id	sid	tid	token	lemma	pos
ejpam-4690	1	1	european	european	PROPN
ejpam-4690	1	2	journal	journal	PROPN
ejpam-4690	1	3	of	of	ADP
ejpam-4690	1	4	pure	pure	ADJ
ejpam-4690	1	5	and	and	CCONJ
ejpam-4690	1	6	applied	apply	VERB
ejpam-4690	1	7	mathematics	mathematic	NOUN
ejpam-4690	1	8	vol	vol	NOUN
ejpam-4690	1	9	.	.	PUNCT
ejpam-4690	2	1	16	16	NUM
ejpam-4690	2	2	,	,	PUNCT
ejpam-4690	2	3	no	no	INTJ
ejpam-4690	2	4	.	.	NOUN
ejpam-4690	2	5	2	2	NUM
ejpam-4690	2	6	,	,	PUNCT
ejpam-4690	2	7	2023	2023	NUM
ejpam-4690	2	8	,	,	PUNCT
ejpam-4690	2	9	1154	1154	NUM
ejpam-4690	2	10	-	-	SYM
ejpam-4690	2	11	1166	1166	NUM
ejpam-4690	2	12	issn	issn	VERB
ejpam-4690	2	13	1307	1307	NUM
ejpam-4690	2	14	-	-	SYM
ejpam-4690	2	15	5543	5543	NUM
ejpam-4690	2	16	–	–	PUNCT
ejpam-4690	2	17	ejpam.com	ejpam.com	X
ejpam-4690	2	18	published	publish	VERB
ejpam-4690	2	19	by	by	ADP
ejpam-4690	2	20	new	new	PROPN
ejpam-4690	2	21	york	york	PROPN
ejpam-4690	2	22	business	business	PROPN
ejpam-4690	2	23	global	global	PROPN
ejpam-4690	2	24	grundy	grundy	PROPN
ejpam-4690	2	25	dominating	dominating	NOUN
ejpam-4690	2	26	and	and	CCONJ
ejpam-4690	2	27	grundy	grundy	PROPN
ejpam-4690	2	28	hop	hop	NOUN
ejpam-4690	2	29	dominating	dominate	VERB
ejpam-4690	2	30	sequences	sequence	NOUN
ejpam-4690	2	31	in	in	ADP
ejpam-4690	2	32	graphs	graph	NOUN
ejpam-4690	2	33	:	:	PUNCT
ejpam-4690	2	34	relationships	relationship	NOUN
ejpam-4690	2	35	and	and	CCONJ
ejpam-4690	2	36	some	some	DET
ejpam-4690	2	37	structural	structural	ADJ
ejpam-4690	2	38	properties	property	NOUN
ejpam-4690	2	39	javier	javier	PROPN
ejpam-4690	2	40	a.	a.	PROPN
ejpam-4690	2	41	hassan1,∗	hassan1,∗	PROPN
ejpam-4690	2	42	,	,	PUNCT
ejpam-4690	2	43	sergio	sergio	PROPN
ejpam-4690	2	44	r.	r.	PROPN
ejpam-4690	2	45	canoy	canoy	PROPN
ejpam-4690	2	46	,	,	PUNCT
ejpam-4690	2	47	jr.2,3	jr.2,3	PROPN
ejpam-4690	2	48	1mathematics	1mathematics	NUM
ejpam-4690	2	49	and	and	CCONJ
ejpam-4690	2	50	sciences	sciences	PROPN
ejpam-4690	2	51	department	department	PROPN
ejpam-4690	2	52	,	,	PUNCT
ejpam-4690	2	53	college	college	NOUN
ejpam-4690	2	54	of	of	ADP
ejpam-4690	2	55	arts	art	NOUN
ejpam-4690	2	56	and	and	CCONJ
ejpam-4690	2	57	sciences	science	NOUN
ejpam-4690	2	58	,	,	PUNCT
ejpam-4690	2	59	msu	msu	PROPN
ejpam-4690	2	60	tawi	tawi	PROPN
ejpam-4690	2	61	-	-	PUNCT
ejpam-4690	2	62	tawi	tawi	PROPN
ejpam-4690	2	63	college	college	PROPN
ejpam-4690	2	64	of	of	ADP
ejpam-4690	2	65	technology	technology	NOUN
ejpam-4690	2	66	and	and	CCONJ
ejpam-4690	2	67	oceanography	oceanography	NOUN
ejpam-4690	2	68	,	,	PUNCT
ejpam-4690	2	69	bongao	bongao	NOUN
ejpam-4690	2	70	,	,	PUNCT
ejpam-4690	2	71	tawi	tawi	NOUN
ejpam-4690	2	72	-	-	PUNCT
ejpam-4690	2	73	tawi	tawi	NOUN
ejpam-4690	2	74	,	,	PUNCT
ejpam-4690	2	75	philippines	philippine	NOUN
ejpam-4690	2	76	2department	2department	NUM
ejpam-4690	2	77	of	of	ADP
ejpam-4690	2	78	mathematics	mathematic	NOUN
ejpam-4690	2	79	and	and	CCONJ
ejpam-4690	2	80	statistics	statistic	NOUN
ejpam-4690	2	81	,	,	PUNCT
ejpam-4690	2	82	college	college	NOUN
ejpam-4690	2	83	of	of	ADP
ejpam-4690	2	84	science	science	NOUN
ejpam-4690	2	85	and	and	CCONJ
ejpam-4690	2	86	mathematics	mathematic	NOUN
ejpam-4690	2	87	3center	3center	NUM
ejpam-4690	2	88	for	for	ADP
ejpam-4690	2	89	mathematical	mathematical	ADJ
ejpam-4690	2	90	and	and	CCONJ
ejpam-4690	2	91	theoretical	theoretical	ADJ
ejpam-4690	2	92	physical	physical	ADJ
ejpam-4690	2	93	sciences	science	NOUN
ejpam-4690	2	94	,	,	PUNCT
ejpam-4690	2	95	premier	premier	PROPN
ejpam-4690	2	96	research	research	PROPN
ejpam-4690	2	97	institute	institute	PROPN
ejpam-4690	2	98	of	of	ADP
ejpam-4690	2	99	science	science	NOUN
ejpam-4690	2	100	and	and	CCONJ
ejpam-4690	2	101	mathematics	mathematic	NOUN
ejpam-4690	2	102	,	,	PUNCT
ejpam-4690	2	103	msu	msu	PROPN
ejpam-4690	2	104	-	-	PUNCT
ejpam-4690	2	105	iligan	iligan	PROPN
ejpam-4690	2	106	institute	institute	PROPN
ejpam-4690	2	107	of	of	ADP
ejpam-4690	2	108	technology	technology	PROPN
ejpam-4690	2	109	,	,	PUNCT
ejpam-4690	2	110	9200	9200	NUM
ejpam-4690	2	111	iligan	iligan	ADJ
ejpam-4690	2	112	city	city	NOUN
ejpam-4690	2	113	,	,	PUNCT
ejpam-4690	2	114	philippines	philippine	NOUN
ejpam-4690	2	115	abstract	abstract	ADJ
ejpam-4690	2	116	.	.	PUNCT
ejpam-4690	3	1	in	in	ADP
ejpam-4690	3	2	this	this	DET
ejpam-4690	3	3	paper	paper	NOUN
ejpam-4690	3	4	,	,	PUNCT
ejpam-4690	3	5	we	we	PRON
ejpam-4690	3	6	revisit	revisit	VERB
ejpam-4690	3	7	the	the	DET
ejpam-4690	3	8	concepts	concept	NOUN
ejpam-4690	3	9	of	of	ADP
ejpam-4690	3	10	grundy	grundy	PROPN
ejpam-4690	3	11	domination	domination	PROPN
ejpam-4690	3	12	and	and	CCONJ
ejpam-4690	3	13	grundy	grundy	PROPN
ejpam-4690	3	14	hop	hop	PROPN
ejpam-4690	3	15	domination	domination	NOUN
ejpam-4690	3	16	in	in	ADP
ejpam-4690	3	17	graphs	graph	NOUN
ejpam-4690	3	18	and	and	CCONJ
ejpam-4690	3	19	give	give	VERB
ejpam-4690	3	20	some	some	DET
ejpam-4690	3	21	realization	realization	NOUN
ejpam-4690	3	22	results	result	NOUN
ejpam-4690	3	23	involving	involve	VERB
ejpam-4690	3	24	these	these	DET
ejpam-4690	3	25	parameters	parameter	NOUN
ejpam-4690	3	26	.	.	PUNCT
ejpam-4690	4	1	we	we	PRON
ejpam-4690	4	2	show	show	VERB
ejpam-4690	4	3	that	that	SCONJ
ejpam-4690	4	4	the	the	DET
ejpam-4690	4	5	grundy	grundy	PROPN
ejpam-4690	4	6	domination	domination	NOUN
ejpam-4690	4	7	number	number	NOUN
ejpam-4690	4	8	and	and	CCONJ
ejpam-4690	4	9	grundy	grundy	PROPN
ejpam-4690	4	10	hop	hop	PROPN
ejpam-4690	4	11	domination	domination	NOUN
ejpam-4690	4	12	number	number	NOUN
ejpam-4690	4	13	of	of	ADP
ejpam-4690	4	14	a	a	DET
ejpam-4690	4	15	graph	graph	NOUN
ejpam-4690	4	16	g	g	NOUN
ejpam-4690	4	17	are	be	AUX
ejpam-4690	4	18	generally	generally	ADV
ejpam-4690	4	19	incomparable	incomparable	ADJ
ejpam-4690	4	20	(	(	PUNCT
ejpam-4690	4	21	one	one	NUM
ejpam-4690	4	22	is	be	AUX
ejpam-4690	4	23	not	not	PART
ejpam-4690	4	24	always	always	ADV
ejpam-4690	4	25	less	less	ADJ
ejpam-4690	4	26	than	than	ADP
ejpam-4690	4	27	or	or	CCONJ
ejpam-4690	4	28	equal	equal	VERB
ejpam-4690	4	29	the	the	DET
ejpam-4690	4	30	other	other	ADJ
ejpam-4690	4	31	)	)	PUNCT
ejpam-4690	4	32	.	.	PUNCT
ejpam-4690	5	1	it	it	PRON
ejpam-4690	5	2	is	be	AUX
ejpam-4690	5	3	shown	show	VERB
ejpam-4690	5	4	that	that	SCONJ
ejpam-4690	5	5	their	their	PRON
ejpam-4690	5	6	absolute	absolute	ADJ
ejpam-4690	5	7	difference	difference	NOUN
ejpam-4690	5	8	can	can	AUX
ejpam-4690	5	9	be	be	AUX
ejpam-4690	5	10	made	make	VERB
ejpam-4690	5	11	arbitrarily	arbitrarily	ADV
ejpam-4690	5	12	large	large	ADJ
ejpam-4690	5	13	.	.	PUNCT
ejpam-4690	6	1	moreover	moreover	ADV
ejpam-4690	6	2	,	,	PUNCT
ejpam-4690	6	3	the	the	DET
ejpam-4690	6	4	grundy	grundy	PROPN
ejpam-4690	6	5	domination	domination	NOUN
ejpam-4690	6	6	numbers	number	NOUN
ejpam-4690	6	7	of	of	ADP
ejpam-4690	6	8	some	some	DET
ejpam-4690	6	9	graphs	graph	NOUN
ejpam-4690	6	10	are	be	AUX
ejpam-4690	6	11	determined	determine	VERB
ejpam-4690	6	12	.	.	PUNCT
ejpam-4690	7	1	2020	2020	NUM
ejpam-4690	7	2	mathematics	mathematic	NOUN
ejpam-4690	7	3	subject	subject	NOUN
ejpam-4690	7	4	classifications	classification	NOUN
ejpam-4690	7	5	:	:	PUNCT
ejpam-4690	7	6	05c69	05c69	X
ejpam-4690	7	7	key	key	ADJ
ejpam-4690	7	8	words	word	NOUN
ejpam-4690	7	9	and	and	CCONJ
ejpam-4690	7	10	phrases	phrase	NOUN
ejpam-4690	7	11	:	:	PUNCT
ejpam-4690	7	12	grundy	grundy	PROPN
ejpam-4690	7	13	dominating	dominating	NOUN
ejpam-4690	7	14	sequence	sequence	NOUN
ejpam-4690	7	15	,	,	PUNCT
ejpam-4690	7	16	grundy	grundy	PROPN
ejpam-4690	7	17	hop	hop	NOUN
ejpam-4690	7	18	dominating	dominating	NOUN
ejpam-4690	7	19	sequence	sequence	NOUN
ejpam-4690	7	20	,	,	PUNCT
ejpam-4690	7	21	grundy	grundy	PROPN
ejpam-4690	7	22	domination	domination	NOUN
ejpam-4690	7	23	number	number	NOUN
ejpam-4690	7	24	,	,	PUNCT
ejpam-4690	7	25	grundy	grundy	PROPN
ejpam-4690	7	26	hop	hop	PROPN
ejpam-4690	7	27	domination	domination	PROPN
ejpam-4690	7	28	number	number	NOUN
ejpam-4690	7	29	1	1	NUM
ejpam-4690	7	30	.	.	PUNCT
ejpam-4690	7	31	introduction	introduction	NOUN
ejpam-4690	7	32	the	the	DET
ejpam-4690	7	33	concept	concept	NOUN
ejpam-4690	7	34	of	of	ADP
ejpam-4690	7	35	grundy	grundy	PROPN
ejpam-4690	7	36	domination	domination	NOUN
ejpam-4690	7	37	in	in	ADP
ejpam-4690	7	38	a	a	DET
ejpam-4690	7	39	graph	graph	NOUN
ejpam-4690	7	40	was	be	AUX
ejpam-4690	7	41	introduced	introduce	VERB
ejpam-4690	7	42	and	and	CCONJ
ejpam-4690	7	43	initially	initially	ADV
ejpam-4690	7	44	studied	study	VERB
ejpam-4690	7	45	by	by	ADP
ejpam-4690	7	46	bresar	bresar	VERB
ejpam-4690	7	47	et	et	PROPN
ejpam-4690	7	48	al	al	PROPN
ejpam-4690	7	49	.	.	PUNCT
ejpam-4690	8	1	[	[	X
ejpam-4690	8	2	6	6	NUM
ejpam-4690	8	3	]	]	PUNCT
ejpam-4690	8	4	.	.	PUNCT
ejpam-4690	9	1	this	this	DET
ejpam-4690	9	2	concept	concept	NOUN
ejpam-4690	9	3	was	be	AUX
ejpam-4690	9	4	also	also	ADV
ejpam-4690	9	5	considered	consider	VERB
ejpam-4690	9	6	in	in	ADP
ejpam-4690	9	7	other	other	ADJ
ejpam-4690	9	8	previous	previous	ADJ
ejpam-4690	9	9	studies	study	NOUN
ejpam-4690	9	10	(	(	PUNCT
ejpam-4690	9	11	see	see	VERB
ejpam-4690	9	12	[	[	X
ejpam-4690	9	13	3	3	NUM
ejpam-4690	9	14	]	]	PUNCT
ejpam-4690	9	15	,	,	PUNCT
ejpam-4690	9	16	[	[	X
ejpam-4690	9	17	4	4	NUM
ejpam-4690	9	18	]	]	PUNCT
ejpam-4690	9	19	,	,	PUNCT
ejpam-4690	9	20	[	[	X
ejpam-4690	9	21	5	5	NUM
ejpam-4690	9	22	]	]	PUNCT
ejpam-4690	9	23	,	,	PUNCT
ejpam-4690	10	1	[	[	X
ejpam-4690	10	2	7	7	NUM
ejpam-4690	10	3	]	]	NUM
ejpam-4690	10	4	)	)	PUNCT
ejpam-4690	10	5	.	.	PUNCT
ejpam-4690	11	1	in	in	ADP
ejpam-4690	11	2	[	[	X
ejpam-4690	11	3	5	5	NUM
ejpam-4690	11	4	]	]	PUNCT
ejpam-4690	11	5	,	,	PUNCT
ejpam-4690	11	6	exact	exact	ADJ
ejpam-4690	11	7	formulas	formula	NOUN
ejpam-4690	11	8	for	for	ADP
ejpam-4690	11	9	grundy	grundy	PROPN
ejpam-4690	11	10	domination	domination	NOUN
ejpam-4690	11	11	numbers	number	NOUN
ejpam-4690	11	12	of	of	ADP
ejpam-4690	11	13	sierpinski	sierpinski	ADJ
ejpam-4690	11	14	graphs	graph	NOUN
ejpam-4690	11	15	were	be	AUX
ejpam-4690	11	16	generated	generate	VERB
ejpam-4690	11	17	and	and	CCONJ
ejpam-4690	11	18	a	a	DET
ejpam-4690	11	19	linear	linear	ADJ
ejpam-4690	11	20	algorithm	algorithm	NOUN
ejpam-4690	11	21	for	for	ADP
ejpam-4690	11	22	determining	determine	VERB
ejpam-4690	11	23	these	these	DET
ejpam-4690	11	24	numbers	number	NOUN
ejpam-4690	11	25	in	in	ADP
ejpam-4690	11	26	arbitrary	arbitrary	ADJ
ejpam-4690	11	27	interval	interval	NOUN
ejpam-4690	11	28	graphs	graph	NOUN
ejpam-4690	11	29	was	be	AUX
ejpam-4690	11	30	given	give	VERB
ejpam-4690	11	31	.	.	PUNCT
ejpam-4690	12	1	grundy	grundy	PROPN
ejpam-4690	12	2	domination	domination	NOUN
ejpam-4690	12	3	number	number	NOUN
ejpam-4690	12	4	was	be	AUX
ejpam-4690	12	5	studied	study	VERB
ejpam-4690	12	6	for	for	ADP
ejpam-4690	12	7	kneser	kneser	NOUN
ejpam-4690	12	8	graphs	graph	NOUN
ejpam-4690	12	9	in	in	ADP
ejpam-4690	12	10	[	[	X
ejpam-4690	12	11	7	7	NUM
ejpam-4690	12	12	]	]	PUNCT
ejpam-4690	12	13	and	and	CCONJ
ejpam-4690	12	14	graph	graph	NOUN
ejpam-4690	12	15	products	product	NOUN
ejpam-4690	12	16	in	in	ADP
ejpam-4690	12	17	[	[	X
ejpam-4690	12	18	3	3	NUM
ejpam-4690	12	19	]	]	PUNCT
ejpam-4690	12	20	and	and	CCONJ
ejpam-4690	12	21	[	[	X
ejpam-4690	12	22	14	14	NUM
ejpam-4690	12	23	]	]	PUNCT
ejpam-4690	12	24	.	.	PUNCT
ejpam-4690	13	1	recently	recently	ADV
ejpam-4690	13	2	,	,	PUNCT
ejpam-4690	13	3	hassan	hassan	PROPN
ejpam-4690	13	4	and	and	CCONJ
ejpam-4690	13	5	canoy	canoy	ADJ
ejpam-4690	13	6	[	[	X
ejpam-4690	13	7	8	8	NUM
ejpam-4690	13	8	]	]	PUNCT
ejpam-4690	13	9	introduced	introduce	VERB
ejpam-4690	13	10	and	and	CCONJ
ejpam-4690	13	11	investigated	investigate	VERB
ejpam-4690	13	12	the	the	DET
ejpam-4690	13	13	concept	concept	NOUN
ejpam-4690	13	14	of	of	ADP
ejpam-4690	13	15	grundy	grundy	PROPN
ejpam-4690	13	16	hop	hop	PROPN
ejpam-4690	13	17	domination	domination	NOUN
ejpam-4690	13	18	in	in	ADP
ejpam-4690	13	19	a	a	DET
ejpam-4690	13	20	graph	graph	NOUN
ejpam-4690	13	21	.	.	PUNCT
ejpam-4690	14	1	they	they	PRON
ejpam-4690	14	2	showed	show	VERB
ejpam-4690	14	3	that	that	SCONJ
ejpam-4690	14	4	the	the	DET
ejpam-4690	14	5	parameter	parameter	NOUN
ejpam-4690	14	6	is	be	AUX
ejpam-4690	14	7	at	at	ADP
ejpam-4690	14	8	least	least	ADJ
ejpam-4690	14	9	equal	equal	ADJ
ejpam-4690	14	10	to	to	ADP
ejpam-4690	14	11	the	the	DET
ejpam-4690	14	12	hop	hop	NOUN
ejpam-4690	14	13	domination	domination	NOUN
ejpam-4690	14	14	number	number	NOUN
ejpam-4690	14	15	of	of	ADP
ejpam-4690	14	16	a	a	DET
ejpam-4690	14	17	graph	graph	NOUN
ejpam-4690	14	18	g.	g.	NOUN
ejpam-4690	14	19	the	the	DET
ejpam-4690	14	20	authors	author	NOUN
ejpam-4690	14	21	also	also	ADV
ejpam-4690	14	22	characterized	characterize	VERB
ejpam-4690	14	23	the	the	DET
ejpam-4690	14	24	grundy	grundy	PROPN
ejpam-4690	14	25	hop	hop	NOUN
ejpam-4690	14	26	∗corresponding	∗corresponde	VERB
ejpam-4690	14	27	author	author	NOUN
ejpam-4690	14	28	.	.	PUNCT
ejpam-4690	15	1	doi	doi	NOUN
ejpam-4690	15	2	:	:	PUNCT
ejpam-4690	15	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4690	https://doi.org/10.29020/nybg.ejpam.v16i2.4690	PROPN
ejpam-4690	15	4	email	email	NOUN
ejpam-4690	15	5	addresses	address	NOUN
ejpam-4690	15	6	:	:	PUNCT
ejpam-4690	15	7	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-4690	15	8	(	(	PUNCT
ejpam-4690	15	9	j.	j.	PROPN
ejpam-4690	15	10	hassan	hassan	PROPN
ejpam-4690	15	11	)	)	PUNCT
ejpam-4690	15	12	,	,	PUNCT
ejpam-4690	15	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4690	15	14	(	(	PUNCT
ejpam-4690	15	15	s.	s.	PROPN
ejpam-4690	15	16	canoy	canoy	PROPN
ejpam-4690	15	17	)	)	PUNCT
ejpam-4690	15	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4690	15	19	1154	1154	NUM
ejpam-4690	15	20	©	©	PROPN
ejpam-4690	15	21	2023	2023	NUM
ejpam-4690	15	22	ejpam	ejpam	NOUN
ejpam-4690	15	23	all	all	DET
ejpam-4690	15	24	rights	right	NOUN
ejpam-4690	15	25	reserved	reserve	VERB
ejpam-4690	15	26	.	.	PUNCT
ejpam-4690	16	1	j.	j.	PROPN
ejpam-4690	16	2	hassan	hassan	PROPN
ejpam-4690	16	3	,	,	PUNCT
ejpam-4690	16	4	s.	s.	PROPN
ejpam-4690	16	5	canoy	canoy	PROPN
ejpam-4690	16	6	jr	jr	PROPN
ejpam-4690	16	7	.	.	PROPN
ejpam-4690	16	8	/	/	SYM
ejpam-4690	16	9	eur	eur	PROPN
ejpam-4690	16	10	.	.	PUNCT
ejpam-4690	17	1	j.	j.	PROPN
ejpam-4690	17	2	pure	pure	PROPN
ejpam-4690	17	3	appl	appl	PROPN
ejpam-4690	17	4	.	.	PROPN
ejpam-4690	17	5	math	math	PROPN
ejpam-4690	17	6	,	,	PUNCT
ejpam-4690	17	7	16	16	NUM
ejpam-4690	17	8	(	(	PUNCT
ejpam-4690	17	9	2	2	NUM
ejpam-4690	17	10	)	)	PUNCT
ejpam-4690	17	11	(	(	PUNCT
ejpam-4690	17	12	2023	2023	NUM
ejpam-4690	17	13	)	)	PUNCT
ejpam-4690	17	14	,	,	PUNCT
ejpam-4690	17	15	1154	1154	NUM
ejpam-4690	17	16	-	-	SYM
ejpam-4690	17	17	1166	1166	NUM
ejpam-4690	17	18	1155	1155	NUM
ejpam-4690	17	19	dominating	dominating	NOUN
ejpam-4690	17	20	sequences	sequence	NOUN
ejpam-4690	17	21	in	in	ADP
ejpam-4690	17	22	graphs	graph	NOUN
ejpam-4690	17	23	under	under	ADP
ejpam-4690	17	24	some	some	DET
ejpam-4690	17	25	binary	binary	ADJ
ejpam-4690	17	26	operations	operation	NOUN
ejpam-4690	17	27	.	.	PUNCT
ejpam-4690	18	1	previous	previous	ADJ
ejpam-4690	18	2	studies	study	NOUN
ejpam-4690	18	3	on	on	ADP
ejpam-4690	18	4	hop	hop	NOUN
ejpam-4690	18	5	domination	domination	NOUN
ejpam-4690	18	6	can	can	AUX
ejpam-4690	18	7	be	be	AUX
ejpam-4690	18	8	found	find	VERB
ejpam-4690	18	9	in	in	ADP
ejpam-4690	18	10	[	[	X
ejpam-4690	18	11	1	1	NUM
ejpam-4690	18	12	]	]	PUNCT
ejpam-4690	18	13	,	,	PUNCT
ejpam-4690	18	14	[	[	X
ejpam-4690	18	15	2	2	NUM
ejpam-4690	18	16	]	]	PUNCT
ejpam-4690	18	17	,	,	PUNCT
ejpam-4690	18	18	[	[	X
ejpam-4690	18	19	9	9	NUM
ejpam-4690	18	20	]	]	PUNCT
ejpam-4690	18	21	,	,	PUNCT
ejpam-4690	18	22	[	[	X
ejpam-4690	18	23	10	10	NUM
ejpam-4690	18	24	]	]	PUNCT
ejpam-4690	18	25	,	,	PUNCT
ejpam-4690	18	26	[	[	X
ejpam-4690	18	27	11	11	NUM
ejpam-4690	18	28	]	]	PUNCT
ejpam-4690	18	29	,	,	PUNCT
ejpam-4690	18	30	[	[	X
ejpam-4690	18	31	12	12	NUM
ejpam-4690	18	32	]	]	PUNCT
ejpam-4690	18	33	,	,	PUNCT
ejpam-4690	18	34	[	[	X
ejpam-4690	18	35	13	13	NUM
ejpam-4690	18	36	]	]	PUNCT
ejpam-4690	18	37	,	,	PUNCT
ejpam-4690	18	38	[	[	X
ejpam-4690	18	39	15	15	NUM
ejpam-4690	18	40	]	]	PUNCT
ejpam-4690	18	41	,	,	PUNCT
ejpam-4690	18	42	and	and	CCONJ
ejpam-4690	18	43	[	[	X
ejpam-4690	18	44	16	16	NUM
ejpam-4690	18	45	]	]	PUNCT
ejpam-4690	18	46	.	.	PUNCT
ejpam-4690	19	1	this	this	DET
ejpam-4690	19	2	paper	paper	NOUN
ejpam-4690	19	3	revisits	revisit	VERB
ejpam-4690	19	4	the	the	DET
ejpam-4690	19	5	concepts	concept	NOUN
ejpam-4690	19	6	of	of	ADP
ejpam-4690	19	7	grundy	grundy	PROPN
ejpam-4690	19	8	domination	domination	PROPN
ejpam-4690	19	9	and	and	CCONJ
ejpam-4690	19	10	grundy	grundy	PROPN
ejpam-4690	19	11	hop	hop	PROPN
ejpam-4690	19	12	domination	domination	NOUN
ejpam-4690	19	13	in	in	ADP
ejpam-4690	19	14	a	a	DET
ejpam-4690	19	15	graph	graph	NOUN
ejpam-4690	19	16	and	and	CCONJ
ejpam-4690	19	17	shows	show	NOUN
ejpam-4690	19	18	,	,	PUNCT
ejpam-4690	19	19	as	as	ADP
ejpam-4690	19	20	a	a	DET
ejpam-4690	19	21	particular	particular	ADJ
ejpam-4690	19	22	case	case	NOUN
ejpam-4690	19	23	of	of	ADP
ejpam-4690	19	24	a	a	DET
ejpam-4690	19	25	realization	realization	NOUN
ejpam-4690	19	26	result	result	NOUN
ejpam-4690	19	27	,	,	PUNCT
ejpam-4690	19	28	that	that	SCONJ
ejpam-4690	19	29	the	the	DET
ejpam-4690	19	30	absolute	absolute	ADJ
ejpam-4690	19	31	difference	difference	NOUN
ejpam-4690	19	32	of	of	ADP
ejpam-4690	19	33	the	the	DET
ejpam-4690	19	34	grundy	grundy	PROPN
ejpam-4690	19	35	domination	domination	PROPN
ejpam-4690	19	36	and	and	CCONJ
ejpam-4690	19	37	grundy	grundy	PROPN
ejpam-4690	19	38	hop	hop	PROPN
ejpam-4690	19	39	domination	domination	NOUN
ejpam-4690	19	40	numbers	number	NOUN
ejpam-4690	19	41	can	can	AUX
ejpam-4690	19	42	be	be	AUX
ejpam-4690	19	43	made	make	VERB
ejpam-4690	19	44	arbitrarily	arbitrarily	ADV
ejpam-4690	19	45	large	large	ADJ
ejpam-4690	19	46	.	.	PUNCT
ejpam-4690	20	1	moreover	moreover	ADV
ejpam-4690	20	2	,	,	PUNCT
ejpam-4690	20	3	the	the	DET
ejpam-4690	20	4	grundy	grundy	PROPN
ejpam-4690	20	5	domination	domination	NOUN
ejpam-4690	20	6	numbers	number	NOUN
ejpam-4690	20	7	of	of	ADP
ejpam-4690	20	8	some	some	DET
ejpam-4690	20	9	graphs	graph	NOUN
ejpam-4690	20	10	are	be	AUX
ejpam-4690	20	11	given	give	VERB
ejpam-4690	20	12	.	.	PUNCT
ejpam-4690	21	1	2	2	X
ejpam-4690	21	2	.	.	X
ejpam-4690	21	3	terminology	terminology	NOUN
ejpam-4690	21	4	and	and	CCONJ
ejpam-4690	21	5	notation	notation	NOUN
ejpam-4690	21	6	let	let	VERB
ejpam-4690	21	7	g	g	PRON
ejpam-4690	21	8	be	be	AUX
ejpam-4690	21	9	a	a	DET
ejpam-4690	21	10	simple	simple	ADJ
ejpam-4690	21	11	undirected	undirected	ADJ
ejpam-4690	21	12	graph	graph	NOUN
ejpam-4690	21	13	.	.	PUNCT
ejpam-4690	22	1	a	a	DET
ejpam-4690	22	2	set	set	NOUN
ejpam-4690	22	3	d	d	NOUN
ejpam-4690	22	4	⊆	⊆	NUM
ejpam-4690	22	5	v	v	ADP
ejpam-4690	22	6	(	(	PUNCT
ejpam-4690	22	7	g	g	NOUN
ejpam-4690	22	8	)	)	PUNCT
ejpam-4690	22	9	is	be	AUX
ejpam-4690	22	10	a	a	DET
ejpam-4690	22	11	dominating	dominating	NOUN
ejpam-4690	22	12	set	set	NOUN
ejpam-4690	22	13	of	of	ADP
ejpam-4690	22	14	g	g	PROPN
ejpam-4690	22	15	if	if	SCONJ
ejpam-4690	22	16	for	for	ADP
ejpam-4690	22	17	every	every	DET
ejpam-4690	22	18	v	v	NUM
ejpam-4690	22	19	∈	∈	NOUN
ejpam-4690	22	20	v	v	NOUN
ejpam-4690	22	21	(	(	PUNCT
ejpam-4690	22	22	g)\d	g)\d	NOUN
ejpam-4690	22	23	,	,	PUNCT
ejpam-4690	22	24	there	there	PRON
ejpam-4690	22	25	exists	exist	VERB
ejpam-4690	22	26	u	u	NOUN
ejpam-4690	22	27	∈	∈	PROPN
ejpam-4690	22	28	d	d	ADP
ejpam-4690	22	29	such	such	ADJ
ejpam-4690	22	30	that	that	DET
ejpam-4690	22	31	uv	uv	PROPN
ejpam-4690	22	32	∈	∈	PROPN
ejpam-4690	22	33	e(g	e(g	PROPN
ejpam-4690	22	34	)	)	PUNCT
ejpam-4690	22	35	,	,	PUNCT
ejpam-4690	22	36	that	that	ADV
ejpam-4690	22	37	is	is	ADV
ejpam-4690	22	38	,	,	PUNCT
ejpam-4690	22	39	ng[d	ng[d	PROPN
ejpam-4690	22	40	]	]	PUNCT
ejpam-4690	22	41	=	=	SYM
ejpam-4690	22	42	v	v	X
ejpam-4690	22	43	(	(	PUNCT
ejpam-4690	22	44	g	g	NOUN
ejpam-4690	22	45	)	)	PUNCT
ejpam-4690	22	46	.	.	PUNCT
ejpam-4690	23	1	the	the	DET
ejpam-4690	23	2	domination	domination	NOUN
ejpam-4690	23	3	number	number	NOUN
ejpam-4690	23	4	of	of	ADP
ejpam-4690	23	5	g	g	NOUN
ejpam-4690	23	6	,	,	PUNCT
ejpam-4690	23	7	denoted	denote	VERB
ejpam-4690	23	8	by	by	ADP
ejpam-4690	23	9	γ(g	γ(g	PROPN
ejpam-4690	23	10	)	)	PUNCT
ejpam-4690	23	11	,	,	PUNCT
ejpam-4690	23	12	is	be	AUX
ejpam-4690	23	13	the	the	DET
ejpam-4690	23	14	minimum	minimum	ADJ
ejpam-4690	23	15	cardinality	cardinality	NOUN
ejpam-4690	23	16	of	of	ADP
ejpam-4690	23	17	a	a	DET
ejpam-4690	23	18	dominating	dominating	NOUN
ejpam-4690	23	19	set	set	NOUN
ejpam-4690	23	20	of	of	ADP
ejpam-4690	23	21	g.	g.	PROPN
ejpam-4690	23	22	any	any	DET
ejpam-4690	23	23	dominating	dominating	NOUN
ejpam-4690	23	24	set	set	VERB
ejpam-4690	23	25	with	with	ADP
ejpam-4690	23	26	cardinality	cardinality	NOUN
ejpam-4690	23	27	equal	equal	ADJ
ejpam-4690	23	28	to	to	ADP
ejpam-4690	23	29	γ(g	γ(g	PROPN
ejpam-4690	23	30	)	)	PUNCT
ejpam-4690	23	31	is	be	AUX
ejpam-4690	23	32	called	call	VERB
ejpam-4690	23	33	a	a	DET
ejpam-4690	23	34	γ	γ	NOUN
ejpam-4690	23	35	-	-	PUNCT
ejpam-4690	23	36	set	set	NOUN
ejpam-4690	23	37	.	.	PUNCT
ejpam-4690	24	1	let	let	VERB
ejpam-4690	24	2	s	s	PRON
ejpam-4690	24	3	=	=	PUNCT
ejpam-4690	24	4	(	(	PUNCT
ejpam-4690	24	5	v1	v1	PROPN
ejpam-4690	24	6	,	,	PUNCT
ejpam-4690	24	7	v2	v2	PROPN
ejpam-4690	24	8	,	,	PUNCT
ejpam-4690	24	9	·	·	PUNCT
ejpam-4690	24	10	·	·	PUNCT
ejpam-4690	24	11	·	·	PUNCT
ejpam-4690	24	12	,	,	PUNCT
ejpam-4690	24	13	vk	vk	AUX
ejpam-4690	24	14	)	)	PUNCT
ejpam-4690	24	15	be	be	AUX
ejpam-4690	24	16	a	a	DET
ejpam-4690	24	17	sequence	sequence	NOUN
ejpam-4690	24	18	of	of	ADP
ejpam-4690	24	19	distinct	distinct	ADJ
ejpam-4690	24	20	vertices	vertex	NOUN
ejpam-4690	24	21	of	of	ADP
ejpam-4690	24	22	a	a	DET
ejpam-4690	24	23	graph	graph	NOUN
ejpam-4690	24	24	g	g	NOUN
ejpam-4690	24	25	and	and	CCONJ
ejpam-4690	24	26	let	let	VERB
ejpam-4690	24	27	ŝ	ŝ	X
ejpam-4690	24	28	=	=	SYM
ejpam-4690	24	29	{	{	PUNCT
ejpam-4690	24	30	v1	v1	PROPN
ejpam-4690	24	31	,	,	PUNCT
ejpam-4690	24	32	v2	v2	PROPN
ejpam-4690	24	33	,	,	PUNCT
ejpam-4690	24	34	·	·	PUNCT
ejpam-4690	24	35	·	·	PUNCT
ejpam-4690	24	36	·	·	PUNCT
ejpam-4690	24	37	,	,	PUNCT
ejpam-4690	24	38	vk	vk	PART
ejpam-4690	24	39	}	}	PUNCT
ejpam-4690	24	40	be	be	AUX
ejpam-4690	24	41	its	its	PRON
ejpam-4690	24	42	corresponding	corresponding	ADJ
ejpam-4690	24	43	set	set	NOUN
ejpam-4690	24	44	.	.	PUNCT
ejpam-4690	25	1	then	then	ADV
ejpam-4690	25	2	s	s	VERB
ejpam-4690	25	3	is	be	AUX
ejpam-4690	25	4	a	a	DET
ejpam-4690	25	5	legal	legal	ADJ
ejpam-4690	25	6	closed	closed	ADJ
ejpam-4690	25	7	neighborhood	neighborhood	NOUN
ejpam-4690	25	8	sequence	sequence	NOUN
ejpam-4690	25	9	if	if	SCONJ
ejpam-4690	25	10	ng[vi	ng[vi	PROPN
ejpam-4690	25	11	]	]	PUNCT
ejpam-4690	25	12	\	\	PROPN
ejpam-4690	25	13	⋃i−1	⋃i−1	NOUN
ejpam-4690	25	14	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4690	25	15	]	]	PUNCT
ejpam-4690	25	16	̸=	̸=	PROPN
ejpam-4690	25	17	∅	∅	NOUN
ejpam-4690	25	18	for	for	ADP
ejpam-4690	25	19	every	every	DET
ejpam-4690	25	20	i	i	PROPN
ejpam-4690	25	21	∈	∈	PROPN
ejpam-4690	25	22	{	{	PUNCT
ejpam-4690	25	23	2	2	NUM
ejpam-4690	25	24	,	,	PUNCT
ejpam-4690	25	25	·	·	PUNCT
ejpam-4690	25	26	·	·	PUNCT
ejpam-4690	25	27	·	·	PUNCT
ejpam-4690	25	28	,	,	PUNCT
ejpam-4690	25	29	k	k	NOUN
ejpam-4690	25	30	}	}	PUNCT
ejpam-4690	25	31	.	.	PUNCT
ejpam-4690	26	1	if	if	SCONJ
ejpam-4690	26	2	,	,	PUNCT
ejpam-4690	26	3	in	in	ADP
ejpam-4690	26	4	addition	addition	NOUN
ejpam-4690	26	5	,	,	PUNCT
ejpam-4690	26	6	ŝ	ŝ	X
ejpam-4690	26	7	is	be	AUX
ejpam-4690	26	8	a	a	DET
ejpam-4690	26	9	dominating	dominating	NOUN
ejpam-4690	26	10	set	set	NOUN
ejpam-4690	26	11	of	of	ADP
ejpam-4690	26	12	g	g	NOUN
ejpam-4690	26	13	,	,	PUNCT
ejpam-4690	26	14	then	then	ADV
ejpam-4690	26	15	s	s	VERB
ejpam-4690	26	16	is	be	AUX
ejpam-4690	26	17	called	call	VERB
ejpam-4690	26	18	a	a	DET
ejpam-4690	26	19	grundy	grundy	PROPN
ejpam-4690	26	20	dominating	dominating	NOUN
ejpam-4690	26	21	sequence	sequence	NOUN
ejpam-4690	26	22	.	.	PUNCT
ejpam-4690	27	1	the	the	DET
ejpam-4690	27	2	maximum	maximum	ADJ
ejpam-4690	27	3	length	length	NOUN
ejpam-4690	27	4	of	of	ADP
ejpam-4690	27	5	a	a	DET
ejpam-4690	27	6	grundy	grundy	PROPN
ejpam-4690	27	7	dominating	dominating	NOUN
ejpam-4690	27	8	sequence	sequence	NOUN
ejpam-4690	27	9	in	in	ADP
ejpam-4690	27	10	a	a	DET
ejpam-4690	27	11	graph	graph	NOUN
ejpam-4690	27	12	g	g	NOUN
ejpam-4690	27	13	,	,	PUNCT
ejpam-4690	27	14	denoted	denote	VERB
ejpam-4690	27	15	by	by	ADP
ejpam-4690	27	16	γgr(g	γgr(g	PROPN
ejpam-4690	27	17	)	)	PUNCT
ejpam-4690	27	18	,	,	PUNCT
ejpam-4690	27	19	is	be	AUX
ejpam-4690	27	20	called	call	VERB
ejpam-4690	27	21	the	the	DET
ejpam-4690	27	22	grundy	grundy	PROPN
ejpam-4690	27	23	domination	domination	NOUN
ejpam-4690	27	24	number	number	NOUN
ejpam-4690	27	25	of	of	ADP
ejpam-4690	27	26	g.	g.	PROPN
ejpam-4690	27	27	we	we	PRON
ejpam-4690	27	28	say	say	VERB
ejpam-4690	27	29	that	that	SCONJ
ejpam-4690	27	30	vertex	vertex	PROPN
ejpam-4690	27	31	vi	vi	PROPN
ejpam-4690	27	32	footprints	footprint	NOUN
ejpam-4690	27	33	the	the	DET
ejpam-4690	27	34	vertices	vertex	NOUN
ejpam-4690	27	35	from	from	ADP
ejpam-4690	27	36	ng[vi	ng[vi	PROPN
ejpam-4690	27	37	]	]	PUNCT
ejpam-4690	27	38	\	\	PROPN
ejpam-4690	27	39	∪i	∪i	PROPN
ejpam-4690	27	40	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4690	27	41	]	]	PUNCT
ejpam-4690	27	42	,	,	PUNCT
ejpam-4690	27	43	and	and	CCONJ
ejpam-4690	27	44	that	that	DET
ejpam-4690	27	45	vi	vi	PROPN
ejpam-4690	27	46	is	be	AUX
ejpam-4690	27	47	their	their	PRON
ejpam-4690	27	48	footprinter	footprinter	NOUN
ejpam-4690	27	49	.	.	PUNCT
ejpam-4690	28	1	any	any	DET
ejpam-4690	28	2	grundy	grundy	PROPN
ejpam-4690	28	3	dominating	dominating	NOUN
ejpam-4690	28	4	sequence	sequence	NOUN
ejpam-4690	28	5	s	s	PART
ejpam-4690	28	6	with	with	ADP
ejpam-4690	28	7	|ŝ|	|ŝ|	PROPN
ejpam-4690	28	8	=	=	SYM
ejpam-4690	28	9	γgr(g	γgr(g	PROPN
ejpam-4690	28	10	)	)	PUNCT
ejpam-4690	28	11	is	be	AUX
ejpam-4690	28	12	called	call	VERB
ejpam-4690	28	13	a	a	DET
ejpam-4690	28	14	maximum	maximum	ADJ
ejpam-4690	28	15	grundy	grundy	PROPN
ejpam-4690	28	16	dominating	dominating	NOUN
ejpam-4690	28	17	sequence	sequence	NOUN
ejpam-4690	28	18	or	or	CCONJ
ejpam-4690	28	19	a	a	DET
ejpam-4690	28	20	γgr	γgr	NOUN
ejpam-4690	28	21	-	-	PUNCT
ejpam-4690	28	22	sequence	sequence	NOUN
ejpam-4690	28	23	of	of	ADP
ejpam-4690	28	24	g.	g.	PROPN
ejpam-4690	28	25	in	in	ADP
ejpam-4690	28	26	this	this	DET
ejpam-4690	28	27	case	case	NOUN
ejpam-4690	28	28	,	,	PUNCT
ejpam-4690	28	29	we	we	PRON
ejpam-4690	28	30	call	call	VERB
ejpam-4690	28	31	ŝ	ŝ	NOUN
ejpam-4690	28	32	a	a	DET
ejpam-4690	28	33	γgr	γgr	NOUN
ejpam-4690	28	34	-	-	PUNCT
ejpam-4690	28	35	set	set	NOUN
ejpam-4690	28	36	of	of	ADP
ejpam-4690	28	37	g.	g.	PROPN
ejpam-4690	28	38	a	a	DET
ejpam-4690	28	39	legal	legal	ADJ
