id	sid	tid	token	lemma	pos
ejpam-4350	1	1	european	european	PROPN
ejpam-4350	1	2	journal	journal	PROPN
ejpam-4350	1	3	of	of	ADP
ejpam-4350	1	4	pure	pure	ADJ
ejpam-4350	1	5	and	and	CCONJ
ejpam-4350	1	6	applied	apply	VERB
ejpam-4350	1	7	mathematics	mathematic	NOUN
ejpam-4350	1	8	vol	vol	NOUN
ejpam-4350	1	9	.	.	PROPN
ejpam-4350	2	1	15	15	NUM
ejpam-4350	2	2	,	,	PUNCT
ejpam-4350	2	3	no	no	INTJ
ejpam-4350	2	4	.	.	NOUN
ejpam-4350	2	5	2	2	NUM
ejpam-4350	2	6	,	,	PUNCT
ejpam-4350	2	7	2022	2022	NUM
ejpam-4350	2	8	,	,	PUNCT
ejpam-4350	2	9	467	467	NUM
ejpam-4350	2	10	-	-	SYM
ejpam-4350	2	11	477	477	NUM
ejpam-4350	2	12	issn	issn	PROPN
ejpam-4350	2	13	1307	1307	NUM
ejpam-4350	2	14	-	-	SYM
ejpam-4350	2	15	5543	5543	NUM
ejpam-4350	2	16	–	–	PUNCT
ejpam-4350	2	17	ejpam.com	ejpam.com	X
ejpam-4350	2	18	published	publish	VERB
ejpam-4350	2	19	by	by	ADP
ejpam-4350	2	20	new	new	PROPN
ejpam-4350	2	21	york	york	PROPN
ejpam-4350	2	22	business	business	PROPN
ejpam-4350	2	23	global	global	PROPN
ejpam-4350	2	24	hop	hop	PROPN
ejpam-4350	2	25	independent	independent	ADJ
ejpam-4350	2	26	sets	set	NOUN
ejpam-4350	2	27	in	in	ADP
ejpam-4350	2	28	graphs	graph	NOUN
ejpam-4350	2	29	javier	javier	PROPN
ejpam-4350	2	30	a.	a.	PROPN
ejpam-4350	2	31	hassan1,∗	hassan1,∗	PROPN
ejpam-4350	2	32	,	,	PUNCT
ejpam-4350	2	33	sergio	sergio	PROPN
ejpam-4350	2	34	r.	r.	PROPN
ejpam-4350	2	35	canoy	canoy	PROPN
ejpam-4350	2	36	,	,	PUNCT
ejpam-4350	2	37	jr.1	jr.1	NOUN
ejpam-4350	2	38	,	,	PUNCT
ejpam-4350	3	1	alkajim	alkajim	NOUN
ejpam-4350	3	2	a.	a.	NOUN
ejpam-4350	3	3	aradais2	aradais2	PROPN
ejpam-4350	3	4	1	1	NUM
ejpam-4350	3	5	department	department	NOUN
ejpam-4350	3	6	of	of	ADP
ejpam-4350	3	7	mathematics	mathematic	NOUN
ejpam-4350	3	8	and	and	CCONJ
ejpam-4350	3	9	statistics	statistic	NOUN
ejpam-4350	3	10	,	,	PUNCT
ejpam-4350	3	11	college	college	NOUN
ejpam-4350	3	12	of	of	ADP
ejpam-4350	3	13	science	science	NOUN
ejpam-4350	3	14	and	and	CCONJ
ejpam-4350	3	15	mathematics	mathematic	NOUN
ejpam-4350	3	16	,	,	PUNCT
ejpam-4350	3	17	center	center	NOUN
ejpam-4350	3	18	for	for	ADP
ejpam-4350	3	19	graph	graph	NOUN
ejpam-4350	3	20	theory	theory	NOUN
ejpam-4350	3	21	,	,	PUNCT
ejpam-4350	3	22	algebra	algebra	NOUN
ejpam-4350	3	23	and	and	CCONJ
ejpam-4350	3	24	analysis	analysis	NOUN
ejpam-4350	3	25	-	-	PUNCT
ejpam-4350	3	26	prism	prism	NOUN
ejpam-4350	3	27	,	,	PUNCT
ejpam-4350	3	28	msu	msu	PROPN
ejpam-4350	3	29	-	-	PUNCT
ejpam-4350	3	30	iligan	iligan	PROPN
ejpam-4350	3	31	institute	institute	PROPN
ejpam-4350	3	32	of	of	ADP
ejpam-4350	3	33	technology	technology	PROPN
ejpam-4350	3	34	,	,	PUNCT
ejpam-4350	3	35	9200	9200	NUM
ejpam-4350	3	36	iligan	iligan	ADJ
ejpam-4350	3	37	city	city	NOUN
ejpam-4350	3	38	,	,	PUNCT
ejpam-4350	3	39	philippines	philippine	NOUN
ejpam-4350	3	40	2	2	NUM
ejpam-4350	3	41	integrated	integrate	VERB
ejpam-4350	3	42	laboratory	laboratory	NOUN
ejpam-4350	3	43	school	school	NOUN
ejpam-4350	3	44	,	,	PUNCT
ejpam-4350	3	45	college	college	NOUN
ejpam-4350	3	46	of	of	ADP
ejpam-4350	3	47	education	education	NOUN
ejpam-4350	3	48	,	,	PUNCT
ejpam-4350	3	49	mindanao	mindanao	PROPN
ejpam-4350	3	50	state	state	PROPN
ejpam-4350	3	51	university	university	NOUN
ejpam-4350	3	52	-	-	PUNCT
ejpam-4350	3	53	tcto	tcto	VERB
ejpam-4350	3	54	,	,	PUNCT
ejpam-4350	3	55	tawi	tawi	PROPN
ejpam-4350	3	56	-	-	PUNCT
ejpam-4350	3	57	tawi	tawi	NOUN
ejpam-4350	3	58	,	,	PUNCT
ejpam-4350	3	59	philippines	philippine	NOUN
ejpam-4350	3	60	abstract	abstract	ADJ
ejpam-4350	3	61	.	.	PUNCT
ejpam-4350	4	1	let	let	VERB
ejpam-4350	4	2	g	g	PRON
ejpam-4350	4	3	be	be	AUX
ejpam-4350	4	4	an	an	DET
ejpam-4350	4	5	undirected	undirected	ADJ
ejpam-4350	4	6	graph	graph	NOUN
ejpam-4350	4	7	with	with	ADP
ejpam-4350	4	8	vertex	vertex	NOUN
ejpam-4350	4	9	and	and	CCONJ
ejpam-4350	4	10	edge	edge	NOUN
ejpam-4350	4	11	sets	set	NOUN
ejpam-4350	4	12	v	v	ADP
ejpam-4350	4	13	(	(	PUNCT
ejpam-4350	4	14	g	g	NOUN
ejpam-4350	4	15	)	)	PUNCT
ejpam-4350	4	16	and	and	CCONJ
ejpam-4350	4	17	e(g	e(g	PROPN
ejpam-4350	4	18	)	)	PUNCT
ejpam-4350	4	19	,	,	PUNCT
ejpam-4350	4	20	respectively	respectively	ADV
ejpam-4350	4	21	.	.	PUNCT
ejpam-4350	5	1	a	a	DET
ejpam-4350	5	2	set	set	NOUN
ejpam-4350	5	3	s	s	NOUN
ejpam-4350	5	4	⊆	⊆	NUM
ejpam-4350	5	5	v	v	NOUN
ejpam-4350	5	6	(	(	PUNCT
ejpam-4350	5	7	g	g	NOUN
ejpam-4350	5	8	)	)	PUNCT
ejpam-4350	5	9	is	be	AUX
ejpam-4350	5	10	a	a	DET
ejpam-4350	5	11	hop	hop	NOUN
ejpam-4350	5	12	independent	independent	ADJ
ejpam-4350	5	13	set	set	NOUN
ejpam-4350	5	14	of	of	ADP
ejpam-4350	5	15	g	g	PROPN
ejpam-4350	5	16	if	if	SCONJ
ejpam-4350	5	17	any	any	DET
ejpam-4350	5	18	two	two	NUM
ejpam-4350	5	19	distinct	distinct	ADJ
ejpam-4350	5	20	vertices	vertex	NOUN
ejpam-4350	5	21	in	in	ADP
ejpam-4350	5	22	s	s	NOUN
ejpam-4350	5	23	are	be	AUX
ejpam-4350	5	24	not	not	PART
ejpam-4350	5	25	at	at	ADP
ejpam-4350	5	26	a	a	DET
ejpam-4350	5	27	distance	distance	NOUN
ejpam-4350	5	28	two	two	NUM
ejpam-4350	5	29	from	from	ADP
ejpam-4350	5	30	each	each	DET
ejpam-4350	5	31	other	other	ADJ
ejpam-4350	5	32	,	,	PUNCT
ejpam-4350	5	33	that	that	ADV
ejpam-4350	5	34	is	is	ADV
ejpam-4350	5	35	,	,	PUNCT
ejpam-4350	5	36	dg(v	dg(v	X
ejpam-4350	5	37	,	,	PUNCT
ejpam-4350	5	38	w	w	NOUN
ejpam-4350	5	39	)	)	PUNCT
ejpam-4350	5	40	6=	6=	ADP
ejpam-4350	5	41	2	2	NUM
ejpam-4350	5	42	for	for	ADP
ejpam-4350	5	43	any	any	DET
ejpam-4350	5	44	distinct	distinct	ADJ
ejpam-4350	5	45	vertices	vertex	NOUN
ejpam-4350	5	46	v	v	ADP
ejpam-4350	5	47	,	,	PUNCT
ejpam-4350	5	48	w	w	PROPN
ejpam-4350	5	49	∈	∈	PROPN
ejpam-4350	5	50	s.	s.	PROPN
ejpam-4350	5	51	the	the	DET
ejpam-4350	5	52	maximum	maximum	PROPN
ejpam-4350	5	53	cardinality	cardinality	NOUN
ejpam-4350	5	54	of	of	ADP
ejpam-4350	5	55	a	a	DET
ejpam-4350	5	56	hop	hop	NOUN
ejpam-4350	5	57	independent	independent	ADJ
ejpam-4350	5	58	set	set	NOUN
ejpam-4350	5	59	of	of	ADP
ejpam-4350	5	60	g	g	NOUN
ejpam-4350	5	61	,	,	PUNCT
ejpam-4350	5	62	denoted	denote	VERB
ejpam-4350	5	63	by	by	ADP
ejpam-4350	5	64	αh(g	αh(g	NOUN
ejpam-4350	5	65	)	)	PUNCT
ejpam-4350	5	66	,	,	PUNCT
ejpam-4350	5	67	is	be	AUX
ejpam-4350	5	68	called	call	VERB
ejpam-4350	5	69	the	the	DET
ejpam-4350	5	70	hop	hop	NOUN
ejpam-4350	5	71	independence	independence	NOUN
ejpam-4350	5	72	number	number	NOUN
ejpam-4350	5	73	of	of	ADP
ejpam-4350	5	74	g.	g.	PROPN
ejpam-4350	5	75	in	in	ADP
ejpam-4350	5	76	this	this	DET
ejpam-4350	5	77	paper	paper	NOUN
ejpam-4350	5	78	,	,	PUNCT
ejpam-4350	5	79	we	we	PRON
ejpam-4350	5	80	show	show	VERB
ejpam-4350	5	81	that	that	SCONJ
ejpam-4350	5	82	the	the	DET
ejpam-4350	5	83	absolute	absolute	ADJ
ejpam-4350	5	84	difference	difference	NOUN
ejpam-4350	5	85	of	of	ADP
ejpam-4350	5	86	the	the	DET
ejpam-4350	5	87	independence	independence	NOUN
ejpam-4350	5	88	number	number	NOUN
ejpam-4350	5	89	and	and	CCONJ
ejpam-4350	5	90	the	the	DET
ejpam-4350	5	91	hop	hop	NOUN
ejpam-4350	5	92	independence	independence	NOUN
ejpam-4350	5	93	number	number	NOUN
ejpam-4350	5	94	of	of	ADP
ejpam-4350	5	95	a	a	DET
ejpam-4350	5	96	graph	graph	NOUN
ejpam-4350	5	97	can	can	AUX
ejpam-4350	5	98	be	be	AUX
ejpam-4350	5	99	made	make	VERB
ejpam-4350	5	100	arbitrarily	arbitrarily	ADV
ejpam-4350	5	101	large	large	ADJ
ejpam-4350	5	102	.	.	PUNCT
ejpam-4350	6	1	furthermore	furthermore	ADV
ejpam-4350	6	2	,	,	PUNCT
ejpam-4350	6	3	we	we	PRON
ejpam-4350	6	4	determine	determine	VERB
ejpam-4350	6	5	the	the	DET
ejpam-4350	6	6	hop	hop	NOUN
ejpam-4350	6	7	independence	independence	NOUN
ejpam-4350	6	8	numbers	number	NOUN
ejpam-4350	6	9	of	of	ADP
ejpam-4350	6	10	some	some	DET
ejpam-4350	6	11	graphs	graph	NOUN
ejpam-4350	6	12	including	include	VERB
ejpam-4350	6	13	those	those	PRON
ejpam-4350	6	14	resulting	result	VERB
ejpam-4350	6	15	from	from	ADP
ejpam-4350	6	16	some	some	DET
ejpam-4350	6	17	binary	binary	ADJ
ejpam-4350	6	18	operations	operation	NOUN
ejpam-4350	6	19	of	of	ADP
ejpam-4350	6	20	graphs	graph	NOUN
ejpam-4350	6	21	.	.	PUNCT
ejpam-4350	7	1	2020	2020	NUM
ejpam-4350	7	2	mathematics	mathematic	NOUN
ejpam-4350	7	3	subject	subject	NOUN
ejpam-4350	7	4	classifications	classification	NOUN
ejpam-4350	7	5	:	:	PUNCT
ejpam-4350	7	6	05c69	05c69	X
ejpam-4350	7	7	key	key	ADJ
ejpam-4350	7	8	words	word	NOUN
ejpam-4350	7	9	and	and	CCONJ
ejpam-4350	7	10	phrases	phrase	NOUN
ejpam-4350	7	11	:	:	PUNCT
ejpam-4350	7	12	locating	locate	VERB
ejpam-4350	7	13	,	,	PUNCT
ejpam-4350	7	14	stable	stable	ADJ
ejpam-4350	7	15	,	,	PUNCT
ejpam-4350	7	16	domination	domination	NOUN
ejpam-4350	7	17	,	,	PUNCT
ejpam-4350	7	18	join	join	NOUN
ejpam-4350	7	19	,	,	PUNCT
ejpam-4350	7	20	corona	corona	PROPN
ejpam-4350	7	21	1	1	NUM
ejpam-4350	7	22	.	.	PUNCT
ejpam-4350	8	1	introduction	introduction	NOUN
ejpam-4350	8	2	in	in	ADP
ejpam-4350	8	3	this	this	DET
ejpam-4350	8	4	paper	paper	NOUN
ejpam-4350	8	5	we	we	PRON
ejpam-4350	8	6	explore	explore	VERB
ejpam-4350	8	7	a	a	DET
ejpam-4350	8	8	parameter	parameter	NOUN
ejpam-4350	8	9	that	that	PRON
ejpam-4350	8	10	is	be	AUX
ejpam-4350	8	11	,	,	PUNCT
ejpam-4350	8	12	in	in	ADP
ejpam-4350	8	13	some	some	DET
ejpam-4350	8	14	sense	sense	NOUN
ejpam-4350	8	15	,	,	PUNCT
ejpam-4350	8	16	defined	define	VERB
ejpam-4350	8	17	in	in	ADP
ejpam-4350	8	18	a	a	DET
ejpam-4350	8	19	similar	similar	ADJ
ejpam-4350	8	20	way	way	NOUN
ejpam-4350	8	21	that	that	PRON
ejpam-4350	8	22	the	the	DET
ejpam-4350	8	23	well	well	ADV
ejpam-4350	8	24	-	-	PUNCT
ejpam-4350	8	25	known	know	VERB
ejpam-4350	8	26	independence	independence	NOUN
ejpam-4350	8	27	number	number	NOUN
ejpam-4350	8	28	of	of	ADP
ejpam-4350	8	29	a	a	DET
ejpam-4350	8	30	graph	graph	NOUN
ejpam-4350	8	31	is	be	AUX
ejpam-4350	8	32	.	.	PUNCT
ejpam-4350	9	1	indeed	indeed	ADV
ejpam-4350	9	2	,	,	PUNCT
ejpam-4350	9	3	while	while	SCONJ
ejpam-4350	9	4	an	an	DET
ejpam-4350	9	5	independent	independent	ADJ
ejpam-4350	9	6	set	set	NOUN
ejpam-4350	9	7	of	of	ADP
ejpam-4350	9	8	graph	graph	NOUN
ejpam-4350	9	9	requires	require	VERB
ejpam-4350	9	10	that	that	SCONJ
ejpam-4350	9	11	no	no	DET
ejpam-4350	9	12	two	two	NUM
ejpam-4350	9	13	distinct	distinct	ADJ
ejpam-4350	9	14	vertices	vertex	NOUN
ejpam-4350	9	15	in	in	ADP
ejpam-4350	9	16	the	the	DET
ejpam-4350	9	17	set	set	NOUN
ejpam-4350	9	18	are	be	AUX
ejpam-4350	9	19	at	at	ADP
ejpam-4350	9	20	distance	distance	NOUN
ejpam-4350	9	21	one	one	NUM
ejpam-4350	9	22	from	from	ADP
ejpam-4350	9	23	each	each	DET
ejpam-4350	9	24	other	other	ADJ
ejpam-4350	9	25	,	,	PUNCT
ejpam-4350	9	26	the	the	DET
ejpam-4350	9	27	concept	concept	NOUN
ejpam-4350	9	28	that	that	SCONJ
ejpam-4350	9	29	we	we	PRON
ejpam-4350	9	30	will	will	AUX
ejpam-4350	9	31	be	be	AUX
ejpam-4350	9	32	dealing	deal	VERB
ejpam-4350	9	33	with	with	ADP
ejpam-4350	9	34	here	here	ADV
ejpam-4350	9	35	imposes	impose	VERB
ejpam-4350	9	36	the	the	DET
ejpam-4350	9	37	condition	condition	NOUN
ejpam-4350	9	38	that	that	SCONJ
ejpam-4350	9	39	no	no	DET
ejpam-4350	9	40	two	two	NUM
ejpam-4350	9	41	distinct	distinct	ADJ
ejpam-4350	9	42	vertices	vertex	NOUN
ejpam-4350	9	43	in	in	ADP
ejpam-4350	9	44	the	the	DET
ejpam-4350	9	45	set	set	NOUN
ejpam-4350	9	46	are	be	AUX
ejpam-4350	9	47	at	at	ADP
ejpam-4350	9	48	distance	distance	NOUN
ejpam-4350	9	49	two	two	NUM
ejpam-4350	9	50	from	from	ADP
ejpam-4350	9	51	each	each	DET
ejpam-4350	9	52	other	other	ADJ
ejpam-4350	9	53	.	.	PUNCT
ejpam-4350	10	1	the	the	DET
ejpam-4350	10	2	motivation	motivation	NOUN
ejpam-4350	10	3	of	of	ADP
ejpam-4350	10	4	introducing	introduce	VERB
ejpam-4350	10	5	the	the	DET
ejpam-4350	10	6	concept	concept	NOUN
ejpam-4350	10	7	is	be	AUX
ejpam-4350	10	8	the	the	DET
ejpam-4350	10	9	ever	ever	ADV
ejpam-4350	10	10	increasing	increase	VERB
ejpam-4350	10	11	number	number	NOUN
ejpam-4350	10	12	of	of	ADP
ejpam-4350	10	13	studies	study	NOUN
ejpam-4350	10	14	on	on	ADP
ejpam-4350	10	15	hop	hop	NOUN
ejpam-4350	10	16	domination	domination	NOUN
ejpam-4350	10	17	and	and	CCONJ
ejpam-4350	10	18	some	some	PRON
ejpam-4350	10	19	of	of	ADP
ejpam-4350	10	20	its	its	PRON
ejpam-4350	10	21	variations	variation	NOUN
ejpam-4350	10	22	.	.	PUNCT
ejpam-4350	11	1	in	in	ADP
ejpam-4350	11	2	fact	fact	NOUN
ejpam-4350	11	3	,	,	PUNCT
ejpam-4350	11	4	it	it	PRON
ejpam-4350	11	5	can	can	AUX
ejpam-4350	11	6	be	be	AUX
ejpam-4350	11	7	shown	show	VERB
ejpam-4350	11	8	that	that	SCONJ
ejpam-4350	11	9	every	every	DET
ejpam-4350	11	10	maximum	maximum	ADJ
ejpam-4350	11	11	hop	hop	NOUN
ejpam-4350	11	12	independent	independent	ADJ
ejpam-4350	11	13	set	set	NOUN
ejpam-4350	11	14	of	of	ADP
ejpam-4350	11	15	a	a	DET
ejpam-4350	11	16	graph	graph	NOUN
ejpam-4350	11	17	is	be	AUX
ejpam-4350	11	18	a	a	DET
ejpam-4350	11	19	hop	hop	NOUN
ejpam-4350	11	20	dominating	dominating	NOUN
ejpam-4350	11	21	set	set	NOUN
ejpam-4350	11	22	.	.	PUNCT
ejpam-4350	12	1	consequently	consequently	ADV
ejpam-4350	12	2	,	,	PUNCT
ejpam-4350	12	3	the	the	DET
ejpam-4350	12	4	hop	hop	NOUN
ejpam-4350	12	5	domination	domination	NOUN
ejpam-4350	12	6	number	number	NOUN
ejpam-4350	12	7	of	of	ADP
ejpam-4350	12	8	a	a	DET
ejpam-4350	12	9	graph	graph	NOUN
ejpam-4350	12	10	is	be	AUX
ejpam-4350	12	11	at	at	ADP
ejpam-4350	12	12	most	most	ADV
ejpam-4350	12	13	equal	equal	ADJ
ejpam-4350	12	14	to	to	ADP
ejpam-4350	12	15	the	the	DET
ejpam-4350	12	16	hop	hop	NOUN
ejpam-4350	12	17	independence	independence	NOUN
ejpam-4350	12	18	number	number	NOUN
ejpam-4350	12	19	of	of	ADP
ejpam-4350	12	20	the	the	DET
ejpam-4350	12	21	graph	graph	NOUN
ejpam-4350	12	22	.	.	PUNCT
ejpam-4350	13	1	the	the	DET
ejpam-4350	13	2	concept	concept	NOUN
ejpam-4350	13	3	of	of	ADP
ejpam-4350	13	4	hop	hop	NOUN
ejpam-4350	13	5	domination	domination	NOUN
ejpam-4350	13	6	was	be	AUX
ejpam-4350	13	7	introduced	introduce	VERB
ejpam-4350	13	8	and	and	CCONJ
ejpam-4350	13	9	studied	study	VERB
ejpam-4350	13	10	by	by	ADP
ejpam-4350	13	11	natarajan	natarajan	PROPN
ejpam-4350	13	12	and	and	CCONJ
ejpam-4350	13	13	ayyaswamy	ayyaswamy	ADV
ejpam-4350	13	14	in	in	ADP
ejpam-4350	13	15	[	[	X
ejpam-4350	13	16	4	4	NUM
ejpam-4350	13	17	]	]	PUNCT
ejpam-4350	13	18	.	.	PUNCT
ejpam-4350	14	1	the	the	DET
ejpam-4350	14	2	concept	concept	NOUN
ejpam-4350	14	3	and	and	CCONJ
ejpam-4350	14	4	some	some	PRON
ejpam-4350	14	5	of	of	ADP
ejpam-4350	14	6	its	its	PRON
ejpam-4350	14	7	variants	variant	NOUN
ejpam-4350	14	8	are	be	AUX
ejpam-4350	14	9	also	also	ADV
ejpam-4350	14	10	studied	study	VERB
ejpam-4350	14	11	in	in	ADP
ejpam-4350	14	12	[	[	X
ejpam-4350	14	13	1	1	NUM
ejpam-4350	14	14	]	]	PUNCT
ejpam-4350	14	15	,	,	PUNCT
ejpam-4350	14	16	[	[	X
ejpam-4350	14	17	2	2	NUM
ejpam-4350	14	18	]	]	PUNCT
ejpam-4350	14	19	,	,	PUNCT
ejpam-4350	14	20	∗corresponding	∗corresponde	VERB
ejpam-4350	14	21	author	author	NOUN
ejpam-4350	14	22	.	.	PUNCT
ejpam-4350	15	1	doi	doi	NOUN
ejpam-4350	15	2	:	:	PUNCT
ejpam-4350	15	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4350	https://doi.org/10.29020/nybg.ejpam.v15i2.4350	PROPN
ejpam-4350	15	4	email	email	NOUN
ejpam-4350	15	5	addresses	address	NOUN
ejpam-4350	15	6	:	:	PUNCT
ejpam-4350	16	1	javier.hassan@g.msuiit.edu.ph	javier.hassan@g.msuiit.edu.ph	PROPN
ejpam-4350	16	2	(	(	PUNCT
ejpam-4350	16	3	j.	j.	PROPN
ejpam-4350	16	4	hassan	hassan	PROPN
ejpam-4350	16	5	)	)	PUNCT
ejpam-4350	16	6	,	,	PUNCT
ejpam-4350	16	7	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4350	16	8	(	(	PUNCT
ejpam-4350	16	9	s.	s.	PROPN
ejpam-4350	16	10	canoy	canoy	PROPN
ejpam-4350	16	11	,	,	PUNCT
ejpam-4350	16	12	jr	jr	PROPN
ejpam-4350	16	13	.	.	PROPN
ejpam-4350	16	14	)	)	PUNCT
ejpam-4350	16	15	,	,	PUNCT
ejpam-4350	16	16	alkajim.aradais@g.msuiit.edu.ph	alkajim.aradais@g.msuiit.edu.ph	PROPN
ejpam-4350	16	17	(	(	PUNCT
ejpam-4350	16	18	a.	a.	NOUN
ejpam-4350	16	19	aradais	aradais	PROPN
ejpam-4350	16	20	)	)	PUNCT
ejpam-4350	16	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4350	16	22	467	467	NUM
ejpam-4350	16	23	©	©	PROPN
ejpam-4350	16	24	2022	2022	NUM
ejpam-4350	16	25	ejpam	ejpam	VERB
ejpam-4350	16	26	all	all	DET
ejpam-4350	16	27	rights	right	NOUN
ejpam-4350	16	28	reserved	reserve	VERB
ejpam-4350	16	29	.	.	PUNCT
ejpam-4350	17	1	j.	j.	PROPN
ejpam-4350	17	2	hassan	hassan	PROPN
ejpam-4350	17	3	,	,	PUNCT
ejpam-4350	17	4	s.	s.	PROPN
ejpam-4350	17	5	canoy	canoy	PROPN
ejpam-4350	17	6	,	,	PUNCT
ejpam-4350	17	7	jr	jr	PROPN
ejpam-4350	17	8	.	.	PROPN
ejpam-4350	17	9	,	,	PUNCT
ejpam-4350	17	10	a.	a.	PROPN
ejpam-4350	17	11	aradais	aradais	PROPN
ejpam-4350	17	12	/	/	SYM
ejpam-4350	17	13	eur	eur	PROPN
ejpam-4350	17	14	.	.	PUNCT
ejpam-4350	18	1	j.	j.	PROPN
ejpam-4350	18	2	pure	pure	PROPN
ejpam-4350	18	3	appl	appl	PROPN
ejpam-4350	18	4	.	.	PROPN
ejpam-4350	18	5	math	math	PROPN
ejpam-4350	18	6	,	,	PUNCT
ejpam-4350	18	7	15	15	NUM
ejpam-4350	18	8	(	(	PUNCT
ejpam-4350	18	9	2	2	NUM
ejpam-4350	18	10	)	)	PUNCT
ejpam-4350	18	11	(	(	PUNCT
ejpam-4350	18	12	2022	2022	NUM
ejpam-4350	18	13	)	)	PUNCT
ejpam-4350	18	14	,	,	PUNCT
ejpam-4350	18	15	467	467	NUM
ejpam-4350	18	16	-	-	SYM
ejpam-4350	18	17	477	477	NUM
ejpam-4350	18	18	468	468	NUM
ejpam-4350	19	1	[	[	X
ejpam-4350	19	2	3	3	NUM
ejpam-4350	19	3	]	]	PUNCT
ejpam-4350	19	4	,	,	PUNCT
ejpam-4350	19	5	[	[	X
ejpam-4350	19	6	5	5	NUM
ejpam-4350	19	7	]	]	PUNCT
ejpam-4350	19	8	,	,	PUNCT
ejpam-4350	19	9	[	[	X
ejpam-4350	19	10	6	6	NUM
ejpam-4350	19	11	]	]	PUNCT
ejpam-4350	19	12	,	,	PUNCT
ejpam-4350	19	13	[	[	X
ejpam-4350	19	14	7	7	NUM
ejpam-4350	19	15	]	]	PUNCT
ejpam-4350	19	16	,	,	PUNCT
ejpam-4350	19	17	[	[	X
ejpam-4350	19	18	8	8	NUM
ejpam-4350	19	19	]	]	PUNCT
ejpam-4350	19	20	,	,	PUNCT
ejpam-4350	19	21	and	and	CCONJ
ejpam-4350	19	22	[	[	X
ejpam-4350	19	23	9	9	NUM
ejpam-4350	19	24	]	]	PUNCT
ejpam-4350	19	25	.	.	PUNCT
ejpam-4350	20	1	alongside	alongside	ADP
ejpam-4350	20	2	other	other	ADJ
ejpam-4350	20	3	previously	previously	ADV
ejpam-4350	20	4	defined	define	VERB
ejpam-4350	20	5	parameters	parameter	NOUN
ejpam-4350	20	6	in	in	ADP
ejpam-4350	20	7	a	a	DET
ejpam-4350	20	8	graph	graph	NOUN
ejpam-4350	20	9	,	,	PUNCT
ejpam-4350	20	10	the	the	DET
ejpam-4350	20	11	hop	hop	NOUN
ejpam-4350	20	12	independence	independence	NOUN
ejpam-4350	20	13	number	number	NOUN
ejpam-4350	20	14	of	of	ADP
ejpam-4350	20	15	a	a	DET
ejpam-4350	20	16	graph	graph	NOUN
ejpam-4350	20	17	may	may	AUX
ejpam-4350	20	18	be	be	AUX
ejpam-4350	20	19	used	use	VERB
ejpam-4350	20	20	to	to	PART
ejpam-4350	20	21	give	give	VERB
ejpam-4350	20	22	bounds	bound	NOUN
ejpam-4350	20	23	on	on	ADP
ejpam-4350	20	24	some	some	DET
ejpam-4350	20	25	hop	hop	NOUN
ejpam-4350	20	26	-	-	PUNCT
ejpam-4350	20	27	domination	domination	NOUN
ejpam-4350	20	28	related	related	ADJ
ejpam-4350	20	29	parameters	parameter	NOUN
ejpam-4350	20	30	.	.	PUNCT
ejpam-4350	21	1	moreover	moreover	ADV
ejpam-4350	21	2	,	,	PUNCT
ejpam-4350	21	3	this	this	DET
ejpam-4350	21	4	newly	newly	ADV
ejpam-4350	21	5	defined	define	VERB
ejpam-4350	21	6	concept	concept	NOUN
ejpam-4350	21	7	may	may	AUX
ejpam-4350	21	8	be	be	AUX
ejpam-4350	21	9	utilized	utilize	VERB
ejpam-4350	21	10	to	to	PART
ejpam-4350	21	11	introduce	introduce	VERB
ejpam-4350	21	12	some	some	DET
ejpam-4350	21	13	concepts	concept	NOUN
ejpam-4350	21	14	(	(	PUNCT
ejpam-4350	21	15	say	say	INTJ
ejpam-4350	21	16	,	,	PUNCT
ejpam-4350	21	17	a	a	DET
ejpam-4350	21	18	variant	variant	NOUN
ejpam-4350	21	19	of	of	ADP
ejpam-4350	21	20	hop	hop	NOUN
ejpam-4350	21	21	domination	domination	NOUN
ejpam-4350	21	22	)	)	PUNCT
ejpam-4350	21	23	in	in	ADP
ejpam-4350	21	24	the	the	DET
ejpam-4350	21	25	future	future	NOUN
ejpam-4350	21	26	.	.	PUNCT
ejpam-4350	22	1	2	2	X
ejpam-4350	22	2	.	.	X
ejpam-4350	22	3	terminology	terminology	NOUN
ejpam-4350	22	4	and	and	CCONJ
ejpam-4350	22	5	notation	notation	NOUN
ejpam-4350	22	6	for	for	ADP
ejpam-4350	22	7	any	any	DET
ejpam-4350	22	8	two	two	NUM
ejpam-4350	22	9	vertices	vertex	NOUN
ejpam-4350	22	10	u	u	NOUN
ejpam-4350	22	11	and	and	CCONJ
ejpam-4350	22	12	v	v	NOUN
ejpam-4350	22	13	in	in	ADP
ejpam-4350	22	14	an	an	DET
ejpam-4350	22	15	undirected	undirected	ADJ
ejpam-4350	22	16	connected	connected	ADJ
ejpam-4350	22	17	graph	graph	NOUN
ejpam-4350	22	18	g	g	PROPN
ejpam-4350	22	19	,	,	PUNCT
ejpam-4350	22	20	the	the	DET
ejpam-4350	22	21	distance	distance	NOUN
ejpam-4350	22	22	dg(u	dg(u	X
ejpam-4350	22	23	,	,	PUNCT
ejpam-4350	22	24	v	v	NOUN
ejpam-4350	22	25	)	)	PUNCT
ejpam-4350	22	26	is	be	AUX
ejpam-4350	22	27	the	the	DET
ejpam-4350	22	28	length	length	NOUN
ejpam-4350	22	29	of	of	ADP
ejpam-4350	22	30	a	a	DET
ejpam-4350	22	31	shortest	short	ADJ
ejpam-4350	22	32	path	path	NOUN
ejpam-4350	22	33	joining	join	VERB
ejpam-4350	22	34	u	u	NOUN
ejpam-4350	22	35	and	and	CCONJ
ejpam-4350	22	36	v.	v.	ADP
ejpam-4350	22	37	any	any	DET
ejpam-4350	22	38	u	u	NOUN
ejpam-4350	22	39	-	-	NOUN
ejpam-4350	22	40	v	v	ADJ
ejpam-4350	22	41	path	path	NOUN
ejpam-4350	22	42	of	of	ADP
ejpam-4350	22	43	length	length	NOUN
ejpam-4350	22	44	dg(u	dg(u	PROPN
ejpam-4350	22	45	,	,	PUNCT
ejpam-4350	22	46	v	v	NOUN
ejpam-4350	22	47	)	)	PUNCT
ejpam-4350	22	48	is	be	AUX
ejpam-4350	22	49	called	call	VERB
ejpam-4350	22	50	a	a	DET
ejpam-4350	22	51	u	u	NOUN
ejpam-4350	22	52	-	-	NOUN
ejpam-4350	22	53	v	v	ADJ
ejpam-4350	22	54	geodesic	geodesic	NOUN
ejpam-4350	22	55	.	.	PUNCT
ejpam-4350	23	1	the	the	DET
ejpam-4350	23	2	open	open	ADJ
ejpam-4350	23	3	neighborhood	neighborhood	NOUN
ejpam-4350	23	4	of	of	ADP
ejpam-4350	23	5	a	a	DET
ejpam-4350	23	6	point	point	NOUN
ejpam-4350	23	7	u	u	NOUN
ejpam-4350	23	8	is	be	AUX
ejpam-4350	23	9	the	the	DET
ejpam-4350	23	10	set	set	NOUN
ejpam-4350	23	11	ng(u	ng(u	NOUN
ejpam-4350	23	12	)	)	PUNCT
ejpam-4350	23	13	consisting	consist	VERB
ejpam-4350	23	14	of	of	ADP
ejpam-4350	23	15	all	all	DET
ejpam-4350	23	16	points	point	NOUN
ejpam-4350	23	17	v	v	NUM
ejpam-4350	23	18	which	which	PRON
ejpam-4350	23	19	are	be	AUX
ejpam-4350	23	20	adjacent	adjacent	ADJ
ejpam-4350	23	21	to	to	PART
ejpam-4350	23	22	u.	u.	VERB
ejpam-4350	23	23	the	the	DET
ejpam-4350	23	24	closed	closed	ADJ
ejpam-4350	23	25	neighborhood	neighborhood	NOUN
ejpam-4350	23	26	of	of	ADP
ejpam-4350	23	27	u	u	NOUN
ejpam-4350	23	28	is	be	AUX
ejpam-4350	23	29	ng[u	ng[u	PROPN
ejpam-4350	23	30	]	]	X
ejpam-4350	23	31	=	=	SYM
ejpam-4350	23	32	ng(u	ng(u	PROPN
ejpam-4350	23	33	)	)	PUNCT
ejpam-4350	23	34	∪	∪	NOUN
ejpam-4350	23	35	{	{	PUNCT
ejpam-4350	23	36	u	u	NOUN
ejpam-4350	23	37	}	}	PUNCT
ejpam-4350	23	38	.	.	PUNCT
ejpam-4350	24	1	for	for	ADP
ejpam-4350	24	2	any	any	DET
ejpam-4350	24	3	a	a	DET
ejpam-4350	24	4	⊆	⊆	NUM
ejpam-4350	24	5	v	v	NOUN
ejpam-4350	24	6	(	(	PUNCT
ejpam-4350	24	7	g	g	NOUN
ejpam-4350	24	8	)	)	PUNCT
ejpam-4350	24	9	,	,	PUNCT
ejpam-4350	24	10	ng(a	ng(a	X
ejpam-4350	24	11	)	)	PUNCT
ejpam-4350	24	12	=	=	PUNCT
ejpam-4350	24	13	⋃	⋃	NOUN
ejpam-4350	24	14	v∈a	v∈a	NOUN
ejpam-4350	24	15	ng(v	ng(v	PUNCT
ejpam-4350	24	16	)	)	PUNCT
ejpam-4350	24	17	is	be	AUX
ejpam-4350	24	18	called	call	VERB
ejpam-4350	24	19	the	the	DET
ejpam-4350	24	20	open	open	ADJ
ejpam-4350	24	21	neighborhood	neighborhood	NOUN
ejpam-4350	24	22	of	of	ADP
ejpam-4350	24	23	a	a	PRON
ejpam-4350	24	24	and	and	CCONJ
ejpam-4350	24	25	ng[a	ng[a	NOUN
ejpam-4350	24	26	]	]	X
ejpam-4350	24	27	=	=	PUNCT
ejpam-4350	24	28	ng(a	ng(a	X
ejpam-4350	24	29	)	)	PUNCT
ejpam-4350	24	30	∪	∪	ADP
ejpam-4350	24	31	a	a	PRON
ejpam-4350	24	32	is	be	AUX
ejpam-4350	24	33	called	call	VERB
ejpam-4350	24	34	the	the	DET
ejpam-4350	24	35	closed	closed	ADJ
ejpam-4350	24	36	neighborhood	neighborhood	NOUN
ejpam-4350	24	37	of	of	ADP
ejpam-4350	24	38	a.	a.	NOUN
ejpam-4350	24	39	the	the	DET
ejpam-4350	24	40	open	open	ADJ
ejpam-4350	24	41	hop	hop	NOUN
ejpam-4350	24	42	neighborhood	neighborhood	NOUN
ejpam-4350	24	43	of	of	ADP
ejpam-4350	24	44	a	a	DET
ejpam-4350	24	45	point	point	NOUN
ejpam-4350	24	46	u	u	NOUN
ejpam-4350	24	47	is	be	AUX
ejpam-4350	24	48	the	the	DET
ejpam-4350	24	49	set	set	ADJ
ejpam-4350	24	50	n2	n2	ADJ
ejpam-4350	24	51	g(u	g(u	PROPN
ejpam-4350	24	52	)	)	PUNCT
ejpam-4350	24	53	=	=	PRON
ejpam-4350	24	54	{	{	PUNCT
ejpam-4350	24	55	v	v	NUM
ejpam-4350	24	56	∈	∈	NOUN
ejpam-4350	24	57	v	v	NOUN
ejpam-4350	24	58	(	(	PUNCT
ejpam-4350	24	59	g	g	NOUN
ejpam-4350	24	60	)	)	PUNCT
ejpam-4350	24	61	:	:	PUNCT
ejpam-4350	24	62	dg(v	dg(v	X
ejpam-4350	24	63	,	,	PUNCT
ejpam-4350	24	64	u	u	NOUN
ejpam-4350	24	65	)	)	PUNCT
ejpam-4350	24	66	=	=	SYM
ejpam-4350	24	67	2	2	NUM
ejpam-4350	24	68	}	}	PUNCT
ejpam-4350	24	69	.	.	PUNCT
ejpam-4350	25	1	the	the	DET
ejpam-4350	25	2	closed	closed	ADJ
ejpam-4350	25	3	hop	hop	NOUN
ejpam-4350	25	4	neighborhood	neighborhood	NOUN
ejpam-4350	25	5	of	of	ADP
ejpam-4350	25	6	u	u	NOUN
ejpam-4350	25	7	is	be	AUX
ejpam-4350	25	8	n2	n2	ADJ
ejpam-4350	25	9	g[u	g[u	X
ejpam-4350	25	10	]	]	X
ejpam-4350	25	11	=	=	SYM
ejpam-4350	25	12	n2	n2	ADJ
ejpam-4350	25	13	g(u	g(u	PROPN
ejpam-4350	25	14	)	)	PUNCT
ejpam-4350	25	15	∪	∪	NOUN
ejpam-4350	25	16	{	{	PUNCT
ejpam-4350	25	17	u	u	NOUN
ejpam-4350	25	18	}	}	PUNCT
ejpam-4350	25	19	.	.	PUNCT
ejpam-4350	26	1	for	for	ADP
ejpam-4350	26	2	any	any	DET
ejpam-4350	26	3	a	a	DET
ejpam-4350	26	4	⊆	⊆	NUM
ejpam-4350	26	5	v	v	NOUN
ejpam-4350	26	6	(	(	PUNCT
ejpam-4350	26	7	g	g	NOUN
ejpam-4350	26	8	)	)	PUNCT
ejpam-4350	26	9	,	,	PUNCT
ejpam-4350	26	10	n2	n2	PROPN
ejpam-4350	26	11	g(a	g(a	PROPN
ejpam-4350	26	12	)	)	PUNCT
ejpam-4350	26	13	=	=	SYM
ejpam-4350	26	14	⋃	⋃	NOUN
ejpam-4350	26	15	v∈a	v∈a	NOUN
ejpam-4350	26	16	n2	n2	ADJ
ejpam-4350	26	17	g(v	g(v	PROPN
ejpam-4350	26	18	)	)	PUNCT
ejpam-4350	26	19	is	be	AUX
ejpam-4350	26	20	called	call	VERB
ejpam-4350	26	21	the	the	DET
ejpam-4350	26	22	open	open	ADJ
ejpam-4350	26	23	hop	hop	NOUN
ejpam-4350	26	24	neighborhood	neighborhood	NOUN
ejpam-4350	26	25	of	of	ADP
ejpam-4350	26	26	a	a	DET
ejpam-4350	26	27	and	and	CCONJ
ejpam-4350	26	28	n2	n2	ADJ
ejpam-4350	26	29	g[a	g[a	NOUN
ejpam-4350	26	30	]	]	X
ejpam-4350	26	31	=	=	SYM
ejpam-4350	26	32	n2	n2	PROPN
ejpam-4350	26	33	g(a	g(a	PROPN
ejpam-4350	26	34	)	)	PUNCT
ejpam-4350	26	35	∪a	∪a	NUM
ejpam-4350	26	36	is	be	AUX
ejpam-4350	26	37	called	call	VERB
ejpam-4350	26	38	the	the	DET
ejpam-4350	26	39	closed	closed	ADJ
ejpam-4350	26	40	hop	hop	NOUN
ejpam-4350	26	41	neighborhood	neighborhood	NOUN
ejpam-4350	26	42	of	of	ADP
ejpam-4350	26	43	a.	a.	NOUN
ejpam-4350	26	44	a	a	DET
ejpam-4350	26	45	set	set	NOUN
ejpam-4350	26	46	s	s	NOUN
ejpam-4350	26	47	⊆	⊆	NUM
ejpam-4350	26	48	v	v	NOUN
ejpam-4350	26	49	(	(	PUNCT
ejpam-4350	26	50	g	g	NOUN
ejpam-4350	26	51	)	)	PUNCT
ejpam-4350	26	52	is	be	AUX
ejpam-4350	26	53	a	a	DET
ejpam-4350	26	54	hop	hop	NOUN
ejpam-4350	26	55	dominating	dominating	NOUN
ejpam-4350	26	56	set	set	NOUN
ejpam-4350	26	57	if	if	SCONJ
ejpam-4350	26	58	n2	n2	ADJ
ejpam-4350	26	59	g[s	g[s	PROPN
ejpam-4350	26	60	]	]	X
