ejpam-4963	245	10	+	+	CCONJ
ejpam-4963	245	11	h	h	NOUN
ejpam-4963	245	12	is	be	AUX
ejpam-4963	245	13	equal	equal	ADJ
ejpam-4963	245	14	to	to	ADP
ejpam-4963	245	15	the	the	DET
ejpam-4963	245	16	degree	degree	NOUN
ejpam-4963	245	17	of	of	ADP
ejpam-4963	245	18	u	u	NOUN
ejpam-4963	245	19	in	in	ADP
ejpam-4963	245	20	g	g	PROPN
ejpam-4963	245	21	plus	plus	CCONJ
ejpam-4963	245	22	the	the	DET
ejpam-4963	245	23	cardinality	cardinality	NOUN
ejpam-4963	245	24	of	of	ADP
ejpam-4963	245	25	h.	h.	PROPN
ejpam-4963	245	26	since	since	SCONJ
ejpam-4963	245	27	g	g	PROPN
ejpam-4963	245	28	is	be	AUX
ejpam-4963	245	29	nontrivial	nontrivial	ADJ
ejpam-4963	245	30	,	,	PUNCT
ejpam-4963	245	31	deg(u	deg(u	PROPN
ejpam-4963	245	32	)	)	PUNCT
ejpam-4963	245	33	≥	≥	NOUN
ejpam-4963	245	34	1	1	NUM
ejpam-4963	245	35	in	in	ADP
ejpam-4963	245	36	g.	g.	PROPN
ejpam-4963	245	37	thus	thus	ADV
ejpam-4963	245	38	,	,	PUNCT
ejpam-4963	245	39	deg(u	deg(u	PROPN
ejpam-4963	245	40	)	)	PUNCT
ejpam-4963	245	41	≥	≥	NOUN
ejpam-4963	245	42	1	1	NUM
ejpam-4963	246	1	+	+	NOUN
ejpam-4963	246	2	m	m	VERB
ejpam-4963	246	3	in	in	ADP
ejpam-4963	246	4	g	g	PROPN
ejpam-4963	246	5	+	+	PROPN
ejpam-4963	246	6	h.	h.	PROPN
ejpam-4963	247	1	but	but	CCONJ
ejpam-4963	247	2	every	every	DET
ejpam-4963	247	3	vertex	vertex	NOUN
ejpam-4963	247	4	v	v	ADP
ejpam-4963	247	5	∈	∈	PROPN
ejpam-4963	247	6	v	v	NOUN
ejpam-4963	247	7	(	(	PUNCT
ejpam-4963	247	8	h	h	NOUN
ejpam-4963	247	9	)	)	PUNCT
ejpam-4963	247	10	has	have	VERB
ejpam-4963	247	11	at	at	ADP
ejpam-4963	247	12	most	most	ADJ
ejpam-4963	247	13	m	m	VERB
ejpam-4963	247	14	−	−	NUM
ejpam-4963	247	15	1	1	NUM
ejpam-4963	247	16	degree	degree	NOUN
ejpam-4963	247	17	.	.	PUNCT
ejpam-4963	248	1	hence	hence	ADV
ejpam-4963	248	2	,	,	PUNCT
ejpam-4963	248	3	it	it	PRON
ejpam-4963	248	4	follows	follow	VERB
ejpam-4963	248	5	that	that	SCONJ
ejpam-4963	248	6	|deg(u)−	|deg(u)−	VERB
ejpam-4963	248	7	deg(v)|	deg(v)|	PROPN
ejpam-4963	248	8	≥	≥	NUM
ejpam-4963	248	9	1	1	NUM
ejpam-4963	248	10	,	,	PUNCT
ejpam-4963	248	11	a	a	DET
ejpam-4963	248	12	contradiction	contradiction	NOUN
ejpam-4963	248	13	.	.	PUNCT
ejpam-4963	249	1	similarly	similarly	ADV
ejpam-4963	249	2	,	,	PUNCT
ejpam-4963	249	3	assume	assume	VERB
ejpam-4963	249	4	s	s	PRON
ejpam-4963	249	5	⊆	⊆	NUM
ejpam-4963	249	6	v	v	NOUN
ejpam-4963	249	7	(	(	PUNCT
ejpam-4963	249	8	h	h	NOUN
ejpam-4963	249	9	)	)	PUNCT
ejpam-4963	249	10	and	and	CCONJ
ejpam-4963	249	11	let	let	VERB
ejpam-4963	249	12	w	w	PROPN
ejpam-4963	249	13	∈	∈	PROPN
ejpam-4963	249	14	s.	s.	PROPN
ejpam-4963	249	15	then	then	ADV
ejpam-4963	249	16	w	w	PROPN
ejpam-4963	249	17	∈	∈	PROPN
ejpam-4963	249	18	v	v	ADP
ejpam-4963	249	19	(	(	PUNCT
ejpam-4963	249	20	h	h	NOUN
ejpam-4963	249	21	)	)	PUNCT
ejpam-4963	249	22	.	.	PUNCT
ejpam-4963	250	1	this	this	PRON
ejpam-4963	250	2	means	mean	VERB
ejpam-4963	250	3	that	that	SCONJ
ejpam-4963	250	4	the	the	DET
ejpam-4963	250	5	degree	degree	NOUN
ejpam-4963	250	6	of	of	ADP
ejpam-4963	250	7	w	w	NOUN
ejpam-4963	250	8	in	in	ADP
ejpam-4963	250	9	g	g	PROPN
ejpam-4963	250	10	+	+	NOUN
ejpam-4963	250	11	h	h	NOUN
ejpam-4963	250	12	is	be	AUX
ejpam-4963	250	13	equal	equal	ADJ
ejpam-4963	250	14	to	to	ADP
ejpam-4963	250	15	the	the	DET
ejpam-4963	250	16	degree	degree	NOUN
ejpam-4963	250	17	of	of	ADP
ejpam-4963	250	18	w	w	NOUN
ejpam-4963	250	19	in	in	ADP
ejpam-4963	250	20	h	h	PROPN
ejpam-4963	250	21	plus	plus	CCONJ
ejpam-4963	250	22	the	the	DET
ejpam-4963	250	23	cardinality	cardinality	NOUN
ejpam-4963	250	24	of	of	ADP
ejpam-4963	250	25	g.	g.	PROPN
ejpam-4963	250	26	since	since	SCONJ
ejpam-4963	250	27	h	h	PROPN
ejpam-4963	250	28	is	be	AUX
ejpam-4963	250	29	nontrivial	nontrivial	ADJ
ejpam-4963	250	30	,	,	PUNCT
