id	sid	tid	token	lemma	pos
ejpam-5044	1	1	european	european	PROPN
ejpam-5044	1	2	journal	journal	PROPN
ejpam-5044	1	3	of	of	ADP
ejpam-5044	1	4	pure	pure	ADJ
ejpam-5044	1	5	and	and	CCONJ
ejpam-5044	1	6	applied	apply	VERB
ejpam-5044	1	7	mathematics	mathematic	NOUN
ejpam-5044	1	8	vol	vol	NOUN
ejpam-5044	1	9	.	.	PROPN
ejpam-5044	2	1	17	17	NUM
ejpam-5044	2	2	,	,	PUNCT
ejpam-5044	2	3	no	no	INTJ
ejpam-5044	2	4	.	.	NOUN
ejpam-5044	2	5	1	1	NUM
ejpam-5044	2	6	,	,	PUNCT
ejpam-5044	2	7	2024	2024	NUM
ejpam-5044	2	8	,	,	PUNCT
ejpam-5044	2	9	435	435	NUM
ejpam-5044	2	10	-	-	SYM
ejpam-5044	2	11	444	444	NUM
ejpam-5044	2	12	issn	issn	PROPN
ejpam-5044	2	13	1307	1307	NUM
ejpam-5044	2	14	-	-	SYM
ejpam-5044	2	15	5543	5543	NUM
ejpam-5044	2	16	–	–	PUNCT
ejpam-5044	2	17	ejpam.com	ejpam.com	X
ejpam-5044	2	18	published	publish	VERB
ejpam-5044	2	19	by	by	ADP
ejpam-5044	2	20	new	new	PROPN
ejpam-5044	2	21	york	york	PROPN
ejpam-5044	2	22	business	business	PROPN
ejpam-5044	2	23	global	global	PROPN
ejpam-5044	2	24	certified	certify	VERB
ejpam-5044	2	25	hop	hop	NOUN
ejpam-5044	2	26	independence	independence	NOUN
ejpam-5044	2	27	:	:	PUNCT
ejpam-5044	2	28	properties	property	NOUN
ejpam-5044	2	29	and	and	CCONJ
ejpam-5044	2	30	connections	connection	NOUN
ejpam-5044	2	31	with	with	ADP
ejpam-5044	2	32	other	other	ADJ
ejpam-5044	2	33	variants	variant	NOUN
ejpam-5044	2	34	of	of	ADP
ejpam-5044	2	35	independence	independence	NOUN
ejpam-5044	3	1	sharmia	sharmia	PROPN
ejpam-5044	3	2	h.	h.	PROPN
ejpam-5044	3	3	kaida1	kaida1	PROPN
ejpam-5044	3	4	,	,	PUNCT
ejpam-5044	3	5	kaimar	kaimar	PROPN
ejpam-5044	3	6	jay	jay	PROPN
ejpam-5044	3	7	s.	s.	PROPN
ejpam-5044	3	8	maharajul1	maharajul1	PROPN
ejpam-5044	3	9	,	,	PUNCT
ejpam-5044	3	10	javier	javier	PROPN
ejpam-5044	3	11	a.	a.	PROPN
ejpam-5044	3	12	hassan1,∗	hassan1,∗	PROPN
ejpam-5044	3	13	,	,	PUNCT
ejpam-5044	3	14	ladznar	ladznar	ADJ
ejpam-5044	3	15	s.	s.	PROPN
ejpam-5044	3	16	laja1	laja1	PROPN
ejpam-5044	3	17	,	,	PUNCT
ejpam-5044	3	18	abdurajan	abdurajan	PROPN
ejpam-5044	3	19	b.	b.	PROPN
ejpam-5044	3	20	lintasan1	lintasan1	PROPN
ejpam-5044	3	21	,	,	PUNCT
ejpam-5044	3	22	aljon	aljon	NOUN
ejpam-5044	3	23	a.	a.	NOUN
ejpam-5044	3	24	pablo2	pablo2	NOUN
ejpam-5044	4	1	1mathematics	1mathematics	NUM
ejpam-5044	4	2	and	and	CCONJ
ejpam-5044	4	3	sciences	sciences	PROPN
ejpam-5044	4	4	department	department	PROPN
ejpam-5044	4	5	,	,	PUNCT
ejpam-5044	4	6	college	college	NOUN
ejpam-5044	4	7	of	of	ADP
ejpam-5044	4	8	arts	art	NOUN
ejpam-5044	4	9	and	and	CCONJ
ejpam-5044	4	10	sciences	science	NOUN
ejpam-5044	4	11	,	,	PUNCT
ejpam-5044	4	12	msu	msu	PROPN
ejpam-5044	4	13	-	-	PUNCT
ejpam-5044	4	14	tawi	tawi	NOUN
ejpam-5044	4	15	-	-	PUNCT
ejpam-5044	4	16	tawi	tawi	NOUN
ejpam-5044	4	17	college	college	PROPN
ejpam-5044	4	18	of	of	ADP
ejpam-5044	4	19	technology	technology	NOUN
ejpam-5044	4	20	and	and	CCONJ
ejpam-5044	4	21	oceanography	oceanography	NOUN
ejpam-5044	4	22	,	,	PUNCT
ejpam-5044	4	23	bongao	bongao	NOUN
ejpam-5044	4	24	,	,	PUNCT
ejpam-5044	4	25	tawi	tawi	NOUN
ejpam-5044	4	26	-	-	PUNCT
ejpam-5044	4	27	tawi	tawi	NOUN
ejpam-5044	4	28	,	,	PUNCT
ejpam-5044	4	29	philippines	philippines	PROPN
ejpam-5044	4	30	2	2	NUM
ejpam-5044	4	31	banaran	banaran	VERB
ejpam-5044	4	32	main	main	ADJ
ejpam-5044	4	33	junior	junior	ADJ
ejpam-5044	4	34	high	high	ADJ
ejpam-5044	4	35	school	school	NOUN
ejpam-5044	4	36	,	,	PUNCT
ejpam-5044	4	37	secondary	secondary	ADJ
ejpam-5044	4	38	education	education	NOUN
ejpam-5044	4	39	department	department	PROPN
ejpam-5044	4	40	,	,	PUNCT
ejpam-5044	4	41	msu	msu	PROPN
ejpam-5044	4	42	-	-	PUNCT
ejpam-5044	4	43	tawi	tawi	NOUN
ejpam-5044	4	44	-	-	PUNCT
ejpam-5044	4	45	tawi	tawi	NOUN
ejpam-5044	4	46	college	college	PROPN
ejpam-5044	4	47	of	of	ADP
ejpam-5044	4	48	technology	technology	NOUN
ejpam-5044	4	49	and	and	CCONJ
ejpam-5044	4	50	oceanography	oceanography	NOUN
ejpam-5044	4	51	,	,	PUNCT
ejpam-5044	4	52	bongao	bongao	NOUN
ejpam-5044	4	53	,	,	PUNCT
ejpam-5044	4	54	tawi	tawi	NOUN
ejpam-5044	4	55	-	-	PUNCT
ejpam-5044	4	56	tawi	tawi	NOUN
ejpam-5044	4	57	,	,	PUNCT
ejpam-5044	4	58	philippines	philippine	NOUN
ejpam-5044	4	59	abstract	abstract	ADJ
ejpam-5044	4	60	.	.	PUNCT
ejpam-5044	5	1	let	let	VERB
ejpam-5044	5	2	g	g	PRON
ejpam-5044	5	3	be	be	AUX
ejpam-5044	5	4	a	a	DET
ejpam-5044	5	5	graph	graph	NOUN
ejpam-5044	5	6	.	.	PUNCT
ejpam-5044	6	1	then	then	ADV
ejpam-5044	6	2	b	b	PROPN
ejpam-5044	6	3	⊆	⊆	NUM
ejpam-5044	6	4	v	v	NOUN
ejpam-5044	6	5	(	(	PUNCT
ejpam-5044	6	6	g	g	NOUN
ejpam-5044	6	7	)	)	PUNCT
ejpam-5044	6	8	is	be	AUX
ejpam-5044	6	9	called	call	VERB
ejpam-5044	6	10	a	a	DET
ejpam-5044	6	11	certified	certify	VERB
ejpam-5044	6	12	hop	hop	NOUN
ejpam-5044	6	13	independent	independent	ADJ
ejpam-5044	6	14	set	set	NOUN
ejpam-5044	6	15	of	of	ADP
ejpam-5044	6	16	g	g	PROPN
ejpam-5044	6	17	if	if	SCONJ
ejpam-5044	6	18	for	for	ADP
ejpam-5044	6	19	every	every	DET
ejpam-5044	6	20	a	a	PROPN
ejpam-5044	6	21	,	,	PUNCT
ejpam-5044	6	22	b	b	PROPN
ejpam-5044	6	23	∈	∈	PROPN
ejpam-5044	6	24	b	b	PROPN
ejpam-5044	6	25	,	,	PUNCT
ejpam-5044	6	26	dg(a	dg(a	X
ejpam-5044	6	27	,	,	PUNCT
ejpam-5044	6	28	b	b	X
ejpam-5044	6	29	)	)	PUNCT
ejpam-5044	6	30	̸=	̸=	PROPN
ejpam-5044	6	31	2	2	NUM
ejpam-5044	6	32	and	and	CCONJ
ejpam-5044	6	33	for	for	ADP
ejpam-5044	6	34	every	every	DET
ejpam-5044	6	35	x	x	SYM
ejpam-5044	6	36	∈	∈	PROPN
ejpam-5044	6	37	b	b	PROPN
ejpam-5044	6	38	has	have	VERB
ejpam-5044	6	39	either	either	CCONJ
ejpam-5044	6	40	zero	zero	NUM
ejpam-5044	6	41	or	or	CCONJ
ejpam-5044	6	42	at	at	ADP
ejpam-5044	6	43	least	least	ADV
ejpam-5044	6	44	two	two	NUM
ejpam-5044	6	45	neighbors	neighbor	NOUN
ejpam-5044	6	46	in	in	ADP
ejpam-5044	6	47	v	v	NOUN
ejpam-5044	6	48	(	(	PUNCT
ejpam-5044	6	49	g	g	NOUN
ejpam-5044	6	50	)	)	PUNCT
ejpam-5044	6	51	\	\	PROPN
ejpam-5044	7	1	b.	b.	PROPN
ejpam-5044	7	2	the	the	DET
ejpam-5044	7	3	maximum	maximum	PROPN
ejpam-5044	7	4	cardinality	cardinality	NOUN
ejpam-5044	7	5	among	among	ADP
ejpam-5044	7	6	all	all	DET
ejpam-5044	7	7	certified	certify	VERB
ejpam-5044	7	8	hop	hop	NOUN
ejpam-5044	7	9	independent	independent	ADJ
ejpam-5044	7	10	sets	set	NOUN
ejpam-5044	7	11	in	in	ADP
ejpam-5044	7	12	g	g	NOUN
ejpam-5044	7	13	,	,	PUNCT
ejpam-5044	7	14	denoted	denote	VERB
ejpam-5044	7	15	by	by	ADP
ejpam-5044	7	16	αch(g	αch(g	NOUN
ejpam-5044	7	17	)	)	PUNCT
ejpam-5044	7	18	,	,	PUNCT
ejpam-5044	7	19	is	be	AUX
ejpam-5044	7	20	called	call	VERB
ejpam-5044	7	21	the	the	DET
ejpam-5044	7	22	certified	certify	VERB
ejpam-5044	7	23	hop	hop	NOUN
ejpam-5044	7	24	independence	independence	NOUN
ejpam-5044	7	25	number	number	NOUN
ejpam-5044	7	26	of	of	ADP
ejpam-5044	7	27	g.	g.	PROPN
ejpam-5044	7	28	in	in	ADP
ejpam-5044	7	29	this	this	DET
ejpam-5044	7	30	paper	paper	NOUN
ejpam-5044	7	31	,	,	PUNCT
ejpam-5044	7	32	we	we	PRON
ejpam-5044	7	33	initiate	initiate	VERB
ejpam-5044	7	34	the	the	DET
ejpam-5044	7	35	study	study	NOUN
ejpam-5044	7	36	of	of	ADP
ejpam-5044	7	37	certified	certify	VERB
ejpam-5044	7	38	hop	hop	NOUN
ejpam-5044	7	39	independence	independence	NOUN
ejpam-5044	7	40	in	in	ADP
ejpam-5044	7	41	graphs	graph	NOUN
ejpam-5044	7	42	and	and	CCONJ
ejpam-5044	7	43	we	we	PRON
ejpam-5044	7	44	establish	establish	VERB
ejpam-5044	7	45	some	some	PRON
ejpam-5044	7	46	of	of	ADP
ejpam-5044	7	47	its	its	PRON
ejpam-5044	7	48	properties	property	NOUN
ejpam-5044	7	49	.	.	PUNCT
ejpam-5044	8	1	we	we	PRON
ejpam-5044	8	2	give	give	VERB
ejpam-5044	8	3	realization	realization	NOUN
ejpam-5044	8	4	results	result	NOUN
ejpam-5044	8	5	involving	involve	VERB
ejpam-5044	8	6	hop	hop	NOUN
ejpam-5044	8	7	independence	independence	NOUN
ejpam-5044	8	8	and	and	CCONJ
ejpam-5044	8	9	certified	certify	VERB
ejpam-5044	8	10	hop	hop	NOUN
ejpam-5044	8	11	independence	independence	NOUN
ejpam-5044	8	12	parameters	parameter	NOUN
ejpam-5044	8	13	,	,	PUNCT
ejpam-5044	8	14	and	and	CCONJ
ejpam-5044	8	15	we	we	PRON
ejpam-5044	8	16	show	show	VERB
ejpam-5044	8	17	that	that	SCONJ
ejpam-5044	8	18	the	the	DET
ejpam-5044	8	19	difference	difference	NOUN
ejpam-5044	8	20	between	between	ADP
ejpam-5044	8	21	these	these	DET
ejpam-5044	8	22	two	two	NUM
ejpam-5044	8	23	parameters	parameter	NOUN
ejpam-5044	8	24	can	can	AUX
ejpam-5044	8	25	be	be	AUX
ejpam-5044	8	26	made	make	VERB
ejpam-5044	8	27	arbitrarily	arbitrarily	ADV
ejpam-5044	8	28	large	large	ADJ
ejpam-5044	8	29	.	.	PUNCT
ejpam-5044	9	1	we	we	PRON
ejpam-5044	9	2	characterize	characterize	VERB
ejpam-5044	9	3	certified	certify	VERB
ejpam-5044	9	4	hop	hop	NOUN
ejpam-5044	9	5	independent	independent	ADJ
ejpam-5044	9	6	sets	set	NOUN
ejpam-5044	9	7	in	in	ADP
ejpam-5044	9	8	some	some	DET
ejpam-5044	9	9	graphs	graph	NOUN
ejpam-5044	9	10	and	and	CCONJ
ejpam-5044	9	11	we	we	PRON
ejpam-5044	9	12	use	use	VERB
ejpam-5044	9	13	these	these	DET
ejpam-5044	9	14	results	result	NOUN
ejpam-5044	9	15	to	to	PART
ejpam-5044	9	16	obtain	obtain	VERB
ejpam-5044	9	17	the	the	DET
ejpam-5044	9	18	exact	exact	ADJ
ejpam-5044	9	19	values	value	NOUN
ejpam-5044	9	20	or	or	CCONJ
ejpam-5044	9	21	bounds	bound	NOUN
ejpam-5044	9	22	of	of	ADP
ejpam-5044	9	23	the	the	DET
ejpam-5044	9	24	parameter	parameter	NOUN
ejpam-5044	9	25	.	.	PUNCT
ejpam-5044	10	1	moreover	moreover	ADV
ejpam-5044	10	2	,	,	PUNCT
ejpam-5044	10	3	we	we	PRON
ejpam-5044	10	4	show	show	VERB
ejpam-5044	10	5	that	that	SCONJ
ejpam-5044	10	6	the	the	DET
ejpam-5044	10	7	certified	certify	VERB
ejpam-5044	10	8	hop	hop	NOUN
ejpam-5044	10	9	independence	independence	NOUN
ejpam-5044	10	10	and	and	CCONJ
ejpam-5044	10	11	independence	independence	NOUN
ejpam-5044	10	12	parameters	parameter	NOUN
ejpam-5044	10	13	are	be	AUX
ejpam-5044	10	14	incomparable	incomparable	ADJ
ejpam-5044	10	15	.	.	PUNCT
ejpam-5044	11	1	2020	2020	NUM
ejpam-5044	11	2	mathematics	mathematic	NOUN
ejpam-5044	11	3	subject	subject	NOUN
ejpam-5044	11	4	classifications	classification	NOUN
ejpam-5044	11	5	:	:	PUNCT
ejpam-5044	11	6	05c69	05c69	X
ejpam-5044	11	7	key	key	ADJ
ejpam-5044	11	8	words	word	NOUN
ejpam-5044	11	9	and	and	CCONJ
ejpam-5044	11	10	phrases	phrase	NOUN
ejpam-5044	11	11	:	:	PUNCT
ejpam-5044	11	12	hop	hop	NOUN
ejpam-5044	11	13	independence	independence	NOUN
ejpam-5044	11	14	,	,	PUNCT
ejpam-5044	11	15	certified	certify	VERB
ejpam-5044	11	16	independent	independent	ADJ
ejpam-5044	11	17	set	set	NOUN
ejpam-5044	11	18	,	,	PUNCT
ejpam-5044	11	19	certified	certify	VERB
ejpam-5044	11	20	hop	hop	NOUN
ejpam-5044	11	21	independence	independence	NOUN
ejpam-5044	11	22	number	number	NOUN
ejpam-5044	11	23	1	1	NUM
ejpam-5044	11	24	.	.	PUNCT
ejpam-5044	12	1	introduction	introduction	NOUN
ejpam-5044	12	2	in	in	ADP
ejpam-5044	12	3	this	this	DET
ejpam-5044	12	4	paper	paper	NOUN
ejpam-5044	12	5	,	,	PUNCT
ejpam-5044	12	6	we	we	PRON
ejpam-5044	12	7	introduce	introduce	VERB
ejpam-5044	12	8	a	a	DET
ejpam-5044	12	9	new	new	ADJ
ejpam-5044	12	10	variant	variant	NOUN
ejpam-5044	12	11	of	of	ADP
ejpam-5044	12	12	hop	hop	NOUN
ejpam-5044	12	13	independence	independence	NOUN
ejpam-5044	12	14	called	call	VERB
ejpam-5044	12	15	certified	certify	VERB
ejpam-5044	12	16	hop	hop	NOUN
ejpam-5044	12	17	independence	independence	NOUN
ejpam-5044	12	18	.	.	PUNCT
ejpam-5044	13	1	indeed	indeed	ADV
ejpam-5044	13	2	,	,	PUNCT
ejpam-5044	13	3	while	while	SCONJ
ejpam-5044	13	4	a	a	DET
ejpam-5044	13	5	hop	hop	NOUN
ejpam-5044	13	6	independent	independent	ADJ
ejpam-5044	13	7	set	set	NOUN
ejpam-5044	13	8	of	of	ADP
ejpam-5044	13	9	a	a	DET
ejpam-5044	13	10	graph	graph	NOUN
ejpam-5044	13	11	requires	require	VERB
ejpam-5044	13	12	that	that	SCONJ
ejpam-5044	13	13	no	no	DET
ejpam-5044	13	14	two	two	NUM
ejpam-5044	13	15	distinct	distinct	ADJ
ejpam-5044	13	16	vertices	vertex	NOUN
ejpam-5044	13	17	in	in	ADP
ejpam-5044	13	18	the	the	DET
ejpam-5044	13	19	set	set	NOUN
ejpam-5044	13	20	are	be	AUX
ejpam-5044	13	21	at	at	ADP
ejpam-5044	13	22	distance	distance	NOUN
ejpam-5044	13	23	two	two	NUM
ejpam-5044	13	24	from	from	ADP
ejpam-5044	13	25	each	each	DET
ejpam-5044	13	26	other	other	ADJ
ejpam-5044	13	27	,	,	PUNCT
ejpam-5044	13	28	the	the	DET
ejpam-5044	13	29	concept	concept	NOUN
ejpam-5044	13	30	that	that	SCONJ
ejpam-5044	13	31	we	we	PRON
ejpam-5044	13	32	will	will	AUX
ejpam-5044	13	33	be	be	AUX
ejpam-5044	13	34	dealing	deal	VERB
ejpam-5044	13	35	with	with	ADP
ejpam-5044	13	36	here	here	ADV
ejpam-5044	13	37	imposes	impose	VERB
ejpam-5044	13	38	additional	additional	ADJ
ejpam-5044	13	39	condition	condition	NOUN
ejpam-5044	13	40	that	that	SCONJ
ejpam-5044	13	41	each	each	DET
ejpam-5044	13	42	vertex	vertex	NOUN
ejpam-5044	13	43	in	in	ADP
ejpam-5044	13	44	the	the	DET
ejpam-5044	13	45	set	set	NOUN
ejpam-5044	13	46	must	must	AUX
ejpam-5044	13	47	have	have	AUX
ejpam-5044	13	48	either	either	CCONJ
ejpam-5044	13	49	zero	zero	NUM
ejpam-5044	13	50	∗corresponding	∗corresponde	VERB
ejpam-5044	13	51	author	author	NOUN
ejpam-5044	13	52	.	.	PUNCT
ejpam-5044	14	1	doi	doi	NOUN
ejpam-5044	14	2	:	:	PUNCT
ejpam-5044	14	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5044	https://doi.org/10.29020/nybg.ejpam.v17i1.5044	PRON
ejpam-5044	14	4	email	email	NOUN
ejpam-5044	14	5	addresses	address	VERB
ejpam-5044	14	6	:	:	PUNCT
ejpam-5044	15	1	sharmiakaida@msutawi-tawi.edu.ph	sharmiakaida@msutawi-tawi.edu.ph	PROPN
ejpam-5044	15	2	(	(	PUNCT
ejpam-5044	15	3	s.	s.	PROPN
ejpam-5044	15	4	kaida	kaida	PROPN
ejpam-5044	15	5	)	)	PUNCT
ejpam-5044	15	6	kaimarjaymaharajul@msutawi-tawi.edu.ph	kaimarjaymaharajul@msutawi-tawi.edu.ph	PROPN
ejpam-5044	15	7	(	(	PUNCT
ejpam-5044	15	8	k.	k.	PROPN
ejpam-5044	15	9	maharajul	maharajul	PROPN
ejpam-5044	15	10	)	)	PUNCT
ejpam-5044	15	11	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-5044	15	12	(	(	PUNCT
ejpam-5044	15	13	j.	j.	PROPN
ejpam-5044	15	14	hassan	hassan	PROPN
ejpam-5044	15	15	)	)	PUNCT
ejpam-5044	15	16	ladznarlaja@msutawi-tawi.edu.ph	ladznarlaja@msutawi-tawi.edu.ph	PROPN
ejpam-5044	15	17	(	(	PUNCT
ejpam-5044	15	18	l.	l.	PROPN
ejpam-5044	15	19	laja	laja	PROPN
ejpam-5044	15	20	)	)	PUNCT
ejpam-5044	16	1	abdurajanlintasan@msutawi-tawi.edu.ph	abdurajanlintasan@msutawi-tawi.edu.ph	PROPN
ejpam-5044	16	2	(	(	PUNCT
ejpam-5044	16	3	a.	a.	NOUN
ejpam-5044	16	4	lintasan	lintasan	NOUN
ejpam-5044	16	5	)	)	PUNCT
ejpam-5044	16	6	aljonpablo@msutawi-tawi.edu.ph	aljonpablo@msutawi-tawi.edu.ph	PROPN
ejpam-5044	16	7	(	(	PUNCT
ejpam-5044	16	8	a.	a.	NOUN
ejpam-5044	16	9	pablo	pablo	PROPN
ejpam-5044	16	10	)	)	PUNCT
ejpam-5044	16	11	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5044	17	1	435	435	NUM
ejpam-5044	17	2	©	©	ADP
ejpam-5044	17	3	2024	2024	NUM
ejpam-5044	17	4	ejpam	ejpam	NOUN
ejpam-5044	17	5	all	all	DET
ejpam-5044	17	6	rights	right	NOUN
ejpam-5044	17	7	reserved	reserve	VERB
ejpam-5044	17	8	.	.	PUNCT
ejpam-5044	18	1	j.	j.	PROPN
ejpam-5044	18	2	a.	a.	PROPN
ejpam-5044	18	3	hassan	hassan	PROPN
ejpam-5044	18	4	et	et	PROPN
ejpam-5044	18	5	al	al	PROPN
ejpam-5044	18	6	.	.	PUNCT
ejpam-5044	18	7	/	/	SYM
ejpam-5044	18	8	eur	eur	PROPN
ejpam-5044	18	9	.	.	PUNCT
ejpam-5044	19	1	j.	j.	PROPN
ejpam-5044	19	2	pure	pure	PROPN
ejpam-5044	19	3	appl	appl	PROPN
ejpam-5044	19	4	.	.	PROPN
ejpam-5044	19	5	math	math	PROPN
ejpam-5044	19	6	,	,	PUNCT
ejpam-5044	19	7	17	17	NUM
ejpam-5044	19	8	(	(	PUNCT
ejpam-5044	19	9	1	1	NUM
ejpam-5044	19	10	)	)	PUNCT
ejpam-5044	19	11	(	(	PUNCT
ejpam-5044	19	12	2024	2024	NUM
ejpam-5044	19	13	)	)	PUNCT
ejpam-5044	19	14	,	,	PUNCT
ejpam-5044	19	15	435	435	NUM
ejpam-5044	19	16	-	-	SYM
ejpam-5044	19	17	444	444	NUM
ejpam-5044	19	18	436	436	NUM
ejpam-5044	19	19	or	or	CCONJ
ejpam-5044	19	20	at	at	ADP
ejpam-5044	19	21	least	least	ADV
ejpam-5044	19	22	two	two	NUM
ejpam-5044	19	23	neighbors	neighbor	NOUN
ejpam-5044	19	24	outside	outside	ADP
ejpam-5044	19	25	the	the	DET
ejpam-5044	19	26	set	set	NOUN
ejpam-5044	19	27	.	.	PUNCT
ejpam-5044	20	1	some	some	DET
ejpam-5044	20	2	related	related	ADJ
ejpam-5044	20	3	studies	study	NOUN
ejpam-5044	20	4	on	on	ADP
ejpam-5044	20	5	hop	hop	NOUN
ejpam-5044	20	6	independence	independence	NOUN
ejpam-5044	20	7	can	can	AUX
ejpam-5044	20	8	be	be	AUX
ejpam-5044	20	9	found	find	VERB
ejpam-5044	20	10	in	in	ADP
