id	sid	tid	token	lemma	pos
ejpam-5065	1	1	european	european	PROPN
ejpam-5065	1	2	journal	journal	PROPN
ejpam-5065	1	3	of	of	ADP
ejpam-5065	1	4	pure	pure	ADJ
ejpam-5065	1	5	and	and	CCONJ
ejpam-5065	1	6	applied	apply	VERB
ejpam-5065	1	7	mathematics	mathematic	NOUN
ejpam-5065	1	8	vol	vol	NOUN
ejpam-5065	1	9	.	.	PROPN
ejpam-5065	2	1	17	17	NUM
ejpam-5065	2	2	,	,	PUNCT
ejpam-5065	2	3	no	no	INTJ
ejpam-5065	2	4	.	.	NOUN
ejpam-5065	2	5	2	2	NUM
ejpam-5065	2	6	,	,	PUNCT
ejpam-5065	2	7	2024	2024	NUM
ejpam-5065	2	8	,	,	PUNCT
ejpam-5065	2	9	852	852	NUM
ejpam-5065	2	10	-	-	SYM
ejpam-5065	2	11	859	859	NUM
ejpam-5065	2	12	issn	issn	PROPN
ejpam-5065	2	13	1307	1307	NUM
ejpam-5065	2	14	-	-	SYM
ejpam-5065	2	15	5543	5543	NUM
ejpam-5065	2	16	–	–	PUNCT
ejpam-5065	2	17	ejpam.com	ejpam.com	X
ejpam-5065	2	18	published	publish	VERB
ejpam-5065	2	19	by	by	ADP
ejpam-5065	2	20	new	new	PROPN
ejpam-5065	2	21	york	york	PROPN
ejpam-5065	2	22	business	business	NOUN
ejpam-5065	2	23	global	global	ADJ
ejpam-5065	2	24	formulas	formula	NOUN
ejpam-5065	2	25	and	and	CCONJ
ejpam-5065	2	26	properties	property	NOUN
ejpam-5065	2	27	of	of	ADP
ejpam-5065	2	28	2	2	NUM
ejpam-5065	2	29	-	-	PUNCT
ejpam-5065	2	30	hop	hop	NOUN
ejpam-5065	2	31	domination	domination	NOUN
ejpam-5065	2	32	in	in	ADP
ejpam-5065	2	33	some	some	DET
ejpam-5065	2	34	graphs	graph	NOUN
ejpam-5065	2	35	javier	javier	PROPN
ejpam-5065	2	36	a.	a.	PROPN
ejpam-5065	2	37	hassan1,∗	hassan1,∗	PROPN
ejpam-5065	2	38	,	,	PUNCT
ejpam-5065	2	39	anabel	anabel	PROPN
ejpam-5065	2	40	e.	e.	PROPN
ejpam-5065	2	41	gomorez2	gomorez2	PROPN
ejpam-5065	2	42	,	,	PUNCT
ejpam-5065	2	43	ladznar	ladznar	ADJ
ejpam-5065	2	44	s.	s.	PROPN
ejpam-5065	2	45	laja1	laja1	PROPN
ejpam-5065	2	46	,	,	PUNCT
ejpam-5065	2	47	eman	eman	PROPN
ejpam-5065	2	48	c.	c.	PROPN
ejpam-5065	2	49	ahmad2	ahmad2	PROPN
ejpam-5065	2	50	1mathematics	1mathematics	PROPN
ejpam-5065	2	51	and	and	CCONJ
ejpam-5065	2	52	statistics	statistics	PROPN
ejpam-5065	2	53	department	department	PROPN
ejpam-5065	2	54	,	,	PUNCT
ejpam-5065	2	55	college	college	NOUN
ejpam-5065	2	56	of	of	ADP
ejpam-5065	2	57	arts	art	NOUN
ejpam-5065	2	58	and	and	CCONJ
ejpam-5065	2	59	sciences	science	NOUN
ejpam-5065	2	60	,	,	PUNCT
ejpam-5065	2	61	msu	msu	PROPN
ejpam-5065	2	62	tawi	tawi	PROPN
ejpam-5065	2	63	-	-	PUNCT
ejpam-5065	2	64	tawi	tawi	PROPN
ejpam-5065	2	65	college	college	PROPN
ejpam-5065	2	66	of	of	ADP
ejpam-5065	2	67	technology	technology	NOUN
ejpam-5065	2	68	and	and	CCONJ
ejpam-5065	2	69	oceanography	oceanography	NOUN
ejpam-5065	2	70	,	,	PUNCT
ejpam-5065	2	71	bongao	bongao	NOUN
ejpam-5065	2	72	,	,	PUNCT
ejpam-5065	2	73	tawi	tawi	NOUN
ejpam-5065	2	74	-	-	PUNCT
ejpam-5065	2	75	tawi	tawi	NOUN
ejpam-5065	2	76	,	,	PUNCT
ejpam-5065	3	1	philippines	philippine	NOUN
ejpam-5065	3	2	2department	2department	NUM
ejpam-5065	3	3	of	of	ADP
ejpam-5065	3	4	mathematics	mathematic	NOUN
ejpam-5065	3	5	and	and	CCONJ
ejpam-5065	3	6	statistics	statistic	NOUN
ejpam-5065	3	7	,	,	PUNCT
ejpam-5065	3	8	college	college	NOUN
ejpam-5065	3	9	of	of	ADP
ejpam-5065	3	10	science	science	NOUN
ejpam-5065	3	11	and	and	CCONJ
ejpam-5065	3	12	mathematics	mathematic	NOUN
ejpam-5065	3	13	,	,	PUNCT
ejpam-5065	3	14	western	western	ADJ
ejpam-5065	3	15	mindanao	mindanao	PROPN
ejpam-5065	3	16	state	state	PROPN
ejpam-5065	3	17	university	university	PROPN
ejpam-5065	3	18	,	,	PUNCT
ejpam-5065	3	19	zamboanga	zamboanga	PROPN
ejpam-5065	3	20	city	city	PROPN
ejpam-5065	3	21	,	,	PUNCT
ejpam-5065	3	22	philippines	philippine	NOUN
ejpam-5065	3	23	abstract	abstract	ADJ
ejpam-5065	3	24	.	.	PUNCT
ejpam-5065	4	1	in	in	ADP
ejpam-5065	4	2	this	this	DET
ejpam-5065	4	3	paper	paper	NOUN
ejpam-5065	4	4	,	,	PUNCT
ejpam-5065	4	5	2	2	NUM
ejpam-5065	4	6	-	-	PUNCT
ejpam-5065	4	7	hop	hop	NOUN
ejpam-5065	4	8	domination	domination	NOUN
ejpam-5065	4	9	parameter	parameter	NOUN
ejpam-5065	4	10	is	be	AUX
ejpam-5065	4	11	introduced	introduce	VERB
ejpam-5065	4	12	and	and	CCONJ
ejpam-5065	4	13	investigated	investigate	VERB
ejpam-5065	4	14	on	on	ADP
ejpam-5065	4	15	some	some	DET
ejpam-5065	4	16	special	special	ADJ
ejpam-5065	4	17	graphs	graph	NOUN
ejpam-5065	4	18	and	and	CCONJ
ejpam-5065	4	19	on	on	ADP
ejpam-5065	4	20	the	the	DET
ejpam-5065	4	21	join	join	NOUN
ejpam-5065	4	22	of	of	ADP
ejpam-5065	4	23	two	two	NUM
ejpam-5065	4	24	graphs	graph	NOUN
ejpam-5065	4	25	.	.	PUNCT
ejpam-5065	5	1	characterizations	characterization	NOUN
ejpam-5065	5	2	of	of	ADP
ejpam-5065	5	3	2	2	NUM
ejpam-5065	5	4	-	-	PUNCT
ejpam-5065	5	5	hop	hop	NOUN
ejpam-5065	5	6	dominating	dominating	NOUN
ejpam-5065	5	7	sets	set	NOUN
ejpam-5065	5	8	in	in	ADP
ejpam-5065	5	9	some	some	DET
ejpam-5065	5	10	special	special	ADJ
ejpam-5065	5	11	graphs	graph	NOUN
ejpam-5065	5	12	are	be	AUX
ejpam-5065	5	13	formulated	formulate	VERB
ejpam-5065	5	14	to	to	PART
ejpam-5065	5	15	derive	derive	VERB
ejpam-5065	5	16	bounds	bound	NOUN
ejpam-5065	5	17	or	or	CCONJ
ejpam-5065	5	18	formulas	formula	NOUN
ejpam-5065	5	19	of	of	ADP
ejpam-5065	5	20	the	the	DET
ejpam-5065	5	21	parameter	parameter	NOUN
ejpam-5065	5	22	of	of	ADP
ejpam-5065	5	23	these	these	DET
ejpam-5065	5	24	graphs	graph	NOUN
ejpam-5065	5	25	.	.	PUNCT
ejpam-5065	6	1	moreover	moreover	ADV
ejpam-5065	6	2	,	,	PUNCT
ejpam-5065	6	3	new	new	ADJ
ejpam-5065	6	4	variant	variant	NOUN
ejpam-5065	6	5	of	of	ADP
ejpam-5065	6	6	pointwise	pointwise	PROPN
ejpam-5065	6	7	non	non	ADJ
ejpam-5065	6	8	-	-	ADJ
ejpam-5065	6	9	domination	domination	NOUN
ejpam-5065	6	10	is	be	AUX
ejpam-5065	6	11	introduced	introduce	VERB
ejpam-5065	6	12	to	to	PART
ejpam-5065	6	13	characterize	characterize	VERB
ejpam-5065	6	14	2	2	NUM
ejpam-5065	6	15	-	-	PUNCT
ejpam-5065	6	16	hop	hop	NOUN
ejpam-5065	6	17	dominating	dominating	NOUN
ejpam-5065	6	18	sets	set	NOUN
ejpam-5065	6	19	in	in	ADP
ejpam-5065	6	20	the	the	DET
ejpam-5065	6	21	join	join	NOUN
ejpam-5065	6	22	of	of	ADP
ejpam-5065	6	23	two	two	NUM
ejpam-5065	6	24	graphs	graph	NOUN
ejpam-5065	6	25	.	.	PUNCT
ejpam-5065	7	1	this	this	DET
ejpam-5065	7	2	characterization	characterization	NOUN
ejpam-5065	7	3	is	be	AUX
ejpam-5065	7	4	used	use	VERB
ejpam-5065	7	5	to	to	PART
ejpam-5065	7	6	calculate	calculate	VERB
ejpam-5065	7	7	the	the	DET
ejpam-5065	7	8	exact	exact	ADJ
ejpam-5065	7	9	value	value	NOUN
ejpam-5065	7	10	of	of	ADP
ejpam-5065	7	11	2	2	NUM
ejpam-5065	7	12	-	-	PUNCT
ejpam-5065	7	13	hop	hop	NOUN
ejpam-5065	7	14	domination	domination	NOUN
ejpam-5065	7	15	number	number	NOUN
ejpam-5065	7	16	of	of	ADP
ejpam-5065	7	17	the	the	DET
ejpam-5065	7	18	join	join	NOUN
ejpam-5065	7	19	of	of	ADP
ejpam-5065	7	20	two	two	NUM
ejpam-5065	7	21	graphs	graph	NOUN
ejpam-5065	7	22	.	.	PUNCT
ejpam-5065	8	1	2020	2020	NUM
ejpam-5065	8	2	mathematics	mathematic	NOUN
ejpam-5065	8	3	subject	subject	NOUN
ejpam-5065	8	4	classifications	classification	NOUN
ejpam-5065	8	5	:	:	PUNCT
ejpam-5065	8	6	05c69	05c69	X
ejpam-5065	8	7	key	key	ADJ
ejpam-5065	8	8	words	word	NOUN
ejpam-5065	8	9	and	and	CCONJ
ejpam-5065	8	10	phrases	phrase	NOUN
ejpam-5065	8	11	:	:	PUNCT
ejpam-5065	8	12	hop	hop	NOUN
ejpam-5065	8	13	dominating	dominating	NOUN
ejpam-5065	8	14	,	,	PUNCT
ejpam-5065	8	15	2	2	NUM
ejpam-5065	8	16	-	-	PUNCT
ejpam-5065	8	17	hop	hop	NOUN
ejpam-5065	8	18	dominating	dominating	NOUN
ejpam-5065	8	19	set	set	NOUN
ejpam-5065	8	20	,	,	PUNCT
ejpam-5065	8	21	2	2	NUM
ejpam-5065	8	22	-	-	PUNCT
ejpam-5065	8	23	hop	hop	NOUN
ejpam-5065	8	24	domination	domination	NOUN
ejpam-5065	8	25	number	number	NOUN
ejpam-5065	8	26	1	1	NUM
ejpam-5065	8	27	.	.	PUNCT
ejpam-5065	9	1	introduction	introduction	NOUN
ejpam-5065	9	2	hop	hop	PROPN
ejpam-5065	9	3	domination	domination	NOUN
ejpam-5065	9	4	is	be	AUX
ejpam-5065	9	5	the	the	DET
ejpam-5065	9	6	variant	variant	NOUN
ejpam-5065	9	7	of	of	ADP
ejpam-5065	9	8	the	the	DET
ejpam-5065	9	9	standard	standard	ADJ
ejpam-5065	9	10	domination	domination	NOUN
ejpam-5065	9	11	and	and	CCONJ
ejpam-5065	9	12	was	be	AUX
ejpam-5065	9	13	introduced	introduce	VERB
ejpam-5065	9	14	by	by	ADP
ejpam-5065	9	15	natarajan	natarajan	PROPN
ejpam-5065	9	16	et	et	PROPN
ejpam-5065	9	17	al	al	PROPN
ejpam-5065	9	18	.	.	PUNCT
ejpam-5065	10	1	in	in	ADP
ejpam-5065	10	2	[	[	X
ejpam-5065	10	3	12	12	NUM
ejpam-5065	10	4	]	]	PUNCT
ejpam-5065	10	5	.	.	PUNCT
ejpam-5065	11	1	hop	hop	PROPN
ejpam-5065	11	2	domination	domination	NOUN
ejpam-5065	11	3	has	have	VERB
ejpam-5065	11	4	applications	application	NOUN
ejpam-5065	11	5	in	in	ADP
ejpam-5065	11	6	various	various	ADJ
ejpam-5065	11	7	fields	field	NOUN
ejpam-5065	11	8	such	such	ADJ
ejpam-5065	11	9	as	as	ADP
ejpam-5065	11	10	network	network	NOUN
ejpam-5065	11	11	design	design	NOUN
ejpam-5065	11	12	,	,	PUNCT
ejpam-5065	11	13	communication	communication	NOUN
ejpam-5065	11	14	networks	network	NOUN
ejpam-5065	11	15	,	,	PUNCT
ejpam-5065	11	16	and	and	CCONJ
ejpam-5065	11	17	facility	facility	NOUN
ejpam-5065	11	18	location	location	NOUN
ejpam-5065	11	19	problems	problem	NOUN
ejpam-5065	11	20	.	.	PUNCT
ejpam-5065	12	1	researchers	researcher	NOUN
ejpam-5065	12	2	continue	continue	VERB
ejpam-5065	12	3	to	to	PART
ejpam-5065	12	4	explore	explore	VERB
ejpam-5065	12	5	various	various	ADJ
ejpam-5065	12	6	aspects	aspect	NOUN
ejpam-5065	12	7	of	of	ADP
ejpam-5065	12	8	hop	hop	NOUN
ejpam-5065	12	9	domination	domination	NOUN
ejpam-5065	12	10	,	,	PUNCT
ejpam-5065	12	11	including	include	VERB
ejpam-5065	12	12	its	its	PRON
ejpam-5065	12	13	computational	computational	ADJ
ejpam-5065	12	14	complexity	complexity	NOUN
ejpam-5065	12	15	,	,	PUNCT
ejpam-5065	12	16	structural	structural	ADJ
ejpam-5065	12	17	properties	property	NOUN
ejpam-5065	12	18	,	,	PUNCT
ejpam-5065	12	19	and	and	CCONJ
ejpam-5065	12	20	applications	application	NOUN
ejpam-5065	12	21	in	in	ADP
ejpam-5065	12	22	real	real	ADJ
ejpam-5065	12	23	-	-	PUNCT
ejpam-5065	12	24	world	world	NOUN
ejpam-5065	12	25	networks	network	NOUN
ejpam-5065	12	26	.	.	PUNCT
ejpam-5065	13	1	as	as	SCONJ
ejpam-5065	13	2	graph	graph	NOUN
ejpam-5065	13	3	theory	theory	NOUN
ejpam-5065	13	4	and	and	CCONJ
ejpam-5065	13	5	its	its	PRON
ejpam-5065	13	6	applications	application	NOUN
ejpam-5065	13	7	continue	continue	VERB
ejpam-5065	13	8	to	to	PART
ejpam-5065	13	9	evolve	evolve	VERB
ejpam-5065	13	10	,	,	PUNCT
ejpam-5065	13	11	hop	hop	NOUN
ejpam-5065	13	12	domination	domination	NOUN
ejpam-5065	13	13	remains	remain	VERB
ejpam-5065	13	14	an	an	DET
ejpam-5065	13	15	active	active	ADJ
ejpam-5065	13	16	area	area	NOUN
ejpam-5065	13	17	of	of	ADP
ejpam-5065	13	18	research	research	NOUN
ejpam-5065	13	19	,	,	PUNCT
ejpam-5065	13	20	contributing	contribute	VERB
ejpam-5065	13	21	to	to	ADP
ejpam-5065	13	22	our	our	PRON
ejpam-5065	13	23	understanding	understanding	NOUN
ejpam-5065	13	24	of	of	ADP
ejpam-5065	13	25	network	network	NOUN
ejpam-5065	13	26	dynamics	dynamic	NOUN
ejpam-5065	13	27	and	and	CCONJ
ejpam-5065	13	28	optimization	optimization	NOUN
ejpam-5065	13	29	.	.	PUNCT
ejpam-5065	14	1	researchers	researcher	NOUN
ejpam-5065	14	2	in	in	ADP
ejpam-5065	14	3	the	the	DET
ejpam-5065	14	4	field	field	NOUN
ejpam-5065	14	5	had	have	AUX
ejpam-5065	14	6	further	far	ADV
ejpam-5065	14	7	investigated	investigate	VERB
ejpam-5065	14	8	this	this	DET
ejpam-5065	14	9	concept	concept	NOUN
ejpam-5065	14	10	,	,	PUNCT
ejpam-5065	14	11	and	and	CCONJ
ejpam-5065	14	12	its	its	PRON
ejpam-5065	14	13	variants	variant	NOUN
ejpam-5065	14	14	.	.	PUNCT
ejpam-5065	15	1	they	they	PRON
ejpam-5065	15	2	have	have	AUX
ejpam-5065	15	3	obtained	obtain	VERB
ejpam-5065	15	4	some	some	DET
ejpam-5065	15	5	significant	significant	ADJ
ejpam-5065	15	6	results	result	NOUN
ejpam-5065	15	7	that	that	PRON
ejpam-5065	15	8	contributed	contribute	VERB
ejpam-5065	15	9	a	a	DET
ejpam-5065	15	10	lot	lot	NOUN
ejpam-5065	15	11	to	to	ADP
ejpam-5065	15	12	the	the	DET
ejpam-5065	15	13	hop	hop	NOUN
ejpam-5065	15	14	domination	domination	NOUN
ejpam-5065	15	15	theory	theory	NOUN
ejpam-5065	15	16	(	(	PUNCT
ejpam-5065	15	17	see	see	VERB
ejpam-5065	15	18	[	[	X
ejpam-5065	15	19	1–11	1–11	X
ejpam-5065	15	20	]	]	PUNCT
ejpam-5065	15	21	)	)	PUNCT
ejpam-5065	15	22	.	.	PUNCT
ejpam-5065	16	1	in	in	ADP
ejpam-5065	16	2	this	this	DET
ejpam-5065	16	3	paper	paper	NOUN
ejpam-5065	16	4	,	,	PUNCT
ejpam-5065	16	5	new	new	ADJ
ejpam-5065	16	6	variant	variant	NOUN
ejpam-5065	16	7	of	of	ADP
ejpam-5065	16	8	hop	hop	NOUN
ejpam-5065	16	9	domination	domination	NOUN
ejpam-5065	16	10	called	call	VERB
ejpam-5065	16	11	2	2	NUM
ejpam-5065	16	12	-	-	PUNCT
ejpam-5065	16	13	hop	hop	NOUN
ejpam-5065	16	14	domination	domination	NOUN
ejpam-5065	16	15	is	be	AUX
ejpam-5065	16	16	introduced	introduce	VERB
ejpam-5065	16	17	and	and	CCONJ
ejpam-5065	16	18	studied	study	VERB
ejpam-5065	16	19	on	on	ADP
ejpam-5065	16	20	some	some	DET
ejpam-5065	16	21	special	special	ADJ
ejpam-5065	16	22	graphs	graph	NOUN
ejpam-5065	16	23	and	and	CCONJ
ejpam-5065	16	24	on	on	ADP
ejpam-5065	16	25	the	the	DET
ejpam-5065	16	26	join	join	NOUN
ejpam-5065	16	27	of	of	ADP
ejpam-5065	16	28	two	two	NUM
ejpam-5065	16	29	graphs	graph	NOUN
ejpam-5065	16	30	.	.	PUNCT
ejpam-5065	17	1	the	the	DET
ejpam-5065	17	2	researchers	researcher	NOUN
ejpam-5065	17	3	believe	believe	VERB
ejpam-5065	17	4	that	that	SCONJ
ejpam-5065	17	5	this	this	DET
ejpam-5065	17	6	parameter	parameter	NOUN
ejpam-5065	17	7	and	and	CCONJ
ejpam-5065	17	8	its	its	PRON
ejpam-5065	17	9	results	result	NOUN
ejpam-5065	17	10	would	would	AUX
ejpam-5065	17	11	contribute	contribute	VERB
ejpam-5065	17	12	positively	positively	ADV
ejpam-5065	17	13	to	to	ADP
ejpam-5065	17	14	the	the	DET
ejpam-5065	17	15	field	field	NOUN
ejpam-5065	17	16	of	of	ADP
ejpam-5065	17	17	graph	graph	NOUN
ejpam-5065	17	18	theory	theory	NOUN
ejpam-5065	17	19	and	and	CCONJ
ejpam-5065	17	20	would	would	AUX
ejpam-5065	17	21	help	help	VERB
ejpam-5065	17	22	other	other	ADJ
ejpam-5065	17	23	researchers	researcher	NOUN
ejpam-5065	17	24	in	in	ADP
ejpam-5065	17	25	the	the	DET
ejpam-5065	17	26	field	field	NOUN
ejpam-5065	17	27	for	for	ADP
ejpam-5065	17	28	more	more	ADJ
ejpam-5065	17	29	research	research	NOUN
ejpam-5065	17	30	directions	direction	NOUN
ejpam-5065	17	31	in	in	ADP
ejpam-5065	17	32	the	the	DET
ejpam-5065	17	33	future	future	NOUN
ejpam-5065	17	34	.	.	PUNCT
ejpam-5065	18	1	doi	doi	NOUN
ejpam-5065	18	2	:	:	PUNCT
ejpam-5065	18	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5065	https://doi.org/10.29020/nybg.ejpam.v17i2.5065	NOUN
ejpam-5065	18	4	email	email	NOUN
ejpam-5065	18	5	address	address	NOUN
ejpam-5065	18	6	:	:	PUNCT
ejpam-5065	18	7	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-5065	18	8	(	(	PUNCT
ejpam-5065	18	9	j.	j.	PROPN
ejpam-5065	18	10	hassan	hassan	PROPN
ejpam-5065	18	11	)	)	PUNCT
ejpam-5065	18	12	,	,	PUNCT
ejpam-5065	18	13	anabel.gamorez@wmsu.edu.ph	anabel.gamorez@wmsu.edu.ph	X
ejpam-5065	18	14	(	(	PUNCT
ejpam-5065	18	15	a.	a.	NOUN
ejpam-5065	18	16	gamorez	gamorez	PROPN
ejpam-5065	18	17	)	)	PUNCT
ejpam-5065	18	18	,	,	PUNCT
ejpam-5065	18	19	ladznarlaja@msutawi-tawi.edu.ph	ladznarlaja@msutawi-tawi.edu.ph	PROPN
ejpam-5065	18	20	(	(	PUNCT
ejpam-5065	18	21	l.	l.	PROPN
ejpam-5065	18	22	laja	laja	PROPN
ejpam-5065	18	23	)	)	PUNCT
ejpam-5065	18	24	,	,	PUNCT
ejpam-5065	18	25	ahmad.eman@wmsu.edu.ph	ahmad.eman@wmsu.edu.ph	PROPN
ejpam-5065	18	26	(	(	PUNCT
ejpam-5065	18	27	e.	e.	PROPN
ejpam-5065	18	28	ahmad	ahmad	PROPN
ejpam-5065	18	29	)	)	PUNCT
ejpam-5065	18	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5065	19	1	852	852	NUM
ejpam-5065	19	2	©	©	ADP
ejpam-5065	19	3	2024	2024	NUM
ejpam-5065	19	4	ejpam	ejpam	NOUN
ejpam-5065	19	5	all	all	DET
ejpam-5065	19	6	rights	right	NOUN
ejpam-5065	19	7	reserved	reserve	VERB
ejpam-5065	19	8	.	.	PUNCT
ejpam-5065	20	1	j.	j.	PROPN
ejpam-5065	20	2	hassan	hassan	PROPN
ejpam-5065	20	3	,	,	PUNCT
ejpam-5065	20	4	a.	a.	PROPN
ejpam-5065	20	5	gomorez	gomorez	PROPN
ejpam-5065	20	6	,	,	PUNCT
ejpam-5065	20	7	l.	l.	PROPN
ejpam-5065	20	8	laja	laja	PROPN
ejpam-5065	20	9	,	,	PUNCT
ejpam-5065	20	10	e.	e.	PROPN
ejpam-5065	20	11	ahmad	ahmad	PROPN
ejpam-5065	20	12	/	/	SYM
ejpam-5065	20	13	eur	eur	PROPN
ejpam-5065	20	14	.	.	PUNCT
ejpam-5065	21	1	j.	j.	PROPN
ejpam-5065	21	2	pure	pure	PROPN
ejpam-5065	21	3	appl	appl	PROPN
ejpam-5065	21	4	.	.	PROPN
ejpam-5065	21	5	math	math	PROPN
ejpam-5065	21	6	,	,	PUNCT
ejpam-5065	21	7	17	17	NUM
ejpam-5065	21	8	(	(	PUNCT
ejpam-5065	21	9	2	2	NUM
ejpam-5065	21	10	)	)	PUNCT
ejpam-5065	21	11	(	(	PUNCT
ejpam-5065	21	12	2024	2024	NUM
ejpam-5065	21	13	)	)	PUNCT
ejpam-5065	21	14	,	,	PUNCT
ejpam-5065	21	15	852	852	NUM
ejpam-5065	21	16	-	-	SYM
ejpam-5065	21	17	859	859	NUM
ejpam-5065	21	18	853	853	NUM
ejpam-5065	21	19	2	2	NUM
ejpam-5065	21	20	.	.	PUNCT
ejpam-5065	21	21	terminology	terminology	NOUN
ejpam-5065	21	22	and	and	CCONJ
ejpam-5065	21	23	notation	notation	NOUN
ejpam-5065	21	24	let	let	VERB
ejpam-5065	21	25	g	g	NOUN
ejpam-5065	21	26	=	=	SYM
ejpam-5065	21	27	(	(	PUNCT
ejpam-5065	21	28	v	v	NOUN
ejpam-5065	21	29	(	(	PUNCT
ejpam-5065	21	30	g	g	NOUN
ejpam-5065	21	31	)	)	PUNCT
ejpam-5065	21	32	,	,	PUNCT
ejpam-5065	21	33	e(g	e(g	PROPN
ejpam-5065	21	34	)	)	PUNCT
ejpam-5065	21	35	)	)	PUNCT
ejpam-5065	21	36	be	be	AUX
ejpam-5065	21	37	a	a	DET
ejpam-5065	21	38	simple	simple	ADJ
ejpam-5065	21	39	and	and	CCONJ
ejpam-5065	21	40	undirected	undirected	ADJ
ejpam-5065	21	41	graph	graph	NOUN
ejpam-5065	21	42	.	.	PUNCT
ejpam-5065	22	1	the	the	DET
ejpam-5065	22	2	distance	distance	NOUN
ejpam-5065	22	3	dg(a	dg(a	PROPN
ejpam-5065	22	4	,	,	PUNCT
ejpam-5065	22	5	b	b	X
ejpam-5065	22	6	)	)	PUNCT
ejpam-5065	22	7	in	in	ADP
ejpam-5065	22	8	g	g	NOUN
ejpam-5065	22	9	of	of	ADP
ejpam-5065	22	10	two	two	NUM
ejpam-5065	22	11	vertices	vertex	NOUN
ejpam-5065	22	12	a	a	PRON
ejpam-5065	22	13	,	,	PUNCT
ejpam-5065	22	14	b	b	PROPN
ejpam-5065	22	15	is	be	AUX
ejpam-5065	22	16	the	the	DET
ejpam-5065	22	17	length	length	NOUN
ejpam-5065	22	18	of	of	ADP
ejpam-5065	22	19	a	a	DET
ejpam-5065	22	20	shortest	short	ADJ
ejpam-5065	22	21	a	a	PRON
ejpam-5065	22	22	-	-	PUNCT
ejpam-5065	22	23	b	b	NOUN
ejpam-5065	22	24	path	path	NOUN
ejpam-5065	22	25	in	in	ADP
ejpam-5065	22	26	g.	g.	PROPN
ejpam-5065	22	27	two	two	NUM
ejpam-5065	22	28	vertices	vertice	VERB
ejpam-5065	22	29	x	x	X
ejpam-5065	22	30	,	,	PUNCT
ejpam-5065	22	31	y	y	PROPN
ejpam-5065	22	32	of	of	ADP
ejpam-5065	22	33	g	g	PROPN
ejpam-5065	22	34	are	be	AUX
ejpam-5065	22	35	adjacent	adjacent	ADJ
ejpam-5065	22	36	or	or	CCONJ
ejpam-5065	22	37	neighbors	neighbor	NOUN
ejpam-5065	22	38	,	,	PUNCT
ejpam-5065	22	39	if	if	SCONJ
ejpam-5065	22	40	dg(x	dg(x	NUM
ejpam-5065	22	41	,	,	PUNCT
ejpam-5065	22	42	y	y	NOUN
ejpam-5065	22	43	)	)	PUNCT
ejpam-5065	22	44	=	=	SYM
ejpam-5065	23	1	1	1	X
ejpam-5065	23	2	.	.	PUNCT
ejpam-5065	24	1	the	the	DET
ejpam-5065	24	2	open	open	ADJ
ejpam-5065	24	3	neighborhood	neighborhood	NOUN
ejpam-5065	24	4	of	of	ADP
ejpam-5065	24	5	x	x	PUNCT
ejpam-5065	24	6	in	in	ADP
ejpam-5065	24	7	g	g	PROPN
ejpam-5065	24	8	is	be	AUX
ejpam-5065	24	9	the	the	DET
ejpam-5065	24	10	set	set	NOUN
ejpam-5065	24	11	ng(x	ng(x	NUM
ejpam-5065	24	12	)	)	PUNCT
