id	sid	tid	token	lemma	pos
ejpam-5084	1	1	european	european	PROPN
ejpam-5084	1	2	journal	journal	PROPN
ejpam-5084	1	3	of	of	ADP
ejpam-5084	1	4	pure	pure	ADJ
ejpam-5084	1	5	and	and	CCONJ
ejpam-5084	1	6	applied	apply	VERB
ejpam-5084	1	7	mathematics	mathematic	NOUN
ejpam-5084	1	8	vol	vol	NOUN
ejpam-5084	1	9	.	.	PROPN
ejpam-5084	2	1	17	17	NUM
ejpam-5084	2	2	,	,	PUNCT
ejpam-5084	2	3	no	no	INTJ
ejpam-5084	2	4	.	.	NOUN
ejpam-5084	2	5	2	2	NUM
ejpam-5084	2	6	,	,	PUNCT
ejpam-5084	2	7	2024	2024	NUM
ejpam-5084	2	8	,	,	PUNCT
ejpam-5084	2	9	922	922	NUM
ejpam-5084	2	10	-	-	SYM
ejpam-5084	2	11	930	930	NUM
ejpam-5084	2	12	issn	issn	PROPN
ejpam-5084	2	13	1307	1307	NUM
ejpam-5084	2	14	-	-	SYM
ejpam-5084	2	15	5543	5543	NUM
ejpam-5084	2	16	–	–	PUNCT
ejpam-5084	2	17	ejpam.com	ejpam.com	X
ejpam-5084	2	18	published	publish	VERB
ejpam-5084	2	19	by	by	ADP
ejpam-5084	2	20	new	new	PROPN
ejpam-5084	2	21	york	york	PROPN
ejpam-5084	2	22	business	business	PROPN
ejpam-5084	2	23	global	global	PROPN
ejpam-5084	2	24	j	j	PROPN
ejpam-5084	2	25	-	-	ADJ
ejpam-5084	2	26	open	open	ADJ
ejpam-5084	2	27	independent	independent	ADJ
ejpam-5084	2	28	sets	set	NOUN
ejpam-5084	2	29	in	in	ADP
ejpam-5084	2	30	graphs	graph	NOUN
ejpam-5084	2	31	javier	javier	PROPN
ejpam-5084	2	32	a.	a.	PROPN
ejpam-5084	2	33	hassan1,∗	hassan1,∗	PROPN
ejpam-5084	2	34	,	,	PUNCT
ejpam-5084	2	35	nuruddina	nuruddina	PROPN
ejpam-5084	2	36	m.	m.	PROPN
ejpam-5084	2	37	bakar1	bakar1	PROPN
ejpam-5084	2	38	,	,	PUNCT
ejpam-5084	2	39	norwajir	norwajir	PROPN
ejpam-5084	2	40	s.	s.	PROPN
ejpam-5084	2	41	dagsaan1	dagsaan1	PROPN
ejpam-5084	2	42	,	,	PUNCT
ejpam-5084	3	1	mercedita	mercedita	PROPN
ejpam-5084	3	2	a.	a.	NOUN
ejpam-5084	3	3	langamin1	langamin1	PROPN
ejpam-5084	3	4	,	,	PUNCT
ejpam-5084	3	5	nurijam	nurijam	PROPN
ejpam-5084	3	6	hanna	hanna	PROPN
ejpam-5084	3	7	m.	m.	PROPN
ejpam-5084	3	8	mohammad1	mohammad1	PROPN
ejpam-5084	3	9	,	,	PUNCT
ejpam-5084	3	10	sisteta	sisteta	PROPN
ejpam-5084	3	11	u.	u.	PROPN
ejpam-5084	3	12	kamdon1	kamdon1	PROPN
ejpam-5084	3	13	1	1	NUM
ejpam-5084	3	14	mathematics	mathematic	NOUN
ejpam-5084	3	15	and	and	CCONJ
ejpam-5084	3	16	sciences	sciences	PROPN
ejpam-5084	3	17	department	department	PROPN
ejpam-5084	3	18	,	,	PUNCT
ejpam-5084	3	19	college	college	NOUN
ejpam-5084	3	20	of	of	ADP
ejpam-5084	3	21	arts	art	NOUN
ejpam-5084	3	22	and	and	CCONJ
ejpam-5084	3	23	sciences	science	NOUN
ejpam-5084	3	24	,	,	PUNCT
ejpam-5084	3	25	msu	msu	PROPN
ejpam-5084	3	26	-	-	PUNCT
ejpam-5084	3	27	tawi	tawi	NOUN
ejpam-5084	3	28	-	-	PUNCT
ejpam-5084	3	29	tawi	tawi	NOUN
ejpam-5084	3	30	college	college	PROPN
ejpam-5084	3	31	of	of	ADP
ejpam-5084	3	32	technology	technology	NOUN
ejpam-5084	3	33	and	and	CCONJ
ejpam-5084	3	34	oceanography	oceanography	NOUN
ejpam-5084	3	35	,	,	PUNCT
ejpam-5084	3	36	bongao	bongao	NOUN
ejpam-5084	3	37	,	,	PUNCT
ejpam-5084	3	38	tawi	tawi	NOUN
ejpam-5084	3	39	-	-	PUNCT
ejpam-5084	3	40	tawi	tawi	NOUN
ejpam-5084	3	41	,	,	PUNCT
ejpam-5084	3	42	philippines	philippine	NOUN
ejpam-5084	3	43	abstract	abstract	ADJ
ejpam-5084	3	44	.	.	PUNCT
ejpam-5084	4	1	let	let	VERB
ejpam-5084	4	2	g	g	PRON
ejpam-5084	4	3	be	be	AUX
ejpam-5084	4	4	a	a	DET
ejpam-5084	4	5	graph	graph	NOUN
ejpam-5084	4	6	with	with	ADP
ejpam-5084	4	7	vertex	vertex	NOUN
ejpam-5084	4	8	and	and	CCONJ
ejpam-5084	4	9	edge	edge	NOUN
ejpam-5084	4	10	-	-	PUNCT
ejpam-5084	4	11	sets	set	NOUN
ejpam-5084	4	12	v	v	NOUN
ejpam-5084	4	13	(	(	PUNCT
ejpam-5084	4	14	g	g	NOUN
ejpam-5084	4	15	)	)	PUNCT
ejpam-5084	4	16	and	and	CCONJ
ejpam-5084	4	17	e(g	e(g	PROPN
ejpam-5084	4	18	)	)	PUNCT
ejpam-5084	4	19	,	,	PUNCT
ejpam-5084	4	20	respectively	respectively	ADV
ejpam-5084	4	21	.	.	PUNCT
ejpam-5084	5	1	then	then	ADV
ejpam-5084	5	2	o	o	X
ejpam-5084	5	3	⊆	⊆	NUM
ejpam-5084	5	4	v	v	ADP
ejpam-5084	5	5	(	(	PUNCT
ejpam-5084	5	6	g	g	NOUN
ejpam-5084	5	7	)	)	PUNCT
ejpam-5084	5	8	is	be	AUX
ejpam-5084	5	9	called	call	VERB
ejpam-5084	5	10	a	a	DET
ejpam-5084	5	11	j	j	NOUN
ejpam-5084	5	12	-	-	ADJ
ejpam-5084	5	13	open	open	ADJ
ejpam-5084	5	14	independent	independent	ADJ
ejpam-5084	5	15	set	set	NOUN
ejpam-5084	5	16	of	of	ADP
ejpam-5084	5	17	g	g	PROPN
ejpam-5084	5	18	if	if	SCONJ
ejpam-5084	5	19	o	o	NOUN
ejpam-5084	5	20	is	be	AUX
ejpam-5084	5	21	a	a	DET
ejpam-5084	5	22	singleton	singleton	NOUN
ejpam-5084	5	23	set	set	NOUN
ejpam-5084	5	24	or	or	CCONJ
ejpam-5084	5	25	o	o	NOUN
ejpam-5084	5	26	is	be	AUX
ejpam-5084	5	27	an	an	DET
ejpam-5084	5	28	independent	independent	ADJ
ejpam-5084	5	29	set	set	NOUN
ejpam-5084	5	30	of	of	ADP
ejpam-5084	5	31	g	g	NOUN
ejpam-5084	5	32	and	and	CCONJ
ejpam-5084	5	33	for	for	ADP
ejpam-5084	5	34	every	every	DET
ejpam-5084	5	35	a	a	PROPN
ejpam-5084	5	36	,	,	PUNCT
ejpam-5084	5	37	b	b	PROPN
ejpam-5084	5	38	∈	∈	PROPN
ejpam-5084	5	39	v	v	NOUN
ejpam-5084	5	40	(	(	PUNCT
ejpam-5084	5	41	g	g	NOUN
ejpam-5084	5	42	)	)	PUNCT
ejpam-5084	5	43	,	,	PUNCT
ejpam-5084	5	44	ng(a)\ng(b	ng(a)\ng(b	ADJ
ejpam-5084	5	45	)	)	PUNCT
ejpam-5084	5	46	̸=	̸=	PROPN
ejpam-5084	5	47	∅	∅	NOUN
ejpam-5084	5	48	and	and	CCONJ
ejpam-5084	5	49	ng(b)\ng(a	ng(b)\ng(a	NOUN
ejpam-5084	5	50	)	)	PUNCT
ejpam-5084	5	51	̸=	̸=	PROPN
ejpam-5084	5	52	∅.	∅.	ADP
ejpam-5084	5	53	the	the	DET
ejpam-5084	5	54	maximum	maximum	ADJ
ejpam-5084	5	55	cardinality	cardinality	NOUN
ejpam-5084	5	56	of	of	ADP
ejpam-5084	5	57	a	a	DET
ejpam-5084	5	58	j	j	NOUN
ejpam-5084	5	59	-	-	ADJ
ejpam-5084	5	60	open	open	ADJ
ejpam-5084	5	61	independent	independent	ADJ
ejpam-5084	5	62	set	set	NOUN
ejpam-5084	5	63	of	of	ADP
ejpam-5084	5	64	g	g	NOUN
ejpam-5084	5	65	,	,	PUNCT
ejpam-5084	5	66	denoted	denote	VERB
ejpam-5084	5	67	by	by	ADP
ejpam-5084	5	68	αj(g	αj(g	NOUN
ejpam-5084	5	69	)	)	PUNCT
ejpam-5084	5	70	,	,	PUNCT
ejpam-5084	5	71	is	be	AUX
ejpam-5084	5	72	called	call	VERB
ejpam-5084	5	73	the	the	DET
ejpam-5084	5	74	j	j	NOUN
ejpam-5084	5	75	-	-	ADJ
ejpam-5084	5	76	open	open	ADJ
ejpam-5084	5	77	independence	independence	NOUN
ejpam-5084	5	78	number	number	NOUN
ejpam-5084	5	79	of	of	ADP
ejpam-5084	5	80	g.	g.	PROPN
ejpam-5084	5	81	in	in	ADP
ejpam-5084	5	82	this	this	DET
ejpam-5084	5	83	paper	paper	NOUN
ejpam-5084	5	84	,	,	PUNCT
ejpam-5084	5	85	we	we	PRON
ejpam-5084	5	86	introduce	introduce	VERB
ejpam-5084	5	87	this	this	DET
ejpam-5084	5	88	parameter	parameter	NOUN
ejpam-5084	5	89	and	and	CCONJ
ejpam-5084	5	90	we	we	PRON
ejpam-5084	5	91	show	show	VERB
ejpam-5084	5	92	that	that	SCONJ
ejpam-5084	5	93	it	it	PRON
ejpam-5084	5	94	is	be	AUX
ejpam-5084	5	95	always	always	ADV
ejpam-5084	5	96	less	less	ADJ
ejpam-5084	5	97	than	than	ADP
ejpam-5084	5	98	or	or	CCONJ
ejpam-5084	5	99	equal	equal	ADJ
ejpam-5084	5	100	to	to	ADP
ejpam-5084	5	101	the	the	DET
ejpam-5084	5	102	standard	standard	ADJ
ejpam-5084	5	103	independence	independence	NOUN
ejpam-5084	5	104	(	(	PUNCT
ejpam-5084	5	105	resp	resp	NOUN
ejpam-5084	5	106	.	.	PUNCT
ejpam-5084	6	1	j	j	PROPN
ejpam-5084	6	2	-	-	ADJ
ejpam-5084	6	3	total	total	ADJ
ejpam-5084	6	4	domination	domination	NOUN
ejpam-5084	6	5	)	)	PUNCT
ejpam-5084	6	6	parameter	parameter	NOUN
ejpam-5084	6	7	of	of	ADP
ejpam-5084	6	8	a	a	DET
ejpam-5084	6	9	graph	graph	NOUN
ejpam-5084	6	10	.	.	PUNCT
ejpam-5084	7	1	in	in	ADP
ejpam-5084	7	2	fact	fact	NOUN
ejpam-5084	7	3	,	,	PUNCT
ejpam-5084	7	4	their	their	PRON
ejpam-5084	7	5	differences	difference	NOUN
ejpam-5084	7	6	can	can	AUX
ejpam-5084	7	7	be	be	AUX
ejpam-5084	7	8	made	make	VERB
ejpam-5084	7	9	arbitrarily	arbitrarily	ADV
ejpam-5084	7	10	large	large	ADJ
ejpam-5084	7	11	.	.	PUNCT
ejpam-5084	8	1	in	in	ADP
ejpam-5084	8	2	addition	addition	NOUN
ejpam-5084	8	3	,	,	PUNCT
ejpam-5084	8	4	we	we	PRON
ejpam-5084	8	5	show	show	VERB
ejpam-5084	8	6	that	that	SCONJ
ejpam-5084	8	7	j	j	PROPN
ejpam-5084	8	8	-	-	ADJ
ejpam-5084	8	9	open	open	ADJ
ejpam-5084	8	10	independence	independence	NOUN
ejpam-5084	8	11	parameter	parameter	NOUN
ejpam-5084	8	12	is	be	AUX
ejpam-5084	8	13	incomparable	incomparable	ADJ
ejpam-5084	8	14	with	with	ADP
ejpam-5084	8	15	hop	hop	PROPN
ejpam-5084	8	16	independence	independence	NOUN
ejpam-5084	8	17	parameter	parameter	NOUN
ejpam-5084	8	18	.	.	PUNCT
ejpam-5084	9	1	moreover	moreover	ADV
ejpam-5084	9	2	,	,	PUNCT
ejpam-5084	9	3	we	we	PRON
ejpam-5084	9	4	derive	derive	VERB
ejpam-5084	9	5	some	some	DET
ejpam-5084	9	6	formulas	formula	NOUN
ejpam-5084	9	7	and	and	CCONJ
ejpam-5084	9	8	bounds	bound	NOUN
ejpam-5084	9	9	of	of	ADP
ejpam-5084	9	10	the	the	DET
ejpam-5084	9	11	parameter	parameter	NOUN
ejpam-5084	9	12	for	for	ADP
ejpam-5084	9	13	some	some	DET
ejpam-5084	9	14	classes	class	NOUN
ejpam-5084	9	15	of	of	ADP
ejpam-5084	9	16	graphs	graph	NOUN
ejpam-5084	9	17	and	and	CCONJ
ejpam-5084	9	18	the	the	DET
ejpam-5084	9	19	join	join	NOUN
ejpam-5084	9	20	of	of	ADP
ejpam-5084	9	21	two	two	NUM
ejpam-5084	9	22	graphs	graph	NOUN
ejpam-5084	9	23	.	.	PUNCT
ejpam-5084	10	1	2020	2020	NUM
ejpam-5084	10	2	mathematics	mathematic	NOUN
ejpam-5084	10	3	subject	subject	NOUN
ejpam-5084	10	4	classifications	classification	NOUN
ejpam-5084	10	5	:	:	PUNCT
ejpam-5084	10	6	05c69	05c69	X
ejpam-5084	10	7	key	key	ADJ
ejpam-5084	10	8	words	word	NOUN
ejpam-5084	10	9	and	and	CCONJ
ejpam-5084	10	10	phrases	phrase	NOUN
ejpam-5084	10	11	:	:	PUNCT
ejpam-5084	10	12	j	j	NOUN
ejpam-5084	10	13	-	-	ADJ
ejpam-5084	10	14	open	open	ADJ
ejpam-5084	10	15	set	set	NOUN
ejpam-5084	10	16	,	,	PUNCT
ejpam-5084	10	17	j	j	NOUN
ejpam-5084	10	18	-	-	ADJ
ejpam-5084	10	19	open	open	ADJ
ejpam-5084	10	20	independent	independent	ADJ
ejpam-5084	10	21	set	set	NOUN
ejpam-5084	10	22	,	,	PUNCT
ejpam-5084	10	23	j	j	NOUN
ejpam-5084	10	24	-	-	ADJ
ejpam-5084	10	25	open	open	ADJ
ejpam-5084	10	26	independence	independence	NOUN
ejpam-5084	10	27	number	number	NOUN
ejpam-5084	10	28	1	1	NUM
ejpam-5084	10	29	.	.	PUNCT
ejpam-5084	10	30	introduction	introduction	NOUN
ejpam-5084	10	31	an	an	DET
ejpam-5084	10	32	independent	independent	ADJ
ejpam-5084	10	33	set	set	NOUN
ejpam-5084	10	34	in	in	ADP
ejpam-5084	10	35	a	a	DET
ejpam-5084	10	36	graph	graph	NOUN
ejpam-5084	10	37	is	be	AUX
ejpam-5084	10	38	a	a	DET
ejpam-5084	10	39	subset	subset	NOUN
ejpam-5084	10	40	of	of	ADP
ejpam-5084	10	41	a	a	DET
ejpam-5084	10	42	vertex	vertex	NOUN
ejpam-5084	10	43	-	-	PUNCT
ejpam-5084	10	44	set	set	NOUN
ejpam-5084	10	45	of	of	ADP
ejpam-5084	10	46	a	a	DET
ejpam-5084	10	47	graph	graph	NOUN
ejpam-5084	10	48	where	where	SCONJ
ejpam-5084	10	49	each	each	DET
ejpam-5084	10	50	pair	pair	NOUN
ejpam-5084	10	51	of	of	ADP
ejpam-5084	10	52	distinct	distinct	ADJ
ejpam-5084	10	53	vertices	vertex	NOUN
ejpam-5084	10	54	are	be	AUX
ejpam-5084	10	55	not	not	PART
ejpam-5084	10	56	of	of	ADP
ejpam-5084	10	57	distance	distance	NOUN
ejpam-5084	10	58	one	one	NUM
ejpam-5084	10	59	.	.	PUNCT
ejpam-5084	11	1	in	in	ADP
ejpam-5084	11	2	other	other	ADJ
ejpam-5084	11	3	words	word	NOUN
ejpam-5084	11	4	,	,	PUNCT
ejpam-5084	11	5	it	it	PRON
ejpam-5084	11	6	is	be	AUX
ejpam-5084	11	7	a	a	DET
ejpam-5084	11	8	set	set	NOUN
ejpam-5084	11	9	of	of	ADP
ejpam-5084	11	10	vertices	vertex	NOUN
ejpam-5084	11	11	that	that	PRON
ejpam-5084	11	12	are	be	AUX
ejpam-5084	11	13	not	not	PART
ejpam-5084	11	14	connected	connect	VERB
ejpam-5084	11	15	by	by	ADP
ejpam-5084	11	16	an	an	DET
ejpam-5084	11	17	edge	edge	NOUN
ejpam-5084	11	18	.	.	PUNCT
ejpam-5084	12	1	this	this	DET
ejpam-5084	12	2	concept	concept	NOUN
ejpam-5084	12	3	is	be	AUX
ejpam-5084	12	4	fundamental	fundamental	ADJ
ejpam-5084	12	5	in	in	ADP
ejpam-5084	12	6	graph	graph	NOUN
ejpam-5084	12	7	theory	theory	NOUN
ejpam-5084	12	8	and	and	CCONJ
ejpam-5084	12	9	has	have	VERB
ejpam-5084	12	10	a	a	DET
ejpam-5084	12	11	wide	wide	ADJ
ejpam-5084	12	12	range	range	NOUN
ejpam-5084	12	13	of	of	ADP
ejpam-5084	12	14	applications	application	NOUN
ejpam-5084	12	15	in	in	ADP
ejpam-5084	12	16	various	various	ADJ
ejpam-5084	12	17	field	field	NOUN
ejpam-5084	12	18	.	.	PUNCT
ejpam-5084	13	1	some	some	DET
ejpam-5084	13	2	studies	study	NOUN
ejpam-5084	13	3	on	on	ADP
ejpam-5084	13	4	independent	independent	ADJ
ejpam-5084	13	5	sets	set	NOUN
ejpam-5084	13	6	in	in	ADP
ejpam-5084	13	7	graphs	graph	NOUN
ejpam-5084	13	8	can	can	AUX
ejpam-5084	13	9	be	be	AUX
ejpam-5084	13	10	found	find	VERB
ejpam-5084	13	11	in	in	ADP
ejpam-5084	13	12	[	[	X
ejpam-5084	13	13	2–4	2–4	NUM
ejpam-5084	13	14	,	,	PUNCT
ejpam-5084	13	15	12	12	NUM
ejpam-5084	13	16	,	,	PUNCT
ejpam-5084	13	17	17	17	NUM
ejpam-5084	13	18	,	,	PUNCT
ejpam-5084	13	19	18	18	NUM
ejpam-5084	13	20	]	]	PUNCT
ejpam-5084	13	21	.	.	PUNCT
ejpam-5084	14	1	in	in	ADP
ejpam-5084	14	2	2022	2022	NUM
ejpam-5084	14	3	,	,	PUNCT
ejpam-5084	14	4	hop	hop	NOUN
ejpam-5084	14	5	independent	independent	ADJ
ejpam-5084	14	6	set	set	NOUN
ejpam-5084	14	7	in	in	ADP
ejpam-5084	14	8	a	a	DET
ejpam-5084	14	9	graph	graph	NOUN
ejpam-5084	14	10	and	and	CCONJ
ejpam-5084	14	11	its	its	PRON
ejpam-5084	14	12	parameter	parameter	NOUN
ejpam-5084	14	13	was	be	AUX
ejpam-5084	14	14	introduced	introduce	VERB
ejpam-5084	14	15	by	by	ADP
ejpam-5084	14	16	hassan	hassan	PROPN
ejpam-5084	14	17	et	et	PROPN
ejpam-5084	14	18	al	al	PROPN
ejpam-5084	14	19	.	.	PUNCT
ejpam-5084	15	1	[	[	X
ejpam-5084	15	2	8	8	NUM
ejpam-5084	15	3	]	]	PUNCT
ejpam-5084	15	4	.	.	PUNCT
ejpam-5084	16	1	they	they	PRON
ejpam-5084	16	2	defined	define	VERB
ejpam-5084	16	3	a	a	DET
ejpam-5084	16	4	set	set	NOUN
ejpam-5084	16	5	s	s	NOUN
ejpam-5084	16	6	⊆	⊆	NUM
ejpam-5084	16	7	v	v	NOUN
ejpam-5084	16	8	(	(	PUNCT
ejpam-5084	16	9	g	g	NOUN
ejpam-5084	16	10	)	)	PUNCT
ejpam-5084	16	11	is	be	AUX
ejpam-5084	16	12	a	a	DET
ejpam-5084	16	13	hop	hop	NOUN
ejpam-5084	16	14	independet	independet	NOUN
ejpam-5084	16	15	set	set	NOUN
ejpam-5084	16	16	of	of	ADP
ejpam-5084	16	17	g	g	PROPN
ejpam-5084	16	18	if	if	SCONJ
ejpam-5084	16	19	any	any	DET
ejpam-5084	16	20	two	two	NUM
ejpam-5084	16	21	distinct	distinct	ADJ
ejpam-5084	16	22	vertices	vertex	NOUN
ejpam-5084	16	23	in	in	ADP
ejpam-5084	16	24	s	s	NOUN
ejpam-5084	16	25	are	be	AUX
ejpam-5084	16	26	not	not	PART
ejpam-5084	16	27	at	at	ADP
ejpam-5084	16	28	a	a	DET
ejpam-5084	16	29	distance	distance	NOUN
ejpam-5084	16	30	two	two	NUM
ejpam-5084	16	31	from	from	ADP
ejpam-5084	16	32	each	each	DET
ejpam-5084	16	33	other	other	ADJ
ejpam-5084	16	34	,	,	PUNCT
ejpam-5084	16	35	that	that	ADV
ejpam-5084	16	36	is	is	ADV
ejpam-5084	16	37	,	,	PUNCT
ejpam-5084	16	38	dg(u	dg(u	X
ejpam-5084	16	39	,	,	PUNCT
ejpam-5084	16	40	w	w	NOUN
ejpam-5084	16	41	)	)	PUNCT
ejpam-5084	16	42	̸=	̸=	PROPN
ejpam-5084	16	43	2	2	NUM
ejpam-5084	16	44	for	for	ADP
ejpam-5084	16	45	any	any	DET
ejpam-5084	16	46	distinct	distinct	ADJ
ejpam-5084	16	47	vertices	vertex	NOUN
ejpam-5084	16	48	u	u	NOUN
ejpam-5084	16	49	,	,	PUNCT
ejpam-5084	16	50	w	w	PROPN
ejpam-5084	16	51	∈	∈	PROPN
ejpam-5084	16	52	s.	s.	PROPN
ejpam-5084	16	53	the	the	DET
ejpam-5084	16	54	maximum	maximum	PROPN
ejpam-5084	16	55	cardinality	cardinality	NOUN
ejpam-5084	16	56	of	of	ADP
ejpam-5084	16	57	a	a	DET
ejpam-5084	16	58	hop	hop	NOUN
ejpam-5084	16	59	independent	independent	ADJ
ejpam-5084	16	60	set	set	NOUN
ejpam-5084	16	61	of	of	ADP
ejpam-5084	16	62	g	g	NOUN
ejpam-5084	16	63	,	,	PUNCT
ejpam-5084	16	64	∗corresponding	∗corresponde	VERB
ejpam-5084	16	65	author	author	NOUN
ejpam-5084	16	66	.	.	PUNCT
ejpam-5084	17	1	doi	doi	NOUN
ejpam-5084	17	2	:	:	PUNCT
ejpam-5084	17	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5084	https://doi.org/10.29020/nybg.ejpam.v17i2.5084	ADP
ejpam-5084	17	4	email	email	NOUN
ejpam-5084	17	5	addresses	address	NOUN
ejpam-5084	17	6	:	:	PUNCT
ejpam-5084	17	7	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-5084	17	8	(	(	PUNCT
ejpam-5084	17	9	j.	j.	PROPN
ejpam-5084	17	10	a.	a.	PROPN
ejpam-5084	17	11	hassan	hassan	PROPN
ejpam-5084	17	12	)	)	PUNCT
ejpam-5084	17	13	,	,	PUNCT
ejpam-5084	17	14	nuruddinabakar@msutawi-tawi.edu.ph	nuruddinabakar@msutawi-tawi.edu.ph	PROPN
ejpam-5084	17	15	(	(	PUNCT
ejpam-5084	17	16	n.	n.	PROPN
ejpam-5084	17	17	m.	m.	NOUN