ejpam-5044	20	11	[	[	X
ejpam-5044	20	12	1–4	1–4	NOUN
ejpam-5044	20	13	]	]	X
ejpam-5044	20	14	.	.	PUNCT
ejpam-5044	21	1	the	the	DET
ejpam-5044	21	2	motivation	motivation	NOUN
ejpam-5044	21	3	of	of	ADP
ejpam-5044	21	4	introducing	introduce	VERB
ejpam-5044	21	5	the	the	DET
ejpam-5044	21	6	concept	concept	NOUN
ejpam-5044	21	7	is	be	AUX
ejpam-5044	21	8	the	the	DET
ejpam-5044	21	9	ever	ever	ADV
ejpam-5044	21	10	increasing	increase	VERB
ejpam-5044	21	11	number	number	NOUN
ejpam-5044	21	12	of	of	ADP
ejpam-5044	21	13	studies	study	NOUN
ejpam-5044	21	14	on	on	ADP
ejpam-5044	21	15	independence	independence	NOUN
ejpam-5044	21	16	and	and	CCONJ
ejpam-5044	21	17	some	some	PRON
ejpam-5044	21	18	of	of	ADP
ejpam-5044	21	19	its	its	PRON
ejpam-5044	21	20	variations	variation	NOUN
ejpam-5044	21	21	.	.	PUNCT
ejpam-5044	22	1	we	we	PRON
ejpam-5044	22	2	show	show	VERB
ejpam-5044	22	3	that	that	SCONJ
ejpam-5044	22	4	the	the	DET
ejpam-5044	22	5	certified	certify	VERB
ejpam-5044	22	6	hop	hop	NOUN
ejpam-5044	22	7	independence	independence	NOUN
ejpam-5044	22	8	and	and	CCONJ
ejpam-5044	22	9	the	the	DET
ejpam-5044	22	10	standard	standard	ADJ
ejpam-5044	22	11	independence	independence	NOUN
ejpam-5044	22	12	parameters	parameter	NOUN
ejpam-5044	22	13	of	of	ADP
ejpam-5044	22	14	a	a	DET
ejpam-5044	22	15	graph	graph	NOUN
ejpam-5044	22	16	are	be	AUX
ejpam-5044	22	17	incomparable	incomparable	ADJ
ejpam-5044	22	18	.	.	PUNCT
ejpam-5044	23	1	moreover	moreover	ADV
ejpam-5044	23	2	,	,	PUNCT
ejpam-5044	23	3	we	we	PRON
ejpam-5044	23	4	give	give	VERB
ejpam-5044	23	5	realization	realization	NOUN
ejpam-5044	23	6	results	result	NOUN
ejpam-5044	23	7	involving	involve	VERB
ejpam-5044	23	8	certified	certify	VERB
ejpam-5044	23	9	hop	hop	NOUN
ejpam-5044	23	10	independence	independence	NOUN
ejpam-5044	23	11	and	and	CCONJ
ejpam-5044	23	12	hop	hop	NOUN
ejpam-5044	23	13	independence	independence	NOUN
ejpam-5044	23	14	parameters	parameter	NOUN
ejpam-5044	23	15	,	,	PUNCT
ejpam-5044	23	16	and	and	CCONJ
ejpam-5044	23	17	we	we	PRON
ejpam-5044	23	18	show	show	VERB
ejpam-5044	23	19	that	that	SCONJ
ejpam-5044	23	20	the	the	DET
ejpam-5044	23	21	latter	latter	ADJ
ejpam-5044	23	22	is	be	AUX
ejpam-5044	23	23	always	always	ADV
ejpam-5044	23	24	at	at	ADP
ejpam-5044	23	25	most	most	ADV
ejpam-5044	23	26	equal	equal	ADJ
ejpam-5044	23	27	to	to	ADP
ejpam-5044	23	28	the	the	DET
ejpam-5044	23	29	hop	hop	NOUN
ejpam-5044	23	30	independence	independence	NOUN
ejpam-5044	23	31	parameter	parameter	NOUN
ejpam-5044	23	32	.	.	PUNCT
ejpam-5044	24	1	2	2	X
ejpam-5044	24	2	.	.	X
ejpam-5044	24	3	terminology	terminology	NOUN
ejpam-5044	24	4	and	and	CCONJ
ejpam-5044	24	5	notation	notation	NOUN
ejpam-5044	24	6	let	let	VERB
ejpam-5044	24	7	g	g	NOUN
ejpam-5044	24	8	=	=	SYM
ejpam-5044	24	9	(	(	PUNCT
ejpam-5044	24	10	v	v	NOUN
ejpam-5044	24	11	(	(	PUNCT
ejpam-5044	24	12	g	g	NOUN
ejpam-5044	24	13	)	)	PUNCT
ejpam-5044	24	14	,	,	PUNCT
ejpam-5044	24	15	e(g	e(g	PROPN
ejpam-5044	24	16	)	)	PUNCT
ejpam-5044	24	17	)	)	PUNCT
ejpam-5044	24	18	be	be	AUX
ejpam-5044	24	19	a	a	DET
ejpam-5044	24	20	simple	simple	ADJ
ejpam-5044	24	21	and	and	CCONJ
ejpam-5044	24	22	undirected	undirected	ADJ
ejpam-5044	24	23	graph	graph	NOUN
ejpam-5044	24	24	.	.	PUNCT
ejpam-5044	25	1	two	two	NUM
ejpam-5044	25	2	vertices	vertex	NOUN
ejpam-5044	25	3	x	x	X
ejpam-5044	25	4	,	,	PUNCT
ejpam-5044	25	5	y	y	PROPN
ejpam-5044	25	6	of	of	ADP
ejpam-5044	25	7	g	g	PROPN
ejpam-5044	25	8	are	be	AUX
ejpam-5044	25	9	adjacent	adjacent	ADJ
ejpam-5044	25	10	,	,	PUNCT
ejpam-5044	25	11	or	or	CCONJ
ejpam-5044	25	12	neighbors	neighbor	NOUN
ejpam-5044	25	13	,	,	PUNCT
ejpam-5044	25	14	if	if	SCONJ
ejpam-5044	25	15	xy	xy	PROPN
ejpam-5044	25	16	is	be	AUX
ejpam-5044	25	17	an	an	DET
ejpam-5044	25	18	edge	edge	NOUN
ejpam-5044	25	19	of	of	ADP
ejpam-5044	25	20	g.	g.	PROPN
ejpam-5044	25	21	the	the	DET
ejpam-5044	25	22	open	open	ADJ
ejpam-5044	25	23	neighborhood	neighborhood	NOUN
ejpam-5044	25	24	of	of	ADP
ejpam-5044	25	25	x	x	PUNCT
ejpam-5044	25	26	in	in	ADP
ejpam-5044	25	27	g	g	PROPN
ejpam-5044	25	28	is	be	AUX
ejpam-5044	25	29	the	the	DET
ejpam-5044	25	30	set	set	NOUN
ejpam-5044	25	31	ng(x	ng(x	NUM
ejpam-5044	25	32	)	)	PUNCT
ejpam-5044	26	1	=	=	PRON
ejpam-5044	26	2	{	{	PUNCT
ejpam-5044	26	3	y	y	PROPN
ejpam-5044	26	4	∈	∈	PROPN
ejpam-5044	26	5	v	v	NOUN
ejpam-5044	26	6	(	(	PUNCT
ejpam-5044	26	7	g	g	NOUN
ejpam-5044	26	8	)	)	PUNCT
ejpam-5044	26	9	:	:	PUNCT
ejpam-5044	26	10	xy	xy	PROPN
ejpam-5044	26	11	∈	∈	PROPN
ejpam-5044	26	12	e(g	e(g	PROPN
ejpam-5044	26	13	)	)	PUNCT
ejpam-5044	26	14	}	}	PUNCT
ejpam-5044	26	15	.	.	PUNCT
ejpam-5044	27	1	the	the	DET
ejpam-5044	27	2	closed	closed	ADJ
ejpam-5044	27	3	neighborhood	neighborhood	NOUN
ejpam-5044	27	4	of	of	ADP
ejpam-5044	27	5	x	x	PUNCT
ejpam-5044	27	6	in	in	ADP
ejpam-5044	27	7	g	g	PROPN
ejpam-5044	27	8	is	be	AUX
ejpam-5044	27	9	the	the	DET
ejpam-5044	27	10	set	set	NOUN
ejpam-5044	27	11	ng[x	ng[x	PROPN
ejpam-5044	27	12	]	]	X
ejpam-5044	27	13	=	=	PUNCT
ejpam-5044	27	14	ng(x	ng(x	X
ejpam-5044	27	15	)	)	PUNCT
ejpam-5044	27	16	∪	∪	ADP
ejpam-5044	27	17	{	{	PUNCT
ejpam-5044	27	18	x	x	NOUN
ejpam-5044	27	19	}	}	PUNCT
ejpam-5044	27	20	.	.	PUNCT
ejpam-5044	28	1	if	if	SCONJ
ejpam-5044	28	2	x	x	PROPN
ejpam-5044	28	3	⊆	⊆	NUM
ejpam-5044	28	4	v	v	X
ejpam-5044	28	5	(	(	PUNCT
ejpam-5044	28	6	g	g	NOUN
ejpam-5044	28	7	)	)	PUNCT
ejpam-5044	28	8	,	,	PUNCT
ejpam-5044	28	9	the	the	DET
ejpam-5044	28	10	open	open	ADJ
ejpam-5044	28	11	neighborhood	neighborhood	NOUN
ejpam-5044	28	12	of	of	ADP
ejpam-5044	28	13	x	x	PUNCT
ejpam-5044	28	14	in	in	ADP
ejpam-5044	28	15	g	g	PROPN
ejpam-5044	28	16	is	be	AUX
ejpam-5044	28	17	the	the	DET
ejpam-5044	28	18	set	set	NOUN
ejpam-5044	28	19	ng(x	ng(x	NUM
ejpam-5044	28	20	)	)	PUNCT
ejpam-5044	29	1	=	=	SYM
ejpam-5044	29	2	⋃	⋃	NOUN
ejpam-5044	29	3	x∈x	x∈x	NOUN
ejpam-5044	29	4	ng(x	ng(x	NUM
ejpam-5044	29	5	)	)	PUNCT
ejpam-5044	29	6	.	.	PUNCT
ejpam-5044	30	1	the	the	DET
ejpam-5044	30	2	closed	closed	ADJ
ejpam-5044	30	3	neighborhood	neighborhood	NOUN
ejpam-5044	30	4	of	of	ADP
ejpam-5044	30	5	x	x	PUNCT
ejpam-5044	30	6	in	in	ADP
ejpam-5044	30	7	g	g	PROPN
ejpam-5044	30	8	is	be	AUX
ejpam-5044	30	9	the	the	DET
ejpam-5044	30	10	set	set	NOUN
ejpam-5044	30	11	ng[x	ng[x	PROPN
ejpam-5044	30	12	]	]	X
ejpam-5044	30	13	=	=	SYM
ejpam-5044	30	14	ng(x)∪x	ng(x)∪x	PROPN
ejpam-5044	30	15	.	.	PUNCT
ejpam-5044	31	1	a	a	DET
ejpam-5044	31	2	path	path	NOUN
ejpam-5044	31	3	graph	graph	NOUN
ejpam-5044	31	4	is	be	AUX
ejpam-5044	31	5	non	non	ADJ
ejpam-5044	31	6	-	-	ADJ
ejpam-5044	31	7	empty	empty	ADJ
ejpam-5044	31	8	graph	graph	NOUN
ejpam-5044	31	9	with	with	ADP
ejpam-5044	31	10	vertex	vertex	NOUN
ejpam-5044	31	11	-	-	PUNCT
ejpam-5044	31	12	set	set	VERB
ejpam-5044	31	13	{	{	PUNCT
ejpam-5044	31	14	x1	x1	PROPN
ejpam-5044	31	15	,	,	PUNCT
ejpam-5044	31	16	x2	x2	PROPN
ejpam-5044	31	17	,	,	PUNCT
ejpam-5044	31	18	...	...	PUNCT
ejpam-5044	31	19	,	,	PUNCT
ejpam-5044	31	20	xn	xn	PROPN
ejpam-5044	31	21	}	}	PUNCT
ejpam-5044	31	22	and	and	CCONJ
ejpam-5044	31	23	edge	edge	NOUN
ejpam-5044	31	24	-	-	PUNCT
ejpam-5044	31	25	set	set	NOUN
ejpam-5044	31	26	{	{	PUNCT
ejpam-5044	31	27	x1x2	x1x2	NOUN
ejpam-5044	31	28	,	,	PUNCT
ejpam-5044	31	29	x2x3	x2x3	PROPN
ejpam-5044	31	30	,	,	PUNCT
ejpam-5044	31	31	...	...	PUNCT
ejpam-5044	31	32	,	,	PUNCT
ejpam-5044	31	33	xn−1xn	xn−1xn	NUM
ejpam-5044	31	34	}	}	PUNCT
ejpam-5044	31	35	,	,	PUNCT
ejpam-5044	31	36	where	where	SCONJ
ejpam-5044	31	37	the	the	DET
ejpam-5044	31	38	x′is	x′is	PROPN
ejpam-5044	31	39	are	be	AUX
ejpam-5044	31	40	all	all	ADV
ejpam-5044	31	41	distinct	distinct	ADJ
ejpam-5044	31	42	.	.	PUNCT
ejpam-5044	32	1	the	the	DET
ejpam-5044	32	2	path	path	NOUN
ejpam-5044	32	3	of	of	ADP
ejpam-5044	32	4	order	order	NOUN
ejpam-5044	32	5	n	n	NOUN
ejpam-5044	32	6	is	be	AUX
ejpam-5044	32	7	denoted	denote	VERB
ejpam-5044	32	8	by	by	ADP
ejpam-5044	32	9	pn	pn	PROPN
ejpam-5044	32	10	.	.	PUNCT
ejpam-5044	33	1	if	if	SCONJ
ejpam-5044	33	2	g	g	PROPN
ejpam-5044	33	3	is	be	AUX
ejpam-5044	33	4	a	a	DET
ejpam-5044	33	5	graph	graph	NOUN
ejpam-5044	33	6	and	and	CCONJ
ejpam-5044	33	7	u	u	NOUN
ejpam-5044	33	8	and	and	CCONJ
ejpam-5044	33	9	v	v	NOUN
ejpam-5044	33	10	are	be	AUX
ejpam-5044	33	11	vertices	vertex	NOUN
ejpam-5044	33	12	of	of	ADP
ejpam-5044	33	13	g	g	NOUN
ejpam-5044	33	14	,	,	PUNCT
ejpam-5044	33	15	then	then	ADV
ejpam-5044	33	16	a	a	DET
ejpam-5044	33	17	path	path	NOUN
ejpam-5044	33	18	from	from	ADP
ejpam-5044	33	19	vertex	vertex	NOUN
ejpam-5044	33	20	u	u	NOUN
ejpam-5044	33	21	to	to	PART
ejpam-5044	33	22	vertex	vertex	NOUN
ejpam-5044	33	23	v	v	NOUN
ejpam-5044	33	24	is	be	AUX
ejpam-5044	33	25	called	call	VERB
ejpam-5044	33	26	u	u	NOUN
ejpam-5044	33	27	−	−	PROPN
ejpam-5044	33	28	v	v	ADP
ejpam-5044	33	29	path	path	NOUN
ejpam-5044	33	30	.	.	PUNCT
ejpam-5044	34	1	the	the	DET
ejpam-5044	34	2	cycle	cycle	NOUN
ejpam-5044	34	3	graph	graph	NOUN
ejpam-5044	34	4	cn	cn	PROPN
ejpam-5044	34	5	is	be	AUX
ejpam-5044	34	6	the	the	DET
ejpam-5044	34	7	graph	graph	NOUN
ejpam-5044	34	8	of	of	ADP
ejpam-5044	34	9	order	order	NOUN
ejpam-5044	34	10	n	n	PRON
ejpam-5044	34	11	≥	≥	NOUN
ejpam-5044	34	12	3	3	NUM
ejpam-5044	34	13	with	with	ADP
ejpam-5044	34	14	vertex	vertex	NOUN
ejpam-5044	34	15	-	-	PUNCT
ejpam-5044	34	16	set	set	VERB
ejpam-5044	34	17	{	{	PUNCT
ejpam-5044	34	18	x1	x1	PROPN
ejpam-5044	34	19	,	,	PUNCT
ejpam-5044	34	20	x2	x2	PROPN
ejpam-5044	34	21	,	,	PUNCT
ejpam-5044	34	22	.	.	PUNCT
ejpam-5044	34	23	.	.	PUNCT
ejpam-5044	34	24	.	.	PUNCT
ejpam-5044	35	1	,	,	PUNCT
ejpam-5044	35	2	xn	xn	X
ejpam-5044	35	3	}	}	PUNCT
ejpam-5044	35	4	and	and	CCONJ
ejpam-5044	35	5	edge	edge	NOUN
ejpam-5044	35	6	-	-	PUNCT
ejpam-5044	35	7	set	set	NOUN
ejpam-5044	35	8	{	{	PUNCT
ejpam-5044	35	9	x1x2	x1x2	NOUN
ejpam-5044	35	10	,	,	PUNCT
ejpam-5044	35	11	x2x3	x2x3	PROPN
ejpam-5044	35	12	,	,	PUNCT
ejpam-5044	35	13	.	.	PUNCT
ejpam-5044	35	14	.	.	PUNCT
ejpam-5044	36	1	.	.	PUNCT
ejpam-5044	37	1	,	,	PUNCT
ejpam-5044	37	2	xn−1xn	xn−1xn	PROPN
ejpam-5044	37	3	,	,	PUNCT
ejpam-5044	37	4	xnx1	xnx1	PROPN
ejpam-5044	37	5	}	}	PUNCT
ejpam-5044	37	6	.	.	PUNCT
ejpam-5044	38	1	a	a	DET
ejpam-5044	38	2	graph	graph	NOUN
ejpam-5044	38	3	is	be	AUX
ejpam-5044	38	4	complete	complete	ADJ
ejpam-5044	38	5	if	if	SCONJ
ejpam-5044	38	6	every	every	DET
ejpam-5044	38	7	pair	pair	NOUN
ejpam-5044	38	8	of	of	ADP
ejpam-5044	38	9	distinct	distinct	ADJ
ejpam-5044	38	10	vertices	vertex	NOUN
ejpam-5044	38	11	are	be	AUX
ejpam-5044	38	12	adjacent	adjacent	ADJ
ejpam-5044	38	13	.	.	PUNCT
ejpam-5044	39	1	a	a	DET
ejpam-5044	39	2	complete	complete	ADJ
ejpam-5044	39	3	graph	graph	NOUN
ejpam-5044	39	4	of	of	ADP
ejpam-5044	39	5	order	order	NOUN
ejpam-5044	39	6	n	n	NOUN
ejpam-5044	39	7	is	be	AUX
ejpam-5044	39	8	denoted	denote	VERB
ejpam-5044	39	9	by	by	ADP
ejpam-5044	39	10	kn	kn	PROPN
ejpam-5044	39	11	.	.	PUNCT
ejpam-5044	40	1	a	a	DET
ejpam-5044	40	2	subset	subset	NOUN
ejpam-5044	40	3	c	c	NOUN
ejpam-5044	40	4	of	of	ADP
ejpam-5044	40	5	a	a	DET
ejpam-5044	40	6	vertex	vertex	NOUN
ejpam-5044	40	7	-	-	PUNCT
ejpam-5044	40	8	set	set	VERB
ejpam-5044	40	9	v	v	NOUN
ejpam-5044	40	10	(	(	PUNCT
ejpam-5044	40	11	g	g	NOUN
ejpam-5044	40	12	)	)	PUNCT
ejpam-5044	40	13	of	of	ADP
ejpam-5044	40	14	g	g	PROPN
ejpam-5044	40	15	is	be	AUX
ejpam-5044	40	16	a	a	DET
ejpam-5044	40	17	clique	clique	NOUN
ejpam-5044	40	18	if	if	SCONJ
ejpam-5044	40	19	the	the	DET
ejpam-5044	40	20	graph	graph	NOUN
ejpam-5044	40	21	⟨c⟩	⟨c⟩	PROPN
ejpam-5044	40	22	induced	induce	VERB
ejpam-5044	40	23	by	by	ADP
ejpam-5044	40	24	c	c	PROPN
ejpam-5044	40	25	is	be	AUX
ejpam-5044	40	26	complete	complete	ADJ
ejpam-5044	40	27	.	.	PUNCT
ejpam-5044	41	1	the	the	DET
ejpam-5044	41	2	maximum	maximum	ADJ
ejpam-5044	41	3	cardinality	cardinality	NOUN
ejpam-5044	41	4	of	of	ADP
ejpam-5044	41	5	a	a	DET
ejpam-5044	41	6	clique	clique	NOUN
ejpam-5044	41	7	of	of	ADP
ejpam-5044	41	8	g	g	NOUN
ejpam-5044	41	9	,	,	PUNCT
ejpam-5044	41	10	denoted	denote	VERB
ejpam-5044	41	11	by	by	ADP
ejpam-5044	41	12	ω(g	ω(g	NOUN
ejpam-5044	41	13	)	)	PUNCT
ejpam-5044	41	14	,	,	PUNCT
ejpam-5044	41	15	is	be	AUX
ejpam-5044	41	16	called	call	VERB
ejpam-5044	41	17	the	the	DET
ejpam-5044	41	18	clique	clique	ADJ
ejpam-5044	41	19	number	number	NOUN
ejpam-5044	41	20	of	of	ADP
ejpam-5044	41	21	g.	g.	PROPN
ejpam-5044	41	22	a	a	DET
ejpam-5044	41	23	graph	graph	NOUN
ejpam-5044	41	24	g	g	NOUN
ejpam-5044	41	25	is	be	AUX
ejpam-5044	41	26	connected	connect	VERB
ejpam-5044	41	27	if	if	SCONJ
ejpam-5044	41	28	every	every	DET
ejpam-5044	41	29	pair	pair	NOUN
ejpam-5044	41	30	of	of	ADP
ejpam-5044	41	31	its	its	PRON
ejpam-5044	41	32	vertices	vertex	NOUN
ejpam-5044	41	33	can	can	AUX
ejpam-5044	41	34	be	be	AUX
ejpam-5044	41	35	joined	join	VERB
ejpam-5044	41	36	by	by	ADP
ejpam-5044	41	37	a	a	DET
ejpam-5044	41	38	path	path	NOUN
ejpam-5044	41	39	.	.	PUNCT
ejpam-5044	42	1	otherwise	otherwise	ADV
ejpam-5044	42	2	,	,	PUNCT
ejpam-5044	42	3	g	g	PROPN
ejpam-5044	42	4	is	be	AUX
ejpam-5044	42	5	disconnected	disconnect	VERB
ejpam-5044	42	6	.	.	PUNCT
ejpam-5044	43	1	a	a	DET
ejpam-5044	43	2	maximal	maximal	ADJ
ejpam-5044	43	3	connected	connected	ADJ
ejpam-5044	43	4	subgraph	subgraph	NOUN
ejpam-5044	43	5	(	(	PUNCT
ejpam-5044	43	6	not	not	PART
ejpam-5044	43	7	a	a	DET
ejpam-5044	43	8	subgraph	subgraph	NOUN
ejpam-5044	43	9	of	of	ADP
ejpam-5044	43	10	any	any	DET
ejpam-5044	43	11	connected	connected	ADJ
ejpam-5044	43	12	subgraph	subgraph	NOUN
ejpam-5044	43	13	)	)	PUNCT
ejpam-5044	43	14	of	of	ADP
ejpam-5044	43	15	g	g	PROPN
ejpam-5044	43	16	is	be	AUX
ejpam-5044	43	17	called	call	VERB
ejpam-5044	43	18	a	a	DET
ejpam-5044	43	19	component	component	NOUN
ejpam-5044	43	20	of	of	ADP
ejpam-5044	43	21	g.	g.	PROPN
ejpam-5044	43	22	let	let	VERB
ejpam-5044	43	23	g	g	NOUN
ejpam-5044	43	24	and	and	CCONJ
ejpam-5044	43	25	h	h	NOUN
ejpam-5044	43	26	be	be	VERB
ejpam-5044	43	27	two	two	NUM
ejpam-5044	43	28	graphs	graph	NOUN
ejpam-5044	43	29	.	.	PUNCT
ejpam-5044	44	1	the	the	DET
ejpam-5044	44	2	join	join	NOUN
ejpam-5044	44	3	g+h	g+h	PROPN
ejpam-5044	44	4	of	of	ADP
ejpam-5044	44	5	g	g	PROPN
ejpam-5044	44	6	and	and	CCONJ
ejpam-5044	44	7	h	h	NOUN
ejpam-5044	44	8	is	be	AUX
ejpam-5044	44	9	the	the	DET
ejpam-5044	44	10	graph	graph	NOUN
ejpam-5044	44	11	with	with	ADP
ejpam-5044	44	12	vertex	vertex	NOUN
ejpam-5044	44	13	set	set	VERB
ejpam-5044	44	14	v	v	NOUN
ejpam-5044	44	15	(	(	PUNCT
ejpam-5044	44	16	g+h	g+h	NOUN
ejpam-5044	44	17	)	)	PUNCT
ejpam-5044	44	18	=	=	SYM
ejpam-5044	44	19	v	v	X
ejpam-5044	44	20	(	(	PUNCT
ejpam-5044	44	21	g	g	NOUN
ejpam-5044	44	22	)	)	PUNCT
ejpam-5044	44	23	∪	∪	NOUN
ejpam-5044	44	24	v	v	NOUN
ejpam-5044	44	25	(	(	PUNCT
ejpam-5044	44	26	h	h	NOUN
ejpam-5044	44	27	)	)	PUNCT
ejpam-5044	44	28	and	and	CCONJ
ejpam-5044	44	29	edge	edge	NOUN
ejpam-5044	44	30	set	set	VERB
ejpam-5044	44	31	e(g+h	e(g+h	NUM
ejpam-5044	44	32	)	)	PUNCT
ejpam-5044	44	33	=	=	SYM
ejpam-5044	44	34	e(g	e(g	NOUN
ejpam-5044	44	35	)	)	PUNCT
ejpam-5044	44	36	∪	∪	ADP
ejpam-5044	44	37	e(h	e(h	PROPN
ejpam-5044	44	38	)	)	PUNCT
ejpam-5044	44	39	∪	∪	NOUN
ejpam-5044	44	40	{	{	PUNCT
ejpam-5044	44	41	ab	ab	NOUN
ejpam-5044	44	42	:	:	PUNCT
ejpam-5044	44	43	a	a	DET
ejpam-5044	44	44	∈	∈	PROPN
ejpam-5044	44	45	v	v	NOUN
ejpam-5044	44	46	(	(	PUNCT
ejpam-5044	44	47	g	g	NOUN
ejpam-5044	44	48	)	)	PUNCT
ejpam-5044	44	49	,	,	PUNCT
ejpam-5044	45	1	b	b	X
ejpam-5044	45	2	∈	∈	PROPN
ejpam-5044	45	3	v	v	ADP
ejpam-5044	45	4	(	(	PUNCT
ejpam-5044	45	5	h	h	NOUN
ejpam-5044	45	6	)	)	PUNCT
ejpam-5044	45	7	}	}	PUNCT
ejpam-5044	45	8	.	.	PUNCT
ejpam-5044	46	1	the	the	DET
ejpam-5044	46	2	distance	distance	NOUN
ejpam-5044	46	3	dg(u	dg(u	NOUN
ejpam-5044	46	4	,	,	PUNCT
ejpam-5044	46	5	v	v	NOUN
ejpam-5044	46	6	)	)	PUNCT
ejpam-5044	46	7	in	in	ADP
ejpam-5044	46	8	g	g	NOUN
ejpam-5044	46	9	of	of	ADP
ejpam-5044	46	10	two	two	NUM
ejpam-5044	46	11	vertices	vertex	NOUN
ejpam-5044	46	12	u	u	NOUN
ejpam-5044	46	13	,	,	PUNCT
ejpam-5044	46	14	v	v	PROPN
ejpam-5044	46	15	is	be	AUX
ejpam-5044	46	16	the	the	DET
ejpam-5044	46	17	length	length	NOUN
ejpam-5044	46	18	of	of	ADP