ejpam-4963	250	31	deg(w	deg(w	PROPN
ejpam-4963	250	32	)	)	PUNCT
ejpam-4963	250	33	≥	≥	NOUN
ejpam-4963	250	34	1	1	NUM
ejpam-4963	250	35	in	in	ADP
ejpam-4963	250	36	h.	h.	PROPN
ejpam-4963	250	37	thus	thus	ADV
ejpam-4963	250	38	,	,	PUNCT
ejpam-4963	250	39	deg(w	deg(w	PROPN
ejpam-4963	250	40	)	)	PUNCT
ejpam-4963	250	41	≥	≥	NOUN
ejpam-4963	250	42	1	1	NUM
ejpam-4963	250	43	+	+	CCONJ
ejpam-4963	250	44	n	n	X
ejpam-4963	250	45	in	in	ADP
ejpam-4963	250	46	g	g	PROPN
ejpam-4963	250	47	+	+	PROPN
ejpam-4963	250	48	h.	h.	PROPN
ejpam-4963	251	1	but	but	CCONJ
ejpam-4963	251	2	every	every	DET
ejpam-4963	251	3	vertex	vertex	NOUN
ejpam-4963	251	4	z	z	PROPN
ejpam-4963	251	5	∈	∈	PROPN
ejpam-4963	251	6	v	v	ADP
ejpam-4963	251	7	(	(	PUNCT
ejpam-4963	251	8	g	g	NOUN
ejpam-4963	251	9	)	)	PUNCT
ejpam-4963	251	10	has	have	VERB
ejpam-4963	251	11	at	at	ADP
ejpam-4963	251	12	most	most	ADJ
ejpam-4963	251	13	n	n	CCONJ
ejpam-4963	251	14	−	−	NUM
ejpam-4963	251	15	1	1	NUM
ejpam-4963	251	16	degree	degree	NOUN
ejpam-4963	251	17	.	.	PUNCT
ejpam-4963	252	1	hence	hence	ADV
ejpam-4963	252	2	,	,	PUNCT
ejpam-4963	252	3	it	it	PRON
ejpam-4963	252	4	follows	follow	VERB
ejpam-4963	252	5	that	that	SCONJ
ejpam-4963	252	6	|deg(w)−	|deg(w)−	NOUN
ejpam-4963	252	7	deg(z)|	deg(z)|	PROPN
ejpam-4963	252	8	≥	≥	NUM
ejpam-4963	252	9	1	1	NUM
ejpam-4963	252	10	,	,	PUNCT
ejpam-4963	252	11	a	a	DET
ejpam-4963	252	12	contradiction	contradiction	NOUN
ejpam-4963	252	13	.	.	PUNCT
ejpam-4963	253	1	lastly	lastly	ADV
ejpam-4963	253	2	,	,	PUNCT
ejpam-4963	253	3	suppose	suppose	VERB
ejpam-4963	253	4	s	s	VERB
ejpam-4963	253	5	⊆	⊆	NUM
ejpam-4963	253	6	v	v	NOUN
ejpam-4963	253	7	(	(	PUNCT
ejpam-4963	253	8	g+h	g+h	PROPN
ejpam-4963	253	9	)	)	PUNCT
ejpam-4963	253	10	.	.	PUNCT
ejpam-4963	254	1	then	then	ADV
ejpam-4963	254	2	there	there	PRON
ejpam-4963	254	3	exist	exist	VERB
ejpam-4963	254	4	u1	u1	NOUN
ejpam-4963	254	5	,	,	PUNCT
ejpam-4963	254	6	u2	u2	PROPN
ejpam-4963	254	7	∈	∈	PROPN
ejpam-4963	254	8	s	s	VERB
ejpam-4963	254	9	such	such	ADJ
ejpam-4963	254	10	that	that	DET
ejpam-4963	254	11	u1	u1	PROPN
ejpam-4963	254	12	∈	∈	PROPN
ejpam-4963	254	13	v	v	ADP
ejpam-4963	254	14	(	(	PUNCT
ejpam-4963	254	15	g	g	NOUN
ejpam-4963	254	16	)	)	PUNCT
ejpam-4963	254	17	and	and	CCONJ
ejpam-4963	254	18	u2	u2	PROPN
ejpam-4963	254	19	∈	∈	PROPN
ejpam-4963	254	20	v	v	ADP
ejpam-4963	254	21	(	(	PUNCT
ejpam-4963	254	22	h	h	NOUN
ejpam-4963	254	23	)	)	PUNCT
ejpam-4963	254	24	.	.	PUNCT
ejpam-4963	255	1	since	since	SCONJ
ejpam-4963	255	2	every	every	DET
ejpam-4963	255	3	vertices	vertex	NOUN
ejpam-4963	255	4	in	in	ADP
ejpam-4963	255	5	h	h	NOUN
ejpam-4963	255	6	are	be	AUX
ejpam-4963	255	7	adjacent	adjacent	ADJ
ejpam-4963	255	8	to	to	PART
ejpam-4963	255	9	u1	u1	VERB
ejpam-4963	255	10	,	,	PUNCT
ejpam-4963	255	11	this	this	PRON
ejpam-4963	255	12	means	mean	VERB
ejpam-4963	255	13	that	that	SCONJ
ejpam-4963	255	14	there	there	PRON
ejpam-4963	255	15	are	be	VERB
ejpam-4963	255	16	vertices	vertex	NOUN
ejpam-4963	255	17	in	in	ADP
ejpam-4963	255	18	h	h	NOUN
ejpam-4963	255	19	adjacent	adjacent	ADJ
ejpam-4963	255	20	to	to	ADP
ejpam-4963	255	21	both	both	PRON
ejpam-4963	255	22	u1	u1	NOUN
ejpam-4963	255	23	and	and	CCONJ
ejpam-4963	255	24	u2	u2	NOUN
ejpam-4963	255	25	,	,	PUNCT
ejpam-4963	255	26	a	a	DET
ejpam-4963	255	27	contradiction	contradiction	NOUN
ejpam-4963	255	28	.	.	PUNCT
ejpam-4963	256	1	hence	hence	ADV
ejpam-4963	256	2	,	,	PUNCT
ejpam-4963	256	3	all	all	PRON
ejpam-4963	256	4	of	of	ADP
ejpam-4963	256	5	the	the	DET
ejpam-4963	256	6	cases	case	NOUN
ejpam-4963	256	7	lead	lead	VERB
ejpam-4963	256	8	to	to	ADP
ejpam-4963	256	9	contradiction	contradiction	NOUN
ejpam-4963	256	10	.	.	PUNCT
ejpam-4963	257	1	therefore	therefore	ADV
