id	sid	tid	token	lemma	pos
ejpam-5061	1	1	european	european	PROPN
ejpam-5061	1	2	journal	journal	PROPN
ejpam-5061	1	3	of	of	ADP
ejpam-5061	1	4	pure	pure	ADJ
ejpam-5061	1	5	and	and	CCONJ
ejpam-5061	1	6	applied	apply	VERB
ejpam-5061	1	7	mathematics	mathematic	NOUN
ejpam-5061	1	8	vol	vol	NOUN
ejpam-5061	1	9	.	.	PROPN
ejpam-5061	2	1	17	17	NUM
ejpam-5061	2	2	,	,	PUNCT
ejpam-5061	2	3	no	no	INTJ
ejpam-5061	2	4	.	.	NOUN
ejpam-5061	2	5	2	2	NUM
ejpam-5061	2	6	,	,	PUNCT
ejpam-5061	2	7	2024	2024	NUM
ejpam-5061	2	8	,	,	PUNCT
ejpam-5061	2	9	725	725	NUM
ejpam-5061	2	10	-	-	SYM
ejpam-5061	2	11	735	735	NUM
ejpam-5061	2	12	issn	issn	PROPN
ejpam-5061	2	13	1307	1307	NUM
ejpam-5061	2	14	-	-	SYM
ejpam-5061	2	15	5543	5543	NUM
ejpam-5061	2	16	–	–	PUNCT
ejpam-5061	3	1	ejpam.com	ejpam.com	X
ejpam-5061	3	2	published	publish	VERB
ejpam-5061	3	3	by	by	ADP
ejpam-5061	3	4	new	new	PROPN
ejpam-5061	3	5	york	york	PROPN
ejpam-5061	3	6	business	business	PROPN
ejpam-5061	3	7	global	global	ADJ
ejpam-5061	3	8	legal	legal	ADJ
ejpam-5061	3	9	hop	hop	NOUN
ejpam-5061	3	10	independent	independent	ADJ
ejpam-5061	3	11	sequences	sequence	NOUN
ejpam-5061	3	12	in	in	ADP
ejpam-5061	3	13	graphs	graph	NOUN
ejpam-5061	3	14	javier	javier	PROPN
ejpam-5061	3	15	a.	a.	PROPN
ejpam-5061	3	16	hassan1,∗	hassan1,∗	PROPN
ejpam-5061	3	17	,	,	PUNCT
ejpam-5061	3	18	mercedita	mercedita	NOUN
ejpam-5061	3	19	a.	a.	NOUN
ejpam-5061	3	20	langamin1	langamin1	PROPN
ejpam-5061	3	21	,	,	PUNCT
ejpam-5061	3	22	amy	amy	PROPN
ejpam-5061	3	23	a.	a.	PROPN
ejpam-5061	3	24	laja1	laja1	PROPN
ejpam-5061	3	25	,	,	PUNCT
ejpam-5061	3	26	bayah	bayah	NOUN
ejpam-5061	3	27	j.	j.	PROPN
ejpam-5061	3	28	amiruddin	amiruddin	PROPN
ejpam-5061	3	29	-	-	PUNCT
ejpam-5061	3	30	rajik1	rajik1	PROPN
ejpam-5061	3	31	,	,	PUNCT
ejpam-5061	3	32	eman	eman	PROPN
ejpam-5061	3	33	c.	c.	PROPN
ejpam-5061	3	34	ahmad2	ahmad2	PROPN
ejpam-5061	3	35	,	,	PUNCT
ejpam-5061	3	36	jahiri	jahiri	PROPN
ejpam-5061	3	37	u.	u.	PROPN
ejpam-5061	3	38	manditong1	manditong1	PROPN
ejpam-5061	3	39	1	1	NUM
ejpam-5061	3	40	mathematics	mathematic	NOUN
ejpam-5061	3	41	and	and	CCONJ
ejpam-5061	3	42	sciences	sciences	PROPN
ejpam-5061	3	43	department	department	PROPN
ejpam-5061	3	44	,	,	PUNCT
ejpam-5061	3	45	college	college	NOUN
ejpam-5061	3	46	of	of	ADP
ejpam-5061	3	47	arts	art	NOUN
ejpam-5061	3	48	and	and	CCONJ
ejpam-5061	3	49	sciences	science	NOUN
ejpam-5061	3	50	,	,	PUNCT
ejpam-5061	3	51	msu	msu	PROPN
ejpam-5061	3	52	tawi	tawi	PROPN
ejpam-5061	3	53	-	-	PUNCT
ejpam-5061	3	54	tawi	tawi	PROPN
ejpam-5061	3	55	college	college	PROPN
ejpam-5061	3	56	of	of	ADP
ejpam-5061	3	57	technology	technology	NOUN
ejpam-5061	3	58	and	and	CCONJ
ejpam-5061	3	59	oceanography	oceanography	NOUN
ejpam-5061	3	60	,	,	PUNCT
ejpam-5061	3	61	bongao	bongao	NOUN
ejpam-5061	3	62	,	,	PUNCT
ejpam-5061	3	63	tawi	tawi	NOUN
ejpam-5061	3	64	-	-	PUNCT
ejpam-5061	3	65	tawi	tawi	NOUN
ejpam-5061	3	66	,	,	PUNCT
ejpam-5061	3	67	philippines	philippines	PROPN
ejpam-5061	3	68	1	1	NUM
ejpam-5061	3	69	department	department	NOUN
ejpam-5061	3	70	of	of	ADP
ejpam-5061	3	71	mathematics	mathematic	NOUN
ejpam-5061	3	72	and	and	CCONJ
ejpam-5061	3	73	statistics	statistic	NOUN
ejpam-5061	3	74	,	,	PUNCT
ejpam-5061	3	75	college	college	NOUN
ejpam-5061	3	76	of	of	ADP
ejpam-5061	3	77	science	science	NOUN
ejpam-5061	3	78	and	and	CCONJ
ejpam-5061	3	79	mathematics	mathematic	NOUN
ejpam-5061	3	80	,	,	PUNCT
ejpam-5061	3	81	western	western	ADJ
ejpam-5061	3	82	mindanao	mindanao	PROPN
ejpam-5061	3	83	state	state	PROPN
ejpam-5061	3	84	university	university	PROPN
ejpam-5061	3	85	,	,	PUNCT
ejpam-5061	3	86	zamboanga	zamboanga	PROPN
ejpam-5061	3	87	city	city	PROPN
ejpam-5061	3	88	,	,	PUNCT
ejpam-5061	4	1	philippines	philippine	NOUN
ejpam-5061	4	2	abstract	abstract	ADJ
ejpam-5061	4	3	.	.	PUNCT
ejpam-5061	5	1	let	let	VERB
ejpam-5061	5	2	g	g	NOUN
ejpam-5061	5	3	be	be	AUX
ejpam-5061	5	4	any	any	DET
ejpam-5061	5	5	graph	graph	NOUN
ejpam-5061	5	6	.	.	PUNCT
ejpam-5061	6	1	a	a	DET
ejpam-5061	6	2	sequence	sequence	NOUN
ejpam-5061	6	3	l	l	NOUN
ejpam-5061	6	4	=	=	SYM
ejpam-5061	6	5	(	(	PUNCT
ejpam-5061	6	6	w1	w1	NOUN
ejpam-5061	6	7	,	,	PUNCT
ejpam-5061	6	8	.	.	PUNCT
ejpam-5061	6	9	.	.	PUNCT
ejpam-5061	6	10	.	.	PUNCT
ejpam-5061	7	1	,	,	PUNCT
ejpam-5061	7	2	wk	wk	X
ejpam-5061	7	3	)	)	PUNCT
ejpam-5061	7	4	of	of	ADP
ejpam-5061	7	5	distinct	distinct	ADJ
ejpam-5061	7	6	vertices	vertex	NOUN
ejpam-5061	7	7	of	of	ADP
ejpam-5061	7	8	g	g	PROPN
ejpam-5061	7	9	is	be	AUX
ejpam-5061	7	10	called	call	VERB
ejpam-5061	7	11	a	a	DET
ejpam-5061	7	12	legal	legal	ADJ
ejpam-5061	7	13	hop	hop	NOUN
ejpam-5061	7	14	independent	independent	ADJ
ejpam-5061	7	15	sequence	sequence	NOUN
ejpam-5061	7	16	if	if	SCONJ
ejpam-5061	7	17	k	k	PROPN
ejpam-5061	7	18	=	=	SYM
ejpam-5061	7	19	1	1	NUM
ejpam-5061	7	20	or	or	CCONJ
ejpam-5061	7	21	l	l	NOUN
ejpam-5061	7	22	is	be	AUX
ejpam-5061	7	23	a	a	DET
ejpam-5061	7	24	hop	hop	NOUN
ejpam-5061	7	25	independent	independent	ADJ
ejpam-5061	7	26	and	and	CCONJ
ejpam-5061	7	27	ng[wi	ng[wi	PROPN
ejpam-5061	7	28	]	]	X
ejpam-5061	7	29	\	\	PROPN
ejpam-5061	7	30	⋃i−1	⋃i−1	NOUN
ejpam-5061	7	31	j=1	j=1	PROPN
ejpam-5061	7	32	ng[wj	ng[wj	PROPN
ejpam-5061	7	33	]	]	PUNCT
ejpam-5061	7	34	̸=	̸=	PROPN
ejpam-5061	7	35	∅	∅	NOUN
ejpam-5061	7	36	for	for	ADP
ejpam-5061	7	37	every	every	DET
ejpam-5061	7	38	i	i	PROPN
ejpam-5061	7	39	∈	∈	PROPN
ejpam-5061	7	40	{	{	PUNCT
ejpam-5061	7	41	2	2	NUM
ejpam-5061	7	42	,	,	PUNCT
ejpam-5061	7	43	·	·	PUNCT
ejpam-5061	7	44	·	·	PUNCT
ejpam-5061	7	45	·	·	PUNCT
ejpam-5061	7	46	,	,	PUNCT
ejpam-5061	7	47	k	k	X
ejpam-5061	7	48	}	}	PUNCT
ejpam-5061	7	49	.	.	PUNCT
ejpam-5061	8	1	the	the	DET
ejpam-5061	8	2	maximum	maximum	ADJ
ejpam-5061	8	3	length	length	NOUN
ejpam-5061	8	4	of	of	ADP
ejpam-5061	8	5	a	a	DET
ejpam-5061	8	6	legal	legal	ADJ
ejpam-5061	8	7	hop	hop	NOUN
ejpam-5061	8	8	independent	independent	ADJ
ejpam-5061	8	9	sequence	sequence	NOUN
ejpam-5061	8	10	in	in	ADP
ejpam-5061	8	11	g	g	NOUN
ejpam-5061	8	12	,	,	PUNCT
ejpam-5061	8	13	denoted	denote	VERB
ejpam-5061	8	14	by	by	ADP
ejpam-5061	8	15	αℓh(g	αℓh(g	NOUN
ejpam-5061	8	16	)	)	PUNCT
ejpam-5061	8	17	,	,	PUNCT
ejpam-5061	8	18	is	be	AUX
ejpam-5061	8	19	called	call	VERB
ejpam-5061	8	20	the	the	DET
ejpam-5061	8	21	legal	legal	ADJ
ejpam-5061	8	22	hop	hop	NOUN
ejpam-5061	8	23	independence	independence	NOUN
ejpam-5061	8	24	number	number	NOUN
ejpam-5061	8	25	of	of	ADP
ejpam-5061	8	26	g.	g.	PROPN
ejpam-5061	8	27	in	in	ADP
ejpam-5061	8	28	this	this	DET
ejpam-5061	8	29	paper	paper	NOUN
ejpam-5061	8	30	,	,	PUNCT
ejpam-5061	8	31	we	we	PRON
ejpam-5061	8	32	investigate	investigate	VERB
ejpam-5061	8	33	its	its	PRON
ejpam-5061	8	34	relationships	relationship	NOUN
ejpam-5061	8	35	with	with	ADP
ejpam-5061	8	36	the	the	DET
ejpam-5061	8	37	hop	hop	NOUN
ejpam-5061	8	38	independence	independence	NOUN
ejpam-5061	8	39	and	and	CCONJ
ejpam-5061	8	40	grundy	grundy	PROPN
ejpam-5061	8	41	domination	domination	NOUN
ejpam-5061	8	42	parameter	parameter	NOUN
ejpam-5061	8	43	of	of	ADP
ejpam-5061	8	44	a	a	DET
ejpam-5061	8	45	graph	graph	NOUN
ejpam-5061	8	46	,	,	PUNCT
ejpam-5061	8	47	respectively	respectively	ADV
ejpam-5061	8	48	.	.	PUNCT
ejpam-5061	9	1	in	in	ADP
ejpam-5061	9	2	fact	fact	NOUN
ejpam-5061	9	3	,	,	PUNCT
ejpam-5061	9	4	the	the	DET
ejpam-5061	9	5	legal	legal	ADJ
ejpam-5061	9	6	hop	hop	NOUN
ejpam-5061	9	7	independence	independence	NOUN
ejpam-5061	9	8	parameter	parameter	NOUN
ejpam-5061	9	9	is	be	AUX
ejpam-5061	9	10	at	at	ADP
ejpam-5061	9	11	most	most	ADV
ejpam-5061	9	12	equal	equal	ADJ
ejpam-5061	9	13	to	to	ADP
ejpam-5061	9	14	the	the	DET
ejpam-5061	9	15	grundy	grundy	PROPN
ejpam-5061	9	16	domination	domination	NOUN
ejpam-5061	9	17	(	(	PUNCT
ejpam-5061	9	18	resp	resp	NOUN
ejpam-5061	9	19	.	.	PUNCT
ejpam-5061	10	1	hop	hop	PROPN
ejpam-5061	10	2	independence	independence	NOUN
ejpam-5061	10	3	)	)	PUNCT
ejpam-5061	10	4	parameter	parameter	NOUN
ejpam-5061	10	5	on	on	ADP
ejpam-5061	10	6	any	any	DET
ejpam-5061	10	7	graph	graph	NOUN
ejpam-5061	10	8	g.	g.	NOUN
ejpam-5061	11	1	moreover	moreover	ADV
ejpam-5061	11	2	,	,	PUNCT
ejpam-5061	11	3	we	we	PRON
ejpam-5061	11	4	derive	derive	VERB
ejpam-5061	11	5	some	some	DET
ejpam-5061	11	6	formulas	formula	NOUN
ejpam-5061	11	7	and	and	CCONJ
ejpam-5061	11	8	bounds	bound	NOUN
ejpam-5061	11	9	of	of	ADP
ejpam-5061	11	10	this	this	DET
ejpam-5061	11	11	parameter	parameter	NOUN
ejpam-5061	11	12	on	on	ADP
ejpam-5061	11	13	some	some	DET
ejpam-5061	11	14	families	family	NOUN
ejpam-5061	11	15	of	of	ADP
ejpam-5061	11	16	graphs	graph	NOUN
ejpam-5061	11	17	,	,	PUNCT
ejpam-5061	11	18	join	join	NOUN
ejpam-5061	11	19	,	,	PUNCT
ejpam-5061	11	20	and	and	CCONJ
ejpam-5061	11	21	corona	corona	NOUN
ejpam-5061	11	22	of	of	ADP
ejpam-5061	11	23	two	two	NUM
ejpam-5061	11	24	graphs	graph	NOUN
ejpam-5061	11	25	.	.	PUNCT
ejpam-5061	12	1	2020	2020	NUM
ejpam-5061	12	2	mathematics	mathematic	NOUN
ejpam-5061	12	3	subject	subject	NOUN
ejpam-5061	12	4	classifications	classification	NOUN
ejpam-5061	12	5	:	:	PUNCT
ejpam-5061	12	6	05c69	05c69	X
ejpam-5061	12	7	key	key	ADJ
ejpam-5061	12	8	words	word	NOUN
ejpam-5061	12	9	and	and	CCONJ
ejpam-5061	12	10	phrases	phrase	NOUN
ejpam-5061	12	11	:	:	PUNCT
ejpam-5061	12	12	legal	legal	ADJ
ejpam-5061	12	13	sequence	sequence	NOUN
ejpam-5061	12	14	,	,	PUNCT
ejpam-5061	12	15	hop	hop	NOUN
ejpam-5061	12	16	independent	independent	ADJ
ejpam-5061	12	17	set	set	NOUN
ejpam-5061	12	18	,	,	PUNCT
ejpam-5061	12	19	legal	legal	ADJ
ejpam-5061	12	20	hop	hop	NOUN
ejpam-5061	12	21	independent	independent	ADJ
ejpam-5061	12	22	sequence	sequence	NOUN
ejpam-5061	12	23	,	,	PUNCT
ejpam-5061	12	24	legal	legal	ADJ
ejpam-5061	12	25	hop	hop	NOUN
ejpam-5061	12	26	independence	independence	NOUN
ejpam-5061	12	27	number	number	NOUN
ejpam-5061	12	28	1	1	NUM
ejpam-5061	12	29	.	.	PUNCT
ejpam-5061	13	1	introduction	introduction	NOUN
ejpam-5061	13	2	independent	independent	ADJ
ejpam-5061	13	3	sets	set	NOUN
ejpam-5061	13	4	are	be	AUX
ejpam-5061	13	5	used	use	VERB
ejpam-5061	13	6	to	to	PART
ejpam-5061	13	7	model	model	VERB
ejpam-5061	13	8	relationships	relationship	NOUN
ejpam-5061	13	9	in	in	ADP
ejpam-5061	13	10	networks	network	NOUN
ejpam-5061	13	11	,	,	PUNCT
ejpam-5061	13	12	such	such	ADJ
ejpam-5061	13	13	as	as	ADP
ejpam-5061	13	14	social	social	ADJ
ejpam-5061	13	15	networks	network	NOUN
ejpam-5061	13	16	,	,	PUNCT
ejpam-5061	13	17	computer	computer	NOUN
ejpam-5061	13	18	networks	network	NOUN
ejpam-5061	13	19	,	,	PUNCT
ejpam-5061	13	20	and	and	CCONJ
ejpam-5061	13	21	biological	biological	ADJ
ejpam-5061	13	22	networks	network	NOUN
ejpam-5061	13	23	.	.	PUNCT
ejpam-5061	14	1	for	for	ADP
ejpam-5061	14	2	example	example	NOUN
ejpam-5061	14	3	,	,	PUNCT
ejpam-5061	14	4	in	in	ADP
ejpam-5061	14	5	a	a	DET
ejpam-5061	14	6	social	social	ADJ
ejpam-5061	14	7	network	network	NOUN
ejpam-5061	14	8	,	,	PUNCT
ejpam-5061	14	9	an	an	DET
ejpam-5061	14	10	independent	independent	ADJ
ejpam-5061	14	11	set	set	NOUN
ejpam-5061	14	12	could	could	AUX
ejpam-5061	14	13	represent	represent	VERB
ejpam-5061	14	14	a	a	DET
ejpam-5061	14	15	group	group	NOUN
ejpam-5061	14	16	of	of	ADP
ejpam-5061	14	17	individuals	individual	NOUN
ejpam-5061	14	18	who	who	PRON
ejpam-5061	14	19	are	be	AUX
ejpam-5061	14	20	not	not	PART
ejpam-5061	14	21	directly	directly	ADV
ejpam-5061	14	22	connected	connect	VERB
ejpam-5061	14	23	or	or	CCONJ
ejpam-5061	14	24	acquainted	acquaint	VERB
ejpam-5061	14	25	with	with	ADP
ejpam-5061	14	26	each	each	DET
ejpam-5061	14	27	other	other	ADJ
ejpam-5061	14	28	.	.	PUNCT
ejpam-5061	15	1	independent	independent	ADJ
ejpam-5061	15	2	sets	set	NOUN
ejpam-5061	15	3	in	in	ADP
ejpam-5061	15	4	graphs	graph	NOUN
ejpam-5061	15	5	had	have	AUX
ejpam-5061	15	6	studied	study	VERB
ejpam-5061	15	7	on	on	ADP
ejpam-5061	15	8	different	different	ADJ
ejpam-5061	15	9	kinds	kind	NOUN
ejpam-5061	15	10	of	of	ADP
ejpam-5061	15	11	graphs	graph	NOUN
ejpam-5061	15	12	(	(	PUNCT
ejpam-5061	15	13	see	see	VERB
ejpam-5061	15	14	[	[	X
ejpam-5061	15	15	2	2	NUM
ejpam-5061	15	16	,	,	PUNCT
ejpam-5061	15	17	11	11	NUM
ejpam-5061	15	18	,	,	PUNCT
ejpam-5061	15	19	17	17	NUM
ejpam-5061	15	20	,	,	PUNCT
ejpam-5061	15	21	18	18	NUM
ejpam-5061	15	22	]	]	PUNCT
ejpam-5061	15	23	)	)	PUNCT
ejpam-5061	15	24	.	.	PUNCT
ejpam-5061	16	1	in	in	ADP
ejpam-5061	16	2	2022	2022	NUM
ejpam-5061	16	3	,	,	PUNCT
ejpam-5061	16	4	hop	hop	NOUN
ejpam-5061	16	5	independent	independent	ADJ
ejpam-5061	16	6	set	set	NOUN
ejpam-5061	16	7	in	in	ADP
ejpam-5061	16	8	a	a	DET
ejpam-5061	16	9	graph	graph	NOUN
ejpam-5061	16	10	and	and	CCONJ
ejpam-5061	16	11	its	its	PRON
ejpam-5061	16	12	parameter	parameter	NOUN
ejpam-5061	16	13	was	be	AUX
ejpam-5061	16	14	introduced	introduce	VERB
ejpam-5061	16	15	by	by	ADP
ejpam-5061	16	16	j.	j.	PROPN
ejpam-5061	16	17	hassan	hassan	PROPN
ejpam-5061	16	18	et	et	PROPN
ejpam-5061	16	19	al	al	PROPN
ejpam-5061	16	20	.	.	PUNCT
ejpam-5061	17	1	[	[	X
ejpam-5061	17	2	8	8	NUM
ejpam-5061	17	3	]	]	PUNCT
ejpam-5061	17	4	.	.	PUNCT
ejpam-5061	18	1	they	they	PRON
ejpam-5061	18	2	defined	define	VERB
ejpam-5061	18	3	a	a	DET
ejpam-5061	18	4	set	set	NOUN
ejpam-5061	18	5	s	s	NOUN
ejpam-5061	18	6	⊆	⊆	NUM
ejpam-5061	18	7	v	v	NOUN
ejpam-5061	18	8	(	(	PUNCT
ejpam-5061	18	9	g	g	NOUN
ejpam-5061	18	10	)	)	PUNCT
ejpam-5061	18	11	is	be	AUX
ejpam-5061	18	12	a	a	DET
ejpam-5061	18	13	hop	hop	NOUN
ejpam-5061	18	14	independet	independet	NOUN
ejpam-5061	18	15	set	set	NOUN
ejpam-5061	18	16	of	of	ADP
ejpam-5061	18	17	g	g	PROPN
ejpam-5061	18	18	if	if	SCONJ
ejpam-5061	18	19	any	any	DET
ejpam-5061	18	20	two	two	NUM
ejpam-5061	18	21	distinct	distinct	ADJ
ejpam-5061	18	22	vertices	vertex	NOUN
ejpam-5061	18	23	in	in	ADP
ejpam-5061	18	24	s	s	NOUN
ejpam-5061	18	25	are	be	AUX
ejpam-5061	18	26	not	not	PART
ejpam-5061	18	27	at	at	ADP
ejpam-5061	18	28	a	a	DET
ejpam-5061	18	29	distance	distance	NOUN
ejpam-5061	18	30	two	two	NUM
ejpam-5061	18	31	from	from	ADP
ejpam-5061	18	32	each	each	DET
ejpam-5061	18	33	other	other	ADJ
ejpam-5061	18	34	,	,	PUNCT
ejpam-5061	18	35	that	that	ADV
ejpam-5061	18	36	is	is	ADV
ejpam-5061	18	37	,	,	PUNCT
ejpam-5061	18	38	dg(u	dg(u	X
ejpam-5061	18	39	,	,	PUNCT
ejpam-5061	18	40	w	w	NOUN
ejpam-5061	18	41	)	)	PUNCT
ejpam-5061	18	42	̸=	̸=	PROPN
ejpam-5061	18	43	2	2	NUM
ejpam-5061	18	44	for	for	ADP
ejpam-5061	18	45	any	any	DET
ejpam-5061	18	46	distinct	distinct	ADJ
ejpam-5061	18	47	vertices	vertex	NOUN
ejpam-5061	18	48	u	u	NOUN
ejpam-5061	18	49	,	,	PUNCT
ejpam-5061	18	50	w	w	PROPN
ejpam-5061	18	51	∈	∈	PROPN
ejpam-5061	18	52	s.	s.	PROPN
ejpam-5061	18	53	the	the	DET
ejpam-5061	18	54	maximum	maximum	PROPN
ejpam-5061	18	55	cardinality	cardinality	NOUN
ejpam-5061	18	56	of	of	ADP
ejpam-5061	18	57	a	a	DET
ejpam-5061	18	58	hop	hop	NOUN
ejpam-5061	18	59	independent	independent	ADJ
ejpam-5061	18	60	set	set	NOUN
ejpam-5061	18	61	of	of	ADP
ejpam-5061	18	62	g	g	NOUN
ejpam-5061	18	63	,	,	PUNCT
ejpam-5061	18	64	∗corresponding	∗corresponde	VERB
ejpam-5061	18	65	author	author	NOUN
ejpam-5061	18	66	.	.	PUNCT
ejpam-5061	19	1	doi	doi	NOUN
ejpam-5061	19	2	:	:	PUNCT
ejpam-5061	19	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5061	https://doi.org/10.29020/nybg.ejpam.v17i2.5061	PROPN
ejpam-5061	19	4	email	email	NOUN
ejpam-5061	19	5	addresses	address	NOUN
ejpam-5061	19	6	:	:	PUNCT
ejpam-5061	19	7	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-5061	19	8	(	(	PUNCT
ejpam-5061	19	9	j.	j.	PROPN
ejpam-5061	19	10	hassan	hassan	PROPN
ejpam-5061	19	11	)	)	PUNCT
ejpam-5061	19	12	merceditalangamin@msutawi-tawi.edu.ph	merceditalangamin@msutawi-tawi.edu.ph	PROPN
ejpam-5061	19	13	(	(	PUNCT
ejpam-5061	19	14	m.	m.	NOUN
ejpam-5061	19	15	langamin	langamin	PROPN
ejpam-5061	19	16	)	)	PUNCT
ejpam-5061	19	17	amylaja@msutawi-tawi.edu.ph	amylaja@msutawi-tawi.edu.ph	PROPN
ejpam-5061	19	18	(	(	PUNCT
ejpam-5061	19	19	a.	a.	NOUN
ejpam-5061	19	20	laja	laja	PROPN
ejpam-5061	19	21	)	)	PUNCT
ejpam-5061	20	1	bayahamiruddin@msutawi-tawi.edu.ph	bayahamiruddin@msutawi-tawi.edu.ph	PROPN
ejpam-5061	20	2	(	(	PUNCT
ejpam-5061	20	3	b.	b.	PROPN
ejpam-5061	20	4	amiruddin	amiruddin	PROPN
ejpam-5061	20	5	)	)	PUNCT
ejpam-5061	21	1	ahmad.eman@wmsu.edu.ph	ahmad.eman@wmsu.edu.ph	PROPN
ejpam-5061	21	2	(	(	PUNCT
ejpam-5061	21	3	e.	e.	PROPN
ejpam-5061	21	4	ahmad	ahmad	PROPN
ejpam-5061	21	5	)	)	PUNCT
ejpam-5061	21	6	jahirimanditong@msutawi-tawi.edu.ph	jahirimanditong@msutawi-tawi.edu.ph	PROPN
ejpam-5061	21	7	(	(	PUNCT
ejpam-5061	21	8	j.	j.	PROPN
ejpam-5061	21	9	manditong	manditong	PROPN
ejpam-5061	21	10	)	)	PUNCT
ejpam-5061	21	11	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5061	22	1	725	725	NUM
ejpam-5061	22	2	©	©	PROPN
ejpam-5061	22	3	2024	2024	NUM
ejpam-5061	22	4	ejpam	ejpam	NOUN
ejpam-5061	22	5	all	all	DET
ejpam-5061	22	6	rights	right	NOUN
ejpam-5061	22	7	reserved	reserve	VERB
ejpam-5061	22	8	.	.	PUNCT
ejpam-5061	23	1	j.	j.	PROPN
ejpam-5061	23	2	hassan	hassan	PROPN
ejpam-5061	23	3	et	et	PROPN
ejpam-5061	23	4	al	al	PROPN
ejpam-5061	23	5	.	.	PUNCT
ejpam-5061	23	6	/	/	SYM
ejpam-5061	23	7	eur	eur	PROPN
ejpam-5061	23	8	.	.	PUNCT
ejpam-5061	24	1	j.	j.	PROPN
ejpam-5061	24	2	pure	pure	PROPN
ejpam-5061	24	3	appl	appl	PROPN
ejpam-5061	24	4	.	.	PROPN
ejpam-5061	24	5	math	math	PROPN
ejpam-5061	24	6	,	,	PUNCT
ejpam-5061	24	7	17	17	NUM
ejpam-5061	24	8	(	(	PUNCT
ejpam-5061	24	9	2	2	NUM
ejpam-5061	24	10	)	)	PUNCT
ejpam-5061	24	11	(	(	PUNCT
ejpam-5061	24	12	2024	2024	NUM
ejpam-5061	24	13	)	)	PUNCT
ejpam-5061	24	14	,	,	PUNCT
ejpam-5061	24	15	725	725	NUM
ejpam-5061	24	16	-	-	SYM
ejpam-5061	24	17	735	735	NUM
ejpam-5061	24	18	726	726	NUM
ejpam-5061	24	19	denoted	denote	VERB
ejpam-5061	24	20	by	by	ADP
ejpam-5061	24	21	αh(g	αh(g	NOUN
ejpam-5061	24	22	)	)	PUNCT
ejpam-5061	24	23	,	,	PUNCT
ejpam-5061	24	24	is	be	AUX
ejpam-5061	24	25	called	call	VERB
ejpam-5061	24	26	the	the	DET
ejpam-5061	24	27	hop	hop	NOUN
ejpam-5061	24	28	independence	independence	NOUN
ejpam-5061	24	29	number	number	NOUN
ejpam-5061	24	30	of	of	ADP
ejpam-5061	24	31	g.	g.	PROPN
ejpam-5061	24	32	they	they	PRON
ejpam-5061	24	33	have	have	AUX
ejpam-5061	24	34	shown	show	VERB
ejpam-5061	24	35	that	that	SCONJ
ejpam-5061	24	36	any	any	DET
ejpam-5061	24	37	maximum	maximum	ADJ
ejpam-5061	24	38	hop	hop	NOUN
ejpam-5061	24	39	independent	independent	ADJ
ejpam-5061	24	40	set	set	NOUN
ejpam-5061	24	41	s	s	PRON
ejpam-5061	24	42	of	of	ADP
ejpam-5061	24	43	g	g	PROPN
ejpam-5061	24	44	is	be	AUX
ejpam-5061	24	45	always	always	ADV
ejpam-5061	24	46	a	a	DET
ejpam-5061	24	47	hop	hop	NOUN
ejpam-5061	24	48	dominating	dominating	NOUN
ejpam-5061	24	49	,	,	PUNCT
ejpam-5061	24	50	that	that	ADV
ejpam-5061	24	51	is	is	ADV
ejpam-5061	24	52	,	,	PUNCT
ejpam-5061	24	53	the	the	DET
ejpam-5061	24	54	hop	hop	NOUN
ejpam-5061	24	55	indpendence	indpendence	NOUN
ejpam-5061	24	56	number	number	NOUN
ejpam-5061	24	57	of	of	ADP
ejpam-5061	24	58	a	a	DET
ejpam-5061	24	59	graph	graph	NOUN
ejpam-5061	24	60	is	be	AUX
ejpam-5061	24	61	always	always	ADV
ejpam-5061	24	62	greater	great	ADJ
ejpam-5061	24	63	than	than	ADP
ejpam-5061	24	64	or	or	CCONJ
ejpam-5061	24	65	equal	equal	ADJ
ejpam-5061	24	66	to	to	ADP
ejpam-5061	24	67	the	the	DET
ejpam-5061	24	68	hop	hop	NOUN
ejpam-5061	24	69	domination	domination	PROPN
ejpam-5061	24	70	parameter	parameter	NOUN
ejpam-5061	24	71	.	.	PUNCT
ejpam-5061	25	1	moreover	moreover	ADV
ejpam-5061	25	2	,	,	PUNCT
ejpam-5061	25	3	they	they	PRON
ejpam-5061	25	4	derived	derive	VERB
ejpam-5061	25	5	some	some	DET
ejpam-5061	25	6	bounds	bound	NOUN
ejpam-5061	25	7	and	and	CCONJ
ejpam-5061	25	8	formulas	formula	NOUN
ejpam-5061	25	9	for	for	ADP
ejpam-5061	25	10	some	some	DET
ejpam-5061	25	11	special	special	ADJ
ejpam-5061	25	12	graphs	graph	NOUN
ejpam-5061	25	13	and	and	CCONJ
ejpam-5061	25	14	graphs	graph	NOUN
ejpam-5061	25	15	under	under	ADP
ejpam-5061	25	16	some	some	DET
ejpam-5061	25	17	binary	binary	ADJ
ejpam-5061	25	18	operations	operation	NOUN
ejpam-5061	25	19	.	.	PUNCT
ejpam-5061	26	1	some	some	DET
ejpam-5061	26	2	studies	study	NOUN
ejpam-5061	26	3	related	relate	VERB
ejpam-5061	26	4	to	to	ADP
ejpam-5061	26	5	hop	hop	NOUN
ejpam-5061	26	6	independent	independent	ADJ
ejpam-5061	26	7	sets	set	NOUN
ejpam-5061	26	8	,	,	PUNCT
ejpam-5061	26	9	its	its	PRON
ejpam-5061	26	10	variations	variation	NOUN
ejpam-5061	26	11	,	,	PUNCT
ejpam-5061	26	12	and	and	CCONJ
ejpam-5061	26	13	other	other	ADJ
ejpam-5061	26	14	hop	hop	ADV
ejpam-5061	26	15	-	-	PUNCT
ejpam-5061	26	16	related	relate	VERB
ejpam-5061	26	17	concepts	concept	NOUN
ejpam-5061	26	18	can	can	AUX
ejpam-5061	26	19	be	be	AUX
ejpam-5061	26	20	found	find	VERB
ejpam-5061	26	21	in	in	ADP
ejpam-5061	26	22	[	[	X
ejpam-5061	26	23	3	3	NUM
ejpam-5061	26	24	,	,	PUNCT
ejpam-5061	26	25	9	9	NUM
ejpam-5061	26	26	,	,	PUNCT
ejpam-5061	26	27	10	10	NUM
ejpam-5061	26	28	,	,	PUNCT
ejpam-5061	26	29	13	13	NUM
ejpam-5061	26	30	,	,	PUNCT
ejpam-5061	26	31	14	14	NUM
ejpam-5061	26	32	]	]	PUNCT
ejpam-5061	26	33	.	.	PUNCT
ejpam-5061	27	1	recently	recently	ADV
ejpam-5061	27	2	,	,	PUNCT
ejpam-5061	27	3	j.	j.	PROPN
ejpam-5061	27	4	hassan	hassan	PROPN
ejpam-5061	27	5	and	and	CCONJ
ejpam-5061	27	6	s.	s.	PROPN
ejpam-5061	27	7	canoy	canoy	PROPN
ejpam-5061	27	8	[	[	X
ejpam-5061	27	9	5	5	NUM
ejpam-5061	27	10	]	]	PUNCT
ejpam-5061	27	11	,	,	PUNCT
ejpam-5061	27	12	introduced	introduce	VERB
ejpam-5061	27	13	another	another	DET
ejpam-5061	27	14	variant	variant	NOUN
ejpam-5061	27	15	of	of	ADP
ejpam-5061	27	16	hop	hop	NOUN
ejpam-5061	27	17	independence	independence	NOUN
ejpam-5061	27	18	in	in	ADP
ejpam-5061	27	19	a	a	DET
ejpam-5061	27	20	graph	graph	NOUN
ejpam-5061	27	21	called	call	VERB
ejpam-5061	27	22	hop	hop	PROPN
ejpam-5061	27	23	independent	independent	ADJ
ejpam-5061	27	24	hop	hop	NOUN
ejpam-5061	27	25	domination	domination	NOUN
ejpam-5061	27	26	.	.	PUNCT
ejpam-5061	28	1	they	they	PRON
ejpam-5061	28	2	have	have	AUX
ejpam-5061	28	3	shown	show	VERB
ejpam-5061	28	4	that	that	SCONJ
ejpam-5061	28	5	the	the	DET