ejpam-5065	25	1	=	=	PRON
ejpam-5065	25	2	{	{	PUNCT
ejpam-5065	25	3	y	y	PROPN
ejpam-5065	25	4	∈	∈	PROPN
ejpam-5065	25	5	v	v	NOUN
ejpam-5065	25	6	(	(	PUNCT
ejpam-5065	25	7	g	g	NOUN
ejpam-5065	25	8	)	)	PUNCT
ejpam-5065	25	9	:	:	PUNCT
ejpam-5065	25	10	dg(x	dg(x	NUM
ejpam-5065	25	11	,	,	PUNCT
ejpam-5065	25	12	y	y	NOUN
ejpam-5065	25	13	)	)	PUNCT
ejpam-5065	25	14	=	=	PUNCT
ejpam-5065	25	15	1	1	NUM
ejpam-5065	25	16	}	}	PUNCT
ejpam-5065	25	17	.	.	PUNCT
ejpam-5065	26	1	the	the	DET
ejpam-5065	26	2	closed	closed	ADJ
ejpam-5065	26	3	neighborhood	neighborhood	NOUN
ejpam-5065	26	4	of	of	ADP
ejpam-5065	26	5	x	x	PUNCT
ejpam-5065	26	6	in	in	ADP
ejpam-5065	26	7	g	g	PROPN
ejpam-5065	26	8	is	be	AUX
ejpam-5065	26	9	the	the	DET
ejpam-5065	26	10	set	set	NOUN
ejpam-5065	26	11	ng[x	ng[x	PROPN
ejpam-5065	26	12	]	]	X
ejpam-5065	26	13	=	=	PUNCT
ejpam-5065	26	14	ng(x	ng(x	X
ejpam-5065	26	15	)	)	PUNCT
ejpam-5065	26	16	∪	∪	ADP
ejpam-5065	26	17	{	{	PUNCT
ejpam-5065	26	18	x	x	NOUN
ejpam-5065	26	19	}	}	PUNCT
ejpam-5065	26	20	.	.	PUNCT
ejpam-5065	27	1	if	if	SCONJ
ejpam-5065	27	2	x	x	PROPN
ejpam-5065	27	3	⊆	⊆	NUM
ejpam-5065	27	4	v	v	X
ejpam-5065	27	5	(	(	PUNCT
ejpam-5065	27	6	g	g	NOUN
ejpam-5065	27	7	)	)	PUNCT
ejpam-5065	27	8	,	,	PUNCT
ejpam-5065	27	9	the	the	DET
ejpam-5065	27	10	open	open	ADJ
ejpam-5065	27	11	neighborhood	neighborhood	NOUN
ejpam-5065	27	12	of	of	ADP
ejpam-5065	27	13	x	x	PUNCT
ejpam-5065	27	14	in	in	ADP
ejpam-5065	27	15	g	g	PROPN
ejpam-5065	27	16	is	be	AUX
ejpam-5065	27	17	the	the	DET
ejpam-5065	27	18	set	set	NOUN
ejpam-5065	27	19	ng(x	ng(x	NUM
ejpam-5065	27	20	)	)	PUNCT
ejpam-5065	28	1	=	=	SYM
ejpam-5065	28	2	⋃	⋃	NOUN
ejpam-5065	28	3	x∈x	x∈x	NOUN
ejpam-5065	28	4	ng(x	ng(x	NUM
ejpam-5065	28	5	)	)	PUNCT
ejpam-5065	28	6	.	.	PUNCT
ejpam-5065	29	1	the	the	DET
ejpam-5065	29	2	closed	closed	ADJ
ejpam-5065	29	3	neighborhood	neighborhood	NOUN
ejpam-5065	29	4	of	of	ADP
ejpam-5065	29	5	x	x	PUNCT
ejpam-5065	29	6	in	in	ADP
ejpam-5065	29	7	g	g	PROPN
ejpam-5065	29	8	is	be	AUX
ejpam-5065	29	9	the	the	DET
ejpam-5065	29	10	set	set	NOUN
ejpam-5065	29	11	ng[x	ng[x	PROPN
ejpam-5065	29	12	]	]	X
ejpam-5065	29	13	=	=	PUNCT
ejpam-5065	29	14	ng(x	ng(x	X
ejpam-5065	29	15	)	)	PUNCT
ejpam-5065	30	1	∪x	∪x	ADP
ejpam-5065	30	2	.	.	PUNCT
ejpam-5065	31	1	a	a	DET
ejpam-5065	31	2	vertex	vertex	NOUN
ejpam-5065	31	3	a	a	PRON
ejpam-5065	31	4	in	in	ADP
ejpam-5065	31	5	g	g	PROPN
ejpam-5065	31	6	is	be	AUX
ejpam-5065	31	7	a	a	DET
ejpam-5065	31	8	hop	hop	NOUN
ejpam-5065	31	9	neighbor	neighbor	NOUN
ejpam-5065	31	10	of	of	ADP
ejpam-5065	31	11	a	a	DET
ejpam-5065	31	12	vertex	vertex	NOUN
ejpam-5065	31	13	b	b	NOUN
ejpam-5065	31	14	in	in	ADP
ejpam-5065	31	15	g	g	PROPN
ejpam-5065	31	16	if	if	SCONJ
ejpam-5065	31	17	dg(a	dg(a	X
ejpam-5065	31	18	,	,	PUNCT
ejpam-5065	31	19	b	b	X
ejpam-5065	31	20	)	)	PUNCT
ejpam-5065	31	21	=	=	SYM
ejpam-5065	31	22	2	2	X
ejpam-5065	31	23	.	.	X
ejpam-5065	31	24	the	the	DET
ejpam-5065	31	25	set	set	ADJ
ejpam-5065	31	26	n2	n2	PROPN
ejpam-5065	31	27	g(a	g(a	PROPN
ejpam-5065	31	28	)	)	PUNCT
ejpam-5065	31	29	=	=	PRON
ejpam-5065	32	1	{	{	PUNCT
ejpam-5065	32	2	b	b	PROPN
ejpam-5065	32	3	∈	∈	ADJ
ejpam-5065	32	4	v	v	NOUN
ejpam-5065	32	5	(	(	PUNCT
ejpam-5065	32	6	g	g	NOUN
ejpam-5065	32	7	)	)	PUNCT
ejpam-5065	32	8	:	:	PUNCT
ejpam-5065	33	1	dg(a	dg(a	X
ejpam-5065	33	2	,	,	PUNCT
ejpam-5065	33	3	b	b	X
ejpam-5065	33	4	)	)	PUNCT
ejpam-5065	33	5	=	=	SYM
ejpam-5065	33	6	2	2	X
ejpam-5065	33	7	}	}	PUNCT
ejpam-5065	33	8	is	be	AUX
ejpam-5065	33	9	called	call	VERB
ejpam-5065	33	10	the	the	DET
ejpam-5065	33	11	open	open	ADJ
ejpam-5065	33	12	hop	hop	NOUN
ejpam-5065	33	13	neighborhood	neighborhood	NOUN
ejpam-5065	33	14	of	of	ADP
ejpam-5065	33	15	a.	a.	NOUN
ejpam-5065	33	16	the	the	DET
ejpam-5065	33	17	closed	closed	ADJ
ejpam-5065	33	18	hop	hop	NOUN
ejpam-5065	33	19	neighborhood	neighborhood	NOUN
ejpam-5065	33	20	of	of	ADP
ejpam-5065	33	21	a	a	PRON
ejpam-5065	33	22	in	in	ADP
ejpam-5065	33	23	g	g	PROPN
ejpam-5065	33	24	is	be	AUX
ejpam-5065	33	25	given	give	VERB
ejpam-5065	33	26	by	by	ADP
ejpam-5065	33	27	n2	n2	ADJ
ejpam-5065	33	28	g[a	g[a	PROPN
ejpam-5065	33	29	]	]	X
ejpam-5065	33	30	=	=	SYM
ejpam-5065	33	31	n2	n2	PROPN
ejpam-5065	33	32	g(a	g(a	PROPN
ejpam-5065	33	33	)	)	PUNCT
ejpam-5065	33	34	∪	∪	ADP
ejpam-5065	33	35	{	{	PUNCT
ejpam-5065	33	36	a	a	NOUN
ejpam-5065	33	37	}	}	PUNCT
ejpam-5065	33	38	.	.	PUNCT
ejpam-5065	34	1	the	the	DET
ejpam-5065	34	2	open	open	ADJ
ejpam-5065	34	3	hop	hop	NOUN
ejpam-5065	34	4	neighborhood	neighborhood	NOUN
ejpam-5065	34	5	of	of	ADP
ejpam-5065	34	6	s	s	NOUN
ejpam-5065	34	7	⊆	⊆	NUM
ejpam-5065	34	8	v	v	NOUN
ejpam-5065	34	9	(	(	PUNCT
ejpam-5065	34	10	g	g	NOUN
ejpam-5065	34	11	)	)	PUNCT
ejpam-5065	34	12	is	be	AUX
ejpam-5065	34	13	the	the	DET
ejpam-5065	34	14	set	set	ADJ
ejpam-5065	34	15	n2	n2	ADJ
ejpam-5065	34	16	g(s	g(s	PROPN
ejpam-5065	34	17	)	)	PUNCT
ejpam-5065	34	18	=	=	SYM
ejpam-5065	35	1	⋃	⋃	ADP
ejpam-5065	35	2	a∈s	a∈s	ADJ
ejpam-5065	35	3	n2	n2	NOUN
ejpam-5065	35	4	g(a	g(a	PROPN
ejpam-5065	35	5	)	)	PUNCT
ejpam-5065	35	6	.	.	PUNCT
ejpam-5065	36	1	the	the	DET
ejpam-5065	36	2	closed	closed	ADJ
ejpam-5065	36	3	hop	hop	NOUN
ejpam-5065	36	4	neighborhood	neighborhood	NOUN
ejpam-5065	36	5	of	of	ADP
ejpam-5065	36	6	s	s	PRON
ejpam-5065	36	7	in	in	ADP
ejpam-5065	36	8	g	g	PROPN
ejpam-5065	36	9	is	be	AUX
ejpam-5065	36	10	the	the	DET
ejpam-5065	36	11	set	set	ADJ
ejpam-5065	36	12	n2	n2	ADJ
ejpam-5065	36	13	g[s	g[s	PROPN
ejpam-5065	36	14	]	]	PUNCT
ejpam-5065	36	15	=	=	SYM
ejpam-5065	36	16	n2	n2	PROPN
ejpam-5065	36	17	g(s)∪s	g(s)∪s	PROPN
ejpam-5065	36	18	.	.	PUNCT
ejpam-5065	37	1	a	a	DET
ejpam-5065	37	2	subset	subset	NOUN
ejpam-5065	37	3	s	s	X
ejpam-5065	37	4	of	of	ADP
ejpam-5065	37	5	v	v	NOUN
ejpam-5065	37	6	(	(	PUNCT
ejpam-5065	37	7	g	g	NOUN
ejpam-5065	37	8	)	)	PUNCT
ejpam-5065	37	9	is	be	AUX
ejpam-5065	37	10	a	a	DET
ejpam-5065	37	11	hop	hop	NOUN
ejpam-5065	37	12	dominating	dominating	NOUN
ejpam-5065	37	13	of	of	ADP
ejpam-5065	37	14	g	g	PROPN
ejpam-5065	37	15	if	if	SCONJ
ejpam-5065	37	16	for	for	ADP
ejpam-5065	37	17	every	every	DET
ejpam-5065	37	18	a	a	DET
ejpam-5065	37	19	∈	∈	PROPN
ejpam-5065	37	20	v	v	NOUN
ejpam-5065	37	21	(	(	PUNCT
ejpam-5065	37	22	g)\s	g)\s	NOUN
ejpam-5065	37	23	,	,	PUNCT
ejpam-5065	37	24	there	there	PRON
ejpam-5065	37	25	exists	exist	VERB
ejpam-5065	37	26	b	b	PROPN
ejpam-5065	37	27	∈	∈	PROPN
ejpam-5065	37	28	s	s	VERB
ejpam-5065	37	29	such	such	ADJ
ejpam-5065	37	30	that	that	SCONJ
ejpam-5065	37	31	dg(a	dg(a	PROPN
ejpam-5065	37	32	,	,	PUNCT
ejpam-5065	37	33	b	b	X
ejpam-5065	37	34	)	)	PUNCT
ejpam-5065	37	35	=	=	SYM
ejpam-5065	37	36	2	2	X
ejpam-5065	37	37	.	.	PUNCT
ejpam-5065	37	38	the	the	DET
ejpam-5065	37	39	minimum	minimum	ADJ
ejpam-5065	37	40	cardinality	cardinality	NOUN
ejpam-5065	37	41	among	among	ADP
ejpam-5065	37	42	all	all	DET
ejpam-5065	37	43	hop	hop	NOUN
ejpam-5065	37	44	dominating	dominating	NOUN
ejpam-5065	37	45	sets	set	NOUN
ejpam-5065	37	46	of	of	ADP
ejpam-5065	37	47	g	g	NOUN
ejpam-5065	37	48	,	,	PUNCT
ejpam-5065	37	49	denoted	denote	VERB
ejpam-5065	37	50	by	by	ADP
ejpam-5065	37	51	γh(g	γh(g	NOUN
ejpam-5065	37	52	)	)	PUNCT
ejpam-5065	37	53	,	,	PUNCT
ejpam-5065	37	54	is	be	AUX
ejpam-5065	37	55	called	call	VERB
ejpam-5065	37	56	the	the	DET
ejpam-5065	37	57	hop	hop	NOUN
ejpam-5065	37	58	domination	domination	NOUN
ejpam-5065	37	59	number	number	NOUN
ejpam-5065	37	60	of	of	ADP
ejpam-5065	37	61	g.	g.	PROPN
ejpam-5065	37	62	any	any	DET
ejpam-5065	37	63	hop	hop	NOUN
ejpam-5065	37	64	dominating	dominating	NOUN
ejpam-5065	37	65	set	set	VERB
ejpam-5065	37	66	with	with	ADP
ejpam-5065	37	67	cardinality	cardinality	NOUN
ejpam-5065	37	68	equal	equal	ADJ
ejpam-5065	37	69	to	to	ADP
ejpam-5065	37	70	γh(g	γh(g	NOUN
ejpam-5065	37	71	)	)	PUNCT
ejpam-5065	37	72	is	be	AUX
ejpam-5065	37	73	called	call	VERB
ejpam-5065	37	74	a	a	DET
ejpam-5065	37	75	γh	γh	ADV
ejpam-5065	37	76	-	-	PUNCT
ejpam-5065	37	77	set	set	NOUN
ejpam-5065	37	78	of	of	ADP
ejpam-5065	37	79	g.	g.	PROPN
ejpam-5065	37	80	a	a	DET
ejpam-5065	37	81	subset	subset	NOUN
ejpam-5065	37	82	c	c	NOUN
ejpam-5065	37	83	of	of	ADP
ejpam-5065	37	84	v	v	PROPN
ejpam-5065	37	85	(	(	PUNCT
ejpam-5065	37	86	g	g	NOUN
ejpam-5065	37	87	)	)	PUNCT
ejpam-5065	37	88	is	be	AUX
ejpam-5065	37	89	a	a	DET
ejpam-5065	37	90	pointwise	pointwise	ADJ
ejpam-5065	37	91	non	non	ADJ
ejpam-5065	37	92	-	-	ADJ
ejpam-5065	37	93	dominating	dominating	ADJ
ejpam-5065	37	94	set	set	NOUN
ejpam-5065	37	95	if	if	SCONJ
ejpam-5065	37	96	for	for	ADP
ejpam-5065	37	97	every	every	DET
ejpam-5065	37	98	v	v	NUM
ejpam-5065	37	99	∈	∈	NOUN
ejpam-5065	37	100	v	v	NOUN
ejpam-5065	37	101	(	(	PUNCT
ejpam-5065	37	102	g)\c	g)\c	NOUN
ejpam-5065	37	103	,	,	PUNCT
ejpam-5065	37	104	there	there	PRON
ejpam-5065	37	105	exists	exist	VERB
ejpam-5065	37	106	u	u	PROPN
ejpam-5065	37	107	∈	∈	PROPN
ejpam-5065	37	108	c	c	NOUN
ejpam-5065	37	109	such	such	ADJ
ejpam-5065	37	110	that	that	DET
ejpam-5065	37	111	v	v	NOUN
ejpam-5065	37	112	/∈	/∈	PUNCT
ejpam-5065	37	113	ng(u	ng(u	NOUN
ejpam-5065	37	114	)	)	PUNCT
ejpam-5065	37	115	.	.	PUNCT
ejpam-5065	38	1	the	the	DET
ejpam-5065	38	2	minimum	minimum	ADJ
ejpam-5065	38	3	cardinality	cardinality	NOUN
ejpam-5065	38	4	of	of	ADP
ejpam-5065	38	5	a	a	DET
ejpam-5065	38	6	pointwise	pointwise	ADJ
ejpam-5065	38	7	nondominating	nondominate	VERB
ejpam-5065	38	8	set	set	NOUN
ejpam-5065	38	9	in	in	ADP
ejpam-5065	38	10	g	g	NOUN
ejpam-5065	38	11	,	,	PUNCT
ejpam-5065	38	12	denoted	denote	VERB
ejpam-5065	38	13	by	by	ADP
ejpam-5065	38	14	pnd(g	pnd(g	PROPN
ejpam-5065	38	15	)	)	PUNCT
ejpam-5065	38	16	,	,	PUNCT
ejpam-5065	38	17	is	be	AUX
ejpam-5065	38	18	called	call	VERB
ejpam-5065	38	19	a	a	DET
ejpam-5065	38	20	pointwise	pointwise	ADJ
ejpam-5065	38	21	non	non	ADJ
ejpam-5065	38	22	-	-	ADJ
ejpam-5065	38	23	domination	domination	ADJ
ejpam-5065	38	24	number	number	NOUN
ejpam-5065	38	25	of	of	ADP
ejpam-5065	38	26	g.	g.	PROPN
ejpam-5065	38	27	let	let	VERB
ejpam-5065	38	28	g	g	NOUN
ejpam-5065	38	29	and	and	CCONJ
ejpam-5065	38	30	h	h	NOUN
ejpam-5065	38	31	be	be	VERB
ejpam-5065	38	32	any	any	DET
ejpam-5065	38	33	two	two	NUM
ejpam-5065	38	34	graphs	graph	NOUN
ejpam-5065	38	35	.	.	PUNCT
ejpam-5065	39	1	the	the	DET
ejpam-5065	39	2	join	join	NOUN
ejpam-5065	39	3	of	of	ADP
ejpam-5065	39	4	g	g	PROPN
ejpam-5065	39	5	and	and	CCONJ
ejpam-5065	39	6	h	h	NOUN
ejpam-5065	39	7	,	,	PUNCT
ejpam-5065	39	8	denoted	denote	VERB
ejpam-5065	39	9	by	by	ADP
ejpam-5065	39	10	g+h	g+h	PROPN
ejpam-5065	39	11	is	be	AUX
ejpam-5065	39	12	the	the	DET
ejpam-5065	39	13	graph	graph	NOUN
ejpam-5065	39	14	with	with	ADP
ejpam-5065	39	15	vertex	vertex	NOUN
ejpam-5065	39	16	set	set	VERB
ejpam-5065	39	17	v	v	NOUN
ejpam-5065	39	18	(	(	PUNCT
ejpam-5065	39	19	g+h	g+h	NOUN
ejpam-5065	39	20	)	)	PUNCT
ejpam-5065	40	1	=	=	SYM
ejpam-5065	40	2	v	v	X
ejpam-5065	40	3	(	(	PUNCT
ejpam-5065	40	4	g	g	NOUN
ejpam-5065	40	5	)	)	PUNCT
ejpam-5065	40	6	∪	∪	NOUN
ejpam-5065	40	7	v	v	NOUN
ejpam-5065	40	8	(	(	PUNCT
ejpam-5065	40	9	h	h	NOUN
ejpam-5065	40	10	)	)	PUNCT
ejpam-5065	40	11	and	and	CCONJ
ejpam-5065	40	12	edge	edge	NOUN
ejpam-5065	40	13	set	set	VERB
ejpam-5065	40	14	e(g+h	e(g+h	NUM
ejpam-5065	40	15	)	)	PUNCT
ejpam-5065	40	16	=	=	SYM
ejpam-5065	40	17	e(g	e(g	NOUN
ejpam-5065	40	18	)	)	PUNCT
ejpam-5065	40	19	∪	∪	ADP
ejpam-5065	40	20	e(h	e(h	PROPN
ejpam-5065	40	21	)	)	PUNCT
ejpam-5065	40	22	∪	∪	NOUN
ejpam-5065	40	23	{	{	PUNCT
ejpam-5065	40	24	uv	uv	NOUN
ejpam-5065	40	25	:	:	PUNCT
ejpam-5065	40	26	u	u	PROPN
ejpam-5065	40	27	∈	∈	PROPN
ejpam-5065	40	28	v	v	ADP
ejpam-5065	40	29	(	(	PUNCT
ejpam-5065	40	30	g	g	NOUN
ejpam-5065	40	31	)	)	PUNCT
ejpam-5065	40	32	,	,	PUNCT
ejpam-5065	40	33	v	v	X
ejpam-5065	40	34	∈	∈	PROPN
ejpam-5065	40	35	v	v	NOUN
ejpam-5065	40	36	(	(	PUNCT
ejpam-5065	40	37	h	h	NOUN
ejpam-5065	40	38	)	)	PUNCT
ejpam-5065	40	39	}	}	PUNCT
ejpam-5065	40	40	.	.	PUNCT
ejpam-5065	41	1	3	3	X
ejpam-5065	41	2	.	.	X
ejpam-5065	41	3	results	result	NOUN
ejpam-5065	41	4	we	we	PRON
ejpam-5065	41	5	begin	begin	VERB
ejpam-5065	41	6	this	this	DET
ejpam-5065	41	7	section	section	NOUN
ejpam-5065	41	8	by	by	ADP
ejpam-5065	41	9	introducing	introduce	VERB
ejpam-5065	41	10	the	the	DET
ejpam-5065	41	11	concept	concept	NOUN
ejpam-5065	41	12	of	of	ADP
ejpam-5065	41	13	2	2	NUM
ejpam-5065	41	14	-	-	PUNCT
ejpam-5065	41	15	hop	hop	NOUN
ejpam-5065	41	16	domination	domination	NOUN
ejpam-5065	41	17	in	in	ADP
ejpam-5065	41	18	a	a	DET
ejpam-5065	41	19	graph	graph	NOUN
ejpam-5065	41	20	.	.	PUNCT
ejpam-5065	42	1	definition	definition	NOUN
ejpam-5065	42	2	1	1	NUM
ejpam-5065	42	3	.	.	PUNCT
ejpam-5065	43	1	let	let	VERB
ejpam-5065	43	2	g	g	PRON
ejpam-5065	43	3	be	be	AUX
ejpam-5065	43	4	a	a	DET
ejpam-5065	43	5	simple	simple	ADJ
ejpam-5065	43	6	and	and	CCONJ
ejpam-5065	43	7	undirected	undirected	ADJ
ejpam-5065	43	8	graph	graph	NOUN
ejpam-5065	43	9	.	.	PUNCT
ejpam-5065	44	1	a	a	DET
ejpam-5065	44	2	subset	subset	NOUN
ejpam-5065	44	3	p	p	NOUN
ejpam-5065	44	4	of	of	ADP
ejpam-5065	44	5	a	a	DET
ejpam-5065	44	6	vertex	vertex	NOUN
ejpam-5065	44	7	-	-	PUNCT
ejpam-5065	44	8	set	set	VERB
ejpam-5065	44	9	v	v	NOUN
ejpam-5065	44	10	(	(	PUNCT
ejpam-5065	44	11	g	g	NOUN
ejpam-5065	44	12	)	)	PUNCT
ejpam-5065	44	13	of	of	ADP
ejpam-5065	44	14	g	g	PROPN
ejpam-5065	44	15	is	be	AUX
ejpam-5065	44	16	called	call	VERB
ejpam-5065	44	17	a	a	DET
ejpam-5065	44	18	2	2	NUM
ejpam-5065	44	19	-	-	PUNCT
ejpam-5065	44	20	hop	hop	NOUN
ejpam-5065	44	21	dominating	dominating	NOUN
ejpam-5065	44	22	if	if	SCONJ
ejpam-5065	44	23	for	for	SCONJ
ejpam-5065	44	24	every	every	DET
ejpam-5065	44	25	x	x	SYM
ejpam-5065	44	26	∈	∈	PROPN
ejpam-5065	44	27	v	v	NOUN
ejpam-5065	44	28	(	(	PUNCT
ejpam-5065	44	29	g)\p	g)\p	NOUN
ejpam-5065	44	30	,	,	PUNCT
ejpam-5065	44	31	x	x	PRON
ejpam-5065	44	32	has	have	VERB
ejpam-5065	44	33	at	at	ADV
ejpam-5065	44	34	least	least	ADV
ejpam-5065	44	35	two	two	NUM
ejpam-5065	44	36	hop	hop	NOUN
ejpam-5065	44	37	neighbors	neighbor	NOUN
ejpam-5065	44	38	in	in	ADP
ejpam-5065	44	39	p	p	PROPN
ejpam-5065	44	40	.	.	PUNCT
ejpam-5065	45	1	the	the	DET
ejpam-5065	45	2	2	2	NUM
ejpam-5065	45	3	-	-	PUNCT
ejpam-5065	45	4	hop	hop	NOUN
ejpam-5065	45	5	domination	domination	NOUN
ejpam-5065	45	6	number	number	NOUN
ejpam-5065	45	7	of	of	ADP
ejpam-5065	45	8	g	g	NOUN
ejpam-5065	45	9	,	,	PUNCT
ejpam-5065	45	10	denoted	denote	VERB
ejpam-5065	45	11	by	by	ADP
ejpam-5065	45	12	γ2h(g	γ2h(g	NOUN
ejpam-5065	45	13	)	)	PUNCT
ejpam-5065	45	14	,	,	PUNCT
ejpam-5065	45	15	is	be	AUX
ejpam-5065	45	16	the	the	DET
ejpam-5065	45	17	minimum	minimum	ADJ
ejpam-5065	45	18	cardinality	cardinality	NOUN
ejpam-5065	45	19	of	of	ADP
ejpam-5065	45	20	a	a	DET
ejpam-5065	45	21	2	2	NUM
ejpam-5065	45	22	-	-	PUNCT
ejpam-5065	45	23	hop	hop	NOUN
ejpam-5065	45	24	dominating	dominating	NOUN
ejpam-5065	45	25	set	set	NOUN
ejpam-5065	45	26	of	of	ADP
ejpam-5065	45	27	g.	g.	PROPN
ejpam-5065	45	28	to	to	PART
ejpam-5065	45	29	further	far	ADV
ejpam-5065	45	30	understand	understand	VERB
ejpam-5065	45	31	the	the	DET
ejpam-5065	45	32	aforementioned	aforementioned	ADJ
ejpam-5065	45	33	concept	concept	NOUN
ejpam-5065	45	34	,	,	PUNCT
ejpam-5065	45	35	consider	consider	VERB
ejpam-5065	45	36	the	the	DET
ejpam-5065	45	37	following	follow	VERB
ejpam-5065	45	38	example	example	NOUN
ejpam-5065	45	39	:	:	PUNCT
ejpam-5065	45	40	example	example	NOUN
ejpam-5065	45	41	1	1	X
ejpam-5065	45	42	.	.	X
ejpam-5065	45	43	consider	consider	VERB
ejpam-5065	45	44	the	the	DET
ejpam-5065	45	45	graph	graph	NOUN
ejpam-5065	45	46	g	g	NOUN
ejpam-5065	45	47	below	below	ADV
ejpam-5065	45	48	.	.	PUNCT
ejpam-5065	46	1	j.	j.	PROPN
ejpam-5065	46	2	hassan	hassan	PROPN
ejpam-5065	46	3	,	,	PUNCT
ejpam-5065	46	4	a.	a.	PROPN
ejpam-5065	46	5	gomorez	gomorez	PROPN
ejpam-5065	46	6	,	,	PUNCT
ejpam-5065	46	7	l.	l.	PROPN
ejpam-5065	46	8	laja	laja	PROPN
ejpam-5065	46	9	,	,	PUNCT
ejpam-5065	46	10	e.	e.	PROPN
ejpam-5065	46	11	ahmad	ahmad	PROPN
ejpam-5065	46	12	/	/	SYM
ejpam-5065	46	13	eur	eur	PROPN
ejpam-5065	46	14	.	.	PUNCT
ejpam-5065	47	1	j.	j.	PROPN
ejpam-5065	47	2	pure	pure	PROPN
ejpam-5065	47	3	appl	appl	PROPN
ejpam-5065	47	4	.	.	PROPN
ejpam-5065	47	5	math	math	PROPN
ejpam-5065	47	6	,	,	PUNCT
ejpam-5065	47	7	17	17	NUM
ejpam-5065	47	8	(	(	PUNCT
ejpam-5065	47	9	2	2	NUM
ejpam-5065	47	10	)	)	PUNCT
ejpam-5065	47	11	(	(	PUNCT
ejpam-5065	47	12	2024	2024	NUM
ejpam-5065	47	13	)	)	PUNCT
ejpam-5065	47	14	,	,	PUNCT
ejpam-5065	47	15	852	852	NUM
ejpam-5065	47	16	-	-	SYM
ejpam-5065	47	17	859	859	NUM
ejpam-5065	47	18	854	854	NUM
ejpam-5065	47	19	a	a	DET
ejpam-5065	47	20	b	b	NOUN
ejpam-5065	47	21	c	c	NOUN
ejpam-5065	47	22	d	d	PROPN
ejpam-5065	47	23	e	e	X
ejpam-5065	47	24	f	f	X
ejpam-5065	47	25	g	g	PROPN
ejpam-5065	47	26	h	h	NOUN
ejpam-5065	47	27	g	g	NOUN
ejpam-5065	47	28	:	:	PUNCT
ejpam-5065	47	29	figure	figure	NOUN
ejpam-5065	47	30	1	1	NUM
ejpam-5065	47	31	:	:	PUNCT
ejpam-5065	47	32	graph	graph	VERB
ejpam-5065	47	33	g	g	NOUN
ejpam-5065	47	34	with	with	ADP
ejpam-5065	47	35	γ2h(g	γ2h(g	NOUN
ejpam-5065	47	36	)	)	PUNCT
ejpam-5065	47	37	=	=	SYM
ejpam-5065	48	1	5	5	NUM
ejpam-5065	48	2	let	let	VERB
ejpam-5065	48	3	p	p	NOUN
ejpam-5065	48	4	=	=	PUNCT
ejpam-5065	48	5	{	{	PUNCT
ejpam-5065	48	6	b	b	PROPN
ejpam-5065	48	7	,	,	PUNCT
ejpam-5065	48	8	c	c	NOUN
ejpam-5065	48	9	,	,	PUNCT
ejpam-5065	48	10	d	d	NOUN
ejpam-5065	48	11	,	,	PUNCT
ejpam-5065	48	12	e	e	NOUN
ejpam-5065	48	13	,	,	PUNCT
ejpam-5065	48	14	h	h	NOUN
ejpam-5065	48	15	}	}	PUNCT
ejpam-5065	48	16	.	.	PUNCT
ejpam-5065	49	1	then	then	ADV
ejpam-5065	49	2	v	v	X
ejpam-5065	49	3	(	(	PUNCT
ejpam-5065	49	4	g)\p	g)\p	NOUN
ejpam-5065	49	5	=	=	PUNCT
ejpam-5065	49	6	{	{	PUNCT
ejpam-5065	49	7	a	a	X
ejpam-5065	49	8	,	,	PUNCT
ejpam-5065	49	9	f	f	X
ejpam-5065	49	10	,	,	PUNCT
ejpam-5065	49	11	g	g	NOUN
ejpam-5065	49	12	}	}	PUNCT
ejpam-5065	49	13	.	.	PUNCT
ejpam-5065	50	1	observe	observe	VERB
ejpam-5065	50	2	that	that	DET
ejpam-5065	50	3	vertex	vertex	NOUN
ejpam-5065	50	4	a	a	PRON
ejpam-5065	50	5	has	have	VERB
ejpam-5065	50	6	two	two	NUM
ejpam-5065	50	7	hop	hop	NOUN
ejpam-5065	50	8	neighbors	neighbor	NOUN
ejpam-5065	50	9	c	c	PROPN
ejpam-5065	50	10	and	and	CCONJ
ejpam-5065	50	11	d	d	PROPN
ejpam-5065	50	12	in	in	ADP
ejpam-5065	50	13	p	p	PROPN
ejpam-5065	50	14	,	,	PUNCT
ejpam-5065	50	15	f	f	PROPN
ejpam-5065	50	16	has	have	VERB
ejpam-5065	50	17	three	three	NUM
ejpam-5065	50	18	hop	hop	NOUN
ejpam-5065	50	19	neighbors	neighbor	NOUN
ejpam-5065	50	20	b	b	PROPN
ejpam-5065	50	21	,	,	PUNCT
ejpam-5065	50	22	c	c	PROPN
ejpam-5065	50	23	and	and	CCONJ
ejpam-5065	50	24	h	h	NOUN
ejpam-5065	50	25	in	in	ADP
ejpam-5065	50	26	p	p	NOUN
ejpam-5065	50	27	,	,	PUNCT
ejpam-5065	50	28	and	and	CCONJ
ejpam-5065	50	29	g	g	NOUN
ejpam-5065	50	30	has	have	VERB
ejpam-5065	50	31	two	two	NUM
ejpam-5065	50	32	neighbors	neighbor	NOUN
ejpam-5065	50	33	d	d	NOUN
ejpam-5065	50	34	and	and	CCONJ
ejpam-5065	50	35	e	e	NOUN
ejpam-5065	50	36	in	in	ADP
ejpam-5065	50	37	p	p	PROPN
ejpam-5065	50	38	.	.	PUNCT