ejpam-5084	17	18	bakar	bakar	PROPN
ejpam-5084	17	19	)	)	PUNCT
ejpam-5084	17	20	,	,	PUNCT
ejpam-5084	17	21	norwajirdagsaan@msutawi-tawi.edu.ph	norwajirdagsaan@msutawi-tawi.edu.ph	PROPN
ejpam-5084	17	22	(	(	PUNCT
ejpam-5084	17	23	n.	n.	PROPN
ejpam-5084	17	24	s.	s.	PROPN
ejpam-5084	17	25	dagsaan	dagsaan	PROPN
ejpam-5084	17	26	)	)	PUNCT
ejpam-5084	17	27	,	,	PUNCT
ejpam-5084	17	28	merceditalangamin@msutawi-tawi.edu.ph	merceditalangamin@msutawi-tawi.edu.ph	PROPN
ejpam-5084	17	29	(	(	PUNCT
ejpam-5084	17	30	m.	m.	NOUN
ejpam-5084	17	31	a.	a.	PROPN
ejpam-5084	17	32	langamin	langamin	PROPN
ejpam-5084	17	33	)	)	PUNCT
ejpam-5084	17	34	,	,	PUNCT
ejpam-5084	17	35	hannamohammad@msu-tawi-tawi.edu.ph	hannamohammad@msu-tawi-tawi.edu.ph	PROPN
ejpam-5084	17	36	(	(	PUNCT
ejpam-5084	17	37	h.	h.	PROPN
ejpam-5084	17	38	m.	m.	PROPN
ejpam-5084	17	39	mohammad	mohammad	PROPN
ejpam-5084	17	40	)	)	PUNCT
ejpam-5084	17	41	,	,	PUNCT
ejpam-5084	17	42	sistetakamdon@msu-tawi-tawi.edu.ph	sistetakamdon@msu-tawi-tawi.edu.ph	PROPN
ejpam-5084	17	43	(	(	PUNCT
ejpam-5084	17	44	s.	s.	PROPN
ejpam-5084	17	45	u.	u.	PROPN
ejpam-5084	17	46	kamdon	kamdon	PROPN
ejpam-5084	17	47	)	)	PUNCT
ejpam-5084	17	48	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5084	17	49	922	922	NUM
ejpam-5084	17	50	©	©	ADP
ejpam-5084	17	51	2024	2024	NUM
ejpam-5084	17	52	ejpam	ejpam	NOUN
ejpam-5084	17	53	all	all	DET
ejpam-5084	17	54	rights	right	NOUN
ejpam-5084	17	55	reserved	reserve	VERB
ejpam-5084	17	56	.	.	PUNCT
ejpam-5084	18	1	j.	j.	PROPN
ejpam-5084	18	2	a.	a.	PROPN
ejpam-5084	18	3	hassan	hassan	PROPN
ejpam-5084	18	4	et	et	PROPN
ejpam-5084	18	5	al	al	PROPN
ejpam-5084	18	6	.	.	PUNCT
ejpam-5084	18	7	/	/	SYM
ejpam-5084	18	8	eur	eur	PROPN
ejpam-5084	18	9	.	.	PUNCT
ejpam-5084	19	1	j.	j.	PROPN
ejpam-5084	19	2	pure	pure	PROPN
ejpam-5084	19	3	appl	appl	PROPN
ejpam-5084	19	4	.	.	PROPN
ejpam-5084	19	5	math	math	PROPN
ejpam-5084	19	6	,	,	PUNCT
ejpam-5084	19	7	17	17	NUM
ejpam-5084	19	8	(	(	PUNCT
ejpam-5084	19	9	2	2	NUM
ejpam-5084	19	10	)	)	PUNCT
ejpam-5084	19	11	(	(	PUNCT
ejpam-5084	19	12	2024	2024	NUM
ejpam-5084	19	13	)	)	PUNCT
ejpam-5084	19	14	,	,	PUNCT
ejpam-5084	19	15	922	922	NUM
ejpam-5084	19	16	-	-	SYM
ejpam-5084	19	17	930	930	NUM
ejpam-5084	19	18	923	923	NUM
ejpam-5084	19	19	denoted	denote	VERB
ejpam-5084	19	20	by	by	ADP
ejpam-5084	19	21	αh(g	αh(g	NOUN
ejpam-5084	19	22	)	)	PUNCT
ejpam-5084	19	23	,	,	PUNCT
ejpam-5084	19	24	is	be	AUX
ejpam-5084	19	25	called	call	VERB
ejpam-5084	19	26	the	the	DET
ejpam-5084	19	27	hop	hop	NOUN
ejpam-5084	19	28	independence	independence	NOUN
ejpam-5084	19	29	number	number	NOUN
ejpam-5084	19	30	of	of	ADP
ejpam-5084	19	31	g.	g.	PROPN
ejpam-5084	19	32	they	they	PRON
ejpam-5084	19	33	have	have	AUX
ejpam-5084	19	34	shown	show	VERB
ejpam-5084	19	35	that	that	SCONJ
ejpam-5084	19	36	any	any	DET
ejpam-5084	19	37	maximum	maximum	ADJ
ejpam-5084	19	38	hop	hop	NOUN
ejpam-5084	19	39	independent	independent	ADJ
ejpam-5084	19	40	set	set	NOUN
ejpam-5084	19	41	s	s	PRON
ejpam-5084	19	42	of	of	ADP
ejpam-5084	19	43	g	g	PROPN
ejpam-5084	19	44	is	be	AUX
ejpam-5084	19	45	always	always	ADV
ejpam-5084	19	46	a	a	DET
ejpam-5084	19	47	hop	hop	NOUN
ejpam-5084	19	48	dominating	dominating	NOUN
ejpam-5084	19	49	,	,	PUNCT
ejpam-5084	19	50	that	that	ADV
ejpam-5084	19	51	is	is	ADV
ejpam-5084	19	52	,	,	PUNCT
ejpam-5084	19	53	the	the	DET
ejpam-5084	19	54	hop	hop	NOUN
ejpam-5084	19	55	independence	independence	NOUN
ejpam-5084	19	56	number	number	NOUN
ejpam-5084	19	57	of	of	ADP
ejpam-5084	19	58	a	a	DET
ejpam-5084	19	59	graph	graph	NOUN
ejpam-5084	19	60	is	be	AUX
ejpam-5084	19	61	always	always	ADV
ejpam-5084	19	62	greater	great	ADJ
ejpam-5084	19	63	than	than	ADP
ejpam-5084	19	64	or	or	CCONJ
ejpam-5084	19	65	equal	equal	ADJ
ejpam-5084	19	66	to	to	ADP
ejpam-5084	19	67	the	the	DET
ejpam-5084	19	68	hop	hop	NOUN
ejpam-5084	19	69	domination	domination	PROPN
ejpam-5084	19	70	parameter	parameter	NOUN
ejpam-5084	19	71	.	.	PUNCT
ejpam-5084	20	1	moreover	moreover	ADV
ejpam-5084	20	2	,	,	PUNCT
ejpam-5084	20	3	they	they	PRON
ejpam-5084	20	4	derived	derive	VERB
ejpam-5084	20	5	some	some	DET
ejpam-5084	20	6	bounds	bound	NOUN
ejpam-5084	20	7	and	and	CCONJ
ejpam-5084	20	8	formulas	formula	NOUN
ejpam-5084	20	9	for	for	ADP
ejpam-5084	20	10	some	some	DET
ejpam-5084	20	11	special	special	ADJ
ejpam-5084	20	12	graphs	graph	NOUN
ejpam-5084	20	13	and	and	CCONJ
ejpam-5084	20	14	graphs	graph	NOUN
ejpam-5084	20	15	under	under	ADP
ejpam-5084	20	16	some	some	DET
ejpam-5084	20	17	binary	binary	ADJ
ejpam-5084	20	18	operations	operation	NOUN
ejpam-5084	20	19	.	.	PUNCT
ejpam-5084	21	1	some	some	DET
ejpam-5084	21	2	studies	study	NOUN
ejpam-5084	21	3	on	on	ADP
ejpam-5084	21	4	variants	variant	NOUN
ejpam-5084	21	5	of	of	ADP
ejpam-5084	21	6	hop	hop	NOUN
ejpam-5084	21	7	independent	independent	ADJ
ejpam-5084	21	8	sets	set	NOUN
ejpam-5084	21	9	and	and	CCONJ
ejpam-5084	21	10	other	other	ADJ
ejpam-5084	21	11	hop	hop	ADV
ejpam-5084	21	12	-	-	PUNCT
ejpam-5084	21	13	related	relate	VERB
ejpam-5084	21	14	concepts	concept	NOUN
ejpam-5084	21	15	can	can	AUX
ejpam-5084	21	16	be	be	AUX
ejpam-5084	21	17	found	find	VERB
ejpam-5084	21	18	in	in	ADP
ejpam-5084	21	19	[	[	X
ejpam-5084	21	20	1	1	NUM
ejpam-5084	21	21	,	,	PUNCT
ejpam-5084	21	22	5–7	5–7	NUM
ejpam-5084	21	23	,	,	PUNCT
ejpam-5084	21	24	9	9	NUM
ejpam-5084	21	25	,	,	PUNCT
ejpam-5084	21	26	11	11	NUM
ejpam-5084	21	27	,	,	PUNCT
ejpam-5084	21	28	13–16	13–16	NUM
ejpam-5084	21	29	]	]	PUNCT
ejpam-5084	21	30	in	in	ADP
ejpam-5084	21	31	this	this	DET
ejpam-5084	21	32	paper	paper	NOUN
ejpam-5084	21	33	,	,	PUNCT
ejpam-5084	21	34	we	we	PRON
ejpam-5084	21	35	introduce	introduce	VERB
ejpam-5084	21	36	new	new	ADJ
ejpam-5084	21	37	independence	independence	NOUN
ejpam-5084	21	38	parameter	parameter	NOUN
ejpam-5084	21	39	called	call	VERB
ejpam-5084	21	40	j	j	NOUN
ejpam-5084	21	41	-	-	ADJ
ejpam-5084	21	42	open	open	ADJ
ejpam-5084	21	43	independence	independence	NOUN
ejpam-5084	21	44	.	.	PUNCT
ejpam-5084	22	1	we	we	PRON
ejpam-5084	22	2	investigate	investigate	VERB
ejpam-5084	22	3	this	this	DET
ejpam-5084	22	4	concept	concept	NOUN
ejpam-5084	22	5	on	on	ADP
ejpam-5084	22	6	some	some	DET
ejpam-5084	22	7	families	family	NOUN
ejpam-5084	22	8	of	of	ADP
ejpam-5084	22	9	graphs	graph	NOUN
ejpam-5084	22	10	and	and	CCONJ
ejpam-5084	22	11	on	on	ADP
ejpam-5084	22	12	the	the	DET
ejpam-5084	22	13	join	join	NOUN
ejpam-5084	22	14	of	of	ADP
ejpam-5084	22	15	two	two	NUM
ejpam-5084	22	16	graphs	graph	NOUN
ejpam-5084	22	17	.	.	PUNCT
ejpam-5084	23	1	we	we	PRON
ejpam-5084	23	2	believe	believe	VERB
ejpam-5084	23	3	,	,	PUNCT
ejpam-5084	23	4	the	the	DET
ejpam-5084	23	5	results	result	NOUN
ejpam-5084	23	6	of	of	ADP
ejpam-5084	23	7	this	this	DET
ejpam-5084	23	8	study	study	NOUN
ejpam-5084	23	9	could	could	AUX
ejpam-5084	23	10	led	lead	VERB
ejpam-5084	23	11	to	to	ADP
ejpam-5084	23	12	other	other	ADJ
ejpam-5084	23	13	interesting	interesting	ADJ
ejpam-5084	23	14	research	research	NOUN
ejpam-5084	23	15	directions	direction	NOUN
ejpam-5084	23	16	in	in	ADP
ejpam-5084	23	17	the	the	DET
ejpam-5084	23	18	future	future	NOUN
ejpam-5084	23	19	.	.	PUNCT
ejpam-5084	24	1	2	2	X
ejpam-5084	24	2	.	.	X
ejpam-5084	24	3	terminology	terminology	NOUN
ejpam-5084	24	4	and	and	CCONJ
ejpam-5084	24	5	notation	notation	NOUN
ejpam-5084	24	6	let	let	VERB
ejpam-5084	24	7	g	g	NOUN
ejpam-5084	24	8	=	=	SYM
ejpam-5084	24	9	(	(	PUNCT
ejpam-5084	24	10	v	v	NOUN
ejpam-5084	24	11	(	(	PUNCT
ejpam-5084	24	12	g	g	NOUN
ejpam-5084	24	13	)	)	PUNCT
ejpam-5084	24	14	,	,	PUNCT
ejpam-5084	24	15	e(g	e(g	PROPN
ejpam-5084	24	16	)	)	PUNCT
ejpam-5084	24	17	)	)	PUNCT
ejpam-5084	24	18	be	be	AUX
ejpam-5084	24	19	a	a	DET
ejpam-5084	24	20	simple	simple	ADJ
ejpam-5084	24	21	and	and	CCONJ
ejpam-5084	24	22	undirected	undirected	ADJ
ejpam-5084	24	23	graph	graph	NOUN
ejpam-5084	24	24	.	.	PUNCT
ejpam-5084	25	1	the	the	DET
ejpam-5084	25	2	distance	distance	NOUN
ejpam-5084	25	3	dg(u	dg(u	NOUN
ejpam-5084	25	4	,	,	PUNCT
ejpam-5084	25	5	v	v	NOUN
ejpam-5084	25	6	)	)	PUNCT
ejpam-5084	25	7	in	in	ADP
ejpam-5084	25	8	g	g	NOUN
ejpam-5084	25	9	of	of	ADP
ejpam-5084	25	10	two	two	NUM
ejpam-5084	25	11	vertices	vertex	NOUN
ejpam-5084	25	12	u	u	NOUN
ejpam-5084	25	13	,	,	PUNCT
ejpam-5084	25	14	v	v	PROPN
ejpam-5084	25	15	is	be	AUX
ejpam-5084	25	16	the	the	DET
ejpam-5084	25	17	length	length	NOUN
ejpam-5084	25	18	of	of	ADP
ejpam-5084	25	19	a	a	DET
ejpam-5084	25	20	shortest	short	ADJ
ejpam-5084	25	21	u	u	NOUN
ejpam-5084	25	22	-	-	NOUN
ejpam-5084	25	23	v	v	ADJ
ejpam-5084	25	24	path	path	NOUN
ejpam-5084	25	25	in	in	ADP
ejpam-5084	25	26	g.	g.	PROPN
ejpam-5084	25	27	the	the	DET
ejpam-5084	25	28	greatest	great	ADJ
ejpam-5084	25	29	distance	distance	NOUN
ejpam-5084	25	30	between	between	ADP
ejpam-5084	25	31	any	any	DET
ejpam-5084	25	32	two	two	NUM
ejpam-5084	25	33	vertices	vertex	NOUN
ejpam-5084	25	34	in	in	ADP
ejpam-5084	25	35	g	g	NOUN
ejpam-5084	25	36	,	,	PUNCT
ejpam-5084	25	37	denoted	denote	VERB
ejpam-5084	25	38	by	by	ADP
ejpam-5084	25	39	diam(g	diam(g	PROPN
ejpam-5084	25	40	)	)	PUNCT
ejpam-5084	25	41	,	,	PUNCT
ejpam-5084	25	42	is	be	AUX
ejpam-5084	25	43	called	call	VERB
ejpam-5084	25	44	the	the	DET
ejpam-5084	25	45	diameter	diameter	NOUN
ejpam-5084	25	46	of	of	ADP
ejpam-5084	25	47	g.	g.	PROPN
ejpam-5084	25	48	two	two	NUM
ejpam-5084	25	49	vertices	vertice	VERB
ejpam-5084	25	50	x	x	X
ejpam-5084	25	51	,	,	PUNCT
ejpam-5084	25	52	y	y	PROPN
ejpam-5084	25	53	of	of	ADP
ejpam-5084	25	54	g	g	PROPN
ejpam-5084	25	55	are	be	AUX
ejpam-5084	25	56	adjacent	adjacent	ADJ
ejpam-5084	25	57	,	,	PUNCT
ejpam-5084	25	58	or	or	CCONJ
ejpam-5084	25	59	neighbors	neighbor	NOUN
ejpam-5084	25	60	,	,	PUNCT
ejpam-5084	25	61	if	if	SCONJ
ejpam-5084	25	62	xy	xy	PROPN
ejpam-5084	25	63	is	be	AUX
ejpam-5084	25	64	an	an	DET
ejpam-5084	25	65	edge	edge	NOUN
ejpam-5084	25	66	of	of	ADP
ejpam-5084	25	67	g.	g.	PROPN
ejpam-5084	25	68	the	the	DET
ejpam-5084	25	69	open	open	ADJ
ejpam-5084	25	70	neighborhood	neighborhood	NOUN
ejpam-5084	25	71	of	of	ADP
ejpam-5084	25	72	x	x	PUNCT
ejpam-5084	25	73	in	in	ADP
ejpam-5084	25	74	g	g	PROPN
ejpam-5084	25	75	is	be	AUX
ejpam-5084	25	76	the	the	DET
ejpam-5084	25	77	set	set	NOUN
ejpam-5084	25	78	ng(x	ng(x	NUM
ejpam-5084	25	79	)	)	PUNCT
ejpam-5084	25	80	=	=	PRON
ejpam-5084	25	81	{	{	PUNCT
ejpam-5084	25	82	y	y	PROPN
ejpam-5084	25	83	∈	∈	PROPN
ejpam-5084	25	84	v	v	NOUN
ejpam-5084	25	85	(	(	PUNCT
ejpam-5084	25	86	g	g	NOUN
ejpam-5084	25	87	)	)	PUNCT
ejpam-5084	25	88	:	:	PUNCT
ejpam-5084	25	89	xy	xy	PROPN
ejpam-5084	25	90	∈	∈	PROPN
ejpam-5084	25	91	e(g	e(g	PROPN
ejpam-5084	25	92	)	)	PUNCT
ejpam-5084	25	93	}	}	PUNCT
ejpam-5084	25	94	.	.	PUNCT
ejpam-5084	26	1	the	the	DET
ejpam-5084	26	2	closed	closed	ADJ
ejpam-5084	26	3	neighborhood	neighborhood	NOUN
ejpam-5084	26	4	of	of	ADP
ejpam-5084	26	5	x	x	SYM
ejpam-5084	26	6	ing	ing	NOUN
ejpam-5084	26	7	is	be	AUX
ejpam-5084	26	8	the	the	DET
ejpam-5084	26	9	setng[x	setng[x	NOUN
ejpam-5084	26	10	]	]	X
ejpam-5084	26	11	=	=	SYM
ejpam-5084	26	12	ng(x)∪{x	ng(x)∪{x	NOUN
ejpam-5084	26	13	}	}	PUNCT
ejpam-5084	26	14	.	.	PUNCT
ejpam-5084	27	1	ifx	ifx	PROPN
ejpam-5084	27	2	⊆	⊆	NUM
ejpam-5084	27	3	v	v	NOUN
ejpam-5084	27	4	(	(	PUNCT
ejpam-5084	27	5	g	g	NOUN
ejpam-5084	27	6	)	)	PUNCT
ejpam-5084	27	7	,	,	PUNCT
ejpam-5084	27	8	the	the	DET
ejpam-5084	27	9	open	open	ADJ
ejpam-5084	27	10	neighborhood	neighborhood	NOUN
ejpam-5084	27	11	of	of	ADP
ejpam-5084	27	12	x	x	PUNCT
ejpam-5084	27	13	in	in	ADP
ejpam-5084	27	14	g	g	PROPN
ejpam-5084	27	15	is	be	AUX
ejpam-5084	27	16	the	the	DET
ejpam-5084	27	17	set	set	NOUN
ejpam-5084	27	18	ng(x	ng(x	NUM
ejpam-5084	27	19	)	)	PUNCT
ejpam-5084	28	1	=	=	SYM
ejpam-5084	28	2	⋃	⋃	NOUN
ejpam-5084	28	3	x∈x	x∈x	NOUN
ejpam-5084	28	4	ng(x	ng(x	NUM
ejpam-5084	28	5	)	)	PUNCT
ejpam-5084	28	6	.	.	PUNCT
ejpam-5084	29	1	the	the	DET
ejpam-5084	29	2	closed	closed	ADJ
ejpam-5084	29	3	neighborhood	neighborhood	NOUN
ejpam-5084	29	4	of	of	ADP
ejpam-5084	29	5	x	x	PUNCT
ejpam-5084	29	6	in	in	ADP
ejpam-5084	29	7	g	g	PROPN
ejpam-5084	29	8	is	be	AUX
ejpam-5084	29	9	the	the	DET
ejpam-5084	29	10	set	set	NOUN
ejpam-5084	29	11	ng[x	ng[x	PROPN
ejpam-5084	29	12	]	]	X
ejpam-5084	29	13	=	=	PUNCT
ejpam-5084	29	14	ng(x	ng(x	X
ejpam-5084	29	15	)	)	PUNCT
ejpam-5084	30	1	∪x	∪x	PROPN
ejpam-5084	30	2	.	.	PUNCT
ejpam-5084	31	1	a	a	DET
ejpam-5084	31	2	subset	subset	NOUN
ejpam-5084	31	3	d	d	NOUN
ejpam-5084	31	4	=	=	PUNCT
ejpam-5084	31	5	{	{	PUNCT
ejpam-5084	31	6	d1	d1	PROPN
ejpam-5084	31	7	,	,	PUNCT
ejpam-5084	31	8	d2	d2	PROPN
ejpam-5084	31	9	,	,	PUNCT
ejpam-5084	31	10	·	·	PUNCT
ejpam-5084	31	11	·	·	PUNCT
ejpam-5084	31	12	·	·	PUNCT
ejpam-5084	31	13	,	,	PUNCT
ejpam-5084	31	14	dm	dm	INTJ
ejpam-5084	31	15	}	}	PUNCT
ejpam-5084	31	16	of	of	ADP
ejpam-5084	31	17	vertices	vertex	NOUN
ejpam-5084	31	18	of	of	ADP
ejpam-5084	31	19	g	g	PROPN
ejpam-5084	31	20	is	be	AUX
ejpam-5084	31	21	called	call	VERB
ejpam-5084	31	22	a	a	DET
ejpam-5084	31	23	j	j	NOUN
ejpam-5084	31	24	-	-	ADJ
ejpam-5084	31	25	open	open	ADJ
ejpam-5084	31	26	set	set	NOUN
ejpam-5084	31	27	if	if	SCONJ
ejpam-5084	31	28	ng(di	ng(di	NOUN
ejpam-5084	31	29	)	)	PUNCT
ejpam-5084	31	30	\ng(dj	\ng(dj	NOUN
ejpam-5084	31	31	)	)	PUNCT
ejpam-5084	31	32	̸=	̸=	NOUN
ejpam-5084	31	33	∅	∅	NOUN
ejpam-5084	31	34	for	for	ADP
ejpam-5084	31	35	every	every	DET
ejpam-5084	31	36	i	i	PROPN
ejpam-5084	31	37	̸=	̸=	PROPN
ejpam-5084	31	38	j	j	PROPN
ejpam-5084	31	39	,	,	PUNCT
ejpam-5084	31	40	where	where	SCONJ
ejpam-5084	31	41	i	i	PRON
ejpam-5084	31	42	,	,	PUNCT
ejpam-5084	31	43	j	j	PROPN
ejpam-5084	31	44	∈	∈	PROPN
ejpam-5084	31	45	{	{	PUNCT
ejpam-5084	31	46	1	1	NUM
ejpam-5084	31	47	,	,	PUNCT
ejpam-5084	31	48	2	2	NUM
ejpam-5084	31	49	,	,	PUNCT
ejpam-5084	31	50	.	.	PUNCT
ejpam-5084	31	51	.	.	PUNCT
ejpam-5084	32	1	.	.	PUNCT
ejpam-5084	33	1	,	,	PUNCT
ejpam-5084	33	2	m	m	VERB
ejpam-5084	33	3	}	}	PUNCT
ejpam-5084	33	4	.	.	PUNCT
ejpam-5084	34	1	a	a	DET
ejpam-5084	34	2	j	j	NOUN
ejpam-5084	34	3	-	-	ADJ
ejpam-5084	34	4	open	open	ADJ
ejpam-5084	34	5	set	set	NOUN
ejpam-5084	34	6	is	be	AUX
ejpam-5084	34	7	called	call	VERB
ejpam-5084	34	8	a	a	DET
ejpam-5084	34	9	j	j	PROPN
ejpam-5084	34	10	-	-	ADJ
ejpam-5084	34	11	total	total	ADJ
ejpam-5084	34	12	dominating	dominating	NOUN
ejpam-5084	34	13	set	set	NOUN
ejpam-5084	34	14	of	of	ADP
ejpam-5084	34	15	g	g	PROPN
ejpam-5084	34	16	if	if	SCONJ
ejpam-5084	34	17	d	d	PROPN
ejpam-5084	34	18	=	=	PRON
ejpam-5084	34	19	{	{	PUNCT
ejpam-5084	34	20	d1	d1	PROPN
ejpam-5084	34	21	,	,	PUNCT
ejpam-5084	34	22	d2	d2	PROPN
ejpam-5084	34	23	,	,	PUNCT
ejpam-5084	34	24	.	.	PUNCT
ejpam-5084	34	25	.	.	PUNCT
ejpam-5084	35	1	.	.	PUNCT
ejpam-5084	36	1	,	,	PUNCT
ejpam-5084	36	2	dm	dm	PROPN
ejpam-5084	36	3	}	}	PUNCT
ejpam-5084	36	4	is	be	AUX
ejpam-5084	36	5	a	a	DET
ejpam-5084	36	6	total	total	ADJ
ejpam-5084	36	7	dominating	dominating	NOUN
ejpam-5084	36	8	set	set	NOUN
ejpam-5084	36	9	of	of	ADP
ejpam-5084	36	10	g.	g.	PROPN
ejpam-5084	36	11	the	the	DET
ejpam-5084	36	12	j	j	PROPN
ejpam-5084	36	13	-	-	ADJ
ejpam-5084	36	14	total	total	ADJ
ejpam-5084	36	15	domination	domination	NOUN
ejpam-5084	36	16	number	number	NOUN
ejpam-5084	36	17	of	of	ADP
ejpam-5084	36	18	g	g	NOUN
ejpam-5084	36	19	,	,	PUNCT
ejpam-5084	36	20	denoted	denote	VERB
ejpam-5084	36	21	by	by	ADP
ejpam-5084	36	22	γjt(g	γjt(g	PROPN
ejpam-5084	36	23	)	)	PUNCT
ejpam-5084	36	24	,	,	PUNCT
ejpam-5084	36	25	is	be	AUX
ejpam-5084	36	26	the	the	DET
ejpam-5084	36	27	maximum	maximum	ADJ
ejpam-5084	36	28	cardinality	cardinality	NOUN
ejpam-5084	36	29	of	of	ADP
ejpam-5084	36	30	a	a	DET
ejpam-5084	36	31	j	j	PROPN
ejpam-5084	36	32	-	-	ADJ
ejpam-5084	36	33	total	total	ADJ
ejpam-5084	36	34	dominating	dominating	NOUN
ejpam-5084	36	35	set	set	NOUN
ejpam-5084	36	36	of	of	ADP
ejpam-5084	36	37	g	g	PROPN
ejpam-5084	36	38	[	[	X
ejpam-5084	36	39	10	10	NUM