ejpam-5061	28	6	hop	hop	NOUN
ejpam-5061	28	7	independent	independent	ADJ
ejpam-5061	28	8	hop	hop	NOUN
ejpam-5061	28	9	domination	domination	NOUN
ejpam-5061	28	10	number	number	NOUN
ejpam-5061	28	11	of	of	ADP
ejpam-5061	28	12	a	a	DET
ejpam-5061	28	13	graph	graph	NOUN
ejpam-5061	28	14	g	g	NOUN
ejpam-5061	28	15	lies	lie	NOUN
ejpam-5061	28	16	between	between	ADP
ejpam-5061	28	17	the	the	DET
ejpam-5061	28	18	hop	hop	NOUN
ejpam-5061	28	19	domination	domination	NOUN
ejpam-5061	28	20	number	number	NOUN
ejpam-5061	28	21	and	and	CCONJ
ejpam-5061	28	22	the	the	DET
ejpam-5061	28	23	hop	hop	NOUN
ejpam-5061	28	24	independence	independence	NOUN
ejpam-5061	28	25	number	number	NOUN
ejpam-5061	28	26	of	of	ADP
ejpam-5061	28	27	graph	graph	NOUN
ejpam-5061	28	28	g.	g.	PROPN
ejpam-5061	28	29	they	they	PRON
ejpam-5061	28	30	have	have	AUX
ejpam-5061	28	31	characterized	characterize	VERB
ejpam-5061	28	32	hop	hop	NOUN
ejpam-5061	28	33	independent	independent	ADJ
ejpam-5061	28	34	hop	hop	NOUN
ejpam-5061	28	35	dominating	dominating	NOUN
ejpam-5061	28	36	sets	set	NOUN
ejpam-5061	28	37	in	in	ADP
ejpam-5061	28	38	the	the	DET
ejpam-5061	28	39	shadow	shadow	NOUN
ejpam-5061	28	40	graph	graph	NOUN
ejpam-5061	28	41	,	,	PUNCT
ejpam-5061	28	42	join	join	NOUN
ejpam-5061	28	43	,	,	PUNCT
ejpam-5061	28	44	corona	corona	PROPN
ejpam-5061	28	45	,	,	PUNCT
ejpam-5061	28	46	and	and	CCONJ
ejpam-5061	28	47	lexicographic	lexicographic	ADJ
ejpam-5061	28	48	product	product	NOUN
ejpam-5061	28	49	of	of	ADP
ejpam-5061	28	50	two	two	NUM
ejpam-5061	28	51	graphs	graph	NOUN
ejpam-5061	28	52	.	.	PUNCT
ejpam-5061	29	1	moreover	moreover	ADV
ejpam-5061	29	2	,	,	PUNCT
ejpam-5061	29	3	they	they	PRON
ejpam-5061	29	4	have	have	AUX
ejpam-5061	29	5	obtained	obtain	VERB
ejpam-5061	29	6	exact	exact	ADJ
ejpam-5061	29	7	values	value	NOUN
ejpam-5061	29	8	or	or	CCONJ
ejpam-5061	29	9	bounds	bound	NOUN
ejpam-5061	29	10	of	of	ADP
ejpam-5061	29	11	the	the	DET
ejpam-5061	29	12	hop	hop	NOUN
ejpam-5061	29	13	independent	independent	ADJ
ejpam-5061	29	14	hop	hop	NOUN
ejpam-5061	29	15	domination	domination	NOUN
ejpam-5061	29	16	numbers	number	NOUN
ejpam-5061	29	17	of	of	ADP
ejpam-5061	29	18	these	these	DET
ejpam-5061	29	19	graphs	graph	NOUN
ejpam-5061	29	20	.	.	PUNCT
ejpam-5061	30	1	furthermore	furthermore	ADV
ejpam-5061	30	2	,	,	PUNCT
ejpam-5061	30	3	researchers	researcher	NOUN
ejpam-5061	30	4	had	have	AUX
ejpam-5061	30	5	studied	study	VERB
ejpam-5061	30	6	variants	variant	NOUN
ejpam-5061	30	7	of	of	ADP
ejpam-5061	30	8	hop	hop	PROPN
ejpam-5061	30	9	independent	independent	ADJ
ejpam-5061	30	10	hop	hop	NOUN
ejpam-5061	30	11	domination	domination	NOUN
ejpam-5061	30	12	and	and	CCONJ
ejpam-5061	30	13	other	other	ADJ
ejpam-5061	30	14	related	related	ADJ
ejpam-5061	30	15	studies	study	NOUN
ejpam-5061	30	16	on	on	ADP
ejpam-5061	30	17	different	different	ADJ
ejpam-5061	30	18	types	type	NOUN
ejpam-5061	30	19	of	of	ADP
ejpam-5061	30	20	graphs	graph	NOUN
ejpam-5061	30	21	(	(	PUNCT
ejpam-5061	30	22	see	see	VERB
ejpam-5061	30	23	[	[	X
ejpam-5061	30	24	1	1	NUM
ejpam-5061	30	25	,	,	PUNCT
ejpam-5061	30	26	4	4	NUM
ejpam-5061	30	27	,	,	PUNCT
ejpam-5061	30	28	6	6	NUM
ejpam-5061	30	29	,	,	PUNCT
ejpam-5061	30	30	7	7	NUM
ejpam-5061	30	31	,	,	PUNCT
ejpam-5061	30	32	12	12	NUM
ejpam-5061	30	33	,	,	PUNCT
ejpam-5061	30	34	15	15	NUM
ejpam-5061	30	35	,	,	PUNCT
ejpam-5061	30	36	16	16	NUM
ejpam-5061	30	37	]	]	PUNCT
ejpam-5061	30	38	)	)	PUNCT
ejpam-5061	30	39	.	.	PUNCT
ejpam-5061	31	1	in	in	ADP
ejpam-5061	31	2	this	this	DET
ejpam-5061	31	3	paper	paper	NOUN
ejpam-5061	31	4	,	,	PUNCT
ejpam-5061	31	5	new	new	ADJ
ejpam-5061	31	6	variant	variant	NOUN
ejpam-5061	31	7	of	of	ADP
ejpam-5061	31	8	hop	hop	NOUN
ejpam-5061	31	9	independence	independence	NOUN
ejpam-5061	31	10	called	call	VERB
ejpam-5061	31	11	legal	legal	ADJ
ejpam-5061	31	12	hop	hop	NOUN
ejpam-5061	31	13	independent	independent	ADJ
ejpam-5061	31	14	sequences	sequence	NOUN
ejpam-5061	31	15	in	in	ADP
ejpam-5061	31	16	a	a	DET
ejpam-5061	31	17	graph	graph	NOUN
ejpam-5061	31	18	is	be	AUX
ejpam-5061	31	19	introduced	introduce	VERB
ejpam-5061	31	20	and	and	CCONJ
ejpam-5061	31	21	investigated	investigate	VERB
ejpam-5061	31	22	.	.	PUNCT
ejpam-5061	32	1	the	the	DET
ejpam-5061	32	2	main	main	ADJ
ejpam-5061	32	3	focus	focus	NOUN
ejpam-5061	32	4	of	of	ADP
ejpam-5061	32	5	this	this	DET
ejpam-5061	32	6	concept	concept	NOUN
ejpam-5061	32	7	is	be	AUX
ejpam-5061	32	8	on	on	ADP
ejpam-5061	32	9	the	the	DET
ejpam-5061	32	10	sequence	sequence	NOUN
ejpam-5061	32	11	of	of	ADP
ejpam-5061	32	12	vertices	vertex	NOUN
ejpam-5061	32	13	of	of	ADP
ejpam-5061	32	14	a	a	DET
ejpam-5061	32	15	graph	graph	NOUN
ejpam-5061	32	16	wherein	wherein	SCONJ
ejpam-5061	32	17	it	it	PRON
ejpam-5061	32	18	must	must	AUX
ejpam-5061	32	19	satisfy	satisfy	VERB
ejpam-5061	32	20	a	a	DET
ejpam-5061	32	21	certain	certain	ADJ
ejpam-5061	32	22	condition	condition	NOUN
ejpam-5061	32	23	aside	aside	ADV
ejpam-5061	32	24	from	from	ADP
ejpam-5061	32	25	being	be	AUX
ejpam-5061	32	26	a	a	DET
ejpam-5061	32	27	hop	hop	NOUN
ejpam-5061	32	28	independent	independent	ADJ
ejpam-5061	32	29	.	.	PUNCT
ejpam-5061	33	1	the	the	DET
ejpam-5061	33	2	authors	author	NOUN
ejpam-5061	33	3	believe	believe	VERB
ejpam-5061	33	4	that	that	SCONJ
ejpam-5061	33	5	this	this	DET
ejpam-5061	33	6	study	study	NOUN
ejpam-5061	33	7	may	may	AUX
ejpam-5061	33	8	provide	provide	VERB
ejpam-5061	33	9	interesting	interesting	ADJ
ejpam-5061	33	10	results	result	NOUN
ejpam-5061	33	11	that	that	PRON
ejpam-5061	33	12	would	would	AUX
ejpam-5061	33	13	positively	positively	ADV
ejpam-5061	33	14	contribute	contribute	VERB
ejpam-5061	33	15	to	to	ADP
ejpam-5061	33	16	the	the	DET
ejpam-5061	33	17	independence	independence	NOUN
ejpam-5061	33	18	theory	theory	NOUN
ejpam-5061	33	19	and	and	CCONJ
ejpam-5061	33	20	could	could	AUX
ejpam-5061	33	21	lead	lead	VERB
ejpam-5061	33	22	to	to	ADP
ejpam-5061	33	23	another	another	DET
ejpam-5061	33	24	interesting	interesting	ADJ
ejpam-5061	33	25	studies	study	NOUN
ejpam-5061	33	26	and	and	CCONJ
ejpam-5061	33	27	application	application	NOUN
ejpam-5061	33	28	of	of	ADP
ejpam-5061	33	29	the	the	DET
ejpam-5061	33	30	parameter	parameter	NOUN
ejpam-5061	33	31	.	.	PUNCT
ejpam-5061	34	1	2	2	X
ejpam-5061	34	2	.	.	X
ejpam-5061	34	3	terminology	terminology	NOUN
ejpam-5061	34	4	and	and	CCONJ
ejpam-5061	34	5	notation	notation	NOUN
ejpam-5061	34	6	let	let	VERB
ejpam-5061	34	7	g	g	NOUN
ejpam-5061	34	8	=	=	SYM
ejpam-5061	34	9	(	(	PUNCT
ejpam-5061	34	10	v	v	NOUN
ejpam-5061	34	11	(	(	PUNCT
ejpam-5061	34	12	g	g	NOUN
ejpam-5061	34	13	)	)	PUNCT
ejpam-5061	34	14	,	,	PUNCT
ejpam-5061	34	15	e(g	e(g	PROPN
ejpam-5061	34	16	)	)	PUNCT
ejpam-5061	34	17	)	)	PUNCT
ejpam-5061	34	18	be	be	AUX
ejpam-5061	34	19	a	a	DET
ejpam-5061	34	20	simple	simple	ADJ
ejpam-5061	34	21	and	and	CCONJ
ejpam-5061	34	22	undirected	undirected	ADJ
ejpam-5061	34	23	graph	graph	NOUN
ejpam-5061	34	24	.	.	PUNCT
ejpam-5061	35	1	the	the	DET
ejpam-5061	35	2	distance	distance	NOUN
ejpam-5061	35	3	dg(u	dg(u	NOUN
ejpam-5061	35	4	,	,	PUNCT
ejpam-5061	35	5	v	v	NOUN
ejpam-5061	35	6	)	)	PUNCT
ejpam-5061	35	7	in	in	ADP
ejpam-5061	35	8	g	g	NOUN
ejpam-5061	35	9	of	of	ADP
ejpam-5061	35	10	two	two	NUM
ejpam-5061	35	11	vertices	vertex	NOUN
ejpam-5061	35	12	u	u	NOUN
ejpam-5061	35	13	,	,	PUNCT
ejpam-5061	35	14	v	v	PROPN
ejpam-5061	35	15	is	be	AUX
ejpam-5061	35	16	the	the	DET
ejpam-5061	35	17	length	length	NOUN
ejpam-5061	35	18	of	of	ADP
ejpam-5061	35	19	a	a	DET
ejpam-5061	35	20	shortest	short	ADJ
ejpam-5061	35	21	u	u	NOUN
ejpam-5061	35	22	-	-	NOUN
ejpam-5061	35	23	v	v	ADJ
ejpam-5061	35	24	path	path	NOUN
ejpam-5061	35	25	in	in	ADP
ejpam-5061	35	26	g.	g.	PROPN
ejpam-5061	35	27	the	the	DET
ejpam-5061	35	28	greatest	great	ADJ
ejpam-5061	35	29	distance	distance	NOUN
ejpam-5061	35	30	between	between	ADP
ejpam-5061	35	31	any	any	DET
ejpam-5061	35	32	two	two	NUM
ejpam-5061	35	33	vertices	vertex	NOUN
ejpam-5061	35	34	in	in	ADP
ejpam-5061	35	35	g	g	NOUN
ejpam-5061	35	36	,	,	PUNCT
ejpam-5061	35	37	denoted	denote	VERB
ejpam-5061	35	38	by	by	ADP
ejpam-5061	35	39	diam(g	diam(g	PROPN
ejpam-5061	35	40	)	)	PUNCT
ejpam-5061	35	41	,	,	PUNCT
ejpam-5061	35	42	is	be	AUX
ejpam-5061	35	43	called	call	VERB
ejpam-5061	35	44	the	the	DET
ejpam-5061	35	45	diameter	diameter	NOUN
ejpam-5061	35	46	of	of	ADP
ejpam-5061	35	47	g.	g.	PROPN
ejpam-5061	35	48	a	a	DET
ejpam-5061	35	49	subset	subset	NOUN
ejpam-5061	35	50	d	d	NOUN
ejpam-5061	35	51	of	of	ADP
ejpam-5061	35	52	v	v	NOUN
ejpam-5061	35	53	(	(	PUNCT
ejpam-5061	35	54	g	g	NOUN
ejpam-5061	35	55	)	)	PUNCT
ejpam-5061	35	56	is	be	AUX
ejpam-5061	35	57	called	call	VERB
ejpam-5061	35	58	a	a	DET
ejpam-5061	35	59	dominating	dominating	NOUN
ejpam-5061	35	60	of	of	ADP
ejpam-5061	35	61	g	g	PROPN
ejpam-5061	35	62	if	if	SCONJ
ejpam-5061	35	63	for	for	ADP
ejpam-5061	35	64	every	every	DET
ejpam-5061	35	65	x	x	SYM
ejpam-5061	35	66	∈	∈	PROPN
ejpam-5061	35	67	v	v	ADP
ejpam-5061	35	68	(	(	PUNCT
ejpam-5061	35	69	g	g	NOUN
ejpam-5061	35	70	)	)	PUNCT
ejpam-5061	35	71	\	\	PUNCT
ejpam-5061	36	1	d	d	X
ejpam-5061	36	2	,	,	PUNCT
ejpam-5061	36	3	there	there	PRON
ejpam-5061	36	4	exists	exist	VERB
ejpam-5061	36	5	y	y	PROPN
ejpam-5061	36	6	∈	∈	PROPN
ejpam-5061	37	1	d	d	X
ejpam-5061	37	2	such	such	ADJ
ejpam-5061	37	3	that	that	SCONJ
ejpam-5061	37	4	xy	xy	PROPN
ejpam-5061	37	5	∈	∈	PROPN
ejpam-5061	37	6	e(g	e(g	PROPN
ejpam-5061	37	7	)	)	PUNCT
ejpam-5061	37	8	.	.	PUNCT
ejpam-5061	38	1	the	the	DET
ejpam-5061	38	2	domination	domination	NOUN
ejpam-5061	38	3	number	number	NOUN
ejpam-5061	38	4	of	of	ADP
ejpam-5061	38	5	g	g	NOUN
ejpam-5061	38	6	,	,	PUNCT
ejpam-5061	38	7	denoted	denote	VERB
ejpam-5061	38	8	by	by	ADP
ejpam-5061	38	9	γ(g	γ(g	PROPN
ejpam-5061	38	10	)	)	PUNCT
ejpam-5061	38	11	,	,	PUNCT
ejpam-5061	38	12	is	be	AUX
ejpam-5061	38	13	the	the	DET
ejpam-5061	38	14	minimum	minimum	ADJ
ejpam-5061	38	15	cardinality	cardinality	NOUN
ejpam-5061	38	16	of	of	ADP
ejpam-5061	38	17	a	a	DET
ejpam-5061	38	18	dominating	dominating	NOUN
ejpam-5061	38	19	set	set	VERB
ejpam-5061	38	20	in	in	ADP
ejpam-5061	38	21	g.	g.	PROPN
ejpam-5061	38	22	let	let	VERB
ejpam-5061	38	23	s	s	AUX
ejpam-5061	38	24	=	=	PUNCT
ejpam-5061	38	25	(	(	PUNCT
ejpam-5061	38	26	v1	v1	PROPN
ejpam-5061	38	27	,	,	PUNCT
ejpam-5061	38	28	v2	v2	PROPN
ejpam-5061	38	29	,	,	PUNCT
ejpam-5061	38	30	·	·	PUNCT
ejpam-5061	38	31	·	·	PUNCT
ejpam-5061	38	32	·	·	PUNCT
ejpam-5061	38	33	,	,	PUNCT
ejpam-5061	38	34	vk	vk	AUX
ejpam-5061	38	35	)	)	PUNCT
ejpam-5061	38	36	be	be	AUX
ejpam-5061	38	37	a	a	DET
ejpam-5061	38	38	sequence	sequence	NOUN
ejpam-5061	38	39	of	of	ADP
ejpam-5061	38	40	distinct	distinct	ADJ
ejpam-5061	38	41	vertices	vertex	NOUN
ejpam-5061	38	42	of	of	ADP
ejpam-5061	38	43	a	a	DET
ejpam-5061	38	44	graph	graph	NOUN
ejpam-5061	38	45	g	g	NOUN
ejpam-5061	38	46	,	,	PUNCT
ejpam-5061	38	47	and	and	CCONJ
ejpam-5061	38	48	let	let	VERB
ejpam-5061	38	49	ŝ	ŝ	X
ejpam-5061	38	50	=	=	SYM
ejpam-5061	38	51	{	{	PUNCT
ejpam-5061	38	52	v1	v1	PROPN
ejpam-5061	38	53	,	,	PUNCT
ejpam-5061	38	54	v2	v2	PROPN
ejpam-5061	38	55	,	,	PUNCT
ejpam-5061	38	56	·	·	PUNCT
ejpam-5061	38	57	·	·	PUNCT
ejpam-5061	38	58	·	·	PUNCT
ejpam-5061	38	59	,	,	PUNCT
ejpam-5061	38	60	vk	vk	PART
ejpam-5061	38	61	}	}	PUNCT
ejpam-5061	38	62	be	be	AUX
ejpam-5061	38	63	a	a	DET
ejpam-5061	38	64	corresponding	corresponding	ADJ
ejpam-5061	38	65	set	set	NOUN
ejpam-5061	38	66	of	of	ADP
ejpam-5061	38	67	a	a	DET
ejpam-5061	38	68	sequence	sequence	NOUN
ejpam-5061	38	69	s.	s.	PROPN
ejpam-5061	39	1	then	then	ADV
ejpam-5061	39	2	s	s	VERB
ejpam-5061	39	3	is	be	AUX
ejpam-5061	39	4	called	call	VERB
ejpam-5061	39	5	a	a	DET
ejpam-5061	39	6	legal	legal	ADJ
ejpam-5061	39	7	closed	closed	ADJ
ejpam-5061	39	8	neighborhood	neighborhood	NOUN
ejpam-5061	39	9	sequence(legal	sequence(legal	ADJ
ejpam-5061	39	10	sequence	sequence	NOUN
ejpam-5061	39	11	)	)	PUNCT
ejpam-5061	39	12	if	if	SCONJ
ejpam-5061	39	13	ng[vi]\	ng[vi]\	PROPN
ejpam-5061	39	14	⋃i−1	⋃i−1	PROPN
ejpam-5061	39	15	j=1ng[vj	j=1ng[vj	PROPN
ejpam-5061	39	16	]	]	PUNCT
ejpam-5061	39	17	̸=	̸=	PROPN
ejpam-5061	39	18	∅	∅	NOUN
ejpam-5061	39	19	for	for	ADP
ejpam-5061	39	20	every	every	DET
ejpam-5061	39	21	i	i	PROPN
ejpam-5061	39	22	∈	∈	PROPN
ejpam-5061	39	23	{	{	PUNCT
ejpam-5061	39	24	2	2	NUM
ejpam-5061	39	25	,	,	PUNCT
ejpam-5061	39	26	·	·	PUNCT
ejpam-5061	39	27	·	·	PUNCT
ejpam-5061	39	28	·	·	PUNCT
ejpam-5061	39	29	,	,	PUNCT
ejpam-5061	39	30	k	k	NOUN
ejpam-5061	39	31	}	}	PUNCT
ejpam-5061	39	32	.	.	PUNCT
ejpam-5061	40	1	if	if	SCONJ
ejpam-5061	40	2	,	,	PUNCT
ejpam-5061	40	3	in	in	ADP
ejpam-5061	40	4	addition	addition	NOUN
ejpam-5061	40	5	,	,	PUNCT
ejpam-5061	40	6	ŝ	ŝ	X
ejpam-5061	40	7	is	be	AUX
ejpam-5061	40	8	a	a	DET
ejpam-5061	40	9	dominating	dominating	NOUN
ejpam-5061	40	10	set	set	NOUN
ejpam-5061	40	11	of	of	ADP
ejpam-5061	40	12	g	g	NOUN
ejpam-5061	40	13	,	,	PUNCT
ejpam-5061	40	14	then	then	ADV
ejpam-5061	40	15	s	s	VERB
ejpam-5061	40	16	is	be	AUX
ejpam-5061	40	17	called	call	VERB
ejpam-5061	40	18	a	a	DET
ejpam-5061	40	19	grundy	grundy	PROPN
ejpam-5061	40	20	dominating	dominating	NOUN
ejpam-5061	40	21	sequence	sequence	NOUN
ejpam-5061	40	22	.	.	PUNCT
ejpam-5061	41	1	the	the	DET
ejpam-5061	41	2	maximum	maximum	ADJ
ejpam-5061	41	3	length	length	NOUN
ejpam-5061	41	4	of	of	ADP
ejpam-5061	41	5	a	a	DET
ejpam-5061	41	6	grundy	grundy	PROPN
ejpam-5061	41	7	dominating	dominating	NOUN
ejpam-5061	41	8	sequence	sequence	NOUN
ejpam-5061	41	9	in	in	ADP
ejpam-5061	41	10	a	a	DET
ejpam-5061	41	11	graph	graph	NOUN
ejpam-5061	41	12	g	g	NOUN
ejpam-5061	41	13	is	be	AUX
ejpam-5061	41	14	called	call	VERB
ejpam-5061	41	15	the	the	DET
ejpam-5061	41	16	grundy	grundy	PROPN
ejpam-5061	41	17	domination	domination	NOUN
ejpam-5061	41	18	number	number	NOUN
ejpam-5061	41	19	of	of	ADP
ejpam-5061	41	20	g	g	NOUN
ejpam-5061	41	21	,	,	PUNCT
ejpam-5061	41	22	and	and	CCONJ
ejpam-5061	41	23	is	be	AUX
ejpam-5061	41	24	denoted	denote	VERB
ejpam-5061	41	25	by	by	ADP
ejpam-5061	41	26	γgr(g	γgr(g	PROPN
ejpam-5061	41	27	)	)	PUNCT
ejpam-5061	41	28	.	.	PUNCT
ejpam-5061	42	1	any	any	DET
ejpam-5061	42	2	grundy	grundy	PROPN
ejpam-5061	42	3	dominating	dominating	NOUN
ejpam-5061	42	4	sequence	sequence	NOUN
ejpam-5061	42	5	with	with	ADP
ejpam-5061	42	6	length	length	NOUN
ejpam-5061	42	7	equal	equal	ADJ
ejpam-5061	42	8	to	to	ADP
ejpam-5061	42	9	γgr(g	γgr(g	PROPN
ejpam-5061	42	10	)	)	PUNCT
ejpam-5061	42	11	is	be	AUX
ejpam-5061	42	12	called	call	VERB
ejpam-5061	42	13	a	a	DET
ejpam-5061	42	14	γgr	γgr	NOUN
ejpam-5061	42	15	-	-	PUNCT
ejpam-5061	42	16	sequence	sequence	NOUN
ejpam-5061	42	17	of	of	ADP
ejpam-5061	42	18	g.	g.	NOUN
ejpam-5061	42	19	let	let	VERB
ejpam-5061	42	20	s1	s1	PROPN
ejpam-5061	42	21	=	=	SYM
ejpam-5061	42	22	(	(	PUNCT
ejpam-5061	42	23	v1	v1	PROPN
ejpam-5061	42	24	,	,	PUNCT
ejpam-5061	42	25	.	.	PUNCT
ejpam-5061	42	26	.	.	PUNCT
ejpam-5061	43	1	.	.	PUNCT
ejpam-5061	44	1	,	,	PUNCT
ejpam-5061	44	2	vn	vn	PROPN
ejpam-5061	44	3	)	)	PUNCT
ejpam-5061	44	4	and	and	CCONJ
ejpam-5061	44	5	s2	s2	NOUN
ejpam-5061	44	6	=	=	SYM
ejpam-5061	44	7	(	(	PUNCT
ejpam-5061	44	8	u1	u1	PROPN
ejpam-5061	44	9	,	,	PUNCT
ejpam-5061	44	10	.	.	PUNCT
ejpam-5061	44	11	.	.	PUNCT
ejpam-5061	44	12	.	.	PUNCT
ejpam-5061	45	1	,	,	PUNCT
ejpam-5061	45	2	um	um	INTJ
ejpam-5061	45	3	)	)	PUNCT
ejpam-5061	45	4	be	be	AUX
ejpam-5061	45	5	two	two	NUM
ejpam-5061	45	6	sequences	sequence	NOUN
ejpam-5061	45	7	of	of	ADP
ejpam-5061	45	8	distinct	distinct	ADJ
ejpam-5061	45	9	vertices	vertex	NOUN
ejpam-5061	45	10	of	of	ADP
ejpam-5061	45	11	g.	g.	PROPN
ejpam-5061	45	12	the	the	DET
ejpam-5061	45	13	concatenation	concatenation	NOUN
ejpam-5061	45	14	of	of	ADP
ejpam-5061	45	15	s1	s1	PROPN
ejpam-5061	45	16	and	and	CCONJ
ejpam-5061	45	17	s2	s2	PROPN
ejpam-5061	45	18	,	,	PUNCT
ejpam-5061	45	19	denoted	denote	VERB
ejpam-5061	45	20	by	by	ADP
ejpam-5061	45	21	s1	s1	PROPN
ejpam-5061	45	22	⊕	⊕	PROPN
ejpam-5061	45	23	s2	s2	PROPN
ejpam-5061	45	24	,	,	PUNCT
ejpam-5061	45	25	is	be	AUX
ejpam-5061	45	26	the	the	DET
ejpam-5061	45	27	sequence	sequence	NOUN
ejpam-5061	45	28	given	give	VERB
ejpam-5061	45	29	by	by	ADP
ejpam-5061	45	30	s1	s1	PROPN
ejpam-5061	45	31	⊕	⊕	PROPN
ejpam-5061	45	32	s2	s2	PROPN
ejpam-5061	45	33	=	=	SYM
ejpam-5061	45	34	(	(	PUNCT
ejpam-5061	45	35	v1	v1	PROPN
ejpam-5061	45	36	,	,	PUNCT
ejpam-5061	45	37	.	.	PUNCT
ejpam-5061	45	38	.	.	PUNCT
ejpam-5061	46	1	.	.	PUNCT
ejpam-5061	47	1	,	,	PUNCT
ejpam-5061	47	2	vn	vn	PROPN
ejpam-5061	47	3	,	,	PUNCT
ejpam-5061	47	4	u1	u1	NOUN
ejpam-5061	47	5	,	,	PUNCT
ejpam-5061	47	6	.	.	PUNCT
ejpam-5061	47	7	.	.	PUNCT
ejpam-5061	47	8	.	.	PUNCT
ejpam-5061	48	1	,	,	PUNCT
ejpam-5061	48	2	um	um	INTJ
ejpam-5061	48	3	)	)	PUNCT
ejpam-5061	48	4	.	.	PUNCT
ejpam-5061	49	1	a	a	DET
ejpam-5061	49	2	subset	subset	NOUN
ejpam-5061	49	3	s	s	X
ejpam-5061	49	4	of	of	ADP
ejpam-5061	49	5	v	v	NOUN
ejpam-5061	49	6	(	(	PUNCT
ejpam-5061	49	7	g	g	NOUN
ejpam-5061	49	8	)	)	PUNCT
ejpam-5061	49	9	is	be	AUX
ejpam-5061	49	10	called	call	VERB
ejpam-5061	49	11	a	a	DET
ejpam-5061	49	12	hop	hop	NOUN
ejpam-5061	49	13	independent	independent	ADJ
ejpam-5061	49	14	if	if	SCONJ
ejpam-5061	49	15	for	for	ADP
ejpam-5061	49	16	every	every	DET
ejpam-5061	49	17	pair	pair	NOUN
ejpam-5061	49	18	of	of	ADP
ejpam-5061	49	19	distinct	distinct	ADJ
ejpam-5061	49	20	vertices	vertex	NOUN
ejpam-5061	49	21	x	x	X
ejpam-5061	49	22	,	,	PUNCT
ejpam-5061	49	23	y	y	PROPN
ejpam-5061	49	24	∈	∈	PROPN
ejpam-5061	49	25	s	s	PROPN
ejpam-5061	49	26	,	,	PUNCT
ejpam-5061	49	27	dg(x	dg(x	NUM
ejpam-5061	49	28	,	,	PUNCT
ejpam-5061	49	29	y	y	NOUN
ejpam-5061	49	30	)	)	PUNCT
ejpam-5061	49	31	̸=	̸=	PROPN
ejpam-5061	49	32	2	2	NUM
ejpam-5061	49	33	.	.	PUNCT
ejpam-5061	50	1	the	the	DET
ejpam-5061	50	2	maximum	maximum	ADJ
ejpam-5061	50	3	cardinality	cardinality	NOUN
ejpam-5061	50	4	of	of	ADP
ejpam-5061	50	5	a	a	DET
ejpam-5061	50	6	hop	hop	NOUN
ejpam-5061	50	7	independent	independent	ADJ
ejpam-5061	50	8	set	set	NOUN
ejpam-5061	50	9	in	in	ADP
ejpam-5061	50	10	g	g	NOUN
ejpam-5061	50	11	,	,	PUNCT
ejpam-5061	50	12	denoted	denote	VERB
ejpam-5061	50	13	j.	j.	PROPN
ejpam-5061	50	14	hassan	hassan	PROPN
ejpam-5061	50	15	et	et	PROPN
ejpam-5061	50	16	al	al	PROPN
ejpam-5061	50	17	.	.	PUNCT
ejpam-5061	50	18	/	/	SYM
ejpam-5061	50	19	eur	eur	PROPN
ejpam-5061	50	20	.	.	PUNCT
ejpam-5061	51	1	j.	j.	PROPN
ejpam-5061	51	2	pure	pure	PROPN
ejpam-5061	51	3	appl	appl	PROPN
ejpam-5061	51	4	.	.	PROPN
ejpam-5061	51	5	math	math	PROPN
ejpam-5061	51	6	,	,	PUNCT
ejpam-5061	51	7	17	17	NUM
ejpam-5061	51	8	(	(	PUNCT
ejpam-5061	51	9	2	2	NUM
ejpam-5061	51	10	)	)	PUNCT
ejpam-5061	51	11	(	(	PUNCT
ejpam-5061	51	12	2024	2024	NUM
ejpam-5061	51	13	)	)	PUNCT
ejpam-5061	51	14	,	,	PUNCT
ejpam-5061	51	15	725	725	NUM
ejpam-5061	51	16	-	-	SYM
ejpam-5061	51	17	735	735	NUM
ejpam-5061	51	18	727	727	NUM
ejpam-5061	51	19	by	by	ADP
ejpam-5061	51	20	αh(g	αh(g	NOUN
ejpam-5061	51	21	)	)	PUNCT
ejpam-5061	51	22	,	,	PUNCT
ejpam-5061	51	23	is	be	AUX
ejpam-5061	51	24	called	call	VERB
ejpam-5061	51	25	the	the	DET
ejpam-5061	51	26	hop	hop	NOUN
ejpam-5061	51	27	independence	independence	NOUN
ejpam-5061	51	28	number	number	NOUN
ejpam-5061	51	29	of	of	ADP
ejpam-5061	51	30	g.	g.	PROPN
ejpam-5061	51	31	any	any	DET
ejpam-5061	51	32	hop	hop	NOUN
ejpam-5061	51	33	independent	independent	ADJ
ejpam-5061	51	34	set	set	NOUN
ejpam-5061	51	35	s	s	PROPN
ejpam-5061	51	36	with	with	ADP
ejpam-5061	51	37	cardinality	cardinality	NOUN
ejpam-5061	51	38	equal	equal	ADJ
ejpam-5061	51	39	to	to	ADP
ejpam-5061	51	40	αh(g	αh(g	NOUN
ejpam-5061	51	41	)	)	PUNCT
ejpam-5061	51	42	is	be	AUX
ejpam-5061	51	43	called	call	VERB
ejpam-5061	51	44	an	an	DET
ejpam-5061	51	45	αh	αh	NOUN
ejpam-5061	51	46	-	-	PUNCT
ejpam-5061	51	47	set	set	NOUN
ejpam-5061	51	48	of	of	ADP
ejpam-5061	51	49	g.	g.	PROPN
ejpam-5061	51	50	a	a	DET
ejpam-5061	51	51	graph	graph	NOUN
ejpam-5061	51	52	is	be	AUX
ejpam-5061	51	53	complete	complete	ADJ
ejpam-5061	51	54	if	if	SCONJ
ejpam-5061	51	55	every	every	DET
ejpam-5061	51	56	pair	pair	NOUN
ejpam-5061	51	57	of	of	ADP
ejpam-5061	51	58	distinct	distinct	ADJ
ejpam-5061	51	59	vertices	vertex	NOUN
ejpam-5061	51	60	are	be	AUX
ejpam-5061	51	61	adjacent	adjacent	ADJ
ejpam-5061	51	62	.	.	PUNCT
ejpam-5061	52	1	a	a	DET
ejpam-5061	52	2	complete	complete	ADJ
ejpam-5061	52	3	graph	graph	NOUN
ejpam-5061	52	4	of	of	ADP
ejpam-5061	52	5	order	order	NOUN
ejpam-5061	52	6	n	n	NOUN
ejpam-5061	52	7	is	be	AUX
ejpam-5061	52	8	denoted	denote	VERB
ejpam-5061	52	9	by	by	ADP
ejpam-5061	52	10	kn	kn	PROPN
ejpam-5061	52	11	.	.	PUNCT
ejpam-5061	53	1	a	a	DET
ejpam-5061	53	2	set	set	NOUN
ejpam-5061	53	3	s	s	NOUN
ejpam-5061	53	4	⊆	⊆	NUM
ejpam-5061	53	5	v	v	NOUN
ejpam-5061	53	6	(	(	PUNCT
ejpam-5061	53	7	g	g	NOUN
ejpam-5061	53	8	)	)	PUNCT
ejpam-5061	53	9	is	be	AUX
ejpam-5061	53	10	called	call	VERB
ejpam-5061	53	11	a	a	DET
ejpam-5061	53	12	clique	clique	NOUN
ejpam-5061	53	13	in	in	ADP
ejpam-5061	53	14	g	g	PROPN
ejpam-5061	53	15	if	if	SCONJ
ejpam-5061	53	16	the	the	DET
ejpam-5061	53	17	subgraph	subgraph	NOUN
ejpam-5061	53	18	⟨s⟩	⟨s⟩	PROPN
ejpam-5061	53	19	induced	induce	VERB
ejpam-5061	53	20	by	by	ADP
ejpam-5061	53	21	s	s	PROPN
ejpam-5061	53	22	is	be	AUX
ejpam-5061	53	23	a	a	DET
ejpam-5061	53	24	complete	complete	ADJ
ejpam-5061	53	25	graph	graph	NOUN
ejpam-5061	53	26	.	.	PUNCT
ejpam-5061	54	1	the	the	DET
ejpam-5061	54	2	maximum	maximum	ADJ
ejpam-5061	54	3	size	size	NOUN
ejpam-5061	54	4	or	or	CCONJ
ejpam-5061	54	5	cardinality	cardinality	NOUN
ejpam-5061	54	6	of	of	ADP
ejpam-5061	54	7	a	a	DET
ejpam-5061	54	8	clique	clique	NOUN
ejpam-5061	54	9	of	of	ADP
ejpam-5061	54	10	g	g	NOUN
ejpam-5061	54	11	,	,	PUNCT
ejpam-5061	54	12	denoted	denote	VERB
ejpam-5061	54	13	by	by	ADP
ejpam-5061	54	14	ω(g	ω(g	NOUN
ejpam-5061	54	15	)	)	PUNCT
ejpam-5061	54	16	,	,	PUNCT
ejpam-5061	54	17	is	be	AUX
ejpam-5061	54	18	called	call	VERB
ejpam-5061	54	19	the	the	DET
ejpam-5061	54	20	clique	clique	ADJ
