id	sid	tid	token	lemma	pos
ejpam-4511	1	1	european	european	PROPN
ejpam-4511	1	2	journal	journal	PROPN
ejpam-4511	1	3	of	of	ADP
ejpam-4511	1	4	pure	pure	ADJ
ejpam-4511	1	5	and	and	CCONJ
ejpam-4511	1	6	applied	apply	VERB
ejpam-4511	1	7	mathematics	mathematic	NOUN
ejpam-4511	1	8	vol	vol	NOUN
ejpam-4511	1	9	.	.	PROPN
ejpam-4511	2	1	15	15	NUM
ejpam-4511	2	2	,	,	PUNCT
ejpam-4511	2	3	no	no	INTJ
ejpam-4511	2	4	.	.	NOUN
ejpam-4511	2	5	4	4	NUM
ejpam-4511	2	6	,	,	PUNCT
ejpam-4511	2	7	2022	2022	NUM
ejpam-4511	2	8	,	,	PUNCT
ejpam-4511	2	9	1623	1623	NUM
ejpam-4511	2	10	-	-	SYM
ejpam-4511	2	11	1636	1636	NUM
ejpam-4511	2	12	issn	issn	PROPN
ejpam-4511	2	13	1307	1307	NUM
ejpam-4511	2	14	-	-	SYM
ejpam-4511	2	15	5543	5543	NUM
ejpam-4511	2	16	–	–	PUNCT
ejpam-4511	2	17	ejpam.com	ejpam.com	X
ejpam-4511	2	18	published	publish	VERB
ejpam-4511	2	19	by	by	ADP
ejpam-4511	2	20	new	new	PROPN
ejpam-4511	2	21	york	york	PROPN
ejpam-4511	2	22	business	business	PROPN
ejpam-4511	2	23	global	global	PROPN
ejpam-4511	2	24	grundy	grundy	PROPN
ejpam-4511	2	25	hop	hop	PROPN
ejpam-4511	2	26	domination	domination	NOUN
ejpam-4511	2	27	in	in	ADP
ejpam-4511	2	28	graphs	graph	NOUN
ejpam-4511	2	29	javier	javier	PROPN
ejpam-4511	2	30	a.	a.	PROPN
ejpam-4511	2	31	hassan1,∗	hassan1,∗	PROPN
ejpam-4511	2	32	,	,	PUNCT
ejpam-4511	2	33	sergio	sergio	PROPN
ejpam-4511	2	34	r.	r.	PROPN
ejpam-4511	2	35	canoy	canoy	PROPN
ejpam-4511	2	36	,	,	PUNCT
ejpam-4511	2	37	jr.2	jr.2	PROPN
ejpam-4511	2	38	1,2	1,2	NUM
ejpam-4511	2	39	department	department	NOUN
ejpam-4511	2	40	of	of	ADP
ejpam-4511	2	41	mathematics	mathematic	NOUN
ejpam-4511	2	42	and	and	CCONJ
ejpam-4511	2	43	statistics	statistic	NOUN
ejpam-4511	2	44	,	,	PUNCT
ejpam-4511	2	45	college	college	NOUN
ejpam-4511	2	46	of	of	ADP
ejpam-4511	2	47	science	science	NOUN
ejpam-4511	2	48	and	and	CCONJ
ejpam-4511	2	49	mathematics	mathematic	NOUN
ejpam-4511	2	50	,	,	PUNCT
ejpam-4511	2	51	center	center	NOUN
ejpam-4511	2	52	for	for	ADP
ejpam-4511	2	53	graph	graph	NOUN
ejpam-4511	2	54	theory	theory	NOUN
ejpam-4511	2	55	,	,	PUNCT
ejpam-4511	2	56	premier	premier	PROPN
ejpam-4511	2	57	research	research	PROPN
ejpam-4511	2	58	institute	institute	PROPN
ejpam-4511	2	59	of	of	ADP
ejpam-4511	2	60	science	science	NOUN
ejpam-4511	2	61	and	and	CCONJ
ejpam-4511	2	62	mathematics	mathematic	NOUN
ejpam-4511	2	63	,	,	PUNCT
ejpam-4511	2	64	msu	msu	PROPN
ejpam-4511	2	65	-	-	PUNCT
ejpam-4511	2	66	iligan	iligan	PROPN
ejpam-4511	2	67	institute	institute	PROPN
ejpam-4511	2	68	of	of	ADP
ejpam-4511	2	69	technology	technology	PROPN
ejpam-4511	2	70	,	,	PUNCT
ejpam-4511	2	71	9200	9200	NUM
ejpam-4511	2	72	iligan	iligan	ADJ
ejpam-4511	2	73	city	city	NOUN
ejpam-4511	2	74	,	,	PUNCT
ejpam-4511	2	75	philippines	philippine	NOUN
ejpam-4511	2	76	abstract	abstract	ADJ
ejpam-4511	2	77	.	.	PUNCT
ejpam-4511	3	1	let	let	VERB
ejpam-4511	3	2	g	g	PRON
ejpam-4511	3	3	be	be	AUX
ejpam-4511	3	4	an	an	DET
ejpam-4511	3	5	undirected	undirected	ADJ
ejpam-4511	3	6	graph	graph	NOUN
ejpam-4511	3	7	with	with	ADP
ejpam-4511	3	8	vertex	vertex	NOUN
ejpam-4511	3	9	and	and	CCONJ
ejpam-4511	3	10	edge	edge	NOUN
ejpam-4511	3	11	sets	set	NOUN
ejpam-4511	3	12	v	v	ADP
ejpam-4511	3	13	(	(	PUNCT
ejpam-4511	3	14	g	g	NOUN
ejpam-4511	3	15	)	)	PUNCT
ejpam-4511	3	16	and	and	CCONJ
ejpam-4511	3	17	e(g	e(g	PROPN
ejpam-4511	3	18	)	)	PUNCT
ejpam-4511	3	19	,	,	PUNCT
ejpam-4511	3	20	respectively	respectively	ADV
ejpam-4511	3	21	.	.	PUNCT
ejpam-4511	4	1	let	let	VERB
ejpam-4511	4	2	s	s	PRON
ejpam-4511	4	3	=	=	PUNCT
ejpam-4511	4	4	(	(	PUNCT
ejpam-4511	4	5	v1	v1	PROPN
ejpam-4511	4	6	,	,	PUNCT
ejpam-4511	4	7	v2	v2	PROPN
ejpam-4511	4	8	,	,	PUNCT
ejpam-4511	4	9	·	·	PUNCT
ejpam-4511	4	10	·	·	PUNCT
ejpam-4511	4	11	·	·	PUNCT
ejpam-4511	4	12	,	,	PUNCT
ejpam-4511	4	13	vk	vk	AUX
ejpam-4511	4	14	)	)	PUNCT
ejpam-4511	4	15	be	be	AUX
ejpam-4511	4	16	a	a	DET
ejpam-4511	4	17	sequence	sequence	NOUN
ejpam-4511	4	18	of	of	ADP
ejpam-4511	4	19	distinct	distinct	ADJ
ejpam-4511	4	20	vertices	vertex	NOUN
ejpam-4511	4	21	of	of	ADP
ejpam-4511	4	22	g	g	NOUN
ejpam-4511	4	23	and	and	CCONJ
ejpam-4511	4	24	let	let	VERB
ejpam-4511	4	25	ŝ	ŝ	X
ejpam-4511	4	26	=	=	SYM
ejpam-4511	4	27	{	{	PUNCT
ejpam-4511	4	28	v1	v1	PROPN
ejpam-4511	4	29	,	,	PUNCT
ejpam-4511	4	30	v2	v2	PROPN
ejpam-4511	4	31	,	,	PUNCT
ejpam-4511	4	32	.	.	PUNCT
ejpam-4511	4	33	.	.	PUNCT
ejpam-4511	5	1	.	.	PUNCT
ejpam-4511	6	1	,	,	PUNCT
ejpam-4511	6	2	vk	vk	ADP
ejpam-4511	6	3	}	}	PUNCT
ejpam-4511	6	4	.	.	PUNCT
ejpam-4511	7	1	then	then	ADV
ejpam-4511	7	2	s	s	VERB
ejpam-4511	7	3	is	be	AUX
ejpam-4511	7	4	a	a	DET
ejpam-4511	7	5	legal	legal	ADJ
ejpam-4511	7	6	closed	close	VERB
ejpam-4511	7	7	hop	hop	NOUN
ejpam-4511	7	8	neighborhood	neighborhood	NOUN
ejpam-4511	7	9	sequence	sequence	NOUN
ejpam-4511	7	10	of	of	ADP
ejpam-4511	7	11	g	g	PROPN
ejpam-4511	7	12	if	if	SCONJ
ejpam-4511	7	13	n2	n2	ADJ
ejpam-4511	7	14	g[vi]\∪	g[vi]\∪	VERB
ejpam-4511	7	15	i−1	i−1	PROPN
ejpam-4511	7	16	j=1n	j=1n	PROPN
ejpam-4511	7	17	2	2	NUM
ejpam-4511	7	18	g[vj	g[vj	PROPN
ejpam-4511	7	19	]	]	PUNCT
ejpam-4511	7	20	̸=	̸=	PROPN
ejpam-4511	7	21	∅	∅	NOUN
ejpam-4511	7	22	for	for	ADP
ejpam-4511	7	23	each	each	DET
ejpam-4511	7	24	i	i	PRON
ejpam-4511	7	25	∈	∈	PROPN
ejpam-4511	7	26	{	{	PUNCT
ejpam-4511	7	27	2	2	NUM
ejpam-4511	7	28	,	,	PUNCT
ejpam-4511	7	29	·	·	PUNCT
ejpam-4511	7	30	·	·	PUNCT
ejpam-4511	7	31	·	·	PUNCT
ejpam-4511	7	32	,	,	PUNCT
ejpam-4511	7	33	k	k	NOUN
ejpam-4511	7	34	}	}	PUNCT
ejpam-4511	7	35	.	.	PUNCT
ejpam-4511	8	1	if	if	SCONJ
ejpam-4511	8	2	,	,	PUNCT
ejpam-4511	8	3	in	in	ADP
ejpam-4511	8	4	addition	addition	NOUN
ejpam-4511	8	5	,	,	PUNCT
ejpam-4511	8	6	ŝ	ŝ	X
ejpam-4511	8	7	is	be	AUX
ejpam-4511	8	8	a	a	DET
ejpam-4511	8	9	hop	hop	NOUN
ejpam-4511	8	10	dominating	dominating	NOUN
ejpam-4511	8	11	set	set	NOUN
ejpam-4511	8	12	of	of	ADP
ejpam-4511	8	13	g	g	PROPN
ejpam-4511	8	14	,	,	PUNCT
ejpam-4511	8	15	then	then	ADV
ejpam-4511	8	16	s	s	VERB
ejpam-4511	8	17	is	be	AUX
ejpam-4511	8	18	called	call	VERB
ejpam-4511	8	19	a	a	DET
ejpam-4511	8	20	grundy	grundy	PROPN
ejpam-4511	8	21	hop	hop	NOUN
ejpam-4511	8	22	dominating	dominating	NOUN
ejpam-4511	8	23	sequence	sequence	NOUN
ejpam-4511	8	24	.	.	PUNCT
ejpam-4511	9	1	the	the	DET
ejpam-4511	9	2	maximum	maximum	ADJ
ejpam-4511	9	3	length	length	NOUN
ejpam-4511	9	4	of	of	ADP
ejpam-4511	9	5	a	a	DET
ejpam-4511	9	6	grundy	grundy	PROPN
ejpam-4511	9	7	hop	hop	NOUN
ejpam-4511	9	8	dominating	dominating	NOUN
ejpam-4511	9	9	sequence	sequence	NOUN
ejpam-4511	9	10	in	in	ADP
ejpam-4511	9	11	a	a	DET
ejpam-4511	9	12	graph	graph	NOUN
ejpam-4511	9	13	g	g	NOUN
ejpam-4511	9	14	,	,	PUNCT
ejpam-4511	9	15	denoted	denote	VERB
ejpam-4511	9	16	by	by	ADP
ejpam-4511	9	17	γh	γh	X
ejpam-4511	9	18	gr(g	gr(g	PROPN
ejpam-4511	9	19	)	)	PUNCT
ejpam-4511	9	20	,	,	PUNCT
ejpam-4511	9	21	is	be	AUX
ejpam-4511	9	22	called	call	VERB
ejpam-4511	9	23	the	the	DET
ejpam-4511	9	24	grundy	grundy	PROPN
ejpam-4511	9	25	hop	hop	PROPN
ejpam-4511	9	26	domination	domination	NOUN
ejpam-4511	9	27	number	number	NOUN
ejpam-4511	9	28	of	of	ADP
ejpam-4511	9	29	g.	g.	PROPN
ejpam-4511	9	30	in	in	ADP
ejpam-4511	9	31	this	this	DET
ejpam-4511	9	32	paper	paper	NOUN
ejpam-4511	9	33	,	,	PUNCT
ejpam-4511	9	34	we	we	PRON
ejpam-4511	9	35	determine	determine	VERB
ejpam-4511	9	36	some	some	DET
ejpam-4511	9	37	(	(	PUNCT
ejpam-4511	9	38	extreme	extreme	ADJ
ejpam-4511	9	39	)	)	PUNCT
ejpam-4511	9	40	values	value	NOUN
ejpam-4511	9	41	for	for	ADP
ejpam-4511	9	42	the	the	DET
ejpam-4511	9	43	grundy	grundy	PROPN
ejpam-4511	9	44	hop	hop	PROPN
ejpam-4511	9	45	domination	domination	NOUN
ejpam-4511	9	46	number	number	NOUN
ejpam-4511	9	47	.	.	PUNCT
ejpam-4511	10	1	it	it	PRON
ejpam-4511	10	2	is	be	AUX
ejpam-4511	10	3	pointed	point	VERB
ejpam-4511	10	4	out	out	ADP
ejpam-4511	10	5	that	that	SCONJ
ejpam-4511	10	6	the	the	DET
ejpam-4511	10	7	grundy	grundy	PROPN
ejpam-4511	10	8	hop	hop	PROPN
ejpam-4511	10	9	domination	domination	NOUN
ejpam-4511	10	10	number	number	NOUN
ejpam-4511	10	11	is	be	AUX
ejpam-4511	10	12	at	at	ADP
ejpam-4511	10	13	least	least	ADJ
ejpam-4511	10	14	equal	equal	ADJ
ejpam-4511	10	15	to	to	ADP
ejpam-4511	10	16	the	the	DET
ejpam-4511	10	17	hop	hop	NOUN
ejpam-4511	10	18	domination	domination	NOUN
ejpam-4511	10	19	.	.	PUNCT
ejpam-4511	11	1	bounds	bound	VERB
ejpam-4511	11	2	for	for	ADP
ejpam-4511	11	3	the	the	DET
ejpam-4511	11	4	grundy	grundy	PROPN
ejpam-4511	11	5	hop	hop	PROPN
ejpam-4511	11	6	domination	domination	NOUN
ejpam-4511	11	7	numbers	number	NOUN
ejpam-4511	11	8	of	of	ADP
ejpam-4511	11	9	some	some	DET
ejpam-4511	11	10	graphs	graph	NOUN
ejpam-4511	11	11	resulting	result	VERB
ejpam-4511	11	12	from	from	ADP
ejpam-4511	11	13	some	some	DET
ejpam-4511	11	14	binary	binary	ADJ
ejpam-4511	11	15	operations	operation	NOUN
ejpam-4511	11	16	of	of	ADP
ejpam-4511	11	17	two	two	NUM
ejpam-4511	11	18	graphs	graph	NOUN
ejpam-4511	11	19	are	be	AUX
ejpam-4511	11	20	also	also	ADV
ejpam-4511	11	21	obtained	obtain	VERB
ejpam-4511	11	22	.	.	PUNCT
ejpam-4511	12	1	2020	2020	NUM
ejpam-4511	12	2	mathematics	mathematic	NOUN
ejpam-4511	12	3	subject	subject	NOUN
ejpam-4511	12	4	classifications	classification	NOUN
ejpam-4511	12	5	:	:	PUNCT
ejpam-4511	12	6	05c69	05c69	X
ejpam-4511	12	7	key	key	ADJ
ejpam-4511	12	8	words	word	NOUN
ejpam-4511	12	9	and	and	CCONJ
ejpam-4511	12	10	phrases	phrase	NOUN
ejpam-4511	12	11	:	:	PUNCT
ejpam-4511	12	12	hop	hop	NOUN
ejpam-4511	12	13	domination	domination	NOUN
ejpam-4511	12	14	,	,	PUNCT
ejpam-4511	12	15	hop	hop	NOUN
ejpam-4511	12	16	domination	domination	NOUN
ejpam-4511	12	17	number	number	NOUN
ejpam-4511	12	18	,	,	PUNCT
ejpam-4511	12	19	closed	close	VERB
ejpam-4511	12	20	hop	hop	NOUN
ejpam-4511	12	21	neighborhood	neighborhood	NOUN
ejpam-4511	12	22	sequence	sequence	NOUN
ejpam-4511	12	23	,	,	PUNCT
ejpam-4511	12	24	grundy	grundy	PROPN
ejpam-4511	12	25	hop	hop	NOUN
ejpam-4511	12	26	dominating	dominating	NOUN
ejpam-4511	12	27	sequence	sequence	NOUN
ejpam-4511	12	28	,	,	PUNCT
ejpam-4511	12	29	grundy	grundy	PROPN
ejpam-4511	12	30	hop	hop	PROPN
ejpam-4511	12	31	domination	domination	PROPN
ejpam-4511	12	32	number	number	NOUN
ejpam-4511	12	33	1	1	NUM
ejpam-4511	12	34	.	.	PUNCT
ejpam-4511	13	1	introduction	introduction	NOUN
ejpam-4511	13	2	one	one	NUM
ejpam-4511	13	3	of	of	ADP
ejpam-4511	13	4	the	the	DET
ejpam-4511	13	5	several	several	ADJ
ejpam-4511	13	6	considered	consider	VERB
ejpam-4511	13	7	variations	variation	NOUN
ejpam-4511	13	8	of	of	ADP
ejpam-4511	13	9	the	the	DET
ejpam-4511	13	10	standard	standard	ADJ
ejpam-4511	13	11	domination	domination	NOUN
ejpam-4511	13	12	concept	concept	NOUN
ejpam-4511	13	13	is	be	AUX
ejpam-4511	13	14	hop	hop	NOUN
ejpam-4511	13	15	domination	domination	NOUN
ejpam-4511	13	16	.	.	PUNCT
ejpam-4511	14	1	this	this	DET
ejpam-4511	14	2	concept	concept	NOUN
ejpam-4511	14	3	was	be	AUX
ejpam-4511	14	4	introduced	introduce	VERB
ejpam-4511	14	5	and	and	CCONJ
ejpam-4511	14	6	initially	initially	ADV
ejpam-4511	14	7	studied	study	VERB
ejpam-4511	14	8	by	by	ADP
ejpam-4511	14	9	natarajan	natarajan	PROPN
ejpam-4511	14	10	and	and	CCONJ
ejpam-4511	14	11	ayyaswamy	ayyaswamy	ADV
ejpam-4511	14	12	in	in	ADP
ejpam-4511	14	13	[	[	X
ejpam-4511	14	14	15	15	NUM
ejpam-4511	14	15	]	]	PUNCT
ejpam-4511	14	16	.	.	PUNCT
ejpam-4511	15	1	just	just	ADV
ejpam-4511	15	2	like	like	ADP
ejpam-4511	15	3	domination	domination	NOUN
ejpam-4511	15	4	,	,	PUNCT
ejpam-4511	15	5	hop	hop	NOUN
ejpam-4511	15	6	domination	domination	NOUN
ejpam-4511	15	7	and	and	CCONJ
ejpam-4511	15	8	its	its	PRON
ejpam-4511	15	9	variations	variation	NOUN
ejpam-4511	15	10	find	find	VERB
ejpam-4511	15	11	plenty	plenty	NOUN
ejpam-4511	15	12	of	of	ADP
ejpam-4511	15	13	applications	application	NOUN
ejpam-4511	15	14	in	in	ADP
ejpam-4511	15	15	various	various	ADJ
ejpam-4511	15	16	fields	field	NOUN
ejpam-4511	15	17	and	and	CCONJ
ejpam-4511	15	18	networks	network	NOUN
ejpam-4511	15	19	.	.	PUNCT
ejpam-4511	16	1	in	in	ADP
ejpam-4511	16	2	fact	fact	NOUN
ejpam-4511	16	3	,	,	PUNCT
ejpam-4511	16	4	some	some	DET
ejpam-4511	16	5	real	real	ADJ
ejpam-4511	16	6	-	-	PUNCT
ejpam-4511	16	7	life	life	NOUN
ejpam-4511	16	8	problems	problem	NOUN
ejpam-4511	16	9	(	(	PUNCT
ejpam-4511	16	10	including	include	VERB
ejpam-4511	16	11	protection	protection	NOUN
ejpam-4511	16	12	strategies	strategy	NOUN
ejpam-4511	16	13	and	and	CCONJ
ejpam-4511	16	14	facility	facility	NOUN
ejpam-4511	16	15	location	location	NOUN
ejpam-4511	16	16	)	)	PUNCT
ejpam-4511	16	17	that	that	PRON
ejpam-4511	16	18	can	can	AUX
ejpam-4511	16	19	be	be	AUX
ejpam-4511	16	20	modeled	model	VERB
ejpam-4511	16	21	by	by	ADP
ejpam-4511	16	22	the	the	DET
ejpam-4511	16	23	concept	concept	NOUN
ejpam-4511	16	24	of	of	ADP
ejpam-4511	16	25	domination	domination	NOUN
ejpam-4511	16	26	can	can	AUX
ejpam-4511	16	27	be	be	AUX
ejpam-4511	16	28	slighty	slighty	ADV
ejpam-4511	16	29	modified	modify	VERB
ejpam-4511	16	30	for	for	ADP
ejpam-4511	16	31	the	the	DET
ejpam-4511	16	32	concept	concept	NOUN
ejpam-4511	16	33	of	of	ADP
ejpam-4511	16	34	hop	hop	NOUN
ejpam-4511	16	35	domination	domination	NOUN
ejpam-4511	16	36	.	.	PUNCT
ejpam-4511	17	1	domination	domination	NOUN
ejpam-4511	17	2	,	,	PUNCT
ejpam-4511	17	3	hop	hop	NOUN
ejpam-4511	17	4	domination	domination	NOUN
ejpam-4511	17	5	,	,	PUNCT
ejpam-4511	17	6	and	and	CCONJ
ejpam-4511	17	7	some	some	PRON
ejpam-4511	17	8	of	of	ADP
ejpam-4511	17	9	their	their	PRON
ejpam-4511	17	10	variations	variation	NOUN
ejpam-4511	17	11	are	be	AUX
ejpam-4511	17	12	also	also	ADV
ejpam-4511	17	13	studied	study	VERB
ejpam-4511	17	14	in	in	ADP
ejpam-4511	17	15	[	[	X
ejpam-4511	17	16	1	1	NUM
ejpam-4511	17	17	]	]	PUNCT
ejpam-4511	17	18	,	,	PUNCT
ejpam-4511	18	1	[	[	X
ejpam-4511	18	2	2	2	NUM
ejpam-4511	18	3	]	]	PUNCT
ejpam-4511	18	4	,	,	PUNCT
ejpam-4511	19	1	[	[	X
ejpam-4511	19	2	9	9	NUM
ejpam-4511	19	3	]	]	PUNCT
ejpam-4511	19	4	,	,	PUNCT
ejpam-4511	19	5	[	[	X
ejpam-4511	19	6	10	10	NUM
ejpam-4511	19	7	]	]	PUNCT
ejpam-4511	19	8	,	,	PUNCT
ejpam-4511	20	1	[	[	X
ejpam-4511	20	2	11	11	NUM
ejpam-4511	20	3	]	]	PUNCT
ejpam-4511	20	4	,	,	PUNCT
ejpam-4511	20	5	[	[	X
ejpam-4511	20	6	12	12	NUM
ejpam-4511	20	7	]	]	PUNCT
ejpam-4511	20	8	,	,	PUNCT
ejpam-4511	20	9	[	[	X
ejpam-4511	20	10	13	13	NUM
ejpam-4511	20	11	]	]	PUNCT
ejpam-4511	20	12	,	,	PUNCT
ejpam-4511	20	13	and	and	CCONJ
ejpam-4511	20	14	[	[	X
ejpam-4511	20	15	16	16	NUM
ejpam-4511	20	16	]	]	PUNCT
ejpam-4511	20	17	.	.	PUNCT
ejpam-4511	21	1	in	in	ADP
ejpam-4511	21	2	2014	2014	NUM
ejpam-4511	21	3	,	,	PUNCT
ejpam-4511	21	4	the	the	DET
ejpam-4511	21	5	concept	concept	NOUN
ejpam-4511	21	6	of	of	ADP
ejpam-4511	21	7	grundy	grundy	PROPN
ejpam-4511	21	8	domination	domination	NOUN
ejpam-4511	21	9	in	in	ADP
ejpam-4511	21	10	graphs	graph	NOUN
ejpam-4511	21	11	was	be	AUX
ejpam-4511	21	12	introduced	introduce	VERB
ejpam-4511	21	13	by	by	ADP
ejpam-4511	21	14	bresar	bresar	VERB
ejpam-4511	21	15	et	et	PROPN
ejpam-4511	21	16	al	al	PROPN
ejpam-4511	21	17	.	.	PUNCT
ejpam-4511	22	1	[	[	X
ejpam-4511	22	2	6	6	NUM
ejpam-4511	22	3	]	]	PUNCT
ejpam-4511	22	4	.	.	PUNCT
ejpam-4511	23	1	the	the	DET
ejpam-4511	23	2	newly	newly	ADV
ejpam-4511	23	3	defined	define	VERB
ejpam-4511	23	4	parameter	parameter	NOUN
ejpam-4511	23	5	has	have	AUX
ejpam-4511	23	6	subsequently	subsequently	ADV
ejpam-4511	23	7	attracted	attract	VERB
ejpam-4511	23	8	other	other	ADJ
ejpam-4511	23	9	researchers	researcher	NOUN
ejpam-4511	23	10	in	in	ADP
ejpam-4511	23	11	the	the	DET
ejpam-4511	23	12	area	area	NOUN
ejpam-4511	23	13	who	who	PRON
ejpam-4511	23	14	generated	generate	VERB
ejpam-4511	23	15	more	more	ADV
ejpam-4511	23	16	interesting	interesting	ADJ
ejpam-4511	23	17	results	result	NOUN
ejpam-4511	23	18	(	(	PUNCT
ejpam-4511	23	19	see	see	VERB
ejpam-4511	23	20	[	[	X
ejpam-4511	23	21	3	3	NUM
ejpam-4511	23	22	]	]	PUNCT
ejpam-4511	23	23	,	,	PUNCT
ejpam-4511	23	24	[	[	X
ejpam-4511	23	25	4	4	NUM
ejpam-4511	23	26	]	]	PUNCT
ejpam-4511	23	27	,	,	PUNCT
ejpam-4511	23	28	[	[	X
ejpam-4511	23	29	5	5	NUM
ejpam-4511	23	30	]	]	PUNCT
ejpam-4511	23	31	,	,	PUNCT
ejpam-4511	23	32	and	and	CCONJ
ejpam-4511	23	33	[	[	X
ejpam-4511	23	34	7	7	NUM
ejpam-4511	23	35	]	]	NUM
ejpam-4511	23	36	)	)	PUNCT
ejpam-4511	23	37	.	.	PUNCT
ejpam-4511	24	1	grundy	grundy	PROPN
ejpam-4511	24	2	domination	domination	NOUN
ejpam-4511	24	3	was	be	AUX
ejpam-4511	24	4	further	far	ADV
ejpam-4511	24	5	studied	study	VERB
ejpam-4511	24	6	in	in	ADP
ejpam-4511	24	7	[	[	X
ejpam-4511	24	8	5	5	NUM
ejpam-4511	24	9	]	]	PUNCT
ejpam-4511	24	10	,	,	PUNCT
ejpam-4511	24	11	where	where	SCONJ
ejpam-4511	24	12	exact	exact	ADJ
ejpam-4511	24	13	formulas	formula	NOUN
ejpam-4511	24	14	for	for	ADP
ejpam-4511	24	15	grundy	grundy	PROPN
ejpam-4511	24	16	domination	domination	NOUN
ejpam-4511	24	17	numbers	number	NOUN
ejpam-4511	24	18	of	of	ADP
ejpam-4511	24	19	sierpinski	sierpinski	ADJ
ejpam-4511	24	20	∗corresponding	∗corresponding	NOUN
ejpam-4511	24	21	author	author	NOUN
ejpam-4511	24	22	.	.	PUNCT
ejpam-4511	25	1	doi	doi	NOUN
ejpam-4511	25	2	:	:	PUNCT
ejpam-4511	25	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4511	https://doi.org/10.29020/nybg.ejpam.v15i4.4511	PROPN
ejpam-4511	25	4	email	email	NOUN
ejpam-4511	25	5	addresses	address	NOUN
ejpam-4511	25	6	:	:	PUNCT
ejpam-4511	26	1	javier.hassan@g.msuiit.edu.ph	javier.hassan@g.msuiit.edu.ph	PROPN
ejpam-4511	26	2	(	(	PUNCT
ejpam-4511	26	3	j.	j.	PROPN
ejpam-4511	26	4	hassan	hassan	PROPN
ejpam-4511	26	5	)	)	PUNCT
ejpam-4511	26	6	,	,	PUNCT
ejpam-4511	26	7	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4511	26	8	(	(	PUNCT
ejpam-4511	26	9	s.	s.	PROPN
ejpam-4511	26	10	canoy	canoy	PROPN
ejpam-4511	26	11	)	)	PUNCT
ejpam-4511	26	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4511	26	13	1623	1623	NUM
ejpam-4511	27	1	©	©	PROPN
ejpam-4511	27	2	2022	2022	NUM
ejpam-4511	27	3	ejpam	ejpam	VERB
ejpam-4511	27	4	all	all	DET
ejpam-4511	27	5	rights	right	NOUN
ejpam-4511	27	6	reserved	reserve	VERB
ejpam-4511	27	7	.	.	PUNCT
ejpam-4511	28	1	j.	j.	PROPN
ejpam-4511	28	2	hassan	hassan	PROPN
ejpam-4511	28	3	,	,	PUNCT
ejpam-4511	28	4	s.	s.	PROPN
ejpam-4511	28	5	canoy	canoy	PROPN
ejpam-4511	28	6	/	/	SYM
ejpam-4511	28	7	eur	eur	PROPN
ejpam-4511	28	8	.	.	PUNCT
ejpam-4511	29	1	j.	j.	PROPN
ejpam-4511	29	2	pure	pure	PROPN
ejpam-4511	29	3	appl	appl	PROPN
ejpam-4511	29	4	.	.	PROPN
ejpam-4511	29	5	math	math	PROPN
ejpam-4511	29	6	,	,	PUNCT
ejpam-4511	29	7	15	15	NUM
ejpam-4511	29	8	(	(	PUNCT
ejpam-4511	29	9	4	4	NUM
ejpam-4511	29	10	)	)	PUNCT
ejpam-4511	29	11	(	(	PUNCT
ejpam-4511	29	12	2022	2022	NUM
ejpam-4511	29	13	)	)	PUNCT
ejpam-4511	29	14	,	,	PUNCT
ejpam-4511	29	15	1623	1623	NUM
ejpam-4511	29	16	-	-	SYM
ejpam-4511	29	17	1636	1636	NUM
ejpam-4511	29	18	1624	1624	NUM
ejpam-4511	29	19	graphs	graph	NOUN
ejpam-4511	29	20	were	be	AUX
ejpam-4511	29	21	proven	prove	VERB
ejpam-4511	29	22	and	and	CCONJ
ejpam-4511	29	23	a	a	DET
ejpam-4511	29	24	linear	linear	ADJ
ejpam-4511	29	25	algorithm	algorithm	NOUN
ejpam-4511	29	26	for	for	ADP
ejpam-4511	29	27	determining	determine	VERB
ejpam-4511	29	28	these	these	DET
ejpam-4511	29	29	numbers	number	NOUN
ejpam-4511	29	30	in	in	ADP
ejpam-4511	29	31	arbitrary	arbitrary	ADJ
ejpam-4511	29	32	interval	interval	NOUN
ejpam-4511	29	33	graphs	graph	NOUN
ejpam-4511	29	34	was	be	AUX
ejpam-4511	29	35	given	give	VERB
ejpam-4511	29	36	.	.	PUNCT
ejpam-4511	30	1	grundy	grundy	PROPN
ejpam-4511	30	2	domination	domination	NOUN
ejpam-4511	30	3	number	number	NOUN
ejpam-4511	30	4	was	be	AUX
ejpam-4511	30	5	also	also	ADV
ejpam-4511	30	6	studied	study	VERB
ejpam-4511	30	7	in	in	ADP
ejpam-4511	30	8	kneser	kneser	NOUN
ejpam-4511	30	9	graphs	graph	NOUN
ejpam-4511	30	10	[	[	X
ejpam-4511	30	11	7	7	X
ejpam-4511	30	12	]	]	PUNCT
ejpam-4511	30	13	and	and	CCONJ
ejpam-4511	30	14	graph	graph	NOUN
ejpam-4511	30	15	products	product	NOUN
ejpam-4511	30	16	in	in	ADP
ejpam-4511	30	17	[	[	X
ejpam-4511	30	18	3	3	NUM
ejpam-4511	30	19	]	]	PUNCT
ejpam-4511	30	20	and	and	CCONJ
ejpam-4511	30	21	[	[	X
ejpam-4511	30	22	14	14	NUM
ejpam-4511	30	23	]	]	PUNCT
ejpam-4511	30	24	.	.	PUNCT
ejpam-4511	31	1	in	in	ADP
ejpam-4511	31	2	this	this	DET
ejpam-4511	31	3	study	study	NOUN
ejpam-4511	31	4	,	,	PUNCT
ejpam-4511	31	5	the	the	DET
ejpam-4511	31	6	concept	concept	NOUN
ejpam-4511	31	7	of	of	ADP
ejpam-4511	31	8	grundy	grundy	PROPN
ejpam-4511	31	9	hop	hop	PROPN
ejpam-4511	31	10	domination	domination	NOUN
ejpam-4511	31	11	in	in	ADP
ejpam-4511	31	12	a	a	DET
ejpam-4511	31	13	graph	graph	NOUN
ejpam-4511	31	14	will	will	AUX
ejpam-4511	31	15	be	be	AUX
ejpam-4511	31	16	introduced	introduce	VERB
ejpam-4511	31	17	and	and	CCONJ
ejpam-4511	31	18	initially	initially	ADV
ejpam-4511	31	19	investigated	investigate	VERB
ejpam-4511	31	20	.	.	PUNCT
ejpam-4511	32	1	in	in	ADP
ejpam-4511	32	2	particular	particular	ADJ
ejpam-4511	32	3	,	,	PUNCT
ejpam-4511	32	4	bounds	bound	VERB
ejpam-4511	32	5	for	for	ADP
ejpam-4511	32	6	the	the	DET
ejpam-4511	32	7	parameter	parameter	NOUN
ejpam-4511	32	8	will	will	AUX
ejpam-4511	32	9	be	be	AUX
ejpam-4511	32	10	given	give	VERB
ejpam-4511	32	11	for	for	ADP
ejpam-4511	32	12	the	the	DET
ejpam-4511	32	13	join	join	NOUN
ejpam-4511	32	14	,	,	PUNCT
ejpam-4511	32	15	corona	corona	PROPN
ejpam-4511	32	16	,	,	PUNCT
ejpam-4511	32	17	and	and	CCONJ
ejpam-4511	32	18	lexicographic	lexicographic	ADJ
ejpam-4511	32	19	product	product	NOUN
ejpam-4511	32	20	of	of	ADP
ejpam-4511	32	21	graphs	graph	NOUN
ejpam-4511	32	22	.	.	PUNCT
ejpam-4511	33	1	2	2	X
ejpam-4511	33	2	.	.	X
ejpam-4511	33	3	terminology	terminology	NOUN
ejpam-4511	33	4	and	and	CCONJ
ejpam-4511	33	5	notation	notation	NOUN
ejpam-4511	33	6	two	two	NUM
ejpam-4511	33	7	vertices	vertex	NOUN
ejpam-4511	33	8	u	u	NOUN
ejpam-4511	33	9	,	,	PUNCT
ejpam-4511	33	10	v	v	NOUN
ejpam-4511	33	11	of	of	ADP
ejpam-4511	33	12	a	a	DET
ejpam-4511	33	13	graph	graph	NOUN
ejpam-4511	33	14	g	g	NOUN
ejpam-4511	33	15	are	be	AUX
ejpam-4511	33	16	adjacent	adjacent	ADJ
ejpam-4511	33	17	,	,	PUNCT
ejpam-4511	33	18	or	or	CCONJ
ejpam-4511	33	19	neighbors	neighbor	NOUN
ejpam-4511	33	20	,	,	PUNCT
ejpam-4511	33	21	if	if	SCONJ
ejpam-4511	33	22	uv	uv	NOUN
ejpam-4511	33	23	is	be	AUX
ejpam-4511	33	24	an	an	DET
ejpam-4511	33	25	edge	edge	NOUN
ejpam-4511	33	26	of	of	ADP
ejpam-4511	33	27	g.	g.	PROPN
ejpam-4511	33	28	moreover	moreover	ADV
ejpam-4511	33	29	,	,	PUNCT
ejpam-4511	33	30	an	an	DET
ejpam-4511	33	31	edge	edge	NOUN
ejpam-4511	33	32	uv	uv	NOUN
ejpam-4511	33	33	of	of	ADP
ejpam-4511	33	34	g	g	PROPN
ejpam-4511	33	35	is	be	AUX
ejpam-4511	33	36	incident	incident	NOUN
ejpam-4511	33	37	to	to	ADP
ejpam-4511	33	38	two	two	NUM
ejpam-4511	33	39	vertices	vertex	NOUN
ejpam-4511	33	40	u	u	NOUN
ejpam-4511	33	41	,	,	PUNCT
ejpam-4511	33	42	v	v	NOUN
ejpam-4511	33	43	of	of	ADP
ejpam-4511	33	44	g.	g.	PROPN
ejpam-4511	33	45	the	the	DET
ejpam-4511	33	46	set	set	NOUN
ejpam-4511	33	47	of	of	ADP
ejpam-4511	33	48	neighbors	neighbor	NOUN
ejpam-4511	33	49	of	of	ADP
ejpam-4511	33	50	a	a	DET
ejpam-4511	33	51	vertex	vertex	NOUN
ejpam-4511	33	52	u	u	NOUN
ejpam-4511	33	53	in	in	ADP
ejpam-4511	33	54	g	g	NOUN
ejpam-4511	33	55	,	,	PUNCT
ejpam-4511	33	56	denoted	denote	VERB
ejpam-4511	33	57	by	by	ADP
ejpam-4511	33	58	ng(u	ng(u	NOUN
ejpam-4511	33	59	)	)	PUNCT
ejpam-4511	33	60	,	,	PUNCT
ejpam-4511	33	61	is	be	AUX
ejpam-4511	33	62	called	call	VERB
ejpam-4511	33	63	the	the	DET
ejpam-4511	33	64	open	open	ADJ
ejpam-4511	33	65	neighborhood	neighborhood	NOUN
ejpam-4511	33	66	of	of	ADP
ejpam-4511	33	67	u	u	PROPN
ejpam-4511	33	68	in	in	ADP
ejpam-4511	33	69	g.	g.	PROPN
ejpam-4511	33	70	the	the	DET
ejpam-4511	33	71	closed	close	VERB
ejpam-4511	33	72	neighborhood	neighborhood	NOUN
ejpam-4511	33	73	of	of	ADP
ejpam-4511	33	74	u	u	NOUN
ejpam-4511	33	75	in	in	ADP
ejpam-4511	33	76	g	g	PROPN
ejpam-4511	33	77	is	be	AUX
ejpam-4511	33	78	the	the	DET
ejpam-4511	33	79	set	set	NOUN
ejpam-4511	33	80	ng[u	ng[u	PROPN
ejpam-4511	33	81	]	]	X
ejpam-4511	33	82	=	=	SYM
ejpam-4511	33	83	ng(u	ng(u	PROPN
ejpam-4511	33	84	)	)	PUNCT
ejpam-4511	33	85	∪	∪	NOUN
ejpam-4511	33	86	{	{	PUNCT
ejpam-4511	33	87	u	u	NOUN
ejpam-4511	33	88	}	}	PUNCT
ejpam-4511	33	89	.	.	PUNCT
ejpam-4511	34	1	if	if	SCONJ
ejpam-4511	34	2	x	x	PROPN
ejpam-4511	34	3	⊆	⊆	NUM
ejpam-4511	34	4	v	v	X
ejpam-4511	34	5	(	(	PUNCT
ejpam-4511	34	6	g	g	NOUN
ejpam-4511	34	7	)	)	PUNCT
ejpam-4511	34	8	,	,	PUNCT
ejpam-4511	34	9	the	the	DET
ejpam-4511	34	10	open	open	ADJ
ejpam-4511	34	11	neighborhood	neighborhood	NOUN
ejpam-4511	34	12	of	of	ADP
ejpam-4511	34	13	x	x	PUNCT
ejpam-4511	34	14	in	in	ADP
ejpam-4511	34	15	g	g	PROPN
ejpam-4511	34	16	is	be	AUX
ejpam-4511	34	17	the	the	DET
ejpam-4511	34	18	set	set	NOUN
ejpam-4511	34	19	ng(x	ng(x	NUM
ejpam-4511	34	20	)	)	PUNCT
ejpam-4511	35	1	=	=	SYM
ejpam-4511	35	2	⋃	⋃	NOUN
ejpam-4511	35	3	u∈x	u∈x	NOUN
ejpam-4511	35	4	ng(u	ng(u	NOUN
ejpam-4511	35	5	)	)	PUNCT
ejpam-4511	35	6	.	.	PUNCT
ejpam-4511	36	1	the	the	DET
ejpam-4511	36	2	closed	closed	ADJ
ejpam-4511	36	3	neighborhood	neighborhood	NOUN
ejpam-4511	36	4	of	of	ADP
ejpam-4511	36	5	x	x	PUNCT
ejpam-4511	36	6	in	in	ADP
ejpam-4511	36	7	g	g	PROPN
ejpam-4511	36	8	is	be	AUX
ejpam-4511	36	9	the	the	DET
ejpam-4511	36	10	set	set	NOUN
ejpam-4511	36	11	ng[x	ng[x	PROPN
ejpam-4511	36	12	]	]	X
ejpam-4511	36	13	=	=	PUNCT
ejpam-4511	36	14	ng(x	ng(x	X
ejpam-4511	36	15	)	)	PUNCT
ejpam-4511	36	16	∪x	∪x	X
ejpam-4511	36	17	.	.	PUNCT
ejpam-4511	37	1	let	let	VERB
ejpam-4511	37	2	g	g	PRON
ejpam-4511	37	3	be	be	AUX
ejpam-4511	37	4	a	a	DET
ejpam-4511	37	5	graph	graph	NOUN
ejpam-4511	37	6	.	.	PUNCT
ejpam-4511	38	1	a	a	DET
ejpam-4511	38	2	set	set	NOUN
ejpam-4511	38	3	d	d	NOUN
ejpam-4511	38	4	⊆	⊆	NUM
ejpam-4511	38	5	v	v	ADP
ejpam-4511	38	6	(	(	PUNCT
ejpam-4511	38	7	g	g	NOUN
ejpam-4511	38	8	)	)	PUNCT
ejpam-4511	38	9	is	be	AUX
ejpam-4511	38	10	a	a	DET
ejpam-4511	38	11	dominating	dominating	NOUN
ejpam-4511	38	12	set	set	NOUN
ejpam-4511	38	13	of	of	ADP
ejpam-4511	38	14	g	g	PROPN
ejpam-4511	38	15	if	if	SCONJ
ejpam-4511	38	16	for	for	ADP
ejpam-4511	38	17	every	every	DET
ejpam-4511	38	18	v	v	NUM
ejpam-4511	38	19	∈	∈	NOUN
ejpam-4511	38	20	v	v	NOUN
ejpam-4511	38	21	(	(	PUNCT
ejpam-4511	38	22	g	g	NOUN
ejpam-4511	38	23	)	)	PUNCT
ejpam-4511	38	24	\d	\d	NOUN
ejpam-4511	38	25	,	,	PUNCT
ejpam-4511	38	26	there	there	PRON
ejpam-4511	38	27	exists	exist	VERB
ejpam-4511	38	28	u	u	NOUN
ejpam-4511	38	29	∈	∈	PROPN
ejpam-4511	38	30	d	d	ADP
ejpam-4511	38	31	such	such	ADJ
ejpam-4511	38	32	that	that	DET
ejpam-4511	38	33	uv	uv	PROPN
ejpam-4511	38	34	∈	∈	PROPN
ejpam-4511	38	35	e(g	e(g	PROPN
ejpam-4511	38	36	)	)	PUNCT
ejpam-4511	38	37	,	,	PUNCT
ejpam-4511	38	38	that	that	ADV
ejpam-4511	38	39	is	is	ADV
ejpam-4511	38	40	,	,	PUNCT
ejpam-4511	38	41	ng[d	ng[d	PROPN
ejpam-4511	38	42	]	]	PUNCT
ejpam-4511	38	43	=	=	SYM
ejpam-4511	38	44	v	v	X
ejpam-4511	38	45	(	(	PUNCT
ejpam-4511	38	46	g	g	NOUN
ejpam-4511	38	47	)	)	PUNCT
ejpam-4511	38	48	.	.	PUNCT
ejpam-4511	39	1	the	the	DET
ejpam-4511	39	2	domination	domination	NOUN
ejpam-4511	39	3	number	number	NOUN
ejpam-4511	39	4	of	of	ADP
ejpam-4511	39	5	g	g	NOUN
ejpam-4511	39	6	,	,	PUNCT
ejpam-4511	39	7	denoted	denote	VERB
ejpam-4511	39	8	by	by	ADP
ejpam-4511	39	9	γ(g	γ(g	PROPN
ejpam-4511	39	10	)	)	PUNCT
ejpam-4511	39	11	,	,	PUNCT
ejpam-4511	39	12	is	be	AUX
ejpam-4511	39	13	the	the	DET
ejpam-4511	39	14	minimum	minimum	ADJ
ejpam-4511	39	15	cardinality	cardinality	NOUN
ejpam-4511	39	16	of	of	ADP
ejpam-4511	39	17	a	a	DET
ejpam-4511	39	18	dominating	dominating	NOUN
ejpam-4511	39	19	set	set	NOUN
ejpam-4511	39	20	of	of	ADP
ejpam-4511	39	21	g.	g.	PROPN
ejpam-4511	39	22	let	let	VERB
ejpam-4511	39	23	s	s	AUX
ejpam-4511	39	24	=	=	PUNCT
ejpam-4511	39	25	(	(	PUNCT
ejpam-4511	39	26	v1	v1	PROPN
ejpam-4511	39	27	,	,	PUNCT
ejpam-4511	39	28	v2	v2	PROPN
ejpam-4511	39	29	,	,	PUNCT
ejpam-4511	39	30	·	·	PUNCT
ejpam-4511	39	31	·	·	PUNCT
ejpam-4511	39	32	·	·	PUNCT
ejpam-4511	39	33	,	,	PUNCT
ejpam-4511	39	34	vk	vk	AUX
ejpam-4511	39	35	)	)	PUNCT
ejpam-4511	39	36	be	be	AUX
ejpam-4511	39	37	a	a	DET
ejpam-4511	39	38	sequence	sequence	NOUN
ejpam-4511	39	39	of	of	ADP
ejpam-4511	39	40	distinct	distinct	ADJ
ejpam-4511	39	41	vertices	vertex	NOUN
ejpam-4511	39	42	of	of	ADP
ejpam-4511	39	43	a	a	DET
ejpam-4511	39	44	graph	graph	NOUN
ejpam-4511	39	45	g	g	NOUN
ejpam-4511	39	46	,	,	PUNCT
ejpam-4511	39	47	and	and	CCONJ
ejpam-4511	39	48	let	let	VERB
ejpam-4511	39	49	ŝ	ŝ	X
ejpam-4511	39	50	=	=	SYM
ejpam-4511	39	51	{	{	PUNCT
ejpam-4511	39	52	v1	v1	PROPN
ejpam-4511	39	53	,	,	PUNCT
ejpam-4511	39	54	v2	v2	PROPN
ejpam-4511	39	55	,	,	PUNCT
ejpam-4511	39	56	·	·	PUNCT
ejpam-4511	39	57	·	·	PUNCT
ejpam-4511	39	58	·	·	PUNCT
ejpam-4511	39	59	,	,	PUNCT
ejpam-4511	39	60	vk	vk	ADP
ejpam-4511	39	61	}	}	PUNCT
ejpam-4511	39	62	.	.	PUNCT
ejpam-4511	40	1	then	then	ADV
ejpam-4511	40	2	s	s	VERB
ejpam-4511	40	3	is	be	AUX
ejpam-4511	40	4	a	a	DET
ejpam-4511	40	5	legal	legal	ADJ
ejpam-4511	40	6	closed	closed	ADJ
ejpam-4511	40	7	neighborhood	neighborhood	NOUN
ejpam-4511	40	8	sequence	sequence	NOUN
ejpam-4511	40	9	if	if	SCONJ
ejpam-4511	40	10	ng[vi]\	ng[vi]\	PROPN
ejpam-4511	40	11	⋃i−1	⋃i−1	PROPN
ejpam-4511	40	12	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4511	40	13	]	]	PUNCT
ejpam-4511	40	14	̸=	̸=	PROPN
ejpam-4511	40	15	∅	∅	NOUN
ejpam-4511	40	16	for	for	ADP
ejpam-4511	40	17	every	every	DET
ejpam-4511	40	18	i	i	PROPN
ejpam-4511	40	19	∈	∈	PROPN
ejpam-4511	40	20	{	{	PUNCT
ejpam-4511	40	21	2	2	NUM
ejpam-4511	40	22	,	,	PUNCT
ejpam-4511	40	23	·	·	PUNCT
ejpam-4511	40	24	·	·	PUNCT
ejpam-4511	40	25	·	·	PUNCT
ejpam-4511	40	26	,	,	PUNCT
ejpam-4511	40	27	k	k	NOUN
ejpam-4511	40	28	}	}	PUNCT
ejpam-4511	40	29	.	.	PUNCT
ejpam-4511	41	1	if	if	SCONJ
ejpam-4511	41	2	,	,	PUNCT
ejpam-4511	41	3	in	in	ADP
ejpam-4511	41	4	addition	addition	NOUN
ejpam-4511	41	5	,	,	PUNCT
ejpam-4511	41	6	ŝ	ŝ	X
ejpam-4511	41	7	is	be	AUX
ejpam-4511	41	8	a	a	DET
ejpam-4511	41	9	dominating	dominating	NOUN
ejpam-4511	41	10	set	set	NOUN
ejpam-4511	41	11	of	of	ADP
ejpam-4511	41	12	g	g	NOUN
ejpam-4511	41	13	,	,	PUNCT
ejpam-4511	41	14	then	then	ADV
ejpam-4511	41	15	s	s	VERB
ejpam-4511	41	16	is	be	AUX
ejpam-4511	41	17	called	call	VERB
ejpam-4511	41	18	a	a	DET
ejpam-4511	41	19	grundy	grundy	PROPN
ejpam-4511	41	20	dominating	dominating	NOUN
ejpam-4511	41	21	sequence	sequence	NOUN
ejpam-4511	41	22	.	.	PUNCT
ejpam-4511	42	1	the	the	DET
ejpam-4511	42	2	maximum	maximum	ADJ
ejpam-4511	42	3	length	length	NOUN
ejpam-4511	42	4	of	of	ADP
ejpam-4511	42	5	a	a	DET
ejpam-4511	42	6	grundy	grundy	PROPN
ejpam-4511	42	7	dominating	dominating	NOUN
ejpam-4511	42	8	sequence	sequence	NOUN
ejpam-4511	42	9	in	in	ADP
ejpam-4511	42	10	a	a	DET
ejpam-4511	42	11	graph	graph	NOUN
ejpam-4511	42	12	g	g	NOUN
ejpam-4511	42	13	is	be	AUX
ejpam-4511	42	14	called	call	VERB
ejpam-4511	42	15	the	the	DET
ejpam-4511	42	16	grundy	grundy	PROPN
ejpam-4511	42	17	domination	domination	NOUN
ejpam-4511	42	18	number	number	NOUN
ejpam-4511	42	19	of	of	ADP
ejpam-4511	42	20	g	g	NOUN
ejpam-4511	42	21	,	,	PUNCT
ejpam-4511	42	22	and	and	CCONJ
ejpam-4511	42	23	is	be	AUX
ejpam-4511	42	24	denoted	denote	VERB
ejpam-4511	42	25	by	by	ADP
ejpam-4511	42	26	γgr(g	γgr(g	PROPN
ejpam-4511	42	27	)	)	PUNCT
ejpam-4511	42	28	.	.	PUNCT
ejpam-4511	43	1	a	a	DET
ejpam-4511	43	2	vertex	vertex	NOUN
ejpam-4511	43	3	v	v	NOUN
ejpam-4511	43	4	in	in	ADP
ejpam-4511	43	5	g	g	PROPN
ejpam-4511	43	6	is	be	AUX
ejpam-4511	43	7	a	a	DET
ejpam-4511	43	8	hop	hop	NOUN
ejpam-4511	43	9	neighbor	neighbor	NOUN
ejpam-4511	43	10	of	of	ADP
ejpam-4511	43	11	vertex	vertex	NOUN
ejpam-4511	43	12	u	u	NOUN
ejpam-4511	43	13	in	in	ADP
ejpam-4511	43	14	g	g	PROPN
ejpam-4511	43	15	if	if	SCONJ
ejpam-4511	43	16	dg(u	dg(u	NOUN
ejpam-4511	43	17	,	,	PUNCT
ejpam-4511	43	18	v	v	NOUN
ejpam-4511	43	19	)	)	PUNCT
ejpam-4511	43	20	=	=	SYM
ejpam-4511	43	21	2	2	X
ejpam-4511	43	22	.	.	X
ejpam-4511	44	1	the	the	DET
ejpam-4511	44	2	set	set	ADJ
ejpam-4511	44	3	n2	n2	ADJ
ejpam-4511	44	4	g(u	g(u	PROPN
ejpam-4511	44	5	)	)	PUNCT
ejpam-4511	44	6	=	=	PRON
ejpam-4511	44	7	{	{	PUNCT
ejpam-4511	44	8	v	v	NUM
ejpam-4511	44	9	∈	∈	NOUN
ejpam-4511	44	10	v	v	NOUN
ejpam-4511	44	11	(	(	PUNCT
ejpam-4511	44	12	g	g	NOUN
ejpam-4511	44	13	)	)	PUNCT
ejpam-4511	44	14	:	:	PUNCT
ejpam-4511	44	15	dg(v	dg(v	X
ejpam-4511	44	16	,	,	PUNCT
ejpam-4511	44	17	u	u	NOUN
ejpam-4511	44	18	)	)	PUNCT
ejpam-4511	44	19	=	=	SYM
ejpam-4511	44	20	2	2	X
ejpam-4511	44	21	}	}	PUNCT
ejpam-4511	44	22	is	be	AUX
ejpam-4511	44	23	called	call	VERB
ejpam-4511	44	24	the	the	DET
ejpam-4511	44	25	open	open	ADJ
ejpam-4511	44	26	hop	hop	NOUN
ejpam-4511	44	27	neighborhood	neighborhood	NOUN
ejpam-4511	44	28	of	of	ADP
ejpam-4511	44	29	u.	u.	PROPN
ejpam-4511	44	30	the	the	DET
ejpam-4511	44	31	closed	closed	ADJ
ejpam-4511	44	32	hop	hop	NOUN
ejpam-4511	44	33	neighborhood	neighborhood	NOUN
ejpam-4511	44	34	of	of	ADP
ejpam-4511	44	35	u	u	PROPN
ejpam-4511	44	36	in	in	ADP
ejpam-4511	44	37	g	g	PROPN