ejpam-5084	36	40	]	]	PUNCT
ejpam-5084	36	41	.	.	PUNCT
ejpam-5084	37	1	a	a	DET
ejpam-5084	37	2	path	path	NOUN
ejpam-5084	37	3	graph	graph	NOUN
ejpam-5084	37	4	is	be	AUX
ejpam-5084	37	5	a	a	DET
ejpam-5084	37	6	non	non	ADJ
ejpam-5084	37	7	-	-	ADJ
ejpam-5084	37	8	empty	empty	ADJ
ejpam-5084	37	9	graph	graph	NOUN
ejpam-5084	37	10	with	with	ADP
ejpam-5084	37	11	vertex	vertex	NOUN
ejpam-5084	37	12	-	-	PUNCT
ejpam-5084	37	13	set	set	VERB
ejpam-5084	37	14	{	{	PUNCT
ejpam-5084	37	15	x1	x1	PROPN
ejpam-5084	37	16	,	,	PUNCT
ejpam-5084	37	17	x2	x2	PROPN
ejpam-5084	37	18	,	,	PUNCT
ejpam-5084	37	19	.	.	PUNCT
ejpam-5084	37	20	.	.	PUNCT
ejpam-5084	38	1	.	.	PUNCT
ejpam-5084	39	1	,	,	PUNCT
ejpam-5084	39	2	xn	xn	X
ejpam-5084	39	3	}	}	PUNCT
ejpam-5084	39	4	and	and	CCONJ
ejpam-5084	39	5	edge	edge	NOUN
ejpam-5084	39	6	-	-	PUNCT
ejpam-5084	39	7	set	set	NOUN
ejpam-5084	39	8	{	{	PUNCT
ejpam-5084	39	9	x1x2	x1x2	NOUN
ejpam-5084	39	10	,	,	PUNCT
ejpam-5084	39	11	x2x3	x2x3	PROPN
ejpam-5084	39	12	,	,	PUNCT
ejpam-5084	39	13	.	.	PUNCT
ejpam-5084	39	14	.	.	PUNCT
ejpam-5084	40	1	.	.	PUNCT
ejpam-5084	41	1	,	,	PUNCT
ejpam-5084	41	2	xn−1xn	xn−1xn	PROPN
ejpam-5084	41	3	}	}	PUNCT
ejpam-5084	41	4	,	,	PUNCT
ejpam-5084	41	5	where	where	SCONJ
ejpam-5084	41	6	the	the	DET
ejpam-5084	41	7	x	x	NOUN
ejpam-5084	41	8	′	′	NOUN
ejpam-5084	41	9	is	be	AUX
ejpam-5084	41	10	are	be	AUX
ejpam-5084	41	11	all	all	ADV
ejpam-5084	41	12	distinct	distinct	ADJ
ejpam-5084	41	13	.	.	PUNCT
ejpam-5084	42	1	the	the	DET
ejpam-5084	42	2	path	path	NOUN
ejpam-5084	42	3	of	of	ADP
ejpam-5084	42	4	order	order	NOUN
ejpam-5084	42	5	n	n	NOUN
ejpam-5084	42	6	is	be	AUX
ejpam-5084	42	7	denoted	denote	VERB
ejpam-5084	42	8	by	by	ADP
ejpam-5084	42	9	pn	pn	PROPN
ejpam-5084	42	10	.	.	PUNCT
ejpam-5084	43	1	if	if	SCONJ
ejpam-5084	43	2	g	g	PROPN
ejpam-5084	43	3	is	be	AUX
ejpam-5084	43	4	a	a	DET
ejpam-5084	43	5	graph	graph	NOUN
ejpam-5084	43	6	and	and	CCONJ
ejpam-5084	43	7	u	u	NOUN
ejpam-5084	43	8	and	and	CCONJ
ejpam-5084	43	9	v	v	NOUN
ejpam-5084	43	10	are	be	AUX
ejpam-5084	43	11	vertices	vertex	NOUN
ejpam-5084	43	12	of	of	ADP
ejpam-5084	43	13	g	g	NOUN
ejpam-5084	43	14	,	,	PUNCT
ejpam-5084	43	15	then	then	ADV
ejpam-5084	43	16	a	a	DET
ejpam-5084	43	17	path	path	NOUN
ejpam-5084	43	18	from	from	ADP
ejpam-5084	43	19	vertex	vertex	NOUN
ejpam-5084	43	20	u	u	NOUN
ejpam-5084	43	21	to	to	PART
ejpam-5084	43	22	vertex	vertex	NOUN
ejpam-5084	43	23	v	v	NOUN
ejpam-5084	43	24	is	be	AUX
ejpam-5084	43	25	sometimes	sometimes	ADV
ejpam-5084	43	26	called	call	VERB
ejpam-5084	43	27	a	a	DET
ejpam-5084	43	28	u	u	NOUN
ejpam-5084	43	29	-	-	NOUN
ejpam-5084	43	30	v	v	ADJ
ejpam-5084	43	31	path	path	NOUN
ejpam-5084	43	32	.	.	PUNCT
ejpam-5084	44	1	the	the	DET
ejpam-5084	44	2	cycle	cycle	NOUN
ejpam-5084	44	3	graph	graph	NOUN
ejpam-5084	44	4	cn	cn	PROPN
ejpam-5084	44	5	is	be	AUX
ejpam-5084	44	6	the	the	DET
ejpam-5084	44	7	graph	graph	NOUN
ejpam-5084	44	8	of	of	ADP
ejpam-5084	44	9	order	order	NOUN
ejpam-5084	44	10	n	n	PRON
ejpam-5084	44	11	≥	≥	NOUN
ejpam-5084	44	12	3	3	NUM
ejpam-5084	44	13	with	with	ADP
ejpam-5084	44	14	vertex	vertex	NOUN
ejpam-5084	44	15	-	-	PUNCT
ejpam-5084	44	16	set	set	VERB
ejpam-5084	44	17	{	{	PUNCT
ejpam-5084	44	18	x1	x1	PROPN
ejpam-5084	44	19	,	,	PUNCT
ejpam-5084	44	20	x2	x2	PROPN
ejpam-5084	44	21	,	,	PUNCT
ejpam-5084	44	22	.	.	PUNCT
ejpam-5084	44	23	.	.	PUNCT
ejpam-5084	44	24	.	.	PUNCT
ejpam-5084	45	1	,	,	PUNCT
ejpam-5084	45	2	xn	xn	X
ejpam-5084	45	3	}	}	PUNCT
ejpam-5084	45	4	and	and	CCONJ
ejpam-5084	45	5	edge	edge	NOUN
ejpam-5084	45	6	-	-	PUNCT
ejpam-5084	45	7	set	set	NOUN
ejpam-5084	45	8	{	{	PUNCT
ejpam-5084	45	9	x1x2	x1x2	NOUN
ejpam-5084	45	10	,	,	PUNCT
ejpam-5084	45	11	x2x3	x2x3	PROPN
ejpam-5084	45	12	,	,	PUNCT
ejpam-5084	45	13	.	.	PUNCT
ejpam-5084	45	14	.	.	PUNCT
ejpam-5084	46	1	.	.	PUNCT
ejpam-5084	47	1	,	,	PUNCT
ejpam-5084	47	2	xn−1xn	xn−1xn	PROPN
ejpam-5084	47	3	,	,	PUNCT
ejpam-5084	47	4	xnx1	xnx1	PROPN
ejpam-5084	47	5	}	}	PUNCT
ejpam-5084	47	6	.	.	PUNCT
ejpam-5084	48	1	let	let	VERB
ejpam-5084	48	2	g	g	NOUN
ejpam-5084	48	3	and	and	CCONJ
ejpam-5084	48	4	h	h	NOUN
ejpam-5084	48	5	be	be	VERB
ejpam-5084	48	6	any	any	DET
ejpam-5084	48	7	two	two	NUM
ejpam-5084	48	8	graphs	graph	NOUN
ejpam-5084	48	9	.	.	PUNCT
ejpam-5084	49	1	the	the	DET
ejpam-5084	49	2	join	join	NOUN
ejpam-5084	49	3	of	of	ADP
ejpam-5084	49	4	g	g	PROPN
ejpam-5084	49	5	and	and	CCONJ
ejpam-5084	49	6	h	h	NOUN
ejpam-5084	49	7	,	,	PUNCT
ejpam-5084	49	8	denoted	denote	VERB
ejpam-5084	49	9	by	by	ADP
ejpam-5084	49	10	g	g	PROPN
ejpam-5084	49	11	+	+	CCONJ
ejpam-5084	49	12	h	h	NOUN
ejpam-5084	49	13	is	be	AUX
ejpam-5084	49	14	the	the	DET
ejpam-5084	49	15	graph	graph	NOUN
ejpam-5084	49	16	with	with	ADP
ejpam-5084	49	17	vertex	vertex	NOUN
ejpam-5084	49	18	set	set	VERB
ejpam-5084	49	19	v	v	NOUN
ejpam-5084	49	20	(	(	PUNCT
ejpam-5084	49	21	g+h	g+h	NOUN
ejpam-5084	49	22	)	)	PUNCT
ejpam-5084	49	23	=	=	SYM
ejpam-5084	49	24	v	v	X
ejpam-5084	49	25	(	(	PUNCT
ejpam-5084	49	26	g	g	NOUN
ejpam-5084	49	27	)	)	PUNCT
ejpam-5084	49	28	∪	∪	NOUN
ejpam-5084	49	29	v	v	NOUN
ejpam-5084	49	30	(	(	PUNCT
ejpam-5084	49	31	h	h	NOUN
ejpam-5084	49	32	)	)	PUNCT
ejpam-5084	49	33	and	and	CCONJ
ejpam-5084	49	34	edge	edge	NOUN
ejpam-5084	49	35	set	set	VERB
ejpam-5084	49	36	e(g+h	e(g+h	NUM
ejpam-5084	49	37	)	)	PUNCT
ejpam-5084	49	38	=	=	SYM
ejpam-5084	49	39	e(g	e(g	NOUN
ejpam-5084	49	40	)	)	PUNCT
ejpam-5084	49	41	∪	∪	ADP
ejpam-5084	49	42	e(h	e(h	PROPN
ejpam-5084	49	43	)	)	PUNCT
ejpam-5084	49	44	∪	∪	NOUN
ejpam-5084	49	45	{	{	PUNCT
ejpam-5084	49	46	uv	uv	NOUN
ejpam-5084	49	47	:	:	PUNCT
ejpam-5084	49	48	u	u	PROPN
ejpam-5084	49	49	∈	∈	PROPN
ejpam-5084	49	50	v	v	ADP
ejpam-5084	49	51	(	(	PUNCT
ejpam-5084	49	52	g	g	NOUN
ejpam-5084	49	53	)	)	PUNCT
ejpam-5084	49	54	,	,	PUNCT
ejpam-5084	49	55	v	v	X
ejpam-5084	49	56	∈	∈	PROPN
ejpam-5084	49	57	v	v	NOUN
ejpam-5084	49	58	(	(	PUNCT
ejpam-5084	49	59	h	h	NOUN
ejpam-5084	49	60	)	)	PUNCT
ejpam-5084	49	61	}	}	PUNCT
ejpam-5084	49	62	.	.	PUNCT
ejpam-5084	50	1	a	a	DET
ejpam-5084	50	2	subset	subset	NOUN
ejpam-5084	50	3	s	s	X
ejpam-5084	50	4	of	of	ADP
ejpam-5084	50	5	v	v	NOUN
ejpam-5084	50	6	(	(	PUNCT
ejpam-5084	50	7	g	g	NOUN
ejpam-5084	50	8	)	)	PUNCT
ejpam-5084	50	9	is	be	AUX
ejpam-5084	50	10	called	call	VERB
ejpam-5084	50	11	a	a	DET
ejpam-5084	50	12	independent	independent	ADJ
ejpam-5084	50	13	if	if	SCONJ
ejpam-5084	50	14	for	for	ADP
ejpam-5084	50	15	every	every	DET
ejpam-5084	50	16	pair	pair	NOUN
ejpam-5084	50	17	of	of	ADP
ejpam-5084	50	18	distinct	distinct	ADJ
ejpam-5084	50	19	vertices	vertex	NOUN
ejpam-5084	50	20	x	x	X
ejpam-5084	50	21	,	,	PUNCT
ejpam-5084	50	22	y	y	PROPN
ejpam-5084	50	23	∈	∈	PROPN
ejpam-5084	50	24	s	s	PROPN
ejpam-5084	50	25	,	,	PUNCT
ejpam-5084	50	26	dg(x	dg(x	NUM
ejpam-5084	50	27	,	,	PUNCT
ejpam-5084	50	28	y	y	NOUN
ejpam-5084	50	29	)	)	PUNCT
ejpam-5084	50	30	̸=	̸=	PROPN
ejpam-5084	50	31	1	1	NUM
ejpam-5084	50	32	.	.	PUNCT
ejpam-5084	51	1	the	the	DET
ejpam-5084	51	2	maximum	maximum	ADJ
ejpam-5084	51	3	cardinality	cardinality	NOUN
ejpam-5084	51	4	of	of	ADP
ejpam-5084	51	5	a	a	DET
ejpam-5084	51	6	independent	independent	ADJ
ejpam-5084	51	7	set	set	NOUN
ejpam-5084	51	8	in	in	ADP
ejpam-5084	51	9	g	g	NOUN
ejpam-5084	51	10	,	,	PUNCT
ejpam-5084	51	11	denoted	denote	VERB
ejpam-5084	51	12	by	by	ADP
ejpam-5084	51	13	α(g	α(g	NOUN
ejpam-5084	51	14	)	)	PUNCT
ejpam-5084	51	15	,	,	PUNCT
ejpam-5084	51	16	is	be	AUX
ejpam-5084	51	17	called	call	VERB
ejpam-5084	51	18	the	the	DET
ejpam-5084	51	19	independence	independence	NOUN
ejpam-5084	51	20	number	number	NOUN
ejpam-5084	51	21	of	of	ADP
ejpam-5084	51	22	g.	g.	PROPN
ejpam-5084	51	23	any	any	DET
ejpam-5084	51	24	independent	independent	ADJ
ejpam-5084	51	25	set	set	NOUN
ejpam-5084	51	26	s	s	PROPN
ejpam-5084	51	27	with	with	ADP
ejpam-5084	51	28	cardinality	cardinality	NOUN
ejpam-5084	51	29	equal	equal	ADJ
ejpam-5084	51	30	to	to	ADP
ejpam-5084	51	31	α(g	α(g	NUM
ejpam-5084	51	32	)	)	PUNCT
ejpam-5084	51	33	is	be	AUX
ejpam-5084	51	34	called	call	VERB
ejpam-5084	51	35	an	an	DET
ejpam-5084	51	36	α	α	NOUN
ejpam-5084	51	37	-	-	PUNCT
ejpam-5084	51	38	set	set	NOUN
ejpam-5084	51	39	of	of	ADP
ejpam-5084	51	40	g.	g.	PROPN
ejpam-5084	51	41	a	a	DET
ejpam-5084	51	42	subset	subset	NOUN
ejpam-5084	51	43	s	s	NOUN
ejpam-5084	51	44	of	of	ADP
ejpam-5084	51	45	v	v	NOUN
ejpam-5084	51	46	(	(	PUNCT
ejpam-5084	51	47	g	g	NOUN
ejpam-5084	51	48	)	)	PUNCT
ejpam-5084	51	49	is	be	AUX
ejpam-5084	51	50	called	call	VERB
ejpam-5084	51	51	a	a	DET
ejpam-5084	51	52	hop	hop	NOUN
ejpam-5084	51	53	independent	independent	ADJ
ejpam-5084	51	54	set	set	NOUN
ejpam-5084	51	55	of	of	ADP
ejpam-5084	51	56	g	g	PROPN
ejpam-5084	51	57	if	if	SCONJ
ejpam-5084	51	58	any	any	DET
ejpam-5084	51	59	two	two	NUM
ejpam-5084	51	60	distinct	distinct	ADJ
ejpam-5084	51	61	vertices	vertex	NOUN
ejpam-5084	51	62	in	in	ADP
ejpam-5084	51	63	s	s	NOUN
ejpam-5084	51	64	are	be	AUX
ejpam-5084	51	65	not	not	PART
ejpam-5084	51	66	at	at	ADP
ejpam-5084	51	67	distance	distance	NOUN
ejpam-5084	51	68	two	two	NUM
ejpam-5084	51	69	from	from	ADP
ejpam-5084	51	70	each	each	DET
ejpam-5084	51	71	other	other	ADJ
ejpam-5084	51	72	,	,	PUNCT
ejpam-5084	51	73	that	that	ADV
ejpam-5084	51	74	is	is	ADV
ejpam-5084	51	75	,	,	PUNCT
ejpam-5084	51	76	dg(v	dg(v	X
ejpam-5084	51	77	,	,	PUNCT
ejpam-5084	51	78	w	w	NOUN
ejpam-5084	51	79	)	)	PUNCT
ejpam-5084	51	80	̸=	̸=	PROPN
ejpam-5084	51	81	2	2	NUM
ejpam-5084	51	82	for	for	ADP
ejpam-5084	51	83	any	any	DET
ejpam-5084	51	84	two	two	NUM
ejpam-5084	51	85	distinct	distinct	ADJ
ejpam-5084	51	86	j.	j.	PROPN
ejpam-5084	51	87	a.	a.	PROPN
ejpam-5084	51	88	hassan	hassan	PROPN
ejpam-5084	51	89	et	et	PROPN
ejpam-5084	51	90	al	al	PROPN
ejpam-5084	51	91	.	.	PUNCT
ejpam-5084	51	92	/	/	SYM
ejpam-5084	51	93	eur	eur	PROPN
ejpam-5084	51	94	.	.	PUNCT
ejpam-5084	52	1	j.	j.	PROPN
ejpam-5084	52	2	pure	pure	PROPN
ejpam-5084	52	3	appl	appl	PROPN
ejpam-5084	52	4	.	.	PROPN
ejpam-5084	52	5	math	math	PROPN
ejpam-5084	52	6	,	,	PUNCT
ejpam-5084	52	7	17	17	NUM
ejpam-5084	52	8	(	(	PUNCT
ejpam-5084	52	9	2	2	NUM
ejpam-5084	52	10	)	)	PUNCT
ejpam-5084	52	11	(	(	PUNCT
ejpam-5084	52	12	2024	2024	NUM
ejpam-5084	52	13	)	)	PUNCT
ejpam-5084	52	14	,	,	PUNCT
ejpam-5084	52	15	922	922	NUM
ejpam-5084	52	16	-	-	SYM
ejpam-5084	52	17	930	930	NUM
ejpam-5084	52	18	924	924	NUM
ejpam-5084	52	19	vertices	vertex	NOUN
ejpam-5084	52	20	v	v	NOUN
ejpam-5084	52	21	,	,	PUNCT
ejpam-5084	52	22	w	w	PROPN
ejpam-5084	52	23	∈	∈	PROPN
ejpam-5084	52	24	s.	s.	PROPN
ejpam-5084	52	25	the	the	DET
ejpam-5084	52	26	hop	hop	PROPN
ejpam-5084	52	27	independence	independence	NOUN
ejpam-5084	52	28	number	number	NOUN
ejpam-5084	52	29	of	of	ADP
ejpam-5084	52	30	g	g	NOUN
ejpam-5084	52	31	,	,	PUNCT
ejpam-5084	52	32	denoted	denote	VERB
ejpam-5084	52	33	by	by	ADP
ejpam-5084	52	34	αh(g	αh(g	NOUN
ejpam-5084	52	35	)	)	PUNCT
ejpam-5084	52	36	,	,	PUNCT
ejpam-5084	52	37	is	be	AUX
ejpam-5084	52	38	the	the	DET
ejpam-5084	52	39	maximum	maximum	ADJ
ejpam-5084	52	40	cardinality	cardinality	NOUN
ejpam-5084	52	41	of	of	ADP
ejpam-5084	52	42	a	a	DET
ejpam-5084	52	43	hop	hop	NOUN
ejpam-5084	52	44	independent	independent	ADJ
ejpam-5084	52	45	set	set	NOUN
ejpam-5084	52	46	of	of	ADP
ejpam-5084	52	47	g	g	PROPN
ejpam-5084	52	48	[	[	X
ejpam-5084	52	49	8	8	NUM
ejpam-5084	52	50	]	]	SYM
ejpam-5084	52	51	.	.	PUNCT
ejpam-5084	53	1	3	3	X
ejpam-5084	53	2	.	.	X
ejpam-5084	53	3	results	result	NOUN
ejpam-5084	53	4	we	we	PRON
ejpam-5084	53	5	begin	begin	VERB
ejpam-5084	53	6	this	this	DET
ejpam-5084	53	7	section	section	NOUN
ejpam-5084	53	8	by	by	ADP
ejpam-5084	53	9	introducing	introduce	VERB
ejpam-5084	53	10	the	the	DET
ejpam-5084	53	11	concept	concept	NOUN
ejpam-5084	53	12	of	of	ADP
ejpam-5084	53	13	j	j	NOUN
ejpam-5084	53	14	-	-	ADJ
ejpam-5084	53	15	open	open	ADJ
ejpam-5084	53	16	independence	independence	NOUN
ejpam-5084	53	17	in	in	ADP
ejpam-5084	53	18	graphs	graph	NOUN
ejpam-5084	53	19	.	.	PUNCT
ejpam-5084	54	1	definition	definition	NOUN
ejpam-5084	54	2	1	1	NUM
ejpam-5084	54	3	.	.	PUNCT
ejpam-5084	55	1	let	let	VERB
ejpam-5084	55	2	g	g	PRON
ejpam-5084	55	3	be	be	AUX
ejpam-5084	55	4	a	a	DET
ejpam-5084	55	5	graph	graph	NOUN
ejpam-5084	55	6	with	with	ADP
ejpam-5084	55	7	vertex	vertex	NOUN
ejpam-5084	55	8	and	and	CCONJ
ejpam-5084	55	9	edge	edge	NOUN
ejpam-5084	55	10	-	-	PUNCT
ejpam-5084	55	11	sets	set	NOUN
ejpam-5084	55	12	v	v	NOUN
ejpam-5084	55	13	(	(	PUNCT
ejpam-5084	55	14	g	g	NOUN
ejpam-5084	55	15	)	)	PUNCT
ejpam-5084	55	16	and	and	CCONJ
ejpam-5084	55	17	e(g	e(g	PROPN
ejpam-5084	55	18	)	)	PUNCT
ejpam-5084	55	19	,	,	PUNCT
ejpam-5084	55	20	respectively	respectively	ADV
ejpam-5084	55	21	.	.	PUNCT
ejpam-5084	56	1	then	then	ADV
ejpam-5084	56	2	o	o	X
ejpam-5084	56	3	⊆	⊆	NUM
ejpam-5084	56	4	v	v	ADP
ejpam-5084	56	5	(	(	PUNCT
ejpam-5084	56	6	g	g	NOUN
ejpam-5084	56	7	)	)	PUNCT
ejpam-5084	56	8	is	be	AUX
ejpam-5084	56	9	called	call	VERB
ejpam-5084	56	10	a	a	DET
ejpam-5084	56	11	j	j	NOUN
ejpam-5084	56	12	-	-	ADJ
ejpam-5084	56	13	open	open	ADJ
ejpam-5084	56	14	independent	independent	ADJ
ejpam-5084	56	15	set	set	NOUN
ejpam-5084	56	16	of	of	ADP
ejpam-5084	56	17	g	g	PROPN
ejpam-5084	56	18	if	if	SCONJ
ejpam-5084	56	19	o	o	NOUN
ejpam-5084	56	20	is	be	AUX
ejpam-5084	56	21	a	a	DET
ejpam-5084	56	22	singleton	singleton	NOUN
ejpam-5084	56	23	set	set	NOUN
ejpam-5084	56	24	or	or	CCONJ
ejpam-5084	56	25	o	o	NOUN
ejpam-5084	56	26	is	be	AUX
ejpam-5084	56	27	an	an	DET
ejpam-5084	56	28	independent	independent	ADJ
ejpam-5084	56	29	set	set	NOUN
ejpam-5084	56	30	of	of	ADP
ejpam-5084	56	31	g	g	NOUN
ejpam-5084	56	32	and	and	CCONJ
ejpam-5084	56	33	for	for	ADP
ejpam-5084	56	34	every	every	DET
ejpam-5084	56	35	a	a	PROPN
ejpam-5084	56	36	,	,	PUNCT
ejpam-5084	56	37	b	b	PROPN
ejpam-5084	56	38	∈	∈	PROPN
ejpam-5084	56	39	v	v	NOUN
ejpam-5084	56	40	(	(	PUNCT
ejpam-5084	56	41	g	g	NOUN
ejpam-5084	56	42	)	)	PUNCT
ejpam-5084	56	43	,	,	PUNCT
ejpam-5084	56	44	ng(a)\ng(b	ng(a)\ng(b	ADJ
ejpam-5084	56	45	)	)	PUNCT
ejpam-5084	56	46	̸=	̸=	PROPN
ejpam-5084	56	47	∅	∅	NOUN
ejpam-5084	56	48	and	and	CCONJ
ejpam-5084	56	49	ng(b)\ng(a	ng(b)\ng(a	NOUN
ejpam-5084	56	50	)	)	PUNCT
ejpam-5084	56	51	̸=	̸=	PROPN
ejpam-5084	56	52	∅.	∅.	ADP
ejpam-5084	56	53	the	the	DET
ejpam-5084	56	54	maximum	maximum	ADJ
ejpam-5084	56	55	cardinality	cardinality	NOUN
ejpam-5084	56	56	of	of	ADP
ejpam-5084	56	57	a	a	DET
ejpam-5084	56	58	j	j	NOUN
ejpam-5084	56	59	-	-	ADJ
ejpam-5084	56	60	open	open	ADJ
ejpam-5084	56	61	independent	independent	ADJ
ejpam-5084	56	62	set	set	NOUN
ejpam-5084	56	63	of	of	ADP
ejpam-5084	56	64	g	g	NOUN
ejpam-5084	56	65	,	,	PUNCT
ejpam-5084	56	66	denoted	denote	VERB
ejpam-5084	56	67	by	by	ADP
ejpam-5084	56	68	αj(g	αj(g	NOUN
ejpam-5084	56	69	)	)	PUNCT
ejpam-5084	56	70	,	,	PUNCT
ejpam-5084	56	71	is	be	AUX
ejpam-5084	56	72	called	call	VERB
ejpam-5084	56	73	the	the	DET
ejpam-5084	56	74	j	j	NOUN
ejpam-5084	56	75	-	-	ADJ
ejpam-5084	56	76	open	open	ADJ
ejpam-5084	56	77	independence	independence	NOUN
ejpam-5084	56	78	number	number	NOUN
ejpam-5084	56	79	of	of	ADP
ejpam-5084	56	80	g.	g.	PROPN
ejpam-5084	56	81	example	example	NOUN
ejpam-5084	57	1	1	1	X
ejpam-5084	57	2	.	.	X
ejpam-5084	57	3	consider	consider	VERB
ejpam-5084	57	4	the	the	DET
ejpam-5084	57	5	graph	graph	NOUN
ejpam-5084	57	6	g	g	NOUN
ejpam-5084	57	7	=	=	ADJ
ejpam-5084	57	8	p4	p4	ADJ
ejpam-5084	57	9	in	in	ADP
ejpam-5084	57	10	figure	figure	NOUN
ejpam-5084	57	11	1	1	NUM
ejpam-5084	57	12	below	below	ADV
ejpam-5084	57	13	.	.	PUNCT
ejpam-5084	58	1	let	let	VERB
ejpam-5084	58	2	o	o	NOUN
ejpam-5084	58	3	=	=	PUNCT
ejpam-5084	58	4	{	{	PUNCT
ejpam-5084	58	5	a	a	X
ejpam-5084	58	6	,	,	PUNCT
ejpam-5084	58	7	d	d	NOUN
ejpam-5084	58	8	}	}	PUNCT
ejpam-5084	58	9	.	.	PUNCT
ejpam-5084	59	1	then	then	ADV
ejpam-5084	59	2	dg(a	dg(a	NUM
ejpam-5084	59	3	,	,	PUNCT
ejpam-5084	59	4	d	d	X