ejpam-4350	26	61	=	=	SYM
ejpam-4350	26	62	v	v	NOUN
ejpam-4350	26	63	(	(	PUNCT
ejpam-4350	26	64	g	g	NOUN
ejpam-4350	26	65	)	)	PUNCT
ejpam-4350	26	66	.	.	PUNCT
ejpam-4350	27	1	the	the	DET
ejpam-4350	27	2	minimum	minimum	ADJ
ejpam-4350	27	3	cardinality	cardinality	NOUN
ejpam-4350	27	4	of	of	ADP
ejpam-4350	27	5	a	a	DET
ejpam-4350	27	6	hop	hop	NOUN
ejpam-4350	27	7	dominating	dominating	NOUN
ejpam-4350	27	8	set	set	NOUN
ejpam-4350	27	9	of	of	ADP
ejpam-4350	27	10	a	a	DET
ejpam-4350	27	11	graph	graph	NOUN
ejpam-4350	27	12	g	g	NOUN
ejpam-4350	27	13	,	,	PUNCT
ejpam-4350	27	14	denoted	denote	VERB
ejpam-4350	27	15	by	by	ADP
ejpam-4350	27	16	γh(g	γh(g	NOUN
ejpam-4350	27	17	)	)	PUNCT
ejpam-4350	27	18	,	,	PUNCT
ejpam-4350	27	19	is	be	AUX
ejpam-4350	27	20	called	call	VERB
ejpam-4350	27	21	the	the	DET
ejpam-4350	27	22	hop	hop	NOUN
ejpam-4350	27	23	domination	domination	NOUN
ejpam-4350	27	24	number	number	NOUN
ejpam-4350	27	25	of	of	ADP
ejpam-4350	27	26	g.	g.	PROPN
ejpam-4350	27	27	a	a	DET
ejpam-4350	27	28	set	set	NOUN
ejpam-4350	27	29	s	s	PROPN
ejpam-4350	27	30	⊆	⊆	NUM
ejpam-4350	27	31	v	v	NOUN
ejpam-4350	27	32	(	(	PUNCT
ejpam-4350	27	33	g	g	NOUN
ejpam-4350	27	34	)	)	PUNCT
ejpam-4350	27	35	is	be	AUX
ejpam-4350	27	36	an	an	DET
ejpam-4350	27	37	independent	independent	ADJ
ejpam-4350	27	38	set	set	NOUN
ejpam-4350	27	39	of	of	ADP
ejpam-4350	27	40	g	g	PROPN
ejpam-4350	27	41	if	if	SCONJ
ejpam-4350	27	42	no	no	DET
ejpam-4350	27	43	two	two	NUM
ejpam-4350	27	44	pair	pair	NOUN
ejpam-4350	27	45	of	of	ADP
ejpam-4350	27	46	distinct	distinct	ADJ
ejpam-4350	27	47	vertices	vertex	NOUN
ejpam-4350	27	48	of	of	ADP
ejpam-4350	27	49	s	s	NOUN
ejpam-4350	27	50	are	be	AUX
ejpam-4350	27	51	adjacent	adjacent	ADJ
ejpam-4350	27	52	.	.	PUNCT
ejpam-4350	28	1	the	the	DET
ejpam-4350	28	2	maximum	maximum	ADJ
ejpam-4350	28	3	cardinality	cardinality	NOUN
ejpam-4350	28	4	of	of	ADP
ejpam-4350	28	5	an	an	DET
ejpam-4350	28	6	independent	independent	ADJ
ejpam-4350	28	7	set	set	NOUN
ejpam-4350	28	8	of	of	ADP
ejpam-4350	28	9	g	g	NOUN
ejpam-4350	28	10	,	,	PUNCT
ejpam-4350	28	11	denoted	denote	VERB
ejpam-4350	28	12	by	by	ADP
ejpam-4350	28	13	α(g	α(g	NOUN
ejpam-4350	28	14	)	)	PUNCT
ejpam-4350	28	15	,	,	PUNCT
ejpam-4350	28	16	is	be	AUX
ejpam-4350	28	17	called	call	VERB
ejpam-4350	28	18	the	the	DET
ejpam-4350	28	19	independence	independence	NOUN
ejpam-4350	28	20	number	number	NOUN
ejpam-4350	28	21	of	of	ADP
ejpam-4350	28	22	g.	g.	PROPN
ejpam-4350	28	23	set	set	PROPN
ejpam-4350	28	24	s	s	VERB
ejpam-4350	28	25	is	be	AUX
ejpam-4350	28	26	a	a	DET
ejpam-4350	28	27	hop	hop	NOUN
ejpam-4350	28	28	independent	independent	ADJ
ejpam-4350	28	29	set	set	NOUN
ejpam-4350	28	30	of	of	ADP
ejpam-4350	28	31	g	g	PROPN
ejpam-4350	28	32	if	if	SCONJ
ejpam-4350	28	33	for	for	ADP
ejpam-4350	28	34	any	any	DET
ejpam-4350	28	35	two	two	NUM
ejpam-4350	28	36	distinct	distinct	ADJ
ejpam-4350	28	37	vertices	vertex	NOUN
ejpam-4350	28	38	v	v	NOUN
ejpam-4350	28	39	and	and	CCONJ
ejpam-4350	28	40	w	w	NOUN
ejpam-4350	28	41	of	of	ADP
ejpam-4350	28	42	s	s	NOUN
ejpam-4350	28	43	,	,	PUNCT
ejpam-4350	28	44	dg(v	dg(v	X
ejpam-4350	28	45	,	,	PUNCT
ejpam-4350	28	46	w	w	NOUN
ejpam-4350	28	47	)	)	PUNCT
ejpam-4350	28	48	6=	6=	ADP
ejpam-4350	28	49	2	2	X
ejpam-4350	28	50	.	.	X
ejpam-4350	29	1	the	the	DET
ejpam-4350	29	2	maximum	maximum	ADJ
ejpam-4350	29	3	cardinality	cardinality	NOUN
ejpam-4350	29	4	of	of	ADP
ejpam-4350	29	5	a	a	DET
ejpam-4350	29	6	hop	hop	NOUN
ejpam-4350	29	7	independent	independent	ADJ
ejpam-4350	29	8	set	set	NOUN
ejpam-4350	29	9	of	of	ADP
ejpam-4350	29	10	g	g	NOUN
ejpam-4350	29	11	,	,	PUNCT
ejpam-4350	29	12	denoted	denote	VERB
ejpam-4350	29	13	by	by	ADP
ejpam-4350	29	14	αh(g	αh(g	NOUN
ejpam-4350	29	15	)	)	PUNCT
ejpam-4350	29	16	,	,	PUNCT
ejpam-4350	29	17	is	be	AUX
ejpam-4350	29	18	called	call	VERB
ejpam-4350	29	19	the	the	DET
ejpam-4350	29	20	hop	hop	NOUN
ejpam-4350	29	21	independence	independence	NOUN
ejpam-4350	29	22	number	number	NOUN
ejpam-4350	29	23	of	of	ADP
ejpam-4350	29	24	g.	g.	PROPN
ejpam-4350	29	25	any	any	DET
ejpam-4350	29	26	independent	independent	ADJ
ejpam-4350	29	27	(	(	PUNCT
ejpam-4350	29	28	hop	hop	NOUN
ejpam-4350	29	29	independent	independent	ADJ
ejpam-4350	29	30	)	)	PUNCT
ejpam-4350	29	31	set	set	VERB
ejpam-4350	29	32	with	with	ADP
ejpam-4350	29	33	cardinality	cardinality	NOUN
ejpam-4350	29	34	α(g	α(g	NUM
ejpam-4350	29	35	)	)	PUNCT
ejpam-4350	29	36	(	(	PUNCT
ejpam-4350	29	37	resp	resp	NOUN
ejpam-4350	29	38	.	.	PUNCT
ejpam-4350	29	39	αh(g	αh(g	NOUN
ejpam-4350	29	40	)	)	PUNCT
ejpam-4350	29	41	)	)	PUNCT
ejpam-4350	29	42	is	be	AUX
ejpam-4350	29	43	referred	refer	VERB
ejpam-4350	29	44	to	to	ADP
ejpam-4350	29	45	as	as	ADP
ejpam-4350	29	46	a	a	DET
ejpam-4350	29	47	maximum	maximum	ADJ
ejpam-4350	29	48	independent	independent	ADJ
ejpam-4350	29	49	set	set	NOUN
ejpam-4350	29	50	or	or	CCONJ
ejpam-4350	29	51	α	α	NOUN
ejpam-4350	29	52	-	-	PUNCT
ejpam-4350	29	53	set	set	VERB
ejpam-4350	29	54	(	(	PUNCT
ejpam-4350	29	55	resp	resp	NOUN
ejpam-4350	29	56	.	.	PUNCT
ejpam-4350	30	1	maximum	maximum	ADJ
ejpam-4350	30	2	hop	hop	PROPN
ejpam-4350	30	3	independent	independent	ADJ
ejpam-4350	30	4	set	set	NOUN
ejpam-4350	30	5	or	or	CCONJ
ejpam-4350	30	6	αh	αh	NOUN
ejpam-4350	30	7	-	-	PUNCT
ejpam-4350	30	8	set	set	NOUN
ejpam-4350	30	9	)	)	PUNCT
ejpam-4350	30	10	of	of	ADP
ejpam-4350	30	11	g.	g.	PROPN
ejpam-4350	30	12	a	a	DET
ejpam-4350	30	13	set	set	NOUN
ejpam-4350	30	14	s	s	PART
ejpam-4350	30	15	is	be	AUX
ejpam-4350	30	16	clique	clique	NOUN
ejpam-4350	30	17	of	of	ADP
ejpam-4350	30	18	a	a	DET
ejpam-4350	30	19	graph	graph	NOUN
ejpam-4350	30	20	g	g	NOUN
ejpam-4350	30	21	if	if	SCONJ
ejpam-4350	30	22	the	the	DET
ejpam-4350	30	23	graph	graph	NOUN
ejpam-4350	30	24	〈	〈	PROPN
ejpam-4350	30	25	s	s	PART
ejpam-4350	30	26	〉	〉	NOUN
ejpam-4350	30	27	induced	induce	VERB
ejpam-4350	30	28	by	by	ADP
ejpam-4350	30	29	s	s	PROPN
ejpam-4350	30	30	is	be	AUX
ejpam-4350	30	31	a	a	DET
ejpam-4350	30	32	complete	complete	ADJ
ejpam-4350	30	33	graph	graph	NOUN
ejpam-4350	30	34	.	.	PUNCT
ejpam-4350	31	1	the	the	DET
ejpam-4350	31	2	maximum	maximum	ADJ
ejpam-4350	31	3	size	size	NOUN
ejpam-4350	31	4	or	or	CCONJ
ejpam-4350	31	5	cardinality	cardinality	NOUN
ejpam-4350	31	6	of	of	ADP
ejpam-4350	31	7	a	a	DET
ejpam-4350	31	8	clique	clique	NOUN
ejpam-4350	31	9	of	of	ADP
ejpam-4350	31	10	g	g	NOUN
ejpam-4350	31	11	,	,	PUNCT
ejpam-4350	31	12	denoted	denote	VERB
ejpam-4350	31	13	by	by	ADP
ejpam-4350	31	14	ω(g	ω(g	NOUN
ejpam-4350	31	15	)	)	PUNCT
ejpam-4350	31	16	,	,	PUNCT
ejpam-4350	31	17	is	be	AUX
ejpam-4350	31	18	called	call	VERB
ejpam-4350	31	19	the	the	DET
ejpam-4350	31	20	clique	clique	ADJ
ejpam-4350	31	21	number	number	NOUN
ejpam-4350	31	22	of	of	ADP
ejpam-4350	31	23	g.	g.	PROPN
ejpam-4350	31	24	any	any	DET
ejpam-4350	31	25	clique	clique	NOUN
ejpam-4350	31	26	in	in	ADP
ejpam-4350	31	27	g	g	PROPN
ejpam-4350	31	28	with	with	ADP
ejpam-4350	31	29	cardinality	cardinality	NOUN
ejpam-4350	31	30	ω(g	ω(g	NOUN
ejpam-4350	31	31	)	)	PUNCT
ejpam-4350	31	32	is	be	AUX
ejpam-4350	31	33	called	call	VERB
ejpam-4350	31	34	an	an	DET
ejpam-4350	31	35	ω	ω	NOUN
ejpam-4350	31	36	-	-	PUNCT
ejpam-4350	31	37	set	set	NOUN
ejpam-4350	31	38	in	in	ADP
ejpam-4350	31	39	g.	g.	PROPN
ejpam-4350	31	40	3	3	NUM
ejpam-4350	31	41	.	.	PUNCT
ejpam-4350	32	1	results	result	NOUN
ejpam-4350	32	2	proposition	proposition	NOUN
ejpam-4350	32	3	1	1	X
ejpam-4350	32	4	.	.	PUNCT
ejpam-4350	33	1	let	let	VERB
ejpam-4350	33	2	g	g	NOUN
ejpam-4350	33	3	be	be	AUX
ejpam-4350	33	4	any	any	DET
ejpam-4350	33	5	graph	graph	NOUN
ejpam-4350	33	6	on	on	ADP
ejpam-4350	33	7	n	n	DET
ejpam-4350	33	8	vertices	vertex	NOUN
ejpam-4350	33	9	.	.	PUNCT
ejpam-4350	34	1	if	if	SCONJ
ejpam-4350	34	2	s	s	NOUN
ejpam-4350	34	3	is	be	AUX
ejpam-4350	34	4	a	a	DET
ejpam-4350	34	5	maximun	maximun	PROPN
ejpam-4350	34	6	hop	hop	PROPN
ejpam-4350	34	7	independent	independent	ADJ
ejpam-4350	34	8	set	set	NOUN
ejpam-4350	34	9	of	of	ADP
ejpam-4350	34	10	g	g	NOUN
ejpam-4350	34	11	,	,	PUNCT
ejpam-4350	34	12	then	then	ADV
ejpam-4350	34	13	s	s	VERB
ejpam-4350	34	14	is	be	AUX
ejpam-4350	34	15	a	a	DET
ejpam-4350	34	16	hop	hop	NOUN
ejpam-4350	34	17	dominating	dominating	NOUN
ejpam-4350	34	18	set	set	NOUN
ejpam-4350	34	19	.	.	PUNCT
ejpam-4350	35	1	in	in	ADP
ejpam-4350	35	2	particular	particular	ADJ
ejpam-4350	35	3	,	,	PUNCT
ejpam-4350	35	4	γh(g	γh(g	NOUN
ejpam-4350	35	5	)	)	PUNCT
ejpam-4350	35	6	≤	≤	NOUN
ejpam-4350	35	7	αh(g	αh(g	NOUN
ejpam-4350	35	8	)	)	PUNCT
ejpam-4350	35	9	.	.	PUNCT
ejpam-4350	36	1	proof	proof	NOUN
ejpam-4350	36	2	.	.	PUNCT
ejpam-4350	37	1	let	let	VERB
ejpam-4350	37	2	s	s	PRON
ejpam-4350	37	3	be	be	AUX
ejpam-4350	37	4	a	a	DET
ejpam-4350	37	5	maximun	maximun	PROPN
ejpam-4350	37	6	hop	hop	PROPN
ejpam-4350	37	7	independent	independent	ADJ
ejpam-4350	37	8	set	set	NOUN
ejpam-4350	37	9	of	of	ADP
ejpam-4350	37	10	g	g	NOUN
ejpam-4350	37	11	and	and	CCONJ
ejpam-4350	37	12	let	let	VERB
ejpam-4350	37	13	v	v	NUM
ejpam-4350	37	14	∈	∈	PROPN
ejpam-4350	37	15	v	v	NOUN
ejpam-4350	37	16	(	(	PUNCT
ejpam-4350	37	17	g	g	NOUN
ejpam-4350	37	18	)	)	PUNCT
ejpam-4350	37	19	\	\	PUNCT
ejpam-4350	38	1	s.	s.	PROPN
ejpam-4350	39	1	if	if	SCONJ
ejpam-4350	39	2	dg(v	dg(v	NOUN
ejpam-4350	39	3	,	,	PUNCT
ejpam-4350	39	4	w	w	NOUN
ejpam-4350	39	5	)	)	PUNCT
ejpam-4350	39	6	6=	6=	ADP
ejpam-4350	39	7	2	2	NUM
ejpam-4350	39	8	for	for	ADP
ejpam-4350	39	9	all	all	DET
ejpam-4350	39	10	w	w	NOUN
ejpam-4350	39	11	∈	∈	PROPN
ejpam-4350	39	12	s	s	NOUN
ejpam-4350	39	13	,	,	PUNCT
ejpam-4350	39	14	then	then	ADV
ejpam-4350	39	15	s	s	VERB
ejpam-4350	39	16	∪	∪	X
ejpam-4350	39	17	{	{	PUNCT
ejpam-4350	39	18	v	v	NOUN
ejpam-4350	39	19	}	}	PUNCT
ejpam-4350	39	20	is	be	AUX
ejpam-4350	39	21	a	a	DET
ejpam-4350	39	22	hop	hop	NOUN
ejpam-4350	39	23	independent	independent	ADJ
ejpam-4350	39	24	set	set	NOUN
ejpam-4350	39	25	of	of	ADP
ejpam-4350	39	26	g	g	NOUN
ejpam-4350	39	27	,	,	PUNCT
ejpam-4350	39	28	contradicting	contradict	VERB
ejpam-4350	39	29	the	the	DET
ejpam-4350	39	30	maximality	maximality	NOUN
ejpam-4350	39	31	of	of	ADP
ejpam-4350	39	32	s.	s.	PROPN
ejpam-4350	39	33	thus	thus	ADV
ejpam-4350	39	34	,	,	PUNCT
ejpam-4350	39	35	there	there	PRON
ejpam-4350	39	36	exists	exist	VERB
ejpam-4350	39	37	z	z	PROPN
ejpam-4350	39	38	∈	∈	PROPN
ejpam-4350	39	39	s	s	VERB
ejpam-4350	39	40	such	such	ADJ
ejpam-4350	39	41	that	that	PRON
ejpam-4350	39	42	dg(v	dg(v	ADJ
ejpam-4350	39	43	,	,	PUNCT
ejpam-4350	39	44	z	z	NOUN
ejpam-4350	39	45	)	)	PUNCT
ejpam-4350	39	46	=	=	SYM
ejpam-4350	39	47	2	2	NUM
ejpam-4350	39	48	,	,	PUNCT
ejpam-4350	39	49	showing	show	VERB
ejpam-4350	39	50	that	that	SCONJ
ejpam-4350	39	51	s	s	VERB
ejpam-4350	39	52	is	be	AUX
ejpam-4350	39	53	a	a	DET
ejpam-4350	39	54	hop	hop	NOUN
ejpam-4350	39	55	dominating	dominating	NOUN
ejpam-4350	39	56	set	set	NOUN
ejpam-4350	39	57	of	of	ADP
ejpam-4350	39	58	g.	g.	PROPN
ejpam-4350	39	59	therefore	therefore	ADV
ejpam-4350	39	60	γh(g	γh(g	NOUN
ejpam-4350	39	61	)	)	PUNCT
ejpam-4350	39	62	≤	≤	NOUN
ejpam-4350	39	63	αh(g	αh(g	NOUN
ejpam-4350	39	64	)	)	PUNCT
ejpam-4350	39	65	.	.	PUNCT
ejpam-4350	40	1	theorem	theorem	NOUN
ejpam-4350	40	2	1	1	X
ejpam-4350	40	3	.	.	PUNCT
ejpam-4350	41	1	let	let	VERB
ejpam-4350	41	2	g	g	NOUN
ejpam-4350	41	3	be	be	AUX
ejpam-4350	41	4	any	any	DET
ejpam-4350	41	5	graph	graph	NOUN
ejpam-4350	41	6	on	on	ADP
ejpam-4350	41	7	n	n	DET
ejpam-4350	41	8	vertices	vertex	NOUN
ejpam-4350	41	9	.	.	PUNCT
ejpam-4350	42	1	if	if	SCONJ
ejpam-4350	42	2	s	s	PROPN
ejpam-4350	42	3	is	be	AUX
ejpam-4350	42	4	a	a	DET
ejpam-4350	42	5	hop	hop	NOUN
ejpam-4350	42	6	independent	independent	ADJ
ejpam-4350	42	7	set	set	NOUN
ejpam-4350	42	8	of	of	ADP
ejpam-4350	42	9	g	g	NOUN
ejpam-4350	42	10	,	,	PUNCT
ejpam-4350	42	11	then	then	ADV
ejpam-4350	42	12	every	every	DET
ejpam-4350	42	13	component	component	NOUN
ejpam-4350	42	14	of	of	ADP
ejpam-4350	42	15	〈	〈	PROPN
ejpam-4350	42	16	s	s	PART
ejpam-4350	42	17	〉	〉	NOUN
ejpam-4350	42	18	is	be	AUX
ejpam-4350	42	19	complete	complete	ADJ
ejpam-4350	42	20	.	.	PUNCT
ejpam-4350	43	1	moreover	moreover	ADV
ejpam-4350	43	2	,	,	PUNCT
ejpam-4350	43	3	j.	j.	PROPN
ejpam-4350	43	4	hassan	hassan	PROPN
ejpam-4350	43	5	,	,	PUNCT
ejpam-4350	43	6	s.	s.	PROPN
ejpam-4350	43	7	canoy	canoy	PROPN
ejpam-4350	43	8	,	,	PUNCT
ejpam-4350	43	9	jr	jr	PROPN
ejpam-4350	43	10	.	.	PROPN
ejpam-4350	43	11	,	,	PUNCT
ejpam-4350	43	12	a.	a.	PROPN
ejpam-4350	43	13	aradais	aradais	PROPN
ejpam-4350	43	14	/	/	SYM
ejpam-4350	43	15	eur	eur	PROPN
ejpam-4350	43	16	.	.	PUNCT
ejpam-4350	44	1	j.	j.	PROPN
ejpam-4350	44	2	pure	pure	PROPN
ejpam-4350	44	3	appl	appl	PROPN
ejpam-4350	44	4	.	.	PROPN
ejpam-4350	44	5	math	math	PROPN
ejpam-4350	44	6	,	,	PUNCT
ejpam-4350	44	7	15	15	NUM
ejpam-4350	44	8	(	(	PUNCT
ejpam-4350	44	9	2	2	NUM
ejpam-4350	44	10	)	)	PUNCT
ejpam-4350	44	11	(	(	PUNCT
ejpam-4350	44	12	2022	2022	NUM
ejpam-4350	44	13	)	)	PUNCT
ejpam-4350	44	14	,	,	PUNCT
ejpam-4350	44	15	467	467	NUM
ejpam-4350	44	16	-	-	SYM
ejpam-4350	44	17	477	477	NUM
ejpam-4350	44	18	469	469	NUM
ejpam-4350	44	19	(	(	PUNCT
ejpam-4350	44	20	i	i	NOUN
ejpam-4350	44	21	)	)	PUNCT
ejpam-4350	44	22	αh(g	αh(g	NOUN
ejpam-4350	44	23	)	)	PUNCT
ejpam-4350	44	24	=	=	SYM
ejpam-4350	45	1	n	n	NOUN
ejpam-4350	45	2	if	if	SCONJ
ejpam-4350	45	3	and	and	CCONJ
ejpam-4350	45	4	only	only	ADV
ejpam-4350	45	5	if	if	SCONJ
ejpam-4350	45	6	every	every	DET
ejpam-4350	45	7	component	component	NOUN
ejpam-4350	45	8	of	of	ADP
ejpam-4350	45	9	g	g	PROPN
ejpam-4350	45	10	is	be	AUX
ejpam-4350	45	11	complete	complete	ADJ
ejpam-4350	45	12	;	;	PUNCT
ejpam-4350	45	13	and	and	CCONJ
ejpam-4350	45	14	(	(	PUNCT
ejpam-4350	45	15	ii	ii	NOUN
ejpam-4350	45	16	)	)	PUNCT
ejpam-4350	45	17	for	for	ADP
ejpam-4350	45	18	n	n	X
ejpam-4350	45	19	≥	≥	NUM
ejpam-4350	45	20	3	3	NUM
ejpam-4350	45	21	,	,	PUNCT
ejpam-4350	45	22	αh(g	αh(g	NOUN
ejpam-4350	45	23	)	)	PUNCT
ejpam-4350	45	24	=	=	SYM
ejpam-4350	45	25	n	n	CCONJ
ejpam-4350	45	26	−	−	PROPN
ejpam-4350	45	27	1	1	NUM
ejpam-4350	45	28	if	if	SCONJ
ejpam-4350	45	29	and	and	CCONJ
ejpam-4350	45	30	only	only	ADV
ejpam-4350	45	31	if	if	SCONJ
ejpam-4350	45	32	all	all	PRON
ejpam-4350	45	33	but	but	SCONJ
ejpam-4350	45	34	a	a	DET
ejpam-4350	45	35	single	single	ADJ
ejpam-4350	45	36	component	component	NOUN
ejpam-4350	45	37	c	c	PROPN
ejpam-4350	45	38	of	of	ADP
ejpam-4350	45	39	g	g	PROPN
ejpam-4350	45	40	are	be	AUX
ejpam-4350	45	41	complete	complete	ADJ
ejpam-4350	45	42	and	and	CCONJ
ejpam-4350	45	43	c	c	NOUN
ejpam-4350	45	44	\	\	PROPN
ejpam-4350	45	45	v	v	NOUN
ejpam-4350	45	46	is	be	AUX
ejpam-4350	45	47	a	a	DET
ejpam-4350	45	48	complete	complete	ADJ
ejpam-4350	45	49	graph	graph	NOUN
ejpam-4350	45	50	for	for	ADP
ejpam-4350	45	51	some	some	DET
ejpam-4350	45	52	vertex	vertex	NOUN
ejpam-4350	45	53	v	v	ADP
ejpam-4350	45	54	∈	∈	NOUN
ejpam-4350	45	55	v	v	NOUN
ejpam-4350	45	56	(	(	PUNCT
ejpam-4350	45	57	c	c	NOUN
ejpam-4350	45	58	)	)	PUNCT
ejpam-4350	45	59	.	.	PUNCT
ejpam-4350	46	1	proof	proof	NOUN
ejpam-4350	46	2	.	.	PUNCT
ejpam-4350	47	1	let	let	VERB
ejpam-4350	47	2	s	s	PRON
ejpam-4350	47	3	be	be	AUX
ejpam-4350	47	4	a	a	DET
ejpam-4350	47	5	hop	hop	NOUN
ejpam-4350	47	6	independent	independent	ADJ
ejpam-4350	47	7	set	set	NOUN
ejpam-4350	47	8	of	of	ADP
ejpam-4350	47	9	g.	g.	PROPN
ejpam-4350	47	10	if	if	SCONJ
ejpam-4350	47	11	some	some	DET
ejpam-4350	47	12	component	component	NOUN
ejpam-4350	47	13	c	c	NOUN
ejpam-4350	47	14	of	of	ADP
ejpam-4350	47	15	〈	〈	PROPN
ejpam-4350	47	16	s	s	PART
ejpam-4350	47	17	〉	〉	NOUN
ejpam-4350	47	18	is	be	AUX
ejpam-4350	47	19	not	not	PART
ejpam-4350	47	20	complete	complete	ADJ
ejpam-4350	47	21	,	,	PUNCT
ejpam-4350	47	22	then	then	ADV
ejpam-4350	47	23	there	there	PRON
ejpam-4350	47	24	exist	exist	VERB
ejpam-4350	47	25	distinct	distinct	ADJ
ejpam-4350	47	26	vertices	vertex	NOUN
ejpam-4350	47	27	x	x	X
ejpam-4350	47	28	,	,	PUNCT
ejpam-4350	47	29	y	y	PROPN
ejpam-4350	47	30	∈	∈	PROPN
ejpam-4350	47	31	c	c	NOUN
ejpam-4350	47	32	such	such	ADJ
ejpam-4350	47	33	that	that	DET
ejpam-4350	47	34	dg(x	dg(x	PROPN
ejpam-4350	47	35	,	,	PUNCT
ejpam-4350	47	36	y	y	NOUN
ejpam-4350	47	37	)	)	PUNCT
ejpam-4350	47	38	=	=	SYM
ejpam-4350	47	39	dc(x	dc(x	NOUN
ejpam-4350	47	40	,	,	PUNCT
ejpam-4350	47	41	y	y	NOUN
ejpam-4350	47	42	)	)	PUNCT
ejpam-4350	48	1	=	=	SYM
ejpam-4350	48	2	2	2	X
ejpam-4350	48	3	.	.	X
ejpam-4350	49	1	this	this	PRON
ejpam-4350	49	2	,	,	PUNCT
ejpam-4350	49	3	however	however	ADV
ejpam-4350	49	4	,	,	PUNCT
ejpam-4350	49	5	contradicts	contradict	VERB
ejpam-4350	49	6	our	our	PRON
ejpam-4350	49	7	assumption	assumption	NOUN
ejpam-4350	49	8	of	of	ADP
ejpam-4350	49	9	s.	s.	PROPN
ejpam-4350	49	10	hence	hence	PROPN
ejpam-4350	49	11	,	,	PUNCT
ejpam-4350	49	12	every	every	DET
ejpam-4350	49	13	component	component	NOUN
ejpam-4350	49	14	of	of	ADP
ejpam-4350	49	15	〈	〈	PROPN
ejpam-4350	49	16	s	s	PART
ejpam-4350	49	17	〉	〉	NOUN
ejpam-4350	49	18	is	be	AUX
ejpam-4350	49	19	complete	complete	ADJ
ejpam-4350	49	20	.	.	PUNCT
ejpam-4350	50	1	(	(	PUNCT
ejpam-4350	50	2	i	i	NOUN
ejpam-4350	50	3	)	)	PUNCT
ejpam-4350	50	4	now	now	ADV
ejpam-4350	50	5	,	,	PUNCT
ejpam-4350	50	6	if	if	SCONJ
ejpam-4350	50	7	αh(g	αh(g	NOUN
ejpam-4350	50	8	)	)	PUNCT
ejpam-4350	50	9	=	=	SYM
ejpam-4350	51	1	n	n	CCONJ
ejpam-4350	51	2	,	,	PUNCT
ejpam-4350	51	3	then	then	ADV
ejpam-4350	51	4	v	v	X
ejpam-4350	51	5	(	(	PUNCT
ejpam-4350	51	6	g	g	NOUN
ejpam-4350	51	7	)	)	PUNCT
ejpam-4350	51	8	is	be	AUX
ejpam-4350	51	9	a	a	DET
ejpam-4350	51	10	hop	hop	NOUN
ejpam-4350	51	11	independent	independent	ADJ
ejpam-4350	51	12	set	set	NOUN
ejpam-4350	51	13	of	of	ADP
ejpam-4350	51	14	g.	g.	PROPN
ejpam-4350	51	15	by	by	ADP
ejpam-4350	51	16	the	the	DET
ejpam-4350	51	17	first	first	ADJ
ejpam-4350	51	18	part	part	NOUN
ejpam-4350	51	19	,	,	PUNCT
ejpam-4350	51	20	this	this	PRON
ejpam-4350	51	21	would	would	AUX
ejpam-4350	51	22	imply	imply	VERB
ejpam-4350	51	23	that	that	SCONJ
ejpam-4350	51	24	every	every	DET
ejpam-4350	51	25	component	component	NOUN
ejpam-4350	51	26	of	of	ADP
ejpam-4350	51	27	g	g	PROPN
ejpam-4350	51	28	is	be	AUX
ejpam-4350	51	29	complete	complete	ADJ
ejpam-4350	51	30	.	.	PUNCT
ejpam-4350	52	1	conversely	conversely	ADV
ejpam-4350	52	2	,	,	PUNCT
ejpam-4350	52	3	suppose	suppose	VERB
ejpam-4350	52	4	that	that	SCONJ
ejpam-4350	52	5	every	every	DET
ejpam-4350	52	6	component	component	NOUN
ejpam-4350	52	7	of	of	ADP
ejpam-4350	52	8	g	g	PROPN
ejpam-4350	52	9	is	be	AUX
ejpam-4350	52	10	complete	complete	ADJ
ejpam-4350	52	11	.	.	PUNCT
ejpam-4350	53	1	then	then	ADV
ejpam-4350	53	2	clearly	clearly	ADV
ejpam-4350	53	3	,	,	PUNCT
ejpam-4350	53	4	v	v	INTJ
ejpam-4350	53	5	(	(	PUNCT
ejpam-4350	53	6	g	g	NOUN
ejpam-4350	53	7	)	)	PUNCT
ejpam-4350	53	8	is	be	AUX
ejpam-4350	53	9	a	a	DET
ejpam-4350	53	10	hop	hop	NOUN
ejpam-4350	53	11	independent	independent	ADJ
ejpam-4350	53	12	set	set	NOUN
ejpam-4350	53	13	of	of	ADP
ejpam-4350	53	14	g.	g.	PROPN
ejpam-4350	53	15	thus	thus	ADV
ejpam-4350	53	16	,	,	PUNCT
ejpam-4350	53	17	αh(g	αh(g	NOUN
ejpam-4350	53	18	)	)	PUNCT
ejpam-4350	53	19	=	=	VERB
ejpam-4350	53	20	n.	n.	NOUN
ejpam-4350	53	21	this	this	PRON
ejpam-4350	53	22	proves	prove	VERB
ejpam-4350	53	23	(	(	PUNCT
ejpam-4350	53	24	i	i	NOUN
ejpam-4350	53	25	)	)	PUNCT
ejpam-4350	53	26	.	.	PUNCT
ejpam-4350	54	1	(	(	PUNCT
ejpam-4350	54	2	ii	ii	NOUN
ejpam-4350	54	3	)	)	PUNCT
ejpam-4350	54	4	suppose	suppose	VERB
ejpam-4350	54	5	that	that	SCONJ
ejpam-4350	54	6	αh(g	αh(g	NOUN
ejpam-4350	54	7	)	)	PUNCT
ejpam-4350	54	8	=	=	SYM
ejpam-4350	54	9	n−	n−	NOUN
ejpam-4350	54	10	1	1	NUM
ejpam-4350	54	11	.	.	PUNCT
ejpam-4350	54	12	then	then	ADV
ejpam-4350	54	13	there	there	PRON
ejpam-4350	54	14	exists	exist	VERB
ejpam-4350	54	15	v	v	ADP
ejpam-4350	54	16	∈	∈	PROPN
ejpam-4350	54	17	v	v	NOUN
ejpam-4350	54	18	(	(	PUNCT
ejpam-4350	54	19	g	g	NOUN
ejpam-4350	54	20	)	)	PUNCT
ejpam-4350	54	21	such	such	ADJ
ejpam-4350	54	22	that	that	PRON
ejpam-4350	54	23	s	s	PART
ejpam-4350	54	24	=	=	X
ejpam-4350	54	25	v	v	X
ejpam-4350	54	26	(	(	PUNCT
ejpam-4350	54	27	g	g	NOUN
ejpam-4350	54	28	)	)	PUNCT
ejpam-4350	54	29	\	\	NOUN
ejpam-4350	54	30	{	{	PUNCT
ejpam-4350	54	31	v	v	NOUN
ejpam-4350	54	32	}	}	PUNCT
ejpam-4350	54	33	is	be	AUX
ejpam-4350	54	34	a	a	DET
ejpam-4350	54	35	hop	hop	NOUN
ejpam-4350	54	36	independent	independent	ADJ
ejpam-4350	54	37	set	set	NOUN
ejpam-4350	54	38	of	of	ADP
ejpam-4350	54	39	g.	g.	PROPN
ejpam-4350	54	40	let	let	VERB
ejpam-4350	54	41	ω	ω	PROPN
ejpam-4350	54	42	=	=	PRON
ejpam-4350	54	43	{	{	PUNCT
ejpam-4350	54	44	c1	c1	PROPN
ejpam-4350	54	45	,	,	PUNCT
ejpam-4350	54	46	c2	c2	PROPN
ejpam-4350	54	47	,	,	PUNCT
ejpam-4350	54	48	.	.	PUNCT
ejpam-4350	54	49	.	.	PUNCT
ejpam-4350	55	1	.	.	PUNCT
ejpam-4350	56	1	,	,	PUNCT
ejpam-4350	56	2	ck	ck	X
ejpam-4350	56	3	}	}	PUNCT
ejpam-4350	56	4	be	be	AUX
ejpam-4350	56	5	the	the	DET
ejpam-4350	56	6	set	set	NOUN
ejpam-4350	56	7	consisting	consisting	NOUN
ejpam-4350	56	8	of	of	ADP
ejpam-4350	56	9	the	the	DET
ejpam-4350	56	10	components	component	NOUN
ejpam-4350	56	11	of	of	ADP
ejpam-4350	56	12	〈	〈	PROPN
ejpam-4350	56	13	s	s	PROPN
ejpam-4350	56	14	〉	〉	PROPN
ejpam-4350	56	15	.	.	PUNCT
ejpam-4350	57	1	again	again	ADV
ejpam-4350	57	2	,	,	PUNCT
ejpam-4350	57	3	by	by	ADP
ejpam-4350	57	4	the	the	DET
ejpam-4350	57	5	first	first	ADJ
ejpam-4350	57	6	part	part	NOUN
ejpam-4350	57	7	,	,	PUNCT
ejpam-4350	57	8	every	every	DET
ejpam-4350	57	9	component	component	NOUN
ejpam-4350	57	10	cj	cj	NOUN
ejpam-4350	57	11	of	of	ADP
ejpam-4350	57	12	〈	〈	PROPN
ejpam-4350	57	13	s	s	PART
ejpam-4350	57	14	〉	〉	PROPN
ejpam-4350	57	15	is	be	AUX
ejpam-4350	57	16	complete	complete	ADJ
ejpam-4350	57	17	.	.	PUNCT
ejpam-4350	58	1	now	now	ADV
ejpam-4350	58	2	,	,	PUNCT
ejpam-4350	58	3	by	by	ADP
ejpam-4350	58	4	(	(	PUNCT
ejpam-4350	58	5	i	i	NOUN
ejpam-4350	58	6	)	)	PUNCT
ejpam-4350	58	7	and	and	CCONJ
ejpam-4350	58	8	the	the	DET
ejpam-4350	58	9	assumption	assumption	NOUN
ejpam-4350	58	10	,	,	PUNCT
ejpam-4350	58	11	it	it	PRON
ejpam-4350	58	12	follows	follow	VERB
ejpam-4350	58	13	that	that	SCONJ
ejpam-4350	58	14	g	g	PROPN
ejpam-4350	58	15	has	have	VERB
ejpam-4350	58	16	a	a	DET
ejpam-4350	58	17	component	component	NOUN
ejpam-4350	58	18	c	c	NOUN
ejpam-4350	58	19	that	that	PRON
ejpam-4350	58	20	is	be	AUX
ejpam-4350	58	21	not	not	PART
ejpam-4350	58	22	complete	complete	ADJ
ejpam-4350	58	23	.	.	PUNCT
ejpam-4350	59	1	hence	hence	ADV
ejpam-4350	59	2	,	,	PUNCT
ejpam-4350	59	3	〈	〈	PROPN
ejpam-4350	59	4	{	{	PUNCT
ejpam-4350	59	5	v	v	NOUN
ejpam-4350	59	6	}	}	PUNCT
ejpam-4350	59	7	〉	〉	NOUN
ejpam-4350	59	8	is	be	AUX
ejpam-4350	59	9	not	not	PART
ejpam-4350	59	10	a	a	DET
ejpam-4350	59	11	component	component	NOUN
ejpam-4350	59	12	of	of	ADP
ejpam-4350	59	13	g	g	NOUN
ejpam-4350	59	14	;	;	PUNCT
ejpam-4350	59	15	otherwise	otherwise	ADV
ejpam-4350	59	16	,	,	PUNCT
ejpam-4350	59	17	c1	c1	PROPN
ejpam-4350	59	18	,	,	PUNCT
ejpam-4350	59	19	c2	c2	PROPN
ejpam-4350	59	20	,	,	PUNCT
ejpam-4350	59	21	.	.	PUNCT
ejpam-4350	59	22	.	.	PUNCT
ejpam-4350	60	1	.	.	PUNCT
ejpam-4350	61	1	,	,	PUNCT
ejpam-4350	61	2	ck	ck	INTJ
ejpam-4350	61	3	,	,	PUNCT
ejpam-4350	61	4	〈	〈	PROPN
ejpam-4350	61	5	{	{	PUNCT
ejpam-4350	61	6	v	v	NOUN
ejpam-4350	61	7	}	}	PUNCT
ejpam-4350	61	8	〉	〉	NOUN
ejpam-4350	61	9	are	be	AUX
ejpam-4350	61	10	the	the	DET
ejpam-4350	61	11	components	component	NOUN
ejpam-4350	61	12	of	of	ADP
ejpam-4350	61	13	g	g	PROPN
ejpam-4350	61	14	which	which	PRON
ejpam-4350	61	15	is	be	AUX
ejpam-4350	61	16	not	not	PART
ejpam-4350	61	17	possible	possible	ADJ
ejpam-4350	61	18	.	.	PUNCT
ejpam-4350	62	1	this	this	PRON
ejpam-4350	62	2	implies	imply	VERB
ejpam-4350	62	3	that	that	SCONJ
ejpam-4350	62	4	there	there	PRON
ejpam-4350	62	5	exists	exist	VERB
ejpam-4350	62	6	z	z	PROPN
ejpam-4350	62	7	∈	∈	PROPN
ejpam-4350	62	8	s	s	VERB
ejpam-4350	62	9	such	such	ADJ
ejpam-4350	62	10	that	that	SCONJ
ejpam-4350	62	11	vz	vz	PROPN
ejpam-4350	62	12	∈	∈	PROPN
ejpam-4350	62	13	e(g	e(g	PROPN
ejpam-4350	62	14	)	)	PUNCT
ejpam-4350	62	15	.	.	PUNCT
ejpam-4350	63	1	let	let	VERB
ejpam-4350	63	2	cr	cr	NOUN
ejpam-4350	63	3	be	be	AUX
ejpam-4350	63	4	the	the	DET
ejpam-4350	63	5	component	component	NOUN
ejpam-4350	63	6	of	of	ADP
ejpam-4350	63	7	〈	〈	PROPN
ejpam-4350	63	8	s	s	PROPN
ejpam-4350	63	9	〉	〉	NOUN
ejpam-4350	63	10	containing	contain	VERB
ejpam-4350	63	11	z.	z.	PROPN
ejpam-4350	63	12	since	since	SCONJ
ejpam-4350	63	13	s	s	PROPN
ejpam-4350	63	14	is	be	AUX
ejpam-4350	63	15	a	a	DET
ejpam-4350	63	16	hop	hop	NOUN
ejpam-4350	63	17	independent	independent	ADJ
ejpam-4350	63	18	set	set	NOUN
ejpam-4350	63	19	,	,	PUNCT
ejpam-4350	63	20	vq	vq	PROPN
ejpam-4350	63	21	/∈	/∈	PROPN
ejpam-4350	63	22	e(g	e(g	PROPN
ejpam-4350	63	23	)	)	PUNCT
ejpam-4350	63	24	for	for	ADP
ejpam-4350	63	25	all	all	DET
ejpam-4350	63	26	q	q	PROPN
ejpam-4350	63	27	∈	∈	PROPN
ejpam-4350	63	28	∪j	∪j	NUM
ejpam-4350	63	29	6	6	NUM
ejpam-4350	63	30	=	=	SYM
ejpam-4350	63	31	rv	rv	PROPN
ejpam-4350	63	32	(	(	PUNCT
ejpam-4350	63	33	cj	cj	NOUN
ejpam-4350	63	34	)	)	PUNCT
ejpam-4350	63	35	.	.	PUNCT
ejpam-4350	64	1	let	let	VERB
ejpam-4350	64	2	d	d	NOUN
ejpam-4350	64	3	=	=	SYM
ejpam-4350	64	4	v	v	PROPN
ejpam-4350	64	5	(	(	PUNCT
ejpam-4350	64	6	cr	cr	NOUN
ejpam-4350	64	7	)	)	PUNCT
ejpam-4350	64	8	∪	∪	NOUN
ejpam-4350	64	9	{	{	PUNCT
ejpam-4350	64	10	v	v	NOUN
ejpam-4350	64	11	}	}	PUNCT
ejpam-4350	64	12	and	and	CCONJ
ejpam-4350	64	13	let	let	VERB
ejpam-4350	64	14	c	c	NOUN
ejpam-4350	64	15	=	=	SYM
ejpam-4350	64	16	〈	〈	PROPN
ejpam-4350	64	17	d	d	PROPN
ejpam-4350	64	18	〉	〉	PROPN
ejpam-4350	64	19	.	.	PUNCT
ejpam-4350	65	1	then	then	ADV
ejpam-4350	65	2	(	(	PUNCT
ejpam-4350	65	3	ω	ω	PROPN
ejpam-4350	65	4	\	\	PROPN
ejpam-4350	65	5	{	{	PUNCT
ejpam-4350	65	6	cr	cr	NOUN
ejpam-4350	65	7	}	}	PUNCT
ejpam-4350	65	8	)	)	PUNCT
ejpam-4350	65	9	∪	∪	ADP
ejpam-4350	65	10	{	{	PUNCT
ejpam-4350	65	11	c	c	NOUN
ejpam-4350	65	12	}	}	PUNCT
ejpam-4350	65	13	contains	contain	VERB
ejpam-4350	65	14	all	all	DET
ejpam-4350	65	15	the	the	DET
ejpam-4350	65	16	components	component	NOUN
ejpam-4350	65	17	of	of	ADP
ejpam-4350	65	18	g.	g.	PROPN
ejpam-4350	65	19	consequently	consequently	ADV
ejpam-4350	65	20	,	,	PUNCT
ejpam-4350	65	21	c	c	PROPN
ejpam-4350	65	22	is	be	AUX
ejpam-4350	65	23	not	not	PART
ejpam-4350	65	24	complete	complete	ADJ
ejpam-4350	65	25	and	and	CCONJ
ejpam-4350	65	26	c	c	NOUN
ejpam-4350	65	27	\	\	PROPN
ejpam-4350	65	28	v	v	PROPN
ejpam-4350	65	29	=	=	SYM
ejpam-4350	65	30	cr	cr	PROPN
ejpam-4350	65	31	is	be	AUX
ejpam-4350	65	32	complete	complete	ADJ
ejpam-4350	65	33	.	.	PUNCT
