id	sid	tid	token	lemma	pos
ejpam-4978	1	1	european	european	PROPN
ejpam-4978	1	2	journal	journal	PROPN
ejpam-4978	1	3	of	of	ADP
ejpam-4978	1	4	pure	pure	ADJ
ejpam-4978	1	5	and	and	CCONJ
ejpam-4978	1	6	applied	apply	VERB
ejpam-4978	1	7	mathematics	mathematic	NOUN
ejpam-4978	1	8	vol	vol	NOUN
ejpam-4978	1	9	.	.	PROPN
ejpam-4978	2	1	17	17	NUM
ejpam-4978	2	2	,	,	PUNCT
ejpam-4978	2	3	no	no	INTJ
ejpam-4978	2	4	.	.	NOUN
ejpam-4978	2	5	1	1	NUM
ejpam-4978	2	6	,	,	PUNCT
ejpam-4978	2	7	2024	2024	NUM
ejpam-4978	2	8	,	,	PUNCT
ejpam-4978	2	9	93	93	NUM
ejpam-4978	2	10	-	-	SYM
ejpam-4978	2	11	104	104	NUM
ejpam-4978	2	12	issn	issn	PROPN
ejpam-4978	2	13	1307	1307	NUM
ejpam-4978	2	14	-	-	SYM
ejpam-4978	2	15	5543	5543	NUM
ejpam-4978	2	16	–	–	PUNCT
ejpam-4978	2	17	ejpam.com	ejpam.com	X
ejpam-4978	2	18	published	publish	VERB
ejpam-4978	2	19	by	by	ADP
ejpam-4978	2	20	new	new	PROPN
ejpam-4978	2	21	york	york	PROPN
ejpam-4978	2	22	business	business	PROPN
ejpam-4978	2	23	global	global	ADJ
ejpam-4978	2	24	vertex	vertex	NOUN
ejpam-4978	2	25	cover	cover	VERB
ejpam-4978	2	26	hop	hop	NOUN
ejpam-4978	2	27	dominating	dominating	NOUN
ejpam-4978	2	28	sets	set	NOUN
ejpam-4978	2	29	in	in	ADP
ejpam-4978	2	30	graphs	graph	NOUN
ejpam-4978	2	31	vergel	vergel	NOUN
ejpam-4978	2	32	t.	t.	PROPN
ejpam-4978	2	33	bilar1,∗	bilar1,∗	PROPN
ejpam-4978	2	34	,	,	PUNCT
ejpam-4978	2	35	maria	maria	PROPN
ejpam-4978	2	36	andrea	andrea	PROPN
ejpam-4978	2	37	o.	o.	PROPN
ejpam-4978	2	38	bonsocan1	bonsocan1	PROPN
ejpam-4978	2	39	,	,	PUNCT
ejpam-4978	2	40	javier	javier	PROPN
ejpam-4978	2	41	a.	a.	PROPN
ejpam-4978	2	42	hassan2	hassan2	PROPN
ejpam-4978	2	43	,	,	PUNCT
ejpam-4978	2	44	susan	susan	PROPN
ejpam-4978	2	45	c.	c.	PROPN
ejpam-4978	2	46	dagondon1	dagondon1	PROPN
ejpam-4978	3	1	1department	1department	NUM
ejpam-4978	3	2	of	of	ADP
ejpam-4978	3	3	mathematics	mathematic	NOUN
ejpam-4978	3	4	and	and	CCONJ
ejpam-4978	3	5	statistics	statistic	NOUN
ejpam-4978	3	6	,	,	PUNCT
ejpam-4978	3	7	college	college	NOUN
ejpam-4978	3	8	of	of	ADP
ejpam-4978	3	9	science	science	NOUN
ejpam-4978	3	10	and	and	CCONJ
ejpam-4978	3	11	mathematics	mathematic	NOUN
ejpam-4978	3	12	,	,	PUNCT
ejpam-4978	3	13	msu	msu	PROPN
ejpam-4978	3	14	-	-	PUNCT
ejpam-4978	3	15	iligan	iligan	PROPN
ejpam-4978	3	16	institute	institute	PROPN
ejpam-4978	3	17	of	of	ADP
ejpam-4978	3	18	technology	technology	PROPN
ejpam-4978	3	19	,	,	PUNCT
ejpam-4978	3	20	9200	9200	NUM
ejpam-4978	3	21	iligan	iligan	ADJ
ejpam-4978	3	22	city	city	NOUN
ejpam-4978	3	23	,	,	PUNCT
ejpam-4978	3	24	philippines	philippine	VERB
ejpam-4978	3	25	2mathematics	2mathematics	NUM
ejpam-4978	3	26	and	and	CCONJ
ejpam-4978	3	27	sciences	sciences	PROPN
ejpam-4978	3	28	department	department	PROPN
ejpam-4978	3	29	,	,	PUNCT
ejpam-4978	3	30	college	college	NOUN
ejpam-4978	3	31	of	of	ADP
ejpam-4978	3	32	arts	art	NOUN
ejpam-4978	3	33	and	and	CCONJ
ejpam-4978	3	34	sciences	science	NOUN
ejpam-4978	3	35	,	,	PUNCT
ejpam-4978	3	36	msu	msu	PROPN
ejpam-4978	3	37	tawi	tawi	PROPN
ejpam-4978	3	38	-	-	PUNCT
ejpam-4978	3	39	tawi	tawi	PROPN
ejpam-4978	3	40	college	college	PROPN
ejpam-4978	3	41	of	of	ADP
ejpam-4978	3	42	technology	technology	NOUN
ejpam-4978	3	43	and	and	CCONJ
ejpam-4978	3	44	oceanography	oceanography	NOUN
ejpam-4978	3	45	,	,	PUNCT
ejpam-4978	3	46	bongao	bongao	NOUN
ejpam-4978	3	47	,	,	PUNCT
ejpam-4978	3	48	tawi	tawi	NOUN
ejpam-4978	3	49	-	-	PUNCT
ejpam-4978	3	50	tawi	tawi	NOUN
ejpam-4978	3	51	,	,	PUNCT
ejpam-4978	3	52	philippines	philippine	NOUN
ejpam-4978	3	53	abstract	abstract	ADJ
ejpam-4978	3	54	.	.	PUNCT
ejpam-4978	4	1	let	let	VERB
ejpam-4978	4	2	g	g	PRON
ejpam-4978	4	3	be	be	AUX
ejpam-4978	4	4	a	a	DET
ejpam-4978	4	5	graph	graph	NOUN
ejpam-4978	4	6	.	.	PUNCT
ejpam-4978	5	1	then	then	ADV
ejpam-4978	5	2	a	a	DET
ejpam-4978	5	3	subset	subset	NOUN
ejpam-4978	5	4	c	c	NOUN
ejpam-4978	5	5	of	of	ADP
ejpam-4978	5	6	vertices	vertex	NOUN
ejpam-4978	5	7	of	of	ADP
ejpam-4978	5	8	g	g	PROPN
ejpam-4978	5	9	is	be	AUX
ejpam-4978	5	10	called	call	VERB
ejpam-4978	5	11	a	a	DET
ejpam-4978	5	12	vertex	vertex	NOUN
ejpam-4978	5	13	cover	cover	NOUN
ejpam-4978	5	14	hop	hop	NOUN
ejpam-4978	5	15	dominating	dominating	NOUN
ejpam-4978	5	16	if	if	SCONJ
ejpam-4978	5	17	c	c	PROPN
ejpam-4978	5	18	is	be	AUX
ejpam-4978	5	19	both	both	CCONJ
ejpam-4978	5	20	a	a	DET
ejpam-4978	5	21	vertex	vertex	NOUN
ejpam-4978	5	22	cover	cover	NOUN
ejpam-4978	5	23	and	and	CCONJ
ejpam-4978	5	24	a	a	DET
ejpam-4978	5	25	hop	hop	NOUN
ejpam-4978	5	26	dominating	dominating	NOUN
ejpam-4978	5	27	of	of	ADP
ejpam-4978	5	28	g.	g.	PROPN
ejpam-4978	5	29	the	the	DET
ejpam-4978	5	30	vertex	vertex	NOUN
ejpam-4978	5	31	cover	cover	VERB
ejpam-4978	5	32	hop	hop	NOUN
ejpam-4978	5	33	domination	domination	NOUN
ejpam-4978	5	34	number	number	NOUN
ejpam-4978	5	35	of	of	ADP
ejpam-4978	5	36	g	g	NOUN
ejpam-4978	5	37	,	,	PUNCT
ejpam-4978	5	38	denoted	denote	VERB
ejpam-4978	5	39	by	by	ADP
ejpam-4978	5	40	γvch(g	γvch(g	NOUN
ejpam-4978	5	41	)	)	PUNCT
ejpam-4978	5	42	,	,	PUNCT
ejpam-4978	5	43	is	be	AUX
ejpam-4978	5	44	the	the	DET
ejpam-4978	5	45	minimum	minimum	ADJ
ejpam-4978	5	46	cardinality	cardinality	NOUN
ejpam-4978	5	47	among	among	ADP
ejpam-4978	5	48	all	all	DET
ejpam-4978	5	49	vertex	vertex	NOUN
ejpam-4978	5	50	cover	cover	NOUN
ejpam-4978	5	51	hop	hop	NOUN
ejpam-4978	5	52	dominating	dominating	NOUN
ejpam-4978	5	53	sets	set	NOUN
ejpam-4978	5	54	in	in	ADP
ejpam-4978	5	55	g.	g.	PROPN
ejpam-4978	5	56	in	in	ADP
ejpam-4978	5	57	this	this	DET
ejpam-4978	5	58	paper	paper	NOUN
ejpam-4978	5	59	,	,	PUNCT
ejpam-4978	5	60	we	we	PRON
ejpam-4978	5	61	initiate	initiate	VERB
ejpam-4978	5	62	the	the	DET
ejpam-4978	5	63	study	study	NOUN
ejpam-4978	5	64	of	of	ADP
ejpam-4978	5	65	vertex	vertex	NOUN
ejpam-4978	5	66	cover	cover	VERB
ejpam-4978	5	67	hop	hop	NOUN
ejpam-4978	5	68	domination	domination	NOUN
ejpam-4978	5	69	in	in	ADP
ejpam-4978	5	70	a	a	DET
ejpam-4978	5	71	graph	graph	NOUN
ejpam-4978	5	72	and	and	CCONJ
ejpam-4978	5	73	we	we	PRON
ejpam-4978	5	74	determine	determine	VERB
ejpam-4978	5	75	its	its	PRON
ejpam-4978	5	76	relations	relation	NOUN
ejpam-4978	5	77	with	with	ADP
ejpam-4978	5	78	other	other	ADJ
ejpam-4978	5	79	parameters	parameter	NOUN
ejpam-4978	5	80	in	in	ADP
ejpam-4978	5	81	graph	graph	NOUN
ejpam-4978	5	82	theory	theory	NOUN
ejpam-4978	5	83	.	.	PUNCT
ejpam-4978	6	1	we	we	PRON
ejpam-4978	6	2	characterize	characterize	VERB
ejpam-4978	6	3	the	the	DET
ejpam-4978	6	4	vertex	vertex	NOUN
ejpam-4978	6	5	cover	cover	NOUN
ejpam-4978	6	6	hop	hop	NOUN
ejpam-4978	6	7	dominating	dominating	NOUN
ejpam-4978	6	8	sets	set	NOUN
ejpam-4978	6	9	in	in	ADP
ejpam-4978	6	10	some	some	DET
ejpam-4978	6	11	special	special	ADJ
ejpam-4978	6	12	graphs	graph	NOUN
ejpam-4978	6	13	,	,	PUNCT
ejpam-4978	6	14	join	join	NOUN
ejpam-4978	6	15	,	,	PUNCT
ejpam-4978	6	16	and	and	CCONJ
ejpam-4978	6	17	corona	corona	NOUN
ejpam-4978	6	18	of	of	ADP
ejpam-4978	6	19	two	two	NUM
ejpam-4978	6	20	graphs	graph	NOUN
ejpam-4978	6	21	and	and	CCONJ
ejpam-4978	6	22	we	we	PRON
ejpam-4978	6	23	finally	finally	ADV
ejpam-4978	6	24	obtain	obtain	VERB
ejpam-4978	6	25	the	the	DET
ejpam-4978	6	26	exact	exact	ADJ
ejpam-4978	6	27	values	value	NOUN
ejpam-4978	6	28	or	or	CCONJ
ejpam-4978	6	29	bounds	bound	NOUN
ejpam-4978	6	30	of	of	ADP
ejpam-4978	6	31	the	the	DET
ejpam-4978	6	32	parameters	parameter	NOUN
ejpam-4978	6	33	of	of	ADP
ejpam-4978	6	34	these	these	DET
ejpam-4978	6	35	graphs	graph	NOUN
ejpam-4978	6	36	.	.	PUNCT
ejpam-4978	7	1	2020	2020	NUM
ejpam-4978	7	2	mathematics	mathematic	NOUN
ejpam-4978	7	3	subject	subject	NOUN
ejpam-4978	7	4	classifications	classification	NOUN
ejpam-4978	7	5	:	:	PUNCT
ejpam-4978	7	6	05c69	05c69	X
ejpam-4978	7	7	key	key	ADJ
ejpam-4978	7	8	words	word	NOUN
ejpam-4978	7	9	and	and	CCONJ
ejpam-4978	7	10	phrases	phrase	NOUN
ejpam-4978	7	11	:	:	PUNCT
ejpam-4978	7	12	vertex	vertex	NOUN
ejpam-4978	7	13	cover	cover	NOUN
ejpam-4978	7	14	,	,	PUNCT
ejpam-4978	7	15	vertex	vertex	NOUN
ejpam-4978	7	16	cover	cover	NOUN
ejpam-4978	7	17	hop	hop	NOUN
ejpam-4978	7	18	dominating	dominating	NOUN
ejpam-4978	7	19	set	set	NOUN
ejpam-4978	7	20	,	,	PUNCT
ejpam-4978	7	21	vertex	vertex	NOUN
ejpam-4978	7	22	cover	cover	VERB
ejpam-4978	7	23	hop	hop	NOUN
ejpam-4978	7	24	domination	domination	NOUN
ejpam-4978	7	25	number	number	NOUN
ejpam-4978	7	26	1	1	NUM
ejpam-4978	7	27	.	.	PUNCT
ejpam-4978	8	1	introduction	introduction	NOUN
ejpam-4978	8	2	one	one	NUM
ejpam-4978	8	3	of	of	ADP
ejpam-4978	8	4	the	the	DET
ejpam-4978	8	5	rapidly	rapidly	ADV
ejpam-4978	8	6	developing	develop	VERB
ejpam-4978	8	7	areas	area	NOUN
ejpam-4978	8	8	of	of	ADP
ejpam-4978	8	9	research	research	NOUN
ejpam-4978	8	10	in	in	ADP
ejpam-4978	8	11	graph	graph	NOUN
ejpam-4978	8	12	theory	theory	NOUN
ejpam-4978	8	13	is	be	AUX
ejpam-4978	8	14	the	the	DET
ejpam-4978	8	15	study	study	NOUN
ejpam-4978	8	16	of	of	ADP
ejpam-4978	8	17	domination	domination	NOUN
ejpam-4978	8	18	.	.	PUNCT
ejpam-4978	9	1	the	the	DET
ejpam-4978	9	2	idea	idea	NOUN
ejpam-4978	9	3	was	be	AUX
ejpam-4978	9	4	first	first	ADV
ejpam-4978	9	5	introduced	introduce	VERB
ejpam-4978	9	6	by	by	ADP
ejpam-4978	9	7	claude	claude	PROPN
ejpam-4978	9	8	berge	berge	NOUN
ejpam-4978	10	1	[	[	X
ejpam-4978	10	2	1	1	X
ejpam-4978	10	3	]	]	PUNCT
ejpam-4978	10	4	in	in	ADP
ejpam-4978	10	5	1958	1958	NUM
ejpam-4978	10	6	and	and	CCONJ
ejpam-4978	10	7	ore	ore	NOUN
ejpam-4978	11	1	[	[	X
ejpam-4978	11	2	6	6	NUM
ejpam-4978	11	3	]	]	PUNCT
ejpam-4978	11	4	in	in	ADP
ejpam-4978	11	5	1962	1962	NUM
ejpam-4978	11	6	.	.	PUNCT
ejpam-4978	12	1	moreover	moreover	ADV
ejpam-4978	12	2	,	,	PUNCT
ejpam-4978	12	3	graph	graph	NOUN
ejpam-4978	12	4	theory	theory	NOUN
ejpam-4978	12	5	has	have	AUX
ejpam-4978	12	6	also	also	ADV
ejpam-4978	12	7	witnessed	witness	VERB
ejpam-4978	12	8	a	a	DET
ejpam-4978	12	9	surge	surge	NOUN
ejpam-4978	12	10	of	of	ADP
ejpam-4978	12	11	interest	interest	NOUN
ejpam-4978	12	12	in	in	ADP
ejpam-4978	12	13	recent	recent	ADJ
ejpam-4978	12	14	research	research	NOUN
ejpam-4978	12	15	,	,	PUNCT
ejpam-4978	12	16	with	with	ADP
ejpam-4978	12	17	hop	hop	NOUN
ejpam-4978	12	18	domination	domination	NOUN
ejpam-4978	12	19	as	as	ADP
ejpam-4978	12	20	an	an	DET
ejpam-4978	12	21	intriguing	intriguing	ADJ
ejpam-4978	12	22	area	area	NOUN
ejpam-4978	12	23	of	of	ADP
ejpam-4978	12	24	investigation	investigation	NOUN
ejpam-4978	12	25	which	which	PRON
ejpam-4978	12	26	is	be	AUX
ejpam-4978	12	27	one	one	NUM
ejpam-4978	12	28	of	of	ADP
ejpam-4978	12	29	the	the	DET
ejpam-4978	12	30	variations	variation	NOUN
ejpam-4978	12	31	of	of	ADP
ejpam-4978	12	32	domination	domination	NOUN
ejpam-4978	12	33	in	in	ADP
ejpam-4978	12	34	graphs	graph	NOUN
ejpam-4978	12	35	.	.	PUNCT
ejpam-4978	13	1	first	first	ADV
ejpam-4978	13	2	introduced	introduce	VERB
ejpam-4978	13	3	and	and	CCONJ
ejpam-4978	13	4	investigated	investigate	VERB
ejpam-4978	13	5	by	by	ADP
ejpam-4978	13	6	natarajan	natarajan	PROPN
ejpam-4978	13	7	et	et	PROPN
ejpam-4978	13	8	al	al	PROPN
ejpam-4978	13	9	.	.	PUNCT
ejpam-4978	14	1	[	[	X
ejpam-4978	14	2	5	5	NUM
ejpam-4978	14	3	]	]	PUNCT
ejpam-4978	14	4	,	,	PUNCT
ejpam-4978	14	5	this	this	DET
ejpam-4978	14	6	concept	concept	NOUN
ejpam-4978	14	7	can	can	AUX
ejpam-4978	14	8	be	be	AUX
ejpam-4978	14	9	used	use	VERB
ejpam-4978	14	10	in	in	ADP
ejpam-4978	14	11	modelling	model	VERB
ejpam-4978	14	12	social	social	ADJ
ejpam-4978	14	13	networks	network	NOUN
ejpam-4978	14	14	.	.	PUNCT
ejpam-4978	15	1	over	over	ADP
ejpam-4978	15	2	time	time	NOUN
ejpam-4978	15	3	,	,	PUNCT
ejpam-4978	15	4	researchers	researcher	NOUN
ejpam-4978	15	5	have	have	AUX
ejpam-4978	15	6	extensively	extensively	ADV
ejpam-4978	15	7	studied	study	VERB
ejpam-4978	15	8	hop	hop	NOUN
ejpam-4978	15	9	domination	domination	NOUN
ejpam-4978	15	10	and	and	CCONJ
ejpam-4978	15	11	its	its	PRON
ejpam-4978	15	12	numerous	numerous	ADJ
ejpam-4978	15	13	variants	variant	NOUN
ejpam-4978	15	14	,	,	PUNCT
ejpam-4978	15	15	as	as	SCONJ
ejpam-4978	15	16	evidenced	evidence	VERB
ejpam-4978	15	17	by	by	ADP
ejpam-4978	15	18	a	a	DET
ejpam-4978	15	19	range	range	NOUN
ejpam-4978	15	20	of	of	ADP
ejpam-4978	15	21	notable	notable	ADJ
ejpam-4978	15	22	studies	study	NOUN
ejpam-4978	15	23	found	find	VERB
ejpam-4978	15	24	in	in	ADP
ejpam-4978	15	25	[	[	X
ejpam-4978	15	26	2–4	2–4	NUM
ejpam-4978	15	27	,	,	PUNCT
ejpam-4978	15	28	7–11	7–11	NOUN
ejpam-4978	15	29	]	]	PUNCT
ejpam-4978	15	30	.	.	PUNCT
ejpam-4978	16	1	in	in	ADP
ejpam-4978	16	2	this	this	DET
ejpam-4978	16	3	study	study	NOUN
ejpam-4978	16	4	,	,	PUNCT
ejpam-4978	16	5	we	we	PRON
ejpam-4978	16	6	will	will	AUX
ejpam-4978	16	7	introduce	introduce	VERB
ejpam-4978	16	8	the	the	DET
ejpam-4978	16	9	concept	concept	NOUN
ejpam-4978	16	10	of	of	ADP
ejpam-4978	16	11	vertex	vertex	NOUN
ejpam-4978	16	12	cover	cover	VERB
ejpam-4978	16	13	hop	hop	NOUN
ejpam-4978	16	14	domination	domination	NOUN
ejpam-4978	16	15	in	in	ADP
ejpam-4978	16	16	a	a	DET
ejpam-4978	16	17	graph	graph	NOUN
ejpam-4978	16	18	.	.	PUNCT
ejpam-4978	17	1	we	we	PRON
ejpam-4978	17	2	will	will	AUX
ejpam-4978	17	3	investigate	investigate	VERB
ejpam-4978	17	4	and	and	CCONJ
ejpam-4978	17	5	characterize	characterize	VERB
ejpam-4978	17	6	these	these	DET
ejpam-4978	17	7	sets	set	NOUN
ejpam-4978	17	8	in	in	ADP
ejpam-4978	17	9	some	some	DET
ejpam-4978	17	10	special	special	ADJ
ejpam-4978	17	11	graphs	graph	NOUN
ejpam-4978	17	12	and	and	CCONJ
ejpam-4978	17	13	graphs	graph	NOUN
ejpam-4978	17	14	obtained	obtain	VERB
ejpam-4978	17	15	from	from	ADP
ejpam-4978	17	16	some	some	DET
ejpam-4978	17	17	binary	binary	ADJ
ejpam-4978	17	18	operations	operation	NOUN
ejpam-4978	17	19	.	.	PUNCT
ejpam-4978	18	1	moreover	moreover	ADV
ejpam-4978	18	2	,	,	PUNCT
ejpam-4978	18	3	some	some	DET
ejpam-4978	18	4	bounds	bound	NOUN
ejpam-4978	18	5	or	or	CCONJ
ejpam-4978	18	6	exact	exact	ADJ
ejpam-4978	18	7	values	value	NOUN
ejpam-4978	18	8	of	of	ADP
ejpam-4978	18	9	these	these	DET
ejpam-4978	18	10	graphs	graph	NOUN
ejpam-4978	18	11	will	will	AUX
ejpam-4978	18	12	be	be	AUX
ejpam-4978	18	13	presented	present	VERB
ejpam-4978	18	14	.	.	PUNCT
ejpam-4978	19	1	∗corresponding	∗corresponde	VERB
ejpam-4978	19	2	author	author	NOUN
ejpam-4978	19	3	.	.	PUNCT
ejpam-4978	20	1	doi	doi	NOUN
ejpam-4978	20	2	:	:	PUNCT
ejpam-4978	20	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4978	https://doi.org/10.29020/nybg.ejpam.v17i1.4978	DET
ejpam-4978	20	4	email	email	NOUN
ejpam-4978	20	5	addresses	address	VERB
ejpam-4978	20	6	:	:	PUNCT
ejpam-4978	20	7	vergel.bilar@g.msuiit.edu.ph	vergel.bilar@g.msuiit.edu.ph	PROPN
ejpam-4978	20	8	(	(	PUNCT
ejpam-4978	20	9	v.t	v.t	PROPN
ejpam-4978	20	10	.	.	PROPN
ejpam-4978	20	11	bilar	bilar	PROPN
ejpam-4978	20	12	)	)	PUNCT
ejpam-4978	20	13	mariaandrea.bonsocan@g.msuiit.edu.ph	mariaandrea.bonsocan@g.msuiit.edu.ph	PROPN
ejpam-4978	20	14	(	(	PUNCT
ejpam-4978	20	15	m.a	m.a	PROPN
ejpam-4978	20	16	.	.	PROPN
ejpam-4978	20	17	bonsocan	bonsocan	PROPN
ejpam-4978	20	18	)	)	PUNCT
ejpam-4978	20	19	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-4978	20	20	(	(	PUNCT
ejpam-4978	20	21	j.	j.	PROPN
ejpam-4978	20	22	hassan	hassan	PROPN
ejpam-4978	20	23	)	)	PUNCT
ejpam-4978	20	24	susan.dagondon@g.msuiit.edu.ph	susan.dagondon@g.msuiit.edu.ph	PROPN
ejpam-4978	20	25	(	(	PUNCT
ejpam-4978	20	26	s.c	s.c	PROPN
ejpam-4978	20	27	.	.	PROPN
ejpam-4978	20	28	dagondon	dagondon	PROPN
ejpam-4978	20	29	)	)	PUNCT
ejpam-4978	20	30	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4978	21	1	93	93	NUM
ejpam-4978	21	2	©	©	ADP
ejpam-4978	21	3	2024	2024	NUM
ejpam-4978	21	4	ejpam	ejpam	NOUN
ejpam-4978	21	5	all	all	DET
ejpam-4978	21	6	rights	right	NOUN
ejpam-4978	21	7	reserved	reserve	VERB
ejpam-4978	21	8	.	.	PUNCT
ejpam-4978	22	1	v.	v.	ADP
ejpam-4978	22	2	t.	t.	PROPN
ejpam-4978	22	3	bilar	bilar	PROPN
ejpam-4978	22	4	et	et	PROPN
ejpam-4978	22	5	al	al	PROPN
ejpam-4978	22	6	.	.	PUNCT
ejpam-4978	22	7	/	/	SYM
ejpam-4978	22	8	eur	eur	PROPN
ejpam-4978	22	9	.	.	PUNCT
ejpam-4978	23	1	j.	j.	PROPN
ejpam-4978	23	2	pure	pure	PROPN
ejpam-4978	23	3	appl	appl	PROPN
ejpam-4978	23	4	.	.	PROPN
ejpam-4978	23	5	math	math	PROPN
ejpam-4978	23	6	,	,	PUNCT
ejpam-4978	23	7	17	17	NUM
ejpam-4978	23	8	(	(	PUNCT
ejpam-4978	23	9	1	1	NUM
ejpam-4978	23	10	)	)	PUNCT
ejpam-4978	23	11	(	(	PUNCT
ejpam-4978	23	12	2024	2024	NUM
ejpam-4978	23	13	)	)	PUNCT
ejpam-4978	23	14	,	,	PUNCT
ejpam-4978	23	15	93	93	NUM
ejpam-4978	23	16	-	-	SYM
ejpam-4978	23	17	104	104	NUM
ejpam-4978	23	18	94	94	NUM
ejpam-4978	23	19	2	2	NUM
ejpam-4978	23	20	.	.	PUNCT
ejpam-4978	23	21	terminology	terminology	NOUN
ejpam-4978	23	22	and	and	CCONJ
ejpam-4978	23	23	notation	notation	NOUN
ejpam-4978	23	24	let	let	VERB
ejpam-4978	23	25	g	g	PRON
ejpam-4978	23	26	be	be	AUX
ejpam-4978	23	27	a	a	DET
ejpam-4978	23	28	graph	graph	NOUN
ejpam-4978	23	29	.	.	PUNCT
ejpam-4978	24	1	a	a	DET
ejpam-4978	24	2	subset	subset	NOUN
ejpam-4978	24	3	b	b	NOUN
ejpam-4978	24	4	of	of	ADP
ejpam-4978	24	5	v	v	NOUN
ejpam-4978	24	6	(	(	PUNCT
ejpam-4978	24	7	g	g	NOUN
ejpam-4978	24	8	)	)	PUNCT
ejpam-4978	24	9	is	be	AUX
ejpam-4978	24	10	an	an	DET
ejpam-4978	24	11	independent	independent	ADJ
ejpam-4978	24	12	if	if	SCONJ
ejpam-4978	24	13	for	for	ADP
ejpam-4978	24	14	every	every	DET
ejpam-4978	24	15	pair	pair	NOUN
ejpam-4978	24	16	of	of	ADP
ejpam-4978	24	17	distinct	distinct	ADJ
ejpam-4978	24	18	vertices	vertex	NOUN
ejpam-4978	24	19	v	v	ADP
ejpam-4978	24	20	,	,	PUNCT
ejpam-4978	24	21	w	w	PROPN
ejpam-4978	24	22	∈	∈	PROPN
ejpam-4978	24	23	b	b	PROPN
ejpam-4978	24	24	,	,	PUNCT
ejpam-4978	24	25	dg(v	dg(v	X
ejpam-4978	24	26	,	,	PUNCT
ejpam-4978	24	27	w	w	NOUN
ejpam-4978	24	28	)	)	PUNCT
ejpam-4978	24	29	̸=	̸=	PROPN
ejpam-4978	24	30	1	1	NUM
ejpam-4978	24	31	.	.	PUNCT
ejpam-4978	25	1	the	the	DET
ejpam-4978	25	2	maximum	maximum	ADJ
ejpam-4978	25	3	cardinality	cardinality	NOUN
ejpam-4978	25	4	of	of	ADP
ejpam-4978	25	5	an	an	DET
ejpam-4978	25	6	independent	independent	ADJ
ejpam-4978	25	7	set	set	NOUN
ejpam-4978	25	8	in	in	ADP
ejpam-4978	25	9	g	g	NOUN
ejpam-4978	25	10	,	,	PUNCT
ejpam-4978	25	11	denoted	denote	VERB
ejpam-4978	25	12	by	by	ADP
ejpam-4978	25	13	α(g	α(g	NOUN
ejpam-4978	25	14	)	)	PUNCT
ejpam-4978	25	15	,	,	PUNCT
ejpam-4978	25	16	is	be	AUX
ejpam-4978	25	17	called	call	VERB
ejpam-4978	25	18	the	the	DET
ejpam-4978	25	19	independence	independence	NOUN
ejpam-4978	25	20	number	number	NOUN
ejpam-4978	25	21	of	of	ADP
ejpam-4978	25	22	g.	g.	PROPN
ejpam-4978	25	23	any	any	DET
ejpam-4978	25	24	independent	independent	ADJ
ejpam-4978	25	25	set	set	NOUN
ejpam-4978	25	26	b	b	PROPN
ejpam-4978	25	27	with	with	ADP
ejpam-4978	25	28	cardinality	cardinality	NOUN
ejpam-4978	25	29	equal	equal	ADJ
ejpam-4978	25	30	to	to	ADP
ejpam-4978	25	31	α(g	α(g	NUM
ejpam-4978	25	32	)	)	PUNCT
ejpam-4978	25	33	is	be	AUX
ejpam-4978	25	34	called	call	VERB
ejpam-4978	25	35	an	an	DET
ejpam-4978	25	36	α	α	NOUN
ejpam-4978	25	37	-	-	PUNCT
ejpam-4978	25	38	set	set	NOUN
ejpam-4978	25	39	of	of	ADP
ejpam-4978	25	40	g.	g.	PROPN
ejpam-4978	25	41	a	a	DET
ejpam-4978	25	42	vertex	vertex	NOUN
ejpam-4978	25	43	a	a	PRON
ejpam-4978	25	44	in	in	ADP
ejpam-4978	25	45	g	g	PROPN
ejpam-4978	25	46	is	be	AUX
ejpam-4978	25	47	a	a	DET
ejpam-4978	25	48	hop	hop	NOUN
ejpam-4978	25	49	neighbor	neighbor	NOUN
ejpam-4978	25	50	of	of	ADP
ejpam-4978	25	51	a	a	DET
ejpam-4978	25	52	vertex	vertex	NOUN
ejpam-4978	25	53	b	b	NOUN
ejpam-4978	25	54	in	in	ADP
ejpam-4978	25	55	g	g	PROPN
ejpam-4978	25	56	if	if	SCONJ
ejpam-4978	25	57	dg(a	dg(a	X
ejpam-4978	25	58	,	,	PUNCT
ejpam-4978	25	59	b	b	X
ejpam-4978	25	60	)	)	PUNCT
ejpam-4978	26	1	=	=	SYM
ejpam-4978	26	2	2	2	X
ejpam-4978	26	3	.	.	X
ejpam-4978	26	4	the	the	DET
ejpam-4978	26	5	set	set	ADJ
ejpam-4978	26	6	n2	n2	PROPN
ejpam-4978	26	7	g(a	g(a	PROPN
ejpam-4978	26	8	)	)	PUNCT
ejpam-4978	26	9	=	=	PRON
ejpam-4978	27	1	{	{	PUNCT
ejpam-4978	27	2	b	b	PROPN
ejpam-4978	27	3	∈	∈	ADJ
ejpam-4978	27	4	v	v	NOUN
ejpam-4978	27	5	(	(	PUNCT
ejpam-4978	27	6	g	g	NOUN
ejpam-4978	27	7	)	)	PUNCT
ejpam-4978	27	8	:	:	PUNCT
ejpam-4978	28	1	dg(a	dg(a	X
ejpam-4978	28	2	,	,	PUNCT
ejpam-4978	28	3	b	b	X
ejpam-4978	28	4	)	)	PUNCT
ejpam-4978	28	5	=	=	SYM
ejpam-4978	28	6	2	2	X
ejpam-4978	28	7	}	}	PUNCT
ejpam-4978	28	8	is	be	AUX
ejpam-4978	28	9	called	call	VERB
ejpam-4978	28	10	the	the	DET
ejpam-4978	28	11	open	open	ADJ
ejpam-4978	28	12	hop	hop	NOUN
ejpam-4978	28	13	neighborhood	neighborhood	NOUN
ejpam-4978	28	14	of	of	ADP
ejpam-4978	28	15	a.	a.	NOUN
ejpam-4978	28	16	the	the	DET
ejpam-4978	28	17	closed	closed	ADJ
ejpam-4978	28	18	hop	hop	NOUN
ejpam-4978	28	19	neighborhood	neighborhood	NOUN
ejpam-4978	28	20	of	of	ADP
ejpam-4978	28	21	a	a	PRON
ejpam-4978	28	22	in	in	ADP
ejpam-4978	28	23	g	g	PROPN
ejpam-4978	28	24	is	be	AUX
ejpam-4978	28	25	given	give	VERB
ejpam-4978	28	26	by	by	ADP
ejpam-4978	28	27	n2	n2	ADJ
ejpam-4978	28	28	g[a	g[a	PROPN
ejpam-4978	28	29	]	]	X
ejpam-4978	28	30	=	=	SYM
ejpam-4978	28	31	n2	n2	PROPN
ejpam-4978	28	32	g(a	g(a	PROPN
ejpam-4978	28	33	)	)	PUNCT
ejpam-4978	28	34	∪	∪	ADP
ejpam-4978	28	35	{	{	PUNCT
ejpam-4978	28	36	a	a	NOUN
ejpam-4978	28	37	}	}	PUNCT
ejpam-4978	28	38	.	.	PUNCT
ejpam-4978	29	1	the	the	DET
ejpam-4978	29	2	open	open	ADJ
ejpam-4978	29	3	hop	hop	NOUN
ejpam-4978	29	4	neighborhood	neighborhood	NOUN
ejpam-4978	29	5	of	of	ADP
ejpam-4978	29	6	s	s	NOUN
ejpam-4978	29	7	⊆	⊆	NUM
ejpam-4978	29	8	v	v	NOUN
ejpam-4978	29	9	(	(	PUNCT
ejpam-4978	29	10	g	g	NOUN
ejpam-4978	29	11	)	)	PUNCT
ejpam-4978	29	12	is	be	AUX
ejpam-4978	29	13	the	the	DET
ejpam-4978	29	14	set	set	ADJ
ejpam-4978	29	15	n2	n2	ADJ
ejpam-4978	29	16	g(s	g(s	PROPN
ejpam-4978	29	17	)	)	PUNCT
ejpam-4978	29	18	=	=	SYM
ejpam-4978	30	1	⋃	⋃	ADP
ejpam-4978	30	2	a∈s	a∈s	ADJ
ejpam-4978	30	3	n2	n2	NOUN
ejpam-4978	30	4	g(a	g(a	PROPN
ejpam-4978	30	5	)	)	PUNCT
ejpam-4978	30	6	.	.	PUNCT
ejpam-4978	31	1	the	the	DET
ejpam-4978	31	2	closed	closed	ADJ
ejpam-4978	31	3	hop	hop	NOUN
ejpam-4978	31	4	neighborhood	neighborhood	NOUN
ejpam-4978	31	5	of	of	ADP
ejpam-4978	31	6	s	s	PRON
ejpam-4978	31	7	in	in	ADP
ejpam-4978	31	8	g	g	PROPN
ejpam-4978	31	9	is	be	AUX
ejpam-4978	31	10	the	the	DET
ejpam-4978	31	11	set	set	ADJ
ejpam-4978	31	12	n2	n2	ADJ
ejpam-4978	31	13	g[s	g[s	PROPN
ejpam-4978	31	14	]	]	PUNCT
ejpam-4978	31	15	=	=	SYM
ejpam-4978	31	16	n2	n2	ADJ
ejpam-4978	31	17	g(s	g(s	PROPN
ejpam-4978	31	18	)	)	PUNCT
ejpam-4978	31	19	∪	∪	ADP
ejpam-4978	31	20	s.	s.	PROPN
ejpam-4978	31	21	a	a	DET
ejpam-4978	31	22	subset	subset	NOUN
ejpam-4978	31	23	s	s	X
ejpam-4978	31	24	of	of	ADP
ejpam-4978	31	25	v	v	NOUN
ejpam-4978	31	26	(	(	PUNCT
ejpam-4978	31	27	g	g	NOUN
ejpam-4978	31	28	)	)	PUNCT
ejpam-4978	31	29	is	be	AUX
ejpam-4978	31	30	a	a	DET
ejpam-4978	31	31	hop	hop	NOUN
ejpam-4978	31	32	dominating	dominating	NOUN
ejpam-4978	31	33	of	of	ADP
ejpam-4978	31	34	g	g	PROPN
ejpam-4978	31	35	if	if	SCONJ
ejpam-4978	31	36	for	for	ADP
ejpam-4978	31	37	every	every	DET
ejpam-4978	31	38	a	a	DET
ejpam-4978	31	39	∈	∈	PROPN
ejpam-4978	31	40	v	v	NOUN
ejpam-4978	31	41	(	(	PUNCT
ejpam-4978	31	42	g)\s	g)\s	NOUN
ejpam-4978	31	43	,	,	PUNCT
ejpam-4978	31	44	there	there	PRON
ejpam-4978	31	45	exists	exist	VERB
ejpam-4978	31	46	b	b	PROPN
ejpam-4978	31	47	∈	∈	PROPN
ejpam-4978	31	48	s	s	VERB
ejpam-4978	31	49	such	such	ADJ
ejpam-4978	31	50	that	that	SCONJ
ejpam-4978	31	51	dg(a	dg(a	PROPN
ejpam-4978	31	52	,	,	PUNCT
ejpam-4978	31	53	b	b	X
ejpam-4978	31	54	)	)	PUNCT
ejpam-4978	31	55	=	=	SYM
ejpam-4978	31	56	2	2	X
ejpam-4978	31	57	.	.	PUNCT
ejpam-4978	31	58	the	the	DET
ejpam-4978	31	59	minimum	minimum	ADJ
ejpam-4978	31	60	cardinality	cardinality	NOUN
ejpam-4978	31	61	among	among	ADP
ejpam-4978	31	62	all	all	DET
ejpam-4978	31	63	hop	hop	NOUN
ejpam-4978	31	64	dominating	dominating	NOUN
ejpam-4978	31	65	sets	set	NOUN
ejpam-4978	31	66	of	of	ADP
ejpam-4978	31	67	g	g	NOUN