ejpam-5044	46	19	a	a	DET
ejpam-5044	46	20	shortest	short	ADJ
ejpam-5044	46	21	u	u	NOUN
ejpam-5044	46	22	-	-	NOUN
ejpam-5044	46	23	v	v	ADJ
ejpam-5044	46	24	path	path	NOUN
ejpam-5044	46	25	in	in	ADP
ejpam-5044	46	26	g.	g.	PROPN
ejpam-5044	46	27	the	the	DET
ejpam-5044	46	28	greatest	great	ADJ
ejpam-5044	46	29	distance	distance	NOUN
ejpam-5044	46	30	between	between	ADP
ejpam-5044	46	31	any	any	DET
ejpam-5044	46	32	two	two	NUM
ejpam-5044	46	33	vertices	vertex	NOUN
ejpam-5044	46	34	in	in	ADP
ejpam-5044	46	35	g	g	NOUN
ejpam-5044	46	36	,	,	PUNCT
ejpam-5044	46	37	denoted	denote	VERB
ejpam-5044	46	38	by	by	ADP
ejpam-5044	46	39	diam(g	diam(g	PROPN
ejpam-5044	46	40	)	)	PUNCT
ejpam-5044	46	41	,	,	PUNCT
ejpam-5044	46	42	is	be	AUX
ejpam-5044	46	43	called	call	VERB
ejpam-5044	46	44	the	the	DET
ejpam-5044	46	45	diameter	diameter	NOUN
ejpam-5044	46	46	of	of	ADP
ejpam-5044	46	47	g.	g.	PROPN
ejpam-5044	46	48	a	a	DET
ejpam-5044	46	49	subset	subset	NOUN
ejpam-5044	46	50	i	i	PRON
ejpam-5044	46	51	of	of	ADP
ejpam-5044	46	52	v	v	NOUN
ejpam-5044	46	53	(	(	PUNCT
ejpam-5044	46	54	g	g	NOUN
ejpam-5044	46	55	)	)	PUNCT
ejpam-5044	46	56	is	be	AUX
ejpam-5044	46	57	called	call	VERB
ejpam-5044	46	58	an	an	DET
ejpam-5044	46	59	independent	independent	ADJ
ejpam-5044	46	60	if	if	SCONJ
ejpam-5044	46	61	for	for	ADP
ejpam-5044	46	62	every	every	DET
ejpam-5044	46	63	pair	pair	NOUN
ejpam-5044	46	64	of	of	ADP
ejpam-5044	46	65	distinct	distinct	ADJ
ejpam-5044	46	66	vertices	vertex	NOUN
ejpam-5044	46	67	x	x	X
ejpam-5044	46	68	,	,	PUNCT
ejpam-5044	46	69	y	y	PROPN
ejpam-5044	46	70	∈	∈	PROPN
ejpam-5044	46	71	i	i	PRON
ejpam-5044	46	72	,	,	PUNCT
ejpam-5044	46	73	dg(x	dg(x	X
ejpam-5044	46	74	,	,	PUNCT
ejpam-5044	46	75	y	y	NOUN
ejpam-5044	46	76	)	)	PUNCT
ejpam-5044	46	77	̸=	̸=	PROPN
ejpam-5044	46	78	1	1	NUM
ejpam-5044	46	79	.	.	PUNCT
ejpam-5044	47	1	the	the	DET
ejpam-5044	47	2	maximum	maximum	ADJ
ejpam-5044	47	3	cardinality	cardinality	NOUN
ejpam-5044	47	4	of	of	ADP
ejpam-5044	47	5	an	an	DET
ejpam-5044	47	6	independent	independent	ADJ
ejpam-5044	47	7	set	set	NOUN
ejpam-5044	47	8	in	in	ADP
ejpam-5044	47	9	g	g	NOUN
ejpam-5044	47	10	,	,	PUNCT
ejpam-5044	47	11	denoted	denote	VERB
ejpam-5044	47	12	by	by	ADP
ejpam-5044	47	13	α(g	α(g	NOUN
ejpam-5044	47	14	)	)	PUNCT
ejpam-5044	47	15	,	,	PUNCT
ejpam-5044	47	16	is	be	AUX
ejpam-5044	47	17	called	call	VERB
ejpam-5044	47	18	the	the	DET
ejpam-5044	47	19	independence	independence	NOUN
ejpam-5044	47	20	number	number	NOUN
ejpam-5044	47	21	of	of	ADP
ejpam-5044	47	22	g.	g.	PROPN
ejpam-5044	47	23	any	any	DET
ejpam-5044	47	24	independent	independent	ADJ
ejpam-5044	47	25	set	set	NOUN
ejpam-5044	47	26	i	i	PRON
ejpam-5044	47	27	with	with	ADP
ejpam-5044	47	28	cardinality	cardinality	NOUN
ejpam-5044	47	29	equal	equal	ADJ
ejpam-5044	47	30	to	to	ADP
ejpam-5044	47	31	α(g	α(g	NUM
ejpam-5044	47	32	)	)	PUNCT
ejpam-5044	47	33	is	be	AUX
ejpam-5044	47	34	called	call	VERB
ejpam-5044	47	35	an	an	DET
ejpam-5044	47	36	α	α	NOUN
ejpam-5044	47	37	-	-	PUNCT
ejpam-5044	47	38	set	set	NOUN
ejpam-5044	47	39	of	of	ADP
ejpam-5044	47	40	g.	g.	PROPN
ejpam-5044	47	41	a	a	DET
ejpam-5044	47	42	subset	subset	NOUN
ejpam-5044	47	43	s	s	NOUN
ejpam-5044	47	44	of	of	ADP
ejpam-5044	47	45	v	v	NOUN
ejpam-5044	47	46	(	(	PUNCT
ejpam-5044	47	47	g	g	NOUN
ejpam-5044	47	48	)	)	PUNCT
ejpam-5044	47	49	is	be	AUX
ejpam-5044	47	50	called	call	VERB
ejpam-5044	47	51	a	a	DET
ejpam-5044	47	52	hop	hop	NOUN
ejpam-5044	47	53	independent	independent	ADJ
ejpam-5044	47	54	set	set	NOUN
ejpam-5044	47	55	of	of	ADP
ejpam-5044	47	56	g	g	PROPN
ejpam-5044	47	57	if	if	SCONJ
ejpam-5044	47	58	any	any	DET
ejpam-5044	47	59	two	two	NUM
ejpam-5044	47	60	distinct	distinct	ADJ
ejpam-5044	47	61	vertices	vertex	NOUN
ejpam-5044	47	62	in	in	ADP
ejpam-5044	47	63	s	s	NOUN
ejpam-5044	47	64	are	be	AUX
ejpam-5044	47	65	not	not	PART
ejpam-5044	47	66	at	at	ADP
ejpam-5044	47	67	distance	distance	NOUN
ejpam-5044	47	68	two	two	NUM
ejpam-5044	47	69	from	from	ADP
ejpam-5044	47	70	each	each	DET
ejpam-5044	47	71	other	other	ADJ
ejpam-5044	47	72	,	,	PUNCT
ejpam-5044	47	73	that	that	ADV
ejpam-5044	47	74	is	is	ADV
ejpam-5044	47	75	,	,	PUNCT
ejpam-5044	47	76	dg(v	dg(v	X
ejpam-5044	47	77	,	,	PUNCT
ejpam-5044	47	78	w	w	NOUN
ejpam-5044	47	79	)	)	PUNCT
ejpam-5044	47	80	̸=	̸=	PROPN
ejpam-5044	47	81	2	2	NUM
ejpam-5044	47	82	for	for	ADP
ejpam-5044	47	83	any	any	DET
ejpam-5044	47	84	two	two	NUM
ejpam-5044	47	85	distinct	distinct	ADJ
ejpam-5044	47	86	vertices	vertex	NOUN
ejpam-5044	47	87	v	v	ADP
ejpam-5044	47	88	,	,	PUNCT
ejpam-5044	47	89	w	w	PROPN
ejpam-5044	47	90	∈	∈	PROPN
ejpam-5044	47	91	s.	s.	PROPN
ejpam-5044	47	92	the	the	DET
ejpam-5044	47	93	hop	hop	PROPN
ejpam-5044	47	94	independence	independence	NOUN
ejpam-5044	47	95	number	number	NOUN
ejpam-5044	47	96	of	of	ADP
ejpam-5044	47	97	g	g	NOUN
ejpam-5044	47	98	,	,	PUNCT
ejpam-5044	47	99	denoted	denote	VERB
ejpam-5044	47	100	by	by	ADP
ejpam-5044	47	101	αh(g	αh(g	NOUN
ejpam-5044	47	102	)	)	PUNCT
ejpam-5044	47	103	,	,	PUNCT
ejpam-5044	47	104	is	be	AUX
ejpam-5044	47	105	the	the	DET
ejpam-5044	47	106	maximum	maximum	ADJ
ejpam-5044	47	107	j.	j.	PROPN
ejpam-5044	47	108	a.	a.	PROPN
ejpam-5044	47	109	hassan	hassan	PROPN
ejpam-5044	47	110	et	et	PROPN
ejpam-5044	47	111	al	al	PROPN
ejpam-5044	47	112	.	.	PUNCT
ejpam-5044	47	113	/	/	SYM
ejpam-5044	47	114	eur	eur	PROPN
ejpam-5044	47	115	.	.	PUNCT
ejpam-5044	48	1	j.	j.	PROPN
ejpam-5044	48	2	pure	pure	PROPN
ejpam-5044	48	3	appl	appl	PROPN
ejpam-5044	48	4	.	.	PROPN
ejpam-5044	48	5	math	math	PROPN
ejpam-5044	48	6	,	,	PUNCT
ejpam-5044	48	7	17	17	NUM
ejpam-5044	48	8	(	(	PUNCT
ejpam-5044	48	9	1	1	NUM
ejpam-5044	48	10	)	)	PUNCT
ejpam-5044	48	11	(	(	PUNCT
ejpam-5044	48	12	2024	2024	NUM
ejpam-5044	48	13	)	)	PUNCT
ejpam-5044	48	14	,	,	PUNCT
ejpam-5044	48	15	435	435	NUM
ejpam-5044	48	16	-	-	SYM
ejpam-5044	48	17	444	444	NUM
ejpam-5044	48	18	437	437	NUM
ejpam-5044	48	19	cardinality	cardinality	NOUN
ejpam-5044	48	20	of	of	ADP
ejpam-5044	48	21	a	a	DET
ejpam-5044	48	22	hop	hop	NOUN
ejpam-5044	48	23	independent	independent	ADJ
ejpam-5044	48	24	set	set	NOUN
ejpam-5044	48	25	of	of	ADP
ejpam-5044	48	26	g.	g.	PROPN
ejpam-5044	48	27	3	3	NUM
ejpam-5044	48	28	.	.	PUNCT
ejpam-5044	48	29	results	result	NOUN
ejpam-5044	48	30	we	we	PRON
ejpam-5044	48	31	begin	begin	VERB
ejpam-5044	48	32	this	this	DET
ejpam-5044	48	33	section	section	NOUN
ejpam-5044	48	34	by	by	ADP
ejpam-5044	48	35	introducing	introduce	VERB
ejpam-5044	48	36	the	the	DET
ejpam-5044	48	37	concept	concept	NOUN
ejpam-5044	48	38	of	of	ADP
ejpam-5044	48	39	certified	certify	VERB
ejpam-5044	48	40	hop	hop	NOUN
ejpam-5044	48	41	independence	independence	NOUN
ejpam-5044	48	42	in	in	ADP
ejpam-5044	48	43	a	a	DET
ejpam-5044	48	44	graph	graph	NOUN
ejpam-5044	48	45	.	.	PUNCT
ejpam-5044	49	1	definition	definition	NOUN
ejpam-5044	49	2	1	1	NUM
ejpam-5044	49	3	.	.	PUNCT
ejpam-5044	50	1	let	let	VERB
ejpam-5044	50	2	g	g	PRON
ejpam-5044	50	3	be	be	AUX
ejpam-5044	50	4	a	a	DET
ejpam-5044	50	5	graph	graph	NOUN
ejpam-5044	50	6	.	.	PUNCT
ejpam-5044	51	1	then	then	ADV
ejpam-5044	51	2	b	b	PROPN
ejpam-5044	51	3	⊆	⊆	NUM
ejpam-5044	51	4	v	v	NOUN
ejpam-5044	51	5	(	(	PUNCT
ejpam-5044	51	6	g	g	NOUN
ejpam-5044	51	7	)	)	PUNCT
ejpam-5044	51	8	is	be	AUX
ejpam-5044	51	9	called	call	VERB
ejpam-5044	51	10	a	a	DET
ejpam-5044	51	11	certified	certify	VERB
ejpam-5044	51	12	hop	hop	NOUN
ejpam-5044	51	13	independent	independent	ADJ
ejpam-5044	51	14	set	set	NOUN
ejpam-5044	51	15	of	of	ADP
ejpam-5044	51	16	g	g	PROPN
ejpam-5044	51	17	if	if	SCONJ
ejpam-5044	51	18	for	for	ADP
ejpam-5044	51	19	every	every	DET
ejpam-5044	51	20	a	a	PROPN
ejpam-5044	51	21	,	,	PUNCT
ejpam-5044	51	22	b	b	PROPN
ejpam-5044	51	23	∈	∈	PROPN
ejpam-5044	51	24	b	b	PROPN
ejpam-5044	51	25	,	,	PUNCT
ejpam-5044	51	26	dg(a	dg(a	X
ejpam-5044	51	27	,	,	PUNCT
ejpam-5044	51	28	b	b	X
ejpam-5044	51	29	)	)	PUNCT
ejpam-5044	51	30	̸=	̸=	PROPN
ejpam-5044	51	31	2	2	NUM
ejpam-5044	51	32	and	and	CCONJ
ejpam-5044	51	33	for	for	ADP
ejpam-5044	51	34	every	every	DET
ejpam-5044	51	35	x	x	SYM
ejpam-5044	51	36	∈	∈	PROPN
ejpam-5044	51	37	b	b	PROPN
ejpam-5044	51	38	has	have	VERB
ejpam-5044	51	39	either	either	CCONJ
ejpam-5044	51	40	zero	zero	NUM
ejpam-5044	51	41	or	or	CCONJ
ejpam-5044	51	42	at	at	ADP
ejpam-5044	51	43	least	least	ADV
ejpam-5044	51	44	two	two	NUM
ejpam-5044	51	45	neighbors	neighbor	NOUN
ejpam-5044	51	46	in	in	ADP
ejpam-5044	51	47	v	v	NOUN
ejpam-5044	51	48	(	(	PUNCT
ejpam-5044	51	49	g	g	NOUN
ejpam-5044	51	50	)	)	PUNCT
ejpam-5044	51	51	\	\	PROPN
ejpam-5044	52	1	b.	b.	PROPN
ejpam-5044	52	2	the	the	DET
ejpam-5044	52	3	maximum	maximum	PROPN
ejpam-5044	52	4	cardinality	cardinality	NOUN
ejpam-5044	52	5	among	among	ADP
ejpam-5044	52	6	all	all	DET
ejpam-5044	52	7	certified	certify	VERB
ejpam-5044	52	8	hop	hop	NOUN
ejpam-5044	52	9	independent	independent	ADJ
ejpam-5044	52	10	sets	set	NOUN
ejpam-5044	52	11	in	in	ADP
ejpam-5044	52	12	g	g	NOUN
ejpam-5044	52	13	,	,	PUNCT
ejpam-5044	52	14	denoted	denote	VERB
ejpam-5044	52	15	by	by	ADP
ejpam-5044	52	16	αch(g	αch(g	NOUN
ejpam-5044	52	17	)	)	PUNCT
ejpam-5044	52	18	,	,	PUNCT
ejpam-5044	52	19	is	be	AUX
ejpam-5044	52	20	called	call	VERB
ejpam-5044	52	21	the	the	DET
ejpam-5044	52	22	certified	certify	VERB
ejpam-5044	52	23	hop	hop	NOUN
ejpam-5044	52	24	independence	independence	NOUN
ejpam-5044	52	25	number	number	NOUN
ejpam-5044	52	26	of	of	ADP
ejpam-5044	52	27	g.	g.	PROPN
ejpam-5044	52	28	any	any	DET
ejpam-5044	52	29	certified	certify	VERB
ejpam-5044	52	30	hop	hop	NOUN
ejpam-5044	52	31	independent	independent	ADJ
ejpam-5044	52	32	set	set	PROPN
ejpam-5044	52	33	b	b	PROPN
ejpam-5044	52	34	with	with	ADP
ejpam-5044	52	35	|b|	|b|	PROPN
ejpam-5044	52	36	=	=	SYM
ejpam-5044	52	37	αch(g	αch(g	NOUN
ejpam-5044	52	38	)	)	PUNCT
ejpam-5044	52	39	is	be	AUX
ejpam-5044	52	40	called	call	VERB
ejpam-5044	52	41	the	the	DET
ejpam-5044	52	42	maximum	maximum	ADJ
ejpam-5044	52	43	certified	certify	VERB
ejpam-5044	52	44	hop	hop	NOUN
ejpam-5044	52	45	independent	independent	ADJ
ejpam-5044	52	46	set	set	NOUN
ejpam-5044	52	47	of	of	ADP
ejpam-5044	52	48	g	g	NOUN
ejpam-5044	52	49	or	or	CCONJ
ejpam-5044	52	50	an	an	DET
ejpam-5044	52	51	αch	αch	ADV
ejpam-5044	52	52	-	-	PUNCT
ejpam-5044	52	53	set	set	NOUN
ejpam-5044	52	54	of	of	ADP
ejpam-5044	52	55	g.	g.	PROPN
ejpam-5044	52	56	example	example	NOUN
ejpam-5044	53	1	1	1	X
ejpam-5044	53	2	.	.	X
ejpam-5044	53	3	consider	consider	VERB
ejpam-5044	53	4	the	the	DET
ejpam-5044	53	5	graph	graph	NOUN
ejpam-5044	53	6	g	g	NOUN
ejpam-5044	53	7	in	in	ADP
ejpam-5044	53	8	figure	figure	NOUN
ejpam-5044	53	9	1	1	NUM
ejpam-5044	53	10	.	.	PUNCT
ejpam-5044	54	1	g	g	NOUN
ejpam-5044	54	2	:	:	PUNCT
ejpam-5044	54	3	a	a	DET
ejpam-5044	54	4	f	f	X
ejpam-5044	54	5	b	b	PROPN
ejpam-5044	54	6	e	e	X
ejpam-5044	54	7	c	c	NOUN
ejpam-5044	54	8	d	d	NOUN
ejpam-5044	54	9	figure	figure	NOUN
ejpam-5044	54	10	1	1	NUM
ejpam-5044	54	11	:	:	PUNCT
ejpam-5044	54	12	graph	graph	VERB
ejpam-5044	54	13	g	g	NOUN
ejpam-5044	54	14	with	with	ADP
ejpam-5044	54	15	αch(g	αch(g	NOUN
ejpam-5044	54	16	)	)	PUNCT
ejpam-5044	54	17	=	=	SYM
ejpam-5044	54	18	2	2	NUM
ejpam-5044	54	19	let	let	VERB
ejpam-5044	54	20	b	b	NOUN
ejpam-5044	54	21	=	=	PRON
ejpam-5044	54	22	{	{	PUNCT
ejpam-5044	54	23	a	a	X
ejpam-5044	54	24	,	,	PUNCT
ejpam-5044	54	25	d	d	NOUN
ejpam-5044	54	26	}	}	PUNCT
ejpam-5044	54	27	.	.	PUNCT
ejpam-5044	55	1	then	then	ADV
ejpam-5044	55	2	dg(a	dg(a	NUM
ejpam-5044	55	3	,	,	PUNCT
ejpam-5044	55	4	d	d	X
ejpam-5044	55	5	)	)	PUNCT
ejpam-5044	55	6	=	=	SYM
ejpam-5044	55	7	3	3	X
ejpam-5044	55	8	.	.	PUNCT
ejpam-5044	55	9	thus	thus	ADV
ejpam-5044	55	10	,	,	PUNCT
ejpam-5044	55	11	b	b	PROPN
ejpam-5044	55	12	is	be	AUX
ejpam-5044	55	13	a	a	DET
ejpam-5044	55	14	hop	hop	NOUN
ejpam-5044	55	15	independent	independent	ADJ
ejpam-5044	55	16	set	set	NOUN
ejpam-5044	55	17	of	of	ADP
ejpam-5044	55	18	b.	b.	PROPN
ejpam-5044	55	19	now	now	ADV
ejpam-5044	55	20	,	,	PUNCT
ejpam-5044	55	21	observe	observe	VERB
ejpam-5044	55	22	that	that	PRON
ejpam-5044	55	23	b	b	NOUN
ejpam-5044	55	24	,	,	PUNCT
ejpam-5044	55	25	f	f	PROPN
ejpam-5044	55	26	∈	∈	PROPN
ejpam-5044	55	27	ng(a	ng(a	NOUN
ejpam-5044	55	28	)	)	PUNCT
ejpam-5044	55	29	and	and	CCONJ
ejpam-5044	55	30	c	c	X
ejpam-5044	55	31	,	,	PUNCT
ejpam-5044	55	32	e	e	PROPN
ejpam-5044	55	33	∈	∈	PROPN
ejpam-5044	55	34	ng(d	ng(d	NOUN
ejpam-5044	55	35	)	)	PUNCT
ejpam-5044	55	36	,	,	PUNCT
ejpam-5044	55	37	where	where	SCONJ
ejpam-5044	55	38	b	b	NOUN
ejpam-5044	55	39	,	,	PUNCT
ejpam-5044	55	40	c	c	NOUN
ejpam-5044	55	41	,	,	PUNCT
ejpam-5044	55	42	f	f	X
ejpam-5044	55	43	,	,	PUNCT
ejpam-5044	55	44	e	e	PROPN
ejpam-5044	55	45	∈	∈	PROPN
ejpam-5044	55	46	v	v	ADP
ejpam-5044	55	47	(	(	PUNCT
ejpam-5044	55	48	g	g	NOUN
ejpam-5044	55	49	)	)	PUNCT
ejpam-5044	55	50	\	\	PROPN
ejpam-5044	55	51	b.	b.	PROPN
ejpam-5044	56	1	it	it	PRON
ejpam-5044	56	2	follows	follow	VERB
ejpam-5044	56	3	that	that	SCONJ
ejpam-5044	56	4	b	b	NOUN
ejpam-5044	56	5	is	be	AUX
ejpam-5044	56	6	a	a	DET
ejpam-5044	56	7	certified	certified	ADJ
ejpam-5044	56	8	hop	hop	NOUN
ejpam-5044	56	9	independent	independent	ADJ
ejpam-5044	56	10	set	set	NOUN
ejpam-5044	56	11	of	of	ADP
ejpam-5044	56	12	g.	g.	PROPN
ejpam-5044	56	13	moreover	moreover	ADV
ejpam-5044	56	14	,	,	PUNCT
ejpam-5044	56	15	it	it	PRON
ejpam-5044	56	16	can	can	AUX
ejpam-5044	56	17	be	be	AUX
ejpam-5044	56	18	verified	verify	VERB
ejpam-5044	56	19	that	that	SCONJ
ejpam-5044	56	20	αch(g	αch(g	NOUN
ejpam-5044	56	21	)	)	PUNCT
ejpam-5044	56	22	=	=	SYM
ejpam-5044	56	23	2	2	X
ejpam-5044	56	24	.	.	X
ejpam-5044	56	25	theorem	theorem	NOUN
ejpam-5044	56	26	1	1	NUM
ejpam-5044	56	27	.	.	PUNCT
ejpam-5044	57	1	let	let	VERB
ejpam-5044	57	2	g	g	PRON
ejpam-5044	57	3	be	be	AUX
ejpam-5044	57	4	a	a	DET
ejpam-5044	57	5	graph	graph	NOUN
ejpam-5044	57	6	.	.	PUNCT
ejpam-5044	58	1	then	then	ADV
ejpam-5044	58	2	(	(	PUNCT
ejpam-5044	58	3	i	i	NOUN
ejpam-5044	58	4	)	)	PUNCT
ejpam-5044	58	5	αch(g	αch(g	PROPN
ejpam-5044	58	6	)	)	PUNCT
ejpam-5044	58	7	≤	≤	NOUN
ejpam-5044	58	8	αh(g	αh(g	NOUN
ejpam-5044	58	9	)	)	PUNCT
ejpam-5044	58	10	;	;	PUNCT
ejpam-5044	58	11	and	and	CCONJ
ejpam-5044	58	12	(	(	PUNCT
ejpam-5044	58	13	ii	ii	NOUN
ejpam-5044	58	14	)	)	PUNCT
ejpam-5044	58	15	1	1	NUM
ejpam-5044	58	16	≤	≤	NUM
ejpam-5044	58	17	αch(g	αch(g	NOUN
ejpam-5044	58	18	)	)	PUNCT
ejpam-5044	58	19	≤	≤	NOUN
ejpam-5044	58	20	|v	|v	X
ejpam-5044	58	21	(	(	PUNCT
ejpam-5044	58	22	g)|	g)|	NOUN
ejpam-5044	58	23	.	.	PUNCT
ejpam-5044	59	1	proof	proof	NOUN
ejpam-5044	59	2	.	.	PUNCT
ejpam-5044	60	1	(	(	PUNCT
ejpam-5044	60	2	i	i	NOUN
ejpam-5044	60	3	)	)	PUNCT
ejpam-5044	60	4	let	let	VERB
ejpam-5044	61	1	b	b	NOUN
ejpam-5044	61	2	⊆	⊆	NUM
ejpam-5044	61	3	v	v	NOUN
ejpam-5044	61	4	(	(	PUNCT
ejpam-5044	61	5	g	g	NOUN
ejpam-5044	61	6	)	)	PUNCT
ejpam-5044	61	7	be	be	AUX
ejpam-5044	61	8	a	a	DET
ejpam-5044	61	9	maximum	maximum	ADV
ejpam-5044	61	10	certified	certify	VERB
ejpam-5044	61	11	hop	hop	NOUN
ejpam-5044	61	12	independent	independent	ADJ
ejpam-5044	61	13	set	set	NOUN
ejpam-5044	61	14	of	of	ADP
ejpam-5044	61	15	g.	g.	PROPN
ejpam-5044	61	16	then	then	ADV
ejpam-5044	61	17	αch(g	αch(g	NOUN
ejpam-5044	61	18	)	)	PUNCT
ejpam-5044	61	19	=	=	SYM
ejpam-5044	61	20	|b|	|b|	PROPN
ejpam-5044	61	21	and	and	CCONJ
ejpam-5044	61	22	b	b	PROPN
ejpam-5044	61	23	is	be	AUX
ejpam-5044	61	24	a	a	DET
ejpam-5044	61	25	hop	hop	NOUN
ejpam-5044	61	26	independent	independent	ADJ
ejpam-5044	61	27	set	set	NOUN
ejpam-5044	61	28	of	of	ADP
ejpam-5044	61	29	g.	g.	PROPN
ejpam-5044	61	30	since	since	SCONJ
ejpam-5044	61	31	αh(g	αh(g	NOUN
ejpam-5044	61	32	)	)	PUNCT
ejpam-5044	61	33	is	be	AUX
ejpam-5044	61	34	the	the	DET
ejpam-5044	61	35	maximum	maximum	ADJ
ejpam-5044	61	36	cardinality	cardinality	NOUN
ejpam-5044	61	37	among	among	ADP
ejpam-5044	61	38	all	all	DET
ejpam-5044	61	39	hop	hop	NOUN
ejpam-5044	61	40	independent	independent	ADJ
ejpam-5044	61	41	sets	set	NOUN
ejpam-5044	61	42	in	in	ADP
ejpam-5044	61	43	g	g	NOUN
ejpam-5044	61	44	,	,	PUNCT
ejpam-5044	61	45	it	it	PRON
ejpam-5044	61	46	follows	follow	VERB