ejpam-4350	66	1	next	next	ADV
ejpam-4350	66	2	,	,	PUNCT
ejpam-4350	66	3	suppose	suppose	VERB
ejpam-4350	66	4	that	that	SCONJ
ejpam-4350	66	5	all	all	PRON
ejpam-4350	66	6	but	but	SCONJ
ejpam-4350	66	7	a	a	DET
ejpam-4350	66	8	single	single	ADJ
ejpam-4350	66	9	component	component	NOUN
ejpam-4350	66	10	c	c	PROPN
ejpam-4350	66	11	of	of	ADP
ejpam-4350	66	12	g	g	PROPN
ejpam-4350	66	13	are	be	AUX
ejpam-4350	66	14	complete	complete	ADJ
ejpam-4350	66	15	and	and	CCONJ
ejpam-4350	66	16	c	c	NOUN
ejpam-4350	66	17	\	\	PROPN
ejpam-4350	66	18	v	v	NOUN
ejpam-4350	66	19	is	be	AUX
ejpam-4350	66	20	a	a	DET
ejpam-4350	66	21	complete	complete	ADJ
ejpam-4350	66	22	graph	graph	NOUN
ejpam-4350	66	23	for	for	ADP
ejpam-4350	66	24	some	some	DET
ejpam-4350	66	25	vertex	vertex	NOUN
ejpam-4350	66	26	v	v	ADP
ejpam-4350	66	27	∈	∈	NOUN
ejpam-4350	66	28	v	v	NOUN
ejpam-4350	66	29	(	(	PUNCT
ejpam-4350	66	30	c	c	NOUN
ejpam-4350	66	31	)	)	PUNCT
ejpam-4350	66	32	.	.	PUNCT
ejpam-4350	67	1	then	then	ADV
ejpam-4350	67	2	αh(g	αh(g	PRON
ejpam-4350	67	3	≤	≤	NUM
ejpam-4350	67	4	n−1	n−1	PROPN
ejpam-4350	67	5	by	by	ADP
ejpam-4350	67	6	(	(	PUNCT
ejpam-4350	67	7	i	i	NOUN
ejpam-4350	67	8	)	)	PUNCT
ejpam-4350	67	9	.	.	PUNCT
ejpam-4350	68	1	since	since	SCONJ
ejpam-4350	68	2	s′	s′	ADJ
ejpam-4350	68	3	=	=	SYM
ejpam-4350	68	4	v	v	X
ejpam-4350	68	5	(	(	PUNCT
ejpam-4350	68	6	g)\{v	g)\{v	PROPN
ejpam-4350	68	7	}	}	PUNCT
ejpam-4350	68	8	is	be	AUX
ejpam-4350	68	9	a	a	DET
ejpam-4350	68	10	hop	hop	NOUN
ejpam-4350	68	11	independent	independent	ADJ
ejpam-4350	68	12	set	set	NOUN
ejpam-4350	68	13	of	of	ADP
ejpam-4350	68	14	g	g	NOUN
ejpam-4350	68	15	,	,	PUNCT
ejpam-4350	68	16	it	it	PRON
ejpam-4350	68	17	follows	follow	VERB
ejpam-4350	68	18	that	that	SCONJ
ejpam-4350	68	19	αh(g	αh(g	NOUN
ejpam-4350	68	20	)	)	PUNCT
ejpam-4350	69	1	=	=	SYM
ejpam-4350	69	2	n−	n−	NOUN
ejpam-4350	69	3	1	1	NUM
ejpam-4350	69	4	.	.	PUNCT
ejpam-4350	70	1	the	the	DET
ejpam-4350	70	2	next	next	ADJ
ejpam-4350	70	3	result	result	NOUN
ejpam-4350	70	4	is	be	AUX
ejpam-4350	70	5	immediate	immediate	ADJ
ejpam-4350	70	6	from	from	ADP
ejpam-4350	70	7	theorem	theorem	ADJ
ejpam-4350	70	8	1	1	NUM
ejpam-4350	71	1	.	.	PUNCT
ejpam-4350	71	2	corollary	corollary	ADJ
ejpam-4350	71	3	1	1	NUM
ejpam-4350	71	4	.	.	PUNCT
ejpam-4350	72	1	let	let	VERB
ejpam-4350	72	2	g	g	PRON
ejpam-4350	72	3	be	be	AUX
ejpam-4350	72	4	a	a	DET
ejpam-4350	72	5	connected	connected	ADJ
ejpam-4350	72	6	graph	graph	NOUN
ejpam-4350	72	7	on	on	ADP
ejpam-4350	72	8	n	n	DET
ejpam-4350	72	9	vertices	vertex	NOUN
ejpam-4350	72	10	.	.	PUNCT
ejpam-4350	73	1	then	then	ADV
ejpam-4350	73	2	(	(	PUNCT
ejpam-4350	73	3	i	i	NOUN
ejpam-4350	73	4	)	)	PUNCT
ejpam-4350	73	5	αh(g	αh(g	NOUN
ejpam-4350	73	6	)	)	PUNCT
ejpam-4350	73	7	=	=	SYM
ejpam-4350	74	1	n	n	NOUN
ejpam-4350	74	2	if	if	SCONJ
ejpam-4350	74	3	and	and	CCONJ
ejpam-4350	74	4	only	only	ADV
ejpam-4350	74	5	if	if	SCONJ
ejpam-4350	74	6	g	g	PROPN
ejpam-4350	74	7	=	=	SYM
ejpam-4350	74	8	kn	kn	PROPN
ejpam-4350	74	9	;	;	PUNCT
ejpam-4350	74	10	and	and	CCONJ
ejpam-4350	74	11	(	(	PUNCT
ejpam-4350	74	12	ii	ii	NOUN
ejpam-4350	74	13	)	)	PUNCT
ejpam-4350	74	14	for	for	ADP
ejpam-4350	74	15	n	n	X
ejpam-4350	74	16	≥	≥	NUM
ejpam-4350	74	17	3	3	NUM
ejpam-4350	74	18	,	,	PUNCT
ejpam-4350	74	19	αh(g	αh(g	NOUN
ejpam-4350	74	20	)	)	PUNCT
ejpam-4350	74	21	=	=	SYM
ejpam-4350	74	22	n−	n−	NOUN
ejpam-4350	74	23	1	1	NUM
ejpam-4350	74	24	if	if	SCONJ
ejpam-4350	74	25	and	and	CCONJ
ejpam-4350	74	26	only	only	ADV
ejpam-4350	74	27	if	if	SCONJ
ejpam-4350	74	28	g	g	PROPN
ejpam-4350	74	29	6=	6=	PROPN
ejpam-4350	74	30	kn	kn	PROPN
ejpam-4350	74	31	and	and	CCONJ
ejpam-4350	74	32	there	there	PRON
ejpam-4350	74	33	exists	exist	VERB
ejpam-4350	74	34	v	v	ADP
ejpam-4350	74	35	∈	∈	PROPN
ejpam-4350	74	36	v	v	NOUN
ejpam-4350	74	37	(	(	PUNCT
ejpam-4350	74	38	g	g	NOUN
ejpam-4350	74	39	)	)	PUNCT
ejpam-4350	74	40	such	such	ADJ
ejpam-4350	74	41	that	that	SCONJ
ejpam-4350	74	42	g	g	PROPN
ejpam-4350	74	43	\	\	PROPN
ejpam-4350	74	44	v	v	PROPN
ejpam-4350	74	45	=	=	SYM
ejpam-4350	74	46	kn−1	kn−1	PROPN
ejpam-4350	74	47	.	.	PROPN
ejpam-4350	74	48	proposition	proposition	NOUN
ejpam-4350	74	49	2	2	NUM
ejpam-4350	74	50	.	.	PUNCT
ejpam-4350	75	1	let	let	VERB
ejpam-4350	75	2	n	n	PRON
ejpam-4350	75	3	be	be	AUX
ejpam-4350	75	4	a	a	DET
ejpam-4350	75	5	positive	positive	ADJ
ejpam-4350	75	6	integer	integer	NOUN
ejpam-4350	75	7	.	.	PUNCT
ejpam-4350	76	1	(	(	PUNCT
ejpam-4350	76	2	i	i	NOUN
ejpam-4350	76	3	)	)	PUNCT
ejpam-4350	76	4	there	there	PRON
ejpam-4350	76	5	exists	exist	VERB
ejpam-4350	76	6	a	a	DET
ejpam-4350	76	7	connected	connected	ADJ
ejpam-4350	76	8	graph	graph	NOUN
ejpam-4350	76	9	g	g	ADP
ejpam-4350	76	10	such	such	ADJ
ejpam-4350	76	11	αh(g)−	αh(g)−	NOUN
ejpam-4350	76	12	α(g	α(g	NUM
ejpam-4350	76	13	)	)	PUNCT
ejpam-4350	76	14	=	=	SYM
ejpam-4350	76	15	n.	n.	NOUN
ejpam-4350	76	16	(	(	PUNCT
ejpam-4350	76	17	ii	ii	NOUN
ejpam-4350	76	18	)	)	PUNCT
ejpam-4350	76	19	there	there	PRON
ejpam-4350	76	20	exists	exist	VERB
ejpam-4350	76	21	a	a	DET
ejpam-4350	76	22	connected	connected	ADJ
ejpam-4350	76	23	graph	graph	NOUN
ejpam-4350	76	24	g	g	ADP
ejpam-4350	76	25	such	such	ADJ
ejpam-4350	76	26	α(g)−	α(g)−	NOUN
ejpam-4350	76	27	αh(g	αh(g	NOUN
ejpam-4350	76	28	)	)	PUNCT
ejpam-4350	76	29	=	=	SYM
ejpam-4350	76	30	n.	n.	NOUN
ejpam-4350	76	31	proof	proof	NOUN
ejpam-4350	76	32	.	.	PUNCT
ejpam-4350	77	1	for	for	ADP
ejpam-4350	77	2	(	(	PUNCT
ejpam-4350	77	3	i	i	NOUN
ejpam-4350	77	4	)	)	PUNCT
ejpam-4350	77	5	,	,	PUNCT
ejpam-4350	77	6	consider	consider	VERB
ejpam-4350	77	7	g	g	PROPN
ejpam-4350	77	8	=	=	SYM
ejpam-4350	77	9	kn+1	kn+1	PROPN
ejpam-4350	77	10	.	.	PUNCT
ejpam-4350	77	11	then	then	ADV
ejpam-4350	77	12	α(g	α(g	NUM
ejpam-4350	77	13	)	)	PUNCT
ejpam-4350	77	14	=	=	SYM
ejpam-4350	77	15	1	1	NUM
ejpam-4350	77	16	,	,	PUNCT
ejpam-4350	77	17	and	and	CCONJ
ejpam-4350	77	18	by	by	ADP
ejpam-4350	77	19	corollary	corollary	ADJ
ejpam-4350	77	20	1	1	NUM
ejpam-4350	77	21	,	,	PUNCT
ejpam-4350	77	22	αh(g	αh(g	NOUN
ejpam-4350	77	23	)	)	PUNCT
ejpam-4350	77	24	=	=	SYM
ejpam-4350	78	1	n+1	n+1	PROPN
ejpam-4350	78	2	.	.	PUNCT
ejpam-4350	79	1	hence	hence	ADV
ejpam-4350	79	2	,	,	PUNCT
ejpam-4350	79	3	αh(g)−	αh(g)−	NOUN
ejpam-4350	79	4	α(g	α(g	NUM
ejpam-4350	79	5	)	)	PUNCT
ejpam-4350	79	6	=	=	SYM
ejpam-4350	79	7	n.	n.	PROPN
ejpam-4350	79	8	j.	j.	PROPN
ejpam-4350	79	9	hassan	hassan	PROPN
ejpam-4350	79	10	,	,	PUNCT
ejpam-4350	79	11	s.	s.	PROPN
ejpam-4350	79	12	canoy	canoy	PROPN
ejpam-4350	79	13	,	,	PUNCT
ejpam-4350	79	14	jr	jr	PROPN
ejpam-4350	79	15	.	.	PROPN
ejpam-4350	79	16	,	,	PUNCT
ejpam-4350	79	17	a.	a.	PROPN
ejpam-4350	79	18	aradais	aradais	PROPN
ejpam-4350	79	19	/	/	SYM
ejpam-4350	79	20	eur	eur	PROPN
ejpam-4350	79	21	.	.	PUNCT
ejpam-4350	80	1	j.	j.	PROPN
ejpam-4350	80	2	pure	pure	PROPN
ejpam-4350	80	3	appl	appl	PROPN
ejpam-4350	80	4	.	.	PROPN
ejpam-4350	80	5	math	math	PROPN
ejpam-4350	80	6	,	,	PUNCT
ejpam-4350	80	7	15	15	NUM
ejpam-4350	80	8	(	(	PUNCT
ejpam-4350	80	9	2	2	NUM
ejpam-4350	80	10	)	)	PUNCT
ejpam-4350	80	11	(	(	PUNCT
ejpam-4350	80	12	2022	2022	NUM
ejpam-4350	80	13	)	)	PUNCT
ejpam-4350	80	14	,	,	PUNCT
ejpam-4350	80	15	467	467	NUM
ejpam-4350	80	16	-	-	SYM
ejpam-4350	80	17	477	477	NUM
ejpam-4350	80	18	470	470	NUM
ejpam-4350	80	19	for	for	ADP
ejpam-4350	80	20	(	(	PUNCT
ejpam-4350	80	21	ii	ii	NOUN
ejpam-4350	80	22	)	)	PUNCT
ejpam-4350	80	23	,	,	PUNCT
ejpam-4350	80	24	consider	consider	VERB
ejpam-4350	80	25	g	g	PROPN
ejpam-4350	80	26	=	=	SYM
ejpam-4350	80	27	k1,n+2	k1,n+2	PROPN
ejpam-4350	80	28	.	.	PUNCT
ejpam-4350	81	1	then	then	ADV
ejpam-4350	81	2	α(g	α(g	NUM
ejpam-4350	81	3	)	)	PUNCT
ejpam-4350	81	4	=	=	SYM
ejpam-4350	82	1	n	n	PROPN
ejpam-4350	82	2	+	+	CCONJ
ejpam-4350	82	3	2	2	NUM
ejpam-4350	82	4	and	and	CCONJ
ejpam-4350	82	5	αh(g	αh(g	NOUN
ejpam-4350	82	6	)	)	PUNCT
ejpam-4350	82	7	=	=	SYM
ejpam-4350	82	8	2	2	X
ejpam-4350	82	9	.	.	PUNCT
ejpam-4350	82	10	thus	thus	ADV
ejpam-4350	82	11	,	,	PUNCT
ejpam-4350	82	12	α(g	α(g	NUM
ejpam-4350	82	13	)	)	PUNCT
ejpam-4350	82	14	−	−	NOUN
ejpam-4350	82	15	αh(g	αh(g	NOUN
ejpam-4350	82	16	)	)	PUNCT
ejpam-4350	82	17	=	=	SYM
ejpam-4350	82	18	n.	n.	NOUN
ejpam-4350	82	19	note	note	VERB
ejpam-4350	82	20	that	that	SCONJ
ejpam-4350	82	21	proposition	proposition	NOUN
ejpam-4350	82	22	2	2	NUM
ejpam-4350	82	23	implies	imply	VERB
ejpam-4350	82	24	that	that	SCONJ
ejpam-4350	82	25	given	give	VERB
ejpam-4350	82	26	a	a	DET
ejpam-4350	82	27	positive	positive	ADJ
ejpam-4350	82	28	integer	integer	NOUN
ejpam-4350	82	29	n	n	CCONJ
ejpam-4350	82	30	,	,	PUNCT
ejpam-4350	82	31	there	there	PRON
ejpam-4350	82	32	exists	exist	VERB
ejpam-4350	82	33	a	a	DET
ejpam-4350	82	34	connected	connected	ADJ
ejpam-4350	82	35	graph	graph	NOUN
ejpam-4350	82	36	g	g	ADP
ejpam-4350	82	37	such	such	ADJ
ejpam-4350	82	38	that	that	PRON
ejpam-4350	82	39	|α(g)−αh(g)|	|α(g)−αh(g)|	SYM
ejpam-4350	82	40	=	=	SYM
ejpam-4350	82	41	n	n	CCONJ
ejpam-4350	82	42	,	,	PUNCT
ejpam-4350	82	43	i.e.	i.e.	X
ejpam-4350	82	44	,	,	PUNCT
ejpam-4350	82	45	the	the	DET
ejpam-4350	82	46	absolute	absolute	ADJ
ejpam-4350	82	47	difference	difference	NOUN
ejpam-4350	82	48	of	of	ADP
ejpam-4350	82	49	these	these	DET
ejpam-4350	82	50	two	two	NUM
ejpam-4350	82	51	parameters	parameter	NOUN
ejpam-4350	82	52	can	can	AUX
ejpam-4350	82	53	be	be	AUX
ejpam-4350	82	54	made	make	VERB
ejpam-4350	82	55	arbitrarily	arbitrarily	ADV
ejpam-4350	82	56	large	large	ADJ
ejpam-4350	82	57	.	.	PUNCT
ejpam-4350	83	1	theorem	theorem	NOUN
ejpam-4350	83	2	2	2	NUM
ejpam-4350	83	3	.	.	PUNCT
ejpam-4350	83	4	let	let	VERB
ejpam-4350	83	5	a	a	PRON
ejpam-4350	83	6	and	and	CCONJ
ejpam-4350	83	7	b	b	NOUN
ejpam-4350	83	8	be	be	AUX
ejpam-4350	83	9	positive	positive	ADJ
ejpam-4350	83	10	integers	integer	NOUN
ejpam-4350	83	11	such	such	ADJ
ejpam-4350	83	12	that	that	SCONJ
ejpam-4350	83	13	3	3	NUM
ejpam-4350	83	14	≤	≤	NOUN
ejpam-4350	83	15	a	a	DET
ejpam-4350	83	16	≤	≤	PROPN
ejpam-4350	83	17	b.	b.	NOUN
ejpam-4350	84	1	then	then	ADV
ejpam-4350	84	2	(	(	PUNCT
ejpam-4350	84	3	i	i	NOUN
ejpam-4350	84	4	)	)	PUNCT
ejpam-4350	84	5	there	there	PRON
ejpam-4350	84	6	exists	exist	VERB
ejpam-4350	84	7	a	a	DET
ejpam-4350	84	8	connected	connected	ADJ
ejpam-4350	84	9	graph	graph	NOUN
ejpam-4350	84	10	g	g	ADP
ejpam-4350	84	11	such	such	ADJ
ejpam-4350	84	12	αh(g	αh(g	NOUN
ejpam-4350	84	13	)	)	PUNCT
ejpam-4350	84	14	=	=	SYM
ejpam-4350	84	15	a	a	PRON
ejpam-4350	84	16	and	and	CCONJ
ejpam-4350	84	17	α(g	α(g	NUM
ejpam-4350	84	18	)	)	PUNCT
ejpam-4350	84	19	=	=	SYM
ejpam-4350	84	20	b	b	NOUN
ejpam-4350	84	21	,	,	PUNCT
ejpam-4350	84	22	and	and	CCONJ
ejpam-4350	84	23	(	(	PUNCT
ejpam-4350	84	24	ii	ii	NOUN
ejpam-4350	84	25	)	)	PUNCT
ejpam-4350	84	26	there	there	PRON
ejpam-4350	84	27	exists	exist	VERB
ejpam-4350	84	28	a	a	DET
ejpam-4350	84	29	connected	connected	ADJ
ejpam-4350	84	30	graph	graph	NOUN
ejpam-4350	84	31	g′	g′	NOUN
ejpam-4350	84	32	such	such	ADJ
ejpam-4350	84	33	α(g′	α(g′	NUM
ejpam-4350	84	34	)	)	PUNCT
ejpam-4350	84	35	=	=	PUNCT
ejpam-4350	84	36	a	a	PRON
ejpam-4350	84	37	and	and	CCONJ
ejpam-4350	84	38	αh(g	αh(g	NUM
ejpam-4350	84	39	′	′	NUM
ejpam-4350	84	40	)	)	PUNCT
ejpam-4350	84	41	=	=	SYM
ejpam-4350	84	42	b.	b.	PROPN
ejpam-4350	84	43	proof	proof	NOUN
ejpam-4350	84	44	.	.	PUNCT
ejpam-4350	85	1	suppose	suppose	VERB
ejpam-4350	85	2	first	first	ADV
ejpam-4350	85	3	that	that	SCONJ
ejpam-4350	85	4	a	a	DET
ejpam-4350	85	5	=	=	X
ejpam-4350	85	6	b.	b.	NOUN
ejpam-4350	85	7	consider	consider	VERB
ejpam-4350	85	8	the	the	DET
ejpam-4350	85	9	graph	graph	NOUN
ejpam-4350	85	10	g	g	NOUN
ejpam-4350	85	11	in	in	ADP
ejpam-4350	85	12	figure	figure	NOUN
ejpam-4350	85	13	1	1	NUM
ejpam-4350	85	14	.	.	PUNCT
ejpam-4350	86	1	clearly	clearly	ADV
ejpam-4350	86	2	,	,	PUNCT
ejpam-4350	86	3	s1	s1	PROPN
ejpam-4350	86	4	=	=	PUNCT
ejpam-4350	86	5	{	{	PUNCT
ejpam-4350	86	6	y1	y1	PROPN
ejpam-4350	86	7	,	,	PUNCT
ejpam-4350	86	8	y2	y2	PROPN
ejpam-4350	86	9	,	,	PUNCT
ejpam-4350	86	10	.	.	PUNCT
ejpam-4350	86	11	.	.	PUNCT
ejpam-4350	87	1	.	.	PUNCT
ejpam-4350	88	1	,	,	PUNCT
ejpam-4350	88	2	ya	ya	PRON
ejpam-4350	88	3	}	}	PUNCT
ejpam-4350	88	4	is	be	AUX
ejpam-4350	88	5	both	both	PRON
ejpam-4350	88	6	an	an	DET
ejpam-4350	88	7	α	α	NOUN
ejpam-4350	88	8	-	-	PUNCT
ejpam-4350	88	9	set	set	VERB
ejpam-4350	88	10	and	and	CCONJ
ejpam-4350	88	11	an	an	DET
ejpam-4350	88	12	αh	αh	NOUN
ejpam-4350	88	13	-	-	PUNCT
ejpam-4350	88	14	set	set	NOUN
ejpam-4350	88	15	of	of	ADP
ejpam-4350	88	16	g.	g.	PROPN
ejpam-4350	88	17	hence	hence	ADV
ejpam-4350	88	18	,	,	PUNCT
ejpam-4350	88	19	α(g	α(g	NUM
ejpam-4350	88	20	)	)	PUNCT
ejpam-4350	88	21	=	=	NOUN
ejpam-4350	88	22	αh(g	αh(g	NOUN
ejpam-4350	88	23	)	)	PUNCT
ejpam-4350	89	1	=	=	SYM
ejpam-4350	89	2	a.	a.	NOUN
ejpam-4350	89	3	.........	.........	PUNCT
ejpam-4350	89	4	........	........	PUNCT
ejpam-4350	89	5	........	........	PUNCT
ejpam-4350	89	6	........	........	PUNCT
ejpam-4350	89	7	........	........	PUNCT
ejpam-4350	89	8	........	........	PUNCT
ejpam-4350	89	9	........	........	PUNCT
ejpam-4350	89	10	........	........	PUNCT
ejpam-4350	89	11	........	........	PUNCT
ejpam-4350	89	12	...	...	PUNCT
ejpam-4350	89	13	....................................	....................................	PUNCT
ejpam-4350	89	14	....................................	....................................	PUNCT
ejpam-4350	89	15	.........	.........	PUNCT
ejpam-4350	89	16	........	........	PUNCT
ejpam-4350	89	17	........	........	PUNCT
ejpam-4350	89	18	........	........	PUNCT
ejpam-4350	89	19	........	........	PUNCT
ejpam-4350	89	20	........	........	PUNCT
ejpam-4350	89	21	........	........	PUNCT
ejpam-4350	89	22	........	........	PUNCT
ejpam-4350	89	23	........	........	PUNCT
ejpam-4350	89	24	...	...	PUNCT
ejpam-4350	89	25	....................................	....................................	PUNCT
ejpam-4350	89	26	....................................	....................................	PUNCT
ejpam-4350	89	27	.........	.........	PUNCT
ejpam-4350	89	28	........	........	PUNCT
ejpam-4350	89	29	........	........	PUNCT
ejpam-4350	89	30	........	........	PUNCT
ejpam-4350	89	31	........	........	PUNCT
ejpam-4350	89	32	........	........	PUNCT
ejpam-4350	89	33	........	........	PUNCT
ejpam-4350	89	34	........	........	PUNCT
ejpam-4350	89	35	........	........	PUNCT
ejpam-4350	89	36	...	...	PUNCT
ejpam-4350	89	37	....................................	....................................	PUNCT
ejpam-4350	89	38	....................................	....................................	PUNCT
ejpam-4350	89	39	.........	.........	PUNCT
ejpam-4350	89	40	........	........	PUNCT
ejpam-4350	89	41	........	........	PUNCT
ejpam-4350	89	42	........	........	PUNCT
ejpam-4350	89	43	........	........	PUNCT
ejpam-4350	89	44	........	........	PUNCT
ejpam-4350	89	45	........	........	PUNCT
ejpam-4350	89	46	........	........	PUNCT
ejpam-4350	89	47	........	........	PUNCT
ejpam-4350	89	48	...	...	PUNCT
ejpam-4350	89	49	....................................	....................................	PUNCT
ejpam-4350	89	50	....................................	....................................	PUNCT
ejpam-4350	89	51	.........	.........	PUNCT
ejpam-4350	89	52	........	........	PUNCT
ejpam-4350	89	53	........	........	PUNCT
ejpam-4350	89	54	........	........	PUNCT
ejpam-4350	89	55	........	........	PUNCT
ejpam-4350	89	56	........	........	PUNCT
ejpam-4350	89	57	........	........	PUNCT
ejpam-4350	89	58	........	........	PUNCT
ejpam-4350	89	59	........	........	PUNCT
ejpam-4350	89	60	...	...	PUNCT
ejpam-4350	90	1	....................................	....................................	PUNCT
ejpam-4350	90	2	....................................	....................................	PUNCT
ejpam-4350	91	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4350	91	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4350	92	1	....................................	....................................	PUNCT
ejpam-4350	92	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4350	93	1	....................................	....................................	PUNCT
ejpam-4350	94	1	y1	y1	INTJ
ejpam-4350	94	2	y2	y2	NOUN
ejpam-4350	94	3	y3	y3	NOUN
ejpam-4350	94	4	ya−1	ya−1	NOUN
ejpam-4350	94	5	ya	ya	PROPN
ejpam-4350	94	6	x1	x1	NOUN
ejpam-4350	95	1	x2	x2	PROPN
ejpam-4350	95	2	x3	x3	PROPN
ejpam-4350	95	3	xa−1	xa−1	PROPN
ejpam-4350	95	4	xa	xa	PROPN
ejpam-4350	95	5	.	.	PUNCT
ejpam-4350	95	6	.	.	PUNCT
ejpam-4350	95	7	.	.	PUNCT
ejpam-4350	96	1	g	g	NOUN
ejpam-4350	96	2	figure	figure	NOUN
ejpam-4350	96	3	1	1	NUM
ejpam-4350	96	4	next	next	ADV
ejpam-4350	96	5	,	,	PUNCT
ejpam-4350	96	6	suppose	suppose	VERB
ejpam-4350	96	7	that	that	SCONJ
ejpam-4350	96	8	a	a	DET
ejpam-4350	96	9	<	<	X
ejpam-4350	96	10	b	b	NOUN
ejpam-4350	96	11	and	and	CCONJ
ejpam-4350	96	12	let	let	VERB
ejpam-4350	96	13	m	m	NOUN
ejpam-4350	96	14	=	=	VERB
ejpam-4350	97	1	b	b	X
ejpam-4350	97	2	−	−	PROPN
ejpam-4350	97	3	a	a	DET
ejpam-4350	97	4	+	+	NOUN
ejpam-4350	97	5	1	1	NUM
ejpam-4350	97	6	.	.	X
ejpam-4350	97	7	consider	consider	VERB
ejpam-4350	97	8	the	the	DET
ejpam-4350	97	9	graph	graph	NOUN
ejpam-4350	97	10	g	g	NOUN
ejpam-4350	97	11	in	in	ADP
ejpam-4350	97	12	figure	figure	NOUN
ejpam-4350	97	13	2	2	NUM
ejpam-4350	97	14	.	.	PUNCT
ejpam-4350	98	1	it	it	PRON
ejpam-4350	98	2	can	can	AUX
ejpam-4350	98	3	easily	easily	ADV
ejpam-4350	98	4	be	be	AUX
ejpam-4350	98	5	verified	verify	VERB
ejpam-4350	98	6	that	that	SCONJ
ejpam-4350	98	7	the	the	DET
ejpam-4350	98	8	set	set	NOUN
ejpam-4350	98	9	s1	s1	NOUN
ejpam-4350	98	10	=	=	SYM
ejpam-4350	98	11	{	{	PUNCT
ejpam-4350	98	12	y1	y1	PROPN
ejpam-4350	98	13	,	,	PUNCT
ejpam-4350	98	14	y2	y2	PROPN
ejpam-4350	98	15	,	,	PUNCT
ejpam-4350	98	16	.	.	PUNCT
ejpam-4350	98	17	.	.	PUNCT
ejpam-4350	98	18	.	.	PUNCT
ejpam-4350	99	1	,	,	PUNCT
ejpam-4350	99	2	ya−2	ya−2	PROPN
ejpam-4350	99	3	,	,	PUNCT
ejpam-4350	99	4	xa	xa	PROPN
ejpam-4350	99	5	,	,	PUNCT
ejpam-4350	99	6	z1	z1	PROPN
ejpam-4350	99	7	}	}	PUNCT
ejpam-4350	99	8	is	be	AUX
ejpam-4350	99	9	an	an	DET
ejpam-4350	99	10	αh	αh	NOUN
ejpam-4350	99	11	-	-	PUNCT
ejpam-4350	99	12	set	set	VERB
ejpam-4350	99	13	and	and	CCONJ
ejpam-4350	99	14	s2	s2	NOUN
ejpam-4350	99	15	=	=	SYM
ejpam-4350	99	16	{	{	PUNCT
ejpam-4350	99	17	y1	y1	PROPN
ejpam-4350	99	18	,	,	PUNCT
ejpam-4350	99	19	.	.	PUNCT
ejpam-4350	99	20	.	.	PUNCT
ejpam-4350	100	1	.	.	PUNCT
ejpam-4350	101	1	,	,	PUNCT
ejpam-4350	101	2	ya−1	ya−1	NOUN
ejpam-4350	101	3	,	,	PUNCT
ejpam-4350	101	4	z1	z1	PROPN
ejpam-4350	101	5	,	,	PUNCT
ejpam-4350	101	6	.	.	PUNCT
ejpam-4350	101	7	.	.	PUNCT
ejpam-4350	102	1	.	.	PUNCT
ejpam-4350	103	1	,	,	PUNCT
ejpam-4350	103	2	zm	zm	PROPN
ejpam-4350	103	3	}	}	PUNCT
ejpam-4350	103	4	is	be	AUX
ejpam-4350	103	5	an	an	DET
ejpam-4350	103	6	α	α	NOUN
ejpam-4350	103	7	-	-	PUNCT
ejpam-4350	103	8	set	set	NOUN
ejpam-4350	103	9	of	of	ADP
ejpam-4350	103	10	g.	g.	PROPN
ejpam-4350	103	11	thus	thus	ADV
ejpam-4350	103	12	,	,	PUNCT
ejpam-4350	103	13	αh(g	αh(g	NOUN
ejpam-4350	103	14	)	)	PUNCT
ejpam-4350	103	15	=	=	SYM
ejpam-4350	103	16	a	a	PRON
ejpam-4350	103	17	and	and	CCONJ
ejpam-4350	103	18	α(g	α(g	NUM
ejpam-4350	103	19	)	)	PUNCT
ejpam-4350	103	20	=	=	SYM
ejpam-4350	103	21	b.	b.	PROPN
ejpam-4350	103	22	.........	.........	PUNCT
ejpam-4350	103	23	........	........	PUNCT
ejpam-4350	103	24	........	........	PUNCT
ejpam-4350	103	25	........	........	PUNCT
ejpam-4350	103	26	........	........	PUNCT
ejpam-4350	103	27	........	........	PUNCT
ejpam-4350	103	28	........	........	PUNCT
ejpam-4350	103	29	........	........	PUNCT
ejpam-4350	103	30	........	........	PUNCT
ejpam-4350	103	31	...	...	PUNCT
ejpam-4350	104	1	....................................	....................................	PUNCT
ejpam-4350	104	2	....................................	....................................	PUNCT
ejpam-4350	104	3	.........	.........	PUNCT
ejpam-4350	104	4	........	........	PUNCT
ejpam-4350	104	5	........	........	PUNCT
ejpam-4350	104	6	........	........	PUNCT
ejpam-4350	104	7	........	........	PUNCT
ejpam-4350	104	8	........	........	PUNCT
ejpam-4350	104	9	........	........	PUNCT
ejpam-4350	104	10	........	........	PUNCT
ejpam-4350	104	11	........	........	PUNCT
ejpam-4350	104	12	...	...	PUNCT
ejpam-4350	105	1	....................................	....................................	PUNCT
ejpam-4350	105	2	....................................	....................................	PUNCT
ejpam-4350	105	3	.........	.........	PUNCT
ejpam-4350	105	4	........	........	PUNCT
ejpam-4350	105	5	........	........	PUNCT
ejpam-4350	105	6	........	........	PUNCT
ejpam-4350	105	7	........	........	PUNCT
ejpam-4350	105	8	........	........	PUNCT
ejpam-4350	105	9	........	........	PUNCT
ejpam-4350	105	10	........	........	PUNCT
ejpam-4350	105	11	........	........	PUNCT
ejpam-4350	105	12	...	...	PUNCT
ejpam-4350	106	1	....................................	....................................	PUNCT
ejpam-4350	106	2	....................................	....................................	PUNCT
ejpam-4350	106	3	.........	.........	PUNCT
ejpam-4350	106	4	........	........	PUNCT
ejpam-4350	106	5	........	........	PUNCT
ejpam-4350	106	6	........	........	PUNCT
ejpam-4350	106	7	........	........	PUNCT
ejpam-4350	106	8	........	........	PUNCT
ejpam-4350	106	9	........	........	PUNCT
ejpam-4350	106	10	........	........	PUNCT
ejpam-4350	106	11	........	........	PUNCT
ejpam-4350	106	12	...	...	PUNCT
ejpam-4350	107	1	....................................	....................................	PUNCT
ejpam-4350	107	2	....................................	....................................	PUNCT
ejpam-4350	108	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4350	108	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4350	109	1	....................................	....................................	PUNCT
ejpam-4350	109	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4350	110	1	....................................	....................................	PUNCT
ejpam-4350	110	2	............	............	PUNCT
ejpam-4350	110	3	...........	...........	PUNCT
ejpam-4350	110	4	...........	...........	PUNCT
ejpam-4350	110	5	...........	...........	PUNCT
ejpam-4350	110	6	...........	...........	PUNCT
ejpam-4350	110	7	...........	...........	PUNCT
ejpam-4350	110	8	....	....	PUNCT
ejpam-4350	110	9	....................................	....................................	PUNCT
ejpam-4350	111	1	....................................	....................................	PUNCT
ejpam-4350	111	2	.........................................	.........................................	PUNCT
ejpam-4350	111	3	......................	......................	PUNCT
ejpam-4350	112	1	....................................	....................................	PUNCT
ejpam-4350	112	2	....................................	....................................	PUNCT
ejpam-4350	112	3	.......................................................................	.......................................................................	PUNCT
ejpam-4350	113	1	....................................	....................................	PUNCT
ejpam-4350	113	2	....................................	....................................	PUNCT
ejpam-4350	114	1	y1	y1	INTJ
ejpam-4350	114	2	y2	y2	NOUN
ejpam-4350	114	3	y3	y3	NOUN
ejpam-4350	114	4	ya−1	ya−1	NOUN
ejpam-4350	114	5	x1	x1	PROPN
ejpam-4350	115	1	x2	x2	PROPN
ejpam-4350	115	2	x3	x3	PROPN
ejpam-4350	115	3	xa−1	xa−1	PROPN
ejpam-4350	115	4	xa	xa	PROPN
ejpam-4350	115	5	z1	z1	PROPN
ejpam-4350	115	6	z2	z2	PROPN
ejpam-4350	115	7	zm	zm	PROPN
ejpam-4350	115	8	.	.	PUNCT
ejpam-4350	115	9	.	.	PUNCT
ejpam-4350	115	10	.	.	PUNCT
ejpam-4350	116	1	...	...	PUNCT
ejpam-4350	117	1	g	g	NOUN
ejpam-4350	117	2	figure	figure	NOUN
ejpam-4350	117	3	2	2	NUM
ejpam-4350	117	4	(	(	PUNCT
ejpam-4350	117	5	ii	ii	NOUN
ejpam-4350	117	6	)	)	PUNCT
ejpam-4350	117	7	suppose	suppose	VERB
ejpam-4350	117	8	a	a	DET
ejpam-4350	117	9	<	<	X
ejpam-4350	117	10	b	b	NOUN
ejpam-4350	117	11	and	and	CCONJ
ejpam-4350	117	12	let	let	VERB
ejpam-4350	117	13	m	m	PROPN
ejpam-4350	117	14	=	=	VERB
ejpam-4350	117	15	b−a+1	b−a+1	PROPN
ejpam-4350	117	16	.	.	PUNCT
ejpam-4350	117	17	consider	consider	VERB
ejpam-4350	117	18	the	the	DET
ejpam-4350	117	19	graph	graph	NOUN
ejpam-4350	117	20	g′	g′	NOUN
ejpam-4350	117	21	in	in	ADP
ejpam-4350	117	22	figure	figure	NOUN
ejpam-4350	117	23	3	3	X
ejpam-4350	117	24	.	.	PUNCT
ejpam-4350	118	1	it	it	PRON
ejpam-4350	118	2	can	can	AUX
ejpam-4350	118	3	easily	easily	ADV
ejpam-4350	118	4	be	be	AUX
ejpam-4350	118	5	verified	verify	VERB
ejpam-4350	118	6	that	that	SCONJ
ejpam-4350	118	7	the	the	DET
ejpam-4350	118	8	set	set	NOUN
ejpam-4350	118	9	s	s	PART
ejpam-4350	118	10	=	=	SYM
ejpam-4350	118	11	{	{	PUNCT
ejpam-4350	118	12	y1	y1	PROPN
ejpam-4350	118	13	,	,	PUNCT
ejpam-4350	118	14	y2	y2	PROPN
ejpam-4350	118	15	,	,	PUNCT
ejpam-4350	118	16	.	.	PUNCT
ejpam-4350	118	17	.	.	PUNCT
ejpam-4350	119	1	.	.	PUNCT
ejpam-4350	120	1	,	,	PUNCT
ejpam-4350	120	2	ya−1	ya−1	PROPN
ejpam-4350	120	3	,	,	PUNCT
ejpam-4350	120	4	xa	xa	PROPN
ejpam-4350	120	5	}	}	PUNCT
ejpam-4350	120	6	is	be	AUX
ejpam-4350	120	7	an	an	DET
ejpam-4350	120	8	α	α	NOUN
ejpam-4350	120	9	-	-	PUNCT
ejpam-4350	120	10	set	set	VERB
ejpam-4350	120	11	and	and	CCONJ
ejpam-4350	120	12	s′	s′	ADJ
ejpam-4350	120	13	=	=	PUNCT
ejpam-4350	120	14	{	{	PUNCT
ejpam-4350	120	15	y1	y1	NOUN
ejpam-4350	120	16	,	,	PUNCT
ejpam-4350	120	17	.	.	PUNCT
ejpam-4350	120	18	.	.	PUNCT
ejpam-4350	121	1	.	.	PUNCT
ejpam-4350	122	1	,	,	PUNCT
ejpam-4350	122	2	ya−1	ya−1	NOUN
ejpam-4350	122	3	,	,	PUNCT
ejpam-4350	122	4	z1	z1	PROPN
ejpam-4350	122	5	,	,	PUNCT
ejpam-4350	122	6	.	.	PUNCT
ejpam-4350	122	7	.	.	PUNCT
ejpam-4350	123	1	.	.	PUNCT
ejpam-4350	124	1	,	,	PUNCT
ejpam-4350	124	2	zm	zm	PROPN
ejpam-4350	124	3	}	}	PUNCT
ejpam-4350	124	4	is	be	AUX
ejpam-4350	124	5	an	an	DET
ejpam-4350	124	6	αh	αh	NOUN
ejpam-4350	124	7	-	-	PUNCT
ejpam-4350	124	8	set	set	NOUN
ejpam-4350	124	9	of	of	ADP
ejpam-4350	124	10	g′.	g′.	X
ejpam-4350	124	11	thus	thus	ADV
ejpam-4350	124	12	,	,	PUNCT
ejpam-4350	124	13	α(g′	α(g′	X
ejpam-4350	124	14	)	)	PUNCT
ejpam-4350	124	15	=	=	PUNCT
ejpam-4350	124	16	a	a	PRON
ejpam-4350	124	17	and	and	CCONJ
ejpam-4350	124	18	αh(g	αh(g	NUM
ejpam-4350	124	19	′	′	NUM
ejpam-4350	124	20	)	)	PUNCT
ejpam-4350	124	21	=	=	SYM
ejpam-4350	124	22	b.	b.	PROPN
