id	sid	tid	token	lemma	pos
ejpam-4920	1	1	european	european	PROPN
ejpam-4920	1	2	journal	journal	PROPN
ejpam-4920	1	3	of	of	ADP
ejpam-4920	1	4	pure	pure	ADJ
ejpam-4920	1	5	and	and	CCONJ
ejpam-4920	1	6	applied	apply	VERB
ejpam-4920	1	7	mathematics	mathematic	NOUN
ejpam-4920	1	8	vol	vol	NOUN
ejpam-4920	1	9	.	.	PROPN
ejpam-4920	2	1	17	17	NUM
ejpam-4920	2	2	,	,	PUNCT
ejpam-4920	2	3	no	no	INTJ
ejpam-4920	2	4	.	.	NOUN
ejpam-4920	2	5	1	1	NUM
ejpam-4920	2	6	,	,	PUNCT
ejpam-4920	2	7	2024	2024	NUM
ejpam-4920	2	8	,	,	PUNCT
ejpam-4920	2	9	324	324	NUM
ejpam-4920	2	10	-	-	SYM
ejpam-4920	2	11	337	337	NUM
ejpam-4920	2	12	issn	issn	PROPN
ejpam-4920	2	13	1307	1307	NUM
ejpam-4920	2	14	-	-	SYM
ejpam-4920	2	15	5543	5543	NUM
ejpam-4920	2	16	–	–	PUNCT
ejpam-4920	2	17	ejpam.com	ejpam.com	X
ejpam-4920	2	18	published	publish	VERB
ejpam-4920	2	19	by	by	ADP
ejpam-4920	2	20	new	new	PROPN
ejpam-4920	2	21	york	york	PROPN
ejpam-4920	2	22	business	business	PROPN
ejpam-4920	2	23	global	global	VERB
ejpam-4920	2	24	some	some	DET
ejpam-4920	2	25	properties	property	NOUN
ejpam-4920	2	26	of	of	ADP
ejpam-4920	2	27	zero	zero	NUM
ejpam-4920	2	28	forcing	force	VERB
ejpam-4920	2	29	hop	hop	NOUN
ejpam-4920	2	30	dominating	dominating	NOUN
ejpam-4920	2	31	sets	set	NOUN
ejpam-4920	2	32	in	in	ADP
ejpam-4920	2	33	a	a	DET
ejpam-4920	2	34	graph	graph	NOUN
ejpam-4920	2	35	jahiri	jahiri	NOUN
ejpam-4920	2	36	u.	u.	PROPN
ejpam-4920	2	37	manditong1,∗	manditong1,∗	PROPN
ejpam-4920	2	38	,	,	PUNCT
ejpam-4920	2	39	aziz	aziz	PROPN
ejpam-4920	2	40	b.	b.	PROPN
ejpam-4920	3	1	tapeing1	tapeing1	PROPN
ejpam-4920	3	2	,	,	PUNCT
ejpam-4920	3	3	javier	javier	PROPN
ejpam-4920	3	4	a.	a.	PROPN
ejpam-4920	3	5	hassan1	hassan1	PROPN
ejpam-4920	3	6	,	,	PUNCT
ejpam-4920	3	7	alcyn	alcyn	PROPN
ejpam-4920	3	8	r.	r.	PROPN
ejpam-4920	3	9	bakkang2	bakkang2	PROPN
ejpam-4920	3	10	,	,	PUNCT
ejpam-4920	3	11	nurijam	nurijam	PROPN
ejpam-4920	3	12	hanna	hanna	PROPN
ejpam-4920	3	13	m.	m.	PROPN
ejpam-4920	3	14	mohommad1	mohommad1	PROPN
ejpam-4920	3	15	,	,	PUNCT
ejpam-4920	3	16	sisteta	sisteta	PROPN
ejpam-4920	3	17	u.	u.	PROPN
ejpam-4920	3	18	kamdon1	kamdon1	PROPN
ejpam-4920	4	1	1mathematics	1mathematics	NUM
ejpam-4920	4	2	and	and	CCONJ
ejpam-4920	4	3	sciences	sciences	PROPN
ejpam-4920	4	4	department	department	PROPN
ejpam-4920	4	5	,	,	PUNCT
ejpam-4920	4	6	college	college	NOUN
ejpam-4920	4	7	of	of	ADP
ejpam-4920	4	8	arts	art	NOUN
ejpam-4920	4	9	and	and	CCONJ
ejpam-4920	4	10	sciences	science	NOUN
ejpam-4920	4	11	,	,	PUNCT
ejpam-4920	4	12	msu	msu	PROPN
ejpam-4920	4	13	tawi	tawi	PROPN
ejpam-4920	4	14	-	-	PUNCT
ejpam-4920	4	15	tawi	tawi	PROPN
ejpam-4920	4	16	college	college	PROPN
ejpam-4920	4	17	of	of	ADP
ejpam-4920	4	18	technology	technology	NOUN
ejpam-4920	4	19	and	and	CCONJ
ejpam-4920	4	20	oceanography	oceanography	NOUN
ejpam-4920	4	21	,	,	PUNCT
ejpam-4920	4	22	bongao	bongao	NOUN
ejpam-4920	4	23	,	,	PUNCT
ejpam-4920	4	24	tawi	tawi	NOUN
ejpam-4920	4	25	-	-	PUNCT
ejpam-4920	4	26	tawi	tawi	NOUN
ejpam-4920	4	27	,	,	PUNCT
ejpam-4920	4	28	philippines	philippine	NOUN
ejpam-4920	4	29	2	2	NUM
ejpam-4920	4	30	secondary	secondary	ADJ
ejpam-4920	4	31	education	education	NOUN
ejpam-4920	4	32	department	department	NOUN
ejpam-4920	4	33	,	,	PUNCT
ejpam-4920	4	34	college	college	NOUN
ejpam-4920	4	35	of	of	ADP
ejpam-4920	4	36	education	education	NOUN
ejpam-4920	4	37	,	,	PUNCT
ejpam-4920	4	38	msu	msu	PROPN
ejpam-4920	4	39	tawi	tawi	PROPN
ejpam-4920	4	40	-	-	PUNCT
ejpam-4920	4	41	tawi	tawi	PROPN
ejpam-4920	4	42	college	college	PROPN
ejpam-4920	4	43	of	of	ADP
ejpam-4920	4	44	technology	technology	NOUN
ejpam-4920	4	45	and	and	CCONJ
ejpam-4920	4	46	oceanography	oceanography	NOUN
ejpam-4920	4	47	,	,	PUNCT
ejpam-4920	4	48	bongao	bongao	NOUN
ejpam-4920	4	49	,	,	PUNCT
ejpam-4920	4	50	tawi	tawi	NOUN
ejpam-4920	4	51	-	-	PUNCT
ejpam-4920	4	52	tawi	tawi	NOUN
ejpam-4920	4	53	,	,	PUNCT
ejpam-4920	4	54	philippines	philippine	NOUN
ejpam-4920	4	55	abstract	abstract	ADJ
ejpam-4920	4	56	.	.	PUNCT
ejpam-4920	5	1	in	in	ADP
ejpam-4920	5	2	this	this	DET
ejpam-4920	5	3	paper	paper	NOUN
ejpam-4920	5	4	,	,	PUNCT
ejpam-4920	5	5	we	we	PRON
ejpam-4920	5	6	initiate	initiate	VERB
ejpam-4920	5	7	the	the	DET
ejpam-4920	5	8	study	study	NOUN
ejpam-4920	5	9	of	of	ADP
ejpam-4920	5	10	a	a	DET
ejpam-4920	5	11	zero	zero	NUM
ejpam-4920	5	12	forcing	force	VERB
ejpam-4920	5	13	hop	hop	NOUN
ejpam-4920	5	14	domination	domination	NOUN
ejpam-4920	5	15	in	in	ADP
ejpam-4920	5	16	a	a	DET
ejpam-4920	5	17	graph	graph	NOUN
ejpam-4920	5	18	.	.	PUNCT
ejpam-4920	6	1	we	we	PRON
ejpam-4920	6	2	establish	establish	VERB
ejpam-4920	6	3	some	some	DET
ejpam-4920	6	4	properties	property	NOUN
ejpam-4920	6	5	of	of	ADP
ejpam-4920	6	6	this	this	DET
ejpam-4920	6	7	parameter	parameter	NOUN
ejpam-4920	6	8	and	and	CCONJ
ejpam-4920	6	9	we	we	PRON
ejpam-4920	6	10	determine	determine	VERB
ejpam-4920	6	11	its	its	PRON
ejpam-4920	6	12	connections	connection	NOUN
ejpam-4920	6	13	with	with	ADP
ejpam-4920	6	14	other	other	ADJ
ejpam-4920	6	15	known	know	VERB
ejpam-4920	6	16	parameters	parameter	NOUN
ejpam-4920	6	17	in	in	ADP
ejpam-4920	6	18	graph	graph	NOUN
ejpam-4920	6	19	theory	theory	NOUN
ejpam-4920	6	20	.	.	PUNCT
ejpam-4920	7	1	moreover	moreover	ADV
ejpam-4920	7	2	,	,	PUNCT
ejpam-4920	7	3	we	we	PRON
ejpam-4920	7	4	obtain	obtain	VERB
ejpam-4920	7	5	some	some	DET
ejpam-4920	7	6	exact	exact	ADJ
ejpam-4920	7	7	values	value	NOUN
ejpam-4920	7	8	or	or	CCONJ
ejpam-4920	7	9	bounds	bound	NOUN
ejpam-4920	7	10	of	of	ADP
ejpam-4920	7	11	the	the	DET
ejpam-4920	7	12	parameter	parameter	NOUN
ejpam-4920	7	13	on	on	ADP
ejpam-4920	7	14	the	the	DET
ejpam-4920	7	15	generalized	generalized	ADJ
ejpam-4920	7	16	graph	graph	NOUN
ejpam-4920	7	17	,	,	PUNCT
ejpam-4920	7	18	some	some	DET
ejpam-4920	7	19	families	family	NOUN
ejpam-4920	7	20	of	of	ADP
ejpam-4920	7	21	graphs	graph	NOUN
ejpam-4920	7	22	,	,	PUNCT
ejpam-4920	7	23	and	and	CCONJ
ejpam-4920	7	24	graphs	graph	NOUN
ejpam-4920	7	25	under	under	ADP
ejpam-4920	7	26	some	some	DET
ejpam-4920	7	27	operations	operation	NOUN
ejpam-4920	7	28	via	via	ADP
ejpam-4920	7	29	characterizations	characterization	NOUN
ejpam-4920	7	30	.	.	PUNCT
ejpam-4920	8	1	2020	2020	NUM
ejpam-4920	8	2	mathematics	mathematic	NOUN
ejpam-4920	8	3	subject	subject	NOUN
ejpam-4920	8	4	classifications	classification	NOUN
ejpam-4920	8	5	:	:	PUNCT
ejpam-4920	8	6	05c69	05c69	X
ejpam-4920	8	7	key	key	ADJ
ejpam-4920	8	8	words	word	NOUN
ejpam-4920	8	9	and	and	CCONJ
ejpam-4920	8	10	phrases	phrase	NOUN
ejpam-4920	8	11	:	:	PUNCT
ejpam-4920	8	12	zero	zero	NUM
ejpam-4920	8	13	forcing	force	VERB
ejpam-4920	8	14	hop	hop	NOUN
ejpam-4920	8	15	dominating	dominating	NOUN
ejpam-4920	8	16	set	set	NOUN
ejpam-4920	8	17	,	,	PUNCT
ejpam-4920	8	18	zero	zero	NUM
ejpam-4920	8	19	forcing	force	VERB
ejpam-4920	8	20	hop	hop	NOUN
ejpam-4920	8	21	domination	domination	NOUN
ejpam-4920	8	22	number	number	NOUN
ejpam-4920	8	23	,	,	PUNCT
ejpam-4920	8	24	zero	zero	NUM
ejpam-4920	8	25	forcing	force	VERB
ejpam-4920	8	26	pointwise	pointwise	PROPN
ejpam-4920	8	27	non	non	ADJ
ejpam-4920	8	28	-	-	ADJ
ejpam-4920	8	29	domination	domination	ADJ
ejpam-4920	8	30	1	1	NUM
ejpam-4920	8	31	.	.	PUNCT
ejpam-4920	9	1	introduction	introduction	NOUN
ejpam-4920	9	2	hop	hop	PROPN
ejpam-4920	9	3	domination	domination	NOUN
ejpam-4920	9	4	was	be	AUX
ejpam-4920	9	5	introduced	introduce	VERB
ejpam-4920	9	6	by	by	ADP
ejpam-4920	9	7	natarajan	natarajan	PROPN
ejpam-4920	9	8	et	et	PROPN
ejpam-4920	9	9	al	al	PROPN
ejpam-4920	9	10	.	.	PUNCT
ejpam-4920	10	1	in	in	ADP
ejpam-4920	10	2	[	[	X
ejpam-4920	10	3	12	12	NUM
ejpam-4920	10	4	]	]	PUNCT
ejpam-4920	10	5	.	.	PUNCT
ejpam-4920	11	1	this	this	DET
ejpam-4920	11	2	parameter	parameter	NOUN
ejpam-4920	11	3	is	be	AUX
ejpam-4920	11	4	incomparable	incomparable	ADJ
ejpam-4920	11	5	with	with	ADP
ejpam-4920	11	6	the	the	DET
ejpam-4920	11	7	standard	standard	ADJ
ejpam-4920	11	8	domination	domination	NOUN
ejpam-4920	11	9	and	and	CCONJ
ejpam-4920	11	10	just	just	ADV
ejpam-4920	11	11	like	like	ADP
ejpam-4920	11	12	domination	domination	NOUN
ejpam-4920	11	13	,	,	PUNCT
ejpam-4920	11	14	hop	hop	NOUN
ejpam-4920	11	15	domination	domination	NOUN
ejpam-4920	11	16	has	have	VERB
ejpam-4920	11	17	many	many	ADJ
ejpam-4920	11	18	applications	application	NOUN
ejpam-4920	11	19	in	in	ADP
ejpam-4920	11	20	different	different	ADJ
ejpam-4920	11	21	fields	field	NOUN
ejpam-4920	11	22	and	and	CCONJ
ejpam-4920	11	23	in	in	ADP
ejpam-4920	11	24	networks	network	NOUN
ejpam-4920	11	25	.	.	PUNCT
ejpam-4920	12	1	a	a	DET
ejpam-4920	12	2	subset	subset	NOUN
ejpam-4920	12	3	s	s	NOUN
ejpam-4920	12	4	of	of	ADP
ejpam-4920	12	5	a	a	DET
ejpam-4920	12	6	vertex	vertex	NOUN
ejpam-4920	12	7	set	set	VERB
ejpam-4920	12	8	v	v	NOUN
ejpam-4920	12	9	(	(	PUNCT
ejpam-4920	12	10	g	g	NOUN
ejpam-4920	12	11	)	)	PUNCT
ejpam-4920	12	12	is	be	AUX
ejpam-4920	12	13	called	call	VERB
ejpam-4920	12	14	a	a	DET
ejpam-4920	12	15	hop	hop	NOUN
ejpam-4920	12	16	dominating	dominating	NOUN
ejpam-4920	12	17	in	in	ADP
ejpam-4920	12	18	g	g	PROPN
ejpam-4920	12	19	if	if	SCONJ
ejpam-4920	12	20	n2	n2	ADJ
ejpam-4920	12	21	g[s	g[s	PROPN
ejpam-4920	12	22	]	]	X
ejpam-4920	12	23	=	=	SYM
ejpam-4920	12	24	v	v	NOUN
ejpam-4920	12	25	(	(	PUNCT
ejpam-4920	12	26	g	g	NOUN
ejpam-4920	12	27	)	)	PUNCT
ejpam-4920	12	28	,	,	PUNCT
ejpam-4920	12	29	where	where	SCONJ
ejpam-4920	12	30	n2	n2	ADJ
ejpam-4920	12	31	g[s	g[s	PROPN
ejpam-4920	12	32	]	]	PUNCT
ejpam-4920	12	33	is	be	AUX
ejpam-4920	12	34	the	the	DET
ejpam-4920	12	35	closed	closed	ADJ
ejpam-4920	12	36	hop	hop	NOUN
ejpam-4920	12	37	neighborhood	neighborhood	NOUN
ejpam-4920	12	38	of	of	ADP
ejpam-4920	12	39	s	s	PRON
ejpam-4920	12	40	in	in	ADP
ejpam-4920	12	41	g.	g.	PROPN
ejpam-4920	12	42	the	the	DET
ejpam-4920	12	43	minimum	minimum	ADJ
ejpam-4920	12	44	cardinality	cardinality	NOUN
ejpam-4920	12	45	among	among	ADP
ejpam-4920	12	46	all	all	DET
ejpam-4920	12	47	hop	hop	NOUN
ejpam-4920	12	48	dominating	dominating	NOUN
ejpam-4920	12	49	sets	set	NOUN
ejpam-4920	12	50	in	in	ADP
ejpam-4920	12	51	g	g	NOUN
ejpam-4920	12	52	,	,	PUNCT
ejpam-4920	12	53	denoted	denote	VERB
ejpam-4920	12	54	by	by	ADP
ejpam-4920	12	55	γh(g	γh(g	NOUN
ejpam-4920	12	56	)	)	PUNCT
ejpam-4920	12	57	,	,	PUNCT
ejpam-4920	12	58	is	be	AUX
ejpam-4920	12	59	called	call	VERB
ejpam-4920	12	60	the	the	DET
ejpam-4920	12	61	hop	hop	NOUN
ejpam-4920	12	62	domination	domination	NOUN
ejpam-4920	12	63	number	number	NOUN
ejpam-4920	12	64	of	of	ADP
ejpam-4920	12	65	g.	g.	PROPN
ejpam-4920	12	66	this	this	DET
ejpam-4920	12	67	concept	concept	NOUN
ejpam-4920	12	68	had	have	AUX
ejpam-4920	12	69	been	be	AUX
ejpam-4920	12	70	studied	study	VERB
ejpam-4920	12	71	on	on	ADP
ejpam-4920	12	72	different	different	ADJ
ejpam-4920	12	73	types	type	NOUN
ejpam-4920	12	74	of	of	ADP
ejpam-4920	12	75	graphs	graph	NOUN
ejpam-4920	12	76	and	and	CCONJ
ejpam-4920	12	77	graph	graph	NOUN
ejpam-4920	12	78	theorists	theorist	NOUN
ejpam-4920	12	79	found	find	VERB
ejpam-4920	12	80	some	some	DET
ejpam-4920	12	81	interesting	interesting	ADJ
ejpam-4920	12	82	results	result	NOUN
ejpam-4920	12	83	(	(	PUNCT
ejpam-4920	12	84	see	see	VERB
ejpam-4920	12	85	[	[	X
ejpam-4920	12	86	1	1	NUM
ejpam-4920	12	87	,	,	PUNCT
ejpam-4920	12	88	2	2	NUM
ejpam-4920	12	89	,	,	PUNCT
ejpam-4920	12	90	10	10	NUM
ejpam-4920	12	91	]	]	PUNCT
ejpam-4920	12	92	)	)	PUNCT
ejpam-4920	12	93	.	.	PUNCT
ejpam-4920	13	1	since	since	SCONJ
ejpam-4920	13	2	then	then	ADV
ejpam-4920	13	3	,	,	PUNCT
ejpam-4920	13	4	several	several	ADJ
ejpam-4920	13	5	researchers	researcher	NOUN
ejpam-4920	13	6	had	have	AUX
ejpam-4920	13	7	studied	study	VERB
ejpam-4920	13	8	this	this	DET
ejpam-4920	13	9	concepts	concept	NOUN
ejpam-4920	13	10	and	and	CCONJ
ejpam-4920	13	11	they	they	PRON
ejpam-4920	13	12	had	have	AUX
ejpam-4920	13	13	extended	extend	VERB
ejpam-4920	13	14	this	this	DET
ejpam-4920	13	15	parameter	parameter	NOUN
ejpam-4920	13	16	by	by	ADP
ejpam-4920	13	17	∗corresponding	∗corresponde	VERB
ejpam-4920	13	18	author	author	NOUN
ejpam-4920	13	19	.	.	PUNCT
ejpam-4920	14	1	doi	doi	NOUN
ejpam-4920	14	2	:	:	PUNCT
ejpam-4920	14	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4920	https://doi.org/10.29020/nybg.ejpam.v17i1.4920	CCONJ
ejpam-4920	14	4	email	email	NOUN
ejpam-4920	14	5	addresses	address	NOUN
ejpam-4920	14	6	:	:	PUNCT
ejpam-4920	14	7	jahirimanditong@msutawi-tawi.edu.ph	jahirimanditong@msutawi-tawi.edu.ph	PROPN
ejpam-4920	14	8	(	(	PUNCT
ejpam-4920	14	9	j.	j.	PROPN
ejpam-4920	14	10	u.	u.	PROPN
ejpam-4920	14	11	manditong	manditong	PROPN
ejpam-4920	14	12	)	)	PUNCT
ejpam-4920	14	13	aziztapeing@msutawi-tawi.edu.ph	aziztapeing@msutawi-tawi.edu.ph	PROPN
ejpam-4920	14	14	(	(	PUNCT
ejpam-4920	14	15	a.	a.	NOUN
ejpam-4920	14	16	tapeing	tapeing	NOUN
ejpam-4920	14	17	)	)	PUNCT
ejpam-4920	14	18	,	,	PUNCT
ejpam-4920	14	19	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-4920	14	20	(	(	PUNCT
ejpam-4920	14	21	j.	j.	PROPN
ejpam-4920	14	22	hassan	hassan	PROPN
ejpam-4920	14	23	)	)	PUNCT
ejpam-4920	14	24	,	,	PUNCT
ejpam-4920	14	25	hannamohammadg@msutawi-tawi.edu.ph	hannamohammadg@msutawi-tawi.edu.ph	PROPN
ejpam-4920	14	26	(	(	PUNCT
ejpam-4920	14	27	n.	n.	PROPN
ejpam-4920	14	28	h.	h.	PROPN
ejpam-4920	14	29	mohammad	mohammad	PROPN
ejpam-4920	14	30	)	)	PUNCT
ejpam-4920	14	31	,	,	PUNCT
ejpam-4920	14	32	sistetakamdon@msutawi-tawi.edu.ph	sistetakamdon@msutawi-tawi.edu.ph	PROPN
ejpam-4920	14	33	(	(	PUNCT
ejpam-4920	14	34	s.	s.	PROPN
ejpam-4920	14	35	kamdon	kamdon	PROPN
ejpam-4920	14	36	)	)	PUNCT
ejpam-4920	14	37	,	,	PUNCT
ejpam-4920	14	38	alcynbakkang@msutawi-tawi.edu.ph	alcynbakkang@msutawi-tawi.edu.ph	PROPN
ejpam-4920	14	39	(	(	PUNCT
ejpam-4920	14	40	a.	a.	PROPN
ejpam-4920	14	41	bakkang	bakkang	PROPN
ejpam-4920	14	42	)	)	PUNCT
ejpam-4920	14	43	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4920	15	1	324	324	NUM
ejpam-4920	16	1	©	©	ADP
ejpam-4920	16	2	2024	2024	NUM
ejpam-4920	16	3	ejpam	ejpam	NOUN
ejpam-4920	16	4	all	all	DET
ejpam-4920	16	5	rights	right	NOUN
ejpam-4920	16	6	reserved	reserve	VERB
ejpam-4920	16	7	.	.	PUNCT
ejpam-4920	17	1	j.	j.	PROPN
ejpam-4920	17	2	u.	u.	PROPN
ejpam-4920	17	3	manditong	manditong	PROPN
ejpam-4920	17	4	et	et	PROPN
ejpam-4920	17	5	al	al	PROPN
ejpam-4920	17	6	.	.	PUNCT
ejpam-4920	17	7	/	/	SYM
ejpam-4920	17	8	eur	eur	PROPN
ejpam-4920	17	9	.	.	PUNCT
ejpam-4920	18	1	j.	j.	PROPN
ejpam-4920	18	2	pure	pure	PROPN
ejpam-4920	18	3	appl	appl	PROPN
ejpam-4920	18	4	.	.	PROPN
ejpam-4920	18	5	math	math	PROPN
ejpam-4920	18	6	,	,	PUNCT
ejpam-4920	18	7	17	17	NUM
ejpam-4920	18	8	(	(	PUNCT
ejpam-4920	18	9	1	1	NUM
ejpam-4920	18	10	)	)	PUNCT
ejpam-4920	18	11	(	(	PUNCT
ejpam-4920	18	12	2024	2024	NUM
ejpam-4920	18	13	)	)	PUNCT
ejpam-4920	18	14	,	,	PUNCT
ejpam-4920	18	15	324	324	NUM
ejpam-4920	18	16	-	-	SYM
ejpam-4920	18	17	337	337	NUM
ejpam-4920	18	18	325	325	NUM
ejpam-4920	18	19	introducing	introduce	VERB
ejpam-4920	18	20	variants	variant	NOUN
ejpam-4920	18	21	,	,	PUNCT
ejpam-4920	18	22	that	that	ADV
ejpam-4920	18	23	is	is	ADV
ejpam-4920	18	24	,	,	PUNCT
ejpam-4920	18	25	imposing	impose	VERB
ejpam-4920	18	26	additional	additional	ADJ
ejpam-4920	18	27	properties	property	NOUN
ejpam-4920	18	28	or	or	CCONJ
ejpam-4920	18	29	conditions	condition	NOUN
ejpam-4920	18	30	on	on	ADP
ejpam-4920	18	31	the	the	DET
ejpam-4920	18	32	standard	standard	ADJ
ejpam-4920	18	33	hop	hop	NOUN
ejpam-4920	18	34	domination	domination	NOUN
ejpam-4920	18	35	(	(	PUNCT
ejpam-4920	18	36	see	see	VERB
ejpam-4920	18	37	[	[	X
ejpam-4920	18	38	3–9	3–9	NUM
ejpam-4920	18	39	,	,	PUNCT
ejpam-4920	18	40	11	11	NUM
ejpam-4920	18	41	]	]	NUM
ejpam-4920	18	42	)	)	PUNCT
ejpam-4920	18	43	.	.	PUNCT
ejpam-4920	19	1	in	in	ADP
ejpam-4920	19	2	this	this	DET
ejpam-4920	19	3	paper	paper	NOUN
ejpam-4920	19	4	,	,	PUNCT
ejpam-4920	19	5	we	we	PRON
ejpam-4920	19	6	introduce	introduce	VERB
ejpam-4920	19	7	and	and	CCONJ
ejpam-4920	19	8	investigate	investigate	VERB
ejpam-4920	19	9	zero	zero	NUM
ejpam-4920	19	10	forcing	force	VERB
ejpam-4920	19	11	hop	hop	NOUN
ejpam-4920	19	12	domination	domination	NOUN
ejpam-4920	19	13	in	in	ADP
ejpam-4920	19	14	a	a	DET
ejpam-4920	19	15	graph	graph	NOUN
ejpam-4920	19	16	.	.	PUNCT
ejpam-4920	20	1	let	let	VERB
ejpam-4920	20	2	g	g	PRON
ejpam-4920	20	3	be	be	AUX
ejpam-4920	20	4	a	a	DET
ejpam-4920	20	5	graph	graph	NOUN
ejpam-4920	20	6	.	.	PUNCT
ejpam-4920	21	1	a	a	DET
ejpam-4920	21	2	subset	subset	NOUN
ejpam-4920	21	3	z	z	NOUN
ejpam-4920	21	4	of	of	ADP
ejpam-4920	21	5	a	a	DET
ejpam-4920	21	6	vertex	vertex	NOUN
ejpam-4920	21	7	-	-	PUNCT
ejpam-4920	21	8	set	set	VERB
ejpam-4920	21	9	v	v	NOUN
ejpam-4920	21	10	(	(	PUNCT
ejpam-4920	21	11	g	g	NOUN
ejpam-4920	21	12	)	)	PUNCT
ejpam-4920	21	13	of	of	ADP
ejpam-4920	21	14	g	g	PROPN
ejpam-4920	21	15	is	be	AUX
ejpam-4920	21	16	said	say	VERB
ejpam-4920	21	17	to	to	PART
ejpam-4920	21	18	be	be	AUX
ejpam-4920	21	19	a	a	DET
ejpam-4920	21	20	zero	zero	NUM
ejpam-4920	21	21	forcing	force	VERB
ejpam-4920	21	22	hop	hop	NOUN
ejpam-4920	21	23	dominating	dominating	NOUN
ejpam-4920	21	24	if	if	SCONJ
ejpam-4920	21	25	z	z	NOUN
ejpam-4920	21	26	is	be	AUX
ejpam-4920	21	27	both	both	PRON
ejpam-4920	21	28	zero	zero	NUM
ejpam-4920	21	29	forcing	forcing	NOUN
ejpam-4920	21	30	and	and	CCONJ
ejpam-4920	21	31	hop	hop	NOUN
ejpam-4920	21	32	dominating	dominating	NOUN
ejpam-4920	21	33	in	in	ADP
ejpam-4920	21	34	g.	g.	PROPN
ejpam-4920	21	35	the	the	DET
ejpam-4920	21	36	minimum	minimum	ADJ
ejpam-4920	21	37	cardinality	cardinality	NOUN
ejpam-4920	21	38	among	among	ADP
ejpam-4920	21	39	all	all	DET
ejpam-4920	21	40	zero	zero	NUM
ejpam-4920	21	41	forcing	force	VERB
ejpam-4920	21	42	hop	hop	NOUN
ejpam-4920	21	43	dominating	dominating	NOUN
ejpam-4920	21	44	sets	set	NOUN
ejpam-4920	21	45	in	in	ADP
ejpam-4920	21	46	g	g	NOUN
ejpam-4920	21	47	,	,	PUNCT
ejpam-4920	21	48	denoted	denote	VERB
ejpam-4920	21	49	by	by	ADP
ejpam-4920	21	50	γzh(g	γzh(g	NOUN
ejpam-4920	21	51	)	)	PUNCT
ejpam-4920	21	52	,	,	PUNCT
ejpam-4920	21	53	is	be	AUX
ejpam-4920	21	54	called	call	VERB
ejpam-4920	21	55	the	the	DET
ejpam-4920	21	56	zero	zero	NUM
ejpam-4920	21	57	forcing	force	VERB
ejpam-4920	21	58	hop	hop	NOUN
ejpam-4920	21	59	domination	domination	NOUN
ejpam-4920	21	60	number	number	NOUN
ejpam-4920	21	61	of	of	ADP
ejpam-4920	21	62	g.	g.	NOUN
ejpam-4920	21	63	we	we	PRON
ejpam-4920	21	64	study	study	VERB
ejpam-4920	21	65	this	this	DET
ejpam-4920	21	66	parameter	parameter	NOUN
ejpam-4920	21	67	on	on	ADP
ejpam-4920	21	68	some	some	DET
ejpam-4920	21	69	classes	class	NOUN
