id	sid	tid	token	lemma	pos
ejpam-6383	1	1	european	european	PROPN
ejpam-6383	1	2	journal	journal	PROPN
ejpam-6383	1	3	of	of	ADP
ejpam-6383	1	4	pure	pure	ADJ
ejpam-6383	1	5	and	and	CCONJ
ejpam-6383	1	6	applied	applied	ADJ
ejpam-6383	1	7	mathematics	mathematic	NOUN
ejpam-6383	1	8	2025	2025	NUM
ejpam-6383	1	9	,	,	PUNCT
ejpam-6383	1	10	vol	vol	NOUN
ejpam-6383	1	11	.	.	PROPN
ejpam-6383	1	12	18	18	NUM
ejpam-6383	1	13	,	,	PUNCT
ejpam-6383	1	14	issue	issue	NOUN
ejpam-6383	1	15	3	3	NUM
ejpam-6383	1	16	,	,	PUNCT
ejpam-6383	1	17	article	article	NOUN
ejpam-6383	1	18	number	number	NOUN
ejpam-6383	1	19	6383	6383	NUM
ejpam-6383	1	20	issn	issn	VERB
ejpam-6383	1	21	1307	1307	NUM
ejpam-6383	1	22	-	-	SYM
ejpam-6383	1	23	5543	5543	NUM
ejpam-6383	1	24	–	–	PUNCT
ejpam-6383	1	25	ejpam.com	ejpam.com	X
ejpam-6383	1	26	published	publish	VERB
ejpam-6383	1	27	by	by	ADP
ejpam-6383	1	28	new	new	PROPN
ejpam-6383	1	29	york	york	PROPN
ejpam-6383	1	30	business	business	PROPN
ejpam-6383	1	31	global	global	PROPN
ejpam-6383	1	32	l	l	PROPN
ejpam-6383	1	33	-	-	ADJ
ejpam-6383	1	34	hop	hop	ADJ
ejpam-6383	1	35	independent	independent	ADJ
ejpam-6383	1	36	sequences	sequence	NOUN
ejpam-6383	1	37	in	in	ADP
ejpam-6383	1	38	graphs	graph	NOUN
ejpam-6383	1	39	kaimar	kaimar	PROPN
ejpam-6383	1	40	jay	jay	PROPN
ejpam-6383	1	41	s.	s.	PROPN
ejpam-6383	1	42	maharajul1	maharajul1	PROPN
ejpam-6383	1	43	,	,	PUNCT
ejpam-6383	1	44	javier	javier	PROPN
ejpam-6383	1	45	a.	a.	PROPN
ejpam-6383	1	46	hassan1,2,∗	hassan1,2,∗	PROPN
ejpam-6383	1	47	,	,	PUNCT
ejpam-6383	1	48	ladznar	ladznar	ADJ
ejpam-6383	1	49	s.	s.	PROPN
ejpam-6383	1	50	laja1	laja1	PUNCT
ejpam-6383	2	1	1department	1department	NUM
ejpam-6383	2	2	of	of	ADP
ejpam-6383	2	3	mathematics	mathematic	NOUN
ejpam-6383	2	4	,	,	PUNCT
ejpam-6383	2	5	college	college	NOUN
ejpam-6383	2	6	of	of	ADP
ejpam-6383	2	7	arts	art	NOUN
ejpam-6383	2	8	and	and	CCONJ
ejpam-6383	2	9	sciences	science	NOUN
ejpam-6383	2	10	,	,	PUNCT
ejpam-6383	2	11	msu	msu	PROPN
ejpam-6383	2	12	-	-	PUNCT
ejpam-6383	2	13	tawi	tawi	NOUN
ejpam-6383	2	14	-	-	PUNCT
ejpam-6383	2	15	tawi	tawi	NOUN
ejpam-6383	2	16	college	college	PROPN
ejpam-6383	2	17	of	of	ADP
ejpam-6383	2	18	technology	technology	NOUN
ejpam-6383	2	19	and	and	CCONJ
ejpam-6383	2	20	oceanography	oceanography	NOUN
ejpam-6383	2	21	,	,	PUNCT
ejpam-6383	2	22	bongao	bongao	NOUN
ejpam-6383	2	23	,	,	PUNCT
ejpam-6383	2	24	tawi	tawi	NOUN
ejpam-6383	2	25	-	-	PUNCT
ejpam-6383	2	26	tawi	tawi	NOUN
ejpam-6383	2	27	,	,	PUNCT
ejpam-6383	2	28	philippines	philippine	NOUN
ejpam-6383	2	29	2department	2department	NUM
ejpam-6383	2	30	of	of	ADP
ejpam-6383	2	31	mathematics	mathematic	NOUN
ejpam-6383	2	32	,	,	PUNCT
ejpam-6383	2	33	college	college	NOUN
ejpam-6383	2	34	of	of	ADP
ejpam-6383	2	35	science	science	PROPN
ejpam-6383	2	36	,	,	PUNCT
ejpam-6383	2	37	korea	korea	PROPN
ejpam-6383	2	38	university	university	PROPN
ejpam-6383	2	39	,	,	PUNCT
ejpam-6383	2	40	seoul	seoul	PROPN
ejpam-6383	2	41	,	,	PUNCT
ejpam-6383	2	42	south	south	PROPN
ejpam-6383	2	43	korea	korea	PROPN
ejpam-6383	2	44	abstract	abstract	NOUN
ejpam-6383	2	45	.	.	PUNCT
ejpam-6383	3	1	let	let	VERB
ejpam-6383	3	2	g	g	PRON
ejpam-6383	3	3	be	be	AUX
ejpam-6383	3	4	a	a	DET
ejpam-6383	3	5	graph	graph	NOUN
ejpam-6383	3	6	.	.	PUNCT
ejpam-6383	4	1	a	a	DET
ejpam-6383	4	2	sequence	sequence	NOUN
ejpam-6383	4	3	of	of	ADP
ejpam-6383	4	4	distinct	distinct	ADJ
ejpam-6383	4	5	vertices	vertex	NOUN
ejpam-6383	4	6	q	q	NOUN
ejpam-6383	4	7	=	=	PUNCT
ejpam-6383	4	8	(	(	PUNCT
ejpam-6383	4	9	a1	a1	PROPN
ejpam-6383	4	10	,	,	PUNCT
ejpam-6383	4	11	a2	a2	PROPN
ejpam-6383	4	12	,	,	PUNCT
ejpam-6383	4	13	.	.	PUNCT
ejpam-6383	4	14	.	.	PUNCT
ejpam-6383	5	1	.	.	PUNCT
ejpam-6383	6	1	,	,	PUNCT
ejpam-6383	6	2	an	an	X
ejpam-6383	6	3	)	)	PUNCT
ejpam-6383	6	4	of	of	ADP
ejpam-6383	6	5	g	g	PROPN
ejpam-6383	6	6	is	be	AUX
ejpam-6383	6	7	called	call	VERB
ejpam-6383	6	8	an	an	DET
ejpam-6383	6	9	l	l	NOUN
ejpam-6383	6	10	-	-	ADJ
ejpam-6383	6	11	hop	hop	ADJ
ejpam-6383	6	12	independent	independent	ADJ
ejpam-6383	6	13	sequence	sequence	NOUN
ejpam-6383	6	14	if	if	SCONJ
ejpam-6383	6	15	n	n	NOUN
ejpam-6383	6	16	=	=	SYM
ejpam-6383	6	17	1	1	NUM
ejpam-6383	6	18	or	or	CCONJ
ejpam-6383	6	19	if	if	SCONJ
ejpam-6383	6	20	dg(ai	dg(ai	PROPN
ejpam-6383	6	21	,	,	PUNCT
ejpam-6383	6	22	aj	aj	PROPN
ejpam-6383	6	23	)	)	PUNCT
ejpam-6383	6	24	̸=	̸=	PROPN
ejpam-6383	6	25	2	2	NUM
ejpam-6383	6	26	for	for	ADP
ejpam-6383	6	27	each	each	DET
ejpam-6383	6	28	i	i	PRON
ejpam-6383	6	29	̸=	̸=	PROPN
ejpam-6383	6	30	j	j	PROPN
ejpam-6383	6	31	,	,	PUNCT
ejpam-6383	6	32	where	where	SCONJ
ejpam-6383	6	33	i	i	PRON
ejpam-6383	6	34	,	,	PUNCT
ejpam-6383	6	35	j	j	PROPN
ejpam-6383	6	36	∈	∈	PROPN
ejpam-6383	6	37	{	{	PUNCT
ejpam-6383	6	38	1	1	NUM
ejpam-6383	6	39	,	,	PUNCT
ejpam-6383	6	40	2	2	NUM
ejpam-6383	6	41	,	,	PUNCT
ejpam-6383	6	42	.	.	PUNCT
ejpam-6383	6	43	.	.	PUNCT
ejpam-6383	7	1	.	.	PUNCT
ejpam-6383	7	2	,	,	PUNCT
ejpam-6383	8	1	n	n	CCONJ
ejpam-6383	8	2	}	}	PUNCT
ejpam-6383	8	3	and	and	CCONJ
ejpam-6383	8	4	ng[as]\	ng[as]\	PRON
ejpam-6383	8	5	s−1⋃	s−1⋃	PROPN
ejpam-6383	8	6	t=1	t=1	PROPN
ejpam-6383	8	7	ng(at	ng(at	PROPN
ejpam-6383	8	8	)	)	PUNCT
ejpam-6383	8	9	̸=	̸=	PROPN
ejpam-6383	8	10	∅	∅	NOUN
ejpam-6383	8	11	for	for	ADP
ejpam-6383	8	12	each	each	DET
ejpam-6383	8	13	s	s	X
ejpam-6383	8	14	∈	∈	PROPN
ejpam-6383	8	15	{	{	PUNCT
ejpam-6383	8	16	2	2	NUM
ejpam-6383	8	17	,	,	PUNCT
ejpam-6383	8	18	.	.	PUNCT
ejpam-6383	8	19	.	.	PUNCT
ejpam-6383	9	1	.	.	PUNCT
ejpam-6383	9	2	,	,	PUNCT
ejpam-6383	9	3	n	n	CCONJ
ejpam-6383	9	4	}	}	PUNCT
ejpam-6383	9	5	.	.	PUNCT
ejpam-6383	10	1	the	the	DET
ejpam-6383	10	2	l	l	ADJ
ejpam-6383	10	3	-	-	ADJ
ejpam-6383	10	4	hop	hop	ADJ
ejpam-6383	10	5	independence	independence	NOUN
ejpam-6383	10	6	number	number	NOUN
ejpam-6383	10	7	of	of	ADP
ejpam-6383	10	8	g	g	NOUN
ejpam-6383	10	9	,	,	PUNCT
ejpam-6383	10	10	denoted	denote	VERB
ejpam-6383	10	11	by	by	ADP
ejpam-6383	10	12	αlh(g	αlh(g	NOUN
ejpam-6383	10	13	)	)	PUNCT
ejpam-6383	10	14	,	,	PUNCT
ejpam-6383	10	15	is	be	AUX
ejpam-6383	10	16	the	the	DET
ejpam-6383	10	17	maximum	maximum	ADJ
ejpam-6383	10	18	length	length	NOUN
ejpam-6383	10	19	among	among	ADP
ejpam-6383	10	20	all	all	DET
ejpam-6383	10	21	l	l	ADJ
ejpam-6383	10	22	-	-	ADJ
ejpam-6383	10	23	hop	hop	ADJ
ejpam-6383	10	24	independent	independent	ADJ
ejpam-6383	10	25	sequences	sequence	NOUN
ejpam-6383	10	26	in	in	ADP
ejpam-6383	10	27	g.	g.	PROPN
ejpam-6383	10	28	this	this	DET
ejpam-6383	10	29	study	study	NOUN
ejpam-6383	10	30	explores	explore	NOUN
ejpam-6383	10	31	and	and	CCONJ
ejpam-6383	10	32	characterizes	characterize	VERB
ejpam-6383	10	33	the	the	DET
ejpam-6383	10	34	l	l	ADJ
ejpam-6383	10	35	-	-	ADJ
ejpam-6383	10	36	hop	hop	ADJ
ejpam-6383	10	37	independent	independent	ADJ
ejpam-6383	10	38	sequences	sequence	NOUN
ejpam-6383	10	39	in	in	ADP
ejpam-6383	10	40	some	some	DET
ejpam-6383	10	41	graphs	graph	NOUN
ejpam-6383	10	42	,	,	PUNCT
ejpam-6383	10	43	and	and	CCONJ
ejpam-6383	10	44	in	in	ADP
ejpam-6383	10	45	the	the	DET
ejpam-6383	10	46	join	join	NOUN
ejpam-6383	10	47	of	of	ADP
ejpam-6383	10	48	two	two	NUM
ejpam-6383	10	49	graphs	graph	NOUN
ejpam-6383	10	50	.	.	PUNCT
ejpam-6383	11	1	some	some	DET
ejpam-6383	11	2	formulas	formula	NOUN
ejpam-6383	11	3	and	and	CCONJ
ejpam-6383	11	4	bounds	bound	NOUN
ejpam-6383	11	5	of	of	ADP
ejpam-6383	11	6	l	l	NOUN
ejpam-6383	11	7	-	-	ADJ
ejpam-6383	11	8	hop	hop	ADJ
ejpam-6383	11	9	independence	independence	NOUN
ejpam-6383	11	10	number	number	NOUN
ejpam-6383	11	11	with	with	ADP
ejpam-6383	11	12	respect	respect	NOUN
ejpam-6383	11	13	to	to	ADP
ejpam-6383	11	14	the	the	DET
ejpam-6383	11	15	order	order	NOUN
ejpam-6383	11	16	of	of	ADP
ejpam-6383	11	17	a	a	DET
ejpam-6383	11	18	graph	graph	NOUN
ejpam-6383	11	19	and	and	CCONJ
ejpam-6383	11	20	other	other	ADJ
ejpam-6383	11	21	parameters	parameter	NOUN
ejpam-6383	11	22	in	in	ADP
ejpam-6383	11	23	graph	graph	NOUN
ejpam-6383	11	24	theory	theory	NOUN
ejpam-6383	11	25	are	be	AUX
ejpam-6383	11	26	derived	derive	VERB
ejpam-6383	11	27	.	.	PUNCT
ejpam-6383	12	1	moreover	moreover	ADV
ejpam-6383	12	2	,	,	PUNCT
ejpam-6383	12	3	some	some	DET
ejpam-6383	12	4	relationships	relationship	NOUN
ejpam-6383	12	5	of	of	ADP
ejpam-6383	12	6	l	l	ADJ
ejpam-6383	12	7	-	-	ADJ
ejpam-6383	12	8	hop	hop	ADJ
ejpam-6383	12	9	independence	independence	NOUN
ejpam-6383	12	10	with	with	ADP
ejpam-6383	12	11	hop	hop	NOUN
ejpam-6383	12	12	independence	independence	NOUN
ejpam-6383	12	13	and	and	CCONJ
ejpam-6383	12	14	legal	legal	ADJ
ejpam-6383	12	15	hop	hop	NOUN
ejpam-6383	12	16	independence	independence	NOUN
ejpam-6383	12	17	are	be	AUX
ejpam-6383	12	18	established	establish	VERB
ejpam-6383	12	19	.	.	PUNCT
ejpam-6383	13	1	2020	2020	NUM
ejpam-6383	13	2	mathematics	mathematics	PROPN
ejpam-6383	13	3	subject	subject	NOUN
ejpam-6383	13	4	classifications	classification	NOUN
ejpam-6383	13	5	:	:	PUNCT
ejpam-6383	13	6	05c69	05c69	X
ejpam-6383	13	7	key	key	ADJ
ejpam-6383	13	8	words	word	NOUN
ejpam-6383	13	9	and	and	CCONJ
ejpam-6383	13	10	phrases	phrase	NOUN
ejpam-6383	13	11	:	:	PUNCT
ejpam-6383	14	1	l	l	NOUN
ejpam-6383	14	2	-	-	NOUN
ejpam-6383	14	3	sequence	sequence	NOUN
ejpam-6383	14	4	,	,	PUNCT
ejpam-6383	14	5	clique	clique	NOUN
ejpam-6383	14	6	l	l	NOUN
ejpam-6383	14	7	-	-	NOUN
ejpam-6383	14	8	sequence	sequence	NOUN
ejpam-6383	14	9	,	,	PUNCT
ejpam-6383	14	10	clique	clique	NOUN
ejpam-6383	14	11	l	l	PROPN
ejpam-6383	14	12	-	-	ADJ
ejpam-6383	14	13	grundy	grundy	ADJ
ejpam-6383	14	14	dominating	dominating	NOUN
ejpam-6383	14	15	sequence	sequence	NOUN
ejpam-6383	14	16	,	,	PUNCT
ejpam-6383	14	17	l	l	NOUN
ejpam-6383	14	18	-	-	ADJ
ejpam-6383	14	19	hop	hop	ADJ
ejpam-6383	14	20	independent	independent	ADJ
ejpam-6383	14	21	sequence	sequence	NOUN
ejpam-6383	14	22	,	,	PUNCT
ejpam-6383	14	23	l	l	NOUN
ejpam-6383	14	24	-	-	NOUN
ejpam-6383	14	25	independence	independence	NOUN
ejpam-6383	14	26	number	number	NOUN
ejpam-6383	14	27	1	1	NUM
ejpam-6383	14	28	.	.	PUNCT
ejpam-6383	14	29	introduction	introduction	NOUN
ejpam-6383	14	30	graph	graph	NOUN
ejpam-6383	14	31	theory	theory	NOUN
ejpam-6383	14	32	is	be	AUX
ejpam-6383	14	33	relatively	relatively	ADV
ejpam-6383	14	34	new	new	ADJ
ejpam-6383	14	35	area	area	NOUN
ejpam-6383	14	36	of	of	ADP
ejpam-6383	14	37	mathematics	mathematic	NOUN
ejpam-6383	14	38	,	,	PUNCT
ejpam-6383	14	39	first	first	ADV
ejpam-6383	14	40	studied	study	VERB
ejpam-6383	14	41	by	by	ADP
ejpam-6383	14	42	the	the	DET
ejpam-6383	14	43	super	super	ADV
ejpam-6383	14	44	famous	famous	ADJ
ejpam-6383	14	45	mathematician	mathematician	ADJ
ejpam-6383	14	46	leonhard	leonhard	PROPN
ejpam-6383	14	47	euler	euler	NOUN
ejpam-6383	14	48	in	in	ADP
ejpam-6383	14	49	1735	1735	NUM
ejpam-6383	14	50	.	.	PUNCT
ejpam-6383	15	1	since	since	SCONJ
ejpam-6383	15	2	then	then	ADV
ejpam-6383	15	3	it	it	PRON
ejpam-6383	15	4	has	have	AUX
ejpam-6383	15	5	blossomed	blossom	VERB
ejpam-6383	15	6	into	into	ADP
ejpam-6383	15	7	a	a	DET
ejpam-6383	15	8	powerful	powerful	ADJ
ejpam-6383	15	9	tool	tool	NOUN
ejpam-6383	15	10	used	use	VERB
ejpam-6383	15	11	in	in	ADP
ejpam-6383	15	12	nearly	nearly	ADV
ejpam-6383	15	13	every	every	PRON
ejpam-6383	15	14	branch	branch	NOUN
ejpam-6383	15	15	of	of	ADP
ejpam-6383	15	16	science	science	NOUN
ejpam-6383	15	17	and	and	CCONJ
ejpam-6383	15	18	is	be	AUX
ejpam-6383	15	19	currently	currently	ADV
ejpam-6383	15	20	an	an	DET
ejpam-6383	15	21	active	active	ADJ
ejpam-6383	15	22	area	area	NOUN
ejpam-6383	15	23	of	of	ADP
ejpam-6383	15	24	mathematics	mathematics	PROPN
ejpam-6383	15	25	research	research	NOUN
ejpam-6383	15	26	.	.	PUNCT
ejpam-6383	16	1	one	one	NUM
ejpam-6383	16	2	of	of	ADP
ejpam-6383	16	3	the	the	DET
ejpam-6383	16	4	hottest	hot	ADJ
ejpam-6383	16	5	topics	topic	NOUN
ejpam-6383	16	6	in	in	ADP
ejpam-6383	16	7	graph	graph	NOUN
ejpam-6383	16	8	theory	theory	NOUN
ejpam-6383	16	9	is	be	AUX
ejpam-6383	16	10	the	the	DET
ejpam-6383	16	11	concept	concept	NOUN
ejpam-6383	16	12	of	of	ADP
ejpam-6383	16	13	independent	independent	ADJ
ejpam-6383	16	14	sets	set	NOUN
ejpam-6383	16	15	in	in	ADP
ejpam-6383	16	16	graphs	graph	NOUN
ejpam-6383	16	17	.	.	PUNCT
ejpam-6383	17	1	a	a	DET
ejpam-6383	17	2	set	set	NOUN
ejpam-6383	17	3	s	s	NOUN
ejpam-6383	17	4	⊆	⊆	NUM
ejpam-6383	17	5	v	v	NOUN
ejpam-6383	17	6	(	(	PUNCT
ejpam-6383	17	7	g	g	NOUN
ejpam-6383	17	8	)	)	PUNCT
ejpam-6383	17	9	is	be	AUX
ejpam-6383	17	10	called	call	VERB
ejpam-6383	17	11	an	an	DET
ejpam-6383	17	12	independent	independent	ADJ
ejpam-6383	17	13	set	set	NOUN
ejpam-6383	17	14	of	of	ADP
ejpam-6383	17	15	g	g	PROPN
ejpam-6383	17	16	if	if	SCONJ
ejpam-6383	17	17	no	no	DET
ejpam-6383	17	18	two	two	NUM
ejpam-6383	17	19	pair	pair	NOUN
ejpam-6383	17	20	of	of	ADP
ejpam-6383	17	21	distinct	distinct	ADJ
ejpam-6383	17	22	vertices	vertex	NOUN
ejpam-6383	17	23	of	of	ADP
ejpam-6383	17	24	s	s	NOUN
ejpam-6383	17	25	are	be	AUX
ejpam-6383	17	26	adjacent	adjacent	ADJ
ejpam-6383	17	27	.	.	PUNCT
ejpam-6383	18	1	the	the	DET
ejpam-6383	18	2	maximum	maximum	ADJ
ejpam-6383	18	3	cardinality	cardinality	NOUN
ejpam-6383	18	4	of	of	ADP
ejpam-6383	18	5	an	an	DET
ejpam-6383	18	6	independent	independent	ADJ
ejpam-6383	18	7	set	set	NOUN
ejpam-6383	18	8	of	of	ADP
ejpam-6383	18	9	g	g	NOUN
ejpam-6383	18	10	,	,	PUNCT
ejpam-6383	18	11	denoted	denote	VERB
ejpam-6383	18	12	by	by	ADP
ejpam-6383	18	13	α(g	α(g	NOUN
ejpam-6383	18	14	)	)	PUNCT
ejpam-6383	18	15	,	,	PUNCT
ejpam-6383	18	16	is	be	AUX
ejpam-6383	18	17	called	call	VERB
ejpam-6383	18	18	the	the	DET
ejpam-6383	18	19	independence	independence	NOUN
ejpam-6383	18	20	number	number	NOUN
ejpam-6383	18	21	of	of	ADP
ejpam-6383	18	22	g	g	PROPN
ejpam-6383	18	23	[	[	X
ejpam-6383	18	24	1	1	NUM
ejpam-6383	18	25	]	]	PUNCT
ejpam-6383	18	26	.	.	PUNCT
ejpam-6383	19	1	the	the	DET
ejpam-6383	19	2	concept	concept	NOUN
ejpam-6383	19	3	of	of	ADP
ejpam-6383	19	4	an	an	DET
ejpam-6383	19	5	independent	independent	ADJ
ejpam-6383	19	6	set	set	NOUN
ejpam-6383	19	7	is	be	AUX
ejpam-6383	19	8	often	often	ADV
ejpam-6383	19	9	studied	study	VERB
ejpam-6383	19	10	in	in	ADP
ejpam-6383	19	11	the	the	DET
ejpam-6383	19	12	context	context	NOUN
ejpam-6383	19	13	of	of	ADP
ejpam-6383	19	14	maximum	maximum	ADJ
ejpam-6383	19	15	independent	independent	ADJ
ejpam-6383	19	16	sets	set	NOUN
ejpam-6383	19	17	,	,	PUNCT
ejpam-6383	19	18	which	which	PRON
ejpam-6383	19	19	refers	refer	VERB
ejpam-6383	19	20	to	to	ADP
ejpam-6383	19	21	the	the	DET
ejpam-6383	19	22	largest	large	ADJ
ejpam-6383	19	23	possible	possible	ADJ
ejpam-6383	19	24	∗corresponding	∗corresponding	NOUN
ejpam-6383	19	25	author	author	NOUN
ejpam-6383	19	26	.	.	PUNCT
ejpam-6383	20	1	doi	doi	NOUN
ejpam-6383	20	2	:	:	PUNCT
ejpam-6383	20	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6383	https://doi.org/10.29020/nybg.ejpam.v18i3.6383	PROPN
ejpam-6383	20	4	email	email	NOUN
ejpam-6383	20	5	addresses	address	NOUN
ejpam-6383	20	6	:	:	PUNCT
ejpam-6383	20	7	kaimarjaymaharajul@msutawi-tawi.edu.ph	kaimarjaymaharajul@msutawi-tawi.edu.ph	PROPN
ejpam-6383	20	8	(	(	PUNCT
ejpam-6383	20	9	k.	k.	PROPN
ejpam-6383	20	10	j.	j.	PROPN
ejpam-6383	20	11	maharajul	maharajul	PROPN
ejpam-6383	20	12	)	)	PUNCT
ejpam-6383	20	13	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-6383	20	14	(	(	PUNCT
ejpam-6383	20	15	j.	j.	PROPN
ejpam-6383	20	16	a.	a.	PROPN
ejpam-6383	20	17	hassan	hassan	PROPN
ejpam-6383	20	18	)	)	PUNCT
ejpam-6383	20	19	.	.	PUNCT
ejpam-6383	21	1	ladznarlaja@msutawi-tawi.edu.ph	ladznarlaja@msutawi-tawi.edu.ph	PROPN
ejpam-6383	21	2	(	(	PUNCT
ejpam-6383	21	3	l.	l.	PROPN
ejpam-6383	21	4	s.	s.	PROPN
ejpam-6383	21	5	laja	laja	PROPN
ejpam-6383	21	6	)	)	PUNCT
ejpam-6383	21	7	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6383	22	1	1	1	NUM
ejpam-6383	22	2	copyright	copyright	NOUN
ejpam-6383	22	3	:	:	PUNCT
ejpam-6383	22	4	©	©	PROPN
ejpam-6383	22	5	2025	2025	NUM
ejpam-6383	22	6	the	the	DET
ejpam-6383	22	7	author(s	author(s	NOUN
ejpam-6383	22	8	)	)	PUNCT
ejpam-6383	22	9	.	.	PUNCT
ejpam-6383	23	1	(	(	PUNCT
ejpam-6383	23	2	cc	cc	NOUN
ejpam-6383	23	3	by	by	ADP
ejpam-6383	23	4	-	-	PUNCT
ejpam-6383	23	5	nc	nc	PROPN
ejpam-6383	23	6	4.0	4.0	NUM
ejpam-6383	23	7	)	)	PUNCT
ejpam-6383	23	8	k.	k.	PROPN
ejpam-6383	23	9	maharajul	maharajul	PROPN
ejpam-6383	23	10	,	,	PUNCT
ejpam-6383	23	11	j.	j.	PROPN
ejpam-6383	23	12	a.	a.	PROPN
ejpam-6383	23	13	hassan	hassan	PROPN
ejpam-6383	23	14	,	,	PUNCT
ejpam-6383	23	15	l.	l.	PROPN
ejpam-6383	23	16	laja	laja	PROPN
ejpam-6383	23	17	/	/	SYM
ejpam-6383	23	18	eur	eur	PROPN
ejpam-6383	23	19	.	.	PUNCT
ejpam-6383	24	1	j.	j.	PROPN
ejpam-6383	24	2	pure	pure	PROPN
ejpam-6383	24	3	appl	appl	PROPN
ejpam-6383	24	4	.	.	PROPN
ejpam-6383	24	5	math	math	PROPN
ejpam-6383	24	6	,	,	PUNCT
ejpam-6383	24	7	18	18	NUM
ejpam-6383	24	8	(	(	PUNCT
ejpam-6383	24	9	3	3	NUM
ejpam-6383	24	10	)	)	PUNCT
ejpam-6383	24	11	(	(	PUNCT
ejpam-6383	24	12	2025	2025	NUM
ejpam-6383	24	13	)	)	PUNCT
ejpam-6383	24	14	,	,	PUNCT
ejpam-6383	24	15	6383	6383	NUM
ejpam-6383	24	16	2	2	NUM
ejpam-6383	24	17	of	of	ADP
ejpam-6383	24	18	10	10	NUM
ejpam-6383	24	19	independent	independent	ADJ
ejpam-6383	24	20	set	set	NOUN
ejpam-6383	24	21	within	within	ADP
ejpam-6383	24	22	a	a	DET
ejpam-6383	24	23	graph	graph	NOUN
ejpam-6383	24	24	.	.	PUNCT
ejpam-6383	25	1	this	this	DET
ejpam-6383	25	2	set	set	NOUN
ejpam-6383	25	3	has	have	VERB
ejpam-6383	25	4	applications	application	NOUN
ejpam-6383	25	5	in	in	ADP
ejpam-6383	25	6	areas	area	NOUN
ejpam-6383	25	7	like	like	ADP
ejpam-6383	25	8	scheduling	scheduling	NOUN
ejpam-6383	25	9	,	,	PUNCT
ejpam-6383	25	10	resource	resource	NOUN
ejpam-6383	25	11	allocation	allocation	NOUN
ejpam-6383	25	12	,	,	PUNCT
ejpam-6383	25	13	and	and	CCONJ
ejpam-6383	25	14	even	even	ADV
ejpam-6383	25	15	social	social	ADJ
ejpam-6383	25	16	network	network	NOUN
ejpam-6383	25	17	analysis	analysis	NOUN
ejpam-6383	25	18	,	,	PUNCT
ejpam-6383	25	19	where	where	SCONJ
ejpam-6383	25	20	finding	find	VERB
ejpam-6383	25	21	independent	independent	ADJ
ejpam-6383	25	22	sets	set	NOUN
ejpam-6383	25	23	can	can	AUX
ejpam-6383	25	24	represent	represent	VERB
ejpam-6383	25	25	groups	group	NOUN
ejpam-6383	25	26	of	of	ADP
ejpam-6383	25	27	individuals	individual	NOUN
ejpam-6383	25	28	or	or	CCONJ
ejpam-6383	25	29	resources	resource	NOUN
ejpam-6383	25	30	that	that	PRON
ejpam-6383	25	31	do	do	AUX
ejpam-6383	25	32	not	not	PART
ejpam-6383	25	33	interfere	interfere	VERB
ejpam-6383	25	34	with	with	ADP
ejpam-6383	25	35	one	one	NUM
ejpam-6383	25	36	another	another	DET
ejpam-6383	25	37	.	.	PUNCT
ejpam-6383	26	1	in	in	ADP
ejpam-6383	26	2	2022	2022	NUM
ejpam-6383	26	3	,	,	PUNCT
ejpam-6383	26	4	hop	hop	NOUN
ejpam-6383	26	5	independent	independent	ADJ
ejpam-6383	26	6	set	set	NOUN
ejpam-6383	26	7	in	in	ADP
ejpam-6383	26	8	a	a	DET
ejpam-6383	26	9	graph	graph	NOUN
ejpam-6383	26	10	and	and	CCONJ
ejpam-6383	26	11	its	its	PRON
ejpam-6383	26	12	parameter	parameter	NOUN
ejpam-6383	26	13	was	be	AUX
ejpam-6383	26	14	introduced	introduce	VERB
ejpam-6383	26	15	by	by	ADP
ejpam-6383	26	16	j.	j.	PROPN
ejpam-6383	26	17	hassan	hassan	PROPN
ejpam-6383	26	18	et	et	PROPN
ejpam-6383	26	19	al	al	PROPN
ejpam-6383	26	20	.	.	PUNCT
ejpam-6383	27	1	[	[	X
ejpam-6383	27	2	2	2	NUM
ejpam-6383	27	3	]	]	PUNCT
ejpam-6383	27	4	.	.	PUNCT
ejpam-6383	28	1	a	a	DET
ejpam-6383	28	2	set	set	NOUN
ejpam-6383	28	3	s	s	NOUN
ejpam-6383	28	4	⊆	⊆	NUM
ejpam-6383	28	5	v	v	NOUN
ejpam-6383	28	6	(	(	PUNCT
ejpam-6383	28	7	g	g	NOUN
ejpam-6383	28	8	)	)	PUNCT
ejpam-6383	28	9	is	be	AUX
ejpam-6383	28	10	called	call	VERB
ejpam-6383	28	11	a	a	DET
ejpam-6383	28	12	hop	hop	NOUN
ejpam-6383	28	13	independent	independent	ADJ
ejpam-6383	28	14	set	set	NOUN
ejpam-6383	28	15	of	of	ADP
ejpam-6383	28	16	g	g	PROPN
ejpam-6383	28	17	if	if	SCONJ
ejpam-6383	28	18	dg(u	dg(u	NOUN
ejpam-6383	28	19	,	,	PUNCT
ejpam-6383	28	20	w	w	NOUN
ejpam-6383	28	21	)	)	PUNCT
ejpam-6383	28	22	̸=	̸=	PROPN
ejpam-6383	28	23	2	2	NUM
ejpam-6383	28	24	for	for	ADP
ejpam-6383	28	25	any	any	DET
ejpam-6383	28	26	distinct	distinct	ADJ
ejpam-6383	28	27	vertices	vertex	NOUN
ejpam-6383	28	28	u	u	NOUN
ejpam-6383	28	29	,	,	PUNCT
ejpam-6383	28	30	w	w	PROPN
ejpam-6383	28	31	∈	∈	PROPN
ejpam-6383	28	32	s.	s.	PROPN
ejpam-6383	28	33	the	the	DET
ejpam-6383	28	34	maximum	maximum	PROPN
ejpam-6383	28	35	cardinality	cardinality	NOUN
ejpam-6383	28	36	of	of	ADP
ejpam-6383	28	37	a	a	DET
ejpam-6383	28	38	hop	hop	NOUN
ejpam-6383	28	39	independent	independent	ADJ
ejpam-6383	28	40	set	set	NOUN
ejpam-6383	28	41	of	of	ADP
ejpam-6383	28	42	g	g	NOUN
ejpam-6383	28	43	,	,	PUNCT
ejpam-6383	28	44	is	be	AUX
ejpam-6383	28	45	called	call	VERB
ejpam-6383	28	46	the	the	DET
ejpam-6383	28	47	hop	hop	NOUN
ejpam-6383	28	48	independence	independence	NOUN
ejpam-6383	28	49	number	number	NOUN
ejpam-6383	28	50	of	of	ADP
ejpam-6383	28	51	g	g	NOUN
ejpam-6383	28	52	,	,	PUNCT
ejpam-6383	28	53	and	and	CCONJ
ejpam-6383	28	54	is	be	AUX
ejpam-6383	28	55	denoted	denote	VERB
ejpam-6383	28	56	by	by	ADP
ejpam-6383	28	57	αh(g	αh(g	NOUN
ejpam-6383	28	58	)	)	PUNCT
ejpam-6383	28	59	.	.	PUNCT
ejpam-6383	29	1	they	they	PRON
ejpam-6383	29	2	have	have	AUX
ejpam-6383	29	3	shown	show	VERB
ejpam-6383	29	4	that	that	SCONJ
ejpam-6383	29	5	the	the	DET
ejpam-6383	29	6	hop	hop	NOUN
ejpam-6383	29	7	independence	independence	NOUN
ejpam-6383	29	8	number	number	NOUN
ejpam-6383	29	9	of	of	ADP
ejpam-6383	29	10	a	a	DET
ejpam-6383	29	11	graph	graph	NOUN
ejpam-6383	29	12	is	be	AUX
ejpam-6383	29	13	always	always	ADV
ejpam-6383	29	14	greater	great	ADJ
ejpam-6383	29	15	than	than	ADP
ejpam-6383	29	16	or	or	CCONJ