ejpam-4978	31	68	,	,	PUNCT
ejpam-4978	31	69	denoted	denote	VERB
ejpam-4978	31	70	by	by	ADP
ejpam-4978	31	71	γh(g	γh(g	NOUN
ejpam-4978	31	72	)	)	PUNCT
ejpam-4978	31	73	,	,	PUNCT
ejpam-4978	31	74	is	be	AUX
ejpam-4978	31	75	called	call	VERB
ejpam-4978	31	76	the	the	DET
ejpam-4978	31	77	hop	hop	NOUN
ejpam-4978	31	78	domination	domination	NOUN
ejpam-4978	31	79	number	number	NOUN
ejpam-4978	31	80	of	of	ADP
ejpam-4978	31	81	g.	g.	PROPN
ejpam-4978	31	82	any	any	DET
ejpam-4978	31	83	hop	hop	NOUN
ejpam-4978	31	84	dominating	dominating	NOUN
ejpam-4978	31	85	set	set	VERB
ejpam-4978	31	86	with	with	ADP
ejpam-4978	31	87	cardinality	cardinality	NOUN
ejpam-4978	31	88	equal	equal	ADJ
ejpam-4978	31	89	to	to	ADP
ejpam-4978	31	90	γh(g	γh(g	NOUN
ejpam-4978	31	91	)	)	PUNCT
ejpam-4978	31	92	is	be	AUX
ejpam-4978	31	93	called	call	VERB
ejpam-4978	31	94	a	a	DET
ejpam-4978	31	95	γh	γh	ADV
ejpam-4978	31	96	-	-	PUNCT
ejpam-4978	31	97	set	set	NOUN
ejpam-4978	31	98	.	.	PUNCT
ejpam-4978	32	1	a	a	DET
ejpam-4978	32	2	subset	subset	ADJ
ejpam-4978	32	3	u	u	NOUN
ejpam-4978	32	4	of	of	ADP
ejpam-4978	32	5	vertices	vertex	NOUN
ejpam-4978	32	6	of	of	ADP
ejpam-4978	32	7	a	a	DET
ejpam-4978	32	8	graph	graph	NOUN
ejpam-4978	32	9	g	g	NOUN
ejpam-4978	32	10	is	be	AUX
ejpam-4978	32	11	called	call	VERB
ejpam-4978	32	12	a	a	DET
ejpam-4978	32	13	vertex	vertex	NOUN
ejpam-4978	32	14	cover	cover	NOUN
ejpam-4978	32	15	of	of	ADP
ejpam-4978	32	16	g	g	PROPN
ejpam-4978	32	17	if	if	SCONJ
ejpam-4978	32	18	every	every	DET
ejpam-4978	32	19	edge	edge	NOUN
ejpam-4978	32	20	in	in	ADP
ejpam-4978	32	21	g	g	PROPN
ejpam-4978	32	22	is	be	AUX
ejpam-4978	32	23	incident	incident	NOUN
ejpam-4978	32	24	with	with	ADP
ejpam-4978	32	25	a	a	DET
ejpam-4978	32	26	vertex	vertex	NOUN
ejpam-4978	32	27	in	in	ADP
ejpam-4978	32	28	u	u	PROPN
ejpam-4978	32	29	.	.	PUNCT
ejpam-4978	33	1	the	the	DET
ejpam-4978	33	2	minimum	minimum	ADJ
ejpam-4978	33	3	cardinality	cardinality	NOUN
ejpam-4978	33	4	of	of	ADP
ejpam-4978	33	5	such	such	ADJ
ejpam-4978	33	6	set	set	NOUN
ejpam-4978	33	7	is	be	AUX
ejpam-4978	33	8	the	the	DET
ejpam-4978	33	9	vertex	vertex	NOUN
ejpam-4978	33	10	covering	cover	VERB
ejpam-4978	33	11	number	number	NOUN
ejpam-4978	33	12	of	of	ADP
ejpam-4978	33	13	g	g	NOUN
ejpam-4978	33	14	and	and	CCONJ
ejpam-4978	33	15	is	be	AUX
ejpam-4978	33	16	denoted	denote	VERB
ejpam-4978	33	17	by	by	ADP
ejpam-4978	33	18	β(g	β(g	PROPN
ejpam-4978	33	19	)	)	PUNCT
ejpam-4978	33	20	.	.	PUNCT
ejpam-4978	34	1	a	a	DET
ejpam-4978	34	2	subset	subset	NOUN
ejpam-4978	34	3	c	c	NOUN
ejpam-4978	34	4	of	of	ADP
ejpam-4978	34	5	v	v	PROPN
ejpam-4978	34	6	(	(	PUNCT
ejpam-4978	34	7	g	g	NOUN
ejpam-4978	34	8	)	)	PUNCT
ejpam-4978	34	9	is	be	AUX
ejpam-4978	34	10	a	a	DET
ejpam-4978	34	11	pointwise	pointwise	ADJ
ejpam-4978	34	12	non	non	ADJ
ejpam-4978	34	13	-	-	ADJ
ejpam-4978	34	14	dominating	dominating	ADJ
ejpam-4978	34	15	set	set	NOUN
ejpam-4978	34	16	if	if	SCONJ
ejpam-4978	34	17	for	for	ADP
ejpam-4978	34	18	every	every	PRON
ejpam-4978	34	19	v	v	NUM
ejpam-4978	34	20	∈	∈	NOUN
ejpam-4978	34	21	v	v	NOUN
ejpam-4978	34	22	(	(	PUNCT
ejpam-4978	34	23	g	g	NOUN
ejpam-4978	34	24	)	)	PUNCT
ejpam-4978	34	25	\	\	PUNCT
ejpam-4978	35	1	c	c	X
ejpam-4978	35	2	,	,	PUNCT
ejpam-4978	35	3	there	there	PRON
ejpam-4978	35	4	exists	exist	VERB
ejpam-4978	35	5	u	u	PROPN
ejpam-4978	35	6	∈	∈	PROPN
ejpam-4978	35	7	c	c	NOUN
ejpam-4978	35	8	such	such	ADJ
ejpam-4978	35	9	that	that	DET
ejpam-4978	35	10	v	v	NOUN
ejpam-4978	35	11	/∈	/∈	PUNCT
ejpam-4978	35	12	ng(u	ng(u	NOUN
ejpam-4978	35	13	)	)	PUNCT
ejpam-4978	35	14	.	.	PUNCT
ejpam-4978	36	1	the	the	DET
ejpam-4978	36	2	minimum	minimum	ADJ
ejpam-4978	36	3	cardinality	cardinality	NOUN
ejpam-4978	36	4	of	of	ADP
ejpam-4978	36	5	a	a	DET
ejpam-4978	36	6	pointwise	pointwise	ADJ
ejpam-4978	36	7	nondominating	nondominate	VERB
ejpam-4978	36	8	set	set	NOUN
ejpam-4978	36	9	of	of	ADP
ejpam-4978	36	10	g	g	NOUN
ejpam-4978	36	11	,	,	PUNCT
ejpam-4978	36	12	denoted	denote	VERB
ejpam-4978	36	13	by	by	ADP
ejpam-4978	36	14	pnd(g	pnd(g	PROPN
ejpam-4978	36	15	)	)	PUNCT
ejpam-4978	36	16	,	,	PUNCT
ejpam-4978	36	17	is	be	AUX
ejpam-4978	36	18	called	call	VERB
ejpam-4978	36	19	a	a	DET
ejpam-4978	36	20	pointwise	pointwise	ADJ
ejpam-4978	36	21	non	non	ADJ
ejpam-4978	36	22	-	-	ADJ
ejpam-4978	36	23	domination	domination	ADJ
ejpam-4978	36	24	number	number	NOUN
ejpam-4978	36	25	of	of	ADP
ejpam-4978	36	26	g.	g.	PROPN
ejpam-4978	36	27	any	any	DET
ejpam-4978	36	28	pointwise	pointwise	PROPN
ejpam-4978	36	29	non	non	ADJ
ejpam-4978	36	30	-	-	ADJ
ejpam-4978	36	31	dominating	dominating	ADJ
ejpam-4978	36	32	set	set	NOUN
ejpam-4978	36	33	of	of	ADP
ejpam-4978	36	34	g	g	PROPN
ejpam-4978	36	35	with	with	ADP
ejpam-4978	36	36	cardinality	cardinality	NOUN
ejpam-4978	36	37	pnd(g	pnd(g	PROPN
ejpam-4978	36	38	)	)	PUNCT
ejpam-4978	36	39	is	be	AUX
ejpam-4978	36	40	called	call	VERB
ejpam-4978	36	41	a	a	DET
ejpam-4978	36	42	pnd	pnd	NOUN
ejpam-4978	36	43	-	-	PUNCT
ejpam-4978	36	44	set	set	NOUN
ejpam-4978	36	45	of	of	ADP
ejpam-4978	36	46	g.	g.	PROPN
ejpam-4978	36	47	let	let	VERB
ejpam-4978	36	48	g	g	NOUN
ejpam-4978	36	49	and	and	CCONJ
ejpam-4978	36	50	h	h	NOUN
ejpam-4978	36	51	be	be	VERB
ejpam-4978	36	52	any	any	DET
ejpam-4978	36	53	two	two	NUM
ejpam-4978	36	54	graphs	graph	NOUN
ejpam-4978	36	55	.	.	PUNCT
ejpam-4978	37	1	the	the	DET
ejpam-4978	37	2	join	join	NOUN
ejpam-4978	37	3	g	g	PROPN
ejpam-4978	37	4	+	+	CCONJ
ejpam-4978	37	5	h	h	NOUN
ejpam-4978	37	6	is	be	AUX
ejpam-4978	37	7	the	the	DET
ejpam-4978	37	8	graph	graph	NOUN
ejpam-4978	37	9	with	with	ADP
ejpam-4978	37	10	vertex	vertex	NOUN
ejpam-4978	37	11	set	set	VERB
ejpam-4978	37	12	v	v	NOUN
ejpam-4978	37	13	(	(	PUNCT
ejpam-4978	37	14	g+h	g+h	NOUN
ejpam-4978	37	15	)	)	PUNCT
ejpam-4978	37	16	=	=	SYM
ejpam-4978	37	17	v	v	X
ejpam-4978	37	18	(	(	PUNCT
ejpam-4978	37	19	g	g	NOUN
ejpam-4978	37	20	)	)	PUNCT
ejpam-4978	37	21	∪	∪	NOUN
ejpam-4978	37	22	v	v	NOUN
ejpam-4978	37	23	(	(	PUNCT
ejpam-4978	37	24	h	h	NOUN
ejpam-4978	37	25	)	)	PUNCT
ejpam-4978	37	26	and	and	CCONJ
ejpam-4978	37	27	edge	edge	NOUN
ejpam-4978	37	28	set	set	VERB
ejpam-4978	37	29	e(g+h	e(g+h	NUM
ejpam-4978	37	30	)	)	PUNCT
ejpam-4978	37	31	=	=	SYM
ejpam-4978	37	32	e(g	e(g	NOUN
ejpam-4978	37	33	)	)	PUNCT
ejpam-4978	37	34	∪	∪	ADP
ejpam-4978	37	35	e(h	e(h	PROPN
ejpam-4978	37	36	)	)	PUNCT
ejpam-4978	37	37	∪	∪	NOUN
ejpam-4978	37	38	{	{	PUNCT
ejpam-4978	37	39	uv	uv	NOUN
ejpam-4978	37	40	:	:	PUNCT
ejpam-4978	37	41	u	u	PROPN
ejpam-4978	37	42	∈	∈	PROPN
ejpam-4978	37	43	v	v	ADP
ejpam-4978	37	44	(	(	PUNCT
ejpam-4978	37	45	g	g	NOUN
ejpam-4978	37	46	)	)	PUNCT
ejpam-4978	37	47	,	,	PUNCT
ejpam-4978	37	48	v	v	X
ejpam-4978	37	49	∈	∈	PROPN
ejpam-4978	37	50	v	v	NOUN
ejpam-4978	37	51	(	(	PUNCT
ejpam-4978	37	52	h	h	NOUN
ejpam-4978	37	53	)	)	PUNCT
ejpam-4978	37	54	}	}	PUNCT
ejpam-4978	37	55	.	.	PUNCT
ejpam-4978	38	1	the	the	DET
ejpam-4978	38	2	corona	corona	NOUN
ejpam-4978	38	3	g	g	PROPN
ejpam-4978	38	4	◦	◦	NOUN
ejpam-4978	38	5	h	h	NOUN
ejpam-4978	38	6	is	be	AUX
ejpam-4978	38	7	the	the	DET
ejpam-4978	38	8	graph	graph	NOUN
ejpam-4978	38	9	obtained	obtain	VERB
ejpam-4978	38	10	by	by	ADP
ejpam-4978	38	11	taking	take	VERB
ejpam-4978	38	12	one	one	NUM
ejpam-4978	38	13	copy	copy	NOUN
ejpam-4978	38	14	of	of	ADP
ejpam-4978	38	15	g	g	PROPN
ejpam-4978	38	16	and	and	CCONJ
ejpam-4978	38	17	|v	|v	PROPN
ejpam-4978	38	18	(	(	PUNCT
ejpam-4978	38	19	g)|	g)|	NOUN
ejpam-4978	38	20	copies	copy	NOUN
ejpam-4978	38	21	of	of	ADP
ejpam-4978	38	22	h	h	NOUN
ejpam-4978	38	23	,	,	PUNCT
ejpam-4978	38	24	and	and	CCONJ
ejpam-4978	38	25	then	then	ADV
ejpam-4978	38	26	joining	join	VERB
ejpam-4978	38	27	the	the	DET
ejpam-4978	38	28	ith	ith	PROPN
ejpam-4978	38	29	vertex	vertex	NOUN
ejpam-4978	38	30	of	of	ADP
ejpam-4978	38	31	g	g	NOUN
ejpam-4978	38	32	to	to	ADP
ejpam-4978	38	33	every	every	DET
ejpam-4978	38	34	vertex	vertex	NOUN
ejpam-4978	38	35	of	of	ADP
ejpam-4978	38	36	the	the	DET
ejpam-4978	38	37	ith	ith	PROPN
ejpam-4978	38	38	copy	copy	NOUN
ejpam-4978	38	39	of	of	ADP
ejpam-4978	38	40	h.	h.	PROPN
ejpam-4978	38	41	we	we	PRON
ejpam-4978	38	42	denote	denote	VERB
ejpam-4978	38	43	by	by	ADP
ejpam-4978	38	44	hv	hv	PROPN
ejpam-4978	38	45	the	the	DET
ejpam-4978	38	46	copy	copy	NOUN
ejpam-4978	38	47	of	of	ADP
ejpam-4978	38	48	h	h	NOUN
ejpam-4978	38	49	in	in	ADP
ejpam-4978	38	50	g	g	PROPN
ejpam-4978	38	51	◦	◦	NOUN
ejpam-4978	38	52	h	h	NOUN
ejpam-4978	38	53	corresponding	correspond	VERB
ejpam-4978	38	54	to	to	ADP
ejpam-4978	38	55	the	the	DET
ejpam-4978	38	56	vertex	vertex	NOUN
ejpam-4978	38	57	v	v	ADP
ejpam-4978	38	58	∈	∈	PROPN
ejpam-4978	38	59	g	g	NOUN
ejpam-4978	38	60	and	and	CCONJ
ejpam-4978	38	61	write	write	VERB
ejpam-4978	38	62	v	v	ADP
ejpam-4978	38	63	+	+	CCONJ
ejpam-4978	38	64	hv	hv	NOUN
ejpam-4978	38	65	for	for	ADP
ejpam-4978	38	66	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4978	38	67	.	.	PUNCT
ejpam-4978	39	1	3	3	X
ejpam-4978	39	2	.	.	X
ejpam-4978	39	3	results	result	NOUN
ejpam-4978	39	4	we	we	PRON
ejpam-4978	39	5	shall	shall	AUX
ejpam-4978	39	6	define	define	VERB
ejpam-4978	39	7	the	the	DET
ejpam-4978	39	8	concept	concept	NOUN
ejpam-4978	39	9	of	of	ADP
ejpam-4978	39	10	vertex	vertex	NOUN
ejpam-4978	39	11	cover	cover	VERB
ejpam-4978	39	12	hop	hop	NOUN
ejpam-4978	39	13	domination	domination	NOUN
ejpam-4978	39	14	in	in	ADP
ejpam-4978	39	15	a	a	DET
ejpam-4978	39	16	graph	graph	NOUN
ejpam-4978	39	17	as	as	SCONJ
ejpam-4978	39	18	follows	follow	VERB
ejpam-4978	39	19	:	:	PUNCT
ejpam-4978	39	20	definition	definition	NOUN
ejpam-4978	39	21	1	1	NUM
ejpam-4978	39	22	.	.	PUNCT
ejpam-4978	40	1	let	let	VERB
ejpam-4978	40	2	g	g	PRON
ejpam-4978	40	3	be	be	AUX
ejpam-4978	40	4	a	a	DET
ejpam-4978	40	5	graph	graph	NOUN
ejpam-4978	40	6	.	.	PUNCT
ejpam-4978	41	1	a	a	DET
ejpam-4978	41	2	subset	subset	NOUN
ejpam-4978	41	3	c	c	NOUN
ejpam-4978	41	4	of	of	ADP
ejpam-4978	41	5	vertices	vertex	NOUN
ejpam-4978	41	6	v	v	X
ejpam-4978	41	7	(	(	PUNCT
ejpam-4978	41	8	g	g	NOUN
ejpam-4978	41	9	)	)	PUNCT
ejpam-4978	41	10	of	of	ADP
ejpam-4978	41	11	g	g	PROPN
ejpam-4978	41	12	is	be	AUX
ejpam-4978	41	13	said	say	VERB
ejpam-4978	41	14	to	to	PART
ejpam-4978	41	15	be	be	AUX
ejpam-4978	41	16	a	a	DET
ejpam-4978	41	17	vertex	vertex	NOUN
ejpam-4978	41	18	cover	cover	NOUN
ejpam-4978	41	19	hop	hop	NOUN
ejpam-4978	41	20	dominating	dominating	NOUN
ejpam-4978	41	21	if	if	SCONJ
ejpam-4978	41	22	c	c	PROPN
ejpam-4978	41	23	is	be	AUX
ejpam-4978	41	24	both	both	CCONJ
ejpam-4978	41	25	a	a	DET
ejpam-4978	41	26	vertex	vertex	NOUN
ejpam-4978	41	27	cover	cover	NOUN
ejpam-4978	41	28	and	and	CCONJ
ejpam-4978	41	29	a	a	DET
ejpam-4978	41	30	hop	hop	NOUN
ejpam-4978	41	31	dominating	dominating	NOUN
ejpam-4978	41	32	set	set	VERB
ejpam-4978	41	33	in	in	ADP
ejpam-4978	41	34	g.	g.	PROPN
ejpam-4978	41	35	the	the	DET
ejpam-4978	41	36	vertex	vertex	NOUN
ejpam-4978	41	37	cover	cover	VERB
ejpam-4978	41	38	hop	hop	NOUN
ejpam-4978	41	39	domination	domination	NOUN
ejpam-4978	41	40	number	number	NOUN
ejpam-4978	41	41	of	of	ADP
ejpam-4978	41	42	g	g	NOUN
ejpam-4978	41	43	,	,	PUNCT
ejpam-4978	41	44	denoted	denote	VERB
ejpam-4978	41	45	by	by	ADP
ejpam-4978	41	46	γvch(g	γvch(g	NOUN
ejpam-4978	41	47	)	)	PUNCT
ejpam-4978	41	48	,	,	PUNCT
ejpam-4978	41	49	is	be	AUX
ejpam-4978	41	50	the	the	DET
ejpam-4978	41	51	minimum	minimum	ADJ
ejpam-4978	41	52	cardinality	cardinality	NOUN
ejpam-4978	41	53	among	among	ADP
ejpam-4978	41	54	all	all	DET
ejpam-4978	41	55	vertex	vertex	NOUN
ejpam-4978	41	56	cover	cover	NOUN
ejpam-4978	41	57	hop	hop	NOUN
ejpam-4978	41	58	dominating	dominating	NOUN
ejpam-4978	41	59	sets	set	NOUN
ejpam-4978	41	60	in	in	ADP
ejpam-4978	41	61	g.	g.	PROPN
ejpam-4978	41	62	any	any	DET
ejpam-4978	41	63	vertex	vertex	NOUN
ejpam-4978	41	64	cover	cover	NOUN
ejpam-4978	41	65	hop	hop	NOUN
ejpam-4978	41	66	dominating	dominating	NOUN
ejpam-4978	41	67	set	set	VERB
ejpam-4978	41	68	with	with	ADP
ejpam-4978	41	69	cardinality	cardinality	NOUN
ejpam-4978	41	70	equal	equal	ADJ
ejpam-4978	41	71	to	to	ADP
ejpam-4978	41	72	γvch(g	γvch(g	NOUN
ejpam-4978	41	73	)	)	PUNCT
ejpam-4978	41	74	is	be	AUX
ejpam-4978	41	75	called	call	VERB
ejpam-4978	41	76	a	a	DET
ejpam-4978	41	77	γvch	γvch	NOUN
ejpam-4978	41	78	-	-	PUNCT
ejpam-4978	41	79	set	set	NOUN
ejpam-4978	41	80	of	of	ADP
ejpam-4978	41	81	g.	g.	PROPN
ejpam-4978	41	82	v.	v.	PROPN
ejpam-4978	41	83	t.	t.	PROPN
ejpam-4978	41	84	bilar	bilar	PROPN
ejpam-4978	41	85	et	et	PROPN
ejpam-4978	41	86	al	al	PROPN
ejpam-4978	41	87	.	.	PUNCT
ejpam-4978	41	88	/	/	SYM
ejpam-4978	41	89	eur	eur	PROPN
ejpam-4978	41	90	.	.	PUNCT
ejpam-4978	42	1	j.	j.	PROPN
ejpam-4978	42	2	pure	pure	PROPN
ejpam-4978	42	3	appl	appl	PROPN
ejpam-4978	42	4	.	.	PROPN
ejpam-4978	42	5	math	math	PROPN
ejpam-4978	42	6	,	,	PUNCT
ejpam-4978	42	7	17	17	NUM
ejpam-4978	42	8	(	(	PUNCT
ejpam-4978	42	9	1	1	NUM
ejpam-4978	42	10	)	)	PUNCT
ejpam-4978	42	11	(	(	PUNCT
ejpam-4978	42	12	2024	2024	NUM
ejpam-4978	42	13	)	)	PUNCT
ejpam-4978	42	14	,	,	PUNCT
ejpam-4978	42	15	93	93	NUM
ejpam-4978	42	16	-	-	SYM
ejpam-4978	42	17	104	104	NUM
ejpam-4978	42	18	95	95	NUM
ejpam-4978	42	19	example	example	NOUN
ejpam-4978	42	20	1	1	NUM
ejpam-4978	42	21	.	.	X
ejpam-4978	42	22	consider	consider	VERB
ejpam-4978	42	23	the	the	DET
ejpam-4978	42	24	graph	graph	NOUN
ejpam-4978	42	25	g	g	NOUN
ejpam-4978	42	26	in	in	ADP
ejpam-4978	42	27	figure	figure	NOUN
ejpam-4978	42	28	1	1	NUM
ejpam-4978	42	29	.	.	PUNCT
ejpam-4978	43	1	let	let	VERB
ejpam-4978	43	2	c	c	NOUN
ejpam-4978	43	3	=	=	PUNCT
ejpam-4978	43	4	{	{	PUNCT
ejpam-4978	43	5	e	e	PROPN
ejpam-4978	43	6	,	,	PUNCT
ejpam-4978	43	7	f	f	PROPN
ejpam-4978	43	8	,	,	PUNCT
ejpam-4978	43	9	g	g	PROPN
ejpam-4978	43	10	,	,	PUNCT
ejpam-4978	43	11	h	h	NOUN
ejpam-4978	43	12	}	}	PUNCT
ejpam-4978	43	13	.	.	PUNCT
ejpam-4978	44	1	notice	notice	VERB
ejpam-4978	44	2	that	that	SCONJ
ejpam-4978	44	3	every	every	DET
ejpam-4978	44	4	edge	edge	NOUN
ejpam-4978	44	5	of	of	ADP
ejpam-4978	44	6	g	g	PROPN
ejpam-4978	44	7	is	be	AUX
ejpam-4978	44	8	incident	incident	NOUN
ejpam-4978	44	9	to	to	ADP
ejpam-4978	44	10	atleast	atleast	VERB
ejpam-4978	44	11	one	one	NUM
ejpam-4978	44	12	vertex	vertex	NOUN
ejpam-4978	44	13	in	in	ADP
ejpam-4978	44	14	c.	c.	PROPN
ejpam-4978	44	15	thus	thus	ADV
ejpam-4978	44	16	,	,	PUNCT
ejpam-4978	44	17	c	c	PROPN
ejpam-4978	44	18	is	be	AUX
ejpam-4978	44	19	a	a	DET
ejpam-4978	44	20	vertex	vertex	NOUN
ejpam-4978	44	21	cover	cover	NOUN
ejpam-4978	44	22	set	set	NOUN
ejpam-4978	44	23	of	of	ADP
ejpam-4978	44	24	g.	g.	PROPN
ejpam-4978	44	25	observe	observe	VERB
ejpam-4978	44	26	that	that	SCONJ
ejpam-4978	44	27	a	a	DET
ejpam-4978	44	28	,	,	PUNCT
ejpam-4978	44	29	d	d	PROPN
ejpam-4978	44	30	∈	∈	PROPN
ejpam-4978	44	31	n2	n2	ADJ
ejpam-4978	44	32	g(f	g(f	PROPN
ejpam-4978	44	33	)	)	PUNCT
ejpam-4978	44	34	,	,	PUNCT
ejpam-4978	44	35	b	b	X
ejpam-4978	44	36	∈	∈	PROPN
ejpam-4978	44	37	n2	n2	NOUN
ejpam-4978	44	38	g(g	g(g	PROPN
ejpam-4978	44	39	)	)	PUNCT
ejpam-4978	44	40	and	and	CCONJ
ejpam-4978	44	41	c	c	NOUN
ejpam-4978	44	42	∈	∈	PROPN
ejpam-4978	44	43	n2	n2	PROPN
ejpam-4978	44	44	g(e	g(e	PROPN
ejpam-4978	44	45	)	)	PUNCT
ejpam-4978	44	46	.	.	PUNCT
ejpam-4978	45	1	it	it	PRON
ejpam-4978	45	2	follows	follow	VERB
ejpam-4978	45	3	that	that	SCONJ
ejpam-4978	45	4	n	n	PROPN
ejpam-4978	45	5	2	2	NUM
ejpam-4978	45	6	g[c	g[c	NOUN
ejpam-4978	45	7	]	]	X
ejpam-4978	45	8	=	=	SYM
ejpam-4978	45	9	v	v	X
ejpam-4978	45	10	(	(	PUNCT
ejpam-4978	45	11	g	g	NOUN
ejpam-4978	45	12	)	)	PUNCT
ejpam-4978	45	13	,	,	PUNCT
ejpam-4978	45	14	showing	show	VERB
ejpam-4978	45	15	that	that	SCONJ
ejpam-4978	45	16	c	c	PROPN
ejpam-4978	45	17	is	be	AUX
ejpam-4978	45	18	a	a	DET
ejpam-4978	45	19	hop	hop	NOUN
ejpam-4978	45	20	dominating	dominating	NOUN
ejpam-4978	45	21	set	set	VERB
ejpam-4978	45	22	in	in	ADP
ejpam-4978	45	23	g.	g.	PROPN
ejpam-4978	45	24	therefore	therefore	ADV
ejpam-4978	45	25	,	,	PUNCT
ejpam-4978	45	26	c	c	PROPN
ejpam-4978	45	27	is	be	AUX
ejpam-4978	45	28	a	a	DET
ejpam-4978	45	29	vertex	vertex	NOUN
ejpam-4978	45	30	cover	cover	NOUN
ejpam-4978	45	31	hop	hop	NOUN
ejpam-4978	45	32	dominating	dominating	NOUN
ejpam-4978	45	33	set	set	NOUN
ejpam-4978	45	34	of	of	ADP
ejpam-4978	45	35	g.	g.	PROPN
ejpam-4978	45	36	moreover	moreover	ADV
ejpam-4978	45	37	,	,	PUNCT
ejpam-4978	45	38	it	it	PRON
ejpam-4978	45	39	can	can	AUX
ejpam-4978	45	40	be	be	AUX
ejpam-4978	45	41	verified	verify	VERB
ejpam-4978	45	42	that	that	SCONJ
ejpam-4978	45	43	γvch(g	γvch(g	X
ejpam-4978	45	44	)	)	PUNCT
ejpam-4978	45	45	=	=	PUNCT
ejpam-4978	46	1	4	4	X
ejpam-4978	46	2	.	.	PUNCT
ejpam-4978	46	3	a	a	DET
ejpam-4978	46	4	b	b	NOUN
ejpam-4978	46	5	c	c	NOUN
ejpam-4978	46	6	d	d	X
ejpam-4978	46	7	e	e	X
ejpam-4978	46	8	f	f	X
ejpam-4978	46	9	g	g	PROPN
ejpam-4978	46	10	h	h	NOUN
ejpam-4978	46	11	g	g	NOUN
ejpam-4978	46	12	:	:	PUNCT
ejpam-4978	46	13	figure	figure	NOUN
ejpam-4978	46	14	1	1	NUM
ejpam-4978	46	15	:	:	PUNCT
ejpam-4978	46	16	graph	graph	VERB
ejpam-4978	46	17	g	g	NOUN
ejpam-4978	46	18	with	with	ADP
ejpam-4978	46	19	γvch(g	γvch(g	NOUN
ejpam-4978	46	20	)	)	PUNCT
ejpam-4978	46	21	=	=	SYM
ejpam-4978	46	22	4	4	NUM
ejpam-4978	46	23	proposition	proposition	NOUN
ejpam-4978	46	24	1	1	NUM
ejpam-4978	46	25	.	.	PUNCT
ejpam-4978	47	1	let	let	VERB
ejpam-4978	47	2	g	g	NOUN
ejpam-4978	47	3	be	be	AUX
ejpam-4978	47	4	any	any	DET
ejpam-4978	47	5	graph	graph	NOUN
ejpam-4978	47	6	.	.	PUNCT
ejpam-4978	48	1	then	then	ADV
ejpam-4978	48	2	each	each	PRON
ejpam-4978	48	3	of	of	ADP
ejpam-4978	48	4	the	the	DET
ejpam-4978	48	5	following	following	NOUN
ejpam-4978	48	6	is	be	AUX
ejpam-4978	48	7	true	true	ADJ
ejpam-4978	48	8	.	.	PUNCT
ejpam-4978	49	1	(	(	PUNCT
ejpam-4978	49	2	i	i	NOUN
ejpam-4978	49	3	)	)	PUNCT
ejpam-4978	49	4	a	a	DET
ejpam-4978	49	5	vertex	vertex	NOUN
ejpam-4978	49	6	cover	cover	NOUN
ejpam-4978	49	7	may	may	AUX
ejpam-4978	49	8	not	not	PART
ejpam-4978	49	9	be	be	AUX
ejpam-4978	49	10	a	a	DET
ejpam-4978	49	11	hop	hop	NOUN
ejpam-4978	49	12	dominating	dominating	NOUN
ejpam-4978	49	13	.	.	PUNCT
ejpam-4978	50	1	(	(	PUNCT
ejpam-4978	50	2	ii	ii	NOUN
ejpam-4978	50	3	)	)	PUNCT
ejpam-4978	50	4	a	a	DET
ejpam-4978	50	5	hop	hop	NOUN
ejpam-4978	50	6	dominating	dominating	NOUN
ejpam-4978	50	7	may	may	AUX
ejpam-4978	50	8	not	not	PART
ejpam-4978	50	9	be	be	AUX
ejpam-4978	50	10	a	a	DET
ejpam-4978	50	11	vertex	vertex	NOUN
ejpam-4978	50	12	cover	cover	NOUN
ejpam-4978	50	13	.	.	PUNCT
ejpam-4978	51	1	proof	proof	NOUN
ejpam-4978	51	2	.	.	PUNCT
ejpam-4978	52	1	(	(	PUNCT
ejpam-4978	52	2	i	i	NOUN
ejpam-4978	52	3	)	)	PUNCT
ejpam-4978	52	4	consider	consider	VERB
ejpam-4978	52	5	the	the	DET
ejpam-4978	52	6	graph	graph	NOUN
ejpam-4978	52	7	h	h	NOUN
ejpam-4978	52	8	given	give	VERB
ejpam-4978	52	9	in	in	ADP
ejpam-4978	52	10	figure	figure	NOUN
ejpam-4978	52	11	2	2	NUM
ejpam-4978	52	12	.	.	PUNCT
ejpam-4978	53	1	let	let	VERB
ejpam-4978	53	2	c	c	NOUN
ejpam-4978	53	3	′	′	VERB
ejpam-4978	54	1	=	=	PUNCT
ejpam-4978	54	2	{	{	PUNCT
ejpam-4978	54	3	b	b	PROPN
ejpam-4978	54	4	,	,	PUNCT
ejpam-4978	54	5	d	d	NOUN
ejpam-4978	54	6	,	,	PUNCT
ejpam-4978	54	7	e	e	NOUN
ejpam-4978	54	8	,	,	PUNCT
ejpam-4978	54	9	f	f	X
ejpam-4978	54	10	,	,	PUNCT
ejpam-4978	54	11	g	g	NOUN
ejpam-4978	54	12	}	}	PUNCT
ejpam-4978	54	13	.	.	PUNCT
ejpam-4978	55	1	observe	observe	VERB
ejpam-4978	55	2	that	that	SCONJ
ejpam-4978	55	3	every	every	DET
ejpam-4978	55	4	edge	edge	NOUN
ejpam-4978	55	5	of	of	ADP
ejpam-4978	55	6	h	h	NOUN
ejpam-4978	55	7	is	be	AUX
ejpam-4978	55	8	incident	incident	NOUN
ejpam-4978	55	9	to	to	ADP
ejpam-4978	55	10	at	at	ADV
ejpam-4978	55	11	least	least	ADV
ejpam-4978	55	12	one	one	NUM
ejpam-4978	55	13	vertex	vertex	NOUN
ejpam-4978	55	14	in	in	ADP
ejpam-4978	55	15	c	c	NOUN
ejpam-4978	55	16	′	′	NOUN
ejpam-4978	55	17	,	,	PUNCT
ejpam-4978	55	18	and	and	CCONJ
ejpam-4978	55	19	so	so	ADV
ejpam-4978	55	20	c	c	NOUN
ejpam-4978	55	21	′	′	NOUN
ejpam-4978	55	22	is	be	AUX
ejpam-4978	55	23	a	a	DET
ejpam-4978	55	24	vertex	vertex	NOUN
ejpam-4978	55	25	cover	cover	NOUN
ejpam-4978	55	26	set	set	NOUN
ejpam-4978	55	27	of	of	ADP
ejpam-4978	55	28	h.	h.	PROPN
ejpam-4978	56	1	however	however	ADV
ejpam-4978	56	2	c	c	PROPN
ejpam-4978	56	3	′	′	NOUN
ejpam-4978	56	4	is	be	AUX
ejpam-4978	56	5	not	not	PART
ejpam-4978	56	6	a	a	DET
ejpam-4978	56	7	hop	hop	NOUN
ejpam-4978	56	8	dominating	dominating	NOUN
ejpam-4978	56	9	set	set	NOUN
ejpam-4978	56	10	of	of	ADP
ejpam-4978	56	11	h	h	NOUN
ejpam-4978	56	12	since	since	SCONJ
ejpam-4978	56	13	i	i	PRON
ejpam-4978	56	14	/∈	/∈	PUNCT
ejpam-4978	57	1	n2	n2	PROPN
ejpam-4978	57	2	g[x	g[x	X
ejpam-4978	57	3	]	]	X
ejpam-4978	57	4	∀x	∀x	X
ejpam-4978	57	5	∈	∈	PROPN
ejpam-4978	57	6	c	c	NOUN
ejpam-4978	57	7	′.	′.	PROPN
ejpam-4978	57	8	h	h	NOUN
ejpam-4978	57	9	h	h	NOUN
ejpam-4978	57	10	:	:	PUNCT
ejpam-4978	57	11	b	b	X
ejpam-4978	57	12	d	d	X
ejpam-4978	57	13	e	e	X
ejpam-4978	57	14	f	f	PROPN
ejpam-4978	57	15	ga	ga	PROPN
ejpam-4978	57	16	c	c	NOUN
ejpam-4978	57	17	i	i	PRON
ejpam-4978	57	18	figure	figure	VERB
ejpam-4978	57	19	2	2	NUM
ejpam-4978	57	20	:	:	PUNCT
ejpam-4978	57	21	graph	graph	NOUN
ejpam-4978	57	22	h	h	PROPN
ejpam-4978	57	23	(	(	PUNCT
ejpam-4978	57	24	ii	ii	NOUN
ejpam-4978	57	25	)	)	PUNCT
ejpam-4978	57	26	consider	consider	VERB
ejpam-4978	57	27	again	again	ADV
ejpam-4978	57	28	the	the	DET
ejpam-4978	57	29	graph	graph	NOUN
ejpam-4978	57	30	g	g	NOUN
ejpam-4978	57	31	in	in	ADP
ejpam-4978	57	32	figure	figure	NOUN
ejpam-4978	57	33	1	1	NUM
ejpam-4978	57	34	.	.	PUNCT
ejpam-4978	58	1	let	let	VERB
ejpam-4978	58	2	m	m	VERB
ejpam-4978	58	3	=	=	VERB
ejpam-4978	58	4	{	{	PUNCT
ejpam-4978	58	5	c	c	NOUN
ejpam-4978	58	6	,	,	PUNCT
ejpam-4978	58	7	f	f	X
ejpam-4978	58	8	,	,	PUNCT
ejpam-4978	58	9	g	g	NOUN
ejpam-4978	58	10	}	}	PUNCT
ejpam-4978	58	11	.	.	PUNCT
ejpam-4978	59	1	notice	notice	VERB
ejpam-4978	59	2	that	that	SCONJ
ejpam-4978	59	3	a	a	DET
ejpam-4978	59	4	,	,	PUNCT
ejpam-4978	59	5	d	d	NOUN
ejpam-4978	59	6	,	,	PUNCT
ejpam-4978	59	7	h	h	PROPN
ejpam-4978	59	8	∈	∈	PROPN
ejpam-4978	59	9	n2	n2	ADJ
ejpam-4978	59	10	g(f	g(f	PROPN
ejpam-4978	59	11	)	)	PUNCT
ejpam-4978	59	12	and	and	CCONJ
ejpam-4978	59	13	b	b	NOUN
ejpam-4978	59	14	,	,	PUNCT
ejpam-4978	59	15	e	e	PROPN
ejpam-4978	59	16	∈	∈	PROPN
ejpam-4978	59	17	n2	n2	ADJ
ejpam-4978	59	18	g(g	g(g	PROPN
ejpam-4978	59	19	)	)	PUNCT
ejpam-4978	59	20	.	.	PUNCT
ejpam-4978	60	1	thus	thus	ADV
ejpam-4978	60	2	,	,	PUNCT
ejpam-4978	60	3	n2	n2	ADJ
ejpam-4978	60	4	g[m	g[m	NOUN
ejpam-4978	60	5	]	]	PUNCT
ejpam-4978	60	6	=	=	SYM
ejpam-4978	60	7	v	v	X
ejpam-4978	60	8	(	(	PUNCT
ejpam-4978	60	9	g	g	NOUN
ejpam-4978	60	10	)	)	PUNCT
ejpam-4978	60	11	,	,	PUNCT
ejpam-4978	60	12	showing	show	VERB
ejpam-4978	60	13	that	that	SCONJ
ejpam-4978	60	14	m	m	NOUN
ejpam-4978	60	15	is	be	AUX
ejpam-4978	60	16	a	a	DET
ejpam-4978	60	17	hop	hop	NOUN
ejpam-4978	60	18	v.	v.	ADP
ejpam-4978	60	19	t.	t.	PROPN
ejpam-4978	60	20	bilar	bilar	PROPN
ejpam-4978	60	21	et	et	PROPN
ejpam-4978	60	22	al	al	PROPN
ejpam-4978	60	23	.	.	PUNCT
ejpam-4978	60	24	/	/	SYM
ejpam-4978	60	25	eur	eur	PROPN
ejpam-4978	60	26	.	.	PUNCT
ejpam-4978	61	1	j.	j.	PROPN
ejpam-4978	61	2	pure	pure	PROPN
ejpam-4978	61	3	appl	appl	PROPN
ejpam-4978	61	4	.	.	PROPN
ejpam-4978	61	5	math	math	PROPN
ejpam-4978	61	6	,	,	PUNCT
ejpam-4978	61	7	17	17	NUM
ejpam-4978	61	8	(	(	PUNCT
ejpam-4978	61	9	1	1	NUM
ejpam-4978	61	10	)	)	PUNCT
ejpam-4978	61	11	(	(	PUNCT
ejpam-4978	61	12	2024	2024	NUM
ejpam-4978	61	13	)	)	PUNCT
ejpam-4978	61	14	,	,	PUNCT
ejpam-4978	61	15	93	93	NUM
ejpam-4978	61	16	-	-	SYM
ejpam-4978	61	17	104	104	NUM
ejpam-4978	61	18	96	96	NUM
ejpam-4978	61	19	dominating	dominating	NOUN
ejpam-4978	61	20	set	set	NOUN
ejpam-4978	61	21	of	of	ADP
ejpam-4978	61	22	g.	g.	PROPN
ejpam-4978	61	23	however	however	ADV
ejpam-4978	61	24	,	,	PUNCT
ejpam-4978	61	25	m	m	VERB