ejpam-5084	59	5	)	)	PUNCT
ejpam-5084	59	6	=	=	SYM
ejpam-5084	59	7	3	3	X
ejpam-5084	59	8	.	.	PUNCT
ejpam-5084	59	9	thus	thus	ADV
ejpam-5084	59	10	,	,	PUNCT
ejpam-5084	59	11	o	o	PROPN
ejpam-5084	59	12	is	be	AUX
ejpam-5084	59	13	an	an	DET
ejpam-5084	59	14	independent	independent	ADJ
ejpam-5084	59	15	set	set	NOUN
ejpam-5084	59	16	of	of	ADP
ejpam-5084	59	17	g.	g.	PROPN
ejpam-5084	59	18	observe	observe	VERB
ejpam-5084	59	19	that	that	PRON
ejpam-5084	59	20	ng(a	ng(a	NOUN
ejpam-5084	59	21	)	)	PUNCT
ejpam-5084	59	22	=	=	PUNCT
ejpam-5084	59	23	{	{	PUNCT
ejpam-5084	59	24	b	b	NOUN
ejpam-5084	59	25	}	}	PUNCT
ejpam-5084	59	26	and	and	CCONJ
ejpam-5084	59	27	ng(d	ng(d	NUM
ejpam-5084	59	28	)	)	PUNCT
ejpam-5084	59	29	=	=	PRON
ejpam-5084	60	1	{	{	PUNCT
ejpam-5084	60	2	c	c	NOUN
ejpam-5084	60	3	}	}	PUNCT
ejpam-5084	60	4	.	.	PUNCT
ejpam-5084	61	1	hence	hence	ADV
ejpam-5084	61	2	,	,	PUNCT
ejpam-5084	61	3	ng(a)\ng(d	ng(a)\ng(d	PROPN
ejpam-5084	61	4	)	)	PUNCT
ejpam-5084	61	5	=	=	PRON
ejpam-5084	61	6	{	{	PUNCT
ejpam-5084	61	7	b}\{c	b}\{c	NOUN
ejpam-5084	61	8	}	}	PUNCT
ejpam-5084	61	9	=	=	PUNCT
ejpam-5084	61	10	{	{	PUNCT
ejpam-5084	61	11	b	b	NOUN
ejpam-5084	61	12	}	}	PUNCT
ejpam-5084	61	13	,	,	PUNCT
ejpam-5084	61	14	andng(d)\ng(a	andng(d)\ng(a	PROPN
ejpam-5084	61	15	)	)	PUNCT
ejpam-5084	61	16	=	=	PRON
ejpam-5084	61	17	{	{	PUNCT
ejpam-5084	61	18	c}\{b	c}\{b	PROPN
ejpam-5084	61	19	}	}	PUNCT
ejpam-5084	61	20	=	=	PUNCT
ejpam-5084	61	21	{	{	PUNCT
ejpam-5084	61	22	c	c	NOUN
ejpam-5084	61	23	}	}	PUNCT
ejpam-5084	61	24	.	.	PUNCT
ejpam-5084	62	1	therefore	therefore	ADV
ejpam-5084	62	2	,	,	PUNCT
ejpam-5084	62	3	o	o	PROPN
ejpam-5084	62	4	is	be	AUX
ejpam-5084	62	5	a	a	DET
ejpam-5084	62	6	j	j	NOUN
ejpam-5084	62	7	-	-	ADJ
ejpam-5084	62	8	open	open	ADJ
ejpam-5084	62	9	independent	independent	ADJ
ejpam-5084	62	10	set	set	NOUN
ejpam-5084	62	11	of	of	ADP
ejpam-5084	62	12	g.	g.	PROPN
ejpam-5084	62	13	moreover	moreover	ADV
ejpam-5084	62	14	,	,	PUNCT
ejpam-5084	62	15	it	it	PRON
ejpam-5084	62	16	can	can	AUX
ejpam-5084	62	17	be	be	AUX
ejpam-5084	62	18	verified	verify	VERB
ejpam-5084	62	19	that	that	SCONJ
ejpam-5084	62	20	αj(g	αj(g	NUM
ejpam-5084	62	21	)	)	PUNCT
ejpam-5084	63	1	=	=	SYM
ejpam-5084	63	2	2	2	X
ejpam-5084	63	3	.	.	PUNCT
ejpam-5084	63	4	a	a	DET
ejpam-5084	63	5	b	b	NOUN
ejpam-5084	63	6	c	c	NOUN
ejpam-5084	63	7	d	d	X
ejpam-5084	63	8	p4	p4	ADJ
ejpam-5084	63	9	:	:	PUNCT
ejpam-5084	63	10	figure	figure	NOUN
ejpam-5084	63	11	1	1	NUM
ejpam-5084	63	12	:	:	PUNCT
ejpam-5084	63	13	graph	graph	NOUN
ejpam-5084	63	14	g	g	NOUN
ejpam-5084	63	15	=	=	NOUN
ejpam-5084	63	16	p4	p4	ADJ
ejpam-5084	63	17	with	with	ADP
ejpam-5084	63	18	αj	αj	PROPN
ejpam-5084	63	19	(	(	PUNCT
ejpam-5084	63	20	p4	p4	ADJ
ejpam-5084	63	21	)	)	PUNCT
ejpam-5084	63	22	=	=	SYM
ejpam-5084	63	23	2	2	NUM
ejpam-5084	63	24	remark	remark	NOUN
ejpam-5084	63	25	1	1	NUM
ejpam-5084	63	26	.	.	PUNCT
ejpam-5084	64	1	let	let	VERB
ejpam-5084	64	2	g	g	PRON
ejpam-5084	64	3	be	be	AUX
ejpam-5084	64	4	a	a	DET
ejpam-5084	64	5	graph	graph	NOUN
ejpam-5084	64	6	.	.	PUNCT
ejpam-5084	65	1	then	then	ADV
ejpam-5084	65	2	each	each	PRON
ejpam-5084	65	3	of	of	ADP
ejpam-5084	65	4	the	the	DET
ejpam-5084	65	5	following	follow	VERB
ejpam-5084	65	6	holds	hold	VERB
ejpam-5084	65	7	:	:	PUNCT
ejpam-5084	65	8	(	(	PUNCT
ejpam-5084	65	9	i	i	NOUN
ejpam-5084	65	10	)	)	PUNCT
ejpam-5084	65	11	a	a	DET
ejpam-5084	65	12	j	j	NOUN
ejpam-5084	65	13	-	-	ADJ
ejpam-5084	65	14	open	open	ADJ
ejpam-5084	65	15	set	set	ADJ
ejpam-5084	65	16	o	o	NOUN
ejpam-5084	65	17	of	of	ADP
ejpam-5084	65	18	g	g	NOUN
ejpam-5084	65	19	may	may	AUX
ejpam-5084	65	20	not	not	PART
ejpam-5084	65	21	be	be	AUX
ejpam-5084	65	22	an	an	DET
ejpam-5084	65	23	independent	independent	ADJ
ejpam-5084	65	24	set	set	NOUN
ejpam-5084	65	25	of	of	ADP
ejpam-5084	65	26	g.	g.	PROPN
ejpam-5084	65	27	(	(	PUNCT
ejpam-5084	65	28	ii	ii	PROPN
ejpam-5084	65	29	)	)	PUNCT
ejpam-5084	65	30	an	an	DET
ejpam-5084	65	31	independent	independent	ADJ
ejpam-5084	65	32	set	set	NOUN
ejpam-5084	65	33	of	of	ADP
ejpam-5084	65	34	g	g	NOUN
ejpam-5084	65	35	may	may	AUX
ejpam-5084	65	36	not	not	PART
ejpam-5084	65	37	be	be	AUX
ejpam-5084	65	38	a	a	DET
ejpam-5084	65	39	j	j	NOUN
ejpam-5084	65	40	-	-	ADJ
ejpam-5084	65	41	open	open	ADJ
ejpam-5084	65	42	set	set	NOUN
ejpam-5084	65	43	of	of	ADP
ejpam-5084	65	44	g.	g.	PROPN
ejpam-5084	65	45	the	the	DET
ejpam-5084	65	46	remark	remark	NOUN
ejpam-5084	65	47	above	above	ADV
ejpam-5084	65	48	says	say	VERB
ejpam-5084	65	49	that	that	SCONJ
ejpam-5084	65	50	the	the	DET
ejpam-5084	65	51	definition	definition	NOUN
ejpam-5084	65	52	of	of	ADP
ejpam-5084	65	53	a	a	DET
ejpam-5084	65	54	j	j	NOUN
ejpam-5084	65	55	-	-	ADJ
ejpam-5084	65	56	open	open	ADJ
ejpam-5084	65	57	independence	independence	NOUN
ejpam-5084	65	58	makes	make	VERB
ejpam-5084	65	59	sense	sense	NOUN
ejpam-5084	65	60	.	.	PUNCT
ejpam-5084	66	1	4	4	X
ejpam-5084	66	2	.	.	X
ejpam-5084	66	3	relationships	relationship	NOUN
ejpam-5084	66	4	of	of	ADP
ejpam-5084	66	5	j	j	NOUN
ejpam-5084	66	6	-	-	ADJ
ejpam-5084	66	7	open	open	ADJ
ejpam-5084	66	8	independence	independence	NOUN
ejpam-5084	66	9	and	and	CCONJ
ejpam-5084	66	10	independence	independence	NOUN
ejpam-5084	66	11	parameters	parameter	NOUN
ejpam-5084	66	12	theorem	theorem	VERB
ejpam-5084	66	13	1	1	X
ejpam-5084	66	14	.	.	PUNCT
ejpam-5084	67	1	let	let	VERB
ejpam-5084	67	2	g	g	PRON
ejpam-5084	67	3	be	be	AUX
ejpam-5084	67	4	a	a	DET
ejpam-5084	67	5	graph	graph	NOUN
ejpam-5084	67	6	.	.	PUNCT
ejpam-5084	68	1	then	then	ADV
ejpam-5084	68	2	(	(	PUNCT
ejpam-5084	68	3	i	i	NOUN
ejpam-5084	68	4	)	)	PUNCT
ejpam-5084	68	5	αj(g	αj(g	NOUN
ejpam-5084	68	6	)	)	PUNCT
ejpam-5084	68	7	≤	≤	NOUN
ejpam-5084	68	8	α(g	α(g	NUM
ejpam-5084	68	9	)	)	PUNCT
ejpam-5084	68	10	;	;	PUNCT
ejpam-5084	68	11	and	and	CCONJ
ejpam-5084	68	12	(	(	PUNCT
ejpam-5084	68	13	ii	ii	NOUN
ejpam-5084	68	14	)	)	PUNCT
ejpam-5084	68	15	1	1	NUM
ejpam-5084	68	16	≤	≤	NOUN
ejpam-5084	68	17	αj(g	αj(g	NOUN
ejpam-5084	68	18	)	)	PUNCT
ejpam-5084	68	19	≤	≤	NOUN
ejpam-5084	68	20	|v	|v	X
ejpam-5084	68	21	(	(	PUNCT
ejpam-5084	68	22	g)|	g)|	INTJ
ejpam-5084	68	23	−	−	NOUN
ejpam-5084	68	24	1	1	NUM
ejpam-5084	68	25	.	.	PUNCT
ejpam-5084	69	1	proof	proof	NOUN
ejpam-5084	69	2	.	.	PUNCT
ejpam-5084	70	1	(	(	PUNCT
ejpam-5084	70	2	i	i	NOUN
ejpam-5084	70	3	)	)	PUNCT
ejpam-5084	70	4	let	let	VERB
ejpam-5084	70	5	g	g	NOUN
ejpam-5084	70	6	be	be	AUX
ejpam-5084	70	7	a	a	DET
ejpam-5084	70	8	graph	graph	NOUN
ejpam-5084	70	9	and	and	CCONJ
ejpam-5084	70	10	let	let	VERB
ejpam-5084	70	11	o	o	NOUN
ejpam-5084	70	12	be	be	AUX
ejpam-5084	70	13	a	a	DET
ejpam-5084	70	14	maximum	maximum	ADJ
ejpam-5084	70	15	j	j	NOUN
ejpam-5084	70	16	-	-	ADJ
ejpam-5084	70	17	open	open	ADJ
ejpam-5084	70	18	independent	independent	ADJ
ejpam-5084	70	19	set	set	NOUN
ejpam-5084	70	20	of	of	ADP
ejpam-5084	70	21	g.	g.	PROPN
ejpam-5084	71	1	then	then	ADV
ejpam-5084	71	2	o	o	PROPN
ejpam-5084	71	3	is	be	AUX
ejpam-5084	71	4	an	an	DET
ejpam-5084	71	5	independent	independent	ADJ
ejpam-5084	71	6	set	set	NOUN
ejpam-5084	71	7	of	of	ADP
ejpam-5084	71	8	g	g	PROPN
ejpam-5084	71	9	and	and	CCONJ
ejpam-5084	71	10	αj(g)=|o|	αj(g)=|o|	PROPN
ejpam-5084	71	11	.	.	PUNCT
ejpam-5084	72	1	since	since	SCONJ
ejpam-5084	72	2	α(g	α(g	NUM
ejpam-5084	72	3	)	)	PUNCT
ejpam-5084	72	4	is	be	AUX
ejpam-5084	72	5	the	the	DET
ejpam-5084	72	6	maximum	maximum	ADJ
ejpam-5084	72	7	cardinality	cardinality	NOUN
ejpam-5084	72	8	among	among	ADP
ejpam-5084	72	9	all	all	DET
ejpam-5084	72	10	independent	independent	ADJ
ejpam-5084	72	11	sets	set	NOUN
ejpam-5084	72	12	in	in	ADP
ejpam-5084	72	13	g	g	NOUN
ejpam-5084	72	14	,	,	PUNCT
ejpam-5084	72	15	if	if	SCONJ
ejpam-5084	72	16	follows	follow	VERB
ejpam-5084	72	17	that	that	SCONJ
ejpam-5084	72	18	α(g	α(g	NUM
ejpam-5084	72	19	)	)	PUNCT
ejpam-5084	72	20	≥	≥	NOUN
ejpam-5084	72	21	|o|=αj(g	|o|=αj(g	PROPN
ejpam-5084	72	22	)	)	PUNCT
ejpam-5084	72	23	.	.	PUNCT
ejpam-5084	73	1	(	(	PUNCT
ejpam-5084	73	2	ii	ii	NOUN
ejpam-5084	73	3	)	)	PUNCT
ejpam-5084	73	4	let	let	VERB
ejpam-5084	73	5	g	g	NOUN
ejpam-5084	73	6	be	be	AUX
ejpam-5084	73	7	a	a	DET
ejpam-5084	73	8	graph	graph	NOUN
ejpam-5084	73	9	and	and	CCONJ
ejpam-5084	73	10	let	let	VERB
ejpam-5084	73	11	v	v	NOUN
ejpam-5084	73	12	(	(	PUNCT
ejpam-5084	73	13	g	g	NOUN
ejpam-5084	73	14	)	)	PUNCT
ejpam-5084	73	15	=	=	SYM
ejpam-5084	73	16	{	{	PUNCT
ejpam-5084	73	17	a1	a1	PROPN
ejpam-5084	73	18	,	,	PUNCT
ejpam-5084	73	19	a2	a2	PROPN
ejpam-5084	73	20	,	,	PUNCT
ejpam-5084	73	21	...	...	PUNCT
ejpam-5084	73	22	,	,	PUNCT
ejpam-5084	73	23	an	an	PRON
ejpam-5084	73	24	}	}	PUNCT
ejpam-5084	73	25	.	.	PUNCT
ejpam-5084	74	1	then	then	ADV
ejpam-5084	74	2	{	{	PUNCT
ejpam-5084	74	3	a1	a1	NOUN
ejpam-5084	74	4	}	}	PUNCT
ejpam-5084	74	5	is	be	AUX
ejpam-5084	74	6	a	a	DET
ejpam-5084	74	7	j	j	NOUN
ejpam-5084	74	8	-	-	ADJ
ejpam-5084	74	9	open	open	ADJ
ejpam-5084	74	10	independent	independent	ADJ
ejpam-5084	74	11	set	set	NOUN
ejpam-5084	74	12	of	of	ADP
ejpam-5084	74	13	g.	g.	PROPN
ejpam-5084	74	14	thus	thus	ADV
ejpam-5084	74	15	,	,	PUNCT
ejpam-5084	74	16	αj(g	αj(g	NUM
ejpam-5084	74	17	)	)	PUNCT
ejpam-5084	74	18	≥	≥	NOUN
ejpam-5084	74	19	|{a1}|=1	|{a1}|=1	NOUN
ejpam-5084	74	20	.	.	PUNCT
ejpam-5084	75	1	to	to	PART
ejpam-5084	75	2	show	show	VERB
ejpam-5084	75	3	that	that	SCONJ
ejpam-5084	75	4	αj(g	αj(g	NUM
ejpam-5084	75	5	)	)	PUNCT
ejpam-5084	75	6	≤	≤	NOUN
ejpam-5084	75	7	|v	|v	X
ejpam-5084	75	8	(	(	PUNCT
ejpam-5084	75	9	g)|	g)|	INTJ
ejpam-5084	75	10	−	−	NOUN
ejpam-5084	75	11	1	1	NUM
ejpam-5084	75	12	.	.	PUNCT
ejpam-5084	75	13	suppose	suppose	VERB
ejpam-5084	75	14	that	that	SCONJ
ejpam-5084	75	15	j.	j.	PROPN
ejpam-5084	75	16	a.	a.	PROPN
ejpam-5084	75	17	hassan	hassan	PROPN
ejpam-5084	75	18	et	et	PROPN
ejpam-5084	75	19	al	al	PROPN
ejpam-5084	75	20	.	.	PUNCT
ejpam-5084	75	21	/	/	SYM
ejpam-5084	75	22	eur	eur	PROPN
ejpam-5084	75	23	.	.	PUNCT
ejpam-5084	76	1	j.	j.	PROPN
ejpam-5084	76	2	pure	pure	PROPN
ejpam-5084	76	3	appl	appl	PROPN
ejpam-5084	76	4	.	.	PROPN
ejpam-5084	76	5	math	math	PROPN
ejpam-5084	76	6	,	,	PUNCT
ejpam-5084	76	7	17	17	NUM
ejpam-5084	76	8	(	(	PUNCT
ejpam-5084	76	9	2	2	NUM
ejpam-5084	76	10	)	)	PUNCT
ejpam-5084	76	11	(	(	PUNCT
ejpam-5084	76	12	2024	2024	NUM
ejpam-5084	76	13	)	)	PUNCT
ejpam-5084	76	14	,	,	PUNCT
ejpam-5084	76	15	922	922	NUM
ejpam-5084	76	16	-	-	SYM
ejpam-5084	76	17	930	930	NUM
ejpam-5084	76	18	925	925	NUM
ejpam-5084	76	19	g	g	NOUN
ejpam-5084	76	20	is	be	AUX
ejpam-5084	76	21	connected	connect	VERB
ejpam-5084	76	22	.	.	PUNCT
ejpam-5084	77	1	let	let	AUX
ejpam-5084	77	2	ai	ai	VERB
ejpam-5084	77	3	,	,	PUNCT
ejpam-5084	77	4	aj	aj	PROPN
ejpam-5084	77	5	∈	∈	PROPN
ejpam-5084	77	6	v	v	ADP
ejpam-5084	77	7	(	(	PUNCT
ejpam-5084	77	8	g	g	NOUN
ejpam-5084	77	9	)	)	PUNCT
ejpam-5084	77	10	such	such	ADJ
ejpam-5084	77	11	that	that	SCONJ
ejpam-5084	77	12	dg(ai	dg(ai	PROPN
ejpam-5084	77	13	,	,	PUNCT
ejpam-5084	77	14	aj	aj	PROPN
ejpam-5084	77	15	)	)	PUNCT
ejpam-5084	77	16	=	=	SYM
ejpam-5084	77	17	1	1	NUM
ejpam-5084	77	18	for	for	ADP
ejpam-5084	77	19	some	some	DET
ejpam-5084	77	20	i	i	PROPN
ejpam-5084	77	21	,	,	PUNCT
ejpam-5084	77	22	j	j	PROPN
ejpam-5084	77	23	∈	∈	PROPN
ejpam-5084	77	24	{	{	PUNCT
ejpam-5084	77	25	1	1	NUM
ejpam-5084	77	26	,	,	PUNCT
ejpam-5084	77	27	2	2	NUM
ejpam-5084	77	28	,	,	PUNCT
ejpam-5084	77	29	.	.	PUNCT
ejpam-5084	77	30	.	.	PUNCT
ejpam-5084	78	1	.	.	PUNCT
ejpam-5084	78	2	,	,	PUNCT
ejpam-5084	78	3	n	n	CCONJ
ejpam-5084	78	4	}	}	PUNCT
ejpam-5084	78	5	.	.	PUNCT
ejpam-5084	79	1	then	then	ADV
ejpam-5084	79	2	ai	ai	VERB
ejpam-5084	79	3	and	and	CCONJ
ejpam-5084	79	4	aj	aj	PROPN
ejpam-5084	79	5	can	can	AUX
ejpam-5084	79	6	not	not	PART
ejpam-5084	79	7	be	be	AUX
ejpam-5084	79	8	both	both	PRON
ejpam-5084	79	9	in	in	ADP
ejpam-5084	79	10	an	an	DET
ejpam-5084	79	11	independent	independent	ADJ
ejpam-5084	79	12	set	set	NOUN
ejpam-5084	79	13	s	s	PROPN
ejpam-5084	79	14	of	of	ADP
ejpam-5084	79	15	g.	g.	PROPN
ejpam-5084	79	16	hence	hence	ADV
ejpam-5084	79	17	,	,	PUNCT
ejpam-5084	79	18	if	if	SCONJ
ejpam-5084	79	19	ai	ai	VERB
ejpam-5084	79	20	∈	∈	PROPN
ejpam-5084	79	21	s	s	PROPN
ejpam-5084	79	22	,	,	PUNCT
ejpam-5084	79	23	then	then	ADV
ejpam-5084	79	24	aj	aj	PROPN
ejpam-5084	79	25	/∈	/∈	PROPN
ejpam-5084	79	26	s	s	PART
ejpam-5084	79	27	or	or	CCONJ
ejpam-5084	79	28	if	if	SCONJ
ejpam-5084	79	29	aj	aj	PROPN
ejpam-5084	79	30	∈	∈	PROPN
ejpam-5084	79	31	s	s	PART
ejpam-5084	79	32	,	,	PUNCT
ejpam-5084	79	33	then	then	ADV
ejpam-5084	79	34	ai	ai	VERB
ejpam-5084	79	35	/∈	/∈	PROPN
ejpam-5084	79	36	s.	s.	PROPN
ejpam-5084	79	37	thus	thus	ADV
ejpam-5084	79	38	,	,	PUNCT
ejpam-5084	79	39	α(g	α(g	NUM
ejpam-5084	79	40	)	)	PUNCT
ejpam-5084	79	41	≤	≤	NOUN
ejpam-5084	79	42	|v	|v	X
ejpam-5084	79	43	(	(	PUNCT
ejpam-5084	79	44	g)|	g)|	INTJ
ejpam-5084	79	45	−	−	NOUN
ejpam-5084	79	46	1	1	NUM
ejpam-5084	79	47	.	.	PUNCT
ejpam-5084	80	1	by	by	ADP
ejpam-5084	80	2	(	(	PUNCT
ejpam-5084	80	3	i	i	NOUN
ejpam-5084	80	4	)	)	PUNCT
ejpam-5084	80	5	,	,	PUNCT
ejpam-5084	80	6	αj(g	αj(g	NUM
ejpam-5084	80	7	)	)	PUNCT
ejpam-5084	80	8	≤	≤	NOUN
ejpam-5084	80	9	|v	|v	X
ejpam-5084	80	10	(	(	PUNCT
ejpam-5084	80	11	g)|	g)|	INTJ
ejpam-5084	80	12	−	−	NOUN
ejpam-5084	80	13	1	1	NUM
ejpam-5084	80	14	.	.	PUNCT
ejpam-5084	81	1	now	now	ADV
ejpam-5084	81	2	,	,	PUNCT
ejpam-5084	81	3	suppose	suppose	VERB
ejpam-5084	81	4	that	that	SCONJ
ejpam-5084	81	5	g	g	PROPN
ejpam-5084	81	6	is	be	AUX
ejpam-5084	81	7	disconnected	disconnect	VERB
ejpam-5084	81	8	.	.	PUNCT
ejpam-5084	82	1	let	let	VERB
ejpam-5084	82	2	q1	q1	PROPN
ejpam-5084	82	3	,	,	PUNCT
ejpam-5084	82	4	...	...	PUNCT
ejpam-5084	82	5	,	,	PUNCT
ejpam-5084	82	6	qk	qk	INTJ
ejpam-5084	82	7	,	,	PUNCT
ejpam-5084	82	8	k	k	PROPN
ejpam-5084	82	9	≥	≥	NUM
ejpam-5084	82	10	2	2	NUM
ejpam-5084	82	11	be	be	AUX
ejpam-5084	82	12	components	component	NOUN
ejpam-5084	82	13	of	of	ADP
ejpam-5084	82	14	g.	g.	PROPN
ejpam-5084	82	15	since	since	SCONJ
ejpam-5084	82	16	g	g	PROPN
ejpam-5084	82	17	̸=	̸=	PROPN
ejpam-5084	82	18	kn	kn	PROPN
ejpam-5084	82	19	,	,	PUNCT
ejpam-5084	82	20	it	it	PRON
ejpam-5084	82	21	follows	follow	VERB
ejpam-5084	82	22	that	that	SCONJ
ejpam-5084	82	23	qi	qi	PROPN
ejpam-5084	82	24	is	be	AUX
ejpam-5084	82	25	non	non	ADJ
ejpam-5084	82	26	-	-	ADJ
ejpam-5084	82	27	trivial	trivial	ADJ
ejpam-5084	82	28	for	for	ADP
ejpam-5084	82	29	each	each	DET
ejpam-5084	82	30	i	i	PRON
ejpam-5084	82	31	∈	∈	PROPN
ejpam-5084	82	32	{	{	PUNCT
ejpam-5084	82	33	1	1	NUM
ejpam-5084	82	34	,	,	PUNCT
ejpam-5084	82	35	...	...	PUNCT
ejpam-5084	82	36	,	,	PUNCT
ejpam-5084	82	37	k	k	NOUN
ejpam-5084	82	38	}	}	PUNCT
ejpam-5084	82	39	.	.	PUNCT
ejpam-5084	83	1	thus	thus	ADV
ejpam-5084	83	2	,	,	PUNCT
ejpam-5084	83	3	α(qi	α(qi	NUM
ejpam-5084	83	4	)	)	PUNCT
ejpam-5084	83	5	≤	≤	NOUN
ejpam-5084	83	6	|v	|v	X
ejpam-5084	83	7	(	(	PUNCT
ejpam-5084	83	8	qi)|−	qi)|−	ADP
ejpam-5084	83	9	1	1	NUM
ejpam-5084	83	10	for	for	ADP
ejpam-5084	83	11	each	each	DET
ejpam-5084	83	12	i	i	PRON
ejpam-5084	83	13	∈	∈	PROPN
ejpam-5084	83	14	{	{	PUNCT
ejpam-5084	83	15	1	1	NUM
ejpam-5084	83	16	,	,	PUNCT
ejpam-5084	83	17	...	...	PUNCT
ejpam-5084	83	18	,	,	PUNCT
ejpam-5084	83	19	k	k	NOUN
ejpam-5084	83	20	}	}	PUNCT
ejpam-5084	83	21	.	.	PUNCT
ejpam-5084	84	1	therefore	therefore	ADV
ejpam-5084	84	2	,	,	PUNCT
ejpam-5084	84	3	α(g	α(g	NUM
ejpam-5084	84	4	)	)	PUNCT
ejpam-5084	84	5	=	=	PUNCT
ejpam-5084	84	6	α(q1	α(q1	PRON
ejpam-5084	84	7	)	)	PUNCT
ejpam-5084	84	8	+	+	CCONJ
ejpam-5084	84	9	...	...	PUNCT
ejpam-5084	85	1	+	+	CCONJ
ejpam-5084	85	2	α(qk	α(qk	NOUN
ejpam-5084	85	3	)	)	PUNCT
ejpam-5084	85	4	=	=	SYM
ejpam-5084	85	5	|v	|v	X
ejpam-5084	85	6	(	(	PUNCT
ejpam-5084	85	7	qi)|	qi)|	INTJ
ejpam-5084	85	8	−	−	PROPN
ejpam-5084	85	9	1	1	NUM
ejpam-5084	85	10	+	+	CCONJ
ejpam-5084	85	11	...	...	PUNCT
ejpam-5084	85	12	+	+	CCONJ
ejpam-5084	85	13	|v	|v	X
ejpam-5084	85	14	(	(	PUNCT