ejpam-5065	51	1	thus	thus	ADV
ejpam-5065	51	2	,	,	PUNCT
ejpam-5065	51	3	p	p	PROPN
ejpam-5065	51	4	is	be	AUX
ejpam-5065	51	5	a	a	DET
ejpam-5065	51	6	2	2	NUM
ejpam-5065	51	7	-	-	PUNCT
ejpam-5065	51	8	hop	hop	NOUN
ejpam-5065	51	9	dominating	dominating	NOUN
ejpam-5065	51	10	set	set	NOUN
ejpam-5065	51	11	of	of	ADP
ejpam-5065	51	12	g.	g.	PROPN
ejpam-5065	51	13	moreover	moreover	ADV
ejpam-5065	51	14	,	,	PUNCT
ejpam-5065	51	15	it	it	PRON
ejpam-5065	51	16	can	can	AUX
ejpam-5065	51	17	be	be	AUX
ejpam-5065	51	18	verified	verify	VERB
ejpam-5065	51	19	that	that	SCONJ
ejpam-5065	51	20	γ2h(g	γ2h(g	NOUN
ejpam-5065	51	21	)	)	PUNCT
ejpam-5065	51	22	=	=	SYM
ejpam-5065	51	23	5	5	X
ejpam-5065	51	24	.	.	NOUN
ejpam-5065	51	25	remark	remark	NOUN
ejpam-5065	51	26	1	1	NUM
ejpam-5065	51	27	.	.	PUNCT
ejpam-5065	52	1	let	let	VERB
ejpam-5065	52	2	g	g	PRON
ejpam-5065	52	3	be	be	AUX
ejpam-5065	52	4	a	a	DET
ejpam-5065	52	5	graph	graph	NOUN
ejpam-5065	52	6	.	.	PUNCT
ejpam-5065	53	1	then	then	ADV
ejpam-5065	53	2	(	(	PUNCT
ejpam-5065	53	3	i	i	NOUN
ejpam-5065	53	4	)	)	PUNCT
ejpam-5065	53	5	a	a	DET
ejpam-5065	53	6	2	2	NUM
ejpam-5065	53	7	-	-	PUNCT
ejpam-5065	53	8	hop	hop	NOUN
ejpam-5065	53	9	dominating	dominating	NOUN
ejpam-5065	53	10	set	set	NOUN
ejpam-5065	53	11	p	p	NOUN
ejpam-5065	53	12	of	of	ADP
ejpam-5065	53	13	g	g	PROPN
ejpam-5065	53	14	is	be	AUX
ejpam-5065	53	15	always	always	ADV
ejpam-5065	53	16	a	a	DET
ejpam-5065	53	17	hop	hop	NOUN
ejpam-5065	53	18	dominating	dominating	NOUN
ejpam-5065	53	19	;	;	PUNCT
ejpam-5065	53	20	and	and	CCONJ
ejpam-5065	53	21	(	(	PUNCT
ejpam-5065	53	22	ii	ii	NOUN
ejpam-5065	53	23	)	)	PUNCT
ejpam-5065	53	24	g	g	PROPN
ejpam-5065	53	25	admits	admit	VERB
ejpam-5065	53	26	a	a	DET
ejpam-5065	53	27	2	2	NUM
ejpam-5065	53	28	-	-	PUNCT
ejpam-5065	53	29	hop	hop	NOUN
ejpam-5065	53	30	domination	domination	NOUN
ejpam-5065	53	31	.	.	PUNCT
ejpam-5065	54	1	theorem	theorem	NOUN
ejpam-5065	54	2	1	1	X
ejpam-5065	54	3	.	.	PUNCT
ejpam-5065	55	1	let	let	VERB
ejpam-5065	55	2	g	g	PRON
ejpam-5065	55	3	be	be	AUX
ejpam-5065	55	4	a	a	DET
ejpam-5065	55	5	graph	graph	NOUN
ejpam-5065	55	6	.	.	PUNCT
ejpam-5065	56	1	then	then	ADV
ejpam-5065	56	2	(	(	PUNCT
ejpam-5065	56	3	i	i	NOUN
ejpam-5065	56	4	)	)	PUNCT
ejpam-5065	56	5	γh(g	γh(g	NOUN
ejpam-5065	56	6	)	)	PUNCT
ejpam-5065	56	7	≤	≤	NUM
ejpam-5065	56	8	γ2h(g	γ2h(g	NOUN
ejpam-5065	56	9	)	)	PUNCT
ejpam-5065	56	10	,	,	PUNCT
ejpam-5065	56	11	and	and	CCONJ
ejpam-5065	56	12	this	this	DET
ejpam-5065	56	13	bound	bind	VERB
ejpam-5065	56	14	is	be	AUX
ejpam-5065	56	15	tight	tight	ADJ
ejpam-5065	56	16	;	;	PUNCT
ejpam-5065	56	17	(	(	PUNCT
ejpam-5065	56	18	ii	ii	NOUN
ejpam-5065	56	19	)	)	PUNCT
ejpam-5065	56	20	1	1	NUM
ejpam-5065	56	21	≤	≤	NUM
ejpam-5065	56	22	γ2h(g	γ2h(g	PROPN
ejpam-5065	56	23	)	)	PUNCT
ejpam-5065	56	24	≤	≤	NUM
ejpam-5065	56	25	|v	|v	X
ejpam-5065	56	26	(	(	PUNCT
ejpam-5065	56	27	g)|	g)|	NOUN
ejpam-5065	56	28	;	;	PUNCT
ejpam-5065	56	29	and	and	CCONJ
ejpam-5065	56	30	(	(	PUNCT
ejpam-5065	56	31	iii	iii	X
ejpam-5065	56	32	)	)	PUNCT
ejpam-5065	56	33	if	if	SCONJ
ejpam-5065	56	34	g	g	PROPN
ejpam-5065	56	35	has	have	VERB
ejpam-5065	56	36	|v	|v	X
ejpam-5065	56	37	(	(	PUNCT
ejpam-5065	56	38	g)|	g)|	X
ejpam-5065	56	39	≥	≥	NOUN
ejpam-5065	56	40	2	2	NUM
ejpam-5065	56	41	,	,	PUNCT
ejpam-5065	56	42	then	then	ADV
ejpam-5065	56	43	γ2h(g	γ2h(g	NOUN
ejpam-5065	56	44	)	)	PUNCT
ejpam-5065	56	45	≥	≥	NOUN
ejpam-5065	56	46	2	2	NUM
ejpam-5065	56	47	.	.	PUNCT
ejpam-5065	57	1	proof	proof	NOUN
ejpam-5065	57	2	.	.	PUNCT
ejpam-5065	58	1	(	(	PUNCT
ejpam-5065	58	2	i	i	NOUN
ejpam-5065	58	3	)	)	PUNCT
ejpam-5065	58	4	let	let	VERB
ejpam-5065	58	5	g	g	NOUN
ejpam-5065	58	6	be	be	AUX
ejpam-5065	58	7	a	a	DET
ejpam-5065	58	8	graph	graph	NOUN
ejpam-5065	58	9	and	and	CCONJ
ejpam-5065	58	10	let	let	VERB
ejpam-5065	58	11	p	p	PRON
ejpam-5065	58	12	be	be	AUX
ejpam-5065	58	13	a	a	DET
ejpam-5065	58	14	minimum	minimum	ADJ
ejpam-5065	58	15	2	2	NUM
ejpam-5065	58	16	-	-	PUNCT
ejpam-5065	58	17	hop	hop	NOUN
ejpam-5065	58	18	dominating	dominating	NOUN
ejpam-5065	58	19	set	set	NOUN
ejpam-5065	58	20	of	of	ADP
ejpam-5065	58	21	g.	g.	PROPN
ejpam-5065	58	22	then	then	ADV
ejpam-5065	58	23	γ2h(g	γ2h(g	PROPN
ejpam-5065	58	24	)	)	PUNCT
ejpam-5065	59	1	=	=	SYM
ejpam-5065	59	2	|p	|p	PUNCT
ejpam-5065	59	3	|	|	ADV
ejpam-5065	59	4	.	.	PUNCT
ejpam-5065	60	1	since	since	SCONJ
ejpam-5065	60	2	every	every	DET
ejpam-5065	60	3	2	2	NUM
ejpam-5065	60	4	-	-	PUNCT
ejpam-5065	60	5	hop	hop	NOUN
ejpam-5065	60	6	dominating	dominating	NOUN
ejpam-5065	60	7	is	be	AUX
ejpam-5065	60	8	a	a	DET
ejpam-5065	60	9	hop	hop	NOUN
ejpam-5065	60	10	dominating	dominating	NOUN
ejpam-5065	60	11	,	,	PUNCT
ejpam-5065	60	12	it	it	PRON
ejpam-5065	60	13	follows	follow	VERB
ejpam-5065	60	14	that	that	SCONJ
ejpam-5065	60	15	γh(g	γh(g	NOUN
ejpam-5065	60	16	)	)	PUNCT
ejpam-5065	60	17	≤	≤	NUM
ejpam-5065	60	18	|p	|p	NOUN
ejpam-5065	61	1	|	|	NOUN
ejpam-5065	61	2	=	=	SYM
ejpam-5065	61	3	γ2h(g	γ2h(g	NOUN
ejpam-5065	61	4	)	)	PUNCT
ejpam-5065	61	5	.	.	PUNCT
ejpam-5065	62	1	for	for	ADP
ejpam-5065	62	2	tightness	tightness	NOUN
ejpam-5065	62	3	,	,	PUNCT
ejpam-5065	62	4	consider	consider	VERB
ejpam-5065	62	5	kn	kn	PROPN
ejpam-5065	62	6	.	.	PUNCT
ejpam-5065	63	1	then	then	ADV
ejpam-5065	63	2	γ2h(kn	γ2h(kn	NUM
ejpam-5065	63	3	)	)	PUNCT
ejpam-5065	63	4	=	=	SYM
ejpam-5065	64	1	n	n	NOUN
ejpam-5065	64	2	=	=	NOUN
ejpam-5065	64	3	γh(g	γh(g	NOUN
ejpam-5065	64	4	)	)	PUNCT
ejpam-5065	64	5	.	.	PUNCT
ejpam-5065	65	1	(	(	PUNCT
ejpam-5065	65	2	ii	ii	NOUN
ejpam-5065	65	3	)	)	PUNCT
ejpam-5065	65	4	since	since	SCONJ
ejpam-5065	65	5	γh(g	γh(g	NOUN
ejpam-5065	65	6	)	)	PUNCT
ejpam-5065	65	7	≥	≥	NOUN
ejpam-5065	65	8	1	1	NUM
ejpam-5065	65	9	for	for	ADP
ejpam-5065	65	10	any	any	DET
ejpam-5065	65	11	graph	graph	NOUN
ejpam-5065	65	12	g	g	NOUN
ejpam-5065	65	13	,	,	PUNCT
ejpam-5065	65	14	by(i	by(i	PROPN
ejpam-5065	65	15	)	)	PUNCT
ejpam-5065	65	16	,	,	PUNCT
ejpam-5065	65	17	γ2h(g	γ2h(g	PROPN
ejpam-5065	65	18	)	)	PUNCT
ejpam-5065	65	19	≥	≥	NOUN
ejpam-5065	65	20	1	1	NUM
ejpam-5065	65	21	.	.	PUNCT
ejpam-5065	66	1	now	now	ADV
ejpam-5065	66	2	,	,	PUNCT
ejpam-5065	66	3	since	since	SCONJ
ejpam-5065	66	4	every	every	DET
ejpam-5065	66	5	2	2	NUM
ejpam-5065	66	6	-	-	PUNCT
ejpam-5065	66	7	hop	hop	NOUN
ejpam-5065	66	8	dominating	dominating	NOUN
ejpam-5065	66	9	set	set	NOUN
ejpam-5065	66	10	p	p	NOUN
ejpam-5065	66	11	is	be	AUX
ejpam-5065	66	12	always	always	ADV
ejpam-5065	66	13	a	a	DET
ejpam-5065	66	14	subset	subset	NOUN
ejpam-5065	66	15	of	of	ADP
ejpam-5065	66	16	v	v	NOUN
ejpam-5065	66	17	(	(	PUNCT
ejpam-5065	66	18	g	g	NOUN
ejpam-5065	66	19	)	)	PUNCT
ejpam-5065	66	20	,	,	PUNCT
ejpam-5065	66	21	it	it	PRON
ejpam-5065	66	22	follows	follow	VERB
ejpam-5065	66	23	that	that	SCONJ
ejpam-5065	66	24	γ2h(g	γ2h(g	NOUN
ejpam-5065	66	25	)	)	PUNCT
ejpam-5065	66	26	≤	≤	NUM
ejpam-5065	66	27	|v	|v	X
ejpam-5065	66	28	(	(	PUNCT
ejpam-5065	66	29	g)|	g)|	PROPN
ejpam-5065	66	30	.	.	PUNCT
ejpam-5065	67	1	therefore	therefore	ADV
ejpam-5065	67	2	,	,	PUNCT
ejpam-5065	67	3	1	1	NUM
ejpam-5065	67	4	≤	≤	NUM
ejpam-5065	67	5	γ2h(g	γ2h(g	PROPN
ejpam-5065	67	6	)	)	PUNCT
ejpam-5065	67	7	≤	≤	NUM
ejpam-5065	67	8	|v	|v	X
ejpam-5065	67	9	(	(	PUNCT
ejpam-5065	67	10	g)|	g)|	NOUN
ejpam-5065	67	11	.	.	PUNCT
ejpam-5065	68	1	(	(	PUNCT
ejpam-5065	69	1	iii	iii	X
ejpam-5065	69	2	)	)	PUNCT
ejpam-5065	69	3	suppose	suppose	VERB
ejpam-5065	69	4	that	that	SCONJ
ejpam-5065	69	5	γ2h(g	γ2h(g	NOUN
ejpam-5065	69	6	)	)	PUNCT
ejpam-5065	69	7	=	=	SYM
ejpam-5065	70	1	1	1	X
ejpam-5065	70	2	.	.	PUNCT
ejpam-5065	70	3	then	then	ADV
ejpam-5065	70	4	p	p	NOUN
ejpam-5065	70	5	=	=	X
ejpam-5065	70	6	{	{	PUNCT
ejpam-5065	70	7	a	a	NOUN
ejpam-5065	70	8	}	}	PUNCT
ejpam-5065	70	9	⊆	⊆	NUM
ejpam-5065	70	10	v	v	NOUN
ejpam-5065	70	11	(	(	PUNCT
ejpam-5065	70	12	g	g	NOUN
ejpam-5065	70	13	)	)	PUNCT
ejpam-5065	70	14	is	be	AUX
ejpam-5065	70	15	minimum	minimum	ADJ
ejpam-5065	70	16	2	2	NUM
ejpam-5065	70	17	-	-	PUNCT
ejpam-5065	70	18	hop	hop	NOUN
ejpam-5065	70	19	dominating	dominating	NOUN
ejpam-5065	70	20	set	set	NOUN
ejpam-5065	70	21	of	of	ADP
ejpam-5065	70	22	g	g	NOUN
ejpam-5065	70	23	for	for	ADP
ejpam-5065	70	24	some	some	PRON
ejpam-5065	70	25	a	a	DET
ejpam-5065	70	26	∈	∈	PROPN
ejpam-5065	70	27	v	v	NOUN
ejpam-5065	70	28	(	(	PUNCT
ejpam-5065	70	29	g	g	NOUN
ejpam-5065	70	30	)	)	PUNCT
ejpam-5065	70	31	.	.	PUNCT
ejpam-5065	71	1	since	since	SCONJ
ejpam-5065	71	2	every	every	DET
ejpam-5065	71	3	2	2	NUM
ejpam-5065	71	4	-	-	PUNCT
ejpam-5065	71	5	hop	hop	NOUN
ejpam-5065	71	6	dominating	dominating	NOUN
ejpam-5065	71	7	is	be	AUX
ejpam-5065	71	8	a	a	DET
ejpam-5065	71	9	hop	hop	NOUN
ejpam-5065	71	10	dominating	dominating	NOUN
ejpam-5065	71	11	,	,	PUNCT
ejpam-5065	71	12	n2	n2	NOUN
ejpam-5065	71	13	g[a	g[a	NOUN
ejpam-5065	71	14	]	]	X
ejpam-5065	71	15	=	=	SYM
ejpam-5065	71	16	v	v	X
ejpam-5065	71	17	(	(	PUNCT
ejpam-5065	71	18	g	g	NOUN
ejpam-5065	71	19	)	)	PUNCT
ejpam-5065	71	20	.	.	PUNCT
ejpam-5065	72	1	assume	assume	VERB
ejpam-5065	72	2	that	that	SCONJ
ejpam-5065	72	3	there	there	PRON
ejpam-5065	72	4	is	be	VERB
ejpam-5065	72	5	b	b	PROPN
ejpam-5065	72	6	∈	∈	NUM
ejpam-5065	72	7	v	v	NOUN
ejpam-5065	72	8	(	(	PUNCT
ejpam-5065	72	9	g)\p	g)\p	VERB
ejpam-5065	72	10	such	such	DET
ejpam-5065	72	11	that	that	DET
ejpam-5065	72	12	b	b	PROPN
ejpam-5065	72	13	∈	∈	PROPN
ejpam-5065	72	14	n2	n2	NOUN
ejpam-5065	72	15	g[a	g[a	PROPN
ejpam-5065	72	16	]	]	PUNCT
ejpam-5065	72	17	.	.	PUNCT
ejpam-5065	73	1	let	let	VERB
ejpam-5065	73	2	x	x	PUNCT
ejpam-5065	73	3	∈	∈	PROPN
ejpam-5065	73	4	ng(a	ng(a	NOUN
ejpam-5065	73	5	)	)	PUNCT
ejpam-5065	73	6	∩ng(b	∩ng(b	NOUN
ejpam-5065	73	7	)	)	PUNCT
ejpam-5065	73	8	.	.	PUNCT
ejpam-5065	74	1	then	then	ADV
ejpam-5065	74	2	x	x	X
ejpam-5065	74	3	/∈	/∈	PUNCT
ejpam-5065	74	4	n2	n2	PROPN
ejpam-5065	74	5	g[a	g[a	PROPN
ejpam-5065	74	6	]	]	X
ejpam-5065	74	7	,	,	PUNCT
ejpam-5065	74	8	a	a	DET
ejpam-5065	74	9	contradiction	contradiction	NOUN
ejpam-5065	74	10	.	.	PUNCT
ejpam-5065	75	1	therefore	therefore	ADV
ejpam-5065	75	2	,	,	PUNCT
ejpam-5065	75	3	n2	n2	PROPN
ejpam-5065	75	4	g[a	g[a	NOUN
ejpam-5065	75	5	]	]	X
ejpam-5065	75	6	=	=	X
ejpam-5065	75	7	{	{	PUNCT
ejpam-5065	75	8	a	a	NOUN
ejpam-5065	75	9	}	}	PUNCT
ejpam-5065	75	10	,	,	PUNCT
ejpam-5065	75	11	and	and	CCONJ
ejpam-5065	75	12	so	so	ADV
ejpam-5065	75	13	g	g	PROPN
ejpam-5065	75	14	is	be	AUX
ejpam-5065	75	15	trivial	trivial	ADJ
ejpam-5065	75	16	.	.	PUNCT
ejpam-5065	76	1	consequently	consequently	ADV
ejpam-5065	76	2	,	,	PUNCT
ejpam-5065	76	3	|v	|v	PROPN
ejpam-5065	76	4	(	(	PUNCT
ejpam-5065	76	5	g)|	g)|	NOUN
ejpam-5065	76	6	=	=	SYM
ejpam-5065	76	7	1	1	NUM
ejpam-5065	76	8	,	,	PUNCT
ejpam-5065	76	9	a	a	DET
ejpam-5065	76	10	contradiction	contradiction	NOUN
ejpam-5065	76	11	.	.	PUNCT
ejpam-5065	77	1	theorem	theorem	NOUN
ejpam-5065	77	2	2	2	NUM
ejpam-5065	77	3	.	.	PUNCT
ejpam-5065	78	1	let	let	VERB
ejpam-5065	78	2	g	g	PRON
ejpam-5065	78	3	be	be	AUX
ejpam-5065	78	4	a	a	DET
ejpam-5065	78	5	graph	graph	NOUN
ejpam-5065	78	6	.	.	PUNCT
ejpam-5065	79	1	then	then	ADV
ejpam-5065	79	2	γ2h(g	γ2h(g	NOUN
ejpam-5065	79	3	)	)	PUNCT
ejpam-5065	79	4	=	=	SYM
ejpam-5065	79	5	2	2	NUM
ejpam-5065	79	6	if	if	SCONJ
ejpam-5065	79	7	and	and	CCONJ
ejpam-5065	79	8	only	only	ADV
ejpam-5065	79	9	if	if	SCONJ
ejpam-5065	79	10	g	g	PROPN
ejpam-5065	79	11	=	=	SYM
ejpam-5065	79	12	k2	k2	PROPN
ejpam-5065	79	13	or	or	CCONJ
ejpam-5065	79	14	g	g	NOUN
ejpam-5065	79	15	=	=	SYM
ejpam-5065	79	16	k2	k2	PROPN
ejpam-5065	79	17	.	.	PUNCT
ejpam-5065	80	1	proof	proof	NOUN
ejpam-5065	80	2	.	.	PUNCT
ejpam-5065	81	1	suppose	suppose	VERB
ejpam-5065	81	2	that	that	SCONJ
ejpam-5065	81	3	γ2h(g	γ2h(g	NOUN
ejpam-5065	81	4	)	)	PUNCT
ejpam-5065	81	5	=	=	SYM
ejpam-5065	81	6	2	2	X
ejpam-5065	81	7	,	,	PUNCT
ejpam-5065	81	8	say	say	VERB
ejpam-5065	81	9	p	p	NOUN
ejpam-5065	81	10	=	=	X
ejpam-5065	81	11	{	{	PUNCT
ejpam-5065	81	12	a	a	PROPN
ejpam-5065	81	13	,	,	PUNCT
ejpam-5065	81	14	b	b	NOUN
ejpam-5065	81	15	}	}	PUNCT
ejpam-5065	81	16	is	be	AUX
ejpam-5065	81	17	a	a	DET
ejpam-5065	81	18	minimum	minimum	ADJ
ejpam-5065	81	19	2	2	NUM
ejpam-5065	81	20	-	-	PUNCT
ejpam-5065	81	21	hop	hop	NOUN
ejpam-5065	81	22	dominating	dominating	NOUN
ejpam-5065	81	23	set	set	NOUN
ejpam-5065	81	24	of	of	ADP
ejpam-5065	81	25	g.	g.	PROPN
ejpam-5065	81	26	then	then	ADV
ejpam-5065	81	27	n2	n2	PROPN
ejpam-5065	81	28	g[p	g[p	PROPN
ejpam-5065	81	29	]	]	PUNCT
ejpam-5065	81	30	=	=	SYM
ejpam-5065	81	31	v	v	X
ejpam-5065	81	32	(	(	PUNCT
ejpam-5065	81	33	g	g	NOUN
ejpam-5065	81	34	)	)	PUNCT
ejpam-5065	81	35	since	since	SCONJ
ejpam-5065	81	36	every	every	DET
ejpam-5065	81	37	2	2	NUM
ejpam-5065	81	38	-	-	PUNCT
ejpam-5065	81	39	hop	hop	NOUN
ejpam-5065	81	40	dominating	dominating	NOUN
ejpam-5065	81	41	set	set	NOUN
ejpam-5065	81	42	p	p	NOUN
ejpam-5065	81	43	is	be	AUX
ejpam-5065	81	44	a	a	DET
ejpam-5065	81	45	hop	hop	NOUN
ejpam-5065	81	46	dominating	dominating	NOUN
ejpam-5065	81	47	.	.	PUNCT
ejpam-5065	82	1	assume	assume	VERB
ejpam-5065	82	2	that	that	SCONJ
ejpam-5065	82	3	g	g	PROPN
ejpam-5065	82	4	is	be	AUX
ejpam-5065	82	5	connected	connect	VERB
ejpam-5065	82	6	.	.	PUNCT
ejpam-5065	83	1	if	if	SCONJ
ejpam-5065	83	2	dg(a	dg(a	NUM
ejpam-5065	83	3	,	,	PUNCT
ejpam-5065	83	4	b	b	X
ejpam-5065	83	5	)	)	PUNCT
ejpam-5065	83	6	=	=	SYM
ejpam-5065	83	7	2	2	NUM
ejpam-5065	83	8	,	,	PUNCT
ejpam-5065	83	9	then	then	ADV
ejpam-5065	83	10	there	there	PRON
ejpam-5065	83	11	exists	exist	VERB
ejpam-5065	83	12	y	y	PROPN
ejpam-5065	83	13	∈	∈	PROPN
ejpam-5065	83	14	v	v	PROPN
ejpam-5065	83	15	(	(	PUNCT
ejpam-5065	83	16	g)\p	g)\p	NOUN
ejpam-5065	83	17	j.	j.	PROPN
ejpam-5065	83	18	hassan	hassan	PROPN
ejpam-5065	83	19	,	,	PUNCT
ejpam-5065	83	20	a.	a.	PROPN
ejpam-5065	83	21	gomorez	gomorez	PROPN
ejpam-5065	83	22	,	,	PUNCT
ejpam-5065	83	23	l.	l.	PROPN
ejpam-5065	83	24	laja	laja	PROPN
ejpam-5065	83	25	,	,	PUNCT
ejpam-5065	83	26	e.	e.	PROPN
ejpam-5065	83	27	ahmad	ahmad	PROPN
ejpam-5065	83	28	/	/	SYM
ejpam-5065	83	29	eur	eur	PROPN
ejpam-5065	83	30	.	.	PUNCT
ejpam-5065	84	1	j.	j.	PROPN
ejpam-5065	84	2	pure	pure	PROPN
ejpam-5065	84	3	appl	appl	PROPN
ejpam-5065	84	4	.	.	PROPN
ejpam-5065	84	5	math	math	PROPN
ejpam-5065	84	6	,	,	PUNCT
ejpam-5065	84	7	17	17	NUM
ejpam-5065	84	8	(	(	PUNCT
ejpam-5065	84	9	2	2	NUM
ejpam-5065	84	10	)	)	PUNCT
ejpam-5065	84	11	(	(	PUNCT
ejpam-5065	84	12	2024	2024	NUM
ejpam-5065	84	13	)	)	PUNCT
ejpam-5065	84	14	,	,	PUNCT
ejpam-5065	84	15	852	852	NUM
ejpam-5065	84	16	-	-	SYM
ejpam-5065	84	17	859	859	NUM
ejpam-5065	84	18	855	855	NUM
ejpam-5065	84	19	such	such	ADJ
ejpam-5065	84	20	that	that	SCONJ
ejpam-5065	84	21	y	y	PROPN
ejpam-5065	84	22	∈	∈	PROPN
ejpam-5065	84	23	ng(a	ng(a	NOUN
ejpam-5065	84	24	)	)	PUNCT
ejpam-5065	84	25	∩	∩	NOUN
ejpam-5065	84	26	ng(b	ng(b	NOUN
ejpam-5065	84	27	)	)	PUNCT
ejpam-5065	84	28	.	.	PUNCT
ejpam-5065	85	1	however	however	ADV
ejpam-5065	85	2	,	,	PUNCT
ejpam-5065	85	3	y	y	PROPN
ejpam-5065	85	4	/∈	/∈	PROPN
ejpam-5065	85	5	n2	n2	PROPN
ejpam-5065	85	6	g[p	g[p	PROPN
ejpam-5065	85	7	]	]	PUNCT
ejpam-5065	85	8	,	,	PUNCT
ejpam-5065	85	9	a	a	DET
ejpam-5065	85	10	contradiction	contradiction	NOUN
ejpam-5065	85	11	.	.	PUNCT
ejpam-5065	86	1	similarly	similarly	ADV
ejpam-5065	86	2	,	,	PUNCT
ejpam-5065	86	3	when	when	SCONJ
ejpam-5065	86	4	dg(a	dg(a	X
ejpam-5065	86	5	,	,	PUNCT
ejpam-5065	86	6	b	b	X
ejpam-5065	86	7	)	)	PUNCT
ejpam-5065	86	8	=	=	SYM
ejpam-5065	86	9	3	3	NUM
ejpam-5065	86	10	,	,	PUNCT
ejpam-5065	86	11	4	4	NUM
ejpam-5065	86	12	,	,	PUNCT
ejpam-5065	86	13	.	.	PUNCT
ejpam-5065	86	14	.	.	PUNCT
ejpam-5065	86	15	.	.	PUNCT
ejpam-5065	87	1	,	,	PUNCT
ejpam-5065	87	2	n−	n−	NOUN
ejpam-5065	87	3	1	1	NUM
ejpam-5065	87	4	,	,	PUNCT
ejpam-5065	87	5	where	where	SCONJ
ejpam-5065	87	6	n	n	X
ejpam-5065	87	7	is	be	AUX
ejpam-5065	87	8	the	the	DET
ejpam-5065	87	9	order	order	NOUN
ejpam-5065	87	10	of	of	ADP
ejpam-5065	87	11	g.	g.	PROPN
ejpam-5065	87	12	thus	thus	ADV
ejpam-5065	87	13	,	,	PUNCT
ejpam-5065	87	14	dg(a	dg(a	X
ejpam-5065	87	15	,	,	PUNCT
ejpam-5065	87	16	b	b	X
ejpam-5065	87	17	)	)	PUNCT
ejpam-5065	87	18	=	=	SYM
ejpam-5065	87	19	1	1	NUM
ejpam-5065	87	20	,	,	PUNCT
ejpam-5065	87	21	and	and	CCONJ
ejpam-5065	87	22	so	so	ADV
ejpam-5065	87	23	g	g	PROPN
ejpam-5065	87	24	=	=	SYM
ejpam-5065	87	25	k2	k2	PROPN
ejpam-5065	87	26	.	.	PUNCT
ejpam-5065	88	1	now	now	ADV
ejpam-5065	88	2	,	,	PUNCT
ejpam-5065	88	3	assume	assume	VERB
ejpam-5065	88	4	that	that	SCONJ
ejpam-5065	88	5	g	g	PROPN
ejpam-5065	88	6	is	be	AUX
ejpam-5065	88	7	disconnected	disconnect	VERB
ejpam-5065	88	8	.	.	PUNCT
ejpam-5065	89	1	let	let	VERB
ejpam-5065	89	2	g1	g1	PROPN
ejpam-5065	89	3	,	,	PUNCT
ejpam-5065	89	4	.	.	PUNCT
ejpam-5065	89	5	.	.	PUNCT
ejpam-5065	90	1	.	.	PUNCT
ejpam-5065	91	1	,	,	PUNCT
ejpam-5065	91	2	gk	gk	PROPN
ejpam-5065	91	3	,	,	PUNCT
ejpam-5065	91	4	k	k	PROPN
ejpam-5065	91	5	≥	≥	NUM
ejpam-5065	91	6	2	2	NUM
ejpam-5065	91	7	,	,	PUNCT
ejpam-5065	91	8	be	be	AUX
ejpam-5065	91	9	conponents	conponent	NOUN
ejpam-5065	91	10	of	of	ADP
ejpam-5065	91	11	g.	g.	NOUN
ejpam-5065	91	12	since	since	SCONJ
ejpam-5065	91	13	γ2h(g	γ2h(g	NOUN
ejpam-5065	91	14	)	)	PUNCT
ejpam-5065	92	1	=	=	SYM
ejpam-5065	92	2	2	2	X
ejpam-5065	93	1	,	,	PUNCT
ejpam-5065	93	2	it	it	PRON
ejpam-5065	93	3	follows	follow	VERB
ejpam-5065	93	4	that	that	SCONJ
ejpam-5065	93	5	k	k	PROPN
ejpam-5065	93	6	=	=	PUNCT
ejpam-5065	93	7	2	2	X
ejpam-5065	93	8	.	.	X
ejpam-5065	93	9	that	that	PRON
ejpam-5065	93	10	is	is	ADV
ejpam-5065	93	11	,	,	PUNCT
ejpam-5065	93	12	there	there	PRON
ejpam-5065	93	13	are	be	VERB
ejpam-5065	93	14	only	only	ADV
ejpam-5065	93	15	2	2	NUM
ejpam-5065	93	16	components	component	NOUN
ejpam-5065	93	17	of	of	ADP
ejpam-5065	93	18	g.	g.	PROPN
ejpam-5065	93	19	if	if	SCONJ
ejpam-5065	93	20	g1	g1	PROPN
ejpam-5065	93	21	is	be	AUX
ejpam-5065	93	22	non	non	ADJ
ejpam-5065	93	23	-	-	ADJ
ejpam-5065	93	24	trivial	trivial	ADJ
ejpam-5065	93	25	,	,	PUNCT
ejpam-5065	93	26	then	then	ADV
ejpam-5065	93	27	γ2h(g1	γ2h(g1	PROPN
ejpam-5065	93	28	)	)	PUNCT
ejpam-5065	93	29	≥	≥	NOUN
ejpam-5065	93	30	2	2	NUM
ejpam-5065	93	31	by	by	ADP
ejpam-5065	93	32	theorem	theorem	NOUN
ejpam-5065	93	33	1	1	NUM
ejpam-5065	93	34	(	(	PUNCT
ejpam-5065	93	35	iii	iii	NOUN
ejpam-5065	93	36	)	)	PUNCT
ejpam-5065	93	37	.	.	PUNCT
ejpam-5065	94	1	since	since	SCONJ
ejpam-5065	94	2	g	g	PROPN
ejpam-5065	94	3	has	have	VERB
ejpam-5065	94	4	two	two	NUM
ejpam-5065	94	5	components	component	NOUN
ejpam-5065	94	6	,	,	PUNCT
ejpam-5065	94	7	it	it	PRON
ejpam-5065	94	8	follows	follow	VERB
ejpam-5065	94	9	that	that	SCONJ
ejpam-5065	94	10	γ2h(g	γ2h(g	NOUN
ejpam-5065	94	11	)	)	PUNCT
ejpam-5065	94	12	≥	≥	NOUN
ejpam-5065	94	13	3	3	NUM
ejpam-5065	94	14	,	,	PUNCT
ejpam-5065	94	15	a	a	DET
ejpam-5065	94	16	contradiction	contradiction	NOUN
ejpam-5065	94	17	.	.	PUNCT
ejpam-5065	95	1	similarly	similarly	ADV
ejpam-5065	95	2	,	,	PUNCT
ejpam-5065	95	3	when	when	SCONJ
ejpam-5065	95	4	g2	g2	PROPN
ejpam-5065	95	5	is	be	AUX
ejpam-5065	95	6	non	non	ADJ
ejpam-5065	95	7	-	-	ADJ