ejpam-4963	257	2	,	,	PUNCT
ejpam-4963	257	3	there	there	PRON
ejpam-4963	257	4	does	do	AUX
ejpam-4963	257	5	not	not	PART
ejpam-4963	257	6	exist	exist	VERB
ejpam-4963	257	7	a	a	DET
ejpam-4963	257	8	γpe0	γpe0	NOUN
ejpam-4963	257	9	-	-	PUNCT
ejpam-4963	257	10	set	set	NOUN
ejpam-4963	257	11	of	of	ADP
ejpam-4963	257	12	g	g	PROPN
ejpam-4963	257	13	◦	◦	NOUN
ejpam-4963	257	14	h	h	NOUN
ejpam-4963	257	15	for	for	ADP
ejpam-4963	257	16	any	any	DET
ejpam-4963	257	17	non	non	ADJ
ejpam-4963	257	18	-	-	ADJ
ejpam-4963	257	19	trivial	trivial	ADJ
ejpam-4963	257	20	graphs	graph	NOUN
ejpam-4963	257	21	g	g	PROPN
ejpam-4963	257	22	and	and	CCONJ
ejpam-4963	257	23	h.	h.	PROPN
ejpam-4963	257	24	theorem	theorem	PROPN
ejpam-4963	257	25	13	13	NUM
ejpam-4963	257	26	.	.	PUNCT
ejpam-4963	258	1	let	let	VERB
ejpam-4963	258	2	g	g	NOUN
ejpam-4963	258	3	and	and	CCONJ
ejpam-4963	258	4	h	h	NOUN
ejpam-4963	258	5	be	be	VERB
ejpam-4963	258	6	any	any	DET
ejpam-4963	258	7	graphs	graph	NOUN
ejpam-4963	258	8	having	have	VERB
ejpam-4963	258	9	γpe0	γpe0	NOUN
ejpam-4963	258	10	-	-	PUNCT
ejpam-4963	258	11	sets	set	NOUN
ejpam-4963	258	12	.	.	PUNCT
ejpam-4963	259	1	then	then	ADV
ejpam-4963	259	2	g	g	PROPN
ejpam-4963	259	3	◦	◦	NOUN
ejpam-4963	259	4	h	h	NOUN
ejpam-4963	259	5	does	do	AUX
ejpam-4963	259	6	not	not	PART
ejpam-4963	259	7	have	have	VERB
ejpam-4963	259	8	γpe0	γpe0	NOUN
ejpam-4963	259	9	-	-	PUNCT
ejpam-4963	259	10	set	set	NOUN
ejpam-4963	259	11	,	,	PUNCT
ejpam-4963	259	12	but	but	CCONJ
ejpam-4963	259	13	g+h	g+h	PROPN
ejpam-4963	259	14	has	have	VERB
ejpam-4963	259	15	a	a	DET
ejpam-4963	259	16	γe	γe	NOUN
ejpam-4963	259	17	-	-	PUNCT
ejpam-4963	259	18	set	set	NOUN
ejpam-4963	259	19	.	.	PUNCT
ejpam-4963	260	1	proof	proof	NOUN
ejpam-4963	260	2	.	.	PUNCT
ejpam-4963	261	1	suppose	suppose	VERB
ejpam-4963	261	2	u	u	PRON
ejpam-4963	261	3	∈	∈	PROPN
ejpam-4963	261	4	s1	s1	PROPN
ejpam-4963	261	5	⊆	⊆	NUM
ejpam-4963	261	6	v	v	NOUN
ejpam-4963	261	7	(	(	PUNCT
ejpam-4963	261	8	g	g	NOUN
ejpam-4963	261	9	)	)	PUNCT
ejpam-4963	261	10	.	.	PUNCT
ejpam-4963	262	1	then	then	ADV
ejpam-4963	262	2	uvi	uvi	PROPN
ejpam-4963	262	3	∈	∈	PROPN
ejpam-4963	262	4	e(g	e(g	PROPN
ejpam-4963	262	5	◦	◦	PROPN
ejpam-4963	262	6	h	h	NOUN
ejpam-4963	262	7	)	)	PUNCT
ejpam-4963	262	8	for	for	ADP
ejpam-4963	262	9	all	all	DET
ejpam-4963	262	10	vi	vi	PROPN
ejpam-4963	262	11	∈	∈	NOUN
ejpam-4963	262	12	v	v	NOUN
ejpam-4963	262	13	(	(	PUNCT
ejpam-4963	262	14	h	h	NOUN
ejpam-4963	262	15	)	)	PUNCT
ejpam-4963	262	16	\	\	NOUN
ejpam-4963	262	17	s2	s2	PROPN
ejpam-4963	262	18	,	,	PUNCT
ejpam-4963	262	19	where	where	SCONJ
ejpam-4963	262	20	s2	s2	PROPN
ejpam-4963	262	21	is	be	AUX
ejpam-4963	262	22	a	a	DET
ejpam-4963	262	23	γpe0	γpe0	NOUN
ejpam-4963	262	24	-	-	PUNCT
ejpam-4963	262	25	set	set	NOUN
ejpam-4963	262	26	of	of	ADP
ejpam-4963	262	27	h.	h.	PROPN
ejpam-4963	262	28	but	but	CCONJ
ejpam-4963	262	29	vivj	vivj	PROPN
ejpam-4963	262	30	∈	∈	PROPN
ejpam-4963	262	31	e(g	e(g	PROPN
ejpam-4963	262	32	◦	◦	PROPN
ejpam-4963	262	33	h	h	NOUN
ejpam-4963	262	34	)	)	PUNCT
ejpam-4963	262	35	for	for	ADP
ejpam-4963	262	36	some	some	DET
ejpam-4963	262	37	vj	vj	PRON
ejpam-4963	262	38	∈	∈	PROPN
ejpam-4963	262	39	s2	s2	PROPN
ejpam-4963	262	40	,	,	PUNCT
ejpam-4963	262	41	i	i	PROPN
ejpam-4963	262	42	̸=	̸=	PROPN
ejpam-4963	262	43	j.	j.	PROPN
ejpam-4963	262	44	this	this	PRON
ejpam-4963	262	45	means	mean	VERB
ejpam-4963	262	46	that	that	SCONJ
ejpam-4963	262	47	s1	s1	NOUN
ejpam-4963	262	48	∪	∪	NOUN
ejpam-4963	262	49	s2	s2	NOUN
ejpam-4963	262	50	is	be	AUX
ejpam-4963	262	51	no	no	ADV
ejpam-4963	262	52	longer	long	ADV
ejpam-4963	262	53	γp	γp	NOUN
ejpam-4963	262	54	-	-	PUNCT
ejpam-4963	262	55	set	set	NOUN
ejpam-4963	262	56	.	.	PUNCT