ejpam-4920	21	70	of	of	ADP
ejpam-4920	21	71	graphs	graph	NOUN
ejpam-4920	21	72	and	and	CCONJ
ejpam-4920	21	73	graphs	graph	NOUN
ejpam-4920	21	74	under	under	ADP
ejpam-4920	21	75	some	some	DET
ejpam-4920	21	76	operations	operation	NOUN
ejpam-4920	21	77	.	.	PUNCT
ejpam-4920	22	1	we	we	PRON
ejpam-4920	22	2	determine	determine	VERB
ejpam-4920	22	3	its	its	PRON
ejpam-4920	22	4	connections	connection	NOUN
ejpam-4920	22	5	with	with	ADP
ejpam-4920	22	6	other	other	ADJ
ejpam-4920	22	7	known	know	VERB
ejpam-4920	22	8	parameters	parameter	NOUN
ejpam-4920	22	9	in	in	ADP
ejpam-4920	22	10	graph	graph	NOUN
ejpam-4920	22	11	theory	theory	NOUN
ejpam-4920	22	12	such	such	ADJ
ejpam-4920	22	13	as	as	ADP
ejpam-4920	22	14	zero	zero	NUM
ejpam-4920	22	15	forcing	forcing	NOUN
ejpam-4920	22	16	and	and	CCONJ
ejpam-4920	22	17	hop	hop	NOUN
ejpam-4920	22	18	domination	domination	NOUN
ejpam-4920	22	19	.	.	PUNCT
ejpam-4920	23	1	we	we	PRON
ejpam-4920	23	2	believe	believe	VERB
ejpam-4920	23	3	that	that	SCONJ
ejpam-4920	23	4	this	this	DET
ejpam-4920	23	5	study	study	NOUN
ejpam-4920	23	6	and	and	CCONJ
ejpam-4920	23	7	its	its	PRON
ejpam-4920	23	8	results	result	NOUN
ejpam-4920	23	9	would	would	AUX
ejpam-4920	23	10	contribute	contribute	VERB
ejpam-4920	23	11	a	a	DET
ejpam-4920	23	12	lot	lot	NOUN
ejpam-4920	23	13	to	to	ADP
ejpam-4920	23	14	the	the	DET
ejpam-4920	23	15	rapidly	rapidly	ADV
ejpam-4920	23	16	increasing	increase	VERB
ejpam-4920	23	17	number	number	NOUN
ejpam-4920	23	18	of	of	ADP
ejpam-4920	23	19	studies	study	NOUN
ejpam-4920	23	20	in	in	ADP
ejpam-4920	23	21	domination	domination	NOUN
ejpam-4920	23	22	theory	theory	NOUN
ejpam-4920	23	23	.	.	PUNCT
ejpam-4920	24	1	2	2	X
ejpam-4920	24	2	.	.	X
ejpam-4920	24	3	terminology	terminology	NOUN
ejpam-4920	24	4	and	and	CCONJ
ejpam-4920	24	5	notation	notation	NOUN
ejpam-4920	24	6	let	let	VERB
ejpam-4920	24	7	g	g	PRON
ejpam-4920	24	8	be	be	AUX
ejpam-4920	24	9	a	a	DET
ejpam-4920	24	10	graph	graph	NOUN
ejpam-4920	24	11	.	.	PUNCT
ejpam-4920	25	1	the	the	DET
ejpam-4920	25	2	distance	distance	NOUN
ejpam-4920	25	3	dg(u	dg(u	NOUN
ejpam-4920	25	4	,	,	PUNCT
ejpam-4920	25	5	v	v	NOUN
ejpam-4920	25	6	)	)	PUNCT
ejpam-4920	25	7	of	of	ADP
ejpam-4920	25	8	two	two	NUM
ejpam-4920	25	9	vertices	vertex	NOUN
ejpam-4920	25	10	u	u	NOUN
ejpam-4920	25	11	,	,	PUNCT
ejpam-4920	25	12	v	v	NOUN
ejpam-4920	25	13	in	in	ADP
ejpam-4920	25	14	g	g	PROPN
ejpam-4920	25	15	is	be	AUX
ejpam-4920	25	16	the	the	DET
ejpam-4920	25	17	length	length	NOUN
ejpam-4920	25	18	of	of	ADP
ejpam-4920	25	19	a	a	DET
ejpam-4920	25	20	shortest	short	ADJ
ejpam-4920	25	21	u	u	NOUN
ejpam-4920	25	22	-	-	NOUN
ejpam-4920	25	23	v	v	ADJ
ejpam-4920	25	24	path	path	NOUN
ejpam-4920	25	25	in	in	ADP
ejpam-4920	25	26	g.	g.	PROPN
ejpam-4920	25	27	the	the	DET
ejpam-4920	25	28	greatest	great	ADJ
ejpam-4920	25	29	distance	distance	NOUN
ejpam-4920	25	30	between	between	ADP
ejpam-4920	25	31	any	any	DET
ejpam-4920	25	32	two	two	NUM
ejpam-4920	25	33	vertices	vertex	NOUN
ejpam-4920	25	34	in	in	ADP
ejpam-4920	25	35	g	g	NOUN
ejpam-4920	25	36	,	,	PUNCT
ejpam-4920	25	37	denoted	denote	VERB
ejpam-4920	25	38	by	by	ADP
ejpam-4920	25	39	diam(g	diam(g	PROPN
ejpam-4920	25	40	)	)	PUNCT
ejpam-4920	25	41	,	,	PUNCT
ejpam-4920	25	42	is	be	AUX
ejpam-4920	25	43	called	call	VERB
ejpam-4920	25	44	the	the	DET
ejpam-4920	25	45	diameter	diameter	NOUN
ejpam-4920	25	46	of	of	ADP
ejpam-4920	25	47	g.	g.	PROPN
ejpam-4920	25	48	two	two	NUM
ejpam-4920	25	49	distinct	distinct	ADJ
ejpam-4920	25	50	vertices	vertex	NOUN
ejpam-4920	25	51	v	v	ADP
ejpam-4920	25	52	,	,	PUNCT
ejpam-4920	25	53	w	w	NOUN
ejpam-4920	25	54	of	of	ADP
ejpam-4920	25	55	g	g	NOUN
ejpam-4920	25	56	are	be	AUX
ejpam-4920	25	57	said	say	VERB
ejpam-4920	25	58	to	to	PART
ejpam-4920	25	59	be	be	AUX
ejpam-4920	25	60	neighbors	neighbor	NOUN
ejpam-4920	25	61	,	,	PUNCT
ejpam-4920	25	62	if	if	SCONJ
ejpam-4920	25	63	dg(v	dg(v	NOUN
ejpam-4920	25	64	,	,	PUNCT
ejpam-4920	25	65	w	w	NOUN
ejpam-4920	25	66	)	)	PUNCT
ejpam-4920	26	1	=	=	SYM
ejpam-4920	26	2	1	1	X
ejpam-4920	26	3	.	.	PUNCT
ejpam-4920	27	1	the	the	DET
ejpam-4920	27	2	open	open	ADJ
ejpam-4920	27	3	neighborhood	neighborhood	NOUN
ejpam-4920	27	4	(	(	PUNCT
ejpam-4920	27	5	resp	resp	NOUN
ejpam-4920	27	6	.	.	PUNCT
ejpam-4920	28	1	closed	closed	ADJ
ejpam-4920	28	2	neighborhood	neighborhood	NOUN
ejpam-4920	28	3	)	)	PUNCT
ejpam-4920	28	4	of	of	ADP
ejpam-4920	28	5	v	v	NOUN
ejpam-4920	28	6	in	in	ADP
ejpam-4920	28	7	g	g	PROPN
ejpam-4920	28	8	is	be	AUX
ejpam-4920	28	9	the	the	DET
ejpam-4920	28	10	set	set	NOUN
ejpam-4920	28	11	defined	define	VERB
ejpam-4920	28	12	by	by	ADP
ejpam-4920	28	13	ng(v	ng(v	NOUN
ejpam-4920	28	14	)	)	PUNCT
ejpam-4920	28	15	=	=	PRON
ejpam-4920	28	16	{	{	PUNCT
ejpam-4920	28	17	w	w	NOUN
ejpam-4920	28	18	∈	∈	PROPN
ejpam-4920	28	19	v	v	ADP
ejpam-4920	28	20	(	(	PUNCT
ejpam-4920	28	21	g	g	NOUN
ejpam-4920	28	22	)	)	PUNCT
ejpam-4920	28	23	:	:	PUNCT
ejpam-4920	28	24	dg(v	dg(v	X
ejpam-4920	28	25	,	,	PUNCT
ejpam-4920	28	26	w	w	NOUN
ejpam-4920	28	27	)	)	PUNCT
ejpam-4920	28	28	=	=	SYM
ejpam-4920	28	29	1	1	X
ejpam-4920	28	30	}	}	PUNCT
ejpam-4920	28	31	(	(	PUNCT
ejpam-4920	28	32	resp	resp	NOUN
ejpam-4920	28	33	.	.	PUNCT
ejpam-4920	29	1	ng[v	ng[v	PUNCT
ejpam-4920	29	2	]	]	X
ejpam-4920	29	3	=	=	SYM
ejpam-4920	29	4	ng(v	ng(v	X
ejpam-4920	29	5	)	)	PUNCT
ejpam-4920	29	6	∪	∪	ADP
ejpam-4920	29	7	{	{	PUNCT
ejpam-4920	29	8	v	v	NOUN
ejpam-4920	29	9	}	}	PUNCT
ejpam-4920	29	10	)	)	PUNCT
ejpam-4920	29	11	.	.	PUNCT
ejpam-4920	30	1	if	if	SCONJ
ejpam-4920	30	2	x	x	PROPN
ejpam-4920	30	3	⊆	⊆	NUM
ejpam-4920	30	4	v	v	X
ejpam-4920	30	5	(	(	PUNCT
ejpam-4920	30	6	g	g	NOUN
ejpam-4920	30	7	)	)	PUNCT
ejpam-4920	30	8	,	,	PUNCT
ejpam-4920	30	9	then	then	ADV
ejpam-4920	30	10	the	the	DET
ejpam-4920	30	11	open	open	ADJ
ejpam-4920	30	12	neighborhood	neighborhood	NOUN
ejpam-4920	30	13	(	(	PUNCT
ejpam-4920	30	14	resp	resp	NOUN
ejpam-4920	30	15	.	.	PUNCT
ejpam-4920	30	16	closed	closed	ADJ
ejpam-4920	30	17	neighborhood	neighborhood	NOUN
ejpam-4920	30	18	)	)	PUNCT
ejpam-4920	30	19	of	of	ADP
ejpam-4920	30	20	x	x	X
ejpam-4920	30	21	in	in	ADP
ejpam-4920	30	22	g	g	PROPN
ejpam-4920	30	23	is	be	AUX
ejpam-4920	30	24	the	the	DET
ejpam-4920	30	25	set	set	NOUN
ejpam-4920	30	26	defined	define	VERB
ejpam-4920	30	27	by	by	ADP
ejpam-4920	30	28	ng(x	ng(x	NUM
ejpam-4920	30	29	)	)	PUNCT
ejpam-4920	31	1	=	=	VERB
ejpam-4920	31	2	⋃	⋃	NOUN
ejpam-4920	31	3	x∈x	x∈x	NOUN
ejpam-4920	31	4	ng(x	ng(x	NUM
ejpam-4920	31	5	)	)	PUNCT
ejpam-4920	31	6	(	(	PUNCT
ejpam-4920	31	7	resp	resp	NOUN
ejpam-4920	31	8	.	.	PUNCT
ejpam-4920	32	1	ng[x	ng[x	PROPN
ejpam-4920	32	2	]	]	PUNCT
ejpam-4920	32	3	=	=	PUNCT
ejpam-4920	32	4	ng(x	ng(x	X
ejpam-4920	32	5	)	)	PUNCT
ejpam-4920	32	6	∪x	∪x	NOUN
ejpam-4920	32	7	)	)	PUNCT
ejpam-4920	32	8	.	.	PUNCT
ejpam-4920	33	1	the	the	DET
ejpam-4920	33	2	color	color	NOUN
ejpam-4920	33	3	change	change	NOUN
ejpam-4920	33	4	rule	rule	NOUN
ejpam-4920	33	5	is	be	AUX
ejpam-4920	33	6	:	:	PUNCT
ejpam-4920	33	7	if	if	SCONJ
ejpam-4920	33	8	u	u	NOUN
ejpam-4920	33	9	is	be	AUX
ejpam-4920	33	10	a	a	DET
ejpam-4920	33	11	blue	blue	ADJ
ejpam-4920	33	12	vertex	vertex	NOUN
ejpam-4920	33	13	and	and	CCONJ
ejpam-4920	33	14	exactly	exactly	ADV
ejpam-4920	33	15	one	one	NUM
ejpam-4920	33	16	neighbor	neighbor	NOUN
ejpam-4920	33	17	w	w	PROPN
ejpam-4920	33	18	of	of	ADP
ejpam-4920	33	19	u	u	NOUN
ejpam-4920	33	20	is	be	AUX
ejpam-4920	33	21	white	white	ADJ
ejpam-4920	33	22	,	,	PUNCT
ejpam-4920	33	23	then	then	ADV
ejpam-4920	33	24	change	change	VERB
ejpam-4920	33	25	the	the	DET
ejpam-4920	33	26	color	color	NOUN
ejpam-4920	33	27	of	of	ADP
ejpam-4920	33	28	w	w	PROPN
ejpam-4920	33	29	to	to	PART
ejpam-4920	33	30	blue	blue	VERB
ejpam-4920	33	31	.	.	PUNCT
ejpam-4920	34	1	we	we	PRON
ejpam-4920	34	2	say	say	VERB
ejpam-4920	34	3	u	u	PRON
ejpam-4920	34	4	forces	force	NOUN
ejpam-4920	34	5	w	w	ADV
ejpam-4920	34	6	and	and	CCONJ
ejpam-4920	34	7	denote	denote	VERB
ejpam-4920	34	8	this	this	PRON
ejpam-4920	34	9	by	by	ADP
ejpam-4920	34	10	u	u	PROPN
ejpam-4920	34	11	→	→	PUNCT
ejpam-4920	34	12	w.	w.	PROPN
ejpam-4920	34	13	a	a	DET
ejpam-4920	34	14	zero	zero	NUM
ejpam-4920	34	15	forcing	forcing	NOUN
ejpam-4920	34	16	set	set	NOUN
ejpam-4920	34	17	for	for	ADP
ejpam-4920	34	18	g	g	PROPN
ejpam-4920	34	19	is	be	AUX
ejpam-4920	34	20	a	a	DET
ejpam-4920	34	21	subset	subset	NOUN
ejpam-4920	34	22	of	of	ADP
ejpam-4920	34	23	vertices	vertex	NOUN
ejpam-4920	34	24	b	b	X
ejpam-4920	34	25	such	such	ADJ
ejpam-4920	34	26	that	that	SCONJ
ejpam-4920	34	27	when	when	SCONJ
ejpam-4920	34	28	the	the	DET
ejpam-4920	34	29	vertices	vertex	NOUN
ejpam-4920	34	30	in	in	ADP
ejpam-4920	34	31	z	z	NOUN
ejpam-4920	34	32	are	be	AUX
ejpam-4920	34	33	colored	color	VERB
ejpam-4920	34	34	blue	blue	ADJ
ejpam-4920	34	35	and	and	CCONJ
ejpam-4920	34	36	the	the	DET
ejpam-4920	34	37	remaining	remain	VERB
ejpam-4920	34	38	vertices	vertex	NOUN
ejpam-4920	34	39	are	be	AUX
ejpam-4920	34	40	colored	color	VERB
ejpam-4920	34	41	white	white	ADJ
ejpam-4920	34	42	initially	initially	ADV
ejpam-4920	34	43	,	,	PUNCT
ejpam-4920	34	44	repeated	repeat	VERB
ejpam-4920	34	45	application	application	NOUN
ejpam-4920	34	46	of	of	ADP
ejpam-4920	34	47	the	the	DET
ejpam-4920	34	48	color	color	NOUN
ejpam-4920	34	49	change	change	NOUN
ejpam-4920	34	50	rule	rule	NOUN
ejpam-4920	34	51	can	can	AUX
ejpam-4920	34	52	color	color	VERB
ejpam-4920	34	53	all	all	DET
ejpam-4920	34	54	vertices	vertex	NOUN
ejpam-4920	34	55	of	of	ADP
ejpam-4920	34	56	g	g	PROPN
ejpam-4920	34	57	blue	blue	NOUN
ejpam-4920	34	58	.	.	PUNCT
ejpam-4920	35	1	the	the	DET
ejpam-4920	35	2	zero	zero	NUM
ejpam-4920	35	3	forcing	force	VERB
ejpam-4920	35	4	number	number	NOUN
ejpam-4920	35	5	of	of	ADP
ejpam-4920	35	6	g	g	NOUN
ejpam-4920	35	7	,	,	PUNCT
ejpam-4920	35	8	denoted	denote	VERB
ejpam-4920	35	9	by	by	ADP
ejpam-4920	35	10	z(g	z(g	NOUN
ejpam-4920	35	11	)	)	PUNCT
ejpam-4920	35	12	,	,	PUNCT
ejpam-4920	35	13	is	be	AUX
ejpam-4920	35	14	the	the	DET
ejpam-4920	35	15	minimum	minimum	ADJ
ejpam-4920	35	16	cardinality	cardinality	NOUN
ejpam-4920	35	17	among	among	ADP
ejpam-4920	35	18	all	all	DET
ejpam-4920	35	19	zero	zero	NUM
ejpam-4920	35	20	forcing	force	VERB
ejpam-4920	35	21	sets	set	NOUN
ejpam-4920	35	22	in	in	ADP
ejpam-4920	35	23	g.	g.	PROPN
ejpam-4920	35	24	a	a	DET
ejpam-4920	35	25	vertex	vertex	NOUN
ejpam-4920	35	26	v	v	NOUN
ejpam-4920	35	27	in	in	ADP
ejpam-4920	35	28	g	g	PROPN
ejpam-4920	35	29	is	be	AUX
ejpam-4920	35	30	a	a	DET
ejpam-4920	35	31	hop	hop	NOUN
ejpam-4920	35	32	neighbor	neighbor	NOUN
ejpam-4920	35	33	of	of	ADP
ejpam-4920	35	34	vertex	vertex	NOUN
ejpam-4920	35	35	u	u	NOUN
ejpam-4920	35	36	in	in	ADP
ejpam-4920	35	37	g	g	PROPN
ejpam-4920	35	38	if	if	SCONJ
ejpam-4920	35	39	dg(u	dg(u	NOUN
ejpam-4920	35	40	,	,	PUNCT
ejpam-4920	35	41	v	v	NOUN
ejpam-4920	35	42	)	)	PUNCT
ejpam-4920	35	43	=	=	SYM
ejpam-4920	35	44	2	2	X
ejpam-4920	35	45	.	.	X
ejpam-4920	35	46	the	the	DET
ejpam-4920	35	47	set	set	ADJ
ejpam-4920	35	48	n2	n2	ADJ
ejpam-4920	35	49	g(u	g(u	PROPN
ejpam-4920	35	50	)	)	PUNCT
ejpam-4920	35	51	=	=	PRON
ejpam-4920	35	52	{	{	PUNCT
ejpam-4920	35	53	v	v	NUM
ejpam-4920	35	54	∈	∈	NOUN
ejpam-4920	35	55	v	v	NOUN
ejpam-4920	35	56	(	(	PUNCT
ejpam-4920	35	57	g	g	NOUN
ejpam-4920	35	58	)	)	PUNCT
ejpam-4920	35	59	:	:	PUNCT
ejpam-4920	35	60	dg(v	dg(v	X
ejpam-4920	35	61	,	,	PUNCT
ejpam-4920	35	62	u	u	NOUN
ejpam-4920	35	63	)	)	PUNCT
ejpam-4920	35	64	=	=	SYM
ejpam-4920	35	65	2	2	X
ejpam-4920	35	66	}	}	PUNCT
ejpam-4920	35	67	(	(	PUNCT
ejpam-4920	35	68	resp	resp	NOUN
ejpam-4920	35	69	.	.	PUNCT
ejpam-4920	36	1	n2	n2	PROPN
ejpam-4920	36	2	g[u	g[u	PROPN
ejpam-4920	36	3	]	]	X
ejpam-4920	36	4	=	=	SYM
ejpam-4920	36	5	n2	n2	ADJ
ejpam-4920	36	6	g(u	g(u	PROPN
ejpam-4920	36	7	)	)	PUNCT
ejpam-4920	36	8	∪	∪	NOUN
ejpam-4920	36	9	{	{	PUNCT
ejpam-4920	36	10	u	u	NOUN
ejpam-4920	36	11	}	}	PUNCT
ejpam-4920	36	12	)	)	PUNCT
ejpam-4920	36	13	is	be	AUX
ejpam-4920	36	14	called	call	VERB
ejpam-4920	36	15	the	the	DET
ejpam-4920	36	16	open	open	ADJ
ejpam-4920	36	17	hop	hop	NOUN
ejpam-4920	36	18	neighborhood	neighborhood	NOUN
ejpam-4920	36	19	(	(	PUNCT
ejpam-4920	36	20	resp	resp	NOUN
ejpam-4920	36	21	.	.	PUNCT
ejpam-4920	37	1	closed	close	VERB
ejpam-4920	37	2	hop	hop	PROPN
ejpam-4920	37	3	neighborhood	neighborhood	NOUN
ejpam-4920	37	4	)	)	PUNCT
ejpam-4920	37	5	of	of	ADP
ejpam-4920	37	6	u.	u.	NOUN
ejpam-4920	37	7	let	let	VERB
ejpam-4920	37	8	a	a	PRON
ejpam-4920	37	9	be	be	AUX
ejpam-4920	37	10	a	a	DET
ejpam-4920	37	11	subset	subset	NOUN
ejpam-4920	37	12	of	of	ADP
ejpam-4920	37	13	v	v	NOUN
ejpam-4920	37	14	(	(	PUNCT
ejpam-4920	37	15	g	g	NOUN
ejpam-4920	37	16	)	)	PUNCT
ejpam-4920	37	17	.	.	PUNCT
ejpam-4920	38	1	then	then	ADV
ejpam-4920	38	2	the	the	DET
ejpam-4920	38	3	open	open	ADJ
ejpam-4920	38	4	hop	hop	NOUN
ejpam-4920	38	5	neighborhood	neighborhood	NOUN
ejpam-4920	38	6	(	(	PUNCT
ejpam-4920	38	7	resp	resp	NOUN
ejpam-4920	38	8	.	.	PUNCT
ejpam-4920	39	1	closed	close	VERB
ejpam-4920	39	2	hop	hop	PROPN
ejpam-4920	39	3	neighborhood	neighborhood	NOUN
ejpam-4920	39	4	)	)	PUNCT
ejpam-4920	39	5	of	of	ADP
ejpam-4920	39	6	a	a	PRON
ejpam-4920	39	7	is	be	AUX
ejpam-4920	39	8	the	the	DET
ejpam-4920	39	9	set	set	NOUN
ejpam-4920	39	10	defined	define	VERB
ejpam-4920	39	11	by	by	ADP
ejpam-4920	39	12	n2	n2	PROPN
ejpam-4920	39	13	g(a	g(a	PROPN
ejpam-4920	39	14	)	)	PUNCT
ejpam-4920	40	1	=	=	PUNCT
ejpam-4920	40	2	⋃	⋃	PUNCT
ejpam-4920	40	3	u∈a	u∈a	NOUN
ejpam-4920	40	4	n2	n2	ADJ
ejpam-4920	40	5	g(u	g(u	PROPN
ejpam-4920	40	6	)	)	PUNCT
ejpam-4920	40	7	(	(	PUNCT
ejpam-4920	40	8	resp	resp	NOUN
ejpam-4920	40	9	.	.	PUNCT
ejpam-4920	41	1	n	n	CCONJ
ejpam-4920	41	2	2	2	NUM
ejpam-4920	41	3	g[a	g[a	NOUN
ejpam-4920	41	4	]	]	X
ejpam-4920	41	5	=	=	SYM
ejpam-4920	41	6	n2	n2	PROPN
ejpam-4920	41	7	g(a	g(a	PROPN
ejpam-4920	41	8	)	)	PUNCT
ejpam-4920	41	9	∪a	∪a	NUM
ejpam-4920	41	10	)	)	PUNCT
ejpam-4920	41	11	.	.	PUNCT
ejpam-4920	42	1	a	a	DET
ejpam-4920	42	2	subset	subset	NOUN
ejpam-4920	42	3	s	s	X
ejpam-4920	42	4	of	of	ADP
ejpam-4920	42	5	v	v	NOUN
ejpam-4920	42	6	(	(	PUNCT
ejpam-4920	42	7	g	g	NOUN
ejpam-4920	42	8	)	)	PUNCT
ejpam-4920	42	9	is	be	AUX
ejpam-4920	42	10	called	call	VERB
ejpam-4920	42	11	a	a	DET
ejpam-4920	42	12	hop	hop	NOUN
ejpam-4920	42	13	dominating	dominating	NOUN
ejpam-4920	42	14	ofg	ofg	PROPN
ejpam-4920	42	15	if	if	SCONJ
ejpam-4920	42	16	for	for	ADP
ejpam-4920	42	17	every	every	DET
ejpam-4920	42	18	v	v	NUM
ejpam-4920	42	19	∈	∈	NOUN
ejpam-4920	42	20	v	v	NOUN
ejpam-4920	42	21	(	(	PUNCT
ejpam-4920	42	22	g)\s	g)\s	NOUN
ejpam-4920	42	23	,	,	PUNCT
ejpam-4920	42	24	there	there	PRON
ejpam-4920	42	25	exists	exist	VERB
ejpam-4920	42	26	u	u	PROPN
ejpam-4920	42	27	∈	∈	PROPN
ejpam-4920	42	28	s	s	VERB
ejpam-4920	42	29	such	such	ADJ
ejpam-4920	42	30	that	that	DET
ejpam-4920	42	31	dg(u	dg(u	ADJ
ejpam-4920	42	32	,	,	PUNCT
ejpam-4920	42	33	v	v	NOUN
ejpam-4920	42	34	)	)	PUNCT
ejpam-4920	42	35	=	=	SYM
ejpam-4920	43	1	2	2	X
ejpam-4920	43	2	.	.	PUNCT
ejpam-4920	43	3	the	the	DET
ejpam-4920	43	4	minimum	minimum	ADJ
ejpam-4920	43	5	cardinality	cardinality	NOUN
ejpam-4920	43	6	among	among	ADP
ejpam-4920	43	7	all	all	DET
ejpam-4920	43	8	hop	hop	NOUN
ejpam-4920	43	9	dominating	dominating	NOUN
ejpam-4920	43	10	sets	set	NOUN
ejpam-4920	43	11	of	of	ADP
ejpam-4920	43	12	g	g	NOUN
ejpam-4920	43	13	,	,	PUNCT
ejpam-4920	43	14	denoted	denote	VERB
ejpam-4920	43	15	by	by	ADP
ejpam-4920	43	16	γh(g	γh(g	NOUN
ejpam-4920	43	17	)	)	PUNCT
ejpam-4920	43	18	,	,	PUNCT
ejpam-4920	43	19	is	be	AUX
ejpam-4920	43	20	called	call	VERB
ejpam-4920	43	21	the	the	DET
ejpam-4920	43	22	hop	hop	NOUN
ejpam-4920	43	23	domination	domination	NOUN
ejpam-4920	43	24	number	number	NOUN
ejpam-4920	43	25	of	of	ADP
ejpam-4920	43	26	g.	g.	PROPN
ejpam-4920	43	27	any	any	DET
ejpam-4920	43	28	hop	hop	NOUN
ejpam-4920	43	29	dominating	dominating	NOUN
ejpam-4920	43	30	set	set	VERB
ejpam-4920	43	31	with	with	ADP
ejpam-4920	43	32	cardinality	cardinality	NOUN
ejpam-4920	43	33	equal	equal	ADJ
ejpam-4920	43	34	to	to	ADP
ejpam-4920	43	35	γh(g	γh(g	NOUN
ejpam-4920	43	36	)	)	PUNCT
ejpam-4920	43	37	is	be	AUX
ejpam-4920	43	38	called	call	VERB
ejpam-4920	43	39	a	a	DET
ejpam-4920	43	40	γh	γh	ADV
ejpam-4920	43	41	-	-	PUNCT
ejpam-4920	43	42	set	set	NOUN
ejpam-4920	43	43	of	of	ADP
ejpam-4920	43	44	g.	g.	PROPN
ejpam-4920	43	45	a	a	DET
ejpam-4920	43	46	subset	subset	NOUN
ejpam-4920	43	47	c	c	NOUN
ejpam-4920	43	48	of	of	ADP
ejpam-4920	43	49	v	v	PROPN
ejpam-4920	43	50	(	(	PUNCT
ejpam-4920	43	51	g	g	NOUN
ejpam-4920	43	52	)	)	PUNCT
ejpam-4920	43	53	is	be	AUX
ejpam-4920	43	54	called	call	VERB
ejpam-4920	43	55	a	a	DET
ejpam-4920	43	56	pointwise	pointwise	ADJ
ejpam-4920	43	57	non	non	ADJ
ejpam-4920	43	58	-	-	ADJ
ejpam-4920	43	59	dominating	dominating	ADJ
ejpam-4920	43	60	(	(	PUNCT
ejpam-4920	43	61	pnd	pnd	NOUN
ejpam-4920	43	62	)	)	PUNCT
ejpam-4920	43	63	if	if	SCONJ
ejpam-4920	43	64	for	for	ADP
ejpam-4920	43	65	every	every	PRON
ejpam-4920	43	66	v	v	NUM
ejpam-4920	43	67	∈	∈	NOUN
ejpam-4920	43	68	v	v	NOUN
ejpam-4920	43	69	(	(	PUNCT
ejpam-4920	43	70	g	g	NOUN
ejpam-4920	43	71	)	)	PUNCT
ejpam-4920	43	72	\	\	PUNCT
ejpam-4920	44	1	c	c	X
ejpam-4920	44	2	,	,	PUNCT
ejpam-4920	44	3	there	there	PRON
ejpam-4920	44	4	exists	exist	VERB
ejpam-4920	44	5	u	u	PROPN
ejpam-4920	44	6	∈	∈	PROPN
ejpam-4920	44	7	c	c	NOUN
ejpam-4920	44	8	such	such	ADJ
ejpam-4920	44	9	that	that	DET
ejpam-4920	44	10	v	v	NOUN
ejpam-4920	44	11	/∈	/∈	PUNCT
ejpam-4920	44	12	ng(u	ng(u	NOUN
ejpam-4920	44	13	)	)	PUNCT
ejpam-4920	44	14	.	.	PUNCT
ejpam-4920	45	1	the	the	DET
ejpam-4920	45	2	minimum	minimum	ADJ
ejpam-4920	45	3	cardinality	cardinality	NOUN
ejpam-4920	45	4	of	of	ADP
ejpam-4920	45	5	a	a	DET
ejpam-4920	45	6	pointwise	pointwise	ADJ
ejpam-4920	45	7	non	non	ADJ
ejpam-4920	45	8	-	-	ADJ
ejpam-4920	45	9	dominating	dominating	ADJ
ejpam-4920	45	10	(	(	PUNCT
ejpam-4920	45	11	pnd	pnd	NOUN
ejpam-4920	45	12	)	)	PUNCT
ejpam-4920	45	13	set	set	NOUN
ejpam-4920	45	14	of	of	ADP
ejpam-4920	45	15	g	g	NOUN
ejpam-4920	45	16	,	,	PUNCT
ejpam-4920	45	17	denoted	denote	VERB
ejpam-4920	45	18	by	by	ADP
ejpam-4920	45	19	pnd(g	pnd(g	PROPN
ejpam-4920	45	20	)	)	PUNCT
ejpam-4920	45	21	,	,	PUNCT
ejpam-4920	45	22	is	be	AUX
ejpam-4920	45	23	called	call	VERB
ejpam-4920	45	24	the	the	DET
ejpam-4920	45	25	pointwise	pointwise	ADJ
ejpam-4920	45	26	non	non	ADJ
ejpam-4920	45	27	-	-	ADJ
ejpam-4920	45	28	domination	domination	ADJ
ejpam-4920	45	29	number	number	NOUN
ejpam-4920	45	30	of	of	ADP
ejpam-4920	45	31	g.	g.	PROPN