ejpam-4978	61	26	is	be	AUX
ejpam-4978	61	27	not	not	PART
ejpam-4978	61	28	a	a	DET
ejpam-4978	61	29	vertex	vertex	NOUN
ejpam-4978	61	30	cover	cover	NOUN
ejpam-4978	61	31	of	of	ADP
ejpam-4978	61	32	g	g	NOUN
ejpam-4978	61	33	since	since	SCONJ
ejpam-4978	61	34	edges	edge	NOUN
ejpam-4978	61	35	ae	ae	PROPN
ejpam-4978	61	36	,	,	PUNCT
ejpam-4978	61	37	be	be	VERB
ejpam-4978	61	38	and	and	CCONJ
ejpam-4978	61	39	dh	dh	NOUN
ejpam-4978	61	40	are	be	AUX
ejpam-4978	61	41	not	not	PART
ejpam-4978	61	42	incident	incident	NOUN
ejpam-4978	61	43	to	to	ADP
ejpam-4978	61	44	any	any	DET
ejpam-4978	61	45	vertex	vertex	NOUN
ejpam-4978	61	46	in	in	ADP
ejpam-4978	61	47	m	m	PROPN
ejpam-4978	61	48	.	.	PUNCT
ejpam-4978	62	1	proposition	proposition	NOUN
ejpam-4978	62	2	2	2	NUM
ejpam-4978	62	3	.	.	PUNCT
ejpam-4978	63	1	let	let	VERB
ejpam-4978	63	2	g	g	NOUN
ejpam-4978	63	3	be	be	AUX
ejpam-4978	63	4	any	any	DET
ejpam-4978	63	5	graph	graph	NOUN
ejpam-4978	63	6	.	.	PUNCT
ejpam-4978	64	1	then	then	ADV
ejpam-4978	64	2	each	each	PRON
ejpam-4978	64	3	of	of	ADP
ejpam-4978	64	4	the	the	DET
ejpam-4978	64	5	following	follow	VERB
ejpam-4978	64	6	holds	hold	VERB
ejpam-4978	64	7	:	:	PUNCT
ejpam-4978	64	8	(	(	PUNCT
ejpam-4978	64	9	i	i	NOUN
ejpam-4978	64	10	)	)	PUNCT
ejpam-4978	64	11	γh(g	γh(g	PUNCT
ejpam-4978	64	12	)	)	PUNCT
ejpam-4978	64	13	≤	≤	NUM
ejpam-4978	64	14	γvch(g	γvch(g	NOUN
ejpam-4978	64	15	)	)	PUNCT
ejpam-4978	64	16	,	,	PUNCT
ejpam-4978	64	17	and	and	CCONJ
ejpam-4978	64	18	this	this	DET
ejpam-4978	64	19	bound	bind	VERB
ejpam-4978	64	20	is	be	AUX
ejpam-4978	64	21	sharp	sharp	ADJ
ejpam-4978	64	22	.	.	PUNCT
ejpam-4978	65	1	(	(	PUNCT
ejpam-4978	65	2	ii	ii	NOUN
ejpam-4978	65	3	)	)	PUNCT
ejpam-4978	65	4	β(g	β(g	PROPN
ejpam-4978	65	5	)	)	PUNCT
ejpam-4978	66	1	≤	≤	NOUN
ejpam-4978	66	2	γvch(g	γvch(g	NOUN
ejpam-4978	66	3	)	)	PUNCT
ejpam-4978	66	4	,	,	PUNCT
ejpam-4978	66	5	and	and	CCONJ
ejpam-4978	66	6	this	this	DET
ejpam-4978	66	7	bound	bind	VERB
ejpam-4978	66	8	is	be	AUX
ejpam-4978	66	9	sharp	sharp	ADJ
ejpam-4978	66	10	.	.	PUNCT
ejpam-4978	67	1	proof	proof	NOUN
ejpam-4978	67	2	.	.	PUNCT
ejpam-4978	68	1	(	(	PUNCT
ejpam-4978	68	2	i	i	NOUN
ejpam-4978	68	3	)	)	PUNCT
ejpam-4978	68	4	let	let	VERB
ejpam-4978	68	5	c	c	NOUN
ejpam-4978	68	6	be	be	AUX
ejpam-4978	68	7	a	a	DET
ejpam-4978	68	8	minimum	minimum	ADJ
ejpam-4978	68	9	vertex	vertex	NOUN
ejpam-4978	68	10	cover	cover	NOUN
ejpam-4978	68	11	hop	hop	NOUN
ejpam-4978	68	12	dominating	dominating	NOUN
ejpam-4978	68	13	set	set	NOUN
ejpam-4978	68	14	of	of	ADP
ejpam-4978	68	15	g.	g.	PROPN
ejpam-4978	68	16	then	then	ADV
ejpam-4978	68	17	c	c	PROPN
ejpam-4978	68	18	is	be	AUX
ejpam-4978	68	19	a	a	DET
ejpam-4978	68	20	hop	hop	NOUN
ejpam-4978	68	21	dominating	dominating	NOUN
ejpam-4978	68	22	in	in	ADP
ejpam-4978	68	23	g	g	PROPN
ejpam-4978	68	24	(	(	PUNCT
ejpam-4978	68	25	by	by	ADP
ejpam-4978	68	26	definition	definition	NOUN
ejpam-4978	68	27	)	)	PUNCT
ejpam-4978	68	28	.	.	PUNCT
ejpam-4978	69	1	since	since	SCONJ
ejpam-4978	69	2	γh(g	γh(g	NOUN
ejpam-4978	69	3	)	)	PUNCT
ejpam-4978	69	4	is	be	AUX
ejpam-4978	69	5	the	the	DET
ejpam-4978	69	6	minimum	minimum	ADJ
ejpam-4978	69	7	cardinality	cardinality	NOUN
ejpam-4978	69	8	among	among	ADP
ejpam-4978	69	9	all	all	DET
ejpam-4978	69	10	hop	hop	NOUN
ejpam-4978	69	11	dominating	dominating	NOUN
ejpam-4978	69	12	sets	set	NOUN
ejpam-4978	69	13	in	in	ADP
ejpam-4978	69	14	g	g	NOUN
ejpam-4978	69	15	,	,	PUNCT
ejpam-4978	69	16	it	it	PRON
ejpam-4978	69	17	follows	follow	VERB
ejpam-4978	69	18	that	that	SCONJ
ejpam-4978	69	19	γh(g	γh(g	NOUN
ejpam-4978	69	20	)	)	PUNCT
ejpam-4978	69	21	≤	≤	NUM
ejpam-4978	69	22	|c|	|c|	PROPN
ejpam-4978	69	23	=	=	SYM
ejpam-4978	69	24	γvch(g	γvch(g	PROPN
ejpam-4978	69	25	)	)	PUNCT
ejpam-4978	69	26	.	.	PUNCT
ejpam-4978	70	1	to	to	PART
ejpam-4978	70	2	see	see	VERB
ejpam-4978	70	3	that	that	SCONJ
ejpam-4978	70	4	the	the	DET
ejpam-4978	70	5	bound	bind	VERB
ejpam-4978	70	6	is	be	AUX
ejpam-4978	70	7	sharp	sharp	ADJ
ejpam-4978	70	8	,	,	PUNCT
ejpam-4978	70	9	consider	consider	VERB
ejpam-4978	70	10	g	g	NOUN
ejpam-4978	70	11	=	=	SYM
ejpam-4978	70	12	k1,n	k1,n	PROPN
ejpam-4978	70	13	.	.	PUNCT
ejpam-4978	71	1	then	then	ADV
ejpam-4978	71	2	γh(g	γh(g	NOUN
ejpam-4978	71	3	)	)	PUNCT
ejpam-4978	71	4	=	=	SYM
ejpam-4978	71	5	γvch(g	γvch(g	X
ejpam-4978	71	6	)	)	PUNCT
ejpam-4978	71	7	=	=	SYM
ejpam-4978	71	8	2	2	X
ejpam-4978	71	9	.	.	PUNCT
ejpam-4978	71	10	(	(	PUNCT
ejpam-4978	71	11	ii	ii	NOUN
ejpam-4978	71	12	)	)	PUNCT
ejpam-4978	71	13	let	let	VERB
ejpam-4978	71	14	c	c	NOUN
ejpam-4978	71	15	be	be	AUX
ejpam-4978	71	16	a	a	DET
ejpam-4978	71	17	minimum	minimum	ADJ
ejpam-4978	71	18	vertex	vertex	NOUN
ejpam-4978	71	19	cover	cover	NOUN
ejpam-4978	71	20	hop	hop	NOUN
ejpam-4978	71	21	dominating	dominating	NOUN
ejpam-4978	71	22	set	set	NOUN
ejpam-4978	71	23	of	of	ADP
ejpam-4978	71	24	g.	g.	PROPN
ejpam-4978	71	25	then	then	ADV
ejpam-4978	71	26	c	c	PROPN
ejpam-4978	71	27	is	be	AUX
ejpam-4978	71	28	a	a	DET
ejpam-4978	71	29	vertex	vertex	NOUN
ejpam-4978	71	30	cover	cover	NOUN
ejpam-4978	71	31	in	in	ADP
ejpam-4978	71	32	g	g	PROPN
ejpam-4978	71	33	(	(	PUNCT
ejpam-4978	71	34	by	by	ADP
ejpam-4978	71	35	definition	definition	NOUN
ejpam-4978	71	36	)	)	PUNCT
ejpam-4978	71	37	.	.	PUNCT
ejpam-4978	72	1	since	since	SCONJ
ejpam-4978	72	2	β(g	β(g	PROPN
ejpam-4978	72	3	)	)	PUNCT
ejpam-4978	72	4	is	be	AUX
ejpam-4978	72	5	the	the	DET
ejpam-4978	72	6	minimum	minimum	ADJ
ejpam-4978	72	7	cardinality	cardinality	NOUN
ejpam-4978	72	8	of	of	ADP
ejpam-4978	72	9	a	a	DET
ejpam-4978	72	10	vertex	vertex	NOUN
ejpam-4978	72	11	cover	cover	NOUN
ejpam-4978	72	12	set	set	VERB
ejpam-4978	72	13	in	in	ADP
ejpam-4978	72	14	g	g	NOUN
ejpam-4978	72	15	,	,	PUNCT
ejpam-4978	72	16	it	it	PRON
ejpam-4978	72	17	follows	follow	VERB
ejpam-4978	72	18	that	that	SCONJ
ejpam-4978	72	19	β(g	β(g	PROPN
ejpam-4978	72	20	)	)	PUNCT
ejpam-4978	72	21	≤	≤	NOUN
ejpam-4978	72	22	|c|	|c|	PROPN
ejpam-4978	72	23	=	=	SYM
ejpam-4978	72	24	γvch(g	γvch(g	PROPN
ejpam-4978	72	25	)	)	PUNCT
ejpam-4978	72	26	.	.	PUNCT
ejpam-4978	73	1	to	to	PART
ejpam-4978	73	2	see	see	VERB
ejpam-4978	73	3	that	that	DET
ejpam-4978	73	4	sharpness	sharpness	NOUN
ejpam-4978	73	5	is	be	AUX
ejpam-4978	73	6	attainable	attainable	ADJ
ejpam-4978	73	7	,	,	PUNCT
ejpam-4978	73	8	consider	consider	VERB
ejpam-4978	73	9	the	the	DET
ejpam-4978	73	10	graph	graph	NOUN
ejpam-4978	73	11	g	g	NOUN
ejpam-4978	73	12	in	in	ADP
ejpam-4978	73	13	figure	figure	NOUN
ejpam-4978	73	14	3	3	NUM
ejpam-4978	73	15	.	.	PUNCT
ejpam-4978	74	1	let	let	VERB
ejpam-4978	74	2	t	t	NOUN
ejpam-4978	74	3	=	=	SYM
ejpam-4978	74	4	{	{	PUNCT
ejpam-4978	74	5	b	b	PROPN
ejpam-4978	74	6	,	,	PUNCT
ejpam-4978	74	7	d	d	NOUN
ejpam-4978	74	8	,	,	PUNCT
ejpam-4978	74	9	e	e	NOUN
ejpam-4978	74	10	}	}	PUNCT
ejpam-4978	74	11	.	.	PUNCT
ejpam-4978	75	1	then	then	ADV
ejpam-4978	75	2	t	t	PROPN
ejpam-4978	75	3	is	be	AUX
ejpam-4978	75	4	a	a	DET
ejpam-4978	75	5	vertex	vertex	NOUN
ejpam-4978	75	6	cover	cover	NOUN
ejpam-4978	75	7	set	set	NOUN
ejpam-4978	75	8	of	of	ADP
ejpam-4978	75	9	g	g	NOUN
ejpam-4978	75	10	,	,	PUNCT
ejpam-4978	75	11	and	and	CCONJ
ejpam-4978	75	12	so	so	ADV
ejpam-4978	75	13	β(g	β(g	PROPN
ejpam-4978	75	14	)	)	PUNCT
ejpam-4978	75	15	≤	≤	NUM
ejpam-4978	75	16	3	3	NUM
ejpam-4978	75	17	.	.	PUNCT
ejpam-4978	76	1	since	since	SCONJ
ejpam-4978	76	2	{	{	PUNCT
ejpam-4978	76	3	x	x	NOUN
ejpam-4978	76	4	,	,	PUNCT
ejpam-4978	76	5	y	y	NOUN
ejpam-4978	76	6	}	}	PUNCT
ejpam-4978	76	7	is	be	AUX
ejpam-4978	76	8	not	not	PART
ejpam-4978	76	9	a	a	DET
ejpam-4978	76	10	vertex	vertex	NOUN
ejpam-4978	76	11	cover	cover	NOUN
ejpam-4978	76	12	of	of	ADP
ejpam-4978	76	13	g	g	NOUN
ejpam-4978	76	14	for	for	ADP
ejpam-4978	76	15	any	any	DET
ejpam-4978	76	16	pair	pair	NOUN
ejpam-4978	76	17	of	of	ADP
ejpam-4978	76	18	distinct	distinct	ADJ
ejpam-4978	76	19	vertices	vertex	NOUN
ejpam-4978	76	20	x	x	X
ejpam-4978	76	21	,	,	PUNCT
ejpam-4978	76	22	y	y	PROPN
ejpam-4978	76	23	∈	∈	PROPN
ejpam-4978	76	24	v	v	NOUN
ejpam-4978	76	25	(	(	PUNCT
ejpam-4978	76	26	g	g	NOUN
ejpam-4978	76	27	)	)	PUNCT
ejpam-4978	76	28	,	,	PUNCT
ejpam-4978	76	29	it	it	PRON
ejpam-4978	76	30	follows	follow	VERB
ejpam-4978	76	31	that	that	SCONJ
ejpam-4978	76	32	β(g	β(g	PROPN
ejpam-4978	76	33	)	)	PUNCT
ejpam-4978	76	34	≥	≥	NOUN
ejpam-4978	76	35	3	3	NUM
ejpam-4978	76	36	.	.	PUNCT
ejpam-4978	76	37	thus	thus	ADV
ejpam-4978	76	38	,	,	PUNCT
ejpam-4978	76	39	β(g	β(g	PROPN
ejpam-4978	76	40	)	)	PUNCT
ejpam-4978	76	41	=	=	SYM
ejpam-4978	77	1	3	3	X
ejpam-4978	77	2	.	.	PUNCT
ejpam-4978	77	3	now	now	ADV
ejpam-4978	77	4	,	,	PUNCT
ejpam-4978	77	5	observe	observe	VERB
ejpam-4978	77	6	that	that	SCONJ
ejpam-4978	77	7	n2	n2	PROPN
ejpam-4978	77	8	g[b	g[b	PROPN
ejpam-4978	77	9	]	]	X
ejpam-4978	77	10	=	=	PUNCT
ejpam-4978	77	11	{	{	PUNCT
ejpam-4978	77	12	b	b	PROPN
ejpam-4978	77	13	,	,	PUNCT
ejpam-4978	77	14	c	c	X
ejpam-4978	77	15	,	,	PUNCT
ejpam-4978	77	16	f	f	X
ejpam-4978	77	17	,	,	PUNCT
ejpam-4978	77	18	g	g	NOUN
ejpam-4978	77	19	}	}	PUNCT
ejpam-4978	77	20	,	,	PUNCT
ejpam-4978	77	21	n2	n2	PROPN
ejpam-4978	77	22	g[d	g[d	PROPN
ejpam-4978	77	23	]	]	X
ejpam-4978	77	24	=	=	X
ejpam-4978	77	25	{	{	PUNCT
ejpam-4978	77	26	a	a	X
ejpam-4978	77	27	,	,	PUNCT
ejpam-4978	77	28	d	d	NOUN
ejpam-4978	77	29	,	,	PUNCT
ejpam-4978	77	30	f	f	X
ejpam-4978	77	31	,	,	PUNCT
ejpam-4978	77	32	g	g	NOUN
ejpam-4978	77	33	}	}	PUNCT
ejpam-4978	77	34	and	and	CCONJ
ejpam-4978	77	35	n2	n2	ADJ
ejpam-4978	77	36	g[e	g[e	X
ejpam-4978	77	37	]	]	X
ejpam-4978	77	38	=	=	X
ejpam-4978	77	39	{	{	PUNCT
ejpam-4978	77	40	a	a	X
ejpam-4978	77	41	,	,	PUNCT
ejpam-4978	77	42	c	c	NOUN
ejpam-4978	77	43	,	,	PUNCT
ejpam-4978	77	44	e	e	NOUN
ejpam-4978	77	45	}	}	PUNCT
ejpam-4978	77	46	.	.	PUNCT
ejpam-4978	78	1	thus	thus	ADV
ejpam-4978	78	2	,	,	PUNCT
ejpam-4978	78	3	n2	n2	ADJ
ejpam-4978	78	4	g[t	g[t	NOUN
ejpam-4978	78	5	]	]	PUNCT
ejpam-4978	78	6	=	=	SYM
ejpam-4978	78	7	v	v	X
ejpam-4978	78	8	(	(	PUNCT
ejpam-4978	78	9	g	g	NOUN
ejpam-4978	78	10	)	)	PUNCT
ejpam-4978	78	11	,	,	PUNCT
ejpam-4978	78	12	showing	show	VERB
ejpam-4978	78	13	that	that	SCONJ
ejpam-4978	78	14	t	t	PROPN
ejpam-4978	78	15	is	be	AUX
ejpam-4978	78	16	a	a	DET
ejpam-4978	78	17	vertex	vertex	NOUN
ejpam-4978	78	18	cover	cover	NOUN
ejpam-4978	78	19	hop	hop	NOUN
ejpam-4978	78	20	dominating	dominating	NOUN
ejpam-4978	78	21	set	set	NOUN
ejpam-4978	78	22	of	of	ADP
ejpam-4978	78	23	g.	g.	PROPN
ejpam-4978	78	24	since	since	SCONJ
ejpam-4978	78	25	t	t	PROPN
ejpam-4978	78	26	is	be	AUX
ejpam-4978	78	27	a	a	DET
ejpam-4978	78	28	minimum	minimum	ADJ
ejpam-4978	78	29	vertex	vertex	NOUN
ejpam-4978	78	30	cover	cover	NOUN
ejpam-4978	78	31	of	of	ADP
ejpam-4978	78	32	g	g	NOUN
ejpam-4978	78	33	,	,	PUNCT
ejpam-4978	78	34	it	it	PRON
ejpam-4978	78	35	follows	follow	VERB
ejpam-4978	78	36	that	that	SCONJ
ejpam-4978	78	37	t	t	PROPN
ejpam-4978	78	38	is	be	AUX
ejpam-4978	78	39	a	a	DET
ejpam-4978	78	40	minimum	minimum	ADJ
ejpam-4978	78	41	vertex	vertex	NOUN
ejpam-4978	78	42	cover	cover	NOUN
ejpam-4978	78	43	hop	hop	NOUN
ejpam-4978	78	44	dominating	dominating	NOUN
ejpam-4978	78	45	set	set	NOUN
ejpam-4978	78	46	of	of	ADP
ejpam-4978	78	47	g	g	NOUN
ejpam-4978	78	48	,	,	PUNCT
ejpam-4978	78	49	and	and	CCONJ
ejpam-4978	78	50	so	so	ADV
ejpam-4978	78	51	γvch(g	γvch(g	NOUN
ejpam-4978	78	52	)	)	PUNCT
ejpam-4978	78	53	=	=	SYM
ejpam-4978	79	1	3	3	X
ejpam-4978	79	2	.	.	PUNCT
ejpam-4978	79	3	consequently	consequently	ADV
ejpam-4978	79	4	,	,	PUNCT
ejpam-4978	79	5	γvch(g	γvch(g	NOUN
ejpam-4978	79	6	)	)	PUNCT
ejpam-4978	79	7	=	=	SYM
ejpam-4978	79	8	3	3	X
ejpam-4978	79	9	=	=	SYM
ejpam-4978	79	10	β(g	β(g	PROPN
ejpam-4978	79	11	)	)	PUNCT
ejpam-4978	79	12	.	.	PUNCT
ejpam-4978	80	1	a	a	DET
ejpam-4978	80	2	b	b	X
ejpam-4978	80	3	c	c	NOUN
ejpam-4978	80	4	d	d	X
ejpam-4978	80	5	e	e	X
ejpam-4978	80	6	f	f	PROPN
ejpam-4978	80	7	g	g	PROPN
ejpam-4978	80	8	g	g	PROPN
ejpam-4978	80	9	:	:	PUNCT
ejpam-4978	80	10	figure	figure	VERB
ejpam-4978	80	11	3	3	NUM
ejpam-4978	80	12	:	:	PUNCT
ejpam-4978	80	13	graph	graph	VERB
ejpam-4978	80	14	g	g	NOUN
ejpam-4978	80	15	with	with	ADP
ejpam-4978	80	16	β(g	β(g	PROPN
ejpam-4978	80	17	)	)	PUNCT
ejpam-4978	81	1	=	=	SYM
ejpam-4978	81	2	γvch(g	γvch(g	PROPN
ejpam-4978	81	3	)	)	PUNCT
ejpam-4978	81	4	theorem	theorem	NOUN
ejpam-4978	81	5	1	1	NUM
ejpam-4978	81	6	.	.	PUNCT
ejpam-4978	82	1	let	let	VERB
ejpam-4978	82	2	g	g	NOUN
ejpam-4978	82	3	be	be	AUX
ejpam-4978	82	4	any	any	DET
ejpam-4978	82	5	graph	graph	NOUN
ejpam-4978	82	6	on	on	ADP
ejpam-4978	82	7	n	n	PRON
ejpam-4978	82	8	≥	≥	NUM
ejpam-4978	82	9	1	1	NUM
ejpam-4978	82	10	vertices	vertex	NOUN
ejpam-4978	82	11	.	.	PUNCT
ejpam-4978	83	1	then	then	ADV
ejpam-4978	83	2	1	1	NUM
ejpam-4978	83	3	≤	≤	NUM
ejpam-4978	83	4	γvch(g	γvch(g	NOUN
ejpam-4978	83	5	)	)	PUNCT
ejpam-4978	83	6	≤	≤	PROPN
ejpam-4978	83	7	n.	n.	NOUN
ejpam-4978	83	8	moreover	moreover	ADV
ejpam-4978	83	9	,	,	PUNCT
ejpam-4978	83	10	(	(	PUNCT
ejpam-4978	83	11	i	i	NOUN
ejpam-4978	83	12	)	)	PUNCT
ejpam-4978	83	13	γvch(g	γvch(g	X
ejpam-4978	83	14	)	)	PUNCT
ejpam-4978	83	15	=	=	SYM
ejpam-4978	83	16	1	1	NUM
ejpam-4978	83	17	if	if	SCONJ
ejpam-4978	83	18	and	and	CCONJ
ejpam-4978	83	19	only	only	ADV
ejpam-4978	83	20	if	if	SCONJ
ejpam-4978	83	21	g	g	PROPN
ejpam-4978	83	22	is	be	AUX
ejpam-4978	83	23	trivial	trivial	ADJ
ejpam-4978	83	24	.	.	PUNCT
ejpam-4978	84	1	(	(	PUNCT
ejpam-4978	84	2	ii	ii	X
ejpam-4978	84	3	)	)	PUNCT
ejpam-4978	84	4	γvch(g	γvch(g	PROPN
ejpam-4978	84	5	)	)	PUNCT
ejpam-4978	84	6	=	=	SYM
ejpam-4978	84	7	2	2	NUM
ejpam-4978	84	8	if	if	SCONJ
ejpam-4978	84	9	and	and	CCONJ
ejpam-4978	84	10	only	only	ADV
ejpam-4978	84	11	if	if	SCONJ
ejpam-4978	84	12	γh(g	γh(g	NOUN
ejpam-4978	84	13	)	)	PUNCT
ejpam-4978	84	14	=	=	SYM
ejpam-4978	84	15	2	2	X
ejpam-4978	84	16	=	=	NUM
ejpam-4978	84	17	|t	|t	VERB
ejpam-4978	85	1	|	|	ADV
ejpam-4978	85	2	such	such	ADJ
ejpam-4978	85	3	that	that	PRON
ejpam-4978	85	4	v	v	NOUN
ejpam-4978	85	5	(	(	PUNCT
ejpam-4978	85	6	g	g	NOUN
ejpam-4978	85	7	)	)	PUNCT
ejpam-4978	85	8	\t	\t	VERB
ejpam-4978	85	9	is	be	AUX
ejpam-4978	85	10	an	an	DET
ejpam-4978	85	11	independent	independent	ADJ
ejpam-4978	85	12	set	set	NOUN
ejpam-4978	85	13	of	of	ADP
ejpam-4978	85	14	g.	g.	PROPN
ejpam-4978	85	15	v.	v.	PROPN
ejpam-4978	85	16	t.	t.	PROPN
ejpam-4978	85	17	bilar	bilar	PROPN
ejpam-4978	85	18	et	et	PROPN
ejpam-4978	85	19	al	al	PROPN
ejpam-4978	85	20	.	.	PUNCT
ejpam-4978	85	21	/	/	SYM
ejpam-4978	85	22	eur	eur	PROPN
ejpam-4978	85	23	.	.	PUNCT
ejpam-4978	86	1	j.	j.	PROPN
ejpam-4978	86	2	pure	pure	PROPN
ejpam-4978	86	3	appl	appl	PROPN
ejpam-4978	86	4	.	.	PROPN
ejpam-4978	86	5	math	math	PROPN
ejpam-4978	86	6	,	,	PUNCT
ejpam-4978	86	7	17	17	NUM
ejpam-4978	86	8	(	(	PUNCT
ejpam-4978	86	9	1	1	NUM
ejpam-4978	86	10	)	)	PUNCT
ejpam-4978	86	11	(	(	PUNCT
ejpam-4978	86	12	2024	2024	NUM
ejpam-4978	86	13	)	)	PUNCT
ejpam-4978	86	14	,	,	PUNCT
ejpam-4978	86	15	93	93	NUM
ejpam-4978	86	16	-	-	SYM
ejpam-4978	86	17	104	104	NUM
ejpam-4978	86	18	97	97	NUM
ejpam-4978	86	19	(	(	PUNCT
ejpam-4978	86	20	iii	iii	NOUN
ejpam-4978	86	21	)	)	PUNCT
ejpam-4978	86	22	γvch(g	γvch(g	NOUN
ejpam-4978	86	23	)	)	PUNCT
ejpam-4978	86	24	=	=	SYM
ejpam-4978	87	1	n	n	NOUN
ejpam-4978	87	2	if	if	SCONJ
ejpam-4978	87	3	and	and	CCONJ
ejpam-4978	87	4	only	only	ADV
ejpam-4978	87	5	if	if	SCONJ
ejpam-4978	87	6	every	every	DET
ejpam-4978	87	7	component	component	NOUN
ejpam-4978	87	8	of	of	ADP
ejpam-4978	87	9	g	g	PROPN
ejpam-4978	87	10	is	be	AUX
ejpam-4978	87	11	complete	complete	ADJ
ejpam-4978	87	12	.	.	PUNCT
ejpam-4978	88	1	proof	proof	NOUN
ejpam-4978	88	2	.	.	PUNCT
ejpam-4978	89	1	clearly	clearly	ADV
ejpam-4978	89	2	,	,	PUNCT
ejpam-4978	89	3	1	1	NUM
ejpam-4978	89	4	≤	≤	NUM
ejpam-4978	89	5	γvch(g	γvch(g	ADP
ejpam-4978	89	6	)	)	PUNCT
ejpam-4978	89	7	≤	≤	NOUN
ejpam-4978	89	8	n.	n.	NOUN
ejpam-4978	89	9	(	(	PUNCT
ejpam-4978	89	10	i	i	NOUN
ejpam-4978	89	11	)	)	PUNCT
ejpam-4978	89	12	suppose	suppose	VERB
ejpam-4978	89	13	γvch(g	γvch(g	NOUN
ejpam-4978	89	14	)	)	PUNCT
ejpam-4978	89	15	=	=	SYM
ejpam-4978	90	1	1	1	X
ejpam-4978	90	2	.	.	PUNCT
ejpam-4978	91	1	if	if	SCONJ
ejpam-4978	91	2	g	g	PROPN
ejpam-4978	91	3	is	be	AUX
ejpam-4978	91	4	not	not	PART
ejpam-4978	91	5	trivial	trivial	ADJ
ejpam-4978	91	6	graph	graph	NOUN
ejpam-4978	91	7	,	,	PUNCT
ejpam-4978	91	8	then	then	ADV
ejpam-4978	91	9	γh(g	γh(g	PUNCT
ejpam-4978	91	10	)	)	PUNCT
ejpam-4978	91	11	≥	≥	NOUN
ejpam-4978	91	12	2	2	NUM
ejpam-4978	91	13	.	.	PUNCT
ejpam-4978	91	14	by	by	ADP
ejpam-4978	91	15	proposition	proposition	NOUN
ejpam-4978	91	16	2	2	NUM
ejpam-4978	91	17	,	,	PUNCT
ejpam-4978	91	18	γvch(g	γvch(g	NOUN
ejpam-4978	91	19	)	)	PUNCT
ejpam-4978	91	20	≥	≥	NOUN
ejpam-4978	91	21	2	2	NUM
ejpam-4978	91	22	,	,	PUNCT
ejpam-4978	91	23	a	a	DET
ejpam-4978	91	24	contradiction	contradiction	NOUN
ejpam-4978	91	25	.	.	PUNCT
ejpam-4978	92	1	hence	hence	ADV
ejpam-4978	92	2	,	,	PUNCT
ejpam-4978	92	3	g	g	PROPN
ejpam-4978	92	4	is	be	AUX
ejpam-4978	92	5	trivial	trivial	ADJ
ejpam-4978	92	6	.	.	PUNCT
ejpam-4978	93	1	conversely	conversely	ADV
ejpam-4978	93	2	,	,	PUNCT
ejpam-4978	93	3	suppose	suppose	VERB
ejpam-4978	93	4	g	g	PROPN
ejpam-4978	93	5	is	be	AUX
ejpam-4978	93	6	trivial	trivial	ADJ
ejpam-4978	93	7	graph	graph	NOUN
ejpam-4978	93	8	.	.	PUNCT
ejpam-4978	94	1	clearly	clearly	ADV
ejpam-4978	94	2	,	,	PUNCT
ejpam-4978	94	3	γvch	γvch	PROPN
ejpam-4978	94	4	=	=	PUNCT
ejpam-4978	94	5	1	1	X
ejpam-4978	94	6	.	.	PUNCT
ejpam-4978	94	7	(	(	PUNCT
ejpam-4978	94	8	ii	ii	NOUN
ejpam-4978	94	9	)	)	PUNCT
ejpam-4978	94	10	γvch(g	γvch(g	PROPN
ejpam-4978	94	11	)	)	PUNCT
ejpam-4978	94	12	=	=	SYM
ejpam-4978	94	13	2	2	NUM
ejpam-4978	94	14	,	,	PUNCT
ejpam-4978	94	15	say	say	VERB
ejpam-4978	94	16	t	t	NOUN
ejpam-4978	94	17	=	=	PUNCT
ejpam-4978	94	18	{	{	PUNCT
ejpam-4978	94	19	a	a	DET
ejpam-4978	94	20	,	,	PUNCT
ejpam-4978	94	21	b	b	NOUN
ejpam-4978	94	22	}	}	PUNCT
ejpam-4978	94	23	is	be	AUX
ejpam-4978	94	24	a	a	DET
ejpam-4978	94	25	minimum	minimum	ADJ
ejpam-4978	94	26	vertex	vertex	NOUN
ejpam-4978	94	27	cover	cover	NOUN
ejpam-4978	94	28	hop	hop	NOUN
ejpam-4978	94	29	dominating	dominating	NOUN
ejpam-4978	94	30	set	set	NOUN
ejpam-4978	94	31	of	of	ADP
ejpam-4978	94	32	g.	g.	PROPN
ejpam-4978	94	33	then	then	ADV
ejpam-4978	94	34	by	by	ADP
ejpam-4978	94	35	(	(	PUNCT
ejpam-4978	94	36	i	i	NOUN
ejpam-4978	94	37	)	)	PUNCT
ejpam-4978	94	38	,	,	PUNCT
ejpam-4978	94	39	g	g	PROPN
ejpam-4978	94	40	is	be	AUX
ejpam-4978	94	41	non	non	ADJ
ejpam-4978	94	42	-	-	ADJ
ejpam-4978	94	43	trivial	trivial	ADJ
ejpam-4978	94	44	and	and	CCONJ
ejpam-4978	94	45	so	so	ADV
ejpam-4978	94	46	γh(g	γh(g	PUNCT
ejpam-4978	94	47	)	)	PUNCT
ejpam-4978	94	48	≥	≥	NOUN
ejpam-4978	95	1	2	2	NUM
ejpam-4978	95	2	.	.	PUNCT
ejpam-4978	95	3	by	by	ADP
ejpam-4978	95	4	assumption	assumption	NOUN
ejpam-4978	95	5	and	and	CCONJ
ejpam-4978	95	6	proposition	proposition	NOUN
ejpam-4978	95	7	2	2	NUM
ejpam-4978	95	8	,	,	PUNCT
ejpam-4978	95	9	we	we	PRON
ejpam-4978	95	10	have	have	VERB
ejpam-4978	95	11	γh(g	γh(g	NOUN
ejpam-4978	95	12	)	)	PUNCT
ejpam-4978	95	13	=	=	SYM
ejpam-4978	96	1	2	2	X
ejpam-4978	96	2	.	.	PUNCT
ejpam-4978	96	3	now	now	ADV
ejpam-4978	96	4	,	,	PUNCT
ejpam-4978	96	5	suppose	suppose	VERB
ejpam-4978	96	6	that	that	SCONJ
ejpam-4978	96	7	v	v	X
ejpam-4978	96	8	(	(	PUNCT
ejpam-4978	96	9	g	g	NOUN
ejpam-4978	96	10	)	)	PUNCT
ejpam-4978	96	11	\	\	PROPN
ejpam-4978	96	12	t	t	PROPN
ejpam-4978	96	13	is	be	AUX
ejpam-4978	96	14	not	not	PART
ejpam-4978	96	15	an	an	DET
ejpam-4978	96	16	independent	independent	ADJ
ejpam-4978	96	17	set	set	NOUN
ejpam-4978	96	18	in	in	ADP
ejpam-4978	96	19	g.	g.	PROPN
ejpam-4978	96	20	then	then	ADV
ejpam-4978	96	21	there	there	PRON
ejpam-4978	96	22	exist	exist	VERB
ejpam-4978	96	23	a	a	DET
ejpam-4978	96	24	,	,	PUNCT
ejpam-4978	96	25	b	b	PROPN
ejpam-4978	96	26	∈	∈	PROPN
ejpam-4978	96	27	v	v	NOUN
ejpam-4978	96	28	(	(	PUNCT
ejpam-4978	96	29	g	g	NOUN
ejpam-4978	96	30	)	)	PUNCT
ejpam-4978	96	31	\	\	PROPN
ejpam-4978	96	32	t	t	NOUN
ejpam-4978	96	33	such	such	ADJ
ejpam-4978	96	34	that	that	PRON
ejpam-4978	96	35	dg(a	dg(a	PROPN
ejpam-4978	96	36	,	,	PUNCT
ejpam-4978	96	37	b	b	X
ejpam-4978	96	38	)	)	PUNCT
ejpam-4978	96	39	=	=	SYM
ejpam-4978	96	40	1	1	NUM
ejpam-4978	96	41	,	,	PUNCT
ejpam-4978	96	42	a	a	DET
ejpam-4978	96	43	contradiction	contradiction	NOUN
ejpam-4978	96	44	to	to	ADP
ejpam-4978	96	45	the	the	DET
ejpam-4978	96	46	fact	fact	NOUN
ejpam-4978	96	47	that	that	SCONJ
ejpam-4978	96	48	t	t	PROPN
ejpam-4978	96	49	is	be	AUX
ejpam-4978	96	50	a	a	DET
ejpam-4978	96	51	vertex	vertex	NOUN
ejpam-4978	96	52	cover	cover	NOUN
ejpam-4978	96	53	of	of	ADP
ejpam-4978	96	54	g.	g.	PROPN
ejpam-4978	96	55	hence	hence	ADV
ejpam-4978	96	56	,	,	PUNCT
ejpam-4978	96	57	v	v	X
ejpam-4978	96	58	(	(	PUNCT
ejpam-4978	96	59	g	g	NOUN
ejpam-4978	96	60	)	)	PUNCT
ejpam-4978	96	61	\	\	PROPN
ejpam-4978	96	62	t	t	PROPN
ejpam-4978	96	63	is	be	AUX
ejpam-4978	96	64	an	an	DET
ejpam-4978	96	65	independent	independent	ADJ
ejpam-4978	96	66	set	set	NOUN
ejpam-4978	96	67	in	in	ADP
ejpam-4978	96	68	g.	g.	NOUN
ejpam-4978	96	69	conversely	conversely	ADV
ejpam-4978	96	70	,	,	PUNCT
ejpam-4978	96	71	suppose	suppose	VERB
ejpam-4978	96	72	γh(g	γh(g	NOUN
ejpam-4978	96	73	)	)	PUNCT
ejpam-4978	96	74	=	=	SYM
ejpam-4978	96	75	2	2	X
ejpam-4978	96	76	=	=	SYM
ejpam-4978	96	77	|t	|t	NOUN
ejpam-4978	96	78	|	|	ADV
ejpam-4978	96	79	,	,	PUNCT
ejpam-4978	96	80	say	say	VERB
ejpam-4978	96	81	t	t	NOUN
ejpam-4978	96	82	=	=	PUNCT
ejpam-4978	96	83	{	{	PUNCT
ejpam-4978	96	84	a	a	PRON
ejpam-4978	96	85	,	,	PUNCT
ejpam-4978	96	86	b	b	NOUN
ejpam-4978	96	87	}	}	PUNCT
ejpam-4978	96	88	is	be	AUX
ejpam-4978	96	89	a	a	DET
ejpam-4978	96	90	γh	γh	ADV
ejpam-4978	96	91	-	-	PUNCT
ejpam-4978	96	92	set	set	NOUN
ejpam-4978	96	93	of	of	ADP
ejpam-4978	96	94	g	g	NOUN
ejpam-4978	96	95	such	such	ADJ
ejpam-4978	96	96	that	that	DET
ejpam-4978	96	97	v	v	NOUN
ejpam-4978	96	98	(	(	PUNCT
ejpam-4978	96	99	g)\t	g)\t	NOUN
ejpam-4978	96	100	is	be	AUX
ejpam-4978	96	101	an	an	DET
ejpam-4978	96	102	independent	independent	ADJ
ejpam-4978	96	103	set	set	NOUN
ejpam-4978	96	104	in	in	ADP
ejpam-4978	96	105	g.	g.	PROPN
ejpam-4978	96	106	then	then	ADV
ejpam-4978	96	107	γvch(g	γvch(g	PROPN
ejpam-4978	96	108	)	)	PUNCT
ejpam-4978	96	109	≥	≥	NOUN
ejpam-4978	96	110	2	2	NUM
ejpam-4978	96	111	by	by	ADP
ejpam-4978	96	112	proposition	proposition	NOUN
ejpam-4978	96	113	2	2	NUM
ejpam-4978	96	114	.	.	PUNCT
ejpam-4978	96	115	now	now	ADV
ejpam-4978	96	116	,	,	PUNCT
ejpam-4978	96	117	suppose	suppose	VERB
ejpam-4978	96	118	t	t	NOUN
ejpam-4978	96	119	is	be	AUX
ejpam-4978	96	120	not	not	PART
ejpam-4978	96	121	a	a	DET
ejpam-4978	96	122	vertex	vertex	NOUN
ejpam-4978	96	123	cover	cover	NOUN
ejpam-4978	96	124	of	of	ADP
ejpam-4978	96	125	g.	g.	PROPN
ejpam-4978	96	126	then	then	ADV
ejpam-4978	96	127	there	there	PRON
ejpam-4978	96	128	exist	exist	VERB
ejpam-4978	96	129	an	an	DET
ejpam-4978	96	130	edge	edge	NOUN
ejpam-4978	96	131	e	e	NOUN
ejpam-4978	96	132	=	=	PUNCT
ejpam-4978	97	1	xy	xy	PROPN
ejpam-4978	97	2	such	such	ADJ
ejpam-4978	97	3	that	that	SCONJ
ejpam-4978	97	4	x	x	NOUN
ejpam-4978	97	5	,	,	PUNCT
ejpam-4978	97	6	y	y	PROPN
ejpam-4978	97	7	/∈	/∈	PROPN
ejpam-4978	97	8	t	t	PROPN
ejpam-4978	97	9	.	.	PUNCT
ejpam-4978	98	1	it	it	PRON
ejpam-4978	98	2	follows	follow	VERB
ejpam-4978	98	3	that	that	SCONJ
ejpam-4978	98	4	x	x	SYM
ejpam-4978	98	5	,	,	PUNCT
ejpam-4978	98	6	y	y	PROPN
ejpam-4978	98	7	∈	∈	PROPN
ejpam-4978	98	8	v	v	ADP
ejpam-4978	98	9	(	(	PUNCT
ejpam-4978	98	10	g	g	NOUN
ejpam-4978	98	11	)	)	PUNCT
ejpam-4978	98	12	\	\	PROPN
ejpam-4978	98	13	t	t	PROPN
ejpam-4978	98	14	,	,	PUNCT
ejpam-4978	98	15	a	a	DET
ejpam-4978	98	16	contradiction	contradiction	NOUN
ejpam-4978	98	17	to	to	ADP
ejpam-4978	98	18	the	the	DET
ejpam-4978	98	19	fact	fact	NOUN