ejpam-4350	124	23	j.	j.	PROPN
ejpam-4350	124	24	hassan	hassan	PROPN
ejpam-4350	124	25	,	,	PUNCT
ejpam-4350	124	26	s.	s.	PROPN
ejpam-4350	124	27	canoy	canoy	PROPN
ejpam-4350	124	28	,	,	PUNCT
ejpam-4350	124	29	jr	jr	PROPN
ejpam-4350	124	30	.	.	PROPN
ejpam-4350	124	31	,	,	PUNCT
ejpam-4350	124	32	a.	a.	PROPN
ejpam-4350	124	33	aradais	aradais	PROPN
ejpam-4350	124	34	/	/	SYM
ejpam-4350	124	35	eur	eur	PROPN
ejpam-4350	124	36	.	.	PUNCT
ejpam-4350	125	1	j.	j.	PROPN
ejpam-4350	125	2	pure	pure	PROPN
ejpam-4350	125	3	appl	appl	PROPN
ejpam-4350	125	4	.	.	PROPN
ejpam-4350	125	5	math	math	PROPN
ejpam-4350	125	6	,	,	PUNCT
ejpam-4350	125	7	15	15	NUM
ejpam-4350	125	8	(	(	PUNCT
ejpam-4350	125	9	2	2	NUM
ejpam-4350	125	10	)	)	PUNCT
ejpam-4350	125	11	(	(	PUNCT
ejpam-4350	125	12	2022	2022	NUM
ejpam-4350	125	13	)	)	PUNCT
ejpam-4350	125	14	,	,	PUNCT
ejpam-4350	125	15	467	467	NUM
ejpam-4350	125	16	-	-	SYM
ejpam-4350	125	17	477	477	NUM
ejpam-4350	125	18	471	471	NUM
ejpam-4350	125	19	.........	.........	PUNCT
ejpam-4350	125	20	........	........	PUNCT
ejpam-4350	125	21	........	........	PUNCT
ejpam-4350	125	22	........	........	PUNCT
ejpam-4350	125	23	........	........	PUNCT
ejpam-4350	125	24	........	........	PUNCT
ejpam-4350	125	25	........	........	PUNCT
ejpam-4350	125	26	........	........	PUNCT
ejpam-4350	125	27	........	........	PUNCT
ejpam-4350	125	28	...	...	PUNCT
ejpam-4350	126	1	....................................	....................................	PUNCT
ejpam-4350	126	2	....................................	....................................	PUNCT
ejpam-4350	126	3	.........	.........	PUNCT
ejpam-4350	126	4	........	........	PUNCT
ejpam-4350	126	5	........	........	PUNCT
ejpam-4350	126	6	........	........	PUNCT
ejpam-4350	126	7	........	........	PUNCT
ejpam-4350	126	8	........	........	PUNCT
ejpam-4350	126	9	........	........	PUNCT
ejpam-4350	126	10	........	........	PUNCT
ejpam-4350	126	11	........	........	PUNCT
ejpam-4350	126	12	...	...	PUNCT
ejpam-4350	127	1	....................................	....................................	PUNCT
ejpam-4350	127	2	....................................	....................................	PUNCT
ejpam-4350	127	3	.........	.........	PUNCT
ejpam-4350	127	4	........	........	PUNCT
ejpam-4350	127	5	........	........	PUNCT
ejpam-4350	127	6	........	........	PUNCT
ejpam-4350	127	7	........	........	PUNCT
ejpam-4350	127	8	........	........	PUNCT
ejpam-4350	127	9	........	........	PUNCT
ejpam-4350	127	10	........	........	PUNCT
ejpam-4350	127	11	........	........	PUNCT
ejpam-4350	127	12	...	...	PUNCT
ejpam-4350	128	1	....................................	....................................	PUNCT
ejpam-4350	128	2	....................................	....................................	PUNCT
ejpam-4350	128	3	.........	.........	PUNCT
ejpam-4350	128	4	........	........	PUNCT
ejpam-4350	128	5	........	........	PUNCT
ejpam-4350	128	6	........	........	PUNCT
ejpam-4350	128	7	........	........	PUNCT
ejpam-4350	128	8	........	........	PUNCT
ejpam-4350	128	9	........	........	PUNCT
ejpam-4350	128	10	........	........	PUNCT
ejpam-4350	128	11	........	........	PUNCT
ejpam-4350	128	12	...	...	PUNCT
ejpam-4350	129	1	....................................	....................................	PUNCT
ejpam-4350	129	2	....................................	....................................	PUNCT
ejpam-4350	130	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4350	130	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4350	131	1	....................................	....................................	PUNCT
ejpam-4350	131	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4350	132	1	....................................	....................................	PUNCT
ejpam-4350	132	2	............	............	PUNCT
ejpam-4350	132	3	...........	...........	PUNCT
ejpam-4350	132	4	...........	...........	PUNCT
ejpam-4350	132	5	...........	...........	PUNCT
ejpam-4350	132	6	...........	...........	PUNCT
ejpam-4350	132	7	...........	...........	PUNCT
ejpam-4350	132	8	....	....	PUNCT
ejpam-4350	133	1	....................................	....................................	PUNCT
ejpam-4350	133	2	....................................	....................................	PUNCT
ejpam-4350	134	1	................................................	................................................	PUNCT
ejpam-4350	134	2	.............................	.............................	PUNCT
ejpam-4350	135	1	....................................	....................................	PUNCT
ejpam-4350	135	2	....................................	....................................	PUNCT
ejpam-4350	135	3	.......................................................................	.......................................................................	PUNCT
ejpam-4350	136	1	....................................	....................................	PUNCT
ejpam-4350	136	2	....................................	....................................	PUNCT
ejpam-4350	137	1	..........................................	..........................................	PUNCT
ejpam-4350	137	2	....................................	....................................	PUNCT
ejpam-4350	138	1	....................................	....................................	PUNCT
ejpam-4350	138	2	..........	..........	PUNCT
ejpam-4350	139	1	.........	.........	PUNCT
ejpam-4350	139	2	.........	.........	PUNCT
ejpam-4350	140	1	.........	.........	PUNCT
ejpam-4350	140	2	.........	.........	PUNCT
ejpam-4350	141	1	.........	.........	PUNCT
ejpam-4350	141	2	.........	.........	PUNCT
ejpam-4350	141	3	...	...	PUNCT
ejpam-4350	141	4	.	.	PUNCT
ejpam-4350	142	1	...................................	...................................	PUNCT
ejpam-4350	142	2	....................................	....................................	PUNCT
ejpam-4350	143	1	.........	.........	PUNCT
ejpam-4350	143	2	........	........	PUNCT
ejpam-4350	143	3	........	........	PUNCT
ejpam-4350	143	4	........	........	PUNCT
ejpam-4350	143	5	........	........	PUNCT
ejpam-4350	143	6	........	........	PUNCT
ejpam-4350	143	7	........	........	PUNCT
ejpam-4350	143	8	........	........	PUNCT
ejpam-4350	143	9	........	........	PUNCT
ejpam-4350	143	10	........	........	PUNCT
ejpam-4350	143	11	........	........	PUNCT
ejpam-4350	143	12	........	........	PUNCT
ejpam-4350	143	13	.......	.......	PUNCT
ejpam-4350	144	1	....................................	....................................	PUNCT
ejpam-4350	144	2	....................................	....................................	PUNCT
ejpam-4350	145	1	y1	y1	INTJ
ejpam-4350	145	2	y2	y2	NOUN
ejpam-4350	145	3	y3	y3	NOUN
ejpam-4350	145	4	ya−1	ya−1	NOUN
ejpam-4350	145	5	x1	x1	PROPN
ejpam-4350	146	1	x2	x2	PROPN
ejpam-4350	146	2	x3	x3	PROPN
ejpam-4350	146	3	xa−1	xa−1	PROPN
ejpam-4350	146	4	xa	xa	PROPN
ejpam-4350	146	5	z1	z1	PROPN
ejpam-4350	146	6	z2	z2	PROPN
ejpam-4350	146	7	zm	zm	PROPN
ejpam-4350	146	8	.	.	PUNCT
ejpam-4350	146	9	.	.	PUNCT
ejpam-4350	146	10	.	.	PUNCT
ejpam-4350	147	1	...	...	PUNCT
ejpam-4350	148	1	g′	g′	NOUN
ejpam-4350	148	2	figure	figure	NOUN
ejpam-4350	148	3	3	3	NUM
ejpam-4350	148	4	this	this	PRON
ejpam-4350	148	5	proves	prove	VERB
ejpam-4350	148	6	the	the	DET
ejpam-4350	148	7	assertion	assertion	NOUN
ejpam-4350	148	8	.	.	PUNCT
ejpam-4350	149	1	for	for	ADP
ejpam-4350	149	2	any	any	DET
ejpam-4350	149	3	graph	graph	NOUN
ejpam-4350	149	4	g	g	NOUN
ejpam-4350	149	5	,	,	PUNCT
ejpam-4350	149	6	let	let	VERB
ejpam-4350	149	7	δh(g	δh(g	NOUN
ejpam-4350	149	8	)	)	PUNCT
ejpam-4350	150	1	=	=	SYM
ejpam-4350	150	2	min{|n2	min{|n2	NOUN
ejpam-4350	150	3	g(v)|	g(v)|	VERB
ejpam-4350	150	4	:	:	PUNCT
ejpam-4350	150	5	v	v	NUM
ejpam-4350	150	6	∈	∈	PROPN
ejpam-4350	150	7	v	v	NOUN
ejpam-4350	150	8	(	(	PUNCT
ejpam-4350	150	9	g	g	NOUN
ejpam-4350	150	10	)	)	PUNCT
ejpam-4350	150	11	}	}	PUNCT
ejpam-4350	150	12	.	.	PUNCT
ejpam-4350	151	1	theorem	theorem	NOUN
ejpam-4350	151	2	3	3	NUM
ejpam-4350	151	3	.	.	X
ejpam-4350	151	4	for	for	ADP
ejpam-4350	151	5	any	any	DET
ejpam-4350	151	6	graph	graph	NOUN
ejpam-4350	151	7	g	g	NOUN
ejpam-4350	151	8	on	on	ADP
ejpam-4350	151	9	n	n	DET
ejpam-4350	151	10	vertices	vertex	NOUN
ejpam-4350	151	11	,	,	PUNCT
ejpam-4350	151	12	αh(g	αh(g	NOUN
ejpam-4350	151	13	)	)	PUNCT
ejpam-4350	151	14	≤	≤	NUM
ejpam-4350	151	15	n−	n−	NOUN
ejpam-4350	151	16	δh(g	δh(g	NOUN
ejpam-4350	151	17	)	)	PUNCT
ejpam-4350	151	18	.	.	PUNCT
ejpam-4350	152	1	proof	proof	NOUN
ejpam-4350	152	2	.	.	PUNCT
ejpam-4350	153	1	let	let	VERB
ejpam-4350	153	2	s	s	PRON
ejpam-4350	153	3	be	be	AUX
ejpam-4350	153	4	a	a	DET
ejpam-4350	153	5	maximum	maximum	ADJ
ejpam-4350	153	6	hop	hop	NOUN
ejpam-4350	153	7	independent	independent	ADJ
ejpam-4350	153	8	set	set	NOUN
ejpam-4350	153	9	of	of	ADP
ejpam-4350	153	10	g	g	NOUN
ejpam-4350	153	11	and	and	CCONJ
ejpam-4350	153	12	let	let	VERB
ejpam-4350	153	13	v	v	X
ejpam-4350	153	14	∈	∈	VERB
ejpam-4350	153	15	s.	s.	PROPN
ejpam-4350	153	16	by	by	ADP
ejpam-4350	153	17	definition	definition	NOUN
ejpam-4350	153	18	,	,	PUNCT
ejpam-4350	153	19	δh(g	δh(g	NOUN
ejpam-4350	153	20	)	)	PUNCT
ejpam-4350	153	21	≤	≤	NUM
ejpam-4350	153	22	|n2	|n2	PROPN
ejpam-4350	153	23	g(v)|	g(v)|	NOUN
ejpam-4350	153	24	.	.	PUNCT
ejpam-4350	154	1	since	since	SCONJ
ejpam-4350	154	2	s	s	PROPN
ejpam-4350	154	3	is	be	AUX
ejpam-4350	154	4	a	a	DET
ejpam-4350	154	5	hop	hop	NOUN
ejpam-4350	154	6	independent	independent	ADJ
ejpam-4350	154	7	set	set	NOUN
ejpam-4350	154	8	of	of	ADP
ejpam-4350	154	9	g	g	PROPN
ejpam-4350	154	10	and	and	CCONJ
ejpam-4350	154	11	v	v	ADP
ejpam-4350	154	12	∈	∈	PROPN
ejpam-4350	154	13	s	s	NOUN
ejpam-4350	154	14	,	,	PUNCT
ejpam-4350	154	15	n2	n2	ADJ
ejpam-4350	154	16	g(v	g(v	X
ejpam-4350	154	17	)	)	PUNCT
ejpam-4350	154	18	⊆	⊆	NUM
ejpam-4350	154	19	v	v	NOUN
ejpam-4350	154	20	(	(	PUNCT
ejpam-4350	154	21	g	g	NOUN
ejpam-4350	154	22	)	)	PUNCT
ejpam-4350	154	23	\	\	NOUN
ejpam-4350	155	1	s.	s.	PROPN
ejpam-4350	155	2	hence	hence	ADV
ejpam-4350	155	3	,	,	PUNCT
ejpam-4350	155	4	δh(g	δh(g	NOUN
ejpam-4350	155	5	)	)	PUNCT
ejpam-4350	155	6	≤	≤	NUM
ejpam-4350	155	7	|n2	|n2	PROPN
ejpam-4350	155	8	g(v)|	g(v)|	NOUN
ejpam-4350	155	9	≤	≤	ADJ
ejpam-4350	155	10	n−	n−	NOUN
ejpam-4350	155	11	|s|	|s|	NOUN
ejpam-4350	155	12	=	=	SYM
ejpam-4350	155	13	n−	n−	NOUN
ejpam-4350	155	14	αh(g	αh(g	NOUN
ejpam-4350	155	15	)	)	PUNCT
ejpam-4350	155	16	.	.	PUNCT
ejpam-4350	156	1	therefore	therefore	ADV
ejpam-4350	156	2	,	,	PUNCT
ejpam-4350	156	3	αh(g	αh(g	NOUN
ejpam-4350	156	4	)	)	PUNCT
ejpam-4350	156	5	≤	≤	NUM
ejpam-4350	156	6	n−	n−	NOUN
ejpam-4350	156	7	δh(g	δh(g	NOUN
ejpam-4350	156	8	)	)	PUNCT
ejpam-4350	156	9	.	.	PUNCT
ejpam-4350	157	1	the	the	DET
ejpam-4350	157	2	join	join	NOUN
ejpam-4350	157	3	of	of	ADP
ejpam-4350	157	4	two	two	NUM
ejpam-4350	157	5	graphs	graph	NOUN
ejpam-4350	157	6	g	g	NOUN
ejpam-4350	157	7	and	and	CCONJ
ejpam-4350	157	8	h	h	NOUN
ejpam-4350	157	9	,	,	PUNCT
ejpam-4350	157	10	denoted	denote	VERB
ejpam-4350	157	11	by	by	ADP
ejpam-4350	157	12	g	g	PROPN
ejpam-4350	157	13	+	+	CCONJ
ejpam-4350	157	14	h	h	NOUN
ejpam-4350	157	15	is	be	AUX
ejpam-4350	157	16	the	the	DET
ejpam-4350	157	17	graph	graph	NOUN
ejpam-4350	157	18	with	with	ADP
ejpam-4350	157	19	vertex	vertex	NOUN
ejpam-4350	157	20	set	set	VERB
ejpam-4350	157	21	v	v	NOUN
ejpam-4350	157	22	(	(	PUNCT
ejpam-4350	157	23	g+h	g+h	NOUN
ejpam-4350	157	24	)	)	PUNCT
ejpam-4350	157	25	=	=	SYM
ejpam-4350	157	26	v	v	NOUN
ejpam-4350	157	27	(	(	PUNCT
ejpam-4350	157	28	g)∪	g)∪	VERB
ejpam-4350	157	29	v	v	NUM
ejpam-4350	157	30	(	(	PUNCT
ejpam-4350	157	31	h	h	NOUN
ejpam-4350	157	32	)	)	PUNCT
ejpam-4350	157	33	and	and	CCONJ
ejpam-4350	157	34	edge	edge	NOUN
ejpam-4350	157	35	set	set	VERB
ejpam-4350	157	36	e(g+h	e(g+h	NUM
ejpam-4350	157	37	)	)	PUNCT
ejpam-4350	158	1	=	=	SYM
ejpam-4350	158	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-4350	158	3	{	{	PUNCT
ejpam-4350	158	4	uv	uv	NOUN
ejpam-4350	158	5	:	:	PUNCT
ejpam-4350	158	6	u	u	PROPN
ejpam-4350	158	7	∈	∈	PROPN
ejpam-4350	158	8	v	v	ADP
ejpam-4350	158	9	(	(	PUNCT
ejpam-4350	158	10	g	g	NOUN
ejpam-4350	158	11	)	)	PUNCT
ejpam-4350	158	12	,	,	PUNCT
ejpam-4350	158	13	v	v	X
ejpam-4350	158	14	∈	∈	PROPN
ejpam-4350	158	15	v	v	NOUN
ejpam-4350	158	16	(	(	PUNCT
ejpam-4350	158	17	h	h	NOUN
ejpam-4350	158	18	)	)	PUNCT
ejpam-4350	158	19	}	}	PUNCT
ejpam-4350	158	20	.	.	PUNCT
ejpam-4350	159	1	theorem	theorem	ADJ
ejpam-4350	159	2	4	4	NUM
ejpam-4350	159	3	.	.	PUNCT
ejpam-4350	160	1	let	let	VERB
ejpam-4350	160	2	g	g	NOUN
ejpam-4350	160	3	and	and	CCONJ
ejpam-4350	160	4	h	h	PROPN
ejpam-4350	160	5	be	be	AUX
ejpam-4350	160	6	graphs	graph	NOUN
ejpam-4350	160	7	.	.	PUNCT
ejpam-4350	161	1	then	then	ADV
ejpam-4350	161	2	s	s	VERB
ejpam-4350	161	3	is	be	AUX
ejpam-4350	161	4	a	a	DET
ejpam-4350	161	5	non	non	ADJ
ejpam-4350	161	6	-	-	ADJ
ejpam-4350	161	7	empty	empty	ADJ
ejpam-4350	161	8	hop	hop	NOUN
ejpam-4350	161	9	independent	independent	ADJ
ejpam-4350	161	10	set	set	NOUN
ejpam-4350	161	11	of	of	ADP
ejpam-4350	161	12	g+h	g+h	PROPN
ejpam-4350	161	13	if	if	SCONJ
ejpam-4350	161	14	and	and	CCONJ
ejpam-4350	161	15	only	only	ADV
ejpam-4350	161	16	if	if	SCONJ
ejpam-4350	161	17	one	one	NUM
ejpam-4350	161	18	of	of	ADP
ejpam-4350	161	19	the	the	DET
ejpam-4350	161	20	following	following	ADJ
ejpam-4350	161	21	statements	statement	NOUN
ejpam-4350	161	22	holds	hold	VERB
ejpam-4350	161	23	:	:	PUNCT
ejpam-4350	161	24	(	(	PUNCT
ejpam-4350	161	25	i	i	NOUN
ejpam-4350	161	26	)	)	PUNCT
ejpam-4350	161	27	s	s	PART
ejpam-4350	161	28	∩	∩	ADJ
ejpam-4350	161	29	v	v	ADJ
ejpam-4350	161	30	(	(	PUNCT
ejpam-4350	161	31	h	h	NOUN
ejpam-4350	161	32	)	)	PUNCT
ejpam-4350	161	33	=	=	NOUN
ejpam-4350	161	34	∅	∅	NOUN
ejpam-4350	161	35	and	and	CCONJ
ejpam-4350	161	36	s	s	X
ejpam-4350	161	37	∩	∩	ADJ
ejpam-4350	161	38	v	v	ADJ
ejpam-4350	161	39	(	(	PUNCT
ejpam-4350	161	40	g	g	NOUN
ejpam-4350	161	41	)	)	PUNCT
ejpam-4350	161	42	is	be	AUX
ejpam-4350	161	43	a	a	DET
ejpam-4350	161	44	clique	clique	NOUN
ejpam-4350	161	45	in	in	ADP
ejpam-4350	161	46	g.	g.	PROPN
ejpam-4350	161	47	(	(	PUNCT
ejpam-4350	161	48	ii	ii	PROPN
ejpam-4350	161	49	)	)	PUNCT
ejpam-4350	161	50	s	s	PART
ejpam-4350	161	51	∩	∩	ADJ
ejpam-4350	161	52	v	v	X
ejpam-4350	161	53	(	(	PUNCT
ejpam-4350	161	54	g	g	NOUN
ejpam-4350	161	55	)	)	PUNCT
ejpam-4350	161	56	=	=	NOUN
ejpam-4350	161	57	∅	∅	NOUN
ejpam-4350	161	58	and	and	CCONJ
ejpam-4350	161	59	s	s	X
ejpam-4350	161	60	∩	∩	ADJ
ejpam-4350	161	61	v	v	ADJ
ejpam-4350	161	62	(	(	PUNCT
ejpam-4350	161	63	h	h	NOUN
ejpam-4350	161	64	)	)	PUNCT
ejpam-4350	161	65	is	be	AUX
ejpam-4350	161	66	a	a	DET
ejpam-4350	161	67	clique	clique	NOUN
ejpam-4350	161	68	in	in	ADP
ejpam-4350	161	69	h	h	PROPN
ejpam-4350	161	70	(	(	PUNCT
ejpam-4350	161	71	iii	iii	NOUN
ejpam-4350	161	72	)	)	PUNCT
ejpam-4350	161	73	s	s	PART
ejpam-4350	161	74	∩	∩	ADJ
ejpam-4350	161	75	v	v	X
ejpam-4350	161	76	(	(	PUNCT
ejpam-4350	161	77	g	g	NOUN
ejpam-4350	161	78	)	)	PUNCT
ejpam-4350	161	79	and	and	CCONJ
ejpam-4350	161	80	s	s	VERB
ejpam-4350	161	81	∩	∩	ADJ
ejpam-4350	161	82	v	v	ADJ
ejpam-4350	161	83	(	(	PUNCT
ejpam-4350	161	84	g	g	NOUN
ejpam-4350	161	85	)	)	PUNCT
ejpam-4350	161	86	are	be	AUX
ejpam-4350	161	87	cliques	clique	NOUN
ejpam-4350	161	88	in	in	ADP
ejpam-4350	161	89	g	g	PROPN
ejpam-4350	161	90	and	and	CCONJ
ejpam-4350	161	91	h	h	NOUN
ejpam-4350	161	92	,	,	PUNCT
ejpam-4350	161	93	respectively	respectively	ADV
ejpam-4350	161	94	.	.	PUNCT
ejpam-4350	162	1	proof	proof	NOUN
ejpam-4350	162	2	.	.	PUNCT
ejpam-4350	163	1	suppose	suppose	VERB
ejpam-4350	163	2	s	s	PRON
ejpam-4350	163	3	is	be	AUX
ejpam-4350	163	4	a	a	DET
ejpam-4350	163	5	hop	hop	NOUN
ejpam-4350	163	6	independent	independent	ADJ
ejpam-4350	163	7	set	set	NOUN
ejpam-4350	163	8	of	of	ADP
ejpam-4350	163	9	g	g	PROPN
ejpam-4350	163	10	+	+	CCONJ
ejpam-4350	163	11	h	h	NOUN
ejpam-4350	163	12	and	and	CCONJ
ejpam-4350	163	13	let	let	VERB
ejpam-4350	163	14	sg	sg	VERB
ejpam-4350	163	15	=	=	SYM
ejpam-4350	163	16	s	s	PART
ejpam-4350	163	17	∩	∩	ADJ
ejpam-4350	163	18	v	v	X
ejpam-4350	163	19	(	(	PUNCT
ejpam-4350	163	20	g	g	NOUN
ejpam-4350	163	21	)	)	PUNCT
ejpam-4350	163	22	and	and	CCONJ
ejpam-4350	163	23	sh	sh	INTJ
ejpam-4350	163	24	=	=	SYM
ejpam-4350	163	25	s	s	PROPN
ejpam-4350	163	26	∩	∩	ADJ
ejpam-4350	163	27	v	v	ADJ
ejpam-4350	163	28	(	(	PUNCT
ejpam-4350	163	29	h	h	NOUN
ejpam-4350	163	30	)	)	PUNCT
ejpam-4350	163	31	.	.	PUNCT
ejpam-4350	164	1	suppose	suppose	VERB
ejpam-4350	164	2	sh	sh	AUX
ejpam-4350	164	3	=	=	PUNCT
ejpam-4350	164	4	∅.	∅.	VERB
ejpam-4350	164	5	then	then	ADV
ejpam-4350	164	6	sg	sg	PROPN
ejpam-4350	164	7	6=	6=	ADP
ejpam-4350	164	8	∅.	∅.	ADV
ejpam-4350	164	9	let	let	VERB
ejpam-4350	164	10	a	a	DET
ejpam-4350	164	11	,	,	PUNCT
ejpam-4350	164	12	b	b	PROPN
ejpam-4350	164	13	∈	∈	PROPN
ejpam-4350	164	14	sg	sg	PROPN
ejpam-4350	164	15	.	.	PUNCT
ejpam-4350	165	1	since	since	SCONJ
ejpam-4350	165	2	s	s	PROPN
ejpam-4350	165	3	is	be	AUX
ejpam-4350	165	4	a	a	DET
ejpam-4350	165	5	hop	hop	NOUN
ejpam-4350	165	6	independent	independent	ADJ
ejpam-4350	165	7	set	set	NOUN
ejpam-4350	165	8	of	of	ADP
ejpam-4350	165	9	g	g	PROPN
ejpam-4350	165	10	+	+	CCONJ
ejpam-4350	165	11	h	h	NOUN
ejpam-4350	165	12	,	,	PUNCT
ejpam-4350	165	13	it	it	PRON
ejpam-4350	165	14	follows	follow	VERB
ejpam-4350	165	15	that	that	DET
ejpam-4350	165	16	dg+h(a	dg+h(a	NOUN
ejpam-4350	165	17	,	,	PUNCT
ejpam-4350	165	18	b	b	NOUN
ejpam-4350	165	19	)	)	PUNCT
ejpam-4350	165	20	=	=	SYM
ejpam-4350	165	21	dg(a	dg(a	X
ejpam-4350	165	22	,	,	PUNCT
ejpam-4350	165	23	b	b	NOUN
ejpam-4350	165	24	)	)	PUNCT
ejpam-4350	165	25	6=	6=	ADP
ejpam-4350	165	26	2	2	X
ejpam-4350	165	27	.	.	PUNCT
ejpam-4350	166	1	this	this	PRON
ejpam-4350	166	2	implies	imply	VERB
ejpam-4350	166	3	that	that	SCONJ
ejpam-4350	166	4	dg(a	dg(a	PROPN
ejpam-4350	166	5	,	,	PUNCT
ejpam-4350	166	6	b	b	X
ejpam-4350	166	7	)	)	PUNCT
ejpam-4350	166	8	=	=	SYM
ejpam-4350	166	9	1	1	NUM
ejpam-4350	166	10	,	,	PUNCT
ejpam-4350	166	11	showing	show	VERB
ejpam-4350	166	12	that	that	SCONJ
ejpam-4350	166	13	sg	sg	PROPN
ejpam-4350	166	14	is	be	AUX
ejpam-4350	166	15	a	a	DET
ejpam-4350	166	16	clique	clique	NOUN
ejpam-4350	166	17	in	in	ADP
ejpam-4350	166	18	g.	g.	PROPN
ejpam-4350	166	19	hence	hence	ADV
ejpam-4350	166	20	,	,	PUNCT
ejpam-4350	166	21	(	(	PUNCT
ejpam-4350	166	22	i	i	NOUN
ejpam-4350	166	23	)	)	PUNCT
ejpam-4350	166	24	holds	hold	VERB
ejpam-4350	166	25	.	.	PUNCT
ejpam-4350	167	1	similarly	similarly	ADV
ejpam-4350	167	2	,	,	PUNCT
ejpam-4350	167	3	(	(	PUNCT
ejpam-4350	167	4	ii	ii	NOUN
ejpam-4350	167	5	)	)	PUNCT
ejpam-4350	167	6	holds	hold	VERB
ejpam-4350	167	7	.	.	PUNCT
ejpam-4350	168	1	next	next	ADV
ejpam-4350	168	2	,	,	PUNCT
ejpam-4350	168	3	suppose	suppose	VERB
ejpam-4350	168	4	that	that	SCONJ
ejpam-4350	168	5	sg	sg	PROPN
ejpam-4350	168	6	6=	6=	ADP
ejpam-4350	168	7	∅	∅	NOUN
ejpam-4350	168	8	and	and	CCONJ
ejpam-4350	168	9	sh	sh	PROPN
ejpam-4350	168	10	6=	6=	PROPN
ejpam-4350	168	11	∅.	∅.	ADP
ejpam-4350	168	12	then	then	ADV
ejpam-4350	168	13	,	,	PUNCT
ejpam-4350	168	14	clearly	clearly	ADV
ejpam-4350	168	15	,	,	PUNCT
ejpam-4350	168	16	sg	sg	PROPN
ejpam-4350	168	17	and	and	CCONJ
ejpam-4350	168	18	sh	sh	PROPN
ejpam-4350	168	19	are	be	AUX
ejpam-4350	168	20	cliques	clique	NOUN
ejpam-4350	168	21	in	in	ADP
ejpam-4350	168	22	g	g	PROPN
ejpam-4350	168	23	and	and	CCONJ
ejpam-4350	168	24	h	h	NOUN
ejpam-4350	168	25	,	,	PUNCT
ejpam-4350	168	26	respectively	respectively	ADV
ejpam-4350	168	27	.	.	PUNCT
ejpam-4350	169	1	the	the	DET
ejpam-4350	169	2	converse	converse	NOUN
ejpam-4350	169	3	is	be	AUX
ejpam-4350	169	4	clear	clear	ADJ
ejpam-4350	169	5	.	.	PUNCT
ejpam-4350	170	1	the	the	DET
ejpam-4350	170	2	next	next	ADJ
ejpam-4350	170	3	result	result	NOUN
ejpam-4350	170	4	is	be	AUX
ejpam-4350	170	5	a	a	DET
ejpam-4350	170	6	consequence	consequence	NOUN
ejpam-4350	170	7	of	of	ADP
ejpam-4350	170	8	theorem	theorem	ADJ
ejpam-4350	170	9	4	4	NUM
ejpam-4350	170	10	.	.	PUNCT
ejpam-4350	170	11	corollary	corollary	ADJ
ejpam-4350	170	12	2	2	NUM
ejpam-4350	170	13	.	.	PUNCT
ejpam-4350	171	1	let	let	VERB
ejpam-4350	171	2	g	g	NOUN
ejpam-4350	171	3	and	and	CCONJ
ejpam-4350	171	4	h	h	PROPN
ejpam-4350	171	5	be	be	AUX
ejpam-4350	171	6	graphs	graph	NOUN
ejpam-4350	171	7	.	.	PUNCT
ejpam-4350	172	1	then	then	ADV
ejpam-4350	172	2	αh(g	αh(g	PRON
ejpam-4350	172	3	+	+	ADJ
ejpam-4350	172	4	h	h	NOUN
ejpam-4350	172	5	)	)	PUNCT
ejpam-4350	172	6	=	=	SYM
ejpam-4350	172	7	ω(g	ω(g	NOUN
ejpam-4350	172	8	)	)	PUNCT
ejpam-4350	172	9	+	+	NUM
ejpam-4350	172	10	ω(h	ω(h	NUM
ejpam-4350	172	11	)	)	PUNCT
ejpam-4350	172	12	.	.	PUNCT
ejpam-4350	173	1	in	in	ADP
ejpam-4350	173	2	particular	particular	ADJ
ejpam-4350	173	3	,	,	PUNCT
ejpam-4350	173	4	we	we	PRON
ejpam-4350	173	5	have	have	VERB
ejpam-4350	173	6	j.	j.	PROPN
ejpam-4350	173	7	hassan	hassan	PROPN
ejpam-4350	173	8	,	,	PUNCT
ejpam-4350	173	9	s.	s.	PROPN
ejpam-4350	173	10	canoy	canoy	PROPN
ejpam-4350	173	11	,	,	PUNCT
ejpam-4350	173	12	jr	jr	PROPN
ejpam-4350	173	13	.	.	PROPN
ejpam-4350	173	14	,	,	PUNCT
ejpam-4350	173	15	a.	a.	PROPN
ejpam-4350	173	16	aradais	aradais	PROPN
ejpam-4350	173	17	/	/	SYM
ejpam-4350	173	18	eur	eur	PROPN
ejpam-4350	173	19	.	.	PUNCT
ejpam-4350	174	1	j.	j.	PROPN
ejpam-4350	174	2	pure	pure	PROPN
ejpam-4350	174	3	appl	appl	PROPN
ejpam-4350	174	4	.	.	PROPN
ejpam-4350	174	5	math	math	PROPN
ejpam-4350	174	6	,	,	PUNCT
ejpam-4350	174	7	15	15	NUM
ejpam-4350	174	8	(	(	PUNCT
ejpam-4350	174	9	2	2	NUM
ejpam-4350	174	10	)	)	PUNCT
ejpam-4350	174	11	(	(	PUNCT
ejpam-4350	174	12	2022	2022	NUM
ejpam-4350	174	13	)	)	PUNCT
ejpam-4350	174	14	,	,	PUNCT
ejpam-4350	174	15	467	467	NUM
ejpam-4350	174	16	-	-	SYM
ejpam-4350	174	17	477	477	NUM
ejpam-4350	174	18	472	472	NUM
ejpam-4350	174	19	(	(	PUNCT
ejpam-4350	174	20	i	i	NOUN
ejpam-4350	174	21	)	)	PUNCT
ejpam-4350	174	22	αh(kn	αh(kn	PROPN
ejpam-4350	175	1	+	+	PROPN
ejpam-4350	175	2	h	h	NOUN
ejpam-4350	175	3	)	)	PUNCT
ejpam-4350	175	4	=	=	SYM
ejpam-4350	175	5	n+	n+	NOUN
ejpam-4350	175	6	ω(h	ω(h	NUM
ejpam-4350	175	7	)	)	PUNCT
ejpam-4350	175	8	for	for	ADP
ejpam-4350	175	9	all	all	DET
ejpam-4350	175	10	n	n	PRON
ejpam-4350	175	11	≥	≥	NOUN
ejpam-4350	175	12	1	1	NUM
ejpam-4350	175	13	;	;	PUNCT
ejpam-4350	175	14	(	(	PUNCT
ejpam-4350	175	15	ii	ii	NOUN
ejpam-4350	175	16	)	)	PUNCT
ejpam-4350	175	17	αh(wn	αh(wn	PROPN
ejpam-4350	175	18	)	)	PUNCT
ejpam-4350	176	1	=	=	SYM
ejpam-4350	176	2	αh(k1	αh(k1	PROPN
ejpam-4350	176	3	+	+	CCONJ
ejpam-4350	176	4	cn	cn	ADJ
ejpam-4350	176	5	)	)	PUNCT
ejpam-4350	176	6	=	=	SYM
ejpam-4350	176	7	3	3	NUM
ejpam-4350	176	8	for	for	ADP
ejpam-4350	176	9	all	all	DET
ejpam-4350	176	10	n	n	PRON
ejpam-4350	176	11	≥	≥	NOUN
ejpam-4350	176	12	4	4	NUM
ejpam-4350	176	13	;	;	PUNCT
ejpam-4350	176	14	(	(	PUNCT
ejpam-4350	176	15	iii	iii	NOUN
ejpam-4350	176	16	)	)	PUNCT
ejpam-4350	176	17	αh(fn	αh(fn	NOUN
ejpam-4350	176	18	)	)	PUNCT
ejpam-4350	176	19	=	=	SYM
ejpam-4350	176	20	αh(k1	αh(k1	PROPN
ejpam-4350	176	21	+	+	CCONJ
ejpam-4350	176	22	pn	pn	NOUN
ejpam-4350	176	23	)	)	PUNCT
ejpam-4350	176	24	=	=	SYM
ejpam-4350	176	25	3	3	NUM
ejpam-4350	176	26	for	for	ADP
ejpam-4350	176	27	all	all	DET
ejpam-4350	176	28	n	n	PRON
ejpam-4350	176	29	≥	≥	NOUN
ejpam-4350	176	30	1	1	NUM
ejpam-4350	176	31	;	;	PUNCT
ejpam-4350	176	32	and	and	CCONJ
ejpam-4350	176	33	(	(	PUNCT
ejpam-4350	176	34	iv	iv	X
ejpam-4350	176	35	)	)	PUNCT
ejpam-4350	176	36	αh(k1,n	αh(k1,n	PROPN
ejpam-4350	176	37	)	)	PUNCT
ejpam-4350	176	38	=	=	PUNCT
ejpam-4350	177	1	αh(k1	αh(k1	PROPN
ejpam-4350	178	1	+	+	PROPN
ejpam-4350	178	2	kn	kn	PROPN
ejpam-4350	178	3	)	)	PUNCT
ejpam-4350	178	4	=	=	SYM
ejpam-4350	178	5	2	2	NUM
ejpam-4350	178	6	for	for	ADP
ejpam-4350	178	7	all	all	DET
ejpam-4350	178	8	n	n	PRON
ejpam-4350	178	9	≥	≥	NOUN
ejpam-4350	178	10	1	1	NUM
ejpam-4350	178	11	.	.	PUNCT
ejpam-4350	179	1	the	the	DET
ejpam-4350	179	2	corona	corona	NOUN
ejpam-4350	179	3	of	of	ADP
ejpam-4350	179	4	graphs	graph	NOUN
ejpam-4350	179	5	g	g	PROPN
ejpam-4350	179	6	and	and	CCONJ
ejpam-4350	179	7	h	h	NOUN
ejpam-4350	179	8	,	,	PUNCT
ejpam-4350	179	9	denoted	denote	VERB
ejpam-4350	179	10	by	by	ADP
ejpam-4350	179	11	g	g	PROPN
ejpam-4350	179	12	◦	◦	NOUN
ejpam-4350	179	13	h	h	NOUN
ejpam-4350	179	14	,	,	PUNCT
ejpam-4350	179	15	is	be	AUX
ejpam-4350	179	16	the	the	DET
ejpam-4350	179	17	graph	graph	NOUN
ejpam-4350	179	18	obtained	obtain	VERB
ejpam-4350	179	19	from	from	ADP
ejpam-4350	179	20	g	g	NOUN
ejpam-4350	179	21	by	by	ADP
ejpam-4350	179	22	taking	take	VERB
ejpam-4350	179	23	a	a	DET
ejpam-4350	179	24	copy	copy	NOUN
ejpam-4350	179	25	hv	hv	PROPN
ejpam-4350	179	26	of	of	ADP
ejpam-4350	179	27	h	h	PROPN
ejpam-4350	179	28	and	and	CCONJ
ejpam-4350	179	29	forming	form	VERB
ejpam-4350	179	30	the	the	DET
ejpam-4350	179	31	join	join	NOUN
ejpam-4350	179	32	〈	〈	PROPN
ejpam-4350	179	33	v〉+hv	v〉+hv	NOUN
ejpam-4350	179	34	=	=	SYM
ejpam-4350	179	35	v	v	ADP
ejpam-4350	179	36	+	+	NOUN
ejpam-4350	179	37	hv	hv	NOUN
ejpam-4350	179	38	for	for	ADP
ejpam-4350	179	39	each	each	DET
ejpam-4350	179	40	v	v	NUM
ejpam-4350	179	41	∈	∈	PROPN
ejpam-4350	179	42	v	v	NOUN
ejpam-4350	179	43	(	(	PUNCT
ejpam-4350	179	44	g	g	NOUN
ejpam-4350	179	45	)	)	PUNCT
ejpam-4350	179	46	.	.	PUNCT
ejpam-4350	180	1	theorem	theorem	NOUN
ejpam-4350	180	2	5	5	NUM
ejpam-4350	180	3	.	.	PUNCT
ejpam-4350	181	1	let	let	VERB
ejpam-4350	181	2	g	g	PRON
ejpam-4350	181	3	be	be	AUX
ejpam-4350	181	4	a	a	DET
ejpam-4350	181	5	non	non	ADJ
ejpam-4350	181	6	-	-	ADJ
ejpam-4350	181	7	trivial	trivial	ADJ
ejpam-4350	181	8	connected	connected	ADJ
ejpam-4350	181	9	graph	graph	NOUN
ejpam-4350	181	10	and	and	CCONJ
ejpam-4350	181	11	let	let	VERB
ejpam-4350	181	12	h	h	NOUN
ejpam-4350	181	13	be	be	AUX
ejpam-4350	181	14	any	any	DET
ejpam-4350	181	15	graph	graph	NOUN
ejpam-4350	181	16	.	.	PUNCT
ejpam-4350	182	1	then	then	ADV
ejpam-4350	182	2	s	s	VERB
ejpam-4350	182	3	is	be	AUX
ejpam-4350	182	4	a	a	DET
ejpam-4350	182	5	hop	hop	NOUN
ejpam-4350	182	6	independent	independent	ADJ
ejpam-4350	182	7	set	set	NOUN
ejpam-4350	182	8	in	in	ADP
ejpam-4350	182	9	g	g	PROPN
ejpam-4350	182	10	◦	◦	NOUN
ejpam-4350	182	11	h	h	NOUN
ejpam-4350	182	12	if	if	SCONJ
ejpam-4350	183	1	and	and	CCONJ
ejpam-4350	183	2	only	only	ADV
ejpam-4350	183	3	if	if	SCONJ
ejpam-4350	183	4	s	s	X
ejpam-4350	183	5	=	=	VERB
ejpam-4350	183	6	a∪	a∪	X
ejpam-4350	183	7	(	(	PUNCT
ejpam-4350	183	8	∪v∈v	∪v∈v	X
ejpam-4350	183	9	(	(	PUNCT