ejpam-4920	45	32	any	any	DET
ejpam-4920	45	33	pnd	pnd	NOUN
ejpam-4920	45	34	set	set	NOUN
ejpam-4920	45	35	of	of	ADP
ejpam-4920	45	36	g	g	NOUN
ejpam-4920	45	37	with	with	ADP
ejpam-4920	45	38	cardinality	cardinality	NOUN
ejpam-4920	45	39	pnd(g	pnd(g	PROPN
ejpam-4920	45	40	)	)	PUNCT
ejpam-4920	45	41	is	be	AUX
ejpam-4920	45	42	called	call	VERB
ejpam-4920	45	43	a	a	DET
ejpam-4920	45	44	j.	j.	PROPN
ejpam-4920	45	45	u.	u.	PROPN
ejpam-4920	45	46	manditong	manditong	PROPN
ejpam-4920	46	1	et	et	PROPN
ejpam-4920	46	2	al	al	PROPN
ejpam-4920	46	3	.	.	PUNCT
ejpam-4920	46	4	/	/	SYM
ejpam-4920	46	5	eur	eur	PROPN
ejpam-4920	46	6	.	.	PUNCT
ejpam-4920	47	1	j.	j.	PROPN
ejpam-4920	47	2	pure	pure	PROPN
ejpam-4920	47	3	appl	appl	PROPN
ejpam-4920	47	4	.	.	PROPN
ejpam-4920	47	5	math	math	PROPN
ejpam-4920	47	6	,	,	PUNCT
ejpam-4920	47	7	17	17	NUM
ejpam-4920	47	8	(	(	PUNCT
ejpam-4920	47	9	1	1	NUM
ejpam-4920	47	10	)	)	PUNCT
ejpam-4920	47	11	(	(	PUNCT
ejpam-4920	47	12	2024	2024	NUM
ejpam-4920	47	13	)	)	PUNCT
ejpam-4920	47	14	,	,	PUNCT
ejpam-4920	47	15	324	324	NUM
ejpam-4920	47	16	-	-	SYM
ejpam-4920	47	17	337	337	NUM
ejpam-4920	47	18	326	326	NUM
ejpam-4920	47	19	minimum	minimum	ADJ
ejpam-4920	47	20	pnd	pnd	NOUN
ejpam-4920	47	21	set	set	NOUN
ejpam-4920	47	22	or	or	CCONJ
ejpam-4920	47	23	a	a	DET
ejpam-4920	47	24	pnd	pnd	NOUN
ejpam-4920	47	25	-	-	PUNCT
ejpam-4920	47	26	set	set	NOUN
ejpam-4920	47	27	of	of	ADP
ejpam-4920	47	28	g.	g.	PROPN
ejpam-4920	47	29	let	let	VERB
ejpam-4920	47	30	g	g	NOUN
ejpam-4920	47	31	and	and	CCONJ
ejpam-4920	47	32	h	h	NOUN
ejpam-4920	47	33	be	be	VERB
ejpam-4920	47	34	two	two	NUM
ejpam-4920	47	35	graphs	graph	NOUN
ejpam-4920	47	36	.	.	PUNCT
ejpam-4920	48	1	the	the	DET
ejpam-4920	48	2	join	join	NOUN
ejpam-4920	48	3	g+h	g+h	PROPN
ejpam-4920	48	4	of	of	ADP
ejpam-4920	48	5	g	g	PROPN
ejpam-4920	48	6	and	and	CCONJ
ejpam-4920	48	7	h	h	NOUN
ejpam-4920	48	8	is	be	AUX
ejpam-4920	48	9	the	the	DET
ejpam-4920	48	10	graph	graph	NOUN
ejpam-4920	48	11	with	with	ADP
ejpam-4920	48	12	vertex	vertex	NOUN
ejpam-4920	48	13	set	set	VERB
ejpam-4920	48	14	v	v	NOUN
ejpam-4920	48	15	(	(	PUNCT
ejpam-4920	48	16	g+h	g+h	NOUN
ejpam-4920	48	17	)	)	PUNCT
ejpam-4920	48	18	=	=	SYM
ejpam-4920	48	19	v	v	X
ejpam-4920	48	20	(	(	PUNCT
ejpam-4920	48	21	g	g	NOUN
ejpam-4920	48	22	)	)	PUNCT
ejpam-4920	48	23	∪	∪	NOUN
ejpam-4920	48	24	v	v	NOUN
ejpam-4920	48	25	(	(	PUNCT
ejpam-4920	48	26	h	h	NOUN
ejpam-4920	48	27	)	)	PUNCT
ejpam-4920	48	28	and	and	CCONJ
ejpam-4920	48	29	edge	edge	NOUN
ejpam-4920	48	30	set	set	VERB
ejpam-4920	48	31	e(g+h	e(g+h	NUM
ejpam-4920	48	32	)	)	PUNCT
ejpam-4920	48	33	=	=	SYM
ejpam-4920	48	34	e(g	e(g	NOUN
ejpam-4920	48	35	)	)	PUNCT
ejpam-4920	48	36	∪	∪	ADP
ejpam-4920	48	37	e(h	e(h	PROPN
ejpam-4920	48	38	)	)	PUNCT
ejpam-4920	48	39	∪	∪	NOUN
ejpam-4920	48	40	{	{	PUNCT
ejpam-4920	48	41	ab	ab	NOUN
ejpam-4920	48	42	:	:	PUNCT
ejpam-4920	48	43	a	a	DET
ejpam-4920	48	44	∈	∈	PROPN
ejpam-4920	48	45	v	v	NOUN
ejpam-4920	48	46	(	(	PUNCT
ejpam-4920	48	47	g	g	NOUN
ejpam-4920	48	48	)	)	PUNCT
ejpam-4920	48	49	,	,	PUNCT
ejpam-4920	49	1	b	b	X
ejpam-4920	49	2	∈	∈	PROPN
ejpam-4920	49	3	v	v	ADP
ejpam-4920	49	4	(	(	PUNCT
ejpam-4920	49	5	h	h	NOUN
ejpam-4920	49	6	)	)	PUNCT
ejpam-4920	49	7	}	}	PUNCT
ejpam-4920	49	8	.	.	PUNCT
ejpam-4920	50	1	the	the	DET
ejpam-4920	50	2	corona	corona	NOUN
ejpam-4920	50	3	g	g	PROPN
ejpam-4920	50	4	◦	◦	NOUN
ejpam-4920	50	5	h	h	NOUN
ejpam-4920	50	6	of	of	ADP
ejpam-4920	50	7	g	g	PROPN
ejpam-4920	50	8	and	and	CCONJ
ejpam-4920	50	9	h	h	NOUN
ejpam-4920	50	10	is	be	AUX
ejpam-4920	50	11	the	the	DET
ejpam-4920	50	12	graph	graph	NOUN
ejpam-4920	50	13	obtained	obtain	VERB
ejpam-4920	50	14	by	by	ADP
ejpam-4920	50	15	taking	take	VERB
ejpam-4920	50	16	one	one	NUM
ejpam-4920	50	17	copy	copy	NOUN
ejpam-4920	50	18	of	of	ADP
ejpam-4920	50	19	g	g	PROPN
ejpam-4920	50	20	and	and	CCONJ
ejpam-4920	50	21	|v	|v	PROPN
ejpam-4920	50	22	(	(	PUNCT
ejpam-4920	50	23	g)|	g)|	NOUN
ejpam-4920	50	24	copies	copy	NOUN
ejpam-4920	50	25	of	of	ADP
ejpam-4920	50	26	h	h	NOUN
ejpam-4920	50	27	,	,	PUNCT
ejpam-4920	50	28	and	and	CCONJ
ejpam-4920	50	29	then	then	ADV
ejpam-4920	50	30	joining	join	VERB
ejpam-4920	50	31	the	the	DET
ejpam-4920	50	32	ith	ith	PROPN
ejpam-4920	50	33	vertex	vertex	NOUN
ejpam-4920	50	34	of	of	ADP
ejpam-4920	50	35	g	g	NOUN
ejpam-4920	50	36	to	to	ADP
ejpam-4920	50	37	every	every	DET
ejpam-4920	50	38	vertex	vertex	NOUN
ejpam-4920	50	39	of	of	ADP
ejpam-4920	50	40	the	the	DET
ejpam-4920	50	41	ith	ith	PROPN
ejpam-4920	50	42	copy	copy	NOUN
ejpam-4920	50	43	of	of	ADP
ejpam-4920	50	44	h.	h.	PROPN
ejpam-4920	50	45	we	we	PRON
ejpam-4920	50	46	denote	denote	VERB
ejpam-4920	50	47	by	by	ADP
ejpam-4920	50	48	ha	ha	INTJ
ejpam-4920	50	49	the	the	DET
ejpam-4920	50	50	copy	copy	NOUN
ejpam-4920	50	51	of	of	ADP
ejpam-4920	50	52	h	h	NOUN
ejpam-4920	50	53	in	in	ADP
ejpam-4920	50	54	g	g	PROPN
ejpam-4920	50	55	◦	◦	NOUN
ejpam-4920	50	56	h	h	NOUN
ejpam-4920	50	57	corresponding	correspond	VERB
ejpam-4920	50	58	to	to	ADP
ejpam-4920	50	59	the	the	DET
ejpam-4920	50	60	vertex	vertex	NOUN
ejpam-4920	50	61	a	a	DET
ejpam-4920	50	62	∈	∈	NOUN
ejpam-4920	50	63	v	v	NOUN
ejpam-4920	50	64	(	(	PUNCT
ejpam-4920	50	65	g	g	NOUN
ejpam-4920	50	66	)	)	PUNCT
ejpam-4920	50	67	.	.	PUNCT
ejpam-4920	51	1	3	3	X
ejpam-4920	51	2	.	.	X
ejpam-4920	51	3	results	result	NOUN
ejpam-4920	51	4	we	we	PRON
ejpam-4920	51	5	begin	begin	VERB
ejpam-4920	51	6	this	this	DET
ejpam-4920	51	7	section	section	NOUN
ejpam-4920	51	8	by	by	ADP
ejpam-4920	51	9	defining	define	VERB
ejpam-4920	51	10	the	the	DET
ejpam-4920	51	11	concept	concept	NOUN
ejpam-4920	51	12	of	of	ADP
ejpam-4920	51	13	zero	zero	NUM
ejpam-4920	51	14	forcing	force	VERB
ejpam-4920	51	15	hop	hop	NOUN
ejpam-4920	51	16	domination	domination	NOUN
ejpam-4920	51	17	in	in	ADP
ejpam-4920	51	18	a	a	DET
ejpam-4920	51	19	graph	graph	NOUN
ejpam-4920	51	20	as	as	SCONJ
ejpam-4920	51	21	follows	follow	VERB
ejpam-4920	51	22	:	:	PUNCT
ejpam-4920	51	23	definition	definition	NOUN
ejpam-4920	51	24	1	1	NUM
ejpam-4920	51	25	.	.	PUNCT
ejpam-4920	52	1	let	let	VERB
ejpam-4920	52	2	g	g	PRON
ejpam-4920	52	3	be	be	AUX
ejpam-4920	52	4	a	a	DET
ejpam-4920	52	5	graph	graph	NOUN
ejpam-4920	52	6	.	.	PUNCT
ejpam-4920	53	1	a	a	DET
ejpam-4920	53	2	subset	subset	NOUN
ejpam-4920	53	3	z	z	NOUN
ejpam-4920	53	4	of	of	ADP
ejpam-4920	53	5	v	v	PROPN
ejpam-4920	53	6	(	(	PUNCT
ejpam-4920	53	7	g	g	NOUN
ejpam-4920	53	8	)	)	PUNCT
ejpam-4920	53	9	is	be	AUX
ejpam-4920	53	10	said	say	VERB
ejpam-4920	53	11	to	to	PART
ejpam-4920	53	12	be	be	AUX
ejpam-4920	53	13	a	a	DET
ejpam-4920	53	14	zero	zero	NUM
ejpam-4920	53	15	forcing	force	VERB
ejpam-4920	53	16	hop	hop	NOUN
ejpam-4920	53	17	dominating	dominating	NOUN
ejpam-4920	53	18	if	if	SCONJ
ejpam-4920	53	19	z	z	NOUN
ejpam-4920	53	20	is	be	AUX
ejpam-4920	53	21	both	both	PRON
ejpam-4920	53	22	a	a	DET
ejpam-4920	53	23	zero	zero	NUM
ejpam-4920	53	24	forcing	forcing	NOUN
ejpam-4920	53	25	and	and	CCONJ
ejpam-4920	53	26	a	a	DET
ejpam-4920	53	27	hop	hop	NOUN
ejpam-4920	53	28	dominating	dominating	NOUN
ejpam-4920	53	29	in	in	ADP
ejpam-4920	53	30	g.	g.	PROPN
ejpam-4920	53	31	the	the	DET
ejpam-4920	53	32	minimum	minimum	ADJ
ejpam-4920	53	33	cardinality	cardinality	NOUN
ejpam-4920	53	34	among	among	ADP
ejpam-4920	53	35	all	all	DET
ejpam-4920	53	36	zero	zero	NUM
ejpam-4920	53	37	forcing	force	VERB
ejpam-4920	53	38	hop	hop	NOUN
ejpam-4920	53	39	dominating	dominating	NOUN
ejpam-4920	53	40	sets	set	NOUN
ejpam-4920	53	41	in	in	ADP
ejpam-4920	53	42	g	g	NOUN
ejpam-4920	53	43	,	,	PUNCT
ejpam-4920	53	44	denoted	denote	VERB
ejpam-4920	53	45	by	by	ADP
ejpam-4920	53	46	γzh(g	γzh(g	NOUN
ejpam-4920	53	47	)	)	PUNCT
ejpam-4920	53	48	,	,	PUNCT
ejpam-4920	53	49	is	be	AUX
ejpam-4920	53	50	called	call	VERB
ejpam-4920	53	51	the	the	DET
ejpam-4920	53	52	zero	zero	NUM
ejpam-4920	53	53	forcing	force	VERB
ejpam-4920	53	54	hop	hop	NOUN
ejpam-4920	53	55	domination	domination	NOUN
ejpam-4920	53	56	number	number	NOUN
ejpam-4920	53	57	of	of	ADP
ejpam-4920	53	58	g.	g.	PROPN
ejpam-4920	53	59	a	a	DET
ejpam-4920	53	60	zero	zero	NUM
ejpam-4920	53	61	forcing	force	VERB
ejpam-4920	53	62	hop	hop	NOUN
ejpam-4920	53	63	dominating	dominating	NOUN
ejpam-4920	53	64	set	set	NOUN
ejpam-4920	53	65	z	z	NOUN
ejpam-4920	53	66	with	with	ADP
ejpam-4920	53	67	|z|	|z|	NOUN
ejpam-4920	53	68	=	=	SYM
ejpam-4920	53	69	γzh(g	γzh(g	NOUN
ejpam-4920	53	70	)	)	PUNCT
ejpam-4920	53	71	,	,	PUNCT
ejpam-4920	53	72	is	be	AUX
ejpam-4920	53	73	called	call	VERB
ejpam-4920	53	74	the	the	DET
ejpam-4920	53	75	minimum	minimum	ADJ
ejpam-4920	53	76	zero	zero	NUM
ejpam-4920	53	77	forcing	force	VERB
ejpam-4920	53	78	hop	hop	NOUN
ejpam-4920	53	79	dominating	dominating	NOUN
ejpam-4920	53	80	set	set	NOUN
ejpam-4920	53	81	of	of	ADP
ejpam-4920	53	82	g	g	PROPN
ejpam-4920	53	83	or	or	CCONJ
ejpam-4920	53	84	a	a	DET
ejpam-4920	53	85	γzh	γzh	NOUN
ejpam-4920	53	86	-	-	PUNCT
ejpam-4920	53	87	set	set	NOUN
ejpam-4920	53	88	of	of	ADP
ejpam-4920	53	89	g.	g.	PROPN
ejpam-4920	53	90	example	example	NOUN
ejpam-4920	53	91	1	1	X
ejpam-4920	53	92	.	.	X
ejpam-4920	53	93	consider	consider	VERB
ejpam-4920	53	94	the	the	DET
ejpam-4920	53	95	graph	graph	NOUN
ejpam-4920	53	96	g	g	NOUN
ejpam-4920	53	97	below	below	ADV
ejpam-4920	53	98	.	.	PUNCT
ejpam-4920	54	1	g2	g2	PROPN
ejpam-4920	54	2	:	:	PUNCT
ejpam-4920	55	1	h	h	NOUN
ejpam-4920	56	1	g	g	NOUN
ejpam-4920	56	2	f	f	PROPN
ejpam-4920	57	1	ed	ed	NOUN
ejpam-4920	57	2	c	c	PROPN
ejpam-4920	57	3	b	b	PROPN
ejpam-4920	57	4	a	a	DET
ejpam-4920	57	5	figure	figure	NOUN
ejpam-4920	57	6	1	1	NUM
ejpam-4920	57	7	:	:	PUNCT
ejpam-4920	57	8	graph	graph	VERB
ejpam-4920	57	9	g	g	NOUN
ejpam-4920	57	10	with	with	ADP
ejpam-4920	57	11	γzh(g	γzh(g	NOUN
ejpam-4920	57	12	)	)	PUNCT
ejpam-4920	57	13	=	=	SYM
ejpam-4920	58	1	5	5	NUM
ejpam-4920	58	2	let	let	VERB
ejpam-4920	58	3	z	z	NOUN
ejpam-4920	58	4	=	=	PRON
ejpam-4920	58	5	{	{	PUNCT
ejpam-4920	58	6	a	a	DET
ejpam-4920	58	7	,	,	PUNCT
ejpam-4920	58	8	b	b	NOUN
ejpam-4920	58	9	,	,	PUNCT
ejpam-4920	58	10	e	e	NOUN
ejpam-4920	58	11	,	,	PUNCT
ejpam-4920	58	12	f	f	X
ejpam-4920	58	13	,	,	PUNCT
ejpam-4920	58	14	g	g	NOUN
ejpam-4920	58	15	}	}	PUNCT
ejpam-4920	58	16	.	.	PUNCT
ejpam-4920	59	1	then	then	ADV
ejpam-4920	59	2	z	z	PROPN
ejpam-4920	59	3	is	be	AUX
ejpam-4920	59	4	a	a	DET
ejpam-4920	59	5	zero	zero	NUM
ejpam-4920	59	6	forcing	forcing	NOUN
ejpam-4920	59	7	set	set	NOUN
ejpam-4920	59	8	in	in	ADP
ejpam-4920	59	9	g.	g.	PROPN
ejpam-4920	59	10	observe	observe	VERB
ejpam-4920	59	11	that	that	DET
ejpam-4920	59	12	n2	n2	ADJ
ejpam-4920	59	13	g[a	g[a	NOUN
ejpam-4920	59	14	]	]	X
ejpam-4920	59	15	=	=	X
ejpam-4920	59	16	{	{	PUNCT
ejpam-4920	59	17	a	a	PRON
ejpam-4920	59	18	,	,	PUNCT
ejpam-4920	59	19	b	b	NOUN
ejpam-4920	59	20	,	,	PUNCT
ejpam-4920	59	21	c	c	X
ejpam-4920	59	22	,	,	PUNCT
ejpam-4920	59	23	e	e	NOUN
ejpam-4920	59	24	}	}	PUNCT
ejpam-4920	59	25	=	=	SYM
ejpam-4920	59	26	n2	n2	PROPN
ejpam-4920	59	27	g[b	g[b	PROPN
ejpam-4920	59	28	]	]	PUNCT
ejpam-4920	59	29	=	=	SYM
ejpam-4920	59	30	n2	n2	NOUN
ejpam-4920	59	31	g[e	g[e	X
ejpam-4920	59	32	]	]	PUNCT
ejpam-4920	59	33	and	and	CCONJ
ejpam-4920	59	34	n2	n2	PROPN
ejpam-4920	59	35	g[f	g[f	X
ejpam-4920	59	36	]	]	PUNCT
ejpam-4920	59	37	=	=	PUNCT
ejpam-4920	59	38	{	{	PUNCT
ejpam-4920	59	39	d	d	PROPN
ejpam-4920	59	40	,	,	PUNCT
ejpam-4920	59	41	f	f	PROPN
ejpam-4920	59	42	,	,	PUNCT
ejpam-4920	59	43	g	g	PROPN
ejpam-4920	59	44	,	,	PUNCT
ejpam-4920	59	45	h	h	NOUN
ejpam-4920	59	46	}	}	PUNCT
ejpam-4920	59	47	=	=	SYM
ejpam-4920	59	48	n2	n2	NOUN
ejpam-4920	59	49	g[g	g[g	NOUN
ejpam-4920	59	50	]	]	PUNCT
ejpam-4920	59	51	.	.	PUNCT
ejpam-4920	60	1	thus	thus	ADV
ejpam-4920	60	2	,	,	PUNCT
ejpam-4920	60	3	n2	n2	PROPN
ejpam-4920	60	4	g[z	g[z	PROPN
ejpam-4920	60	5	]	]	X
ejpam-4920	60	6	=	=	X
ejpam-4920	60	7	{	{	PUNCT
ejpam-4920	60	8	a	a	PRON
ejpam-4920	60	9	,	,	PUNCT
ejpam-4920	60	10	b	b	NOUN
ejpam-4920	60	11	,	,	PUNCT
ejpam-4920	60	12	c	c	NOUN
ejpam-4920	60	13	,	,	PUNCT
ejpam-4920	60	14	d	d	NOUN
ejpam-4920	60	15	,	,	PUNCT
ejpam-4920	60	16	e	e	NOUN
ejpam-4920	60	17	,	,	PUNCT
ejpam-4920	60	18	f	f	PROPN
ejpam-4920	60	19	,	,	PUNCT
ejpam-4920	60	20	g	g	PROPN
ejpam-4920	60	21	,	,	PUNCT
ejpam-4920	60	22	h	h	NOUN
ejpam-4920	60	23	}	}	PUNCT
ejpam-4920	60	24	=	=	SYM
ejpam-4920	60	25	v	v	NOUN
ejpam-4920	60	26	(	(	PUNCT
ejpam-4920	60	27	g	g	NOUN
ejpam-4920	60	28	)	)	PUNCT
ejpam-4920	60	29	,	,	PUNCT
ejpam-4920	60	30	showing	show	VERB
ejpam-4920	60	31	that	that	SCONJ
ejpam-4920	60	32	z	z	NOUN
ejpam-4920	60	33	is	be	AUX
ejpam-4920	60	34	a	a	DET
ejpam-4920	60	35	hop	hop	NOUN
ejpam-4920	60	36	dominating	dominating	NOUN
ejpam-4920	60	37	set	set	VERB
ejpam-4920	60	38	in	in	ADP
ejpam-4920	60	39	g.	g.	PROPN
ejpam-4920	60	40	hence	hence	ADV
ejpam-4920	60	41	,	,	PUNCT
ejpam-4920	60	42	z	z	PROPN
ejpam-4920	60	43	is	be	AUX
ejpam-4920	60	44	a	a	DET
ejpam-4920	60	45	zero	zero	NUM
ejpam-4920	60	46	forcing	force	VERB
ejpam-4920	60	47	hop	hop	NOUN
ejpam-4920	60	48	dominating	dominating	NOUN
ejpam-4920	60	49	set	set	NOUN
ejpam-4920	60	50	of	of	ADP
ejpam-4920	60	51	g.	g.	PROPN
ejpam-4920	60	52	moreover	moreover	ADV
ejpam-4920	60	53	,	,	PUNCT
ejpam-4920	60	54	since	since	SCONJ
ejpam-4920	60	55	z	z	NOUN
ejpam-4920	60	56	is	be	AUX
ejpam-4920	60	57	a	a	DET
ejpam-4920	60	58	minimum	minimum	ADJ
ejpam-4920	60	59	zero	zero	NUM
ejpam-4920	60	60	forcing	force	VERB
ejpam-4920	60	61	set	set	NOUN
ejpam-4920	60	62	of	of	ADP
ejpam-4920	60	63	g	g	NOUN
ejpam-4920	60	64	,	,	PUNCT
ejpam-4920	60	65	it	it	PRON
ejpam-4920	60	66	follows	follow	VERB
ejpam-4920	60	67	that	that	SCONJ
ejpam-4920	60	68	z	z	PROPN
ejpam-4920	60	69	is	be	AUX
ejpam-4920	60	70	a	a	DET
ejpam-4920	60	71	minimum	minimum	ADJ
ejpam-4920	60	72	zero	zero	NUM
ejpam-4920	60	73	forcing	force	VERB
ejpam-4920	60	74	hop	hop	NOUN
ejpam-4920	60	75	dominating	dominating	NOUN
ejpam-4920	60	76	set	set	NOUN
ejpam-4920	60	77	of	of	ADP
ejpam-4920	60	78	g	g	NOUN
ejpam-4920	60	79	,	,	PUNCT
ejpam-4920	60	80	and	and	CCONJ
ejpam-4920	60	81	so	so	ADV
ejpam-4920	60	82	γzh(g	γzh(g	NOUN
ejpam-4920	60	83	)	)	PUNCT
ejpam-4920	60	84	=	=	SYM
ejpam-4920	61	1	5	5	X
ejpam-4920	61	2	.	.	PUNCT
ejpam-4920	61	3	j.	j.	PROPN
ejpam-4920	61	4	u.	u.	PROPN
ejpam-4920	61	5	manditong	manditong	PROPN
ejpam-4920	61	6	et	et	PROPN
ejpam-4920	61	7	al	al	PROPN
ejpam-4920	61	8	.	.	PUNCT
ejpam-4920	61	9	/	/	SYM
ejpam-4920	61	10	eur	eur	PROPN
ejpam-4920	61	11	.	.	PUNCT
ejpam-4920	62	1	j.	j.	PROPN
ejpam-4920	62	2	pure	pure	PROPN
ejpam-4920	62	3	appl	appl	PROPN
ejpam-4920	62	4	.	.	PROPN
ejpam-4920	62	5	math	math	PROPN
ejpam-4920	62	6	,	,	PUNCT
ejpam-4920	62	7	17	17	NUM
ejpam-4920	62	8	(	(	PUNCT
ejpam-4920	62	9	1	1	NUM
ejpam-4920	62	10	)	)	PUNCT
ejpam-4920	62	11	(	(	PUNCT
ejpam-4920	62	12	2024	2024	NUM
ejpam-4920	62	13	)	)	PUNCT
ejpam-4920	62	14	,	,	PUNCT
ejpam-4920	62	15	324	324	NUM
ejpam-4920	62	16	-	-	SYM
ejpam-4920	62	17	337	337	NUM
ejpam-4920	62	18	327	327	NUM
ejpam-4920	62	19	proposition	proposition	NOUN
ejpam-4920	62	20	1	1	NUM
ejpam-4920	62	21	.	.	PUNCT
ejpam-4920	63	1	let	let	VERB
ejpam-4920	63	2	g	g	PRON
ejpam-4920	63	3	be	be	AUX
ejpam-4920	63	4	a	a	DET
ejpam-4920	63	5	graph	graph	NOUN
ejpam-4920	63	6	.	.	PUNCT
ejpam-4920	64	1	then	then	ADV
ejpam-4920	64	2	(	(	PUNCT
ejpam-4920	64	3	i	i	NOUN
ejpam-4920	64	4	)	)	PUNCT
ejpam-4920	64	5	a	a	DET
ejpam-4920	64	6	zero	zero	NUM
ejpam-4920	64	7	forcing	force	VERB
ejpam-4920	64	8	set	set	NOUN
ejpam-4920	64	9	may	may	AUX
ejpam-4920	64	10	not	not	PART
ejpam-4920	64	11	be	be	AUX
ejpam-4920	64	12	a	a	DET
ejpam-4920	64	13	hop	hop	NOUN
ejpam-4920	64	14	dominating	dominating	NOUN
ejpam-4920	64	15	;	;	PUNCT
ejpam-4920	64	16	and	and	CCONJ
ejpam-4920	64	17	(	(	PUNCT
ejpam-4920	64	18	ii	ii	NOUN
ejpam-4920	64	19	)	)	PUNCT
ejpam-4920	64	20	a	a	DET
ejpam-4920	64	21	hop	hop	NOUN
ejpam-4920	64	22	dominating	dominating	NOUN
ejpam-4920	64	23	set	set	NOUN
ejpam-4920	64	24	may	may	AUX
ejpam-4920	64	25	not	not	PART
ejpam-4920	64	26	be	be	AUX
ejpam-4920	64	27	a	a	DET
ejpam-4920	64	28	zero	zero	NUM
ejpam-4920	64	29	forcing	forcing	NOUN
ejpam-4920	64	30	.	.	PUNCT
ejpam-4920	65	1	proof	proof	NOUN
ejpam-4920	65	2	.	.	PUNCT
ejpam-4920	66	1	(	(	PUNCT
ejpam-4920	66	2	i	i	NOUN
ejpam-4920	66	3	)	)	PUNCT
ejpam-4920	66	4	consider	consider	VERB
ejpam-4920	66	5	the	the	DET
ejpam-4920	66	6	graph	graph	NOUN
ejpam-4920	66	7	g	g	NOUN
ejpam-4920	66	8	below	below	ADV
ejpam-4920	66	9	.	.	PUNCT
ejpam-4920	67	1	g	g	NOUN
ejpam-4920	67	2	:	:	PUNCT
ejpam-4920	67	3	g	g	PROPN
ejpam-4920	67	4	h	h	PROPN
ejpam-4920	68	1	fec	fec	PROPN
ejpam-4920	68	2	b	b	PROPN
ejpam-4920	68	3	d	d	PROPN
ejpam-4920	68	4	a	a	DET
ejpam-4920	68	5	let	let	NOUN
ejpam-4920	68	6	z	z	NOUN
ejpam-4920	68	7	=	=	PUNCT
ejpam-4920	68	8	{	{	PUNCT
ejpam-4920	68	9	a	a	DET
ejpam-4920	68	10	,	,	PUNCT
ejpam-4920	68	11	b	b	NOUN
ejpam-4920	68	12	,	,	PUNCT
ejpam-4920	68	13	e	e	NOUN
ejpam-4920	68	14	,	,	PUNCT
ejpam-4920	68	15	h	h	NOUN
ejpam-4920	68	16	}	}	PUNCT
ejpam-4920	68	17	.	.	PUNCT
ejpam-4920	69	1	then	then	ADV
ejpam-4920	69	2	,	,	PUNCT
ejpam-4920	69	3	z	z	PROPN
ejpam-4920	69	4	is	be	AUX
ejpam-4920	69	5	a	a	DET
ejpam-4920	69	6	zero	zero	NUM
ejpam-4920	69	7	forcing	forcing	NOUN
ejpam-4920	69	8	set	set	NOUN
ejpam-4920	69	9	in	in	ADP
ejpam-4920	69	10	g.	g.	PROPN
ejpam-4920	69	11	however	however	ADV
ejpam-4920	69	12	,	,	PUNCT
ejpam-4920	69	13	c	c	X
ejpam-4920	69	14	,	,	PUNCT
ejpam-4920	69	15	f	f	PROPN
ejpam-4920	69	16	/∈	/∈	PROPN
ejpam-4920	69	17	n2	n2	PROPN
ejpam-4920	69	18	g[z	g[z	PROPN
ejpam-4920	69	19	]	]	PUNCT
ejpam-4920	69	20	.	.	PUNCT
ejpam-4920	70	1	thus	thus	ADV
ejpam-4920	70	2	,	,	PUNCT
ejpam-4920	70	3	n2	n2	PROPN
ejpam-4920	70	4	g[z	g[z	PROPN
ejpam-4920	70	5	]	]	X
ejpam-4920	70	6	̸=	̸=	PROPN
ejpam-4920	70	7	v	v	NOUN
ejpam-4920	70	8	(	(	PUNCT
ejpam-4920	70	9	g	g	NOUN
ejpam-4920	70	10	)	)	PUNCT
ejpam-4920	70	11	,	,	PUNCT
ejpam-4920	70	12	showing	show	VERB
ejpam-4920	70	13	that	that	SCONJ
ejpam-4920	70	14	z	z	NOUN
ejpam-4920	70	15	is	be	AUX
ejpam-4920	70	16	not	not	PART
ejpam-4920	70	17	a	a	DET
ejpam-4920	70	18	hop	hop	NOUN
ejpam-4920	70	19	dominating	dominating	NOUN
ejpam-4920	70	20	set	set	NOUN
ejpam-4920	70	21	of	of	ADP
ejpam-4920	70	22	g.	g.	PROPN
ejpam-4920	70	23	hence	hence	ADV
ejpam-4920	70	24	,	,	PUNCT
ejpam-4920	70	25	the	the	DET
ejpam-4920	70	26	result	result	NOUN
ejpam-4920	70	27	follows	follow	VERB
ejpam-4920	70	28	.	.	PUNCT
ejpam-4920	71	1	(	(	PUNCT
ejpam-4920	71	2	ii	ii	NOUN
ejpam-4920	71	3	)	)	PUNCT
ejpam-4920	71	4	consider	consider	VERB