ejpam-4978	98	20	that	that	SCONJ
ejpam-4978	98	21	v	v	X
ejpam-4978	98	22	(	(	PUNCT
ejpam-4978	98	23	g	g	NOUN
ejpam-4978	98	24	)	)	PUNCT
ejpam-4978	98	25	\	\	PROPN
ejpam-4978	99	1	t	t	PROPN
ejpam-4978	99	2	is	be	AUX
ejpam-4978	99	3	an	an	DET
ejpam-4978	99	4	independent	independent	ADJ
ejpam-4978	99	5	set	set	NOUN
ejpam-4978	99	6	in	in	ADP
ejpam-4978	99	7	g.	g.	PROPN
ejpam-4978	99	8	hence	hence	ADV
ejpam-4978	99	9	,	,	PUNCT
ejpam-4978	99	10	t	t	PROPN
ejpam-4978	99	11	is	be	AUX
ejpam-4978	99	12	a	a	DET
ejpam-4978	99	13	vertex	vertex	NOUN
ejpam-4978	99	14	cover	cover	NOUN
ejpam-4978	99	15	of	of	ADP
ejpam-4978	99	16	g	g	NOUN
ejpam-4978	99	17	,	,	PUNCT
ejpam-4978	99	18	and	and	CCONJ
ejpam-4978	99	19	so	so	ADV
ejpam-4978	99	20	t	t	PROPN
ejpam-4978	99	21	is	be	AUX
ejpam-4978	99	22	a	a	DET
ejpam-4978	99	23	vertex	vertex	NOUN
ejpam-4978	99	24	cover	cover	NOUN
ejpam-4978	99	25	hop	hop	NOUN
ejpam-4978	99	26	dominating	dominating	NOUN
ejpam-4978	99	27	of	of	ADP
ejpam-4978	99	28	g.	g.	PROPN
ejpam-4978	99	29	consequently	consequently	ADV
ejpam-4978	99	30	,	,	PUNCT
ejpam-4978	99	31	γvch(g	γvch(g	NOUN
ejpam-4978	99	32	)	)	PUNCT
ejpam-4978	99	33	=	=	SYM
ejpam-4978	99	34	2	2	X
ejpam-4978	99	35	.	.	PUNCT
ejpam-4978	99	36	(	(	PUNCT
ejpam-4978	99	37	iii	iii	NOUN
ejpam-4978	99	38	)	)	PUNCT
ejpam-4978	99	39	suppose	suppose	VERB
ejpam-4978	99	40	that	that	SCONJ
ejpam-4978	99	41	γvch(g	γvch(g	X
ejpam-4978	99	42	)	)	PUNCT
ejpam-4978	99	43	=	=	VERB
ejpam-4978	99	44	n.	n.	NOUN
ejpam-4978	99	45	suppose	suppose	VERB
ejpam-4978	99	46	there	there	PRON
ejpam-4978	99	47	is	be	VERB
ejpam-4978	99	48	a	a	DET
ejpam-4978	99	49	component	component	NOUN
ejpam-4978	99	50	h	h	NOUN
ejpam-4978	99	51	of	of	ADP
ejpam-4978	99	52	g	g	NOUN
ejpam-4978	99	53	which	which	PRON
ejpam-4978	99	54	is	be	AUX
ejpam-4978	99	55	noncomplete	noncomplete	ADJ
ejpam-4978	99	56	.	.	PUNCT
ejpam-4978	100	1	then	then	ADV
ejpam-4978	100	2	dh(a	dh(a	NUM
ejpam-4978	100	3	,	,	PUNCT
ejpam-4978	100	4	b	b	NOUN
ejpam-4978	100	5	)	)	PUNCT
ejpam-4978	100	6	=	=	SYM
ejpam-4978	100	7	2	2	NUM
ejpam-4978	100	8	=	=	SYM
ejpam-4978	100	9	dg(a	dg(a	X
ejpam-4978	100	10	,	,	PUNCT
ejpam-4978	100	11	b	b	NOUN
ejpam-4978	100	12	)	)	PUNCT
ejpam-4978	100	13	for	for	ADP
ejpam-4978	100	14	some	some	PRON
ejpam-4978	100	15	a	a	PRON
ejpam-4978	100	16	,	,	PUNCT
ejpam-4978	100	17	b	b	PROPN
ejpam-4978	100	18	∈	∈	PROPN
ejpam-4978	100	19	v	v	NOUN
ejpam-4978	100	20	(	(	PUNCT
ejpam-4978	100	21	h	h	NOUN
ejpam-4978	100	22	)	)	PUNCT
ejpam-4978	100	23	.	.	PUNCT
ejpam-4978	101	1	let	let	VERB
ejpam-4978	102	1	c	c	NOUN
ejpam-4978	102	2	′	′	NOUN
ejpam-4978	103	1	=	=	SYM
ejpam-4978	103	2	v	v	NOUN
ejpam-4978	103	3	(	(	PUNCT
ejpam-4978	103	4	g	g	NOUN
ejpam-4978	103	5	)	)	PUNCT
ejpam-4978	103	6	\	\	NOUN
ejpam-4978	103	7	{	{	PUNCT
ejpam-4978	103	8	a	a	NOUN
ejpam-4978	103	9	}	}	PUNCT
ejpam-4978	103	10	.	.	PUNCT
ejpam-4978	104	1	then	then	ADV
ejpam-4978	104	2	c	c	X
ejpam-4978	104	3	′	′	PROPN
ejpam-4978	104	4	is	be	AUX
ejpam-4978	104	5	a	a	DET
ejpam-4978	104	6	vertex	vertex	NOUN
ejpam-4978	104	7	cover	cover	NOUN
ejpam-4978	104	8	hop	hop	NOUN
ejpam-4978	104	9	dominating	dominating	NOUN
ejpam-4978	104	10	set	set	NOUN
ejpam-4978	104	11	of	of	ADP
ejpam-4978	104	12	g.	g.	PROPN
ejpam-4978	104	13	it	it	PRON
ejpam-4978	104	14	follows	follow	VERB
ejpam-4978	104	15	that	that	SCONJ
ejpam-4978	104	16	γvch(g	γvch(g	ADP
ejpam-4978	104	17	)	)	PUNCT
ejpam-4978	104	18	≤	≤	NOUN
ejpam-4978	104	19	n	n	CCONJ
ejpam-4978	104	20	−	−	PROPN
ejpam-4978	104	21	1	1	NUM
ejpam-4978	104	22	,	,	PUNCT
ejpam-4978	104	23	a	a	DET
ejpam-4978	104	24	contradiction	contradiction	NOUN
ejpam-4978	104	25	.	.	PUNCT
ejpam-4978	105	1	thus	thus	ADV
ejpam-4978	105	2	,	,	PUNCT
ejpam-4978	105	3	every	every	DET
ejpam-4978	105	4	component	component	NOUN
ejpam-4978	105	5	of	of	ADP
ejpam-4978	105	6	g	g	PROPN
ejpam-4978	105	7	is	be	AUX
ejpam-4978	105	8	complete	complete	ADJ
ejpam-4978	105	9	.	.	PUNCT
ejpam-4978	106	1	conversely	conversely	ADV
ejpam-4978	106	2	,	,	PUNCT
ejpam-4978	106	3	suppose	suppose	VERB
ejpam-4978	106	4	that	that	SCONJ
ejpam-4978	106	5	every	every	DET
ejpam-4978	106	6	component	component	NOUN
ejpam-4978	106	7	of	of	ADP
ejpam-4978	106	8	g	g	PROPN
ejpam-4978	106	9	is	be	AUX
ejpam-4978	106	10	complete	complete	ADJ
ejpam-4978	106	11	.	.	PUNCT
ejpam-4978	107	1	then	then	ADV
ejpam-4978	107	2	γh(g	γh(g	NOUN
ejpam-4978	107	3	)	)	PUNCT
ejpam-4978	107	4	=	=	VERB
ejpam-4978	107	5	n.	n.	NOUN
ejpam-4978	107	6	by	by	ADP
ejpam-4978	107	7	proposition	proposition	NOUN
ejpam-4978	107	8	2	2	NUM
ejpam-4978	107	9	,	,	PUNCT
ejpam-4978	107	10	γvch(g	γvch(g	NOUN
ejpam-4978	107	11	)	)	PUNCT
ejpam-4978	107	12	=	=	VERB
ejpam-4978	107	13	n.	n.	NOUN
ejpam-4978	107	14	the	the	DET
ejpam-4978	107	15	next	next	ADJ
ejpam-4978	107	16	result	result	NOUN
ejpam-4978	107	17	is	be	AUX
ejpam-4978	107	18	a	a	DET
ejpam-4978	107	19	direct	direct	ADJ
ejpam-4978	107	20	consequence	consequence	NOUN
ejpam-4978	107	21	of	of	ADP
ejpam-4978	107	22	theorem	theorem	NOUN
ejpam-4978	107	23	1	1	NUM
ejpam-4978	107	24	.	.	PUNCT
ejpam-4978	107	25	corollary	corollary	ADJ
ejpam-4978	107	26	1	1	NUM
ejpam-4978	107	27	.	.	PUNCT
ejpam-4978	108	1	let	let	VERB
ejpam-4978	108	2	g	g	NOUN
ejpam-4978	108	3	be	be	AUX
ejpam-4978	108	4	any	any	DET
ejpam-4978	108	5	graph	graph	NOUN
ejpam-4978	108	6	of	of	ADP
ejpam-4978	108	7	order	order	NOUN
ejpam-4978	108	8	n	n	PRON
ejpam-4978	108	9	≥	≥	NOUN
ejpam-4978	108	10	1	1	NUM
ejpam-4978	108	11	.	.	PUNCT
ejpam-4978	109	1	then	then	ADV
ejpam-4978	109	2	each	each	PRON
ejpam-4978	109	3	of	of	ADP
ejpam-4978	109	4	the	the	DET
ejpam-4978	109	5	following	following	ADJ
ejpam-4978	109	6	statements	statement	NOUN
ejpam-4978	109	7	holds	hold	VERB
ejpam-4978	109	8	.	.	PUNCT
ejpam-4978	110	1	(	(	PUNCT
ejpam-4978	110	2	i	i	NOUN
ejpam-4978	110	3	)	)	PUNCT
ejpam-4978	110	4	γvch(g	γvch(g	PROPN
ejpam-4978	110	5	)	)	PUNCT
ejpam-4978	110	6	≥	≥	NOUN
ejpam-4978	110	7	2	2	NUM
ejpam-4978	110	8	if	if	SCONJ
ejpam-4978	110	9	and	and	CCONJ
ejpam-4978	110	10	only	only	ADV
ejpam-4978	110	11	if	if	SCONJ
ejpam-4978	110	12	g	g	PROPN
ejpam-4978	110	13	is	be	AUX
ejpam-4978	110	14	non	non	ADJ
ejpam-4978	110	15	-	-	ADJ
ejpam-4978	110	16	trivial	trivial	ADJ
ejpam-4978	110	17	.	.	PUNCT
ejpam-4978	111	1	(	(	PUNCT
ejpam-4978	111	2	ii	ii	X
ejpam-4978	111	3	)	)	PUNCT
ejpam-4978	111	4	γvch(g	γvch(g	PROPN
ejpam-4978	111	5	)	)	PUNCT
ejpam-4978	111	6	=	=	SYM
ejpam-4978	112	1	n	n	NOUN
ejpam-4978	112	2	if	if	SCONJ
ejpam-4978	112	3	g	g	PROPN
ejpam-4978	112	4	=	=	PROPN
ejpam-4978	112	5	kn	kn	PROPN
ejpam-4978	112	6	.	.	PUNCT
ejpam-4978	113	1	(	(	PUNCT
ejpam-4978	113	2	iii	iii	X
ejpam-4978	113	3	)	)	PUNCT
ejpam-4978	113	4	γvch(g	γvch(g	PROPN
ejpam-4978	113	5	)	)	PUNCT
ejpam-4978	113	6	≤	≤	NUM
ejpam-4978	113	7	n−	n−	NOUN
ejpam-4978	113	8	1	1	NUM
ejpam-4978	113	9	if	if	SCONJ
ejpam-4978	113	10	g	g	PROPN
ejpam-4978	113	11	has	have	VERB
ejpam-4978	113	12	non	non	ADJ
ejpam-4978	113	13	-	-	ADJ
ejpam-4978	113	14	complete	complete	ADJ
ejpam-4978	113	15	component	component	NOUN
ejpam-4978	113	16	.	.	PUNCT
ejpam-4978	114	1	(	(	PUNCT
ejpam-4978	114	2	iv	iv	X
ejpam-4978	114	3	)	)	PUNCT
ejpam-4978	114	4	γvch(g	γvch(g	NOUN
ejpam-4978	114	5	)	)	PUNCT
ejpam-4978	115	1	+	+	PUNCT
ejpam-4978	115	2	γvch(g	γvch(g	X
ejpam-4978	115	3	)	)	PUNCT
ejpam-4978	115	4	=	=	SYM
ejpam-4978	115	5	2n	2n	NUM
ejpam-4978	115	6	if	if	SCONJ
ejpam-4978	115	7	g	g	PROPN
ejpam-4978	115	8	=	=	PROPN
ejpam-4978	115	9	kn	kn	PROPN
ejpam-4978	115	10	or	or	CCONJ
ejpam-4978	115	11	g	g	PROPN
ejpam-4978	115	12	=	=	PROPN
ejpam-4978	115	13	kn	kn	PROPN
ejpam-4978	115	14	.	.	PUNCT
ejpam-4978	116	1	(	(	PUNCT
ejpam-4978	116	2	v	v	NOUN
ejpam-4978	116	3	)	)	PUNCT
ejpam-4978	116	4	γvch(g	γvch(g	PROPN
ejpam-4978	116	5	)	)	PUNCT
ejpam-4978	116	6	·	·	PUNCT
ejpam-4978	117	1	γvch(g	γvch(g	X
ejpam-4978	117	2	)	)	PUNCT
ejpam-4978	117	3	=	=	SYM
ejpam-4978	117	4	n2	n2	NOUN
ejpam-4978	117	5	if	if	SCONJ
ejpam-4978	117	6	g	g	PROPN
ejpam-4978	117	7	=	=	VERB
ejpam-4978	117	8	kn	kn	PROPN
ejpam-4978	117	9	or	or	CCONJ
ejpam-4978	117	10	g	g	PROPN
ejpam-4978	117	11	=	=	PROPN
ejpam-4978	117	12	kn	kn	PROPN
ejpam-4978	117	13	.	.	PUNCT
ejpam-4978	117	14	theorem	theorem	PROPN
ejpam-4978	117	15	2	2	NUM
ejpam-4978	117	16	.	.	PUNCT
ejpam-4978	118	1	let	let	VERB
ejpam-4978	118	2	g	g	PRON
ejpam-4978	118	3	be	be	AUX
ejpam-4978	118	4	a	a	DET
ejpam-4978	118	5	graph	graph	NOUN
ejpam-4978	118	6	of	of	ADP
ejpam-4978	118	7	order	order	NOUN
ejpam-4978	118	8	n	n	PRON
ejpam-4978	118	9	≥	≥	NOUN
ejpam-4978	118	10	1	1	NUM
ejpam-4978	118	11	.	.	PUNCT
ejpam-4978	119	1	then	then	ADV
ejpam-4978	119	2	each	each	PRON
ejpam-4978	119	3	of	of	ADP
ejpam-4978	119	4	the	the	DET
ejpam-4978	119	5	following	following	ADJ
ejpam-4978	119	6	statements	statement	NOUN
ejpam-4978	119	7	holds	hold	VERB
ejpam-4978	119	8	.	.	PUNCT
ejpam-4978	120	1	(	(	PUNCT
ejpam-4978	120	2	i	i	NOUN
ejpam-4978	120	3	)	)	PUNCT
ejpam-4978	120	4	let	let	VERB
ejpam-4978	120	5	g	g	NOUN
ejpam-4978	120	6	be	be	AUX
ejpam-4978	120	7	a	a	DET
ejpam-4978	120	8	connected	connected	ADJ
ejpam-4978	120	9	graph	graph	NOUN
ejpam-4978	120	10	.	.	PUNCT
ejpam-4978	121	1	then	then	ADV
ejpam-4978	121	2	γvch(g	γvch(g	X
ejpam-4978	121	3	)	)	PUNCT
ejpam-4978	121	4	=	=	SYM
ejpam-4978	122	1	n	n	NOUN
ejpam-4978	122	2	if	if	SCONJ
ejpam-4978	122	3	and	and	CCONJ
ejpam-4978	122	4	only	only	ADV
ejpam-4978	122	5	if	if	SCONJ
ejpam-4978	122	6	g	g	PROPN
ejpam-4978	122	7	=	=	PROPN
ejpam-4978	122	8	kn	kn	PROPN
ejpam-4978	122	9	.	.	PUNCT
ejpam-4978	123	1	v.	v.	ADP
ejpam-4978	123	2	t.	t.	PROPN
ejpam-4978	123	3	bilar	bilar	PROPN
ejpam-4978	123	4	et	et	PROPN
ejpam-4978	123	5	al	al	PROPN
ejpam-4978	123	6	.	.	PUNCT
ejpam-4978	123	7	/	/	SYM
ejpam-4978	123	8	eur	eur	PROPN
ejpam-4978	123	9	.	.	PUNCT
ejpam-4978	124	1	j.	j.	PROPN
ejpam-4978	124	2	pure	pure	PROPN
ejpam-4978	124	3	appl	appl	PROPN
ejpam-4978	124	4	.	.	PROPN
ejpam-4978	124	5	math	math	PROPN
ejpam-4978	124	6	,	,	PUNCT
ejpam-4978	124	7	17	17	NUM
ejpam-4978	124	8	(	(	PUNCT
ejpam-4978	124	9	1	1	NUM
ejpam-4978	124	10	)	)	PUNCT
ejpam-4978	124	11	(	(	PUNCT
ejpam-4978	124	12	2024	2024	NUM
ejpam-4978	124	13	)	)	PUNCT
ejpam-4978	124	14	,	,	PUNCT
ejpam-4978	124	15	93	93	NUM
ejpam-4978	124	16	-	-	SYM
ejpam-4978	124	17	104	104	NUM
ejpam-4978	124	18	98	98	NUM
ejpam-4978	124	19	(	(	PUNCT
ejpam-4978	124	20	ii	ii	NOUN
ejpam-4978	124	21	)	)	PUNCT
ejpam-4978	124	22	4	4	NUM
ejpam-4978	124	23	≤	≤	NUM
ejpam-4978	124	24	γvch(g	γvch(g	NOUN
ejpam-4978	124	25	)	)	PUNCT
ejpam-4978	124	26	+	+	NUM
ejpam-4978	125	1	γvch(g	γvch(g	X
ejpam-4978	125	2	)	)	PUNCT
ejpam-4978	125	3	≤	≤	NOUN
ejpam-4978	126	1	2n−	2n−	NUM
ejpam-4978	126	2	1	1	NUM
ejpam-4978	126	3	if	if	SCONJ
ejpam-4978	126	4	g	g	PROPN
ejpam-4978	126	5	has	have	VERB
ejpam-4978	126	6	one	one	NUM
ejpam-4978	126	7	non	non	ADJ
ejpam-4978	126	8	-	-	ADJ
ejpam-4978	126	9	complete	complete	ADJ
ejpam-4978	126	10	component	component	NOUN
ejpam-4978	126	11	.	.	PUNCT
ejpam-4978	127	1	(	(	PUNCT
ejpam-4978	127	2	iii	iii	NOUN
ejpam-4978	127	3	)	)	PUNCT
ejpam-4978	127	4	4	4	NUM
ejpam-4978	127	5	≤	≤	NUM
ejpam-4978	127	6	γvch(g	γvch(g	X
ejpam-4978	127	7	)	)	PUNCT
ejpam-4978	127	8	·	·	PUNCT
ejpam-4978	128	1	γvch(g	γvch(g	X
ejpam-4978	128	2	)	)	PUNCT
ejpam-4978	128	3	≤	≤	NOUN
ejpam-4978	128	4	n2	n2	NOUN
ejpam-4978	128	5	−	−	PROPN
ejpam-4978	129	1	n	n	NOUN
ejpam-4978	130	1	if	if	SCONJ
ejpam-4978	130	2	g	g	PROPN
ejpam-4978	130	3	has	have	VERB
ejpam-4978	130	4	one	one	NUM
ejpam-4978	130	5	non	non	ADJ
ejpam-4978	130	6	-	-	ADJ
ejpam-4978	130	7	complete	complete	ADJ
ejpam-4978	130	8	component	component	NOUN
ejpam-4978	130	9	.	.	PUNCT
ejpam-4978	131	1	proof	proof	NOUN
ejpam-4978	131	2	.	.	PUNCT
ejpam-4978	132	1	(	(	PUNCT
ejpam-4978	132	2	i	i	NOUN
ejpam-4978	132	3	)	)	PUNCT
ejpam-4978	132	4	suppose	suppose	VERB
ejpam-4978	132	5	γvch(g	γvch(g	NOUN
ejpam-4978	132	6	)	)	PUNCT
ejpam-4978	132	7	=	=	VERB
ejpam-4978	133	1	n.	n.	NOUN
ejpam-4978	133	2	then	then	ADV
ejpam-4978	133	3	by	by	ADP
ejpam-4978	133	4	theorem	theorem	NOUN
ejpam-4978	133	5	1(iii	1(iii	NUM
ejpam-4978	133	6	)	)	PUNCT
ejpam-4978	133	7	,	,	PUNCT
ejpam-4978	133	8	every	every	DET
ejpam-4978	133	9	component	component	NOUN
ejpam-4978	133	10	of	of	ADP
ejpam-4978	133	11	g	g	PROPN
ejpam-4978	133	12	is	be	AUX
ejpam-4978	133	13	complete	complete	ADJ
ejpam-4978	133	14	.	.	PUNCT
ejpam-4978	134	1	since	since	SCONJ
ejpam-4978	134	2	g	g	PROPN
ejpam-4978	134	3	is	be	AUX
ejpam-4978	134	4	connected	connect	VERB
ejpam-4978	134	5	,	,	PUNCT
ejpam-4978	134	6	it	it	PRON
ejpam-4978	134	7	follows	follow	VERB
ejpam-4978	134	8	that	that	SCONJ
ejpam-4978	134	9	g	g	PROPN
ejpam-4978	134	10	=	=	PROPN
ejpam-4978	134	11	kn	kn	PROPN
ejpam-4978	134	12	.	.	PUNCT
ejpam-4978	135	1	the	the	DET
ejpam-4978	135	2	converse	converse	NOUN
ejpam-4978	135	3	follows	follow	VERB
ejpam-4978	135	4	from	from	ADP
ejpam-4978	135	5	corollary	corollary	ADJ
ejpam-4978	135	6	1(ii	1(ii	NUM
ejpam-4978	135	7	)	)	PUNCT
ejpam-4978	135	8	.	.	PUNCT
ejpam-4978	136	1	(	(	PUNCT
ejpam-4978	136	2	ii	ii	NOUN
ejpam-4978	136	3	)	)	PUNCT
ejpam-4978	136	4	,	,	PUNCT
ejpam-4978	136	5	(	(	PUNCT
ejpam-4978	136	6	iii	iii	X
ejpam-4978	136	7	)	)	PUNCT
ejpam-4978	136	8	suppose	suppose	VERB
ejpam-4978	136	9	that	that	SCONJ
ejpam-4978	136	10	g	g	PROPN
ejpam-4978	136	11	has	have	VERB
ejpam-4978	136	12	one	one	NUM
ejpam-4978	136	13	non	non	ADJ
ejpam-4978	136	14	-	-	ADJ
ejpam-4978	136	15	complete	complete	ADJ
ejpam-4978	136	16	component	component	NOUN
ejpam-4978	136	17	.	.	PUNCT
ejpam-4978	137	1	then	then	ADV
ejpam-4978	137	2	by	by	ADP
ejpam-4978	137	3	corollary	corollary	ADJ
ejpam-4978	137	4	1(iii	1(iii	NUM
ejpam-4978	137	5	)	)	PUNCT
ejpam-4978	137	6	,	,	PUNCT
ejpam-4978	137	7	γvch(g	γvch(g	NOUN
ejpam-4978	137	8	)	)	PUNCT
ejpam-4978	137	9	≤	≤	NOUN
ejpam-4978	137	10	n	n	CCONJ
ejpam-4978	137	11	−	−	PROPN
ejpam-4978	137	12	1	1	NUM
ejpam-4978	137	13	.	.	PUNCT
ejpam-4978	137	14	by	by	ADP
ejpam-4978	137	15	theorem	theorem	NOUN
ejpam-4978	137	16	1	1	NUM
ejpam-4978	137	17	,	,	PUNCT
ejpam-4978	137	18	γvch(g	γvch(g	NOUN
ejpam-4978	137	19	)	)	PUNCT
ejpam-4978	137	20	≤	≤	PROPN
ejpam-4978	137	21	n.	n.	NOUN
ejpam-4978	137	22	thus	thus	ADV
ejpam-4978	137	23	,	,	PUNCT
ejpam-4978	137	24	γvch(g	γvch(g	NOUN
ejpam-4978	137	25	)	)	PUNCT
ejpam-4978	137	26	+	+	NUM
ejpam-4978	138	1	γvch(g	γvch(g	X
ejpam-4978	138	2	)	)	PUNCT
ejpam-4978	138	3	≤	≤	NOUN
ejpam-4978	138	4	2n	2n	NUM
ejpam-4978	138	5	−	−	ADP
ejpam-4978	138	6	1	1	NUM
ejpam-4978	138	7	and	and	CCONJ
ejpam-4978	138	8	γvch(g	γvch(g	PROPN
ejpam-4978	138	9	)	)	PUNCT
ejpam-4978	138	10	·	·	PUNCT
ejpam-4978	139	1	γvch(g	γvch(g	X
ejpam-4978	139	2	)	)	PUNCT
ejpam-4978	139	3	≤	≤	NOUN
ejpam-4978	139	4	n2	n2	NOUN
ejpam-4978	139	5	−	−	PROPN
ejpam-4978	139	6	n.	n.	NOUN
ejpam-4978	139	7	since	since	SCONJ
ejpam-4978	139	8	g	g	PROPN
ejpam-4978	139	9	is	be	AUX
ejpam-4978	139	10	non	non	ADJ
ejpam-4978	139	11	-	-	ADJ
ejpam-4978	139	12	trivial	trivial	ADJ
ejpam-4978	139	13	,	,	PUNCT
ejpam-4978	139	14	γvch(g	γvch(g	NOUN
ejpam-4978	139	15	)	)	PUNCT
ejpam-4978	139	16	≥	≥	NOUN
ejpam-4978	139	17	2	2	NUM
ejpam-4978	139	18	and	and	CCONJ
ejpam-4978	139	19	γvch(g	γvch(g	PROPN
ejpam-4978	139	20	)	)	PUNCT
ejpam-4978	139	21	≥	≥	NOUN
ejpam-4978	139	22	2	2	NUM
ejpam-4978	139	23	by	by	ADP
ejpam-4978	139	24	corollary	corollary	NOUN
ejpam-4978	139	25	1(i	1(i	NUM
ejpam-4978	139	26	)	)	PUNCT
ejpam-4978	139	27	.	.	PUNCT
ejpam-4978	140	1	therefore	therefore	ADV
ejpam-4978	140	2	,	,	PUNCT
ejpam-4978	140	3	γvch(g)+γvch(g	γvch(g)+γvch(g	PROPN
ejpam-4978	140	4	)	)	PUNCT
ejpam-4978	140	5	≥	≥	NOUN
ejpam-4978	140	6	4	4	NUM
ejpam-4978	140	7	and	and	CCONJ
ejpam-4978	140	8	γvch(g	γvch(g	NOUN
ejpam-4978	140	9	)	)	PUNCT
ejpam-4978	140	10	·	·	PUNCT
ejpam-4978	140	11	γvch(g	γvch(g	X
ejpam-4978	140	12	)	)	PUNCT
ejpam-4978	140	13	≥	≥	NOUN
ejpam-4978	140	14	4	4	NUM
ejpam-4978	140	15	.	.	PUNCT
ejpam-4978	140	16	consequently	consequently	ADV
ejpam-4978	140	17	,	,	PUNCT
ejpam-4978	140	18	4	4	NUM
ejpam-4978	140	19	≤	≤	NUM
ejpam-4978	140	20	γvch(g	γvch(g	NOUN
ejpam-4978	140	21	)	)	PUNCT
ejpam-4978	140	22	+	+	NUM
ejpam-4978	140	23	γvch(g	γvch(g	X
ejpam-4978	140	24	)	)	PUNCT
ejpam-4978	140	25	≤	≤	NOUN
ejpam-4978	141	1	2n−	2n−	NUM
ejpam-4978	141	2	1	1	NUM
ejpam-4978	141	3	and	and	CCONJ
ejpam-4978	141	4	4	4	NUM
ejpam-4978	141	5	≤	≤	NUM
ejpam-4978	141	6	γvch(g	γvch(g	NOUN
ejpam-4978	141	7	)	)	PUNCT
ejpam-4978	141	8	·	·	PUNCT
ejpam-4978	142	1	γvch(g	γvch(g	X
ejpam-4978	142	2	)	)	PUNCT
ejpam-4978	142	3	≤	≤	NOUN
ejpam-4978	142	4	n2	n2	NOUN
ejpam-4978	142	5	−	−	PROPN
ejpam-4978	142	6	n.	n.	NOUN
ejpam-4978	142	7	proposition	proposition	NOUN
ejpam-4978	142	8	3	3	X
ejpam-4978	142	9	.	.	PUNCT
ejpam-4978	143	1	let	let	VERB
ejpam-4978	143	2	g	g	NOUN
ejpam-4978	143	3	be	be	AUX
ejpam-4978	143	4	any	any	DET
ejpam-4978	143	5	graph	graph	NOUN
ejpam-4978	143	6	on	on	ADP
ejpam-4978	143	7	n	n	PRON
ejpam-4978	143	8	≥	≥	NUM
ejpam-4978	143	9	2	2	NUM
ejpam-4978	143	10	vertices	vertex	NOUN
ejpam-4978	143	11	.	.	PUNCT
ejpam-4978	144	1	if	if	SCONJ
ejpam-4978	144	2	γvch(g	γvch(g	NOUN
ejpam-4978	144	3	)	)	PUNCT
ejpam-4978	144	4	=	=	SYM
ejpam-4978	144	5	2	2	NUM
ejpam-4978	144	6	,	,	PUNCT
ejpam-4978	144	7	then	then	ADV
ejpam-4978	144	8	γh(g	γh(g	PUNCT
ejpam-4978	144	9	)	)	PUNCT
ejpam-4978	144	10	=	=	SYM
ejpam-4978	144	11	2	2	X
ejpam-4978	144	12	.	.	PUNCT
ejpam-4978	145	1	however	however	ADV
ejpam-4978	145	2	,	,	PUNCT
ejpam-4978	145	3	the	the	DET
ejpam-4978	145	4	converse	converse	NOUN
ejpam-4978	145	5	of	of	ADP
ejpam-4978	145	6	is	be	AUX
ejpam-4978	145	7	not	not	PART
ejpam-4978	145	8	always	always	ADV
ejpam-4978	145	9	true	true	ADJ
ejpam-4978	145	10	.	.	PUNCT
ejpam-4978	146	1	proof	proof	NOUN
ejpam-4978	146	2	.	.	PUNCT
ejpam-4978	147	1	suppose	suppose	VERB
ejpam-4978	147	2	γvch(g	γvch(g	NOUN
ejpam-4978	147	3	)	)	PUNCT
ejpam-4978	147	4	=	=	SYM
ejpam-4978	148	1	2	2	X
ejpam-4978	148	2	.	.	PUNCT
ejpam-4978	148	3	then	then	ADV
ejpam-4978	148	4	γh(g	γh(g	PUNCT
ejpam-4978	148	5	)	)	PUNCT
ejpam-4978	148	6	≤	≤	NUM
ejpam-4978	148	7	2	2	NUM
ejpam-4978	148	8	by	by	ADP
ejpam-4978	148	9	proposition	proposition	NOUN
ejpam-4978	148	10	2	2	NUM
ejpam-4978	148	11	.	.	PUNCT
ejpam-4978	148	12	since	since	SCONJ
ejpam-4978	148	13	γh(g	γh(g	NOUN
ejpam-4978	148	14	)	)	PUNCT
ejpam-4978	148	15	≥	≥	NOUN
ejpam-4978	148	16	2	2	NUM
ejpam-4978	148	17	for	for	ADP
ejpam-4978	148	18	any	any	DET
ejpam-4978	148	19	graph	graph	NOUN
ejpam-4978	148	20	of	of	ADP
ejpam-4978	148	21	order	order	NOUN
ejpam-4978	148	22	n	n	PRON
ejpam-4978	148	23	≥	≥	NOUN
ejpam-4978	148	24	2	2	NUM
ejpam-4978	148	25	,	,	PUNCT
ejpam-4978	148	26	it	it	PRON
ejpam-4978	148	27	follows	follow	VERB
ejpam-4978	148	28	that	that	PRON
ejpam-4978	148	29	γh(g	γh(g	PUNCT
ejpam-4978	148	30	)	)	PUNCT
ejpam-4978	148	31	=	=	SYM
ejpam-4978	148	32	2	2	X
ejpam-4978	148	33	.	.	PUNCT
ejpam-4978	148	34	to	to	PART
ejpam-4978	148	35	see	see	VERB
ejpam-4978	148	36	the	the	DET
ejpam-4978	148	37	converse	converse	NOUN
ejpam-4978	148	38	is	be	AUX
ejpam-4978	148	39	not	not	PART
ejpam-4978	148	40	necessarily	necessarily	ADV
ejpam-4978	148	41	true	true	ADJ
ejpam-4978	148	42	,	,	PUNCT
ejpam-4978	148	43	consider	consider	VERB
ejpam-4978	148	44	p5	p5	ADJ
ejpam-4978	148	45	=	=	PUNCT
ejpam-4978	149	1	[	[	X
ejpam-4978	149	2	v1	v1	NOUN
ejpam-4978	149	3	,	,	PUNCT
ejpam-4978	149	4	v2	v2	PROPN
ejpam-4978	149	5	,	,	PUNCT
ejpam-4978	149	6	v3	v3	PROPN
ejpam-4978	149	7	,	,	PUNCT
ejpam-4978	149	8	v4	v4	PROPN
ejpam-4978	149	9	,	,	PUNCT
ejpam-4978	149	10	v5	v5	PROPN
ejpam-4978	149	11	]	]	PUNCT
ejpam-4978	149	12	.	.	PUNCT
ejpam-4978	150	1	let	let	VERB
ejpam-4978	150	2	c	c	NOUN
ejpam-4978	150	3	=	=	PUNCT
ejpam-4978	150	4	{	{	PUNCT
ejpam-4978	150	5	v2	v2	PROPN
ejpam-4978	150	6	,	,	PUNCT
ejpam-4978	150	7	v3	v3	PROPN
ejpam-4978	150	8	}	}	PUNCT
ejpam-4978	150	9	.	.	PUNCT
ejpam-4978	151	1	then	then	ADV
ejpam-4978	151	2	c	c	PROPN
ejpam-4978	151	3	is	be	AUX
ejpam-4978	151	4	a	a	DET
ejpam-4978	151	5	γh	γh	ADV
ejpam-4978	151	6	-	-	PUNCT
ejpam-4978	151	7	set	set	NOUN
ejpam-4978	151	8	of	of	ADP
ejpam-4978	151	9	p5	p5	ADJ
ejpam-4978	151	10	and	and	CCONJ
ejpam-4978	151	11	so	so	ADV
ejpam-4978	151	12	γh(p5	γh(p5	NOUN
ejpam-4978	151	13	)	)	PUNCT
ejpam-4978	151	14	=	=	SYM
ejpam-4978	151	15	2	2	X
ejpam-4978	151	16	.	.	PUNCT
ejpam-4978	152	1	however	however	ADV
ejpam-4978	152	2	,	,	PUNCT
ejpam-4978	152	3	γvch(p5	γvch(p5	ADJ
ejpam-4978	152	4	)	)	PUNCT
ejpam-4978	152	5	=	=	SYM
ejpam-4978	153	1	3	3	X
ejpam-4978	153	2	.	.	X
ejpam-4978	153	3	definition	definition	NOUN
ejpam-4978	153	4	2	2	NUM
ejpam-4978	153	5	.	.	PUNCT
ejpam-4978	153	6	a	a	DET
ejpam-4978	153	7	pointwise	pointwise	ADJ
ejpam-4978	153	8	non	non	ADJ
ejpam-4978	153	9	-	-	ADJ
ejpam-4978	153	10	dominating	dominating	ADJ
ejpam-4978	153	11	set	set	NOUN
ejpam-4978	153	12	c	c	PROPN
ejpam-4978	153	13	⊆	⊆	NUM
ejpam-4978	153	14	v	v	NOUN
ejpam-4978	153	15	(	(	PUNCT
ejpam-4978	153	16	g	g	NOUN
ejpam-4978	153	17	)	)	PUNCT
ejpam-4978	153	18	is	be	AUX
ejpam-4978	153	19	called	call	VERB
ejpam-4978	153	20	a	a	DET
ejpam-4978	153	21	vertex	vertex	NOUN
ejpam-4978	153	22	cover	cover	NOUN
ejpam-4978	153	23	pointwise	pointwise	PROPN
ejpam-4978	153	24	non	non	ADJ
ejpam-4978	153	25	-	-	ADJ
ejpam-4978	153	26	dominating	dominating	ADJ
ejpam-4978	153	27	set	set	NOUN
ejpam-4978	153	28	of	of	ADP
ejpam-4978	153	29	g	g	PROPN
ejpam-4978	153	30	if	if	SCONJ
ejpam-4978	153	31	it	it	PRON
ejpam-4978	153	32	is	be	AUX
ejpam-4978	153	33	a	a	DET
ejpam-4978	153	34	vertex	vertex	NOUN
ejpam-4978	153	35	cover	cover	NOUN
ejpam-4978	153	36	of	of	ADP
ejpam-4978	153	37	g.	g.	PROPN
ejpam-4978	153	38	the	the	DET
ejpam-4978	153	39	minimum	minimum	ADJ
ejpam-4978	153	40	cardinality	cardinality	NOUN
ejpam-4978	153	41	of	of	ADP
ejpam-4978	153	42	a	a	DET
ejpam-4978	153	43	vertex	vertex	NOUN
ejpam-4978	153	44	cover	cover	NOUN
ejpam-4978	153	45	pointwise	pointwise	PROPN
ejpam-4978	153	46	non	non	ADJ
ejpam-4978	153	47	-	-	ADJ
ejpam-4978	153	48	dominating	dominating	ADJ
ejpam-4978	153	49	set	set	NOUN
ejpam-4978	153	50	of	of	ADP
ejpam-4978	153	51	g	g	NOUN
ejpam-4978	153	52	,	,	PUNCT
ejpam-4978	153	53	denoted	denote	VERB
ejpam-4978	153	54	by	by	ADP
ejpam-4978	153	55	vcpnd(g	vcpnd(g	PROPN
ejpam-4978	153	56	)	)	PUNCT
ejpam-4978	153	57	,	,	PUNCT
ejpam-4978	153	58	is	be	AUX
ejpam-4978	153	59	called	call	VERB
ejpam-4978	153	60	a	a	DET
ejpam-4978	153	61	vertex	vertex	NOUN
ejpam-4978	153	62	cover	cover	NOUN
ejpam-4978	153	63	pointwise	pointwise	PROPN
ejpam-4978	153	64	non	non	ADJ
ejpam-4978	153	65	-	-	ADJ
ejpam-4978	153	66	domination	domination	ADJ
ejpam-4978	153	67	number	number	NOUN
ejpam-4978	153	68	of	of	ADP
ejpam-4978	153	69	g.	g.	PROPN
ejpam-4978	153	70	any	any	DET
ejpam-4978	153	71	vertex	vertex	NOUN
ejpam-4978	153	72	cover	cover	NOUN
ejpam-4978	153	73	pointwise	pointwise	PROPN
ejpam-4978	153	74	non	non	ADJ
ejpam-4978	153	75	-	-	ADJ
ejpam-4978	153	76	dominating	dominating	ADJ
ejpam-4978	153	77	set	set	NOUN
ejpam-4978	153	78	of	of	ADP
ejpam-4978	153	79	g	g	PROPN
ejpam-4978	153	80	with	with	ADP
ejpam-4978	153	81	cardinality	cardinality	NOUN
ejpam-4978	153	82	equal	equal	ADJ
ejpam-4978	153	83	to	to	ADP
ejpam-4978	153	84	vcpnd(g	vcpnd(g	PROPN
ejpam-4978	153	85	)	)	PUNCT
ejpam-4978	153	86	is	be	AUX
ejpam-4978	153	87	called	call	VERB
ejpam-4978	153	88	a	a	DET
ejpam-4978	153	89	vcpnd	vcpnd	NOUN
ejpam-4978	153	90	-	-	PUNCT
ejpam-4978	153	91	set	set	NOUN
ejpam-4978	153	92	of	of	ADP
ejpam-4978	153	93	g.	g.	PROPN
ejpam-4978	153	94	example	example	NOUN
ejpam-4978	154	1	2	2	X
ejpam-4978	154	2	.	.	X
ejpam-4978	154	3	consider	consider	VERB
ejpam-4978	154	4	the	the	DET
ejpam-4978	154	5	graph	graph	NOUN