ejpam-5061	54	21	number	number	NOUN
ejpam-5061	54	22	of	of	ADP
ejpam-5061	54	23	g.	g.	PROPN
ejpam-5061	54	24	any	any	DET
ejpam-5061	54	25	clique	clique	NOUN
ejpam-5061	54	26	in	in	ADP
ejpam-5061	54	27	g	g	PROPN
ejpam-5061	54	28	with	with	ADP
ejpam-5061	54	29	cardinality	cardinality	NOUN
ejpam-5061	54	30	ω(g	ω(g	NOUN
ejpam-5061	54	31	)	)	PUNCT
ejpam-5061	54	32	is	be	AUX
ejpam-5061	54	33	called	call	VERB
ejpam-5061	54	34	an	an	DET
ejpam-5061	54	35	ω	ω	NOUN
ejpam-5061	54	36	-	-	PUNCT
ejpam-5061	54	37	set	set	NOUN
ejpam-5061	54	38	in	in	ADP
ejpam-5061	54	39	g.	g.	PROPN
ejpam-5061	54	40	the	the	DET
ejpam-5061	54	41	complement	complement	NOUN
ejpam-5061	54	42	of	of	ADP
ejpam-5061	54	43	a	a	DET
ejpam-5061	54	44	graph	graph	NOUN
ejpam-5061	54	45	g	g	NOUN
ejpam-5061	54	46	,	,	PUNCT
ejpam-5061	54	47	denoted	denote	VERB
ejpam-5061	54	48	by	by	ADP
ejpam-5061	54	49	g	g	NOUN
ejpam-5061	54	50	,	,	PUNCT
ejpam-5061	54	51	is	be	AUX
ejpam-5061	54	52	the	the	DET
ejpam-5061	54	53	graph	graph	NOUN
ejpam-5061	54	54	with	with	ADP
ejpam-5061	54	55	v	v	NOUN
ejpam-5061	54	56	(	(	PUNCT
ejpam-5061	54	57	g	g	NOUN
ejpam-5061	54	58	)	)	PUNCT
ejpam-5061	55	1	=	=	NOUN
ejpam-5061	55	2	v	v	X
ejpam-5061	55	3	(	(	PUNCT
ejpam-5061	55	4	g	g	NOUN
ejpam-5061	55	5	)	)	PUNCT
ejpam-5061	55	6	and	and	CCONJ
ejpam-5061	55	7	e(g	e(g	PROPN
ejpam-5061	55	8	)	)	PUNCT
ejpam-5061	56	1	=	=	PRON
ejpam-5061	56	2	{	{	PUNCT
ejpam-5061	56	3	uv	uv	NOUN
ejpam-5061	56	4	:	:	PUNCT
ejpam-5061	56	5	u	u	NOUN
ejpam-5061	56	6	,	,	PUNCT
ejpam-5061	56	7	v	v	PROPN
ejpam-5061	56	8	∈	∈	PROPN
ejpam-5061	56	9	v	v	NOUN
ejpam-5061	56	10	(	(	PUNCT
ejpam-5061	56	11	g	g	NOUN
ejpam-5061	56	12	)	)	PUNCT
ejpam-5061	56	13	and	and	CCONJ
ejpam-5061	56	14	uv	uv	NOUN
ejpam-5061	56	15	/∈	/∈	PROPN
ejpam-5061	56	16	e(g	e(g	PROPN
ejpam-5061	56	17	)	)	PUNCT
ejpam-5061	56	18	}	}	PUNCT
ejpam-5061	56	19	.	.	PUNCT
ejpam-5061	57	1	let	let	VERB
ejpam-5061	57	2	g	g	NOUN
ejpam-5061	57	3	and	and	CCONJ
ejpam-5061	57	4	h	h	NOUN
ejpam-5061	57	5	be	be	VERB
ejpam-5061	57	6	any	any	DET
ejpam-5061	57	7	two	two	NUM
ejpam-5061	57	8	graphs	graph	NOUN
ejpam-5061	57	9	.	.	PUNCT
ejpam-5061	58	1	the	the	DET
ejpam-5061	58	2	join	join	NOUN
ejpam-5061	58	3	of	of	ADP
ejpam-5061	58	4	g	g	PROPN
ejpam-5061	58	5	and	and	CCONJ
ejpam-5061	58	6	h	h	NOUN
ejpam-5061	58	7	,	,	PUNCT
ejpam-5061	58	8	denoted	denote	VERB
ejpam-5061	58	9	by	by	ADP
ejpam-5061	58	10	g+h	g+h	PROPN
ejpam-5061	58	11	is	be	AUX
ejpam-5061	58	12	the	the	DET
ejpam-5061	58	13	graph	graph	NOUN
ejpam-5061	58	14	with	with	ADP
ejpam-5061	58	15	vertex	vertex	NOUN
ejpam-5061	58	16	set	set	VERB
ejpam-5061	58	17	v	v	NOUN
ejpam-5061	58	18	(	(	PUNCT
ejpam-5061	58	19	g+h	g+h	NOUN
ejpam-5061	58	20	)	)	PUNCT
ejpam-5061	59	1	=	=	SYM
ejpam-5061	59	2	v	v	X
ejpam-5061	59	3	(	(	PUNCT
ejpam-5061	59	4	g	g	NOUN
ejpam-5061	59	5	)	)	PUNCT
ejpam-5061	59	6	∪	∪	NOUN
ejpam-5061	59	7	v	v	NOUN
ejpam-5061	59	8	(	(	PUNCT
ejpam-5061	59	9	h	h	NOUN
ejpam-5061	59	10	)	)	PUNCT
ejpam-5061	59	11	and	and	CCONJ
ejpam-5061	59	12	edge	edge	NOUN
ejpam-5061	59	13	set	set	VERB
ejpam-5061	59	14	e(g+h	e(g+h	NUM
ejpam-5061	59	15	)	)	PUNCT
ejpam-5061	59	16	=	=	SYM
ejpam-5061	59	17	e(g	e(g	NOUN
ejpam-5061	59	18	)	)	PUNCT
ejpam-5061	59	19	∪	∪	ADP
ejpam-5061	59	20	e(h	e(h	PROPN
ejpam-5061	59	21	)	)	PUNCT
ejpam-5061	59	22	∪	∪	NOUN
ejpam-5061	59	23	{	{	PUNCT
ejpam-5061	59	24	uv	uv	NOUN
ejpam-5061	59	25	:	:	PUNCT
ejpam-5061	59	26	u	u	PROPN
ejpam-5061	59	27	∈	∈	PROPN
ejpam-5061	59	28	v	v	ADP
ejpam-5061	59	29	(	(	PUNCT
ejpam-5061	59	30	g	g	NOUN
ejpam-5061	59	31	)	)	PUNCT
ejpam-5061	59	32	,	,	PUNCT
ejpam-5061	59	33	v	v	X
ejpam-5061	59	34	∈	∈	PROPN
ejpam-5061	59	35	v	v	NOUN
ejpam-5061	59	36	(	(	PUNCT
ejpam-5061	59	37	h	h	NOUN
ejpam-5061	59	38	)	)	PUNCT
ejpam-5061	59	39	}	}	PUNCT
ejpam-5061	59	40	.	.	PUNCT
ejpam-5061	60	1	the	the	DET
ejpam-5061	60	2	corona	corona	NOUN
ejpam-5061	60	3	g	g	PROPN
ejpam-5061	60	4	and	and	CCONJ
ejpam-5061	60	5	h	h	NOUN
ejpam-5061	60	6	,	,	PUNCT
ejpam-5061	60	7	denoted	denote	VERB
ejpam-5061	60	8	by	by	ADP
ejpam-5061	60	9	g	g	PROPN
ejpam-5061	60	10	◦	◦	NOUN
ejpam-5061	60	11	h	h	NOUN
ejpam-5061	60	12	,	,	PUNCT
ejpam-5061	60	13	the	the	DET
ejpam-5061	60	14	graph	graph	NOUN
ejpam-5061	60	15	obtained	obtain	VERB
ejpam-5061	60	16	by	by	ADP
ejpam-5061	60	17	taking	take	VERB
ejpam-5061	60	18	one	one	NUM
ejpam-5061	60	19	copy	copy	NOUN
ejpam-5061	60	20	of	of	ADP
ejpam-5061	60	21	g	g	PROPN
ejpam-5061	60	22	and	and	CCONJ
ejpam-5061	60	23	|v	|v	PROPN
ejpam-5061	60	24	(	(	PUNCT
ejpam-5061	60	25	g)|	g)|	NOUN
ejpam-5061	60	26	copies	copy	NOUN
ejpam-5061	60	27	of	of	ADP
ejpam-5061	60	28	h	h	NOUN
ejpam-5061	60	29	,	,	PUNCT
ejpam-5061	60	30	and	and	CCONJ
ejpam-5061	60	31	then	then	ADV
ejpam-5061	60	32	joining	join	VERB
ejpam-5061	60	33	the	the	DET
ejpam-5061	60	34	ith	ith	PROPN
ejpam-5061	60	35	vertex	vertex	NOUN
ejpam-5061	60	36	of	of	ADP
ejpam-5061	60	37	g	g	NOUN
ejpam-5061	60	38	to	to	ADP
ejpam-5061	60	39	every	every	DET
ejpam-5061	60	40	vertex	vertex	NOUN
ejpam-5061	60	41	of	of	ADP
ejpam-5061	60	42	the	the	DET
ejpam-5061	60	43	ith	ith	PROPN
ejpam-5061	60	44	copy	copy	NOUN
ejpam-5061	60	45	of	of	ADP
ejpam-5061	60	46	h.	h.	PROPN
ejpam-5061	60	47	we	we	PRON
ejpam-5061	60	48	denote	denote	VERB
ejpam-5061	60	49	by	by	ADP
ejpam-5061	60	50	hv	hv	PROPN
ejpam-5061	61	1	the	the	DET
ejpam-5061	61	2	copy	copy	NOUN
ejpam-5061	61	3	of	of	ADP
ejpam-5061	61	4	h	h	NOUN
ejpam-5061	61	5	in	in	ADP
ejpam-5061	61	6	g	g	PROPN
ejpam-5061	61	7	◦	◦	NOUN
ejpam-5061	61	8	h	h	NOUN
ejpam-5061	61	9	corresponding	correspond	VERB
ejpam-5061	61	10	to	to	ADP
ejpam-5061	61	11	the	the	DET
ejpam-5061	61	12	vertex	vertex	NOUN
ejpam-5061	61	13	v	v	ADP
ejpam-5061	61	14	∈	∈	PROPN
ejpam-5061	61	15	g	g	NOUN
ejpam-5061	61	16	and	and	CCONJ
ejpam-5061	61	17	write	write	VERB
ejpam-5061	61	18	v	v	ADP
ejpam-5061	61	19	+	+	PROPN
ejpam-5061	61	20	hv	hv	NOUN
ejpam-5061	61	21	for	for	ADP
ejpam-5061	61	22	⟨{v}+hv⟩.	⟨{v}+hv⟩.	X
ejpam-5061	61	23	3	3	X
ejpam-5061	61	24	.	.	X
ejpam-5061	61	25	results	result	NOUN
ejpam-5061	61	26	we	we	PRON
ejpam-5061	61	27	begin	begin	VERB
ejpam-5061	61	28	this	this	DET
ejpam-5061	61	29	section	section	NOUN
ejpam-5061	61	30	by	by	ADP
ejpam-5061	61	31	introducing	introduce	VERB
ejpam-5061	61	32	the	the	DET
ejpam-5061	61	33	concept	concept	NOUN
ejpam-5061	61	34	of	of	ADP
ejpam-5061	61	35	a	a	DET
ejpam-5061	61	36	legal	legal	ADJ
ejpam-5061	61	37	hop	hop	NOUN
ejpam-5061	61	38	independence	independence	NOUN
ejpam-5061	61	39	in	in	ADP
ejpam-5061	61	40	a	a	DET
ejpam-5061	61	41	graph	graph	NOUN
ejpam-5061	61	42	.	.	PUNCT
ejpam-5061	62	1	definition	definition	NOUN
ejpam-5061	62	2	1	1	NUM
ejpam-5061	62	3	.	.	PUNCT
ejpam-5061	63	1	let	let	VERB
ejpam-5061	63	2	g	g	NOUN
ejpam-5061	63	3	be	be	AUX
ejpam-5061	63	4	any	any	DET
ejpam-5061	63	5	graph	graph	NOUN
ejpam-5061	63	6	.	.	PUNCT
ejpam-5061	64	1	a	a	DET
ejpam-5061	64	2	sequence	sequence	NOUN
ejpam-5061	64	3	l	l	NOUN
ejpam-5061	64	4	=	=	SYM
ejpam-5061	64	5	(	(	PUNCT
ejpam-5061	64	6	w1	w1	NOUN
ejpam-5061	64	7	,	,	PUNCT
ejpam-5061	64	8	.	.	PUNCT
ejpam-5061	64	9	.	.	PUNCT
ejpam-5061	64	10	.	.	PUNCT
ejpam-5061	65	1	,	,	PUNCT
ejpam-5061	65	2	wk	wk	X
ejpam-5061	65	3	)	)	PUNCT
ejpam-5061	65	4	of	of	ADP
ejpam-5061	65	5	distinct	distinct	ADJ
ejpam-5061	65	6	vertices	vertex	NOUN
ejpam-5061	65	7	of	of	ADP
ejpam-5061	65	8	g	g	PROPN
ejpam-5061	65	9	is	be	AUX
ejpam-5061	65	10	called	call	VERB
ejpam-5061	65	11	a	a	DET
ejpam-5061	65	12	legal	legal	ADJ
ejpam-5061	65	13	hop	hop	NOUN
ejpam-5061	65	14	independent	independent	ADJ
ejpam-5061	65	15	sequence	sequence	NOUN
ejpam-5061	65	16	if	if	SCONJ
ejpam-5061	65	17	k	k	PROPN
ejpam-5061	65	18	=	=	SYM
ejpam-5061	65	19	1	1	NUM
ejpam-5061	65	20	or	or	CCONJ
ejpam-5061	65	21	l	l	NOUN
ejpam-5061	65	22	is	be	AUX
ejpam-5061	65	23	a	a	DET
ejpam-5061	65	24	hop	hop	NOUN
ejpam-5061	65	25	independent	independent	ADJ
ejpam-5061	65	26	and	and	CCONJ
ejpam-5061	65	27	ng[wi	ng[wi	PROPN
ejpam-5061	66	1	]	]	X
ejpam-5061	66	2	\	\	PROPN
ejpam-5061	66	3	⋃i−1	⋃i−1	NOUN
ejpam-5061	66	4	j=1ng[wj	j=1ng[wj	PROPN
ejpam-5061	66	5	]	]	PUNCT
ejpam-5061	66	6	̸=	̸=	PROPN
ejpam-5061	66	7	∅	∅	NOUN
ejpam-5061	66	8	for	for	ADP
ejpam-5061	66	9	every	every	DET
ejpam-5061	66	10	i	i	PROPN
ejpam-5061	66	11	∈	∈	PROPN
ejpam-5061	66	12	{	{	PUNCT
ejpam-5061	66	13	2	2	NUM
ejpam-5061	66	14	,	,	PUNCT
ejpam-5061	66	15	·	·	PUNCT
ejpam-5061	66	16	·	·	PUNCT
ejpam-5061	66	17	·	·	PUNCT
ejpam-5061	66	18	,	,	PUNCT
ejpam-5061	66	19	k	k	X
ejpam-5061	66	20	}	}	PUNCT
ejpam-5061	66	21	.	.	PUNCT
ejpam-5061	67	1	the	the	DET
ejpam-5061	67	2	maximum	maximum	ADJ
ejpam-5061	67	3	length	length	NOUN
ejpam-5061	67	4	of	of	ADP
ejpam-5061	67	5	a	a	DET
ejpam-5061	67	6	legal	legal	ADJ
ejpam-5061	67	7	hop	hop	NOUN
ejpam-5061	67	8	independent	independent	ADJ
ejpam-5061	67	9	sequence	sequence	NOUN
ejpam-5061	67	10	in	in	ADP
ejpam-5061	67	11	g	g	NOUN
ejpam-5061	67	12	,	,	PUNCT
ejpam-5061	67	13	denoted	denote	VERB
ejpam-5061	67	14	by	by	ADP
ejpam-5061	67	15	αℓh(g	αℓh(g	NOUN
ejpam-5061	67	16	)	)	PUNCT
ejpam-5061	67	17	,	,	PUNCT
ejpam-5061	67	18	is	be	AUX
ejpam-5061	67	19	called	call	VERB
ejpam-5061	67	20	the	the	DET
ejpam-5061	67	21	legal	legal	ADJ
ejpam-5061	67	22	hop	hop	NOUN
ejpam-5061	67	23	independence	independence	NOUN
ejpam-5061	67	24	number	number	NOUN
ejpam-5061	67	25	of	of	ADP
ejpam-5061	67	26	g.	g.	PROPN
ejpam-5061	67	27	any	any	DET
ejpam-5061	67	28	legal	legal	ADJ
ejpam-5061	67	29	hop	hop	NOUN
ejpam-5061	67	30	independent	independent	ADJ
ejpam-5061	67	31	sequence	sequence	NOUN
ejpam-5061	67	32	l	l	NOUN
ejpam-5061	67	33	of	of	ADP
ejpam-5061	67	34	g	g	NOUN
ejpam-5061	67	35	with	with	ADP
ejpam-5061	67	36	|l̂|	|l̂|	PROPN
ejpam-5061	67	37	=	=	PROPN
ejpam-5061	67	38	αlh(g	αlh(g	NUM
ejpam-5061	67	39	)	)	PUNCT
ejpam-5061	67	40	,	,	PUNCT
ejpam-5061	67	41	where	where	SCONJ
ejpam-5061	67	42	l̂	l̂	X
ejpam-5061	67	43	=	=	PUNCT
ejpam-5061	67	44	{	{	PUNCT
ejpam-5061	67	45	w1	w1	NOUN
ejpam-5061	67	46	,	,	PUNCT
ejpam-5061	67	47	.	.	PUNCT
ejpam-5061	67	48	.	.	PUNCT
ejpam-5061	68	1	.	.	PUNCT
ejpam-5061	69	1	,	,	PUNCT
ejpam-5061	69	2	wk	wk	PROPN
ejpam-5061	69	3	}	}	PUNCT
ejpam-5061	69	4	,	,	PUNCT
ejpam-5061	69	5	is	be	AUX
ejpam-5061	69	6	called	call	VERB
ejpam-5061	69	7	an	an	DET
ejpam-5061	69	8	αlh	αlh	NOUN
ejpam-5061	69	9	-	-	PUNCT
ejpam-5061	69	10	sequence	sequence	NOUN
ejpam-5061	69	11	or	or	CCONJ
ejpam-5061	69	12	a	a	DET
ejpam-5061	69	13	maximum	maximum	ADJ
ejpam-5061	69	14	legal	legal	ADJ
ejpam-5061	69	15	hop	hop	NOUN
ejpam-5061	69	16	independent	independent	ADJ
ejpam-5061	69	17	sequence	sequence	NOUN
ejpam-5061	69	18	of	of	ADP
ejpam-5061	69	19	g.	g.	PROPN
ejpam-5061	69	20	moreover	moreover	ADV
ejpam-5061	69	21	,	,	PUNCT
ejpam-5061	69	22	we	we	PRON
ejpam-5061	69	23	call	call	VERB
ejpam-5061	69	24	l̂	l̂	VERB
ejpam-5061	69	25	an	an	DET
ejpam-5061	69	26	αlh	αlh	NOUN
ejpam-5061	69	27	-	-	PUNCT
ejpam-5061	69	28	set	set	NOUN
ejpam-5061	69	29	of	of	ADP
ejpam-5061	69	30	g.	g.	PROPN
ejpam-5061	69	31	example	example	NOUN
ejpam-5061	70	1	1	1	X
ejpam-5061	70	2	.	.	X
ejpam-5061	70	3	consider	consider	VERB
ejpam-5061	70	4	the	the	DET
ejpam-5061	70	5	graph	graph	NOUN
ejpam-5061	70	6	g	g	NOUN
ejpam-5061	70	7	=	=	NOUN
ejpam-5061	70	8	c4	c4	NOUN
ejpam-5061	70	9	in	in	ADP
ejpam-5061	70	10	figure	figure	NOUN
ejpam-5061	70	11	1	1	NUM
ejpam-5061	70	12	.	.	PUNCT
ejpam-5061	71	1	let	let	VERB
ejpam-5061	71	2	l	l	NOUN
ejpam-5061	71	3	=	=	SYM
ejpam-5061	71	4	(	(	PUNCT
ejpam-5061	71	5	w1	w1	NOUN
ejpam-5061	71	6	,	,	PUNCT
ejpam-5061	71	7	w2	w2	NOUN
ejpam-5061	71	8	)	)	PUNCT
ejpam-5061	71	9	.	.	PUNCT
ejpam-5061	72	1	then	then	ADV
ejpam-5061	72	2	ng[w1	ng[w1	NOUN
ejpam-5061	72	3	]	]	X
ejpam-5061	72	4	=	=	SYM
ejpam-5061	72	5	{	{	PUNCT
ejpam-5061	72	6	w1	w1	NOUN
ejpam-5061	72	7	,	,	PUNCT
ejpam-5061	72	8	w2	w2	NOUN
ejpam-5061	72	9	,	,	PUNCT
ejpam-5061	72	10	w4	w4	NOUN
ejpam-5061	72	11	}	}	PUNCT
ejpam-5061	72	12	and	and	CCONJ
ejpam-5061	72	13	ng[w2	ng[w2	PROPN
ejpam-5061	72	14	]	]	PUNCT
ejpam-5061	72	15	=	=	PUNCT
ejpam-5061	72	16	{	{	PUNCT
ejpam-5061	72	17	w1	w1	NOUN
ejpam-5061	72	18	,	,	PUNCT
ejpam-5061	72	19	w2	w2	NOUN
ejpam-5061	72	20	,	,	PUNCT
ejpam-5061	72	21	w3	w3	PROPN
ejpam-5061	72	22	}	}	PUNCT
ejpam-5061	72	23	.	.	PUNCT
ejpam-5061	73	1	from	from	ADP
ejpam-5061	73	2	the	the	DET
ejpam-5061	73	3	equations	equation	NOUN
ejpam-5061	73	4	above	above	ADV
ejpam-5061	73	5	,	,	PUNCT
ejpam-5061	73	6	we	we	PRON
ejpam-5061	73	7	have	have	VERB
ejpam-5061	73	8	ng[w2]\ng[w1	ng[w2]\ng[w1	NOUN
ejpam-5061	73	9	]	]	PUNCT
ejpam-5061	74	1	=	=	PUNCT
ejpam-5061	74	2	{	{	PUNCT
ejpam-5061	74	3	w1	w1	NOUN
ejpam-5061	74	4	,	,	PUNCT
ejpam-5061	74	5	w2	w2	NOUN
ejpam-5061	74	6	,	,	PUNCT
ejpam-5061	74	7	w3}\{w1	w3}\{w1	PROPN
ejpam-5061	74	8	,	,	PUNCT
ejpam-5061	74	9	w2	w2	NOUN
ejpam-5061	74	10	,	,	PUNCT
ejpam-5061	74	11	w4	w4	NOUN
ejpam-5061	74	12	}	}	PUNCT
ejpam-5061	74	13	=	=	SYM
ejpam-5061	74	14	{	{	PUNCT
ejpam-5061	74	15	w3	w3	PROPN
ejpam-5061	74	16	}	}	PUNCT
ejpam-5061	74	17	=	=	PROPN
ejpam-5061	74	18	̸	̸	X
ejpam-5061	74	19	∅.	∅.	NOUN
ejpam-5061	74	20	it	it	PRON
ejpam-5061	74	21	follows	follow	VERB
ejpam-5061	74	22	that	that	SCONJ
ejpam-5061	74	23	l	l	NOUN
ejpam-5061	74	24	is	be	AUX
ejpam-5061	74	25	a	a	DET
ejpam-5061	74	26	legal	legal	ADJ
ejpam-5061	74	27	sequence	sequence	NOUN
ejpam-5061	74	28	in	in	ADP
ejpam-5061	74	29	g.	g.	PROPN
ejpam-5061	74	30	since	since	SCONJ
ejpam-5061	74	31	dg(w1	dg(w1	NOUN
ejpam-5061	74	32	,	,	PUNCT
ejpam-5061	74	33	w2	w2	NOUN
ejpam-5061	74	34	)	)	PUNCT
ejpam-5061	74	35	=	=	SYM
ejpam-5061	75	1	1	1	NUM
ejpam-5061	75	2	̸=	̸=	PROPN
ejpam-5061	75	3	2	2	NUM
ejpam-5061	75	4	,	,	PUNCT
ejpam-5061	75	5	this	this	PRON
ejpam-5061	75	6	means	mean	VERB
ejpam-5061	75	7	that	that	SCONJ
ejpam-5061	75	8	l̂	l̂	VERB
ejpam-5061	75	9	=	=	PUNCT
ejpam-5061	75	10	{	{	PUNCT
ejpam-5061	75	11	w1	w1	NOUN
ejpam-5061	75	12	,	,	PUNCT
ejpam-5061	75	13	w2	w2	NOUN
ejpam-5061	75	14	}	}	PUNCT
ejpam-5061	75	15	is	be	AUX
ejpam-5061	75	16	a	a	DET
ejpam-5061	75	17	hop	hop	NOUN
ejpam-5061	75	18	independent	independent	ADJ
ejpam-5061	75	19	set	set	NOUN
ejpam-5061	75	20	of	of	ADP
ejpam-5061	75	21	g.	g.	PROPN
ejpam-5061	75	22	thus	thus	ADV
ejpam-5061	75	23	,	,	PUNCT
ejpam-5061	75	24	l	l	PROPN
ejpam-5061	75	25	=	=	SYM
ejpam-5061	75	26	(	(	PUNCT
ejpam-5061	75	27	w1	w1	NOUN
ejpam-5061	75	28	,	,	PUNCT
ejpam-5061	75	29	w2	w2	NOUN
ejpam-5061	75	30	)	)	PUNCT
ejpam-5061	75	31	is	be	AUX
ejpam-5061	75	32	a	a	DET
ejpam-5061	75	33	legal	legal	ADJ
ejpam-5061	75	34	hop	hop	NOUN
ejpam-5061	75	35	independent	independent	ADJ
ejpam-5061	75	36	sequence	sequence	NOUN
ejpam-5061	75	37	of	of	ADP
ejpam-5061	75	38	g.	g.	PROPN
ejpam-5061	75	39	moreover	moreover	ADV
ejpam-5061	75	40	,	,	PUNCT
ejpam-5061	75	41	since	since	SCONJ
ejpam-5061	75	42	dg(w1	dg(w1	NOUN
ejpam-5061	75	43	,	,	PUNCT
ejpam-5061	75	44	w3	w3	PROPN
ejpam-5061	75	45	)	)	PUNCT
ejpam-5061	75	46	=	=	SYM
ejpam-5061	75	47	2	2	NUM
ejpam-5061	75	48	and	and	CCONJ
ejpam-5061	75	49	dg(w2	dg(w2	NOUN
ejpam-5061	75	50	,	,	PUNCT
ejpam-5061	75	51	w4	w4	NOUN
ejpam-5061	75	52	)	)	PUNCT
ejpam-5061	75	53	=	=	SYM
ejpam-5061	75	54	2	2	NUM
ejpam-5061	75	55	,	,	PUNCT
ejpam-5061	75	56	it	it	PRON
ejpam-5061	75	57	follows	follow	VERB
ejpam-5061	75	58	that	that	SCONJ
ejpam-5061	75	59	l	l	NOUN
ejpam-5061	75	60	is	be	AUX
ejpam-5061	75	61	a	a	DET
ejpam-5061	75	62	maximum	maximum	ADJ
ejpam-5061	75	63	legal	legal	ADJ
ejpam-5061	75	64	hop	hop	NOUN
ejpam-5061	75	65	independent	independent	ADJ
ejpam-5061	75	66	sequence	sequence	NOUN
ejpam-5061	75	67	of	of	ADP
ejpam-5061	75	68	g.	g.	PROPN
ejpam-5061	75	69	therefore	therefore	ADV
ejpam-5061	75	70	,	,	PUNCT
ejpam-5061	75	71	αℓh(g	αℓh(g	X
ejpam-5061	75	72	)	)	PUNCT
ejpam-5061	76	1	=	=	SYM
ejpam-5061	76	2	2	2	X
ejpam-5061	76	3	.	.	PUNCT
ejpam-5061	76	4	j.	j.	PROPN
ejpam-5061	76	5	hassan	hassan	PROPN
ejpam-5061	76	6	et	et	PROPN
ejpam-5061	76	7	al	al	PROPN
ejpam-5061	76	8	.	.	PUNCT
ejpam-5061	76	9	/	/	SYM
ejpam-5061	76	10	eur	eur	PROPN
ejpam-5061	76	11	.	.	PUNCT
ejpam-5061	77	1	j.	j.	PROPN
ejpam-5061	77	2	pure	pure	PROPN
ejpam-5061	77	3	appl	appl	PROPN
ejpam-5061	77	4	.	.	PROPN
ejpam-5061	77	5	math	math	PROPN
ejpam-5061	77	6	,	,	PUNCT
ejpam-5061	77	7	17	17	NUM
ejpam-5061	77	8	(	(	PUNCT
ejpam-5061	77	9	2	2	NUM
ejpam-5061	77	10	)	)	PUNCT
ejpam-5061	77	11	(	(	PUNCT
ejpam-5061	77	12	2024	2024	NUM
ejpam-5061	77	13	)	)	PUNCT
ejpam-5061	77	14	,	,	PUNCT
ejpam-5061	77	15	725	725	NUM
ejpam-5061	77	16	-	-	SYM
ejpam-5061	77	17	735	735	NUM
ejpam-5061	77	18	728	728	NUM
ejpam-5061	77	19	w1	w1	NOUN
ejpam-5061	77	20	w2	w2	NOUN
ejpam-5061	77	21	w3w4	w3w4	PROPN
ejpam-5061	77	22	g	g	NOUN
ejpam-5061	77	23	:	:	PUNCT
ejpam-5061	77	24	figure	figure	NOUN
ejpam-5061	77	25	1	1	NUM
ejpam-5061	77	26	:	:	PUNCT
ejpam-5061	77	27	graph	graph	VERB
ejpam-5061	77	28	g	g	NOUN
ejpam-5061	77	29	with	with	ADP
ejpam-5061	77	30	αlh(g	αlh(g	NUM
ejpam-5061	77	31	)	)	PUNCT
ejpam-5061	77	32	=	=	SYM
ejpam-5061	77	33	2	2	NUM
ejpam-5061	77	34	remark	remark	NOUN
ejpam-5061	77	35	1	1	NUM
ejpam-5061	77	36	.	.	PUNCT
ejpam-5061	78	1	let	let	VERB
ejpam-5061	78	2	g	g	PRON
ejpam-5061	78	3	be	be	AUX
ejpam-5061	78	4	a	a	DET
ejpam-5061	78	5	graph	graph	NOUN
ejpam-5061	78	6	.	.	PUNCT
ejpam-5061	79	1	then	then	ADV
ejpam-5061	79	2	(	(	PUNCT
ejpam-5061	79	3	i	i	NOUN
ejpam-5061	79	4	)	)	PUNCT
ejpam-5061	79	5	a	a	DET
ejpam-5061	79	6	legal	legal	ADJ
ejpam-5061	79	7	sequence	sequence	NOUN
ejpam-5061	79	8	of	of	ADP
ejpam-5061	79	9	g	g	NOUN
ejpam-5061	79	10	may	may	AUX
ejpam-5061	79	11	not	not	PART
ejpam-5061	79	12	form	form	VERB
ejpam-5061	79	13	a	a	DET
ejpam-5061	79	14	hop	hop	NOUN
ejpam-5061	79	15	independent	independent	ADJ
ejpam-5061	79	16	set	set	NOUN
ejpam-5061	79	17	of	of	ADP
ejpam-5061	79	18	g	g	NOUN
ejpam-5061	79	19	;	;	PUNCT
ejpam-5061	79	20	(	(	PUNCT
ejpam-5061	79	21	ii	ii	NOUN
ejpam-5061	79	22	)	)	PUNCT
ejpam-5061	79	23	a	a	DET
ejpam-5061	79	24	hop	hop	NOUN
ejpam-5061	79	25	independent	independent	ADJ
ejpam-5061	79	26	set	set	NOUN
ejpam-5061	79	27	of	of	ADP
ejpam-5061	79	28	g	g	NOUN
ejpam-5061	79	29	may	may	AUX
ejpam-5061	79	30	not	not	PART
ejpam-5061	79	31	form	form	VERB
ejpam-5061	79	32	a	a	DET
ejpam-5061	79	33	legal	legal	ADJ
ejpam-5061	79	34	sequence	sequence	NOUN
ejpam-5061	79	35	of	of	ADP
ejpam-5061	79	36	g	g	NOUN
ejpam-5061	79	37	;	;	PUNCT
ejpam-5061	79	38	(	(	PUNCT
ejpam-5061	79	39	iii	iii	X
ejpam-5061	79	40	)	)	PUNCT
ejpam-5061	79	41	if	if	SCONJ
ejpam-5061	79	42	ŝ	ŝ	NUM
ejpam-5061	79	43	is	be	AUX
ejpam-5061	79	44	an	an	DET
ejpam-5061	79	45	αh	αh	NOUN
ejpam-5061	79	46	-	-	PUNCT
ejpam-5061	79	47	set	set	NOUN
ejpam-5061	79	48	of	of	ADP
ejpam-5061	79	49	g	g	NOUN
ejpam-5061	79	50	and	and	CCONJ
ejpam-5061	79	51	form	form	VERB
ejpam-5061	79	52	a	a	DET
ejpam-5061	79	53	legal	legal	ADJ
ejpam-5061	79	54	sequence	sequence	NOUN
ejpam-5061	79	55	,	,	PUNCT
ejpam-5061	79	56	then	then	ADV
ejpam-5061	79	57	s	s	VERB
ejpam-5061	79	58	is	be	AUX
ejpam-5061	79	59	an	an	DET
ejpam-5061	79	60	αℓh	αℓh	NOUN
ejpam-5061	79	61	-	-	PUNCT
ejpam-5061	79	62	sequence	sequence	NOUN
ejpam-5061	79	63	of	of	ADP
ejpam-5061	79	64	g	g	NOUN
ejpam-5061	79	65	and	and	CCONJ
ejpam-5061	79	66	αℓh(g	αℓh(g	NOUN
ejpam-5061	79	67	)	)	PUNCT
ejpam-5061	79	68	=	=	PUNCT
ejpam-5061	79	69	|ŝ|	|ŝ|	NUM
ejpam-5061	79	70	;	;	PUNCT
ejpam-5061	79	71	and	and	CCONJ
ejpam-5061	79	72	(	(	PUNCT
ejpam-5061	79	73	iv	iv	X
ejpam-5061	79	74	)	)	PUNCT
ejpam-5061	79	75	if	if	SCONJ
ejpam-5061	79	76	l	l	NOUN
ejpam-5061	79	77	is	be	AUX
ejpam-5061	79	78	a	a	DET
ejpam-5061	79	79	maximum	maximum	ADJ
ejpam-5061	79	80	legal	legal	ADJ
ejpam-5061	79	81	sequence	sequence	NOUN
ejpam-5061	79	82	of	of	ADP
ejpam-5061	79	83	g	g	PROPN
ejpam-5061	79	84	and	and	CCONJ
ejpam-5061	79	85	l̂	l̂	NUM
ejpam-5061	79	86	is	be	AUX
ejpam-5061	79	87	a	a	DET
ejpam-5061	79	88	hop	hop	NOUN
ejpam-5061	79	89	independent	independent	ADJ
ejpam-5061	79	90	set	set	NOUN
ejpam-5061	79	91	of	of	ADP
ejpam-5061	79	92	g	g	NOUN
ejpam-5061	79	93	,	,	PUNCT
ejpam-5061	79	94	then	then	ADV
ejpam-5061	79	95	l	l	NOUN
ejpam-5061	79	96	is	be	AUX
ejpam-5061	79	97	an	an	DET
ejpam-5061	79	98	αℓh	αℓh	NOUN
ejpam-5061	79	99	-	-	PUNCT
ejpam-5061	79	100	sequence	sequence	NOUN
ejpam-5061	79	101	of	of	ADP
ejpam-5061	79	102	g	g	NOUN
ejpam-5061	79	103	and	and	CCONJ
ejpam-5061	79	104	αℓh(g	αℓh(g	NOUN
ejpam-5061	79	105	)	)	PUNCT
ejpam-5061	79	106	=	=	SYM
ejpam-5061	80	1	|l̂|	|l̂|	PROPN
ejpam-5061	80	2	.	.	PUNCT
ejpam-5061	80	3	theorem	theorem	NOUN
ejpam-5061	80	4	1	1	NUM
ejpam-5061	80	5	.	.	PUNCT
ejpam-5061	81	1	let	let	VERB
ejpam-5061	81	2	g	g	NOUN
ejpam-5061	81	3	be	be	AUX
ejpam-5061	81	4	any	any	DET
ejpam-5061	81	5	graph	graph	NOUN
ejpam-5061	81	6	.	.	PUNCT
ejpam-5061	82	1	then	then	ADV
ejpam-5061	82	2	(	(	PUNCT
ejpam-5061	82	3	i	i	NOUN
ejpam-5061	82	4	)	)	PUNCT
ejpam-5061	82	5	αℓh(g	αℓh(g	PROPN
ejpam-5061	82	6	)	)	PUNCT
ejpam-5061	82	7	≤	≤	NOUN
ejpam-5061	82	8	αh(g	αh(g	NOUN
ejpam-5061	82	9	)	)	PUNCT
ejpam-5061	82	10	;	;	PUNCT
ejpam-5061	82	11	(	(	PUNCT
ejpam-5061	82	12	ii	ii	NOUN
ejpam-5061	82	13	)	)	PUNCT
ejpam-5061	82	14	1	1	NUM
ejpam-5061	82	15	≤	≤	NUM
ejpam-5061	82	16	αℓh(g	αℓh(g	NOUN
ejpam-5061	82	17	)	)	PUNCT
ejpam-5061	82	18	≤	≤	NUM
ejpam-5061	82	19	|v	|v	X
ejpam-5061	82	20	(	(	PUNCT
ejpam-5061	82	21	g)|	g)|	NOUN
ejpam-5061	82	22	;	;	PUNCT
ejpam-5061	82	23	and	and	CCONJ
ejpam-5061	82	24	(	(	PUNCT
ejpam-5061	82	25	iii	iii	X
ejpam-5061	82	26	)	)	PUNCT
ejpam-5061	82	27	αℓh(g	αℓh(g	PROPN
ejpam-5061	82	28	)	)	PUNCT
ejpam-5061	82	29	≤	≤	NUM
ejpam-5061	82	30	γgr(g	γgr(g	PROPN
ejpam-5061	82	31	)	)	PUNCT
ejpam-5061	82	32	.	.	PUNCT
ejpam-5061	83	1	proof	proof	NOUN
ejpam-5061	83	2	.	.	PUNCT
ejpam-5061	84	1	(	(	PUNCT
ejpam-5061	84	2	i	i	NOUN
ejpam-5061	84	3	)	)	PUNCT
ejpam-5061	84	4	let	let	VERB
ejpam-5061	84	5	g	g	NOUN
ejpam-5061	84	6	be	be	AUX
ejpam-5061	84	7	any	any	DET
ejpam-5061	84	8	graph	graph	NOUN