ejpam-6383	29	17	equal	equal	ADJ
ejpam-6383	29	18	to	to	ADP
ejpam-6383	29	19	the	the	DET
ejpam-6383	29	20	hop	hop	NOUN
ejpam-6383	29	21	domination	domination	NOUN
ejpam-6383	29	22	number	number	NOUN
ejpam-6383	29	23	.	.	PUNCT
ejpam-6383	30	1	moreover	moreover	ADV
ejpam-6383	30	2	,	,	PUNCT
ejpam-6383	30	3	they	they	PRON
ejpam-6383	30	4	derived	derive	VERB
ejpam-6383	30	5	some	some	DET
ejpam-6383	30	6	bounds	bound	NOUN
ejpam-6383	30	7	and	and	CCONJ
ejpam-6383	30	8	formulas	formula	NOUN
ejpam-6383	30	9	of	of	ADP
ejpam-6383	30	10	hop	hop	NOUN
ejpam-6383	30	11	independence	independence	NOUN
ejpam-6383	30	12	numbers	number	NOUN
ejpam-6383	30	13	of	of	ADP
ejpam-6383	30	14	some	some	DET
ejpam-6383	30	15	special	special	ADJ
ejpam-6383	30	16	graphs	graph	NOUN
ejpam-6383	30	17	and	and	CCONJ
ejpam-6383	30	18	graphs	graph	NOUN
ejpam-6383	30	19	under	under	ADP
ejpam-6383	30	20	some	some	DET
ejpam-6383	30	21	binary	binary	ADJ
ejpam-6383	30	22	operations	operation	NOUN
ejpam-6383	30	23	.	.	PUNCT
ejpam-6383	31	1	some	some	DET
ejpam-6383	31	2	studies	study	NOUN
ejpam-6383	31	3	related	relate	VERB
ejpam-6383	31	4	to	to	ADP
ejpam-6383	31	5	independent	independent	ADJ
ejpam-6383	31	6	sets	set	NOUN
ejpam-6383	31	7	,	,	PUNCT
ejpam-6383	31	8	its	its	PRON
ejpam-6383	31	9	variations	variation	NOUN
ejpam-6383	31	10	,	,	PUNCT
ejpam-6383	31	11	and	and	CCONJ
ejpam-6383	31	12	other	other	ADJ
ejpam-6383	31	13	hop	hop	ADV
ejpam-6383	31	14	-	-	PUNCT
ejpam-6383	31	15	related	relate	VERB
ejpam-6383	31	16	concepts	concept	NOUN
ejpam-6383	31	17	can	can	AUX
ejpam-6383	31	18	be	be	AUX
ejpam-6383	31	19	found	find	VERB
ejpam-6383	31	20	in	in	ADP
ejpam-6383	31	21	[	[	X
ejpam-6383	31	22	3–11	3–11	NOUN
ejpam-6383	31	23	]	]	PUNCT
ejpam-6383	31	24	.	.	PUNCT
ejpam-6383	32	1	in	in	ADP
ejpam-6383	32	2	this	this	DET
ejpam-6383	32	3	paper	paper	NOUN
ejpam-6383	32	4	,	,	PUNCT
ejpam-6383	32	5	new	new	ADJ
ejpam-6383	32	6	variant	variant	NOUN
ejpam-6383	32	7	of	of	ADP
ejpam-6383	32	8	hop	hop	NOUN
ejpam-6383	32	9	independence	independence	NOUN
ejpam-6383	32	10	called	call	VERB
ejpam-6383	32	11	l	l	NOUN
ejpam-6383	32	12	-	-	ADJ
ejpam-6383	32	13	hop	hop	ADJ
ejpam-6383	32	14	independence	independence	NOUN
ejpam-6383	32	15	sequence	sequence	NOUN
ejpam-6383	32	16	in	in	ADP
ejpam-6383	32	17	a	a	DET
ejpam-6383	32	18	graph	graph	NOUN
ejpam-6383	32	19	is	be	AUX
ejpam-6383	32	20	introduced	introduce	VERB
ejpam-6383	32	21	.	.	PUNCT
ejpam-6383	33	1	the	the	DET
ejpam-6383	33	2	authors	author	NOUN
ejpam-6383	33	3	add	add	VERB
ejpam-6383	33	4	some	some	DET
ejpam-6383	33	5	properties	property	NOUN
ejpam-6383	33	6	to	to	PART
ejpam-6383	33	7	hop	hop	VERB
ejpam-6383	33	8	independence	independence	NOUN
ejpam-6383	33	9	wherein	wherein	SCONJ
ejpam-6383	33	10	the	the	DET
ejpam-6383	33	11	order	order	NOUN
ejpam-6383	33	12	of	of	ADP
ejpam-6383	33	13	choosing	choose	VERB
ejpam-6383	33	14	vertices	vertex	NOUN
ejpam-6383	33	15	and	and	CCONJ
ejpam-6383	33	16	its	its	PRON
ejpam-6383	33	17	neighborhoods	neighborhood	NOUN
ejpam-6383	33	18	are	be	AUX
ejpam-6383	33	19	important	important	ADJ
ejpam-6383	33	20	.	.	PUNCT
ejpam-6383	34	1	this	this	DET
ejpam-6383	34	2	parameter	parameter	NOUN
ejpam-6383	34	3	is	be	AUX
ejpam-6383	34	4	investigated	investigate	VERB
ejpam-6383	34	5	on	on	ADP
ejpam-6383	34	6	some	some	DET
ejpam-6383	34	7	special	special	ADJ
ejpam-6383	34	8	graphs	graph	NOUN
ejpam-6383	34	9	,	,	PUNCT
ejpam-6383	34	10	and	and	CCONJ
ejpam-6383	34	11	on	on	ADP
ejpam-6383	34	12	the	the	DET
ejpam-6383	34	13	join	join	NOUN
ejpam-6383	34	14	of	of	ADP
ejpam-6383	34	15	any	any	DET
ejpam-6383	34	16	two	two	NUM
ejpam-6383	34	17	graphs	graph	NOUN
ejpam-6383	34	18	.	.	PUNCT
ejpam-6383	35	1	some	some	DET
ejpam-6383	35	2	bounds	bound	NOUN
ejpam-6383	35	3	and	and	CCONJ
ejpam-6383	35	4	exact	exact	ADJ
ejpam-6383	35	5	values	value	NOUN
ejpam-6383	35	6	are	be	AUX
ejpam-6383	35	7	determined	determine	VERB
ejpam-6383	35	8	.	.	PUNCT
ejpam-6383	36	1	moreover	moreover	ADV
ejpam-6383	36	2	,	,	PUNCT
ejpam-6383	36	3	some	some	DET
ejpam-6383	36	4	characterizations	characterization	NOUN
ejpam-6383	36	5	of	of	ADP
ejpam-6383	36	6	this	this	DET
ejpam-6383	36	7	newly	newly	ADV
ejpam-6383	36	8	defined	define	VERB
ejpam-6383	36	9	sequence	sequence	NOUN
ejpam-6383	36	10	are	be	AUX
ejpam-6383	36	11	presented	present	VERB
ejpam-6383	36	12	,	,	PUNCT
ejpam-6383	36	13	and	and	CCONJ
ejpam-6383	36	14	used	use	VERB
ejpam-6383	36	15	to	to	PART
ejpam-6383	36	16	solve	solve	VERB
ejpam-6383	36	17	the	the	DET
ejpam-6383	36	18	said	say	VERB
ejpam-6383	36	19	bounds	bound	NOUN
ejpam-6383	36	20	and	and	CCONJ
ejpam-6383	36	21	exact	exact	ADJ
ejpam-6383	36	22	values	value	NOUN
ejpam-6383	36	23	.	.	PUNCT
ejpam-6383	37	1	the	the	DET
ejpam-6383	37	2	authors	author	NOUN
ejpam-6383	37	3	are	be	AUX
ejpam-6383	37	4	confident	confident	ADJ
ejpam-6383	37	5	that	that	SCONJ
ejpam-6383	37	6	this	this	DET
ejpam-6383	37	7	study	study	NOUN
ejpam-6383	37	8	would	would	AUX
ejpam-6383	37	9	lead	lead	VERB
ejpam-6383	37	10	to	to	ADP
ejpam-6383	37	11	another	another	DET
ejpam-6383	37	12	interesting	interesting	ADJ
ejpam-6383	37	13	studies	study	NOUN
ejpam-6383	37	14	and	and	CCONJ
ejpam-6383	37	15	application	application	NOUN
ejpam-6383	37	16	in	in	ADP
ejpam-6383	37	17	the	the	DET
ejpam-6383	37	18	future	future	NOUN
ejpam-6383	37	19	.	.	PUNCT
ejpam-6383	38	1	2	2	X
ejpam-6383	38	2	.	.	X
ejpam-6383	38	3	terminology	terminology	NOUN
ejpam-6383	38	4	and	and	CCONJ
ejpam-6383	38	5	notation	notation	NOUN
ejpam-6383	38	6	let	let	VERB
ejpam-6383	38	7	g	g	NOUN
ejpam-6383	38	8	=	=	SYM
ejpam-6383	38	9	(	(	PUNCT
ejpam-6383	38	10	v	v	NOUN
ejpam-6383	38	11	(	(	PUNCT
ejpam-6383	38	12	g	g	NOUN
ejpam-6383	38	13	)	)	PUNCT
ejpam-6383	38	14	,	,	PUNCT
ejpam-6383	38	15	e(g	e(g	PROPN
ejpam-6383	38	16	)	)	PUNCT
ejpam-6383	38	17	)	)	PUNCT
ejpam-6383	38	18	be	be	AUX
ejpam-6383	38	19	a	a	DET
ejpam-6383	38	20	simple	simple	ADJ
ejpam-6383	38	21	and	and	CCONJ
ejpam-6383	38	22	undirected	undirected	ADJ
ejpam-6383	38	23	graph	graph	NOUN
ejpam-6383	38	24	.	.	PUNCT
ejpam-6383	39	1	the	the	DET
ejpam-6383	39	2	distance	distance	NOUN
ejpam-6383	39	3	dg(u	dg(u	NOUN
ejpam-6383	39	4	,	,	PUNCT
ejpam-6383	39	5	v	v	NOUN
ejpam-6383	39	6	)	)	PUNCT
ejpam-6383	39	7	in	in	ADP
ejpam-6383	39	8	g	g	NOUN
ejpam-6383	39	9	of	of	ADP
ejpam-6383	39	10	two	two	NUM
ejpam-6383	39	11	vertices	vertex	NOUN
ejpam-6383	39	12	u	u	NOUN
ejpam-6383	39	13	,	,	PUNCT
ejpam-6383	39	14	v	v	PROPN
ejpam-6383	39	15	is	be	AUX
ejpam-6383	39	16	the	the	DET
ejpam-6383	39	17	length	length	NOUN
ejpam-6383	39	18	of	of	ADP
ejpam-6383	39	19	a	a	DET
ejpam-6383	39	20	shortest	short	ADJ
ejpam-6383	39	21	u	u	NOUN
ejpam-6383	39	22	-	-	NOUN
ejpam-6383	39	23	v	v	ADJ
ejpam-6383	39	24	path	path	NOUN
ejpam-6383	39	25	in	in	ADP
ejpam-6383	39	26	g.	g.	PROPN
ejpam-6383	39	27	a	a	DET
ejpam-6383	39	28	subset	subset	VERB
ejpam-6383	39	29	i	i	PRON
ejpam-6383	39	30	of	of	ADP
ejpam-6383	39	31	v	v	NOUN
ejpam-6383	39	32	(	(	PUNCT
ejpam-6383	39	33	g	g	NOUN
ejpam-6383	39	34	)	)	PUNCT
ejpam-6383	39	35	is	be	AUX
ejpam-6383	39	36	called	call	VERB
ejpam-6383	39	37	an	an	DET
ejpam-6383	39	38	independent	independent	ADJ
ejpam-6383	39	39	if	if	SCONJ
ejpam-6383	39	40	for	for	ADP
ejpam-6383	39	41	every	every	DET
ejpam-6383	39	42	pair	pair	NOUN
ejpam-6383	39	43	of	of	ADP
ejpam-6383	39	44	distinct	distinct	ADJ
ejpam-6383	39	45	vertices	vertex	NOUN
ejpam-6383	39	46	x	x	X
ejpam-6383	39	47	,	,	PUNCT
ejpam-6383	39	48	y	y	PROPN
ejpam-6383	39	49	∈	∈	PROPN
ejpam-6383	39	50	i	i	PRON
ejpam-6383	39	51	,	,	PUNCT
ejpam-6383	39	52	dg(x	dg(x	X
ejpam-6383	39	53	,	,	PUNCT
ejpam-6383	39	54	y	y	NOUN
ejpam-6383	39	55	)	)	PUNCT
ejpam-6383	39	56	̸=	̸=	PROPN
ejpam-6383	39	57	1	1	NUM
ejpam-6383	39	58	.	.	PUNCT
ejpam-6383	40	1	the	the	DET
ejpam-6383	40	2	maximum	maximum	ADJ
ejpam-6383	40	3	cardinality	cardinality	NOUN
ejpam-6383	40	4	of	of	ADP
ejpam-6383	40	5	an	an	DET
ejpam-6383	40	6	independent	independent	ADJ
ejpam-6383	40	7	set	set	NOUN
ejpam-6383	40	8	in	in	ADP
ejpam-6383	40	9	g	g	NOUN
ejpam-6383	40	10	,	,	PUNCT
ejpam-6383	40	11	denoted	denote	VERB
ejpam-6383	40	12	by	by	ADP
ejpam-6383	40	13	α(g	α(g	NOUN
ejpam-6383	40	14	)	)	PUNCT
ejpam-6383	40	15	,	,	PUNCT
ejpam-6383	40	16	is	be	AUX
ejpam-6383	40	17	called	call	VERB
ejpam-6383	40	18	the	the	DET
ejpam-6383	40	19	independence	independence	NOUN
ejpam-6383	40	20	number	number	NOUN
ejpam-6383	40	21	of	of	ADP
ejpam-6383	40	22	g.	g.	PROPN
ejpam-6383	40	23	any	any	DET
ejpam-6383	40	24	independent	independent	ADJ
ejpam-6383	40	25	set	set	NOUN
ejpam-6383	40	26	i	i	PRON
ejpam-6383	40	27	with	with	ADP
ejpam-6383	40	28	cardinality	cardinality	NOUN
ejpam-6383	40	29	equal	equal	ADJ
ejpam-6383	40	30	to	to	ADP
ejpam-6383	40	31	α(g	α(g	NUM
ejpam-6383	40	32	)	)	PUNCT
ejpam-6383	40	33	is	be	AUX
ejpam-6383	40	34	called	call	VERB
ejpam-6383	40	35	an	an	DET
ejpam-6383	40	36	α	α	NOUN
ejpam-6383	40	37	-	-	PUNCT
ejpam-6383	40	38	set	set	NOUN
ejpam-6383	40	39	of	of	ADP
ejpam-6383	40	40	g.	g.	PROPN
ejpam-6383	40	41	a	a	DET
ejpam-6383	40	42	subset	subset	NOUN
ejpam-6383	40	43	s	s	NOUN
ejpam-6383	40	44	of	of	ADP
ejpam-6383	40	45	v	v	NOUN
ejpam-6383	40	46	(	(	PUNCT
ejpam-6383	40	47	g	g	NOUN
ejpam-6383	40	48	)	)	PUNCT
ejpam-6383	40	49	is	be	AUX
ejpam-6383	40	50	called	call	VERB
ejpam-6383	40	51	a	a	DET
ejpam-6383	40	52	hop	hop	NOUN
ejpam-6383	40	53	independent	independent	ADJ
ejpam-6383	40	54	set	set	NOUN
ejpam-6383	40	55	of	of	ADP
ejpam-6383	40	56	g	g	PROPN
ejpam-6383	40	57	if	if	SCONJ
ejpam-6383	40	58	dg(u	dg(u	NOUN
ejpam-6383	40	59	,	,	PUNCT
ejpam-6383	40	60	v	v	NOUN
ejpam-6383	40	61	)	)	PUNCT
ejpam-6383	40	62	̸=	̸=	PROPN
ejpam-6383	40	63	2	2	NUM
ejpam-6383	40	64	for	for	ADP
ejpam-6383	40	65	any	any	DET
ejpam-6383	40	66	two	two	NUM
ejpam-6383	40	67	distinct	distinct	ADJ
ejpam-6383	40	68	vertices	vertex	NOUN
ejpam-6383	40	69	u	u	NOUN
ejpam-6383	40	70	,	,	PUNCT
ejpam-6383	40	71	v	v	PROPN
ejpam-6383	40	72	∈	∈	PROPN
ejpam-6383	40	73	s.	s.	PROPN
ejpam-6383	40	74	the	the	DET
ejpam-6383	40	75	hop	hop	PROPN
ejpam-6383	40	76	independence	independence	NOUN
ejpam-6383	40	77	number	number	NOUN
ejpam-6383	40	78	of	of	ADP
ejpam-6383	40	79	g	g	NOUN
ejpam-6383	40	80	,	,	PUNCT
ejpam-6383	40	81	denoted	denote	VERB
ejpam-6383	40	82	by	by	ADP
ejpam-6383	40	83	αh(g	αh(g	NOUN
ejpam-6383	40	84	)	)	PUNCT
ejpam-6383	40	85	,	,	PUNCT
ejpam-6383	40	86	is	be	AUX
ejpam-6383	40	87	the	the	DET
ejpam-6383	40	88	maximum	maximum	ADJ
ejpam-6383	40	89	cardinality	cardinality	NOUN
ejpam-6383	40	90	of	of	ADP
ejpam-6383	40	91	a	a	DET
ejpam-6383	40	92	hop	hop	NOUN
ejpam-6383	40	93	independent	independent	ADJ
ejpam-6383	40	94	set	set	NOUN
ejpam-6383	40	95	of	of	ADP
ejpam-6383	40	96	g.	g.	PROPN
ejpam-6383	40	97	given	give	VERB
ejpam-6383	40	98	a	a	DET
ejpam-6383	40	99	graph	graph	NOUN
ejpam-6383	40	100	g	g	NOUN
ejpam-6383	40	101	and	and	CCONJ
ejpam-6383	40	102	a	a	DET
ejpam-6383	40	103	sequence	sequence	NOUN
ejpam-6383	40	104	s	s	PART
ejpam-6383	40	105	=	=	PUNCT
ejpam-6383	40	106	(	(	PUNCT
ejpam-6383	40	107	v1	v1	PROPN
ejpam-6383	40	108	,	,	PUNCT
ejpam-6383	40	109	.	.	PUNCT
ejpam-6383	40	110	.	.	PUNCT
ejpam-6383	41	1	.	.	PUNCT
ejpam-6383	42	1	,	,	PUNCT
ejpam-6383	42	2	vk	vk	PROPN
ejpam-6383	42	3	)	)	PUNCT
ejpam-6383	42	4	of	of	ADP
ejpam-6383	42	5	distinct	distinct	ADJ
ejpam-6383	42	6	vertices	vertex	NOUN
ejpam-6383	42	7	of	of	ADP
ejpam-6383	42	8	g	g	NOUN
ejpam-6383	42	9	,	,	PUNCT
ejpam-6383	42	10	for	for	ADP
ejpam-6383	42	11	every	every	DET
ejpam-6383	42	12	i	i	PROPN
ejpam-6383	42	13	∈	∈	PROPN
ejpam-6383	42	14	{	{	PUNCT
ejpam-6383	42	15	2	2	NUM
ejpam-6383	42	16	,	,	PUNCT
ejpam-6383	42	17	3	3	NUM
ejpam-6383	42	18	,	,	PUNCT
ejpam-6383	42	19	·	·	PUNCT
ejpam-6383	42	20	·	·	PUNCT
ejpam-6383	42	21	·	·	PUNCT
ejpam-6383	42	22	,	,	PUNCT
ejpam-6383	42	23	k	k	X
ejpam-6383	42	24	}	}	PUNCT
ejpam-6383	42	25	we	we	PRON
ejpam-6383	42	26	define	define	VERB
ejpam-6383	42	27	the	the	DET
ejpam-6383	42	28	set	set	NOUN
ejpam-6383	42	29	ϕs	ϕs	INTJ
ejpam-6383	42	30	by	by	ADP
ejpam-6383	42	31	ϕs(v	ϕs(v	NOUN
ejpam-6383	43	1	i	i	NOUN
ejpam-6383	43	2	)	)	PUNCT
ejpam-6383	43	3	=	=	SYM
ejpam-6383	44	1	n	n	PROPN
ejpam-6383	44	2	[	[	X
ejpam-6383	44	3	vi]\	vi]\	NOUN
ejpam-6383	44	4	i−1⋃	i−1⋃	PROPN
ejpam-6383	44	5	j=1	j=1	PROPN
ejpam-6383	44	6	n(vj	n(vj	PROPN
ejpam-6383	44	7	)	)	PUNCT
ejpam-6383	44	8	.	.	PUNCT
ejpam-6383	45	1	the	the	DET
ejpam-6383	45	2	sequence	sequence	NOUN
ejpam-6383	45	3	is	be	AUX
ejpam-6383	45	4	called	call	VERB
ejpam-6383	45	5	l	l	NOUN
ejpam-6383	45	6	-	-	NOUN
ejpam-6383	45	7	sequence	sequence	NOUN
ejpam-6383	45	8	if	if	SCONJ
ejpam-6383	45	9	ϕs(vi	ϕs(vi	NOUN
ejpam-6383	45	10	)	)	PUNCT
ejpam-6383	45	11	̸=	̸=	PROPN
ejpam-6383	45	12	∅	∅	NOUN
ejpam-6383	45	13	for	for	ADP
ejpam-6383	45	14	every	every	DET
ejpam-6383	45	15	i	i	PROPN
ejpam-6383	45	16	∈	∈	PROPN
ejpam-6383	45	17	{	{	PUNCT
ejpam-6383	45	18	2	2	NUM
ejpam-6383	45	19	,	,	PUNCT
ejpam-6383	45	20	3	3	NUM
ejpam-6383	45	21	,	,	PUNCT
ejpam-6383	45	22	·	·	PUNCT
ejpam-6383	45	23	·	·	PUNCT
ejpam-6383	45	24	·	·	PUNCT
ejpam-6383	45	25	,	,	PUNCT
ejpam-6383	45	26	k	k	X
ejpam-6383	45	27	}	}	PUNCT
ejpam-6383	45	28	.	.	PUNCT
ejpam-6383	46	1	let	let	VERB
ejpam-6383	46	2	s1	s1	PROPN
ejpam-6383	46	3	=	=	SYM
ejpam-6383	46	4	(	(	PUNCT
ejpam-6383	46	5	v1	v1	PROPN
ejpam-6383	46	6	,	,	PUNCT
ejpam-6383	46	7	.	.	PUNCT
ejpam-6383	46	8	.	.	PUNCT
ejpam-6383	47	1	.	.	PUNCT
ejpam-6383	48	1	,	,	PUNCT
ejpam-6383	48	2	vn	vn	PROPN
ejpam-6383	48	3	)	)	PUNCT
ejpam-6383	48	4	and	and	CCONJ
ejpam-6383	48	5	s2	s2	NOUN
ejpam-6383	48	6	=	=	SYM
ejpam-6383	48	7	(	(	PUNCT
ejpam-6383	48	8	u1	u1	PROPN
ejpam-6383	48	9	,	,	PUNCT
ejpam-6383	48	10	.	.	PUNCT
ejpam-6383	48	11	.	.	PUNCT
ejpam-6383	48	12	.	.	PUNCT
ejpam-6383	49	1	,	,	PUNCT
ejpam-6383	49	2	um	um	INTJ
ejpam-6383	49	3	)	)	PUNCT
ejpam-6383	49	4	be	be	AUX
ejpam-6383	49	5	two	two	NUM
ejpam-6383	49	6	sequences	sequence	NOUN
ejpam-6383	49	7	of	of	ADP
ejpam-6383	49	8	distinct	distinct	ADJ
ejpam-6383	49	9	vertices	vertex	NOUN
ejpam-6383	49	10	of	of	ADP
ejpam-6383	49	11	g.	g.	PROPN
ejpam-6383	49	12	the	the	DET
ejpam-6383	49	13	concatenation	concatenation	NOUN
ejpam-6383	49	14	of	of	ADP
ejpam-6383	49	15	s1	s1	PROPN
ejpam-6383	49	16	and	and	CCONJ
ejpam-6383	49	17	s2	s2	PROPN
ejpam-6383	49	18	,	,	PUNCT
ejpam-6383	49	19	denoted	denote	VERB
ejpam-6383	49	20	by	by	ADP
ejpam-6383	49	21	s1	s1	PROPN
ejpam-6383	49	22	⊕	⊕	PROPN
ejpam-6383	49	23	s2	s2	PROPN
ejpam-6383	49	24	,	,	PUNCT
ejpam-6383	49	25	is	be	AUX
ejpam-6383	49	26	the	the	DET
ejpam-6383	49	27	sequence	sequence	NOUN
ejpam-6383	49	28	given	give	VERB
ejpam-6383	49	29	by	by	ADP
ejpam-6383	49	30	s1	s1	PROPN
ejpam-6383	49	31	⊕	⊕	PROPN
ejpam-6383	49	32	s2	s2	PROPN
ejpam-6383	49	33	=	=	SYM
ejpam-6383	49	34	(	(	PUNCT
ejpam-6383	49	35	v1	v1	PROPN
ejpam-6383	49	36	,	,	PUNCT
ejpam-6383	49	37	.	.	PUNCT
ejpam-6383	49	38	.	.	PUNCT
ejpam-6383	50	1	.	.	PUNCT
ejpam-6383	51	1	,	,	PUNCT
ejpam-6383	51	2	vn	vn	PROPN
ejpam-6383	51	3	,	,	PUNCT
ejpam-6383	51	4	u1	u1	NOUN
ejpam-6383	51	5	,	,	PUNCT
ejpam-6383	51	6	.	.	PUNCT
ejpam-6383	51	7	.	.	PUNCT
ejpam-6383	51	8	.	.	PUNCT
ejpam-6383	52	1	,	,	PUNCT
ejpam-6383	52	2	um	um	INTJ
ejpam-6383	52	3	)	)	PUNCT
ejpam-6383	52	4	.	.	PUNCT
ejpam-6383	53	1	a	a	DET
ejpam-6383	53	2	sequence	sequence	NOUN
ejpam-6383	53	3	l	l	NOUN
ejpam-6383	53	4	=	=	SYM
ejpam-6383	53	5	(	(	PUNCT
ejpam-6383	53	6	w1	w1	NOUN
ejpam-6383	53	7	,	,	PUNCT
ejpam-6383	53	8	.	.	PUNCT
ejpam-6383	53	9	.	.	PUNCT
ejpam-6383	53	10	.	.	PUNCT
ejpam-6383	54	1	,	,	PUNCT
ejpam-6383	54	2	wk	wk	X
ejpam-6383	54	3	)	)	PUNCT
ejpam-6383	54	4	of	of	ADP
ejpam-6383	54	5	distinct	distinct	ADJ
ejpam-6383	54	6	vertices	vertex	NOUN
ejpam-6383	54	7	of	of	ADP
ejpam-6383	54	8	g	g	PROPN
ejpam-6383	54	9	is	be	AUX
ejpam-6383	54	10	called	call	VERB
ejpam-6383	54	11	a	a	DET
ejpam-6383	54	12	legal	legal	ADJ
ejpam-6383	54	13	hop	hop	NOUN
ejpam-6383	54	14	independent	independent	ADJ
ejpam-6383	54	15	sequence	sequence	NOUN
ejpam-6383	54	16	if	if	SCONJ
ejpam-6383	54	17	k	k	PROPN
ejpam-6383	54	18	=	=	SYM
ejpam-6383	54	19	1	1	NUM
ejpam-6383	54	20	or	or	CCONJ
ejpam-6383	54	21	l	l	NOUN
ejpam-6383	54	22	is	be	AUX
ejpam-6383	54	23	a	a	DET
ejpam-6383	54	24	hop	hop	NOUN
ejpam-6383	54	25	independent	independent	ADJ
ejpam-6383	54	26	and	and	CCONJ
ejpam-6383	54	27	ng[wi	ng[wi	PROPN
ejpam-6383	55	1	]	]	X
ejpam-6383	55	2	\	\	PROPN
ejpam-6383	55	3	⋃i−1	⋃i−1	NOUN
ejpam-6383	55	4	j=1ng[wj	j=1ng[wj	PROPN
ejpam-6383	55	5	]	]	PUNCT
ejpam-6383	55	6	̸=	̸=	PROPN
ejpam-6383	55	7	∅	∅	NOUN
ejpam-6383	55	8	for	for	ADP
ejpam-6383	55	9	every	every	DET
ejpam-6383	55	10	i	i	PROPN
ejpam-6383	55	11	∈	∈	PROPN
ejpam-6383	55	12	{	{	PUNCT
ejpam-6383	55	13	2	2	NUM
ejpam-6383	55	14	,	,	PUNCT
ejpam-6383	55	15	·	·	PUNCT
ejpam-6383	55	16	·	·	PUNCT
ejpam-6383	55	17	·	·	PUNCT
ejpam-6383	55	18	,	,	PUNCT
ejpam-6383	55	19	k	k	X
ejpam-6383	55	20	}	}	PUNCT
ejpam-6383	55	21	.	.	PUNCT
ejpam-6383	56	1	the	the	DET
ejpam-6383	56	2	maximum	maximum	ADJ
ejpam-6383	56	3	length	length	NOUN
ejpam-6383	56	4	of	of	ADP
ejpam-6383	56	5	a	a	DET
ejpam-6383	56	6	legal	legal	ADJ
ejpam-6383	56	7	hop	hop	NOUN
ejpam-6383	56	8	independent	independent	ADJ
ejpam-6383	56	9	sequence	sequence	NOUN
ejpam-6383	56	10	in	in	ADP
ejpam-6383	56	11	g	g	NOUN
ejpam-6383	56	12	,	,	PUNCT
ejpam-6383	56	13	denoted	denote	VERB
ejpam-6383	56	14	k.	k.	PROPN
ejpam-6383	56	15	maharajul	maharajul	PROPN
ejpam-6383	56	16	,	,	PUNCT
ejpam-6383	56	17	j.	j.	PROPN
ejpam-6383	56	18	a.	a.	PROPN
ejpam-6383	56	19	hassan	hassan	PROPN
ejpam-6383	56	20	,	,	PUNCT
ejpam-6383	56	21	l.	l.	PROPN
ejpam-6383	56	22	laja	laja	PROPN
ejpam-6383	56	23	/	/	SYM
ejpam-6383	56	24	eur	eur	PROPN
ejpam-6383	56	25	.	.	PUNCT
ejpam-6383	57	1	j.	j.	PROPN
ejpam-6383	57	2	pure	pure	PROPN
ejpam-6383	57	3	appl	appl	PROPN
ejpam-6383	57	4	.	.	PROPN
ejpam-6383	57	5	math	math	PROPN
ejpam-6383	57	6	,	,	PUNCT
ejpam-6383	57	7	18	18	NUM
ejpam-6383	57	8	(	(	PUNCT
ejpam-6383	57	9	3	3	NUM
ejpam-6383	57	10	)	)	PUNCT
ejpam-6383	57	11	(	(	PUNCT
ejpam-6383	57	12	2025	2025	NUM
ejpam-6383	57	13	)	)	PUNCT
ejpam-6383	57	14	,	,	PUNCT
ejpam-6383	57	15	6383	6383	NUM
ejpam-6383	57	16	3	3	NUM
ejpam-6383	57	17	of	of	ADP
ejpam-6383	57	18	10	10	NUM
ejpam-6383	57	19	by	by	ADP
ejpam-6383	57	20	αℓh(g	αℓh(g	NOUN
ejpam-6383	57	21	)	)	PUNCT
ejpam-6383	57	22	,	,	PUNCT
ejpam-6383	57	23	is	be	AUX
ejpam-6383	57	24	called	call	VERB
ejpam-6383	57	25	the	the	DET
ejpam-6383	57	26	legal	legal	ADJ
ejpam-6383	57	27	hop	hop	NOUN
ejpam-6383	57	28	independence	independence	NOUN
ejpam-6383	57	29	number	number	NOUN
ejpam-6383	57	30	of	of	ADP
ejpam-6383	57	31	g.	g.	PROPN
ejpam-6383	57	32	a	a	DET
ejpam-6383	57	33	graph	graph	NOUN
ejpam-6383	57	34	is	be	AUX
ejpam-6383	57	35	complete	complete	ADJ
ejpam-6383	57	36	if	if	SCONJ
ejpam-6383	57	37	every	every	DET
ejpam-6383	57	38	pair	pair	NOUN
ejpam-6383	57	39	of	of	ADP
ejpam-6383	57	40	distinct	distinct	ADJ
ejpam-6383	57	41	vertices	vertex	NOUN
ejpam-6383	57	42	are	be	AUX
ejpam-6383	57	43	adjacent	adjacent	ADJ
ejpam-6383	57	44	.	.	PUNCT
ejpam-6383	58	1	a	a	DET
ejpam-6383	58	2	complete	complete	ADJ
ejpam-6383	58	3	graph	graph	NOUN
ejpam-6383	58	4	of	of	ADP
ejpam-6383	58	5	order	order	NOUN
ejpam-6383	58	6	n	n	NOUN
ejpam-6383	58	7	is	be	AUX
ejpam-6383	58	8	denoted	denote	VERB
ejpam-6383	58	9	by	by	ADP
ejpam-6383	58	10	kn	kn	PROPN
ejpam-6383	58	11	.	.	PUNCT
ejpam-6383	59	1	a	a	DET
ejpam-6383	59	2	set	set	NOUN
ejpam-6383	59	3	s	s	NOUN
ejpam-6383	59	4	⊆	⊆	NUM
ejpam-6383	59	5	v	v	NOUN
ejpam-6383	59	6	(	(	PUNCT
ejpam-6383	59	7	g	g	NOUN
ejpam-6383	59	8	)	)	PUNCT
ejpam-6383	59	9	is	be	AUX
ejpam-6383	59	10	called	call	VERB
ejpam-6383	59	11	a	a	DET
ejpam-6383	59	12	clique	clique	NOUN
ejpam-6383	59	13	in	in	ADP
ejpam-6383	59	14	g	g	PROPN
ejpam-6383	59	15	if	if	SCONJ
ejpam-6383	59	16	the	the	DET
ejpam-6383	59	17	subgraph	subgraph	NOUN
ejpam-6383	59	18	⟨s⟩	⟨s⟩	PROPN
ejpam-6383	59	19	induced	induce	VERB
ejpam-6383	59	20	by	by	ADP
ejpam-6383	59	21	s	s	PROPN
ejpam-6383	59	22	is	be	AUX
ejpam-6383	59	23	a	a	DET
ejpam-6383	59	24	complete	complete	ADJ
ejpam-6383	59	25	graph	graph	NOUN
ejpam-6383	59	26	.	.	PUNCT
ejpam-6383	60	1	the	the	DET
ejpam-6383	60	2	maximum	maximum	ADJ
ejpam-6383	60	3	size	size	NOUN
ejpam-6383	60	4	or	or	CCONJ
ejpam-6383	60	5	cardinality	cardinality	NOUN
ejpam-6383	60	6	of	of	ADP
ejpam-6383	60	7	a	a	DET
ejpam-6383	60	8	clique	clique	NOUN
ejpam-6383	60	9	of	of	ADP
ejpam-6383	60	10	g	g	NOUN
ejpam-6383	60	11	,	,	PUNCT
ejpam-6383	60	12	denoted	denote	VERB
ejpam-6383	60	13	by	by	ADP
ejpam-6383	60	14	ω(g	ω(g	NOUN
ejpam-6383	60	15	)	)	PUNCT
ejpam-6383	60	16	,	,	PUNCT
ejpam-6383	60	17	is	be	AUX
ejpam-6383	60	18	called	call	VERB
ejpam-6383	60	19	the	the	DET
ejpam-6383	60	20	clique	clique	ADJ
ejpam-6383	60	21	number	number	NOUN
ejpam-6383	60	22	of	of	ADP
ejpam-6383	60	23	g.	g.	PROPN
ejpam-6383	60	24	let	let	VERB
ejpam-6383	60	25	g	g	NOUN
ejpam-6383	61	1	and	and	CCONJ
ejpam-6383	61	2	h	h	NOUN
ejpam-6383	61	3	be	be	VERB
ejpam-6383	61	4	any	any	DET
ejpam-6383	61	5	two	two	NUM
ejpam-6383	61	6	graphs	graph	NOUN
ejpam-6383	61	7	.	.	PUNCT
ejpam-6383	62	1	the	the	DET
ejpam-6383	62	2	join	join	NOUN
ejpam-6383	62	3	g	g	PROPN
ejpam-6383	62	4	+	+	CCONJ
ejpam-6383	62	5	h	h	NOUN
ejpam-6383	62	6	is	be	AUX
ejpam-6383	62	7	the	the	DET
ejpam-6383	62	8	graph	graph	NOUN
ejpam-6383	62	9	with	with	ADP
ejpam-6383	62	10	vertex	vertex	NOUN
ejpam-6383	62	11	set	set	VERB
ejpam-6383	62	12	v	v	NOUN
ejpam-6383	62	13	(	(	PUNCT