ejpam-4978	154	6	g	g	NOUN
ejpam-4978	154	7	in	in	ADP
ejpam-4978	154	8	figure	figure	NOUN
ejpam-4978	154	9	4	4	NUM
ejpam-4978	154	10	.	.	PUNCT
ejpam-4978	155	1	let	let	VERB
ejpam-4978	155	2	c	c	NOUN
ejpam-4978	155	3	=	=	PUNCT
ejpam-4978	155	4	{	{	PUNCT
ejpam-4978	155	5	a	a	PRON
ejpam-4978	155	6	,	,	PUNCT
ejpam-4978	155	7	b	b	NOUN
ejpam-4978	155	8	,	,	PUNCT
ejpam-4978	155	9	f	f	NOUN
ejpam-4978	155	10	}	}	PUNCT
ejpam-4978	155	11	.	.	PUNCT
ejpam-4978	156	1	notice	notice	VERB
ejpam-4978	156	2	that	that	SCONJ
ejpam-4978	156	3	every	every	DET
ejpam-4978	156	4	edge	edge	NOUN
ejpam-4978	156	5	of	of	ADP
ejpam-4978	156	6	g	g	PROPN
ejpam-4978	156	7	is	be	AUX
ejpam-4978	156	8	incident	incident	NOUN
ejpam-4978	156	9	to	to	ADP
ejpam-4978	156	10	atleast	atleast	VERB
ejpam-4978	156	11	one	one	NUM
ejpam-4978	156	12	vertex	vertex	NOUN
ejpam-4978	156	13	in	in	ADP
ejpam-4978	156	14	c.	c.	PROPN
ejpam-4978	156	15	thus	thus	ADV
ejpam-4978	156	16	,	,	PUNCT
ejpam-4978	156	17	c	c	PROPN
ejpam-4978	156	18	is	be	AUX
ejpam-4978	156	19	a	a	DET
ejpam-4978	156	20	vertex	vertex	NOUN
ejpam-4978	156	21	cover	cover	NOUN
ejpam-4978	156	22	set	set	NOUN
ejpam-4978	156	23	of	of	ADP
ejpam-4978	156	24	g.	g.	PROPN
ejpam-4978	156	25	now	now	ADV
ejpam-4978	156	26	,	,	PUNCT
ejpam-4978	156	27	since	since	SCONJ
ejpam-4978	156	28	c	c	X
ejpam-4978	156	29	,	,	PUNCT
ejpam-4978	156	30	d	d	NOUN
ejpam-4978	156	31	,	,	PUNCT
ejpam-4978	156	32	e	e	NOUN
ejpam-4978	156	33	/∈	/∈	PUNCT
ejpam-4978	156	34	ng(a	ng(a	NUM
ejpam-4978	156	35	)	)	PUNCT
ejpam-4978	156	36	,	,	PUNCT
ejpam-4978	156	37	it	it	PRON
ejpam-4978	156	38	follows	follow	VERB
ejpam-4978	156	39	that	that	SCONJ
ejpam-4978	156	40	c	c	PROPN
ejpam-4978	156	41	is	be	AUX
ejpam-4978	156	42	a	a	DET
ejpam-4978	156	43	pointwise	pointwise	ADJ
ejpam-4978	156	44	non	non	ADJ
ejpam-4978	156	45	-	-	ADJ
ejpam-4978	156	46	dominating	dominating	ADJ
ejpam-4978	156	47	set	set	NOUN
ejpam-4978	156	48	of	of	ADP
ejpam-4978	156	49	g.	g.	PROPN
ejpam-4978	156	50	hence	hence	ADV
ejpam-4978	156	51	,	,	PUNCT
ejpam-4978	156	52	c	c	PROPN
ejpam-4978	156	53	is	be	AUX
ejpam-4978	156	54	a	a	DET
ejpam-4978	156	55	vertex	vertex	NOUN
ejpam-4978	156	56	cover	cover	NOUN
ejpam-4978	156	57	pointwise	pointwise	PROPN
ejpam-4978	156	58	non	non	ADJ
ejpam-4978	156	59	-	-	ADJ
ejpam-4978	156	60	dominating	dominating	ADJ
ejpam-4978	156	61	set	set	NOUN
ejpam-4978	156	62	of	of	ADP
ejpam-4978	156	63	g.	g.	PROPN
ejpam-4978	156	64	moreover	moreover	ADV
ejpam-4978	156	65	,	,	PUNCT
ejpam-4978	156	66	it	it	PRON
ejpam-4978	156	67	can	can	AUX
ejpam-4978	156	68	be	be	AUX
ejpam-4978	156	69	verified	verify	VERB
ejpam-4978	156	70	that	that	SCONJ
ejpam-4978	156	71	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	156	72	)	)	PUNCT
ejpam-4978	156	73	=	=	SYM
ejpam-4978	157	1	3	3	X
ejpam-4978	157	2	.	.	X
ejpam-4978	158	1	v.	v.	ADP
ejpam-4978	158	2	t.	t.	PROPN
ejpam-4978	158	3	bilar	bilar	PROPN
ejpam-4978	158	4	et	et	PROPN
ejpam-4978	158	5	al	al	PROPN
ejpam-4978	158	6	.	.	PUNCT
ejpam-4978	158	7	/	/	SYM
ejpam-4978	158	8	eur	eur	PROPN
ejpam-4978	158	9	.	.	PUNCT
ejpam-4978	159	1	j.	j.	PROPN
ejpam-4978	159	2	pure	pure	PROPN
ejpam-4978	159	3	appl	appl	PROPN
ejpam-4978	159	4	.	.	PROPN
ejpam-4978	159	5	math	math	PROPN
ejpam-4978	159	6	,	,	PUNCT
ejpam-4978	159	7	17	17	NUM
ejpam-4978	159	8	(	(	PUNCT
ejpam-4978	159	9	1	1	NUM
ejpam-4978	159	10	)	)	PUNCT
ejpam-4978	159	11	(	(	PUNCT
ejpam-4978	159	12	2024	2024	NUM
ejpam-4978	159	13	)	)	PUNCT
ejpam-4978	159	14	,	,	PUNCT
ejpam-4978	159	15	93	93	NUM
ejpam-4978	159	16	-	-	SYM
ejpam-4978	159	17	104	104	NUM
ejpam-4978	159	18	99	99	NUM
ejpam-4978	159	19	b	b	NOUN
ejpam-4978	159	20	a	a	DET
ejpam-4978	159	21	c	c	NOUN
ejpam-4978	159	22	d	d	X
ejpam-4978	159	23	e	e	PROPN
ejpam-4978	159	24	f	f	PROPN
ejpam-4978	159	25	g	g	NOUN
ejpam-4978	159	26	:	:	PUNCT
ejpam-4978	159	27	figure	figure	VERB
ejpam-4978	159	28	4	4	NUM
ejpam-4978	159	29	:	:	PUNCT
ejpam-4978	159	30	graph	graph	VERB
ejpam-4978	159	31	g	g	NOUN
ejpam-4978	159	32	with	with	ADP
ejpam-4978	159	33	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	159	34	)	)	PUNCT
ejpam-4978	159	35	=	=	SYM
ejpam-4978	159	36	3	3	NUM
ejpam-4978	159	37	theorem	theorem	NOUN
ejpam-4978	159	38	3	3	X
ejpam-4978	159	39	.	.	PUNCT
ejpam-4978	160	1	let	let	VERB
ejpam-4978	160	2	g	g	NOUN
ejpam-4978	160	3	be	be	AUX
ejpam-4978	160	4	any	any	DET
ejpam-4978	160	5	graph	graph	NOUN
ejpam-4978	160	6	of	of	ADP
ejpam-4978	160	7	order	order	NOUN
ejpam-4978	161	1	n.	n.	NOUN
ejpam-4978	161	2	then	then	ADV
ejpam-4978	161	3	each	each	PRON
ejpam-4978	161	4	of	of	ADP
ejpam-4978	161	5	the	the	DET
ejpam-4978	161	6	following	following	NOUN
ejpam-4978	161	7	is	be	AUX
ejpam-4978	161	8	true	true	ADJ
ejpam-4978	161	9	.	.	PUNCT
ejpam-4978	162	1	(	(	PUNCT
ejpam-4978	162	2	i	i	NOUN
ejpam-4978	162	3	)	)	PUNCT
ejpam-4978	162	4	1	1	NUM
ejpam-4978	162	5	≤	≤	NUM
ejpam-4978	162	6	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	162	7	)	)	PUNCT
ejpam-4978	162	8	≤	≤	NUM
ejpam-4978	162	9	n	n	CCONJ
ejpam-4978	162	10	(	(	PUNCT
ejpam-4978	162	11	ii	ii	NOUN
ejpam-4978	162	12	)	)	PUNCT
ejpam-4978	162	13	pnd(g	pnd(g	PROPN
ejpam-4978	162	14	)	)	PUNCT
ejpam-4978	162	15	≤	≤	NUM
ejpam-4978	162	16	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	162	17	)	)	PUNCT
ejpam-4978	162	18	.	.	PUNCT
ejpam-4978	163	1	(	(	PUNCT
ejpam-4978	163	2	iii	iii	X
ejpam-4978	163	3	)	)	PUNCT
ejpam-4978	163	4	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	163	5	)	)	PUNCT
ejpam-4978	163	6	=	=	SYM
ejpam-4978	163	7	1	1	NUM
ejpam-4978	163	8	if	if	SCONJ
ejpam-4978	163	9	and	and	CCONJ
ejpam-4978	163	10	only	only	ADV
ejpam-4978	163	11	if	if	SCONJ
ejpam-4978	163	12	every	every	DET
ejpam-4978	163	13	component	component	NOUN
ejpam-4978	163	14	of	of	ADP
ejpam-4978	163	15	g	g	PROPN
ejpam-4978	163	16	is	be	AUX
ejpam-4978	163	17	trivial	trivial	ADJ
ejpam-4978	163	18	.	.	PUNCT
ejpam-4978	164	1	(	(	PUNCT
ejpam-4978	164	2	iv	iv	X
ejpam-4978	164	3	)	)	PUNCT
ejpam-4978	164	4	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	164	5	)	)	PUNCT
ejpam-4978	165	1	=	=	SYM
ejpam-4978	166	1	n	n	NOUN
ejpam-4978	166	2	if	if	SCONJ
ejpam-4978	166	3	and	and	CCONJ
ejpam-4978	166	4	only	only	ADV
ejpam-4978	166	5	if	if	SCONJ
ejpam-4978	166	6	every	every	DET
ejpam-4978	166	7	component	component	NOUN
ejpam-4978	166	8	of	of	ADP
ejpam-4978	166	9	g	g	PROPN
ejpam-4978	166	10	is	be	AUX
ejpam-4978	166	11	a	a	DET
ejpam-4978	166	12	non	non	ADJ
ejpam-4978	166	13	-	-	ADJ
ejpam-4978	166	14	trivial	trivial	ADJ
ejpam-4978	166	15	complete	complete	ADJ
ejpam-4978	166	16	graph	graph	NOUN
ejpam-4978	166	17	.	.	PUNCT
ejpam-4978	167	1	proof	proof	NOUN
ejpam-4978	167	2	.	.	PUNCT
ejpam-4978	168	1	(	(	PUNCT
ejpam-4978	168	2	i	i	NOUN
ejpam-4978	168	3	)	)	PUNCT
ejpam-4978	168	4	since	since	SCONJ
ejpam-4978	168	5	any	any	DET
ejpam-4978	168	6	vertex	vertex	NOUN
ejpam-4978	168	7	cover	cover	NOUN
ejpam-4978	168	8	pointwise	pointwise	ADP
ejpam-4978	168	9	non	non	ADJ
ejpam-4978	168	10	-	-	ADJ
ejpam-4978	168	11	dominating	dominating	ADJ
ejpam-4978	168	12	set	set	NOUN
ejpam-4978	168	13	in	in	ADP
ejpam-4978	168	14	g	g	PROPN
ejpam-4978	168	15	is	be	AUX
ejpam-4978	168	16	a	a	DET
ejpam-4978	168	17	non	non	ADJ
ejpam-4978	168	18	-	-	ADJ
ejpam-4978	168	19	empty	empty	ADJ
ejpam-4978	168	20	,	,	PUNCT
ejpam-4978	168	21	it	it	PRON
ejpam-4978	168	22	follows	follow	VERB
ejpam-4978	168	23	that	that	PRON
ejpam-4978	168	24	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	168	25	)	)	PUNCT
ejpam-4978	168	26	≥	≥	NOUN
ejpam-4978	168	27	1	1	NUM
ejpam-4978	168	28	.	.	PUNCT
ejpam-4978	169	1	also	also	ADV
ejpam-4978	169	2	,	,	PUNCT
ejpam-4978	169	3	since	since	SCONJ
ejpam-4978	169	4	every	every	DET
ejpam-4978	169	5	vertex	vertex	NOUN
ejpam-4978	169	6	cover	cover	VERB
ejpam-4978	169	7	pointwise	pointwise	ADP
ejpam-4978	169	8	non	non	ADJ
ejpam-4978	169	9	-	-	ADJ
ejpam-4978	169	10	dominating	dominating	ADJ
ejpam-4978	169	11	set	set	NOUN
ejpam-4978	169	12	c	c	NOUN
ejpam-4978	169	13	is	be	AUX
ejpam-4978	169	14	contained	contain	VERB
ejpam-4978	169	15	in	in	ADP
ejpam-4978	169	16	v	v	NOUN
ejpam-4978	169	17	(	(	PUNCT
ejpam-4978	169	18	g	g	NOUN
ejpam-4978	169	19	)	)	PUNCT
ejpam-4978	169	20	,	,	PUNCT
ejpam-4978	169	21	we	we	PRON
ejpam-4978	169	22	have	have	VERB
ejpam-4978	169	23	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	169	24	)	)	PUNCT
ejpam-4978	169	25	≤	≤	NOUN
ejpam-4978	169	26	n.	n.	NOUN
ejpam-4978	169	27	therefore	therefore	ADV
ejpam-4978	169	28	,	,	PUNCT
ejpam-4978	169	29	1	1	NUM
ejpam-4978	169	30	≤	≤	NUM
ejpam-4978	169	31	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	169	32	)	)	PUNCT
ejpam-4978	169	33	≤	≤	NOUN
ejpam-4978	169	34	n.	n.	NOUN
ejpam-4978	169	35	(	(	PUNCT
ejpam-4978	169	36	ii	ii	NOUN
ejpam-4978	169	37	)	)	PUNCT
ejpam-4978	169	38	let	let	VERB
ejpam-4978	169	39	c	c	NOUN
ejpam-4978	169	40	be	be	AUX
ejpam-4978	169	41	a	a	DET
ejpam-4978	169	42	minimum	minimum	ADJ
ejpam-4978	169	43	vertex	vertex	NOUN
ejpam-4978	169	44	cover	cover	NOUN
ejpam-4978	169	45	pointwise	pointwise	PROPN
ejpam-4978	169	46	non	non	ADJ
ejpam-4978	169	47	-	-	ADJ
ejpam-4978	169	48	dominating	dominating	ADJ
ejpam-4978	169	49	set	set	NOUN
ejpam-4978	169	50	of	of	ADP
ejpam-4978	169	51	g.	g.	PROPN
ejpam-4978	169	52	then	then	ADV
ejpam-4978	169	53	c	c	PROPN
ejpam-4978	169	54	is	be	AUX
ejpam-4978	169	55	a	a	DET
ejpam-4978	169	56	pointwise	pointwise	ADJ
ejpam-4978	169	57	non	non	ADJ
ejpam-4978	169	58	-	-	ADJ
ejpam-4978	169	59	dominating	dominating	ADJ
ejpam-4978	169	60	(	(	PUNCT
ejpam-4978	169	61	by	by	ADP
ejpam-4978	169	62	definition	definition	NOUN
ejpam-4978	169	63	)	)	PUNCT
ejpam-4978	169	64	.	.	PUNCT
ejpam-4978	170	1	since	since	SCONJ
ejpam-4978	170	2	pnd(g	pnd(g	PROPN
ejpam-4978	170	3	)	)	PUNCT
ejpam-4978	170	4	is	be	AUX
ejpam-4978	170	5	the	the	DET
ejpam-4978	170	6	minimum	minimum	ADJ
ejpam-4978	170	7	cardinality	cardinality	NOUN
ejpam-4978	170	8	among	among	ADP
ejpam-4978	170	9	all	all	DET
ejpam-4978	170	10	pointwise	pointwise	PROPN
ejpam-4978	170	11	non	non	ADJ
ejpam-4978	170	12	-	-	ADJ
ejpam-4978	170	13	dominating	dominating	ADJ
ejpam-4978	170	14	sets	set	NOUN
ejpam-4978	170	15	in	in	ADP
ejpam-4978	170	16	g	g	NOUN
ejpam-4978	170	17	,	,	PUNCT
ejpam-4978	170	18	we	we	PRON
ejpam-4978	170	19	have	have	VERB
ejpam-4978	170	20	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	170	21	)	)	PUNCT
ejpam-4978	171	1	=	=	SYM
ejpam-4978	171	2	|c|	|c|	PROPN
ejpam-4978	171	3	≥	≥	NOUN
ejpam-4978	171	4	pnd(g	pnd(g	ADP
ejpam-4978	171	5	)	)	PUNCT
ejpam-4978	171	6	.	.	PUNCT
ejpam-4978	172	1	(	(	PUNCT
ejpam-4978	172	2	iii	iii	X
ejpam-4978	172	3	)	)	PUNCT
ejpam-4978	172	4	suppose	suppose	VERB
ejpam-4978	172	5	vcpnd(g	vcpnd(g	ADP
ejpam-4978	172	6	)	)	PUNCT
ejpam-4978	172	7	=	=	SYM
ejpam-4978	172	8	1	1	X
ejpam-4978	172	9	,	,	PUNCT
ejpam-4978	172	10	say	say	VERB
ejpam-4978	172	11	,	,	PUNCT
ejpam-4978	172	12	{	{	PUNCT
ejpam-4978	172	13	v	v	NOUN
ejpam-4978	172	14	}	}	PUNCT
ejpam-4978	172	15	is	be	AUX
ejpam-4978	172	16	a	a	DET
ejpam-4978	172	17	vcpnd	vcpnd	NOUN
ejpam-4978	172	18	-	-	PUNCT
ejpam-4978	172	19	set	set	NOUN
ejpam-4978	172	20	of	of	ADP
ejpam-4978	172	21	g.	g.	PROPN
ejpam-4978	172	22	suppose	suppose	VERB
ejpam-4978	172	23	there	there	PRON
ejpam-4978	172	24	is	be	VERB
ejpam-4978	172	25	a	a	DET
ejpam-4978	172	26	component	component	NOUN
ejpam-4978	172	27	w	w	NOUN
ejpam-4978	172	28	of	of	ADP
ejpam-4978	172	29	g	g	NOUN
ejpam-4978	172	30	which	which	PRON
ejpam-4978	172	31	is	be	AUX
ejpam-4978	172	32	non	non	ADJ
ejpam-4978	172	33	-	-	ADJ
ejpam-4978	172	34	trivial	trivial	ADJ
ejpam-4978	172	35	.	.	PUNCT
ejpam-4978	173	1	then	then	ADV
ejpam-4978	173	2	there	there	PRON
ejpam-4978	173	3	exist	exist	VERB
ejpam-4978	173	4	a	a	PRON
ejpam-4978	173	5	,	,	PUNCT
ejpam-4978	173	6	b	b	PROPN
ejpam-4978	173	7	∈	∈	PROPN
ejpam-4978	173	8	v	v	ADP
ejpam-4978	173	9	(	(	PUNCT
ejpam-4978	173	10	w	w	NOUN
ejpam-4978	173	11	)	)	PUNCT
ejpam-4978	173	12	such	such	ADJ
ejpam-4978	173	13	that	that	SCONJ
ejpam-4978	173	14	ab	ab	PROPN
ejpam-4978	173	15	∈	∈	PROPN
ejpam-4978	173	16	e(w	e(w	PROPN
ejpam-4978	173	17	)	)	PUNCT
ejpam-4978	173	18	⊆	⊆	NUM
ejpam-4978	173	19	e(g	e(g	NOUN
ejpam-4978	173	20	)	)	PUNCT
ejpam-4978	173	21	.	.	PUNCT
ejpam-4978	174	1	if	if	SCONJ
ejpam-4978	174	2	v	v	ADP
ejpam-4978	174	3	̸=	̸=	PROPN
ejpam-4978	174	4	a	a	PRON
ejpam-4978	174	5	,	,	PUNCT
ejpam-4978	174	6	b	b	NOUN
ejpam-4978	174	7	,	,	PUNCT
ejpam-4978	174	8	then	then	ADV
ejpam-4978	174	9	vcpnd(g	vcpnd(g	PROPN
ejpam-4978	174	10	)	)	PUNCT
ejpam-4978	174	11	≥	≥	NOUN
ejpam-4978	174	12	2	2	NUM
ejpam-4978	174	13	,	,	PUNCT
ejpam-4978	174	14	a	a	DET
ejpam-4978	174	15	contradiction	contradiction	NOUN
ejpam-4978	174	16	.	.	PUNCT
ejpam-4978	175	1	suppose	suppose	VERB
ejpam-4978	175	2	v	v	X
ejpam-4978	175	3	=	=	NOUN
ejpam-4978	175	4	a.	a.	NOUN
ejpam-4978	175	5	then	then	ADV
ejpam-4978	175	6	b	b	X
ejpam-4978	175	7	must	must	AUX
ejpam-4978	175	8	also	also	ADV
ejpam-4978	175	9	be	be	AUX
ejpam-4978	175	10	in	in	ADP
ejpam-4978	175	11	the	the	DET
ejpam-4978	175	12	vertex	vertex	NOUN
ejpam-4978	175	13	cover	cover	NOUN
ejpam-4978	175	14	pointwise	pointwise	PROPN
ejpam-4978	175	15	non	non	ADJ
ejpam-4978	175	16	-	-	ADJ
ejpam-4978	175	17	dominating	dominating	ADJ
ejpam-4978	175	18	set	set	NOUN
ejpam-4978	175	19	s	s	PROPN
ejpam-4978	175	20	of	of	ADP
ejpam-4978	175	21	g.	g.	PROPN
ejpam-4978	175	22	hence	hence	ADV
ejpam-4978	175	23	,	,	PUNCT
ejpam-4978	175	24	vcpnd(g	vcpnd(g	PROPN
ejpam-4978	175	25	)	)	PUNCT
ejpam-4978	175	26	≥	≥	NOUN
ejpam-4978	175	27	2	2	NUM
ejpam-4978	175	28	,	,	PUNCT
ejpam-4978	175	29	a	a	DET
ejpam-4978	175	30	contradiction	contradiction	NOUN
ejpam-4978	175	31	.	.	PUNCT
ejpam-4978	176	1	therefore	therefore	ADV
ejpam-4978	176	2	,	,	PUNCT
ejpam-4978	176	3	every	every	DET
ejpam-4978	176	4	component	component	NOUN
ejpam-4978	176	5	of	of	ADP
ejpam-4978	176	6	g	g	PROPN
ejpam-4978	176	7	is	be	AUX
ejpam-4978	176	8	trivial	trivial	ADJ
ejpam-4978	176	9	.	.	PUNCT
ejpam-4978	177	1	the	the	DET
ejpam-4978	177	2	converse	converse	NOUN
ejpam-4978	177	3	is	be	AUX
ejpam-4978	177	4	clear	clear	ADJ
ejpam-4978	177	5	.	.	PUNCT
ejpam-4978	178	1	(	(	PUNCT
ejpam-4978	178	2	iv	iv	X
ejpam-4978	178	3	)	)	PUNCT
ejpam-4978	178	4	suppose	suppose	VERB
ejpam-4978	178	5	vcpnd(g	vcpnd(g	ADP
ejpam-4978	178	6	)	)	PUNCT
ejpam-4978	178	7	=	=	SYM
ejpam-4978	178	8	n	n	CCONJ
ejpam-4978	178	9	,	,	PUNCT
ejpam-4978	178	10	say	say	INTJ
ejpam-4978	178	11	,	,	PUNCT
ejpam-4978	178	12	c	c	PROPN
ejpam-4978	178	13	=	=	SYM
ejpam-4978	178	14	v	v	PROPN
ejpam-4978	178	15	(	(	PUNCT
ejpam-4978	178	16	g	g	NOUN
ejpam-4978	178	17	)	)	PUNCT
ejpam-4978	178	18	is	be	AUX
ejpam-4978	178	19	the	the	DET
ejpam-4978	178	20	vcpnd	vcpnd	NOUN
ejpam-4978	178	21	-	-	PUNCT
ejpam-4978	178	22	set	set	NOUN
ejpam-4978	178	23	of	of	ADP
ejpam-4978	178	24	g.	g.	PROPN
ejpam-4978	178	25	then	then	ADV
ejpam-4978	178	26	by	by	ADP
ejpam-4978	178	27	(	(	PUNCT
ejpam-4978	178	28	iii	iii	NOUN
ejpam-4978	178	29	)	)	PUNCT
ejpam-4978	178	30	,	,	PUNCT
ejpam-4978	178	31	every	every	DET
ejpam-4978	178	32	component	component	NOUN
ejpam-4978	178	33	of	of	ADP
ejpam-4978	178	34	g	g	PROPN
ejpam-4978	178	35	is	be	AUX
ejpam-4978	178	36	a	a	DET
ejpam-4978	178	37	non	non	ADJ
ejpam-4978	178	38	-	-	ADJ
ejpam-4978	178	39	trivial	trivial	ADJ
ejpam-4978	178	40	graph	graph	NOUN
ejpam-4978	178	41	.	.	PUNCT
ejpam-4978	179	1	now	now	ADV
ejpam-4978	179	2	,	,	PUNCT
ejpam-4978	179	3	suppose	suppose	VERB
ejpam-4978	179	4	there	there	PRON
ejpam-4978	179	5	is	be	VERB
ejpam-4978	179	6	a	a	DET
ejpam-4978	179	7	component	component	NOUN
ejpam-4978	179	8	c	c	NOUN
ejpam-4978	179	9	of	of	ADP
ejpam-4978	179	10	g	g	NOUN
ejpam-4978	179	11	which	which	PRON
ejpam-4978	179	12	is	be	AUX
ejpam-4978	179	13	non	non	ADJ
ejpam-4978	179	14	-	-	ADJ
ejpam-4978	179	15	complete	complete	ADJ
ejpam-4978	179	16	.	.	PUNCT
ejpam-4978	180	1	then	then	ADV
ejpam-4978	180	2	there	there	PRON
ejpam-4978	180	3	exist	exist	VERB
ejpam-4978	180	4	u	u	NOUN
ejpam-4978	180	5	,	,	PUNCT
ejpam-4978	180	6	v	v	NOUN
ejpam-4978	180	7	∈	∈	PROPN
ejpam-4978	180	8	v	v	NOUN
ejpam-4978	180	9	(	(	PUNCT
ejpam-4978	180	10	c	c	NOUN
ejpam-4978	180	11	)	)	PUNCT
ejpam-4978	180	12	⊆	⊆	NUM
ejpam-4978	180	13	v	v	NOUN
ejpam-4978	180	14	(	(	PUNCT
ejpam-4978	180	15	g	g	NOUN
ejpam-4978	180	16	)	)	PUNCT
ejpam-4978	180	17	such	such	ADJ
ejpam-4978	180	18	that	that	PRON
ejpam-4978	180	19	dc(u	dc(u	PROPN
ejpam-4978	180	20	,	,	PUNCT
ejpam-4978	180	21	v	v	NOUN
ejpam-4978	180	22	)	)	PUNCT
ejpam-4978	180	23	=	=	SYM
ejpam-4978	180	24	2	2	NUM
ejpam-4978	180	25	=	=	SYM
ejpam-4978	180	26	dg(u	dg(u	X
ejpam-4978	180	27	,	,	PUNCT
ejpam-4978	180	28	v	v	NOUN
ejpam-4978	180	29	)	)	PUNCT
ejpam-4978	180	30	=	=	SYM
ejpam-4978	180	31	2	2	X
ejpam-4978	180	32	.	.	PUNCT
ejpam-4978	180	33	clearly	clearly	ADV
ejpam-4978	180	34	,	,	PUNCT
ejpam-4978	180	35	v	v	X
ejpam-4978	180	36	(	(	PUNCT
ejpam-4978	180	37	g	g	NOUN
ejpam-4978	180	38	)	)	PUNCT
ejpam-4978	180	39	\	\	NOUN
ejpam-4978	180	40	{	{	PUNCT
ejpam-4978	180	41	u	u	NOUN
ejpam-4978	180	42	}	}	PUNCT
ejpam-4978	180	43	is	be	AUX
ejpam-4978	180	44	a	a	DET
ejpam-4978	180	45	vertex	vertex	NOUN
ejpam-4978	180	46	cover	cover	NOUN
ejpam-4978	180	47	pointwise	pointwise	PROPN
ejpam-4978	180	48	non	non	ADJ
ejpam-4978	180	49	-	-	ADJ
ejpam-4978	180	50	dominating	dominating	ADJ
ejpam-4978	180	51	set	set	NOUN
ejpam-4978	180	52	in	in	ADP
ejpam-4978	180	53	g.	g.	PROPN
ejpam-4978	180	54	hence	hence	ADV
ejpam-4978	180	55	,	,	PUNCT
ejpam-4978	180	56	vcpnd(g	vcpnd(g	PROPN
ejpam-4978	180	57	)	)	PUNCT
ejpam-4978	180	58	≤	≤	NUM
ejpam-4978	180	59	n−	n−	NOUN
ejpam-4978	180	60	1	1	NUM
ejpam-4978	180	61	,	,	PUNCT
ejpam-4978	180	62	a	a	DET
ejpam-4978	180	63	contradiction	contradiction	NOUN
ejpam-4978	180	64	.	.	PUNCT
ejpam-4978	181	1	therefore	therefore	ADV
ejpam-4978	181	2	,	,	PUNCT
ejpam-4978	181	3	every	every	DET
ejpam-4978	181	4	component	component	NOUN
ejpam-4978	181	5	of	of	ADP
ejpam-4978	181	6	g	g	PROPN
ejpam-4978	181	7	is	be	AUX
ejpam-4978	181	8	non	non	ADJ
ejpam-4978	181	9	-	-	ADJ
ejpam-4978	181	10	trivial	trivial	ADJ
ejpam-4978	181	11	complete	complete	ADJ
ejpam-4978	181	12	graph	graph	NOUN
ejpam-4978	181	13	.	.	PUNCT
ejpam-4978	182	1	conversely	conversely	ADV
ejpam-4978	182	2	,	,	PUNCT
ejpam-4978	182	3	suppose	suppose	VERB
ejpam-4978	182	4	that	that	SCONJ
ejpam-4978	182	5	every	every	DET
ejpam-4978	182	6	component	component	NOUN
ejpam-4978	182	7	of	of	ADP
ejpam-4978	182	8	g	g	PROPN
ejpam-4978	182	9	is	be	AUX
ejpam-4978	182	10	a	a	DET
ejpam-4978	182	11	non	non	ADJ
ejpam-4978	182	12	-	-	ADJ
ejpam-4978	182	13	trivial	trivial	ADJ
ejpam-4978	182	14	complete	complete	ADJ
ejpam-4978	182	15	graph	graph	NOUN
ejpam-4978	182	16	.	.	PUNCT
ejpam-4978	183	1	then	then	ADV
ejpam-4978	183	2	pnd(g	pnd(g	ADP
ejpam-4978	183	3	)	)	PUNCT
ejpam-4978	183	4	=	=	VERB
ejpam-4978	184	1	n.	n.	NOUN
ejpam-4978	184	2	by	by	ADP
ejpam-4978	184	3	(	(	PUNCT
ejpam-4978	184	4	i	i	NOUN
ejpam-4978	184	5	)	)	PUNCT
ejpam-4978	184	6	and	and	CCONJ
ejpam-4978	184	7	(	(	PUNCT
ejpam-4978	184	8	ii	ii	NOUN
ejpam-4978	184	9	)	)	PUNCT
ejpam-4978	184	10	,	,	PUNCT
ejpam-4978	184	11	we	we	PRON
ejpam-4978	184	12	have	have	VERB
ejpam-4978	184	13	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	184	14	)	)	PUNCT
ejpam-4978	185	1	=	=	VERB
ejpam-4978	185	2	n.	n.	NOUN
ejpam-4978	185	3	v.	v.	ADP
ejpam-4978	185	4	t.	t.	PROPN
ejpam-4978	185	5	bilar	bilar	PROPN
ejpam-4978	185	6	et	et	PROPN
ejpam-4978	185	7	al	al	PROPN
ejpam-4978	185	8	.	.	PUNCT
ejpam-4978	185	9	/	/	SYM
ejpam-4978	185	10	eur	eur	PROPN
ejpam-4978	185	11	.	.	PUNCT
ejpam-4978	186	1	j.	j.	PROPN
ejpam-4978	186	2	pure	pure	PROPN
ejpam-4978	186	3	appl	appl	PROPN
ejpam-4978	186	4	.	.	PROPN
ejpam-4978	186	5	math	math	PROPN
ejpam-4978	186	6	,	,	PUNCT
ejpam-4978	186	7	17	17	NUM
ejpam-4978	186	8	(	(	PUNCT
ejpam-4978	186	9	1	1	NUM
ejpam-4978	186	10	)	)	PUNCT
ejpam-4978	186	11	(	(	PUNCT
ejpam-4978	186	12	2024	2024	NUM
ejpam-4978	186	13	)	)	PUNCT
ejpam-4978	186	14	,	,	PUNCT
ejpam-4978	186	15	93	93	NUM
ejpam-4978	186	16	-	-	SYM
ejpam-4978	186	17	104	104	NUM
ejpam-4978	186	18	100	100	NUM
ejpam-4978	186	19	observation	observation	NOUN
ejpam-4978	186	20	1	1	NUM
ejpam-4978	186	21	.	.	PUNCT
ejpam-4978	187	1	let	let	VERB
ejpam-4978	187	2	n	n	PRON
ejpam-4978	187	3	be	be	AUX
ejpam-4978	187	4	any	any	DET
ejpam-4978	187	5	positive	positive	ADJ
ejpam-4978	187	6	integer	integer	NOUN
ejpam-4978	187	7	.	.	PUNCT
ejpam-4978	188	1	then	then	ADV
ejpam-4978	188	2	(	(	PUNCT
ejpam-4978	188	3	i	i	NOUN
ejpam-4978	188	4	)	)	PUNCT
ejpam-4978	188	5	vcpnd(pn	vcpnd(pn	NOUN
ejpam-4978	188	6	)	)	PUNCT
ejpam-4978	188	7	=	=	PUNCT
ejpam-4978	188	8			NOUN
ejpam-4978	188	9	2	2	NUM
ejpam-4978	188	10	if	if	SCONJ
ejpam-4978	188	11	n	n	NOUN
ejpam-4978	188	12	=	=	SYM
ejpam-4978	188	13	2	2	NUM
ejpam-4978	188	14	,	,	PUNCT
ejpam-4978	188	15	3	3	NUM
ejpam-4978	188	16	3	3	NUM
ejpam-4978	188	17	if	if	SCONJ
ejpam-4978	188	18	n	n	NOUN
ejpam-4978	188	19	=	=	SYM
ejpam-4978	188	20	5	5	NUM
ejpam-4978	188	21	n	n	NUM
ejpam-4978	188	22	2	2	NUM
ejpam-4978	188	23	if	if	SCONJ
ejpam-4978	188	24	n	n	PRON
ejpam-4978	188	25	≥	≥	NOUN
ejpam-4978	188	26	4	4	NUM
ejpam-4978	188	27	and	and	CCONJ
ejpam-4978	188	28	even	even	ADV
ejpam-4978	188	29	⌊n2	⌊n2	X
ejpam-4978	188	30	⌋	⌋	NOUN
ejpam-4978	188	31	if	if	SCONJ
ejpam-4978	188	32	n	n	NUM
ejpam-4978	188	33	≥	≥	VERB
ejpam-4978	188	34	7	7	NUM
ejpam-4978	188	35	and	and	CCONJ
ejpam-4978	188	36	odd	odd	ADJ
ejpam-4978	188	37	.	.	PUNCT
ejpam-4978	189	1	(	(	PUNCT
ejpam-4978	189	2	ii	ii	NOUN
ejpam-4978	189	3	)	)	PUNCT
ejpam-4978	189	4	vcpnd(cn	vcpnd(cn	PROPN
ejpam-4978	189	5	)	)	PUNCT
ejpam-4978	189	6	=	=	PUNCT
ejpam-4978	190	1			NOUN
ejpam-4978	190	2	3	3	NUM
ejpam-4978	190	3	if	if	SCONJ
ejpam-4978	190	4	n	n	NOUN
ejpam-4978	190	5	=	=	SYM
ejpam-4978	190	6	3	3	NUM
ejpam-4978	190	7	n	n	NUM
ejpam-4978	190	8	2	2	NUM
ejpam-4978	190	9	if	if	SCONJ
ejpam-4978	190	10	n	n	PRON
ejpam-4978	190	11	≥	≥	NOUN
ejpam-4978	190	12	4	4	NUM
ejpam-4978	190	13	and	and	CCONJ
ejpam-4978	190	14	even	even	ADV
ejpam-4978	190	15	⌈n2	⌈n2	NOUN
ejpam-4978	190	16	⌉	⌉	PUNCT
ejpam-4978	190	17	if	if	SCONJ
ejpam-4978	190	18	n	n	PRON
ejpam-4978	190	19	≥	≥	NOUN
ejpam-4978	190	20	5	5	NUM
ejpam-4978	190	21	and	and	CCONJ
ejpam-4978	190	22	odd	odd	ADJ
ejpam-4978	190	23	.	.	PUNCT
ejpam-4978	191	1	theorem	theorem	VERB
ejpam-4978	191	2	4	4	NUM
ejpam-4978	191	3	.	.	PUNCT
ejpam-4978	192	1	[	[	X
ejpam-4978	192	2	10	10	NUM
ejpam-4978	192	3	]	]	PUNCT
ejpam-4978	192	4	let	let	VERB
ejpam-4978	192	5	g	g	NOUN
ejpam-4978	192	6	and	and	CCONJ
ejpam-4978	192	7	h	h	NOUN
ejpam-4978	192	8	be	be	VERB
ejpam-4978	192	9	any	any	DET
ejpam-4978	192	10	two	two	NUM
ejpam-4978	192	11	graphs	graph	NOUN
ejpam-4978	192	12	.	.	PUNCT
ejpam-4978	193	1	a	a	DET
ejpam-4978	193	2	set	set	NOUN
ejpam-4978	193	3	s	s	NOUN
ejpam-4978	193	4	⊆	⊆	NUM
ejpam-4978	193	5	v	v	NOUN
ejpam-4978	193	6	(	(	PUNCT
ejpam-4978	193	7	g+h	g+h	PROPN
ejpam-4978	193	8	)	)	PUNCT
ejpam-4978	193	9	is	be	AUX
ejpam-4978	193	10	hop	hop	NOUN
ejpam-4978	193	11	dominating	dominate	VERB
ejpam-4978	193	12	set	set	NOUN
ejpam-4978	193	13	of	of	ADP
ejpam-4978	193	14	g+h	g+h	PROPN
ejpam-4978	193	15	if	if	SCONJ
ejpam-4978	194	1	and	and	CCONJ
ejpam-4978	194	2	only	only	ADV
ejpam-4978	194	3	if	if	SCONJ
ejpam-4978	194	4	s	s	NOUN
ejpam-4978	194	5	=	=	PUNCT
ejpam-4978	194	6	sg	sg	PROPN
ejpam-4978	194	7	∪sh	∪sh	NOUN
ejpam-4978	194	8	,	,	PUNCT
ejpam-4978	194	9	where	where	SCONJ
ejpam-4978	194	10	sg	sg	PROPN
ejpam-4978	194	11	and	and	CCONJ
ejpam-4978	194	12	sh	sh	PROPN
ejpam-4978	194	13	are	be	AUX
ejpam-4978	194	14	pointwise	pointwise	PROPN
ejpam-4978	194	15	non	non	ADJ
ejpam-4978	194	16	-	-	ADJ