ejpam-5065	95	8	trivial	trivial	ADJ
ejpam-5065	95	9	.	.	PUNCT
ejpam-5065	96	1	therefore	therefore	ADV
ejpam-5065	96	2	,	,	PUNCT
ejpam-5065	96	3	both	both	CCONJ
ejpam-5065	96	4	g1	g1	PROPN
ejpam-5065	96	5	and	and	CCONJ
ejpam-5065	96	6	g2	g2	PROPN
ejpam-5065	96	7	are	be	AUX
ejpam-5065	96	8	trivial	trivial	ADJ
ejpam-5065	96	9	,	,	PUNCT
ejpam-5065	96	10	and	and	CCONJ
ejpam-5065	96	11	so	so	ADV
ejpam-5065	96	12	g	g	PROPN
ejpam-5065	96	13	=	=	SYM
ejpam-5065	96	14	k2	k2	PROPN
ejpam-5065	96	15	.	.	PUNCT
ejpam-5065	97	1	conversely	conversely	ADV
ejpam-5065	97	2	,	,	PUNCT
ejpam-5065	97	3	suppose	suppose	VERB
ejpam-5065	97	4	that	that	SCONJ
ejpam-5065	97	5	g	g	PROPN
ejpam-5065	97	6	=	=	SYM
ejpam-5065	97	7	k2	k2	PROPN
ejpam-5065	97	8	.	.	PUNCT
ejpam-5065	98	1	then	then	ADV
ejpam-5065	98	2	γh(g	γh(g	NOUN
ejpam-5065	98	3	)	)	PUNCT
ejpam-5065	98	4	=	=	SYM
ejpam-5065	98	5	2	2	X
ejpam-5065	98	6	.	.	PUNCT
ejpam-5065	98	7	since	since	SCONJ
ejpam-5065	98	8	γ2h(g	γ2h(g	NOUN
ejpam-5065	98	9	)	)	PUNCT
ejpam-5065	98	10	≥	≥	NOUN
ejpam-5065	98	11	γh(g	γh(g	NOUN
ejpam-5065	98	12	)	)	PUNCT
ejpam-5065	98	13	,	,	PUNCT
ejpam-5065	98	14	it	it	PRON
ejpam-5065	98	15	follows	follow	VERB
ejpam-5065	98	16	that	that	SCONJ
ejpam-5065	98	17	γ2h(g	γ2h(g	NOUN
ejpam-5065	98	18	)	)	PUNCT
ejpam-5065	98	19	≥	≥	NOUN
ejpam-5065	98	20	2	2	NUM
ejpam-5065	98	21	.	.	PUNCT
ejpam-5065	99	1	since	since	SCONJ
ejpam-5065	99	2	|v	|v	PROPN
ejpam-5065	99	3	(	(	PUNCT
ejpam-5065	99	4	g)|	g)|	NOUN
ejpam-5065	99	5	=	=	SYM
ejpam-5065	99	6	2	2	NUM
ejpam-5065	99	7	,	,	PUNCT
ejpam-5065	99	8	γ2h(g	γ2h(g	PROPN
ejpam-5065	99	9	)	)	PUNCT
ejpam-5065	99	10	=	=	SYM
ejpam-5065	99	11	2	2	NUM
ejpam-5065	99	12	by	by	ADP
ejpam-5065	99	13	theorem	theorem	NOUN
ejpam-5065	99	14	1(ii	1(ii	NUM
ejpam-5065	99	15	)	)	PUNCT
ejpam-5065	99	16	.	.	PUNCT
ejpam-5065	100	1	similarly	similarly	ADV
ejpam-5065	100	2	,	,	PUNCT
ejpam-5065	100	3	if	if	SCONJ
ejpam-5065	100	4	g	g	PROPN
ejpam-5065	100	5	=	=	SYM
ejpam-5065	100	6	k2	k2	PROPN
ejpam-5065	100	7	,	,	PUNCT
ejpam-5065	100	8	then	then	ADV
ejpam-5065	100	9	γ2h(g	γ2h(g	NOUN
ejpam-5065	100	10	)	)	PUNCT
ejpam-5065	100	11	=	=	SYM
ejpam-5065	100	12	2	2	X
ejpam-5065	100	13	.	.	X
ejpam-5065	100	14	theorem	theorem	NOUN
ejpam-5065	100	15	3	3	X
ejpam-5065	100	16	.	.	PUNCT
ejpam-5065	101	1	let	let	VERB
ejpam-5065	101	2	g	g	PRON
ejpam-5065	101	3	be	be	AUX
ejpam-5065	101	4	a	a	DET
ejpam-5065	101	5	graph	graph	NOUN
ejpam-5065	101	6	.	.	PUNCT
ejpam-5065	102	1	then	then	ADV
ejpam-5065	102	2	(	(	PUNCT
ejpam-5065	102	3	i	i	NOUN
ejpam-5065	102	4	)	)	PUNCT
ejpam-5065	102	5	γ2h(g	γ2h(g	PROPN
ejpam-5065	102	6	)	)	PUNCT
ejpam-5065	102	7	=	=	SYM
ejpam-5065	102	8	|v	|v	PROPN
ejpam-5065	102	9	(	(	PUNCT
ejpam-5065	102	10	g)|	g)|	VERB
ejpam-5065	102	11	if	if	SCONJ
ejpam-5065	102	12	and	and	CCONJ
ejpam-5065	102	13	only	only	ADV
ejpam-5065	102	14	if	if	SCONJ
ejpam-5065	102	15	|n2	|n2	PROPN
ejpam-5065	102	16	g[x]|	g[x]|	PROPN
ejpam-5065	102	17	≤	≤	ADV
ejpam-5065	102	18	2	2	NUM
ejpam-5065	102	19	for	for	ADP
ejpam-5065	102	20	every	every	DET
ejpam-5065	102	21	x	x	SYM
ejpam-5065	102	22	∈	∈	PROPN
ejpam-5065	102	23	v	v	NOUN
ejpam-5065	102	24	(	(	PUNCT
ejpam-5065	102	25	g	g	NOUN
ejpam-5065	102	26	)	)	PUNCT
ejpam-5065	102	27	;	;	PUNCT
ejpam-5065	102	28	and	and	CCONJ
ejpam-5065	102	29	(	(	PUNCT
ejpam-5065	102	30	ii	ii	NOUN
ejpam-5065	102	31	)	)	PUNCT
ejpam-5065	102	32	if	if	SCONJ
ejpam-5065	102	33	γh(g	γh(g	NOUN
ejpam-5065	102	34	)	)	PUNCT
ejpam-5065	102	35	=	=	SYM
ejpam-5065	102	36	|v	|v	PROPN
ejpam-5065	102	37	(	(	PUNCT
ejpam-5065	102	38	g)|	g)|	PROPN
ejpam-5065	102	39	,	,	PUNCT
ejpam-5065	102	40	then	then	ADV
ejpam-5065	102	41	γ2h(g	γ2h(g	NOUN
ejpam-5065	102	42	)	)	PUNCT
ejpam-5065	102	43	=	=	SYM
ejpam-5065	102	44	|v	|v	PROPN
ejpam-5065	102	45	(	(	PUNCT
ejpam-5065	102	46	g)|	g)|	NOUN
ejpam-5065	102	47	.	.	PUNCT
ejpam-5065	103	1	however	however	ADV
ejpam-5065	103	2	,	,	PUNCT
ejpam-5065	103	3	the	the	DET
ejpam-5065	103	4	converse	converse	NOUN
ejpam-5065	103	5	is	be	AUX
ejpam-5065	103	6	not	not	PART
ejpam-5065	103	7	true	true	ADJ
ejpam-5065	103	8	.	.	PUNCT
ejpam-5065	104	1	proof	proof	NOUN
ejpam-5065	104	2	.	.	PUNCT
ejpam-5065	105	1	(	(	PUNCT
ejpam-5065	105	2	i	i	NOUN
ejpam-5065	105	3	)	)	PUNCT
ejpam-5065	105	4	suppose	suppose	VERB
ejpam-5065	105	5	that	that	SCONJ
ejpam-5065	105	6	γ2h(g	γ2h(g	NOUN
ejpam-5065	105	7	)	)	PUNCT
ejpam-5065	105	8	=	=	SYM
ejpam-5065	105	9	|v	|v	PROPN
ejpam-5065	105	10	(	(	PUNCT
ejpam-5065	105	11	g)|	g)|	PROPN
ejpam-5065	105	12	.	.	PUNCT
ejpam-5065	106	1	then	then	ADV
ejpam-5065	106	2	v	v	X
ejpam-5065	106	3	(	(	PUNCT
ejpam-5065	106	4	g	g	NOUN
ejpam-5065	106	5	)	)	PUNCT
ejpam-5065	106	6	is	be	AUX
ejpam-5065	106	7	the	the	DET
ejpam-5065	106	8	minimum	minimum	ADJ
ejpam-5065	106	9	2	2	NUM
ejpam-5065	106	10	-	-	PUNCT
ejpam-5065	106	11	hop	hop	NOUN
ejpam-5065	106	12	dominating	dominating	NOUN
ejpam-5065	106	13	set	set	NOUN
ejpam-5065	106	14	of	of	ADP
ejpam-5065	106	15	g	g	PROPN
ejpam-5065	106	16	,	,	PUNCT
ejpam-5065	106	17	that	that	ADV
ejpam-5065	106	18	is	is	ADV
ejpam-5065	106	19	,	,	PUNCT
ejpam-5065	106	20	n2	n2	PROPN
ejpam-5065	106	21	g[v	g[v	PROPN
ejpam-5065	106	22	(	(	PUNCT
ejpam-5065	106	23	g	g	NOUN
ejpam-5065	106	24	)	)	PUNCT
ejpam-5065	106	25	]	]	PUNCT
ejpam-5065	107	1	=	=	SYM
ejpam-5065	107	2	v	v	X
ejpam-5065	107	3	(	(	PUNCT
ejpam-5065	107	4	g	g	NOUN
ejpam-5065	107	5	)	)	PUNCT
ejpam-5065	107	6	.	.	PUNCT
ejpam-5065	108	1	assume	assume	VERB
ejpam-5065	108	2	that	that	SCONJ
ejpam-5065	108	3	|n2	|n2	PROPN
ejpam-5065	108	4	g[x]|	g[x]|	PROPN
ejpam-5065	108	5	≥	≥	NUM
ejpam-5065	108	6	3	3	NUM
ejpam-5065	108	7	for	for	ADP
ejpam-5065	108	8	some	some	DET
ejpam-5065	108	9	x	x	SYM
ejpam-5065	108	10	∈	∈	PROPN
ejpam-5065	108	11	v	v	NOUN
ejpam-5065	108	12	(	(	PUNCT
ejpam-5065	108	13	g	g	NOUN
ejpam-5065	108	14	)	)	PUNCT
ejpam-5065	108	15	.	.	PUNCT
ejpam-5065	109	1	then	then	ADV
ejpam-5065	109	2	there	there	PRON
ejpam-5065	109	3	exist	exist	VERB
ejpam-5065	109	4	u	u	NOUN
ejpam-5065	109	5	,	,	PUNCT
ejpam-5065	109	6	v	v	NOUN
ejpam-5065	109	7	∈	∈	PROPN
ejpam-5065	109	8	v	v	NOUN
ejpam-5065	109	9	(	(	PUNCT
ejpam-5065	109	10	g	g	NOUN
ejpam-5065	109	11	)	)	PUNCT
ejpam-5065	109	12	such	such	ADJ
ejpam-5065	109	13	that	that	SCONJ
ejpam-5065	109	14	u	u	NOUN
ejpam-5065	109	15	,	,	PUNCT
ejpam-5065	109	16	v	v	PROPN
ejpam-5065	109	17	∈	∈	PROPN
ejpam-5065	109	18	n2	n2	NOUN
ejpam-5065	109	19	g(x	g(x	PROPN
ejpam-5065	109	20	)	)	PUNCT
ejpam-5065	109	21	.	.	PUNCT
ejpam-5065	110	1	let	let	VERB
ejpam-5065	110	2	p	p	NOUN
ejpam-5065	110	3	=	=	X
ejpam-5065	110	4	v	v	X
ejpam-5065	110	5	(	(	PUNCT
ejpam-5065	110	6	g)\{x	g)\{x	PROPN
ejpam-5065	110	7	}	}	PUNCT
ejpam-5065	110	8	.	.	PUNCT
ejpam-5065	111	1	then	then	ADV
ejpam-5065	111	2	p	p	PROPN
ejpam-5065	111	3	is	be	AUX
ejpam-5065	111	4	a	a	DET
ejpam-5065	111	5	2	2	NUM
ejpam-5065	111	6	-	-	PUNCT
ejpam-5065	111	7	hop	hop	NOUN
ejpam-5065	111	8	dominating	dominating	NOUN
ejpam-5065	111	9	set	set	NOUN
ejpam-5065	111	10	of	of	ADP
ejpam-5065	111	11	g.	g.	PROPN
ejpam-5065	111	12	thus	thus	ADV
ejpam-5065	111	13	,	,	PUNCT
ejpam-5065	111	14	γ2h(g	γ2h(g	PROPN
ejpam-5065	111	15	)	)	PUNCT
ejpam-5065	111	16	≤	≤	NUM
ejpam-5065	111	17	|v	|v	X
ejpam-5065	111	18	(	(	PUNCT
ejpam-5065	111	19	g)|	g)|	INTJ
ejpam-5065	111	20	−	−	PROPN
ejpam-5065	111	21	1	1	NUM
ejpam-5065	111	22	,	,	PUNCT
ejpam-5065	111	23	a	a	DET
ejpam-5065	111	24	contradiction	contradiction	NOUN
ejpam-5065	111	25	.	.	PUNCT
ejpam-5065	112	1	therefore	therefore	ADV
ejpam-5065	112	2	,	,	PUNCT
ejpam-5065	112	3	|n2	|n2	PROPN
ejpam-5065	112	4	g[x]|	g[x]|	PROPN
ejpam-5065	112	5	≤	≤	ADV
ejpam-5065	112	6	2	2	NUM
ejpam-5065	112	7	for	for	ADP
ejpam-5065	112	8	all	all	PRON
ejpam-5065	112	9	x	x	SYM
ejpam-5065	112	10	∈	∈	NOUN
ejpam-5065	112	11	v	v	NOUN
ejpam-5065	112	12	(	(	PUNCT
ejpam-5065	112	13	g	g	NOUN
ejpam-5065	112	14	)	)	PUNCT
ejpam-5065	112	15	.	.	PUNCT
ejpam-5065	113	1	conversely	conversely	ADV
ejpam-5065	113	2	,	,	PUNCT
ejpam-5065	113	3	suppose	suppose	VERB
ejpam-5065	113	4	that	that	SCONJ
ejpam-5065	113	5	|n2	|n2	PROPN
ejpam-5065	113	6	g[x]|	g[x]|	PROPN
ejpam-5065	113	7	≤	≤	ADV
ejpam-5065	113	8	2	2	NUM
ejpam-5065	113	9	for	for	ADP
ejpam-5065	113	10	all	all	PRON
ejpam-5065	113	11	x	x	SYM
ejpam-5065	113	12	∈	∈	NOUN
ejpam-5065	113	13	v	v	NOUN
ejpam-5065	113	14	(	(	PUNCT
ejpam-5065	113	15	g	g	NOUN
ejpam-5065	113	16	)	)	PUNCT
ejpam-5065	113	17	.	.	PUNCT
ejpam-5065	114	1	ifn2	ifn2	PROPN
ejpam-5065	114	2	g[x	g[x	PROPN
ejpam-5065	114	3	]	]	X
ejpam-5065	114	4	=	=	SYM
ejpam-5065	114	5	{	{	PUNCT
ejpam-5065	114	6	x	x	NOUN
ejpam-5065	114	7	}	}	PUNCT
ejpam-5065	114	8	for	for	ADP
ejpam-5065	114	9	all	all	PRON
ejpam-5065	114	10	x	x	SYM
ejpam-5065	114	11	∈	∈	PROPN
ejpam-5065	114	12	v	v	NOUN
ejpam-5065	114	13	(	(	PUNCT
ejpam-5065	114	14	g	g	NOUN
ejpam-5065	114	15	)	)	PUNCT
ejpam-5065	114	16	,	,	PUNCT
ejpam-5065	114	17	then	then	ADV
ejpam-5065	114	18	we	we	PRON
ejpam-5065	114	19	are	be	AUX
ejpam-5065	114	20	done	do	VERB
ejpam-5065	114	21	.	.	PUNCT
ejpam-5065	115	1	assume	assume	VERB
ejpam-5065	115	2	that	that	SCONJ
ejpam-5065	115	3	|n2	|n2	PROPN
ejpam-5065	115	4	g[x]|	g[x]|	PROPN
ejpam-5065	115	5	=	=	PUNCT
ejpam-5065	115	6	2	2	NUM
ejpam-5065	115	7	for	for	ADP
ejpam-5065	115	8	all	all	PRON
ejpam-5065	115	9	x	x	SYM
ejpam-5065	115	10	∈	∈	NOUN
ejpam-5065	115	11	v	v	NOUN
ejpam-5065	115	12	(	(	PUNCT
ejpam-5065	115	13	g	g	NOUN
ejpam-5065	115	14	)	)	PUNCT
ejpam-5065	115	15	.	.	PUNCT
ejpam-5065	116	1	then	then	ADV
ejpam-5065	116	2	there	there	PRON
ejpam-5065	116	3	exists	exist	VERB
ejpam-5065	116	4	a	a	DET
ejpam-5065	116	5	unique	unique	ADJ
ejpam-5065	116	6	y	y	PROPN
ejpam-5065	116	7	∈	∈	PROPN
ejpam-5065	116	8	v	v	ADP
ejpam-5065	116	9	(	(	PUNCT
ejpam-5065	116	10	g	g	NOUN
ejpam-5065	116	11	)	)	PUNCT
ejpam-5065	116	12	such	such	ADJ
ejpam-5065	116	13	that	that	SCONJ
ejpam-5065	116	14	y	y	PROPN
ejpam-5065	116	15	∈	∈	PROPN
ejpam-5065	116	16	n2	n2	NOUN
ejpam-5065	116	17	g(x	g(x	PROPN
ejpam-5065	116	18	)	)	PUNCT
ejpam-5065	116	19	.	.	PUNCT
ejpam-5065	117	1	let	let	VERB
ejpam-5065	117	2	p	p	PRON
ejpam-5065	117	3	be	be	AUX
ejpam-5065	117	4	a	a	DET
ejpam-5065	117	5	2	2	NUM
ejpam-5065	117	6	-	-	PUNCT
ejpam-5065	117	7	hop	hop	NOUN
ejpam-5065	117	8	dominating	dominating	NOUN
ejpam-5065	117	9	set	set	NOUN
ejpam-5065	117	10	of	of	ADP
ejpam-5065	117	11	g.	g.	PROPN
ejpam-5065	117	12	since	since	SCONJ
ejpam-5065	117	13	p	p	PROPN
ejpam-5065	117	14	is	be	AUX
ejpam-5065	117	15	a	a	DET
ejpam-5065	117	16	hop	hop	NOUN
ejpam-5065	117	17	dominating	dominating	NOUN
ejpam-5065	117	18	,	,	PUNCT
ejpam-5065	117	19	either	either	CCONJ
ejpam-5065	117	20	x	x	SYM
ejpam-5065	117	21	or	or	CCONJ
ejpam-5065	117	22	y	y	PROPN
ejpam-5065	117	23	is	be	AUX
ejpam-5065	117	24	in	in	ADP
ejpam-5065	117	25	p	p	PROPN
ejpam-5065	117	26	.	.	PUNCT
ejpam-5065	118	1	assume	assume	VERB
ejpam-5065	118	2	that	that	SCONJ
ejpam-5065	118	3	x	x	SYM
ejpam-5065	118	4	∈	∈	PROPN
ejpam-5065	118	5	p	p	X
ejpam-5065	118	6	.	.	PUNCT
ejpam-5065	119	1	assume	assume	VERB
ejpam-5065	119	2	further	far	ADV
ejpam-5065	119	3	that	that	SCONJ
ejpam-5065	119	4	y	y	PROPN
ejpam-5065	119	5	/∈	/∈	PUNCT
ejpam-5065	120	1	p	p	X
ejpam-5065	120	2	.	.	PUNCT
ejpam-5065	121	1	since	since	SCONJ
ejpam-5065	121	2	p	p	NOUN
ejpam-5065	121	3	is	be	AUX
ejpam-5065	121	4	a	a	DET
ejpam-5065	121	5	2	2	NUM
ejpam-5065	121	6	-	-	PUNCT
ejpam-5065	121	7	hop	hop	NOUN
ejpam-5065	121	8	dominating	dominating	NOUN
ejpam-5065	121	9	,	,	PUNCT
ejpam-5065	121	10	there	there	PRON
ejpam-5065	121	11	exists	exist	VERB
ejpam-5065	121	12	w	w	PROPN
ejpam-5065	121	13	∈	∈	PROPN
ejpam-5065	121	14	p	p	NOUN
ejpam-5065	121	15	such	such	ADJ
ejpam-5065	121	16	that	that	SCONJ
ejpam-5065	121	17	dg(w	dg(w	NUM
ejpam-5065	121	18	,	,	PUNCT
ejpam-5065	121	19	y	y	NOUN
ejpam-5065	121	20	)	)	PUNCT
ejpam-5065	121	21	=	=	SYM
ejpam-5065	122	1	2	2	X
ejpam-5065	122	2	.	.	PUNCT
ejpam-5065	122	3	it	it	PRON
ejpam-5065	122	4	follows	follow	VERB
ejpam-5065	122	5	that	that	PRON
ejpam-5065	122	6	w	w	ADP
ejpam-5065	122	7	,	,	PUNCT
ejpam-5065	122	8	x	x	SYM
ejpam-5065	122	9	∈	∈	PROPN
ejpam-5065	122	10	n2	n2	NOUN
ejpam-5065	122	11	g(y	g(y	PROPN
ejpam-5065	122	12	)	)	PUNCT
ejpam-5065	122	13	.	.	PUNCT
ejpam-5065	123	1	thus	thus	ADV
ejpam-5065	123	2	|n2	|n2	PROPN
ejpam-5065	123	3	g[y]|	g[y]|	PROPN
ejpam-5065	123	4	≥	≥	NOUN
ejpam-5065	123	5	3	3	NUM
ejpam-5065	123	6	,	,	PUNCT
ejpam-5065	123	7	a	a	DET
ejpam-5065	123	8	contradiction	contradiction	NOUN
ejpam-5065	123	9	.	.	PUNCT
ejpam-5065	124	1	therefore	therefore	ADV
ejpam-5065	124	2	,	,	PUNCT
ejpam-5065	124	3	y	y	PROPN
ejpam-5065	124	4	∈	∈	PROPN
ejpam-5065	124	5	p	p	PROPN
ejpam-5065	124	6	.	.	PUNCT
ejpam-5065	125	1	similarly	similarly	ADV
ejpam-5065	125	2	,	,	PUNCT
ejpam-5065	125	3	when	when	SCONJ
ejpam-5065	125	4	y	y	PROPN
ejpam-5065	125	5	∈	∈	PROPN
ejpam-5065	125	6	p	p	X
ejpam-5065	125	7	,	,	PUNCT
ejpam-5065	125	8	then	then	ADV
ejpam-5065	125	9	x	x	X
ejpam-5065	125	10	∈	∈	PROPN
ejpam-5065	125	11	p	p	NOUN
ejpam-5065	125	12	.	.	PUNCT
ejpam-5065	126	1	since	since	SCONJ
ejpam-5065	126	2	x	x	PRON
ejpam-5065	126	3	is	be	AUX
ejpam-5065	126	4	arbitrary	arbitrary	ADJ
ejpam-5065	126	5	,	,	PUNCT
ejpam-5065	126	6	it	it	PRON
ejpam-5065	126	7	follows	follow	VERB
ejpam-5065	126	8	that	that	SCONJ
ejpam-5065	126	9	v	v	X
ejpam-5065	126	10	(	(	PUNCT
ejpam-5065	126	11	g	g	NOUN
ejpam-5065	126	12	)	)	PUNCT
ejpam-5065	126	13	is	be	AUX
ejpam-5065	126	14	the	the	DET
ejpam-5065	126	15	minimum	minimum	ADJ
ejpam-5065	126	16	2	2	NUM
ejpam-5065	126	17	-	-	PUNCT
ejpam-5065	126	18	hop	hop	NOUN
ejpam-5065	126	19	dominating	dominating	NOUN
ejpam-5065	126	20	set	set	NOUN
ejpam-5065	126	21	of	of	ADP
ejpam-5065	126	22	g.	g.	PROPN
ejpam-5065	126	23	consequently	consequently	ADV
ejpam-5065	126	24	,	,	PUNCT
ejpam-5065	126	25	γ2h(g	γ2h(g	PROPN
ejpam-5065	126	26	)	)	PUNCT
ejpam-5065	127	1	=	=	SYM
ejpam-5065	127	2	|v	|v	PROPN
ejpam-5065	127	3	(	(	PUNCT
ejpam-5065	127	4	g)|	g)|	PROPN
ejpam-5065	127	5	.	.	PUNCT
ejpam-5065	128	1	(	(	PUNCT
ejpam-5065	128	2	ii	ii	NOUN
ejpam-5065	128	3	)	)	PUNCT
ejpam-5065	128	4	suppose	suppose	VERB
ejpam-5065	128	5	that	that	SCONJ
ejpam-5065	128	6	γh(g	γh(g	NOUN
ejpam-5065	128	7	)	)	PUNCT
ejpam-5065	128	8	=	=	SYM
ejpam-5065	128	9	|v	|v	PROPN
ejpam-5065	128	10	(	(	PUNCT
ejpam-5065	128	11	g)|	g)|	NOUN
ejpam-5065	128	12	.	.	PUNCT
ejpam-5065	129	1	then	then	ADV
ejpam-5065	129	2	by	by	ADP
ejpam-5065	129	3	theorem	theorem	NOUN
ejpam-5065	129	4	1	1	NUM
ejpam-5065	129	5	,	,	PUNCT
ejpam-5065	129	6	γ2h(g	γ2h(g	PROPN
ejpam-5065	129	7	)	)	PUNCT
ejpam-5065	130	1	=	=	SYM
ejpam-5065	130	2	|v	|v	PROPN
ejpam-5065	130	3	(	(	PUNCT
ejpam-5065	130	4	g)|	g)|	NOUN
ejpam-5065	130	5	.	.	PUNCT
ejpam-5065	130	6	to	to	PART
ejpam-5065	130	7	see	see	VERB
ejpam-5065	130	8	that	that	SCONJ
ejpam-5065	130	9	the	the	DET
ejpam-5065	130	10	converse	converse	NOUN
ejpam-5065	130	11	is	be	AUX
ejpam-5065	130	12	not	not	PART
ejpam-5065	130	13	true	true	ADJ
ejpam-5065	130	14	,	,	PUNCT
ejpam-5065	130	15	conisder	conisder	VERB
ejpam-5065	130	16	p4	p4	ADJ
ejpam-5065	130	17	.	.	PUNCT
ejpam-5065	131	1	then	then	ADV
ejpam-5065	131	2	γ2h(p4	γ2h(p4	PROPN
ejpam-5065	131	3	)	)	PUNCT
ejpam-5065	131	4	=	=	SYM
ejpam-5065	131	5	4	4	NUM
ejpam-5065	131	6	by	by	ADP
ejpam-5065	131	7	(	(	PUNCT
ejpam-5065	131	8	i	i	NOUN
ejpam-5065	131	9	)	)	PUNCT
ejpam-5065	131	10	.	.	PUNCT
ejpam-5065	132	1	however	however	ADV
ejpam-5065	132	2	,	,	PUNCT
ejpam-5065	132	3	γh(p4	γh(p4	NOUN
ejpam-5065	132	4	)	)	PUNCT
ejpam-5065	132	5	=	=	SYM
ejpam-5065	132	6	2	2	X
ejpam-5065	132	7	.	.	X
ejpam-5065	133	1	the	the	DET
ejpam-5065	133	2	following	follow	VERB
ejpam-5065	133	3	definition	definition	NOUN
ejpam-5065	133	4	will	will	AUX
ejpam-5065	133	5	be	be	AUX
ejpam-5065	133	6	used	use	VERB
ejpam-5065	133	7	to	to	PART
ejpam-5065	133	8	characterize	characterize	VERB
ejpam-5065	133	9	2	2	NUM
ejpam-5065	133	10	-	-	PUNCT
ejpam-5065	133	11	hop	hop	NOUN
ejpam-5065	133	12	dominating	dominating	NOUN
ejpam-5065	133	13	sets	set	NOUN
ejpam-5065	133	14	in	in	ADP
ejpam-5065	133	15	the	the	DET
ejpam-5065	133	16	join	join	NOUN
ejpam-5065	133	17	of	of	ADP
ejpam-5065	133	18	two	two	NUM
ejpam-5065	133	19	graphs	graph	NOUN
ejpam-5065	133	20	.	.	PUNCT
ejpam-5065	134	1	definition	definition	NOUN
ejpam-5065	134	2	2	2	NUM
ejpam-5065	134	3	.	.	PUNCT
ejpam-5065	135	1	let	let	VERB
ejpam-5065	135	2	g	g	PRON
ejpam-5065	135	3	be	be	AUX
ejpam-5065	135	4	a	a	DET
ejpam-5065	135	5	graph	graph	NOUN
ejpam-5065	135	6	.	.	PUNCT
ejpam-5065	136	1	a	a	DET
ejpam-5065	136	2	subset	subset	NOUN
ejpam-5065	136	3	n	n	NOUN
ejpam-5065	136	4	of	of	ADP
ejpam-5065	136	5	a	a	DET
ejpam-5065	136	6	vertex	vertex	NOUN
ejpam-5065	136	7	-	-	PUNCT
ejpam-5065	136	8	set	set	VERB
ejpam-5065	136	9	v	v	NOUN
ejpam-5065	136	10	(	(	PUNCT
ejpam-5065	136	11	g	g	NOUN
ejpam-5065	136	12	)	)	PUNCT
ejpam-5065	136	13	of	of	ADP
ejpam-5065	136	14	g	g	PROPN
ejpam-5065	136	15	is	be	AUX
ejpam-5065	136	16	called	call	VERB
ejpam-5065	136	17	a	a	DET
ejpam-5065	136	18	2	2	NUM
ejpam-5065	136	19	-	-	PUNCT
ejpam-5065	136	20	pointwise	pointwise	ADJ
ejpam-5065	136	21	non	non	ADJ
ejpam-5065	136	22	-	-	ADJ
ejpam-5065	136	23	dominating	dominating	ADJ
ejpam-5065	136	24	if	if	SCONJ
ejpam-5065	136	25	for	for	ADP
ejpam-5065	136	26	every	every	DET
ejpam-5065	136	27	x	x	SYM
ejpam-5065	136	28	∈	∈	PROPN
ejpam-5065	136	29	v	v	NOUN
ejpam-5065	136	30	(	(	PUNCT
ejpam-5065	136	31	g)\n	g)\n	PROPN
ejpam-5065	136	32	,	,	PUNCT
ejpam-5065	136	33	there	there	PRON
ejpam-5065	136	34	exist	exist	VERB
ejpam-5065	136	35	at	at	ADV
ejpam-5065	136	36	least	least	ADV
ejpam-5065	136	37	two	two	NUM
ejpam-5065	136	38	distinct	distinct	ADJ
ejpam-5065	136	39	vertices	vertex	NOUN
ejpam-5065	136	40	a	a	DET
ejpam-5065	136	41	,	,	PUNCT
ejpam-5065	136	42	b	b	X
ejpam-5065	136	43	∈	∈	PROPN
ejpam-5065	136	44	n	n	PRON
ejpam-5065	137	1	such	such	ADJ
ejpam-5065	137	2	that	that	SCONJ
ejpam-5065	137	3	x	x	SYM
ejpam-5065	137	4	/∈	/∈	PUNCT
ejpam-5065	137	5	ng(a	ng(a	NUM
ejpam-5065	137	6	)	)	PUNCT
ejpam-5065	137	7	and	and	CCONJ
ejpam-5065	137	8	x	x	PART
ejpam-5065	137	9	/∈	/∈	NOUN
ejpam-5065	137	10	ng(b	ng(b	NUM
ejpam-5065	137	11	)	)	PUNCT
ejpam-5065	137	12	.	.	PUNCT
ejpam-5065	138	1	the	the	DET
ejpam-5065	138	2	minimum	minimum	ADJ
ejpam-5065	138	3	cardinality	cardinality	NOUN
ejpam-5065	138	4	of	of	ADP
ejpam-5065	138	5	a	a	DET
ejpam-5065	138	6	2	2	NUM
ejpam-5065	138	7	-	-	PUNCT
ejpam-5065	138	8	pointwise	pointwise	ADJ
ejpam-5065	138	9	non	non	ADJ
ejpam-5065	138	10	-	-	ADJ
ejpam-5065	138	11	dominating	dominating	ADJ
ejpam-5065	138	12	set	set	NOUN
ejpam-5065	138	13	of	of	ADP
ejpam-5065	138	14	g	g	PROPN
ejpam-5065	138	15	is	be	AUX
ejpam-5065	138	16	the	the	DET
ejpam-5065	138	17	2	2	NUM
ejpam-5065	138	18	-	-	PUNCT
ejpam-5065	138	19	pointwise	pointwise	ADJ
ejpam-5065	138	20	non	non	ADJ
ejpam-5065	138	21	-	-	ADJ
ejpam-5065	138	22	domination	domination	ADJ