ejpam-4350	183	10	g)sv	g)sv	PROPN
ejpam-4350	183	11	)	)	PUNCT
ejpam-4350	183	12	and	and	CCONJ
ejpam-4350	183	13	satisfies	satisfy	VERB
ejpam-4350	183	14	the	the	DET
ejpam-4350	183	15	following	follow	VERB
ejpam-4350	183	16	conditions	condition	NOUN
ejpam-4350	183	17	:	:	PUNCT
ejpam-4350	183	18	(	(	PUNCT
ejpam-4350	183	19	i	i	NOUN
ejpam-4350	183	20	)	)	PUNCT
ejpam-4350	183	21	a	a	PRON
ejpam-4350	183	22	is	be	AUX
ejpam-4350	183	23	a	a	DET
ejpam-4350	183	24	hop	hop	NOUN
ejpam-4350	183	25	independent	independent	ADJ
ejpam-4350	183	26	set	set	NOUN
ejpam-4350	183	27	in	in	ADP
ejpam-4350	183	28	g.	g.	PROPN
ejpam-4350	183	29	(	(	PUNCT
ejpam-4350	183	30	ii	ii	PROPN
ejpam-4350	183	31	)	)	PUNCT
ejpam-4350	183	32	sv	sv	PROPN
ejpam-4350	183	33	is	be	AUX
ejpam-4350	183	34	empty	empty	ADJ
ejpam-4350	183	35	or	or	CCONJ
ejpam-4350	183	36	a	a	DET
ejpam-4350	183	37	clique	clique	NOUN
ejpam-4350	183	38	in	in	ADP
ejpam-4350	183	39	hv	hv	PROPN
ejpam-4350	183	40	for	for	ADP
ejpam-4350	183	41	each	each	DET
ejpam-4350	183	42	v	v	NUM
ejpam-4350	183	43	∈	∈	PROPN
ejpam-4350	183	44	v	v	NOUN
ejpam-4350	183	45	(	(	PUNCT
ejpam-4350	183	46	g	g	NOUN
ejpam-4350	183	47	)	)	PUNCT
ejpam-4350	183	48	\ng(a	\ng(a	PROPN
ejpam-4350	183	49	)	)	PUNCT
ejpam-4350	183	50	.	.	PUNCT
ejpam-4350	184	1	(	(	PUNCT
ejpam-4350	184	2	iii	iii	X
ejpam-4350	184	3	)	)	PUNCT
ejpam-4350	184	4	sv	sv	NOUN
ejpam-4350	185	1	=	=	NOUN
ejpam-4350	185	2	∅	∅	NOUN
ejpam-4350	185	3	for	for	ADP
ejpam-4350	185	4	each	each	DET
ejpam-4350	185	5	v	v	ADP
ejpam-4350	185	6	∈	∈	PROPN
ejpam-4350	185	7	ng(a	ng(a	NOUN
ejpam-4350	185	8	)	)	PUNCT
ejpam-4350	185	9	.	.	PUNCT
ejpam-4350	186	1	proof	proof	NOUN
ejpam-4350	186	2	.	.	PUNCT
ejpam-4350	187	1	suppose	suppose	VERB
ejpam-4350	187	2	s	s	PRON
ejpam-4350	187	3	is	be	AUX
ejpam-4350	187	4	a	a	DET
ejpam-4350	187	5	hop	hop	NOUN
ejpam-4350	187	6	independent	independent	ADJ
ejpam-4350	187	7	set	set	NOUN
ejpam-4350	187	8	in	in	ADP
ejpam-4350	187	9	g	g	PROPN
ejpam-4350	187	10	◦	◦	NOUN
ejpam-4350	187	11	h	h	NOUN
ejpam-4350	187	12	and	and	CCONJ
ejpam-4350	187	13	let	let	VERB
ejpam-4350	187	14	a	a	DET
ejpam-4350	187	15	=	=	X
ejpam-4350	187	16	s	s	NOUN
ejpam-4350	187	17	∩	∩	ADJ
ejpam-4350	187	18	v	v	X
ejpam-4350	187	19	(	(	PUNCT
ejpam-4350	187	20	g	g	NOUN
ejpam-4350	187	21	)	)	PUNCT
ejpam-4350	187	22	and	and	CCONJ
ejpam-4350	187	23	sv	sv	X
ejpam-4350	187	24	=	=	SYM
ejpam-4350	187	25	s	s	PROPN
ejpam-4350	187	26	∩	∩	ADJ
ejpam-4350	187	27	v	v	X
ejpam-4350	187	28	(	(	PUNCT
ejpam-4350	187	29	hv	hv	PROPN
ejpam-4350	187	30	)	)	PUNCT
ejpam-4350	187	31	for	for	ADP
ejpam-4350	187	32	each	each	DET
ejpam-4350	187	33	v	v	NUM
ejpam-4350	187	34	∈	∈	PROPN
ejpam-4350	187	35	v	v	NOUN
ejpam-4350	187	36	(	(	PUNCT
ejpam-4350	187	37	g	g	NOUN
ejpam-4350	187	38	)	)	PUNCT
ejpam-4350	187	39	.	.	PUNCT
ejpam-4350	188	1	since	since	SCONJ
ejpam-4350	188	2	s	s	PROPN
ejpam-4350	188	3	is	be	AUX
ejpam-4350	188	4	a	a	DET
ejpam-4350	188	5	hop	hop	NOUN
ejpam-4350	188	6	independent	independent	ADJ
ejpam-4350	188	7	set	set	NOUN
ejpam-4350	188	8	in	in	ADP
ejpam-4350	188	9	g	g	PROPN
ejpam-4350	188	10	◦	◦	NOUN
ejpam-4350	188	11	h	h	NOUN
ejpam-4350	188	12	,	,	PUNCT
ejpam-4350	188	13	a	a	PRON
ejpam-4350	188	14	is	be	AUX
ejpam-4350	188	15	a	a	DET
ejpam-4350	188	16	hop	hop	NOUN
ejpam-4350	188	17	independent	independent	ADJ
ejpam-4350	188	18	set	set	NOUN
ejpam-4350	188	19	in	in	ADP
ejpam-4350	188	20	g.	g.	PROPN
ejpam-4350	188	21	this	this	PRON
ejpam-4350	188	22	shows	show	VERB
ejpam-4350	188	23	that	that	SCONJ
ejpam-4350	188	24	(	(	PUNCT
ejpam-4350	188	25	i	i	NOUN
ejpam-4350	188	26	)	)	PUNCT
ejpam-4350	188	27	holds	hold	VERB
ejpam-4350	188	28	.	.	PUNCT
ejpam-4350	189	1	next	next	ADV
ejpam-4350	189	2	,	,	PUNCT
ejpam-4350	189	3	let	let	VERB
ejpam-4350	189	4	v	v	NUM
ejpam-4350	189	5	∈	∈	PROPN
ejpam-4350	189	6	v	v	NOUN
ejpam-4350	189	7	(	(	PUNCT
ejpam-4350	189	8	g	g	NOUN
ejpam-4350	189	9	)	)	PUNCT
ejpam-4350	189	10	.	.	PUNCT
ejpam-4350	190	1	suppose	suppose	VERB
ejpam-4350	190	2	first	first	ADV
ejpam-4350	190	3	that	that	SCONJ
ejpam-4350	190	4	v	v	NUM
ejpam-4350	190	5	∈	∈	PROPN
ejpam-4350	190	6	v	v	NOUN
ejpam-4350	190	7	(	(	PUNCT
ejpam-4350	190	8	g	g	NOUN
ejpam-4350	190	9	)	)	PUNCT
ejpam-4350	190	10	\	\	NOUN
ejpam-4350	190	11	ng(a	ng(a	NOUN
ejpam-4350	190	12	)	)	PUNCT
ejpam-4350	190	13	.	.	PUNCT
ejpam-4350	191	1	suppose	suppose	VERB
ejpam-4350	191	2	further	far	ADV
ejpam-4350	191	3	that	that	DET
ejpam-4350	191	4	sv	sv	PROPN
ejpam-4350	191	5	6=	6=	X
ejpam-4350	191	6	∅.	∅.	VERB
ejpam-4350	191	7	clearly	clearly	ADV
ejpam-4350	191	8	,	,	PUNCT
ejpam-4350	191	9	if	if	SCONJ
ejpam-4350	191	10	|sv|	|sv|	PROPN
ejpam-4350	191	11	=	=	SYM
ejpam-4350	191	12	1	1	NUM
ejpam-4350	191	13	,	,	PUNCT
ejpam-4350	191	14	then	then	ADV
ejpam-4350	191	15	it	it	PRON
ejpam-4350	191	16	is	be	AUX
ejpam-4350	191	17	a	a	DET
ejpam-4350	191	18	clique	clique	NOUN
ejpam-4350	191	19	.	.	PUNCT
ejpam-4350	192	1	so	so	ADV
ejpam-4350	192	2	suppose	suppose	VERB
ejpam-4350	192	3	|sv|	|sv|	PROPN
ejpam-4350	192	4	≥	≥	NOUN
ejpam-4350	192	5	2	2	NUM
ejpam-4350	192	6	and	and	CCONJ
ejpam-4350	192	7	let	let	VERB
ejpam-4350	192	8	x	x	PRON
ejpam-4350	192	9	,	,	PUNCT
ejpam-4350	192	10	y	y	PROPN
ejpam-4350	192	11	∈	∈	PROPN
ejpam-4350	193	1	sv	sv	INTJ
ejpam-4350	193	2	.	.	PUNCT
ejpam-4350	194	1	since	since	SCONJ
ejpam-4350	194	2	s	s	PROPN
ejpam-4350	194	3	is	be	AUX
ejpam-4350	194	4	a	a	DET
ejpam-4350	194	5	hop	hop	NOUN
ejpam-4350	194	6	independent	independent	ADJ
ejpam-4350	194	7	set	set	NOUN
ejpam-4350	194	8	,	,	PUNCT
ejpam-4350	194	9	dg	dg	PROPN
ejpam-4350	194	10	◦	◦	NOUN
ejpam-4350	194	11	h(x	h(x	PROPN
ejpam-4350	194	12	,	,	PUNCT
ejpam-4350	194	13	y	y	PROPN
ejpam-4350	194	14	)	)	PUNCT
ejpam-4350	194	15	=	=	SYM
ejpam-4350	194	16	dhv(x	dhv(x	PROPN
ejpam-4350	194	17	,	,	PUNCT
ejpam-4350	194	18	y	y	PROPN
ejpam-4350	194	19	)	)	PUNCT
ejpam-4350	194	20	6=	6=	ADP
ejpam-4350	194	21	2	2	NUM
ejpam-4350	194	22	,	,	PUNCT
ejpam-4350	194	23	i.e.	i.e.	X
ejpam-4350	194	24	,	,	PUNCT
ejpam-4350	194	25	dhv(x	dhv(x	PROPN
ejpam-4350	194	26	,	,	PUNCT
ejpam-4350	194	27	y	y	NOUN
ejpam-4350	194	28	)	)	PUNCT
ejpam-4350	194	29	=	=	SYM
ejpam-4350	195	1	1	1	X
ejpam-4350	195	2	.	.	PUNCT
ejpam-4350	196	1	this	this	PRON
ejpam-4350	196	2	shows	show	VERB
ejpam-4350	196	3	that	that	SCONJ
ejpam-4350	196	4	(	(	PUNCT
ejpam-4350	196	5	ii	ii	NOUN
ejpam-4350	196	6	)	)	PUNCT
ejpam-4350	196	7	holds	hold	VERB
ejpam-4350	196	8	.	.	PUNCT
ejpam-4350	197	1	suppose	suppose	VERB
ejpam-4350	197	2	now	now	ADV
ejpam-4350	197	3	that	that	SCONJ
ejpam-4350	197	4	v	v	ADP
ejpam-4350	197	5	∈	∈	PROPN
ejpam-4350	197	6	ng(a	ng(a	NOUN
ejpam-4350	197	7	)	)	PUNCT
ejpam-4350	197	8	,	,	PUNCT
ejpam-4350	197	9	say	say	VERB
ejpam-4350	197	10	vw	vw	PROPN
ejpam-4350	197	11	∈	∈	PROPN
ejpam-4350	197	12	e(g	e(g	PROPN
ejpam-4350	197	13	◦	◦	PROPN
ejpam-4350	197	14	h	h	NOUN
ejpam-4350	197	15	)	)	PUNCT
ejpam-4350	197	16	for	for	ADP
ejpam-4350	197	17	some	some	DET
ejpam-4350	197	18	w	w	PROPN
ejpam-4350	197	19	∈	∈	PROPN
ejpam-4350	197	20	a.	a.	NOUN
ejpam-4350	197	21	since	since	SCONJ
ejpam-4350	197	22	s	s	PROPN
ejpam-4350	197	23	is	be	AUX
ejpam-4350	197	24	a	a	DET
ejpam-4350	197	25	hop	hop	NOUN
ejpam-4350	197	26	independent	independent	ADJ
ejpam-4350	197	27	set	set	NOUN
ejpam-4350	197	28	and	and	CCONJ
ejpam-4350	197	29	dg	dg	NOUN
ejpam-4350	197	30	◦	◦	NOUN
ejpam-4350	197	31	h(w	h(w	PROPN
ejpam-4350	197	32	,	,	PUNCT
ejpam-4350	197	33	z	z	NOUN
ejpam-4350	197	34	)	)	PUNCT
ejpam-4350	197	35	=	=	SYM
ejpam-4350	197	36	2	2	NUM
ejpam-4350	197	37	for	for	ADP
ejpam-4350	197	38	all	all	DET
ejpam-4350	197	39	z	z	NOUN
ejpam-4350	197	40	∈	∈	PROPN
ejpam-4350	197	41	v	v	ADP
ejpam-4350	197	42	(	(	PUNCT
ejpam-4350	197	43	hv	hv	PROPN
ejpam-4350	197	44	)	)	PUNCT
ejpam-4350	197	45	,	,	PUNCT
ejpam-4350	197	46	it	it	PRON
ejpam-4350	197	47	follows	follow	VERB
ejpam-4350	197	48	that	that	SCONJ
ejpam-4350	197	49	sv	sv	NOUN
ejpam-4350	197	50	=	=	NOUN
ejpam-4350	197	51	∅	∅	NOUN
ejpam-4350	197	52	,	,	PUNCT
ejpam-4350	197	53	showing	show	VERB
ejpam-4350	197	54	that	that	SCONJ
ejpam-4350	197	55	(	(	PUNCT
ejpam-4350	197	56	iii	iii	NOUN
ejpam-4350	197	57	)	)	PUNCT
ejpam-4350	197	58	holds	hold	VERB
ejpam-4350	197	59	.	.	PUNCT
ejpam-4350	198	1	for	for	ADP
ejpam-4350	198	2	the	the	DET
ejpam-4350	198	3	converse	converse	NOUN
ejpam-4350	198	4	,	,	PUNCT
ejpam-4350	198	5	suppose	suppose	VERB
ejpam-4350	198	6	that	that	SCONJ
ejpam-4350	198	7	s	s	VERB
ejpam-4350	198	8	has	have	VERB
ejpam-4350	198	9	the	the	DET
ejpam-4350	198	10	given	give	VERB
ejpam-4350	198	11	form	form	NOUN
ejpam-4350	198	12	and	and	CCONJ
ejpam-4350	198	13	satisfies	satisfie	NOUN
ejpam-4350	198	14	(	(	PUNCT
ejpam-4350	198	15	i	i	NOUN
ejpam-4350	198	16	)	)	PUNCT
ejpam-4350	198	17	,	,	PUNCT
ejpam-4350	198	18	(	(	PUNCT
ejpam-4350	198	19	ii	ii	NOUN
ejpam-4350	198	20	)	)	PUNCT
ejpam-4350	198	21	,	,	PUNCT
ejpam-4350	198	22	and	and	CCONJ
ejpam-4350	198	23	(	(	PUNCT
ejpam-4350	198	24	iii	iii	NOUN
ejpam-4350	198	25	)	)	PUNCT
ejpam-4350	198	26	.	.	PUNCT
ejpam-4350	199	1	let	let	VERB
ejpam-4350	199	2	a	a	DET
ejpam-4350	199	3	,	,	PUNCT
ejpam-4350	199	4	b	b	PROPN
ejpam-4350	199	5	∈	∈	PROPN
ejpam-4350	199	6	s	s	NOUN
ejpam-4350	199	7	,	,	PUNCT
ejpam-4350	199	8	where	where	SCONJ
ejpam-4350	199	9	a	a	DET
ejpam-4350	199	10	6=	6=	PROPN
ejpam-4350	199	11	b	b	NOUN
ejpam-4350	199	12	,	,	PUNCT
ejpam-4350	199	13	and	and	CCONJ
ejpam-4350	199	14	let	let	VERB
ejpam-4350	199	15	v	v	NOUN
ejpam-4350	199	16	,	,	PUNCT
ejpam-4350	199	17	w	w	PROPN
ejpam-4350	199	18	∈	∈	PROPN
ejpam-4350	199	19	v	v	ADP
ejpam-4350	199	20	(	(	PUNCT
ejpam-4350	199	21	g	g	NOUN
ejpam-4350	199	22	)	)	PUNCT
ejpam-4350	199	23	such	such	ADJ
ejpam-4350	199	24	that	that	SCONJ
ejpam-4350	199	25	a	a	DET
ejpam-4350	199	26	∈	∈	PROPN
ejpam-4350	199	27	v	v	NOUN
ejpam-4350	199	28	(	(	PUNCT
ejpam-4350	199	29	v	v	PROPN
ejpam-4350	199	30	+	+	NOUN
ejpam-4350	199	31	hv	hv	NOUN
ejpam-4350	199	32	)	)	PUNCT
ejpam-4350	199	33	and	and	CCONJ
ejpam-4350	199	34	b	b	X
ejpam-4350	199	35	∈	∈	PROPN
ejpam-4350	199	36	v	v	NOUN
ejpam-4350	199	37	(	(	PUNCT
ejpam-4350	199	38	w	w	NOUN
ejpam-4350	199	39	+	+	NOUN
ejpam-4350	199	40	hw	hw	NOUN
ejpam-4350	199	41	)	)	PUNCT
ejpam-4350	199	42	.	.	PUNCT
ejpam-4350	200	1	consider	consider	VERB
ejpam-4350	200	2	the	the	DET
ejpam-4350	200	3	following	follow	VERB
ejpam-4350	200	4	cases	case	NOUN
ejpam-4350	200	5	:	:	PUNCT
ejpam-4350	200	6	case	case	NOUN
ejpam-4350	200	7	1	1	NUM
ejpam-4350	200	8	.	.	NUM
ejpam-4350	200	9	v	v	NOUN
ejpam-4350	200	10	6=	6=	NOUN
ejpam-4350	200	11	w.	w.	PROPN
ejpam-4350	200	12	suppose	suppose	VERB
ejpam-4350	200	13	a	a	DET
ejpam-4350	200	14	=	=	X
ejpam-4350	200	15	v	v	NOUN
ejpam-4350	200	16	and	and	CCONJ
ejpam-4350	200	17	b	b	NOUN
ejpam-4350	200	18	=	=	SYM
ejpam-4350	200	19	w.	w.	PROPN
ejpam-4350	200	20	then	then	ADV
ejpam-4350	200	21	a	a	DET
ejpam-4350	200	22	,	,	PUNCT
ejpam-4350	200	23	b	b	X
ejpam-4350	200	24	∈	∈	PROPN
ejpam-4350	200	25	a.	a.	NOUN
ejpam-4350	200	26	since	since	SCONJ
ejpam-4350	200	27	a	a	PRON
ejpam-4350	200	28	is	be	AUX
ejpam-4350	200	29	a	a	DET
ejpam-4350	200	30	hop	hop	NOUN
ejpam-4350	200	31	independent	independent	ADJ
ejpam-4350	200	32	set	set	NOUN
ejpam-4350	200	33	of	of	ADP
ejpam-4350	200	34	g	g	PROPN
ejpam-4350	200	35	,	,	PUNCT
ejpam-4350	200	36	dg	dg	PROPN
ejpam-4350	200	37	◦	◦	PROPN
ejpam-4350	200	38	h(a	h(a	PROPN
ejpam-4350	200	39	,	,	PUNCT
ejpam-4350	200	40	b	b	NOUN
ejpam-4350	200	41	)	)	PUNCT
ejpam-4350	200	42	=	=	SYM
ejpam-4350	200	43	dg(a	dg(a	X
ejpam-4350	200	44	,	,	PUNCT
ejpam-4350	200	45	b	b	NOUN
ejpam-4350	200	46	)	)	PUNCT
ejpam-4350	200	47	6=	6=	ADP
ejpam-4350	200	48	2	2	X
ejpam-4350	200	49	.	.	PUNCT
ejpam-4350	200	50	suppose	suppose	VERB
ejpam-4350	200	51	now	now	ADV
ejpam-4350	200	52	that	that	SCONJ
ejpam-4350	200	53	a	a	DET
ejpam-4350	200	54	=	=	SYM
ejpam-4350	200	55	v	v	NOUN
ejpam-4350	200	56	and	and	CCONJ
ejpam-4350	200	57	b	b	NOUN
ejpam-4350	200	58	6=	6=	ADP
ejpam-4350	200	59	w	w	PROPN
ejpam-4350	200	60	(	(	PUNCT
ejpam-4350	200	61	or	or	CCONJ
ejpam-4350	200	62	a	a	DET
ejpam-4350	200	63	6=	6=	NOUN
ejpam-4350	200	64	v	v	NOUN
ejpam-4350	200	65	and	and	CCONJ
ejpam-4350	200	66	b	b	NOUN
ejpam-4350	200	67	=	=	SYM
ejpam-4350	200	68	w	w	PROPN
ejpam-4350	200	69	)	)	PUNCT
ejpam-4350	200	70	.	.	PUNCT
ejpam-4350	201	1	then	then	ADV
ejpam-4350	201	2	a	a	DET
ejpam-4350	201	3	∈	∈	PROPN
ejpam-4350	201	4	a	a	PRON
ejpam-4350	201	5	and	and	CCONJ
ejpam-4350	201	6	b	b	PROPN
ejpam-4350	201	7	∈	∈	PROPN
ejpam-4350	201	8	sw	sw	PROPN
ejpam-4350	201	9	.	.	PUNCT
ejpam-4350	202	1	by	by	ADP
ejpam-4350	202	2	(	(	PUNCT
ejpam-4350	202	3	iii	iii	NOUN
ejpam-4350	202	4	)	)	PUNCT
ejpam-4350	202	5	,	,	PUNCT
ejpam-4350	202	6	w	w	PROPN
ejpam-4350	202	7	/∈	/∈	NOUN
ejpam-4350	202	8	ng(a	ng(a	NOUN
ejpam-4350	202	9	)	)	PUNCT
ejpam-4350	202	10	.	.	PUNCT
ejpam-4350	203	1	hence	hence	ADV
ejpam-4350	203	2	,	,	PUNCT
ejpam-4350	203	3	wv	wv	PROPN
ejpam-4350	203	4	/∈	/∈	PUNCT
ejpam-4350	203	5	e(g	e(g	PROPN
ejpam-4350	203	6	)	)	PUNCT
ejpam-4350	203	7	and	and	CCONJ
ejpam-4350	203	8	dg	dg	PROPN
ejpam-4350	203	9	◦	◦	PROPN
ejpam-4350	203	10	h(a	h(a	PROPN
ejpam-4350	203	11	,	,	PUNCT
ejpam-4350	203	12	b	b	NOUN
ejpam-4350	203	13	)	)	PUNCT
ejpam-4350	203	14	6=	6=	ADP
ejpam-4350	203	15	2	2	X
ejpam-4350	203	16	.	.	PUNCT
ejpam-4350	204	1	if	if	SCONJ
ejpam-4350	204	2	if	if	SCONJ
ejpam-4350	204	3	a	a	DET
ejpam-4350	204	4	6=	6=	NUM
ejpam-4350	204	5	v	v	NOUN
ejpam-4350	204	6	and	and	CCONJ
ejpam-4350	204	7	b	b	NOUN
ejpam-4350	204	8	6=	6=	ADP
ejpam-4350	204	9	w	w	PROPN
ejpam-4350	204	10	,	,	PUNCT
ejpam-4350	204	11	then	then	ADV
ejpam-4350	204	12	a	a	DET
ejpam-4350	204	13	∈	∈	PROPN
ejpam-4350	204	14	sv	sv	NOUN
ejpam-4350	204	15	and	and	CCONJ
ejpam-4350	204	16	b	b	PROPN
ejpam-4350	204	17	∈	∈	PROPN
ejpam-4350	204	18	sw	sw	PROPN
ejpam-4350	204	19	.	.	PUNCT
ejpam-4350	205	1	clearly	clearly	ADV
ejpam-4350	205	2	,	,	PUNCT
ejpam-4350	205	3	dg	dg	PROPN
ejpam-4350	205	4	◦	◦	PROPN
ejpam-4350	205	5	h(a	h(a	PROPN
ejpam-4350	205	6	,	,	PUNCT
ejpam-4350	205	7	b	b	NOUN
ejpam-4350	205	8	)	)	PUNCT
ejpam-4350	205	9	6=	6=	ADP
ejpam-4350	205	10	2	2	NUM
ejpam-4350	205	11	.	.	X
ejpam-4350	205	12	case	case	NOUN
ejpam-4350	205	13	2	2	NUM
ejpam-4350	205	14	.	.	NOUN
ejpam-4350	206	1	v	v	NOUN
ejpam-4350	206	2	=	=	PUNCT
ejpam-4350	206	3	w.	w.	NOUN
ejpam-4350	206	4	if	if	SCONJ
ejpam-4350	206	5	one	one	NUM
ejpam-4350	206	6	of	of	ADP
ejpam-4350	206	7	a	a	PRON
ejpam-4350	206	8	and	and	CCONJ
ejpam-4350	206	9	b	b	NOUN
ejpam-4350	206	10	is	be	AUX
ejpam-4350	206	11	v	v	ADJ
ejpam-4350	206	12	,	,	PUNCT
ejpam-4350	206	13	say	say	VERB
ejpam-4350	206	14	a	a	DET
ejpam-4350	206	15	=	=	ADJ
ejpam-4350	206	16	v	v	NOUN
ejpam-4350	206	17	,	,	PUNCT
ejpam-4350	207	1	then	then	ADV
ejpam-4350	207	2	b	b	PROPN
ejpam-4350	207	3	∈	∈	PROPN
ejpam-4350	207	4	sv	sv	PROPN
ejpam-4350	207	5	and	and	CCONJ
ejpam-4350	207	6	dg	dg	PROPN
ejpam-4350	207	7	◦	◦	PROPN
ejpam-4350	207	8	h(a	h(a	PROPN
ejpam-4350	207	9	,	,	PUNCT
ejpam-4350	207	10	b	b	NOUN
ejpam-4350	207	11	)	)	PUNCT
ejpam-4350	207	12	=	=	SYM
ejpam-4350	207	13	1	1	NUM
ejpam-4350	207	14	6=	6=	NUM
ejpam-4350	207	15	2	2	NUM
ejpam-4350	207	16	.	.	PUNCT
ejpam-4350	208	1	if	if	SCONJ
ejpam-4350	208	2	a	a	DET
ejpam-4350	208	3	6=	6=	NUM
ejpam-4350	208	4	v	v	NOUN
ejpam-4350	208	5	and	and	CCONJ
ejpam-4350	208	6	b	b	NOUN
ejpam-4350	208	7	6=	6=	ADP
ejpam-4350	208	8	w	w	PROPN
ejpam-4350	208	9	,	,	PUNCT
ejpam-4350	208	10	then	then	ADV
ejpam-4350	208	11	a	a	PRON
ejpam-4350	208	12	,	,	PUNCT
ejpam-4350	208	13	b	b	PROPN
ejpam-4350	208	14	∈	∈	PROPN
ejpam-4350	208	15	sv	sv	PROPN
ejpam-4350	208	16	.	.	PUNCT
ejpam-4350	208	17	by	by	ADP
ejpam-4350	208	18	(	(	PUNCT
ejpam-4350	208	19	ii	ii	NOUN
ejpam-4350	208	20	)	)	PUNCT
ejpam-4350	208	21	,	,	PUNCT
ejpam-4350	208	22	sv	sv	PROPN
ejpam-4350	208	23	is	be	AUX
ejpam-4350	208	24	a	a	DET
ejpam-4350	208	25	clique	clique	NOUN
ejpam-4350	208	26	in	in	ADP
ejpam-4350	208	27	hv	hv	PROPN
ejpam-4350	208	28	and	and	CCONJ
ejpam-4350	208	29	so	so	ADV
ejpam-4350	208	30	dg	dg	PROPN
ejpam-4350	208	31	◦	◦	PROPN
ejpam-4350	208	32	h(a	h(a	PROPN
ejpam-4350	208	33	,	,	PUNCT
ejpam-4350	208	34	b	b	NOUN
ejpam-4350	208	35	)	)	PUNCT
ejpam-4350	208	36	=	=	SYM
ejpam-4350	208	37	1	1	NUM
ejpam-4350	208	38	6=	6=	NUM
ejpam-4350	208	39	2	2	NUM
ejpam-4350	208	40	.	.	PUNCT
ejpam-4350	209	1	therefore	therefore	ADV
ejpam-4350	209	2	,	,	PUNCT
ejpam-4350	209	3	s	s	VERB
ejpam-4350	209	4	is	be	AUX
ejpam-4350	209	5	a	a	DET
ejpam-4350	209	6	hop	hop	NOUN
ejpam-4350	209	7	independent	independent	ADJ
ejpam-4350	209	8	set	set	NOUN
ejpam-4350	209	9	of	of	ADP
ejpam-4350	209	10	g	g	PROPN
ejpam-4350	209	11	◦	◦	PROPN
ejpam-4350	209	12	h.	h.	PROPN
ejpam-4350	209	13	lemma	lemma	PROPN
ejpam-4350	210	1	1	1	X
ejpam-4350	210	2	.	.	PUNCT
ejpam-4350	211	1	let	let	VERB
ejpam-4350	211	2	g	g	PRON
ejpam-4350	211	3	be	be	AUX
ejpam-4350	211	4	a	a	DET
ejpam-4350	211	5	non	non	ADJ
ejpam-4350	211	6	-	-	ADJ
ejpam-4350	211	7	trivial	trivial	ADJ
ejpam-4350	211	8	connected	connected	ADJ
ejpam-4350	211	9	graph	graph	NOUN
ejpam-4350	211	10	and	and	CCONJ
ejpam-4350	211	11	let	let	VERB
ejpam-4350	211	12	a	a	PRON
ejpam-4350	211	13	be	be	AUX
ejpam-4350	211	14	a	a	DET
ejpam-4350	211	15	hop	hop	NOUN
ejpam-4350	211	16	independent	independent	ADJ
ejpam-4350	211	17	set	set	NOUN
ejpam-4350	211	18	of	of	ADP
ejpam-4350	211	19	g.	g.	PROPN
ejpam-4350	212	1	then	then	ADV
ejpam-4350	212	2	|a|	|a|	PROPN
ejpam-4350	212	3	≤	≤	PROPN
ejpam-4350	212	4	|ng(a)|	|ng(a)|	PROPN
ejpam-4350	212	5	.	.	PUNCT
ejpam-4350	213	1	j.	j.	PROPN
ejpam-4350	213	2	hassan	hassan	PROPN
ejpam-4350	213	3	,	,	PUNCT
ejpam-4350	213	4	s.	s.	PROPN
ejpam-4350	213	5	canoy	canoy	PROPN
ejpam-4350	213	6	,	,	PUNCT
ejpam-4350	213	7	jr	jr	PROPN
ejpam-4350	213	8	.	.	PROPN
ejpam-4350	213	9	,	,	PUNCT
ejpam-4350	213	10	a.	a.	PROPN
ejpam-4350	213	11	aradais	aradais	PROPN
ejpam-4350	213	12	/	/	SYM
ejpam-4350	213	13	eur	eur	PROPN
ejpam-4350	213	14	.	.	PUNCT
ejpam-4350	214	1	j.	j.	PROPN
ejpam-4350	214	2	pure	pure	PROPN
ejpam-4350	214	3	appl	appl	PROPN
ejpam-4350	214	4	.	.	PROPN
ejpam-4350	214	5	math	math	PROPN
ejpam-4350	214	6	,	,	PUNCT
ejpam-4350	214	7	15	15	NUM
ejpam-4350	214	8	(	(	PUNCT
ejpam-4350	214	9	2	2	NUM
ejpam-4350	214	10	)	)	PUNCT
ejpam-4350	214	11	(	(	PUNCT
ejpam-4350	214	12	2022	2022	NUM
ejpam-4350	214	13	)	)	PUNCT
ejpam-4350	214	14	,	,	PUNCT
ejpam-4350	214	15	467	467	NUM
ejpam-4350	214	16	-	-	SYM
ejpam-4350	214	17	477	477	NUM
ejpam-4350	214	18	473	473	NUM
ejpam-4350	214	19	proof	proof	NOUN
ejpam-4350	214	20	.	.	PUNCT
ejpam-4350	215	1	note	note	VERB
ejpam-4350	215	2	that	that	SCONJ
ejpam-4350	215	3	a	a	DET
ejpam-4350	215	4	=	=	X
ejpam-4350	215	5	(	(	PUNCT
ejpam-4350	215	6	a	a	DET
ejpam-4350	215	7	\ng(a	\ng(a	NOUN
ejpam-4350	215	8	)	)	PUNCT
ejpam-4350	215	9	)	)	PUNCT
ejpam-4350	215	10	∪	∪	NOUN
ejpam-4350	215	11	(	(	PUNCT
ejpam-4350	215	12	a	a	DET
ejpam-4350	215	13	∩ng(a	∩ng(a	NOUN
ejpam-4350	215	14	)	)	PUNCT
ejpam-4350	215	15	)	)	PUNCT
ejpam-4350	215	16	.	.	PUNCT
ejpam-4350	216	1	since	since	SCONJ
ejpam-4350	216	2	g	g	PROPN
ejpam-4350	216	3	is	be	AUX
ejpam-4350	216	4	a	a	DET
ejpam-4350	216	5	non	non	ADJ
ejpam-4350	216	6	-	-	ADJ
ejpam-4350	216	7	trivial	trivial	ADJ
ejpam-4350	216	8	connected	connected	ADJ
ejpam-4350	216	9	graph	graph	NOUN
ejpam-4350	216	10	,	,	PUNCT
ejpam-4350	216	11	ng(a	ng(a	PRON
ejpam-4350	216	12	)	)	PUNCT
ejpam-4350	216	13	6=	6=	ADP
ejpam-4350	216	14	∅	∅	NOUN
ejpam-4350	216	15	for	for	ADP
ejpam-4350	216	16	each	each	PRON
ejpam-4350	216	17	a	a	DET
ejpam-4350	216	18	∈	∈	PROPN
ejpam-4350	216	19	a	a	DET
ejpam-4350	216	20	\	\	NOUN
ejpam-4350	216	21	ng(a	ng(a	NOUN
ejpam-4350	216	22	)	)	PUNCT
ejpam-4350	216	23	.	.	PUNCT
ejpam-4350	217	1	now	now	ADV
ejpam-4350	217	2	let	let	VERB
ejpam-4350	217	3	a	a	DET
ejpam-4350	217	4	,	,	PUNCT
ejpam-4350	217	5	b	b	X
ejpam-4350	217	6	∈	∈	PROPN
ejpam-4350	217	7	a	a	DET
ejpam-4350	217	8	\	\	NOUN
ejpam-4350	217	9	ng(a	ng(a	NOUN
ejpam-4350	217	10	)	)	PUNCT
ejpam-4350	217	11	with	with	ADP
ejpam-4350	217	12	a	a	PRON
ejpam-4350	217	13	6=	6=	PROPN
ejpam-4350	217	14	b.	b.	PROPN
ejpam-4350	217	15	suppose	suppose	VERB
ejpam-4350	217	16	ng(a	ng(a	NOUN
ejpam-4350	217	17	)	)	PUNCT
ejpam-4350	217	18	∩	∩	NOUN
ejpam-4350	217	19	ng(b	ng(b	X
ejpam-4350	217	20	)	)	PUNCT
ejpam-4350	217	21	6=	6=	ADP
ejpam-4350	217	22	∅	∅	NOUN
ejpam-4350	217	23	,	,	PUNCT
ejpam-4350	217	24	say	say	VERB
ejpam-4350	217	25	x	x	SYM
ejpam-4350	217	26	∈	∈	PROPN
ejpam-4350	217	27	ng(a	ng(a	NOUN
ejpam-4350	217	28	)	)	PUNCT
ejpam-4350	217	29	∩	∩	NOUN
ejpam-4350	217	30	ng(b	ng(b	NOUN
ejpam-4350	217	31	)	)	PUNCT
ejpam-4350	217	32	.	.	PUNCT
ejpam-4350	218	1	since	since	SCONJ
ejpam-4350	218	2	a	a	PRON
ejpam-4350	218	3	is	be	AUX
ejpam-4350	218	4	a	a	DET
ejpam-4350	218	5	hop	hop	NOUN
ejpam-4350	218	6	independent	independent	ADJ
ejpam-4350	218	7	set	set	NOUN
ejpam-4350	218	8	of	of	ADP
ejpam-4350	218	9	g	g	NOUN
ejpam-4350	218	10	,	,	PUNCT
ejpam-4350	218	11	dg(a	dg(a	X
ejpam-4350	218	12	,	,	PUNCT
ejpam-4350	218	13	b	b	NOUN
ejpam-4350	218	14	)	)	PUNCT
ejpam-4350	218	15	6=	6=	ADP
ejpam-4350	218	16	2	2	NUM
ejpam-4350	218	17	.	.	PUNCT
ejpam-4350	219	1	hence	hence	ADV
ejpam-4350	219	2	,	,	PUNCT
ejpam-4350	219	3	ab	ab	PROPN
ejpam-4350	219	4	∈	∈	PROPN
ejpam-4350	219	5	e(g	e(g	PROPN
ejpam-4350	219	6	)	)	PUNCT
ejpam-4350	219	7	,	,	PUNCT
ejpam-4350	219	8	implying	imply	VERB
ejpam-4350	219	9	that	that	SCONJ
ejpam-4350	219	10	a	a	DET
ejpam-4350	219	11	∈	∈	PROPN
ejpam-4350	219	12	a	a	DET
ejpam-4350	219	13	∩	∩	NOUN
ejpam-4350	219	14	ng(a	ng(a	NOUN
ejpam-4350	219	15	)	)	PUNCT
ejpam-4350	219	16	.	.	PUNCT
ejpam-4350	220	1	this	this	PRON
ejpam-4350	220	2	contradicts	contradict	VERB
ejpam-4350	220	3	the	the	DET
ejpam-4350	220	4	assumption	assumption	NOUN
ejpam-4350	220	5	that	that	SCONJ
ejpam-4350	220	6	a	a	DET
ejpam-4350	220	7	∈	∈	PROPN
ejpam-4350	220	8	a	a	DET
ejpam-4350	220	9	\ng(a	\ng(a	NOUN
ejpam-4350	220	10	)	)	PUNCT
ejpam-4350	220	11	.	.	PUNCT
ejpam-4350	221	1	therefore	therefore	ADV
ejpam-4350	221	2	,	,	PUNCT
ejpam-4350	221	3	ng(a	ng(a	PRON
ejpam-4350	221	4	)	)	PUNCT
ejpam-4350	221	5	∩ng(b	∩ng(b	PROPN
ejpam-4350	221	6	)	)	PUNCT
ejpam-4350	221	7	=	=	PUNCT
ejpam-4350	221	8	∅	∅	NOUN
ejpam-4350	221	9	for	for	ADP
ejpam-4350	221	10	any	any	DET
ejpam-4350	221	11	two	two	NUM
ejpam-4350	221	12	distinct	distinct	ADJ
ejpam-4350	221	13	vertices	vertex	NOUN
ejpam-4350	221	14	a	a	PRON
ejpam-4350	221	15	and	and	CCONJ
ejpam-4350	221	16	b	b	NOUN
ejpam-4350	221	17	in	in	ADP
ejpam-4350	221	18	a\ng(a	a\ng(a	PROPN
ejpam-4350	221	19	)	)	PUNCT
ejpam-4350	221	20	.	.	PUNCT
ejpam-4350	222	1	for	for	ADP
ejpam-4350	222	2	each	each	PRON
ejpam-4350	222	3	a	a	DET
ejpam-4350	222	4	∈	∈	PROPN
ejpam-4350	222	5	a\ng(a	a\ng(a	PROPN
ejpam-4350	222	6	)	)	PUNCT
ejpam-4350	222	7	,	,	PUNCT
ejpam-4350	222	8	choose	choose	VERB
ejpam-4350	222	9	va	va	PROPN
ejpam-4350	222	10	∈	∈	PROPN
ejpam-4350	222	11	(	(	PUNCT
ejpam-4350	222	12	v	v	NOUN
ejpam-4350	222	13	(	(	PUNCT
ejpam-4350	222	14	g)\a)∩ng(a	g)\a)∩ng(a	PROPN
ejpam-4350	222	15	)	)	PUNCT
ejpam-4350	222	16	(	(	PUNCT
ejpam-4350	222	17	such	such	ADJ
ejpam-4350	222	18	vertex	vertex	NOUN
ejpam-4350	222	19	va	va	NOUN
ejpam-4350	222	20	exists	exist	VERB
ejpam-4350	222	21	because	because	SCONJ
ejpam-4350	222	22	g	g	PROPN
ejpam-4350	222	23	is	be	AUX
ejpam-4350	222	24	non	non	ADJ
ejpam-4350	222	25	-	-	ADJ
ejpam-4350	222	26	trivial	trivial	ADJ
ejpam-4350	222	27	and	and	CCONJ
ejpam-4350	222	28	connected	connect	VERB
ejpam-4350	222	29	)	)	PUNCT
ejpam-4350	222	30	and	and	CCONJ
ejpam-4350	222	31	let	let	VERB
ejpam-4350	222	32	d	d	NOUN
ejpam-4350	222	33	=	=	SYM
ejpam-4350	222	34	{	{	PUNCT
ejpam-4350	222	35	va	va	NOUN
ejpam-4350	222	36	:	:	PUNCT
ejpam-4350	222	37	a	a	DET
ejpam-4350	222	38	∈	∈	PROPN
ejpam-4350	222	39	a\ng(a	a\ng(a	PROPN
ejpam-4350	222	40	)	)	PUNCT
ejpam-4350	222	41	}	}	PUNCT
ejpam-4350	222	42	.	.	PUNCT
ejpam-4350	223	1	then	then	ADV
ejpam-4350	223	2	d	d	X
ejpam-4350	223	3	⊆	⊆	NUM
ejpam-4350	223	4	ng(a	ng(a	NOUN
ejpam-4350	223	5	)	)	PUNCT
ejpam-4350	223	6	and	and	CCONJ
ejpam-4350	223	7	|d|	|d|	PROPN
ejpam-4350	223	8	=	=	PROPN
ejpam-4350	223	9	|a	|a	VERB
ejpam-4350	223	10	\ng(a)|	\ng(a)|	X
ejpam-4350	223	11	.	.	PUNCT
ejpam-4350	223	12	thus	thus	ADV
ejpam-4350	223	13	,	,	PUNCT
ejpam-4350	223	14	|a|	|a|	NOUN
ejpam-4350	223	15	=	=	NOUN
ejpam-4350	223	16	|a	|a	PUNCT
ejpam-4350	223	17	∩ng(a)|+	∩ng(a)|+	ADJ
ejpam-4350	223	18	|a	|a	VERB
ejpam-4350	223	19	\ng(a)|	\ng(a)|	X
ejpam-4350	223	20	=	=	PUNCT
ejpam-4350	223	21	|a	|a	VERB
ejpam-4350	223	22	∩ng(a)|+	∩ng(a)|+	ADJ
ejpam-4350	223	23	|d|	|d|	PROPN
ejpam-4350	223	24	≤	≤	PROPN
ejpam-4350	223	25	|ng(a)|	|ng(a)|	PROPN
ejpam-4350	223	26	.	.	PUNCT
ejpam-4350	224	1	this	this	PRON
ejpam-4350	224	2	proves	prove	VERB
ejpam-4350	224	3	the	the	DET
ejpam-4350	224	4	assertion	assertion	NOUN
ejpam-4350	224	5	.	.	PUNCT
ejpam-4350	225	1	corollary	corollary	ADJ
ejpam-4350	225	2	3	3	X
ejpam-4350	225	3	.	.	PUNCT
ejpam-4350	226	1	let	let	VERB
ejpam-4350	226	2	g	g	PRON
ejpam-4350	226	3	be	be	AUX
ejpam-4350	226	4	a	a	DET
ejpam-4350	226	5	non	non	ADJ
ejpam-4350	226	6	-	-	ADJ
ejpam-4350	226	7	trivial	trivial	ADJ
ejpam-4350	226	8	connected	connected	ADJ
ejpam-4350	226	9	graph	graph	NOUN
ejpam-4350	226	10	and	and	CCONJ
ejpam-4350	226	11	let	let	VERB
ejpam-4350	226	12	h	h	NOUN
ejpam-4350	226	13	be	be	AUX
ejpam-4350	226	14	any	any	DET
ejpam-4350	226	15	graph	graph	NOUN
ejpam-4350	226	16	.	.	PUNCT
ejpam-4350	227	1	then	then	ADV
ejpam-4350	227	2	αh(g	αh(g	ADP
ejpam-4350	227	3	◦	◦	NOUN
ejpam-4350	227	4	h	h	NOUN
ejpam-4350	227	5	)	)	PUNCT
ejpam-4350	227	6	=	=	SYM
ejpam-4350	227	7	|v	|v	X
ejpam-4350	227	8	(	(	PUNCT
ejpam-4350	227	9	g)|ω(h	g)|ω(h	PROPN
ejpam-4350	227	10	)	)	PUNCT
ejpam-4350	227	11	.	.	PUNCT
ejpam-4350	228	1	proof	proof	NOUN
ejpam-4350	228	2	.	.	PUNCT
ejpam-4350	229	1	let	let	VERB
ejpam-4350	229	2	sv	sv	INTJ
ejpam-4350	229	3	be	be	AUX
ejpam-4350	229	4	an	an	DET
ejpam-4350	229	5	ω	ω	NOUN
ejpam-4350	229	6	-	-	PUNCT
ejpam-4350	229	7	set	set	NOUN
ejpam-4350	229	8	of	of	ADP
ejpam-4350	229	9	hv	hv	PROPN
ejpam-4350	229	10	for	for	ADP
ejpam-4350	229	11	each	each	DET
ejpam-4350	229	12	v	v	NUM
ejpam-4350	229	13	∈	∈	PROPN
ejpam-4350	229	14	v	v	NOUN
ejpam-4350	229	15	(	(	PUNCT
ejpam-4350	229	16	g	g	NOUN
ejpam-4350	229	17	)	)	PUNCT
ejpam-4350	229	18	.	.	PUNCT
ejpam-4350	230	1	then	then	ADV
ejpam-4350	230	2	s	s	VERB