ejpam-4690	28	40	closed	closed	ADJ
ejpam-4690	28	41	neighborhood	neighborhood	NOUN
ejpam-4690	28	42	sequence	sequence	NOUN
ejpam-4690	28	43	s	s	PART
ejpam-4690	28	44	=	=	PUNCT
ejpam-4690	28	45	(	(	PUNCT
ejpam-4690	28	46	v1	v1	PROPN
ejpam-4690	28	47	,	,	PUNCT
ejpam-4690	28	48	v2	v2	PROPN
ejpam-4690	28	49	,	,	PUNCT
ejpam-4690	28	50	·	·	PUNCT
ejpam-4690	28	51	·	·	PUNCT
ejpam-4690	28	52	·	·	PUNCT
ejpam-4690	28	53	,	,	PUNCT
ejpam-4690	28	54	vk	vk	PROPN
ejpam-4690	28	55	)	)	PUNCT
ejpam-4690	28	56	of	of	ADP
ejpam-4690	28	57	g	g	PROPN
ejpam-4690	28	58	is	be	AUX
ejpam-4690	28	59	a	a	DET
ejpam-4690	28	60	maximum	maximum	ADJ
ejpam-4690	28	61	legal	legal	ADJ
ejpam-4690	28	62	closed	closed	ADJ
ejpam-4690	28	63	neighborhood	neighborhood	NOUN
ejpam-4690	28	64	sequence	sequence	NOUN
ejpam-4690	28	65	if	if	SCONJ
ejpam-4690	28	66	for	for	ADP
ejpam-4690	28	67	any	any	DET
ejpam-4690	28	68	legal	legal	ADJ
ejpam-4690	28	69	closed	closed	ADJ
ejpam-4690	28	70	neighborhood	neighborhood	NOUN
ejpam-4690	28	71	sequence	sequence	NOUN
ejpam-4690	28	72	(	(	PUNCT
ejpam-4690	28	73	w1	w1	NOUN
ejpam-4690	28	74	,	,	PUNCT
ejpam-4690	28	75	w2	w2	NOUN
ejpam-4690	28	76	,	,	PUNCT
ejpam-4690	28	77	·	·	PUNCT
ejpam-4690	28	78	·	·	PUNCT
ejpam-4690	28	79	·	·	PUNCT
ejpam-4690	28	80	,	,	PUNCT
ejpam-4690	28	81	wt	wt	NOUN
ejpam-4690	28	82	)	)	PUNCT
ejpam-4690	28	83	of	of	ADP
ejpam-4690	28	84	g	g	PROPN
ejpam-4690	28	85	,	,	PUNCT
ejpam-4690	28	86	we	we	PRON
ejpam-4690	28	87	have	have	VERB
ejpam-4690	28	88	t	t	NOUN
ejpam-4690	28	89	≤	≤	PROPN
ejpam-4690	28	90	k.	k.	PROPN
ejpam-4690	29	1	a	a	DET
ejpam-4690	29	2	legal	legal	ADJ
ejpam-4690	29	3	closed	closed	ADJ
ejpam-4690	29	4	neighborhood	neighborhood	NOUN
ejpam-4690	29	5	sequence	sequence	NOUN
ejpam-4690	29	6	s	s	VERB
ejpam-4690	29	7	is	be	AUX
ejpam-4690	29	8	non	non	ADJ
ejpam-4690	29	9	-	-	ADJ
ejpam-4690	29	10	dominating	dominating	ADJ
ejpam-4690	29	11	if	if	SCONJ
ejpam-4690	29	12	ŝ	ŝ	NUM
ejpam-4690	29	13	is	be	AUX
ejpam-4690	29	14	a	a	DET
ejpam-4690	29	15	non	non	ADJ
ejpam-4690	29	16	-	-	ADJ
ejpam-4690	29	17	dominating	dominating	ADJ
ejpam-4690	29	18	set	set	NOUN
ejpam-4690	29	19	of	of	ADP
ejpam-4690	29	20	g.	g.	PROPN
ejpam-4690	29	21	a	a	DET
ejpam-4690	29	22	vertex	vertex	NOUN
ejpam-4690	29	23	v	v	NOUN
ejpam-4690	29	24	in	in	ADP
ejpam-4690	29	25	g	g	PROPN
ejpam-4690	29	26	is	be	AUX
ejpam-4690	29	27	a	a	DET
ejpam-4690	29	28	hop	hop	NOUN
ejpam-4690	29	29	neighbor	neighbor	NOUN
ejpam-4690	29	30	of	of	ADP
ejpam-4690	29	31	vertex	vertex	NOUN
ejpam-4690	29	32	u	u	NOUN
ejpam-4690	29	33	in	in	ADP
ejpam-4690	29	34	g	g	PROPN
ejpam-4690	30	1	if	if	SCONJ
ejpam-4690	30	2	dg(u	dg(u	NOUN
ejpam-4690	30	3	,	,	PUNCT
ejpam-4690	30	4	v	v	NOUN
ejpam-4690	30	5	)	)	PUNCT
ejpam-4690	30	6	=	=	SYM
ejpam-4690	30	7	2	2	X
ejpam-4690	30	8	.	.	X
ejpam-4690	31	1	the	the	DET
ejpam-4690	31	2	set	set	ADJ
ejpam-4690	31	3	n2	n2	ADJ
ejpam-4690	31	4	g(u	g(u	PROPN
ejpam-4690	31	5	)	)	PUNCT
ejpam-4690	31	6	=	=	PRON
ejpam-4690	31	7	{	{	PUNCT
ejpam-4690	31	8	v	v	NUM
ejpam-4690	31	9	∈	∈	NOUN
ejpam-4690	31	10	v	v	NOUN
ejpam-4690	31	11	(	(	PUNCT
ejpam-4690	31	12	g	g	NOUN
ejpam-4690	31	13	)	)	PUNCT
ejpam-4690	31	14	:	:	PUNCT
ejpam-4690	31	15	dg(v	dg(v	X
ejpam-4690	31	16	,	,	PUNCT
ejpam-4690	31	17	u	u	NOUN
ejpam-4690	31	18	)	)	PUNCT
ejpam-4690	31	19	=	=	SYM
ejpam-4690	31	20	2	2	X
ejpam-4690	31	21	}	}	PUNCT
ejpam-4690	31	22	is	be	AUX
ejpam-4690	31	23	called	call	VERB
ejpam-4690	31	24	the	the	DET
ejpam-4690	31	25	open	open	ADJ
ejpam-4690	31	26	hop	hop	NOUN
ejpam-4690	31	27	neighborhood	neighborhood	NOUN
ejpam-4690	31	28	of	of	ADP
ejpam-4690	31	29	u.	u.	PROPN
ejpam-4690	31	30	the	the	DET
ejpam-4690	31	31	closed	closed	ADJ
ejpam-4690	31	32	hop	hop	NOUN
ejpam-4690	31	33	neighborhood	neighborhood	NOUN
ejpam-4690	31	34	of	of	ADP
ejpam-4690	31	35	u	u	PROPN
ejpam-4690	31	36	in	in	ADP
ejpam-4690	31	37	g	g	PROPN
ejpam-4690	31	38	is	be	AUX
ejpam-4690	31	39	given	give	VERB
ejpam-4690	31	40	by	by	ADP
ejpam-4690	31	41	n2	n2	PROPN
ejpam-4690	31	42	g[u	g[u	PROPN
ejpam-4690	31	43	]	]	X
ejpam-4690	31	44	=	=	SYM
ejpam-4690	31	45	n2	n2	ADJ
ejpam-4690	31	46	g(u	g(u	PROPN
ejpam-4690	31	47	)	)	PUNCT
ejpam-4690	31	48	∪	∪	NOUN
ejpam-4690	31	49	{	{	PUNCT
ejpam-4690	31	50	u	u	NOUN
ejpam-4690	31	51	}	}	PUNCT
ejpam-4690	31	52	.	.	PUNCT
ejpam-4690	32	1	the	the	DET
ejpam-4690	32	2	open	open	ADJ
ejpam-4690	32	3	hop	hop	NOUN
ejpam-4690	32	4	neighborhood	neighborhood	NOUN
ejpam-4690	32	5	of	of	ADP
ejpam-4690	32	6	x	x	PROPN
ejpam-4690	32	7	⊆	⊆	NUM
ejpam-4690	32	8	v	v	ADP
ejpam-4690	32	9	(	(	PUNCT
ejpam-4690	32	10	g	g	NOUN
ejpam-4690	32	11	)	)	PUNCT
ejpam-4690	32	12	is	be	AUX
ejpam-4690	32	13	the	the	DET
ejpam-4690	32	14	set	set	ADJ
ejpam-4690	32	15	n2	n2	ADJ
ejpam-4690	32	16	g(x	g(x	NOUN
ejpam-4690	32	17	)	)	PUNCT
ejpam-4690	33	1	=	=	SYM
ejpam-4690	33	2	⋃	⋃	NOUN
ejpam-4690	33	3	u∈x	u∈x	ADJ
ejpam-4690	33	4	n2	n2	NOUN
ejpam-4690	33	5	g(u	g(u	PROPN
ejpam-4690	33	6	)	)	PUNCT
ejpam-4690	33	7	.	.	PUNCT
ejpam-4690	34	1	the	the	DET
ejpam-4690	34	2	closed	closed	ADJ
ejpam-4690	34	3	hop	hop	NOUN
ejpam-4690	34	4	neighborhood	neighborhood	NOUN
ejpam-4690	34	5	of	of	ADP
ejpam-4690	34	6	x	x	PUNCT
ejpam-4690	34	7	in	in	ADP
ejpam-4690	34	8	g	g	PROPN
ejpam-4690	34	9	is	be	AUX
ejpam-4690	34	10	the	the	DET
ejpam-4690	34	11	set	set	ADJ
ejpam-4690	34	12	n2	n2	NOUN
ejpam-4690	34	13	g[x	g[x	PROPN
ejpam-4690	34	14	]	]	X
ejpam-4690	34	15	=	=	SYM
ejpam-4690	34	16	n2	n2	PROPN
ejpam-4690	34	17	g(x	g(x	NOUN
ejpam-4690	34	18	)	)	PUNCT
ejpam-4690	34	19	∪x	∪x	NUM
ejpam-4690	34	20	.	.	PUNCT
ejpam-4690	35	1	a	a	DET
ejpam-4690	35	2	set	set	NOUN
ejpam-4690	35	3	s	s	NOUN
ejpam-4690	35	4	⊆	⊆	NUM
ejpam-4690	35	5	v	v	NOUN
ejpam-4690	35	6	(	(	PUNCT
ejpam-4690	35	7	g	g	NOUN
ejpam-4690	35	8	)	)	PUNCT
ejpam-4690	35	9	is	be	AUX
ejpam-4690	35	10	a	a	DET
ejpam-4690	35	11	hop	hop	NOUN
ejpam-4690	35	12	dominating	dominating	NOUN
ejpam-4690	35	13	set	set	NOUN
ejpam-4690	35	14	of	of	ADP
ejpam-4690	35	15	g	g	PROPN
ejpam-4690	35	16	if	if	SCONJ
ejpam-4690	35	17	n2	n2	ADJ
ejpam-4690	35	18	g[s	g[s	PROPN
ejpam-4690	35	19	]	]	X
ejpam-4690	35	20	=	=	SYM
ejpam-4690	35	21	v	v	NOUN
ejpam-4690	35	22	(	(	PUNCT
ejpam-4690	35	23	g	g	NOUN
ejpam-4690	35	24	)	)	PUNCT
ejpam-4690	35	25	,	,	PUNCT
ejpam-4690	35	26	that	that	ADV
ejpam-4690	35	27	is	is	ADV
ejpam-4690	35	28	,	,	PUNCT
ejpam-4690	35	29	for	for	ADP
ejpam-4690	35	30	every	every	DET
ejpam-4690	35	31	v	v	NUM
ejpam-4690	35	32	∈	∈	NOUN
ejpam-4690	35	33	v	v	NOUN
ejpam-4690	35	34	(	(	PUNCT
ejpam-4690	35	35	g)\s	g)\s	NOUN
ejpam-4690	35	36	,	,	PUNCT
ejpam-4690	35	37	there	there	PRON
ejpam-4690	35	38	exists	exist	VERB
ejpam-4690	35	39	u	u	PROPN
ejpam-4690	35	40	∈	∈	PROPN
ejpam-4690	35	41	s	s	VERB
ejpam-4690	35	42	such	such	ADJ
ejpam-4690	35	43	that	that	DET
ejpam-4690	35	44	dg(u	dg(u	ADJ
ejpam-4690	35	45	,	,	PUNCT
ejpam-4690	35	46	v	v	NOUN
ejpam-4690	35	47	)	)	PUNCT
ejpam-4690	36	1	=	=	SYM
ejpam-4690	36	2	2	2	X
ejpam-4690	36	3	.	.	PUNCT
ejpam-4690	37	1	the	the	DET
ejpam-4690	37	2	minimum	minimum	ADJ
ejpam-4690	37	3	cardinality	cardinality	NOUN
ejpam-4690	37	4	among	among	ADP
ejpam-4690	37	5	all	all	DET
ejpam-4690	37	6	hop	hop	NOUN
ejpam-4690	37	7	dominating	dominating	NOUN
ejpam-4690	37	8	sets	set	NOUN
ejpam-4690	37	9	of	of	ADP
ejpam-4690	37	10	g	g	NOUN
ejpam-4690	37	11	,	,	PUNCT
ejpam-4690	37	12	denoted	denote	VERB
ejpam-4690	37	13	by	by	ADP
ejpam-4690	37	14	γh(g	γh(g	NOUN
ejpam-4690	37	15	)	)	PUNCT
ejpam-4690	37	16	,	,	PUNCT
ejpam-4690	37	17	is	be	AUX
ejpam-4690	37	18	called	call	VERB
ejpam-4690	37	19	the	the	DET
ejpam-4690	37	20	hop	hop	NOUN
ejpam-4690	37	21	domination	domination	NOUN
ejpam-4690	37	22	number	number	NOUN
ejpam-4690	37	23	of	of	ADP
ejpam-4690	37	24	g.	g.	PROPN
ejpam-4690	37	25	any	any	DET
ejpam-4690	37	26	hop	hop	NOUN
ejpam-4690	37	27	dominating	dominating	NOUN
ejpam-4690	37	28	set	set	VERB
ejpam-4690	37	29	with	with	ADP
ejpam-4690	37	30	cardinality	cardinality	NOUN
ejpam-4690	37	31	equal	equal	ADJ
ejpam-4690	37	32	to	to	ADP
ejpam-4690	37	33	γh(g	γh(g	NOUN
ejpam-4690	37	34	)	)	PUNCT
ejpam-4690	37	35	is	be	AUX
ejpam-4690	37	36	called	call	VERB
ejpam-4690	37	37	a	a	DET
ejpam-4690	37	38	γh	γh	ADV
ejpam-4690	37	39	-	-	PUNCT
ejpam-4690	37	40	set	set	NOUN
ejpam-4690	37	41	.	.	PUNCT
ejpam-4690	38	1	let	let	VERB
ejpam-4690	38	2	s	s	PRON
ejpam-4690	38	3	=	=	PUNCT
ejpam-4690	38	4	(	(	PUNCT
ejpam-4690	38	5	v1	v1	PROPN
ejpam-4690	38	6	,	,	PUNCT
ejpam-4690	38	7	v2	v2	PROPN
ejpam-4690	38	8	,	,	PUNCT
ejpam-4690	38	9	·	·	PUNCT
ejpam-4690	38	10	·	·	PUNCT
ejpam-4690	38	11	·	·	PUNCT
ejpam-4690	38	12	,	,	PUNCT
ejpam-4690	38	13	vk	vk	AUX
ejpam-4690	38	14	)	)	PUNCT
ejpam-4690	38	15	be	be	AUX
ejpam-4690	38	16	a	a	DET
ejpam-4690	38	17	sequence	sequence	NOUN
ejpam-4690	38	18	of	of	ADP
ejpam-4690	38	19	distinct	distinct	ADJ
ejpam-4690	38	20	vertices	vertex	NOUN
ejpam-4690	38	21	of	of	ADP
ejpam-4690	38	22	g	g	NOUN
ejpam-4690	38	23	and	and	CCONJ
ejpam-4690	38	24	let	let	VERB
ejpam-4690	38	25	ŝ	ŝ	X
ejpam-4690	38	26	=	=	SYM
ejpam-4690	38	27	{	{	PUNCT
ejpam-4690	38	28	v1	v1	PROPN
ejpam-4690	38	29	,	,	PUNCT
ejpam-4690	38	30	·	·	PUNCT
ejpam-4690	38	31	·	·	PUNCT
ejpam-4690	38	32	·	·	PUNCT
ejpam-4690	38	33	,	,	PUNCT
ejpam-4690	38	34	vk	vk	PART
ejpam-4690	38	35	}	}	PUNCT
ejpam-4690	38	36	be	be	AUX
ejpam-4690	38	37	the	the	DET
ejpam-4690	38	38	set	set	NOUN
ejpam-4690	38	39	induced	induce	VERB
ejpam-4690	38	40	by	by	ADP
ejpam-4690	38	41	s.	s.	PROPN
ejpam-4690	38	42	then	then	ADV
ejpam-4690	38	43	s	s	VERB
ejpam-4690	38	44	is	be	AUX
ejpam-4690	38	45	a	a	DET
ejpam-4690	38	46	legal	legal	ADJ
ejpam-4690	38	47	closed	close	VERB
ejpam-4690	38	48	hop	hop	NOUN
ejpam-4690	38	49	neighborhood	neighborhood	NOUN
ejpam-4690	38	50	sequence	sequence	NOUN
ejpam-4690	38	51	of	of	ADP
ejpam-4690	38	52	g	g	PROPN
ejpam-4690	38	53	if	if	SCONJ
ejpam-4690	38	54	n2	n2	PROPN
ejpam-4690	38	55	g[vi	g[vi	PROPN
ejpam-4690	38	56	]	]	PUNCT
ejpam-4690	38	57	\	\	X
ejpam-4690	39	1	∪i−1	∪i−1	PUNCT
ejpam-4690	39	2	j=1n	j=1n	PROPN
ejpam-4690	39	3	2	2	NUM
ejpam-4690	39	4	g[vj	g[vj	PROPN
ejpam-4690	39	5	]	]	PUNCT
ejpam-4690	39	6	̸=	̸=	PROPN
ejpam-4690	39	7	∅	∅	NOUN
ejpam-4690	39	8	for	for	ADP
ejpam-4690	39	9	each	each	DET
ejpam-4690	39	10	i	i	PRON
ejpam-4690	39	11	∈	∈	PROPN
ejpam-4690	39	12	{	{	PUNCT
ejpam-4690	39	13	2	2	NUM
ejpam-4690	39	14	,	,	PUNCT
ejpam-4690	39	15	·	·	PUNCT
ejpam-4690	39	16	·	·	PUNCT
ejpam-4690	39	17	·	·	PUNCT
ejpam-4690	39	18	,	,	PUNCT
ejpam-4690	39	19	k	k	NOUN
ejpam-4690	39	20	}	}	PUNCT
ejpam-4690	39	21	.	.	PUNCT
ejpam-4690	40	1	if	if	SCONJ
ejpam-4690	40	2	,	,	PUNCT
ejpam-4690	40	3	in	in	ADP
ejpam-4690	40	4	addition	addition	NOUN
ejpam-4690	40	5	,	,	PUNCT
ejpam-4690	40	6	ŝ	ŝ	X
ejpam-4690	40	7	is	be	AUX
ejpam-4690	40	8	a	a	DET
ejpam-4690	40	9	hop	hop	NOUN
ejpam-4690	40	10	dominating	dominating	NOUN
ejpam-4690	40	11	set	set	NOUN
ejpam-4690	40	12	of	of	ADP
ejpam-4690	40	13	g	g	PROPN
ejpam-4690	40	14	,	,	PUNCT
ejpam-4690	40	15	then	then	ADV
ejpam-4690	40	16	s	s	VERB
ejpam-4690	40	17	is	be	AUX
ejpam-4690	40	18	called	call	VERB
ejpam-4690	40	19	a	a	DET
ejpam-4690	40	20	grundy	grundy	PROPN
ejpam-4690	40	21	hop	hop	NOUN
ejpam-4690	40	22	dominating	dominating	NOUN
ejpam-4690	40	23	sequence	sequence	NOUN
ejpam-4690	40	24	.	.	PUNCT
ejpam-4690	41	1	the	the	DET
ejpam-4690	41	2	maximum	maximum	ADJ
ejpam-4690	41	3	length	length	NOUN
ejpam-4690	41	4	of	of	ADP
ejpam-4690	41	5	a	a	DET
ejpam-4690	41	6	grundy	grundy	PROPN
ejpam-4690	41	7	hop	hop	NOUN
ejpam-4690	41	8	dominating	dominating	NOUN
ejpam-4690	41	9	sequence	sequence	NOUN
ejpam-4690	41	10	in	in	ADP
ejpam-4690	41	11	a	a	DET
ejpam-4690	41	12	graph	graph	NOUN
ejpam-4690	41	13	g	g	NOUN
ejpam-4690	41	14	,	,	PUNCT
ejpam-4690	41	15	denoted	denote	VERB
ejpam-4690	41	16	by	by	ADP
ejpam-4690	41	17	γhgr(g	γhgr(g	PROPN
ejpam-4690	41	18	)	)	PUNCT
ejpam-4690	41	19	,	,	PUNCT
ejpam-4690	41	20	is	be	AUX
ejpam-4690	41	21	called	call	VERB
ejpam-4690	41	22	the	the	DET
ejpam-4690	41	23	grundy	grundy	PROPN
ejpam-4690	41	24	hop	hop	PROPN
ejpam-4690	41	25	domination	domination	NOUN
ejpam-4690	41	26	number	number	NOUN
ejpam-4690	41	27	of	of	ADP
ejpam-4690	41	28	g.	g.	PROPN
ejpam-4690	41	29	we	we	PRON
ejpam-4690	41	30	say	say	VERB
ejpam-4690	41	31	that	that	DET
ejpam-4690	41	32	vertex	vertex	NOUN
ejpam-4690	41	33	vi	vi	PROPN
ejpam-4690	41	34	hop	hop	NOUN
ejpam-4690	41	35	-	-	PUNCT
ejpam-4690	41	36	footprints	footprint	NOUN
ejpam-4690	41	37	the	the	DET
ejpam-4690	41	38	vertices	vertex	NOUN
ejpam-4690	41	39	from	from	ADP
ejpam-4690	41	40	n2	n2	PROPN
ejpam-4690	41	41	g[vi	g[vi	PROPN
ejpam-4690	41	42	]	]	PUNCT
ejpam-4690	41	43	\	\	NOUN
ejpam-4690	42	1	∪i	∪i	PUNCT
ejpam-4690	42	2	j=1n	j=1n	PROPN
ejpam-4690	42	3	2	2	NUM
ejpam-4690	42	4	g[vj	g[vj	PROPN
ejpam-4690	42	5	]	]	PUNCT
ejpam-4690	42	6	,	,	PUNCT
ejpam-4690	42	7	and	and	CCONJ
ejpam-4690	42	8	that	that	DET
ejpam-4690	42	9	vi	vi	PROPN
ejpam-4690	42	10	is	be	AUX
ejpam-4690	42	11	their	their	PRON
ejpam-4690	42	12	hop	hop	NOUN
ejpam-4690	42	13	-	-	PUNCT
ejpam-4690	42	14	footprinter	footprinter	NOUN
ejpam-4690	42	15	.	.	PUNCT
ejpam-4690	43	1	any	any	PRON
ejpam-4690	43	2	grundy	grundy	PROPN
ejpam-4690	43	3	hop	hop	NOUN
ejpam-4690	43	4	dominating	dominate	VERB
ejpam-4690	43	5	j.	j.	PROPN
ejpam-4690	43	6	hassan	hassan	PROPN
ejpam-4690	43	7	,	,	PUNCT
ejpam-4690	43	8	s.	s.	PROPN
ejpam-4690	43	9	canoy	canoy	PROPN
ejpam-4690	43	10	jr	jr	PROPN
ejpam-4690	43	11	.	.	PROPN
ejpam-4690	43	12	/	/	SYM
ejpam-4690	43	13	eur	eur	PROPN
ejpam-4690	43	14	.	.	PUNCT
ejpam-4690	44	1	j.	j.	PROPN
ejpam-4690	44	2	pure	pure	PROPN
ejpam-4690	44	3	appl	appl	PROPN
ejpam-4690	44	4	.	.	PROPN
ejpam-4690	44	5	math	math	PROPN
ejpam-4690	44	6	,	,	PUNCT
ejpam-4690	44	7	16	16	NUM
ejpam-4690	44	8	(	(	PUNCT
ejpam-4690	44	9	2	2	NUM
ejpam-4690	44	10	)	)	PUNCT
ejpam-4690	44	11	(	(	PUNCT
ejpam-4690	44	12	2023	2023	NUM
ejpam-4690	44	13	)	)	PUNCT
ejpam-4690	44	14	,	,	PUNCT
ejpam-4690	44	15	1154	1154	NUM
ejpam-4690	44	16	-	-	SYM
ejpam-4690	44	17	1166	1166	NUM
ejpam-4690	44	18	1156	1156	NUM
ejpam-4690	44	19	sequence	sequence	NOUN
ejpam-4690	44	20	s	s	PART
ejpam-4690	44	21	with	with	ADP
ejpam-4690	44	22	|ŝ|	|ŝ|	PROPN
ejpam-4690	44	23	=	=	SYM
ejpam-4690	44	24	γhgr(g	γhgr(g	PROPN
ejpam-4690	44	25	)	)	PUNCT
ejpam-4690	44	26	is	be	AUX
ejpam-4690	44	27	called	call	VERB
ejpam-4690	44	28	a	a	DET
ejpam-4690	44	29	maximum	maximum	ADJ
ejpam-4690	44	30	grundy	grundy	PROPN
ejpam-4690	44	31	hop	hop	NOUN
ejpam-4690	44	32	dominating	dominating	NOUN
ejpam-4690	44	33	sequence	sequence	NOUN
ejpam-4690	44	34	or	or	CCONJ
ejpam-4690	44	35	a	a	DET
ejpam-4690	44	36	γhgr	γhgr	ADJ
ejpam-4690	44	37	-	-	PUNCT
ejpam-4690	44	38	sequence	sequence	NOUN
ejpam-4690	44	39	of	of	ADP
ejpam-4690	44	40	g.	g.	PROPN
ejpam-4690	44	41	in	in	ADP
ejpam-4690	44	42	this	this	DET
ejpam-4690	44	43	case	case	NOUN
ejpam-4690	44	44	,	,	PUNCT
ejpam-4690	44	45	we	we	PRON
ejpam-4690	44	46	call	call	VERB
ejpam-4690	44	47	ŝ	ŝ	NOUN
ejpam-4690	44	48	a	a	DET
ejpam-4690	44	49	γhgr	γhgr	VERB
ejpam-4690	44	50	-	-	PUNCT
ejpam-4690	44	51	set	set	NOUN
ejpam-4690	44	52	of	of	ADP
ejpam-4690	44	53	g.	g.	PROPN
ejpam-4690	44	54	a	a	DET
ejpam-4690	44	55	set	set	NOUN
ejpam-4690	44	56	s	s	PROPN
ejpam-4690	44	57	⊆	⊆	NUM
ejpam-4690	44	58	v	v	NOUN
ejpam-4690	44	59	(	(	PUNCT
ejpam-4690	44	60	g	g	NOUN
ejpam-4690	44	61	)	)	PUNCT
ejpam-4690	44	62	is	be	AUX
ejpam-4690	44	63	an	an	DET
ejpam-4690	44	64	independent	independent	ADJ
ejpam-4690	44	65	set	set	NOUN
ejpam-4690	44	66	of	of	ADP
ejpam-4690	44	67	g	g	PROPN
ejpam-4690	44	68	if	if	SCONJ
ejpam-4690	44	69	for	for	ADP
ejpam-4690	44	70	any	any	DET
ejpam-4690	44	71	two	two	NUM
ejpam-4690	44	72	distinct	distinct	ADJ
ejpam-4690	44	73	vertices	vertex	NOUN
ejpam-4690	44	74	v	v	NOUN
ejpam-4690	44	75	and	and	CCONJ
ejpam-4690	44	76	w	w	NOUN
ejpam-4690	44	77	of	of	ADP
ejpam-4690	44	78	s	s	NOUN
ejpam-4690	44	79	,	,	PUNCT
ejpam-4690	44	80	dg(v	dg(v	X
ejpam-4690	44	81	,	,	PUNCT
ejpam-4690	44	82	w	w	NOUN
ejpam-4690	44	83	)	)	PUNCT
ejpam-4690	44	84	̸=	̸=	PROPN
ejpam-4690	44	85	1	1	NUM
ejpam-4690	44	86	.	.	PUNCT
ejpam-4690	45	1	the	the	DET
ejpam-4690	45	2	maximum	maximum	ADJ
ejpam-4690	45	3	cardinality	cardinality	NOUN
ejpam-4690	45	4	of	of	ADP
ejpam-4690	45	5	an	an	DET
ejpam-4690	45	6	independent	independent	ADJ
ejpam-4690	45	7	set	set	NOUN
ejpam-4690	45	8	of	of	ADP
ejpam-4690	45	9	g	g	NOUN
ejpam-4690	45	10	,	,	PUNCT
ejpam-4690	45	11	denoted	denote	VERB
ejpam-4690	45	12	by	by	ADP
ejpam-4690	45	13	α(g	α(g	NOUN
ejpam-4690	45	14	)	)	PUNCT
ejpam-4690	45	15	,	,	PUNCT
ejpam-4690	45	16	is	be	AUX
ejpam-4690	45	17	called	call	VERB
ejpam-4690	45	18	the	the	DET
ejpam-4690	45	19	independence	independence	NOUN
ejpam-4690	45	20	number	number	NOUN
ejpam-4690	45	21	of	of	ADP
ejpam-4690	45	22	g.	g.	PROPN
ejpam-4690	45	23	any	any	DET
ejpam-4690	45	24	independent	independent	ADJ
ejpam-4690	45	25	set	set	NOUN
ejpam-4690	45	26	with	with	ADP
ejpam-4690	45	27	cardinality	cardinality	PROPN
ejpam-4690	45	28	α(g	α(g	NUM
ejpam-4690	45	29	)	)	PUNCT
ejpam-4690	45	30	is	be	AUX
ejpam-4690	45	31	referred	refer	VERB
ejpam-4690	45	32	to	to	ADP
ejpam-4690	45	33	as	as	ADP
ejpam-4690	45	34	a	a	DET
ejpam-4690	45	35	maximum	maximum	ADJ
ejpam-4690	45	36	independent	independent	ADJ
ejpam-4690	45	37	set	set	NOUN
ejpam-4690	45	38	or	or	CCONJ
ejpam-4690	45	39	α	α	NOUN
ejpam-4690	45	40	-	-	PUNCT
ejpam-4690	45	41	set	set	NOUN
ejpam-4690	45	42	of	of	ADP
ejpam-4690	45	43	g.	g.	PROPN
ejpam-4690	45	44	let	let	VERB
ejpam-4690	45	45	s1	s1	PROPN
ejpam-4690	45	46	=	=	SYM
ejpam-4690	45	47	(	(	PUNCT
ejpam-4690	45	48	v1	v1	PROPN
ejpam-4690	45	49	,	,	PUNCT
ejpam-4690	45	50	·	·	PUNCT
ejpam-4690	45	51	·	·	PUNCT
ejpam-4690	45	52	·	·	PUNCT
ejpam-4690	45	53	,	,	PUNCT
ejpam-4690	45	54	vn	vn	PROPN
ejpam-4690	45	55	)	)	PUNCT
ejpam-4690	45	56	and	and	CCONJ
ejpam-4690	45	57	s2	s2	NOUN
ejpam-4690	45	58	=	=	SYM
ejpam-4690	45	59	(	(	PUNCT
ejpam-4690	45	60	u1	u1	PROPN
ejpam-4690	45	61	,	,	PUNCT
ejpam-4690	45	62	·	·	PUNCT
ejpam-4690	45	63	·	·	PUNCT
ejpam-4690	45	64	·	·	PUNCT
ejpam-4690	45	65	,	,	PUNCT
ejpam-4690	45	66	um	um	INTJ
ejpam-4690	45	67	)	)	PUNCT
ejpam-4690	45	68	,	,	PUNCT
ejpam-4690	45	69	n	n	CCONJ
ejpam-4690	45	70	,	,	PUNCT
ejpam-4690	45	71	m	m	VERB
ejpam-4690	45	72	≥	≥	NOUN
ejpam-4690	45	73	1	1	NUM
ejpam-4690	45	74	be	be	AUX
ejpam-4690	45	75	two	two	NUM
ejpam-4690	45	76	sequences	sequence	NOUN
ejpam-4690	45	77	of	of	ADP
ejpam-4690	45	78	distinct	distinct	ADJ
ejpam-4690	45	79	vertices	vertex	NOUN
ejpam-4690	45	80	of	of	ADP
ejpam-4690	45	81	g.	g.	PROPN
ejpam-4690	45	82	the	the	DET
ejpam-4690	45	83	concatenation	concatenation	NOUN
ejpam-4690	45	84	of	of	ADP
ejpam-4690	45	85	s1	s1	PROPN
ejpam-4690	45	86	and	and	CCONJ
ejpam-4690	45	87	s2	s2	PROPN
ejpam-4690	45	88	,	,	PUNCT
ejpam-4690	45	89	denoted	denote	VERB
ejpam-4690	45	90	by	by	ADP
ejpam-4690	45	91	s1	s1	PROPN
ejpam-4690	45	92	⊕	⊕	PROPN
ejpam-4690	45	93	s2	s2	PROPN
ejpam-4690	45	94	,	,	PUNCT
ejpam-4690	45	95	is	be	AUX
ejpam-4690	45	96	the	the	DET
ejpam-4690	45	97	sequence	sequence	NOUN
ejpam-4690	45	98	given	give	VERB
ejpam-4690	45	99	by	by	ADP
ejpam-4690	45	100	s1	s1	PROPN
ejpam-4690	45	101	⊕	⊕	PROPN
ejpam-4690	45	102	s2	s2	PROPN
ejpam-4690	45	103	=	=	SYM
ejpam-4690	45	104	(	(	PUNCT
ejpam-4690	45	105	v1	v1	PROPN
ejpam-4690	45	106	,	,	PUNCT
ejpam-4690	45	107	·	·	PUNCT
ejpam-4690	45	108	·	·	PUNCT
ejpam-4690	45	109	·	·	PUNCT
ejpam-4690	45	110	,	,	PUNCT
ejpam-4690	45	111	vn	vn	PROPN
ejpam-4690	45	112	,	,	PUNCT
ejpam-4690	45	113	u1	u1	NOUN
ejpam-4690	45	114	,	,	PUNCT
ejpam-4690	45	115	·	·	PUNCT
ejpam-4690	45	116	·	·	PUNCT
ejpam-4690	45	117	·	·	PUNCT
ejpam-4690	45	118	,	,	PUNCT
ejpam-4690	45	119	um	um	INTJ
ejpam-4690	45	120	)	)	PUNCT
ejpam-4690	45	121	.	.	PUNCT
ejpam-4690	46	1	let	let	VERB
ejpam-4690	46	2	g	g	NOUN
ejpam-4690	46	3	and	and	CCONJ
ejpam-4690	46	4	h	h	NOUN
ejpam-4690	46	5	be	be	VERB
ejpam-4690	46	6	any	any	DET
ejpam-4690	46	7	two	two	NUM
ejpam-4690	46	8	graphs	graph	NOUN
ejpam-4690	46	9	.	.	PUNCT
ejpam-4690	47	1	the	the	DET
ejpam-4690	47	2	join	join	NOUN
ejpam-4690	47	3	of	of	ADP
ejpam-4690	47	4	g	g	PROPN
ejpam-4690	47	5	and	and	CCONJ
ejpam-4690	47	6	h	h	NOUN
ejpam-4690	47	7	,	,	PUNCT
ejpam-4690	47	8	denoted	denote	VERB
ejpam-4690	47	9	by	by	ADP
ejpam-4690	47	10	g+h	g+h	PROPN
ejpam-4690	47	11	,	,	PUNCT
ejpam-4690	47	12	is	be	AUX
ejpam-4690	47	13	the	the	DET
ejpam-4690	47	14	graph	graph	NOUN
ejpam-4690	47	15	with	with	ADP
ejpam-4690	47	16	vertex	vertex	NOUN
ejpam-4690	47	17	set	set	VERB
ejpam-4690	47	18	v	v	NOUN
ejpam-4690	47	19	(	(	PUNCT
ejpam-4690	47	20	g+h	g+h	NOUN
ejpam-4690	47	21	)	)	PUNCT
ejpam-4690	47	22	=	=	SYM
ejpam-4690	47	23	v	v	X
ejpam-4690	47	24	(	(	PUNCT
ejpam-4690	47	25	g)∪v	g)∪v	NOUN
ejpam-4690	47	26	(	(	PUNCT
ejpam-4690	47	27	h	h	NOUN
ejpam-4690	47	28	)	)	PUNCT
ejpam-4690	47	29	and	and	CCONJ
ejpam-4690	47	30	edge	edge	NOUN
ejpam-4690	47	31	set	set	VERB
ejpam-4690	47	32	e(g+h	e(g+h	NUM
ejpam-4690	47	33	)	)	PUNCT
ejpam-4690	48	1	=	=	SYM
ejpam-4690	48	2	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	X
ejpam-4690	48	3	:	:	PUNCT
ejpam-4690	48	4	u	u	PROPN
ejpam-4690	48	5	∈	∈	PROPN
ejpam-4690	48	6	v	v	NOUN
ejpam-4690	48	7	(	(	PUNCT
ejpam-4690	48	8	g	g	NOUN
ejpam-4690	48	9	)	)	PUNCT
ejpam-4690	48	10	,	,	PUNCT
ejpam-4690	48	11	v	v	X
ejpam-4690	48	12	∈	∈	PROPN
ejpam-4690	48	13	v	v	NOUN
ejpam-4690	48	14	(	(	PUNCT
ejpam-4690	48	15	h	h	NOUN
ejpam-4690	48	16	)	)	PUNCT
ejpam-4690	48	17	}	}	PUNCT
ejpam-4690	48	18	.	.	PUNCT
ejpam-4690	49	1	3	3	X
ejpam-4690	49	2	.	.	X
ejpam-4690	49	3	main	main	ADJ
ejpam-4690	49	4	results	result	NOUN
ejpam-4690	49	5	theorem	theorem	VERB
ejpam-4690	49	6	1	1	NUM
ejpam-4690	49	7	.	.	PUNCT
ejpam-4690	50	1	let	let	VERB
ejpam-4690	50	2	a	a	PRON
ejpam-4690	50	3	and	and	CCONJ
ejpam-4690	50	4	b	b	NOUN
ejpam-4690	50	5	be	be	AUX
ejpam-4690	50	6	positive	positive	ADJ
ejpam-4690	50	7	integers	integer	NOUN
ejpam-4690	50	8	such	such	ADJ
ejpam-4690	50	9	that	that	SCONJ
ejpam-4690	50	10	3	3	NUM
ejpam-4690	50	11	≤	≤	NOUN
ejpam-4690	50	12	a	a	DET
ejpam-4690	50	13	≤	≤	PROPN
ejpam-4690	50	14	b.	b.	NOUN
ejpam-4690	51	1	then	then	ADV
ejpam-4690	51	2	(	(	PUNCT
ejpam-4690	51	3	i	i	NOUN
ejpam-4690	51	4	)	)	PUNCT
ejpam-4690	51	5	there	there	PRON
ejpam-4690	51	6	exists	exist	VERB
ejpam-4690	51	7	a	a	DET
ejpam-4690	51	8	connected	connected	ADJ
ejpam-4690	51	9	graph	graph	NOUN
ejpam-4690	51	10	g	g	ADP
ejpam-4690	51	11	such	such	ADJ
ejpam-4690	51	12	that	that	DET
ejpam-4690	51	13	γgr(g	γgr(g	PROPN
ejpam-4690	51	14	)	)	PUNCT
ejpam-4690	51	15	=	=	PUNCT
ejpam-4690	52	1	a	a	PRON
ejpam-4690	52	2	and	and	CCONJ
ejpam-4690	52	3	γhgr(g	γhgr(g	NUM
ejpam-4690	52	4	)	)	PUNCT
ejpam-4690	52	5	=	=	SYM
ejpam-4690	52	6	b	b	NOUN
ejpam-4690	52	7	,	,	PUNCT
ejpam-4690	52	8	and	and	CCONJ
ejpam-4690	52	9	(	(	PUNCT
ejpam-4690	52	10	ii	ii	NOUN
ejpam-4690	52	11	)	)	PUNCT
ejpam-4690	52	12	there	there	PRON
ejpam-4690	52	13	exists	exist	VERB
ejpam-4690	52	14	a	a	DET
ejpam-4690	52	15	connected	connected	ADJ
ejpam-4690	52	16	graph	graph	NOUN
ejpam-4690	52	17	g′	g′	NOUN
ejpam-4690	53	1	such	such	ADJ
ejpam-4690	53	2	that	that	SCONJ
ejpam-4690	53	3	γhgr(g	γhgr(g	NOUN
ejpam-4690	53	4	′	′	NUM
ejpam-4690	53	5	)	)	PUNCT
ejpam-4690	53	6	=	=	PUNCT
ejpam-4690	53	7	a	a	PROPN
ejpam-4690	53	8	and	and	CCONJ
ejpam-4690	53	9	γgr(g	γgr(g	PROPN
ejpam-4690	53	10	′	′	NUM
ejpam-4690	53	11	)	)	PUNCT
ejpam-4690	53	12	=	=	SYM
ejpam-4690	53	13	b.	b.	PROPN
ejpam-4690	53	14	proof	proof	NOUN
ejpam-4690	53	15	.	.	PUNCT
ejpam-4690	54	1	for	for	ADP
ejpam-4690	54	2	a	a	DET
ejpam-4690	54	3	=	=	SYM
ejpam-4690	54	4	b	b	NOUN
ejpam-4690	54	5	,	,	PUNCT
ejpam-4690	54	6	consider	consider	VERB
ejpam-4690	54	7	the	the	DET
ejpam-4690	54	8	graphg	graphg	NOUN
ejpam-4690	54	9	given	give	VERB
ejpam-4690	54	10	in	in	ADP
ejpam-4690	54	11	figure	figure	NOUN
ejpam-4690	54	12	1	1	NUM
ejpam-4690	54	13	.	.	PUNCT
ejpam-4690	55	1	let	let	VERB
ejpam-4690	55	2	s	s	PRON
ejpam-4690	55	3	=	=	PUNCT
ejpam-4690	55	4	(	(	PUNCT
ejpam-4690	55	5	u1	u1	PROPN
ejpam-4690	55	6	,	,	PUNCT
ejpam-4690	55	7	u2	u2	NOUN
ejpam-4690	55	8	,	,	PUNCT
ejpam-4690	55	9	.	.	PUNCT
ejpam-4690	55	10	.	.	PUNCT
ejpam-4690	56	1	.	.	PUNCT
ejpam-4690	57	1	,	,	PUNCT
ejpam-4690	57	2	ua−1	ua−1	PROPN
ejpam-4690	57	3	,	,	PUNCT
ejpam-4690	57	4	ua	ua	PROPN
ejpam-4690	57	5	)	)	PUNCT
ejpam-4690	57	6	.	.	PUNCT
ejpam-4690	58	1	then	then	ADV
ejpam-4690	58	2	s	s	VERB
ejpam-4690	58	3	is	be	AUX
ejpam-4690	58	4	both	both	PRON
ejpam-4690	58	5	a	a	DET
ejpam-4690	58	6	γgr	γgr	NOUN
ejpam-4690	58	7	-	-	PUNCT
ejpam-4690	58	8	sequence	sequence	NOUN
ejpam-4690	58	9	and	and	CCONJ
ejpam-4690	58	10	a	a	DET
ejpam-4690	58	11	γhgr	γhgr	ADJ
ejpam-4690	58	12	-	-	PUNCT
ejpam-4690	58	13	sequence	sequence	NOUN
ejpam-4690	58	14	of	of	ADP
ejpam-4690	58	15	g.	g.	PROPN
ejpam-4690	58	16	hence	hence	ADV
ejpam-4690	58	17	,	,	PUNCT
ejpam-4690	58	18	γgr(g	γgr(g	PROPN
ejpam-4690	58	19	)	)	PUNCT
ejpam-4690	58	20	=	=	PUNCT
ejpam-4690	59	1	a	a	DET
ejpam-4690	59	2	=	=	SYM
ejpam-4690	59	3	γhgr(g	γhgr(g	NOUN
ejpam-4690	59	4	)	)	PUNCT
ejpam-4690	59	5	.	.	PUNCT
ejpam-4690	60	1	u2	u2	PROPN
ejpam-4690	60	2	ua−1u1	ua−1u1	PROPN
ejpam-4690	60	3	g	g	PROPN
ejpam-4690	60	4	:	:	PUNCT
ejpam-4690	60	5	.	.	PUNCT
ejpam-4690	60	6	.	.	PUNCT
ejpam-4690	60	7	.	.	PUNCT
ejpam-4690	61	1	ua	ua	PROPN
ejpam-4690	61	2	figure	figure	VERB
ejpam-4690	61	3	1	1	NUM
ejpam-4690	61	4	:	:	PUNCT
ejpam-4690	61	5	a	a	DET
ejpam-4690	61	6	graph	graph	NOUN
ejpam-4690	61	7	g	g	NOUN
ejpam-4690	61	8	with	with	ADP
ejpam-4690	61	9	γgr(g	γgr(g	PROPN
ejpam-4690	61	10	)	)	PUNCT
ejpam-4690	61	11	=	=	PRON
ejpam-4690	61	12	γh	γh	X
ejpam-4690	61	13	gr(g	gr(g	PROPN
ejpam-4690	61	14	)	)	PUNCT
ejpam-4690	61	15	next	next	ADV
ejpam-4690	61	16	,	,	PUNCT
ejpam-4690	61	17	suppose	suppose	VERB
ejpam-4690	61	18	a	a	DET
ejpam-4690	61	19	<	<	X
ejpam-4690	61	20	b	b	NOUN
ejpam-4690	61	21	and	and	CCONJ
ejpam-4690	61	22	let	let	VERB
ejpam-4690	61	23	m	m	NOUN
ejpam-4690	61	24	=	=	VERB
ejpam-4690	61	25	b−	b−	ADJ
ejpam-4690	61	26	a.	a.	NOUN
ejpam-4690	61	27	for	for	ADP
ejpam-4690	61	28	(	(	PUNCT
ejpam-4690	61	29	i	i	NOUN
ejpam-4690	61	30	)	)	PUNCT
ejpam-4690	61	31	,	,	PUNCT
ejpam-4690	61	32	consider	consider	VERB
ejpam-4690	61	33	the	the	DET
ejpam-4690	61	34	graph	graph	NOUN
ejpam-4690	61	35	g	g	NOUN
ejpam-4690	61	36	given	give	VERB
ejpam-4690	61	37	in	in	ADP
ejpam-4690	61	38	figure	figure	NOUN
ejpam-4690	61	39	2	2	NUM
ejpam-4690	61	40	,	,	PUNCT
ejpam-4690	61	41	where	where	SCONJ
ejpam-4690	61	42	the	the	DET
ejpam-4690	61	43	graph	graph	NOUN
ejpam-4690	61	44	g[{xa	g[{xa	NOUN
ejpam-4690	61	45	,	,	PUNCT
ejpam-4690	61	46	z1	z1	VERB
ejpam-4690	61	47	,	,	PUNCT
ejpam-4690	61	48	z2	z2	PROPN
ejpam-4690	61	49	,	,	PUNCT
ejpam-4690	61	50	.	.	PUNCT