ejpam-6383	62	14	g+h	g+h	NOUN
ejpam-6383	62	15	)	)	PUNCT
ejpam-6383	62	16	=	=	SYM
ejpam-6383	62	17	v	v	NOUN
ejpam-6383	62	18	(	(	PUNCT
ejpam-6383	62	19	g)∪	g)∪	VERB
ejpam-6383	62	20	v	v	NUM
ejpam-6383	62	21	(	(	PUNCT
ejpam-6383	62	22	h	h	NOUN
ejpam-6383	62	23	)	)	PUNCT
ejpam-6383	62	24	and	and	CCONJ
ejpam-6383	62	25	edge	edge	NOUN
ejpam-6383	62	26	set	set	VERB
ejpam-6383	62	27	e(g+h	e(g+h	NUM
ejpam-6383	62	28	)	)	PUNCT
ejpam-6383	63	1	=	=	SYM
ejpam-6383	63	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-6383	63	3	{	{	PUNCT
ejpam-6383	63	4	uv	uv	NOUN
ejpam-6383	63	5	:	:	PUNCT
ejpam-6383	63	6	u	u	PROPN
ejpam-6383	63	7	∈	∈	PROPN
ejpam-6383	63	8	v	v	ADP
ejpam-6383	63	9	(	(	PUNCT
ejpam-6383	63	10	g	g	NOUN
ejpam-6383	63	11	)	)	PUNCT
ejpam-6383	63	12	,	,	PUNCT
ejpam-6383	63	13	v	v	X
ejpam-6383	63	14	∈	∈	PROPN
ejpam-6383	63	15	v	v	NOUN
ejpam-6383	63	16	(	(	PUNCT
ejpam-6383	63	17	h	h	NOUN
ejpam-6383	63	18	)	)	PUNCT
ejpam-6383	63	19	}	}	PUNCT
ejpam-6383	63	20	.	.	PUNCT
ejpam-6383	64	1	3	3	X
ejpam-6383	64	2	.	.	X
ejpam-6383	64	3	results	result	NOUN
ejpam-6383	64	4	we	we	PRON
ejpam-6383	64	5	shall	shall	AUX
ejpam-6383	64	6	now	now	ADV
ejpam-6383	64	7	define	define	VERB
ejpam-6383	64	8	the	the	DET
ejpam-6383	64	9	l	l	ADJ
ejpam-6383	64	10	-	-	ADJ
ejpam-6383	64	11	hop	hop	ADJ
ejpam-6383	64	12	independent	independent	ADJ
ejpam-6383	64	13	sequence	sequence	NOUN
ejpam-6383	64	14	and	and	CCONJ
ejpam-6383	64	15	l	l	NOUN
ejpam-6383	64	16	-	-	ADJ
ejpam-6383	64	17	hop	hop	ADJ
ejpam-6383	64	18	independence	independence	NOUN
ejpam-6383	64	19	number	number	NOUN
ejpam-6383	64	20	of	of	ADP
ejpam-6383	64	21	a	a	DET
ejpam-6383	64	22	graph	graph	NOUN
ejpam-6383	64	23	as	as	SCONJ
ejpam-6383	64	24	follows	follow	VERB
ejpam-6383	64	25	:	:	PUNCT
ejpam-6383	64	26	definition	definition	NOUN
ejpam-6383	64	27	1	1	NUM
ejpam-6383	64	28	.	.	PUNCT
ejpam-6383	65	1	let	let	VERB
ejpam-6383	65	2	g	g	PRON
ejpam-6383	65	3	be	be	AUX
ejpam-6383	65	4	a	a	DET
ejpam-6383	65	5	graph	graph	NOUN
ejpam-6383	65	6	.	.	PUNCT
ejpam-6383	66	1	a	a	DET
ejpam-6383	66	2	sequence	sequence	NOUN
ejpam-6383	66	3	of	of	ADP
ejpam-6383	66	4	distinct	distinct	ADJ
ejpam-6383	66	5	vertices	vertex	NOUN
ejpam-6383	66	6	q	q	NOUN
ejpam-6383	66	7	=	=	PUNCT
ejpam-6383	66	8	(	(	PUNCT
ejpam-6383	66	9	a1	a1	PROPN
ejpam-6383	66	10	,	,	PUNCT
ejpam-6383	66	11	a2	a2	PROPN
ejpam-6383	66	12	,	,	PUNCT
ejpam-6383	66	13	.	.	PUNCT
ejpam-6383	66	14	.	.	PUNCT
ejpam-6383	67	1	.	.	PUNCT
ejpam-6383	68	1	,	,	PUNCT
ejpam-6383	68	2	an	an	X
ejpam-6383	68	3	)	)	PUNCT
ejpam-6383	68	4	of	of	ADP
ejpam-6383	68	5	g	g	PROPN
ejpam-6383	68	6	is	be	AUX
ejpam-6383	68	7	called	call	VERB
ejpam-6383	68	8	an	an	DET
ejpam-6383	68	9	l	l	NOUN
ejpam-6383	68	10	-	-	ADJ
ejpam-6383	68	11	hop	hop	ADJ
ejpam-6383	68	12	independent	independent	ADJ
ejpam-6383	68	13	sequence	sequence	NOUN
ejpam-6383	68	14	if	if	SCONJ
ejpam-6383	68	15	n	n	NOUN
ejpam-6383	68	16	=	=	SYM
ejpam-6383	68	17	1	1	NUM
ejpam-6383	68	18	or	or	CCONJ
ejpam-6383	68	19	if	if	SCONJ
ejpam-6383	68	20	dg(ai	dg(ai	PROPN
ejpam-6383	68	21	,	,	PUNCT
ejpam-6383	68	22	aj	aj	PROPN
ejpam-6383	68	23	)	)	PUNCT
ejpam-6383	68	24	̸=	̸=	PROPN
ejpam-6383	68	25	2	2	NUM
ejpam-6383	68	26	for	for	ADP
ejpam-6383	68	27	each	each	DET
ejpam-6383	68	28	i	i	PRON
ejpam-6383	68	29	̸=	̸=	PROPN
ejpam-6383	68	30	j	j	PROPN
ejpam-6383	68	31	,	,	PUNCT
ejpam-6383	68	32	where	where	SCONJ
ejpam-6383	68	33	i	i	PRON
ejpam-6383	68	34	,	,	PUNCT
ejpam-6383	68	35	j	j	PROPN
ejpam-6383	68	36	∈	∈	PROPN
ejpam-6383	68	37	{	{	PUNCT
ejpam-6383	68	38	1	1	NUM
ejpam-6383	68	39	,	,	PUNCT
ejpam-6383	68	40	2	2	NUM
ejpam-6383	68	41	,	,	PUNCT
ejpam-6383	68	42	.	.	PUNCT
ejpam-6383	68	43	.	.	PUNCT
ejpam-6383	69	1	.	.	PUNCT
ejpam-6383	69	2	,	,	PUNCT
ejpam-6383	70	1	n	n	CCONJ
ejpam-6383	70	2	}	}	PUNCT
ejpam-6383	70	3	and	and	CCONJ
ejpam-6383	70	4	ng[as]\	ng[as]\	PRON
ejpam-6383	70	5	s−1⋃	s−1⋃	PROPN
ejpam-6383	70	6	t=1	t=1	PROPN
ejpam-6383	70	7	ng(at	ng(at	PROPN
ejpam-6383	70	8	)	)	PUNCT
ejpam-6383	70	9	̸=	̸=	PROPN
ejpam-6383	70	10	∅	∅	NOUN
ejpam-6383	70	11	for	for	ADP
ejpam-6383	70	12	each	each	DET
ejpam-6383	70	13	s	s	X
ejpam-6383	70	14	∈	∈	PROPN
ejpam-6383	70	15	{	{	PUNCT
ejpam-6383	70	16	2	2	NUM
ejpam-6383	70	17	,	,	PUNCT
ejpam-6383	70	18	.	.	PUNCT
ejpam-6383	70	19	.	.	PUNCT
ejpam-6383	71	1	.	.	PUNCT
ejpam-6383	71	2	,	,	PUNCT
ejpam-6383	71	3	n	n	CCONJ
ejpam-6383	71	4	}	}	PUNCT
ejpam-6383	71	5	.	.	PUNCT
ejpam-6383	72	1	the	the	DET
ejpam-6383	72	2	lhop	lhop	ADJ
ejpam-6383	72	3	independence	independence	NOUN
ejpam-6383	72	4	number	number	NOUN
ejpam-6383	72	5	of	of	ADP
ejpam-6383	72	6	g	g	NOUN
ejpam-6383	72	7	,	,	PUNCT
ejpam-6383	72	8	denoted	denote	VERB
ejpam-6383	72	9	by	by	ADP
ejpam-6383	72	10	αlh(g	αlh(g	NOUN
ejpam-6383	72	11	)	)	PUNCT
ejpam-6383	72	12	,	,	PUNCT
ejpam-6383	72	13	is	be	AUX
ejpam-6383	72	14	the	the	DET
ejpam-6383	72	15	maximum	maximum	ADJ
ejpam-6383	72	16	length	length	NOUN
ejpam-6383	72	17	among	among	ADP
ejpam-6383	72	18	all	all	DET
ejpam-6383	72	19	l	l	ADJ
ejpam-6383	72	20	-	-	ADJ
ejpam-6383	72	21	hop	hop	ADJ
ejpam-6383	72	22	independent	independent	ADJ
ejpam-6383	72	23	sequences	sequence	NOUN
ejpam-6383	72	24	in	in	ADP
ejpam-6383	72	25	g.	g.	PROPN
ejpam-6383	72	26	moreover	moreover	ADV
ejpam-6383	72	27	,	,	PUNCT
ejpam-6383	72	28	we	we	PRON
ejpam-6383	72	29	call	call	VERB
ejpam-6383	72	30	q̂	q̂	PUNCT
ejpam-6383	72	31	=	=	SYM
ejpam-6383	72	32	{	{	PUNCT
ejpam-6383	72	33	a1	a1	PROPN
ejpam-6383	72	34	,	,	PUNCT
ejpam-6383	72	35	a2	a2	PROPN
ejpam-6383	72	36	,	,	PUNCT
ejpam-6383	72	37	·	·	PUNCT
ejpam-6383	72	38	·	·	PUNCT
ejpam-6383	72	39	·	·	PUNCT
ejpam-6383	72	40	,	,	PUNCT
ejpam-6383	72	41	ak	ak	PROPN
ejpam-6383	72	42	}	}	PUNCT
ejpam-6383	72	43	an	an	DET
ejpam-6383	72	44	l−hop	l−hop	NOUN
ejpam-6383	72	45	independent	independent	ADJ
ejpam-6383	72	46	set	set	NOUN
ejpam-6383	72	47	of	of	ADP
ejpam-6383	72	48	g.	g.	PROPN
ejpam-6383	72	49	example	example	NOUN
ejpam-6383	72	50	1	1	X
ejpam-6383	72	51	.	.	X
ejpam-6383	72	52	consider	consider	VERB
ejpam-6383	72	53	the	the	DET
ejpam-6383	72	54	graph	graph	NOUN
ejpam-6383	72	55	in	in	ADP
ejpam-6383	72	56	figure	figure	NOUN
ejpam-6383	72	57	1	1	NUM
ejpam-6383	72	58	.	.	PUNCT
ejpam-6383	73	1	let	let	VERB
ejpam-6383	73	2	l	l	NOUN
ejpam-6383	73	3	=	=	SYM
ejpam-6383	73	4	(	(	PUNCT
ejpam-6383	73	5	a1	a1	PROPN
ejpam-6383	73	6	,	,	PUNCT
ejpam-6383	73	7	a2	a2	PROPN
ejpam-6383	73	8	)	)	PUNCT
ejpam-6383	73	9	.	.	PUNCT
ejpam-6383	74	1	then	then	ADV
ejpam-6383	74	2	dp4(a1	dp4(a1	PROPN
ejpam-6383	74	3	,	,	PUNCT
ejpam-6383	74	4	a2	a2	PROPN
ejpam-6383	74	5	)	)	PUNCT
ejpam-6383	74	6	=	=	SYM
ejpam-6383	74	7	1	1	X
ejpam-6383	74	8	.	.	X
ejpam-6383	74	9	observe	observe	VERB
ejpam-6383	74	10	that	that	SCONJ
ejpam-6383	74	11	np4(a1	np4(a1	X
ejpam-6383	74	12	)	)	PUNCT
ejpam-6383	74	13	=	=	SYM
ejpam-6383	74	14	{	{	PUNCT
ejpam-6383	74	15	a2	a2	PROPN
ejpam-6383	74	16	}	}	PUNCT
ejpam-6383	74	17	and	and	CCONJ
ejpam-6383	74	18	np4	np4	PROPN
ejpam-6383	74	19	[	[	X
ejpam-6383	74	20	a2	a2	X
ejpam-6383	74	21	]	]	X
ejpam-6383	74	22	=	=	SYM
ejpam-6383	74	23	{	{	PUNCT
ejpam-6383	74	24	a1	a1	PROPN
ejpam-6383	74	25	,	,	PUNCT
ejpam-6383	74	26	a2	a2	PROPN
ejpam-6383	74	27	,	,	PUNCT
ejpam-6383	74	28	a3	a3	NOUN
ejpam-6383	74	29	}	}	PUNCT
ejpam-6383	74	30	.	.	PUNCT
ejpam-6383	75	1	thus	thus	ADV
ejpam-6383	75	2	,	,	PUNCT
ejpam-6383	75	3	np4	np4	PROPN
ejpam-6383	75	4	[	[	X
ejpam-6383	75	5	a2]\np4(a1	a2]\np4(a1	INTJ
ejpam-6383	75	6	)	)	PUNCT
ejpam-6383	75	7	=	=	SYM
ejpam-6383	75	8	{	{	PUNCT
ejpam-6383	75	9	a1	a1	PROPN
ejpam-6383	75	10	,	,	PUNCT
ejpam-6383	75	11	a2	a2	PROPN
ejpam-6383	75	12	,	,	PUNCT
ejpam-6383	75	13	a3}\{a2	a3}\{a2	NOUN
ejpam-6383	75	14	}	}	PUNCT
ejpam-6383	75	15	=	=	SYM
ejpam-6383	75	16	{	{	PUNCT
ejpam-6383	75	17	a1	a1	NOUN
ejpam-6383	75	18	,	,	PUNCT
ejpam-6383	75	19	a3	a3	NOUN
ejpam-6383	75	20	}	}	PUNCT
ejpam-6383	75	21	=	=	SYM
ejpam-6383	75	22	̸	̸	X
ejpam-6383	75	23	∅.	∅.	VERB
ejpam-6383	75	24	therefore	therefore	ADV
ejpam-6383	75	25	,	,	PUNCT
ejpam-6383	75	26	l	l	NOUN
ejpam-6383	75	27	=	=	SYM
ejpam-6383	75	28	(	(	PUNCT
ejpam-6383	75	29	a1	a1	PROPN
ejpam-6383	75	30	,	,	PUNCT
ejpam-6383	75	31	a2	a2	PROPN
ejpam-6383	75	32	)	)	PUNCT
ejpam-6383	75	33	is	be	AUX
ejpam-6383	75	34	an	an	DET
ejpam-6383	75	35	l	l	ADJ
ejpam-6383	75	36	-	-	ADJ
ejpam-6383	75	37	hop	hop	ADJ
ejpam-6383	75	38	independent	independent	ADJ
ejpam-6383	75	39	sequence	sequence	NOUN
ejpam-6383	75	40	of	of	ADP
ejpam-6383	75	41	p4	p4	ADJ
ejpam-6383	75	42	,	,	PUNCT
ejpam-6383	75	43	and	and	CCONJ
ejpam-6383	75	44	so	so	ADV
ejpam-6383	75	45	αlh(p4	αlh(p4	NOUN
ejpam-6383	75	46	)	)	PUNCT
ejpam-6383	75	47	≥	≥	NOUN
ejpam-6383	76	1	2	2	NUM
ejpam-6383	76	2	.	.	PUNCT
ejpam-6383	76	3	now	now	ADV
ejpam-6383	76	4	,	,	PUNCT
ejpam-6383	76	5	since	since	SCONJ
ejpam-6383	76	6	dp4(a1	dp4(a1	NOUN
ejpam-6383	76	7	,	,	PUNCT
ejpam-6383	76	8	a3	a3	NOUN
ejpam-6383	76	9	)	)	PUNCT
ejpam-6383	76	10	=	=	SYM
ejpam-6383	76	11	2	2	NUM
ejpam-6383	76	12	,	,	PUNCT
ejpam-6383	76	13	it	it	PRON
ejpam-6383	76	14	follows	follow	VERB
ejpam-6383	76	15	that	that	SCONJ
ejpam-6383	76	16	αlh(p4	αlh(p4	NOUN
ejpam-6383	76	17	)	)	PUNCT
ejpam-6383	76	18	̸=	̸=	PROPN
ejpam-6383	76	19	4	4	NUM
ejpam-6383	76	20	.	.	PUNCT
ejpam-6383	77	1	since	since	SCONJ
ejpam-6383	77	2	dp4(a1	dp4(a1	NOUN
ejpam-6383	77	3	,	,	PUNCT
ejpam-6383	77	4	a3	a3	NOUN
ejpam-6383	77	5	)	)	PUNCT
ejpam-6383	77	6	=	=	SYM
ejpam-6383	77	7	2	2	NUM
ejpam-6383	77	8	=	=	SYM
ejpam-6383	77	9	dp4(a2	dp4(a2	NOUN
ejpam-6383	77	10	,	,	PUNCT
ejpam-6383	77	11	a4	a4	NOUN
ejpam-6383	77	12	)	)	PUNCT
ejpam-6383	77	13	,	,	PUNCT
ejpam-6383	77	14	it	it	PRON
ejpam-6383	77	15	follows	follow	VERB
ejpam-6383	77	16	that	that	SCONJ
ejpam-6383	77	17	l	l	NOUN
ejpam-6383	77	18	is	be	AUX
ejpam-6383	77	19	a	a	DET
ejpam-6383	77	20	maximum	maximum	ADJ
ejpam-6383	77	21	l	l	NOUN
ejpam-6383	77	22	-	-	ADJ
ejpam-6383	77	23	hop	hop	ADJ
ejpam-6383	77	24	independent	independent	ADJ
ejpam-6383	77	25	sequence	sequence	NOUN
ejpam-6383	77	26	of	of	ADP
ejpam-6383	77	27	p4	p4	ADJ
ejpam-6383	77	28	.	.	PUNCT
ejpam-6383	78	1	therefore	therefore	ADV
ejpam-6383	78	2	,	,	PUNCT
ejpam-6383	78	3	αlh(p4	αlh(p4	NOUN
ejpam-6383	78	4	)	)	PUNCT
ejpam-6383	78	5	=	=	SYM
ejpam-6383	78	6	2	2	X
ejpam-6383	78	7	.	.	X
ejpam-6383	78	8	a1	a1	NOUN
ejpam-6383	78	9	a2	a2	PROPN
ejpam-6383	78	10	a3	a3	PROPN
ejpam-6383	78	11	a4p4	a4p4	X
ejpam-6383	78	12	:	:	PUNCT
ejpam-6383	78	13	figure	figure	NOUN
ejpam-6383	78	14	1	1	NUM
ejpam-6383	78	15	:	:	PUNCT
ejpam-6383	78	16	a	a	DET
ejpam-6383	78	17	path	path	NOUN
ejpam-6383	78	18	graph	graph	NOUN
ejpam-6383	78	19	of	of	ADP
ejpam-6383	78	20	order	order	NOUN
ejpam-6383	78	21	4	4	NUM
ejpam-6383	78	22	.	.	PUNCT
ejpam-6383	78	23	k.	k.	PROPN
ejpam-6383	78	24	maharajul	maharajul	PROPN
ejpam-6383	78	25	,	,	PUNCT
ejpam-6383	78	26	j.	j.	PROPN
ejpam-6383	78	27	a.	a.	PROPN
ejpam-6383	78	28	hassan	hassan	PROPN
ejpam-6383	78	29	,	,	PUNCT
ejpam-6383	78	30	l.	l.	PROPN
ejpam-6383	78	31	laja	laja	PROPN
ejpam-6383	78	32	/	/	SYM
ejpam-6383	78	33	eur	eur	PROPN
ejpam-6383	78	34	.	.	PUNCT
ejpam-6383	79	1	j.	j.	PROPN
ejpam-6383	79	2	pure	pure	PROPN
ejpam-6383	79	3	appl	appl	PROPN
ejpam-6383	79	4	.	.	PROPN
ejpam-6383	79	5	math	math	PROPN
ejpam-6383	79	6	,	,	PUNCT
ejpam-6383	79	7	18	18	NUM
ejpam-6383	79	8	(	(	PUNCT
ejpam-6383	79	9	3	3	NUM
ejpam-6383	79	10	)	)	PUNCT
ejpam-6383	79	11	(	(	PUNCT
ejpam-6383	79	12	2025	2025	NUM
ejpam-6383	79	13	)	)	PUNCT
ejpam-6383	79	14	,	,	PUNCT
ejpam-6383	79	15	6383	6383	NUM
ejpam-6383	79	16	4	4	NUM
ejpam-6383	79	17	of	of	ADP
ejpam-6383	79	18	10	10	NUM
ejpam-6383	79	19	theorem	theorem	NOUN
ejpam-6383	79	20	1	1	NUM
ejpam-6383	79	21	.	.	PUNCT
ejpam-6383	80	1	let	let	VERB
ejpam-6383	80	2	g	g	PRON
ejpam-6383	80	3	be	be	AUX
ejpam-6383	80	4	a	a	DET
ejpam-6383	80	5	graph	graph	NOUN
ejpam-6383	80	6	.	.	PUNCT
ejpam-6383	81	1	then	then	ADV
ejpam-6383	81	2	i.	i.	PROPN
ejpam-6383	81	3	αlh(g	αlh(g	PROPN
ejpam-6383	81	4	)	)	PUNCT
ejpam-6383	81	5	≤	≤	NOUN
ejpam-6383	81	6	αh(g	αh(g	NOUN
ejpam-6383	81	7	)	)	PUNCT
ejpam-6383	81	8	;	;	PUNCT
ejpam-6383	81	9	ii	ii	X
ejpam-6383	81	10	.	.	PROPN
ejpam-6383	81	11	1	1	NUM
ejpam-6383	81	12	≤	≤	NUM
ejpam-6383	81	13	αlh(g	αlh(g	NOUN
ejpam-6383	81	14	)	)	PUNCT
ejpam-6383	81	15	≤	≤	NUM
ejpam-6383	81	16	|v	|v	X
ejpam-6383	81	17	(	(	PUNCT
ejpam-6383	81	18	g)|	g)|	NOUN
ejpam-6383	81	19	;	;	PUNCT
ejpam-6383	81	20	and	and	CCONJ
ejpam-6383	81	21	iii	iii	X
ejpam-6383	81	22	.	.	PROPN
ejpam-6383	82	1	αlh(g	αlh(g	NOUN
ejpam-6383	82	2	)	)	PUNCT
ejpam-6383	82	3	≥	≥	NOUN
ejpam-6383	82	4	αℓh(g	αℓh(g	NOUN
ejpam-6383	82	5	)	)	PUNCT
ejpam-6383	82	6	.	.	PUNCT
ejpam-6383	83	1	proof	proof	NOUN
ejpam-6383	83	2	.	.	PUNCT
ejpam-6383	84	1	[	[	X
ejpam-6383	84	2	i.	i.	X
ejpam-6383	84	3	]	]	X
ejpam-6383	84	4	let	let	VERB
ejpam-6383	84	5	g	g	PRON
ejpam-6383	84	6	be	be	AUX
ejpam-6383	84	7	a	a	DET
ejpam-6383	84	8	graph	graph	NOUN
ejpam-6383	84	9	and	and	CCONJ
ejpam-6383	84	10	let	let	VERB
ejpam-6383	84	11	d	d	PRON
ejpam-6383	84	12	be	be	AUX
ejpam-6383	84	13	a	a	DET
ejpam-6383	84	14	maximum	maximum	ADJ
ejpam-6383	84	15	l	l	NOUN
ejpam-6383	84	16	-	-	ADJ
ejpam-6383	84	17	hop	hop	ADJ
ejpam-6383	84	18	independent	independent	ADJ
ejpam-6383	84	19	sequence	sequence	NOUN
ejpam-6383	84	20	of	of	ADP
ejpam-6383	84	21	g.	g.	PROPN
ejpam-6383	84	22	then	then	ADV
ejpam-6383	84	23	αlh(g	αlh(g	NUM
ejpam-6383	84	24	)	)	PUNCT
ejpam-6383	84	25	=	=	SYM
ejpam-6383	84	26	|d̂|	|d̂|	PROPN
ejpam-6383	84	27	and	and	CCONJ
ejpam-6383	84	28	d̂	d̂	PROPN
ejpam-6383	84	29	is	be	AUX
ejpam-6383	84	30	a	a	DET
ejpam-6383	84	31	hop	hop	NOUN
ejpam-6383	84	32	independent	independent	ADJ
ejpam-6383	84	33	set	set	NOUN
ejpam-6383	84	34	of	of	ADP
ejpam-6383	84	35	g	g	NOUN
ejpam-6383	84	36	,	,	PUNCT
ejpam-6383	84	37	where	where	SCONJ
ejpam-6383	84	38	d̂	d̂	PRON
ejpam-6383	84	39	is	be	AUX
ejpam-6383	84	40	a	a	DET
ejpam-6383	84	41	corresponding	corresponding	ADJ
ejpam-6383	84	42	set	set	NOUN
ejpam-6383	84	43	of	of	ADP
ejpam-6383	84	44	d.	d.	PROPN
ejpam-6383	84	45	since	since	SCONJ
ejpam-6383	84	46	,	,	PUNCT
ejpam-6383	84	47	αh(g	αh(g	NOUN
ejpam-6383	84	48	)	)	PUNCT
ejpam-6383	84	49	is	be	AUX
ejpam-6383	84	50	the	the	DET
ejpam-6383	84	51	maximum	maximum	ADJ
ejpam-6383	84	52	cardinality	cardinality	NOUN
ejpam-6383	84	53	among	among	ADP
ejpam-6383	84	54	all	all	DET
ejpam-6383	84	55	hop	hop	NOUN
ejpam-6383	84	56	independent	independent	ADJ
ejpam-6383	84	57	sets	set	NOUN
ejpam-6383	84	58	in	in	ADP
ejpam-6383	84	59	g	g	NOUN
ejpam-6383	84	60	,	,	PUNCT
ejpam-6383	84	61	it	it	PRON
ejpam-6383	84	62	follows	follow	VERB
ejpam-6383	84	63	that	that	SCONJ
ejpam-6383	84	64	αh(g	αh(g	NOUN
ejpam-6383	84	65	)	)	PUNCT
ejpam-6383	84	66	≥	≥	NUM
ejpam-6383	84	67	|d̂	|d̂	NOUN
ejpam-6383	84	68	=	=	SYM
ejpam-6383	84	69	αlh(g	αlh(g	NOUN
ejpam-6383	84	70	)	)	PUNCT
ejpam-6383	84	71	.	.	PUNCT
ejpam-6383	85	1	[	[	X
ejpam-6383	85	2	ii	ii	X
ejpam-6383	85	3	.	.	PUNCT
ejpam-6383	85	4	]	]	PUNCT
ejpam-6383	86	1	since	since	SCONJ
ejpam-6383	86	2	any	any	DET
ejpam-6383	86	3	sequence	sequence	NOUN
ejpam-6383	86	4	(	(	PUNCT
ejpam-6383	86	5	v	v	NOUN
ejpam-6383	86	6	)	)	PUNCT
ejpam-6383	86	7	,	,	PUNCT
ejpam-6383	86	8	where	where	SCONJ
ejpam-6383	86	9	v	v	X
ejpam-6383	86	10	∈	∈	PROPN
ejpam-6383	86	11	v	v	NOUN
ejpam-6383	86	12	(	(	PUNCT
ejpam-6383	86	13	g	g	NOUN
ejpam-6383	86	14	)	)	PUNCT
ejpam-6383	86	15	,	,	PUNCT
ejpam-6383	86	16	is	be	AUX
ejpam-6383	86	17	an	an	DET
ejpam-6383	86	18	l	l	ADJ
ejpam-6383	86	19	-	-	ADJ
ejpam-6383	86	20	hop	hop	ADJ
ejpam-6383	86	21	independent	independent	ADJ
ejpam-6383	86	22	sequence	sequence	NOUN
ejpam-6383	86	23	of	of	ADP
ejpam-6383	86	24	g	g	NOUN
ejpam-6383	86	25	,	,	PUNCT
ejpam-6383	86	26	we	we	PRON
ejpam-6383	86	27	have	have	VERB
ejpam-6383	86	28	αlh(g	αlh(g	NOUN
ejpam-6383	86	29	)	)	PUNCT
ejpam-6383	86	30	≥	≥	NOUN
ejpam-6383	86	31	1	1	NUM
ejpam-6383	86	32	.	.	PUNCT
ejpam-6383	87	1	since	since	SCONJ
ejpam-6383	87	2	αh(g	αh(g	NOUN
ejpam-6383	87	3	)	)	PUNCT
ejpam-6383	87	4	≤	≤	NUM
ejpam-6383	87	5	|v	|v	X
ejpam-6383	87	6	(	(	PUNCT
ejpam-6383	87	7	g)|	g)|	INTJ
ejpam-6383	87	8	,	,	PUNCT
ejpam-6383	87	9	it	it	PRON
ejpam-6383	87	10	follows	follow	VERB
ejpam-6383	87	11	that	that	SCONJ
ejpam-6383	87	12	αlh(g	αlh(g	NUM
ejpam-6383	87	13	)	)	PUNCT
ejpam-6383	87	14	≤	≤	NOUN
ejpam-6383	87	15	|v	|v	X
ejpam-6383	87	16	(	(	PUNCT
ejpam-6383	87	17	g)|	g)|	NOUN
ejpam-6383	87	18	by	by	ADP
ejpam-6383	87	19	(	(	PUNCT
ejpam-6383	87	20	i	i	NOUN
ejpam-6383	87	21	)	)	PUNCT
ejpam-6383	87	22	.	.	PUNCT
ejpam-6383	88	1	consequently	consequently	ADV
ejpam-6383	88	2	,	,	PUNCT
ejpam-6383	88	3	1	1	NUM
ejpam-6383	88	4	≤	≤	NUM
ejpam-6383	88	5	αlh(g	αlh(g	NOUN
ejpam-6383	88	6	)	)	PUNCT
ejpam-6383	88	7	≤	≤	NUM
ejpam-6383	88	8	|v	|v	X
ejpam-6383	88	9	(	(	PUNCT
ejpam-6383	88	10	g)|	g)|	NOUN
ejpam-6383	88	11	.	.	PUNCT
ejpam-6383	89	1	[	[	X
ejpam-6383	89	2	iii	iii	X
ejpam-6383	89	3	.	.	PUNCT
ejpam-6383	89	4	]	]	PUNCT
ejpam-6383	90	1	let	let	VERB
ejpam-6383	90	2	s	s	PRON
ejpam-6383	90	3	=	=	PUNCT
ejpam-6383	90	4	(	(	PUNCT
ejpam-6383	90	5	v1	v1	PROPN
ejpam-6383	90	6	,	,	PUNCT
ejpam-6383	90	7	v2	v2	NOUN
ejpam-6383	90	8	,	,	PUNCT
ejpam-6383	90	9	.	.	PUNCT
ejpam-6383	90	10	.	.	PUNCT
ejpam-6383	91	1	.	.	PUNCT
ejpam-6383	92	1	,	,	PUNCT
ejpam-6383	92	2	vn	vn	AUX
ejpam-6383	92	3	)	)	PUNCT
ejpam-6383	92	4	be	be	AUX
ejpam-6383	92	5	a	a	DET
ejpam-6383	92	6	maximum	maximum	ADJ
ejpam-6383	92	7	legal	legal	ADJ
ejpam-6383	92	8	hop	hop	NOUN
ejpam-6383	92	9	independent	independent	ADJ
ejpam-6383	92	10	sequence	sequence	NOUN
ejpam-6383	92	11	in	in	ADP
ejpam-6383	92	12	g.	g.	PROPN
ejpam-6383	93	1	then	then	ADV
ejpam-6383	93	2	ng[vi]\	ng[vi]\	PROPN
ejpam-6383	93	3	i−1⋃	i−1⋃	PROPN
ejpam-6383	93	4	j=1	j=1	PROPN
ejpam-6383	93	5	ng[vj	ng[vj	PROPN
ejpam-6383	93	6	]	]	PUNCT
ejpam-6383	94	1	̸=	̸=	PROPN
ejpam-6383	94	2	∅	∅	NOUN
ejpam-6383	94	3	for	for	ADP
ejpam-6383	94	4	each	each	DET
ejpam-6383	94	5	i	i	PRON
ejpam-6383	94	6	∈	∈	PROPN
ejpam-6383	94	7	{	{	PUNCT
ejpam-6383	94	8	2	2	NUM
ejpam-6383	94	9	,	,	PUNCT
ejpam-6383	94	10	3	3	NUM
ejpam-6383	94	11	,	,	PUNCT
ejpam-6383	94	12	.	.	PUNCT
ejpam-6383	94	13	.	.	PUNCT
ejpam-6383	94	14	.	.	PUNCT
ejpam-6383	94	15	,	,	PUNCT
ejpam-6383	94	16	n	n	CCONJ
ejpam-6383	94	17	}	}	PUNCT
ejpam-6383	94	18	.	.	PUNCT
ejpam-6383	95	1	since	since	SCONJ
ejpam-6383	95	2	ng(a	ng(a	NOUN
ejpam-6383	95	3	)	)	PUNCT
ejpam-6383	95	4	⊆	⊆	NUM
ejpam-6383	95	5	ng[a	ng[a	NOUN
ejpam-6383	95	6	]	]	PUNCT
ejpam-6383	95	7	for	for	ADP
ejpam-6383	95	8	all	all	DET
ejpam-6383	95	9	a	a	DET
ejpam-6383	95	10	∈	∈	PROPN
ejpam-6383	95	11	v	v	NOUN
ejpam-6383	95	12	(	(	PUNCT
ejpam-6383	95	13	g	g	NOUN
ejpam-6383	95	14	)	)	PUNCT
ejpam-6383	95	15	,	,	PUNCT
ejpam-6383	95	16	it	it	PRON
ejpam-6383	95	17	follows	follow	VERB
ejpam-6383	95	18	that	that	SCONJ
ejpam-6383	95	19	∅	∅	NOUN
ejpam-6383	95	20	̸=	̸=	PROPN
ejpam-6383	95	21	ng[vi]\	ng[vi]\	NOUN
ejpam-6383	95	22	i−1⋃	i−1⋃	PROPN
ejpam-6383	95	23	j=1	j=1	PROPN
ejpam-6383	95	24	ng[vj	ng[vj	PRON
ejpam-6383	95	25	]	]	PUNCT
ejpam-6383	96	1	⊆	⊆	NUM
ejpam-6383	96	2	ng[vi]\	ng[vi]\	NOUN
ejpam-6383	96	3	i−1⋃	i−1⋃	PROPN
ejpam-6383	96	4	j=1	j=1	PROPN
ejpam-6383	96	5	ng(vj	ng(vj	PROPN
ejpam-6383	96	6	)	)	PUNCT
ejpam-6383	96	7	.	.	PUNCT
ejpam-6383	97	1	hence	hence	ADV
ejpam-6383	97	2	,	,	PUNCT
ejpam-6383	97	3	ng[vi]\	ng[vi]\	PROPN
ejpam-6383	97	4	i−1⋃	i−1⋃	PROPN
ejpam-6383	97	5	j=1	j=1	PROPN
ejpam-6383	97	6	ng(vj	ng(vj	PROPN
ejpam-6383	97	7	)	)	PUNCT
ejpam-6383	97	8	̸=	̸=	PROPN
ejpam-6383	97	9	∅	∅	NOUN
ejpam-6383	97	10	for	for	ADP
ejpam-6383	97	11	each	each	DET
ejpam-6383	97	12	i	i	PRON
ejpam-6383	97	13	∈	∈	PROPN
ejpam-6383	97	14	{	{	PUNCT
ejpam-6383	97	15	2	2	NUM
ejpam-6383	97	16	,	,	PUNCT
ejpam-6383	97	17	3	3	NUM
ejpam-6383	97	18	,	,	PUNCT
ejpam-6383	97	19	.	.	PUNCT
ejpam-6383	97	20	.	.	PUNCT
ejpam-6383	97	21	.	.	PUNCT
ejpam-6383	97	22	,	,	PUNCT
ejpam-6383	97	23	n	n	CCONJ
ejpam-6383	97	24	}	}	PUNCT
ejpam-6383	97	25	.	.	PUNCT
ejpam-6383	98	1	therefore	therefore	ADV
ejpam-6383	98	2	,	,	PUNCT
ejpam-6383	98	3	s	s	VERB
ejpam-6383	98	4	is	be	AUX
ejpam-6383	98	5	an	an	DET
ejpam-6383	98	6	l	l	NOUN
ejpam-6383	98	7	-	-	NOUN
ejpam-6383	98	8	sequence	sequence	NOUN
ejpam-6383	98	9	in	in	ADP
ejpam-6383	98	10	g.	g.	PROPN
ejpam-6383	98	11	since	since	SCONJ
ejpam-6383	98	12	ŝ	ŝ	NUM
ejpam-6383	98	13	is	be	AUX
ejpam-6383	98	14	a	a	DET
ejpam-6383	98	15	hop	hop	NOUN
ejpam-6383	98	16	independent	independent	ADJ
ejpam-6383	98	17	set	set	NOUN
ejpam-6383	98	18	of	of	ADP
ejpam-6383	98	19	g	g	NOUN
ejpam-6383	98	20	,	,	PUNCT
ejpam-6383	98	21	it	it	PRON
ejpam-6383	98	22	follows	follow	VERB
ejpam-6383	98	23	that	that	SCONJ
ejpam-6383	98	24	s	s	VERB
ejpam-6383	98	25	is	be	AUX
ejpam-6383	98	26	an	an	DET
ejpam-6383	98	27	l	l	ADJ
ejpam-6383	98	28	-	-	ADJ
ejpam-6383	98	29	hop	hop	ADJ
ejpam-6383	98	30	independent	independent	ADJ
ejpam-6383	98	31	sequence	sequence	NOUN
ejpam-6383	98	32	in	in	ADP
ejpam-6383	98	33	g.	g.	PROPN
ejpam-6383	98	34	since	since	SCONJ
ejpam-6383	98	35	αlh(g	αlh(g	NOUN
ejpam-6383	98	36	)	)	PUNCT
ejpam-6383	98	37	refers	refer	VERB
ejpam-6383	98	38	to	to	ADP
ejpam-6383	98	39	the	the	DET
ejpam-6383	98	40	maximum	maximum	ADJ
ejpam-6383	98	41	length	length	NOUN
ejpam-6383	98	42	of	of	ADP
ejpam-6383	98	43	an	an	DET
ejpam-6383	98	44	l	l	NOUN
ejpam-6383	98	45	-	-	ADJ
ejpam-6383	98	46	hop	hop	ADJ
ejpam-6383	98	47	independent	independent	ADJ
ejpam-6383	98	48	sequence	sequence	NOUN
ejpam-6383	98	49	in	in	ADP
ejpam-6383	98	50	g	g	PROPN