ejpam-4511	44	38	is	be	AUX
ejpam-4511	44	39	given	give	VERB
ejpam-4511	44	40	by	by	ADP
ejpam-4511	44	41	n2	n2	PROPN
ejpam-4511	44	42	g[u	g[u	PROPN
ejpam-4511	44	43	]	]	X
ejpam-4511	44	44	=	=	SYM
ejpam-4511	44	45	n2	n2	ADJ
ejpam-4511	44	46	g(u	g(u	PROPN
ejpam-4511	44	47	)	)	PUNCT
ejpam-4511	44	48	∪	∪	NOUN
ejpam-4511	44	49	{	{	PUNCT
ejpam-4511	44	50	u	u	NOUN
ejpam-4511	44	51	}	}	PUNCT
ejpam-4511	44	52	.	.	PUNCT
ejpam-4511	45	1	the	the	DET
ejpam-4511	45	2	open	open	ADJ
ejpam-4511	45	3	hop	hop	NOUN
ejpam-4511	45	4	neighborhood	neighborhood	NOUN
ejpam-4511	45	5	of	of	ADP
ejpam-4511	45	6	x	x	PROPN
ejpam-4511	45	7	⊆	⊆	NUM
ejpam-4511	45	8	v	v	ADP
ejpam-4511	45	9	(	(	PUNCT
ejpam-4511	45	10	g	g	NOUN
ejpam-4511	45	11	)	)	PUNCT
ejpam-4511	45	12	is	be	AUX
ejpam-4511	45	13	the	the	DET
ejpam-4511	45	14	set	set	ADJ
ejpam-4511	45	15	n2	n2	ADJ
ejpam-4511	45	16	g(x	g(x	NOUN
ejpam-4511	45	17	)	)	PUNCT
ejpam-4511	46	1	=	=	SYM
ejpam-4511	46	2	⋃	⋃	NOUN
ejpam-4511	46	3	u∈x	u∈x	ADJ
ejpam-4511	46	4	n2	n2	NOUN
ejpam-4511	46	5	g(u	g(u	PROPN
ejpam-4511	46	6	)	)	PUNCT
ejpam-4511	46	7	.	.	PUNCT
ejpam-4511	47	1	the	the	DET
ejpam-4511	47	2	closed	closed	ADJ
ejpam-4511	47	3	hop	hop	NOUN
ejpam-4511	47	4	neighborhood	neighborhood	NOUN
ejpam-4511	47	5	of	of	ADP
ejpam-4511	47	6	x	x	PUNCT
ejpam-4511	47	7	in	in	ADP
ejpam-4511	47	8	g	g	PROPN
ejpam-4511	47	9	is	be	AUX
ejpam-4511	47	10	the	the	DET
ejpam-4511	47	11	set	set	ADJ
ejpam-4511	47	12	n2	n2	NOUN
ejpam-4511	47	13	g[x	g[x	PROPN
ejpam-4511	47	14	]	]	X
ejpam-4511	47	15	=	=	SYM
ejpam-4511	47	16	n2	n2	PROPN
ejpam-4511	47	17	g(x	g(x	NOUN
ejpam-4511	47	18	)	)	PUNCT
ejpam-4511	47	19	∪x	∪x	NUM
ejpam-4511	47	20	.	.	PUNCT
ejpam-4511	48	1	a	a	DET
ejpam-4511	48	2	set	set	NOUN
ejpam-4511	48	3	s	s	NOUN
ejpam-4511	48	4	⊆	⊆	NUM
ejpam-4511	48	5	v	v	NOUN
ejpam-4511	48	6	(	(	PUNCT
ejpam-4511	48	7	g	g	NOUN
ejpam-4511	48	8	)	)	PUNCT
ejpam-4511	48	9	is	be	AUX
ejpam-4511	48	10	a	a	DET
ejpam-4511	48	11	hop	hop	NOUN
ejpam-4511	48	12	dominating	dominating	NOUN
ejpam-4511	48	13	set	set	NOUN
ejpam-4511	48	14	of	of	ADP
ejpam-4511	48	15	g	g	PROPN
ejpam-4511	48	16	if	if	SCONJ
ejpam-4511	48	17	n2	n2	ADJ
ejpam-4511	48	18	g[s	g[s	PROPN
ejpam-4511	48	19	]	]	X
ejpam-4511	48	20	=	=	SYM
ejpam-4511	48	21	v	v	NOUN
ejpam-4511	48	22	(	(	PUNCT
ejpam-4511	48	23	g	g	NOUN
ejpam-4511	48	24	)	)	PUNCT
ejpam-4511	48	25	,	,	PUNCT
ejpam-4511	48	26	that	that	ADV
ejpam-4511	48	27	is	is	ADV
ejpam-4511	48	28	,	,	PUNCT
ejpam-4511	48	29	for	for	ADP
ejpam-4511	48	30	every	every	DET
ejpam-4511	48	31	v	v	NUM
ejpam-4511	48	32	∈	∈	NOUN
ejpam-4511	48	33	v	v	NOUN
ejpam-4511	48	34	(	(	PUNCT
ejpam-4511	48	35	g)\s	g)\s	NOUN
ejpam-4511	48	36	,	,	PUNCT
ejpam-4511	48	37	there	there	PRON
ejpam-4511	48	38	exists	exist	VERB
ejpam-4511	48	39	u	u	PROPN
ejpam-4511	48	40	∈	∈	PROPN
ejpam-4511	48	41	s	s	VERB
ejpam-4511	48	42	such	such	ADJ
ejpam-4511	48	43	that	that	DET
ejpam-4511	48	44	dg(u	dg(u	ADJ
ejpam-4511	48	45	,	,	PUNCT
ejpam-4511	48	46	v	v	NOUN
ejpam-4511	48	47	)	)	PUNCT
ejpam-4511	49	1	=	=	SYM
ejpam-4511	49	2	2	2	X
ejpam-4511	49	3	.	.	PUNCT
ejpam-4511	50	1	the	the	DET
ejpam-4511	50	2	minimum	minimum	ADJ
ejpam-4511	50	3	cardinality	cardinality	NOUN
ejpam-4511	50	4	among	among	ADP
ejpam-4511	50	5	all	all	DET
ejpam-4511	50	6	hop	hop	NOUN
ejpam-4511	50	7	dominating	dominating	NOUN
ejpam-4511	50	8	sets	set	NOUN
ejpam-4511	50	9	of	of	ADP
ejpam-4511	50	10	g	g	NOUN
ejpam-4511	50	11	,	,	PUNCT
ejpam-4511	50	12	denoted	denote	VERB
ejpam-4511	50	13	by	by	ADP
ejpam-4511	50	14	γh(g	γh(g	NOUN
ejpam-4511	50	15	)	)	PUNCT
ejpam-4511	50	16	,	,	PUNCT
ejpam-4511	50	17	is	be	AUX
ejpam-4511	50	18	called	call	VERB
ejpam-4511	50	19	the	the	DET
ejpam-4511	50	20	hop	hop	NOUN
ejpam-4511	50	21	domination	domination	NOUN
ejpam-4511	50	22	number	number	NOUN
ejpam-4511	50	23	of	of	ADP
ejpam-4511	50	24	g.	g.	PROPN
ejpam-4511	50	25	any	any	DET
ejpam-4511	50	26	hop	hop	NOUN
ejpam-4511	50	27	dominating	dominating	NOUN
ejpam-4511	50	28	set	set	VERB
ejpam-4511	50	29	with	with	ADP
ejpam-4511	50	30	cardinality	cardinality	NOUN
ejpam-4511	50	31	equal	equal	ADJ
ejpam-4511	50	32	to	to	ADP
ejpam-4511	50	33	γh(g	γh(g	NOUN
ejpam-4511	50	34	)	)	PUNCT
ejpam-4511	50	35	is	be	AUX
ejpam-4511	50	36	called	call	VERB
ejpam-4511	50	37	a	a	DET
ejpam-4511	50	38	γh	γh	ADV
ejpam-4511	50	39	-	-	PUNCT
ejpam-4511	50	40	set	set	NOUN
ejpam-4511	50	41	.	.	PUNCT
ejpam-4511	51	1	let	let	VERB
ejpam-4511	51	2	s	s	PRON
ejpam-4511	51	3	=	=	PUNCT
ejpam-4511	51	4	(	(	PUNCT
ejpam-4511	51	5	v1	v1	PROPN
ejpam-4511	51	6	,	,	PUNCT
ejpam-4511	51	7	v2	v2	PROPN
ejpam-4511	51	8	,	,	PUNCT
ejpam-4511	51	9	·	·	PUNCT
ejpam-4511	51	10	·	·	PUNCT
ejpam-4511	51	11	·	·	PUNCT
ejpam-4511	51	12	,	,	PUNCT
ejpam-4511	51	13	vk	vk	AUX
ejpam-4511	51	14	)	)	PUNCT
ejpam-4511	51	15	be	be	AUX
ejpam-4511	51	16	a	a	DET
ejpam-4511	51	17	sequence	sequence	NOUN
ejpam-4511	51	18	of	of	ADP
ejpam-4511	51	19	distinct	distinct	ADJ
ejpam-4511	51	20	vertices	vertex	NOUN
ejpam-4511	51	21	of	of	ADP
ejpam-4511	51	22	g	g	NOUN
ejpam-4511	51	23	and	and	CCONJ
ejpam-4511	51	24	let	let	VERB
ejpam-4511	51	25	ŝ	ŝ	X
ejpam-4511	51	26	=	=	SYM
ejpam-4511	51	27	{	{	PUNCT
ejpam-4511	51	28	v1	v1	PROPN
ejpam-4511	51	29	,	,	PUNCT
ejpam-4511	51	30	·	·	PUNCT
ejpam-4511	51	31	·	·	PUNCT
ejpam-4511	51	32	·	·	PUNCT
ejpam-4511	51	33	,	,	PUNCT
ejpam-4511	51	34	vk	vk	ADP
ejpam-4511	51	35	}	}	PUNCT
ejpam-4511	51	36	.	.	PUNCT
ejpam-4511	52	1	then	then	ADV
ejpam-4511	52	2	s	s	VERB
ejpam-4511	52	3	is	be	AUX
ejpam-4511	52	4	a	a	DET
ejpam-4511	52	5	legal	legal	ADJ
ejpam-4511	52	6	closed	close	VERB
ejpam-4511	52	7	hop	hop	NOUN
ejpam-4511	52	8	neighborhood	neighborhood	NOUN
ejpam-4511	52	9	sequence	sequence	NOUN
ejpam-4511	52	10	of	of	ADP
ejpam-4511	52	11	g	g	PROPN
ejpam-4511	52	12	if	if	SCONJ
ejpam-4511	52	13	n2	n2	ADJ
ejpam-4511	52	14	g[vi]\∪	g[vi]\∪	VERB
ejpam-4511	52	15	i−1	i−1	PROPN
ejpam-4511	52	16	j=1n	j=1n	PROPN
ejpam-4511	52	17	2	2	NUM
ejpam-4511	52	18	g[vj	g[vj	PROPN
ejpam-4511	52	19	]	]	PUNCT
ejpam-4511	52	20	̸=	̸=	PROPN
ejpam-4511	52	21	∅	∅	NOUN
ejpam-4511	52	22	for	for	ADP
ejpam-4511	52	23	each	each	DET
ejpam-4511	52	24	i	i	PRON
ejpam-4511	52	25	∈	∈	PROPN
ejpam-4511	52	26	{	{	PUNCT
ejpam-4511	52	27	2	2	NUM
ejpam-4511	52	28	,	,	PUNCT
ejpam-4511	52	29	·	·	PUNCT
ejpam-4511	52	30	·	·	PUNCT
ejpam-4511	52	31	·	·	PUNCT
ejpam-4511	52	32	,	,	PUNCT
ejpam-4511	52	33	k	k	NOUN
ejpam-4511	52	34	}	}	PUNCT
ejpam-4511	52	35	.	.	PUNCT
ejpam-4511	53	1	if	if	SCONJ
ejpam-4511	53	2	,	,	PUNCT
ejpam-4511	53	3	in	in	ADP
ejpam-4511	53	4	addition	addition	NOUN
ejpam-4511	53	5	,	,	PUNCT
ejpam-4511	53	6	ŝ	ŝ	X
ejpam-4511	53	7	is	be	AUX
ejpam-4511	53	8	a	a	DET
ejpam-4511	53	9	hop	hop	NOUN
ejpam-4511	53	10	dominating	dominating	NOUN
ejpam-4511	53	11	set	set	NOUN
ejpam-4511	53	12	of	of	ADP
ejpam-4511	53	13	g	g	PROPN
ejpam-4511	53	14	,	,	PUNCT
ejpam-4511	53	15	then	then	ADV
ejpam-4511	53	16	s	s	VERB
ejpam-4511	53	17	is	be	AUX
ejpam-4511	53	18	called	call	VERB
ejpam-4511	53	19	a	a	DET
ejpam-4511	53	20	grundy	grundy	PROPN
ejpam-4511	53	21	hop	hop	NOUN
ejpam-4511	53	22	dominating	dominating	NOUN
ejpam-4511	53	23	sequence	sequence	NOUN
ejpam-4511	53	24	.	.	PUNCT
ejpam-4511	54	1	the	the	DET
ejpam-4511	54	2	maximum	maximum	ADJ
ejpam-4511	54	3	length	length	NOUN
ejpam-4511	54	4	of	of	ADP
ejpam-4511	54	5	a	a	DET
ejpam-4511	54	6	grundy	grundy	PROPN
ejpam-4511	54	7	hop	hop	NOUN
ejpam-4511	54	8	dominating	dominating	NOUN
ejpam-4511	54	9	sequence	sequence	NOUN
ejpam-4511	54	10	in	in	ADP
ejpam-4511	54	11	a	a	DET
ejpam-4511	54	12	graph	graph	NOUN
ejpam-4511	54	13	g	g	NOUN
ejpam-4511	54	14	,	,	PUNCT
ejpam-4511	54	15	denoted	denote	VERB
ejpam-4511	54	16	by	by	ADP
ejpam-4511	54	17	γhgr(g	γhgr(g	PROPN
ejpam-4511	54	18	)	)	PUNCT
ejpam-4511	54	19	,	,	PUNCT
ejpam-4511	54	20	is	be	AUX
ejpam-4511	54	21	called	call	VERB
ejpam-4511	54	22	the	the	DET
ejpam-4511	54	23	grundy	grundy	PROPN
ejpam-4511	54	24	hop	hop	PROPN
ejpam-4511	54	25	domination	domination	NOUN
ejpam-4511	54	26	number	number	NOUN
ejpam-4511	54	27	of	of	ADP
ejpam-4511	54	28	g.	g.	PROPN
ejpam-4511	54	29	we	we	PRON
ejpam-4511	54	30	say	say	VERB
ejpam-4511	54	31	that	that	DET
ejpam-4511	54	32	vertex	vertex	NOUN
ejpam-4511	54	33	vi	vi	PROPN
ejpam-4511	54	34	hop	hop	NOUN
ejpam-4511	54	35	-	-	PUNCT
ejpam-4511	54	36	footprints	footprint	NOUN
ejpam-4511	54	37	the	the	DET
ejpam-4511	54	38	vertices	vertex	NOUN
ejpam-4511	54	39	from	from	ADP
ejpam-4511	54	40	n2	n2	ADJ
ejpam-4511	55	1	g[vi]\∪i	g[vi]\∪i	PROPN
ejpam-4511	55	2	j=1n	j=1n	PROPN
ejpam-4511	55	3	2	2	NUM
ejpam-4511	55	4	g[vj	g[vj	PROPN
ejpam-4511	55	5	]	]	PUNCT
ejpam-4511	55	6	,	,	PUNCT
ejpam-4511	55	7	and	and	CCONJ
ejpam-4511	55	8	that	that	DET
ejpam-4511	55	9	vi	vi	PROPN
ejpam-4511	55	10	is	be	AUX
ejpam-4511	55	11	their	their	PRON
ejpam-4511	55	12	hopfootprinter	hopfootprinter	NOUN
ejpam-4511	55	13	.	.	PUNCT
ejpam-4511	56	1	a	a	DET
ejpam-4511	56	2	legal	legal	ADJ
ejpam-4511	56	3	closed	close	VERB
ejpam-4511	56	4	hop	hop	NOUN
ejpam-4511	56	5	neighborhood	neighborhood	NOUN
ejpam-4511	56	6	sequence	sequence	NOUN
ejpam-4511	56	7	s	s	PART
ejpam-4511	56	8	=	=	PUNCT
ejpam-4511	56	9	(	(	PUNCT
ejpam-4511	56	10	v1	v1	PROPN
ejpam-4511	56	11	,	,	PUNCT
ejpam-4511	56	12	v2	v2	PROPN
ejpam-4511	56	13	,	,	PUNCT
ejpam-4511	56	14	·	·	PUNCT
ejpam-4511	56	15	·	·	PUNCT
ejpam-4511	56	16	·	·	PUNCT
ejpam-4511	56	17	,	,	PUNCT
ejpam-4511	56	18	vk	vk	PROPN
ejpam-4511	56	19	)	)	PUNCT
ejpam-4511	56	20	with	with	ADP
ejpam-4511	56	21	maximum	maximum	ADJ
ejpam-4511	56	22	length	length	NOUN
ejpam-4511	56	23	,	,	PUNCT
ejpam-4511	56	24	i.e.	i.e.	X
ejpam-4511	56	25	,	,	PUNCT
ejpam-4511	56	26	k	k	NOUN
ejpam-4511	56	27	=	=	PUNCT
ejpam-4511	56	28	max{p	max{p	NOUN
ejpam-4511	56	29	∈	∈	PROPN
ejpam-4511	56	30	n	n	NOUN
ejpam-4511	56	31	:	:	PUNCT
ejpam-4511	56	32	∃	∃	PROPN
ejpam-4511	56	33	a	a	DET
ejpam-4511	56	34	legal	legal	ADJ
ejpam-4511	56	35	closed	closed	ADJ
ejpam-4511	56	36	hop	hop	NOUN
ejpam-4511	56	37	neighborhood	neighborhood	NOUN
ejpam-4511	56	38	sequence	sequence	NOUN
ejpam-4511	56	39	(	(	PUNCT
ejpam-4511	56	40	x1	x1	PROPN
ejpam-4511	56	41	,	,	PUNCT
ejpam-4511	56	42	·	·	PUNCT
ejpam-4511	56	43	·	·	PUNCT
ejpam-4511	56	44	·	·	PUNCT
ejpam-4511	56	45	,	,	PUNCT
ejpam-4511	56	46	xp	xp	X
ejpam-4511	56	47	)	)	PUNCT
ejpam-4511	56	48	ofg	ofg	PROPN
ejpam-4511	56	49	}	}	PUNCT
ejpam-4511	56	50	,	,	PUNCT
ejpam-4511	56	51	will	will	AUX
ejpam-4511	56	52	be	be	AUX
ejpam-4511	56	53	referred	refer	VERB
ejpam-4511	56	54	to	to	ADP
ejpam-4511	56	55	as	as	ADP
ejpam-4511	56	56	a	a	DET
ejpam-4511	56	57	maximum	maximum	ADJ
ejpam-4511	56	58	legal	legal	ADJ
ejpam-4511	56	59	closed	closed	ADJ
ejpam-4511	56	60	hop	hop	NOUN
ejpam-4511	56	61	neighborhood	neighborhood	NOUN
ejpam-4511	56	62	sequence	sequence	NOUN
ejpam-4511	56	63	.	.	PUNCT
ejpam-4511	57	1	j.	j.	PROPN
ejpam-4511	57	2	hassan	hassan	PROPN
ejpam-4511	57	3	,	,	PUNCT
ejpam-4511	57	4	s.	s.	PROPN
ejpam-4511	57	5	canoy	canoy	PROPN
ejpam-4511	57	6	/	/	SYM
ejpam-4511	57	7	eur	eur	PROPN
ejpam-4511	57	8	.	.	PUNCT
ejpam-4511	58	1	j.	j.	PROPN
ejpam-4511	58	2	pure	pure	PROPN
ejpam-4511	58	3	appl	appl	PROPN
ejpam-4511	58	4	.	.	PROPN
ejpam-4511	58	5	math	math	PROPN
ejpam-4511	58	6	,	,	PUNCT
ejpam-4511	58	7	15	15	NUM
ejpam-4511	58	8	(	(	PUNCT
ejpam-4511	58	9	4	4	NUM
ejpam-4511	58	10	)	)	PUNCT
ejpam-4511	58	11	(	(	PUNCT
ejpam-4511	58	12	2022	2022	NUM
ejpam-4511	58	13	)	)	PUNCT
ejpam-4511	58	14	,	,	PUNCT
ejpam-4511	58	15	1623	1623	NUM
ejpam-4511	58	16	-	-	SYM
ejpam-4511	58	17	1636	1636	NUM
ejpam-4511	58	18	1625	1625	NUM
ejpam-4511	58	19	let	let	VERB
ejpam-4511	58	20	s1	s1	NOUN
ejpam-4511	58	21	=	=	SYM
ejpam-4511	58	22	(	(	PUNCT
ejpam-4511	58	23	v1	v1	PROPN
ejpam-4511	58	24	,	,	PUNCT
ejpam-4511	58	25	·	·	PUNCT
ejpam-4511	58	26	·	·	PUNCT
ejpam-4511	58	27	·	·	PUNCT
ejpam-4511	58	28	,	,	PUNCT
ejpam-4511	58	29	vn	vn	PROPN
ejpam-4511	58	30	)	)	PUNCT
ejpam-4511	58	31	and	and	CCONJ
ejpam-4511	58	32	s2	s2	NOUN
ejpam-4511	58	33	=	=	SYM
ejpam-4511	58	34	(	(	PUNCT
ejpam-4511	58	35	u1	u1	PROPN
ejpam-4511	58	36	,	,	PUNCT
ejpam-4511	58	37	·	·	PUNCT
ejpam-4511	58	38	·	·	PUNCT
ejpam-4511	58	39	·	·	PUNCT
ejpam-4511	58	40	,	,	PUNCT
ejpam-4511	58	41	um	um	INTJ
ejpam-4511	58	42	)	)	PUNCT
ejpam-4511	58	43	,	,	PUNCT
ejpam-4511	58	44	n	n	CCONJ
ejpam-4511	58	45	,	,	PUNCT
ejpam-4511	58	46	m	m	VERB
ejpam-4511	58	47	≥	≥	NOUN
ejpam-4511	58	48	1	1	NUM
ejpam-4511	58	49	be	be	AUX
ejpam-4511	58	50	two	two	NUM
ejpam-4511	58	51	sequences	sequence	NOUN
ejpam-4511	58	52	of	of	ADP
ejpam-4511	58	53	distinct	distinct	ADJ
ejpam-4511	58	54	vertices	vertex	NOUN
ejpam-4511	58	55	of	of	ADP
ejpam-4511	58	56	g.	g.	PROPN
ejpam-4511	58	57	the	the	DET
ejpam-4511	58	58	concatenation	concatenation	NOUN
ejpam-4511	58	59	of	of	ADP
ejpam-4511	58	60	s1	s1	PROPN
ejpam-4511	58	61	and	and	CCONJ
ejpam-4511	58	62	s2	s2	PROPN
ejpam-4511	58	63	,	,	PUNCT
ejpam-4511	58	64	denoted	denote	VERB
ejpam-4511	58	65	by	by	ADP
ejpam-4511	58	66	s1	s1	PROPN
ejpam-4511	58	67	⊕	⊕	PROPN
ejpam-4511	58	68	s2	s2	PROPN
ejpam-4511	58	69	,	,	PUNCT
ejpam-4511	58	70	is	be	AUX
ejpam-4511	58	71	the	the	DET
ejpam-4511	58	72	sequence	sequence	NOUN
ejpam-4511	58	73	given	give	VERB
ejpam-4511	58	74	by	by	ADP
ejpam-4511	58	75	s1	s1	PROPN
ejpam-4511	58	76	⊕	⊕	PROPN
ejpam-4511	58	77	s2	s2	PROPN
ejpam-4511	58	78	=	=	SYM
ejpam-4511	58	79	(	(	PUNCT
ejpam-4511	58	80	v1	v1	PROPN
ejpam-4511	58	81	,	,	PUNCT
ejpam-4511	58	82	·	·	PUNCT
ejpam-4511	58	83	·	·	PUNCT
ejpam-4511	58	84	·	·	PUNCT
ejpam-4511	58	85	,	,	PUNCT
ejpam-4511	58	86	vn	vn	PROPN
ejpam-4511	58	87	,	,	PUNCT
ejpam-4511	58	88	u1	u1	NOUN
ejpam-4511	58	89	,	,	PUNCT
ejpam-4511	58	90	·	·	PUNCT
ejpam-4511	58	91	·	·	PUNCT
ejpam-4511	58	92	·	·	PUNCT
ejpam-4511	58	93	,	,	PUNCT
ejpam-4511	58	94	um	um	INTJ
ejpam-4511	58	95	)	)	PUNCT
ejpam-4511	58	96	.	.	PUNCT
ejpam-4511	59	1	a	a	DET
ejpam-4511	59	2	sequence	sequence	NOUN
ejpam-4511	59	3	s	s	PART
ejpam-4511	59	4	=	=	PUNCT
ejpam-4511	59	5	(	(	PUNCT
ejpam-4511	59	6	v1	v1	PROPN
ejpam-4511	59	7	,	,	PUNCT
ejpam-4511	59	8	v2	v2	PROPN
ejpam-4511	59	9	,	,	PUNCT
ejpam-4511	59	10	·	·	PUNCT
ejpam-4511	59	11	·	·	PUNCT
ejpam-4511	59	12	·	·	PUNCT
ejpam-4511	59	13	,	,	PUNCT
ejpam-4511	59	14	vk	vk	PROPN
ejpam-4511	59	15	)	)	PUNCT
ejpam-4511	59	16	of	of	ADP
ejpam-4511	59	17	distinct	distinct	ADJ
ejpam-4511	59	18	vertices	vertex	NOUN
ejpam-4511	59	19	of	of	ADP
ejpam-4511	59	20	a	a	DET
ejpam-4511	59	21	graph	graph	NOUN
ejpam-4511	59	22	g	g	NOUN
ejpam-4511	59	23	is	be	AUX
ejpam-4511	59	24	a	a	DET
ejpam-4511	59	25	co	co	ADJ
ejpam-4511	59	26	-	-	ADJ
ejpam-4511	59	27	legal	legal	ADJ
ejpam-4511	59	28	closed	closed	ADJ
ejpam-4511	59	29	neighborhood	neighborhood	NOUN
ejpam-4511	59	30	sequence	sequence	NOUN
ejpam-4511	59	31	in	in	ADP
ejpam-4511	59	32	g	g	PROPN
ejpam-4511	59	33	if	if	SCONJ
ejpam-4511	59	34	[	[	X
ejpam-4511	59	35	v	v	X
ejpam-4511	59	36	(	(	PUNCT
ejpam-4511	59	37	g	g	NOUN
ejpam-4511	59	38	)	)	PUNCT
ejpam-4511	59	39	\ng(vi	\ng(vi	NOUN
ejpam-4511	59	40	)	)	PUNCT
ejpam-4511	59	41	]	]	PUNCT
ejpam-4511	59	42	\	\	X
ejpam-4511	60	1	∪i−1	∪i−1	PROPN
ejpam-4511	60	2	j=1[v	j=1[v	X
ejpam-4511	60	3	(	(	PUNCT
ejpam-4511	60	4	g	g	NOUN
ejpam-4511	60	5	)	)	PUNCT
ejpam-4511	60	6	\ng(vj	\ng(vj	ADP
ejpam-4511	60	7	)	)	PUNCT
ejpam-4511	60	8	]	]	PUNCT
ejpam-4511	60	9	̸=	̸=	NOUN
ejpam-4511	60	10	∅	∅	NOUN
ejpam-4511	60	11	for	for	ADP
ejpam-4511	60	12	each	each	DET
ejpam-4511	60	13	i	i	PRON
ejpam-4511	60	14	∈	∈	PROPN
ejpam-4511	60	15	{	{	PUNCT
ejpam-4511	60	16	2	2	NUM
ejpam-4511	60	17	,	,	PUNCT
ejpam-4511	60	18	.	.	PUNCT
ejpam-4511	60	19	.	.	PUNCT
ejpam-4511	60	20	.	.	PUNCT
ejpam-4511	61	1	,	,	PUNCT
ejpam-4511	61	2	k	k	X
ejpam-4511	61	3	}	}	PUNCT
ejpam-4511	61	4	.	.	PUNCT
ejpam-4511	62	1	a	a	DET
ejpam-4511	62	2	co	co	ADJ
ejpam-4511	62	3	-	-	ADJ
ejpam-4511	62	4	legal	legal	ADJ
ejpam-4511	62	5	sequence	sequence	NOUN
ejpam-4511	62	6	s	s	PART
ejpam-4511	62	7	=	=	PUNCT
ejpam-4511	62	8	(	(	PUNCT
ejpam-4511	62	9	v1	v1	PROPN
ejpam-4511	62	10	,	,	PUNCT
ejpam-4511	62	11	v2	v2	NOUN
ejpam-4511	62	12	,	,	PUNCT
ejpam-4511	62	13	.	.	PUNCT
ejpam-4511	62	14	.	.	PUNCT
ejpam-4511	62	15	.	.	PUNCT
ejpam-4511	63	1	,	,	PUNCT
ejpam-4511	63	2	vk	vk	PROPN
ejpam-4511	63	3	)	)	PUNCT
ejpam-4511	63	4	is	be	AUX
ejpam-4511	63	5	a	a	DET
ejpam-4511	63	6	co	co	ADJ
ejpam-4511	63	7	-	-	ADJ
ejpam-4511	63	8	grundy	grundy	ADJ
ejpam-4511	63	9	dominating	dominating	NOUN
ejpam-4511	63	10	sequence	sequence	NOUN
ejpam-4511	63	11	if	if	SCONJ
ejpam-4511	63	12	v	v	X
ejpam-4511	63	13	(	(	PUNCT
ejpam-4511	63	14	g	g	NOUN
ejpam-4511	63	15	)	)	PUNCT
ejpam-4511	63	16	=	=	PUNCT
ejpam-4511	64	1	∪k	∪k	NUM
ejpam-4511	64	2	i=1[v	i=1[v	X
ejpam-4511	64	3	(	(	PUNCT
ejpam-4511	64	4	g)\ng(vi	g)\ng(vi	PROPN
ejpam-4511	64	5	)	)	PUNCT
ejpam-4511	64	6	]	]	PUNCT
ejpam-4511	64	7	.	.	PUNCT
ejpam-4511	65	1	the	the	DET
ejpam-4511	65	2	maximum	maximum	ADJ
ejpam-4511	65	3	length	length	NOUN
ejpam-4511	65	4	of	of	ADP
ejpam-4511	65	5	a	a	DET
ejpam-4511	65	6	co	co	ADJ
ejpam-4511	65	7	-	-	ADJ
ejpam-4511	65	8	grundy	grundy	ADJ
ejpam-4511	65	9	dominating	dominating	NOUN
ejpam-4511	65	10	sequence	sequence	NOUN
ejpam-4511	65	11	in	in	ADP
ejpam-4511	65	12	a	a	DET
ejpam-4511	65	13	graph	graph	NOUN
ejpam-4511	65	14	g	g	NOUN
ejpam-4511	65	15	is	be	AUX
ejpam-4511	65	16	called	call	VERB
ejpam-4511	65	17	the	the	DET
ejpam-4511	65	18	co	co	ADJ
ejpam-4511	65	19	-	-	ADJ
ejpam-4511	65	20	grundy	grundy	ADJ
ejpam-4511	65	21	domination	domination	NOUN
ejpam-4511	65	22	number	number	NOUN
ejpam-4511	65	23	of	of	ADP
ejpam-4511	65	24	g	g	NOUN
ejpam-4511	65	25	,	,	PUNCT
ejpam-4511	65	26	and	and	CCONJ
ejpam-4511	65	27	is	be	AUX
ejpam-4511	65	28	denoted	denote	VERB
ejpam-4511	65	29	by	by	ADP
ejpam-4511	65	30	γcogr(g	γcogr(g	PROPN
ejpam-4511	65	31	)	)	PUNCT
ejpam-4511	65	32	.	.	PUNCT
ejpam-4511	66	1	a	a	DET
ejpam-4511	66	2	set	set	NOUN
ejpam-4511	66	3	d	d	NOUN
ejpam-4511	66	4	⊆	⊆	NUM
ejpam-4511	66	5	v	v	ADP
ejpam-4511	66	6	(	(	PUNCT
ejpam-4511	66	7	g	g	NOUN
ejpam-4511	66	8	)	)	PUNCT
ejpam-4511	66	9	is	be	AUX
ejpam-4511	66	10	hop	hop	ADV
ejpam-4511	66	11	independent	independent	ADJ
ejpam-4511	66	12	if	if	SCONJ
ejpam-4511	66	13	for	for	ADP
ejpam-4511	66	14	every	every	DET
ejpam-4511	66	15	pair	pair	NOUN
ejpam-4511	66	16	of	of	ADP
ejpam-4511	66	17	distinct	distinct	ADJ
ejpam-4511	66	18	vertices	vertex	NOUN
ejpam-4511	66	19	v	v	ADP
ejpam-4511	66	20	,	,	PUNCT
ejpam-4511	66	21	w	w	PROPN
ejpam-4511	66	22	∈	∈	PROPN
ejpam-4511	66	23	d	d	X
ejpam-4511	66	24	,	,	PUNCT
ejpam-4511	66	25	we	we	PRON
ejpam-4511	66	26	have	have	VERB
ejpam-4511	66	27	dg(v	dg(v	NOUN
ejpam-4511	66	28	,	,	PUNCT
ejpam-4511	66	29	w	w	NOUN
ejpam-4511	66	30	)	)	PUNCT
ejpam-4511	66	31	̸=	̸=	PROPN
ejpam-4511	66	32	2	2	NUM
ejpam-4511	66	33	.	.	PUNCT
ejpam-4511	67	1	this	this	DET
ejpam-4511	67	2	concept	concept	NOUN
ejpam-4511	67	3	was	be	AUX
ejpam-4511	67	4	introduced	introduce	VERB
ejpam-4511	67	5	and	and	CCONJ
ejpam-4511	67	6	studied	study	VERB
ejpam-4511	67	7	in	in	ADP
ejpam-4511	67	8	[	[	X
ejpam-4511	67	9	8	8	NUM
ejpam-4511	67	10	]	]	PUNCT
ejpam-4511	67	11	.	.	PUNCT
ejpam-4511	68	1	let	let	VERB
ejpam-4511	68	2	s	s	AUX
ejpam-4511	68	3	=	=	PUNCT
ejpam-4511	68	4	(	(	PUNCT
ejpam-4511	68	5	v1	v1	PROPN
ejpam-4511	68	6	,	,	PUNCT
ejpam-4511	68	7	v2	v2	PROPN
ejpam-4511	68	8	,	,	PUNCT
ejpam-4511	68	9	·	·	PUNCT
ejpam-4511	68	10	·	·	PUNCT
ejpam-4511	68	11	·	·	PUNCT
ejpam-4511	68	12	,	,	PUNCT
ejpam-4511	68	13	vk	vk	AUX
ejpam-4511	68	14	)	)	PUNCT
ejpam-4511	68	15	be	be	AUX
ejpam-4511	68	16	a	a	DET
ejpam-4511	68	17	sequence	sequence	NOUN
ejpam-4511	68	18	of	of	ADP
ejpam-4511	68	19	distinct	distinct	ADJ
ejpam-4511	68	20	vertices	vertex	NOUN
ejpam-4511	68	21	of	of	ADP
ejpam-4511	68	22	a	a	DET
ejpam-4511	68	23	graph	graph	NOUN
ejpam-4511	68	24	g	g	NOUN
ejpam-4511	68	25	and	and	CCONJ
ejpam-4511	68	26	let	let	VERB
ejpam-4511	68	27	ŝ	ŝ	X
ejpam-4511	68	28	=	=	SYM
ejpam-4511	68	29	{	{	PUNCT
ejpam-4511	68	30	v1	v1	PROPN
ejpam-4511	68	31	,	,	PUNCT
ejpam-4511	68	32	v2	v2	PROPN
ejpam-4511	68	33	,	,	PUNCT
ejpam-4511	68	34	.	.	PUNCT
ejpam-4511	68	35	.	.	PUNCT
ejpam-4511	69	1	.	.	PUNCT
ejpam-4511	70	1	,	,	PUNCT
ejpam-4511	70	2	vk	vk	ADP
ejpam-4511	70	3	}	}	PUNCT
ejpam-4511	70	4	.	.	PUNCT
ejpam-4511	71	1	then	then	ADV
ejpam-4511	71	2	s	s	VERB
ejpam-4511	71	3	is	be	AUX
ejpam-4511	71	4	a	a	DET
ejpam-4511	71	5	legal	legal	ADJ
ejpam-4511	71	6	closed	close	VERB
ejpam-4511	71	7	hop	hop	NOUN
ejpam-4511	71	8	independent	independent	ADJ
ejpam-4511	71	9	neighborhood	neighborhood	NOUN
ejpam-4511	71	10	sequence	sequence	NOUN
ejpam-4511	71	11	in	in	ADP
ejpam-4511	71	12	g	g	PROPN
ejpam-4511	71	13	if	if	SCONJ
ejpam-4511	71	14	it	it	PRON
ejpam-4511	71	15	is	be	AUX
ejpam-4511	71	16	a	a	DET
ejpam-4511	71	17	legal	legal	ADJ
ejpam-4511	71	18	closed	close	VERB
ejpam-4511	71	19	hop	hop	NOUN
ejpam-4511	71	20	neighborhood	neighborhood	NOUN
ejpam-4511	71	21	sequence	sequence	NOUN
ejpam-4511	71	22	and	and	CCONJ
ejpam-4511	71	23	ŝ	ŝ	X
ejpam-4511	71	24	is	be	AUX
ejpam-4511	71	25	a	a	DET
ejpam-4511	71	26	hop	hop	NOUN
ejpam-4511	71	27	independent	independent	ADJ
ejpam-4511	71	28	set	set	NOUN
ejpam-4511	71	29	.	.	PUNCT
ejpam-4511	72	1	a	a	DET
ejpam-4511	72	2	legal	legal	ADJ
ejpam-4511	72	3	closed	close	VERB
ejpam-4511	72	4	hop	hop	NOUN
ejpam-4511	72	5	independent	independent	ADJ
ejpam-4511	72	6	neighborhood	neighborhood	NOUN
ejpam-4511	72	7	sequence	sequence	NOUN
ejpam-4511	72	8	s	s	PART
ejpam-4511	72	9	=	=	PUNCT
ejpam-4511	72	10	(	(	PUNCT
ejpam-4511	72	11	v1	v1	PROPN
ejpam-4511	72	12	,	,	PUNCT
ejpam-4511	72	13	v2	v2	NOUN
ejpam-4511	72	14	,	,	PUNCT
ejpam-4511	72	15	.	.	PUNCT
ejpam-4511	72	16	.	.	PUNCT
ejpam-4511	72	17	.	.	PUNCT
ejpam-4511	73	1	,	,	PUNCT
ejpam-4511	73	2	vk	vk	PROPN
ejpam-4511	73	3	)	)	PUNCT
ejpam-4511	73	4	is	be	AUX
ejpam-4511	73	5	a	a	DET
ejpam-4511	73	6	grundy	grundy	PROPN
ejpam-4511	73	7	hop	hop	NOUN
ejpam-4511	73	8	independent	independent	ADJ
ejpam-4511	73	9	hop	hop	NOUN
ejpam-4511	73	10	dominating	dominating	NOUN
ejpam-4511	73	11	sequence	sequence	NOUN
ejpam-4511	73	12	if	if	SCONJ
ejpam-4511	73	13	ŝ	ŝ	NUM
ejpam-4511	73	14	is	be	AUX
ejpam-4511	73	15	a	a	DET
ejpam-4511	73	16	hop	hop	NOUN
ejpam-4511	73	17	independent	independent	ADJ
ejpam-4511	73	18	hop	hop	NOUN
ejpam-4511	73	19	dominating	dominating	NOUN
ejpam-4511	73	20	set	set	NOUN
ejpam-4511	73	21	of	of	ADP
ejpam-4511	73	22	g.	g.	PROPN
ejpam-4511	73	23	the	the	DET
ejpam-4511	73	24	maximum	maximum	ADJ
ejpam-4511	73	25	length	length	NOUN
ejpam-4511	73	26	of	of	ADP
ejpam-4511	73	27	a	a	DET
ejpam-4511	73	28	grundy	grundy	PROPN
ejpam-4511	73	29	hop	hop	NOUN
ejpam-4511	73	30	independent	independent	ADJ
ejpam-4511	73	31	hop	hop	NOUN
ejpam-4511	73	32	dominating	dominating	NOUN
ejpam-4511	73	33	sequence	sequence	NOUN
ejpam-4511	73	34	in	in	ADP
ejpam-4511	73	35	a	a	DET
ejpam-4511	73	36	graph	graph	NOUN
ejpam-4511	73	37	g	g	NOUN
ejpam-4511	73	38	is	be	AUX
ejpam-4511	73	39	called	call	VERB
ejpam-4511	73	40	the	the	DET
ejpam-4511	73	41	grundy	grundy	PROPN
ejpam-4511	73	42	hop	hop	PROPN
ejpam-4511	73	43	independent	independent	PROPN
ejpam-4511	73	44	hop	hop	NOUN
ejpam-4511	73	45	domination	domination	NOUN
ejpam-4511	73	46	number	number	NOUN
ejpam-4511	73	47	of	of	ADP
ejpam-4511	73	48	g	g	NOUN
ejpam-4511	73	49	,	,	PUNCT
ejpam-4511	73	50	and	and	CCONJ
ejpam-4511	73	51	is	be	AUX
ejpam-4511	73	52	denoted	denote	VERB
ejpam-4511	73	53	by	by	ADP
ejpam-4511	73	54	γhihgr	γhihgr	NOUN
ejpam-4511	73	55	(	(	PUNCT
ejpam-4511	73	56	g	g	NOUN
ejpam-4511	73	57	)	)	PUNCT
ejpam-4511	73	58	.	.	PUNCT
ejpam-4511	74	1	let	let	VERB
ejpam-4511	74	2	g	g	NOUN
ejpam-4511	74	3	and	and	CCONJ
ejpam-4511	74	4	h	h	NOUN
ejpam-4511	74	5	be	be	VERB
ejpam-4511	74	6	any	any	DET
ejpam-4511	74	7	two	two	NUM
ejpam-4511	74	8	graphs	graph	NOUN
ejpam-4511	74	9	.	.	PUNCT
ejpam-4511	75	1	the	the	DET
ejpam-4511	75	2	join	join	NOUN
ejpam-4511	75	3	of	of	ADP
ejpam-4511	75	4	g	g	PROPN
ejpam-4511	75	5	and	and	CCONJ
ejpam-4511	75	6	h	h	NOUN
ejpam-4511	75	7	,	,	PUNCT
ejpam-4511	75	8	denoted	denote	VERB
ejpam-4511	75	9	by	by	ADP
ejpam-4511	75	10	g+h	g+h	PROPN
ejpam-4511	75	11	is	be	AUX
ejpam-4511	75	12	the	the	DET
ejpam-4511	75	13	graph	graph	NOUN
ejpam-4511	75	14	with	with	ADP
ejpam-4511	75	15	vertex	vertex	NOUN
ejpam-4511	75	16	set	set	VERB
ejpam-4511	75	17	v	v	NOUN
ejpam-4511	75	18	(	(	PUNCT
ejpam-4511	75	19	g+h	g+h	NOUN
ejpam-4511	75	20	)	)	PUNCT
ejpam-4511	76	1	=	=	SYM
ejpam-4511	76	2	v	v	X
ejpam-4511	76	3	(	(	PUNCT
ejpam-4511	76	4	g)∪v	g)∪v	NOUN
ejpam-4511	76	5	(	(	PUNCT
ejpam-4511	76	6	h	h	NOUN
ejpam-4511	76	7	)	)	PUNCT
ejpam-4511	76	8	and	and	CCONJ
ejpam-4511	76	9	edge	edge	NOUN
ejpam-4511	76	10	set	set	VERB
ejpam-4511	76	11	e(g+h	e(g+h	NUM
ejpam-4511	76	12	)	)	PUNCT
ejpam-4511	77	1	=	=	SYM
ejpam-4511	77	2	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	X
ejpam-4511	77	3	:	:	PUNCT
ejpam-4511	77	4	u	u	PROPN
ejpam-4511	77	5	∈	∈	PROPN
ejpam-4511	77	6	v	v	NOUN
ejpam-4511	77	7	(	(	PUNCT
ejpam-4511	77	8	g	g	NOUN
ejpam-4511	77	9	)	)	PUNCT
ejpam-4511	77	10	,	,	PUNCT
ejpam-4511	77	11	v	v	X
ejpam-4511	77	12	∈	∈	PROPN
ejpam-4511	77	13	v	v	NOUN
ejpam-4511	77	14	(	(	PUNCT
ejpam-4511	77	15	h	h	NOUN
ejpam-4511	77	16	)	)	PUNCT
ejpam-4511	77	17	}	}	PUNCT
ejpam-4511	77	18	.	.	PUNCT
ejpam-4511	78	1	the	the	DET
ejpam-4511	78	2	corona	corona	NOUN
ejpam-4511	78	3	g	g	PROPN
ejpam-4511	78	4	and	and	CCONJ
ejpam-4511	78	5	h	h	NOUN
ejpam-4511	78	6	,	,	PUNCT
ejpam-4511	78	7	denoted	denote	VERB
ejpam-4511	78	8	by	by	ADP
ejpam-4511	78	9	g	g	PROPN
ejpam-4511	78	10	◦	◦	NOUN
ejpam-4511	78	11	h	h	NOUN
ejpam-4511	78	12	,	,	PUNCT
ejpam-4511	78	13	the	the	DET
ejpam-4511	78	14	graph	graph	NOUN
ejpam-4511	78	15	obtained	obtain	VERB
ejpam-4511	78	16	by	by	ADP
ejpam-4511	78	17	taking	take	VERB
ejpam-4511	78	18	one	one	NUM
ejpam-4511	78	19	copy	copy	NOUN
ejpam-4511	78	20	of	of	ADP
ejpam-4511	78	21	g	g	PROPN
ejpam-4511	78	22	and	and	CCONJ
ejpam-4511	78	23	|v	|v	PROPN
ejpam-4511	78	24	(	(	PUNCT
ejpam-4511	78	25	g)|	g)|	NOUN
ejpam-4511	78	26	copies	copy	NOUN
ejpam-4511	78	27	of	of	ADP
ejpam-4511	78	28	h	h	NOUN
ejpam-4511	78	29	,	,	PUNCT
ejpam-4511	78	30	and	and	CCONJ
ejpam-4511	78	31	then	then	ADV
ejpam-4511	78	32	joining	join	VERB
ejpam-4511	78	33	the	the	DET
ejpam-4511	78	34	ith	ith	PROPN
ejpam-4511	78	35	vertex	vertex	NOUN
ejpam-4511	78	36	of	of	ADP
ejpam-4511	78	37	g	g	NOUN
ejpam-4511	78	38	to	to	ADP
ejpam-4511	78	39	every	every	DET
ejpam-4511	78	40	vertex	vertex	NOUN
ejpam-4511	78	41	of	of	ADP
ejpam-4511	78	42	the	the	DET
ejpam-4511	78	43	ith	ith	PROPN
ejpam-4511	78	44	copy	copy	NOUN
ejpam-4511	78	45	of	of	ADP
ejpam-4511	78	46	h.	h.	PROPN
ejpam-4511	78	47	we	we	PRON
ejpam-4511	78	48	denote	denote	VERB
ejpam-4511	78	49	by	by	ADP
ejpam-4511	78	50	hv	hv	PROPN
ejpam-4511	78	51	the	the	DET
ejpam-4511	78	52	copy	copy	NOUN
ejpam-4511	78	53	of	of	ADP
ejpam-4511	78	54	h	h	NOUN
ejpam-4511	78	55	in	in	ADP
ejpam-4511	78	56	g	g	PROPN
ejpam-4511	78	57	◦	◦	NOUN
ejpam-4511	78	58	h	h	NOUN
ejpam-4511	78	59	corresponding	correspond	VERB
ejpam-4511	78	60	to	to	ADP
ejpam-4511	78	61	the	the	DET
ejpam-4511	78	62	vertex	vertex	NOUN
ejpam-4511	78	63	v	v	ADP
ejpam-4511	78	64	∈	∈	PROPN
ejpam-4511	78	65	g	g	NOUN
ejpam-4511	78	66	and	and	CCONJ
ejpam-4511	78	67	write	write	VERB
ejpam-4511	78	68	v	v	ADP
ejpam-4511	78	69	+	+	PROPN
ejpam-4511	78	70	hv	hv	PROPN
ejpam-4511	78	71	for	for	ADP
ejpam-4511	78	72	⟨{v	⟨{v	PROPN
ejpam-4511	78	73	}	}	PUNCT
ejpam-4511	79	1	+	+	PROPN
ejpam-4511	79	2	hv⟩.	hv⟩.	PROPN
ejpam-4511	79	3	the	the	DET
ejpam-4511	79	4	lexicographic	lexicographic	ADJ
ejpam-4511	79	5	product	product	NOUN
ejpam-4511	79	6	of	of	ADP
ejpam-4511	79	7	graphs	graph	NOUN
ejpam-4511	79	8	g	g	PROPN
ejpam-4511	79	9	and	and	CCONJ
ejpam-4511	79	10	h	h	NOUN
ejpam-4511	79	11	,	,	PUNCT
ejpam-4511	79	12	denoted	denote	VERB
ejpam-4511	79	13	by	by	ADP
ejpam-4511	79	14	g[h	g[h	NOUN
ejpam-4511	79	15	]	]	PUNCT
ejpam-4511	79	16	,	,	PUNCT
ejpam-4511	79	17	is	be	AUX
ejpam-4511	79	18	the	the	DET
ejpam-4511	79	19	graph	graph	NOUN
ejpam-4511	79	20	with	with	ADP
ejpam-4511	79	21	vertex	vertex	NOUN
ejpam-4511	79	22	set	set	VERB
ejpam-4511	79	23	v	v	NOUN
ejpam-4511	79	24	(	(	PUNCT
ejpam-4511	79	25	g[h	g[h	PROPN
ejpam-4511	79	26	]	]	PUNCT
ejpam-4511	79	27	)	)	PUNCT
ejpam-4511	79	28	=	=	SYM
ejpam-4511	79	29	v	v	X
ejpam-4511	79	30	(	(	PUNCT
ejpam-4511	79	31	g	g	NOUN
ejpam-4511	79	32	)	)	PUNCT
ejpam-4511	79	33	×	×	NOUN
ejpam-4511	79	34	v	v	NOUN
ejpam-4511	79	35	(	(	PUNCT
ejpam-4511	79	36	h	h	NOUN
ejpam-4511	79	37	)	)	PUNCT
ejpam-4511	79	38	and	and	CCONJ
ejpam-4511	79	39	(	(	PUNCT
ejpam-4511	79	40	v	v	NOUN
ejpam-4511	79	41	,	,	PUNCT
ejpam-4511	79	42	a)(u	a)(u	ADJ
ejpam-4511	79	43	,	,	PUNCT
ejpam-4511	79	44	b	b	X
ejpam-4511	79	45	)	)	PUNCT
ejpam-4511	79	46	∈	∈	NOUN
ejpam-4511	79	47	e(g[h	e(g[h	NOUN
ejpam-4511	79	48	]	]	PUNCT
ejpam-4511	79	49	)	)	PUNCT
ejpam-4511	80	1	if	if	SCONJ
ejpam-4511	80	2	and	and	CCONJ
ejpam-4511	80	3	only	only	ADV
ejpam-4511	80	4	if	if	SCONJ
ejpam-4511	80	5	either	either	DET
ejpam-4511	80	6	uv	uv	PROPN
ejpam-4511	80	7	∈	∈	PROPN
ejpam-4511	80	8	e(g	e(g	PROPN
ejpam-4511	80	9	)	)	PUNCT
ejpam-4511	80	10	or	or	CCONJ
ejpam-4511	80	11	u	u	X
ejpam-4511	80	12	=	=	PROPN
ejpam-4511	80	13	v	v	PROPN
ejpam-4511	80	14	and	and	CCONJ
ejpam-4511	80	15	ab	ab	PROPN
ejpam-4511	80	16	∈	∈	PROPN
ejpam-4511	80	17	e(h	e(h	PROPN
ejpam-4511	80	18	)	)	PUNCT
ejpam-4511	80	19	.	.	PUNCT
ejpam-4511	81	1	we	we	PRON
ejpam-4511	81	2	note	note	VERB
ejpam-4511	81	3	that	that	SCONJ
ejpam-4511	81	4	any	any	DET
ejpam-4511	81	5	non	non	ADJ
ejpam-4511	81	6	-	-	ADJ
ejpam-4511	81	7	empty	empty	ADJ
ejpam-4511	81	8	set	set	NOUN
ejpam-4511	81	9	c	c	NOUN
ejpam-4511	81	10	⊆	⊆	NUM
ejpam-4511	81	11	v	v	NOUN
ejpam-4511	81	12	(	(	PUNCT
ejpam-4511	81	13	g	g	NOUN
ejpam-4511	81	14	)	)	PUNCT
ejpam-4511	81	15	×	×	NOUN
ejpam-4511	81	16	v	v	NOUN
ejpam-4511	81	17	(	(	PUNCT
ejpam-4511	81	18	h	h	NOUN
ejpam-4511	81	19	)	)	PUNCT
ejpam-4511	81	20	can	can	AUX
ejpam-4511	81	21	be	be	AUX
ejpam-4511	81	22	written	write	VERB
ejpam-4511	81	23	as	as	ADP
ejpam-4511	81	24	c	c	NOUN
ejpam-4511	81	25	=	=	PUNCT
ejpam-4511	81	26	⋃	⋃	PROPN
ejpam-4511	81	27	x∈s	x∈s	NOUN
ejpam-4511	82	1	[	[	X
ejpam-4511	82	2	{	{	PUNCT
ejpam-4511	82	3	x	x	NOUN
ejpam-4511	82	4	}	}	PUNCT
ejpam-4511	82	5	×	×	PROPN
ejpam-4511	82	6	tx	tx	PROPN
ejpam-4511	82	7	]	]	X
ejpam-4511	82	8	,	,	PUNCT
ejpam-4511	82	9	where	where	SCONJ
ejpam-4511	82	10	s	s	VERB
ejpam-4511	82	11	⊆	⊆	NUM
ejpam-4511	82	12	v	v	NOUN
ejpam-4511	82	13	(	(	PUNCT
ejpam-4511	82	14	g	g	NOUN
ejpam-4511	82	15	)	)	PUNCT
ejpam-4511	82	16	and	and	CCONJ
ejpam-4511	82	17	tx	tx	VERB
ejpam-4511	82	18	⊆	⊆	NUM
ejpam-4511	82	19	v	v	NOUN
ejpam-4511	82	20	(	(	PUNCT
ejpam-4511	82	21	h	h	NOUN
ejpam-4511	82	22	)	)	PUNCT
ejpam-4511	82	23	for	for	ADP
ejpam-4511	82	24	each	each	DET
ejpam-4511	82	25	x	x	PROPN
ejpam-4511	82	26	∈	∈	PROPN
ejpam-4511	82	27	s.	s.	PROPN
ejpam-4511	82	28	specifically	specifically	ADV
ejpam-4511	82	29	,	,	PUNCT
ejpam-4511	82	30	tx	tx	PROPN
ejpam-4511	82	31	=	=	PUNCT
ejpam-4511	82	32	{	{	PUNCT
ejpam-4511	82	33	a	a	DET
ejpam-4511	82	34	∈	∈	PROPN
ejpam-4511	82	35	v	v	ADP
ejpam-4511	82	36	(	(	PUNCT
ejpam-4511	82	37	h	h	NOUN
ejpam-4511	82	38	)	)	PUNCT
ejpam-4511	82	39	:	:	PUNCT
ejpam-4511	82	40	(	(	PUNCT
ejpam-4511	82	41	x	x	X
ejpam-4511	82	42	,	,	PUNCT
ejpam-4511	82	43	a	a	PRON
ejpam-4511	82	44	)	)	PUNCT
ejpam-4511	82	45	∈	∈	PROPN
ejpam-4511	82	46	c	c	NOUN
ejpam-4511	82	47	}	}	PUNCT
ejpam-4511	82	48	for	for	ADP
ejpam-4511	82	49	each	each	DET
ejpam-4511	82	50	x	x	PROPN
ejpam-4511	82	51	∈	∈	PROPN
ejpam-4511	82	52	s.	s.	PROPN
ejpam-4511	82	53	3	3	X
ejpam-4511	82	54	.	.	PROPN
ejpam-4511	82	55	results	result	NOUN
ejpam-4511	82	56	remark	remark	VERB
ejpam-4511	82	57	1	1	NUM
ejpam-4511	82	58	.	.	PUNCT
ejpam-4511	83	1	the	the	DET
ejpam-4511	83	2	vertex	vertex	NOUN
ejpam-4511	83	3	set	set	NOUN
ejpam-4511	83	4	of	of	ADP
ejpam-4511	83	5	a	a	DET
ejpam-4511	83	6	graph	graph	NOUN
ejpam-4511	83	7	need	need	AUX
ejpam-4511	83	8	not	not	PART
ejpam-4511	83	9	form	form	VERB
ejpam-4511	83	10	a	a	DET
ejpam-4511	83	11	legal	legal	ADJ
ejpam-4511	83	12	closed	closed	ADJ
ejpam-4511	83	13	hop	hop	NOUN
ejpam-4511	83	14	neighborhood	neighborhood	NOUN
ejpam-4511	83	15	sequence	sequence	NOUN
ejpam-4511	83	16	(	(	PUNCT
ejpam-4511	83	17	a	a	DET
ejpam-4511	83	18	grundy	grundy	PROPN
ejpam-4511	83	19	hop	hop	NOUN
ejpam-4511	83	20	dominating	dominating	NOUN
ejpam-4511	83	21	sequence	sequence	NOUN
ejpam-4511	83	22	)	)	PUNCT
ejpam-4511	83	23	.	.	PUNCT
ejpam-4511	84	1	to	to	PART
ejpam-4511	84	2	see	see	VERB
ejpam-4511	84	3	this	this	PRON
ejpam-4511	84	4	,	,	PUNCT
ejpam-4511	84	5	consider	consider	VERB
ejpam-4511	84	6	the	the	DET
ejpam-4511	84	7	graph	graph	NOUN
ejpam-4511	84	8	g	g	PROPN
ejpam-4511	84	9	=	=	PROPN
ejpam-4511	84	10	c5	c5	PROPN