ejpam-4690	61	51	.	.	PUNCT
ejpam-4690	61	52	.	.	PUNCT
ejpam-4690	62	1	,	,	PUNCT
ejpam-4690	62	2	zm	zm	PROPN
ejpam-4690	62	3	}	}	PUNCT
ejpam-4690	62	4	]	]	PUNCT
ejpam-4690	62	5	induced	induce	VERB
ejpam-4690	62	6	by	by	ADP
ejpam-4690	62	7	{	{	PUNCT
ejpam-4690	62	8	xa	xa	PROPN
ejpam-4690	62	9	,	,	PUNCT
ejpam-4690	62	10	z1	z1	PROPN
ejpam-4690	62	11	,	,	PUNCT
ejpam-4690	62	12	z2	z2	PROPN
ejpam-4690	62	13	,	,	PUNCT
ejpam-4690	62	14	.	.	PUNCT
ejpam-4690	62	15	.	.	PUNCT
ejpam-4690	63	1	.	.	PUNCT
ejpam-4690	64	1	,	,	PUNCT
ejpam-4690	64	2	zm	zm	PROPN
ejpam-4690	64	3	}	}	PUNCT
ejpam-4690	64	4	is	be	AUX
ejpam-4690	64	5	complete	complete	ADJ
ejpam-4690	64	6	.	.	PUNCT
ejpam-4690	65	1	it	it	PRON
ejpam-4690	65	2	can	can	AUX
ejpam-4690	65	3	easily	easily	ADV
ejpam-4690	65	4	be	be	AUX
ejpam-4690	65	5	verified	verify	VERB
ejpam-4690	65	6	that	that	SCONJ
ejpam-4690	65	7	s1	s1	NOUN
ejpam-4690	65	8	=	=	PUNCT
ejpam-4690	65	9	(	(	PUNCT
ejpam-4690	65	10	x1	x1	PROPN
ejpam-4690	65	11	,	,	PUNCT
ejpam-4690	65	12	x2	x2	PROPN
ejpam-4690	65	13	,	,	PUNCT
ejpam-4690	65	14	·	·	PUNCT
ejpam-4690	65	15	·	·	PUNCT
ejpam-4690	65	16	·	·	PUNCT
ejpam-4690	65	17	,	,	PUNCT
ejpam-4690	65	18	xa	xa	PROPN
ejpam-4690	65	19	)	)	PUNCT
ejpam-4690	65	20	and	and	CCONJ
ejpam-4690	65	21	s2	s2	NOUN
ejpam-4690	65	22	=	=	SYM
ejpam-4690	65	23	(	(	PUNCT
ejpam-4690	65	24	u	u	NOUN
ejpam-4690	65	25	,	,	PUNCT
ejpam-4690	65	26	v	v	NOUN
ejpam-4690	65	27	,	,	PUNCT
ejpam-4690	65	28	x1	x1	PROPN
ejpam-4690	65	29	,	,	PUNCT
ejpam-4690	65	30	.	.	PUNCT
ejpam-4690	65	31	.	.	PUNCT
ejpam-4690	66	1	.	.	PUNCT
ejpam-4690	67	1	,	,	PUNCT
ejpam-4690	67	2	xa−2	xa−2	PROPN
ejpam-4690	67	3	,	,	PUNCT
ejpam-4690	67	4	z1	z1	NOUN
ejpam-4690	67	5	,	,	PUNCT
ejpam-4690	67	6	·	·	PUNCT
ejpam-4690	67	7	·	·	PUNCT
ejpam-4690	67	8	·	·	PUNCT
ejpam-4690	67	9	,	,	PUNCT
ejpam-4690	67	10	zm	zm	PROPN
ejpam-4690	67	11	)	)	PUNCT
ejpam-4690	67	12	are	be	AUX
ejpam-4690	67	13	γgr	γgr	NOUN
ejpam-4690	67	14	-	-	PUNCT
ejpam-4690	67	15	sequence	sequence	NOUN
ejpam-4690	67	16	and	and	CCONJ
ejpam-4690	67	17	γhgr	γhgr	ADJ
ejpam-4690	67	18	-	-	PUNCT
ejpam-4690	67	19	sequence	sequence	NOUN
ejpam-4690	67	20	of	of	ADP
ejpam-4690	67	21	g	g	NOUN
ejpam-4690	67	22	,	,	PUNCT
ejpam-4690	67	23	respectively	respectively	ADV
ejpam-4690	67	24	.	.	PUNCT
ejpam-4690	68	1	therefore	therefore	ADV
ejpam-4690	68	2	,	,	PUNCT
ejpam-4690	68	3	γgr(g	γgr(g	PROPN
ejpam-4690	68	4	)	)	PUNCT
ejpam-4690	68	5	=	=	PUNCT
ejpam-4690	68	6	a	a	PRON
ejpam-4690	68	7	and	and	CCONJ
ejpam-4690	68	8	γhgr(g	γhgr(g	NUM
ejpam-4690	68	9	)	)	PUNCT
ejpam-4690	69	1	=	=	VERB
ejpam-4690	69	2	m+	m+	NUM
ejpam-4690	69	3	a	a	DET
ejpam-4690	69	4	=	=	PROPN
ejpam-4690	69	5	b.	b.	PROPN
ejpam-4690	69	6	j.	j.	PROPN
ejpam-4690	69	7	hassan	hassan	PROPN
ejpam-4690	69	8	,	,	PUNCT
ejpam-4690	69	9	s.	s.	PROPN
ejpam-4690	69	10	canoy	canoy	PROPN
ejpam-4690	69	11	jr	jr	PROPN
ejpam-4690	69	12	.	.	PROPN
ejpam-4690	69	13	/	/	SYM
ejpam-4690	69	14	eur	eur	PROPN
ejpam-4690	69	15	.	.	PUNCT
ejpam-4690	70	1	j.	j.	PROPN
ejpam-4690	70	2	pure	pure	PROPN
ejpam-4690	70	3	appl	appl	PROPN
ejpam-4690	70	4	.	.	PROPN
ejpam-4690	70	5	math	math	PROPN
ejpam-4690	70	6	,	,	PUNCT
ejpam-4690	70	7	16	16	NUM
ejpam-4690	70	8	(	(	PUNCT
ejpam-4690	70	9	2	2	NUM
ejpam-4690	70	10	)	)	PUNCT
ejpam-4690	70	11	(	(	PUNCT
ejpam-4690	70	12	2023	2023	NUM
ejpam-4690	70	13	)	)	PUNCT
ejpam-4690	70	14	,	,	PUNCT
ejpam-4690	70	15	1154	1154	NUM
ejpam-4690	70	16	-	-	SYM
ejpam-4690	70	17	1166	1166	NUM
ejpam-4690	70	18	1157	1157	NUM
ejpam-4690	70	19	u	u	NOUN
ejpam-4690	70	20	v	v	ADP
ejpam-4690	70	21	x1	x1	PROPN
ejpam-4690	71	1	x2	x2	PROPN
ejpam-4690	71	2	g	g	PROPN
ejpam-4690	71	3	:	:	PUNCT
ejpam-4690	71	4	x3	x3	ADJ
ejpam-4690	71	5	.	.	PUNCT
ejpam-4690	71	6	.	.	PUNCT
ejpam-4690	71	7	.	.	PUNCT
ejpam-4690	72	1	xa−1	xa−1	PROPN
ejpam-4690	72	2	xa	xa	PROPN
ejpam-4690	73	1	z1	z1	PROPN
ejpam-4690	73	2	z2	z2	PROPN
ejpam-4690	73	3	zm	zm	PROPN
ejpam-4690	73	4	.	.	PUNCT
ejpam-4690	73	5	.	.	PUNCT
ejpam-4690	74	1	.	.	PUNCT
ejpam-4690	75	1	figure	figure	VERB
ejpam-4690	75	2	2	2	NUM
ejpam-4690	75	3	:	:	PUNCT
ejpam-4690	75	4	a	a	DET
ejpam-4690	75	5	graph	graph	NOUN
ejpam-4690	75	6	g	g	NOUN
ejpam-4690	75	7	with	with	ADP
ejpam-4690	75	8	γgr(g	γgr(g	PROPN
ejpam-4690	75	9	)	)	PUNCT
ejpam-4690	75	10	=	=	PUNCT
ejpam-4690	76	1	a	a	PRON
ejpam-4690	76	2	<	<	X
ejpam-4690	76	3	γh	γh	X
ejpam-4690	76	4	gr(g	gr(g	PUNCT
ejpam-4690	76	5	)	)	PUNCT
ejpam-4690	77	1	=	=	SYM
ejpam-4690	77	2	b	b	X
ejpam-4690	77	3	for	for	ADP
ejpam-4690	77	4	(	(	PUNCT
ejpam-4690	77	5	ii	ii	NOUN
ejpam-4690	77	6	)	)	PUNCT
ejpam-4690	77	7	,	,	PUNCT
ejpam-4690	77	8	consider	consider	VERB
ejpam-4690	77	9	the	the	DET
ejpam-4690	77	10	graph	graph	NOUN
ejpam-4690	77	11	g′	g′	NOUN
ejpam-4690	77	12	given	give	VERB
ejpam-4690	77	13	in	in	ADP
ejpam-4690	77	14	figure	figure	NOUN
ejpam-4690	77	15	3	3	NUM
ejpam-4690	77	16	.	.	PUNCT
ejpam-4690	78	1	let	let	VERB
ejpam-4690	78	2	s1	s1	PROPN
ejpam-4690	78	3	=	=	SYM
ejpam-4690	78	4	(	(	PUNCT
ejpam-4690	78	5	s1	s1	PROPN
ejpam-4690	78	6	,	,	PUNCT
ejpam-4690	78	7	s2	s2	PROPN
ejpam-4690	78	8	,	,	PUNCT
ejpam-4690	78	9	·	·	PUNCT
ejpam-4690	78	10	·	·	PUNCT
ejpam-4690	78	11	·	·	PUNCT
ejpam-4690	78	12	,	,	PUNCT
ejpam-4690	78	13	sa	sa	PROPN
ejpam-4690	78	14	)	)	PUNCT
ejpam-4690	78	15	and	and	CCONJ
ejpam-4690	78	16	s2	s2	VERB
ejpam-4690	78	17	=	=	SYM
ejpam-4690	78	18	(	(	PUNCT
ejpam-4690	78	19	s1	s1	PROPN
ejpam-4690	78	20	,	,	PUNCT
ejpam-4690	78	21	s2	s2	NOUN
ejpam-4690	78	22	,	,	PUNCT
ejpam-4690	78	23	.	.	PUNCT
ejpam-4690	78	24	.	.	PUNCT
ejpam-4690	79	1	.	.	PUNCT
ejpam-4690	80	1	,	,	PUNCT
ejpam-4690	80	2	sa	sa	PROPN
ejpam-4690	80	3	,	,	PUNCT
ejpam-4690	80	4	u1	u1	NOUN
ejpam-4690	80	5	,	,	PUNCT
ejpam-4690	80	6	u2	u2	NOUN
ejpam-4690	80	7	,	,	PUNCT
ejpam-4690	80	8	·	·	PUNCT
ejpam-4690	80	9	·	·	PUNCT
ejpam-4690	80	10	·	·	PUNCT
ejpam-4690	80	11	,	,	PUNCT
ejpam-4690	80	12	um	um	INTJ
ejpam-4690	80	13	)	)	PUNCT
ejpam-4690	80	14	.	.	PUNCT
ejpam-4690	81	1	then	then	ADV
ejpam-4690	81	2	s1	s1	PROPN
ejpam-4690	81	3	and	and	CCONJ
ejpam-4690	81	4	s2	s2	PROPN
ejpam-4690	81	5	are	be	AUX
ejpam-4690	81	6	γhgr	γhgr	ADJ
ejpam-4690	81	7	-	-	PUNCT
ejpam-4690	81	8	sequence	sequence	NOUN
ejpam-4690	81	9	and	and	CCONJ
ejpam-4690	81	10	γgr	γgr	NOUN
ejpam-4690	81	11	-	-	PUNCT
ejpam-4690	81	12	sequence	sequence	NOUN
ejpam-4690	81	13	of	of	ADP
ejpam-4690	81	14	g′	g′	NOUN
ejpam-4690	81	15	,	,	PUNCT
ejpam-4690	81	16	respectively	respectively	ADV
ejpam-4690	81	17	.	.	PUNCT
ejpam-4690	82	1	thus	thus	ADV
ejpam-4690	82	2	,	,	PUNCT
ejpam-4690	82	3	γhgr(g	γhgr(g	NOUN
ejpam-4690	82	4	′	′	NUM
ejpam-4690	82	5	)	)	PUNCT
ejpam-4690	82	6	=	=	PUNCT
ejpam-4690	82	7	a	a	PROPN
ejpam-4690	82	8	and	and	CCONJ
ejpam-4690	82	9	γgr(g	γgr(g	PROPN
ejpam-4690	82	10	′	′	NUM
ejpam-4690	82	11	)	)	PUNCT
ejpam-4690	83	1	=	=	PRON
ejpam-4690	83	2	m+	m+	NUM
ejpam-4690	83	3	a	a	DET
ejpam-4690	83	4	=	=	X
ejpam-4690	83	5	b.	b.	PROPN
ejpam-4690	83	6	g′	g′	NOUN
ejpam-4690	83	7	:	:	PUNCT
ejpam-4690	83	8	.	.	PUNCT
ejpam-4690	83	9	.	.	PUNCT
ejpam-4690	83	10	.	.	PUNCT
ejpam-4690	84	1	s1	s1	PROPN
ejpam-4690	84	2	s2	s2	PROPN
ejpam-4690	84	3	um	um	INTJ
ejpam-4690	84	4	sa	sa	PROPN
ejpam-4690	84	5	u1	u1	PROPN
ejpam-4690	84	6	u2	u2	PROPN
ejpam-4690	84	7	.	.	PUNCT
ejpam-4690	84	8	.	.	PUNCT
ejpam-4690	84	9	.	.	PUNCT
ejpam-4690	85	1	figure	figure	VERB
ejpam-4690	85	2	3	3	NUM
ejpam-4690	85	3	:	:	PUNCT
ejpam-4690	85	4	a	a	DET
ejpam-4690	85	5	graph	graph	NOUN
ejpam-4690	85	6	g′	g′	NOUN
ejpam-4690	85	7	with	with	ADP
ejpam-4690	85	8	γh	γh	PROPN
ejpam-4690	85	9	gr(g	gr(g	PROPN
ejpam-4690	85	10	′	′	NUM
ejpam-4690	85	11	)	)	PUNCT
ejpam-4690	86	1	=	=	PUNCT
ejpam-4690	86	2	a	a	DET
ejpam-4690	86	3	<	<	X
ejpam-4690	86	4	γgr(g′	γgr(g′	NOUN
ejpam-4690	86	5	)	)	PUNCT
ejpam-4690	87	1	=	=	SYM
ejpam-4690	87	2	b	b	NOUN
ejpam-4690	87	3	this	this	PRON
ejpam-4690	87	4	proves	prove	VERB
ejpam-4690	87	5	the	the	DET
ejpam-4690	87	6	assertion	assertion	NOUN
ejpam-4690	87	7	.	.	PUNCT
ejpam-4690	88	1	corollary	corollary	ADJ
ejpam-4690	88	2	1	1	NUM
ejpam-4690	88	3	.	.	PUNCT
ejpam-4690	89	1	let	let	VERB
ejpam-4690	89	2	n	n	PRON
ejpam-4690	89	3	be	be	AUX
ejpam-4690	89	4	a	a	DET
ejpam-4690	89	5	positive	positive	ADJ
ejpam-4690	89	6	integer	integer	NOUN
ejpam-4690	89	7	.	.	PUNCT
ejpam-4690	90	1	then	then	ADV
ejpam-4690	90	2	each	each	PRON
ejpam-4690	90	3	of	of	ADP
ejpam-4690	90	4	the	the	DET
ejpam-4690	90	5	following	following	ADJ
ejpam-4690	90	6	statements	statement	NOUN
ejpam-4690	90	7	holds	hold	VERB
ejpam-4690	90	8	.	.	PUNCT
ejpam-4690	91	1	(	(	PUNCT
ejpam-4690	91	2	i	i	NOUN
ejpam-4690	91	3	)	)	PUNCT
ejpam-4690	91	4	there	there	PRON
ejpam-4690	91	5	exists	exist	VERB
ejpam-4690	91	6	a	a	DET
ejpam-4690	91	7	connected	connected	ADJ
ejpam-4690	91	8	graph	graph	NOUN
ejpam-4690	91	9	g	g	ADP
ejpam-4690	91	10	such	such	ADJ
ejpam-4690	91	11	that	that	PRON
ejpam-4690	91	12	γhgr(g)−	γhgr(g)−	ADJ
ejpam-4690	91	13	γgr(g	γgr(g	PROPN
ejpam-4690	91	14	)	)	PUNCT
ejpam-4690	91	15	=	=	SYM
ejpam-4690	91	16	n.	n.	NOUN
ejpam-4690	91	17	(	(	PUNCT
ejpam-4690	91	18	ii	ii	NOUN
ejpam-4690	91	19	)	)	PUNCT
ejpam-4690	91	20	there	there	PRON
ejpam-4690	91	21	exists	exist	VERB
ejpam-4690	91	22	a	a	DET
ejpam-4690	91	23	connected	connected	ADJ
ejpam-4690	91	24	graph	graph	NOUN
ejpam-4690	91	25	h	h	NOUN
ejpam-4690	91	26	such	such	ADJ
ejpam-4690	91	27	that	that	DET
ejpam-4690	91	28	γgr(h)−	γgr(h)−	PROPN
ejpam-4690	91	29	γhgr(h	γhgr(h	NOUN
ejpam-4690	91	30	)	)	PUNCT
ejpam-4690	92	1	=	=	VERB
ejpam-4690	92	2	n.	n.	NOUN
ejpam-4690	92	3	in	in	ADP
ejpam-4690	92	4	other	other	ADJ
ejpam-4690	92	5	words	word	NOUN
ejpam-4690	92	6	,	,	PUNCT
ejpam-4690	92	7	the	the	DET
ejpam-4690	92	8	absolute	absolute	ADJ
ejpam-4690	92	9	difference	difference	NOUN
ejpam-4690	92	10	|γhgr(g)−	|γhgr(g)−	NOUN
ejpam-4690	92	11	γgr(g)|	γgr(g)|	NOUN
ejpam-4690	92	12	can	can	AUX
ejpam-4690	92	13	be	be	AUX
ejpam-4690	92	14	made	make	VERB
ejpam-4690	92	15	arbitrarily	arbitrarily	ADV
ejpam-4690	92	16	large	large	ADJ
ejpam-4690	92	17	.	.	PUNCT
ejpam-4690	93	1	proof	proof	NOUN
ejpam-4690	93	2	.	.	PUNCT
ejpam-4690	94	1	let	let	VERB
ejpam-4690	94	2	n	n	PRON
ejpam-4690	94	3	be	be	AUX
ejpam-4690	94	4	a	a	DET
ejpam-4690	94	5	positive	positive	ADJ
ejpam-4690	94	6	integer	integer	NOUN
ejpam-4690	94	7	and	and	CCONJ
ejpam-4690	94	8	let	let	VERB
ejpam-4690	94	9	a	a	DET
ejpam-4690	94	10	=	=	PUNCT
ejpam-4690	94	11	n	n	NOUN
ejpam-4690	94	12	+	+	CCONJ
ejpam-4690	94	13	2	2	NUM
ejpam-4690	94	14	and	and	CCONJ
ejpam-4690	94	15	b	b	NOUN
ejpam-4690	94	16	=	=	SYM
ejpam-4690	94	17	2n	2n	NUM
ejpam-4690	95	1	+	+	CCONJ
ejpam-4690	95	2	2	2	X
ejpam-4690	95	3	.	.	PUNCT
ejpam-4690	95	4	by	by	ADP
ejpam-4690	95	5	theorem	theorem	NOUN
ejpam-4690	95	6	1(i	1(i	NUM
ejpam-4690	95	7	)	)	PUNCT
ejpam-4690	95	8	,	,	PUNCT
ejpam-4690	95	9	there	there	PRON
ejpam-4690	95	10	exists	exist	VERB
ejpam-4690	95	11	a	a	DET
ejpam-4690	95	12	connected	connected	ADJ
ejpam-4690	95	13	graph	graph	NOUN
ejpam-4690	95	14	g	g	NOUN
ejpam-4690	95	15	with	with	ADP
ejpam-4690	95	16	γgr(g	γgr(g	PROPN
ejpam-4690	95	17	)	)	PUNCT
ejpam-4690	95	18	=	=	PUNCT
ejpam-4690	96	1	a	a	PRON
ejpam-4690	96	2	and	and	CCONJ
ejpam-4690	96	3	γhgr(g	γhgr(g	NUM
ejpam-4690	96	4	)	)	PUNCT
ejpam-4690	96	5	=	=	SYM
ejpam-4690	96	6	b.	b.	PROPN
ejpam-4690	96	7	hence	hence	ADV
ejpam-4690	96	8	,	,	PUNCT
ejpam-4690	96	9	γhgr(g)−	γhgr(g)−	ADJ
ejpam-4690	96	10	γgr(g	γgr(g	PROPN
ejpam-4690	96	11	)	)	PUNCT
ejpam-4690	96	12	=	=	VERB
ejpam-4690	97	1	n.	n.	NOUN
ejpam-4690	97	2	by	by	ADP
ejpam-4690	97	3	theorem	theorem	NOUN
ejpam-4690	97	4	1(ii	1(ii	NUM
ejpam-4690	97	5	)	)	PUNCT
ejpam-4690	97	6	,	,	PUNCT
ejpam-4690	97	7	there	there	PRON
ejpam-4690	97	8	exists	exist	VERB
ejpam-4690	97	9	a	a	DET
ejpam-4690	97	10	connected	connected	ADJ
ejpam-4690	97	11	graph	graph	NOUN
ejpam-4690	97	12	h	h	NOUN
ejpam-4690	97	13	such	such	ADJ
ejpam-4690	97	14	that	that	DET
ejpam-4690	97	15	γhgr(h	γhgr(h	NOUN
ejpam-4690	97	16	)	)	PUNCT
ejpam-4690	97	17	=	=	PUNCT
ejpam-4690	98	1	a	a	PRON
ejpam-4690	98	2	and	and	CCONJ
ejpam-4690	98	3	γgr(h	γgr(h	PROPN
ejpam-4690	98	4	)	)	PUNCT
ejpam-4690	98	5	=	=	SYM
ejpam-4690	98	6	b.	b.	PROPN
ejpam-4690	99	1	hence	hence	ADV
ejpam-4690	99	2	,	,	PUNCT
ejpam-4690	99	3	γgr(h)−	γgr(h)−	PROPN
ejpam-4690	99	4	γhgr(h	γhgr(h	NOUN
ejpam-4690	99	5	)	)	PUNCT
ejpam-4690	99	6	=	=	VERB
ejpam-4690	100	1	n.	n.	PROPN
ejpam-4690	100	2	j.	j.	PROPN
ejpam-4690	100	3	hassan	hassan	PROPN
ejpam-4690	100	4	,	,	PUNCT
ejpam-4690	100	5	s.	s.	PROPN
ejpam-4690	100	6	canoy	canoy	PROPN
ejpam-4690	100	7	jr	jr	PROPN
ejpam-4690	100	8	.	.	PROPN
ejpam-4690	100	9	/	/	SYM
ejpam-4690	100	10	eur	eur	PROPN
ejpam-4690	100	11	.	.	PUNCT
ejpam-4690	101	1	j.	j.	PROPN
ejpam-4690	101	2	pure	pure	PROPN
ejpam-4690	101	3	appl	appl	PROPN
ejpam-4690	101	4	.	.	PROPN
ejpam-4690	101	5	math	math	PROPN
ejpam-4690	101	6	,	,	PUNCT
ejpam-4690	101	7	16	16	NUM
ejpam-4690	101	8	(	(	PUNCT
ejpam-4690	101	9	2	2	NUM
ejpam-4690	101	10	)	)	PUNCT
ejpam-4690	101	11	(	(	PUNCT
ejpam-4690	101	12	2023	2023	NUM
ejpam-4690	101	13	)	)	PUNCT
ejpam-4690	101	14	,	,	PUNCT
ejpam-4690	101	15	1154	1154	NUM
ejpam-4690	101	16	-	-	SYM
ejpam-4690	101	17	1166	1166	NUM
ejpam-4690	101	18	1158	1158	NUM
ejpam-4690	101	19	the	the	DET
ejpam-4690	101	20	following	following	ADJ
ejpam-4690	101	21	result	result	NOUN
ejpam-4690	101	22	shows	show	VERB
ejpam-4690	101	23	that	that	SCONJ
ejpam-4690	101	24	difference	difference	NOUN
ejpam-4690	101	25	of	of	ADP
ejpam-4690	101	26	the	the	DET
ejpam-4690	101	27	grundy	grundy	PROPN
ejpam-4690	101	28	domination	domination	NOUN
ejpam-4690	101	29	number	number	NOUN
ejpam-4690	101	30	(	(	PUNCT
ejpam-4690	101	31	grundy	grundy	PROPN
ejpam-4690	101	32	hop	hop	PROPN
ejpam-4690	101	33	domination	domination	NOUN
ejpam-4690	101	34	number	number	NOUN
ejpam-4690	101	35	)	)	PUNCT
ejpam-4690	101	36	and	and	CCONJ
ejpam-4690	101	37	domination	domination	NOUN
ejpam-4690	101	38	number	number	NOUN
ejpam-4690	101	39	(	(	PUNCT
ejpam-4690	101	40	resp	resp	NOUN
ejpam-4690	101	41	.	.	PUNCT
ejpam-4690	102	1	hop	hop	PROPN
ejpam-4690	102	2	domination	domination	NOUN
ejpam-4690	102	3	number	number	NOUN
ejpam-4690	102	4	)	)	PUNCT
ejpam-4690	102	5	of	of	ADP
ejpam-4690	102	6	a	a	DET
ejpam-4690	102	7	graph	graph	NOUN
ejpam-4690	102	8	g	g	NOUN
ejpam-4690	102	9	can	can	AUX
ejpam-4690	102	10	be	be	AUX
ejpam-4690	102	11	made	make	VERB
ejpam-4690	102	12	arbitrarily	arbitrarily	ADV
ejpam-4690	102	13	large	large	ADJ
ejpam-4690	102	14	.	.	PUNCT
ejpam-4690	103	1	proposition	proposition	NOUN
ejpam-4690	103	2	1	1	NUM
ejpam-4690	103	3	.	.	PUNCT
ejpam-4690	104	1	let	let	VERB
ejpam-4690	104	2	n	n	PRON
ejpam-4690	104	3	be	be	AUX
ejpam-4690	104	4	a	a	DET
ejpam-4690	104	5	positive	positive	ADJ
ejpam-4690	104	6	integer	integer	NOUN
ejpam-4690	104	7	.	.	PUNCT
ejpam-4690	105	1	then	then	ADV
ejpam-4690	105	2	each	each	PRON
ejpam-4690	105	3	of	of	ADP
ejpam-4690	105	4	the	the	DET
ejpam-4690	105	5	following	following	ADJ
ejpam-4690	105	6	statements	statement	NOUN
ejpam-4690	105	7	holds	hold	VERB
ejpam-4690	105	8	.	.	PUNCT
ejpam-4690	106	1	(	(	PUNCT
ejpam-4690	106	2	i	i	NOUN
ejpam-4690	106	3	)	)	PUNCT
ejpam-4690	106	4	there	there	PRON
ejpam-4690	106	5	exists	exist	VERB
ejpam-4690	106	6	a	a	DET
ejpam-4690	106	7	connected	connected	ADJ
ejpam-4690	106	8	graph	graph	NOUN
ejpam-4690	106	9	g	g	ADP
ejpam-4690	106	10	such	such	ADJ
ejpam-4690	106	11	that	that	SCONJ
ejpam-4690	106	12	γgr(g)−	γgr(g)−	PROPN
ejpam-4690	106	13	γ(g	γ(g	PROPN
ejpam-4690	106	14	)	)	PUNCT
ejpam-4690	107	1	=	=	SYM
ejpam-4690	107	2	n.	n.	NOUN
ejpam-4690	107	3	(	(	PUNCT
ejpam-4690	107	4	ii	ii	NOUN
ejpam-4690	107	5	)	)	PUNCT
ejpam-4690	107	6	there	there	PRON
ejpam-4690	107	7	exists	exist	VERB
ejpam-4690	107	8	a	a	DET
ejpam-4690	107	9	connected	connected	ADJ
ejpam-4690	107	10	graph	graph	NOUN
ejpam-4690	107	11	g′	g′	NOUN
ejpam-4690	107	12	such	such	ADJ
ejpam-4690	107	13	that	that	SCONJ
ejpam-4690	107	14	γhgr(g	γhgr(g	PROPN
ejpam-4690	107	15	′)−	′)−	PROPN
ejpam-4690	107	16	γh(g	γh(g	PUNCT
ejpam-4690	107	17	′	′	NUM
ejpam-4690	107	18	)	)	PUNCT
ejpam-4690	107	19	=	=	SYM
ejpam-4690	108	1	n.	n.	NOUN
ejpam-4690	108	2	proof	proof	NOUN
ejpam-4690	108	3	.	.	PUNCT
ejpam-4690	109	1	(	(	PUNCT
ejpam-4690	109	2	i	i	NOUN
ejpam-4690	109	3	)	)	PUNCT
ejpam-4690	109	4	consider	consider	VERB
ejpam-4690	109	5	the	the	DET
ejpam-4690	109	6	graph	graph	NOUN
ejpam-4690	109	7	g	g	NOUN
ejpam-4690	109	8	in	in	ADP
ejpam-4690	109	9	figure	figure	NOUN
ejpam-4690	109	10	4	4	NUM
ejpam-4690	109	11	.	.	PUNCT
ejpam-4690	110	1	let	let	VERB
ejpam-4690	110	2	d	d	NOUN
ejpam-4690	110	3	=	=	PUNCT
ejpam-4690	110	4	{	{	PUNCT
ejpam-4690	110	5	u	u	NOUN
ejpam-4690	110	6	}	}	PUNCT
ejpam-4690	110	7	and	and	CCONJ
ejpam-4690	110	8	s	s	PROPN
ejpam-4690	110	9	=	=	PUNCT
ejpam-4690	110	10	(	(	PUNCT
ejpam-4690	110	11	v1	v1	PROPN
ejpam-4690	110	12	,	,	PUNCT
ejpam-4690	110	13	v2	v2	NOUN
ejpam-4690	110	14	,	,	PUNCT
ejpam-4690	110	15	.	.	PUNCT
ejpam-4690	110	16	.	.	PUNCT
ejpam-4690	111	1	.	.	PUNCT
ejpam-4690	112	1	,	,	PUNCT
ejpam-4690	112	2	vn+1	vn+1	PROPN
ejpam-4690	112	3	)	)	PUNCT
ejpam-4690	112	4	.	.	PUNCT
ejpam-4690	113	1	then	then	ADV
ejpam-4690	113	2	d	d	PROPN
ejpam-4690	113	3	is	be	AUX
ejpam-4690	113	4	a	a	DET
ejpam-4690	113	5	γ	γ	NOUN
ejpam-4690	113	6	-	-	PUNCT
ejpam-4690	113	7	set	set	VERB
ejpam-4690	113	8	and	and	CCONJ
ejpam-4690	113	9	s	s	NOUN
ejpam-4690	113	10	is	be	AUX
ejpam-4690	113	11	a	a	DET
ejpam-4690	113	12	γgr	γgr	NOUN
ejpam-4690	113	13	-	-	PUNCT
ejpam-4690	113	14	sequence	sequence	NOUN
ejpam-4690	113	15	of	of	ADP
ejpam-4690	113	16	g.	g.	PROPN
ejpam-4690	113	17	hence	hence	ADV
ejpam-4690	113	18	,	,	PUNCT
ejpam-4690	113	19	γ(g	γ(g	PROPN
ejpam-4690	113	20	)	)	PUNCT
ejpam-4690	114	1	=	=	SYM
ejpam-4690	114	2	1	1	NUM
ejpam-4690	114	3	and	and	CCONJ
ejpam-4690	114	4	γgr(g	γgr(g	PROPN
ejpam-4690	114	5	)	)	PUNCT
ejpam-4690	114	6	=	=	SYM
ejpam-4690	115	1	n	n	PROPN
ejpam-4690	115	2	+	+	NUM
ejpam-4690	115	3	1	1	NUM
ejpam-4690	115	4	,	,	PUNCT
ejpam-4690	115	5	that	that	ADV
ejpam-4690	115	6	is	is	ADV
ejpam-4690	115	7	,	,	PUNCT
ejpam-4690	115	8	γgr(g)−	γgr(g)−	ADJ
ejpam-4690	115	9	γ(g	γ(g	PROPN
ejpam-4690	115	10	)	)	PUNCT
ejpam-4690	116	1	=	=	VERB
ejpam-4690	116	2	n.	n.	NOUN
ejpam-4690	116	3	g	g	NOUN
ejpam-4690	116	4	:	:	PUNCT
ejpam-4690	116	5	v1	v1	VERB
ejpam-4690	116	6	v2	v2	PROPN
ejpam-4690	116	7	vn+1	vn+1	PROPN
ejpam-4690	116	8	u	u	NOUN
ejpam-4690	116	9	.	.	PUNCT
ejpam-4690	116	10	.	.	PUNCT
ejpam-4690	116	11	.	.	PUNCT
ejpam-4690	117	1	figure	figure	VERB
ejpam-4690	117	2	4	4	NUM
ejpam-4690	117	3	:	:	PUNCT
ejpam-4690	117	4	a	a	DET
ejpam-4690	117	5	graph	graph	NOUN
ejpam-4690	117	6	g	g	NOUN
ejpam-4690	117	7	with	with	ADP
ejpam-4690	117	8	γgr(g)−	γgr(g)−	NOUN
ejpam-4690	117	9	γ(g	γ(g	PROPN
ejpam-4690	117	10	)	)	PUNCT
ejpam-4690	118	1	=	=	SYM
ejpam-4690	118	2	n	n	PROPN
ejpam-4690	118	3	(	(	PUNCT
ejpam-4690	118	4	ii	ii	NOUN
ejpam-4690	118	5	)	)	PUNCT
ejpam-4690	118	6	consider	consider	VERB
ejpam-4690	118	7	the	the	DET
ejpam-4690	118	8	graph	graph	NOUN
ejpam-4690	118	9	g′	g′	NOUN
ejpam-4690	118	10	given	give	VERB
ejpam-4690	118	11	in	in	ADP
ejpam-4690	118	12	figure	figure	NOUN
ejpam-4690	118	13	5	5	NUM
ejpam-4690	118	14	.	.	PUNCT
ejpam-4690	119	1	let	let	VERB
ejpam-4690	119	2	s1	s1	PROPN
ejpam-4690	119	3	=	=	PUNCT
ejpam-4690	119	4	{	{	PUNCT
ejpam-4690	119	5	u	u	NOUN
ejpam-4690	119	6	,	,	PUNCT
ejpam-4690	119	7	w	w	NOUN
ejpam-4690	119	8	}	}	PUNCT
ejpam-4690	119	9	and	and	CCONJ
ejpam-4690	119	10	s2	s2	VERB
ejpam-4690	119	11	=	=	SYM
ejpam-4690	119	12	(	(	PUNCT
ejpam-4690	119	13	x1	x1	PROPN
ejpam-4690	119	14	,	,	PUNCT
ejpam-4690	119	15	x2	x2	PROPN
ejpam-4690	119	16	,	,	PUNCT
ejpam-4690	119	17	.	.	PUNCT
ejpam-4690	119	18	.	.	PUNCT
ejpam-4690	120	1	.	.	PUNCT
ejpam-4690	121	1	,	,	PUNCT
ejpam-4690	121	2	xn+1	xn+1	PROPN
ejpam-4690	121	3	,	,	PUNCT
ejpam-4690	121	4	w	w	NOUN
ejpam-4690	121	5	)	)	PUNCT
ejpam-4690	121	6	.	.	PUNCT
ejpam-4690	122	1	then	then	ADV
ejpam-4690	122	2	s1	s1	PROPN
ejpam-4690	122	3	is	be	AUX
ejpam-4690	122	4	a	a	DET
ejpam-4690	122	5	γh	γh	ADV
ejpam-4690	122	6	-	-	PUNCT
ejpam-4690	122	7	set	set	VERB
ejpam-4690	122	8	and	and	CCONJ
ejpam-4690	122	9	s2	s2	NOUN
ejpam-4690	122	10	is	be	AUX
ejpam-4690	122	11	a	a	DET
ejpam-4690	122	12	γhgr	γhgr	ADJ
ejpam-4690	122	13	-	-	PUNCT
ejpam-4690	122	14	sequence	sequence	NOUN
ejpam-4690	122	15	of	of	ADP
ejpam-4690	122	16	g′.	g′.	NOUN
ejpam-4690	122	17	therefore	therefore	ADV
ejpam-4690	122	18	,	,	PUNCT
ejpam-4690	122	19	γh(g	γh(g	PUNCT
ejpam-4690	122	20	′	′	NUM
ejpam-4690	122	21	)	)	PUNCT
ejpam-4690	122	22	=	=	SYM
ejpam-4690	122	23	2	2	NUM
ejpam-4690	122	24	and	and	CCONJ
ejpam-4690	122	25	γhgr(g	γhgr(g	PRON
ejpam-4690	122	26	′	′	NUM
ejpam-4690	122	27	)	)	PUNCT
ejpam-4690	122	28	=	=	PRON
ejpam-4690	122	29	n+	n+	PUNCT
ejpam-4690	122	30	2	2	NUM
ejpam-4690	122	31	,	,	PUNCT
ejpam-4690	122	32	that	that	ADV
ejpam-4690	122	33	is	is	ADV
ejpam-4690	122	34	,	,	PUNCT
ejpam-4690	122	35	γhgr(g	γhgr(g	PROPN
ejpam-4690	122	36	′)−	′)−	PROPN
ejpam-4690	122	37	γh(g	γh(g	PUNCT
ejpam-4690	122	38	′	′	NUM
ejpam-4690	122	39	)	)	PUNCT
ejpam-4690	123	1	=	=	VERB
ejpam-4690	123	2	n.	n.	NOUN
ejpam-4690	124	1	x2	x2	PROPN
ejpam-4690	125	1	xn+1x1	xn+1x1	PROPN
ejpam-4690	125	2	g′	g′	NOUN
ejpam-4690	125	3	:	:	PUNCT
ejpam-4690	125	4	.	.	PUNCT
ejpam-4690	125	5	.	.	PUNCT
ejpam-4690	125	6	.	.	PUNCT
ejpam-4690	126	1	w	w	NOUN
ejpam-4690	126	2	u	u	NOUN
ejpam-4690	126	3	figure	figure	NOUN
ejpam-4690	126	4	5	5	NUM
ejpam-4690	126	5	:	:	PUNCT
ejpam-4690	126	6	a	a	DET
ejpam-4690	126	7	graph	graph	NOUN
ejpam-4690	126	8	g′	g′	NOUN
ejpam-4690	126	9	with	with	ADP
ejpam-4690	126	10	γh	γh	X
ejpam-4690	126	11	gr(g	gr(g	X
ejpam-4690	126	12	′)−	′)−	PROPN
ejpam-4690	126	13	γh(g	γh(g	PUNCT
ejpam-4690	126	14	′	′	NUM
ejpam-4690	126	15	)	)	PUNCT
ejpam-4690	126	16	=	=	SYM
ejpam-4690	127	1	n	n	CCONJ
ejpam-4690	127	2	this	this	PRON
ejpam-4690	127	3	proves	prove	VERB
ejpam-4690	127	4	the	the	DET
ejpam-4690	127	5	assertion	assertion	NOUN
ejpam-4690	127	6	.	.	PUNCT
ejpam-4690	128	1	j.	j.	PROPN
ejpam-4690	128	2	hassan	hassan	PROPN
ejpam-4690	128	3	,	,	PUNCT
ejpam-4690	128	4	s.	s.	PROPN
ejpam-4690	128	5	canoy	canoy	PROPN
ejpam-4690	128	6	jr	jr	PROPN
ejpam-4690	128	7	.	.	PROPN
ejpam-4690	128	8	/	/	SYM
ejpam-4690	128	9	eur	eur	PROPN
ejpam-4690	128	10	.	.	PUNCT
ejpam-4690	129	1	j.	j.	PROPN
ejpam-4690	129	2	pure	pure	PROPN
ejpam-4690	129	3	appl	appl	PROPN
ejpam-4690	129	4	.	.	PROPN
ejpam-4690	129	5	math	math	PROPN
ejpam-4690	129	6	,	,	PUNCT
ejpam-4690	129	7	16	16	NUM
ejpam-4690	129	8	(	(	PUNCT
ejpam-4690	129	9	2	2	NUM
ejpam-4690	129	10	)	)	PUNCT
ejpam-4690	129	11	(	(	PUNCT
ejpam-4690	129	12	2023	2023	NUM
ejpam-4690	129	13	)	)	PUNCT
ejpam-4690	129	14	,	,	PUNCT
ejpam-4690	129	15	1154	1154	NUM
ejpam-4690	129	16	-	-	SYM
ejpam-4690	129	17	1166	1166	NUM
ejpam-4690	129	18	1159	1159	NUM
ejpam-4690	129	19	proposition	proposition	NOUN
ejpam-4690	129	20	2	2	NUM
ejpam-4690	129	21	.	.	PUNCT
ejpam-4690	130	1	if	if	SCONJ
ejpam-4690	130	2	d	d	NOUN
ejpam-4690	130	3	=	=	SYM
ejpam-4690	130	4	{	{	PUNCT
ejpam-4690	130	5	v1	v1	NOUN
ejpam-4690	130	6	,	,	PUNCT
ejpam-4690	130	7	.	.	PUNCT
ejpam-4690	130	8	.	.	PUNCT
ejpam-4690	131	1	.	.	PUNCT
ejpam-4690	132	1	,	,	PUNCT
ejpam-4690	132	2	vk	vk	PROPN
ejpam-4690	132	3	}	}	PUNCT
ejpam-4690	132	4	is	be	AUX
ejpam-4690	132	5	a	a	DET
ejpam-4690	132	6	γ	γ	NOUN
ejpam-4690	132	7	-	-	PUNCT
ejpam-4690	132	8	set	set	NOUN
ejpam-4690	132	9	of	of	ADP
ejpam-4690	132	10	g	g	NOUN
ejpam-4690	132	11	,	,	PUNCT
ejpam-4690	132	12	then	then	ADV
ejpam-4690	132	13	(	(	PUNCT
ejpam-4690	132	14	v1	v1	NOUN
ejpam-4690	132	15	,	,	PUNCT
ejpam-4690	132	16	.	.	PUNCT
ejpam-4690	132	17	.	.	PUNCT
ejpam-4690	133	1	.	.	PUNCT
ejpam-4690	134	1	,	,	PUNCT
ejpam-4690	134	2	vk	vk	PROPN
ejpam-4690	134	3	)	)	PUNCT
ejpam-4690	134	4	is	be	AUX
ejpam-4690	134	5	a	a	DET
ejpam-4690	134	6	grundy	grundy	PROPN
ejpam-4690	134	7	dominating	dominating	NOUN
ejpam-4690	134	8	sequence	sequence	NOUN
ejpam-4690	134	9	.	.	PUNCT
ejpam-4690	135	1	in	in	ADP
ejpam-4690	135	2	particular	particular	ADJ
ejpam-4690	135	3	,	,	PUNCT
ejpam-4690	135	4	γ(g	γ(g	PROPN
ejpam-4690	135	5	)	)	PUNCT
ejpam-4690	135	6	≤	≤	PROPN
ejpam-4690	135	7	γgr(g	γgr(g	PROPN
ejpam-4690	135	8	)	)	PUNCT
ejpam-4690	135	9	.	.	PUNCT
ejpam-4690	136	1	proof	proof	NOUN
ejpam-4690	136	2	.	.	PUNCT
ejpam-4690	137	1	let	let	VERB
ejpam-4690	137	2	d	d	NOUN
ejpam-4690	137	3	=	=	SYM
ejpam-4690	137	4	{	{	PUNCT
ejpam-4690	137	5	v1	v1	PROPN
ejpam-4690	137	6	,	,	PUNCT
ejpam-4690	137	7	.	.	PUNCT
ejpam-4690	137	8	.	.	PUNCT
ejpam-4690	138	1	.	.	PUNCT
ejpam-4690	139	1	,	,	PUNCT
ejpam-4690	139	2	vk	vk	PART
ejpam-4690	139	3	}	}	PUNCT
ejpam-4690	139	4	be	be	AUX
ejpam-4690	139	5	a	a	DET
ejpam-4690	139	6	γ	γ	NOUN
ejpam-4690	139	7	-	-	PUNCT
ejpam-4690	139	8	set	set	NOUN
ejpam-4690	139	9	of	of	ADP
ejpam-4690	139	10	g.	g.	PROPN
ejpam-4690	139	11	suppose	suppose	VERB
ejpam-4690	139	12	s	s	VERB
ejpam-4690	139	13	=	=	SYM
ejpam-4690	139	14	(	(	PUNCT
ejpam-4690	139	15	v1	v1	PROPN
ejpam-4690	139	16	,	,	PUNCT
ejpam-4690	139	17	v2	v2	NOUN
ejpam-4690	139	18	,	,	PUNCT
ejpam-4690	139	19	.	.	PUNCT
ejpam-4690	139	20	.	.	PUNCT
ejpam-4690	140	1	.	.	PUNCT
ejpam-4690	141	1	,	,	PUNCT
ejpam-4690	141	2	vk	vk	PROPN
ejpam-4690	141	3	)	)	PUNCT
ejpam-4690	141	4	is	be	AUX
ejpam-4690	141	5	not	not	PART
ejpam-4690	141	6	a	a	DET
ejpam-4690	141	7	legal	legal	ADJ
ejpam-4690	141	8	closed	closed	ADJ
ejpam-4690	141	9	neighborhood	neighborhood	NOUN
ejpam-4690	141	10	sequence	sequence	NOUN
ejpam-4690	141	11	of	of	ADP
ejpam-4690	141	12	g.	g.	PROPN
ejpam-4690	141	13	then	then	ADV
ejpam-4690	141	14	there	there	PRON
ejpam-4690	141	15	exists	exist	VERB
ejpam-4690	141	16	i	i	PRON
ejpam-4690	141	17	∈	∈	PROPN
ejpam-4690	141	18	{	{	PUNCT
ejpam-4690	141	19	2	2	NUM
ejpam-4690	141	20	,	,	PUNCT
ejpam-4690	141	21	3	3	NUM
ejpam-4690	141	22	,	,	PUNCT
ejpam-4690	141	23	.	.	PUNCT
ejpam-4690	141	24	.	.	PUNCT
ejpam-4690	142	1	.	.	PUNCT
ejpam-4690	143	1	,	,	PUNCT
ejpam-4690	143	2	k	k	X
ejpam-4690	143	3	}	}	PUNCT
ejpam-4690	143	4	such	such	ADJ
ejpam-4690	143	5	that	that	SCONJ
ejpam-4690	143	6	ng[vi	ng[vi	PROPN
ejpam-4690	143	7	]	]	PUNCT
ejpam-4690	143	8	\	\	X
ejpam-4690	143	9	∪i−1	∪i−1	PROPN
ejpam-4690	143	10	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4690	143	11	]	]	PUNCT
ejpam-4690	143	12	=	=	PUNCT
ejpam-4690	143	13	∅.	∅.	PRON
ejpam-4690	143	14	this	this	PRON
ejpam-4690	143	15	implies	imply	VERB
ejpam-4690	143	16	that	that	SCONJ
ejpam-4690	143	17	ng[vi	ng[vi	PROPN
ejpam-4690	143	18	]	]	X
ejpam-4690	143	19	⊆	⊆	NUM
ejpam-4690	143	20	∪i−1	∪i−1	X
ejpam-4690	143	21	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4690	143	22	]	]	PUNCT
ejpam-4690	143	23	.	.	PUNCT