ejpam-6383	98	51	,	,	PUNCT
ejpam-6383	98	52	it	it	PRON
ejpam-6383	98	53	follows	follow	VERB
ejpam-6383	98	54	that	that	SCONJ
ejpam-6383	98	55	αlh(g	αlh(g	NUM
ejpam-6383	98	56	)	)	PUNCT
ejpam-6383	98	57	≥	≥	NOUN
ejpam-6383	98	58	|ŝ|	|ŝ|	PROPN
ejpam-6383	98	59	=	=	SYM
ejpam-6383	98	60	αℓh(g	αℓh(g	NOUN
ejpam-6383	98	61	)	)	PUNCT
ejpam-6383	98	62	.	.	PUNCT
ejpam-6383	99	1	remark	remark	PROPN
ejpam-6383	99	2	1	1	NUM
ejpam-6383	99	3	.	.	PUNCT
ejpam-6383	100	1	the	the	DET
ejpam-6383	100	2	strict	strict	ADJ
ejpam-6383	100	3	inequality	inequality	NOUN
ejpam-6383	100	4	of	of	ADP
ejpam-6383	100	5	theorem	theorem	NOUN
ejpam-6383	100	6	1(i	1(i	NUM
ejpam-6383	100	7	)	)	PUNCT
ejpam-6383	100	8	is	be	AUX
ejpam-6383	100	9	attainable	attainable	ADJ
ejpam-6383	100	10	.	.	PUNCT
ejpam-6383	101	1	moreover	moreover	ADV
ejpam-6383	101	2	,	,	PUNCT
ejpam-6383	101	3	the	the	DET
ejpam-6383	101	4	inequality	inequality	NOUN
ejpam-6383	101	5	is	be	AUX
ejpam-6383	101	6	also	also	ADV
ejpam-6383	101	7	attainable	attainable	ADJ
ejpam-6383	101	8	.	.	PUNCT
ejpam-6383	102	1	consider	consider	VERB
ejpam-6383	102	2	the	the	DET
ejpam-6383	102	3	following	follow	VERB
ejpam-6383	102	4	two	two	NUM
ejpam-6383	102	5	examples	example	NOUN
ejpam-6383	102	6	below	below	ADP
ejpam-6383	102	7	:	:	PUNCT
ejpam-6383	102	8	example	example	NOUN
ejpam-6383	102	9	2	2	X
ejpam-6383	102	10	.	.	X
ejpam-6383	102	11	consider	consider	VERB
ejpam-6383	102	12	the	the	DET
ejpam-6383	102	13	graph	graph	NOUN
ejpam-6383	102	14	g	g	NOUN
ejpam-6383	102	15	below	below	ADV
ejpam-6383	102	16	.	.	PUNCT
ejpam-6383	103	1	g	g	NOUN
ejpam-6383	103	2	:	:	PUNCT
ejpam-6383	104	1	x1	x1	PROPN
ejpam-6383	104	2	x2	x2	NOUN
ejpam-6383	104	3	x3	x3	PROPN
ejpam-6383	104	4	x4	x4	PROPN
ejpam-6383	104	5	let	let	VERB
ejpam-6383	104	6	s	s	PRON
ejpam-6383	104	7	=	=	PUNCT
ejpam-6383	104	8	{	{	PUNCT
ejpam-6383	104	9	x1	x1	PROPN
ejpam-6383	104	10	,	,	PUNCT
ejpam-6383	104	11	x2	x2	PROPN
ejpam-6383	104	12	,	,	PUNCT
ejpam-6383	104	13	x3	x3	ADJ
ejpam-6383	104	14	,	,	PUNCT
ejpam-6383	104	15	x4	x4	PROPN
ejpam-6383	104	16	}	}	PUNCT
ejpam-6383	104	17	.	.	PUNCT
ejpam-6383	105	1	then	then	ADV
ejpam-6383	105	2	s	s	VERB
ejpam-6383	105	3	is	be	AUX
ejpam-6383	105	4	a	a	DET
ejpam-6383	105	5	maximum	maximum	ADJ
ejpam-6383	105	6	hop	hop	NOUN
ejpam-6383	105	7	independent	independent	ADJ
ejpam-6383	105	8	set	set	NOUN
ejpam-6383	105	9	of	of	ADP
ejpam-6383	105	10	g.	g.	PROPN
ejpam-6383	105	11	thus	thus	ADV
ejpam-6383	105	12	,	,	PUNCT
ejpam-6383	105	13	αh(g	αh(g	NOUN
ejpam-6383	105	14	)	)	PUNCT
ejpam-6383	105	15	=	=	SYM
ejpam-6383	106	1	4	4	X
ejpam-6383	106	2	.	.	PUNCT
ejpam-6383	107	1	next	next	ADV
ejpam-6383	107	2	,	,	PUNCT
ejpam-6383	107	3	let	let	VERB
ejpam-6383	107	4	b	b	X
ejpam-6383	107	5	=	=	SYM
ejpam-6383	107	6	(	(	PUNCT
ejpam-6383	107	7	x1	x1	PROPN
ejpam-6383	107	8	,	,	PUNCT
ejpam-6383	107	9	x2	x2	PROPN
ejpam-6383	107	10	)	)	PUNCT
ejpam-6383	107	11	.	.	PUNCT
ejpam-6383	108	1	then	then	ADV
ejpam-6383	108	2	ng[x2	ng[x2	PROPN
ejpam-6383	108	3	]	]	X
ejpam-6383	108	4	=	=	SYM
ejpam-6383	108	5	v	v	X
ejpam-6383	108	6	(	(	PUNCT
ejpam-6383	108	7	g	g	NOUN
ejpam-6383	108	8	)	)	PUNCT
ejpam-6383	108	9	and	and	CCONJ
ejpam-6383	108	10	ng(x1	ng(x1	NOUN
ejpam-6383	108	11	)	)	PUNCT
ejpam-6383	108	12	=	=	PRON
ejpam-6383	108	13	{	{	PUNCT
ejpam-6383	108	14	x2	x2	PROPN
ejpam-6383	108	15	,	,	PUNCT
ejpam-6383	108	16	x3	x3	ADJ
ejpam-6383	108	17	,	,	PUNCT
ejpam-6383	108	18	x4	x4	PROPN
ejpam-6383	108	19	}	}	PUNCT
ejpam-6383	108	20	.	.	PUNCT
ejpam-6383	109	1	hence	hence	ADV
ejpam-6383	109	2	,	,	PUNCT
ejpam-6383	109	3	ng[x2	ng[x2	PROPN
ejpam-6383	109	4	]	]	PUNCT
ejpam-6383	109	5	\	\	PROPN
ejpam-6383	109	6	ng(x1	ng(x1	NOUN
ejpam-6383	109	7	)	)	PUNCT
ejpam-6383	109	8	=	=	PRON
ejpam-6383	109	9	{	{	PUNCT
ejpam-6383	109	10	x1	x1	PROPN
ejpam-6383	109	11	}	}	PUNCT
ejpam-6383	109	12	̸=	̸=	PROPN
ejpam-6383	109	13	∅	∅	NOUN
ejpam-6383	109	14	,	,	PUNCT
ejpam-6383	109	15	showing	show	VERB
ejpam-6383	109	16	that	that	SCONJ
ejpam-6383	109	17	b	b	NOUN
ejpam-6383	109	18	is	be	AUX
ejpam-6383	109	19	an	an	DET
ejpam-6383	109	20	l	l	ADJ
ejpam-6383	109	21	-	-	ADJ
ejpam-6383	109	22	hop	hop	ADJ
ejpam-6383	109	23	independent	independent	ADJ
ejpam-6383	109	24	sequence	sequence	NOUN
ejpam-6383	109	25	of	of	ADP
ejpam-6383	109	26	g.	g.	PROPN
ejpam-6383	109	27	since	since	SCONJ
ejpam-6383	109	28	ng(xi	ng(xi	PROPN
ejpam-6383	109	29	)	)	PUNCT
ejpam-6383	109	30	∪ng(xj	∪ng(xj	ADV
ejpam-6383	109	31	)	)	PUNCT
ejpam-6383	109	32	=	=	SYM
ejpam-6383	109	33	v	v	X
ejpam-6383	109	34	(	(	PUNCT
ejpam-6383	109	35	g	g	NOUN
ejpam-6383	109	36	)	)	PUNCT
ejpam-6383	109	37	for	for	ADP
ejpam-6383	109	38	all	all	DET
ejpam-6383	109	39	i	i	PROPN
ejpam-6383	109	40	,	,	PUNCT
ejpam-6383	109	41	j	j	PROPN
ejpam-6383	109	42	∈	∈	PROPN
ejpam-6383	109	43	{	{	PUNCT
ejpam-6383	109	44	1	1	NUM
ejpam-6383	109	45	,	,	PUNCT
ejpam-6383	109	46	2	2	NUM
ejpam-6383	109	47	,	,	PUNCT
ejpam-6383	109	48	3	3	NUM
ejpam-6383	109	49	,	,	PUNCT
ejpam-6383	109	50	4	4	NUM
ejpam-6383	109	51	}	}	PUNCT
ejpam-6383	109	52	,	,	PUNCT
ejpam-6383	109	53	where	where	SCONJ
ejpam-6383	109	54	i	i	PRON
ejpam-6383	109	55	̸=	̸=	PROPN
ejpam-6383	109	56	j	j	PROPN
ejpam-6383	109	57	,	,	PUNCT
ejpam-6383	109	58	it	it	PRON
ejpam-6383	109	59	follows	follow	VERB
ejpam-6383	109	60	that	that	SCONJ
ejpam-6383	109	61	b	b	NOUN
ejpam-6383	109	62	is	be	AUX
ejpam-6383	109	63	a	a	DET
ejpam-6383	109	64	maximum	maximum	ADJ
ejpam-6383	109	65	l	l	NOUN
ejpam-6383	109	66	-	-	ADJ
ejpam-6383	109	67	hop	hop	ADJ
ejpam-6383	109	68	independent	independent	ADJ
ejpam-6383	109	69	sequence	sequence	NOUN
ejpam-6383	109	70	of	of	ADP
ejpam-6383	109	71	g	g	PROPN
ejpam-6383	109	72	.	.	PUNCT
ejpam-6383	110	1	that	that	PRON
ejpam-6383	110	2	is	is	ADV
ejpam-6383	110	3	,	,	PUNCT
ejpam-6383	110	4	αlh(g	αlh(g	X
ejpam-6383	110	5	)	)	PUNCT
ejpam-6383	110	6	=	=	SYM
ejpam-6383	111	1	2	2	X
ejpam-6383	111	2	.	.	PUNCT
ejpam-6383	111	3	k.	k.	PROPN
ejpam-6383	111	4	maharajul	maharajul	PROPN
ejpam-6383	111	5	,	,	PUNCT
ejpam-6383	111	6	j.	j.	PROPN
ejpam-6383	111	7	a.	a.	PROPN
ejpam-6383	111	8	hassan	hassan	PROPN
ejpam-6383	111	9	,	,	PUNCT
ejpam-6383	111	10	l.	l.	PROPN
ejpam-6383	111	11	laja	laja	PROPN
ejpam-6383	111	12	/	/	SYM
ejpam-6383	111	13	eur	eur	PROPN
ejpam-6383	111	14	.	.	PUNCT
ejpam-6383	112	1	j.	j.	PROPN
ejpam-6383	112	2	pure	pure	PROPN
ejpam-6383	112	3	appl	appl	PROPN
ejpam-6383	112	4	.	.	PROPN
ejpam-6383	112	5	math	math	PROPN
ejpam-6383	112	6	,	,	PUNCT
ejpam-6383	112	7	18	18	NUM
ejpam-6383	112	8	(	(	PUNCT
ejpam-6383	112	9	3	3	NUM
ejpam-6383	112	10	)	)	PUNCT
ejpam-6383	112	11	(	(	PUNCT
ejpam-6383	112	12	2025	2025	NUM
ejpam-6383	112	13	)	)	PUNCT
ejpam-6383	112	14	,	,	PUNCT
ejpam-6383	112	15	6383	6383	NUM
ejpam-6383	112	16	5	5	NUM
ejpam-6383	112	17	of	of	ADP
ejpam-6383	112	18	10	10	NUM
ejpam-6383	112	19	example	example	NOUN
ejpam-6383	112	20	3	3	NUM
ejpam-6383	112	21	.	.	X
ejpam-6383	112	22	consider	consider	VERB
ejpam-6383	112	23	the	the	DET
ejpam-6383	112	24	graph	graph	NOUN
ejpam-6383	112	25	g′	g′	NOUN
ejpam-6383	112	26	below	below	ADV
ejpam-6383	112	27	.	.	PUNCT
ejpam-6383	113	1	g′	g′	NOUN
ejpam-6383	113	2	:	:	PUNCT
ejpam-6383	114	1	x1	x1	PROPN
ejpam-6383	114	2	x2	x2	NOUN
ejpam-6383	114	3	x3	x3	PROPN
ejpam-6383	114	4	x4	x4	PROPN
ejpam-6383	115	1	x5	x5	PROPN
ejpam-6383	115	2	x8	x8	PROPN
ejpam-6383	115	3	x9	x9	NOUN
ejpam-6383	115	4	x7	x7	VERB
ejpam-6383	115	5	x10	x10	NOUN
ejpam-6383	115	6	x11x6	x11x6	PROPN
ejpam-6383	115	7	x12	x12	NUM
ejpam-6383	115	8	let	let	VERB
ejpam-6383	115	9	p	p	NOUN
ejpam-6383	115	10	=	=	X
ejpam-6383	115	11	(	(	PUNCT
ejpam-6383	115	12	x1	x1	PROPN
ejpam-6383	115	13	,	,	PUNCT
ejpam-6383	115	14	x2	x2	PROPN
ejpam-6383	115	15	,	,	PUNCT
ejpam-6383	115	16	x5	x5	PROPN
ejpam-6383	115	17	,	,	PUNCT
ejpam-6383	115	18	x6	x6	PROPN
ejpam-6383	115	19	,	,	PUNCT
ejpam-6383	115	20	x8	x8	PROPN
ejpam-6383	115	21	,	,	PUNCT
ejpam-6383	115	22	x9	x9	PROPN
ejpam-6383	115	23	,	,	PUNCT
ejpam-6383	115	24	x11	x11	NOUN
ejpam-6383	115	25	,	,	PUNCT
ejpam-6383	115	26	x12	x12	NUM
ejpam-6383	115	27	)	)	PUNCT
ejpam-6383	115	28	and	and	CCONJ
ejpam-6383	115	29	let	let	VERB
ejpam-6383	115	30	p̂	p̂	NOUN
ejpam-6383	115	31	=	=	PUNCT
ejpam-6383	115	32	{	{	PUNCT
ejpam-6383	115	33	x1	x1	PROPN
ejpam-6383	115	34	,	,	PUNCT
ejpam-6383	115	35	x2	x2	PROPN
ejpam-6383	115	36	,	,	PUNCT
ejpam-6383	115	37	x5	x5	PROPN
ejpam-6383	115	38	,	,	PUNCT
ejpam-6383	115	39	x6	x6	PROPN
ejpam-6383	115	40	,	,	PUNCT
ejpam-6383	115	41	x8	x8	PROPN
ejpam-6383	115	42	,	,	PUNCT
ejpam-6383	115	43	x9	x9	PROPN
ejpam-6383	115	44	,	,	PUNCT
ejpam-6383	115	45	x11	x11	NOUN
ejpam-6383	115	46	,	,	PUNCT
ejpam-6383	115	47	x12	x12	NUM
ejpam-6383	115	48	}	}	PUNCT
ejpam-6383	115	49	.	.	PUNCT
ejpam-6383	116	1	then	then	ADV
ejpam-6383	116	2	p̂	p̂	NOUN
ejpam-6383	116	3	is	be	AUX
ejpam-6383	116	4	a	a	DET
ejpam-6383	116	5	maximum	maximum	ADJ
ejpam-6383	116	6	hop	hop	NOUN
ejpam-6383	116	7	independent	independent	ADJ
ejpam-6383	116	8	set	set	NOUN
ejpam-6383	116	9	of	of	ADP
ejpam-6383	116	10	g′	g′	NOUN
ejpam-6383	116	11	and	and	CCONJ
ejpam-6383	116	12	p	p	NOUN
ejpam-6383	116	13	is	be	AUX
ejpam-6383	116	14	a	a	DET
ejpam-6383	116	15	maximum	maximum	ADJ
ejpam-6383	116	16	l	l	NOUN
ejpam-6383	116	17	-	-	ADJ
ejpam-6383	116	18	hop	hop	ADJ
ejpam-6383	116	19	independent	independent	ADJ
ejpam-6383	116	20	sequence	sequence	NOUN
ejpam-6383	116	21	of	of	ADP
ejpam-6383	116	22	g′.	g′.	X
ejpam-6383	116	23	therefore	therefore	ADV
ejpam-6383	116	24	,	,	PUNCT
ejpam-6383	116	25	αh(g	αh(g	PRON
ejpam-6383	116	26	′	′	NOUN
ejpam-6383	116	27	)	)	PUNCT
ejpam-6383	116	28	=	=	SYM
ejpam-6383	116	29	8	8	NUM
ejpam-6383	116	30	=	=	SYM
ejpam-6383	116	31	αlh(g	αlh(g	NUM
ejpam-6383	116	32	′	′	NUM
ejpam-6383	116	33	)	)	PUNCT
ejpam-6383	116	34	.	.	PUNCT
ejpam-6383	117	1	we	we	PRON
ejpam-6383	117	2	shall	shall	AUX
ejpam-6383	117	3	now	now	ADV
ejpam-6383	117	4	state	state	VERB
ejpam-6383	117	5	the	the	DET
ejpam-6383	117	6	following	follow	VERB
ejpam-6383	117	7	remark	remark	NOUN
ejpam-6383	117	8	:	:	PUNCT
ejpam-6383	117	9	remark	remark	NOUN
ejpam-6383	117	10	2	2	NUM
ejpam-6383	117	11	.	.	PUNCT
ejpam-6383	118	1	let	let	VERB
ejpam-6383	118	2	g	g	PRON
ejpam-6383	118	3	be	be	AUX
ejpam-6383	118	4	a	a	DET
ejpam-6383	118	5	graph	graph	NOUN
ejpam-6383	118	6	.	.	PUNCT
ejpam-6383	119	1	then	then	ADV
ejpam-6383	119	2	each	each	PRON
ejpam-6383	119	3	of	of	ADP
ejpam-6383	119	4	the	the	DET
ejpam-6383	119	5	following	follow	VERB
ejpam-6383	119	6	holds	hold	VERB
ejpam-6383	119	7	:	:	PUNCT
ejpam-6383	119	8	(	(	PUNCT
ejpam-6383	119	9	i	i	NOUN
ejpam-6383	119	10	)	)	PUNCT
ejpam-6383	119	11	every	every	DET
ejpam-6383	119	12	legal	legal	ADJ
ejpam-6383	119	13	hop	hop	NOUN
ejpam-6383	119	14	independent	independent	ADJ
ejpam-6383	119	15	sequence	sequence	NOUN
ejpam-6383	119	16	of	of	ADP
ejpam-6383	119	17	g	g	PROPN
ejpam-6383	119	18	is	be	AUX
ejpam-6383	119	19	an	an	DET
ejpam-6383	119	20	l	l	ADJ
ejpam-6383	119	21	-	-	ADJ
ejpam-6383	119	22	hop	hop	ADJ
ejpam-6383	119	23	independent	independent	ADJ
ejpam-6383	119	24	sequence	sequence	NOUN
ejpam-6383	119	25	.	.	PUNCT
ejpam-6383	120	1	(	(	PUNCT
ejpam-6383	120	2	ii	ii	NOUN
ejpam-6383	120	3	)	)	PUNCT
ejpam-6383	120	4	every	every	DET
ejpam-6383	120	5	l	l	NOUN
ejpam-6383	120	6	-	-	ADJ
ejpam-6383	120	7	hop	hop	ADJ
ejpam-6383	120	8	independent	independent	ADJ
ejpam-6383	120	9	set	set	NOUN
ejpam-6383	120	10	is	be	AUX
ejpam-6383	120	11	a	a	DET
ejpam-6383	120	12	hop	hop	NOUN
ejpam-6383	120	13	independent	independent	ADJ
ejpam-6383	120	14	set	set	NOUN
ejpam-6383	120	15	,	,	PUNCT
ejpam-6383	120	16	however	however	ADV
ejpam-6383	120	17	,	,	PUNCT
ejpam-6383	120	18	the	the	DET
ejpam-6383	120	19	converse	converse	NOUN
ejpam-6383	120	20	need	need	AUX
ejpam-6383	120	21	not	not	PART
ejpam-6383	120	22	be	be	AUX
ejpam-6383	120	23	true	true	ADJ
ejpam-6383	120	24	.	.	PUNCT
ejpam-6383	121	1	proposition	proposition	NOUN
ejpam-6383	121	2	1	1	NUM
ejpam-6383	121	3	.	.	PUNCT
ejpam-6383	122	1	let	let	VERB
ejpam-6383	122	2	n	n	PRON
ejpam-6383	122	3	be	be	AUX
ejpam-6383	122	4	a	a	DET
ejpam-6383	122	5	positive	positive	ADJ
ejpam-6383	122	6	integer	integer	NOUN
ejpam-6383	122	7	.	.	PUNCT
ejpam-6383	123	1	then	then	ADV
ejpam-6383	123	2	αlh(kn	αlh(kn	X
ejpam-6383	123	3	)	)	PUNCT
ejpam-6383	123	4	=	=	PRON
ejpam-6383	123	5	{	{	PUNCT
ejpam-6383	123	6	1	1	NUM
ejpam-6383	123	7	if	if	SCONJ
ejpam-6383	123	8	n	n	CCONJ
ejpam-6383	123	9	=	=	SYM
ejpam-6383	123	10	1	1	NUM
ejpam-6383	123	11	2	2	NUM
ejpam-6383	123	12	if	if	SCONJ
ejpam-6383	123	13	n	n	PRON
ejpam-6383	123	14	≥	≥	NOUN
ejpam-6383	123	15	2	2	NUM
ejpam-6383	123	16	.	.	PUNCT
ejpam-6383	124	1	proof	proof	NOUN
ejpam-6383	124	2	.	.	PUNCT
ejpam-6383	125	1	clearly	clearly	ADV
ejpam-6383	125	2	,	,	PUNCT
ejpam-6383	125	3	αlh(k1	αlh(k1	PROPN
ejpam-6383	125	4	)	)	PUNCT
ejpam-6383	125	5	=	=	SYM
ejpam-6383	126	1	1	1	X
ejpam-6383	126	2	.	.	X
ejpam-6383	126	3	for	for	ADP
ejpam-6383	126	4	n	n	NOUN
ejpam-6383	126	5	=	=	SYM
ejpam-6383	126	6	2	2	NUM
ejpam-6383	126	7	,	,	PUNCT
ejpam-6383	126	8	let	let	VERB
ejpam-6383	126	9	v	v	NOUN
ejpam-6383	126	10	(	(	PUNCT
ejpam-6383	126	11	k2	k2	NOUN
ejpam-6383	126	12	)	)	PUNCT
ejpam-6383	126	13	=	=	SYM
ejpam-6383	126	14	{	{	PUNCT
ejpam-6383	126	15	v1	v1	NOUN
ejpam-6383	126	16	,	,	PUNCT
ejpam-6383	126	17	v2	v2	PROPN
ejpam-6383	126	18	}	}	PUNCT
ejpam-6383	126	19	.	.	PUNCT
ejpam-6383	127	1	then	then	ADV
ejpam-6383	127	2	nk2	nk2	PROPN
ejpam-6383	127	3	[	[	X
ejpam-6383	127	4	v2	v2	X
ejpam-6383	127	5	]	]	X
ejpam-6383	127	6	=	=	SYM
ejpam-6383	127	7	{	{	PUNCT
ejpam-6383	127	8	v1	v1	PROPN
ejpam-6383	127	9	,	,	PUNCT
ejpam-6383	127	10	v2	v2	NOUN
ejpam-6383	127	11	}	}	PUNCT
ejpam-6383	127	12	and	and	CCONJ
ejpam-6383	127	13	nk2(v1	nk2(v1	NOUN
ejpam-6383	127	14	)	)	PUNCT
ejpam-6383	127	15	=	=	SYM
ejpam-6383	127	16	v2	v2	NOUN
ejpam-6383	127	17	.	.	PUNCT
ejpam-6383	128	1	thus	thus	ADV
ejpam-6383	128	2	,	,	PUNCT
ejpam-6383	128	3	nk2	nk2	X
ejpam-6383	128	4	[	[	X
ejpam-6383	128	5	v2]\nk2(v1	v2]\nk2(v1	X
ejpam-6383	128	6	)	)	PUNCT
ejpam-6383	128	7	=	=	SYM
ejpam-6383	128	8	v1	v1	PROPN
ejpam-6383	128	9	̸=	̸=	PROPN
ejpam-6383	128	10	∅	∅	NOUN
ejpam-6383	128	11	,	,	PUNCT
ejpam-6383	128	12	showing	show	VERB
ejpam-6383	128	13	that	that	SCONJ
ejpam-6383	128	14	c	c	NOUN
ejpam-6383	128	15	=	=	SYM
ejpam-6383	128	16	(	(	PUNCT
ejpam-6383	128	17	v1	v1	PROPN
ejpam-6383	128	18	,	,	PUNCT
ejpam-6383	128	19	v2	v2	PROPN
ejpam-6383	128	20	)	)	PUNCT
ejpam-6383	128	21	is	be	AUX
ejpam-6383	128	22	an	an	DET
ejpam-6383	128	23	l	l	NOUN
ejpam-6383	128	24	-	-	NOUN
ejpam-6383	128	25	sequence	sequence	NOUN
ejpam-6383	128	26	of	of	ADP
ejpam-6383	128	27	k2	k2	NOUN
ejpam-6383	128	28	.	.	PUNCT
ejpam-6383	129	1	since	since	SCONJ
ejpam-6383	129	2	dk2(v2	dk2(v2	NOUN
ejpam-6383	129	3	,	,	PUNCT
ejpam-6383	129	4	v1	v1	NOUN
ejpam-6383	129	5	)	)	PUNCT
ejpam-6383	129	6	=	=	SYM
ejpam-6383	129	7	1	1	NUM
ejpam-6383	129	8	,	,	PUNCT
ejpam-6383	129	9	it	it	PRON
ejpam-6383	129	10	follows	follow	VERB
ejpam-6383	129	11	that	that	SCONJ
ejpam-6383	129	12	c	c	PROPN
ejpam-6383	129	13	is	be	AUX
ejpam-6383	129	14	an	an	DET
ejpam-6383	129	15	l	l	ADJ
ejpam-6383	129	16	-	-	ADJ
ejpam-6383	129	17	hop	hop	ADJ
ejpam-6383	129	18	independent	independent	ADJ
ejpam-6383	129	19	sequence	sequence	NOUN
ejpam-6383	129	20	of	of	ADP
ejpam-6383	129	21	k2	k2	PROPN
ejpam-6383	129	22	.	.	PUNCT
ejpam-6383	130	1	therefore	therefore	ADV
ejpam-6383	130	2	,	,	PUNCT
ejpam-6383	130	3	αlh(k2	αlh(k2	X
ejpam-6383	130	4	)	)	PUNCT
ejpam-6383	130	5	=	=	SYM
ejpam-6383	131	1	2	2	X
ejpam-6383	131	2	.	.	PUNCT
ejpam-6383	132	1	next	next	ADV
ejpam-6383	132	2	,	,	PUNCT
ejpam-6383	132	3	suppose	suppose	VERB
ejpam-6383	132	4	that	that	SCONJ
ejpam-6383	132	5	n	n	PROPN
ejpam-6383	132	6	≥	≥	NUM
ejpam-6383	132	7	3	3	X
ejpam-6383	132	8	.	.	PUNCT
ejpam-6383	133	1	let	let	VERB
ejpam-6383	133	2	v	v	X
ejpam-6383	133	3	(	(	PUNCT
ejpam-6383	133	4	kn	kn	PROPN
ejpam-6383	133	5	)	)	PUNCT
ejpam-6383	133	6	=	=	SYM
ejpam-6383	133	7	{	{	PUNCT
ejpam-6383	133	8	v1	v1	PROPN
ejpam-6383	133	9	,	,	PUNCT
ejpam-6383	133	10	v2	v2	PROPN
ejpam-6383	133	11	,	,	PUNCT
ejpam-6383	133	12	.	.	PUNCT
ejpam-6383	133	13	.	.	PUNCT
ejpam-6383	134	1	.	.	PUNCT
ejpam-6383	135	1	,	,	PUNCT
ejpam-6383	135	2	vn	vn	PROPN
ejpam-6383	135	3	}	}	PUNCT
ejpam-6383	135	4	.	.	PUNCT
ejpam-6383	136	1	then	then	ADV
ejpam-6383	136	2	c	c	NOUN
ejpam-6383	136	3	′	′	NOUN
ejpam-6383	137	1	=	=	SYM
ejpam-6383	137	2	(	(	PUNCT
ejpam-6383	137	3	v1	v1	NOUN
ejpam-6383	137	4	,	,	PUNCT
ejpam-6383	137	5	v2	v2	PROPN
ejpam-6383	137	6	)	)	PUNCT
ejpam-6383	137	7	is	be	AUX
ejpam-6383	137	8	an	an	DET
ejpam-6383	137	9	l	l	ADJ
ejpam-6383	137	10	-	-	ADJ
ejpam-6383	137	11	hop	hop	ADJ
ejpam-6383	137	12	independent	independent	ADJ
ejpam-6383	137	13	sequence	sequence	NOUN
ejpam-6383	137	14	of	of	ADP
ejpam-6383	137	15	kn	kn	PROPN
ejpam-6383	137	16	.	.	PUNCT
ejpam-6383	138	1	hence	hence	ADV
ejpam-6383	138	2	,	,	PUNCT
ejpam-6383	138	3	αlh(kn	αlh(kn	NUM
ejpam-6383	138	4	)	)	PUNCT
ejpam-6383	138	5	≥	≥	NOUN
ejpam-6383	138	6	2	2	NUM
ejpam-6383	138	7	.	.	PUNCT
ejpam-6383	138	8	suppose	suppose	VERB
ejpam-6383	138	9	that	that	SCONJ
ejpam-6383	138	10	αlh(kn	αlh(kn	NOUN
ejpam-6383	138	11	)	)	PUNCT
ejpam-6383	138	12	≥	≥	NOUN
ejpam-6383	138	13	3	3	NUM
ejpam-6383	138	14	,	,	PUNCT
ejpam-6383	138	15	say	say	VERB
ejpam-6383	138	16	l	l	NOUN
ejpam-6383	138	17	=	=	SYM
ejpam-6383	138	18	(	(	PUNCT
ejpam-6383	138	19	v1	v1	PROPN
ejpam-6383	138	20	,	,	PUNCT
ejpam-6383	138	21	v2	v2	NOUN
ejpam-6383	138	22	,	,	PUNCT
ejpam-6383	138	23	.	.	PUNCT
ejpam-6383	138	24	.	.	PUNCT
ejpam-6383	138	25	.	.	PUNCT
ejpam-6383	139	1	,	,	PUNCT
ejpam-6383	139	2	vm	vm	PROPN
ejpam-6383	139	3	)	)	PUNCT
ejpam-6383	139	4	is	be	AUX
ejpam-6383	139	5	a	a	DET
ejpam-6383	139	6	maximum	maximum	ADJ
ejpam-6383	139	7	l	l	NOUN
ejpam-6383	139	8	-	-	ADJ
ejpam-6383	139	9	hop	hop	ADJ
ejpam-6383	139	10	independent	independent	ADJ
ejpam-6383	139	11	sequence	sequence	NOUN
ejpam-6383	139	12	of	of	ADP
ejpam-6383	139	13	kn	kn	PROPN
ejpam-6383	139	14	,	,	PUNCT
ejpam-6383	139	15	where	where	SCONJ
ejpam-6383	139	16	m	m	PROPN
ejpam-6383	139	17	≥	≥	NOUN
ejpam-6383	139	18	3	3	NUM
ejpam-6383	139	19	.	.	X
ejpam-6383	139	20	note	note	VERB
ejpam-6383	139	21	that	that	SCONJ
ejpam-6383	139	22	nkn(v1)∪nkn(v2	nkn(v1)∪nkn(v2	NOUN
ejpam-6383	139	23	)	)	PUNCT
ejpam-6383	139	24	=	=	SYM
ejpam-6383	139	25	v	v	X
ejpam-6383	139	26	(	(	PUNCT
ejpam-6383	139	27	kn	kn	PROPN
ejpam-6383	139	28	)	)	PUNCT
ejpam-6383	139	29	.	.	PUNCT
ejpam-6383	140	1	it	it	PRON
ejpam-6383	140	2	follows	follow	VERB
ejpam-6383	140	3	that	that	DET
ejpam-6383	140	4	nkn	nkn	PROPN
ejpam-6383	141	1	[	[	X
ejpam-6383	141	2	vs]\	vs]\	VERB
ejpam-6383	141	3	s−1⋃	s−1⋃	PROPN
ejpam-6383	141	4	i=1	i=1	PROPN
ejpam-6383	141	5	nkn(vi	nkn(vi	NOUN
ejpam-6383	141	6	)	)	PUNCT
ejpam-6383	141	7	=	=	SYM
ejpam-6383	141	8	∅	∅	NOUN
ejpam-6383	141	9	for	for	ADP
ejpam-6383	141	10	all	all	DET
ejpam-6383	141	11	3	3	NUM
ejpam-6383	141	12	≤	≤	NUM
ejpam-6383	141	13	s	s	PART
ejpam-6383	141	14	≤	≤	NUM
ejpam-6383	141	15	m	m	PROPN
ejpam-6383	141	16	,	,	PUNCT
ejpam-6383	141	17	a	a	DET
ejpam-6383	141	18	contradiction	contradiction	NOUN
ejpam-6383	141	19	.	.	PUNCT
ejpam-6383	142	1	therefore	therefore	ADV
ejpam-6383	142	2	,	,	PUNCT
ejpam-6383	142	3	αlh(kn	αlh(kn	NUM
ejpam-6383	142	4	)	)	PUNCT
ejpam-6383	142	5	=	=	SYM
ejpam-6383	142	6	2	2	NUM
ejpam-6383	142	7	for	for	ADP
ejpam-6383	142	8	all	all	DET
ejpam-6383	142	9	n	n	PRON
ejpam-6383	142	10	≥	≥	NOUN
ejpam-6383	142	11	2	2	NUM
ejpam-6383	142	12	.	.	PUNCT
ejpam-6383	143	1	proposition	proposition	NOUN
ejpam-6383	143	2	2	2	NUM
ejpam-6383	143	3	.	.	PUNCT
ejpam-6383	144	1	let	let	VERB
ejpam-6383	144	2	g	g	PRON
ejpam-6383	144	3	be	be	AUX
ejpam-6383	144	4	a	a	DET
ejpam-6383	144	5	graph	graph	NOUN
ejpam-6383	144	6	.	.	PUNCT
ejpam-6383	145	1	if	if	SCONJ
ejpam-6383	145	2	αlh(g	αlh(g	NOUN
ejpam-6383	145	3	)	)	PUNCT
ejpam-6383	145	4	=	=	SYM
ejpam-6383	145	5	|v	|v	PROPN
ejpam-6383	145	6	(	(	PUNCT
ejpam-6383	145	7	g)|	g)|	NOUN
ejpam-6383	145	8	,	,	PUNCT
ejpam-6383	145	9	then	then	ADV
ejpam-6383	145	10	αh(g	αh(g	NOUN
ejpam-6383	145	11	)	)	PUNCT
ejpam-6383	145	12	=	=	SYM
ejpam-6383	145	13	|v	|v	PROPN
ejpam-6383	145	14	(	(	PUNCT
ejpam-6383	145	15	g)|	g)|	NOUN
ejpam-6383	145	16	.	.	PUNCT
ejpam-6383	146	1	however	however	ADV
ejpam-6383	146	2	,	,	PUNCT
ejpam-6383	146	3	the	the	DET
ejpam-6383	146	4	converse	converse	NOUN
ejpam-6383	146	5	is	be	AUX
ejpam-6383	146	6	not	not	PART
ejpam-6383	146	7	necessarily	necessarily	ADV
ejpam-6383	146	8	true	true	ADJ
ejpam-6383	146	9	.	.	PUNCT
ejpam-6383	147	1	k.	k.	PROPN
ejpam-6383	147	2	maharajul	maharajul	PROPN
ejpam-6383	147	3	,	,	PUNCT
ejpam-6383	147	4	j.	j.	PROPN
ejpam-6383	147	5	a.	a.	PROPN
ejpam-6383	147	6	hassan	hassan	PROPN
ejpam-6383	147	7	,	,	PUNCT
ejpam-6383	147	8	l.	l.	PROPN
ejpam-6383	147	9	laja	laja	PROPN
ejpam-6383	147	10	/	/	SYM
ejpam-6383	147	11	eur	eur	PROPN
ejpam-6383	147	12	.	.	PUNCT
ejpam-6383	148	1	j.	j.	PROPN
ejpam-6383	148	2	pure	pure	PROPN
ejpam-6383	148	3	appl	appl	PROPN
ejpam-6383	148	4	.	.	PROPN
ejpam-6383	148	5	math	math	PROPN
ejpam-6383	148	6	,	,	PUNCT
ejpam-6383	148	7	18	18	NUM
ejpam-6383	148	8	(	(	PUNCT
ejpam-6383	148	9	3	3	NUM
ejpam-6383	148	10	)	)	PUNCT
ejpam-6383	148	11	(	(	PUNCT
ejpam-6383	148	12	2025	2025	NUM
ejpam-6383	148	13	)	)	PUNCT
ejpam-6383	148	14	,	,	PUNCT
ejpam-6383	148	15	6383	6383	NUM
ejpam-6383	148	16	6	6	NUM
ejpam-6383	148	17	of	of	ADP
ejpam-6383	148	18	10	10	NUM
ejpam-6383	148	19	proof	proof	NOUN