ejpam-4350	230	3	=	=	SYM
ejpam-4350	230	4	∪v∈v	∪v∈v	X
ejpam-4350	230	5	(	(	PUNCT
ejpam-4350	230	6	g)sv	g)sv	PROPN
ejpam-4350	230	7	is	be	AUX
ejpam-4350	230	8	a	a	DET
ejpam-4350	230	9	hop	hop	NOUN
ejpam-4350	230	10	independent	independent	ADJ
ejpam-4350	230	11	set	set	NOUN
ejpam-4350	230	12	of	of	ADP
ejpam-4350	230	13	g	g	NOUN
ejpam-4350	230	14	◦	◦	NOUN
ejpam-4350	230	15	h	h	NOUN
ejpam-4350	230	16	by	by	ADP
ejpam-4350	230	17	theorem	theorem	NOUN
ejpam-4350	230	18	5	5	NUM
ejpam-4350	230	19	.	.	PUNCT
ejpam-4350	231	1	this	this	PRON
ejpam-4350	231	2	implies	imply	VERB
ejpam-4350	231	3	that	that	SCONJ
ejpam-4350	231	4	αh(g	αh(g	VERB
ejpam-4350	231	5	◦	◦	NOUN
ejpam-4350	231	6	h	h	NOUN
ejpam-4350	231	7	)	)	PUNCT
ejpam-4350	231	8	≥	≥	NOUN
ejpam-4350	231	9	|s|	|s|	NOUN
ejpam-4350	231	10	=	=	SYM
ejpam-4350	231	11	|v	|v	X
ejpam-4350	231	12	(	(	PUNCT
ejpam-4350	231	13	g)|ω(h	g)|ω(h	PROPN
ejpam-4350	231	14	)	)	PUNCT
ejpam-4350	231	15	.	.	PUNCT
ejpam-4350	232	1	next	next	ADV
ejpam-4350	232	2	,	,	PUNCT
ejpam-4350	232	3	let	let	VERB
ejpam-4350	232	4	s∗	s∗	PROPN
ejpam-4350	232	5	be	be	AUX
ejpam-4350	232	6	a	a	DET
ejpam-4350	232	7	αh	αh	NOUN
ejpam-4350	232	8	-	-	PUNCT
ejpam-4350	232	9	set	set	NOUN
ejpam-4350	232	10	of	of	ADP
ejpam-4350	232	11	g	g	PROPN
ejpam-4350	232	12	◦	◦	NOUN
ejpam-4350	232	13	h.	h.	PROPN
ejpam-4350	232	14	then	then	ADV
ejpam-4350	232	15	s∗	s∗	PROPN
ejpam-4350	232	16	=	=	PUNCT
ejpam-4350	232	17	a	a	DET
ejpam-4350	232	18	∪	∪	X
ejpam-4350	232	19	(	(	PUNCT
ejpam-4350	232	20	∪v∈v	∪v∈v	X
ejpam-4350	232	21	(	(	PUNCT
ejpam-4350	232	22	g)rv	g)rv	PROPN
ejpam-4350	232	23	)	)	PUNCT
ejpam-4350	232	24	and	and	CCONJ
ejpam-4350	232	25	satisfies	satisfie	NOUN
ejpam-4350	232	26	(	(	PUNCT
ejpam-4350	232	27	i	i	NOUN
ejpam-4350	232	28	)	)	PUNCT
ejpam-4350	232	29	,	,	PUNCT
ejpam-4350	232	30	(	(	PUNCT
ejpam-4350	232	31	ii	ii	NOUN
ejpam-4350	232	32	)	)	PUNCT
ejpam-4350	232	33	,	,	PUNCT
ejpam-4350	232	34	and	and	CCONJ
ejpam-4350	232	35	(	(	PUNCT
ejpam-4350	232	36	iii	iii	NOUN
ejpam-4350	232	37	)	)	PUNCT
ejpam-4350	232	38	of	of	ADP
ejpam-4350	232	39	theorem	theorem	NOUN
ejpam-4350	232	40	5	5	NUM
ejpam-4350	232	41	.	.	PUNCT
ejpam-4350	232	42	hence	hence	ADV
ejpam-4350	232	43	,	,	PUNCT
ejpam-4350	232	44	by	by	ADP
ejpam-4350	232	45	theorem	theorem	NOUN
ejpam-4350	232	46	5	5	NUM
ejpam-4350	232	47	and	and	CCONJ
ejpam-4350	232	48	lemma	lemma	PROPN
ejpam-4350	232	49	1	1	NUM
ejpam-4350	232	50	,	,	PUNCT
ejpam-4350	232	51	we	we	PRON
ejpam-4350	232	52	have	have	VERB
ejpam-4350	232	53	αh(g	αh(g	PRON
ejpam-4350	232	54	◦	◦	NOUN
ejpam-4350	232	55	h	h	NOUN
ejpam-4350	232	56	)	)	PUNCT
ejpam-4350	232	57	=	=	NOUN
ejpam-4350	232	58	|s∗|	|s∗|	NOUN
ejpam-4350	232	59	=	=	PUNCT
ejpam-4350	232	60	|a|+	|a|+	VERB
ejpam-4350	232	61	∑	∑	PUNCT
ejpam-4350	232	62	v∈v	v∈v	NOUN
ejpam-4350	232	63	(	(	PUNCT
ejpam-4350	232	64	g	g	NOUN
ejpam-4350	232	65	)	)	PUNCT
ejpam-4350	232	66	|rv|	|rv|	NOUN
ejpam-4350	233	1	=	=	PUNCT
ejpam-4350	233	2	|a|+	|a|+	VERB
ejpam-4350	233	3	∑	∑	PUNCT
ejpam-4350	233	4	u∈ng(a	u∈ng(a	PROPN
ejpam-4350	233	5	)	)	PUNCT
ejpam-4350	233	6	|ru|+	|ru|+	NOUN
ejpam-4350	233	7	∑	∑	PUNCT
ejpam-4350	233	8	v/∈ng(a	v/∈ng(a	X
ejpam-4350	233	9	)	)	PUNCT
ejpam-4350	233	10	|rv|	|rv|	NOUN
ejpam-4350	234	1	=	=	PUNCT
ejpam-4350	234	2	|a|+	|a|+	VERB
ejpam-4350	234	3	∑	∑	PUNCT
ejpam-4350	234	4	v/∈ng(a	v/∈ng(a	X
ejpam-4350	234	5	)	)	PUNCT
ejpam-4350	234	6	|rv|	|rv|	NOUN
ejpam-4350	235	1	≤	≤	ADJ
ejpam-4350	235	2	|a|+	|a|+	NOUN
ejpam-4350	235	3	(	(	PUNCT
ejpam-4350	235	4	|v	|v	X
ejpam-4350	235	5	(	(	PUNCT
ejpam-4350	235	6	g)|	g)|	NOUN
ejpam-4350	235	7	−	−	PROPN
ejpam-4350	235	8	|ng(a)|)ω(h	|ng(a)|)ω(h	NOUN
ejpam-4350	235	9	)	)	PUNCT
ejpam-4350	235	10	=	=	SYM
ejpam-4350	235	11	|a|	|a|	PROPN
ejpam-4350	235	12	−	−	PROPN
ejpam-4350	235	13	|ng(a)|ω(h	|ng(a)|ω(h	NOUN
ejpam-4350	235	14	)	)	PUNCT
ejpam-4350	236	1	+	+	CCONJ
ejpam-4350	236	2	|v	|v	X
ejpam-4350	236	3	(	(	PUNCT
ejpam-4350	236	4	g)|ω(h	g)|ω(h	PROPN
ejpam-4350	236	5	)	)	PUNCT
ejpam-4350	236	6	≤	≤	NUM
ejpam-4350	236	7	|a|	|a|	ADP
ejpam-4350	236	8	−	−	PROPN
ejpam-4350	236	9	|ng(a)|+	|ng(a)|+	PUNCT
ejpam-4350	236	10	|v	|v	X
ejpam-4350	236	11	(	(	PUNCT
ejpam-4350	236	12	g)|ω(h	g)|ω(h	PROPN
ejpam-4350	236	13	)	)	PUNCT
ejpam-4350	236	14	≤	≤	NOUN
ejpam-4350	236	15	|v	|v	X
ejpam-4350	236	16	(	(	PUNCT
ejpam-4350	236	17	g)|ω(h	g)|ω(h	PROPN
ejpam-4350	236	18	)	)	PUNCT
ejpam-4350	236	19	.	.	PUNCT
ejpam-4350	237	1	this	this	PRON
ejpam-4350	237	2	proves	prove	VERB
ejpam-4350	237	3	the	the	DET
ejpam-4350	237	4	desired	desire	VERB
ejpam-4350	237	5	equality	equality	NOUN
ejpam-4350	237	6	.	.	PUNCT
ejpam-4350	238	1	the	the	DET
ejpam-4350	238	2	lexicographic	lexicographic	ADJ
ejpam-4350	238	3	product	product	NOUN
ejpam-4350	238	4	of	of	ADP
ejpam-4350	238	5	graphs	graph	NOUN
ejpam-4350	238	6	g	g	PROPN
ejpam-4350	238	7	and	and	CCONJ
ejpam-4350	238	8	h	h	NOUN
ejpam-4350	238	9	,	,	PUNCT
ejpam-4350	238	10	denoted	denote	VERB
ejpam-4350	238	11	by	by	ADP
ejpam-4350	238	12	g[h	g[h	NOUN
ejpam-4350	238	13	]	]	PUNCT
ejpam-4350	238	14	,	,	PUNCT
ejpam-4350	238	15	is	be	AUX
ejpam-4350	238	16	the	the	DET
ejpam-4350	238	17	graph	graph	NOUN
ejpam-4350	238	18	with	with	ADP
ejpam-4350	238	19	vertex	vertex	NOUN
ejpam-4350	238	20	set	set	VERB
ejpam-4350	238	21	v	v	NOUN
ejpam-4350	238	22	(	(	PUNCT
ejpam-4350	238	23	g[h	g[h	PROPN
ejpam-4350	238	24	]	]	PUNCT
ejpam-4350	238	25	)	)	PUNCT
ejpam-4350	238	26	=	=	SYM
ejpam-4350	238	27	v	v	X
ejpam-4350	238	28	(	(	PUNCT
ejpam-4350	238	29	g	g	NOUN
ejpam-4350	238	30	)	)	PUNCT
ejpam-4350	238	31	×	×	NOUN
ejpam-4350	238	32	v	v	NOUN
ejpam-4350	238	33	(	(	PUNCT
ejpam-4350	238	34	h	h	NOUN
ejpam-4350	238	35	)	)	PUNCT
ejpam-4350	238	36	and	and	CCONJ
ejpam-4350	238	37	(	(	PUNCT
ejpam-4350	238	38	v	v	NOUN
ejpam-4350	238	39	,	,	PUNCT
ejpam-4350	238	40	a)(u	a)(u	ADJ
ejpam-4350	238	41	,	,	PUNCT
ejpam-4350	238	42	b	b	X
ejpam-4350	238	43	)	)	PUNCT
ejpam-4350	238	44	∈	∈	NOUN
ejpam-4350	238	45	e(g[h	e(g[h	NOUN
ejpam-4350	238	46	]	]	PUNCT
ejpam-4350	238	47	)	)	PUNCT
ejpam-4350	239	1	if	if	SCONJ
ejpam-4350	239	2	and	and	CCONJ
ejpam-4350	239	3	only	only	ADV
ejpam-4350	239	4	if	if	SCONJ
ejpam-4350	239	5	either	either	DET
ejpam-4350	239	6	uv	uv	PROPN
ejpam-4350	239	7	∈	∈	PROPN
ejpam-4350	239	8	e(g	e(g	PROPN
ejpam-4350	239	9	)	)	PUNCT
ejpam-4350	239	10	or	or	CCONJ
ejpam-4350	239	11	u	u	X
ejpam-4350	239	12	=	=	PROPN
ejpam-4350	239	13	v	v	PROPN
ejpam-4350	239	14	and	and	CCONJ
ejpam-4350	239	15	ab	ab	PROPN
ejpam-4350	239	16	∈	∈	PROPN
ejpam-4350	239	17	e(h	e(h	PROPN
ejpam-4350	239	18	)	)	PUNCT
ejpam-4350	239	19	.	.	PUNCT
ejpam-4350	239	20	note	note	VERB
ejpam-4350	239	21	that	that	SCONJ
ejpam-4350	239	22	any	any	DET
ejpam-4350	239	23	non	non	ADJ
ejpam-4350	239	24	-	-	ADJ
ejpam-4350	239	25	empty	empty	ADJ
ejpam-4350	239	26	set	set	NOUN
ejpam-4350	239	27	c	c	NOUN
ejpam-4350	239	28	⊆	⊆	NUM
ejpam-4350	239	29	v	v	NOUN
ejpam-4350	239	30	(	(	PUNCT
ejpam-4350	239	31	g)×	g)×	NOUN
ejpam-4350	239	32	v	v	NOUN
ejpam-4350	239	33	(	(	PUNCT
ejpam-4350	239	34	h	h	NOUN
ejpam-4350	239	35	)	)	PUNCT
ejpam-4350	239	36	can	can	AUX
ejpam-4350	239	37	be	be	AUX
ejpam-4350	239	38	written	write	VERB
ejpam-4350	239	39	as	as	ADP
ejpam-4350	239	40	c	c	NOUN
ejpam-4350	239	41	=	=	PUNCT
ejpam-4350	239	42	⋃	⋃	PROPN
ejpam-4350	239	43	x∈s	x∈s	NOUN
ejpam-4350	240	1	[	[	X
ejpam-4350	240	2	{	{	PUNCT
ejpam-4350	240	3	x}×	x}×	PROPN
ejpam-4350	240	4	tx	tx	PROPN
ejpam-4350	240	5	]	]	X
ejpam-4350	240	6	,	,	PUNCT
ejpam-4350	240	7	where	where	SCONJ
ejpam-4350	240	8	s	s	VERB
ejpam-4350	240	9	⊆	⊆	NUM
ejpam-4350	240	10	v	v	NOUN
ejpam-4350	240	11	(	(	PUNCT
ejpam-4350	240	12	g	g	NOUN
ejpam-4350	240	13	)	)	PUNCT
ejpam-4350	240	14	and	and	CCONJ
ejpam-4350	240	15	tx	tx	VERB
ejpam-4350	240	16	⊆	⊆	NUM
ejpam-4350	240	17	v	v	NOUN
ejpam-4350	240	18	(	(	PUNCT
ejpam-4350	240	19	h	h	NOUN
ejpam-4350	240	20	)	)	PUNCT
ejpam-4350	240	21	for	for	ADP
ejpam-4350	240	22	each	each	DET
ejpam-4350	240	23	x	x	PROPN
ejpam-4350	240	24	∈	∈	PROPN
ejpam-4350	240	25	s.	s.	PROPN
ejpam-4350	240	26	theorem	theorem	VERB
ejpam-4350	240	27	6	6	NUM
ejpam-4350	240	28	.	.	PUNCT
ejpam-4350	241	1	let	let	VERB
ejpam-4350	241	2	g	g	NOUN
ejpam-4350	241	3	and	and	CCONJ
ejpam-4350	241	4	h	h	PROPN
ejpam-4350	241	5	be	be	VERB
ejpam-4350	241	6	non	non	ADJ
ejpam-4350	241	7	-	-	ADJ
ejpam-4350	241	8	trivial	trivial	ADJ
ejpam-4350	241	9	connected	connected	ADJ
ejpam-4350	241	10	graphs	graph	NOUN
ejpam-4350	241	11	.	.	PUNCT
ejpam-4350	242	1	then	then	ADV
ejpam-4350	242	2	c	c	NOUN
ejpam-4350	242	3	=	=	PUNCT
ejpam-4350	242	4	⋃	⋃	PROPN
ejpam-4350	242	5	x∈s	x∈s	NOUN
ejpam-4350	243	1	[	[	X
ejpam-4350	243	2	{	{	PUNCT
ejpam-4350	243	3	x	x	NOUN
ejpam-4350	243	4	}	}	PUNCT
ejpam-4350	243	5	×	×	PROPN
ejpam-4350	243	6	tx	tx	PROPN
ejpam-4350	243	7	]	]	PUNCT
ejpam-4350	243	8	,	,	PUNCT
ejpam-4350	243	9	j.	j.	PROPN
ejpam-4350	243	10	hassan	hassan	PROPN
ejpam-4350	243	11	,	,	PUNCT
ejpam-4350	243	12	s.	s.	PROPN
ejpam-4350	243	13	canoy	canoy	PROPN
ejpam-4350	243	14	,	,	PUNCT
ejpam-4350	243	15	jr	jr	PROPN
ejpam-4350	243	16	.	.	PROPN
ejpam-4350	243	17	,	,	PUNCT
ejpam-4350	243	18	a.	a.	PROPN
ejpam-4350	243	19	aradais	aradais	PROPN
ejpam-4350	243	20	/	/	SYM
ejpam-4350	243	21	eur	eur	PROPN
ejpam-4350	243	22	.	.	PUNCT
ejpam-4350	244	1	j.	j.	PROPN
ejpam-4350	244	2	pure	pure	PROPN
ejpam-4350	244	3	appl	appl	PROPN
ejpam-4350	244	4	.	.	PROPN
ejpam-4350	244	5	math	math	PROPN
ejpam-4350	244	6	,	,	PUNCT
ejpam-4350	244	7	15	15	NUM
ejpam-4350	244	8	(	(	PUNCT
ejpam-4350	244	9	2	2	NUM
ejpam-4350	244	10	)	)	PUNCT
ejpam-4350	244	11	(	(	PUNCT
ejpam-4350	244	12	2022	2022	NUM
ejpam-4350	244	13	)	)	PUNCT
ejpam-4350	244	14	,	,	PUNCT
ejpam-4350	244	15	467	467	NUM
ejpam-4350	244	16	-	-	SYM
ejpam-4350	244	17	477	477	NUM
ejpam-4350	244	18	474	474	NUM
ejpam-4350	244	19	where	where	SCONJ
ejpam-4350	244	20	s	s	VERB
ejpam-4350	244	21	⊆	⊆	NUM
ejpam-4350	244	22	v	v	NOUN
ejpam-4350	244	23	(	(	PUNCT
ejpam-4350	244	24	g	g	NOUN
ejpam-4350	244	25	)	)	PUNCT
ejpam-4350	244	26	and	and	CCONJ
ejpam-4350	244	27	tx	tx	VERB
ejpam-4350	244	28	⊆	⊆	NUM
ejpam-4350	244	29	v	v	NOUN
ejpam-4350	244	30	(	(	PUNCT
ejpam-4350	244	31	h	h	NOUN
ejpam-4350	244	32	)	)	PUNCT
ejpam-4350	244	33	for	for	ADP
ejpam-4350	244	34	each	each	DET
ejpam-4350	244	35	x	x	SYM
ejpam-4350	244	36	∈	∈	PROPN
ejpam-4350	244	37	s	s	NOUN
ejpam-4350	244	38	,	,	PUNCT
ejpam-4350	244	39	is	be	AUX
ejpam-4350	244	40	a	a	DET
ejpam-4350	244	41	hop	hop	NOUN
ejpam-4350	244	42	independent	independent	ADJ
ejpam-4350	244	43	set	set	NOUN
ejpam-4350	244	44	of	of	ADP
ejpam-4350	244	45	g[h	g[h	NOUN
ejpam-4350	244	46	]	]	PUNCT
ejpam-4350	244	47	if	if	SCONJ
ejpam-4350	245	1	and	and	CCONJ
ejpam-4350	245	2	only	only	ADV
ejpam-4350	245	3	if	if	SCONJ
ejpam-4350	245	4	the	the	DET
ejpam-4350	245	5	following	follow	VERB
ejpam-4350	245	6	conditions	condition	NOUN
ejpam-4350	245	7	hold	hold	VERB
ejpam-4350	245	8	.	.	PUNCT
ejpam-4350	246	1	(	(	PUNCT
ejpam-4350	246	2	i	i	NOUN
ejpam-4350	246	3	)	)	PUNCT
ejpam-4350	246	4	s	s	VERB
ejpam-4350	246	5	is	be	AUX
ejpam-4350	246	6	a	a	DET
ejpam-4350	246	7	hop	hop	NOUN
ejpam-4350	246	8	independent	independent	ADJ
ejpam-4350	246	9	set	set	NOUN
ejpam-4350	246	10	of	of	ADP
ejpam-4350	246	11	g.	g.	PROPN
ejpam-4350	246	12	(	(	PUNCT
ejpam-4350	246	13	ii	ii	PROPN
ejpam-4350	246	14	)	)	PUNCT
ejpam-4350	246	15	tx	tx	PROPN
ejpam-4350	246	16	is	be	AUX
ejpam-4350	246	17	a	a	DET
ejpam-4350	246	18	clique	clique	NOUN
ejpam-4350	246	19	in	in	ADP
ejpam-4350	246	20	h	h	NOUN
ejpam-4350	246	21	for	for	ADP
ejpam-4350	246	22	each	each	DET
ejpam-4350	246	23	x	x	SYM
ejpam-4350	246	24	∈	∈	PROPN
ejpam-4350	246	25	s.	s.	PROPN
ejpam-4350	246	26	proof	proof	PROPN
ejpam-4350	246	27	.	.	PUNCT
ejpam-4350	247	1	suppose	suppose	VERB
ejpam-4350	247	2	c	c	NOUN
ejpam-4350	247	3	=	=	PUNCT
ejpam-4350	247	4	⋃	⋃	PROPN
ejpam-4350	247	5	x∈s	x∈s	NOUN
ejpam-4350	248	1	[	[	X
ejpam-4350	248	2	{	{	PUNCT
ejpam-4350	248	3	x	x	NOUN
ejpam-4350	248	4	}	}	PUNCT
ejpam-4350	248	5	×	×	PROPN
ejpam-4350	248	6	tx	tx	PROPN
ejpam-4350	248	7	]	]	PUNCT
ejpam-4350	248	8	is	be	AUX
ejpam-4350	248	9	a	a	DET
ejpam-4350	248	10	hop	hop	NOUN
ejpam-4350	248	11	independent	independent	ADJ
ejpam-4350	248	12	set	set	NOUN
ejpam-4350	248	13	of	of	ADP
ejpam-4350	248	14	g[h	g[h	NOUN
ejpam-4350	248	15	]	]	PUNCT
ejpam-4350	248	16	.	.	PUNCT
ejpam-4350	249	1	let	let	VERB
ejpam-4350	249	2	v	v	NOUN
ejpam-4350	249	3	,	,	PUNCT
ejpam-4350	249	4	w	w	PROPN
ejpam-4350	249	5	∈	∈	PROPN
ejpam-4350	249	6	s	s	PART
ejpam-4350	249	7	with	with	ADP
ejpam-4350	249	8	v	v	NOUN
ejpam-4350	249	9	6=	6=	ADP
ejpam-4350	249	10	w	w	NOUN
ejpam-4350	249	11	and	and	CCONJ
ejpam-4350	249	12	let	let	VERB
ejpam-4350	249	13	a	a	DET
ejpam-4350	249	14	∈	∈	NOUN
ejpam-4350	249	15	tv	tv	NOUN
ejpam-4350	249	16	and	and	CCONJ
ejpam-4350	249	17	b	b	PROPN
ejpam-4350	249	18	∈	∈	PROPN
ejpam-4350	249	19	tw	tw	NOUN
ejpam-4350	249	20	.	.	PUNCT
ejpam-4350	250	1	since	since	SCONJ
ejpam-4350	250	2	(	(	PUNCT
ejpam-4350	250	3	v	v	NOUN
ejpam-4350	250	4	,	,	PUNCT
ejpam-4350	250	5	a	a	PRON
ejpam-4350	250	6	)	)	PUNCT
ejpam-4350	250	7	,	,	PUNCT
ejpam-4350	250	8	(	(	PUNCT
ejpam-4350	250	9	w	w	PROPN
ejpam-4350	250	10	,	,	PUNCT
ejpam-4350	250	11	b	b	NOUN
ejpam-4350	250	12	)	)	PUNCT
ejpam-4350	250	13	∈	∈	PROPN
ejpam-4350	250	14	c	c	NOUN
ejpam-4350	250	15	and	and	CCONJ
ejpam-4350	250	16	c	c	PROPN
ejpam-4350	250	17	is	be	AUX
ejpam-4350	250	18	a	a	DET
ejpam-4350	250	19	hop	hop	NOUN
ejpam-4350	250	20	independent	independent	ADJ
ejpam-4350	250	21	set	set	NOUN
ejpam-4350	250	22	of	of	ADP
ejpam-4350	250	23	g[h	g[h	PROPN
ejpam-4350	250	24	]	]	PUNCT
ejpam-4350	250	25	,	,	PUNCT
ejpam-4350	250	26	it	it	PRON
ejpam-4350	250	27	follows	follow	VERB
ejpam-4350	250	28	that	that	DET
ejpam-4350	250	29	dg[h]((v	dg[h]((v	NOUN
ejpam-4350	250	30	,	,	PUNCT
ejpam-4350	250	31	a	a	NOUN
ejpam-4350	250	32	)	)	PUNCT
ejpam-4350	250	33	,	,	PUNCT
ejpam-4350	250	34	(	(	PUNCT
ejpam-4350	250	35	w	w	PROPN
ejpam-4350	250	36	,	,	PUNCT
ejpam-4350	250	37	b	b	NOUN
ejpam-4350	250	38	)	)	PUNCT
ejpam-4350	250	39	)	)	PUNCT
ejpam-4350	250	40	=	=	SYM
ejpam-4350	251	1	dg(v	dg(v	X
ejpam-4350	251	2	,	,	PUNCT
ejpam-4350	251	3	w	w	NOUN
ejpam-4350	251	4	)	)	PUNCT
ejpam-4350	251	5	6=	6=	ADP
ejpam-4350	251	6	2	2	X
ejpam-4350	251	7	.	.	PUNCT
ejpam-4350	252	1	this	this	PRON
ejpam-4350	252	2	implies	imply	VERB
ejpam-4350	252	3	that	that	SCONJ
ejpam-4350	252	4	s	s	VERB
ejpam-4350	252	5	is	be	AUX
ejpam-4350	252	6	a	a	DET
ejpam-4350	252	7	hop	hop	NOUN
ejpam-4350	252	8	independent	independent	ADJ
ejpam-4350	252	9	set	set	NOUN
ejpam-4350	252	10	of	of	ADP
ejpam-4350	252	11	g	g	NOUN
ejpam-4350	252	12	,	,	PUNCT
ejpam-4350	252	13	showing	show	VERB
ejpam-4350	252	14	that	that	SCONJ
ejpam-4350	252	15	(	(	PUNCT
ejpam-4350	252	16	i	i	NOUN
ejpam-4350	252	17	)	)	PUNCT
ejpam-4350	252	18	holds	hold	VERB
ejpam-4350	252	19	.	.	PUNCT
ejpam-4350	253	1	next	next	ADV
ejpam-4350	253	2	,	,	PUNCT
ejpam-4350	253	3	let	let	VERB
ejpam-4350	253	4	x	x	PROPN
ejpam-4350	253	5	∈	∈	PROPN
ejpam-4350	253	6	s.	s.	PROPN
ejpam-4350	254	1	if	if	SCONJ
ejpam-4350	254	2	|tx|	|tx|	NOUN
ejpam-4350	254	3	=	=	SYM
ejpam-4350	254	4	1	1	NUM
ejpam-4350	254	5	,	,	PUNCT
ejpam-4350	254	6	then	then	ADV
ejpam-4350	254	7	tx	tx	PROPN
ejpam-4350	254	8	is	be	AUX
ejpam-4350	254	9	a	a	DET
ejpam-4350	254	10	clique	clique	NOUN
ejpam-4350	254	11	in	in	ADP
ejpam-4350	254	12	h.	h.	PROPN
ejpam-4350	254	13	suppose	suppose	VERB
ejpam-4350	254	14	|tx|	|tx|	PROPN
ejpam-4350	254	15	≥	≥	NUM
ejpam-4350	254	16	2	2	NUM
ejpam-4350	254	17	and	and	CCONJ
ejpam-4350	254	18	let	let	VERB
ejpam-4350	254	19	p	p	PRON
ejpam-4350	254	20	,	,	PUNCT
ejpam-4350	254	21	q	q	PROPN
ejpam-4350	254	22	∈	∈	PROPN
ejpam-4350	254	23	tx	tx	PROPN
ejpam-4350	254	24	,	,	PUNCT
ejpam-4350	254	25	where	where	SCONJ
ejpam-4350	254	26	p	p	PROPN
ejpam-4350	254	27	6=	6=	PROPN
ejpam-4350	254	28	q.	q.	PROPN
ejpam-4350	254	29	then	then	ADV
ejpam-4350	254	30	(	(	PUNCT
ejpam-4350	254	31	x	x	X
ejpam-4350	254	32	,	,	PUNCT
ejpam-4350	254	33	p	p	NOUN
ejpam-4350	254	34	)	)	PUNCT
ejpam-4350	254	35	and	and	CCONJ
ejpam-4350	254	36	(	(	PUNCT
ejpam-4350	254	37	x	x	X
ejpam-4350	254	38	,	,	PUNCT
ejpam-4350	254	39	q	q	X
ejpam-4350	254	40	)	)	PUNCT
ejpam-4350	254	41	are	be	AUX
ejpam-4350	254	42	distinct	distinct	ADJ
ejpam-4350	254	43	elements	element	NOUN
ejpam-4350	254	44	of	of	ADP
ejpam-4350	254	45	c.	c.	NOUN
ejpam-4350	254	46	since	since	SCONJ
ejpam-4350	254	47	c	c	PROPN
ejpam-4350	254	48	is	be	AUX
ejpam-4350	254	49	a	a	DET
ejpam-4350	254	50	hop	hop	NOUN
ejpam-4350	254	51	independent	independent	ADJ
ejpam-4350	254	52	set	set	NOUN
ejpam-4350	254	53	of	of	ADP
ejpam-4350	254	54	g[h	g[h	PROPN
ejpam-4350	254	55	]	]	PUNCT
ejpam-4350	254	56	,	,	PUNCT
ejpam-4350	254	57	dg[h]((x	dg[h]((x	PROPN
ejpam-4350	254	58	,	,	PUNCT
ejpam-4350	254	59	p	p	NOUN
ejpam-4350	254	60	)	)	PUNCT
ejpam-4350	254	61	,	,	PUNCT
ejpam-4350	254	62	(	(	PUNCT
ejpam-4350	254	63	x	x	X
ejpam-4350	254	64	,	,	PUNCT
ejpam-4350	254	65	q	q	NOUN
ejpam-4350	254	66	)	)	PUNCT
ejpam-4350	254	67	)	)	PUNCT
ejpam-4350	254	68	6=	6=	ADP
ejpam-4350	255	1	2	2	X
ejpam-4350	255	2	.	.	PUNCT
ejpam-4350	255	3	now	now	ADV
ejpam-4350	255	4	,	,	PUNCT
ejpam-4350	255	5	since	since	SCONJ
ejpam-4350	255	6	g	g	PROPN
ejpam-4350	255	7	is	be	AUX
ejpam-4350	255	8	non	non	ADJ
ejpam-4350	255	9	-	-	ADJ
ejpam-4350	255	10	trivial	trivial	ADJ
ejpam-4350	255	11	and	and	CCONJ
ejpam-4350	255	12	connected	connected	ADJ
ejpam-4350	255	13	,	,	PUNCT
ejpam-4350	255	14	it	it	PRON
ejpam-4350	255	15	follows	follow	VERB
ejpam-4350	255	16	that	that	SCONJ
ejpam-4350	255	17	dh(p	dh(p	NOUN
ejpam-4350	255	18	,	,	PUNCT
ejpam-4350	255	19	q	q	X
ejpam-4350	255	20	)	)	PUNCT
ejpam-4350	255	21	=	=	SYM
ejpam-4350	255	22	1	1	X
ejpam-4350	255	23	.	.	PUNCT
ejpam-4350	256	1	thus	thus	ADV
ejpam-4350	256	2	,	,	PUNCT
ejpam-4350	256	3	tx	tx	PROPN
ejpam-4350	256	4	is	be	AUX
ejpam-4350	256	5	a	a	DET
ejpam-4350	256	6	clique	clique	NOUN
ejpam-4350	256	7	in	in	ADP
ejpam-4350	256	8	h	h	NOUN
ejpam-4350	256	9	,	,	PUNCT
ejpam-4350	256	10	showing	show	VERB
ejpam-4350	256	11	that	that	SCONJ
ejpam-4350	256	12	(	(	PUNCT
ejpam-4350	256	13	ii	ii	NOUN
ejpam-4350	256	14	)	)	PUNCT
ejpam-4350	256	15	holds	hold	VERB
ejpam-4350	256	16	.	.	PUNCT
ejpam-4350	257	1	for	for	ADP
ejpam-4350	257	2	the	the	DET
ejpam-4350	257	3	converse	converse	NOUN
ejpam-4350	257	4	,	,	PUNCT
ejpam-4350	257	5	suppose	suppose	VERB
ejpam-4350	257	6	that	that	SCONJ
ejpam-4350	257	7	c	c	PROPN
ejpam-4350	257	8	=	=	PUNCT
ejpam-4350	257	9	⋃	⋃	PROPN
ejpam-4350	257	10	x∈s	x∈s	NOUN
ejpam-4350	258	1	[	[	X
ejpam-4350	258	2	{	{	PUNCT
ejpam-4350	258	3	x	x	NOUN
ejpam-4350	258	4	}	}	PUNCT
ejpam-4350	258	5	×	×	PROPN
ejpam-4350	258	6	tx	tx	PROPN
ejpam-4350	258	7	]	]	PUNCT
ejpam-4350	258	8	and	and	CCONJ
ejpam-4350	258	9	satisfies	satisfie	NOUN
ejpam-4350	258	10	(	(	PUNCT
ejpam-4350	258	11	i	i	NOUN
ejpam-4350	258	12	)	)	PUNCT
ejpam-4350	258	13	and	and	CCONJ
ejpam-4350	258	14	(	(	PUNCT
ejpam-4350	258	15	ii	ii	NOUN
ejpam-4350	258	16	)	)	PUNCT
ejpam-4350	258	17	.	.	PUNCT
ejpam-4350	259	1	let	let	VERB
ejpam-4350	259	2	(	(	PUNCT
ejpam-4350	259	3	y	y	NOUN
ejpam-4350	259	4	,	,	PUNCT
ejpam-4350	259	5	a	a	PRON
ejpam-4350	259	6	)	)	PUNCT
ejpam-4350	259	7	,	,	PUNCT
ejpam-4350	259	8	(	(	PUNCT
ejpam-4350	259	9	z	z	X
ejpam-4350	259	10	,	,	PUNCT
ejpam-4350	259	11	b	b	NOUN
ejpam-4350	259	12	)	)	PUNCT
ejpam-4350	259	13	∈	∈	PROPN
ejpam-4350	259	14	c	c	NOUN
ejpam-4350	259	15	with	with	ADP
ejpam-4350	259	16	(	(	PUNCT
ejpam-4350	259	17	y	y	PROPN
ejpam-4350	259	18	,	,	PUNCT
ejpam-4350	259	19	a	a	PRON
ejpam-4350	259	20	)	)	PUNCT
ejpam-4350	259	21	6=	6=	ADP
ejpam-4350	259	22	(	(	PUNCT
ejpam-4350	259	23	z	z	NOUN
ejpam-4350	259	24	,	,	PUNCT
ejpam-4350	259	25	b	b	NOUN
ejpam-4350	259	26	)	)	PUNCT
ejpam-4350	259	27	.	.	PUNCT
ejpam-4350	260	1	consider	consider	VERB
ejpam-4350	260	2	the	the	DET
ejpam-4350	260	3	following	follow	VERB
ejpam-4350	260	4	cases	case	NOUN
ejpam-4350	260	5	:	:	PUNCT
ejpam-4350	260	6	case	case	NOUN
ejpam-4350	260	7	1	1	NUM
ejpam-4350	260	8	.	.	PUNCT
ejpam-4350	261	1	y	y	PROPN
ejpam-4350	261	2	=	=	PUNCT
ejpam-4350	261	3	z.	z.	PROPN
ejpam-4350	261	4	then	then	ADV
ejpam-4350	261	5	a	a	PRON
ejpam-4350	261	6	,	,	PUNCT
ejpam-4350	261	7	b	b	PROPN
ejpam-4350	261	8	∈	∈	PROPN
ejpam-4350	261	9	ty	ty	INTJ
ejpam-4350	261	10	.	.	PUNCT
ejpam-4350	262	1	from	from	ADP
ejpam-4350	262	2	condition	condition	NOUN
ejpam-4350	262	3	(	(	PUNCT
ejpam-4350	262	4	ii	ii	NOUN
ejpam-4350	262	5	)	)	PUNCT
ejpam-4350	262	6	,	,	PUNCT
ejpam-4350	262	7	tx	tx	PROPN
ejpam-4350	262	8	is	be	AUX
ejpam-4350	262	9	a	a	DET
ejpam-4350	262	10	clique	clique	NOUN
ejpam-4350	262	11	in	in	ADP
ejpam-4350	262	12	h	h	NOUN
ejpam-4350	262	13	and	and	CCONJ
ejpam-4350	262	14	so	so	ADV
ejpam-4350	262	15	dh(a	dh(a	ADJ
ejpam-4350	262	16	,	,	PUNCT
ejpam-4350	262	17	b	b	NOUN
ejpam-4350	262	18	)	)	PUNCT
ejpam-4350	262	19	=	=	SYM
ejpam-4350	262	20	1	1	X
ejpam-4350	262	21	.	.	PUNCT
ejpam-4350	263	1	hence	hence	ADV
ejpam-4350	263	2	,	,	PUNCT
ejpam-4350	263	3	dg[h]((y	dg[h]((y	PROPN
ejpam-4350	263	4	,	,	PUNCT
ejpam-4350	263	5	a	a	PRON
ejpam-4350	263	6	)	)	PUNCT
ejpam-4350	263	7	,	,	PUNCT
ejpam-4350	263	8	(	(	PUNCT
ejpam-4350	263	9	y	y	PROPN
ejpam-4350	263	10	,	,	PUNCT
ejpam-4350	263	11	b	b	NOUN
ejpam-4350	263	12	)	)	PUNCT
ejpam-4350	263	13	)	)	PUNCT
ejpam-4350	264	1	=	=	SYM
ejpam-4350	264	2	1	1	NUM
ejpam-4350	264	3	6=	6=	NUM
ejpam-4350	264	4	2	2	NUM
ejpam-4350	264	5	.	.	X
ejpam-4350	264	6	case	case	NOUN
ejpam-4350	264	7	2	2	NUM
ejpam-4350	264	8	.	.	X
ejpam-4350	265	1	y	y	PROPN
ejpam-4350	265	2	6=	6=	PROPN
ejpam-4350	265	3	z.	z.	PROPN
ejpam-4350	265	4	since	since	SCONJ
ejpam-4350	265	5	y	y	PROPN
ejpam-4350	265	6	,	,	PUNCT
ejpam-4350	265	7	z	z	PROPN
ejpam-4350	265	8	∈	∈	PROPN
ejpam-4350	265	9	s	s	PART
ejpam-4350	265	10	and	and	CCONJ
ejpam-4350	265	11	s	s	VERB
ejpam-4350	265	12	is	be	AUX
ejpam-4350	265	13	a	a	DET
ejpam-4350	265	14	hop	hop	NOUN
ejpam-4350	265	15	independent	independent	ADJ
ejpam-4350	265	16	set	set	NOUN
ejpam-4350	265	17	of	of	ADP
ejpam-4350	265	18	g	g	NOUN
ejpam-4350	265	19	,	,	PUNCT
ejpam-4350	265	20	dg(y	dg(y	ADJ
ejpam-4350	265	21	,	,	PUNCT
ejpam-4350	265	22	z	z	NOUN
ejpam-4350	265	23	)	)	PUNCT
ejpam-4350	265	24	6=	6=	ADP
ejpam-4350	265	25	2	2	X
ejpam-4350	265	26	.	.	PUNCT
ejpam-4350	266	1	it	it	PRON
ejpam-4350	266	2	follows	follow	VERB
ejpam-4350	266	3	that	that	SCONJ
ejpam-4350	266	4	dg[h]((y	dg[h]((y	NOUN
ejpam-4350	266	5	,	,	PUNCT
ejpam-4350	266	6	a	a	PRON
ejpam-4350	266	7	)	)	PUNCT
ejpam-4350	266	8	,	,	PUNCT
ejpam-4350	266	9	(	(	PUNCT
ejpam-4350	266	10	z	z	X
ejpam-4350	266	11	,	,	PUNCT
ejpam-4350	266	12	b	b	NOUN
ejpam-4350	266	13	)	)	PUNCT
ejpam-4350	266	14	)	)	PUNCT
ejpam-4350	266	15	=	=	SYM
ejpam-4350	267	1	dg(y	dg(y	ADJ
ejpam-4350	267	2	,	,	PUNCT
ejpam-4350	267	3	z	z	NOUN
ejpam-4350	267	4	)	)	PUNCT
ejpam-4350	267	5	6=	6=	ADP
ejpam-4350	267	6	2	2	X
ejpam-4350	267	7	.	.	PUNCT
ejpam-4350	267	8	accordingly	accordingly	ADV
ejpam-4350	267	9	,	,	PUNCT
ejpam-4350	267	10	c	c	PROPN
ejpam-4350	267	11	is	be	AUX
ejpam-4350	267	12	a	a	DET
ejpam-4350	267	13	hop	hop	NOUN
ejpam-4350	267	14	independent	independent	ADJ
ejpam-4350	267	15	set	set	NOUN
ejpam-4350	267	16	of	of	ADP
ejpam-4350	267	17	g[h	g[h	PROPN
ejpam-4350	267	18	]	]	PUNCT
ejpam-4350	267	19	.	.	PUNCT
ejpam-4350	268	1	corollary	corollary	ADJ
ejpam-4350	268	2	4	4	NUM
ejpam-4350	268	3	.	.	PUNCT
ejpam-4350	269	1	let	let	VERB
ejpam-4350	269	2	g	g	NOUN
ejpam-4350	269	3	and	and	CCONJ
ejpam-4350	269	4	h	h	PROPN
ejpam-4350	269	5	be	be	VERB
ejpam-4350	269	6	non	non	ADJ
ejpam-4350	269	7	-	-	ADJ
ejpam-4350	269	8	trivial	trivial	ADJ
ejpam-4350	269	9	connected	connected	ADJ
ejpam-4350	269	10	graphs	graph	NOUN
ejpam-4350	269	11	.	.	PUNCT
ejpam-4350	270	1	then	then	ADV
ejpam-4350	270	2	αh(g[h	αh(g[h	ADV
ejpam-4350	270	3	]	]	X
ejpam-4350	270	4	)	)	PUNCT
ejpam-4350	270	5	=	=	SYM
ejpam-4350	270	6	αh(g)ω(h	αh(g)ω(h	NOUN
ejpam-4350	270	7	)	)	PUNCT
ejpam-4350	270	8	.	.	PUNCT
ejpam-4350	271	1	proof	proof	NOUN
ejpam-4350	271	2	.	.	PUNCT
ejpam-4350	272	1	let	let	VERB
ejpam-4350	272	2	s	s	PRON
ejpam-4350	272	3	be	be	AUX
ejpam-4350	272	4	a	a	DET
ejpam-4350	272	5	αh	αh	NOUN
ejpam-4350	272	6	-	-	PUNCT
ejpam-4350	272	7	set	set	NOUN
ejpam-4350	272	8	of	of	ADP
ejpam-4350	272	9	g	g	NOUN
ejpam-4350	272	10	and	and	CCONJ
ejpam-4350	272	11	let	let	VERB
ejpam-4350	272	12	d	d	PRON
ejpam-4350	272	13	be	be	AUX
ejpam-4350	272	14	a	a	DET
ejpam-4350	272	15	clique	clique	NOUN
ejpam-4350	272	16	in	in	ADP
ejpam-4350	272	17	h	h	NOUN
ejpam-4350	272	18	with	with	ADP
ejpam-4350	272	19	|d|	|d|	PROPN
ejpam-4350	272	20	=	=	SYM
ejpam-4350	272	21	ω(h	ω(h	NUM
ejpam-4350	272	22	)	)	PUNCT
ejpam-4350	272	23	.	.	PUNCT
ejpam-4350	273	1	for	for	ADP
ejpam-4350	273	2	each	each	DET
ejpam-4350	273	3	x	x	SYM
ejpam-4350	273	4	∈	∈	PROPN
ejpam-4350	273	5	s	s	NOUN
ejpam-4350	273	6	,	,	PUNCT
ejpam-4350	273	7	set	set	VERB
ejpam-4350	273	8	tx	tx	PROPN
ejpam-4350	273	9	=	=	SYM
ejpam-4350	273	10	d.	d.	PROPN
ejpam-4350	273	11	then	then	ADV
ejpam-4350	273	12	c	c	PROPN
ejpam-4350	274	1	=	=	PUNCT
ejpam-4350	274	2	⋃	⋃	PROPN
ejpam-4350	274	3	x∈s	x∈s	NOUN
ejpam-4350	275	1	[	[	X
ejpam-4350	275	2	{	{	PUNCT
ejpam-4350	275	3	x}×tx	x}×tx	X
ejpam-4350	275	4	]	]	X
ejpam-4350	275	5	=	=	PUNCT
ejpam-4350	275	6	s×d	s×d	PROPN
ejpam-4350	275	7	is	be	AUX
ejpam-4350	275	8	a	a	DET
ejpam-4350	275	9	hop	hop	NOUN
ejpam-4350	275	10	independent	independent	ADJ
ejpam-4350	275	11	set	set	NOUN
ejpam-4350	275	12	of	of	ADP
ejpam-4350	275	13	g[h	g[h	PROPN
ejpam-4350	275	14	]	]	PUNCT
ejpam-4350	275	15	by	by	ADP
ejpam-4350	275	16	theorem	theorem	NOUN
ejpam-4350	275	17	6	6	NUM
ejpam-4350	275	18	.	.	PUNCT
ejpam-4350	276	1	hence	hence	ADV
ejpam-4350	276	2	,	,	PUNCT
ejpam-4350	276	3	αh(g[h	αh(g[h	NOUN
ejpam-4350	276	4	]	]	X
ejpam-4350	276	5	)	)	PUNCT
ejpam-4350	276	6	≥	≥	NOUN
ejpam-4350	276	7	|c|	|c|	NOUN
ejpam-4350	276	8	=	=	SYM
ejpam-4350	276	9	αh(g)ω(h	αh(g)ω(h	PROPN
ejpam-4350	276	10	)	)	PUNCT
ejpam-4350	276	11	.	.	PUNCT
ejpam-4350	277	1	next	next	ADV
ejpam-4350	277	2	,	,	PUNCT
ejpam-4350	277	3	let	let	VERB
ejpam-4350	277	4	c0	c0	PROPN
ejpam-4350	277	5	=	=	PUNCT
ejpam-4350	278	1	⋃	⋃	PROPN
ejpam-4350	278	2	x∈s0	x∈s0	NOUN
ejpam-4350	279	1	[	[	X
ejpam-4350	279	2	{	{	PUNCT
ejpam-4350	279	3	x	x	NOUN
ejpam-4350	279	4	}	}	PUNCT
ejpam-4350	279	5	×	×	NOUN
ejpam-4350	279	6	rx	rx	AUX
ejpam-4350	279	7	]	]	PUNCT