ejpam-4690	144	1	thus	thus	ADV
ejpam-4690	144	2	,	,	PUNCT
ejpam-4690	144	3	ŝ	ŝ	CCONJ
ejpam-4690	144	4	\	\	PROPN
ejpam-4690	144	5	{	{	PUNCT
ejpam-4690	144	6	vi	vi	NOUN
ejpam-4690	144	7	}	}	PUNCT
ejpam-4690	144	8	=	=	SYM
ejpam-4690	144	9	d	d	X
ejpam-4690	144	10	\	\	PROPN
ejpam-4690	144	11	{	{	PUNCT
ejpam-4690	144	12	vi	vi	NOUN
ejpam-4690	144	13	}	}	PUNCT
ejpam-4690	144	14	is	be	AUX
ejpam-4690	144	15	a	a	DET
ejpam-4690	144	16	dominating	dominating	NOUN
ejpam-4690	144	17	set	set	NOUN
ejpam-4690	144	18	of	of	ADP
ejpam-4690	144	19	g	g	NOUN
ejpam-4690	144	20	,	,	PUNCT
ejpam-4690	144	21	contradicting	contradict	VERB
ejpam-4690	144	22	the	the	DET
ejpam-4690	144	23	the	the	DET
ejpam-4690	144	24	minimality	minimality	NOUN
ejpam-4690	144	25	of	of	ADP
ejpam-4690	144	26	d.	d.	PROPN
ejpam-4690	144	27	therefore	therefore	ADV
ejpam-4690	144	28	,	,	PUNCT
ejpam-4690	144	29	ng[vi]\∪i−1	ng[vi]\∪i−1	PROPN
ejpam-4690	144	30	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4690	144	31	]	]	PUNCT
ejpam-4690	144	32	̸=	̸=	PROPN
ejpam-4690	144	33	∅	∅	NOUN
ejpam-4690	144	34	for	for	ADP
ejpam-4690	144	35	each	each	DET
ejpam-4690	144	36	i	i	PRON
ejpam-4690	144	37	∈	∈	PROPN
ejpam-4690	144	38	{	{	PUNCT
ejpam-4690	144	39	2	2	NUM
ejpam-4690	144	40	,	,	PUNCT
ejpam-4690	144	41	3	3	NUM
ejpam-4690	144	42	,	,	PUNCT
ejpam-4690	144	43	.	.	PUNCT
ejpam-4690	144	44	.	.	PUNCT
ejpam-4690	144	45	.	.	PUNCT
ejpam-4690	145	1	,	,	PUNCT
ejpam-4690	145	2	k	k	X
ejpam-4690	145	3	}	}	PUNCT
ejpam-4690	145	4	,	,	PUNCT
ejpam-4690	145	5	showing	show	VERB
ejpam-4690	145	6	that	that	SCONJ
ejpam-4690	145	7	s	s	VERB
ejpam-4690	145	8	is	be	AUX
ejpam-4690	145	9	a	a	DET
ejpam-4690	145	10	grundy	grundy	PROPN
ejpam-4690	145	11	dominating	dominating	NOUN
ejpam-4690	145	12	sequence	sequence	NOUN
ejpam-4690	145	13	of	of	ADP
ejpam-4690	145	14	g.	g.	PROPN
ejpam-4690	145	15	proposition	proposition	PROPN
ejpam-4690	145	16	3	3	X
ejpam-4690	145	17	.	.	PUNCT
ejpam-4690	146	1	let	let	VERB
ejpam-4690	146	2	g	g	PRON
ejpam-4690	146	3	be	be	AUX
ejpam-4690	146	4	a	a	DET
ejpam-4690	146	5	graph	graph	NOUN
ejpam-4690	146	6	on	on	ADP
ejpam-4690	146	7	n	n	DET
ejpam-4690	146	8	vertices	vertex	NOUN
ejpam-4690	146	9	.	.	PUNCT
ejpam-4690	147	1	if	if	SCONJ
ejpam-4690	147	2	s	s	PRON
ejpam-4690	147	3	=	=	PUNCT
ejpam-4690	147	4	(	(	PUNCT
ejpam-4690	147	5	u1	u1	PROPN
ejpam-4690	147	6	,	,	PUNCT
ejpam-4690	147	7	v2	v2	PROPN
ejpam-4690	147	8	,	,	PUNCT
ejpam-4690	147	9	·	·	PUNCT
ejpam-4690	147	10	·	·	PUNCT
ejpam-4690	147	11	·	·	PUNCT
ejpam-4690	147	12	,	,	PUNCT
ejpam-4690	147	13	uk	uk	PROPN
ejpam-4690	147	14	)	)	PUNCT
ejpam-4690	147	15	is	be	AUX
ejpam-4690	147	16	a	a	DET
ejpam-4690	147	17	grundy	grundy	PROPN
ejpam-4690	147	18	dominating	dominating	NOUN
ejpam-4690	147	19	sequence	sequence	NOUN
ejpam-4690	147	20	of	of	ADP
ejpam-4690	147	21	smallest	small	ADJ
ejpam-4690	147	22	length	length	NOUN
ejpam-4690	147	23	k	k	NOUN
ejpam-4690	147	24	,	,	PUNCT
ejpam-4690	147	25	then	then	ADV
ejpam-4690	147	26	γ(g	γ(g	PROPN
ejpam-4690	147	27	)	)	PUNCT
ejpam-4690	148	1	=	=	PUNCT
ejpam-4690	148	2	|ŝ|	|ŝ|	PUNCT
ejpam-4690	148	3	=	=	SYM
ejpam-4690	148	4	k.	k.	NOUN
ejpam-4690	148	5	proof	proof	NOUN
ejpam-4690	148	6	.	.	PUNCT
ejpam-4690	149	1	since	since	SCONJ
ejpam-4690	149	2	ŝ	ŝ	NUM
ejpam-4690	149	3	is	be	AUX
ejpam-4690	149	4	a	a	DET
ejpam-4690	149	5	dominating	dominating	NOUN
ejpam-4690	149	6	set	set	NOUN
ejpam-4690	149	7	of	of	ADP
ejpam-4690	149	8	g	g	NOUN
ejpam-4690	149	9	,	,	PUNCT
ejpam-4690	149	10	it	it	PRON
ejpam-4690	149	11	follows	follow	VERB
ejpam-4690	149	12	that	that	SCONJ
ejpam-4690	149	13	γ(g	γ(g	PROPN
ejpam-4690	149	14	)	)	PUNCT
ejpam-4690	149	15	≤	≤	PUNCT
ejpam-4690	149	16	|ŝ|	|ŝ|	PROPN
ejpam-4690	149	17	.	.	PUNCT
ejpam-4690	150	1	on	on	ADP
ejpam-4690	150	2	the	the	DET
ejpam-4690	150	3	other	other	ADJ
ejpam-4690	150	4	hand	hand	NOUN
ejpam-4690	150	5	,	,	PUNCT
ejpam-4690	150	6	by	by	ADP
ejpam-4690	150	7	proposition	proposition	NOUN
ejpam-4690	150	8	2	2	NUM
ejpam-4690	150	9	and	and	CCONJ
ejpam-4690	150	10	the	the	DET
ejpam-4690	150	11	assumption	assumption	NOUN
ejpam-4690	150	12	that	that	PRON
ejpam-4690	150	13	s	s	VERB
ejpam-4690	150	14	a	a	DET
ejpam-4690	150	15	grundy	grundy	PROPN
ejpam-4690	150	16	dominating	dominating	NOUN
ejpam-4690	150	17	sequence	sequence	NOUN
ejpam-4690	150	18	of	of	ADP
ejpam-4690	150	19	smallest	small	ADJ
ejpam-4690	150	20	length	length	NOUN
ejpam-4690	150	21	k	k	NOUN
ejpam-4690	150	22	,	,	PUNCT
ejpam-4690	150	23	|ŝ|	|ŝ|	PROPN
ejpam-4690	150	24	≤	≤	PROPN
ejpam-4690	150	25	γ(g	γ(g	PROPN
ejpam-4690	150	26	)	)	PUNCT
ejpam-4690	150	27	.	.	PUNCT
ejpam-4690	151	1	consequently	consequently	ADV
ejpam-4690	151	2	,	,	PUNCT
ejpam-4690	151	3	γ(g	γ(g	PROPN
ejpam-4690	151	4	)	)	PUNCT
ejpam-4690	151	5	=	=	PUNCT
ejpam-4690	151	6	|ŝ|	|ŝ|	PUNCT
ejpam-4690	151	7	=	=	SYM
ejpam-4690	151	8	k.	k.	NOUN
ejpam-4690	151	9	theorem	theorem	NOUN
ejpam-4690	151	10	2	2	X
ejpam-4690	151	11	.	.	PUNCT
ejpam-4690	152	1	let	let	VERB
ejpam-4690	152	2	g	g	PRON
ejpam-4690	152	3	be	be	AUX
ejpam-4690	152	4	a	a	DET
ejpam-4690	152	5	graph	graph	NOUN
ejpam-4690	152	6	.	.	PUNCT
ejpam-4690	153	1	then	then	ADV
ejpam-4690	153	2	s	s	VERB
ejpam-4690	153	3	=	=	SYM
ejpam-4690	153	4	(	(	PUNCT
ejpam-4690	153	5	s1	s1	PROPN
ejpam-4690	153	6	,	,	PUNCT
ejpam-4690	153	7	s2	s2	PROPN
ejpam-4690	153	8	,	,	PUNCT
ejpam-4690	153	9	·	·	PUNCT
ejpam-4690	153	10	·	·	PUNCT
ejpam-4690	153	11	·	·	PUNCT
ejpam-4690	153	12	,	,	PUNCT
ejpam-4690	153	13	sk	sk	PROPN
ejpam-4690	153	14	)	)	PUNCT
ejpam-4690	153	15	is	be	AUX
ejpam-4690	153	16	a	a	DET
ejpam-4690	153	17	maximum	maximum	ADJ
ejpam-4690	153	18	legal	legal	ADJ
ejpam-4690	153	19	closed	closed	ADJ
ejpam-4690	153	20	neighborhood	neighborhood	NOUN
ejpam-4690	153	21	sequence	sequence	NOUN
ejpam-4690	153	22	of	of	ADP
ejpam-4690	153	23	g	g	PROPN
ejpam-4690	153	24	if	if	SCONJ
ejpam-4690	154	1	and	and	CCONJ
ejpam-4690	154	2	only	only	ADV
ejpam-4690	154	3	if	if	SCONJ
ejpam-4690	154	4	s	s	NOUN
ejpam-4690	154	5	is	be	AUX
ejpam-4690	154	6	a	a	DET
ejpam-4690	154	7	grundy	grundy	PROPN
ejpam-4690	154	8	dominating	dominating	NOUN
ejpam-4690	154	9	sequence	sequence	NOUN
ejpam-4690	154	10	of	of	ADP
ejpam-4690	154	11	g	g	NOUN
ejpam-4690	154	12	with	with	ADP
ejpam-4690	154	13	γgr(g	γgr(g	PROPN
ejpam-4690	154	14	)	)	PUNCT
ejpam-4690	155	1	=	=	PUNCT
ejpam-4690	155	2	k.	k.	NOUN
ejpam-4690	155	3	proof	proof	NOUN
ejpam-4690	155	4	.	.	PUNCT
ejpam-4690	156	1	let	let	VERB
ejpam-4690	156	2	s	s	PRON
ejpam-4690	156	3	=	=	PUNCT
ejpam-4690	156	4	(	(	PUNCT
ejpam-4690	156	5	s1	s1	PROPN
ejpam-4690	156	6	,	,	PUNCT
ejpam-4690	156	7	s2	s2	PROPN
ejpam-4690	156	8	,	,	PUNCT
ejpam-4690	156	9	·	·	PUNCT
ejpam-4690	156	10	·	·	PUNCT
ejpam-4690	156	11	·	·	PUNCT
ejpam-4690	156	12	,	,	PUNCT
ejpam-4690	156	13	sk	sk	PART
ejpam-4690	156	14	)	)	PUNCT
ejpam-4690	156	15	be	be	AUX
ejpam-4690	156	16	a	a	DET
ejpam-4690	156	17	maximum	maximum	ADJ
ejpam-4690	156	18	legal	legal	ADJ
ejpam-4690	156	19	closed	closed	ADJ
ejpam-4690	156	20	neighborhood	neighborhood	NOUN
ejpam-4690	156	21	sequence	sequence	NOUN
ejpam-4690	156	22	of	of	ADP
ejpam-4690	156	23	g.	g.	PROPN
ejpam-4690	156	24	suppose	suppose	VERB
ejpam-4690	156	25	ŝ	ŝ	PROPN
ejpam-4690	156	26	is	be	AUX
ejpam-4690	156	27	not	not	PART
ejpam-4690	156	28	a	a	DET
ejpam-4690	156	29	dominating	dominating	NOUN
ejpam-4690	156	30	set	set	NOUN
ejpam-4690	156	31	of	of	ADP
ejpam-4690	156	32	g.	g.	PROPN
ejpam-4690	156	33	then	then	ADV
ejpam-4690	156	34	there	there	PRON
ejpam-4690	156	35	exists	exist	VERB
ejpam-4690	156	36	v	v	ADP
ejpam-4690	156	37	∈	∈	PROPN
ejpam-4690	156	38	v	v	NOUN
ejpam-4690	156	39	(	(	PUNCT
ejpam-4690	156	40	g)\ng[ŝ	g)\ng[ŝ	PROPN
ejpam-4690	156	41	]	]	X
ejpam-4690	156	42	.	.	PUNCT
ejpam-4690	157	1	this	this	PRON
ejpam-4690	157	2	implies	imply	VERB
ejpam-4690	157	3	that	that	PRON
ejpam-4690	157	4	v	v	X
ejpam-4690	157	5	/∈	/∈	PUNCT
ejpam-4690	158	1	ng[u	ng[u	PROPN
ejpam-4690	158	2	]	]	PUNCT
ejpam-4690	158	3	for	for	ADP
ejpam-4690	158	4	every	every	DET
ejpam-4690	158	5	u	u	PROPN
ejpam-4690	158	6	∈	∈	PROPN
ejpam-4690	158	7	ŝ.	ŝ.	NOUN
ejpam-4690	158	8	let	let	VERB
ejpam-4690	158	9	s∗	s∗	PROPN
ejpam-4690	158	10	=	=	SYM
ejpam-4690	158	11	(	(	PUNCT
ejpam-4690	158	12	s1	s1	NOUN
ejpam-4690	158	13	,	,	PUNCT
ejpam-4690	158	14	s2	s2	PROPN
ejpam-4690	158	15	,	,	PUNCT
ejpam-4690	158	16	·	·	PUNCT
ejpam-4690	158	17	·	·	PUNCT
ejpam-4690	158	18	·	·	PUNCT
ejpam-4690	158	19	,	,	PUNCT
ejpam-4690	158	20	sk	sk	INTJ
ejpam-4690	158	21	,	,	PUNCT
ejpam-4690	158	22	v	v	NOUN
ejpam-4690	158	23	)	)	PUNCT
ejpam-4690	158	24	.	.	PUNCT
ejpam-4690	159	1	then	then	ADV
ejpam-4690	159	2	ng[v]\∪k	ng[v]\∪k	VERB
ejpam-4690	159	3	j=1ng[si	j=1ng[si	PROPN
ejpam-4690	159	4	]	]	X
ejpam-4690	159	5	̸=	̸=	PROPN
ejpam-4690	159	6	∅.	∅.	ADV
ejpam-4690	159	7	it	it	PRON
ejpam-4690	159	8	follows	follow	VERB
ejpam-4690	159	9	that	that	SCONJ
ejpam-4690	159	10	s∗	s∗	PROPN
ejpam-4690	159	11	is	be	AUX
ejpam-4690	159	12	a	a	DET
ejpam-4690	159	13	legal	legal	ADJ
ejpam-4690	159	14	closed	closed	ADJ
ejpam-4690	159	15	neighborhood	neighborhood	NOUN
ejpam-4690	159	16	sequence	sequence	NOUN
ejpam-4690	159	17	of	of	ADP
ejpam-4690	159	18	g	g	NOUN
ejpam-4690	159	19	,	,	PUNCT
ejpam-4690	159	20	a	a	DET
ejpam-4690	159	21	contradiction	contradiction	NOUN
ejpam-4690	159	22	to	to	ADP
ejpam-4690	159	23	the	the	DET
ejpam-4690	159	24	maximality	maximality	NOUN
ejpam-4690	159	25	of	of	ADP
ejpam-4690	159	26	s.	s.	PROPN
ejpam-4690	159	27	thus	thus	ADV
ejpam-4690	159	28	,	,	PUNCT
ejpam-4690	159	29	ŝ	ŝ	X
ejpam-4690	159	30	is	be	AUX
ejpam-4690	159	31	a	a	DET
ejpam-4690	159	32	dominating	dominating	NOUN
ejpam-4690	159	33	set	set	NOUN
ejpam-4690	159	34	of	of	ADP
ejpam-4690	159	35	g.	g.	PROPN
ejpam-4690	159	36	therefore	therefore	ADV
ejpam-4690	159	37	,	,	PUNCT
ejpam-4690	159	38	by	by	ADP
ejpam-4690	159	39	assumption	assumption	NOUN
ejpam-4690	159	40	,	,	PUNCT
ejpam-4690	159	41	s	s	X
ejpam-4690	159	42	is	be	AUX
ejpam-4690	159	43	a	a	DET
ejpam-4690	159	44	grundy	grundy	PROPN
ejpam-4690	159	45	dominating	dominating	NOUN
ejpam-4690	159	46	sequence	sequence	NOUN
ejpam-4690	159	47	of	of	ADP
ejpam-4690	159	48	g	g	PROPN
ejpam-4690	159	49	and	and	CCONJ
ejpam-4690	159	50	γgr(g	γgr(g	PROPN
ejpam-4690	159	51	)	)	PUNCT
ejpam-4690	159	52	=	=	VERB
ejpam-4690	160	1	k.	k.	NOUN
ejpam-4690	161	1	the	the	DET
ejpam-4690	161	2	converse	converse	NOUN
ejpam-4690	161	3	is	be	AUX
ejpam-4690	161	4	clear	clear	ADJ
ejpam-4690	161	5	.	.	PUNCT
ejpam-4690	162	1	the	the	DET
ejpam-4690	162	2	next	next	ADJ
ejpam-4690	162	3	result	result	NOUN
ejpam-4690	162	4	follows	follow	VERB
ejpam-4690	162	5	from	from	ADP
ejpam-4690	162	6	theorem	theorem	ADJ
ejpam-4690	162	7	2	2	NUM
ejpam-4690	162	8	corollary	corollary	NOUN
ejpam-4690	162	9	2	2	NUM
ejpam-4690	162	10	.	.	PUNCT
ejpam-4690	163	1	let	let	VERB
ejpam-4690	163	2	g	g	PRON
ejpam-4690	163	3	be	be	AUX
ejpam-4690	163	4	a	a	DET
ejpam-4690	163	5	graph	graph	NOUN
ejpam-4690	163	6	and	and	CCONJ
ejpam-4690	163	7	let	let	VERB
ejpam-4690	163	8	s	s	PRON
ejpam-4690	163	9	=	=	PUNCT
ejpam-4690	163	10	(	(	PUNCT
ejpam-4690	163	11	s1	s1	PROPN
ejpam-4690	163	12	,	,	PUNCT
ejpam-4690	163	13	s2	s2	NOUN
ejpam-4690	163	14	,	,	PUNCT
ejpam-4690	163	15	.	.	PUNCT
ejpam-4690	163	16	.	.	PUNCT
ejpam-4690	164	1	.	.	PUNCT
ejpam-4690	165	1	,	,	PUNCT
ejpam-4690	165	2	sm	sm	X
ejpam-4690	165	3	)	)	PUNCT
ejpam-4690	165	4	be	be	VERB
ejpam-4690	165	5	a	a	DET
ejpam-4690	165	6	legal	legal	ADJ
ejpam-4690	165	7	closed	closed	ADJ
ejpam-4690	165	8	neighborhood	neighborhood	NOUN
ejpam-4690	165	9	sequence	sequence	NOUN
ejpam-4690	165	10	of	of	ADP
ejpam-4690	165	11	g.	g.	PROPN
ejpam-4690	165	12	then	then	ADV
ejpam-4690	165	13	|ŝ|	|ŝ|	PROPN
ejpam-4690	165	14	=	=	SYM
ejpam-4690	165	15	m	m	VERB
ejpam-4690	165	16	≤	≤	ADJ
ejpam-4690	165	17	γgr(g	γgr(g	PROPN
ejpam-4690	165	18	)	)	PUNCT
ejpam-4690	165	19	.	.	PUNCT
ejpam-4690	166	1	theorem	theorem	NOUN
ejpam-4690	166	2	3	3	X
ejpam-4690	166	3	.	.	PUNCT
ejpam-4690	167	1	let	let	VERB
ejpam-4690	167	2	g	g	PRON
ejpam-4690	167	3	be	be	AUX
ejpam-4690	167	4	a	a	DET
ejpam-4690	167	5	graph	graph	NOUN
ejpam-4690	167	6	on	on	ADP
ejpam-4690	167	7	n	n	DET
ejpam-4690	167	8	vertices	vertex	NOUN
ejpam-4690	167	9	.	.	PUNCT
ejpam-4690	168	1	then	then	ADV
ejpam-4690	168	2	γgr(g	γgr(g	PROPN
ejpam-4690	168	3	)	)	PUNCT
ejpam-4690	168	4	=	=	SYM
ejpam-4690	168	5	α(g	α(g	NUM
ejpam-4690	168	6	)	)	PUNCT
ejpam-4690	168	7	if	if	SCONJ
ejpam-4690	168	8	and	and	CCONJ
ejpam-4690	168	9	only	only	ADV
ejpam-4690	168	10	if	if	SCONJ
ejpam-4690	168	11	every	every	DET
ejpam-4690	168	12	α	α	NOUN
ejpam-4690	168	13	-	-	PUNCT
ejpam-4690	168	14	set	set	NOUN
ejpam-4690	168	15	is	be	AUX
ejpam-4690	168	16	induced	induce	VERB
ejpam-4690	168	17	by	by	ADP
ejpam-4690	168	18	a	a	DET
ejpam-4690	168	19	maximum	maximum	ADJ
ejpam-4690	168	20	legal	legal	ADJ
ejpam-4690	168	21	closed	closed	ADJ
ejpam-4690	168	22	neighborhood	neighborhood	NOUN
ejpam-4690	168	23	sequence	sequence	NOUN
ejpam-4690	168	24	of	of	ADP
ejpam-4690	168	25	g.	g.	PROPN
ejpam-4690	168	26	proof	proof	PROPN
ejpam-4690	168	27	.	.	PUNCT
ejpam-4690	169	1	suppose	suppose	VERB
ejpam-4690	169	2	γgr(g	γgr(g	PROPN
ejpam-4690	169	3	)	)	PUNCT
ejpam-4690	169	4	=	=	SYM
ejpam-4690	169	5	α(g	α(g	NUM
ejpam-4690	169	6	)	)	PUNCT
ejpam-4690	169	7	.	.	PUNCT
ejpam-4690	170	1	let	let	VERB
ejpam-4690	170	2	d	d	NOUN
ejpam-4690	170	3	=	=	SYM
ejpam-4690	170	4	{	{	PUNCT
ejpam-4690	170	5	v1	v1	PROPN
ejpam-4690	170	6	,	,	PUNCT
ejpam-4690	170	7	.	.	PUNCT
ejpam-4690	170	8	.	.	PUNCT
ejpam-4690	171	1	.	.	PUNCT
ejpam-4690	172	1	,	,	PUNCT
ejpam-4690	172	2	vk	vk	PART
ejpam-4690	172	3	}	}	PUNCT
ejpam-4690	172	4	be	be	AUX
ejpam-4690	172	5	a	a	DET
ejpam-4690	172	6	maximum	maximum	ADJ
ejpam-4690	172	7	independent	independent	ADJ
ejpam-4690	172	8	set	set	NOUN
ejpam-4690	172	9	of	of	ADP
ejpam-4690	172	10	g	g	NOUN
ejpam-4690	172	11	and	and	CCONJ
ejpam-4690	172	12	let	let	VERB
ejpam-4690	172	13	s	s	AUX
ejpam-4690	172	14	=	=	PUNCT
ejpam-4690	172	15	(	(	PUNCT
ejpam-4690	172	16	v1	v1	PROPN
ejpam-4690	172	17	,	,	PUNCT
ejpam-4690	172	18	.	.	PUNCT
ejpam-4690	172	19	.	.	PUNCT
ejpam-4690	173	1	.	.	PUNCT
ejpam-4690	174	1	,	,	PUNCT
ejpam-4690	174	2	vk	vk	PROPN
ejpam-4690	174	3	)	)	PUNCT
ejpam-4690	174	4	.	.	PUNCT
ejpam-4690	175	1	then	then	ADV
ejpam-4690	175	2	ŝ	ŝ	VERB
ejpam-4690	176	1	=	=	PUNCT
ejpam-4690	176	2	d	d	NOUN
ejpam-4690	176	3	is	be	AUX
ejpam-4690	176	4	a	a	DET
ejpam-4690	176	5	dominating	dominating	NOUN
ejpam-4690	176	6	set	set	NOUN
ejpam-4690	176	7	of	of	ADP
ejpam-4690	176	8	g.	g.	PROPN
ejpam-4690	176	9	moreover	moreover	ADV
ejpam-4690	176	10	,	,	PUNCT
ejpam-4690	176	11	since	since	SCONJ
ejpam-4690	176	12	ŝ	ŝ	NUM
ejpam-4690	176	13	is	be	AUX
ejpam-4690	176	14	an	an	DET
ejpam-4690	176	15	independent	independent	ADJ
ejpam-4690	176	16	set	set	NOUN
ejpam-4690	176	17	,	,	PUNCT
ejpam-4690	176	18	vi	vi	PROPN
ejpam-4690	176	19	∈	∈	PROPN
ejpam-4690	176	20	ng[vi	ng[vi	PROPN
ejpam-4690	176	21	]	]	PUNCT
ejpam-4690	176	22	\	\	PROPN
ejpam-4690	176	23	⋃i−1	⋃i−1	NOUN
ejpam-4690	176	24	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4690	176	25	]	]	PUNCT
ejpam-4690	176	26	for	for	ADP
ejpam-4690	176	27	each	each	DET
ejpam-4690	176	28	i	i	PRON
ejpam-4690	176	29	∈	∈	PROPN
ejpam-4690	176	30	{	{	PUNCT
ejpam-4690	176	31	2	2	NUM
ejpam-4690	176	32	,	,	PUNCT
ejpam-4690	176	33	.	.	PUNCT
ejpam-4690	176	34	.	.	PUNCT
ejpam-4690	177	1	.	.	PUNCT
ejpam-4690	178	1	,	,	PUNCT
ejpam-4690	178	2	k	k	X
ejpam-4690	178	3	}	}	PUNCT
ejpam-4690	178	4	.	.	PUNCT
ejpam-4690	179	1	hence	hence	ADV
ejpam-4690	179	2	,	,	PUNCT
ejpam-4690	179	3	s	s	VERB
ejpam-4690	179	4	is	be	AUX
ejpam-4690	179	5	a	a	DET
ejpam-4690	179	6	legal	legal	ADJ
ejpam-4690	179	7	closed	closed	ADJ
ejpam-4690	179	8	neighborhood	neighborhood	NOUN
ejpam-4690	179	9	sequence	sequence	NOUN
ejpam-4690	179	10	of	of	ADP
ejpam-4690	179	11	g.	g.	PROPN
ejpam-4690	179	12	since	since	SCONJ
ejpam-4690	179	13	γgr(g	γgr(g	PROPN
ejpam-4690	179	14	)	)	PUNCT
ejpam-4690	179	15	=	=	SYM
ejpam-4690	180	1	α(g	α(g	NUM
ejpam-4690	180	2	)	)	PUNCT
ejpam-4690	180	3	,	,	PUNCT
ejpam-4690	180	4	s	s	VERB
ejpam-4690	180	5	is	be	AUX
ejpam-4690	180	6	a	a	DET
ejpam-4690	180	7	maximum	maximum	ADJ
ejpam-4690	180	8	legal	legal	ADJ
ejpam-4690	180	9	closed	closed	ADJ
ejpam-4690	180	10	neighborhood	neighborhood	NOUN
ejpam-4690	180	11	sequence	sequence	NOUN
ejpam-4690	180	12	of	of	ADP
ejpam-4690	180	13	g	g	NOUN
ejpam-4690	180	14	by	by	ADP
ejpam-4690	180	15	theorem	theorem	NOUN
ejpam-4690	180	16	2	2	NUM
ejpam-4690	180	17	.	.	PUNCT
ejpam-4690	181	1	therefore	therefore	ADV
ejpam-4690	181	2	,	,	PUNCT
ejpam-4690	181	3	α	α	X
ejpam-4690	181	4	-	-	PUNCT
ejpam-4690	181	5	set	set	NOUN
ejpam-4690	181	6	is	be	AUX
ejpam-4690	181	7	induced	induce	VERB
ejpam-4690	181	8	by	by	ADP
ejpam-4690	181	9	a	a	DET
ejpam-4690	181	10	maximum	maximum	ADJ
ejpam-4690	181	11	legal	legal	ADJ
ejpam-4690	181	12	closed	closed	ADJ
ejpam-4690	181	13	neighborhood	neighborhood	NOUN
ejpam-4690	181	14	sequence	sequence	NOUN
ejpam-4690	181	15	of	of	ADP
ejpam-4690	181	16	g.	g.	PROPN
ejpam-4690	181	17	for	for	ADP
ejpam-4690	181	18	the	the	DET
ejpam-4690	181	19	converse	converse	NOUN
ejpam-4690	181	20	,	,	PUNCT
ejpam-4690	181	21	suppose	suppose	VERB
ejpam-4690	181	22	that	that	SCONJ
ejpam-4690	181	23	every	every	DET
ejpam-4690	181	24	α	α	X
ejpam-4690	181	25	-	-	PUNCT
ejpam-4690	181	26	set	set	NOUN
ejpam-4690	181	27	is	be	AUX
ejpam-4690	181	28	induced	induce	VERB
ejpam-4690	181	29	by	by	ADP
ejpam-4690	181	30	a	a	DET
ejpam-4690	181	31	maximum	maximum	ADJ
ejpam-4690	181	32	legal	legal	ADJ
ejpam-4690	181	33	closed	closed	ADJ
ejpam-4690	181	34	neighborhood	neighborhood	NOUN
ejpam-4690	181	35	sequence	sequence	NOUN
ejpam-4690	181	36	of	of	ADP
ejpam-4690	181	37	g.	g.	PROPN
ejpam-4690	181	38	by	by	ADP
ejpam-4690	181	39	theorem	theorem	NOUN
ejpam-4690	181	40	2	2	NUM
ejpam-4690	181	41	,	,	PUNCT
ejpam-4690	181	42	γgr(g	γgr(g	PROPN
ejpam-4690	181	43	)	)	PUNCT
ejpam-4690	181	44	=	=	SYM
ejpam-4690	182	1	α(g	α(g	NUM
ejpam-4690	182	2	)	)	PUNCT
ejpam-4690	182	3	.	.	PUNCT
ejpam-4690	183	1	j.	j.	PROPN
ejpam-4690	183	2	hassan	hassan	PROPN
ejpam-4690	183	3	,	,	PUNCT
ejpam-4690	183	4	s.	s.	PROPN
ejpam-4690	183	5	canoy	canoy	PROPN
ejpam-4690	183	6	jr	jr	PROPN
ejpam-4690	183	7	.	.	PROPN
ejpam-4690	183	8	/	/	SYM
ejpam-4690	183	9	eur	eur	PROPN
ejpam-4690	183	10	.	.	PUNCT
ejpam-4690	184	1	j.	j.	PROPN
ejpam-4690	184	2	pure	pure	PROPN
ejpam-4690	184	3	appl	appl	PROPN
ejpam-4690	184	4	.	.	PROPN
ejpam-4690	184	5	math	math	PROPN
ejpam-4690	184	6	,	,	PUNCT
ejpam-4690	184	7	16	16	NUM
ejpam-4690	184	8	(	(	PUNCT
ejpam-4690	184	9	2	2	NUM
ejpam-4690	184	10	)	)	PUNCT
ejpam-4690	184	11	(	(	PUNCT
ejpam-4690	184	12	2023	2023	NUM
ejpam-4690	184	13	)	)	PUNCT
ejpam-4690	184	14	,	,	PUNCT
ejpam-4690	184	15	1154	1154	NUM
ejpam-4690	184	16	-	-	SYM
ejpam-4690	184	17	1166	1166	NUM
ejpam-4690	184	18	1160	1160	NUM
ejpam-4690	184	19	corollary	corollary	NOUN
ejpam-4690	184	20	3	3	NUM
ejpam-4690	184	21	.	.	PUNCT
ejpam-4690	184	22	γgr(k1,n	γgr(k1,n	PROPN
ejpam-4690	184	23	)	)	PUNCT
ejpam-4690	185	1	=	=	SYM
ejpam-4690	185	2	α(k1,n	α(k1,n	X
ejpam-4690	185	3	)	)	PUNCT
ejpam-4690	185	4	=	=	SYM
ejpam-4690	186	1	n	n	CCONJ
ejpam-4690	186	2	for	for	ADP
ejpam-4690	186	3	every	every	DET
ejpam-4690	186	4	positive	positive	ADJ
ejpam-4690	186	5	integer	integer	NOUN
ejpam-4690	186	6	n.	n.	NOUN
ejpam-4690	186	7	proposition	proposition	NOUN
ejpam-4690	186	8	4	4	NUM
ejpam-4690	186	9	.	.	PUNCT
ejpam-4690	187	1	let	let	VERB
ejpam-4690	187	2	g	g	PRON
ejpam-4690	187	3	be	be	AUX
ejpam-4690	187	4	a	a	DET
ejpam-4690	187	5	graph	graph	NOUN
ejpam-4690	187	6	with	with	ADP
ejpam-4690	187	7	components	component	NOUN
ejpam-4690	187	8	g1	g1	PROPN
ejpam-4690	187	9	,	,	PUNCT
ejpam-4690	187	10	g2	g2	PROPN
ejpam-4690	187	11	,	,	PUNCT
ejpam-4690	187	12	.	.	PUNCT
ejpam-4690	187	13	.	.	PUNCT
ejpam-4690	188	1	.	.	PUNCT
ejpam-4690	189	1	,	,	PUNCT
ejpam-4690	189	2	gk	gk	PROPN
ejpam-4690	189	3	,	,	PUNCT
ejpam-4690	189	4	k	k	PROPN
ejpam-4690	189	5	≥	≥	NUM
ejpam-4690	189	6	2	2	NUM
ejpam-4690	189	7	.	.	PUNCT
ejpam-4690	189	8	then	then	ADV
ejpam-4690	189	9	γgr(g	γgr(g	PROPN
ejpam-4690	189	10	)	)	PUNCT
ejpam-4690	189	11	=	=	SYM
ejpam-4690	190	1	k∑	k∑	PROPN
ejpam-4690	190	2	i=1	i=1	PROPN
ejpam-4690	190	3	γgr(gi	γgr(gi	PROPN
ejpam-4690	190	4	)	)	PUNCT
ejpam-4690	190	5	.	.	PUNCT
ejpam-4690	191	1	proof	proof	NOUN
ejpam-4690	191	2	.	.	PUNCT
ejpam-4690	192	1	for	for	ADP
ejpam-4690	192	2	each	each	DET
ejpam-4690	192	3	i	i	PRON
ejpam-4690	192	4	∈	∈	PROPN
ejpam-4690	192	5	{	{	PUNCT
ejpam-4690	192	6	1	1	NUM
ejpam-4690	192	7	,	,	PUNCT
ejpam-4690	192	8	2	2	NUM
ejpam-4690	192	9	,	,	PUNCT
ejpam-4690	192	10	.	.	PUNCT
ejpam-4690	192	11	.	.	PUNCT
ejpam-4690	192	12	.	.	PUNCT
ejpam-4690	193	1	,	,	PUNCT
ejpam-4690	193	2	k	k	X
ejpam-4690	193	3	}	}	PUNCT
ejpam-4690	193	4	,	,	PUNCT
ejpam-4690	193	5	let	let	VERB
ejpam-4690	193	6	si	si	PART
ejpam-4690	193	7	be	be	AUX
ejpam-4690	193	8	a	a	DET
ejpam-4690	193	9	γgr	γgr	NOUN
ejpam-4690	193	10	-	-	PUNCT
ejpam-4690	193	11	sequence	sequence	NOUN
ejpam-4690	193	12	of	of	ADP
ejpam-4690	193	13	gi	gi	NOUN
ejpam-4690	193	14	.	.	PUNCT
ejpam-4690	194	1	then	then	ADV
ejpam-4690	194	2	s	s	VERB
ejpam-4690	194	3	=	=	PROPN
ejpam-4690	194	4	s1	s1	PROPN
ejpam-4690	194	5	⊕	⊕	PROPN
ejpam-4690	194	6	s2	s2	PROPN
ejpam-4690	194	7	⊕	⊕	PROPN
ejpam-4690	194	8	·	·	PUNCT
ejpam-4690	194	9	·	·	PUNCT
ejpam-4690	194	10	·	·	PUNCT
ejpam-4690	195	1	⊕	⊕	NOUN
ejpam-4690	195	2	sk	sk	PROPN
ejpam-4690	195	3	is	be	AUX
ejpam-4690	195	4	a	a	DET
ejpam-4690	195	5	grundy	grundy	PROPN
ejpam-4690	195	6	dominating	dominating	NOUN
ejpam-4690	195	7	sequence	sequence	NOUN
ejpam-4690	195	8	of	of	ADP
ejpam-4690	195	9	g.	g.	PROPN
ejpam-4690	195	10	thus	thus	ADV
ejpam-4690	195	11	,	,	PUNCT
ejpam-4690	195	12	γgr(g	γgr(g	PROPN
ejpam-4690	195	13	)	)	PUNCT
ejpam-4690	195	14	≥	≥	NOUN
ejpam-4690	196	1	|ŝ|	|ŝ|	PROPN
ejpam-4690	196	2	=	=	SYM
ejpam-4690	196	3	k∑	k∑	PROPN
ejpam-4690	196	4	i=1	i=1	PROPN
ejpam-4690	196	5	|ŝi|	|ŝi|	PROPN
ejpam-4690	196	6	=	=	SYM
ejpam-4690	196	7	k∑	k∑	PROPN
ejpam-4690	196	8	i=1	i=1	PROPN
ejpam-4690	196	9	γgr(gi	γgr(gi	PROPN
ejpam-4690	196	10	)	)	PUNCT
ejpam-4690	196	11	.	.	PUNCT
ejpam-4690	197	1	next	next	ADV
ejpam-4690	197	2	,	,	PUNCT
ejpam-4690	197	3	suppose	suppose	VERB
ejpam-4690	197	4	that	that	SCONJ
ejpam-4690	197	5	s′	s′	ADJ
ejpam-4690	197	6	=	=	SYM
ejpam-4690	197	7	(	(	PUNCT
ejpam-4690	197	8	w1	w1	NOUN
ejpam-4690	197	9	,	,	PUNCT
ejpam-4690	197	10	w2	w2	NOUN
ejpam-4690	197	11	,	,	PUNCT
ejpam-4690	197	12	.	.	PUNCT
ejpam-4690	197	13	.	.	PUNCT
ejpam-4690	197	14	.	.	PUNCT
ejpam-4690	198	1	,	,	PUNCT
ejpam-4690	198	2	wm	wm	PROPN
ejpam-4690	198	3	)	)	PUNCT
ejpam-4690	198	4	is	be	AUX
ejpam-4690	198	5	a	a	DET
ejpam-4690	198	6	γgr	γgr	NOUN
ejpam-4690	198	7	-	-	PUNCT
ejpam-4690	198	8	sequence	sequence	NOUN
ejpam-4690	198	9	of	of	ADP
ejpam-4690	198	10	g.	g.	PROPN
ejpam-4690	198	11	for	for	ADP
ejpam-4690	198	12	each	each	DET
ejpam-4690	198	13	i	i	PRON
ejpam-4690	198	14	∈	∈	PROPN
ejpam-4690	198	15	{	{	PUNCT
ejpam-4690	198	16	1	1	NUM
ejpam-4690	198	17	,	,	PUNCT
ejpam-4690	198	18	2	2	NUM
ejpam-4690	198	19	,	,	PUNCT
ejpam-4690	198	20	.	.	PUNCT
ejpam-4690	198	21	.	.	PUNCT
ejpam-4690	199	1	.	.	PUNCT
ejpam-4690	200	1	,	,	PUNCT
ejpam-4690	200	2	k	k	X
ejpam-4690	200	3	}	}	PUNCT
ejpam-4690	200	4	,	,	PUNCT
ejpam-4690	200	5	let	let	VERB
ejpam-4690	200	6	s′	s′	ADJ
ejpam-4690	200	7	i	i	X
ejpam-4690	200	8	=	=	SYM
ejpam-4690	200	9	(	(	PUNCT
ejpam-4690	200	10	wi,1	wi,1	PROPN
ejpam-4690	200	11	,	,	PUNCT
ejpam-4690	200	12	wi,2	wi,2	PROPN
ejpam-4690	200	13	,	,	PUNCT
ejpam-4690	200	14	.	.	PUNCT
ejpam-4690	200	15	.	.	PUNCT
ejpam-4690	201	1	.	.	PUNCT
ejpam-4690	202	1	,	,	PUNCT
ejpam-4690	202	2	wi	wi	PROPN
ejpam-4690	202	3	,	,	PUNCT
ejpam-4690	202	4	mi	mi	PROPN
ejpam-4690	202	5	)	)	PUNCT
ejpam-4690	202	6	be	be	AUX
ejpam-4690	202	7	a	a	DET
ejpam-4690	202	8	subsequence	subsequence	NOUN
ejpam-4690	202	9	of	of	ADP
ejpam-4690	202	10	s′	s′	NUM
ejpam-4690	202	11	such	such	ADJ
ejpam-4690	202	12	that	that	DET
ejpam-4690	202	13	ŝ′	ŝ′	PROPN
ejpam-4690	203	1	i	i	PROPN
ejpam-4690	203	2	=	=	SYM
ejpam-4690	203	3	ŝ′	ŝ′	PROPN
ejpam-4690	203	4	∩	∩	ADJ
ejpam-4690	203	5	v	v	NOUN
ejpam-4690	203	6	(	(	PUNCT
ejpam-4690	203	7	gi	gi	NOUN
ejpam-4690	203	8	)	)	PUNCT
ejpam-4690	203	9	.	.	PUNCT
ejpam-4690	204	1	since	since	SCONJ
ejpam-4690	204	2	s′	s′	ADJ
ejpam-4690	204	3	is	be	AUX
ejpam-4690	204	4	a	a	DET
ejpam-4690	204	5	grundy	grundy	PROPN
ejpam-4690	204	6	dominating	dominating	NOUN
ejpam-4690	204	7	sequence	sequence	NOUN
ejpam-4690	204	8	of	of	ADP
ejpam-4690	204	9	g	g	NOUN
ejpam-4690	204	10	,	,	PUNCT
ejpam-4690	204	11	s′	s′	PUNCT
ejpam-4690	204	12	i	i	PRON
ejpam-4690	204	13	is	be	AUX
ejpam-4690	204	14	a	a	DET
ejpam-4690	204	15	grundy	grundy	PROPN
ejpam-4690	204	16	dominating	dominating	NOUN
ejpam-4690	204	17	sequence	sequence	NOUN
ejpam-4690	204	18	of	of	ADP
ejpam-4690	204	19	gi	gi	NOUN
ejpam-4690	204	20	for	for	ADP
ejpam-4690	204	21	each	each	DET
ejpam-4690	204	22	i	i	PRON
ejpam-4690	204	23	∈	∈	PROPN
ejpam-4690	204	24	{	{	PUNCT
ejpam-4690	204	25	1	1	NUM
ejpam-4690	204	26	,	,	PUNCT
ejpam-4690	204	27	2	2	NUM
ejpam-4690	204	28	,	,	PUNCT
ejpam-4690	204	29	.	.	PUNCT
ejpam-4690	204	30	.	.	PUNCT
ejpam-4690	205	1	.	.	PUNCT
ejpam-4690	206	1	,	,	PUNCT
ejpam-4690	206	2	k	k	X
ejpam-4690	206	3	}	}	PUNCT
ejpam-4690	206	4	.	.	PUNCT
ejpam-4690	207	1	hence	hence	ADV
ejpam-4690	207	2	,	,	PUNCT
ejpam-4690	207	3	s∗	s∗	PROPN
ejpam-4690	207	4	=	=	PUNCT
ejpam-4690	207	5	s′	s′	NUM
ejpam-4690	207	6	1	1	NUM
ejpam-4690	207	7	⊕	⊕	PROPN
ejpam-4690	207	8	s′	s′	ADJ
ejpam-4690	207	9	2	2	NUM
ejpam-4690	207	10	⊕	⊕	PROPN
ejpam-4690	207	11	·	·	PUNCT
ejpam-4690	207	12	·	·	PUNCT
ejpam-4690	208	1	·	·	PUNCT
ejpam-4690	208	2	⊕	⊕	NOUN
ejpam-4690	208	3	s′	s′	VERB
ejpam-4690	209	1	k	k	PROPN
ejpam-4690	209	2	is	be	AUX
ejpam-4690	209	3	a	a	DET
ejpam-4690	209	4	grundy	grundy	PROPN
ejpam-4690	209	5	dominating	dominating	NOUN
ejpam-4690	209	6	sequence	sequence	NOUN
ejpam-4690	209	7	of	of	ADP
ejpam-4690	209	8	g.	g.	PROPN
ejpam-4690	209	9	therefore	therefore	ADV
ejpam-4690	209	10	,	,	PUNCT
ejpam-4690	209	11	γgr(g	γgr(g	PROPN
ejpam-4690	209	12	)	)	PUNCT
ejpam-4690	210	1	=	=	SYM
ejpam-4690	210	2	|ŝ′|	|ŝ′|	ADJ
ejpam-4690	210	3	=	=	SYM
ejpam-4690	210	4	|ŝ∗|	|ŝ∗|	X
ejpam-4690	210	5	=	=	SYM
ejpam-4690	210	6	k∑	k∑	PROPN
ejpam-4690	210	7	i=1	i=1	PROPN
ejpam-4690	211	1	|ŝ′	|ŝ′	PROPN
ejpam-4690	211	2	i|	i|	PROPN
ejpam-4690	211	3	≤	≤	PROPN
ejpam-4690	211	4	k∑	k∑	PROPN
ejpam-4690	211	5	i=1	i=1	PROPN
ejpam-4690	211	6	γgr(gi	γgr(gi	PROPN
ejpam-4690	211	7	)	)	PUNCT
ejpam-4690	211	8	.	.	PUNCT
ejpam-4690	212	1	consequently	consequently	ADV