ejpam-5084	85	15	qk)|	qk)|	NOUN
ejpam-5084	85	16	−	−	PROPN
ejpam-5084	85	17	1	1	NUM
ejpam-5084	85	18	=	=	SYM
ejpam-5084	85	19	|v	|v	X
ejpam-5084	85	20	(	(	PUNCT
ejpam-5084	85	21	g)|	g)|	PROPN
ejpam-5084	85	22	−	−	PROPN
ejpam-5084	85	23	k	k	PROPN
ejpam-5084	85	24	≤	≤	PROPN
ejpam-5084	85	25	|v	|v	X
ejpam-5084	85	26	(	(	PUNCT
ejpam-5084	85	27	g)|	g)|	INTJ
ejpam-5084	85	28	−	−	NOUN
ejpam-5084	85	29	1	1	NUM
ejpam-5084	85	30	.	.	PUNCT
ejpam-5084	85	31	consequently	consequently	ADV
ejpam-5084	85	32	,	,	PUNCT
ejpam-5084	85	33	αj(g	αj(g	NUM
ejpam-5084	85	34	)	)	PUNCT
ejpam-5084	85	35	≤	≤	NOUN
ejpam-5084	85	36	|v	|v	X
ejpam-5084	85	37	(	(	PUNCT
ejpam-5084	85	38	g)|	g)|	INTJ
ejpam-5084	85	39	−	−	NOUN
ejpam-5084	85	40	1	1	NUM
ejpam-5084	85	41	by	by	ADP
ejpam-5084	85	42	(	(	PUNCT
ejpam-5084	85	43	i	i	NOUN
ejpam-5084	85	44	)	)	PUNCT
ejpam-5084	85	45	.	.	PUNCT
ejpam-5084	86	1	theorem	theorem	NOUN
ejpam-5084	86	2	2	2	NUM
ejpam-5084	86	3	.	.	PUNCT
ejpam-5084	87	1	let	let	VERB
ejpam-5084	87	2	s	s	PROPN
ejpam-5084	87	3	,	,	PUNCT
ejpam-5084	87	4	t	t	PROPN
ejpam-5084	87	5	be	be	AUX
ejpam-5084	87	6	positive	positive	ADJ
ejpam-5084	87	7	integers	integer	NOUN
ejpam-5084	87	8	such	such	ADJ
ejpam-5084	87	9	that	that	SCONJ
ejpam-5084	87	10	1	1	NUM
ejpam-5084	87	11	≤	≤	NOUN
ejpam-5084	87	12	s	s	PART
ejpam-5084	87	13	≤	≤	ADJ
ejpam-5084	87	14	t.	t.	NOUN
ejpam-5084	87	15	then	then	ADV
ejpam-5084	87	16	there	there	PRON
ejpam-5084	87	17	exists	exist	VERB
ejpam-5084	87	18	a	a	DET
ejpam-5084	87	19	connected	connected	ADJ
ejpam-5084	87	20	graph	graph	NOUN
ejpam-5084	87	21	h	h	NOUN
ejpam-5084	87	22	such	such	ADJ
ejpam-5084	87	23	that	that	SCONJ
ejpam-5084	87	24	αj(h)=s	αj(h)=s	NUM
ejpam-5084	87	25	and	and	CCONJ
ejpam-5084	87	26	α(h)=t	α(h)=t	PROPN
ejpam-5084	87	27	.	.	PUNCT
ejpam-5084	88	1	in	in	ADP
ejpam-5084	88	2	other	other	ADJ
ejpam-5084	88	3	words	word	NOUN
ejpam-5084	88	4	,	,	PUNCT
ejpam-5084	88	5	α(h	α(h	NOUN
ejpam-5084	88	6	)	)	PUNCT
ejpam-5084	88	7	−	−	PROPN
ejpam-5084	88	8	αj(h	αj(h	CCONJ
ejpam-5084	88	9	)	)	PUNCT
ejpam-5084	88	10	can	can	AUX
ejpam-5084	88	11	be	be	AUX
ejpam-5084	88	12	made	make	VERB
ejpam-5084	88	13	arbitrarily	arbitrarily	ADV
ejpam-5084	88	14	large	large	ADJ
ejpam-5084	88	15	.	.	PUNCT
ejpam-5084	89	1	proof	proof	NOUN
ejpam-5084	89	2	.	.	PUNCT
ejpam-5084	90	1	consider	consider	VERB
ejpam-5084	90	2	the	the	DET
ejpam-5084	90	3	following	follow	VERB
ejpam-5084	90	4	two	two	NUM
ejpam-5084	90	5	cases	case	NOUN
ejpam-5084	90	6	.	.	PUNCT
ejpam-5084	91	1	case	case	NOUN
ejpam-5084	91	2	1	1	NUM
ejpam-5084	91	3	.	.	X
ejpam-5084	91	4	s	s	PART
ejpam-5084	92	1	=	=	X
ejpam-5084	92	2	t	t	PROPN
ejpam-5084	92	3	consider	consider	VERB
ejpam-5084	92	4	the	the	DET
ejpam-5084	92	5	graph	graph	NOUN
ejpam-5084	92	6	h	h	NOUN
ejpam-5084	92	7	below	below	ADV
ejpam-5084	92	8	.	.	PUNCT
ejpam-5084	92	9	.	.	PUNCT
ejpam-5084	92	10	.	.	PUNCT
ejpam-5084	92	11	.	.	PUNCT
ejpam-5084	93	1	a1	a1	NOUN
ejpam-5084	93	2	a2	a2	PROPN
ejpam-5084	93	3	a3	a3	NOUN
ejpam-5084	93	4	b2b1	b2b1	ADP
ejpam-5084	93	5	b3	b3	PROPN
ejpam-5084	93	6	as−1	as−1	NOUN
ejpam-5084	93	7	bs−1	bs−1	ADJ
ejpam-5084	93	8	as	as	ADP
ejpam-5084	93	9	bs	bs	PROPN
ejpam-5084	93	10	h	h	NOUN
ejpam-5084	93	11	:	:	PUNCT
ejpam-5084	93	12	let	let	VERB
ejpam-5084	93	13	o	o	NOUN
ejpam-5084	93	14	=	=	PUNCT
ejpam-5084	93	15	{	{	PUNCT
ejpam-5084	93	16	a1	a1	PROPN
ejpam-5084	93	17	,	,	PUNCT
ejpam-5084	93	18	a2	a2	PROPN
ejpam-5084	93	19	,	,	PUNCT
ejpam-5084	93	20	·	·	PUNCT
ejpam-5084	93	21	·	·	PUNCT
ejpam-5084	93	22	·	·	PUNCT
ejpam-5084	93	23	,	,	PUNCT
ejpam-5084	93	24	as	as	ADP
ejpam-5084	93	25	}	}	PUNCT
ejpam-5084	93	26	.	.	PUNCT
ejpam-5084	94	1	then	then	ADV
ejpam-5084	94	2	o	o	NOUN
ejpam-5084	94	3	is	be	AUX
ejpam-5084	94	4	both	both	CCONJ
ejpam-5084	94	5	a	a	DET
ejpam-5084	94	6	maximum	maximum	ADJ
ejpam-5084	94	7	j	j	NOUN
ejpam-5084	94	8	-	-	ADJ
ejpam-5084	94	9	open	open	ADJ
ejpam-5084	94	10	independent	independent	ADJ
ejpam-5084	94	11	and	and	CCONJ
ejpam-5084	94	12	maximum	maximum	ADJ
ejpam-5084	94	13	independet	independet	NOUN
ejpam-5084	94	14	set	set	NOUN
ejpam-5084	94	15	of	of	ADP
ejpam-5084	94	16	h.	h.	PROPN
ejpam-5084	94	17	thus	thus	ADV
ejpam-5084	94	18	,	,	PUNCT
ejpam-5084	94	19	αj(h	αj(h	PUNCT
ejpam-5084	94	20	)	)	PUNCT
ejpam-5084	94	21	=	=	SYM
ejpam-5084	94	22	g	g	NOUN
ejpam-5084	94	23	=	=	SYM
ejpam-5084	94	24	α(h	α(h	NOUN
ejpam-5084	94	25	)	)	PUNCT
ejpam-5084	94	26	.	.	PUNCT
ejpam-5084	95	1	case	case	NOUN
ejpam-5084	95	2	2	2	NUM
ejpam-5084	95	3	:	:	PUNCT
ejpam-5084	95	4	s	s	X
ejpam-5084	95	5	<	<	X
ejpam-5084	95	6	t	t	X
ejpam-5084	95	7	let	let	VERB
ejpam-5084	95	8	q	q	NOUN
ejpam-5084	95	9	=	=	PUNCT
ejpam-5084	95	10	t−	t−	PROPN
ejpam-5084	95	11	s	s	PART
ejpam-5084	95	12	and	and	CCONJ
ejpam-5084	95	13	consider	consider	VERB
ejpam-5084	95	14	the	the	DET
ejpam-5084	95	15	graph	graph	NOUN
ejpam-5084	95	16	h	h	NOUN
ejpam-5084	95	17	′	′	NUM
ejpam-5084	95	18	below	below	ADV
ejpam-5084	95	19	.	.	PUNCT
ejpam-5084	96	1	x1	x1	NUM
ejpam-5084	96	2	x3	x3	ADJ
ejpam-5084	97	1	x2	x2	PROPN
ejpam-5084	97	2	.	.	PUNCT
ejpam-5084	97	3	.	.	PUNCT
ejpam-5084	97	4	.	.	PUNCT
ejpam-5084	98	1	xs	xs	PROPN
ejpam-5084	99	1	y2	y2	PROPN
ejpam-5084	99	2	y1	y1	INTJ
ejpam-5084	99	3	yq	yq	PROPN
ejpam-5084	99	4	...	...	PUNCT
ejpam-5084	100	1	xs−1	xs−1	PROPN
ejpam-5084	100	2	h	h	NOUN
ejpam-5084	100	3	′	′	NOUN
ejpam-5084	100	4	:	:	PUNCT
ejpam-5084	100	5	let	let	VERB
ejpam-5084	100	6	o1	o1	NOUN
ejpam-5084	100	7	=	=	SYM
ejpam-5084	100	8	{	{	PUNCT
ejpam-5084	100	9	x1	x1	PROPN
ejpam-5084	100	10	,	,	PUNCT
ejpam-5084	100	11	x2	x2	PROPN
ejpam-5084	100	12	,	,	PUNCT
ejpam-5084	100	13	·	·	PUNCT
ejpam-5084	100	14	·	·	PUNCT
ejpam-5084	100	15	·	·	PUNCT
ejpam-5084	100	16	,	,	PUNCT
ejpam-5084	100	17	xs	xs	PROPN
ejpam-5084	100	18	}	}	PUNCT
ejpam-5084	100	19	and	and	CCONJ
ejpam-5084	100	20	o2	o2	PROPN
ejpam-5084	100	21	=	=	SYM
ejpam-5084	100	22	o1	o1	PROPN
ejpam-5084	100	23	∪	∪	X
ejpam-5084	100	24	{	{	PUNCT
ejpam-5084	100	25	y1	y1	NOUN
ejpam-5084	100	26	,	,	PUNCT
ejpam-5084	100	27	y2	y2	PROPN
ejpam-5084	100	28	·	·	PUNCT
ejpam-5084	100	29	·	·	PUNCT
ejpam-5084	100	30	·	·	PUNCT
ejpam-5084	100	31	,	,	PUNCT
ejpam-5084	100	32	yq	yq	PROPN
ejpam-5084	100	33	}	}	PUNCT
ejpam-5084	100	34	then	then	ADV
ejpam-5084	100	35	o1	o1	PROPN
ejpam-5084	100	36	and	and	CCONJ
ejpam-5084	100	37	o2	o2	PROPN
ejpam-5084	100	38	are	be	AUX
ejpam-5084	100	39	maximum	maximum	ADJ
ejpam-5084	100	40	j	j	ADJ
ejpam-5084	100	41	-	-	ADJ
ejpam-5084	100	42	open	open	ADJ
ejpam-5084	100	43	independent	independent	ADJ
ejpam-5084	100	44	and	and	CCONJ
ejpam-5084	100	45	maximum	maximum	ADJ
ejpam-5084	100	46	independent	independent	ADJ
ejpam-5084	100	47	sets	set	NOUN
ejpam-5084	100	48	of	of	ADP
ejpam-5084	100	49	h	h	NOUN
ejpam-5084	100	50	′	′	NOUN
ejpam-5084	100	51	,	,	PUNCT
ejpam-5084	100	52	respectively	respectively	ADV
ejpam-5084	100	53	.	.	PUNCT
ejpam-5084	101	1	therefore	therefore	ADV
ejpam-5084	101	2	,	,	PUNCT
ejpam-5084	101	3	αj(h	αj(h	ADV
ejpam-5084	101	4	′	′	NUM
ejpam-5084	101	5	)	)	PUNCT
ejpam-5084	102	1	=	=	SYM
ejpam-5084	102	2	s	s	PROPN
ejpam-5084	102	3	and	and	CCONJ
ejpam-5084	102	4	α(h	α(h	NOUN
ejpam-5084	102	5	′	′	NOUN
ejpam-5084	102	6	)	)	PUNCT
ejpam-5084	103	1	=	=	PUNCT
ejpam-5084	103	2	s+	s+	PUNCT
ejpam-5084	103	3	q	q	X
ejpam-5084	104	1	=	=	PUNCT
ejpam-5084	104	2	t.	t.	NOUN
ejpam-5084	104	3	consequently	consequently	ADV
ejpam-5084	104	4	,	,	PUNCT
ejpam-5084	104	5	αj(h	αj(h	ADV
ejpam-5084	104	6	′	′	NUM
ejpam-5084	104	7	)	)	PUNCT
ejpam-5084	105	1	=	=	SYM
ejpam-5084	105	2	s	s	PART
ejpam-5084	105	3	<	<	X
ejpam-5084	105	4	t	t	NOUN
ejpam-5084	105	5	=	=	SYM
ejpam-5084	105	6	α(h	α(h	NOUN
ejpam-5084	105	7	′	′	NUM
ejpam-5084	105	8	)	)	PUNCT
ejpam-5084	105	9	.	.	PUNCT
ejpam-5084	106	1	j.	j.	PROPN
ejpam-5084	106	2	a.	a.	PROPN
ejpam-5084	106	3	hassan	hassan	PROPN
ejpam-5084	106	4	et	et	PROPN
ejpam-5084	106	5	al	al	PROPN
ejpam-5084	106	6	.	.	PUNCT
ejpam-5084	106	7	/	/	SYM
ejpam-5084	106	8	eur	eur	PROPN
ejpam-5084	106	9	.	.	PUNCT
ejpam-5084	107	1	j.	j.	PROPN
ejpam-5084	107	2	pure	pure	PROPN
ejpam-5084	107	3	appl	appl	PROPN
ejpam-5084	107	4	.	.	PROPN
ejpam-5084	107	5	math	math	PROPN
ejpam-5084	107	6	,	,	PUNCT
ejpam-5084	107	7	17	17	NUM
ejpam-5084	107	8	(	(	PUNCT
ejpam-5084	107	9	2	2	NUM
ejpam-5084	107	10	)	)	PUNCT
ejpam-5084	107	11	(	(	PUNCT
ejpam-5084	107	12	2024	2024	NUM
ejpam-5084	107	13	)	)	PUNCT
ejpam-5084	107	14	,	,	PUNCT
ejpam-5084	107	15	922	922	NUM
ejpam-5084	107	16	-	-	SYM
ejpam-5084	107	17	930	930	NUM
ejpam-5084	107	18	926	926	NUM
ejpam-5084	107	19	5	5	NUM
ejpam-5084	107	20	.	.	PUNCT
ejpam-5084	108	1	relationships	relationship	NOUN
ejpam-5084	108	2	of	of	ADP
ejpam-5084	108	3	j	j	NOUN
ejpam-5084	108	4	-	-	ADJ
ejpam-5084	108	5	open	open	ADJ
ejpam-5084	108	6	independence	independence	NOUN
ejpam-5084	108	7	and	and	CCONJ
ejpam-5084	108	8	j	j	PROPN
ejpam-5084	108	9	-	-	ADJ
ejpam-5084	108	10	total	total	ADJ
ejpam-5084	108	11	domination	domination	NOUN
ejpam-5084	108	12	parameters	parameter	NOUN
ejpam-5084	108	13	proposition	proposition	VERB
ejpam-5084	108	14	1	1	X
ejpam-5084	108	15	.	.	PUNCT
ejpam-5084	109	1	let	let	VERB
ejpam-5084	109	2	g	g	PRON
ejpam-5084	109	3	be	be	AUX
ejpam-5084	109	4	a	a	DET
ejpam-5084	109	5	graph	graph	NOUN
ejpam-5084	109	6	such	such	ADJ
ejpam-5084	109	7	that	that	SCONJ
ejpam-5084	109	8	g	g	PROPN
ejpam-5084	109	9	̸=	̸=	PROPN
ejpam-5084	109	10	kn	kn	PROPN
ejpam-5084	109	11	.	.	PUNCT
ejpam-5084	110	1	then	then	ADV
ejpam-5084	110	2	αj(g	αj(g	NUM
ejpam-5084	110	3	)	)	PUNCT
ejpam-5084	110	4	≤	≤	NUM
ejpam-5084	110	5	γjt(g	γjt(g	PROPN
ejpam-5084	110	6	)	)	PUNCT
ejpam-5084	110	7	,	,	PUNCT
ejpam-5084	110	8	and	and	CCONJ
ejpam-5084	110	9	its	its	PRON
ejpam-5084	110	10	bound	bind	VERB
ejpam-5084	110	11	is	be	AUX
ejpam-5084	110	12	tight	tight	ADJ
ejpam-5084	110	13	.	.	PUNCT
ejpam-5084	111	1	proof	proof	NOUN
ejpam-5084	111	2	.	.	PUNCT
ejpam-5084	112	1	let	let	VERB
ejpam-5084	112	2	g	g	PRON
ejpam-5084	112	3	be	be	AUX
ejpam-5084	112	4	a	a	DET
ejpam-5084	112	5	graph	graph	NOUN
ejpam-5084	112	6	such	such	ADJ
ejpam-5084	112	7	that	that	SCONJ
ejpam-5084	112	8	g	g	PROPN
ejpam-5084	112	9	̸=	̸=	PROPN
ejpam-5084	112	10	kn	kn	PROPN
ejpam-5084	112	11	.	.	PUNCT
ejpam-5084	113	1	and	and	CCONJ
ejpam-5084	113	2	let	let	VERB
ejpam-5084	113	3	q	q	PUNCT
ejpam-5084	113	4	be	be	AUX
ejpam-5084	113	5	a	a	DET
ejpam-5084	113	6	maximum	maximum	ADJ
ejpam-5084	113	7	j	j	NOUN
ejpam-5084	113	8	-	-	ADJ
ejpam-5084	113	9	open	open	ADJ
ejpam-5084	113	10	independent	independent	ADJ
ejpam-5084	113	11	set	set	NOUN
ejpam-5084	113	12	of	of	ADP
ejpam-5084	113	13	g.	g.	PROPN
ejpam-5084	114	1	then	then	ADV
ejpam-5084	114	2	q	q	X
ejpam-5084	114	3	is	be	AUX
ejpam-5084	114	4	a	a	DET
ejpam-5084	114	5	j	j	NOUN
ejpam-5084	114	6	-	-	ADJ
ejpam-5084	114	7	open	open	ADJ
ejpam-5084	114	8	set	set	NOUN
ejpam-5084	114	9	in	in	ADP
ejpam-5084	114	10	g.	g.	PROPN
ejpam-5084	114	11	since	since	SCONJ
ejpam-5084	114	12	γjt(g	γjt(g	PROPN
ejpam-5084	114	13	)	)	PUNCT
ejpam-5084	114	14	is	be	AUX
ejpam-5084	114	15	a	a	DET
ejpam-5084	114	16	maximum	maximum	ADJ
ejpam-5084	114	17	cardinality	cardinality	NOUN
ejpam-5084	114	18	of	of	ADP
ejpam-5084	114	19	a	a	DET
ejpam-5084	114	20	j	j	NOUN
ejpam-5084	114	21	-	-	ADJ
ejpam-5084	114	22	open	open	ADJ
ejpam-5084	114	23	set	set	NOUN
ejpam-5084	114	24	of	of	ADP
ejpam-5084	114	25	g	g	NOUN
ejpam-5084	114	26	,	,	PUNCT
ejpam-5084	114	27	it	it	PRON
ejpam-5084	114	28	follows	follow	VERB
ejpam-5084	114	29	that	that	SCONJ
ejpam-5084	114	30	γjt(g	γjt(g	PROPN
ejpam-5084	114	31	)	)	PUNCT
ejpam-5084	114	32	≥	≥	PRON
ejpam-5084	114	33	|q|	|q|	VERB
ejpam-5084	114	34	=	=	SYM
ejpam-5084	114	35	αj(g	αj(g	NUM
ejpam-5084	114	36	)	)	PUNCT
ejpam-5084	114	37	.	.	PUNCT
ejpam-5084	115	1	for	for	ADP
ejpam-5084	115	2	the	the	DET
ejpam-5084	115	3	tightness	tightness	NOUN
ejpam-5084	115	4	,	,	PUNCT
ejpam-5084	115	5	consider	consider	VERB
ejpam-5084	115	6	p4	p4	ADJ
ejpam-5084	115	7	.	.	PUNCT
ejpam-5084	116	1	then	then	ADV
ejpam-5084	116	2	αj(p4	αj(p4	NOUN
ejpam-5084	116	3	)	)	PUNCT
ejpam-5084	116	4	=	=	SYM
ejpam-5084	116	5	2	2	NUM
ejpam-5084	116	6	=	=	SYM
ejpam-5084	116	7	γjt(p4	γjt(p4	NOUN
ejpam-5084	116	8	)	)	PUNCT
ejpam-5084	116	9	.	.	PUNCT
ejpam-5084	117	1	theorem	theorem	NOUN
ejpam-5084	117	2	3	3	X
ejpam-5084	117	3	.	.	PUNCT
ejpam-5084	118	1	let	let	VERB
ejpam-5084	118	2	a	a	PRON
ejpam-5084	118	3	and	and	CCONJ
ejpam-5084	118	4	b	b	NOUN
ejpam-5084	118	5	be	be	AUX
ejpam-5084	118	6	positive	positive	ADJ
ejpam-5084	118	7	integers	integer	NOUN
ejpam-5084	118	8	such	such	ADJ
ejpam-5084	118	9	that	that	SCONJ
ejpam-5084	118	10	1	1	NUM
ejpam-5084	118	11	≤	≤	NUM
ejpam-5084	118	12	a	a	DET
ejpam-5084	118	13	≤	≤	PROPN
ejpam-5084	118	14	b.	b.	NOUN
ejpam-5084	119	1	then	then	ADV
ejpam-5084	119	2	there	there	PRON
ejpam-5084	119	3	exists	exist	VERB
ejpam-5084	119	4	a	a	DET
ejpam-5084	119	5	connected	connected	ADJ
ejpam-5084	119	6	graph	graph	NOUN
ejpam-5084	119	7	g	g	ADP
ejpam-5084	119	8	such	such	ADJ
ejpam-5084	119	9	that	that	DET
ejpam-5084	119	10	αj(g	αj(g	NUM
ejpam-5084	119	11	)	)	PUNCT
ejpam-5084	119	12	=	=	SYM
ejpam-5084	119	13	a	a	PRON
ejpam-5084	119	14	and	and	CCONJ
ejpam-5084	119	15	γjt(g	γjt(g	NOUN
ejpam-5084	119	16	)	)	PUNCT
ejpam-5084	119	17	=	=	SYM
ejpam-5084	119	18	b.	b.	PROPN
ejpam-5084	119	19	proof	proof	NOUN
ejpam-5084	119	20	.	.	PUNCT
ejpam-5084	120	1	suppose	suppose	VERB
ejpam-5084	120	2	that	that	SCONJ
ejpam-5084	120	3	a	a	DET
ejpam-5084	120	4	=	=	X
ejpam-5084	120	5	b.	b.	NOUN
ejpam-5084	120	6	consider	consider	VERB
ejpam-5084	120	7	the	the	DET
ejpam-5084	120	8	graph	graph	NOUN
ejpam-5084	120	9	g	g	NOUN
ejpam-5084	120	10	below	below	ADV
ejpam-5084	120	11	.	.	PUNCT
ejpam-5084	120	12	.	.	PUNCT
ejpam-5084	120	13	.	.	PUNCT
ejpam-5084	120	14	.	.	PUNCT
ejpam-5084	121	1	v1	v1	PROPN
ejpam-5084	121	2	v2	v2	PROPN
ejpam-5084	121	3	v3	v3	PROPN
ejpam-5084	121	4	v4	v4	PROPN
ejpam-5084	121	5	u1	u1	NOUN
ejpam-5084	121	6	u2	u2	PROPN
ejpam-5084	121	7	u3	u3	PROPN
ejpam-5084	121	8	u4	u4	PROPN
ejpam-5084	121	9	ua−2	ua−2	PROPN
ejpam-5084	121	10	ua−1	ua−1	PROPN
ejpam-5084	121	11	ua	ua	PROPN
ejpam-5084	121	12	va−2	va−2	PROPN
ejpam-5084	121	13	va−1	va−1	PROPN
ejpam-5084	121	14	va	va	PROPN
ejpam-5084	121	15	g	g	PROPN
ejpam-5084	121	16	:	:	PUNCT
ejpam-5084	121	17	let	let	VERB
ejpam-5084	121	18	o1	o1	NOUN
ejpam-5084	121	19	=	=	SYM
ejpam-5084	121	20	{	{	PUNCT
ejpam-5084	121	21	u1	u1	NOUN
ejpam-5084	121	22	,	,	PUNCT
ejpam-5084	121	23	u2	u2	NOUN
ejpam-5084	121	24	,	,	PUNCT
ejpam-5084	121	25	.	.	PUNCT
ejpam-5084	121	26	.	.	PUNCT
ejpam-5084	122	1	.	.	PUNCT
ejpam-5084	123	1	,	,	PUNCT
ejpam-5084	123	2	ua	ua	PROPN
ejpam-5084	123	3	}	}	PUNCT
ejpam-5084	123	4	and	and	CCONJ
ejpam-5084	123	5	o2	o2	PROPN
ejpam-5084	123	6	=	=	SYM
ejpam-5084	123	7	{	{	PUNCT
ejpam-5084	123	8	v1	v1	PROPN
ejpam-5084	123	9	,	,	PUNCT
ejpam-5084	123	10	v2	v2	PROPN
ejpam-5084	123	11	,	,	PUNCT
ejpam-5084	123	12	.	.	PUNCT
ejpam-5084	123	13	.	.	PUNCT
ejpam-5084	124	1	.	.	PUNCT
ejpam-5084	125	1	,	,	PUNCT
ejpam-5084	125	2	va	va	PROPN
ejpam-5084	125	3	}	}	PUNCT
ejpam-5084	125	4	,	,	PUNCT
ejpam-5084	125	5	then	then	ADV
ejpam-5084	125	6	o1	o1	PROPN
ejpam-5084	125	7	and	and	CCONJ
ejpam-5084	125	8	o2	o2	PROPN
ejpam-5084	125	9	are	be	AUX
ejpam-5084	125	10	maximum	maximum	ADJ
ejpam-5084	125	11	jopen	jopen	ADJ
ejpam-5084	125	12	independent	independent	ADJ
ejpam-5084	125	13	and	and	CCONJ
ejpam-5084	125	14	maximumu	maximumu	PROPN
ejpam-5084	125	15	j	j	PROPN
ejpam-5084	125	16	-	-	ADJ
ejpam-5084	125	17	total	total	ADJ
ejpam-5084	125	18	dominating	dominating	NOUN
ejpam-5084	125	19	sets	set	NOUN
ejpam-5084	125	20	of	of	ADP
ejpam-5084	125	21	g	g	NOUN
ejpam-5084	125	22	,	,	PUNCT
ejpam-5084	125	23	respectively	respectively	ADV
ejpam-5084	125	24	.	.	PUNCT
ejpam-5084	126	1	therefore	therefore	ADV