ejpam-4511	84	11	in	in	ADP
ejpam-4511	84	12	figure	figure	NOUN
ejpam-4511	84	13	1	1	NUM
ejpam-4511	84	14	.	.	PUNCT
ejpam-4511	85	1	let	let	VERB
ejpam-4511	85	2	s	s	PRON
ejpam-4511	85	3	=	=	PUNCT
ejpam-4511	85	4	(	(	PUNCT
ejpam-4511	85	5	v1	v1	PROPN
ejpam-4511	85	6	,	,	PUNCT
ejpam-4511	85	7	v2	v2	PROPN
ejpam-4511	85	8	,	,	PUNCT
ejpam-4511	85	9	v3	v3	PROPN
ejpam-4511	85	10	,	,	PUNCT
ejpam-4511	85	11	v4	v4	NOUN
ejpam-4511	85	12	,	,	PUNCT
ejpam-4511	85	13	v5	v5	PROPN
ejpam-4511	85	14	)	)	PUNCT
ejpam-4511	85	15	.	.	PUNCT
ejpam-4511	86	1	notice	notice	VERB
ejpam-4511	86	2	that	that	SCONJ
ejpam-4511	86	3	n2	n2	ADJ
ejpam-4511	86	4	g[v5	g[v5	NOUN
ejpam-4511	86	5	]	]	X
ejpam-4511	86	6	=	=	SYM
ejpam-4511	86	7	{	{	PUNCT
ejpam-4511	86	8	v2	v2	PROPN
ejpam-4511	86	9	,	,	PUNCT
ejpam-4511	86	10	v3	v3	PROPN
ejpam-4511	86	11	,	,	PUNCT
ejpam-4511	86	12	v5	v5	PROPN
ejpam-4511	86	13	}	}	PUNCT
ejpam-4511	86	14	⊆	⊆	NUM
ejpam-4511	86	15	n2	n2	ADJ
ejpam-4511	86	16	g[v1	g[v1	PROPN
ejpam-4511	86	17	]	]	PUNCT
ejpam-4511	86	18	∪n2	∪n2	PROPN
ejpam-4511	86	19	g[v2	g[v2	PROPN
ejpam-4511	86	20	]	]	X
ejpam-4511	86	21	=	=	SYM
ejpam-4511	86	22	{	{	PUNCT
ejpam-4511	86	23	v1	v1	PROPN
ejpam-4511	86	24	,	,	PUNCT
ejpam-4511	86	25	v2	v2	PROPN
ejpam-4511	86	26	,	,	PUNCT
ejpam-4511	86	27	v3	v3	PROPN
ejpam-4511	86	28	,	,	PUNCT
ejpam-4511	86	29	v4	v4	PROPN
ejpam-4511	86	30	,	,	PUNCT
ejpam-4511	86	31	v5	v5	PROPN
ejpam-4511	86	32	}	}	PUNCT
ejpam-4511	86	33	.	.	PUNCT
ejpam-4511	87	1	j.	j.	PROPN
ejpam-4511	87	2	hassan	hassan	PROPN
ejpam-4511	87	3	,	,	PUNCT
ejpam-4511	87	4	s.	s.	PROPN
ejpam-4511	87	5	canoy	canoy	PROPN
ejpam-4511	87	6	/	/	SYM
ejpam-4511	87	7	eur	eur	PROPN
ejpam-4511	87	8	.	.	PUNCT
ejpam-4511	88	1	j.	j.	PROPN
ejpam-4511	88	2	pure	pure	PROPN
ejpam-4511	88	3	appl	appl	PROPN
ejpam-4511	88	4	.	.	PROPN
ejpam-4511	88	5	math	math	PROPN
ejpam-4511	88	6	,	,	PUNCT
ejpam-4511	88	7	15	15	NUM
ejpam-4511	88	8	(	(	PUNCT
ejpam-4511	88	9	4	4	NUM
ejpam-4511	88	10	)	)	PUNCT
ejpam-4511	88	11	(	(	PUNCT
ejpam-4511	88	12	2022	2022	NUM
ejpam-4511	88	13	)	)	PUNCT
ejpam-4511	88	14	,	,	PUNCT
ejpam-4511	88	15	1623	1623	NUM
ejpam-4511	88	16	-	-	SYM
ejpam-4511	88	17	1636	1636	NUM
ejpam-4511	88	18	1626	1626	NUM
ejpam-4511	88	19	hence	hence	ADV
ejpam-4511	88	20	,	,	PUNCT
ejpam-4511	88	21	n2	n2	ADJ
ejpam-4511	88	22	g[v5	g[v5	NOUN
ejpam-4511	88	23	]	]	PUNCT
ejpam-4511	88	24	\	\	NOUN
ejpam-4511	88	25	∪4	∪4	NOUN
ejpam-4511	88	26	j=1n	j=1n	NOUN
ejpam-4511	88	27	2	2	NUM
ejpam-4511	88	28	g[vj	g[vj	PROPN
ejpam-4511	88	29	]	]	PUNCT
ejpam-4511	88	30	=	=	PUNCT
ejpam-4511	88	31	∅.	∅.	VERB
ejpam-4511	88	32	thus	thus	ADV
ejpam-4511	88	33	,	,	PUNCT
ejpam-4511	88	34	s	s	VERB
ejpam-4511	88	35	is	be	AUX
ejpam-4511	88	36	not	not	PART
ejpam-4511	88	37	a	a	DET
ejpam-4511	88	38	legal	legal	ADJ
ejpam-4511	88	39	closed	close	VERB
ejpam-4511	88	40	hop	hop	NOUN
ejpam-4511	88	41	neighborhood	neighborhood	NOUN
ejpam-4511	88	42	sequence	sequence	NOUN
ejpam-4511	88	43	(	(	PUNCT
ejpam-4511	88	44	hence	hence	ADV
ejpam-4511	88	45	,	,	PUNCT
ejpam-4511	88	46	not	not	PART
ejpam-4511	88	47	a	a	DET
ejpam-4511	88	48	grundy	grundy	PROPN
ejpam-4511	88	49	hop	hop	NOUN
ejpam-4511	88	50	dominating	dominating	NOUN
ejpam-4511	88	51	sequence	sequence	NOUN
ejpam-4511	88	52	)	)	PUNCT
ejpam-4511	88	53	.	.	PUNCT
ejpam-4511	89	1	it	it	PRON
ejpam-4511	89	2	is	be	AUX
ejpam-4511	89	3	routine	routine	ADJ
ejpam-4511	89	4	to	to	PART
ejpam-4511	89	5	show	show	VERB
ejpam-4511	89	6	that	that	SCONJ
ejpam-4511	89	7	any	any	DET
ejpam-4511	89	8	rearrangement	rearrangement	NOUN
ejpam-4511	89	9	of	of	ADP
ejpam-4511	89	10	the	the	DET
ejpam-4511	89	11	terms	term	NOUN
ejpam-4511	89	12	of	of	ADP
ejpam-4511	89	13	s	s	NOUN
ejpam-4511	89	14	is	be	AUX
ejpam-4511	89	15	not	not	PART
ejpam-4511	89	16	legal	legal	ADJ
ejpam-4511	89	17	closed	close	VERB
ejpam-4511	89	18	hop	hop	NOUN
ejpam-4511	89	19	neighborhood	neighborhood	NOUN
ejpam-4511	89	20	sequence	sequence	NOUN
ejpam-4511	89	21	of	of	ADP
ejpam-4511	89	22	g.	g.	PROPN
ejpam-4511	89	23	g	g	PROPN
ejpam-4511	89	24	:	:	PUNCT
ejpam-4511	89	25	v1	v1	VERB
ejpam-4511	89	26	v2	v2	PROPN
ejpam-4511	90	1	v3v4	v3v4	PUNCT
ejpam-4511	90	2	v5	v5	PROPN
ejpam-4511	90	3	figure	figure	NOUN
ejpam-4511	90	4	1	1	NUM
ejpam-4511	90	5	:	:	PUNCT
ejpam-4511	90	6	a	a	DET
ejpam-4511	90	7	graph	graph	NOUN
ejpam-4511	90	8	g	g	ADP
ejpam-4511	90	9	such	such	DET
ejpam-4511	90	10	that	that	PRON
ejpam-4511	90	11	v	v	NOUN
ejpam-4511	90	12	(	(	PUNCT
ejpam-4511	90	13	g	g	NOUN
ejpam-4511	90	14	)	)	PUNCT
ejpam-4511	90	15	does	do	AUX
ejpam-4511	90	16	not	not	PART
ejpam-4511	90	17	form	form	VERB
ejpam-4511	90	18	a	a	DET
ejpam-4511	90	19	legal	legal	ADJ
ejpam-4511	90	20	closed	closed	ADJ
ejpam-4511	90	21	hop	hop	NOUN
ejpam-4511	90	22	neighborhood	neighborhood	NOUN
ejpam-4511	90	23	sequence	sequence	NOUN
ejpam-4511	90	24	remark	remark	NOUN
ejpam-4511	90	25	2	2	NUM
ejpam-4511	90	26	.	.	PUNCT
ejpam-4511	91	1	a	a	DET
ejpam-4511	91	2	proper	proper	ADJ
ejpam-4511	91	3	hop	hop	NOUN
ejpam-4511	91	4	dominating	dominating	NOUN
ejpam-4511	91	5	set	set	NOUN
ejpam-4511	91	6	need	need	AUX
ejpam-4511	91	7	not	not	PART
ejpam-4511	91	8	form	form	VERB
ejpam-4511	91	9	a	a	DET
ejpam-4511	91	10	legal	legal	ADJ
ejpam-4511	91	11	closed	closed	ADJ
ejpam-4511	91	12	hop	hop	NOUN
ejpam-4511	91	13	neighborhood	neighborhood	NOUN
ejpam-4511	91	14	sequence	sequence	NOUN
ejpam-4511	91	15	(	(	PUNCT
ejpam-4511	91	16	a	a	DET
ejpam-4511	91	17	grundy	grundy	PROPN
ejpam-4511	91	18	hop	hop	NOUN
ejpam-4511	91	19	dominating	dominating	NOUN
ejpam-4511	91	20	sequence	sequence	NOUN
ejpam-4511	91	21	)	)	PUNCT
ejpam-4511	91	22	.	.	PUNCT
ejpam-4511	92	1	consider	consider	VERB
ejpam-4511	92	2	the	the	DET
ejpam-4511	92	3	graph	graph	NOUN
ejpam-4511	92	4	g	g	NOUN
ejpam-4511	92	5	in	in	ADP
ejpam-4511	92	6	figure	figure	NOUN
ejpam-4511	92	7	2	2	NUM
ejpam-4511	92	8	.	.	PUNCT
ejpam-4511	93	1	let	let	VERB
ejpam-4511	93	2	s	s	PRON
ejpam-4511	93	3	=	=	PUNCT
ejpam-4511	93	4	(	(	PUNCT
ejpam-4511	93	5	v1	v1	PROPN
ejpam-4511	93	6	,	,	PUNCT
ejpam-4511	93	7	v2	v2	PROPN
ejpam-4511	93	8	,	,	PUNCT
ejpam-4511	93	9	v3	v3	PROPN
ejpam-4511	93	10	)	)	PUNCT
ejpam-4511	93	11	.	.	PUNCT
ejpam-4511	94	1	clearly	clearly	ADV
ejpam-4511	94	2	,	,	PUNCT
ejpam-4511	94	3	ŝ	ŝ	X
ejpam-4511	94	4	is	be	AUX
ejpam-4511	94	5	a	a	DET
ejpam-4511	94	6	proper	proper	ADJ
ejpam-4511	94	7	hop	hop	NOUN
ejpam-4511	94	8	dominating	dominating	NOUN
ejpam-4511	94	9	set	set	NOUN
ejpam-4511	94	10	of	of	ADP
ejpam-4511	94	11	g.	g.	PROPN
ejpam-4511	94	12	observe	observe	VERB
ejpam-4511	94	13	that	that	DET
ejpam-4511	94	14	n2	n2	ADJ
ejpam-4511	94	15	g[v3	g[v3	NOUN
ejpam-4511	94	16	]	]	X
ejpam-4511	94	17	=	=	PRON
ejpam-4511	94	18	{	{	PUNCT
ejpam-4511	94	19	v2	v2	PROPN
ejpam-4511	94	20	,	,	PUNCT
ejpam-4511	94	21	v3	v3	PROPN
ejpam-4511	94	22	,	,	PUNCT
ejpam-4511	94	23	v5	v5	NOUN
ejpam-4511	94	24	}	}	PUNCT
ejpam-4511	94	25	=	=	SYM
ejpam-4511	94	26	n2	n2	PROPN
ejpam-4511	94	27	g[v2	g[v2	NOUN
ejpam-4511	94	28	]	]	PUNCT
ejpam-4511	94	29	.	.	PUNCT
ejpam-4511	95	1	hence	hence	ADV
ejpam-4511	95	2	,	,	PUNCT
ejpam-4511	95	3	n2	n2	ADJ
ejpam-4511	95	4	g[v3	g[v3	NOUN
ejpam-4511	95	5	]	]	PUNCT
ejpam-4511	95	6	\	\	NOUN
ejpam-4511	95	7	∪2	∪2	PRON
ejpam-4511	95	8	j=1n	j=1n	VERB
ejpam-4511	95	9	2	2	NUM
ejpam-4511	95	10	g[vj	g[vj	PROPN
ejpam-4511	95	11	]	]	PUNCT
ejpam-4511	95	12	=	=	PUNCT
ejpam-4511	95	13	∅.	∅.	VERB
ejpam-4511	95	14	thus	thus	ADV
ejpam-4511	95	15	,	,	PUNCT
ejpam-4511	95	16	s	s	VERB
ejpam-4511	95	17	is	be	AUX
ejpam-4511	95	18	not	not	PART
ejpam-4511	95	19	a	a	DET
ejpam-4511	95	20	legal	legal	ADJ
ejpam-4511	95	21	closed	close	VERB
ejpam-4511	95	22	hop	hop	NOUN
ejpam-4511	95	23	neighborhood	neighborhood	NOUN
ejpam-4511	95	24	sequence	sequence	NOUN
ejpam-4511	95	25	(	(	PUNCT
ejpam-4511	95	26	not	not	PART
ejpam-4511	95	27	a	a	DET
ejpam-4511	95	28	grundy	grundy	PROPN
ejpam-4511	95	29	hop	hop	NOUN
ejpam-4511	95	30	dominating	dominating	NOUN
ejpam-4511	95	31	sequence	sequence	NOUN
ejpam-4511	95	32	)	)	PUNCT
ejpam-4511	95	33	.	.	PUNCT
ejpam-4511	96	1	v1	v1	PROPN
ejpam-4511	96	2	v2	v2	PROPN
ejpam-4511	96	3	v4	v4	PROPN
ejpam-4511	96	4	v3	v3	PROPN
ejpam-4511	96	5	v5	v5	PROPN
ejpam-4511	96	6	g	g	PROPN
ejpam-4511	96	7	:	:	PUNCT
ejpam-4511	96	8	figure	figure	NOUN
ejpam-4511	96	9	2	2	NUM
ejpam-4511	96	10	:	:	PUNCT
ejpam-4511	96	11	a	a	DET
ejpam-4511	96	12	graph	graph	NOUN
ejpam-4511	96	13	g	g	NOUN
ejpam-4511	96	14	with	with	ADP
ejpam-4511	96	15	a	a	DET
ejpam-4511	96	16	proper	proper	ADJ
ejpam-4511	96	17	hop	hop	NOUN
ejpam-4511	96	18	dominating	dominating	NOUN
ejpam-4511	96	19	set	set	NOUN
ejpam-4511	96	20	which	which	PRON
ejpam-4511	96	21	does	do	AUX
ejpam-4511	96	22	not	not	PART
ejpam-4511	96	23	form	form	VERB
ejpam-4511	96	24	a	a	DET
ejpam-4511	96	25	legal	legal	ADJ
ejpam-4511	96	26	closed	closed	ADJ
ejpam-4511	96	27	hop	hop	NOUN
ejpam-4511	96	28	neighborhood	neighborhood	NOUN
ejpam-4511	96	29	sequence	sequence	NOUN
ejpam-4511	96	30	our	our	PRON
ejpam-4511	96	31	first	first	ADJ
ejpam-4511	96	32	result	result	NOUN
ejpam-4511	96	33	shows	show	VERB
ejpam-4511	96	34	that	that	SCONJ
ejpam-4511	96	35	every	every	DET
ejpam-4511	96	36	graph	graph	NOUN
ejpam-4511	96	37	g	g	PROPN
ejpam-4511	96	38	admits	admit	VERB
ejpam-4511	96	39	a	a	DET
ejpam-4511	96	40	grundy	grundy	PROPN
ejpam-4511	96	41	hop	hop	NOUN
ejpam-4511	96	42	dominating	dominating	NOUN
ejpam-4511	96	43	sequence	sequence	NOUN
ejpam-4511	96	44	.	.	PUNCT
ejpam-4511	97	1	theorem	theorem	NOUN
ejpam-4511	97	2	1	1	NUM
ejpam-4511	97	3	.	.	PUNCT
ejpam-4511	98	1	let	let	VERB
ejpam-4511	98	2	g	g	NOUN
ejpam-4511	98	3	be	be	AUX
ejpam-4511	98	4	any	any	DET
ejpam-4511	98	5	graph	graph	NOUN
ejpam-4511	98	6	on	on	ADP
ejpam-4511	98	7	n	n	DET
ejpam-4511	98	8	vertices	vertex	NOUN
ejpam-4511	98	9	.	.	PUNCT
ejpam-4511	99	1	then	then	ADV
ejpam-4511	99	2	the	the	DET
ejpam-4511	99	3	following	follow	VERB
ejpam-4511	99	4	statements	statement	NOUN
ejpam-4511	99	5	hold	hold	VERB
ejpam-4511	99	6	.	.	PUNCT
ejpam-4511	100	1	(	(	PUNCT
ejpam-4511	100	2	i	i	NOUN
ejpam-4511	100	3	)	)	PUNCT
ejpam-4511	100	4	if	if	SCONJ
ejpam-4511	100	5	γh(g	γh(g	NOUN
ejpam-4511	100	6	)	)	PUNCT
ejpam-4511	100	7	=	=	SYM
ejpam-4511	101	1	k	k	PROPN
ejpam-4511	101	2	and	and	CCONJ
ejpam-4511	101	3	d	d	NOUN
ejpam-4511	101	4	=	=	PUNCT
ejpam-4511	101	5	{	{	PUNCT
ejpam-4511	101	6	v1	v1	PROPN
ejpam-4511	101	7	,	,	PUNCT
ejpam-4511	101	8	v2	v2	PROPN
ejpam-4511	101	9	,	,	PUNCT
ejpam-4511	101	10	.	.	PUNCT
ejpam-4511	101	11	.	.	PUNCT
ejpam-4511	102	1	.	.	PUNCT
ejpam-4511	103	1	,	,	PUNCT
ejpam-4511	103	2	vk	vk	PROPN
ejpam-4511	103	3	}	}	PUNCT
ejpam-4511	103	4	is	be	AUX
ejpam-4511	103	5	a	a	DET
ejpam-4511	103	6	minimum	minimum	ADJ
ejpam-4511	103	7	hop	hop	NOUN
ejpam-4511	103	8	dominating	dominating	NOUN
ejpam-4511	103	9	set	set	NOUN
ejpam-4511	103	10	of	of	ADP
ejpam-4511	103	11	g	g	NOUN
ejpam-4511	103	12	,	,	PUNCT
ejpam-4511	103	13	then	then	ADV
ejpam-4511	103	14	s	s	VERB
ejpam-4511	103	15	=	=	PUNCT
ejpam-4511	103	16	(	(	PUNCT
ejpam-4511	103	17	v1	v1	PROPN
ejpam-4511	103	18	,	,	PUNCT
ejpam-4511	103	19	v2	v2	PROPN
ejpam-4511	103	20	,	,	PUNCT
ejpam-4511	103	21	·	·	PUNCT
ejpam-4511	103	22	·	·	PUNCT
ejpam-4511	103	23	·	·	PUNCT
ejpam-4511	103	24	,	,	PUNCT
ejpam-4511	103	25	vk	vk	PROPN
ejpam-4511	103	26	)	)	PUNCT
ejpam-4511	103	27	is	be	AUX
ejpam-4511	103	28	a	a	DET
ejpam-4511	103	29	grundy	grundy	PROPN
ejpam-4511	103	30	hop	hop	NOUN
ejpam-4511	103	31	dominating	dominating	NOUN
ejpam-4511	103	32	sequence	sequence	NOUN
ejpam-4511	103	33	.	.	PUNCT
ejpam-4511	104	1	in	in	ADP
ejpam-4511	104	2	particular	particular	ADJ
ejpam-4511	104	3	,	,	PUNCT
ejpam-4511	104	4	γh(g	γh(g	NOUN
ejpam-4511	104	5	)	)	PUNCT
ejpam-4511	104	6	≤	≤	NOUN
ejpam-4511	104	7	γhgr(g	γhgr(g	NOUN
ejpam-4511	104	8	)	)	PUNCT
ejpam-4511	104	9	.	.	PUNCT
ejpam-4511	105	1	(	(	PUNCT
ejpam-4511	105	2	ii	ii	X
ejpam-4511	105	3	)	)	PUNCT
ejpam-4511	105	4	if	if	SCONJ
ejpam-4511	105	5	s	s	VERB
ejpam-4511	105	6	=	=	PUNCT
ejpam-4511	105	7	(	(	PUNCT
ejpam-4511	105	8	v1	v1	PROPN
ejpam-4511	105	9	,	,	PUNCT
ejpam-4511	105	10	v2	v2	PROPN
ejpam-4511	105	11	,	,	PUNCT
ejpam-4511	105	12	·	·	PUNCT
ejpam-4511	105	13	·	·	PUNCT
ejpam-4511	105	14	·	·	PUNCT
ejpam-4511	105	15	,	,	PUNCT
ejpam-4511	105	16	vm	vm	NOUN
ejpam-4511	105	17	)	)	PUNCT
ejpam-4511	105	18	is	be	AUX
ejpam-4511	105	19	a	a	DET
ejpam-4511	105	20	minimum	minimum	ADJ
ejpam-4511	105	21	grundy	grundy	PROPN
ejpam-4511	105	22	hop	hop	NOUN
ejpam-4511	105	23	dominating	dominating	NOUN
ejpam-4511	105	24	sequence	sequence	NOUN
ejpam-4511	105	25	,	,	PUNCT
ejpam-4511	105	26	then	then	ADV
ejpam-4511	105	27	γh(g	γh(g	PUNCT
ejpam-4511	105	28	)	)	PUNCT
ejpam-4511	105	29	=	=	SYM
ejpam-4511	106	1	|ŝ|	|ŝ|	PROPN
ejpam-4511	106	2	.	.	PUNCT
ejpam-4511	106	3	j.	j.	PROPN
ejpam-4511	106	4	hassan	hassan	PROPN
ejpam-4511	106	5	,	,	PUNCT
ejpam-4511	106	6	s.	s.	PROPN
ejpam-4511	106	7	canoy	canoy	PROPN
ejpam-4511	106	8	/	/	SYM
ejpam-4511	106	9	eur	eur	PROPN
ejpam-4511	106	10	.	.	PUNCT
ejpam-4511	107	1	j.	j.	PROPN
ejpam-4511	107	2	pure	pure	PROPN
ejpam-4511	107	3	appl	appl	PROPN
ejpam-4511	107	4	.	.	PROPN
ejpam-4511	107	5	math	math	PROPN
ejpam-4511	107	6	,	,	PUNCT
ejpam-4511	107	7	15	15	NUM
ejpam-4511	107	8	(	(	PUNCT
ejpam-4511	107	9	4	4	NUM
ejpam-4511	107	10	)	)	PUNCT
ejpam-4511	107	11	(	(	PUNCT
ejpam-4511	107	12	2022	2022	NUM
ejpam-4511	107	13	)	)	PUNCT
ejpam-4511	107	14	,	,	PUNCT
ejpam-4511	107	15	1623	1623	NUM
ejpam-4511	107	16	-	-	SYM
ejpam-4511	107	17	1636	1636	NUM
ejpam-4511	107	18	1627	1627	NUM
ejpam-4511	107	19	proof	proof	NOUN
ejpam-4511	107	20	.	.	PUNCT
ejpam-4511	108	1	(	(	PUNCT
ejpam-4511	108	2	i	i	NOUN
ejpam-4511	108	3	)	)	PUNCT
ejpam-4511	108	4	suppose	suppose	VERB
ejpam-4511	108	5	there	there	PRON
ejpam-4511	108	6	exists	exist	VERB
ejpam-4511	108	7	i	i	PRON
ejpam-4511	108	8	∈	∈	PROPN
ejpam-4511	108	9	{	{	PUNCT
ejpam-4511	108	10	2	2	NUM
ejpam-4511	108	11	,	,	PUNCT
ejpam-4511	108	12	3	3	NUM
ejpam-4511	108	13	,	,	PUNCT
ejpam-4511	108	14	.	.	PUNCT
ejpam-4511	108	15	.	.	PUNCT
ejpam-4511	109	1	.	.	PUNCT
ejpam-4511	110	1	,	,	PUNCT
ejpam-4511	110	2	k	k	X
ejpam-4511	110	3	}	}	PUNCT
ejpam-4511	110	4	such	such	ADJ
ejpam-4511	110	5	that	that	PRON
ejpam-4511	110	6	n2	n2	ADJ
ejpam-4511	110	7	g[vi	g[vi	PROPN
ejpam-4511	110	8	]	]	PUNCT
ejpam-4511	110	9	\	\	NOUN
ejpam-4511	110	10	∪	∪	X
ejpam-4511	110	11	i−1	i−1	PROPN
ejpam-4511	110	12	j=1n	j=1n	PROPN
ejpam-4511	110	13	2	2	NUM
ejpam-4511	110	14	g[vj	g[vj	PROPN
ejpam-4511	110	15	]	]	PUNCT
ejpam-4511	110	16	=	=	PUNCT
ejpam-4511	110	17	∅.	∅.	X
ejpam-4511	110	18	then	then	ADV
ejpam-4511	110	19	n2	n2	PROPN
ejpam-4511	110	20	g[vi	g[vi	PROPN
ejpam-4511	110	21	]	]	X
ejpam-4511	110	22	⊆	⊆	NUM
ejpam-4511	110	23	∪i−1	∪i−1	PROPN
ejpam-4511	110	24	j=1n	j=1n	PROPN
ejpam-4511	110	25	2	2	NUM
ejpam-4511	110	26	g[vj	g[vj	PROPN
ejpam-4511	110	27	]	]	PUNCT
ejpam-4511	110	28	.	.	PUNCT
ejpam-4511	111	1	it	it	PRON
ejpam-4511	111	2	follows	follow	VERB
ejpam-4511	111	3	that	that	SCONJ
ejpam-4511	111	4	d	d	SCONJ
ejpam-4511	111	5	\	\	PROPN
ejpam-4511	111	6	{	{	PUNCT
ejpam-4511	111	7	vi	vi	NOUN
ejpam-4511	111	8	}	}	PUNCT
ejpam-4511	111	9	is	be	AUX
ejpam-4511	111	10	a	a	DET
ejpam-4511	111	11	hop	hop	NOUN
ejpam-4511	111	12	dominating	dominating	NOUN
ejpam-4511	111	13	set	set	NOUN
ejpam-4511	111	14	of	of	ADP
ejpam-4511	111	15	g	g	NOUN
ejpam-4511	111	16	,	,	PUNCT
ejpam-4511	111	17	contradicting	contradict	VERB
ejpam-4511	111	18	the	the	DET
ejpam-4511	111	19	minimality	minimality	NOUN
ejpam-4511	111	20	of	of	ADP
ejpam-4511	111	21	d.	d.	PROPN
ejpam-4511	111	22	therefore	therefore	ADV
ejpam-4511	111	23	,	,	PUNCT
ejpam-4511	111	24	n2	n2	ADJ
ejpam-4511	111	25	g[vi]\∪	g[vi]\∪	NOUN
ejpam-4511	111	26	i−1	i−1	PROPN
ejpam-4511	111	27	j=1n	j=1n	PROPN
ejpam-4511	111	28	2	2	NUM
ejpam-4511	111	29	g[vj	g[vj	PROPN
ejpam-4511	111	30	]	]	PUNCT
ejpam-4511	111	31	̸=	̸=	PROPN
ejpam-4511	111	32	∅	∅	NOUN
ejpam-4511	111	33	for	for	ADP
ejpam-4511	111	34	each	each	DET
ejpam-4511	111	35	i	i	PRON
ejpam-4511	111	36	∈	∈	PROPN
ejpam-4511	111	37	{	{	PUNCT
ejpam-4511	111	38	2	2	NUM
ejpam-4511	111	39	,	,	PUNCT
ejpam-4511	111	40	3	3	NUM
ejpam-4511	111	41	,	,	PUNCT
ejpam-4511	111	42	.	.	PUNCT
ejpam-4511	111	43	.	.	PUNCT
ejpam-4511	112	1	.	.	PUNCT
ejpam-4511	113	1	,	,	PUNCT
ejpam-4511	113	2	k	k	X
ejpam-4511	113	3	}	}	PUNCT
ejpam-4511	113	4	.	.	PUNCT
ejpam-4511	114	1	consequently	consequently	ADV
ejpam-4511	114	2	,	,	PUNCT
ejpam-4511	114	3	γh(g	γh(g	NOUN
ejpam-4511	114	4	)	)	PUNCT
ejpam-4511	114	5	≤	≤	NOUN
ejpam-4511	114	6	γhgr(g	γhgr(g	NOUN
ejpam-4511	114	7	)	)	PUNCT
ejpam-4511	114	8	.	.	PUNCT
ejpam-4511	115	1	(	(	PUNCT
ejpam-4511	115	2	ii	ii	NOUN
ejpam-4511	115	3	)	)	PUNCT
ejpam-4511	115	4	note	note	VERB
ejpam-4511	115	5	that	that	SCONJ
ejpam-4511	115	6	from	from	ADP
ejpam-4511	115	7	(	(	PUNCT
ejpam-4511	115	8	i	i	NOUN
ejpam-4511	115	9	)	)	PUNCT
ejpam-4511	115	10	,	,	PUNCT
ejpam-4511	115	11	every	every	DET
ejpam-4511	115	12	γh	γh	ADV
ejpam-4511	115	13	-	-	PUNCT
ejpam-4511	115	14	set	set	NOUN
ejpam-4511	115	15	of	of	ADP
ejpam-4511	115	16	g	g	PROPN
ejpam-4511	115	17	forms	form	VERB
ejpam-4511	115	18	a	a	DET
ejpam-4511	115	19	grundy	grundy	PROPN
ejpam-4511	115	20	hop	hop	NOUN
ejpam-4511	115	21	dominating	dominating	NOUN
ejpam-4511	115	22	sequence	sequence	NOUN
ejpam-4511	115	23	.	.	PUNCT
ejpam-4511	116	1	since	since	SCONJ
ejpam-4511	116	2	s	s	PROPN
ejpam-4511	116	3	is	be	AUX
ejpam-4511	116	4	a	a	DET
ejpam-4511	116	5	minimum	minimum	ADJ
ejpam-4511	116	6	grundy	grundy	PROPN
ejpam-4511	116	7	hop	hop	NOUN
ejpam-4511	116	8	dominating	dominating	NOUN
ejpam-4511	116	9	sequence	sequence	NOUN
ejpam-4511	116	10	,	,	PUNCT
ejpam-4511	116	11	it	it	PRON
ejpam-4511	116	12	follows	follow	VERB
ejpam-4511	116	13	that	that	SCONJ
ejpam-4511	116	14	|ŝ|	|ŝ|	PROPN
ejpam-4511	116	15	≤	≤	NUM
ejpam-4511	116	16	γh(g	γh(g	NOUN
ejpam-4511	116	17	)	)	PUNCT
ejpam-4511	116	18	.	.	PUNCT
ejpam-4511	117	1	on	on	ADP
ejpam-4511	117	2	the	the	DET
ejpam-4511	117	3	other	other	ADJ
ejpam-4511	117	4	hand	hand	NOUN
ejpam-4511	117	5	,	,	PUNCT
ejpam-4511	117	6	since	since	SCONJ
ejpam-4511	117	7	every	every	DET
ejpam-4511	117	8	grundy	grundy	PROPN
ejpam-4511	117	9	hop	hop	NOUN
ejpam-4511	117	10	dominating	dominating	NOUN
ejpam-4511	117	11	sequence	sequence	NOUN
ejpam-4511	117	12	forms	form	VERB
ejpam-4511	117	13	a	a	DET
ejpam-4511	117	14	hop	hop	NOUN
ejpam-4511	117	15	dominating	dominating	NOUN
ejpam-4511	117	16	set	set	NOUN
ejpam-4511	117	17	(	(	PUNCT
ejpam-4511	117	18	by	by	ADP
ejpam-4511	117	19	definition	definition	NOUN
ejpam-4511	117	20	)	)	PUNCT
ejpam-4511	117	21	,	,	PUNCT
ejpam-4511	117	22	it	it	PRON
ejpam-4511	117	23	follows	follow	VERB
ejpam-4511	117	24	that	that	SCONJ
ejpam-4511	117	25	γh(g	γh(g	NOUN
ejpam-4511	117	26	)	)	PUNCT
ejpam-4511	117	27	≤	≤	NOUN
ejpam-4511	118	1	|ŝ|	|ŝ|	NUM
ejpam-4511	118	2	.	.	PUNCT
ejpam-4511	119	1	this	this	PRON
ejpam-4511	119	2	establishes	establish	VERB
ejpam-4511	119	3	the	the	DET
ejpam-4511	119	4	desired	desire	VERB
ejpam-4511	119	5	equality	equality	NOUN
ejpam-4511	119	6	.	.	PUNCT
ejpam-4511	120	1	theorem	theorem	NOUN
ejpam-4511	120	2	2	2	NUM
ejpam-4511	120	3	.	.	PUNCT
ejpam-4511	121	1	let	let	VERB
ejpam-4511	121	2	g	g	NOUN
ejpam-4511	121	3	be	be	AUX
ejpam-4511	121	4	any	any	DET
ejpam-4511	121	5	graph	graph	NOUN
ejpam-4511	121	6	.	.	PUNCT
ejpam-4511	122	1	then	then	ADV
ejpam-4511	122	2	s	s	VERB
ejpam-4511	122	3	=	=	PUNCT
ejpam-4511	122	4	(	(	PUNCT
ejpam-4511	122	5	v1	v1	PROPN
ejpam-4511	122	6	,	,	PUNCT
ejpam-4511	122	7	v2	v2	PROPN
ejpam-4511	122	8	,	,	PUNCT
ejpam-4511	122	9	·	·	PUNCT
ejpam-4511	122	10	·	·	PUNCT
ejpam-4511	122	11	·	·	PUNCT
ejpam-4511	122	12	,	,	PUNCT
ejpam-4511	122	13	vk	vk	PROPN
ejpam-4511	122	14	)	)	PUNCT
ejpam-4511	122	15	is	be	AUX
ejpam-4511	122	16	a	a	DET
ejpam-4511	122	17	maximum	maximum	ADJ
ejpam-4511	122	18	legal	legal	ADJ
ejpam-4511	122	19	closed	closed	ADJ
ejpam-4511	122	20	hop	hop	NOUN
ejpam-4511	122	21	neighborhood	neighborhood	NOUN
ejpam-4511	122	22	sequence	sequence	NOUN
ejpam-4511	122	23	of	of	ADP
ejpam-4511	122	24	g	g	PROPN
ejpam-4511	122	25	if	if	SCONJ
ejpam-4511	122	26	and	and	CCONJ
ejpam-4511	122	27	only	only	ADV
ejpam-4511	122	28	if	if	SCONJ
ejpam-4511	122	29	s	s	NOUN
ejpam-4511	122	30	is	be	AUX
ejpam-4511	122	31	a	a	DET
ejpam-4511	122	32	grundy	grundy	PROPN
ejpam-4511	122	33	hop	hop	NOUN
ejpam-4511	122	34	dominating	dominating	NOUN
ejpam-4511	122	35	sequence	sequence	NOUN
ejpam-4511	122	36	of	of	ADP
ejpam-4511	122	37	g	g	PROPN
ejpam-4511	122	38	and	and	CCONJ
ejpam-4511	122	39	γhgr(g	γhgr(g	NUM
ejpam-4511	122	40	)	)	PUNCT
ejpam-4511	122	41	=	=	PUNCT
ejpam-4511	123	1	k.	k.	NOUN
ejpam-4511	123	2	proof	proof	NOUN
ejpam-4511	123	3	.	.	PUNCT
ejpam-4511	124	1	let	let	VERB
ejpam-4511	124	2	s	s	AUX
ejpam-4511	124	3	=	=	PUNCT
ejpam-4511	124	4	(	(	PUNCT
ejpam-4511	124	5	v1	v1	PROPN
ejpam-4511	124	6	,	,	PUNCT
ejpam-4511	124	7	·	·	PUNCT
ejpam-4511	124	8	·	·	PUNCT
ejpam-4511	124	9	·	·	PUNCT
ejpam-4511	124	10	,	,	PUNCT
ejpam-4511	124	11	vk	vk	AUX
ejpam-4511	124	12	)	)	PUNCT
ejpam-4511	124	13	be	be	AUX
ejpam-4511	124	14	a	a	DET
ejpam-4511	124	15	maximum	maximum	ADJ
ejpam-4511	124	16	legal	legal	ADJ
ejpam-4511	124	17	closed	closed	ADJ
ejpam-4511	124	18	hop	hop	NOUN
ejpam-4511	124	19	neighborhood	neighborhood	NOUN
ejpam-4511	124	20	sequence	sequence	NOUN
ejpam-4511	124	21	of	of	ADP
ejpam-4511	124	22	g.	g.	PROPN
ejpam-4511	124	23	suppose	suppose	VERB
ejpam-4511	124	24	ŝ	ŝ	PROPN
ejpam-4511	124	25	is	be	AUX
ejpam-4511	124	26	not	not	PART
ejpam-4511	124	27	a	a	DET
ejpam-4511	124	28	hop	hop	NOUN
ejpam-4511	124	29	dominating	dominating	NOUN
ejpam-4511	124	30	set	set	NOUN
ejpam-4511	124	31	of	of	ADP
ejpam-4511	124	32	g.	g.	PROPN
ejpam-4511	124	33	then	then	ADV
ejpam-4511	124	34	there	there	PRON
ejpam-4511	124	35	exists	exist	VERB
ejpam-4511	124	36	v	v	ADP
ejpam-4511	124	37	∈	∈	PROPN
ejpam-4511	124	38	v	v	NOUN
ejpam-4511	124	39	(	(	PUNCT
ejpam-4511	124	40	g)\n2	g)\n2	PROPN
ejpam-4511	124	41	g[ŝ	g[ŝ	PROPN
ejpam-4511	124	42	]	]	PUNCT
ejpam-4511	124	43	.	.	PUNCT
ejpam-4511	125	1	this	this	PRON
ejpam-4511	125	2	implies	imply	VERB
ejpam-4511	125	3	that	that	SCONJ
ejpam-4511	125	4	v	v	X
ejpam-4511	125	5	/∈	/∈	PUNCT
ejpam-4511	125	6	n2	n2	PROPN
ejpam-4511	125	7	g[u	g[u	PROPN
ejpam-4511	125	8	]	]	PUNCT
ejpam-4511	125	9	for	for	ADP
ejpam-4511	125	10	every	every	DET
ejpam-4511	125	11	u	u	PROPN
ejpam-4511	125	12	∈	∈	PROPN
ejpam-4511	125	13	ŝ.	ŝ.	NOUN
ejpam-4511	125	14	let	let	VERB
ejpam-4511	125	15	s′	s′	ADJ
ejpam-4511	125	16	=	=	SYM
ejpam-4511	125	17	(	(	PUNCT
ejpam-4511	125	18	v1	v1	PROPN
ejpam-4511	125	19	,	,	PUNCT
ejpam-4511	125	20	·	·	PUNCT
ejpam-4511	125	21	·	·	PUNCT
ejpam-4511	125	22	·	·	PUNCT
ejpam-4511	125	23	,	,	PUNCT
ejpam-4511	125	24	vk	vk	X
ejpam-4511	125	25	,	,	PUNCT
ejpam-4511	125	26	v	v	NOUN
ejpam-4511	125	27	)	)	PUNCT
ejpam-4511	125	28	.	.	PUNCT
ejpam-4511	126	1	since	since	SCONJ
ejpam-4511	126	2	s	s	PROPN
ejpam-4511	126	3	is	be	AUX
ejpam-4511	126	4	a	a	DET
ejpam-4511	126	5	legal	legal	ADJ
ejpam-4511	126	6	closed	close	VERB
ejpam-4511	126	7	hop	hop	NOUN
ejpam-4511	126	8	neighborhood	neighborhood	NOUN
ejpam-4511	126	9	sequence	sequence	NOUN
ejpam-4511	126	10	,	,	PUNCT
ejpam-4511	126	11	n2	n2	PROPN
ejpam-4511	126	12	g[vi	g[vi	PROPN
ejpam-4511	126	13	]	]	PUNCT
ejpam-4511	126	14	\	\	X
ejpam-4511	127	1	∪i−1	∪i−1	PUNCT
ejpam-4511	127	2	j=1n	j=1n	PROPN
ejpam-4511	127	3	2	2	NUM
ejpam-4511	127	4	g[vj	g[vj	PROPN
ejpam-4511	127	5	]	]	PUNCT
ejpam-4511	127	6	̸=	̸=	PROPN
ejpam-4511	127	7	∅	∅	NOUN
ejpam-4511	127	8	for	for	ADP
ejpam-4511	127	9	each	each	DET
ejpam-4511	127	10	i	i	PRON
ejpam-4511	127	11	∈	∈	PROPN
ejpam-4511	127	12	{	{	PUNCT
ejpam-4511	127	13	2	2	NUM
ejpam-4511	127	14	,	,	PUNCT
ejpam-4511	127	15	3	3	NUM
ejpam-4511	127	16	,	,	PUNCT
ejpam-4511	127	17	.	.	PUNCT
ejpam-4511	127	18	.	.	PUNCT
ejpam-4511	127	19	.	.	PUNCT
ejpam-4511	128	1	,	,	PUNCT
ejpam-4511	128	2	k	k	X
ejpam-4511	128	3	}	}	PUNCT
ejpam-4511	128	4	.	.	PUNCT
ejpam-4511	129	1	also	also	ADV
ejpam-4511	129	2	,	,	PUNCT
ejpam-4511	129	3	since	since	SCONJ
ejpam-4511	129	4	v	v	NUM
ejpam-4511	129	5	∈	∈	PROPN
ejpam-4511	129	6	n2	n2	ADJ
ejpam-4511	129	7	g[v	g[v	PROPN
ejpam-4511	129	8	]	]	PUNCT
ejpam-4511	129	9	and	and	CCONJ
ejpam-4511	129	10	v	v	NOUN
ejpam-4511	129	11	/∈	/∈	PROPN
ejpam-4511	129	12	n2	n2	PROPN
ejpam-4511	129	13	g[u	g[u	PROPN
ejpam-4511	129	14	]	]	PUNCT
ejpam-4511	129	15	for	for	ADP
ejpam-4511	129	16	every	every	DET
ejpam-4511	129	17	u	u	PROPN
ejpam-4511	129	18	∈	∈	PROPN
ejpam-4511	129	19	ŝ	ŝ	NOUN
ejpam-4511	129	20	,	,	PUNCT
ejpam-4511	129	21	it	it	PRON
ejpam-4511	129	22	follows	follow	VERB
ejpam-4511	129	23	that	that	DET
ejpam-4511	129	24	n2	n2	ADJ
ejpam-4511	129	25	g[v	g[v	PROPN
ejpam-4511	129	26	]	]	PUNCT
ejpam-4511	129	27	\	\	PROPN
ejpam-4511	130	1	∪k	∪k	PROPN
ejpam-4511	130	2	j=1n	j=1n	PROPN
ejpam-4511	130	3	2	2	NUM
ejpam-4511	130	4	g[vi	g[vi	PROPN
ejpam-4511	130	5	]	]	X
ejpam-4511	130	6	̸=	̸=	PROPN
ejpam-4511	130	7	∅.	∅.	PRON
ejpam-4511	130	8	hence	hence	ADV
ejpam-4511	130	9	,	,	PUNCT
ejpam-4511	130	10	s′	s′	PROPN
ejpam-4511	130	11	is	be	AUX
ejpam-4511	130	12	a	a	DET
ejpam-4511	130	13	legal	legal	ADJ
ejpam-4511	130	14	closed	close	VERB
ejpam-4511	130	15	hop	hop	NOUN
ejpam-4511	130	16	neighborhood	neighborhood	NOUN
ejpam-4511	130	17	sequence	sequence	NOUN
ejpam-4511	130	18	of	of	ADP
ejpam-4511	130	19	g	g	NOUN
ejpam-4511	130	20	,	,	PUNCT
ejpam-4511	130	21	contradicting	contradict	VERB
ejpam-4511	130	22	the	the	DET
ejpam-4511	130	23	maximality	maximality	NOUN
ejpam-4511	130	24	of	of	ADP
ejpam-4511	130	25	s.	s.	PROPN
ejpam-4511	130	26	therefore	therefore	ADV
ejpam-4511	130	27	,	,	PUNCT
ejpam-4511	130	28	ŝ	ŝ	X
ejpam-4511	130	29	is	be	AUX
ejpam-4511	130	30	a	a	DET
ejpam-4511	130	31	hop	hop	NOUN
ejpam-4511	130	32	dominating	dominating	NOUN
ejpam-4511	130	33	set	set	NOUN
ejpam-4511	130	34	of	of	ADP
ejpam-4511	130	35	g.	g.	PROPN
ejpam-4511	130	36	since	since	SCONJ
ejpam-4511	130	37	s	s	PROPN
ejpam-4511	130	38	is	be	AUX
ejpam-4511	130	39	a	a	DET
ejpam-4511	130	40	maximum	maximum	ADJ
ejpam-4511	130	41	legal	legal	ADJ
ejpam-4511	130	42	closed	closed	ADJ
ejpam-4511	130	43	hop	hop	NOUN
ejpam-4511	130	44	neighborhood	neighborhood	NOUN
ejpam-4511	130	45	sequence	sequence	NOUN
ejpam-4511	130	46	of	of	ADP
ejpam-4511	130	47	g	g	NOUN
ejpam-4511	130	48	,	,	PUNCT
ejpam-4511	130	49	it	it	PRON
ejpam-4511	130	50	is	be	AUX
ejpam-4511	130	51	a	a	DET
ejpam-4511	130	52	grundy	grundy	PROPN
ejpam-4511	130	53	hop	hop	NOUN
ejpam-4511	130	54	dominating	dominating	NOUN
ejpam-4511	130	55	sequence	sequence	NOUN
ejpam-4511	130	56	and	and	CCONJ
ejpam-4511	130	57	γhgr(g	γhgr(g	NOUN
ejpam-4511	130	58	)	)	PUNCT
ejpam-4511	130	59	=	=	VERB
ejpam-4511	130	60	k.	k.	PROPN
ejpam-4511	130	61	for	for	ADP
ejpam-4511	130	62	the	the	DET
ejpam-4511	130	63	converse	converse	NOUN
ejpam-4511	130	64	,	,	PUNCT
ejpam-4511	130	65	suppose	suppose	VERB
ejpam-4511	130	66	that	that	SCONJ
ejpam-4511	130	67	s	s	VERB
ejpam-4511	130	68	is	be	AUX
ejpam-4511	130	69	a	a	DET
ejpam-4511	130	70	grundy	grundy	PROPN
ejpam-4511	130	71	hop	hop	NOUN
ejpam-4511	130	72	dominating	dominating	NOUN
ejpam-4511	130	73	sequence	sequence	NOUN
ejpam-4511	130	74	and	and	CCONJ
ejpam-4511	130	75	γhgr(g	γhgr(g	NOUN
ejpam-4511	130	76	)	)	PUNCT
ejpam-4511	131	1	=	=	VERB
ejpam-4511	131	2	k.	k.	PROPN
ejpam-4511	132	1	then	then	ADV
ejpam-4511	132	2	s	s	VERB
ejpam-4511	132	3	is	be	AUX
ejpam-4511	132	4	a	a	DET
ejpam-4511	132	5	maximum	maximum	ADJ
ejpam-4511	132	6	legal	legal	ADJ
ejpam-4511	132	7	closed	closed	ADJ
ejpam-4511	132	8	hop	hop	NOUN
ejpam-4511	132	9	neighborhood	neighborhood	NOUN
ejpam-4511	132	10	sequence	sequence	NOUN
ejpam-4511	132	11	of	of	ADP
ejpam-4511	132	12	g.	g.	PROPN
ejpam-4511	132	13	corollary	corollary	NOUN
ejpam-4511	132	14	1	1	PROPN
ejpam-4511	132	15	.	.	PUNCT
ejpam-4511	133	1	let	let	VERB
ejpam-4511	133	2	g	g	PRON
ejpam-4511	133	3	be	be	AUX
ejpam-4511	133	4	a	a	DET
ejpam-4511	133	5	graph	graph	NOUN
ejpam-4511	133	6	and	and	CCONJ
ejpam-4511	133	7	let	let	VERB
ejpam-4511	133	8	d	d	NOUN
ejpam-4511	133	9	=	=	SYM
ejpam-4511	133	10	(	(	PUNCT
ejpam-4511	133	11	x1	x1	PROPN
ejpam-4511	133	12	,	,	PUNCT
ejpam-4511	133	13	·	·	PUNCT
ejpam-4511	133	14	·	·	PUNCT
ejpam-4511	133	15	·	·	PUNCT
ejpam-4511	133	16	,	,	PUNCT
ejpam-4511	133	17	xt	xt	AUX
ejpam-4511	133	18	)	)	PUNCT
ejpam-4511	133	19	be	be	AUX
ejpam-4511	133	20	a	a	DET
ejpam-4511	133	21	legal	legal	ADJ
ejpam-4511	133	22	closed	close	VERB
ejpam-4511	133	23	hop	hop	NOUN
ejpam-4511	133	24	neighborhood	neighborhood	NOUN
ejpam-4511	133	25	sequence	sequence	NOUN
ejpam-4511	133	26	of	of	ADP
ejpam-4511	133	27	g.	g.	PROPN
ejpam-4511	133	28	then	then	ADV
ejpam-4511	133	29	|d̂|	|d̂|	PROPN
ejpam-4511	134	1	=	=	SYM
ejpam-4511	134	2	t	t	PROPN
ejpam-4511	134	3	≤	≤	NOUN
ejpam-4511	134	4	γhgr(g	γhgr(g	PROPN
ejpam-4511	134	5	)	)	PUNCT
ejpam-4511	134	6	.	.	PUNCT
ejpam-4511	135	1	proof	proof	NOUN
ejpam-4511	135	2	.	.	PUNCT
ejpam-4511	136	1	let	let	VERB
ejpam-4511	136	2	k	k	PRON
ejpam-4511	136	3	be	be	AUX
ejpam-4511	136	4	the	the	DET
ejpam-4511	136	5	length	length	NOUN
ejpam-4511	136	6	of	of	ADP
ejpam-4511	136	7	a	a	DET
ejpam-4511	136	8	maximum	maximum	ADJ
ejpam-4511	136	9	legal	legal	ADJ
ejpam-4511	136	10	closed	closed	ADJ
ejpam-4511	136	11	hop	hop	NOUN
ejpam-4511	136	12	neighborhood	neighborhood	NOUN
ejpam-4511	136	13	sequence	sequence	NOUN
ejpam-4511	136	14	of	of	ADP
ejpam-4511	136	15	g.	g.	PROPN
ejpam-4511	136	16	then	then	ADV
ejpam-4511	136	17	t	t	X
ejpam-4511	136	18	≤	≤	PROPN
ejpam-4511	136	19	k.	k.	PROPN
ejpam-4511	136	20	by	by	ADP
ejpam-4511	136	21	theorem	theorem	NOUN
ejpam-4511	136	22	2	2	NUM
ejpam-4511	136	23	,	,	PUNCT
ejpam-4511	136	24	|d̂|	|d̂|	PROPN
ejpam-4511	136	25	=	=	SYM
ejpam-4511	136	26	t	t	PROPN
ejpam-4511	136	27	≤	≤	NOUN
ejpam-4511	136	28	γhgr(g	γhgr(g	PROPN
ejpam-4511	136	29	)	)	PUNCT
ejpam-4511	136	30	.	.	PUNCT
ejpam-4511	137	1	throughout	throughout	ADP
ejpam-4511	137	2	,	,	PUNCT
ejpam-4511	137	3	[	[	X
ejpam-4511	137	4	n	n	X
ejpam-4511	137	5	]	]	X
ejpam-4511	137	6	=	=	PUNCT
ejpam-4511	137	7	{	{	PUNCT
ejpam-4511	137	8	1	1	NUM
ejpam-4511	137	9	,	,	PUNCT
ejpam-4511	137	10	2	2	NUM
ejpam-4511	137	11	,	,	PUNCT
ejpam-4511	137	12	.	.	PUNCT
ejpam-4511	137	13	.	.	PUNCT
ejpam-4511	138	1	.	.	PUNCT
ejpam-4511	139	1	,	,	PUNCT
ejpam-4511	139	2	n	n	CCONJ
ejpam-4511	139	3	}	}	PUNCT
ejpam-4511	139	4	for	for	SCONJ
ejpam-4511	139	5	each	each	DET
ejpam-4511	139	6	positive	positive	ADJ
ejpam-4511	139	7	integer	integer	NOUN
ejpam-4511	139	8	n.	n.	NOUN
ejpam-4511	139	9	theorem	theorem	VERB
ejpam-4511	139	10	3	3	X
ejpam-4511	139	11	.	.	PUNCT
ejpam-4511	140	1	let	let	VERB
ejpam-4511	140	2	g	g	NOUN
ejpam-4511	140	3	be	be	AUX
ejpam-4511	140	4	any	any	DET
ejpam-4511	140	5	graph	graph	NOUN
ejpam-4511	140	6	on	on	ADP
ejpam-4511	140	7	n	n	PRON
ejpam-4511	140	8	≥	≥	NUM
ejpam-4511	140	9	2	2	NUM
ejpam-4511	140	10	vertices	vertex	NOUN
ejpam-4511	140	11	.	.	PUNCT
ejpam-4511	141	1	then	then	ADV
ejpam-4511	141	2	2	2	NUM
ejpam-4511	141	3	≤	≤	NOUN
ejpam-4511	141	4	γhgr(g	γhgr(g	PROPN
ejpam-4511	141	5	)	)	PUNCT
ejpam-4511	141	6	≤	≤	NOUN
ejpam-4511	141	7	n.	n.	NOUN
ejpam-4511	141	8	moreover	moreover	ADV
ejpam-4511	141	9	,	,	PUNCT
ejpam-4511	141	10	each	each	PRON
ejpam-4511	141	11	of	of	ADP
ejpam-4511	141	12	the	the	DET
ejpam-4511	141	13	following	following	ADJ
ejpam-4511	141	14	statements	statement	NOUN
ejpam-4511	141	15	holds	hold	VERB
ejpam-4511	141	16	.	.	PUNCT
ejpam-4511	142	1	(	(	PUNCT
ejpam-4511	142	2	i	i	NOUN
ejpam-4511	142	3	)	)	PUNCT
ejpam-4511	142	4	γhgr(g	γhgr(g	X
ejpam-4511	142	5	)	)	PUNCT
ejpam-4511	142	6	=	=	SYM
ejpam-4511	142	7	2	2	NUM
ejpam-4511	143	1	if	if	SCONJ
ejpam-4511	143	2	and	and	CCONJ
ejpam-4511	143	3	only	only	ADV
ejpam-4511	143	4	if	if	SCONJ
ejpam-4511	143	5	for	for	ADP
ejpam-4511	143	6	each	each	DET
ejpam-4511	143	7	pair	pair	NOUN
ejpam-4511	143	8	of	of	ADP
ejpam-4511	143	9	distinct	distinct	ADJ
ejpam-4511	143	10	vertices	vertex	NOUN
ejpam-4511	143	11	x	x	X
ejpam-4511	143	12	,	,	PUNCT
ejpam-4511	143	13	y	y	PROPN
ejpam-4511	143	14	∈	∈	PROPN
ejpam-4511	143	15	v	v	ADP
ejpam-4511	143	16	(	(	PUNCT
ejpam-4511	143	17	g	g	NOUN
ejpam-4511	143	18	)	)	PUNCT
ejpam-4511	143	19	such	such	ADJ
ejpam-4511	143	20	that	that	DET
ejpam-4511	143	21	n2	n2	PROPN
ejpam-4511	143	22	g[x	g[x	PROPN
ejpam-4511	143	23	]	]	X
ejpam-4511	143	24	̸=	̸=	PROPN
ejpam-4511	143	25	n2	n2	PROPN
ejpam-4511	143	26	g[y	g[y	PROPN
ejpam-4511	143	27	]	]	PUNCT
ejpam-4511	143	28	,	,	PUNCT
ejpam-4511	143	29	we	we	PRON
ejpam-4511	143	30	have	have	VERB
ejpam-4511	143	31	v	v	NUM
ejpam-4511	143	32	(	(	PUNCT
ejpam-4511	143	33	g	g	NOUN
ejpam-4511	143	34	)	)	PUNCT
ejpam-4511	143	35	=	=	SYM
ejpam-4511	143	36	n2	n2	PROPN
ejpam-4511	143	37	g[x]∪n2	g[x]∪n2	PROPN