ejpam-6383	148	20	.	.	PUNCT
ejpam-6383	148	21	suppose	suppose	VERB
ejpam-6383	148	22	that	that	SCONJ
ejpam-6383	148	23	αlh(g	αlh(g	NOUN
ejpam-6383	148	24	)	)	PUNCT
ejpam-6383	148	25	=	=	SYM
ejpam-6383	148	26	|v	|v	PROPN
ejpam-6383	148	27	(	(	PUNCT
ejpam-6383	148	28	g)|	g)|	PROPN
ejpam-6383	148	29	.	.	PUNCT
ejpam-6383	149	1	then	then	ADV
ejpam-6383	149	2	αh(g	αh(g	NOUN
ejpam-6383	149	3	)	)	PUNCT
ejpam-6383	149	4	≥	≥	NOUN
ejpam-6383	149	5	|v	|v	NOUN
ejpam-6383	149	6	(	(	PUNCT
ejpam-6383	149	7	g)|	g)|	NOUN
ejpam-6383	149	8	by	by	ADP
ejpam-6383	149	9	theorem	theorem	NOUN
ejpam-6383	149	10	1	1	NUM
ejpam-6383	149	11	.	.	PUNCT
ejpam-6383	149	12	since	since	SCONJ
ejpam-6383	149	13	αh(g	αh(g	NOUN
ejpam-6383	149	14	)	)	PUNCT
ejpam-6383	149	15	≤	≤	NUM
ejpam-6383	149	16	|v	|v	X
ejpam-6383	149	17	(	(	PUNCT
ejpam-6383	149	18	g)|	g)|	INTJ
ejpam-6383	149	19	,	,	PUNCT
ejpam-6383	149	20	it	it	PRON
ejpam-6383	149	21	follows	follow	VERB
ejpam-6383	149	22	that	that	SCONJ
ejpam-6383	149	23	αh(g	αh(g	NOUN
ejpam-6383	149	24	)	)	PUNCT
ejpam-6383	150	1	=	=	SYM
ejpam-6383	150	2	|v	|v	PROPN
ejpam-6383	150	3	(	(	PUNCT
ejpam-6383	150	4	g)|	g)|	NOUN
ejpam-6383	150	5	.	.	PUNCT
ejpam-6383	151	1	now	now	ADV
ejpam-6383	151	2	,	,	PUNCT
ejpam-6383	151	3	consider	consider	VERB
ejpam-6383	151	4	k5	k5	PROPN
ejpam-6383	151	5	and	and	CCONJ
ejpam-6383	151	6	let	let	VERB
ejpam-6383	151	7	v	v	NOUN
ejpam-6383	151	8	(	(	PUNCT
ejpam-6383	151	9	k5	k5	PROPN
ejpam-6383	151	10	)	)	PUNCT
ejpam-6383	151	11	=	=	PRON
ejpam-6383	152	1	{	{	PUNCT
ejpam-6383	152	2	x1	x1	PROPN
ejpam-6383	152	3	,	,	PUNCT
ejpam-6383	152	4	x2	x2	PROPN
ejpam-6383	152	5	,	,	PUNCT
ejpam-6383	152	6	x3	x3	PROPN
ejpam-6383	152	7	,	,	PUNCT
ejpam-6383	152	8	x4	x4	PROPN
ejpam-6383	152	9	,	,	PUNCT
ejpam-6383	152	10	x5	x5	PROPN
ejpam-6383	152	11	}	}	PUNCT
ejpam-6383	152	12	.	.	PUNCT
ejpam-6383	153	1	observe	observe	VERB
ejpam-6383	153	2	that	that	SCONJ
ejpam-6383	153	3	dk5(xi	dk5(xi	PROPN
ejpam-6383	153	4	,	,	PUNCT
ejpam-6383	153	5	xj	xj	PROPN
ejpam-6383	153	6	)	)	PUNCT
ejpam-6383	153	7	=	=	SYM
ejpam-6383	153	8	1	1	NUM
ejpam-6383	153	9	for	for	ADP
ejpam-6383	153	10	all	all	DET
ejpam-6383	153	11	i	i	PROPN
ejpam-6383	153	12	,	,	PUNCT
ejpam-6383	153	13	j	j	PROPN
ejpam-6383	153	14	∈	∈	PROPN
ejpam-6383	153	15	{	{	PUNCT
ejpam-6383	153	16	1	1	NUM
ejpam-6383	153	17	,	,	PUNCT
ejpam-6383	153	18	2	2	NUM
ejpam-6383	153	19	,	,	PUNCT
ejpam-6383	153	20	3	3	NUM
ejpam-6383	153	21	,	,	PUNCT
ejpam-6383	153	22	4	4	NUM
ejpam-6383	153	23	,	,	PUNCT
ejpam-6383	153	24	5	5	NUM
ejpam-6383	153	25	}	}	PUNCT
ejpam-6383	153	26	,	,	PUNCT
ejpam-6383	153	27	where	where	SCONJ
ejpam-6383	153	28	i	i	PRON
ejpam-6383	153	29	̸=	̸=	PROPN
ejpam-6383	153	30	j.	j.	PROPN
ejpam-6383	153	31	it	it	PRON
ejpam-6383	153	32	follows	follow	VERB
ejpam-6383	153	33	that	that	SCONJ
ejpam-6383	153	34	v	v	X
ejpam-6383	153	35	(	(	PUNCT
ejpam-6383	153	36	k5	k5	PROPN
ejpam-6383	153	37	)	)	PUNCT
ejpam-6383	153	38	is	be	AUX
ejpam-6383	153	39	a	a	DET
ejpam-6383	153	40	maximum	maximum	ADJ
ejpam-6383	153	41	hop	hop	NOUN
ejpam-6383	153	42	independent	independent	ADJ
ejpam-6383	153	43	set	set	NOUN
ejpam-6383	153	44	of	of	ADP
ejpam-6383	153	45	k5	k5	PROPN
ejpam-6383	153	46	.	.	PUNCT
ejpam-6383	154	1	thus	thus	ADV
ejpam-6383	154	2	,	,	PUNCT
ejpam-6383	154	3	αh(k5	αh(k5	NOUN
ejpam-6383	154	4	)	)	PUNCT
ejpam-6383	154	5	=	=	SYM
ejpam-6383	154	6	5	5	X
ejpam-6383	154	7	.	.	PUNCT
ejpam-6383	154	8	now	now	ADV
ejpam-6383	154	9	,	,	PUNCT
ejpam-6383	154	10	by	by	ADP
ejpam-6383	154	11	proposition	proposition	NOUN
ejpam-6383	154	12	1	1	NUM
ejpam-6383	154	13	,	,	PUNCT
ejpam-6383	154	14	αlh(k5	αlh(k5	NOUN
ejpam-6383	154	15	)	)	PUNCT
ejpam-6383	154	16	=	=	SYM
ejpam-6383	154	17	2	2	X
ejpam-6383	154	18	.	.	X
ejpam-6383	154	19	hence	hence	ADV
ejpam-6383	154	20	,	,	PUNCT
ejpam-6383	154	21	the	the	DET
ejpam-6383	154	22	assertion	assertion	NOUN
ejpam-6383	154	23	follows	follow	VERB
ejpam-6383	154	24	.	.	PUNCT
ejpam-6383	155	1	theorem	theorem	NOUN
ejpam-6383	155	2	2	2	NUM
ejpam-6383	155	3	.	.	PUNCT
ejpam-6383	156	1	[	[	X
ejpam-6383	156	2	2	2	X
ejpam-6383	156	3	]	]	PUNCT
ejpam-6383	156	4	let	let	VERB
ejpam-6383	156	5	g	g	NOUN
ejpam-6383	156	6	be	be	AUX
ejpam-6383	156	7	any	any	DET
ejpam-6383	156	8	graph	graph	NOUN
ejpam-6383	156	9	on	on	ADP
ejpam-6383	156	10	n	n	DET
ejpam-6383	156	11	vertices	vertex	NOUN
ejpam-6383	156	12	.	.	PUNCT
ejpam-6383	157	1	then	then	ADV
ejpam-6383	157	2	i.	i.	PROPN
ejpam-6383	157	3	αh(g	αh(g	PUNCT
ejpam-6383	157	4	)	)	PUNCT
ejpam-6383	158	1	=	=	SYM
ejpam-6383	158	2	n	n	NOUN
ejpam-6383	158	3	if	if	SCONJ
ejpam-6383	158	4	and	and	CCONJ
ejpam-6383	158	5	only	only	ADV
ejpam-6383	158	6	if	if	SCONJ
ejpam-6383	158	7	every	every	DET
ejpam-6383	158	8	component	component	NOUN
ejpam-6383	158	9	of	of	ADP
ejpam-6383	158	10	g	g	PROPN
ejpam-6383	158	11	is	be	AUX
ejpam-6383	158	12	complete	complete	ADJ
ejpam-6383	158	13	;	;	PUNCT
ejpam-6383	158	14	and	and	CCONJ
ejpam-6383	158	15	ii	ii	X
ejpam-6383	158	16	.	.	PROPN
ejpam-6383	159	1	for	for	ADP
ejpam-6383	159	2	n	n	PROPN
ejpam-6383	159	3	≥	≥	NUM
ejpam-6383	159	4	3	3	NUM
ejpam-6383	159	5	,	,	PUNCT
ejpam-6383	159	6	αh(g	αh(g	NOUN
ejpam-6383	159	7	)	)	PUNCT
ejpam-6383	159	8	=	=	SYM
ejpam-6383	159	9	n	n	CCONJ
ejpam-6383	159	10	−	−	PROPN
ejpam-6383	159	11	1	1	NUM
ejpam-6383	159	12	if	if	SCONJ
ejpam-6383	159	13	and	and	CCONJ
ejpam-6383	159	14	only	only	ADV
ejpam-6383	159	15	if	if	SCONJ
ejpam-6383	159	16	all	all	PRON
ejpam-6383	159	17	but	but	SCONJ
ejpam-6383	159	18	a	a	DET
ejpam-6383	159	19	single	single	ADJ
ejpam-6383	159	20	component	component	NOUN
ejpam-6383	159	21	c	c	PROPN
ejpam-6383	159	22	of	of	ADP
ejpam-6383	159	23	g	g	PROPN
ejpam-6383	159	24	are	be	AUX
ejpam-6383	159	25	complete	complete	ADJ
ejpam-6383	159	26	and	and	CCONJ
ejpam-6383	159	27	c\v	c\v	PROPN
ejpam-6383	159	28	is	be	AUX
ejpam-6383	159	29	a	a	DET
ejpam-6383	159	30	complete	complete	ADJ
ejpam-6383	159	31	graph	graph	NOUN
ejpam-6383	159	32	for	for	ADP
ejpam-6383	159	33	some	some	DET
ejpam-6383	159	34	vertex	vertex	NOUN
ejpam-6383	159	35	v	v	ADP
ejpam-6383	159	36	∈	∈	NOUN
ejpam-6383	159	37	v	v	NOUN
ejpam-6383	159	38	(	(	PUNCT
ejpam-6383	159	39	c	c	NOUN
ejpam-6383	159	40	)	)	PUNCT
ejpam-6383	159	41	.	.	PUNCT
ejpam-6383	160	1	theorem	theorem	NOUN
ejpam-6383	160	2	3	3	X
ejpam-6383	160	3	.	.	PUNCT
ejpam-6383	161	1	let	let	VERB
ejpam-6383	161	2	g	g	PRON
ejpam-6383	161	3	be	be	AUX
ejpam-6383	161	4	a	a	DET
ejpam-6383	161	5	graph	graph	NOUN
ejpam-6383	161	6	.	.	PUNCT
ejpam-6383	162	1	then	then	ADV
ejpam-6383	162	2	αlh(g	αlh(g	NUM
ejpam-6383	162	3	)	)	PUNCT
ejpam-6383	162	4	=	=	SYM
ejpam-6383	162	5	|v	|v	PROPN
ejpam-6383	162	6	(	(	PUNCT
ejpam-6383	162	7	g)|	g)|	VERB
ejpam-6383	162	8	if	if	SCONJ
ejpam-6383	162	9	and	and	CCONJ
ejpam-6383	162	10	only	only	ADV
ejpam-6383	162	11	if	if	SCONJ
ejpam-6383	162	12	every	every	DET
ejpam-6383	162	13	component	component	NOUN
ejpam-6383	162	14	of	of	ADP
ejpam-6383	162	15	g	g	PROPN
ejpam-6383	162	16	is	be	AUX
ejpam-6383	162	17	either	either	CCONJ
ejpam-6383	162	18	k1	k1	NOUN
ejpam-6383	162	19	or	or	CCONJ
ejpam-6383	162	20	k2	k2	NOUN
ejpam-6383	162	21	.	.	PUNCT
ejpam-6383	163	1	proof	proof	NOUN
ejpam-6383	163	2	.	.	PUNCT
ejpam-6383	164	1	suppose	suppose	VERB
ejpam-6383	164	2	that	that	SCONJ
ejpam-6383	164	3	αlh(g	αlh(g	NOUN
ejpam-6383	164	4	)	)	PUNCT
ejpam-6383	164	5	=	=	SYM
ejpam-6383	164	6	|v	|v	PROPN
ejpam-6383	164	7	(	(	PUNCT
ejpam-6383	164	8	g)|	g)|	PROPN
ejpam-6383	164	9	.	.	PUNCT
ejpam-6383	165	1	then	then	ADV
ejpam-6383	165	2	by	by	ADP
ejpam-6383	165	3	proposition	proposition	NOUN
ejpam-6383	165	4	2	2	NUM
ejpam-6383	165	5	,	,	PUNCT
ejpam-6383	165	6	αh(g	αh(g	NOUN
ejpam-6383	165	7	)	)	PUNCT
ejpam-6383	166	1	=	=	SYM
ejpam-6383	166	2	|v	|v	PROPN
ejpam-6383	166	3	(	(	PUNCT
ejpam-6383	166	4	g)|	g)|	NOUN
ejpam-6383	166	5	.	.	PUNCT
ejpam-6383	166	6	by	by	ADP
ejpam-6383	166	7	theorem	theorem	NOUN
ejpam-6383	166	8	2(i	2(i	NUM
ejpam-6383	166	9	)	)	PUNCT
ejpam-6383	166	10	,	,	PUNCT
ejpam-6383	166	11	every	every	DET
ejpam-6383	166	12	component	component	NOUN
ejpam-6383	166	13	of	of	ADP
ejpam-6383	166	14	g	g	PROPN
ejpam-6383	166	15	is	be	AUX
ejpam-6383	166	16	complete	complete	ADJ
ejpam-6383	166	17	.	.	PUNCT
ejpam-6383	167	1	if	if	SCONJ
ejpam-6383	167	2	it	it	PRON
ejpam-6383	167	3	is	be	AUX
ejpam-6383	167	4	either	either	CCONJ
ejpam-6383	167	5	k1	k1	NOUN
ejpam-6383	167	6	or	or	CCONJ
ejpam-6383	167	7	k2	k2	NOUN
ejpam-6383	167	8	,	,	PUNCT
ejpam-6383	167	9	then	then	ADV
ejpam-6383	167	10	we	we	PRON
ejpam-6383	167	11	are	be	AUX
ejpam-6383	167	12	done	do	VERB
ejpam-6383	167	13	.	.	PUNCT
ejpam-6383	168	1	now	now	ADV
ejpam-6383	168	2	,	,	PUNCT
ejpam-6383	168	3	suppose	suppose	VERB
ejpam-6383	168	4	that	that	SCONJ
ejpam-6383	168	5	every	every	DET
ejpam-6383	168	6	component	component	NOUN
ejpam-6383	168	7	of	of	ADP
ejpam-6383	168	8	g	g	PROPN
ejpam-6383	168	9	is	be	AUX
ejpam-6383	168	10	kn	kn	PROPN
ejpam-6383	168	11	,	,	PUNCT
ejpam-6383	168	12	where	where	SCONJ
ejpam-6383	168	13	n	n	PRON
ejpam-6383	168	14	≥	≥	NOUN
ejpam-6383	168	15	3	3	NUM
ejpam-6383	168	16	.	.	PUNCT
ejpam-6383	168	17	then	then	ADV
ejpam-6383	168	18	by	by	ADP
ejpam-6383	168	19	proposition	proposition	NOUN
ejpam-6383	168	20	1	1	NUM
ejpam-6383	168	21	,	,	PUNCT
ejpam-6383	168	22	αlh(kn	αlh(kn	NUM
ejpam-6383	168	23	)	)	PUNCT
ejpam-6383	168	24	=	=	SYM
ejpam-6383	168	25	2	2	NUM
ejpam-6383	168	26	for	for	ADP
ejpam-6383	168	27	all	all	DET
ejpam-6383	168	28	n	n	PRON
ejpam-6383	168	29	≥	≥	NOUN
ejpam-6383	168	30	3	3	NUM
ejpam-6383	168	31	.	.	PUNCT
ejpam-6383	169	1	it	it	PRON
ejpam-6383	169	2	follows	follow	VERB
ejpam-6383	169	3	that	that	SCONJ
ejpam-6383	169	4	αlh(g	αlh(g	NUM
ejpam-6383	169	5	)	)	PUNCT
ejpam-6383	169	6	≤	≤	NOUN
ejpam-6383	169	7	|v	|v	X
ejpam-6383	169	8	(	(	PUNCT
ejpam-6383	169	9	g)|	g)|	INTJ
ejpam-6383	169	10	−	−	PROPN
ejpam-6383	169	11	1	1	NUM
ejpam-6383	169	12	,	,	PUNCT
ejpam-6383	169	13	a	a	DET
ejpam-6383	169	14	contradiction	contradiction	NOUN
ejpam-6383	169	15	.	.	PUNCT
ejpam-6383	170	1	therefore	therefore	ADV
ejpam-6383	170	2	,	,	PUNCT
ejpam-6383	170	3	the	the	DET
ejpam-6383	170	4	assertion	assertion	NOUN
ejpam-6383	170	5	is	be	AUX
ejpam-6383	170	6	true	true	ADJ
ejpam-6383	170	7	.	.	PUNCT
ejpam-6383	171	1	conversely	conversely	ADV
ejpam-6383	171	2	,	,	PUNCT
ejpam-6383	171	3	suppose	suppose	VERB
ejpam-6383	171	4	that	that	SCONJ
ejpam-6383	171	5	every	every	DET
ejpam-6383	171	6	component	component	NOUN
ejpam-6383	171	7	of	of	ADP
ejpam-6383	171	8	g	g	PROPN
ejpam-6383	171	9	is	be	AUX
ejpam-6383	171	10	either	either	CCONJ
ejpam-6383	171	11	k1	k1	NOUN
ejpam-6383	171	12	or	or	CCONJ
ejpam-6383	171	13	k2	k2	NOUN
ejpam-6383	171	14	.	.	PUNCT
ejpam-6383	172	1	if	if	SCONJ
ejpam-6383	172	2	every	every	DET
ejpam-6383	172	3	component	component	NOUN
ejpam-6383	172	4	of	of	ADP
ejpam-6383	172	5	g	g	PROPN
ejpam-6383	172	6	is	be	AUX
ejpam-6383	172	7	k1	k1	PROPN
ejpam-6383	172	8	.	.	PUNCT
ejpam-6383	173	1	then	then	ADV
ejpam-6383	173	2	by	by	SCONJ
ejpam-6383	173	3	theorem	theorem	NOUN
ejpam-6383	173	4	1	1	NUM
ejpam-6383	173	5	,	,	PUNCT
ejpam-6383	173	6	αlh(k1	αlh(k1	PROPN
ejpam-6383	173	7	)	)	PUNCT
ejpam-6383	173	8	=	=	SYM
ejpam-6383	173	9	1	1	X
ejpam-6383	173	10	.	.	PUNCT
ejpam-6383	173	11	let	let	VERB
ejpam-6383	173	12	m	m	PRON
ejpam-6383	173	13	be	be	AUX
ejpam-6383	173	14	the	the	DET
ejpam-6383	173	15	number	number	NOUN
ejpam-6383	173	16	of	of	ADP
ejpam-6383	173	17	components	component	NOUN
ejpam-6383	173	18	k1	k1	PROPN
ejpam-6383	173	19	of	of	ADP
ejpam-6383	173	20	g.	g.	PROPN
ejpam-6383	173	21	then	then	ADV
ejpam-6383	173	22	αlh(g	αlh(g	NUM
ejpam-6383	173	23	)	)	PUNCT
ejpam-6383	174	1	=	=	PUNCT
ejpam-6383	174	2	m∑	m∑	PROPN
ejpam-6383	174	3	i=1	i=1	PROPN
ejpam-6383	174	4	αlh(k1	αlh(k1	PROPN
ejpam-6383	174	5	)	)	PUNCT
ejpam-6383	174	6	=	=	SYM
ejpam-6383	175	1	m	m	X
ejpam-6383	175	2	=	=	NOUN
ejpam-6383	175	3	|v	|v	PROPN
ejpam-6383	175	4	(	(	PUNCT
ejpam-6383	175	5	g)|	g)|	PROPN
ejpam-6383	175	6	.	.	PUNCT
ejpam-6383	176	1	next	next	ADV
ejpam-6383	176	2	,	,	PUNCT
ejpam-6383	176	3	assume	assume	VERB
ejpam-6383	176	4	that	that	SCONJ
ejpam-6383	176	5	every	every	DET
ejpam-6383	176	6	component	component	NOUN
ejpam-6383	176	7	of	of	ADP
ejpam-6383	176	8	g	g	PROPN
ejpam-6383	176	9	is	be	AUX
ejpam-6383	176	10	k2	k2	ADJ
ejpam-6383	176	11	.	.	PUNCT
ejpam-6383	177	1	then	then	ADV
ejpam-6383	177	2	by	by	ADP
ejpam-6383	177	3	proposition	proposition	NOUN
ejpam-6383	177	4	1	1	NUM
ejpam-6383	177	5	,	,	PUNCT
ejpam-6383	177	6	αlh(k2	αlh(k2	X
ejpam-6383	177	7	)	)	PUNCT
ejpam-6383	177	8	=	=	SYM
ejpam-6383	177	9	2	2	X
ejpam-6383	177	10	.	.	X
ejpam-6383	177	11	let	let	VERB
ejpam-6383	177	12	s	s	PRON
ejpam-6383	177	13	be	be	AUX
ejpam-6383	177	14	the	the	DET
ejpam-6383	177	15	number	number	NOUN
ejpam-6383	177	16	of	of	ADP
ejpam-6383	177	17	components	component	NOUN
ejpam-6383	177	18	k2	k2	PROPN
ejpam-6383	177	19	of	of	ADP
ejpam-6383	177	20	g.	g.	PROPN
ejpam-6383	177	21	then	then	ADV
ejpam-6383	177	22	αlh(g	αlh(g	NUM
ejpam-6383	177	23	)	)	PUNCT
ejpam-6383	178	1	=	=	SYM
ejpam-6383	178	2	s∑	s∑	PROPN
ejpam-6383	178	3	j=1	j=1	NOUN
ejpam-6383	178	4	αlh(k2	αlh(k2	NOUN
ejpam-6383	178	5	)	)	PUNCT
ejpam-6383	178	6	=	=	SYM
ejpam-6383	179	1	2s	2s	NUM
ejpam-6383	179	2	=	=	SYM
ejpam-6383	179	3	|v	|v	PROPN
ejpam-6383	179	4	(	(	PUNCT
ejpam-6383	179	5	g)|	g)|	NOUN
ejpam-6383	179	6	.	.	PUNCT
ejpam-6383	180	1	now	now	ADV
ejpam-6383	180	2	,	,	PUNCT
ejpam-6383	180	3	let	let	VERB
ejpam-6383	180	4	r	r	NOUN
ejpam-6383	180	5	and	and	CCONJ
ejpam-6383	180	6	q	q	NOUN
ejpam-6383	180	7	be	be	AUX
ejpam-6383	180	8	the	the	DET
ejpam-6383	180	9	number	number	NOUN
ejpam-6383	180	10	of	of	ADP
ejpam-6383	180	11	k1	k1	NOUN
ejpam-6383	180	12	and	and	CCONJ
ejpam-6383	180	13	k2	k2	ADJ
ejpam-6383	180	14	components	component	NOUN
ejpam-6383	180	15	of	of	ADP
ejpam-6383	180	16	g	g	NOUN
ejpam-6383	180	17	,	,	PUNCT
ejpam-6383	180	18	respectively	respectively	ADV
ejpam-6383	180	19	.	.	PUNCT
ejpam-6383	181	1	then	then	ADV
ejpam-6383	181	2	by	by	ADP
ejpam-6383	181	3	proposition	proposition	NOUN
ejpam-6383	181	4	1	1	NUM
ejpam-6383	181	5	,	,	PUNCT
ejpam-6383	181	6	αlh(g	αlh(g	NUM
ejpam-6383	181	7	)	)	PUNCT
ejpam-6383	181	8	=	=	SYM
ejpam-6383	181	9	r	r	NOUN
ejpam-6383	181	10	+	+	NOUN
ejpam-6383	181	11	q	q	NOUN
ejpam-6383	181	12	=	=	X
ejpam-6383	181	13	|v	|v	X
ejpam-6383	181	14	(	(	PUNCT
ejpam-6383	181	15	g)|	g)|	PROPN
ejpam-6383	181	16	.	.	PUNCT
ejpam-6383	181	17	corollary	corollary	ADJ
ejpam-6383	181	18	1	1	NUM
ejpam-6383	181	19	.	.	PUNCT
ejpam-6383	182	1	(	(	PUNCT
ejpam-6383	182	2	i	i	NOUN
ejpam-6383	182	3	)	)	PUNCT
ejpam-6383	182	4	let	let	VERB
ejpam-6383	182	5	n	n	PRON
ejpam-6383	182	6	be	be	AUX
ejpam-6383	182	7	a	a	DET
ejpam-6383	182	8	positive	positive	ADJ
ejpam-6383	182	9	integer	integer	NOUN
ejpam-6383	182	10	.	.	PUNCT
ejpam-6383	183	1	then	then	ADV
ejpam-6383	183	2	αlh(kn	αlh(kn	X
ejpam-6383	183	3	)	)	PUNCT
ejpam-6383	183	4	=	=	SYM
ejpam-6383	183	5	n	n	PROPN
ejpam-6383	183	6	for	for	ADP
ejpam-6383	183	7	all	all	DET
ejpam-6383	183	8	n	n	PRON
ejpam-6383	183	9	≥	≥	NOUN
ejpam-6383	183	10	1	1	NUM
ejpam-6383	183	11	.	.	PUNCT
ejpam-6383	183	12	(	(	PUNCT
ejpam-6383	183	13	ii	ii	NOUN
ejpam-6383	183	14	)	)	PUNCT
ejpam-6383	183	15	αlh(g	αlh(g	PROPN
ejpam-6383	183	16	)	)	PUNCT
ejpam-6383	184	1	=	=	NOUN
ejpam-6383	184	2	αh(g	αh(g	NOUN
ejpam-6383	184	3	)	)	PUNCT
ejpam-6383	184	4	=	=	SYM
ejpam-6383	184	5	|v	|v	PROPN
ejpam-6383	184	6	(	(	PUNCT
ejpam-6383	184	7	g)|	g)|	VERB
ejpam-6383	184	8	if	if	SCONJ
ejpam-6383	184	9	and	and	CCONJ
ejpam-6383	184	10	only	only	ADV
ejpam-6383	184	11	if	if	SCONJ
ejpam-6383	184	12	every	every	DET
ejpam-6383	184	13	component	component	NOUN
ejpam-6383	184	14	of	of	ADP
ejpam-6383	184	15	g	g	PROPN
ejpam-6383	184	16	is	be	AUX
ejpam-6383	184	17	either	either	CCONJ
ejpam-6383	184	18	k1	k1	NOUN
ejpam-6383	184	19	or	or	CCONJ
ejpam-6383	184	20	k2	k2	NOUN
ejpam-6383	184	21	.	.	PUNCT
ejpam-6383	185	1	to	to	PART
ejpam-6383	185	2	characterize	characterize	VERB
ejpam-6383	185	3	the	the	DET
ejpam-6383	185	4	l	l	NOUN
ejpam-6383	185	5	-	-	ADJ
ejpam-6383	185	6	hop	hop	ADJ
ejpam-6383	185	7	independent	independent	ADJ
ejpam-6383	185	8	sequences	sequence	NOUN
ejpam-6383	185	9	and	and	CCONJ
ejpam-6383	185	10	the	the	DET
ejpam-6383	185	11	join	join	NOUN
ejpam-6383	185	12	of	of	ADP
ejpam-6383	185	13	two	two	NUM
ejpam-6383	185	14	graphs	graph	NOUN
ejpam-6383	185	15	,	,	PUNCT
ejpam-6383	185	16	we	we	PRON
ejpam-6383	185	17	first	first	ADV
ejpam-6383	185	18	define	define	VERB
ejpam-6383	185	19	the	the	DET
ejpam-6383	185	20	following	follow	VERB
ejpam-6383	185	21	concepts	concept	NOUN
ejpam-6383	185	22	:	:	PUNCT
ejpam-6383	185	23	definition	definition	NOUN
ejpam-6383	185	24	2	2	NUM
ejpam-6383	185	25	.	.	PUNCT
ejpam-6383	186	1	let	let	VERB
ejpam-6383	186	2	g	g	PRON
ejpam-6383	186	3	be	be	AUX
ejpam-6383	186	4	a	a	DET
ejpam-6383	186	5	graph	graph	NOUN
ejpam-6383	186	6	.	.	PUNCT
ejpam-6383	187	1	a	a	DET
ejpam-6383	187	2	sequence	sequence	NOUN
ejpam-6383	187	3	l	l	NOUN
ejpam-6383	187	4	=	=	SYM
ejpam-6383	187	5	(	(	PUNCT
ejpam-6383	187	6	a1	a1	PROPN
ejpam-6383	187	7	,	,	PUNCT
ejpam-6383	187	8	.	.	PUNCT
ejpam-6383	187	9	.	.	PUNCT
ejpam-6383	188	1	.	.	PUNCT
ejpam-6383	189	1	,	,	PUNCT
ejpam-6383	189	2	an	an	X
ejpam-6383	189	3	)	)	PUNCT
ejpam-6383	189	4	of	of	ADP
ejpam-6383	189	5	distinct	distinct	ADJ
ejpam-6383	189	6	vertices	vertex	NOUN
ejpam-6383	189	7	of	of	ADP
ejpam-6383	189	8	g	g	PROPN
ejpam-6383	189	9	is	be	AUX
ejpam-6383	189	10	called	call	VERB
ejpam-6383	189	11	a	a	DET
ejpam-6383	189	12	clique	clique	ADJ
ejpam-6383	189	13	l	l	NOUN
ejpam-6383	189	14	-	-	NOUN
ejpam-6383	189	15	sequence	sequence	NOUN
ejpam-6383	189	16	if	if	SCONJ
ejpam-6383	189	17	n	n	NOUN
ejpam-6383	189	18	=	=	SYM
ejpam-6383	189	19	1	1	NUM
ejpam-6383	189	20	or	or	CCONJ
ejpam-6383	189	21	if	if	SCONJ
ejpam-6383	189	22	l	l	NOUN
ejpam-6383	189	23	is	be	AUX
ejpam-6383	189	24	an	an	DET
ejpam-6383	189	25	l	l	NOUN
ejpam-6383	189	26	-	-	NOUN
ejpam-6383	189	27	sequence	sequence	NOUN
ejpam-6383	189	28	and	and	CCONJ
ejpam-6383	189	29	its	its	PRON
ejpam-6383	189	30	corresponding	corresponding	ADJ
ejpam-6383	189	31	set	set	NOUN
ejpam-6383	189	32	l̂	l̂	X
ejpam-6383	189	33	=	=	SYM
ejpam-6383	189	34	{	{	PUNCT
ejpam-6383	189	35	a1	a1	PROPN
ejpam-6383	189	36	,	,	PUNCT
ejpam-6383	189	37	a2	a2	PROPN
ejpam-6383	189	38	,	,	PUNCT
ejpam-6383	189	39	·	·	PUNCT
ejpam-6383	189	40	·	·	PUNCT
ejpam-6383	189	41	·	·	PUNCT
ejpam-6383	189	42	,	,	PUNCT
ejpam-6383	189	43	an	an	PRON
ejpam-6383	189	44	}	}	PUNCT
ejpam-6383	189	45	induces	induce	VERB
ejpam-6383	189	46	a	a	DET
ejpam-6383	189	47	complete	complete	ADJ
ejpam-6383	189	48	graph	graph	NOUN
ejpam-6383	189	49	.	.	PUNCT
ejpam-6383	190	1	the	the	DET
ejpam-6383	190	2	maximum	maximum	ADJ
ejpam-6383	190	3	length	length	NOUN
ejpam-6383	190	4	of	of	ADP
ejpam-6383	190	5	a	a	DET
ejpam-6383	190	6	clique	clique	NOUN
ejpam-6383	190	7	lsequence	lsequence	NOUN
ejpam-6383	190	8	in	in	ADP
ejpam-6383	190	9	g	g	NOUN
ejpam-6383	190	10	,	,	PUNCT
ejpam-6383	190	11	denoted	denote	VERB
ejpam-6383	190	12	by	by	ADP
ejpam-6383	190	13	αl	αl	ADP
ejpam-6383	190	14	ch(g	ch(g	NOUN
ejpam-6383	190	15	)	)	PUNCT
ejpam-6383	190	16	,	,	PUNCT
ejpam-6383	190	17	is	be	AUX
ejpam-6383	190	18	called	call	VERB
ejpam-6383	190	19	the	the	DET
ejpam-6383	190	20	l	l	NOUN
ejpam-6383	190	21	-	-	ADJ
ejpam-6383	190	22	clique	clique	ADJ
ejpam-6383	190	23	number	number	NOUN
ejpam-6383	190	24	of	of	ADP
ejpam-6383	190	25	g.	g.	PROPN
ejpam-6383	190	26	moreover	moreover	ADV
ejpam-6383	190	27	,	,	PUNCT
ejpam-6383	190	28	we	we	PRON
ejpam-6383	190	29	call	call	VERB
ejpam-6383	190	30	l̂	l̂	VERB
ejpam-6383	190	31	a	a	DET
ejpam-6383	190	32	clique	clique	NOUN
ejpam-6383	190	33	l	l	NOUN
ejpam-6383	190	34	-	-	NOUN
ejpam-6383	190	35	set	set	NOUN
ejpam-6383	190	36	of	of	ADP
ejpam-6383	190	37	g.	g.	PROPN
ejpam-6383	190	38	k.	k.	PROPN
ejpam-6383	190	39	maharajul	maharajul	PROPN
ejpam-6383	190	40	,	,	PUNCT
ejpam-6383	190	41	j.	j.	PROPN
ejpam-6383	190	42	a.	a.	PROPN
ejpam-6383	190	43	hassan	hassan	PROPN
ejpam-6383	190	44	,	,	PUNCT
ejpam-6383	190	45	l.	l.	PROPN
ejpam-6383	190	46	laja	laja	PROPN
ejpam-6383	190	47	/	/	SYM
ejpam-6383	190	48	eur	eur	PROPN
ejpam-6383	190	49	.	.	PUNCT
ejpam-6383	191	1	j.	j.	PROPN
ejpam-6383	191	2	pure	pure	PROPN
ejpam-6383	191	3	appl	appl	PROPN
ejpam-6383	191	4	.	.	PROPN
ejpam-6383	191	5	math	math	PROPN
ejpam-6383	191	6	,	,	PUNCT
ejpam-6383	191	7	18	18	NUM
ejpam-6383	191	8	(	(	PUNCT
ejpam-6383	191	9	3	3	NUM
ejpam-6383	191	10	)	)	PUNCT
ejpam-6383	191	11	(	(	PUNCT
ejpam-6383	191	12	2025	2025	NUM
ejpam-6383	191	13	)	)	PUNCT
ejpam-6383	191	14	,	,	PUNCT
ejpam-6383	191	15	6383	6383	NUM
ejpam-6383	191	16	7	7	NUM
ejpam-6383	191	17	of	of	ADP
ejpam-6383	191	18	10	10	NUM
ejpam-6383	191	19	definition	definition	NOUN
ejpam-6383	191	20	3	3	NUM
ejpam-6383	191	21	.	.	PUNCT
ejpam-6383	192	1	let	let	VERB
ejpam-6383	192	2	g	g	NOUN
ejpam-6383	192	3	be	be	AUX
ejpam-6383	192	4	any	any	DET
ejpam-6383	192	5	graph	graph	NOUN
ejpam-6383	192	6	.	.	PUNCT
ejpam-6383	193	1	a	a	DET
ejpam-6383	193	2	clique	clique	ADJ
ejpam-6383	193	3	l	l	NOUN
ejpam-6383	193	4	-	-	NOUN
ejpam-6383	193	5	sequence	sequence	NOUN
ejpam-6383	193	6	l	l	NOUN
ejpam-6383	193	7	is	be	AUX
ejpam-6383	193	8	called	call	VERB
ejpam-6383	193	9	a	a	DET
ejpam-6383	193	10	clique	clique	ADJ
ejpam-6383	193	11	l	l	NOUN
ejpam-6383	193	12	-	-	ADJ
ejpam-6383	193	13	dominating	dominate	VERB