ejpam-4963	263	1	moreover	moreover	ADV
ejpam-4963	263	2	,	,	PUNCT
ejpam-4963	263	3	by	by	ADP
ejpam-4963	263	4	theorem	theorem	NOUN
ejpam-4963	263	5	12	12	NUM
ejpam-4963	263	6	,	,	PUNCT
ejpam-4963	263	7	s1	s1	NOUN
ejpam-4963	263	8	and	and	CCONJ
ejpam-4963	263	9	s2	s2	NOUN
ejpam-4963	263	10	are	be	AUX
ejpam-4963	263	11	no	no	ADV
ejpam-4963	263	12	longer	long	ADJ
ejpam-4963	263	13	γpe0	γpe0	NOUN
ejpam-4963	263	14	-	-	PUNCT
ejpam-4963	263	15	sets	set	NOUN
ejpam-4963	263	16	.	.	PUNCT
ejpam-4963	264	1	consequently	consequently	ADV
ejpam-4963	264	2	,	,	PUNCT
ejpam-4963	264	3	s1	s1	NOUN
ejpam-4963	264	4	,	,	PUNCT
ejpam-4963	264	5	s2	s2	NOUN
ejpam-4963	264	6	and	and	CCONJ
ejpam-4963	264	7	s1	s1	PROPN
ejpam-4963	264	8	∪	∪	X
ejpam-4963	264	9	s2	s2	NOUN
ejpam-4963	264	10	are	be	AUX
ejpam-4963	264	11	no	no	ADV
ejpam-4963	264	12	longer	long	ADV
ejpam-4963	264	13	γ0	γ0	NOUN
ejpam-4963	264	14	-	-	PUNCT
ejpam-4963	264	15	sets	set	NOUN
ejpam-4963	264	16	since	since	SCONJ
ejpam-4963	264	17	the	the	DET
ejpam-4963	264	18	elements	element	NOUN
ejpam-4963	264	19	are	be	AUX
ejpam-4963	264	20	adjacents	adjacent	NOUN
ejpam-4963	264	21	.	.	PUNCT
ejpam-4963	265	1	lastly	lastly	ADV
ejpam-4963	265	2	,	,	PUNCT
ejpam-4963	265	3	since	since	SCONJ
ejpam-4963	265	4	every	every	DET
ejpam-4963	265	5	vertices	vertex	NOUN
ejpam-4963	265	6	in	in	ADP
ejpam-4963	265	7	v	v	NOUN
ejpam-4963	265	8	(	(	PUNCT
ejpam-4963	265	9	g	g	PROPN
ejpam-4963	265	10	◦	◦	NOUN
ejpam-4963	265	11	h	h	NOUN
ejpam-4963	265	12	)	)	PUNCT
ejpam-4963	265	13	\	\	PUNCT
ejpam-4963	265	14	(	(	PUNCT
ejpam-4963	265	15	s1	s1	PROPN
ejpam-4963	265	16	∪	∪	X
ejpam-4963	265	17	s2	s2	PROPN
ejpam-4963	265	18	)	)	PUNCT
ejpam-4963	265	19	,	,	PUNCT
ejpam-4963	265	20	it	it	PRON
ejpam-4963	265	21	follows	follow	VERB
ejpam-4963	265	22	that	that	SCONJ
ejpam-4963	265	23	s1	s1	PROPN
ejpam-4963	265	24	∪	∪	NOUN
ejpam-4963	265	25	s2	s2	PROPN
ejpam-4963	265	26	is	be	AUX
ejpam-4963	265	27	γe	γe	NOUN
ejpam-4963	265	28	-	-	PUNCT
ejpam-4963	265	29	set	set	ADJ
ejpam-4963	265	30	.	.	PUNCT
ejpam-4963	266	1	this	this	PRON
ejpam-4963	266	2	proves	prove	VERB
ejpam-4963	266	3	the	the	DET
ejpam-4963	266	4	claim	claim	NOUN
ejpam-4963	266	5	.	.	PUNCT
ejpam-4963	267	1	remark	remark	NOUN
ejpam-4963	267	2	2	2	NUM
ejpam-4963	267	3	.	.	PUNCT
ejpam-4963	268	1	the	the	DET
ejpam-4963	268	2	γe	γe	NOUN
ejpam-4963	268	3	-	-	PUNCT
ejpam-4963	268	4	set	set	NOUN
ejpam-4963	268	5	of	of	ADP
ejpam-4963	268	6	g	g	PROPN
ejpam-4963	268	7	◦	◦	NOUN
ejpam-4963	268	8	h	h	NOUN
ejpam-4963	268	9	of	of	ADP
ejpam-4963	268	10	theorem	theorem	NOUN
ejpam-4963	268	11	13	13	NUM
ejpam-4963	268	12	is	be	AUX
ejpam-4963	268	13	not	not	PART
ejpam-4963	268	14	necessarily	necessarily	ADV
ejpam-4963	268	15	minimal	minimal	ADJ
ejpam-4963	268	16	.	.	PUNCT
ejpam-4963	269	1	proposition	proposition	NOUN
ejpam-4963	269	2	6	6	NUM
ejpam-4963	269	3	.	.	PUNCT
ejpam-4963	270	1	let	let	VERB
ejpam-4963	270	2	g	g	PRON
ejpam-4963	270	3	be	be	AUX
ejpam-4963	270	4	a	a	DET
ejpam-4963	270	5	trivial	trivial	ADJ
ejpam-4963	270	6	graph	graph	NOUN
ejpam-4963	270	7	.	.	PUNCT
ejpam-4963	271	1	then	then	ADV
ejpam-4963	271	2	γpe0(g	γpe0(g	X
ejpam-4963	271	3	◦	◦	PROPN
ejpam-4963	271	4	kn	kn	PROPN
ejpam-4963	271	5	)	)	PUNCT
ejpam-4963	271	6	=	=	SYM
ejpam-4963	271	7	γpe0(kn	γpe0(kn	PROPN
ejpam-4963	271	8	◦	◦	NOUN
ejpam-4963	271	9	g	g	NOUN
ejpam-4963	271	10	)	)	PUNCT
ejpam-4963	271	11	=	=	SYM
ejpam-4963	271	12	1	1	X
ejpam-4963	271	13	.	.	PUNCT
ejpam-4963	272	1	acknowledgements	acknowledgement	NOUN
ejpam-4963	272	2	thank	thank	VERB
ejpam-4963	272	3	you	you	PRON
ejpam-4963	272	4	,	,	PUNCT
ejpam-4963	272	5	adamson	adamson	PROPN
ejpam-4963	272	6	university	university	PROPN