ejpam-4511	143	38	g[y	g[y	PROPN
ejpam-4511	143	39	]	]	X
ejpam-4511	143	40	(	(	PUNCT
ejpam-4511	143	41	i.e.	i.e.	X
ejpam-4511	143	42	,	,	PUNCT
ejpam-4511	143	43	{	{	PUNCT
ejpam-4511	143	44	x	x	NOUN
ejpam-4511	143	45	,	,	PUNCT
ejpam-4511	143	46	y	y	PRON
ejpam-4511	143	47	}	}	PUNCT
ejpam-4511	143	48	is	be	AUX
ejpam-4511	143	49	a	a	DET
ejpam-4511	143	50	hop	hop	NOUN
ejpam-4511	143	51	dominating	dominating	NOUN
ejpam-4511	143	52	set	set	NOUN
ejpam-4511	143	53	of	of	ADP
ejpam-4511	143	54	g	g	NOUN
ejpam-4511	143	55	)	)	PUNCT
ejpam-4511	143	56	.	.	PUNCT
ejpam-4511	144	1	(	(	PUNCT
ejpam-4511	144	2	ii	ii	X
ejpam-4511	144	3	)	)	PUNCT
ejpam-4511	144	4	γhgr(g	γhgr(g	NOUN
ejpam-4511	144	5	)	)	PUNCT
ejpam-4511	144	6	=	=	SYM
ejpam-4511	145	1	n	n	NOUN
ejpam-4511	145	2	if	if	SCONJ
ejpam-4511	145	3	and	and	CCONJ
ejpam-4511	145	4	only	only	ADV
ejpam-4511	145	5	if	if	SCONJ
ejpam-4511	145	6	every	every	DET
ejpam-4511	145	7	component	component	NOUN
ejpam-4511	145	8	c	c	NOUN
ejpam-4511	145	9	of	of	ADP
ejpam-4511	145	10	g	g	PROPN
ejpam-4511	145	11	is	be	AUX
ejpam-4511	145	12	complete	complete	ADJ
ejpam-4511	145	13	.	.	PUNCT
ejpam-4511	146	1	proof	proof	NOUN
ejpam-4511	146	2	.	.	PUNCT
ejpam-4511	147	1	clearly	clearly	ADV
ejpam-4511	147	2	,	,	PUNCT
ejpam-4511	147	3	2	2	NUM
ejpam-4511	147	4	≤	≤	NUM
ejpam-4511	147	5	γhgr(g	γhgr(g	NUM
ejpam-4511	147	6	)	)	PUNCT
ejpam-4511	147	7	≤	≤	PROPN
ejpam-4511	147	8	n.	n.	PROPN
ejpam-4511	147	9	j.	j.	PROPN
ejpam-4511	147	10	hassan	hassan	PROPN
ejpam-4511	147	11	,	,	PUNCT
ejpam-4511	147	12	s.	s.	PROPN
ejpam-4511	147	13	canoy	canoy	PROPN
ejpam-4511	147	14	/	/	SYM
ejpam-4511	147	15	eur	eur	PROPN
ejpam-4511	147	16	.	.	PUNCT
ejpam-4511	148	1	j.	j.	PROPN
ejpam-4511	148	2	pure	pure	PROPN
ejpam-4511	148	3	appl	appl	PROPN
ejpam-4511	148	4	.	.	PROPN
ejpam-4511	148	5	math	math	PROPN
ejpam-4511	148	6	,	,	PUNCT
ejpam-4511	148	7	15	15	NUM
ejpam-4511	148	8	(	(	PUNCT
ejpam-4511	148	9	4	4	NUM
ejpam-4511	148	10	)	)	PUNCT
ejpam-4511	148	11	(	(	PUNCT
ejpam-4511	148	12	2022	2022	NUM
ejpam-4511	148	13	)	)	PUNCT
ejpam-4511	148	14	,	,	PUNCT
ejpam-4511	148	15	1623	1623	NUM
ejpam-4511	148	16	-	-	SYM
ejpam-4511	148	17	1636	1636	NUM
ejpam-4511	148	18	1628	1628	NUM
ejpam-4511	148	19	(	(	PUNCT
ejpam-4511	148	20	i	i	NOUN
ejpam-4511	148	21	)	)	PUNCT
ejpam-4511	148	22	suppose	suppose	VERB
ejpam-4511	148	23	γhgr(g	γhgr(g	NUM
ejpam-4511	148	24	)	)	PUNCT
ejpam-4511	148	25	=	=	SYM
ejpam-4511	148	26	2	2	X
ejpam-4511	148	27	.	.	PUNCT
ejpam-4511	148	28	then	then	ADV
ejpam-4511	148	29	by	by	ADP
ejpam-4511	148	30	theorem	theorem	NOUN
ejpam-4511	148	31	2	2	NUM
ejpam-4511	148	32	,	,	PUNCT
ejpam-4511	148	33	the	the	DET
ejpam-4511	148	34	maximum	maximum	ADJ
ejpam-4511	148	35	length	length	NOUN
ejpam-4511	148	36	of	of	ADP
ejpam-4511	148	37	a	a	DET
ejpam-4511	148	38	legal	legal	ADJ
ejpam-4511	148	39	closed	closed	ADJ
ejpam-4511	148	40	hop	hop	NOUN
ejpam-4511	148	41	neighborhood	neighborhood	NOUN
ejpam-4511	148	42	sequence	sequence	NOUN
ejpam-4511	148	43	of	of	ADP
ejpam-4511	148	44	g	g	PROPN
ejpam-4511	148	45	is	be	AUX
ejpam-4511	148	46	2	2	NUM
ejpam-4511	148	47	.	.	PUNCT
ejpam-4511	149	1	let	let	VERB
ejpam-4511	149	2	x	x	PRON
ejpam-4511	149	3	and	and	CCONJ
ejpam-4511	149	4	y	y	PROPN
ejpam-4511	149	5	be	be	AUX
ejpam-4511	149	6	distinct	distinct	ADJ
ejpam-4511	149	7	vertices	vertex	NOUN
ejpam-4511	149	8	of	of	ADP
ejpam-4511	149	9	g	g	PROPN
ejpam-4511	149	10	such	such	ADJ
ejpam-4511	149	11	that	that	DET
ejpam-4511	149	12	n2	n2	PROPN
ejpam-4511	149	13	g[x	g[x	PROPN
ejpam-4511	149	14	]	]	X
ejpam-4511	149	15	̸=	̸=	PROPN
ejpam-4511	149	16	n2	n2	PROPN
ejpam-4511	149	17	g[y	g[y	NOUN
ejpam-4511	149	18	]	]	PUNCT
ejpam-4511	149	19	.	.	PUNCT
ejpam-4511	150	1	we	we	PRON
ejpam-4511	150	2	may	may	AUX
ejpam-4511	150	3	assume	assume	VERB
ejpam-4511	150	4	that	that	SCONJ
ejpam-4511	150	5	n2	n2	ADJ
ejpam-4511	150	6	g[y	g[y	NOUN
ejpam-4511	150	7	]	]	PUNCT
ejpam-4511	150	8	\	\	PROPN
ejpam-4511	150	9	n2	n2	PROPN
ejpam-4511	150	10	g[x	g[x	PROPN
ejpam-4511	150	11	]	]	X
ejpam-4511	150	12	̸=	̸=	PROPN
ejpam-4511	150	13	∅.	∅.	NOUN
ejpam-4511	150	14	then	then	ADV
ejpam-4511	150	15	(	(	PUNCT
ejpam-4511	150	16	x	x	X
ejpam-4511	150	17	,	,	PUNCT
ejpam-4511	150	18	y	y	NOUN
ejpam-4511	150	19	)	)	PUNCT
ejpam-4511	150	20	is	be	AUX
ejpam-4511	150	21	a	a	DET
ejpam-4511	150	22	legal	legal	ADJ
ejpam-4511	150	23	closed	close	VERB
ejpam-4511	150	24	hop	hop	NOUN
ejpam-4511	150	25	neighborhood	neighborhood	NOUN
ejpam-4511	150	26	sequence	sequence	NOUN
ejpam-4511	150	27	of	of	ADP
ejpam-4511	150	28	g.	g.	PROPN
ejpam-4511	150	29	suppose	suppose	VERB
ejpam-4511	150	30	there	there	PRON
ejpam-4511	150	31	exists	exist	VERB
ejpam-4511	150	32	z	z	PROPN
ejpam-4511	150	33	∈	∈	PROPN
ejpam-4511	150	34	v	v	ADP
ejpam-4511	150	35	(	(	PUNCT
ejpam-4511	150	36	g	g	NOUN
ejpam-4511	150	37	)	)	PUNCT
ejpam-4511	150	38	\	\	PUNCT
ejpam-4511	151	1	(	(	PUNCT
ejpam-4511	151	2	n2	n2	PROPN
ejpam-4511	151	3	g[x]∪n2	g[x]∪n2	PROPN
ejpam-4511	151	4	g[y	g[y	PROPN
ejpam-4511	151	5	]	]	PUNCT
ejpam-4511	151	6	)	)	PUNCT
ejpam-4511	151	7	.	.	PUNCT
ejpam-4511	152	1	since	since	SCONJ
ejpam-4511	152	2	z	z	PROPN
ejpam-4511	152	3	∈	∈	PROPN
ejpam-4511	152	4	n2	n2	PROPN
ejpam-4511	152	5	g[z	g[z	PROPN
ejpam-4511	152	6	]	]	PUNCT
ejpam-4511	152	7	,	,	PUNCT
ejpam-4511	152	8	it	it	PRON
ejpam-4511	152	9	follows	follow	VERB
ejpam-4511	152	10	that	that	DET
ejpam-4511	152	11	n2	n2	PROPN
ejpam-4511	152	12	g[z	g[z	PROPN
ejpam-4511	152	13	]	]	PUNCT
ejpam-4511	152	14	\	\	PUNCT
ejpam-4511	153	1	(	(	PUNCT
ejpam-4511	153	2	n2	n2	PROPN
ejpam-4511	153	3	g[x	g[x	PROPN
ejpam-4511	153	4	]	]	PUNCT
ejpam-4511	153	5	∪	∪	ADP
ejpam-4511	153	6	n2	n2	ADJ
ejpam-4511	153	7	g[y	g[y	NOUN
ejpam-4511	153	8	]	]	PUNCT
ejpam-4511	153	9	)	)	PUNCT
ejpam-4511	153	10	̸=	̸=	PROPN
ejpam-4511	153	11	∅.	∅.	ADP
ejpam-4511	153	12	this	this	PRON
ejpam-4511	153	13	implies	imply	VERB
ejpam-4511	153	14	that	that	SCONJ
ejpam-4511	153	15	(	(	PUNCT
ejpam-4511	153	16	x	x	X
ejpam-4511	153	17	,	,	PUNCT
ejpam-4511	153	18	y	y	PROPN
ejpam-4511	153	19	,	,	PUNCT
ejpam-4511	153	20	z	z	NOUN
ejpam-4511	153	21	)	)	PUNCT
ejpam-4511	153	22	is	be	AUX
ejpam-4511	153	23	a	a	DET
ejpam-4511	153	24	legal	legal	ADJ
ejpam-4511	153	25	closed	close	VERB
ejpam-4511	153	26	hop	hop	NOUN
ejpam-4511	153	27	neighborhood	neighborhood	NOUN
ejpam-4511	153	28	sequence	sequence	NOUN
ejpam-4511	153	29	of	of	ADP
ejpam-4511	153	30	g	g	NOUN
ejpam-4511	153	31	,	,	PUNCT
ejpam-4511	153	32	contrary	contrary	ADV
ejpam-4511	153	33	to	to	ADP
ejpam-4511	153	34	the	the	DET
ejpam-4511	153	35	assumption	assumption	NOUN
ejpam-4511	153	36	that	that	SCONJ
ejpam-4511	153	37	γhgr(g	γhgr(g	X
ejpam-4511	153	38	)	)	PUNCT
ejpam-4511	153	39	=	=	SYM
ejpam-4511	154	1	2	2	X
ejpam-4511	154	2	.	.	X
ejpam-4511	154	3	hence	hence	ADV
ejpam-4511	154	4	,	,	PUNCT
ejpam-4511	154	5	v	v	X
ejpam-4511	154	6	(	(	PUNCT
ejpam-4511	154	7	g	g	NOUN
ejpam-4511	154	8	)	)	PUNCT
ejpam-4511	154	9	=	=	SYM
ejpam-4511	154	10	n2	n2	PROPN
ejpam-4511	154	11	g[x	g[x	PROPN
ejpam-4511	154	12	]	]	X
ejpam-4511	154	13	∪n2	∪n2	PROPN
ejpam-4511	154	14	g[y	g[y	PROPN
ejpam-4511	154	15	]	]	PUNCT
ejpam-4511	154	16	.	.	PUNCT
ejpam-4511	155	1	for	for	ADP
ejpam-4511	155	2	the	the	DET
ejpam-4511	155	3	converse	converse	NOUN
ejpam-4511	155	4	,	,	PUNCT
ejpam-4511	155	5	suppose	suppose	VERB
ejpam-4511	155	6	that	that	SCONJ
ejpam-4511	155	7	for	for	ADP
ejpam-4511	155	8	each	each	DET
ejpam-4511	155	9	pair	pair	NOUN
ejpam-4511	155	10	of	of	ADP
ejpam-4511	155	11	distinct	distinct	ADJ
ejpam-4511	155	12	vertices	vertex	NOUN
ejpam-4511	155	13	x	x	X
ejpam-4511	155	14	,	,	PUNCT
ejpam-4511	155	15	y	y	PROPN
ejpam-4511	155	16	∈	∈	PROPN
ejpam-4511	155	17	v	v	ADP
ejpam-4511	155	18	(	(	PUNCT
ejpam-4511	155	19	g	g	NOUN
ejpam-4511	155	20	)	)	PUNCT
ejpam-4511	155	21	such	such	ADJ
ejpam-4511	155	22	that	that	DET
ejpam-4511	155	23	n2	n2	PROPN
ejpam-4511	155	24	g[x	g[x	PROPN
ejpam-4511	155	25	]	]	X
ejpam-4511	155	26	̸=	̸=	PROPN
ejpam-4511	155	27	n2	n2	PROPN
ejpam-4511	155	28	g[y	g[y	PROPN
ejpam-4511	155	29	]	]	PUNCT
ejpam-4511	155	30	,	,	PUNCT
ejpam-4511	155	31	we	we	PRON
ejpam-4511	155	32	have	have	VERB
ejpam-4511	155	33	v	v	NUM
ejpam-4511	155	34	(	(	PUNCT
ejpam-4511	155	35	g	g	NOUN
ejpam-4511	155	36	)	)	PUNCT
ejpam-4511	155	37	=	=	SYM
ejpam-4511	155	38	n2	n2	PROPN
ejpam-4511	155	39	g[x	g[x	PROPN
ejpam-4511	155	40	]	]	PUNCT
ejpam-4511	155	41	∪	∪	ADP
ejpam-4511	155	42	n2	n2	ADJ
ejpam-4511	155	43	g[y	g[y	NOUN
ejpam-4511	155	44	]	]	PUNCT
ejpam-4511	155	45	.	.	PUNCT
ejpam-4511	156	1	since	since	SCONJ
ejpam-4511	156	2	g	g	PROPN
ejpam-4511	156	3	is	be	AUX
ejpam-4511	156	4	a	a	DET
ejpam-4511	156	5	non	non	ADJ
ejpam-4511	156	6	-	-	ADJ
ejpam-4511	156	7	trivial	trivial	ADJ
ejpam-4511	156	8	graph	graph	NOUN
ejpam-4511	156	9	,	,	PUNCT
ejpam-4511	156	10	the	the	DET
ejpam-4511	156	11	assumption	assumption	NOUN
ejpam-4511	156	12	implies	imply	VERB
ejpam-4511	156	13	that	that	SCONJ
ejpam-4511	156	14	γh(g	γh(g	NOUN
ejpam-4511	156	15	)	)	PUNCT
ejpam-4511	156	16	=	=	SYM
ejpam-4511	156	17	2	2	X
ejpam-4511	156	18	.	.	X
ejpam-4511	156	19	hence	hence	ADV
ejpam-4511	156	20	,	,	PUNCT
ejpam-4511	156	21	γhgr(g	γhgr(g	NOUN
ejpam-4511	156	22	)	)	PUNCT
ejpam-4511	156	23	=	=	SYM
ejpam-4511	157	1	k	k	PROPN
ejpam-4511	157	2	≥	≥	NUM
ejpam-4511	157	3	2	2	X
ejpam-4511	157	4	.	.	PUNCT
ejpam-4511	158	1	let	let	VERB
ejpam-4511	158	2	(	(	PUNCT
ejpam-4511	158	3	v1	v1	VERB
ejpam-4511	158	4	,	,	PUNCT
ejpam-4511	158	5	v2	v2	PROPN
ejpam-4511	158	6	,	,	PUNCT
ejpam-4511	158	7	·	·	PUNCT
ejpam-4511	158	8	·	·	PUNCT
ejpam-4511	158	9	·	·	PUNCT
ejpam-4511	158	10	,	,	PUNCT
ejpam-4511	158	11	vk	vk	AUX
ejpam-4511	158	12	)	)	PUNCT
ejpam-4511	158	13	be	be	AUX
ejpam-4511	158	14	a	a	DET
ejpam-4511	158	15	grundy	grundy	PROPN
ejpam-4511	158	16	hop	hop	NOUN
ejpam-4511	158	17	dominating	dominating	NOUN
ejpam-4511	158	18	sequence	sequence	NOUN
ejpam-4511	158	19	of	of	ADP
ejpam-4511	158	20	g.	g.	PROPN
ejpam-4511	158	21	because	because	SCONJ
ejpam-4511	158	22	n2	n2	PROPN
ejpam-4511	158	23	g[v2	g[v2	PROPN
ejpam-4511	158	24	]	]	PUNCT
ejpam-4511	158	25	\	\	PROPN
ejpam-4511	158	26	n2	n2	PROPN
ejpam-4511	158	27	g[v1	g[v1	PROPN
ejpam-4511	158	28	]	]	PUNCT
ejpam-4511	158	29	̸=	̸=	PROPN
ejpam-4511	158	30	∅	∅	NOUN
ejpam-4511	158	31	,	,	PUNCT
ejpam-4511	158	32	v	v	PROPN
ejpam-4511	158	33	(	(	PUNCT
ejpam-4511	158	34	g	g	NOUN
ejpam-4511	158	35	)	)	PUNCT
ejpam-4511	158	36	=	=	SYM
ejpam-4511	158	37	n2	n2	PROPN
ejpam-4511	158	38	g[v1	g[v1	PROPN
ejpam-4511	158	39	]	]	PUNCT
ejpam-4511	158	40	∪n2	∪n2	PROPN
ejpam-4511	158	41	g[v2	g[v2	PROPN
ejpam-4511	158	42	]	]	X
ejpam-4511	158	43	,	,	PUNCT
ejpam-4511	158	44	by	by	ADP
ejpam-4511	158	45	assumption	assumption	NOUN
ejpam-4511	158	46	.	.	PUNCT
ejpam-4511	159	1	therefore	therefore	ADV
ejpam-4511	159	2	,	,	PUNCT
ejpam-4511	159	3	γhgr(g	γhgr(g	NOUN
ejpam-4511	159	4	)	)	PUNCT
ejpam-4511	159	5	=	=	PUNCT
ejpam-4511	160	1	k	k	NOUN
ejpam-4511	160	2	=	=	SYM
ejpam-4511	160	3	2	2	X
ejpam-4511	160	4	.	.	PUNCT
ejpam-4511	160	5	(	(	PUNCT
ejpam-4511	160	6	ii	ii	NOUN
ejpam-4511	160	7	)	)	PUNCT
ejpam-4511	160	8	suppose	suppose	VERB
ejpam-4511	160	9	γhgr(g	γhgr(g	ADP
ejpam-4511	160	10	)	)	PUNCT
ejpam-4511	160	11	=	=	SYM
ejpam-4511	160	12	n	n	NOUN
ejpam-4511	160	13	and	and	CCONJ
ejpam-4511	160	14	let	let	VERB
ejpam-4511	160	15	s	s	AUX
ejpam-4511	160	16	=	=	PUNCT
ejpam-4511	160	17	(	(	PUNCT
ejpam-4511	160	18	v1	v1	PROPN
ejpam-4511	160	19	,	,	PUNCT
ejpam-4511	160	20	v2	v2	PROPN
ejpam-4511	160	21	,	,	PUNCT
ejpam-4511	160	22	·	·	PUNCT
ejpam-4511	160	23	·	·	PUNCT
ejpam-4511	160	24	·	·	PUNCT
ejpam-4511	160	25	,	,	PUNCT
ejpam-4511	160	26	vn	vn	AUX
ejpam-4511	160	27	)	)	PUNCT
ejpam-4511	160	28	be	be	AUX
ejpam-4511	160	29	a	a	DET
ejpam-4511	160	30	grundy	grundy	PROPN
ejpam-4511	160	31	hop	hop	NOUN
ejpam-4511	160	32	dominating	dominating	NOUN
ejpam-4511	160	33	sequence	sequence	NOUN
ejpam-4511	160	34	of	of	ADP
ejpam-4511	160	35	g.	g.	PROPN
ejpam-4511	160	36	note	note	VERB
ejpam-4511	160	37	that	that	SCONJ
ejpam-4511	160	38	since	since	SCONJ
ejpam-4511	160	39	n2	n2	ADJ
ejpam-4511	160	40	g[vn	g[vn	PROPN
ejpam-4511	160	41	]	]	PUNCT
ejpam-4511	160	42	\	\	X
ejpam-4511	160	43	∪n−1	∪n−1	PROPN
ejpam-4511	160	44	j=1n	j=1n	VERB
ejpam-4511	160	45	2	2	NUM
ejpam-4511	160	46	g[vj	g[vj	PROPN
ejpam-4511	160	47	]	]	PUNCT
ejpam-4511	160	48	̸=	̸=	PROPN
ejpam-4511	160	49	∅	∅	NOUN
ejpam-4511	160	50	and	and	CCONJ
ejpam-4511	160	51	vj	vj	PRON
ejpam-4511	160	52	∈	∈	PROPN
ejpam-4511	160	53	n2	n2	PROPN
ejpam-4511	160	54	g[vj	g[vj	PROPN
ejpam-4511	160	55	]	]	PUNCT
ejpam-4511	160	56	for	for	ADP
ejpam-4511	160	57	each	each	DET
ejpam-4511	160	58	j	j	PROPN
ejpam-4511	160	59	∈	∈	PROPN
ejpam-4511	161	1	[	[	X
ejpam-4511	161	2	n	n	X
ejpam-4511	161	3	]	]	PUNCT
ejpam-4511	161	4	,	,	PUNCT
ejpam-4511	161	5	n2	n2	ADJ
ejpam-4511	161	6	g[vn	g[vn	PROPN
ejpam-4511	161	7	]	]	PUNCT
ejpam-4511	161	8	\	\	X
ejpam-4511	161	9	∪n−1	∪n−1	PROPN
ejpam-4511	161	10	j=1n	j=1n	VERB
ejpam-4511	161	11	2	2	NUM
ejpam-4511	161	12	g[vj	g[vj	PROPN
ejpam-4511	161	13	]	]	PUNCT
ejpam-4511	161	14	=	=	PUNCT
ejpam-4511	161	15	{	{	PUNCT
ejpam-4511	161	16	vn	vn	NOUN
ejpam-4511	161	17	}	}	PUNCT
ejpam-4511	161	18	.	.	PUNCT
ejpam-4511	162	1	this	this	PRON
ejpam-4511	162	2	implies	imply	VERB
ejpam-4511	162	3	that	that	PRON
ejpam-4511	162	4	vn	vn	PROPN
ejpam-4511	162	5	/∈	/∈	PUNCT
ejpam-4511	162	6	n2	n2	PROPN
ejpam-4511	162	7	g[vj	g[vj	PROPN
ejpam-4511	162	8	]	]	PUNCT
ejpam-4511	162	9	for	for	ADP
ejpam-4511	162	10	all	all	DET
ejpam-4511	162	11	j	j	PROPN
ejpam-4511	162	12	∈	∈	PROPN
ejpam-4511	163	1	[	[	X
ejpam-4511	163	2	n	n	CCONJ
ejpam-4511	163	3	−	−	PROPN
ejpam-4511	163	4	1	1	NUM
ejpam-4511	163	5	]	]	PUNCT
ejpam-4511	163	6	,	,	PUNCT
ejpam-4511	163	7	i.e.	i.e.	X
ejpam-4511	163	8	,	,	PUNCT
ejpam-4511	163	9	n2	n2	ADJ
ejpam-4511	163	10	g[vn	g[vn	PROPN
ejpam-4511	163	11	]	]	X
ejpam-4511	163	12	=	=	X
ejpam-4511	163	13	{	{	PUNCT
ejpam-4511	163	14	vn	vn	NOUN
ejpam-4511	163	15	}	}	PUNCT
ejpam-4511	163	16	.	.	PUNCT
ejpam-4511	164	1	this	this	PRON
ejpam-4511	164	2	would	would	AUX
ejpam-4511	164	3	imply	imply	VERB
ejpam-4511	164	4	that	that	DET
ejpam-4511	164	5	n2	n2	NOUN
ejpam-4511	164	6	g[vn−1	g[vn−1	PROPN
ejpam-4511	164	7	]	]	PUNCT
ejpam-4511	164	8	\	\	X
ejpam-4511	165	1	∪n−2	∪n−2	PUNCT
ejpam-4511	165	2	j=1n	j=1n	PROPN
ejpam-4511	165	3	2	2	NUM
ejpam-4511	165	4	g[vj	g[vj	PROPN
ejpam-4511	165	5	]	]	PUNCT
ejpam-4511	165	6	=	=	PUNCT
ejpam-4511	165	7	{	{	PUNCT
ejpam-4511	165	8	vn−1	vn−1	PROPN
ejpam-4511	165	9	}	}	PUNCT
ejpam-4511	165	10	.	.	PUNCT
ejpam-4511	166	1	using	use	VERB
ejpam-4511	166	2	the	the	DET
ejpam-4511	166	3	same	same	ADJ
ejpam-4511	166	4	argument	argument	NOUN
ejpam-4511	166	5	as	as	ADP
ejpam-4511	166	6	earlier	early	ADV
ejpam-4511	166	7	,	,	PUNCT
ejpam-4511	166	8	n2	n2	PROPN
ejpam-4511	166	9	g[vn−1	g[vn−1	PROPN
ejpam-4511	166	10	]	]	PUNCT
ejpam-4511	166	11	=	=	X
ejpam-4511	166	12	{	{	PUNCT
ejpam-4511	166	13	vn−1	vn−1	PROPN
ejpam-4511	166	14	}	}	PUNCT
ejpam-4511	166	15	.	.	PUNCT
ejpam-4511	167	1	continuing	continue	VERB
ejpam-4511	167	2	in	in	ADP
ejpam-4511	167	3	this	this	DET
ejpam-4511	167	4	fashion	fashion	NOUN
ejpam-4511	167	5	,	,	PUNCT
ejpam-4511	167	6	we	we	PRON
ejpam-4511	167	7	find	find	VERB
ejpam-4511	167	8	that	that	SCONJ
ejpam-4511	167	9	n2	n2	ADJ
ejpam-4511	167	10	g[vi	g[vi	PROPN
ejpam-4511	167	11	]	]	X
ejpam-4511	167	12	=	=	SYM
ejpam-4511	167	13	{	{	PUNCT
ejpam-4511	167	14	vi	vi	NOUN
ejpam-4511	167	15	}	}	PUNCT
ejpam-4511	167	16	for	for	ADP
ejpam-4511	167	17	each	each	DET
ejpam-4511	167	18	i	i	PRON
ejpam-4511	167	19	∈	∈	PROPN
ejpam-4511	168	1	[	[	X
ejpam-4511	168	2	n	n	X
ejpam-4511	168	3	]	]	PUNCT
ejpam-4511	168	4	,	,	PUNCT
ejpam-4511	168	5	i.e.	i.e.	X
ejpam-4511	168	6	,	,	PUNCT
ejpam-4511	168	7	degg(vi	degg(vi	NOUN
ejpam-4511	168	8	)	)	PUNCT
ejpam-4511	168	9	=	=	SYM
ejpam-4511	168	10	0	0	NUM
ejpam-4511	168	11	or	or	CCONJ
ejpam-4511	168	12	vi	vi	PROPN
ejpam-4511	168	13	is	be	AUX
ejpam-4511	168	14	adjacent	adjacent	ADJ
ejpam-4511	168	15	to	to	ADP
ejpam-4511	168	16	every	every	DET
ejpam-4511	168	17	other	other	ADJ
ejpam-4511	168	18	vertex	vertex	NOUN
ejpam-4511	168	19	in	in	ADP
ejpam-4511	168	20	the	the	DET
ejpam-4511	168	21	component	component	NOUN
ejpam-4511	168	22	it	it	PRON
ejpam-4511	168	23	belongs	belong	VERB
ejpam-4511	168	24	.	.	PUNCT
ejpam-4511	169	1	therefore	therefore	ADV
ejpam-4511	169	2	,	,	PUNCT
ejpam-4511	169	3	every	every	DET
ejpam-4511	169	4	component	component	NOUN
ejpam-4511	169	5	of	of	ADP
ejpam-4511	169	6	g	g	PROPN
ejpam-4511	169	7	is	be	AUX
ejpam-4511	169	8	complete	complete	ADJ
ejpam-4511	169	9	.	.	PUNCT
ejpam-4511	170	1	conversely	conversely	ADV
ejpam-4511	170	2	,	,	PUNCT
ejpam-4511	170	3	if	if	SCONJ
ejpam-4511	170	4	every	every	DET
ejpam-4511	170	5	component	component	NOUN
ejpam-4511	170	6	of	of	ADP
ejpam-4511	170	7	g	g	PROPN
ejpam-4511	170	8	is	be	AUX
ejpam-4511	170	9	complete	complete	ADJ
ejpam-4511	170	10	,	,	PUNCT
ejpam-4511	170	11	then	then	ADV
ejpam-4511	170	12	n2	n2	PROPN
ejpam-4511	170	13	g[v	g[v	PROPN
ejpam-4511	170	14	]	]	X
ejpam-4511	170	15	=	=	SYM
ejpam-4511	170	16	{	{	PUNCT
ejpam-4511	170	17	v	v	NOUN
ejpam-4511	170	18	}	}	PUNCT
ejpam-4511	170	19	for	for	ADP
ejpam-4511	170	20	each	each	DET
ejpam-4511	170	21	v	v	NUM
ejpam-4511	170	22	∈	∈	PROPN
ejpam-4511	170	23	v	v	NOUN
ejpam-4511	170	24	(	(	PUNCT
ejpam-4511	170	25	g	g	NOUN
ejpam-4511	170	26	)	)	PUNCT
ejpam-4511	170	27	.	.	PUNCT
ejpam-4511	171	1	hence	hence	ADV
ejpam-4511	171	2	,	,	PUNCT
ejpam-4511	171	3	if	if	SCONJ
ejpam-4511	171	4	v	v	X
ejpam-4511	171	5	(	(	PUNCT
ejpam-4511	171	6	g	g	NOUN
ejpam-4511	171	7	)	)	PUNCT
ejpam-4511	171	8	=	=	SYM
ejpam-4511	171	9	{	{	PUNCT
ejpam-4511	171	10	v1	v1	PROPN
ejpam-4511	171	11	,	,	PUNCT
ejpam-4511	171	12	v2	v2	PROPN
ejpam-4511	171	13	,	,	PUNCT
ejpam-4511	171	14	.	.	PUNCT
ejpam-4511	171	15	.	.	PUNCT
ejpam-4511	171	16	.	.	PUNCT
ejpam-4511	172	1	,	,	PUNCT
ejpam-4511	172	2	vn	vn	PROPN
ejpam-4511	172	3	}	}	PUNCT
ejpam-4511	172	4	,	,	PUNCT
ejpam-4511	172	5	then	then	ADV
ejpam-4511	172	6	n2	n2	PROPN
ejpam-4511	172	7	g[vi	g[vi	PROPN
ejpam-4511	172	8	]	]	PUNCT
ejpam-4511	172	9	\	\	X
ejpam-4511	172	10	∪i−1	∪i−1	PUNCT
ejpam-4511	172	11	j=1n	j=1n	PROPN
ejpam-4511	172	12	2	2	NUM
ejpam-4511	172	13	g[vj	g[vj	PROPN
ejpam-4511	172	14	]	]	PUNCT
ejpam-4511	172	15	=	=	PUNCT
ejpam-4511	172	16	{	{	PUNCT
ejpam-4511	172	17	vi	vi	PROPN
ejpam-4511	172	18	}	}	PUNCT
ejpam-4511	172	19	\	\	NOUN
ejpam-4511	172	20	{	{	PUNCT
ejpam-4511	172	21	vj	vj	INTJ
ejpam-4511	172	22	:	:	PUNCT
ejpam-4511	172	23	j	j	PROPN
ejpam-4511	172	24	̸=	̸=	PROPN
ejpam-4511	172	25	i	i	PRON
ejpam-4511	172	26	}	}	PUNCT
ejpam-4511	172	27	=	=	SYM
ejpam-4511	172	28	{	{	PUNCT
ejpam-4511	172	29	vi	vi	NOUN
ejpam-4511	172	30	}	}	PUNCT
ejpam-4511	172	31	=	=	NOUN
ejpam-4511	172	32	̸	̸	X
ejpam-4511	172	33	∅.	∅.	ADJ
ejpam-4511	172	34	for	for	ADP
ejpam-4511	172	35	each	each	DET
ejpam-4511	172	36	i	i	PRON
ejpam-4511	172	37	∈	∈	PROPN
ejpam-4511	172	38	{	{	PUNCT
ejpam-4511	172	39	2	2	NUM
ejpam-4511	172	40	,	,	PUNCT
ejpam-4511	172	41	3	3	NUM
ejpam-4511	172	42	,	,	PUNCT
ejpam-4511	172	43	.	.	PUNCT
ejpam-4511	172	44	.	.	PUNCT
ejpam-4511	173	1	.	.	PUNCT
ejpam-4511	173	2	,	,	PUNCT
ejpam-4511	173	3	n	n	CCONJ
ejpam-4511	173	4	}	}	PUNCT
ejpam-4511	173	5	.	.	PUNCT
ejpam-4511	174	1	this	this	PRON
ejpam-4511	174	2	shows	show	VERB
ejpam-4511	174	3	that	that	SCONJ
ejpam-4511	174	4	(	(	PUNCT
ejpam-4511	174	5	v1	v1	NOUN
ejpam-4511	174	6	,	,	PUNCT
ejpam-4511	174	7	v2	v2	PROPN
ejpam-4511	174	8	,	,	PUNCT
ejpam-4511	174	9	·	·	PUNCT
ejpam-4511	174	10	·	·	PUNCT
ejpam-4511	174	11	·	·	PUNCT
ejpam-4511	174	12	,	,	PUNCT
ejpam-4511	174	13	vn	vn	PROPN
ejpam-4511	174	14	)	)	PUNCT
ejpam-4511	174	15	is	be	AUX
ejpam-4511	174	16	a	a	DET
ejpam-4511	174	17	grundy	grundy	PROPN
ejpam-4511	174	18	hop	hop	NOUN
ejpam-4511	174	19	dominating	dominating	NOUN
ejpam-4511	174	20	sequence	sequence	NOUN
ejpam-4511	174	21	of	of	ADP
ejpam-4511	174	22	g.	g.	PROPN
ejpam-4511	174	23	therefore	therefore	ADV
ejpam-4511	174	24	γhgr(g	γhgr(g	PROPN
ejpam-4511	174	25	)	)	PUNCT
ejpam-4511	174	26	=	=	VERB
ejpam-4511	175	1	n.	n.	NOUN
ejpam-4511	175	2	the	the	DET
ejpam-4511	175	3	next	next	ADJ
ejpam-4511	175	4	result	result	NOUN
ejpam-4511	175	5	is	be	AUX
ejpam-4511	175	6	immediate	immediate	ADJ
ejpam-4511	175	7	from	from	ADP
ejpam-4511	175	8	the	the	DET
ejpam-4511	175	9	theorem	theorem	NOUN
ejpam-4511	175	10	3(ii	3(ii	NUM
ejpam-4511	175	11	)	)	PUNCT
ejpam-4511	175	12	.	.	PUNCT
ejpam-4511	176	1	corollary	corollary	ADJ
ejpam-4511	176	2	2	2	NUM
ejpam-4511	176	3	.	.	PUNCT
ejpam-4511	177	1	let	let	VERB
ejpam-4511	177	2	g	g	PRON
ejpam-4511	177	3	be	be	AUX
ejpam-4511	177	4	a	a	DET
ejpam-4511	177	5	connected	connected	ADJ
ejpam-4511	177	6	graph	graph	NOUN
ejpam-4511	177	7	on	on	ADP
ejpam-4511	177	8	n	n	DET
ejpam-4511	177	9	vertices	vertex	NOUN
ejpam-4511	177	10	.	.	PUNCT
ejpam-4511	178	1	then	then	ADV
ejpam-4511	178	2	each	each	PRON
ejpam-4511	178	3	of	of	ADP
ejpam-4511	178	4	the	the	DET
ejpam-4511	178	5	following	following	ADJ
ejpam-4511	178	6	statements	statement	NOUN
ejpam-4511	178	7	holds	hold	VERB
ejpam-4511	178	8	.	.	PUNCT
ejpam-4511	179	1	(	(	PUNCT
ejpam-4511	179	2	i	i	NOUN
ejpam-4511	179	3	)	)	PUNCT
ejpam-4511	179	4	γhgr(g	γhgr(g	X
ejpam-4511	179	5	)	)	PUNCT
ejpam-4511	179	6	=	=	SYM
ejpam-4511	180	1	n	n	NOUN
ejpam-4511	180	2	if	if	SCONJ
ejpam-4511	181	1	and	and	CCONJ
ejpam-4511	181	2	only	only	ADV
ejpam-4511	181	3	if	if	SCONJ
ejpam-4511	181	4	g	g	PROPN
ejpam-4511	181	5	=	=	PROPN
ejpam-4511	181	6	kn	kn	PROPN
ejpam-4511	181	7	.	.	PUNCT
ejpam-4511	182	1	(	(	PUNCT
ejpam-4511	182	2	ii	ii	NOUN
ejpam-4511	182	3	)	)	PUNCT
ejpam-4511	182	4	if	if	SCONJ
ejpam-4511	182	5	g	g	PROPN
ejpam-4511	182	6	is	be	AUX
ejpam-4511	182	7	non	non	ADJ
ejpam-4511	182	8	-	-	ADJ
ejpam-4511	182	9	complete	complete	ADJ
ejpam-4511	182	10	,	,	PUNCT
ejpam-4511	182	11	then	then	ADV
ejpam-4511	182	12	γhgr(g	γhgr(g	NOUN
ejpam-4511	182	13	)	)	PUNCT
ejpam-4511	182	14	≤	≤	NUM
ejpam-4511	182	15	n−	n−	NOUN
ejpam-4511	182	16	1	1	NUM
ejpam-4511	182	17	.	.	PUNCT
ejpam-4511	182	18	theorem	theorem	VERB
ejpam-4511	182	19	4	4	NUM
ejpam-4511	182	20	.	.	PUNCT
ejpam-4511	183	1	let	let	VERB
ejpam-4511	183	2	g	g	PRON
ejpam-4511	183	3	be	be	AUX
ejpam-4511	183	4	a	a	DET
ejpam-4511	183	5	graph	graph	NOUN
ejpam-4511	183	6	on	on	ADP
ejpam-4511	183	7	n	n	DET
ejpam-4511	183	8	vertices	vertex	NOUN
ejpam-4511	183	9	.	.	PUNCT
ejpam-4511	184	1	(	(	PUNCT
ejpam-4511	184	2	i	i	NOUN
ejpam-4511	184	3	)	)	PUNCT
ejpam-4511	184	4	if	if	SCONJ
ejpam-4511	184	5	g	g	PROPN
ejpam-4511	184	6	is	be	AUX
ejpam-4511	184	7	complete	complete	ADJ
ejpam-4511	184	8	,	,	PUNCT
ejpam-4511	184	9	then	then	ADV
ejpam-4511	184	10	γhgr(g	γhgr(g	NOUN
ejpam-4511	184	11	)	)	PUNCT
ejpam-4511	185	1	+	+	X
ejpam-4511	185	2	γhgr(g	γhgr(g	X
ejpam-4511	185	3	)	)	PUNCT
ejpam-4511	185	4	=	=	SYM
ejpam-4511	185	5	2n	2n	X
ejpam-4511	185	6	.	.	PUNCT
ejpam-4511	186	1	(	(	PUNCT
ejpam-4511	186	2	ii	ii	NOUN
ejpam-4511	186	3	)	)	PUNCT
ejpam-4511	186	4	if	if	SCONJ
ejpam-4511	186	5	g	g	PROPN
ejpam-4511	186	6	is	be	AUX
ejpam-4511	186	7	non	non	ADJ
ejpam-4511	186	8	-	-	ADJ
ejpam-4511	186	9	complete	complete	ADJ
ejpam-4511	186	10	,	,	PUNCT
ejpam-4511	186	11	then	then	ADV
ejpam-4511	186	12	(	(	PUNCT
ejpam-4511	186	13	a	a	X
ejpam-4511	186	14	)	)	PUNCT
ejpam-4511	186	15	4	4	NUM
ejpam-4511	186	16	≤	≤	NOUN
ejpam-4511	186	17	γhgr(g	γhgr(g	PROPN
ejpam-4511	186	18	)	)	PUNCT
ejpam-4511	187	1	+	+	X
ejpam-4511	187	2	γhgr(g	γhgr(g	X
ejpam-4511	187	3	)	)	PUNCT
ejpam-4511	187	4	≤	≤	NOUN
ejpam-4511	188	1	2n−	2n−	NUM
ejpam-4511	188	2	1	1	NUM
ejpam-4511	188	3	,	,	PUNCT
ejpam-4511	188	4	and	and	CCONJ
ejpam-4511	188	5	(	(	PUNCT
ejpam-4511	188	6	b	b	NOUN
ejpam-4511	188	7	)	)	PUNCT
ejpam-4511	188	8	4	4	NUM
ejpam-4511	188	9	≤	≤	NOUN
ejpam-4511	188	10	γhgr(g	γhgr(g	PROPN
ejpam-4511	188	11	)	)	PUNCT
ejpam-4511	188	12	·	·	PUNCT
ejpam-4511	189	1	γhgr(g	γhgr(g	X
ejpam-4511	189	2	)	)	PUNCT
ejpam-4511	189	3	≤	≤	NOUN
ejpam-4511	189	4	n2	n2	NOUN
ejpam-4511	189	5	−	−	PROPN
ejpam-4511	189	6	n.	n.	PROPN
ejpam-4511	189	7	j.	j.	PROPN
ejpam-4511	189	8	hassan	hassan	PROPN
ejpam-4511	189	9	,	,	PUNCT
ejpam-4511	189	10	s.	s.	PROPN
ejpam-4511	189	11	canoy	canoy	PROPN
ejpam-4511	189	12	/	/	SYM
ejpam-4511	189	13	eur	eur	PROPN
ejpam-4511	189	14	.	.	PUNCT
ejpam-4511	190	1	j.	j.	PROPN
ejpam-4511	190	2	pure	pure	PROPN
ejpam-4511	190	3	appl	appl	PROPN
ejpam-4511	190	4	.	.	PROPN
ejpam-4511	190	5	math	math	PROPN
ejpam-4511	190	6	,	,	PUNCT
ejpam-4511	190	7	15	15	NUM
ejpam-4511	190	8	(	(	PUNCT
ejpam-4511	190	9	4	4	NUM
ejpam-4511	190	10	)	)	PUNCT
ejpam-4511	190	11	(	(	PUNCT
ejpam-4511	190	12	2022	2022	NUM
ejpam-4511	190	13	)	)	PUNCT
ejpam-4511	190	14	,	,	PUNCT
ejpam-4511	190	15	1623	1623	NUM
ejpam-4511	190	16	-	-	SYM
ejpam-4511	190	17	1636	1636	NUM
ejpam-4511	190	18	1629	1629	NUM
ejpam-4511	190	19	proof	proof	NOUN
ejpam-4511	190	20	.	.	PUNCT
ejpam-4511	191	1	(	(	PUNCT
ejpam-4511	191	2	i	i	NOUN
ejpam-4511	191	3	)	)	PUNCT
ejpam-4511	191	4	the	the	DET
ejpam-4511	191	5	equality	equality	NOUN
ejpam-4511	191	6	follows	follow	VERB
ejpam-4511	191	7	from	from	ADP
ejpam-4511	191	8	theorem	theorem	ADJ
ejpam-4511	191	9	3(ii	3(ii	NUM
ejpam-4511	191	10	)	)	PUNCT
ejpam-4511	191	11	.	.	PUNCT
ejpam-4511	192	1	(	(	PUNCT
ejpam-4511	192	2	ii	ii	NOUN
ejpam-4511	192	3	)	)	PUNCT
ejpam-4511	192	4	by	by	ADP
ejpam-4511	192	5	corollary	corollary	ADJ
ejpam-4511	192	6	2(ii	2(ii	NUM
ejpam-4511	192	7	)	)	PUNCT
ejpam-4511	192	8	,	,	PUNCT
ejpam-4511	192	9	γhgr(g	γhgr(g	NOUN
ejpam-4511	192	10	)	)	PUNCT
ejpam-4511	192	11	≤	≤	NUM
ejpam-4511	192	12	n−	n−	NOUN
ejpam-4511	192	13	1	1	NUM
ejpam-4511	192	14	and	and	CCONJ
ejpam-4511	192	15	by	by	ADP
ejpam-4511	192	16	theorem	theorem	NOUN
ejpam-4511	192	17	3	3	NUM
ejpam-4511	192	18	,	,	PUNCT
ejpam-4511	192	19	γhgr(g	γhgr(g	NOUN
ejpam-4511	192	20	)	)	PUNCT
ejpam-4511	192	21	≤	≤	NOUN
ejpam-4511	192	22	n.	n.	NOUN
ejpam-4511	192	23	these	these	PRON
ejpam-4511	192	24	imply	imply	VERB
ejpam-4511	192	25	that	that	SCONJ
ejpam-4511	192	26	γhgr(g	γhgr(g	NOUN
ejpam-4511	192	27	)	)	PUNCT
ejpam-4511	193	1	+	+	X
ejpam-4511	193	2	γhgr(g	γhgr(g	X
ejpam-4511	193	3	)	)	PUNCT
ejpam-4511	193	4	≤	≤	NUM
ejpam-4511	193	5	n−	n−	NOUN
ejpam-4511	193	6	1	1	NUM
ejpam-4511	193	7	+	+	CCONJ
ejpam-4511	193	8	n	n	PROPN
ejpam-4511	193	9	=	=	SYM
ejpam-4511	194	1	2n−	2n−	PROPN
ejpam-4511	194	2	1	1	NUM
ejpam-4511	194	3	,	,	PUNCT
ejpam-4511	194	4	and	and	CCONJ
ejpam-4511	194	5	γhgr(g	γhgr(g	X
ejpam-4511	194	6	)	)	PUNCT
ejpam-4511	194	7	·	·	PUNCT
ejpam-4511	195	1	γhgr(g	γhgr(g	X
ejpam-4511	195	2	)	)	PUNCT
ejpam-4511	195	3	≤	≤	NOUN
ejpam-4511	195	4	(	(	PUNCT
ejpam-4511	195	5	n−	n−	NOUN
ejpam-4511	195	6	1)n	1)n	X
ejpam-4511	195	7	=	=	SYM
ejpam-4511	195	8	n2	n2	PROPN
ejpam-4511	195	9	−	−	PROPN
ejpam-4511	195	10	n.	n.	NOUN
ejpam-4511	195	11	the	the	DET
ejpam-4511	195	12	left	left	ADJ
ejpam-4511	195	13	inequalities	inequality	NOUN
ejpam-4511	195	14	follow	follow	VERB
ejpam-4511	195	15	from	from	ADP
ejpam-4511	195	16	theorem	theorem	ADJ
ejpam-4511	195	17	3	3	NUM
ejpam-4511	195	18	.	.	PUNCT
ejpam-4511	196	1	the	the	DET
ejpam-4511	196	2	bounds	bound	NOUN
ejpam-4511	196	3	in	in	ADP
ejpam-4511	196	4	theorem	theorem	ADJ
ejpam-4511	196	5	4(ii	4(ii	NUM
ejpam-4511	196	6	)	)	PUNCT
ejpam-4511	196	7	are	be	AUX
ejpam-4511	196	8	tight	tight	ADJ
ejpam-4511	196	9	.	.	PUNCT
ejpam-4511	197	1	indeed	indeed	ADV
ejpam-4511	197	2	,	,	PUNCT
ejpam-4511	197	3	one	one	PRON
ejpam-4511	197	4	can	can	AUX
ejpam-4511	197	5	easily	easily	ADV
ejpam-4511	197	6	verify	verify	VERB
ejpam-4511	197	7	that	that	SCONJ
ejpam-4511	197	8	γhgr(p4	γhgr(p4	NOUN
ejpam-4511	197	9	)	)	PUNCT
ejpam-4511	198	1	+	+	CCONJ
ejpam-4511	198	2	γhgr(p	γhgr(p	NOUN
ejpam-4511	198	3	4	4	NUM
ejpam-4511	198	4	)	)	PUNCT
ejpam-4511	198	5	=	=	NOUN
ejpam-4511	198	6	γhgr(p4	γhgr(p4	NOUN
ejpam-4511	198	7	)	)	PUNCT
ejpam-4511	198	8	·	·	PUNCT
ejpam-4511	198	9	γhgr(p	γhgr(p	NOUN
ejpam-4511	198	10	4	4	NUM
ejpam-4511	198	11	)	)	PUNCT
ejpam-4511	198	12	=	=	SYM
ejpam-4511	198	13	4	4	NUM
ejpam-4511	198	14	,	,	PUNCT
ejpam-4511	198	15	γhgr(p3	γhgr(p3	ADJ
ejpam-4511	198	16	)	)	PUNCT
ejpam-4511	199	1	+	+	CCONJ
ejpam-4511	199	2	γhgr(p	γhgr(p	NOUN
ejpam-4511	199	3	3	3	NUM
ejpam-4511	199	4	)	)	PUNCT
ejpam-4511	199	5	=	=	SYM
ejpam-4511	199	6	5	5	NUM
ejpam-4511	199	7	=	=	SYM
ejpam-4511	199	8	2(3)−	2(3)−	PROPN
ejpam-4511	199	9	1	1	NUM
ejpam-4511	199	10	,	,	PUNCT
ejpam-4511	199	11	and	and	CCONJ
ejpam-4511	199	12	γhgr(p3	γhgr(p3	PROPN
ejpam-4511	199	13	)	)	PUNCT
ejpam-4511	199	14	·	·	PUNCT
ejpam-4511	199	15	γhgr(p	γhgr(p	NOUN
ejpam-4511	199	16	3	3	NUM
ejpam-4511	199	17	)	)	PUNCT
ejpam-4511	199	18	=	=	SYM
ejpam-4511	199	19	6	6	NUM
ejpam-4511	199	20	=	=	SYM
ejpam-4511	199	21	32	32	NUM
ejpam-4511	199	22	−	−	NOUN
ejpam-4511	199	23	3	3	X
ejpam-4511	199	24	.	.	PUNCT
ejpam-4511	199	25	proposition	proposition	NOUN
ejpam-4511	199	26	1	1	NUM
ejpam-4511	199	27	.	.	PUNCT
ejpam-4511	200	1	for	for	ADP
ejpam-4511	200	2	any	any	DET
ejpam-4511	200	3	positive	positive	ADJ
ejpam-4511	200	4	integer	integer	NOUN
ejpam-4511	200	5	n	n	PRON
ejpam-4511	200	6	≥	≥	NUM
ejpam-4511	200	7	2	2	NUM
ejpam-4511	200	8	,	,	PUNCT
ejpam-4511	200	9	γhgr(pn	γhgr(pn	ADJ
ejpam-4511	200	10	)	)	PUNCT
ejpam-4511	200	11	=	=	SYM
ejpam-4511	200	12	{	{	PUNCT
ejpam-4511	200	13	2	2	NUM
ejpam-4511	200	14	if	if	SCONJ
ejpam-4511	200	15	n	n	X
ejpam-4511	200	16	=	=	SYM
ejpam-4511	200	17	2	2	NUM
ejpam-4511	200	18	,	,	PUNCT
ejpam-4511	200	19	3	3	NUM
ejpam-4511	200	20	n−	n−	NOUN
ejpam-4511	200	21	2	2	NUM
ejpam-4511	200	22	if	if	SCONJ
ejpam-4511	200	23	n	n	PRON
ejpam-4511	200	24	≥	≥	NOUN
ejpam-4511	200	25	4	4	NUM
ejpam-4511	200	26	.	.	PUNCT
ejpam-4511	201	1	proof	proof	NOUN
ejpam-4511	201	2	.	.	PUNCT
ejpam-4511	202	1	let	let	VERB
ejpam-4511	202	2	g	g	NOUN
ejpam-4511	202	3	=	=	PUNCT
ejpam-4511	202	4	pn	pn	PROPN
ejpam-4511	202	5	=	=	PUNCT
ejpam-4511	203	1	[	[	X
ejpam-4511	203	2	v1	v1	NOUN
ejpam-4511	203	3	,	,	PUNCT
ejpam-4511	203	4	v2	v2	PROPN
ejpam-4511	203	5	,	,	PUNCT
ejpam-4511	203	6	·	·	PUNCT
ejpam-4511	203	7	·	·	PUNCT
ejpam-4511	203	8	·	·	PUNCT
ejpam-4511	203	9	,	,	PUNCT
ejpam-4511	203	10	vn	vn	X
ejpam-4511	203	11	]	]	PUNCT
ejpam-4511	203	12	.	.	PUNCT
ejpam-4511	204	1	clearly	clearly	ADV
ejpam-4511	204	2	,	,	PUNCT
ejpam-4511	204	3	γhgr(pn	γhgr(pn	ADJ
ejpam-4511	204	4	)	)	PUNCT
ejpam-4511	204	5	=	=	SYM
ejpam-4511	204	6	2	2	NUM
ejpam-4511	204	7	for	for	ADP
ejpam-4511	204	8	n	n	NOUN
ejpam-4511	204	9	=	=	SYM
ejpam-4511	204	10	2	2	NUM
ejpam-4511	204	11	,	,	PUNCT
ejpam-4511	204	12	3	3	NUM
ejpam-4511	204	13	.	.	PUNCT
ejpam-4511	205	1	so	so	ADV
ejpam-4511	205	2	suppose	suppose	VERB
ejpam-4511	205	3	that	that	SCONJ
ejpam-4511	205	4	n	n	PROPN
ejpam-4511	205	5	≥	≥	NUM
ejpam-4511	205	6	4	4	NUM
ejpam-4511	205	7	.	.	PUNCT
ejpam-4511	206	1	let	let	VERB
ejpam-4511	206	2	s′	s′	ADJ
ejpam-4511	206	3	=	=	SYM
ejpam-4511	206	4	(	(	PUNCT
ejpam-4511	206	5	v1	v1	PROPN
ejpam-4511	206	6	,	,	PUNCT
ejpam-4511	206	7	·	·	PUNCT
ejpam-4511	206	8	·	·	PUNCT
ejpam-4511	206	9	·	·	PUNCT
ejpam-4511	206	10	,	,	PUNCT
ejpam-4511	206	11	vn−2	vn−2	PROPN
ejpam-4511	206	12	)	)	PUNCT
ejpam-4511	206	13	.	.	PUNCT
ejpam-4511	207	1	clearly	clearly	ADV
ejpam-4511	207	2	,	,	PUNCT
ejpam-4511	207	3	s′	s′	PROPN
ejpam-4511	207	4	is	be	AUX
ejpam-4511	207	5	a	a	DET
ejpam-4511	207	6	grundy	grundy	PROPN
ejpam-4511	207	7	hop	hop	NOUN
ejpam-4511	207	8	dominating	dominating	NOUN
ejpam-4511	207	9	sequence	sequence	NOUN
ejpam-4511	207	10	in	in	ADP
ejpam-4511	207	11	g.	g.	PROPN
ejpam-4511	207	12	since	since	SCONJ
ejpam-4511	207	13	g	g	PROPN
ejpam-4511	207	14	is	be	AUX
ejpam-4511	207	15	not	not	PART
ejpam-4511	207	16	a	a	DET
ejpam-4511	207	17	complete	complete	ADJ
ejpam-4511	207	18	graph	graph	NOUN
ejpam-4511	207	19	,	,	PUNCT
ejpam-4511	207	20	γhgr(g	γhgr(g	NOUN
ejpam-4511	207	21	)	)	PUNCT
ejpam-4511	207	22	≤	≤	NOUN
ejpam-4511	208	1	n	n	CCONJ
ejpam-4511	208	2	−	−	PROPN
ejpam-4511	208	3	1	1	NUM
ejpam-4511	208	4	by	by	ADP
ejpam-4511	208	5	corollary	corollary	ADJ
ejpam-4511	208	6	2(ii	2(ii	NUM
ejpam-4511	208	7	)	)	PUNCT
ejpam-4511	208	8	.	.	PUNCT
ejpam-4511	209	1	thus	thus	ADV
ejpam-4511	209	2	,	,	PUNCT
ejpam-4511	209	3	n	n	CCONJ
ejpam-4511	209	4	−	−	PROPN
ejpam-4511	209	5	2	2	NUM
ejpam-4511	209	6	≤	≤	NOUN
ejpam-4511	209	7	γhgr(g	γhgr(g	PROPN
ejpam-4511	209	8	)	)	PUNCT
ejpam-4511	209	9	≤	≤	NOUN
ejpam-4511	209	10	n	n	CCONJ
ejpam-4511	209	11	−	−	PROPN
ejpam-4511	209	12	1	1	NUM
ejpam-4511	209	13	.	.	PUNCT
ejpam-4511	209	14	suppose	suppose	VERB
ejpam-4511	209	15	γhgr(g	γhgr(g	ADP
ejpam-4511	209	16	)	)	PUNCT
ejpam-4511	209	17	=	=	SYM
ejpam-4511	209	18	n	n	CCONJ
ejpam-4511	209	19	−	−	PROPN
ejpam-4511	209	20	1	1	NUM
ejpam-4511	209	21	,	,	PUNCT
ejpam-4511	209	22	say	say	VERB