ejpam-4920	71	5	again	again	ADV
ejpam-4920	71	6	the	the	DET
ejpam-4920	71	7	graph	graph	NOUN
ejpam-4920	71	8	g	g	PROPN
ejpam-4920	71	9	in	in	ADP
ejpam-4920	71	10	(	(	PUNCT
ejpam-4920	71	11	i	i	NOUN
ejpam-4920	71	12	)	)	PUNCT
ejpam-4920	71	13	and	and	CCONJ
ejpam-4920	71	14	let	let	VERB
ejpam-4920	71	15	s	s	PRON
ejpam-4920	71	16	=	=	X
ejpam-4920	71	17	{	{	PUNCT
ejpam-4920	71	18	c	c	NOUN
ejpam-4920	71	19	,	,	PUNCT
ejpam-4920	71	20	d	d	NOUN
ejpam-4920	71	21	,	,	PUNCT
ejpam-4920	71	22	e	e	NOUN
ejpam-4920	71	23	}	}	PUNCT
ejpam-4920	71	24	.	.	PUNCT
ejpam-4920	72	1	then	then	ADV
ejpam-4920	72	2	,	,	PUNCT
ejpam-4920	72	3	n2	n2	ADJ
ejpam-4920	72	4	g	g	PROPN
ejpam-4920	72	5	[	[	X
ejpam-4920	72	6	s	s	X
ejpam-4920	72	7	]	]	X
ejpam-4920	72	8	=	=	SYM
ejpam-4920	72	9	v	v	NOUN
ejpam-4920	72	10	(	(	PUNCT
ejpam-4920	72	11	g	g	NOUN
ejpam-4920	72	12	)	)	PUNCT
ejpam-4920	72	13	,	,	PUNCT
ejpam-4920	72	14	and	and	CCONJ
ejpam-4920	72	15	so	so	ADV
ejpam-4920	72	16	s	s	VERB
ejpam-4920	72	17	is	be	AUX
ejpam-4920	72	18	a	a	DET
ejpam-4920	72	19	hop	hop	NOUN
ejpam-4920	72	20	dominating	dominating	NOUN
ejpam-4920	72	21	set	set	VERB
ejpam-4920	72	22	in	in	ADP
ejpam-4920	72	23	g.	g.	PROPN
ejpam-4920	72	24	however	however	ADV
ejpam-4920	72	25	,	,	PUNCT
ejpam-4920	72	26	s	s	X
ejpam-4920	72	27	is	be	AUX
ejpam-4920	72	28	not	not	PART
ejpam-4920	72	29	a	a	DET
ejpam-4920	72	30	zero	zero	NUM
ejpam-4920	72	31	forcing	forcing	NOUN
ejpam-4920	72	32	set	set	NOUN
ejpam-4920	72	33	in	in	ADP
ejpam-4920	72	34	g	g	PROPN
ejpam-4920	72	35	since	since	SCONJ
ejpam-4920	72	36	it	it	PRON
ejpam-4920	72	37	can	can	AUX
ejpam-4920	72	38	not	not	PART
ejpam-4920	72	39	forces	force	VERB
ejpam-4920	72	40	vertices	vertice	VERB
ejpam-4920	72	41	a	a	DET
ejpam-4920	72	42	,	,	PUNCT
ejpam-4920	72	43	b	b	NOUN
ejpam-4920	72	44	,	,	PUNCT
ejpam-4920	72	45	g	g	PROPN
ejpam-4920	72	46	and	and	CCONJ
ejpam-4920	72	47	h	h	PROPN
ejpam-4920	72	48	in	in	ADP
ejpam-4920	72	49	g.	g.	PROPN
ejpam-4920	72	50	thus	thus	ADV
ejpam-4920	72	51	,	,	PUNCT
ejpam-4920	72	52	the	the	DET
ejpam-4920	72	53	assertion	assertion	NOUN
ejpam-4920	72	54	follows	follow	VERB
ejpam-4920	72	55	.	.	PUNCT
ejpam-4920	73	1	remark	remark	PROPN
ejpam-4920	73	2	1	1	NUM
ejpam-4920	73	3	.	.	PUNCT
ejpam-4920	74	1	the	the	DET
ejpam-4920	74	2	proposition	proposition	NOUN
ejpam-4920	74	3	1	1	NUM
ejpam-4920	74	4	says	say	VERB
ejpam-4920	74	5	that	that	SCONJ
ejpam-4920	74	6	a	a	DET
ejpam-4920	74	7	zero	zero	NUM
ejpam-4920	74	8	forcing	force	VERB
ejpam-4920	74	9	(	(	PUNCT
ejpam-4920	74	10	resp	resp	NOUN
ejpam-4920	74	11	.	.	PUNCT
ejpam-4920	74	12	hop	hop	PROPN
ejpam-4920	74	13	dominating	dominating	NOUN
ejpam-4920	74	14	)	)	PUNCT
ejpam-4920	74	15	set	set	NOUN
ejpam-4920	74	16	may	may	AUX
ejpam-4920	74	17	not	not	PART
ejpam-4920	74	18	be	be	AUX
ejpam-4920	74	19	a	a	PRON
ejpam-4920	74	20	zero	zero	NUM
ejpam-4920	74	21	forcing	force	VERB
ejpam-4920	74	22	hop	hop	NOUN
ejpam-4920	74	23	dominating	dominating	NOUN
ejpam-4920	74	24	set	set	NOUN
ejpam-4920	74	25	.	.	PUNCT
ejpam-4920	75	1	theorem	theorem	NOUN
ejpam-4920	75	2	1	1	NUM
ejpam-4920	75	3	.	.	PUNCT
ejpam-4920	76	1	let	let	VERB
ejpam-4920	76	2	g	g	NOUN
ejpam-4920	76	3	be	be	AUX
ejpam-4920	76	4	any	any	DET
ejpam-4920	76	5	graph	graph	NOUN
ejpam-4920	76	6	.	.	PUNCT
ejpam-4920	77	1	then	then	ADV
ejpam-4920	77	2	(	(	PUNCT
ejpam-4920	77	3	i	i	NOUN
ejpam-4920	77	4	)	)	PUNCT
ejpam-4920	77	5	z(g	z(g	NOUN
ejpam-4920	77	6	)	)	PUNCT
ejpam-4920	77	7	≤	≤	NOUN
ejpam-4920	77	8	γzh(g	γzh(g	NOUN
ejpam-4920	77	9	)	)	PUNCT
ejpam-4920	77	10	;	;	PUNCT
ejpam-4920	77	11	(	(	PUNCT
ejpam-4920	77	12	ii	ii	NOUN
ejpam-4920	77	13	)	)	PUNCT
ejpam-4920	77	14	γh(g	γh(g	NOUN
ejpam-4920	77	15	)	)	PUNCT
ejpam-4920	77	16	≤	≤	NUM
ejpam-4920	77	17	γzh(g	γzh(g	NOUN
ejpam-4920	77	18	)	)	PUNCT
ejpam-4920	77	19	;	;	PUNCT
ejpam-4920	77	20	(	(	PUNCT
ejpam-4920	77	21	iii	iii	X
ejpam-4920	77	22	)	)	PUNCT
ejpam-4920	77	23	1	1	NUM
ejpam-4920	77	24	≤	≤	NUM
ejpam-4920	77	25	γzh(g	γzh(g	NOUN
ejpam-4920	77	26	)	)	PUNCT
ejpam-4920	77	27	≤	≤	PUNCT
ejpam-4920	77	28	|v	|v	X
ejpam-4920	77	29	(	(	PUNCT
ejpam-4920	77	30	g)|	g)|	NOUN
ejpam-4920	77	31	;	;	PUNCT
ejpam-4920	77	32	and	and	CCONJ
ejpam-4920	77	33	(	(	PUNCT
ejpam-4920	77	34	iv	iv	X
ejpam-4920	77	35	)	)	PUNCT
ejpam-4920	77	36	γzh(g	γzh(g	NOUN
ejpam-4920	77	37	)	)	PUNCT
ejpam-4920	78	1	=	=	SYM
ejpam-4920	78	2	|v	|v	PROPN
ejpam-4920	78	3	(	(	PUNCT
ejpam-4920	78	4	g)|	g)|	VERB
ejpam-4920	78	5	if	if	SCONJ
ejpam-4920	78	6	and	and	CCONJ
ejpam-4920	78	7	only	only	ADV
ejpam-4920	78	8	if	if	SCONJ
ejpam-4920	78	9	γh(g	γh(g	NOUN
ejpam-4920	78	10	)	)	PUNCT
ejpam-4920	78	11	=	=	SYM
ejpam-4920	78	12	|v	|v	PROPN
ejpam-4920	78	13	(	(	PUNCT
ejpam-4920	78	14	g)|	g)|	NOUN
ejpam-4920	78	15	.	.	PUNCT
ejpam-4920	79	1	proof	proof	NOUN
ejpam-4920	79	2	.	.	PUNCT
ejpam-4920	80	1	(	(	PUNCT
ejpam-4920	80	2	i	i	NOUN
ejpam-4920	80	3	)	)	PUNCT
ejpam-4920	80	4	let	let	VERB
ejpam-4920	80	5	g	g	NOUN
ejpam-4920	80	6	be	be	AUX
ejpam-4920	80	7	a	a	DET
ejpam-4920	80	8	graph	graph	NOUN
ejpam-4920	80	9	and	and	CCONJ
ejpam-4920	80	10	let	let	VERB
ejpam-4920	80	11	z	z	PRON
ejpam-4920	80	12	be	be	AUX
ejpam-4920	80	13	a	a	DET
ejpam-4920	80	14	γzh	γzh	NOUN
ejpam-4920	80	15	-	-	PUNCT
ejpam-4920	80	16	set	set	NOUN
ejpam-4920	80	17	of	of	ADP
ejpam-4920	80	18	g.	g.	PROPN
ejpam-4920	81	1	then	then	ADV
ejpam-4920	81	2	z	z	PROPN
ejpam-4920	81	3	is	be	AUX
ejpam-4920	81	4	a	a	DET
ejpam-4920	81	5	zero	zero	NUM
ejpam-4920	81	6	forcing	force	VERB
ejpam-4920	81	7	in	in	ADP
ejpam-4920	81	8	g	g	NOUN
ejpam-4920	81	9	and	and	CCONJ
ejpam-4920	81	10	|z|	|z|	NOUN
ejpam-4920	81	11	=	=	SYM
ejpam-4920	81	12	γzh(g	γzh(g	NOUN
ejpam-4920	81	13	)	)	PUNCT
ejpam-4920	81	14	.	.	PUNCT
ejpam-4920	82	1	since	since	SCONJ
ejpam-4920	82	2	z(g	z(g	NOUN
ejpam-4920	82	3	)	)	PUNCT
ejpam-4920	82	4	is	be	AUX
ejpam-4920	82	5	the	the	DET
ejpam-4920	82	6	minimum	minimum	ADJ
ejpam-4920	82	7	cardinality	cardinality	NOUN
ejpam-4920	82	8	among	among	ADP
ejpam-4920	82	9	all	all	DET
ejpam-4920	82	10	zero	zero	NUM
ejpam-4920	82	11	forcing	force	VERB
ejpam-4920	82	12	sets	set	NOUN
ejpam-4920	82	13	in	in	ADP
ejpam-4920	82	14	g	g	NOUN
ejpam-4920	82	15	,	,	PUNCT
ejpam-4920	82	16	we	we	PRON
ejpam-4920	82	17	have	have	VERB
ejpam-4920	82	18	z(g	z(g	NOUN
ejpam-4920	82	19	)	)	PUNCT
ejpam-4920	82	20	≤	≤	NUM
ejpam-4920	82	21	|z|	|z|	NOUN
ejpam-4920	82	22	=	=	SYM
ejpam-4920	82	23	γzh(g	γzh(g	NOUN
ejpam-4920	82	24	)	)	PUNCT
ejpam-4920	82	25	.	.	PUNCT
ejpam-4920	83	1	j.	j.	PROPN
ejpam-4920	83	2	u.	u.	PROPN
ejpam-4920	83	3	manditong	manditong	PROPN
ejpam-4920	83	4	et	et	PROPN
ejpam-4920	83	5	al	al	PROPN
ejpam-4920	83	6	.	.	PUNCT
ejpam-4920	83	7	/	/	SYM
ejpam-4920	83	8	eur	eur	PROPN
ejpam-4920	83	9	.	.	PUNCT
ejpam-4920	84	1	j.	j.	PROPN
ejpam-4920	84	2	pure	pure	PROPN
ejpam-4920	84	3	appl	appl	PROPN
ejpam-4920	84	4	.	.	PROPN
ejpam-4920	84	5	math	math	PROPN
ejpam-4920	84	6	,	,	PUNCT
ejpam-4920	84	7	17	17	NUM
ejpam-4920	84	8	(	(	PUNCT
ejpam-4920	84	9	1	1	NUM
ejpam-4920	84	10	)	)	PUNCT
ejpam-4920	84	11	(	(	PUNCT
ejpam-4920	84	12	2024	2024	NUM
ejpam-4920	84	13	)	)	PUNCT
ejpam-4920	84	14	,	,	PUNCT
ejpam-4920	84	15	324	324	NUM
ejpam-4920	84	16	-	-	SYM
ejpam-4920	84	17	337	337	NUM
ejpam-4920	84	18	328	328	NUM
ejpam-4920	84	19	(	(	PUNCT
ejpam-4920	84	20	ii	ii	NOUN
ejpam-4920	84	21	)	)	PUNCT
ejpam-4920	84	22	let	let	VERB
ejpam-4920	84	23	s	s	PRON
ejpam-4920	84	24	be	be	AUX
ejpam-4920	84	25	a	a	DET
ejpam-4920	84	26	γzh	γzh	ADJ
ejpam-4920	84	27	-	-	PUNCT
ejpam-4920	84	28	set	set	NOUN
ejpam-4920	84	29	of	of	ADP
ejpam-4920	84	30	g.	g.	PROPN
ejpam-4920	85	1	then	then	ADV
ejpam-4920	85	2	s	s	VERB
ejpam-4920	85	3	is	be	AUX
ejpam-4920	85	4	a	a	DET
ejpam-4920	85	5	hop	hop	NOUN
ejpam-4920	85	6	dominating	dominating	NOUN
ejpam-4920	85	7	set	set	VERB
ejpam-4920	85	8	in	in	ADP
ejpam-4920	85	9	g	g	PROPN
ejpam-4920	85	10	and	and	CCONJ
ejpam-4920	85	11	|s|	|s|	PROPN
ejpam-4920	85	12	=	=	SYM
ejpam-4920	85	13	γzh(g	γzh(g	PROPN
ejpam-4920	85	14	)	)	PUNCT
ejpam-4920	85	15	.	.	PUNCT
ejpam-4920	86	1	since	since	SCONJ
ejpam-4920	86	2	γh(g	γh(g	NOUN
ejpam-4920	86	3	)	)	PUNCT
ejpam-4920	86	4	is	be	AUX
ejpam-4920	86	5	the	the	DET
ejpam-4920	86	6	minimum	minimum	ADJ
ejpam-4920	86	7	cardinality	cardinality	NOUN
ejpam-4920	86	8	among	among	ADP
ejpam-4920	86	9	all	all	DET
ejpam-4920	86	10	hop	hop	NOUN
ejpam-4920	86	11	dominating	dominating	NOUN
ejpam-4920	86	12	sets	set	NOUN
ejpam-4920	86	13	in	in	ADP
ejpam-4920	86	14	g	g	NOUN
ejpam-4920	86	15	,	,	PUNCT
ejpam-4920	86	16	hence	hence	ADV
ejpam-4920	86	17	γh(g	γh(g	PUNCT
ejpam-4920	86	18	)	)	PUNCT
ejpam-4920	86	19	≤|	≤|	NOUN
ejpam-4920	86	20	s	s	PART
ejpam-4920	86	21	|=	|=	NOUN
ejpam-4920	86	22	γzh(g	γzh(g	NOUN
ejpam-4920	86	23	)	)	PUNCT
ejpam-4920	86	24	.	.	PUNCT
ejpam-4920	87	1	(	(	PUNCT
ejpam-4920	87	2	iii	iii	NOUN
ejpam-4920	87	3	)	)	PUNCT
ejpam-4920	87	4	since	since	SCONJ
ejpam-4920	87	5	γh(g	γh(g	NOUN
ejpam-4920	87	6	)	)	PUNCT
ejpam-4920	87	7	≥	≥	NOUN
ejpam-4920	87	8	1	1	NUM
ejpam-4920	87	9	for	for	ADP
ejpam-4920	87	10	any	any	DET
ejpam-4920	87	11	graph	graph	NOUN
ejpam-4920	87	12	g	g	NOUN
ejpam-4920	87	13	,	,	PUNCT
ejpam-4920	87	14	it	it	PRON
ejpam-4920	87	15	follows	follow	VERB
ejpam-4920	87	16	that	that	SCONJ
ejpam-4920	87	17	γzh(g	γzh(g	NOUN
ejpam-4920	87	18	)	)	PUNCT
ejpam-4920	87	19	≥	≥	NOUN
ejpam-4920	87	20	1	1	NUM
ejpam-4920	87	21	by	by	ADP
ejpam-4920	87	22	(	(	PUNCT
ejpam-4920	87	23	ii	ii	NOUN
ejpam-4920	87	24	)	)	PUNCT
ejpam-4920	87	25	.	.	PUNCT
ejpam-4920	88	1	since	since	SCONJ
ejpam-4920	88	2	any	any	DET
ejpam-4920	88	3	zero	zero	NUM
ejpam-4920	88	4	forcing	force	VERB
ejpam-4920	88	5	hop	hop	NOUN
ejpam-4920	88	6	dominating	dominating	NOUN
ejpam-4920	88	7	set	set	NOUN
ejpam-4920	88	8	s′	s′	PUNCT
ejpam-4920	88	9	is	be	AUX
ejpam-4920	88	10	always	always	ADV
ejpam-4920	88	11	a	a	DET
ejpam-4920	88	12	subset	subset	NOUN
ejpam-4920	88	13	of	of	ADP
ejpam-4920	88	14	v	v	NOUN
ejpam-4920	88	15	(	(	PUNCT
ejpam-4920	88	16	g	g	NOUN
ejpam-4920	88	17	)	)	PUNCT
ejpam-4920	88	18	,	,	PUNCT
ejpam-4920	88	19	we	we	PRON
ejpam-4920	88	20	have	have	VERB
ejpam-4920	88	21	γzh(g	γzh(g	NOUN
ejpam-4920	88	22	)	)	PUNCT
ejpam-4920	88	23	≤|	≤|	NOUN
ejpam-4920	88	24	v	v	ADP
ejpam-4920	88	25	(	(	PUNCT
ejpam-4920	88	26	g	g	NOUN
ejpam-4920	88	27	)	)	PUNCT
ejpam-4920	88	28	|	|	ADV
ejpam-4920	88	29	.	.	PUNCT
ejpam-4920	89	1	consequently	consequently	ADV
ejpam-4920	89	2	,	,	PUNCT
ejpam-4920	89	3	1	1	NUM
ejpam-4920	89	4	≤	≤	NUM
ejpam-4920	89	5	γzh(g	γzh(g	NOUN
ejpam-4920	89	6	)	)	PUNCT
ejpam-4920	89	7	≤	≤	PUNCT
ejpam-4920	89	8	|v	|v	X
ejpam-4920	89	9	(	(	PUNCT
ejpam-4920	89	10	g)|	g)|	NOUN
ejpam-4920	89	11	.	.	PUNCT
ejpam-4920	90	1	(	(	PUNCT
ejpam-4920	90	2	iv	iv	X
ejpam-4920	90	3	)	)	PUNCT
ejpam-4920	90	4	suppose	suppose	VERB
ejpam-4920	90	5	that	that	SCONJ
ejpam-4920	90	6	γzh(g	γzh(g	NOUN
ejpam-4920	90	7	)	)	PUNCT
ejpam-4920	90	8	=	=	SYM
ejpam-4920	90	9	|v	|v	PROPN
ejpam-4920	90	10	(	(	PUNCT
ejpam-4920	90	11	g)|	g)|	PROPN
ejpam-4920	90	12	.	.	PUNCT
ejpam-4920	91	1	then	then	ADV
ejpam-4920	91	2	v	v	X
ejpam-4920	91	3	(	(	PUNCT
ejpam-4920	91	4	g	g	NOUN
ejpam-4920	91	5	)	)	PUNCT
ejpam-4920	91	6	is	be	AUX
ejpam-4920	91	7	the	the	DET
ejpam-4920	91	8	minimum	minimum	ADJ
ejpam-4920	91	9	zero	zero	NUM
ejpam-4920	91	10	forcing	force	VERB
ejpam-4920	91	11	hop	hop	NOUN
ejpam-4920	91	12	dominating	dominating	NOUN
ejpam-4920	91	13	set	set	VERB
ejpam-4920	91	14	in	in	ADP
ejpam-4920	91	15	g.	g.	PROPN
ejpam-4920	91	16	assume	assume	VERB
ejpam-4920	91	17	that	that	SCONJ
ejpam-4920	91	18	g	g	PROPN
ejpam-4920	91	19	is	be	AUX
ejpam-4920	91	20	connected	connect	VERB
ejpam-4920	91	21	.	.	PUNCT
ejpam-4920	92	1	suppose	suppose	VERB
ejpam-4920	92	2	further	far	ADV
ejpam-4920	92	3	that	that	SCONJ
ejpam-4920	92	4	g	g	PROPN
ejpam-4920	92	5	is	be	AUX
ejpam-4920	92	6	noncomplete	noncomplete	ADJ
ejpam-4920	92	7	.	.	PUNCT
ejpam-4920	93	1	then	then	ADV
ejpam-4920	93	2	dg(v	dg(v	NOUN
ejpam-4920	93	3	,	,	PUNCT
ejpam-4920	93	4	w	w	NOUN
ejpam-4920	93	5	)	)	PUNCT
ejpam-4920	93	6	=	=	SYM
ejpam-4920	93	7	2	2	NUM
ejpam-4920	93	8	for	for	ADP
ejpam-4920	93	9	some	some	DET
ejpam-4920	93	10	v	v	NOUN
ejpam-4920	93	11	,	,	PUNCT
ejpam-4920	93	12	w	w	PROPN
ejpam-4920	93	13	∈	∈	PROPN
ejpam-4920	93	14	v	v	ADP
ejpam-4920	93	15	(	(	PUNCT
ejpam-4920	93	16	g	g	NOUN
ejpam-4920	93	17	)	)	PUNCT
ejpam-4920	93	18	.	.	PUNCT
ejpam-4920	94	1	hence	hence	ADV
ejpam-4920	94	2	,	,	PUNCT
ejpam-4920	94	3	z	z	NOUN
ejpam-4920	94	4	′	′	NUM
ejpam-4920	94	5	=	=	SYM
ejpam-4920	94	6	v	v	NOUN
ejpam-4920	94	7	(	(	PUNCT
ejpam-4920	94	8	g	g	NOUN
ejpam-4920	94	9	)	)	PUNCT
ejpam-4920	94	10	\	\	NOUN
ejpam-4920	94	11	{	{	PUNCT
ejpam-4920	94	12	w	w	NOUN
ejpam-4920	94	13	}	}	PUNCT
ejpam-4920	94	14	is	be	AUX
ejpam-4920	94	15	a	a	DET
ejpam-4920	94	16	zero	zero	NUM
ejpam-4920	94	17	forcing	force	VERB
ejpam-4920	94	18	hop	hop	NOUN
ejpam-4920	94	19	dominating	dominating	NOUN
ejpam-4920	94	20	set	set	NOUN
ejpam-4920	94	21	of	of	ADP
ejpam-4920	94	22	g	g	NOUN
ejpam-4920	94	23	,	,	PUNCT
ejpam-4920	94	24	showing	show	VERB
ejpam-4920	94	25	that	that	SCONJ
ejpam-4920	94	26	γzh(g	γzh(g	NOUN
ejpam-4920	94	27	)	)	PUNCT
ejpam-4920	94	28	≤	≤	NUM
ejpam-4920	94	29	|v	|v	X
ejpam-4920	94	30	(	(	PUNCT
ejpam-4920	94	31	g)|	g)|	INTJ
ejpam-4920	94	32	−	−	PROPN
ejpam-4920	94	33	1	1	NUM
ejpam-4920	94	34	,	,	PUNCT
ejpam-4920	94	35	which	which	PRON
ejpam-4920	94	36	is	be	AUX
ejpam-4920	94	37	a	a	DET
ejpam-4920	94	38	contradiction	contradiction	NOUN
ejpam-4920	94	39	.	.	PUNCT
ejpam-4920	95	1	therefore	therefore	ADV
ejpam-4920	95	2	,	,	PUNCT
ejpam-4920	95	3	g	g	PROPN
ejpam-4920	95	4	is	be	AUX
ejpam-4920	95	5	complete	complete	ADJ
ejpam-4920	95	6	,	,	PUNCT
ejpam-4920	95	7	and	and	CCONJ
ejpam-4920	95	8	so	so	ADV
ejpam-4920	95	9	γh(g	γh(g	PUNCT
ejpam-4920	95	10	)	)	PUNCT
ejpam-4920	95	11	=	=	SYM
ejpam-4920	95	12	|v	|v	PROPN
ejpam-4920	95	13	(	(	PUNCT
ejpam-4920	95	14	g)|	g)|	NOUN
ejpam-4920	95	15	.	.	PUNCT
ejpam-4920	96	1	now	now	ADV
ejpam-4920	96	2	,	,	PUNCT
ejpam-4920	96	3	let	let	VERB
ejpam-4920	96	4	g1	g1	NOUN
ejpam-4920	96	5	,	,	PUNCT
ejpam-4920	96	6	.	.	PUNCT
ejpam-4920	96	7	.	.	PUNCT
ejpam-4920	97	1	.	.	PUNCT
ejpam-4920	98	1	,	,	PUNCT
ejpam-4920	98	2	gk	gk	PROPN
ejpam-4920	98	3	,	,	PUNCT
ejpam-4920	98	4	k	k	PROPN
ejpam-4920	98	5	≥	≥	NUM
ejpam-4920	98	6	2	2	NUM
ejpam-4920	98	7	be	be	AUX
ejpam-4920	98	8	components	component	NOUN
ejpam-4920	98	9	of	of	ADP
ejpam-4920	98	10	g.	g.	PROPN
ejpam-4920	98	11	suppose	suppose	VERB
ejpam-4920	98	12	that	that	SCONJ
ejpam-4920	98	13	gi	gi	PROPN
ejpam-4920	98	14	is	be	AUX
ejpam-4920	98	15	non	non	ADJ
ejpam-4920	98	16	-	-	ADJ
ejpam-4920	98	17	complete	complete	ADJ
ejpam-4920	98	18	for	for	ADP
ejpam-4920	98	19	some	some	DET
ejpam-4920	98	20	i	i	PRON
ejpam-4920	98	21	∈	∈	PROPN
ejpam-4920	98	22	{	{	PUNCT
ejpam-4920	98	23	1	1	NUM
ejpam-4920	98	24	,	,	PUNCT
ejpam-4920	98	25	.	.	PUNCT
ejpam-4920	98	26	.	.	PUNCT
ejpam-4920	99	1	.	.	PUNCT
ejpam-4920	100	1	,	,	PUNCT
ejpam-4920	100	2	k	k	X
ejpam-4920	100	3	}	}	PUNCT
ejpam-4920	100	4	.	.	PUNCT
ejpam-4920	101	1	then	then	ADV
ejpam-4920	101	2	dgi(s	dgi(s	PROPN
ejpam-4920	101	3	,	,	PUNCT
ejpam-4920	101	4	t	t	PROPN
ejpam-4920	101	5	)	)	PUNCT
ejpam-4920	101	6	=	=	SYM
ejpam-4920	101	7	2	2	NUM
ejpam-4920	101	8	=	=	SYM
ejpam-4920	101	9	dg(s	dg(s	NOUN
ejpam-4920	101	10	,	,	PUNCT
ejpam-4920	101	11	t	t	PROPN
ejpam-4920	101	12	)	)	PUNCT
ejpam-4920	101	13	for	for	ADP
ejpam-4920	101	14	some	some	DET
ejpam-4920	101	15	s	s	NOUN
ejpam-4920	101	16	,	,	PUNCT
ejpam-4920	101	17	t	t	PROPN
ejpam-4920	101	18	∈	∈	PROPN
ejpam-4920	101	19	v	v	PROPN
ejpam-4920	101	20	(	(	PUNCT
ejpam-4920	101	21	gi	gi	NOUN
ejpam-4920	101	22	)	)	PUNCT
ejpam-4920	101	23	.	.	PUNCT
ejpam-4920	102	1	thus	thus	ADV
ejpam-4920	102	2	,	,	PUNCT
ejpam-4920	102	3	z	z	X
ejpam-4920	102	4	′′	′′	NOUN
ejpam-4920	102	5	=	=	SYM
ejpam-4920	102	6	v	v	PROPN
ejpam-4920	102	7	(	(	PUNCT
ejpam-4920	102	8	g	g	NOUN
ejpam-4920	102	9	)	)	PUNCT
ejpam-4920	102	10	\	\	NOUN
ejpam-4920	102	11	{	{	PUNCT
ejpam-4920	102	12	t	t	PROPN
ejpam-4920	102	13	}	}	PUNCT
ejpam-4920	102	14	is	be	AUX
ejpam-4920	102	15	a	a	DET
ejpam-4920	102	16	zero	zero	NUM
ejpam-4920	102	17	forcing	force	VERB
ejpam-4920	102	18	hop	hop	NOUN
ejpam-4920	102	19	dominating	dominating	NOUN
ejpam-4920	102	20	set	set	NOUN
ejpam-4920	102	21	of	of	ADP
ejpam-4920	102	22	g	g	NOUN
ejpam-4920	102	23	,	,	PUNCT
ejpam-4920	102	24	and	and	CCONJ
ejpam-4920	102	25	so	so	ADV
ejpam-4920	102	26	γzh(g	γzh(g	NOUN
ejpam-4920	102	27	)	)	PUNCT
ejpam-4920	102	28	≤	≤	NUM
ejpam-4920	102	29	|v	|v	X
ejpam-4920	102	30	(	(	PUNCT
ejpam-4920	102	31	g)|	g)|	INTJ
ejpam-4920	102	32	−	−	PROPN
ejpam-4920	102	33	1	1	NUM
ejpam-4920	102	34	,	,	PUNCT
ejpam-4920	102	35	a	a	DET
ejpam-4920	102	36	contradiction	contradiction	NOUN
ejpam-4920	102	37	.	.	PUNCT
ejpam-4920	103	1	hence	hence	ADV
ejpam-4920	103	2	,	,	PUNCT
ejpam-4920	103	3	every	every	DET
ejpam-4920	103	4	component	component	NOUN
ejpam-4920	103	5	of	of	ADP
ejpam-4920	103	6	g	g	PROPN
ejpam-4920	103	7	is	be	AUX
ejpam-4920	103	8	complete	complete	ADJ
ejpam-4920	103	9	.	.	PUNCT
ejpam-4920	104	1	therefore	therefore	ADV
ejpam-4920	104	2	,	,	PUNCT
ejpam-4920	104	3	γh(gi	γh(gi	PROPN
ejpam-4920	104	4	)	)	PUNCT
ejpam-4920	105	1	=	=	PUNCT
ejpam-4920	105	2	|v	|v	PROPN
ejpam-4920	105	3	(	(	PUNCT
ejpam-4920	105	4	gi)|	gi)|	INTJ
ejpam-4920	105	5	for	for	ADP
ejpam-4920	105	6	each	each	DET
ejpam-4920	105	7	i	i	PRON
ejpam-4920	105	8	∈	∈	PROPN
ejpam-4920	105	9	{	{	PUNCT
ejpam-4920	105	10	1	1	NUM
ejpam-4920	105	11	.	.	PUNCT
ejpam-4920	105	12	.	.	PUNCT
ejpam-4920	105	13	.	.	PUNCT
ejpam-4920	105	14	,	,	PUNCT
ejpam-4920	105	15	k	k	X
ejpam-4920	105	16	}	}	PUNCT
ejpam-4920	105	17	.	.	PUNCT
ejpam-4920	106	1	consequently	consequently	ADV
ejpam-4920	106	2	,	,	PUNCT
ejpam-4920	106	3	γh(g	γh(g	NOUN
ejpam-4920	106	4	)	)	PUNCT
ejpam-4920	106	5	=	=	SYM
ejpam-4920	106	6	γh(g1	γh(g1	X
ejpam-4920	106	7	)	)	PUNCT
ejpam-4920	106	8	+	+	CCONJ
ejpam-4920	106	9	·	·	PUNCT
ejpam-4920	106	10	·	·	PUNCT
ejpam-4920	106	11	·	·	PUNCT
ejpam-4920	106	12	+	+	NUM
ejpam-4920	106	13	γh(gk	γh(gk	NOUN
ejpam-4920	106	14	)	)	PUNCT
ejpam-4920	106	15	=	=	SYM
ejpam-4920	106	16	|v	|v	X
ejpam-4920	106	17	(	(	PUNCT
ejpam-4920	106	18	g1)|+	g1)|+	X
ejpam-4920	106	19	·	·	PUNCT
ejpam-4920	106	20	·	·	PUNCT
ejpam-4920	106	21	·	·	PUNCT
ejpam-4920	107	1	+	+	CCONJ
ejpam-4920	107	2	|v	|v	X
ejpam-4920	107	3	(	(	PUNCT
ejpam-4920	107	4	gk)|	gk)|	NOUN
ejpam-4920	107	5	=	=	SYM
ejpam-4920	107	6	|v	|v	PROPN