ejpam-4978	194	17	dominating	dominating	ADJ
ejpam-4978	194	18	sets	set	NOUN
ejpam-4978	194	19	of	of	ADP
ejpam-4978	194	20	g	g	PROPN
ejpam-4978	194	21	and	and	CCONJ
ejpam-4978	194	22	h	h	NOUN
ejpam-4978	194	23	,	,	PUNCT
ejpam-4978	194	24	respectively	respectively	ADV
ejpam-4978	194	25	.	.	PUNCT
ejpam-4978	195	1	theorem	theorem	NOUN
ejpam-4978	195	2	5	5	NUM
ejpam-4978	195	3	.	.	PUNCT
ejpam-4978	196	1	let	let	VERB
ejpam-4978	196	2	g	g	NOUN
ejpam-4978	196	3	and	and	CCONJ
ejpam-4978	196	4	h	h	NOUN
ejpam-4978	196	5	be	be	VERB
ejpam-4978	196	6	two	two	NUM
ejpam-4978	196	7	non	non	ADJ
ejpam-4978	196	8	-	-	ADJ
ejpam-4978	196	9	complete	complete	ADJ
ejpam-4978	196	10	graphs	graph	NOUN
ejpam-4978	196	11	.	.	PUNCT
ejpam-4978	197	1	a	a	DET
ejpam-4978	197	2	subset	subset	NOUN
ejpam-4978	197	3	c	c	NOUN
ejpam-4978	198	1	=	=	PUNCT
ejpam-4978	198	2	cg	cg	NOUN
ejpam-4978	198	3	∪	∪	NOUN
ejpam-4978	198	4	ch	ch	NOUN
ejpam-4978	198	5	of	of	ADP
ejpam-4978	198	6	v	v	NOUN
ejpam-4978	198	7	(	(	PUNCT
ejpam-4978	198	8	g+h	g+h	PROPN
ejpam-4978	198	9	)	)	PUNCT
ejpam-4978	198	10	is	be	AUX
ejpam-4978	198	11	a	a	DET
ejpam-4978	198	12	vertex	vertex	NOUN
ejpam-4978	198	13	cover	cover	NOUN
ejpam-4978	198	14	hop	hop	NOUN
ejpam-4978	198	15	dominating	dominating	NOUN
ejpam-4978	198	16	set	set	NOUN
ejpam-4978	198	17	of	of	ADP
ejpam-4978	198	18	g+h	g+h	PROPN
ejpam-4978	199	1	if	if	SCONJ
ejpam-4978	199	2	and	and	CCONJ
ejpam-4978	199	3	only	only	ADV
ejpam-4978	199	4	if	if	SCONJ
ejpam-4978	199	5	c	c	PROPN
ejpam-4978	199	6	satisfies	satisfy	VERB
ejpam-4978	199	7	one	one	NUM
ejpam-4978	199	8	of	of	ADP
ejpam-4978	199	9	the	the	DET
ejpam-4978	199	10	following	following	ADJ
ejpam-4978	199	11	conditions	condition	NOUN
ejpam-4978	199	12	:	:	PUNCT
ejpam-4978	199	13	(	(	PUNCT
ejpam-4978	199	14	i	i	NOUN
ejpam-4978	199	15	)	)	PUNCT
ejpam-4978	199	16	cg	cg	NOUN
ejpam-4978	199	17	=	=	SYM
ejpam-4978	199	18	v	v	PROPN
ejpam-4978	199	19	(	(	PUNCT
ejpam-4978	199	20	g	g	NOUN
ejpam-4978	199	21	)	)	PUNCT
ejpam-4978	199	22	and	and	CCONJ
ejpam-4978	199	23	ch	ch	NOUN
ejpam-4978	199	24	is	be	AUX
ejpam-4978	199	25	a	a	DET
ejpam-4978	199	26	vertex	vertex	NOUN
ejpam-4978	199	27	cover	cover	NOUN
ejpam-4978	199	28	pointwise	pointwise	PROPN
ejpam-4978	199	29	non	non	ADJ
ejpam-4978	199	30	-	-	ADJ
ejpam-4978	199	31	dominating	dominating	ADJ
ejpam-4978	199	32	set	set	NOUN
ejpam-4978	199	33	of	of	ADP
ejpam-4978	199	34	h.	h.	PROPN
ejpam-4978	199	35	(	(	PUNCT
ejpam-4978	199	36	ii	ii	PROPN
ejpam-4978	199	37	)	)	PUNCT
ejpam-4978	199	38	ch	ch	NOUN
ejpam-4978	199	39	=	=	SYM
ejpam-4978	199	40	v	v	PROPN
ejpam-4978	199	41	(	(	PUNCT
ejpam-4978	199	42	h	h	NOUN
ejpam-4978	199	43	)	)	PUNCT
ejpam-4978	199	44	and	and	CCONJ
ejpam-4978	199	45	cg	cg	NOUN
ejpam-4978	199	46	is	be	AUX
ejpam-4978	199	47	a	a	DET
ejpam-4978	199	48	vertex	vertex	NOUN
ejpam-4978	199	49	cover	cover	NOUN
ejpam-4978	199	50	pointwise	pointwise	PROPN
ejpam-4978	199	51	non	non	ADJ
ejpam-4978	199	52	-	-	ADJ
ejpam-4978	199	53	dominating	dominating	ADJ
ejpam-4978	199	54	set	set	NOUN
ejpam-4978	199	55	of	of	ADP
ejpam-4978	199	56	g.	g.	PROPN
ejpam-4978	199	57	proof	proof	PROPN
ejpam-4978	199	58	.	.	PUNCT
ejpam-4978	200	1	suppose	suppose	VERB
ejpam-4978	200	2	c	c	NOUN
ejpam-4978	200	3	is	be	AUX
ejpam-4978	200	4	a	a	DET
ejpam-4978	200	5	vertex	vertex	NOUN
ejpam-4978	200	6	cover	cover	NOUN
ejpam-4978	200	7	hop	hop	NOUN
ejpam-4978	200	8	dominating	dominating	NOUN
ejpam-4978	200	9	set	set	NOUN
ejpam-4978	200	10	of	of	ADP
ejpam-4978	200	11	g	g	PROPN
ejpam-4978	200	12	+	+	PROPN
ejpam-4978	200	13	h.	h.	PROPN
ejpam-4978	200	14	suppose	suppose	VERB
ejpam-4978	200	15	cg	cg	NOUN
ejpam-4978	200	16	=	=	PUNCT
ejpam-4978	200	17	∅.	∅.	AUX
ejpam-4978	200	18	observe	observe	VERB
ejpam-4978	200	19	that	that	PRON
ejpam-4978	200	20	v	v	NOUN
ejpam-4978	200	21	(	(	PUNCT
ejpam-4978	200	22	g	g	NOUN
ejpam-4978	200	23	)	)	PUNCT
ejpam-4978	200	24	⊈	⊈	PROPN
ejpam-4978	200	25	n2	n2	PROPN
ejpam-4978	200	26	g[c	g[c	PROPN
ejpam-4978	200	27	]	]	PUNCT
ejpam-4978	200	28	.	.	PUNCT
ejpam-4978	201	1	since	since	SCONJ
ejpam-4978	201	2	c	c	PROPN
ejpam-4978	201	3	is	be	AUX
ejpam-4978	201	4	a	a	DET
ejpam-4978	201	5	hop	hop	NOUN
ejpam-4978	201	6	dominating	dominating	NOUN
ejpam-4978	201	7	set	set	NOUN
ejpam-4978	201	8	of	of	ADP
ejpam-4978	201	9	g	g	PROPN
ejpam-4978	201	10	+	+	PROPN
ejpam-4978	201	11	h	h	NOUN
ejpam-4978	201	12	,	,	PUNCT
ejpam-4978	201	13	it	it	PRON
ejpam-4978	201	14	follows	follow	VERB
ejpam-4978	201	15	that	that	SCONJ
ejpam-4978	201	16	v	v	X
ejpam-4978	201	17	(	(	PUNCT
ejpam-4978	201	18	g	g	NOUN
ejpam-4978	201	19	)	)	PUNCT
ejpam-4978	201	20	⊆	⊆	NUM
ejpam-4978	201	21	n2	n2	NOUN
ejpam-4978	201	22	g[c	g[c	PROPN
ejpam-4978	201	23	]	]	PUNCT
ejpam-4978	201	24	,	,	PUNCT
ejpam-4978	201	25	a	a	DET
ejpam-4978	201	26	contradiction	contradiction	NOUN
ejpam-4978	201	27	.	.	PUNCT
ejpam-4978	202	1	thus	thus	ADV
ejpam-4978	202	2	,	,	PUNCT
ejpam-4978	202	3	cg	cg	PROPN
ejpam-4978	202	4	̸=	̸=	PROPN
ejpam-4978	202	5	∅.	∅.	PRON
ejpam-4978	202	6	similarly	similarly	ADV
ejpam-4978	202	7	,	,	PUNCT
ejpam-4978	202	8	ch	ch	NOUN
ejpam-4978	202	9	̸=	̸=	PROPN
ejpam-4978	202	10	∅.	∅.	VERB
ejpam-4978	202	11	if	if	SCONJ
ejpam-4978	202	12	cg	cg	NOUN
ejpam-4978	202	13	=	=	SYM
ejpam-4978	202	14	v	v	NOUN
ejpam-4978	202	15	(	(	PUNCT
ejpam-4978	202	16	g	g	NOUN
ejpam-4978	202	17	)	)	PUNCT
ejpam-4978	202	18	and	and	CCONJ
ejpam-4978	202	19	ch	ch	NOUN
ejpam-4978	202	20	=	=	SYM
ejpam-4978	202	21	v	v	PROPN
ejpam-4978	202	22	(	(	PUNCT
ejpam-4978	202	23	h	h	NOUN
ejpam-4978	202	24	)	)	PUNCT
ejpam-4978	202	25	,	,	PUNCT
ejpam-4978	202	26	then	then	ADV
ejpam-4978	202	27	we	we	PRON
ejpam-4978	202	28	are	be	AUX
ejpam-4978	202	29	done	do	VERB
ejpam-4978	202	30	.	.	PUNCT
ejpam-4978	203	1	suppose	suppose	VERB
ejpam-4978	203	2	that	that	SCONJ
ejpam-4978	203	3	ch	ch	NOUN
ejpam-4978	203	4	̸=	̸=	PROPN
ejpam-4978	203	5	v	v	NOUN
ejpam-4978	203	6	(	(	PUNCT
ejpam-4978	203	7	h	h	NOUN
ejpam-4978	203	8	)	)	PUNCT
ejpam-4978	203	9	.	.	PUNCT
ejpam-4978	204	1	then	then	ADV
ejpam-4978	204	2	there	there	PRON
ejpam-4978	204	3	exists	exist	VERB
ejpam-4978	204	4	a	a	DET
ejpam-4978	204	5	∈	∈	PROPN
ejpam-4978	204	6	v	v	NOUN
ejpam-4978	204	7	(	(	PUNCT
ejpam-4978	204	8	h)\ch	h)\ch	PROPN
ejpam-4978	204	9	such	such	ADJ
ejpam-4978	204	10	that	that	SCONJ
ejpam-4978	204	11	a	a	DET
ejpam-4978	204	12	/∈	/∈	NOUN
ejpam-4978	204	13	c.	c.	NOUN
ejpam-4978	204	14	if	if	SCONJ
ejpam-4978	204	15	cg	cg	NOUN
ejpam-4978	204	16	̸=	̸=	PROPN
ejpam-4978	204	17	v	v	NOUN
ejpam-4978	204	18	(	(	PUNCT
ejpam-4978	204	19	g	g	NOUN
ejpam-4978	204	20	)	)	PUNCT
ejpam-4978	204	21	,	,	PUNCT
ejpam-4978	204	22	then	then	ADV
ejpam-4978	204	23	there	there	PRON
ejpam-4978	204	24	exists	exist	VERB
ejpam-4978	204	25	b	b	PROPN
ejpam-4978	204	26	∈	∈	PROPN
ejpam-4978	204	27	v	v	NOUN
ejpam-4978	204	28	(	(	PUNCT
ejpam-4978	204	29	g)\cg	g)\cg	VERB
ejpam-4978	204	30	such	such	ADJ
ejpam-4978	204	31	that	that	SCONJ
ejpam-4978	204	32	ab	ab	PROPN
ejpam-4978	204	33	∈	∈	PROPN
ejpam-4978	204	34	e(g+h	e(g+h	PROPN
ejpam-4978	204	35	)	)	PUNCT
ejpam-4978	204	36	.	.	PUNCT
ejpam-4978	205	1	however	however	ADV
ejpam-4978	205	2	,	,	PUNCT
ejpam-4978	205	3	a	a	DET
ejpam-4978	205	4	,	,	PUNCT
ejpam-4978	205	5	b	b	PROPN
ejpam-4978	205	6	/∈	/∈	PUNCT
ejpam-4978	206	1	c	c	X
ejpam-4978	206	2	,	,	PUNCT
ejpam-4978	206	3	a	a	DET
ejpam-4978	206	4	contradiction	contradiction	NOUN
ejpam-4978	206	5	to	to	ADP
ejpam-4978	206	6	the	the	DET
ejpam-4978	206	7	fact	fact	NOUN
ejpam-4978	206	8	that	that	SCONJ
ejpam-4978	206	9	c	c	PROPN
ejpam-4978	206	10	is	be	AUX
ejpam-4978	206	11	a	a	DET
ejpam-4978	206	12	vertex	vertex	NOUN
ejpam-4978	206	13	cover	cover	NOUN
ejpam-4978	206	14	of	of	ADP
ejpam-4978	206	15	g+h	g+h	PROPN
ejpam-4978	206	16	.	.	PUNCT
ejpam-4978	207	1	hence	hence	ADV
ejpam-4978	207	2	,	,	PUNCT
ejpam-4978	207	3	cg	cg	NOUN
ejpam-4978	207	4	=	=	SYM
ejpam-4978	207	5	v	v	NOUN
ejpam-4978	207	6	(	(	PUNCT
ejpam-4978	207	7	g	g	NOUN
ejpam-4978	207	8	)	)	PUNCT
ejpam-4978	207	9	.	.	PUNCT
ejpam-4978	208	1	since	since	SCONJ
ejpam-4978	208	2	c	c	PROPN
ejpam-4978	208	3	is	be	AUX
ejpam-4978	208	4	a	a	DET
ejpam-4978	208	5	hop	hop	NOUN
ejpam-4978	208	6	dominating	dominating	NOUN
ejpam-4978	208	7	set	set	VERB
ejpam-4978	208	8	in	in	ADP
ejpam-4978	208	9	g+h	g+h	PROPN
ejpam-4978	208	10	,	,	PUNCT
ejpam-4978	208	11	it	it	PRON
ejpam-4978	208	12	follows	follow	VERB
ejpam-4978	208	13	that	that	SCONJ
ejpam-4978	208	14	ch	ch	NOUN
ejpam-4978	208	15	is	be	AUX
ejpam-4978	208	16	a	a	DET
ejpam-4978	208	17	pointwise	pointwise	ADJ
ejpam-4978	208	18	non	non	ADJ
ejpam-4978	208	19	-	-	ADJ
ejpam-4978	208	20	dominating	dominating	ADJ
ejpam-4978	208	21	set	set	NOUN
ejpam-4978	208	22	of	of	ADP
ejpam-4978	208	23	h	h	NOUN
ejpam-4978	208	24	by	by	ADP
ejpam-4978	208	25	theorem	theorem	NOUN
ejpam-4978	208	26	4	4	NUM
ejpam-4978	208	27	.	.	PUNCT
ejpam-4978	208	28	also	also	ADV
ejpam-4978	208	29	,	,	PUNCT
ejpam-4978	208	30	since	since	SCONJ
ejpam-4978	208	31	c	c	PROPN
ejpam-4978	208	32	is	be	AUX
ejpam-4978	208	33	a	a	DET
ejpam-4978	208	34	vertex	vertex	NOUN
ejpam-4978	208	35	cover	cover	NOUN
ejpam-4978	208	36	of	of	ADP
ejpam-4978	208	37	g+h	g+h	PROPN
ejpam-4978	208	38	,	,	PUNCT
ejpam-4978	208	39	ch	ch	PROPN
ejpam-4978	208	40	is	be	AUX
ejpam-4978	208	41	a	a	DET
ejpam-4978	208	42	vertex	vertex	NOUN
ejpam-4978	208	43	cover	cover	NOUN
ejpam-4978	208	44	of	of	ADP
ejpam-4978	208	45	h.	h.	PROPN
ejpam-4978	208	46	thus	thus	ADV
ejpam-4978	208	47	,	,	PUNCT
ejpam-4978	208	48	(	(	PUNCT
ejpam-4978	208	49	i	i	NOUN
ejpam-4978	208	50	)	)	PUNCT
ejpam-4978	208	51	holds	hold	VERB
ejpam-4978	208	52	.	.	PUNCT
ejpam-4978	209	1	similarly	similarly	ADV
ejpam-4978	209	2	,	,	PUNCT
ejpam-4978	209	3	(	(	PUNCT
ejpam-4978	209	4	ii	ii	NOUN
ejpam-4978	209	5	)	)	PUNCT
ejpam-4978	209	6	holds	hold	VERB
ejpam-4978	209	7	.	.	PUNCT
ejpam-4978	210	1	conversely	conversely	ADV
ejpam-4978	210	2	,	,	PUNCT
ejpam-4978	210	3	suppose	suppose	VERB
ejpam-4978	210	4	that	that	SCONJ
ejpam-4978	210	5	(	(	PUNCT
ejpam-4978	210	6	i	i	NOUN
ejpam-4978	210	7	)	)	PUNCT
ejpam-4978	210	8	holds	hold	VERB
ejpam-4978	210	9	.	.	PUNCT
ejpam-4978	211	1	then	then	ADV
ejpam-4978	211	2	c	c	X
ejpam-4978	211	3	=	=	SYM
ejpam-4978	211	4	v	v	PROPN
ejpam-4978	211	5	(	(	PUNCT
ejpam-4978	211	6	g	g	NOUN
ejpam-4978	211	7	)	)	PUNCT
ejpam-4978	211	8	∪	∪	ADP
ejpam-4978	211	9	ch	ch	NOUN
ejpam-4978	211	10	is	be	AUX
ejpam-4978	211	11	a	a	DET
ejpam-4978	211	12	vertex	vertex	NOUN
ejpam-4978	211	13	cover	cover	NOUN
ejpam-4978	211	14	of	of	ADP
ejpam-4978	211	15	g+h	g+h	PROPN
ejpam-4978	211	16	.	.	PUNCT
ejpam-4978	212	1	since	since	SCONJ
ejpam-4978	212	2	ch	ch	NOUN
ejpam-4978	212	3	is	be	AUX
ejpam-4978	212	4	a	a	DET
ejpam-4978	212	5	pointwise	pointwise	ADJ
ejpam-4978	212	6	non	non	ADJ
ejpam-4978	212	7	-	-	ADJ
ejpam-4978	212	8	dominating	dominating	ADJ
ejpam-4978	212	9	set	set	NOUN
ejpam-4978	212	10	,	,	PUNCT
ejpam-4978	212	11	it	it	PRON
ejpam-4978	212	12	follows	follow	VERB
ejpam-4978	212	13	that	that	SCONJ
ejpam-4978	212	14	c	c	PROPN
ejpam-4978	212	15	=	=	SYM
ejpam-4978	212	16	v	v	PROPN
ejpam-4978	212	17	(	(	PUNCT
ejpam-4978	212	18	g	g	NOUN
ejpam-4978	212	19	)	)	PUNCT
ejpam-4978	212	20	∪	∪	ADP
ejpam-4978	212	21	ch	ch	NOUN
ejpam-4978	212	22	is	be	AUX
ejpam-4978	212	23	a	a	DET
ejpam-4978	212	24	hop	hop	NOUN
ejpam-4978	212	25	dominating	dominating	NOUN
ejpam-4978	212	26	set	set	VERB
ejpam-4978	212	27	in	in	ADP
ejpam-4978	212	28	g	g	PROPN
ejpam-4978	212	29	+	+	PROPN
ejpam-4978	212	30	h	h	NOUN
ejpam-4978	212	31	by	by	ADP
ejpam-4978	212	32	theorem	theorem	NOUN
ejpam-4978	212	33	4	4	NUM
ejpam-4978	212	34	.	.	PUNCT
ejpam-4978	213	1	therefore	therefore	ADV
ejpam-4978	213	2	,	,	PUNCT
ejpam-4978	213	3	c	c	PROPN
ejpam-4978	213	4	=	=	PUNCT
ejpam-4978	213	5	cg	cg	NOUN
ejpam-4978	213	6	∪	∪	NOUN
ejpam-4978	213	7	ch	ch	NOUN
ejpam-4978	213	8	is	be	AUX
ejpam-4978	213	9	a	a	DET
ejpam-4978	213	10	vertex	vertex	NOUN
ejpam-4978	213	11	cover	cover	NOUN
ejpam-4978	213	12	hop	hop	NOUN
ejpam-4978	213	13	dominating	dominating	NOUN
ejpam-4978	213	14	set	set	NOUN
ejpam-4978	213	15	of	of	ADP
ejpam-4978	213	16	g+h	g+h	PROPN
ejpam-4978	213	17	.	.	PUNCT
ejpam-4978	214	1	similarly	similarly	ADV
ejpam-4978	214	2	,	,	PUNCT
ejpam-4978	214	3	if	if	SCONJ
ejpam-4978	214	4	(	(	PUNCT
ejpam-4978	214	5	ii	ii	NOUN
ejpam-4978	214	6	)	)	PUNCT
ejpam-4978	214	7	holds	hold	VERB
ejpam-4978	214	8	,	,	PUNCT
ejpam-4978	214	9	then	then	ADV
ejpam-4978	214	10	c	c	X
ejpam-4978	214	11	=	=	SYM
ejpam-4978	215	1	cg	cg	PROPN
ejpam-4978	215	2	∪ch	∪ch	PROPN
ejpam-4978	215	3	is	be	AUX
ejpam-4978	215	4	a	a	DET
ejpam-4978	215	5	vertex	vertex	NOUN
ejpam-4978	215	6	cover	cover	NOUN
ejpam-4978	215	7	hop	hop	NOUN
ejpam-4978	215	8	dominating	dominating	NOUN
ejpam-4978	215	9	set	set	NOUN
ejpam-4978	215	10	of	of	ADP
ejpam-4978	215	11	g+h	g+h	PROPN
ejpam-4978	215	12	.	.	PUNCT
ejpam-4978	216	1	theorem	theorem	VERB
ejpam-4978	216	2	6	6	NUM
ejpam-4978	216	3	.	.	PUNCT
ejpam-4978	217	1	let	let	VERB
ejpam-4978	217	2	g	g	NOUN
ejpam-4978	217	3	and	and	CCONJ
ejpam-4978	217	4	h	h	NOUN
ejpam-4978	217	5	be	be	VERB
ejpam-4978	217	6	two	two	NUM
ejpam-4978	217	7	non	non	ADJ
ejpam-4978	217	8	-	-	ADJ
ejpam-4978	217	9	complete	complete	ADJ
ejpam-4978	217	10	graphs	graph	NOUN
ejpam-4978	217	11	.	.	PUNCT
ejpam-4978	218	1	then	then	ADV
ejpam-4978	218	2	γvch(g+h	γvch(g+h	ADJ
ejpam-4978	218	3	)	)	PUNCT
ejpam-4978	219	1	=	=	SYM
ejpam-4978	219	2	min{|v	min{|v	PROPN
ejpam-4978	219	3	(	(	PUNCT
ejpam-4978	219	4	g)|+	g)|+	NOUN
ejpam-4978	219	5	vcpnd(h	vcpnd(h	PROPN
ejpam-4978	219	6	)	)	PUNCT
ejpam-4978	219	7	,	,	PUNCT
ejpam-4978	219	8	|v	|v	PROPN
ejpam-4978	219	9	(	(	PUNCT
ejpam-4978	219	10	h)|+	h)|+	PROPN
ejpam-4978	219	11	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	219	12	)	)	PUNCT
ejpam-4978	219	13	}	}	PUNCT
ejpam-4978	219	14	.	.	PUNCT
ejpam-4978	220	1	proof	proof	NOUN
ejpam-4978	220	2	.	.	PUNCT
ejpam-4978	221	1	let	let	VERB
ejpam-4978	221	2	c	c	NOUN
ejpam-4978	221	3	=	=	PUNCT
ejpam-4978	221	4	cg	cg	NOUN
ejpam-4978	221	5	∪	∪	NOUN
ejpam-4978	221	6	ch	ch	NOUN
ejpam-4978	221	7	be	be	AUX
ejpam-4978	221	8	a	a	DET
ejpam-4978	221	9	minimum	minimum	ADJ
ejpam-4978	221	10	vertex	vertex	NOUN
ejpam-4978	221	11	cover	cover	NOUN
ejpam-4978	221	12	hop	hop	NOUN
ejpam-4978	221	13	dominating	dominating	NOUN
ejpam-4978	221	14	set	set	NOUN
ejpam-4978	221	15	of	of	ADP
ejpam-4978	221	16	g	g	PROPN
ejpam-4978	221	17	+	+	PROPN
ejpam-4978	221	18	h.	h.	PROPN
ejpam-4978	221	19	then	then	ADV
ejpam-4978	221	20	by	by	ADP
ejpam-4978	221	21	theorem	theorem	NOUN
ejpam-4978	221	22	5	5	NUM
ejpam-4978	221	23	,	,	PUNCT
ejpam-4978	221	24	c	c	PROPN
ejpam-4978	221	25	satisfies	satisfy	VERB
ejpam-4978	221	26	one	one	NUM
ejpam-4978	221	27	of	of	ADP
ejpam-4978	221	28	the	the	DET
ejpam-4978	221	29	following	following	NOUN
ejpam-4978	221	30	:	:	PUNCT
ejpam-4978	222	1	v.	v.	PROPN
ejpam-4978	222	2	t.	t.	PROPN
ejpam-4978	222	3	bilar	bilar	PROPN
ejpam-4978	222	4	et	et	PROPN
ejpam-4978	222	5	al	al	PROPN
ejpam-4978	222	6	.	.	PUNCT
ejpam-4978	222	7	/	/	SYM
ejpam-4978	222	8	eur	eur	PROPN
ejpam-4978	222	9	.	.	PUNCT
ejpam-4978	223	1	j.	j.	PROPN
ejpam-4978	223	2	pure	pure	PROPN
ejpam-4978	223	3	appl	appl	PROPN
ejpam-4978	223	4	.	.	PROPN
ejpam-4978	223	5	math	math	PROPN
ejpam-4978	223	6	,	,	PUNCT
ejpam-4978	223	7	17	17	NUM
ejpam-4978	223	8	(	(	PUNCT
ejpam-4978	223	9	1	1	NUM
ejpam-4978	223	10	)	)	PUNCT
ejpam-4978	223	11	(	(	PUNCT
ejpam-4978	223	12	2024	2024	NUM
ejpam-4978	223	13	)	)	PUNCT
ejpam-4978	223	14	,	,	PUNCT
ejpam-4978	223	15	93	93	NUM
ejpam-4978	223	16	-	-	SYM
ejpam-4978	223	17	104	104	NUM
ejpam-4978	223	18	101	101	NUM
ejpam-4978	223	19	(	(	PUNCT
ejpam-4978	223	20	i	i	NOUN
ejpam-4978	223	21	)	)	PUNCT
ejpam-4978	223	22	cg	cg	NOUN
ejpam-4978	224	1	=	=	SYM
ejpam-4978	224	2	v	v	PROPN
ejpam-4978	224	3	(	(	PUNCT
ejpam-4978	224	4	g	g	NOUN
ejpam-4978	224	5	)	)	PUNCT
ejpam-4978	224	6	and	and	CCONJ
ejpam-4978	224	7	ch	ch	NOUN
ejpam-4978	224	8	is	be	AUX
ejpam-4978	224	9	a	a	DET
ejpam-4978	224	10	vertex	vertex	NOUN
ejpam-4978	224	11	cover	cover	NOUN
ejpam-4978	224	12	pointwise	pointwise	PROPN
ejpam-4978	224	13	non	non	ADJ
ejpam-4978	224	14	-	-	ADJ
ejpam-4978	224	15	dominating	dominating	ADJ
ejpam-4978	224	16	set	set	NOUN
ejpam-4978	224	17	of	of	ADP
ejpam-4978	224	18	h.	h.	PROPN
ejpam-4978	224	19	(	(	PUNCT
ejpam-4978	224	20	ii	ii	PROPN
ejpam-4978	224	21	)	)	PUNCT
ejpam-4978	224	22	ch	ch	NOUN
ejpam-4978	224	23	=	=	SYM
ejpam-4978	224	24	v	v	PROPN
ejpam-4978	224	25	(	(	PUNCT
ejpam-4978	224	26	h	h	NOUN
ejpam-4978	224	27	)	)	PUNCT
ejpam-4978	224	28	and	and	CCONJ
ejpam-4978	224	29	cg	cg	NOUN
ejpam-4978	224	30	is	be	AUX
ejpam-4978	224	31	a	a	DET
ejpam-4978	224	32	vertex	vertex	NOUN
ejpam-4978	224	33	cover	cover	NOUN
ejpam-4978	224	34	pointwise	pointwise	PROPN
ejpam-4978	224	35	non	non	ADJ
ejpam-4978	224	36	-	-	ADJ
ejpam-4978	224	37	dominating	dominating	ADJ
ejpam-4978	224	38	set	set	NOUN
ejpam-4978	224	39	of	of	ADP
ejpam-4978	224	40	g.	g.	PROPN
ejpam-4978	224	41	thus	thus	ADV
ejpam-4978	224	42	,	,	PUNCT
ejpam-4978	224	43	γvch(g+h	γvch(g+h	NOUN
ejpam-4978	224	44	)	)	PUNCT
ejpam-4978	224	45	=	=	SYM
ejpam-4978	224	46	|c|	|c|	PROPN
ejpam-4978	224	47	=	=	PUNCT
ejpam-4978	224	48	|cg|+	|cg|+	NOUN
ejpam-4978	224	49	|ch	|ch	PROPN
ejpam-4978	224	50	|	|	ADV
ejpam-4978	224	51	≥	≥	NOUN
ejpam-4978	224	52	v	v	NOUN
ejpam-4978	224	53	(	(	PUNCT
ejpam-4978	224	54	g)|+	g)|+	NOUN
ejpam-4978	224	55	vcpnd(h	vcpnd(h	PROPN
ejpam-4978	224	56	)	)	PUNCT
ejpam-4978	224	57	and	and	CCONJ
ejpam-4978	224	58	γvch(g+h	γvch(g+h	NOUN
ejpam-4978	224	59	)	)	PUNCT
ejpam-4978	224	60	=	=	SYM
ejpam-4978	224	61	|c|	|c|	PROPN
ejpam-4978	224	62	=	=	PUNCT
ejpam-4978	224	63	|cg|+	|cg|+	NOUN
ejpam-4978	224	64	|ch	|ch	PROPN
ejpam-4978	224	65	|	|	ADV
ejpam-4978	224	66	≥	≥	NOUN
ejpam-4978	224	67	v	v	NOUN
ejpam-4978	224	68	(	(	PUNCT
ejpam-4978	224	69	h)|+	h)|+	PROPN
ejpam-4978	224	70	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	224	71	)	)	PUNCT
ejpam-4978	224	72	.	.	PUNCT
ejpam-4978	225	1	consequently	consequently	ADV
ejpam-4978	225	2	,	,	PUNCT
ejpam-4978	225	3	γvch(g+h	γvch(g+h	PROPN
ejpam-4978	225	4	)	)	PUNCT
ejpam-4978	225	5	≥	≥	PROPN
ejpam-4978	225	6	min{|v	min{|v	PROPN
ejpam-4978	225	7	(	(	PUNCT
ejpam-4978	225	8	g)|+	g)|+	NOUN
ejpam-4978	225	9	vcpnd(h	vcpnd(h	PROPN
ejpam-4978	225	10	)	)	PUNCT
ejpam-4978	225	11	,	,	PUNCT
ejpam-4978	225	12	|v	|v	PROPN
ejpam-4978	225	13	(	(	PUNCT
ejpam-4978	225	14	h)|+	h)|+	PROPN
ejpam-4978	225	15	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	225	16	)	)	PUNCT
ejpam-4978	225	17	}	}	PUNCT
ejpam-4978	225	18	.	.	PUNCT
ejpam-4978	226	1	on	on	ADP
ejpam-4978	226	2	the	the	DET
ejpam-4978	226	3	other	other	ADJ
ejpam-4978	226	4	hand	hand	NOUN
ejpam-4978	226	5	,	,	PUNCT
ejpam-4978	226	6	suppose	suppose	VERB
ejpam-4978	226	7	that	that	SCONJ
ejpam-4978	226	8	c	c	PROPN
ejpam-4978	226	9	=	=	SYM
ejpam-4978	226	10	v	v	PROPN
ejpam-4978	226	11	(	(	PUNCT
ejpam-4978	226	12	g	g	NOUN
ejpam-4978	226	13	)	)	PUNCT
ejpam-4978	226	14	∪	∪	NOUN
ejpam-4978	226	15	ch	ch	NOUN
ejpam-4978	226	16	,	,	PUNCT
ejpam-4978	226	17	where	where	SCONJ
ejpam-4978	226	18	ch	ch	NOUN
ejpam-4978	226	19	is	be	AUX
ejpam-4978	226	20	a	a	DET
ejpam-4978	226	21	minimum	minimum	ADJ
ejpam-4978	226	22	vertex	vertex	NOUN
ejpam-4978	226	23	cover	cover	NOUN
ejpam-4978	226	24	pointwise	pointwise	PROPN
ejpam-4978	226	25	non	non	ADJ
ejpam-4978	226	26	-	-	ADJ
ejpam-4978	226	27	dominating	dominating	ADJ
ejpam-4978	226	28	set	set	NOUN
ejpam-4978	226	29	of	of	ADP
ejpam-4978	226	30	h.	h.	PROPN
ejpam-4978	226	31	then	then	ADV
ejpam-4978	226	32	c	c	PROPN
ejpam-4978	226	33	is	be	AUX
ejpam-4978	226	34	a	a	DET
ejpam-4978	226	35	vertex	vertex	NOUN
ejpam-4978	226	36	cover	cover	NOUN
ejpam-4978	226	37	hop	hop	NOUN
ejpam-4978	226	38	dominating	dominating	NOUN
ejpam-4978	226	39	set	set	VERB
ejpam-4978	226	40	in	in	ADP
ejpam-4978	226	41	g+h	g+h	PROPN
ejpam-4978	226	42	by	by	ADP
ejpam-4978	226	43	theorem	theorem	NOUN
ejpam-4978	226	44	5	5	NUM
ejpam-4978	226	45	.	.	PUNCT
ejpam-4978	226	46	thus	thus	ADV
ejpam-4978	226	47	,	,	PUNCT
ejpam-4978	226	48	|v	|v	PROPN
ejpam-4978	226	49	(	(	PUNCT
ejpam-4978	226	50	g)|+	g)|+	NOUN
ejpam-4978	226	51	vcpnd(h	vcpnd(h	NOUN
ejpam-4978	226	52	)	)	PUNCT
ejpam-4978	226	53	=	=	SYM
ejpam-4978	226	54	|c|	|c|	PROPN
ejpam-4978	226	55	≥	≥	NOUN
ejpam-4978	226	56	γvch(g+h	γvch(g+h	NOUN
ejpam-4978	226	57	)	)	PUNCT
ejpam-4978	226	58	.	.	PUNCT
ejpam-4978	227	1	next	next	ADV
ejpam-4978	227	2	,	,	PUNCT
ejpam-4978	227	3	suppose	suppose	VERB
ejpam-4978	227	4	that	that	SCONJ
ejpam-4978	227	5	c	c	PROPN
ejpam-4978	227	6	=	=	SYM
ejpam-4978	227	7	v	v	PROPN
ejpam-4978	227	8	(	(	PUNCT
ejpam-4978	227	9	h	h	NOUN
ejpam-4978	227	10	)	)	PUNCT
ejpam-4978	227	11	∪	∪	PROPN
ejpam-4978	227	12	cg	cg	NOUN
ejpam-4978	227	13	,	,	PUNCT
ejpam-4978	227	14	where	where	SCONJ
ejpam-4978	227	15	cg	cg	NOUN
ejpam-4978	227	16	is	be	AUX
ejpam-4978	227	17	a	a	DET
ejpam-4978	227	18	minimum	minimum	ADJ
ejpam-4978	227	19	vertex	vertex	NOUN
ejpam-4978	227	20	cover	cover	NOUN
ejpam-4978	227	21	pointwise	pointwise	PROPN
ejpam-4978	227	22	non	non	ADJ
ejpam-4978	227	23	-	-	ADJ
ejpam-4978	227	24	dominating	dominating	ADJ
ejpam-4978	227	25	set	set	NOUN
ejpam-4978	227	26	of	of	ADP
ejpam-4978	227	27	g.	g.	PROPN
ejpam-4978	227	28	then	then	ADV
ejpam-4978	227	29	c	c	PROPN
ejpam-4978	227	30	is	be	AUX
ejpam-4978	227	31	a	a	DET
ejpam-4978	227	32	vertex	vertex	NOUN
ejpam-4978	227	33	cover	cover	NOUN
ejpam-4978	227	34	hop	hop	NOUN
ejpam-4978	227	35	dominating	dominating	NOUN
ejpam-4978	227	36	set	set	VERB
ejpam-4978	227	37	in	in	ADP
ejpam-4978	227	38	g	g	PROPN
ejpam-4978	227	39	+	+	CCONJ
ejpam-4978	227	40	h	h	NOUN
ejpam-4978	227	41	by	by	ADP
ejpam-4978	227	42	theorem	theorem	NOUN
ejpam-4978	227	43	5	5	NUM
ejpam-4978	227	44	.	.	PUNCT
ejpam-4978	227	45	thus	thus	ADV
ejpam-4978	227	46	,	,	PUNCT
ejpam-4978	227	47	|v	|v	PROPN
ejpam-4978	227	48	(	(	PUNCT
ejpam-4978	227	49	h)|+	h)|+	ADJ
ejpam-4978	227	50	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	227	51	)	)	PUNCT
ejpam-4978	227	52	=	=	SYM
ejpam-4978	227	53	|c|	|c|	PROPN
ejpam-4978	227	54	≥	≥	NOUN
ejpam-4978	227	55	γvch(g+h	γvch(g+h	NOUN
ejpam-4978	227	56	)	)	PUNCT
ejpam-4978	227	57	.	.	PUNCT
ejpam-4978	228	1	therefore	therefore	ADV
ejpam-4978	228	2	,	,	PUNCT
ejpam-4978	228	3	γvch(g+h	γvch(g+h	NOUN
ejpam-4978	228	4	)	)	PUNCT
ejpam-4978	229	1	=	=	SYM
ejpam-4978	229	2	min{|v	min{|v	PROPN
ejpam-4978	229	3	(	(	PUNCT
ejpam-4978	229	4	g)|+	g)|+	NOUN
ejpam-4978	229	5	vcpnd(h	vcpnd(h	PROPN
ejpam-4978	229	6	)	)	PUNCT
ejpam-4978	229	7	,	,	PUNCT
ejpam-4978	229	8	|v	|v	PROPN
ejpam-4978	229	9	(	(	PUNCT
ejpam-4978	229	10	h)|+	h)|+	PROPN
ejpam-4978	229	11	vcpnd(g	vcpnd(g	NOUN
ejpam-4978	229	12	)	)	PUNCT
ejpam-4978	229	13	}	}	PUNCT
ejpam-4978	229	14	.	.	PUNCT
ejpam-4978	230	1	the	the	DET
ejpam-4978	230	2	following	following	ADJ
ejpam-4978	230	3	result	result	NOUN
ejpam-4978	230	4	follows	follow	VERB
ejpam-4978	230	5	from	from	ADP
ejpam-4978	230	6	observation	observation	NOUN
ejpam-4978	230	7	1	1	NUM
ejpam-4978	230	8	and	and	CCONJ
ejpam-4978	230	9	theorem	theorem	VERB
ejpam-4978	230	10	6	6	NUM
ejpam-4978	230	11	.	.	PUNCT
ejpam-4978	230	12	corollary	corollary	ADJ
ejpam-4978	230	13	2	2	NUM
ejpam-4978	230	14	.	.	PUNCT
ejpam-4978	231	1	let	let	VERB
ejpam-4978	231	2	n	n	PRON
ejpam-4978	231	3	be	be	AUX
ejpam-4978	231	4	any	any	DET
ejpam-4978	231	5	positive	positive	ADJ
ejpam-4978	231	6	integer	integer	NOUN
ejpam-4978	231	7	.	.	PUNCT
ejpam-4978	232	1	then	then	ADV
ejpam-4978	232	2	each	each	PRON
ejpam-4978	232	3	of	of	ADP
ejpam-4978	232	4	the	the	DET
ejpam-4978	232	5	following	following	NOUN
ejpam-4978	232	6	is	be	AUX