ejpam-6383	193	14	sequence	sequence	NOUN
ejpam-6383	193	15	or	or	CCONJ
ejpam-6383	193	16	a	a	DET
ejpam-6383	193	17	clique	clique	ADJ
ejpam-6383	193	18	l	l	PROPN
ejpam-6383	193	19	-	-	ADJ
ejpam-6383	193	20	grundy	grundy	ADJ
ejpam-6383	193	21	dominating	dominating	NOUN
ejpam-6383	193	22	sequence	sequence	NOUN
ejpam-6383	193	23	if	if	SCONJ
ejpam-6383	193	24	its	its	PRON
ejpam-6383	193	25	corresponding	corresponding	ADJ
ejpam-6383	193	26	set	set	NOUN
ejpam-6383	193	27	l̂	l̂	VERB
ejpam-6383	193	28	is	be	AUX
ejpam-6383	193	29	a	a	DET
ejpam-6383	193	30	dominating	dominating	NOUN
ejpam-6383	193	31	set	set	NOUN
ejpam-6383	193	32	of	of	ADP
ejpam-6383	193	33	g.	g.	PROPN
ejpam-6383	193	34	the	the	DET
ejpam-6383	193	35	maximum	maximum	ADJ
ejpam-6383	193	36	length	length	NOUN
ejpam-6383	193	37	of	of	ADP
ejpam-6383	193	38	a	a	DET
ejpam-6383	193	39	clique	clique	ADJ
ejpam-6383	193	40	l	l	PROPN
ejpam-6383	193	41	-	-	ADJ
ejpam-6383	193	42	grundy	grundy	ADJ
ejpam-6383	193	43	dominating	dominating	NOUN
ejpam-6383	193	44	sequence	sequence	NOUN
ejpam-6383	193	45	in	in	ADP
ejpam-6383	193	46	g	g	NOUN
ejpam-6383	193	47	,	,	PUNCT
ejpam-6383	193	48	denoted	denote	VERB
ejpam-6383	193	49	by	by	ADP
ejpam-6383	193	50	γlcgr(g	γlcgr(g	PROPN
ejpam-6383	193	51	)	)	PUNCT
ejpam-6383	193	52	,	,	PUNCT
ejpam-6383	193	53	is	be	AUX
ejpam-6383	193	54	called	call	VERB
ejpam-6383	193	55	the	the	DET
ejpam-6383	193	56	clique	clique	ADJ
ejpam-6383	193	57	l	l	PROPN
ejpam-6383	193	58	-	-	ADJ
ejpam-6383	193	59	grundy	grundy	ADJ
ejpam-6383	193	60	domination	domination	NOUN
ejpam-6383	193	61	number	number	NOUN
ejpam-6383	193	62	of	of	ADP
ejpam-6383	193	63	g.	g.	PROPN
ejpam-6383	193	64	moreover	moreover	ADV
ejpam-6383	193	65	,	,	PUNCT
ejpam-6383	193	66	a	a	DET
ejpam-6383	193	67	clique	clique	ADJ
ejpam-6383	193	68	l	l	NOUN
ejpam-6383	193	69	-	-	NOUN
ejpam-6383	193	70	sequence	sequence	NOUN
ejpam-6383	193	71	l	l	NOUN
ejpam-6383	193	72	of	of	ADP
ejpam-6383	193	73	g	g	PROPN
ejpam-6383	193	74	is	be	AUX
ejpam-6383	193	75	called	call	VERB
ejpam-6383	193	76	a	a	DET
ejpam-6383	193	77	clique	clique	ADJ
ejpam-6383	193	78	non	non	ADJ
ejpam-6383	193	79	-	-	ADJ
ejpam-6383	193	80	dominating	dominating	ADJ
ejpam-6383	193	81	l	l	NOUN
ejpam-6383	193	82	-	-	NOUN
ejpam-6383	193	83	sequence	sequence	NOUN
ejpam-6383	193	84	if	if	SCONJ
ejpam-6383	193	85	l̂	l̂	PRON
ejpam-6383	193	86	is	be	AUX
ejpam-6383	193	87	not	not	PART
ejpam-6383	193	88	a	a	DET
ejpam-6383	193	89	dominating	dominating	NOUN
ejpam-6383	193	90	set	set	NOUN
ejpam-6383	193	91	of	of	ADP
ejpam-6383	193	92	g.	g.	PROPN
ejpam-6383	193	93	theorem	theorem	VERB
ejpam-6383	193	94	4	4	NUM
ejpam-6383	193	95	.	.	PUNCT
ejpam-6383	194	1	[	[	X
ejpam-6383	194	2	2]let	2]let	NOUN
ejpam-6383	194	3	g	g	NOUN
ejpam-6383	194	4	and	and	CCONJ
ejpam-6383	194	5	h	h	NOUN
ejpam-6383	194	6	be	be	AUX
ejpam-6383	194	7	graphs	graph	NOUN
ejpam-6383	194	8	.	.	PUNCT
ejpam-6383	195	1	then	then	ADV
ejpam-6383	195	2	s	s	VERB
ejpam-6383	195	3	is	be	AUX
ejpam-6383	195	4	a	a	DET
ejpam-6383	195	5	non	non	ADJ
ejpam-6383	195	6	-	-	ADJ
ejpam-6383	195	7	empty	empty	ADJ
ejpam-6383	195	8	hop	hop	NOUN
ejpam-6383	195	9	independent	independent	ADJ
ejpam-6383	195	10	set	set	NOUN
ejpam-6383	195	11	of	of	ADP
ejpam-6383	195	12	g+h	g+h	PROPN
ejpam-6383	195	13	if	if	SCONJ
ejpam-6383	195	14	and	and	CCONJ
ejpam-6383	195	15	only	only	ADV
ejpam-6383	195	16	if	if	SCONJ
ejpam-6383	195	17	one	one	NUM
ejpam-6383	195	18	of	of	ADP
ejpam-6383	195	19	the	the	DET
ejpam-6383	195	20	following	follow	VERB
ejpam-6383	195	21	statement	statement	NOUN
ejpam-6383	195	22	holds	hold	VERB
ejpam-6383	195	23	:	:	PUNCT
ejpam-6383	195	24	(	(	PUNCT
ejpam-6383	195	25	i	i	NOUN
ejpam-6383	195	26	)	)	PUNCT
ejpam-6383	195	27	s	s	PART
ejpam-6383	195	28	∩	∩	ADJ
ejpam-6383	195	29	v	v	ADJ
ejpam-6383	195	30	(	(	PUNCT
ejpam-6383	195	31	h	h	NOUN
ejpam-6383	195	32	)	)	PUNCT
ejpam-6383	195	33	=	=	NOUN
ejpam-6383	195	34	∅	∅	NOUN
ejpam-6383	195	35	and	and	CCONJ
ejpam-6383	195	36	s	s	X
ejpam-6383	195	37	∩	∩	ADJ
ejpam-6383	195	38	v	v	ADJ
ejpam-6383	195	39	(	(	PUNCT
ejpam-6383	195	40	g	g	NOUN
ejpam-6383	195	41	)	)	PUNCT
ejpam-6383	195	42	is	be	AUX
ejpam-6383	195	43	a	a	DET
ejpam-6383	195	44	clique	clique	NOUN
ejpam-6383	195	45	of	of	ADP
ejpam-6383	195	46	g.	g.	PROPN
ejpam-6383	195	47	(	(	PUNCT
ejpam-6383	195	48	ii	ii	PROPN
ejpam-6383	195	49	)	)	PUNCT
ejpam-6383	195	50	s	s	PART
ejpam-6383	195	51	∩	∩	ADJ
ejpam-6383	195	52	v	v	X
ejpam-6383	195	53	(	(	PUNCT
ejpam-6383	195	54	g	g	NOUN
ejpam-6383	195	55	)	)	PUNCT
ejpam-6383	195	56	=	=	NOUN
ejpam-6383	195	57	∅	∅	NOUN
ejpam-6383	195	58	and	and	CCONJ
ejpam-6383	195	59	s	s	X
ejpam-6383	195	60	∩	∩	ADJ
ejpam-6383	195	61	v	v	ADJ
ejpam-6383	195	62	(	(	PUNCT
ejpam-6383	195	63	h	h	NOUN
ejpam-6383	195	64	)	)	PUNCT
ejpam-6383	195	65	is	be	AUX
ejpam-6383	195	66	a	a	DET
ejpam-6383	195	67	clique	clique	NOUN
ejpam-6383	195	68	of	of	ADP
ejpam-6383	195	69	h.	h.	PROPN
ejpam-6383	195	70	(	(	PUNCT
ejpam-6383	195	71	iii	iii	NOUN
ejpam-6383	195	72	)	)	PUNCT
ejpam-6383	195	73	s	s	PART
ejpam-6383	195	74	∩	∩	ADJ
ejpam-6383	195	75	v	v	X
ejpam-6383	195	76	(	(	PUNCT
ejpam-6383	195	77	g	g	NOUN
ejpam-6383	195	78	)	)	PUNCT
ejpam-6383	195	79	and	and	CCONJ
ejpam-6383	195	80	s	s	VERB
ejpam-6383	195	81	∩	∩	ADJ
ejpam-6383	195	82	v	v	ADJ
ejpam-6383	195	83	(	(	PUNCT
ejpam-6383	195	84	h	h	NOUN
ejpam-6383	195	85	)	)	PUNCT
ejpam-6383	195	86	are	be	AUX
ejpam-6383	195	87	cliques	clique	NOUN
ejpam-6383	195	88	in	in	ADP
ejpam-6383	195	89	g	g	PROPN
ejpam-6383	195	90	and	and	CCONJ
ejpam-6383	195	91	h	h	NOUN
ejpam-6383	195	92	,	,	PUNCT
ejpam-6383	195	93	respectively	respectively	ADV
ejpam-6383	195	94	.	.	PUNCT
ejpam-6383	196	1	theorem	theorem	VERB
ejpam-6383	196	2	5	5	NUM
ejpam-6383	196	3	.	.	PUNCT
ejpam-6383	197	1	[	[	X
ejpam-6383	197	2	12	12	NUM
ejpam-6383	197	3	]	]	PUNCT
ejpam-6383	197	4	let	let	VERB
ejpam-6383	197	5	g	g	NOUN
ejpam-6383	197	6	and	and	CCONJ
ejpam-6383	197	7	h	h	NOUN
ejpam-6383	197	8	be	be	VERB
ejpam-6383	197	9	two	two	NUM
ejpam-6383	197	10	non	non	ADJ
ejpam-6383	197	11	-	-	ADJ
ejpam-6383	197	12	complete	complete	ADJ
ejpam-6383	197	13	graphs	graph	NOUN
ejpam-6383	197	14	.	.	PUNCT
ejpam-6383	198	1	a	a	DET
ejpam-6383	198	2	sequence	sequence	NOUN
ejpam-6383	198	3	d	d	NOUN
ejpam-6383	198	4	of	of	ADP
ejpam-6383	198	5	distinct	distinct	ADJ
ejpam-6383	198	6	verices	verice	NOUN
ejpam-6383	198	7	of	of	ADP
ejpam-6383	198	8	g	g	PROPN
ejpam-6383	198	9	+	+	CCONJ
ejpam-6383	198	10	h	h	NOUN
ejpam-6383	198	11	is	be	AUX
ejpam-6383	198	12	a	a	DET
ejpam-6383	198	13	grundy	grundy	PROPN
ejpam-6383	198	14	dominating	dominating	NOUN
ejpam-6383	198	15	sequence	sequence	NOUN
ejpam-6383	198	16	in	in	ADP
ejpam-6383	198	17	g	g	PROPN
ejpam-6383	199	1	+	+	NOUN
ejpam-6383	199	2	h	h	NOUN
ejpam-6383	199	3	if	if	SCONJ
ejpam-6383	199	4	and	and	CCONJ
ejpam-6383	199	5	only	only	ADV
ejpam-6383	199	6	if	if	SCONJ
ejpam-6383	199	7	one	one	NUM
ejpam-6383	199	8	of	of	ADP
ejpam-6383	199	9	the	the	DET
ejpam-6383	199	10	following	follow	VERB
ejpam-6383	199	11	conditions	condition	NOUN
ejpam-6383	199	12	holds	hold	VERB
ejpam-6383	199	13	:	:	PUNCT
ejpam-6383	199	14	(	(	PUNCT
ejpam-6383	199	15	i	i	NOUN
ejpam-6383	199	16	)	)	PUNCT
ejpam-6383	200	1	d	d	PRON
ejpam-6383	200	2	is	be	AUX
ejpam-6383	200	3	a	a	DET
ejpam-6383	200	4	grundy	grundy	PROPN
ejpam-6383	200	5	dominating	dominating	NOUN
ejpam-6383	200	6	sequence	sequence	NOUN
ejpam-6383	200	7	of	of	ADP
ejpam-6383	200	8	g.	g.	PROPN
ejpam-6383	200	9	(	(	PUNCT
ejpam-6383	200	10	ii	ii	PROPN
ejpam-6383	200	11	)	)	PUNCT
ejpam-6383	200	12	d	d	NOUN
ejpam-6383	200	13	is	be	AUX
ejpam-6383	200	14	a	a	DET
ejpam-6383	200	15	grundy	grundy	PROPN
ejpam-6383	200	16	dominating	dominating	NOUN
ejpam-6383	200	17	sequence	sequence	NOUN
ejpam-6383	200	18	of	of	ADP
ejpam-6383	200	19	h.	h.	PROPN
ejpam-6383	200	20	(	(	PUNCT
ejpam-6383	200	21	iii	iii	NOUN
ejpam-6383	200	22	)	)	PUNCT
ejpam-6383	200	23	d	d	NOUN
ejpam-6383	200	24	=	=	SYM
ejpam-6383	200	25	dg	dg	PROPN
ejpam-6383	200	26	⊕	⊕	PROPN
ejpam-6383	200	27	(	(	PUNCT
ejpam-6383	200	28	w	w	NOUN
ejpam-6383	200	29	)	)	PUNCT
ejpam-6383	200	30	for	for	ADP
ejpam-6383	200	31	some	some	DET
ejpam-6383	200	32	non	non	ADJ
ejpam-6383	200	33	-	-	ADJ
ejpam-6383	200	34	dominating	dominating	ADJ
ejpam-6383	200	35	legal	legal	ADJ
ejpam-6383	200	36	closed	close	VERB
ejpam-6383	200	37	neighborhood	neighborhood	NOUN
ejpam-6383	200	38	sequence	sequence	NOUN
ejpam-6383	200	39	dg	dg	NOUN
ejpam-6383	200	40	of	of	ADP
ejpam-6383	200	41	g	g	PROPN
ejpam-6383	200	42	and	and	CCONJ
ejpam-6383	200	43	w	w	PROPN
ejpam-6383	200	44	∈	∈	PROPN
ejpam-6383	200	45	v	v	ADP
ejpam-6383	200	46	(	(	PUNCT
ejpam-6383	200	47	h	h	NOUN
ejpam-6383	200	48	)	)	PUNCT
ejpam-6383	200	49	.	.	PUNCT
ejpam-6383	201	1	(	(	PUNCT
ejpam-6383	201	2	iv	iv	X
ejpam-6383	201	3	)	)	PUNCT
ejpam-6383	201	4	d	d	NOUN
ejpam-6383	201	5	=	=	SYM
ejpam-6383	201	6	dh	dh	PROPN
ejpam-6383	201	7	⊕	⊕	PROPN
ejpam-6383	201	8	(	(	PUNCT
ejpam-6383	201	9	v	v	NOUN
ejpam-6383	201	10	)	)	PUNCT
ejpam-6383	201	11	for	for	ADP
ejpam-6383	201	12	some	some	DET
ejpam-6383	201	13	non	non	ADJ
ejpam-6383	201	14	-	-	ADJ
ejpam-6383	201	15	dominating	dominating	ADJ
ejpam-6383	201	16	legal	legal	ADJ
ejpam-6383	201	17	closed	close	VERB
ejpam-6383	201	18	neighborhood	neighborhood	NOUN
ejpam-6383	201	19	sequence	sequence	NOUN
ejpam-6383	201	20	dh	dh	NOUN
ejpam-6383	201	21	of	of	ADP
ejpam-6383	201	22	h	h	NOUN
ejpam-6383	201	23	and	and	CCONJ
ejpam-6383	201	24	v	v	ADP
ejpam-6383	201	25	∈	∈	PROPN
ejpam-6383	201	26	v	v	NOUN
ejpam-6383	201	27	(	(	PUNCT
ejpam-6383	201	28	g	g	NOUN
ejpam-6383	201	29	)	)	PUNCT
ejpam-6383	201	30	.	.	PUNCT
ejpam-6383	202	1	theorem	theorem	ADJ
ejpam-6383	202	2	6	6	NUM
ejpam-6383	202	3	.	.	PUNCT
ejpam-6383	203	1	let	let	VERB
ejpam-6383	203	2	h	h	NOUN
ejpam-6383	203	3	and	and	CCONJ
ejpam-6383	203	4	k	k	PROPN
ejpam-6383	203	5	be	be	AUX
ejpam-6383	203	6	two	two	NUM
ejpam-6383	203	7	non	non	ADJ
ejpam-6383	203	8	-	-	ADJ
ejpam-6383	203	9	complete	complete	ADJ
ejpam-6383	203	10	graphs	graph	NOUN
ejpam-6383	203	11	.	.	PUNCT
ejpam-6383	204	1	a	a	DET
ejpam-6383	204	2	sequence	sequence	NOUN
ejpam-6383	204	3	a	a	PRON
ejpam-6383	204	4	of	of	ADP
ejpam-6383	204	5	distinct	distinct	ADJ
ejpam-6383	204	6	vertices	vertex	NOUN
ejpam-6383	204	7	of	of	ADP
ejpam-6383	204	8	h	h	NOUN
ejpam-6383	205	1	+	+	NOUN
ejpam-6383	205	2	k	k	PROPN
ejpam-6383	205	3	is	be	AUX
ejpam-6383	205	4	an	an	DET
ejpam-6383	205	5	l	l	ADJ
ejpam-6383	205	6	-	-	ADJ
ejpam-6383	205	7	hop	hop	ADJ
ejpam-6383	205	8	independent	independent	ADJ
ejpam-6383	205	9	sequence	sequence	NOUN
ejpam-6383	205	10	in	in	ADP
ejpam-6383	205	11	h	h	PROPN
ejpam-6383	206	1	+	+	PROPN
ejpam-6383	206	2	k	k	X
ejpam-6383	206	3	if	if	SCONJ
ejpam-6383	206	4	and	and	CCONJ
ejpam-6383	206	5	only	only	ADV
ejpam-6383	206	6	if	if	SCONJ
ejpam-6383	206	7	one	one	NUM
ejpam-6383	206	8	of	of	ADP
ejpam-6383	206	9	the	the	DET
ejpam-6383	206	10	following	follow	VERB
ejpam-6383	206	11	conditions	condition	NOUN
ejpam-6383	206	12	holds	hold	VERB
ejpam-6383	206	13	:	:	PUNCT
ejpam-6383	206	14	(	(	PUNCT
ejpam-6383	206	15	i	i	NOUN
ejpam-6383	206	16	)	)	PUNCT
ejpam-6383	206	17	a	a	PRON
ejpam-6383	206	18	is	be	AUX
ejpam-6383	206	19	a	a	DET
ejpam-6383	206	20	clique	clique	ADJ
ejpam-6383	206	21	l	l	NOUN
ejpam-6383	206	22	-	-	NOUN
ejpam-6383	206	23	sequence	sequence	NOUN
ejpam-6383	206	24	in	in	ADP
ejpam-6383	206	25	h	h	PROPN
ejpam-6383	206	26	(	(	PUNCT
ejpam-6383	206	27	ii	ii	PROPN
ejpam-6383	206	28	)	)	PUNCT
ejpam-6383	206	29	a	a	PRON
ejpam-6383	206	30	is	be	AUX
ejpam-6383	206	31	a	a	DET
ejpam-6383	206	32	clique	clique	ADJ
ejpam-6383	206	33	l	l	NOUN
ejpam-6383	206	34	-	-	NOUN
ejpam-6383	206	35	sequence	sequence	NOUN
ejpam-6383	206	36	in	in	ADP
ejpam-6383	206	37	k	k	PROPN
ejpam-6383	206	38	(	(	PUNCT
ejpam-6383	206	39	iii	iii	NOUN
ejpam-6383	206	40	)	)	PUNCT
ejpam-6383	206	41	a	a	DET
ejpam-6383	206	42	=	=	SYM
ejpam-6383	206	43	ah⊕(a	ah⊕(a	NOUN
ejpam-6383	206	44	)	)	PUNCT
ejpam-6383	206	45	,	,	PUNCT
ejpam-6383	206	46	where	where	SCONJ
ejpam-6383	206	47	ah	ah	INTJ
ejpam-6383	206	48	is	be	AUX
ejpam-6383	206	49	a	a	DET
ejpam-6383	206	50	clique	clique	ADJ
ejpam-6383	206	51	non	non	ADJ
ejpam-6383	206	52	-	-	ADJ
ejpam-6383	206	53	dominating	dominating	ADJ
ejpam-6383	206	54	l	l	NOUN
ejpam-6383	206	55	-	-	NOUN
ejpam-6383	206	56	sequence	sequence	NOUN
ejpam-6383	206	57	in	in	ADP
ejpam-6383	206	58	h	h	NOUN
ejpam-6383	206	59	and	and	CCONJ
ejpam-6383	206	60	a	a	DET
ejpam-6383	206	61	∈	∈	NOUN
ejpam-6383	206	62	v	v	NOUN
ejpam-6383	206	63	(	(	PUNCT
ejpam-6383	206	64	k	k	NOUN
ejpam-6383	206	65	)	)	PUNCT
ejpam-6383	206	66	.	.	PUNCT
ejpam-6383	207	1	(	(	PUNCT
ejpam-6383	207	2	iv	iv	X
ejpam-6383	207	3	)	)	PUNCT
ejpam-6383	207	4	a	a	DET
ejpam-6383	207	5	=	=	PROPN
ejpam-6383	207	6	ak	ak	PROPN
ejpam-6383	207	7	⊕	⊕	PROPN
ejpam-6383	207	8	(	(	PUNCT
ejpam-6383	207	9	b	b	NOUN
ejpam-6383	207	10	)	)	PUNCT
ejpam-6383	207	11	,	,	PUNCT
ejpam-6383	207	12	where	where	SCONJ
ejpam-6383	207	13	ak	ak	PROPN
ejpam-6383	207	14	is	be	AUX
ejpam-6383	207	15	a	a	DET
ejpam-6383	207	16	clique	clique	ADJ
ejpam-6383	207	17	non	non	ADJ
ejpam-6383	207	18	-	-	ADJ
ejpam-6383	207	19	dominating	dominating	ADJ
ejpam-6383	207	20	l	l	NOUN
ejpam-6383	207	21	-	-	NOUN
ejpam-6383	207	22	sequence	sequence	NOUN
ejpam-6383	207	23	in	in	ADP
ejpam-6383	207	24	k	k	PROPN
ejpam-6383	207	25	and	and	CCONJ
ejpam-6383	207	26	b	b	PROPN
ejpam-6383	207	27	∈	∈	PROPN
ejpam-6383	207	28	v	v	ADP
ejpam-6383	207	29	(	(	PUNCT
ejpam-6383	207	30	h	h	NOUN
ejpam-6383	207	31	)	)	PUNCT
ejpam-6383	207	32	.	.	PUNCT
ejpam-6383	208	1	(	(	PUNCT
ejpam-6383	208	2	v	v	NOUN
ejpam-6383	208	3	)	)	PUNCT
ejpam-6383	208	4	a	a	PRON
ejpam-6383	208	5	=	=	SYM
ejpam-6383	208	6	(	(	PUNCT
ejpam-6383	208	7	x	x	NOUN
ejpam-6383	208	8	,	,	PUNCT
ejpam-6383	208	9	y	y	NOUN
ejpam-6383	208	10	)	)	PUNCT
ejpam-6383	208	11	for	for	ADP
ejpam-6383	208	12	some	some	PRON
ejpam-6383	208	13	x	x	SYM
ejpam-6383	208	14	∈	∈	PROPN
ejpam-6383	208	15	v	v	ADP
ejpam-6383	208	16	(	(	PUNCT
ejpam-6383	208	17	h	h	NOUN
ejpam-6383	208	18	)	)	PUNCT
ejpam-6383	208	19	and	and	CCONJ
ejpam-6383	208	20	y	y	PROPN
ejpam-6383	208	21	∈	∈	PROPN
ejpam-6383	208	22	v	v	PROPN
ejpam-6383	208	23	(	(	PUNCT
ejpam-6383	208	24	k	k	NOUN
ejpam-6383	208	25	)	)	PUNCT
ejpam-6383	208	26	.	.	PUNCT
ejpam-6383	209	1	proof	proof	NOUN
ejpam-6383	209	2	.	.	PUNCT
ejpam-6383	210	1	suppose	suppose	VERB
ejpam-6383	210	2	that	that	SCONJ
ejpam-6383	210	3	a	a	PRON
ejpam-6383	210	4	is	be	AUX
ejpam-6383	210	5	a	a	DET
ejpam-6383	210	6	l	l	ADJ
ejpam-6383	210	7	-	-	ADJ
ejpam-6383	210	8	hop	hop	ADJ
ejpam-6383	210	9	independent	independent	ADJ
ejpam-6383	210	10	sequence	sequence	NOUN
ejpam-6383	210	11	of	of	ADP
ejpam-6383	210	12	h	h	PROPN
ejpam-6383	211	1	+	+	CCONJ
ejpam-6383	211	2	k.	k.	PROPN
ejpam-6383	211	3	assume	assume	VERB
ejpam-6383	211	4	that	that	SCONJ
ejpam-6383	211	5	â	â	PROPN
ejpam-6383	211	6	⊆	⊆	NUM
ejpam-6383	211	7	v	v	NOUN
ejpam-6383	211	8	(	(	PUNCT
ejpam-6383	211	9	h	h	NOUN
ejpam-6383	211	10	)	)	PUNCT
ejpam-6383	211	11	.	.	PUNCT
ejpam-6383	212	1	then	then	ADV
ejpam-6383	212	2	â	â	X
ejpam-6383	212	3	is	be	AUX
ejpam-6383	212	4	a	a	DET
ejpam-6383	212	5	clique	clique	NOUN
ejpam-6383	212	6	in	in	ADP
ejpam-6383	212	7	h	h	NOUN
ejpam-6383	212	8	by	by	ADP
ejpam-6383	212	9	theorem	theorem	NOUN
ejpam-6383	212	10	4	4	NUM
ejpam-6383	212	11	.	.	PUNCT
ejpam-6383	212	12	by	by	ADP
ejpam-6383	212	13	theorem	theorem	NOUN
ejpam-6383	212	14	5	5	NUM
ejpam-6383	212	15	,	,	PUNCT
ejpam-6383	212	16	a	a	PRON
ejpam-6383	212	17	is	be	AUX
ejpam-6383	212	18	a	a	DET
ejpam-6383	212	19	legal	legal	ADJ
ejpam-6383	212	20	sequence	sequence	NOUN
ejpam-6383	212	21	in	in	ADP
ejpam-6383	212	22	h.	h.	PROPN
ejpam-6383	212	23	thus	thus	ADV
ejpam-6383	212	24	,	,	PUNCT
ejpam-6383	212	25	a	a	PRON
ejpam-6383	212	26	is	be	AUX
ejpam-6383	212	27	an	an	DET
ejpam-6383	212	28	l	l	NOUN
ejpam-6383	212	29	-	-	NOUN
ejpam-6383	212	30	sequence	sequence	NOUN
ejpam-6383	212	31	in	in	ADP
ejpam-6383	212	32	h	h	NOUN
ejpam-6383	212	33	,	,	PUNCT
ejpam-6383	212	34	showing	show	VERB
ejpam-6383	212	35	that	that	SCONJ
ejpam-6383	212	36	a	a	PRON
ejpam-6383	212	37	is	be	AUX
ejpam-6383	212	38	a	a	DET
ejpam-6383	212	39	clique	clique	ADJ
ejpam-6383	212	40	l	l	NOUN
ejpam-6383	212	41	-	-	NOUN
ejpam-6383	212	42	sequence	sequence	NOUN
ejpam-6383	212	43	in	in	ADP
ejpam-6383	212	44	h	h	NOUN
ejpam-6383	212	45	,	,	PUNCT
ejpam-6383	212	46	that	that	SCONJ
ejpam-6383	212	47	k.	k.	PROPN
ejpam-6383	212	48	maharajul	maharajul	PROPN
ejpam-6383	212	49	,	,	PUNCT
ejpam-6383	212	50	j.	j.	PROPN
ejpam-6383	212	51	a.	a.	PROPN
ejpam-6383	212	52	hassan	hassan	PROPN
ejpam-6383	212	53	,	,	PUNCT
ejpam-6383	212	54	l.	l.	PROPN
ejpam-6383	212	55	laja	laja	PROPN
ejpam-6383	212	56	/	/	SYM
ejpam-6383	212	57	eur	eur	PROPN
ejpam-6383	212	58	.	.	PUNCT
ejpam-6383	213	1	j.	j.	PROPN
ejpam-6383	213	2	pure	pure	PROPN
ejpam-6383	213	3	appl	appl	PROPN
ejpam-6383	213	4	.	.	PROPN
ejpam-6383	213	5	math	math	PROPN
ejpam-6383	213	6	,	,	PUNCT
ejpam-6383	213	7	18	18	NUM
ejpam-6383	213	8	(	(	PUNCT
ejpam-6383	213	9	3	3	NUM
ejpam-6383	213	10	)	)	PUNCT
ejpam-6383	213	11	(	(	PUNCT
ejpam-6383	213	12	2025	2025	NUM
ejpam-6383	213	13	)	)	PUNCT
ejpam-6383	213	14	,	,	PUNCT
ejpam-6383	213	15	6383	6383	NUM
ejpam-6383	213	16	8	8	NUM
ejpam-6383	213	17	of	of	ADP
ejpam-6383	213	18	10	10	NUM
ejpam-6383	213	19	is	be	AUX
ejpam-6383	213	20	,	,	PUNCT
ejpam-6383	213	21	(	(	PUNCT
ejpam-6383	213	22	i	i	NOUN
ejpam-6383	213	23	)	)	PUNCT
ejpam-6383	213	24	holds	hold	VERB
ejpam-6383	213	25	.	.	PUNCT
ejpam-6383	214	1	similarly	similarly	ADV
ejpam-6383	214	2	,	,	PUNCT
ejpam-6383	214	3	if	if	SCONJ
ejpam-6383	214	4	â	â	ADP
ejpam-6383	214	5	⊆	⊆	NUM
ejpam-6383	214	6	v	v	X
ejpam-6383	214	7	(	(	PUNCT
ejpam-6383	214	8	k	k	NOUN
ejpam-6383	214	9	)	)	PUNCT
ejpam-6383	214	10	,	,	PUNCT
ejpam-6383	214	11	then	then	ADV
ejpam-6383	214	12	a	a	PRON
ejpam-6383	214	13	is	be	AUX
ejpam-6383	214	14	a	a	DET
ejpam-6383	214	15	clique	clique	ADJ
ejpam-6383	214	16	l	l	ADJ
ejpam-6383	214	17	-	-	NOUN
ejpam-6383	214	18	sequence	sequence	NOUN
ejpam-6383	214	19	ink	ink	NOUN
ejpam-6383	214	20	.	.	PUNCT
ejpam-6383	215	1	that	that	PRON
ejpam-6383	215	2	is	is	ADV
ejpam-6383	215	3	,	,	PUNCT
ejpam-6383	215	4	(	(	PUNCT
ejpam-6383	215	5	ii	ii	NOUN
ejpam-6383	215	6	)	)	PUNCT
ejpam-6383	215	7	holds	hold	VERB
ejpam-6383	215	8	.	.	PUNCT
ejpam-6383	216	1	now	now	ADV
ejpam-6383	216	2	,	,	PUNCT
ejpam-6383	216	3	let	let	VERB
ejpam-6383	216	4	ah	ah	INTJ
ejpam-6383	216	5	and	and	CCONJ
ejpam-6383	216	6	ak	ak	PROPN
ejpam-6383	216	7	be	be	AUX
ejpam-6383	216	8	subsequences	subsequence	NOUN
ejpam-6383	216	9	of	of	ADP
ejpam-6383	216	10	a	a	DET
ejpam-6383	216	11	such	such	ADJ
ejpam-6383	216	12	that	that	DET
ejpam-6383	216	13	âh	âh	NOUN
ejpam-6383	216	14	=	=	SYM
ejpam-6383	216	15	â	â	X
ejpam-6383	216	16	∩	∩	PROPN
ejpam-6383	216	17	v	v	X
ejpam-6383	216	18	(	(	PUNCT
ejpam-6383	216	19	h	h	NOUN
ejpam-6383	216	20	)	)	PUNCT
ejpam-6383	216	21	and	and	CCONJ
ejpam-6383	216	22	âk	âk	X
ejpam-6383	216	23	=	=	SYM
ejpam-6383	217	1	â	â	X
ejpam-6383	217	2	∩	∩	PROPN
ejpam-6383	217	3	v	v	X
ejpam-6383	217	4	(	(	PUNCT
ejpam-6383	217	5	k	k	NOUN
ejpam-6383	217	6	)	)	PUNCT
ejpam-6383	217	7	,	,	PUNCT
ejpam-6383	217	8	where	where	SCONJ
ejpam-6383	217	9	âh	âh	NOUN
ejpam-6383	217	10	̸=	̸=	PROPN
ejpam-6383	217	11	∅	∅	NOUN
ejpam-6383	217	12	and	and	CCONJ
ejpam-6383	217	13	âk	âk	PRON
ejpam-6383	217	14	̸=	̸=	PROPN
ejpam-6383	217	15	∅.	∅.	VERB
ejpam-6383	217	16	then	then	ADV
ejpam-6383	217	17	a	a	DET
ejpam-6383	217	18	=	=	X
ejpam-6383	217	19	ah	ah	INTJ
ejpam-6383	217	20	⊕	⊕	PROPN
ejpam-6383	217	21	(	(	PUNCT
ejpam-6383	217	22	a	a	NOUN
ejpam-6383	217	23	)	)	PUNCT
ejpam-6383	217	24	for	for	ADP
ejpam-6383	217	25	some	some	DET
ejpam-6383	217	26	non	non	ADJ
ejpam-6383	217	27	-	-	ADJ
ejpam-6383	217	28	dominating	dominating	ADJ
ejpam-6383	217	29	legal	legal	ADJ
ejpam-6383	217	30	sequence	sequence	NOUN
ejpam-6383	217	31	ah	ah	INTJ
ejpam-6383	217	32	in	in	ADP
ejpam-6383	217	33	h	h	NOUN
ejpam-6383	217	34	and	and	CCONJ
ejpam-6383	217	35	a	a	DET
ejpam-6383	217	36	∈	∈	NOUN
ejpam-6383	217	37	v	v	NOUN
ejpam-6383	217	38	(	(	PUNCT
ejpam-6383	217	39	k	k	NOUN
ejpam-6383	217	40	)	)	PUNCT
ejpam-6383	217	41	by	by	ADP
ejpam-6383	217	42	theorem	theorem	NOUN
ejpam-6383	217	43	5	5	NUM
ejpam-6383	217	44	.	.	PUNCT
ejpam-6383	218	1	since	since	SCONJ
ejpam-6383	218	2	every	every	DET
ejpam-6383	218	3	legal	legal	ADJ
ejpam-6383	218	4	sequence	sequence	NOUN
ejpam-6383	218	5	is	be	AUX
ejpam-6383	218	6	an	an	DET
ejpam-6383	218	7	l	l	NOUN
ejpam-6383	218	8	-	-	NOUN
ejpam-6383	218	9	sequence	sequence	NOUN
ejpam-6383	218	10	,	,	PUNCT
ejpam-6383	218	11	ah	ah	INTJ
ejpam-6383	218	12	is	be	AUX
ejpam-6383	218	13	a	a	DET
ejpam-6383	218	14	non	non	ADJ
ejpam-6383	218	15	-	-	ADJ
ejpam-6383	218	16	dominating	dominating	ADJ
ejpam-6383	218	17	l	l	NOUN
ejpam-6383	218	18	-	-	NOUN
ejpam-6383	218	19	sequence	sequence	NOUN
ejpam-6383	218	20	in	in	ADP
ejpam-6383	218	21	h.	h.	PROPN
ejpam-6383	218	22	by	by	ADP
ejpam-6383	218	23	theorem	theorem	NOUN
ejpam-6383	218	24	4	4	NUM
ejpam-6383	218	25	,	,	PUNCT
ejpam-6383	218	26	ah	ah	INTJ
ejpam-6383	218	27	is	be	AUX
ejpam-6383	218	28	clique	clique	NOUN
ejpam-6383	218	29	in	in	ADP
ejpam-6383	218	30	h.	h.	PROPN
ejpam-6383	218	31	thus	thus	ADV
ejpam-6383	218	32	,	,	PUNCT
ejpam-6383	218	33	ah	ah	INTJ
ejpam-6383	218	34	is	be	AUX
ejpam-6383	218	35	a	a	DET