ejpam-4511	209	23	,	,	PUNCT
ejpam-4511	209	24	s	s	PART
ejpam-4511	209	25	=	=	PUNCT
ejpam-4511	209	26	(	(	PUNCT
ejpam-4511	209	27	w1	w1	NOUN
ejpam-4511	209	28	,	,	PUNCT
ejpam-4511	209	29	·	·	PUNCT
ejpam-4511	209	30	·	·	PUNCT
ejpam-4511	209	31	·	·	PUNCT
ejpam-4511	209	32	,	,	PUNCT
ejpam-4511	209	33	wn−1	wn−1	PROPN
ejpam-4511	209	34	)	)	PUNCT
ejpam-4511	209	35	is	be	AUX
ejpam-4511	209	36	a	a	DET
ejpam-4511	209	37	grundy	grundy	PROPN
ejpam-4511	209	38	hop	hop	NOUN
ejpam-4511	209	39	dominating	dominating	NOUN
ejpam-4511	209	40	sequence	sequence	NOUN
ejpam-4511	209	41	.	.	PUNCT
ejpam-4511	210	1	then	then	ADV
ejpam-4511	210	2	n2	n2	PROPN
ejpam-4511	210	3	g[wn−1	g[wn−1	PROPN
ejpam-4511	210	4	]	]	PUNCT
ejpam-4511	210	5	\	\	PROPN
ejpam-4511	210	6	⋃n−2	⋃n−2	NOUN
ejpam-4511	210	7	j=1	j=1	PROPN
ejpam-4511	210	8	n	n	CCONJ
ejpam-4511	210	9	2	2	NUM
ejpam-4511	210	10	g[wj	g[wj	PROPN
ejpam-4511	210	11	]	]	PUNCT
ejpam-4511	211	1	̸=	̸=	PROPN
ejpam-4511	211	2	∅.	∅.	AUX
ejpam-4511	211	3	notice	notice	VERB
ejpam-4511	211	4	that	that	SCONJ
ejpam-4511	211	5	n2	n2	ADJ
ejpam-4511	211	6	g[wn−1	g[wn−1	PROPN
ejpam-4511	211	7	]	]	PUNCT
ejpam-4511	211	8	\	\	PROPN
ejpam-4511	211	9	⋃n−2	⋃n−2	NOUN
ejpam-4511	212	1	j=1	j=1	PROPN
ejpam-4511	212	2	n	n	CCONJ
ejpam-4511	212	3	2	2	NUM
ejpam-4511	212	4	g[wj	g[wj	PROPN
ejpam-4511	212	5	]	]	PUNCT
ejpam-4511	212	6	⊆	⊆	NUM
ejpam-4511	212	7	{	{	PUNCT
ejpam-4511	212	8	wn−1	wn−1	PROPN
ejpam-4511	212	9	,	,	PUNCT
ejpam-4511	212	10	vr	vr	NOUN
ejpam-4511	212	11	}	}	PUNCT
ejpam-4511	212	12	for	for	ADP
ejpam-4511	212	13	some	some	DET
ejpam-4511	212	14	r	r	NOUN
ejpam-4511	212	15	∈	∈	PROPN
ejpam-4511	212	16	{	{	PUNCT
ejpam-4511	212	17	1	1	NUM
ejpam-4511	212	18	,	,	PUNCT
ejpam-4511	212	19	.	.	PUNCT
ejpam-4511	212	20	.	.	PUNCT
ejpam-4511	212	21	.	.	PUNCT
ejpam-4511	212	22	,	,	PUNCT
ejpam-4511	212	23	n	n	CCONJ
ejpam-4511	212	24	}	}	PUNCT
ejpam-4511	212	25	,	,	PUNCT
ejpam-4511	212	26	vr	vr	PROPN
ejpam-4511	212	27	̸=	̸=	PROPN
ejpam-4511	212	28	wn−1	wn−1	PROPN
ejpam-4511	212	29	.	.	PUNCT
ejpam-4511	213	1	consider	consider	VERB
ejpam-4511	213	2	the	the	DET
ejpam-4511	213	3	following	follow	VERB
ejpam-4511	213	4	two	two	NUM
ejpam-4511	213	5	cases	case	NOUN
ejpam-4511	213	6	:	:	PUNCT
ejpam-4511	213	7	case	case	NOUN
ejpam-4511	213	8	1	1	NUM
ejpam-4511	213	9	:	:	PUNCT
ejpam-4511	213	10	n2	n2	PROPN
ejpam-4511	213	11	g[wn−1	g[wn−1	PROPN
ejpam-4511	213	12	]	]	PUNCT
ejpam-4511	213	13	\	\	PROPN
ejpam-4511	213	14	⋃n−2	⋃n−2	NOUN
ejpam-4511	214	1	j=1	j=1	PROPN
ejpam-4511	214	2	n	n	CCONJ
ejpam-4511	214	3	2	2	NUM
ejpam-4511	214	4	g[wj	g[wj	PROPN
ejpam-4511	214	5	]	]	PUNCT
ejpam-4511	214	6	=	=	PUNCT
ejpam-4511	214	7	{	{	PUNCT
ejpam-4511	214	8	wn−1	wn−1	PROPN
ejpam-4511	214	9	,	,	PUNCT
ejpam-4511	214	10	vr	vr	NOUN
ejpam-4511	214	11	}	}	PUNCT
ejpam-4511	214	12	for	for	ADP
ejpam-4511	214	13	some	some	DET
ejpam-4511	214	14	vr	vr	PROPN
ejpam-4511	214	15	∈	∈	PROPN
ejpam-4511	214	16	v	v	ADP
ejpam-4511	214	17	(	(	PUNCT
ejpam-4511	214	18	g	g	NOUN
ejpam-4511	214	19	)	)	PUNCT
ejpam-4511	214	20	\	\	NOUN
ejpam-4511	214	21	{	{	PUNCT
ejpam-4511	214	22	w1	w1	NOUN
ejpam-4511	214	23	,	,	PUNCT
ejpam-4511	214	24	.	.	PUNCT
ejpam-4511	214	25	.	.	PUNCT
ejpam-4511	214	26	.	.	PUNCT
ejpam-4511	215	1	,	,	PUNCT
ejpam-4511	215	2	wn−1	wn−1	PROPN
ejpam-4511	215	3	}	}	PUNCT
ejpam-4511	215	4	.	.	PUNCT
ejpam-4511	216	1	let	let	VERB
ejpam-4511	216	2	wn−1	wn−1	PROPN
ejpam-4511	216	3	=	=	SYM
ejpam-4511	216	4	vq	vq	PROPN
ejpam-4511	216	5	.	.	PROPN
ejpam-4511	217	1	then	then	ADV
ejpam-4511	217	2	vq	vq	PROPN
ejpam-4511	217	3	and	and	CCONJ
ejpam-4511	217	4	vr	vr	PROPN
ejpam-4511	217	5	are	be	AUX
ejpam-4511	217	6	not	not	PART
ejpam-4511	217	7	hop	hop	ADV
ejpam-4511	217	8	dominated	dominate	VERB
ejpam-4511	217	9	by	by	ADP
ejpam-4511	217	10	each	each	DET
ejpam-4511	217	11	wj	wj	PROPN
ejpam-4511	217	12	,	,	PUNCT
ejpam-4511	217	13	where	where	SCONJ
ejpam-4511	217	14	j	j	PROPN
ejpam-4511	217	15	∈	∈	PROPN
ejpam-4511	217	16	{	{	PUNCT
ejpam-4511	217	17	1	1	NUM
ejpam-4511	217	18	,	,	PUNCT
ejpam-4511	217	19	2	2	NUM
ejpam-4511	217	20	,	,	PUNCT
ejpam-4511	217	21	.	.	PUNCT
ejpam-4511	217	22	.	.	PUNCT
ejpam-4511	218	1	.	.	PUNCT
ejpam-4511	219	1	,	,	PUNCT
ejpam-4511	220	1	n	n	CCONJ
ejpam-4511	220	2	−	−	PROPN
ejpam-4511	220	3	2	2	NUM
ejpam-4511	220	4	}	}	PUNCT
ejpam-4511	220	5	.	.	PUNCT
ejpam-4511	221	1	if	if	SCONJ
ejpam-4511	221	2	q	q	X
ejpam-4511	221	3	<	<	X
ejpam-4511	221	4	r	r	NOUN
ejpam-4511	221	5	,	,	PUNCT
ejpam-4511	221	6	then	then	ADV
ejpam-4511	221	7	vq	vq	PROPN
ejpam-4511	221	8	is	be	AUX
ejpam-4511	221	9	v1	v1	NOUN
ejpam-4511	221	10	or	or	CCONJ
ejpam-4511	221	11	v2	v2	NOUN
ejpam-4511	221	12	.	.	PUNCT
ejpam-4511	222	1	if	if	SCONJ
ejpam-4511	222	2	vq	vq	PROPN
ejpam-4511	222	3	=	=	SYM
ejpam-4511	222	4	v1	v1	PROPN
ejpam-4511	222	5	,	,	PUNCT
ejpam-4511	222	6	then	then	ADV
ejpam-4511	222	7	vr	vr	PROPN
ejpam-4511	222	8	=	=	PROPN
ejpam-4511	222	9	v3	v3	PROPN
ejpam-4511	222	10	and	and	CCONJ
ejpam-4511	222	11	vn	vn	PROPN
ejpam-4511	222	12	=	=	PUNCT
ejpam-4511	222	13	v4	v4	PROPN
ejpam-4511	222	14	.	.	PUNCT
ejpam-4511	223	1	this	this	PRON
ejpam-4511	223	2	is	be	AUX
ejpam-4511	223	3	not	not	PART
ejpam-4511	223	4	possible	possible	ADJ
ejpam-4511	223	5	because	because	SCONJ
ejpam-4511	223	6	n2	n2	ADJ
ejpam-4511	223	7	g[v2	g[v2	NOUN
ejpam-4511	223	8	]	]	X
ejpam-4511	223	9	=	=	SYM
ejpam-4511	223	10	n2	n2	ADJ
ejpam-4511	223	11	g[v4	g[v4	NOUN
ejpam-4511	223	12	]	]	X
ejpam-4511	223	13	=	=	SYM
ejpam-4511	223	14	{	{	PUNCT
ejpam-4511	223	15	v2	v2	PROPN
ejpam-4511	223	16	,	,	PUNCT
ejpam-4511	223	17	v4	v4	NOUN
ejpam-4511	223	18	}	}	PUNCT
ejpam-4511	223	19	where	where	SCONJ
ejpam-4511	223	20	v2	v2	PROPN
ejpam-4511	223	21	,	,	PUNCT
ejpam-4511	223	22	v4	v4	NOUN
ejpam-4511	223	23	∈	∈	NOUN
ejpam-4511	223	24	ŝ.	ŝ.	NOUN
ejpam-4511	223	25	if	if	SCONJ
ejpam-4511	223	26	vq	vq	PROPN
ejpam-4511	223	27	=	=	SYM
ejpam-4511	223	28	v2	v2	PROPN
ejpam-4511	223	29	,	,	PUNCT
ejpam-4511	223	30	then	then	ADV
ejpam-4511	223	31	vr	vr	PROPN
ejpam-4511	223	32	=	=	SYM
ejpam-4511	223	33	v4	v4	PROPN
ejpam-4511	223	34	and	and	CCONJ
ejpam-4511	223	35	n	n	CCONJ
ejpam-4511	223	36	=	=	SYM
ejpam-4511	223	37	4	4	NUM
ejpam-4511	223	38	or	or	CCONJ
ejpam-4511	223	39	5	5	NUM
ejpam-4511	223	40	.	.	PUNCT
ejpam-4511	223	41	again	again	ADV
ejpam-4511	223	42	,	,	PUNCT
ejpam-4511	223	43	this	this	PRON
ejpam-4511	223	44	is	be	AUX
ejpam-4511	223	45	not	not	PART
ejpam-4511	223	46	possible	possible	ADJ
ejpam-4511	223	47	.	.	PUNCT
ejpam-4511	224	1	a	a	DET
ejpam-4511	224	2	similar	similar	ADJ
ejpam-4511	224	3	situation	situation	NOUN
ejpam-4511	224	4	happens	happen	VERB
ejpam-4511	224	5	when	when	SCONJ
ejpam-4511	224	6	q	q	X
ejpam-4511	224	7	>	>	X
ejpam-4511	224	8	r.	r.	PROPN
ejpam-4511	224	9	case	case	NOUN
ejpam-4511	224	10	2	2	NUM
ejpam-4511	224	11	:	:	PUNCT
ejpam-4511	224	12	n2	n2	ADJ
ejpam-4511	224	13	g[wn−1	g[wn−1	PROPN
ejpam-4511	224	14	]	]	PUNCT
ejpam-4511	224	15	\	\	PROPN
ejpam-4511	224	16	⋃n−2	⋃n−2	NOUN
ejpam-4511	224	17	j=1	j=1	PROPN
ejpam-4511	224	18	n	n	CCONJ
ejpam-4511	224	19	2	2	NUM
ejpam-4511	224	20	g[wj	g[wj	PROPN
ejpam-4511	224	21	]	]	PUNCT
ejpam-4511	225	1	=	=	PUNCT
ejpam-4511	225	2	{	{	PUNCT
ejpam-4511	225	3	wn−1	wn−1	PROPN
ejpam-4511	225	4	}	}	PUNCT
ejpam-4511	225	5	.	.	PUNCT
ejpam-4511	226	1	then	then	ADV
ejpam-4511	226	2	wn−1	wn−1	PROPN
ejpam-4511	226	3	is	be	AUX
ejpam-4511	226	4	not	not	PART
ejpam-4511	226	5	hop	hop	ADV
ejpam-4511	226	6	dominated	dominate	VERB
ejpam-4511	226	7	by	by	ADP
ejpam-4511	226	8	any	any	PRON
ejpam-4511	226	9	of	of	ADP
ejpam-4511	226	10	the	the	DET
ejpam-4511	226	11	vertices	vertex	NOUN
ejpam-4511	226	12	w1	w1	NOUN
ejpam-4511	226	13	,	,	PUNCT
ejpam-4511	226	14	·	·	PUNCT
ejpam-4511	226	15	·	·	PUNCT
ejpam-4511	226	16	·	·	PUNCT
ejpam-4511	226	17	,	,	PUNCT
ejpam-4511	226	18	wn−2	wn−2	PROPN
ejpam-4511	226	19	.	.	PUNCT
ejpam-4511	227	1	moreover	moreover	ADV
ejpam-4511	227	2	,	,	PUNCT
ejpam-4511	227	3	since	since	SCONJ
ejpam-4511	227	4	n	n	NUM
ejpam-4511	227	5	≥	≥	X
ejpam-4511	227	6	4	4	NUM
ejpam-4511	227	7	,	,	PUNCT
ejpam-4511	227	8	dg(wn−1	dg(wn−1	PROPN
ejpam-4511	227	9	,	,	PUNCT
ejpam-4511	227	10	vt	vt	NOUN
ejpam-4511	227	11	)	)	PUNCT
ejpam-4511	227	12	=	=	SYM
ejpam-4511	227	13	2	2	NUM
ejpam-4511	227	14	for	for	ADP
ejpam-4511	227	15	some	some	DET
ejpam-4511	227	16	vertex	vertex	NOUN
ejpam-4511	227	17	vt	vt	PROPN
ejpam-4511	227	18	∈	∈	PROPN
ejpam-4511	227	19	v	v	PROPN
ejpam-4511	227	20	(	(	PUNCT
ejpam-4511	227	21	g	g	NOUN
ejpam-4511	227	22	)	)	PUNCT
ejpam-4511	227	23	\	\	NOUN
ejpam-4511	227	24	ŝ.	ŝ.	NOUN
ejpam-4511	227	25	now	now	ADV
ejpam-4511	227	26	,	,	PUNCT
ejpam-4511	227	27	because	because	SCONJ
ejpam-4511	227	28	n2	n2	ADJ
ejpam-4511	227	29	g[wn−1	g[wn−1	PROPN
ejpam-4511	227	30	]	]	PUNCT
ejpam-4511	227	31	\⋃n−2	\⋃n−2	PROPN
ejpam-4511	227	32	j=1	j=1	PROPN
ejpam-4511	227	33	n	n	CCONJ
ejpam-4511	227	34	2	2	NUM
ejpam-4511	227	35	g[wj	g[wj	PROPN
ejpam-4511	227	36	]	]	PUNCT
ejpam-4511	227	37	=	=	PUNCT
ejpam-4511	227	38	{	{	PUNCT
ejpam-4511	227	39	wn−1	wn−1	PROPN
ejpam-4511	227	40	}	}	PUNCT
ejpam-4511	227	41	,	,	PUNCT
ejpam-4511	227	42	vt	vt	PROPN
ejpam-4511	227	43	must	must	AUX
ejpam-4511	227	44	be	be	AUX
ejpam-4511	227	45	hop	hop	NOUN
ejpam-4511	227	46	-	-	PUNCT
ejpam-4511	227	47	dominated	dominate	VERB
ejpam-4511	227	48	by	by	ADP
ejpam-4511	227	49	some	some	DET
ejpam-4511	227	50	vertex	vertex	NOUN
ejpam-4511	227	51	wj	wj	X
ejpam-4511	227	52	where	where	SCONJ
ejpam-4511	227	53	1	1	NUM
ejpam-4511	227	54	≤	≤	NUM
ejpam-4511	227	55	j	j	PROPN
ejpam-4511	227	56	≤	≤	PROPN
ejpam-4511	227	57	n−2	n−2	PROPN
ejpam-4511	227	58	.	.	PUNCT
ejpam-4511	228	1	this	this	PRON
ejpam-4511	228	2	is	be	AUX
ejpam-4511	228	3	not	not	PART
ejpam-4511	228	4	possible	possible	ADJ
ejpam-4511	228	5	when	when	SCONJ
ejpam-4511	228	6	n	n	X
ejpam-4511	228	7	=	=	SYM
ejpam-4511	228	8	4	4	NUM
ejpam-4511	228	9	,	,	PUNCT
ejpam-4511	228	10	and	and	CCONJ
ejpam-4511	228	11	so	so	ADV
ejpam-4511	228	12	n	n	PRON
ejpam-4511	228	13	≥	≥	NOUN
ejpam-4511	228	14	5	5	NUM
ejpam-4511	228	15	.	.	PUNCT
ejpam-4511	229	1	this	this	PRON
ejpam-4511	229	2	would	would	AUX
ejpam-4511	229	3	imply	imply	VERB
ejpam-4511	229	4	that	that	SCONJ
ejpam-4511	229	5	wn−1	wn−1	PROPN
ejpam-4511	229	6	is	be	AUX
ejpam-4511	229	7	either	either	CCONJ
ejpam-4511	229	8	v1	v1	NOUN
ejpam-4511	229	9	,	,	PUNCT
ejpam-4511	229	10	v2	v2	PROPN
ejpam-4511	229	11	,	,	PUNCT
ejpam-4511	229	12	vn−1	vn−1	ADJ
ejpam-4511	229	13	,	,	PUNCT
ejpam-4511	229	14	or	or	CCONJ
ejpam-4511	229	15	vn	vn	NOUN
ejpam-4511	229	16	.	.	PUNCT
ejpam-4511	230	1	it	it	PRON
ejpam-4511	230	2	is	be	AUX
ejpam-4511	230	3	routine	routine	ADJ
ejpam-4511	230	4	to	to	PART
ejpam-4511	230	5	show	show	VERB
ejpam-4511	230	6	that	that	SCONJ
ejpam-4511	230	7	any	any	PRON
ejpam-4511	230	8	of	of	ADP
ejpam-4511	230	9	these	these	DET
ejpam-4511	230	10	vertices	vertex	NOUN
ejpam-4511	230	11	will	will	AUX
ejpam-4511	230	12	contradict	contradict	VERB
ejpam-4511	230	13	the	the	DET
ejpam-4511	230	14	assumption	assumption	NOUN
ejpam-4511	230	15	that	that	SCONJ
ejpam-4511	230	16	s	s	VERB
ejpam-4511	230	17	is	be	AUX
ejpam-4511	230	18	a	a	DET
ejpam-4511	230	19	legal	legal	ADJ
ejpam-4511	230	20	closed	close	VERB
ejpam-4511	230	21	hop	hop	NOUN
ejpam-4511	230	22	neighborhood	neighborhood	NOUN
ejpam-4511	230	23	sequence	sequence	NOUN
ejpam-4511	230	24	.	.	PUNCT
ejpam-4511	231	1	therefore	therefore	ADV
ejpam-4511	231	2	,	,	PUNCT
ejpam-4511	231	3	γhgr(pn	γhgr(pn	ADJ
ejpam-4511	231	4	)	)	PUNCT
ejpam-4511	231	5	=	=	SYM
ejpam-4511	231	6	n−	n−	NOUN
ejpam-4511	231	7	2	2	NUM
ejpam-4511	232	1	when	when	SCONJ
ejpam-4511	232	2	n	n	X
ejpam-4511	232	3	≥	≥	X
ejpam-4511	232	4	4	4	NUM
ejpam-4511	232	5	.	.	PUNCT
ejpam-4511	232	6	lemma	lemma	PROPN
ejpam-4511	232	7	1	1	X
ejpam-4511	232	8	.	.	PUNCT
ejpam-4511	233	1	let	let	VERB
ejpam-4511	233	2	g	g	PRON
ejpam-4511	233	3	be	be	AUX
ejpam-4511	233	4	a	a	DET
ejpam-4511	233	5	graph	graph	NOUN
ejpam-4511	233	6	on	on	ADP
ejpam-4511	233	7	n	n	DET
ejpam-4511	233	8	vertices	vertex	NOUN
ejpam-4511	233	9	.	.	PUNCT
ejpam-4511	234	1	if	if	SCONJ
ejpam-4511	234	2	|n2	|n2	PROPN
ejpam-4511	234	3	g[v]|	g[v]|	PROPN
ejpam-4511	234	4	=	=	SYM
ejpam-4511	234	5	3	3	NUM
ejpam-4511	234	6	for	for	ADP
ejpam-4511	234	7	every	every	PRON
ejpam-4511	234	8	v	v	NUM
ejpam-4511	234	9	∈	∈	NOUN
ejpam-4511	234	10	v	v	NOUN
ejpam-4511	234	11	(	(	PUNCT
ejpam-4511	234	12	g	g	NOUN
ejpam-4511	234	13	)	)	PUNCT
ejpam-4511	234	14	,	,	PUNCT
ejpam-4511	234	15	then	then	ADV
ejpam-4511	234	16	γhgr(g	γhgr(g	X
ejpam-4511	234	17	)	)	PUNCT
ejpam-4511	234	18	≤	≤	NUM
ejpam-4511	234	19	n−	n−	NOUN
ejpam-4511	234	20	2	2	NUM
ejpam-4511	234	21	.	.	PUNCT
ejpam-4511	234	22	j.	j.	PROPN
ejpam-4511	234	23	hassan	hassan	PROPN
ejpam-4511	234	24	,	,	PUNCT
ejpam-4511	234	25	s.	s.	PROPN
ejpam-4511	234	26	canoy	canoy	PROPN
ejpam-4511	234	27	/	/	SYM
ejpam-4511	234	28	eur	eur	PROPN
ejpam-4511	234	29	.	.	PUNCT
ejpam-4511	235	1	j.	j.	PROPN
ejpam-4511	235	2	pure	pure	PROPN
ejpam-4511	235	3	appl	appl	PROPN
ejpam-4511	235	4	.	.	PROPN
ejpam-4511	235	5	math	math	PROPN
ejpam-4511	235	6	,	,	PUNCT
ejpam-4511	235	7	15	15	NUM
ejpam-4511	235	8	(	(	PUNCT
ejpam-4511	235	9	4	4	NUM
ejpam-4511	235	10	)	)	PUNCT
ejpam-4511	235	11	(	(	PUNCT
ejpam-4511	235	12	2022	2022	NUM
ejpam-4511	235	13	)	)	PUNCT
ejpam-4511	235	14	,	,	PUNCT
ejpam-4511	235	15	1623	1623	NUM
ejpam-4511	235	16	-	-	SYM
ejpam-4511	235	17	1636	1636	NUM
ejpam-4511	235	18	1630	1630	NUM
ejpam-4511	235	19	proof	proof	NOUN
ejpam-4511	235	20	.	.	PUNCT
ejpam-4511	235	21	suppose	suppose	VERB
ejpam-4511	235	22	that	that	SCONJ
ejpam-4511	235	23	|n2	|n2	PROPN
ejpam-4511	235	24	g[v]|	g[v]|	PROPN
ejpam-4511	235	25	=	=	SYM
ejpam-4511	235	26	3	3	NUM
ejpam-4511	235	27	for	for	ADP
ejpam-4511	235	28	every	every	DET
ejpam-4511	235	29	v	v	NUM
ejpam-4511	235	30	∈	∈	NOUN
ejpam-4511	235	31	v	v	NOUN
ejpam-4511	235	32	(	(	PUNCT
ejpam-4511	235	33	g	g	NOUN
ejpam-4511	235	34	)	)	PUNCT
ejpam-4511	235	35	.	.	PUNCT
ejpam-4511	236	1	then	then	ADV
ejpam-4511	236	2	g	g	PROPN
ejpam-4511	236	3	̸=	̸=	PROPN
ejpam-4511	236	4	kn	kn	PROPN
ejpam-4511	236	5	.	.	PUNCT
ejpam-4511	237	1	thus	thus	ADV
ejpam-4511	237	2	,	,	PUNCT
ejpam-4511	237	3	γhgr(g	γhgr(g	NOUN
ejpam-4511	237	4	)	)	PUNCT
ejpam-4511	237	5	≤	≤	NUM
ejpam-4511	237	6	n−	n−	NOUN
ejpam-4511	237	7	1	1	NUM
ejpam-4511	237	8	.	.	PUNCT
ejpam-4511	237	9	suppose	suppose	VERB
ejpam-4511	237	10	that	that	SCONJ
ejpam-4511	237	11	γhgr(g	γhgr(g	NOUN
ejpam-4511	237	12	)	)	PUNCT
ejpam-4511	238	1	=	=	VERB
ejpam-4511	238	2	n−	n−	NOUN
ejpam-4511	238	3	1	1	NUM
ejpam-4511	238	4	,	,	PUNCT
ejpam-4511	238	5	say	say	VERB
ejpam-4511	238	6	,	,	PUNCT
ejpam-4511	238	7	s	s	PART
ejpam-4511	238	8	=	=	PUNCT
ejpam-4511	238	9	(	(	PUNCT
ejpam-4511	238	10	v1	v1	PROPN
ejpam-4511	238	11	,	,	PUNCT
ejpam-4511	238	12	·	·	PUNCT
ejpam-4511	238	13	·	·	PUNCT
ejpam-4511	238	14	·	·	PUNCT
ejpam-4511	238	15	,	,	PUNCT
ejpam-4511	238	16	vn−1	vn−1	PROPN
ejpam-4511	238	17	)	)	PUNCT
ejpam-4511	238	18	is	be	AUX
ejpam-4511	238	19	a	a	DET
ejpam-4511	238	20	grundy	grundy	PROPN
ejpam-4511	238	21	hop	hop	NOUN
ejpam-4511	238	22	dominating	dominating	NOUN
ejpam-4511	238	23	sequence	sequence	NOUN
ejpam-4511	238	24	of	of	ADP
ejpam-4511	238	25	g.	g.	PROPN
ejpam-4511	238	26	then	then	ADV
ejpam-4511	238	27	n2	n2	PROPN
ejpam-4511	238	28	g[vi	g[vi	PROPN
ejpam-4511	238	29	]	]	PUNCT
ejpam-4511	238	30	\	\	PROPN
ejpam-4511	238	31	⋃i−1	⋃i−1	NOUN
ejpam-4511	238	32	j=1n	j=1n	PROPN
ejpam-4511	238	33	2	2	NUM
ejpam-4511	238	34	g[vj	g[vj	PROPN
ejpam-4511	238	35	]	]	PUNCT
ejpam-4511	238	36	̸=	̸=	PROPN
ejpam-4511	238	37	∅	∅	NOUN
ejpam-4511	238	38	for	for	ADP
ejpam-4511	238	39	each	each	DET
ejpam-4511	238	40	i	i	PRON
ejpam-4511	238	41	∈	∈	PROPN
ejpam-4511	238	42	{	{	PUNCT
ejpam-4511	238	43	2	2	NUM
ejpam-4511	238	44	,	,	PUNCT
ejpam-4511	238	45	.	.	PUNCT
ejpam-4511	238	46	.	.	PUNCT
ejpam-4511	239	1	.	.	PUNCT
ejpam-4511	240	1	,	,	PUNCT
ejpam-4511	240	2	n	n	CCONJ
ejpam-4511	240	3	−	−	PROPN
ejpam-4511	240	4	1	1	NUM
ejpam-4511	240	5	}	}	PUNCT
ejpam-4511	240	6	.	.	PUNCT
ejpam-4511	241	1	let	let	VERB
ejpam-4511	241	2	p	p	PRON
ejpam-4511	241	3	,	,	PUNCT
ejpam-4511	241	4	q	q	PROPN
ejpam-4511	241	5	∈	∈	PROPN
ejpam-4511	241	6	n2	n2	NOUN
ejpam-4511	241	7	g(vn−1	g(vn−1	PROPN
ejpam-4511	241	8	)	)	PUNCT
ejpam-4511	241	9	.	.	PUNCT
ejpam-4511	242	1	since	since	SCONJ
ejpam-4511	242	2	n	n	ADV
ejpam-4511	242	3	2	2	NUM
ejpam-4511	242	4	g[vn−1]\	g[vn−1]\	NUM
ejpam-4511	242	5	⋃n−2	⋃n−2	NOUN
ejpam-4511	242	6	j=1	j=1	PROPN
ejpam-4511	242	7	n	n	CCONJ
ejpam-4511	242	8	2	2	NUM
ejpam-4511	242	9	g[vj	g[vj	PROPN
ejpam-4511	242	10	]	]	PUNCT
ejpam-4511	242	11	̸=	̸=	PROPN
ejpam-4511	242	12	∅	∅	NOUN
ejpam-4511	242	13	,	,	PUNCT
ejpam-4511	242	14	p	p	NOUN
ejpam-4511	242	15	/∈	/∈	PUNCT
ejpam-4511	242	16	s	s	NOUN
ejpam-4511	242	17	or	or	CCONJ
ejpam-4511	242	18	q	q	NOUN
ejpam-4511	242	19	/∈	/∈	PUNCT
ejpam-4511	243	1	s	s	X
ejpam-4511	243	2	,	,	PUNCT
ejpam-4511	243	3	say	say	VERB
ejpam-4511	243	4	p	p	PROPN
ejpam-4511	243	5	/∈	/∈	PUNCT
ejpam-4511	243	6	s.	s.	PROPN
ejpam-4511	244	1	then	then	ADV
ejpam-4511	244	2	q	q	X
ejpam-4511	244	3	=	=	NOUN
ejpam-4511	244	4	vk	vk	ADP
ejpam-4511	244	5	∈	∈	PROPN
ejpam-4511	244	6	ŝ	ŝ	NOUN
ejpam-4511	244	7	for	for	ADP
ejpam-4511	244	8	some	some	DET
ejpam-4511	244	9	k	k	PROPN
ejpam-4511	244	10	̸=	̸=	PROPN
ejpam-4511	244	11	n−	n−	NOUN
ejpam-4511	244	12	1	1	NUM
ejpam-4511	244	13	and	and	CCONJ
ejpam-4511	244	14	vk	vk	PROPN
ejpam-4511	244	15	,	,	PUNCT
ejpam-4511	244	16	vn−1	vn−1	PROPN
ejpam-4511	244	17	∈	∈	PROPN
ejpam-4511	244	18	n2	n2	PROPN
ejpam-4511	244	19	g[vk	g[vk	PROPN
ejpam-4511	244	20	]	]	PUNCT
ejpam-4511	244	21	.	.	PUNCT
ejpam-4511	245	1	now	now	ADV
ejpam-4511	245	2	,	,	PUNCT
ejpam-4511	245	3	since	since	SCONJ
ejpam-4511	245	4	|n2	|n2	PROPN
ejpam-4511	245	5	g[p]|	g[p]|	PROPN
ejpam-4511	245	6	=	=	PUNCT
ejpam-4511	246	1	3	3	NUM
ejpam-4511	246	2	,	,	PUNCT
ejpam-4511	246	3	there	there	PRON
ejpam-4511	246	4	exists	exist	VERB
ejpam-4511	246	5	j	j	PROPN
ejpam-4511	246	6	̸=	̸=	PROPN
ejpam-4511	246	7	n−	n−	NOUN
ejpam-4511	246	8	1	1	NUM
ejpam-4511	246	9	such	such	ADJ
ejpam-4511	246	10	that	that	SCONJ
ejpam-4511	246	11	p	p	PROPN
ejpam-4511	246	12	∈	∈	PROPN
ejpam-4511	246	13	n2(vj	n2(vj	PROPN
ejpam-4511	246	14	)	)	PUNCT
ejpam-4511	246	15	.	.	PUNCT
ejpam-4511	247	1	it	it	PRON
ejpam-4511	247	2	follows	follow	VERB
ejpam-4511	247	3	that	that	SCONJ
ejpam-4511	247	4	vk	vk	VERB
ejpam-4511	247	5	,	,	PUNCT
ejpam-4511	247	6	p	p	X
ejpam-4511	247	7	,	,	PUNCT
ejpam-4511	247	8	vn−1	vn−1	PROPN
ejpam-4511	247	9	∈	∈	PROPN
ejpam-4511	247	10	n2	n2	PROPN
ejpam-4511	247	11	g[vk	g[vk	PROPN
ejpam-4511	247	12	]	]	PUNCT
ejpam-4511	247	13	∪	∪	ADP
ejpam-4511	247	14	n2	n2	PROPN
ejpam-4511	247	15	g[vj	g[vj	PROPN
ejpam-4511	247	16	]	]	PUNCT
ejpam-4511	247	17	,	,	PUNCT
ejpam-4511	247	18	a	a	DET
ejpam-4511	247	19	contradiction	contradiction	NOUN
ejpam-4511	247	20	.	.	PUNCT
ejpam-4511	248	1	therefore	therefore	ADV
ejpam-4511	248	2	,	,	PUNCT
ejpam-4511	248	3	γhgr(g	γhgr(g	NOUN
ejpam-4511	248	4	)	)	PUNCT
ejpam-4511	248	5	≤	≤	NUM
ejpam-4511	248	6	n−	n−	NOUN
ejpam-4511	248	7	2	2	NUM
ejpam-4511	248	8	.	.	PUNCT
ejpam-4511	249	1	the	the	DET
ejpam-4511	249	2	next	next	ADJ
ejpam-4511	249	3	result	result	NOUN
ejpam-4511	249	4	shows	show	VERB
ejpam-4511	249	5	that	that	SCONJ
ejpam-4511	249	6	the	the	DET
ejpam-4511	249	7	bound	bind	VERB
ejpam-4511	249	8	in	in	ADP
ejpam-4511	249	9	lemma	lemma	PROPN
ejpam-4511	249	10	1	1	NUM
ejpam-4511	249	11	is	be	AUX
ejpam-4511	249	12	tight	tight	ADJ
ejpam-4511	249	13	.	.	PUNCT
ejpam-4511	250	1	proposition	proposition	NOUN
ejpam-4511	250	2	2	2	NUM
ejpam-4511	250	3	.	.	X
ejpam-4511	251	1	for	for	ADP
ejpam-4511	251	2	any	any	DET
ejpam-4511	251	3	positive	positive	ADJ
ejpam-4511	251	4	integer	integer	NOUN
ejpam-4511	251	5	n	n	PRON
ejpam-4511	251	6	≥	≥	NOUN
ejpam-4511	251	7	3	3	NUM
ejpam-4511	251	8	,	,	PUNCT
ejpam-4511	251	9	γhgr(cn	γhgr(cn	NOUN
ejpam-4511	251	10	)	)	PUNCT
ejpam-4511	251	11	=	=	PUNCT
ejpam-4511	251	12			NOUN
ejpam-4511	251	13	3	3	NUM
ejpam-4511	251	14	if	if	SCONJ
ejpam-4511	251	15	n	n	NOUN
ejpam-4511	251	16	=	=	SYM
ejpam-4511	251	17	3	3	NUM
ejpam-4511	251	18	2	2	NUM
ejpam-4511	251	19	if	if	SCONJ
ejpam-4511	251	20	n	n	NOUN
ejpam-4511	251	21	=	=	SYM
ejpam-4511	251	22	4	4	NUM
ejpam-4511	251	23	n−	n−	NOUN
ejpam-4511	251	24	4	4	NUM
ejpam-4511	251	25	if	if	SCONJ
ejpam-4511	251	26	n	n	PRON
ejpam-4511	251	27	≥	≥	NOUN
ejpam-4511	251	28	6	6	NUM
ejpam-4511	251	29	and	and	CCONJ
ejpam-4511	251	30	even	even	ADV
ejpam-4511	251	31	n−	n−	PROPN
ejpam-4511	251	32	2	2	NUM
ejpam-4511	251	33	if	if	SCONJ
ejpam-4511	251	34	n	n	PRON
ejpam-4511	251	35	≥	≥	NOUN
ejpam-4511	251	36	5	5	NUM
ejpam-4511	251	37	and	and	CCONJ
ejpam-4511	251	38	odd	odd	ADJ
ejpam-4511	251	39	.	.	PUNCT
ejpam-4511	252	1	proof	proof	NOUN
ejpam-4511	252	2	.	.	PUNCT
ejpam-4511	253	1	let	let	VERB
ejpam-4511	253	2	g	g	NOUN
ejpam-4511	253	3	=	=	PUNCT
ejpam-4511	253	4	cn	cn	PROPN
ejpam-4511	253	5	=	=	PUNCT
ejpam-4511	254	1	[	[	X
ejpam-4511	254	2	v1	v1	NOUN
ejpam-4511	254	3	,	,	PUNCT
ejpam-4511	254	4	v2	v2	PROPN
ejpam-4511	254	5	,	,	PUNCT
ejpam-4511	254	6	·	·	PUNCT
ejpam-4511	254	7	·	·	PUNCT
ejpam-4511	254	8	·	·	PUNCT
ejpam-4511	254	9	,	,	PUNCT
ejpam-4511	254	10	vn	vn	X
ejpam-4511	254	11	,	,	PUNCT
ejpam-4511	254	12	v1	v1	PROPN
ejpam-4511	254	13	]	]	PUNCT
ejpam-4511	254	14	.	.	PUNCT
ejpam-4511	255	1	clearly	clearly	ADV
ejpam-4511	255	2	,	,	PUNCT
ejpam-4511	255	3	γhgr(c3	γhgr(c3	NOUN
ejpam-4511	255	4	)	)	PUNCT
ejpam-4511	256	1	=	=	SYM
ejpam-4511	256	2	3	3	NUM
ejpam-4511	256	3	and	and	CCONJ
ejpam-4511	256	4	γhgr(c4	γhgr(c4	NOUN
ejpam-4511	256	5	)	)	PUNCT
ejpam-4511	257	1	=	=	SYM
ejpam-4511	258	1	2	2	X
ejpam-4511	258	2	.	.	X
ejpam-4511	258	3	let	let	VERB
ejpam-4511	258	4	n	n	PRON
ejpam-4511	258	5	≥	≥	NOUN
ejpam-4511	258	6	6	6	NUM
ejpam-4511	258	7	.	.	PUNCT
ejpam-4511	259	1	let	let	VERB
ejpam-4511	259	2	s0	s0	PROPN
ejpam-4511	259	3	=	=	SYM
ejpam-4511	259	4	(	(	PUNCT
ejpam-4511	259	5	v1	v1	PROPN
ejpam-4511	259	6	,	,	PUNCT
ejpam-4511	259	7	v2	v2	PROPN
ejpam-4511	259	8	,	,	PUNCT
ejpam-4511	259	9	·	·	PUNCT
ejpam-4511	259	10	·	·	PUNCT
ejpam-4511	259	11	·	·	PUNCT
ejpam-4511	259	12	,	,	PUNCT
ejpam-4511	259	13	vn−4	vn−4	NOUN
ejpam-4511	259	14	)	)	PUNCT
ejpam-4511	259	15	.	.	PUNCT
ejpam-4511	260	1	then	then	ADV
ejpam-4511	260	2	n2	n2	PROPN
ejpam-4511	260	3	g[v2	g[v2	PROPN
ejpam-4511	260	4	]	]	PUNCT
ejpam-4511	260	5	\	\	PROPN
ejpam-4511	260	6	n2	n2	PROPN
ejpam-4511	260	7	g[v1	g[v1	PROPN
ejpam-4511	260	8	]	]	X
ejpam-4511	260	9	=	=	PRON
ejpam-4511	260	10	{	{	PUNCT
ejpam-4511	260	11	v2	v2	PROPN
ejpam-4511	260	12	,	,	PUNCT
ejpam-4511	260	13	v4	v4	NOUN
ejpam-4511	260	14	,	,	PUNCT
ejpam-4511	260	15	vn	vn	PROPN
ejpam-4511	260	16	}	}	PUNCT
ejpam-4511	260	17	̸=	̸=	PROPN
ejpam-4511	260	18	∅	∅	NOUN
ejpam-4511	260	19	and	and	CCONJ
ejpam-4511	260	20	vi+2	vi+2	NUM
ejpam-4511	260	21	∈	∈	PROPN
ejpam-4511	260	22	n2	n2	PROPN
ejpam-4511	260	23	g[vi	g[vi	PROPN
ejpam-4511	260	24	]	]	PUNCT
ejpam-4511	260	25	\∪	\∪	PUNCT
ejpam-4511	260	26	i−1	i−1	PROPN
ejpam-4511	260	27	j=1n	j=1n	VERB
ejpam-4511	260	28	2	2	NUM
ejpam-4511	260	29	g[vj	g[vj	PROPN
ejpam-4511	260	30	]	]	PUNCT
ejpam-4511	260	31	for	for	ADP
ejpam-4511	260	32	all	all	PRON
ejpam-4511	260	33	i	i	PRON
ejpam-4511	260	34	∈	∈	PROPN
ejpam-4511	260	35	{	{	PUNCT
ejpam-4511	260	36	3	3	NUM
ejpam-4511	260	37	,	,	PUNCT
ejpam-4511	260	38	4	4	NUM
ejpam-4511	260	39	,	,	PUNCT
ejpam-4511	260	40	·	·	PUNCT
ejpam-4511	260	41	·	·	PUNCT
ejpam-4511	260	42	·	·	PUNCT
ejpam-4511	260	43	,	,	PUNCT
ejpam-4511	260	44	n−	n−	NOUN
ejpam-4511	260	45	4	4	NUM
ejpam-4511	260	46	}	}	PUNCT
ejpam-4511	260	47	.	.	PUNCT
ejpam-4511	261	1	it	it	PRON
ejpam-4511	261	2	follows	follow	VERB
ejpam-4511	261	3	that	that	SCONJ
ejpam-4511	261	4	s0	s0	PROPN
ejpam-4511	261	5	is	be	AUX
ejpam-4511	261	6	a	a	DET
ejpam-4511	261	7	grundy	grundy	PROPN
ejpam-4511	261	8	hop	hop	NOUN
ejpam-4511	261	9	dominating	dominating	NOUN
ejpam-4511	261	10	sequence	sequence	NOUN
ejpam-4511	261	11	and	and	CCONJ
ejpam-4511	261	12	γhgr(cn	γhgr(cn	NOUN
ejpam-4511	261	13	)	)	PUNCT
ejpam-4511	261	14	≥	≥	NOUN
ejpam-4511	261	15	|ŝ0|	|ŝ0|	NOUN
ejpam-4511	261	16	=	=	PUNCT
ejpam-4511	261	17	n	n	CCONJ
ejpam-4511	261	18	−	−	PROPN
ejpam-4511	261	19	4	4	NUM
ejpam-4511	261	20	.	.	PUNCT
ejpam-4511	261	21	suppose	suppose	VERB
ejpam-4511	261	22	that	that	SCONJ
ejpam-4511	261	23	n	n	PRON
ejpam-4511	261	24	is	be	AUX
ejpam-4511	261	25	even	even	ADV
ejpam-4511	261	26	and	and	CCONJ
ejpam-4511	261	27	suppose	suppose	VERB
ejpam-4511	261	28	that	that	SCONJ
ejpam-4511	261	29	s	s	VERB
ejpam-4511	261	30	is	be	AUX
ejpam-4511	261	31	a	a	DET
ejpam-4511	261	32	grundy	grundy	PROPN
ejpam-4511	261	33	hop	hop	NOUN
ejpam-4511	261	34	dominating	dominating	NOUN
ejpam-4511	261	35	sequence	sequence	NOUN
ejpam-4511	261	36	of	of	ADP
ejpam-4511	261	37	cn	cn	PROPN
ejpam-4511	261	38	with	with	ADP
ejpam-4511	261	39	γhgr(cn	γhgr(cn	NOUN
ejpam-4511	261	40	)	)	PUNCT
ejpam-4511	261	41	=	=	PUNCT
ejpam-4511	262	1	|ŝ|	|ŝ|	PROPN
ejpam-4511	262	2	.	.	X
ejpam-4511	262	3	observe	observe	VERB
ejpam-4511	262	4	that	that	SCONJ
ejpam-4511	262	5	if	if	SCONJ
ejpam-4511	262	6	i	i	PRON
ejpam-4511	262	7	is	be	AUX
ejpam-4511	262	8	even	even	ADV
ejpam-4511	262	9	and	and	CCONJ
ejpam-4511	262	10	j	j	PROPN
ejpam-4511	262	11	is	be	AUX
ejpam-4511	262	12	odd	odd	ADJ
ejpam-4511	262	13	,	,	PUNCT
ejpam-4511	262	14	then	then	ADV
ejpam-4511	262	15	n2	n2	PROPN
ejpam-4511	262	16	g[vi]∩n2	g[vi]∩n2	PROPN
ejpam-4511	262	17	g[vj	g[vj	PROPN
ejpam-4511	262	18	]	]	X
ejpam-4511	262	19	=	=	PUNCT
ejpam-4511	262	20	∅.	∅.	VERB
ejpam-4511	262	21	hence	hence	ADV
ejpam-4511	262	22	,	,	PUNCT
ejpam-4511	262	23	we	we	PRON
ejpam-4511	262	24	may	may	AUX
ejpam-4511	262	25	express	express	VERB
ejpam-4511	262	26	s	s	PRON
ejpam-4511	262	27	as	as	ADP
ejpam-4511	262	28	concatenation	concatenation	NOUN
ejpam-4511	262	29	s1⊕s2	s1⊕s2	ADJ
ejpam-4511	262	30	where	where	SCONJ
ejpam-4511	262	31	the	the	DET
ejpam-4511	262	32	subscripts	subscript	NOUN
ejpam-4511	262	33	of	of	ADP
ejpam-4511	262	34	the	the	DET
ejpam-4511	262	35	terms	term	NOUN
ejpam-4511	262	36	of	of	ADP
ejpam-4511	262	37	s1	s1	NOUN
ejpam-4511	262	38	and	and	CCONJ
ejpam-4511	262	39	s2	s2	NOUN
ejpam-4511	262	40	are	be	AUX
ejpam-4511	262	41	even	even	ADV
ejpam-4511	262	42	and	and	CCONJ
ejpam-4511	262	43	odd	odd	ADJ
ejpam-4511	262	44	,	,	PUNCT
ejpam-4511	262	45	respectively	respectively	ADV
ejpam-4511	262	46	.	.	PUNCT
ejpam-4511	263	1	now	now	ADV
ejpam-4511	263	2	,	,	PUNCT
ejpam-4511	263	3	since	since	SCONJ
ejpam-4511	263	4	n2	n2	PROPN
ejpam-4511	263	5	g[v1	g[v1	PROPN
ejpam-4511	263	6	]	]	X
ejpam-4511	263	7	=	=	SYM
ejpam-4511	263	8	{	{	PUNCT
ejpam-4511	263	9	v1	v1	PROPN
ejpam-4511	263	10	,	,	PUNCT
ejpam-4511	263	11	v3	v3	PROPN
ejpam-4511	263	12	,	,	PUNCT
ejpam-4511	263	13	vn−1	vn−1	ADJ
ejpam-4511	263	14	}	}	PUNCT
ejpam-4511	263	15	,	,	PUNCT
ejpam-4511	263	16	n2	n2	ADJ
ejpam-4511	263	17	g[v2	g[v2	NOUN
ejpam-4511	263	18	]	]	X
ejpam-4511	263	19	=	=	SYM
ejpam-4511	263	20	{	{	PUNCT
ejpam-4511	263	21	v2	v2	PROPN
ejpam-4511	263	22	,	,	PUNCT
ejpam-4511	263	23	v4	v4	NOUN
ejpam-4511	263	24	,	,	PUNCT
ejpam-4511	263	25	vn	vn	NOUN
ejpam-4511	263	26	}	}	PUNCT
ejpam-4511	263	27	,	,	PUNCT
ejpam-4511	263	28	n2	n2	ADJ
ejpam-4511	263	29	g[vn	g[vn	PROPN
ejpam-4511	263	30	]	]	X
ejpam-4511	263	31	=	=	SYM
ejpam-4511	263	32	{	{	PUNCT
ejpam-4511	263	33	v2	v2	PROPN
ejpam-4511	263	34	,	,	PUNCT
ejpam-4511	263	35	vn−2	vn−2	PROPN
ejpam-4511	263	36	,	,	PUNCT
ejpam-4511	263	37	vn	vn	NOUN
ejpam-4511	263	38	}	}	PUNCT
ejpam-4511	263	39	,	,	PUNCT
ejpam-4511	263	40	n2	n2	PROPN
ejpam-4511	263	41	g[vn−1	g[vn−1	PROPN
ejpam-4511	263	42	]	]	PUNCT
ejpam-4511	263	43	=	=	PRON
ejpam-4511	263	44	{	{	PUNCT
ejpam-4511	263	45	v1	v1	PROPN
ejpam-4511	263	46	,	,	PUNCT
ejpam-4511	263	47	vn−3	vn−3	PROPN
ejpam-4511	263	48	,	,	PUNCT
ejpam-4511	263	49	vn−1	vn−1	ADJ
ejpam-4511	263	50	}	}	PUNCT
ejpam-4511	263	51	,	,	PUNCT
ejpam-4511	263	52	and	and	CCONJ
ejpam-4511	263	53	n2	n2	PROPN
ejpam-4511	263	54	g[vi	g[vi	PROPN
ejpam-4511	263	55	]	]	X
ejpam-4511	263	56	=	=	SYM
ejpam-4511	263	57	{	{	PUNCT
ejpam-4511	263	58	vi−2	vi−2	PROPN
ejpam-4511	263	59	,	,	PUNCT
ejpam-4511	263	60	vi	vi	NOUN
ejpam-4511	263	61	,	,	PUNCT
ejpam-4511	263	62	vi+2	vi+2	NUM
ejpam-4511	263	63	}	}	PUNCT
ejpam-4511	263	64	for	for	ADP
ejpam-4511	263	65	i	i	PROPN
ejpam-4511	263	66	∈	∈	PROPN
ejpam-4511	263	67	{	{	PUNCT
ejpam-4511	263	68	3	3	NUM
ejpam-4511	263	69	,	,	PUNCT
ejpam-4511	263	70	4	4	NUM
ejpam-4511	263	71	,	,	PUNCT
ejpam-4511	263	72	·	·	PUNCT
ejpam-4511	263	73	·	·	PUNCT
ejpam-4511	263	74	·	·	PUNCT
ejpam-4511	263	75	,	,	PUNCT
ejpam-4511	263	76	n−	n−	NOUN
ejpam-4511	263	77	4	4	NUM
ejpam-4511	263	78	}	}	PUNCT
ejpam-4511	263	79	,	,	PUNCT
ejpam-4511	263	80	it	it	PRON
ejpam-4511	263	81	follows	follow	VERB
ejpam-4511	263	82	that	that	SCONJ
ejpam-4511	263	83	each	each	PRON
ejpam-4511	263	84	of	of	ADP
ejpam-4511	263	85	s1	s1	PROPN
ejpam-4511	263	86	and	and	CCONJ
ejpam-4511	263	87	s2	s2	PROPN
ejpam-4511	263	88	can	can	AUX
ejpam-4511	263	89	only	only	ADV
ejpam-4511	263	90	have	have	VERB
ejpam-4511	263	91	at	at	ADP
ejpam-4511	263	92	most	most	ADJ
ejpam-4511	263	93	n	n	DET
ejpam-4511	263	94	2	2	NUM
ejpam-4511	263	95	−	−	NUM
ejpam-4511	263	96	2	2	NUM
ejpam-4511	263	97	terms	term	NOUN
ejpam-4511	263	98	.	.	PUNCT
ejpam-4511	264	1	thus	thus	ADV
ejpam-4511	264	2	,	,	PUNCT
ejpam-4511	264	3	γhgr(cn	γhgr(cn	NOUN
ejpam-4511	264	4	)	)	PUNCT
ejpam-4511	264	5	=	=	PUNCT
ejpam-4511	265	1	n−	n−	NOUN
ejpam-4511	265	2	4	4	NUM
ejpam-4511	265	3	.	.	PUNCT
ejpam-4511	266	1	next	next	ADV
ejpam-4511	266	2	,	,	PUNCT
ejpam-4511	266	3	suppose	suppose	VERB
ejpam-4511	266	4	that	that	SCONJ
ejpam-4511	266	5	n	n	PROPN
ejpam-4511	266	6	≥	≥	NUM
ejpam-4511	266	7	5	5	NUM
ejpam-4511	266	8	and	and	CCONJ
ejpam-4511	266	9	is	be	AUX
ejpam-4511	266	10	odd	odd	ADJ
ejpam-4511	266	11	.	.	PUNCT
ejpam-4511	267	1	clearly	clearly	ADV
ejpam-4511	267	2	,	,	PUNCT
ejpam-4511	267	3	γhgr(cn	γhgr(cn	NOUN
ejpam-4511	267	4	)	)	PUNCT
ejpam-4511	267	5	=	=	SYM
ejpam-4511	267	6	3	3	NUM
ejpam-4511	267	7	if	if	SCONJ
ejpam-4511	267	8	n	n	X
ejpam-4511	267	9	=	=	SYM
ejpam-4511	267	10	5	5	X
ejpam-4511	267	11	.	.	X
ejpam-4511	267	12	for	for	ADP
ejpam-4511	267	13	n	n	X
ejpam-4511	267	14	≥	≥	NUM
ejpam-4511	267	15	7	7	NUM
ejpam-4511	267	16	,	,	PUNCT
ejpam-4511	267	17	the	the	DET
ejpam-4511	267	18	sequence	sequence	NOUN
ejpam-4511	267	19	s	s	PART
ejpam-4511	267	20	=	=	PUNCT
ejpam-4511	267	21	(	(	PUNCT
ejpam-4511	267	22	v1	v1	PROPN
ejpam-4511	267	23	,	,	PUNCT
ejpam-4511	267	24	v3	v3	PROPN
ejpam-4511	267	25	,	,	PUNCT
ejpam-4511	267	26	·	·	PUNCT
ejpam-4511	267	27	·	·	PUNCT
ejpam-4511	267	28	·	·	PUNCT
ejpam-4511	267	29	,	,	PUNCT
ejpam-4511	267	30	vn	vn	X
ejpam-4511	267	31	,	,	PUNCT
ejpam-4511	267	32	v2	v2	PROPN
ejpam-4511	267	33	,	,	PUNCT
ejpam-4511	267	34	v4	v4	NOUN
ejpam-4511	267	35	,	,	PUNCT
ejpam-4511	267	36	·	·	PUNCT
ejpam-4511	267	37	·	·	PUNCT
ejpam-4511	267	38	·	·	PUNCT
ejpam-4511	267	39	,	,	PUNCT
ejpam-4511	267	40	vn−5	vn−5	PROPN
ejpam-4511	267	41	)	)	PUNCT
ejpam-4511	267	42	=	=	PUNCT
ejpam-4511	267	43	(	(	PUNCT
ejpam-4511	267	44	v1	v1	PROPN
ejpam-4511	267	45	,	,	PUNCT
ejpam-4511	267	46	v3	v3	PROPN
ejpam-4511	267	47	,	,	PUNCT
ejpam-4511	267	48	·	·	PUNCT
ejpam-4511	267	49	·	·	PUNCT
ejpam-4511	267	50	·	·	PUNCT
ejpam-4511	267	51	,	,	PUNCT
ejpam-4511	267	52	vn)⊕(v2	vn)⊕(v2	X
ejpam-4511	267	53	,	,	PUNCT
ejpam-4511	267	54	v4	v4	PROPN
ejpam-4511	267	55	,	,	PUNCT
ejpam-4511	267	56	·	·	PUNCT
ejpam-4511	267	57	·	·	PUNCT
ejpam-4511	267	58	·	·	PUNCT
ejpam-4511	267	59	,	,	PUNCT
ejpam-4511	267	60	vn−5	vn−5	PROPN
ejpam-4511	267	61	)	)	PUNCT
ejpam-4511	267	62	can	can	AUX
ejpam-4511	267	63	be	be	AUX
ejpam-4511	267	64	verified	verify	VERB
ejpam-4511	267	65	to	to	PART
ejpam-4511	267	66	be	be	AUX
ejpam-4511	267	67	a	a	DET
ejpam-4511	267	68	grundy	grundy	PROPN
ejpam-4511	267	69	hop	hop	NOUN
ejpam-4511	267	70	dominating	dominating	NOUN
ejpam-4511	267	71	sequence	sequence	NOUN
ejpam-4511	267	72	of	of	ADP
ejpam-4511	267	73	cn	cn	PROPN
ejpam-4511	267	74	.	.	PUNCT
ejpam-4511	268	1	this	this	PRON
ejpam-4511	268	2	and	and	CCONJ
ejpam-4511	268	3	lemma	lemma	PROPN
ejpam-4511	268	4	1	1	NUM
ejpam-4511	268	5	would	would	AUX
ejpam-4511	268	6	imply	imply	VERB
ejpam-4511	268	7	that	that	PRON
ejpam-4511	268	8	γhgr(g	γhgr(g	NOUN
ejpam-4511	268	9	)	)	PUNCT
ejpam-4511	268	10	=	=	VERB
ejpam-4511	268	11	n−	n−	NOUN
ejpam-4511	268	12	2	2	NUM
ejpam-4511	268	13	.	.	PUNCT
ejpam-4511	269	1	lemma	lemma	PROPN
ejpam-4511	269	2	2	2	X
ejpam-4511	269	3	.	.	PUNCT
ejpam-4511	270	1	let	let	VERB
ejpam-4511	270	2	g	g	PRON
ejpam-4511	270	3	be	be	AUX
ejpam-4511	270	4	a	a	DET
ejpam-4511	270	5	graph	graph	NOUN