ejpam-4920	107	7	(	(	PUNCT
ejpam-4920	107	8	g)|	g)|	NOUN
ejpam-4920	107	9	.	.	PUNCT
ejpam-4920	108	1	conversely	conversely	ADV
ejpam-4920	108	2	,	,	PUNCT
ejpam-4920	108	3	suppose	suppose	VERB
ejpam-4920	108	4	that	that	SCONJ
ejpam-4920	108	5	γh(g	γh(g	NOUN
ejpam-4920	108	6	)	)	PUNCT
ejpam-4920	108	7	=	=	SYM
ejpam-4920	108	8	|v	|v	PROPN
ejpam-4920	108	9	(	(	PUNCT
ejpam-4920	108	10	g)|	g)|	PROPN
ejpam-4920	108	11	.	.	PUNCT
ejpam-4920	109	1	then	then	ADV
ejpam-4920	109	2	by	by	ADP
ejpam-4920	109	3	(	(	PUNCT
ejpam-4920	109	4	ii	ii	NOUN
ejpam-4920	109	5	)	)	PUNCT
ejpam-4920	109	6	and	and	CCONJ
ejpam-4920	109	7	(	(	PUNCT
ejpam-4920	109	8	iii	iii	NOUN
ejpam-4920	109	9	)	)	PUNCT
ejpam-4920	109	10	,	,	PUNCT
ejpam-4920	109	11	γzh(g	γzh(g	NUM
ejpam-4920	109	12	)	)	PUNCT
ejpam-4920	109	13	=	=	SYM
ejpam-4920	109	14	|v	|v	PROPN
ejpam-4920	109	15	(	(	PUNCT
ejpam-4920	109	16	g)|	g)|	NOUN
ejpam-4920	109	17	.	.	PUNCT
ejpam-4920	110	1	the	the	DET
ejpam-4920	110	2	following	following	ADJ
ejpam-4920	110	3	result	result	NOUN
ejpam-4920	110	4	follows	follow	VERB
ejpam-4920	110	5	immediately	immediately	ADV
ejpam-4920	110	6	from	from	ADP
ejpam-4920	110	7	theorem	theorem	ADJ
ejpam-4920	110	8	1(iv	1(iv	NUM
ejpam-4920	110	9	)	)	PUNCT
ejpam-4920	110	10	.	.	PUNCT
ejpam-4920	111	1	corollary	corollary	ADJ
ejpam-4920	111	2	1	1	NUM
ejpam-4920	111	3	.	.	NOUN
ejpam-4920	111	4	γzh(kr	γzh(kr	X
ejpam-4920	111	5	)	)	PUNCT
ejpam-4920	112	1	=	=	SYM
ejpam-4920	112	2	r	r	NOUN
ejpam-4920	112	3	=	=	SYM
ejpam-4920	112	4	γzh(kr	γzh(kr	X
ejpam-4920	112	5	)	)	PUNCT
ejpam-4920	112	6	for	for	ADP
ejpam-4920	112	7	all	all	DET
ejpam-4920	112	8	positive	positive	ADJ
ejpam-4920	112	9	integer	integer	NOUN
ejpam-4920	112	10	r	r	NOUN
ejpam-4920	112	11	≥	≥	NUM
ejpam-4920	112	12	1	1	NUM
ejpam-4920	112	13	.	.	PUNCT
ejpam-4920	112	14	proposition	proposition	NOUN
ejpam-4920	112	15	2	2	NUM
ejpam-4920	112	16	.	.	PUNCT
ejpam-4920	113	1	let	let	VERB
ejpam-4920	113	2	g	g	NOUN
ejpam-4920	113	3	be	be	AUX
ejpam-4920	113	4	any	any	DET
ejpam-4920	113	5	graph	graph	NOUN
ejpam-4920	113	6	with	with	ADP
ejpam-4920	113	7	|v	|v	PROPN
ejpam-4920	113	8	(	(	PUNCT
ejpam-4920	113	9	g)|	g)|	X
ejpam-4920	113	10	≥	≥	NOUN
ejpam-4920	113	11	2	2	NUM
ejpam-4920	113	12	.	.	PUNCT
ejpam-4920	114	1	if	if	SCONJ
ejpam-4920	114	2	γzh(g	γzh(g	NOUN
ejpam-4920	114	3	)	)	PUNCT
ejpam-4920	114	4	=	=	SYM
ejpam-4920	115	1	2	2	NUM
ejpam-4920	115	2	,	,	PUNCT
ejpam-4920	115	3	then	then	ADV
ejpam-4920	115	4	γh(g	γh(g	PUNCT
ejpam-4920	115	5	)	)	PUNCT
ejpam-4920	115	6	=	=	SYM
ejpam-4920	116	1	2	2	X
ejpam-4920	116	2	.	.	PUNCT
ejpam-4920	117	1	however	however	ADV
ejpam-4920	117	2	,	,	PUNCT
ejpam-4920	117	3	the	the	DET
ejpam-4920	117	4	converse	converse	NOUN
ejpam-4920	117	5	is	be	AUX
ejpam-4920	117	6	not	not	PART
ejpam-4920	117	7	true	true	ADJ
ejpam-4920	117	8	.	.	PUNCT
ejpam-4920	118	1	proof	proof	NOUN
ejpam-4920	118	2	.	.	PUNCT
ejpam-4920	119	1	let	let	VERB
ejpam-4920	119	2	g	g	PRON
ejpam-4920	119	3	be	be	AUX
ejpam-4920	119	4	a	a	DET
ejpam-4920	119	5	graph	graph	NOUN
ejpam-4920	119	6	with	with	ADP
ejpam-4920	119	7	|v	|v	PROPN
ejpam-4920	119	8	(	(	PUNCT
ejpam-4920	119	9	g)|	g)|	X
ejpam-4920	119	10	≥	≥	NOUN
ejpam-4920	119	11	2	2	NUM
ejpam-4920	119	12	.	.	PUNCT
ejpam-4920	119	13	then	then	ADV
ejpam-4920	119	14	γh(g	γh(g	PUNCT
ejpam-4920	119	15	)	)	PUNCT
ejpam-4920	119	16	≥	≥	NOUN
ejpam-4920	119	17	2	2	NUM
ejpam-4920	119	18	.	.	PUNCT
ejpam-4920	119	19	since	since	SCONJ
ejpam-4920	119	20	γzh(g	γzh(g	NUM
ejpam-4920	119	21	)	)	PUNCT
ejpam-4920	120	1	=	=	SYM
ejpam-4920	120	2	2	2	NUM
ejpam-4920	120	3	,	,	PUNCT
ejpam-4920	120	4	γh(g	γh(g	NOUN
ejpam-4920	120	5	)	)	PUNCT
ejpam-4920	120	6	≤	≤	NUM
ejpam-4920	120	7	2	2	NUM
ejpam-4920	120	8	by	by	ADP
ejpam-4920	120	9	theorem	theorem	NOUN
ejpam-4920	120	10	1(ii	1(ii	NUM
ejpam-4920	120	11	)	)	PUNCT
ejpam-4920	120	12	.	.	PUNCT
ejpam-4920	121	1	hence	hence	ADV
ejpam-4920	121	2	,	,	PUNCT
ejpam-4920	121	3	γh(g	γh(g	NOUN
ejpam-4920	121	4	)	)	PUNCT
ejpam-4920	121	5	=	=	SYM
ejpam-4920	121	6	2	2	X
ejpam-4920	121	7	.	.	PUNCT
ejpam-4920	121	8	to	to	PART
ejpam-4920	121	9	see	see	VERB
ejpam-4920	121	10	that	that	SCONJ
ejpam-4920	121	11	the	the	DET
ejpam-4920	121	12	converse	converse	NOUN
ejpam-4920	121	13	is	be	AUX
ejpam-4920	121	14	not	not	PART
ejpam-4920	121	15	true	true	ADJ
ejpam-4920	121	16	,	,	PUNCT
ejpam-4920	121	17	consider	consider	VERB
ejpam-4920	121	18	the	the	DET
ejpam-4920	121	19	graph	graph	NOUN
ejpam-4920	121	20	g	g	NOUN
ejpam-4920	121	21	below	below	ADV
ejpam-4920	121	22	.	.	PUNCT
ejpam-4920	122	1	g	g	NOUN
ejpam-4920	122	2	:	:	PUNCT
ejpam-4920	122	3	c	c	X
ejpam-4920	122	4	d	d	X
ejpam-4920	122	5	e	e	PROPN
ejpam-4920	122	6	b	b	PROPN
ejpam-4920	122	7	a	a	DET
ejpam-4920	122	8	j.	j.	PROPN
ejpam-4920	122	9	u.	u.	PROPN
ejpam-4920	122	10	manditong	manditong	PROPN
ejpam-4920	122	11	et	et	PROPN
ejpam-4920	122	12	al	al	PROPN
ejpam-4920	122	13	.	.	PUNCT
ejpam-4920	122	14	/	/	SYM
ejpam-4920	122	15	eur	eur	PROPN
ejpam-4920	122	16	.	.	PUNCT
ejpam-4920	123	1	j.	j.	PROPN
ejpam-4920	123	2	pure	pure	PROPN
ejpam-4920	123	3	appl	appl	PROPN
ejpam-4920	123	4	.	.	PROPN
ejpam-4920	123	5	math	math	PROPN
ejpam-4920	123	6	,	,	PUNCT
ejpam-4920	123	7	17	17	NUM
ejpam-4920	123	8	(	(	PUNCT
ejpam-4920	123	9	1	1	NUM
ejpam-4920	123	10	)	)	PUNCT
ejpam-4920	123	11	(	(	PUNCT
ejpam-4920	123	12	2024	2024	NUM
ejpam-4920	123	13	)	)	PUNCT
ejpam-4920	123	14	,	,	PUNCT
ejpam-4920	123	15	324	324	NUM
ejpam-4920	123	16	-	-	SYM
ejpam-4920	123	17	337	337	NUM
ejpam-4920	123	18	329	329	NUM
ejpam-4920	123	19	let	let	VERB
ejpam-4920	123	20	z1	z1	NOUN
ejpam-4920	123	21	=	=	SYM
ejpam-4920	123	22	{	{	PUNCT
ejpam-4920	123	23	a	a	X
ejpam-4920	123	24	,	,	PUNCT
ejpam-4920	123	25	e	e	NOUN
ejpam-4920	123	26	}	}	PUNCT
ejpam-4920	123	27	.	.	PUNCT
ejpam-4920	124	1	then	then	ADV
ejpam-4920	124	2	n2	n2	PROPN
ejpam-4920	124	3	g[z1	g[z1	PROPN
ejpam-4920	124	4	]	]	X
ejpam-4920	124	5	=	=	SYM
ejpam-4920	124	6	v	v	X
ejpam-4920	124	7	(	(	PUNCT
ejpam-4920	124	8	g	g	NOUN
ejpam-4920	124	9	)	)	PUNCT
ejpam-4920	124	10	,	,	PUNCT
ejpam-4920	124	11	showing	show	VERB
ejpam-4920	124	12	that	that	SCONJ
ejpam-4920	124	13	z1	z1	PROPN
ejpam-4920	124	14	is	be	AUX
ejpam-4920	124	15	a	a	DET
ejpam-4920	124	16	hop	hop	NOUN
ejpam-4920	124	17	dominating	dominating	NOUN
ejpam-4920	124	18	set	set	NOUN
ejpam-4920	124	19	of	of	ADP
ejpam-4920	124	20	g.	g.	PROPN
ejpam-4920	124	21	thus	thus	ADV
ejpam-4920	124	22	,	,	PUNCT
ejpam-4920	124	23	γh(g	γh(g	NOUN
ejpam-4920	124	24	)	)	PUNCT
ejpam-4920	124	25	≤	≤	NUM
ejpam-4920	124	26	2	2	NUM
ejpam-4920	124	27	.	.	PUNCT
ejpam-4920	124	28	since	since	ADV
ejpam-4920	124	29	,	,	PUNCT
ejpam-4920	124	30	|v	|v	PROPN
ejpam-4920	124	31	(	(	PUNCT
ejpam-4920	124	32	g)|	g)|	X
ejpam-4920	124	33	≥	≥	NOUN
ejpam-4920	124	34	2	2	NUM
ejpam-4920	124	35	,	,	PUNCT
ejpam-4920	124	36	it	it	PRON
ejpam-4920	124	37	follows	follow	VERB
ejpam-4920	124	38	that	that	PRON
ejpam-4920	124	39	γh(g	γh(g	NOUN
ejpam-4920	124	40	)	)	PUNCT
ejpam-4920	124	41	≥	≥	NOUN
ejpam-4920	125	1	2	2	NUM
ejpam-4920	125	2	.	.	PUNCT
ejpam-4920	125	3	hence	hence	ADV
ejpam-4920	125	4	,	,	PUNCT
ejpam-4920	125	5	γh(g	γh(g	NOUN
ejpam-4920	125	6	)	)	PUNCT
ejpam-4920	125	7	=	=	SYM
ejpam-4920	125	8	2	2	X
ejpam-4920	125	9	.	.	PUNCT
ejpam-4920	126	1	now	now	ADV
ejpam-4920	126	2	,	,	PUNCT
ejpam-4920	126	3	let	let	VERB
ejpam-4920	126	4	z2	z2	PROPN
ejpam-4920	126	5	=	=	SYM
ejpam-4920	126	6	{	{	PUNCT
ejpam-4920	126	7	a	a	PRON
ejpam-4920	126	8	,	,	PUNCT
ejpam-4920	126	9	b	b	NOUN
ejpam-4920	126	10	,	,	PUNCT
ejpam-4920	126	11	c	c	X
ejpam-4920	126	12	,	,	PUNCT
ejpam-4920	126	13	e	e	NOUN
ejpam-4920	126	14	}	}	PUNCT
ejpam-4920	126	15	.	.	PUNCT
ejpam-4920	127	1	then	then	ADV
ejpam-4920	127	2	,	,	PUNCT
ejpam-4920	127	3	z2	z2	PROPN
ejpam-4920	127	4	is	be	AUX
ejpam-4920	127	5	minimum	minimum	ADJ
ejpam-4920	127	6	zero	zero	NUM
ejpam-4920	127	7	forcing	force	VERB
ejpam-4920	127	8	hop	hop	NOUN
ejpam-4920	127	9	dominating	dominating	NOUN
ejpam-4920	127	10	set	set	VERB
ejpam-4920	127	11	in	in	ADP
ejpam-4920	127	12	g.	g.	PROPN
ejpam-4920	127	13	thus	thus	ADV
ejpam-4920	127	14	,	,	PUNCT
ejpam-4920	127	15	fzg(g	fzg(g	X
ejpam-4920	127	16	)	)	PUNCT
ejpam-4920	127	17	=	=	SYM
ejpam-4920	127	18	4	4	NUM
ejpam-4920	127	19	theorem	theorem	NOUN
ejpam-4920	127	20	2	2	NUM
ejpam-4920	127	21	.	.	PUNCT
ejpam-4920	128	1	let	let	VERB
ejpam-4920	128	2	r	r	NOUN
ejpam-4920	128	3	,	,	PUNCT
ejpam-4920	128	4	q	q	NOUN
ejpam-4920	128	5	∈	∈	PROPN
ejpam-4920	128	6	n	n	NOUN
ejpam-4920	128	7	with	with	ADP
ejpam-4920	128	8	2	2	NUM
ejpam-4920	128	9	≤	≤	NOUN
ejpam-4920	128	10	r	r	NOUN
ejpam-4920	128	11	≤	≤	PUNCT
ejpam-4920	128	12	q.	q.	NOUN
ejpam-4920	128	13	then	then	ADV
ejpam-4920	128	14	there	there	PRON
ejpam-4920	128	15	exists	exist	VERB
ejpam-4920	128	16	a	a	DET
ejpam-4920	128	17	connected	connected	ADJ
ejpam-4920	128	18	graph	graph	NOUN
ejpam-4920	128	19	k	k	PRON
ejpam-4920	128	20	such	such	ADJ
ejpam-4920	128	21	that	that	PRON
ejpam-4920	128	22	γh(k	γh(k	PUNCT
ejpam-4920	128	23	)	)	PUNCT
ejpam-4920	129	1	=	=	SYM
ejpam-4920	129	2	r	r	NOUN
ejpam-4920	129	3	and	and	CCONJ
ejpam-4920	129	4	γzh(k	γzh(k	PROPN
ejpam-4920	129	5	)	)	PUNCT
ejpam-4920	129	6	=	=	PUNCT
ejpam-4920	129	7	q.	q.	NOUN
ejpam-4920	129	8	proof	proof	NOUN
ejpam-4920	129	9	.	.	PUNCT
ejpam-4920	130	1	suppose	suppose	VERB
ejpam-4920	130	2	that	that	SCONJ
ejpam-4920	130	3	r	r	NOUN
ejpam-4920	130	4	<	<	X
ejpam-4920	130	5	q.	q.	NOUN
ejpam-4920	130	6	let	let	VERB
ejpam-4920	130	7	l	l	NOUN
ejpam-4920	130	8	=	=	PUNCT
ejpam-4920	130	9	q	q	NOUN
ejpam-4920	131	1	−	−	NOUN
ejpam-4920	131	2	r	r	NOUN
ejpam-4920	131	3	and	and	CCONJ
ejpam-4920	131	4	consider	consider	VERB
ejpam-4920	131	5	the	the	DET
ejpam-4920	131	6	graph	graph	NOUN
ejpam-4920	131	7	k	k	ADV
ejpam-4920	131	8	below	below	ADV
ejpam-4920	131	9	.	.	PUNCT
ejpam-4920	132	1	k	k	X
ejpam-4920	132	2	:	:	PUNCT
ejpam-4920	133	1	x1	x1	NUM
ejpam-4920	134	1	x2	x2	NOUN
ejpam-4920	134	2	x3	x3	VERB
ejpam-4920	135	1	xr−1	xr−1	PROPN
ejpam-4920	135	2	xr	xr	PROPN
ejpam-4920	135	3	.	.	PUNCT
ejpam-4920	135	4	..	..	PUNCT
ejpam-4920	135	5	.	.	PUNCT
ejpam-4920	135	6	.	.	PUNCT
ejpam-4920	135	7	.	.	PUNCT
ejpam-4920	136	1	y1	y1	INTJ
ejpam-4920	136	2	y2	y2	NOUN
ejpam-4920	136	3	yl−1	yl−1	NOUN
ejpam-4920	136	4	yl	yl	NOUN
ejpam-4920	136	5	figure	figure	NOUN
ejpam-4920	136	6	2	2	NUM
ejpam-4920	136	7	:	:	PUNCT
ejpam-4920	136	8	graph	graph	NOUN
ejpam-4920	136	9	k	k	PROPN
ejpam-4920	136	10	with	with	ADP
ejpam-4920	136	11	γh(k	γh(k	NUM
ejpam-4920	136	12	)	)	PUNCT
ejpam-4920	136	13	<	<	X
ejpam-4920	136	14	γzh(k	γzh(k	PROPN
ejpam-4920	136	15	)	)	PUNCT
ejpam-4920	136	16	let	let	VERB
ejpam-4920	136	17	a	a	PRON
ejpam-4920	136	18	=	=	SYM
ejpam-4920	136	19	{	{	PUNCT
ejpam-4920	136	20	x1	x1	PROPN
ejpam-4920	136	21	,	,	PUNCT
ejpam-4920	136	22	x2	x2	PROPN
ejpam-4920	136	23	,	,	PUNCT
ejpam-4920	136	24	.	.	PUNCT
ejpam-4920	136	25	.	.	PUNCT
ejpam-4920	137	1	.	.	PUNCT
ejpam-4920	138	1	,	,	PUNCT
ejpam-4920	138	2	xr	xr	X
ejpam-4920	138	3	}	}	PUNCT
ejpam-4920	138	4	and	and	CCONJ
ejpam-4920	138	5	b	b	X
ejpam-4920	138	6	=	=	SYM
ejpam-4920	138	7	{	{	PUNCT
ejpam-4920	138	8	x1	x1	PROPN
ejpam-4920	138	9	,	,	PUNCT
ejpam-4920	138	10	x2	x2	PROPN
ejpam-4920	138	11	,	,	PUNCT
ejpam-4920	138	12	.	.	PUNCT
ejpam-4920	138	13	.	.	PUNCT
ejpam-4920	139	1	.	.	PUNCT
ejpam-4920	140	1	,	,	PUNCT
ejpam-4920	140	2	xr	xr	PROPN
ejpam-4920	140	3	,	,	PUNCT
ejpam-4920	140	4	y1	y1	PROPN
ejpam-4920	140	5	,	,	PUNCT
ejpam-4920	140	6	y2	y2	PROPN
ejpam-4920	140	7	,	,	PUNCT
ejpam-4920	140	8	.	.	PUNCT
ejpam-4920	140	9	.	.	PUNCT
ejpam-4920	141	1	.	.	PUNCT
ejpam-4920	142	1	,	,	PUNCT
ejpam-4920	142	2	yl	yl	NOUN
ejpam-4920	142	3	}	}	PUNCT
ejpam-4920	142	4	.	.	PUNCT
ejpam-4920	143	1	then	then	ADV
ejpam-4920	143	2	a	a	PRON
ejpam-4920	143	3	is	be	AUX
ejpam-4920	143	4	a	a	DET
ejpam-4920	143	5	minimum	minimum	ADJ
ejpam-4920	143	6	hop	hop	NOUN
ejpam-4920	143	7	dominating	dominating	NOUN
ejpam-4920	143	8	set	set	NOUN
ejpam-4920	143	9	of	of	ADP
ejpam-4920	143	10	k.	k.	PROPN
ejpam-4920	143	11	thus	thus	ADV
ejpam-4920	143	12	,	,	PUNCT
ejpam-4920	143	13	γh(k	γh(k	X
ejpam-4920	143	14	)	)	PUNCT
ejpam-4920	144	1	=	=	VERB
ejpam-4920	144	2	r.	r.	PROPN
ejpam-4920	144	3	observe	observe	VERB
ejpam-4920	144	4	that	that	SCONJ
ejpam-4920	144	5	b	b	PROPN
ejpam-4920	144	6	is	be	AUX
ejpam-4920	144	7	a	a	DET
ejpam-4920	144	8	minimum	minimum	ADJ
ejpam-4920	144	9	zero	zero	NUM
ejpam-4920	144	10	forcing	force	VERB
ejpam-4920	144	11	set	set	NOUN
ejpam-4920	144	12	of	of	ADP
ejpam-4920	144	13	k.	k.	PROPN
ejpam-4920	144	14	since	since	SCONJ
ejpam-4920	144	15	a	a	DET
ejpam-4920	144	16	⊆	⊆	NUM
ejpam-4920	144	17	b	b	NOUN
ejpam-4920	144	18	,	,	PUNCT
ejpam-4920	144	19	it	it	PRON
ejpam-4920	144	20	follows	follow	VERB
ejpam-4920	144	21	that	that	SCONJ
ejpam-4920	144	22	b	b	NOUN
ejpam-4920	144	23	is	be	AUX
ejpam-4920	144	24	also	also	ADV
ejpam-4920	144	25	a	a	DET
ejpam-4920	144	26	hop	hop	NOUN
ejpam-4920	144	27	dominating	dominating	NOUN
ejpam-4920	144	28	set	set	NOUN
ejpam-4920	144	29	of	of	ADP
ejpam-4920	144	30	k.	k.	PROPN
ejpam-4920	144	31	hence	hence	PROPN
ejpam-4920	144	32	,	,	PUNCT
ejpam-4920	144	33	b	b	PROPN
ejpam-4920	144	34	is	be	AUX
ejpam-4920	144	35	a	a	DET
ejpam-4920	144	36	minimum	minimum	ADJ
ejpam-4920	144	37	zero	zero	NUM
ejpam-4920	144	38	forcing	force	VERB
ejpam-4920	144	39	hop	hop	NOUN
ejpam-4920	144	40	dominating	dominating	NOUN
ejpam-4920	144	41	set	set	NOUN
ejpam-4920	144	42	of	of	ADP
ejpam-4920	144	43	k.	k.	PROPN
ejpam-4920	144	44	consequently	consequently	ADV
ejpam-4920	144	45	,	,	PUNCT
ejpam-4920	144	46	γh(k	γh(k	X
ejpam-4920	144	47	)	)	PUNCT
ejpam-4920	145	1	=	=	PUNCT
ejpam-4920	145	2	r	r	NOUN
ejpam-4920	145	3	<	<	X
ejpam-4920	145	4	q	q	NOUN
ejpam-4920	145	5	=	=	PUNCT
ejpam-4920	145	6	l	l	NOUN
ejpam-4920	146	1	+	+	CCONJ
ejpam-4920	146	2	r	r	NOUN
ejpam-4920	146	3	=	=	SYM
ejpam-4920	146	4	γzh(k	γzh(k	PROPN
ejpam-4920	146	5	)	)	PUNCT
ejpam-4920	146	6	.	.	PUNCT
ejpam-4920	147	1	for	for	ADP
ejpam-4920	147	2	r	r	NOUN
ejpam-4920	147	3	=	=	SYM
ejpam-4920	147	4	q	q	NOUN
ejpam-4920	147	5	,	,	PUNCT
ejpam-4920	147	6	consider	consider	VERB
ejpam-4920	147	7	a	a	DET
ejpam-4920	147	8	complete	complete	ADJ
ejpam-4920	147	9	graph	graph	NOUN
ejpam-4920	147	10	g	g	NOUN
ejpam-4920	147	11	with	with	ADP
ejpam-4920	147	12	order	order	NOUN
ejpam-4920	147	13	r.	r.	PROPN
ejpam-4920	147	14	then	then	ADV
ejpam-4920	147	15	the	the	DET
ejpam-4920	147	16	sharpness	sharpness	NOUN
ejpam-4920	147	17	of	of	ADP
ejpam-4920	147	18	γzh(g	γzh(g	NOUN
ejpam-4920	147	19	)	)	PUNCT
ejpam-4920	147	20	and	and	CCONJ
ejpam-4920	147	21	γh(g	γh(g	NOUN
ejpam-4920	147	22	)	)	PUNCT
ejpam-4920	147	23	follows	follow	VERB
ejpam-4920	147	24	.	.	PUNCT
ejpam-4920	148	1	j.	j.	PROPN
ejpam-4920	148	2	u.	u.	PROPN
ejpam-4920	148	3	manditong	manditong	PROPN
ejpam-4920	148	4	et	et	PROPN
ejpam-4920	148	5	al	al	PROPN
ejpam-4920	148	6	.	.	PUNCT
ejpam-4920	148	7	/	/	SYM
ejpam-4920	148	8	eur	eur	PROPN
ejpam-4920	148	9	.	.	PUNCT
ejpam-4920	149	1	j.	j.	PROPN
ejpam-4920	149	2	pure	pure	PROPN
ejpam-4920	149	3	appl	appl	PROPN
ejpam-4920	149	4	.	.	PROPN
ejpam-4920	149	5	math	math	PROPN
ejpam-4920	149	6	,	,	PUNCT
ejpam-4920	149	7	17	17	NUM
ejpam-4920	149	8	(	(	PUNCT
ejpam-4920	149	9	1	1	NUM
ejpam-4920	149	10	)	)	PUNCT
ejpam-4920	149	11	(	(	PUNCT
ejpam-4920	149	12	2024	2024	NUM
ejpam-4920	149	13	)	)	PUNCT
ejpam-4920	149	14	,	,	PUNCT
ejpam-4920	149	15	324	324	NUM
ejpam-4920	149	16	-	-	SYM
ejpam-4920	149	17	337	337	NUM
ejpam-4920	149	18	330	330	NUM
ejpam-4920	149	19	the	the	DET
ejpam-4920	149	20	next	next	ADJ
ejpam-4920	149	21	definition	definition	NOUN
ejpam-4920	149	22	will	will	AUX
ejpam-4920	149	23	be	be	AUX
ejpam-4920	149	24	used	use	VERB
ejpam-4920	149	25	to	to	PART
ejpam-4920	149	26	calculate	calculate	VERB
ejpam-4920	149	27	the	the	DET
ejpam-4920	149	28	exact	exact	ADJ
ejpam-4920	149	29	value	value	NOUN
ejpam-4920	149	30	of	of	ADP
ejpam-4920	149	31	parameter	parameter	NOUN
ejpam-4920	149	32	of	of	ADP
ejpam-4920	149	33	the	the	DET
ejpam-4920	149	34	join	join	NOUN
ejpam-4920	149	35	of	of	ADP
ejpam-4920	149	36	two	two	NUM
ejpam-4920	149	37	graphs	graph	NOUN
ejpam-4920	149	38	.	.	PUNCT
ejpam-4920	150	1	definition	definition	NOUN
ejpam-4920	150	2	2	2	NUM
ejpam-4920	150	3	.	.	PUNCT
ejpam-4920	151	1	let	let	VERB
ejpam-4920	151	2	j	j	PROPN
ejpam-4920	151	3	be	be	AUX
ejpam-4920	151	4	any	any	DET
ejpam-4920	151	5	graph	graph	NOUN
ejpam-4920	151	6	.	.	PUNCT
ejpam-4920	152	1	then	then	ADV
ejpam-4920	152	2	f	f	PROPN
ejpam-4920	152	3	⊆	⊆	NUM
ejpam-4920	152	4	v	v	PROPN
ejpam-4920	152	5	(	(	PUNCT
ejpam-4920	152	6	j	j	NOUN
ejpam-4920	152	7	)	)	PUNCT
ejpam-4920	152	8	is	be	AUX
ejpam-4920	152	9	called	call	VERB
ejpam-4920	152	10	a	a	DET
ejpam-4920	152	11	zero	zero	NUM
ejpam-4920	152	12	forcing	force	VERB
ejpam-4920	152	13	pointwise	pointwise	PROPN
ejpam-4920	152	14	non	non	ADJ
ejpam-4920	152	15	-	-	ADJ
ejpam-4920	152	16	dominating	dominating	ADJ
ejpam-4920	152	17	(	(	PUNCT
ejpam-4920	152	18	zfpnd	zfpnd	NOUN
ejpam-4920	152	19	)	)	PUNCT
ejpam-4920	152	20	in	in	ADP
ejpam-4920	152	21	j	j	PROPN
ejpam-4920	152	22	if	if	SCONJ
ejpam-4920	152	23	f	f	PROPN
ejpam-4920	152	24	is	be	AUX
ejpam-4920	152	25	both	both	PRON
ejpam-4920	152	26	a	a	DET
ejpam-4920	152	27	zero	zero	NUM
ejpam-4920	152	28	forcing	forcing	NOUN
ejpam-4920	152	29	and	and	CCONJ
ejpam-4920	152	30	a	a	DET
ejpam-4920	152	31	pointwise	pointwise	ADJ
ejpam-4920	152	32	nondominating	nondominate	VERB
ejpam-4920	152	33	(	(	PUNCT
ejpam-4920	152	34	pnd	pnd	NOUN
ejpam-4920	152	35	)	)	PUNCT
ejpam-4920	152	36	in	in	ADP
ejpam-4920	152	37	j	j	PROPN
ejpam-4920	152	38	.	.	PUNCT
ejpam-4920	153	1	the	the	DET
ejpam-4920	153	2	minimum	minimum	ADJ
ejpam-4920	153	3	cardinality	cardinality	NOUN
ejpam-4920	153	4	among	among	ADP
ejpam-4920	153	5	all	all	DET
ejpam-4920	153	6	zero	zero	NUM
ejpam-4920	153	7	forcing	force	VERB
ejpam-4920	153	8	pointwise	pointwise	NOUN
ejpam-4920	153	9	nondominating	nondominate	VERB
ejpam-4920	153	10	(	(	PUNCT
ejpam-4920	153	11	zfpnd	zfpnd	NOUN
ejpam-4920	153	12	)	)	PUNCT
ejpam-4920	153	13	sets	set	NOUN
ejpam-4920	153	14	in	in	ADP
ejpam-4920	153	15	j	j	PROPN
ejpam-4920	153	16	,	,	PUNCT
ejpam-4920	153	17	denoted	denote	VERB
ejpam-4920	153	18	by	by	ADP
ejpam-4920	153	19	zfpnd(j	zfpnd(j	PROPN
ejpam-4920	153	20	)	)	PUNCT
ejpam-4920	153	21	,	,	PUNCT
ejpam-4920	153	22	is	be	AUX
ejpam-4920	153	23	called	call	VERB
ejpam-4920	153	24	the	the	DET