ejpam-5065	138	23	number	number	NOUN
ejpam-5065	138	24	of	of	ADP
ejpam-5065	138	25	g	g	NOUN
ejpam-5065	138	26	,	,	PUNCT
ejpam-5065	138	27	and	and	CCONJ
ejpam-5065	138	28	is	be	AUX
ejpam-5065	138	29	denoted	denote	VERB
ejpam-5065	138	30	by	by	ADP
ejpam-5065	138	31	pnd2(g	pnd2(g	NOUN
ejpam-5065	138	32	)	)	PUNCT
ejpam-5065	138	33	.	.	PUNCT
ejpam-5065	139	1	remark	remark	NOUN
ejpam-5065	139	2	2	2	NUM
ejpam-5065	139	3	.	.	PUNCT
ejpam-5065	140	1	let	let	VERB
ejpam-5065	140	2	g	g	PRON
ejpam-5065	140	3	be	be	AUX
ejpam-5065	140	4	a	a	DET
ejpam-5065	140	5	graph	graph	NOUN
ejpam-5065	140	6	.	.	PUNCT
ejpam-5065	141	1	then	then	ADV
ejpam-5065	141	2	j.	j.	PROPN
ejpam-5065	141	3	hassan	hassan	PROPN
ejpam-5065	141	4	,	,	PUNCT
ejpam-5065	141	5	a.	a.	PROPN
ejpam-5065	141	6	gomorez	gomorez	PROPN
ejpam-5065	141	7	,	,	PUNCT
ejpam-5065	141	8	l.	l.	PROPN
ejpam-5065	141	9	laja	laja	PROPN
ejpam-5065	141	10	,	,	PUNCT
ejpam-5065	141	11	e.	e.	PROPN
ejpam-5065	141	12	ahmad	ahmad	PROPN
ejpam-5065	141	13	/	/	SYM
ejpam-5065	141	14	eur	eur	PROPN
ejpam-5065	141	15	.	.	PUNCT
ejpam-5065	142	1	j.	j.	PROPN
ejpam-5065	142	2	pure	pure	PROPN
ejpam-5065	142	3	appl	appl	PROPN
ejpam-5065	142	4	.	.	PROPN
ejpam-5065	142	5	math	math	PROPN
ejpam-5065	142	6	,	,	PUNCT
ejpam-5065	142	7	17	17	NUM
ejpam-5065	142	8	(	(	PUNCT
ejpam-5065	142	9	2	2	NUM
ejpam-5065	142	10	)	)	PUNCT
ejpam-5065	142	11	(	(	PUNCT
ejpam-5065	142	12	2024	2024	NUM
ejpam-5065	142	13	)	)	PUNCT
ejpam-5065	142	14	,	,	PUNCT
ejpam-5065	142	15	852	852	NUM
ejpam-5065	142	16	-	-	SYM
ejpam-5065	142	17	859	859	NUM
ejpam-5065	142	18	856	856	NUM
ejpam-5065	142	19	(	(	PUNCT
ejpam-5065	142	20	i	i	NOUN
ejpam-5065	142	21	)	)	PUNCT
ejpam-5065	142	22	every	every	DET
ejpam-5065	142	23	2	2	NUM
ejpam-5065	142	24	-	-	PUNCT
ejpam-5065	142	25	pointwise	pointwise	ADJ
ejpam-5065	142	26	non	non	ADJ
ejpam-5065	142	27	-	-	ADJ
ejpam-5065	142	28	dominating	dominating	ADJ
ejpam-5065	142	29	set	set	NOUN
ejpam-5065	142	30	is	be	AUX
ejpam-5065	142	31	a	a	DET
ejpam-5065	142	32	pointwise	pointwise	ADJ
ejpam-5065	142	33	non	non	ADJ
ejpam-5065	142	34	-	-	ADJ
ejpam-5065	142	35	dominating	dominating	ADJ
ejpam-5065	142	36	;	;	PUNCT
ejpam-5065	142	37	(	(	PUNCT
ejpam-5065	142	38	ii	ii	NOUN
ejpam-5065	142	39	)	)	PUNCT
ejpam-5065	142	40	pnd(g	pnd(g	PROPN
ejpam-5065	142	41	)	)	PUNCT
ejpam-5065	142	42	≤	≤	NOUN
ejpam-5065	142	43	pnd2(g	pnd2(g	NOUN
ejpam-5065	142	44	)	)	PUNCT
ejpam-5065	142	45	;	;	PUNCT
ejpam-5065	142	46	(	(	PUNCT
ejpam-5065	142	47	iii	iii	X
ejpam-5065	142	48	)	)	PUNCT
ejpam-5065	142	49	pnd2(kn	pnd2(kn	NOUN
ejpam-5065	142	50	)	)	PUNCT
ejpam-5065	142	51	=	=	SYM
ejpam-5065	143	1	n	n	PROPN
ejpam-5065	143	2	for	for	ADP
ejpam-5065	143	3	all	all	DET
ejpam-5065	143	4	positive	positive	ADJ
ejpam-5065	143	5	integer	integer	NOUN
ejpam-5065	143	6	n	n	PRON
ejpam-5065	143	7	≥	≥	NOUN
ejpam-5065	143	8	1	1	NUM
ejpam-5065	143	9	;	;	PUNCT
ejpam-5065	143	10	(	(	PUNCT
ejpam-5065	143	11	iv	iv	X
ejpam-5065	143	12	)	)	PUNCT
ejpam-5065	143	13	pnd2(kn	pnd2(kn	NUM
ejpam-5065	143	14	)	)	PUNCT
ejpam-5065	144	1	=	=	PRON
ejpam-5065	144	2	{	{	PUNCT
ejpam-5065	144	3	1	1	NUM
ejpam-5065	144	4	,	,	PUNCT
ejpam-5065	144	5	n	n	NOUN
ejpam-5065	144	6	=	=	SYM
ejpam-5065	144	7	1	1	NUM
ejpam-5065	144	8	2	2	NUM
ejpam-5065	144	9	,	,	PUNCT
ejpam-5065	144	10	n	n	PRON
ejpam-5065	144	11	≥	≥	NOUN
ejpam-5065	144	12	2	2	NUM
ejpam-5065	144	13	;	;	PUNCT
ejpam-5065	144	14	and	and	CCONJ
ejpam-5065	144	15	(	(	PUNCT
ejpam-5065	144	16	v	v	NOUN
ejpam-5065	144	17	)	)	PUNCT
ejpam-5065	144	18	1	1	NUM
ejpam-5065	144	19	≤	≤	NOUN
ejpam-5065	144	20	pnd2(g	pnd2(g	NOUN
ejpam-5065	144	21	)	)	PUNCT
ejpam-5065	144	22	≤	≤	NUM
ejpam-5065	144	23	|v	|v	X
ejpam-5065	144	24	(	(	PUNCT
ejpam-5065	144	25	g)|	g)|	NOUN
ejpam-5065	144	26	.	.	PUNCT
ejpam-5065	144	27	proposition	proposition	NOUN
ejpam-5065	144	28	1	1	NUM
ejpam-5065	144	29	.	.	PUNCT
ejpam-5065	145	1	let	let	VERB
ejpam-5065	145	2	n	n	PRON
ejpam-5065	145	3	be	be	AUX
ejpam-5065	145	4	a	a	DET
ejpam-5065	145	5	positive	positive	ADJ
ejpam-5065	145	6	integer	integer	NOUN
ejpam-5065	145	7	.	.	PUNCT
ejpam-5065	146	1	then	then	ADV
ejpam-5065	146	2	(	(	PUNCT
ejpam-5065	146	3	i	i	NOUN
ejpam-5065	146	4	)	)	PUNCT
ejpam-5065	146	5	pnd2(pn	pnd2(pn	PROPN
ejpam-5065	146	6	)	)	PUNCT
ejpam-5065	146	7	=	=	SYM
ejpam-5065	146	8	{	{	PUNCT
ejpam-5065	146	9	n	n	NOUN
ejpam-5065	146	10	,	,	PUNCT
ejpam-5065	146	11	1	1	NUM
ejpam-5065	146	12	≤	≤	NUM
ejpam-5065	146	13	n	n	PRON
ejpam-5065	146	14	≤	≤	NUM
ejpam-5065	146	15	3	3	NUM
ejpam-5065	146	16	3	3	NUM
ejpam-5065	146	17	,	,	PUNCT
ejpam-5065	146	18	otherwise	otherwise	ADV
ejpam-5065	146	19	(	(	PUNCT
ejpam-5065	146	20	ii	ii	NOUN
ejpam-5065	146	21	)	)	PUNCT
ejpam-5065	146	22	pnd2(cn	pnd2(cn	PROPN
ejpam-5065	146	23	)	)	PUNCT
ejpam-5065	146	24	=	=	PUNCT
ejpam-5065	146	25	{	{	PUNCT
ejpam-5065	146	26	n	n	NOUN
ejpam-5065	146	27	,	,	PUNCT
ejpam-5065	146	28	n	n	NOUN
ejpam-5065	146	29	=	=	SYM
ejpam-5065	146	30	3	3	NUM
ejpam-5065	146	31	,	,	PUNCT
ejpam-5065	146	32	4	4	NUM
ejpam-5065	146	33	3	3	NUM
ejpam-5065	146	34	,	,	PUNCT
ejpam-5065	146	35	otherwise	otherwise	ADV
ejpam-5065	146	36	proof	proof	NOUN
ejpam-5065	146	37	.	.	PUNCT
ejpam-5065	147	1	(	(	PUNCT
ejpam-5065	147	2	i	i	NOUN
ejpam-5065	147	3	)	)	PUNCT
ejpam-5065	147	4	since	since	SCONJ
ejpam-5065	147	5	pnd(pn	pnd(pn	NOUN
ejpam-5065	147	6	)	)	PUNCT
ejpam-5065	147	7	=	=	SYM
ejpam-5065	147	8	n	n	NOUN
ejpam-5065	147	9	for	for	ADP
ejpam-5065	147	10	n	n	NOUN
ejpam-5065	147	11	=	=	SYM
ejpam-5065	147	12	1	1	NUM
ejpam-5065	147	13	,	,	PUNCT
ejpam-5065	147	14	2	2	NUM
ejpam-5065	147	15	,	,	PUNCT
ejpam-5065	147	16	it	it	PRON
ejpam-5065	147	17	follows	follow	VERB
ejpam-5065	147	18	that	that	SCONJ
ejpam-5065	147	19	pnd2(pn	pnd2(pn	NOUN
ejpam-5065	147	20	)	)	PUNCT
ejpam-5065	147	21	=	=	SYM
ejpam-5065	148	1	n	n	NOUN
ejpam-5065	148	2	for	for	ADP
ejpam-5065	148	3	n	n	NOUN
ejpam-5065	148	4	=	=	SYM
ejpam-5065	148	5	1	1	NUM
ejpam-5065	148	6	,	,	PUNCT
ejpam-5065	148	7	2	2	NUM
ejpam-5065	148	8	.	.	X
ejpam-5065	149	1	for	for	ADP
ejpam-5065	149	2	n	n	NOUN
ejpam-5065	149	3	=	=	SYM
ejpam-5065	149	4	3	3	NUM
ejpam-5065	149	5	,	,	PUNCT
ejpam-5065	149	6	let	let	VERB
ejpam-5065	149	7	v	v	NOUN
ejpam-5065	149	8	(	(	PUNCT
ejpam-5065	149	9	p3	p3	PROPN
ejpam-5065	149	10	)	)	PUNCT
ejpam-5065	150	1	=	=	PRON
ejpam-5065	150	2	{	{	PUNCT
ejpam-5065	150	3	v1	v1	PROPN
ejpam-5065	150	4	,	,	PUNCT
ejpam-5065	150	5	v2	v2	PROPN
ejpam-5065	150	6	,	,	PUNCT
ejpam-5065	150	7	v3	v3	PROPN
ejpam-5065	150	8	}	}	PUNCT
ejpam-5065	150	9	.	.	PUNCT
ejpam-5065	151	1	since	since	SCONJ
ejpam-5065	151	2	pnd(p3	pnd(p3	PROPN
ejpam-5065	151	3	)	)	PUNCT
ejpam-5065	151	4	=	=	SYM
ejpam-5065	151	5	2	2	NUM
ejpam-5065	151	6	,	,	PUNCT
ejpam-5065	151	7	pnd2(p3	pnd2(p3	PROPN
ejpam-5065	151	8	)	)	PUNCT
ejpam-5065	151	9	≥	≥	NOUN
ejpam-5065	151	10	2	2	NUM
ejpam-5065	151	11	.	.	PUNCT
ejpam-5065	151	12	if	if	SCONJ
ejpam-5065	151	13	pnd2(p3	pnd2(p3	PROPN
ejpam-5065	151	14	)	)	PUNCT
ejpam-5065	151	15	=	=	SYM
ejpam-5065	151	16	2	2	NUM
ejpam-5065	151	17	,	,	PUNCT
ejpam-5065	151	18	then	then	ADV
ejpam-5065	151	19	there	there	PRON
ejpam-5065	151	20	exists	exist	VERB
ejpam-5065	151	21	vi	vi	PROPN
ejpam-5065	151	22	∈	∈	PROPN
ejpam-5065	151	23	v	v	NOUN
ejpam-5065	151	24	(	(	PUNCT
ejpam-5065	151	25	p3	p3	PROPN
ejpam-5065	151	26	)	)	PUNCT
ejpam-5065	151	27	such	such	ADJ
ejpam-5065	151	28	that	that	DET
ejpam-5065	151	29	vi	vi	PROPN
ejpam-5065	152	1	/∈	/∈	PROPN
ejpam-5065	153	1	p	p	NOUN
ejpam-5065	153	2	,	,	PUNCT
ejpam-5065	153	3	where	where	SCONJ
ejpam-5065	153	4	p	p	NOUN
ejpam-5065	153	5	is	be	AUX
ejpam-5065	153	6	a	a	DET
ejpam-5065	153	7	minimum	minimum	ADJ
ejpam-5065	153	8	2	2	NUM
ejpam-5065	153	9	-	-	PUNCT
ejpam-5065	153	10	pointwise	pointwise	ADV
ejpam-5065	153	11	nondominating	nondominate	VERB
ejpam-5065	153	12	set	set	NOUN
ejpam-5065	153	13	of	of	ADP
ejpam-5065	153	14	p3	p3	PROPN
ejpam-5065	153	15	for	for	ADP
ejpam-5065	153	16	some	some	DET
ejpam-5065	153	17	i	i	PRON
ejpam-5065	153	18	∈	∈	PROPN
ejpam-5065	153	19	{	{	PUNCT
ejpam-5065	153	20	1	1	NUM
ejpam-5065	153	21	,	,	PUNCT
ejpam-5065	153	22	2	2	NUM
ejpam-5065	153	23	,	,	PUNCT
ejpam-5065	153	24	3	3	NUM
ejpam-5065	153	25	}	}	PUNCT
ejpam-5065	153	26	.	.	PUNCT
ejpam-5065	154	1	suppose	suppose	VERB
ejpam-5065	154	2	that	that	SCONJ
ejpam-5065	154	3	vi	vi	PROPN
ejpam-5065	154	4	=	=	SYM
ejpam-5065	154	5	v1	v1	NOUN
ejpam-5065	154	6	.	.	PUNCT
ejpam-5065	155	1	then	then	ADV
ejpam-5065	155	2	v3	v3	PROPN
ejpam-5065	155	3	is	be	AUX
ejpam-5065	155	4	the	the	DET
ejpam-5065	155	5	only	only	ADJ
ejpam-5065	155	6	vertex	vertex	NOUN
ejpam-5065	155	7	in	in	ADP
ejpam-5065	155	8	p	p	PRON
ejpam-5065	155	9	such	such	ADJ
ejpam-5065	155	10	that	that	DET
ejpam-5065	155	11	v1	v1	NOUN
ejpam-5065	155	12	/∈	/∈	PUNCT
ejpam-5065	156	1	ng(v3	ng(v3	NOUN
ejpam-5065	156	2	)	)	PUNCT
ejpam-5065	156	3	,	,	PUNCT
ejpam-5065	156	4	which	which	PRON
ejpam-5065	156	5	is	be	AUX
ejpam-5065	156	6	a	a	DET
ejpam-5065	156	7	contradiction	contradiction	NOUN
ejpam-5065	156	8	.	.	PUNCT
ejpam-5065	157	1	similarly	similarly	ADV
ejpam-5065	157	2	,	,	PUNCT
ejpam-5065	157	3	if	if	SCONJ
ejpam-5065	157	4	vi	vi	PROPN
ejpam-5065	157	5	=	=	SYM
ejpam-5065	157	6	v3	v3	PROPN
ejpam-5065	157	7	.	.	PUNCT
ejpam-5065	158	1	now	now	ADV
ejpam-5065	158	2	,	,	PUNCT
ejpam-5065	158	3	assume	assume	VERB
ejpam-5065	158	4	that	that	SCONJ
ejpam-5065	158	5	vi	vi	NOUN
ejpam-5065	158	6	=	=	SYM
ejpam-5065	158	7	v2	v2	PROPN
ejpam-5065	158	8	.	.	PUNCT
ejpam-5065	159	1	observe	observe	VERB
ejpam-5065	159	2	that	that	SCONJ
ejpam-5065	159	3	vertices	vertice	VERB
ejpam-5065	159	4	v1	v1	VERB
ejpam-5065	159	5	and	and	CCONJ
ejpam-5065	159	6	v3	v3	PROPN
ejpam-5065	159	7	are	be	AUX
ejpam-5065	159	8	both	both	ADV
ejpam-5065	159	9	adjacent	adjacent	ADJ
ejpam-5065	159	10	to	to	PART
ejpam-5065	159	11	v2	v2	VERB
ejpam-5065	159	12	,	,	PUNCT
ejpam-5065	159	13	that	that	ADV
ejpam-5065	159	14	is	is	ADV
ejpam-5065	159	15	,	,	PUNCT
ejpam-5065	159	16	v1	v1	PROPN
ejpam-5065	159	17	,	,	PUNCT
ejpam-5065	159	18	v3	v3	PROPN
ejpam-5065	159	19	∈	∈	PROPN
ejpam-5065	159	20	np3(v2	np3(v2	ADV
ejpam-5065	159	21	)	)	PUNCT
ejpam-5065	159	22	,	,	PUNCT
ejpam-5065	159	23	a	a	DET
ejpam-5065	159	24	contradiction	contradiction	NOUN
ejpam-5065	159	25	.	.	PUNCT
ejpam-5065	160	1	therefore	therefore	ADV
ejpam-5065	160	2	,	,	PUNCT
ejpam-5065	160	3	pnd2(p3	pnd2(p3	PROPN
ejpam-5065	160	4	)	)	PUNCT
ejpam-5065	160	5	=	=	SYM
ejpam-5065	160	6	3	3	X
ejpam-5065	160	7	.	.	PUNCT
ejpam-5065	160	8	suppose	suppose	VERB
ejpam-5065	160	9	that	that	SCONJ
ejpam-5065	160	10	n	n	PROPN
ejpam-5065	160	11	≥	≥	NUM
ejpam-5065	160	12	4	4	NUM
ejpam-5065	160	13	.	.	PUNCT
ejpam-5065	161	1	let	let	VERB
ejpam-5065	161	2	v	v	X
ejpam-5065	161	3	(	(	PUNCT
ejpam-5065	161	4	pn	pn	NOUN
ejpam-5065	161	5	)	)	PUNCT
ejpam-5065	161	6	=	=	SYM
ejpam-5065	161	7	{	{	PUNCT
ejpam-5065	161	8	v1	v1	PROPN
ejpam-5065	161	9	,	,	PUNCT
ejpam-5065	161	10	v2	v2	PROPN
ejpam-5065	161	11	,	,	PUNCT
ejpam-5065	161	12	v3	v3	PROPN
ejpam-5065	161	13	,	,	PUNCT
ejpam-5065	161	14	.	.	PUNCT
ejpam-5065	161	15	.	.	PUNCT
ejpam-5065	162	1	.	.	PUNCT
ejpam-5065	163	1	,	,	PUNCT
ejpam-5065	163	2	vn	vn	PROPN
ejpam-5065	163	3	}	}	PUNCT
ejpam-5065	163	4	.	.	PUNCT
ejpam-5065	164	1	since	since	SCONJ
ejpam-5065	164	2	pnd(pn	pnd(pn	NOUN
ejpam-5065	164	3	)	)	PUNCT
ejpam-5065	164	4	=	=	SYM
ejpam-5065	164	5	2	2	NUM
ejpam-5065	164	6	for	for	ADP
ejpam-5065	164	7	all	all	DET
ejpam-5065	164	8	n	n	PRON
ejpam-5065	164	9	≥	≥	NOUN
ejpam-5065	164	10	4	4	NUM
ejpam-5065	164	11	,	,	PUNCT
ejpam-5065	164	12	it	it	PRON
ejpam-5065	164	13	follows	follow	VERB
ejpam-5065	164	14	that	that	SCONJ
ejpam-5065	164	15	pnd2(pn	pnd2(pn	PROPN
ejpam-5065	164	16	)	)	PUNCT
ejpam-5065	164	17	≥	≥	NOUN
ejpam-5065	164	18	2	2	NUM
ejpam-5065	164	19	for	for	ADP
ejpam-5065	164	20	all	all	DET
ejpam-5065	164	21	n	n	PRON
ejpam-5065	164	22	≥	≥	NOUN
ejpam-5065	164	23	4	4	NUM
ejpam-5065	164	24	.	.	PUNCT
ejpam-5065	165	1	assume	assume	VERB
ejpam-5065	165	2	that	that	SCONJ
ejpam-5065	165	3	pnd2(pn	pnd2(pn	NOUN
ejpam-5065	165	4	)	)	PUNCT
ejpam-5065	165	5	=	=	SYM
ejpam-5065	165	6	2	2	NUM
ejpam-5065	165	7	for	for	ADP
ejpam-5065	165	8	all	all	DET
ejpam-5065	165	9	n	n	PRON
ejpam-5065	165	10	≥	≥	NOUN
ejpam-5065	165	11	4	4	NUM
ejpam-5065	165	12	.	.	PUNCT
ejpam-5065	166	1	let	let	VERB
ejpam-5065	166	2	q	q	NOUN
ejpam-5065	166	3	=	=	PUNCT
ejpam-5065	166	4	{	{	PUNCT
ejpam-5065	166	5	vi	vi	PROPN
ejpam-5065	166	6	,	,	PUNCT
ejpam-5065	166	7	vj	vj	AUX
ejpam-5065	166	8	}	}	PUNCT
ejpam-5065	166	9	be	be	AUX
ejpam-5065	166	10	a	a	DET
ejpam-5065	166	11	minimum	minimum	ADJ
ejpam-5065	166	12	2	2	NUM
ejpam-5065	166	13	-	-	PUNCT
ejpam-5065	166	14	pointwise	pointwise	ADJ
ejpam-5065	166	15	non	non	ADJ
ejpam-5065	166	16	-	-	ADJ
ejpam-5065	166	17	dominating	dominating	ADJ
ejpam-5065	166	18	set	set	NOUN
ejpam-5065	166	19	of	of	ADP
ejpam-5065	166	20	pn	pn	PROPN
ejpam-5065	166	21	,	,	PUNCT
ejpam-5065	166	22	where	where	SCONJ
ejpam-5065	166	23	j	j	PROPN
ejpam-5065	166	24	<	<	X
ejpam-5065	166	25	i	i	PROPN
ejpam-5065	166	26	,	,	PUNCT
ejpam-5065	166	27	i	i	PRON
ejpam-5065	166	28	,	,	PUNCT
ejpam-5065	166	29	j	j	PROPN
ejpam-5065	166	30	∈	∈	PROPN
ejpam-5065	166	31	{	{	PUNCT
ejpam-5065	166	32	1	1	NUM
ejpam-5065	166	33	,	,	PUNCT
ejpam-5065	166	34	2	2	NUM
ejpam-5065	166	35	,	,	PUNCT
ejpam-5065	166	36	.	.	PUNCT
ejpam-5065	166	37	.	.	PUNCT
ejpam-5065	167	1	.	.	PUNCT
ejpam-5065	167	2	,	,	PUNCT
ejpam-5065	167	3	n	n	CCONJ
ejpam-5065	167	4	}	}	PUNCT
ejpam-5065	167	5	.	.	PUNCT
ejpam-5065	168	1	assume	assume	VERB
ejpam-5065	168	2	that	that	SCONJ
ejpam-5065	168	3	⟨q⟩	⟨q⟩	PUNCT
ejpam-5065	168	4	is	be	AUX
ejpam-5065	168	5	connected	connect	VERB
ejpam-5065	168	6	.	.	PUNCT
ejpam-5065	169	1	if	if	SCONJ
ejpam-5065	169	2	vi	vi	PROPN
ejpam-5065	169	3	=	=	SYM
ejpam-5065	169	4	vn	vn	PROPN
ejpam-5065	169	5	,	,	PUNCT
ejpam-5065	169	6	then	then	ADV
ejpam-5065	169	7	vj	vj	INTJ
ejpam-5065	169	8	=	=	PUNCT
ejpam-5065	169	9	vn−1	vn−1	PROPN
ejpam-5065	169	10	.	.	PUNCT
ejpam-5065	170	1	thus	thus	ADV
ejpam-5065	170	2	,	,	PUNCT
ejpam-5065	170	3	vi	vi	PROPN
ejpam-5065	170	4	=	=	SYM
ejpam-5065	170	5	vn	vn	PROPN
ejpam-5065	170	6	is	be	AUX
ejpam-5065	170	7	the	the	DET
ejpam-5065	170	8	only	only	ADJ
ejpam-5065	170	9	vertex	vertex	NOUN
ejpam-5065	170	10	in	in	ADP
ejpam-5065	170	11	q	q	NOUN
ejpam-5065	170	12	such	such	ADJ
ejpam-5065	170	13	that	that	DET
ejpam-5065	170	14	vn−2	vn−2	PROPN
ejpam-5065	170	15	/∈	/∈	PUNCT
ejpam-5065	170	16	npn(vi	npn(vi	NOUN
ejpam-5065	170	17	)	)	PUNCT
ejpam-5065	170	18	,	,	PUNCT
ejpam-5065	170	19	a	a	DET
ejpam-5065	170	20	contradiction	contradiction	NOUN
ejpam-5065	170	21	.	.	PUNCT
ejpam-5065	171	1	if	if	SCONJ
ejpam-5065	171	2	vi	vi	NOUN
ejpam-5065	171	3	=	=	SYM
ejpam-5065	171	4	v2	v2	PROPN
ejpam-5065	171	5	,	,	PUNCT
ejpam-5065	171	6	then	then	ADV
ejpam-5065	171	7	vj	vj	PROPN
ejpam-5065	171	8	=	=	PUNCT
ejpam-5065	171	9	v1	v1	PROPN
ejpam-5065	171	10	.	.	PUNCT
ejpam-5065	172	1	thus	thus	ADV
ejpam-5065	172	2	,	,	PUNCT
ejpam-5065	172	3	vj	vj	ADP
ejpam-5065	172	4	=	=	PUNCT
ejpam-5065	172	5	v1	v1	PROPN
ejpam-5065	172	6	is	be	AUX
ejpam-5065	172	7	the	the	DET
ejpam-5065	172	8	only	only	ADJ
ejpam-5065	172	9	vertex	vertex	NOUN
ejpam-5065	172	10	in	in	ADP
ejpam-5065	172	11	q	q	NOUN
ejpam-5065	172	12	such	such	ADJ
ejpam-5065	172	13	that	that	DET
ejpam-5065	172	14	v3	v3	PROPN
ejpam-5065	172	15	/∈	/∈	PUNCT
ejpam-5065	172	16	npn(vj	npn(vj	NOUN
ejpam-5065	172	17	)	)	PUNCT
ejpam-5065	172	18	,	,	PUNCT
ejpam-5065	172	19	a	a	DET
ejpam-5065	172	20	contradiction	contradiction	NOUN
ejpam-5065	172	21	.	.	PUNCT
ejpam-5065	173	1	similarly	similarly	ADV
ejpam-5065	173	2	,	,	PUNCT
ejpam-5065	173	3	when	when	SCONJ
ejpam-5065	173	4	vi	vi	PROPN
ejpam-5065	173	5	=	=	SYM
ejpam-5065	173	6	vr	vr	PROPN
ejpam-5065	173	7	,	,	PUNCT
ejpam-5065	173	8	where	where	SCONJ
ejpam-5065	173	9	r	r	NOUN
ejpam-5065	173	10	∈	∈	PROPN
ejpam-5065	173	11	{	{	PUNCT
ejpam-5065	173	12	3	3	NUM
ejpam-5065	173	13	,	,	PUNCT
ejpam-5065	173	14	4	4	NUM
ejpam-5065	173	15	,	,	PUNCT
ejpam-5065	173	16	.	.	PUNCT
ejpam-5065	173	17	.	.	PUNCT
ejpam-5065	173	18	.	.	PUNCT
ejpam-5065	174	1	,	,	PUNCT
ejpam-5065	174	2	n−	n−	NOUN
ejpam-5065	174	3	1	1	NUM
ejpam-5065	174	4	}	}	PUNCT
ejpam-5065	174	5	.	.	PUNCT
ejpam-5065	175	1	next	next	ADV
ejpam-5065	175	2	,	,	PUNCT
ejpam-5065	175	3	assume	assume	VERB
ejpam-5065	175	4	that	that	SCONJ
ejpam-5065	175	5	⟨q⟩	⟨q⟩	PUNCT
ejpam-5065	175	6	is	be	AUX
ejpam-5065	175	7	disconnected	disconnect	VERB
ejpam-5065	175	8	.	.	PUNCT
ejpam-5065	176	1	if	if	SCONJ
ejpam-5065	176	2	dpn(vi	dpn(vi	NOUN
ejpam-5065	176	3	,	,	PUNCT
ejpam-5065	176	4	vj	vj	ADJ
ejpam-5065	176	5	)	)	PUNCT
ejpam-5065	176	6	=	=	SYM
ejpam-5065	176	7	2	2	NUM
ejpam-5065	176	8	,	,	PUNCT
ejpam-5065	176	9	then	then	ADV
ejpam-5065	176	10	there	there	PRON
ejpam-5065	176	11	exists	exist	VERB
ejpam-5065	176	12	vs	vs	ADP
ejpam-5065	176	13	∈	∈	PROPN
ejpam-5065	176	14	v	v	NOUN
ejpam-5065	176	15	(	(	PUNCT
ejpam-5065	176	16	pn)\q	pn)\q	NOUN
ejpam-5065	176	17	such	such	ADJ
ejpam-5065	176	18	that	that	SCONJ
ejpam-5065	176	19	vs	vs	ADP
ejpam-5065	176	20	∈	∈	PROPN
ejpam-5065	176	21	npn(vi	npn(vi	NOUN
ejpam-5065	176	22	)	)	PUNCT
ejpam-5065	176	23	∩	∩	NOUN
ejpam-5065	176	24	npn(vj	npn(vj	NOUN
ejpam-5065	176	25	)	)	PUNCT
ejpam-5065	176	26	for	for	ADP
ejpam-5065	176	27	some	some	PRON
ejpam-5065	176	28	s	s	VERB
ejpam-5065	176	29	̸=	̸=	PROPN
ejpam-5065	176	30	i	i	PROPN
ejpam-5065	176	31	,	,	PUNCT
ejpam-5065	176	32	j	j	PROPN
ejpam-5065	176	33	,	,	PUNCT
ejpam-5065	176	34	which	which	PRON
ejpam-5065	176	35	is	be	AUX
ejpam-5065	176	36	a	a	DET
ejpam-5065	176	37	contradiction	contradiction	NOUN
ejpam-5065	176	38	.	.	PUNCT
ejpam-5065	177	1	thus	thus	ADV
ejpam-5065	177	2	,	,	PUNCT
ejpam-5065	177	3	dpn(vi	dpn(vi	NOUN
ejpam-5065	177	4	,	,	PUNCT
ejpam-5065	177	5	vj	vj	PROPN
ejpam-5065	177	6	)	)	PUNCT
ejpam-5065	177	7	≥	≥	NOUN
ejpam-5065	177	8	3	3	NUM
ejpam-5065	177	9	.	.	PUNCT
ejpam-5065	178	1	let	let	VERB
ejpam-5065	178	2	vk	vk	VERB
ejpam-5065	178	3	∈	∈	PROPN
ejpam-5065	178	4	npn(vi	npn(vi	NOUN
ejpam-5065	178	5	)	)	PUNCT
ejpam-5065	178	6	.	.	PUNCT
ejpam-5065	179	1	then	then	ADV
ejpam-5065	179	2	vj	vj	INTJ
ejpam-5065	179	3	is	be	AUX
ejpam-5065	179	4	the	the	DET
ejpam-5065	179	5	only	only	ADJ
ejpam-5065	179	6	vertex	vertex	NOUN
ejpam-5065	179	7	in	in	ADP
ejpam-5065	179	8	q	q	NOUN
ejpam-5065	179	9	such	such	ADJ
ejpam-5065	179	10	that	that	DET
ejpam-5065	179	11	vk	vk	NOUN
ejpam-5065	179	12	/∈	/∈	PUNCT
ejpam-5065	179	13	npn(vj	npn(vj	NOUN
ejpam-5065	179	14	)	)	PUNCT
ejpam-5065	179	15	,	,	PUNCT
ejpam-5065	179	16	a	a	DET
ejpam-5065	179	17	contradiction	contradiction	NOUN
ejpam-5065	179	18	.	.	PUNCT
ejpam-5065	180	1	therefore	therefore	ADV
ejpam-5065	180	2	,	,	PUNCT
ejpam-5065	180	3	pnd2(pn	pnd2(pn	PROPN
ejpam-5065	180	4	)	)	PUNCT
ejpam-5065	180	5	≥	≥	NOUN
ejpam-5065	180	6	3	3	NUM
ejpam-5065	180	7	for	for	ADP
ejpam-5065	180	8	all	all	DET