ejpam-5061	84	9	and	and	CCONJ
ejpam-5061	84	10	let	let	VERB
ejpam-5061	84	11	l	l	NOUN
ejpam-5061	84	12	be	be	AUX
ejpam-5061	84	13	an	an	DET
ejpam-5061	84	14	αℓh	αℓh	NOUN
ejpam-5061	84	15	-	-	PUNCT
ejpam-5061	84	16	sequence	sequence	NOUN
ejpam-5061	84	17	of	of	ADP
ejpam-5061	84	18	g.	g.	PROPN
ejpam-5061	84	19	then	then	ADV
ejpam-5061	84	20	its	its	PRON
ejpam-5061	84	21	corresponding	corresponding	ADJ
ejpam-5061	84	22	set	set	NOUN
ejpam-5061	84	23	l̂	l̂	X
ejpam-5061	84	24	is	be	AUX
ejpam-5061	84	25	a	a	DET
ejpam-5061	84	26	hop	hop	NOUN
ejpam-5061	84	27	independent	independent	ADJ
ejpam-5061	84	28	set	set	NOUN
ejpam-5061	84	29	of	of	ADP
ejpam-5061	84	30	g.	g.	PROPN
ejpam-5061	84	31	since	since	SCONJ
ejpam-5061	84	32	αh(g	αh(g	NOUN
ejpam-5061	84	33	)	)	PUNCT
ejpam-5061	84	34	is	be	AUX
ejpam-5061	84	35	the	the	DET
ejpam-5061	84	36	maximum	maximum	ADJ
ejpam-5061	84	37	cardinality	cardinality	NOUN
ejpam-5061	84	38	of	of	ADP
ejpam-5061	84	39	a	a	DET
ejpam-5061	84	40	hop	hop	NOUN
ejpam-5061	84	41	independent	independent	ADJ
ejpam-5061	84	42	set	set	NOUN
ejpam-5061	84	43	in	in	ADP
ejpam-5061	84	44	g	g	PROPN
ejpam-5061	84	45	,	,	PUNCT
ejpam-5061	84	46	it	it	PRON
ejpam-5061	84	47	follows	follow	VERB
ejpam-5061	84	48	that	that	SCONJ
ejpam-5061	84	49	αh(g	αh(g	NOUN
ejpam-5061	84	50	)	)	PUNCT
ejpam-5061	84	51	≥	≥	NOUN
ejpam-5061	84	52	∣∣∣l̂∣∣∣	∣∣∣l̂∣∣∣	PROPN
ejpam-5061	84	53	=	=	SYM
ejpam-5061	84	54	αℓh(g	αℓh(g	NOUN
ejpam-5061	84	55	)	)	PUNCT
ejpam-5061	84	56	.	.	PUNCT
ejpam-5061	85	1	(	(	PUNCT
ejpam-5061	85	2	ii	ii	NOUN
ejpam-5061	85	3	)	)	PUNCT
ejpam-5061	85	4	let	let	VERB
ejpam-5061	85	5	g	g	NOUN
ejpam-5061	85	6	be	be	AUX
ejpam-5061	85	7	any	any	DET
ejpam-5061	85	8	graph	graph	NOUN
ejpam-5061	85	9	and	and	CCONJ
ejpam-5061	85	10	let	let	VERB
ejpam-5061	85	11	x	x	SYM
ejpam-5061	85	12	∈	∈	PROPN
ejpam-5061	85	13	v	v	X
ejpam-5061	85	14	(	(	PUNCT
ejpam-5061	85	15	g	g	NOUN
ejpam-5061	85	16	)	)	PUNCT
ejpam-5061	85	17	.	.	PUNCT
ejpam-5061	86	1	then	then	ADV
ejpam-5061	86	2	(	(	PUNCT
ejpam-5061	86	3	x	x	X
ejpam-5061	86	4	)	)	PUNCT
ejpam-5061	86	5	is	be	AUX
ejpam-5061	86	6	a	a	DET
ejpam-5061	86	7	legal	legal	ADJ
ejpam-5061	86	8	hop	hop	NOUN
ejpam-5061	86	9	independent	independent	ADJ
ejpam-5061	86	10	sequence	sequence	NOUN
ejpam-5061	86	11	of	of	ADP
ejpam-5061	86	12	g.	g.	PROPN
ejpam-5061	86	13	hence	hence	ADV
ejpam-5061	86	14	,	,	PUNCT
ejpam-5061	86	15	αℓh(g	αℓh(g	PROPN
ejpam-5061	86	16	)	)	PUNCT
ejpam-5061	86	17	≥	≥	NOUN
ejpam-5061	86	18	1	1	NUM
ejpam-5061	86	19	.	.	PUNCT
ejpam-5061	87	1	since	since	SCONJ
ejpam-5061	87	2	αh(g	αh(g	NOUN
ejpam-5061	87	3	)	)	PUNCT
ejpam-5061	87	4	≤	≤	NUM
ejpam-5061	87	5	|v	|v	X
ejpam-5061	87	6	(	(	PUNCT
ejpam-5061	87	7	g)|	g)|	NOUN
ejpam-5061	87	8	for	for	ADP
ejpam-5061	87	9	any	any	DET
ejpam-5061	87	10	graph	graph	NOUN
ejpam-5061	87	11	g	g	NOUN
ejpam-5061	87	12	,	,	PUNCT
ejpam-5061	87	13	it	it	PRON
ejpam-5061	87	14	follows	follow	VERB
ejpam-5061	87	15	that	that	SCONJ
ejpam-5061	87	16	αℓh(g	αℓh(g	NOUN
ejpam-5061	87	17	)	)	PUNCT
ejpam-5061	87	18	≤	≤	NUM
ejpam-5061	87	19	|v	|v	X
ejpam-5061	87	20	(	(	PUNCT
ejpam-5061	87	21	g)|	g)|	NOUN
ejpam-5061	87	22	by	by	ADP
ejpam-5061	87	23	(	(	PUNCT
ejpam-5061	87	24	i	i	NOUN
ejpam-5061	87	25	)	)	PUNCT
ejpam-5061	87	26	.	.	PUNCT
ejpam-5061	88	1	consequently	consequently	ADV
ejpam-5061	88	2	,	,	PUNCT
ejpam-5061	88	3	1	1	NUM
ejpam-5061	88	4	≤	≤	NUM
ejpam-5061	88	5	αℓh(g	αℓh(g	NOUN
ejpam-5061	88	6	)	)	PUNCT
ejpam-5061	88	7	≤	≤	NUM
ejpam-5061	88	8	|v	|v	X
ejpam-5061	88	9	(	(	PUNCT
ejpam-5061	88	10	g)|	g)|	NOUN
ejpam-5061	88	11	.	.	PUNCT
ejpam-5061	89	1	(	(	PUNCT
ejpam-5061	89	2	iii	iii	X
ejpam-5061	89	3	)	)	PUNCT
ejpam-5061	89	4	let	let	VERB
ejpam-5061	89	5	g	g	NOUN
ejpam-5061	89	6	be	be	AUX
ejpam-5061	89	7	any	any	DET
ejpam-5061	89	8	graph	graph	NOUN
ejpam-5061	89	9	and	and	CCONJ
ejpam-5061	89	10	let	let	VERB
ejpam-5061	89	11	l	l	NOUN
ejpam-5061	89	12	be	be	AUX
ejpam-5061	89	13	an	an	DET
ejpam-5061	89	14	αℓh	αℓh	NOUN
ejpam-5061	89	15	-	-	PUNCT
ejpam-5061	89	16	sequence	sequence	NOUN
ejpam-5061	89	17	of	of	ADP
ejpam-5061	89	18	g.	g.	PROPN
ejpam-5061	90	1	then	then	ADV
ejpam-5061	90	2	l	l	PROPN
ejpam-5061	90	3	is	be	AUX
ejpam-5061	90	4	a	a	DET
ejpam-5061	90	5	legal	legal	ADJ
ejpam-5061	90	6	sequence	sequence	NOUN
ejpam-5061	90	7	of	of	ADP
ejpam-5061	90	8	g.	g.	PROPN
ejpam-5061	90	9	since	since	SCONJ
ejpam-5061	90	10	any	any	DET
ejpam-5061	90	11	γgr	γgr	NOUN
ejpam-5061	90	12	-	-	PUNCT
ejpam-5061	90	13	sequence	sequence	NOUN
ejpam-5061	90	14	is	be	AUX
ejpam-5061	90	15	a	a	DET
ejpam-5061	90	16	maximum	maximum	ADJ
ejpam-5061	90	17	legal	legal	ADJ
ejpam-5061	90	18	sequence	sequence	NOUN
ejpam-5061	90	19	,	,	PUNCT
ejpam-5061	90	20	we	we	PRON
ejpam-5061	90	21	have	have	VERB
ejpam-5061	90	22	αℓh(g	αℓh(g	NOUN
ejpam-5061	90	23	)	)	PUNCT
ejpam-5061	90	24	=	=	SYM
ejpam-5061	91	1	|l̂|	|l̂|	PRON
ejpam-5061	91	2	≤	≤	ADJ
ejpam-5061	91	3	γgr(g	γgr(g	PROPN
ejpam-5061	91	4	)	)	PUNCT
ejpam-5061	91	5	.	.	PUNCT
ejpam-5061	92	1	theorem	theorem	VERB
ejpam-5061	92	2	2	2	NUM
ejpam-5061	92	3	.	.	PUNCT
ejpam-5061	92	4	αℓh(g	αℓh(g	NOUN
ejpam-5061	92	5	)	)	PUNCT
ejpam-5061	92	6	=	=	SYM
ejpam-5061	93	1	1	1	NUM
ejpam-5061	93	2	if	if	SCONJ
ejpam-5061	93	3	and	and	CCONJ
ejpam-5061	93	4	only	only	ADV
ejpam-5061	93	5	if	if	SCONJ
ejpam-5061	93	6	g	g	PROPN
ejpam-5061	93	7	is	be	AUX
ejpam-5061	93	8	complete	complete	ADJ
ejpam-5061	93	9	graph	graph	NOUN
ejpam-5061	93	10	.	.	PUNCT
ejpam-5061	94	1	proof	proof	NOUN
ejpam-5061	94	2	.	.	PUNCT
ejpam-5061	95	1	let	let	VERB
ejpam-5061	95	2	αℓh(g	αℓh(g	NOUN
ejpam-5061	95	3	)	)	PUNCT
ejpam-5061	95	4	=	=	SYM
ejpam-5061	95	5	1	1	X
ejpam-5061	95	6	.	.	PUNCT
ejpam-5061	95	7	suppose	suppose	VERB
ejpam-5061	95	8	g	g	PROPN
ejpam-5061	95	9	is	be	AUX
ejpam-5061	95	10	non	non	ADJ
ejpam-5061	95	11	-	-	ADJ
ejpam-5061	95	12	complete	complete	ADJ
ejpam-5061	95	13	.	.	PUNCT
ejpam-5061	96	1	if	if	SCONJ
ejpam-5061	96	2	g	g	PROPN
ejpam-5061	96	3	is	be	AUX
ejpam-5061	96	4	connected	connect	VERB
ejpam-5061	96	5	,	,	PUNCT
ejpam-5061	96	6	there	there	PRON
ejpam-5061	96	7	exist	exist	VERB
ejpam-5061	96	8	u	u	NOUN
ejpam-5061	96	9	,	,	PUNCT
ejpam-5061	96	10	w	w	PROPN
ejpam-5061	96	11	∈	∈	PROPN
ejpam-5061	96	12	v	v	ADP
ejpam-5061	96	13	(	(	PUNCT
ejpam-5061	96	14	g	g	NOUN
ejpam-5061	96	15	)	)	PUNCT
ejpam-5061	96	16	such	such	ADJ
ejpam-5061	96	17	that	that	SCONJ
ejpam-5061	96	18	dg(u	dg(u	ADJ
ejpam-5061	96	19	,	,	PUNCT
ejpam-5061	96	20	w	w	NOUN
ejpam-5061	96	21	)	)	PUNCT
ejpam-5061	96	22	=	=	SYM
ejpam-5061	96	23	2	2	X
ejpam-5061	96	24	.	.	X
ejpam-5061	96	25	let	let	VERB
ejpam-5061	96	26	x	x	SYM
ejpam-5061	96	27	∈	∈	PROPN
ejpam-5061	96	28	ng(u	ng(u	NOUN
ejpam-5061	96	29	)	)	PUNCT
ejpam-5061	96	30	∩	∩	NOUN
ejpam-5061	96	31	ng(w	ng(w	NOUN
ejpam-5061	96	32	)	)	PUNCT
ejpam-5061	96	33	.	.	PUNCT
ejpam-5061	97	1	then	then	ADV
ejpam-5061	97	2	w	w	PROPN
ejpam-5061	97	3	∈	∈	PROPN
ejpam-5061	97	4	ng[x]\ng[u	ng[x]\ng[u	NOUN
ejpam-5061	97	5	]	]	PUNCT
ejpam-5061	97	6	,	,	PUNCT
ejpam-5061	97	7	j.	j.	PROPN
ejpam-5061	97	8	hassan	hassan	PROPN
ejpam-5061	97	9	et	et	PROPN
ejpam-5061	97	10	al	al	PROPN
ejpam-5061	97	11	.	.	PUNCT
ejpam-5061	97	12	/	/	SYM
ejpam-5061	97	13	eur	eur	PROPN
ejpam-5061	97	14	.	.	PUNCT
ejpam-5061	98	1	j.	j.	PROPN
ejpam-5061	98	2	pure	pure	PROPN
ejpam-5061	98	3	appl	appl	PROPN
ejpam-5061	98	4	.	.	PROPN
ejpam-5061	98	5	math	math	PROPN
ejpam-5061	98	6	,	,	PUNCT
ejpam-5061	98	7	17	17	NUM
ejpam-5061	98	8	(	(	PUNCT
ejpam-5061	98	9	2	2	NUM
ejpam-5061	98	10	)	)	PUNCT
ejpam-5061	98	11	(	(	PUNCT
ejpam-5061	98	12	2024	2024	NUM
ejpam-5061	98	13	)	)	PUNCT
ejpam-5061	98	14	,	,	PUNCT
ejpam-5061	98	15	725	725	NUM
ejpam-5061	98	16	-	-	SYM
ejpam-5061	98	17	735	735	NUM
ejpam-5061	98	18	729	729	NUM
ejpam-5061	98	19	and	and	CCONJ
ejpam-5061	98	20	so	so	ADV
ejpam-5061	98	21	ng[x]\ng[u	ng[x]\ng[u	ADV
ejpam-5061	98	22	]	]	X
ejpam-5061	98	23	̸=	̸=	PROPN
ejpam-5061	98	24	∅.	∅.	ADV
ejpam-5061	98	25	thus	thus	ADV
ejpam-5061	98	26	,	,	PUNCT
ejpam-5061	98	27	l	l	NOUN
ejpam-5061	98	28	=	=	SYM
ejpam-5061	98	29	(	(	PUNCT
ejpam-5061	98	30	u	u	NOUN
ejpam-5061	98	31	,	,	PUNCT
ejpam-5061	98	32	x	x	X
ejpam-5061	98	33	)	)	PUNCT
ejpam-5061	98	34	is	be	AUX
ejpam-5061	98	35	a	a	DET
ejpam-5061	98	36	legal	legal	ADJ
ejpam-5061	98	37	sequence	sequence	NOUN
ejpam-5061	98	38	of	of	ADP
ejpam-5061	98	39	g.	g.	PROPN
ejpam-5061	98	40	since	since	SCONJ
ejpam-5061	98	41	dg(u	dg(u	NOUN
ejpam-5061	98	42	,	,	PUNCT
ejpam-5061	98	43	x	x	X
ejpam-5061	98	44	)	)	PUNCT
ejpam-5061	98	45	=	=	SYM
ejpam-5061	98	46	1	1	NUM
ejpam-5061	98	47	,	,	PUNCT
ejpam-5061	98	48	it	it	PRON
ejpam-5061	98	49	follows	follow	VERB
ejpam-5061	98	50	that	that	SCONJ
ejpam-5061	98	51	l	l	NOUN
ejpam-5061	98	52	=	=	SYM
ejpam-5061	98	53	(	(	PUNCT
ejpam-5061	98	54	u	u	NOUN
ejpam-5061	98	55	,	,	PUNCT
ejpam-5061	98	56	x	x	X
ejpam-5061	98	57	)	)	PUNCT
ejpam-5061	98	58	is	be	AUX
ejpam-5061	98	59	a	a	DET
ejpam-5061	98	60	legal	legal	ADJ
ejpam-5061	98	61	hop	hop	NOUN
ejpam-5061	98	62	independent	independent	ADJ
ejpam-5061	98	63	sequence	sequence	NOUN
ejpam-5061	98	64	of	of	ADP
ejpam-5061	98	65	g.	g.	PROPN
ejpam-5061	98	66	therefore	therefore	ADV
ejpam-5061	98	67	,	,	PUNCT
ejpam-5061	98	68	αℓh(g	αℓh(g	NOUN
ejpam-5061	98	69	)	)	PUNCT
ejpam-5061	98	70	≥	≥	NOUN
ejpam-5061	98	71	2	2	NUM
ejpam-5061	98	72	,	,	PUNCT
ejpam-5061	98	73	which	which	PRON
ejpam-5061	98	74	is	be	AUX
ejpam-5061	98	75	a	a	DET
ejpam-5061	98	76	contradiction	contradiction	NOUN
ejpam-5061	98	77	.	.	PUNCT
ejpam-5061	99	1	now	now	ADV
ejpam-5061	99	2	,	,	PUNCT
ejpam-5061	99	3	suppose	suppose	VERB
ejpam-5061	99	4	that	that	SCONJ
ejpam-5061	99	5	g	g	PROPN
ejpam-5061	99	6	is	be	AUX
ejpam-5061	99	7	disconnected	disconnected	ADJ
ejpam-5061	99	8	graph	graph	NOUN
ejpam-5061	99	9	.	.	PUNCT
ejpam-5061	100	1	let	let	VERB
ejpam-5061	100	2	g1	g1	PROPN
ejpam-5061	100	3	,	,	PUNCT
ejpam-5061	100	4	...	...	PUNCT
ejpam-5061	100	5	,	,	PUNCT
ejpam-5061	100	6	gm	gm	PROPN
ejpam-5061	100	7	,	,	PUNCT
ejpam-5061	100	8	where	where	SCONJ
ejpam-5061	100	9	m	m	PROPN
ejpam-5061	100	10	≥	≥	NUM
ejpam-5061	100	11	2	2	NUM
ejpam-5061	100	12	be	be	AUX
ejpam-5061	100	13	components	component	NOUN
ejpam-5061	100	14	of	of	ADP
ejpam-5061	100	15	g.	g.	PROPN
ejpam-5061	100	16	then	then	ADV
ejpam-5061	100	17	αℓh(gi	αℓh(gi	NUM
ejpam-5061	100	18	)	)	PUNCT
ejpam-5061	100	19	≥	≥	NOUN
ejpam-5061	100	20	1	1	NUM
ejpam-5061	100	21	for	for	ADP
ejpam-5061	100	22	each	each	DET
ejpam-5061	100	23	i	i	PRON
ejpam-5061	100	24	∈	∈	PROPN
ejpam-5061	100	25	{	{	PUNCT
ejpam-5061	100	26	1	1	NUM
ejpam-5061	100	27	,	,	PUNCT
ejpam-5061	100	28	...	...	PUNCT
ejpam-5061	100	29	,	,	PUNCT
ejpam-5061	100	30	m	m	VERB
ejpam-5061	100	31	}	}	PUNCT
ejpam-5061	100	32	.	.	PUNCT
ejpam-5061	101	1	thus	thus	ADV
ejpam-5061	101	2	,	,	PUNCT
ejpam-5061	101	3	αℓh(g	αℓh(g	NOUN
ejpam-5061	101	4	)	)	PUNCT
ejpam-5061	101	5	=	=	SYM
ejpam-5061	101	6	αℓh(g1	αℓh(g1	NOUN
ejpam-5061	101	7	)	)	PUNCT
ejpam-5061	101	8	+	+	CCONJ
ejpam-5061	101	9	...	...	PUNCT
ejpam-5061	101	10	+	+	NUM
ejpam-5061	101	11	αℓh(gm	αℓh(gm	NOUN
ejpam-5061	101	12	)	)	PUNCT
ejpam-5061	101	13	≥	≥	NOUN
ejpam-5061	101	14	1	1	NUM
ejpam-5061	101	15	+	+	CCONJ
ejpam-5061	101	16	...	...	PUNCT
ejpam-5061	102	1	+	+	CCONJ
ejpam-5061	102	2	1	1	NUM
ejpam-5061	102	3	≥	≥	NOUN
ejpam-5061	102	4	2	2	NUM
ejpam-5061	102	5	since	since	SCONJ
ejpam-5061	102	6	m	m	PROPN
ejpam-5061	102	7	≥	≥	NUM
ejpam-5061	102	8	2	2	NUM
ejpam-5061	102	9	.	.	PUNCT
ejpam-5061	103	1	however	however	ADV
ejpam-5061	103	2	,	,	PUNCT
ejpam-5061	103	3	this	this	DET
ejpam-5061	103	4	a	a	DET
ejpam-5061	103	5	contradiction	contradiction	NOUN
ejpam-5061	103	6	to	to	ADP
ejpam-5061	103	7	our	our	PRON
ejpam-5061	103	8	assumption	assumption	NOUN
ejpam-5061	103	9	.	.	PUNCT
ejpam-5061	104	1	consequently	consequently	ADV
ejpam-5061	104	2	,	,	PUNCT
ejpam-5061	104	3	g	g	PROPN
ejpam-5061	104	4	must	must	AUX
ejpam-5061	104	5	be	be	AUX
ejpam-5061	104	6	complete	complete	ADJ
ejpam-5061	104	7	graph	graph	NOUN
ejpam-5061	104	8	.	.	PUNCT
ejpam-5061	105	1	for	for	ADP
ejpam-5061	105	2	the	the	DET
ejpam-5061	105	3	converse	converse	NOUN
ejpam-5061	105	4	,	,	PUNCT
ejpam-5061	105	5	suppose	suppose	VERB
ejpam-5061	105	6	that	that	SCONJ
ejpam-5061	105	7	g	g	PROPN
ejpam-5061	105	8	is	be	AUX
ejpam-5061	105	9	complete	complete	ADJ
ejpam-5061	105	10	.	.	PUNCT
ejpam-5061	106	1	then	then	ADV
ejpam-5061	106	2	γgr(g	γgr(g	PROPN
ejpam-5061	106	3	)	)	PUNCT
ejpam-5061	106	4	=	=	SYM
ejpam-5061	107	1	1	1	X
ejpam-5061	107	2	.	.	PUNCT
ejpam-5061	107	3	therefore	therefore	ADV
ejpam-5061	107	4	,	,	PUNCT
ejpam-5061	107	5	αℓh(g	αℓh(g	NOUN
ejpam-5061	107	6	)	)	PUNCT
ejpam-5061	107	7	=	=	SYM
ejpam-5061	107	8	1	1	NUM
ejpam-5061	107	9	by	by	ADP
ejpam-5061	107	10	theorem	theorem	NOUN
ejpam-5061	107	11	3	3	NUM
ejpam-5061	107	12	(	(	PUNCT
ejpam-5061	107	13	ii	ii	NOUN
ejpam-5061	107	14	)	)	PUNCT
ejpam-5061	107	15	and	and	CCONJ
ejpam-5061	107	16	(	(	PUNCT
ejpam-5061	107	17	iii	iii	NOUN
ejpam-5061	107	18	)	)	PUNCT
ejpam-5061	107	19	.	.	PUNCT
ejpam-5061	108	1	theorem	theorem	NOUN
ejpam-5061	108	2	3	3	X
ejpam-5061	108	3	.	.	PUNCT
ejpam-5061	109	1	let	let	VERB
ejpam-5061	109	2	g	g	NOUN
ejpam-5061	109	3	be	be	AUX
ejpam-5061	109	4	any	any	DET
ejpam-5061	109	5	graph	graph	NOUN
ejpam-5061	109	6	.	.	PUNCT
ejpam-5061	110	1	then	then	ADV
ejpam-5061	110	2	αℓh(g	αℓh(g	NUM
ejpam-5061	110	3	)	)	PUNCT
ejpam-5061	110	4	=	=	SYM
ejpam-5061	110	5	|v	|v	PROPN
ejpam-5061	110	6	(	(	PUNCT
ejpam-5061	110	7	g)|	g)|	VERB
ejpam-5061	110	8	if	if	SCONJ
ejpam-5061	110	9	and	and	CCONJ
ejpam-5061	110	10	only	only	ADV
ejpam-5061	110	11	if	if	SCONJ
ejpam-5061	110	12	every	every	DET
ejpam-5061	110	13	component	component	NOUN
ejpam-5061	110	14	of	of	ADP
ejpam-5061	110	15	g	g	PROPN
ejpam-5061	110	16	is	be	AUX
ejpam-5061	110	17	trivial	trivial	ADJ
ejpam-5061	110	18	.	.	PUNCT
ejpam-5061	111	1	proof	proof	NOUN
ejpam-5061	111	2	.	.	PUNCT
ejpam-5061	112	1	suppose	suppose	VERB
ejpam-5061	112	2	that	that	SCONJ
ejpam-5061	112	3	αℓh(g	αℓh(g	NOUN
ejpam-5061	112	4	)	)	PUNCT
ejpam-5061	112	5	=	=	SYM
ejpam-5061	112	6	|v	|v	PROPN
ejpam-5061	112	7	(	(	PUNCT
ejpam-5061	112	8	g)|	g)|	NOUN
ejpam-5061	112	9	.	.	PUNCT
ejpam-5061	113	1	then	then	ADV
ejpam-5061	113	2	v	v	X
ejpam-5061	113	3	(	(	PUNCT
ejpam-5061	113	4	g	g	NOUN
ejpam-5061	113	5	)	)	PUNCT
ejpam-5061	113	6	is	be	AUX
ejpam-5061	113	7	the	the	DET
ejpam-5061	113	8	maximum	maximum	ADJ
ejpam-5061	113	9	αℓh	αℓh	NOUN
ejpam-5061	113	10	-	-	PUNCT
ejpam-5061	113	11	set	set	NOUN
ejpam-5061	113	12	of	of	ADP
ejpam-5061	113	13	g.	g.	PROPN
ejpam-5061	113	14	suppose	suppose	VERB
ejpam-5061	113	15	there	there	PRON
ejpam-5061	113	16	is	be	VERB
ejpam-5061	113	17	a	a	DET
ejpam-5061	113	18	component	component	NOUN
ejpam-5061	113	19	k	k	NOUN
ejpam-5061	113	20	of	of	ADP
ejpam-5061	113	21	g	g	PROPN
ejpam-5061	113	22	which	which	PRON
ejpam-5061	113	23	is	be	AUX
ejpam-5061	113	24	non	non	ADJ
ejpam-5061	113	25	-	-	ADJ
ejpam-5061	113	26	trivial	trivial	ADJ
ejpam-5061	113	27	.	.	PUNCT
ejpam-5061	114	1	if	if	SCONJ
ejpam-5061	114	2	k	k	PROPN
ejpam-5061	114	3	is	be	AUX
ejpam-5061	114	4	complete	complete	ADJ
ejpam-5061	114	5	,	,	PUNCT
ejpam-5061	114	6	then	then	ADV
ejpam-5061	114	7	αℓh(k	αℓh(k	X
ejpam-5061	114	8	)	)	PUNCT
ejpam-5061	114	9	=	=	SYM
ejpam-5061	114	10	1	1	X
ejpam-5061	114	11	.	.	PUNCT
ejpam-5061	114	12	thus	thus	ADV
ejpam-5061	114	13	,	,	PUNCT
ejpam-5061	114	14	αℓh(g	αℓh(g	NOUN
ejpam-5061	114	15	)	)	PUNCT
ejpam-5061	114	16	≤	≤	NOUN
ejpam-5061	114	17	|v	|v	X
ejpam-5061	114	18	(	(	PUNCT
ejpam-5061	114	19	g)|−	g)|−	DET
ejpam-5061	114	20	|v	|v	PROPN
ejpam-5061	114	21	(	(	PUNCT
ejpam-5061	114	22	k)|	k)|	PROPN
ejpam-5061	114	23	≤	≤	PUNCT
ejpam-5061	114	24	|v	|v	X
ejpam-5061	114	25	(	(	PUNCT
ejpam-5061	114	26	g)|−	g)|−	PRON
ejpam-5061	114	27	1	1	NUM
ejpam-5061	114	28	,	,	PUNCT
ejpam-5061	114	29	a	a	DET
ejpam-5061	114	30	contradiction	contradiction	NOUN
ejpam-5061	114	31	.	.	PUNCT
ejpam-5061	115	1	if	if	SCONJ
ejpam-5061	115	2	k	k	PROPN
ejpam-5061	115	3	is	be	AUX
ejpam-5061	115	4	noncomplete	noncomplete	ADJ
ejpam-5061	115	5	,	,	PUNCT
ejpam-5061	115	6	then	then	ADV
ejpam-5061	115	7	αh(k	αh(k	NUM
ejpam-5061	115	8	)	)	PUNCT
ejpam-5061	115	9	≤	≤	NOUN
ejpam-5061	115	10	|v	|v	X
ejpam-5061	115	11	(	(	PUNCT
ejpam-5061	115	12	k)|−1.hence	k)|−1.hence	NOUN
ejpam-5061	115	13	,	,	PUNCT
ejpam-5061	115	14	αh(g	αh(g	NOUN
ejpam-5061	115	15	)	)	PUNCT
ejpam-5061	115	16	≤	≤	NUM
ejpam-5061	115	17	|v	|v	X
ejpam-5061	115	18	(	(	PUNCT
ejpam-5061	115	19	g)|−1	g)|−1	PROPN
ejpam-5061	115	20	,	,	PUNCT
ejpam-5061	115	21	and	and	CCONJ
ejpam-5061	115	22	so	so	ADV
ejpam-5061	115	23	αℓh(g	αℓh(g	NOUN
ejpam-5061	115	24	)	)	PUNCT
ejpam-5061	115	25	≤	≤	NUM
ejpam-5061	115	26	|v	|v	NOUN
ejpam-5061	115	27	(	(	PUNCT
ejpam-5061	115	28	g)|−1	g)|−1	PROPN
ejpam-5061	115	29	by	by	ADP
ejpam-5061	115	30	theorem	theorem	NOUN
ejpam-5061	115	31	3(i	3(i	NUM
ejpam-5061	115	32	)	)	PUNCT
ejpam-5061	115	33	,	,	PUNCT
ejpam-5061	115	34	a	a	DET
ejpam-5061	115	35	contradiction	contradiction	NOUN
ejpam-5061	115	36	.	.	PUNCT
ejpam-5061	116	1	therefore	therefore	ADV
ejpam-5061	116	2	,	,	PUNCT
ejpam-5061	116	3	every	every	DET
ejpam-5061	116	4	component	component	NOUN
ejpam-5061	116	5	of	of	ADP
ejpam-5061	116	6	g	g	PROPN
ejpam-5061	116	7	is	be	AUX
ejpam-5061	116	8	trivial	trivial	ADJ
ejpam-5061	116	9	.	.	PUNCT
ejpam-5061	117	1	conversely	conversely	ADV
ejpam-5061	117	2	,	,	PUNCT
ejpam-5061	117	3	suppose	suppose	VERB
ejpam-5061	117	4	that	that	SCONJ
ejpam-5061	117	5	every	every	DET
ejpam-5061	117	6	component	component	NOUN
ejpam-5061	117	7	of	of	ADP
ejpam-5061	117	8	g	g	PROPN
ejpam-5061	117	9	is	be	AUX
ejpam-5061	117	10	trivial	trivial	ADJ
ejpam-5061	117	11	.	.	PUNCT
ejpam-5061	118	1	let	let	VERB
ejpam-5061	118	2	v	v	X
ejpam-5061	118	3	(	(	PUNCT
ejpam-5061	118	4	g	g	NOUN
ejpam-5061	118	5	)	)	PUNCT
ejpam-5061	118	6	=	=	SYM
ejpam-5061	118	7	{	{	PUNCT
ejpam-5061	118	8	v1	v1	PROPN
ejpam-5061	118	9	,	,	PUNCT
ejpam-5061	118	10	v2	v2	PROPN
ejpam-5061	118	11	,	,	PUNCT
ejpam-5061	118	12	...	...	PUNCT
ejpam-5061	118	13	,	,	PUNCT
ejpam-5061	118	14	vm	vm	NOUN
ejpam-5061	118	15	}	}	PUNCT
ejpam-5061	118	16	.	.	PUNCT
ejpam-5061	119	1	then	then	ADV
ejpam-5061	119	2	⟨{x1}⟩	⟨{x1}⟩	PROPN
ejpam-5061	119	3	,	,	PUNCT
ejpam-5061	119	4	⟨{x2}⟩	⟨{x2}⟩	ADV
ejpam-5061	119	5	,	,	PUNCT
ejpam-5061	119	6	...	...	PUNCT
ejpam-5061	119	7	,	,	PUNCT
ejpam-5061	119	8	⟨{xm}⟩	⟨{xm}⟩	VERB
ejpam-5061	119	9	are	be	AUX
ejpam-5061	119	10	the	the	DET
ejpam-5061	119	11	components	component	NOUN
ejpam-5061	119	12	of	of	ADP
ejpam-5061	119	13	g.	g.	PROPN
ejpam-5061	119	14	thus	thus	ADV
ejpam-5061	119	15	,	,	PUNCT
ejpam-5061	119	16	ng[xi	ng[xi	NOUN
ejpam-5061	119	17	]	]	X
ejpam-5061	119	18	=	=	X
ejpam-5061	119	19	{	{	PUNCT
ejpam-5061	119	20	xi	xi	X
ejpam-5061	119	21	}	}	PUNCT
ejpam-5061	119	22	for	for	ADP
ejpam-5061	119	23	each	each	DET
ejpam-5061	119	24	i	i	PRON
ejpam-5061	119	25	∈	∈	PROPN
ejpam-5061	119	26	{	{	PUNCT
ejpam-5061	119	27	1	1	NUM
ejpam-5061	119	28	,	,	PUNCT
ejpam-5061	119	29	2	2	NUM
ejpam-5061	119	30	,	,	PUNCT
ejpam-5061	119	31	...	...	PUNCT
ejpam-5061	119	32	,	,	PUNCT
ejpam-5061	119	33	m	m	VERB
ejpam-5061	119	34	}	}	PUNCT
ejpam-5061	119	35	,	,	PUNCT
ejpam-5061	119	36	and	and	CCONJ
ejpam-5061	119	37	so	so	ADV
ejpam-5061	119	38	xj	xj	PROPN
ejpam-5061	119	39	∈	∈	PROPN
ejpam-5061	119	40	ng[xj	ng[xj	NOUN
ejpam-5061	119	41	]	]	PUNCT
ejpam-5061	119	42	\	\	PROPN
ejpam-5061	119	43	j−1⋃	j−1⋃	PROPN
ejpam-5061	119	44	k=1	k=1	PROPN
ejpam-5061	119	45	ng[xk	ng[xk	PROPN
ejpam-5061	119	46	]	]	X
ejpam-5061	119	47	∀	∀	PUNCT
ejpam-5061	119	48	j	j	PROPN
ejpam-5061	119	49	∈	∈	PROPN
ejpam-5061	119	50	{	{	PUNCT
ejpam-5061	119	51	2	2	NUM
ejpam-5061	119	52	,	,	PUNCT
ejpam-5061	119	53	...	...	PUNCT
ejpam-5061	119	54	,	,	PUNCT
ejpam-5061	119	55	m	m	VERB
ejpam-5061	119	56	}	}	PUNCT
ejpam-5061	119	57	.	.	PUNCT
ejpam-5061	120	1	that	that	PRON
ejpam-5061	120	2	is	be	AUX
ejpam-5061	120	3	,	,	PUNCT
ejpam-5061	120	4	s	s	PART
ejpam-5061	120	5	=	=	PUNCT
ejpam-5061	120	6	(	(	PUNCT
ejpam-5061	120	7	v1	v1	PROPN
ejpam-5061	120	8	,	,	PUNCT
ejpam-5061	120	9	v2	v2	PROPN
ejpam-5061	120	10	,	,	PUNCT
ejpam-5061	120	11	...	...	PUNCT
ejpam-5061	120	12	,	,	PUNCT
ejpam-5061	120	13	vm	vm	PROPN
ejpam-5061	120	14	)	)	PUNCT
ejpam-5061	120	15	is	be	AUX
ejpam-5061	120	16	a	a	DET
ejpam-5061	120	17	legal	legal	ADJ
ejpam-5061	120	18	sequence	sequence	NOUN
ejpam-5061	120	19	of	of	ADP
ejpam-5061	120	20	g.	g.	PROPN
ejpam-5061	120	21	notice	notice	VERB
ejpam-5061	120	22	that	that	SCONJ
ejpam-5061	120	23	dg(xs	dg(xs	NOUN
ejpam-5061	120	24	,	,	PUNCT
ejpam-5061	120	25	xt	xt	ADJ
ejpam-5061	120	26	)	)	PUNCT
ejpam-5061	120	27	̸=	̸=	NOUN
ejpam-5061	120	28	2	2	NUM
ejpam-5061	120	29	∀	∀	NOUN
ejpam-5061	120	30	s	s	PART
ejpam-5061	120	31	̸=	̸=	PROPN
ejpam-5061	120	32	t	t	PROPN
ejpam-5061	120	33	,	,	PUNCT
ejpam-5061	120	34	where	where	SCONJ
ejpam-5061	120	35	s	s	X
ejpam-5061	120	36	,	,	PUNCT
ejpam-5061	120	37	t	t	PROPN
ejpam-5061	120	38	∈	∈	PROPN
ejpam-5061	120	39	{	{	PUNCT
ejpam-5061	120	40	1	1	NUM
ejpam-5061	120	41	,	,	PUNCT
ejpam-5061	120	42	2	2	NUM
ejpam-5061	120	43	,	,	PUNCT
ejpam-5061	120	44	...	...	PUNCT
ejpam-5061	120	45	,	,	PUNCT
ejpam-5061	120	46	m	m	VERB
ejpam-5061	120	47	}	}	PUNCT
ejpam-5061	120	48	.	.	PUNCT
ejpam-5061	121	1	therefore	therefore	ADV
ejpam-5061	121	2	,	,	PUNCT
ejpam-5061	121	3	s	s	VERB
ejpam-5061	121	4	is	be	AUX
ejpam-5061	121	5	a	a	DET
ejpam-5061	121	6	legal	legal	ADJ
ejpam-5061	121	7	hop	hop	NOUN
ejpam-5061	121	8	independent	independent	ADJ
ejpam-5061	121	9	sequence	sequence	NOUN
ejpam-5061	121	10	of	of	ADP
ejpam-5061	121	11	g.	g.	PROPN
ejpam-5061	121	12	consequently	consequently	ADV
ejpam-5061	121	13	,	,	PUNCT
ejpam-5061	121	14	αℓh(g	αℓh(g	NUM
ejpam-5061	121	15	)	)	PUNCT
ejpam-5061	121	16	=	=	SYM
ejpam-5061	121	17	|v	|v	PROPN
ejpam-5061	121	18	(	(	PUNCT