ejpam-6383	218	36	clique	clique	ADJ
ejpam-6383	218	37	non	non	ADJ
ejpam-6383	218	38	-	-	ADJ
ejpam-6383	218	39	dominating	dominating	ADJ
ejpam-6383	218	40	l	l	NOUN
ejpam-6383	218	41	-	-	NOUN
ejpam-6383	218	42	sequence	sequence	NOUN
ejpam-6383	218	43	in	in	ADP
ejpam-6383	218	44	h	h	NOUN
ejpam-6383	218	45	,	,	PUNCT
ejpam-6383	218	46	and	and	CCONJ
ejpam-6383	218	47	so	so	ADV
ejpam-6383	218	48	(	(	PUNCT
ejpam-6383	218	49	iii	iii	NOUN
ejpam-6383	218	50	)	)	PUNCT
ejpam-6383	218	51	holds	hold	VERB
ejpam-6383	218	52	.	.	PUNCT
ejpam-6383	219	1	similarly	similarly	ADV
ejpam-6383	219	2	,	,	PUNCT
ejpam-6383	219	3	by	by	ADP
ejpam-6383	219	4	theorem	theorem	NOUN
ejpam-6383	219	5	4	4	NUM
ejpam-6383	219	6	and	and	CCONJ
ejpam-6383	219	7	theorem	theorem	VERB
ejpam-6383	219	8	5	5	NUM
ejpam-6383	219	9	,	,	PUNCT
ejpam-6383	219	10	(	(	PUNCT
ejpam-6383	219	11	iv	iv	X
ejpam-6383	219	12	)	)	PUNCT
ejpam-6383	219	13	holds	hold	NOUN
ejpam-6383	219	14	.	.	PUNCT
ejpam-6383	220	1	now	now	ADV
ejpam-6383	220	2	,	,	PUNCT
ejpam-6383	220	3	it	it	PRON
ejpam-6383	220	4	is	be	AUX
ejpam-6383	220	5	also	also	ADV
ejpam-6383	220	6	easy	easy	ADJ
ejpam-6383	220	7	to	to	PART
ejpam-6383	220	8	see	see	VERB
ejpam-6383	220	9	that	that	PRON
ejpam-6383	220	10	(	(	PUNCT
ejpam-6383	220	11	v	v	NOUN
ejpam-6383	220	12	)	)	PUNCT
ejpam-6383	220	13	follows	follow	VERB
ejpam-6383	220	14	whenever	whenever	SCONJ
ejpam-6383	220	15	ah	ah	INTJ
ejpam-6383	220	16	or	or	CCONJ
ejpam-6383	220	17	ak	ak	PROPN
ejpam-6383	220	18	is	be	AUX
ejpam-6383	220	19	a	a	DET
ejpam-6383	220	20	clique	clique	ADJ
ejpam-6383	220	21	l	l	NOUN
ejpam-6383	220	22	-	-	ADJ
ejpam-6383	220	23	grundy	grundy	ADJ
ejpam-6383	220	24	dominating	dominating	NOUN
ejpam-6383	220	25	sequence	sequence	NOUN
ejpam-6383	220	26	of	of	ADP
ejpam-6383	220	27	h	h	NOUN
ejpam-6383	220	28	or	or	CCONJ
ejpam-6383	220	29	k.	k.	NOUN
ejpam-6383	220	30	conversely	conversely	ADV
ejpam-6383	220	31	,	,	PUNCT
ejpam-6383	220	32	assume	assume	VERB
ejpam-6383	220	33	that	that	SCONJ
ejpam-6383	220	34	(	(	PUNCT
ejpam-6383	220	35	i	i	NOUN
ejpam-6383	220	36	)	)	PUNCT
ejpam-6383	220	37	holds	hold	VERB
ejpam-6383	220	38	.	.	PUNCT
ejpam-6383	221	1	then	then	ADV
ejpam-6383	221	2	by	by	ADP
ejpam-6383	221	3	theorem	theorem	NOUN
ejpam-6383	221	4	4	4	NUM
ejpam-6383	221	5	,	,	PUNCT
ejpam-6383	221	6	â	â	X
ejpam-6383	221	7	is	be	AUX
ejpam-6383	221	8	a	a	DET
ejpam-6383	221	9	hop	hop	NOUN
ejpam-6383	221	10	independent	independent	ADJ
ejpam-6383	221	11	set	set	NOUN
ejpam-6383	221	12	of	of	ADP
ejpam-6383	221	13	h	h	NOUN
ejpam-6383	222	1	+	+	PROPN
ejpam-6383	222	2	k.	k.	PROPN
ejpam-6383	222	3	since	since	SCONJ
ejpam-6383	222	4	a	a	PRON
ejpam-6383	222	5	is	be	AUX
ejpam-6383	222	6	an	an	DET
ejpam-6383	222	7	l	l	NOUN
ejpam-6383	222	8	-	-	NOUN
ejpam-6383	222	9	sequence	sequence	NOUN
ejpam-6383	222	10	,	,	PUNCT
ejpam-6383	222	11	it	it	PRON
ejpam-6383	222	12	follows	follow	VERB
ejpam-6383	222	13	that	that	SCONJ
ejpam-6383	222	14	a	a	PRON
ejpam-6383	222	15	is	be	AUX
ejpam-6383	222	16	an	an	DET
ejpam-6383	222	17	l	l	ADJ
ejpam-6383	222	18	-	-	ADJ
ejpam-6383	222	19	hop	hop	ADJ
ejpam-6383	222	20	independent	independent	ADJ
ejpam-6383	222	21	sequence	sequence	NOUN
ejpam-6383	222	22	of	of	ADP
ejpam-6383	222	23	h	h	PROPN
ejpam-6383	223	1	+	+	X
ejpam-6383	223	2	k.	k.	PROPN
ejpam-6383	223	3	similarly	similarly	ADV
ejpam-6383	223	4	,	,	PUNCT
ejpam-6383	223	5	the	the	DET
ejpam-6383	223	6	assertion	assertion	NOUN
ejpam-6383	223	7	follows	follow	VERB
ejpam-6383	223	8	whenever	whenever	SCONJ
ejpam-6383	223	9	(	(	PUNCT
ejpam-6383	223	10	ii	ii	NOUN
ejpam-6383	223	11	)	)	PUNCT
ejpam-6383	223	12	holds	hold	VERB
ejpam-6383	223	13	.	.	PUNCT
ejpam-6383	224	1	suppose	suppose	VERB
ejpam-6383	224	2	that	that	SCONJ
ejpam-6383	224	3	(	(	PUNCT
ejpam-6383	224	4	iii	iii	NOUN
ejpam-6383	224	5	)	)	PUNCT
ejpam-6383	224	6	holds	hold	VERB
ejpam-6383	224	7	.	.	PUNCT
ejpam-6383	225	1	then	then	ADV
ejpam-6383	225	2	the	the	DET
ejpam-6383	225	3	corresponding	corresponding	ADJ
ejpam-6383	225	4	set	set	NOUN
ejpam-6383	225	5	of	of	ADP
ejpam-6383	225	6	ah	ah	INTJ
ejpam-6383	225	7	⊕	⊕	PROPN
ejpam-6383	225	8	(	(	PUNCT
ejpam-6383	225	9	a	a	NOUN
ejpam-6383	225	10	)	)	PUNCT
ejpam-6383	225	11	is	be	AUX
ejpam-6383	225	12	a	a	DET
ejpam-6383	225	13	hop	hop	NOUN
ejpam-6383	225	14	independent	independent	ADJ
ejpam-6383	225	15	set	set	NOUN
ejpam-6383	225	16	of	of	ADP
ejpam-6383	225	17	h	h	NOUN
ejpam-6383	226	1	+	+	PROPN
ejpam-6383	226	2	k.	k.	PROPN
ejpam-6383	226	3	since	since	SCONJ
ejpam-6383	226	4	ah	ah	INTJ
ejpam-6383	226	5	is	be	VERB
ejpam-6383	226	6	a	a	DET
ejpam-6383	226	7	non	non	ADJ
ejpam-6383	226	8	-	-	ADJ
ejpam-6383	226	9	dominating	dominating	ADJ
ejpam-6383	226	10	,	,	PUNCT
ejpam-6383	226	11	there	there	PRON
ejpam-6383	226	12	exists	exist	VERB
ejpam-6383	226	13	x	x	X
ejpam-6383	226	14	∈	∈	PROPN
ejpam-6383	226	15	v	v	ADP
ejpam-6383	226	16	(	(	PUNCT
ejpam-6383	226	17	h	h	NOUN
ejpam-6383	226	18	)	)	PUNCT
ejpam-6383	226	19	\	\	NOUN
ejpam-6383	226	20	âh	âh	NOUN
ejpam-6383	226	21	such	such	ADJ
ejpam-6383	226	22	that	that	SCONJ
ejpam-6383	226	23	x	x	PROPN
ejpam-6383	226	24	/∈	/∈	PUNCT
ejpam-6383	226	25	nh+k(âh	nh+k(âh	PROPN
ejpam-6383	226	26	)	)	PUNCT
ejpam-6383	226	27	.	.	PUNCT
ejpam-6383	227	1	it	it	PRON
ejpam-6383	227	2	follows	follow	VERB
ejpam-6383	227	3	that	that	SCONJ
ejpam-6383	227	4	x	x	PUNCT
ejpam-6383	227	5	∈	∈	PRON
ejpam-6383	227	6	nh+k	nh+k	NOUN
ejpam-6383	228	1	[	[	X
ejpam-6383	228	2	a	a	X
ejpam-6383	228	3	]	]	PUNCT
ejpam-6383	228	4	\	\	PROPN
ejpam-6383	228	5	nh+k(âh	nh+k(âh	PROPN
ejpam-6383	228	6	)	)	PUNCT
ejpam-6383	228	7	.	.	PUNCT
ejpam-6383	229	1	thus	thus	ADV
ejpam-6383	229	2	,	,	PUNCT
ejpam-6383	229	3	a	a	DET
ejpam-6383	229	4	=	=	X
ejpam-6383	229	5	ah	ah	INTJ
ejpam-6383	229	6	⊕	⊕	PROPN
ejpam-6383	229	7	(	(	PUNCT
ejpam-6383	229	8	a	a	NOUN
ejpam-6383	229	9	)	)	PUNCT
ejpam-6383	229	10	is	be	AUX
ejpam-6383	229	11	an	an	DET
ejpam-6383	229	12	l	l	ADJ
ejpam-6383	229	13	-	-	ADJ
ejpam-6383	229	14	hop	hop	ADJ
ejpam-6383	229	15	independent	independent	ADJ
ejpam-6383	229	16	sequence	sequence	NOUN
ejpam-6383	229	17	of	of	ADP
ejpam-6383	229	18	h+k	h+k	NUM
ejpam-6383	229	19	.	.	PUNCT
ejpam-6383	230	1	similarly	similarly	ADV
ejpam-6383	230	2	,	,	PUNCT
ejpam-6383	230	3	the	the	DET
ejpam-6383	230	4	result	result	NOUN
ejpam-6383	230	5	follows	follow	VERB
ejpam-6383	230	6	when	when	SCONJ
ejpam-6383	230	7	(	(	PUNCT
ejpam-6383	230	8	iv	iv	X
ejpam-6383	230	9	)	)	PUNCT
ejpam-6383	230	10	is	be	AUX
ejpam-6383	230	11	true	true	ADJ
ejpam-6383	230	12	.	.	PUNCT
ejpam-6383	231	1	moreover	moreover	ADV
ejpam-6383	231	2	,	,	PUNCT
ejpam-6383	231	3	it	it	PRON
ejpam-6383	231	4	is	be	AUX
ejpam-6383	231	5	clear	clear	ADJ
ejpam-6383	231	6	that	that	SCONJ
ejpam-6383	231	7	a	a	PRON
ejpam-6383	231	8	=	=	X
ejpam-6383	231	9	(	(	PUNCT
ejpam-6383	231	10	x	x	NOUN
ejpam-6383	231	11	,	,	PUNCT
ejpam-6383	231	12	y	y	NOUN
ejpam-6383	231	13	)	)	PUNCT
ejpam-6383	231	14	for	for	ADP
ejpam-6383	231	15	some	some	DET
ejpam-6383	231	16	x	x	SYM
ejpam-6383	231	17	∈	∈	PROPN
ejpam-6383	231	18	v	v	ADP
ejpam-6383	231	19	(	(	PUNCT
ejpam-6383	231	20	h	h	NOUN
ejpam-6383	231	21	)	)	PUNCT
ejpam-6383	231	22	and	and	CCONJ
ejpam-6383	231	23	y	y	PROPN
ejpam-6383	231	24	∈	∈	PROPN
ejpam-6383	231	25	v	v	ADP
ejpam-6383	231	26	(	(	PUNCT
ejpam-6383	231	27	k	k	NOUN
ejpam-6383	231	28	)	)	PUNCT
ejpam-6383	231	29	is	be	AUX
ejpam-6383	231	30	an	an	DET
ejpam-6383	231	31	l	l	ADJ
ejpam-6383	231	32	-	-	ADJ
ejpam-6383	231	33	hop	hop	ADJ
ejpam-6383	231	34	independent	independent	ADJ
ejpam-6383	231	35	sequence	sequence	NOUN
ejpam-6383	231	36	of	of	ADP
ejpam-6383	231	37	h	h	PROPN
ejpam-6383	231	38	+	+	PROPN
ejpam-6383	231	39	k.	k.	PROPN
ejpam-6383	231	40	theorem	theorem	VERB
ejpam-6383	231	41	7	7	NUM
ejpam-6383	231	42	.	.	PUNCT
ejpam-6383	232	1	[	[	X
ejpam-6383	232	2	12]let	12]let	NUM
ejpam-6383	232	3	g	g	NOUN
ejpam-6383	232	4	be	be	AUX
ejpam-6383	232	5	a	a	DET
ejpam-6383	232	6	complete	complete	ADJ
ejpam-6383	232	7	graph	graph	NOUN
ejpam-6383	232	8	and	and	CCONJ
ejpam-6383	232	9	let	let	VERB
ejpam-6383	232	10	h	h	PRON
ejpam-6383	232	11	be	be	AUX
ejpam-6383	232	12	a	a	DET
ejpam-6383	232	13	non	non	ADJ
ejpam-6383	232	14	-	-	ADJ
ejpam-6383	232	15	complete	complete	ADJ
ejpam-6383	232	16	graph	graph	NOUN
ejpam-6383	232	17	.	.	PUNCT
ejpam-6383	233	1	a	a	DET
ejpam-6383	233	2	sequence	sequence	NOUN
ejpam-6383	233	3	d	d	NOUN
ejpam-6383	233	4	of	of	ADP
ejpam-6383	233	5	distinct	distinct	ADJ
ejpam-6383	233	6	vertices	vertex	NOUN
ejpam-6383	233	7	of	of	ADP
ejpam-6383	233	8	g	g	PROPN
ejpam-6383	233	9	+	+	CCONJ
ejpam-6383	233	10	h	h	NOUN
ejpam-6383	233	11	is	be	AUX
ejpam-6383	233	12	a	a	DET
ejpam-6383	233	13	grundy	grundy	PROPN
ejpam-6383	233	14	dominating	dominating	NOUN
ejpam-6383	233	15	sequence	sequence	NOUN
ejpam-6383	233	16	in	in	ADP
ejpam-6383	233	17	g	g	PROPN
ejpam-6383	234	1	+	+	NOUN
ejpam-6383	234	2	h	h	NOUN
ejpam-6383	234	3	if	if	SCONJ
ejpam-6383	234	4	and	and	CCONJ
ejpam-6383	234	5	only	only	ADV
ejpam-6383	234	6	if	if	SCONJ
ejpam-6383	234	7	one	one	NUM
ejpam-6383	234	8	of	of	ADP
ejpam-6383	234	9	the	the	DET
ejpam-6383	234	10	following	follow	VERB
ejpam-6383	234	11	condition	condition	NOUN
ejpam-6383	234	12	holds	hold	VERB
ejpam-6383	234	13	:	:	PUNCT
ejpam-6383	234	14	(	(	PUNCT
ejpam-6383	234	15	i	i	NOUN
ejpam-6383	234	16	)	)	PUNCT
ejpam-6383	235	1	d	d	PROPN
ejpam-6383	235	2	=	=	SYM
ejpam-6383	235	3	(	(	PUNCT
ejpam-6383	235	4	v	v	NOUN
ejpam-6383	235	5	)	)	PUNCT
ejpam-6383	235	6	for	for	ADP
ejpam-6383	235	7	some	some	PRON
ejpam-6383	235	8	v	v	ADP
ejpam-6383	235	9	∈	∈	PROPN
ejpam-6383	235	10	v	v	NOUN
ejpam-6383	235	11	(	(	PUNCT
ejpam-6383	235	12	g	g	NOUN
ejpam-6383	235	13	)	)	PUNCT
ejpam-6383	235	14	.	.	PUNCT
ejpam-6383	236	1	(	(	PUNCT
ejpam-6383	236	2	ii	ii	NOUN
ejpam-6383	236	3	)	)	PUNCT
ejpam-6383	236	4	d	d	NOUN
ejpam-6383	236	5	is	be	AUX
ejpam-6383	236	6	a	a	DET
ejpam-6383	236	7	grundy	grundy	PROPN
ejpam-6383	236	8	dominating	dominating	NOUN
ejpam-6383	236	9	sequence	sequence	NOUN
ejpam-6383	236	10	of	of	ADP
ejpam-6383	236	11	h.	h.	PROPN
ejpam-6383	236	12	(	(	PUNCT
ejpam-6383	236	13	iii	iii	NOUN
ejpam-6383	236	14	)	)	PUNCT
ejpam-6383	236	15	d	d	NOUN
ejpam-6383	236	16	=	=	SYM
ejpam-6383	236	17	dh	dh	PROPN
ejpam-6383	236	18	⊕	⊕	PROPN
ejpam-6383	236	19	(	(	PUNCT
ejpam-6383	236	20	v	v	NOUN
ejpam-6383	236	21	)	)	PUNCT
ejpam-6383	236	22	for	for	ADP
ejpam-6383	236	23	some	some	DET
ejpam-6383	236	24	non	non	ADJ
ejpam-6383	236	25	-	-	ADJ
ejpam-6383	236	26	dominating	dominating	ADJ
ejpam-6383	236	27	legal	legal	ADJ
ejpam-6383	236	28	closed	close	VERB
ejpam-6383	236	29	neighborhood	neighborhood	NOUN
ejpam-6383	236	30	sequence	sequence	NOUN
ejpam-6383	236	31	dh	dh	NOUN
ejpam-6383	236	32	of	of	ADP
ejpam-6383	236	33	h	h	NOUN
ejpam-6383	236	34	and	and	CCONJ
ejpam-6383	236	35	v	v	ADP
ejpam-6383	236	36	∈	∈	PROPN
ejpam-6383	236	37	v	v	NOUN
ejpam-6383	236	38	(	(	PUNCT
ejpam-6383	236	39	g	g	NOUN
ejpam-6383	236	40	)	)	PUNCT
ejpam-6383	236	41	.	.	PUNCT
ejpam-6383	237	1	theorem	theorem	ADJ
ejpam-6383	237	2	8	8	NUM
ejpam-6383	237	3	.	.	PUNCT
ejpam-6383	238	1	let	let	VERB
ejpam-6383	238	2	q	q	NOUN
ejpam-6383	238	3	and	and	CCONJ
ejpam-6383	238	4	r	r	NOUN
ejpam-6383	238	5	be	be	AUX
ejpam-6383	238	6	complete	complete	ADJ
ejpam-6383	238	7	and	and	CCONJ
ejpam-6383	238	8	non	non	ADJ
ejpam-6383	238	9	-	-	ADJ
ejpam-6383	238	10	complete	complete	ADJ
ejpam-6383	238	11	graph	graph	NOUN
ejpam-6383	238	12	,	,	PUNCT
ejpam-6383	238	13	respectively	respectively	ADV
ejpam-6383	238	14	.	.	PUNCT
ejpam-6383	239	1	a	a	DET
ejpam-6383	239	2	sequence	sequence	NOUN
ejpam-6383	239	3	b	b	NOUN
ejpam-6383	239	4	of	of	ADP
ejpam-6383	239	5	distinct	distinct	ADJ
ejpam-6383	239	6	vertices	vertex	NOUN
ejpam-6383	239	7	of	of	ADP
ejpam-6383	239	8	q+r	q+r	NUM
ejpam-6383	239	9	is	be	AUX
ejpam-6383	239	10	an	an	DET
ejpam-6383	239	11	l	l	ADJ
ejpam-6383	239	12	-	-	ADJ
ejpam-6383	239	13	hop	hop	ADJ
ejpam-6383	239	14	independent	independent	ADJ
ejpam-6383	239	15	sequence	sequence	NOUN
ejpam-6383	239	16	if	if	SCONJ
ejpam-6383	239	17	and	and	CCONJ
ejpam-6383	239	18	only	only	ADV
ejpam-6383	239	19	if	if	SCONJ
ejpam-6383	239	20	one	one	NUM
ejpam-6383	239	21	of	of	ADP
ejpam-6383	239	22	the	the	DET
ejpam-6383	239	23	following	follow	VERB
ejpam-6383	239	24	conditions	condition	NOUN
ejpam-6383	239	25	holds	hold	VERB
ejpam-6383	239	26	:	:	PUNCT
ejpam-6383	239	27	(	(	PUNCT
ejpam-6383	239	28	i	i	NOUN
ejpam-6383	239	29	)	)	PUNCT
ejpam-6383	239	30	b	b	PROPN
ejpam-6383	239	31	is	be	AUX
ejpam-6383	239	32	a	a	DET
ejpam-6383	239	33	clique	clique	ADJ
ejpam-6383	239	34	l	l	NOUN
ejpam-6383	239	35	-	-	NOUN
ejpam-6383	239	36	sequence	sequence	NOUN
ejpam-6383	239	37	of	of	ADP
ejpam-6383	239	38	q.	q.	PROPN
ejpam-6383	239	39	(	(	PUNCT
ejpam-6383	239	40	ii	ii	PROPN
ejpam-6383	239	41	)	)	PUNCT
ejpam-6383	239	42	b	b	PROPN
ejpam-6383	239	43	is	be	AUX
ejpam-6383	239	44	a	a	DET
ejpam-6383	239	45	clique	clique	ADJ
ejpam-6383	239	46	l	l	NOUN
ejpam-6383	239	47	-	-	NOUN
ejpam-6383	239	48	sequence	sequence	NOUN
ejpam-6383	239	49	of	of	ADP
ejpam-6383	239	50	r.	r.	PROPN
ejpam-6383	239	51	(	(	PUNCT
ejpam-6383	239	52	iii	iii	PROPN
ejpam-6383	239	53	)	)	PUNCT
ejpam-6383	239	54	b	b	NOUN
ejpam-6383	239	55	=	=	SYM
ejpam-6383	239	56	br	br	PROPN
ejpam-6383	239	57	⊕	⊕	PROPN
ejpam-6383	239	58	(	(	PUNCT
ejpam-6383	239	59	w	w	NOUN
ejpam-6383	239	60	)	)	PUNCT
ejpam-6383	239	61	,	,	PUNCT
ejpam-6383	239	62	where	where	SCONJ
ejpam-6383	239	63	br	br	PROPN
ejpam-6383	239	64	is	be	AUX
ejpam-6383	239	65	a	a	DET
ejpam-6383	239	66	clique	clique	ADJ
ejpam-6383	239	67	non	non	ADJ
ejpam-6383	239	68	-	-	ADJ
ejpam-6383	239	69	dominating	dominating	ADJ
ejpam-6383	239	70	l	l	NOUN
ejpam-6383	239	71	-	-	NOUN
ejpam-6383	239	72	sequence	sequence	NOUN
ejpam-6383	239	73	in	in	ADP
ejpam-6383	239	74	r	r	NOUN
ejpam-6383	239	75	and	and	CCONJ
ejpam-6383	239	76	w	w	NOUN
ejpam-6383	239	77	∈	∈	PROPN
ejpam-6383	239	78	v	v	ADP
ejpam-6383	239	79	(	(	PUNCT
ejpam-6383	239	80	q	q	NOUN
ejpam-6383	239	81	)	)	PUNCT
ejpam-6383	239	82	.	.	PUNCT
ejpam-6383	240	1	(	(	PUNCT
ejpam-6383	240	2	iv	iv	X
ejpam-6383	240	3	)	)	PUNCT
ejpam-6383	240	4	a	a	PRON
ejpam-6383	240	5	=	=	SYM
ejpam-6383	240	6	(	(	PUNCT
ejpam-6383	240	7	x	x	NOUN
ejpam-6383	240	8	,	,	PUNCT
ejpam-6383	240	9	y	y	NOUN
ejpam-6383	240	10	)	)	PUNCT
ejpam-6383	240	11	for	for	ADP
ejpam-6383	240	12	some	some	PRON
ejpam-6383	240	13	x	x	SYM
ejpam-6383	240	14	∈	∈	PROPN
ejpam-6383	240	15	v	v	ADP
ejpam-6383	240	16	(	(	PUNCT
ejpam-6383	240	17	h	h	NOUN
ejpam-6383	240	18	)	)	PUNCT
ejpam-6383	240	19	and	and	CCONJ
ejpam-6383	240	20	y	y	PROPN
ejpam-6383	240	21	∈	∈	PROPN
ejpam-6383	240	22	v	v	PROPN
ejpam-6383	240	23	(	(	PUNCT
ejpam-6383	240	24	k	k	NOUN
ejpam-6383	240	25	)	)	PUNCT
ejpam-6383	240	26	.	.	PUNCT
ejpam-6383	241	1	proof	proof	NOUN
ejpam-6383	241	2	.	.	PUNCT
ejpam-6383	242	1	let	let	VERB
ejpam-6383	242	2	b	b	X
ejpam-6383	242	3	be	be	AUX
ejpam-6383	242	4	an	an	DET
ejpam-6383	242	5	l	l	NOUN
ejpam-6383	242	6	-	-	ADJ
ejpam-6383	242	7	hop	hop	ADJ
ejpam-6383	242	8	independent	independent	ADJ
ejpam-6383	242	9	sequence	sequence	NOUN
ejpam-6383	242	10	of	of	ADP
ejpam-6383	242	11	q	q	PROPN
ejpam-6383	243	1	+	+	PROPN
ejpam-6383	243	2	r.	r.	PROPN
ejpam-6383	243	3	assume	assume	VERB
ejpam-6383	243	4	that	that	SCONJ
ejpam-6383	243	5	b̂	b̂	NOUN
ejpam-6383	243	6	⊆	⊆	NUM
ejpam-6383	243	7	v	v	NOUN
ejpam-6383	243	8	(	(	PUNCT
ejpam-6383	243	9	q	q	NOUN
ejpam-6383	243	10	)	)	PUNCT
ejpam-6383	243	11	.	.	PUNCT
ejpam-6383	244	1	since	since	SCONJ
ejpam-6383	244	2	b̂	b̂	NOUN
ejpam-6383	244	3	is	be	AUX
ejpam-6383	244	4	hop	hop	ADV
ejpam-6383	244	5	independent	independent	ADJ
ejpam-6383	244	6	in	in	ADP
ejpam-6383	244	7	q+	q+	ADP
ejpam-6383	244	8	r	r	NOUN
ejpam-6383	244	9	,	,	PUNCT
ejpam-6383	244	10	b̂	b̂	NOUN
ejpam-6383	244	11	is	be	AUX
ejpam-6383	244	12	clique	clique	ADJ
ejpam-6383	244	13	in	in	ADP
ejpam-6383	244	14	r	r	NOUN
ejpam-6383	244	15	by	by	ADP
ejpam-6383	244	16	theorem	theorem	NOUN
ejpam-6383	244	17	4	4	NUM
ejpam-6383	244	18	.	.	PUNCT
ejpam-6383	245	1	hence	hence	ADV
ejpam-6383	245	2	,	,	PUNCT
ejpam-6383	245	3	(	(	PUNCT
ejpam-6383	245	4	i	i	NOUN
ejpam-6383	245	5	)	)	PUNCT
ejpam-6383	245	6	follows	follow	VERB
ejpam-6383	245	7	since	since	SCONJ
ejpam-6383	245	8	b	b	NOUN
ejpam-6383	245	9	is	be	AUX
ejpam-6383	245	10	an	an	DET
ejpam-6383	245	11	l	l	NOUN
ejpam-6383	245	12	-	-	NOUN
ejpam-6383	245	13	sequence	sequence	NOUN
ejpam-6383	245	14	in	in	ADP
ejpam-6383	245	15	q+r	q+r	NUM
ejpam-6383	245	16	.	.	PUNCT
ejpam-6383	246	1	similarly	similarly	ADV
ejpam-6383	246	2	,	,	PUNCT
ejpam-6383	246	3	(	(	PUNCT
ejpam-6383	246	4	ii	ii	NOUN
ejpam-6383	246	5	)	)	PUNCT
ejpam-6383	246	6	follows	follow	VERB
ejpam-6383	246	7	whenever	whenever	SCONJ
ejpam-6383	246	8	b̂	b̂	NOUN
ejpam-6383	246	9	⊆	⊆	NUM
ejpam-6383	246	10	v	v	NOUN
ejpam-6383	246	11	(	(	PUNCT
ejpam-6383	246	12	r	r	NOUN
ejpam-6383	246	13	)	)	PUNCT
ejpam-6383	246	14	.	.	PUNCT
ejpam-6383	247	1	k.	k.	PROPN
ejpam-6383	247	2	maharajul	maharajul	PROPN
ejpam-6383	247	3	,	,	PUNCT
ejpam-6383	247	4	j.	j.	PROPN
ejpam-6383	247	5	a.	a.	PROPN
ejpam-6383	247	6	hassan	hassan	PROPN
ejpam-6383	247	7	,	,	PUNCT
ejpam-6383	247	8	l.	l.	PROPN
ejpam-6383	247	9	laja	laja	PROPN
ejpam-6383	247	10	/	/	SYM
ejpam-6383	247	11	eur	eur	PROPN
ejpam-6383	247	12	.	.	PUNCT
ejpam-6383	248	1	j.	j.	PROPN
ejpam-6383	248	2	pure	pure	PROPN
ejpam-6383	248	3	appl	appl	PROPN
ejpam-6383	248	4	.	.	PROPN
ejpam-6383	248	5	math	math	PROPN
ejpam-6383	248	6	,	,	PUNCT
ejpam-6383	248	7	18	18	NUM
ejpam-6383	248	8	(	(	PUNCT
ejpam-6383	248	9	3	3	NUM
ejpam-6383	248	10	)	)	PUNCT
ejpam-6383	248	11	(	(	PUNCT
ejpam-6383	248	12	2025	2025	NUM
ejpam-6383	248	13	)	)	PUNCT
ejpam-6383	248	14	,	,	PUNCT
ejpam-6383	248	15	6383	6383	NUM
ejpam-6383	248	16	9	9	NUM
ejpam-6383	248	17	of	of	ADP
ejpam-6383	248	18	10	10	NUM
ejpam-6383	248	19	now	now	ADV
ejpam-6383	248	20	,	,	PUNCT
ejpam-6383	248	21	assume	assume	VERB
ejpam-6383	248	22	that	that	SCONJ
ejpam-6383	248	23	b̂	b̂	NOUN
ejpam-6383	248	24	=	=	NOUN
ejpam-6383	248	25	b̂q∪	b̂q∪	ADP
ejpam-6383	248	26	b̂r	b̂r	NOUN
ejpam-6383	248	27	,	,	PUNCT
ejpam-6383	248	28	where	where	SCONJ
ejpam-6383	248	29	b̂q	b̂q	NOUN
ejpam-6383	248	30	=	=	PUNCT
ejpam-6383	248	31	b̂∩v	b̂∩v	VERB
ejpam-6383	248	32	(	(	PUNCT
ejpam-6383	248	33	q	q	X
ejpam-6383	248	34	)	)	PUNCT
ejpam-6383	248	35	̸=	̸=	PROPN
ejpam-6383	248	36	∅	∅	NOUN
ejpam-6383	248	37	and	and	CCONJ
ejpam-6383	248	38	b̂r	b̂r	NOUN
ejpam-6383	248	39	=	=	NUM
ejpam-6383	248	40	b̂∩v	b̂∩v	NOUN
ejpam-6383	248	41	(	(	PUNCT
ejpam-6383	248	42	r	r	NOUN
ejpam-6383	248	43	)	)	PUNCT
ejpam-6383	248	44	̸=	̸=	PROPN
ejpam-6383	248	45	∅.	∅.	VERB
ejpam-6383	248	46	by	by	ADP
ejpam-6383	248	47	theorem	theorem	ADJ
ejpam-6383	248	48	7	7	NUM
ejpam-6383	248	49	,	,	PUNCT
ejpam-6383	248	50	b	b	NOUN
ejpam-6383	248	51	=	=	SYM
ejpam-6383	248	52	br	br	PROPN
ejpam-6383	248	53	⊕	⊕	PROPN
ejpam-6383	248	54	(	(	PUNCT
ejpam-6383	248	55	w	w	NOUN
ejpam-6383	248	56	)	)	PUNCT
ejpam-6383	248	57	for	for	ADP
ejpam-6383	248	58	some	some	DET
ejpam-6383	248	59	non	non	ADJ
ejpam-6383	248	60	-	-	ADJ
ejpam-6383	248	61	dominating	dominating	ADJ
ejpam-6383	248	62	legal	legal	ADJ
ejpam-6383	248	63	closed	close	VERB
ejpam-6383	248	64	neighborhhood	neighborhhood	NOUN
ejpam-6383	248	65	sequence	sequence	NOUN
ejpam-6383	248	66	br	br	NOUN
ejpam-6383	248	67	of	of	ADP
ejpam-6383	248	68	r	r	NOUN
ejpam-6383	248	69	and	and	CCONJ
ejpam-6383	248	70	w	w	NOUN
ejpam-6383	248	71	∈	∈	PROPN
ejpam-6383	248	72	v	v	ADP
ejpam-6383	248	73	(	(	PUNCT
ejpam-6383	248	74	q	q	NOUN
ejpam-6383	248	75	)	)	PUNCT
ejpam-6383	248	76	.	.	PUNCT
ejpam-6383	249	1	since	since	SCONJ
ejpam-6383	249	2	every	every	DET
ejpam-6383	249	3	legal	legal	ADJ
ejpam-6383	249	4	closed	closed	ADJ
ejpam-6383	249	5	neighborhood	neighborhood	NOUN
ejpam-6383	249	6	sequence	sequence	NOUN
ejpam-6383	249	7	is	be	AUX
ejpam-6383	249	8	an	an	DET
ejpam-6383	249	9	l	l	NOUN
ejpam-6383	249	10	-	-	NOUN
ejpam-6383	249	11	sequence	sequence	NOUN
ejpam-6383	249	12	and	and	CCONJ
ejpam-6383	249	13	b̂	b̂	NOUN
ejpam-6383	249	14	is	be	AUX
ejpam-6383	249	15	a	a	DET
ejpam-6383	249	16	hop	hop	NOUN
ejpam-6383	249	17	independent	independent	ADJ
ejpam-6383	249	18	set	set	NOUN
ejpam-6383	249	19	in	in	ADP
ejpam-6383	249	20	q+r	q+r	NUM
ejpam-6383	249	21	,	,	PUNCT
ejpam-6383	249	22	br	br	PROPN
ejpam-6383	249	23	must	must	AUX
ejpam-6383	249	24	be	be	AUX
ejpam-6383	249	25	a	a	DET
ejpam-6383	249	26	clique	clique	ADJ
ejpam-6383	249	27	non	non	ADJ
ejpam-6383	249	28	-	-	ADJ
ejpam-6383	249	29	dominating	dominating	ADJ
ejpam-6383	249	30	l	l	NOUN
ejpam-6383	249	31	-	-	NOUN
ejpam-6383	249	32	sequence	sequence	NOUN
ejpam-6383	249	33	in	in	ADP
ejpam-6383	249	34	r.	r.	PROPN
ejpam-6383	249	35	hence	hence	ADV
ejpam-6383	249	36	,	,	PUNCT
ejpam-6383	249	37	(	(	PUNCT
ejpam-6383	249	38	iii	iii	NOUN
ejpam-6383	249	39	)	)	PUNCT
ejpam-6383	249	40	holds	hold	VERB
ejpam-6383	249	41	.	.	PUNCT
ejpam-6383	250	1	the	the	DET
ejpam-6383	250	2	converse	converse	NOUN
ejpam-6383	250	3	can	can	AUX
ejpam-6383	250	4	be	be	AUX
ejpam-6383	250	5	proved	prove	VERB
ejpam-6383	250	6	easily	easily	ADV
ejpam-6383	250	7	.	.	PUNCT
ejpam-6383	251	1	the	the	DET
ejpam-6383	251	2	following	follow	VERB
ejpam-6383	251	3	theorem	theorem	NOUN
ejpam-6383	251	4	can	can	AUX
ejpam-6383	251	5	be	be	AUX
ejpam-6383	251	6	proved	prove	VERB
ejpam-6383	251	7	easily	easily	ADV
ejpam-6383	251	8	.	.	PUNCT
ejpam-6383	252	1	theorem	theorem	VERB
ejpam-6383	252	2	9	9	NUM