ejpam-4511	270	6	.	.	PUNCT
ejpam-4511	271	1	a	a	DET
ejpam-4511	271	2	sequence	sequence	NOUN
ejpam-4511	271	3	s	s	PART
ejpam-4511	271	4	is	be	AUX
ejpam-4511	271	5	a	a	DET
ejpam-4511	271	6	co	co	ADJ
ejpam-4511	271	7	-	-	ADJ
ejpam-4511	271	8	legal	legal	ADJ
ejpam-4511	271	9	closed	closed	ADJ
ejpam-4511	271	10	neighborhood	neighborhood	NOUN
ejpam-4511	271	11	sequence	sequence	NOUN
ejpam-4511	271	12	in	in	ADP
ejpam-4511	271	13	g	g	PROPN
ejpam-4511	271	14	if	if	SCONJ
ejpam-4511	272	1	and	and	CCONJ
ejpam-4511	272	2	only	only	ADV
ejpam-4511	272	3	if	if	SCONJ
ejpam-4511	272	4	s	s	NOUN
ejpam-4511	272	5	is	be	AUX
ejpam-4511	272	6	a	a	DET
ejpam-4511	272	7	legal	legal	ADJ
ejpam-4511	272	8	closed	closed	ADJ
ejpam-4511	272	9	neighborhood	neighborhood	NOUN
ejpam-4511	272	10	sequence	sequence	NOUN
ejpam-4511	272	11	in	in	ADP
ejpam-4511	272	12	g.	g.	PROPN
ejpam-4511	272	13	moreover	moreover	ADV
ejpam-4511	272	14	,	,	PUNCT
ejpam-4511	272	15	s	s	VERB
ejpam-4511	272	16	is	be	AUX
ejpam-4511	272	17	a	a	DET
ejpam-4511	272	18	co	co	ADJ
ejpam-4511	272	19	-	-	ADJ
ejpam-4511	272	20	grundy	grundy	ADJ
ejpam-4511	272	21	dominating	dominating	NOUN
ejpam-4511	272	22	sequence	sequence	NOUN
ejpam-4511	272	23	in	in	ADP
ejpam-4511	272	24	g	g	PROPN
ejpam-4511	272	25	if	if	SCONJ
ejpam-4511	273	1	and	and	CCONJ
ejpam-4511	273	2	only	only	ADV
ejpam-4511	273	3	if	if	SCONJ
ejpam-4511	273	4	it	it	PRON
ejpam-4511	273	5	is	be	AUX
ejpam-4511	273	6	a	a	DET
ejpam-4511	273	7	grundy	grundy	PROPN
ejpam-4511	273	8	dominating	dominating	NOUN
ejpam-4511	273	9	sequence	sequence	NOUN
ejpam-4511	273	10	in	in	ADP
ejpam-4511	273	11	g.	g.	PROPN
ejpam-4511	273	12	in	in	ADP
ejpam-4511	273	13	particular	particular	ADJ
ejpam-4511	273	14	,	,	PUNCT
ejpam-4511	273	15	γcogr(g	γcogr(g	NOUN
ejpam-4511	273	16	)	)	PUNCT
ejpam-4511	273	17	=	=	SYM
ejpam-4511	273	18	γgr(g	γgr(g	PROPN
ejpam-4511	273	19	)	)	PUNCT
ejpam-4511	273	20	.	.	PUNCT
ejpam-4511	274	1	proof	proof	NOUN
ejpam-4511	274	2	.	.	PUNCT
ejpam-4511	275	1	let	let	VERB
ejpam-4511	275	2	s	s	AUX
ejpam-4511	275	3	=	=	PUNCT
ejpam-4511	275	4	(	(	PUNCT
ejpam-4511	275	5	v1	v1	PROPN
ejpam-4511	275	6	,	,	PUNCT
ejpam-4511	275	7	·	·	PUNCT
ejpam-4511	275	8	·	·	PUNCT
ejpam-4511	275	9	·	·	PUNCT
ejpam-4511	275	10	,	,	PUNCT
ejpam-4511	275	11	vk	vk	AUX
ejpam-4511	275	12	)	)	PUNCT
ejpam-4511	275	13	be	be	AUX
ejpam-4511	275	14	a	a	DET
ejpam-4511	275	15	sequence	sequence	NOUN
ejpam-4511	275	16	in	in	ADP
ejpam-4511	275	17	g.	g.	PROPN
ejpam-4511	275	18	since	since	SCONJ
ejpam-4511	275	19	v	v	PROPN
ejpam-4511	275	20	(	(	PUNCT
ejpam-4511	275	21	g	g	NOUN
ejpam-4511	275	22	)	)	PUNCT
ejpam-4511	275	23	\	\	NOUN
ejpam-4511	275	24	ng(vi	ng(vi	PROPN
ejpam-4511	275	25	)	)	PUNCT
ejpam-4511	275	26	=	=	PUNCT
ejpam-4511	276	1	ng[vi	ng[vi	PROPN
ejpam-4511	276	2	]	]	X
ejpam-4511	276	3	for	for	ADP
ejpam-4511	276	4	each	each	DET
ejpam-4511	276	5	i	i	PRON
ejpam-4511	276	6	∈	∈	PROPN
ejpam-4511	277	1	[	[	X
ejpam-4511	277	2	k	k	X
ejpam-4511	277	3	]	]	X
ejpam-4511	277	4	,	,	PUNCT
ejpam-4511	277	5	it	it	PRON
ejpam-4511	277	6	follows	follow	VERB
ejpam-4511	277	7	that	that	SCONJ
ejpam-4511	278	1	[	[	X
ejpam-4511	278	2	v	v	X
ejpam-4511	278	3	(	(	PUNCT
ejpam-4511	278	4	g	g	NOUN
ejpam-4511	278	5	)	)	PUNCT
ejpam-4511	278	6	\ng(vi	\ng(vi	NOUN
ejpam-4511	278	7	)	)	PUNCT
ejpam-4511	278	8	]	]	PUNCT
ejpam-4511	278	9	\	\	X
ejpam-4511	279	1	∪i−1	∪i−1	PROPN
ejpam-4511	279	2	j=1[v	j=1[v	X
ejpam-4511	279	3	(	(	PUNCT
ejpam-4511	279	4	g	g	NOUN
ejpam-4511	279	5	)	)	PUNCT
ejpam-4511	279	6	\ng(vj	\ng(vj	ADP
ejpam-4511	279	7	)	)	PUNCT
ejpam-4511	279	8	]	]	PUNCT
ejpam-4511	280	1	=	=	PUNCT
ejpam-4511	280	2	ng[vi	ng[vi	PROPN
ejpam-4511	280	3	]	]	X
ejpam-4511	280	4	\	\	NOUN
ejpam-4511	280	5	∪	∪	X
ejpam-4511	280	6	i−1	i−1	PROPN
ejpam-4511	280	7	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4511	280	8	]	]	PUNCT
ejpam-4511	280	9	.	.	PUNCT
ejpam-4511	281	1	hence	hence	ADV
ejpam-4511	281	2	,	,	PUNCT
ejpam-4511	281	3	s	s	VERB
ejpam-4511	281	4	is	be	AUX
ejpam-4511	281	5	a	a	DET
ejpam-4511	281	6	co	co	ADJ
ejpam-4511	281	7	-	-	ADJ
ejpam-4511	281	8	legal	legal	ADJ
ejpam-4511	281	9	closed	closed	ADJ
ejpam-4511	281	10	neighborhood	neighborhood	NOUN
ejpam-4511	281	11	sequence	sequence	NOUN
ejpam-4511	281	12	in	in	ADP
ejpam-4511	281	13	g	g	PROPN
ejpam-4511	281	14	if	if	SCONJ
ejpam-4511	282	1	and	and	CCONJ
ejpam-4511	282	2	only	only	ADV
ejpam-4511	282	3	if	if	SCONJ
ejpam-4511	282	4	it	it	PRON
ejpam-4511	282	5	is	be	AUX
ejpam-4511	282	6	a	a	DET
ejpam-4511	282	7	legal	legal	ADJ
ejpam-4511	282	8	closed	closed	ADJ
ejpam-4511	282	9	neighborhood	neighborhood	NOUN
ejpam-4511	282	10	sequence	sequence	NOUN
ejpam-4511	282	11	in	in	ADP
ejpam-4511	282	12	g.	g.	PROPN
ejpam-4511	282	13	clearly	clearly	ADV
ejpam-4511	282	14	,	,	PUNCT
ejpam-4511	282	15	a	a	DET
ejpam-4511	282	16	co	co	ADJ
ejpam-4511	282	17	-	-	ADJ
ejpam-4511	282	18	legal	legal	ADJ
ejpam-4511	282	19	closed	closed	ADJ
ejpam-4511	282	20	neighborhood	neighborhood	NOUN
ejpam-4511	282	21	sequence	sequence	NOUN
ejpam-4511	282	22	in	in	ADP
ejpam-4511	282	23	g	g	PROPN
ejpam-4511	282	24	is	be	AUX
ejpam-4511	282	25	a	a	DET
ejpam-4511	282	26	j.	j.	PROPN
ejpam-4511	282	27	hassan	hassan	PROPN
ejpam-4511	282	28	,	,	PUNCT
ejpam-4511	282	29	s.	s.	PROPN
ejpam-4511	282	30	canoy	canoy	PROPN
ejpam-4511	282	31	/	/	SYM
ejpam-4511	282	32	eur	eur	PROPN
ejpam-4511	282	33	.	.	PUNCT
ejpam-4511	283	1	j.	j.	PROPN
ejpam-4511	283	2	pure	pure	PROPN
ejpam-4511	283	3	appl	appl	PROPN
ejpam-4511	283	4	.	.	PROPN
ejpam-4511	283	5	math	math	PROPN
ejpam-4511	283	6	,	,	PUNCT
ejpam-4511	283	7	15	15	NUM
ejpam-4511	283	8	(	(	PUNCT
ejpam-4511	283	9	4	4	NUM
ejpam-4511	283	10	)	)	PUNCT
ejpam-4511	283	11	(	(	PUNCT
ejpam-4511	283	12	2022	2022	NUM
ejpam-4511	283	13	)	)	PUNCT
ejpam-4511	283	14	,	,	PUNCT
ejpam-4511	283	15	1623	1623	NUM
ejpam-4511	283	16	-	-	SYM
ejpam-4511	283	17	1636	1636	NUM
ejpam-4511	283	18	1631	1631	NUM
ejpam-4511	283	19	co	co	NOUN
ejpam-4511	283	20	-	-	ADJ
ejpam-4511	283	21	grundy	grundy	ADJ
ejpam-4511	283	22	dominating	dominating	NOUN
ejpam-4511	283	23	sequence	sequence	NOUN
ejpam-4511	283	24	if	if	SCONJ
ejpam-4511	283	25	and	and	CCONJ
ejpam-4511	283	26	only	only	ADV
ejpam-4511	283	27	if	if	SCONJ
ejpam-4511	283	28	it	it	PRON
ejpam-4511	283	29	is	be	AUX
ejpam-4511	283	30	a	a	DET
ejpam-4511	283	31	grundy	grundy	PROPN
ejpam-4511	283	32	dominating	dominating	NOUN
ejpam-4511	283	33	sequence	sequence	NOUN
ejpam-4511	283	34	in	in	ADP
ejpam-4511	283	35	g.	g.	PROPN
ejpam-4511	283	36	hence	hence	ADV
ejpam-4511	283	37	,	,	PUNCT
ejpam-4511	283	38	γcogr(g	γcogr(g	NOUN
ejpam-4511	283	39	)	)	PUNCT
ejpam-4511	283	40	=	=	SYM
ejpam-4511	283	41	γgr(g	γgr(g	PROPN
ejpam-4511	283	42	)	)	PUNCT
ejpam-4511	283	43	.	.	PUNCT
ejpam-4511	284	1	theorem	theorem	NOUN
ejpam-4511	284	2	5	5	NUM
ejpam-4511	284	3	.	.	PUNCT
ejpam-4511	285	1	let	let	VERB
ejpam-4511	285	2	g	g	NOUN
ejpam-4511	285	3	and	and	CCONJ
ejpam-4511	285	4	h	h	NOUN
ejpam-4511	285	5	be	be	VERB
ejpam-4511	285	6	any	any	DET
ejpam-4511	285	7	two	two	NUM
ejpam-4511	285	8	graphs	graph	NOUN
ejpam-4511	285	9	.	.	PUNCT
ejpam-4511	286	1	a	a	DET
ejpam-4511	286	2	sequence	sequence	NOUN
ejpam-4511	286	3	s	s	VERB
ejpam-4511	286	4	of	of	ADP
ejpam-4511	286	5	distinct	distinct	ADJ
ejpam-4511	286	6	vertices	vertex	NOUN
ejpam-4511	286	7	of	of	ADP
ejpam-4511	286	8	g+h	g+h	PROPN
ejpam-4511	286	9	is	be	AUX
ejpam-4511	286	10	a	a	DET
ejpam-4511	286	11	legal	legal	ADJ
ejpam-4511	286	12	closed	closed	ADJ
ejpam-4511	286	13	hop	hop	NOUN
ejpam-4511	286	14	neighborhood	neighborhood	NOUN
ejpam-4511	286	15	sequence	sequence	NOUN
ejpam-4511	286	16	if	if	SCONJ
ejpam-4511	286	17	and	and	CCONJ
ejpam-4511	286	18	only	only	ADV
ejpam-4511	286	19	if	if	SCONJ
ejpam-4511	286	20	one	one	NUM
ejpam-4511	286	21	of	of	ADP
ejpam-4511	286	22	the	the	DET
ejpam-4511	286	23	following	follow	VERB
ejpam-4511	286	24	holds	hold	VERB
ejpam-4511	286	25	:	:	PUNCT
ejpam-4511	286	26	(	(	PUNCT
ejpam-4511	286	27	i	i	NOUN
ejpam-4511	286	28	)	)	PUNCT
ejpam-4511	286	29	s	s	VERB
ejpam-4511	286	30	is	be	AUX
ejpam-4511	286	31	a	a	DET
ejpam-4511	286	32	co	co	ADJ
ejpam-4511	286	33	-	-	ADJ
ejpam-4511	286	34	legal	legal	ADJ
ejpam-4511	286	35	closed	closed	ADJ
ejpam-4511	286	36	neighborhood	neighborhood	NOUN
ejpam-4511	286	37	sequence	sequence	NOUN
ejpam-4511	286	38	in	in	ADP
ejpam-4511	286	39	g	g	PROPN
ejpam-4511	286	40	(	(	PUNCT
ejpam-4511	286	41	legal	legal	ADJ
ejpam-4511	286	42	closed	close	VERB
ejpam-4511	286	43	neighborhood	neighborhood	NOUN
ejpam-4511	286	44	sequence	sequence	NOUN
ejpam-4511	286	45	in	in	ADP
ejpam-4511	286	46	g	g	NOUN
ejpam-4511	286	47	)	)	PUNCT
ejpam-4511	286	48	.	.	PUNCT
ejpam-4511	287	1	(	(	PUNCT
ejpam-4511	287	2	ii	ii	X
ejpam-4511	287	3	)	)	PUNCT
ejpam-4511	287	4	s	s	VERB
ejpam-4511	287	5	is	be	AUX
ejpam-4511	287	6	a	a	DET
ejpam-4511	287	7	co	co	ADJ
ejpam-4511	287	8	-	-	ADJ
ejpam-4511	287	9	legal	legal	ADJ
ejpam-4511	287	10	closed	closed	ADJ
ejpam-4511	287	11	neighborhood	neighborhood	NOUN
ejpam-4511	287	12	sequence	sequence	NOUN
ejpam-4511	287	13	in	in	ADP
ejpam-4511	287	14	h	h	PROPN
ejpam-4511	287	15	(	(	PUNCT
ejpam-4511	287	16	legal	legal	ADJ
ejpam-4511	287	17	closed	close	VERB
ejpam-4511	287	18	neighborhood	neighborhood	NOUN
ejpam-4511	287	19	sequence	sequence	NOUN
ejpam-4511	287	20	in	in	ADP
ejpam-4511	287	21	h	h	NOUN
ejpam-4511	287	22	)	)	PUNCT
ejpam-4511	287	23	.	.	PUNCT
ejpam-4511	288	1	(	(	PUNCT
ejpam-4511	288	2	iii	iii	X
ejpam-4511	288	3	)	)	PUNCT
ejpam-4511	288	4	s	s	AUX
ejpam-4511	288	5	is	be	AUX
ejpam-4511	288	6	a	a	DET
ejpam-4511	288	7	concatenation	concatenation	NOUN
ejpam-4511	288	8	sg	sg	ADP
ejpam-4511	288	9	⊕	⊕	PROPN
ejpam-4511	288	10	sh	sh	INTJ
ejpam-4511	288	11	,	,	PUNCT
ejpam-4511	288	12	where	where	SCONJ
ejpam-4511	288	13	sg	sg	PROPN
ejpam-4511	288	14	and	and	CCONJ
ejpam-4511	288	15	sh	sh	PROPN
ejpam-4511	288	16	are	be	AUX
ejpam-4511	288	17	co	co	ADJ
ejpam-4511	288	18	-	-	ADJ
ejpam-4511	288	19	legal	legal	ADJ
ejpam-4511	288	20	closed	closed	ADJ
ejpam-4511	288	21	neighborhood	neighborhood	NOUN
ejpam-4511	288	22	sequences	sequence	NOUN
ejpam-4511	288	23	in	in	ADP
ejpam-4511	288	24	g	g	PROPN
ejpam-4511	288	25	and	and	CCONJ
ejpam-4511	288	26	h	h	NOUN
ejpam-4511	288	27	,	,	PUNCT
ejpam-4511	288	28	respectively	respectively	ADV
ejpam-4511	288	29	.	.	PUNCT
ejpam-4511	289	1	proof	proof	NOUN
ejpam-4511	289	2	.	.	PUNCT
ejpam-4511	290	1	suppose	suppose	VERB
ejpam-4511	290	2	that	that	SCONJ
ejpam-4511	290	3	s	s	VERB
ejpam-4511	290	4	=	=	X
ejpam-4511	290	5	(	(	PUNCT
ejpam-4511	290	6	w1	w1	NOUN
ejpam-4511	290	7	,	,	PUNCT
ejpam-4511	290	8	·	·	PUNCT
ejpam-4511	290	9	·	·	PUNCT
ejpam-4511	290	10	·	·	PUNCT
ejpam-4511	290	11	,	,	PUNCT
ejpam-4511	290	12	wk	wk	X
ejpam-4511	290	13	)	)	PUNCT
ejpam-4511	290	14	is	be	AUX
ejpam-4511	290	15	a	a	DET
ejpam-4511	290	16	legal	legal	ADJ
ejpam-4511	290	17	closed	close	VERB
ejpam-4511	290	18	hop	hop	NOUN
ejpam-4511	290	19	neighborhood	neighborhood	NOUN
ejpam-4511	290	20	sequence	sequence	NOUN
ejpam-4511	290	21	in	in	ADP
ejpam-4511	290	22	g+h	g+h	PROPN
ejpam-4511	290	23	and	and	CCONJ
ejpam-4511	290	24	let	let	VERB
ejpam-4511	290	25	ŝ	ŝ	X
ejpam-4511	290	26	=	=	PUNCT
ejpam-4511	290	27	{	{	PUNCT
ejpam-4511	290	28	w1	w1	NOUN
ejpam-4511	290	29	,	,	PUNCT
ejpam-4511	290	30	.	.	PUNCT
ejpam-4511	290	31	.	.	PUNCT
ejpam-4511	291	1	.	.	PUNCT
ejpam-4511	292	1	,	,	PUNCT
ejpam-4511	292	2	wk	wk	X
ejpam-4511	292	3	}	}	PUNCT
ejpam-4511	292	4	.	.	PUNCT
ejpam-4511	293	1	suppose	suppose	VERB
ejpam-4511	293	2	ŝ	ŝ	VERB
ejpam-4511	293	3	⊆	⊆	NUM
ejpam-4511	293	4	v	v	NOUN
ejpam-4511	293	5	(	(	PUNCT
ejpam-4511	293	6	g	g	NOUN
ejpam-4511	293	7	)	)	PUNCT
ejpam-4511	293	8	.	.	PUNCT
ejpam-4511	294	1	by	by	ADP
ejpam-4511	294	2	the	the	DET
ejpam-4511	294	3	legality	legality	NOUN
ejpam-4511	294	4	condition	condition	NOUN
ejpam-4511	294	5	in	in	ADP
ejpam-4511	294	6	s	s	PROPN
ejpam-4511	294	7	,	,	PUNCT
ejpam-4511	294	8	we	we	PRON
ejpam-4511	294	9	have	have	VERB
ejpam-4511	294	10	n2	n2	PROPN
ejpam-4511	294	11	g+h	g+h	PROPN
ejpam-4511	295	1	[	[	X
ejpam-4511	295	2	wi	wi	X
ejpam-4511	295	3	]	]	PUNCT
ejpam-4511	295	4	\	\	X
ejpam-4511	296	1	∪i−1	∪i−1	PROPN
ejpam-4511	296	2	j=1n	j=1n	PROPN
ejpam-4511	296	3	2	2	NUM
ejpam-4511	296	4	g+h	g+h	PROPN
ejpam-4511	297	1	[	[	X
ejpam-4511	297	2	wj	wj	X
ejpam-4511	297	3	]	]	PUNCT
ejpam-4511	297	4	̸=	̸=	PROPN
ejpam-4511	297	5	∅	∅	NOUN
ejpam-4511	297	6	for	for	ADP
ejpam-4511	297	7	all	all	PRON
ejpam-4511	297	8	i	i	PRON
ejpam-4511	297	9	∈	∈	PROPN
ejpam-4511	297	10	{	{	PUNCT
ejpam-4511	297	11	2	2	NUM
ejpam-4511	297	12	,	,	PUNCT
ejpam-4511	297	13	3	3	NUM
ejpam-4511	297	14	,	,	PUNCT
ejpam-4511	297	15	.	.	PUNCT
ejpam-4511	297	16	.	.	PUNCT
ejpam-4511	297	17	.	.	PUNCT
ejpam-4511	298	1	,	,	PUNCT
ejpam-4511	298	2	k	k	X
ejpam-4511	298	3	}	}	PUNCT
ejpam-4511	298	4	.	.	PUNCT
ejpam-4511	299	1	since	since	SCONJ
ejpam-4511	299	2	n2	n2	PROPN
ejpam-4511	299	3	g+h	g+h	PROPN
ejpam-4511	300	1	[	[	X
ejpam-4511	300	2	wi	wi	X
ejpam-4511	300	3	]	]	X
ejpam-4511	300	4	=	=	SYM
ejpam-4511	300	5	v	v	X
ejpam-4511	300	6	(	(	PUNCT
ejpam-4511	300	7	g	g	NOUN
ejpam-4511	300	8	)	)	PUNCT
ejpam-4511	300	9	\ng(wi	\ng(wi	VERB
ejpam-4511	300	10	)	)	PUNCT
ejpam-4511	300	11	for	for	ADP
ejpam-4511	300	12	each	each	DET
ejpam-4511	300	13	i	i	PRON
ejpam-4511	300	14	∈	∈	PROPN
ejpam-4511	301	1	[	[	X
ejpam-4511	301	2	k	k	X
ejpam-4511	301	3	]	]	X
ejpam-4511	301	4	,	,	PUNCT
ejpam-4511	301	5	it	it	PRON
ejpam-4511	301	6	follows	follow	VERB
ejpam-4511	301	7	that	that	SCONJ
ejpam-4511	302	1	[	[	X
ejpam-4511	302	2	v	v	X
ejpam-4511	302	3	(	(	PUNCT
ejpam-4511	302	4	g	g	NOUN
ejpam-4511	302	5	)	)	PUNCT
ejpam-4511	302	6	\ng(wi	\ng(wi	NOUN
ejpam-4511	302	7	)	)	PUNCT
ejpam-4511	302	8	]	]	PUNCT
ejpam-4511	302	9	\	\	X
ejpam-4511	302	10	∪i−1	∪i−1	PROPN
ejpam-4511	302	11	j=1[v	j=1[v	X
ejpam-4511	302	12	(	(	PUNCT
ejpam-4511	302	13	g	g	NOUN
ejpam-4511	302	14	)	)	PUNCT
ejpam-4511	302	15	\ng(wj	\ng(wj	NOUN
ejpam-4511	302	16	)	)	PUNCT
ejpam-4511	302	17	]	]	PUNCT
ejpam-4511	303	1	̸=	̸=	NOUN
ejpam-4511	303	2	∅	∅	NOUN
ejpam-4511	303	3	for	for	ADP
ejpam-4511	303	4	all	all	PRON
ejpam-4511	303	5	i	i	PRON
ejpam-4511	303	6	∈	∈	PROPN
ejpam-4511	303	7	{	{	PUNCT
ejpam-4511	303	8	2	2	NUM
ejpam-4511	303	9	,	,	PUNCT
ejpam-4511	303	10	3	3	NUM
ejpam-4511	303	11	,	,	PUNCT
ejpam-4511	303	12	.	.	PUNCT
ejpam-4511	303	13	.	.	PUNCT
ejpam-4511	303	14	.	.	PUNCT
ejpam-4511	303	15	,	,	PUNCT
ejpam-4511	303	16	k	k	X
ejpam-4511	303	17	}	}	PUNCT
ejpam-4511	303	18	.	.	PUNCT
ejpam-4511	304	1	therefore	therefore	ADV
ejpam-4511	304	2	,	,	PUNCT
ejpam-4511	304	3	s	s	VERB
ejpam-4511	304	4	is	be	AUX
ejpam-4511	304	5	a	a	DET
ejpam-4511	304	6	co	co	ADJ
ejpam-4511	304	7	-	-	ADJ
ejpam-4511	304	8	legal	legal	ADJ
ejpam-4511	304	9	closed	closed	ADJ
ejpam-4511	304	10	neighborhood	neighborhood	NOUN
ejpam-4511	304	11	sequence	sequence	NOUN
ejpam-4511	304	12	in	in	ADP
ejpam-4511	304	13	g	g	NOUN
ejpam-4511	304	14	,	,	PUNCT
ejpam-4511	304	15	showing	show	VERB
ejpam-4511	304	16	that	that	SCONJ
ejpam-4511	304	17	(	(	PUNCT
ejpam-4511	304	18	i	i	NOUN
ejpam-4511	304	19	)	)	PUNCT
ejpam-4511	304	20	holds	hold	VERB
ejpam-4511	304	21	.	.	PUNCT
ejpam-4511	305	1	similarly	similarly	ADV
ejpam-4511	305	2	,	,	PUNCT
ejpam-4511	305	3	(	(	PUNCT
ejpam-4511	305	4	ii	ii	NOUN
ejpam-4511	305	5	)	)	PUNCT
ejpam-4511	305	6	holds	hold	VERB
ejpam-4511	305	7	if	if	SCONJ
ejpam-4511	305	8	ŝ	ŝ	ADP
ejpam-4511	305	9	⊆	⊆	NUM
ejpam-4511	305	10	v	v	NOUN
ejpam-4511	305	11	(	(	PUNCT
ejpam-4511	305	12	h	h	NOUN
ejpam-4511	305	13	)	)	PUNCT
ejpam-4511	305	14	.	.	PUNCT
ejpam-4511	306	1	next	next	ADV
ejpam-4511	306	2	,	,	PUNCT
ejpam-4511	306	3	suppose	suppose	VERB
ejpam-4511	306	4	that	that	SCONJ
ejpam-4511	306	5	ŝg	ŝg	NOUN
ejpam-4511	306	6	=	=	SYM
ejpam-4511	306	7	ŝ	ŝ	X
ejpam-4511	306	8	∩	∩	PROPN
ejpam-4511	306	9	v	v	X
ejpam-4511	306	10	(	(	PUNCT
ejpam-4511	306	11	g	g	NOUN
ejpam-4511	306	12	)	)	PUNCT
ejpam-4511	306	13	̸=	̸=	PROPN
ejpam-4511	306	14	∅	∅	NOUN
ejpam-4511	306	15	and	and	CCONJ
ejpam-4511	306	16	ŝh	ŝh	PRON
ejpam-4511	306	17	=	=	SYM
ejpam-4511	306	18	ŝ	ŝ	X
ejpam-4511	306	19	∩	∩	PROPN
ejpam-4511	306	20	v	v	X
ejpam-4511	306	21	(	(	PUNCT
ejpam-4511	306	22	h	h	NOUN
ejpam-4511	306	23	)	)	PUNCT
ejpam-4511	306	24	̸=	̸=	PROPN
ejpam-4511	306	25	∅.	∅.	ADV
ejpam-4511	306	26	since	since	SCONJ
ejpam-4511	306	27	n2	n2	PROPN
ejpam-4511	306	28	g+h	g+h	PROPN
ejpam-4511	307	1	[	[	X
ejpam-4511	307	2	wj	wj	X
ejpam-4511	307	3	]	]	PUNCT
ejpam-4511	307	4	⊆	⊆	NUM
ejpam-4511	307	5	v	v	NOUN
ejpam-4511	307	6	(	(	PUNCT
ejpam-4511	307	7	g	g	NOUN
ejpam-4511	307	8	)	)	PUNCT
ejpam-4511	307	9	for	for	ADP
ejpam-4511	307	10	all	all	DET
ejpam-4511	307	11	wj	wj	PROPN
ejpam-4511	307	12	∈	∈	PROPN
ejpam-4511	307	13	ŝg	ŝg	NOUN
ejpam-4511	307	14	and	and	CCONJ
ejpam-4511	307	15	n2	n2	PROPN
ejpam-4511	307	16	g+h	g+h	PROPN
ejpam-4511	308	1	[	[	X
ejpam-4511	308	2	ws	ws	X
ejpam-4511	308	3	]	]	X
ejpam-4511	308	4	⊆	⊆	NUM
ejpam-4511	308	5	v	v	NOUN
ejpam-4511	308	6	(	(	PUNCT
ejpam-4511	308	7	h	h	NOUN
ejpam-4511	308	8	)	)	PUNCT
ejpam-4511	308	9	for	for	ADP
ejpam-4511	308	10	all	all	DET
ejpam-4511	308	11	ws	ws	NOUN
ejpam-4511	308	12	∈	∈	PROPN
ejpam-4511	308	13	ŝh	ŝh	PROPN
ejpam-4511	308	14	,	,	PUNCT
ejpam-4511	308	15	we	we	PRON
ejpam-4511	308	16	may	may	AUX
ejpam-4511	308	17	assume	assume	VERB
ejpam-4511	308	18	that	that	SCONJ
ejpam-4511	308	19	ŝg	ŝg	NOUN
ejpam-4511	308	20	=	=	NOUN
ejpam-4511	308	21	{	{	PUNCT
ejpam-4511	308	22	w1	w1	NOUN
ejpam-4511	308	23	,	,	PUNCT
ejpam-4511	308	24	w2	w2	NOUN
ejpam-4511	308	25	,	,	PUNCT
ejpam-4511	308	26	.	.	PUNCT
ejpam-4511	308	27	.	.	PUNCT
ejpam-4511	308	28	.	.	PUNCT
ejpam-4511	309	1	,	,	PUNCT
ejpam-4511	309	2	wm	wm	PROPN
ejpam-4511	309	3	}	}	PUNCT
ejpam-4511	309	4	and	and	CCONJ
ejpam-4511	309	5	ŝh	ŝh	PRON
ejpam-4511	309	6	=	=	SYM
ejpam-4511	309	7	{	{	PUNCT
ejpam-4511	309	8	wm+1	wm+1	PROPN
ejpam-4511	309	9	,	,	PUNCT
ejpam-4511	309	10	wm+1	wm+1	X
ejpam-4511	309	11	,	,	PUNCT
ejpam-4511	309	12	.	.	PUNCT
ejpam-4511	309	13	.	.	PUNCT
ejpam-4511	309	14	.	.	PUNCT
ejpam-4511	310	1	,	,	PUNCT
ejpam-4511	310	2	wk	wk	ADP
ejpam-4511	310	3	}	}	PUNCT
ejpam-4511	310	4	.	.	PUNCT
ejpam-4511	311	1	then	then	ADV
ejpam-4511	311	2	s	s	VERB
ejpam-4511	311	3	=	=	PUNCT
ejpam-4511	311	4	sg	sg	PROPN
ejpam-4511	311	5	⊕	⊕	PROPN
ejpam-4511	311	6	sh	sh	INTJ
ejpam-4511	311	7	.	.	PUNCT
ejpam-4511	312	1	since	since	SCONJ
ejpam-4511	312	2	s	s	PROPN
ejpam-4511	312	3	is	be	AUX
ejpam-4511	312	4	a	a	DET
ejpam-4511	312	5	legal	legal	ADJ
ejpam-4511	312	6	closed	close	VERB
ejpam-4511	312	7	hop	hop	NOUN
ejpam-4511	312	8	neighborhood	neighborhood	NOUN
ejpam-4511	312	9	sequence	sequence	NOUN
ejpam-4511	312	10	,	,	PUNCT
ejpam-4511	312	11	[	[	X
ejpam-4511	312	12	v	v	X
ejpam-4511	312	13	(	(	PUNCT
ejpam-4511	312	14	g	g	NOUN
ejpam-4511	312	15	)	)	PUNCT
ejpam-4511	312	16	\ng(wi	\ng(wi	NOUN
ejpam-4511	312	17	)	)	PUNCT
ejpam-4511	312	18	]	]	PUNCT
ejpam-4511	312	19	\	\	X
ejpam-4511	313	1	∪i−1	∪i−1	PROPN
ejpam-4511	313	2	j=1[v	j=1[v	X
ejpam-4511	313	3	(	(	PUNCT
ejpam-4511	313	4	g	g	NOUN
ejpam-4511	313	5	)	)	PUNCT
ejpam-4511	313	6	\ng(wj	\ng(wj	NOUN
ejpam-4511	313	7	)	)	PUNCT
ejpam-4511	313	8	]	]	PUNCT
ejpam-4511	313	9	=	=	SYM
ejpam-4511	313	10	n2	n2	PROPN
ejpam-4511	313	11	g+h	g+h	PROPN
ejpam-4511	314	1	[	[	X
ejpam-4511	314	2	wi	wi	X
ejpam-4511	314	3	]	]	PUNCT
ejpam-4511	314	4	\	\	X
ejpam-4511	315	1	∪i−1	∪i−1	PROPN
ejpam-4511	315	2	j=1n	j=1n	PROPN
ejpam-4511	315	3	2	2	NUM
ejpam-4511	315	4	g+h	g+h	PROPN
ejpam-4511	316	1	[	[	X
ejpam-4511	316	2	wj	wj	X
ejpam-4511	316	3	]	]	PUNCT
ejpam-4511	316	4	̸=	̸=	PROPN
ejpam-4511	316	5	∅	∅	NOUN
ejpam-4511	316	6	for	for	ADP
ejpam-4511	316	7	all	all	PRON
ejpam-4511	316	8	i	i	PRON
ejpam-4511	316	9	∈	∈	PROPN
ejpam-4511	316	10	{	{	PUNCT
ejpam-4511	316	11	2	2	NUM
ejpam-4511	316	12	,	,	PUNCT
ejpam-4511	316	13	3	3	NUM
ejpam-4511	316	14	,	,	PUNCT
ejpam-4511	316	15	.	.	PUNCT
ejpam-4511	316	16	.	.	PUNCT
ejpam-4511	316	17	.	.	PUNCT
ejpam-4511	317	1	,	,	PUNCT
ejpam-4511	317	2	m	m	VERB
ejpam-4511	317	3	}	}	PUNCT
ejpam-4511	317	4	,	,	PUNCT
ejpam-4511	317	5	showing	show	VERB
ejpam-4511	317	6	that	that	SCONJ
ejpam-4511	317	7	sg	sg	PROPN
ejpam-4511	317	8	is	be	AUX
ejpam-4511	317	9	a	a	DET
ejpam-4511	317	10	co	co	ADJ
ejpam-4511	317	11	-	-	ADJ
ejpam-4511	317	12	legal	legal	ADJ
ejpam-4511	317	13	closed	closed	ADJ
ejpam-4511	317	14	neighborhood	neighborhood	NOUN
ejpam-4511	317	15	sequence	sequence	NOUN
ejpam-4511	317	16	in	in	ADP
ejpam-4511	317	17	g.	g.	PROPN
ejpam-4511	317	18	similarly	similarly	ADV
ejpam-4511	317	19	,	,	PUNCT
ejpam-4511	317	20	sh	sh	PROPN
ejpam-4511	317	21	is	be	AUX
ejpam-4511	317	22	a	a	DET
ejpam-4511	317	23	co	co	ADJ
ejpam-4511	317	24	-	-	ADJ
ejpam-4511	317	25	legal	legal	ADJ
ejpam-4511	317	26	closed	closed	ADJ
ejpam-4511	317	27	neighborhood	neighborhood	NOUN
ejpam-4511	317	28	sequence	sequence	NOUN
ejpam-4511	317	29	in	in	ADP
ejpam-4511	317	30	h.	h.	PROPN
ejpam-4511	318	1	this	this	PRON
ejpam-4511	318	2	shows	show	VERB
ejpam-4511	318	3	that	that	SCONJ
ejpam-4511	318	4	(	(	PUNCT
ejpam-4511	318	5	iii	iii	NOUN
ejpam-4511	318	6	)	)	PUNCT
ejpam-4511	318	7	holds	hold	VERB
ejpam-4511	318	8	.	.	PUNCT
ejpam-4511	319	1	the	the	DET
ejpam-4511	319	2	converse	converse	NOUN
ejpam-4511	319	3	is	be	AUX
ejpam-4511	319	4	clear	clear	ADJ
ejpam-4511	319	5	.	.	PUNCT
ejpam-4511	320	1	corollary	corollary	ADJ
ejpam-4511	320	2	3	3	X
ejpam-4511	320	3	.	.	PUNCT
ejpam-4511	321	1	let	let	VERB
ejpam-4511	321	2	g	g	NOUN
ejpam-4511	322	1	and	and	CCONJ
ejpam-4511	322	2	h	h	NOUN
ejpam-4511	322	3	be	be	VERB
ejpam-4511	322	4	any	any	DET
ejpam-4511	322	5	two	two	NUM
ejpam-4511	322	6	graphs	graph	NOUN
ejpam-4511	322	7	.	.	PUNCT
ejpam-4511	323	1	a	a	DET
ejpam-4511	323	2	sequence	sequence	NOUN
ejpam-4511	323	3	s	s	VERB
ejpam-4511	323	4	of	of	ADP
ejpam-4511	323	5	distinct	distinct	ADJ
ejpam-4511	323	6	vertices	vertex	NOUN
ejpam-4511	323	7	of	of	ADP
ejpam-4511	323	8	g+h	g+h	PROPN
ejpam-4511	323	9	is	be	AUX
ejpam-4511	323	10	a	a	DET
ejpam-4511	323	11	grundy	grundy	PROPN
ejpam-4511	323	12	hop	hop	NOUN
ejpam-4511	323	13	dominating	dominating	NOUN
ejpam-4511	323	14	sequence	sequence	NOUN
ejpam-4511	323	15	in	in	ADP
ejpam-4511	323	16	g+h	g+h	PROPN
ejpam-4511	324	1	if	if	SCONJ
ejpam-4511	324	2	and	and	CCONJ
ejpam-4511	324	3	only	only	ADV
ejpam-4511	324	4	if	if	SCONJ
ejpam-4511	324	5	s	s	VERB
ejpam-4511	324	6	=	=	ADJ
ejpam-4511	324	7	sg⊕sh	sg⊕sh	NOUN
ejpam-4511	324	8	,	,	PUNCT
ejpam-4511	324	9	where	where	SCONJ
ejpam-4511	324	10	sh	sh	PROPN
ejpam-4511	324	11	and	and	CCONJ
ejpam-4511	324	12	sh	sh	PROPN
ejpam-4511	324	13	are	be	AUX
ejpam-4511	324	14	co	co	ADJ
ejpam-4511	324	15	-	-	ADJ
ejpam-4511	324	16	grundy	grundy	ADJ
ejpam-4511	324	17	dominating	dominating	NOUN
ejpam-4511	324	18	sequences	sequence	NOUN
ejpam-4511	324	19	in	in	ADP
ejpam-4511	324	20	g	g	PROPN
ejpam-4511	324	21	and	and	CCONJ
ejpam-4511	324	22	h	h	NOUN
ejpam-4511	324	23	,	,	PUNCT
ejpam-4511	324	24	respectively	respectively	ADV
ejpam-4511	324	25	(	(	PUNCT
ejpam-4511	324	26	grundy	grundy	PROPN
ejpam-4511	324	27	dominating	dominating	NOUN
ejpam-4511	324	28	sequences	sequence	NOUN
ejpam-4511	324	29	in	in	ADP
ejpam-4511	324	30	g	g	PROPN
ejpam-4511	324	31	and	and	CCONJ
ejpam-4511	324	32	h	h	NOUN
ejpam-4511	324	33	,	,	PUNCT
ejpam-4511	324	34	respectively	respectively	ADV
ejpam-4511	324	35	)	)	PUNCT
ejpam-4511	324	36	.	.	PUNCT
ejpam-4511	325	1	moreover	moreover	ADV
ejpam-4511	325	2	,	,	PUNCT
ejpam-4511	325	3	γhgr(g+h	γhgr(g+h	PROPN
ejpam-4511	325	4	)	)	PUNCT
ejpam-4511	325	5	=	=	SYM
ejpam-4511	326	1	γcogr(g	γcogr(g	NOUN
ejpam-4511	326	2	)	)	PUNCT
ejpam-4511	327	1	+	+	CCONJ
ejpam-4511	327	2	γcogr(h	γcogr(h	NOUN
ejpam-4511	327	3	)	)	PUNCT
ejpam-4511	327	4	=	=	SYM
ejpam-4511	327	5	γgr(g	γgr(g	PROPN
ejpam-4511	327	6	)	)	PUNCT
ejpam-4511	327	7	+	+	CCONJ
ejpam-4511	327	8	γgr(h	γgr(h	PROPN
ejpam-4511	327	9	)	)	PUNCT
ejpam-4511	327	10	.	.	PUNCT
ejpam-4511	328	1	in	in	ADP
ejpam-4511	328	2	particular	particular	ADJ
ejpam-4511	328	3	,	,	PUNCT
ejpam-4511	328	4	each	each	PRON
ejpam-4511	328	5	of	of	ADP
ejpam-4511	328	6	the	the	DET
ejpam-4511	328	7	following	follow	VERB
ejpam-4511	328	8	holds	hold	NOUN
ejpam-4511	328	9	.	.	PUNCT
ejpam-4511	329	1	j.	j.	PROPN
ejpam-4511	329	2	hassan	hassan	PROPN
ejpam-4511	329	3	,	,	PUNCT
ejpam-4511	329	4	s.	s.	PROPN
ejpam-4511	329	5	canoy	canoy	PROPN
ejpam-4511	329	6	/	/	SYM
ejpam-4511	329	7	eur	eur	PROPN
ejpam-4511	329	8	.	.	PUNCT
ejpam-4511	330	1	j.	j.	PROPN
ejpam-4511	330	2	pure	pure	PROPN
ejpam-4511	330	3	appl	appl	PROPN
ejpam-4511	330	4	.	.	PROPN
ejpam-4511	330	5	math	math	PROPN
ejpam-4511	330	6	,	,	PUNCT
ejpam-4511	330	7	15	15	NUM
ejpam-4511	330	8	(	(	PUNCT
ejpam-4511	330	9	4	4	NUM
ejpam-4511	330	10	)	)	PUNCT
ejpam-4511	330	11	(	(	PUNCT
ejpam-4511	330	12	2022	2022	NUM
ejpam-4511	330	13	)	)	PUNCT
ejpam-4511	330	14	,	,	PUNCT
ejpam-4511	330	15	1623	1623	NUM
ejpam-4511	330	16	-	-	SYM
ejpam-4511	330	17	1636	1636	NUM
ejpam-4511	330	18	1632	1632	NUM
ejpam-4511	330	19	(	(	PUNCT
ejpam-4511	330	20	i	i	NOUN
ejpam-4511	330	21	)	)	PUNCT
ejpam-4511	330	22	γhgr(k1	γhgr(k1	PUNCT
ejpam-4511	331	1	+	+	NOUN
ejpam-4511	331	2	g	g	NOUN
ejpam-4511	331	3	)	)	PUNCT
ejpam-4511	331	4	=	=	SYM
ejpam-4511	332	1	1	1	NUM
ejpam-4511	332	2	+	+	NUM
ejpam-4511	332	3	γcogr(g	γcogr(g	NOUN
ejpam-4511	332	4	)	)	PUNCT
ejpam-4511	332	5	=	=	SYM
ejpam-4511	333	1	1	1	NUM
ejpam-4511	333	2	+	+	NUM
ejpam-4511	333	3	γgr(g	γgr(g	PROPN
ejpam-4511	333	4	)	)	PUNCT
ejpam-4511	333	5	.	.	PUNCT
ejpam-4511	334	1	(	(	PUNCT
ejpam-4511	334	2	ii	ii	X
ejpam-4511	334	3	)	)	PUNCT
ejpam-4511	334	4	γhgr(km	γhgr(km	NOUN
ejpam-4511	334	5	,	,	PUNCT
ejpam-4511	334	6	n	n	CCONJ
ejpam-4511	334	7	)	)	PUNCT
ejpam-4511	334	8	=	=	SYM
ejpam-4511	334	9	2	2	NUM
ejpam-4511	334	10	for	for	ADP
ejpam-4511	334	11	m	m	PROPN
ejpam-4511	334	12	,	,	PUNCT
ejpam-4511	334	13	n	n	PRON
ejpam-4511	334	14	≥	≥	NOUN
ejpam-4511	334	15	1	1	NUM
ejpam-4511	334	16	.	.	PUNCT
ejpam-4511	335	1	(	(	PUNCT
ejpam-4511	335	2	iii	iii	NOUN
ejpam-4511	335	3	)	)	PUNCT
ejpam-4511	335	4	γhgr(wn	γhgr(wn	NOUN
ejpam-4511	335	5	)	)	PUNCT
ejpam-4511	335	6	=	=	SYM
ejpam-4511	336	1	1	1	NUM
ejpam-4511	336	2	+	+	X
ejpam-4511	336	3	γcogr(cn	γcogr(cn	NOUN
ejpam-4511	336	4	)	)	PUNCT
ejpam-4511	336	5	=	=	SYM
ejpam-4511	336	6	1	1	NUM
ejpam-4511	336	7	+	+	NUM
ejpam-4511	336	8	γgr(cn	γgr(cn	NOUN
ejpam-4511	336	9	)	)	PUNCT
ejpam-4511	336	10	for	for	ADP
ejpam-4511	336	11	all	all	DET
ejpam-4511	336	12	n	n	PRON
ejpam-4511	336	13	≥	≥	NOUN
ejpam-4511	336	14	3	3	NUM
ejpam-4511	336	15	.	.	PUNCT
ejpam-4511	336	16	(	(	PUNCT
ejpam-4511	336	17	iv	iv	X
ejpam-4511	336	18	)	)	PUNCT
ejpam-4511	336	19	γhgr(fn	γhgr(fn	NOUN
ejpam-4511	336	20	)	)	PUNCT
ejpam-4511	336	21	=	=	SYM
ejpam-4511	336	22	1	1	NUM
ejpam-4511	336	23	+	+	SYM
ejpam-4511	336	24	γcogr(pn	γcogr(pn	ADJ
ejpam-4511	336	25	)	)	PUNCT
ejpam-4511	336	26	=	=	SYM
ejpam-4511	336	27	1	1	NUM
ejpam-4511	336	28	+	+	NUM
ejpam-4511	336	29	γgr(pn	γgr(pn	NOUN
ejpam-4511	336	30	)	)	PUNCT
ejpam-4511	336	31	for	for	ADP
ejpam-4511	336	32	all	all	PRON
ejpam-4511	336	33	n	n	PRON
ejpam-4511	336	34	≥	≥	NUM
ejpam-4511	336	35	1	1	NUM
ejpam-4511	336	36	.	.	PUNCT
ejpam-4511	336	37	theorem	theorem	NOUN
ejpam-4511	336	38	6	6	NUM
ejpam-4511	336	39	.	.	PUNCT
ejpam-4511	337	1	let	let	VERB
ejpam-4511	337	2	g	g	PRON
ejpam-4511	337	3	be	be	AUX
ejpam-4511	337	4	a	a	DET
ejpam-4511	337	5	non	non	ADJ
ejpam-4511	337	6	-	-	ADJ
ejpam-4511	337	7	trivial	trivial	ADJ
ejpam-4511	337	8	connected	connected	ADJ
ejpam-4511	337	9	graph	graph	NOUN
ejpam-4511	337	10	on	on	ADP
ejpam-4511	337	11	m	m	NOUN
ejpam-4511	337	12	vertices	vertex	NOUN
ejpam-4511	337	13	and	and	CCONJ
ejpam-4511	337	14	let	let	VERB
ejpam-4511	337	15	h	h	NOUN
ejpam-4511	337	16	be	be	AUX
ejpam-4511	337	17	any	any	DET
ejpam-4511	337	18	graph	graph	NOUN
ejpam-4511	337	19	.	.	PUNCT
ejpam-4511	338	1	then	then	ADV
ejpam-4511	338	2	γhgr(g	γhgr(g	VERB
ejpam-4511	338	3	◦	◦	NOUN
ejpam-4511	338	4	h	h	NOUN
ejpam-4511	338	5	)	)	PUNCT
ejpam-4511	338	6	≥	≥	PROPN
ejpam-4511	338	7	m	m	PROPN
ejpam-4511	338	8	·	·	PUNCT
ejpam-4511	338	9	γcogr(h	γcogr(h	NOUN
ejpam-4511	338	10	)	)	PUNCT
ejpam-4511	338	11	=	=	PUNCT
ejpam-4511	338	12	m	m	PROPN
ejpam-4511	338	13	·	·	PUNCT
ejpam-4511	338	14	γgr(h	γgr(h	PROPN
ejpam-4511	338	15	)	)	PUNCT
ejpam-4511	338	16	.	.	PUNCT
ejpam-4511	339	1	proof	proof	NOUN
ejpam-4511	339	2	.	.	PUNCT
ejpam-4511	340	1	let	let	VERB
ejpam-4511	340	2	v	v	X
ejpam-4511	340	3	(	(	PUNCT
ejpam-4511	340	4	g	g	NOUN
ejpam-4511	340	5	)	)	PUNCT
ejpam-4511	340	6	=	=	SYM
ejpam-4511	340	7	{	{	PUNCT
ejpam-4511	340	8	v1	v1	PROPN
ejpam-4511	340	9	,	,	PUNCT
ejpam-4511	340	10	v2	v2	PROPN
ejpam-4511	340	11	,	,	PUNCT
ejpam-4511	340	12	.	.	PUNCT
ejpam-4511	340	13	.	.	PUNCT
ejpam-4511	341	1	.	.	PUNCT
ejpam-4511	342	1	,	,	PUNCT
ejpam-4511	342	2	vm	vm	NOUN
ejpam-4511	342	3	}	}	PUNCT
ejpam-4511	342	4	and	and	CCONJ
ejpam-4511	342	5	let	let	VERB
ejpam-4511	342	6	svi	svi	PROPN
ejpam-4511	342	7	=	=	SYM
ejpam-4511	342	8	(	(	PUNCT
ejpam-4511	342	9	w1	w1	PROPN
ejpam-4511	342	10	vi	vi	PROPN
ejpam-4511	342	11	,	,	PUNCT
ejpam-4511	342	12	w	w	PROPN
ejpam-4511	342	13	2	2	NUM
ejpam-4511	342	14	vi	vi	NOUN
ejpam-4511	342	15	,	,	PUNCT
ejpam-4511	342	16	·	·	PUNCT
ejpam-4511	342	17	·	·	PUNCT
ejpam-4511	342	18	·	·	PUNCT
ejpam-4511	342	19	,	,	PUNCT
ejpam-4511	342	20	w	w	PROPN
ejpam-4511	342	21	k	k	PROPN
ejpam-4511	342	22	vi	vi	X
ejpam-4511	342	23	)	)	PUNCT
ejpam-4511	342	24	be	be	VERB
ejpam-4511	342	25	a	a	DET
ejpam-4511	342	26	co	co	ADJ
ejpam-4511	342	27	-	-	ADJ
ejpam-4511	342	28	grundy	grundy	ADJ
ejpam-4511	342	29	dominating	dominating	NOUN
ejpam-4511	342	30	sequence	sequence	NOUN
ejpam-4511	342	31	in	in	ADP
ejpam-4511	342	32	hvi	hvi	NOUN
ejpam-4511	342	33	for	for	ADP
ejpam-4511	342	34	each	each	DET
ejpam-4511	342	35	i	i	PRON
ejpam-4511	342	36	∈	∈	PROPN
ejpam-4511	343	1	[	[	X
ejpam-4511	343	2	m	m	X
ejpam-4511	343	3	]	]	X
ejpam-4511	343	4	=	=	X
ejpam-4511	343	5	{	{	PUNCT
ejpam-4511	343	6	1	1	NUM
ejpam-4511	343	7	,	,	PUNCT
ejpam-4511	343	8	2	2	NUM
ejpam-4511	343	9	,	,	PUNCT
ejpam-4511	343	10	.	.	PUNCT
ejpam-4511	343	11	.	.	PUNCT
ejpam-4511	344	1	.	.	PUNCT
ejpam-4511	345	1	,	,	PUNCT
ejpam-4511	345	2	m	m	VERB
ejpam-4511	345	3	}	}	PUNCT
ejpam-4511	345	4	,	,	PUNCT
ejpam-4511	345	5	where	where	SCONJ
ejpam-4511	345	6	k	k	PROPN
ejpam-4511	345	7	=	=	SYM
ejpam-4511	345	8	γcogr(h	γcogr(h	PROPN
ejpam-4511	345	9	)	)	PUNCT
ejpam-4511	345	10	.	.	PUNCT
ejpam-4511	346	1	let	let	VERB
ejpam-4511	346	2	s	s	PRON
ejpam-4511	346	3	=	=	PUNCT
ejpam-4511	346	4	sv1	sv1	PROPN
ejpam-4511	346	5	⊕	⊕	PROPN
ejpam-4511	346	6	sv2	sv2	PROPN
ejpam-4511	346	7	⊕	⊕	PROPN
ejpam-4511	346	8	·	·	PUNCT
ejpam-4511	346	9	·	·	PUNCT
ejpam-4511	346	10	·	·	PUNCT
ejpam-4511	347	1	⊕	⊕	NOUN
ejpam-4511	347	2	svm	svm	VERB
ejpam-4511	347	3	.	.	PUNCT
ejpam-4511	348	1	let	let	VERB
ejpam-4511	348	2	x	x	SYM
ejpam-4511	348	3	∈	∈	PROPN
ejpam-4511	348	4	v	v	X
ejpam-4511	348	5	(	(	PUNCT
ejpam-4511	348	6	g	g	PROPN
ejpam-4511	348	7	◦	◦	NOUN
ejpam-4511	348	8	h	h	NOUN
ejpam-4511	348	9	)	)	PUNCT
ejpam-4511	348	10	\	\	NOUN
ejpam-4511	348	11	ŝ	ŝ	NOUN
ejpam-4511	348	12	and	and	CCONJ
ejpam-4511	348	13	let	let	VERB
ejpam-4511	348	14	vt	vt	PROPN
ejpam-4511	348	15	∈	∈	PROPN
ejpam-4511	348	16	v	v	X
ejpam-4511	348	17	(	(	PUNCT
ejpam-4511	348	18	g	g	NOUN
ejpam-4511	348	19	)	)	PUNCT
ejpam-4511	348	20	such	such	ADJ
ejpam-4511	348	21	that	that	SCONJ
ejpam-4511	348	22	x	x	SYM
ejpam-4511	348	23	∈	∈	NOUN
ejpam-4511	348	24	v	v	X
ejpam-4511	348	25	(	(	PUNCT
ejpam-4511	348	26	vt	vt	PROPN
ejpam-4511	348	27	+	+	PROPN
ejpam-4511	348	28	hvt	hvt	PROPN
ejpam-4511	348	29	)	)	PUNCT
ejpam-4511	348	30	.	.	PUNCT
ejpam-4511	349	1	suppose	suppose	VERB
ejpam-4511	349	2	first	first	ADV
ejpam-4511	349	3	that	that	SCONJ
ejpam-4511	349	4	x	x	X
ejpam-4511	349	5	=	=	SYM
ejpam-4511	349	6	vt	vt	PROPN
ejpam-4511	349	7	.	.	PUNCT
ejpam-4511	349	8	let	let	VERB
ejpam-4511	349	9	vs	vs	ADP
ejpam-4511	349	10	∈	∈	PROPN
ejpam-4511	349	11	ng(vt	ng(vt	PROPN
ejpam-4511	349	12	)	)	PUNCT
ejpam-4511	349	13	and	and	CCONJ
ejpam-4511	349	14	pick	pick	VERB
ejpam-4511	349	15	any	any	DET
ejpam-4511	349	16	wj	wj	PROPN
ejpam-4511	349	17	vs	vs	ADP
ejpam-4511	349	18	∈	∈	PROPN
ejpam-4511	349	19	ŝvs	ŝvs	NOUN
ejpam-4511	349	20	.	.	PUNCT
ejpam-4511	350	1	then	then	ADV
ejpam-4511	350	2	wj	wj	PROPN
ejpam-4511	350	3	vs	vs	ADP
ejpam-4511	350	4	∈	∈	PROPN
ejpam-4511	350	5	ŝ	ŝ	NOUN
ejpam-4511	350	6	∩	∩	PROPN
ejpam-4511	350	7	n2	n2	NOUN
ejpam-4511	350	8	g	g	PROPN
ejpam-4511	350	9	◦	◦	NOUN
ejpam-4511	350	10	h(vt	h(vt	NOUN
ejpam-4511	350	11	)	)	PUNCT
ejpam-4511	350	12	.	.	PUNCT
ejpam-4511	351	1	suppose	suppose	VERB
ejpam-4511	351	2	x	x	SYM
ejpam-4511	351	3	̸=	̸=	PROPN
ejpam-4511	351	4	vt	vt	PROPN
ejpam-4511	351	5	.	.	PUNCT
ejpam-4511	352	1	then	then	ADV
ejpam-4511	352	2	x	x	SYM