ejpam-4963	272	7	center	center	NOUN
ejpam-4963	272	8	for	for	ADP
ejpam-4963	272	9	research	research	NOUN
ejpam-4963	272	10	and	and	CCONJ
ejpam-4963	272	11	development	development	NOUN
ejpam-4963	272	12	for	for	ADP
ejpam-4963	272	13	the	the	DET
ejpam-4963	272	14	funding	funding	NOUN
ejpam-4963	272	15	of	of	ADP
ejpam-4963	272	16	this	this	DET
ejpam-4963	272	17	research	research	NOUN
ejpam-4963	272	18	works	work	VERB
ejpam-4963	272	19	.	.	PUNCT
ejpam-4963	273	1	references	reference	NOUN
ejpam-4963	273	2	[	[	X
ejpam-4963	273	3	1	1	NUM
ejpam-4963	273	4	]	]	X
ejpam-4963	273	5	c	c	PROPN
ejpam-4963	273	6	armada	armada	PROPN
ejpam-4963	273	7	and	and	CCONJ
ejpam-4963	273	8	j	j	PROPN
ejpam-4963	273	9	hamja	hamja	PROPN
ejpam-4963	273	10	.	.	PUNCT
ejpam-4963	274	1	perfect	perfect	PROPN
ejpam-4963	274	2	isolate	isolate	NOUN
ejpam-4963	274	3	domination	domination	NOUN
ejpam-4963	274	4	in	in	ADP
ejpam-4963	274	5	graphs	graph	NOUN
ejpam-4963	274	6	.	.	PUNCT
ejpam-4963	275	1	european	european	ADJ
ejpam-4963	275	2	journal	journal	PROPN
ejpam-4963	275	3	of	of	ADP
ejpam-4963	275	4	pure	pure	ADJ
ejpam-4963	275	5	and	and	CCONJ
ejpam-4963	275	6	applied	applied	ADJ
ejpam-4963	275	7	mathematics	mathematic	NOUN
ejpam-4963	275	8	,	,	PUNCT
ejpam-4963	275	9	16(22):1362–1341	16(22):1362–1341	NUM
ejpam-4963	275	10	,	,	PUNCT
ejpam-4963	275	11	2023	2023	NUM
ejpam-4963	275	12	.	.	PUNCT
ejpam-4963	276	1	[	[	X
ejpam-4963	276	2	2	2	NUM
ejpam-4963	276	3	]	]	X
ejpam-4963	276	4	c	c	NOUN
ejpam-4963	276	5	berge	berge	NOUN
ejpam-4963	276	6	.	.	PUNCT
ejpam-4963	277	1	the	the	DET
ejpam-4963	277	2	theory	theory	NOUN
ejpam-4963	277	3	of	of	ADP
ejpam-4963	277	4	graphs	graph	NOUN
ejpam-4963	277	5	and	and	CCONJ
ejpam-4963	277	6	its	its	PRON
ejpam-4963	277	7	applications	application	NOUN
ejpam-4963	277	8	.	.	PUNCT
ejpam-4963	278	1	greenwood	greenwood	PROPN
ejpam-4963	278	2	press	press	PROPN
ejpam-4963	278	3	,	,	PUNCT
ejpam-4963	278	4	1982	1982	NUM
ejpam-4963	278	5	.	.	PUNCT
ejpam-4963	279	1	references	reference	NOUN
ejpam-4963	279	2	978	978	NUM
ejpam-4963	280	1	[	[	X
ejpam-4963	280	2	3	3	NUM
ejpam-4963	280	3	]	]	PUNCT
ejpam-4963	280	4	m	m	AUX
ejpam-4963	280	5	caay	caay	VERB
ejpam-4963	280	6	.	.	PUNCT
ejpam-4963	281	1	equitable	equitable	ADJ
ejpam-4963	281	2	rings	ring	NOUN
ejpam-4963	281	3	domination	domination	NOUN
ejpam-4963	281	4	in	in	ADP
ejpam-4963	281	5	graphs	graph	NOUN
ejpam-4963	281	6	.	.	PUNCT
ejpam-4963	282	1	journal	journal	NOUN
ejpam-4963	282	2	of	of	ADP
ejpam-4963	282	3	algebraic	algebraic	PROPN
ejpam-4963	282	4	systems	system	NOUN
ejpam-4963	282	5	,	,	PUNCT
ejpam-4963	282	6	(	(	PUNCT
ejpam-4963	282	7	(	(	PUNCT
ejpam-4963	282	8	in	in	ADP
ejpam-4963	282	9	preparation	preparation	NOUN
ejpam-4963	282	10	)	)	PUNCT
ejpam-4963	282	11	,	,	PUNCT
ejpam-4963	282	12	2024	2024	NUM
ejpam-4963	282	13	.	.	PUNCT
ejpam-4963	283	1	[	[	X
ejpam-4963	283	2	4	4	X
ejpam-4963	283	3	]	]	PUNCT
ejpam-4963	283	4	m	m	AUX
ejpam-4963	283	5	caay	caay	ADJ
ejpam-4963	283	6	and	and	CCONJ
ejpam-4963	283	7	e	e	NOUN
ejpam-4963	283	8	arugay	arugay	NOUN
ejpam-4963	283	9	.	.	PUNCT
ejpam-4963	284	1	perfect	perfect	ADJ
ejpam-4963	284	2	equitable	equitable	ADJ
ejpam-4963	284	3	domination	domination	NOUN
ejpam-4963	284	4	of	of	ADP
ejpam-4963	284	5	some	some	DET
ejpam-4963	284	6	graphs	graph	NOUN
ejpam-4963	284	7	.	.	PUNCT
ejpam-4963	285	1	international	international	ADJ
ejpam-4963	285	2	mathematical	mathematical	PROPN
ejpam-4963	285	3	forum	forum	PROPN
ejpam-4963	285	4	,	,	PUNCT
ejpam-4963	285	5	1(9):891–900	1(9):891–900	NUM
ejpam-4963	285	6	,	,	PUNCT
ejpam-4963	285	7	2017	2017	NUM
ejpam-4963	285	8	.	.	PUNCT
ejpam-4963	286	1	[	[	X
ejpam-4963	286	2	5	5	NUM