ejpam-4690	212	2	,	,	PUNCT
ejpam-4690	212	3	γgr(g	γgr(g	PROPN
ejpam-4690	212	4	)	)	PUNCT
ejpam-4690	212	5	=	=	SYM
ejpam-4690	212	6	k∑	k∑	PROPN
ejpam-4690	212	7	i=1	i=1	PROPN
ejpam-4690	212	8	γgr(gi	γgr(gi	PROPN
ejpam-4690	212	9	)	)	PUNCT
ejpam-4690	212	10	.	.	PUNCT
ejpam-4690	213	1	lemma	lemma	PROPN
ejpam-4690	213	2	1	1	X
ejpam-4690	213	3	.	.	PUNCT
ejpam-4690	214	1	let	let	VERB
ejpam-4690	214	2	g	g	PRON
ejpam-4690	214	3	be	be	AUX
ejpam-4690	214	4	a	a	DET
ejpam-4690	214	5	graph	graph	NOUN
ejpam-4690	214	6	on	on	ADP
ejpam-4690	214	7	n	n	DET
ejpam-4690	214	8	vertices	vertex	NOUN
ejpam-4690	214	9	and	and	CCONJ
ejpam-4690	214	10	k	k	PROPN
ejpam-4690	214	11	be	be	AUX
ejpam-4690	214	12	any	any	DET
ejpam-4690	214	13	positive	positive	ADJ
ejpam-4690	214	14	integer	integer	NOUN
ejpam-4690	214	15	.	.	PUNCT
ejpam-4690	215	1	if	if	SCONJ
ejpam-4690	215	2	|ng[a]|	|ng[a]|	PRON
ejpam-4690	215	3	≥	≥	AUX
ejpam-4690	215	4	k	k	X
ejpam-4690	215	5	for	for	ADP
ejpam-4690	215	6	every	every	DET
ejpam-4690	215	7	a	a	DET
ejpam-4690	215	8	∈	∈	PROPN
ejpam-4690	215	9	v	v	NOUN
ejpam-4690	215	10	(	(	PUNCT
ejpam-4690	215	11	g	g	NOUN
ejpam-4690	215	12	)	)	PUNCT
ejpam-4690	215	13	,	,	PUNCT
ejpam-4690	215	14	then	then	ADV
ejpam-4690	215	15	γgr(g	γgr(g	PROPN
ejpam-4690	215	16	)	)	PUNCT
ejpam-4690	215	17	≤	≤	NUM
ejpam-4690	215	18	n−	n−	NOUN
ejpam-4690	215	19	k	k	NOUN
ejpam-4690	216	1	+	+	PROPN
ejpam-4690	216	2	1	1	X
ejpam-4690	216	3	.	.	X
ejpam-4690	216	4	proof	proof	NOUN
ejpam-4690	216	5	.	.	PUNCT
ejpam-4690	217	1	suppose	suppose	VERB
ejpam-4690	217	2	s	s	X
ejpam-4690	217	3	=	=	SYM
ejpam-4690	217	4	(	(	PUNCT
ejpam-4690	217	5	s1	s1	PROPN
ejpam-4690	217	6	,	,	PUNCT
ejpam-4690	217	7	s2	s2	NOUN
ejpam-4690	217	8	,	,	PUNCT
ejpam-4690	217	9	.	.	PUNCT
ejpam-4690	217	10	.	.	PUNCT
ejpam-4690	218	1	.	.	PUNCT
ejpam-4690	219	1	,	,	PUNCT
ejpam-4690	219	2	st	st	PROPN
ejpam-4690	219	3	)	)	PUNCT
ejpam-4690	219	4	is	be	AUX
ejpam-4690	219	5	γgr	γgr	NOUN
ejpam-4690	219	6	-	-	PUNCT
ejpam-4690	219	7	sequence	sequence	NOUN
ejpam-4690	219	8	of	of	ADP
ejpam-4690	219	9	g.	g.	PROPN
ejpam-4690	220	1	then	then	ADV
ejpam-4690	220	2	|ng[s1]|	|ng[s1]|	PROPN
ejpam-4690	220	3	≥	≥	PROPN
ejpam-4690	220	4	k	k	X
ejpam-4690	220	5	by	by	ADP
ejpam-4690	220	6	assumption	assumption	NOUN
ejpam-4690	220	7	.	.	PUNCT
ejpam-4690	221	1	it	it	PRON
ejpam-4690	221	2	follows	follow	VERB
ejpam-4690	221	3	that	that	SCONJ
ejpam-4690	221	4	there	there	PRON
ejpam-4690	221	5	are	be	VERB
ejpam-4690	221	6	only	only	ADV
ejpam-4690	221	7	at	at	ADP
ejpam-4690	221	8	most	most	ADJ
ejpam-4690	221	9	n	n	ADP
ejpam-4690	221	10	−	−	NOUN
ejpam-4690	221	11	k	k	NOUN
ejpam-4690	221	12	remaining	remain	VERB
ejpam-4690	221	13	vertices	vertex	NOUN
ejpam-4690	221	14	that	that	PRON
ejpam-4690	221	15	can	can	AUX
ejpam-4690	221	16	be	be	AUX
ejpam-4690	221	17	footprinted	footprinte	VERB
ejpam-4690	221	18	by	by	ADP
ejpam-4690	221	19	the	the	DET
ejpam-4690	221	20	remaining	remain	VERB
ejpam-4690	221	21	terms	term	NOUN
ejpam-4690	221	22	of	of	ADP
ejpam-4690	221	23	s.	s.	PROPN
ejpam-4690	221	24	thus	thus	ADV
ejpam-4690	221	25	,	,	PUNCT
ejpam-4690	221	26	γgr(g	γgr(g	PROPN
ejpam-4690	221	27	)	)	PUNCT
ejpam-4690	221	28	=	=	PUNCT
ejpam-4690	221	29	t	t	NOUN
ejpam-4690	221	30	≤	≤	NUM
ejpam-4690	221	31	n−	n−	PROPN
ejpam-4690	221	32	k	k	PROPN
ejpam-4690	222	1	+	+	PROPN
ejpam-4690	222	2	1	1	X
ejpam-4690	222	3	.	.	X
ejpam-4690	222	4	theorem	theorem	NOUN
ejpam-4690	222	5	4	4	NUM
ejpam-4690	222	6	.	.	PUNCT
ejpam-4690	223	1	let	let	VERB
ejpam-4690	223	2	g	g	NOUN
ejpam-4690	223	3	be	be	AUX
ejpam-4690	223	4	any	any	DET
ejpam-4690	223	5	non	non	ADJ
ejpam-4690	223	6	-	-	ADJ
ejpam-4690	223	7	trivial	trivial	ADJ
ejpam-4690	223	8	graph	graph	NOUN
ejpam-4690	223	9	on	on	ADP
ejpam-4690	223	10	n	n	PRON
ejpam-4690	223	11	≥	≥	NUM
ejpam-4690	223	12	1	1	NUM
ejpam-4690	223	13	vertices	vertex	NOUN
ejpam-4690	223	14	.	.	PUNCT
ejpam-4690	224	1	then	then	ADV
ejpam-4690	224	2	1	1	NUM
ejpam-4690	224	3	≤	≤	NUM
ejpam-4690	224	4	γgr(g	γgr(g	PROPN
ejpam-4690	224	5	)	)	PUNCT
ejpam-4690	224	6	≤	≤	NOUN
ejpam-4690	224	7	n.	n.	NOUN
ejpam-4690	224	8	moreover	moreover	ADV
ejpam-4690	224	9	,	,	PUNCT
ejpam-4690	224	10	each	each	PRON
ejpam-4690	224	11	of	of	ADP
ejpam-4690	224	12	the	the	DET
ejpam-4690	224	13	following	following	ADJ
ejpam-4690	224	14	statements	statement	NOUN
ejpam-4690	224	15	holds	hold	VERB
ejpam-4690	224	16	.	.	PUNCT
ejpam-4690	225	1	(	(	PUNCT
ejpam-4690	225	2	i	i	NOUN
ejpam-4690	225	3	)	)	PUNCT
ejpam-4690	225	4	γgr(g	γgr(g	PROPN
ejpam-4690	225	5	)	)	PUNCT
ejpam-4690	225	6	=	=	PUNCT
ejpam-4690	225	7	1	1	NUM
ejpam-4690	225	8	if	if	SCONJ
ejpam-4690	225	9	and	and	CCONJ
ejpam-4690	225	10	only	only	ADV
ejpam-4690	225	11	if	if	SCONJ
ejpam-4690	225	12	g	g	PROPN
ejpam-4690	225	13	is	be	AUX
ejpam-4690	225	14	a	a	DET
ejpam-4690	225	15	complete	complete	ADJ
ejpam-4690	225	16	graph	graph	NOUN
ejpam-4690	225	17	.	.	PUNCT
ejpam-4690	226	1	(	(	PUNCT
ejpam-4690	226	2	ii	ii	NOUN
ejpam-4690	226	3	)	)	PUNCT
ejpam-4690	226	4	γgr(g	γgr(g	PROPN
ejpam-4690	226	5	)	)	PUNCT
ejpam-4690	226	6	=	=	SYM
ejpam-4690	226	7	2	2	NUM
ejpam-4690	226	8	if	if	SCONJ
ejpam-4690	226	9	and	and	CCONJ
ejpam-4690	226	10	only	only	ADV
ejpam-4690	226	11	if	if	SCONJ
ejpam-4690	226	12	g	g	PROPN
ejpam-4690	226	13	is	be	AUX
ejpam-4690	226	14	non	non	ADJ
ejpam-4690	226	15	-	-	ADJ
ejpam-4690	226	16	complete	complete	ADJ
ejpam-4690	226	17	and	and	CCONJ
ejpam-4690	226	18	{	{	PUNCT
ejpam-4690	226	19	a	a	DET
ejpam-4690	226	20	,	,	PUNCT
ejpam-4690	226	21	b	b	NOUN
ejpam-4690	226	22	}	}	PUNCT
ejpam-4690	226	23	is	be	AUX
ejpam-4690	226	24	a	a	DET
ejpam-4690	226	25	dominating	dominating	NOUN
ejpam-4690	226	26	set	set	NOUN
ejpam-4690	226	27	of	of	ADP
ejpam-4690	226	28	g	g	NOUN
ejpam-4690	226	29	for	for	ADP
ejpam-4690	226	30	each	each	DET
ejpam-4690	226	31	pair	pair	NOUN
ejpam-4690	226	32	of	of	ADP
ejpam-4690	226	33	distinct	distinct	ADJ
ejpam-4690	226	34	vertices	vertex	NOUN
ejpam-4690	226	35	a	a	DET
ejpam-4690	226	36	,	,	PUNCT
ejpam-4690	226	37	b	b	PROPN
ejpam-4690	226	38	∈	∈	PROPN
ejpam-4690	226	39	v	v	NOUN
ejpam-4690	226	40	(	(	PUNCT
ejpam-4690	226	41	g	g	NOUN
ejpam-4690	226	42	)	)	PUNCT
ejpam-4690	226	43	with	with	ADP
ejpam-4690	226	44	ng[a	ng[a	NOUN
ejpam-4690	226	45	]	]	PUNCT
ejpam-4690	226	46	̸=	̸=	PROPN
ejpam-4690	226	47	ng[b	ng[b	NOUN
ejpam-4690	226	48	]	]	PUNCT
ejpam-4690	226	49	.	.	PUNCT
ejpam-4690	227	1	(	(	PUNCT
ejpam-4690	227	2	iii	iii	X
ejpam-4690	227	3	)	)	PUNCT
ejpam-4690	227	4	γgr(g	γgr(g	PROPN
ejpam-4690	227	5	)	)	PUNCT
ejpam-4690	228	1	=	=	SYM
ejpam-4690	229	1	n	n	NOUN
ejpam-4690	229	2	if	if	SCONJ
ejpam-4690	230	1	and	and	CCONJ
ejpam-4690	230	2	only	only	ADV
ejpam-4690	230	3	if	if	SCONJ
ejpam-4690	230	4	g	g	PROPN
ejpam-4690	230	5	=	=	PROPN
ejpam-4690	230	6	kn	kn	PROPN
ejpam-4690	230	7	.	.	PUNCT
ejpam-4690	231	1	j.	j.	PROPN
ejpam-4690	231	2	hassan	hassan	PROPN
ejpam-4690	231	3	,	,	PUNCT
ejpam-4690	231	4	s.	s.	PROPN
ejpam-4690	231	5	canoy	canoy	PROPN
ejpam-4690	231	6	jr	jr	PROPN
ejpam-4690	231	7	.	.	PROPN
ejpam-4690	231	8	/	/	SYM
ejpam-4690	231	9	eur	eur	PROPN
ejpam-4690	231	10	.	.	PUNCT
ejpam-4690	232	1	j.	j.	PROPN
ejpam-4690	232	2	pure	pure	PROPN
ejpam-4690	232	3	appl	appl	PROPN
ejpam-4690	232	4	.	.	PROPN
ejpam-4690	232	5	math	math	PROPN
ejpam-4690	232	6	,	,	PUNCT
ejpam-4690	232	7	16	16	NUM
ejpam-4690	232	8	(	(	PUNCT
ejpam-4690	232	9	2	2	NUM
ejpam-4690	232	10	)	)	PUNCT
ejpam-4690	232	11	(	(	PUNCT
ejpam-4690	232	12	2023	2023	NUM
ejpam-4690	232	13	)	)	PUNCT
ejpam-4690	232	14	,	,	PUNCT
ejpam-4690	232	15	1154	1154	NUM
ejpam-4690	232	16	-	-	SYM
ejpam-4690	232	17	1166	1166	NUM
ejpam-4690	232	18	1161	1161	NUM
ejpam-4690	232	19	proof	proof	NOUN
ejpam-4690	232	20	.	.	PUNCT
ejpam-4690	233	1	clearly	clearly	ADV
ejpam-4690	233	2	,	,	PUNCT
ejpam-4690	233	3	1	1	NUM
ejpam-4690	233	4	≤	≤	NUM
ejpam-4690	233	5	γgr(g	γgr(g	PROPN
ejpam-4690	233	6	)	)	PUNCT
ejpam-4690	233	7	≤	≤	NOUN
ejpam-4690	233	8	n.	n.	NOUN
ejpam-4690	233	9	(	(	PUNCT
ejpam-4690	233	10	i	i	NOUN
ejpam-4690	233	11	)	)	PUNCT
ejpam-4690	233	12	assume	assume	VERB
ejpam-4690	233	13	that	that	SCONJ
ejpam-4690	233	14	γgr(g	γgr(g	PROPN
ejpam-4690	233	15	)	)	PUNCT
ejpam-4690	233	16	=	=	SYM
ejpam-4690	233	17	1	1	X
ejpam-4690	233	18	.	.	PUNCT
ejpam-4690	233	19	suppose	suppose	VERB
ejpam-4690	233	20	g	g	PROPN
ejpam-4690	233	21	is	be	AUX
ejpam-4690	233	22	not	not	PART
ejpam-4690	233	23	a	a	DET
ejpam-4690	233	24	complete	complete	ADJ
ejpam-4690	233	25	graph	graph	NOUN
ejpam-4690	233	26	.	.	PUNCT
ejpam-4690	234	1	then	then	ADV
ejpam-4690	234	2	there	there	PRON
ejpam-4690	234	3	exists	exist	VERB
ejpam-4690	234	4	a	a	DET
ejpam-4690	234	5	,	,	PUNCT
ejpam-4690	234	6	b	b	PROPN
ejpam-4690	234	7	∈	∈	PROPN
ejpam-4690	234	8	v	v	NOUN
ejpam-4690	234	9	(	(	PUNCT
ejpam-4690	234	10	g	g	NOUN
ejpam-4690	234	11	)	)	PUNCT
ejpam-4690	234	12	such	such	ADJ
ejpam-4690	234	13	that	that	SCONJ
ejpam-4690	234	14	dg(a	dg(a	PROPN
ejpam-4690	234	15	,	,	PUNCT
ejpam-4690	234	16	b	b	X
ejpam-4690	234	17	)	)	PUNCT
ejpam-4690	234	18	=	=	SYM
ejpam-4690	234	19	2	2	X
ejpam-4690	234	20	.	.	PUNCT
ejpam-4690	235	1	this	this	PRON
ejpam-4690	235	2	implies	imply	VERB
ejpam-4690	235	3	that	that	SCONJ
ejpam-4690	235	4	b	b	PROPN
ejpam-4690	235	5	∈	∈	PROPN
ejpam-4690	235	6	ng[b	ng[b	NOUN
ejpam-4690	235	7	]	]	PUNCT
ejpam-4690	235	8	\ng[a	\ng[a	NOUN
ejpam-4690	235	9	]	]	PUNCT
ejpam-4690	235	10	.	.	PUNCT
ejpam-4690	236	1	hence	hence	ADV
ejpam-4690	236	2	,	,	PUNCT
ejpam-4690	236	3	(	(	PUNCT
ejpam-4690	236	4	a	a	DET
ejpam-4690	236	5	,	,	PUNCT
ejpam-4690	236	6	b	b	NOUN
ejpam-4690	236	7	)	)	PUNCT
ejpam-4690	236	8	is	be	AUX
ejpam-4690	236	9	a	a	DET
ejpam-4690	236	10	legal	legal	ADJ
ejpam-4690	236	11	closed	closed	ADJ
ejpam-4690	236	12	neighborhood	neighborhood	NOUN
ejpam-4690	236	13	sequence	sequence	NOUN
ejpam-4690	236	14	of	of	ADP
ejpam-4690	236	15	g.	g.	PROPN
ejpam-4690	236	16	therefore	therefore	ADV
ejpam-4690	236	17	,	,	PUNCT
ejpam-4690	236	18	γgr(g	γgr(g	PROPN
ejpam-4690	236	19	)	)	PUNCT
ejpam-4690	236	20	≥	≥	NOUN
ejpam-4690	236	21	2	2	NUM
ejpam-4690	236	22	,	,	PUNCT
ejpam-4690	236	23	a	a	DET
ejpam-4690	236	24	contradiction	contradiction	NOUN
ejpam-4690	236	25	.	.	PUNCT
ejpam-4690	237	1	conversely	conversely	ADV
ejpam-4690	237	2	,	,	PUNCT
ejpam-4690	237	3	suppose	suppose	VERB
ejpam-4690	237	4	g	g	PROPN
ejpam-4690	237	5	is	be	AUX
ejpam-4690	237	6	a	a	DET
ejpam-4690	237	7	complete	complete	ADJ
ejpam-4690	237	8	graph	graph	NOUN
ejpam-4690	237	9	.	.	PUNCT
ejpam-4690	238	1	then	then	ADV
ejpam-4690	238	2	γgr(g	γgr(g	PROPN
ejpam-4690	238	3	)	)	PUNCT
ejpam-4690	238	4	=	=	SYM
ejpam-4690	238	5	1	1	X
ejpam-4690	238	6	.	.	PUNCT
ejpam-4690	238	7	(	(	PUNCT
ejpam-4690	238	8	ii	ii	NOUN
ejpam-4690	238	9	)	)	PUNCT
ejpam-4690	238	10	suppose	suppose	VERB
ejpam-4690	238	11	that	that	SCONJ
ejpam-4690	238	12	γgr(g	γgr(g	PROPN
ejpam-4690	238	13	)	)	PUNCT
ejpam-4690	238	14	=	=	SYM
ejpam-4690	238	15	2	2	X
ejpam-4690	238	16	.	.	PUNCT
ejpam-4690	238	17	then	then	ADV
ejpam-4690	238	18	g	g	PROPN
ejpam-4690	238	19	is	be	AUX
ejpam-4690	238	20	non	non	ADJ
ejpam-4690	238	21	-	-	ADJ
ejpam-4690	238	22	complete	complete	ADJ
ejpam-4690	238	23	by	by	ADP
ejpam-4690	238	24	(	(	PUNCT
ejpam-4690	238	25	i	i	NOUN
ejpam-4690	238	26	)	)	PUNCT
ejpam-4690	238	27	.	.	PUNCT
ejpam-4690	239	1	let	let	VERB
ejpam-4690	239	2	a	a	PRON
ejpam-4690	239	3	,	,	PUNCT
ejpam-4690	239	4	b	b	NOUN
ejpam-4690	239	5	be	be	AUX
ejpam-4690	239	6	two	two	NUM
ejpam-4690	239	7	distinct	distinct	ADJ
ejpam-4690	239	8	vertices	vertex	NOUN
ejpam-4690	239	9	of	of	ADP
ejpam-4690	239	10	g	g	NOUN
ejpam-4690	239	11	such	such	ADJ
ejpam-4690	239	12	that	that	DET
ejpam-4690	239	13	ng[a	ng[a	NOUN
ejpam-4690	239	14	]	]	PUNCT
ejpam-4690	239	15	̸=	̸=	PROPN
ejpam-4690	239	16	ng[b	ng[b	NOUN
ejpam-4690	239	17	]	]	PUNCT
ejpam-4690	239	18	.	.	PUNCT
ejpam-4690	240	1	then	then	ADV
ejpam-4690	240	2	ng[a]\ng[b	ng[a]\ng[b	NOUN
ejpam-4690	240	3	]	]	X
ejpam-4690	240	4	̸=	̸=	PROPN
ejpam-4690	240	5	∅	∅	NOUN
ejpam-4690	240	6	or	or	CCONJ
ejpam-4690	240	7	ng[b]\ng[a	ng[b]\ng[a	NOUN
ejpam-4690	240	8	]	]	X
ejpam-4690	241	1	̸=	̸=	PROPN
ejpam-4690	241	2	∅.	∅.	ADV
ejpam-4690	241	3	we	we	PRON
ejpam-4690	241	4	may	may	AUX
ejpam-4690	241	5	ssume	ssume	VERB
ejpam-4690	241	6	that	that	SCONJ
ejpam-4690	241	7	ng[b	ng[b	NOUN
ejpam-4690	241	8	]	]	PUNCT
ejpam-4690	241	9	\ng[a	\ng[a	NOUN
ejpam-4690	241	10	]	]	X
ejpam-4690	241	11	̸=	̸=	PROPN
ejpam-4690	241	12	∅.	∅.	ADP
ejpam-4690	241	13	this	this	PRON
ejpam-4690	241	14	implies	imply	VERB
ejpam-4690	241	15	that	that	SCONJ
ejpam-4690	241	16	(	(	PUNCT
ejpam-4690	241	17	a	a	DET
ejpam-4690	241	18	,	,	PUNCT
ejpam-4690	241	19	b	b	NOUN
ejpam-4690	241	20	)	)	PUNCT
ejpam-4690	241	21	is	be	AUX
ejpam-4690	241	22	a	a	DET
ejpam-4690	241	23	legal	legal	ADJ
ejpam-4690	241	24	closed	closed	ADJ
ejpam-4690	241	25	neighborhood	neighborhood	NOUN
ejpam-4690	241	26	sequence	sequence	NOUN
ejpam-4690	241	27	of	of	ADP
ejpam-4690	241	28	g.	g.	PROPN
ejpam-4690	241	29	suppose	suppose	VERB
ejpam-4690	241	30	there	there	PRON
ejpam-4690	241	31	exists	exist	VERB
ejpam-4690	241	32	c	c	PROPN
ejpam-4690	241	33	∈	∈	PROPN
ejpam-4690	241	34	v	v	NOUN
ejpam-4690	241	35	(	(	PUNCT
ejpam-4690	241	36	g)\(ng[a]∪ng[b	g)\(ng[a]∪ng[b	NOUN
ejpam-4690	241	37	]	]	PUNCT
ejpam-4690	241	38	)	)	PUNCT
ejpam-4690	241	39	.	.	PUNCT
ejpam-4690	242	1	since	since	SCONJ
ejpam-4690	242	2	c	c	PROPN
ejpam-4690	242	3	∈	∈	PROPN
ejpam-4690	242	4	ng[c	ng[c	PROPN
ejpam-4690	242	5	]	]	PUNCT
ejpam-4690	242	6	,	,	PUNCT
ejpam-4690	242	7	it	it	PRON
ejpam-4690	242	8	follows	follow	VERB
ejpam-4690	242	9	that	that	SCONJ
ejpam-4690	242	10	ng[c	ng[c	PROPN
ejpam-4690	242	11	]	]	PUNCT
ejpam-4690	242	12	\	\	PUNCT
ejpam-4690	243	1	(	(	PUNCT
ejpam-4690	243	2	ng[a	ng[a	PROPN
ejpam-4690	243	3	]	]	X
ejpam-4690	243	4	∪ng[b	∪ng[b	X
ejpam-4690	243	5	]	]	PUNCT
ejpam-4690	243	6	)	)	PUNCT
ejpam-4690	243	7	̸=	̸=	PROPN
ejpam-4690	243	8	∅.	∅.	PRON
ejpam-4690	243	9	hence	hence	ADV
ejpam-4690	243	10	,	,	PUNCT
ejpam-4690	243	11	(	(	PUNCT
ejpam-4690	243	12	a	a	DET
ejpam-4690	243	13	,	,	PUNCT
ejpam-4690	243	14	b	b	NOUN
ejpam-4690	243	15	,	,	PUNCT
ejpam-4690	243	16	c	c	NOUN
ejpam-4690	243	17	)	)	PUNCT
ejpam-4690	243	18	is	be	AUX
ejpam-4690	243	19	a	a	DET
ejpam-4690	243	20	legal	legal	ADJ
ejpam-4690	243	21	closed	closed	ADJ
ejpam-4690	243	22	neighborhood	neighborhood	NOUN
ejpam-4690	243	23	sequence	sequence	NOUN
ejpam-4690	243	24	of	of	ADP
ejpam-4690	243	25	g.	g.	PROPN
ejpam-4690	243	26	thus	thus	ADV
ejpam-4690	243	27	,	,	PUNCT
ejpam-4690	243	28	γgr(g	γgr(g	PROPN
ejpam-4690	243	29	)	)	PUNCT
ejpam-4690	243	30	≥	≥	NOUN
ejpam-4690	243	31	3	3	NUM
ejpam-4690	243	32	,	,	PUNCT
ejpam-4690	243	33	a	a	DET
ejpam-4690	243	34	contradiction	contradiction	NOUN
ejpam-4690	243	35	to	to	ADP
ejpam-4690	243	36	the	the	DET
ejpam-4690	243	37	assumption	assumption	NOUN
ejpam-4690	243	38	that	that	SCONJ
ejpam-4690	243	39	γgr(g	γgr(g	PROPN
ejpam-4690	243	40	)	)	PUNCT
ejpam-4690	243	41	=	=	SYM
ejpam-4690	243	42	2	2	X
ejpam-4690	243	43	.	.	PUNCT
ejpam-4690	243	44	therefore	therefore	ADV
ejpam-4690	243	45	,	,	PUNCT
ejpam-4690	243	46	{	{	PUNCT
ejpam-4690	243	47	a	a	DET
ejpam-4690	243	48	,	,	PUNCT
ejpam-4690	243	49	b	b	NOUN
ejpam-4690	243	50	}	}	PUNCT
ejpam-4690	243	51	is	be	AUX
ejpam-4690	243	52	a	a	DET
ejpam-4690	243	53	dominating	dominating	NOUN
ejpam-4690	243	54	set	set	NOUN
ejpam-4690	243	55	of	of	ADP
ejpam-4690	243	56	g.	g.	PROPN
ejpam-4690	243	57	conversely	conversely	ADV
ejpam-4690	243	58	,	,	PUNCT
ejpam-4690	243	59	suppose	suppose	VERB
ejpam-4690	243	60	that	that	SCONJ
ejpam-4690	243	61	g	g	PROPN
ejpam-4690	243	62	is	be	AUX
ejpam-4690	243	63	non	non	ADJ
ejpam-4690	243	64	-	-	ADJ
ejpam-4690	243	65	complete	complete	ADJ
ejpam-4690	243	66	and	and	CCONJ
ejpam-4690	243	67	{	{	PUNCT
ejpam-4690	243	68	a	a	DET
ejpam-4690	243	69	,	,	PUNCT
ejpam-4690	243	70	b	b	NOUN
ejpam-4690	243	71	}	}	PUNCT
ejpam-4690	243	72	is	be	AUX
ejpam-4690	243	73	a	a	DET
ejpam-4690	243	74	dominating	dominating	NOUN
ejpam-4690	243	75	set	set	NOUN
ejpam-4690	243	76	of	of	ADP
ejpam-4690	243	77	g	g	NOUN
ejpam-4690	243	78	for	for	ADP
ejpam-4690	243	79	each	each	DET
ejpam-4690	243	80	pair	pair	NOUN
ejpam-4690	243	81	of	of	ADP
ejpam-4690	243	82	distinct	distinct	ADJ
ejpam-4690	243	83	vertices	vertex	NOUN
ejpam-4690	243	84	a	a	DET
ejpam-4690	243	85	,	,	PUNCT
ejpam-4690	243	86	b	b	PROPN
ejpam-4690	243	87	∈	∈	PROPN
ejpam-4690	243	88	v	v	NOUN
ejpam-4690	243	89	(	(	PUNCT
ejpam-4690	243	90	g	g	NOUN
ejpam-4690	243	91	)	)	PUNCT
ejpam-4690	243	92	with	with	ADP
ejpam-4690	243	93	ng[a	ng[a	NOUN
ejpam-4690	243	94	]	]	PUNCT
ejpam-4690	243	95	̸=	̸=	PROPN
ejpam-4690	243	96	ng[b	ng[b	NOUN
ejpam-4690	243	97	]	]	PUNCT
ejpam-4690	243	98	.	.	PUNCT
ejpam-4690	244	1	then	then	ADV
ejpam-4690	244	2	γgr(g	γgr(g	PROPN
ejpam-4690	244	3	)	)	PUNCT
ejpam-4690	244	4	≥	≥	NOUN
ejpam-4690	244	5	2	2	NUM
ejpam-4690	244	6	.	.	PUNCT
ejpam-4690	245	1	let	let	AUX
ejpam-4690	245	2	(	(	PUNCT
ejpam-4690	245	3	s1	s1	NOUN
ejpam-4690	245	4	,	,	PUNCT
ejpam-4690	245	5	s2	s2	PROPN
ejpam-4690	245	6	,	,	PUNCT
ejpam-4690	245	7	·	·	PUNCT
ejpam-4690	245	8	·	·	PUNCT
ejpam-4690	245	9	·	·	PUNCT
ejpam-4690	245	10	,	,	PUNCT
ejpam-4690	245	11	st	st	PROPN
ejpam-4690	245	12	)	)	PUNCT
ejpam-4690	245	13	be	be	AUX
ejpam-4690	245	14	a	a	DET
ejpam-4690	245	15	γgr	γgr	NOUN
ejpam-4690	245	16	-	-	PUNCT
ejpam-4690	245	17	sequence	sequence	NOUN
ejpam-4690	245	18	of	of	ADP
ejpam-4690	245	19	g.	g.	PROPN
ejpam-4690	245	20	thenng[s2]\ng[s1	thenng[s2]\ng[s1	PROPN
ejpam-4690	245	21	]	]	PUNCT
ejpam-4690	245	22	̸=	̸=	PROPN
ejpam-4690	245	23	∅	∅	NOUN
ejpam-4690	245	24	,	,	PUNCT
ejpam-4690	245	25	that	that	ADV
ejpam-4690	245	26	is	is	ADV
ejpam-4690	245	27	,	,	PUNCT
ejpam-4690	245	28	ng[s2	ng[s2	PROPN
ejpam-4690	245	29	]	]	X
ejpam-4690	245	30	̸=	̸=	PROPN
ejpam-4690	245	31	ng[s1	ng[s1	PROPN
ejpam-4690	245	32	]	]	PUNCT
ejpam-4690	245	33	.	.	PUNCT
ejpam-4690	246	1	by	by	ADP
ejpam-4690	246	2	assumption	assumption	NOUN
ejpam-4690	246	3	,	,	PUNCT
ejpam-4690	246	4	{	{	PUNCT
ejpam-4690	246	5	s1	s1	NOUN
ejpam-4690	246	6	,	,	PUNCT
ejpam-4690	246	7	s2	s2	PROPN
ejpam-4690	246	8	}	}	PUNCT
ejpam-4690	246	9	is	be	AUX
ejpam-4690	246	10	a	a	DET
ejpam-4690	246	11	dominating	dominating	NOUN
ejpam-4690	246	12	set	set	NOUN
ejpam-4690	246	13	of	of	ADP
ejpam-4690	246	14	g	g	NOUN
ejpam-4690	246	15	,	,	PUNCT
ejpam-4690	246	16	that	that	ADV
ejpam-4690	246	17	is	is	ADV
ejpam-4690	246	18	,	,	PUNCT
ejpam-4690	246	19	v	v	INTJ
ejpam-4690	246	20	(	(	PUNCT
ejpam-4690	246	21	g	g	NOUN
ejpam-4690	246	22	)	)	PUNCT
ejpam-4690	247	1	=	=	SYM
ejpam-4690	247	2	n2	n2	PROPN
ejpam-4690	247	3	g[s1]∪n2	g[s1]∪n2	PROPN
ejpam-4690	247	4	g[s2	g[s2	NOUN
ejpam-4690	247	5	]	]	PUNCT
ejpam-4690	247	6	.	.	PUNCT
ejpam-4690	248	1	therefore	therefore	ADV
ejpam-4690	248	2	,	,	PUNCT
ejpam-4690	248	3	γgr(g	γgr(g	PROPN
ejpam-4690	248	4	)	)	PUNCT
ejpam-4690	248	5	=	=	SYM
ejpam-4690	248	6	t	t	NOUN
ejpam-4690	248	7	=	=	SYM
ejpam-4690	248	8	2	2	X
ejpam-4690	248	9	.	.	PUNCT
ejpam-4690	248	10	(	(	PUNCT
ejpam-4690	248	11	iii	iii	NOUN
ejpam-4690	248	12	)	)	PUNCT
ejpam-4690	248	13	suppose	suppose	VERB
ejpam-4690	248	14	γgr(g	γgr(g	PROPN
ejpam-4690	248	15	)	)	PUNCT
ejpam-4690	248	16	=	=	SYM
ejpam-4690	248	17	n.	n.	NOUN
ejpam-4690	248	18	suppose	suppose	VERB
ejpam-4690	248	19	there	there	PRON
ejpam-4690	248	20	exists	exist	VERB
ejpam-4690	248	21	component	component	NOUN
ejpam-4690	248	22	c	c	PROPN
ejpam-4690	248	23	of	of	ADP
ejpam-4690	248	24	g	g	NOUN
ejpam-4690	248	25	which	which	PRON
ejpam-4690	248	26	is	be	AUX
ejpam-4690	248	27	non	non	ADJ
ejpam-4690	248	28	-	-	ADJ
ejpam-4690	248	29	trivial	trivial	ADJ
ejpam-4690	248	30	.	.	PUNCT
ejpam-4690	249	1	then	then	ADV
ejpam-4690	249	2	|nc	|nc	NUM
ejpam-4690	249	3	[	[	X
ejpam-4690	249	4	v]|	v]|	PROPN
ejpam-4690	249	5	≥	≥	NOUN
ejpam-4690	249	6	2	2	NUM
ejpam-4690	249	7	for	for	ADP
ejpam-4690	249	8	every	every	DET
ejpam-4690	249	9	v	v	NUM
ejpam-4690	249	10	∈	∈	NOUN
ejpam-4690	249	11	v	v	NOUN
ejpam-4690	249	12	(	(	PUNCT
ejpam-4690	249	13	c	c	NOUN
ejpam-4690	249	14	)	)	PUNCT
ejpam-4690	249	15	.	.	PUNCT
ejpam-4690	250	1	by	by	ADP
ejpam-4690	250	2	lemma	lemma	PROPN
ejpam-4690	250	3	1	1	NUM
ejpam-4690	250	4	,	,	PUNCT
ejpam-4690	250	5	γgr(c	γgr(c	NUM
ejpam-4690	250	6	)	)	PUNCT
ejpam-4690	250	7	≤	≤	NOUN
ejpam-4690	250	8	|v	|v	X
ejpam-4690	250	9	(	(	PUNCT
ejpam-4690	250	10	c)|	c)|	NOUN
ejpam-4690	250	11	−	−	PROPN
ejpam-4690	250	12	1	1	X
ejpam-4690	250	13	.	.	PUNCT
ejpam-4690	250	14	by	by	ADP
ejpam-4690	250	15	proposition	proposition	NOUN
ejpam-4690	250	16	4	4	NUM
ejpam-4690	250	17	,	,	PUNCT
ejpam-4690	250	18	it	it	PRON
ejpam-4690	250	19	follows	follow	VERB
ejpam-4690	250	20	that	that	SCONJ
ejpam-4690	250	21	γgr(g	γgr(g	PROPN
ejpam-4690	250	22	)	)	PUNCT
ejpam-4690	250	23	≤	≤	NUM
ejpam-4690	250	24	n−	n−	NOUN
ejpam-4690	250	25	1	1	NUM
ejpam-4690	250	26	,	,	PUNCT
ejpam-4690	250	27	a	a	DET
ejpam-4690	250	28	contradiction	contradiction	NOUN
ejpam-4690	250	29	.	.	PUNCT
ejpam-4690	251	1	therefore	therefore	ADV
ejpam-4690	251	2	,	,	PUNCT
ejpam-4690	251	3	every	every	DET
ejpam-4690	251	4	component	component	NOUN
ejpam-4690	251	5	c	c	NOUN
ejpam-4690	251	6	of	of	ADP
ejpam-4690	251	7	g	g	PROPN
ejpam-4690	251	8	is	be	AUX
ejpam-4690	251	9	trivial	trivial	ADJ
ejpam-4690	251	10	,	,	PUNCT
ejpam-4690	251	11	i.e.	i.e.	X
ejpam-4690	251	12	,	,	PUNCT
ejpam-4690	251	13	g	g	PROPN
ejpam-4690	251	14	=	=	SYM
ejpam-4690	251	15	kn	kn	PROPN
ejpam-4690	251	16	.	.	PUNCT
ejpam-4690	252	1	conversely	conversely	ADV
ejpam-4690	252	2	,	,	PUNCT
ejpam-4690	252	3	suppose	suppose	VERB
ejpam-4690	252	4	that	that	SCONJ
ejpam-4690	252	5	every	every	DET
ejpam-4690	252	6	component	component	NOUN
ejpam-4690	252	7	c	c	NOUN
ejpam-4690	252	8	of	of	ADP
ejpam-4690	252	9	g	g	PROPN
ejpam-4690	252	10	is	be	AUX
ejpam-4690	252	11	trivial	trivial	ADJ
ejpam-4690	252	12	.	.	PUNCT
ejpam-4690	253	1	then	then	ADV
ejpam-4690	253	2	by	by	ADP
ejpam-4690	253	3	(	(	PUNCT
ejpam-4690	253	4	i	i	NOUN
ejpam-4690	253	5	)	)	PUNCT
ejpam-4690	253	6	and	and	CCONJ
ejpam-4690	253	7	proposition	proposition	NOUN
ejpam-4690	253	8	4	4	NUM
ejpam-4690	253	9	,	,	PUNCT
ejpam-4690	253	10	γgr(g	γgr(g	PROPN
ejpam-4690	253	11	)	)	PUNCT
ejpam-4690	253	12	=	=	VERB
ejpam-4690	254	1	n.	n.	NOUN
ejpam-4690	254	2	the	the	DET
ejpam-4690	254	3	next	next	ADJ
ejpam-4690	254	4	result	result	NOUN
ejpam-4690	254	5	follows	follow	VERB
ejpam-4690	254	6	from	from	ADP
ejpam-4690	254	7	theorem	theorem	ADJ
ejpam-4690	254	8	4	4	NUM
ejpam-4690	254	9	and	and	CCONJ
ejpam-4690	254	10	proposition	proposition	NOUN
ejpam-4690	254	11	4	4	NUM
ejpam-4690	254	12	.	.	PUNCT
ejpam-4690	254	13	corollary	corollary	ADJ
ejpam-4690	254	14	4	4	NUM
ejpam-4690	254	15	.	.	PUNCT
ejpam-4690	255	1	let	let	VERB
ejpam-4690	255	2	g	g	PRON
ejpam-4690	255	3	be	be	AUX
ejpam-4690	255	4	a	a	DET
ejpam-4690	255	5	graph	graph	NOUN
ejpam-4690	255	6	on	on	ADP
ejpam-4690	255	7	n	n	DET
ejpam-4690	255	8	vertices	vertex	NOUN
ejpam-4690	255	9	.	.	PUNCT
ejpam-4690	256	1	then	then	ADV
ejpam-4690	256	2	each	each	PRON
ejpam-4690	256	3	of	of	ADP
ejpam-4690	256	4	the	the	DET
ejpam-4690	256	5	following	following	ADJ
ejpam-4690	256	6	statements	statement	NOUN
ejpam-4690	256	7	holds	hold	VERB
ejpam-4690	256	8	.	.	PUNCT
ejpam-4690	257	1	(	(	PUNCT
ejpam-4690	257	2	i	i	NOUN
ejpam-4690	257	3	)	)	PUNCT
ejpam-4690	257	4	γgr(g	γgr(g	PROPN
ejpam-4690	257	5	)	)	PUNCT
ejpam-4690	257	6	≥	≥	NOUN
ejpam-4690	257	7	2	2	NUM
ejpam-4690	257	8	if	if	SCONJ
ejpam-4690	257	9	and	and	CCONJ
ejpam-4690	257	10	only	only	ADV
ejpam-4690	257	11	if	if	SCONJ
ejpam-4690	257	12	g	g	PROPN
ejpam-4690	257	13	is	be	AUX
ejpam-4690	257	14	non	non	ADJ
ejpam-4690	257	15	-	-	ADJ
ejpam-4690	257	16	complete	complete	ADJ
ejpam-4690	257	17	graph	graph	NOUN
ejpam-4690	257	18	.	.	PUNCT
ejpam-4690	258	1	(	(	PUNCT
ejpam-4690	258	2	ii	ii	NOUN
ejpam-4690	258	3	)	)	PUNCT
ejpam-4690	258	4	if	if	SCONJ
ejpam-4690	258	5	g	g	PROPN
ejpam-4690	258	6	has	have	VERB
ejpam-4690	258	7	k	k	PROPN
ejpam-4690	258	8	components	component	NOUN
ejpam-4690	258	9	and	and	CCONJ
ejpam-4690	258	10	every	every	DET
ejpam-4690	258	11	component	component	NOUN
ejpam-4690	258	12	is	be	AUX
ejpam-4690	258	13	complete	complete	ADJ
ejpam-4690	258	14	,	,	PUNCT
ejpam-4690	258	15	then	then	ADV
ejpam-4690	258	16	γgr(g	γgr(g	PROPN
ejpam-4690	258	17	)	)	PUNCT
ejpam-4690	258	18	=	=	SYM
ejpam-4690	259	1	k.	k.	PROPN
ejpam-4690	259	2	(	(	PUNCT
ejpam-4690	259	3	iii	iii	X
ejpam-4690	259	4	)	)	PUNCT
ejpam-4690	259	5	if	if	SCONJ
ejpam-4690	259	6	g	g	PROPN
ejpam-4690	259	7	is	be	AUX
ejpam-4690	259	8	complete	complete	ADJ
ejpam-4690	259	9	,	,	PUNCT
ejpam-4690	259	10	then	then	ADV
ejpam-4690	259	11	γgr(g	γgr(g	PROPN
ejpam-4690	259	12	)	)	PUNCT
ejpam-4690	260	1	+	+	CCONJ
ejpam-4690	260	2	γgr(g	γgr(g	PROPN
ejpam-4690	260	3	)	)	PUNCT
ejpam-4690	260	4	=	=	PUNCT
ejpam-4690	260	5	n+	n+	PUNCT
ejpam-4690	260	6	1	1	X
ejpam-4690	260	7	.	.	PUNCT
ejpam-4690	260	8	(	(	PUNCT
ejpam-4690	260	9	iv	iv	X
ejpam-4690	260	10	)	)	PUNCT
ejpam-4690	260	11	if	if	SCONJ
ejpam-4690	260	12	g	g	PROPN
ejpam-4690	260	13	is	be	AUX
ejpam-4690	260	14	non	non	ADJ
ejpam-4690	260	15	-	-	ADJ
ejpam-4690	260	16	complete	complete	ADJ
ejpam-4690	260	17	,	,	PUNCT
ejpam-4690	260	18	then	then	ADV
ejpam-4690	260	19	(	(	PUNCT
ejpam-4690	260	20	a	a	X
ejpam-4690	260	21	)	)	PUNCT
ejpam-4690	260	22	3	3	NUM
ejpam-4690	260	23	≤	≤	NUM
ejpam-4690	260	24	γgr(g	γgr(g	PROPN
ejpam-4690	260	25	)	)	PUNCT
ejpam-4690	261	1	+	+	CCONJ
ejpam-4690	261	2	γgr(g	γgr(g	PROPN
ejpam-4690	261	3	)	)	PUNCT
ejpam-4690	261	4	≤	≤	NOUN
ejpam-4690	262	1	2n−	2n−	NUM
ejpam-4690	262	2	1	1	NUM
ejpam-4690	262	3	,	,	PUNCT
ejpam-4690	262	4	and	and	CCONJ
ejpam-4690	262	5	(	(	PUNCT
ejpam-4690	262	6	b	b	NOUN
ejpam-4690	262	7	)	)	PUNCT
ejpam-4690	262	8	2	2	NUM
ejpam-4690	262	9	≤	≤	NUM
ejpam-4690	262	10	γgr(g	γgr(g	PROPN
ejpam-4690	262	11	)	)	PUNCT
ejpam-4690	262	12	·	·	PUNCT
ejpam-4690	262	13	γgr(g	γgr(g	PROPN
ejpam-4690	262	14	)	)	PUNCT
ejpam-4690	262	15	≤	≤	NUM
ejpam-4690	262	16	n2	n2	NOUN
ejpam-4690	262	17	−	−	PROPN
ejpam-4690	262	18	n.	n.	NOUN
ejpam-4690	262	19	in	in	ADP
ejpam-4690	262	20	particular	particular	ADJ
ejpam-4690	262	21	,	,	PUNCT
ejpam-4690	262	22	equality	equality	NOUN
ejpam-4690	262	23	in	in	ADP
ejpam-4690	262	24	(	(	PUNCT
ejpam-4690	262	25	a	a	NOUN
ejpam-4690	262	26	)	)	PUNCT
ejpam-4690	262	27	and	and	CCONJ
ejpam-4690	262	28	(	(	PUNCT
ejpam-4690	262	29	b	b	X
ejpam-4690	262	30	)	)	PUNCT
ejpam-4690	262	31	holds	hold	VERB
ejpam-4690	262	32	if	if	SCONJ
ejpam-4690	262	33	and	and	CCONJ
ejpam-4690	262	34	only	only	ADV
ejpam-4690	262	35	if	if	SCONJ
ejpam-4690	262	36	g	g	PROPN
ejpam-4690	262	37	=	=	SYM
ejpam-4690	262	38	k2	k2	PROPN