ejpam-4920	153	25	zero	zero	NUM
ejpam-4920	153	26	forcing	force	VERB
ejpam-4920	153	27	pointwise	pointwise	PROPN
ejpam-4920	153	28	non	non	ADJ
ejpam-4920	153	29	-	-	ADJ
ejpam-4920	153	30	domination	domination	ADJ
ejpam-4920	153	31	number	number	NOUN
ejpam-4920	153	32	of	of	ADP
ejpam-4920	153	33	j	j	PROPN
ejpam-4920	153	34	.	.	PUNCT
ejpam-4920	154	1	any	any	DET
ejpam-4920	154	2	zfpnd	zfpnd	NOUN
ejpam-4920	154	3	set	set	VERB
ejpam-4920	154	4	f	f	PROPN
ejpam-4920	154	5	with	with	ADP
ejpam-4920	154	6	|f	|f	PROPN
ejpam-4920	155	1	|	|	ADV
ejpam-4920	155	2	=	=	SYM
ejpam-4920	155	3	zfpnd(j	zfpnd(j	NUM
ejpam-4920	155	4	)	)	PUNCT
ejpam-4920	155	5	,	,	PUNCT
ejpam-4920	155	6	is	be	AUX
ejpam-4920	155	7	called	call	VERB
ejpam-4920	155	8	the	the	DET
ejpam-4920	155	9	minimum	minimum	ADJ
ejpam-4920	155	10	zfpnd	zfpnd	NOUN
ejpam-4920	155	11	set	set	VERB
ejpam-4920	155	12	or	or	CCONJ
ejpam-4920	155	13	a	a	DET
ejpam-4920	155	14	zfpnd	zfpnd	NOUN
ejpam-4920	155	15	-	-	PUNCT
ejpam-4920	155	16	set	set	NOUN
ejpam-4920	155	17	of	of	ADP
ejpam-4920	155	18	j	j	PROPN
ejpam-4920	155	19	.	.	PUNCT
ejpam-4920	155	20	example	example	NOUN
ejpam-4920	156	1	2	2	NUM
ejpam-4920	156	2	.	.	X
ejpam-4920	156	3	consider	consider	VERB
ejpam-4920	156	4	the	the	DET
ejpam-4920	156	5	graph	graph	NOUN
ejpam-4920	156	6	g	g	NOUN
ejpam-4920	156	7	below	below	ADV
ejpam-4920	156	8	.	.	PUNCT
ejpam-4920	157	1	a	a	DET
ejpam-4920	157	2	b	b	NOUN
ejpam-4920	157	3	c	c	NOUN
ejpam-4920	157	4	d	d	X
ejpam-4920	157	5	e	e	X
ejpam-4920	157	6	f	f	PROPN
ejpam-4920	157	7	g	g	PROPN
ejpam-4920	157	8	hg	hg	X
ejpam-4920	157	9	:	:	PUNCT
ejpam-4920	157	10	i	i	PRON
ejpam-4920	157	11	figure	figure	VERB
ejpam-4920	157	12	3	3	NUM
ejpam-4920	157	13	:	:	PUNCT
ejpam-4920	157	14	a	a	DET
ejpam-4920	157	15	graph	graph	NOUN
ejpam-4920	157	16	g	g	NOUN
ejpam-4920	157	17	with	with	ADP
ejpam-4920	157	18	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	157	19	)	)	PUNCT
ejpam-4920	157	20	=	=	SYM
ejpam-4920	157	21	5	5	NUM
ejpam-4920	157	22	let	let	VERB
ejpam-4920	157	23	f	f	NOUN
ejpam-4920	157	24	=	=	PRON
ejpam-4920	157	25	{	{	PUNCT
ejpam-4920	157	26	a	a	DET
ejpam-4920	157	27	,	,	PUNCT
ejpam-4920	157	28	b	b	NOUN
ejpam-4920	157	29	,	,	PUNCT
ejpam-4920	157	30	e	e	NOUN
ejpam-4920	157	31	,	,	PUNCT
ejpam-4920	157	32	g	g	PROPN
ejpam-4920	157	33	,	,	PUNCT
ejpam-4920	157	34	h	h	NOUN
ejpam-4920	157	35	}	}	PUNCT
ejpam-4920	157	36	.	.	PUNCT
ejpam-4920	158	1	notice	notice	VERB
ejpam-4920	158	2	that	that	SCONJ
ejpam-4920	158	3	c	c	X
ejpam-4920	158	4	,	,	PUNCT
ejpam-4920	158	5	f	f	AUX
ejpam-4920	158	6	,	,	PUNCT
ejpam-4920	158	7	i	i	PRON
ejpam-4920	158	8	/∈	/∈	PUNCT
ejpam-4920	158	9	ng(a	ng(a	NUM
ejpam-4920	158	10	)	)	PUNCT
ejpam-4920	158	11	and	and	CCONJ
ejpam-4920	158	12	d	d	NOUN
ejpam-4920	158	13	/∈	/∈	NOUN
ejpam-4920	158	14	ng(g	ng(g	NUM
ejpam-4920	158	15	)	)	PUNCT
ejpam-4920	158	16	.	.	PUNCT
ejpam-4920	159	1	it	it	PRON
ejpam-4920	159	2	follows	follow	VERB
ejpam-4920	159	3	that	that	SCONJ
ejpam-4920	159	4	f	f	PROPN
ejpam-4920	159	5	is	be	AUX
ejpam-4920	159	6	a	a	DET
ejpam-4920	159	7	pnd	pnd	NOUN
ejpam-4920	159	8	set	set	NOUN
ejpam-4920	159	9	of	of	ADP
ejpam-4920	159	10	g.	g.	PROPN
ejpam-4920	159	11	since	since	SCONJ
ejpam-4920	159	12	f	f	PROPN
ejpam-4920	159	13	is	be	AUX
ejpam-4920	159	14	a	a	DET
ejpam-4920	159	15	minimum	minimum	ADJ
ejpam-4920	159	16	zero	zero	NUM
ejpam-4920	159	17	forcing	force	VERB
ejpam-4920	159	18	set	set	NOUN
ejpam-4920	159	19	of	of	ADP
ejpam-4920	159	20	g	g	PROPN
ejpam-4920	159	21	,	,	PUNCT
ejpam-4920	159	22	f	f	PROPN
ejpam-4920	159	23	is	be	AUX
ejpam-4920	159	24	a	a	DET
ejpam-4920	159	25	minimum	minimum	ADJ
ejpam-4920	159	26	zfpnd	zfpnd	NOUN
ejpam-4920	159	27	set	set	NOUN
ejpam-4920	159	28	of	of	ADP
ejpam-4920	159	29	g.	g.	PROPN
ejpam-4920	159	30	thus	thus	ADV
ejpam-4920	159	31	,	,	PUNCT
ejpam-4920	159	32	zfpnd(g	zfpnd(g	ADJ
ejpam-4920	159	33	)	)	PUNCT
ejpam-4920	160	1	=	=	SYM
ejpam-4920	160	2	5	5	X
ejpam-4920	160	3	.	.	PUNCT
ejpam-4920	160	4	consequently	consequently	ADV
ejpam-4920	160	5	,	,	PUNCT
ejpam-4920	160	6	f	f	PROPN
ejpam-4920	160	7	is	be	AUX
ejpam-4920	160	8	a	a	DET
ejpam-4920	160	9	zfpnd	zfpnd	NOUN
ejpam-4920	160	10	-	-	PUNCT
ejpam-4920	160	11	set	set	NOUN
ejpam-4920	160	12	of	of	ADP
ejpam-4920	160	13	g.	g.	PROPN
ejpam-4920	160	14	proposition	proposition	PROPN
ejpam-4920	160	15	3	3	X
ejpam-4920	160	16	.	.	PUNCT
ejpam-4920	161	1	let	let	VERB
ejpam-4920	161	2	g	g	NOUN
ejpam-4920	161	3	be	be	AUX
ejpam-4920	161	4	any	any	DET
ejpam-4920	161	5	graph	graph	NOUN
ejpam-4920	161	6	.	.	PUNCT
ejpam-4920	162	1	then	then	ADV
ejpam-4920	162	2	every	every	DET
ejpam-4920	162	3	zfpnd	zfpnd	NOUN
ejpam-4920	162	4	set	set	VERB
ejpam-4920	162	5	f	f	PROPN
ejpam-4920	162	6	⊆	⊆	NUM
ejpam-4920	162	7	v	v	NOUN
ejpam-4920	162	8	(	(	PUNCT
ejpam-4920	162	9	g	g	NOUN
ejpam-4920	162	10	)	)	PUNCT
ejpam-4920	162	11	is	be	AUX
ejpam-4920	162	12	a	a	DET
ejpam-4920	162	13	pnd	pnd	NOUN
ejpam-4920	162	14	.	.	PUNCT
ejpam-4920	163	1	but	but	CCONJ
ejpam-4920	163	2	the	the	DET
ejpam-4920	163	3	converse	converse	NOUN
ejpam-4920	163	4	is	be	AUX
ejpam-4920	163	5	not	not	PART
ejpam-4920	163	6	true	true	ADJ
ejpam-4920	163	7	.	.	PUNCT
ejpam-4920	164	1	proof	proof	NOUN
ejpam-4920	164	2	.	.	PUNCT
ejpam-4920	165	1	let	let	VERB
ejpam-4920	165	2	f	f	PRON
ejpam-4920	165	3	be	be	AUX
ejpam-4920	165	4	a	a	DET
ejpam-4920	165	5	zfpnd	zfpnd	NOUN
ejpam-4920	165	6	.	.	PUNCT
ejpam-4920	166	1	then	then	ADV
ejpam-4920	166	2	f	f	PROPN
ejpam-4920	166	3	is	be	AUX
ejpam-4920	166	4	a	a	DET
ejpam-4920	166	5	pnd	pnd	NOUN
ejpam-4920	166	6	set	set	NOUN
ejpam-4920	166	7	(	(	PUNCT
ejpam-4920	166	8	by	by	ADP
ejpam-4920	166	9	definition	definition	NOUN
ejpam-4920	166	10	)	)	PUNCT
ejpam-4920	166	11	.	.	PUNCT
ejpam-4920	167	1	to	to	PART
ejpam-4920	167	2	see	see	VERB
ejpam-4920	167	3	that	that	SCONJ
ejpam-4920	167	4	the	the	DET
ejpam-4920	167	5	converse	converse	NOUN
ejpam-4920	167	6	is	be	AUX
ejpam-4920	167	7	not	not	PART
ejpam-4920	167	8	true	true	ADJ
ejpam-4920	167	9	,	,	PUNCT
ejpam-4920	167	10	consider	consider	VERB
ejpam-4920	167	11	the	the	DET
ejpam-4920	167	12	graph	graph	NOUN
ejpam-4920	167	13	g	g	NOUN
ejpam-4920	167	14	below	below	ADV
ejpam-4920	167	15	.	.	PUNCT
ejpam-4920	168	1	g	g	NOUN
ejpam-4920	168	2	:	:	PUNCT
ejpam-4920	168	3	f	f	PROPN
ejpam-4920	168	4	e	e	PROPN
ejpam-4920	168	5	dc	dc	PROPN
ejpam-4920	168	6	b	b	PROPN
ejpam-4920	168	7	a	a	DET
ejpam-4920	168	8	j.	j.	PROPN
ejpam-4920	168	9	u.	u.	PROPN
ejpam-4920	168	10	manditong	manditong	PROPN
ejpam-4920	168	11	et	et	PROPN
ejpam-4920	168	12	al	al	PROPN
ejpam-4920	168	13	.	.	PUNCT
ejpam-4920	168	14	/	/	SYM
ejpam-4920	168	15	eur	eur	PROPN
ejpam-4920	168	16	.	.	PUNCT
ejpam-4920	169	1	j.	j.	PROPN
ejpam-4920	169	2	pure	pure	PROPN
ejpam-4920	169	3	appl	appl	PROPN
ejpam-4920	169	4	.	.	PROPN
ejpam-4920	169	5	math	math	PROPN
ejpam-4920	169	6	,	,	PUNCT
ejpam-4920	169	7	17	17	NUM
ejpam-4920	169	8	(	(	PUNCT
ejpam-4920	169	9	1	1	NUM
ejpam-4920	169	10	)	)	PUNCT
ejpam-4920	169	11	(	(	PUNCT
ejpam-4920	169	12	2024	2024	NUM
ejpam-4920	169	13	)	)	PUNCT
ejpam-4920	169	14	,	,	PUNCT
ejpam-4920	169	15	324	324	NUM
ejpam-4920	169	16	-	-	SYM
ejpam-4920	169	17	337	337	NUM
ejpam-4920	169	18	331	331	NUM
ejpam-4920	169	19	let	let	VERB
ejpam-4920	169	20	n	n	NOUN
ejpam-4920	169	21	=	=	PRON
ejpam-4920	169	22	{	{	PUNCT
ejpam-4920	169	23	a	a	DET
ejpam-4920	169	24	,	,	PUNCT
ejpam-4920	169	25	b	b	NOUN
ejpam-4920	169	26	,	,	PUNCT
ejpam-4920	169	27	c	c	NOUN
ejpam-4920	169	28	}	}	PUNCT
ejpam-4920	169	29	.	.	PUNCT
ejpam-4920	170	1	observe	observe	VERB
ejpam-4920	170	2	that	that	SCONJ
ejpam-4920	170	3	d	d	NOUN
ejpam-4920	170	4	,	,	PUNCT
ejpam-4920	170	5	e	e	NOUN
ejpam-4920	170	6	,	,	PUNCT
ejpam-4920	170	7	f	f	PROPN
ejpam-4920	170	8	/∈	/∈	PUNCT
ejpam-4920	170	9	ng(a	ng(a	NUM
ejpam-4920	170	10	)	)	PUNCT
ejpam-4920	170	11	.	.	PUNCT
ejpam-4920	171	1	it	it	PRON
ejpam-4920	171	2	follows	follow	VERB
ejpam-4920	171	3	that	that	SCONJ
ejpam-4920	171	4	n	n	PRON
ejpam-4920	171	5	is	be	AUX
ejpam-4920	171	6	a	a	DET
ejpam-4920	171	7	pnd	pnd	NOUN
ejpam-4920	171	8	set	set	VERB
ejpam-4920	171	9	in	in	ADP
ejpam-4920	171	10	g.	g.	PROPN
ejpam-4920	171	11	however	however	ADV
ejpam-4920	171	12	,	,	PUNCT
ejpam-4920	171	13	n	n	PRON
ejpam-4920	171	14	is	be	AUX
ejpam-4920	171	15	not	not	PART
ejpam-4920	171	16	a	a	DET
ejpam-4920	171	17	zero	zero	NUM
ejpam-4920	171	18	forcing	forcing	NOUN
ejpam-4920	171	19	set	set	NOUN
ejpam-4920	171	20	in	in	ADP
ejpam-4920	171	21	g	g	PROPN
ejpam-4920	171	22	since	since	SCONJ
ejpam-4920	171	23	it	it	PRON
ejpam-4920	171	24	can	can	AUX
ejpam-4920	171	25	not	not	PART
ejpam-4920	171	26	forces	force	VERB
ejpam-4920	171	27	vertices	vertex	NOUN
ejpam-4920	171	28	e	e	NOUN
ejpam-4920	171	29	and	and	CCONJ
ejpam-4920	171	30	f	f	PROPN
ejpam-4920	171	31	.	.	PUNCT
ejpam-4920	172	1	hence	hence	ADV
ejpam-4920	172	2	,	,	PUNCT
ejpam-4920	172	3	n	n	PRON
ejpam-4920	172	4	is	be	AUX
ejpam-4920	172	5	not	not	PART
ejpam-4920	172	6	a	a	DET
ejpam-4920	172	7	zfpnd	zfpnd	NOUN
ejpam-4920	172	8	set	set	NOUN
ejpam-4920	172	9	of	of	ADP
ejpam-4920	172	10	g	g	NOUN
ejpam-4920	172	11	,	,	PUNCT
ejpam-4920	172	12	and	and	CCONJ
ejpam-4920	172	13	so	so	ADV
ejpam-4920	172	14	the	the	DET
ejpam-4920	172	15	assertion	assertion	NOUN
ejpam-4920	172	16	follows	follow	VERB
ejpam-4920	172	17	.	.	PUNCT
ejpam-4920	173	1	theorem	theorem	NOUN
ejpam-4920	173	2	3	3	X
ejpam-4920	173	3	.	.	PUNCT
ejpam-4920	174	1	let	let	VERB
ejpam-4920	174	2	g	g	NOUN
ejpam-4920	174	3	be	be	AUX
ejpam-4920	174	4	any	any	DET
ejpam-4920	174	5	graph	graph	NOUN
ejpam-4920	174	6	.	.	PUNCT
ejpam-4920	175	1	then	then	ADV
ejpam-4920	175	2	(	(	PUNCT
ejpam-4920	175	3	i	i	NOUN
ejpam-4920	175	4	)	)	PUNCT
ejpam-4920	175	5	pnd(g	pnd(g	ADP
ejpam-4920	175	6	)	)	PUNCT
ejpam-4920	175	7	≤	≤	NOUN
ejpam-4920	176	1	zfpnd(g	zfpnd(g	PROPN
ejpam-4920	176	2	)	)	PUNCT
ejpam-4920	176	3	;	;	PUNCT
ejpam-4920	176	4	(	(	PUNCT
ejpam-4920	176	5	ii	ii	NOUN
ejpam-4920	176	6	)	)	PUNCT
ejpam-4920	176	7	1	1	NUM
ejpam-4920	176	8	≤	≤	NUM
ejpam-4920	176	9	zfpnd(g	zfpnd(g	ADJ
ejpam-4920	176	10	)	)	PUNCT
ejpam-4920	177	1	≤	≤	NOUN
ejpam-4920	177	2	|v	|v	X
ejpam-4920	177	3	(	(	PUNCT
ejpam-4920	177	4	g)|	g)|	NOUN
ejpam-4920	177	5	;	;	PUNCT
ejpam-4920	177	6	and	and	CCONJ
ejpam-4920	177	7	(	(	PUNCT
ejpam-4920	177	8	iii	iii	X
ejpam-4920	177	9	)	)	PUNCT
ejpam-4920	177	10	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	177	11	)	)	PUNCT
ejpam-4920	177	12	=	=	SYM
ejpam-4920	177	13	1	1	NUM
ejpam-4920	177	14	if	if	SCONJ
ejpam-4920	177	15	and	and	CCONJ
ejpam-4920	177	16	only	only	ADV
ejpam-4920	177	17	if	if	SCONJ
ejpam-4920	177	18	g	g	PROPN
ejpam-4920	177	19	=	=	SYM
ejpam-4920	177	20	k1	k1	PROPN
ejpam-4920	177	21	.	.	PUNCT
ejpam-4920	178	1	proof	proof	NOUN
ejpam-4920	178	2	.	.	PUNCT
ejpam-4920	179	1	(	(	PUNCT
ejpam-4920	179	2	i	i	NOUN
ejpam-4920	179	3	)	)	PUNCT
ejpam-4920	179	4	let	let	VERB
ejpam-4920	179	5	g	g	NOUN
ejpam-4920	179	6	be	be	AUX
ejpam-4920	179	7	any	any	DET
ejpam-4920	179	8	graph	graph	NOUN
ejpam-4920	179	9	and	and	CCONJ
ejpam-4920	179	10	let	let	VERB
ejpam-4920	179	11	f	f	PRON
ejpam-4920	179	12	be	be	AUX
ejpam-4920	179	13	a	a	DET
ejpam-4920	179	14	minimum	minimum	ADJ
ejpam-4920	179	15	zfpnd	zfpnd	NOUN
ejpam-4920	179	16	set	set	NOUN
ejpam-4920	179	17	of	of	ADP
ejpam-4920	179	18	g.	g.	PROPN
ejpam-4920	179	19	then	then	ADV
ejpam-4920	179	20	zfpnd(g	zfpnd(g	X
ejpam-4920	179	21	)	)	PUNCT
ejpam-4920	179	22	=	=	SYM
ejpam-4920	180	1	|f	|f	PROPN
ejpam-4920	181	1	|	|	ADV
ejpam-4920	181	2	and	and	CCONJ
ejpam-4920	181	3	f	f	PROPN
ejpam-4920	181	4	is	be	AUX
ejpam-4920	181	5	a	a	DET
ejpam-4920	181	6	pnd	pnd	NOUN
ejpam-4920	181	7	set	set	NOUN
ejpam-4920	181	8	of	of	ADP
ejpam-4920	181	9	g.	g.	PROPN
ejpam-4920	181	10	since	since	SCONJ
ejpam-4920	181	11	pnd(g	pnd(g	PROPN
ejpam-4920	181	12	)	)	PUNCT
ejpam-4920	181	13	is	be	AUX
ejpam-4920	181	14	the	the	DET
ejpam-4920	181	15	minimum	minimum	ADJ
ejpam-4920	181	16	cardinality	cardinality	NOUN
ejpam-4920	181	17	among	among	ADP
ejpam-4920	181	18	all	all	DET
ejpam-4920	181	19	pnd	pnd	NOUN
ejpam-4920	181	20	sets	set	NOUN
ejpam-4920	181	21	in	in	ADP
ejpam-4920	181	22	g	g	NOUN
ejpam-4920	181	23	,	,	PUNCT
ejpam-4920	181	24	it	it	PRON
ejpam-4920	181	25	follows	follow	VERB
ejpam-4920	181	26	that	that	SCONJ
ejpam-4920	181	27	pnd(g	pnd(g	ADP
ejpam-4920	181	28	)	)	PUNCT
ejpam-4920	181	29	≤	≤	NOUN
ejpam-4920	181	30	|f	|f	PUNCT
ejpam-4920	182	1	|	|	ADV
ejpam-4920	182	2	=	=	SYM
ejpam-4920	182	3	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	182	4	)	)	PUNCT
ejpam-4920	182	5	.	.	PUNCT
ejpam-4920	183	1	(	(	PUNCT
ejpam-4920	183	2	ii	ii	NOUN
ejpam-4920	183	3	)	)	PUNCT
ejpam-4920	183	4	since	since	SCONJ
ejpam-4920	183	5	pnd(g	pnd(g	PROPN
ejpam-4920	183	6	)	)	PUNCT
ejpam-4920	183	7	≥	≥	NOUN
ejpam-4920	183	8	1	1	NUM
ejpam-4920	183	9	for	for	ADP
ejpam-4920	183	10	any	any	DET
ejpam-4920	183	11	graph	graph	NOUN
ejpam-4920	183	12	g	g	NOUN
ejpam-4920	183	13	,	,	PUNCT
ejpam-4920	183	14	we	we	PRON
ejpam-4920	183	15	have	have	VERB
ejpam-4920	183	16	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	183	17	)	)	PUNCT
ejpam-4920	183	18	≥	≥	NOUN
ejpam-4920	183	19	1	1	NUM
ejpam-4920	183	20	by	by	ADP
ejpam-4920	183	21	(	(	PUNCT
ejpam-4920	183	22	i	i	NOUN
ejpam-4920	183	23	)	)	PUNCT
ejpam-4920	183	24	.	.	PUNCT
ejpam-4920	184	1	moreover	moreover	ADV
ejpam-4920	184	2	,	,	PUNCT
ejpam-4920	184	3	since	since	SCONJ
ejpam-4920	184	4	any	any	DET
ejpam-4920	184	5	zfpnd	zfpnd	NOUN
ejpam-4920	184	6	set	set	NOUN
ejpam-4920	184	7	f	f	PROPN
ejpam-4920	184	8	is	be	AUX
ejpam-4920	184	9	always	always	ADV
ejpam-4920	184	10	a	a	DET
ejpam-4920	184	11	subset	subset	NOUN
ejpam-4920	184	12	of	of	ADP
ejpam-4920	184	13	v	v	NOUN
ejpam-4920	184	14	(	(	PUNCT
ejpam-4920	184	15	g	g	NOUN
ejpam-4920	184	16	)	)	PUNCT
ejpam-4920	184	17	,	,	PUNCT
ejpam-4920	184	18	it	it	PRON
ejpam-4920	184	19	follows	follow	VERB
ejpam-4920	184	20	that	that	SCONJ
ejpam-4920	184	21	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	184	22	)	)	PUNCT
ejpam-4920	185	1	≤	≤	NOUN
ejpam-4920	185	2	|v	|v	X
ejpam-4920	185	3	(	(	PUNCT
ejpam-4920	185	4	g)|	g)|	PROPN
ejpam-4920	185	5	.	.	PUNCT
ejpam-4920	186	1	therefore	therefore	ADV
ejpam-4920	186	2	,	,	PUNCT
ejpam-4920	186	3	1	1	NUM
ejpam-4920	186	4	≤	≤	NUM
ejpam-4920	186	5	zfpnd(g	zfpnd(g	ADJ
ejpam-4920	186	6	)	)	PUNCT
ejpam-4920	186	7	≤	≤	NOUN
ejpam-4920	186	8	|v	|v	X
ejpam-4920	186	9	(	(	PUNCT
ejpam-4920	186	10	g)|	g)|	NOUN
ejpam-4920	186	11	.	.	PUNCT
ejpam-4920	187	1	(	(	PUNCT
ejpam-4920	187	2	iii	iii	X
ejpam-4920	187	3	)	)	PUNCT
ejpam-4920	187	4	suppose	suppose	VERB
ejpam-4920	187	5	that	that	SCONJ
ejpam-4920	187	6	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	187	7	)	)	PUNCT
ejpam-4920	187	8	=	=	SYM
ejpam-4920	187	9	1	1	X
ejpam-4920	187	10	.	.	X
ejpam-4920	187	11	assume	assume	VERB
ejpam-4920	187	12	that	that	SCONJ
ejpam-4920	187	13	g	g	PROPN
ejpam-4920	187	14	̸=	̸=	PROPN
ejpam-4920	187	15	k1	k1	NOUN
ejpam-4920	187	16	.	.	PUNCT
ejpam-4920	188	1	if	if	SCONJ
ejpam-4920	188	2	g	g	PROPN
ejpam-4920	188	3	is	be	AUX
ejpam-4920	188	4	connected	connect	VERB
ejpam-4920	188	5	,	,	PUNCT
ejpam-4920	188	6	then	then	ADV
ejpam-4920	188	7	pnd(g	pnd(g	ADP
ejpam-4920	188	8	)	)	PUNCT
ejpam-4920	188	9	≥	≥	NOUN
ejpam-4920	188	10	2	2	NUM
ejpam-4920	188	11	,	,	PUNCT
ejpam-4920	188	12	a	a	DET
ejpam-4920	188	13	contradiction	contradiction	NOUN
ejpam-4920	188	14	.	.	PUNCT
ejpam-4920	189	1	assume	assume	VERB
ejpam-4920	189	2	that	that	SCONJ
ejpam-4920	189	3	g	g	PROPN
ejpam-4920	189	4	is	be	AUX
ejpam-4920	189	5	disconnected	disconnect	VERB
ejpam-4920	189	6	.	.	PUNCT
ejpam-4920	190	1	let	let	VERB
ejpam-4920	190	2	g1	g1	PROPN
ejpam-4920	190	3	,	,	PUNCT
ejpam-4920	190	4	.	.	PUNCT
ejpam-4920	190	5	.	.	PUNCT
ejpam-4920	191	1	.	.	PUNCT
ejpam-4920	192	1	,	,	PUNCT
ejpam-4920	192	2	gk	gk	PROPN
ejpam-4920	192	3	,	,	PUNCT
ejpam-4920	192	4	k	k	PROPN
ejpam-4920	192	5	≥	≥	NUM
ejpam-4920	192	6	2	2	NUM
ejpam-4920	192	7	be	be	AUX
ejpam-4920	192	8	components	component	NOUN
ejpam-4920	192	9	of	of	ADP
ejpam-4920	192	10	g.	g.	PROPN
ejpam-4920	192	11	then	then	ADV
ejpam-4920	192	12	z(g	z(g	NOUN
ejpam-4920	192	13	)	)	PUNCT
ejpam-4920	192	14	≥	≥	NOUN
ejpam-4920	192	15	2	2	NUM
ejpam-4920	192	16	.	.	PUNCT
ejpam-4920	193	1	since	since	SCONJ
ejpam-4920	193	2	every	every	DET
ejpam-4920	193	3	zfpnd	zfpnd	NOUN
ejpam-4920	193	4	set	set	VERB
ejpam-4920	193	5	is	be	AUX
ejpam-4920	193	6	a	a	DET
ejpam-4920	193	7	zero	zero	NUM
ejpam-4920	193	8	forcing	forcing	NOUN
ejpam-4920	193	9	,	,	PUNCT
ejpam-4920	193	10	we	we	PRON
ejpam-4920	193	11	have	have	VERB
ejpam-4920	193	12	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	193	13	)	)	PUNCT
ejpam-4920	193	14	≥	≥	NOUN
ejpam-4920	193	15	z(g	z(g	NOUN
ejpam-4920	193	16	)	)	PUNCT
ejpam-4920	193	17	.	.	PUNCT
ejpam-4920	194	1	thus	thus	ADV
ejpam-4920	194	2	,	,	PUNCT
ejpam-4920	194	3	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	194	4	)	)	PUNCT
ejpam-4920	194	5	≥	≥	NOUN
ejpam-4920	194	6	2	2	NUM
ejpam-4920	194	7	,	,	PUNCT
ejpam-4920	194	8	a	a	DET
ejpam-4920	194	9	contradiction	contradiction	NOUN
ejpam-4920	194	10	.	.	PUNCT
ejpam-4920	195	1	therefore	therefore	ADV
ejpam-4920	195	2	,	,	PUNCT
ejpam-4920	195	3	g	g	PROPN
ejpam-4920	195	4	=	=	SYM
ejpam-4920	195	5	k1	k1	PROPN
ejpam-4920	195	6	.	.	PUNCT
ejpam-4920	196	1	the	the	DET
ejpam-4920	196	2	converse	converse	NOUN
ejpam-4920	196	3	is	be	AUX
ejpam-4920	196	4	clear	clear	ADJ
ejpam-4920	196	5	.	.	PUNCT
ejpam-4920	197	1	theorem	theorem	ADJ
ejpam-4920	197	2	4	4	NUM
ejpam-4920	197	3	.	.	PUNCT
ejpam-4920	198	1	let	let	VERB
ejpam-4920	198	2	g	g	NOUN
ejpam-4920	198	3	be	be	AUX
ejpam-4920	198	4	non	non	ADJ
ejpam-4920	198	5	-	-	ADJ
ejpam-4920	198	6	trivial	trivial	ADJ
ejpam-4920	198	7	graph	graph	NOUN
ejpam-4920	198	8	.	.	PUNCT
ejpam-4920	199	1	then	then	ADV
ejpam-4920	199	2	zfpnd(g	zfpnd(g	X
ejpam-4920	199	3	)	)	PUNCT
ejpam-4920	199	4	=	=	SYM
ejpam-4920	200	1	|v	|v	PROPN
ejpam-4920	200	2	(	(	PUNCT
ejpam-4920	200	3	g)|	g)|	VERB
ejpam-4920	200	4	if	if	SCONJ
ejpam-4920	201	1	and	and	CCONJ
ejpam-4920	201	2	only	only	ADV
ejpam-4920	201	3	if	if	SCONJ
ejpam-4920	201	4	every	every	DET
ejpam-4920	201	5	component	component	NOUN
ejpam-4920	201	6	of	of	ADP
ejpam-4920	201	7	g	g	PROPN
ejpam-4920	201	8	is	be	AUX
ejpam-4920	201	9	complete	complete	ADJ
ejpam-4920	201	10	.	.	PUNCT
ejpam-4920	202	1	proof	proof	NOUN
ejpam-4920	202	2	.	.	PUNCT
ejpam-4920	203	1	suppose	suppose	VERB