ejpam-4963	286	3	]	]	PUNCT
ejpam-4963	286	4	m	m	AUX
ejpam-4963	286	5	caay	caay	ADJ
ejpam-4963	286	6	and	and	CCONJ
ejpam-4963	286	7	m	m	AUX
ejpam-4963	286	8	durog	durog	VERB
ejpam-4963	286	9	.	.	PUNCT
ejpam-4963	287	1	on	on	ADP
ejpam-4963	287	2	some	some	DET
ejpam-4963	287	3	independent	independent	ADJ
ejpam-4963	287	4	equitable	equitable	ADJ
ejpam-4963	287	5	domination	domination	NOUN
ejpam-4963	287	6	of	of	ADP
ejpam-4963	287	7	graphs	graph	NOUN
ejpam-4963	287	8	.	.	PUNCT
ejpam-4963	288	1	gulf	gulf	PROPN
ejpam-4963	288	2	journal	journal	PROPN
ejpam-4963	288	3	of	of	ADP
ejpam-4963	288	4	mathematics	mathematic	NOUN
ejpam-4963	288	5	,	,	PUNCT
ejpam-4963	288	6	11(1):57–64	11(1):57–64	NUM
ejpam-4963	288	7	,	,	PUNCT
ejpam-4963	288	8	2021	2021	NUM
ejpam-4963	288	9	.	.	PUNCT
ejpam-4963	289	1	[	[	X
ejpam-4963	289	2	6	6	NUM
ejpam-4963	289	3	]	]	PUNCT
ejpam-4963	289	4	m	m	AUX
ejpam-4963	289	5	caay	caay	ADJ
ejpam-4963	289	6	and	and	CCONJ
ejpam-4963	289	7	s	s	VERB
ejpam-4963	289	8	palahang	palahang	NOUN
ejpam-4963	289	9	.	.	PUNCT
ejpam-4963	290	1	on	on	ADP
ejpam-4963	290	2	some	some	DET
ejpam-4963	290	3	results	result	NOUN
ejpam-4963	290	4	of	of	ADP
ejpam-4963	290	5	perfect	perfect	ADJ
ejpam-4963	290	6	dominations	domination	NOUN
ejpam-4963	290	7	of	of	ADP
ejpam-4963	290	8	some	some	DET
ejpam-4963	290	9	graphs	graph	NOUN
ejpam-4963	290	10	.	.	PUNCT
ejpam-4963	291	1	twms	twms	PROPN
ejpam-4963	291	2	journal	journal	PROPN
ejpam-4963	291	3	of	of	ADP
ejpam-4963	291	4	applied	apply	VERB
ejpam-4963	291	5	and	and	CCONJ
ejpam-4963	291	6	engineering	engineering	NOUN
ejpam-4963	291	7	mathematics	mathematic	NOUN
ejpam-4963	291	8	,	,	PUNCT
ejpam-4963	291	9	12(2):600–607	12(2):600–607	PROPN
ejpam-4963	291	10	,	,	PUNCT
ejpam-4963	291	11	2022	2022	NUM
ejpam-4963	291	12	.	.	PUNCT
ejpam-4963	292	1	[	[	X
ejpam-4963	292	2	7	7	X
ejpam-4963	292	3	]	]	X
ejpam-4963	292	4	g	g	PROPN
ejpam-4963	292	5	chartrand	chartrand	NOUN
ejpam-4963	292	6	.	.	PUNCT
ejpam-4963	293	1	introductory	introductory	ADJ
ejpam-4963	293	2	graph	graph	NOUN
ejpam-4963	293	3	theory	theory	NOUN
ejpam-4963	293	4	.	.	PUNCT
ejpam-4963	294	1	dover	dover	PROPN
ejpam-4963	294	2	publications	publication	NOUN
ejpam-4963	294	3	,	,	PUNCT
ejpam-4963	294	4	1984	1984	NUM
ejpam-4963	294	5	.	.	PUNCT
ejpam-4963	295	1	[	[	X
ejpam-4963	295	2	8	8	NUM
ejpam-4963	295	3	]	]	PUNCT
ejpam-4963	295	4	a	a	DET
ejpam-4963	295	5	anitha	anitha	ADJ
ejpam-4963	295	6	et.al	et.al	PROPN
ejpam-4963	295	7	.	.	PUNCT
ejpam-4963	296	1	equitable	equitable	ADJ
ejpam-4963	296	2	domination	domination	NOUN
ejpam-4963	296	3	in	in	ADP
ejpam-4963	296	4	graphs	graph	NOUN
ejpam-4963	296	5	.	.	PUNCT
ejpam-4963	297	1	discrete	discrete	ADJ
ejpam-4963	297	2	mathematics	mathematic	NOUN
ejpam-4963	297	3	,	,	PUNCT
ejpam-4963	297	4	algorithm	algorithm	NOUN
ejpam-4963	297	5	and	and	CCONJ
ejpam-4963	297	6	applications	application	NOUN
ejpam-4963	297	7	,	,	PUNCT
ejpam-4963	297	8	3(3):1726–1732	3(3):1726–1732	NUM
ejpam-4963	297	9	,	,	PUNCT
ejpam-4963	297	10	2011	2011	NUM
ejpam-4963	297	11	.	.	PUNCT
ejpam-4963	298	1	[	[	X
ejpam-4963	298	2	9	9	NUM
ejpam-4963	298	3	]	]	PUNCT
ejpam-4963	298	4	g	g	PROPN
ejpam-4963	298	5	deepak	deepak	PROPN
ejpam-4963	298	6	et.al	et.al	PROPN
ejpam-4963	298	7	.	.	PUNCT
ejpam-4963	299	1	the	the	DET
ejpam-4963	299	2	equitable	equitable	ADJ
ejpam-4963	299	3	bondage	bondage	NOUN
ejpam-4963	299	4	number	number	NOUN
ejpam-4963	299	5	of	of	ADP
ejpam-4963	299	6	a	a	DET
ejpam-4963	299	7	graph	graph	NOUN
ejpam-4963	299	8	.	.	PUNCT
ejpam-4963	300	1	research	research	NOUN
ejpam-4963	300	2	journal	journal	NOUN
ejpam-4963	300	3	of	of	ADP
ejpam-4963	300	4	pure	pure	ADJ
ejpam-4963	300	5	algebra	algebra	NOUN