ejpam-4690	262	39	.	.	PUNCT
ejpam-4690	263	1	proposition	proposition	NOUN
ejpam-4690	263	2	5	5	NUM
ejpam-4690	263	3	.	.	PUNCT
ejpam-4690	264	1	for	for	ADP
ejpam-4690	264	2	any	any	DET
ejpam-4690	264	3	positive	positive	ADJ
ejpam-4690	264	4	integer	integer	NOUN
ejpam-4690	264	5	n	n	CCONJ
ejpam-4690	264	6	,	,	PUNCT
ejpam-4690	264	7	each	each	PRON
ejpam-4690	264	8	of	of	ADP
ejpam-4690	264	9	the	the	DET
ejpam-4690	264	10	following	follow	VERB
ejpam-4690	264	11	holds	hold	NOUN
ejpam-4690	264	12	.	.	PUNCT
ejpam-4690	265	1	(	(	PUNCT
ejpam-4690	265	2	i	i	NOUN
ejpam-4690	265	3	)	)	PUNCT
ejpam-4690	265	4	γgr(cn	γgr(cn	ADV
ejpam-4690	265	5	)	)	PUNCT
ejpam-4690	265	6	=	=	PRON
ejpam-4690	265	7	{	{	PUNCT
ejpam-4690	265	8	1	1	NUM
ejpam-4690	265	9	if	if	SCONJ
ejpam-4690	265	10	n	n	NOUN
ejpam-4690	265	11	=	=	SYM
ejpam-4690	265	12	3	3	NUM
ejpam-4690	265	13	n−	n−	NOUN
ejpam-4690	265	14	2	2	NUM
ejpam-4690	265	15	if	if	SCONJ
ejpam-4690	265	16	n	n	PRON
ejpam-4690	265	17	≥	≥	NOUN
ejpam-4690	265	18	4	4	NUM
ejpam-4690	265	19	.	.	PUNCT
ejpam-4690	266	1	j.	j.	PROPN
ejpam-4690	266	2	hassan	hassan	PROPN
ejpam-4690	266	3	,	,	PUNCT
ejpam-4690	266	4	s.	s.	PROPN
ejpam-4690	266	5	canoy	canoy	PROPN
ejpam-4690	266	6	jr	jr	PROPN
ejpam-4690	266	7	.	.	PROPN
ejpam-4690	266	8	/	/	SYM
ejpam-4690	266	9	eur	eur	PROPN
ejpam-4690	266	10	.	.	PUNCT
ejpam-4690	267	1	j.	j.	PROPN
ejpam-4690	267	2	pure	pure	PROPN
ejpam-4690	267	3	appl	appl	PROPN
ejpam-4690	267	4	.	.	PROPN
ejpam-4690	267	5	math	math	PROPN
ejpam-4690	267	6	,	,	PUNCT
ejpam-4690	267	7	16	16	NUM
ejpam-4690	267	8	(	(	PUNCT
ejpam-4690	267	9	2	2	NUM
ejpam-4690	267	10	)	)	PUNCT
ejpam-4690	267	11	(	(	PUNCT
ejpam-4690	267	12	2023	2023	NUM
ejpam-4690	267	13	)	)	PUNCT
ejpam-4690	267	14	,	,	PUNCT
ejpam-4690	267	15	1154	1154	NUM
ejpam-4690	267	16	-	-	SYM
ejpam-4690	267	17	1166	1166	NUM
ejpam-4690	267	18	1162	1162	NUM
ejpam-4690	267	19	(	(	PUNCT
ejpam-4690	267	20	ii	ii	NOUN
ejpam-4690	267	21	)	)	PUNCT
ejpam-4690	267	22	γgr(pn	γgr(pn	NOUN
ejpam-4690	267	23	)	)	PUNCT
ejpam-4690	267	24	=	=	NOUN
ejpam-4690	267	25	{	{	PUNCT
ejpam-4690	267	26	1	1	NUM
ejpam-4690	267	27	if	if	SCONJ
ejpam-4690	267	28	n	n	CCONJ
ejpam-4690	267	29	=	=	SYM
ejpam-4690	267	30	1	1	NUM
ejpam-4690	267	31	,	,	PUNCT
ejpam-4690	267	32	2	2	NUM
ejpam-4690	267	33	n−	n−	NOUN
ejpam-4690	267	34	1	1	NUM
ejpam-4690	267	35	if	if	SCONJ
ejpam-4690	267	36	n	n	PRON
ejpam-4690	267	37	≥	≥	NOUN
ejpam-4690	267	38	3	3	NUM
ejpam-4690	267	39	.	.	PUNCT
ejpam-4690	267	40	(	(	PUNCT
ejpam-4690	267	41	iii	iii	NOUN
ejpam-4690	267	42	)	)	PUNCT
ejpam-4690	267	43	γgr(pn	γgr(pn	NOUN
ejpam-4690	267	44	)	)	PUNCT
ejpam-4690	267	45	=	=	NOUN
ejpam-4690	267	46	{	{	PUNCT
ejpam-4690	267	47	2	2	NUM
ejpam-4690	267	48	,	,	PUNCT
ejpam-4690	267	49	n	n	NOUN
ejpam-4690	267	50	=	=	SYM
ejpam-4690	267	51	2	2	NUM
ejpam-4690	267	52	,	,	PUNCT
ejpam-4690	267	53	3	3	NUM
ejpam-4690	267	54	3	3	NUM
ejpam-4690	267	55	,	,	PUNCT
ejpam-4690	267	56	n	n	PRON
ejpam-4690	267	57	≥	≥	NOUN
ejpam-4690	267	58	4	4	NUM
ejpam-4690	267	59	.	.	PUNCT
ejpam-4690	267	60	(	(	PUNCT
ejpam-4690	267	61	iv	iv	X
ejpam-4690	267	62	)	)	PUNCT
ejpam-4690	267	63	γgr(cn	γgr(cn	ADV
ejpam-4690	267	64	)	)	PUNCT
ejpam-4690	267	65	=	=	PRON
ejpam-4690	267	66	{	{	PUNCT
ejpam-4690	267	67	2	2	NUM
ejpam-4690	267	68	,	,	PUNCT
ejpam-4690	267	69	ifn	ifn	NOUN
ejpam-4690	267	70	=	=	SYM
ejpam-4690	267	71	4	4	NUM
ejpam-4690	267	72	3	3	NUM
ejpam-4690	267	73	,	,	PUNCT
ejpam-4690	267	74	if	if	SCONJ
ejpam-4690	267	75	n	n	CCONJ
ejpam-4690	267	76	=	=	SYM
ejpam-4690	267	77	3	3	NUM
ejpam-4690	267	78	or	or	CCONJ
ejpam-4690	267	79	n	n	PRON
ejpam-4690	267	80	≥	≥	NOUN
ejpam-4690	267	81	5	5	NUM
ejpam-4690	267	82	.	.	PUNCT
ejpam-4690	268	1	proof	proof	NOUN
ejpam-4690	268	2	.	.	PUNCT
ejpam-4690	269	1	(	(	PUNCT
ejpam-4690	269	2	i	i	NOUN
ejpam-4690	269	3	)	)	PUNCT
ejpam-4690	269	4	clearly	clearly	ADV
ejpam-4690	269	5	,	,	PUNCT
ejpam-4690	269	6	γgr(cn	γgr(cn	ADV
ejpam-4690	269	7	)	)	PUNCT
ejpam-4690	269	8	=	=	SYM
ejpam-4690	269	9	1	1	NUM
ejpam-4690	269	10	for	for	ADP
ejpam-4690	269	11	n	n	NOUN
ejpam-4690	269	12	=	=	SYM
ejpam-4690	269	13	3	3	X
ejpam-4690	269	14	.	.	PUNCT
ejpam-4690	269	15	suppose	suppose	VERB
ejpam-4690	269	16	n	n	PRON
ejpam-4690	269	17	≥	≥	NUM
ejpam-4690	269	18	4	4	NUM
ejpam-4690	269	19	.	.	PUNCT
ejpam-4690	270	1	let	let	VERB
ejpam-4690	270	2	cn	cn	PROPN
ejpam-4690	270	3	=	=	PUNCT
ejpam-4690	271	1	[	[	X
ejpam-4690	271	2	v1	v1	NOUN
ejpam-4690	271	3	,	,	PUNCT
ejpam-4690	271	4	v2	v2	NOUN
ejpam-4690	271	5	,	,	PUNCT
ejpam-4690	271	6	.	.	PUNCT
ejpam-4690	271	7	.	.	PUNCT
ejpam-4690	271	8	.	.	PUNCT
ejpam-4690	272	1	,	,	PUNCT
ejpam-4690	272	2	vn	vn	X
ejpam-4690	272	3	,	,	PUNCT
ejpam-4690	272	4	v1	v1	PROPN
ejpam-4690	272	5	]	]	PUNCT
ejpam-4690	272	6	and	and	CCONJ
ejpam-4690	272	7	s	s	NOUN
ejpam-4690	272	8	=	=	PUNCT
ejpam-4690	272	9	(	(	PUNCT
ejpam-4690	272	10	v1	v1	PROPN
ejpam-4690	272	11	,	,	PUNCT
ejpam-4690	272	12	v2	v2	PROPN
ejpam-4690	272	13	,	,	PUNCT
ejpam-4690	272	14	·	·	PUNCT
ejpam-4690	272	15	·	·	PUNCT
ejpam-4690	272	16	·	·	PUNCT
ejpam-4690	272	17	,	,	PUNCT
ejpam-4690	272	18	vn−2	vn−2	PROPN
ejpam-4690	272	19	)	)	PUNCT
ejpam-4690	272	20	.	.	PUNCT
ejpam-4690	273	1	clearly	clearly	ADV
ejpam-4690	273	2	,	,	PUNCT
ejpam-4690	273	3	ŝ	ŝ	X
ejpam-4690	273	4	is	be	AUX
ejpam-4690	273	5	a	a	DET
ejpam-4690	273	6	dominating	dominating	NOUN
ejpam-4690	273	7	set	set	NOUN
ejpam-4690	273	8	of	of	ADP
ejpam-4690	273	9	cn	cn	PROPN
ejpam-4690	273	10	.	.	PROPN
ejpam-4690	273	11	observe	observe	VERB
ejpam-4690	273	12	that	that	SCONJ
ejpam-4690	273	13	vi+1	vi+1	NUM
ejpam-4690	273	14	∈	∈	PROPN
ejpam-4690	273	15	ng[vi]\	ng[vi]\	NOUN
ejpam-4690	273	16	⋃i−1	⋃i−1	PROPN
ejpam-4690	273	17	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4690	273	18	]	]	PUNCT
ejpam-4690	273	19	for	for	ADP
ejpam-4690	273	20	each	each	DET
ejpam-4690	273	21	i	i	PRON
ejpam-4690	273	22	∈	∈	PROPN
ejpam-4690	273	23	{	{	PUNCT
ejpam-4690	273	24	2	2	NUM
ejpam-4690	273	25	,	,	PUNCT
ejpam-4690	273	26	.	.	PUNCT
ejpam-4690	273	27	.	.	PUNCT
ejpam-4690	274	1	.	.	PUNCT
ejpam-4690	275	1	,	,	PUNCT
ejpam-4690	275	2	n−2	n−2	PROPN
ejpam-4690	275	3	}	}	PUNCT
ejpam-4690	275	4	.	.	PUNCT
ejpam-4690	276	1	thus	thus	ADV
ejpam-4690	276	2	,	,	PUNCT
ejpam-4690	276	3	s	s	VERB
ejpam-4690	276	4	is	be	AUX
ejpam-4690	276	5	a	a	DET
ejpam-4690	276	6	grundy	grundy	PROPN
ejpam-4690	276	7	dominating	dominating	NOUN
ejpam-4690	276	8	sequence	sequence	NOUN
ejpam-4690	276	9	of	of	ADP
ejpam-4690	276	10	cn	cn	PROPN
ejpam-4690	276	11	and	and	CCONJ
ejpam-4690	276	12	γgr(cn	γgr(cn	NUM
ejpam-4690	276	13	)	)	PUNCT
ejpam-4690	276	14	≥	≥	PROPN
ejpam-4690	276	15	n	n	CCONJ
ejpam-4690	276	16	−	−	NOUN
ejpam-4690	276	17	2	2	NUM
ejpam-4690	276	18	.	.	PUNCT
ejpam-4690	277	1	on	on	ADP
ejpam-4690	277	2	the	the	DET
ejpam-4690	277	3	other	other	ADJ
ejpam-4690	277	4	hand	hand	NOUN
ejpam-4690	277	5	,	,	PUNCT
ejpam-4690	277	6	let	let	VERB
ejpam-4690	277	7	s0	s0	PROPN
ejpam-4690	277	8	=	=	SYM
ejpam-4690	277	9	(	(	PUNCT
ejpam-4690	277	10	a1	a1	PROPN
ejpam-4690	277	11	,	,	PUNCT
ejpam-4690	277	12	a2	a2	PROPN
ejpam-4690	277	13	,	,	PUNCT
ejpam-4690	277	14	.	.	PUNCT
ejpam-4690	277	15	.	.	PUNCT
ejpam-4690	278	1	.	.	PUNCT
ejpam-4690	279	1	,	,	PUNCT
ejpam-4690	279	2	ak	ak	AUX
ejpam-4690	279	3	)	)	PUNCT
ejpam-4690	279	4	be	be	AUX
ejpam-4690	279	5	a	a	DET
ejpam-4690	279	6	grundy	grundy	PROPN
ejpam-4690	279	7	dominating	dominating	NOUN
ejpam-4690	279	8	sequence	sequence	NOUN
ejpam-4690	279	9	of	of	ADP
ejpam-4690	279	10	cn	cn	PROPN
ejpam-4690	279	11	.	.	PUNCT
ejpam-4690	280	1	since	since	SCONJ
ejpam-4690	280	2	|ng[vi]|	|ng[vi]|	NOUN
ejpam-4690	280	3	=	=	SYM
ejpam-4690	280	4	3	3	NUM
ejpam-4690	280	5	for	for	ADP
ejpam-4690	280	6	each	each	DET
ejpam-4690	280	7	i	i	PRON
ejpam-4690	280	8	∈	∈	PROPN
ejpam-4690	280	9	{	{	PUNCT
ejpam-4690	280	10	1	1	NUM
ejpam-4690	280	11	,	,	PUNCT
ejpam-4690	280	12	.	.	PUNCT
ejpam-4690	280	13	.	.	PUNCT
ejpam-4690	281	1	.	.	PUNCT
ejpam-4690	282	1	,	,	PUNCT
ejpam-4690	282	2	n	n	CCONJ
ejpam-4690	282	3	}	}	PUNCT
ejpam-4690	282	4	,	,	PUNCT
ejpam-4690	282	5	it	it	PRON
ejpam-4690	282	6	follows	follow	VERB
ejpam-4690	282	7	that	that	PRON
ejpam-4690	282	8	γgr(cn	γgr(cn	ADP
ejpam-4690	282	9	)	)	PUNCT
ejpam-4690	283	1	=	=	SYM
ejpam-4690	283	2	k	k	X
ejpam-4690	283	3	≤	≤	ADJ
ejpam-4690	283	4	n−	n−	NOUN
ejpam-4690	283	5	2	2	NUM
ejpam-4690	283	6	by	by	ADP
ejpam-4690	283	7	lemma	lemma	PROPN
ejpam-4690	283	8	1	1	NUM
ejpam-4690	283	9	.	.	PUNCT
ejpam-4690	283	10	consequently	consequently	ADV
ejpam-4690	283	11	,	,	PUNCT
ejpam-4690	283	12	γgr(g	γgr(g	PROPN
ejpam-4690	283	13	)	)	PUNCT
ejpam-4690	283	14	=	=	PUNCT
ejpam-4690	283	15	n−	n−	NOUN
ejpam-4690	283	16	2	2	NUM
ejpam-4690	283	17	for	for	ADP
ejpam-4690	283	18	all	all	DET
ejpam-4690	283	19	n	n	PRON
ejpam-4690	283	20	≥	≥	NOUN
ejpam-4690	283	21	4	4	NUM
ejpam-4690	283	22	.	.	PUNCT
ejpam-4690	283	23	(	(	PUNCT
ejpam-4690	283	24	ii	ii	NOUN
ejpam-4690	283	25	)	)	PUNCT
ejpam-4690	283	26	clearly	clearly	ADV
ejpam-4690	283	27	,	,	PUNCT
ejpam-4690	283	28	γgr(pn	γgr(pn	ADJ
ejpam-4690	283	29	)	)	PUNCT
ejpam-4690	283	30	=	=	SYM
ejpam-4690	283	31	1	1	NUM
ejpam-4690	283	32	for	for	ADP
ejpam-4690	283	33	n	n	NOUN
ejpam-4690	283	34	=	=	SYM
ejpam-4690	283	35	1	1	NUM
ejpam-4690	283	36	,	,	PUNCT
ejpam-4690	283	37	2	2	NUM
ejpam-4690	283	38	.	.	PUNCT
ejpam-4690	283	39	suppose	suppose	VERB
ejpam-4690	283	40	n	n	PRON
ejpam-4690	283	41	≥	≥	NUM
ejpam-4690	283	42	3	3	X
ejpam-4690	283	43	.	.	PUNCT
ejpam-4690	284	1	let	let	VERB
ejpam-4690	284	2	pn	pn	VERB
ejpam-4690	284	3	=	=	PUNCT
ejpam-4690	285	1	[	[	X
ejpam-4690	285	2	v1	v1	NOUN
ejpam-4690	285	3	,	,	PUNCT
ejpam-4690	285	4	v2	v2	NOUN
ejpam-4690	285	5	,	,	PUNCT
ejpam-4690	285	6	.	.	PUNCT
ejpam-4690	285	7	.	.	PUNCT
ejpam-4690	285	8	.	.	PUNCT
ejpam-4690	286	1	,	,	PUNCT
ejpam-4690	286	2	vn	vn	X
ejpam-4690	286	3	]	]	PUNCT
ejpam-4690	286	4	and	and	CCONJ
ejpam-4690	286	5	let	let	VERB
ejpam-4690	286	6	d	d	X
ejpam-4690	286	7	=	=	PUNCT
ejpam-4690	286	8	(	(	PUNCT
ejpam-4690	286	9	v1	v1	PROPN
ejpam-4690	286	10	,	,	PUNCT
ejpam-4690	286	11	v2	v2	PROPN
ejpam-4690	286	12	,	,	PUNCT
ejpam-4690	286	13	·	·	PUNCT
ejpam-4690	286	14	·	·	PUNCT
ejpam-4690	286	15	·	·	PUNCT
ejpam-4690	286	16	,	,	PUNCT
ejpam-4690	286	17	vn−1	vn−1	PROPN
ejpam-4690	286	18	)	)	PUNCT
ejpam-4690	286	19	.	.	PUNCT
ejpam-4690	287	1	clearly	clearly	ADV
ejpam-4690	287	2	,	,	PUNCT
ejpam-4690	287	3	d̂	d̂	PROPN
ejpam-4690	287	4	is	be	AUX
ejpam-4690	287	5	a	a	DET
ejpam-4690	287	6	dominating	dominating	NOUN
ejpam-4690	287	7	set	set	NOUN
ejpam-4690	287	8	of	of	ADP
ejpam-4690	287	9	pn	pn	PROPN
ejpam-4690	287	10	.	.	PROPN
ejpam-4690	287	11	observe	observe	VERB
ejpam-4690	287	12	that	that	SCONJ
ejpam-4690	287	13	vi+1	vi+1	NUM
ejpam-4690	287	14	∈	∈	PROPN
ejpam-4690	287	15	ng[vi	ng[vi	PROPN
ejpam-4690	287	16	]	]	PUNCT
ejpam-4690	287	17	\	\	PROPN
ejpam-4690	287	18	⋃i−1	⋃i−1	NOUN
ejpam-4690	287	19	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4690	287	20	]	]	PUNCT
ejpam-4690	287	21	for	for	ADP
ejpam-4690	287	22	each	each	DET
ejpam-4690	287	23	i	i	PRON
ejpam-4690	287	24	∈	∈	PROPN
ejpam-4690	287	25	{	{	PUNCT
ejpam-4690	287	26	2	2	NUM
ejpam-4690	287	27	,	,	PUNCT
ejpam-4690	287	28	.	.	PUNCT
ejpam-4690	287	29	.	.	PUNCT
ejpam-4690	288	1	.	.	PUNCT
ejpam-4690	289	1	,	,	PUNCT
ejpam-4690	289	2	n−	n−	NOUN
ejpam-4690	289	3	2	2	NUM
ejpam-4690	289	4	}	}	PUNCT
ejpam-4690	289	5	.	.	PUNCT
ejpam-4690	290	1	thus	thus	ADV
ejpam-4690	290	2	,	,	PUNCT
ejpam-4690	290	3	d	d	PRON
ejpam-4690	290	4	is	be	AUX
ejpam-4690	290	5	a	a	DET
ejpam-4690	290	6	grundy	grundy	PROPN
ejpam-4690	290	7	dominating	dominating	NOUN
ejpam-4690	290	8	sequence	sequence	NOUN
ejpam-4690	290	9	of	of	ADP
ejpam-4690	290	10	pn	pn	PROPN
ejpam-4690	290	11	showing	show	VERB
ejpam-4690	290	12	that	that	DET
ejpam-4690	290	13	γgr(pn	γgr(pn	NOUN
ejpam-4690	290	14	)	)	PUNCT
ejpam-4690	290	15	≥	≥	NOUN
ejpam-4690	290	16	n	n	CCONJ
ejpam-4690	290	17	−	−	PROPN
ejpam-4690	290	18	1	1	NUM
ejpam-4690	290	19	.	.	PUNCT
ejpam-4690	291	1	since	since	SCONJ
ejpam-4690	291	2	|npn	|npn	NOUN
ejpam-4690	291	3	[	[	X
ejpam-4690	291	4	a]|	a]|	NOUN
ejpam-4690	291	5	≥	≥	NUM
ejpam-4690	291	6	2	2	NUM
ejpam-4690	291	7	for	for	ADP
ejpam-4690	291	8	every	every	PRON
ejpam-4690	291	9	a	a	PRON
ejpam-4690	291	10	∈	∈	PROPN
ejpam-4690	291	11	v	v	NOUN
ejpam-4690	291	12	(	(	PUNCT
ejpam-4690	291	13	pn	pn	NOUN
ejpam-4690	291	14	)	)	PUNCT
ejpam-4690	291	15	,	,	PUNCT
ejpam-4690	291	16	γgr(pn	γgr(pn	NOUN
ejpam-4690	291	17	)	)	PUNCT
ejpam-4690	291	18	≤	≤	NUM
ejpam-4690	291	19	n−	n−	NOUN
ejpam-4690	291	20	1	1	NUM
ejpam-4690	291	21	by	by	ADP
ejpam-4690	291	22	lemma	lemma	PROPN
ejpam-4690	291	23	1	1	NUM
ejpam-4690	291	24	.	.	PUNCT
ejpam-4690	291	25	therefore	therefore	ADV
ejpam-4690	291	26	,	,	PUNCT
ejpam-4690	291	27	γgr(pn	γgr(pn	X
ejpam-4690	291	28	)	)	PUNCT
ejpam-4690	291	29	=	=	PUNCT
ejpam-4690	291	30	n−	n−	NOUN
ejpam-4690	291	31	1	1	NUM
ejpam-4690	291	32	for	for	ADP
ejpam-4690	291	33	all	all	DET
ejpam-4690	291	34	n	n	PRON
ejpam-4690	291	35	≥	≥	NOUN
ejpam-4690	291	36	3	3	NUM
ejpam-4690	291	37	.	.	PUNCT
ejpam-4690	291	38	(	(	PUNCT
ejpam-4690	291	39	iii	iii	NOUN
ejpam-4690	291	40	)	)	PUNCT
ejpam-4690	291	41	clearly	clearly	ADV
ejpam-4690	291	42	,	,	PUNCT
ejpam-4690	291	43	γgr(pn	γgr(pn	ADJ
ejpam-4690	291	44	)	)	PUNCT
ejpam-4690	291	45	=	=	SYM
ejpam-4690	291	46	2	2	NUM
ejpam-4690	291	47	for	for	ADP
ejpam-4690	291	48	n	n	NOUN
ejpam-4690	291	49	=	=	SYM
ejpam-4690	291	50	2	2	NUM
ejpam-4690	291	51	,	,	PUNCT
ejpam-4690	291	52	3	3	NUM
ejpam-4690	291	53	.	.	PUNCT
ejpam-4690	291	54	suppose	suppose	VERB
ejpam-4690	291	55	n	n	PRON
ejpam-4690	291	56	≥	≥	NUM
ejpam-4690	291	57	4	4	NUM
ejpam-4690	291	58	.	.	PUNCT
ejpam-4690	292	1	let	let	AUX
ejpam-4690	292	2	{	{	PUNCT
ejpam-4690	292	3	v1	v1	VERB
ejpam-4690	292	4	,	,	PUNCT
ejpam-4690	292	5	v2	v2	PROPN
ejpam-4690	292	6	,	,	PUNCT
ejpam-4690	292	7	·	·	PUNCT
ejpam-4690	292	8	·	·	PUNCT
ejpam-4690	292	9	·	·	PUNCT
ejpam-4690	292	10	,	,	PUNCT
ejpam-4690	292	11	vn	vn	PART
ejpam-4690	292	12	}	}	PUNCT
ejpam-4690	292	13	be	be	AUX
ejpam-4690	292	14	a	a	DET
ejpam-4690	292	15	vertex	vertex	NOUN
ejpam-4690	292	16	set	set	NOUN
ejpam-4690	292	17	of	of	ADP
ejpam-4690	292	18	pn	pn	PROPN
ejpam-4690	292	19	and	and	CCONJ
ejpam-4690	292	20	consider	consider	VERB
ejpam-4690	292	21	s	s	PRON
ejpam-4690	292	22	=	=	X
ejpam-4690	292	23	(	(	PUNCT
ejpam-4690	292	24	v2	v2	PROPN
ejpam-4690	292	25	,	,	PUNCT
ejpam-4690	292	26	v4	v4	NOUN
ejpam-4690	292	27	,	,	PUNCT
ejpam-4690	292	28	v3	v3	PROPN
ejpam-4690	292	29	)	)	PUNCT
ejpam-4690	292	30	.	.	PUNCT
ejpam-4690	293	1	then	then	ADV
ejpam-4690	293	2	s	s	VERB
ejpam-4690	293	3	is	be	AUX
ejpam-4690	293	4	a	a	DET
ejpam-4690	293	5	grundy	grundy	PROPN
ejpam-4690	293	6	dominating	dominating	NOUN
ejpam-4690	293	7	sequence	sequence	NOUN
ejpam-4690	293	8	of	of	ADP
ejpam-4690	293	9	pn	pn	PROPN
ejpam-4690	293	10	.	.	PROPN
ejpam-4690	294	1	hence	hence	ADV
ejpam-4690	294	2	,	,	PUNCT
ejpam-4690	294	3	γgr(pn	γgr(pn	NUM
ejpam-4690	294	4	)	)	PUNCT
ejpam-4690	294	5	≥	≥	NOUN
ejpam-4690	295	1	3	3	NUM
ejpam-4690	295	2	.	.	PUNCT
ejpam-4690	296	1	on	on	ADP
ejpam-4690	296	2	the	the	DET
ejpam-4690	296	3	other	other	ADJ
ejpam-4690	296	4	hand	hand	NOUN
ejpam-4690	296	5	,	,	PUNCT
ejpam-4690	296	6	let	let	VERB
ejpam-4690	296	7	s′	s′	ADJ
ejpam-4690	296	8	=	=	SYM
ejpam-4690	296	9	(	(	PUNCT
ejpam-4690	296	10	w1	w1	NOUN
ejpam-4690	296	11	,	,	PUNCT
ejpam-4690	296	12	·	·	PUNCT
ejpam-4690	296	13	·	·	PUNCT
ejpam-4690	296	14	·	·	PUNCT
ejpam-4690	296	15	,	,	PUNCT
ejpam-4690	296	16	wk	wk	AUX
ejpam-4690	296	17	)	)	PUNCT
ejpam-4690	296	18	be	be	AUX
ejpam-4690	296	19	a	a	DET
ejpam-4690	296	20	grundy	grundy	PROPN
ejpam-4690	296	21	dominating	dominating	NOUN
ejpam-4690	296	22	sequence	sequence	NOUN
ejpam-4690	296	23	of	of	ADP
ejpam-4690	296	24	pn	pn	PROPN
ejpam-4690	296	25	.	.	PROPN
ejpam-4690	296	26	notice	notice	VERB
ejpam-4690	296	27	that	that	SCONJ
ejpam-4690	296	28	|npn	|npn	NOUN
ejpam-4690	296	29	[	[	X
ejpam-4690	296	30	vi]|	vi]|	VERB
ejpam-4690	296	31	≥	≥	NOUN
ejpam-4690	296	32	n−	n−	NOUN
ejpam-4690	296	33	2	2	NUM
ejpam-4690	296	34	for	for	ADP
ejpam-4690	296	35	every	every	DET
ejpam-4690	296	36	i	i	PROPN
ejpam-4690	296	37	∈	∈	PROPN
ejpam-4690	296	38	{	{	PUNCT
ejpam-4690	296	39	1	1	NUM
ejpam-4690	296	40	,	,	PUNCT
ejpam-4690	296	41	.	.	PUNCT
ejpam-4690	296	42	.	.	PUNCT
ejpam-4690	296	43	.	.	PUNCT
ejpam-4690	297	1	,	,	PUNCT
ejpam-4690	298	1	n	n	CCONJ
ejpam-4690	298	2	}	}	PUNCT
ejpam-4690	298	3	.	.	PUNCT
ejpam-4690	299	1	thus	thus	ADV
ejpam-4690	299	2	,	,	PUNCT
ejpam-4690	299	3	γgr(pn	γgr(pn	NOUN
ejpam-4690	299	4	)	)	PUNCT
ejpam-4690	299	5	=	=	SYM
ejpam-4690	300	1	k	k	NOUN
ejpam-4690	300	2	≤	≤	ADV
ejpam-4690	300	3	3	3	NUM
ejpam-4690	300	4	by	by	ADP
ejpam-4690	300	5	lemma	lemma	PROPN
ejpam-4690	300	6	1	1	NUM
ejpam-4690	300	7	.	.	PUNCT
ejpam-4690	300	8	consequently	consequently	ADV
ejpam-4690	300	9	,	,	PUNCT
ejpam-4690	300	10	γgr(pn	γgr(pn	ADJ
ejpam-4690	300	11	)	)	PUNCT
ejpam-4690	300	12	=	=	SYM
ejpam-4690	300	13	3	3	NUM
ejpam-4690	300	14	for	for	ADP
ejpam-4690	300	15	all	all	DET
ejpam-4690	300	16	n	n	PRON
ejpam-4690	300	17	≥	≥	NOUN
ejpam-4690	300	18	4	4	NUM
ejpam-4690	300	19	.	.	PUNCT
ejpam-4690	300	20	(	(	PUNCT
ejpam-4690	300	21	iv	iv	X
ejpam-4690	300	22	)	)	PUNCT
ejpam-4690	300	23	clearly	clearly	ADV
ejpam-4690	300	24	,	,	PUNCT
ejpam-4690	300	25	γgr(c3	γgr(c3	NOUN
ejpam-4690	300	26	)	)	PUNCT
ejpam-4690	300	27	=	=	SYM
ejpam-4690	300	28	3	3	NUM
ejpam-4690	300	29	and	and	CCONJ
ejpam-4690	300	30	γgr(c4	γgr(c4	NOUN
ejpam-4690	300	31	)	)	PUNCT
ejpam-4690	300	32	=	=	SYM
ejpam-4690	301	1	2	2	X
ejpam-4690	301	2	.	.	X
ejpam-4690	301	3	suppose	suppose	VERB
ejpam-4690	301	4	n	n	PRON
ejpam-4690	301	5	≥	≥	NUM
ejpam-4690	301	6	5	5	NUM
ejpam-4690	301	7	.	.	PUNCT
ejpam-4690	302	1	let	let	AUX
ejpam-4690	302	2	{	{	PUNCT
ejpam-4690	302	3	v1	v1	VERB
ejpam-4690	302	4	,	,	PUNCT
ejpam-4690	302	5	v2	v2	PROPN
ejpam-4690	302	6	,	,	PUNCT
ejpam-4690	302	7	·	·	PUNCT
ejpam-4690	302	8	·	·	PUNCT
ejpam-4690	302	9	·	·	PUNCT
ejpam-4690	302	10	,	,	PUNCT
ejpam-4690	302	11	vn	vn	PART
ejpam-4690	302	12	}	}	PUNCT
ejpam-4690	302	13	be	be	AUX
ejpam-4690	302	14	a	a	DET
ejpam-4690	302	15	vertex	vertex	NOUN
ejpam-4690	302	16	set	set	NOUN
ejpam-4690	302	17	of	of	ADP
ejpam-4690	302	18	cn	cn	PROPN
ejpam-4690	302	19	and	and	CCONJ
ejpam-4690	302	20	consider	consider	VERB
ejpam-4690	302	21	s′	s′	ADJ
ejpam-4690	302	22	=	=	PUNCT
ejpam-4690	302	23	{	{	PUNCT
ejpam-4690	302	24	v1	v1	PROPN
ejpam-4690	302	25	,	,	PUNCT
ejpam-4690	302	26	v3	v3	PROPN
ejpam-4690	302	27	,	,	PUNCT
ejpam-4690	302	28	v2	v2	PROPN
ejpam-4690	302	29	}	}	PUNCT
ejpam-4690	302	30	.	.	PUNCT
ejpam-4690	303	1	then	then	ADV
ejpam-4690	303	2	s′	s′	PROPN
ejpam-4690	303	3	is	be	AUX
ejpam-4690	303	4	a	a	DET
ejpam-4690	303	5	grundy	grundy	PROPN
ejpam-4690	303	6	dominating	dominating	NOUN
ejpam-4690	303	7	sequence	sequence	NOUN
ejpam-4690	303	8	of	of	ADP
ejpam-4690	303	9	cn	cn	PROPN
ejpam-4690	303	10	.	.	PUNCT
ejpam-4690	304	1	hence	hence	ADV
ejpam-4690	304	2	,	,	PUNCT
ejpam-4690	304	3	γgr(cn	γgr(cn	NUM
ejpam-4690	304	4	)	)	PUNCT
ejpam-4690	304	5	≥	≥	NOUN
ejpam-4690	304	6	3	3	NUM
ejpam-4690	304	7	.	.	PUNCT
ejpam-4690	305	1	on	on	ADP
ejpam-4690	305	2	the	the	DET
ejpam-4690	305	3	other	other	ADJ
ejpam-4690	305	4	hand	hand	NOUN
ejpam-4690	305	5	,	,	PUNCT
ejpam-4690	305	6	let	let	VERB
ejpam-4690	305	7	s′′	s′′	PROPN
ejpam-4690	305	8	=	=	SYM
ejpam-4690	305	9	(	(	PUNCT
ejpam-4690	305	10	u1	u1	PROPN
ejpam-4690	305	11	,	,	PUNCT
ejpam-4690	305	12	·	·	PUNCT
ejpam-4690	305	13	·	·	PUNCT
ejpam-4690	305	14	·	·	PUNCT
ejpam-4690	305	15	,	,	PUNCT
ejpam-4690	305	16	ul	ul	AUX
ejpam-4690	305	17	)	)	PUNCT
ejpam-4690	305	18	be	be	VERB
ejpam-4690	305	19	a	a	DET
ejpam-4690	305	20	grundy	grundy	PROPN
ejpam-4690	305	21	dominating	dominating	NOUN
ejpam-4690	305	22	sequence	sequence	NOUN
ejpam-4690	305	23	of	of	ADP
ejpam-4690	305	24	cn	cn	PROPN
ejpam-4690	305	25	.	.	PROPN
ejpam-4690	305	26	observe	observe	VERB
ejpam-4690	305	27	that	that	DET
ejpam-4690	305	28	|ncn	|ncn	NOUN
ejpam-4690	306	1	[	[	X
ejpam-4690	306	2	vi]|	vi]|	NOUN
ejpam-4690	306	3	=	=	SYM
ejpam-4690	306	4	n	n	CCONJ
ejpam-4690	306	5	−	−	NUM
ejpam-4690	306	6	2	2	NUM
ejpam-4690	306	7	for	for	ADP
ejpam-4690	306	8	every	every	DET
ejpam-4690	306	9	i	i	PROPN
ejpam-4690	306	10	∈	∈	PROPN
ejpam-4690	306	11	{	{	PUNCT
ejpam-4690	306	12	1	1	NUM
ejpam-4690	306	13	,	,	PUNCT
ejpam-4690	306	14	·	·	PUNCT
ejpam-4690	306	15	·	·	PUNCT
ejpam-4690	306	16	·	·	PUNCT
ejpam-4690	306	17	,	,	PUNCT
ejpam-4690	306	18	n	n	CCONJ
ejpam-4690	306	19	}	}	PUNCT
ejpam-4690	306	20	.	.	PUNCT
ejpam-4690	307	1	thus	thus	ADV
ejpam-4690	307	2	,	,	PUNCT
ejpam-4690	307	3	γgr(cn	γgr(cn	ADV
ejpam-4690	307	4	)	)	PUNCT
ejpam-4690	308	1	=	=	PUNCT
ejpam-4690	308	2	l	l	NOUN
ejpam-4690	308	3	≤	≤	NUM
ejpam-4690	308	4	3	3	NUM
ejpam-4690	308	5	by	by	ADP
ejpam-4690	308	6	lemma	lemma	PROPN
ejpam-4690	308	7	1	1	NUM
ejpam-4690	308	8	.	.	PUNCT
ejpam-4690	308	9	therefore	therefore	ADV
ejpam-4690	308	10	,	,	PUNCT
ejpam-4690	308	11	γgr(cn	γgr(cn	ADV
ejpam-4690	308	12	)	)	PUNCT
ejpam-4690	308	13	=	=	SYM
ejpam-4690	308	14	3	3	NUM
ejpam-4690	308	15	for	for	ADP
ejpam-4690	308	16	all	all	DET
ejpam-4690	308	17	n	n	PRON
ejpam-4690	308	18	≥	≥	NUM
ejpam-4690	308	19	5	5	NUM
ejpam-4690	308	20	.	.	PUNCT
ejpam-4690	308	21	theorem	theorem	NOUN
ejpam-4690	308	22	5	5	NUM
ejpam-4690	308	23	.	.	PUNCT
ejpam-4690	309	1	let	let	VERB
ejpam-4690	309	2	g	g	NOUN
ejpam-4690	309	3	and	and	CCONJ
ejpam-4690	309	4	h	h	NOUN
ejpam-4690	309	5	be	be	VERB
ejpam-4690	309	6	two	two	NUM
ejpam-4690	309	7	non	non	ADJ
ejpam-4690	309	8	-	-	ADJ
ejpam-4690	309	9	complete	complete	ADJ
ejpam-4690	309	10	graphs	graph	NOUN
ejpam-4690	309	11	.	.	PUNCT
ejpam-4690	310	1	a	a	DET
ejpam-4690	310	2	sequence	sequence	NOUN
ejpam-4690	310	3	d	d	NOUN
ejpam-4690	310	4	of	of	ADP
ejpam-4690	310	5	distinct	distinct	ADJ
ejpam-4690	310	6	vertices	vertex	NOUN
ejpam-4690	310	7	of	of	ADP
ejpam-4690	310	8	g	g	PROPN
ejpam-4690	310	9	+	+	NOUN
ejpam-4690	310	10	h	h	NOUN
ejpam-4690	310	11	is	be	AUX
ejpam-4690	310	12	a	a	DET
ejpam-4690	310	13	grundy	grundy	PROPN
ejpam-4690	310	14	dominating	dominating	NOUN
ejpam-4690	310	15	sequence	sequence	NOUN
ejpam-4690	310	16	in	in	ADP
ejpam-4690	310	17	g	g	PROPN
ejpam-4690	311	1	+	+	NOUN
ejpam-4690	311	2	h	h	NOUN
ejpam-4690	311	3	if	if	SCONJ
ejpam-4690	311	4	and	and	CCONJ
ejpam-4690	311	5	only	only	ADV
ejpam-4690	311	6	if	if	SCONJ
ejpam-4690	311	7	one	one	NUM
ejpam-4690	311	8	of	of	ADP
ejpam-4690	311	9	the	the	DET
ejpam-4690	311	10	following	follow	VERB
ejpam-4690	311	11	condition	condition	NOUN
ejpam-4690	311	12	holds	hold	VERB
ejpam-4690	311	13	:	:	PUNCT
ejpam-4690	311	14	(	(	PUNCT
ejpam-4690	311	15	i	i	NOUN
ejpam-4690	311	16	)	)	PUNCT
ejpam-4690	312	1	d	d	PRON
ejpam-4690	312	2	is	be	AUX
ejpam-4690	312	3	a	a	DET
ejpam-4690	312	4	grundy	grundy	PROPN
ejpam-4690	312	5	dominating	dominating	NOUN
ejpam-4690	312	6	sequence	sequence	NOUN
ejpam-4690	312	7	of	of	ADP
ejpam-4690	312	8	g.	g.	PROPN
ejpam-4690	312	9	(	(	PUNCT
ejpam-4690	312	10	ii	ii	PROPN
ejpam-4690	312	11	)	)	PUNCT
ejpam-4690	312	12	d	d	NOUN
ejpam-4690	312	13	is	be	AUX
ejpam-4690	312	14	a	a	DET
ejpam-4690	312	15	grundy	grundy	PROPN
ejpam-4690	312	16	dominating	dominating	NOUN
ejpam-4690	312	17	sequence	sequence	NOUN
ejpam-4690	312	18	of	of	ADP
ejpam-4690	312	19	h.	h.	PROPN
ejpam-4690	312	20	(	(	PUNCT
ejpam-4690	312	21	iii	iii	NOUN
ejpam-4690	312	22	)	)	PUNCT
ejpam-4690	312	23	d	d	NOUN
ejpam-4690	312	24	=	=	SYM
ejpam-4690	312	25	dg	dg	PROPN
ejpam-4690	312	26	⊕	⊕	PROPN
ejpam-4690	312	27	(	(	PUNCT
ejpam-4690	312	28	w	w	NOUN
ejpam-4690	312	29	)	)	PUNCT
ejpam-4690	312	30	for	for	ADP
ejpam-4690	312	31	some	some	DET
ejpam-4690	312	32	non	non	ADJ
ejpam-4690	312	33	-	-	ADJ
ejpam-4690	312	34	dominating	dominating	ADJ
ejpam-4690	312	35	legal	legal	ADJ
ejpam-4690	312	36	closed	close	VERB
ejpam-4690	312	37	neighborhood	neighborhood	NOUN
ejpam-4690	312	38	sequence	sequence	NOUN
ejpam-4690	312	39	dg	dg	NOUN
ejpam-4690	312	40	of	of	ADP
ejpam-4690	312	41	g	g	PROPN
ejpam-4690	312	42	and	and	CCONJ
ejpam-4690	312	43	w	w	PROPN
ejpam-4690	312	44	∈	∈	PROPN
ejpam-4690	312	45	v	v	ADP
ejpam-4690	312	46	(	(	PUNCT
ejpam-4690	312	47	h	h	NOUN
ejpam-4690	312	48	)	)	PUNCT
ejpam-4690	312	49	.	.	PUNCT
ejpam-4690	313	1	j.	j.	PROPN
ejpam-4690	313	2	hassan	hassan	PROPN
ejpam-4690	313	3	,	,	PUNCT
ejpam-4690	313	4	s.	s.	PROPN
ejpam-4690	313	5	canoy	canoy	PROPN
ejpam-4690	313	6	jr	jr	PROPN
ejpam-4690	313	7	.	.	PROPN
ejpam-4690	313	8	/	/	SYM
ejpam-4690	313	9	eur	eur	PROPN
ejpam-4690	313	10	.	.	PUNCT
ejpam-4690	314	1	j.	j.	PROPN
ejpam-4690	314	2	pure	pure	PROPN
ejpam-4690	314	3	appl	appl	PROPN
ejpam-4690	314	4	.	.	PROPN
ejpam-4690	314	5	math	math	PROPN
ejpam-4690	314	6	,	,	PUNCT
ejpam-4690	314	7	16	16	NUM
ejpam-4690	314	8	(	(	PUNCT
ejpam-4690	314	9	2	2	NUM
ejpam-4690	314	10	)	)	PUNCT
ejpam-4690	314	11	(	(	PUNCT
ejpam-4690	314	12	2023	2023	NUM
ejpam-4690	314	13	)	)	PUNCT
ejpam-4690	314	14	,	,	PUNCT
ejpam-4690	314	15	1154	1154	NUM
ejpam-4690	314	16	-	-	SYM
ejpam-4690	314	17	1166	1166	NUM
ejpam-4690	314	18	1163	1163	NUM
ejpam-4690	314	19	(	(	PUNCT
ejpam-4690	314	20	iv	iv	X
ejpam-4690	314	21	)	)	PUNCT
ejpam-4690	314	22	d	d	NOUN
ejpam-4690	314	23	=	=	SYM
ejpam-4690	314	24	dh	dh	PROPN
ejpam-4690	314	25	⊕	⊕	PROPN
ejpam-4690	314	26	(	(	PUNCT
ejpam-4690	314	27	v	v	NOUN
ejpam-4690	314	28	)	)	PUNCT
ejpam-4690	314	29	for	for	ADP
ejpam-4690	314	30	some	some	DET
ejpam-4690	314	31	non	non	ADJ
ejpam-4690	314	32	-	-	ADJ
ejpam-4690	314	33	dominating	dominating	ADJ
ejpam-4690	314	34	legal	legal	ADJ
ejpam-4690	314	35	closed	close	VERB
ejpam-4690	314	36	neighborhood	neighborhood	NOUN
ejpam-4690	314	37	sequence	sequence	NOUN
ejpam-4690	314	38	dh	dh	NOUN
ejpam-4690	314	39	of	of	ADP
ejpam-4690	314	40	h	h	NOUN
ejpam-4690	314	41	and	and	CCONJ
ejpam-4690	314	42	v	v	ADP
ejpam-4690	314	43	∈	∈	PROPN
ejpam-4690	314	44	v	v	NOUN
ejpam-4690	314	45	(	(	PUNCT
ejpam-4690	314	46	g	g	NOUN
ejpam-4690	314	47	)	)	PUNCT
ejpam-4690	314	48	.	.	PUNCT
ejpam-4690	315	1	proof	proof	NOUN
ejpam-4690	315	2	.	.	PUNCT
ejpam-4690	316	1	let	let	VERB
ejpam-4690	316	2	dg	dg	PRON
ejpam-4690	316	3	and	and	CCONJ
ejpam-4690	316	4	dh	dh	PROPN
ejpam-4690	316	5	be	be	AUX
ejpam-4690	316	6	subsequences	subsequence	NOUN
ejpam-4690	316	7	d	d	X
ejpam-4690	316	8	such	such	ADJ
ejpam-4690	316	9	that	that	DET
ejpam-4690	316	10	d̂g	d̂g	NOUN
ejpam-4690	316	11	=	=	PUNCT
ejpam-4690	316	12	d̂	d̂	PROPN
ejpam-4690	316	13	∩	∩	PROPN
ejpam-4690	316	14	v	v	X
ejpam-4690	316	15	(	(	PUNCT
ejpam-4690	316	16	g	g	NOUN
ejpam-4690	316	17	)	)	PUNCT
ejpam-4690	316	18	and	and	CCONJ
ejpam-4690	316	19	d̂h	d̂h	NOUN