ejpam-5044	61	47	that	that	SCONJ
ejpam-5044	61	48	αh(g	αh(g	NOUN
ejpam-5044	61	49	)	)	PUNCT
ejpam-5044	61	50	≥	≥	NOUN
ejpam-5044	61	51	|b|	|b|	X
ejpam-5044	61	52	=	=	PUNCT
ejpam-5044	61	53	αch(g	αch(g	NOUN
ejpam-5044	61	54	)	)	PUNCT
ejpam-5044	61	55	.	.	PUNCT
ejpam-5044	62	1	(	(	PUNCT
ejpam-5044	62	2	ii	ii	NOUN
ejpam-5044	62	3	)	)	PUNCT
ejpam-5044	62	4	since	since	SCONJ
ejpam-5044	62	5	an	an	DET
ejpam-5044	62	6	empty	empty	ADJ
ejpam-5044	62	7	set	set	NOUN
ejpam-5044	62	8	can	can	AUX
ejpam-5044	62	9	not	not	PART
ejpam-5044	62	10	be	be	AUX
ejpam-5044	62	11	a	a	DET
ejpam-5044	62	12	certified	certified	ADJ
ejpam-5044	62	13	hop	hop	NOUN
ejpam-5044	62	14	independent	independent	ADJ
ejpam-5044	62	15	,	,	PUNCT
ejpam-5044	62	16	we	we	PRON
ejpam-5044	62	17	have	have	VERB
ejpam-5044	62	18	αch(g	αch(g	NOUN
ejpam-5044	62	19	)	)	PUNCT
ejpam-5044	62	20	≥	≥	NOUN
ejpam-5044	62	21	1	1	NUM
ejpam-5044	62	22	.	.	PUNCT
ejpam-5044	63	1	since	since	SCONJ
ejpam-5044	63	2	αh(g	αh(g	NOUN
ejpam-5044	63	3	)	)	PUNCT
ejpam-5044	63	4	≤	≤	NUM
ejpam-5044	63	5	|v	|v	X
ejpam-5044	63	6	(	(	PUNCT
ejpam-5044	63	7	g)|	g)|	INTJ
ejpam-5044	63	8	,	,	PUNCT
ejpam-5044	63	9	we	we	PRON
ejpam-5044	63	10	have	have	VERB
ejpam-5044	63	11	αch(g	αch(g	NOUN
ejpam-5044	63	12	)	)	PUNCT
ejpam-5044	63	13	≤	≤	NOUN
ejpam-5044	63	14	|v	|v	X
ejpam-5044	63	15	(	(	PUNCT
ejpam-5044	63	16	g)|	g)|	NOUN
ejpam-5044	63	17	by	by	ADP
ejpam-5044	63	18	(	(	PUNCT
ejpam-5044	63	19	i	i	NOUN
ejpam-5044	63	20	)	)	PUNCT
ejpam-5044	63	21	.	.	PUNCT
ejpam-5044	64	1	consequently	consequently	ADV
ejpam-5044	64	2	,	,	PUNCT
ejpam-5044	64	3	1	1	NUM
ejpam-5044	64	4	≤	≤	NUM
ejpam-5044	64	5	αch(g	αch(g	NOUN
ejpam-5044	64	6	)	)	PUNCT
ejpam-5044	64	7	≤	≤	NOUN
ejpam-5044	64	8	|v	|v	X
ejpam-5044	64	9	(	(	PUNCT
ejpam-5044	64	10	g)|	g)|	PROPN
ejpam-5044	64	11	.	.	PUNCT
ejpam-5044	65	1	j.	j.	PROPN
ejpam-5044	65	2	a.	a.	PROPN
ejpam-5044	65	3	hassan	hassan	PROPN
ejpam-5044	65	4	et	et	PROPN
ejpam-5044	65	5	al	al	PROPN
ejpam-5044	65	6	.	.	PUNCT
ejpam-5044	65	7	/	/	SYM
ejpam-5044	65	8	eur	eur	PROPN
ejpam-5044	65	9	.	.	PUNCT
ejpam-5044	66	1	j.	j.	PROPN
ejpam-5044	66	2	pure	pure	PROPN
ejpam-5044	66	3	appl	appl	PROPN
ejpam-5044	66	4	.	.	PROPN
ejpam-5044	66	5	math	math	PROPN
ejpam-5044	66	6	,	,	PUNCT
ejpam-5044	66	7	17	17	NUM
ejpam-5044	66	8	(	(	PUNCT
ejpam-5044	66	9	1	1	NUM
ejpam-5044	66	10	)	)	PUNCT
ejpam-5044	66	11	(	(	PUNCT
ejpam-5044	66	12	2024	2024	NUM
ejpam-5044	66	13	)	)	PUNCT
ejpam-5044	66	14	,	,	PUNCT
ejpam-5044	66	15	435	435	NUM
ejpam-5044	66	16	-	-	SYM
ejpam-5044	66	17	444	444	NUM
ejpam-5044	66	18	438	438	NUM
ejpam-5044	66	19	theorem	theorem	NOUN
ejpam-5044	66	20	2	2	NUM
ejpam-5044	66	21	.	.	PUNCT
ejpam-5044	67	1	let	let	VERB
ejpam-5044	67	2	g	g	PRON
ejpam-5044	67	3	be	be	AUX
ejpam-5044	67	4	a	a	DET
ejpam-5044	67	5	graph	graph	NOUN
ejpam-5044	67	6	.	.	PUNCT
ejpam-5044	68	1	then	then	ADV
ejpam-5044	68	2	αch(g	αch(g	NOUN
ejpam-5044	68	3	)	)	PUNCT
ejpam-5044	68	4	=	=	SYM
ejpam-5044	69	1	|v	|v	X
ejpam-5044	69	2	(	(	PUNCT
ejpam-5044	69	3	g)|	g)|	VERB
ejpam-5044	69	4	if	if	SCONJ
ejpam-5044	69	5	and	and	CCONJ
ejpam-5044	69	6	only	only	ADV
ejpam-5044	69	7	if	if	SCONJ
ejpam-5044	69	8	diam(h	diam(h	ADJ
ejpam-5044	69	9	)	)	PUNCT
ejpam-5044	69	10	≤	≤	NOUN
ejpam-5044	69	11	1	1	NUM
ejpam-5044	69	12	for	for	ADP
ejpam-5044	69	13	each	each	DET
ejpam-5044	69	14	component	component	NOUN
ejpam-5044	69	15	h	h	NOUN
ejpam-5044	69	16	of	of	ADP
ejpam-5044	69	17	g.	g.	PROPN
ejpam-5044	69	18	proof	proof	PROPN
ejpam-5044	69	19	.	.	PUNCT
ejpam-5044	69	20	suppose	suppose	VERB
ejpam-5044	69	21	that	that	SCONJ
ejpam-5044	69	22	αch(g	αch(g	NOUN
ejpam-5044	69	23	)	)	PUNCT
ejpam-5044	69	24	=	=	SYM
ejpam-5044	69	25	|v	|v	PROPN
ejpam-5044	69	26	(	(	PUNCT
ejpam-5044	69	27	g)|	g)|	PROPN
ejpam-5044	69	28	.	.	PUNCT
ejpam-5044	70	1	then	then	ADV
ejpam-5044	70	2	v	v	X
ejpam-5044	70	3	(	(	PUNCT
ejpam-5044	70	4	g	g	NOUN
ejpam-5044	70	5	)	)	PUNCT
ejpam-5044	70	6	is	be	AUX
ejpam-5044	70	7	the	the	DET
ejpam-5044	70	8	maximum	maximum	ADJ
ejpam-5044	70	9	certified	certify	VERB
ejpam-5044	70	10	hop	hop	NOUN
ejpam-5044	70	11	independent	independent	ADJ
ejpam-5044	70	12	set	set	NOUN
ejpam-5044	70	13	of	of	ADP
ejpam-5044	70	14	g.	g.	PROPN
ejpam-5044	70	15	assume	assume	VERB
ejpam-5044	70	16	that	that	SCONJ
ejpam-5044	70	17	g	g	PROPN
ejpam-5044	70	18	is	be	AUX
ejpam-5044	70	19	connected	connect	VERB
ejpam-5044	70	20	.	.	PUNCT
ejpam-5044	71	1	suppose	suppose	VERB
ejpam-5044	71	2	further	far	ADV
ejpam-5044	71	3	that	that	DET
ejpam-5044	71	4	diam(g	diam(g	NOUN
ejpam-5044	71	5	)	)	PUNCT
ejpam-5044	71	6	≥	≥	NOUN
ejpam-5044	72	1	2	2	NUM
ejpam-5044	72	2	.	.	X
ejpam-5044	72	3	there	there	PRON
ejpam-5044	72	4	exist	exist	VERB
ejpam-5044	72	5	a	a	PRON
ejpam-5044	72	6	,	,	PUNCT
ejpam-5044	72	7	b	b	PROPN
ejpam-5044	72	8	∈	∈	PROPN
ejpam-5044	72	9	v	v	NOUN
ejpam-5044	72	10	(	(	PUNCT
ejpam-5044	72	11	g	g	NOUN
ejpam-5044	72	12	)	)	PUNCT
ejpam-5044	72	13	such	such	ADJ
ejpam-5044	72	14	that	that	SCONJ
ejpam-5044	72	15	dg(a	dg(a	PROPN
ejpam-5044	72	16	,	,	PUNCT
ejpam-5044	72	17	b	b	X
ejpam-5044	72	18	)	)	PUNCT
ejpam-5044	72	19	=	=	SYM
ejpam-5044	72	20	2	2	X
ejpam-5044	72	21	.	.	PUNCT
ejpam-5044	73	1	this	this	PRON
ejpam-5044	73	2	means	mean	VERB
ejpam-5044	73	3	that	that	SCONJ
ejpam-5044	73	4	a	a	PRON
ejpam-5044	73	5	and	and	CCONJ
ejpam-5044	73	6	b	b	NOUN
ejpam-5044	73	7	can	can	AUX
ejpam-5044	73	8	not	not	PART
ejpam-5044	73	9	be	be	AUX
ejpam-5044	73	10	both	both	DET
ejpam-5044	73	11	elements	element	NOUN
ejpam-5044	73	12	of	of	ADP
ejpam-5044	73	13	any	any	DET
ejpam-5044	73	14	certified	certify	VERB
ejpam-5044	73	15	hop	hop	NOUN
ejpam-5044	73	16	independent	independent	ADJ
ejpam-5044	73	17	set	set	NOUN
ejpam-5044	73	18	of	of	ADP
ejpam-5044	73	19	g.	g.	PROPN
ejpam-5044	73	20	thus	thus	ADV
ejpam-5044	73	21	,	,	PUNCT
ejpam-5044	73	22	αch(g	αch(g	NOUN
ejpam-5044	73	23	)	)	PUNCT
ejpam-5044	73	24	≤	≤	NOUN
ejpam-5044	73	25	|v	|v	X
ejpam-5044	73	26	(	(	PUNCT
ejpam-5044	73	27	g)|	g)|	INTJ
ejpam-5044	73	28	−	−	PROPN
ejpam-5044	73	29	1	1	NUM
ejpam-5044	73	30	,	,	PUNCT
ejpam-5044	73	31	a	a	DET
ejpam-5044	73	32	contradiction	contradiction	NOUN
ejpam-5044	73	33	.	.	PUNCT
ejpam-5044	74	1	next	next	ADV
ejpam-5044	74	2	,	,	PUNCT
ejpam-5044	74	3	suppose	suppose	VERB
ejpam-5044	74	4	that	that	SCONJ
ejpam-5044	74	5	g	g	PROPN
ejpam-5044	74	6	is	be	AUX
ejpam-5044	74	7	disconnected	disconnect	VERB
ejpam-5044	74	8	.	.	PUNCT
ejpam-5044	75	1	suppose	suppose	VERB
ejpam-5044	75	2	further	far	ADV
ejpam-5044	75	3	that	that	DET
ejpam-5044	75	4	diam(h	diam(h	NOUN
ejpam-5044	75	5	)	)	PUNCT
ejpam-5044	75	6	≥	≥	NOUN
ejpam-5044	75	7	2	2	NUM
ejpam-5044	75	8	for	for	ADP
ejpam-5044	75	9	some	some	DET
ejpam-5044	75	10	component	component	NOUN
ejpam-5044	75	11	h	h	NOUN
ejpam-5044	75	12	of	of	ADP
ejpam-5044	75	13	g.	g.	PROPN
ejpam-5044	75	14	then	then	ADV
ejpam-5044	75	15	there	there	PRON
ejpam-5044	75	16	exist	exist	VERB
ejpam-5044	75	17	x	x	NOUN
ejpam-5044	75	18	,	,	PUNCT
ejpam-5044	75	19	y,∈	y,∈	PROPN
ejpam-5044	75	20	v	v	NOUN
ejpam-5044	75	21	(	(	PUNCT
ejpam-5044	75	22	h	h	NOUN
ejpam-5044	75	23	)	)	PUNCT
ejpam-5044	75	24	such	such	ADJ
ejpam-5044	75	25	that	that	SCONJ
ejpam-5044	75	26	dh(x	dh(x	NOUN
ejpam-5044	75	27	,	,	PUNCT
ejpam-5044	75	28	y	y	NOUN
ejpam-5044	75	29	)	)	PUNCT
ejpam-5044	75	30	=	=	SYM
ejpam-5044	75	31	2	2	NUM
ejpam-5044	75	32	=	=	SYM
ejpam-5044	75	33	dg(x	dg(x	NUM
ejpam-5044	75	34	,	,	PUNCT
ejpam-5044	75	35	y	y	NOUN
ejpam-5044	75	36	)	)	PUNCT
ejpam-5044	75	37	.	.	PUNCT
ejpam-5044	76	1	then	then	ADV
ejpam-5044	76	2	either	either	CCONJ
ejpam-5044	76	3	x	x	SYM
ejpam-5044	76	4	or	or	CCONJ
ejpam-5044	76	5	y	y	PROPN
ejpam-5044	76	6	can	can	AUX
ejpam-5044	76	7	not	not	PART
ejpam-5044	76	8	be	be	AUX
ejpam-5044	76	9	an	an	DET
ejpam-5044	76	10	element	element	NOUN
ejpam-5044	76	11	of	of	ADP
ejpam-5044	76	12	a	a	DET
ejpam-5044	76	13	certified	certify	VERB
ejpam-5044	76	14	hop	hop	NOUN
ejpam-5044	76	15	independent	independent	ADJ
ejpam-5044	76	16	set	set	NOUN
ejpam-5044	76	17	of	of	ADP
ejpam-5044	76	18	g.	g.	PROPN
ejpam-5044	76	19	thus	thus	ADV
ejpam-5044	76	20	αch(g	αch(g	NOUN
ejpam-5044	76	21	)	)	PUNCT
ejpam-5044	76	22	≤	≤	NOUN
ejpam-5044	76	23	|v	|v	X
ejpam-5044	76	24	(	(	PUNCT
ejpam-5044	76	25	g)|	g)|	INTJ
ejpam-5044	76	26	−	−	PROPN
ejpam-5044	76	27	1	1	NUM
ejpam-5044	76	28	,	,	PUNCT
ejpam-5044	76	29	a	a	DET
ejpam-5044	76	30	contradiction	contradiction	NOUN
ejpam-5044	76	31	.	.	PUNCT
ejpam-5044	77	1	therefore	therefore	ADV
ejpam-5044	77	2	,	,	PUNCT
ejpam-5044	77	3	diam(h	diam(h	INTJ
ejpam-5044	77	4	)	)	PUNCT
ejpam-5044	77	5	≤	≤	NOUN
ejpam-5044	77	6	1	1	NUM
ejpam-5044	77	7	for	for	ADP
ejpam-5044	77	8	each	each	DET
ejpam-5044	77	9	component	component	NOUN
ejpam-5044	77	10	h	h	NOUN
ejpam-5044	77	11	of	of	ADP
ejpam-5044	77	12	g.	g.	PROPN
ejpam-5044	77	13	conversely	conversely	ADV
ejpam-5044	77	14	,	,	PUNCT
ejpam-5044	77	15	suppose	suppose	VERB
ejpam-5044	77	16	that	that	SCONJ
ejpam-5044	77	17	diam(h	diam(h	NOUN
ejpam-5044	77	18	)	)	PUNCT
ejpam-5044	77	19	≤	≤	NOUN
ejpam-5044	77	20	1	1	NUM
ejpam-5044	77	21	for	for	ADP
ejpam-5044	77	22	each	each	DET
ejpam-5044	77	23	component	component	NOUN
ejpam-5044	77	24	h	h	NOUN
ejpam-5044	77	25	of	of	ADP
ejpam-5044	77	26	g.	g.	PROPN
ejpam-5044	77	27	let	let	VERB
ejpam-5044	77	28	u	u	NOUN
ejpam-5044	77	29	,	,	PUNCT
ejpam-5044	77	30	v	v	PROPN
ejpam-5044	77	31	∈	∈	PROPN
ejpam-5044	77	32	v	v	NOUN
ejpam-5044	77	33	(	(	PUNCT
ejpam-5044	77	34	g	g	NOUN
ejpam-5044	77	35	)	)	PUNCT
ejpam-5044	77	36	.	.	PUNCT
ejpam-5044	78	1	if	if	SCONJ
ejpam-5044	78	2	u	u	NOUN
ejpam-5044	78	3	,	,	PUNCT
ejpam-5044	78	4	v	v	NOUN
ejpam-5044	78	5	are	be	AUX
ejpam-5044	78	6	vertices	vertex	NOUN
ejpam-5044	78	7	of	of	ADP
ejpam-5044	78	8	one	one	NUM
ejpam-5044	78	9	component	component	NOUN
ejpam-5044	78	10	k	k	NOUN
ejpam-5044	78	11	of	of	ADP
ejpam-5044	78	12	g	g	PROPN
ejpam-5044	78	13	,	,	PUNCT
ejpam-5044	78	14	then	then	ADV
ejpam-5044	78	15	dk(u	dk(u	NUM
ejpam-5044	78	16	,	,	PUNCT
ejpam-5044	78	17	v	v	NOUN
ejpam-5044	78	18	)	)	PUNCT
ejpam-5044	78	19	=	=	SYM
ejpam-5044	78	20	1	1	NUM
ejpam-5044	78	21	=	=	SYM
ejpam-5044	78	22	dg(u	dg(u	X
ejpam-5044	78	23	,	,	PUNCT
ejpam-5044	78	24	v	v	NOUN
ejpam-5044	78	25	)	)	PUNCT
ejpam-5044	78	26	,	,	PUNCT
ejpam-5044	78	27	and	and	CCONJ
ejpam-5044	78	28	we	we	PRON
ejpam-5044	78	29	are	be	AUX
ejpam-5044	78	30	done	do	VERB
ejpam-5044	78	31	.	.	PUNCT
ejpam-5044	78	32	suppose	suppose	VERB
ejpam-5044	78	33	that	that	SCONJ
ejpam-5044	78	34	u	u	PROPN
ejpam-5044	78	35	∈	∈	PROPN
ejpam-5044	78	36	v	v	ADP
ejpam-5044	78	37	(	(	PUNCT
ejpam-5044	78	38	q	q	NOUN
ejpam-5044	78	39	)	)	PUNCT
ejpam-5044	78	40	and	and	CCONJ
ejpam-5044	78	41	v	v	ADP
ejpam-5044	78	42	∈	∈	PROPN
ejpam-5044	78	43	v	v	NOUN
ejpam-5044	78	44	(	(	PUNCT
ejpam-5044	78	45	t	t	PROPN
ejpam-5044	78	46	)	)	PUNCT
ejpam-5044	78	47	,	,	PUNCT
ejpam-5044	78	48	where	where	SCONJ
ejpam-5044	78	49	q	q	NOUN
ejpam-5044	78	50	and	and	CCONJ
ejpam-5044	78	51	t	t	PROPN
ejpam-5044	78	52	are	be	AUX
ejpam-5044	78	53	components	component	NOUN
ejpam-5044	78	54	of	of	ADP
ejpam-5044	78	55	g.	g.	PROPN
ejpam-5044	78	56	then	then	ADV
ejpam-5044	78	57	dg(u	dg(u	X
ejpam-5044	78	58	,	,	PUNCT
ejpam-5044	78	59	v	v	NOUN
ejpam-5044	78	60	)	)	PUNCT
ejpam-5044	78	61	̸=	̸=	PROPN
ejpam-5044	78	62	2	2	NUM
ejpam-5044	78	63	.	.	PUNCT
ejpam-5044	79	1	since	since	SCONJ
ejpam-5044	79	2	u	u	PROPN
ejpam-5044	79	3	and	and	CCONJ
ejpam-5044	79	4	v	v	NOUN
ejpam-5044	79	5	are	be	AUX
ejpam-5044	79	6	arbitrary	arbitrary	ADJ
ejpam-5044	79	7	,	,	PUNCT
ejpam-5044	79	8	it	it	PRON
ejpam-5044	79	9	follows	follow	VERB
ejpam-5044	79	10	that	that	SCONJ
ejpam-5044	79	11	v	v	X
ejpam-5044	79	12	(	(	PUNCT
ejpam-5044	79	13	g	g	NOUN
ejpam-5044	79	14	)	)	PUNCT
ejpam-5044	79	15	is	be	AUX
ejpam-5044	79	16	a	a	DET
ejpam-5044	79	17	hop	hop	NOUN
ejpam-5044	79	18	independent	independent	ADJ
ejpam-5044	79	19	set	set	NOUN
ejpam-5044	79	20	of	of	ADP
ejpam-5044	79	21	g.	g.	PROPN
ejpam-5044	79	22	since	since	SCONJ
ejpam-5044	79	23	each	each	DET
ejpam-5044	79	24	vertex	vertex	NOUN
ejpam-5044	79	25	in	in	ADP
ejpam-5044	79	26	g	g	PROPN
ejpam-5044	79	27	has	have	VERB
ejpam-5044	79	28	zero	zero	NUM
ejpam-5044	79	29	neighbor	neighbor	NOUN
ejpam-5044	79	30	outside	outside	ADP
ejpam-5044	79	31	v	v	NOUN
ejpam-5044	79	32	(	(	PUNCT
ejpam-5044	79	33	g	g	NOUN
ejpam-5044	79	34	)	)	PUNCT
ejpam-5044	79	35	,	,	PUNCT
ejpam-5044	79	36	v	v	X
ejpam-5044	79	37	(	(	PUNCT
ejpam-5044	79	38	g	g	NOUN
ejpam-5044	79	39	)	)	PUNCT
ejpam-5044	79	40	is	be	AUX
ejpam-5044	79	41	a	a	DET
ejpam-5044	79	42	certified	certified	ADJ
ejpam-5044	79	43	hop	hop	NOUN
ejpam-5044	79	44	independent	independent	ADJ
ejpam-5044	79	45	set	set	NOUN
ejpam-5044	79	46	of	of	ADP
ejpam-5044	79	47	g.	g.	PROPN
ejpam-5044	79	48	consequently	consequently	ADV
ejpam-5044	79	49	,	,	PUNCT
ejpam-5044	79	50	αch(g	αch(g	NOUN
ejpam-5044	79	51	)	)	PUNCT
ejpam-5044	79	52	=	=	SYM
ejpam-5044	80	1	|v	|v	PROPN
ejpam-5044	80	2	(	(	PUNCT
ejpam-5044	80	3	g)|	g)|	PROPN
ejpam-5044	80	4	.	.	PUNCT
ejpam-5044	80	5	corollary	corollary	ADJ
ejpam-5044	81	1	1	1	NUM
ejpam-5044	81	2	.	.	PUNCT
ejpam-5044	82	1	let	let	VERB
ejpam-5044	82	2	m	m	PRON
ejpam-5044	82	3	be	be	AUX
ejpam-5044	82	4	a	a	DET
ejpam-5044	82	5	positive	positive	ADJ
ejpam-5044	82	6	integer	integer	NOUN
ejpam-5044	82	7	.	.	PUNCT
ejpam-5044	83	1	then	then	ADV
ejpam-5044	83	2	αch(km	αch(km	NOUN
ejpam-5044	83	3	)	)	PUNCT
ejpam-5044	84	1	=	=	SYM
ejpam-5044	84	2	m	m	NOUN
ejpam-5044	84	3	=	=	SYM
ejpam-5044	84	4	αch(km	αch(km	NOUN
ejpam-5044	84	5	)	)	PUNCT
ejpam-5044	84	6	for	for	ADP
ejpam-5044	84	7	all	all	DET
ejpam-5044	84	8	m	m	PROPN
ejpam-5044	84	9	≥	≥	NOUN
ejpam-5044	84	10	1	1	NUM
ejpam-5044	84	11	.	.	PUNCT
ejpam-5044	85	1	theorem	theorem	NOUN
ejpam-5044	85	2	3	3	NUM
ejpam-5044	85	3	.	.	PUNCT
ejpam-5044	86	1	if	if	SCONJ
ejpam-5044	86	2	s	s	PROPN
ejpam-5044	86	3	is	be	AUX
ejpam-5044	86	4	a	a	DET
ejpam-5044	86	5	certified	certified	ADJ
ejpam-5044	86	6	hop	hop	NOUN
ejpam-5044	86	7	independent	independent	ADJ
ejpam-5044	86	8	set	set	NOUN
ejpam-5044	86	9	of	of	ADP
ejpam-5044	86	10	a	a	DET
ejpam-5044	86	11	path	path	NOUN
ejpam-5044	86	12	graph	graph	NOUN
ejpam-5044	86	13	pn	pn	PROPN
ejpam-5044	86	14	,	,	PUNCT
ejpam-5044	86	15	then	then	ADV
ejpam-5044	86	16	dpn(x	dpn(x	PROPN
ejpam-5044	86	17	,	,	PUNCT
ejpam-5044	86	18	y	y	PROPN
ejpam-5044	86	19	)	)	PUNCT
ejpam-5044	86	20	≥	≥	NOUN
ejpam-5044	86	21	3	3	NUM
ejpam-5044	86	22	for	for	ADP
ejpam-5044	86	23	all	all	DET
ejpam-5044	86	24	x	x	NOUN
ejpam-5044	86	25	,	,	PUNCT
ejpam-5044	86	26	y	y	PROPN
ejpam-5044	86	27	∈	∈	PROPN
ejpam-5044	86	28	s	s	PROPN
ejpam-5044	86	29	,	,	PUNCT
ejpam-5044	86	30	where	where	SCONJ
ejpam-5044	86	31	x	x	SYM
ejpam-5044	86	32	̸=	̸=	PROPN
ejpam-5044	86	33	y.	y.	NOUN
ejpam-5044	86	34	proof	proof	NOUN
ejpam-5044	86	35	.	.	PUNCT
ejpam-5044	87	1	let	let	VERB
ejpam-5044	87	2	s	s	PRON
ejpam-5044	87	3	⊆	⊆	NUM
ejpam-5044	87	4	v	v	NOUN
ejpam-5044	87	5	(	(	PUNCT
ejpam-5044	87	6	pn	pn	NOUN
ejpam-5044	87	7	)	)	PUNCT
ejpam-5044	87	8	be	be	AUX
ejpam-5044	87	9	a	a	DET
ejpam-5044	87	10	certified	certified	ADJ
ejpam-5044	87	11	hop	hop	NOUN
ejpam-5044	87	12	independent	independent	ADJ
ejpam-5044	87	13	set	set	NOUN
ejpam-5044	87	14	of	of	ADP
ejpam-5044	87	15	pn	pn	PROPN
ejpam-5044	87	16	,	,	PUNCT
ejpam-5044	87	17	where	where	SCONJ
ejpam-5044	87	18	v	v	X
ejpam-5044	87	19	(	(	PUNCT
ejpam-5044	87	20	pn	pn	NOUN
ejpam-5044	87	21	)	)	PUNCT
ejpam-5044	87	22	=	=	SYM
ejpam-5044	87	23	{	{	PUNCT
ejpam-5044	87	24	v1	v1	PROPN
ejpam-5044	87	25	,	,	PUNCT
ejpam-5044	87	26	v2	v2	PROPN
ejpam-5044	87	27	,	,	PUNCT
ejpam-5044	87	28	.	.	PUNCT
ejpam-5044	87	29	.	.	PUNCT
ejpam-5044	88	1	.	.	PUNCT
ejpam-5044	89	1	,	,	PUNCT
ejpam-5044	89	2	vn	vn	PROPN
ejpam-5044	89	3	}	}	PUNCT
ejpam-5044	89	4	.	.	PUNCT
ejpam-5044	90	1	let	let	VERB
ejpam-5044	90	2	x	x	PRON
ejpam-5044	90	3	,	,	PUNCT
ejpam-5044	90	4	y	y	PROPN
ejpam-5044	90	5	∈	∈	PROPN
ejpam-5044	90	6	s.	s.	PROPN