ejpam-5084	126	2	,	,	PUNCT
ejpam-5084	126	3	αj(g	αj(g	NUM
ejpam-5084	126	4	)	)	PUNCT
ejpam-5084	126	5	=	=	SYM
ejpam-5084	126	6	a	a	DET
ejpam-5084	126	7	=	=	SYM
ejpam-5084	126	8	γjt(g	γjt(g	PROPN
ejpam-5084	126	9	)	)	PUNCT
ejpam-5084	126	10	.	.	PUNCT
ejpam-5084	127	1	now	now	ADV
ejpam-5084	127	2	suppose	suppose	VERB
ejpam-5084	127	3	that	that	SCONJ
ejpam-5084	127	4	a	a	DET
ejpam-5084	127	5	<	<	X
ejpam-5084	127	6	b.	b.	NOUN
ejpam-5084	127	7	let	let	VERB
ejpam-5084	127	8	q	q	NOUN
ejpam-5084	127	9	=	=	SYM
ejpam-5084	127	10	b	b	X
ejpam-5084	127	11	−	−	NOUN
ejpam-5084	127	12	a	a	PRON
ejpam-5084	127	13	and	and	CCONJ
ejpam-5084	127	14	consider	consider	VERB
ejpam-5084	127	15	the	the	DET
ejpam-5084	127	16	graph	graph	NOUN
ejpam-5084	127	17	h	h	NOUN
ejpam-5084	127	18	below	below	ADV
ejpam-5084	127	19	,	,	PUNCT
ejpam-5084	127	20	where	where	SCONJ
ejpam-5084	127	21	{	{	PUNCT
ejpam-5084	127	22	va	va	NOUN
ejpam-5084	127	23	,	,	PUNCT
ejpam-5084	127	24	r1	r1	NOUN
ejpam-5084	127	25	,	,	PUNCT
ejpam-5084	127	26	r2	r2	PROPN
ejpam-5084	127	27	,	,	PUNCT
ejpam-5084	127	28	.	.	PUNCT
ejpam-5084	127	29	.	.	PUNCT
ejpam-5084	127	30	.	.	PUNCT
ejpam-5084	128	1	,	,	PUNCT
ejpam-5084	128	2	rq	rq	INTJ
ejpam-5084	128	3	}	}	PUNCT
ejpam-5084	128	4	is	be	AUX
ejpam-5084	128	5	a	a	DET
ejpam-5084	128	6	clique	clique	NOUN
ejpam-5084	128	7	.	.	PUNCT
ejpam-5084	128	8	.	.	PUNCT
ejpam-5084	128	9	.	.	PUNCT
ejpam-5084	129	1	.	.	PUNCT
ejpam-5084	130	1	v1	v1	PROPN
ejpam-5084	130	2	v2	v2	PROPN
ejpam-5084	130	3	v3	v3	PROPN
ejpam-5084	130	4	v4	v4	PROPN
ejpam-5084	130	5	u1	u1	NOUN
ejpam-5084	130	6	u2	u2	PROPN
ejpam-5084	130	7	u3	u3	PROPN
ejpam-5084	130	8	u4	u4	PROPN
ejpam-5084	130	9	ua−2	ua−2	PROPN
ejpam-5084	130	10	ua−1	ua−1	PROPN
ejpam-5084	130	11	ua	ua	PROPN
ejpam-5084	130	12	va−2	va−2	PROPN
ejpam-5084	130	13	va−1	va−1	PROPN
ejpam-5084	130	14	va	va	PROPN
ejpam-5084	130	15	h	h	PROPN
ejpam-5084	130	16	:	:	PUNCT
ejpam-5084	130	17	...	...	PUNCT
ejpam-5084	131	1	rq	rq	AUX
ejpam-5084	131	2	r2	r2	PROPN
ejpam-5084	131	3	r1	r1	PROPN
ejpam-5084	131	4	let	let	VERB
ejpam-5084	131	5	q1	q1	PROPN
ejpam-5084	131	6	=	=	SYM
ejpam-5084	131	7	{	{	PUNCT
ejpam-5084	131	8	u1	u1	NOUN
ejpam-5084	131	9	,	,	PUNCT
ejpam-5084	131	10	u2	u2	NOUN
ejpam-5084	131	11	,	,	PUNCT
ejpam-5084	131	12	.	.	PUNCT
ejpam-5084	131	13	.	.	PUNCT
ejpam-5084	132	1	.	.	PUNCT
ejpam-5084	133	1	,	,	PUNCT
ejpam-5084	133	2	ua	ua	PROPN
ejpam-5084	133	3	}	}	PUNCT
ejpam-5084	133	4	and	and	CCONJ
ejpam-5084	133	5	q2	q2	NOUN
ejpam-5084	133	6	=	=	SYM
ejpam-5084	133	7	{	{	PUNCT
ejpam-5084	133	8	v1	v1	PROPN
ejpam-5084	133	9	,	,	PUNCT
ejpam-5084	133	10	v2	v2	PROPN
ejpam-5084	133	11	,	,	PUNCT
ejpam-5084	133	12	.	.	PUNCT
ejpam-5084	133	13	.	.	PUNCT
ejpam-5084	134	1	.	.	PUNCT
ejpam-5084	135	1	,	,	PUNCT
ejpam-5084	135	2	va	va	PROPN
ejpam-5084	135	3	,	,	PUNCT
ejpam-5084	135	4	r1	r1	NOUN
ejpam-5084	135	5	,	,	PUNCT
ejpam-5084	135	6	.	.	PUNCT
ejpam-5084	135	7	.	.	PUNCT
ejpam-5084	135	8	.	.	PUNCT
ejpam-5084	136	1	,	,	PUNCT
ejpam-5084	136	2	rq	rq	INTJ
ejpam-5084	136	3	}	}	PUNCT
ejpam-5084	136	4	.	.	PUNCT
ejpam-5084	137	1	then	then	ADV
ejpam-5084	137	2	q1	q1	PROPN
ejpam-5084	137	3	and	and	CCONJ
ejpam-5084	137	4	q2	q2	NOUN
ejpam-5084	137	5	are	be	AUX
ejpam-5084	137	6	maximum	maximum	ADJ
ejpam-5084	137	7	j	j	ADJ
ejpam-5084	137	8	-	-	ADJ
ejpam-5084	137	9	open	open	ADJ
ejpam-5084	137	10	independent	independent	ADJ
ejpam-5084	137	11	and	and	CCONJ
ejpam-5084	137	12	maximum	maximum	ADJ
ejpam-5084	137	13	j	j	PROPN
ejpam-5084	137	14	-	-	ADJ
ejpam-5084	137	15	total	total	ADJ
ejpam-5084	137	16	dominating	dominating	NOUN
ejpam-5084	137	17	sets	set	NOUN
ejpam-5084	137	18	of	of	ADP
ejpam-5084	137	19	h	h	NOUN
ejpam-5084	137	20	,	,	PUNCT
ejpam-5084	137	21	respectively	respectively	ADV
ejpam-5084	137	22	.	.	PUNCT
ejpam-5084	138	1	hence	hence	ADV
ejpam-5084	138	2	,	,	PUNCT
ejpam-5084	138	3	αj(h	αj(h	PUNCT
ejpam-5084	138	4	)	)	PUNCT
ejpam-5084	138	5	=	=	SYM
ejpam-5084	139	1	a	a	PRON
ejpam-5084	139	2	and	and	CCONJ
ejpam-5084	139	3	γjt(h	γjt(h	ADJ
ejpam-5084	139	4	)	)	PUNCT
ejpam-5084	140	1	=	=	PRON
ejpam-5084	140	2	a+	a+	PUNCT
ejpam-5084	140	3	q	q	PROPN
ejpam-5084	140	4	=	=	PROPN
ejpam-5084	140	5	b.	b.	PROPN
ejpam-5084	140	6	j.	j.	PROPN
ejpam-5084	140	7	a.	a.	PROPN
ejpam-5084	140	8	hassan	hassan	PROPN
ejpam-5084	140	9	et	et	PROPN
ejpam-5084	140	10	al	al	PROPN
ejpam-5084	140	11	.	.	PUNCT
ejpam-5084	140	12	/	/	SYM
ejpam-5084	140	13	eur	eur	PROPN
ejpam-5084	140	14	.	.	PUNCT
ejpam-5084	141	1	j.	j.	PROPN
ejpam-5084	141	2	pure	pure	PROPN
ejpam-5084	141	3	appl	appl	PROPN
ejpam-5084	141	4	.	.	PROPN
ejpam-5084	141	5	math	math	PROPN
ejpam-5084	141	6	,	,	PUNCT
ejpam-5084	141	7	17	17	NUM
ejpam-5084	141	8	(	(	PUNCT
ejpam-5084	141	9	2	2	NUM
ejpam-5084	141	10	)	)	PUNCT
ejpam-5084	141	11	(	(	PUNCT
ejpam-5084	141	12	2024	2024	NUM
ejpam-5084	141	13	)	)	PUNCT
ejpam-5084	141	14	,	,	PUNCT
ejpam-5084	141	15	922	922	NUM
ejpam-5084	141	16	-	-	SYM
ejpam-5084	141	17	930	930	NUM
ejpam-5084	141	18	927	927	NUM
ejpam-5084	141	19	6	6	NUM
ejpam-5084	141	20	.	.	PUNCT
ejpam-5084	142	1	the	the	DET
ejpam-5084	142	2	incomparability	incomparability	NOUN
ejpam-5084	142	3	of	of	ADP
ejpam-5084	142	4	j	j	PROPN
ejpam-5084	142	5	-	-	ADJ
ejpam-5084	142	6	open	open	ADJ
ejpam-5084	142	7	independence	independence	NOUN
ejpam-5084	142	8	and	and	CCONJ
ejpam-5084	142	9	hop	hop	NOUN
ejpam-5084	142	10	independence	independence	NOUN
ejpam-5084	142	11	parameters	parameter	NOUN
ejpam-5084	142	12	remark	remark	VERB
ejpam-5084	142	13	2	2	NUM
ejpam-5084	142	14	.	.	PUNCT
ejpam-5084	143	1	the	the	DET
ejpam-5084	143	2	hop	hop	NOUN
ejpam-5084	143	3	independence	independence	NOUN
ejpam-5084	143	4	and	and	CCONJ
ejpam-5084	143	5	j	j	NOUN
ejpam-5084	143	6	-	-	ADJ
ejpam-5084	143	7	open	open	ADJ
ejpam-5084	143	8	independence	independence	NOUN
ejpam-5084	143	9	parameters	parameter	NOUN
ejpam-5084	143	10	of	of	ADP
ejpam-5084	143	11	a	a	DET
ejpam-5084	143	12	graph	graph	NOUN
ejpam-5084	143	13	are	be	AUX
ejpam-5084	143	14	incomparable	incomparable	ADJ
ejpam-5084	143	15	.	.	PUNCT
ejpam-5084	144	1	to	to	PART
ejpam-5084	144	2	see	see	VERB
ejpam-5084	144	3	this	this	PRON
ejpam-5084	144	4	,	,	PUNCT
ejpam-5084	144	5	consider	consider	VERB
ejpam-5084	144	6	the	the	DET
ejpam-5084	144	7	graph	graph	NOUN
ejpam-5084	144	8	k2	k2	ADJ
ejpam-5084	144	9	+	+	CCONJ
ejpam-5084	144	10	p5	p5	ADJ
ejpam-5084	144	11	below	below	ADV
ejpam-5084	144	12	.	.	PUNCT
ejpam-5084	145	1	x1	x1	PROPN
ejpam-5084	146	1	x2	x2	NOUN
ejpam-5084	146	2	x3	x3	PROPN
ejpam-5084	147	1	x4	x4	PROPN
ejpam-5084	147	2	x5	x5	PROPN
ejpam-5084	147	3	y1	y1	PROPN
ejpam-5084	147	4	y2	y2	PROPN
ejpam-5084	147	5	k2	k2	NOUN
ejpam-5084	147	6	+	+	CCONJ
ejpam-5084	147	7	p5	p5	ADJ
ejpam-5084	147	8	:	:	PUNCT
ejpam-5084	147	9	let	let	VERB
ejpam-5084	147	10	o1	o1	NOUN
ejpam-5084	147	11	=	=	SYM
ejpam-5084	147	12	{	{	PUNCT
ejpam-5084	147	13	x2	x2	PROPN
ejpam-5084	147	14	,	,	PUNCT
ejpam-5084	147	15	x4	x4	PROPN
ejpam-5084	147	16	}	}	PUNCT
ejpam-5084	147	17	and	and	CCONJ
ejpam-5084	147	18	o2	o2	PROPN
ejpam-5084	147	19	=	=	SYM
ejpam-5084	147	20	{	{	PUNCT
ejpam-5084	147	21	x1	x1	PROPN
ejpam-5084	147	22	,	,	PUNCT
ejpam-5084	147	23	x2	x2	PROPN
ejpam-5084	147	24	,	,	PUNCT
ejpam-5084	147	25	y1	y1	NOUN
ejpam-5084	147	26	,	,	PUNCT
ejpam-5084	147	27	y2	y2	PROPN
ejpam-5084	147	28	}	}	PUNCT
ejpam-5084	147	29	.	.	PUNCT
ejpam-5084	148	1	then	then	ADV
ejpam-5084	148	2	o1	o1	PROPN
ejpam-5084	148	3	and	and	CCONJ
ejpam-5084	148	4	o2	o2	PROPN
ejpam-5084	148	5	are	be	AUX
ejpam-5084	148	6	maximum	maximum	ADJ
ejpam-5084	148	7	j	j	ADJ
ejpam-5084	148	8	-	-	ADJ
ejpam-5084	148	9	open	open	ADJ
ejpam-5084	148	10	independent	independent	ADJ
ejpam-5084	148	11	and	and	CCONJ
ejpam-5084	148	12	maximum	maximum	ADJ
ejpam-5084	148	13	hop	hop	NOUN
ejpam-5084	148	14	independent	independent	ADJ
ejpam-5084	148	15	sets	set	NOUN
ejpam-5084	148	16	of	of	ADP
ejpam-5084	148	17	k2	k2	ADJ
ejpam-5084	148	18	+	+	CCONJ
ejpam-5084	148	19	p5	p5	ADJ
ejpam-5084	148	20	,	,	PUNCT
ejpam-5084	148	21	respectively	respectively	ADV
ejpam-5084	148	22	.	.	PUNCT
ejpam-5084	149	1	hence	hence	ADV
ejpam-5084	149	2	,	,	PUNCT
ejpam-5084	149	3	αj(k2	αj(k2	ADV
ejpam-5084	149	4	+	+	ADJ
ejpam-5084	149	5	p11	p11	NOUN
ejpam-5084	149	6	)	)	PUNCT
ejpam-5084	149	7	=	=	SYM
ejpam-5084	149	8	2	2	NUM
ejpam-5084	149	9	and	and	CCONJ
ejpam-5084	149	10	αh(k2	αh(k2	NOUN
ejpam-5084	149	11	+	+	CCONJ
ejpam-5084	149	12	p5	p5	ADJ
ejpam-5084	149	13	)	)	PUNCT
ejpam-5084	149	14	=	=	SYM
ejpam-5084	150	1	4	4	X
ejpam-5084	150	2	.	.	PUNCT
ejpam-5084	150	3	next	next	ADV
ejpam-5084	150	4	,	,	PUNCT
ejpam-5084	150	5	consider	consider	VERB
ejpam-5084	150	6	the	the	DET
ejpam-5084	150	7	graph	graph	NOUN
ejpam-5084	150	8	c4	c4	NOUN
ejpam-5084	150	9	+	+	CCONJ
ejpam-5084	150	10	p11	p11	ADV
ejpam-5084	150	11	below	below	ADV
ejpam-5084	150	12	.	.	PUNCT
ejpam-5084	151	1	x1	x1	PROPN
ejpam-5084	152	1	x2	x2	PROPN
ejpam-5084	152	2	x3	x3	PROPN
ejpam-5084	152	3	x4	x4	PROPN
ejpam-5084	152	4	x10x9x5	x10x9x5	PROPN
ejpam-5084	152	5	x7x6	x7x6	PROPN
ejpam-5084	153	1	x8	x8	PROPN
ejpam-5084	153	2	x11	x11	NOUN
ejpam-5084	153	3	y1	y1	NOUN
ejpam-5084	153	4	y2	y2	PROPN
ejpam-5084	153	5	y3	y3	PROPN
ejpam-5084	153	6	y4	y4	NOUN
ejpam-5084	153	7	c4	c4	NOUN
ejpam-5084	153	8	+	+	CCONJ
ejpam-5084	153	9	p11	p11	NOUN
ejpam-5084	153	10	:	:	PUNCT
ejpam-5084	153	11	let	let	VERB
ejpam-5084	153	12	o′	o′	X
ejpam-5084	153	13	=	=	SYM
ejpam-5084	153	14	{	{	PUNCT
ejpam-5084	153	15	y1	y1	PROPN
ejpam-5084	153	16	,	,	PUNCT
ejpam-5084	153	17	y2	y2	PROPN
ejpam-5084	153	18	,	,	PUNCT
ejpam-5084	153	19	x10	x10	NOUN
ejpam-5084	153	20	,	,	PUNCT
ejpam-5084	153	21	x11	x11	NOUN
ejpam-5084	153	22	}	}	PUNCT
ejpam-5084	153	23	and	and	CCONJ
ejpam-5084	153	24	o′′	o′′	NOUN
ejpam-5084	153	25	=	=	SYM
ejpam-5084	153	26	{	{	PUNCT
ejpam-5084	153	27	x2	x2	PROPN
ejpam-5084	153	28	,	,	PUNCT
ejpam-5084	153	29	x4	x4	PROPN
ejpam-5084	153	30	,	,	PUNCT
ejpam-5084	153	31	x6	x6	PROPN
ejpam-5084	153	32	,	,	PUNCT
ejpam-5084	153	33	x8	x8	PROPN
ejpam-5084	153	34	,	,	PUNCT
ejpam-5084	153	35	x10	x10	NOUN
ejpam-5084	153	36	}	}	PUNCT
ejpam-5084	153	37	.	.	PUNCT
ejpam-5084	154	1	then	then	ADV
ejpam-5084	154	2	o′	o′	X
ejpam-5084	154	3	and	and	CCONJ
ejpam-5084	154	4	o′′	o′′	NOUN
ejpam-5084	154	5	are	be	AUX
ejpam-5084	154	6	maximum	maximum	ADJ
ejpam-5084	154	7	hop	hop	NOUN
ejpam-5084	154	8	independent	independent	ADJ
ejpam-5084	154	9	and	and	CCONJ
ejpam-5084	154	10	j	j	NOUN
ejpam-5084	154	11	-	-	ADJ
ejpam-5084	154	12	open	open	ADJ
ejpam-5084	154	13	independent	independent	ADJ
ejpam-5084	154	14	sets	set	NOUN
ejpam-5084	154	15	of	of	ADP
ejpam-5084	154	16	c4	c4	NOUN
ejpam-5084	154	17	+	+	CCONJ
ejpam-5084	154	18	p11	p11	NOUN
ejpam-5084	154	19	respectively	respectively	ADV
ejpam-5084	154	20	.	.	PUNCT
ejpam-5084	155	1	thus	thus	ADV
ejpam-5084	155	2	,	,	PUNCT
ejpam-5084	155	3	αh(c4	αh(c4	NOUN
ejpam-5084	155	4	+	+	CCONJ
ejpam-5084	155	5	p11	p11	NOUN
ejpam-5084	155	6	)	)	PUNCT
ejpam-5084	155	7	=	=	SYM
ejpam-5084	155	8	4	4	NUM
ejpam-5084	155	9	and	and	CCONJ
ejpam-5084	155	10	αj(c4	αj(c4	NOUN
ejpam-5084	155	11	+	+	CCONJ
ejpam-5084	155	12	p11	p11	NOUN
ejpam-5084	155	13	)	)	PUNCT
ejpam-5084	155	14	=	=	SYM
ejpam-5084	156	1	5	5	NUM
ejpam-5084	156	2	.	.	NOUN
ejpam-5084	156	3	7	7	NUM
ejpam-5084	156	4	.	.	X
ejpam-5084	157	1	j	j	NOUN
ejpam-5084	157	2	-	-	ADJ
ejpam-5084	157	3	open	open	ADJ
ejpam-5084	157	4	independence	independence	NOUN
ejpam-5084	157	5	in	in	ADP
ejpam-5084	157	6	the	the	DET
ejpam-5084	157	7	join	join	NOUN
ejpam-5084	157	8	of	of	ADP
ejpam-5084	157	9	two	two	NUM
ejpam-5084	157	10	graphs	graph	NOUN
ejpam-5084	157	11	theorem	theorem	VERB
ejpam-5084	157	12	4	4	NUM
ejpam-5084	157	13	.	.	PUNCT
ejpam-5084	158	1	let	let	VERB
ejpam-5084	158	2	g	g	NOUN
ejpam-5084	159	1	and	and	CCONJ
ejpam-5084	159	2	h	h	NOUN
ejpam-5084	159	3	be	be	AUX
ejpam-5084	159	4	a	a	DET
ejpam-5084	159	5	graphs	graph	NOUN
ejpam-5084	159	6	.	.	PUNCT
ejpam-5084	160	1	a	a	DET
ejpam-5084	160	2	subset	subset	ADJ
ejpam-5084	160	3	o	o	NOUN
ejpam-5084	160	4	of	of	ADP
ejpam-5084	160	5	a	a	DET
ejpam-5084	160	6	vertex	vertex	NOUN
ejpam-5084	160	7	-	-	PUNCT
ejpam-5084	160	8	set	set	VERB
ejpam-5084	160	9	v	v	NOUN
ejpam-5084	160	10	(	(	PUNCT
ejpam-5084	160	11	g+h	g+h	NOUN
ejpam-5084	160	12	)	)	PUNCT
ejpam-5084	160	13	of	of	ADP
ejpam-5084	160	14	g+h	g+h	PROPN
ejpam-5084	160	15	is	be	AUX
ejpam-5084	160	16	a	a	DET
ejpam-5084	160	17	j	j	NOUN
ejpam-5084	160	18	-	-	ADJ
ejpam-5084	160	19	open	open	ADJ
ejpam-5084	160	20	independent	independent	ADJ
ejpam-5084	160	21	set	set	NOUN
ejpam-5084	160	22	of	of	ADP
ejpam-5084	160	23	g	g	PROPN
ejpam-5084	161	1	+	+	CCONJ
ejpam-5084	161	2	h	h	NOUN
ejpam-5084	161	3	if	if	SCONJ
ejpam-5084	161	4	and	and	CCONJ
ejpam-5084	161	5	only	only	ADV
ejpam-5084	161	6	if	if	SCONJ
ejpam-5084	161	7	o	o	NOUN
ejpam-5084	161	8	satisfies	satisfy	VERB
ejpam-5084	161	9	one	one	NUM
ejpam-5084	161	10	of	of	ADP
ejpam-5084	161	11	the	the	DET
ejpam-5084	161	12	following	following	ADJ
ejpam-5084	161	13	conditions	condition	NOUN
ejpam-5084	161	14	:	:	PUNCT
ejpam-5084	161	15	(	(	PUNCT
ejpam-5084	161	16	i	i	NOUN
ejpam-5084	161	17	)	)	PUNCT
ejpam-5084	161	18	o	o	NOUN
ejpam-5084	161	19	is	be	AUX
ejpam-5084	161	20	a	a	DET
ejpam-5084	161	21	j	j	NOUN
ejpam-5084	161	22	-	-	ADJ
ejpam-5084	161	23	open	open	ADJ
ejpam-5084	161	24	independent	independent	ADJ
ejpam-5084	161	25	set	set	NOUN
ejpam-5084	161	26	of	of	ADP
ejpam-5084	161	27	g.	g.	PROPN
ejpam-5084	161	28	(	(	PUNCT
ejpam-5084	161	29	ii	ii	PROPN
ejpam-5084	161	30	)	)	PUNCT
ejpam-5084	161	31	o	o	NOUN
ejpam-5084	161	32	is	be	AUX
ejpam-5084	161	33	a	a	DET
ejpam-5084	161	34	j	j	NOUN
ejpam-5084	161	35	-	-	ADJ
ejpam-5084	161	36	open	open	ADJ
ejpam-5084	161	37	independent	independent	ADJ
ejpam-5084	161	38	set	set	NOUN
ejpam-5084	161	39	of	of	ADP
ejpam-5084	161	40	h.	h.	PROPN
ejpam-5084	161	41	references	reference	NOUN
ejpam-5084	161	42	928	928	NUM
ejpam-5084	161	43	proof	proof	NOUN
ejpam-5084	161	44	.	.	PUNCT
ejpam-5084	162	1	let	let	VERB
ejpam-5084	162	2	o	o	NOUN
ejpam-5084	162	3	be	be	AUX
ejpam-5084	162	4	a	a	DET
ejpam-5084	162	5	j	j	NOUN
ejpam-5084	162	6	-	-	ADJ
ejpam-5084	162	7	open	open	ADJ
ejpam-5084	162	8	independent	independent	ADJ
ejpam-5084	162	9	set	set	NOUN
ejpam-5084	162	10	of	of	ADP
ejpam-5084	162	11	g	g	PROPN
ejpam-5084	162	12	+	+	CCONJ
ejpam-5084	162	13	h.	h.	PROPN
ejpam-5084	163	1	then	then	ADV
ejpam-5084	163	2	either	either	CCONJ
ejpam-5084	163	3	o	o	PROPN
ejpam-5084	163	4	⊆	⊆	NUM
ejpam-5084	163	5	v	v	ADP
ejpam-5084	163	6	(	(	PUNCT
ejpam-5084	163	7	h	h	NOUN
ejpam-5084	163	8	)	)	PUNCT
ejpam-5084	163	9	or	or	CCONJ
ejpam-5084	163	10	o	o	NOUN
ejpam-5084	163	11	⊆	⊆	NUM
ejpam-5084	163	12	v	v	NOUN
ejpam-5084	163	13	(	(	PUNCT
ejpam-5084	163	14	g	g	NOUN
ejpam-5084	163	15	)	)	PUNCT
ejpam-5084	163	16	.	.	PUNCT
ejpam-5084	164	1	if	if	SCONJ
ejpam-5084	164	2	o	o	PROPN
ejpam-5084	164	3	⊆	⊆	NUM
ejpam-5084	164	4	v	v	X
ejpam-5084	164	5	(	(	PUNCT
ejpam-5084	164	6	g	g	NOUN
ejpam-5084	164	7	)	)	PUNCT
ejpam-5084	164	8	,	,	PUNCT
ejpam-5084	164	9	then	then	ADV
ejpam-5084	164	10	o	o	NOUN
ejpam-5084	164	11	is	be	AUX
ejpam-5084	164	12	a	a	DET
ejpam-5084	164	13	j	j	NOUN
ejpam-5084	164	14	-	-	ADJ
ejpam-5084	164	15	open	open	ADJ
ejpam-5084	164	16	independent	independent	ADJ
ejpam-5084	164	17	set	set	NOUN
ejpam-5084	164	18	of	of	ADP
ejpam-5084	164	19	g.	g.	PROPN
ejpam-5084	164	20	thus	thus	ADV
ejpam-5084	164	21	,	,	PUNCT
ejpam-5084	164	22	(	(	PUNCT
ejpam-5084	164	23	i	i	NOUN
ejpam-5084	164	24	)	)	PUNCT
ejpam-5084	164	25	holds	hold	VERB
ejpam-5084	164	26	.	.	PUNCT
ejpam-5084	165	1	if	if	SCONJ
ejpam-5084	165	2	o	o	PROPN
ejpam-5084	165	3	⊆	⊆	NUM
ejpam-5084	165	4	v	v	X
ejpam-5084	165	5	(	(	PUNCT
ejpam-5084	165	6	h	h	NOUN
ejpam-5084	165	7	)	)	PUNCT
ejpam-5084	165	8	,	,	PUNCT