ejpam-4690	316	20	=	=	PUNCT
ejpam-4690	316	21	d̂	d̂	PROPN
ejpam-4690	316	22	∩	∩	PROPN
ejpam-4690	316	23	v	v	X
ejpam-4690	316	24	(	(	PUNCT
ejpam-4690	316	25	h	h	NOUN
ejpam-4690	316	26	)	)	PUNCT
ejpam-4690	316	27	.	.	PUNCT
ejpam-4690	317	1	if	if	SCONJ
ejpam-4690	317	2	d̂h	d̂h	NOUN
ejpam-4690	317	3	=	=	SYM
ejpam-4690	317	4	∅	∅	NOUN
ejpam-4690	317	5	,	,	PUNCT
ejpam-4690	317	6	then	then	ADV
ejpam-4690	317	7	d	d	PROPN
ejpam-4690	317	8	=	=	PUNCT
ejpam-4690	317	9	dg	dg	PROPN
ejpam-4690	317	10	is	be	AUX
ejpam-4690	317	11	a	a	DET
ejpam-4690	317	12	grundy	grundy	PROPN
ejpam-4690	317	13	dominating	dominating	NOUN
ejpam-4690	317	14	sequence	sequence	NOUN
ejpam-4690	317	15	of	of	ADP
ejpam-4690	317	16	g.	g.	PROPN
ejpam-4690	317	17	if	if	SCONJ
ejpam-4690	317	18	d̂g	d̂g	NOUN
ejpam-4690	317	19	=	=	SYM
ejpam-4690	317	20	∅	∅	NOUN
ejpam-4690	317	21	,	,	PUNCT
ejpam-4690	317	22	then	then	ADV
ejpam-4690	317	23	d	d	PROPN
ejpam-4690	317	24	=	=	SYM
ejpam-4690	317	25	dh	dh	PROPN
ejpam-4690	317	26	is	be	AUX
ejpam-4690	317	27	a	a	DET
ejpam-4690	317	28	grundy	grundy	PROPN
ejpam-4690	317	29	dominating	dominating	NOUN
ejpam-4690	317	30	sequence	sequence	NOUN
ejpam-4690	317	31	of	of	ADP
ejpam-4690	317	32	h.	h.	PROPN
ejpam-4690	317	33	hence	hence	ADV
ejpam-4690	317	34	,	,	PUNCT
ejpam-4690	317	35	(	(	PUNCT
ejpam-4690	317	36	i	i	NOUN
ejpam-4690	317	37	)	)	PUNCT
ejpam-4690	317	38	or	or	CCONJ
ejpam-4690	317	39	(	(	PUNCT
ejpam-4690	317	40	ii	ii	NOUN
ejpam-4690	317	41	)	)	PUNCT
ejpam-4690	317	42	holds	hold	VERB
ejpam-4690	317	43	.	.	PUNCT
ejpam-4690	318	1	suppose	suppose	VERB
ejpam-4690	318	2	now	now	ADV
ejpam-4690	318	3	that	that	SCONJ
ejpam-4690	318	4	d̂g	d̂g	NOUN
ejpam-4690	318	5	and	and	CCONJ
ejpam-4690	318	6	d̂h	d̂h	PRON
ejpam-4690	318	7	are	be	AUX
ejpam-4690	318	8	both	both	PRON
ejpam-4690	318	9	non	non	ADJ
ejpam-4690	318	10	-	-	ADJ
ejpam-4690	318	11	empty	empty	ADJ
ejpam-4690	318	12	.	.	PUNCT
ejpam-4690	319	1	since	since	SCONJ
ejpam-4690	319	2	d	d	PROPN
ejpam-4690	319	3	is	be	AUX
ejpam-4690	319	4	a	a	DET
ejpam-4690	319	5	legal	legal	ADJ
ejpam-4690	319	6	closed	closed	ADJ
ejpam-4690	319	7	neighborhood	neighborhood	NOUN
ejpam-4690	319	8	sequence	sequence	NOUN
ejpam-4690	319	9	of	of	ADP
ejpam-4690	319	10	g+h	g+h	PROPN
ejpam-4690	319	11	,	,	PUNCT
ejpam-4690	319	12	dg	dg	PROPN
ejpam-4690	319	13	and	and	CCONJ
ejpam-4690	319	14	dh	dh	NOUN
ejpam-4690	319	15	are	be	AUX
ejpam-4690	319	16	legal	legal	ADJ
ejpam-4690	319	17	closed	closed	ADJ
ejpam-4690	319	18	neighborhood	neighborhood	NOUN
ejpam-4690	319	19	sequences	sequence	NOUN
ejpam-4690	319	20	of	of	ADP
ejpam-4690	319	21	g	g	PROPN
ejpam-4690	319	22	and	and	CCONJ
ejpam-4690	319	23	h	h	NOUN
ejpam-4690	319	24	,	,	PUNCT
ejpam-4690	319	25	respectively	respectively	ADV
ejpam-4690	319	26	.	.	PUNCT
ejpam-4690	320	1	if	if	SCONJ
ejpam-4690	320	2	|d̂g|	|d̂g|	PROPN
ejpam-4690	320	3	=	=	SYM
ejpam-4690	320	4	|d̂h	|d̂h	PROPN
ejpam-4690	320	5	|	|	ADV
ejpam-4690	320	6	=	=	SYM
ejpam-4690	320	7	1	1	NUM
ejpam-4690	320	8	,	,	PUNCT
ejpam-4690	320	9	then	then	ADV
ejpam-4690	320	10	both	both	DET
ejpam-4690	320	11	(	(	PUNCT
ejpam-4690	320	12	iii	iii	NOUN
ejpam-4690	320	13	)	)	PUNCT
ejpam-4690	320	14	and	and	CCONJ
ejpam-4690	320	15	(	(	PUNCT
ejpam-4690	320	16	iv	iv	X
ejpam-4690	320	17	)	)	PUNCT
ejpam-4690	320	18	hold	hold	NOUN
ejpam-4690	320	19	.	.	PUNCT
ejpam-4690	321	1	next	next	ADV
ejpam-4690	321	2	,	,	PUNCT
ejpam-4690	321	3	suppose	suppose	VERB
ejpam-4690	321	4	that	that	SCONJ
ejpam-4690	321	5	|d̂g|	|d̂g|	PROPN
ejpam-4690	321	6	≥	≥	NUM
ejpam-4690	321	7	2	2	X
ejpam-4690	321	8	.	.	PUNCT
ejpam-4690	321	9	suppose	suppose	VERB
ejpam-4690	321	10	further	far	ADV
ejpam-4690	321	11	that	that	SCONJ
ejpam-4690	321	12	d̂g	d̂g	PRON
ejpam-4690	321	13	is	be	AUX
ejpam-4690	321	14	dominating	dominate	VERB
ejpam-4690	321	15	.	.	PUNCT
ejpam-4690	322	1	let	let	VERB
ejpam-4690	322	2	d	d	NOUN
ejpam-4690	322	3	=	=	SYM
ejpam-4690	322	4	(	(	PUNCT
ejpam-4690	322	5	x1	x1	PROPN
ejpam-4690	322	6	,	,	PUNCT
ejpam-4690	322	7	x2	x2	PROPN
ejpam-4690	322	8	,	,	PUNCT
ejpam-4690	322	9	.	.	PUNCT
ejpam-4690	322	10	.	.	PUNCT
ejpam-4690	323	1	.	.	PUNCT
ejpam-4690	324	1	,	,	PUNCT
ejpam-4690	324	2	xm	xm	PROPN
ejpam-4690	324	3	)	)	PUNCT
ejpam-4690	324	4	.	.	PUNCT
ejpam-4690	325	1	since	since	SCONJ
ejpam-4690	325	2	d̂g	d̂g	PRON
ejpam-4690	325	3	is	be	AUX
ejpam-4690	325	4	dominating	dominate	VERB
ejpam-4690	325	5	,	,	PUNCT
ejpam-4690	325	6	none	none	NOUN
ejpam-4690	325	7	of	of	ADP
ejpam-4690	325	8	the	the	DET
ejpam-4690	325	9	terms	term	NOUN
ejpam-4690	325	10	in	in	ADP
ejpam-4690	325	11	dh	dh	PROPN
ejpam-4690	325	12	comes	come	VERB
ejpam-4690	325	13	after	after	ADV
ejpam-4690	325	14	(	(	PUNCT
ejpam-4690	325	15	succeeds	succeed	VERB
ejpam-4690	325	16	)	)	PUNCT
ejpam-4690	325	17	all	all	DET
ejpam-4690	325	18	the	the	DET
ejpam-4690	325	19	terms	term	NOUN
ejpam-4690	325	20	of	of	ADP
ejpam-4690	325	21	dg	dg	NOUN
ejpam-4690	325	22	in	in	ADP
ejpam-4690	325	23	d	d	PROPN
ejpam-4690	325	24	by	by	ADP
ejpam-4690	325	25	the	the	DET
ejpam-4690	325	26	legality	legality	NOUN
ejpam-4690	325	27	property	property	NOUN
ejpam-4690	325	28	of	of	ADP
ejpam-4690	325	29	d.	d.	PROPN
ejpam-4690	325	30	hence	hence	ADV
ejpam-4690	325	31	,	,	PUNCT
ejpam-4690	325	32	if	if	SCONJ
ejpam-4690	325	33	xj	xj	PROPN
ejpam-4690	325	34	∈	∈	PROPN
ejpam-4690	325	35	d̂h	d̂h	PRON
ejpam-4690	325	36	and	and	CCONJ
ejpam-4690	325	37	xk	xk	PROPN
ejpam-4690	325	38	∈	∈	PROPN
ejpam-4690	325	39	d̂g	d̂g	PROPN
ejpam-4690	325	40	,	,	PUNCT
ejpam-4690	325	41	then	then	ADV
ejpam-4690	325	42	k	k	PROPN
ejpam-4690	325	43	>	>	X
ejpam-4690	325	44	j.	j.	PROPN
ejpam-4690	325	45	however	however	ADV
ejpam-4690	325	46	,	,	PUNCT
ejpam-4690	325	47	if	if	SCONJ
ejpam-4690	325	48	xj	xj	PROPN
ejpam-4690	325	49	∈	∈	PROPN
ejpam-4690	325	50	d̂h	d̂h	NOUN
ejpam-4690	325	51	for	for	ADP
ejpam-4690	325	52	some	some	DET
ejpam-4690	325	53	j	j	NOUN
ejpam-4690	325	54	,	,	PUNCT
ejpam-4690	325	55	then	then	ADV
ejpam-4690	325	56	v	v	X
ejpam-4690	325	57	(	(	PUNCT
ejpam-4690	325	58	g	g	NOUN
ejpam-4690	325	59	)	)	PUNCT
ejpam-4690	325	60	⊆	⊆	PROPN
ejpam-4690	325	61	ng+h	ng+h	PROPN
ejpam-4690	326	1	[	[	X
ejpam-4690	326	2	xj	xj	X
ejpam-4690	326	3	]	]	PUNCT
ejpam-4690	326	4	.	.	PUNCT
ejpam-4690	327	1	this	this	PRON
ejpam-4690	327	2	would	would	AUX
ejpam-4690	327	3	imply	imply	VERB
ejpam-4690	327	4	that	that	SCONJ
ejpam-4690	327	5	|d̂g|	|d̂g|	PROPN
ejpam-4690	327	6	=	=	SYM
ejpam-4690	327	7	1	1	NUM
ejpam-4690	327	8	,	,	PUNCT
ejpam-4690	327	9	a	a	DET
ejpam-4690	327	10	contradiction	contradiction	NOUN
ejpam-4690	327	11	.	.	PUNCT
ejpam-4690	328	1	thus	thus	ADV
ejpam-4690	328	2	,	,	PUNCT
ejpam-4690	328	3	d̂h	d̂h	X
ejpam-4690	328	4	=	=	SYM
ejpam-4690	328	5	∅	∅	NOUN
ejpam-4690	328	6	,	,	PUNCT
ejpam-4690	328	7	a	a	DET
ejpam-4690	328	8	contradiction	contradiction	NOUN
ejpam-4690	328	9	.	.	PUNCT
ejpam-4690	329	1	thus	thus	ADV
ejpam-4690	329	2	,	,	PUNCT
ejpam-4690	329	3	dg	dg	PROPN
ejpam-4690	329	4	is	be	AUX
ejpam-4690	329	5	a	a	DET
ejpam-4690	329	6	non	non	ADJ
ejpam-4690	329	7	-	-	ADJ
ejpam-4690	329	8	dominating	dominating	ADJ
ejpam-4690	329	9	legal	legal	ADJ
ejpam-4690	329	10	closed	close	VERB
ejpam-4690	329	11	neighborhood	neighborhood	NOUN
ejpam-4690	329	12	sequence	sequence	NOUN
ejpam-4690	329	13	of	of	ADP
ejpam-4690	329	14	g.	g.	PROPN
ejpam-4690	329	15	let	let	VERB
ejpam-4690	329	16	dg	dg	X
ejpam-4690	329	17	=	=	SYM
ejpam-4690	329	18	(	(	PUNCT
ejpam-4690	329	19	v1	v1	PROPN
ejpam-4690	329	20	,	,	PUNCT
ejpam-4690	329	21	v2	v2	NOUN
ejpam-4690	329	22	,	,	PUNCT
ejpam-4690	329	23	.	.	PUNCT
ejpam-4690	329	24	.	.	PUNCT
ejpam-4690	330	1	.	.	PUNCT
ejpam-4690	331	1	,	,	PUNCT
ejpam-4690	331	2	vr	vr	PROPN
ejpam-4690	331	3	)	)	PUNCT
ejpam-4690	331	4	and	and	CCONJ
ejpam-4690	331	5	dh	dh	NOUN
ejpam-4690	331	6	=	=	SYM
ejpam-4690	331	7	(	(	PUNCT
ejpam-4690	331	8	w1	w1	NOUN
ejpam-4690	331	9	,	,	PUNCT
ejpam-4690	331	10	w2	w2	NOUN
ejpam-4690	331	11	,	,	PUNCT
ejpam-4690	331	12	.	.	PUNCT
ejpam-4690	331	13	.	.	PUNCT
ejpam-4690	332	1	.	.	PUNCT
ejpam-4690	333	1	,	,	PUNCT
ejpam-4690	333	2	wt	wt	NOUN
ejpam-4690	333	3	)	)	PUNCT
ejpam-4690	333	4	.	.	PUNCT
ejpam-4690	334	1	if	if	SCONJ
ejpam-4690	334	2	in	in	ADP
ejpam-4690	334	3	d	d	PROPN
ejpam-4690	334	4	the	the	DET
ejpam-4690	334	5	term	term	NOUN
ejpam-4690	334	6	w1	w1	NOUN
ejpam-4690	334	7	does	do	AUX
ejpam-4690	334	8	not	not	PART
ejpam-4690	334	9	precede	precede	VERB
ejpam-4690	334	10	vr	vr	NOUN
ejpam-4690	334	11	,	,	PUNCT
ejpam-4690	334	12	where	where	SCONJ
ejpam-4690	334	13	r	r	NOUN
ejpam-4690	334	14	≥	≥	NOUN
ejpam-4690	334	15	2	2	NUM
ejpam-4690	334	16	,	,	PUNCT
ejpam-4690	334	17	then	then	ADV
ejpam-4690	334	18	vr	vr	PROPN
ejpam-4690	334	19	does	do	AUX
ejpam-4690	334	20	not	not	PART
ejpam-4690	334	21	satisfy	satisfy	VERB
ejpam-4690	334	22	the	the	DET
ejpam-4690	334	23	property	property	NOUN
ejpam-4690	334	24	in	in	ADP
ejpam-4690	334	25	the	the	DET
ejpam-4690	334	26	legality	legality	NOUN
ejpam-4690	334	27	condition	condition	NOUN
ejpam-4690	334	28	,	,	PUNCT
ejpam-4690	334	29	a	a	DET
ejpam-4690	334	30	contradiction	contradiction	NOUN
ejpam-4690	334	31	.	.	PUNCT
ejpam-4690	335	1	hence	hence	ADV
ejpam-4690	335	2	,	,	PUNCT
ejpam-4690	335	3	in	in	ADP
ejpam-4690	335	4	d	d	PROPN
ejpam-4690	335	5	,	,	PUNCT
ejpam-4690	335	6	w1	w1	NOUN
ejpam-4690	335	7	comes	come	VERB
ejpam-4690	335	8	after	after	ADP
ejpam-4690	335	9	the	the	DET
ejpam-4690	335	10	term	term	NOUN
ejpam-4690	335	11	vr	vr	PROPN
ejpam-4690	335	12	in	in	ADP
ejpam-4690	335	13	dg	dg	PROPN
ejpam-4690	335	14	.	.	PUNCT
ejpam-4690	336	1	since	since	SCONJ
ejpam-4690	336	2	v	v	NOUN
ejpam-4690	336	3	(	(	PUNCT
ejpam-4690	336	4	h	h	NOUN
ejpam-4690	336	5	)	)	PUNCT
ejpam-4690	336	6	⊆	⊆	NUM
ejpam-4690	336	7	⋃r	⋃r	PROPN
ejpam-4690	336	8	j=1ng+h	j=1ng+h	PROPN
ejpam-4690	336	9	[	[	X
ejpam-4690	336	10	vj	vj	X
ejpam-4690	336	11	]	]	X
ejpam-4690	336	12	and	and	CCONJ
ejpam-4690	336	13	v	v	X
ejpam-4690	336	14	(	(	PUNCT
ejpam-4690	336	15	g	g	NOUN
ejpam-4690	336	16	)	)	PUNCT
ejpam-4690	336	17	\	\	PUNCT
ejpam-4690	337	1	(	(	PUNCT
ejpam-4690	337	2	⋃r	⋃r	PROPN
ejpam-4690	337	3	j=1ng[vj	j=1ng[vj	PROPN
ejpam-4690	337	4	]	]	PUNCT
ejpam-4690	337	5	)	)	PUNCT
ejpam-4690	337	6	⊆	⊆	NUM
ejpam-4690	337	7	ng+h	ng+h	PROPN
ejpam-4690	338	1	[	[	X
ejpam-4690	338	2	w1	w1	NOUN
ejpam-4690	338	3	]	]	PUNCT
ejpam-4690	338	4	,	,	PUNCT
ejpam-4690	338	5	dh	dh	PROPN
ejpam-4690	338	6	can	can	AUX
ejpam-4690	338	7	not	not	PART
ejpam-4690	338	8	have	have	VERB
ejpam-4690	338	9	other	other	ADJ
ejpam-4690	338	10	terms	term	NOUN
ejpam-4690	338	11	,	,	PUNCT
ejpam-4690	338	12	i.e.	i.e.	X
ejpam-4690	338	13	,	,	PUNCT
ejpam-4690	338	14	t	t	NOUN
ejpam-4690	338	15	=	=	SYM
ejpam-4690	338	16	1	1	NUM
ejpam-4690	338	17	.	.	PUNCT
ejpam-4690	339	1	thus	thus	ADV
ejpam-4690	339	2	,	,	PUNCT
ejpam-4690	339	3	dh	dh	NOUN
ejpam-4690	339	4	=	=	PUNCT
ejpam-4690	339	5	(	(	PUNCT
ejpam-4690	339	6	w	w	NOUN
ejpam-4690	339	7	)	)	PUNCT
ejpam-4690	339	8	,	,	PUNCT
ejpam-4690	339	9	where	where	SCONJ
ejpam-4690	339	10	w	w	NOUN
ejpam-4690	339	11	=	=	SYM
ejpam-4690	339	12	w1	w1	NOUN
ejpam-4690	339	13	,	,	PUNCT
ejpam-4690	339	14	and	and	CCONJ
ejpam-4690	339	15	d	d	NOUN
ejpam-4690	339	16	=	=	SYM
ejpam-4690	339	17	dg	dg	PROPN
ejpam-4690	339	18	⊕	⊕	PROPN
ejpam-4690	339	19	(	(	PUNCT
ejpam-4690	339	20	w	w	NOUN
ejpam-4690	339	21	)	)	PUNCT
ejpam-4690	339	22	.	.	PUNCT
ejpam-4690	340	1	this	this	PRON
ejpam-4690	340	2	shows	show	VERB
ejpam-4690	340	3	that	that	SCONJ
ejpam-4690	340	4	(	(	PUNCT
ejpam-4690	340	5	iii	iii	NOUN
ejpam-4690	340	6	)	)	PUNCT
ejpam-4690	340	7	holds	hold	VERB
ejpam-4690	340	8	.	.	PUNCT
ejpam-4690	341	1	similarly	similarly	ADV
ejpam-4690	341	2	,	,	PUNCT
ejpam-4690	341	3	(	(	PUNCT
ejpam-4690	341	4	iv	iv	X
ejpam-4690	341	5	)	)	PUNCT
ejpam-4690	341	6	holds	hold	VERB
ejpam-4690	341	7	if	if	SCONJ
ejpam-4690	341	8	|d̂h	|d̂h	NOUN
ejpam-4690	341	9	|	|	ADV
ejpam-4690	341	10	≥	≥	NOUN
ejpam-4690	341	11	2	2	NUM
ejpam-4690	341	12	.	.	X
ejpam-4690	342	1	for	for	ADP
ejpam-4690	342	2	the	the	DET
ejpam-4690	342	3	converse	converse	NOUN
ejpam-4690	342	4	,	,	PUNCT
ejpam-4690	342	5	suppose	suppose	VERB
ejpam-4690	342	6	first	first	ADV
ejpam-4690	342	7	that	that	SCONJ
ejpam-4690	342	8	(	(	PUNCT
ejpam-4690	342	9	i	i	NOUN
ejpam-4690	342	10	)	)	PUNCT
ejpam-4690	342	11	or	or	CCONJ
ejpam-4690	342	12	(	(	PUNCT
ejpam-4690	342	13	ii	ii	NOUN
ejpam-4690	342	14	)	)	PUNCT
ejpam-4690	342	15	holds	hold	VERB
ejpam-4690	342	16	.	.	PUNCT
ejpam-4690	343	1	then	then	ADV
ejpam-4690	343	2	clearly	clearly	ADV
ejpam-4690	343	3	,	,	PUNCT
ejpam-4690	343	4	d	d	PRON
ejpam-4690	343	5	is	be	AUX
ejpam-4690	343	6	a	a	DET
ejpam-4690	343	7	grundy	grundy	PROPN
ejpam-4690	343	8	dominating	dominating	NOUN
ejpam-4690	343	9	sequence	sequence	NOUN
ejpam-4690	343	10	of	of	ADP
ejpam-4690	343	11	g	g	PROPN
ejpam-4690	343	12	+	+	PROPN
ejpam-4690	343	13	h.	h.	PROPN
ejpam-4690	343	14	next	next	ADV
ejpam-4690	343	15	,	,	PUNCT
ejpam-4690	343	16	suppose	suppose	VERB
ejpam-4690	343	17	that	that	SCONJ
ejpam-4690	343	18	(	(	PUNCT
ejpam-4690	343	19	iii	iii	NOUN
ejpam-4690	343	20	)	)	PUNCT
ejpam-4690	343	21	holds	hold	VERB
ejpam-4690	343	22	.	.	PUNCT
ejpam-4690	344	1	then	then	ADV
ejpam-4690	344	2	d̂	d̂	PROPN
ejpam-4690	344	3	is	be	AUX
ejpam-4690	344	4	a	a	DET
ejpam-4690	344	5	dominating	dominating	NOUN
ejpam-4690	344	6	set	set	NOUN
ejpam-4690	344	7	of	of	ADP
ejpam-4690	344	8	g+h	g+h	PROPN
ejpam-4690	344	9	.	.	PUNCT
ejpam-4690	345	1	let	let	VERB
ejpam-4690	345	2	dg	dg	X
ejpam-4690	345	3	=	=	SYM
ejpam-4690	345	4	(	(	PUNCT
ejpam-4690	345	5	v1	v1	PROPN
ejpam-4690	345	6	,	,	PUNCT
ejpam-4690	345	7	v2	v2	NOUN
ejpam-4690	345	8	,	,	PUNCT
ejpam-4690	345	9	.	.	PUNCT
ejpam-4690	345	10	.	.	PUNCT
ejpam-4690	346	1	.	.	PUNCT
ejpam-4690	347	1	,	,	PUNCT
ejpam-4690	347	2	vr	vr	PROPN
ejpam-4690	347	3	)	)	PUNCT
ejpam-4690	347	4	.	.	PUNCT
ejpam-4690	348	1	since	since	SCONJ
ejpam-4690	348	2	dg	dg	PROPN
ejpam-4690	348	3	is	be	AUX
ejpam-4690	348	4	a	a	DET
ejpam-4690	348	5	legal	legal	ADJ
ejpam-4690	348	6	closed	closed	ADJ
ejpam-4690	348	7	neighborhood	neighborhood	NOUN
ejpam-4690	348	8	sequence	sequence	NOUN
ejpam-4690	348	9	of	of	ADP
ejpam-4690	348	10	g	g	NOUN
ejpam-4690	348	11	,	,	PUNCT
ejpam-4690	348	12	it	it	PRON
ejpam-4690	348	13	is	be	AUX
ejpam-4690	348	14	legal	legal	ADJ
ejpam-4690	348	15	closed	closed	ADJ
ejpam-4690	348	16	neighborhood	neighborhood	NOUN
ejpam-4690	348	17	sequence	sequence	NOUN
ejpam-4690	348	18	of	of	ADP
ejpam-4690	348	19	g	g	PROPN
ejpam-4690	348	20	+	+	CCONJ
ejpam-4690	348	21	h.	h.	PROPN
ejpam-4690	348	22	moreover	moreover	ADV
ejpam-4690	348	23	,	,	PUNCT
ejpam-4690	348	24	since	since	SCONJ
ejpam-4690	348	25	d̂g	d̂g	PRON
ejpam-4690	348	26	is	be	AUX
ejpam-4690	348	27	nondominating	nondominate	VERB
ejpam-4690	348	28	in	in	ADP
ejpam-4690	348	29	g	g	PROPN
ejpam-4690	348	30	,	,	PUNCT
ejpam-4690	348	31	ng+h	ng+h	PROPN
ejpam-4690	349	1	[	[	X
ejpam-4690	349	2	w	w	X
ejpam-4690	349	3	]	]	PUNCT
ejpam-4690	349	4	\	\	PUNCT
ejpam-4690	350	1	(	(	PUNCT
ejpam-4690	350	2	⋃r	⋃r	PROPN
ejpam-4690	350	3	j=1ng+h	j=1ng+h	PROPN
ejpam-4690	351	1	[	[	X
ejpam-4690	351	2	vj	vj	X
ejpam-4690	351	3	]	]	X
ejpam-4690	351	4	)	)	PUNCT
ejpam-4690	352	1	̸=	̸=	PROPN
ejpam-4690	352	2	∅.	∅.	ADP
ejpam-4690	352	3	thus	thus	ADV
ejpam-4690	352	4	,	,	PUNCT
ejpam-4690	352	5	d	d	PROPN
ejpam-4690	352	6	=	=	X
ejpam-4690	352	7	dg	dg	PROPN
ejpam-4690	352	8	⊕	⊕	PROPN
ejpam-4690	352	9	(	(	PUNCT
ejpam-4690	352	10	w	w	NOUN
ejpam-4690	352	11	)	)	PUNCT
ejpam-4690	352	12	is	be	AUX
ejpam-4690	352	13	a	a	DET
ejpam-4690	352	14	legal	legal	ADJ
ejpam-4690	352	15	closed	closed	ADJ
ejpam-4690	352	16	neighborhood	neighborhood	NOUN
ejpam-4690	352	17	sequence	sequence	NOUN
ejpam-4690	352	18	of	of	ADP
ejpam-4690	352	19	g+h	g+h	PROPN
ejpam-4690	352	20	.	.	PUNCT
ejpam-4690	353	1	similarly	similarly	ADV
ejpam-4690	353	2	,	,	PUNCT
ejpam-4690	353	3	d	d	PRON
ejpam-4690	353	4	is	be	AUX
ejpam-4690	353	5	a	a	DET
ejpam-4690	353	6	grundy	grundy	PROPN
ejpam-4690	353	7	dominating	dominating	NOUN
ejpam-4690	353	8	sequence	sequence	NOUN
ejpam-4690	353	9	of	of	ADP
ejpam-4690	353	10	g+h	g+h	PROPN
ejpam-4690	353	11	if	if	SCONJ
ejpam-4690	353	12	(	(	PUNCT
ejpam-4690	353	13	iv	iv	X
ejpam-4690	353	14	)	)	PUNCT
ejpam-4690	353	15	holds	hold	NOUN
ejpam-4690	353	16	.	.	PUNCT
ejpam-4690	354	1	the	the	DET
ejpam-4690	354	2	next	next	ADJ
ejpam-4690	354	3	result	result	NOUN
ejpam-4690	354	4	follows	follow	VERB
ejpam-4690	354	5	from	from	ADP
ejpam-4690	354	6	proposition	proposition	NOUN
ejpam-4690	354	7	5	5	NUM
ejpam-4690	354	8	and	and	CCONJ
ejpam-4690	354	9	theorem	theorem	VERB
ejpam-4690	354	10	5	5	NUM
ejpam-4690	354	11	.	.	PUNCT
ejpam-4690	354	12	corollary	corollary	ADJ
ejpam-4690	354	13	5	5	NUM
ejpam-4690	354	14	.	.	PUNCT
ejpam-4690	355	1	let	let	VERB
ejpam-4690	355	2	g	g	NOUN
ejpam-4690	355	3	and	and	CCONJ
ejpam-4690	355	4	h	h	NOUN
ejpam-4690	355	5	be	be	VERB
ejpam-4690	355	6	two	two	NUM
ejpam-4690	355	7	non	non	ADJ
ejpam-4690	355	8	-	-	ADJ
ejpam-4690	355	9	complete	complete	ADJ
ejpam-4690	355	10	graphs	graph	NOUN
ejpam-4690	355	11	.	.	PUNCT
ejpam-4690	356	1	then	then	ADV
ejpam-4690	356	2	γgr(g+h	γgr(g+h	NOUN
ejpam-4690	356	3	)	)	PUNCT
ejpam-4690	357	1	=	=	SYM
ejpam-4690	357	2	max{γgr(g	max{γgr(g	ADJ
ejpam-4690	357	3	)	)	PUNCT
ejpam-4690	357	4	,	,	PUNCT
ejpam-4690	357	5	γgr(h	γgr(h	PROPN
ejpam-4690	357	6	)	)	PUNCT
ejpam-4690	357	7	}	}	PUNCT
ejpam-4690	357	8	in	in	ADP
ejpam-4690	357	9	particular	particular	ADJ
ejpam-4690	357	10	,	,	PUNCT
ejpam-4690	357	11	each	each	PRON
ejpam-4690	357	12	of	of	ADP
ejpam-4690	357	13	the	the	DET
ejpam-4690	357	14	following	follow	VERB
ejpam-4690	357	15	holds	hold	VERB
ejpam-4690	357	16	:	:	PUNCT
ejpam-4690	357	17	(	(	PUNCT
ejpam-4690	357	18	i	i	NOUN
ejpam-4690	357	19	)	)	PUNCT
ejpam-4690	357	20	γgr(pn	γgr(pn	PRON
ejpam-4690	357	21	+	+	CCONJ
ejpam-4690	357	22	pm	pm	NOUN
ejpam-4690	357	23	)	)	PUNCT
ejpam-4690	357	24	=	=	PRON
ejpam-4690	357	25	{	{	PUNCT
ejpam-4690	357	26	n−	n−	NOUN
ejpam-4690	357	27	1	1	NUM
ejpam-4690	357	28	if	if	SCONJ
ejpam-4690	357	29	n	n	PRON
ejpam-4690	357	30	≥	≥	NOUN
ejpam-4690	357	31	m	m	VERB
ejpam-4690	357	32	≥	≥	NUM
ejpam-4690	357	33	3	3	NUM
ejpam-4690	357	34	m−	m−	PROPN
ejpam-4690	357	35	1	1	NUM
ejpam-4690	357	36	if	if	SCONJ
ejpam-4690	357	37	m	m	PROPN
ejpam-4690	357	38	≥	≥	VERB
ejpam-4690	357	39	n	n	PRON
ejpam-4690	357	40	≥	≥	NOUN
ejpam-4690	357	41	3	3	NUM
ejpam-4690	357	42	.	.	PUNCT
ejpam-4690	357	43	(	(	PUNCT
ejpam-4690	357	44	ii	ii	NOUN
ejpam-4690	357	45	)	)	PUNCT
ejpam-4690	357	46	γgr(pn	γgr(pn	NOUN
ejpam-4690	357	47	+	+	X
ejpam-4690	357	48	cm	cm	NOUN
ejpam-4690	357	49	)	)	PUNCT
ejpam-4690	357	50	=	=	PRON
ejpam-4690	357	51	{	{	PUNCT
ejpam-4690	357	52	n−	n−	NOUN
ejpam-4690	357	53	1	1	NUM
ejpam-4690	357	54	if	if	SCONJ
ejpam-4690	357	55	n	n	PRON
ejpam-4690	357	56	≥	≥	NOUN
ejpam-4690	357	57	m	m	VERB
ejpam-4690	357	58	=	=	NOUN
ejpam-4690	357	59	4	4	NUM
ejpam-4690	357	60	m−	m−	PROPN
ejpam-4690	357	61	2	2	NUM
ejpam-4690	357	62	if	if	SCONJ
ejpam-4690	357	63	m	m	VERB
ejpam-4690	357	64	≥	≥	NOUN
ejpam-4690	357	65	n+	n+	PUNCT
ejpam-4690	357	66	1	1	NUM
ejpam-4690	357	67	=	=	SYM
ejpam-4690	357	68	4	4	NUM
ejpam-4690	357	69	.	.	PUNCT
ejpam-4690	357	70	(	(	PUNCT
ejpam-4690	357	71	iii	iii	X
ejpam-4690	357	72	)	)	PUNCT
ejpam-4690	357	73	γgr(cn	γgr(cn	NOUN
ejpam-4690	358	1	+	+	X
ejpam-4690	358	2	cm	cm	NOUN
ejpam-4690	358	3	)	)	PUNCT
ejpam-4690	359	1	=	=	PRON
ejpam-4690	359	2	{	{	PUNCT
ejpam-4690	359	3	n−	n−	NOUN
ejpam-4690	359	4	2	2	NUM
ejpam-4690	359	5	if	if	SCONJ
ejpam-4690	359	6	n	n	PRON
ejpam-4690	359	7	≥	≥	NOUN
ejpam-4690	359	8	m	m	VERB
ejpam-4690	359	9	≥	≥	NUM
ejpam-4690	359	10	4	4	NUM
ejpam-4690	359	11	m−	m−	PROPN
ejpam-4690	359	12	2	2	NUM
ejpam-4690	359	13	if	if	SCONJ
ejpam-4690	359	14	m	m	VERB
ejpam-4690	359	15	≥	≥	VERB
ejpam-4690	359	16	n	n	DET
ejpam-4690	359	17	≥	≥	NUM
ejpam-4690	359	18	4	4	NUM
ejpam-4690	359	19	.	.	PUNCT
ejpam-4690	360	1	j.	j.	PROPN
ejpam-4690	360	2	hassan	hassan	PROPN
ejpam-4690	360	3	,	,	PUNCT
ejpam-4690	360	4	s.	s.	PROPN
ejpam-4690	360	5	canoy	canoy	PROPN
ejpam-4690	360	6	jr	jr	PROPN
ejpam-4690	360	7	.	.	PROPN
ejpam-4690	360	8	/	/	SYM
ejpam-4690	360	9	eur	eur	PROPN
ejpam-4690	360	10	.	.	PUNCT
ejpam-4690	361	1	j.	j.	PROPN
ejpam-4690	361	2	pure	pure	PROPN
ejpam-4690	361	3	appl	appl	PROPN
ejpam-4690	361	4	.	.	PROPN
ejpam-4690	361	5	math	math	PROPN
ejpam-4690	361	6	,	,	PUNCT
ejpam-4690	361	7	16	16	NUM
ejpam-4690	361	8	(	(	PUNCT
ejpam-4690	361	9	2	2	NUM
ejpam-4690	361	10	)	)	PUNCT
ejpam-4690	361	11	(	(	PUNCT
ejpam-4690	361	12	2023	2023	NUM
ejpam-4690	361	13	)	)	PUNCT
ejpam-4690	361	14	,	,	PUNCT
ejpam-4690	361	15	1154	1154	NUM
ejpam-4690	361	16	-	-	SYM
ejpam-4690	361	17	1166	1166	NUM
ejpam-4690	361	18	1164	1164	NUM
ejpam-4690	361	19	(	(	PUNCT
ejpam-4690	361	20	iv	iv	X
ejpam-4690	361	21	)	)	PUNCT
ejpam-4690	361	22	γgr(km	γgr(km	PROPN
ejpam-4690	361	23	,	,	PUNCT
ejpam-4690	361	24	n	n	CCONJ
ejpam-4690	361	25	)	)	PUNCT
ejpam-4690	362	1	=	=	SYM
ejpam-4690	362	2	max	max	PROPN
ejpam-4690	362	3	{	{	PUNCT
ejpam-4690	362	4	m	m	PROPN
ejpam-4690	362	5	,	,	PUNCT
ejpam-4690	362	6	n	n	CCONJ
ejpam-4690	362	7	}	}	PUNCT
ejpam-4690	362	8	for	for	ADP
ejpam-4690	362	9	all	all	DET
ejpam-4690	362	10	m	m	PROPN
ejpam-4690	362	11	,	,	PUNCT
ejpam-4690	362	12	n	n	PRON
ejpam-4690	362	13	≥	≥	NOUN
ejpam-4690	362	14	2	2	NUM
ejpam-4690	362	15	.	.	PUNCT
ejpam-4690	363	1	then	then	ADV
ejpam-4690	363	2	next	next	ADJ
ejpam-4690	363	3	result	result	NOUN
ejpam-4690	363	4	can	can	AUX
ejpam-4690	363	5	be	be	AUX
ejpam-4690	363	6	proved	prove	VERB
ejpam-4690	363	7	easily	easily	ADV
ejpam-4690	363	8	.	.	PUNCT
ejpam-4690	364	1	theorem	theorem	ADJ
ejpam-4690	364	2	6	6	NUM
ejpam-4690	364	3	.	.	PUNCT
ejpam-4690	365	1	let	let	VERB
ejpam-4690	365	2	g	g	PRON
ejpam-4690	365	3	be	be	AUX
ejpam-4690	365	4	a	a	DET
ejpam-4690	365	5	complete	complete	ADJ
ejpam-4690	365	6	graph	graph	NOUN
ejpam-4690	365	7	and	and	CCONJ
ejpam-4690	365	8	let	let	VERB
ejpam-4690	365	9	h	h	PRON
ejpam-4690	365	10	be	be	AUX
ejpam-4690	365	11	a	a	DET
ejpam-4690	365	12	non	non	ADJ
ejpam-4690	365	13	-	-	ADJ
ejpam-4690	365	14	complete	complete	ADJ
ejpam-4690	365	15	graph	graph	NOUN
ejpam-4690	365	16	.	.	PUNCT
ejpam-4690	366	1	a	a	DET
ejpam-4690	366	2	sequence	sequence	NOUN
ejpam-4690	366	3	d	d	NOUN
ejpam-4690	366	4	of	of	ADP
ejpam-4690	366	5	distinct	distinct	ADJ
ejpam-4690	366	6	vertices	vertex	NOUN
ejpam-4690	366	7	of	of	ADP
ejpam-4690	366	8	g+h	g+h	PROPN
ejpam-4690	366	9	is	be	AUX
ejpam-4690	366	10	a	a	DET
ejpam-4690	366	11	grundy	grundy	PROPN
ejpam-4690	366	12	dominating	dominating	NOUN
ejpam-4690	366	13	sequence	sequence	NOUN
ejpam-4690	366	14	in	in	ADP
ejpam-4690	366	15	g+h	g+h	PROPN
ejpam-4690	367	1	if	if	SCONJ
ejpam-4690	367	2	and	and	CCONJ
ejpam-4690	367	3	only	only	ADV
ejpam-4690	367	4	if	if	SCONJ
ejpam-4690	367	5	one	one	NUM
ejpam-4690	367	6	of	of	ADP
ejpam-4690	367	7	the	the	DET
ejpam-4690	367	8	following	follow	VERB
ejpam-4690	367	9	condition	condition	NOUN
ejpam-4690	367	10	holds	hold	VERB
ejpam-4690	367	11	:	:	PUNCT
ejpam-4690	367	12	(	(	PUNCT
ejpam-4690	367	13	i	i	NOUN
ejpam-4690	367	14	)	)	PUNCT
ejpam-4690	368	1	d	d	PROPN
ejpam-4690	368	2	=	=	SYM
ejpam-4690	368	3	(	(	PUNCT
ejpam-4690	368	4	v	v	NOUN
ejpam-4690	368	5	)	)	PUNCT
ejpam-4690	368	6	for	for	ADP
ejpam-4690	368	7	some	some	PRON
ejpam-4690	368	8	v	v	ADP
ejpam-4690	368	9	∈	∈	PROPN
ejpam-4690	368	10	v	v	NOUN
ejpam-4690	368	11	(	(	PUNCT
ejpam-4690	368	12	g	g	NOUN
ejpam-4690	368	13	)	)	PUNCT
ejpam-4690	368	14	.	.	PUNCT
ejpam-4690	369	1	(	(	PUNCT
ejpam-4690	369	2	ii	ii	NOUN
ejpam-4690	369	3	)	)	PUNCT
ejpam-4690	369	4	d	d	NOUN
ejpam-4690	369	5	is	be	AUX
ejpam-4690	369	6	a	a	DET
ejpam-4690	369	7	grundy	grundy	PROPN
ejpam-4690	369	8	dominating	dominating	NOUN
ejpam-4690	369	9	sequence	sequence	NOUN
ejpam-4690	369	10	of	of	ADP
ejpam-4690	369	11	h.	h.	PROPN
ejpam-4690	369	12	(	(	PUNCT
ejpam-4690	369	13	iii	iii	NOUN
ejpam-4690	369	14	)	)	PUNCT
ejpam-4690	369	15	d	d	NOUN
ejpam-4690	369	16	=	=	SYM
ejpam-4690	369	17	dh	dh	PROPN
ejpam-4690	369	18	⊕	⊕	PROPN
ejpam-4690	369	19	(	(	PUNCT
ejpam-4690	369	20	v	v	NOUN
ejpam-4690	369	21	)	)	PUNCT
ejpam-4690	369	22	for	for	ADP
ejpam-4690	369	23	some	some	DET
ejpam-4690	369	24	non	non	ADJ
ejpam-4690	369	25	-	-	ADJ
ejpam-4690	369	26	dominating	dominating	ADJ
ejpam-4690	369	27	legal	legal	ADJ
ejpam-4690	369	28	closed	close	VERB
ejpam-4690	369	29	neighborhood	neighborhood	NOUN
ejpam-4690	369	30	sequence	sequence	NOUN
ejpam-4690	369	31	dh	dh	NOUN
ejpam-4690	369	32	of	of	ADP
ejpam-4690	369	33	h	h	NOUN
ejpam-4690	369	34	and	and	CCONJ
ejpam-4690	369	35	v	v	ADP
ejpam-4690	369	36	∈	∈	PROPN
ejpam-4690	369	37	v	v	NOUN
ejpam-4690	369	38	(	(	PUNCT
ejpam-4690	369	39	g	g	NOUN
ejpam-4690	369	40	)	)	PUNCT
ejpam-4690	369	41	.	.	PUNCT
ejpam-4690	370	1	since	since	SCONJ
ejpam-4690	370	2	γgr(h	γgr(h	PROPN
ejpam-4690	370	3	)	)	PUNCT
ejpam-4690	370	4	≥	≥	NOUN
ejpam-4690	370	5	2	2	NUM
ejpam-4690	370	6	for	for	ADP
ejpam-4690	370	7	any	any	DET
ejpam-4690	370	8	non	non	ADJ
ejpam-4690	370	9	-	-	ADJ
ejpam-4690	370	10	complete	complete	ADJ
ejpam-4690	370	11	graph	graph	NOUN
ejpam-4690	370	12	h	h	NOUN
ejpam-4690	370	13	,	,	PUNCT
ejpam-4690	370	14	the	the	DET
ejpam-4690	370	15	following	following	ADJ
ejpam-4690	370	16	result	result	NOUN
ejpam-4690	370	17	follows	follow	VERB
ejpam-4690	370	18	from	from	ADP
ejpam-4690	370	19	theorem	theorem	ADJ
ejpam-4690	370	20	6	6	NUM
ejpam-4690	370	21	.	.	PUNCT
ejpam-4690	370	22	corollary	corollary	ADJ
ejpam-4690	370	23	6	6	NUM
ejpam-4690	370	24	.	.	PUNCT
ejpam-4690	371	1	let	let	VERB
ejpam-4690	371	2	g	g	PRON
ejpam-4690	371	3	be	be	AUX
ejpam-4690	371	4	a	a	DET
ejpam-4690	371	5	complete	complete	ADJ
ejpam-4690	371	6	graph	graph	NOUN
ejpam-4690	371	7	and	and	CCONJ
ejpam-4690	371	8	let	let	VERB
ejpam-4690	371	9	h	h	NOUN
ejpam-4690	371	10	be	be	AUX
ejpam-4690	371	11	any	any	DET
ejpam-4690	371	12	non	non	ADJ
ejpam-4690	371	13	-	-	ADJ
ejpam-4690	371	14	complete	complete	ADJ
ejpam-4690	371	15	graph	graph	NOUN
ejpam-4690	371	16	.	.	PUNCT
ejpam-4690	372	1	then	then	ADV
ejpam-4690	372	2	γgr(g+h	γgr(g+h	NOUN
ejpam-4690	372	3	)	)	PUNCT
ejpam-4690	372	4	=	=	SYM
ejpam-4690	372	5	γgr(h	γgr(h	PROPN
ejpam-4690	372	6	)	)	PUNCT
ejpam-4690	372	7	.	.	PUNCT
ejpam-4690	373	1	in	in	ADP
ejpam-4690	373	2	particular	particular	ADJ
ejpam-4690	373	3	,	,	PUNCT
ejpam-4690	373	4	each	each	PRON
ejpam-4690	373	5	of	of	ADP
ejpam-4690	373	6	the	the	DET
ejpam-4690	373	7	following	follow	VERB
ejpam-4690	373	8	holds	hold	VERB
ejpam-4690	373	9	:	:	PUNCT
ejpam-4690	373	10	(	(	PUNCT
ejpam-4690	373	11	i	i	NOUN
ejpam-4690	373	12	)	)	PUNCT
ejpam-4690	373	13	γgr(k1,n	γgr(k1,n	PROPN
ejpam-4690	373	14	)	)	PUNCT