ejpam-4350	279	8	be	be	AUX
ejpam-4350	279	9	a	a	DET
ejpam-4350	279	10	αh	αh	NOUN
ejpam-4350	279	11	-	-	PUNCT
ejpam-4350	279	12	set	set	NOUN
ejpam-4350	279	13	of	of	ADP
ejpam-4350	279	14	g[h	g[h	NOUN
ejpam-4350	279	15	]	]	PUNCT
ejpam-4350	279	16	.	.	PUNCT
ejpam-4350	280	1	by	by	ADP
ejpam-4350	280	2	theorem	theorem	NOUN
ejpam-4350	280	3	6	6	NUM
ejpam-4350	280	4	,	,	PUNCT
ejpam-4350	280	5	s0	s0	PROPN
ejpam-4350	280	6	is	be	AUX
ejpam-4350	280	7	a	a	DET
ejpam-4350	280	8	hop	hop	NOUN
ejpam-4350	280	9	independent	independent	ADJ
ejpam-4350	280	10	set	set	NOUN
ejpam-4350	280	11	of	of	ADP
ejpam-4350	280	12	g	g	PROPN
ejpam-4350	280	13	and	and	CCONJ
ejpam-4350	280	14	tx	tx	PROPN
ejpam-4350	280	15	is	be	AUX
ejpam-4350	280	16	a	a	DET
ejpam-4350	280	17	clique	clique	NOUN
ejpam-4350	280	18	in	in	ADP
ejpam-4350	280	19	h.	h.	PROPN
ejpam-4350	280	20	hence	hence	ADV
ejpam-4350	280	21	,	,	PUNCT
ejpam-4350	280	22	αh(g[h	αh(g[h	NOUN
ejpam-4350	280	23	]	]	X
ejpam-4350	280	24	)	)	PUNCT
ejpam-4350	281	1	=	=	SYM
ejpam-4350	281	2	|c0|	|c0|	NOUN
ejpam-4350	281	3	=	=	SYM
ejpam-4350	281	4	∑	∑	PUNCT
ejpam-4350	281	5	x∈s0	x∈s0	PROPN
ejpam-4350	281	6	|tx|	|tx|	VERB
ejpam-4350	281	7	≤	≤	NUM
ejpam-4350	281	8	|s0|ω(h	|s0|ω(h	PROPN
ejpam-4350	281	9	)	)	PUNCT
ejpam-4350	281	10	≤	≤	NUM
ejpam-4350	281	11	αh(g)ω(h	αh(g)ω(h	NOUN
ejpam-4350	281	12	)	)	PUNCT
ejpam-4350	281	13	.	.	PUNCT
ejpam-4350	282	1	this	this	PRON
ejpam-4350	282	2	establishes	establish	VERB
ejpam-4350	282	3	the	the	DET
ejpam-4350	282	4	desired	desire	VERB
ejpam-4350	282	5	equality	equality	NOUN
ejpam-4350	282	6	.	.	PUNCT
ejpam-4350	283	1	j.	j.	PROPN
ejpam-4350	283	2	hassan	hassan	PROPN
ejpam-4350	283	3	,	,	PUNCT
ejpam-4350	283	4	s.	s.	PROPN
ejpam-4350	283	5	canoy	canoy	PROPN
ejpam-4350	283	6	,	,	PUNCT
ejpam-4350	283	7	jr	jr	PROPN
ejpam-4350	283	8	.	.	PROPN
ejpam-4350	283	9	,	,	PUNCT
ejpam-4350	283	10	a.	a.	PROPN
ejpam-4350	283	11	aradais	aradais	PROPN
ejpam-4350	283	12	/	/	SYM
ejpam-4350	283	13	eur	eur	PROPN
ejpam-4350	283	14	.	.	PUNCT
ejpam-4350	284	1	j.	j.	PROPN
ejpam-4350	284	2	pure	pure	PROPN
ejpam-4350	284	3	appl	appl	PROPN
ejpam-4350	284	4	.	.	PROPN
ejpam-4350	284	5	math	math	PROPN
ejpam-4350	284	6	,	,	PUNCT
ejpam-4350	284	7	15	15	NUM
ejpam-4350	284	8	(	(	PUNCT
ejpam-4350	284	9	2	2	NUM
ejpam-4350	284	10	)	)	PUNCT
ejpam-4350	284	11	(	(	PUNCT
ejpam-4350	284	12	2022	2022	NUM
ejpam-4350	284	13	)	)	PUNCT
ejpam-4350	284	14	,	,	PUNCT
ejpam-4350	284	15	467	467	NUM
ejpam-4350	284	16	-	-	SYM
ejpam-4350	284	17	477	477	NUM
ejpam-4350	284	18	475	475	NUM
ejpam-4350	284	19	the	the	DET
ejpam-4350	284	20	cartesian	cartesian	ADJ
ejpam-4350	284	21	product	product	NOUN
ejpam-4350	284	22	of	of	ADP
ejpam-4350	284	23	graphs	graph	NOUN
ejpam-4350	284	24	g	g	PROPN
ejpam-4350	284	25	and	and	CCONJ
ejpam-4350	284	26	h	h	NOUN
ejpam-4350	284	27	,	,	PUNCT
ejpam-4350	284	28	denoted	denote	VERB
ejpam-4350	284	29	by	by	ADP
ejpam-4350	284	30	g	g	PROPN
ejpam-4350	284	31	�	�	PROPN
ejpam-4350	284	32	h	h	NOUN
ejpam-4350	284	33	,	,	PUNCT
ejpam-4350	284	34	is	be	AUX
ejpam-4350	284	35	the	the	DET
ejpam-4350	284	36	graph	graph	NOUN
ejpam-4350	284	37	with	with	ADP
ejpam-4350	284	38	vertex	vertex	NOUN
ejpam-4350	284	39	set	set	VERB
ejpam-4350	284	40	v	v	NOUN
ejpam-4350	284	41	(	(	PUNCT
ejpam-4350	284	42	g	g	PROPN
ejpam-4350	284	43	�	�	NOUN
ejpam-4350	284	44	h	h	NOUN
ejpam-4350	284	45	)	)	PUNCT
ejpam-4350	284	46	=	=	NOUN
ejpam-4350	284	47	v	v	X
ejpam-4350	284	48	(	(	PUNCT
ejpam-4350	284	49	g	g	NOUN
ejpam-4350	284	50	)	)	PUNCT
ejpam-4350	284	51	×	×	NOUN
ejpam-4350	284	52	v	v	NOUN
ejpam-4350	284	53	(	(	PUNCT
ejpam-4350	284	54	h	h	NOUN
ejpam-4350	284	55	)	)	PUNCT
ejpam-4350	284	56	and	and	CCONJ
ejpam-4350	284	57	(	(	PUNCT
ejpam-4350	284	58	v	v	NOUN
ejpam-4350	284	59	,	,	PUNCT
ejpam-4350	284	60	a)(u	a)(u	ADJ
ejpam-4350	284	61	,	,	PUNCT
ejpam-4350	284	62	b	b	X
ejpam-4350	284	63	)	)	PUNCT
ejpam-4350	284	64	∈	∈	NOUN
ejpam-4350	284	65	e(g[h	e(g[h	NOUN
ejpam-4350	284	66	]	]	PUNCT
ejpam-4350	284	67	)	)	PUNCT
ejpam-4350	284	68	if	if	SCONJ
ejpam-4350	284	69	and	and	CCONJ
ejpam-4350	284	70	only	only	ADV
ejpam-4350	284	71	if	if	SCONJ
ejpam-4350	284	72	either	either	CCONJ
ejpam-4350	284	73	a	a	DET
ejpam-4350	284	74	=	=	SYM
ejpam-4350	284	75	b	b	NOUN
ejpam-4350	284	76	and	and	CCONJ
ejpam-4350	284	77	uv	uv	PROPN
ejpam-4350	284	78	∈	∈	PROPN
ejpam-4350	284	79	e(g	e(g	PROPN
ejpam-4350	284	80	)	)	PUNCT
ejpam-4350	284	81	or	or	CCONJ
ejpam-4350	284	82	u	u	X
ejpam-4350	284	83	=	=	PROPN
ejpam-4350	284	84	v	v	PROPN
ejpam-4350	284	85	and	and	CCONJ
ejpam-4350	284	86	ab	ab	PROPN
ejpam-4350	284	87	∈	∈	PROPN
ejpam-4350	284	88	e(h	e(h	PROPN
ejpam-4350	284	89	)	)	PUNCT
ejpam-4350	284	90	.	.	PUNCT
ejpam-4350	285	1	theorem	theorem	VERB
ejpam-4350	285	2	7	7	NUM
ejpam-4350	285	3	.	.	PUNCT
ejpam-4350	286	1	let	let	VERB
ejpam-4350	286	2	g	g	NOUN
ejpam-4350	286	3	and	and	CCONJ
ejpam-4350	286	4	h	h	PROPN
ejpam-4350	286	5	be	be	VERB
ejpam-4350	286	6	non	non	ADJ
ejpam-4350	286	7	-	-	ADJ
ejpam-4350	286	8	trivial	trivial	ADJ
ejpam-4350	286	9	connected	connected	ADJ
ejpam-4350	286	10	graphs	graph	NOUN
ejpam-4350	286	11	.	.	PUNCT
ejpam-4350	287	1	then	then	ADV
ejpam-4350	287	2	c	c	NOUN
ejpam-4350	287	3	=	=	PUNCT
ejpam-4350	287	4	⋃	⋃	PROPN
ejpam-4350	287	5	x∈s	x∈s	NOUN
ejpam-4350	288	1	[	[	X
ejpam-4350	288	2	{	{	PUNCT
ejpam-4350	288	3	x	x	NOUN
ejpam-4350	288	4	}	}	PUNCT
ejpam-4350	288	5	×	×	PROPN
ejpam-4350	288	6	tx	tx	PROPN
ejpam-4350	288	7	]	]	X
ejpam-4350	288	8	,	,	PUNCT
ejpam-4350	288	9	where	where	SCONJ
ejpam-4350	288	10	s	s	VERB
ejpam-4350	288	11	⊆	⊆	NUM
ejpam-4350	288	12	v	v	NOUN
ejpam-4350	288	13	(	(	PUNCT
ejpam-4350	288	14	g	g	NOUN
ejpam-4350	288	15	)	)	PUNCT
ejpam-4350	288	16	and	and	CCONJ
ejpam-4350	288	17	tx	tx	VERB
ejpam-4350	288	18	⊆	⊆	NUM
ejpam-4350	288	19	v	v	NOUN
ejpam-4350	288	20	(	(	PUNCT
ejpam-4350	288	21	h	h	NOUN
ejpam-4350	288	22	)	)	PUNCT
ejpam-4350	288	23	for	for	ADP
ejpam-4350	288	24	each	each	DET
ejpam-4350	288	25	x	x	SYM
ejpam-4350	288	26	∈	∈	PROPN
ejpam-4350	288	27	s	s	NOUN
ejpam-4350	288	28	,	,	PUNCT
ejpam-4350	288	29	is	be	AUX
ejpam-4350	288	30	a	a	DET
ejpam-4350	288	31	hop	hop	NOUN
ejpam-4350	288	32	independent	independent	ADJ
ejpam-4350	288	33	set	set	NOUN
ejpam-4350	288	34	of	of	ADP
ejpam-4350	288	35	g	g	PROPN
ejpam-4350	288	36	�	�	PROPN
ejpam-4350	288	37	h	h	NOUN
ejpam-4350	288	38	if	if	SCONJ
ejpam-4350	288	39	and	and	CCONJ
ejpam-4350	288	40	only	only	ADV
ejpam-4350	288	41	if	if	SCONJ
ejpam-4350	288	42	the	the	DET
ejpam-4350	288	43	following	follow	VERB
ejpam-4350	288	44	conditions	condition	NOUN
ejpam-4350	288	45	hold	hold	VERB
ejpam-4350	288	46	.	.	PUNCT
ejpam-4350	289	1	(	(	PUNCT
ejpam-4350	289	2	i	i	NOUN
ejpam-4350	289	3	)	)	PUNCT
ejpam-4350	289	4	tx	tx	PROPN
ejpam-4350	289	5	is	be	AUX
ejpam-4350	289	6	a	a	DET
ejpam-4350	289	7	hop	hop	NOUN
ejpam-4350	289	8	independent	independent	ADJ
ejpam-4350	289	9	set	set	NOUN
ejpam-4350	289	10	of	of	ADP
ejpam-4350	289	11	h	h	NOUN
ejpam-4350	289	12	for	for	ADP
ejpam-4350	289	13	each	each	DET
ejpam-4350	289	14	x	x	SYM
ejpam-4350	289	15	∈	∈	PROPN
ejpam-4350	289	16	s	s	PART
ejpam-4350	289	17	;	;	PUNCT
ejpam-4350	289	18	(	(	PUNCT
ejpam-4350	289	19	ii	ii	NOUN
ejpam-4350	289	20	)	)	PUNCT
ejpam-4350	289	21	for	for	ADP
ejpam-4350	289	22	each	each	DET
ejpam-4350	289	23	x	x	SYM
ejpam-4350	289	24	∈	∈	PROPN
ejpam-4350	289	25	s	s	NOUN
ejpam-4350	289	26	∩ng(s	∩ng(s	NOUN
ejpam-4350	289	27	)	)	PUNCT
ejpam-4350	289	28	and	and	CCONJ
ejpam-4350	289	29	for	for	ADP
ejpam-4350	289	30	each	each	DET
ejpam-4350	289	31	y	y	PROPN
ejpam-4350	289	32	∈	∈	PROPN
ejpam-4350	289	33	s	s	PART
ejpam-4350	289	34	∩ng(x	∩ng(x	NOUN
ejpam-4350	289	35	)	)	PUNCT
ejpam-4350	289	36	,	,	PUNCT
ejpam-4350	289	37	it	it	PRON
ejpam-4350	289	38	holds	hold	VERB
ejpam-4350	289	39	that	that	SCONJ
ejpam-4350	289	40	dh(p	dh(p	NOUN
ejpam-4350	289	41	,	,	PUNCT
ejpam-4350	289	42	q	q	NOUN
ejpam-4350	289	43	)	)	PUNCT
ejpam-4350	289	44	6=	6=	ADP
ejpam-4350	289	45	1	1	NUM
ejpam-4350	289	46	for	for	ADP
ejpam-4350	289	47	all	all	DET
ejpam-4350	289	48	p	p	PROPN
ejpam-4350	289	49	∈	∈	PROPN
ejpam-4350	289	50	tx	tx	NOUN
ejpam-4350	289	51	and	and	CCONJ
ejpam-4350	289	52	q	q	ADJ
ejpam-4350	289	53	∈	∈	PROPN
ejpam-4350	289	54	ty	ty	NUM
ejpam-4350	289	55	;	;	PUNCT
ejpam-4350	289	56	and	and	CCONJ
ejpam-4350	289	57	(	(	PUNCT
ejpam-4350	289	58	iii	iii	NOUN
ejpam-4350	289	59	)	)	PUNCT
ejpam-4350	289	60	for	for	ADP
ejpam-4350	289	61	each	each	DET
ejpam-4350	289	62	v	v	NOUN
ejpam-4350	289	63	∈	∈	NOUN
ejpam-4350	289	64	s	s	PART
ejpam-4350	289	65	∩n2	∩n2	NOUN
ejpam-4350	289	66	g(s	g(s	PROPN
ejpam-4350	289	67	)	)	PUNCT
ejpam-4350	289	68	and	and	CCONJ
ejpam-4350	289	69	for	for	ADP
ejpam-4350	289	70	each	each	DET
ejpam-4350	289	71	w	w	PROPN
ejpam-4350	289	72	∈	∈	PROPN
ejpam-4350	289	73	s	s	PART
ejpam-4350	289	74	∩n2	∩n2	NOUN
ejpam-4350	289	75	g(v	g(v	PROPN
ejpam-4350	289	76	)	)	PUNCT
ejpam-4350	289	77	,	,	PUNCT
ejpam-4350	289	78	it	it	PRON
ejpam-4350	289	79	holds	hold	VERB
ejpam-4350	289	80	that	that	DET
ejpam-4350	289	81	dh(a	dh(a	ADJ
ejpam-4350	289	82	,	,	PUNCT
ejpam-4350	289	83	b	b	NOUN
ejpam-4350	289	84	)	)	PUNCT
ejpam-4350	289	85	≥	≥	NOUN
ejpam-4350	289	86	1	1	NUM
ejpam-4350	289	87	for	for	ADP
ejpam-4350	289	88	all	all	DET
ejpam-4350	289	89	a	a	DET
ejpam-4350	289	90	∈	∈	NOUN
ejpam-4350	289	91	tv	tv	NOUN
ejpam-4350	289	92	and	and	CCONJ
ejpam-4350	289	93	b	b	PROPN
ejpam-4350	289	94	∈	∈	PROPN
ejpam-4350	289	95	tw	tw	NOUN
ejpam-4350	289	96	.	.	PUNCT
ejpam-4350	290	1	proof	proof	NOUN
ejpam-4350	290	2	.	.	PUNCT
ejpam-4350	291	1	suppose	suppose	VERB
ejpam-4350	291	2	c	c	NOUN
ejpam-4350	291	3	=	=	PUNCT
ejpam-4350	291	4	⋃	⋃	PROPN
ejpam-4350	291	5	x∈s	x∈s	NOUN
ejpam-4350	292	1	[	[	X
ejpam-4350	292	2	{	{	PUNCT
ejpam-4350	292	3	x	x	NOUN
ejpam-4350	292	4	}	}	PUNCT
ejpam-4350	292	5	×	×	PROPN
ejpam-4350	292	6	tx	tx	PROPN
ejpam-4350	292	7	]	]	PUNCT
ejpam-4350	292	8	is	be	AUX
ejpam-4350	292	9	a	a	DET
ejpam-4350	292	10	hop	hop	NOUN
ejpam-4350	292	11	independent	independent	ADJ
ejpam-4350	292	12	set	set	NOUN
ejpam-4350	292	13	of	of	ADP
ejpam-4350	292	14	g	g	PROPN
ejpam-4350	292	15	�	�	PROPN
ejpam-4350	292	16	h.	h.	PROPN
ejpam-4350	292	17	let	let	VERB
ejpam-4350	292	18	x	x	PUNCT
ejpam-4350	292	19	∈	∈	NOUN
ejpam-4350	292	20	s	s	PART
ejpam-4350	292	21	and	and	CCONJ
ejpam-4350	292	22	let	let	VERB
ejpam-4350	292	23	a	a	DET
ejpam-4350	292	24	,	,	PUNCT
ejpam-4350	292	25	b	b	X
ejpam-4350	292	26	∈	∈	PROPN
ejpam-4350	292	27	tx	tx	PROPN
ejpam-4350	292	28	with	with	ADP
ejpam-4350	292	29	a	a	DET
ejpam-4350	292	30	6=	6=	ADP
ejpam-4350	292	31	b.	b.	PROPN
ejpam-4350	292	32	since	since	SCONJ
ejpam-4350	292	33	(	(	PUNCT
ejpam-4350	292	34	x	x	X
ejpam-4350	292	35	,	,	PUNCT
ejpam-4350	292	36	a	a	PRON
ejpam-4350	292	37	)	)	PUNCT
ejpam-4350	292	38	and	and	CCONJ
ejpam-4350	292	39	(	(	PUNCT
ejpam-4350	292	40	x	x	NOUN
ejpam-4350	292	41	,	,	PUNCT
ejpam-4350	292	42	b	b	NOUN
ejpam-4350	292	43	)	)	PUNCT
ejpam-4350	292	44	are	be	AUX
ejpam-4350	292	45	distinct	distinct	ADJ
ejpam-4350	292	46	elements	element	NOUN
ejpam-4350	292	47	of	of	ADP
ejpam-4350	292	48	c	c	PROPN
ejpam-4350	292	49	and	and	CCONJ
ejpam-4350	292	50	c	c	PROPN
ejpam-4350	292	51	is	be	AUX
ejpam-4350	292	52	a	a	DET
ejpam-4350	292	53	hop	hop	NOUN
ejpam-4350	292	54	independent	independent	ADJ
ejpam-4350	292	55	set	set	NOUN
ejpam-4350	292	56	of	of	ADP
ejpam-4350	292	57	g	g	PROPN
ejpam-4350	292	58	�	�	PROPN
ejpam-4350	292	59	h	h	PROPN
ejpam-4350	292	60	,	,	PUNCT
ejpam-4350	292	61	dh(a	dh(a	ADJ
ejpam-4350	292	62	,	,	PUNCT
ejpam-4350	292	63	b	b	NOUN
ejpam-4350	292	64	)	)	PUNCT
ejpam-4350	292	65	=	=	SYM
ejpam-4350	292	66	dg	dg	PROPN
ejpam-4350	292	67	�	�	PROPN
ejpam-4350	292	68	h((x	h((x	NOUN
ejpam-4350	292	69	,	,	PUNCT
ejpam-4350	292	70	a	a	PRON
ejpam-4350	292	71	)	)	PUNCT
ejpam-4350	292	72	,	,	PUNCT
ejpam-4350	292	73	(	(	PUNCT
ejpam-4350	292	74	x	x	NOUN
ejpam-4350	292	75	,	,	PUNCT
ejpam-4350	292	76	b	b	NOUN
ejpam-4350	292	77	)	)	PUNCT
ejpam-4350	292	78	)	)	PUNCT
ejpam-4350	293	1	6=	6=	ADP
ejpam-4350	293	2	2	2	NUM
ejpam-4350	293	3	,	,	PUNCT
ejpam-4350	293	4	showing	show	VERB
ejpam-4350	293	5	that	that	SCONJ
ejpam-4350	293	6	(	(	PUNCT
ejpam-4350	293	7	i	i	NOUN
ejpam-4350	293	8	)	)	PUNCT
ejpam-4350	293	9	holds	hold	VERB
ejpam-4350	293	10	,	,	PUNCT
ejpam-4350	293	11	i.e.	i.e.	X
ejpam-4350	293	12	,	,	PUNCT
ejpam-4350	293	13	tx	tx	PROPN
ejpam-4350	293	14	is	be	AUX
ejpam-4350	293	15	a	a	DET
ejpam-4350	293	16	hop	hop	NOUN
ejpam-4350	293	17	independent	independent	ADJ
ejpam-4350	293	18	set	set	NOUN
ejpam-4350	293	19	of	of	ADP
ejpam-4350	293	20	h.	h.	PROPN
ejpam-4350	293	21	next	next	ADV
ejpam-4350	293	22	,	,	PUNCT
ejpam-4350	293	23	let	let	VERB
ejpam-4350	293	24	x	x	X
ejpam-4350	293	25	∈	∈	PROPN
ejpam-4350	293	26	s∩ng(s	s∩ng(s	NOUN
ejpam-4350	293	27	)	)	PUNCT
ejpam-4350	293	28	and	and	CCONJ
ejpam-4350	293	29	let	let	VERB
ejpam-4350	293	30	y	y	PROPN
ejpam-4350	293	31	∈	∈	PROPN
ejpam-4350	293	32	s∩ng(x	s∩ng(x	PROPN
ejpam-4350	293	33	)	)	PUNCT
ejpam-4350	293	34	.	.	PUNCT
ejpam-4350	294	1	take	take	VERB
ejpam-4350	294	2	any	any	DET
ejpam-4350	294	3	p	p	PROPN
ejpam-4350	294	4	∈	∈	PROPN
ejpam-4350	294	5	tx	tx	NOUN
ejpam-4350	294	6	and	and	CCONJ
ejpam-4350	294	7	q	q	ADJ
ejpam-4350	294	8	∈	∈	PROPN
ejpam-4350	294	9	ty	ty	X
ejpam-4350	294	10	.	.	PUNCT
ejpam-4350	294	11	suppose	suppose	VERB
ejpam-4350	295	1	dh(p	dh(p	NOUN
ejpam-4350	295	2	,	,	PUNCT
ejpam-4350	295	3	q	q	X
ejpam-4350	295	4	)	)	PUNCT
ejpam-4350	295	5	=	=	SYM
ejpam-4350	295	6	1	1	X
ejpam-4350	295	7	.	.	PUNCT
ejpam-4350	295	8	clearly	clearly	ADV
ejpam-4350	295	9	,	,	PUNCT
ejpam-4350	295	10	(	(	PUNCT
ejpam-4350	295	11	x	x	X
ejpam-4350	295	12	,	,	PUNCT
ejpam-4350	295	13	p	p	NOUN
ejpam-4350	295	14	)	)	PUNCT
ejpam-4350	295	15	and	and	CCONJ
ejpam-4350	295	16	(	(	PUNCT
ejpam-4350	295	17	y	y	PROPN
ejpam-4350	295	18	,	,	PUNCT
ejpam-4350	295	19	q	q	NOUN
ejpam-4350	295	20	)	)	PUNCT
ejpam-4350	295	21	are	be	AUX
ejpam-4350	295	22	distinct	distinct	ADJ
ejpam-4350	295	23	elements	element	NOUN
ejpam-4350	295	24	of	of	ADP
ejpam-4350	295	25	c	c	PROPN
ejpam-4350	295	26	and	and	CCONJ
ejpam-4350	295	27	since	since	SCONJ
ejpam-4350	295	28	p	p	PROPN
ejpam-4350	295	29	6=	6=	PROPN
ejpam-4350	295	30	q	q	PROPN
ejpam-4350	295	31	,	,	PUNCT
ejpam-4350	295	32	dg	dg	PROPN
ejpam-4350	295	33	�	�	PROPN
ejpam-4350	295	34	h((x	h((x	NOUN
ejpam-4350	295	35	,	,	PUNCT
ejpam-4350	295	36	p	p	NOUN
ejpam-4350	295	37	)	)	PUNCT
ejpam-4350	295	38	,	,	PUNCT
ejpam-4350	295	39	(	(	PUNCT
ejpam-4350	295	40	y	y	NOUN
ejpam-4350	295	41	,	,	PUNCT
ejpam-4350	295	42	q	q	NOUN
ejpam-4350	295	43	)	)	PUNCT
ejpam-4350	295	44	)	)	PUNCT
ejpam-4350	296	1	6=	6=	ADP
ejpam-4350	296	2	1	1	X
ejpam-4350	296	3	.	.	PUNCT
ejpam-4350	297	1	since	since	SCONJ
ejpam-4350	297	2	[	[	X
ejpam-4350	297	3	(	(	PUNCT
ejpam-4350	297	4	x	x	X
ejpam-4350	297	5	,	,	PUNCT
ejpam-4350	297	6	p	p	NOUN
ejpam-4350	297	7	)	)	PUNCT
ejpam-4350	297	8	,	,	PUNCT
ejpam-4350	297	9	(	(	PUNCT
ejpam-4350	297	10	x	x	X
ejpam-4350	297	11	,	,	PUNCT
ejpam-4350	297	12	q	q	NOUN
ejpam-4350	297	13	)	)	PUNCT
ejpam-4350	297	14	,	,	PUNCT
ejpam-4350	297	15	(	(	PUNCT
ejpam-4350	297	16	y	y	NOUN
ejpam-4350	297	17	,	,	PUNCT
ejpam-4350	297	18	q	q	NOUN
ejpam-4350	297	19	)	)	PUNCT
ejpam-4350	297	20	]	]	PUNCT
ejpam-4350	297	21	is	be	AUX
ejpam-4350	297	22	an	an	DET
ejpam-4350	297	23	(	(	PUNCT
ejpam-4350	297	24	x	x	NOUN
ejpam-4350	297	25	,	,	PUNCT
ejpam-4350	297	26	p)-(y	p)-(y	ADJ
ejpam-4350	297	27	,	,	PUNCT
ejpam-4350	297	28	q	q	ADJ
ejpam-4350	297	29	)	)	PUNCT
ejpam-4350	297	30	geodetic	geodetic	ADJ
ejpam-4350	297	31	in	in	ADP
ejpam-4350	297	32	g	g	PROPN
ejpam-4350	297	33	�	�	PROPN
ejpam-4350	297	34	h	h	PROPN
ejpam-4350	297	35	,	,	PUNCT
ejpam-4350	297	36	dg	dg	PROPN
ejpam-4350	297	37	�	�	PROPN
ejpam-4350	297	38	h((x	h((x	NOUN
ejpam-4350	297	39	,	,	PUNCT
ejpam-4350	297	40	p	p	NOUN
ejpam-4350	297	41	)	)	PUNCT
ejpam-4350	297	42	,	,	PUNCT
ejpam-4350	297	43	(	(	PUNCT
ejpam-4350	297	44	y	y	NOUN
ejpam-4350	297	45	,	,	PUNCT
ejpam-4350	297	46	q	q	NOUN
ejpam-4350	297	47	)	)	PUNCT
ejpam-4350	297	48	)	)	PUNCT
ejpam-4350	298	1	=	=	SYM
ejpam-4350	298	2	2	2	NUM
ejpam-4350	298	3	,	,	PUNCT
ejpam-4350	298	4	contrary	contrary	ADV
ejpam-4350	298	5	to	to	ADP
ejpam-4350	298	6	the	the	DET
ejpam-4350	298	7	fact	fact	NOUN
ejpam-4350	298	8	that	that	SCONJ
ejpam-4350	298	9	c	c	PROPN
ejpam-4350	298	10	is	be	AUX
ejpam-4350	298	11	a	a	DET
ejpam-4350	298	12	hop	hop	NOUN
ejpam-4350	298	13	independent	independent	ADJ
ejpam-4350	298	14	set	set	NOUN
ejpam-4350	298	15	of	of	ADP
ejpam-4350	298	16	g	g	PROPN
ejpam-4350	298	17	�	�	PROPN
ejpam-4350	298	18	h.	h.	PROPN
ejpam-4350	298	19	thus	thus	ADV
ejpam-4350	298	20	,	,	PUNCT
ejpam-4350	298	21	dh(p	dh(p	NOUN
ejpam-4350	298	22	,	,	PUNCT
ejpam-4350	298	23	q	q	NOUN
ejpam-4350	298	24	)	)	PUNCT
ejpam-4350	298	25	6=	6=	ADP
ejpam-4350	298	26	1	1	NUM
ejpam-4350	298	27	,	,	PUNCT
ejpam-4350	298	28	showing	show	VERB
ejpam-4350	298	29	that	that	SCONJ
ejpam-4350	298	30	(	(	PUNCT
ejpam-4350	298	31	ii	ii	NOUN
ejpam-4350	298	32	)	)	PUNCT
ejpam-4350	298	33	holds	hold	VERB
ejpam-4350	298	34	.	.	PUNCT
ejpam-4350	299	1	finally	finally	ADV
ejpam-4350	299	2	,	,	PUNCT
ejpam-4350	299	3	let	let	VERB
ejpam-4350	299	4	v	v	NUM
ejpam-4350	299	5	∈	∈	NOUN
ejpam-4350	299	6	s	s	PART
ejpam-4350	299	7	∩n2	∩n2	NOUN
ejpam-4350	299	8	g(s	g(s	PROPN
ejpam-4350	299	9	)	)	PUNCT
ejpam-4350	299	10	and	and	CCONJ
ejpam-4350	299	11	let	let	VERB
ejpam-4350	299	12	w	w	PRON
ejpam-4350	299	13	∈	∈	NOUN
ejpam-4350	299	14	s	s	PART
ejpam-4350	299	15	∩n2	∩n2	NOUN
ejpam-4350	299	16	g(v	g(v	PROPN
ejpam-4350	299	17	)	)	PUNCT
ejpam-4350	299	18	.	.	PUNCT
ejpam-4350	300	1	choose	choose	VERB
ejpam-4350	300	2	any	any	DET
ejpam-4350	300	3	a	a	DET
ejpam-4350	300	4	∈	∈	NOUN
ejpam-4350	300	5	tv	tv	NOUN
ejpam-4350	300	6	and	and	CCONJ
ejpam-4350	300	7	b	b	X
ejpam-4350	300	8	∈	∈	PROPN
ejpam-4350	300	9	tw	tw	PROPN
ejpam-4350	300	10	.	.	PUNCT
ejpam-4350	301	1	then	then	ADV
ejpam-4350	301	2	(	(	PUNCT
ejpam-4350	301	3	v	v	NOUN
ejpam-4350	301	4	,	,	PUNCT
ejpam-4350	301	5	a	a	PRON
ejpam-4350	301	6	)	)	PUNCT
ejpam-4350	301	7	,	,	PUNCT
ejpam-4350	301	8	(	(	PUNCT
ejpam-4350	301	9	w	w	PROPN
ejpam-4350	301	10	,	,	PUNCT
ejpam-4350	301	11	b	b	NOUN
ejpam-4350	301	12	)	)	PUNCT
ejpam-4350	301	13	∈	∈	PROPN
ejpam-4350	301	14	c.	c.	NOUN
ejpam-4350	301	15	again	again	ADV
ejpam-4350	301	16	,	,	PUNCT
ejpam-4350	301	17	since	since	SCONJ
ejpam-4350	301	18	c	c	PROPN
ejpam-4350	301	19	is	be	AUX
ejpam-4350	301	20	a	a	DET
ejpam-4350	301	21	hop	hop	NOUN
ejpam-4350	301	22	independent	independent	ADJ
ejpam-4350	301	23	set	set	NOUN
ejpam-4350	301	24	of	of	ADP
ejpam-4350	301	25	g	g	PROPN
ejpam-4350	301	26	�	�	PROPN
ejpam-4350	301	27	h	h	PROPN
ejpam-4350	301	28	,	,	PUNCT
ejpam-4350	301	29	dg	dg	PROPN
ejpam-4350	301	30	�	�	PROPN
ejpam-4350	301	31	h((v	h((v	NOUN
ejpam-4350	301	32	,	,	PUNCT
ejpam-4350	301	33	a	a	PRON
ejpam-4350	301	34	)	)	PUNCT
ejpam-4350	301	35	,	,	PUNCT
ejpam-4350	301	36	(	(	PUNCT
ejpam-4350	301	37	w	w	PROPN
ejpam-4350	301	38	,	,	PUNCT
ejpam-4350	301	39	b	b	NOUN
ejpam-4350	301	40	)	)	PUNCT
ejpam-4350	301	41	)	)	PUNCT
ejpam-4350	302	1	6=	6=	ADP
ejpam-4350	302	2	2	2	X
ejpam-4350	302	3	.	.	PUNCT
ejpam-4350	302	4	since	since	SCONJ
ejpam-4350	302	5	dg(v	dg(v	NOUN
ejpam-4350	302	6	,	,	PUNCT
ejpam-4350	302	7	w	w	NOUN
ejpam-4350	302	8	)	)	PUNCT
ejpam-4350	302	9	=	=	SYM
ejpam-4350	302	10	2	2	NUM
ejpam-4350	302	11	,	,	PUNCT
ejpam-4350	302	12	a	a	PRON
ejpam-4350	302	13	6=	6=	NUM
ejpam-4350	302	14	b.	b.	PROPN
ejpam-4350	302	15	thus	thus	ADV
ejpam-4350	302	16	,	,	PUNCT
ejpam-4350	302	17	dh(a	dh(a	ADJ
ejpam-4350	302	18	,	,	PUNCT
ejpam-4350	302	19	b	b	NOUN
ejpam-4350	302	20	)	)	PUNCT
ejpam-4350	302	21	≥	≥	NOUN
ejpam-4350	302	22	1	1	NUM
ejpam-4350	302	23	,	,	PUNCT
ejpam-4350	302	24	showing	show	VERB
ejpam-4350	302	25	that	that	SCONJ
ejpam-4350	302	26	(	(	PUNCT
ejpam-4350	302	27	iii	iii	NOUN
ejpam-4350	302	28	)	)	PUNCT
ejpam-4350	302	29	holds	hold	VERB
ejpam-4350	302	30	.	.	PUNCT
ejpam-4350	303	1	for	for	ADP
ejpam-4350	303	2	the	the	DET
ejpam-4350	303	3	converse	converse	NOUN
ejpam-4350	303	4	,	,	PUNCT
ejpam-4350	303	5	suppose	suppose	VERB
ejpam-4350	303	6	that	that	SCONJ
ejpam-4350	303	7	c	c	PROPN
ejpam-4350	303	8	satisfies	satisfy	VERB
ejpam-4350	303	9	conditions	condition	NOUN
ejpam-4350	303	10	(	(	PUNCT
ejpam-4350	303	11	i	i	NOUN
ejpam-4350	303	12	)	)	PUNCT
ejpam-4350	303	13	,	,	PUNCT
ejpam-4350	303	14	(	(	PUNCT
ejpam-4350	303	15	ii	ii	NOUN
ejpam-4350	303	16	)	)	PUNCT
ejpam-4350	303	17	,	,	PUNCT
ejpam-4350	303	18	and	and	CCONJ
ejpam-4350	303	19	(	(	PUNCT
ejpam-4350	303	20	iii	iii	NOUN
ejpam-4350	303	21	)	)	PUNCT
ejpam-4350	303	22	.	.	PUNCT
ejpam-4350	304	1	let	let	VERB
ejpam-4350	304	2	(	(	PUNCT
ejpam-4350	304	3	x	x	X
ejpam-4350	304	4	,	,	PUNCT
ejpam-4350	304	5	p	p	NOUN
ejpam-4350	304	6	)	)	PUNCT
ejpam-4350	304	7	,	,	PUNCT
ejpam-4350	304	8	(	(	PUNCT
ejpam-4350	304	9	y	y	NOUN
ejpam-4350	304	10	,	,	PUNCT
ejpam-4350	304	11	q	q	X
ejpam-4350	304	12	)	)	PUNCT
ejpam-4350	304	13	∈	∈	PROPN
ejpam-4350	304	14	c	c	NOUN
ejpam-4350	304	15	such	such	ADJ
ejpam-4350	304	16	that	that	PRON
ejpam-4350	304	17	(	(	PUNCT
ejpam-4350	304	18	x	x	NOUN
ejpam-4350	304	19	,	,	PUNCT
ejpam-4350	304	20	p	p	NOUN
ejpam-4350	304	21	)	)	PUNCT
ejpam-4350	304	22	6=	6=	ADP
ejpam-4350	305	1	(	(	PUNCT
ejpam-4350	305	2	y	y	NOUN
ejpam-4350	305	3	,	,	PUNCT
ejpam-4350	305	4	q	q	NOUN
ejpam-4350	305	5	)	)	PUNCT
ejpam-4350	305	6	.	.	PUNCT
ejpam-4350	306	1	consider	consider	VERB
ejpam-4350	306	2	the	the	DET
ejpam-4350	306	3	following	follow	VERB
ejpam-4350	306	4	cases	case	NOUN
ejpam-4350	306	5	:	:	PUNCT
ejpam-4350	306	6	case	case	NOUN
ejpam-4350	306	7	1	1	NUM
ejpam-4350	306	8	.	.	PUNCT
ejpam-4350	306	9	x	x	X
ejpam-4350	307	1	=	=	PUNCT
ejpam-4350	307	2	y.	y.	NOUN
ejpam-4350	307	3	then	then	ADV
ejpam-4350	307	4	p	p	PROPN
ejpam-4350	307	5	6=	6=	PROPN
ejpam-4350	307	6	q	q	PROPN
ejpam-4350	308	1	and	and	CCONJ
ejpam-4350	308	2	p	p	X
ejpam-4350	308	3	,	,	PUNCT
ejpam-4350	308	4	q	q	PROPN
ejpam-4350	308	5	∈	∈	PROPN
ejpam-4350	308	6	tx	tx	PROPN
ejpam-4350	308	7	.	.	PUNCT
ejpam-4350	309	1	from	from	ADP
ejpam-4350	309	2	condition	condition	NOUN
ejpam-4350	309	3	(	(	PUNCT
ejpam-4350	309	4	i	i	NOUN
ejpam-4350	309	5	)	)	PUNCT
ejpam-4350	309	6	,	,	PUNCT
ejpam-4350	309	7	it	it	PRON
ejpam-4350	309	8	follows	follow	VERB
ejpam-4350	309	9	that	that	SCONJ
ejpam-4350	309	10	dg	dg	PROPN
ejpam-4350	309	11	�	�	PROPN
ejpam-4350	309	12	h((x	h((x	NOUN
ejpam-4350	309	13	,	,	PUNCT
ejpam-4350	309	14	p	p	NOUN
ejpam-4350	309	15	)	)	PUNCT
ejpam-4350	309	16	,	,	PUNCT
ejpam-4350	309	17	(	(	PUNCT
ejpam-4350	309	18	y	y	NOUN
ejpam-4350	309	19	,	,	PUNCT
ejpam-4350	309	20	q	q	NOUN
ejpam-4350	309	21	)	)	PUNCT
ejpam-4350	309	22	)	)	PUNCT
ejpam-4350	309	23	=	=	SYM
ejpam-4350	310	1	dh(p	dh(p	X
ejpam-4350	310	2	,	,	PUNCT
ejpam-4350	310	3	q	q	NOUN
ejpam-4350	310	4	)	)	PUNCT
ejpam-4350	310	5	6=	6=	ADP
ejpam-4350	310	6	2	2	NUM
ejpam-4350	310	7	.	.	X
ejpam-4350	310	8	case	case	NOUN
ejpam-4350	310	9	2	2	NUM
ejpam-4350	310	10	.	.	NUM
ejpam-4350	310	11	x	x	SYM
ejpam-4350	311	1	6=	6=	X
ejpam-4350	311	2	y.	y.	NOUN
ejpam-4350	311	3	clearly	clearly	ADV
ejpam-4350	311	4	,	,	PUNCT
ejpam-4350	311	5	if	if	SCONJ
ejpam-4350	311	6	dg(x	dg(x	NUM
ejpam-4350	311	7	,	,	PUNCT
ejpam-4350	311	8	y	y	PROPN
ejpam-4350	311	9	)	)	PUNCT
ejpam-4350	311	10	≥	≥	NOUN
ejpam-4350	311	11	3	3	NUM
ejpam-4350	311	12	,	,	PUNCT
ejpam-4350	311	13	then	then	ADV
ejpam-4350	311	14	dg	dg	PROPN
ejpam-4350	311	15	�	�	PROPN
ejpam-4350	311	16	h((x	h((x	NOUN
ejpam-4350	311	17	,	,	PUNCT
ejpam-4350	311	18	p	p	NOUN
ejpam-4350	311	19	)	)	PUNCT
ejpam-4350	311	20	,	,	PUNCT
ejpam-4350	311	21	(	(	PUNCT
ejpam-4350	311	22	y	y	NOUN
ejpam-4350	311	23	,	,	PUNCT
ejpam-4350	311	24	q	q	NOUN
ejpam-4350	311	25	)	)	PUNCT
ejpam-4350	311	26	)	)	PUNCT
ejpam-4350	312	1	6=	6=	ADP
ejpam-4350	313	1	2	2	X
ejpam-4350	313	2	.	.	PUNCT
ejpam-4350	313	3	next	next	ADV
ejpam-4350	313	4	,	,	PUNCT
ejpam-4350	313	5	suppose	suppose	VERB
ejpam-4350	313	6	that	that	SCONJ
ejpam-4350	313	7	dg(x	dg(x	PROPN
ejpam-4350	313	8	,	,	PUNCT
ejpam-4350	313	9	y	y	NOUN
ejpam-4350	313	10	)	)	PUNCT
ejpam-4350	313	11	=	=	SYM
ejpam-4350	314	1	1	1	X
ejpam-4350	314	2	.	.	PUNCT
ejpam-4350	314	3	then	then	ADV
ejpam-4350	314	4	by	by	ADP
ejpam-4350	314	5	condition	condition	NOUN
ejpam-4350	314	6	(	(	PUNCT
ejpam-4350	314	7	ii	ii	NOUN
ejpam-4350	314	8	)	)	PUNCT
ejpam-4350	314	9	,	,	PUNCT
ejpam-4350	314	10	dh(p	dh(p	PROPN
ejpam-4350	314	11	,	,	PUNCT
ejpam-4350	314	12	q	q	NOUN
ejpam-4350	314	13	)	)	PUNCT
ejpam-4350	314	14	6=	6=	ADP
ejpam-4350	314	15	1	1	X
ejpam-4350	314	16	.	.	PUNCT
ejpam-4350	315	1	if	if	SCONJ
ejpam-4350	315	2	dh(p	dh(p	NOUN
ejpam-4350	315	3	,	,	PUNCT
ejpam-4350	315	4	q	q	X
ejpam-4350	315	5	)	)	PUNCT
ejpam-4350	315	6	=	=	SYM
ejpam-4350	315	7	0	0	NUM
ejpam-4350	315	8	,	,	PUNCT
ejpam-4350	315	9	then	then	ADV
ejpam-4350	315	10	dg	dg	PROPN
ejpam-4350	315	11	�	�	PROPN
ejpam-4350	315	12	h((x	h((x	NOUN
ejpam-4350	315	13	,	,	PUNCT
ejpam-4350	315	14	p	p	NOUN
ejpam-4350	315	15	)	)	PUNCT
ejpam-4350	315	16	,	,	PUNCT
ejpam-4350	315	17	(	(	PUNCT
ejpam-4350	315	18	y	y	NOUN
ejpam-4350	315	19	,	,	PUNCT
ejpam-4350	315	20	q	q	NOUN
ejpam-4350	315	21	)	)	PUNCT
ejpam-4350	315	22	)	)	PUNCT
ejpam-4350	316	1	=	=	SYM
ejpam-4350	316	2	1	1	NUM
ejpam-4350	316	3	6=	6=	NUM
ejpam-4350	316	4	2	2	NUM
ejpam-4350	316	5	.	.	PUNCT
ejpam-4350	317	1	if	if	SCONJ
ejpam-4350	317	2	dh(p	dh(p	NOUN
ejpam-4350	317	3	,	,	PUNCT
ejpam-4350	317	4	q	q	X
ejpam-4350	317	5	)	)	PUNCT
ejpam-4350	317	6	≥	≥	NOUN
ejpam-4350	317	7	2	2	NUM
ejpam-4350	317	8	,	,	PUNCT
ejpam-4350	317	9	then	then	ADV
ejpam-4350	317	10	dg	dg	PROPN
ejpam-4350	317	11	�	�	PROPN
ejpam-4350	317	12	h((x	h((x	NOUN
ejpam-4350	317	13	,	,	PUNCT
ejpam-4350	317	14	p	p	NOUN
ejpam-4350	317	15	)	)	PUNCT
ejpam-4350	317	16	,	,	PUNCT
ejpam-4350	317	17	(	(	PUNCT
ejpam-4350	317	18	y	y	NOUN
ejpam-4350	317	19	,	,	PUNCT
ejpam-4350	317	20	q	q	NOUN
ejpam-4350	317	21	)	)	PUNCT
ejpam-4350	317	22	)	)	PUNCT
ejpam-4350	318	1	=	=	PUNCT
ejpam-4350	318	2	1	1	NUM
ejpam-4350	318	3	+	+	NUM
ejpam-4350	318	4	dh(p	dh(p	NOUN
ejpam-4350	318	5	,	,	PUNCT
ejpam-4350	318	6	q	q	NOUN
ejpam-4350	318	7	)	)	PUNCT
ejpam-4350	318	8	≥	≥	NOUN
ejpam-4350	318	9	3	3	NUM
ejpam-4350	318	10	.	.	PUNCT
ejpam-4350	318	11	suppose	suppose	VERB
ejpam-4350	318	12	now	now	ADV
ejpam-4350	318	13	that	that	SCONJ
ejpam-4350	318	14	dg(x	dg(x	ADV