ejpam-5061	121	19	g)|	g)|	NOUN
ejpam-5061	121	20	.	.	PUNCT
ejpam-5061	122	1	the	the	DET
ejpam-5061	122	2	following	following	ADJ
ejpam-5061	122	3	result	result	NOUN
ejpam-5061	122	4	follows	follow	VERB
ejpam-5061	122	5	from	from	ADP
ejpam-5061	122	6	the	the	DET
ejpam-5061	122	7	above	above	ADJ
ejpam-5061	122	8	theorem	theorem	ADJ
ejpam-5061	122	9	.	.	PROPN
ejpam-5061	122	10	corollary	corollary	ADJ
ejpam-5061	122	11	1	1	NUM
ejpam-5061	122	12	.	.	PUNCT
ejpam-5061	123	1	let	let	VERB
ejpam-5061	123	2	m	m	PRON
ejpam-5061	123	3	≥	≥	NOUN
ejpam-5061	123	4	1	1	NUM
ejpam-5061	123	5	be	be	AUX
ejpam-5061	123	6	any	any	DET
ejpam-5061	123	7	positive	positive	ADJ
ejpam-5061	123	8	integer	integer	NOUN
ejpam-5061	123	9	.	.	PUNCT
ejpam-5061	124	1	then	then	ADV
ejpam-5061	124	2	αℓh(km	αℓh(km	NOUN
ejpam-5061	124	3	)	)	PUNCT
ejpam-5061	124	4	=	=	SYM
ejpam-5061	124	5	m.	m.	NOUN
ejpam-5061	124	6	theorem	theorem	VERB
ejpam-5061	124	7	4	4	NUM
ejpam-5061	124	8	.	.	PUNCT
ejpam-5061	125	1	let	let	VERB
ejpam-5061	125	2	s	s	PRON
ejpam-5061	125	3	and	and	CCONJ
ejpam-5061	125	4	t	t	PROPN
ejpam-5061	125	5	be	be	AUX
ejpam-5061	125	6	positive	positive	ADJ
ejpam-5061	125	7	integers	integer	NOUN
ejpam-5061	125	8	that	that	PRON
ejpam-5061	125	9	satisfy	satisfy	VERB
ejpam-5061	125	10	2	2	NUM
ejpam-5061	125	11	≤	≤	NOUN
ejpam-5061	125	12	s	s	PART
ejpam-5061	125	13	≤	≤	ADJ
ejpam-5061	125	14	t.	t.	NOUN
ejpam-5061	125	15	then	then	ADV
ejpam-5061	125	16	there	there	PRON
ejpam-5061	125	17	exists	exist	VERB
ejpam-5061	125	18	a	a	DET
ejpam-5061	125	19	connected	connected	ADJ
ejpam-5061	125	20	graph	graph	NOUN
ejpam-5061	125	21	k	k	PRON
ejpam-5061	125	22	such	such	ADJ
ejpam-5061	125	23	that	that	SCONJ
ejpam-5061	125	24	αℓh(k	αℓh(k	X
ejpam-5061	125	25	)	)	PUNCT
ejpam-5061	125	26	=	=	SYM
ejpam-5061	125	27	s	s	NOUN
ejpam-5061	125	28	and	and	CCONJ
ejpam-5061	125	29	αh(k	αh(k	NUM
ejpam-5061	125	30	)	)	PUNCT
ejpam-5061	125	31	=	=	SYM
ejpam-5061	126	1	t.	t.	NOUN
ejpam-5061	126	2	proof	proof	NOUN
ejpam-5061	126	3	.	.	PUNCT
ejpam-5061	127	1	supose	supose	VERB
ejpam-5061	127	2	that	that	PRON
ejpam-5061	127	3	s	s	VERB
ejpam-5061	127	4	<	<	X
ejpam-5061	127	5	t.	t.	X
ejpam-5061	127	6	let	let	VERB
ejpam-5061	127	7	q	q	PROPN
ejpam-5061	127	8	=	=	PUNCT
ejpam-5061	127	9	t	t	PROPN
ejpam-5061	127	10	−	−	NOUN
ejpam-5061	127	11	s	s	PART
ejpam-5061	127	12	and	and	CCONJ
ejpam-5061	127	13	consider	consider	VERB
ejpam-5061	127	14	the	the	DET
ejpam-5061	127	15	graph	graph	NOUN
ejpam-5061	127	16	k	k	X
ejpam-5061	127	17	in	in	ADP
ejpam-5061	127	18	figure	figure	NOUN
ejpam-5061	127	19	2	2	NUM
ejpam-5061	127	20	,	,	PUNCT
ejpam-5061	127	21	where	where	SCONJ
ejpam-5061	127	22	⟨{x	⟨{x	PROPN
ejpam-5061	127	23	,	,	PUNCT
ejpam-5061	127	24	ws	ws	NOUN
ejpam-5061	127	25	,	,	PUNCT
ejpam-5061	127	26	u1	u1	NOUN
ejpam-5061	127	27	,	,	PUNCT
ejpam-5061	127	28	u2	u2	NOUN
ejpam-5061	127	29	,	,	PUNCT
ejpam-5061	127	30	...	...	PUNCT
ejpam-5061	127	31	uq}⟩	uq}⟩	PROPN
ejpam-5061	127	32	and	and	CCONJ
ejpam-5061	127	33	⟨{y	⟨{y	PROPN
ejpam-5061	127	34	,	,	PUNCT
ejpam-5061	127	35	ws	ws	NOUN
ejpam-5061	127	36	,	,	PUNCT
ejpam-5061	127	37	u1	u1	NOUN
ejpam-5061	127	38	,	,	PUNCT
ejpam-5061	127	39	u2	u2	PROPN
ejpam-5061	127	40	,	,	PUNCT
ejpam-5061	127	41	...	...	PUNCT
ejpam-5061	127	42	uq}⟩	uq}⟩	PROPN
ejpam-5061	127	43	induced	induce	VERB
ejpam-5061	127	44	a	a	DET
ejpam-5061	127	45	complete	complete	ADJ
ejpam-5061	127	46	graph	graph	NOUN
ejpam-5061	127	47	,	,	PUNCT
ejpam-5061	127	48	respectively	respectively	ADV
ejpam-5061	127	49	.	.	PUNCT
ejpam-5061	128	1	let	let	VERB
ejpam-5061	128	2	l	l	NOUN
ejpam-5061	128	3	=	=	SYM
ejpam-5061	128	4	(	(	PUNCT
ejpam-5061	128	5	w1	w1	NOUN
ejpam-5061	128	6	,	,	PUNCT
ejpam-5061	128	7	w2	w2	NOUN
ejpam-5061	128	8	,	,	PUNCT
ejpam-5061	128	9	...	...	PUNCT
ejpam-5061	128	10	,	,	PUNCT
ejpam-5061	128	11	ws	ws	PROPN
ejpam-5061	128	12	)	)	PUNCT
ejpam-5061	128	13	and	and	CCONJ
ejpam-5061	128	14	l̂0	l̂0	NOUN
ejpam-5061	128	15	=	=	PUNCT
ejpam-5061	128	16	{	{	PUNCT
ejpam-5061	128	17	w1	w1	NOUN
ejpam-5061	128	18	,	,	PUNCT
ejpam-5061	128	19	w2	w2	NOUN
ejpam-5061	128	20	,	,	PUNCT
ejpam-5061	128	21	...	...	PUNCT
ejpam-5061	128	22	,	,	PUNCT
ejpam-5061	128	23	ws	ws	PROPN
ejpam-5061	128	24	,	,	PUNCT
ejpam-5061	128	25	u1	u1	NOUN
ejpam-5061	128	26	,	,	PUNCT
ejpam-5061	128	27	u2	u2	NOUN
ejpam-5061	128	28	,	,	PUNCT
ejpam-5061	128	29	...	...	PUNCT
ejpam-5061	128	30	,	,	PUNCT
ejpam-5061	128	31	uq	uq	NOUN
ejpam-5061	128	32	}	}	PUNCT
ejpam-5061	128	33	.	.	PUNCT
ejpam-5061	129	1	then	then	ADV
ejpam-5061	129	2	l	l	PROPN
ejpam-5061	129	3	and	and	CCONJ
ejpam-5061	129	4	l̂0	l̂0	PROPN
ejpam-5061	129	5	are	be	AUX
ejpam-5061	129	6	maximum	maximum	ADJ
ejpam-5061	129	7	legal	legal	ADJ
ejpam-5061	129	8	hop	hop	NOUN
ejpam-5061	129	9	independent	independent	ADJ
ejpam-5061	129	10	sequence	sequence	NOUN
ejpam-5061	129	11	and	and	CCONJ
ejpam-5061	129	12	maximum	maximum	ADJ
ejpam-5061	129	13	hop	hop	NOUN
ejpam-5061	129	14	independent	independent	ADJ
ejpam-5061	129	15	set	set	NOUN
ejpam-5061	129	16	of	of	ADP
ejpam-5061	129	17	k	k	PROPN
ejpam-5061	129	18	,	,	PUNCT
ejpam-5061	129	19	respectively	respectively	ADV
ejpam-5061	129	20	.	.	PUNCT
ejpam-5061	130	1	therefore	therefore	ADV
ejpam-5061	130	2	,	,	PUNCT
ejpam-5061	130	3	αℓh(k	αℓh(k	PROPN
ejpam-5061	130	4	)	)	PUNCT
ejpam-5061	130	5	=	=	SYM
ejpam-5061	130	6	s	s	NOUN
ejpam-5061	130	7	and	and	CCONJ
ejpam-5061	130	8	αh(k	αh(k	NUM
ejpam-5061	130	9	)	)	PUNCT
ejpam-5061	130	10	=	=	SYM
ejpam-5061	131	1	s+q	s+q	PROPN
ejpam-5061	131	2	=	=	SYM
ejpam-5061	131	3	t	t	PROPN
ejpam-5061	131	4	,	,	PUNCT
ejpam-5061	131	5	and	and	CCONJ
ejpam-5061	131	6	so	so	ADV
ejpam-5061	131	7	αℓh(k	αℓh(k	X
ejpam-5061	131	8	)	)	PUNCT
ejpam-5061	131	9	=	=	SYM
ejpam-5061	131	10	s	s	PART
ejpam-5061	131	11	<	<	X
ejpam-5061	131	12	t	t	NOUN
ejpam-5061	131	13	=	=	SYM
ejpam-5061	131	14	αh(k	αh(k	NUM
ejpam-5061	131	15	)	)	PUNCT
ejpam-5061	131	16	.	.	PUNCT
ejpam-5061	132	1	j.	j.	PROPN
ejpam-5061	132	2	hassan	hassan	PROPN
ejpam-5061	132	3	et	et	PROPN
ejpam-5061	132	4	al	al	PROPN
ejpam-5061	132	5	.	.	PUNCT
ejpam-5061	132	6	/	/	SYM
ejpam-5061	132	7	eur	eur	PROPN
ejpam-5061	132	8	.	.	PUNCT
ejpam-5061	133	1	j.	j.	PROPN
ejpam-5061	133	2	pure	pure	PROPN
ejpam-5061	133	3	appl	appl	PROPN
ejpam-5061	133	4	.	.	PROPN
ejpam-5061	133	5	math	math	PROPN
ejpam-5061	133	6	,	,	PUNCT
ejpam-5061	133	7	17	17	NUM
ejpam-5061	133	8	(	(	PUNCT
ejpam-5061	133	9	2	2	NUM
ejpam-5061	133	10	)	)	PUNCT
ejpam-5061	133	11	(	(	PUNCT
ejpam-5061	133	12	2024	2024	NUM
ejpam-5061	133	13	)	)	PUNCT
ejpam-5061	133	14	,	,	PUNCT
ejpam-5061	133	15	725	725	NUM
ejpam-5061	133	16	-	-	SYM
ejpam-5061	133	17	735	735	NUM
ejpam-5061	133	18	730	730	NUM
ejpam-5061	133	19	.	.	PUNCT
ejpam-5061	133	20	.	.	PUNCT
ejpam-5061	133	21	.	.	PUNCT
ejpam-5061	134	1	w1	w1	NOUN
ejpam-5061	134	2	.	.	PUNCT
ejpam-5061	134	3	.	.	PUNCT
ejpam-5061	134	4	.	.	PUNCT
ejpam-5061	135	1	w2	w2	PROPN
ejpam-5061	135	2	w3	w3	PROPN
ejpam-5061	135	3	ws−1	ws−1	PROPN
ejpam-5061	135	4	x	x	PROPN
ejpam-5061	135	5	u1	u1	PROPN
ejpam-5061	135	6	ws	ws	PROPN
ejpam-5061	135	7	uq	uq	PROPN
ejpam-5061	135	8	u2	u2	PROPN
ejpam-5061	135	9	y	y	PROPN
ejpam-5061	135	10	k	k	PROPN
ejpam-5061	135	11	:	:	PUNCT
ejpam-5061	135	12	figure	figure	NOUN
ejpam-5061	135	13	2	2	NUM
ejpam-5061	135	14	:	:	PUNCT
ejpam-5061	135	15	a	a	DET
ejpam-5061	135	16	graph	graph	NOUN
ejpam-5061	135	17	k′	k′	PROPN
ejpam-5061	135	18	with	with	ADP
ejpam-5061	135	19	αlh(k	αlh(k	PROPN
ejpam-5061	135	20	′	′	NOUN
ejpam-5061	135	21	)	)	PUNCT
ejpam-5061	135	22	<	<	X
ejpam-5061	135	23	αh(k	αh(k	X
ejpam-5061	135	24	′	′	NOUN
ejpam-5061	135	25	)	)	PUNCT
ejpam-5061	135	26	for	for	ADP
ejpam-5061	135	27	s	s	PROPN
ejpam-5061	135	28	=	=	SYM
ejpam-5061	135	29	t	t	PROPN
ejpam-5061	135	30	,	,	PUNCT
ejpam-5061	135	31	consider	consider	VERB
ejpam-5061	135	32	the	the	DET
ejpam-5061	135	33	graph	graph	NOUN
ejpam-5061	135	34	k	k	NOUN
ejpam-5061	135	35	′	′	NUM
ejpam-5061	135	36	in	in	ADP
ejpam-5061	135	37	figure	figure	NOUN
ejpam-5061	135	38	3	3	NUM
ejpam-5061	135	39	.	.	PUNCT
ejpam-5061	136	1	let	let	VERB
ejpam-5061	136	2	q	q	NOUN
ejpam-5061	136	3	=	=	SYM
ejpam-5061	136	4	(	(	PUNCT
ejpam-5061	136	5	a1	a1	PROPN
ejpam-5061	136	6	,	,	PUNCT
ejpam-5061	136	7	a2	a2	PROPN
ejpam-5061	136	8	,	,	PUNCT
ejpam-5061	136	9	...	...	PUNCT
ejpam-5061	136	10	,	,	PUNCT
ejpam-5061	136	11	at	at	ADP
ejpam-5061	136	12	)	)	PUNCT
ejpam-5061	136	13	and	and	CCONJ
ejpam-5061	136	14	q̂	q̂	X
ejpam-5061	136	15	=	=	SYM
ejpam-5061	136	16	{	{	PUNCT
ejpam-5061	136	17	a1	a1	PROPN
ejpam-5061	136	18	,	,	PUNCT
ejpam-5061	136	19	a2	a2	PROPN
ejpam-5061	136	20	,	,	PUNCT
ejpam-5061	136	21	...	...	PUNCT
ejpam-5061	136	22	at	at	ADP
ejpam-5061	136	23	}	}	PUNCT
ejpam-5061	136	24	.	.	PUNCT
ejpam-5061	137	1	then	then	ADV
ejpam-5061	137	2	q	q	X
ejpam-5061	137	3	and	and	CCONJ
ejpam-5061	137	4	q̂	q̂	NUM
ejpam-5061	137	5	are	be	AUX
ejpam-5061	137	6	maximum	maximum	ADJ
ejpam-5061	137	7	legal	legal	ADJ
ejpam-5061	137	8	hop	hop	NOUN
ejpam-5061	137	9	independent	independent	ADJ
ejpam-5061	137	10	sequence	sequence	NOUN
ejpam-5061	137	11	and	and	CCONJ
ejpam-5061	137	12	maximum	maximum	ADJ
ejpam-5061	137	13	hop	hop	NOUN
ejpam-5061	137	14	independent	independent	ADJ
ejpam-5061	137	15	set	set	NOUN
ejpam-5061	137	16	of	of	ADP
ejpam-5061	137	17	k	k	PROPN
ejpam-5061	137	18	′	′	PROPN
ejpam-5061	137	19	,	,	PUNCT
ejpam-5061	137	20	respectively	respectively	ADV
ejpam-5061	137	21	.	.	PUNCT
ejpam-5061	138	1	thus	thus	ADV
ejpam-5061	138	2	,	,	PUNCT
ejpam-5061	138	3	αℓh(k	αℓh(k	PROPN
ejpam-5061	138	4	′	′	NOUN
ejpam-5061	138	5	)	)	PUNCT
ejpam-5061	139	1	=	=	SYM
ejpam-5061	139	2	t	t	NOUN
ejpam-5061	139	3	=	=	SYM
ejpam-5061	139	4	s	s	PART
ejpam-5061	139	5	=	=	SYM
ejpam-5061	139	6	αh(k	αh(k	NOUN
ejpam-5061	139	7	′	′	NOUN
ejpam-5061	139	8	)	)	PUNCT
ejpam-5061	139	9	.	.	PUNCT
ejpam-5061	140	1	a1	a1	NOUN
ejpam-5061	140	2	.	.	PUNCT
ejpam-5061	140	3	.	.	PUNCT
ejpam-5061	140	4	.	.	PUNCT
ejpam-5061	141	1	k	k	NOUN
ejpam-5061	142	1	′	′	NUM
ejpam-5061	142	2	:	:	PUNCT
ejpam-5061	143	1	a2	a2	NOUN
ejpam-5061	143	2	a3	a3	VERB
ejpam-5061	143	3	at−1	at−1	PROPN
ejpam-5061	143	4	at	at	ADP
ejpam-5061	143	5	figure	figure	NOUN
ejpam-5061	143	6	3	3	NUM
ejpam-5061	143	7	:	:	PUNCT
ejpam-5061	143	8	a	a	DET
ejpam-5061	143	9	graph	graph	NOUN
ejpam-5061	143	10	k′	k′	PROPN
ejpam-5061	143	11	with	with	ADP
ejpam-5061	143	12	αlh(k	αlh(k	PROPN
ejpam-5061	143	13	′	′	NOUN
ejpam-5061	143	14	)	)	PUNCT
ejpam-5061	143	15	=	=	SYM
ejpam-5061	143	16	αh(k	αh(k	NUM
ejpam-5061	143	17	′	′	NOUN
ejpam-5061	143	18	)	)	PUNCT
ejpam-5061	143	19	definition	definition	NOUN
ejpam-5061	143	20	2	2	NUM
ejpam-5061	143	21	.	.	PUNCT
ejpam-5061	144	1	let	let	VERB
ejpam-5061	144	2	g	g	NOUN
ejpam-5061	144	3	be	be	AUX
ejpam-5061	144	4	any	any	DET
ejpam-5061	144	5	graph	graph	NOUN
ejpam-5061	144	6	.	.	PUNCT
ejpam-5061	145	1	a	a	DET
ejpam-5061	145	2	sequence	sequence	NOUN
ejpam-5061	145	3	l	l	NOUN
ejpam-5061	145	4	=	=	SYM
ejpam-5061	145	5	(	(	PUNCT
ejpam-5061	145	6	a1	a1	PROPN
ejpam-5061	145	7	,	,	PUNCT
ejpam-5061	145	8	.	.	PUNCT
ejpam-5061	145	9	.	.	PUNCT
ejpam-5061	146	1	.	.	PUNCT
ejpam-5061	147	1	,	,	PUNCT
ejpam-5061	147	2	an	an	PRON
ejpam-5061	147	3	)	)	PUNCT
ejpam-5061	147	4	is	be	AUX
ejpam-5061	147	5	called	call	VERB
ejpam-5061	147	6	a	a	DET
ejpam-5061	147	7	clique	clique	ADJ
ejpam-5061	147	8	legal	legal	ADJ
ejpam-5061	147	9	sequence	sequence	NOUN
ejpam-5061	147	10	if	if	SCONJ
ejpam-5061	147	11	n	n	NOUN
ejpam-5061	147	12	=	=	SYM
ejpam-5061	147	13	1	1	NUM
ejpam-5061	147	14	or	or	CCONJ
ejpam-5061	147	15	l	l	NOUN
ejpam-5061	147	16	is	be	AUX
ejpam-5061	147	17	a	a	DET
ejpam-5061	147	18	legal	legal	ADJ
ejpam-5061	147	19	sequence	sequence	NOUN
ejpam-5061	147	20	and	and	CCONJ
ejpam-5061	147	21	its	its	PRON
ejpam-5061	147	22	corresponding	corresponding	ADJ
ejpam-5061	147	23	set	set	NOUN
ejpam-5061	147	24	l̂	l̂	X
ejpam-5061	147	25	induces	induce	VERB
ejpam-5061	147	26	a	a	DET
ejpam-5061	147	27	complete	complete	ADJ
ejpam-5061	147	28	graph	graph	NOUN
ejpam-5061	147	29	.	.	PUNCT
ejpam-5061	148	1	the	the	DET
ejpam-5061	148	2	maximum	maximum	ADJ
ejpam-5061	148	3	length	length	NOUN
ejpam-5061	148	4	of	of	ADP
ejpam-5061	148	5	a	a	DET
ejpam-5061	148	6	clique	clique	ADJ
ejpam-5061	148	7	legal	legal	ADJ
ejpam-5061	148	8	sequence	sequence	NOUN
ejpam-5061	148	9	in	in	ADP
ejpam-5061	148	10	g	g	NOUN
ejpam-5061	148	11	,	,	PUNCT
ejpam-5061	148	12	denoted	denote	VERB
ejpam-5061	148	13	by	by	ADP
ejpam-5061	148	14	αcℓh(g	αcℓh(g	NOUN
ejpam-5061	148	15	)	)	PUNCT
ejpam-5061	148	16	,	,	PUNCT
ejpam-5061	148	17	is	be	AUX
ejpam-5061	148	18	called	call	VERB
ejpam-5061	148	19	the	the	DET
ejpam-5061	148	20	clique	clique	ADJ
ejpam-5061	148	21	legal	legal	ADJ
ejpam-5061	148	22	number	number	NOUN
ejpam-5061	148	23	of	of	ADP
ejpam-5061	148	24	g.	g.	PROPN
ejpam-5061	148	25	moreover	moreover	ADV
ejpam-5061	148	26	,	,	PUNCT
ejpam-5061	148	27	we	we	PRON
ejpam-5061	148	28	call	call	VERB
ejpam-5061	148	29	l̂	l̂	VERB
ejpam-5061	148	30	a	a	DET
ejpam-5061	148	31	clique	clique	ADJ
ejpam-5061	148	32	legal	legal	ADJ
ejpam-5061	148	33	set	set	NOUN
ejpam-5061	148	34	of	of	ADP
ejpam-5061	148	35	g.	g.	PROPN
ejpam-5061	148	36	definition	definition	NOUN
ejpam-5061	148	37	3	3	X
ejpam-5061	148	38	.	.	PUNCT
ejpam-5061	149	1	let	let	VERB
ejpam-5061	149	2	g	g	NOUN
ejpam-5061	149	3	be	be	AUX
ejpam-5061	149	4	any	any	DET
ejpam-5061	149	5	graph	graph	NOUN
ejpam-5061	149	6	.	.	PUNCT
ejpam-5061	150	1	a	a	DET
ejpam-5061	150	2	clique	clique	ADJ
ejpam-5061	150	3	legal	legal	ADJ
ejpam-5061	150	4	sequence	sequence	NOUN
ejpam-5061	150	5	l	l	NOUN
ejpam-5061	150	6	is	be	AUX
ejpam-5061	150	7	called	call	VERB
ejpam-5061	150	8	a	a	DET
ejpam-5061	150	9	clique	clique	ADJ
ejpam-5061	150	10	legal	legal	ADJ
ejpam-5061	150	11	dominating	dominating	NOUN
ejpam-5061	150	12	sequence	sequence	NOUN
ejpam-5061	150	13	or	or	CCONJ
ejpam-5061	150	14	a	a	DET
ejpam-5061	150	15	clique	clique	NOUN
ejpam-5061	150	16	grundy	grundy	PROPN
ejpam-5061	150	17	dominating	dominating	NOUN
ejpam-5061	150	18	sequence	sequence	NOUN
ejpam-5061	150	19	if	if	SCONJ
ejpam-5061	150	20	its	its	PRON
ejpam-5061	150	21	corresponding	corresponding	ADJ
ejpam-5061	150	22	set	set	NOUN
ejpam-5061	150	23	l̂	l̂	VERB
ejpam-5061	150	24	is	be	AUX
ejpam-5061	150	25	a	a	DET
ejpam-5061	150	26	dominating	dominating	NOUN
ejpam-5061	150	27	set	set	NOUN
ejpam-5061	150	28	of	of	ADP
ejpam-5061	150	29	g.	g.	PROPN
ejpam-5061	150	30	the	the	DET
ejpam-5061	150	31	maximum	maximum	ADJ
ejpam-5061	150	32	length	length	NOUN
ejpam-5061	150	33	of	of	ADP
ejpam-5061	150	34	a	a	DET
ejpam-5061	150	35	clique	clique	NOUN
ejpam-5061	150	36	grundy	grundy	PROPN
ejpam-5061	150	37	dominating	dominating	NOUN
ejpam-5061	150	38	sequence	sequence	NOUN
ejpam-5061	150	39	in	in	ADP
ejpam-5061	150	40	g	g	NOUN
ejpam-5061	150	41	,	,	PUNCT
ejpam-5061	150	42	denoted	denote	VERB
ejpam-5061	150	43	by	by	ADP
ejpam-5061	150	44	γcℓgr(g	γcℓgr(g	PROPN
ejpam-5061	150	45	)	)	PUNCT
ejpam-5061	150	46	,	,	PUNCT
ejpam-5061	150	47	is	be	AUX
ejpam-5061	150	48	called	call	VERB
ejpam-5061	150	49	the	the	DET
ejpam-5061	150	50	clique	clique	NOUN
ejpam-5061	150	51	grundy	grundy	PROPN
ejpam-5061	150	52	domination	domination	NOUN
ejpam-5061	150	53	number	number	NOUN
ejpam-5061	150	54	of	of	ADP
ejpam-5061	150	55	g.	g.	PROPN
ejpam-5061	150	56	moreover	moreover	ADV
ejpam-5061	150	57	,	,	PUNCT
ejpam-5061	150	58	a	a	DET
ejpam-5061	150	59	clique	clique	ADJ
ejpam-5061	150	60	legal	legal	ADJ
ejpam-5061	150	61	sequence	sequence	NOUN
ejpam-5061	150	62	l	l	NOUN
ejpam-5061	150	63	of	of	ADP
ejpam-5061	150	64	g	g	PROPN
ejpam-5061	150	65	is	be	AUX
ejpam-5061	150	66	called	call	VERB
ejpam-5061	150	67	a	a	DET
ejpam-5061	150	68	clique	clique	ADJ
ejpam-5061	150	69	legal	legal	ADJ
ejpam-5061	150	70	non	non	ADJ
ejpam-5061	150	71	-	-	ADJ
ejpam-5061	150	72	dominating	dominating	ADJ
ejpam-5061	150	73	sequence	sequence	NOUN
ejpam-5061	150	74	if	if	SCONJ
ejpam-5061	150	75	l̂	l̂	PRON
ejpam-5061	150	76	is	be	AUX
ejpam-5061	150	77	not	not	PART
ejpam-5061	150	78	a	a	DET
ejpam-5061	150	79	dominating	dominating	NOUN
ejpam-5061	150	80	set	set	NOUN
ejpam-5061	150	81	of	of	ADP
ejpam-5061	150	82	g.	g.	PROPN
ejpam-5061	150	83	j.	j.	PROPN
ejpam-5061	150	84	hassan	hassan	PROPN
ejpam-5061	150	85	et	et	PROPN
ejpam-5061	150	86	al	al	PROPN
ejpam-5061	150	87	.	.	PUNCT
ejpam-5061	150	88	/	/	SYM
ejpam-5061	150	89	eur	eur	PROPN
ejpam-5061	150	90	.	.	PUNCT
ejpam-5061	151	1	j.	j.	PROPN
ejpam-5061	151	2	pure	pure	PROPN
ejpam-5061	151	3	appl	appl	PROPN
ejpam-5061	151	4	.	.	PROPN
ejpam-5061	151	5	math	math	PROPN
ejpam-5061	151	6	,	,	PUNCT
ejpam-5061	151	7	17	17	NUM
ejpam-5061	151	8	(	(	PUNCT
ejpam-5061	151	9	2	2	NUM
ejpam-5061	151	10	)	)	PUNCT
ejpam-5061	151	11	(	(	PUNCT
ejpam-5061	151	12	2024	2024	NUM
ejpam-5061	151	13	)	)	PUNCT
ejpam-5061	151	14	,	,	PUNCT
ejpam-5061	151	15	725	725	NUM
ejpam-5061	151	16	-	-	SYM
ejpam-5061	151	17	735	735	NUM
ejpam-5061	151	18	731	731	NUM
ejpam-5061	151	19	theorem	theorem	NOUN
ejpam-5061	151	20	5	5	NUM
ejpam-5061	151	21	.	.	PUNCT
ejpam-5061	152	1	[	[	X
ejpam-5061	152	2	8	8	NUM
ejpam-5061	152	3	]	]	PUNCT
ejpam-5061	152	4	let	let	VERB
ejpam-5061	152	5	g	g	NOUN
ejpam-5061	152	6	and	and	CCONJ
ejpam-5061	152	7	h	h	PROPN
ejpam-5061	152	8	be	be	AUX
ejpam-5061	152	9	graphs	graph	NOUN
ejpam-5061	152	10	.	.	PUNCT
ejpam-5061	153	1	then	then	ADV
ejpam-5061	153	2	s	s	VERB
ejpam-5061	153	3	is	be	AUX
ejpam-5061	153	4	a	a	DET
ejpam-5061	153	5	non	non	ADJ
ejpam-5061	153	6	-	-	ADJ
ejpam-5061	153	7	empty	empty	ADJ
ejpam-5061	153	8	hop	hop	NOUN
ejpam-5061	153	9	independent	independent	ADJ
ejpam-5061	153	10	set	set	NOUN
ejpam-5061	153	11	of	of	ADP
ejpam-5061	153	12	g+h	g+h	PROPN
ejpam-5061	153	13	if	if	SCONJ
ejpam-5061	153	14	and	and	CCONJ
ejpam-5061	153	15	only	only	ADV
ejpam-5061	153	16	if	if	SCONJ
ejpam-5061	153	17	one	one	NUM
ejpam-5061	153	18	of	of	ADP
ejpam-5061	153	19	the	the	DET
ejpam-5061	153	20	following	following	ADJ
ejpam-5061	153	21	statements	statement	NOUN
ejpam-5061	153	22	holds	hold	VERB
ejpam-5061	153	23	:	:	PUNCT
ejpam-5061	153	24	(	(	PUNCT
ejpam-5061	153	25	i	i	NOUN
ejpam-5061	153	26	)	)	PUNCT
ejpam-5061	153	27	s	s	PART
ejpam-5061	153	28	∩	∩	ADJ
ejpam-5061	153	29	v	v	ADJ
ejpam-5061	153	30	(	(	PUNCT
ejpam-5061	153	31	h	h	NOUN
ejpam-5061	153	32	)	)	PUNCT
ejpam-5061	153	33	=	=	NOUN
ejpam-5061	153	34	∅	∅	NOUN
ejpam-5061	153	35	and	and	CCONJ
ejpam-5061	153	36	s	s	X
ejpam-5061	153	37	∩	∩	ADJ
ejpam-5061	153	38	v	v	ADJ
ejpam-5061	153	39	(	(	PUNCT
ejpam-5061	153	40	g	g	NOUN
ejpam-5061	153	41	)	)	PUNCT
ejpam-5061	153	42	is	be	AUX
ejpam-5061	153	43	a	a	DET
ejpam-5061	153	44	clique	clique	NOUN
ejpam-5061	153	45	in	in	ADP
ejpam-5061	153	46	g.	g.	PROPN
ejpam-5061	153	47	(	(	PUNCT
ejpam-5061	153	48	ii	ii	PROPN
ejpam-5061	153	49	)	)	PUNCT
ejpam-5061	153	50	s	s	PART
ejpam-5061	153	51	∩	∩	ADJ
ejpam-5061	153	52	v	v	X
ejpam-5061	153	53	(	(	PUNCT
ejpam-5061	153	54	g	g	NOUN
ejpam-5061	153	55	)	)	PUNCT
ejpam-5061	153	56	=	=	NOUN
ejpam-5061	153	57	∅	∅	NOUN
ejpam-5061	153	58	and	and	CCONJ
ejpam-5061	153	59	s	s	X
ejpam-5061	153	60	∩	∩	ADJ
ejpam-5061	153	61	v	v	ADJ
ejpam-5061	153	62	(	(	PUNCT
ejpam-5061	153	63	h	h	NOUN
ejpam-5061	153	64	)	)	PUNCT
ejpam-5061	153	65	is	be	AUX
ejpam-5061	153	66	a	a	DET
ejpam-5061	153	67	clique	clique	NOUN
ejpam-5061	153	68	in	in	ADP
ejpam-5061	153	69	h.	h.	PROPN
ejpam-5061	153	70	(	(	PUNCT
ejpam-5061	153	71	iii	iii	NOUN
ejpam-5061	153	72	)	)	PUNCT
ejpam-5061	153	73	s	s	PART
ejpam-5061	153	74	∩	∩	ADJ
ejpam-5061	153	75	v	v	X
ejpam-5061	153	76	(	(	PUNCT
ejpam-5061	153	77	g	g	NOUN
ejpam-5061	153	78	)	)	PUNCT
ejpam-5061	153	79	and	and	CCONJ
ejpam-5061	153	80	s	s	VERB
ejpam-5061	153	81	∩	∩	ADJ
ejpam-5061	153	82	v	v	ADJ
ejpam-5061	153	83	(	(	PUNCT
ejpam-5061	153	84	g	g	NOUN
ejpam-5061	153	85	)	)	PUNCT
ejpam-5061	153	86	are	be	AUX
ejpam-5061	153	87	clique	clique	ADJ
ejpam-5061	153	88	in	in	ADP
ejpam-5061	153	89	g	g	PROPN
ejpam-5061	153	90	and	and	CCONJ
ejpam-5061	153	91	h	h	NOUN
ejpam-5061	153	92	,	,	PUNCT
ejpam-5061	153	93	repectively	repectively	NOUN
ejpam-5061	153	94	.	.	PUNCT
ejpam-5061	154	1	theorem	theorem	VERB
ejpam-5061	154	2	6	6	NUM
ejpam-5061	154	3	.	.	PUNCT
ejpam-5061	155	1	[	[	X
ejpam-5061	155	2	6	6	NUM
ejpam-5061	155	3	]	]	PUNCT
ejpam-5061	155	4	let	let	VERB
ejpam-5061	155	5	g	g	NOUN
ejpam-5061	155	6	and	and	CCONJ
ejpam-5061	155	7	h	h	NOUN
ejpam-5061	155	8	be	be	VERB
ejpam-5061	155	9	two	two	NUM
ejpam-5061	155	10	non	non	ADJ
ejpam-5061	155	11	-	-	ADJ
ejpam-5061	155	12	complete	complete	ADJ
ejpam-5061	155	13	graphs	graph	NOUN
ejpam-5061	155	14	.	.	PUNCT
ejpam-5061	156	1	a	a	DET
ejpam-5061	156	2	sequence	sequence	NOUN
ejpam-5061	156	3	d	d	NOUN
ejpam-5061	156	4	of	of	ADP
ejpam-5061	156	5	distinct	distinct	ADJ
ejpam-5061	156	6	verices	verice	NOUN
ejpam-5061	156	7	of	of	ADP
ejpam-5061	156	8	g	g	PROPN
ejpam-5061	156	9	+	+	CCONJ
ejpam-5061	156	10	h	h	NOUN
ejpam-5061	156	11	is	be	AUX
ejpam-5061	156	12	a	a	DET
ejpam-5061	156	13	grundy	grundy	PROPN
ejpam-5061	156	14	dominating	dominating	NOUN
ejpam-5061	156	15	sequence	sequence	NOUN
ejpam-5061	156	16	in	in	ADP
ejpam-5061	156	17	g	g	PROPN
ejpam-5061	157	1	+	+	NOUN
ejpam-5061	157	2	h	h	NOUN
ejpam-5061	157	3	if	if	SCONJ
ejpam-5061	157	4	and	and	CCONJ
ejpam-5061	157	5	only	only	ADV
ejpam-5061	157	6	if	if	SCONJ
ejpam-5061	157	7	one	one	NUM
ejpam-5061	157	8	of	of	ADP
ejpam-5061	157	9	the	the	DET
ejpam-5061	157	10	following	follow	VERB
ejpam-5061	157	11	conditions	condition	NOUN
ejpam-5061	157	12	holds	hold	VERB
ejpam-5061	157	13	:	:	PUNCT
ejpam-5061	157	14	(	(	PUNCT
ejpam-5061	157	15	i	i	NOUN
ejpam-5061	157	16	)	)	PUNCT
ejpam-5061	158	1	d	d	PRON
ejpam-5061	158	2	is	be	AUX
ejpam-5061	158	3	a	a	DET
ejpam-5061	158	4	grundy	grundy	PROPN
ejpam-5061	158	5	dominating	dominating	NOUN
ejpam-5061	158	6	sequence	sequence	NOUN
ejpam-5061	158	7	of	of	ADP