ejpam-5044	90	7	suppose	suppose	VERB
ejpam-5044	90	8	that	that	SCONJ
ejpam-5044	90	9	dpn(x	dpn(x	PROPN
ejpam-5044	90	10	,	,	PUNCT
ejpam-5044	90	11	y	y	NOUN
ejpam-5044	90	12	)	)	PUNCT
ejpam-5044	90	13	=	=	SYM
ejpam-5044	91	1	1	1	X
ejpam-5044	91	2	.	.	PUNCT
ejpam-5044	92	1	if	if	SCONJ
ejpam-5044	92	2	x	x	X
ejpam-5044	92	3	=	=	SYM
ejpam-5044	92	4	v1	v1	NOUN
ejpam-5044	92	5	,	,	PUNCT
ejpam-5044	92	6	then	then	ADV
ejpam-5044	92	7	y	y	PROPN
ejpam-5044	92	8	=	=	SYM
ejpam-5044	92	9	v2	v2	PROPN
ejpam-5044	92	10	and	and	CCONJ
ejpam-5044	92	11	y	y	PROPN
ejpam-5044	92	12	have	have	VERB
ejpam-5044	92	13	only	only	ADV
ejpam-5044	92	14	one	one	NUM
ejpam-5044	92	15	neighbor	neighbor	NOUN
ejpam-5044	92	16	v3	v3	PROPN
ejpam-5044	92	17	outside	outside	ADP
ejpam-5044	92	18	s	s	PROPN
ejpam-5044	92	19	,	,	PUNCT
ejpam-5044	92	20	a	a	DET
ejpam-5044	92	21	contradiction	contradiction	NOUN
ejpam-5044	92	22	.	.	PUNCT
ejpam-5044	93	1	similarly	similarly	ADV
ejpam-5044	93	2	,	,	PUNCT
ejpam-5044	93	3	when	when	SCONJ
ejpam-5044	93	4	y	y	PROPN
ejpam-5044	93	5	=	=	SYM
ejpam-5044	93	6	v1	v1	PROPN
ejpam-5044	93	7	,	,	PUNCT
ejpam-5044	93	8	x	x	X
ejpam-5044	94	1	=	=	PUNCT
ejpam-5044	94	2	vn	vn	PROPN
ejpam-5044	94	3	or	or	CCONJ
ejpam-5044	94	4	y	y	PROPN
ejpam-5044	94	5	=	=	SYM
ejpam-5044	94	6	vn	vn	PROPN
ejpam-5044	94	7	.	.	PUNCT
ejpam-5044	94	8	suppose	suppose	VERB
ejpam-5044	94	9	that	that	SCONJ
ejpam-5044	94	10	x	x	X
ejpam-5044	94	11	=	=	SYM
ejpam-5044	94	12	vi	vi	PROPN
ejpam-5044	94	13	and	and	CCONJ
ejpam-5044	94	14	y	y	PROPN
ejpam-5044	94	15	=	=	SYM
ejpam-5044	94	16	vj	vj	PROPN
ejpam-5044	94	17	,	,	PUNCT
ejpam-5044	94	18	where	where	SCONJ
ejpam-5044	94	19	i	i	PRON
ejpam-5044	94	20	,	,	PUNCT
ejpam-5044	94	21	j	j	PROPN
ejpam-5044	94	22	=	=	PUNCT
ejpam-5044	94	23	{	{	PUNCT
ejpam-5044	94	24	2	2	NUM
ejpam-5044	94	25	,	,	PUNCT
ejpam-5044	94	26	.	.	PUNCT
ejpam-5044	94	27	.	.	PUNCT
ejpam-5044	94	28	.	.	PUNCT
ejpam-5044	95	1	,	,	PUNCT
ejpam-5044	96	1	n	n	CCONJ
ejpam-5044	96	2	−	−	PROPN
ejpam-5044	96	3	1	1	NUM
ejpam-5044	96	4	}	}	PUNCT
ejpam-5044	96	5	.	.	PUNCT
ejpam-5044	97	1	since	since	SCONJ
ejpam-5044	97	2	|npn(vk)|	|npn(vk)|	NOUN
ejpam-5044	97	3	=	=	SYM
ejpam-5044	97	4	2	2	NUM
ejpam-5044	97	5	for	for	ADP
ejpam-5044	97	6	all	all	DET
ejpam-5044	97	7	k	k	PROPN
ejpam-5044	97	8	∈	∈	PROPN
ejpam-5044	97	9	{	{	PUNCT
ejpam-5044	97	10	2	2	NUM
ejpam-5044	97	11	,	,	PUNCT
ejpam-5044	97	12	.	.	PUNCT
ejpam-5044	97	13	.	.	PUNCT
ejpam-5044	97	14	.	.	PUNCT
ejpam-5044	98	1	,	,	PUNCT
ejpam-5044	98	2	n−	n−	NOUN
ejpam-5044	98	3	1	1	NUM
ejpam-5044	98	4	}	}	PUNCT
ejpam-5044	98	5	,	,	PUNCT
ejpam-5044	98	6	x	x	PUNCT
ejpam-5044	98	7	and	and	CCONJ
ejpam-5044	98	8	y	y	PROPN
ejpam-5044	98	9	have	have	VERB
ejpam-5044	98	10	only	only	ADV
ejpam-5044	98	11	one	one	NUM
ejpam-5044	98	12	neighbor	neighbor	NOUN
ejpam-5044	98	13	outside	outside	ADP
ejpam-5044	98	14	s	s	PROPN
ejpam-5044	98	15	,	,	PUNCT
ejpam-5044	98	16	which	which	PRON
ejpam-5044	98	17	is	be	AUX
ejpam-5044	98	18	a	a	DET
ejpam-5044	98	19	contradiction	contradiction	NOUN
ejpam-5044	98	20	.	.	PUNCT
ejpam-5044	99	1	now	now	ADV
ejpam-5044	99	2	,	,	PUNCT
ejpam-5044	99	3	since	since	SCONJ
ejpam-5044	99	4	any	any	DET
ejpam-5044	99	5	certified	certify	VERB
ejpam-5044	99	6	hop	hop	NOUN
ejpam-5044	99	7	independent	independent	ADJ
ejpam-5044	99	8	set	set	NOUN
ejpam-5044	99	9	is	be	AUX
ejpam-5044	99	10	a	a	DET
ejpam-5044	99	11	hop	hop	NOUN
ejpam-5044	99	12	independent	independent	ADJ
ejpam-5044	99	13	,	,	PUNCT
ejpam-5044	99	14	it	it	PRON
ejpam-5044	99	15	follows	follow	VERB
ejpam-5044	99	16	that	that	SCONJ
ejpam-5044	99	17	dpn(x	dpn(x	PROPN
ejpam-5044	99	18	,	,	PUNCT
ejpam-5044	99	19	y	y	NOUN
ejpam-5044	99	20	)	)	PUNCT
ejpam-5044	99	21	̸=	̸=	PROPN
ejpam-5044	99	22	2	2	NUM
ejpam-5044	99	23	.	.	PUNCT
ejpam-5044	100	1	therefore	therefore	ADV
ejpam-5044	100	2	,	,	PUNCT
ejpam-5044	100	3	dpn(x	dpn(x	PROPN
ejpam-5044	100	4	,	,	PUNCT
ejpam-5044	100	5	y	y	PROPN
ejpam-5044	100	6	)	)	PUNCT
ejpam-5044	100	7	≥	≥	NOUN
ejpam-5044	100	8	3	3	NUM
ejpam-5044	100	9	for	for	ADP
ejpam-5044	100	10	all	all	DET
ejpam-5044	100	11	x	x	NOUN
ejpam-5044	100	12	,	,	PUNCT
ejpam-5044	100	13	y	y	PROPN
ejpam-5044	100	14	∈	∈	PROPN
ejpam-5044	100	15	s	s	PROPN
ejpam-5044	100	16	,	,	PUNCT
ejpam-5044	100	17	where	where	SCONJ
ejpam-5044	100	18	x	x	X
ejpam-5044	100	19	̸=	̸=	PROPN
ejpam-5044	100	20	y.	y.	NOUN
ejpam-5044	100	21	the	the	DET
ejpam-5044	100	22	following	following	ADJ
ejpam-5044	100	23	result	result	NOUN
ejpam-5044	100	24	follows	follow	VERB
ejpam-5044	100	25	from	from	ADP
ejpam-5044	100	26	theorem	theorem	ADJ
ejpam-5044	100	27	3	3	NUM
ejpam-5044	100	28	.	.	PUNCT
ejpam-5044	100	29	corollary	corollary	ADJ
ejpam-5044	100	30	2	2	NUM
ejpam-5044	100	31	.	.	PUNCT
ejpam-5044	101	1	let	let	VERB
ejpam-5044	101	2	n	n	PRON
ejpam-5044	101	3	be	be	AUX
ejpam-5044	101	4	a	a	DET
ejpam-5044	101	5	positive	positive	ADJ
ejpam-5044	101	6	integer	integer	NOUN
ejpam-5044	101	7	.	.	PUNCT
ejpam-5044	102	1	then	then	ADV
ejpam-5044	102	2	αch(pn	αch(pn	NOUN
ejpam-5044	102	3	)	)	PUNCT
ejpam-5044	102	4	=	=	SYM
ejpam-5044	102	5	{	{	PUNCT
ejpam-5044	102	6	n	n	NOUN
ejpam-5044	102	7	if	if	SCONJ
ejpam-5044	102	8	n	n	NOUN
ejpam-5044	102	9	=	=	SYM
ejpam-5044	102	10	1	1	NUM
ejpam-5044	102	11	,	,	PUNCT
ejpam-5044	102	12	2	2	NUM
ejpam-5044	102	13	⌊n3	⌊n3	NOUN
ejpam-5044	102	14	⌋	⌋	VERB
ejpam-5044	102	15	if	if	SCONJ
ejpam-5044	102	16	n	n	PRON
ejpam-5044	102	17	≥	≥	NOUN
ejpam-5044	102	18	3	3	NUM
ejpam-5044	102	19	.	.	PUNCT
ejpam-5044	102	20	j.	j.	PROPN
ejpam-5044	102	21	a.	a.	PROPN
ejpam-5044	102	22	hassan	hassan	PROPN
ejpam-5044	102	23	et	et	PROPN
ejpam-5044	102	24	al	al	PROPN
ejpam-5044	102	25	.	.	PUNCT
ejpam-5044	102	26	/	/	SYM
ejpam-5044	102	27	eur	eur	PROPN
ejpam-5044	102	28	.	.	PUNCT
ejpam-5044	103	1	j.	j.	PROPN
ejpam-5044	103	2	pure	pure	PROPN
ejpam-5044	103	3	appl	appl	PROPN
ejpam-5044	103	4	.	.	PROPN
ejpam-5044	103	5	math	math	PROPN
ejpam-5044	103	6	,	,	PUNCT
ejpam-5044	103	7	17	17	NUM
ejpam-5044	103	8	(	(	PUNCT
ejpam-5044	103	9	1	1	NUM
ejpam-5044	103	10	)	)	PUNCT
ejpam-5044	103	11	(	(	PUNCT
ejpam-5044	103	12	2024	2024	NUM
ejpam-5044	103	13	)	)	PUNCT
ejpam-5044	103	14	,	,	PUNCT
ejpam-5044	103	15	435	435	NUM
ejpam-5044	103	16	-	-	SYM
ejpam-5044	103	17	444	444	NUM
ejpam-5044	103	18	439	439	NUM
ejpam-5044	103	19	theorem	theorem	NOUN
ejpam-5044	103	20	4	4	NUM
ejpam-5044	103	21	.	.	PUNCT
ejpam-5044	104	1	if	if	SCONJ
ejpam-5044	104	2	s′	s′	PRON
ejpam-5044	104	3	is	be	AUX
ejpam-5044	104	4	a	a	DET
ejpam-5044	104	5	certified	certified	ADJ
ejpam-5044	104	6	hop	hop	NOUN
ejpam-5044	104	7	independent	independent	ADJ
ejpam-5044	104	8	set	set	NOUN
ejpam-5044	104	9	of	of	ADP
ejpam-5044	104	10	a	a	DET
ejpam-5044	104	11	cycle	cycle	NOUN
ejpam-5044	104	12	graph	graph	NOUN
ejpam-5044	104	13	cn	cn	PROPN
ejpam-5044	104	14	,	,	PUNCT
ejpam-5044	104	15	then	then	ADV
ejpam-5044	104	16	dcn(u	dcn(u	PROPN
ejpam-5044	104	17	,	,	PUNCT
ejpam-5044	104	18	v	v	NOUN
ejpam-5044	104	19	)	)	PUNCT
ejpam-5044	104	20	≥	≥	NOUN
ejpam-5044	104	21	3	3	NUM
ejpam-5044	104	22	for	for	ADP
ejpam-5044	104	23	all	all	DET
ejpam-5044	104	24	u	u	NOUN
ejpam-5044	104	25	,	,	PUNCT
ejpam-5044	104	26	v	v	PROPN
ejpam-5044	104	27	∈	∈	PROPN
ejpam-5044	104	28	s′	s′	NOUN
ejpam-5044	104	29	,	,	PUNCT
ejpam-5044	104	30	where	where	SCONJ
ejpam-5044	104	31	u	u	NOUN
ejpam-5044	104	32	̸=	̸=	PROPN
ejpam-5044	104	33	v.	v.	ADP
ejpam-5044	104	34	proof	proof	NOUN
ejpam-5044	104	35	.	.	PUNCT
ejpam-5044	105	1	let	let	VERB
ejpam-5044	105	2	s′	s′	ADJ
ejpam-5044	105	3	⊆	⊆	NUM
ejpam-5044	105	4	v	v	NOUN
ejpam-5044	105	5	(	(	PUNCT
ejpam-5044	105	6	cn	cn	PROPN
ejpam-5044	105	7	)	)	PUNCT
ejpam-5044	105	8	be	be	AUX
ejpam-5044	105	9	a	a	DET
ejpam-5044	105	10	certified	certified	ADJ
ejpam-5044	105	11	hop	hop	NOUN
ejpam-5044	105	12	independent	independent	ADJ
ejpam-5044	105	13	set	set	NOUN
ejpam-5044	105	14	of	of	ADP
ejpam-5044	105	15	cn	cn	PROPN
ejpam-5044	105	16	.	.	PUNCT
ejpam-5044	106	1	let	let	VERB
ejpam-5044	106	2	u	u	NOUN
ejpam-5044	106	3	,	,	PUNCT
ejpam-5044	106	4	v	v	ADP
ejpam-5044	106	5	∈	∈	NOUN
ejpam-5044	106	6	s′.	s′.	X
ejpam-5044	107	1	if	if	SCONJ
ejpam-5044	107	2	dcn(u	dcn(u	PROPN
ejpam-5044	107	3	,	,	PUNCT
ejpam-5044	107	4	v	v	NOUN
ejpam-5044	107	5	)	)	PUNCT
ejpam-5044	107	6	=	=	SYM
ejpam-5044	107	7	1	1	NUM
ejpam-5044	107	8	,	,	PUNCT
ejpam-5044	107	9	then	then	ADV
ejpam-5044	107	10	both	both	DET
ejpam-5044	107	11	u	u	NOUN
ejpam-5044	107	12	and	and	CCONJ
ejpam-5044	107	13	v	v	NOUN
ejpam-5044	107	14	have	have	VERB
ejpam-5044	107	15	only	only	ADV
ejpam-5044	107	16	one	one	NUM
ejpam-5044	107	17	neighbor	neighbor	NOUN
ejpam-5044	107	18	in	in	ADP
ejpam-5044	107	19	v	v	PROPN
ejpam-5044	107	20	(	(	PUNCT
ejpam-5044	107	21	cn	cn	PROPN
ejpam-5044	107	22	)	)	PUNCT
ejpam-5044	107	23	\	\	PROPN
ejpam-5044	107	24	s′	s′	NOUN
ejpam-5044	107	25	,	,	PUNCT
ejpam-5044	107	26	a	a	DET
ejpam-5044	107	27	contradiction	contradiction	NOUN
ejpam-5044	107	28	.	.	PUNCT
ejpam-5044	108	1	now	now	ADV
ejpam-5044	108	2	,	,	PUNCT
ejpam-5044	108	3	since	since	SCONJ
ejpam-5044	108	4	s′	s′	ADJ
ejpam-5044	108	5	is	be	AUX
ejpam-5044	108	6	a	a	DET
ejpam-5044	108	7	hop	hop	NOUN
ejpam-5044	108	8	independent	independent	ADJ
ejpam-5044	108	9	set	set	NOUN
ejpam-5044	108	10	of	of	ADP
ejpam-5044	108	11	cn	cn	PROPN
ejpam-5044	108	12	,	,	PUNCT
ejpam-5044	108	13	dcn(u	dcn(u	PROPN
ejpam-5044	108	14	,	,	PUNCT
ejpam-5044	108	15	v	v	NOUN
ejpam-5044	108	16	)	)	PUNCT
ejpam-5044	108	17	̸=	̸=	PROPN
ejpam-5044	108	18	2	2	NUM
ejpam-5044	108	19	for	for	ADP
ejpam-5044	108	20	all	all	DET
ejpam-5044	108	21	u	u	NOUN
ejpam-5044	108	22	,	,	PUNCT
ejpam-5044	108	23	v	v	ADP
ejpam-5044	108	24	∈	∈	NOUN
ejpam-5044	108	25	s′.	s′.	X
ejpam-5044	108	26	therefore	therefore	ADV
ejpam-5044	108	27	,	,	PUNCT
ejpam-5044	108	28	dcn(u	dcn(u	PROPN
ejpam-5044	108	29	,	,	PUNCT
ejpam-5044	108	30	v	v	NOUN
ejpam-5044	108	31	)	)	PUNCT
ejpam-5044	108	32	≥	≥	NOUN
ejpam-5044	108	33	3	3	NUM
ejpam-5044	108	34	for	for	ADP
ejpam-5044	108	35	all	all	DET
ejpam-5044	108	36	u	u	NOUN
ejpam-5044	108	37	,	,	PUNCT
ejpam-5044	108	38	v	v	PROPN
ejpam-5044	108	39	∈	∈	PROPN
ejpam-5044	108	40	s′	s′	NOUN
ejpam-5044	108	41	,	,	PUNCT
ejpam-5044	108	42	where	where	SCONJ
ejpam-5044	108	43	u	u	NOUN
ejpam-5044	108	44	̸=	̸=	PROPN
ejpam-5044	108	45	v.	v.	ADP
ejpam-5044	108	46	the	the	DET
ejpam-5044	108	47	following	following	ADJ
ejpam-5044	108	48	result	result	NOUN
ejpam-5044	108	49	follows	follow	VERB
ejpam-5044	108	50	from	from	ADP
ejpam-5044	108	51	theorem	theorem	ADJ
ejpam-5044	108	52	4	4	NUM
ejpam-5044	108	53	.	.	PUNCT
ejpam-5044	108	54	corollary	corollary	ADJ
ejpam-5044	108	55	3	3	X
ejpam-5044	108	56	.	.	PUNCT
ejpam-5044	109	1	let	let	VERB
ejpam-5044	109	2	n	n	PRON
ejpam-5044	109	3	be	be	AUX
ejpam-5044	109	4	a	a	DET
ejpam-5044	109	5	positive	positive	ADJ
ejpam-5044	109	6	integer	integer	NOUN
ejpam-5044	109	7	.	.	PUNCT
ejpam-5044	110	1	then	then	ADV
ejpam-5044	110	2	αch(cn	αch(cn	VERB
ejpam-5044	110	3	)	)	PUNCT
ejpam-5044	111	1	=	=	PRON
ejpam-5044	111	2	{	{	PUNCT
ejpam-5044	111	3	n	n	NOUN
ejpam-5044	111	4	if	if	SCONJ
ejpam-5044	111	5	n	n	ADJ
ejpam-5044	111	6	=	=	SYM
ejpam-5044	111	7	3	3	NUM
ejpam-5044	111	8	⌊n3	⌊n3	NOUN
ejpam-5044	111	9	⌋	⌋	VERB
ejpam-5044	111	10	if	if	SCONJ
ejpam-5044	111	11	n	n	PRON
ejpam-5044	111	12	≥	≥	NOUN
ejpam-5044	111	13	4	4	NUM
ejpam-5044	111	14	.	.	PUNCT
ejpam-5044	112	1	the	the	DET
ejpam-5044	112	2	following	follow	VERB
ejpam-5044	112	3	is	be	AUX
ejpam-5044	112	4	a	a	DET
ejpam-5044	112	5	realization	realization	NOUN
ejpam-5044	112	6	results	result	NOUN
ejpam-5044	112	7	involving	involve	VERB
ejpam-5044	112	8	certified	certify	VERB
ejpam-5044	112	9	hop	hop	NOUN
ejpam-5044	112	10	independence	independence	NOUN
ejpam-5044	112	11	and	and	CCONJ
ejpam-5044	112	12	hop	hop	NOUN
ejpam-5044	112	13	independence	independence	NOUN
ejpam-5044	112	14	parameters	parameter	NOUN
ejpam-5044	112	15	.	.	PUNCT
ejpam-5044	113	1	theorem	theorem	NOUN
ejpam-5044	113	2	5	5	NUM
ejpam-5044	113	3	.	.	PUNCT
ejpam-5044	114	1	let	let	VERB
ejpam-5044	114	2	a	a	PRON
ejpam-5044	114	3	and	and	CCONJ
ejpam-5044	114	4	b	b	NOUN
ejpam-5044	114	5	be	be	AUX
ejpam-5044	114	6	positive	positive	ADJ
ejpam-5044	114	7	integers	integer	NOUN
ejpam-5044	114	8	such	such	ADJ
ejpam-5044	114	9	that	that	SCONJ
ejpam-5044	114	10	2	2	NUM
ejpam-5044	114	11	≤	≤	NUM
ejpam-5044	114	12	a	a	DET
ejpam-5044	114	13	≤	≤	PROPN
ejpam-5044	114	14	b.	b.	NOUN
ejpam-5044	115	1	then	then	ADV
ejpam-5044	115	2	there	there	PRON
ejpam-5044	115	3	exists	exist	VERB
ejpam-5044	115	4	a	a	DET
ejpam-5044	115	5	connected	connected	ADJ
ejpam-5044	115	6	graph	graph	NOUN
ejpam-5044	115	7	g	g	ADP
ejpam-5044	115	8	such	such	ADJ
ejpam-5044	115	9	that	that	SCONJ
ejpam-5044	115	10	αch(g	αch(g	NOUN
ejpam-5044	115	11	)	)	PUNCT
ejpam-5044	115	12	=	=	SYM
ejpam-5044	115	13	a	a	PRON
ejpam-5044	115	14	and	and	CCONJ
ejpam-5044	115	15	αh(g	αh(g	NOUN
ejpam-5044	115	16	)	)	PUNCT
ejpam-5044	115	17	=	=	SYM
ejpam-5044	115	18	b.	b.	NOUN
ejpam-5044	115	19	proof	proof	NOUN
ejpam-5044	115	20	.	.	PUNCT
ejpam-5044	116	1	consider	consider	VERB
ejpam-5044	116	2	the	the	DET
ejpam-5044	116	3	following	follow	VERB
ejpam-5044	116	4	two	two	NUM
ejpam-5044	116	5	cases	case	NOUN
ejpam-5044	116	6	:	:	PUNCT
ejpam-5044	116	7	case	case	NOUN
ejpam-5044	116	8	1	1	NUM
ejpam-5044	116	9	:	:	PUNCT
ejpam-5044	116	10	a	a	DET
ejpam-5044	116	11	=	=	SYM
ejpam-5044	116	12	b	b	NOUN
ejpam-5044	116	13	subcase	subcase	NOUN
ejpam-5044	116	14	1	1	NUM
ejpam-5044	116	15	:	:	PUNCT
ejpam-5044	116	16	a	a	DET
ejpam-5044	116	17	≥	≥	NUM
ejpam-5044	116	18	5	5	NUM
ejpam-5044	116	19	is	be	AUX
ejpam-5044	116	20	odd	odd	ADJ
ejpam-5044	116	21	consider	consider	VERB
ejpam-5044	116	22	the	the	DET
ejpam-5044	116	23	graph	graph	NOUN
ejpam-5044	116	24	g	g	NOUN
ejpam-5044	116	25	in	in	ADP
ejpam-5044	116	26	figure	figure	NOUN
ejpam-5044	116	27	2	2	NUM
ejpam-5044	116	28	.	.	PUNCT
ejpam-5044	117	1	g	g	NOUN
ejpam-5044	117	2	:	:	PUNCT
ejpam-5044	117	3	.	.	PUNCT
ejpam-5044	117	4	.	.	PUNCT
ejpam-5044	117	5	.	.	PUNCT
ejpam-5044	118	1	x1	x1	NUM
ejpam-5044	119	1	x2	x2	NOUN
ejpam-5044	119	2	x3	x3	PROPN
ejpam-5044	120	1	x4	x4	PROPN
ejpam-5044	120	2	xa−3	xa−3	PROPN
ejpam-5044	120	3	xa−1	xa−1	PROPN
ejpam-5044	120	4	xa−4	xa−4	PROPN
ejpam-5044	120	5	xaxa−2	xaxa−2	PROPN
ejpam-5044	120	6	figure	figure	NOUN
ejpam-5044	120	7	2	2	NUM
ejpam-5044	120	8	:	:	PUNCT
ejpam-5044	120	9	graph	graph	VERB
ejpam-5044	120	10	g	g	NOUN
ejpam-5044	120	11	with	with	ADP
ejpam-5044	120	12	αch(g	αch(g	NOUN
ejpam-5044	120	13	)	)	PUNCT
ejpam-5044	120	14	=	=	PUNCT
ejpam-5044	120	15	a	a	DET
ejpam-5044	120	16	=	=	NOUN
ejpam-5044	120	17	αh(g	αh(g	NOUN
ejpam-5044	120	18	)	)	PUNCT
ejpam-5044	120	19	.	.	PUNCT
ejpam-5044	121	1	let	let	VERB
ejpam-5044	121	2	b1	b1	NOUN
ejpam-5044	121	3	=	=	SYM
ejpam-5044	121	4	{	{	PUNCT
ejpam-5044	121	5	x1	x1	PROPN
ejpam-5044	121	6	,	,	PUNCT
ejpam-5044	121	7	x2	x2	PROPN
ejpam-5044	121	8	,	,	PUNCT
ejpam-5044	121	9	...	...	PUNCT
ejpam-5044	121	10	,	,	PUNCT
ejpam-5044	121	11	xa−1	xa−1	PROPN
ejpam-5044	121	12	,	,	PUNCT
ejpam-5044	121	13	xa	xa	PROPN
ejpam-5044	121	14	}	}	PUNCT
ejpam-5044	121	15	.	.	PUNCT
ejpam-5044	122	1	then	then	ADV
ejpam-5044	122	2	b1	b1	PROPN
ejpam-5044	122	3	is	be	AUX
ejpam-5044	122	4	both	both	CCONJ
ejpam-5044	122	5	a	a	DET
ejpam-5044	122	6	maximum	maximum	ADV
ejpam-5044	122	7	certified	certify	VERB
ejpam-5044	122	8	hop	hop	NOUN
ejpam-5044	122	9	independent	independent	ADJ
ejpam-5044	122	10	and	and	CCONJ
ejpam-5044	122	11	a	a	DET
ejpam-5044	122	12	maximum	maximum	ADJ
ejpam-5044	122	13	hop	hop	NOUN
ejpam-5044	122	14	independent	independent	ADJ
ejpam-5044	122	15	set	set	NOUN
ejpam-5044	122	16	of	of	ADP
ejpam-5044	122	17	g.	g.	PROPN
ejpam-5044	122	18	thus	thus	ADV
ejpam-5044	122	19	,	,	PUNCT
ejpam-5044	122	20	αch(g	αch(g	NOUN
ejpam-5044	122	21	)	)	PUNCT
ejpam-5044	122	22	=	=	PUNCT
ejpam-5044	122	23	a	a	DET
ejpam-5044	122	24	=	=	NOUN
ejpam-5044	122	25	αh(g	αh(g	NOUN
ejpam-5044	122	26	)	)	PUNCT