ejpam-4350	318	15	,	,	PUNCT
ejpam-4350	318	16	y	y	NOUN
ejpam-4350	318	17	)	)	PUNCT
ejpam-4350	318	18	=	=	SYM
ejpam-4350	319	1	2	2	X
ejpam-4350	319	2	.	.	PUNCT
ejpam-4350	319	3	then	then	ADV
ejpam-4350	319	4	by	by	ADP
ejpam-4350	319	5	(	(	PUNCT
ejpam-4350	319	6	iii	iii	NOUN
ejpam-4350	319	7	)	)	PUNCT
ejpam-4350	319	8	,	,	PUNCT
ejpam-4350	319	9	dh(p	dh(p	PROPN
ejpam-4350	319	10	,	,	PUNCT
ejpam-4350	319	11	q	q	X
ejpam-4350	319	12	)	)	PUNCT
ejpam-4350	319	13	≥	≥	NOUN
ejpam-4350	319	14	1	1	NUM
ejpam-4350	319	15	.	.	PUNCT
ejpam-4350	319	16	hence	hence	ADV
ejpam-4350	319	17	,	,	PUNCT
ejpam-4350	319	18	dg	dg	PROPN
ejpam-4350	319	19	�	�	PROPN
ejpam-4350	319	20	h((x	h((x	NOUN
ejpam-4350	319	21	,	,	PUNCT
ejpam-4350	319	22	p	p	NOUN
ejpam-4350	319	23	)	)	PUNCT
ejpam-4350	319	24	,	,	PUNCT
ejpam-4350	319	25	(	(	PUNCT
ejpam-4350	319	26	y	y	NOUN
ejpam-4350	319	27	,	,	PUNCT
ejpam-4350	319	28	q	q	NOUN
ejpam-4350	319	29	)	)	PUNCT
ejpam-4350	319	30	)	)	PUNCT
ejpam-4350	320	1	=	=	SYM
ejpam-4350	320	2	dg(x	dg(x	X
ejpam-4350	320	3	,	,	PUNCT
ejpam-4350	320	4	y	y	NOUN
ejpam-4350	320	5	)	)	PUNCT
ejpam-4350	320	6	+	+	NUM
ejpam-4350	320	7	dh(p	dh(p	NOUN
ejpam-4350	320	8	,	,	PUNCT
ejpam-4350	320	9	q	q	NOUN
ejpam-4350	320	10	)	)	PUNCT
ejpam-4350	320	11	≥	≥	NOUN
ejpam-4350	320	12	3	3	NUM
ejpam-4350	320	13	.	.	PUNCT
ejpam-4350	321	1	therefore	therefore	ADV
ejpam-4350	321	2	,	,	PUNCT
ejpam-4350	321	3	c	c	PROPN
ejpam-4350	321	4	is	be	AUX
ejpam-4350	321	5	a	a	DET
ejpam-4350	321	6	hop	hop	NOUN
ejpam-4350	321	7	independent	independent	ADJ
ejpam-4350	321	8	set	set	NOUN
ejpam-4350	321	9	of	of	ADP
ejpam-4350	321	10	g	g	PROPN
ejpam-4350	321	11	�	�	PROPN
ejpam-4350	321	12	h.	h.	PROPN
ejpam-4350	321	13	a	a	DET
ejpam-4350	321	14	set	set	NOUN
ejpam-4350	321	15	s	s	VERB
ejpam-4350	321	16	is	be	AUX
ejpam-4350	321	17	a	a	DET
ejpam-4350	321	18	3	3	NUM
ejpam-4350	321	19	-	-	PUNCT
ejpam-4350	321	20	hop	hop	NOUN
ejpam-4350	321	21	set	set	NOUN
ejpam-4350	321	22	of	of	ADP
ejpam-4350	321	23	a	a	DET
ejpam-4350	321	24	connected	connected	ADJ
ejpam-4350	321	25	graph	graph	NOUN
ejpam-4350	321	26	g	g	NOUN
ejpam-4350	321	27	if	if	SCONJ
ejpam-4350	321	28	dg(v	dg(v	NOUN
ejpam-4350	321	29	,	,	PUNCT
ejpam-4350	321	30	w	w	NOUN
ejpam-4350	321	31	)	)	PUNCT
ejpam-4350	321	32	=	=	SYM
ejpam-4350	321	33	3	3	NUM
ejpam-4350	321	34	for	for	ADP
ejpam-4350	321	35	every	every	DET
ejpam-4350	321	36	pair	pair	NOUN
ejpam-4350	321	37	of	of	ADP
ejpam-4350	321	38	distinct	distinct	ADJ
ejpam-4350	321	39	vertices	vertex	NOUN
ejpam-4350	321	40	v	v	ADP
ejpam-4350	321	41	,	,	PUNCT
ejpam-4350	321	42	w	w	PROPN
ejpam-4350	321	43	∈	∈	PROPN
ejpam-4350	321	44	s.	s.	PROPN
ejpam-4350	321	45	the	the	DET
ejpam-4350	321	46	maximum	maximum	PROPN
ejpam-4350	321	47	cardinality	cardinality	NOUN
ejpam-4350	321	48	of	of	ADP
ejpam-4350	321	49	a	a	DET
ejpam-4350	321	50	3	3	NUM
ejpam-4350	321	51	-	-	PUNCT
ejpam-4350	321	52	hop	hop	NOUN
ejpam-4350	321	53	set	set	NOUN
ejpam-4350	321	54	of	of	ADP
ejpam-4350	321	55	g	g	PROPN
ejpam-4350	321	56	is	be	AUX
ejpam-4350	321	57	denoted	denote	VERB
ejpam-4350	321	58	by	by	ADP
ejpam-4350	321	59	α3	α3	ADJ
ejpam-4350	321	60	h(g	h(g	NOUN
ejpam-4350	321	61	)	)	PUNCT
ejpam-4350	321	62	.	.	PUNCT
ejpam-4350	322	1	references	reference	VERB
ejpam-4350	322	2	476	476	NUM
ejpam-4350	322	3	corollary	corollary	ADJ
ejpam-4350	322	4	5	5	NUM
ejpam-4350	322	5	.	.	PUNCT
ejpam-4350	323	1	let	let	VERB
ejpam-4350	323	2	g	g	NOUN
ejpam-4350	323	3	and	and	CCONJ
ejpam-4350	323	4	h	h	PROPN
ejpam-4350	323	5	be	be	VERB
ejpam-4350	323	6	non	non	ADJ
ejpam-4350	323	7	-	-	ADJ
ejpam-4350	323	8	trivial	trivial	ADJ
ejpam-4350	323	9	connected	connected	ADJ
ejpam-4350	323	10	graphs	graph	NOUN
ejpam-4350	323	11	.	.	PUNCT
ejpam-4350	324	1	then	then	ADV
ejpam-4350	324	2	αh(g	αh(g	NOUN
ejpam-4350	324	3	�	�	PROPN
ejpam-4350	324	4	h	h	NOUN
ejpam-4350	324	5	)	)	PUNCT
ejpam-4350	324	6	≥	≥	NOUN
ejpam-4350	324	7	max{α3	max{α3	ADJ
ejpam-4350	324	8	h(g)αh(h	h(g)αh(h	NOUN
ejpam-4350	324	9	)	)	PUNCT
ejpam-4350	324	10	,	,	PUNCT
ejpam-4350	324	11	α3	α3	NOUN
ejpam-4350	324	12	h(h)αh(g	h(h)αh(g	NOUN
ejpam-4350	324	13	)	)	PUNCT
ejpam-4350	324	14	}	}	PUNCT
ejpam-4350	324	15	.	.	PUNCT
ejpam-4350	325	1	proof	proof	NOUN
ejpam-4350	325	2	.	.	PUNCT
ejpam-4350	326	1	let	let	VERB
ejpam-4350	326	2	s	s	PRON
ejpam-4350	326	3	be	be	AUX
ejpam-4350	326	4	a	a	DET
ejpam-4350	326	5	3	3	NUM
ejpam-4350	326	6	-	-	PUNCT
ejpam-4350	326	7	hop	hop	NOUN
ejpam-4350	326	8	set	set	NOUN
ejpam-4350	326	9	of	of	ADP
ejpam-4350	326	10	g	g	NOUN
ejpam-4350	326	11	with	with	ADP
ejpam-4350	326	12	|s|	|s|	NOUN
ejpam-4350	326	13	=	=	SYM
ejpam-4350	326	14	α3	α3	PROPN
ejpam-4350	326	15	h(g	h(g	NOUN
ejpam-4350	326	16	)	)	PUNCT
ejpam-4350	326	17	and	and	CCONJ
ejpam-4350	326	18	let	let	VERB
ejpam-4350	326	19	d	d	PRON
ejpam-4350	326	20	be	be	AUX
ejpam-4350	326	21	an	an	DET
ejpam-4350	326	22	αh	αh	NOUN
ejpam-4350	326	23	-	-	PUNCT
ejpam-4350	326	24	set	set	NOUN
ejpam-4350	326	25	of	of	ADP
ejpam-4350	326	26	h.	h.	PROPN
ejpam-4350	326	27	set	set	VERB
ejpam-4350	326	28	tx	tx	PROPN
ejpam-4350	327	1	=	=	SYM
ejpam-4350	328	1	d	d	PROPN
ejpam-4350	328	2	for	for	ADP
ejpam-4350	328	3	each	each	DET
ejpam-4350	328	4	x	x	SYM
ejpam-4350	328	5	∈	∈	PROPN
ejpam-4350	328	6	s.	s.	PROPN
ejpam-4350	328	7	then	then	ADV
ejpam-4350	328	8	c	c	PROPN
ejpam-4350	328	9	=	=	PUNCT
ejpam-4350	328	10	⋃	⋃	PROPN
ejpam-4350	328	11	x∈s	x∈s	NOUN
ejpam-4350	329	1	[	[	X
ejpam-4350	329	2	{	{	PUNCT
ejpam-4350	329	3	x	x	NOUN
ejpam-4350	329	4	}	}	PUNCT
ejpam-4350	329	5	×	×	NOUN
ejpam-4350	329	6	tx	tx	NOUN
ejpam-4350	329	7	]	]	X
ejpam-4350	329	8	=	=	SYM
ejpam-4350	329	9	s	s	PART
ejpam-4350	329	10	×	×	PROPN
ejpam-4350	329	11	d	d	NOUN
ejpam-4350	329	12	is	be	AUX
ejpam-4350	329	13	a	a	DET
ejpam-4350	329	14	hop	hop	NOUN
ejpam-4350	329	15	independent	independent	ADJ
ejpam-4350	329	16	set	set	NOUN
ejpam-4350	329	17	of	of	ADP
ejpam-4350	329	18	g	g	PROPN
ejpam-4350	329	19	�	�	PROPN
ejpam-4350	329	20	h	h	NOUN
ejpam-4350	329	21	by	by	ADP
ejpam-4350	329	22	theorem	theorem	NOUN
ejpam-4350	329	23	7	7	NUM
ejpam-4350	329	24	.	.	PUNCT
ejpam-4350	330	1	hence	hence	ADV
ejpam-4350	330	2	,	,	PUNCT
ejpam-4350	330	3	αh(g	αh(g	NOUN
ejpam-4350	330	4	�	�	NOUN
ejpam-4350	330	5	h	h	NOUN
ejpam-4350	330	6	)	)	PUNCT
ejpam-4350	330	7	≥	≥	NOUN
ejpam-4350	330	8	|c|	|c|	PROPN
ejpam-4350	330	9	=	=	SYM
ejpam-4350	330	10	|s||d|	|s||d|	PROPN
ejpam-4350	330	11	=	=	SYM
ejpam-4350	330	12	α3	α3	NOUN
ejpam-4350	330	13	h(g)αh(h	h(g)αh(h	NOUN
ejpam-4350	330	14	)	)	PUNCT
ejpam-4350	330	15	.	.	PUNCT
ejpam-4350	331	1	since	since	SCONJ
ejpam-4350	331	2	g	g	PROPN
ejpam-4350	331	3	�	�	PROPN
ejpam-4350	331	4	h	h	NOUN
ejpam-4350	331	5	and	and	CCONJ
ejpam-4350	331	6	h	h	PROPN
ejpam-4350	331	7	�	�	PROPN
ejpam-4350	331	8	g	g	PROPN
ejpam-4350	331	9	are	be	AUX
ejpam-4350	331	10	isomorphic	isomorphic	ADJ
ejpam-4350	331	11	,	,	PUNCT
ejpam-4350	331	12	the	the	DET
ejpam-4350	331	13	assertion	assertion	NOUN
ejpam-4350	331	14	holds	hold	VERB
ejpam-4350	331	15	.	.	PUNCT
ejpam-4350	332	1	the	the	DET
ejpam-4350	332	2	bound	bind	VERB
ejpam-4350	332	3	given	give	VERB
ejpam-4350	332	4	in	in	ADP
ejpam-4350	332	5	corollary	corollary	ADJ
ejpam-4350	332	6	5	5	NUM
ejpam-4350	332	7	is	be	AUX
ejpam-4350	332	8	attainable	attainable	ADJ
ejpam-4350	332	9	.	.	PUNCT
ejpam-4350	333	1	to	to	PART
ejpam-4350	333	2	see	see	VERB
ejpam-4350	333	3	this	this	PRON
ejpam-4350	333	4	,	,	PUNCT
ejpam-4350	333	5	consider	consider	VERB
ejpam-4350	333	6	p4	p4	ADJ
ejpam-4350	333	7	�	�	NOUN
ejpam-4350	333	8	k4	k4	PROPN
ejpam-4350	333	9	.	.	PUNCT
ejpam-4350	334	1	note	note	VERB
ejpam-4350	334	2	that	that	SCONJ
ejpam-4350	334	3	αh(k4	αh(k4	X
ejpam-4350	334	4	)	)	PUNCT
ejpam-4350	334	5	=	=	SYM
ejpam-4350	334	6	4	4	NUM
ejpam-4350	334	7	and	and	CCONJ
ejpam-4350	334	8	α3	α3	ADJ
ejpam-4350	334	9	h(p4	h(p4	NOUN
ejpam-4350	334	10	)	)	PUNCT
ejpam-4350	335	1	=	=	SYM
ejpam-4350	335	2	2	2	X
ejpam-4350	335	3	.	.	X
ejpam-4350	335	4	one	one	PRON
ejpam-4350	335	5	can	can	AUX
ejpam-4350	335	6	easily	easily	ADV
ejpam-4350	335	7	verify	verify	VERB
ejpam-4350	335	8	that	that	SCONJ
ejpam-4350	335	9	αh(p4	αh(p4	NOUN
ejpam-4350	335	10	�	�	NOUN
ejpam-4350	335	11	k4	k4	NOUN
ejpam-4350	335	12	)	)	PUNCT
ejpam-4350	335	13	=	=	SYM
ejpam-4350	335	14	8	8	NUM
ejpam-4350	335	15	=	=	SYM
ejpam-4350	335	16	α3	α3	NOUN
ejpam-4350	335	17	h(p4)αh(k4	h(p4)αh(k4	NOUN
ejpam-4350	335	18	)	)	PUNCT
ejpam-4350	335	19	.	.	PUNCT
ejpam-4350	336	1	the	the	DET
ejpam-4350	336	2	bound	bind	VERB
ejpam-4350	336	3	,	,	PUNCT
ejpam-4350	336	4	however	however	ADV
ejpam-4350	336	5	,	,	PUNCT
ejpam-4350	336	6	may	may	AUX
ejpam-4350	336	7	not	not	PART
ejpam-4350	336	8	be	be	AUX
ejpam-4350	336	9	attained	attain	VERB
ejpam-4350	336	10	.	.	PUNCT
ejpam-4350	337	1	consider	consider	VERB
ejpam-4350	337	2	,	,	PUNCT
ejpam-4350	337	3	for	for	ADP
ejpam-4350	337	4	example	example	NOUN
ejpam-4350	337	5	,	,	PUNCT
ejpam-4350	337	6	p4	p4	ADJ
ejpam-4350	337	7	�	�	NOUN
ejpam-4350	337	8	p4	p4	ADJ
ejpam-4350	337	9	.	.	PUNCT
ejpam-4350	338	1	it	it	PRON
ejpam-4350	338	2	can	can	AUX
ejpam-4350	338	3	also	also	ADV
ejpam-4350	338	4	be	be	AUX
ejpam-4350	338	5	verified	verify	VERB
ejpam-4350	338	6	that	that	SCONJ
ejpam-4350	338	7	αh(p4	αh(p4	NOUN
ejpam-4350	338	8	�	�	NOUN
ejpam-4350	338	9	k4	k4	NOUN
ejpam-4350	338	10	)	)	PUNCT
ejpam-4350	338	11	=	=	PUNCT
ejpam-4350	338	12	6	6	NUM
ejpam-4350	338	13	>	>	SYM
ejpam-4350	338	14	4	4	NUM
ejpam-4350	338	15	=	=	SYM
ejpam-4350	338	16	α3	α3	NOUN
ejpam-4350	338	17	h(p4)αh(p4	h(p4)αh(p4	NOUN
ejpam-4350	338	18	)	)	PUNCT
ejpam-4350	338	19	.	.	PUNCT
ejpam-4350	339	1	4	4	X
ejpam-4350	339	2	.	.	X
ejpam-4350	339	3	conclusion	conclusion	VERB
ejpam-4350	339	4	the	the	DET
ejpam-4350	339	5	concept	concept	NOUN
ejpam-4350	339	6	of	of	ADP
ejpam-4350	339	7	hop	hop	NOUN
ejpam-4350	339	8	independent	independent	ADJ
ejpam-4350	339	9	set	set	NOUN
ejpam-4350	339	10	in	in	ADP
ejpam-4350	339	11	a	a	DET
ejpam-4350	339	12	graph	graph	NOUN
ejpam-4350	339	13	,	,	PUNCT
ejpam-4350	339	14	though	though	SCONJ
ejpam-4350	339	15	maybe	maybe	ADV
ejpam-4350	339	16	considered	consider	VERB
ejpam-4350	339	17	informally	informally	ADV
ejpam-4350	339	18	previously	previously	ADV
ejpam-4350	339	19	,	,	PUNCT
ejpam-4350	339	20	has	have	AUX
ejpam-4350	339	21	been	be	AUX
ejpam-4350	339	22	introduced	introduce	VERB
ejpam-4350	339	23	formally	formally	ADV
ejpam-4350	339	24	and	and	CCONJ
ejpam-4350	339	25	investigated	investigate	VERB
ejpam-4350	339	26	initially	initially	ADV
ejpam-4350	339	27	in	in	ADP
ejpam-4350	339	28	this	this	DET
ejpam-4350	339	29	study	study	NOUN
ejpam-4350	339	30	.	.	PUNCT
ejpam-4350	340	1	it	it	PRON
ejpam-4350	340	2	is	be	AUX
ejpam-4350	340	3	shown	show	VERB
ejpam-4350	340	4	that	that	SCONJ
ejpam-4350	340	5	the	the	DET
ejpam-4350	340	6	hop	hop	NOUN
ejpam-4350	340	7	independence	independence	NOUN
ejpam-4350	340	8	number	number	NOUN
ejpam-4350	340	9	of	of	ADP
ejpam-4350	340	10	a	a	DET
ejpam-4350	340	11	graph	graph	NOUN
ejpam-4350	340	12	is	be	AUX
ejpam-4350	340	13	an	an	DET
ejpam-4350	340	14	upper	upper	ADJ
ejpam-4350	340	15	bound	bound	NOUN
ejpam-4350	340	16	of	of	ADP
ejpam-4350	340	17	the	the	DET
ejpam-4350	340	18	hop	hop	NOUN
ejpam-4350	340	19	domination	domination	NOUN
ejpam-4350	340	20	number	number	NOUN
ejpam-4350	340	21	of	of	ADP
ejpam-4350	340	22	the	the	DET
ejpam-4350	340	23	graph	graph	NOUN
ejpam-4350	340	24	and	and	CCONJ
ejpam-4350	340	25	that	that	SCONJ
ejpam-4350	340	26	the	the	DET
ejpam-4350	340	27	absolute	absolute	ADJ
ejpam-4350	340	28	difference	difference	NOUN
ejpam-4350	340	29	of	of	ADP
ejpam-4350	340	30	the	the	DET
ejpam-4350	340	31	independence	independence	NOUN
ejpam-4350	340	32	number	number	NOUN
ejpam-4350	340	33	and	and	CCONJ
ejpam-4350	340	34	hop	hop	NOUN
ejpam-4350	340	35	independence	independence	NOUN
ejpam-4350	340	36	number	number	NOUN
ejpam-4350	340	37	can	can	AUX
ejpam-4350	340	38	be	be	AUX
ejpam-4350	340	39	made	make	VERB
ejpam-4350	340	40	arbitrarily	arbitrarily	ADV
ejpam-4350	340	41	large	large	ADJ
ejpam-4350	340	42	.	.	PUNCT
ejpam-4350	341	1	just	just	ADV
ejpam-4350	341	2	like	like	ADP
ejpam-4350	341	3	the	the	DET
ejpam-4350	341	4	independence	independence	NOUN
ejpam-4350	341	5	number	number	NOUN
ejpam-4350	341	6	,	,	PUNCT
ejpam-4350	341	7	the	the	DET
ejpam-4350	341	8	hop	hop	NOUN
ejpam-4350	341	9	independence	independence	NOUN
ejpam-4350	341	10	number	number	NOUN
ejpam-4350	341	11	of	of	ADP
ejpam-4350	341	12	a	a	DET
ejpam-4350	341	13	graph	graph	NOUN
ejpam-4350	341	14	may	may	AUX
ejpam-4350	341	15	be	be	AUX
ejpam-4350	341	16	used	use	VERB
ejpam-4350	341	17	to	to	PART
ejpam-4350	341	18	give	give	VERB
ejpam-4350	341	19	bounds	bound	NOUN
ejpam-4350	341	20	on	on	ADP
ejpam-4350	341	21	some	some	DET
ejpam-4350	341	22	graph	graph	NOUN
ejpam-4350	341	23	-	-	PUNCT
ejpam-4350	341	24	theoretic	theoretic	NOUN
ejpam-4350	341	25	parameters	parameter	NOUN
ejpam-4350	341	26	.	.	PUNCT
ejpam-4350	342	1	in	in	ADP
ejpam-4350	342	2	this	this	DET
ejpam-4350	342	3	paper	paper	NOUN
ejpam-4350	342	4	the	the	DET
ejpam-4350	342	5	concept	concept	NOUN
ejpam-4350	342	6	has	have	AUX
ejpam-4350	342	7	been	be	AUX
ejpam-4350	342	8	investigated	investigate	VERB
ejpam-4350	342	9	for	for	ADP
ejpam-4350	342	10	the	the	DET
ejpam-4350	342	11	join	join	NOUN
ejpam-4350	342	12	,	,	PUNCT
ejpam-4350	342	13	corona	corona	PROPN
ejpam-4350	342	14	,	,	PUNCT
ejpam-4350	342	15	lexicographic	lexicographic	ADJ
ejpam-4350	342	16	and	and	CCONJ
ejpam-4350	342	17	cartesian	cartesian	ADJ
ejpam-4350	342	18	products	product	NOUN
ejpam-4350	342	19	of	of	ADP
ejpam-4350	342	20	graphs	graph	NOUN
ejpam-4350	342	21	.	.	PUNCT
ejpam-4350	343	1	finding	find	VERB
ejpam-4350	343	2	better	well	ADJ
ejpam-4350	343	3	bounds	bound	NOUN
ejpam-4350	343	4	on	on	ADP
ejpam-4350	343	5	the	the	DET
ejpam-4350	343	6	hop	hop	NOUN
ejpam-4350	343	7	independence	independence	NOUN
ejpam-4350	343	8	number	number	NOUN
ejpam-4350	343	9	of	of	ADP
ejpam-4350	343	10	the	the	DET
ejpam-4350	343	11	cartesian	cartesian	ADJ
ejpam-4350	343	12	product	product	NOUN
ejpam-4350	343	13	of	of	ADP
ejpam-4350	343	14	some	some	DET
ejpam-4350	343	15	graphs	graph	NOUN
ejpam-4350	343	16	is	be	AUX
ejpam-4350	343	17	recommended	recommend	VERB
ejpam-4350	343	18	.	.	PUNCT
ejpam-4350	344	1	also	also	ADV
ejpam-4350	344	2	,	,	PUNCT
ejpam-4350	344	3	this	this	DET
ejpam-4350	344	4	newly	newly	ADV
ejpam-4350	344	5	defined	define	VERB
ejpam-4350	344	6	parameter	parameter	NOUN
ejpam-4350	344	7	can	can	AUX
ejpam-4350	344	8	be	be	AUX
ejpam-4350	344	9	studied	study	VERB
ejpam-4350	344	10	further	far	ADV
ejpam-4350	344	11	for	for	ADP
ejpam-4350	344	12	other	other	ADJ
ejpam-4350	344	13	types	type	NOUN
ejpam-4350	344	14	of	of	ADP
ejpam-4350	344	15	graphs	graph	NOUN
ejpam-4350	344	16	.	.	PUNCT
ejpam-4350	345	1	acknowledgements	acknowledgement	NOUN
ejpam-4350	345	2	the	the	DET
ejpam-4350	345	3	authors	author	NOUN
ejpam-4350	345	4	would	would	AUX
ejpam-4350	345	5	like	like	VERB
ejpam-4350	345	6	to	to	PART
ejpam-4350	345	7	thank	thank	VERB
ejpam-4350	345	8	the	the	DET
ejpam-4350	345	9	referees	referee	NOUN
ejpam-4350	345	10	for	for	ADP
ejpam-4350	345	11	the	the	DET
ejpam-4350	345	12	invaluable	invaluable	ADJ
ejpam-4350	345	13	assistance	assistance	NOUN
ejpam-4350	345	14	they	they	PRON
ejpam-4350	345	15	gave	give	VERB
ejpam-4350	345	16	us	we	PRON
ejpam-4350	345	17	through	through	ADP
ejpam-4350	345	18	their	their	PRON
ejpam-4350	345	19	comments	comment	NOUN
ejpam-4350	345	20	and	and	CCONJ
ejpam-4350	345	21	suggestions	suggestion	NOUN
ejpam-4350	345	22	which	which	PRON
ejpam-4350	345	23	led	lead	VERB
ejpam-4350	345	24	to	to	ADP
ejpam-4350	345	25	the	the	DET
ejpam-4350	345	26	improvement	improvement	NOUN
ejpam-4350	345	27	of	of	ADP
ejpam-4350	345	28	the	the	DET
ejpam-4350	345	29	paper	paper	NOUN
ejpam-4350	345	30	.	.	PUNCT
ejpam-4350	346	1	also	also	ADV
ejpam-4350	346	2	,	,	PUNCT
ejpam-4350	346	3	the	the	DET
ejpam-4350	346	4	authors	author	NOUN
ejpam-4350	346	5	would	would	AUX
ejpam-4350	346	6	like	like	VERB
ejpam-4350	346	7	to	to	PART
ejpam-4350	346	8	thank	thank	VERB
ejpam-4350	346	9	the	the	DET
ejpam-4350	346	10	department	department	NOUN
ejpam-4350	346	11	of	of	ADP
ejpam-4350	346	12	science	science	NOUN
ejpam-4350	346	13	and	and	CCONJ
ejpam-4350	346	14	technology	technology	NOUN
ejpam-4350	346	15	accelerated	accelerate	VERB
ejpam-4350	346	16	science	science	NOUN
ejpam-4350	346	17	and	and	CCONJ
ejpam-4350	346	18	technology	technology	NOUN
ejpam-4350	346	19	human	human	ADJ
ejpam-4350	346	20	resource	resource	NOUN
ejpam-4350	346	21	development	development	NOUN
ejpam-4350	346	22	program	program	NOUN
ejpam-4350	346	23	(	(	PUNCT
ejpam-4350	346	24	dost	dost	NOUN
ejpam-4350	346	25	-	-	PUNCT
ejpam-4350	346	26	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4350	346	27	,	,	PUNCT
ejpam-4350	346	28	and	and	CCONJ
ejpam-4350	346	29	msu	msu	PROPN
ejpam-4350	346	30	-	-	PUNCT
ejpam-4350	346	31	iligan	iligan	PROPN
ejpam-4350	346	32	institute	institute	PROPN
ejpam-4350	346	33	of	of	ADP
ejpam-4350	346	34	technology	technology	NOUN
ejpam-4350	346	35	for	for	ADP
ejpam-4350	346	36	funding	fund	VERB
ejpam-4350	346	37	this	this	DET
ejpam-4350	346	38	research	research	NOUN
ejpam-4350	346	39	.	.	PUNCT
ejpam-4350	347	1	references	reference	NOUN
ejpam-4350	347	2	[	[	X
ejpam-4350	347	3	1	1	X
ejpam-4350	347	4	]	]	PUNCT
ejpam-4350	347	5	s.	s.	PROPN
ejpam-4350	347	6	arriola	arriola	PROPN
ejpam-4350	347	7	and	and	CCONJ
ejpam-4350	347	8	jr	jr	PROPN
ejpam-4350	347	9	.	.	PROPN
ejpam-4350	347	10	s.	s.	PROPN
ejpam-4350	347	11	canoy	canoy	PROPN
ejpam-4350	347	12	.	.	PUNCT
ejpam-4350	348	1	(	(	PUNCT
ejpam-4350	348	2	1	1	NUM
ejpam-4350	348	3	,	,	PUNCT
ejpam-4350	348	4	2)∗-domination	2)∗-domination	NOUN
ejpam-4350	348	5	in	in	ADP
ejpam-4350	348	6	graphs	graph	NOUN
ejpam-4350	348	7	.	.	PUNCT
ejpam-4350	349	1	advances	advance	NOUN
ejpam-4350	349	2	and	and	CCONJ
ejpam-4350	349	3	applications	application	NOUN
ejpam-4350	349	4	in	in	ADP
ejpam-4350	349	5	discrete	discrete	ADJ
ejpam-4350	349	6	mathematics	mathematic	NOUN
ejpam-4350	349	7	.	.	PUNCT
ejpam-4350	349	8	,	,	PUNCT
ejpam-4350	349	9	18(2):179–190	18(2):179–190	NUM
ejpam-4350	349	10	,	,	PUNCT
ejpam-4350	349	11	2017	2017	NUM
ejpam-4350	349	12	.	.	PUNCT
ejpam-4350	350	1	[	[	X
ejpam-4350	350	2	2	2	NUM
ejpam-4350	350	3	]	]	PUNCT
ejpam-4350	350	4	s.	s.	PROPN
ejpam-4350	350	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4350	350	6	,	,	PUNCT
ejpam-4350	350	7	b.	b.	PROPN
ejpam-4350	350	8	krishnakumari	krishnakumari	PROPN
ejpam-4350	350	9	,	,	PUNCT
ejpam-4350	350	10	b.	b.	PROPN
ejpam-4350	350	11	natarjan	natarjan	PROPN
ejpam-4350	350	12	,	,	PUNCT
ejpam-4350	350	13	and	and	CCONJ
ejpam-4350	350	14	y.	y.	PROPN
ejpam-4350	350	15	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4350	350	16	.	.	PUNCT
ejpam-4350	351	1	bounds	bound	NOUN
ejpam-4350	351	2	on	on	ADP
ejpam-4350	351	3	the	the	DET
ejpam-4350	351	4	hop	hop	NOUN
ejpam-4350	351	5	domination	domination	NOUN
ejpam-4350	351	6	number	number	NOUN
ejpam-4350	351	7	of	of	ADP
ejpam-4350	351	8	a	a	DET
ejpam-4350	351	9	tree	tree	NOUN
ejpam-4350	351	10	.	.	PUNCT
ejpam-4350	352	1	proceedings	proceeding	NOUN
ejpam-4350	352	2	-	-	PUNCT
ejpam-4350	352	3	mathematical	mathematical	ADJ
ejpam-4350	352	4	sciences	science	NOUN
ejpam-4350	352	5	,	,	PUNCT
ejpam-4350	352	6	125(4):449–455	125(4):449–455	ADP
ejpam-4350	352	7	,	,	PUNCT
ejpam-4350	352	8	2015	2015	NUM
ejpam-4350	352	9	.	.	PUNCT
ejpam-4350	353	1	references	reference	NOUN
ejpam-4350	353	2	477	477	NUM
ejpam-4350	354	1	[	[	X
ejpam-4350	354	2	3	3	NUM
ejpam-4350	354	3	]	]	X
ejpam-4350	354	4	m.	m.	NOUN
ejpam-4350	354	5	henning	henning	PROPN
ejpam-4350	354	6	and	and	CCONJ
ejpam-4350	354	7	n.	n.	PROPN
ejpam-4350	354	8	rad	rad	PROPN
ejpam-4350	354	9	.	.	PROPN
ejpam-4350	355	1	on	on	ADP
ejpam-4350	355	2	2	2	NUM
ejpam-4350	355	3	-	-	PUNCT
ejpam-4350	355	4	step	step	NOUN
ejpam-4350	355	5	and	and	CCONJ
ejpam-4350	355	6	hop	hop	NOUN
ejpam-4350	355	7	dominating	dominating	NOUN
ejpam-4350	355	8	sets	set	NOUN
ejpam-4350	355	9	in	in	ADP
ejpam-4350	355	10	graphs	graph	NOUN
ejpam-4350	355	11	.	.	PUNCT
ejpam-4350	356	1	graphs	graph	NOUN
ejpam-4350	356	2	and	and	CCONJ
ejpam-4350	356	3	combinatorics	combinatoric	NOUN
ejpam-4350	356	4	.	.	PUNCT
ejpam-4350	356	5	,	,	PUNCT
ejpam-4350	356	6	33(4):913–927	33(4):913–927	PROPN
ejpam-4350	356	7	,	,	PUNCT
ejpam-4350	356	8	2017	2017	NUM
ejpam-4350	356	9	.	.	PUNCT
ejpam-4350	357	1	[	[	X
ejpam-4350	357	2	4	4	X
ejpam-4350	357	3	]	]	X
ejpam-4350	357	4	c.	c.	PROPN
ejpam-4350	357	5	natarajan	natarajan	PROPN
ejpam-4350	357	6	and	and	CCONJ
ejpam-4350	357	7	s.	s.	PROPN
ejpam-4350	357	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4350	357	9	.	.	PUNCT
ejpam-4350	358	1	hop	hop	PROPN
ejpam-4350	358	2	domination	domination	NOUN
ejpam-4350	358	3	in	in	ADP
ejpam-4350	358	4	graphs	graphs	PROPN
ejpam-4350	358	5	ii	ii	PROPN
ejpam-4350	358	6	.	.	PUNCT
ejpam-4350	358	7	versita	versita	PROPN
ejpam-4350	358	8	,	,	PUNCT
ejpam-4350	358	9	23(2):187–199	23(2):187–199	PROPN
ejpam-4350	358	10	,	,	PUNCT
ejpam-4350	358	11	2015	2015	NUM
ejpam-4350	358	12	.	.	PUNCT
ejpam-4350	359	1	[	[	X
ejpam-4350	359	2	5	5	NUM
ejpam-4350	359	3	]	]	X
ejpam-4350	359	4	jr	jr	PROPN
ejpam-4350	359	5	.	.	PROPN
ejpam-4350	359	6	s.	s.	PROPN
ejpam-4350	359	7	canoy	canoy	PROPN
ejpam-4350	359	8	and	and	CCONJ
ejpam-4350	359	9	g.	g.	PROPN
ejpam-4350	359	10	malacas	malacas	PROPN
ejpam-4350	359	11	.	.	PUNCT
ejpam-4350	360	1	determining	determine	VERB
ejpam-4350	360	2	the	the	DET
ejpam-4350	360	3	intruder	intruder	NOUN
ejpam-4350	360	4	’s	’s	PART
ejpam-4350	360	5	location	location	NOUN
ejpam-4350	360	6	in	in	ADP
ejpam-4350	360	7	a	a	DET
ejpam-4350	360	8	given	give	VERB
ejpam-4350	360	9	network	network	NOUN
ejpam-4350	360	10	:	:	PUNCT
ejpam-4350	360	11	locating	locate	VERB
ejpam-4350	360	12	-	-	PUNCT
ejpam-4350	360	13	dominating	dominating	NOUN
ejpam-4350	360	14	sets	set	NOUN
ejpam-4350	360	15	in	in	ADP
ejpam-4350	360	16	a	a	DET
ejpam-4350	360	17	graph	graph	NOUN
ejpam-4350	360	18	.	.	PUNCT
ejpam-4350	361	1	nrcp	nrcp	PROPN
ejpam-4350	361	2	research	research	PROPN
ejpam-4350	361	3	journal	journal	PROPN
ejpam-4350	361	4	.	.	PUNCT
ejpam-4350	361	5	,	,	PUNCT
ejpam-4350	361	6	13(1):1–8	13(1):1–8	NUM
ejpam-4350	361	7	,	,	PUNCT
ejpam-4350	361	8	2013	2013	NUM
ejpam-4350	361	9	.	.	PUNCT
ejpam-4350	362	1	[	[	X
ejpam-4350	362	2	6	6	NUM
ejpam-4350	362	3	]	]	X
ejpam-4350	362	4	jr	jr	PROPN
ejpam-4350	362	5	.	.	PROPN
ejpam-4350	362	6	s.	s.	PROPN
ejpam-4350	362	7	canoy	canoy	PROPN
ejpam-4350	362	8	and	and	CCONJ
ejpam-4350	362	9	g.	g.	PROPN
ejpam-4350	362	10	malacas	malacas	PROPN
ejpam-4350	362	11	.	.	PUNCT
ejpam-4350	363	1	differentiating	differentiate	VERB
ejpam-4350	363	2	-	-	PUNCT
ejpam-4350	363	3	dominating	dominating	NOUN
ejpam-4350	363	4	sets	set	NOUN
ejpam-4350	363	5	in	in	ADP
ejpam-4350	363	6	graphs	graph	NOUN
ejpam-4350	363	7	under	under	ADP
ejpam-4350	363	8	binary	binary	ADJ
ejpam-4350	363	9	operations	operation	NOUN
ejpam-4350	363	10	.	.	PUNCT
ejpam-4350	364	1	tamkang	tamkang	PROPN
ejpam-4350	364	2	j.	j.	PROPN
ejpam-4350	364	3	math	math	PROPN
ejpam-4350	364	4	.	.	PUNCT
ejpam-4350	364	5	,	,	PUNCT
ejpam-4350	364	6	46(1):51–60	46(1):51–60	NOUN
ejpam-4350	364	7	,	,	PUNCT
ejpam-4350	364	8	2015	2015	NUM
ejpam-4350	364	9	.	.	PUNCT
ejpam-4350	365	1	[	[	X
ejpam-4350	365	2	7	7	NUM
ejpam-4350	365	3	]	]	X
ejpam-4350	365	4	jr	jr	PROPN
ejpam-4350	365	5	.	.	PROPN
ejpam-4350	365	6	s.	s.	PROPN
ejpam-4350	365	7	canoy	canoy	PROPN
ejpam-4350	365	8	,	,	PUNCT
ejpam-4350	365	9	r.	r.	NOUN
ejpam-4350	365	10	mollejon	mollejon	NOUN
ejpam-4350	365	11	,	,	PUNCT
ejpam-4350	365	12	and	and	CCONJ
ejpam-4350	365	13	j.	j.	PROPN
ejpam-4350	365	14	g.	g.	PROPN
ejpam-4350	365	15	canoy	canoy	PROPN
ejpam-4350	365	16	.	.	PUNCT
ejpam-4350	366	1	hop	hop	PROPN
ejpam-4350	366	2	dominating	dominating	NOUN
ejpam-4350	366	3	sets	set	NOUN
ejpam-4350	366	4	in	in	ADP
ejpam-4350	366	5	graphs	graph	NOUN
ejpam-4350	366	6	under	under	ADP
ejpam-4350	366	7	binary	binary	ADJ
ejpam-4350	366	8	operations	operation	NOUN
ejpam-4350	366	9	.	.	PUNCT
ejpam-4350	367	1	eur	eur	PROPN
ejpam-4350	367	2	.	.	PUNCT
ejpam-4350	368	1	j.	j.	PROPN
ejpam-4350	368	2	pure	pure	PROPN
ejpam-4350	368	3	appl	appl	PROPN
ejpam-4350	368	4	.	.	PUNCT
ejpam-4350	368	5	math	math	PROPN
ejpam-4350	368	6	.	.	PUNCT
ejpam-4350	368	7	,	,	PUNCT
ejpam-4350	369	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4350	369	2	,	,	PUNCT
ejpam-4350	369	3	2019	2019	NUM
ejpam-4350	369	4	.	.	PUNCT
ejpam-4350	370	1	[	[	X
ejpam-4350	370	2	8	8	NUM
ejpam-4350	370	3	]	]	X
ejpam-4350	370	4	jr	jr	PROPN
ejpam-4350	370	5	.	.	PROPN
ejpam-4350	370	6	s.	s.	PROPN
ejpam-4350	370	7	canoy	canoy	PROPN
ejpam-4350	370	8	and	and	CCONJ
ejpam-4350	370	9	g.	g.	PROPN
ejpam-4350	370	10	salasalan	salasalan	NOUN
ejpam-4350	370	11	.	.	PUNCT
ejpam-4350	371	1	locating	locate	VERB
ejpam-4350	371	2	-	-	PUNCT
ejpam-4350	371	3	hop	hop	NOUN
ejpam-4350	371	4	domination	domination	NOUN
ejpam-4350	371	5	in	in	ADP
ejpam-4350	371	6	graphs	graph	NOUN
ejpam-4350	371	7	.	.	PUNCT
ejpam-4350	372	1	kyungpook	kyungpook	PROPN
ejpam-4350	372	2	mathematical	mathematical	PROPN
ejpam-4350	372	3	journal	journal	PROPN
ejpam-4350	372	4	,	,	PUNCT
ejpam-4350	372	5	62:193–204	62:193–204	PROPN
ejpam-4350	372	6	,	,	PUNCT
ejpam-4350	372	7	2022	2022	NUM
ejpam-4350	372	8	.	.	PUNCT
ejpam-4350	373	1	[	[	X
ejpam-4350	373	2	9	9	NUM
ejpam-4350	373	3	]	]	X
ejpam-4350	373	4	g.	g.	NOUN
ejpam-4350	373	5	salasalan	salasalan	NOUN
ejpam-4350	373	6	and	and	CCONJ
ejpam-4350	373	7	jr	jr	PROPN
ejpam-4350	373	8	.	.	PROPN
ejpam-4350	373	9	s.	s.	PROPN
ejpam-4350	373	10	canoy	canoy	PROPN
ejpam-4350	373	11	.	.	PUNCT
ejpam-4350	374	1	global	global	ADJ
ejpam-4350	374	2	hop	hop	PROPN
ejpam-4350	374	3	domination	domination	PROPN
ejpam-4350	374	4	numbers	number	NOUN
ejpam-4350	374	5	of	of	ADP
ejpam-4350	374	6	graphs	graph	NOUN
ejpam-4350	374	7	.	.	PUNCT
ejpam-4350	375	1	eur	eur	PROPN
ejpam-4350	375	2	.	.	PUNCT
ejpam-4350	376	1	j.	j.	PROPN
ejpam-4350	376	2	pure	pure	PROPN
ejpam-4350	376	3	appl	appl	PROPN
ejpam-4350	376	4	.	.	PUNCT
ejpam-4350	376	5	math	math	PROPN
ejpam-4350	376	6	.	.	PUNCT
ejpam-4350	376	7	,	,	PUNCT
ejpam-4350	376	8	14(1):112–125	14(1):112–125	NUM
ejpam-4350	376	9	,	,	PUNCT
ejpam-4350	376	10	2021	2021	NUM
ejpam-4350	376	11	.	.	PUNCT