ejpam-5065	180	9	n	n	PRON
ejpam-5065	180	10	≥	≥	NOUN
ejpam-5065	180	11	4	4	NUM
ejpam-5065	180	12	.	.	PUNCT
ejpam-5065	180	13	now	now	ADV
ejpam-5065	180	14	,	,	PUNCT
ejpam-5065	180	15	let	let	VERB
ejpam-5065	180	16	s	s	PRON
ejpam-5065	180	17	=	=	NOUN
ejpam-5065	180	18	{	{	PUNCT
ejpam-5065	180	19	v1	v1	PROPN
ejpam-5065	180	20	,	,	PUNCT
ejpam-5065	180	21	v2	v2	PROPN
ejpam-5065	180	22	,	,	PUNCT
ejpam-5065	180	23	v3	v3	PROPN
ejpam-5065	180	24	}	}	PUNCT
ejpam-5065	180	25	⊆	⊆	NUM
ejpam-5065	180	26	v	v	NOUN
ejpam-5065	180	27	(	(	PUNCT
ejpam-5065	180	28	pn	pn	NOUN
ejpam-5065	180	29	)	)	PUNCT
ejpam-5065	180	30	.	.	PUNCT
ejpam-5065	181	1	let	let	VERB
ejpam-5065	181	2	vt	vt	PROPN
ejpam-5065	181	3	∈	∈	PROPN
ejpam-5065	181	4	v	v	X
ejpam-5065	181	5	(	(	PUNCT
ejpam-5065	181	6	pn)\s	pn)\s	NOUN
ejpam-5065	181	7	,	,	PUNCT
ejpam-5065	181	8	where	where	SCONJ
ejpam-5065	181	9	t	t	PROPN
ejpam-5065	181	10	∈	∈	PROPN
ejpam-5065	181	11	{	{	PUNCT
ejpam-5065	181	12	4	4	NUM
ejpam-5065	181	13	,	,	PUNCT
ejpam-5065	181	14	5	5	NUM
ejpam-5065	181	15	,	,	PUNCT
ejpam-5065	181	16	.	.	PUNCT
ejpam-5065	181	17	.	.	PUNCT
ejpam-5065	182	1	.	.	PUNCT
ejpam-5065	182	2	,	,	PUNCT
ejpam-5065	182	3	n	n	CCONJ
ejpam-5065	182	4	}	}	PUNCT
ejpam-5065	182	5	.	.	PUNCT
ejpam-5065	183	1	then	then	ADV
ejpam-5065	183	2	vt	vt	PROPN
ejpam-5065	183	3	/∈	/∈	PUNCT
ejpam-5065	183	4	npn(v1	npn(v1	PROPN
ejpam-5065	183	5	)	)	PUNCT
ejpam-5065	183	6	and	and	CCONJ
ejpam-5065	183	7	vt	vt	PROPN
ejpam-5065	183	8	/∈	/∈	PUNCT
ejpam-5065	183	9	npn(v2	npn(v2	PROPN
ejpam-5065	183	10	)	)	PUNCT
ejpam-5065	183	11	.	.	PUNCT
ejpam-5065	184	1	it	it	PRON
ejpam-5065	184	2	follows	follow	VERB
ejpam-5065	184	3	that	that	SCONJ
ejpam-5065	184	4	s	s	VERB
ejpam-5065	184	5	is	be	AUX
ejpam-5065	184	6	a	a	DET
ejpam-5065	184	7	2	2	NUM
ejpam-5065	184	8	-	-	PUNCT
ejpam-5065	184	9	pointwise	pointwise	ADJ
ejpam-5065	184	10	non	non	ADJ
ejpam-5065	184	11	-	-	ADJ
ejpam-5065	184	12	dominating	dominating	ADJ
ejpam-5065	184	13	set	set	NOUN
ejpam-5065	184	14	of	of	ADP
ejpam-5065	184	15	pn	pn	PROPN
ejpam-5065	184	16	.	.	PUNCT
ejpam-5065	184	17	consequently	consequently	ADV
ejpam-5065	184	18	,	,	PUNCT
ejpam-5065	184	19	pnd2(pn	pnd2(pn	PROPN
ejpam-5065	184	20	)	)	PUNCT
ejpam-5065	184	21	=	=	SYM
ejpam-5065	184	22	3	3	NUM
ejpam-5065	184	23	for	for	ADP
ejpam-5065	184	24	all	all	DET
ejpam-5065	184	25	n	n	PRON
ejpam-5065	184	26	≥	≥	NOUN
ejpam-5065	184	27	4	4	NUM
ejpam-5065	184	28	.	.	PUNCT
ejpam-5065	184	29	(	(	PUNCT
ejpam-5065	184	30	ii	ii	NOUN
ejpam-5065	184	31	)	)	PUNCT
ejpam-5065	184	32	clearly	clearly	ADV
ejpam-5065	184	33	,	,	PUNCT
ejpam-5065	184	34	pnd2(c3	pnd2(c3	PROPN
ejpam-5065	184	35	)	)	PUNCT
ejpam-5065	184	36	=	=	SYM
ejpam-5065	185	1	3	3	X
ejpam-5065	185	2	.	.	X
ejpam-5065	185	3	let	let	VERB
ejpam-5065	185	4	n	n	NOUN
ejpam-5065	185	5	=	=	SYM
ejpam-5065	185	6	4	4	NUM
ejpam-5065	185	7	and	and	CCONJ
ejpam-5065	185	8	let	let	VERB
ejpam-5065	185	9	v	v	NOUN
ejpam-5065	185	10	(	(	PUNCT
ejpam-5065	185	11	cn	cn	PROPN
ejpam-5065	185	12	)	)	PUNCT
ejpam-5065	185	13	=	=	SYM
ejpam-5065	185	14	{	{	PUNCT
ejpam-5065	185	15	a1	a1	PROPN
ejpam-5065	185	16	,	,	PUNCT
ejpam-5065	185	17	a2	a2	PROPN
ejpam-5065	185	18	,	,	PUNCT
ejpam-5065	185	19	a3	a3	NOUN
ejpam-5065	185	20	,	,	PUNCT
ejpam-5065	185	21	a4	a4	PROPN
ejpam-5065	185	22	}	}	PUNCT
ejpam-5065	185	23	.	.	PUNCT
ejpam-5065	186	1	since	since	SCONJ
ejpam-5065	186	2	pnd(c4	pnd(c4	NOUN
ejpam-5065	186	3	)	)	PUNCT
ejpam-5065	186	4	=	=	SYM
ejpam-5065	186	5	2	2	NUM
ejpam-5065	186	6	,	,	PUNCT
ejpam-5065	186	7	pnd2(c4	pnd2(c4	PROPN
ejpam-5065	186	8	)	)	PUNCT
ejpam-5065	186	9	≥	≥	NOUN
ejpam-5065	186	10	2	2	NUM
ejpam-5065	186	11	.	.	PUNCT
ejpam-5065	186	12	suppose	suppose	VERB
ejpam-5065	186	13	that	that	SCONJ
ejpam-5065	186	14	pnd2(c4	pnd2(c4	PROPN
ejpam-5065	186	15	)	)	PUNCT
ejpam-5065	186	16	=	=	SYM
ejpam-5065	187	1	2	2	X
ejpam-5065	187	2	.	.	X
ejpam-5065	187	3	let	let	VERB
ejpam-5065	187	4	s	s	PRON
ejpam-5065	187	5	be	be	AUX
ejpam-5065	187	6	a	a	DET
ejpam-5065	187	7	minimum	minimum	ADJ
ejpam-5065	187	8	2pointwise	2pointwise	NUM
ejpam-5065	187	9	non	non	ADJ
ejpam-5065	187	10	-	-	ADJ
ejpam-5065	187	11	dominating	dominating	ADJ
ejpam-5065	187	12	set	set	NOUN
ejpam-5065	187	13	of	of	ADP
ejpam-5065	187	14	c4	c4	NOUN
ejpam-5065	187	15	.	.	PUNCT
ejpam-5065	188	1	since	since	SCONJ
ejpam-5065	188	2	2	2	NUM
ejpam-5065	188	3	-	-	PUNCT
ejpam-5065	188	4	pointwise	pointwise	ADJ
ejpam-5065	188	5	non	non	ADJ
ejpam-5065	188	6	-	-	ADJ
ejpam-5065	188	7	dominating	dominating	NOUN
ejpam-5065	188	8	is	be	AUX
ejpam-5065	188	9	a	a	DET
ejpam-5065	188	10	pointwise	pointwise	PROPN
ejpam-5065	188	11	j.	j.	PROPN
ejpam-5065	188	12	hassan	hassan	PROPN
ejpam-5065	188	13	,	,	PUNCT
ejpam-5065	188	14	a.	a.	PROPN
ejpam-5065	188	15	gomorez	gomorez	PROPN
ejpam-5065	188	16	,	,	PUNCT
ejpam-5065	188	17	l.	l.	PROPN
ejpam-5065	188	18	laja	laja	PROPN
ejpam-5065	188	19	,	,	PUNCT
ejpam-5065	188	20	e.	e.	PROPN
ejpam-5065	188	21	ahmad	ahmad	PROPN
ejpam-5065	188	22	/	/	SYM
ejpam-5065	188	23	eur	eur	PROPN
ejpam-5065	188	24	.	.	PUNCT
ejpam-5065	189	1	j.	j.	PROPN
ejpam-5065	189	2	pure	pure	PROPN
ejpam-5065	189	3	appl	appl	PROPN
ejpam-5065	189	4	.	.	PROPN
ejpam-5065	189	5	math	math	PROPN
ejpam-5065	189	6	,	,	PUNCT
ejpam-5065	189	7	17	17	NUM
ejpam-5065	189	8	(	(	PUNCT
ejpam-5065	189	9	2	2	NUM
ejpam-5065	189	10	)	)	PUNCT
ejpam-5065	189	11	(	(	PUNCT
ejpam-5065	189	12	2024	2024	NUM
ejpam-5065	189	13	)	)	PUNCT
ejpam-5065	189	14	,	,	PUNCT
ejpam-5065	189	15	852	852	NUM
ejpam-5065	189	16	-	-	SYM
ejpam-5065	189	17	859	859	NUM
ejpam-5065	189	18	857	857	NUM
ejpam-5065	189	19	non	non	ADJ
ejpam-5065	189	20	-	-	ADJ
ejpam-5065	189	21	dominating	dominating	ADJ
ejpam-5065	189	22	,	,	PUNCT
ejpam-5065	189	23	⟨s⟩	⟨s⟩	PROPN
ejpam-5065	189	24	is	be	AUX
ejpam-5065	189	25	connected	connect	VERB
ejpam-5065	189	26	.	.	PUNCT
ejpam-5065	190	1	thus	thus	ADV
ejpam-5065	190	2	,	,	PUNCT
ejpam-5065	190	3	{	{	PUNCT
ejpam-5065	190	4	a1	a1	NOUN
ejpam-5065	190	5	,	,	PUNCT
ejpam-5065	190	6	a2	a2	PROPN
ejpam-5065	190	7	}	}	PUNCT
ejpam-5065	190	8	,	,	PUNCT
ejpam-5065	190	9	{	{	PUNCT
ejpam-5065	190	10	a2	a2	NOUN
ejpam-5065	190	11	,	,	PUNCT
ejpam-5065	190	12	a3	a3	NOUN
ejpam-5065	190	13	}	}	PUNCT
ejpam-5065	190	14	,	,	PUNCT
ejpam-5065	190	15	{	{	PUNCT
ejpam-5065	190	16	a3	a3	NOUN
ejpam-5065	190	17	,	,	PUNCT
ejpam-5065	190	18	a4	a4	PROPN
ejpam-5065	190	19	}	}	PUNCT
ejpam-5065	190	20	or	or	CCONJ
ejpam-5065	190	21	{	{	PUNCT
ejpam-5065	190	22	a1	a1	NOUN
ejpam-5065	190	23	,	,	PUNCT
ejpam-5065	190	24	a4	a4	NOUN
ejpam-5065	190	25	}	}	PUNCT
ejpam-5065	190	26	is	be	AUX
ejpam-5065	190	27	the	the	DET
ejpam-5065	190	28	possible	possible	ADJ
ejpam-5065	190	29	set	set	NOUN
ejpam-5065	190	30	s.	s.	PROPN
ejpam-5065	190	31	if	if	SCONJ
ejpam-5065	190	32	s	s	VERB
ejpam-5065	190	33	=	=	PUNCT
ejpam-5065	190	34	{	{	PUNCT
ejpam-5065	190	35	a1	a1	PROPN
ejpam-5065	190	36	,	,	PUNCT
ejpam-5065	190	37	a2	a2	PROPN
ejpam-5065	190	38	}	}	PUNCT
ejpam-5065	190	39	,	,	PUNCT
ejpam-5065	190	40	then	then	ADV
ejpam-5065	190	41	a1	a1	NOUN
ejpam-5065	190	42	is	be	AUX
ejpam-5065	190	43	the	the	DET
ejpam-5065	190	44	only	only	ADJ
ejpam-5065	190	45	vertex	vertex	NOUN
ejpam-5065	190	46	in	in	ADP
ejpam-5065	190	47	s	s	PRON
ejpam-5065	190	48	such	such	ADJ
ejpam-5065	190	49	that	that	DET
ejpam-5065	190	50	a3	a3	NOUN
ejpam-5065	190	51	/∈	/∈	PUNCT
ejpam-5065	191	1	ncn(a1	ncn(a1	VERB
ejpam-5065	191	2	)	)	PUNCT
ejpam-5065	192	1	,	,	PUNCT
ejpam-5065	192	2	a	a	DET
ejpam-5065	192	3	contradiction	contradiction	NOUN
ejpam-5065	192	4	.	.	PUNCT
ejpam-5065	193	1	next	next	ADV
ejpam-5065	193	2	,	,	PUNCT
ejpam-5065	193	3	suppose	suppose	VERB
ejpam-5065	193	4	that	that	SCONJ
ejpam-5065	193	5	s	s	VERB
ejpam-5065	193	6	=	=	SYM
ejpam-5065	193	7	{	{	PUNCT
ejpam-5065	193	8	a2	a2	PROPN
ejpam-5065	193	9	,	,	PUNCT
ejpam-5065	193	10	a3	a3	NOUN
ejpam-5065	193	11	}	}	PUNCT
ejpam-5065	193	12	,	,	PUNCT
ejpam-5065	193	13	then	then	ADV
ejpam-5065	193	14	a2	a2	PROPN
ejpam-5065	193	15	is	be	AUX
ejpam-5065	193	16	the	the	DET
ejpam-5065	193	17	only	only	ADJ
ejpam-5065	193	18	vertex	vertex	NOUN
ejpam-5065	193	19	in	in	ADP
ejpam-5065	193	20	s	s	PRON
ejpam-5065	193	21	such	such	ADJ
ejpam-5065	193	22	that	that	DET
ejpam-5065	193	23	a4	a4	NOUN
ejpam-5065	193	24	/∈	/∈	PUNCT
ejpam-5065	193	25	nc4(a2	nc4(a2	ADJ
ejpam-5065	193	26	)	)	PUNCT
ejpam-5065	193	27	,	,	PUNCT
ejpam-5065	193	28	a	a	DET
ejpam-5065	193	29	contradiction	contradiction	NOUN
ejpam-5065	193	30	.	.	PUNCT
ejpam-5065	194	1	similarly	similarly	ADV
ejpam-5065	194	2	,	,	PUNCT
ejpam-5065	194	3	when	when	SCONJ
ejpam-5065	194	4	s	s	VERB
ejpam-5065	194	5	=	=	SYM
ejpam-5065	194	6	{	{	PUNCT
ejpam-5065	194	7	a3	a3	NOUN
ejpam-5065	194	8	,	,	PUNCT
ejpam-5065	194	9	a4	a4	NOUN
ejpam-5065	194	10	}	}	PUNCT
ejpam-5065	194	11	,	,	PUNCT
ejpam-5065	194	12	or	or	CCONJ
ejpam-5065	194	13	s	s	VERB
ejpam-5065	194	14	=	=	NOUN
ejpam-5065	194	15	{	{	PUNCT
ejpam-5065	194	16	a1	a1	PROPN
ejpam-5065	194	17	,	,	PUNCT
ejpam-5065	194	18	a4	a4	NOUN
ejpam-5065	194	19	}	}	PUNCT
ejpam-5065	194	20	.	.	PUNCT
ejpam-5065	195	1	therefore	therefore	ADV
ejpam-5065	195	2	,	,	PUNCT
ejpam-5065	195	3	pnd2(c4	pnd2(c4	PROPN
ejpam-5065	195	4	)	)	PUNCT
ejpam-5065	195	5	≥	≥	NOUN
ejpam-5065	195	6	3	3	NUM
ejpam-5065	195	7	.	.	PUNCT
ejpam-5065	195	8	suppose	suppose	VERB
ejpam-5065	195	9	that	that	SCONJ
ejpam-5065	195	10	pnd2(c4	pnd2(c4	PROPN
ejpam-5065	195	11	)	)	PUNCT
ejpam-5065	195	12	=	=	SYM
ejpam-5065	196	1	3	3	X
ejpam-5065	196	2	.	.	PUNCT
ejpam-5065	196	3	then	then	ADV
ejpam-5065	196	4	there	there	PRON
ejpam-5065	196	5	exists	exist	VERB
ejpam-5065	196	6	ai	ai	VERB
ejpam-5065	196	7	∈	∈	PROPN
ejpam-5065	196	8	v	v	NOUN
ejpam-5065	196	9	(	(	PUNCT
ejpam-5065	196	10	c4	c4	NOUN
ejpam-5065	196	11	)	)	PUNCT
ejpam-5065	196	12	which	which	PRON
ejpam-5065	196	13	is	be	AUX
ejpam-5065	196	14	not	not	PART
ejpam-5065	196	15	in	in	ADP
ejpam-5065	196	16	2	2	NUM
ejpam-5065	196	17	-	-	PUNCT
ejpam-5065	196	18	pointwise	pointwise	ADJ
ejpam-5065	196	19	non	non	ADJ
ejpam-5065	196	20	-	-	ADJ
ejpam-5065	196	21	dominating	dominating	ADJ
ejpam-5065	196	22	set	set	NOUN
ejpam-5065	196	23	r	r	NOUN
ejpam-5065	196	24	of	of	ADP
ejpam-5065	196	25	c4	c4	NOUN
ejpam-5065	196	26	for	for	ADP
ejpam-5065	196	27	some	some	DET
ejpam-5065	196	28	i	i	PRON
ejpam-5065	196	29	∈	∈	PROPN
ejpam-5065	196	30	{	{	PUNCT
ejpam-5065	196	31	1	1	NUM
ejpam-5065	196	32	,	,	PUNCT
ejpam-5065	196	33	2	2	NUM
ejpam-5065	196	34	,	,	PUNCT
ejpam-5065	196	35	3	3	NUM
ejpam-5065	196	36	,	,	PUNCT
ejpam-5065	196	37	4	4	NUM
ejpam-5065	196	38	}	}	PUNCT
ejpam-5065	196	39	.	.	PUNCT
ejpam-5065	197	1	assume	assume	VERB
ejpam-5065	197	2	that	that	SCONJ
ejpam-5065	197	3	ai	ai	VERB
ejpam-5065	197	4	=	=	ADJ
ejpam-5065	197	5	a1	a1	PROPN
ejpam-5065	197	6	.	.	PUNCT
ejpam-5065	198	1	however	however	ADV
ejpam-5065	198	2	,	,	PUNCT
ejpam-5065	198	3	a3	a3	PROPN
ejpam-5065	198	4	is	be	AUX
ejpam-5065	198	5	the	the	DET
ejpam-5065	198	6	only	only	ADJ
ejpam-5065	198	7	vertex	vertex	NOUN
ejpam-5065	198	8	in	in	ADP
ejpam-5065	198	9	r	r	NOUN
ejpam-5065	198	10	such	such	ADJ
ejpam-5065	198	11	that	that	PRON
ejpam-5065	198	12	ai	ai	VERB
ejpam-5065	198	13	/∈	/∈	CCONJ
ejpam-5065	198	14	nc4(a3	nc4(a3	NOUN
ejpam-5065	198	15	)	)	PUNCT
ejpam-5065	198	16	,	,	PUNCT
ejpam-5065	198	17	a	a	DET
ejpam-5065	198	18	contradiction	contradiction	NOUN
ejpam-5065	198	19	.	.	PUNCT
ejpam-5065	199	1	similarly	similarly	ADV
ejpam-5065	199	2	,	,	PUNCT
ejpam-5065	199	3	when	when	SCONJ
ejpam-5065	199	4	ai	ai	VERB
ejpam-5065	199	5	=	=	PROPN
ejpam-5065	199	6	a2	a2	PROPN
ejpam-5065	199	7	,	,	PUNCT
ejpam-5065	199	8	a3	a3	NOUN
ejpam-5065	199	9	or	or	CCONJ
ejpam-5065	199	10	a4	a4	NOUN
ejpam-5065	199	11	.	.	PUNCT
ejpam-5065	200	1	consequently	consequently	ADV
ejpam-5065	200	2	,	,	PUNCT
ejpam-5065	200	3	pnd2(c4	pnd2(c4	PROPN
ejpam-5065	200	4	)	)	PUNCT
ejpam-5065	200	5	=	=	PUNCT
ejpam-5065	201	1	4	4	X
ejpam-5065	201	2	.	.	PUNCT
ejpam-5065	201	3	now	now	ADV
ejpam-5065	201	4	,	,	PUNCT
ejpam-5065	201	5	assume	assume	VERB
ejpam-5065	201	6	that	that	SCONJ
ejpam-5065	201	7	n	n	NUM
ejpam-5065	201	8	≥	≥	NUM
ejpam-5065	201	9	5	5	NUM
ejpam-5065	201	10	.	.	PUNCT
ejpam-5065	202	1	let	let	VERB
ejpam-5065	202	2	v	v	X
ejpam-5065	202	3	(	(	PUNCT
ejpam-5065	202	4	cn	cn	PROPN
ejpam-5065	202	5	)	)	PUNCT
ejpam-5065	202	6	=	=	SYM
ejpam-5065	202	7	{	{	PUNCT
ejpam-5065	202	8	a1	a1	PROPN
ejpam-5065	202	9	,	,	PUNCT
ejpam-5065	202	10	a2	a2	PROPN
ejpam-5065	202	11	,	,	PUNCT
ejpam-5065	202	12	.	.	PUNCT
ejpam-5065	202	13	.	.	PUNCT
ejpam-5065	203	1	.	.	PUNCT
ejpam-5065	204	1	,	,	PUNCT
ejpam-5065	204	2	an	an	X
ejpam-5065	204	3	}	}	PUNCT
ejpam-5065	204	4	and	and	CCONJ
ejpam-5065	204	5	consider	consider	VERB
ejpam-5065	204	6	b	b	NOUN
ejpam-5065	204	7	=	=	SYM
ejpam-5065	204	8	{	{	PUNCT
ejpam-5065	204	9	a1	a1	PROPN
ejpam-5065	204	10	,	,	PUNCT
ejpam-5065	204	11	a2	a2	PROPN
ejpam-5065	204	12	,	,	PUNCT
ejpam-5065	204	13	a3	a3	NOUN
ejpam-5065	204	14	}	}	PUNCT
ejpam-5065	204	15	.	.	PUNCT
ejpam-5065	205	1	then	then	ADV
ejpam-5065	205	2	,	,	PUNCT
ejpam-5065	205	3	b	b	PROPN
ejpam-5065	205	4	is	be	AUX
ejpam-5065	205	5	a	a	DET
ejpam-5065	205	6	minimum	minimum	ADJ
ejpam-5065	205	7	2	2	NUM
ejpam-5065	205	8	-	-	PUNCT
ejpam-5065	205	9	pointwise	pointwise	ADJ
ejpam-5065	205	10	non	non	ADJ
ejpam-5065	205	11	-	-	ADJ
ejpam-5065	205	12	dominating	dominating	ADJ
ejpam-5065	205	13	set	set	NOUN
ejpam-5065	205	14	of	of	ADP
ejpam-5065	205	15	cn	cn	PROPN
ejpam-5065	205	16	.	.	PUNCT
ejpam-5065	206	1	thus	thus	ADV
ejpam-5065	206	2	,	,	PUNCT
ejpam-5065	206	3	pnd2(cn	pnd2(cn	PROPN
ejpam-5065	206	4	)	)	PUNCT
ejpam-5065	206	5	=	=	SYM
ejpam-5065	206	6	3	3	NUM
ejpam-5065	206	7	for	for	ADP
ejpam-5065	206	8	all	all	DET
ejpam-5065	206	9	n	n	PRON
ejpam-5065	206	10	≥	≥	NUM
ejpam-5065	206	11	5	5	NUM
ejpam-5065	206	12	.	.	PUNCT
ejpam-5065	206	13	theorem	theorem	NOUN
ejpam-5065	206	14	4	4	NUM
ejpam-5065	206	15	.	.	PUNCT
ejpam-5065	207	1	let	let	VERB
ejpam-5065	207	2	g	g	NOUN
ejpam-5065	207	3	and	and	CCONJ
ejpam-5065	207	4	h	h	NOUN
ejpam-5065	207	5	be	be	VERB
ejpam-5065	207	6	two	two	NUM
ejpam-5065	207	7	graphs	graph	NOUN
ejpam-5065	207	8	.	.	PUNCT
ejpam-5065	208	1	then	then	ADV
ejpam-5065	208	2	a	a	DET
ejpam-5065	208	3	subset	subset	NOUN
ejpam-5065	208	4	p	p	NOUN
ejpam-5065	208	5	of	of	ADP
ejpam-5065	208	6	a	a	DET
ejpam-5065	208	7	vertex	vertex	NOUN
ejpam-5065	208	8	-	-	PUNCT
ejpam-5065	208	9	set	set	NOUN
ejpam-5065	208	10	of	of	ADP
ejpam-5065	208	11	g	g	PROPN
ejpam-5065	208	12	+	+	NOUN
ejpam-5065	208	13	h	h	NOUN
ejpam-5065	208	14	is	be	AUX
ejpam-5065	208	15	a	a	DET
ejpam-5065	208	16	2	2	NUM
ejpam-5065	208	17	-	-	PUNCT
ejpam-5065	208	18	hop	hop	NOUN
ejpam-5065	208	19	dominating	dominating	NOUN
ejpam-5065	208	20	if	if	SCONJ
ejpam-5065	208	21	and	and	CCONJ
ejpam-5065	208	22	only	only	ADV
ejpam-5065	208	23	if	if	SCONJ
ejpam-5065	208	24	p	p	X
ejpam-5065	208	25	=	=	X
ejpam-5065	208	26	pg	pg	X
ejpam-5065	208	27	∪	∪	ADJ
ejpam-5065	208	28	ph	ph	NOUN
ejpam-5065	208	29	,	,	PUNCT
ejpam-5065	208	30	where	where	SCONJ
ejpam-5065	208	31	pg	pg	PROPN
ejpam-5065	208	32	⊆	⊆	NUM
ejpam-5065	208	33	v	v	NOUN
ejpam-5065	208	34	(	(	PUNCT
ejpam-5065	208	35	g	g	NOUN
ejpam-5065	208	36	)	)	PUNCT
ejpam-5065	208	37	and	and	CCONJ
ejpam-5065	208	38	ph	ph	VERB
ejpam-5065	208	39	⊆	⊆	NUM
ejpam-5065	208	40	v	v	NOUN
ejpam-5065	208	41	(	(	PUNCT
ejpam-5065	208	42	h	h	NOUN
ejpam-5065	208	43	)	)	PUNCT
ejpam-5065	208	44	are	be	AUX
ejpam-5065	208	45	2	2	NUM
ejpam-5065	208	46	-	-	PUNCT
ejpam-5065	208	47	pointwise	pointwise	ADJ
ejpam-5065	208	48	non	non	ADJ
ejpam-5065	208	49	-	-	ADJ
ejpam-5065	208	50	dominating	dominating	ADJ
ejpam-5065	208	51	sets	set	NOUN
ejpam-5065	208	52	of	of	ADP
ejpam-5065	208	53	g	g	PROPN
ejpam-5065	208	54	and	and	CCONJ
ejpam-5065	208	55	h	h	NOUN
ejpam-5065	208	56	,	,	PUNCT
ejpam-5065	208	57	respectively	respectively	ADV
ejpam-5065	208	58	.	.	PUNCT
ejpam-5065	209	1	proof	proof	NOUN
ejpam-5065	209	2	.	.	PUNCT
ejpam-5065	210	1	suppose	suppose	VERB
ejpam-5065	210	2	that	that	SCONJ
ejpam-5065	210	3	p	p	PROPN
ejpam-5065	210	4	is	be	AUX
ejpam-5065	210	5	a	a	DET
ejpam-5065	210	6	2	2	NUM
ejpam-5065	210	7	-	-	PUNCT
ejpam-5065	210	8	hop	hop	NOUN
ejpam-5065	210	9	dominating	dominating	NOUN
ejpam-5065	210	10	set	set	NOUN
ejpam-5065	210	11	of	of	ADP
ejpam-5065	210	12	g	g	PROPN
ejpam-5065	210	13	+	+	CCONJ
ejpam-5065	210	14	h.	h.	PROPN
ejpam-5065	210	15	assume	assume	VERB
ejpam-5065	210	16	that	that	SCONJ
ejpam-5065	210	17	pg	pg	VERB
ejpam-5065	210	18	=	=	PUNCT
ejpam-5065	210	19	∅.	∅.	VERB
ejpam-5065	210	20	then	then	ADV
ejpam-5065	210	21	p	p	X
ejpam-5065	210	22	=	=	PUNCT
ejpam-5065	210	23	ph	ph	PROPN
ejpam-5065	210	24	⊆	⊆	NUM
ejpam-5065	210	25	v	v	NOUN
ejpam-5065	210	26	(	(	PUNCT
ejpam-5065	210	27	h	h	NOUN
ejpam-5065	210	28	)	)	PUNCT
ejpam-5065	210	29	.	.	PUNCT
ejpam-5065	211	1	since	since	SCONJ
ejpam-5065	211	2	ng+h	ng+h	PROPN
ejpam-5065	211	3	[	[	X
ejpam-5065	211	4	ph	ph	X
ejpam-5065	211	5	]	]	X
ejpam-5065	211	6	⊆	⊆	NUM
ejpam-5065	211	7	v	v	X
ejpam-5065	211	8	(	(	PUNCT
ejpam-5065	211	9	h	h	NOUN
ejpam-5065	211	10	)	)	PUNCT
ejpam-5065	211	11	,	,	PUNCT
ejpam-5065	211	12	ng+h	ng+h	PROPN
ejpam-5065	212	1	[	[	X
ejpam-5065	212	2	ph	ph	X
ejpam-5065	212	3	]	]	X
ejpam-5065	212	4	̸=	̸=	PROPN
ejpam-5065	212	5	v	v	NOUN
ejpam-5065	212	6	(	(	PUNCT
ejpam-5065	212	7	g	g	PROPN
ejpam-5065	212	8	+	+	NOUN
ejpam-5065	212	9	h	h	NOUN
ejpam-5065	212	10	)	)	PUNCT
ejpam-5065	212	11	,	,	PUNCT
ejpam-5065	212	12	which	which	PRON
ejpam-5065	212	13	is	be	AUX
ejpam-5065	212	14	a	a	DET
ejpam-5065	212	15	contradiction	contradiction	NOUN
ejpam-5065	212	16	.	.	PUNCT
ejpam-5065	213	1	therefore	therefore	ADV
ejpam-5065	213	2	,	,	PUNCT
ejpam-5065	213	3	pg	pg	AUX
ejpam-5065	213	4	̸=	̸=	PROPN
ejpam-5065	213	5	∅.	∅.	PRON
ejpam-5065	213	6	similarly	similarly	ADV
ejpam-5065	213	7	,	,	PUNCT
ejpam-5065	213	8	ph	ph	ADJ
ejpam-5065	213	9	̸=	̸=	PROPN
ejpam-5065	213	10	∅.	∅.	ADV
ejpam-5065	213	11	now	now	ADV
ejpam-5065	213	12	,	,	PUNCT
ejpam-5065	213	13	let	let	VERB
ejpam-5065	213	14	x	x	PUNCT
ejpam-5065	213	15	∈	∈	PROPN
ejpam-5065	213	16	v	v	X
ejpam-5065	213	17	(	(	PUNCT
ejpam-5065	213	18	g)\pg	g)\pg	PROPN
ejpam-5065	213	19	.	.	PUNCT
ejpam-5065	214	1	since	since	SCONJ
ejpam-5065	214	2	p	p	NOUN
ejpam-5065	214	3	is	be	AUX
ejpam-5065	214	4	a	a	DET
ejpam-5065	214	5	2	2	NUM
ejpam-5065	214	6	-	-	PUNCT
ejpam-5065	214	7	hop	hop	NOUN
ejpam-5065	214	8	dominating	dominating	NOUN
ejpam-5065	214	9	set	set	VERB
ejpam-5065	214	10	in	in	ADP
ejpam-5065	214	11	g+h	g+h	PROPN
ejpam-5065	214	12	,	,	PUNCT
ejpam-5065	214	13	there	there	PRON
ejpam-5065	214	14	exist	exist	VERB
ejpam-5065	214	15	y	y	PROPN
ejpam-5065	214	16	,	,	PUNCT
ejpam-5065	214	17	w	w	PROPN
ejpam-5065	214	18	∈	∈	PROPN
ejpam-5065	214	19	pg	pg	NOUN
ejpam-5065	214	20	⊆	⊆	NUM
ejpam-5065	214	21	p	p	NOUN
ejpam-5065	214	22	such	such	ADJ
ejpam-5065	214	23	that	that	DET
ejpam-5065	214	24	dg+h(x	dg+h(x	PROPN