ejpam-4920	203	2	that	that	SCONJ
ejpam-4920	203	3	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	203	4	)	)	PUNCT
ejpam-4920	204	1	=	=	SYM
ejpam-4920	204	2	|v	|v	PROPN
ejpam-4920	204	3	(	(	PUNCT
ejpam-4920	204	4	g)|	g)|	PROPN
ejpam-4920	204	5	.	.	PUNCT
ejpam-4920	205	1	then	then	ADV
ejpam-4920	205	2	v	v	X
ejpam-4920	205	3	(	(	PUNCT
ejpam-4920	205	4	g	g	NOUN
ejpam-4920	205	5	)	)	PUNCT
ejpam-4920	205	6	is	be	AUX
ejpam-4920	205	7	the	the	DET
ejpam-4920	205	8	minimum	minimum	ADJ
ejpam-4920	205	9	zfpnd	zfpnd	NOUN
ejpam-4920	205	10	set	set	VERB
ejpam-4920	205	11	in	in	ADP
ejpam-4920	205	12	g.	g.	PROPN
ejpam-4920	205	13	assume	assume	VERB
ejpam-4920	205	14	that	that	SCONJ
ejpam-4920	205	15	g	g	PROPN
ejpam-4920	205	16	is	be	AUX
ejpam-4920	205	17	connected	connect	VERB
ejpam-4920	205	18	.	.	PUNCT
ejpam-4920	206	1	suppose	suppose	VERB
ejpam-4920	206	2	further	far	ADV
ejpam-4920	206	3	that	that	SCONJ
ejpam-4920	206	4	g	g	PROPN
ejpam-4920	206	5	is	be	AUX
ejpam-4920	206	6	non	non	ADJ
ejpam-4920	206	7	-	-	ADJ
ejpam-4920	206	8	complete	complete	ADJ
ejpam-4920	206	9	.	.	PUNCT
ejpam-4920	207	1	then	then	ADV
ejpam-4920	207	2	dg(v	dg(v	NOUN
ejpam-4920	207	3	,	,	PUNCT
ejpam-4920	207	4	w	w	NOUN
ejpam-4920	207	5	)	)	PUNCT
ejpam-4920	207	6	=	=	SYM
ejpam-4920	207	7	2	2	NUM
ejpam-4920	207	8	for	for	ADP
ejpam-4920	207	9	some	some	DET
ejpam-4920	207	10	v	v	NOUN
ejpam-4920	207	11	,	,	PUNCT
ejpam-4920	207	12	w	w	PROPN
ejpam-4920	207	13	∈	∈	PROPN
ejpam-4920	207	14	v	v	ADP
ejpam-4920	207	15	(	(	PUNCT
ejpam-4920	207	16	g	g	NOUN
ejpam-4920	207	17	)	)	PUNCT
ejpam-4920	207	18	.	.	PUNCT
ejpam-4920	208	1	hence	hence	ADV
ejpam-4920	208	2	,	,	PUNCT
ejpam-4920	208	3	z	z	NOUN
ejpam-4920	208	4	′	′	NUM
ejpam-4920	208	5	=	=	SYM
ejpam-4920	208	6	v	v	NOUN
ejpam-4920	208	7	(	(	PUNCT
ejpam-4920	208	8	g	g	NOUN
ejpam-4920	208	9	)	)	PUNCT
ejpam-4920	208	10	\	\	NOUN
ejpam-4920	208	11	{	{	PUNCT
ejpam-4920	208	12	w	w	NOUN
ejpam-4920	208	13	}	}	PUNCT
ejpam-4920	208	14	is	be	AUX
ejpam-4920	208	15	a	a	DET
ejpam-4920	208	16	zfpnd	zfpnd	NOUN
ejpam-4920	208	17	set	set	NOUN
ejpam-4920	208	18	of	of	ADP
ejpam-4920	208	19	g	g	NOUN
ejpam-4920	208	20	,	,	PUNCT
ejpam-4920	208	21	showing	show	VERB
ejpam-4920	208	22	that	that	SCONJ
ejpam-4920	208	23	zfpnd(g	zfpnd(g	NOUN
ejpam-4920	208	24	)	)	PUNCT
ejpam-4920	208	25	≤	≤	NOUN
ejpam-4920	208	26	|v	|v	X
ejpam-4920	208	27	(	(	PUNCT
ejpam-4920	208	28	g)|	g)|	INTJ
ejpam-4920	208	29	−	−	PROPN
ejpam-4920	208	30	1	1	NUM
ejpam-4920	208	31	,	,	PUNCT
ejpam-4920	208	32	a	a	DET
ejpam-4920	208	33	contradiction	contradiction	NOUN
ejpam-4920	208	34	.	.	PUNCT
ejpam-4920	209	1	therefore	therefore	ADV
ejpam-4920	209	2	,	,	PUNCT
ejpam-4920	209	3	g	g	PROPN
ejpam-4920	209	4	is	be	AUX
ejpam-4920	209	5	complete	complete	ADJ
ejpam-4920	209	6	.	.	PUNCT
ejpam-4920	210	1	now	now	ADV
ejpam-4920	210	2	,	,	PUNCT
ejpam-4920	210	3	let	let	VERB
ejpam-4920	210	4	q1	q1	NOUN
ejpam-4920	210	5	,	,	PUNCT
ejpam-4920	210	6	.	.	PUNCT
ejpam-4920	210	7	.	.	PUNCT
ejpam-4920	211	1	.	.	PUNCT
ejpam-4920	212	1	,	,	PUNCT
ejpam-4920	212	2	qk	qk	INTJ
ejpam-4920	212	3	,	,	PUNCT
ejpam-4920	212	4	k	k	PROPN
ejpam-4920	212	5	≥	≥	NUM
ejpam-4920	212	6	2	2	NUM
ejpam-4920	212	7	be	be	AUX
ejpam-4920	212	8	components	component	NOUN
ejpam-4920	212	9	of	of	ADP
ejpam-4920	212	10	g.	g.	PROPN
ejpam-4920	212	11	suppose	suppose	VERB
ejpam-4920	212	12	that	that	SCONJ
ejpam-4920	212	13	qi	qi	PROPN
ejpam-4920	212	14	is	be	AUX
ejpam-4920	212	15	non	non	ADJ
ejpam-4920	212	16	-	-	ADJ
ejpam-4920	212	17	complete	complete	ADJ
ejpam-4920	212	18	for	for	ADP
ejpam-4920	212	19	some	some	DET
ejpam-4920	212	20	i	i	PRON
ejpam-4920	212	21	∈	∈	PROPN
ejpam-4920	212	22	{	{	PUNCT
ejpam-4920	212	23	1	1	NUM
ejpam-4920	212	24	,	,	PUNCT
ejpam-4920	212	25	.	.	PUNCT
ejpam-4920	212	26	.	.	PUNCT
ejpam-4920	213	1	.	.	PUNCT
ejpam-4920	214	1	,	,	PUNCT
ejpam-4920	214	2	k	k	X
ejpam-4920	214	3	}	}	PUNCT
ejpam-4920	214	4	.	.	PUNCT
ejpam-4920	215	1	then	then	ADV
ejpam-4920	215	2	dqi(s	dqi(s	PROPN
ejpam-4920	215	3	,	,	PUNCT
ejpam-4920	215	4	t	t	PROPN
ejpam-4920	215	5	)	)	PUNCT
ejpam-4920	215	6	=	=	SYM
ejpam-4920	215	7	2	2	NUM
ejpam-4920	215	8	=	=	SYM
ejpam-4920	215	9	dg(s	dg(s	NOUN
ejpam-4920	215	10	,	,	PUNCT
ejpam-4920	215	11	t	t	PROPN
ejpam-4920	215	12	)	)	PUNCT
ejpam-4920	215	13	for	for	ADP
ejpam-4920	215	14	some	some	DET
ejpam-4920	215	15	s	s	NOUN
ejpam-4920	215	16	,	,	PUNCT
ejpam-4920	215	17	t	t	PROPN
ejpam-4920	215	18	∈	∈	PROPN
ejpam-4920	215	19	v	v	PROPN
ejpam-4920	215	20	(	(	PUNCT
ejpam-4920	215	21	qi	qi	PROPN
ejpam-4920	215	22	)	)	PUNCT
ejpam-4920	215	23	.	.	PUNCT
ejpam-4920	216	1	thus	thus	ADV
ejpam-4920	216	2	,	,	PUNCT
ejpam-4920	216	3	v	v	INTJ
ejpam-4920	216	4	(	(	PUNCT
ejpam-4920	216	5	g	g	NOUN
ejpam-4920	216	6	)	)	PUNCT
ejpam-4920	216	7	\	\	NOUN
ejpam-4920	216	8	{	{	PUNCT
ejpam-4920	216	9	t	t	PROPN
ejpam-4920	216	10	}	}	PUNCT
ejpam-4920	216	11	is	be	AUX
ejpam-4920	216	12	a	a	DET
ejpam-4920	216	13	zfpnd	zfpnd	NOUN
ejpam-4920	216	14	set	set	NOUN
ejpam-4920	216	15	of	of	ADP
ejpam-4920	216	16	g	g	NOUN
ejpam-4920	216	17	,	,	PUNCT
ejpam-4920	216	18	and	and	CCONJ
ejpam-4920	216	19	so	so	ADV
ejpam-4920	216	20	zfpnd(g	zfpnd(g	ADJ
ejpam-4920	216	21	)	)	PUNCT
ejpam-4920	216	22	≤	≤	NOUN
ejpam-4920	216	23	|v	|v	PROPN
ejpam-4920	216	24	(	(	PUNCT
ejpam-4920	216	25	g)|−1	g)|−1	PROPN
ejpam-4920	216	26	,	,	PUNCT
ejpam-4920	216	27	a	a	DET
ejpam-4920	216	28	contradiction	contradiction	NOUN
ejpam-4920	216	29	.	.	PUNCT
ejpam-4920	217	1	hence	hence	ADV
ejpam-4920	217	2	,	,	PUNCT
ejpam-4920	217	3	every	every	DET
ejpam-4920	217	4	component	component	NOUN
ejpam-4920	217	5	of	of	ADP
ejpam-4920	217	6	g	g	PROPN
ejpam-4920	217	7	is	be	AUX
ejpam-4920	217	8	complete	complete	ADJ
ejpam-4920	217	9	.	.	PUNCT
ejpam-4920	218	1	conversely	conversely	ADV
ejpam-4920	218	2	,	,	PUNCT
ejpam-4920	218	3	let	let	VERB
ejpam-4920	218	4	g1	g1	NOUN
ejpam-4920	218	5	,	,	PUNCT
ejpam-4920	218	6	.	.	PUNCT
ejpam-4920	218	7	.	.	PUNCT
ejpam-4920	219	1	.	.	PUNCT
ejpam-4920	220	1	,	,	PUNCT
ejpam-4920	220	2	gk	gk	PROPN
ejpam-4920	220	3	,	,	PUNCT
ejpam-4920	220	4	k	k	PROPN
ejpam-4920	220	5	≥	≥	NUM
ejpam-4920	220	6	2	2	NUM
ejpam-4920	220	7	be	be	AUX
ejpam-4920	220	8	complete	complete	ADJ
ejpam-4920	220	9	components	component	NOUN
ejpam-4920	220	10	of	of	ADP
ejpam-4920	220	11	g.	g.	PROPN
ejpam-4920	220	12	if	if	SCONJ
ejpam-4920	220	13	gi	gi	PROPN
ejpam-4920	220	14	is	be	AUX
ejpam-4920	220	15	non	non	ADJ
ejpam-4920	220	16	-	-	ADJ
ejpam-4920	220	17	trivial	trivial	ADJ
ejpam-4920	220	18	for	for	ADP
ejpam-4920	220	19	each	each	DET
ejpam-4920	220	20	i	i	PRON
ejpam-4920	220	21	∈	∈	PROPN
ejpam-4920	220	22	{	{	PUNCT
ejpam-4920	220	23	1	1	NUM
ejpam-4920	220	24	,	,	PUNCT
ejpam-4920	220	25	.	.	PUNCT
ejpam-4920	220	26	.	.	PUNCT
ejpam-4920	221	1	.	.	PUNCT
ejpam-4920	222	1	,	,	PUNCT
ejpam-4920	222	2	k	k	X
ejpam-4920	222	3	}	}	PUNCT
ejpam-4920	222	4	,	,	PUNCT
ejpam-4920	222	5	then	then	ADV
ejpam-4920	222	6	pnd(g	pnd(g	ADP
ejpam-4920	222	7	)	)	PUNCT
ejpam-4920	222	8	=	=	SYM
ejpam-4920	222	9	|v	|v	PROPN
ejpam-4920	222	10	(	(	PUNCT
ejpam-4920	222	11	g)|	g)|	PROPN
ejpam-4920	222	12	=	=	PUNCT
ejpam-4920	222	13	k.	k.	PROPN
ejpam-4920	223	1	thus	thus	ADV
ejpam-4920	223	2	,	,	PUNCT
ejpam-4920	223	3	zfpnd(g	zfpnd(g	ADJ
ejpam-4920	223	4	)	)	PUNCT
ejpam-4920	223	5	=	=	SYM
ejpam-4920	224	1	k	k	X
ejpam-4920	224	2	by	by	ADP
ejpam-4920	224	3	theorem	theorem	NOUN
ejpam-4920	224	4	3(i	3(i	NUM
ejpam-4920	224	5	)	)	PUNCT
ejpam-4920	224	6	.	.	PUNCT
ejpam-4920	225	1	assume	assume	VERB
ejpam-4920	225	2	that	that	SCONJ
ejpam-4920	225	3	gi	gi	PROPN
ejpam-4920	225	4	is	be	AUX
ejpam-4920	225	5	trivial	trivial	ADJ
ejpam-4920	225	6	for	for	ADP
ejpam-4920	225	7	some	some	DET
ejpam-4920	225	8	i	i	PRON
ejpam-4920	225	9	∈	∈	PROPN
ejpam-4920	225	10	{	{	PUNCT
ejpam-4920	225	11	1	1	NUM
ejpam-4920	225	12	,	,	PUNCT
ejpam-4920	225	13	.	.	PUNCT
ejpam-4920	225	14	.	.	PUNCT
ejpam-4920	226	1	.	.	PUNCT
ejpam-4920	227	1	,	,	PUNCT
ejpam-4920	227	2	k	k	X
ejpam-4920	227	3	}	}	PUNCT
ejpam-4920	227	4	.	.	PUNCT
ejpam-4920	228	1	since	since	SCONJ
ejpam-4920	228	2	every	every	DET
ejpam-4920	228	3	zfpnd	zfpnd	NOUN
ejpam-4920	228	4	set	set	VERB
ejpam-4920	228	5	f	f	PROPN
ejpam-4920	228	6	is	be	AUX
ejpam-4920	228	7	a	a	DET
ejpam-4920	228	8	zero	zero	NUM
ejpam-4920	228	9	j.	j.	PROPN
ejpam-4920	228	10	u.	u.	PROPN
ejpam-4920	228	11	manditong	manditong	PROPN
ejpam-4920	228	12	et	et	PROPN
ejpam-4920	228	13	al	al	PROPN
ejpam-4920	228	14	.	.	PUNCT
ejpam-4920	228	15	/	/	SYM
ejpam-4920	228	16	eur	eur	PROPN
ejpam-4920	228	17	.	.	PUNCT
ejpam-4920	229	1	j.	j.	PROPN
ejpam-4920	229	2	pure	pure	PROPN
ejpam-4920	229	3	appl	appl	PROPN
ejpam-4920	229	4	.	.	PROPN
ejpam-4920	229	5	math	math	PROPN
ejpam-4920	229	6	,	,	PUNCT
ejpam-4920	229	7	17	17	NUM
ejpam-4920	229	8	(	(	PUNCT
ejpam-4920	229	9	1	1	NUM
ejpam-4920	229	10	)	)	PUNCT
ejpam-4920	229	11	(	(	PUNCT
ejpam-4920	229	12	2024	2024	NUM
ejpam-4920	229	13	)	)	PUNCT
ejpam-4920	229	14	,	,	PUNCT
ejpam-4920	229	15	324	324	NUM
ejpam-4920	229	16	-	-	SYM
ejpam-4920	229	17	337	337	NUM
ejpam-4920	229	18	332	332	NUM
ejpam-4920	229	19	forcing	forcing	NOUN
ejpam-4920	229	20	,	,	PUNCT
ejpam-4920	229	21	v	v	NOUN
ejpam-4920	229	22	(	(	PUNCT
ejpam-4920	229	23	gi	gi	INTJ
ejpam-4920	229	24	)	)	PUNCT
ejpam-4920	229	25	⊆	⊆	NUM
ejpam-4920	229	26	f	f	NOUN
ejpam-4920	229	27	.	.	PUNCT
ejpam-4920	230	1	since	since	SCONJ
ejpam-4920	230	2	vertices	vertex	NOUN
ejpam-4920	230	3	of	of	ADP
ejpam-4920	230	4	every	every	DET
ejpam-4920	230	5	non	non	ADJ
ejpam-4920	230	6	-	-	ADJ
ejpam-4920	230	7	trivial	trivial	ADJ
ejpam-4920	230	8	complete	complete	ADJ
ejpam-4920	230	9	component	component	NOUN
ejpam-4920	230	10	of	of	ADP
ejpam-4920	230	11	g	g	PROPN
ejpam-4920	230	12	are	be	AUX
ejpam-4920	230	13	also	also	ADV
ejpam-4920	230	14	in	in	ADP
ejpam-4920	230	15	any	any	DET
ejpam-4920	230	16	zfpnd	zfpnd	NOUN
ejpam-4920	230	17	set	set	NOUN
ejpam-4920	230	18	of	of	ADP
ejpam-4920	230	19	g	g	PROPN
ejpam-4920	230	20	,	,	PUNCT
ejpam-4920	230	21	it	it	PRON
ejpam-4920	230	22	follows	follow	VERB
ejpam-4920	230	23	that	that	SCONJ
ejpam-4920	230	24	v	v	X
ejpam-4920	230	25	(	(	PUNCT
ejpam-4920	230	26	g	g	NOUN
ejpam-4920	230	27	)	)	PUNCT
ejpam-4920	230	28	is	be	AUX
ejpam-4920	230	29	the	the	DET
ejpam-4920	230	30	minimum	minimum	ADJ
ejpam-4920	230	31	zfpnd	zfpnd	NOUN
ejpam-4920	230	32	set	set	VERB
ejpam-4920	230	33	of	of	ADP
ejpam-4920	230	34	g.	g.	PROPN
ejpam-4920	230	35	thus	thus	ADV
ejpam-4920	230	36	,	,	PUNCT
ejpam-4920	230	37	zfpnd(g	zfpnd(g	ADJ
ejpam-4920	230	38	)	)	PUNCT
ejpam-4920	230	39	=	=	SYM
ejpam-4920	230	40	|v	|v	PROPN
ejpam-4920	230	41	(	(	PUNCT
ejpam-4920	230	42	g)|	g)|	NOUN
ejpam-4920	230	43	.	.	PUNCT
ejpam-4920	231	1	the	the	DET
ejpam-4920	231	2	following	following	ADJ
ejpam-4920	231	3	result	result	NOUN
ejpam-4920	231	4	follows	follow	VERB
ejpam-4920	231	5	from	from	ADP
ejpam-4920	231	6	theorem	theorem	ADJ
ejpam-4920	231	7	3(iii	3(iii	NUM
ejpam-4920	231	8	)	)	PUNCT
ejpam-4920	231	9	and	and	CCONJ
ejpam-4920	231	10	theorem	theorem	VERB
ejpam-4920	231	11	4	4	NUM
ejpam-4920	231	12	.	.	PUNCT
ejpam-4920	231	13	corollary	corollary	ADJ
ejpam-4920	231	14	2	2	NUM
ejpam-4920	231	15	.	.	X
ejpam-4920	231	16	zfpnd(kq	zfpnd(kq	X
ejpam-4920	231	17	)	)	PUNCT
ejpam-4920	231	18	=	=	PUNCT
ejpam-4920	231	19	q	q	NOUN
ejpam-4920	231	20	=	=	PUNCT
ejpam-4920	231	21	zfpnd(kq	zfpnd(kq	PROPN
ejpam-4920	231	22	)	)	PUNCT
ejpam-4920	231	23	for	for	ADP
ejpam-4920	231	24	all	all	DET
ejpam-4920	231	25	positive	positive	ADJ
ejpam-4920	231	26	integer	integer	NOUN
ejpam-4920	231	27	q	q	PROPN
ejpam-4920	231	28	≥	≥	NUM
ejpam-4920	231	29	1	1	NUM
ejpam-4920	231	30	.	.	PUNCT
ejpam-4920	231	31	proposition	proposition	NOUN
ejpam-4920	231	32	4	4	NUM
ejpam-4920	231	33	.	.	PUNCT
ejpam-4920	232	1	let	let	VERB
ejpam-4920	232	2	n	n	PRON
ejpam-4920	232	3	be	be	AUX
ejpam-4920	232	4	any	any	DET
ejpam-4920	232	5	positive	positive	ADJ
ejpam-4920	232	6	integer	integer	NOUN
ejpam-4920	232	7	.	.	PUNCT
ejpam-4920	233	1	then	then	ADV
ejpam-4920	233	2	each	each	PRON
ejpam-4920	233	3	of	of	ADP
ejpam-4920	233	4	the	the	DET
ejpam-4920	233	5	following	follow	VERB
ejpam-4920	233	6	holds	hold	NOUN
ejpam-4920	233	7	.	.	PUNCT
ejpam-4920	234	1	(	(	PUNCT
ejpam-4920	234	2	i	i	NOUN
ejpam-4920	234	3	)	)	PUNCT
ejpam-4920	234	4	zfpnd(pn	zfpnd(pn	PROPN
ejpam-4920	234	5	)	)	PUNCT
ejpam-4920	234	6	=	=	SYM
ejpam-4920	234	7	{	{	PUNCT
ejpam-4920	234	8	n	n	NOUN
ejpam-4920	234	9	if	if	SCONJ
ejpam-4920	234	10	n	n	NOUN
ejpam-4920	234	11	=	=	SYM
ejpam-4920	234	12	1	1	NUM
ejpam-4920	234	13	,	,	PUNCT
ejpam-4920	234	14	2	2	NUM
ejpam-4920	234	15	2	2	NUM
ejpam-4920	234	16	if	if	SCONJ
ejpam-4920	234	17	n	n	PRON
ejpam-4920	234	18	≥	≥	NOUN
ejpam-4920	234	19	3	3	NUM
ejpam-4920	234	20	.	.	PUNCT
ejpam-4920	234	21	(	(	PUNCT
ejpam-4920	234	22	ii	ii	NOUN
ejpam-4920	234	23	)	)	PUNCT
ejpam-4920	234	24	zfpnd(cn	zfpnd(cn	PROPN
ejpam-4920	234	25	)	)	PUNCT
ejpam-4920	234	26	=	=	PUNCT
ejpam-4920	234	27	{	{	PUNCT
ejpam-4920	234	28	3	3	NUM
ejpam-4920	234	29	if	if	SCONJ
ejpam-4920	234	30	n	n	ADV
ejpam-4920	234	31	=	=	SYM
ejpam-4920	234	32	3	3	NUM
ejpam-4920	234	33	2	2	NUM
ejpam-4920	234	34	if	if	SCONJ
ejpam-4920	234	35	n	n	PRON
ejpam-4920	234	36	≥	≥	NOUN
ejpam-4920	234	37	4	4	NUM
ejpam-4920	234	38	.	.	PUNCT
ejpam-4920	235	1	proof	proof	NOUN
ejpam-4920	235	2	.	.	PUNCT
ejpam-4920	236	1	(	(	PUNCT
ejpam-4920	236	2	i	i	NOUN
ejpam-4920	236	3	)	)	PUNCT
ejpam-4920	236	4	clearly	clearly	ADV
ejpam-4920	236	5	,	,	PUNCT
ejpam-4920	236	6	zfpnd(pn	zfpnd(pn	NOUN
ejpam-4920	236	7	)	)	PUNCT
ejpam-4920	236	8	=	=	SYM
ejpam-4920	236	9	n	n	NOUN
ejpam-4920	236	10	for	for	ADP
ejpam-4920	236	11	n	n	NOUN
ejpam-4920	236	12	=	=	SYM
ejpam-4920	236	13	1	1	NUM
ejpam-4920	236	14	,	,	PUNCT
ejpam-4920	236	15	2	2	NUM
ejpam-4920	236	16	.	.	PUNCT
ejpam-4920	236	17	suppose	suppose	VERB
ejpam-4920	236	18	that	that	SCONJ
ejpam-4920	236	19	n	n	PROPN
ejpam-4920	236	20	≥	≥	NUM
ejpam-4920	236	21	3	3	X
ejpam-4920	236	22	.	.	PUNCT
ejpam-4920	237	1	let	let	VERB
ejpam-4920	237	2	v	v	X
ejpam-4920	237	3	(	(	PUNCT
ejpam-4920	237	4	pn	pn	NOUN
ejpam-4920	237	5	)	)	PUNCT
ejpam-4920	237	6	=	=	SYM
ejpam-4920	237	7	{	{	PUNCT
ejpam-4920	237	8	a1	a1	PROPN
ejpam-4920	237	9	,	,	PUNCT
ejpam-4920	237	10	a2	a2	PROPN
ejpam-4920	237	11	,	,	PUNCT
ejpam-4920	237	12	.	.	PUNCT
ejpam-4920	237	13	.	.	PUNCT
ejpam-4920	238	1	.	.	PUNCT
ejpam-4920	239	1	,	,	PUNCT
ejpam-4920	239	2	an	an	X
ejpam-4920	239	3	}	}	PUNCT
ejpam-4920	239	4	and	and	CCONJ
ejpam-4920	239	5	consider	consider	VERB
ejpam-4920	239	6	f	f	NOUN
ejpam-4920	239	7	=	=	PRON
ejpam-4920	239	8	{	{	PUNCT
ejpam-4920	239	9	a1	a1	PROPN
ejpam-4920	239	10	,	,	PUNCT
ejpam-4920	239	11	a2	a2	PROPN
ejpam-4920	239	12	}	}	PUNCT
ejpam-4920	239	13	.	.	PUNCT
ejpam-4920	240	1	clearly	clearly	ADV
ejpam-4920	240	2	,	,	PUNCT
ejpam-4920	240	3	f	f	PROPN
ejpam-4920	240	4	is	be	AUX
ejpam-4920	240	5	a	a	DET
ejpam-4920	240	6	zero	zero	NUM
ejpam-4920	240	7	forcing	force	VERB
ejpam-4920	240	8	set	set	NOUN
ejpam-4920	240	9	of	of	ADP
ejpam-4920	240	10	pn	pn	PROPN
ejpam-4920	240	11	.	.	PROPN
ejpam-4920	240	12	observe	observe	VERB
ejpam-4920	240	13	that	that	SCONJ
ejpam-4920	240	14	for	for	ADP
ejpam-4920	240	15	every	every	PRON
ejpam-4920	240	16	w	w	PROPN
ejpam-4920	240	17	∈	∈	PROPN
ejpam-4920	240	18	v	v	NOUN
ejpam-4920	240	19	(	(	PUNCT
ejpam-4920	240	20	pn	pn	NOUN
ejpam-4920	240	21	)	)	PUNCT
ejpam-4920	240	22	\	\	PROPN
ejpam-4920	240	23	f	f	PROPN
ejpam-4920	240	24	,	,	PUNCT
ejpam-4920	240	25	w	w	PROPN
ejpam-4920	240	26	/∈	/∈	PUNCT
ejpam-4920	240	27	npn(a1	npn(a1	PROPN
ejpam-4920	240	28	)	)	PUNCT
ejpam-4920	240	29	.	.	PUNCT
ejpam-4920	241	1	thus	thus	ADV
ejpam-4920	241	2	,	,	PUNCT
ejpam-4920	241	3	f	f	PROPN
ejpam-4920	241	4	is	be	AUX
ejpam-4920	241	5	a	a	DET
ejpam-4920	241	6	pnd	pnd	NOUN
ejpam-4920	241	7	set	set	NOUN
ejpam-4920	241	8	of	of	ADP
ejpam-4920	241	9	pn	pn	PROPN
ejpam-4920	241	10	,	,	PUNCT
ejpam-4920	241	11	showing	show	VERB
ejpam-4920	241	12	that	that	SCONJ
ejpam-4920	241	13	f	f	PROPN
ejpam-4920	241	14	is	be	AUX
ejpam-4920	241	15	a	a	DET
ejpam-4920	241	16	zfpnd	zfpnd	NOUN
ejpam-4920	241	17	set	set	NOUN
ejpam-4920	241	18	of	of	ADP
ejpam-4920	241	19	pn	pn	PROPN
ejpam-4920	241	20	.	.	PUNCT
ejpam-4920	242	1	since	since	SCONJ
ejpam-4920	242	2	{	{	PUNCT
ejpam-4920	242	3	x	x	X
ejpam-4920	242	4	}	}	PUNCT
ejpam-4920	242	5	is	be	AUX
ejpam-4920	242	6	not	not	PART
ejpam-4920	242	7	a	a	DET
ejpam-4920	242	8	zfpnd	zfpnd	NOUN
ejpam-4920	242	9	set	set	VERB
ejpam-4920	242	10	in	in	ADP
ejpam-4920	242	11	pn	pn	PROPN
ejpam-4920	242	12	∀	∀	X
ejpam-4920	242	13	x	x	X
ejpam-4920	242	14	∈	∈	NOUN
ejpam-4920	242	15	v	v	X
ejpam-4920	242	16	(	(	PUNCT
ejpam-4920	242	17	pn	pn	NOUN
ejpam-4920	242	18	)	)	PUNCT
ejpam-4920	242	19	,	,	PUNCT
ejpam-4920	242	20	it	it	PRON
ejpam-4920	242	21	follows	follow	VERB
ejpam-4920	242	22	that	that	SCONJ
ejpam-4920	242	23	f	f	PROPN
ejpam-4920	242	24	is	be	AUX
ejpam-4920	242	25	a	a	DET
ejpam-4920	242	26	minimum	minimum	ADJ
ejpam-4920	242	27	zfpnd	zfpnd	NOUN
ejpam-4920	242	28	set	set	NOUN
ejpam-4920	242	29	of	of	ADP
ejpam-4920	242	30	pn	pn	PROPN
ejpam-4920	242	31	.	.	PROPN
ejpam-4920	243	1	hence	hence	ADV
ejpam-4920	243	2	,	,	PUNCT
ejpam-4920	243	3	zfpnd(pn	zfpnd(pn	PROPN
ejpam-4920	243	4	)	)	PUNCT
ejpam-4920	243	5	=	=	SYM
ejpam-4920	243	6	2	2	NUM
ejpam-4920	243	7	for	for	ADP
ejpam-4920	243	8	all	all	DET
ejpam-4920	243	9	n	n	PRON
ejpam-4920	243	10	≥	≥	NOUN
ejpam-4920	243	11	3	3	NUM
ejpam-4920	243	12	.	.	PUNCT
ejpam-4920	243	13	(	(	PUNCT
ejpam-4920	243	14	ii	ii	NOUN
ejpam-4920	243	15	)	)	PUNCT
ejpam-4920	243	16	since	since	SCONJ
ejpam-4920	243	17	pnd(c3	pnd(c3	NOUN
ejpam-4920	243	18	)	)	PUNCT
ejpam-4920	243	19	=	=	SYM
ejpam-4920	244	1	3	3	X
ejpam-4920	244	2	,	,	PUNCT
ejpam-4920	244	3	it	it	PRON
ejpam-4920	244	4	follows	follow	VERB
ejpam-4920	244	5	that	that	SCONJ
ejpam-4920	244	6	zfpnd(c3	zfpnd(c3	NOUN
ejpam-4920	244	7	)	)	PUNCT
ejpam-4920	244	8	=	=	SYM
ejpam-4920	244	9	3	3	NUM
ejpam-4920	244	10	by	by	ADP
ejpam-4920	244	11	theorem	theorem	NOUN
ejpam-4920	244	12	3(i)(ii	3(i)(ii	NUM
ejpam-4920	244	13	)	)	PUNCT
ejpam-4920	244	14	.	.	PUNCT
ejpam-4920	245	1	suppose	suppose	VERB
ejpam-4920	245	2	that	that	SCONJ
ejpam-4920	245	3	n	n	PROPN
ejpam-4920	245	4	≥	≥	NUM
ejpam-4920	245	5	4	4	NUM
ejpam-4920	245	6	.	.	PUNCT
ejpam-4920	246	1	let	let	VERB
ejpam-4920	246	2	v	v	X
ejpam-4920	246	3	(	(	PUNCT
ejpam-4920	246	4	cn	cn	PROPN
ejpam-4920	246	5	)	)	PUNCT
ejpam-4920	246	6	=	=	PRON