ejpam-5084	165	9	then	then	ADV
ejpam-5084	165	10	o	o	NOUN
ejpam-5084	165	11	is	be	AUX
ejpam-5084	165	12	a	a	DET
ejpam-5084	165	13	j	j	NOUN
ejpam-5084	165	14	-	-	ADJ
ejpam-5084	165	15	open	open	ADJ
ejpam-5084	165	16	indepedent	indepedent	ADJ
ejpam-5084	165	17	set	set	NOUN
ejpam-5084	165	18	of	of	ADP
ejpam-5084	165	19	h.	h.	PROPN
ejpam-5084	165	20	hence	hence	PROPN
ejpam-5084	165	21	,	,	PUNCT
ejpam-5084	165	22	(	(	PUNCT
ejpam-5084	165	23	ii	ii	NOUN
ejpam-5084	165	24	)	)	PUNCT
ejpam-5084	165	25	holds	hold	VERB
ejpam-5084	165	26	.	.	PUNCT
ejpam-5084	166	1	conversely	conversely	ADV
ejpam-5084	166	2	,	,	PUNCT
ejpam-5084	166	3	suppose	suppose	VERB
ejpam-5084	166	4	that	that	SCONJ
ejpam-5084	166	5	(	(	PUNCT
ejpam-5084	166	6	i	i	NOUN
ejpam-5084	166	7	)	)	PUNCT
ejpam-5084	166	8	holds	hold	VERB
ejpam-5084	166	9	.	.	PUNCT
ejpam-5084	167	1	since	since	SCONJ
ejpam-5084	167	2	v	v	NOUN
ejpam-5084	167	3	(	(	PUNCT
ejpam-5084	167	4	g	g	NOUN
ejpam-5084	167	5	)	)	PUNCT
ejpam-5084	167	6	⊆	⊆	NUM
ejpam-5084	167	7	v	v	NOUN
ejpam-5084	167	8	(	(	PUNCT
ejpam-5084	167	9	g+h	g+h	PROPN
ejpam-5084	167	10	)	)	PUNCT
ejpam-5084	167	11	,	,	PUNCT
ejpam-5084	167	12	o	o	PROPN
ejpam-5084	167	13	is	be	AUX
ejpam-5084	167	14	a	a	DET
ejpam-5084	167	15	j	j	NOUN
ejpam-5084	167	16	-	-	ADJ
ejpam-5084	167	17	open	open	ADJ
ejpam-5084	167	18	independent	independent	ADJ
ejpam-5084	167	19	set	set	NOUN
ejpam-5084	167	20	of	of	ADP
ejpam-5084	167	21	g+h	g+h	PROPN
ejpam-5084	167	22	.	.	PUNCT
ejpam-5084	168	1	assume	assume	VERB
ejpam-5084	168	2	that(ii	that(ii	PROPN
ejpam-5084	168	3	)	)	PUNCT
ejpam-5084	168	4	holds	hold	VERB
ejpam-5084	168	5	.	.	PUNCT
ejpam-5084	169	1	since	since	SCONJ
ejpam-5084	169	2	v	v	NOUN
ejpam-5084	169	3	(	(	PUNCT
ejpam-5084	169	4	h	h	NOUN
ejpam-5084	169	5	)	)	PUNCT
ejpam-5084	169	6	⊆	⊆	NUM
ejpam-5084	169	7	v	v	NOUN
ejpam-5084	169	8	(	(	PUNCT
ejpam-5084	169	9	g+h	g+h	PROPN
ejpam-5084	169	10	)	)	PUNCT
ejpam-5084	169	11	,	,	PUNCT
ejpam-5084	169	12	it	it	PRON
ejpam-5084	169	13	follows	follow	VERB
ejpam-5084	169	14	that	that	SCONJ
ejpam-5084	169	15	o	o	NOUN
ejpam-5084	169	16	is	be	AUX
ejpam-5084	169	17	a	a	DET
ejpam-5084	169	18	j	j	NOUN
ejpam-5084	169	19	-	-	ADJ
ejpam-5084	169	20	open	open	ADJ
ejpam-5084	169	21	independent	independent	ADJ
ejpam-5084	169	22	set	set	NOUN
ejpam-5084	169	23	of	of	ADP
ejpam-5084	169	24	g+h	g+h	PROPN
ejpam-5084	169	25	.	.	PUNCT
ejpam-5084	170	1	corollary	corollary	ADJ
ejpam-5084	170	2	1	1	NUM
ejpam-5084	170	3	.	.	PUNCT
ejpam-5084	171	1	let	let	VERB
ejpam-5084	171	2	g	g	NOUN
ejpam-5084	171	3	and	and	CCONJ
ejpam-5084	171	4	h	h	PROPN
ejpam-5084	171	5	be	be	AUX
ejpam-5084	171	6	graphs	graph	NOUN
ejpam-5084	171	7	.	.	PUNCT
ejpam-5084	172	1	then	then	ADV
ejpam-5084	172	2	αj(g+h	αj(g+h	NUM
ejpam-5084	172	3	)	)	PUNCT
ejpam-5084	172	4	=	=	SYM
ejpam-5084	172	5	max{αj(g	max{αj(g	NOUN
ejpam-5084	172	6	)	)	PUNCT
ejpam-5084	172	7	,	,	PUNCT
ejpam-5084	172	8	αj(h	αj(h	ADV
ejpam-5084	172	9	)	)	PUNCT
ejpam-5084	172	10	}	}	PUNCT
ejpam-5084	172	11	.	.	PUNCT
ejpam-5084	173	1	proof	proof	NOUN
ejpam-5084	173	2	.	.	PUNCT
ejpam-5084	174	1	let	let	VERB
ejpam-5084	174	2	o	o	NOUN
ejpam-5084	174	3	be	be	AUX
ejpam-5084	174	4	a	a	DET
ejpam-5084	174	5	maximum	maximum	ADJ
ejpam-5084	174	6	j	j	NOUN
ejpam-5084	174	7	-	-	ADJ
ejpam-5084	174	8	open	open	ADJ
ejpam-5084	174	9	independent	independent	ADJ
ejpam-5084	174	10	set	set	NOUN
ejpam-5084	174	11	of	of	ADP
ejpam-5084	174	12	g	g	PROPN
ejpam-5084	174	13	+	+	CCONJ
ejpam-5084	174	14	h.	h.	PROPN
ejpam-5084	174	15	then	then	ADV
ejpam-5084	174	16	by	by	ADP
ejpam-5084	174	17	theorem	theorem	NOUN
ejpam-5084	174	18	4	4	NUM
ejpam-5084	174	19	,	,	PUNCT
ejpam-5084	174	20	o	o	NOUN
ejpam-5084	174	21	is	be	AUX
ejpam-5084	174	22	either	either	CCONJ
ejpam-5084	174	23	a	a	DET
ejpam-5084	174	24	j	j	NOUN
ejpam-5084	174	25	-	-	ADJ
ejpam-5084	174	26	open	open	ADJ
ejpam-5084	174	27	independent	independent	ADJ
ejpam-5084	174	28	set	set	NOUN
ejpam-5084	174	29	of	of	ADP
ejpam-5084	174	30	g	g	PROPN
ejpam-5084	174	31	or	or	CCONJ
ejpam-5084	174	32	h.	h.	PROPN
ejpam-5084	174	33	if	if	SCONJ
ejpam-5084	174	34	o	o	PROPN
ejpam-5084	174	35	is	be	AUX
ejpam-5084	174	36	a	a	DET
ejpam-5084	174	37	j	j	NOUN
ejpam-5084	174	38	-	-	ADJ
ejpam-5084	174	39	open	open	ADJ
ejpam-5084	174	40	independent	independent	ADJ
ejpam-5084	174	41	set	set	NOUN
ejpam-5084	174	42	of	of	ADP
ejpam-5084	174	43	g	g	NOUN
ejpam-5084	174	44	,	,	PUNCT
ejpam-5084	174	45	then	then	ADV
ejpam-5084	174	46	αj(g	αj(g	NUM
ejpam-5084	175	1	+	+	CCONJ
ejpam-5084	175	2	h	h	NOUN
ejpam-5084	175	3	)	)	PUNCT
ejpam-5084	175	4	=	=	SYM
ejpam-5084	175	5	|o|	|o|	PROPN
ejpam-5084	175	6	≤	≤	NOUN
ejpam-5084	175	7	αj(g	αj(g	NUM
ejpam-5084	175	8	)	)	PUNCT
ejpam-5084	175	9	.	.	PUNCT
ejpam-5084	176	1	if	if	SCONJ
ejpam-5084	176	2	o	o	PROPN
ejpam-5084	176	3	is	be	AUX
ejpam-5084	176	4	a	a	DET
ejpam-5084	176	5	j	j	NOUN
ejpam-5084	176	6	-	-	ADJ
ejpam-5084	176	7	open	open	ADJ
ejpam-5084	176	8	independent	independent	ADJ
ejpam-5084	176	9	set	set	NOUN
ejpam-5084	176	10	of	of	ADP
ejpam-5084	176	11	h	h	NOUN
ejpam-5084	176	12	,	,	PUNCT
ejpam-5084	176	13	then	then	ADV
ejpam-5084	176	14	αj(g+h	αj(g+h	NUM
ejpam-5084	176	15	)	)	PUNCT
ejpam-5084	176	16	=	=	PUNCT
ejpam-5084	177	1	|o|	|o|	NOUN
ejpam-5084	177	2	≤	≤	NOUN
ejpam-5084	177	3	αj(h	αj(h	CCONJ
ejpam-5084	177	4	)	)	PUNCT
ejpam-5084	177	5	.	.	PUNCT
ejpam-5084	178	1	on	on	ADP
ejpam-5084	178	2	the	the	DET
ejpam-5084	178	3	other	other	ADJ
ejpam-5084	178	4	hand	hand	NOUN
ejpam-5084	178	5	,	,	PUNCT
ejpam-5084	178	6	suppose	suppose	VERB
ejpam-5084	178	7	that	that	SCONJ
ejpam-5084	178	8	o	o	PROPN
ejpam-5084	178	9	is	be	AUX
ejpam-5084	178	10	a	a	DET
ejpam-5084	178	11	maximum	maximum	ADJ
ejpam-5084	178	12	j	j	NOUN
ejpam-5084	178	13	-	-	ADJ
ejpam-5084	178	14	open	open	ADJ
ejpam-5084	178	15	independent	independent	ADJ
ejpam-5084	178	16	set	set	NOUN
ejpam-5084	178	17	of	of	ADP
ejpam-5084	178	18	g.	g.	PROPN
ejpam-5084	178	19	then	then	ADV
ejpam-5084	178	20	by	by	ADP
ejpam-5084	178	21	theorem	theorem	NOUN
ejpam-5084	178	22	4	4	NUM
ejpam-5084	178	23	,	,	PUNCT
ejpam-5084	178	24	o	o	PROPN
ejpam-5084	178	25	is	be	AUX
ejpam-5084	178	26	a	a	DET
ejpam-5084	178	27	j	j	NOUN
ejpam-5084	178	28	-	-	ADJ
ejpam-5084	178	29	open	open	ADJ
ejpam-5084	178	30	independent	independent	ADJ
ejpam-5084	178	31	set	set	NOUN
ejpam-5084	178	32	of	of	ADP
ejpam-5084	178	33	g+h	g+h	PROPN
ejpam-5084	178	34	.	.	PUNCT
ejpam-5084	179	1	thus	thus	ADV
ejpam-5084	179	2	,	,	PUNCT
ejpam-5084	179	3	αj(g	αj(g	NUM
ejpam-5084	179	4	)	)	PUNCT
ejpam-5084	179	5	=	=	SYM
ejpam-5084	180	1	|o|	|o|	PROPN
ejpam-5084	180	2	≤	≤	NUM
ejpam-5084	180	3	αj(g+h	αj(g+h	NUM
ejpam-5084	180	4	)	)	PUNCT
ejpam-5084	180	5	.	.	PUNCT
ejpam-5084	181	1	similarly	similarly	ADV
ejpam-5084	181	2	,	,	PUNCT
ejpam-5084	181	3	if	if	SCONJ
ejpam-5084	181	4	o	o	PROPN
ejpam-5084	181	5	is	be	AUX
ejpam-5084	181	6	a	a	DET
ejpam-5084	181	7	maximum	maximum	ADJ
ejpam-5084	181	8	j	j	NOUN
ejpam-5084	181	9	-	-	ADJ
ejpam-5084	181	10	open	open	ADJ
ejpam-5084	181	11	independent	independent	ADJ
ejpam-5084	181	12	set	set	NOUN
ejpam-5084	181	13	of	of	ADP
ejpam-5084	181	14	h	h	NOUN
ejpam-5084	181	15	,	,	PUNCT
ejpam-5084	181	16	then	then	ADV
ejpam-5084	181	17	o	o	NOUN
ejpam-5084	181	18	is	be	AUX
ejpam-5084	181	19	a	a	DET
ejpam-5084	181	20	j	j	NOUN
ejpam-5084	181	21	-	-	ADJ
ejpam-5084	181	22	open	open	ADJ
ejpam-5084	181	23	independent	independent	ADJ
ejpam-5084	181	24	set	set	NOUN
ejpam-5084	181	25	of	of	ADP
ejpam-5084	181	26	g+h	g+h	PROPN
ejpam-5084	181	27	.	.	PUNCT
ejpam-5084	182	1	hence	hence	ADV
ejpam-5084	182	2	,	,	PUNCT
ejpam-5084	182	3	αj(h	αj(h	PUNCT
ejpam-5084	182	4	)	)	PUNCT
ejpam-5084	182	5	=	=	SYM
ejpam-5084	183	1	|o|	|o|	PROPN
ejpam-5084	183	2	≤	≤	NUM
ejpam-5084	183	3	αj(g+h	αj(g+h	NUM
ejpam-5084	183	4	)	)	PUNCT
ejpam-5084	183	5	.	.	PUNCT
ejpam-5084	184	1	consequently	consequently	ADV
ejpam-5084	184	2	,	,	PUNCT
ejpam-5084	184	3	αj(g+h	αj(g+h	NOUN
ejpam-5084	184	4	)	)	PUNCT
ejpam-5084	184	5	=	=	SYM
ejpam-5084	184	6	max{αj(g	max{αj(g	NOUN
ejpam-5084	184	7	)	)	PUNCT
ejpam-5084	184	8	,	,	PUNCT
ejpam-5084	184	9	αj(h	αj(h	ADV
ejpam-5084	184	10	)	)	PUNCT
ejpam-5084	184	11	}	}	PUNCT
ejpam-5084	184	12	.	.	PUNCT
ejpam-5084	185	1	acknowledgements	acknowledgement	NOUN
ejpam-5084	185	2	the	the	DET
ejpam-5084	185	3	authors	author	NOUN
ejpam-5084	185	4	would	would	AUX
ejpam-5084	185	5	like	like	VERB
ejpam-5084	185	6	to	to	PART
ejpam-5084	185	7	thank	thank	VERB
ejpam-5084	185	8	mindanao	mindanao	PROPN
ejpam-5084	185	9	state	state	PROPN
ejpam-5084	185	10	university	university	PROPN
ejpam-5084	185	11	tawi	tawi	PROPN
ejpam-5084	185	12	-	-	PUNCT
ejpam-5084	185	13	tawi	tawi	PROPN
ejpam-5084	185	14	college	college	PROPN
ejpam-5084	185	15	of	of	ADP
ejpam-5084	185	16	technology	technology	NOUN
ejpam-5084	185	17	and	and	CCONJ
ejpam-5084	185	18	oceanography	oceanography	NOUN
ejpam-5084	185	19	for	for	ADP
ejpam-5084	185	20	funding	fund	VERB
ejpam-5084	185	21	this	this	DET
ejpam-5084	185	22	research	research	NOUN
ejpam-5084	185	23	.	.	PUNCT
ejpam-5084	186	1	also	also	ADV
ejpam-5084	186	2	,	,	PUNCT
ejpam-5084	186	3	the	the	DET
ejpam-5084	186	4	authors	author	NOUN
ejpam-5084	186	5	would	would	AUX
ejpam-5084	186	6	like	like	VERB
ejpam-5084	186	7	to	to	PART
ejpam-5084	186	8	thank	thank	VERB
ejpam-5084	186	9	the	the	DET
ejpam-5084	186	10	referees	referee	NOUN
ejpam-5084	186	11	for	for	ADP
ejpam-5084	186	12	their	their	PRON
ejpam-5084	186	13	invaluable	invaluable	ADJ
ejpam-5084	186	14	comments	comment	NOUN
ejpam-5084	186	15	and	and	CCONJ
ejpam-5084	186	16	suggestions	suggestion	NOUN
ejpam-5084	186	17	that	that	PRON
ejpam-5084	186	18	led	lead	VERB
ejpam-5084	186	19	to	to	ADP
ejpam-5084	186	20	the	the	DET
ejpam-5084	186	21	improvement	improvement	NOUN
ejpam-5084	186	22	of	of	ADP
ejpam-5084	186	23	the	the	DET
ejpam-5084	186	24	paper	paper	NOUN
ejpam-5084	186	25	.	.	PUNCT
ejpam-5084	187	1	references	reference	NOUN
ejpam-5084	187	2	[	[	X
ejpam-5084	187	3	1	1	NUM
ejpam-5084	187	4	]	]	PUNCT
ejpam-5084	187	5	v.	v.	X
ejpam-5084	187	6	bilar	bilar	PROPN
ejpam-5084	187	7	,	,	PUNCT
ejpam-5084	187	8	m.a	m.a	PROPN
ejpam-5084	187	9	.	.	PROPN
ejpam-5084	187	10	bonsocan	bonsocan	PROPN
ejpam-5084	187	11	,	,	PUNCT
ejpam-5084	187	12	j.	j.	PROPN
ejpam-5084	187	13	hassan	hassan	PROPN
ejpam-5084	187	14	,	,	PUNCT
ejpam-5084	187	15	and	and	CCONJ
ejpam-5084	187	16	s.	s.	PROPN
ejpam-5084	187	17	dagondon	dagondon	PROPN
ejpam-5084	187	18	.	.	PUNCT
ejpam-5084	188	1	vertex	vertex	NOUN
ejpam-5084	188	2	cover	cover	VERB
ejpam-5084	188	3	hop	hop	NOUN
ejpam-5084	188	4	dominating	dominating	NOUN
ejpam-5084	188	5	sets	set	NOUN
ejpam-5084	188	6	in	in	ADP
ejpam-5084	188	7	graphs	graph	NOUN
ejpam-5084	188	8	.	.	PUNCT
ejpam-5084	189	1	eur	eur	PROPN
ejpam-5084	189	2	.	.	PUNCT
ejpam-5084	190	1	j.	j.	PROPN
ejpam-5084	190	2	pure	pure	PROPN
ejpam-5084	190	3	appl	appl	PROPN
ejpam-5084	190	4	.	.	PUNCT
ejpam-5084	190	5	math	math	PROPN
ejpam-5084	190	6	.	.	PUNCT
ejpam-5084	190	7	,	,	PUNCT
ejpam-5084	190	8	17(1):93–104	17(1):93–104	NUM
ejpam-5084	190	9	,	,	PUNCT
ejpam-5084	190	10	2024	2024	NUM
ejpam-5084	190	11	.	.	PUNCT
ejpam-5084	191	1	[	[	X
ejpam-5084	191	2	2	2	X
ejpam-5084	191	3	]	]	PUNCT
ejpam-5084	191	4	e.	e.	PROPN
ejpam-5084	191	5	davies	davies	PROPN
ejpam-5084	191	6	,	,	PUNCT
ejpam-5084	191	7	m.	m.	PROPN
ejpam-5084	191	8	jenssen	jenssen	PROPN
ejpam-5084	191	9	,	,	PUNCT
ejpam-5084	191	10	w.	w.	PROPN
ejpam-5084	191	11	perkins	perkins	PROPN
ejpam-5084	191	12	,	,	PUNCT
ejpam-5084	191	13	and	and	CCONJ
ejpam-5084	191	14	b.	b.	PROPN
ejpam-5084	191	15	roberts	roberts	PROPN
ejpam-5084	191	16	.	.	PROPN
ejpam-5084	192	1	ndependent	ndependent	PROPN
ejpam-5084	192	2	sets	set	NOUN
ejpam-5084	192	3	,	,	PUNCT
ejpam-5084	192	4	matchings	matching	NOUN
ejpam-5084	192	5	,	,	PUNCT
ejpam-5084	192	6	and	and	CCONJ
ejpam-5084	192	7	occupancy	occupancy	NOUN
ejpam-5084	192	8	fractions	fraction	NOUN
ejpam-5084	192	9	.	.	PUNCT
ejpam-5084	193	1	j.	j.	PROPN
ejpam-5084	193	2	lond	lond	PROPN
ejpam-5084	193	3	.	.	PUNCT
ejpam-5084	194	1	math	math	PROPN
ejpam-5084	194	2	.	.	PUNCT
ejpam-5084	195	1	soc	soc	PROPN
ejpam-5084	195	2	.	.	PUNCT
ejpam-5084	195	3	,	,	PUNCT
ejpam-5084	195	4	96:211–220	96:211–220	NUM
ejpam-5084	195	5	,	,	PUNCT
ejpam-5084	195	6	2017	2017	NUM
ejpam-5084	195	7	.	.	PUNCT
ejpam-5084	196	1	references	reference	NOUN
ejpam-5084	196	2	929	929	NUM
ejpam-5084	197	1	[	[	X
ejpam-5084	197	2	3	3	NUM
ejpam-5084	197	3	]	]	PUNCT
ejpam-5084	197	4	z.	z.	PROPN
ejpam-5084	197	5	furedi	furedi	PROPN
ejpam-5084	197	6	.	.	PUNCT
ejpam-5084	198	1	the	the	DET
ejpam-5084	198	2	number	number	NOUN
ejpam-5084	198	3	of	of	ADP
ejpam-5084	198	4	maximal	maximal	ADJ
ejpam-5084	198	5	independent	independent	ADJ
ejpam-5084	198	6	sets	set	NOUN
ejpam-5084	198	7	in	in	ADP
ejpam-5084	198	8	connected	connected	ADJ
ejpam-5084	198	9	graphs	graph	NOUN
ejpam-5084	198	10	,	,	PUNCT
ejpam-5084	198	11	.	.	PUNCT
ejpam-5084	199	1	j.	j.	PROPN
ejpam-5084	199	2	graph	graph	PROPN
ejpam-5084	199	3	theory	theory	NOUN
ejpam-5084	199	4	.	.	PUNCT
ejpam-5084	200	1	,	,	PUNCT
ejpam-5084	200	2	11(4):463–470	11(4):463–470	NOUN
ejpam-5084	200	3	,	,	PUNCT
ejpam-5084	200	4	2022	2022	NUM
ejpam-5084	200	5	.	.	PUNCT
ejpam-5084	201	1	[	[	X
ejpam-5084	201	2	4	4	NUM
ejpam-5084	201	3	]	]	X
ejpam-5084	201	4	j.r	j.r	PROPN
ejpam-5084	201	5	.	.	PROPN
ejpam-5084	201	6	griggs	griggs	PROPN
ejpam-5084	201	7	,	,	PUNCT
ejpam-5084	201	8	c.m	c.m	PROPN
ejpam-5084	201	9	.	.	PROPN
ejpam-5084	201	10	grinstead	grinstead	PROPN
ejpam-5084	201	11	,	,	PUNCT
ejpam-5084	201	12	and	and	CCONJ
ejpam-5084	201	13	d.r	d.r	PROPN
ejpam-5084	201	14	.	.	PROPN
ejpam-5084	201	15	guichard	guichard	PROPN
ejpam-5084	201	16	.	.	PUNCT
ejpam-5084	202	1	the	the	DET
ejpam-5084	202	2	number	number	NOUN
ejpam-5084	202	3	of	of	ADP
ejpam-5084	202	4	maximal	maximal	ADJ
ejpam-5084	202	5	independent	independent	ADJ
ejpam-5084	202	6	sets	set	NOUN
ejpam-5084	202	7	in	in	ADP
ejpam-5084	202	8	a	a	DET
ejpam-5084	202	9	connected	connected	ADJ
ejpam-5084	202	10	graph	graph	NOUN
ejpam-5084	202	11	.	.	PUNCT
ejpam-5084	202	12	discrete	discrete	ADJ
ejpam-5084	202	13	mathematics	mathematic	NOUN
ejpam-5084	202	14	.	.	PUNCT
ejpam-5084	202	15	,	,	PUNCT
ejpam-5084	202	16	68:211–220	68:211–220	PROPN
ejpam-5084	202	17	,	,	PUNCT
ejpam-5084	202	18	1988	1988	NUM
ejpam-5084	202	19	.	.	PUNCT
ejpam-5084	203	1	[	[	X
ejpam-5084	203	2	5	5	X
ejpam-5084	203	3	]	]	PUNCT
ejpam-5084	203	4	j.	j.	PROPN
ejpam-5084	203	5	hassan	hassan	PROPN
ejpam-5084	203	6	,	,	PUNCT
ejpam-5084	203	7	ar	ar	PROPN
ejpam-5084	203	8	.	.	PROPN
ejpam-5084	203	9	bakkang	bakkang	PROPN
ejpam-5084	203	10	,	,	PUNCT
ejpam-5084	203	11	and	and	CCONJ
ejpam-5084	203	12	ass	ass	PROPN
ejpam-5084	203	13	.	.	PROPN
ejpam-5084	203	14	sappari	sappari	PROPN
ejpam-5084	203	15	.	.	PUNCT
ejpam-5084	204	1	j2	j2	PROPN
ejpam-5084	204	2	-	-	PUNCT
ejpam-5084	204	3	hop	hop	PROPN
ejpam-5084	204	4	domination	domination	NOUN
ejpam-5084	204	5	in	in	ADP
ejpam-5084	204	6	graphs	graph	NOUN
ejpam-5084	204	7	:	:	PUNCT
ejpam-5084	204	8	properties	property	NOUN
ejpam-5084	204	9	and	and	CCONJ
ejpam-5084	204	10	connections	connection	NOUN
ejpam-5084	204	11	with	with	ADP
ejpam-5084	204	12	other	other	ADJ
ejpam-5084	204	13	parameters	parameter	NOUN
ejpam-5084	204	14	.	.	PUNCT
ejpam-5084	205	1	eur	eur	PROPN
ejpam-5084	205	2	.	.	PUNCT
ejpam-5084	206	1	j.	j.	PROPN
ejpam-5084	206	2	pure	pure	PROPN
ejpam-5084	206	3	appl	appl	PROPN
ejpam-5084	206	4	.	.	PUNCT
ejpam-5084	206	5	math	math	PROPN
ejpam-5084	206	6	.	.	PUNCT
ejpam-5084	206	7	,	,	PUNCT
ejpam-5084	206	8	16(4):2118–2131	16(4):2118–2131	NUM
ejpam-5084	206	9	,	,	PUNCT
ejpam-5084	206	10	2023	2023	NUM
ejpam-5084	206	11	.	.	PUNCT
ejpam-5084	207	1	[	[	X
ejpam-5084	207	2	6	6	NUM
ejpam-5084	207	3	]	]	PUNCT