ejpam-5065	214	25	,	,	PUNCT
ejpam-5065	214	26	y	y	NOUN
ejpam-5065	214	27	)	)	PUNCT
ejpam-5065	214	28	=	=	SYM
ejpam-5065	214	29	2	2	NUM
ejpam-5065	214	30	and	and	CCONJ
ejpam-5065	214	31	dg+h(w	dg+h(w	PROPN
ejpam-5065	214	32	,	,	PUNCT
ejpam-5065	214	33	x	x	X
ejpam-5065	214	34	)	)	PUNCT
ejpam-5065	215	1	=	=	SYM
ejpam-5065	215	2	2	2	X
ejpam-5065	215	3	.	.	PUNCT
ejpam-5065	215	4	thus	thus	ADV
ejpam-5065	215	5	,	,	PUNCT
ejpam-5065	215	6	x	x	X
ejpam-5065	215	7	/∈	/∈	PUNCT
ejpam-5065	215	8	ng(y	ng(y	NOUN
ejpam-5065	215	9	)	)	PUNCT
ejpam-5065	215	10	and	and	CCONJ
ejpam-5065	215	11	x	x	X
ejpam-5065	215	12	/∈	/∈	PUNCT
ejpam-5065	215	13	ng(w	ng(w	NOUN
ejpam-5065	215	14	)	)	PUNCT
ejpam-5065	215	15	.	.	PUNCT
ejpam-5065	216	1	hence	hence	ADV
ejpam-5065	216	2	,	,	PUNCT
ejpam-5065	216	3	pg	pg	PROPN
ejpam-5065	216	4	is	be	AUX
ejpam-5065	216	5	2	2	NUM
ejpam-5065	216	6	-	-	PUNCT
ejpam-5065	216	7	pointwise	pointwise	ADV
ejpam-5065	216	8	nondominating	nondominate	VERB
ejpam-5065	216	9	set	set	NOUN
ejpam-5065	216	10	of	of	ADP
ejpam-5065	216	11	g.	g.	PROPN
ejpam-5065	216	12	similarly	similarly	ADV
ejpam-5065	216	13	,	,	PUNCT
ejpam-5065	216	14	ph	ph	PROPN
ejpam-5065	216	15	is	be	AUX
ejpam-5065	216	16	a	a	DET
ejpam-5065	216	17	2	2	NUM
ejpam-5065	216	18	-	-	PUNCT
ejpam-5065	216	19	pointwise	pointwise	ADJ
ejpam-5065	216	20	non	non	ADJ
ejpam-5065	216	21	-	-	ADJ
ejpam-5065	216	22	dominating	dominating	ADJ
ejpam-5065	216	23	set	set	NOUN
ejpam-5065	216	24	of	of	ADP
ejpam-5065	216	25	h.	h.	NOUN
ejpam-5065	216	26	conversely	conversely	ADV
ejpam-5065	216	27	,	,	PUNCT
ejpam-5065	216	28	suppose	suppose	VERB
ejpam-5065	216	29	that	that	SCONJ
ejpam-5065	216	30	p	p	PRON
ejpam-5065	216	31	=	=	PUNCT
ejpam-5065	216	32	pg	pg	X
ejpam-5065	216	33	∪	∪	ADJ
ejpam-5065	216	34	ph	ph	NOUN
ejpam-5065	216	35	,	,	PUNCT
ejpam-5065	216	36	where	where	SCONJ
ejpam-5065	216	37	pg	pg	NOUN
ejpam-5065	216	38	and	and	CCONJ
ejpam-5065	216	39	ph	ph	NOUN
ejpam-5065	216	40	are	be	AUX
ejpam-5065	216	41	2	2	NUM
ejpam-5065	216	42	-	-	PUNCT
ejpam-5065	216	43	pointwise	pointwise	ADV
ejpam-5065	216	44	nondominating	nondominate	VERB
ejpam-5065	216	45	sets	set	NOUN
ejpam-5065	216	46	of	of	ADP
ejpam-5065	216	47	g	g	NOUN
ejpam-5065	216	48	andh	andh	NOUN
ejpam-5065	216	49	,	,	PUNCT
ejpam-5065	216	50	respectively	respectively	ADV
ejpam-5065	216	51	.	.	PUNCT
ejpam-5065	217	1	let	let	VERB
ejpam-5065	217	2	a	a	DET
ejpam-5065	217	3	∈	∈	PROPN
ejpam-5065	217	4	v	v	NOUN
ejpam-5065	217	5	(	(	PUNCT
ejpam-5065	217	6	g+h)\p	g+h)\p	NUM
ejpam-5065	217	7	.	.	PUNCT
ejpam-5065	218	1	then	then	ADV
ejpam-5065	218	2	either	either	CCONJ
ejpam-5065	218	3	a	a	DET
ejpam-5065	218	4	∈	∈	PROPN
ejpam-5065	218	5	v	v	NOUN
ejpam-5065	218	6	(	(	PUNCT
ejpam-5065	218	7	g)\pg	g)\pg	PROPN
ejpam-5065	218	8	or	or	CCONJ
ejpam-5065	218	9	a	a	DET
ejpam-5065	218	10	∈	∈	NOUN
ejpam-5065	218	11	v	v	NOUN
ejpam-5065	218	12	(	(	PUNCT
ejpam-5065	218	13	h)\ph	h)\ph	PROPN
ejpam-5065	218	14	.	.	PUNCT
ejpam-5065	218	15	suppose	suppose	VERB
ejpam-5065	218	16	that	that	SCONJ
ejpam-5065	218	17	a	a	DET
ejpam-5065	218	18	∈	∈	PROPN
ejpam-5065	218	19	v	v	NOUN
ejpam-5065	218	20	(	(	PUNCT
ejpam-5065	218	21	g)\pg	g)\pg	PROPN
ejpam-5065	218	22	.	.	PUNCT
ejpam-5065	219	1	since	since	SCONJ
ejpam-5065	219	2	pg	pg	PROPN
ejpam-5065	219	3	is	be	AUX
ejpam-5065	219	4	a	a	DET
ejpam-5065	219	5	2	2	NUM
ejpam-5065	219	6	-	-	PUNCT
ejpam-5065	219	7	pointwise	pointwise	ADJ
ejpam-5065	219	8	non	non	ADJ
ejpam-5065	219	9	-	-	ADJ
ejpam-5065	219	10	dominating	dominating	ADJ
ejpam-5065	219	11	set	set	NOUN
ejpam-5065	219	12	of	of	ADP
ejpam-5065	219	13	g	g	NOUN
ejpam-5065	219	14	,	,	PUNCT
ejpam-5065	219	15	there	there	PRON
ejpam-5065	219	16	exist	exist	VERB
ejpam-5065	219	17	u	u	NOUN
ejpam-5065	219	18	,	,	PUNCT
ejpam-5065	219	19	v	v	PROPN
ejpam-5065	219	20	∈	∈	NOUN
ejpam-5065	219	21	pg	pg	NOUN
ejpam-5065	219	22	⊆	⊆	NUM
ejpam-5065	219	23	p	p	NOUN
ejpam-5065	219	24	such	such	ADJ
ejpam-5065	219	25	that	that	DET
ejpam-5065	219	26	dg(a	dg(a	PROPN
ejpam-5065	219	27	,	,	PUNCT
ejpam-5065	219	28	u	u	NOUN
ejpam-5065	219	29	)	)	PUNCT
ejpam-5065	219	30	≥	≥	NOUN
ejpam-5065	219	31	2	2	NUM
ejpam-5065	219	32	and	and	CCONJ
ejpam-5065	219	33	dg(a	dg(a	NUM
ejpam-5065	219	34	,	,	PUNCT
ejpam-5065	219	35	v	v	NOUN
ejpam-5065	219	36	)	)	PUNCT
ejpam-5065	219	37	≥	≥	NOUN
ejpam-5065	219	38	2	2	NUM
ejpam-5065	219	39	.	.	PUNCT
ejpam-5065	220	1	it	it	PRON
ejpam-5065	220	2	follows	follow	VERB
ejpam-5065	220	3	that	that	SCONJ
ejpam-5065	220	4	a	a	DET
ejpam-5065	220	5	∈	∈	PROPN
ejpam-5065	220	6	n2	n2	NOUN
ejpam-5065	220	7	g+h	g+h	PUNCT
ejpam-5065	221	1	[	[	X
ejpam-5065	221	2	u	u	X
ejpam-5065	221	3	]	]	X
ejpam-5065	221	4	and	and	CCONJ
ejpam-5065	221	5	a	a	DET
ejpam-5065	221	6	∈	∈	PROPN
ejpam-5065	221	7	n2	n2	NOUN
ejpam-5065	221	8	g+h	g+h	PUNCT
ejpam-5065	222	1	[	[	X
ejpam-5065	222	2	v	v	X
ejpam-5065	222	3	]	]	PUNCT
ejpam-5065	222	4	.	.	PUNCT
ejpam-5065	223	1	hence	hence	ADV
ejpam-5065	223	2	,	,	PUNCT
ejpam-5065	223	3	p	p	PROPN
ejpam-5065	223	4	is	be	AUX
ejpam-5065	223	5	a	a	DET
ejpam-5065	223	6	2	2	NUM
ejpam-5065	223	7	-	-	PUNCT
ejpam-5065	223	8	hop	hop	NOUN
ejpam-5065	223	9	dominating	dominating	NOUN
ejpam-5065	223	10	set	set	NOUN
ejpam-5065	223	11	of	of	ADP
ejpam-5065	223	12	g+h	g+h	PROPN
ejpam-5065	223	13	.	.	PUNCT
ejpam-5065	224	1	similarly	similarly	ADV
ejpam-5065	224	2	,	,	PUNCT
ejpam-5065	224	3	when	when	SCONJ
ejpam-5065	224	4	a	a	DET
ejpam-5065	224	5	∈	∈	PROPN
ejpam-5065	224	6	v	v	NOUN
ejpam-5065	224	7	(	(	PUNCT
ejpam-5065	224	8	h)\ph	h)\ph	PROPN
ejpam-5065	224	9	,	,	PUNCT
ejpam-5065	224	10	then	then	ADV
ejpam-5065	224	11	p	p	PROPN
ejpam-5065	224	12	is	be	AUX
ejpam-5065	224	13	a	a	DET
ejpam-5065	224	14	2	2	NUM
ejpam-5065	224	15	-	-	PUNCT
ejpam-5065	224	16	hop	hop	NOUN
ejpam-5065	224	17	dominating	dominating	NOUN
ejpam-5065	224	18	set	set	NOUN
ejpam-5065	224	19	of	of	ADP
ejpam-5065	224	20	g+h	g+h	PROPN
ejpam-5065	224	21	.	.	PUNCT
ejpam-5065	225	1	corollary	corollary	ADJ
ejpam-5065	225	2	1	1	NUM
ejpam-5065	225	3	.	.	PUNCT
ejpam-5065	226	1	let	let	VERB
ejpam-5065	226	2	g	g	NOUN
ejpam-5065	226	3	and	and	CCONJ
ejpam-5065	226	4	h	h	NOUN
ejpam-5065	226	5	be	be	VERB
ejpam-5065	226	6	two	two	NUM
ejpam-5065	226	7	graphs	graph	NOUN
ejpam-5065	226	8	.	.	PUNCT
ejpam-5065	227	1	then	then	ADV
ejpam-5065	227	2	γ2h(g+h	γ2h(g+h	PROPN
ejpam-5065	227	3	)	)	PUNCT
ejpam-5065	227	4	=	=	PUNCT
ejpam-5065	227	5	pnd2(g	pnd2(g	X
ejpam-5065	227	6	)	)	PUNCT
ejpam-5065	227	7	+	+	CCONJ
ejpam-5065	227	8	pnd2(h	pnd2(h	NUM
ejpam-5065	227	9	)	)	PUNCT
ejpam-5065	227	10	.	.	PUNCT
ejpam-5065	228	1	in	in	ADP
ejpam-5065	228	2	particular	particular	ADJ
ejpam-5065	228	3	,	,	PUNCT
ejpam-5065	228	4	each	each	PRON
ejpam-5065	228	5	of	of	ADP
ejpam-5065	228	6	the	the	DET
ejpam-5065	228	7	following	follow	VERB
ejpam-5065	228	8	holds	hold	VERB
ejpam-5065	228	9	:	:	PUNCT
ejpam-5065	228	10	(	(	PUNCT
ejpam-5065	228	11	i	i	NOUN
ejpam-5065	228	12	)	)	PUNCT
ejpam-5065	228	13	γ2h(pn	γ2h(pn	PUNCT
ejpam-5065	229	1	+	+	NUM
ejpam-5065	229	2	pm	pm	NOUN
ejpam-5065	229	3	)	)	PUNCT
ejpam-5065	229	4	=	=	PUNCT
ejpam-5065	230	1			PROPN
ejpam-5065	230	2	n+m	n+m	NUM
ejpam-5065	230	3	,	,	PUNCT
ejpam-5065	230	4	if	if	SCONJ
ejpam-5065	230	5	1	1	NUM
ejpam-5065	230	6	≤	≤	NUM
ejpam-5065	230	7	n	n	CCONJ
ejpam-5065	230	8	,	,	PUNCT
ejpam-5065	230	9	m	m	VERB
ejpam-5065	230	10	≤	≤	ADJ
ejpam-5065	230	11	3	3	NUM
ejpam-5065	230	12	n+	n+	SYM
ejpam-5065	230	13	3	3	NUM
ejpam-5065	230	14	,	,	PUNCT
ejpam-5065	230	15	if	if	SCONJ
ejpam-5065	230	16	1	1	NUM
ejpam-5065	230	17	≤	≤	NUM
ejpam-5065	230	18	n	n	PRON
ejpam-5065	230	19	≤	≤	NOUN
ejpam-5065	230	20	3	3	NUM
ejpam-5065	230	21	and	and	CCONJ
ejpam-5065	230	22	m	m	PROPN
ejpam-5065	230	23	≥	≥	NUM
ejpam-5065	230	24	4	4	NUM
ejpam-5065	230	25	m+	m+	NUM
ejpam-5065	230	26	3	3	NUM
ejpam-5065	230	27	,	,	PUNCT
ejpam-5065	230	28	if	if	SCONJ
ejpam-5065	230	29	1	1	NUM
ejpam-5065	230	30	≤	≤	NUM
ejpam-5065	230	31	m	m	VERB
ejpam-5065	230	32	≤	≤	NOUN
ejpam-5065	230	33	3	3	NUM
ejpam-5065	230	34	and	and	CCONJ
ejpam-5065	230	35	n	n	PRON
ejpam-5065	230	36	≥	≥	NOUN
ejpam-5065	230	37	4	4	NUM
ejpam-5065	230	38	6	6	NUM
ejpam-5065	230	39	,	,	PUNCT
ejpam-5065	230	40	if	if	SCONJ
ejpam-5065	230	41	n	n	CCONJ
ejpam-5065	230	42	,	,	PUNCT
ejpam-5065	230	43	m	m	VERB
ejpam-5065	230	44	≥	≥	NOUN
ejpam-5065	230	45	4	4	NUM
ejpam-5065	230	46	.	.	PUNCT
ejpam-5065	231	1	j.	j.	PROPN
ejpam-5065	231	2	hassan	hassan	PROPN
ejpam-5065	231	3	,	,	PUNCT
ejpam-5065	231	4	a.	a.	PROPN
ejpam-5065	231	5	gomorez	gomorez	PROPN
ejpam-5065	231	6	,	,	PUNCT
ejpam-5065	231	7	l.	l.	PROPN
ejpam-5065	231	8	laja	laja	PROPN
ejpam-5065	231	9	,	,	PUNCT
ejpam-5065	231	10	e.	e.	PROPN
ejpam-5065	231	11	ahmad	ahmad	PROPN
ejpam-5065	231	12	/	/	SYM
ejpam-5065	231	13	eur	eur	PROPN
ejpam-5065	231	14	.	.	PUNCT
ejpam-5065	232	1	j.	j.	PROPN
ejpam-5065	232	2	pure	pure	PROPN
ejpam-5065	232	3	appl	appl	PROPN
ejpam-5065	232	4	.	.	PROPN
ejpam-5065	232	5	math	math	PROPN
ejpam-5065	232	6	,	,	PUNCT
ejpam-5065	232	7	17	17	NUM
ejpam-5065	232	8	(	(	PUNCT
ejpam-5065	232	9	2	2	NUM
ejpam-5065	232	10	)	)	PUNCT
ejpam-5065	232	11	(	(	PUNCT
ejpam-5065	232	12	2024	2024	NUM
ejpam-5065	232	13	)	)	PUNCT
ejpam-5065	232	14	,	,	PUNCT
ejpam-5065	232	15	852	852	NUM
ejpam-5065	232	16	-	-	SYM
ejpam-5065	232	17	859	859	NUM
ejpam-5065	232	18	858	858	NUM
ejpam-5065	232	19	(	(	PUNCT
ejpam-5065	232	20	ii	ii	NOUN
ejpam-5065	232	21	)	)	PUNCT
ejpam-5065	232	22	γ2h(cn	γ2h(cn	PROPN
ejpam-5065	233	1	+	+	NUM
ejpam-5065	233	2	cm	cm	NOUN
ejpam-5065	233	3	)	)	PUNCT
ejpam-5065	233	4	=	=	PUNCT
ejpam-5065	234	1			PROPN
ejpam-5065	234	2	n+m	n+m	NUM
ejpam-5065	234	3	,	,	PUNCT
ejpam-5065	234	4	if	if	SCONJ
ejpam-5065	234	5	n	n	CCONJ
ejpam-5065	234	6	,	,	PUNCT
ejpam-5065	234	7	m	m	VERB
ejpam-5065	234	8	=	=	NOUN
ejpam-5065	234	9	3	3	NUM
ejpam-5065	234	10	,	,	PUNCT
ejpam-5065	234	11	4	4	NUM
ejpam-5065	234	12	n+	n+	SYM
ejpam-5065	234	13	3	3	NUM
ejpam-5065	234	14	,	,	PUNCT
ejpam-5065	234	15	if	if	SCONJ
ejpam-5065	234	16	n	n	X
ejpam-5065	234	17	=	=	SYM
ejpam-5065	234	18	3	3	NUM
ejpam-5065	234	19	,	,	PUNCT
ejpam-5065	234	20	4	4	NUM
ejpam-5065	234	21	and	and	CCONJ
ejpam-5065	234	22	m	m	PRON
ejpam-5065	234	23	≥	≥	NUM
ejpam-5065	234	24	5	5	NUM
ejpam-5065	234	25	m+	m+	NUM
ejpam-5065	234	26	3	3	NUM
ejpam-5065	234	27	,	,	PUNCT
ejpam-5065	234	28	if	if	SCONJ
ejpam-5065	234	29	m	m	VERB
ejpam-5065	234	30	=	=	SYM
ejpam-5065	234	31	3	3	NUM
ejpam-5065	234	32	,	,	PUNCT
ejpam-5065	234	33	4	4	NUM
ejpam-5065	234	34	and	and	CCONJ
ejpam-5065	234	35	n	n	PRON
ejpam-5065	234	36	≥	≥	NUM
ejpam-5065	234	37	5	5	NUM
ejpam-5065	234	38	6	6	NUM
ejpam-5065	234	39	,	,	PUNCT
ejpam-5065	234	40	if	if	SCONJ
ejpam-5065	234	41	n	n	CCONJ
ejpam-5065	234	42	,	,	PUNCT
ejpam-5065	234	43	m	m	VERB
ejpam-5065	234	44	≥	≥	NOUN
ejpam-5065	234	45	5	5	NUM
ejpam-5065	234	46	.	.	PUNCT
ejpam-5065	235	1	(	(	PUNCT
ejpam-5065	235	2	iii	iii	X
ejpam-5065	235	3	)	)	PUNCT
ejpam-5065	235	4	γ2h(kn	γ2h(kn	PROPN
ejpam-5065	235	5	+	+	PROPN
ejpam-5065	235	6	km	km	NOUN
ejpam-5065	235	7	)	)	PUNCT
ejpam-5065	235	8	=	=	PUNCT
ejpam-5065	236	1	n+m	n+m	PROPN
ejpam-5065	236	2	for	for	ADP
ejpam-5065	236	3	all	all	DET
ejpam-5065	236	4	positive	positive	ADJ
ejpam-5065	236	5	integer	integer	NOUN
ejpam-5065	236	6	n	n	CCONJ
ejpam-5065	236	7	,	,	PUNCT
ejpam-5065	236	8	m	m	VERB
ejpam-5065	236	9	≥	≥	NOUN
ejpam-5065	236	10	1	1	NUM
ejpam-5065	236	11	.	.	PUNCT
ejpam-5065	236	12	(	(	PUNCT
ejpam-5065	236	13	iv	iv	X
ejpam-5065	236	14	)	)	PUNCT
ejpam-5065	236	15	γ2h(fn	γ2h(fn	PROPN
ejpam-5065	236	16	)	)	PUNCT
ejpam-5065	236	17	=	=	SYM
ejpam-5065	237	1	γ2h(k1	γ2h(k1	PROPN
ejpam-5065	237	2	+	+	CCONJ
ejpam-5065	237	3	pn	pn	NOUN
ejpam-5065	237	4	)	)	PUNCT
ejpam-5065	237	5	=	=	PRON
ejpam-5065	237	6	{	{	PUNCT
ejpam-5065	237	7	n+	n+	NOUN
ejpam-5065	237	8	1	1	NUM
ejpam-5065	237	9	,	,	PUNCT
ejpam-5065	237	10	if	if	SCONJ
ejpam-5065	237	11	1	1	NUM
ejpam-5065	237	12	≤	≤	NUM
ejpam-5065	237	13	n	n	PRON
ejpam-5065	237	14	≤	≤	NUM
ejpam-5065	237	15	3	3	NUM
ejpam-5065	237	16	4	4	NUM
ejpam-5065	237	17	,	,	PUNCT
ejpam-5065	237	18	if	if	SCONJ
ejpam-5065	237	19	n	n	PRON
ejpam-5065	237	20	≥	≥	X
ejpam-5065	237	21	4	4	NUM
ejpam-5065	237	22	(	(	PUNCT
ejpam-5065	237	23	v	v	NOUN
ejpam-5065	237	24	)	)	PUNCT
ejpam-5065	237	25	γ2h(wn	γ2h(wn	NOUN
ejpam-5065	237	26	)	)	PUNCT
ejpam-5065	237	27	=	=	SYM
ejpam-5065	238	1	γ2h(k1	γ2h(k1	PROPN
ejpam-5065	238	2	+	+	CCONJ
ejpam-5065	238	3	cn	cn	ADJ
ejpam-5065	238	4	)	)	PUNCT
ejpam-5065	238	5	=	=	SYM
ejpam-5065	238	6	{	{	PUNCT
ejpam-5065	238	7	n+	n+	NOUN
ejpam-5065	238	8	1	1	NUM
ejpam-5065	238	9	,	,	PUNCT
ejpam-5065	238	10	if	if	SCONJ
ejpam-5065	238	11	n	n	X
ejpam-5065	238	12	=	=	SYM
ejpam-5065	238	13	3	3	NUM
ejpam-5065	238	14	,	,	PUNCT
ejpam-5065	238	15	4	4	NUM
ejpam-5065	238	16	4	4	NUM
ejpam-5065	238	17	,	,	PUNCT
ejpam-5065	238	18	if	if	SCONJ
ejpam-5065	238	19	n	n	PRON
ejpam-5065	238	20	≥	≥	NOUN
ejpam-5065	238	21	5	5	NUM
ejpam-5065	238	22	proof	proof	NOUN
ejpam-5065	238	23	.	.	PUNCT
ejpam-5065	239	1	let	let	VERB
ejpam-5065	239	2	p	p	PRON
ejpam-5065	239	3	be	be	AUX
ejpam-5065	239	4	a	a	DET
ejpam-5065	239	5	minimum	minimum	ADJ
ejpam-5065	239	6	2	2	NUM
ejpam-5065	239	7	-	-	PUNCT
ejpam-5065	239	8	hop	hop	NOUN
ejpam-5065	239	9	dominating	dominating	NOUN
ejpam-5065	239	10	set	set	NOUN
ejpam-5065	239	11	of	of	ADP
ejpam-5065	239	12	g	g	PROPN
ejpam-5065	239	13	+	+	CCONJ
ejpam-5065	239	14	h.	h.	PROPN
ejpam-5065	239	15	then	then	ADV
ejpam-5065	239	16	by	by	ADP
ejpam-5065	239	17	theorem	theorem	NOUN
ejpam-5065	239	18	4	4	NUM
ejpam-5065	239	19	,	,	PUNCT
ejpam-5065	239	20	p	p	NOUN
ejpam-5065	239	21	=	=	PUNCT
ejpam-5065	239	22	pg	pg	X
ejpam-5065	239	23	∪	∪	ADJ
ejpam-5065	239	24	ph	ph	NOUN
ejpam-5065	239	25	,	,	PUNCT
ejpam-5065	239	26	where	where	SCONJ
ejpam-5065	239	27	pg	pg	NOUN
ejpam-5065	239	28	and	and	CCONJ
ejpam-5065	239	29	ph	ph	NOUN
ejpam-5065	239	30	are	be	AUX
ejpam-5065	239	31	2	2	NUM
ejpam-5065	239	32	-	-	PUNCT
ejpam-5065	239	33	pointwise	pointwise	ADJ
ejpam-5065	239	34	non	non	ADJ
ejpam-5065	239	35	-	-	ADJ
ejpam-5065	239	36	dominating	dominating	ADJ
ejpam-5065	239	37	sets	set	NOUN
ejpam-5065	239	38	of	of	ADP
ejpam-5065	239	39	g	g	PROPN
ejpam-5065	239	40	and	and	CCONJ
ejpam-5065	239	41	h	h	NOUN
ejpam-5065	239	42	,	,	PUNCT
ejpam-5065	239	43	respectively	respectively	ADV
ejpam-5065	239	44	.	.	PUNCT
ejpam-5065	240	1	thus	thus	ADV
ejpam-5065	240	2	,	,	PUNCT
ejpam-5065	240	3	pnd2(g	pnd2(g	NOUN
ejpam-5065	240	4	)	)	PUNCT
ejpam-5065	240	5	≤	≤	NUM
ejpam-5065	240	6	|pg|	|pg|	NOUN
ejpam-5065	240	7	and	and	CCONJ
ejpam-5065	240	8	pnd2(h	pnd2(h	NUM
ejpam-5065	240	9	)	)	PUNCT
ejpam-5065	240	10	≤	≤	NOUN
ejpam-5065	241	1	|ph	|ph	PRON
ejpam-5065	241	2	|	|	NOUN
ejpam-5065	241	3	.	.	PUNCT
ejpam-5065	242	1	hence	hence	ADV
ejpam-5065	242	2	,	,	PUNCT
ejpam-5065	242	3	γ2h(g+h	γ2h(g+h	PROPN
ejpam-5065	242	4	)	)	PUNCT
ejpam-5065	243	1	=	=	PRON
ejpam-5065	243	2	|p	|p	X
ejpam-5065	244	1	|	|	ADV
ejpam-5065	244	2	=	=	SYM
ejpam-5065	244	3	|pg|+	|pg|+	NOUN
ejpam-5065	244	4	|ph	|ph	PRON
ejpam-5065	244	5	|	|	ADV
ejpam-5065	244	6	≥	≥	NOUN
ejpam-5065	244	7	pnd2(pg	pnd2(pg	PROPN
ejpam-5065	244	8	)	)	PUNCT
ejpam-5065	245	1	+	+	CCONJ
ejpam-5065	245	2	pnd2(ph	pnd2(ph	NOUN
ejpam-5065	245	3	)	)	PUNCT
ejpam-5065	245	4	.	.	PUNCT
ejpam-5065	246	1	on	on	ADP
ejpam-5065	246	2	the	the	DET
ejpam-5065	246	3	other	other	ADJ
ejpam-5065	246	4	hand	hand	NOUN
ejpam-5065	246	5	,	,	PUNCT
ejpam-5065	246	6	let	let	VERB
ejpam-5065	246	7	p	p	NOUN
ejpam-5065	246	8	=	=	PROPN
ejpam-5065	246	9	pg∪ph	pg∪ph	PROPN
ejpam-5065	246	10	,	,	PUNCT
ejpam-5065	246	11	where	where	SCONJ
ejpam-5065	246	12	pg	pg	NOUN
ejpam-5065	246	13	and	and	CCONJ
ejpam-5065	246	14	ph	ph	NOUN
ejpam-5065	246	15	are	be	AUX
ejpam-5065	246	16	minimum	minimum	ADJ
ejpam-5065	246	17	2	2	NUM
ejpam-5065	246	18	-	-	PUNCT
ejpam-5065	246	19	pointwise	pointwise	ADV
ejpam-5065	246	20	nondominating	nondominate	VERB
ejpam-5065	246	21	sets	set	NOUN
ejpam-5065	246	22	of	of	ADP
ejpam-5065	246	23	g	g	PROPN
ejpam-5065	246	24	and	and	CCONJ
ejpam-5065	246	25	h	h	NOUN
ejpam-5065	246	26	,	,	PUNCT
ejpam-5065	246	27	respectively	respectively	ADV
ejpam-5065	246	28	.	.	PUNCT
ejpam-5065	247	1	then	then	ADV
ejpam-5065	247	2	by	by	ADP
ejpam-5065	247	3	theorem	theorem	NOUN
ejpam-5065	247	4	4	4	NUM
ejpam-5065	247	5	,	,	PUNCT
ejpam-5065	247	6	p	p	PRON
ejpam-5065	247	7	is	be	AUX
ejpam-5065	247	8	a	a	DET
ejpam-5065	247	9	2	2	NUM
ejpam-5065	247	10	-	-	PUNCT
ejpam-5065	247	11	hop	hop	NOUN
ejpam-5065	247	12	dominating	dominating	NOUN
ejpam-5065	247	13	set	set	NOUN
ejpam-5065	247	14	of	of	ADP
ejpam-5065	247	15	g+h	g+h	PROPN
ejpam-5065	247	16	.	.	PUNCT
ejpam-5065	248	1	thus	thus	ADV
ejpam-5065	248	2	,	,	PUNCT
ejpam-5065	248	3	γ2h(g+h	γ2h(g+h	PROPN
ejpam-5065	248	4	)	)	PUNCT
ejpam-5065	248	5	≤	≤	NUM
ejpam-5065	248	6	|p	|p	NOUN
ejpam-5065	249	1	|	|	NOUN
ejpam-5065	249	2	=	=	SYM
ejpam-5065	249	3	|pg|+	|pg|+	NOUN
ejpam-5065	249	4	|ph	|ph	PRON
ejpam-5065	249	5	|	|	NOUN
ejpam-5065	249	6	=	=	SYM
ejpam-5065	249	7	pnd2(g)+pnd2(h	pnd2(g)+pnd2(h	PROPN
ejpam-5065	249	8	)	)	PUNCT
ejpam-5065	249	9	.	.	PUNCT
ejpam-5065	250	1	consequently	consequently	ADV
ejpam-5065	250	2	,	,	PUNCT
ejpam-5065	250	3	γ2h(g+h	γ2h(g+h	PROPN
ejpam-5065	250	4	)	)	PUNCT
ejpam-5065	250	5	=	=	PUNCT
ejpam-5065	250	6	pnd2(g	pnd2(g	X
ejpam-5065	250	7	)	)	PUNCT
ejpam-5065	250	8	+	+	CCONJ
ejpam-5065	250	9	pnd2(h	pnd2(h	NUM
ejpam-5065	250	10	)	)	PUNCT
ejpam-5065	250	11	.	.	PUNCT
ejpam-5065	251	1	moreover	moreover	ADV
ejpam-5065	251	2	,	,	PUNCT
ejpam-5065	251	3	(	(	PUNCT
ejpam-5065	251	4	i),(ii	i),(ii	PROPN
ejpam-5065	251	5	)	)	PUNCT
ejpam-5065	251	6	,	,	PUNCT
ejpam-5065	251	7	(	(	PUNCT
ejpam-5065	251	8	iii),(iv	iii),(iv	NOUN
ejpam-5065	251	9	)	)	PUNCT
ejpam-5065	251	10	and	and	CCONJ
ejpam-5065	251	11	(	(	PUNCT
ejpam-5065	251	12	v	v	NOUN
ejpam-5065	251	13	)	)	PUNCT
ejpam-5065	251	14	follow	follow	VERB
ejpam-5065	251	15	from	from	ADP
ejpam-5065	251	16	remark	remark	NOUN
ejpam-5065	251	17	2	2	NUM
ejpam-5065	251	18	and	and	CCONJ
ejpam-5065	251	19	proposition	proposition	NOUN
ejpam-5065	251	20	1	1	NUM
ejpam-5065	251	21	.	.	NOUN
ejpam-5065	251	22	4	4	NUM
ejpam-5065	251	23	.	.	X
ejpam-5065	251	24	conclusion	conclusion	VERB
ejpam-5065	251	25	the	the	DET
ejpam-5065	251	26	2	2	NUM
ejpam-5065	251	27	-	-	PUNCT
ejpam-5065	251	28	hop	hop	NOUN
ejpam-5065	251	29	domination	domination	NOUN
ejpam-5065	251	30	parameter	parameter	NOUN
ejpam-5065	251	31	has	have	AUX
ejpam-5065	251	32	been	be	AUX
ejpam-5065	251	33	introduced	introduce	VERB
ejpam-5065	251	34	and	and	CCONJ
ejpam-5065	251	35	initially	initially	ADV
ejpam-5065	251	36	investigated	investigate	VERB
ejpam-5065	251	37	in	in	ADP
ejpam-5065	251	38	this	this	DET
ejpam-5065	251	39	paper	paper	NOUN
ejpam-5065	251	40	.	.	PUNCT
ejpam-5065	252	1	this	this	DET
ejpam-5065	252	2	new	new	ADJ
ejpam-5065	252	3	parameter	parameter	NOUN
ejpam-5065	252	4	is	be	AUX