ejpam-4978	232	7	true	true	ADJ
ejpam-4978	232	8	.	.	PUNCT
ejpam-4978	233	1	(	(	PUNCT
ejpam-4978	233	2	i	i	NOUN
ejpam-4978	233	3	)	)	PUNCT
ejpam-4978	233	4	γvch(pn	γvch(pn	NOUN
ejpam-4978	233	5	+	+	CCONJ
ejpam-4978	233	6	pn	pn	NOUN
ejpam-4978	233	7	)	)	PUNCT
ejpam-4978	233	8	=	=	SYM
ejpam-4978	234	1	n+	n+	PUNCT
ejpam-4978	234	2	vcpnd(pn	vcpnd(pn	NOUN
ejpam-4978	234	3	)	)	PUNCT
ejpam-4978	234	4	=	=	PUNCT
ejpam-4978	235	1			NOUN
ejpam-4978	235	2	n+	n+	PUNCT
ejpam-4978	235	3	2	2	NUM
ejpam-4978	235	4	if	if	SCONJ
ejpam-4978	235	5	n	n	NOUN
ejpam-4978	235	6	=	=	SYM
ejpam-4978	235	7	3	3	NUM
ejpam-4978	235	8	n+	n+	SYM
ejpam-4978	235	9	3	3	NUM
ejpam-4978	235	10	if	if	SCONJ
ejpam-4978	235	11	n	n	NOUN
ejpam-4978	235	12	=	=	SYM
ejpam-4978	235	13	5	5	NUM
ejpam-4978	235	14	n+	n+	ADP
ejpam-4978	235	15	n	n	ADV
ejpam-4978	235	16	2	2	NUM
ejpam-4978	235	17	if	if	SCONJ
ejpam-4978	235	18	n	n	PRON
ejpam-4978	235	19	≥	≥	NOUN
ejpam-4978	235	20	4	4	NUM
ejpam-4978	235	21	and	and	CCONJ
ejpam-4978	235	22	even	even	ADV
ejpam-4978	235	23	n+	n+	PRON
ejpam-4978	235	24	⌊n2	⌊n2	X
ejpam-4978	235	25	⌋	⌋	NOUN
ejpam-4978	235	26	if	if	SCONJ
ejpam-4978	235	27	n	n	NUM
ejpam-4978	235	28	≥	≥	VERB
ejpam-4978	235	29	7	7	NUM
ejpam-4978	235	30	and	and	CCONJ
ejpam-4978	235	31	odd	odd	ADJ
ejpam-4978	235	32	.	.	PUNCT
ejpam-4978	236	1	(	(	PUNCT
ejpam-4978	236	2	ii	ii	NOUN
ejpam-4978	236	3	)	)	PUNCT
ejpam-4978	236	4	γvch(cn	γvch(cn	NOUN
ejpam-4978	236	5	+	+	CCONJ
ejpam-4978	236	6	cn	cn	ADJ
ejpam-4978	236	7	)	)	PUNCT
ejpam-4978	236	8	=	=	PROPN
ejpam-4978	236	9	n+	n+	PUNCT
ejpam-4978	236	10	vcpnd(cn	vcpnd(cn	NOUN
ejpam-4978	236	11	)	)	PUNCT
ejpam-4978	236	12	=	=	PRON
ejpam-4978	236	13	{	{	PUNCT
ejpam-4978	236	14	n+	n+	NOUN
ejpam-4978	236	15	n	n	CCONJ
ejpam-4978	236	16	2	2	NUM
ejpam-4978	236	17	if	if	SCONJ
ejpam-4978	236	18	n	n	PRON
ejpam-4978	236	19	≥	≥	NOUN
ejpam-4978	236	20	4	4	NUM
ejpam-4978	236	21	and	and	CCONJ
ejpam-4978	236	22	even	even	ADV
ejpam-4978	236	23	n+	n+	ADP
ejpam-4978	236	24	⌈n2	⌈n2	NOUN
ejpam-4978	236	25	⌉	⌉	PUNCT
ejpam-4978	236	26	if	if	SCONJ
ejpam-4978	236	27	n	n	PRON
ejpam-4978	236	28	≥	≥	NOUN
ejpam-4978	236	29	5	5	NUM
ejpam-4978	236	30	and	and	CCONJ
ejpam-4978	236	31	odd	odd	ADJ
ejpam-4978	236	32	.	.	PUNCT
ejpam-4978	236	33	theorem	theorem	VERB
ejpam-4978	236	34	7	7	NUM
ejpam-4978	236	35	.	.	PUNCT
ejpam-4978	237	1	let	let	VERB
ejpam-4978	237	2	g	g	NOUN
ejpam-4978	237	3	be	be	AUX
ejpam-4978	237	4	any	any	DET
ejpam-4978	237	5	complete	complete	ADJ
ejpam-4978	237	6	graph	graph	NOUN
ejpam-4978	237	7	and	and	CCONJ
ejpam-4978	237	8	h	h	NOUN
ejpam-4978	237	9	be	be	AUX
ejpam-4978	237	10	any	any	DET
ejpam-4978	237	11	graph	graph	NOUN
ejpam-4978	237	12	.	.	PUNCT
ejpam-4978	238	1	a	a	DET
ejpam-4978	238	2	set	set	NOUN
ejpam-4978	238	3	c	c	NOUN
ejpam-4978	238	4	⊆	⊆	NUM
ejpam-4978	238	5	v	v	NOUN
ejpam-4978	238	6	(	(	PUNCT
ejpam-4978	238	7	g+h	g+h	NOUN
ejpam-4978	238	8	)	)	PUNCT
ejpam-4978	238	9	is	be	AUX
ejpam-4978	238	10	vertex	vertex	NOUN
ejpam-4978	238	11	cover	cover	NOUN
ejpam-4978	238	12	hop	hop	NOUN
ejpam-4978	238	13	dominating	dominating	NOUN
ejpam-4978	238	14	set	set	NOUN
ejpam-4978	238	15	of	of	ADP
ejpam-4978	238	16	g+h	g+h	PROPN
ejpam-4978	239	1	if	if	SCONJ
ejpam-4978	239	2	and	and	CCONJ
ejpam-4978	239	3	only	only	ADV
ejpam-4978	239	4	if	if	SCONJ
ejpam-4978	239	5	c	c	PROPN
ejpam-4978	239	6	=	=	SYM
ejpam-4978	239	7	v	v	PROPN
ejpam-4978	239	8	(	(	PUNCT
ejpam-4978	239	9	g	g	NOUN
ejpam-4978	239	10	)	)	PUNCT
ejpam-4978	239	11	∪	∪	NOUN
ejpam-4978	239	12	ch	ch	NOUN
ejpam-4978	239	13	,	,	PUNCT
ejpam-4978	239	14	ch	ch	PROPN
ejpam-4978	239	15	is	be	AUX
ejpam-4978	239	16	a	a	DET
ejpam-4978	239	17	vertex	vertex	NOUN
ejpam-4978	239	18	cover	cover	NOUN
ejpam-4978	239	19	pointwise	pointwise	PROPN
ejpam-4978	239	20	non	non	ADJ
ejpam-4978	239	21	-	-	ADJ
ejpam-4978	239	22	dominating	dominating	ADJ
ejpam-4978	239	23	set	set	NOUN
ejpam-4978	239	24	in	in	ADP
ejpam-4978	239	25	h.	h.	PROPN
ejpam-4978	239	26	proof	proof	NOUN
ejpam-4978	239	27	.	.	PUNCT
ejpam-4978	240	1	suppose	suppose	VERB
ejpam-4978	240	2	c	c	NOUN
ejpam-4978	240	3	is	be	AUX
ejpam-4978	240	4	a	a	DET
ejpam-4978	240	5	vertex	vertex	NOUN
ejpam-4978	240	6	cover	cover	NOUN
ejpam-4978	240	7	hop	hop	NOUN
ejpam-4978	240	8	dominating	dominating	NOUN
ejpam-4978	240	9	set	set	NOUN
ejpam-4978	240	10	of	of	ADP
ejpam-4978	240	11	g	g	PROPN
ejpam-4978	240	12	+	+	PROPN
ejpam-4978	240	13	h.	h.	PROPN
ejpam-4978	240	14	suppose	suppose	VERB
ejpam-4978	240	15	cg	cg	NOUN
ejpam-4978	240	16	=	=	PUNCT
ejpam-4978	240	17	∅.	∅.	AUX
ejpam-4978	240	18	observe	observe	VERB
ejpam-4978	240	19	that	that	PRON
ejpam-4978	240	20	v	v	NOUN
ejpam-4978	240	21	(	(	PUNCT
ejpam-4978	240	22	g	g	NOUN
ejpam-4978	240	23	)	)	PUNCT
ejpam-4978	240	24	⊈	⊈	PROPN
ejpam-4978	240	25	n2	n2	PROPN
ejpam-4978	240	26	g[c	g[c	PROPN
ejpam-4978	240	27	]	]	PUNCT
ejpam-4978	240	28	.	.	PUNCT
ejpam-4978	241	1	since	since	SCONJ
ejpam-4978	241	2	c	c	PROPN
ejpam-4978	241	3	is	be	AUX
ejpam-4978	241	4	a	a	DET
ejpam-4978	241	5	hop	hop	NOUN
ejpam-4978	241	6	dominating	dominating	NOUN
ejpam-4978	241	7	set	set	NOUN
ejpam-4978	241	8	of	of	ADP
ejpam-4978	241	9	g	g	PROPN
ejpam-4978	241	10	+	+	PROPN
ejpam-4978	241	11	h	h	NOUN
ejpam-4978	241	12	,	,	PUNCT
ejpam-4978	241	13	it	it	PRON
ejpam-4978	241	14	follows	follow	VERB
ejpam-4978	241	15	that	that	SCONJ
ejpam-4978	241	16	v	v	X
ejpam-4978	241	17	(	(	PUNCT
ejpam-4978	241	18	g	g	NOUN
ejpam-4978	241	19	)	)	PUNCT
ejpam-4978	241	20	⊆	⊆	NUM
ejpam-4978	241	21	n2	n2	NOUN
ejpam-4978	241	22	g[c	g[c	PROPN
ejpam-4978	241	23	]	]	PUNCT
ejpam-4978	241	24	,	,	PUNCT
ejpam-4978	241	25	a	a	DET
ejpam-4978	241	26	contradiction	contradiction	NOUN
ejpam-4978	241	27	.	.	PUNCT
ejpam-4978	242	1	thus	thus	ADV
ejpam-4978	242	2	,	,	PUNCT
ejpam-4978	242	3	cg	cg	PROPN
ejpam-4978	242	4	̸=	̸=	PROPN
ejpam-4978	242	5	∅.	∅.	PRON
ejpam-4978	242	6	similarly	similarly	ADV
ejpam-4978	242	7	,	,	PUNCT
ejpam-4978	242	8	ch	ch	NOUN
ejpam-4978	242	9	̸=	̸=	PROPN
ejpam-4978	242	10	∅.	∅.	ADV
ejpam-4978	242	11	since	since	SCONJ
ejpam-4978	242	12	c	c	PROPN
ejpam-4978	242	13	is	be	AUX
ejpam-4978	242	14	a	a	DET
ejpam-4978	242	15	hop	hop	NOUN
ejpam-4978	242	16	dominating	dominating	NOUN
ejpam-4978	242	17	set	set	VERB
ejpam-4978	242	18	in	in	ADP
ejpam-4978	242	19	g	g	PROPN
ejpam-4978	242	20	+	+	CCONJ
ejpam-4978	242	21	h	h	NOUN
ejpam-4978	242	22	,	,	PUNCT
ejpam-4978	242	23	it	it	PRON
ejpam-4978	242	24	follows	follow	VERB
ejpam-4978	242	25	that	that	SCONJ
ejpam-4978	242	26	ch	ch	NOUN
ejpam-4978	242	27	is	be	AUX
ejpam-4978	242	28	a	a	DET
ejpam-4978	242	29	pointwise	pointwise	ADJ
ejpam-4978	242	30	non	non	ADJ
ejpam-4978	242	31	-	-	ADJ
ejpam-4978	242	32	dominating	dominating	ADJ
ejpam-4978	242	33	set	set	NOUN
ejpam-4978	242	34	of	of	ADP
ejpam-4978	242	35	h	h	NOUN
ejpam-4978	242	36	by	by	ADP
ejpam-4978	242	37	theorem	theorem	NOUN
ejpam-4978	242	38	4	4	NUM
ejpam-4978	242	39	.	.	PUNCT
ejpam-4978	242	40	also	also	ADV
ejpam-4978	242	41	,	,	PUNCT
ejpam-4978	242	42	since	since	SCONJ
ejpam-4978	242	43	c	c	PROPN
ejpam-4978	242	44	is	be	AUX
ejpam-4978	242	45	a	a	DET
ejpam-4978	242	46	vertex	vertex	NOUN
ejpam-4978	242	47	cover	cover	NOUN
ejpam-4978	242	48	of	of	ADP
ejpam-4978	242	49	g	g	PROPN
ejpam-4978	242	50	+	+	CCONJ
ejpam-4978	242	51	h	h	NOUN
ejpam-4978	242	52	,	,	PUNCT
ejpam-4978	242	53	ch	ch	PROPN
ejpam-4978	242	54	is	be	AUX
ejpam-4978	242	55	a	a	DET
ejpam-4978	242	56	vertex	vertex	NOUN
ejpam-4978	242	57	cover	cover	NOUN
ejpam-4978	242	58	of	of	ADP
ejpam-4978	242	59	h.	h.	PROPN
ejpam-4978	242	60	now	now	ADV
ejpam-4978	242	61	,	,	PUNCT
ejpam-4978	242	62	suppose	suppose	VERB
ejpam-4978	242	63	cg	cg	PRON
ejpam-4978	242	64	̸=	̸=	PROPN
ejpam-4978	242	65	v	v	NOUN
ejpam-4978	242	66	(	(	PUNCT
ejpam-4978	242	67	g	g	NOUN
ejpam-4978	242	68	)	)	PUNCT
ejpam-4978	242	69	.	.	PUNCT
ejpam-4978	243	1	then	then	ADV
ejpam-4978	243	2	there	there	PRON
ejpam-4978	243	3	exists	exist	VERB
ejpam-4978	243	4	a	a	DET
ejpam-4978	243	5	∈	∈	PROPN
ejpam-4978	243	6	v	v	NOUN
ejpam-4978	243	7	(	(	PUNCT
ejpam-4978	243	8	g	g	NOUN
ejpam-4978	243	9	)	)	PUNCT
ejpam-4978	243	10	\	\	PROPN
ejpam-4978	243	11	cg	cg	NOUN
ejpam-4978	243	12	such	such	ADJ
ejpam-4978	243	13	that	that	SCONJ
ejpam-4978	243	14	a	a	DET
ejpam-4978	243	15	/∈	/∈	NOUN
ejpam-4978	243	16	c.	c.	NOUN
ejpam-4978	243	17	since	since	SCONJ
ejpam-4978	243	18	v.	v.	PROPN
ejpam-4978	243	19	t.	t.	PROPN
ejpam-4978	243	20	bilar	bilar	PROPN
ejpam-4978	243	21	et	et	PROPN
ejpam-4978	243	22	al	al	PROPN
ejpam-4978	243	23	.	.	PUNCT
ejpam-4978	243	24	/	/	SYM
ejpam-4978	243	25	eur	eur	PROPN
ejpam-4978	243	26	.	.	PUNCT
ejpam-4978	244	1	j.	j.	PROPN
ejpam-4978	244	2	pure	pure	PROPN
ejpam-4978	244	3	appl	appl	PROPN
ejpam-4978	244	4	.	.	PROPN
ejpam-4978	244	5	math	math	PROPN
ejpam-4978	244	6	,	,	PUNCT
ejpam-4978	244	7	17	17	NUM
ejpam-4978	244	8	(	(	PUNCT
ejpam-4978	244	9	1	1	NUM
ejpam-4978	244	10	)	)	PUNCT
ejpam-4978	244	11	(	(	PUNCT
ejpam-4978	244	12	2024	2024	NUM
ejpam-4978	244	13	)	)	PUNCT
ejpam-4978	244	14	,	,	PUNCT
ejpam-4978	244	15	93	93	NUM
ejpam-4978	244	16	-	-	SYM
ejpam-4978	244	17	104	104	NUM
ejpam-4978	244	18	102	102	NUM
ejpam-4978	244	19	g	g	NOUN
ejpam-4978	244	20	is	be	AUX
ejpam-4978	244	21	complete	complete	ADJ
ejpam-4978	244	22	,	,	PUNCT
ejpam-4978	244	23	it	it	PRON
ejpam-4978	244	24	follows	follow	VERB
ejpam-4978	244	25	that	that	SCONJ
ejpam-4978	244	26	a	a	DET
ejpam-4978	244	27	/∈	/∈	ADJ
ejpam-4978	244	28	n2	n2	NOUN
ejpam-4978	244	29	g+h	g+h	PROPN
ejpam-4978	245	1	[	[	X
ejpam-4978	245	2	c	c	X
ejpam-4978	245	3	]	]	X
ejpam-4978	245	4	,	,	PUNCT
ejpam-4978	245	5	a	a	DET
ejpam-4978	245	6	contradiction	contradiction	NOUN
ejpam-4978	245	7	to	to	ADP
ejpam-4978	245	8	the	the	DET
ejpam-4978	245	9	fact	fact	NOUN
ejpam-4978	245	10	that	that	SCONJ
ejpam-4978	245	11	c	c	PROPN
ejpam-4978	245	12	is	be	AUX
ejpam-4978	245	13	a	a	DET
ejpam-4978	245	14	hop	hop	NOUN
ejpam-4978	245	15	dominating	dominating	NOUN
ejpam-4978	245	16	set	set	VERB
ejpam-4978	245	17	in	in	ADP
ejpam-4978	245	18	g+h	g+h	PROPN
ejpam-4978	245	19	.	.	PUNCT
ejpam-4978	246	1	hence	hence	ADV
ejpam-4978	246	2	,	,	PUNCT
ejpam-4978	246	3	cg	cg	NOUN
ejpam-4978	246	4	=	=	SYM
ejpam-4978	246	5	v	v	NOUN
ejpam-4978	246	6	(	(	PUNCT
ejpam-4978	246	7	g	g	NOUN
ejpam-4978	246	8	)	)	PUNCT
ejpam-4978	246	9	.	.	PUNCT
ejpam-4978	247	1	conversely	conversely	ADV
ejpam-4978	247	2	,	,	PUNCT
ejpam-4978	247	3	suppose	suppose	VERB
ejpam-4978	247	4	that	that	SCONJ
ejpam-4978	247	5	c	c	PROPN
ejpam-4978	247	6	=	=	SYM
ejpam-4978	247	7	v	v	PROPN
ejpam-4978	247	8	(	(	PUNCT
ejpam-4978	247	9	g	g	NOUN
ejpam-4978	247	10	)	)	PUNCT
ejpam-4978	247	11	∪	∪	NOUN
ejpam-4978	247	12	ch	ch	NOUN
ejpam-4978	247	13	,	,	PUNCT
ejpam-4978	247	14	where	where	SCONJ
ejpam-4978	247	15	ch	ch	NOUN
ejpam-4978	247	16	is	be	AUX
ejpam-4978	247	17	a	a	DET
ejpam-4978	247	18	vertex	vertex	NOUN
ejpam-4978	247	19	cover	cover	NOUN
ejpam-4978	247	20	pointwise	pointwise	NOUN
ejpam-4978	247	21	nondominating	nondominate	VERB
ejpam-4978	247	22	set	set	NOUN
ejpam-4978	247	23	in	in	ADP
ejpam-4978	247	24	h.	h.	PROPN
ejpam-4978	247	25	then	then	ADV
ejpam-4978	247	26	c	c	PROPN
ejpam-4978	247	27	is	be	AUX
ejpam-4978	247	28	a	a	DET
ejpam-4978	247	29	vertex	vertex	NOUN
ejpam-4978	247	30	cover	cover	NOUN
ejpam-4978	247	31	set	set	NOUN
ejpam-4978	247	32	of	of	ADP
ejpam-4978	247	33	g+h	g+h	PROPN
ejpam-4978	247	34	.	.	PUNCT
ejpam-4978	248	1	by	by	ADP
ejpam-4978	248	2	theorem	theorem	NOUN
ejpam-4978	248	3	4	4	NUM
ejpam-4978	248	4	,	,	PUNCT
ejpam-4978	248	5	c	c	PROPN
ejpam-4978	248	6	is	be	AUX
ejpam-4978	248	7	a	a	DET
ejpam-4978	248	8	hop	hop	NOUN
ejpam-4978	248	9	dominating	dominating	NOUN
ejpam-4978	248	10	of	of	ADP
ejpam-4978	248	11	g+h	g+h	PROPN
ejpam-4978	248	12	.	.	PUNCT
ejpam-4978	249	1	thus	thus	ADV
ejpam-4978	249	2	,	,	PUNCT
ejpam-4978	249	3	c	c	PROPN
ejpam-4978	249	4	is	be	AUX
ejpam-4978	249	5	a	a	DET
ejpam-4978	249	6	vertex	vertex	NOUN
ejpam-4978	249	7	cover	cover	NOUN
ejpam-4978	249	8	hop	hop	NOUN
ejpam-4978	249	9	dominating	dominating	NOUN
ejpam-4978	249	10	set	set	NOUN
ejpam-4978	249	11	of	of	ADP
ejpam-4978	249	12	g+h	g+h	PROPN
ejpam-4978	249	13	.	.	PUNCT
ejpam-4978	250	1	theorem	theorem	ADJ
ejpam-4978	250	2	8	8	NUM
ejpam-4978	250	3	.	.	PUNCT
ejpam-4978	251	1	let	let	VERB
ejpam-4978	251	2	g	g	NOUN
ejpam-4978	251	3	be	be	AUX
ejpam-4978	251	4	complete	complete	ADJ
ejpam-4978	251	5	graph	graph	NOUN
ejpam-4978	251	6	and	and	CCONJ
ejpam-4978	251	7	h	h	NOUN
ejpam-4978	251	8	be	be	AUX
ejpam-4978	251	9	any	any	DET
ejpam-4978	251	10	graph	graph	NOUN
ejpam-4978	251	11	.	.	PUNCT
ejpam-4978	252	1	then	then	ADV
ejpam-4978	252	2	.	.	PUNCT
ejpam-4978	253	1	γvch(g+h	γvch(g+h	ADJ
ejpam-4978	253	2	)	)	PUNCT
ejpam-4978	254	1	=	=	SYM
ejpam-4978	254	2	|v	|v	PROPN
ejpam-4978	254	3	(	(	PUNCT
ejpam-4978	254	4	g)|+	g)|+	NOUN
ejpam-4978	254	5	vcpnd(h	vcpnd(h	PROPN
ejpam-4978	254	6	)	)	PUNCT
ejpam-4978	254	7	.	.	PUNCT
ejpam-4978	255	1	proof	proof	NOUN
ejpam-4978	255	2	.	.	PUNCT
ejpam-4978	256	1	let	let	VERB
ejpam-4978	256	2	c	c	NOUN
ejpam-4978	256	3	=	=	SYM
ejpam-4978	256	4	v	v	PROPN
ejpam-4978	256	5	(	(	PUNCT
ejpam-4978	256	6	g)∪ch	g)∪ch	NOUN
ejpam-4978	256	7	be	be	AUX
ejpam-4978	256	8	a	a	DET
ejpam-4978	256	9	minimum	minimum	ADJ
ejpam-4978	256	10	vertex	vertex	NOUN
ejpam-4978	256	11	cover	cover	NOUN
ejpam-4978	256	12	hop	hop	NOUN
ejpam-4978	256	13	dominating	dominating	NOUN
ejpam-4978	256	14	set	set	NOUN
ejpam-4978	256	15	of	of	ADP
ejpam-4978	256	16	g+h	g+h	PROPN
ejpam-4978	256	17	.	.	PUNCT
ejpam-4978	257	1	then	then	ADV
ejpam-4978	257	2	by	by	ADP
ejpam-4978	257	3	theorem	theorem	NOUN
ejpam-4978	257	4	7	7	NUM
ejpam-4978	257	5	,	,	PUNCT
ejpam-4978	257	6	c	c	NOUN
ejpam-4978	257	7	=	=	SYM
ejpam-4978	257	8	v	v	PROPN
ejpam-4978	257	9	(	(	PUNCT
ejpam-4978	257	10	g)∪ch	g)∪ch	NOUN
ejpam-4978	257	11	,	,	PUNCT
ejpam-4978	257	12	where	where	SCONJ
ejpam-4978	257	13	ch	ch	NOUN
ejpam-4978	257	14	is	be	AUX
ejpam-4978	257	15	a	a	DET
ejpam-4978	257	16	vertex	vertex	NOUN
ejpam-4978	257	17	cover	cover	NOUN
ejpam-4978	257	18	pointwise	pointwise	PROPN
ejpam-4978	257	19	non	non	ADJ
ejpam-4978	257	20	-	-	ADJ
ejpam-4978	257	21	dominating	dominating	ADJ
ejpam-4978	257	22	set	set	NOUN
ejpam-4978	257	23	of	of	ADP
ejpam-4978	257	24	h.	h.	PROPN
ejpam-4978	257	25	thus	thus	ADV
ejpam-4978	257	26	,	,	PUNCT
ejpam-4978	257	27	γvch(g+h	γvch(g+h	NOUN
ejpam-4978	257	28	)	)	PUNCT
ejpam-4978	258	1	=	=	SYM
ejpam-4978	258	2	|c|	|c|	PROPN
ejpam-4978	258	3	=	=	SYM
ejpam-4978	258	4	|v	|v	PROPN
ejpam-4978	258	5	(	(	PUNCT
ejpam-4978	258	6	g)|+	g)|+	NOUN
ejpam-4978	258	7	|ch	|ch	ADP
ejpam-4978	258	8	|	|	ADV
ejpam-4978	258	9	≥	≥	NOUN
ejpam-4978	258	10	|v	|v	PROPN
ejpam-4978	258	11	(	(	PUNCT
ejpam-4978	258	12	g)|+	g)|+	NOUN
ejpam-4978	258	13	vcpnd(h	vcpnd(h	PROPN
ejpam-4978	258	14	)	)	PUNCT
ejpam-4978	258	15	.	.	PUNCT
ejpam-4978	259	1	next	next	ADV
ejpam-4978	259	2	,	,	PUNCT
ejpam-4978	259	3	suppose	suppose	VERB
ejpam-4978	259	4	that	that	SCONJ
ejpam-4978	259	5	c	c	PROPN
ejpam-4978	259	6	=	=	SYM
ejpam-4978	259	7	v	v	PROPN
ejpam-4978	259	8	(	(	PUNCT
ejpam-4978	259	9	g	g	NOUN
ejpam-4978	259	10	)	)	PUNCT
ejpam-4978	259	11	∪	∪	NOUN
ejpam-4978	259	12	ch	ch	NOUN
ejpam-4978	259	13	,	,	PUNCT
ejpam-4978	259	14	where	where	SCONJ
ejpam-4978	259	15	ch	ch	NOUN
ejpam-4978	259	16	is	be	AUX
ejpam-4978	259	17	a	a	DET
ejpam-4978	259	18	minimum	minimum	ADJ
ejpam-4978	259	19	vertex	vertex	NOUN
ejpam-4978	259	20	cover	cover	NOUN
ejpam-4978	259	21	pointwise	pointwise	PROPN
ejpam-4978	259	22	non	non	ADJ
ejpam-4978	259	23	-	-	ADJ
ejpam-4978	259	24	dominating	dominating	ADJ
ejpam-4978	259	25	set	set	NOUN
ejpam-4978	259	26	of	of	ADP
ejpam-4978	259	27	h.	h.	PROPN
ejpam-4978	259	28	then	then	ADV
ejpam-4978	259	29	c	c	PROPN
ejpam-4978	259	30	is	be	AUX
ejpam-4978	259	31	a	a	DET
ejpam-4978	259	32	vertex	vertex	NOUN
ejpam-4978	259	33	cover	cover	NOUN
ejpam-4978	259	34	hop	hop	NOUN
ejpam-4978	259	35	dominating	dominating	NOUN
ejpam-4978	259	36	set	set	VERB
ejpam-4978	259	37	in	in	ADP
ejpam-4978	259	38	g	g	PROPN
ejpam-4978	259	39	+	+	CCONJ
ejpam-4978	259	40	h	h	NOUN
ejpam-4978	259	41	by	by	ADP
ejpam-4978	259	42	theorem	theorem	NOUN
ejpam-4978	259	43	7	7	NUM
ejpam-4978	259	44	.	.	PUNCT
ejpam-4978	260	1	hence	hence	ADV
ejpam-4978	260	2	,	,	PUNCT
ejpam-4978	260	3	|v	|v	PROPN
ejpam-4978	260	4	(	(	PUNCT
ejpam-4978	260	5	g)|+	g)|+	NOUN
ejpam-4978	260	6	vcpnd(h	vcpnd(h	NOUN
ejpam-4978	260	7	)	)	PUNCT
ejpam-4978	260	8	=	=	SYM
ejpam-4978	260	9	|c|	|c|	PROPN
ejpam-4978	260	10	≥	≥	NOUN
ejpam-4978	260	11	γvch(g+h	γvch(g+h	NOUN
ejpam-4978	260	12	)	)	PUNCT
ejpam-4978	260	13	.	.	PUNCT
ejpam-4978	261	1	therefore	therefore	ADV
ejpam-4978	261	2	,	,	PUNCT
ejpam-4978	261	3	γvch(g+h	γvch(g+h	NOUN
ejpam-4978	261	4	)	)	PUNCT
ejpam-4978	262	1	=	=	SYM
ejpam-4978	262	2	|v	|v	PROPN
ejpam-4978	262	3	(	(	PUNCT
ejpam-4978	262	4	g)|+	g)|+	NOUN
ejpam-4978	262	5	vcpnd(h	vcpnd(h	PROPN
ejpam-4978	262	6	)	)	PUNCT
ejpam-4978	262	7	.	.	PUNCT
ejpam-4978	263	1	the	the	DET
ejpam-4978	263	2	following	follow	VERB
ejpam-4978	263	3	result	result	NOUN
ejpam-4978	263	4	follows	follow	VERB
ejpam-4978	263	5	that	that	SCONJ
ejpam-4978	263	6	from	from	ADP
ejpam-4978	263	7	observation	observation	NOUN
ejpam-4978	263	8	1	1	NUM
ejpam-4978	263	9	and	and	CCONJ
ejpam-4978	263	10	theorem	theorem	VERB
ejpam-4978	263	11	7	7	NUM
ejpam-4978	263	12	.	.	PUNCT
ejpam-4978	263	13	corollary	corollary	ADJ
ejpam-4978	263	14	3	3	X
ejpam-4978	263	15	.	.	PUNCT
ejpam-4978	264	1	let	let	VERB
ejpam-4978	264	2	n	n	PRON
ejpam-4978	264	3	and	and	CCONJ
ejpam-4978	264	4	m	m	AUX
ejpam-4978	264	5	be	be	AUX
ejpam-4978	264	6	positive	positive	ADJ
ejpam-4978	264	7	integers	integer	NOUN
ejpam-4978	264	8	.	.	PUNCT
ejpam-4978	265	1	then	then	ADV
ejpam-4978	265	2	each	each	PRON
ejpam-4978	265	3	of	of	ADP
ejpam-4978	265	4	the	the	DET
ejpam-4978	265	5	following	following	NOUN
ejpam-4978	265	6	is	be	AUX
ejpam-4978	265	7	true	true	ADJ
ejpam-4978	265	8	.	.	PUNCT
ejpam-4978	266	1	(	(	PUNCT
ejpam-4978	266	2	i	i	NOUN
ejpam-4978	266	3	)	)	PUNCT
ejpam-4978	266	4	γvch(kn	γvch(kn	NOUN
ejpam-4978	266	5	+	+	CCONJ
ejpam-4978	266	6	pm	pm	NOUN
ejpam-4978	266	7	)	)	PUNCT
ejpam-4978	266	8	=	=	SYM
ejpam-4978	267	1	n+	n+	PUNCT
ejpam-4978	267	2	vcpnd(pm	vcpnd(pm	NOUN
ejpam-4978	267	3	)	)	PUNCT
ejpam-4978	267	4	=	=	PUNCT
ejpam-4978	268	1			NOUN
ejpam-4978	268	2	n+	n+	PUNCT
ejpam-4978	268	3	2	2	NUM
ejpam-4978	268	4	if	if	SCONJ
ejpam-4978	268	5	m	m	VERB
ejpam-4978	268	6	=	=	SYM
ejpam-4978	268	7	3	3	NUM
ejpam-4978	268	8	n+	n+	SYM
ejpam-4978	268	9	3	3	NUM
ejpam-4978	268	10	if	if	SCONJ
ejpam-4978	268	11	m	m	VERB
ejpam-4978	268	12	=	=	SYM
ejpam-4978	268	13	5	5	NUM
ejpam-4978	268	14	n+	n+	SYM
ejpam-4978	268	15	m	m	VERB
ejpam-4978	268	16	2	2	NUM
ejpam-4978	268	17	if	if	SCONJ
ejpam-4978	268	18	m	m	PROPN
ejpam-4978	268	19	≥	≥	VERB
ejpam-4978	268	20	4	4	NUM
ejpam-4978	268	21	and	and	CCONJ
ejpam-4978	268	22	even	even	ADV
ejpam-4978	268	23	n+	n+	PUNCT
ejpam-4978	268	24	⌊m2	⌊m2	NUM
ejpam-4978	268	25	⌋	⌋	VERB
ejpam-4978	268	26	if	if	SCONJ
ejpam-4978	268	27	m	m	PROPN
ejpam-4978	268	28	≥	≥	VERB
ejpam-4978	268	29	7	7	NUM
ejpam-4978	268	30	and	and	CCONJ
ejpam-4978	268	31	odd	odd	ADJ
ejpam-4978	268	32	.	.	PUNCT
ejpam-4978	269	1	(	(	PUNCT
ejpam-4978	269	2	ii	ii	NOUN
ejpam-4978	269	3	)	)	PUNCT
ejpam-4978	269	4	γvch(kn	γvch(kn	NOUN
ejpam-4978	269	5	+	+	CCONJ
ejpam-4978	269	6	cm	cm	NOUN
ejpam-4978	269	7	)	)	PUNCT
ejpam-4978	270	1	=	=	PUNCT
ejpam-4978	270	2	n+	n+	X
ejpam-4978	270	3	vcpnd(cm	vcpnd(cm	NOUN
ejpam-4978	270	4	)	)	PUNCT
ejpam-4978	270	5	=	=	PRON
ejpam-4978	270	6	{	{	PUNCT
ejpam-4978	270	7	n+	n+	NOUN
ejpam-4978	270	8	m	m	VERB
ejpam-4978	270	9	2	2	NUM
ejpam-4978	270	10	if	if	SCONJ
ejpam-4978	270	11	m	m	PROPN
ejpam-4978	270	12	≥	≥	VERB
ejpam-4978	270	13	4	4	NUM
ejpam-4978	270	14	and	and	CCONJ
ejpam-4978	270	15	even	even	ADV
ejpam-4978	270	16	n+	n+	ADP
ejpam-4978	270	17	⌈m2	⌈m2	PROPN
ejpam-4978	270	18	⌉	⌉	PUNCT
ejpam-4978	270	19	if	if	SCONJ
ejpam-4978	270	20	m	m	PROPN
ejpam-4978	270	21	≥	≥	VERB
ejpam-4978	270	22	5	5	NUM
ejpam-4978	270	23	and	and	CCONJ
ejpam-4978	270	24	odd	odd	ADJ
ejpam-4978	270	25	.	.	PUNCT
ejpam-4978	271	1	(	(	PUNCT
ejpam-4978	271	2	iv	iv	X
ejpam-4978	271	3	)	)	PUNCT
ejpam-4978	271	4	γvch(wn	γvch(wn	NOUN
ejpam-4978	271	5	)	)	PUNCT
ejpam-4978	271	6	=	=	SYM
ejpam-4978	272	1	1	1	NUM
ejpam-4978	272	2	+	+	CCONJ
ejpam-4978	272	3	vcpnd(cm	vcpnd(cm	NOUN
ejpam-4978	272	4	)	)	PUNCT
ejpam-4978	272	5	=	=	PRON
ejpam-4978	272	6	{	{	PUNCT
ejpam-4978	273	1	1	1	NUM
ejpam-4978	273	2	+	+	CCONJ
ejpam-4978	273	3	m	m	VERB
ejpam-4978	273	4	2	2	NUM
ejpam-4978	273	5	if	if	SCONJ
ejpam-4978	273	6	m	m	PROPN
ejpam-4978	273	7	≥	≥	VERB
ejpam-4978	273	8	4	4	NUM
ejpam-4978	273	9	and	and	CCONJ
ejpam-4978	273	10	even	even	ADV
ejpam-4978	273	11	1	1	NUM
ejpam-4978	273	12	+	+	NUM
ejpam-4978	273	13	⌈m2	⌈m2	NOUN
ejpam-4978	273	14	⌉	⌉	PUNCT
ejpam-4978	273	15	if	if	SCONJ
ejpam-4978	273	16	m	m	PROPN
ejpam-4978	273	17	≥	≥	VERB
ejpam-4978	273	18	5	5	NUM
ejpam-4978	273	19	and	and	CCONJ
ejpam-4978	273	20	odd	odd	ADJ
ejpam-4978	273	21	.	.	PUNCT
ejpam-4978	274	1	(	(	PUNCT
ejpam-4978	274	2	v	v	NOUN
ejpam-4978	274	3	)	)	PUNCT
ejpam-4978	274	4	γvch(fn	γvch(fn	NOUN
ejpam-4978	274	5	)	)	PUNCT
ejpam-4978	274	6	=	=	SYM
ejpam-4978	275	1	1	1	NUM
ejpam-4978	275	2	+	+	NUM
ejpam-4978	275	3	vcpnd(pm	vcpnd(pm	NOUN
ejpam-4978	275	4	)	)	PUNCT
ejpam-4978	275	5	=	=	PUNCT
ejpam-4978	275	6			NOUN
ejpam-4978	275	7	3	3	NUM
ejpam-4978	275	8	if	if	SCONJ
ejpam-4978	275	9	m	m	VERB
ejpam-4978	275	10	=	=	NOUN
ejpam-4978	275	11	3	3	NUM
ejpam-4978	275	12	4	4	NUM
ejpam-4978	275	13	if	if	SCONJ
ejpam-4978	275	14	m	m	VERB
ejpam-4978	275	15	=	=	VERB
ejpam-4978	275	16	5	5	NUM
ejpam-4978	275	17	1	1	NUM
ejpam-4978	275	18	+	+	NUM
ejpam-4978	275	19	m	m	PROPN
ejpam-4978	275	20	2	2	NUM
ejpam-4978	275	21	if	if	SCONJ
ejpam-4978	275	22	m	m	PROPN
ejpam-4978	275	23	≥	≥	VERB
ejpam-4978	275	24	4	4	NUM
ejpam-4978	275	25	and	and	CCONJ
ejpam-4978	275	26	even	even	ADV
ejpam-4978	275	27	1	1	NUM
ejpam-4978	275	28	+	+	NUM
ejpam-4978	275	29	⌊m2	⌊m2	NOUN
ejpam-4978	275	30	⌋	⌋	NOUN
ejpam-4978	275	31	if	if	SCONJ
ejpam-4978	275	32	m	m	PROPN
ejpam-4978	275	33	≥	≥	VERB
ejpam-4978	275	34	7	7	NUM
ejpam-4978	275	35	and	and	CCONJ
ejpam-4978	275	36	odd	odd	ADJ
ejpam-4978	275	37	.	.	PUNCT
ejpam-4978	276	1	references	reference	NOUN
ejpam-4978	276	2	103	103	NUM
ejpam-4978	276	3	theorem	theorem	NOUN
ejpam-4978	276	4	9	9	NUM
ejpam-4978	276	5	.	.	PUNCT
ejpam-4978	277	1	let	let	VERB
ejpam-4978	277	2	g	g	PRON
ejpam-4978	277	3	be	be	AUX
ejpam-4978	277	4	a	a	DET
ejpam-4978	277	5	non	non	ADJ
ejpam-4978	277	6	-	-	ADJ
ejpam-4978	277	7	trivial	trivial	ADJ
ejpam-4978	277	8	connected	connected	ADJ
ejpam-4978	277	9	graph	graph	NOUN
ejpam-4978	277	10	and	and	CCONJ
ejpam-4978	277	11	let	let	VERB
ejpam-4978	277	12	h	h	NOUN
ejpam-4978	277	13	be	be	AUX
ejpam-4978	277	14	any	any	DET
ejpam-4978	277	15	graph	graph	NOUN
ejpam-4978	277	16	.	.	PUNCT
ejpam-4978	278	1	if	if	SCONJ
ejpam-4978	278	2	c	c	PROPN
ejpam-4978	278	3	=	=	SYM
ejpam-4978	278	4	v	v	PROPN
ejpam-4978	278	5	(	(	PUNCT
ejpam-4978	278	6	g	g	NOUN
ejpam-4978	278	7	)	)	PUNCT
ejpam-4978	278	8	∪	∪	NOUN
ejpam-4978	278	9	(	(	PUNCT
ejpam-4978	278	10	∪v∈v	∪v∈v	X
ejpam-4978	278	11	(	(	PUNCT
ejpam-4978	278	12	g)cv	g)cv	PROPN
ejpam-4978	278	13	)	)	PUNCT
ejpam-4978	278	14	,	,	PUNCT
ejpam-4978	278	15	where	where	SCONJ
ejpam-4978	278	16	cv	cv	PROPN
ejpam-4978	278	17	⊆	⊆	NUM
ejpam-4978	278	18	v	v	PROPN
ejpam-4978	278	19	(	(	PUNCT
ejpam-4978	278	20	hv	hv	X
ejpam-4978	278	21	)	)	PUNCT
ejpam-4978	278	22	is	be	AUX
ejpam-4978	278	23	a	a	DET
ejpam-4978	278	24	vertex	vertex	NOUN
ejpam-4978	278	25	cover	cover	NOUN