ejpam-5084	207	4	j.	j.	PROPN
ejpam-5084	207	5	hassan	hassan	PROPN
ejpam-5084	207	6	and	and	CCONJ
ejpam-5084	207	7	s.	s.	PROPN
ejpam-5084	207	8	canoy	canoy	PROPN
ejpam-5084	207	9	jr	jr	PROPN
ejpam-5084	207	10	.	.	PUNCT
ejpam-5084	208	1	grundy	grundy	PROPN
ejpam-5084	208	2	dominating	dominating	PROPN
ejpam-5084	208	3	and	and	CCONJ
ejpam-5084	208	4	grundy	grundy	PROPN
ejpam-5084	208	5	hop	hop	NOUN
ejpam-5084	208	6	dominating	dominate	VERB
ejpam-5084	208	7	sequences	sequence	NOUN
ejpam-5084	208	8	in	in	ADP
ejpam-5084	208	9	graphs	graph	NOUN
ejpam-5084	208	10	:	:	PUNCT
ejpam-5084	208	11	relationships	relationship	NOUN
ejpam-5084	208	12	and	and	CCONJ
ejpam-5084	208	13	some	some	DET
ejpam-5084	208	14	structural	structural	ADJ
ejpam-5084	208	15	properties	property	NOUN
ejpam-5084	208	16	.	.	PUNCT
ejpam-5084	209	1	eur	eur	PROPN
ejpam-5084	209	2	.	.	PUNCT
ejpam-5084	210	1	j.	j.	PROPN
ejpam-5084	210	2	pure	pure	PROPN
ejpam-5084	210	3	appl	appl	PROPN
ejpam-5084	210	4	.	.	PUNCT
ejpam-5084	210	5	math	math	PROPN
ejpam-5084	210	6	.	.	PUNCT
ejpam-5084	210	7	,	,	PUNCT
ejpam-5084	211	1	16(2):1154–1166	16(2):1154–1166	NUM
ejpam-5084	211	2	,	,	PUNCT
ejpam-5084	211	3	2023	2023	NUM
ejpam-5084	211	4	.	.	PUNCT
ejpam-5084	212	1	[	[	X
ejpam-5084	212	2	7	7	X
ejpam-5084	212	3	]	]	PUNCT
ejpam-5084	212	4	j.	j.	PROPN
ejpam-5084	212	5	hassan	hassan	PROPN
ejpam-5084	212	6	and	and	CCONJ
ejpam-5084	212	7	s.	s.	PROPN
ejpam-5084	212	8	canoy	canoy	PROPN
ejpam-5084	212	9	jr	jr	PROPN
ejpam-5084	212	10	.	.	PUNCT
ejpam-5084	213	1	grundy	grundy	PROPN
ejpam-5084	213	2	total	total	PROPN
ejpam-5084	213	3	hop	hop	PROPN
ejpam-5084	213	4	dominating	dominate	VERB
ejpam-5084	213	5	sequences	sequence	NOUN
ejpam-5084	213	6	in	in	ADP
ejpam-5084	213	7	graphs	graph	NOUN
ejpam-5084	213	8	.	.	PUNCT
ejpam-5084	214	1	eur	eur	PROPN
ejpam-5084	214	2	.	.	PUNCT
ejpam-5084	215	1	j.	j.	PROPN
ejpam-5084	215	2	pure	pure	PROPN
ejpam-5084	215	3	appl	appl	PROPN
ejpam-5084	215	4	.	.	PUNCT
ejpam-5084	215	5	math	math	PROPN
ejpam-5084	215	6	.	.	PUNCT
ejpam-5084	215	7	,	,	PUNCT
ejpam-5084	215	8	16(4):2597–2612	16(4):2597–2612	NUM
ejpam-5084	215	9	,	,	PUNCT
ejpam-5084	215	10	2023	2023	NUM
ejpam-5084	215	11	.	.	PUNCT
ejpam-5084	216	1	[	[	X
ejpam-5084	216	2	8	8	X
ejpam-5084	216	3	]	]	X
ejpam-5084	216	4	j.	j.	PROPN
ejpam-5084	216	5	hassan	hassan	PROPN
ejpam-5084	216	6	,	,	PUNCT
ejpam-5084	216	7	s.	s.	PROPN
ejpam-5084	216	8	canoy	canoy	PROPN
ejpam-5084	216	9	jr	jr	PROPN
ejpam-5084	216	10	.	.	PROPN
ejpam-5084	216	11	,	,	PUNCT
ejpam-5084	216	12	and	and	CCONJ
ejpam-5084	216	13	a.	a.	PROPN
ejpam-5084	216	14	aradais	aradais	PROPN
ejpam-5084	216	15	.	.	PUNCT
ejpam-5084	217	1	hop	hop	PROPN
ejpam-5084	217	2	independent	independent	ADJ
ejpam-5084	217	3	sets	set	NOUN
ejpam-5084	217	4	in	in	ADP
ejpam-5084	217	5	graphs	graph	NOUN
ejpam-5084	217	6	.	.	PUNCT
ejpam-5084	218	1	eur	eur	PROPN
ejpam-5084	218	2	.	.	PUNCT
ejpam-5084	219	1	j.	j.	PROPN
ejpam-5084	219	2	pure	pure	PROPN
ejpam-5084	219	3	appl	appl	PROPN
ejpam-5084	219	4	.	.	PUNCT
ejpam-5084	219	5	math	math	PROPN
ejpam-5084	219	6	.	.	PUNCT
ejpam-5084	219	7	,	,	PUNCT
ejpam-5084	219	8	15(2):467–477	15(2):467–477	PROPN
ejpam-5084	219	9	,	,	PUNCT
ejpam-5084	219	10	2022	2022	NUM
ejpam-5084	219	11	.	.	PUNCT
ejpam-5084	220	1	[	[	X
ejpam-5084	220	2	9	9	NUM
ejpam-5084	220	3	]	]	PUNCT
ejpam-5084	220	4	j.	j.	PROPN
ejpam-5084	220	5	hassan	hassan	PROPN
ejpam-5084	220	6	,	,	PUNCT
ejpam-5084	220	7	a.	a.	PROPN
ejpam-5084	220	8	lintasan	lintasan	PROPN
ejpam-5084	220	9	,	,	PUNCT
ejpam-5084	220	10	and	and	CCONJ
ejpam-5084	220	11	n.h	n.h	PROPN
ejpam-5084	220	12	.	.	PUNCT
ejpam-5084	221	1	mohammad	mohammad	PROPN
ejpam-5084	221	2	.	.	PUNCT
ejpam-5084	222	1	some	some	DET
ejpam-5084	222	2	properties	property	NOUN
ejpam-5084	222	3	and	and	CCONJ
ejpam-5084	222	4	realization	realization	NOUN
ejpam-5084	222	5	problems	problem	NOUN
ejpam-5084	222	6	involving	involve	VERB
ejpam-5084	222	7	connected	connected	ADJ
ejpam-5084	222	8	outer	outer	ADJ
ejpam-5084	222	9	-	-	PUNCT
ejpam-5084	222	10	hop	hop	NOUN
ejpam-5084	222	11	independent	independent	ADJ
ejpam-5084	222	12	hop	hop	NOUN
ejpam-5084	222	13	domination	domination	NOUN
ejpam-5084	222	14	in	in	ADP
ejpam-5084	222	15	graphs	graph	NOUN
ejpam-5084	222	16	.	.	PUNCT
ejpam-5084	223	1	eur	eur	PROPN
ejpam-5084	223	2	.	.	PUNCT
ejpam-5084	224	1	j.	j.	PROPN
ejpam-5084	224	2	pure	pure	PROPN
ejpam-5084	224	3	appl	appl	PROPN
ejpam-5084	224	4	.	.	PUNCT
ejpam-5084	224	5	math	math	PROPN
ejpam-5084	224	6	.	.	PUNCT
ejpam-5084	224	7	,	,	PUNCT
ejpam-5084	224	8	16(3):1848–1861	16(3):1848–1861	NUM
ejpam-5084	224	9	,	,	PUNCT
ejpam-5084	224	10	2023	2023	NUM
ejpam-5084	224	11	.	.	PUNCT
ejpam-5084	225	1	[	[	X
ejpam-5084	225	2	10	10	NUM
ejpam-5084	225	3	]	]	X
ejpam-5084	225	4	j.	j.	PROPN
ejpam-5084	225	5	hassan	hassan	PROPN
ejpam-5084	225	6	,	,	PUNCT
ejpam-5084	225	7	j.	j.	PROPN
ejpam-5084	225	8	manditong	manditong	PROPN
ejpam-5084	225	9	,	,	PUNCT
ejpam-5084	225	10	a.	a.	PROPN
ejpam-5084	225	11	bakkang	bakkang	PROPN
ejpam-5084	225	12	,	,	PUNCT
ejpam-5084	225	13	s.	s.	PROPN
ejpam-5084	225	14	kamdon	kamdon	PROPN
ejpam-5084	225	15	,	,	PUNCT
ejpam-5084	225	16	and	and	CCONJ
ejpam-5084	225	17	j.	j.	PROPN
ejpam-5084	225	18	salim	salim	PROPN
ejpam-5084	225	19	.	.	PUNCT
ejpam-5084	226	1	characterizations	characterization	NOUN
ejpam-5084	226	2	of	of	ADP
ejpam-5084	226	3	j	j	PROPN
ejpam-5084	226	4	-	-	ADJ
ejpam-5084	226	5	total	total	ADJ
ejpam-5084	226	6	dominating	dominating	NOUN
ejpam-5084	226	7	sets	set	NOUN
ejpam-5084	226	8	of	of	ADP
ejpam-5084	226	9	some	some	DET
ejpam-5084	226	10	graphs	graph	NOUN
ejpam-5084	226	11	.	.	PUNCT
ejpam-5084	227	1	eur	eur	PROPN
ejpam-5084	227	2	.	.	PUNCT
ejpam-5084	228	1	j.	j.	PROPN
ejpam-5084	228	2	pure	pure	PROPN
ejpam-5084	228	3	appl	appl	PROPN
ejpam-5084	228	4	.	.	PUNCT
ejpam-5084	228	5	math	math	PROPN
ejpam-5084	228	6	.	.	PUNCT
ejpam-5084	228	7	,	,	PUNCT
ejpam-5084	228	8	16(4):2106–2117	16(4):2106–2117	NUM
ejpam-5084	228	9	,	,	PUNCT
ejpam-5084	228	10	2023	2023	NUM
ejpam-5084	228	11	.	.	PUNCT
ejpam-5084	229	1	[	[	X
ejpam-5084	229	2	11	11	NUM
ejpam-5084	229	3	]	]	PUNCT
ejpam-5084	229	4	j.	j.	PROPN
ejpam-5084	229	5	hassan	hassan	PROPN
ejpam-5084	229	6	,	,	PUNCT
ejpam-5084	229	7	a.	a.	NOUN
ejpam-5084	229	8	tapeing	tapeing	NOUN
ejpam-5084	229	9	,	,	PUNCT
ejpam-5084	229	10	h.	h.	PROPN
ejpam-5084	229	11	copel	copel	PROPN
ejpam-5084	229	12	,	,	PUNCT
ejpam-5084	229	13	a.r	a.r	PROPN
ejpam-5084	229	14	bakkang	bakkang	PROPN
ejpam-5084	229	15	,	,	PUNCT
ejpam-5084	229	16	and	and	CCONJ
ejpam-5084	229	17	s.d	s.d	PROPN
ejpam-5084	229	18	.	.	PROPN
ejpam-5084	229	19	aming	aming	PROPN
ejpam-5084	229	20	.	.	PUNCT
ejpam-5084	230	1	j2	j2	PROPN
ejpam-5084	230	2	-	-	PUNCT
ejpam-5084	230	3	independence	independence	NOUN
ejpam-5084	230	4	parameters	parameter	NOUN
ejpam-5084	230	5	of	of	ADP
ejpam-5084	230	6	some	some	DET
ejpam-5084	230	7	graphs	graph	NOUN
ejpam-5084	230	8	.	.	PUNCT
ejpam-5084	231	1	eur	eur	PROPN
ejpam-5084	231	2	.	.	PUNCT
ejpam-5084	232	1	j.	j.	PROPN
ejpam-5084	232	2	pure	pure	PROPN
ejpam-5084	232	3	appl	appl	PROPN
ejpam-5084	232	4	.	.	PUNCT
ejpam-5084	232	5	math	math	PROPN
ejpam-5084	232	6	.	.	PUNCT
ejpam-5084	232	7	,	,	PUNCT
ejpam-5084	233	1	17(1):124–134	17(1):124–134	NUM
ejpam-5084	233	2	,	,	PUNCT
ejpam-5084	233	3	2024	2024	NUM
ejpam-5084	233	4	.	.	PUNCT
ejpam-5084	234	1	[	[	X
ejpam-5084	234	2	12	12	NUM
ejpam-5084	234	3	]	]	X
ejpam-5084	234	4	liu	liu	PROPN
ejpam-5084	234	5	jiuqiang	jiuqiang	PROPN
ejpam-5084	234	6	.	.	PUNCT
ejpam-5084	235	1	maximal	maximal	ADJ
ejpam-5084	235	2	and	and	CCONJ
ejpam-5084	235	3	maximum	maximum	ADJ
ejpam-5084	235	4	independent	independent	ADJ
ejpam-5084	235	5	sets	set	NOUN
ejpam-5084	235	6	in	in	ADP
ejpam-5084	235	7	graphs	graph	NOUN
ejpam-5084	235	8	.	.	PUNCT
ejpam-5084	236	1	dissertations	dissertation	NOUN
ejpam-5084	236	2	.	.	PUNCT
ejpam-5084	236	3	,	,	PUNCT
ejpam-5084	236	4	1985	1985	NUM
ejpam-5084	236	5	.	.	PUNCT
ejpam-5084	237	1	[	[	X
ejpam-5084	237	2	13	13	NUM
ejpam-5084	237	3	]	]	PUNCT
ejpam-5084	237	4	s.	s.	PROPN
ejpam-5084	237	5	canoy	canoy	PROPN
ejpam-5084	237	6	jr	jr	PROPN
ejpam-5084	237	7	.	.	PROPN
ejpam-5084	237	8	and	and	CCONJ
ejpam-5084	237	9	j.	j.	PROPN
ejpam-5084	237	10	hassan	hassan	PROPN
ejpam-5084	237	11	.	.	PUNCT
ejpam-5084	238	1	weakly	weakly	ADJ
ejpam-5084	238	2	convex	convex	VERB
ejpam-5084	238	3	hop	hop	NOUN
ejpam-5084	238	4	dominating	dominating	NOUN
ejpam-5084	238	5	sets	set	NOUN
ejpam-5084	238	6	in	in	ADP
ejpam-5084	238	7	graphs	graph	NOUN
ejpam-5084	238	8	.	.	PUNCT
ejpam-5084	239	1	eur	eur	PROPN
ejpam-5084	239	2	.	.	PUNCT
ejpam-5084	240	1	j.	j.	PROPN
ejpam-5084	240	2	pure	pure	PROPN
ejpam-5084	240	3	appl	appl	PROPN
ejpam-5084	240	4	.	.	PUNCT
ejpam-5084	240	5	math	math	PROPN
ejpam-5084	240	6	.	.	PUNCT
ejpam-5084	240	7	,	,	PUNCT
ejpam-5084	240	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-5084	240	9	,	,	PUNCT
ejpam-5084	240	10	2022	2022	NUM
ejpam-5084	240	11	.	.	PUNCT
ejpam-5084	241	1	[	[	X
ejpam-5084	241	2	14	14	NUM
ejpam-5084	241	3	]	]	X
ejpam-5084	241	4	s.	s.	PROPN
ejpam-5084	241	5	kaida	kaida	PROPN
ejpam-5084	241	6	,	,	PUNCT
ejpam-5084	241	7	k.j	k.j	PROPN
ejpam-5084	241	8	.	.	PROPN
ejpam-5084	241	9	maharajul	maharajul	PROPN
ejpam-5084	241	10	,	,	PUNCT
ejpam-5084	241	11	j.	j.	PROPN
ejpam-5084	241	12	hassan	hassan	PROPN
ejpam-5084	241	13	,	,	PUNCT
ejpam-5084	241	14	l.	l.	PROPN
ejpam-5084	241	15	s.	s.	PROPN
ejpam-5084	241	16	laja	laja	PROPN
ejpam-5084	241	17	,	,	PUNCT
ejpam-5084	241	18	a.b	a.b	PROPN
ejpam-5084	241	19	.	.	PROPN
ejpam-5084	241	20	lintasan	lintasan	PROPN
ejpam-5084	241	21	,	,	PUNCT
ejpam-5084	241	22	and	and	CCONJ
ejpam-5084	241	23	a.a	a.a	PROPN
ejpam-5084	241	24	.	.	PROPN
ejpam-5084	241	25	pablo	pablo	PROPN
ejpam-5084	241	26	.	.	PUNCT
ejpam-5084	242	1	certified	certify	VERB
ejpam-5084	242	2	hop	hop	NOUN
ejpam-5084	242	3	independence	independence	NOUN
ejpam-5084	242	4	:	:	PUNCT
ejpam-5084	242	5	properties	property	NOUN
ejpam-5084	242	6	and	and	CCONJ
ejpam-5084	242	7	connections	connection	NOUN
ejpam-5084	242	8	with	with	ADP
ejpam-5084	242	9	other	other	ADJ
ejpam-5084	242	10	variants	variant	NOUN
ejpam-5084	242	11	of	of	ADP
ejpam-5084	242	12	independence	independence	NOUN
ejpam-5084	242	13	.	.	PUNCT
ejpam-5084	243	1	eur	eur	PROPN
ejpam-5084	243	2	.	.	PUNCT
ejpam-5084	244	1	j.	j.	PROPN
ejpam-5084	244	2	pure	pure	PROPN
ejpam-5084	244	3	appl	appl	PROPN
ejpam-5084	244	4	.	.	PUNCT
ejpam-5084	244	5	math	math	PROPN
ejpam-5084	244	6	.	.	PUNCT
ejpam-5084	244	7	,	,	PUNCT
ejpam-5084	244	8	17(1):435–444	17(1):435–444	NUM
ejpam-5084	244	9	,	,	PUNCT
ejpam-5084	244	10	2024	2024	NUM
ejpam-5084	244	11	.	.	PUNCT
ejpam-5084	245	1	[	[	X
ejpam-5084	245	2	15	15	NUM
ejpam-5084	245	3	]	]	X
ejpam-5084	245	4	j.	j.	PROPN
ejpam-5084	245	5	manditong	manditong	PROPN
ejpam-5084	245	6	,	,	PUNCT
ejpam-5084	245	7	j.	j.	PROPN
ejpam-5084	245	8	hassan	hassan	PROPN
ejpam-5084	245	9	,	,	PUNCT
ejpam-5084	245	10	ls	ls	PROPN
ejpam-5084	245	11	laja	laja	PROPN
ejpam-5084	245	12	,	,	PUNCT
ejpam-5084	245	13	aa	aa	INTJ
ejpam-5084	245	14	.	.	PUNCT
ejpam-5084	245	15	laja	laja	PROPN
ejpam-5084	245	16	,	,	PUNCT
ejpam-5084	245	17	nhm	nhm	PROPN
ejpam-5084	245	18	.	.	PUNCT
ejpam-5084	245	19	mohammad	mohammad	PROPN
ejpam-5084	245	20	,	,	PUNCT
ejpam-5084	245	21	and	and	CCONJ
ejpam-5084	245	22	su	su	PROPN
ejpam-5084	245	23	.	.	PROPN
ejpam-5084	245	24	kamdon	kamdon	PROPN
ejpam-5084	245	25	.	.	PUNCT
ejpam-5084	246	1	connected	connected	ADJ
ejpam-5084	246	2	outer	outer	ADJ
ejpam-5084	246	3	-	-	PUNCT
ejpam-5084	246	4	hop	hop	NOUN
ejpam-5084	246	5	independent	independent	ADJ
ejpam-5084	246	6	dominating	dominating	NOUN
ejpam-5084	246	7	sets	set	NOUN
ejpam-5084	246	8	in	in	ADP
ejpam-5084	246	9	graphs	graph	NOUN
ejpam-5084	246	10	under	under	ADP
ejpam-5084	246	11	some	some	DET
ejpam-5084	246	12	binary	binary	ADJ
ejpam-5084	246	13	operations	operation	NOUN
ejpam-5084	246	14	.	.	PUNCT
ejpam-5084	247	1	eur	eur	PROPN
ejpam-5084	247	2	.	.	PUNCT
ejpam-5084	248	1	j.	j.	PROPN
ejpam-5084	248	2	pure	pure	PROPN
ejpam-5084	248	3	appl	appl	PROPN
ejpam-5084	248	4	.	.	PUNCT
ejpam-5084	248	5	math	math	PROPN
ejpam-5084	248	6	.	.	PUNCT
ejpam-5084	248	7	,	,	PUNCT
ejpam-5084	249	1	16(3):1817–1829	16(3):1817–1829	NUM
ejpam-5084	249	2	,	,	PUNCT
ejpam-5084	249	3	2023	2023	NUM
ejpam-5084	249	4	.	.	PUNCT
ejpam-5084	250	1	[	[	X
ejpam-5084	250	2	16	16	NUM
ejpam-5084	250	3	]	]	X
ejpam-5084	250	4	j.	j.	PROPN
ejpam-5084	250	5	manditong	manditong	PROPN
ejpam-5084	250	6	,	,	PUNCT
ejpam-5084	250	7	a.	a.	NOUN
ejpam-5084	250	8	tapeing	tapeing	NOUN
ejpam-5084	250	9	,	,	PUNCT
ejpam-5084	250	10	j.	j.	PROPN
ejpam-5084	250	11	hassan	hassan	PROPN
ejpam-5084	250	12	,	,	PUNCT
ejpam-5084	250	13	a.r	a.r	PROPN
ejpam-5084	250	14	.	.	PROPN
ejpam-5084	250	15	bakkang	bakkang	PROPN
ejpam-5084	250	16	,	,	PUNCT
ejpam-5084	250	17	and	and	CCONJ
ejpam-5084	250	18	n.h	n.h	PROPN
ejpam-5084	250	19	.	.	PROPN
ejpam-5084	250	20	mohammadand	mohammadand	PROPN
ejpam-5084	250	21	s.u	s.u	PROPN
ejpam-5084	250	22	.	.	PROPN
ejpam-5084	250	23	kamdon	kamdon	PROPN
ejpam-5084	250	24	.	.	PUNCT
ejpam-5084	251	1	some	some	DET
ejpam-5084	251	2	properties	property	NOUN
ejpam-5084	251	3	of	of	ADP
ejpam-5084	251	4	zero	zero	NUM
ejpam-5084	251	5	forcing	force	VERB
ejpam-5084	251	6	hop	hop	NOUN
ejpam-5084	251	7	dominating	dominating	NOUN
ejpam-5084	251	8	sets	set	NOUN
ejpam-5084	251	9	in	in	ADP
ejpam-5084	251	10	a	a	DET
ejpam-5084	251	11	graph	graph	NOUN
ejpam-5084	251	12	.	.	PUNCT
ejpam-5084	252	1	eur	eur	PROPN
ejpam-5084	252	2	.	.	PUNCT
ejpam-5084	253	1	j.	j.	PROPN
ejpam-5084	253	2	pure	pure	PROPN
ejpam-5084	253	3	appl	appl	PROPN
ejpam-5084	253	4	.	.	PUNCT
ejpam-5084	253	5	math	math	PROPN
ejpam-5084	253	6	.	.	PUNCT
ejpam-5084	254	1	,	,	PUNCT
ejpam-5084	254	2	17(1):324–337	17(1):324–337	PROPN
ejpam-5084	254	3	,	,	PUNCT
ejpam-5084	254	4	2024	2024	NUM
ejpam-5084	254	5	.	.	PUNCT
ejpam-5084	255	1	references	reference	NOUN
ejpam-5084	255	2	930	930	NUM
ejpam-5084	256	1	[	[	X
ejpam-5084	256	2	17	17	NUM
ejpam-5084	256	3	]	]	X
ejpam-5084	256	4	h.s	h.s	PROPN
ejpam-5084	256	5	.	.	PROPN
ejpam-5084	256	6	wilf	wilf	PROPN
ejpam-5084	256	7	.	.	PUNCT
ejpam-5084	257	1	the	the	DET
ejpam-5084	257	2	number	number	NOUN
ejpam-5084	257	3	of	of	ADP
ejpam-5084	257	4	maximal	maximal	ADJ
ejpam-5084	257	5	independent	independent	ADJ
ejpam-5084	257	6	sets	set	NOUN
ejpam-5084	257	7	in	in	ADP
ejpam-5084	257	8	a	a	DET
ejpam-5084	257	9	tree	tree	NOUN
ejpam-5084	257	10	.	.	PUNCT
ejpam-5084	258	1	siam	siam	PROPN
ejpam-5084	258	2	j.	j.	PROPN
ejpam-5084	258	3	alg	alg	PROPN
ejpam-5084	258	4	.	.	PUNCT
ejpam-5084	259	1	disc	disc	PROPN
ejpam-5084	259	2	.	.	PUNCT
ejpam-5084	260	1	meth	meth	NOUN
ejpam-5084	260	2	.	.	PUNCT
ejpam-5084	260	3	,	,	PUNCT
ejpam-5084	260	4	7:125–130	7:125–130	NUM
ejpam-5084	260	5	,	,	PUNCT
ejpam-5084	260	6	1986	1986	NUM
ejpam-5084	260	7	.	.	PUNCT
ejpam-5084	261	1	[	[	X
ejpam-5084	261	2	18	18	NUM
ejpam-5084	261	3	]	]	PUNCT
ejpam-5084	261	4	j.	j.	PROPN
ejpam-5084	261	5	zito	zito	PROPN
ejpam-5084	261	6	.	.	PUNCT
ejpam-5084	262	1	the	the	DET
ejpam-5084	262	2	structure	structure	NOUN
ejpam-5084	262	3	and	and	CCONJ
ejpam-5084	262	4	maximum	maximum	ADJ
ejpam-5084	262	5	number	number	NOUN
ejpam-5084	262	6	of	of	ADP
ejpam-5084	262	7	maximum	maximum	ADJ
ejpam-5084	262	8	independent	independent	ADJ
ejpam-5084	262	9	sets	set	NOUN
ejpam-5084	262	10	in	in	ADP
ejpam-5084	262	11	trees	tree	NOUN
ejpam-5084	262	12	.	.	PUNCT
ejpam-5084	263	1	j.	j.	PROPN
ejpam-5084	263	2	graph	graph	PROPN
ejpam-5084	263	3	theory	theory	NOUN
ejpam-5084	263	4	.	.	PUNCT
ejpam-5084	263	5	,	,	PUNCT
ejpam-5084	263	6	15(2):207–221	15(2):207–221	NUM
ejpam-5084	263	7	,	,	PUNCT
ejpam-5084	263	8	1991	1991	NUM
ejpam-5084	263	9	.	.	PUNCT