ejpam-4511	352	3	∈	∈	PROPN
ejpam-4511	352	4	v	v	X
ejpam-4511	352	5	(	(	PUNCT
ejpam-4511	352	6	hvt	hvt	PROPN
ejpam-4511	352	7	)	)	PUNCT
ejpam-4511	352	8	\	\	PUNCT
ejpam-4511	353	1	ŝvt	ŝvt	INTJ
ejpam-4511	353	2	.	.	PUNCT
ejpam-4511	354	1	since	since	SCONJ
ejpam-4511	354	2	ŝvt	ŝvt	ADV
ejpam-4511	354	3	is	be	AUX
ejpam-4511	354	4	a	a	DET
ejpam-4511	354	5	co	co	ADJ
ejpam-4511	354	6	-	-	ADJ
ejpam-4511	354	7	grundy	grundy	ADJ
ejpam-4511	354	8	dominating	dominating	NOUN
ejpam-4511	354	9	set	set	VERB
ejpam-4511	354	10	inhvt	inhvt	NOUN
ejpam-4511	354	11	,	,	PUNCT
ejpam-4511	354	12	it	it	PRON
ejpam-4511	354	13	follows	follow	VERB
ejpam-4511	354	14	that	that	SCONJ
ejpam-4511	354	15	there	there	PRON
ejpam-4511	354	16	exists	exist	VERB
ejpam-4511	354	17	wl	wl	PROPN
ejpam-4511	354	18	vt	vt	PROPN
ejpam-4511	354	19	∈	∈	PROPN
ejpam-4511	354	20	ŝvt	ŝvt	ADV
ejpam-4511	354	21	⊆	⊆	NUM
ejpam-4511	354	22	ŝ	ŝ	ADP
ejpam-4511	354	23	such	such	ADJ
ejpam-4511	354	24	that	that	DET
ejpam-4511	354	25	dhvt	dhvt	NOUN
ejpam-4511	354	26	(	(	PUNCT
ejpam-4511	354	27	x	x	X
ejpam-4511	354	28	,	,	PUNCT
ejpam-4511	354	29	wl	wl	PROPN
ejpam-4511	354	30	vt	vt	PROPN
ejpam-4511	354	31	)	)	PUNCT
ejpam-4511	354	32	̸=	̸=	PROPN
ejpam-4511	354	33	1	1	NUM
ejpam-4511	354	34	.	.	PUNCT
ejpam-4511	355	1	it	it	PRON
ejpam-4511	355	2	follows	follow	VERB
ejpam-4511	355	3	that	that	SCONJ
ejpam-4511	355	4	dg	dg	AUX
ejpam-4511	355	5	◦	◦	NOUN
ejpam-4511	355	6	h(x	h(x	PROPN
ejpam-4511	355	7	,	,	PUNCT
ejpam-4511	355	8	wl	wl	PROPN
ejpam-4511	355	9	vt	vt	PROPN
ejpam-4511	355	10	)	)	PUNCT
ejpam-4511	355	11	=	=	SYM
ejpam-4511	356	1	2	2	X
ejpam-4511	356	2	.	.	PUNCT
ejpam-4511	356	3	thus	thus	ADV
ejpam-4511	356	4	,	,	PUNCT
ejpam-4511	356	5	ŝ	ŝ	X
ejpam-4511	356	6	is	be	AUX
ejpam-4511	356	7	a	a	DET
ejpam-4511	356	8	hop	hop	NOUN
ejpam-4511	356	9	dominating	dominating	NOUN
ejpam-4511	356	10	set	set	VERB
ejpam-4511	356	11	in	in	ADP
ejpam-4511	356	12	g	g	PROPN
ejpam-4511	356	13	◦	◦	NOUN
ejpam-4511	356	14	h.	h.	NOUN
ejpam-4511	356	15	we	we	PRON
ejpam-4511	356	16	relabel	relabel	VERB
ejpam-4511	356	17	the	the	DET
ejpam-4511	356	18	terms	term	NOUN
ejpam-4511	356	19	in	in	ADP
ejpam-4511	356	20	s	s	NOUN
ejpam-4511	356	21	,	,	PUNCT
ejpam-4511	356	22	say	say	VERB
ejpam-4511	356	23	s	s	X
ejpam-4511	356	24	=	=	PUNCT
ejpam-4511	356	25	(	(	PUNCT
ejpam-4511	356	26	x1	x1	PROPN
ejpam-4511	356	27	,	,	PUNCT
ejpam-4511	356	28	x2	x2	PROPN
ejpam-4511	356	29	,	,	PUNCT
ejpam-4511	356	30	·	·	PUNCT
ejpam-4511	356	31	·	·	PUNCT
ejpam-4511	356	32	·	·	PUNCT
ejpam-4511	356	33	,	,	PUNCT
ejpam-4511	356	34	xk	xk	PROPN
ejpam-4511	356	35	,	,	PUNCT
ejpam-4511	356	36	·	·	PUNCT
ejpam-4511	356	37	·	·	PUNCT
ejpam-4511	356	38	·	·	PUNCT
ejpam-4511	356	39	,	,	PUNCT
ejpam-4511	356	40	xmk	xmk	PROPN
ejpam-4511	356	41	)	)	PUNCT
ejpam-4511	356	42	.	.	PUNCT
ejpam-4511	357	1	next	next	ADV
ejpam-4511	357	2	,	,	PUNCT
ejpam-4511	357	3	let	let	VERB
ejpam-4511	357	4	i	i	PRON
ejpam-4511	357	5	∈	∈	PROPN
ejpam-4511	358	1	[	[	X
ejpam-4511	358	2	mk	mk	X
ejpam-4511	358	3	]	]	X
ejpam-4511	358	4	\	\	X
ejpam-4511	358	5	{	{	PUNCT
ejpam-4511	358	6	1	1	NUM
ejpam-4511	358	7	}	}	PUNCT
ejpam-4511	358	8	and	and	CCONJ
ejpam-4511	358	9	let	let	VERB
ejpam-4511	358	10	xi	xi	NOUN
ejpam-4511	358	11	=	=	PUNCT
ejpam-4511	358	12	wt	wt	ADP
ejpam-4511	358	13	vr	vr	NOUN
ejpam-4511	358	14	,	,	PUNCT
ejpam-4511	358	15	where	where	SCONJ
ejpam-4511	358	16	r	r	NOUN
ejpam-4511	358	17	∈	∈	PROPN
ejpam-4511	359	1	[	[	X
ejpam-4511	359	2	m	m	X
ejpam-4511	359	3	]	]	X
ejpam-4511	359	4	and	and	CCONJ
ejpam-4511	359	5	t	t	PROPN
ejpam-4511	359	6	∈	∈	PROPN
ejpam-4511	359	7	[	[	X
ejpam-4511	359	8	k	k	X
ejpam-4511	359	9	]	]	X
ejpam-4511	359	10	.	.	PUNCT
ejpam-4511	360	1	then	then	ADV
ejpam-4511	360	2	n2	n2	PROPN
ejpam-4511	360	3	g	g	PROPN
ejpam-4511	360	4	◦	◦	NOUN
ejpam-4511	360	5	h	h	NOUN
ejpam-4511	361	1	[	[	X
ejpam-4511	361	2	xi	xi	X
ejpam-4511	361	3	]	]	PUNCT
ejpam-4511	361	4	\	\	X
ejpam-4511	361	5	∪i−1	∪i−1	PROPN
ejpam-4511	361	6	j=1n	j=1n	NOUN
ejpam-4511	361	7	2	2	NUM
ejpam-4511	361	8	g	g	NOUN
ejpam-4511	361	9	◦	◦	NOUN
ejpam-4511	361	10	h	h	NOUN
ejpam-4511	362	1	[	[	X
ejpam-4511	362	2	xj	xj	X
ejpam-4511	362	3	]	]	X
ejpam-4511	362	4	=	=	PUNCT
ejpam-4511	362	5	n2	n2	PROPN
ejpam-4511	362	6	g	g	PROPN
ejpam-4511	362	7	◦	◦	NOUN
ejpam-4511	362	8	h	h	NOUN
ejpam-4511	363	1	[	[	X
ejpam-4511	363	2	wt	wt	X
ejpam-4511	363	3	vr	vr	X
ejpam-4511	363	4	]	]	PUNCT
ejpam-4511	363	5	\	\	PUNCT
ejpam-4511	364	1	[	[	X
ejpam-4511	364	2	(	(	PUNCT
ejpam-4511	364	3	∪	∪	ADP
ejpam-4511	364	4	t−1	t−1	PROPN
ejpam-4511	364	5	s=1n	s=1n	NOUN
ejpam-4511	364	6	2	2	NUM
ejpam-4511	364	7	g	g	NOUN
ejpam-4511	364	8	◦	◦	NOUN
ejpam-4511	364	9	h	h	NOUN
ejpam-4511	365	1	[	[	X
ejpam-4511	365	2	ws	ws	X
ejpam-4511	365	3	vr	vr	X
ejpam-4511	365	4	]	]	X
ejpam-4511	365	5	)	)	PUNCT
ejpam-4511	365	6	∪	∪	ADV
ejpam-4511	365	7	(	(	PUNCT
ejpam-4511	365	8	∪{n2	∪{n2	NOUN
ejpam-4511	365	9	g	g	PROPN
ejpam-4511	365	10	◦	◦	NOUN
ejpam-4511	365	11	h	h	NOUN
ejpam-4511	366	1	[	[	X
ejpam-4511	366	2	wp	wp	NOUN
ejpam-4511	366	3	vq	vq	NOUN
ejpam-4511	366	4	]	]	X
ejpam-4511	366	5	:	:	PUNCT
ejpam-4511	366	6	p	p	X
ejpam-4511	366	7	∈	∈	PROPN
ejpam-4511	367	1	[	[	X
ejpam-4511	367	2	k	k	X
ejpam-4511	367	3	]	]	X
ejpam-4511	367	4	and	and	CCONJ
ejpam-4511	367	5	1	1	NUM
ejpam-4511	367	6	≤	≤	NUM
ejpam-4511	367	7	q	q	ADJ
ejpam-4511	367	8	≤	≤	NUM
ejpam-4511	367	9	r	r	NOUN
ejpam-4511	367	10	−	−	NOUN
ejpam-4511	367	11	1	1	NUM
ejpam-4511	367	12	}	}	PUNCT
ejpam-4511	367	13	)	)	PUNCT
ejpam-4511	367	14	]	]	PUNCT
ejpam-4511	367	15	.	.	PUNCT
ejpam-4511	368	1	if	if	SCONJ
ejpam-4511	368	2	t	t	NOUN
ejpam-4511	368	3	=	=	SYM
ejpam-4511	368	4	1	1	NUM
ejpam-4511	368	5	,	,	PUNCT
ejpam-4511	368	6	then	then	ADV
ejpam-4511	368	7	n2	n2	PROPN
ejpam-4511	368	8	g	g	PROPN
ejpam-4511	368	9	◦	◦	NOUN
ejpam-4511	368	10	h	h	NOUN
ejpam-4511	368	11	[	[	X
ejpam-4511	368	12	wt	wt	X
ejpam-4511	368	13	vr	vr	X
ejpam-4511	368	14	]	]	PUNCT
ejpam-4511	368	15	\	\	PUNCT
ejpam-4511	368	16	(	(	PUNCT
ejpam-4511	368	17	∪	∪	ADP
ejpam-4511	368	18	t−1	t−1	PROPN
ejpam-4511	368	19	s=1n	s=1n	NOUN
ejpam-4511	368	20	2	2	NUM
ejpam-4511	368	21	g	g	NOUN
ejpam-4511	368	22	◦	◦	NOUN
ejpam-4511	368	23	h	h	NOUN
ejpam-4511	369	1	[	[	X
ejpam-4511	369	2	ws	ws	X
ejpam-4511	369	3	vr	vr	NOUN
ejpam-4511	369	4	]	]	PUNCT
ejpam-4511	369	5	)	)	PUNCT
ejpam-4511	370	1	=	=	SYM
ejpam-4511	370	2	n2	n2	PROPN
ejpam-4511	370	3	g	g	PROPN
ejpam-4511	370	4	◦	◦	NOUN
ejpam-4511	370	5	h	h	NOUN
ejpam-4511	371	1	[	[	X
ejpam-4511	371	2	wt	wt	X
ejpam-4511	371	3	vr	vr	X
ejpam-4511	371	4	]	]	PUNCT
ejpam-4511	371	5	.	.	PUNCT
ejpam-4511	372	1	clearly	clearly	ADV
ejpam-4511	372	2	,	,	PUNCT
ejpam-4511	372	3	wt	wt	PROPN
ejpam-4511	372	4	vr	vr	PROPN
ejpam-4511	372	5	∈	∈	PROPN
ejpam-4511	372	6	n2	n2	NOUN
ejpam-4511	372	7	g	g	PROPN
ejpam-4511	372	8	◦	◦	NOUN
ejpam-4511	372	9	h	h	NOUN
ejpam-4511	373	1	[	[	X
ejpam-4511	373	2	wt	wt	X
ejpam-4511	373	3	vr	vr	X
ejpam-4511	373	4	]	]	PUNCT
ejpam-4511	373	5	\	\	PUNCT
ejpam-4511	374	1	[	[	X
ejpam-4511	374	2	∪{n	∪{n	PROPN
ejpam-4511	374	3	2	2	NUM
ejpam-4511	374	4	g	g	NOUN
ejpam-4511	374	5	◦	◦	NOUN
ejpam-4511	374	6	h	h	NOUN
ejpam-4511	374	7	[	[	X
ejpam-4511	374	8	wp	wp	NOUN
ejpam-4511	374	9	vq	vq	NOUN
ejpam-4511	374	10	]	]	X
ejpam-4511	374	11	:	:	PUNCT
ejpam-4511	374	12	p	p	X
ejpam-4511	374	13	∈	∈	PROPN
ejpam-4511	374	14	[	[	X
ejpam-4511	374	15	k	k	X
ejpam-4511	374	16	]	]	X
ejpam-4511	374	17	and	and	CCONJ
ejpam-4511	374	18	1	1	NUM
ejpam-4511	374	19	≤	≤	NUM
ejpam-4511	374	20	q	q	ADJ
ejpam-4511	374	21	≤	≤	NUM
ejpam-4511	374	22	r	r	NOUN
ejpam-4511	374	23	−	−	NOUN
ejpam-4511	374	24	1	1	NUM
ejpam-4511	374	25	}	}	PUNCT
ejpam-4511	374	26	]	]	PUNCT
ejpam-4511	374	27	.	.	PUNCT
ejpam-4511	375	1	suppose	suppose	VERB
ejpam-4511	376	1	t	t	PROPN
ejpam-4511	376	2	̸=	̸=	PROPN
ejpam-4511	376	3	1	1	NUM
ejpam-4511	376	4	.	.	PUNCT
ejpam-4511	377	1	then	then	ADV
ejpam-4511	377	2	n2	n2	PROPN
ejpam-4511	377	3	g	g	PROPN
ejpam-4511	377	4	◦	◦	NOUN
ejpam-4511	377	5	h	h	NOUN
ejpam-4511	378	1	[	[	X
ejpam-4511	378	2	wt	wt	X
ejpam-4511	378	3	vr	vr	X
ejpam-4511	378	4	]	]	PUNCT
ejpam-4511	378	5	\	\	PUNCT
ejpam-4511	378	6	(	(	PUNCT
ejpam-4511	378	7	∪	∪	ADP
ejpam-4511	378	8	t−1	t−1	PROPN
ejpam-4511	378	9	s=1n	s=1n	NOUN
ejpam-4511	378	10	2	2	NUM
ejpam-4511	378	11	g	g	NOUN
ejpam-4511	378	12	◦	◦	NOUN
ejpam-4511	378	13	h	h	NOUN
ejpam-4511	379	1	[	[	X
ejpam-4511	379	2	ws	ws	X
ejpam-4511	379	3	vr	vr	NOUN
ejpam-4511	379	4	]	]	X
ejpam-4511	379	5	)	)	PUNCT
ejpam-4511	379	6	=	=	PUNCT
ejpam-4511	380	1	[	[	X
ejpam-4511	380	2	v	v	X
ejpam-4511	380	3	(	(	PUNCT
ejpam-4511	380	4	hvr	hvr	PROPN
ejpam-4511	380	5	)	)	PUNCT
ejpam-4511	380	6	\nhvr	\nhvr	PROPN
ejpam-4511	380	7	(	(	PUNCT
ejpam-4511	380	8	wt	wt	PROPN
ejpam-4511	380	9	vr	vr	PROPN
ejpam-4511	380	10	)	)	PUNCT
ejpam-4511	380	11	]	]	PUNCT
ejpam-4511	380	12	\	\	PUNCT
ejpam-4511	381	1	[	[	X
ejpam-4511	381	2	∪t−1	∪t−1	X
ejpam-4511	381	3	s=1(v	s=1(v	X
ejpam-4511	381	4	(	(	PUNCT
ejpam-4511	381	5	hvr	hvr	PROPN
ejpam-4511	381	6	)	)	PUNCT
ejpam-4511	381	7	\nhvr	\nhvr	PROPN
ejpam-4511	381	8	(	(	PUNCT
ejpam-4511	381	9	ws	ws	PROPN
ejpam-4511	381	10	vr	vr	PROPN
ejpam-4511	381	11	)	)	PUNCT
ejpam-4511	381	12	)	)	PUNCT
ejpam-4511	381	13	]	]	PUNCT
ejpam-4511	381	14	̸=	̸=	NOUN
ejpam-4511	381	15	∅	∅	NOUN
ejpam-4511	381	16	because	because	SCONJ
ejpam-4511	381	17	svr	svr	PROPN
ejpam-4511	381	18	is	be	AUX
ejpam-4511	381	19	a	a	DET
ejpam-4511	381	20	co	co	ADJ
ejpam-4511	381	21	-	-	ADJ
ejpam-4511	381	22	legal	legal	ADJ
ejpam-4511	381	23	neighborhood	neighborhood	NOUN
ejpam-4511	381	24	sequence	sequence	NOUN
ejpam-4511	381	25	in	in	ADP
ejpam-4511	381	26	hvr	hvr	PROPN
ejpam-4511	381	27	.	.	PUNCT
ejpam-4511	382	1	since	since	SCONJ
ejpam-4511	382	2	n2	n2	PROPN
ejpam-4511	382	3	g	g	PROPN
ejpam-4511	382	4	◦	◦	NOUN
ejpam-4511	382	5	h	h	NOUN
ejpam-4511	383	1	[	[	X
ejpam-4511	383	2	wt	wt	X
ejpam-4511	383	3	vr	vr	X
ejpam-4511	383	4	]	]	PUNCT
ejpam-4511	383	5	\	\	PUNCT
ejpam-4511	383	6	(	(	PUNCT
ejpam-4511	383	7	∪	∪	ADP
ejpam-4511	383	8	t−1	t−1	PROPN
ejpam-4511	383	9	s=1n	s=1n	NOUN
ejpam-4511	383	10	2	2	NUM
ejpam-4511	383	11	g	g	NOUN
ejpam-4511	383	12	◦	◦	NOUN
ejpam-4511	383	13	h	h	NOUN
ejpam-4511	384	1	[	[	X
ejpam-4511	384	2	ws	ws	X
ejpam-4511	384	3	vr	vr	X
ejpam-4511	384	4	]	]	X
ejpam-4511	384	5	)	)	PUNCT
ejpam-4511	384	6	∩	∩	NOUN
ejpam-4511	385	1	[	[	X
ejpam-4511	385	2	∪{n2	∪{n2	NOUN
ejpam-4511	385	3	g	g	PROPN
ejpam-4511	385	4	◦	◦	NOUN
ejpam-4511	385	5	h	h	NOUN
ejpam-4511	386	1	[	[	X
ejpam-4511	386	2	wp	wp	NOUN
ejpam-4511	386	3	vq	vq	NOUN
ejpam-4511	386	4	]	]	X
ejpam-4511	386	5	:	:	PUNCT
ejpam-4511	386	6	p	p	X
ejpam-4511	386	7	∈	∈	PROPN
ejpam-4511	387	1	[	[	X
ejpam-4511	387	2	k	k	X
ejpam-4511	387	3	]	]	X
ejpam-4511	387	4	and	and	CCONJ
ejpam-4511	387	5	1	1	NUM
ejpam-4511	387	6	≤	≤	NUM
ejpam-4511	387	7	q	q	ADJ
ejpam-4511	387	8	≤	≤	NUM
ejpam-4511	387	9	r	r	NOUN
ejpam-4511	387	10	−	−	NOUN
ejpam-4511	387	11	1	1	NUM
ejpam-4511	387	12	}	}	PUNCT
ejpam-4511	387	13	]	]	PUNCT
ejpam-4511	387	14	=	=	SYM
ejpam-4511	387	15	∅	∅	NOUN
ejpam-4511	387	16	,	,	PUNCT
ejpam-4511	387	17	n2	n2	NOUN
ejpam-4511	387	18	g	g	PROPN
ejpam-4511	387	19	◦	◦	NOUN
ejpam-4511	387	20	h	h	NOUN
ejpam-4511	388	1	[	[	X
ejpam-4511	388	2	xi	xi	X
ejpam-4511	388	3	]	]	PUNCT
ejpam-4511	388	4	\	\	X
ejpam-4511	388	5	∪i−1	∪i−1	PROPN
ejpam-4511	388	6	j=1n	j=1n	NOUN
ejpam-4511	388	7	2	2	NUM
ejpam-4511	388	8	g	g	NOUN
ejpam-4511	388	9	◦	◦	NOUN
ejpam-4511	388	10	h	h	NOUN
ejpam-4511	389	1	[	[	X
ejpam-4511	389	2	xj	xj	X
ejpam-4511	389	3	]	]	X
ejpam-4511	389	4	̸=	̸=	PROPN
ejpam-4511	389	5	∅.	∅.	VERB
ejpam-4511	389	6	therefore	therefore	ADV
ejpam-4511	389	7	,	,	PUNCT
ejpam-4511	389	8	s	s	PART
ejpam-4511	389	9	is	be	AUX
ejpam-4511	389	10	a	a	DET
ejpam-4511	389	11	grundy	grundy	PROPN
ejpam-4511	389	12	hop	hop	NOUN
ejpam-4511	389	13	dominating	dominating	NOUN
ejpam-4511	389	14	sequence	sequence	NOUN
ejpam-4511	389	15	in	in	ADP
ejpam-4511	389	16	g	g	PROPN
ejpam-4511	389	17	◦	◦	NOUN
ejpam-4511	389	18	h.	h.	NOUN
ejpam-4511	389	19	accordingly	accordingly	ADV
ejpam-4511	389	20	,	,	PUNCT
ejpam-4511	389	21	γhgr(g	γhgr(g	VERB
ejpam-4511	389	22	◦	◦	NOUN
ejpam-4511	389	23	h	h	NOUN
ejpam-4511	389	24	)	)	PUNCT
ejpam-4511	389	25	≥	≥	NOUN
ejpam-4511	389	26	|ŝ|	|ŝ|	NUM
ejpam-4511	389	27	=	=	SYM
ejpam-4511	389	28	m∑	m∑	NOUN
ejpam-4511	389	29	i=1	i=1	PROPN
ejpam-4511	389	30	|ŝvi	|ŝvi	PROPN
ejpam-4511	389	31	|	|	PROPN
ejpam-4511	389	32	=	=	PROPN
ejpam-4511	389	33	m	m	PROPN
ejpam-4511	389	34	·	·	PUNCT
ejpam-4511	389	35	γcogr(h	γcogr(h	NOUN
ejpam-4511	389	36	)	)	PUNCT
ejpam-4511	389	37	=	=	PUNCT
ejpam-4511	389	38	m	m	PROPN
ejpam-4511	389	39	·	·	PUNCT
ejpam-4511	389	40	γgr(h	γgr(h	PROPN
ejpam-4511	389	41	)	)	PUNCT
ejpam-4511	389	42	.	.	PUNCT
ejpam-4511	390	1	this	this	PRON
ejpam-4511	390	2	proves	prove	VERB
ejpam-4511	390	3	the	the	DET
ejpam-4511	390	4	assertion	assertion	NOUN
ejpam-4511	390	5	.	.	PUNCT
ejpam-4511	391	1	j.	j.	PROPN
ejpam-4511	391	2	hassan	hassan	PROPN
ejpam-4511	391	3	,	,	PUNCT
ejpam-4511	391	4	s.	s.	PROPN
ejpam-4511	391	5	canoy	canoy	PROPN
ejpam-4511	391	6	/	/	SYM
ejpam-4511	391	7	eur	eur	PROPN
ejpam-4511	391	8	.	.	PUNCT
ejpam-4511	392	1	j.	j.	PROPN
ejpam-4511	392	2	pure	pure	PROPN
ejpam-4511	392	3	appl	appl	PROPN
ejpam-4511	392	4	.	.	PROPN
ejpam-4511	392	5	math	math	PROPN
ejpam-4511	392	6	,	,	PUNCT
ejpam-4511	392	7	15	15	NUM
ejpam-4511	392	8	(	(	PUNCT
ejpam-4511	392	9	4	4	NUM
ejpam-4511	392	10	)	)	PUNCT
ejpam-4511	392	11	(	(	PUNCT
ejpam-4511	392	12	2022	2022	NUM
ejpam-4511	392	13	)	)	PUNCT
ejpam-4511	392	14	,	,	PUNCT
ejpam-4511	392	15	1623	1623	NUM
ejpam-4511	392	16	-	-	SYM
ejpam-4511	392	17	1636	1636	NUM
ejpam-4511	392	18	1633	1633	NUM
ejpam-4511	392	19	remark	remark	NOUN
ejpam-4511	392	20	3	3	NUM
ejpam-4511	392	21	.	.	PUNCT
ejpam-4511	393	1	the	the	DET
ejpam-4511	393	2	bound	bind	VERB
ejpam-4511	393	3	given	give	VERB
ejpam-4511	393	4	in	in	ADP
ejpam-4511	393	5	theorem	theorem	NOUN
ejpam-4511	393	6	6	6	NUM
ejpam-4511	393	7	is	be	AUX
ejpam-4511	393	8	tight	tight	ADJ
ejpam-4511	393	9	.	.	PUNCT
ejpam-4511	394	1	moreover	moreover	ADV
ejpam-4511	394	2	,	,	PUNCT
ejpam-4511	394	3	strict	strict	ADJ
ejpam-4511	394	4	inequality	inequality	NOUN
ejpam-4511	394	5	can	can	AUX
ejpam-4511	394	6	also	also	ADV
ejpam-4511	394	7	be	be	AUX
ejpam-4511	394	8	attained	attain	VERB
ejpam-4511	394	9	.	.	PUNCT
ejpam-4511	395	1	to	to	PART
ejpam-4511	395	2	see	see	VERB
ejpam-4511	395	3	this	this	PRON
ejpam-4511	395	4	,	,	PUNCT
ejpam-4511	395	5	consider	consider	VERB
ejpam-4511	395	6	g	g	NOUN
ejpam-4511	395	7	=	=	PUNCT
ejpam-4511	395	8	k3	k3	ADJ
ejpam-4511	395	9	and	and	CCONJ
ejpam-4511	395	10	h	h	NOUN
ejpam-4511	395	11	=	=	PROPN
ejpam-4511	395	12	p3	p3	PROPN
ejpam-4511	395	13	.	.	PUNCT
ejpam-4511	396	1	then	then	ADV
ejpam-4511	396	2	γcogr(h	γcogr(h	NOUN
ejpam-4511	396	3	)	)	PUNCT
ejpam-4511	396	4	=	=	SYM
ejpam-4511	396	5	2	2	NUM
ejpam-4511	396	6	and	and	CCONJ
ejpam-4511	396	7	γhgr(g	γhgr(g	VERB
ejpam-4511	396	8	◦	◦	NOUN
ejpam-4511	396	9	h	h	NOUN
ejpam-4511	396	10	)	)	PUNCT
ejpam-4511	396	11	=	=	SYM
ejpam-4511	396	12	3γcogr(h	3γcogr(h	NUM
ejpam-4511	396	13	)	)	PUNCT
ejpam-4511	396	14	=	=	PUNCT
ejpam-4511	397	1	6	6	X
ejpam-4511	397	2	.	.	X
ejpam-4511	398	1	for	for	ADP
ejpam-4511	398	2	the	the	DET
ejpam-4511	398	3	strict	strict	ADJ
ejpam-4511	398	4	inequality	inequality	NOUN
ejpam-4511	398	5	,	,	PUNCT
ejpam-4511	398	6	consider	consider	VERB
ejpam-4511	398	7	the	the	DET
ejpam-4511	398	8	graphs	graph	NOUN
ejpam-4511	398	9	g	g	NOUN
ejpam-4511	398	10	and	and	CCONJ
ejpam-4511	398	11	g	g	PROPN
ejpam-4511	398	12	◦	◦	NOUN
ejpam-4511	398	13	k1	k1	NOUN
ejpam-4511	398	14	in	in	ADP
ejpam-4511	398	15	figure	figure	NOUN
ejpam-4511	398	16	3	3	NUM
ejpam-4511	398	17	.	.	PUNCT
ejpam-4511	399	1	then	then	ADV
ejpam-4511	399	2	γcogr(k1	γcogr(k1	NOUN
ejpam-4511	399	3	)	)	PUNCT
ejpam-4511	399	4	=	=	SYM
ejpam-4511	399	5	1	1	NUM
ejpam-4511	399	6	and	and	CCONJ
ejpam-4511	399	7	s	s	NOUN
ejpam-4511	399	8	=	=	X
ejpam-4511	399	9	(	(	PUNCT
ejpam-4511	399	10	7	7	NUM
ejpam-4511	399	11	,	,	PUNCT
ejpam-4511	399	12	5	5	NUM
ejpam-4511	399	13	,	,	PUNCT
ejpam-4511	399	14	1	1	NUM
ejpam-4511	399	15	,	,	PUNCT
ejpam-4511	399	16	4	4	NUM
ejpam-4511	399	17	,	,	PUNCT
ejpam-4511	399	18	3	3	NUM
ejpam-4511	399	19	)	)	PUNCT
ejpam-4511	399	20	is	be	AUX
ejpam-4511	399	21	a	a	DET
ejpam-4511	399	22	grundy	grundy	PROPN
ejpam-4511	399	23	hop	hop	NOUN
ejpam-4511	399	24	dominating	dominating	NOUN
ejpam-4511	399	25	sequence	sequence	NOUN
ejpam-4511	399	26	in	in	ADP
ejpam-4511	399	27	g	g	PROPN
ejpam-4511	399	28	◦	◦	NOUN
ejpam-4511	399	29	k1	k1	NOUN
ejpam-4511	399	30	with	with	ADP
ejpam-4511	399	31	γhgr(g	γhgr(g	PROPN
ejpam-4511	399	32	◦	◦	NOUN
ejpam-4511	399	33	k1	k1	NOUN
ejpam-4511	399	34	)	)	PUNCT
ejpam-4511	399	35	=	=	SYM
ejpam-4511	399	36	|s|	|s|	NOUN
ejpam-4511	399	37	=	=	SYM
ejpam-4511	399	38	5	5	NUM
ejpam-4511	399	39	>	>	SYM
ejpam-4511	399	40	4	4	NUM
ejpam-4511	399	41	=	=	SYM
ejpam-4511	399	42	4γcogr(k1	4γcogr(k1	ADJ
ejpam-4511	399	43	)	)	PUNCT
ejpam-4511	399	44	.	.	PUNCT
ejpam-4511	400	1	g	g	NOUN
ejpam-4511	400	2	:	:	PUNCT
ejpam-4511	400	3	g	g	PROPN
ejpam-4511	400	4	◦	◦	NOUN
ejpam-4511	400	5	k1	k1	NOUN
ejpam-4511	400	6	:	:	PUNCT
ejpam-4511	400	7	1	1	NUM
ejpam-4511	400	8	2	2	NUM
ejpam-4511	400	9	34	34	NUM
ejpam-4511	400	10	5	5	NUM
ejpam-4511	400	11	6	6	NUM
ejpam-4511	400	12	7	7	NUM
ejpam-4511	400	13	8	8	NUM
ejpam-4511	400	14	figure	figure	NOUN
ejpam-4511	400	15	3	3	NUM
ejpam-4511	400	16	:	:	PUNCT
ejpam-4511	400	17	the	the	DET
ejpam-4511	400	18	corona	corona	NOUN
ejpam-4511	400	19	g	g	PROPN
ejpam-4511	400	20	◦	◦	NOUN
ejpam-4511	400	21	k1	k1	NOUN
ejpam-4511	400	22	with	with	ADP
ejpam-4511	400	23	γh	γh	PROPN
ejpam-4511	400	24	gr(g	gr(g	PUNCT
ejpam-4511	400	25	◦	◦	NOUN
ejpam-4511	400	26	k1	k1	NOUN
ejpam-4511	400	27	)	)	PUNCT
ejpam-4511	400	28	=	=	SYM
ejpam-4511	400	29	5	5	NUM
ejpam-4511	400	30	theorem	theorem	VERB
ejpam-4511	400	31	7	7	NUM
ejpam-4511	400	32	.	.	PUNCT
ejpam-4511	401	1	let	let	VERB
ejpam-4511	401	2	g	g	NOUN
ejpam-4511	401	3	and	and	CCONJ
ejpam-4511	401	4	h	h	PROPN
ejpam-4511	401	5	be	be	VERB
ejpam-4511	401	6	non	non	ADJ
ejpam-4511	401	7	-	-	ADJ
ejpam-4511	401	8	trivial	trivial	ADJ
ejpam-4511	401	9	connected	connected	ADJ
ejpam-4511	401	10	graphs	graph	NOUN
ejpam-4511	401	11	.	.	PUNCT
ejpam-4511	402	1	let	let	VERB
ejpam-4511	402	2	sg	sg	VERB
ejpam-4511	402	3	=	=	SYM
ejpam-4511	402	4	(	(	PUNCT
ejpam-4511	402	5	v1	v1	PROPN
ejpam-4511	402	6	,	,	PUNCT
ejpam-4511	402	7	v2	v2	PROPN
ejpam-4511	402	8	,	,	PUNCT
ejpam-4511	402	9	·	·	PUNCT
ejpam-4511	402	10	·	·	PUNCT
ejpam-4511	402	11	·	·	PUNCT
ejpam-4511	402	12	,	,	PUNCT
ejpam-4511	402	13	vk	vk	AUX
ejpam-4511	402	14	)	)	PUNCT
ejpam-4511	402	15	be	be	AUX
ejpam-4511	402	16	a	a	DET
ejpam-4511	402	17	legal	legal	ADJ
ejpam-4511	402	18	closed	close	VERB
ejpam-4511	402	19	hop	hop	NOUN
ejpam-4511	402	20	independent	independent	ADJ
ejpam-4511	402	21	neighborhood	neighborhood	NOUN
ejpam-4511	402	22	sequence	sequence	NOUN
ejpam-4511	402	23	of	of	ADP
ejpam-4511	402	24	g	g	NOUN
ejpam-4511	402	25	and	and	CCONJ
ejpam-4511	402	26	let	let	VERB
ejpam-4511	402	27	sh	sh	NOUN
ejpam-4511	402	28	=	=	SYM
ejpam-4511	402	29	(	(	PUNCT
ejpam-4511	402	30	a1	a1	PROPN
ejpam-4511	402	31	,	,	PUNCT
ejpam-4511	402	32	a2	a2	PROPN
ejpam-4511	402	33	,	,	PUNCT
ejpam-4511	402	34	·	·	PUNCT
ejpam-4511	402	35	·	·	PUNCT
ejpam-4511	402	36	·	·	PUNCT
ejpam-4511	402	37	,	,	PUNCT
ejpam-4511	402	38	at	at	AUX
ejpam-4511	402	39	)	)	PUNCT
ejpam-4511	402	40	be	be	AUX
ejpam-4511	402	41	a	a	DET
ejpam-4511	402	42	co	co	ADJ
ejpam-4511	402	43	-	-	ADJ
ejpam-4511	402	44	legal	legal	ADJ
ejpam-4511	402	45	neighborhood	neighborhood	NOUN
ejpam-4511	402	46	sequence	sequence	NOUN
ejpam-4511	402	47	of	of	ADP
ejpam-4511	402	48	h.	h.	PROPN
ejpam-4511	402	49	then	then	ADV
ejpam-4511	402	50	s	s	VERB
ejpam-4511	402	51	=	=	SYM
ejpam-4511	402	52	(	(	PUNCT
ejpam-4511	402	53	(	(	PUNCT
ejpam-4511	402	54	v1	v1	NOUN
ejpam-4511	402	55	,	,	PUNCT
ejpam-4511	402	56	a1	a1	NOUN
ejpam-4511	402	57	)	)	PUNCT
ejpam-4511	402	58	,	,	PUNCT
ejpam-4511	402	59	(	(	PUNCT
ejpam-4511	402	60	v1	v1	NOUN
ejpam-4511	402	61	,	,	PUNCT
ejpam-4511	402	62	a2	a2	PROPN
ejpam-4511	402	63	)	)	PUNCT
ejpam-4511	402	64	,	,	PUNCT
ejpam-4511	402	65	·	·	PUNCT
ejpam-4511	402	66	·	·	PUNCT
ejpam-4511	402	67	·	·	PUNCT
ejpam-4511	402	68	,	,	PUNCT
ejpam-4511	402	69	(	(	PUNCT
ejpam-4511	402	70	v1	v1	NOUN
ejpam-4511	402	71	,	,	PUNCT
ejpam-4511	402	72	at	at	ADP
ejpam-4511	402	73	)	)	PUNCT
ejpam-4511	402	74	,	,	PUNCT
ejpam-4511	402	75	·	·	PUNCT
ejpam-4511	402	76	·	·	PUNCT
ejpam-4511	402	77	·	·	PUNCT
ejpam-4511	402	78	,	,	PUNCT
ejpam-4511	402	79	(	(	PUNCT
ejpam-4511	402	80	vk	vk	NOUN
ejpam-4511	402	81	,	,	PUNCT
ejpam-4511	402	82	a1	a1	NOUN
ejpam-4511	402	83	)	)	PUNCT
ejpam-4511	402	84	,	,	PUNCT
ejpam-4511	402	85	(	(	PUNCT
ejpam-4511	402	86	vk	vk	PROPN
ejpam-4511	402	87	,	,	PUNCT
ejpam-4511	402	88	a2	a2	PROPN
ejpam-4511	402	89	)	)	PUNCT
ejpam-4511	402	90	,	,	PUNCT
ejpam-4511	402	91	·	·	PUNCT
ejpam-4511	402	92	·	·	PUNCT
ejpam-4511	402	93	·	·	PUNCT
ejpam-4511	402	94	,	,	PUNCT
ejpam-4511	402	95	(	(	PUNCT
ejpam-4511	402	96	vk	vk	INTJ
ejpam-4511	402	97	,	,	PUNCT
ejpam-4511	402	98	at	at	ADP
ejpam-4511	402	99	)	)	PUNCT
ejpam-4511	402	100	)	)	PUNCT
ejpam-4511	402	101	is	be	AUX
ejpam-4511	402	102	a	a	DET
ejpam-4511	402	103	legal	legal	ADJ
ejpam-4511	402	104	closed	close	VERB
ejpam-4511	402	105	hop	hop	NOUN
ejpam-4511	402	106	neighborhood	neighborhood	NOUN
ejpam-4511	402	107	sequence	sequence	NOUN
ejpam-4511	402	108	of	of	ADP
ejpam-4511	402	109	g[h	g[h	NOUN
ejpam-4511	402	110	]	]	PUNCT
ejpam-4511	402	111	.	.	PUNCT
ejpam-4511	403	1	proof	proof	NOUN
ejpam-4511	403	2	.	.	PUNCT
ejpam-4511	404	1	suppose	suppose	VERB
ejpam-4511	404	2	sg	sg	PROPN
ejpam-4511	404	3	is	be	AUX
ejpam-4511	404	4	a	a	DET
ejpam-4511	404	5	legal	legal	ADJ
ejpam-4511	404	6	closed	close	VERB
ejpam-4511	404	7	hop	hop	NOUN
ejpam-4511	404	8	independent	independent	ADJ
ejpam-4511	404	9	neighborhood	neighborhood	NOUN
ejpam-4511	404	10	sequence	sequence	NOUN
ejpam-4511	404	11	of	of	ADP
ejpam-4511	404	12	g	g	NOUN
ejpam-4511	404	13	and	and	CCONJ
ejpam-4511	404	14	let	let	VERB
ejpam-4511	404	15	sh	sh	PRON
ejpam-4511	404	16	be	be	AUX
ejpam-4511	404	17	a	a	DET
ejpam-4511	404	18	co	co	ADJ
ejpam-4511	404	19	-	-	ADJ
ejpam-4511	404	20	legal	legal	ADJ
ejpam-4511	404	21	neighborhood	neighborhood	NOUN
ejpam-4511	404	22	sequence	sequence	NOUN
ejpam-4511	404	23	of	of	ADP
ejpam-4511	404	24	h.	h.	NOUN
ejpam-4511	404	25	let	let	VERB
ejpam-4511	404	26	i	i	PRON
ejpam-4511	404	27	∈	∈	VERB
ejpam-4511	405	1	[	[	X
ejpam-4511	405	2	k	k	X
ejpam-4511	405	3	]	]	X
ejpam-4511	405	4	and	and	CCONJ
ejpam-4511	405	5	j	j	PROPN
ejpam-4511	405	6	∈	∈	PROPN
ejpam-4511	406	1	[	[	X
ejpam-4511	406	2	t	t	X
ejpam-4511	406	3	]	]	PUNCT
ejpam-4511	406	4	.	.	PUNCT
ejpam-4511	407	1	then	then	ADV
ejpam-4511	407	2	n2	n2	PROPN
ejpam-4511	407	3	g[h][(vi	g[h][(vi	PROPN
ejpam-4511	407	4	,	,	PUNCT
ejpam-4511	407	5	aj)]\∪	aj)]\∪	PROPN
ejpam-4511	407	6	j−1	j−1	PROPN
ejpam-4511	407	7	l=1n	l=1n	VERB
ejpam-4511	407	8	2	2	NUM
ejpam-4511	407	9	g[h][(vi	g[h][(vi	PROPN
ejpam-4511	407	10	,	,	PUNCT
ejpam-4511	407	11	al	al	PROPN
ejpam-4511	407	12	)	)	PUNCT
ejpam-4511	407	13	]	]	PUNCT
ejpam-4511	408	1	=	=	PUNCT
ejpam-4511	408	2	(	(	PUNCT
ejpam-4511	408	3	{	{	PUNCT
ejpam-4511	408	4	vi}×v	vi}×v	PROPN
ejpam-4511	408	5	(	(	PUNCT
ejpam-4511	408	6	h)\nh(aj))\({vi}×∪j−1	h)\nh(aj))\({vi}×∪j−1	NOUN
ejpam-4511	408	7	l=1	l=1	PUNCT
ejpam-4511	409	1	[	[	X
ejpam-4511	409	2	v	v	X
ejpam-4511	409	3	(	(	PUNCT
ejpam-4511	409	4	h)\nh(al	h)\nh(al	PROPN
ejpam-4511	409	5	)	)	PUNCT
ejpam-4511	409	6	]	]	PUNCT
ejpam-4511	409	7	)	)	PUNCT
ejpam-4511	409	8	.	.	PUNCT
ejpam-4511	410	1	now	now	ADV
ejpam-4511	410	2	,	,	PUNCT
ejpam-4511	410	3	since	since	SCONJ
ejpam-4511	410	4	sh	sh	PROPN
ejpam-4511	410	5	is	be	AUX
ejpam-4511	410	6	a	a	DET
ejpam-4511	410	7	co	co	ADJ
ejpam-4511	410	8	-	-	ADJ
ejpam-4511	410	9	legal	legal	ADJ
ejpam-4511	410	10	sequence	sequence	NOUN
ejpam-4511	410	11	in	in	ADP
ejpam-4511	410	12	h	h	PROPN
ejpam-4511	410	13	,	,	PUNCT
ejpam-4511	410	14	v	v	ADJ
ejpam-4511	410	15	(	(	PUNCT
ejpam-4511	410	16	h	h	NOUN
ejpam-4511	410	17	)	)	PUNCT
ejpam-4511	410	18	\nh(aj	\nh(aj	NUM
ejpam-4511	410	19	)	)	PUNCT
ejpam-4511	410	20	)	)	PUNCT
ejpam-4511	411	1	\	\	NOUN
ejpam-4511	411	2	∪j−1	∪j−1	X
ejpam-4511	412	1	l=1	l=1	PUNCT
ejpam-4511	412	2	[	[	X
ejpam-4511	412	3	v	v	X
ejpam-4511	412	4	(	(	PUNCT
ejpam-4511	412	5	h	h	NOUN
ejpam-4511	412	6	)	)	PUNCT
ejpam-4511	412	7	\nh(al	\nh(al	ADV
ejpam-4511	412	8	)	)	PUNCT
ejpam-4511	412	9	]	]	PUNCT
ejpam-4511	413	1	̸=	̸=	PROPN
ejpam-4511	413	2	∅.	∅.	PRON
ejpam-4511	413	3	equality	equality	NOUN
ejpam-4511	413	4	implies	imply	VERB
ejpam-4511	413	5	that	that	SCONJ
ejpam-4511	413	6	n2	n2	PROPN
ejpam-4511	413	7	g[h][(vi	g[h][(vi	PROPN
ejpam-4511	413	8	,	,	PUNCT
ejpam-4511	413	9	aj	aj	PROPN
ejpam-4511	413	10	)	)	PUNCT
ejpam-4511	413	11	]	]	PUNCT
ejpam-4511	413	12	\	\	PROPN
ejpam-4511	413	13	∪	∪	X
ejpam-4511	413	14	j−1	j−1	PROPN
ejpam-4511	413	15	l=1n	l=1n	VERB
ejpam-4511	413	16	2	2	NUM
ejpam-4511	413	17	g[h][(vi	g[h][(vi	PROPN
ejpam-4511	413	18	,	,	PUNCT
ejpam-4511	413	19	al	al	PROPN
ejpam-4511	413	20	)	)	PUNCT
ejpam-4511	413	21	]	]	PUNCT
ejpam-4511	414	1	̸=	̸=	PROPN
ejpam-4511	414	2	∅.	∅.	ADP
ejpam-4511	414	3	the	the	DET
ejpam-4511	414	4	assumption	assumption	NOUN
ejpam-4511	414	5	that	that	SCONJ
ejpam-4511	414	6	sg	sg	PROPN
ejpam-4511	414	7	is	be	AUX
ejpam-4511	414	8	a	a	DET
ejpam-4511	414	9	legal	legal	ADJ
ejpam-4511	414	10	closed	close	VERB
ejpam-4511	414	11	hop	hop	NOUN
ejpam-4511	414	12	independent	independent	ADJ
ejpam-4511	414	13	neighborhood	neighborhood	NOUN
ejpam-4511	414	14	sequence	sequence	NOUN
ejpam-4511	414	15	would	would	AUX
ejpam-4511	414	16	imply	imply	VERB
ejpam-4511	414	17	that	that	PRON
ejpam-4511	414	18	(	(	PUNCT
ejpam-4511	414	19	{	{	PUNCT
ejpam-4511	414	20	vi}×	vi}×	PROPN
ejpam-4511	414	21	v	v	PROPN
ejpam-4511	414	22	(	(	PUNCT
ejpam-4511	414	23	h	h	NOUN
ejpam-4511	414	24	)	)	PUNCT
ejpam-4511	414	25	\nh(aj	\nh(aj	NUM
ejpam-4511	414	26	)	)	PUNCT
ejpam-4511	414	27	)	)	PUNCT
ejpam-4511	414	28	\	\	PUNCT
ejpam-4511	415	1	(	(	PUNCT
ejpam-4511	415	2	{	{	PUNCT
ejpam-4511	415	3	vi}×∪j−1	vi}×∪j−1	NOUN
ejpam-4511	415	4	l=1	l=1	PUNCT
ejpam-4511	415	5	[	[	X
ejpam-4511	415	6	v	v	X
ejpam-4511	415	7	(	(	PUNCT
ejpam-4511	415	8	h	h	NOUN
ejpam-4511	415	9	)	)	PUNCT
ejpam-4511	415	10	\nh(al	\nh(al	ADV
ejpam-4511	415	11	)	)	PUNCT
ejpam-4511	415	12	]	]	PUNCT
ejpam-4511	415	13	)	)	PUNCT
ejpam-4511	415	14	and	and	CCONJ
ejpam-4511	415	15	∪{n2	∪{n2	X
ejpam-4511	415	16	g[h][(vr	g[h][(vr	PROPN
ejpam-4511	415	17	,	,	PUNCT
ejpam-4511	415	18	al	al	PROPN
ejpam-4511	415	19	)	)	PUNCT
ejpam-4511	415	20	]	]	PUNCT
ejpam-4511	415	21	:	:	PUNCT
ejpam-4511	415	22	j.	j.	PROPN
ejpam-4511	415	23	hassan	hassan	PROPN
ejpam-4511	415	24	,	,	PUNCT
ejpam-4511	415	25	s.	s.	PROPN
ejpam-4511	415	26	canoy	canoy	PROPN
ejpam-4511	415	27	/	/	SYM
ejpam-4511	415	28	eur	eur	PROPN
ejpam-4511	415	29	.	.	PUNCT
ejpam-4511	416	1	j.	j.	PROPN
ejpam-4511	416	2	pure	pure	PROPN
ejpam-4511	416	3	appl	appl	PROPN
ejpam-4511	416	4	.	.	PROPN
ejpam-4511	416	5	math	math	PROPN
ejpam-4511	416	6	,	,	PUNCT
ejpam-4511	416	7	15	15	NUM
ejpam-4511	416	8	(	(	PUNCT
ejpam-4511	416	9	4	4	NUM
ejpam-4511	416	10	)	)	PUNCT
ejpam-4511	416	11	(	(	PUNCT
ejpam-4511	416	12	2022	2022	NUM
ejpam-4511	416	13	)	)	PUNCT
ejpam-4511	416	14	,	,	PUNCT
ejpam-4511	416	15	1623	1623	NUM
ejpam-4511	416	16	-	-	SYM
ejpam-4511	416	17	1636	1636	NUM
ejpam-4511	416	18	1634	1634	NUM
ejpam-4511	416	19	r	r	NOUN
ejpam-4511	416	20	∈	∈	PROPN
ejpam-4511	417	1	[	[	X
ejpam-4511	417	2	i−	i−	PROPN
ejpam-4511	417	3	1	1	NUM
ejpam-4511	417	4	]	]	PUNCT
ejpam-4511	417	5	and	and	CCONJ
ejpam-4511	417	6	l	l	NOUN
ejpam-4511	417	7	∈	∈	PROPN
ejpam-4511	418	1	[	[	X
ejpam-4511	418	2	t	t	X
ejpam-4511	418	3	]	]	PUNCT
ejpam-4511	418	4	}	}	PUNCT
ejpam-4511	418	5	are	be	AUX
ejpam-4511	418	6	disjoint	disjoint	ADJ
ejpam-4511	418	7	.	.	PUNCT
ejpam-4511	419	1	thus	thus	ADV
ejpam-4511	419	2	,	,	PUNCT
ejpam-4511	419	3	n2	n2	PROPN
ejpam-4511	419	4	g[h][(vi	g[h][(vi	PROPN
ejpam-4511	419	5	,	,	PUNCT
ejpam-4511	419	6	aj	aj	PROPN
ejpam-4511	419	7	)	)	PUNCT
ejpam-4511	419	8	]	]	PUNCT
ejpam-4511	419	9	\	\	PUNCT
ejpam-4511	420	1	∪{n	∪{n	PROPN
ejpam-4511	420	2	2	2	NUM
ejpam-4511	420	3	g[h][(vr	g[h][(vr	PROPN
ejpam-4511	420	4	,	,	PUNCT
ejpam-4511	420	5	al	al	PROPN
ejpam-4511	420	6	)	)	PUNCT
ejpam-4511	420	7	]	]	PUNCT
ejpam-4511	420	8	:	:	PUNCT
ejpam-4511	421	1	r	r	X
ejpam-4511	421	2	∈	∈	PROPN
ejpam-4511	421	3	[	[	X
ejpam-4511	421	4	i	i	X
ejpam-4511	421	5	]	]	X
ejpam-4511	421	6	,	,	PUNCT
ejpam-4511	421	7	l	l	PROPN
ejpam-4511	421	8	∈	∈	PROPN
ejpam-4511	422	1	[	[	X
ejpam-4511	422	2	t	t	X
ejpam-4511	422	3	]	]	PUNCT
ejpam-4511	422	4	with	with	ADP
ejpam-4511	422	5	(	(	PUNCT
ejpam-4511	422	6	vi	vi	PROPN
ejpam-4511	422	7	,	,	PUNCT
ejpam-4511	422	8	aj	aj	ADJ
ejpam-4511	422	9	)	)	PUNCT
ejpam-4511	422	10	̸=	̸=	PROPN
ejpam-4511	422	11	(	(	PUNCT
ejpam-4511	422	12	vr	vr	PROPN
ejpam-4511	422	13	,	,	PUNCT
ejpam-4511	422	14	al	al	PROPN
ejpam-4511	422	15	)	)	PUNCT
ejpam-4511	422	16	}	}	PUNCT
ejpam-4511	422	17	=	=	SYM
ejpam-4511	422	18	̸	̸	X
ejpam-4511	422	19	∅.	∅.	VERB
ejpam-4511	422	20	therefore	therefore	ADV
ejpam-4511	422	21	,	,	PUNCT
ejpam-4511	422	22	s	s	PART
ejpam-4511	422	23	is	be	AUX
ejpam-4511	422	24	a	a	DET
ejpam-4511	422	25	legal	legal	ADJ
ejpam-4511	422	26	closed	closed	ADJ
ejpam-4511	422	27	hop	hop	NOUN
ejpam-4511	422	28	neighborhood	neighborhood	NOUN
ejpam-4511	422	29	sequence	sequence	NOUN
ejpam-4511	422	30	in	in	ADP
ejpam-4511	422	31	g[h	g[h	PROPN
ejpam-4511	422	32	]	]	PUNCT
ejpam-4511	422	33	.	.	PUNCT
ejpam-4511	423	1	theorem	theorem	ADJ
ejpam-4511	423	2	8	8	NUM
ejpam-4511	423	3	.	.	PUNCT
ejpam-4511	424	1	let	let	VERB
ejpam-4511	424	2	g	g	NOUN
ejpam-4511	424	3	and	and	CCONJ
ejpam-4511	424	4	h	h	PROPN
ejpam-4511	424	5	be	be	VERB
ejpam-4511	424	6	non	non	ADJ
ejpam-4511	424	7	-	-	ADJ
ejpam-4511	424	8	trivial	trivial	ADJ
ejpam-4511	424	9	connected	connected	ADJ
ejpam-4511	424	10	graphs	graph	NOUN
ejpam-4511	424	11	.	.	PUNCT
ejpam-4511	425	1	if	if	SCONJ
ejpam-4511	425	2	sg	sg	ADV
ejpam-4511	425	3	=	=	SYM
ejpam-4511	425	4	(	(	PUNCT
ejpam-4511	425	5	v1	v1	PROPN
ejpam-4511	425	6	,	,	PUNCT
ejpam-4511	425	7	v2	v2	PROPN
ejpam-4511	425	8	,	,	PUNCT
ejpam-4511	425	9	·	·	PUNCT
ejpam-4511	425	10	·	·	PUNCT
ejpam-4511	425	11	·	·	PUNCT
ejpam-4511	425	12	,	,	PUNCT
ejpam-4511	425	13	vk	vk	PROPN
ejpam-4511	425	14	)	)	PUNCT
ejpam-4511	425	15	is	be	AUX
ejpam-4511	425	16	a	a	DET
ejpam-4511	425	17	grundy	grundy	PROPN
ejpam-4511	425	18	hop	hop	NOUN
ejpam-4511	425	19	independent	independent	ADJ
ejpam-4511	425	20	hop	hop	NOUN
ejpam-4511	425	21	dominating	dominating	NOUN
ejpam-4511	425	22	sequence	sequence	NOUN
ejpam-4511	425	23	in	in	ADP
ejpam-4511	425	24	g	g	PROPN
ejpam-4511	425	25	and	and	CCONJ
ejpam-4511	425	26	sh	sh	PROPN
ejpam-4511	425	27	=	=	SYM
ejpam-4511	425	28	(	(	PUNCT
ejpam-4511	425	29	a1	a1	PROPN
ejpam-4511	425	30	,	,	PUNCT
ejpam-4511	425	31	a2	a2	PROPN
ejpam-4511	425	32	,	,	PUNCT
ejpam-4511	425	33	·	·	PUNCT
ejpam-4511	425	34	·	·	PUNCT
ejpam-4511	425	35	·	·	PUNCT
ejpam-4511	425	36	,	,	PUNCT
ejpam-4511	425	37	at	at	ADP
ejpam-4511	425	38	)	)	PUNCT
ejpam-4511	425	39	is	be	AUX
ejpam-4511	425	40	a	a	DET
ejpam-4511	425	41	co	co	ADJ
ejpam-4511	425	42	-	-	ADJ
ejpam-4511	425	43	grundy	grundy	ADJ
ejpam-4511	425	44	dominating	dominating	NOUN
ejpam-4511	425	45	sequence	sequence	NOUN
ejpam-4511	425	46	in	in	ADP
ejpam-4511	425	47	h.	h.	PROPN
ejpam-4511	425	48	then	then	ADV
ejpam-4511	425	49	s	s	VERB
ejpam-4511	425	50	=	=	SYM
ejpam-4511	425	51	(	(	PUNCT
ejpam-4511	425	52	(	(	PUNCT
ejpam-4511	425	53	v1	v1	NOUN
ejpam-4511	425	54	,	,	PUNCT
ejpam-4511	425	55	a1	a1	NOUN
ejpam-4511	425	56	)	)	PUNCT
ejpam-4511	425	57	,	,	PUNCT
ejpam-4511	425	58	(	(	PUNCT
ejpam-4511	425	59	v1	v1	NOUN
ejpam-4511	425	60	,	,	PUNCT
ejpam-4511	425	61	a2	a2	PROPN
ejpam-4511	425	62	)	)	PUNCT
ejpam-4511	425	63	,	,	PUNCT
ejpam-4511	425	64	·	·	PUNCT
ejpam-4511	425	65	·	·	PUNCT
ejpam-4511	425	66	·	·	PUNCT
ejpam-4511	425	67	,	,	PUNCT
ejpam-4511	425	68	(	(	PUNCT
ejpam-4511	425	69	v1	v1	NOUN
ejpam-4511	425	70	,	,	PUNCT
ejpam-4511	425	71	at	at	ADP
ejpam-4511	425	72	)	)	PUNCT
ejpam-4511	425	73	,	,	PUNCT
ejpam-4511	425	74	·	·	PUNCT
ejpam-4511	425	75	·	·	PUNCT
ejpam-4511	425	76	·	·	PUNCT
ejpam-4511	425	77	,	,	PUNCT
ejpam-4511	425	78	(	(	PUNCT
ejpam-4511	425	79	vk	vk	NOUN
ejpam-4511	425	80	,	,	PUNCT
ejpam-4511	425	81	a1	a1	NOUN
ejpam-4511	425	82	)	)	PUNCT
ejpam-4511	425	83	,	,	PUNCT
ejpam-4511	425	84	(	(	PUNCT
ejpam-4511	425	85	vk	vk	PROPN
ejpam-4511	425	86	,	,	PUNCT
ejpam-4511	425	87	a2	a2	PROPN