ejpam-5061	158	8	g.	g.	PROPN
ejpam-5061	158	9	(	(	PUNCT
ejpam-5061	158	10	ii	ii	PROPN
ejpam-5061	158	11	)	)	PUNCT
ejpam-5061	158	12	d	d	NOUN
ejpam-5061	158	13	is	be	AUX
ejpam-5061	158	14	a	a	DET
ejpam-5061	158	15	grundy	grundy	PROPN
ejpam-5061	158	16	dominating	dominating	NOUN
ejpam-5061	158	17	sequence	sequence	NOUN
ejpam-5061	158	18	of	of	ADP
ejpam-5061	158	19	h.	h.	PROPN
ejpam-5061	158	20	(	(	PUNCT
ejpam-5061	158	21	iii	iii	NOUN
ejpam-5061	158	22	)	)	PUNCT
ejpam-5061	158	23	d	d	NOUN
ejpam-5061	158	24	=	=	SYM
ejpam-5061	158	25	dg	dg	PROPN
ejpam-5061	158	26	⊕	⊕	PROPN
ejpam-5061	158	27	(	(	PUNCT
ejpam-5061	158	28	w	w	NOUN
ejpam-5061	158	29	)	)	PUNCT
ejpam-5061	158	30	for	for	ADP
ejpam-5061	158	31	some	some	DET
ejpam-5061	158	32	non	non	ADJ
ejpam-5061	158	33	-	-	ADJ
ejpam-5061	158	34	dominating	dominating	ADJ
ejpam-5061	158	35	legal	legal	ADJ
ejpam-5061	158	36	closed	close	VERB
ejpam-5061	158	37	neighborhood	neighborhood	NOUN
ejpam-5061	158	38	sequence	sequence	NOUN
ejpam-5061	158	39	dg	dg	NOUN
ejpam-5061	158	40	of	of	ADP
ejpam-5061	158	41	g	g	PROPN
ejpam-5061	158	42	and	and	CCONJ
ejpam-5061	158	43	w	w	PROPN
ejpam-5061	158	44	∈	∈	PROPN
ejpam-5061	158	45	v	v	ADP
ejpam-5061	158	46	(	(	PUNCT
ejpam-5061	158	47	h	h	NOUN
ejpam-5061	158	48	)	)	PUNCT
ejpam-5061	158	49	.	.	PUNCT
ejpam-5061	159	1	(	(	PUNCT
ejpam-5061	159	2	iv	iv	X
ejpam-5061	159	3	)	)	PUNCT
ejpam-5061	159	4	d	d	NOUN
ejpam-5061	159	5	=	=	SYM
ejpam-5061	159	6	dh	dh	PROPN
ejpam-5061	159	7	⊕	⊕	PROPN
ejpam-5061	159	8	(	(	PUNCT
ejpam-5061	159	9	v	v	NOUN
ejpam-5061	159	10	)	)	PUNCT
ejpam-5061	159	11	for	for	ADP
ejpam-5061	159	12	some	some	DET
ejpam-5061	159	13	non	non	ADJ
ejpam-5061	159	14	-	-	ADJ
ejpam-5061	159	15	dominating	dominating	ADJ
ejpam-5061	159	16	legal	legal	ADJ
ejpam-5061	159	17	closed	close	VERB
ejpam-5061	159	18	neighborhood	neighborhood	NOUN
ejpam-5061	159	19	sequence	sequence	NOUN
ejpam-5061	159	20	dh	dh	NOUN
ejpam-5061	159	21	of	of	ADP
ejpam-5061	159	22	h	h	NOUN
ejpam-5061	159	23	and	and	CCONJ
ejpam-5061	159	24	v	v	ADP
ejpam-5061	159	25	∈	∈	PROPN
ejpam-5061	159	26	v	v	NOUN
ejpam-5061	159	27	(	(	PUNCT
ejpam-5061	159	28	g	g	NOUN
ejpam-5061	159	29	)	)	PUNCT
ejpam-5061	159	30	.	.	PUNCT
ejpam-5061	160	1	theorem	theorem	ADJ
ejpam-5061	160	2	7	7	NUM
ejpam-5061	160	3	.	.	PUNCT
ejpam-5061	161	1	let	let	VERB
ejpam-5061	161	2	h	h	NOUN
ejpam-5061	161	3	and	and	CCONJ
ejpam-5061	161	4	k	k	PROPN
ejpam-5061	161	5	be	be	AUX
ejpam-5061	161	6	two	two	NUM
ejpam-5061	161	7	non	non	ADJ
ejpam-5061	161	8	-	-	ADJ
ejpam-5061	161	9	complete	complete	ADJ
ejpam-5061	161	10	graphs	graph	NOUN
ejpam-5061	161	11	.	.	PUNCT
ejpam-5061	162	1	a	a	DET
ejpam-5061	162	2	sequence	sequence	NOUN
ejpam-5061	162	3	l	l	NOUN
ejpam-5061	162	4	of	of	ADP
ejpam-5061	162	5	distinct	distinct	ADJ
ejpam-5061	162	6	vertices	vertex	NOUN
ejpam-5061	162	7	of	of	ADP
ejpam-5061	162	8	h	h	NOUN
ejpam-5061	163	1	+	+	NOUN
ejpam-5061	163	2	k	k	PROPN
ejpam-5061	163	3	is	be	AUX
ejpam-5061	163	4	a	a	DET
ejpam-5061	163	5	legal	legal	ADJ
ejpam-5061	163	6	hop	hop	NOUN
ejpam-5061	163	7	independent	independent	ADJ
ejpam-5061	163	8	sequence	sequence	NOUN
ejpam-5061	163	9	in	in	ADP
ejpam-5061	163	10	h	h	PROPN
ejpam-5061	164	1	+	+	PROPN
ejpam-5061	164	2	k	k	X
ejpam-5061	164	3	if	if	SCONJ
ejpam-5061	164	4	and	and	CCONJ
ejpam-5061	164	5	only	only	ADV
ejpam-5061	164	6	if	if	SCONJ
ejpam-5061	164	7	one	one	NUM
ejpam-5061	164	8	of	of	ADP
ejpam-5061	164	9	the	the	DET
ejpam-5061	164	10	following	follow	VERB
ejpam-5061	164	11	conditions	condition	NOUN
ejpam-5061	164	12	holds	hold	VERB
ejpam-5061	164	13	:	:	PUNCT
ejpam-5061	164	14	(	(	PUNCT
ejpam-5061	164	15	i	i	NOUN
ejpam-5061	164	16	)	)	PUNCT
ejpam-5061	164	17	l	l	NOUN
ejpam-5061	164	18	is	be	AUX
ejpam-5061	164	19	a	a	DET
ejpam-5061	164	20	clique	clique	ADJ
ejpam-5061	164	21	legal	legal	ADJ
ejpam-5061	164	22	sequence	sequence	NOUN
ejpam-5061	164	23	in	in	ADP
ejpam-5061	164	24	h	h	PROPN
ejpam-5061	164	25	(	(	PUNCT
ejpam-5061	164	26	ii	ii	NOUN
ejpam-5061	164	27	)	)	PUNCT
ejpam-5061	164	28	l	l	NOUN
ejpam-5061	164	29	is	be	AUX
ejpam-5061	164	30	a	a	DET
ejpam-5061	164	31	clique	clique	ADJ
ejpam-5061	164	32	legal	legal	ADJ
ejpam-5061	164	33	sequence	sequence	NOUN
ejpam-5061	164	34	in	in	ADP
ejpam-5061	164	35	k	k	PROPN
ejpam-5061	164	36	(	(	PUNCT
ejpam-5061	164	37	iii	iii	NOUN
ejpam-5061	164	38	)	)	PUNCT
ejpam-5061	164	39	l	l	NOUN
ejpam-5061	165	1	=	=	PUNCT
ejpam-5061	165	2	lh	lh	PROPN
ejpam-5061	165	3	⊕	⊕	PROPN
ejpam-5061	165	4	(	(	PUNCT
ejpam-5061	165	5	a	a	X
ejpam-5061	165	6	)	)	PUNCT
ejpam-5061	165	7	,	,	PUNCT
ejpam-5061	165	8	where	where	SCONJ
ejpam-5061	165	9	lh	lh	PROPN
ejpam-5061	165	10	is	be	AUX
ejpam-5061	165	11	a	a	DET
ejpam-5061	165	12	clique	clique	ADJ
ejpam-5061	165	13	legal	legal	ADJ
ejpam-5061	165	14	non	non	ADJ
ejpam-5061	165	15	-	-	ADJ
ejpam-5061	165	16	dominating	dominating	ADJ
ejpam-5061	165	17	sequence	sequence	NOUN
ejpam-5061	165	18	in	in	ADP
ejpam-5061	165	19	h	h	NOUN
ejpam-5061	165	20	and	and	CCONJ
ejpam-5061	165	21	a	a	DET
ejpam-5061	165	22	∈	∈	NOUN
ejpam-5061	165	23	v	v	NOUN
ejpam-5061	165	24	(	(	PUNCT
ejpam-5061	165	25	k	k	NOUN
ejpam-5061	165	26	)	)	PUNCT
ejpam-5061	165	27	.	.	PUNCT
ejpam-5061	166	1	(	(	PUNCT
ejpam-5061	166	2	iv	iv	X
ejpam-5061	166	3	)	)	PUNCT
ejpam-5061	166	4	l	l	NOUN
ejpam-5061	166	5	=	=	PUNCT
ejpam-5061	166	6	lk	lk	PROPN
ejpam-5061	166	7	⊕	⊕	PROPN
ejpam-5061	166	8	(	(	PUNCT
ejpam-5061	166	9	b	b	NOUN
ejpam-5061	166	10	)	)	PUNCT
ejpam-5061	166	11	,	,	PUNCT
ejpam-5061	166	12	where	where	SCONJ
ejpam-5061	166	13	lk	lk	PROPN
ejpam-5061	166	14	is	be	AUX
ejpam-5061	166	15	a	a	DET
ejpam-5061	166	16	clique	clique	ADJ
ejpam-5061	166	17	legal	legal	ADJ
ejpam-5061	166	18	non	non	ADJ
ejpam-5061	166	19	-	-	ADJ
ejpam-5061	166	20	dominating	dominating	ADJ
ejpam-5061	166	21	sequence	sequence	NOUN
ejpam-5061	166	22	in	in	ADP
ejpam-5061	166	23	k	k	PROPN
ejpam-5061	166	24	and	and	CCONJ
ejpam-5061	166	25	b	b	PROPN
ejpam-5061	166	26	∈	∈	PROPN
ejpam-5061	166	27	v	v	ADP
ejpam-5061	166	28	(	(	PUNCT
ejpam-5061	166	29	h	h	NOUN
ejpam-5061	166	30	)	)	PUNCT
ejpam-5061	166	31	.	.	PUNCT
ejpam-5061	167	1	proof	proof	NOUN
ejpam-5061	167	2	.	.	PUNCT
ejpam-5061	168	1	suppose	suppose	VERB
ejpam-5061	168	2	that	that	SCONJ
ejpam-5061	168	3	l	l	NOUN
ejpam-5061	168	4	is	be	AUX
ejpam-5061	168	5	a	a	DET
ejpam-5061	168	6	legal	legal	ADJ
ejpam-5061	168	7	hop	hop	NOUN
ejpam-5061	168	8	independent	independent	ADJ
ejpam-5061	168	9	sequence	sequence	NOUN
ejpam-5061	168	10	of	of	ADP
ejpam-5061	168	11	h	h	PROPN
ejpam-5061	169	1	+	+	CCONJ
ejpam-5061	169	2	k.	k.	PROPN
ejpam-5061	169	3	assume	assume	VERB
ejpam-5061	169	4	that	that	SCONJ
ejpam-5061	169	5	l̂	l̂	VERB
ejpam-5061	169	6	⊆	⊆	NUM
ejpam-5061	169	7	v	v	X
ejpam-5061	169	8	(	(	PUNCT
ejpam-5061	169	9	h	h	NOUN
ejpam-5061	169	10	)	)	PUNCT
ejpam-5061	169	11	.	.	PUNCT
ejpam-5061	170	1	then	then	ADV
ejpam-5061	170	2	l̂	l̂	PROPN
ejpam-5061	170	3	is	be	AUX
ejpam-5061	170	4	a	a	DET
ejpam-5061	170	5	clique	clique	NOUN
ejpam-5061	170	6	in	in	ADP
ejpam-5061	170	7	h	h	NOUN
ejpam-5061	170	8	by	by	ADP
ejpam-5061	170	9	theorem	theorem	NOUN
ejpam-5061	170	10	5	5	NUM
ejpam-5061	170	11	.	.	PUNCT
ejpam-5061	170	12	by	by	ADP
ejpam-5061	170	13	theorem	theorem	NOUN
ejpam-5061	170	14	6	6	NUM
ejpam-5061	170	15	,	,	PUNCT
ejpam-5061	170	16	l	l	NOUN
ejpam-5061	170	17	is	be	AUX
ejpam-5061	170	18	a	a	DET
ejpam-5061	170	19	legal	legal	ADJ
ejpam-5061	170	20	sequence	sequence	NOUN
ejpam-5061	170	21	in	in	ADP
ejpam-5061	170	22	h.	h.	PROPN
ejpam-5061	170	23	thus	thus	ADV
ejpam-5061	170	24	,	,	PUNCT
ejpam-5061	170	25	l	l	NOUN
ejpam-5061	170	26	is	be	AUX
ejpam-5061	170	27	a	a	DET
ejpam-5061	170	28	clique	clique	ADJ
ejpam-5061	170	29	legal	legal	ADJ
ejpam-5061	170	30	sequence	sequence	NOUN
ejpam-5061	170	31	in	in	ADP
ejpam-5061	170	32	h	h	NOUN
ejpam-5061	170	33	and	and	CCONJ
ejpam-5061	170	34	so	so	ADV
ejpam-5061	170	35	(	(	PUNCT
ejpam-5061	170	36	i	i	NOUN
ejpam-5061	170	37	)	)	PUNCT
ejpam-5061	170	38	holds	hold	VERB
ejpam-5061	170	39	.	.	PUNCT
ejpam-5061	171	1	similarly	similarly	ADV
ejpam-5061	171	2	,	,	PUNCT
ejpam-5061	171	3	if	if	SCONJ
ejpam-5061	171	4	l̂	l̂	NUM
ejpam-5061	171	5	⊆	⊆	NUM
ejpam-5061	171	6	v	v	NOUN
ejpam-5061	171	7	(	(	PUNCT
ejpam-5061	171	8	k	k	NOUN
ejpam-5061	171	9	)	)	PUNCT
ejpam-5061	171	10	,	,	PUNCT
ejpam-5061	171	11	then	then	ADV
ejpam-5061	171	12	l	l	NOUN
ejpam-5061	171	13	is	be	AUX
ejpam-5061	171	14	a	a	DET
ejpam-5061	171	15	clique	clique	ADJ
ejpam-5061	171	16	legal	legal	ADJ
ejpam-5061	171	17	sequence	sequence	NOUN
ejpam-5061	171	18	in	in	ADP
ejpam-5061	171	19	k.	k.	PROPN
ejpam-5061	171	20	that	that	PRON
ejpam-5061	171	21	is	be	AUX
ejpam-5061	171	22	,	,	PUNCT
ejpam-5061	171	23	(	(	PUNCT
ejpam-5061	171	24	ii	ii	NOUN
ejpam-5061	171	25	)	)	PUNCT
ejpam-5061	171	26	holds	hold	VERB
ejpam-5061	171	27	.	.	PUNCT
ejpam-5061	172	1	now	now	ADV
ejpam-5061	172	2	,	,	PUNCT
ejpam-5061	172	3	let	let	VERB
ejpam-5061	172	4	lh	lh	PROPN
ejpam-5061	172	5	and	and	CCONJ
ejpam-5061	172	6	lk	lk	PROPN
ejpam-5061	172	7	be	be	AUX
ejpam-5061	172	8	subsequences	subsequence	NOUN
ejpam-5061	172	9	of	of	ADP
ejpam-5061	172	10	l	l	NOUN
ejpam-5061	172	11	such	such	ADJ
ejpam-5061	172	12	that	that	DET
ejpam-5061	172	13	l̂h	l̂h	NOUN
ejpam-5061	172	14	=	=	SYM
ejpam-5061	172	15	l̂	l̂	X
ejpam-5061	172	16	∩	∩	PROPN
ejpam-5061	172	17	v	v	X
ejpam-5061	172	18	(	(	PUNCT
ejpam-5061	172	19	h	h	NOUN
ejpam-5061	172	20	)	)	PUNCT
ejpam-5061	172	21	and	and	CCONJ
ejpam-5061	172	22	l̂k	l̂k	PROPN
ejpam-5061	172	23	=	=	SYM
ejpam-5061	172	24	l̂	l̂	X
ejpam-5061	172	25	∩	∩	PROPN
ejpam-5061	172	26	v	v	X
ejpam-5061	172	27	(	(	PUNCT
ejpam-5061	172	28	k	k	NOUN
ejpam-5061	172	29	)	)	PUNCT
ejpam-5061	172	30	.	.	PUNCT
ejpam-5061	173	1	suppose	suppose	VERB
ejpam-5061	173	2	that	that	SCONJ
ejpam-5061	173	3	l̂h	l̂h	NUM
ejpam-5061	173	4	̸=	̸=	PROPN
ejpam-5061	173	5	∅	∅	NOUN
ejpam-5061	173	6	and	and	CCONJ
ejpam-5061	173	7	l̂k	l̂k	ADJ
ejpam-5061	173	8	̸=	̸=	PROPN
ejpam-5061	173	9	∅.	∅.	ADV
ejpam-5061	173	10	then	then	ADV
ejpam-5061	173	11	l	l	PROPN
ejpam-5061	173	12	=	=	PUNCT
ejpam-5061	173	13	lh	lh	PROPN
ejpam-5061	173	14	⊕	⊕	PROPN
ejpam-5061	173	15	(	(	PUNCT
ejpam-5061	173	16	a	a	NOUN
ejpam-5061	173	17	)	)	PUNCT
ejpam-5061	173	18	for	for	ADP
ejpam-5061	173	19	some	some	DET
ejpam-5061	173	20	nondominating	nondominate	VERB
ejpam-5061	173	21	legal	legal	ADJ
ejpam-5061	173	22	sequence	sequence	NOUN
ejpam-5061	173	23	lh	lh	PROPN
ejpam-5061	173	24	in	in	ADP
ejpam-5061	173	25	h	h	PROPN
ejpam-5061	173	26	and	and	CCONJ
ejpam-5061	173	27	a	a	DET
ejpam-5061	173	28	∈	∈	NOUN
ejpam-5061	173	29	v	v	NOUN
ejpam-5061	173	30	(	(	PUNCT
ejpam-5061	173	31	k	k	NOUN
ejpam-5061	173	32	)	)	PUNCT
ejpam-5061	173	33	by	by	ADP
ejpam-5061	173	34	theorem	theorem	NOUN
ejpam-5061	173	35	6	6	NUM
ejpam-5061	173	36	.	.	PUNCT
ejpam-5061	173	37	by	by	ADP
ejpam-5061	173	38	theorem	theorem	NOUN
ejpam-5061	173	39	5	5	NUM
ejpam-5061	173	40	,	,	PUNCT
ejpam-5061	173	41	lh	lh	PROPN
ejpam-5061	173	42	is	be	AUX
ejpam-5061	173	43	clique	clique	ADJ
ejpam-5061	173	44	in	in	ADP
ejpam-5061	173	45	h.	h.	PROPN
ejpam-5061	173	46	thus	thus	ADV
ejpam-5061	173	47	,	,	PUNCT
ejpam-5061	173	48	lh	lh	PROPN
ejpam-5061	173	49	is	be	AUX
ejpam-5061	173	50	a	a	DET
ejpam-5061	173	51	clique	clique	ADJ
ejpam-5061	173	52	legal	legal	ADJ
ejpam-5061	173	53	non	non	ADJ
ejpam-5061	173	54	-	-	ADJ
ejpam-5061	173	55	dominating	dominating	ADJ
ejpam-5061	173	56	sequence	sequence	NOUN
ejpam-5061	173	57	in	in	ADP
ejpam-5061	173	58	h	h	NOUN
ejpam-5061	173	59	,	,	PUNCT
ejpam-5061	173	60	and	and	CCONJ
ejpam-5061	173	61	so	so	ADV
ejpam-5061	173	62	(	(	PUNCT
ejpam-5061	173	63	iii	iii	NOUN
ejpam-5061	173	64	)	)	PUNCT
ejpam-5061	173	65	holds	hold	VERB
ejpam-5061	173	66	.	.	PUNCT
ejpam-5061	174	1	similarly	similarly	ADV
ejpam-5061	174	2	,	,	PUNCT
ejpam-5061	174	3	by	by	ADP
ejpam-5061	174	4	theorem	theorem	NOUN
ejpam-5061	174	5	5	5	NUM
ejpam-5061	174	6	and	and	CCONJ
ejpam-5061	174	7	theorem	theorem	VERB
ejpam-5061	174	8	6	6	NUM
ejpam-5061	174	9	,	,	PUNCT
ejpam-5061	174	10	(	(	PUNCT
ejpam-5061	174	11	iv	iv	X
ejpam-5061	174	12	)	)	PUNCT
ejpam-5061	174	13	holds	hold	NOUN
ejpam-5061	174	14	.	.	PUNCT
ejpam-5061	175	1	the	the	DET
ejpam-5061	175	2	converse	converse	NOUN
ejpam-5061	175	3	is	be	AUX
ejpam-5061	175	4	clear	clear	ADJ
ejpam-5061	175	5	.	.	PUNCT
ejpam-5061	176	1	j.	j.	PROPN
ejpam-5061	176	2	hassan	hassan	PROPN
ejpam-5061	176	3	et	et	PROPN
ejpam-5061	176	4	al	al	PROPN
ejpam-5061	176	5	.	.	PUNCT
ejpam-5061	176	6	/	/	SYM
ejpam-5061	176	7	eur	eur	PROPN
ejpam-5061	176	8	.	.	PUNCT
ejpam-5061	177	1	j.	j.	PROPN
ejpam-5061	177	2	pure	pure	PROPN
ejpam-5061	177	3	appl	appl	PROPN
ejpam-5061	177	4	.	.	PROPN
ejpam-5061	177	5	math	math	PROPN
ejpam-5061	177	6	,	,	PUNCT
ejpam-5061	177	7	17	17	NUM
ejpam-5061	177	8	(	(	PUNCT
ejpam-5061	177	9	2	2	NUM
ejpam-5061	177	10	)	)	PUNCT
ejpam-5061	177	11	(	(	PUNCT
ejpam-5061	177	12	2024	2024	NUM
ejpam-5061	177	13	)	)	PUNCT
ejpam-5061	177	14	,	,	PUNCT
ejpam-5061	177	15	725	725	NUM
ejpam-5061	177	16	-	-	SYM
ejpam-5061	177	17	735	735	NUM
ejpam-5061	177	18	732	732	NUM
ejpam-5061	177	19	corollary	corollary	ADJ
ejpam-5061	177	20	2	2	NUM
ejpam-5061	177	21	.	.	PUNCT
ejpam-5061	178	1	let	let	VERB
ejpam-5061	178	2	h	h	NOUN
ejpam-5061	178	3	and	and	CCONJ
ejpam-5061	178	4	k	k	PROPN
ejpam-5061	178	5	be	be	AUX
ejpam-5061	178	6	two	two	NUM
ejpam-5061	178	7	non	non	ADJ
ejpam-5061	178	8	-	-	ADJ
ejpam-5061	178	9	complete	complete	ADJ
ejpam-5061	178	10	graphs	graph	NOUN
ejpam-5061	178	11	.	.	PUNCT
ejpam-5061	179	1	then	then	ADV
ejpam-5061	179	2	αℓh(h	αℓh(h	PROPN
ejpam-5061	179	3	+	+	PROPN
ejpam-5061	179	4	k	k	NOUN
ejpam-5061	179	5	)	)	PUNCT
ejpam-5061	179	6	=	=	SYM
ejpam-5061	179	7			NUM
ejpam-5061	179	8	max{γcℓgr(h	max{γcℓgr(h	NOUN
ejpam-5061	179	9	)	)	PUNCT
ejpam-5061	179	10	,	,	PUNCT
ejpam-5061	179	11	γcℓgr(k	γcℓgr(k	PROPN
ejpam-5061	179	12	)	)	PUNCT
ejpam-5061	179	13	}	}	PUNCT
ejpam-5061	179	14	,	,	PUNCT
ejpam-5061	179	15	if	if	SCONJ
ejpam-5061	179	16	both	both	DET
ejpam-5061	179	17	h	h	NOUN
ejpam-5061	179	18	and	and	CCONJ
ejpam-5061	179	19	k	k	PROPN
ejpam-5061	179	20	admit	admit	VERB
ejpam-5061	179	21	a	a	DET
ejpam-5061	179	22	clique	clique	NOUN
ejpam-5061	179	23	grundy	grundy	PROPN
ejpam-5061	179	24	domination	domination	NOUN
ejpam-5061	179	25	.	.	PUNCT
ejpam-5061	180	1	max{αcℓh(h	max{αcℓh(h	NOUN
ejpam-5061	180	2	)	)	PUNCT
ejpam-5061	181	1	+	+	CCONJ
ejpam-5061	181	2	1	1	NUM
ejpam-5061	181	3	,	,	PUNCT
ejpam-5061	181	4	αclh(k	αclh(k	NOUN
ejpam-5061	181	5	)	)	PUNCT
ejpam-5061	181	6	+	+	CCONJ
ejpam-5061	181	7	1	1	NUM
ejpam-5061	181	8	}	}	PUNCT
ejpam-5061	181	9	,	,	PUNCT
ejpam-5061	181	10	if	if	SCONJ
ejpam-5061	181	11	both	both	DET
ejpam-5061	181	12	h	h	NOUN
ejpam-5061	181	13	and	and	CCONJ
ejpam-5061	181	14	k	k	PROPN
ejpam-5061	181	15	does	do	AUX
ejpam-5061	181	16	not	not	PART
ejpam-5061	181	17	admit	admit	VERB
ejpam-5061	181	18	a	a	DET
ejpam-5061	181	19	clique	clique	NOUN
ejpam-5061	181	20	grundy	grundy	PROPN
ejpam-5061	181	21	domination	domination	NOUN
ejpam-5061	181	22	.	.	PUNCT
ejpam-5061	182	1	max{αcℓh(h	max{αcℓh(h	NOUN
ejpam-5061	182	2	)	)	PUNCT
ejpam-5061	183	1	+	+	CCONJ
ejpam-5061	183	2	1	1	NUM
ejpam-5061	183	3	,	,	PUNCT
ejpam-5061	183	4	γcℓgr(k	γcℓgr(k	PROPN
ejpam-5061	183	5	)	)	PUNCT
ejpam-5061	183	6	}	}	PUNCT
ejpam-5061	183	7	,	,	PUNCT
ejpam-5061	183	8	if	if	SCONJ
ejpam-5061	183	9	k	k	PROPN
ejpam-5061	183	10	admits	admit	VERB
ejpam-5061	183	11	a	a	DET
ejpam-5061	183	12	clique	clique	NOUN
ejpam-5061	183	13	grundy	grundy	PROPN
ejpam-5061	183	14	domination	domination	NOUN
ejpam-5061	183	15	and	and	CCONJ
ejpam-5061	183	16	h	h	NOUN
ejpam-5061	183	17	does	do	VERB
ejpam-5061	183	18	not	not	PART
ejpam-5061	183	19	.	.	PUNCT
ejpam-5061	184	1	max{αcℓh(k	max{αcℓh(k	X
ejpam-5061	184	2	)	)	PUNCT
ejpam-5061	185	1	+	+	CCONJ
ejpam-5061	185	2	1	1	NUM
ejpam-5061	185	3	,	,	PUNCT
ejpam-5061	185	4	γcℓgr(h	γcℓgr(h	NOUN
ejpam-5061	185	5	)	)	PUNCT
ejpam-5061	185	6	}	}	PUNCT
ejpam-5061	185	7	,	,	PUNCT
ejpam-5061	185	8	if	if	SCONJ
ejpam-5061	185	9	h	h	NOUN
ejpam-5061	185	10	admits	admit	VERB
ejpam-5061	185	11	a	a	DET
ejpam-5061	185	12	clique	clique	NOUN
ejpam-5061	185	13	grundy	grundy	PROPN
ejpam-5061	185	14	domination	domination	PROPN
ejpam-5061	185	15	and	and	CCONJ
ejpam-5061	185	16	k	k	PROPN
ejpam-5061	185	17	does	do	VERB
ejpam-5061	185	18	not	not	PART
ejpam-5061	185	19	.	.	PUNCT
ejpam-5061	186	1	theorem	theorem	VERB
ejpam-5061	186	2	8	8	NUM
ejpam-5061	186	3	.	.	PUNCT
ejpam-5061	187	1	[	[	X
ejpam-5061	187	2	6	6	NUM
ejpam-5061	187	3	]	]	PUNCT
ejpam-5061	187	4	let	let	VERB
ejpam-5061	187	5	g	g	PRON
ejpam-5061	187	6	be	be	AUX
ejpam-5061	187	7	a	a	DET
ejpam-5061	187	8	complete	complete	ADJ
ejpam-5061	187	9	graph	graph	NOUN
ejpam-5061	187	10	and	and	CCONJ
ejpam-5061	187	11	let	let	VERB
ejpam-5061	187	12	h	h	PRON
ejpam-5061	187	13	be	be	AUX
ejpam-5061	187	14	a	a	DET
ejpam-5061	187	15	non	non	ADJ
ejpam-5061	187	16	-	-	ADJ
ejpam-5061	187	17	complete	complete	ADJ
ejpam-5061	187	18	graph	graph	NOUN
ejpam-5061	187	19	.	.	PUNCT
ejpam-5061	188	1	a	a	DET
ejpam-5061	188	2	sequence	sequence	NOUN
ejpam-5061	188	3	d	d	NOUN
ejpam-5061	188	4	of	of	ADP
ejpam-5061	188	5	distinct	distinct	ADJ
ejpam-5061	188	6	vertices	vertex	NOUN
ejpam-5061	188	7	of	of	ADP
ejpam-5061	188	8	g+h	g+h	PROPN
ejpam-5061	188	9	is	be	AUX
ejpam-5061	188	10	a	a	DET
ejpam-5061	188	11	grundy	grundy	PROPN
ejpam-5061	188	12	dominating	dominating	NOUN
ejpam-5061	188	13	sequence	sequence	NOUN
ejpam-5061	188	14	in	in	ADP
ejpam-5061	188	15	g+h	g+h	PROPN
ejpam-5061	189	1	if	if	SCONJ
ejpam-5061	189	2	and	and	CCONJ
ejpam-5061	189	3	only	only	ADV
ejpam-5061	189	4	if	if	SCONJ
ejpam-5061	189	5	one	one	NUM
ejpam-5061	189	6	of	of	ADP
ejpam-5061	189	7	the	the	DET
ejpam-5061	189	8	following	follow	VERB
ejpam-5061	189	9	condition	condition	NOUN
ejpam-5061	189	10	holds	hold	VERB
ejpam-5061	189	11	:	:	PUNCT
ejpam-5061	189	12	(	(	PUNCT
ejpam-5061	189	13	i	i	NOUN
ejpam-5061	189	14	)	)	PUNCT
ejpam-5061	190	1	d	d	PROPN
ejpam-5061	190	2	=	=	SYM
ejpam-5061	190	3	(	(	PUNCT
ejpam-5061	190	4	v	v	NOUN
ejpam-5061	190	5	)	)	PUNCT
ejpam-5061	190	6	for	for	ADP
ejpam-5061	190	7	some	some	PRON
ejpam-5061	190	8	v	v	ADP
ejpam-5061	190	9	∈	∈	PROPN
ejpam-5061	190	10	v	v	NOUN
ejpam-5061	190	11	(	(	PUNCT
ejpam-5061	190	12	g	g	NOUN
ejpam-5061	190	13	)	)	PUNCT
ejpam-5061	190	14	.	.	PUNCT
ejpam-5061	191	1	(	(	PUNCT
ejpam-5061	191	2	ii	ii	NOUN
ejpam-5061	191	3	)	)	PUNCT
ejpam-5061	191	4	d	d	NOUN
ejpam-5061	191	5	is	be	AUX
ejpam-5061	191	6	a	a	DET
ejpam-5061	191	7	grundy	grundy	PROPN
ejpam-5061	191	8	dominating	dominating	NOUN
ejpam-5061	191	9	sequence	sequence	NOUN
ejpam-5061	191	10	of	of	ADP
ejpam-5061	191	11	h.	h.	PROPN
ejpam-5061	191	12	(	(	PUNCT
ejpam-5061	191	13	iii	iii	NOUN
ejpam-5061	191	14	)	)	PUNCT
ejpam-5061	191	15	d	d	NOUN
ejpam-5061	191	16	=	=	SYM
ejpam-5061	191	17	dh	dh	PROPN
ejpam-5061	191	18	⊕	⊕	PROPN
ejpam-5061	191	19	(	(	PUNCT
ejpam-5061	191	20	v	v	NOUN
ejpam-5061	191	21	)	)	PUNCT
ejpam-5061	191	22	for	for	ADP
ejpam-5061	191	23	some	some	DET
ejpam-5061	191	24	non	non	ADJ
ejpam-5061	191	25	-	-	ADJ
ejpam-5061	191	26	dominating	dominating	ADJ
ejpam-5061	191	27	legal	legal	ADJ
ejpam-5061	191	28	neighborhood	neighborhood	NOUN
ejpam-5061	191	29	sequence	sequence	NOUN
ejpam-5061	191	30	dh	dh	NOUN
ejpam-5061	191	31	of	of	ADP
ejpam-5061	191	32	h	h	NOUN
ejpam-5061	191	33	and	and	CCONJ
ejpam-5061	191	34	v	v	ADP
ejpam-5061	191	35	∈	∈	PROPN
ejpam-5061	191	36	v	v	NOUN
ejpam-5061	191	37	(	(	PUNCT
ejpam-5061	191	38	g	g	NOUN
ejpam-5061	191	39	)	)	PUNCT
ejpam-5061	191	40	.	.	PUNCT
ejpam-5061	192	1	theorem	theorem	NOUN
ejpam-5061	192	2	9	9	NUM
ejpam-5061	192	3	.	.	PUNCT
ejpam-5061	193	1	let	let	VERB
ejpam-5061	193	2	s	s	PRON
ejpam-5061	193	3	and	and	CCONJ
ejpam-5061	193	4	t	t	PROPN
ejpam-5061	193	5	be	be	AUX
ejpam-5061	193	6	complete	complete	ADJ
ejpam-5061	193	7	and	and	CCONJ
ejpam-5061	193	8	non	non	ADJ
ejpam-5061	193	9	-	-	ADJ
ejpam-5061	193	10	complete	complete	ADJ
ejpam-5061	193	11	graph	graph	NOUN
ejpam-5061	193	12	,	,	PUNCT
ejpam-5061	193	13	respectively	respectively	ADV
ejpam-5061	193	14	.	.	PUNCT
ejpam-5061	194	1	a	a	DET
ejpam-5061	194	2	sequence	sequence	NOUN
ejpam-5061	194	3	l′	l′	NOUN
ejpam-5061	194	4	of	of	ADP
ejpam-5061	194	5	distinct	distinct	ADJ
ejpam-5061	194	6	vertices	vertex	NOUN
ejpam-5061	194	7	of	of	ADP
ejpam-5061	194	8	s	s	NOUN
ejpam-5061	194	9	+	+	NUM
ejpam-5061	194	10	t	t	PROPN
ejpam-5061	194	11	is	be	AUX
ejpam-5061	194	12	a	a	DET
ejpam-5061	194	13	legal	legal	ADJ
ejpam-5061	194	14	hop	hop	NOUN
ejpam-5061	194	15	independent	independent	ADJ
ejpam-5061	194	16	sequence	sequence	NOUN
ejpam-5061	194	17	if	if	SCONJ
ejpam-5061	194	18	and	and	CCONJ
ejpam-5061	194	19	only	only	ADV
ejpam-5061	194	20	if	if	SCONJ
ejpam-5061	194	21	one	one	NUM
ejpam-5061	194	22	of	of	ADP
ejpam-5061	194	23	the	the	DET
ejpam-5061	194	24	following	follow	VERB
ejpam-5061	194	25	conditions	condition	NOUN
ejpam-5061	194	26	holds	hold	VERB
ejpam-5061	194	27	:	:	PUNCT
ejpam-5061	194	28	(	(	PUNCT
ejpam-5061	194	29	i	i	NOUN
ejpam-5061	194	30	)	)	PUNCT
ejpam-5061	194	31	l′	l′	PROPN
ejpam-5061	195	1	=	=	PUNCT
ejpam-5061	195	2	(	(	PUNCT
ejpam-5061	195	3	s	s	NOUN
ejpam-5061	195	4	)	)	PUNCT
ejpam-5061	195	5	for	for	ADP
ejpam-5061	195	6	some	some	PRON
ejpam-5061	195	7	s	s	NOUN
ejpam-5061	195	8	∈	∈	PROPN
ejpam-5061	195	9	v	v	ADP
ejpam-5061	195	10	(	(	PUNCT
ejpam-5061	195	11	s	s	NOUN
ejpam-5061	195	12	)	)	PUNCT
ejpam-5061	195	13	.	.	PUNCT
ejpam-5061	196	1	(	(	PUNCT
ejpam-5061	196	2	ii	ii	NOUN
ejpam-5061	196	3	)	)	PUNCT
ejpam-5061	196	4	l′	l′	PROPN
ejpam-5061	196	5	is	be	AUX
ejpam-5061	196	6	a	a	DET
ejpam-5061	196	7	clique	clique	ADJ
ejpam-5061	196	8	legal	legal	ADJ
ejpam-5061	196	9	sequence	sequence	NOUN
ejpam-5061	196	10	of	of	ADP
ejpam-5061	196	11	t	t	PROPN
ejpam-5061	196	12	.	.	PUNCT