ejpam-6383	252	3	.	.	PUNCT
ejpam-6383	253	1	let	let	VERB
ejpam-6383	253	2	q	q	NOUN
ejpam-6383	254	1	and	and	CCONJ
ejpam-6383	254	2	r	r	NOUN
ejpam-6383	254	3	be	be	AUX
ejpam-6383	254	4	complete	complete	ADJ
ejpam-6383	254	5	graphs	graph	NOUN
ejpam-6383	254	6	.	.	PUNCT
ejpam-6383	255	1	a	a	DET
ejpam-6383	255	2	sequence	sequence	NOUN
ejpam-6383	255	3	b	b	NOUN
ejpam-6383	255	4	of	of	ADP
ejpam-6383	255	5	distinct	distinct	ADJ
ejpam-6383	255	6	vertices	vertex	NOUN
ejpam-6383	255	7	of	of	ADP
ejpam-6383	255	8	q+r	q+r	NUM
ejpam-6383	255	9	is	be	AUX
ejpam-6383	255	10	an	an	DET
ejpam-6383	255	11	l	l	ADJ
ejpam-6383	255	12	-	-	ADJ
ejpam-6383	255	13	hop	hop	ADJ
ejpam-6383	255	14	independent	independent	ADJ
ejpam-6383	255	15	sequence	sequence	NOUN
ejpam-6383	255	16	if	if	SCONJ
ejpam-6383	255	17	and	and	CCONJ
ejpam-6383	255	18	only	only	ADV
ejpam-6383	255	19	if	if	SCONJ
ejpam-6383	255	20	one	one	NUM
ejpam-6383	255	21	of	of	ADP
ejpam-6383	255	22	the	the	DET
ejpam-6383	255	23	following	follow	VERB
ejpam-6383	255	24	conditions	condition	NOUN
ejpam-6383	255	25	holds	hold	VERB
ejpam-6383	255	26	:	:	PUNCT
ejpam-6383	255	27	(	(	PUNCT
ejpam-6383	255	28	i	i	NOUN
ejpam-6383	255	29	)	)	PUNCT
ejpam-6383	255	30	b	b	PROPN
ejpam-6383	255	31	is	be	AUX
ejpam-6383	255	32	a	a	DET
ejpam-6383	255	33	clique	clique	ADJ
ejpam-6383	255	34	l	l	NOUN
ejpam-6383	255	35	-	-	NOUN
ejpam-6383	255	36	sequence	sequence	NOUN
ejpam-6383	255	37	of	of	ADP
ejpam-6383	255	38	q.	q.	PROPN
ejpam-6383	255	39	(	(	PUNCT
ejpam-6383	255	40	ii	ii	PROPN
ejpam-6383	255	41	)	)	PUNCT
ejpam-6383	255	42	b	b	PROPN
ejpam-6383	255	43	is	be	AUX
ejpam-6383	255	44	a	a	DET
ejpam-6383	255	45	clique	clique	ADJ
ejpam-6383	255	46	l	l	NOUN
ejpam-6383	255	47	-	-	NOUN
ejpam-6383	255	48	sequence	sequence	NOUN
ejpam-6383	255	49	of	of	ADP
ejpam-6383	255	50	r.	r.	PROPN
ejpam-6383	255	51	(	(	PUNCT
ejpam-6383	255	52	iii	iii	PROPN
ejpam-6383	255	53	)	)	PUNCT
ejpam-6383	255	54	a	a	PRON
ejpam-6383	255	55	=	=	SYM
ejpam-6383	255	56	(	(	PUNCT
ejpam-6383	255	57	x	x	NOUN
ejpam-6383	255	58	,	,	PUNCT
ejpam-6383	255	59	y	y	NOUN
ejpam-6383	255	60	)	)	PUNCT
ejpam-6383	255	61	for	for	ADP
ejpam-6383	255	62	some	some	PRON
ejpam-6383	255	63	x	x	SYM
ejpam-6383	255	64	∈	∈	PROPN
ejpam-6383	255	65	v	v	ADP
ejpam-6383	255	66	(	(	PUNCT
ejpam-6383	255	67	h	h	NOUN
ejpam-6383	255	68	)	)	PUNCT
ejpam-6383	255	69	and	and	CCONJ
ejpam-6383	255	70	y	y	PROPN
ejpam-6383	255	71	∈	∈	PROPN
ejpam-6383	255	72	v	v	PROPN
ejpam-6383	255	73	(	(	PUNCT
ejpam-6383	255	74	k	k	NOUN
ejpam-6383	255	75	)	)	PUNCT
ejpam-6383	255	76	.	.	PUNCT
ejpam-6383	256	1	the	the	DET
ejpam-6383	256	2	following	following	ADJ
ejpam-6383	256	3	result	result	NOUN
ejpam-6383	256	4	follows	follow	VERB
ejpam-6383	256	5	from	from	ADP
ejpam-6383	256	6	proposition	proposition	NOUN
ejpam-6383	256	7	1	1	NUM
ejpam-6383	256	8	,	,	PUNCT
ejpam-6383	256	9	theorem	theorem	VERB
ejpam-6383	256	10	6	6	NUM
ejpam-6383	256	11	,	,	PUNCT
ejpam-6383	256	12	theorem	theorem	VERB
ejpam-6383	256	13	8	8	NUM
ejpam-6383	256	14	,	,	PUNCT
ejpam-6383	256	15	and	and	CCONJ
ejpam-6383	256	16	theorem	theorem	VERB
ejpam-6383	256	17	9	9	NUM
ejpam-6383	256	18	.	.	PUNCT
ejpam-6383	256	19	corollary	corollary	ADJ
ejpam-6383	256	20	2	2	NUM
ejpam-6383	256	21	.	.	PUNCT
ejpam-6383	257	1	let	let	VERB
ejpam-6383	257	2	h	h	NOUN
ejpam-6383	257	3	and	and	CCONJ
ejpam-6383	257	4	k	k	PROPN
ejpam-6383	257	5	be	be	AUX
ejpam-6383	257	6	two	two	NUM
ejpam-6383	257	7	graphs	graph	NOUN
ejpam-6383	257	8	.	.	PUNCT
ejpam-6383	258	1	then	then	ADV
ejpam-6383	258	2	(	(	PUNCT
ejpam-6383	258	3	i	i	NOUN
ejpam-6383	258	4	)	)	PUNCT
ejpam-6383	258	5	2	2	NUM
ejpam-6383	258	6	≤	≤	PUNCT
ejpam-6383	258	7	αlh(h	αlh(h	PROPN
ejpam-6383	258	8	+	+	PROPN
ejpam-6383	258	9	k	k	NOUN
ejpam-6383	258	10	)	)	PUNCT
ejpam-6383	258	11	≤	≤	NOUN
ejpam-6383	258	12	3	3	NUM
ejpam-6383	258	13	;	;	PUNCT
ejpam-6383	258	14	and	and	CCONJ
ejpam-6383	258	15	(	(	PUNCT
ejpam-6383	258	16	ii	ii	NOUN
ejpam-6383	258	17	)	)	PUNCT
ejpam-6383	258	18	αlh(h	αlh(h	PROPN
ejpam-6383	259	1	+	+	PROPN
ejpam-6383	259	2	k	k	NOUN
ejpam-6383	259	3	)	)	PUNCT
ejpam-6383	259	4	=	=	SYM
ejpam-6383	259	5	2	2	NUM
ejpam-6383	259	6	if	if	SCONJ
ejpam-6383	259	7	both	both	DET
ejpam-6383	259	8	h	h	NOUN
ejpam-6383	259	9	and	and	CCONJ
ejpam-6383	259	10	k	k	PROPN
ejpam-6383	259	11	are	be	AUX
ejpam-6383	259	12	complete	complete	ADJ
ejpam-6383	259	13	graphs	graph	NOUN
ejpam-6383	259	14	.	.	PUNCT
ejpam-6383	260	1	4	4	X
ejpam-6383	260	2	.	.	X
ejpam-6383	260	3	conclusion	conclusion	VERB
ejpam-6383	260	4	the	the	DET
ejpam-6383	260	5	concept	concept	NOUN
ejpam-6383	260	6	of	of	ADP
ejpam-6383	260	7	l	l	ADJ
ejpam-6383	260	8	-	-	ADJ
ejpam-6383	260	9	hop	hop	ADJ
ejpam-6383	260	10	independent	independent	ADJ
ejpam-6383	260	11	sequence	sequence	NOUN
ejpam-6383	260	12	has	have	AUX
ejpam-6383	260	13	been	be	AUX
ejpam-6383	260	14	introduced	introduce	VERB
ejpam-6383	260	15	and	and	CCONJ
ejpam-6383	260	16	initially	initially	ADV
ejpam-6383	260	17	investigated	investigate	VERB
ejpam-6383	260	18	in	in	ADP
ejpam-6383	260	19	this	this	DET
ejpam-6383	260	20	study	study	NOUN
ejpam-6383	260	21	.	.	PUNCT
ejpam-6383	261	1	some	some	DET
ejpam-6383	261	2	characterizations	characterization	NOUN
ejpam-6383	261	3	and	and	CCONJ
ejpam-6383	261	4	formulas	formula	NOUN
ejpam-6383	261	5	have	have	AUX
ejpam-6383	261	6	been	be	AUX
ejpam-6383	261	7	obtained	obtain	VERB
ejpam-6383	261	8	on	on	ADP
ejpam-6383	261	9	some	some	DET
ejpam-6383	261	10	special	special	ADJ
ejpam-6383	261	11	graphs	graph	NOUN
ejpam-6383	261	12	,	,	PUNCT
ejpam-6383	261	13	complementary	complementary	ADJ
ejpam-6383	261	14	prism	prism	NOUN
ejpam-6383	261	15	,	,	PUNCT
ejpam-6383	261	16	and	and	CCONJ
ejpam-6383	261	17	on	on	ADP
ejpam-6383	261	18	the	the	DET
ejpam-6383	261	19	join	join	NOUN
ejpam-6383	261	20	of	of	ADP
ejpam-6383	261	21	any	any	DET
ejpam-6383	261	22	two	two	NUM
ejpam-6383	261	23	graphs	graph	NOUN
ejpam-6383	261	24	.	.	PUNCT
ejpam-6383	262	1	interested	interested	ADJ
ejpam-6383	262	2	researchers	researcher	NOUN
ejpam-6383	262	3	may	may	AUX
ejpam-6383	262	4	consider	consider	VERB
ejpam-6383	262	5	studying	study	VERB
ejpam-6383	262	6	the	the	DET
ejpam-6383	262	7	complexity	complexity	NOUN
ejpam-6383	262	8	of	of	ADP
ejpam-6383	262	9	this	this	DET
ejpam-6383	262	10	newly	newly	ADV
ejpam-6383	262	11	defined	define	VERB
ejpam-6383	262	12	concept	concept	NOUN
ejpam-6383	262	13	,	,	PUNCT
ejpam-6383	262	14	and	and	CCONJ
ejpam-6383	262	15	they	they	PRON
ejpam-6383	262	16	may	may	AUX
ejpam-6383	262	17	also	also	ADV
ejpam-6383	262	18	consider	consider	VERB
ejpam-6383	262	19	providing	provide	VERB
ejpam-6383	262	20	real	real	ADJ
ejpam-6383	262	21	-	-	PUNCT
ejpam-6383	262	22	world	world	NOUN
ejpam-6383	262	23	applications	application	NOUN
ejpam-6383	262	24	.	.	PUNCT
ejpam-6383	263	1	acknowledgements	acknowledgement	NOUN
ejpam-6383	263	2	the	the	DET
ejpam-6383	263	3	authors	author	NOUN
ejpam-6383	263	4	would	would	AUX
ejpam-6383	263	5	like	like	VERB
ejpam-6383	263	6	to	to	PART
ejpam-6383	263	7	thank	thank	VERB
ejpam-6383	263	8	mindanao	mindanao	PROPN
ejpam-6383	263	9	state	state	PROPN
ejpam-6383	263	10	university	university	PROPN
ejpam-6383	263	11	-	-	PUNCT
ejpam-6383	263	12	tawi	tawi	NOUN
ejpam-6383	263	13	-	-	PUNCT
ejpam-6383	263	14	tawi	tawi	NOUN
ejpam-6383	263	15	college	college	PROPN
ejpam-6383	263	16	of	of	ADP
ejpam-6383	263	17	technology	technology	NOUN
ejpam-6383	263	18	and	and	CCONJ
ejpam-6383	263	19	oceanography	oceanography	NOUN
ejpam-6383	263	20	and	and	CCONJ
ejpam-6383	263	21	korea	korea	PROPN
ejpam-6383	263	22	university	university	PROPN
ejpam-6383	263	23	for	for	ADP
ejpam-6383	263	24	funding	fund	VERB
ejpam-6383	263	25	this	this	DET
ejpam-6383	263	26	research	research	NOUN
ejpam-6383	263	27	.	.	PUNCT
ejpam-6383	264	1	references	reference	NOUN
ejpam-6383	264	2	[	[	X
ejpam-6383	264	3	1	1	NUM
ejpam-6383	264	4	]	]	PUNCT
ejpam-6383	264	5	e.	e.	PROPN
ejpam-6383	264	6	davies	davies	PROPN
ejpam-6383	264	7	,	,	PUNCT
ejpam-6383	264	8	m.	m.	PROPN
ejpam-6383	264	9	jenssen	jenssen	PROPN
ejpam-6383	264	10	,	,	PUNCT
ejpam-6383	264	11	w.	w.	PROPN
ejpam-6383	264	12	perkins	perkins	PROPN
ejpam-6383	264	13	,	,	PUNCT
ejpam-6383	264	14	and	and	CCONJ
ejpam-6383	264	15	b.	b.	PROPN
ejpam-6383	264	16	roberts	roberts	PROPN
ejpam-6383	264	17	.	.	PUNCT
ejpam-6383	265	1	independent	independent	ADJ
ejpam-6383	265	2	sets	set	NOUN
ejpam-6383	265	3	,	,	PUNCT
ejpam-6383	265	4	matchings	matching	NOUN
ejpam-6383	265	5	,	,	PUNCT
ejpam-6383	265	6	and	and	CCONJ
ejpam-6383	265	7	occupancy	occupancy	NOUN
ejpam-6383	265	8	fractions	fraction	NOUN
ejpam-6383	265	9	.	.	PUNCT
ejpam-6383	266	1	journal	journal	NOUN
ejpam-6383	266	2	of	of	ADP
ejpam-6383	266	3	the	the	DET
ejpam-6383	266	4	london	london	PROPN
ejpam-6383	266	5	mathematical	mathematical	ADJ
ejpam-6383	266	6	society	society	NOUN
ejpam-6383	266	7	,	,	PUNCT
ejpam-6383	266	8	96(1):47–66	96(1):47–66	NUM
ejpam-6383	266	9	,	,	PUNCT
ejpam-6383	266	10	2017	2017	NUM
ejpam-6383	266	11	.	.	PUNCT
ejpam-6383	267	1	k.	k.	PROPN
ejpam-6383	267	2	maharajul	maharajul	PROPN
ejpam-6383	267	3	,	,	PUNCT
ejpam-6383	267	4	j.	j.	PROPN
ejpam-6383	267	5	a.	a.	PROPN
ejpam-6383	267	6	hassan	hassan	PROPN
ejpam-6383	267	7	,	,	PUNCT
ejpam-6383	267	8	l.	l.	PROPN
ejpam-6383	267	9	laja	laja	PROPN
ejpam-6383	267	10	/	/	SYM
ejpam-6383	267	11	eur	eur	PROPN
ejpam-6383	267	12	.	.	PUNCT
ejpam-6383	268	1	j.	j.	PROPN
ejpam-6383	268	2	pure	pure	PROPN
ejpam-6383	268	3	appl	appl	PROPN
ejpam-6383	268	4	.	.	PROPN
ejpam-6383	268	5	math	math	PROPN
ejpam-6383	268	6	,	,	PUNCT
ejpam-6383	268	7	18	18	NUM
ejpam-6383	268	8	(	(	PUNCT
ejpam-6383	268	9	3	3	NUM
ejpam-6383	268	10	)	)	PUNCT
ejpam-6383	268	11	(	(	PUNCT
ejpam-6383	268	12	2025	2025	NUM
ejpam-6383	268	13	)	)	PUNCT
ejpam-6383	268	14	,	,	PUNCT
ejpam-6383	268	15	6383	6383	NUM
ejpam-6383	268	16	10	10	NUM
ejpam-6383	268	17	of	of	ADP
ejpam-6383	268	18	10	10	NUM
ejpam-6383	268	19	[	[	X
ejpam-6383	268	20	2	2	NUM
ejpam-6383	268	21	]	]	PUNCT
ejpam-6383	268	22	j.	j.	PROPN
ejpam-6383	268	23	hassan	hassan	PROPN
ejpam-6383	268	24	,	,	PUNCT
ejpam-6383	268	25	s.	s.	PROPN
ejpam-6383	268	26	canoy	canoy	PROPN
ejpam-6383	268	27	jr	jr	PROPN
ejpam-6383	268	28	.	.	PROPN
ejpam-6383	268	29	,	,	PUNCT
ejpam-6383	268	30	and	and	CCONJ
ejpam-6383	268	31	a.	a.	PROPN
ejpam-6383	268	32	aradais	aradais	PROPN
ejpam-6383	268	33	.	.	PUNCT
ejpam-6383	269	1	hop	hop	PROPN
ejpam-6383	269	2	independent	independent	ADJ
ejpam-6383	269	3	sets	set	NOUN
ejpam-6383	269	4	in	in	ADP
ejpam-6383	269	5	graphs	graph	NOUN
ejpam-6383	269	6	.	.	PUNCT
ejpam-6383	270	1	european	european	ADJ
ejpam-6383	270	2	journal	journal	PROPN
ejpam-6383	270	3	of	of	ADP
ejpam-6383	270	4	pure	pure	ADJ
ejpam-6383	270	5	and	and	CCONJ
ejpam-6383	270	6	applied	applied	ADJ
ejpam-6383	270	7	mathematics	mathematic	NOUN
ejpam-6383	270	8	,	,	PUNCT
ejpam-6383	270	9	15(2):467–477	15(2):467–477	PROPN
ejpam-6383	270	10	,	,	PUNCT
ejpam-6383	270	11	2022	2022	NUM
ejpam-6383	270	12	.	.	PUNCT
ejpam-6383	271	1	[	[	X
ejpam-6383	271	2	3	3	X
ejpam-6383	271	3	]	]	PUNCT
ejpam-6383	271	4	z.	z.	PROPN
ejpam-6383	271	5	furedi	furedi	PROPN
ejpam-6383	271	6	.	.	PUNCT
ejpam-6383	272	1	the	the	DET
ejpam-6383	272	2	number	number	NOUN
ejpam-6383	272	3	of	of	ADP
ejpam-6383	272	4	maximal	maximal	ADJ
ejpam-6383	272	5	independent	independent	ADJ
ejpam-6383	272	6	sets	set	NOUN
ejpam-6383	272	7	in	in	ADP
ejpam-6383	272	8	connected	connected	ADJ
ejpam-6383	272	9	graphs	graph	NOUN
ejpam-6383	272	10	.	.	PUNCT
ejpam-6383	273	1	journal	journal	NOUN
ejpam-6383	273	2	of	of	ADP
ejpam-6383	273	3	graph	graph	NOUN
ejpam-6383	273	4	theory	theory	NOUN
ejpam-6383	273	5	,	,	PUNCT
ejpam-6383	273	6	11(4):463–470	11(4):463–470	NOUN
ejpam-6383	273	7	,	,	PUNCT
ejpam-6383	273	8	1987	1987	NUM
ejpam-6383	273	9	.	.	PUNCT
ejpam-6383	274	1	[	[	X
ejpam-6383	274	2	4	4	X
ejpam-6383	274	3	]	]	PUNCT
ejpam-6383	274	4	j.	j.	PROPN
ejpam-6383	274	5	r.	r.	PROPN
ejpam-6383	274	6	griggs	griggs	PROPN
ejpam-6383	274	7	,	,	PUNCT
ejpam-6383	274	8	c.	c.	PROPN
ejpam-6383	274	9	m.	m.	PROPN
ejpam-6383	274	10	grinstead	grinstead	PROPN
ejpam-6383	274	11	,	,	PUNCT
ejpam-6383	274	12	and	and	CCONJ
ejpam-6383	274	13	d.	d.	PROPN
ejpam-6383	274	14	r.	r.	PROPN
ejpam-6383	274	15	guichard	guichard	PROPN
ejpam-6383	274	16	.	.	PUNCT
ejpam-6383	275	1	the	the	DET
ejpam-6383	275	2	number	number	NOUN
ejpam-6383	275	3	of	of	ADP
ejpam-6383	275	4	maximal	maximal	ADJ
ejpam-6383	275	5	independent	independent	ADJ
ejpam-6383	275	6	sets	set	NOUN
ejpam-6383	275	7	in	in	ADP
ejpam-6383	275	8	a	a	DET
ejpam-6383	275	9	connected	connected	ADJ
ejpam-6383	275	10	graph	graph	NOUN
ejpam-6383	275	11	.	.	PUNCT
ejpam-6383	275	12	discrete	discrete	ADJ
ejpam-6383	275	13	mathematics	mathematic	NOUN
ejpam-6383	275	14	,	,	PUNCT
ejpam-6383	275	15	68:211–220	68:211–220	PROPN
ejpam-6383	275	16	,	,	PUNCT
ejpam-6383	275	17	1988	1988	NUM
ejpam-6383	275	18	.	.	PUNCT
ejpam-6383	276	1	[	[	X
ejpam-6383	276	2	5	5	X
ejpam-6383	276	3	]	]	PUNCT
ejpam-6383	276	4	j.	j.	PROPN
ejpam-6383	276	5	hassan	hassan	PROPN
ejpam-6383	276	6	,	,	PUNCT
ejpam-6383	276	7	m.	m.	NOUN
ejpam-6383	276	8	langamin	langamin	PROPN
ejpam-6383	276	9	,	,	PUNCT
ejpam-6383	276	10	a.	a.	NOUN
ejpam-6383	276	11	laja	laja	PROPN
ejpam-6383	276	12	,	,	PUNCT
ejpam-6383	276	13	b.	b.	PROPN
ejpam-6383	276	14	amiruddin	amiruddin	PROPN
ejpam-6383	276	15	-	-	PUNCT
ejpam-6383	276	16	rajik	rajik	NOUN
ejpam-6383	276	17	,	,	PUNCT
ejpam-6383	276	18	e.	e.	PROPN
ejpam-6383	276	19	ahmad	ahmad	PROPN
ejpam-6383	276	20	,	,	PUNCT
ejpam-6383	276	21	and	and	CCONJ
ejpam-6383	276	22	j.	j.	PROPN
ejpam-6383	276	23	manditong	manditong	PROPN
ejpam-6383	276	24	.	.	PUNCT
ejpam-6383	277	1	legal	legal	ADJ
ejpam-6383	277	2	hop	hop	NOUN
ejpam-6383	277	3	independent	independent	ADJ
ejpam-6383	277	4	sequences	sequence	NOUN
ejpam-6383	277	5	in	in	ADP
ejpam-6383	277	6	graphs	graph	NOUN
ejpam-6383	277	7	.	.	PUNCT
ejpam-6383	278	1	european	european	ADJ
ejpam-6383	278	2	journal	journal	PROPN
ejpam-6383	278	3	of	of	ADP
ejpam-6383	278	4	pure	pure	ADJ
ejpam-6383	278	5	and	and	CCONJ
ejpam-6383	278	6	applied	applied	ADJ
ejpam-6383	278	7	mathematics	mathematic	NOUN
ejpam-6383	278	8	,	,	PUNCT
ejpam-6383	278	9	17(2):725–735	17(2):725–735	NUM
ejpam-6383	278	10	,	,	PUNCT
ejpam-6383	278	11	2024	2024	NUM
ejpam-6383	278	12	.	.	PUNCT
ejpam-6383	279	1	[	[	X
ejpam-6383	279	2	6	6	NUM
ejpam-6383	279	3	]	]	PUNCT
ejpam-6383	279	4	s.	s.	PROPN
ejpam-6383	279	5	kaida	kaida	PROPN
ejpam-6383	279	6	,	,	PUNCT
ejpam-6383	279	7	k.	k.	PROPN
ejpam-6383	279	8	j.	j.	PROPN
ejpam-6383	279	9	maharajul	maharajul	PROPN
ejpam-6383	279	10	,	,	PUNCT
ejpam-6383	279	11	j.	j.	PROPN
ejpam-6383	279	12	hassan	hassan	PROPN
ejpam-6383	279	13	,	,	PUNCT
ejpam-6383	279	14	l.	l.	PROPN
ejpam-6383	279	15	laja	laja	PROPN
ejpam-6383	279	16	,	,	PUNCT
ejpam-6383	279	17	a.	a.	NOUN
ejpam-6383	279	18	lintasan	lintasan	NOUN
ejpam-6383	279	19	,	,	PUNCT
ejpam-6383	279	20	and	and	CCONJ
ejpam-6383	279	21	a.	a.	NOUN
ejpam-6383	279	22	pablo	pablo	PROPN
ejpam-6383	279	23	.	.	PUNCT
ejpam-6383	280	1	certified	certify	VERB
ejpam-6383	280	2	hop	hop	NOUN
ejpam-6383	280	3	independence	independence	NOUN
ejpam-6383	280	4	:	:	PUNCT
ejpam-6383	280	5	properties	property	NOUN
ejpam-6383	280	6	and	and	CCONJ
ejpam-6383	280	7	connections	connection	NOUN
ejpam-6383	280	8	with	with	ADP
ejpam-6383	280	9	other	other	ADJ
ejpam-6383	280	10	variants	variant	NOUN
ejpam-6383	280	11	of	of	ADP
ejpam-6383	280	12	independence	independence	NOUN
ejpam-6383	280	13	.	.	PUNCT
ejpam-6383	281	1	european	european	ADJ
ejpam-6383	281	2	journal	journal	PROPN
ejpam-6383	281	3	of	of	ADP
ejpam-6383	281	4	pure	pure	ADJ
ejpam-6383	281	5	and	and	CCONJ
ejpam-6383	281	6	applied	applied	ADJ
ejpam-6383	281	7	mathematics	mathematic	NOUN
ejpam-6383	281	8	,	,	PUNCT
ejpam-6383	281	9	17(1):435–444	17(1):435–444	NUM
ejpam-6383	281	10	,	,	PUNCT
ejpam-6383	281	11	2024	2024	NUM
ejpam-6383	281	12	.	.	PUNCT
ejpam-6383	282	1	[	[	X
ejpam-6383	282	2	7	7	X
ejpam-6383	282	3	]	]	X
ejpam-6383	282	4	g.	g.	PROPN
ejpam-6383	282	5	hopkins	hopkins	PROPN
ejpam-6383	282	6	and	and	CCONJ
ejpam-6383	282	7	w.	w.	PROPN
ejpam-6383	282	8	staton	staton	PROPN
ejpam-6383	282	9	.	.	PUNCT
ejpam-6383	283	1	graphs	graph	NOUN
ejpam-6383	283	2	with	with	ADP
ejpam-6383	283	3	unique	unique	ADJ
ejpam-6383	283	4	maximum	maximum	ADJ
ejpam-6383	283	5	independent	independent	ADJ
ejpam-6383	283	6	sets	set	NOUN
ejpam-6383	283	7	.	.	PUNCT
ejpam-6383	284	1	discrete	discrete	ADJ
ejpam-6383	284	2	mathematics	mathematic	NOUN
ejpam-6383	284	3	,	,	PUNCT
ejpam-6383	284	4	57:245–251	57:245–251	PROPN
ejpam-6383	284	5	,	,	PUNCT
ejpam-6383	284	6	1985	1985	NUM
ejpam-6383	284	7	.	.	PUNCT
ejpam-6383	285	1	[	[	X
ejpam-6383	285	2	8	8	NUM
ejpam-6383	285	3	]	]	X
ejpam-6383	285	4	d.	d.	PROPN
ejpam-6383	285	5	g.	g.	PROPN
ejpam-6383	285	6	c.	c.	PROPN
ejpam-6383	285	7	horrocks	horrocks	PROPN
ejpam-6383	285	8	.	.	PUNCT
ejpam-6383	286	1	doubly	doubly	ADV
ejpam-6383	286	2	independent	independent	ADJ
ejpam-6383	286	3	sets	set	NOUN
ejpam-6383	286	4	in	in	ADP
ejpam-6383	286	5	graphs	graph	NOUN
ejpam-6383	286	6	.	.	PUNCT
ejpam-6383	287	1	australasian	australasian	ADJ
ejpam-6383	287	2	journal	journal	NOUN
ejpam-6383	287	3	of	of	ADP
ejpam-6383	287	4	combinatorics	combinatoric	NOUN
ejpam-6383	287	5	,	,	PUNCT
ejpam-6383	287	6	22:105–116	22:105–116	PROPN
ejpam-6383	287	7	,	,	PUNCT
ejpam-6383	287	8	2000	2000	NUM
ejpam-6383	287	9	.	.	PUNCT
ejpam-6383	288	1	[	[	X
ejpam-6383	288	2	9	9	NUM
ejpam-6383	288	3	]	]	PUNCT
ejpam-6383	288	4	m.	m.	NOUN
ejpam-6383	288	5	jou	jou	INTJ
ejpam-6383	288	6	and	and	CCONJ
ejpam-6383	288	7	g.	g.	PROPN
ejpam-6383	288	8	chang	chang	PROPN
ejpam-6383	288	9	.	.	PUNCT
ejpam-6383	289	1	the	the	DET
ejpam-6383	289	2	number	number	NOUN
ejpam-6383	289	3	of	of	ADP
ejpam-6383	289	4	maximum	maximum	ADJ
ejpam-6383	289	5	independent	independent	ADJ
ejpam-6383	289	6	sets	set	NOUN
ejpam-6383	289	7	of	of	ADP
ejpam-6383	289	8	graphs	graph	NOUN
ejpam-6383	289	9	.	.	PUNCT
ejpam-6383	290	1	taiwanese	taiwanese	ADJ
ejpam-6383	290	2	journal	journal	NOUN
ejpam-6383	290	3	of	of	ADP
ejpam-6383	290	4	mathematics	mathematic	NOUN
ejpam-6383	290	5	,	,	PUNCT
ejpam-6383	290	6	4(4):685–695	4(4):685–695	NUM
ejpam-6383	290	7	,	,	PUNCT
ejpam-6383	290	8	2000	2000	NUM
ejpam-6383	290	9	.	.	PUNCT
ejpam-6383	291	1	[	[	X
ejpam-6383	291	2	10	10	NUM
ejpam-6383	291	3	]	]	X
ejpam-6383	291	4	h.	h.	PROPN
ejpam-6383	291	5	s.	s.	PROPN
ejpam-6383	291	6	wilf	wilf	PROPN
ejpam-6383	291	7	.	.	PUNCT
ejpam-6383	292	1	the	the	DET
ejpam-6383	292	2	number	number	NOUN
ejpam-6383	292	3	of	of	ADP
ejpam-6383	292	4	maximal	maximal	ADJ
ejpam-6383	292	5	independent	independent	ADJ
ejpam-6383	292	6	sets	set	NOUN
ejpam-6383	292	7	in	in	ADP
ejpam-6383	292	8	a	a	DET
ejpam-6383	292	9	tree	tree	NOUN
ejpam-6383	292	10	.	.	PUNCT
ejpam-6383	293	1	siam	siam	PROPN
ejpam-6383	293	2	journal	journal	PROPN
ejpam-6383	293	3	on	on	ADP
ejpam-6383	293	4	algebraic	algebraic	ADJ
ejpam-6383	293	5	and	and	CCONJ
ejpam-6383	293	6	discrete	discrete	ADJ
ejpam-6383	293	7	methods	method	NOUN
ejpam-6383	293	8	,	,	PUNCT
ejpam-6383	293	9	7:125–130	7:125–130	NUM
ejpam-6383	293	10	,	,	PUNCT
ejpam-6383	293	11	1986	1986	NUM
ejpam-6383	293	12	.	.	PUNCT
ejpam-6383	294	1	[	[	X
ejpam-6383	294	2	11	11	NUM
ejpam-6383	294	3	]	]	PUNCT
ejpam-6383	294	4	j.	j.	PROPN
ejpam-6383	294	5	zito	zito	PROPN
ejpam-6383	294	6	.	.	PUNCT
ejpam-6383	295	1	the	the	DET
ejpam-6383	295	2	structure	structure	NOUN
ejpam-6383	295	3	and	and	CCONJ
ejpam-6383	295	4	maximum	maximum	ADJ
ejpam-6383	295	5	number	number	NOUN
ejpam-6383	295	6	of	of	ADP
ejpam-6383	295	7	maximum	maximum	ADJ
ejpam-6383	295	8	independent	independent	ADJ
ejpam-6383	295	9	sets	set	NOUN
ejpam-6383	295	10	in	in	ADP
ejpam-6383	295	11	trees	tree	NOUN
ejpam-6383	295	12	.	.	PUNCT
ejpam-6383	296	1	journal	journal	PROPN
ejpam-6383	296	2	of	of	ADP
ejpam-6383	296	3	graph	graph	NOUN
ejpam-6383	296	4	theory	theory	NOUN
ejpam-6383	296	5	,	,	PUNCT
ejpam-6383	296	6	15(2):207–221	15(2):207–221	NUM
ejpam-6383	296	7	,	,	PUNCT
ejpam-6383	296	8	1991	1991	NUM
ejpam-6383	296	9	.	.	PUNCT
ejpam-6383	297	1	[	[	X
ejpam-6383	297	2	12	12	NUM
ejpam-6383	297	3	]	]	PUNCT
ejpam-6383	297	4	j.	j.	PROPN
ejpam-6383	297	5	hassan	hassan	PROPN
ejpam-6383	297	6	and	and	CCONJ
ejpam-6383	297	7	s.	s.	PROPN
ejpam-6383	297	8	canoy	canoy	PROPN
ejpam-6383	297	9	jr	jr	PROPN
ejpam-6383	297	10	.	.	PUNCT
ejpam-6383	298	1	grundy	grundy	PROPN
ejpam-6383	298	2	dominating	dominating	PROPN
ejpam-6383	298	3	and	and	CCONJ
ejpam-6383	298	4	grundy	grundy	PROPN
ejpam-6383	298	5	hop	hop	NOUN
ejpam-6383	298	6	dominating	dominate	VERB
ejpam-6383	298	7	sequences	sequence	NOUN
ejpam-6383	298	8	in	in	ADP
ejpam-6383	298	9	graphs	graph	NOUN
ejpam-6383	298	10	:	:	PUNCT
ejpam-6383	298	11	relationships	relationship	NOUN
ejpam-6383	298	12	and	and	CCONJ
ejpam-6383	298	13	some	some	DET
ejpam-6383	298	14	structural	structural	ADJ
ejpam-6383	298	15	properties	property	NOUN
ejpam-6383	298	16	.	.	PUNCT
ejpam-6383	299	1	european	european	ADJ
ejpam-6383	299	2	journal	journal	PROPN
ejpam-6383	299	3	of	of	ADP
ejpam-6383	299	4	pure	pure	ADJ
ejpam-6383	299	5	and	and	CCONJ
ejpam-6383	299	6	applied	applied	ADJ
ejpam-6383	299	7	mathematics	mathematic	NOUN
ejpam-6383	299	8	,	,	PUNCT
ejpam-6383	299	9	16(2):1154–1166	16(2):1154–1166	NUM
ejpam-6383	299	10	,	,	PUNCT
ejpam-6383	299	11	2023	2023	NUM
ejpam-6383	299	12	.	.	PUNCT