ejpam-4511	425	88	)	)	PUNCT
ejpam-4511	425	89	,	,	PUNCT
ejpam-4511	425	90	·	·	PUNCT
ejpam-4511	425	91	·	·	PUNCT
ejpam-4511	425	92	·	·	PUNCT
ejpam-4511	425	93	,	,	PUNCT
ejpam-4511	425	94	(	(	PUNCT
ejpam-4511	425	95	vk	vk	INTJ
ejpam-4511	425	96	,	,	PUNCT
ejpam-4511	425	97	at	at	ADP
ejpam-4511	425	98	)	)	PUNCT
ejpam-4511	425	99	)	)	PUNCT
ejpam-4511	425	100	is	be	AUX
ejpam-4511	425	101	a	a	DET
ejpam-4511	425	102	grundy	grundy	PROPN
ejpam-4511	425	103	hop	hop	NOUN
ejpam-4511	425	104	dominating	dominating	NOUN
ejpam-4511	425	105	sequence	sequence	NOUN
ejpam-4511	425	106	of	of	ADP
ejpam-4511	425	107	g[h	g[h	NOUN
ejpam-4511	425	108	]	]	PUNCT
ejpam-4511	425	109	.	.	PUNCT
ejpam-4511	426	1	in	in	ADP
ejpam-4511	426	2	particular	particular	ADJ
ejpam-4511	426	3	,	,	PUNCT
ejpam-4511	426	4	γhgr(g[h	γhgr(g[h	PROPN
ejpam-4511	426	5	]	]	PUNCT
ejpam-4511	426	6	)	)	PUNCT
ejpam-4511	426	7	≥	≥	NOUN
ejpam-4511	426	8	γhihgr	γhihgr	NOUN
ejpam-4511	426	9	(	(	PUNCT
ejpam-4511	426	10	g)γcogr(h	g)γcogr(h	NOUN
ejpam-4511	426	11	)	)	PUNCT
ejpam-4511	426	12	.	.	PUNCT
ejpam-4511	427	1	proof	proof	NOUN
ejpam-4511	427	2	.	.	PUNCT
ejpam-4511	428	1	by	by	ADP
ejpam-4511	428	2	theorem	theorem	NOUN
ejpam-4511	428	3	7	7	NUM
ejpam-4511	428	4	,	,	PUNCT
ejpam-4511	428	5	s	s	VERB
ejpam-4511	428	6	is	be	AUX
ejpam-4511	428	7	a	a	DET
ejpam-4511	428	8	legal	legal	ADJ
ejpam-4511	428	9	closed	closed	ADJ
ejpam-4511	428	10	hop	hop	NOUN
ejpam-4511	428	11	neighborhood	neighborhood	NOUN
ejpam-4511	428	12	sequence	sequence	NOUN
ejpam-4511	428	13	in	in	ADP
ejpam-4511	428	14	g[h	g[h	PROPN
ejpam-4511	428	15	]	]	PUNCT
ejpam-4511	428	16	.	.	PUNCT
ejpam-4511	429	1	let	let	VERB
ejpam-4511	429	2	(	(	PUNCT
ejpam-4511	429	3	v	v	NOUN
ejpam-4511	429	4	,	,	PUNCT
ejpam-4511	429	5	a	a	PRON
ejpam-4511	429	6	)	)	PUNCT
ejpam-4511	429	7	∈	∈	NOUN
ejpam-4511	429	8	v	v	NOUN
ejpam-4511	429	9	(	(	PUNCT
ejpam-4511	429	10	g[h])\ŝ.	g[h])\ŝ.	PRON
ejpam-4511	429	11	suppose	suppose	VERB
ejpam-4511	429	12	that	that	SCONJ
ejpam-4511	429	13	v	v	NUM
ejpam-4511	429	14	∈	∈	PROPN
ejpam-4511	429	15	v	v	NOUN
ejpam-4511	429	16	(	(	PUNCT
ejpam-4511	429	17	g)\sg	g)\sg	PROPN
ejpam-4511	429	18	.	.	PROPN
ejpam-4511	429	19	since	since	SCONJ
ejpam-4511	429	20	sg	sg	PROPN
ejpam-4511	429	21	is	be	AUX
ejpam-4511	429	22	a	a	DET
ejpam-4511	429	23	hop	hop	NOUN
ejpam-4511	429	24	dominating	dominating	NOUN
ejpam-4511	429	25	set	set	NOUN
ejpam-4511	429	26	,	,	PUNCT
ejpam-4511	429	27	there	there	PRON
ejpam-4511	429	28	exists	exist	VERB
ejpam-4511	429	29	vj	vj	PROPN
ejpam-4511	429	30	∈	∈	PROPN
ejpam-4511	429	31	sg	sg	ADP
ejpam-4511	429	32	such	such	ADJ
ejpam-4511	429	33	that	that	DET
ejpam-4511	429	34	v	v	PROPN
ejpam-4511	429	35	∈	∈	PROPN
ejpam-4511	429	36	n2	n2	ADJ
ejpam-4511	429	37	g(vj	g(vj	PROPN
ejpam-4511	429	38	)	)	PUNCT
ejpam-4511	429	39	.	.	PUNCT
ejpam-4511	430	1	it	it	PRON
ejpam-4511	430	2	follows	follow	VERB
ejpam-4511	430	3	that	that	SCONJ
ejpam-4511	430	4	(	(	PUNCT
ejpam-4511	430	5	vj	vj	INTJ
ejpam-4511	430	6	,	,	PUNCT
ejpam-4511	430	7	a1	a1	PROPN
ejpam-4511	430	8	)	)	PUNCT
ejpam-4511	430	9	∈	∈	NOUN
ejpam-4511	430	10	ŝ	ŝ	X
ejpam-4511	430	11	and	and	CCONJ
ejpam-4511	430	12	(	(	PUNCT
ejpam-4511	430	13	v	v	NOUN
ejpam-4511	430	14	,	,	PUNCT
ejpam-4511	430	15	a	a	PRON
ejpam-4511	430	16	)	)	PUNCT
ejpam-4511	430	17	∈	∈	PROPN
ejpam-4511	430	18	n2	n2	NOUN
ejpam-4511	430	19	g[h](vj	g[h](vj	PROPN
ejpam-4511	430	20	,	,	PUNCT
ejpam-4511	430	21	a1	a1	PROPN
ejpam-4511	430	22	)	)	PUNCT
ejpam-4511	430	23	.	.	PUNCT
ejpam-4511	431	1	suppose	suppose	VERB
ejpam-4511	431	2	v	v	X
ejpam-4511	431	3	=	=	SYM
ejpam-4511	431	4	vi	vi	PROPN
ejpam-4511	431	5	for	for	ADP
ejpam-4511	431	6	some	some	PRON
ejpam-4511	431	7	i	i	PRON
ejpam-4511	431	8	∈	∈	PROPN
ejpam-4511	432	1	[	[	X
ejpam-4511	432	2	k	k	X
ejpam-4511	432	3	]	]	X
ejpam-4511	432	4	.	.	PUNCT
ejpam-4511	433	1	then	then	ADV
ejpam-4511	434	1	a	a	PRON
ejpam-4511	434	2	∈	∈	PROPN
ejpam-4511	434	3	v	v	ADP
ejpam-4511	434	4	(	(	PUNCT
ejpam-4511	434	5	h	h	NOUN
ejpam-4511	434	6	)	)	PUNCT
ejpam-4511	434	7	\	\	PUNCT
ejpam-4511	435	1	sh	sh	INTJ
ejpam-4511	435	2	.	.	PUNCT
ejpam-4511	436	1	since	since	SCONJ
ejpam-4511	436	2	sh	sh	PROPN
ejpam-4511	436	3	is	be	AUX
ejpam-4511	436	4	a	a	DET
ejpam-4511	436	5	co	co	ADJ
ejpam-4511	436	6	-	-	ADJ
ejpam-4511	436	7	grundy	grundy	ADJ
ejpam-4511	436	8	dominating	dominating	NOUN
ejpam-4511	436	9	sequence	sequence	NOUN
ejpam-4511	436	10	,	,	PUNCT
ejpam-4511	436	11	there	there	PRON
ejpam-4511	436	12	exists	exist	VERB
ejpam-4511	436	13	as	as	ADP
ejpam-4511	436	14	∈	∈	PROPN
ejpam-4511	436	15	sh	sh	INTJ
ejpam-4511	436	16	such	such	ADJ
ejpam-4511	436	17	that	that	SCONJ
ejpam-4511	436	18	a	a	DET
ejpam-4511	436	19	/∈	/∈	INTJ
ejpam-4511	436	20	nh(as	nh(as	ADJ
ejpam-4511	436	21	)	)	PUNCT
ejpam-4511	436	22	.	.	PUNCT
ejpam-4511	437	1	clearly	clearly	ADV
ejpam-4511	437	2	,	,	PUNCT
ejpam-4511	437	3	(	(	PUNCT
ejpam-4511	437	4	vi	vi	NOUN
ejpam-4511	437	5	,	,	PUNCT
ejpam-4511	437	6	as	as	ADP
ejpam-4511	437	7	)	)	PUNCT
ejpam-4511	437	8	∈	∈	PROPN
ejpam-4511	437	9	ŝ	ŝ	X
ejpam-4511	437	10	and	and	CCONJ
ejpam-4511	437	11	(	(	PUNCT
ejpam-4511	437	12	v	v	NOUN
ejpam-4511	437	13	,	,	PUNCT
ejpam-4511	437	14	a	a	PRON
ejpam-4511	437	15	)	)	PUNCT
ejpam-4511	437	16	∈	∈	PROPN
ejpam-4511	437	17	n2	n2	PROPN
ejpam-4511	437	18	g[h](vi	g[h](vi	PROPN
ejpam-4511	437	19	,	,	PUNCT
ejpam-4511	437	20	as	as	ADP
ejpam-4511	437	21	)	)	PUNCT
ejpam-4511	437	22	.	.	PUNCT
ejpam-4511	438	1	thus	thus	ADV
ejpam-4511	438	2	,	,	PUNCT
ejpam-4511	438	3	ŝ	ŝ	X
ejpam-4511	438	4	is	be	AUX
ejpam-4511	438	5	a	a	DET
ejpam-4511	438	6	hop	hop	NOUN
ejpam-4511	438	7	dominating	dominating	NOUN
ejpam-4511	438	8	set	set	NOUN
ejpam-4511	438	9	,	,	PUNCT
ejpam-4511	438	10	showing	show	VERB
ejpam-4511	438	11	that	that	SCONJ
ejpam-4511	438	12	s	s	VERB
ejpam-4511	438	13	is	be	AUX
ejpam-4511	438	14	a	a	DET
ejpam-4511	438	15	grundy	grundy	PROPN
ejpam-4511	438	16	hop	hop	NOUN
ejpam-4511	438	17	dominating	dominating	NOUN
ejpam-4511	438	18	sequence	sequence	NOUN
ejpam-4511	438	19	in	in	ADP
ejpam-4511	438	20	g[h	g[h	PROPN
ejpam-4511	438	21	]	]	PUNCT
ejpam-4511	438	22	.	.	PUNCT
ejpam-4511	439	1	therefore	therefore	ADV
ejpam-4511	439	2	,	,	PUNCT
ejpam-4511	439	3	γhgr(g[h	γhgr(g[h	PROPN
ejpam-4511	439	4	]	]	PUNCT
ejpam-4511	439	5	)	)	PUNCT
ejpam-4511	439	6	≥	≥	NOUN
ejpam-4511	439	7	γhihgr	γhihgr	NOUN
ejpam-4511	439	8	(	(	PUNCT
ejpam-4511	439	9	g)γcogr(h	g)γcogr(h	NOUN
ejpam-4511	439	10	)	)	PUNCT
ejpam-4511	439	11	.	.	PUNCT
ejpam-4511	440	1	remark	remark	PROPN
ejpam-4511	440	2	4	4	NUM
ejpam-4511	440	3	.	.	PUNCT
ejpam-4511	441	1	the	the	DET
ejpam-4511	441	2	bound	bind	VERB
ejpam-4511	441	3	given	give	VERB
ejpam-4511	441	4	in	in	ADP
ejpam-4511	441	5	theorem	theorem	ADJ
ejpam-4511	441	6	8	8	NUM
ejpam-4511	441	7	is	be	AUX
ejpam-4511	441	8	tight	tight	ADJ
ejpam-4511	441	9	.	.	PUNCT
ejpam-4511	442	1	to	to	PART
ejpam-4511	442	2	see	see	VERB
ejpam-4511	442	3	this	this	PRON
ejpam-4511	442	4	,	,	PUNCT
ejpam-4511	442	5	consider	consider	VERB
ejpam-4511	442	6	g	g	NOUN
ejpam-4511	442	7	=	=	NOUN
ejpam-4511	442	8	h	h	PROPN
ejpam-4511	442	9	=	=	PROPN
ejpam-4511	442	10	p3	p3	PROPN
ejpam-4511	442	11	.	.	PUNCT
ejpam-4511	443	1	then	then	ADV
ejpam-4511	443	2	γhihgr	γhihgr	NOUN
ejpam-4511	443	3	(	(	PUNCT
ejpam-4511	443	4	g	g	NOUN
ejpam-4511	443	5	)	)	PUNCT
ejpam-4511	443	6	=	=	SYM
ejpam-4511	443	7	2	2	NUM
ejpam-4511	443	8	and	and	CCONJ
ejpam-4511	443	9	γcogr(h	γcogr(h	NOUN
ejpam-4511	443	10	)	)	PUNCT
ejpam-4511	443	11	=	=	SYM
ejpam-4511	443	12	2	2	X
ejpam-4511	443	13	.	.	X
ejpam-4511	444	1	it	it	PRON
ejpam-4511	444	2	can	can	AUX
ejpam-4511	444	3	easily	easily	ADV
ejpam-4511	444	4	be	be	AUX
ejpam-4511	444	5	verified	verify	VERB
ejpam-4511	444	6	that	that	SCONJ
ejpam-4511	444	7	γhgr(g[h	γhgr(g[h	PROPN
ejpam-4511	444	8	]	]	X
ejpam-4511	444	9	)	)	PUNCT
ejpam-4511	445	1	=	=	SYM
ejpam-4511	445	2	γhihgr	γhihgr	NOUN
ejpam-4511	445	3	(	(	PUNCT
ejpam-4511	445	4	g)γcogr(h	g)γcogr(h	NOUN
ejpam-4511	445	5	)	)	PUNCT
ejpam-4511	445	6	=	=	PUNCT
ejpam-4511	445	7	4	4	NUM
ejpam-4511	445	8	.	.	NOUN
ejpam-4511	445	9	4	4	NUM
ejpam-4511	445	10	.	.	X
ejpam-4511	445	11	conclusion	conclusion	NOUN
ejpam-4511	445	12	this	this	DET
ejpam-4511	445	13	study	study	NOUN
ejpam-4511	445	14	did	do	AUX
ejpam-4511	445	15	introduce	introduce	VERB
ejpam-4511	445	16	the	the	DET
ejpam-4511	445	17	concept	concept	NOUN
ejpam-4511	445	18	of	of	ADP
ejpam-4511	445	19	grundy	grundy	PROPN
ejpam-4511	445	20	hop	hop	PROPN
ejpam-4511	445	21	domination	domination	NOUN
ejpam-4511	445	22	and	and	CCONJ
ejpam-4511	445	23	make	make	VERB
ejpam-4511	445	24	an	an	DET
ejpam-4511	445	25	initial	initial	ADJ
ejpam-4511	445	26	investigation	investigation	NOUN
ejpam-4511	445	27	of	of	ADP
ejpam-4511	445	28	the	the	DET
ejpam-4511	445	29	concept	concept	NOUN
ejpam-4511	445	30	.	.	PUNCT
ejpam-4511	446	1	it	it	PRON
ejpam-4511	446	2	was	be	AUX
ejpam-4511	446	3	pointed	point	VERB
ejpam-4511	446	4	out	out	ADP
ejpam-4511	446	5	and	and	CCONJ
ejpam-4511	446	6	proved	prove	VERB
ejpam-4511	446	7	that	that	SCONJ
ejpam-4511	446	8	every	every	DET
ejpam-4511	446	9	graph	graph	NOUN
ejpam-4511	446	10	admits	admit	VERB
ejpam-4511	446	11	a	a	DET
ejpam-4511	446	12	grundy	grundy	PROPN
ejpam-4511	446	13	hop	hop	NOUN
ejpam-4511	446	14	dominating	dominating	NOUN
ejpam-4511	446	15	sequence	sequence	NOUN
ejpam-4511	446	16	.	.	PUNCT
ejpam-4511	447	1	extremal	extremal	ADJ
ejpam-4511	447	2	values	value	NOUN
ejpam-4511	447	3	of	of	ADP
ejpam-4511	447	4	the	the	DET
ejpam-4511	447	5	grundy	grundy	PROPN
ejpam-4511	447	6	hop	hop	PROPN
ejpam-4511	447	7	domination	domination	NOUN
ejpam-4511	447	8	number	number	NOUN
ejpam-4511	447	9	were	be	AUX
ejpam-4511	447	10	given	give	VERB
ejpam-4511	447	11	.	.	PUNCT
ejpam-4511	448	1	moreover	moreover	ADV
ejpam-4511	448	2	,	,	PUNCT
ejpam-4511	448	3	exact	exact	ADJ
ejpam-4511	448	4	value	value	NOUN
ejpam-4511	448	5	or	or	CCONJ
ejpam-4511	448	6	tight	tight	ADV
ejpam-4511	448	7	lower	lower	ADV
ejpam-4511	448	8	bound	bind	VERB
ejpam-4511	448	9	for	for	ADP
ejpam-4511	448	10	each	each	PRON
ejpam-4511	448	11	of	of	ADP
ejpam-4511	448	12	the	the	DET
ejpam-4511	448	13	grundy	grundy	PROPN
ejpam-4511	448	14	hop	hop	PROPN
ejpam-4511	448	15	domination	domination	NOUN
ejpam-4511	448	16	numbers	number	NOUN
ejpam-4511	448	17	of	of	ADP
ejpam-4511	448	18	the	the	DET
ejpam-4511	448	19	join	join	NOUN
ejpam-4511	448	20	,	,	PUNCT
ejpam-4511	448	21	corona	corona	PROPN
ejpam-4511	448	22	,	,	PUNCT
ejpam-4511	448	23	and	and	CCONJ
ejpam-4511	448	24	lexicographic	lexicographic	ADJ
ejpam-4511	448	25	product	product	NOUN
ejpam-4511	448	26	of	of	ADP
ejpam-4511	448	27	two	two	NUM
ejpam-4511	448	28	graphs	graph	NOUN
ejpam-4511	448	29	was	be	AUX
ejpam-4511	448	30	determined	determine	VERB
ejpam-4511	448	31	.	.	PUNCT
ejpam-4511	449	1	bounds	bound	NOUN
ejpam-4511	449	2	for	for	ADP
ejpam-4511	449	3	this	this	DET
ejpam-4511	449	4	newly	newly	ADV
ejpam-4511	449	5	defined	define	VERB
ejpam-4511	449	6	parameter	parameter	NOUN
ejpam-4511	449	7	in	in	ADP
ejpam-4511	449	8	terms	term	NOUN
ejpam-4511	449	9	of	of	ADP
ejpam-4511	449	10	other	other	ADJ
ejpam-4511	449	11	parameters	parameter	NOUN
ejpam-4511	449	12	(	(	PUNCT
ejpam-4511	449	13	e.g.	e.g.	ADV
ejpam-4511	449	14	minimum	minimum	NOUN
ejpam-4511	449	15	degree	degree	NOUN
ejpam-4511	449	16	,	,	PUNCT
ejpam-4511	449	17	maximum	maximum	ADJ
ejpam-4511	449	18	degree	degree	NOUN
ejpam-4511	449	19	,	,	PUNCT
ejpam-4511	449	20	diameter	diameter	NOUN
ejpam-4511	449	21	,	,	PUNCT
ejpam-4511	449	22	etc	etc	X
ejpam-4511	449	23	.	.	X
ejpam-4511	449	24	)	)	PUNCT
ejpam-4511	449	25	may	may	AUX
ejpam-4511	449	26	be	be	AUX
ejpam-4511	449	27	obtained	obtain	VERB
ejpam-4511	449	28	.	.	PUNCT
ejpam-4511	450	1	the	the	DET
ejpam-4511	450	2	parameter	parameter	NOUN
ejpam-4511	450	3	can	can	AUX
ejpam-4511	450	4	be	be	AUX
ejpam-4511	450	5	investigated	investigate	VERB
ejpam-4511	450	6	further	far	ADV
ejpam-4511	450	7	for	for	ADP
ejpam-4511	450	8	trees	tree	NOUN
ejpam-4511	450	9	and	and	CCONJ
ejpam-4511	450	10	graphs	graph	NOUN
ejpam-4511	450	11	under	under	ADP
ejpam-4511	450	12	other	other	ADJ
ejpam-4511	450	13	binary	binary	ADJ
ejpam-4511	450	14	operations	operation	NOUN
ejpam-4511	450	15	.	.	PUNCT
ejpam-4511	451	1	acknowledgements	acknowledgement	NOUN
ejpam-4511	451	2	the	the	DET
ejpam-4511	451	3	authors	author	NOUN
ejpam-4511	451	4	would	would	AUX
ejpam-4511	451	5	like	like	VERB
ejpam-4511	451	6	to	to	PART
ejpam-4511	451	7	thank	thank	VERB
ejpam-4511	451	8	the	the	DET
ejpam-4511	451	9	referees	referee	NOUN
ejpam-4511	451	10	for	for	ADP
ejpam-4511	451	11	the	the	DET
ejpam-4511	451	12	invaluable	invaluable	ADJ
ejpam-4511	451	13	assistance	assistance	NOUN
ejpam-4511	451	14	they	they	PRON
ejpam-4511	451	15	gave	give	VERB
ejpam-4511	451	16	us	we	PRON
ejpam-4511	451	17	through	through	ADP
ejpam-4511	451	18	their	their	PRON
ejpam-4511	451	19	comments	comment	NOUN
ejpam-4511	451	20	and	and	CCONJ
ejpam-4511	451	21	suggestions	suggestion	NOUN
ejpam-4511	451	22	which	which	PRON
ejpam-4511	451	23	led	lead	VERB
ejpam-4511	451	24	to	to	ADP
ejpam-4511	451	25	the	the	DET
ejpam-4511	451	26	improvement	improvement	NOUN
ejpam-4511	451	27	of	of	ADP
ejpam-4511	451	28	the	the	DET
ejpam-4511	451	29	paper	paper	NOUN
ejpam-4511	451	30	.	.	PUNCT
ejpam-4511	452	1	moreover	moreover	ADV
ejpam-4511	452	2	,	,	PUNCT
ejpam-4511	452	3	the	the	DET
ejpam-4511	452	4	authors	author	NOUN
ejpam-4511	452	5	are	be	AUX
ejpam-4511	452	6	extremely	extremely	ADV
ejpam-4511	452	7	grateful	grateful	ADJ
ejpam-4511	452	8	to	to	ADP
ejpam-4511	452	9	the	the	DET
ejpam-4511	452	10	department	department	NOUN
ejpam-4511	452	11	of	of	ADP
ejpam-4511	452	12	science	science	NOUN
ejpam-4511	452	13	and	and	CCONJ
ejpam-4511	452	14	technology	technology	NOUN
ejpam-4511	452	15	accelerated	accelerate	VERB
ejpam-4511	452	16	science	science	NOUN
ejpam-4511	452	17	and	and	CCONJ
ejpam-4511	452	18	technology	technology	NOUN
ejpam-4511	452	19	human	human	ADJ
ejpam-4511	452	20	resource	resource	NOUN
ejpam-4511	452	21	development	development	NOUN
ejpam-4511	452	22	program	program	NOUN
ejpam-4511	452	23	(	(	PUNCT
ejpam-4511	452	24	dostasthrdp)-philippines	dostasthrdp)-philippine	NOUN
ejpam-4511	452	25	and	and	CCONJ
ejpam-4511	452	26	msu	msu	PROPN
ejpam-4511	452	27	-	-	PUNCT
ejpam-4511	452	28	iligan	iligan	PROPN
ejpam-4511	452	29	institute	institute	PROPN
ejpam-4511	452	30	of	of	ADP
ejpam-4511	452	31	technology	technology	NOUN
ejpam-4511	452	32	for	for	ADP
ejpam-4511	452	33	funding	fund	VERB
ejpam-4511	452	34	this	this	DET
ejpam-4511	452	35	research	research	NOUN
ejpam-4511	452	36	.	.	PUNCT
ejpam-4511	453	1	references	reference	NOUN
ejpam-4511	453	2	1635	1635	NUM
ejpam-4511	453	3	references	reference	NOUN
ejpam-4511	453	4	[	[	X
ejpam-4511	453	5	1	1	NUM
ejpam-4511	453	6	]	]	PUNCT
ejpam-4511	453	7	s.	s.	PROPN
ejpam-4511	453	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4511	453	9	,	,	PUNCT
ejpam-4511	453	10	b.	b.	PROPN
ejpam-4511	453	11	krishnakumari	krishnakumari	PROPN
ejpam-4511	453	12	,	,	PUNCT
ejpam-4511	453	13	b.	b.	PROPN
ejpam-4511	453	14	natarjan	natarjan	PROPN
ejpam-4511	453	15	,	,	PUNCT
ejpam-4511	453	16	and	and	CCONJ
ejpam-4511	453	17	y.	y.	PROPN
ejpam-4511	453	18	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4511	453	19	.	.	PUNCT
ejpam-4511	454	1	bounds	bound	NOUN
ejpam-4511	454	2	on	on	ADP
ejpam-4511	454	3	the	the	DET
ejpam-4511	454	4	hop	hop	NOUN
ejpam-4511	454	5	domination	domination	NOUN
ejpam-4511	454	6	number	number	NOUN
ejpam-4511	454	7	of	of	ADP
ejpam-4511	454	8	a	a	DET
ejpam-4511	454	9	tree	tree	NOUN
ejpam-4511	454	10	.	.	PUNCT
ejpam-4511	455	1	proceedings	proceeding	NOUN
ejpam-4511	455	2	-	-	PUNCT
ejpam-4511	455	3	mathematical	mathematical	ADJ
ejpam-4511	455	4	sciences	science	NOUN
ejpam-4511	455	5	.	.	PUNCT
ejpam-4511	455	6	,	,	PUNCT
ejpam-4511	455	7	125(4):449–455	125(4):449–455	ADP
ejpam-4511	455	8	,	,	PUNCT
ejpam-4511	455	9	2015	2015	NUM
ejpam-4511	455	10	.	.	PUNCT
ejpam-4511	456	1	[	[	X
ejpam-4511	456	2	2	2	NUM
ejpam-4511	456	3	]	]	PUNCT
ejpam-4511	456	4	s.	s.	PROPN
ejpam-4511	456	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4511	456	6	,	,	PUNCT
ejpam-4511	456	7	c.	c.	PROPN
ejpam-4511	456	8	natarajan	natarajan	PROPN
ejpam-4511	456	9	,	,	PUNCT
ejpam-4511	456	10	and	and	CCONJ
ejpam-4511	456	11	g.	g.	PROPN
ejpam-4511	456	12	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4511	456	13	.	.	PUNCT
ejpam-4511	457	1	a	a	DET
ejpam-4511	457	2	note	note	NOUN
ejpam-4511	457	3	on	on	ADP
ejpam-4511	457	4	hop	hop	NOUN
ejpam-4511	457	5	domination	domination	NOUN
ejpam-4511	457	6	number	number	NOUN
ejpam-4511	457	7	of	of	ADP
ejpam-4511	457	8	some	some	DET
ejpam-4511	457	9	special	special	ADJ
ejpam-4511	457	10	families	family	NOUN
ejpam-4511	457	11	of	of	ADP
ejpam-4511	457	12	graphs	graph	NOUN
ejpam-4511	457	13	.	.	PUNCT
ejpam-4511	458	1	international	international	ADJ
ejpam-4511	458	2	journal	journal	NOUN
ejpam-4511	458	3	of	of	ADP
ejpam-4511	458	4	pure	pure	ADJ
ejpam-4511	458	5	and	and	CCONJ
ejpam-4511	458	6	applied	applied	ADJ
ejpam-4511	458	7	mathematics	mathematic	NOUN
ejpam-4511	458	8	.	.	PUNCT
ejpam-4511	458	9	,	,	PUNCT
ejpam-4511	458	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4511	458	11	,	,	PUNCT
ejpam-4511	458	12	2018	2018	NUM
ejpam-4511	458	13	.	.	PUNCT
ejpam-4511	459	1	[	[	X
ejpam-4511	459	2	3	3	X
ejpam-4511	459	3	]	]	X
ejpam-4511	459	4	b.	b.	PROPN
ejpam-4511	459	5	bresar	bresar	PROPN
ejpam-4511	459	6	,	,	PUNCT
ejpam-4511	459	7	cs	cs	PROPN
ejpam-4511	459	8	.	.	PROPN
ejpam-4511	459	9	bujtas	bujtas	PROPN
ejpam-4511	459	10	,	,	PUNCT
ejpam-4511	459	11	t.	t.	NOUN
ejpam-4511	459	12	gologranc	gologranc	PROPN
ejpam-4511	459	13	,	,	PUNCT
ejpam-4511	459	14	s.	s.	PROPN
ejpam-4511	459	15	klavzar	klavzar	PROPN
ejpam-4511	459	16	,	,	PUNCT
ejpam-4511	459	17	g.	g.	PROPN
ejpam-4511	459	18	kosmrlj	kosmrlj	PROPN
ejpam-4511	459	19	,	,	PUNCT
ejpam-4511	459	20	b.	b.	PROPN
ejpam-4511	459	21	patkos	patkos	PROPN
ejpam-4511	459	22	,	,	PUNCT
ejpam-4511	459	23	zs	zs	PROPN
ejpam-4511	459	24	.	.	PUNCT
ejpam-4511	459	25	tuza	tuza	PROPN
ejpam-4511	459	26	,	,	PUNCT
ejpam-4511	459	27	and	and	CCONJ
ejpam-4511	459	28	m.	m.	NOUN
ejpam-4511	459	29	vizer	vizer	NOUN
ejpam-4511	459	30	.	.	PUNCT
ejpam-4511	460	1	dominating	dominate	VERB
ejpam-4511	460	2	sequence	sequence	NOUN
ejpam-4511	460	3	in	in	ADP
ejpam-4511	460	4	grid	grid	NOUN
ejpam-4511	460	5	-	-	PUNCT
ejpam-4511	460	6	like	like	ADJ
ejpam-4511	460	7	and	and	CCONJ
ejpam-4511	460	8	toroidal	toroidal	ADJ
ejpam-4511	460	9	graphs	graph	NOUN
ejpam-4511	460	10	.	.	PUNCT
ejpam-4511	461	1	electron	electron	PROPN
ejpam-4511	461	2	.	.	PUNCT
ejpam-4511	462	1	j.	j.	PROPN
ejpam-4511	462	2	combin	combin	PROPN
ejpam-4511	462	3	.	.	PROPN
ejpam-4511	462	4	,	,	PUNCT
ejpam-4511	462	5	(	(	PUNCT
ejpam-4511	462	6	23):1–17	23):1–17	NUM
ejpam-4511	462	7	,	,	PUNCT
ejpam-4511	462	8	2016	2016	NUM
ejpam-4511	462	9	.	.	PUNCT
ejpam-4511	463	1	[	[	X
ejpam-4511	463	2	4	4	X
ejpam-4511	463	3	]	]	X
ejpam-4511	463	4	b.	b.	PROPN
ejpam-4511	463	5	bresar	bresar	PROPN
ejpam-4511	463	6	,	,	PUNCT
ejpam-4511	463	7	cs	cs	PROPN
ejpam-4511	463	8	.	.	PROPN
ejpam-4511	463	9	bujtas	bujtas	PROPN
ejpam-4511	463	10	,	,	PUNCT
ejpam-4511	463	11	t.	t.	NOUN
ejpam-4511	463	12	gologranc	gologranc	PROPN
ejpam-4511	463	13	,	,	PUNCT
ejpam-4511	463	14	s.	s.	PROPN
ejpam-4511	463	15	klavzar	klavzar	PROPN
ejpam-4511	463	16	,	,	PUNCT
ejpam-4511	463	17	g.	g.	PROPN
ejpam-4511	463	18	kosmrlj	kosmrlj	PROPN
ejpam-4511	463	19	,	,	PUNCT
ejpam-4511	463	20	b.	b.	PROPN
ejpam-4511	463	21	patkos	patkos	PROPN
ejpam-4511	463	22	,	,	PUNCT
ejpam-4511	463	23	zs	zs	PROPN
ejpam-4511	463	24	.	.	PUNCT
ejpam-4511	463	25	tuza	tuza	PROPN
ejpam-4511	463	26	,	,	PUNCT
ejpam-4511	463	27	and	and	CCONJ
ejpam-4511	463	28	m.	m.	NOUN
ejpam-4511	463	29	vizer	vizer	NOUN
ejpam-4511	463	30	.	.	PUNCT
ejpam-4511	464	1	grundy	grundy	PROPN
ejpam-4511	464	2	dominating	dominating	NOUN
ejpam-4511	464	3	sequence	sequence	NOUN
ejpam-4511	464	4	and	and	CCONJ
ejpam-4511	464	5	zero	zero	NUM
ejpam-4511	464	6	forcing	forcing	NOUN
ejpam-4511	464	7	sets	set	NOUN
ejpam-4511	464	8	.	.	PUNCT
ejpam-4511	465	1	discrete	discrete	ADJ
ejpam-4511	465	2	optim	optim	ADJ
ejpam-4511	465	3	.	.	PUNCT
ejpam-4511	465	4	,	,	PUNCT
ejpam-4511	465	5	(	(	PUNCT
ejpam-4511	465	6	26):66–77	26):66–77	NUM
ejpam-4511	465	7	,	,	PUNCT
ejpam-4511	465	8	2017	2017	NUM
ejpam-4511	465	9	.	.	PUNCT
ejpam-4511	466	1	[	[	X
ejpam-4511	466	2	5	5	NUM
ejpam-4511	466	3	]	]	PUNCT
ejpam-4511	466	4	b.	b.	PROPN
ejpam-4511	466	5	bresar	bresar	PROPN
ejpam-4511	466	6	,	,	PUNCT
ejpam-4511	466	7	t.	t.	NOUN
ejpam-4511	466	8	gologranc	gologranc	PROPN
ejpam-4511	466	9	,	,	PUNCT
ejpam-4511	466	10	and	and	CCONJ
ejpam-4511	466	11	t.	t.	PROPN
ejpam-4511	466	12	kos	kos	PROPN
ejpam-4511	466	13	.	.	PUNCT
ejpam-4511	467	1	dominating	dominate	VERB
ejpam-4511	467	2	sequences	sequence	NOUN
ejpam-4511	467	3	under	under	ADP
ejpam-4511	467	4	atomic	atomic	ADJ
ejpam-4511	467	5	changes	change	NOUN
ejpam-4511	467	6	with	with	ADP
ejpam-4511	467	7	applications	application	NOUN
ejpam-4511	467	8	in	in	ADP
ejpam-4511	467	9	sierpinski	sierpinski	ADJ
ejpam-4511	467	10	and	and	CCONJ
ejpam-4511	467	11	interval	interval	NOUN
ejpam-4511	467	12	graphs	graph	NOUN
ejpam-4511	467	13	.	.	PUNCT
ejpam-4511	468	1	appl	appl	PROPN
ejpam-4511	468	2	.	.	PUNCT
ejpam-4511	469	1	anal	anal	PROPN
ejpam-4511	469	2	.	.	PUNCT
ejpam-4511	470	1	discrete	discrete	ADJ
ejpam-4511	470	2	math	math	NOUN
ejpam-4511	470	3	.	.	PUNCT
ejpam-4511	471	1	,	,	PUNCT
ejpam-4511	471	2	(	(	PUNCT
ejpam-4511	471	3	10):518–531	10):518–531	NUM
ejpam-4511	471	4	,	,	PUNCT
ejpam-4511	471	5	2016	2016	NUM
ejpam-4511	471	6	.	.	PUNCT
ejpam-4511	472	1	[	[	X
ejpam-4511	472	2	6	6	NUM
ejpam-4511	472	3	]	]	PUNCT
ejpam-4511	472	4	b.	b.	PROPN
ejpam-4511	472	5	bresar	bresar	PROPN
ejpam-4511	472	6	,	,	PUNCT
ejpam-4511	472	7	t.	t.	NOUN
ejpam-4511	472	8	gologranc	gologranc	PROPN
ejpam-4511	472	9	,	,	PUNCT
ejpam-4511	472	10	m.	m.	NOUN
ejpam-4511	472	11	milanic	milanic	PROPN
ejpam-4511	472	12	,	,	PUNCT
ejpam-4511	472	13	d.	d.	PROPN
ejpam-4511	472	14	rall	rall	PROPN
ejpam-4511	472	15	,	,	PUNCT
ejpam-4511	472	16	and	and	CCONJ
ejpam-4511	472	17	r.	r.	PROPN
ejpam-4511	472	18	rizzi	rizzi	PROPN
ejpam-4511	472	19	.	.	PUNCT
ejpam-4511	473	1	dominating	dominate	VERB
ejpam-4511	473	2	sequence	sequence	NOUN
ejpam-4511	473	3	in	in	ADP
ejpam-4511	473	4	graphs	graph	NOUN
ejpam-4511	473	5	.	.	PUNCT
ejpam-4511	474	1	discrete	discrete	ADJ
ejpam-4511	474	2	math	math	NOUN
ejpam-4511	474	3	.	.	PUNCT
ejpam-4511	475	1	,	,	PUNCT
ejpam-4511	475	2	(	(	PUNCT
ejpam-4511	475	3	336):22–36	336):22–36	NUM
ejpam-4511	475	4	,	,	PUNCT
ejpam-4511	475	5	2014	2014	NUM
ejpam-4511	475	6	.	.	PUNCT
ejpam-4511	476	1	[	[	X
ejpam-4511	476	2	7	7	X
ejpam-4511	476	3	]	]	X
ejpam-4511	476	4	b.	b.	PROPN
ejpam-4511	476	5	bresar	bresar	PROPN
ejpam-4511	476	6	,	,	PUNCT
ejpam-4511	476	7	t.	t.	PROPN
ejpam-4511	476	8	kos	kos	PROPN
ejpam-4511	476	9	,	,	PUNCT
ejpam-4511	476	10	and	and	CCONJ
ejpam-4511	476	11	p.	p.	NOUN
ejpam-4511	476	12	torres	torre	NOUN
ejpam-4511	476	13	.	.	PUNCT
ejpam-4511	477	1	grundy	grundy	PROPN
ejpam-4511	477	2	domination	domination	NOUN
ejpam-4511	477	3	and	and	CCONJ
ejpam-4511	477	4	zero	zero	NUM
ejpam-4511	477	5	forcing	force	VERB
ejpam-4511	477	6	in	in	ADP
ejpam-4511	477	7	kneser	kneser	NOUN
ejpam-4511	477	8	graphs	graph	NOUN
ejpam-4511	477	9	.	.	PUNCT
ejpam-4511	478	1	ars	ar	VERB
ejpam-4511	478	2	math	math	PROPN
ejpam-4511	478	3	.	.	PUNCT
ejpam-4511	479	1	contemp	contemp	NOUN
ejpam-4511	479	2	.	.	PUNCT
ejpam-4511	480	1	,	,	PUNCT
ejpam-4511	480	2	(	(	PUNCT
ejpam-4511	480	3	17):419–430	17):419–430	NUM
ejpam-4511	480	4	,	,	PUNCT
ejpam-4511	480	5	2019	2019	NUM
ejpam-4511	480	6	.	.	PUNCT
ejpam-4511	481	1	[	[	X
ejpam-4511	481	2	8	8	X
ejpam-4511	481	3	]	]	X
ejpam-4511	481	4	j.	j.	PROPN
ejpam-4511	481	5	hassan	hassan	PROPN
ejpam-4511	481	6	,	,	PUNCT
ejpam-4511	481	7	s.	s.	PROPN
ejpam-4511	481	8	canoy	canoy	PROPN
ejpam-4511	481	9	jr	jr	PROPN
ejpam-4511	481	10	.	.	PROPN
ejpam-4511	481	11	,	,	PUNCT
ejpam-4511	481	12	and	and	CCONJ
ejpam-4511	481	13	a.	a.	PROPN
ejpam-4511	481	14	aradais	aradais	PROPN
ejpam-4511	481	15	.	.	PUNCT
ejpam-4511	482	1	hop	hop	PROPN
ejpam-4511	482	2	independent	independent	ADJ
ejpam-4511	482	3	sets	set	NOUN
ejpam-4511	482	4	in	in	ADP
ejpam-4511	482	5	graphs	graph	NOUN
ejpam-4511	482	6	.	.	PUNCT
ejpam-4511	483	1	eur	eur	PROPN
ejpam-4511	483	2	.	.	PUNCT
ejpam-4511	484	1	j.	j.	PROPN
ejpam-4511	484	2	pure	pure	PROPN
ejpam-4511	484	3	appl	appl	PROPN
ejpam-4511	484	4	.	.	PUNCT
ejpam-4511	484	5	math	math	PROPN
ejpam-4511	484	6	.	.	PUNCT
ejpam-4511	484	7	,	,	PUNCT
ejpam-4511	484	8	15(2):467–477	15(2):467–477	PROPN
ejpam-4511	484	9	,	,	PUNCT
ejpam-4511	484	10	2022	2022	NUM
ejpam-4511	484	11	.	.	PUNCT
ejpam-4511	485	1	[	[	X
ejpam-4511	485	2	9	9	NUM
ejpam-4511	485	3	]	]	X
ejpam-4511	485	4	m.	m.	NOUN
ejpam-4511	485	5	henning	henning	PROPN
ejpam-4511	485	6	and	and	CCONJ
ejpam-4511	485	7	n.	n.	PROPN
ejpam-4511	485	8	rad	rad	PROPN
ejpam-4511	485	9	.	.	PROPN
ejpam-4511	486	1	on	on	ADP
ejpam-4511	486	2	2	2	NUM
ejpam-4511	486	3	-	-	PUNCT
ejpam-4511	486	4	step	step	NOUN
ejpam-4511	486	5	and	and	CCONJ
ejpam-4511	486	6	hop	hop	NOUN
ejpam-4511	486	7	dominating	dominating	NOUN
ejpam-4511	486	8	sets	set	NOUN
ejpam-4511	486	9	in	in	ADP
ejpam-4511	486	10	graphs	graph	NOUN
ejpam-4511	486	11	.	.	PUNCT
ejpam-4511	487	1	graphs	graph	NOUN
ejpam-4511	487	2	and	and	CCONJ
ejpam-4511	487	3	combinatorics	combinatoric	NOUN
ejpam-4511	487	4	.	.	PUNCT
ejpam-4511	487	5	,	,	PUNCT
ejpam-4511	487	6	33(4):913–927	33(4):913–927	PROPN
ejpam-4511	487	7	,	,	PUNCT
ejpam-4511	487	8	2017	2017	NUM
ejpam-4511	487	9	.	.	PUNCT
ejpam-4511	488	1	[	[	X
ejpam-4511	488	2	10	10	NUM
ejpam-4511	488	3	]	]	X
ejpam-4511	488	4	s.	s.	PROPN
ejpam-4511	488	5	canoy	canoy	PROPN
ejpam-4511	488	6	jr	jr	PROPN
ejpam-4511	488	7	.	.	PROPN
ejpam-4511	488	8	and	and	CCONJ
ejpam-4511	488	9	g.	g.	PROPN
ejpam-4511	488	10	malacas	malacas	PROPN
ejpam-4511	488	11	.	.	PUNCT
ejpam-4511	489	1	determining	determine	VERB
ejpam-4511	489	2	the	the	DET
ejpam-4511	489	3	intruder	intruder	NOUN
ejpam-4511	489	4	’s	’s	PART
ejpam-4511	489	5	location	location	NOUN
ejpam-4511	489	6	in	in	ADP
ejpam-4511	489	7	a	a	DET
ejpam-4511	489	8	given	give	VERB
ejpam-4511	489	9	network	network	NOUN
ejpam-4511	489	10	:	:	PUNCT
ejpam-4511	489	11	locating	locate	VERB
ejpam-4511	489	12	-	-	PUNCT
ejpam-4511	489	13	dominating	dominating	NOUN
ejpam-4511	489	14	sets	set	NOUN
ejpam-4511	489	15	in	in	ADP
ejpam-4511	489	16	a	a	DET
ejpam-4511	489	17	graph	graph	NOUN
ejpam-4511	489	18	.	.	PUNCT
ejpam-4511	490	1	nrcp	nrcp	PROPN
ejpam-4511	490	2	research	research	PROPN
ejpam-4511	490	3	journal	journal	PROPN
ejpam-4511	490	4	.	.	PUNCT
ejpam-4511	490	5	,	,	PUNCT
ejpam-4511	490	6	13(1):1–8	13(1):1–8	NUM
ejpam-4511	490	7	,	,	PUNCT
ejpam-4511	490	8	2013	2013	NUM
ejpam-4511	490	9	.	.	PUNCT
ejpam-4511	491	1	[	[	X
ejpam-4511	491	2	11	11	NUM
ejpam-4511	491	3	]	]	X
ejpam-4511	491	4	s.	s.	PROPN
ejpam-4511	491	5	canoy	canoy	PROPN
ejpam-4511	491	6	jr	jr	PROPN
ejpam-4511	491	7	.	.	PROPN
ejpam-4511	491	8	and	and	CCONJ
ejpam-4511	491	9	g.	g.	PROPN
ejpam-4511	491	10	malacas	malacas	PROPN
ejpam-4511	491	11	.	.	PUNCT
ejpam-4511	492	1	differentiating	differentiate	VERB
ejpam-4511	492	2	-	-	PUNCT
ejpam-4511	492	3	dominating	dominating	NOUN
ejpam-4511	492	4	sets	set	NOUN
ejpam-4511	492	5	in	in	ADP
ejpam-4511	492	6	graphs	graph	NOUN
ejpam-4511	492	7	under	under	ADP
ejpam-4511	492	8	binary	binary	ADJ
ejpam-4511	492	9	operations	operation	NOUN
ejpam-4511	492	10	.	.	PUNCT
ejpam-4511	493	1	tamkang	tamkang	PROPN
ejpam-4511	493	2	j.	j.	PROPN
ejpam-4511	493	3	math	math	PROPN
ejpam-4511	493	4	.	.	PUNCT
ejpam-4511	493	5	,	,	PUNCT
ejpam-4511	493	6	46(1):51–60	46(1):51–60	NOUN
ejpam-4511	493	7	,	,	PUNCT
ejpam-4511	493	8	2015	2015	NUM
ejpam-4511	493	9	.	.	PUNCT
ejpam-4511	494	1	[	[	X
ejpam-4511	494	2	12	12	NUM
ejpam-4511	494	3	]	]	X
ejpam-4511	494	4	s.	s.	PROPN
ejpam-4511	494	5	canoy	canoy	PROPN
ejpam-4511	494	6	jr	jr	PROPN
ejpam-4511	494	7	.	.	PROPN
ejpam-4511	494	8	,	,	PUNCT
ejpam-4511	494	9	r.	r.	PROPN
ejpam-4511	494	10	mollejon	mollejon	NOUN
ejpam-4511	494	11	,	,	PUNCT
ejpam-4511	494	12	and	and	CCONJ
ejpam-4511	494	13	j.	j.	PROPN
ejpam-4511	494	14	g.	g.	PROPN
ejpam-4511	494	15	canoy	canoy	PROPN
ejpam-4511	494	16	.	.	PUNCT
ejpam-4511	495	1	hop	hop	PROPN
ejpam-4511	495	2	dominating	dominating	NOUN
ejpam-4511	495	3	sets	set	NOUN
ejpam-4511	495	4	in	in	ADP
ejpam-4511	495	5	graphs	graph	NOUN
ejpam-4511	495	6	under	under	ADP
ejpam-4511	495	7	binary	binary	ADJ
ejpam-4511	495	8	operations	operation	NOUN
ejpam-4511	495	9	.	.	PUNCT
ejpam-4511	496	1	eur	eur	PROPN
ejpam-4511	496	2	.	.	PUNCT
ejpam-4511	497	1	j.	j.	PROPN
ejpam-4511	497	2	pure	pure	PROPN
ejpam-4511	497	3	appl	appl	PROPN
ejpam-4511	497	4	.	.	PUNCT
ejpam-4511	497	5	math	math	PROPN
ejpam-4511	497	6	.	.	PUNCT
ejpam-4511	497	7	,	,	PUNCT
ejpam-4511	498	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4511	498	2	,	,	PUNCT
ejpam-4511	498	3	2019	2019	NUM
ejpam-4511	498	4	.	.	PUNCT
ejpam-4511	499	1	[	[	X
ejpam-4511	499	2	13	13	NUM
ejpam-4511	499	3	]	]	PUNCT
ejpam-4511	499	4	s.	s.	PROPN
ejpam-4511	499	5	canoy	canoy	PROPN
ejpam-4511	499	6	jr	jr	PROPN
ejpam-4511	499	7	.	.	PROPN
ejpam-4511	499	8	and	and	CCONJ
ejpam-4511	499	9	g.	g.	PROPN
ejpam-4511	499	10	salasalan	salasalan	NOUN
ejpam-4511	499	11	.	.	PUNCT
ejpam-4511	500	1	locating	locate	VERB
ejpam-4511	500	2	-	-	PUNCT
ejpam-4511	500	3	hop	hop	NOUN
ejpam-4511	500	4	domination	domination	NOUN
ejpam-4511	500	5	in	in	ADP
ejpam-4511	500	6	graphs	graph	NOUN
ejpam-4511	500	7	.	.	PUNCT
ejpam-4511	501	1	kyungpook	kyungpook	PROPN
ejpam-4511	501	2	mathematical	mathematical	PROPN
ejpam-4511	501	3	journal	journal	PROPN
ejpam-4511	501	4	.	.	PUNCT
ejpam-4511	501	5	,	,	PUNCT
ejpam-4511	501	6	62:193–204	62:193–204	NUM
ejpam-4511	501	7	,	,	PUNCT
ejpam-4511	501	8	2022	2022	NUM
ejpam-4511	501	9	.	.	PUNCT
ejpam-4511	502	1	[	[	X
ejpam-4511	502	2	14	14	NUM
ejpam-4511	502	3	]	]	X
ejpam-4511	502	4	g.	g.	PROPN
ejpam-4511	502	5	nasini	nasini	PROPN
ejpam-4511	502	6	and	and	CCONJ
ejpam-4511	502	7	p.	p.	NOUN
ejpam-4511	502	8	torres	torre	NOUN
ejpam-4511	502	9	.	.	PUNCT
ejpam-4511	503	1	grundy	grundy	PROPN
ejpam-4511	503	2	dominating	dominate	VERB
ejpam-4511	503	3	sequences	sequence	NOUN
ejpam-4511	503	4	on	on	ADP
ejpam-4511	503	5	x	x	ADJ
ejpam-4511	503	6	-	-	ADJ
ejpam-4511	503	7	join	join	ADJ
ejpam-4511	503	8	product	product	NOUN
ejpam-4511	503	9	.	.	PUNCT
ejpam-4511	504	1	discrete	discrete	ADJ
ejpam-4511	504	2	applied	applied	ADJ
ejpam-4511	504	3	mathematics	mathematic	NOUN
ejpam-4511	504	4	.	.	PUNCT
ejpam-4511	504	5	,	,	PUNCT
ejpam-4511	504	6	(	(	PUNCT
ejpam-4511	504	7	284):138–149	284):138–149	NOUN
ejpam-4511	504	8	,	,	PUNCT
ejpam-4511	504	9	2020	2020	NUM
ejpam-4511	504	10	.	.	PUNCT
ejpam-4511	505	1	references	reference	NOUN
ejpam-4511	505	2	1636	1636	NUM
ejpam-4511	506	1	[	[	X
ejpam-4511	506	2	15	15	NUM
ejpam-4511	506	3	]	]	X
ejpam-4511	506	4	c.	c.	PROPN
ejpam-4511	506	5	natarajan	natarajan	PROPN
ejpam-4511	506	6	and	and	CCONJ
ejpam-4511	506	7	s.	s.	PROPN
ejpam-4511	506	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4511	506	9	.	.	PUNCT
ejpam-4511	507	1	hop	hop	PROPN
ejpam-4511	507	2	domination	domination	NOUN
ejpam-4511	507	3	in	in	ADP
ejpam-4511	507	4	graphs	graphs	PROPN
ejpam-4511	507	5	ii	ii	PROPN
ejpam-4511	507	6	.	.	PUNCT
ejpam-4511	507	7	versita	versita	PROPN
ejpam-4511	507	8	,	,	PUNCT
ejpam-4511	507	9	23(2):187	23(2):187	NUM
ejpam-4511	507	10	–	–	PUNCT
ejpam-4511	507	11	199	199	NUM
ejpam-4511	507	12	,	,	PUNCT
ejpam-4511	507	13	2015	2015	NUM
ejpam-4511	507	14	.	.	PUNCT
ejpam-4511	508	1	[	[	X
ejpam-4511	508	2	16	16	NUM
ejpam-4511	508	3	]	]	X
ejpam-4511	508	4	g.	g.	PROPN
ejpam-4511	508	5	salasalan	salasalan	NOUN
ejpam-4511	508	6	and	and	CCONJ
ejpam-4511	508	7	s.	s.	PROPN
ejpam-4511	508	8	canoy	canoy	PROPN
ejpam-4511	508	9	jr	jr	PROPN
ejpam-4511	508	10	.	.	PROPN
ejpam-4511	508	11	global	global	PROPN
ejpam-4511	508	12	hop	hop	PROPN
ejpam-4511	508	13	domination	domination	PROPN
ejpam-4511	508	14	numbers	number	NOUN
ejpam-4511	508	15	of	of	ADP
ejpam-4511	508	16	graphs	graph	NOUN
ejpam-4511	508	17	.	.	PUNCT
ejpam-4511	509	1	eur	eur	PROPN
ejpam-4511	509	2	.	.	PUNCT
ejpam-4511	510	1	j.	j.	PROPN
ejpam-4511	510	2	pure	pure	PROPN
ejpam-4511	510	3	appl	appl	PROPN
ejpam-4511	510	4	.	.	PUNCT
ejpam-4511	510	5	math	math	PROPN
ejpam-4511	510	6	.	.	PUNCT
ejpam-4511	510	7	,	,	PUNCT
ejpam-4511	510	8	14(1):112–125	14(1):112–125	NUM
ejpam-4511	510	9	,	,	PUNCT
ejpam-4511	510	10	2021	2021	NUM
ejpam-4511	510	11	.	.	PUNCT