ejpam-4963	300	6	,	,	PUNCT
ejpam-4963	300	7	12(18):209–212	12(18):209–212	NUM
ejpam-4963	300	8	,	,	PUNCT
ejpam-4963	300	9	2011	2011	NUM
ejpam-4963	300	10	.	.	PUNCT
ejpam-4963	301	1	[	[	X
ejpam-4963	301	2	10	10	NUM
ejpam-4963	301	3	]	]	X
ejpam-4963	301	4	l	l	NOUN
ejpam-4963	301	5	rakim	rakim	PROPN
ejpam-4963	301	6	et.al	et.al	PROPN
ejpam-4963	301	7	.	.	PUNCT
ejpam-4963	302	1	perfect	perfect	ADJ
ejpam-4963	302	2	hop	hop	NOUN
ejpam-4963	302	3	domination	domination	NOUN
ejpam-4963	302	4	in	in	ADP
ejpam-4963	302	5	graphs	graph	NOUN
ejpam-4963	302	6	.	.	PUNCT
ejpam-4963	303	1	applied	apply	VERB
ejpam-4963	303	2	mathematical	mathematical	ADJ
ejpam-4963	303	3	sciences	sciences	PROPN
ejpam-4963	303	4	,	,	PUNCT
ejpam-4963	303	5	12(13):635–649	12(13):635–649	NUM
ejpam-4963	303	6	,	,	PUNCT
ejpam-4963	303	7	2002	2002	NUM
ejpam-4963	303	8	.	.	PUNCT
ejpam-4963	304	1	[	[	X
ejpam-4963	304	2	11	11	NUM
ejpam-4963	304	3	]	]	X
ejpam-4963	304	4	s	s	PART
ejpam-4963	304	5	rashmi	rashmi	PROPN
ejpam-4963	304	6	et.al	et.al	PROPN
ejpam-4963	304	7	.	.	PUNCT
ejpam-4963	305	1	perfect	perfect	ADJ
ejpam-4963	305	2	secure	secure	ADJ
ejpam-4963	305	3	domination	domination	NOUN
ejpam-4963	305	4	in	in	ADP
ejpam-4963	305	5	graphs	graph	NOUN
ejpam-4963	305	6	.	.	PUNCT
ejpam-4963	306	1	categories	category	NOUN
ejpam-4963	306	2	and	and	CCONJ
ejpam-4963	306	3	general	general	ADJ
ejpam-4963	306	4	algebraic	algebraic	ADJ
ejpam-4963	306	5	structures	structure	NOUN
ejpam-4963	306	6	with	with	ADP
ejpam-4963	306	7	applications	application	NOUN
ejpam-4963	306	8	.	.	PUNCT
ejpam-4963	307	1	special	special	ADJ
ejpam-4963	307	2	issue	issue	NOUN
ejpam-4963	307	3	on	on	ADP
ejpam-4963	307	4	the	the	DET
ejpam-4963	307	5	occassion	occassion	NOUN
ejpam-4963	307	6	of	of	ADP
ejpam-4963	307	7	banaschewski	banaschewski	PROPN
ejpam-4963	307	8	’s	’s	PART
ejpam-4963	307	9	90th	90th	ADJ
ejpam-4963	307	10	birthday	birthday	NOUN
ejpam-4963	307	11	,	,	PUNCT
ejpam-4963	307	12	page	page	NOUN
ejpam-4963	307	13	125–140	125–140	NUM
ejpam-4963	307	14	.	.	PROPN
ejpam-4963	307	15	,	,	PUNCT
ejpam-4963	307	16	2017	2017	NUM
ejpam-4963	307	17	.	.	PUNCT
ejpam-4963	308	1	[	[	X
ejpam-4963	308	2	12	12	NUM
ejpam-4963	308	3	]	]	X
ejpam-4963	308	4	r	r	NOUN
ejpam-4963	308	5	frucht	frucht	NOUN
ejpam-4963	308	6	and	and	CCONJ
ejpam-4963	308	7	f	f	PROPN
ejpam-4963	308	8	harary	harary	NOUN
ejpam-4963	308	9	.	.	PUNCT
ejpam-4963	309	1	on	on	ADP
ejpam-4963	309	2	the	the	DET
ejpam-4963	309	3	corona	corona	NOUN
ejpam-4963	309	4	of	of	ADP
ejpam-4963	309	5	two	two	NUM
ejpam-4963	309	6	graphs	graph	NOUN
ejpam-4963	309	7	.	.	PUNCT
ejpam-4963	310	1	aequationes	aequatione	NOUN
ejpam-4963	310	2	mathematicae	mathematicae	PROPN
ejpam-4963	310	3	,	,	PUNCT
ejpam-4963	310	4	4:322–325	4:322–325	PROPN
ejpam-4963	310	5	,	,	PUNCT
ejpam-4963	310	6	1970	1970	NUM
ejpam-4963	310	7	.	.	PUNCT
ejpam-4963	311	1	[	[	X
ejpam-4963	311	2	13	13	NUM
ejpam-4963	311	3	]	]	X
ejpam-4963	311	4	s	s	VERB
ejpam-4963	311	5	hamid	hamid	PROPN
ejpam-4963	311	6	and	and	CCONJ
ejpam-4963	311	7	s.	s.	PROPN
ejpam-4963	311	8	balamurugan	balamurugan	VERB
ejpam-4963	311	9	.	.	PUNCT
ejpam-4963	312	1	isolate	isolate	VERB
ejpam-4963	312	2	domination	domination	NOUN
ejpam-4963	312	3	in	in	ADP
ejpam-4963	312	4	graphs	graph	NOUN
ejpam-4963	312	5	.	.	PUNCT
ejpam-4963	313	1	arab	arab	PROPN
ejpam-4963	313	2	journal	journal	PROPN
ejpam-4963	313	3	of	of	ADP
ejpam-4963	313	4	mathematical	mathematical	ADJ
ejpam-4963	313	5	sciences	science	NOUN
ejpam-4963	313	6	,	,	PUNCT
ejpam-4963	313	7	22(2):232–242	22(2):232–242	PROPN
ejpam-4963	313	8	,	,	PUNCT
ejpam-4963	313	9	2015	2015	NUM
ejpam-4963	313	10	.	.	PUNCT
ejpam-4963	314	1	[	[	X
ejpam-4963	314	2	14	14	NUM