ejpam-5044	122	27	.	.	PUNCT
ejpam-5044	123	1	next	next	ADV
ejpam-5044	123	2	,	,	PUNCT
ejpam-5044	123	3	for	for	ADP
ejpam-5044	123	4	a	a	DET
ejpam-5044	123	5	=	=	SYM
ejpam-5044	123	6	3	3	NUM
ejpam-5044	123	7	=	=	SYM
ejpam-5044	123	8	b	b	NOUN
ejpam-5044	123	9	,	,	PUNCT
ejpam-5044	123	10	consider	consider	VERB
ejpam-5044	123	11	k3	k3	VERB
ejpam-5044	123	12	.	.	PUNCT
ejpam-5044	124	1	then	then	ADV
ejpam-5044	124	2	αch(k3	αch(k3	NOUN
ejpam-5044	124	3	)	)	PUNCT
ejpam-5044	124	4	=	=	PUNCT
ejpam-5044	125	1	a	a	DET
ejpam-5044	125	2	=	=	SYM
ejpam-5044	125	3	αh(k3	αh(k3	NUM
ejpam-5044	125	4	)	)	PUNCT
ejpam-5044	125	5	.	.	PUNCT
ejpam-5044	126	1	j.	j.	PROPN
ejpam-5044	126	2	a.	a.	PROPN
ejpam-5044	126	3	hassan	hassan	PROPN
ejpam-5044	126	4	et	et	PROPN
ejpam-5044	126	5	al	al	PROPN
ejpam-5044	126	6	.	.	PUNCT
ejpam-5044	126	7	/	/	SYM
ejpam-5044	126	8	eur	eur	PROPN
ejpam-5044	126	9	.	.	PUNCT
ejpam-5044	127	1	j.	j.	PROPN
ejpam-5044	127	2	pure	pure	PROPN
ejpam-5044	127	3	appl	appl	PROPN
ejpam-5044	127	4	.	.	PROPN
ejpam-5044	127	5	math	math	PROPN
ejpam-5044	127	6	,	,	PUNCT
ejpam-5044	127	7	17	17	NUM
ejpam-5044	127	8	(	(	PUNCT
ejpam-5044	127	9	1	1	NUM
ejpam-5044	127	10	)	)	PUNCT
ejpam-5044	127	11	(	(	PUNCT
ejpam-5044	127	12	2024	2024	NUM
ejpam-5044	127	13	)	)	PUNCT
ejpam-5044	127	14	,	,	PUNCT
ejpam-5044	127	15	435	435	NUM
ejpam-5044	127	16	-	-	SYM
ejpam-5044	127	17	444	444	NUM
ejpam-5044	127	18	440	440	NUM
ejpam-5044	127	19	subcase	subcase	NOUN
ejpam-5044	127	20	2	2	NUM
ejpam-5044	127	21	:	:	PUNCT
ejpam-5044	127	22	a	a	PRON
ejpam-5044	127	23	is	be	AUX
ejpam-5044	127	24	even	even	ADV
ejpam-5044	127	25	consider	consider	VERB
ejpam-5044	127	26	the	the	DET
ejpam-5044	127	27	graph	graph	NOUN
ejpam-5044	127	28	g′	g′	NOUN
ejpam-5044	127	29	below	below	ADV
ejpam-5044	127	30	.	.	PUNCT
ejpam-5044	128	1	g′	g′	NOUN
ejpam-5044	128	2	:	:	PUNCT
ejpam-5044	128	3	.	.	PUNCT
ejpam-5044	128	4	.	.	PUNCT
ejpam-5044	128	5	.	.	PUNCT
ejpam-5044	129	1	y1	y1	INTJ
ejpam-5044	129	2	y2	y2	NOUN
ejpam-5044	129	3	y3	y3	NOUN
ejpam-5044	129	4	y4	y4	PROPN
ejpam-5044	129	5	ya−3	ya−3	PROPN
ejpam-5044	129	6	ya−1	ya−1	PROPN
ejpam-5044	129	7	ya−2	ya−2	PROPN
ejpam-5044	129	8	ya	ya	PROPN
ejpam-5044	129	9	figure	figure	VERB
ejpam-5044	129	10	3	3	NUM
ejpam-5044	129	11	:	:	PUNCT
ejpam-5044	129	12	graph	graph	NOUN
ejpam-5044	129	13	g′	g′	NOUN
ejpam-5044	129	14	with	with	ADP
ejpam-5044	129	15	αh(g	αh(g	NOUN
ejpam-5044	129	16	′	′	NOUN
ejpam-5044	129	17	)	)	PUNCT
ejpam-5044	129	18	=	=	PUNCT
ejpam-5044	130	1	a	a	PRON
ejpam-5044	130	2	=	=	SYM
ejpam-5044	130	3	αch(g	αch(g	PROPN
ejpam-5044	130	4	′	′	NUM
ejpam-5044	130	5	)	)	PUNCT
ejpam-5044	130	6	let	let	VERB
ejpam-5044	130	7	b2	b2	NOUN
ejpam-5044	130	8	=	=	SYM
ejpam-5044	130	9	{	{	PUNCT
ejpam-5044	130	10	y1	y1	PROPN
ejpam-5044	130	11	,	,	PUNCT
ejpam-5044	130	12	y2	y2	PROPN
ejpam-5044	130	13	,	,	PUNCT
ejpam-5044	130	14	.	.	PUNCT
ejpam-5044	130	15	.	.	PUNCT
ejpam-5044	131	1	.	.	PUNCT
ejpam-5044	132	1	,	,	PUNCT
ejpam-5044	132	2	ya	ya	PROPN
ejpam-5044	132	3	}	}	PUNCT
ejpam-5044	132	4	.	.	PUNCT
ejpam-5044	133	1	then	then	ADV
ejpam-5044	133	2	b2	b2	PROPN
ejpam-5044	133	3	is	be	AUX
ejpam-5044	133	4	both	both	CCONJ
ejpam-5044	133	5	a	a	DET
ejpam-5044	133	6	maximum	maximum	ADJ
ejpam-5044	133	7	hop	hop	NOUN
ejpam-5044	133	8	independent	independent	ADJ
ejpam-5044	133	9	and	and	CCONJ
ejpam-5044	133	10	a	a	DET
ejpam-5044	133	11	maximum	maximum	ADJ
ejpam-5044	133	12	certified	certify	VERB
ejpam-5044	133	13	hop	hop	NOUN
ejpam-5044	133	14	independent	independent	ADJ
ejpam-5044	133	15	set	set	NOUN
ejpam-5044	133	16	of	of	ADP
ejpam-5044	133	17	g.	g.	PROPN
ejpam-5044	133	18	therefore	therefore	ADV
ejpam-5044	133	19	,	,	PUNCT
ejpam-5044	133	20	αh(g	αh(g	PRON
ejpam-5044	133	21	′	′	NOUN
ejpam-5044	133	22	)	)	PUNCT
ejpam-5044	133	23	=	=	PUNCT
ejpam-5044	134	1	a	a	PRON
ejpam-5044	134	2	=	=	SYM
ejpam-5044	134	3	αch(g	αch(g	NOUN
ejpam-5044	134	4	′	′	NUM
ejpam-5044	134	5	)	)	PUNCT
ejpam-5044	134	6	.	.	PUNCT
ejpam-5044	135	1	case	case	NOUN
ejpam-5044	135	2	2	2	NUM
ejpam-5044	135	3	:	:	PUNCT
ejpam-5044	135	4	a	a	DET
ejpam-5044	135	5	<	<	X
ejpam-5044	135	6	b	b	X
ejpam-5044	135	7	let	let	VERB
ejpam-5044	135	8	m	m	VERB
ejpam-5044	135	9	=	=	VERB
ejpam-5044	135	10	b−	b−	PROPN
ejpam-5044	135	11	a	a	PRON
ejpam-5044	135	12	and	and	CCONJ
ejpam-5044	135	13	consider	consider	VERB
ejpam-5044	135	14	the	the	DET
ejpam-5044	135	15	following	follow	VERB
ejpam-5044	135	16	cases	case	NOUN
ejpam-5044	135	17	.	.	PUNCT
ejpam-5044	136	1	subcase	subcase	NOUN
ejpam-5044	136	2	1	1	NUM
ejpam-5044	136	3	:	:	PUNCT
ejpam-5044	136	4	a	a	PRON
ejpam-5044	136	5	is	be	AUX
ejpam-5044	136	6	odd	odd	ADJ
ejpam-5044	136	7	.	.	PUNCT
ejpam-5044	137	1	consider	consider	VERB
ejpam-5044	137	2	the	the	DET
ejpam-5044	137	3	graph	graph	NOUN
ejpam-5044	137	4	h	h	NOUN
ejpam-5044	137	5	below	below	ADV
ejpam-5044	137	6	.	.	PUNCT
ejpam-5044	138	1	x1	x1	PROPN
ejpam-5044	138	2	x2	x2	PROPN
ejpam-5044	139	1	xa−2	xa−2	PROPN
ejpam-5044	139	2	xa−1	xa−1	PROPN
ejpam-5044	139	3	u	u	PROPN
ejpam-5044	139	4	xa	xa	PROPN
ejpam-5044	140	1	ym	ym	NOUN
ejpam-5044	140	2	y2	y2	PROPN
ejpam-5044	141	1	y1	y1	INTJ
ejpam-5044	141	2	h	h	NOUN
ejpam-5044	141	3	:	:	PUNCT
ejpam-5044	141	4	.	.	PUNCT
ejpam-5044	141	5	.	.	PUNCT
ejpam-5044	141	6	.	.	PUNCT
ejpam-5044	142	1	...	...	PUNCT
ejpam-5044	142	2	figure	figure	VERB
ejpam-5044	142	3	4	4	NUM
ejpam-5044	142	4	:	:	PUNCT
ejpam-5044	142	5	graph	graph	NOUN
ejpam-5044	142	6	h	h	NOUN
ejpam-5044	142	7	with	with	ADP
ejpam-5044	142	8	αch(h	αch(h	PROPN
ejpam-5044	142	9	)	)	PUNCT
ejpam-5044	142	10	<	<	X
ejpam-5044	142	11	αh(h	αh(h	PRON
ejpam-5044	142	12	)	)	PUNCT
ejpam-5044	142	13	let	let	VERB
ejpam-5044	142	14	b′	b′	NOUN
ejpam-5044	142	15	=	=	PUNCT
ejpam-5044	142	16	{	{	PUNCT
ejpam-5044	142	17	x1	x1	PROPN
ejpam-5044	142	18	,	,	PUNCT
ejpam-5044	142	19	x2	x2	PROPN
ejpam-5044	142	20	,	,	PUNCT
ejpam-5044	142	21	...	...	PUNCT
ejpam-5044	142	22	,	,	PUNCT
ejpam-5044	142	23	xa	xa	PROPN
ejpam-5044	142	24	}	}	PUNCT
ejpam-5044	142	25	and	and	CCONJ
ejpam-5044	142	26	b′′	b′′	PROPN
ejpam-5044	142	27	=	=	PUNCT
ejpam-5044	142	28	{	{	PUNCT
ejpam-5044	142	29	x1	x1	PROPN
ejpam-5044	142	30	,	,	PUNCT
ejpam-5044	142	31	x2	x2	PROPN
ejpam-5044	142	32	,	,	PUNCT
ejpam-5044	142	33	...	...	PUNCT
ejpam-5044	142	34	,	,	PUNCT
ejpam-5044	142	35	xa−1	xa−1	PROPN
ejpam-5044	142	36	,	,	PUNCT
ejpam-5044	142	37	u	u	PROPN
ejpam-5044	142	38	,	,	PUNCT
ejpam-5044	142	39	y1	y1	NOUN
ejpam-5044	142	40	,	,	PUNCT
ejpam-5044	142	41	y2	y2	PROPN
ejpam-5044	142	42	,	,	PUNCT
ejpam-5044	142	43	...	...	PUNCT
ejpam-5044	142	44	,	,	PUNCT
ejpam-5044	142	45	ym	ym	PROPN
ejpam-5044	142	46	}	}	PUNCT
ejpam-5044	142	47	.	.	PUNCT
ejpam-5044	143	1	then	then	ADV
ejpam-5044	143	2	b′	b′	NUM
ejpam-5044	143	3	and	and	CCONJ
ejpam-5044	143	4	b′′	b′′	PROPN
ejpam-5044	143	5	are	be	AUX
ejpam-5044	143	6	maximum	maximum	ADV
ejpam-5044	143	7	certified	certify	VERB
ejpam-5044	143	8	hop	hop	NOUN
ejpam-5044	143	9	independent	independent	ADJ
ejpam-5044	143	10	and	and	CCONJ
ejpam-5044	143	11	maximum	maximum	ADJ
ejpam-5044	143	12	hop	hop	NOUN
ejpam-5044	143	13	independent	independent	ADJ
ejpam-5044	143	14	set	set	NOUN
ejpam-5044	143	15	of	of	ADP
ejpam-5044	143	16	h	h	NOUN
ejpam-5044	143	17	,	,	PUNCT
ejpam-5044	143	18	respectively	respectively	ADV
ejpam-5044	143	19	.	.	PUNCT
ejpam-5044	144	1	hence	hence	ADV
ejpam-5044	144	2	,	,	PUNCT
ejpam-5044	144	3	αch(h	αch(h	PROPN
ejpam-5044	144	4	)	)	PUNCT
ejpam-5044	144	5	=	=	NOUN
ejpam-5044	145	1	a	a	PRON
ejpam-5044	145	2	and	and	CCONJ
ejpam-5044	145	3	αh(h	αh(h	NUM
ejpam-5044	145	4	)	)	PUNCT
ejpam-5044	145	5	=	=	PUNCT
ejpam-5044	145	6	a+m	a+m	NUM
ejpam-5044	146	1	=	=	SYM
ejpam-5044	146	2	b.	b.	PROPN
ejpam-5044	146	3	j.	j.	PROPN
ejpam-5044	146	4	a.	a.	PROPN
ejpam-5044	146	5	hassan	hassan	PROPN
ejpam-5044	146	6	et	et	PROPN
ejpam-5044	146	7	al	al	PROPN
ejpam-5044	146	8	.	.	PUNCT
ejpam-5044	146	9	/	/	SYM
ejpam-5044	146	10	eur	eur	PROPN
ejpam-5044	146	11	.	.	PUNCT
ejpam-5044	147	1	j.	j.	PROPN
ejpam-5044	147	2	pure	pure	PROPN
ejpam-5044	147	3	appl	appl	PROPN
ejpam-5044	147	4	.	.	PROPN
ejpam-5044	147	5	math	math	PROPN
ejpam-5044	147	6	,	,	PUNCT
ejpam-5044	147	7	17	17	NUM
ejpam-5044	147	8	(	(	PUNCT
ejpam-5044	147	9	1	1	NUM
ejpam-5044	147	10	)	)	PUNCT
ejpam-5044	147	11	(	(	PUNCT
ejpam-5044	147	12	2024	2024	NUM
ejpam-5044	147	13	)	)	PUNCT
ejpam-5044	147	14	,	,	PUNCT
ejpam-5044	147	15	435	435	NUM
ejpam-5044	147	16	-	-	SYM
ejpam-5044	147	17	444	444	NUM
ejpam-5044	147	18	441	441	NUM
ejpam-5044	147	19	case	case	NOUN
ejpam-5044	147	20	2	2	NUM
ejpam-5044	147	21	:	:	PUNCT
ejpam-5044	147	22	a	a	PRON
ejpam-5044	147	23	is	be	AUX
ejpam-5044	147	24	even	even	ADV
ejpam-5044	147	25	consider	consider	VERB
ejpam-5044	147	26	the	the	DET
ejpam-5044	147	27	graph	graph	NOUN
ejpam-5044	147	28	h	h	NOUN
ejpam-5044	147	29	′	′	NUM
ejpam-5044	147	30	below	below	ADV
ejpam-5044	147	31	.	.	PUNCT
ejpam-5044	148	1	x1	x1	PROPN
ejpam-5044	149	1	x2	x2	PROPN
ejpam-5044	149	2	xa−3	xa−3	PROPN
ejpam-5044	149	3	xa−2	xa−2	PROPN
ejpam-5044	149	4	v	v	NUM
ejpam-5044	149	5	xa−1	xa−1	PROPN
ejpam-5044	149	6	ym+1	ym+1	PROPN
ejpam-5044	150	1	y2	y2	INTJ
ejpam-5044	150	2	xa	xa	PROPN
ejpam-5044	150	3	h	h	NOUN
ejpam-5044	150	4	′	′	NUM
ejpam-5044	150	5	:	:	PUNCT
ejpam-5044	150	6	.	.	PUNCT
ejpam-5044	150	7	.	.	PUNCT
ejpam-5044	150	8	.	.	PUNCT
ejpam-5044	150	9	.	.	PUNCT
ejpam-5044	150	10	.	.	PUNCT
ejpam-5044	150	11	.	.	PUNCT
ejpam-5044	151	1	y1	y1	INTJ
ejpam-5044	151	2	figure	figure	NOUN
ejpam-5044	151	3	5	5	NUM
ejpam-5044	151	4	:	:	PUNCT
ejpam-5044	151	5	graph	graph	VERB
ejpam-5044	151	6	h′	h′	PROPN
ejpam-5044	151	7	with	with	ADP
ejpam-5044	151	8	αch(h	αch(h	PROPN
ejpam-5044	151	9	′	′	NUM
ejpam-5044	151	10	)	)	PUNCT
ejpam-5044	151	11	<	<	X
ejpam-5044	151	12	αh(h	αh(h	NUM
ejpam-5044	151	13	′	′	NOUN
ejpam-5044	151	14	)	)	PUNCT
ejpam-5044	151	15	let	let	VERB
ejpam-5044	151	16	c1	c1	PROPN
ejpam-5044	151	17	=	=	PUNCT
ejpam-5044	151	18	{	{	PUNCT
ejpam-5044	151	19	x1	x1	PROPN
ejpam-5044	151	20	,	,	PUNCT
ejpam-5044	151	21	x2	x2	PROPN
ejpam-5044	151	22	,	,	PUNCT
ejpam-5044	151	23	...	...	PUNCT
ejpam-5044	151	24	,	,	PUNCT
ejpam-5044	151	25	xa	xa	PRON
ejpam-5044	151	26	}	}	PUNCT
ejpam-5044	151	27	and	and	CCONJ
ejpam-5044	151	28	c2	c2	PROPN
ejpam-5044	151	29	=	=	SYM
ejpam-5044	151	30	{	{	PUNCT
ejpam-5044	151	31	x1	x1	PROPN
ejpam-5044	151	32	,	,	PUNCT
ejpam-5044	151	33	x2	x2	PROPN
ejpam-5044	151	34	,	,	PUNCT
ejpam-5044	151	35	...	...	PUNCT
ejpam-5044	151	36	,	,	PUNCT
ejpam-5044	151	37	xa−2	xa−2	PROPN
ejpam-5044	151	38	,	,	PUNCT
ejpam-5044	151	39	v	v	NOUN
ejpam-5044	151	40	,	,	PUNCT
ejpam-5044	151	41	y1	y1	NOUN
ejpam-5044	151	42	,	,	PUNCT
ejpam-5044	151	43	y2	y2	PROPN
ejpam-5044	151	44	,	,	PUNCT
ejpam-5044	151	45	...	...	PUNCT
ejpam-5044	151	46	,	,	PUNCT
ejpam-5044	151	47	ym+1	ym+1	PROPN
ejpam-5044	151	48	}	}	PUNCT
ejpam-5044	151	49	.	.	PUNCT
ejpam-5044	152	1	then	then	ADV
ejpam-5044	152	2	c1	c1	PROPN
ejpam-5044	152	3	and	and	CCONJ
ejpam-5044	152	4	c2	c2	PROPN
ejpam-5044	152	5	are	be	AUX
ejpam-5044	152	6	maximum	maximum	ADV
ejpam-5044	152	7	certified	certify	VERB
ejpam-5044	152	8	hop	hop	NOUN
ejpam-5044	152	9	independent	independent	ADJ
ejpam-5044	152	10	and	and	CCONJ
ejpam-5044	152	11	maximum	maximum	ADJ
ejpam-5044	152	12	hop	hop	NOUN
ejpam-5044	152	13	independent	independent	ADJ
ejpam-5044	152	14	set	set	NOUN
ejpam-5044	152	15	of	of	ADP
ejpam-5044	152	16	h	h	NOUN
ejpam-5044	152	17	′	′	NOUN
ejpam-5044	152	18	,	,	PUNCT
ejpam-5044	152	19	respectively	respectively	ADV
ejpam-5044	152	20	.	.	PUNCT
ejpam-5044	153	1	thus	thus	ADV
ejpam-5044	153	2	,	,	PUNCT
ejpam-5044	153	3	αch(h	αch(h	PROPN
ejpam-5044	153	4	′	′	NOUN
ejpam-5044	153	5	)	)	PUNCT
ejpam-5044	153	6	=	=	PUNCT
ejpam-5044	153	7	a	a	PRON
ejpam-5044	153	8	and	and	CCONJ
ejpam-5044	153	9	αh(h	αh(h	NUM
ejpam-5044	153	10	′	′	NUM
ejpam-5044	153	11	)	)	PUNCT
ejpam-5044	153	12	=	=	PUNCT
ejpam-5044	154	1	a+m	a+m	NUM
ejpam-5044	154	2	=	=	SYM
ejpam-5044	154	3	b.	b.	PROPN
ejpam-5044	154	4	remark	remark	NOUN
ejpam-5044	154	5	1	1	NUM
ejpam-5044	154	6	.	.	PUNCT
ejpam-5044	155	1	the	the	DET
ejpam-5044	155	2	standard	standard	ADJ
ejpam-5044	155	3	independence	independence	NOUN
ejpam-5044	155	4	and	and	CCONJ
ejpam-5044	155	5	certified	certify	VERB
ejpam-5044	155	6	hop	hop	NOUN
ejpam-5044	155	7	independence	independence	NOUN
ejpam-5044	155	8	parameters	parameter	NOUN
ejpam-5044	155	9	are	be	AUX
ejpam-5044	155	10	incomparable	incomparable	ADJ
ejpam-5044	155	11	.	.	PUNCT
ejpam-5044	156	1	to	to	PART
ejpam-5044	156	2	see	see	VERB
ejpam-5044	156	3	this	this	PRON
ejpam-5044	156	4	,	,	PUNCT
ejpam-5044	156	5	consider	consider	VERB
ejpam-5044	156	6	the	the	DET
ejpam-5044	156	7	graph	graph	NOUN
ejpam-5044	156	8	g	g	NOUN
ejpam-5044	156	9	below	below	ADV
ejpam-5044	156	10	.	.	PUNCT
ejpam-5044	157	1	a	a	DET
ejpam-5044	157	2	b	b	NOUN
ejpam-5044	157	3	c	c	NOUN
ejpam-5044	157	4	d	d	X
ejpam-5044	157	5	e	e	X
ejpam-5044	157	6	f	f	PROPN
ejpam-5044	157	7	g	g	PROPN
ejpam-5044	158	1	h	h	NOUN
ejpam-5044	159	1	i	i	PRON
ejpam-5044	159	2	j	j	PROPN
ejpam-5044	160	1	k	k	PROPN
ejpam-5044	160	2	l	l	PROPN
ejpam-5044	160	3	m	m	AUX
ejpam-5044	160	4	g	g	NOUN
ejpam-5044	160	5	:	:	PUNCT
ejpam-5044	160	6	figure	figure	VERB
ejpam-5044	160	7	6	6	NUM
ejpam-5044	160	8	:	:	PUNCT
ejpam-5044	160	9	graph	graph	VERB
ejpam-5044	160	10	g	g	NOUN
ejpam-5044	160	11	with	with	ADP
ejpam-5044	160	12	α(g	α(g	NUM
ejpam-5044	160	13	)	)	PUNCT
ejpam-5044	160	14	<	<	X
ejpam-5044	160	15	αch(g	αch(g	NOUN
ejpam-5044	160	16	)	)	PUNCT
ejpam-5044	160	17	let	let	VERB
ejpam-5044	160	18	c	c	NOUN
ejpam-5044	160	19	=	=	PUNCT
ejpam-5044	160	20	{	{	PUNCT
ejpam-5044	160	21	a	a	PRON
ejpam-5044	160	22	,	,	PUNCT
ejpam-5044	160	23	b	b	NOUN
ejpam-5044	160	24	,	,	PUNCT
ejpam-5044	160	25	c	c	NOUN
ejpam-5044	160	26	,	,	PUNCT
ejpam-5044	160	27	d	d	NOUN
ejpam-5044	160	28	,	,	PUNCT
ejpam-5044	160	29	i	i	PRON
ejpam-5044	160	30	,	,	PUNCT
ejpam-5044	160	31	k	k	PROPN
ejpam-5044	160	32	,	,	PUNCT
ejpam-5044	160	33	l	l	NOUN
ejpam-5044	160	34	,	,	PUNCT
ejpam-5044	160	35	m	m	NOUN
ejpam-5044	160	36	}	}	PUNCT
ejpam-5044	160	37	.	.	PUNCT
ejpam-5044	161	1	then	then	ADV
ejpam-5044	161	2	c	c	PROPN
ejpam-5044	161	3	is	be	AUX
ejpam-5044	161	4	a	a	DET
ejpam-5044	161	5	maximum	maximum	ADV
ejpam-5044	161	6	certified	certify	VERB
ejpam-5044	161	7	hop	hop	NOUN
ejpam-5044	161	8	independent	independent	ADJ
ejpam-5044	161	9	set	set	NOUN
ejpam-5044	161	10	of	of	ADP
ejpam-5044	161	11	g.	g.	PROPN
ejpam-5044	161	12	thus	thus	ADV
ejpam-5044	161	13	,	,	PUNCT
ejpam-5044	161	14	αch(g	αch(g	NOUN
ejpam-5044	161	15	)	)	PUNCT
ejpam-5044	161	16	=	=	SYM
ejpam-5044	161	17	8	8	X
ejpam-5044	161	18	.	.	PUNCT
ejpam-5044	162	1	next	next	ADV
ejpam-5044	162	2	,	,	PUNCT
ejpam-5044	162	3	let	let	VERB
ejpam-5044	162	4	c	c	NOUN
ejpam-5044	162	5	′	′	VERB
ejpam-5044	162	6	=	=	PUNCT
ejpam-5044	162	7	{	{	PUNCT
ejpam-5044	162	8	a	a	X
ejpam-5044	162	9	,	,	PUNCT
ejpam-5044	162	10	e	e	NOUN
ejpam-5044	162	11	,	,	PUNCT
ejpam-5044	162	12	g	g	PROPN
ejpam-5044	162	13	,	,	PUNCT
ejpam-5044	162	14	h	h	NOUN
ejpam-5044	162	15	,	,	PUNCT
ejpam-5044	162	16	j	j	PROPN
ejpam-5044	162	17	,	,	PUNCT
ejpam-5044	162	18	k	k	NOUN
ejpam-5044	162	19	}	}	PUNCT
ejpam-5044	162	20	.	.	PUNCT
ejpam-5044	163	1	then	then	ADV
ejpam-5044	163	2	c	c	X
ejpam-5044	163	3	′	′	PROPN
ejpam-5044	163	4	is	be	AUX
ejpam-5044	163	5	a	a	DET
ejpam-5044	163	6	maximum	maximum	ADJ
ejpam-5044	163	7	independent	independent	ADJ
ejpam-5044	163	8	set	set	NOUN
ejpam-5044	163	9	of	of	ADP
ejpam-5044	163	10	g.	g.	PROPN
ejpam-5044	163	11	hence	hence	ADV
ejpam-5044	163	12	,	,	PUNCT
ejpam-5044	163	13	α(g	α(g	NUM
ejpam-5044	163	14	)	)	PUNCT
ejpam-5044	163	15	=	=	SYM
ejpam-5044	163	16	6	6	X
ejpam-5044	163	17	.	.	PUNCT
ejpam-5044	164	1	j.	j.	PROPN
ejpam-5044	164	2	a.	a.	PROPN
ejpam-5044	164	3	hassan	hassan	PROPN
ejpam-5044	164	4	et	et	PROPN
ejpam-5044	164	5	al	al	PROPN
ejpam-5044	164	6	.	.	PUNCT
ejpam-5044	164	7	/	/	SYM
ejpam-5044	164	8	eur	eur	PROPN
ejpam-5044	164	9	.	.	PUNCT