ejpam-4690	374	1	=	=	SYM
ejpam-4690	374	2	n	n	PROPN
ejpam-4690	374	3	for	for	ADP
ejpam-4690	374	4	all	all	DET
ejpam-4690	374	5	n	n	PRON
ejpam-4690	374	6	≥	≥	NOUN
ejpam-4690	374	7	1	1	NUM
ejpam-4690	374	8	.	.	PUNCT
ejpam-4690	374	9	(	(	PUNCT
ejpam-4690	374	10	ii	ii	NOUN
ejpam-4690	374	11	)	)	PUNCT
ejpam-4690	374	12	γgr(wn	γgr(wn	NOUN
ejpam-4690	374	13	)	)	PUNCT
ejpam-4690	375	1	=	=	SYM
ejpam-4690	375	2	γgr(k1	γgr(k1	PROPN
ejpam-4690	375	3	+	+	CCONJ
ejpam-4690	375	4	cn	cn	PROPN
ejpam-4690	375	5	)	)	PUNCT
ejpam-4690	375	6	=	=	SYM
ejpam-4690	375	7	γgr(cn	γgr(cn	NOUN
ejpam-4690	375	8	)	)	PUNCT
ejpam-4690	376	1	=	=	VERB
ejpam-4690	376	2	n−	n−	NOUN
ejpam-4690	376	3	2	2	NUM
ejpam-4690	376	4	for	for	ADP
ejpam-4690	376	5	all	all	DET
ejpam-4690	376	6	n	n	PRON
ejpam-4690	376	7	≥	≥	NOUN
ejpam-4690	376	8	4	4	NUM
ejpam-4690	376	9	.	.	PUNCT
ejpam-4690	377	1	(	(	PUNCT
ejpam-4690	377	2	iii	iii	NOUN
ejpam-4690	377	3	)	)	PUNCT
ejpam-4690	377	4	γgr(fn	γgr(fn	NOUN
ejpam-4690	377	5	)	)	PUNCT
ejpam-4690	378	1	=	=	SYM
ejpam-4690	378	2	γgr(k1	γgr(k1	PROPN
ejpam-4690	378	3	+	+	CCONJ
ejpam-4690	378	4	pn	pn	PROPN
ejpam-4690	378	5	)	)	PUNCT
ejpam-4690	378	6	=	=	SYM
ejpam-4690	378	7	γgr(pn	γgr(pn	NOUN
ejpam-4690	378	8	)	)	PUNCT
ejpam-4690	378	9	=	=	PUNCT
ejpam-4690	378	10	n−	n−	NOUN
ejpam-4690	378	11	1	1	NUM
ejpam-4690	378	12	for	for	ADP
ejpam-4690	378	13	all	all	DET
ejpam-4690	378	14	n	n	PRON
ejpam-4690	378	15	≥	≥	NOUN
ejpam-4690	378	16	3	3	NUM
ejpam-4690	378	17	.	.	NOUN
ejpam-4690	378	18	4	4	NUM
ejpam-4690	378	19	.	.	X
ejpam-4690	378	20	conclusion	conclusion	NOUN
ejpam-4690	378	21	the	the	DET
ejpam-4690	378	22	study	study	NOUN
ejpam-4690	378	23	revisited	revisit	VERB
ejpam-4690	378	24	the	the	DET
ejpam-4690	378	25	concepts	concept	NOUN
ejpam-4690	378	26	of	of	ADP
ejpam-4690	378	27	grundy	grundy	PROPN
ejpam-4690	378	28	domination	domination	PROPN
ejpam-4690	378	29	and	and	CCONJ
ejpam-4690	378	30	grundy	grundy	PROPN
ejpam-4690	378	31	hop	hop	PROPN
ejpam-4690	378	32	domination	domination	NOUN
ejpam-4690	378	33	in	in	ADP
ejpam-4690	378	34	graphs	graph	NOUN
ejpam-4690	378	35	which	which	PRON
ejpam-4690	378	36	have	have	AUX
ejpam-4690	378	37	been	be	AUX
ejpam-4690	378	38	considered	consider	VERB
ejpam-4690	378	39	previously	previously	ADV
ejpam-4690	378	40	by	by	ADP
ejpam-4690	378	41	various	various	ADJ
ejpam-4690	378	42	authors	author	NOUN
ejpam-4690	378	43	.	.	PUNCT
ejpam-4690	379	1	in	in	ADP
ejpam-4690	379	2	general	general	ADJ
ejpam-4690	379	3	,	,	PUNCT
ejpam-4690	379	4	the	the	DET
ejpam-4690	379	5	grundy	grundy	PROPN
ejpam-4690	379	6	domination	domination	PROPN
ejpam-4690	379	7	and	and	CCONJ
ejpam-4690	379	8	grundy	grundy	PROPN
ejpam-4690	379	9	hop	hop	PROPN
ejpam-4690	379	10	domination	domination	NOUN
ejpam-4690	379	11	numbers	number	NOUN
ejpam-4690	379	12	do	do	AUX
ejpam-4690	379	13	not	not	PART
ejpam-4690	379	14	satisfy	satisfy	VERB
ejpam-4690	379	15	a	a	DET
ejpam-4690	379	16	consistent	consistent	ADJ
ejpam-4690	379	17	relationship	relationship	NOUN
ejpam-4690	379	18	as	as	ADP
ejpam-4690	379	19	any	any	DET
ejpam-4690	379	20	one	one	NUM
ejpam-4690	379	21	of	of	ADP
ejpam-4690	379	22	them	they	PRON
ejpam-4690	379	23	can	can	AUX
ejpam-4690	379	24	be	be	AUX
ejpam-4690	379	25	larger	large	ADJ
ejpam-4690	379	26	than	than	ADP
ejpam-4690	379	27	the	the	DET
ejpam-4690	379	28	other	other	ADJ
ejpam-4690	379	29	.	.	PUNCT
ejpam-4690	380	1	in	in	ADP
ejpam-4690	380	2	fact	fact	NOUN
ejpam-4690	380	3	,	,	PUNCT
ejpam-4690	380	4	it	it	PRON
ejpam-4690	380	5	was	be	AUX
ejpam-4690	380	6	shown	show	VERB
ejpam-4690	380	7	that	that	SCONJ
ejpam-4690	380	8	the	the	DET
ejpam-4690	380	9	absolute	absolute	ADJ
ejpam-4690	380	10	difference	difference	NOUN
ejpam-4690	380	11	of	of	ADP
ejpam-4690	380	12	these	these	DET
ejpam-4690	380	13	two	two	NUM
ejpam-4690	380	14	parameters	parameter	NOUN
ejpam-4690	380	15	can	can	AUX
ejpam-4690	380	16	be	be	AUX
ejpam-4690	380	17	made	make	VERB
ejpam-4690	380	18	arbitrarily	arbitrarily	ADV
ejpam-4690	380	19	large	large	ADJ
ejpam-4690	380	20	.	.	PUNCT
ejpam-4690	381	1	the	the	DET
ejpam-4690	381	2	grundy	grundy	PROPN
ejpam-4690	381	3	domination	domination	NOUN
ejpam-4690	381	4	numbers	number	NOUN
ejpam-4690	381	5	of	of	ADP
ejpam-4690	381	6	some	some	DET
ejpam-4690	381	7	graphs	graph	NOUN
ejpam-4690	381	8	were	be	AUX
ejpam-4690	381	9	determined	determine	VERB
ejpam-4690	381	10	.	.	PUNCT
ejpam-4690	382	1	for	for	ADP
ejpam-4690	382	2	the	the	DET
ejpam-4690	382	3	join	join	NOUN
ejpam-4690	382	4	of	of	ADP
ejpam-4690	382	5	two	two	NUM
ejpam-4690	382	6	graphs	graph	NOUN
ejpam-4690	382	7	,	,	PUNCT
ejpam-4690	382	8	the	the	DET
ejpam-4690	382	9	grundy	grundy	PROPN
ejpam-4690	382	10	domination	domination	NOUN
ejpam-4690	382	11	number	number	NOUN
ejpam-4690	382	12	was	be	AUX
ejpam-4690	382	13	obtained	obtain	VERB
ejpam-4690	382	14	by	by	ADP
ejpam-4690	382	15	first	first	ADV
ejpam-4690	382	16	characterizing	characterize	VERB
ejpam-4690	382	17	all	all	DET
ejpam-4690	382	18	the	the	DET
ejpam-4690	382	19	grundy	grundy	PROPN
ejpam-4690	382	20	dominating	dominating	NOUN
ejpam-4690	382	21	sequences	sequence	NOUN
ejpam-4690	382	22	in	in	ADP
ejpam-4690	382	23	the	the	DET
ejpam-4690	382	24	graph	graph	NOUN
ejpam-4690	382	25	.	.	PUNCT
ejpam-4690	383	1	these	these	DET
ejpam-4690	383	2	two	two	NUM
ejpam-4690	383	3	parameters	parameter	NOUN
ejpam-4690	383	4	can	can	AUX
ejpam-4690	383	5	still	still	ADV
ejpam-4690	383	6	be	be	AUX
ejpam-4690	383	7	studied	study	VERB
ejpam-4690	383	8	for	for	ADP
ejpam-4690	383	9	other	other	ADJ
ejpam-4690	383	10	graphs	graph	NOUN
ejpam-4690	383	11	;	;	PUNCT
ejpam-4690	383	12	in	in	ADP
ejpam-4690	383	13	particular	particular	ADJ
ejpam-4690	383	14	,	,	PUNCT
ejpam-4690	383	15	for	for	ADP
ejpam-4690	383	16	graphs	graph	NOUN
ejpam-4690	383	17	under	under	ADP
ejpam-4690	383	18	some	some	DET
ejpam-4690	383	19	binary	binary	ADJ
ejpam-4690	383	20	operations	operation	NOUN
ejpam-4690	383	21	not	not	PART
ejpam-4690	383	22	yet	yet	ADV
ejpam-4690	383	23	considered	consider	VERB
ejpam-4690	383	24	in	in	ADP
ejpam-4690	383	25	previous	previous	ADJ
ejpam-4690	383	26	studies	study	NOUN
ejpam-4690	383	27	.	.	PUNCT
ejpam-4690	384	1	moreover	moreover	ADV
ejpam-4690	384	2	,	,	PUNCT
ejpam-4690	384	3	it	it	PRON
ejpam-4690	384	4	still	still	ADV
ejpam-4690	384	5	remains	remain	VERB
ejpam-4690	384	6	a	a	DET
ejpam-4690	384	7	conjecture	conjecture	NOUN
ejpam-4690	384	8	that	that	SCONJ
ejpam-4690	384	9	the	the	DET
ejpam-4690	384	10	grundy	grundy	PROPN
ejpam-4690	384	11	hop	hop	NOUN
ejpam-4690	384	12	dominating	dominating	NOUN
ejpam-4690	384	13	set	set	NOUN
ejpam-4690	384	14	problem	problem	NOUN
ejpam-4690	384	15	is	be	AUX
ejpam-4690	384	16	np	np	NOUN
ejpam-4690	384	17	-	-	PUNCT
ejpam-4690	384	18	complete	complete	ADJ
ejpam-4690	384	19	.	.	PUNCT
ejpam-4690	385	1	acknowledgements	acknowledgement	NOUN
ejpam-4690	385	2	the	the	DET
ejpam-4690	385	3	authors	author	NOUN
ejpam-4690	385	4	would	would	AUX
ejpam-4690	385	5	like	like	VERB
ejpam-4690	385	6	to	to	PART
ejpam-4690	385	7	thank	thank	VERB
ejpam-4690	385	8	the	the	DET
ejpam-4690	385	9	department	department	NOUN
ejpam-4690	385	10	of	of	ADP
ejpam-4690	385	11	science	science	NOUN
ejpam-4690	385	12	and	and	CCONJ
ejpam-4690	385	13	technology	technology	NOUN
ejpam-4690	385	14	accelerated	accelerate	VERB
ejpam-4690	385	15	science	science	NOUN
ejpam-4690	385	16	and	and	CCONJ
ejpam-4690	385	17	technology	technology	NOUN
ejpam-4690	385	18	human	human	ADJ
ejpam-4690	385	19	resource	resource	NOUN
ejpam-4690	385	20	development	development	NOUN
ejpam-4690	385	21	program	program	NOUN
ejpam-4690	385	22	(	(	PUNCT
ejpam-4690	385	23	dost	dost	NOUN
ejpam-4690	385	24	-	-	PUNCT
ejpam-4690	385	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4690	385	26	,	,	PUNCT
ejpam-4690	385	27	msu	msu	PROPN
ejpam-4690	385	28	-	-	PUNCT
ejpam-4690	385	29	iligan	iligan	PROPN
ejpam-4690	385	30	institute	institute	PROPN
ejpam-4690	385	31	of	of	ADP
ejpam-4690	385	32	technology	technology	PROPN
ejpam-4690	385	33	and	and	CCONJ
ejpam-4690	385	34	msu	msu	PROPN
ejpam-4690	385	35	tawi	tawi	PROPN
ejpam-4690	385	36	-	-	PUNCT
ejpam-4690	385	37	tawi	tawi	PROPN
ejpam-4690	385	38	college	college	PROPN
ejpam-4690	385	39	of	of	ADP
ejpam-4690	385	40	technology	technology	NOUN
ejpam-4690	385	41	and	and	CCONJ
ejpam-4690	385	42	oceanography	oceanography	NOUN
ejpam-4690	385	43	for	for	ADP
ejpam-4690	385	44	funding	fund	VERB
ejpam-4690	385	45	this	this	DET
ejpam-4690	385	46	research	research	NOUN
ejpam-4690	385	47	.	.	PUNCT
ejpam-4690	386	1	references	reference	NOUN
ejpam-4690	386	2	1165	1165	NUM
ejpam-4690	386	3	references	reference	NOUN
ejpam-4690	386	4	[	[	X
ejpam-4690	386	5	1	1	NUM
ejpam-4690	386	6	]	]	PUNCT
ejpam-4690	386	7	s.	s.	PROPN
ejpam-4690	386	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4690	386	9	,	,	PUNCT
ejpam-4690	386	10	b.	b.	PROPN
ejpam-4690	386	11	krishnakumari	krishnakumari	PROPN
ejpam-4690	386	12	,	,	PUNCT
ejpam-4690	386	13	b.	b.	PROPN
ejpam-4690	386	14	natarjan	natarjan	PROPN
ejpam-4690	386	15	,	,	PUNCT
ejpam-4690	386	16	and	and	CCONJ
ejpam-4690	386	17	y.	y.	PROPN
ejpam-4690	386	18	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4690	386	19	.	.	PUNCT
ejpam-4690	387	1	bounds	bound	NOUN
ejpam-4690	387	2	on	on	ADP
ejpam-4690	387	3	the	the	DET
ejpam-4690	387	4	hop	hop	NOUN
ejpam-4690	387	5	domination	domination	NOUN
ejpam-4690	387	6	number	number	NOUN
ejpam-4690	387	7	of	of	ADP
ejpam-4690	387	8	a	a	DET
ejpam-4690	387	9	tree	tree	NOUN
ejpam-4690	387	10	.	.	PUNCT
ejpam-4690	388	1	proceedings	proceeding	NOUN
ejpam-4690	388	2	-	-	PUNCT
ejpam-4690	388	3	mathematical	mathematical	ADJ
ejpam-4690	388	4	sciences	science	NOUN
ejpam-4690	388	5	.	.	PUNCT
ejpam-4690	388	6	,	,	PUNCT
ejpam-4690	388	7	125(4):449–455	125(4):449–455	ADP
ejpam-4690	388	8	,	,	PUNCT
ejpam-4690	388	9	2015	2015	NUM
ejpam-4690	388	10	.	.	PUNCT
ejpam-4690	389	1	[	[	X
ejpam-4690	389	2	2	2	NUM
ejpam-4690	389	3	]	]	PUNCT
ejpam-4690	389	4	s.	s.	PROPN
ejpam-4690	389	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4690	389	6	,	,	PUNCT
ejpam-4690	389	7	c.	c.	PROPN
ejpam-4690	389	8	natarajan	natarajan	PROPN
ejpam-4690	389	9	,	,	PUNCT
ejpam-4690	389	10	and	and	CCONJ
ejpam-4690	389	11	g.	g.	PROPN
ejpam-4690	389	12	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4690	389	13	.	.	PUNCT
ejpam-4690	390	1	a	a	DET
ejpam-4690	390	2	note	note	NOUN
ejpam-4690	390	3	on	on	ADP
ejpam-4690	390	4	hop	hop	NOUN
ejpam-4690	390	5	domination	domination	NOUN
ejpam-4690	390	6	number	number	NOUN
ejpam-4690	390	7	of	of	ADP
ejpam-4690	390	8	some	some	DET
ejpam-4690	390	9	special	special	ADJ
ejpam-4690	390	10	families	family	NOUN
ejpam-4690	390	11	of	of	ADP
ejpam-4690	390	12	graphs	graph	NOUN
ejpam-4690	390	13	.	.	PUNCT
ejpam-4690	391	1	international	international	ADJ
ejpam-4690	391	2	journal	journal	NOUN
ejpam-4690	391	3	of	of	ADP
ejpam-4690	391	4	pure	pure	ADJ
ejpam-4690	391	5	and	and	CCONJ
ejpam-4690	391	6	applied	applied	ADJ
ejpam-4690	391	7	mathematics	mathematic	NOUN
ejpam-4690	391	8	.	.	PUNCT
ejpam-4690	391	9	,	,	PUNCT
ejpam-4690	391	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4690	391	11	,	,	PUNCT
ejpam-4690	391	12	2018	2018	NUM
ejpam-4690	391	13	.	.	PUNCT
ejpam-4690	392	1	[	[	X
ejpam-4690	392	2	3	3	X
ejpam-4690	392	3	]	]	X
ejpam-4690	392	4	b.	b.	PROPN
ejpam-4690	392	5	bresar	bresar	PROPN
ejpam-4690	392	6	,	,	PUNCT
ejpam-4690	392	7	cs	cs	PROPN
ejpam-4690	392	8	.	.	PROPN
ejpam-4690	392	9	bujtas	bujtas	PROPN
ejpam-4690	392	10	,	,	PUNCT
ejpam-4690	392	11	t.	t.	NOUN
ejpam-4690	392	12	gologranc	gologranc	PROPN
ejpam-4690	392	13	,	,	PUNCT
ejpam-4690	392	14	s.	s.	PROPN
ejpam-4690	392	15	klavzar	klavzar	PROPN
ejpam-4690	392	16	,	,	PUNCT
ejpam-4690	392	17	g.	g.	PROPN
ejpam-4690	392	18	kosmrlj	kosmrlj	PROPN
ejpam-4690	392	19	,	,	PUNCT
ejpam-4690	392	20	b.	b.	PROPN
ejpam-4690	392	21	patkos	patkos	PROPN
ejpam-4690	392	22	,	,	PUNCT
ejpam-4690	392	23	zs	zs	PROPN
ejpam-4690	392	24	.	.	PUNCT
ejpam-4690	392	25	tuza	tuza	PROPN
ejpam-4690	392	26	,	,	PUNCT
ejpam-4690	392	27	and	and	CCONJ
ejpam-4690	392	28	m.	m.	NOUN
ejpam-4690	392	29	vizer	vizer	NOUN
ejpam-4690	392	30	.	.	PUNCT
ejpam-4690	393	1	dominating	dominate	VERB
ejpam-4690	393	2	sequence	sequence	NOUN
ejpam-4690	393	3	in	in	ADP
ejpam-4690	393	4	grid	grid	NOUN
ejpam-4690	393	5	-	-	PUNCT
ejpam-4690	393	6	like	like	ADJ
ejpam-4690	393	7	and	and	CCONJ
ejpam-4690	393	8	toroidal	toroidal	ADJ
ejpam-4690	393	9	graphs	graph	NOUN
ejpam-4690	393	10	.	.	PUNCT
ejpam-4690	394	1	electron	electron	PROPN
ejpam-4690	394	2	.	.	PUNCT
ejpam-4690	395	1	j.	j.	PROPN
ejpam-4690	395	2	combin	combin	PROPN
ejpam-4690	395	3	.	.	PROPN
ejpam-4690	395	4	,	,	PUNCT
ejpam-4690	395	5	(	(	PUNCT
ejpam-4690	395	6	23):1–17	23):1–17	NUM
ejpam-4690	395	7	,	,	PUNCT
ejpam-4690	395	8	2016	2016	NUM
ejpam-4690	395	9	.	.	PUNCT
ejpam-4690	396	1	[	[	X
ejpam-4690	396	2	4	4	X
ejpam-4690	396	3	]	]	X
ejpam-4690	396	4	b.	b.	PROPN
ejpam-4690	396	5	bresar	bresar	PROPN
ejpam-4690	396	6	,	,	PUNCT
ejpam-4690	396	7	cs	cs	PROPN
ejpam-4690	396	8	.	.	PROPN
ejpam-4690	396	9	bujtas	bujtas	PROPN
ejpam-4690	396	10	,	,	PUNCT
ejpam-4690	396	11	t.	t.	NOUN
ejpam-4690	396	12	gologranc	gologranc	PROPN
ejpam-4690	396	13	,	,	PUNCT
ejpam-4690	396	14	s.	s.	PROPN
ejpam-4690	396	15	klavzar	klavzar	PROPN
ejpam-4690	396	16	,	,	PUNCT
ejpam-4690	396	17	g.	g.	PROPN
ejpam-4690	396	18	kosmrlj	kosmrlj	PROPN
ejpam-4690	396	19	,	,	PUNCT
ejpam-4690	396	20	b.	b.	PROPN
ejpam-4690	396	21	patkos	patkos	PROPN
ejpam-4690	396	22	,	,	PUNCT
ejpam-4690	396	23	zs	zs	PROPN
ejpam-4690	396	24	.	.	PUNCT
ejpam-4690	396	25	tuza	tuza	PROPN
ejpam-4690	396	26	,	,	PUNCT
ejpam-4690	396	27	and	and	CCONJ
ejpam-4690	396	28	m.	m.	NOUN
ejpam-4690	396	29	vizer	vizer	NOUN
ejpam-4690	396	30	.	.	PUNCT
ejpam-4690	397	1	grundy	grundy	PROPN
ejpam-4690	397	2	dominating	dominating	NOUN
ejpam-4690	397	3	sequence	sequence	NOUN
ejpam-4690	397	4	and	and	CCONJ
ejpam-4690	397	5	zero	zero	NUM
ejpam-4690	397	6	forcing	forcing	NOUN
ejpam-4690	397	7	sets	set	NOUN
ejpam-4690	397	8	.	.	PUNCT
ejpam-4690	398	1	discrete	discrete	ADJ
ejpam-4690	398	2	optim	optim	ADJ
ejpam-4690	398	3	.	.	PUNCT
ejpam-4690	398	4	,	,	PUNCT
ejpam-4690	398	5	(	(	PUNCT
ejpam-4690	398	6	26):66–77	26):66–77	NUM
ejpam-4690	398	7	,	,	PUNCT
ejpam-4690	398	8	2017	2017	NUM
ejpam-4690	398	9	.	.	PUNCT
ejpam-4690	399	1	[	[	X
ejpam-4690	399	2	5	5	NUM
ejpam-4690	399	3	]	]	PUNCT
ejpam-4690	399	4	b.	b.	PROPN
ejpam-4690	399	5	bresar	bresar	PROPN
ejpam-4690	399	6	,	,	PUNCT
ejpam-4690	399	7	t.	t.	NOUN
ejpam-4690	399	8	gologranc	gologranc	PROPN
ejpam-4690	399	9	,	,	PUNCT
ejpam-4690	399	10	and	and	CCONJ
ejpam-4690	399	11	t.	t.	PROPN
ejpam-4690	399	12	kos	kos	PROPN
ejpam-4690	399	13	.	.	PUNCT
ejpam-4690	400	1	dominating	dominate	VERB
ejpam-4690	400	2	sequences	sequence	NOUN
ejpam-4690	400	3	under	under	ADP
ejpam-4690	400	4	atomic	atomic	ADJ
ejpam-4690	400	5	changes	change	NOUN
ejpam-4690	400	6	with	with	ADP
ejpam-4690	400	7	applications	application	NOUN
ejpam-4690	400	8	in	in	ADP
ejpam-4690	400	9	sierpinski	sierpinski	ADJ
ejpam-4690	400	10	and	and	CCONJ
ejpam-4690	400	11	interval	interval	NOUN
ejpam-4690	400	12	graphs	graph	NOUN
ejpam-4690	400	13	.	.	PUNCT
ejpam-4690	401	1	appl	appl	PROPN
ejpam-4690	401	2	.	.	PUNCT
ejpam-4690	402	1	anal	anal	PROPN
ejpam-4690	402	2	.	.	PUNCT
ejpam-4690	403	1	discrete	discrete	ADJ
ejpam-4690	403	2	math	math	NOUN
ejpam-4690	403	3	.	.	PUNCT
ejpam-4690	404	1	,	,	PUNCT
ejpam-4690	404	2	(	(	PUNCT
ejpam-4690	404	3	10):518–531	10):518–531	NUM
ejpam-4690	404	4	,	,	PUNCT
ejpam-4690	404	5	2016	2016	NUM
ejpam-4690	404	6	.	.	PUNCT
ejpam-4690	405	1	[	[	X
ejpam-4690	405	2	6	6	NUM
ejpam-4690	405	3	]	]	PUNCT
ejpam-4690	405	4	b.	b.	PROPN
ejpam-4690	405	5	bresar	bresar	PROPN
ejpam-4690	405	6	,	,	PUNCT
ejpam-4690	405	7	t.	t.	NOUN
ejpam-4690	405	8	gologranc	gologranc	PROPN
ejpam-4690	405	9	,	,	PUNCT
ejpam-4690	405	10	m.	m.	NOUN
ejpam-4690	405	11	milanic	milanic	PROPN
ejpam-4690	405	12	,	,	PUNCT
ejpam-4690	405	13	d.	d.	PROPN
ejpam-4690	405	14	rall	rall	PROPN
ejpam-4690	405	15	,	,	PUNCT
ejpam-4690	405	16	and	and	CCONJ
ejpam-4690	405	17	r.	r.	PROPN
ejpam-4690	405	18	rizzi	rizzi	PROPN
ejpam-4690	405	19	.	.	PUNCT
ejpam-4690	406	1	dominating	dominate	VERB
ejpam-4690	406	2	sequence	sequence	NOUN
ejpam-4690	406	3	in	in	ADP
ejpam-4690	406	4	graphs	graph	NOUN
ejpam-4690	406	5	.	.	PUNCT
ejpam-4690	407	1	discrete	discrete	ADJ
ejpam-4690	407	2	math	math	NOUN
ejpam-4690	407	3	.	.	PUNCT
ejpam-4690	408	1	,	,	PUNCT
ejpam-4690	408	2	(	(	PUNCT
ejpam-4690	408	3	336):22–36	336):22–36	NUM
ejpam-4690	408	4	,	,	PUNCT
ejpam-4690	408	5	2014	2014	NUM
ejpam-4690	408	6	.	.	PUNCT
ejpam-4690	409	1	[	[	X
ejpam-4690	409	2	7	7	X
ejpam-4690	409	3	]	]	X
ejpam-4690	409	4	b.	b.	PROPN
ejpam-4690	409	5	bresar	bresar	PROPN
ejpam-4690	409	6	,	,	PUNCT
ejpam-4690	409	7	t.	t.	PROPN
ejpam-4690	409	8	kos	kos	PROPN
ejpam-4690	409	9	,	,	PUNCT
ejpam-4690	409	10	and	and	CCONJ
ejpam-4690	409	11	p.	p.	NOUN
ejpam-4690	409	12	torres	torre	NOUN
ejpam-4690	409	13	.	.	PUNCT
ejpam-4690	410	1	grundy	grundy	PROPN
ejpam-4690	410	2	domination	domination	NOUN
ejpam-4690	410	3	and	and	CCONJ
ejpam-4690	410	4	zero	zero	NUM
ejpam-4690	410	5	forcing	force	VERB
ejpam-4690	410	6	in	in	ADP
ejpam-4690	410	7	kneser	kneser	NOUN
ejpam-4690	410	8	graphs	graph	NOUN
ejpam-4690	410	9	.	.	PUNCT
ejpam-4690	411	1	ars	ar	VERB
ejpam-4690	411	2	math	math	PROPN
ejpam-4690	411	3	.	.	PUNCT
ejpam-4690	412	1	contemp	contemp	NOUN
ejpam-4690	412	2	.	.	PUNCT
ejpam-4690	413	1	,	,	PUNCT
ejpam-4690	413	2	(	(	PUNCT
ejpam-4690	413	3	17):419–430	17):419–430	NUM
ejpam-4690	413	4	,	,	PUNCT
ejpam-4690	413	5	2019	2019	NUM
ejpam-4690	413	6	.	.	PUNCT
ejpam-4690	414	1	[	[	X
ejpam-4690	414	2	8	8	X
ejpam-4690	414	3	]	]	PUNCT
ejpam-4690	414	4	j.	j.	PROPN
ejpam-4690	414	5	hassan	hassan	PROPN
ejpam-4690	414	6	and	and	CCONJ
ejpam-4690	414	7	s.	s.	PROPN
ejpam-4690	414	8	canoy	canoy	PROPN
ejpam-4690	414	9	jr	jr	PROPN
ejpam-4690	414	10	.	.	PUNCT
ejpam-4690	415	1	grundy	grundy	PROPN
ejpam-4690	415	2	hop	hop	PROPN
ejpam-4690	415	3	domination	domination	PROPN
ejpam-4690	415	4	in	in	ADP
ejpam-4690	415	5	graphs	graph	NOUN
ejpam-4690	415	6	.	.	PUNCT
ejpam-4690	416	1	eur	eur	PROPN
ejpam-4690	416	2	.	.	PUNCT
ejpam-4690	417	1	j.	j.	PROPN
ejpam-4690	417	2	pure	pure	PROPN
ejpam-4690	417	3	appl	appl	PROPN
ejpam-4690	417	4	.	.	PUNCT
ejpam-4690	417	5	math	math	PROPN
ejpam-4690	417	6	.	.	PUNCT
ejpam-4690	417	7	,	,	PUNCT
ejpam-4690	417	8	15(4):1623–1636	15(4):1623–1636	NUM
ejpam-4690	417	9	,	,	PUNCT
ejpam-4690	417	10	2022	2022	NUM
ejpam-4690	417	11	.	.	PUNCT
ejpam-4690	418	1	[	[	X
ejpam-4690	418	2	9	9	NUM
ejpam-4690	418	3	]	]	PUNCT
ejpam-4690	418	4	j.	j.	PROPN
ejpam-4690	418	5	hassan	hassan	PROPN
ejpam-4690	418	6	and	and	CCONJ
ejpam-4690	418	7	s.	s.	PROPN
ejpam-4690	418	8	canoy	canoy	PROPN
ejpam-4690	418	9	jr	jr	PROPN
ejpam-4690	418	10	.	.	PROPN
ejpam-4690	418	11	hop	hop	PROPN
ejpam-4690	418	12	independent	independent	ADJ
ejpam-4690	418	13	hop	hop	NOUN
ejpam-4690	418	14	domination	domination	NOUN
ejpam-4690	418	15	in	in	ADP
ejpam-4690	418	16	graphs	graph	NOUN
ejpam-4690	418	17	.	.	PUNCT
ejpam-4690	419	1	eur	eur	PROPN
ejpam-4690	419	2	.	.	PUNCT
ejpam-4690	420	1	j.	j.	PROPN
ejpam-4690	420	2	pure	pure	PROPN
ejpam-4690	420	3	appl	appl	PROPN
ejpam-4690	420	4	.	.	PUNCT
ejpam-4690	420	5	math	math	PROPN
ejpam-4690	420	6	.	.	PUNCT
ejpam-4690	420	7	,	,	PUNCT
ejpam-4690	420	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-4690	420	9	,	,	PUNCT
ejpam-4690	420	10	2022	2022	NUM
ejpam-4690	420	11	.	.	PUNCT
ejpam-4690	421	1	[	[	X
ejpam-4690	421	2	10	10	NUM
ejpam-4690	421	3	]	]	X
ejpam-4690	421	4	j.	j.	PROPN
ejpam-4690	421	5	hassan	hassan	PROPN
ejpam-4690	421	6	,	,	PUNCT
ejpam-4690	421	7	s.	s.	PROPN
ejpam-4690	421	8	canoy	canoy	PROPN
ejpam-4690	421	9	jr	jr	PROPN
ejpam-4690	421	10	.	.	PROPN
ejpam-4690	421	11	,	,	PUNCT
ejpam-4690	421	12	and	and	CCONJ
ejpam-4690	421	13	a.	a.	PROPN
ejpam-4690	421	14	aradais	aradais	PROPN
ejpam-4690	421	15	.	.	PUNCT
ejpam-4690	422	1	hop	hop	PROPN
ejpam-4690	422	2	independent	independent	ADJ
ejpam-4690	422	3	sets	set	NOUN
ejpam-4690	422	4	in	in	ADP
ejpam-4690	422	5	graphs	graph	NOUN
ejpam-4690	422	6	.	.	PUNCT
ejpam-4690	423	1	eur	eur	PROPN
ejpam-4690	423	2	.	.	PUNCT
ejpam-4690	424	1	j.	j.	PROPN
ejpam-4690	424	2	pure	pure	PROPN
ejpam-4690	424	3	appl	appl	PROPN
ejpam-4690	424	4	.	.	PUNCT
ejpam-4690	424	5	math	math	PROPN
ejpam-4690	424	6	.	.	PUNCT
ejpam-4690	424	7	,	,	PUNCT
ejpam-4690	424	8	15(2):467–477	15(2):467–477	PROPN
ejpam-4690	424	9	,	,	PUNCT
ejpam-4690	424	10	2022	2022	NUM
ejpam-4690	424	11	.	.	PUNCT
ejpam-4690	425	1	[	[	X
ejpam-4690	425	2	11	11	NUM
ejpam-4690	425	3	]	]	PUNCT
ejpam-4690	425	4	m.	m.	NOUN
ejpam-4690	425	5	henning	henning	PROPN
ejpam-4690	425	6	and	and	CCONJ
ejpam-4690	425	7	n.	n.	PROPN
ejpam-4690	425	8	rad	rad	PROPN
ejpam-4690	425	9	.	.	PROPN
ejpam-4690	426	1	on	on	ADP
ejpam-4690	426	2	2	2	NUM
ejpam-4690	426	3	-	-	PUNCT
ejpam-4690	426	4	step	step	NOUN
ejpam-4690	426	5	and	and	CCONJ
ejpam-4690	426	6	hop	hop	NOUN
ejpam-4690	426	7	dominating	dominating	NOUN
ejpam-4690	426	8	sets	set	NOUN
ejpam-4690	426	9	in	in	ADP
ejpam-4690	426	10	graphs	graph	NOUN
ejpam-4690	426	11	.	.	PUNCT
ejpam-4690	427	1	graphs	graph	NOUN
ejpam-4690	427	2	and	and	CCONJ
ejpam-4690	427	3	combinatorics	combinatoric	NOUN
ejpam-4690	427	4	.	.	PUNCT
ejpam-4690	427	5	,	,	PUNCT
ejpam-4690	427	6	33(4):913–927	33(4):913–927	PROPN
ejpam-4690	427	7	,	,	PUNCT
ejpam-4690	427	8	2017	2017	NUM
ejpam-4690	427	9	.	.	PUNCT
ejpam-4690	428	1	[	[	X
ejpam-4690	428	2	12	12	NUM
ejpam-4690	428	3	]	]	X
ejpam-4690	428	4	s.	s.	PROPN
ejpam-4690	428	5	canoy	canoy	PROPN
ejpam-4690	428	6	jr	jr	PROPN
ejpam-4690	428	7	.	.	PROPN
ejpam-4690	428	8	,	,	PUNCT
ejpam-4690	428	9	r.	r.	PROPN
ejpam-4690	428	10	mollejon	mollejon	NOUN
ejpam-4690	428	11	,	,	PUNCT
ejpam-4690	428	12	and	and	CCONJ
ejpam-4690	428	13	j.	j.	PROPN
ejpam-4690	428	14	g.	g.	PROPN
ejpam-4690	428	15	canoy	canoy	PROPN
ejpam-4690	428	16	.	.	PUNCT
ejpam-4690	429	1	hop	hop	PROPN
ejpam-4690	429	2	dominating	dominating	NOUN
ejpam-4690	429	3	sets	set	NOUN
ejpam-4690	429	4	in	in	ADP
ejpam-4690	429	5	graphs	graph	NOUN
ejpam-4690	429	6	under	under	ADP
ejpam-4690	429	7	binary	binary	ADJ
ejpam-4690	429	8	operations	operation	NOUN
ejpam-4690	429	9	.	.	PUNCT
ejpam-4690	430	1	eur	eur	PROPN
ejpam-4690	430	2	.	.	PUNCT
ejpam-4690	431	1	j.	j.	PROPN
ejpam-4690	431	2	pure	pure	PROPN
ejpam-4690	431	3	appl	appl	PROPN
ejpam-4690	431	4	.	.	PUNCT
ejpam-4690	431	5	math	math	PROPN
ejpam-4690	431	6	.	.	PUNCT
ejpam-4690	431	7	,	,	PUNCT
ejpam-4690	432	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4690	432	2	,	,	PUNCT
ejpam-4690	432	3	2019	2019	NUM
ejpam-4690	432	4	.	.	PUNCT
ejpam-4690	433	1	[	[	X
ejpam-4690	433	2	13	13	NUM
ejpam-4690	433	3	]	]	PUNCT
ejpam-4690	433	4	s.	s.	PROPN
ejpam-4690	433	5	canoy	canoy	PROPN
ejpam-4690	433	6	jr	jr	PROPN
ejpam-4690	433	7	.	.	PROPN
ejpam-4690	433	8	and	and	CCONJ
ejpam-4690	433	9	g.	g.	PROPN
ejpam-4690	433	10	salasalan	salasalan	NOUN
ejpam-4690	433	11	.	.	PUNCT
ejpam-4690	434	1	revisiting	revisit	VERB
ejpam-4690	434	2	domination	domination	NOUN
ejpam-4690	434	3	,	,	PUNCT
ejpam-4690	434	4	hop	hop	NOUN
ejpam-4690	434	5	domination	domination	NOUN
ejpam-4690	434	6	,	,	PUNCT
ejpam-4690	434	7	and	and	CCONJ
ejpam-4690	434	8	global	global	ADJ
ejpam-4690	434	9	hop	hop	NOUN
ejpam-4690	434	10	domination	domination	NOUN
ejpam-4690	434	11	in	in	ADP
ejpam-4690	434	12	graphs	graph	NOUN
ejpam-4690	434	13	.	.	PUNCT
ejpam-4690	435	1	eur	eur	PROPN
ejpam-4690	435	2	.	.	PUNCT
ejpam-4690	436	1	j.	j.	PROPN
ejpam-4690	436	2	pure	pure	PROPN
ejpam-4690	436	3	appl	appl	PROPN
ejpam-4690	436	4	.	.	PUNCT
ejpam-4690	436	5	math	math	PROPN
ejpam-4690	436	6	.	.	PUNCT
ejpam-4690	436	7	,	,	PUNCT
ejpam-4690	436	8	14:1415–1428	14:1415–1428	NUM
ejpam-4690	436	9	,	,	PUNCT
ejpam-4690	436	10	2021	2021	NUM
ejpam-4690	436	11	.	.	PUNCT
ejpam-4690	437	1	[	[	X
ejpam-4690	437	2	14	14	NUM
ejpam-4690	437	3	]	]	X
ejpam-4690	437	4	g.	g.	PROPN
ejpam-4690	437	5	nasini	nasini	PROPN
ejpam-4690	437	6	and	and	CCONJ
ejpam-4690	437	7	p.	p.	NOUN
ejpam-4690	437	8	torres	torre	NOUN
ejpam-4690	437	9	.	.	PUNCT
ejpam-4690	438	1	grundy	grundy	PROPN
ejpam-4690	438	2	dominating	dominate	VERB
ejpam-4690	438	3	sequences	sequence	NOUN
ejpam-4690	438	4	on	on	ADP
ejpam-4690	438	5	x	x	ADJ
ejpam-4690	438	6	-	-	ADJ
ejpam-4690	438	7	join	join	ADJ
ejpam-4690	438	8	product	product	NOUN
ejpam-4690	438	9	.	.	PUNCT
ejpam-4690	439	1	discrete	discrete	ADJ
ejpam-4690	439	2	applied	applied	ADJ
ejpam-4690	439	3	mathematics	mathematic	NOUN
ejpam-4690	439	4	.	.	PUNCT
ejpam-4690	439	5	,	,	PUNCT
ejpam-4690	439	6	(	(	PUNCT
ejpam-4690	439	7	284):138–149	284):138–149	NOUN
ejpam-4690	439	8	,	,	PUNCT
ejpam-4690	439	9	2020	2020	NUM
ejpam-4690	439	10	.	.	PUNCT
ejpam-4690	440	1	references	reference	NOUN
ejpam-4690	440	2	1166	1166	NUM
ejpam-4690	440	3	[	[	X
ejpam-4690	440	4	15	15	NUM
ejpam-4690	440	5	]	]	X
ejpam-4690	440	6	c.	c.	PROPN
ejpam-4690	440	7	natarajan	natarajan	PROPN
ejpam-4690	440	8	and	and	CCONJ
ejpam-4690	440	9	s.	s.	PROPN
ejpam-4690	440	10	ayyaswamy	ayyaswamy	PROPN
ejpam-4690	440	11	.	.	PUNCT
ejpam-4690	441	1	hop	hop	PROPN
ejpam-4690	441	2	domination	domination	NOUN
ejpam-4690	441	3	in	in	ADP
ejpam-4690	441	4	graphs	graphs	PROPN
ejpam-4690	441	5	ii	ii	PROPN
ejpam-4690	441	6	.	.	PUNCT
ejpam-4690	441	7	versita	versita	PROPN
ejpam-4690	441	8	,	,	PUNCT
ejpam-4690	441	9	23(2):187	23(2):187	NUM
ejpam-4690	441	10	–	–	PUNCT
ejpam-4690	441	11	199	199	NUM
ejpam-4690	441	12	,	,	PUNCT
ejpam-4690	441	13	2015	2015	NUM
ejpam-4690	441	14	.	.	PUNCT
ejpam-4690	442	1	[	[	X
ejpam-4690	442	2	16	16	X
ejpam-4690	442	3	]	]	X
ejpam-4690	442	4	y.	y.	PROPN
ejpam-4690	442	5	pabilona	pabilona	PROPN
ejpam-4690	442	6	and	and	CCONJ
ejpam-4690	442	7	h.	h.	PROPN
ejpam-4690	442	8	rara	rara	PROPN
ejpam-4690	442	9	.	.	PUNCT
ejpam-4690	443	1	connected	connect	VERB
ejpam-4690	443	2	hop	hop	NOUN
ejpam-4690	443	3	domination	domination	NOUN
ejpam-4690	443	4	in	in	ADP
ejpam-4690	443	5	graphs	graph	NOUN
ejpam-4690	443	6	under	under	ADP
ejpam-4690	443	7	some	some	DET
ejpam-4690	443	8	binary	binary	ADJ
ejpam-4690	443	9	operations	operation	NOUN
ejpam-4690	443	10	.	.	PUNCT
ejpam-4690	444	1	asian	asian	ADJ
ejpam-4690	444	2	-	-	PUNCT
ejpam-4690	444	3	eur	eur	NOUN
ejpam-4690	444	4	.	.	PUNCT
ejpam-4690	445	1	j.	j.	PROPN
ejpam-4690	445	2	math	math	PROPN
ejpam-4690	445	3	.	.	PROPN
ejpam-4690	445	4	,	,	PUNCT
ejpam-4690	445	5	11(5):1850075–1–1850075–11	11(5):1850075–1–1850075–11	NUM
ejpam-4690	445	6	,	,	PUNCT
ejpam-4690	445	7	2018	2018	NUM
ejpam-4690	445	8	.	.	PUNCT