ejpam-5065	252	5	always	always	ADV
ejpam-5065	252	6	defined	define	VERB
ejpam-5065	252	7	on	on	ADP
ejpam-5065	252	8	any	any	DET
ejpam-5065	252	9	simple	simple	ADJ
ejpam-5065	252	10	and	and	CCONJ
ejpam-5065	252	11	undirected	undirected	ADJ
ejpam-5065	252	12	graph	graph	NOUN
ejpam-5065	252	13	.	.	PUNCT
ejpam-5065	253	1	its	its	PRON
ejpam-5065	253	2	properties	property	NOUN
ejpam-5065	253	3	and	and	CCONJ
ejpam-5065	253	4	its	its	PRON
ejpam-5065	253	5	connections	connection	NOUN
ejpam-5065	253	6	with	with	ADP
ejpam-5065	253	7	hop	hop	NOUN
ejpam-5065	253	8	domination	domination	NOUN
ejpam-5065	253	9	have	have	AUX
ejpam-5065	253	10	been	be	AUX
ejpam-5065	253	11	presented	present	VERB
ejpam-5065	253	12	.	.	PUNCT
ejpam-5065	254	1	moreover	moreover	ADV
ejpam-5065	254	2	,	,	PUNCT
ejpam-5065	254	3	this	this	DET
ejpam-5065	254	4	parameter	parameter	NOUN
ejpam-5065	254	5	has	have	AUX
ejpam-5065	254	6	been	be	AUX
ejpam-5065	254	7	investigated	investigate	VERB
ejpam-5065	254	8	on	on	ADP
ejpam-5065	254	9	the	the	DET
ejpam-5065	254	10	join	join	NOUN
ejpam-5065	254	11	of	of	ADP
ejpam-5065	254	12	two	two	NUM
ejpam-5065	254	13	graphs	graph	NOUN
ejpam-5065	254	14	.	.	PUNCT
ejpam-5065	255	1	the	the	DET
ejpam-5065	255	2	2	2	NUM
ejpam-5065	255	3	-	-	PUNCT
ejpam-5065	255	4	hop	hop	NOUN
ejpam-5065	255	5	dominating	dominating	NOUN
ejpam-5065	255	6	sets	set	NOUN
ejpam-5065	255	7	in	in	ADP
ejpam-5065	255	8	the	the	DET
ejpam-5065	255	9	join	join	NOUN
ejpam-5065	255	10	of	of	ADP
ejpam-5065	255	11	two	two	NUM
ejpam-5065	255	12	graphs	graph	NOUN
ejpam-5065	255	13	have	have	AUX
ejpam-5065	255	14	been	be	AUX
ejpam-5065	255	15	characterized	characterize	VERB
ejpam-5065	255	16	and	and	CCONJ
ejpam-5065	255	17	used	use	VERB
ejpam-5065	255	18	to	to	PART
ejpam-5065	255	19	derive	derive	VERB
ejpam-5065	255	20	some	some	DET
ejpam-5065	255	21	formulas	formula	NOUN
ejpam-5065	255	22	of	of	ADP
ejpam-5065	255	23	the	the	DET
ejpam-5065	255	24	parameter	parameter	NOUN
ejpam-5065	255	25	.	.	PUNCT
ejpam-5065	256	1	interested	interested	ADJ
ejpam-5065	256	2	researchers	researcher	NOUN
ejpam-5065	256	3	may	may	AUX
ejpam-5065	256	4	further	far	ADV
ejpam-5065	256	5	investigate	investigate	VERB
ejpam-5065	256	6	this	this	DET
ejpam-5065	256	7	concept	concept	NOUN
ejpam-5065	256	8	on	on	ADP
ejpam-5065	256	9	other	other	ADJ
ejpam-5065	256	10	graphs	graph	NOUN
ejpam-5065	256	11	that	that	PRON
ejpam-5065	256	12	were	be	AUX
ejpam-5065	256	13	not	not	PART
ejpam-5065	256	14	considered	consider	VERB
ejpam-5065	256	15	in	in	ADP
ejpam-5065	256	16	this	this	DET
ejpam-5065	256	17	study	study	NOUN
ejpam-5065	256	18	.	.	PUNCT
ejpam-5065	257	1	they	they	PRON
ejpam-5065	257	2	may	may	AUX
ejpam-5065	257	3	also	also	ADV
ejpam-5065	257	4	consider	consider	VERB
ejpam-5065	257	5	the	the	DET
ejpam-5065	257	6	possibility	possibility	NOUN
ejpam-5065	257	7	of	of	ADP
ejpam-5065	257	8	applying	apply	VERB
ejpam-5065	257	9	this	this	DET
ejpam-5065	257	10	newly	newly	ADV
ejpam-5065	257	11	defined	define	VERB
ejpam-5065	257	12	parameter	parameter	NOUN
ejpam-5065	257	13	to	to	ADP
ejpam-5065	257	14	another	another	DET
ejpam-5065	257	15	field	field	NOUN
ejpam-5065	257	16	.	.	PUNCT
ejpam-5065	258	1	acknowledgements	acknowledgement	NOUN
ejpam-5065	258	2	the	the	DET
ejpam-5065	258	3	authors	author	NOUN
ejpam-5065	258	4	would	would	AUX
ejpam-5065	258	5	like	like	VERB
ejpam-5065	258	6	to	to	PART
ejpam-5065	258	7	thank	thank	VERB
ejpam-5065	258	8	mindanao	mindanao	PROPN
ejpam-5065	258	9	state	state	PROPN
ejpam-5065	258	10	university	university	PROPN
ejpam-5065	258	11	tawi	tawi	PROPN
ejpam-5065	258	12	-	-	PUNCT
ejpam-5065	258	13	tawi	tawi	PROPN
ejpam-5065	258	14	college	college	PROPN
ejpam-5065	258	15	of	of	ADP
ejpam-5065	258	16	technology	technology	NOUN
ejpam-5065	258	17	and	and	CCONJ
ejpam-5065	258	18	oceanography	oceanography	NOUN
ejpam-5065	258	19	,	,	PUNCT
ejpam-5065	258	20	and	and	CCONJ
ejpam-5065	258	21	western	western	ADJ
ejpam-5065	258	22	mindanao	mindanao	PROPN
ejpam-5065	258	23	state	state	PROPN
ejpam-5065	258	24	university	university	PROPN
ejpam-5065	258	25	for	for	ADP
ejpam-5065	258	26	funding	fund	VERB
ejpam-5065	258	27	this	this	DET
ejpam-5065	258	28	research	research	NOUN
ejpam-5065	258	29	.	.	PUNCT
ejpam-5065	259	1	references	reference	NOUN
ejpam-5065	259	2	859	859	NUM
ejpam-5065	259	3	references	reference	NOUN
ejpam-5065	259	4	[	[	X
ejpam-5065	259	5	1	1	NUM
ejpam-5065	259	6	]	]	PUNCT
ejpam-5065	259	7	v.	v.	X
ejpam-5065	259	8	bilar	bilar	PROPN
ejpam-5065	259	9	,	,	PUNCT
ejpam-5065	259	10	m.a	m.a	PROPN
ejpam-5065	259	11	.	.	PROPN
ejpam-5065	259	12	bonsocan	bonsocan	PROPN
ejpam-5065	259	13	,	,	PUNCT
ejpam-5065	259	14	j.	j.	PROPN
ejpam-5065	259	15	hassan	hassan	PROPN
ejpam-5065	259	16	,	,	PUNCT
ejpam-5065	259	17	and	and	CCONJ
ejpam-5065	259	18	s.	s.	PROPN
ejpam-5065	259	19	dagondon	dagondon	PROPN
ejpam-5065	259	20	.	.	PUNCT
ejpam-5065	260	1	vertex	vertex	NOUN
ejpam-5065	260	2	cover	cover	VERB
ejpam-5065	260	3	hop	hop	NOUN
ejpam-5065	260	4	dominating	dominating	NOUN
ejpam-5065	260	5	sets	set	NOUN
ejpam-5065	260	6	in	in	ADP
ejpam-5065	260	7	graphs	graph	NOUN
ejpam-5065	260	8	.	.	PUNCT
ejpam-5065	261	1	eur	eur	PROPN
ejpam-5065	261	2	.	.	PUNCT
ejpam-5065	262	1	j.	j.	PROPN
ejpam-5065	262	2	pure	pure	PROPN
ejpam-5065	262	3	appl	appl	PROPN
ejpam-5065	262	4	.	.	PUNCT
ejpam-5065	262	5	math	math	PROPN
ejpam-5065	262	6	.	.	PUNCT
ejpam-5065	262	7	,	,	PUNCT
ejpam-5065	262	8	17(1):93–104	17(1):93–104	NUM
ejpam-5065	262	9	,	,	PUNCT
ejpam-5065	262	10	2024	2024	NUM
ejpam-5065	262	11	.	.	PUNCT
ejpam-5065	263	1	[	[	X
ejpam-5065	263	2	2	2	X
ejpam-5065	263	3	]	]	PUNCT
ejpam-5065	263	4	j.	j.	PROPN
ejpam-5065	263	5	hassan	hassan	PROPN
ejpam-5065	263	6	and	and	CCONJ
ejpam-5065	263	7	ass	ass	PROPN
ejpam-5065	263	8	.	.	PROPN
ejpam-5065	263	9	sappari	sappari	PROPN
ejpam-5065	263	10	ar	ar	PROPN
ejpam-5065	263	11	.	.	PROPN
ejpam-5065	263	12	bakkang	bakkang	PROPN
ejpam-5065	263	13	.	.	PUNCT
ejpam-5065	264	1	j2	j2	PROPN
ejpam-5065	264	2	-	-	PUNCT
ejpam-5065	264	3	hop	hop	PROPN
ejpam-5065	264	4	domination	domination	NOUN
ejpam-5065	264	5	in	in	ADP
ejpam-5065	264	6	graphs	graph	NOUN
ejpam-5065	264	7	:	:	PUNCT
ejpam-5065	264	8	properties	property	NOUN
ejpam-5065	264	9	and	and	CCONJ
ejpam-5065	264	10	connections	connection	NOUN
ejpam-5065	264	11	with	with	ADP
ejpam-5065	264	12	other	other	ADJ
ejpam-5065	264	13	parameters	parameter	NOUN
ejpam-5065	264	14	.	.	PUNCT
ejpam-5065	265	1	eur	eur	PROPN
ejpam-5065	265	2	.	.	PUNCT
ejpam-5065	266	1	j.	j.	PROPN
ejpam-5065	266	2	pure	pure	PROPN
ejpam-5065	266	3	appl	appl	PROPN
ejpam-5065	266	4	.	.	PUNCT
ejpam-5065	266	5	math	math	PROPN
ejpam-5065	266	6	.	.	PUNCT
ejpam-5065	266	7	,	,	PUNCT
ejpam-5065	266	8	16(4):2118–2131	16(4):2118–2131	NUM
ejpam-5065	266	9	,	,	PUNCT
ejpam-5065	266	10	2023	2023	NUM
ejpam-5065	266	11	.	.	PUNCT
ejpam-5065	267	1	[	[	X
ejpam-5065	267	2	3	3	X
ejpam-5065	267	3	]	]	X
ejpam-5065	267	4	j.	j.	PROPN
ejpam-5065	267	5	hassan	hassan	PROPN
ejpam-5065	267	6	and	and	CCONJ
ejpam-5065	267	7	s.	s.	PROPN
ejpam-5065	267	8	canoy	canoy	PROPN
ejpam-5065	267	9	.	.	PUNCT
ejpam-5065	268	1	connected	connect	VERB
ejpam-5065	268	2	grundy	grundy	PROPN
ejpam-5065	268	3	hop	hop	NOUN
ejpam-5065	268	4	dominating	dominate	VERB
ejpam-5065	268	5	sequences	sequence	NOUN
ejpam-5065	268	6	in	in	ADP
ejpam-5065	268	7	graphs	graph	NOUN
ejpam-5065	268	8	.	.	PUNCT
ejpam-5065	269	1	,	,	PUNCT
ejpam-5065	269	2	.	.	PUNCT
ejpam-5065	270	1	eur	eur	PROPN
ejpam-5065	270	2	.	.	PUNCT
ejpam-5065	271	1	j.	j.	PROPN
ejpam-5065	271	2	pure	pure	PROPN
ejpam-5065	271	3	appl	appl	PROPN
ejpam-5065	271	4	.	.	PUNCT
ejpam-5065	271	5	math	math	PROPN
ejpam-5065	271	6	.	.	PUNCT
ejpam-5065	271	7	,	,	PUNCT
ejpam-5065	272	1	16(2):1212–1227	16(2):1212–1227	NUM
ejpam-5065	272	2	,	,	PUNCT
ejpam-5065	272	3	2023	2023	NUM
ejpam-5065	272	4	.	.	PUNCT
ejpam-5065	273	1	[	[	X
ejpam-5065	273	2	4	4	X
ejpam-5065	273	3	]	]	PUNCT
ejpam-5065	273	4	j.	j.	PROPN
ejpam-5065	273	5	hassan	hassan	PROPN
ejpam-5065	273	6	and	and	CCONJ
ejpam-5065	273	7	s.	s.	PROPN
ejpam-5065	273	8	canoy	canoy	PROPN
ejpam-5065	273	9	jr	jr	PROPN
ejpam-5065	273	10	.	.	PUNCT
ejpam-5065	274	1	grundy	grundy	PROPN
ejpam-5065	274	2	dominating	dominating	PROPN
ejpam-5065	274	3	and	and	CCONJ
ejpam-5065	274	4	grundy	grundy	PROPN
ejpam-5065	274	5	hop	hop	NOUN
ejpam-5065	274	6	dominating	dominate	VERB
ejpam-5065	274	7	sequences	sequence	NOUN
ejpam-5065	274	8	in	in	ADP
ejpam-5065	274	9	graphs	graph	NOUN
ejpam-5065	274	10	:	:	PUNCT
ejpam-5065	274	11	relationships	relationship	NOUN
ejpam-5065	274	12	and	and	CCONJ
ejpam-5065	274	13	some	some	DET
ejpam-5065	274	14	structural	structural	ADJ
ejpam-5065	274	15	properties	property	NOUN
ejpam-5065	274	16	.	.	PUNCT
ejpam-5065	275	1	eur	eur	PROPN
ejpam-5065	275	2	.	.	PUNCT
ejpam-5065	276	1	j.	j.	PROPN
ejpam-5065	276	2	pure	pure	PROPN
ejpam-5065	276	3	appl	appl	PROPN
ejpam-5065	276	4	.	.	PUNCT
ejpam-5065	276	5	math	math	PROPN
ejpam-5065	276	6	.	.	PUNCT
ejpam-5065	276	7	,	,	PUNCT
ejpam-5065	277	1	16(2):1154–1166	16(2):1154–1166	NUM
ejpam-5065	277	2	,	,	PUNCT
ejpam-5065	277	3	2023	2023	NUM
ejpam-5065	277	4	.	.	PUNCT
ejpam-5065	278	1	[	[	X
ejpam-5065	278	2	5	5	X
ejpam-5065	278	3	]	]	PUNCT
ejpam-5065	278	4	j.	j.	PROPN
ejpam-5065	278	5	hassan	hassan	PROPN
ejpam-5065	278	6	and	and	CCONJ
ejpam-5065	278	7	s.	s.	PROPN
ejpam-5065	278	8	canoy	canoy	PROPN
ejpam-5065	278	9	jr	jr	PROPN
ejpam-5065	278	10	.	.	PUNCT
ejpam-5065	279	1	grundy	grundy	PROPN
ejpam-5065	279	2	total	total	PROPN
ejpam-5065	279	3	hop	hop	PROPN
ejpam-5065	279	4	dominating	dominate	VERB
ejpam-5065	279	5	sequences	sequence	NOUN
ejpam-5065	279	6	in	in	ADP
ejpam-5065	279	7	graphs	graph	NOUN
ejpam-5065	279	8	.	.	PUNCT
ejpam-5065	280	1	eur	eur	PROPN
ejpam-5065	280	2	.	.	PUNCT
ejpam-5065	281	1	j.	j.	PROPN
ejpam-5065	281	2	pure	pure	PROPN
ejpam-5065	281	3	appl	appl	PROPN
ejpam-5065	281	4	.	.	PUNCT
ejpam-5065	281	5	math	math	PROPN
ejpam-5065	281	6	.	.	PUNCT
ejpam-5065	281	7	,	,	PUNCT
ejpam-5065	281	8	16(4):2597–2612	16(4):2597–2612	NUM
ejpam-5065	281	9	,	,	PUNCT
ejpam-5065	281	10	2023	2023	NUM
ejpam-5065	281	11	.	.	PUNCT
ejpam-5065	282	1	[	[	X
ejpam-5065	282	2	6	6	NUM
ejpam-5065	282	3	]	]	PUNCT
ejpam-5065	282	4	j.	j.	PROPN
ejpam-5065	282	5	hassan	hassan	PROPN
ejpam-5065	282	6	,	,	PUNCT
ejpam-5065	282	7	a.	a.	PROPN
ejpam-5065	282	8	lintasan	lintasan	PROPN
ejpam-5065	282	9	,	,	PUNCT
ejpam-5065	282	10	and	and	CCONJ
ejpam-5065	282	11	n.h	n.h	PROPN
ejpam-5065	282	12	.	.	PUNCT
ejpam-5065	283	1	mohammad	mohammad	PROPN
ejpam-5065	283	2	.	.	PUNCT
ejpam-5065	284	1	some	some	DET
ejpam-5065	284	2	properties	property	NOUN
ejpam-5065	284	3	and	and	CCONJ
ejpam-5065	284	4	realization	realization	NOUN
ejpam-5065	284	5	problems	problem	NOUN
ejpam-5065	284	6	involving	involve	VERB
ejpam-5065	284	7	connected	connected	ADJ
ejpam-5065	284	8	outer	outer	ADJ
ejpam-5065	284	9	-	-	PUNCT
ejpam-5065	284	10	hop	hop	NOUN
ejpam-5065	284	11	independent	independent	ADJ
ejpam-5065	284	12	hop	hop	NOUN
ejpam-5065	284	13	domination	domination	NOUN
ejpam-5065	284	14	in	in	ADP
ejpam-5065	284	15	graphs	graph	NOUN
ejpam-5065	284	16	.	.	PUNCT
ejpam-5065	285	1	eur	eur	PROPN
ejpam-5065	285	2	.	.	PUNCT
ejpam-5065	286	1	j.	j.	PROPN
ejpam-5065	286	2	pure	pure	PROPN
ejpam-5065	286	3	appl	appl	PROPN
ejpam-5065	286	4	.	.	PUNCT
ejpam-5065	286	5	math	math	PROPN
ejpam-5065	286	6	.	.	PUNCT
ejpam-5065	286	7	,	,	PUNCT
ejpam-5065	286	8	16(3):1848–1861	16(3):1848–1861	NUM
ejpam-5065	286	9	,	,	PUNCT
ejpam-5065	286	10	2023	2023	NUM
ejpam-5065	286	11	.	.	PUNCT
ejpam-5065	287	1	[	[	X
ejpam-5065	287	2	7	7	NUM
ejpam-5065	287	3	]	]	X
ejpam-5065	287	4	a.y	a.y	PROPN
ejpam-5065	287	5	.	.	PROPN
ejpam-5065	287	6	isahac	isahac	PROPN
ejpam-5065	287	7	,	,	PUNCT
ejpam-5065	287	8	j.	j.	PROPN
ejpam-5065	287	9	hassan	hassan	PROPN
ejpam-5065	287	10	,	,	PUNCT
ejpam-5065	287	11	ls	ls	PROPN
ejpam-5065	287	12	.	.	PROPN
ejpam-5065	287	13	laja	laja	PROPN
ejpam-5065	287	14	,	,	PUNCT
ejpam-5065	287	15	and	and	CCONJ
ejpam-5065	287	16	hb	hb	PROPN
ejpam-5065	287	17	.	.	PUNCT
ejpam-5065	288	1	copel	copel	ADJ
ejpam-5065	288	2	.	.	PUNCT
ejpam-5065	289	1	outer	outer	ADJ
ejpam-5065	289	2	-	-	PUNCT
ejpam-5065	289	3	convex	convex	ADJ
ejpam-5065	289	4	hop	hop	NOUN
ejpam-5065	289	5	domination	domination	NOUN
ejpam-5065	289	6	in	in	ADP
ejpam-5065	289	7	graphs	graph	NOUN
ejpam-5065	289	8	under	under	ADP
ejpam-5065	289	9	some	some	DET
ejpam-5065	289	10	binary	binary	ADJ
ejpam-5065	289	11	operations	operation	NOUN
ejpam-5065	289	12	.	.	PUNCT
ejpam-5065	290	1	eur	eur	PROPN
ejpam-5065	290	2	.	.	PUNCT
ejpam-5065	291	1	j.	j.	PROPN
ejpam-5065	291	2	pure	pure	PROPN
ejpam-5065	291	3	appl	appl	PROPN
ejpam-5065	291	4	.	.	PUNCT
ejpam-5065	291	5	math	math	PROPN
ejpam-5065	291	6	.	.	PUNCT
ejpam-5065	291	7	,	,	PUNCT
ejpam-5065	291	8	16(4):2035–2048	16(4):2035–2048	NUM
ejpam-5065	291	9	,	,	PUNCT
ejpam-5065	291	10	2023	2023	NUM
ejpam-5065	291	11	.	.	PUNCT
ejpam-5065	292	1	[	[	X
ejpam-5065	292	2	8	8	NUM
ejpam-5065	292	3	]	]	X
ejpam-5065	292	4	s.	s.	PROPN
ejpam-5065	292	5	canoy	canoy	PROPN
ejpam-5065	292	6	jr	jr	PROPN
ejpam-5065	292	7	.	.	PROPN
ejpam-5065	292	8	and	and	CCONJ
ejpam-5065	292	9	j.	j.	PROPN
ejpam-5065	292	10	hassan	hassan	PROPN
ejpam-5065	292	11	.	.	PUNCT
ejpam-5065	293	1	weakly	weakly	ADJ
ejpam-5065	293	2	convex	convex	VERB
ejpam-5065	293	3	hop	hop	NOUN
ejpam-5065	293	4	dominating	dominating	NOUN
ejpam-5065	293	5	sets	set	NOUN
ejpam-5065	293	6	in	in	ADP
ejpam-5065	293	7	graphs	graph	NOUN
ejpam-5065	293	8	.	.	PUNCT
ejpam-5065	294	1	eur	eur	PROPN
ejpam-5065	294	2	.	.	PUNCT
ejpam-5065	295	1	j.	j.	PROPN
ejpam-5065	295	2	pure	pure	PROPN
ejpam-5065	295	3	appl	appl	PROPN
ejpam-5065	295	4	.	.	PUNCT
ejpam-5065	295	5	math	math	PROPN
ejpam-5065	295	6	.	.	PUNCT
ejpam-5065	295	7	,	,	PUNCT
ejpam-5065	295	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-5065	295	9	,	,	PUNCT
ejpam-5065	295	10	2022	2022	NUM
ejpam-5065	295	11	.	.	PUNCT
ejpam-5065	296	1	[	[	X
ejpam-5065	296	2	9	9	X
ejpam-5065	296	3	]	]	PUNCT
ejpam-5065	296	4	j.	j.	PROPN
ejpam-5065	296	5	manditong	manditong	PROPN
ejpam-5065	296	6	,	,	PUNCT
ejpam-5065	296	7	j.	j.	PROPN
ejpam-5065	296	8	hassan	hassan	PROPN
ejpam-5065	296	9	,	,	PUNCT
ejpam-5065	296	10	ls	ls	PROPN
ejpam-5065	296	11	laja	laja	PROPN
ejpam-5065	296	12	,	,	PUNCT
ejpam-5065	296	13	aa	aa	INTJ
ejpam-5065	296	14	.	.	PUNCT
ejpam-5065	296	15	laja	laja	PROPN
ejpam-5065	296	16	,	,	PUNCT
ejpam-5065	296	17	nhm	nhm	PROPN
ejpam-5065	296	18	.	.	PUNCT
ejpam-5065	296	19	mohammad	mohammad	PROPN
ejpam-5065	296	20	,	,	PUNCT
ejpam-5065	296	21	and	and	CCONJ
ejpam-5065	296	22	su	su	PROPN
ejpam-5065	296	23	.	.	PROPN
ejpam-5065	296	24	kamdon	kamdon	PROPN
ejpam-5065	296	25	.	.	PUNCT
ejpam-5065	297	1	connected	connected	ADJ
ejpam-5065	297	2	outer	outer	ADJ
ejpam-5065	297	3	-	-	PUNCT
ejpam-5065	297	4	hop	hop	NOUN
ejpam-5065	297	5	independent	independent	ADJ
ejpam-5065	297	6	dominating	dominating	NOUN
ejpam-5065	297	7	sets	set	NOUN
ejpam-5065	297	8	in	in	ADP
ejpam-5065	297	9	graphs	graph	NOUN
ejpam-5065	297	10	under	under	ADP
ejpam-5065	297	11	some	some	DET
ejpam-5065	297	12	binary	binary	ADJ
ejpam-5065	297	13	operations	operation	NOUN
ejpam-5065	297	14	.	.	PUNCT
ejpam-5065	298	1	eur	eur	PROPN
ejpam-5065	298	2	.	.	PUNCT
ejpam-5065	299	1	j.	j.	PROPN
ejpam-5065	299	2	pure	pure	PROPN
ejpam-5065	299	3	appl	appl	PROPN
ejpam-5065	299	4	.	.	PUNCT
ejpam-5065	299	5	math	math	PROPN
ejpam-5065	299	6	.	.	PUNCT
ejpam-5065	299	7	,	,	PUNCT
ejpam-5065	300	1	16(3):1817–1829	16(3):1817–1829	NUM
ejpam-5065	300	2	,	,	PUNCT
ejpam-5065	300	3	2023	2023	NUM
ejpam-5065	300	4	.	.	PUNCT
ejpam-5065	301	1	[	[	X
ejpam-5065	301	2	10	10	NUM
ejpam-5065	301	3	]	]	X
ejpam-5065	301	4	j.	j.	PROPN
ejpam-5065	301	5	manditong	manditong	PROPN
ejpam-5065	301	6	,	,	PUNCT
ejpam-5065	301	7	a.	a.	NOUN
ejpam-5065	301	8	tapeing	tapeing	NOUN
ejpam-5065	301	9	,	,	PUNCT
ejpam-5065	301	10	j.	j.	PROPN
ejpam-5065	301	11	hassan	hassan	PROPN
ejpam-5065	301	12	,	,	PUNCT
ejpam-5065	301	13	a.r	a.r	PROPN
ejpam-5065	301	14	.	.	PROPN
ejpam-5065	301	15	bakkang	bakkang	PROPN
ejpam-5065	301	16	,	,	PUNCT
ejpam-5065	301	17	n.h	n.h	PROPN
ejpam-5065	301	18	.	.	PUNCT
ejpam-5065	301	19	mohammad	mohammad	PROPN
ejpam-5065	301	20	,	,	PUNCT
ejpam-5065	301	21	and	and	CCONJ
ejpam-5065	301	22	s.u	s.u	PROPN
ejpam-5065	301	23	.	.	PROPN
ejpam-5065	301	24	kamdon	kamdon	PROPN
ejpam-5065	301	25	.	.	PUNCT
ejpam-5065	302	1	some	some	DET
ejpam-5065	302	2	properties	property	NOUN
ejpam-5065	302	3	of	of	ADP
ejpam-5065	302	4	zero	zero	NUM
ejpam-5065	302	5	forcing	force	VERB
ejpam-5065	302	6	hop	hop	NOUN
ejpam-5065	302	7	dominating	dominating	NOUN
ejpam-5065	302	8	sets	set	NOUN
ejpam-5065	302	9	in	in	ADP
ejpam-5065	302	10	a	a	DET
ejpam-5065	302	11	graph	graph	NOUN
ejpam-5065	302	12	.	.	PUNCT
ejpam-5065	303	1	eur	eur	PROPN
ejpam-5065	303	2	.	.	PUNCT
ejpam-5065	304	1	j.	j.	PROPN
ejpam-5065	304	2	pure	pure	PROPN
ejpam-5065	304	3	appl	appl	PROPN
ejpam-5065	304	4	.	.	PUNCT
ejpam-5065	304	5	math	math	PROPN
ejpam-5065	304	6	.	.	PUNCT
ejpam-5065	305	1	,	,	PUNCT
ejpam-5065	305	2	17(1):324–337	17(1):324–337	PROPN
ejpam-5065	305	3	,	,	PUNCT
ejpam-5065	305	4	2024	2024	NUM
ejpam-5065	305	5	.	.	PUNCT
ejpam-5065	306	1	[	[	X
ejpam-5065	306	2	11	11	NUM
ejpam-5065	306	3	]	]	PUNCT
ejpam-5065	306	4	j.	j.	PROPN
ejpam-5065	306	5	mohamad	mohamad	PROPN
ejpam-5065	306	6	and	and	CCONJ
ejpam-5065	306	7	h.	h.	PROPN
ejpam-5065	306	8	rara	rara	PROPN
ejpam-5065	306	9	.	.	PUNCT
ejpam-5065	307	1	on	on	ADP
ejpam-5065	307	2	resolving	resolve	VERB
ejpam-5065	307	3	hop	hop	NOUN
ejpam-5065	307	4	domination	domination	NOUN
ejpam-5065	307	5	in	in	ADP
ejpam-5065	307	6	graphs	graph	NOUN
ejpam-5065	307	7	.	.	PUNCT
ejpam-5065	308	1	eur	eur	PROPN
ejpam-5065	308	2	.	.	PUNCT
ejpam-5065	309	1	j.	j.	PROPN
ejpam-5065	309	2	pure	pure	PROPN
ejpam-5065	309	3	appl	appl	PROPN
ejpam-5065	309	4	.	.	PUNCT
ejpam-5065	309	5	math	math	PROPN
ejpam-5065	309	6	.	.	PUNCT
ejpam-5065	309	7	,	,	PUNCT
ejpam-5065	309	8	14(1):324–337	14(1):324–337	PROPN
ejpam-5065	309	9	,	,	PUNCT
ejpam-5065	309	10	2021	2021	NUM
ejpam-5065	309	11	.	.	PUNCT
ejpam-5065	310	1	[	[	X
ejpam-5065	310	2	12	12	NUM
ejpam-5065	310	3	]	]	X
ejpam-5065	310	4	c.	c.	PROPN
ejpam-5065	310	5	natarajan	natarajan	PROPN
ejpam-5065	310	6	and	and	CCONJ
ejpam-5065	310	7	s.	s.	PROPN
ejpam-5065	310	8	ayyaswamy	ayyaswamy	PROPN
ejpam-5065	310	9	.	.	PUNCT
ejpam-5065	311	1	hop	hop	PROPN
ejpam-5065	311	2	domination	domination	NOUN
ejpam-5065	311	3	in	in	ADP
ejpam-5065	311	4	graphs	graphs	PROPN
ejpam-5065	311	5	ii	ii	PROPN
ejpam-5065	311	6	.	.	PUNCT
ejpam-5065	311	7	versita	versita	PROPN
ejpam-5065	311	8	.	.	PUNCT
ejpam-5065	312	1	,	,	PUNCT
ejpam-5065	312	2	23(2):187	23(2):187	NUM
ejpam-5065	312	3	–	–	PUNCT
ejpam-5065	312	4	199	199	NUM
ejpam-5065	312	5	,	,	PUNCT
ejpam-5065	312	6	2015	2015	NUM
ejpam-5065	312	7	.	.	PUNCT