ejpam-5044	165	1	j.	j.	PROPN
ejpam-5044	165	2	pure	pure	PROPN
ejpam-5044	165	3	appl	appl	PROPN
ejpam-5044	165	4	.	.	PROPN
ejpam-5044	165	5	math	math	PROPN
ejpam-5044	165	6	,	,	PUNCT
ejpam-5044	165	7	17	17	NUM
ejpam-5044	165	8	(	(	PUNCT
ejpam-5044	165	9	1	1	NUM
ejpam-5044	165	10	)	)	PUNCT
ejpam-5044	165	11	(	(	PUNCT
ejpam-5044	165	12	2024	2024	NUM
ejpam-5044	165	13	)	)	PUNCT
ejpam-5044	165	14	,	,	PUNCT
ejpam-5044	165	15	435	435	NUM
ejpam-5044	165	16	-	-	SYM
ejpam-5044	165	17	444	444	NUM
ejpam-5044	165	18	442	442	NUM
ejpam-5044	165	19	on	on	ADP
ejpam-5044	165	20	the	the	DET
ejpam-5044	165	21	other	other	ADJ
ejpam-5044	165	22	hand	hand	NOUN
ejpam-5044	165	23	,	,	PUNCT
ejpam-5044	165	24	consider	consider	VERB
ejpam-5044	165	25	the	the	DET
ejpam-5044	165	26	graph	graph	NOUN
ejpam-5044	165	27	h	h	NOUN
ejpam-5044	165	28	below	below	ADV
ejpam-5044	165	29	.	.	PUNCT
ejpam-5044	166	1	a	a	DET
ejpam-5044	166	2	b	b	NOUN
ejpam-5044	166	3	c	c	NOUN
ejpam-5044	166	4	d	d	X
ejpam-5044	166	5	e	e	X
ejpam-5044	166	6	f	f	PROPN
ejpam-5044	166	7	g	g	PROPN
ejpam-5044	167	1	h	h	NOUN
ejpam-5044	168	1	i	i	PRON
ejpam-5044	168	2	j	j	PROPN
ejpam-5044	169	1	k	k	PROPN
ejpam-5044	169	2	h	h	NOUN
ejpam-5044	169	3	:	:	PUNCT
ejpam-5044	169	4	figure	figure	VERB
ejpam-5044	169	5	7	7	NUM
ejpam-5044	169	6	:	:	PUNCT
ejpam-5044	169	7	graph	graph	NOUN
ejpam-5044	169	8	h	h	NOUN
ejpam-5044	169	9	with	with	ADP
ejpam-5044	169	10	αch(h	αch(h	NUM
ejpam-5044	169	11	)	)	PUNCT
ejpam-5044	169	12	<	<	X
ejpam-5044	169	13	α(h	α(h	NOUN
ejpam-5044	169	14	)	)	PUNCT
ejpam-5044	169	15	let	let	VERB
ejpam-5044	169	16	o1	o1	NOUN
ejpam-5044	169	17	=	=	SYM
ejpam-5044	169	18	{	{	PUNCT
ejpam-5044	169	19	a	a	PRON
ejpam-5044	169	20	,	,	PUNCT
ejpam-5044	169	21	b	b	NOUN
ejpam-5044	169	22	,	,	PUNCT
ejpam-5044	169	23	c	c	X
ejpam-5044	169	24	,	,	PUNCT
ejpam-5044	169	25	f	f	PROPN
ejpam-5044	169	26	,	,	PUNCT
ejpam-5044	169	27	g	g	PROPN
ejpam-5044	169	28	,	,	PUNCT
ejpam-5044	169	29	h	h	NOUN
ejpam-5044	169	30	,	,	PUNCT
ejpam-5044	169	31	j	j	PROPN
ejpam-5044	169	32	,	,	PUNCT
ejpam-5044	169	33	k	k	NOUN
ejpam-5044	169	34	}	}	PUNCT
ejpam-5044	169	35	.	.	PUNCT
ejpam-5044	170	1	then	then	ADV
ejpam-5044	170	2	o1	o1	PROPN
ejpam-5044	170	3	is	be	AUX
ejpam-5044	170	4	a	a	DET
ejpam-5044	170	5	maximum	maximum	ADJ
ejpam-5044	170	6	independent	independent	ADJ
ejpam-5044	170	7	set	set	NOUN
ejpam-5044	170	8	of	of	ADP
ejpam-5044	170	9	h.	h.	PROPN
ejpam-5044	170	10	thus	thus	ADV
ejpam-5044	170	11	,	,	PUNCT
ejpam-5044	170	12	α(h	α(h	NOUN
ejpam-5044	170	13	)	)	PUNCT
ejpam-5044	170	14	=	=	SYM
ejpam-5044	171	1	8	8	X
ejpam-5044	171	2	.	.	PUNCT
ejpam-5044	172	1	next	next	ADV
ejpam-5044	172	2	,	,	PUNCT
ejpam-5044	172	3	let	let	VERB
ejpam-5044	172	4	o2	o2	PROPN
ejpam-5044	172	5	=	=	SYM
ejpam-5044	172	6	{	{	PUNCT
ejpam-5044	172	7	c	c	NOUN
ejpam-5044	172	8	,	,	PUNCT
ejpam-5044	172	9	d	d	NOUN
ejpam-5044	172	10	,	,	PUNCT
ejpam-5044	172	11	i	i	PRON
ejpam-5044	172	12	,	,	PUNCT
ejpam-5044	172	13	j	j	PROPN
ejpam-5044	172	14	}	}	PUNCT
ejpam-5044	172	15	.	.	PUNCT
ejpam-5044	173	1	then	then	ADV
ejpam-5044	173	2	o2	o2	PROPN
ejpam-5044	173	3	is	be	AUX
ejpam-5044	173	4	a	a	DET
ejpam-5044	173	5	maximum	maximum	ADV
ejpam-5044	173	6	certified	certify	VERB
ejpam-5044	173	7	hop	hop	NOUN
ejpam-5044	173	8	independent	independent	ADJ
ejpam-5044	173	9	set	set	NOUN
ejpam-5044	173	10	of	of	ADP
ejpam-5044	173	11	h.	h.	PROPN
ejpam-5044	173	12	therefore	therefore	ADV
ejpam-5044	173	13	,	,	PUNCT
ejpam-5044	173	14	αch(h	αch(h	X
ejpam-5044	173	15	)	)	PUNCT
ejpam-5044	173	16	=	=	SYM
ejpam-5044	173	17	4	4	X
ejpam-5044	173	18	.	.	PUNCT
ejpam-5044	173	19	theorem	theorem	NOUN
ejpam-5044	173	20	6	6	NUM
ejpam-5044	173	21	.	.	PUNCT
ejpam-5044	174	1	let	let	VERB
ejpam-5044	174	2	g	g	NOUN
ejpam-5044	174	3	and	and	CCONJ
ejpam-5044	174	4	h	h	PROPN
ejpam-5044	174	5	be	be	VERB
ejpam-5044	174	6	non	non	ADJ
ejpam-5044	174	7	-	-	ADJ
ejpam-5044	174	8	trivial	trivial	ADJ
ejpam-5044	174	9	graphs	graph	NOUN
ejpam-5044	174	10	such	such	ADJ
ejpam-5044	174	11	that	that	SCONJ
ejpam-5044	174	12	g	g	PROPN
ejpam-5044	174	13	and	and	CCONJ
ejpam-5044	174	14	h	h	NOUN
ejpam-5044	174	15	have	have	VERB
ejpam-5044	174	16	no	no	DET
ejpam-5044	174	17	complete	complete	ADJ
ejpam-5044	174	18	subgraphs	subgraph	NOUN
ejpam-5044	174	19	of	of	ADP
ejpam-5044	174	20	order	order	NOUN
ejpam-5044	174	21	|v	|v	X
ejpam-5044	174	22	(	(	PUNCT
ejpam-5044	174	23	g)|	g)|	INTJ
ejpam-5044	174	24	−	−	PROPN
ejpam-5044	174	25	1	1	NUM
ejpam-5044	174	26	and	and	CCONJ
ejpam-5044	174	27	|v	|v	PROPN
ejpam-5044	174	28	(	(	PUNCT
ejpam-5044	174	29	h)|	h)|	NOUN
ejpam-5044	174	30	−	−	PROPN
ejpam-5044	174	31	1	1	NUM
ejpam-5044	174	32	,	,	PUNCT
ejpam-5044	174	33	respectively	respectively	ADV
ejpam-5044	174	34	.	.	PUNCT
ejpam-5044	175	1	then	then	ADV
ejpam-5044	175	2	l	l	PROPN
ejpam-5044	175	3	⊆	⊆	NUM
ejpam-5044	175	4	v	v	X
ejpam-5044	175	5	(	(	PUNCT
ejpam-5044	175	6	g	g	PROPN
ejpam-5044	175	7	+	+	NOUN
ejpam-5044	175	8	h	h	NOUN
ejpam-5044	175	9	)	)	PUNCT
ejpam-5044	175	10	is	be	AUX
ejpam-5044	175	11	a	a	DET
ejpam-5044	175	12	certified	certified	ADJ
ejpam-5044	175	13	hop	hop	NOUN
ejpam-5044	175	14	independent	independent	ADJ
ejpam-5044	175	15	set	set	NOUN
ejpam-5044	175	16	of	of	ADP
ejpam-5044	175	17	g	g	PROPN
ejpam-5044	176	1	+	+	CCONJ
ejpam-5044	176	2	h	h	NOUN
ejpam-5044	176	3	if	if	SCONJ
ejpam-5044	176	4	and	and	CCONJ
ejpam-5044	176	5	only	only	ADV
ejpam-5044	176	6	if	if	SCONJ
ejpam-5044	176	7	l	l	NOUN
ejpam-5044	176	8	satisfies	satisfy	VERB
ejpam-5044	176	9	one	one	NUM
ejpam-5044	176	10	of	of	ADP
ejpam-5044	176	11	the	the	DET
ejpam-5044	176	12	following	following	ADJ
ejpam-5044	176	13	conditions	condition	NOUN
ejpam-5044	176	14	:	:	PUNCT
ejpam-5044	176	15	(	(	PUNCT
ejpam-5044	176	16	i	i	NOUN
ejpam-5044	176	17	)	)	PUNCT
ejpam-5044	176	18	l	l	NOUN
ejpam-5044	176	19	=	=	SYM
ejpam-5044	176	20	l	l	NOUN
ejpam-5044	176	21	∩	∩	X
ejpam-5044	176	22	v	v	X
ejpam-5044	176	23	(	(	PUNCT
ejpam-5044	176	24	g	g	NOUN
ejpam-5044	176	25	)	)	PUNCT
ejpam-5044	177	1	=	=	SYM
ejpam-5044	177	2	lg	lg	NOUN
ejpam-5044	177	3	is	be	AUX
ejpam-5044	177	4	clique	clique	ADJ
ejpam-5044	177	5	in	in	ADP
ejpam-5044	177	6	g.	g.	PROPN
ejpam-5044	177	7	(	(	PUNCT
ejpam-5044	177	8	ii	ii	PROPN
ejpam-5044	177	9	)	)	PUNCT
ejpam-5044	177	10	l	l	NOUN
ejpam-5044	178	1	=	=	SYM
ejpam-5044	178	2	l	l	NOUN
ejpam-5044	178	3	∩	∩	X
ejpam-5044	178	4	v	v	X
ejpam-5044	178	5	(	(	PUNCT
ejpam-5044	178	6	h	h	NOUN
ejpam-5044	178	7	)	)	PUNCT
ejpam-5044	178	8	=	=	NOUN
ejpam-5044	178	9	lh	lh	PROPN
ejpam-5044	178	10	is	be	AUX
ejpam-5044	178	11	clique	clique	ADJ
ejpam-5044	178	12	in	in	ADP
ejpam-5044	178	13	h.	h.	PROPN
ejpam-5044	178	14	(	(	PUNCT
ejpam-5044	178	15	iii	iii	NOUN
ejpam-5044	178	16	)	)	PUNCT
ejpam-5044	178	17	l	l	NOUN
ejpam-5044	178	18	=	=	PUNCT
ejpam-5044	178	19	lg	lg	NOUN
ejpam-5044	178	20	∪	∪	PROPN
ejpam-5044	178	21	lh	lh	PROPN
ejpam-5044	178	22	,	,	PUNCT
ejpam-5044	178	23	where	where	SCONJ
ejpam-5044	178	24	lg	lg	NOUN
ejpam-5044	178	25	and	and	CCONJ
ejpam-5044	178	26	lh	lh	PROPN
ejpam-5044	178	27	are	be	AUX
ejpam-5044	178	28	cliques	clique	NOUN
ejpam-5044	178	29	in	in	ADP
ejpam-5044	178	30	g	g	PROPN
ejpam-5044	178	31	and	and	CCONJ
ejpam-5044	178	32	h	h	NOUN
ejpam-5044	178	33	,	,	PUNCT
ejpam-5044	178	34	respectively	respectively	ADV
ejpam-5044	178	35	.	.	PUNCT
ejpam-5044	179	1	proof	proof	NOUN
ejpam-5044	179	2	.	.	PUNCT
ejpam-5044	180	1	let	let	VERB
ejpam-5044	180	2	l	l	NOUN
ejpam-5044	180	3	be	be	AUX
ejpam-5044	180	4	a	a	DET
ejpam-5044	180	5	certified	certified	ADJ
ejpam-5044	180	6	hop	hop	NOUN
ejpam-5044	180	7	independent	independent	ADJ
ejpam-5044	180	8	set	set	NOUN
ejpam-5044	180	9	of	of	ADP
ejpam-5044	180	10	g+h	g+h	PROPN
ejpam-5044	180	11	and	and	CCONJ
ejpam-5044	180	12	let	let	VERB
ejpam-5044	180	13	lg	lg	NOUN
ejpam-5044	180	14	=	=	NOUN
ejpam-5044	180	15	l	l	NOUN
ejpam-5044	180	16	∩	∩	X
ejpam-5044	180	17	v	v	X
ejpam-5044	180	18	(	(	PUNCT
ejpam-5044	180	19	g	g	NOUN
ejpam-5044	180	20	)	)	PUNCT
ejpam-5044	180	21	and	and	CCONJ
ejpam-5044	180	22	lh	lh	PROPN
ejpam-5044	180	23	=	=	SYM
ejpam-5044	180	24	l	l	PROPN
ejpam-5044	180	25	∩	∩	X
ejpam-5044	180	26	v	v	X
ejpam-5044	180	27	(	(	PUNCT
ejpam-5044	180	28	h	h	NOUN
ejpam-5044	180	29	)	)	PUNCT
ejpam-5044	180	30	.	.	PUNCT
ejpam-5044	181	1	if	if	SCONJ
ejpam-5044	181	2	lh	lh	PROPN
ejpam-5044	181	3	=	=	NOUN
ejpam-5044	181	4	∅	∅	NOUN
ejpam-5044	181	5	,	,	PUNCT
ejpam-5044	181	6	then	then	ADV
ejpam-5044	181	7	l	l	NOUN
ejpam-5044	181	8	=	=	PUNCT
ejpam-5044	181	9	lg	lg	PROPN
ejpam-5044	181	10	.	.	PROPN
ejpam-5044	181	11	let	let	VERB
ejpam-5044	181	12	x	x	PRON
ejpam-5044	181	13	,	,	PUNCT
ejpam-5044	181	14	y	y	PROPN
ejpam-5044	181	15	∈	∈	PROPN
ejpam-5044	181	16	lg	lg	PROPN
ejpam-5044	181	17	.	.	PROPN
ejpam-5044	182	1	then	then	ADV
ejpam-5044	182	2	dg+h(x	dg+h(x	PROPN
ejpam-5044	182	3	,	,	PUNCT
ejpam-5044	182	4	y	y	PROPN
ejpam-5044	182	5	)	)	PUNCT
ejpam-5044	182	6	=	=	SYM
ejpam-5044	182	7	dg(x	dg(x	X
ejpam-5044	182	8	,	,	PUNCT
ejpam-5044	182	9	y	y	NOUN
ejpam-5044	182	10	)	)	PUNCT
ejpam-5044	182	11	̸=	̸=	PROPN
ejpam-5044	182	12	2	2	NUM
ejpam-5044	182	13	.	.	PUNCT
ejpam-5044	183	1	this	this	PRON
ejpam-5044	183	2	means	mean	VERB
ejpam-5044	183	3	that	that	SCONJ
ejpam-5044	183	4	dg(x	dg(x	ADV
ejpam-5044	183	5	,	,	PUNCT
ejpam-5044	183	6	y	y	NOUN
ejpam-5044	183	7	)	)	PUNCT
ejpam-5044	183	8	=	=	SYM
ejpam-5044	183	9	1	1	X
ejpam-5044	183	10	.	.	PUNCT
ejpam-5044	184	1	thus	thus	ADV
ejpam-5044	184	2	,	,	PUNCT
ejpam-5044	184	3	lg	lg	NOUN
ejpam-5044	184	4	is	be	AUX
ejpam-5044	184	5	a	a	DET
ejpam-5044	184	6	clique	clique	NOUN
ejpam-5044	184	7	in	in	ADP
ejpam-5044	184	8	g.	g.	PROPN
ejpam-5044	184	9	similarly	similarly	ADV
ejpam-5044	184	10	,	,	PUNCT
ejpam-5044	184	11	if	if	SCONJ
ejpam-5044	184	12	lg	lg	NOUN
ejpam-5044	184	13	=	=	NOUN
ejpam-5044	184	14	∅	∅	NOUN
ejpam-5044	184	15	,	,	PUNCT
ejpam-5044	184	16	then	then	ADV
ejpam-5044	184	17	lh	lh	PROPN
ejpam-5044	184	18	=	=	SYM
ejpam-5044	184	19	l	l	PROPN
ejpam-5044	184	20	∩	∩	X
ejpam-5044	184	21	v	v	X
ejpam-5044	184	22	(	(	PUNCT
ejpam-5044	184	23	h	h	NOUN
ejpam-5044	184	24	)	)	PUNCT
ejpam-5044	184	25	is	be	AUX
ejpam-5044	184	26	a	a	DET
ejpam-5044	184	27	clique	clique	NOUN
ejpam-5044	184	28	in	in	ADP
ejpam-5044	184	29	h.	h.	PROPN
ejpam-5044	184	30	suppose	suppose	VERB
ejpam-5044	184	31	that	that	SCONJ
ejpam-5044	184	32	lg	lg	PROPN
ejpam-5044	184	33	̸=	̸=	PROPN
ejpam-5044	184	34	∅	∅	NOUN
ejpam-5044	184	35	and	and	CCONJ
ejpam-5044	184	36	lh	lh	PROPN
ejpam-5044	184	37	̸=	̸=	PROPN
ejpam-5044	184	38	∅.	∅.	ADV
ejpam-5044	184	39	since	since	SCONJ
ejpam-5044	184	40	l	l	NOUN
ejpam-5044	184	41	is	be	AUX
ejpam-5044	184	42	a	a	DET
ejpam-5044	184	43	hop	hop	NOUN
ejpam-5044	184	44	independent	independent	ADJ
ejpam-5044	184	45	,	,	PUNCT
ejpam-5044	184	46	lg	lg	PROPN
ejpam-5044	184	47	and	and	CCONJ
ejpam-5044	184	48	lh	lh	PROPN
ejpam-5044	184	49	are	be	AUX
ejpam-5044	184	50	clique	clique	ADJ
ejpam-5044	184	51	in	in	ADP
ejpam-5044	184	52	g	g	PROPN
ejpam-5044	184	53	and	and	CCONJ
ejpam-5044	184	54	h	h	NOUN
ejpam-5044	184	55	,	,	PUNCT
ejpam-5044	184	56	respectively	respectively	ADV
ejpam-5044	184	57	.	.	PUNCT
ejpam-5044	185	1	conversely	conversely	ADV
ejpam-5044	185	2	,	,	PUNCT
ejpam-5044	185	3	suppose	suppose	VERB
ejpam-5044	185	4	that	that	SCONJ
ejpam-5044	185	5	(	(	PUNCT
ejpam-5044	185	6	i	i	NOUN
ejpam-5044	185	7	)	)	PUNCT
ejpam-5044	185	8	holds	hold	VERB
ejpam-5044	185	9	.	.	PUNCT
ejpam-5044	186	1	then	then	ADV
ejpam-5044	186	2	dg(a	dg(a	NUM
ejpam-5044	186	3	,	,	PUNCT
ejpam-5044	186	4	b	b	X
ejpam-5044	186	5	)	)	PUNCT
ejpam-5044	186	6	=	=	SYM
ejpam-5044	186	7	1	1	NUM
ejpam-5044	186	8	=	=	SYM
ejpam-5044	186	9	dg+h(a	dg+h(a	PROPN
ejpam-5044	186	10	,	,	PUNCT
ejpam-5044	186	11	b	b	NOUN
ejpam-5044	186	12	)	)	PUNCT
ejpam-5044	186	13	for	for	ADP
ejpam-5044	186	14	every	every	DET
ejpam-5044	186	15	a	a	PROPN
ejpam-5044	186	16	,	,	PUNCT
ejpam-5044	186	17	b	b	PROPN
ejpam-5044	186	18	∈	∈	PROPN
ejpam-5044	186	19	l	l	NOUN
ejpam-5044	186	20	=	=	PUNCT
ejpam-5044	186	21	lg	lg	NOUN
ejpam-5044	186	22	.	.	PUNCT
ejpam-5044	187	1	this	this	PRON
ejpam-5044	187	2	means	mean	VERB
ejpam-5044	187	3	that	that	SCONJ
ejpam-5044	187	4	l	l	NOUN
ejpam-5044	187	5	is	be	AUX
ejpam-5044	187	6	a	a	DET
ejpam-5044	187	7	hop	hop	NOUN
ejpam-5044	187	8	independent	independent	ADJ
ejpam-5044	187	9	set	set	NOUN
ejpam-5044	187	10	of	of	ADP
ejpam-5044	187	11	g	g	PROPN
ejpam-5044	187	12	+	+	CCONJ
ejpam-5044	187	13	h.	h.	PROPN
ejpam-5044	187	14	since	since	SCONJ
ejpam-5044	187	15	h	h	PROPN
ejpam-5044	187	16	is	be	AUX
ejpam-5044	187	17	non	non	ADJ
ejpam-5044	187	18	-	-	ADJ
ejpam-5044	187	19	trivial	trivial	ADJ
ejpam-5044	187	20	,	,	PUNCT
ejpam-5044	187	21	there	there	PRON
ejpam-5044	187	22	exist	exist	VERB
ejpam-5044	187	23	at	at	ADV
ejpam-5044	187	24	least	least	ADV
ejpam-5044	187	25	two	two	NUM
ejpam-5044	187	26	vertices	vertex	NOUN
ejpam-5044	187	27	u	u	NOUN
ejpam-5044	187	28	,	,	PUNCT
ejpam-5044	187	29	v	v	NOUN
ejpam-5044	187	30	∈	∈	PROPN
ejpam-5044	187	31	v	v	NOUN
ejpam-5044	187	32	(	(	PUNCT
ejpam-5044	187	33	h	h	NOUN
ejpam-5044	187	34	)	)	PUNCT
ejpam-5044	187	35	such	such	ADJ
ejpam-5044	187	36	that	that	SCONJ
ejpam-5044	187	37	u	u	NOUN
ejpam-5044	187	38	,	,	PUNCT
ejpam-5044	187	39	v	v	PROPN
ejpam-5044	187	40	∈	∈	PROPN
ejpam-5044	187	41	ng+h(a	ng+h(a	NOUN
ejpam-5044	187	42	)	)	PUNCT
ejpam-5044	187	43	and	and	CCONJ
ejpam-5044	187	44	u	u	NOUN
ejpam-5044	187	45	,	,	PUNCT
ejpam-5044	187	46	v	v	ADP
ejpam-5044	187	47	∈	∈	PROPN
ejpam-5044	187	48	ng+h(b	ng+h(b	NUM
ejpam-5044	187	49	)	)	PUNCT
ejpam-5044	187	50	.	.	PUNCT
ejpam-5044	188	1	hence	hence	ADV
ejpam-5044	188	2	,	,	PUNCT
ejpam-5044	188	3	l	l	PROPN
ejpam-5044	188	4	is	be	AUX
ejpam-5044	188	5	a	a	DET
ejpam-5044	188	6	certified	certified	ADJ
ejpam-5044	188	7	hop	hop	NOUN
ejpam-5044	188	8	independent	independent	ADJ
ejpam-5044	188	9	set	set	NOUN
ejpam-5044	188	10	of	of	ADP
ejpam-5044	188	11	g	g	PROPN
ejpam-5044	188	12	+	+	CCONJ
ejpam-5044	188	13	h.	h.	PROPN
ejpam-5044	188	14	similarly	similarly	ADV
ejpam-5044	188	15	,	,	PUNCT
ejpam-5044	188	16	when	when	SCONJ
ejpam-5044	188	17	(	(	PUNCT
ejpam-5044	188	18	ii	ii	NOUN
ejpam-5044	188	19	)	)	PUNCT
ejpam-5044	188	20	holds	hold	VERB
ejpam-5044	188	21	,	,	PUNCT
ejpam-5044	188	22	the	the	DET
ejpam-5044	188	23	assertion	assertion	NOUN
ejpam-5044	188	24	follows	follow	VERB
ejpam-5044	188	25	.	.	PUNCT
ejpam-5044	189	1	now	now	ADV
ejpam-5044	189	2	,	,	PUNCT
ejpam-5044	189	3	suppose	suppose	VERB
ejpam-5044	189	4	that	that	SCONJ
ejpam-5044	189	5	(	(	PUNCT
ejpam-5044	189	6	iii	iii	NOUN
ejpam-5044	189	7	)	)	PUNCT
ejpam-5044	189	8	holds	hold	VERB
ejpam-5044	189	9	.	.	PUNCT
ejpam-5044	190	1	then	then	ADV
ejpam-5044	190	2	l	l	PROPN
ejpam-5044	190	3	is	be	AUX
ejpam-5044	190	4	a	a	DET
ejpam-5044	190	5	hop	hop	NOUN
ejpam-5044	190	6	independent	independent	ADJ
ejpam-5044	190	7	set	set	NOUN
ejpam-5044	190	8	of	of	ADP
ejpam-5044	190	9	g	g	PROPN
ejpam-5044	190	10	+	+	PROPN
ejpam-5044	190	11	h.	h.	PROPN
ejpam-5044	190	12	since	since	SCONJ
ejpam-5044	190	13	g	g	PROPN
ejpam-5044	190	14	and	and	CCONJ
ejpam-5044	190	15	h	h	NOUN
ejpam-5044	190	16	have	have	VERB
ejpam-5044	190	17	no	no	DET
ejpam-5044	190	18	complete	complete	ADJ
ejpam-5044	190	19	subgraphs	subgraph	NOUN
ejpam-5044	190	20	of	of	ADP
ejpam-5044	190	21	order	order	NOUN
ejpam-5044	190	22	|v	|v	X
ejpam-5044	190	23	(	(	PUNCT
ejpam-5044	190	24	g)|	g)|	INTJ
ejpam-5044	190	25	−	−	PROPN
ejpam-5044	190	26	1	1	NUM
ejpam-5044	190	27	and	and	CCONJ
ejpam-5044	190	28	|v	|v	PROPN
ejpam-5044	190	29	(	(	PUNCT
ejpam-5044	190	30	h)|	h)|	NOUN
ejpam-5044	190	31	−	−	PROPN
ejpam-5044	190	32	1	1	NUM
ejpam-5044	190	33	,	,	PUNCT
ejpam-5044	190	34	respectively	respectively	ADV
ejpam-5044	190	35	,	,	PUNCT
ejpam-5044	190	36	clearly	clearly	ADV
ejpam-5044	190	37	,	,	PUNCT
ejpam-5044	190	38	l	l	NOUN
ejpam-5044	190	39	is	be	AUX
ejpam-5044	190	40	a	a	DET
ejpam-5044	190	41	certified	certified	ADJ
ejpam-5044	190	42	hop	hop	NOUN