ejpam-5061	197	1	(	(	PUNCT
ejpam-5061	197	2	iii	iii	NOUN
ejpam-5061	197	3	)	)	PUNCT
ejpam-5061	197	4	l′	l′	NOUN
ejpam-5061	197	5	=	=	SYM
ejpam-5061	197	6	lt	lt	PROPN
ejpam-5061	197	7	⊕	⊕	PROPN
ejpam-5061	197	8	(	(	PUNCT
ejpam-5061	197	9	w	w	PROPN
ejpam-5061	197	10	)	)	PUNCT
ejpam-5061	197	11	,	,	PUNCT
ejpam-5061	197	12	where	where	SCONJ
ejpam-5061	197	13	lt	lt	PRON
ejpam-5061	197	14	is	be	AUX
ejpam-5061	197	15	a	a	DET
ejpam-5061	197	16	clique	clique	ADJ
ejpam-5061	197	17	legal	legal	ADJ
ejpam-5061	197	18	non	non	ADJ
ejpam-5061	197	19	-	-	ADJ
ejpam-5061	197	20	dominating	dominating	ADJ
ejpam-5061	197	21	sequence	sequence	NOUN
ejpam-5061	197	22	in	in	ADP
ejpam-5061	197	23	t	t	PROPN
ejpam-5061	197	24	and	and	CCONJ
ejpam-5061	197	25	w	w	PROPN
ejpam-5061	197	26	∈	∈	PROPN
ejpam-5061	197	27	v	v	ADP
ejpam-5061	197	28	(	(	PUNCT
ejpam-5061	197	29	s	s	NOUN
ejpam-5061	197	30	)	)	PUNCT
ejpam-5061	197	31	.	.	PUNCT
ejpam-5061	198	1	proof	proof	NOUN
ejpam-5061	198	2	.	.	PUNCT
ejpam-5061	199	1	let	let	VERB
ejpam-5061	199	2	l′	l′	PART
ejpam-5061	199	3	be	be	AUX
ejpam-5061	199	4	a	a	DET
ejpam-5061	199	5	legal	legal	ADJ
ejpam-5061	199	6	hop	hop	NOUN
ejpam-5061	199	7	independent	independent	ADJ
ejpam-5061	199	8	sequence	sequence	NOUN
ejpam-5061	199	9	of	of	ADP
ejpam-5061	199	10	s	s	PROPN
ejpam-5061	199	11	+	+	X
ejpam-5061	199	12	t	t	PROPN
ejpam-5061	199	13	.	.	PUNCT
ejpam-5061	200	1	assume	assume	VERB
ejpam-5061	200	2	that	that	SCONJ
ejpam-5061	200	3	l̂′	l̂′	PROPN
ejpam-5061	200	4	⊆	⊆	NUM
ejpam-5061	200	5	v	v	ADP
ejpam-5061	200	6	(	(	PUNCT
ejpam-5061	200	7	s	s	NOUN
ejpam-5061	200	8	)	)	PUNCT
ejpam-5061	200	9	.	.	PUNCT
ejpam-5061	201	1	since	since	SCONJ
ejpam-5061	201	2	s	s	NOUN
ejpam-5061	201	3	is	be	AUX
ejpam-5061	201	4	complete	complete	ADJ
ejpam-5061	201	5	,	,	PUNCT
ejpam-5061	201	6	l′	l′	PUNCT
ejpam-5061	201	7	=	=	PUNCT
ejpam-5061	201	8	(	(	PUNCT
ejpam-5061	201	9	s	s	NOUN
ejpam-5061	201	10	)	)	PUNCT
ejpam-5061	201	11	for	for	ADP
ejpam-5061	201	12	some	some	PRON
ejpam-5061	201	13	s	s	NOUN
ejpam-5061	201	14	∈	∈	PROPN
ejpam-5061	201	15	v	v	NOUN
ejpam-5061	201	16	(	(	PUNCT
ejpam-5061	201	17	g	g	NOUN
ejpam-5061	201	18	)	)	PUNCT
ejpam-5061	201	19	.	.	PUNCT
ejpam-5061	202	1	hence	hence	ADV
ejpam-5061	202	2	,	,	PUNCT
ejpam-5061	202	3	(	(	PUNCT
ejpam-5061	202	4	i	i	NOUN
ejpam-5061	202	5	)	)	PUNCT
ejpam-5061	202	6	holds	hold	VERB
ejpam-5061	202	7	.	.	PUNCT
ejpam-5061	203	1	suppose	suppose	VERB
ejpam-5061	203	2	that	that	SCONJ
ejpam-5061	203	3	l̂′	l̂′	PROPN
ejpam-5061	203	4	⊆	⊆	NUM
ejpam-5061	203	5	v	v	NOUN
ejpam-5061	203	6	(	(	PUNCT
ejpam-5061	203	7	t	t	PROPN
ejpam-5061	203	8	)	)	PUNCT
ejpam-5061	203	9	.	.	PUNCT
ejpam-5061	204	1	since	since	SCONJ
ejpam-5061	204	2	l̂′	l̂′	PROPN
ejpam-5061	204	3	is	be	AUX
ejpam-5061	204	4	hop	hop	ADV
ejpam-5061	204	5	independent	independent	ADJ
ejpam-5061	204	6	in	in	ADP
ejpam-5061	204	7	s	s	PROPN
ejpam-5061	204	8	+	+	PROPN
ejpam-5061	204	9	t	t	NOUN
ejpam-5061	204	10	,	,	PUNCT
ejpam-5061	204	11	l̂′	l̂′	PROPN
ejpam-5061	204	12	is	be	AUX
ejpam-5061	204	13	clique	clique	NOUN
ejpam-5061	204	14	in	in	ADP
ejpam-5061	204	15	t	t	PROPN
ejpam-5061	204	16	by	by	ADP
ejpam-5061	204	17	theorem	theorem	NOUN
ejpam-5061	204	18	5	5	NUM
ejpam-5061	204	19	.	.	PUNCT
ejpam-5061	204	20	by	by	ADP
ejpam-5061	204	21	theorem	theorem	NOUN
ejpam-5061	204	22	7	7	NUM
ejpam-5061	204	23	,	,	PUNCT
ejpam-5061	204	24	l′	l′	NOUN
ejpam-5061	204	25	is	be	AUX
ejpam-5061	204	26	legal	legal	ADJ
ejpam-5061	204	27	sequence	sequence	NOUN
ejpam-5061	204	28	in	in	ADP
ejpam-5061	204	29	t	t	PROPN
ejpam-5061	204	30	.	.	PUNCT
ejpam-5061	205	1	thus	thus	ADV
ejpam-5061	205	2	,	,	PUNCT
ejpam-5061	205	3	l′	l′	PROPN
ejpam-5061	205	4	is	be	AUX
ejpam-5061	205	5	a	a	DET
ejpam-5061	205	6	clique	clique	ADJ
ejpam-5061	205	7	legal	legal	ADJ
ejpam-5061	205	8	sequence	sequence	NOUN
ejpam-5061	205	9	in	in	ADP
ejpam-5061	205	10	t	t	PROPN
ejpam-5061	205	11	,	,	PUNCT
ejpam-5061	205	12	and	and	CCONJ
ejpam-5061	205	13	so	so	ADV
ejpam-5061	205	14	(	(	PUNCT
ejpam-5061	205	15	ii	ii	NOUN
ejpam-5061	205	16	)	)	PUNCT
ejpam-5061	205	17	holds	hold	VERB
ejpam-5061	205	18	.	.	PUNCT
ejpam-5061	206	1	now	now	ADV
ejpam-5061	206	2	,	,	PUNCT
ejpam-5061	206	3	assume	assume	VERB
ejpam-5061	206	4	that	that	SCONJ
ejpam-5061	206	5	l̂′	l̂′	PROPN
ejpam-5061	206	6	=	=	PUNCT
ejpam-5061	206	7	l̂s	l̂s	X
ejpam-5061	206	8	∪	∪	ADJ
ejpam-5061	206	9	l̂t	l̂t	NOUN
ejpam-5061	206	10	,	,	PUNCT
ejpam-5061	206	11	where	where	SCONJ
ejpam-5061	206	12	l̂s	l̂s	ADP
ejpam-5061	206	13	=	=	SYM
ejpam-5061	206	14	l̂′	l̂′	PROPN
ejpam-5061	206	15	∩	∩	PROPN
ejpam-5061	207	1	v	v	X
ejpam-5061	207	2	(	(	PUNCT
ejpam-5061	207	3	s	s	NOUN
ejpam-5061	207	4	)	)	PUNCT
ejpam-5061	207	5	and	and	CCONJ
ejpam-5061	207	6	l̂t	l̂t	NUM
ejpam-5061	207	7	=	=	SYM
ejpam-5061	207	8	l̂′	l̂′	PROPN
ejpam-5061	207	9	∩	∩	PROPN
ejpam-5061	207	10	v	v	PROPN
ejpam-5061	207	11	(	(	PUNCT
ejpam-5061	207	12	t	t	PROPN
ejpam-5061	207	13	)	)	PUNCT
ejpam-5061	207	14	.	.	PUNCT
ejpam-5061	208	1	then	then	ADV
ejpam-5061	208	2	l̂′	l̂′	PROPN
ejpam-5061	208	3	is	be	AUX
ejpam-5061	208	4	a	a	DET
ejpam-5061	208	5	dominating	dominating	NOUN
ejpam-5061	208	6	set	set	NOUN
ejpam-5061	208	7	of	of	ADP
ejpam-5061	208	8	s	s	PROPN
ejpam-5061	208	9	+	+	X
ejpam-5061	208	10	t	t	NOUN
ejpam-5061	208	11	.	.	PUNCT
ejpam-5061	209	1	by	by	ADP
ejpam-5061	209	2	theorem	theorem	NOUN
ejpam-5061	209	3	8	8	NUM
ejpam-5061	209	4	,	,	PUNCT
ejpam-5061	209	5	l′	l′	PUNCT
ejpam-5061	209	6	=	=	PUNCT
ejpam-5061	209	7	lt	lt	PROPN
ejpam-5061	209	8	⊕	⊕	PROPN
ejpam-5061	209	9	(	(	PUNCT
ejpam-5061	209	10	w	w	NOUN
ejpam-5061	209	11	)	)	PUNCT
ejpam-5061	209	12	for	for	ADP
ejpam-5061	209	13	some	some	DET
ejpam-5061	209	14	non	non	ADJ
ejpam-5061	209	15	-	-	ADJ
ejpam-5061	209	16	dominating	dominating	ADJ
ejpam-5061	209	17	legal	legal	ADJ
ejpam-5061	209	18	sequence	sequence	NOUN
ejpam-5061	209	19	lt	lt	PROPN
ejpam-5061	209	20	of	of	ADP
ejpam-5061	209	21	t	t	PROPN
ejpam-5061	209	22	and	and	CCONJ
ejpam-5061	209	23	w	w	PROPN
ejpam-5061	209	24	∈	∈	PROPN
ejpam-5061	209	25	v	v	ADP
ejpam-5061	209	26	(	(	PUNCT
ejpam-5061	209	27	s	s	NOUN
ejpam-5061	209	28	)	)	PUNCT
ejpam-5061	209	29	.	.	PUNCT
ejpam-5061	210	1	since	since	SCONJ
ejpam-5061	210	2	l̂′	l̂′	PROPN
ejpam-5061	210	3	is	be	AUX
ejpam-5061	210	4	a	a	DET
ejpam-5061	210	5	hop	hop	NOUN
ejpam-5061	210	6	independent	independent	ADJ
ejpam-5061	210	7	set	set	NOUN
ejpam-5061	210	8	in	in	ADP
ejpam-5061	210	9	s	s	PROPN
ejpam-5061	210	10	+	+	X
ejpam-5061	210	11	t	t	PROPN
ejpam-5061	210	12	,	,	PUNCT
ejpam-5061	210	13	l̂t	l̂t	PROPN
ejpam-5061	210	14	j.	j.	PROPN
ejpam-5061	210	15	hassan	hassan	PROPN
ejpam-5061	210	16	et	et	PROPN
ejpam-5061	210	17	al	al	PROPN
ejpam-5061	210	18	.	.	PUNCT
ejpam-5061	210	19	/	/	SYM
ejpam-5061	210	20	eur	eur	PROPN
ejpam-5061	210	21	.	.	PUNCT
ejpam-5061	211	1	j.	j.	PROPN
ejpam-5061	211	2	pure	pure	PROPN
ejpam-5061	211	3	appl	appl	PROPN
ejpam-5061	211	4	.	.	PROPN
ejpam-5061	211	5	math	math	PROPN
ejpam-5061	211	6	,	,	PUNCT
ejpam-5061	211	7	17	17	NUM
ejpam-5061	211	8	(	(	PUNCT
ejpam-5061	211	9	2	2	NUM
ejpam-5061	211	10	)	)	PUNCT
ejpam-5061	211	11	(	(	PUNCT
ejpam-5061	211	12	2024	2024	NUM
ejpam-5061	211	13	)	)	PUNCT
ejpam-5061	211	14	,	,	PUNCT
ejpam-5061	211	15	725	725	NUM
ejpam-5061	211	16	-	-	SYM
ejpam-5061	211	17	735	735	NUM
ejpam-5061	211	18	733	733	NUM
ejpam-5061	211	19	must	must	AUX
ejpam-5061	211	20	be	be	AUX
ejpam-5061	211	21	clique	clique	ADJ
ejpam-5061	211	22	in	in	ADP
ejpam-5061	211	23	t	t	PROPN
ejpam-5061	211	24	.	.	PUNCT
ejpam-5061	212	1	hence	hence	ADV
ejpam-5061	212	2	,	,	PUNCT
ejpam-5061	212	3	(	(	PUNCT
ejpam-5061	212	4	iii	iii	NOUN
ejpam-5061	212	5	)	)	PUNCT
ejpam-5061	212	6	holds	hold	VERB
ejpam-5061	212	7	.	.	PUNCT
ejpam-5061	213	1	the	the	DET
ejpam-5061	213	2	converse	converse	NOUN
ejpam-5061	213	3	is	be	AUX
ejpam-5061	213	4	clear	clear	ADJ
ejpam-5061	213	5	.	.	PUNCT
ejpam-5061	214	1	corollary	corollary	ADJ
ejpam-5061	214	2	3	3	X
ejpam-5061	214	3	.	.	PUNCT
ejpam-5061	215	1	let	let	VERB
ejpam-5061	215	2	s	s	PRON
ejpam-5061	215	3	and	and	CCONJ
ejpam-5061	215	4	t	t	PROPN
ejpam-5061	215	5	be	be	AUX
ejpam-5061	215	6	complete	complete	ADJ
ejpam-5061	215	7	and	and	CCONJ
ejpam-5061	215	8	non	non	ADJ
ejpam-5061	215	9	-	-	ADJ
ejpam-5061	215	10	complete	complete	ADJ
ejpam-5061	215	11	graphs	graph	NOUN
ejpam-5061	215	12	,	,	PUNCT
ejpam-5061	215	13	respectively	respectively	ADV
ejpam-5061	215	14	.	.	PUNCT
ejpam-5061	216	1	then	then	ADV
ejpam-5061	216	2	αℓh(s	αℓh(s	NUM
ejpam-5061	216	3	+	+	NUM
ejpam-5061	216	4	t	t	NOUN
ejpam-5061	216	5	)	)	PUNCT
ejpam-5061	217	1	=	=	PRON
ejpam-5061	217	2	{	{	PUNCT
ejpam-5061	217	3	γcℓgr(t	γcℓgr(t	NOUN
ejpam-5061	217	4	)	)	PUNCT
ejpam-5061	217	5	,	,	PUNCT
ejpam-5061	217	6	if	if	SCONJ
ejpam-5061	217	7	t	t	PROPN
ejpam-5061	217	8	admits	admit	VERB
ejpam-5061	217	9	a	a	DET
ejpam-5061	217	10	clique	clique	NOUN
ejpam-5061	217	11	grundy	grundy	PROPN
ejpam-5061	217	12	domination	domination	NOUN
ejpam-5061	217	13	.	.	PUNCT
ejpam-5061	218	1	αcℓh(t	αcℓh(t	NOUN
ejpam-5061	218	2	)	)	PUNCT
ejpam-5061	219	1	+	+	CCONJ
ejpam-5061	219	2	1	1	NUM
ejpam-5061	219	3	,	,	PUNCT
ejpam-5061	219	4	otherwise	otherwise	ADV
ejpam-5061	219	5	.	.	PUNCT
ejpam-5061	220	1	theorem	theorem	NOUN
ejpam-5061	220	2	10	10	NUM
ejpam-5061	220	3	.	.	PUNCT
ejpam-5061	221	1	let	let	VERB
ejpam-5061	221	2	g	g	PRON
ejpam-5061	221	3	be	be	AUX
ejpam-5061	221	4	a	a	DET
ejpam-5061	221	5	connected	connected	ADJ
ejpam-5061	221	6	graph	graph	NOUN
ejpam-5061	221	7	and	and	CCONJ
ejpam-5061	221	8	h	h	NOUN
ejpam-5061	221	9	be	be	AUX
ejpam-5061	221	10	any	any	DET
ejpam-5061	221	11	graph	graph	NOUN
ejpam-5061	221	12	.	.	PUNCT
ejpam-5061	222	1	then	then	ADV
ejpam-5061	222	2	l	l	NOUN
ejpam-5061	222	3	is	be	AUX
ejpam-5061	222	4	a	a	DET
ejpam-5061	222	5	legal	legal	ADJ
ejpam-5061	222	6	hop	hop	NOUN
ejpam-5061	222	7	independent	independent	ADJ
ejpam-5061	222	8	sequence	sequence	NOUN
ejpam-5061	222	9	of	of	ADP
ejpam-5061	222	10	g	g	PROPN
ejpam-5061	222	11	◦	◦	NOUN
ejpam-5061	222	12	h	h	NOUN
ejpam-5061	222	13	if	if	SCONJ
ejpam-5061	222	14	l̂	l̂	X
ejpam-5061	222	15	=	=	SYM
ejpam-5061	223	1	⋃	⋃	ADP
ejpam-5061	223	2	v∈v	v∈v	NOUN
ejpam-5061	223	3	l̂v	l̂v	PROPN
ejpam-5061	223	4	,	,	PUNCT
ejpam-5061	223	5	where	where	SCONJ
ejpam-5061	223	6	l̂v	l̂v	PROPN
ejpam-5061	223	7	is	be	AUX
ejpam-5061	223	8	a	a	DET
ejpam-5061	223	9	clique	clique	ADJ
ejpam-5061	223	10	legal	legal	ADJ
ejpam-5061	223	11	set	set	NOUN
ejpam-5061	223	12	in	in	ADP
ejpam-5061	223	13	hv	hv	PROPN
ejpam-5061	223	14	for	for	ADP
ejpam-5061	223	15	each	each	DET
ejpam-5061	223	16	v	v	NUM
ejpam-5061	223	17	∈	∈	PROPN
ejpam-5061	223	18	v	v	NOUN
ejpam-5061	223	19	(	(	PUNCT
ejpam-5061	223	20	g	g	NOUN
ejpam-5061	223	21	)	)	PUNCT
ejpam-5061	223	22	.	.	PUNCT
ejpam-5061	224	1	moreover	moreover	ADV
ejpam-5061	224	2	,	,	PUNCT
ejpam-5061	224	3	αℓh(g	αℓh(g	NOUN
ejpam-5061	224	4	◦	◦	NOUN
ejpam-5061	224	5	h	h	NOUN
ejpam-5061	224	6	)	)	PUNCT
ejpam-5061	224	7	≥	≥	NOUN
ejpam-5061	224	8	αcℓh(h	αcℓh(h	NOUN
ejpam-5061	224	9	)	)	PUNCT
ejpam-5061	224	10	·	·	PUNCT
ejpam-5061	224	11	|v	|v	PROPN
ejpam-5061	224	12	(	(	PUNCT
ejpam-5061	224	13	g)|	g)|	NOUN
ejpam-5061	224	14	.	.	PUNCT
ejpam-5061	225	1	proof	proof	NOUN
ejpam-5061	225	2	.	.	PUNCT
ejpam-5061	226	1	let	let	VERB
ejpam-5061	226	2	l̂	l̂	X
ejpam-5061	227	1	=	=	PUNCT
ejpam-5061	227	2	⋃	⋃	ADP
ejpam-5061	227	3	v∈v	v∈v	NOUN
ejpam-5061	227	4	l̂v	l̂v	PROPN
ejpam-5061	227	5	,	,	PUNCT
ejpam-5061	227	6	where	where	SCONJ
ejpam-5061	227	7	l̂v	l̂v	PROPN
ejpam-5061	227	8	is	be	AUX
ejpam-5061	227	9	a	a	DET
ejpam-5061	227	10	clique	clique	ADJ
ejpam-5061	227	11	legal	legal	ADJ
ejpam-5061	227	12	set	set	NOUN
ejpam-5061	227	13	in	in	ADP
ejpam-5061	227	14	hv	hv	PROPN
ejpam-5061	227	15	for	for	ADP
ejpam-5061	227	16	some	some	DET
ejpam-5061	227	17	v	v	NUM
ejpam-5061	227	18	∈	∈	PROPN
ejpam-5061	227	19	v	v	NOUN
ejpam-5061	227	20	(	(	PUNCT
ejpam-5061	227	21	g	g	NOUN
ejpam-5061	227	22	)	)	PUNCT
ejpam-5061	227	23	.	.	PUNCT
ejpam-5061	228	1	then	then	ADV
ejpam-5061	228	2	l	l	PROPN
ejpam-5061	228	3	is	be	AUX
ejpam-5061	228	4	a	a	DET
ejpam-5061	228	5	legal	legal	ADJ
ejpam-5061	228	6	sequence	sequence	NOUN
ejpam-5061	228	7	of	of	ADP
ejpam-5061	228	8	g	g	PROPN
ejpam-5061	228	9	◦	◦	NOUN
ejpam-5061	228	10	h.	h.	PROPN
ejpam-5061	228	11	now	now	ADV
ejpam-5061	228	12	,	,	PUNCT
ejpam-5061	228	13	let	let	VERB
ejpam-5061	228	14	a	a	DET
ejpam-5061	228	15	,	,	PUNCT
ejpam-5061	228	16	b	b	X
ejpam-5061	228	17	∈	∈	PROPN
ejpam-5061	228	18	l̂.	l̂.	NOUN
ejpam-5061	228	19	if	if	SCONJ
ejpam-5061	228	20	a	a	DET
ejpam-5061	228	21	,	,	PUNCT
ejpam-5061	228	22	b	b	PROPN
ejpam-5061	228	23	∈	∈	PROPN
ejpam-5061	228	24	l̂v	l̂v	PROPN
ejpam-5061	228	25	,	,	PUNCT
ejpam-5061	228	26	then	then	ADV
ejpam-5061	228	27	dg(a	dg(a	NUM
ejpam-5061	228	28	,	,	PUNCT
ejpam-5061	228	29	b	b	X
ejpam-5061	228	30	)	)	PUNCT
ejpam-5061	228	31	=	=	SYM
ejpam-5061	228	32	1	1	X
ejpam-5061	228	33	.	.	PUNCT
ejpam-5061	229	1	thus	thus	ADV
ejpam-5061	229	2	,	,	PUNCT
ejpam-5061	229	3	l̂	l̂	X
ejpam-5061	229	4	is	be	AUX
ejpam-5061	229	5	a	a	DET
ejpam-5061	229	6	hop	hop	NOUN
ejpam-5061	229	7	independent	independent	ADJ
ejpam-5061	229	8	of	of	ADP
ejpam-5061	229	9	g	g	PROPN
ejpam-5061	229	10	◦	◦	NOUN
ejpam-5061	229	11	h	h	NOUN
ejpam-5061	229	12	,	,	PUNCT
ejpam-5061	229	13	and	and	CCONJ
ejpam-5061	229	14	so	so	ADV
ejpam-5061	229	15	we	we	PRON
ejpam-5061	229	16	are	be	AUX
ejpam-5061	229	17	done	do	VERB
ejpam-5061	229	18	.	.	PUNCT
ejpam-5061	230	1	suppose	suppose	VERB
ejpam-5061	230	2	that	that	SCONJ
ejpam-5061	230	3	a	a	DET
ejpam-5061	230	4	∈	∈	PROPN
ejpam-5061	230	5	lu	lu	NOUN
ejpam-5061	230	6	and	and	CCONJ
ejpam-5061	230	7	b	b	PROPN
ejpam-5061	230	8	∈	∈	PROPN
ejpam-5061	230	9	lw	lw	NOUN
ejpam-5061	230	10	for	for	ADP
ejpam-5061	230	11	some	some	DET
ejpam-5061	230	12	u	u	NOUN
ejpam-5061	230	13	,	,	PUNCT
ejpam-5061	230	14	w	w	PROPN
ejpam-5061	230	15	∈	∈	PROPN
ejpam-5061	230	16	v	v	ADP
ejpam-5061	230	17	(	(	PUNCT
ejpam-5061	230	18	g	g	NOUN
ejpam-5061	230	19	)	)	PUNCT
ejpam-5061	230	20	.	.	PUNCT
ejpam-5061	231	1	clearly	clearly	ADV
ejpam-5061	231	2	,	,	PUNCT
ejpam-5061	231	3	dg	dg	PROPN
ejpam-5061	231	4	◦	◦	PROPN
ejpam-5061	231	5	h(a	h(a	PROPN
ejpam-5061	231	6	,	,	PUNCT
ejpam-5061	231	7	b	b	NOUN
ejpam-5061	231	8	)	)	PUNCT
ejpam-5061	231	9	≥	≥	NOUN
ejpam-5061	231	10	3	3	NUM
ejpam-5061	231	11	.	.	PUNCT
ejpam-5061	232	1	since	since	SCONJ
ejpam-5061	232	2	a	a	PRON
ejpam-5061	232	3	and	and	CCONJ
ejpam-5061	232	4	b	b	NOUN
ejpam-5061	232	5	are	be	AUX
ejpam-5061	232	6	arbitrary	arbitrary	ADJ
ejpam-5061	232	7	,	,	PUNCT
ejpam-5061	232	8	it	it	PRON
ejpam-5061	232	9	follows	follow	VERB
ejpam-5061	232	10	that	that	SCONJ
ejpam-5061	232	11	l̂	l̂	PROPN
ejpam-5061	232	12	is	be	AUX
ejpam-5061	232	13	a	a	DET
ejpam-5061	232	14	hop	hop	NOUN
ejpam-5061	232	15	independent	independent	ADJ
ejpam-5061	232	16	set	set	NOUN
ejpam-5061	232	17	of	of	ADP
ejpam-5061	232	18	g	g	PROPN
ejpam-5061	232	19	◦	◦	PROPN
ejpam-5061	232	20	h.	h.	PROPN
ejpam-5061	232	21	hence	hence	ADV
ejpam-5061	232	22	,	,	PUNCT
ejpam-5061	232	23	l̂	l̂	X
ejpam-5061	232	24	is	be	AUX
ejpam-5061	232	25	legal	legal	ADJ
ejpam-5061	232	26	hop	hop	NOUN
ejpam-5061	232	27	independent	independent	ADJ
ejpam-5061	232	28	set	set	NOUN
ejpam-5061	232	29	of	of	ADP
ejpam-5061	232	30	g	g	PROPN
ejpam-5061	232	31	◦	◦	PROPN
ejpam-5061	232	32	h.	h.	PROPN
ejpam-5061	232	33	consequently	consequently	ADV
ejpam-5061	232	34	,	,	PUNCT
ejpam-5061	232	35	αℓh(g	αℓh(g	PROPN
ejpam-5061	232	36	◦	◦	NOUN
ejpam-5061	232	37	h	h	NOUN
ejpam-5061	232	38	)	)	PUNCT
ejpam-5061	232	39	≥	≥	NOUN
ejpam-5061	232	40	αcℓh(h	αcℓh(h	NOUN
ejpam-5061	232	41	)	)	PUNCT
ejpam-5061	232	42	·	·	PUNCT
ejpam-5061	233	1	|v	|v	PROPN
ejpam-5061	233	2	(	(	PUNCT
ejpam-5061	233	3	g)|	g)|	NOUN
ejpam-5061	233	4	.	.	PUNCT
ejpam-5061	234	1	4	4	X
ejpam-5061	234	2	.	.	X
ejpam-5061	234	3	conclusion	conclusion	VERB
ejpam-5061	234	4	the	the	DET
ejpam-5061	234	5	concept	concept	NOUN
ejpam-5061	234	6	of	of	ADP
ejpam-5061	234	7	legal	legal	ADJ
ejpam-5061	234	8	hop	hop	NOUN
ejpam-5061	234	9	independence	independence	NOUN
ejpam-5061	234	10	in	in	ADP
ejpam-5061	234	11	graphs	graph	NOUN
ejpam-5061	234	12	has	have	AUX
ejpam-5061	234	13	been	be	AUX
ejpam-5061	234	14	introduced	introduce	VERB
ejpam-5061	234	15	and	and	CCONJ
ejpam-5061	234	16	investigated	investigate	VERB
ejpam-5061	234	17	in	in	ADP
ejpam-5061	234	18	this	this	DET
ejpam-5061	234	19	study	study	NOUN
ejpam-5061	234	20	.	.	PUNCT
ejpam-5061	235	1	the	the	DET
ejpam-5061	235	2	parameter	parameter	NOUN
ejpam-5061	235	3	was	be	AUX
ejpam-5061	235	4	defined	define	VERB
ejpam-5061	235	5	on	on	ADP
ejpam-5061	235	6	any	any	DET
ejpam-5061	235	7	simple	simple	ADJ
ejpam-5061	235	8	and	and	CCONJ
ejpam-5061	235	9	undirected	undirected	ADJ
ejpam-5061	235	10	graph	graph	NOUN
ejpam-5061	235	11	.	.	PUNCT
ejpam-5061	236	1	moreover	moreover	ADV
ejpam-5061	236	2	,	,	PUNCT
ejpam-5061	236	3	it	it	PRON
ejpam-5061	236	4	was	be	AUX
ejpam-5061	236	5	found	find	VERB
ejpam-5061	236	6	out	out	ADP
ejpam-5061	236	7	that	that	SCONJ
ejpam-5061	236	8	the	the	DET
ejpam-5061	236	9	legal	legal	ADJ
ejpam-5061	236	10	hop	hop	NOUN
ejpam-5061	236	11	independence	independence	NOUN
ejpam-5061	236	12	number	number	NOUN
ejpam-5061	236	13	of	of	ADP
ejpam-5061	236	14	a	a	DET
ejpam-5061	236	15	graph	graph	NOUN
ejpam-5061	236	16	is	be	AUX
ejpam-5061	236	17	always	always	ADV
ejpam-5061	236	18	less	less	ADJ
ejpam-5061	236	19	than	than	ADP
ejpam-5061	236	20	or	or	CCONJ
ejpam-5061	236	21	equal	equal	ADJ
ejpam-5061	236	22	to	to	ADP
ejpam-5061	236	23	either	either	CCONJ
ejpam-5061	236	24	grundy	grundy	PROPN
ejpam-5061	236	25	domination	domination	NOUN
ejpam-5061	236	26	number	number	NOUN
ejpam-5061	236	27	or	or	CCONJ
ejpam-5061	236	28	hop	hop	NOUN
ejpam-5061	236	29	independence	independence	NOUN
ejpam-5061	236	30	number	number	NOUN
ejpam-5061	236	31	of	of	ADP
ejpam-5061	236	32	a	a	DET
ejpam-5061	236	33	graph	graph	NOUN
ejpam-5061	236	34	.	.	PUNCT
ejpam-5061	237	1	the	the	DET
ejpam-5061	237	2	realization	realization	NOUN
ejpam-5061	237	3	result	result	NOUN
ejpam-5061	237	4	in	in	ADP
ejpam-5061	237	5	theorem	theorem	ADJ
ejpam-5061	237	6	4	4	NUM
ejpam-5061	237	7	says	say	VERB
ejpam-5061	237	8	that	that	SCONJ
ejpam-5061	237	9	the	the	DET
ejpam-5061	237	10	difference	difference	NOUN
ejpam-5061	237	11	between	between	ADP
ejpam-5061	237	12	the	the	DET
ejpam-5061	237	13	hop	hop	NOUN
ejpam-5061	237	14	independence	independence	NOUN
ejpam-5061	237	15	number	number	NOUN
ejpam-5061	237	16	and	and	CCONJ
ejpam-5061	237	17	the	the	DET
ejpam-5061	237	18	legal	legal	ADJ
ejpam-5061	237	19	hop	hop	NOUN
ejpam-5061	237	20	independence	independence	NOUN
ejpam-5061	237	21	number	number	NOUN
ejpam-5061	237	22	of	of	ADP
ejpam-5061	237	23	a	a	DET
ejpam-5061	237	24	graph	graph	NOUN
ejpam-5061	237	25	can	can	AUX
ejpam-5061	237	26	be	be	AUX
ejpam-5061	237	27	made	make	VERB
ejpam-5061	237	28	arbitrarily	arbitrarily	ADV
ejpam-5061	237	29	large	large	ADJ
ejpam-5061	237	30	.	.	PUNCT
ejpam-5061	238	1	furthermore	furthermore	ADV
ejpam-5061	238	2	,	,	PUNCT
ejpam-5061	238	3	some	some	DET
ejpam-5061	238	4	exact	exact	ADJ
ejpam-5061	238	5	values	value	NOUN
ejpam-5061	238	6	and	and	CCONJ
ejpam-5061	238	7	bounds	bound	NOUN
ejpam-5061	238	8	of	of	ADP
ejpam-5061	238	9	the	the	DET
ejpam-5061	238	10	parameter	parameter	NOUN
ejpam-5061	238	11	have	have	AUX
ejpam-5061	238	12	been	be	AUX
ejpam-5061	238	13	obtained	obtain	VERB
ejpam-5061	238	14	on	on	ADP
ejpam-5061	238	15	some	some	DET
ejpam-5061	238	16	special	special	ADJ
ejpam-5061	238	17	graphs	graph	NOUN
ejpam-5061	238	18	,	,	PUNCT
ejpam-5061	238	19	join	join	VERB
ejpam-5061	238	20	and	and	CCONJ
ejpam-5061	238	21	corona	corona	NOUN
ejpam-5061	238	22	of	of	ADP
ejpam-5061	238	23	two	two	NUM
ejpam-5061	238	24	graphs	graph	NOUN
ejpam-5061	238	25	.	.	PUNCT
ejpam-5061	239	1	some	some	DET
ejpam-5061	239	2	graphs	graph	NOUN
ejpam-5061	239	3	that	that	PRON
ejpam-5061	239	4	were	be	AUX
ejpam-5061	239	5	not	not	PART
ejpam-5061	239	6	considered	consider	VERB
ejpam-5061	239	7	in	in	ADP
ejpam-5061	239	8	this	this	DET
ejpam-5061	239	9	study	study	NOUN
ejpam-5061	239	10	could	could	AUX
ejpam-5061	239	11	be	be	AUX
ejpam-5061	239	12	an	an	DET
ejpam-5061	239	13	interesting	interesting	ADJ
ejpam-5061	239	14	cases	case	NOUN
ejpam-5061	239	15	to	to	PART
ejpam-5061	239	16	consider	consider	VERB
ejpam-5061	239	17	for	for	ADP
ejpam-5061	239	18	further	further	ADJ
ejpam-5061	239	19	investigation	investigation	NOUN
ejpam-5061	239	20	of	of	ADP
ejpam-5061	239	21	this	this	DET
ejpam-5061	239	22	newly	newly	ADV
ejpam-5061	239	23	defined	define	VERB
ejpam-5061	239	24	parameter	parameter	NOUN
ejpam-5061	239	25	.	.	PUNCT
ejpam-5061	240	1	in	in	ADP
ejpam-5061	240	2	addition	addition	NOUN
ejpam-5061	240	3	,	,	PUNCT
ejpam-5061	240	4	researchers	researcher	NOUN
ejpam-5061	240	5	may	may	AUX
ejpam-5061	240	6	consider	consider	VERB
ejpam-5061	240	7	to	to	PART
ejpam-5061	240	8	study	study	VERB
ejpam-5061	240	9	the	the	DET
ejpam-5061	240	10	complexity	complexity	NOUN
ejpam-5061	240	11	and	and	CCONJ
ejpam-5061	240	12	algorithm	algorithm	NOUN
ejpam-5061	240	13	of	of	ADP
ejpam-5061	240	14	determining	determine	VERB
ejpam-5061	240	15	the	the	DET
ejpam-5061	240	16	legal	legal	ADJ
ejpam-5061	240	17	hop	hop	NOUN
ejpam-5061	240	18	independence	independence	NOUN
ejpam-5061	240	19	number	number	NOUN
ejpam-5061	240	20	of	of	ADP
ejpam-5061	240	21	any	any	DET
ejpam-5061	240	22	graph	graph	NOUN
ejpam-5061	240	23	.	.	PUNCT
ejpam-5061	241	1	acknowledgements	acknowledgement	NOUN
ejpam-5061	241	2	the	the	DET
ejpam-5061	241	3	authors	author	NOUN
ejpam-5061	241	4	would	would	AUX
ejpam-5061	241	5	like	like	VERB
ejpam-5061	241	6	to	to	PART
ejpam-5061	241	7	thank	thank	VERB
ejpam-5061	241	8	mindanao	mindanao	PROPN
ejpam-5061	241	9	state	state	PROPN