ejpam-4978	278	26	pointwise	pointwise	PROPN
ejpam-4978	278	27	non	non	ADJ
ejpam-4978	278	28	-	-	ADJ
ejpam-4978	278	29	dominating	dominating	ADJ
ejpam-4978	278	30	set	set	NOUN
ejpam-4978	278	31	of	of	ADP
ejpam-4978	278	32	h	h	NOUN
ejpam-4978	278	33	for	for	ADP
ejpam-4978	278	34	each	each	DET
ejpam-4978	278	35	v	v	NUM
ejpam-4978	278	36	∈	∈	PROPN
ejpam-4978	278	37	v	v	NOUN
ejpam-4978	278	38	(	(	PUNCT
ejpam-4978	278	39	g	g	NOUN
ejpam-4978	278	40	)	)	PUNCT
ejpam-4978	278	41	,	,	PUNCT
ejpam-4978	278	42	then	then	ADV
ejpam-4978	278	43	c	c	PROPN
ejpam-4978	278	44	is	be	AUX
ejpam-4978	278	45	a	a	DET
ejpam-4978	278	46	vertex	vertex	NOUN
ejpam-4978	278	47	cover	cover	NOUN
ejpam-4978	278	48	hop	hop	NOUN
ejpam-4978	278	49	dominating	dominating	NOUN
ejpam-4978	278	50	set	set	NOUN
ejpam-4978	278	51	of	of	ADP
ejpam-4978	278	52	g	g	PROPN
ejpam-4978	278	53	◦	◦	NOUN
ejpam-4978	278	54	h.	h.	NOUN
ejpam-4978	278	55	proof	proof	NOUN
ejpam-4978	278	56	.	.	PUNCT
ejpam-4978	279	1	let	let	VERB
ejpam-4978	279	2	c	c	NOUN
ejpam-4978	279	3	=	=	SYM
ejpam-4978	279	4	v	v	PROPN
ejpam-4978	279	5	(	(	PUNCT
ejpam-4978	279	6	g	g	NOUN
ejpam-4978	279	7	)	)	PUNCT
ejpam-4978	279	8	∪	∪	NOUN
ejpam-4978	279	9	(	(	PUNCT
ejpam-4978	279	10	∪cv	∪cv	PROPN
ejpam-4978	279	11	)	)	PUNCT
ejpam-4978	279	12	,	,	PUNCT
ejpam-4978	279	13	where	where	SCONJ
ejpam-4978	279	14	cv	cv	PROPN
ejpam-4978	279	15	is	be	AUX
ejpam-4978	279	16	a	a	DET
ejpam-4978	279	17	vertex	vertex	NOUN
ejpam-4978	279	18	cover	cover	NOUN
ejpam-4978	279	19	pointwise	pointwise	PROPN
ejpam-4978	279	20	non	non	ADJ
ejpam-4978	279	21	-	-	ADJ
ejpam-4978	279	22	dominating	dominating	ADJ
ejpam-4978	279	23	set	set	VERB
ejpam-4978	279	24	hv	hv	NOUN
ejpam-4978	279	25	for	for	ADP
ejpam-4978	279	26	each	each	DET
ejpam-4978	279	27	v	v	NUM
ejpam-4978	279	28	∈	∈	PROPN
ejpam-4978	279	29	v	v	NOUN
ejpam-4978	279	30	(	(	PUNCT
ejpam-4978	279	31	g	g	NOUN
ejpam-4978	279	32	)	)	PUNCT
ejpam-4978	279	33	.	.	PUNCT
ejpam-4978	280	1	since	since	SCONJ
ejpam-4978	280	2	cv	cv	PROPN
ejpam-4978	280	3	is	be	AUX
ejpam-4978	280	4	a	a	DET
ejpam-4978	280	5	pointwise	pointwise	ADJ
ejpam-4978	280	6	non	non	ADJ
ejpam-4978	280	7	-	-	ADJ
ejpam-4978	280	8	dominating	dominating	ADJ
ejpam-4978	280	9	set	set	NOUN
ejpam-4978	280	10	in	in	ADP
ejpam-4978	280	11	hv	hv	PROPN
ejpam-4978	280	12	for	for	ADP
ejpam-4978	280	13	each	each	DET
ejpam-4978	280	14	v	v	NUM
ejpam-4978	280	15	∈	∈	PROPN
ejpam-4978	280	16	v	v	NOUN
ejpam-4978	280	17	(	(	PUNCT
ejpam-4978	280	18	g	g	NOUN
ejpam-4978	280	19	)	)	PUNCT
ejpam-4978	280	20	,	,	PUNCT
ejpam-4978	280	21	it	it	PRON
ejpam-4978	280	22	follows	follow	VERB
ejpam-4978	280	23	that	that	SCONJ
ejpam-4978	280	24	n2	n2	ADJ
ejpam-4978	280	25	⟨v+hv⟩[cv	⟨v+hv⟩[cv	PROPN
ejpam-4978	280	26	]	]	X
ejpam-4978	280	27	=	=	SYM
ejpam-4978	280	28	v	v	X
ejpam-4978	280	29	(	(	PUNCT
ejpam-4978	280	30	hv	hv	PROPN
ejpam-4978	280	31	)	)	PUNCT
ejpam-4978	280	32	for	for	ADP
ejpam-4978	280	33	each	each	DET
ejpam-4978	280	34	v	v	NUM
ejpam-4978	280	35	∈	∈	PROPN
ejpam-4978	280	36	v	v	NOUN
ejpam-4978	280	37	(	(	PUNCT
ejpam-4978	280	38	g	g	NOUN
ejpam-4978	280	39	)	)	PUNCT
ejpam-4978	280	40	.	.	PUNCT
ejpam-4978	281	1	thus	thus	ADV
ejpam-4978	281	2	,	,	PUNCT
ejpam-4978	281	3	n2	n2	ADJ
ejpam-4978	281	4	g	g	PROPN
ejpam-4978	281	5	◦	◦	NOUN
ejpam-4978	281	6	h	h	NOUN
ejpam-4978	282	1	[	[	X
ejpam-4978	282	2	c	c	X
ejpam-4978	282	3	]	]	X
ejpam-4978	282	4	=	=	PUNCT
ejpam-4978	282	5	n2	n2	PROPN
ejpam-4978	282	6	g	g	PROPN
ejpam-4978	282	7	◦	◦	NOUN
ejpam-4978	282	8	h	h	NOUN
ejpam-4978	283	1	[	[	X
ejpam-4978	283	2	v	v	X
ejpam-4978	283	3	(	(	PUNCT
ejpam-4978	283	4	g	g	NOUN
ejpam-4978	283	5	)	)	PUNCT
ejpam-4978	283	6	∪	∪	NOUN
ejpam-4978	283	7	(	(	PUNCT
ejpam-4978	283	8	⋃	⋃	ADJ
ejpam-4978	283	9	v∈v	v∈v	NOUN
ejpam-4978	283	10	(	(	PUNCT
ejpam-4978	283	11	g	g	NOUN
ejpam-4978	283	12	)	)	PUNCT
ejpam-4978	283	13	cv	cv	PROPN
ejpam-4978	283	14	)	)	PUNCT
ejpam-4978	283	15	]	]	PUNCT
ejpam-4978	284	1	=	=	SYM
ejpam-4978	284	2	v	v	X
ejpam-4978	284	3	(	(	PUNCT
ejpam-4978	284	4	g	g	PROPN
ejpam-4978	284	5	◦	◦	NOUN
ejpam-4978	284	6	h	h	NOUN
ejpam-4978	284	7	)	)	PUNCT
ejpam-4978	284	8	,	,	PUNCT
ejpam-4978	284	9	and	and	CCONJ
ejpam-4978	284	10	so	so	ADV
ejpam-4978	284	11	c	c	PROPN
ejpam-4978	284	12	is	be	AUX
ejpam-4978	284	13	a	a	DET
ejpam-4978	284	14	hop	hop	NOUN
ejpam-4978	284	15	dominating	dominating	NOUN
ejpam-4978	284	16	set	set	NOUN
ejpam-4978	284	17	of	of	ADP
ejpam-4978	284	18	g	g	PROPN
ejpam-4978	284	19	◦	◦	PROPN
ejpam-4978	284	20	h.	h.	PROPN
ejpam-4978	284	21	since	since	SCONJ
ejpam-4978	284	22	cv	cv	PROPN
ejpam-4978	284	23	is	be	AUX
ejpam-4978	284	24	a	a	DET
ejpam-4978	284	25	vertex	vertex	NOUN
ejpam-4978	284	26	cover	cover	NOUN
ejpam-4978	284	27	of	of	ADP
ejpam-4978	284	28	hv	hv	PROPN
ejpam-4978	284	29	for	for	ADP
ejpam-4978	284	30	each	each	PRON
ejpam-4978	284	31	v	v	NUM
ejpam-4978	284	32	∈	∈	PROPN
ejpam-4978	284	33	v	v	NOUN
ejpam-4978	284	34	(	(	PUNCT
ejpam-4978	284	35	g	g	NOUN
ejpam-4978	284	36	)	)	PUNCT
ejpam-4978	284	37	,	,	PUNCT
ejpam-4978	284	38	c	c	NOUN
ejpam-4978	284	39	=	=	SYM
ejpam-4978	284	40	v	v	PROPN
ejpam-4978	284	41	(	(	PUNCT
ejpam-4978	284	42	g	g	NOUN
ejpam-4978	284	43	)	)	PUNCT
ejpam-4978	284	44	∪	∪	NOUN
ejpam-4978	284	45	(	(	PUNCT
ejpam-4978	284	46	∪v∈v	∪v∈v	X
ejpam-4978	284	47	(	(	PUNCT
ejpam-4978	284	48	g)cv	g)cv	PROPN
ejpam-4978	284	49	)	)	PUNCT
ejpam-4978	284	50	is	be	AUX
ejpam-4978	284	51	a	a	DET
ejpam-4978	284	52	vertex	vertex	NOUN
ejpam-4978	284	53	cover	cover	NOUN
ejpam-4978	284	54	of	of	ADP
ejpam-4978	284	55	g	g	PROPN
ejpam-4978	284	56	◦	◦	NOUN
ejpam-4978	284	57	h.	h.	PROPN
ejpam-4978	284	58	consequently	consequently	ADV
ejpam-4978	284	59	,	,	PUNCT
ejpam-4978	284	60	c	c	PROPN
ejpam-4978	284	61	is	be	AUX
ejpam-4978	284	62	a	a	DET
ejpam-4978	284	63	vertex	vertex	NOUN
ejpam-4978	284	64	cover	cover	NOUN
ejpam-4978	284	65	hop	hop	NOUN
ejpam-4978	284	66	dominating	dominating	NOUN
ejpam-4978	284	67	set	set	NOUN
ejpam-4978	284	68	of	of	ADP
ejpam-4978	284	69	g	g	PROPN
ejpam-4978	284	70	◦	◦	NOUN
ejpam-4978	284	71	h.	h.	NOUN
ejpam-4978	284	72	corollary	corollary	ADJ
ejpam-4978	284	73	4	4	NUM
ejpam-4978	284	74	.	.	PUNCT
ejpam-4978	285	1	let	let	VERB
ejpam-4978	285	2	g	g	PRON
ejpam-4978	285	3	be	be	AUX
ejpam-4978	285	4	a	a	DET
ejpam-4978	285	5	non	non	ADJ
ejpam-4978	285	6	-	-	ADJ
ejpam-4978	285	7	trivial	trivial	ADJ
ejpam-4978	285	8	connected	connected	ADJ
ejpam-4978	285	9	graph	graph	NOUN
ejpam-4978	285	10	and	and	CCONJ
ejpam-4978	285	11	let	let	VERB
ejpam-4978	285	12	h	h	NOUN
ejpam-4978	285	13	be	be	AUX
ejpam-4978	285	14	any	any	DET
ejpam-4978	285	15	graph	graph	NOUN
ejpam-4978	285	16	.	.	PUNCT
ejpam-4978	286	1	then	then	ADV
ejpam-4978	286	2	γvch(g	γvch(g	ADP
ejpam-4978	286	3	◦	◦	NOUN
ejpam-4978	286	4	h	h	NOUN
ejpam-4978	286	5	)	)	PUNCT
ejpam-4978	286	6	≤	≤	NOUN
ejpam-4978	286	7	|v	|v	X
ejpam-4978	286	8	(	(	PUNCT
ejpam-4978	286	9	g)|+	g)|+	PROPN
ejpam-4978	286	10	|v	|v	PROPN
ejpam-4978	286	11	(	(	PUNCT
ejpam-4978	286	12	g)|	g)|	PROPN
ejpam-4978	286	13	·	·	PUNCT
ejpam-4978	286	14	vcpnd(h	vcpnd(h	NOUN
ejpam-4978	286	15	)	)	PUNCT
ejpam-4978	286	16	.	.	PUNCT
ejpam-4978	287	1	proof	proof	NOUN
ejpam-4978	287	2	.	.	PUNCT
ejpam-4978	288	1	let	let	VERB
ejpam-4978	288	2	c	c	NOUN
ejpam-4978	288	3	=	=	SYM
ejpam-4978	288	4	v	v	PROPN
ejpam-4978	288	5	(	(	PUNCT
ejpam-4978	288	6	g	g	NOUN
ejpam-4978	288	7	)	)	PUNCT
ejpam-4978	288	8	∪	∪	NOUN
ejpam-4978	288	9	(	(	PUNCT
ejpam-4978	288	10	⋃	⋃	ADJ
ejpam-4978	288	11	v∈v	v∈v	NOUN
ejpam-4978	288	12	(	(	PUNCT
ejpam-4978	288	13	g)cv	g)cv	PROPN
ejpam-4978	288	14	)	)	PUNCT
ejpam-4978	288	15	,	,	PUNCT
ejpam-4978	288	16	where	where	SCONJ
ejpam-4978	288	17	cv	cv	PROPN
ejpam-4978	288	18	is	be	AUX
ejpam-4978	288	19	a	a	DET
ejpam-4978	288	20	minimum	minimum	ADJ
ejpam-4978	288	21	vertex	vertex	NOUN
ejpam-4978	288	22	cover	cover	NOUN
ejpam-4978	288	23	pointwise	pointwise	PROPN
ejpam-4978	288	24	non	non	ADJ
ejpam-4978	288	25	-	-	ADJ
ejpam-4978	288	26	dominating	dominating	ADJ
ejpam-4978	288	27	set	set	NOUN
ejpam-4978	288	28	of	of	ADP
ejpam-4978	288	29	h.	h.	PROPN
ejpam-4978	288	30	by	by	ADP
ejpam-4978	288	31	theorem	theorem	NOUN
ejpam-4978	288	32	9	9	NUM
ejpam-4978	288	33	,	,	PUNCT
ejpam-4978	288	34	c	c	PROPN
ejpam-4978	288	35	is	be	AUX
ejpam-4978	288	36	a	a	DET
ejpam-4978	288	37	vertex	vertex	NOUN
ejpam-4978	288	38	cover	cover	NOUN
ejpam-4978	288	39	hop	hop	NOUN
ejpam-4978	288	40	dominating	dominating	NOUN
ejpam-4978	288	41	set	set	NOUN
ejpam-4978	288	42	g	g	PROPN
ejpam-4978	288	43	◦	◦	NOUN
ejpam-4978	288	44	h.	h.	PROPN
ejpam-4978	288	45	thus	thus	ADV
ejpam-4978	288	46	,	,	PUNCT
ejpam-4978	288	47	γvch(g	γvch(g	ADP
ejpam-4978	288	48	◦	◦	NOUN
ejpam-4978	288	49	h	h	NOUN
ejpam-4978	288	50	)	)	PUNCT
ejpam-4978	288	51	≤	≤	NOUN
ejpam-4978	288	52	|c|	|c|	PROPN
ejpam-4978	288	53	=	=	SYM
ejpam-4978	288	54	|v	|v	PROPN
ejpam-4978	288	55	(	(	PUNCT
ejpam-4978	288	56	g)|+	g)|+	PROPN
ejpam-4978	288	57	|v	|v	PROPN
ejpam-4978	288	58	(	(	PUNCT
ejpam-4978	288	59	g)|	g)|	PROPN
ejpam-4978	288	60	·	·	PUNCT
ejpam-4978	288	61	vcpnd(h	vcpnd(h	NOUN
ejpam-4978	288	62	)	)	PUNCT
ejpam-4978	288	63	.	.	PUNCT
ejpam-4978	289	1	4	4	X
ejpam-4978	289	2	.	.	X
ejpam-4978	289	3	conclusion	conclusion	VERB
ejpam-4978	289	4	the	the	DET
ejpam-4978	289	5	concept	concept	NOUN
ejpam-4978	289	6	of	of	ADP
ejpam-4978	289	7	vertex	vertex	NOUN
ejpam-4978	289	8	cover	cover	NOUN
ejpam-4978	289	9	hop	hop	NOUN
ejpam-4978	289	10	domination	domination	NOUN
ejpam-4978	289	11	has	have	AUX
ejpam-4978	289	12	been	be	AUX
ejpam-4978	289	13	introduced	introduce	VERB
ejpam-4978	289	14	and	and	CCONJ
ejpam-4978	289	15	initially	initially	ADV
ejpam-4978	289	16	investigated	investigate	VERB
ejpam-4978	289	17	in	in	ADP
ejpam-4978	289	18	this	this	DET
ejpam-4978	289	19	study	study	NOUN
ejpam-4978	289	20	.	.	PUNCT
ejpam-4978	290	1	graphs	graph	NOUN
ejpam-4978	290	2	that	that	PRON
ejpam-4978	290	3	attained	attain	VERB
ejpam-4978	290	4	some	some	DET
ejpam-4978	290	5	specific	specific	ADJ
ejpam-4978	290	6	vertex	vertex	NOUN
ejpam-4978	290	7	cover	cover	NOUN
ejpam-4978	290	8	hop	hop	NOUN
ejpam-4978	290	9	domination	domination	NOUN
ejpam-4978	290	10	number	number	NOUN
ejpam-4978	290	11	have	have	AUX
ejpam-4978	290	12	been	be	AUX
ejpam-4978	290	13	characterized	characterize	VERB
ejpam-4978	290	14	.	.	PUNCT
ejpam-4978	291	1	the	the	DET
ejpam-4978	291	2	vertex	vertex	NOUN
ejpam-4978	291	3	cover	cover	VERB
ejpam-4978	291	4	hop	hop	NOUN
ejpam-4978	291	5	domination	domination	NOUN
ejpam-4978	291	6	number	number	NOUN
ejpam-4978	291	7	of	of	ADP
ejpam-4978	291	8	the	the	DET
ejpam-4978	291	9	join	join	NOUN
ejpam-4978	291	10	and	and	CCONJ
ejpam-4978	291	11	corona	corona	NOUN
ejpam-4978	291	12	of	of	ADP
ejpam-4978	291	13	two	two	NUM
ejpam-4978	291	14	graphs	graph	NOUN
ejpam-4978	291	15	have	have	AUX
ejpam-4978	291	16	been	be	AUX
ejpam-4978	291	17	obtained	obtain	VERB
ejpam-4978	291	18	.	.	PUNCT
ejpam-4978	292	1	these	these	DET
ejpam-4978	292	2	characterizations	characterization	NOUN
ejpam-4978	292	3	have	have	AUX
ejpam-4978	292	4	been	be	AUX
ejpam-4978	292	5	used	use	VERB
ejpam-4978	292	6	to	to	PART
ejpam-4978	292	7	obtain	obtain	VERB
ejpam-4978	292	8	bounds	bound	NOUN
ejpam-4978	292	9	or	or	CCONJ
ejpam-4978	292	10	exact	exact	ADJ
ejpam-4978	292	11	values	value	NOUN
ejpam-4978	292	12	of	of	ADP
ejpam-4978	292	13	the	the	DET
ejpam-4978	292	14	vertex	vertex	NOUN
ejpam-4978	292	15	cover	cover	NOUN
ejpam-4978	292	16	hop	hop	NOUN
ejpam-4978	292	17	domination	domination	NOUN
ejpam-4978	292	18	number	number	NOUN
ejpam-4978	292	19	of	of	ADP
ejpam-4978	292	20	each	each	PRON
ejpam-4978	292	21	of	of	ADP
ejpam-4978	292	22	these	these	DET
ejpam-4978	292	23	graphs	graph	NOUN
ejpam-4978	292	24	.	.	PUNCT
ejpam-4978	293	1	exploring	explore	VERB
ejpam-4978	293	2	bounds	bound	NOUN
ejpam-4978	293	3	for	for	ADP
ejpam-4978	293	4	this	this	DET
ejpam-4978	293	5	newly	newly	ADV
ejpam-4978	293	6	introduced	introduce	VERB
ejpam-4978	293	7	parameter	parameter	NOUN
ejpam-4978	293	8	in	in	ADP
ejpam-4978	293	9	relation	relation	NOUN
ejpam-4978	293	10	to	to	ADP
ejpam-4978	293	11	other	other	ADJ
ejpam-4978	293	12	known	know	VERB
ejpam-4978	293	13	parameters	parameter	NOUN
ejpam-4978	293	14	possibly	possibly	ADV
ejpam-4978	293	15	provides	provide	VERB
ejpam-4978	293	16	insightful	insightful	ADJ
ejpam-4978	293	17	information	information	NOUN
ejpam-4978	293	18	.	.	PUNCT
ejpam-4978	294	1	acknowledgements	acknowledgement	NOUN
ejpam-4978	294	2	the	the	DET
ejpam-4978	294	3	authors	author	NOUN
ejpam-4978	294	4	would	would	AUX
ejpam-4978	294	5	like	like	VERB
ejpam-4978	294	6	to	to	PART
ejpam-4978	294	7	thank	thank	VERB
ejpam-4978	294	8	msu	msu	PROPN
ejpam-4978	294	9	-	-	PUNCT
ejpam-4978	294	10	iligan	iligan	PROPN
ejpam-4978	294	11	institute	institute	PROPN
ejpam-4978	294	12	of	of	ADP
ejpam-4978	294	13	technology	technology	PROPN
ejpam-4978	294	14	,	,	PUNCT
ejpam-4978	294	15	msu	msu	PROPN
ejpam-4978	294	16	tawi	tawi	PROPN
ejpam-4978	294	17	-	-	PUNCT
ejpam-4978	294	18	tawi	tawi	PROPN
ejpam-4978	294	19	college	college	PROPN
ejpam-4978	294	20	of	of	ADP
ejpam-4978	294	21	technology	technology	NOUN
ejpam-4978	294	22	and	and	CCONJ
ejpam-4978	294	23	oceanography	oceanography	NOUN
ejpam-4978	294	24	and	and	CCONJ
ejpam-4978	294	25	dost	dost	NOUN
ejpam-4978	294	26	-	-	PUNCT
ejpam-4978	294	27	asthrdp	asthrdp	NOUN
ejpam-4978	294	28	for	for	ADP
ejpam-4978	294	29	funding	fund	VERB
ejpam-4978	294	30	this	this	DET
ejpam-4978	294	31	research	research	NOUN
ejpam-4978	294	32	.	.	PUNCT
ejpam-4978	295	1	references	reference	NOUN
ejpam-4978	295	2	[	[	X
ejpam-4978	295	3	1	1	NUM
ejpam-4978	295	4	]	]	PUNCT
ejpam-4978	295	5	c.	c.	PROPN
ejpam-4978	295	6	berge	berge	PROPN
ejpam-4978	295	7	.	.	PUNCT
ejpam-4978	296	1	theory	theory	NOUN
ejpam-4978	296	2	of	of	ADP
ejpam-4978	296	3	graphs	graph	NOUN
ejpam-4978	296	4	and	and	CCONJ
ejpam-4978	296	5	its	its	PRON
ejpam-4978	296	6	applications	application	NOUN
ejpam-4978	296	7	.	.	PUNCT
ejpam-4978	297	1	references	reference	NOUN
ejpam-4978	297	2	104	104	NUM
ejpam-4978	298	1	[	[	X
ejpam-4978	298	2	2	2	X
ejpam-4978	298	3	]	]	PUNCT
ejpam-4978	298	4	s.	s.	PROPN
ejpam-4978	298	5	canoy	canoy	PROPN
ejpam-4978	298	6	jr	jr	PROPN
ejpam-4978	298	7	.	.	PROPN
ejpam-4978	298	8	and	and	CCONJ
ejpam-4978	298	9	j.	j.	PROPN
ejpam-4978	298	10	hassan	hassan	PROPN
ejpam-4978	298	11	.	.	PUNCT
ejpam-4978	299	1	hop	hop	PROPN
ejpam-4978	299	2	independent	independent	ADJ
ejpam-4978	299	3	hop	hop	NOUN
ejpam-4978	299	4	domination	domination	NOUN
ejpam-4978	299	5	in	in	ADP
ejpam-4978	299	6	graphs	graph	NOUN
ejpam-4978	299	7	.	.	PUNCT
ejpam-4978	300	1	eur	eur	PROPN
ejpam-4978	300	2	.	.	PUNCT
ejpam-4978	301	1	j.	j.	PROPN
ejpam-4978	301	2	pure	pure	PROPN
ejpam-4978	301	3	appl	appl	PROPN
ejpam-4978	301	4	.	.	PUNCT
ejpam-4978	301	5	math	math	PROPN
ejpam-4978	301	6	.	.	PUNCT
ejpam-4978	301	7	,	,	PUNCT
ejpam-4978	301	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-4978	301	9	,	,	PUNCT
ejpam-4978	301	10	2022	2022	NUM
ejpam-4978	301	11	.	.	PUNCT
ejpam-4978	302	1	[	[	X
ejpam-4978	302	2	3	3	X
ejpam-4978	302	3	]	]	X
ejpam-4978	302	4	s.	s.	PROPN
ejpam-4978	302	5	canoy	canoy	PROPN
ejpam-4978	302	6	jr	jr	PROPN
ejpam-4978	302	7	.	.	PROPN
ejpam-4978	302	8	and	and	CCONJ
ejpam-4978	302	9	j.	j.	PROPN
ejpam-4978	302	10	hassan	hassan	PROPN
ejpam-4978	302	11	.	.	PUNCT
ejpam-4978	303	1	weakly	weakly	ADJ
ejpam-4978	303	2	convex	convex	VERB
ejpam-4978	303	3	hop	hop	NOUN
ejpam-4978	303	4	dominating	dominating	NOUN
ejpam-4978	303	5	sets	set	NOUN
ejpam-4978	303	6	in	in	ADP
ejpam-4978	303	7	graphs	graph	NOUN
ejpam-4978	303	8	.	.	PUNCT
ejpam-4978	304	1	eur	eur	PROPN
ejpam-4978	304	2	.	.	PUNCT
ejpam-4978	305	1	j.	j.	PROPN
ejpam-4978	305	2	pure	pure	PROPN
ejpam-4978	305	3	appl	appl	PROPN
ejpam-4978	305	4	.	.	PUNCT
ejpam-4978	305	5	math	math	PROPN
ejpam-4978	305	6	.	.	PUNCT
ejpam-4978	305	7	,	,	PUNCT
ejpam-4978	305	8	16(2):1196–1211	16(2):1196–1211	NUM
ejpam-4978	305	9	,	,	PUNCT
ejpam-4978	305	10	2023	2023	NUM
ejpam-4978	305	11	.	.	PUNCT
ejpam-4978	306	1	[	[	X
ejpam-4978	306	2	4	4	X
ejpam-4978	306	3	]	]	X
ejpam-4978	306	4	s.	s.	PROPN
ejpam-4978	306	5	canoy	canoy	PROPN
ejpam-4978	306	6	jr	jr	PROPN
ejpam-4978	306	7	.	.	PROPN
ejpam-4978	306	8	and	and	CCONJ
ejpam-4978	306	9	g.	g.	PROPN
ejpam-4978	306	10	salasalan	salasalan	NOUN
ejpam-4978	306	11	.	.	PUNCT
ejpam-4978	307	1	locating	locate	VERB
ejpam-4978	307	2	-	-	PUNCT
ejpam-4978	307	3	hop	hop	NOUN
ejpam-4978	307	4	domination	domination	NOUN
ejpam-4978	307	5	in	in	ADP
ejpam-4978	307	6	graphs	graph	NOUN
ejpam-4978	307	7	.	.	PUNCT
ejpam-4978	308	1	kyungpook	kyungpook	PROPN
ejpam-4978	308	2	mathematical	mathematical	PROPN
ejpam-4978	308	3	journal	journal	PROPN
ejpam-4978	308	4	.	.	PUNCT
ejpam-4978	308	5	,	,	PUNCT
ejpam-4978	308	6	62:193–204	62:193–204	NUM
ejpam-4978	308	7	,	,	PUNCT
ejpam-4978	308	8	2022	2022	NUM
ejpam-4978	308	9	.	.	PUNCT
ejpam-4978	309	1	[	[	X
ejpam-4978	309	2	5	5	NUM
ejpam-4978	309	3	]	]	PUNCT
ejpam-4978	309	4	c.	c.	PROPN
ejpam-4978	309	5	natarajan	natarajan	PROPN
ejpam-4978	309	6	and	and	CCONJ
ejpam-4978	309	7	s.	s.	PROPN
ejpam-4978	309	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4978	309	9	.	.	PUNCT
ejpam-4978	310	1	hop	hop	PROPN
ejpam-4978	310	2	domination	domination	NOUN
ejpam-4978	310	3	in	in	ADP
ejpam-4978	310	4	graphs	graphs	PROPN
ejpam-4978	310	5	ii	ii	PROPN
ejpam-4978	310	6	.	.	PUNCT
ejpam-4978	310	7	versita	versita	PROPN
ejpam-4978	310	8	,	,	PUNCT
ejpam-4978	310	9	23(2):187	23(2):187	NUM
ejpam-4978	310	10	–	–	PUNCT
ejpam-4978	310	11	199	199	NUM
ejpam-4978	310	12	,	,	PUNCT
ejpam-4978	310	13	2015	2015	NUM
ejpam-4978	310	14	.	.	PUNCT
ejpam-4978	311	1	[	[	X
ejpam-4978	311	2	6	6	NUM
ejpam-4978	311	3	]	]	PUNCT
ejpam-4978	311	4	o.	o.	PROPN
ejpam-4978	311	5	ore	ore	PROPN
ejpam-4978	311	6	.	.	PUNCT
ejpam-4978	312	1	theory	theory	NOUN
ejpam-4978	312	2	of	of	ADP
ejpam-4978	312	3	graphs	graph	NOUN
ejpam-4978	312	4	,	,	PUNCT
ejpam-4978	312	5	volume	volume	NOUN
ejpam-4978	312	6	38	38	NUM
ejpam-4978	312	7	.	.	PUNCT
ejpam-4978	313	1	1962	1962	NUM
ejpam-4978	313	2	.	.	PUNCT
ejpam-4978	314	1	[	[	X
ejpam-4978	314	2	7	7	X
ejpam-4978	314	3	]	]	X
ejpam-4978	314	4	b.	b.	PROPN
ejpam-4978	314	5	natarjan	natarjan	PROPN
ejpam-4978	314	6	s.	s.	PROPN
ejpam-4978	314	7	ayyaswamy	ayyaswamy	PROPN
ejpam-4978	314	8	,	,	PUNCT
ejpam-4978	314	9	b.	b.	PROPN
ejpam-4978	314	10	krishnakumari	krishnakumari	PROPN
ejpam-4978	314	11	and	and	CCONJ
ejpam-4978	314	12	y.	y.	PROPN
ejpam-4978	314	13	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4978	314	14	.	.	PUNCT
ejpam-4978	315	1	bounds	bound	NOUN
ejpam-4978	315	2	on	on	ADP
ejpam-4978	315	3	the	the	DET
ejpam-4978	315	4	hop	hop	NOUN
ejpam-4978	315	5	domination	domination	NOUN
ejpam-4978	315	6	number	number	NOUN
ejpam-4978	315	7	of	of	ADP
ejpam-4978	315	8	a	a	DET
ejpam-4978	315	9	tree	tree	NOUN
ejpam-4978	315	10	.	.	PUNCT
ejpam-4978	316	1	proceedings	proceeding	NOUN
ejpam-4978	316	2	-	-	PUNCT
ejpam-4978	316	3	mathematical	mathematical	ADJ
ejpam-4978	316	4	sciences	science	NOUN
ejpam-4978	316	5	.	.	PUNCT
ejpam-4978	316	6	,	,	PUNCT
ejpam-4978	316	7	125(4):449–455	125(4):449–455	ADP
ejpam-4978	316	8	,	,	PUNCT
ejpam-4978	316	9	2015	2015	NUM
ejpam-4978	316	10	.	.	PUNCT
ejpam-4978	317	1	[	[	X
ejpam-4978	317	2	8	8	NUM
ejpam-4978	317	3	]	]	X
ejpam-4978	317	4	c.	c.	PROPN
ejpam-4978	317	5	natarajan	natarajan	PROPN
ejpam-4978	317	6	s.	s.	PROPN
ejpam-4978	317	7	ayyaswamy	ayyaswamy	PROPN
ejpam-4978	317	8	and	and	CCONJ
ejpam-4978	317	9	g.	g.	PROPN
ejpam-4978	317	10	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4978	317	11	.	.	PUNCT
ejpam-4978	318	1	a	a	DET
ejpam-4978	318	2	note	note	NOUN
ejpam-4978	318	3	on	on	ADP
ejpam-4978	318	4	hop	hop	NOUN
ejpam-4978	318	5	domination	domination	NOUN
ejpam-4978	318	6	number	number	NOUN
ejpam-4978	318	7	of	of	ADP
ejpam-4978	318	8	some	some	DET
ejpam-4978	318	9	special	special	ADJ
ejpam-4978	318	10	families	family	NOUN
ejpam-4978	318	11	of	of	ADP
ejpam-4978	318	12	graphs	graph	NOUN
ejpam-4978	318	13	.	.	PUNCT
ejpam-4978	319	1	international	international	ADJ
ejpam-4978	319	2	journal	journal	NOUN
ejpam-4978	319	3	of	of	ADP
ejpam-4978	319	4	pure	pure	ADJ
ejpam-4978	319	5	and	and	CCONJ
ejpam-4978	319	6	applied	applied	ADJ
ejpam-4978	319	7	mathematics	mathematic	NOUN
ejpam-4978	319	8	.	.	PUNCT
ejpam-4978	319	9	,	,	PUNCT
ejpam-4978	319	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4978	319	11	,	,	PUNCT
ejpam-4978	319	12	2018	2018	NUM
ejpam-4978	319	13	.	.	PUNCT
ejpam-4978	320	1	[	[	X
ejpam-4978	320	2	9	9	NUM
ejpam-4978	320	3	]	]	PUNCT
ejpam-4978	320	4	j.	j.	PROPN
ejpam-4978	320	5	hassan	hassan	PROPN
ejpam-4978	320	6	s.	s.	PROPN
ejpam-4978	320	7	canoy	canoy	PROPN
ejpam-4978	320	8	jr	jr	PROPN
ejpam-4978	320	9	.	.	PROPN
ejpam-4978	320	10	and	and	CCONJ
ejpam-4978	320	11	c.	c.	PROPN
ejpam-4978	320	12	j.	j.	PROPN
ejpam-4978	320	13	saromines	saromines	PROPN
ejpam-4978	320	14	.	.	PUNCT
ejpam-4978	321	1	convex	convex	VERB
ejpam-4978	321	2	hop	hop	NOUN
ejpam-4978	321	3	domination	domination	NOUN
ejpam-4978	321	4	in	in	ADP
ejpam-4978	321	5	graphs	graph	NOUN
ejpam-4978	321	6	.	.	PUNCT
ejpam-4978	322	1	eur	eur	PROPN
ejpam-4978	322	2	.	.	PUNCT
ejpam-4978	323	1	j.	j.	PROPN
ejpam-4978	323	2	pure	pure	PROPN
ejpam-4978	323	3	appl	appl	PROPN
ejpam-4978	323	4	.	.	PUNCT
ejpam-4978	323	5	math	math	PROPN
ejpam-4978	323	6	.	.	PUNCT
ejpam-4978	323	7	,	,	PUNCT
ejpam-4978	323	8	16(1):319–335	16(1):319–335	NOUN
ejpam-4978	323	9	,	,	PUNCT
ejpam-4978	323	10	2023	2023	NUM
ejpam-4978	323	11	.	.	PUNCT
ejpam-4978	324	1	[	[	X
ejpam-4978	324	2	10	10	NUM
ejpam-4978	324	3	]	]	X
ejpam-4978	324	4	r.	r.	PROPN
ejpam-4978	324	5	mollejon	mollejon	PROPN
ejpam-4978	324	6	s.	s.	PROPN
ejpam-4978	324	7	canoy	canoy	PROPN
ejpam-4978	324	8	jr	jr	PROPN
ejpam-4978	324	9	.	.	PROPN
ejpam-4978	324	10	and	and	CCONJ
ejpam-4978	324	11	j.	j.	PROPN
ejpam-4978	324	12	g.	g.	PROPN
ejpam-4978	324	13	canoy	canoy	PROPN
ejpam-4978	324	14	.	.	PUNCT
ejpam-4978	325	1	hop	hop	PROPN
ejpam-4978	325	2	dominating	dominating	NOUN
ejpam-4978	325	3	sets	set	NOUN
ejpam-4978	325	4	in	in	ADP
ejpam-4978	325	5	graphs	graph	NOUN
ejpam-4978	325	6	under	under	ADP
ejpam-4978	325	7	binary	binary	ADJ
ejpam-4978	325	8	operations	operation	NOUN
ejpam-4978	325	9	.	.	PUNCT
ejpam-4978	326	1	eur	eur	PROPN
ejpam-4978	326	2	.	.	PUNCT
ejpam-4978	327	1	j.	j.	PROPN
ejpam-4978	327	2	pure	pure	PROPN
ejpam-4978	327	3	appl	appl	PROPN
ejpam-4978	327	4	.	.	PUNCT
ejpam-4978	327	5	math	math	PROPN
ejpam-4978	327	6	.	.	PUNCT
ejpam-4978	327	7	,	,	PUNCT
ejpam-4978	328	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4978	328	2	,	,	PUNCT
ejpam-4978	328	3	2019	2019	NUM
ejpam-4978	328	4	.	.	PUNCT
ejpam-4978	329	1	[	[	X
ejpam-4978	329	2	11	11	NUM
ejpam-4978	329	3	]	]	X
ejpam-4978	329	4	g.	g.	NOUN
ejpam-4978	329	5	salasalan	salasalan	NOUN
ejpam-4978	329	6	and	and	CCONJ
ejpam-4978	329	7	s.	s.	PROPN
ejpam-4978	329	8	canoy	canoy	PROPN
ejpam-4978	329	9	jr	jr	PROPN
ejpam-4978	329	10	.	.	PROPN
ejpam-4978	329	11	global	global	PROPN
ejpam-4978	329	12	hop	hop	PROPN
ejpam-4978	329	13	domination	domination	PROPN
ejpam-4978	329	14	numbers	number	NOUN
ejpam-4978	329	15	of	of	ADP
ejpam-4978	329	16	graphs	graph	NOUN
ejpam-4978	329	17	.	.	PUNCT
ejpam-4978	330	1	eur	eur	PROPN
ejpam-4978	330	2	.	.	PUNCT
ejpam-4978	331	1	j.	j.	PROPN
ejpam-4978	331	2	pure	pure	PROPN
ejpam-4978	331	3	appl	appl	PROPN
ejpam-4978	331	4	.	.	PUNCT
ejpam-4978	331	5	math	math	PROPN
ejpam-4978	331	6	.	.	PUNCT
ejpam-4978	331	7	,	,	PUNCT
ejpam-4978	331	8	14(1):112–125	14(1):112–125	NUM
ejpam-4978	331	9	,	,	PUNCT
ejpam-4978	331	10	2021	2021	NUM
ejpam-4978	331	11	.	.	PUNCT