ejpam-5044	190	43	independent	independent	ADJ
ejpam-5044	190	44	set	set	NOUN
ejpam-5044	190	45	of	of	ADP
ejpam-5044	190	46	g+h	g+h	PROPN
ejpam-5044	190	47	.	.	PUNCT
ejpam-5044	191	1	references	reference	VERB
ejpam-5044	191	2	443	443	NUM
ejpam-5044	191	3	corollary	corollary	ADJ
ejpam-5044	191	4	4	4	NUM
ejpam-5044	191	5	.	.	PUNCT
ejpam-5044	192	1	let	let	VERB
ejpam-5044	192	2	g	g	NOUN
ejpam-5044	192	3	and	and	CCONJ
ejpam-5044	192	4	h	h	PROPN
ejpam-5044	192	5	be	be	VERB
ejpam-5044	192	6	non	non	ADJ
ejpam-5044	192	7	-	-	ADJ
ejpam-5044	192	8	trivial	trivial	ADJ
ejpam-5044	192	9	graphs	graph	NOUN
ejpam-5044	192	10	such	such	ADJ
ejpam-5044	192	11	that	that	SCONJ
ejpam-5044	192	12	g	g	PROPN
ejpam-5044	192	13	and	and	CCONJ
ejpam-5044	192	14	h	h	NOUN
ejpam-5044	192	15	have	have	VERB
ejpam-5044	192	16	no	no	DET
ejpam-5044	192	17	complete	complete	ADJ
ejpam-5044	192	18	subgraphs	subgraph	NOUN
ejpam-5044	192	19	of	of	ADP
ejpam-5044	192	20	order	order	NOUN
ejpam-5044	192	21	|v	|v	X
ejpam-5044	192	22	(	(	PUNCT
ejpam-5044	192	23	g)|	g)|	INTJ
ejpam-5044	192	24	−	−	PROPN
ejpam-5044	192	25	1	1	NUM
ejpam-5044	192	26	and	and	CCONJ
ejpam-5044	192	27	|v	|v	PROPN
ejpam-5044	192	28	(	(	PUNCT
ejpam-5044	192	29	h)|	h)|	NOUN
ejpam-5044	192	30	−	−	PROPN
ejpam-5044	192	31	1	1	NUM
ejpam-5044	192	32	,	,	PUNCT
ejpam-5044	192	33	respectively	respectively	ADV
ejpam-5044	192	34	.	.	PUNCT
ejpam-5044	193	1	then	then	ADV
ejpam-5044	193	2	αch(g+h	αch(g+h	X
ejpam-5044	193	3	)	)	PUNCT
ejpam-5044	193	4	=	=	SYM
ejpam-5044	193	5	ω(g	ω(g	NOUN
ejpam-5044	193	6	)	)	PUNCT
ejpam-5044	193	7	+	+	NUM
ejpam-5044	193	8	ω(h	ω(h	NUM
ejpam-5044	193	9	)	)	PUNCT
ejpam-5044	193	10	.	.	PUNCT
ejpam-5044	194	1	proof	proof	NOUN
ejpam-5044	194	2	.	.	PUNCT
ejpam-5044	195	1	let	let	VERB
ejpam-5044	195	2	l	l	NOUN
ejpam-5044	195	3	be	be	AUX
ejpam-5044	195	4	a	a	DET
ejpam-5044	195	5	maximum	maximum	ADV
ejpam-5044	195	6	certified	certify	VERB
ejpam-5044	195	7	hop	hop	NOUN
ejpam-5044	195	8	independent	independent	ADJ
ejpam-5044	195	9	set	set	NOUN
ejpam-5044	195	10	of	of	ADP
ejpam-5044	195	11	g+h	g+h	PROPN
ejpam-5044	195	12	.	.	PUNCT
ejpam-5044	196	1	then	then	ADV
ejpam-5044	196	2	by	by	SCONJ
ejpam-5044	196	3	theoorem	theoorem	VERB
ejpam-5044	196	4	6	6	NUM
ejpam-5044	196	5	,	,	PUNCT
ejpam-5044	196	6	l	l	NOUN
ejpam-5044	196	7	=	=	PUNCT
ejpam-5044	196	8	lg	lg	NOUN
ejpam-5044	196	9	∪	∪	PROPN
ejpam-5044	196	10	lh	lh	PROPN
ejpam-5044	196	11	,	,	PUNCT
ejpam-5044	196	12	where	where	SCONJ
ejpam-5044	196	13	lg	lg	NOUN
ejpam-5044	196	14	and	and	CCONJ
ejpam-5044	196	15	lh	lh	PROPN
ejpam-5044	196	16	are	be	AUX
ejpam-5044	196	17	cliques	clique	NOUN
ejpam-5044	196	18	in	in	ADP
ejpam-5044	196	19	g	g	PROPN
ejpam-5044	196	20	and	and	CCONJ
ejpam-5044	196	21	h	h	NOUN
ejpam-5044	196	22	,	,	PUNCT
ejpam-5044	196	23	respectively	respectively	ADV
ejpam-5044	196	24	.	.	PUNCT
ejpam-5044	197	1	it	it	PRON
ejpam-5044	197	2	follows	follow	VERB
ejpam-5044	197	3	that	that	SCONJ
ejpam-5044	197	4	|lg|	|lg|	VERB
ejpam-5044	197	5	≤	≤	ADJ
ejpam-5044	197	6	ω(g	ω(g	NOUN
ejpam-5044	197	7	)	)	PUNCT
ejpam-5044	197	8	and	and	CCONJ
ejpam-5044	197	9	|lh	|lh	DET
ejpam-5044	197	10	|	|	ADV
ejpam-5044	197	11	≤	≤	NUM
ejpam-5044	197	12	ω(h	ω(h	NUM
ejpam-5044	197	13	)	)	PUNCT
ejpam-5044	197	14	.	.	PUNCT
ejpam-5044	198	1	hence	hence	ADV
ejpam-5044	198	2	,	,	PUNCT
ejpam-5044	198	3	αch(g+h	αch(g+h	ADJ
ejpam-5044	198	4	)	)	PUNCT
ejpam-5044	198	5	=	=	PUNCT
ejpam-5044	199	1	|l|	|l|	NOUN
ejpam-5044	199	2	=	=	SYM
ejpam-5044	199	3	|lg|+	|lg|+	PROPN
ejpam-5044	199	4	|lh	|lh	DET
ejpam-5044	199	5	|	|	ADV
ejpam-5044	199	6	≤	≤	NUM
ejpam-5044	199	7	ω(g	ω(g	NOUN
ejpam-5044	199	8	)	)	PUNCT
ejpam-5044	199	9	+	+	NUM
ejpam-5044	199	10	ω(h	ω(h	NUM
ejpam-5044	199	11	)	)	PUNCT
ejpam-5044	199	12	.	.	PUNCT
ejpam-5044	200	1	on	on	ADP
ejpam-5044	200	2	the	the	DET
ejpam-5044	200	3	other	other	ADJ
ejpam-5044	200	4	hand	hand	NOUN
ejpam-5044	200	5	,	,	PUNCT
ejpam-5044	200	6	suppose	suppose	VERB
ejpam-5044	200	7	that	that	SCONJ
ejpam-5044	200	8	l	l	NOUN
ejpam-5044	200	9	=	=	PUNCT
ejpam-5044	200	10	lg	lg	NOUN
ejpam-5044	200	11	∪	∪	PROPN
ejpam-5044	200	12	lh	lh	PROPN
ejpam-5044	200	13	,	,	PUNCT
ejpam-5044	200	14	where	where	SCONJ
ejpam-5044	200	15	lg	lg	NOUN
ejpam-5044	200	16	and	and	CCONJ
ejpam-5044	200	17	lh	lh	PROPN
ejpam-5044	200	18	are	be	AUX
ejpam-5044	200	19	maximum	maximum	ADJ
ejpam-5044	200	20	cliques	clique	NOUN
ejpam-5044	200	21	in	in	ADP
ejpam-5044	200	22	g	g	PROPN
ejpam-5044	200	23	and	and	CCONJ
ejpam-5044	200	24	h	h	NOUN
ejpam-5044	200	25	,	,	PUNCT
ejpam-5044	200	26	respectively	respectively	ADV
ejpam-5044	200	27	.	.	PUNCT
ejpam-5044	201	1	then	then	ADV
ejpam-5044	201	2	by	by	ADP
ejpam-5044	201	3	theorem	theorem	NOUN
ejpam-5044	201	4	6	6	NUM
ejpam-5044	201	5	,	,	PUNCT
ejpam-5044	201	6	l	l	NOUN
ejpam-5044	201	7	is	be	AUX
ejpam-5044	201	8	a	a	DET
ejpam-5044	201	9	certified	certified	ADJ
ejpam-5044	201	10	hop	hop	NOUN
ejpam-5044	201	11	independent	independent	ADJ
ejpam-5044	201	12	set	set	NOUN
ejpam-5044	201	13	of	of	ADP
ejpam-5044	201	14	g+h	g+h	PROPN
ejpam-5044	201	15	.	.	PUNCT
ejpam-5044	202	1	thus	thus	ADV
ejpam-5044	202	2	,	,	PUNCT
ejpam-5044	202	3	αch(g+h	αch(g+h	ADJ
ejpam-5044	202	4	)	)	PUNCT
ejpam-5044	202	5	≥	≥	NOUN
ejpam-5044	202	6	|l|	|l|	NOUN
ejpam-5044	202	7	=	=	SYM
ejpam-5044	202	8	ω(g	ω(g	NOUN
ejpam-5044	202	9	)	)	PUNCT
ejpam-5044	202	10	+	+	NUM
ejpam-5044	202	11	ω(h	ω(h	NUM
ejpam-5044	202	12	)	)	PUNCT
ejpam-5044	202	13	.	.	PUNCT
ejpam-5044	203	1	consequently	consequently	ADV
ejpam-5044	203	2	,	,	PUNCT
ejpam-5044	203	3	αch(g+h	αch(g+h	ADJ
ejpam-5044	203	4	)	)	PUNCT
ejpam-5044	203	5	=	=	SYM
ejpam-5044	203	6	ω(g	ω(g	NOUN
ejpam-5044	203	7	)	)	PUNCT
ejpam-5044	203	8	+	+	NUM
ejpam-5044	203	9	ω(h	ω(h	NUM
ejpam-5044	203	10	)	)	PUNCT
ejpam-5044	203	11	.	.	PUNCT
ejpam-5044	204	1	4	4	X
ejpam-5044	204	2	.	.	X
ejpam-5044	204	3	conclusion	conclusion	VERB
ejpam-5044	204	4	the	the	DET
ejpam-5044	204	5	concept	concept	NOUN
ejpam-5044	204	6	of	of	ADP
ejpam-5044	204	7	certified	certify	VERB
ejpam-5044	204	8	hop	hop	NOUN
ejpam-5044	204	9	independence	independence	NOUN
ejpam-5044	204	10	in	in	ADP
ejpam-5044	204	11	graphs	graph	NOUN
ejpam-5044	204	12	has	have	AUX
ejpam-5044	204	13	been	be	AUX
ejpam-5044	204	14	introduced	introduce	VERB
ejpam-5044	204	15	and	and	CCONJ
ejpam-5044	204	16	investigated	investigate	VERB
ejpam-5044	204	17	in	in	ADP
ejpam-5044	204	18	this	this	DET
ejpam-5044	204	19	study	study	NOUN
ejpam-5044	204	20	.	.	PUNCT
ejpam-5044	205	1	its	its	PRON
ejpam-5044	205	2	relationship	relationship	NOUN
ejpam-5044	205	3	with	with	ADP
ejpam-5044	205	4	hop	hop	PROPN
ejpam-5044	205	5	independence	independence	NOUN
ejpam-5044	205	6	parameter	parameter	NOUN
ejpam-5044	205	7	has	have	AUX
ejpam-5044	205	8	been	be	AUX
ejpam-5044	205	9	presented	present	VERB
ejpam-5044	205	10	.	.	PUNCT
ejpam-5044	206	1	some	some	DET
ejpam-5044	206	2	bounds	bound	VERB
ejpam-5044	206	3	with	with	ADP
ejpam-5044	206	4	respect	respect	NOUN
ejpam-5044	206	5	to	to	ADP
ejpam-5044	206	6	the	the	DET
ejpam-5044	206	7	order	order	NOUN
ejpam-5044	206	8	of	of	ADP
ejpam-5044	206	9	a	a	DET
ejpam-5044	206	10	graph	graph	NOUN
ejpam-5044	206	11	and	and	CCONJ
ejpam-5044	206	12	exact	exact	ADJ
ejpam-5044	206	13	values	value	NOUN
ejpam-5044	206	14	of	of	ADP
ejpam-5044	206	15	parameters	parameter	NOUN
ejpam-5044	206	16	of	of	ADP
ejpam-5044	206	17	some	some	DET
ejpam-5044	206	18	special	special	ADJ
ejpam-5044	206	19	graphs	graph	NOUN
ejpam-5044	206	20	have	have	AUX
ejpam-5044	206	21	been	be	AUX
ejpam-5044	206	22	determined	determine	VERB
ejpam-5044	206	23	.	.	PUNCT
ejpam-5044	207	1	moreover	moreover	ADV
ejpam-5044	207	2	,	,	PUNCT
ejpam-5044	207	3	characterizations	characterization	NOUN
ejpam-5044	207	4	of	of	ADP
ejpam-5044	207	5	certified	certify	VERB
ejpam-5044	207	6	hop	hop	NOUN
ejpam-5044	207	7	independent	independent	ADJ
ejpam-5044	207	8	sets	set	NOUN
ejpam-5044	207	9	in	in	ADP
ejpam-5044	207	10	some	some	DET
ejpam-5044	207	11	graphs	graph	NOUN
ejpam-5044	207	12	have	have	AUX
ejpam-5044	207	13	been	be	AUX
ejpam-5044	207	14	used	use	VERB
ejpam-5044	207	15	to	to	PART
ejpam-5044	207	16	determine	determine	VERB
ejpam-5044	207	17	the	the	DET
ejpam-5044	207	18	exact	exact	ADJ
ejpam-5044	207	19	values	value	NOUN
ejpam-5044	207	20	of	of	ADP
ejpam-5044	207	21	parameters	parameter	NOUN
ejpam-5044	207	22	of	of	ADP
ejpam-5044	207	23	some	some	DET
ejpam-5044	207	24	graphs	graph	NOUN
ejpam-5044	207	25	.	.	PUNCT
ejpam-5044	208	1	some	some	DET
ejpam-5044	208	2	graphs	graph	NOUN
ejpam-5044	208	3	that	that	PRON
ejpam-5044	208	4	were	be	AUX
ejpam-5044	208	5	not	not	PART
ejpam-5044	208	6	considered	consider	VERB
ejpam-5044	208	7	in	in	ADP
ejpam-5044	208	8	this	this	DET
ejpam-5044	208	9	study	study	NOUN
ejpam-5044	208	10	could	could	AUX
ejpam-5044	208	11	be	be	AUX
ejpam-5044	208	12	an	an	DET
ejpam-5044	208	13	interesting	interesting	ADJ
ejpam-5044	208	14	topic	topic	NOUN
ejpam-5044	208	15	to	to	PART
ejpam-5044	208	16	consider	consider	VERB
ejpam-5044	208	17	for	for	ADP
ejpam-5044	208	18	further	further	ADJ
ejpam-5044	208	19	investigation	investigation	NOUN
ejpam-5044	208	20	of	of	ADP
ejpam-5044	208	21	the	the	DET
ejpam-5044	208	22	concept	concept	NOUN
ejpam-5044	208	23	.	.	PUNCT
ejpam-5044	209	1	in	in	ADP
ejpam-5044	209	2	addition	addition	NOUN
ejpam-5044	209	3	,	,	PUNCT
ejpam-5044	209	4	researchers	researcher	NOUN
ejpam-5044	209	5	may	may	AUX
ejpam-5044	209	6	consider	consider	VERB
ejpam-5044	209	7	the	the	DET
ejpam-5044	209	8	complexity	complexity	NOUN
ejpam-5044	209	9	,	,	PUNCT
ejpam-5044	209	10	algorithm	algorithm	NOUN
ejpam-5044	209	11	,	,	PUNCT
ejpam-5044	209	12	and	and	CCONJ
ejpam-5044	209	13	real	real	ADJ
ejpam-5044	209	14	life	life	NOUN
ejpam-5044	209	15	application	application	NOUN
ejpam-5044	209	16	of	of	ADP
ejpam-5044	209	17	the	the	DET
ejpam-5044	209	18	concept	concept	NOUN
ejpam-5044	209	19	.	.	PUNCT
ejpam-5044	210	1	acknowledgements	acknowledgement	NOUN
ejpam-5044	210	2	the	the	DET
ejpam-5044	210	3	authors	author	NOUN
ejpam-5044	210	4	would	would	AUX
ejpam-5044	210	5	like	like	VERB
ejpam-5044	210	6	to	to	PART
ejpam-5044	210	7	thank	thank	VERB
ejpam-5044	210	8	mindanao	mindanao	PROPN
ejpam-5044	210	9	state	state	PROPN
ejpam-5044	210	10	university	university	PROPN
ejpam-5044	210	11	tawi	tawi	PROPN
ejpam-5044	210	12	-	-	PUNCT
ejpam-5044	210	13	tawi	tawi	PROPN
ejpam-5044	210	14	college	college	PROPN
ejpam-5044	210	15	of	of	ADP
ejpam-5044	210	16	technology	technology	NOUN
ejpam-5044	210	17	and	and	CCONJ
ejpam-5044	210	18	oceanography	oceanography	NOUN
ejpam-5044	210	19	for	for	ADP
ejpam-5044	210	20	funding	fund	VERB
ejpam-5044	210	21	this	this	DET
ejpam-5044	210	22	research	research	NOUN
ejpam-5044	210	23	.	.	PUNCT
ejpam-5044	211	1	references	reference	NOUN
ejpam-5044	211	2	[	[	X
ejpam-5044	211	3	1	1	X
ejpam-5044	211	4	]	]	PUNCT
ejpam-5044	211	5	j.	j.	PROPN
ejpam-5044	211	6	hassan	hassan	PROPN
ejpam-5044	211	7	and	and	CCONJ
ejpam-5044	211	8	s.	s.	PROPN
ejpam-5044	211	9	canoy	canoy	PROPN
ejpam-5044	211	10	jr	jr	PROPN
ejpam-5044	211	11	.	.	PROPN
ejpam-5044	211	12	hop	hop	PROPN
ejpam-5044	211	13	independent	independent	ADJ
ejpam-5044	211	14	hop	hop	NOUN
ejpam-5044	211	15	domination	domination	NOUN
ejpam-5044	211	16	in	in	ADP
ejpam-5044	211	17	graphs	graph	NOUN
ejpam-5044	211	18	.	.	PUNCT
ejpam-5044	212	1	eur	eur	PROPN
ejpam-5044	212	2	.	.	PUNCT
ejpam-5044	213	1	j.	j.	PROPN
ejpam-5044	213	2	pure	pure	PROPN
ejpam-5044	213	3	appl	appl	PROPN
ejpam-5044	213	4	.	.	PUNCT
ejpam-5044	213	5	math	math	PROPN
ejpam-5044	213	6	.	.	PUNCT
ejpam-5044	213	7	,	,	PUNCT
ejpam-5044	213	8	15(2):1783–1796	15(2):1783–1796	NUM
ejpam-5044	213	9	,	,	PUNCT
ejpam-5044	213	10	2022	2022	NUM
ejpam-5044	213	11	.	.	PUNCT
ejpam-5044	214	1	[	[	X
ejpam-5044	214	2	2	2	X
ejpam-5044	214	3	]	]	PUNCT
ejpam-5044	214	4	j.	j.	PROPN
ejpam-5044	214	5	hassan	hassan	PROPN
ejpam-5044	214	6	,	,	PUNCT
ejpam-5044	214	7	s.	s.	PROPN
ejpam-5044	214	8	canoy	canoy	PROPN
ejpam-5044	214	9	jr	jr	PROPN
ejpam-5044	214	10	.	.	PROPN
ejpam-5044	214	11	,	,	PUNCT
ejpam-5044	214	12	and	and	CCONJ
ejpam-5044	214	13	a.	a.	PROPN
ejpam-5044	214	14	aradais	aradais	PROPN
ejpam-5044	214	15	.	.	PUNCT
ejpam-5044	215	1	hop	hop	PROPN
ejpam-5044	215	2	independent	independent	ADJ
ejpam-5044	215	3	sets	set	NOUN
ejpam-5044	215	4	in	in	ADP
ejpam-5044	215	5	graphs	graph	NOUN
ejpam-5044	215	6	.	.	PUNCT
ejpam-5044	216	1	eur	eur	PROPN
ejpam-5044	216	2	.	.	PUNCT
ejpam-5044	217	1	j.	j.	PROPN
ejpam-5044	217	2	pure	pure	PROPN
ejpam-5044	217	3	appl	appl	PROPN
ejpam-5044	217	4	.	.	PUNCT
ejpam-5044	217	5	math	math	PROPN
ejpam-5044	217	6	.	.	PUNCT
ejpam-5044	217	7	,	,	PUNCT
ejpam-5044	217	8	15(2):467–477	15(2):467–477	PROPN
ejpam-5044	217	9	,	,	PUNCT
ejpam-5044	217	10	2022	2022	NUM
ejpam-5044	217	11	.	.	PUNCT
ejpam-5044	218	1	references	reference	NOUN
ejpam-5044	218	2	444	444	NUM
ejpam-5044	218	3	[	[	X
ejpam-5044	218	4	3	3	NUM
ejpam-5044	218	5	]	]	PUNCT
ejpam-5044	218	6	j.	j.	PROPN
ejpam-5044	218	7	hassan	hassan	PROPN
ejpam-5044	218	8	,	,	PUNCT
ejpam-5044	218	9	a.	a.	PROPN
ejpam-5044	218	10	lintasan	lintasan	PROPN
ejpam-5044	218	11	,	,	PUNCT
ejpam-5044	218	12	and	and	CCONJ
ejpam-5044	218	13	n.h	n.h	PROPN
ejpam-5044	218	14	.	.	PUNCT
ejpam-5044	219	1	mohammad	mohammad	PROPN
ejpam-5044	219	2	.	.	PUNCT
ejpam-5044	220	1	some	some	DET
ejpam-5044	220	2	properties	property	NOUN
ejpam-5044	220	3	and	and	CCONJ
ejpam-5044	220	4	realization	realization	NOUN
ejpam-5044	220	5	problems	problem	NOUN
ejpam-5044	220	6	involving	involve	VERB
ejpam-5044	220	7	connected	connected	ADJ
ejpam-5044	220	8	outer	outer	ADJ
ejpam-5044	220	9	-	-	PUNCT
ejpam-5044	220	10	hop	hop	NOUN
ejpam-5044	220	11	independent	independent	ADJ
ejpam-5044	220	12	hop	hop	NOUN
ejpam-5044	220	13	domination	domination	NOUN
ejpam-5044	220	14	in	in	ADP
ejpam-5044	220	15	graphs	graph	NOUN
ejpam-5044	220	16	.	.	PUNCT
ejpam-5044	221	1	eur	eur	PROPN
ejpam-5044	221	2	.	.	PUNCT
ejpam-5044	222	1	j.	j.	PROPN
ejpam-5044	222	2	pure	pure	PROPN
ejpam-5044	222	3	appl	appl	PROPN
ejpam-5044	222	4	.	.	PUNCT
ejpam-5044	222	5	math	math	PROPN
ejpam-5044	222	6	.	.	PUNCT
ejpam-5044	222	7	,	,	PUNCT
ejpam-5044	222	8	16(3):1848–1861	16(3):1848–1861	NUM
ejpam-5044	222	9	,	,	PUNCT
ejpam-5044	222	10	2023	2023	NUM
ejpam-5044	222	11	.	.	PUNCT
ejpam-5044	223	1	[	[	X
ejpam-5044	223	2	4	4	X
ejpam-5044	223	3	]	]	PUNCT
ejpam-5044	223	4	j.	j.	PROPN
ejpam-5044	223	5	manditong	manditong	PROPN
ejpam-5044	223	6	,	,	PUNCT
ejpam-5044	223	7	j.	j.	PROPN
ejpam-5044	223	8	hassan	hassan	PROPN
ejpam-5044	223	9	,	,	PUNCT
ejpam-5044	223	10	ls	ls	PROPN
ejpam-5044	223	11	laja	laja	PROPN
ejpam-5044	223	12	,	,	PUNCT
ejpam-5044	223	13	aa	aa	INTJ
ejpam-5044	223	14	.	.	PUNCT
ejpam-5044	223	15	laja	laja	PROPN
ejpam-5044	223	16	,	,	PUNCT
ejpam-5044	223	17	nhm	nhm	PROPN
ejpam-5044	223	18	.	.	PUNCT
ejpam-5044	223	19	mohammad	mohammad	PROPN
ejpam-5044	223	20	,	,	PUNCT
ejpam-5044	223	21	and	and	CCONJ
ejpam-5044	223	22	su	su	PROPN
ejpam-5044	223	23	.	.	PROPN
ejpam-5044	223	24	kamdon	kamdon	PROPN
ejpam-5044	223	25	.	.	PROPN
ejpam-5044	224	1	conneted	connete	VERB
ejpam-5044	224	2	outer	outer	ADJ
ejpam-5044	224	3	-	-	PUNCT
ejpam-5044	224	4	hop	hop	NOUN
ejpam-5044	224	5	independent	independent	ADJ
ejpam-5044	224	6	dominating	dominating	NOUN
ejpam-5044	224	7	sets	set	NOUN
ejpam-5044	224	8	in	in	ADP
ejpam-5044	224	9	graphs	graph	NOUN
ejpam-5044	224	10	under	under	ADP
ejpam-5044	224	11	some	some	DET
ejpam-5044	224	12	binary	binary	ADJ
ejpam-5044	224	13	operations	operation	NOUN
ejpam-5044	224	14	.	.	PUNCT
ejpam-5044	225	1	eur	eur	PROPN
ejpam-5044	225	2	.	.	PUNCT
ejpam-5044	226	1	j.	j.	PROPN
ejpam-5044	226	2	pure	pure	PROPN
ejpam-5044	226	3	appl	appl	PROPN
ejpam-5044	226	4	.	.	PUNCT
ejpam-5044	226	5	math	math	PROPN
ejpam-5044	226	6	.	.	PUNCT
ejpam-5044	226	7	,	,	PUNCT
ejpam-5044	227	1	16(3):1817–1829	16(3):1817–1829	NUM
ejpam-5044	227	2	,	,	PUNCT
ejpam-5044	227	3	2023	2023	NUM
ejpam-5044	227	4	.	.	PUNCT