ejpam-4963	314	3	]	]	X
ejpam-4963	314	4	f	f	PROPN
ejpam-4963	314	5	harary	harary	NOUN
ejpam-4963	314	6	.	.	PUNCT
ejpam-4963	315	1	graph	graph	NOUN
ejpam-4963	315	2	theory	theory	NOUN
ejpam-4963	315	3	.	.	PUNCT
ejpam-4963	316	1	addison	addison	PROPN
ejpam-4963	316	2	-	-	PUNCT
ejpam-4963	316	3	wesley	wesley	PROPN
ejpam-4963	316	4	,	,	PUNCT
ejpam-4963	316	5	1994	1994	NUM
ejpam-4963	316	6	.	.	PUNCT
ejpam-4963	317	1	[	[	X
ejpam-4963	317	2	15	15	NUM
ejpam-4963	317	3	]	]	X
ejpam-4963	317	4	m	m	VERB
ejpam-4963	317	5	livingstout	livingstout	NOUN
ejpam-4963	317	6	and	and	CCONJ
ejpam-4963	317	7	q	q	NOUN
ejpam-4963	317	8	stout	stout	NOUN
ejpam-4963	317	9	.	.	PUNCT
ejpam-4963	318	1	distributing	distribute	VERB
ejpam-4963	318	2	resources	resource	NOUN
ejpam-4963	318	3	in	in	ADP
ejpam-4963	318	4	hypercube	hypercube	ADJ
ejpam-4963	318	5	computers	computer	NOUN
ejpam-4963	318	6	.	.	PUNCT
ejpam-4963	319	1	in	in	ADP
ejpam-4963	319	2	b.n	b.n	PROPN
ejpam-4963	319	3	.	.	PROPN
ejpam-4963	319	4	petrox	petrox	PROPN
ejpam-4963	319	5	and	and	CCONJ
ejpam-4963	319	6	f.	f.	PROPN
ejpam-4963	319	7	csaki	csaki	PROPN
ejpam-4963	319	8	,	,	PUNCT
ejpam-4963	319	9	editors	editor	NOUN
ejpam-4963	319	10	,	,	PUNCT
ejpam-4963	319	11	proc	proc	NOUN
ejpam-4963	319	12	.	.	PUNCT
ejpam-4963	320	1	3rd	3rd	ADJ
ejpam-4963	320	2	conf	conf	NOUN
ejpam-4963	320	3	.	.	PUNCT
ejpam-4963	321	1	on	on	ADP
ejpam-4963	321	2	hypercube	hypercube	ADJ
ejpam-4963	321	3	concurrent	concurrent	ADJ
ejpam-4963	321	4	computers	computer	NOUN
ejpam-4963	321	5	and	and	CCONJ
ejpam-4963	321	6	appl	appl	NOUN
ejpam-4963	321	7	..	..	PUNCT
ejpam-4963	321	8	,	,	PUNCT
ejpam-4963	321	9	page	page	NOUN
ejpam-4963	321	10	222–231	222–231	NUM
ejpam-4963	321	11	,	,	PUNCT
ejpam-4963	321	12	acm	acm	NOUN
ejpam-4963	321	13	,	,	PUNCT
ejpam-4963	321	14	1988	1988	NUM
ejpam-4963	321	15	.	.	PUNCT
ejpam-4963	322	1	[	[	X
ejpam-4963	322	2	16	16	NUM
ejpam-4963	322	3	]	]	X
ejpam-4963	322	4	m	m	VERB
ejpam-4963	322	5	livingstout	livingstout	NOUN
ejpam-4963	322	6	and	and	CCONJ
ejpam-4963	322	7	q	q	NOUN
ejpam-4963	322	8	stout	stout	PROPN
ejpam-4963	322	9	.	.	PUNCT
ejpam-4963	323	1	perfect	perfect	ADJ
ejpam-4963	323	2	dominating	dominating	NOUN
ejpam-4963	323	3	sets	set	NOUN
ejpam-4963	323	4	.	.	PUNCT
ejpam-4963	324	1	in	in	ADP
ejpam-4963	324	2	congressus	congressus	PROPN
ejpam-4963	324	3	numerantium	numerantium	PROPN
ejpam-4963	324	4	,	,	PUNCT
ejpam-4963	324	5	79(5):187–203	79(5):187–203	PROPN
ejpam-4963	324	6	,	,	PUNCT
ejpam-4963	324	7	1990	1990	NUM
ejpam-4963	324	8	.	.	PUNCT
ejpam-4963	325	1	[	[	X
ejpam-4963	325	2	17	17	NUM
ejpam-4963	325	3	]	]	X
ejpam-4963	325	4	g	g	NOUN
ejpam-4963	325	5	rajesekar	rajesekar	NOUN
ejpam-4963	325	6	and	and	CCONJ
ejpam-4963	325	7	a	a	DET
ejpam-4963	325	8	jeslet	jeslet	NOUN
ejpam-4963	325	9	kani	kani	PROPN
ejpam-4963	325	10	bala	bala	PROPN
ejpam-4963	325	11	.	.	PUNCT
ejpam-4963	326	1	k	k	ADJ
ejpam-4963	326	2	-	-	PUNCT
ejpam-4963	326	3	isolate	isolate	VERB
ejpam-4963	326	4	domination	domination	NOUN
ejpam-4963	326	5	number	number	NOUN
ejpam-4963	326	6	of	of	ADP
ejpam-4963	326	7	total	total	ADJ
ejpam-4963	326	8	graphs	graph	NOUN
ejpam-4963	326	9	.	.	PUNCT
ejpam-4963	327	1	international	international	ADJ
ejpam-4963	327	2	journal	journal	NOUN
ejpam-4963	327	3	of	of	ADP
ejpam-4963	327	4	emerging	emerge	VERB
ejpam-4963	327	5	technologies	technology	NOUN
ejpam-4963	327	6	and	and	CCONJ
ejpam-4963	327	7	innovative	innovative	ADJ
ejpam-4963	327	8	research	research	NOUN
ejpam-4963	327	9	,	,	PUNCT
ejpam-4963	327	10	8(3):1726	8(3):1726	NUM
ejpam-4963	327	11	–	–	PUNCT
ejpam-4963	327	12	1732	1732	NUM
ejpam-4963	327	13	,	,	PUNCT
ejpam-4963	327	14	2021	2021	NUM
ejpam-4963	327	15	.	.	PUNCT