ejpam-5061	241	10	university	university	PROPN
ejpam-5061	241	11	-	-	PUNCT
ejpam-5061	241	12	tawi	tawi	NOUN
ejpam-5061	241	13	-	-	PUNCT
ejpam-5061	241	14	tawi	tawi	NOUN
ejpam-5061	241	15	college	college	PROPN
ejpam-5061	241	16	of	of	ADP
ejpam-5061	241	17	technology	technology	NOUN
ejpam-5061	241	18	and	and	CCONJ
ejpam-5061	241	19	oceanography	oceanography	NOUN
ejpam-5061	241	20	for	for	ADP
ejpam-5061	241	21	funding	fund	VERB
ejpam-5061	241	22	this	this	DET
ejpam-5061	241	23	research	research	NOUN
ejpam-5061	241	24	.	.	PUNCT
ejpam-5061	242	1	references	reference	NOUN
ejpam-5061	242	2	734	734	NUM
ejpam-5061	242	3	references	reference	NOUN
ejpam-5061	242	4	[	[	X
ejpam-5061	242	5	1	1	NUM
ejpam-5061	242	6	]	]	PUNCT
ejpam-5061	242	7	v.	v.	X
ejpam-5061	242	8	bilar	bilar	PROPN
ejpam-5061	242	9	,	,	PUNCT
ejpam-5061	242	10	m.a	m.a	PROPN
ejpam-5061	242	11	.	.	PROPN
ejpam-5061	242	12	bonsocan	bonsocan	PROPN
ejpam-5061	242	13	,	,	PUNCT
ejpam-5061	242	14	j.	j.	PROPN
ejpam-5061	242	15	hassan	hassan	PROPN
ejpam-5061	242	16	,	,	PUNCT
ejpam-5061	242	17	and	and	CCONJ
ejpam-5061	242	18	s.	s.	PROPN
ejpam-5061	242	19	dagondon	dagondon	PROPN
ejpam-5061	242	20	.	.	PUNCT
ejpam-5061	243	1	vertex	vertex	NOUN
ejpam-5061	243	2	cover	cover	VERB
ejpam-5061	243	3	hop	hop	NOUN
ejpam-5061	243	4	dominating	dominating	NOUN
ejpam-5061	243	5	sets	set	NOUN
ejpam-5061	243	6	in	in	ADP
ejpam-5061	243	7	graphs	graph	NOUN
ejpam-5061	243	8	.	.	PUNCT
ejpam-5061	244	1	eur	eur	PROPN
ejpam-5061	244	2	.	.	PUNCT
ejpam-5061	245	1	j.	j.	PROPN
ejpam-5061	245	2	pure	pure	PROPN
ejpam-5061	245	3	appl	appl	PROPN
ejpam-5061	245	4	.	.	PUNCT
ejpam-5061	245	5	math	math	PROPN
ejpam-5061	245	6	.	.	PUNCT
ejpam-5061	245	7	,	,	PUNCT
ejpam-5061	245	8	17(1):93–104	17(1):93–104	NUM
ejpam-5061	245	9	,	,	PUNCT
ejpam-5061	245	10	2024	2024	NUM
ejpam-5061	245	11	.	.	PUNCT
ejpam-5061	246	1	[	[	X
ejpam-5061	246	2	2	2	X
ejpam-5061	246	3	]	]	PUNCT
ejpam-5061	246	4	e.	e.	PROPN
ejpam-5061	246	5	davies	davies	PROPN
ejpam-5061	246	6	,	,	PUNCT
ejpam-5061	246	7	m.	m.	PROPN
ejpam-5061	246	8	jenssen	jenssen	PROPN
ejpam-5061	246	9	,	,	PUNCT
ejpam-5061	246	10	w.	w.	PROPN
ejpam-5061	246	11	perkins	perkins	PROPN
ejpam-5061	246	12	,	,	PUNCT
ejpam-5061	246	13	and	and	CCONJ
ejpam-5061	246	14	b.	b.	PROPN
ejpam-5061	246	15	roberts	roberts	PROPN
ejpam-5061	246	16	.	.	PUNCT
ejpam-5061	247	1	independent	independent	ADJ
ejpam-5061	247	2	sets	set	NOUN
ejpam-5061	247	3	,	,	PUNCT
ejpam-5061	247	4	matchings	matching	NOUN
ejpam-5061	247	5	,	,	PUNCT
ejpam-5061	247	6	and	and	CCONJ
ejpam-5061	247	7	occupancy	occupancy	NOUN
ejpam-5061	247	8	fractions	fraction	NOUN
ejpam-5061	247	9	.	.	PUNCT
ejpam-5061	248	1	j.	j.	PROPN
ejpam-5061	248	2	lond	lond	PROPN
ejpam-5061	248	3	.	.	PUNCT
ejpam-5061	249	1	math	math	PROPN
ejpam-5061	249	2	.	.	PUNCT
ejpam-5061	250	1	soc	soc	PROPN
ejpam-5061	250	2	.	.	PUNCT
ejpam-5061	250	3	,	,	PUNCT
ejpam-5061	250	4	96:211–220	96:211–220	NUM
ejpam-5061	250	5	,	,	PUNCT
ejpam-5061	250	6	2017	2017	NUM
ejpam-5061	250	7	.	.	PUNCT
ejpam-5061	251	1	[	[	X
ejpam-5061	251	2	3	3	X
ejpam-5061	251	3	]	]	PUNCT
ejpam-5061	251	4	j.	j.	PROPN
ejpam-5061	251	5	hassan	hassan	PROPN
ejpam-5061	251	6	,	,	PUNCT
ejpam-5061	251	7	ar	ar	PROPN
ejpam-5061	251	8	.	.	PROPN
ejpam-5061	251	9	bakkang	bakkang	PROPN
ejpam-5061	251	10	,	,	PUNCT
ejpam-5061	251	11	and	and	CCONJ
ejpam-5061	251	12	ass	ass	PROPN
ejpam-5061	251	13	.	.	PROPN
ejpam-5061	251	14	sappari	sappari	PROPN
ejpam-5061	251	15	.	.	PUNCT
ejpam-5061	252	1	j2	j2	PROPN
ejpam-5061	252	2	-	-	PUNCT
ejpam-5061	252	3	hop	hop	PROPN
ejpam-5061	252	4	domination	domination	NOUN
ejpam-5061	252	5	in	in	ADP
ejpam-5061	252	6	graphs	graph	NOUN
ejpam-5061	252	7	:	:	PUNCT
ejpam-5061	252	8	properties	property	NOUN
ejpam-5061	252	9	and	and	CCONJ
ejpam-5061	252	10	connections	connection	NOUN
ejpam-5061	252	11	with	with	ADP
ejpam-5061	252	12	other	other	ADJ
ejpam-5061	252	13	parameters	parameter	NOUN
ejpam-5061	252	14	.	.	PUNCT
ejpam-5061	253	1	eur	eur	PROPN
ejpam-5061	253	2	.	.	PUNCT
ejpam-5061	254	1	j.	j.	PROPN
ejpam-5061	254	2	pure	pure	PROPN
ejpam-5061	254	3	appl	appl	PROPN
ejpam-5061	254	4	.	.	PUNCT
ejpam-5061	254	5	math	math	PROPN
ejpam-5061	254	6	.	.	PUNCT
ejpam-5061	254	7	,	,	PUNCT
ejpam-5061	254	8	16(4):2118–2131	16(4):2118–2131	NUM
ejpam-5061	254	9	,	,	PUNCT
ejpam-5061	254	10	2023	2023	NUM
ejpam-5061	254	11	.	.	PUNCT
ejpam-5061	255	1	[	[	X
ejpam-5061	255	2	4	4	X
ejpam-5061	255	3	]	]	PUNCT
ejpam-5061	255	4	j.	j.	PROPN
ejpam-5061	255	5	hassan	hassan	PROPN
ejpam-5061	255	6	and	and	CCONJ
ejpam-5061	255	7	s.	s.	PROPN
ejpam-5061	255	8	canoy	canoy	PROPN
ejpam-5061	255	9	.	.	PUNCT
ejpam-5061	256	1	connected	connect	VERB
ejpam-5061	256	2	grundy	grundy	PROPN
ejpam-5061	256	3	hop	hop	NOUN
ejpam-5061	256	4	dominating	dominate	VERB
ejpam-5061	256	5	sequences	sequence	NOUN
ejpam-5061	256	6	in	in	ADP
ejpam-5061	256	7	graphs	graph	NOUN
ejpam-5061	256	8	.	.	PUNCT
ejpam-5061	257	1	,	,	PUNCT
ejpam-5061	257	2	.	.	PUNCT
ejpam-5061	258	1	eur	eur	PROPN
ejpam-5061	258	2	.	.	PUNCT
ejpam-5061	259	1	j.	j.	PROPN
ejpam-5061	259	2	pure	pure	PROPN
ejpam-5061	259	3	appl	appl	PROPN
ejpam-5061	259	4	.	.	PUNCT
ejpam-5061	259	5	math	math	PROPN
ejpam-5061	259	6	.	.	PUNCT
ejpam-5061	259	7	,	,	PUNCT
ejpam-5061	260	1	16(2):1212–1227	16(2):1212–1227	NUM
ejpam-5061	260	2	,	,	PUNCT
ejpam-5061	260	3	2023	2023	NUM
ejpam-5061	260	4	.	.	PUNCT
ejpam-5061	261	1	[	[	X
ejpam-5061	261	2	5	5	X
ejpam-5061	261	3	]	]	PUNCT
ejpam-5061	261	4	j.	j.	PROPN
ejpam-5061	261	5	hassan	hassan	PROPN
ejpam-5061	261	6	and	and	CCONJ
ejpam-5061	261	7	s.	s.	PROPN
ejpam-5061	261	8	canoy	canoy	PROPN
ejpam-5061	261	9	.	.	PUNCT
ejpam-5061	262	1	hop	hop	PROPN
ejpam-5061	262	2	independent	independent	ADJ
ejpam-5061	262	3	hop	hop	NOUN
ejpam-5061	262	4	domination	domination	NOUN
ejpam-5061	262	5	in	in	ADP
ejpam-5061	262	6	graphs	graph	NOUN
ejpam-5061	262	7	.	.	PUNCT
ejpam-5061	263	1	,	,	PUNCT
ejpam-5061	263	2	.	.	PUNCT
ejpam-5061	264	1	eur	eur	PROPN
ejpam-5061	264	2	.	.	PUNCT
ejpam-5061	265	1	j.	j.	PROPN
ejpam-5061	265	2	pure	pure	PROPN
ejpam-5061	265	3	appl	appl	PROPN
ejpam-5061	265	4	.	.	PUNCT
ejpam-5061	265	5	math	math	PROPN
ejpam-5061	265	6	.	.	PUNCT
ejpam-5061	265	7	,	,	PUNCT
ejpam-5061	265	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-5061	265	9	,	,	PUNCT
ejpam-5061	265	10	2023	2023	NUM
ejpam-5061	265	11	.	.	PUNCT
ejpam-5061	266	1	[	[	X
ejpam-5061	266	2	6	6	NUM
ejpam-5061	266	3	]	]	PUNCT
ejpam-5061	266	4	j.	j.	PROPN
ejpam-5061	266	5	hassan	hassan	PROPN
ejpam-5061	266	6	and	and	CCONJ
ejpam-5061	266	7	s.	s.	PROPN
ejpam-5061	266	8	canoy	canoy	PROPN
ejpam-5061	266	9	jr	jr	PROPN
ejpam-5061	266	10	.	.	PUNCT
ejpam-5061	267	1	grundy	grundy	PROPN
ejpam-5061	267	2	dominating	dominating	PROPN
ejpam-5061	267	3	and	and	CCONJ
ejpam-5061	267	4	grundy	grundy	PROPN
ejpam-5061	267	5	hop	hop	NOUN
ejpam-5061	267	6	dominating	dominate	VERB
ejpam-5061	267	7	sequences	sequence	NOUN
ejpam-5061	267	8	in	in	ADP
ejpam-5061	267	9	graphs	graph	NOUN
ejpam-5061	267	10	:	:	PUNCT
ejpam-5061	267	11	relationships	relationship	NOUN
ejpam-5061	267	12	and	and	CCONJ
ejpam-5061	267	13	some	some	DET
ejpam-5061	267	14	structural	structural	ADJ
ejpam-5061	267	15	properties	property	NOUN
ejpam-5061	267	16	.	.	PUNCT
ejpam-5061	268	1	eur	eur	PROPN
ejpam-5061	268	2	.	.	PUNCT
ejpam-5061	269	1	j.	j.	PROPN
ejpam-5061	269	2	pure	pure	PROPN
ejpam-5061	269	3	appl	appl	PROPN
ejpam-5061	269	4	.	.	PUNCT
ejpam-5061	269	5	math	math	PROPN
ejpam-5061	269	6	.	.	PUNCT
ejpam-5061	269	7	,	,	PUNCT
ejpam-5061	270	1	16(2):1154–1166	16(2):1154–1166	NUM
ejpam-5061	270	2	,	,	PUNCT
ejpam-5061	270	3	2023	2023	NUM
ejpam-5061	270	4	.	.	PUNCT
ejpam-5061	271	1	[	[	X
ejpam-5061	271	2	7	7	X
ejpam-5061	271	3	]	]	PUNCT
ejpam-5061	271	4	j.	j.	PROPN
ejpam-5061	271	5	hassan	hassan	PROPN
ejpam-5061	271	6	and	and	CCONJ
ejpam-5061	271	7	s.	s.	PROPN
ejpam-5061	271	8	canoy	canoy	PROPN
ejpam-5061	271	9	jr	jr	PROPN
ejpam-5061	271	10	.	.	PUNCT
ejpam-5061	272	1	grundy	grundy	PROPN
ejpam-5061	272	2	total	total	PROPN
ejpam-5061	272	3	hop	hop	PROPN
ejpam-5061	272	4	dominating	dominate	VERB
ejpam-5061	272	5	sequences	sequence	NOUN
ejpam-5061	272	6	in	in	ADP
ejpam-5061	272	7	graphs	graph	NOUN
ejpam-5061	272	8	.	.	PUNCT
ejpam-5061	273	1	eur	eur	PROPN
ejpam-5061	273	2	.	.	PUNCT
ejpam-5061	274	1	j.	j.	PROPN
ejpam-5061	274	2	pure	pure	PROPN
ejpam-5061	274	3	appl	appl	PROPN
ejpam-5061	274	4	.	.	PUNCT
ejpam-5061	274	5	math	math	PROPN
ejpam-5061	274	6	.	.	PUNCT
ejpam-5061	274	7	,	,	PUNCT
ejpam-5061	274	8	16(4):2597–2612	16(4):2597–2612	NUM
ejpam-5061	274	9	,	,	PUNCT
ejpam-5061	274	10	2023	2023	NUM
ejpam-5061	274	11	.	.	PUNCT
ejpam-5061	275	1	[	[	X
ejpam-5061	275	2	8	8	X
ejpam-5061	275	3	]	]	X
ejpam-5061	275	4	j.	j.	PROPN
ejpam-5061	275	5	hassan	hassan	PROPN
ejpam-5061	275	6	,	,	PUNCT
ejpam-5061	275	7	s.	s.	PROPN
ejpam-5061	275	8	canoy	canoy	PROPN
ejpam-5061	275	9	jr	jr	PROPN
ejpam-5061	275	10	.	.	PROPN
ejpam-5061	275	11	,	,	PUNCT
ejpam-5061	275	12	and	and	CCONJ
ejpam-5061	275	13	a.	a.	PROPN
ejpam-5061	275	14	aradais	aradais	PROPN
ejpam-5061	275	15	.	.	PUNCT
ejpam-5061	276	1	hop	hop	PROPN
ejpam-5061	276	2	independent	independent	ADJ
ejpam-5061	276	3	sets	set	NOUN
ejpam-5061	276	4	in	in	ADP
ejpam-5061	276	5	graphs	graph	NOUN
ejpam-5061	276	6	.	.	PUNCT
ejpam-5061	277	1	eur	eur	PROPN
ejpam-5061	277	2	.	.	PUNCT
ejpam-5061	278	1	j.	j.	PROPN
ejpam-5061	278	2	pure	pure	PROPN
ejpam-5061	278	3	appl	appl	PROPN
ejpam-5061	278	4	.	.	PUNCT
ejpam-5061	278	5	math	math	PROPN
ejpam-5061	278	6	.	.	PUNCT
ejpam-5061	278	7	,	,	PUNCT
ejpam-5061	278	8	15(2):467–477	15(2):467–477	PROPN
ejpam-5061	278	9	,	,	PUNCT
ejpam-5061	278	10	2022	2022	NUM
ejpam-5061	278	11	.	.	PUNCT
ejpam-5061	279	1	[	[	X
ejpam-5061	279	2	9	9	NUM
ejpam-5061	279	3	]	]	PUNCT
ejpam-5061	279	4	j.	j.	PROPN
ejpam-5061	279	5	hassan	hassan	PROPN
ejpam-5061	279	6	,	,	PUNCT
ejpam-5061	279	7	a.	a.	PROPN
ejpam-5061	279	8	lintasan	lintasan	PROPN
ejpam-5061	279	9	,	,	PUNCT
ejpam-5061	279	10	and	and	CCONJ
ejpam-5061	279	11	n.h	n.h	PROPN
ejpam-5061	279	12	.	.	PUNCT
ejpam-5061	280	1	mohammad	mohammad	PROPN
ejpam-5061	280	2	.	.	PUNCT
ejpam-5061	281	1	some	some	DET
ejpam-5061	281	2	properties	property	NOUN
ejpam-5061	281	3	and	and	CCONJ
ejpam-5061	281	4	realization	realization	NOUN
ejpam-5061	281	5	problems	problem	NOUN
ejpam-5061	281	6	involving	involve	VERB
ejpam-5061	281	7	connected	connected	ADJ
ejpam-5061	281	8	outer	outer	ADJ
ejpam-5061	281	9	-	-	PUNCT
ejpam-5061	281	10	hop	hop	NOUN
ejpam-5061	281	11	independent	independent	ADJ
ejpam-5061	281	12	hop	hop	NOUN
ejpam-5061	281	13	domination	domination	NOUN
ejpam-5061	281	14	in	in	ADP
ejpam-5061	281	15	graphs	graph	NOUN
ejpam-5061	281	16	.	.	PUNCT
ejpam-5061	282	1	eur	eur	PROPN
ejpam-5061	282	2	.	.	PUNCT
ejpam-5061	283	1	j.	j.	PROPN
ejpam-5061	283	2	pure	pure	PROPN
ejpam-5061	283	3	appl	appl	PROPN
ejpam-5061	283	4	.	.	PUNCT
ejpam-5061	283	5	math	math	PROPN
ejpam-5061	283	6	.	.	PUNCT
ejpam-5061	283	7	,	,	PUNCT
ejpam-5061	283	8	16(3):1848–1861	16(3):1848–1861	NUM
ejpam-5061	283	9	,	,	PUNCT
ejpam-5061	283	10	2023	2023	NUM
ejpam-5061	283	11	.	.	PUNCT
ejpam-5061	284	1	[	[	X
ejpam-5061	284	2	10	10	NUM
ejpam-5061	284	3	]	]	X
ejpam-5061	284	4	j.	j.	PROPN
ejpam-5061	284	5	hassan	hassan	PROPN
ejpam-5061	284	6	,	,	PUNCT
ejpam-5061	284	7	a.	a.	NOUN
ejpam-5061	284	8	tapeing	tapeing	NOUN
ejpam-5061	284	9	,	,	PUNCT
ejpam-5061	284	10	h.	h.	PROPN
ejpam-5061	284	11	copel	copel	PROPN
ejpam-5061	284	12	,	,	PUNCT
ejpam-5061	284	13	a.r	a.r	PROPN
ejpam-5061	284	14	bakkang	bakkang	PROPN
ejpam-5061	284	15	,	,	PUNCT
ejpam-5061	284	16	and	and	CCONJ
ejpam-5061	284	17	s.d	s.d	PROPN
ejpam-5061	284	18	.	.	PROPN
ejpam-5061	284	19	aming	aming	PROPN
ejpam-5061	284	20	.	.	PUNCT
ejpam-5061	285	1	j2	j2	PROPN
ejpam-5061	285	2	-	-	PUNCT
ejpam-5061	285	3	independence	independence	NOUN
ejpam-5061	285	4	parameters	parameter	NOUN
ejpam-5061	285	5	of	of	ADP
ejpam-5061	285	6	some	some	DET
ejpam-5061	285	7	graphs	graph	NOUN
ejpam-5061	285	8	.	.	PUNCT
ejpam-5061	286	1	,	,	PUNCT
ejpam-5061	286	2	.	.	PUNCT
ejpam-5061	287	1	eur	eur	PROPN
ejpam-5061	287	2	.	.	PUNCT
ejpam-5061	288	1	j.	j.	PROPN
ejpam-5061	288	2	pure	pure	PROPN
ejpam-5061	288	3	appl	appl	PROPN
ejpam-5061	288	4	.	.	PUNCT
ejpam-5061	288	5	math	math	PROPN
ejpam-5061	288	6	.	.	PUNCT
ejpam-5061	288	7	,	,	PUNCT
ejpam-5061	289	1	17(1):124–134	17(1):124–134	NUM
ejpam-5061	289	2	,	,	PUNCT
ejpam-5061	289	3	2024	2024	NUM
ejpam-5061	289	4	.	.	PUNCT
ejpam-5061	290	1	[	[	X
ejpam-5061	290	2	11	11	NUM
ejpam-5061	290	3	]	]	X
ejpam-5061	290	4	liu	liu	PROPN
ejpam-5061	290	5	jiuqiang	jiuqiang	PROPN
ejpam-5061	290	6	.	.	PUNCT
ejpam-5061	291	1	maximal	maximal	ADJ
ejpam-5061	291	2	and	and	CCONJ
ejpam-5061	291	3	maximum	maximum	ADJ
ejpam-5061	291	4	independent	independent	ADJ
ejpam-5061	291	5	sets	set	NOUN
ejpam-5061	291	6	in	in	ADP
ejpam-5061	291	7	graphs	graph	NOUN
ejpam-5061	291	8	.	.	PUNCT
ejpam-5061	292	1	dissertations	dissertation	NOUN
ejpam-5061	292	2	.	.	PUNCT
ejpam-5061	292	3	,	,	PUNCT
ejpam-5061	292	4	1985	1985	NUM
ejpam-5061	292	5	.	.	PUNCT
ejpam-5061	293	1	[	[	X
ejpam-5061	293	2	12	12	NUM
ejpam-5061	293	3	]	]	X
ejpam-5061	293	4	s.	s.	PROPN
ejpam-5061	293	5	canoy	canoy	PROPN
ejpam-5061	293	6	jr	jr	PROPN
ejpam-5061	293	7	.	.	PROPN
ejpam-5061	293	8	and	and	CCONJ
ejpam-5061	293	9	j.	j.	PROPN
ejpam-5061	293	10	hassan	hassan	PROPN
ejpam-5061	293	11	.	.	PUNCT
ejpam-5061	294	1	weakly	weakly	ADJ
ejpam-5061	294	2	convex	convex	VERB
ejpam-5061	294	3	hop	hop	NOUN
ejpam-5061	294	4	dominating	dominating	NOUN
ejpam-5061	294	5	sets	set	NOUN
ejpam-5061	294	6	in	in	ADP
ejpam-5061	294	7	graphs	graph	NOUN
ejpam-5061	294	8	.	.	PUNCT
ejpam-5061	295	1	eur	eur	PROPN
ejpam-5061	295	2	.	.	PUNCT
ejpam-5061	296	1	j.	j.	PROPN
ejpam-5061	296	2	pure	pure	PROPN
ejpam-5061	296	3	appl	appl	PROPN
ejpam-5061	296	4	.	.	PUNCT
ejpam-5061	296	5	math	math	PROPN
ejpam-5061	296	6	.	.	PUNCT
ejpam-5061	296	7	,	,	PUNCT
ejpam-5061	296	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-5061	296	9	,	,	PUNCT
ejpam-5061	296	10	2022	2022	NUM
ejpam-5061	296	11	.	.	PUNCT
ejpam-5061	297	1	[	[	X
ejpam-5061	297	2	13	13	NUM
ejpam-5061	297	3	]	]	PUNCT
ejpam-5061	297	4	s.	s.	PROPN
ejpam-5061	297	5	kaida	kaida	PROPN
ejpam-5061	297	6	,	,	PUNCT
ejpam-5061	297	7	k.j	k.j	PROPN
ejpam-5061	297	8	.	.	PROPN
ejpam-5061	297	9	maharajul	maharajul	PROPN
ejpam-5061	297	10	,	,	PUNCT
ejpam-5061	297	11	j.	j.	PROPN
ejpam-5061	297	12	hassan	hassan	PROPN
ejpam-5061	297	13	,	,	PUNCT
ejpam-5061	297	14	l.	l.	PROPN
ejpam-5061	297	15	s.	s.	PROPN
ejpam-5061	297	16	laja	laja	PROPN
ejpam-5061	297	17	,	,	PUNCT
ejpam-5061	297	18	a.b	a.b	PROPN
ejpam-5061	297	19	.	.	PROPN
ejpam-5061	297	20	lintasan	lintasan	PROPN
ejpam-5061	297	21	,	,	PUNCT
ejpam-5061	297	22	and	and	CCONJ
ejpam-5061	297	23	a.a	a.a	PROPN
ejpam-5061	297	24	.	.	PROPN
ejpam-5061	297	25	pablo	pablo	PROPN
ejpam-5061	297	26	.	.	PUNCT
ejpam-5061	297	27	certified	certify	VERB
ejpam-5061	297	28	hop	hop	NOUN
ejpam-5061	297	29	independence	independence	NOUN
ejpam-5061	297	30	:	:	PUNCT
ejpam-5061	297	31	properties	property	NOUN
ejpam-5061	297	32	and	and	CCONJ
ejpam-5061	297	33	connections	connection	NOUN
ejpam-5061	297	34	with	with	ADP
ejpam-5061	297	35	other	other	ADJ
ejpam-5061	297	36	variants	variant	NOUN
ejpam-5061	297	37	of	of	ADP
ejpam-5061	297	38	independence	independence	NOUN
ejpam-5061	297	39	.	.	PUNCT
ejpam-5061	298	1	eur	eur	PROPN
ejpam-5061	298	2	.	.	PUNCT
ejpam-5061	299	1	j.	j.	PROPN
ejpam-5061	299	2	pure	pure	PROPN
ejpam-5061	299	3	appl	appl	PROPN
ejpam-5061	299	4	.	.	PUNCT
ejpam-5061	299	5	math	math	PROPN
ejpam-5061	299	6	.	.	PUNCT
ejpam-5061	299	7	,	,	PUNCT
ejpam-5061	299	8	17(1):435–444	17(1):435–444	NUM
ejpam-5061	299	9	,	,	PUNCT
ejpam-5061	299	10	2024	2024	NUM
ejpam-5061	299	11	.	.	PUNCT
ejpam-5061	300	1	[	[	X
ejpam-5061	300	2	14	14	NUM
ejpam-5061	300	3	]	]	X
ejpam-5061	300	4	j.	j.	PROPN
ejpam-5061	300	5	manditong	manditong	PROPN
ejpam-5061	300	6	,	,	PUNCT
ejpam-5061	300	7	j.	j.	PROPN
ejpam-5061	300	8	hassan	hassan	PROPN
ejpam-5061	300	9	,	,	PUNCT
ejpam-5061	300	10	ls	ls	PROPN
ejpam-5061	300	11	laja	laja	PROPN
ejpam-5061	300	12	,	,	PUNCT
ejpam-5061	300	13	aa	aa	INTJ
ejpam-5061	300	14	.	.	PUNCT
ejpam-5061	300	15	laja	laja	PROPN
ejpam-5061	300	16	,	,	PUNCT
ejpam-5061	300	17	nhm	nhm	PROPN
ejpam-5061	300	18	.	.	PUNCT
ejpam-5061	300	19	mohammad	mohammad	PROPN
ejpam-5061	300	20	,	,	PUNCT
ejpam-5061	300	21	and	and	CCONJ
ejpam-5061	300	22	su	su	PROPN
ejpam-5061	300	23	.	.	PROPN
ejpam-5061	300	24	kamdon	kamdon	PROPN
ejpam-5061	300	25	.	.	PUNCT
ejpam-5061	301	1	connected	connected	ADJ
ejpam-5061	301	2	outer	outer	ADJ
ejpam-5061	301	3	-	-	PUNCT
ejpam-5061	301	4	hop	hop	NOUN
ejpam-5061	301	5	independent	independent	ADJ
ejpam-5061	301	6	dominating	dominating	NOUN
ejpam-5061	301	7	sets	set	NOUN
ejpam-5061	301	8	in	in	ADP
ejpam-5061	301	9	graphs	graph	NOUN
ejpam-5061	301	10	under	under	ADP
ejpam-5061	301	11	some	some	DET
ejpam-5061	301	12	binary	binary	ADJ
ejpam-5061	301	13	operations	operation	NOUN
ejpam-5061	301	14	.	.	PUNCT
ejpam-5061	302	1	eur	eur	PROPN
ejpam-5061	302	2	.	.	PUNCT
ejpam-5061	303	1	j.	j.	PROPN
ejpam-5061	303	2	pure	pure	PROPN
ejpam-5061	303	3	appl	appl	PROPN
ejpam-5061	303	4	.	.	PUNCT
ejpam-5061	303	5	math	math	PROPN
ejpam-5061	303	6	.	.	PUNCT
ejpam-5061	303	7	,	,	PUNCT
ejpam-5061	304	1	16(3):1817–1829	16(3):1817–1829	NUM
ejpam-5061	304	2	,	,	PUNCT
ejpam-5061	304	3	2023	2023	NUM
ejpam-5061	304	4	.	.	PUNCT
ejpam-5061	305	1	references	reference	NOUN
ejpam-5061	305	2	735	735	NUM
ejpam-5061	305	3	[	[	X
ejpam-5061	305	4	15	15	NUM
ejpam-5061	305	5	]	]	X
ejpam-5061	305	6	j.	j.	PROPN
ejpam-5061	305	7	manditong	manditong	PROPN
ejpam-5061	305	8	,	,	PUNCT
ejpam-5061	305	9	a.	a.	NOUN
ejpam-5061	305	10	tapeing	tapeing	NOUN
ejpam-5061	305	11	,	,	PUNCT
ejpam-5061	305	12	j.	j.	PROPN
ejpam-5061	305	13	hassan	hassan	PROPN
ejpam-5061	305	14	,	,	PUNCT
ejpam-5061	305	15	a.r	a.r	PROPN
ejpam-5061	305	16	.	.	PROPN
ejpam-5061	305	17	bakkang	bakkang	PROPN
ejpam-5061	305	18	,	,	PUNCT
ejpam-5061	305	19	n.h	n.h	PROPN
ejpam-5061	305	20	.	.	PUNCT
ejpam-5061	305	21	mohammad	mohammad	PROPN
ejpam-5061	305	22	,	,	PUNCT
ejpam-5061	305	23	and	and	CCONJ
ejpam-5061	305	24	s.u	s.u	PROPN
ejpam-5061	305	25	.	.	PROPN
ejpam-5061	305	26	kamdon	kamdon	PROPN
ejpam-5061	305	27	.	.	PUNCT
ejpam-5061	306	1	some	some	DET
ejpam-5061	306	2	properties	property	NOUN
ejpam-5061	306	3	of	of	ADP
ejpam-5061	306	4	zero	zero	NUM
ejpam-5061	306	5	forcing	force	VERB
ejpam-5061	306	6	hop	hop	NOUN
ejpam-5061	306	7	dominating	dominating	NOUN
ejpam-5061	306	8	sets	set	NOUN
ejpam-5061	306	9	in	in	ADP
ejpam-5061	306	10	a	a	DET
ejpam-5061	306	11	graph	graph	NOUN
ejpam-5061	306	12	.	.	PUNCT
ejpam-5061	307	1	eur	eur	PROPN
ejpam-5061	307	2	.	.	PUNCT
ejpam-5061	308	1	j.	j.	PROPN
ejpam-5061	308	2	pure	pure	PROPN
ejpam-5061	308	3	appl	appl	PROPN
ejpam-5061	308	4	.	.	PUNCT
ejpam-5061	308	5	math	math	PROPN
ejpam-5061	308	6	.	.	PUNCT
ejpam-5061	309	1	,	,	PUNCT
ejpam-5061	309	2	17(1):324–337	17(1):324–337	PROPN
ejpam-5061	309	3	,	,	PUNCT
ejpam-5061	309	4	2024	2024	NUM
ejpam-5061	309	5	.	.	PUNCT
ejpam-5061	310	1	[	[	X
ejpam-5061	310	2	16	16	NUM
ejpam-5061	310	3	]	]	X
ejpam-5061	310	4	j.	j.	PROPN
ejpam-5061	310	5	mohamad	mohamad	PROPN
ejpam-5061	310	6	and	and	CCONJ
ejpam-5061	310	7	h.	h.	PROPN
ejpam-5061	310	8	rara	rara	PROPN
ejpam-5061	310	9	.	.	PUNCT
ejpam-5061	311	1	on	on	ADP
ejpam-5061	311	2	resolving	resolve	VERB
ejpam-5061	311	3	hop	hop	NOUN
ejpam-5061	311	4	domination	domination	NOUN
ejpam-5061	311	5	in	in	ADP
ejpam-5061	311	6	graphs	graph	NOUN
ejpam-5061	311	7	.	.	PUNCT
ejpam-5061	312	1	eur	eur	PROPN
ejpam-5061	312	2	.	.	PUNCT
ejpam-5061	313	1	j.	j.	PROPN
ejpam-5061	313	2	pure	pure	PROPN
ejpam-5061	313	3	appl	appl	PROPN
ejpam-5061	313	4	.	.	PUNCT
ejpam-5061	313	5	math	math	PROPN
ejpam-5061	313	6	.	.	PUNCT
ejpam-5061	313	7	,	,	PUNCT
ejpam-5061	313	8	14(1):324–337	14(1):324–337	PROPN
ejpam-5061	313	9	,	,	PUNCT
ejpam-5061	313	10	2021	2021	NUM
ejpam-5061	313	11	.	.	PUNCT
ejpam-5061	314	1	[	[	X
ejpam-5061	314	2	17	17	NUM
ejpam-5061	314	3	]	]	X
ejpam-5061	314	4	h.s	h.s	PROPN
ejpam-5061	314	5	.	.	PROPN
ejpam-5061	314	6	wilf	wilf	PROPN
ejpam-5061	314	7	.	.	PUNCT
ejpam-5061	315	1	the	the	DET
ejpam-5061	315	2	number	number	NOUN
ejpam-5061	315	3	of	of	ADP
ejpam-5061	315	4	maximal	maximal	ADJ
ejpam-5061	315	5	independent	independent	ADJ
ejpam-5061	315	6	sets	set	NOUN
ejpam-5061	315	7	in	in	ADP
ejpam-5061	315	8	a	a	DET
ejpam-5061	315	9	tree	tree	NOUN
ejpam-5061	315	10	.	.	PUNCT
ejpam-5061	316	1	siam	siam	PROPN
ejpam-5061	316	2	j.	j.	PROPN
ejpam-5061	316	3	alg	alg	PROPN
ejpam-5061	316	4	.	.	PUNCT
ejpam-5061	317	1	disc	disc	PROPN
ejpam-5061	317	2	.	.	PUNCT
ejpam-5061	318	1	meth	meth	NOUN
ejpam-5061	318	2	.	.	PUNCT
ejpam-5061	318	3	,	,	PUNCT
ejpam-5061	318	4	7:125–130	7:125–130	NUM
ejpam-5061	318	5	,	,	PUNCT
ejpam-5061	318	6	1986	1986	NUM
ejpam-5061	318	7	.	.	PUNCT
ejpam-5061	319	1	[	[	X
ejpam-5061	319	2	18	18	NUM
ejpam-5061	319	3	]	]	PUNCT
ejpam-5061	319	4	j.	j.	PROPN
ejpam-5061	319	5	zito	zito	PROPN
ejpam-5061	319	6	.	.	PUNCT
ejpam-5061	320	1	the	the	DET
ejpam-5061	320	2	structure	structure	NOUN
ejpam-5061	320	3	and	and	CCONJ
ejpam-5061	320	4	maximum	maximum	ADJ
ejpam-5061	320	5	number	number	NOUN
ejpam-5061	320	6	of	of	ADP
ejpam-5061	320	7	maximum	maximum	ADJ
ejpam-5061	320	8	independent	independent	ADJ
ejpam-5061	320	9	sets	set	NOUN
ejpam-5061	320	10	in	in	ADP
ejpam-5061	320	11	trees	tree	NOUN
ejpam-5061	320	12	.	.	PUNCT
ejpam-5061	321	1	j.	j.	PROPN
ejpam-5061	321	2	graph	graph	PROPN
ejpam-5061	321	3	theory	theory	NOUN
ejpam-5061	321	4	.	.	PUNCT
ejpam-5061	321	5	,	,	PUNCT
ejpam-5061	321	6	15(2):207–221	15(2):207–221	NUM
ejpam-5061	321	7	,	,	PUNCT
ejpam-5061	321	8	1991	1991	NUM
ejpam-5061	321	9	.	.	PUNCT