ejpam-4920	246	7	{	{	PUNCT
ejpam-4920	246	8	x1	x1	PROPN
ejpam-4920	246	9	,	,	PUNCT
ejpam-4920	246	10	x2	x2	PROPN
ejpam-4920	246	11	,	,	PUNCT
ejpam-4920	246	12	.	.	PUNCT
ejpam-4920	246	13	.	.	PUNCT
ejpam-4920	247	1	.	.	PUNCT
ejpam-4920	248	1	,	,	PUNCT
ejpam-4920	248	2	xn	xn	X
ejpam-4920	248	3	}	}	PUNCT
ejpam-4920	248	4	and	and	CCONJ
ejpam-4920	248	5	consider	consider	VERB
ejpam-4920	248	6	f	f	NOUN
ejpam-4920	248	7	′	′	NUM
ejpam-4920	248	8	=	=	PUNCT
ejpam-4920	248	9	{	{	PUNCT
ejpam-4920	248	10	x1	x1	PROPN
ejpam-4920	248	11	,	,	PUNCT
ejpam-4920	248	12	x2	x2	PROPN
ejpam-4920	248	13	}	}	PUNCT
ejpam-4920	248	14	.	.	PUNCT
ejpam-4920	249	1	notice	notice	VERB
ejpam-4920	249	2	that	that	SCONJ
ejpam-4920	249	3	for	for	ADP
ejpam-4920	249	4	all	all	DET
ejpam-4920	249	5	j	j	PROPN
ejpam-4920	249	6	∈	∈	PROPN
ejpam-4920	249	7	{	{	PUNCT
ejpam-4920	249	8	3	3	NUM
ejpam-4920	249	9	,	,	PUNCT
ejpam-4920	249	10	4	4	NUM
ejpam-4920	249	11	,	,	PUNCT
ejpam-4920	249	12	...	...	PUNCT
ejpam-4920	249	13	n	n	CCONJ
ejpam-4920	249	14	}	}	PUNCT
ejpam-4920	249	15	xj	xj	PROPN
ejpam-4920	249	16	/∈	/∈	PUNCT
ejpam-4920	249	17	ncn(x1	ncn(x1	NOUN
ejpam-4920	249	18	)	)	PUNCT
ejpam-4920	249	19	and	and	CCONJ
ejpam-4920	249	20	xn	xn	PROPN
ejpam-4920	249	21	/∈	/∈	PUNCT
ejpam-4920	249	22	ncn(x2	ncn(x2	NOUN
ejpam-4920	249	23	)	)	PUNCT
ejpam-4920	249	24	.	.	PUNCT
ejpam-4920	250	1	thus	thus	ADV
ejpam-4920	250	2	,	,	PUNCT
ejpam-4920	250	3	f	f	PROPN
ejpam-4920	250	4	′	′	PROPN
ejpam-4920	250	5	is	be	AUX
ejpam-4920	250	6	a	a	DET
ejpam-4920	250	7	pnd	pnd	NOUN
ejpam-4920	250	8	set	set	NOUN
ejpam-4920	250	9	of	of	ADP
ejpam-4920	250	10	cn	cn	PROPN
ejpam-4920	250	11	,	,	PUNCT
ejpam-4920	250	12	and	and	CCONJ
ejpam-4920	250	13	so	so	ADV
ejpam-4920	250	14	f	f	PROPN
ejpam-4920	250	15	′	′	NUM
ejpam-4920	250	16	is	be	AUX
ejpam-4920	250	17	a	a	DET
ejpam-4920	250	18	zfpnd	zfpnd	NOUN
ejpam-4920	250	19	set	set	NOUN
ejpam-4920	250	20	of	of	ADP
ejpam-4920	250	21	cn	cn	PROPN
ejpam-4920	250	22	.	.	PUNCT
ejpam-4920	251	1	since	since	SCONJ
ejpam-4920	251	2	{	{	PUNCT
ejpam-4920	251	3	xi	xi	NOUN
ejpam-4920	251	4	}	}	PUNCT
ejpam-4920	251	5	is	be	AUX
ejpam-4920	251	6	not	not	PART
ejpam-4920	251	7	a	a	DET
ejpam-4920	251	8	zfpnd	zfpnd	NOUN
ejpam-4920	251	9	set	set	VERB
ejpam-4920	251	10	of	of	ADP
ejpam-4920	251	11	cn	cn	PROPN
ejpam-4920	251	12	for	for	ADP
ejpam-4920	251	13	each	each	DET
ejpam-4920	251	14	i	i	PRON
ejpam-4920	251	15	∈	∈	PROPN
ejpam-4920	251	16	{	{	PUNCT
ejpam-4920	251	17	1	1	NUM
ejpam-4920	251	18	,	,	PUNCT
ejpam-4920	251	19	2	2	NUM
ejpam-4920	251	20	,	,	PUNCT
ejpam-4920	251	21	.	.	PUNCT
ejpam-4920	251	22	.	.	PUNCT
ejpam-4920	252	1	.	.	PUNCT
ejpam-4920	253	1	,	,	PUNCT
ejpam-4920	253	2	n	n	CCONJ
ejpam-4920	253	3	}	}	PUNCT
ejpam-4920	253	4	,	,	PUNCT
ejpam-4920	253	5	it	it	PRON
ejpam-4920	253	6	follows	follow	VERB
ejpam-4920	253	7	that	that	SCONJ
ejpam-4920	254	1	f	f	PROPN
ejpam-4920	254	2	′	′	NOUN
ejpam-4920	254	3	is	be	AUX
ejpam-4920	254	4	a	a	DET
ejpam-4920	254	5	minimum	minimum	ADJ
ejpam-4920	254	6	zfpnd	zfpnd	NOUN
ejpam-4920	254	7	set	set	NOUN
ejpam-4920	254	8	of	of	ADP
ejpam-4920	254	9	cn	cn	PROPN
ejpam-4920	254	10	.	.	PUNCT
ejpam-4920	255	1	consequently	consequently	ADV
ejpam-4920	255	2	,	,	PUNCT
ejpam-4920	255	3	zfpnd(cn	zfpnd(cn	PROPN
ejpam-4920	255	4	)	)	PUNCT
ejpam-4920	255	5	=	=	SYM
ejpam-4920	255	6	2	2	NUM
ejpam-4920	255	7	for	for	ADP
ejpam-4920	255	8	all	all	DET
ejpam-4920	255	9	n	n	PRON
ejpam-4920	255	10	≥	≥	NUM
ejpam-4920	255	11	4	4	NUM
ejpam-4920	255	12	.	.	PUNCT
ejpam-4920	255	13	theorem	theorem	NOUN
ejpam-4920	255	14	5	5	NUM
ejpam-4920	255	15	.	.	PUNCT
ejpam-4920	256	1	[	[	X
ejpam-4920	256	2	10	10	NUM
ejpam-4920	256	3	]	]	PUNCT
ejpam-4920	256	4	let	let	VERB
ejpam-4920	256	5	g	g	NOUN
ejpam-4920	256	6	and	and	CCONJ
ejpam-4920	256	7	h	h	NOUN
ejpam-4920	256	8	be	be	VERB
ejpam-4920	256	9	two	two	NUM
ejpam-4920	256	10	graphs	graph	NOUN
ejpam-4920	256	11	.	.	PUNCT
ejpam-4920	257	1	a	a	DET
ejpam-4920	257	2	set	set	NOUN
ejpam-4920	257	3	s	s	NOUN
ejpam-4920	257	4	⊆	⊆	NUM
ejpam-4920	257	5	v	v	NOUN
ejpam-4920	257	6	(	(	PUNCT
ejpam-4920	257	7	g	g	PROPN
ejpam-4920	257	8	+	+	NOUN
ejpam-4920	257	9	h	h	NOUN
ejpam-4920	257	10	)	)	PUNCT
ejpam-4920	257	11	is	be	AUX
ejpam-4920	257	12	hop	hop	NOUN
ejpam-4920	257	13	dominating	dominate	VERB
ejpam-4920	257	14	set	set	NOUN
ejpam-4920	257	15	of	of	ADP
ejpam-4920	257	16	g	g	PROPN
ejpam-4920	257	17	+	+	PROPN
ejpam-4920	257	18	h	h	NOUN
ejpam-4920	257	19	if	if	SCONJ
ejpam-4920	258	1	and	and	CCONJ
ejpam-4920	258	2	only	only	ADV
ejpam-4920	258	3	if	if	SCONJ
ejpam-4920	258	4	s	s	VERB
ejpam-4920	258	5	=	=	PUNCT
ejpam-4920	258	6	sg	sg	X
ejpam-4920	258	7	∪	∪	ADJ
ejpam-4920	259	1	sh	sh	PROPN
ejpam-4920	259	2	,	,	PUNCT
ejpam-4920	259	3	where	where	SCONJ
ejpam-4920	259	4	sg	sg	PROPN
ejpam-4920	259	5	and	and	CCONJ
ejpam-4920	259	6	sh	sh	PROPN
ejpam-4920	259	7	are	be	AUX
ejpam-4920	259	8	pnd	pnd	NOUN
ejpam-4920	259	9	sets	set	NOUN
ejpam-4920	259	10	of	of	ADP
ejpam-4920	259	11	g	g	PROPN
ejpam-4920	259	12	and	and	CCONJ
ejpam-4920	259	13	h	h	NOUN
ejpam-4920	259	14	,	,	PUNCT
ejpam-4920	259	15	respectively	respectively	ADV
ejpam-4920	259	16	.	.	PUNCT
ejpam-4920	260	1	theorem	theorem	VERB
ejpam-4920	260	2	6	6	NUM
ejpam-4920	260	3	.	.	PUNCT
ejpam-4920	261	1	let	let	VERB
ejpam-4920	261	2	s	s	PRON
ejpam-4920	261	3	and	and	CCONJ
ejpam-4920	261	4	t	t	PROPN
ejpam-4920	261	5	be	be	AUX
ejpam-4920	261	6	two	two	NUM
ejpam-4920	261	7	non	non	ADJ
ejpam-4920	261	8	-	-	ADJ
ejpam-4920	261	9	complete	complete	ADJ
ejpam-4920	261	10	graphs	graph	NOUN
ejpam-4920	261	11	.	.	PUNCT
ejpam-4920	262	1	a	a	DET
ejpam-4920	262	2	subset	subset	NOUN
ejpam-4920	262	3	z	z	NOUN
ejpam-4920	262	4	of	of	ADP
ejpam-4920	262	5	v	v	NOUN
ejpam-4920	262	6	(	(	PUNCT
ejpam-4920	262	7	s	s	NOUN
ejpam-4920	262	8	+	+	X
ejpam-4920	262	9	t	t	NOUN
ejpam-4920	262	10	)	)	PUNCT
ejpam-4920	262	11	is	be	AUX
ejpam-4920	262	12	a	a	DET
ejpam-4920	262	13	zero	zero	NUM
ejpam-4920	262	14	forcing	force	VERB
ejpam-4920	262	15	hop	hop	NOUN
ejpam-4920	262	16	dominating	dominating	NOUN
ejpam-4920	262	17	set	set	VERB
ejpam-4920	262	18	in	in	ADP
ejpam-4920	262	19	s	s	PROPN
ejpam-4920	262	20	+	+	X
ejpam-4920	262	21	t	t	NOUN
ejpam-4920	263	1	if	if	SCONJ
ejpam-4920	264	1	and	and	CCONJ
ejpam-4920	264	2	only	only	ADV
ejpam-4920	264	3	if	if	SCONJ
ejpam-4920	264	4	z	z	NOUN
ejpam-4920	264	5	=	=	SYM
ejpam-4920	264	6	zs	zs	PROPN
ejpam-4920	264	7	∪	∪	ADP
ejpam-4920	264	8	zt	zt	PROPN
ejpam-4920	264	9	and	and	CCONJ
ejpam-4920	264	10	satisfies	satisfy	VERB
ejpam-4920	264	11	one	one	NUM
ejpam-4920	264	12	of	of	ADP
ejpam-4920	264	13	the	the	DET
ejpam-4920	264	14	following	following	ADJ
ejpam-4920	264	15	conditions	condition	NOUN
ejpam-4920	264	16	:	:	PUNCT
ejpam-4920	264	17	(	(	PUNCT
ejpam-4920	264	18	i	i	NOUN
ejpam-4920	264	19	)	)	PUNCT
ejpam-4920	265	1	zs	zs	PROPN
ejpam-4920	265	2	=	=	SYM
ejpam-4920	265	3	v	v	PROPN
ejpam-4920	265	4	(	(	PUNCT
ejpam-4920	265	5	s	s	NOUN
ejpam-4920	265	6	)	)	PUNCT
ejpam-4920	265	7	and	and	CCONJ
ejpam-4920	265	8	zt	zt	PROPN
ejpam-4920	265	9	is	be	AUX
ejpam-4920	265	10	a	a	DET
ejpam-4920	265	11	zfpnd	zfpnd	NOUN
ejpam-4920	265	12	set	set	VERB
ejpam-4920	265	13	in	in	ADP
ejpam-4920	265	14	t	t	PROPN
ejpam-4920	265	15	.	.	PUNCT
ejpam-4920	266	1	(	(	PUNCT
ejpam-4920	266	2	ii	ii	NOUN
ejpam-4920	266	3	)	)	PUNCT
ejpam-4920	266	4	zt	zt	PROPN
ejpam-4920	266	5	=	=	SYM
ejpam-4920	266	6	v	v	PROPN
ejpam-4920	266	7	(	(	PUNCT
ejpam-4920	266	8	t	t	PROPN
ejpam-4920	266	9	)	)	PUNCT
ejpam-4920	266	10	and	and	CCONJ
ejpam-4920	266	11	zs	zs	PROPN
ejpam-4920	266	12	is	be	AUX
ejpam-4920	266	13	a	a	DET
ejpam-4920	266	14	zfpnd	zfpnd	NOUN
ejpam-4920	266	15	set	set	VERB
ejpam-4920	266	16	in	in	ADP
ejpam-4920	266	17	s.	s.	PROPN
ejpam-4920	266	18	(	(	PUNCT
ejpam-4920	266	19	iii	iii	X
ejpam-4920	266	20	)	)	PUNCT
ejpam-4920	266	21	zs	zs	NOUN
ejpam-4920	266	22	=	=	SYM
ejpam-4920	266	23	v	v	PROPN
ejpam-4920	266	24	(	(	PUNCT
ejpam-4920	266	25	s	s	NOUN
ejpam-4920	266	26	)	)	PUNCT
ejpam-4920	266	27	\	\	NOUN
ejpam-4920	266	28	{	{	PUNCT
ejpam-4920	266	29	a	a	NOUN
ejpam-4920	266	30	}	}	PUNCT
ejpam-4920	266	31	and	and	CCONJ
ejpam-4920	266	32	zt	zt	PROPN
ejpam-4920	266	33	=	=	SYM
ejpam-4920	266	34	v	v	PROPN
ejpam-4920	266	35	(	(	PUNCT
ejpam-4920	266	36	t	t	PROPN
ejpam-4920	266	37	)	)	PUNCT
ejpam-4920	266	38	\	\	NOUN
ejpam-4920	267	1	{	{	PUNCT
ejpam-4920	267	2	b	b	X
ejpam-4920	267	3	}	}	PUNCT
ejpam-4920	267	4	are	be	AUX
ejpam-4920	267	5	zfpnd	zfpnd	NOUN
ejpam-4920	267	6	sets	set	NOUN
ejpam-4920	267	7	in	in	ADP
ejpam-4920	267	8	s	s	PRON
ejpam-4920	267	9	and	and	CCONJ
ejpam-4920	267	10	t	t	PROPN
ejpam-4920	267	11	,	,	PUNCT
ejpam-4920	267	12	respectively	respectively	ADV
ejpam-4920	267	13	,	,	PUNCT
ejpam-4920	267	14	for	for	ADP
ejpam-4920	267	15	some	some	PRON
ejpam-4920	267	16	a	a	DET
ejpam-4920	267	17	∈	∈	PROPN
ejpam-4920	267	18	v	v	ADP
ejpam-4920	267	19	(	(	PUNCT
ejpam-4920	267	20	s	s	NOUN
ejpam-4920	267	21	)	)	PUNCT
ejpam-4920	267	22	,	,	PUNCT
ejpam-4920	267	23	b	b	X
ejpam-4920	267	24	∈	∈	PROPN
ejpam-4920	267	25	v	v	NOUN
ejpam-4920	267	26	(	(	PUNCT
ejpam-4920	267	27	t	t	PROPN
ejpam-4920	267	28	)	)	PUNCT
ejpam-4920	267	29	.	.	PUNCT
ejpam-4920	268	1	j.	j.	PROPN
ejpam-4920	268	2	u.	u.	PROPN
ejpam-4920	268	3	manditong	manditong	PROPN
ejpam-4920	268	4	et	et	PROPN
ejpam-4920	268	5	al	al	PROPN
ejpam-4920	268	6	.	.	PUNCT
ejpam-4920	268	7	/	/	SYM
ejpam-4920	268	8	eur	eur	PROPN
ejpam-4920	268	9	.	.	PUNCT
ejpam-4920	269	1	j.	j.	PROPN
ejpam-4920	269	2	pure	pure	PROPN
ejpam-4920	269	3	appl	appl	PROPN
ejpam-4920	269	4	.	.	PROPN
ejpam-4920	269	5	math	math	PROPN
ejpam-4920	269	6	,	,	PUNCT
ejpam-4920	269	7	17	17	NUM
ejpam-4920	269	8	(	(	PUNCT
ejpam-4920	269	9	1	1	NUM
ejpam-4920	269	10	)	)	PUNCT
ejpam-4920	269	11	(	(	PUNCT
ejpam-4920	269	12	2024	2024	NUM
ejpam-4920	269	13	)	)	PUNCT
ejpam-4920	269	14	,	,	PUNCT
ejpam-4920	269	15	324	324	NUM
ejpam-4920	269	16	-	-	SYM
ejpam-4920	269	17	337	337	NUM
ejpam-4920	269	18	333	333	NUM
ejpam-4920	269	19	proof	proof	NOUN
ejpam-4920	269	20	.	.	PUNCT
ejpam-4920	270	1	let	let	VERB
ejpam-4920	270	2	z	z	NOUN
ejpam-4920	270	3	=	=	PUNCT
ejpam-4920	270	4	zs	zs	PROPN
ejpam-4920	270	5	∪	∪	NOUN
ejpam-4920	270	6	zt	zt	PROPN
ejpam-4920	270	7	be	be	AUX
ejpam-4920	270	8	a	a	DET
ejpam-4920	270	9	zero	zero	NUM
ejpam-4920	270	10	forcing	force	VERB
ejpam-4920	270	11	hop	hop	NOUN
ejpam-4920	270	12	dominating	dominating	NOUN
ejpam-4920	270	13	set	set	VERB
ejpam-4920	270	14	in	in	ADP
ejpam-4920	270	15	s	s	PROPN
ejpam-4920	270	16	+	+	X
ejpam-4920	270	17	t	t	NOUN
ejpam-4920	270	18	.	.	PUNCT
ejpam-4920	271	1	then	then	ADV
ejpam-4920	271	2	z	z	PROPN
ejpam-4920	271	3	is	be	AUX
ejpam-4920	271	4	a	a	DET
ejpam-4920	271	5	zero	zero	NUM
ejpam-4920	271	6	forcing	forcing	NOUN
ejpam-4920	271	7	in	in	ADP
ejpam-4920	271	8	s+t	s+t	PROPN
ejpam-4920	271	9	.	.	PUNCT
ejpam-4920	272	1	suppose	suppose	VERB
ejpam-4920	272	2	that	that	SCONJ
ejpam-4920	272	3	zs	zs	PROPN
ejpam-4920	272	4	=	=	SYM
ejpam-4920	272	5	v	v	PROPN
ejpam-4920	272	6	(	(	PUNCT
ejpam-4920	272	7	s	s	NOUN
ejpam-4920	272	8	)	)	PUNCT
ejpam-4920	272	9	.	.	PUNCT
ejpam-4920	273	1	if	if	SCONJ
ejpam-4920	273	2	zt	zt	PROPN
ejpam-4920	273	3	=	=	SYM
ejpam-4920	273	4	v	v	PROPN
ejpam-4920	273	5	(	(	PUNCT
ejpam-4920	273	6	t	t	PROPN
ejpam-4920	273	7	)	)	PUNCT
ejpam-4920	273	8	,	,	PUNCT
ejpam-4920	273	9	then	then	ADV
ejpam-4920	273	10	we	we	PRON
ejpam-4920	273	11	are	be	AUX
ejpam-4920	273	12	done	do	VERB
ejpam-4920	273	13	.	.	PUNCT
ejpam-4920	274	1	assume	assume	VERB
ejpam-4920	274	2	that	that	SCONJ
ejpam-4920	274	3	zt	zt	PROPN
ejpam-4920	274	4	̸=	̸=	PROPN
ejpam-4920	274	5	v	v	PROPN
ejpam-4920	274	6	(	(	PUNCT
ejpam-4920	274	7	t	t	PROPN
ejpam-4920	274	8	)	)	PUNCT
ejpam-4920	274	9	.	.	PUNCT
ejpam-4920	275	1	suppose	suppose	VERB
ejpam-4920	275	2	zt	zt	PROPN
ejpam-4920	275	3	is	be	AUX
ejpam-4920	275	4	not	not	PART
ejpam-4920	275	5	a	a	DET
ejpam-4920	275	6	zero	zero	NUM
ejpam-4920	275	7	forcing	forcing	NOUN
ejpam-4920	275	8	set	set	NOUN
ejpam-4920	275	9	in	in	ADP
ejpam-4920	275	10	t	t	PROPN
ejpam-4920	275	11	.	.	PUNCT
ejpam-4920	276	1	then	then	ADV
ejpam-4920	276	2	there	there	PRON
ejpam-4920	276	3	exists	exist	VERB
ejpam-4920	276	4	w	w	PROPN
ejpam-4920	276	5	∈	∈	PROPN
ejpam-4920	276	6	zt	zt	PROPN
ejpam-4920	276	7	such	such	ADJ
ejpam-4920	276	8	that	that	SCONJ
ejpam-4920	276	9	w	w	NOUN
ejpam-4920	276	10	can	can	AUX
ejpam-4920	276	11	not	not	PART
ejpam-4920	276	12	be	be	AUX
ejpam-4920	276	13	forced	force	VERB
ejpam-4920	276	14	by	by	ADP
ejpam-4920	276	15	any	any	DET
ejpam-4920	276	16	element	element	NOUN
ejpam-4920	276	17	in	in	ADP
ejpam-4920	276	18	zt	zt	PROPN
ejpam-4920	276	19	.	.	PUNCT
ejpam-4920	277	1	thus	thus	ADV
ejpam-4920	277	2	,	,	PUNCT
ejpam-4920	277	3	w	w	PROPN
ejpam-4920	277	4	can	can	AUX
ejpam-4920	277	5	not	not	PART
ejpam-4920	277	6	be	be	AUX
ejpam-4920	277	7	forced	force	VERB
ejpam-4920	277	8	by	by	ADP
ejpam-4920	277	9	any	any	DET
ejpam-4920	277	10	element	element	NOUN
ejpam-4920	277	11	of	of	ADP
ejpam-4920	277	12	z	z	PROPN
ejpam-4920	277	13	,	,	PUNCT
ejpam-4920	277	14	which	which	PRON
ejpam-4920	277	15	is	be	AUX
ejpam-4920	277	16	a	a	DET
ejpam-4920	277	17	contradiction	contradiction	NOUN
ejpam-4920	277	18	.	.	PUNCT
ejpam-4920	278	1	hence	hence	ADV
ejpam-4920	278	2	,	,	PUNCT
ejpam-4920	278	3	zt	zt	PROPN
ejpam-4920	278	4	is	be	AUX
ejpam-4920	278	5	a	a	DET
ejpam-4920	278	6	zero	zero	NUM
ejpam-4920	278	7	forcing	forcing	NOUN
ejpam-4920	278	8	set	set	NOUN
ejpam-4920	278	9	in	in	ADP
ejpam-4920	278	10	t	t	PROPN
ejpam-4920	278	11	.	.	PUNCT
ejpam-4920	279	1	since	since	SCONJ
ejpam-4920	279	2	z	z	PROPN
ejpam-4920	279	3	is	be	AUX
ejpam-4920	279	4	a	a	DET
ejpam-4920	279	5	hop	hop	NOUN
ejpam-4920	279	6	dominating	dominating	NOUN
ejpam-4920	279	7	,	,	PUNCT
ejpam-4920	279	8	zt	zt	PROPN
ejpam-4920	279	9	is	be	AUX
ejpam-4920	279	10	a	a	DET
ejpam-4920	279	11	pnd	pnd	NOUN
ejpam-4920	279	12	set	set	VERB
ejpam-4920	279	13	in	in	ADP
ejpam-4920	279	14	t	t	NOUN
ejpam-4920	279	15	by	by	ADP
ejpam-4920	279	16	theorem	theorem	NOUN
ejpam-4920	279	17	5	5	NUM
ejpam-4920	279	18	.	.	PUNCT
ejpam-4920	280	1	consequently	consequently	ADV
ejpam-4920	280	2	,	,	PUNCT
ejpam-4920	280	3	zt	zt	PROPN
ejpam-4920	280	4	is	be	AUX
ejpam-4920	280	5	a	a	DET
ejpam-4920	280	6	zfpnd	zfpnd	NOUN
ejpam-4920	280	7	set	set	VERB
ejpam-4920	280	8	in	in	ADP
ejpam-4920	280	9	t	t	PROPN
ejpam-4920	280	10	,	,	PUNCT
ejpam-4920	280	11	and	and	CCONJ
ejpam-4920	280	12	so	so	ADV
ejpam-4920	280	13	(	(	PUNCT
ejpam-4920	280	14	i	i	NOUN
ejpam-4920	280	15	)	)	PUNCT
ejpam-4920	280	16	holds	hold	VERB
ejpam-4920	280	17	.	.	PUNCT
ejpam-4920	281	1	the	the	DET
ejpam-4920	281	2	(	(	PUNCT
ejpam-4920	281	3	ii	ii	NOUN
ejpam-4920	281	4	)	)	PUNCT
ejpam-4920	281	5	can	can	AUX
ejpam-4920	281	6	be	be	AUX
ejpam-4920	281	7	proved	prove	VERB
ejpam-4920	281	8	in	in	ADP
ejpam-4920	281	9	similar	similar	ADJ
ejpam-4920	281	10	manner	manner	NOUN
ejpam-4920	281	11	.	.	PUNCT
ejpam-4920	282	1	next	next	ADV
ejpam-4920	282	2	,	,	PUNCT
ejpam-4920	282	3	suppose	suppose	VERB
ejpam-4920	282	4	that	that	SCONJ
ejpam-4920	282	5	zs	zs	PROPN
ejpam-4920	282	6	̸=	̸=	PROPN
ejpam-4920	282	7	v	v	PROPN
ejpam-4920	282	8	(	(	PUNCT
ejpam-4920	282	9	s	s	NOUN
ejpam-4920	282	10	)	)	PUNCT
ejpam-4920	282	11	and	and	CCONJ
ejpam-4920	282	12	zt	zt	PROPN
ejpam-4920	282	13	̸=	̸=	PROPN
ejpam-4920	282	14	v	v	PROPN
ejpam-4920	282	15	(	(	PUNCT
ejpam-4920	282	16	t	t	PROPN
ejpam-4920	282	17	)	)	PUNCT
ejpam-4920	282	18	then	then	ADV
ejpam-4920	282	19	there	there	PRON
ejpam-4920	282	20	exists	exist	VERB
ejpam-4920	282	21	u	u	PROPN
ejpam-4920	282	22	∈	∈	PROPN
ejpam-4920	282	23	v	v	ADP
ejpam-4920	282	24	(	(	PUNCT
ejpam-4920	282	25	s	s	NOUN
ejpam-4920	282	26	)	)	PUNCT
ejpam-4920	282	27	\	\	NOUN
ejpam-4920	282	28	zs	zs	PROPN
ejpam-4920	282	29	and	and	CCONJ
ejpam-4920	282	30	v	v	ADP
ejpam-4920	282	31	∈	∈	PROPN
ejpam-4920	282	32	v	v	NOUN
ejpam-4920	282	33	(	(	PUNCT
ejpam-4920	282	34	t	t	PROPN
ejpam-4920	282	35	)	)	PUNCT
ejpam-4920	282	36	\	\	PROPN
ejpam-4920	283	1	zt	zt	PROPN
ejpam-4920	283	2	.	.	PUNCT
ejpam-4920	284	1	if	if	SCONJ
ejpam-4920	284	2	|zs	|zs	PRON
ejpam-4920	284	3	|	|	ADV
ejpam-4920	284	4	≤	≤	NUM
ejpam-4920	284	5	|v	|v	X
ejpam-4920	284	6	(	(	PUNCT
ejpam-4920	284	7	g)|−2	g)|−2	NOUN
ejpam-4920	284	8	,	,	PUNCT
ejpam-4920	284	9	then	then	ADV
ejpam-4920	284	10	there	there	PRON
ejpam-4920	284	11	exist	exist	VERB
ejpam-4920	284	12	at	at	ADV
ejpam-4920	284	13	least	least	ADV
ejpam-4920	284	14	two	two	NUM
ejpam-4920	284	15	vertices	vertex	NOUN
ejpam-4920	284	16	s	s	PART
ejpam-4920	284	17	,	,	PUNCT
ejpam-4920	284	18	t	t	PROPN
ejpam-4920	284	19	∈	∈	PROPN
ejpam-4920	284	20	v	v	NOUN
ejpam-4920	284	21	(	(	PUNCT
ejpam-4920	284	22	s)\zs	s)\zs	PROPN
ejpam-4920	284	23	.	.	PUNCT
ejpam-4920	285	1	however	however	ADV
ejpam-4920	285	2	,	,	PUNCT
ejpam-4920	285	3	any	any	DET
ejpam-4920	285	4	element	element	NOUN
ejpam-4920	285	5	of	of	ADP
ejpam-4920	285	6	zs	zs	PROPN
ejpam-4920	285	7	and	and	CCONJ
ejpam-4920	285	8	zt	zt	PROPN
ejpam-4920	285	9	can	can	AUX
ejpam-4920	285	10	not	not	PART
ejpam-4920	285	11	forces	force	VERB
ejpam-4920	285	12	vertices	vertex	NOUN
ejpam-4920	285	13	s	s	PART
ejpam-4920	285	14	and	and	CCONJ
ejpam-4920	285	15	t	t	PROPN
ejpam-4920	285	16	,	,	PUNCT
ejpam-4920	285	17	a	a	DET
ejpam-4920	285	18	contradiction	contradiction	NOUN
ejpam-4920	285	19	.	.	PUNCT
ejpam-4920	286	1	thus	thus	ADV
ejpam-4920	286	2	,	,	PUNCT
ejpam-4920	286	3	|zs	|zs	PRON
ejpam-4920	286	4	|	|	ADV
ejpam-4920	286	5	=	=	SYM
ejpam-4920	286	6	|v	|v	PROPN
ejpam-4920	286	7	(	(	PUNCT
ejpam-4920	286	8	s)|−1	s)|−1	VERB
ejpam-4920	286	9	.	.	PUNCT
ejpam-4920	287	1	similarly	similarly	ADV
ejpam-4920	287	2	,	,	PUNCT
ejpam-4920	287	3	|zt	|zt	NUM
ejpam-4920	287	4	|	|	ADV
ejpam-4920	287	5	=	=	SYM
ejpam-4920	287	6	|v	|v	X
ejpam-4920	287	7	(	(	PUNCT
ejpam-4920	287	8	t	t	NOUN
ejpam-4920	287	9	)	)	PUNCT
ejpam-4920	287	10	|−1	|−1	PUNCT
ejpam-4920	287	11	.	.	PUNCT
ejpam-4920	288	1	let	let	VERB
ejpam-4920	288	2	v	v	NOUN
ejpam-4920	288	3	(	(	PUNCT
ejpam-4920	288	4	s	s	NOUN
ejpam-4920	288	5	)	)	PUNCT
ejpam-4920	288	6	=	=	SYM
ejpam-4920	288	7	{	{	PUNCT
ejpam-4920	288	8	v1	v1	PROPN
ejpam-4920	288	9	,	,	PUNCT
ejpam-4920	288	10	v2	v2	PROPN
ejpam-4920	288	11	,	,	PUNCT
ejpam-4920	288	12	.	.	PUNCT
ejpam-4920	288	13	.	.	PUNCT
ejpam-4920	289	1	.	.	PUNCT
ejpam-4920	290	1	,	,	PUNCT
ejpam-4920	290	2	vm	vm	NOUN
ejpam-4920	290	3	}	}	PUNCT
ejpam-4920	290	4	and	and	CCONJ
ejpam-4920	290	5	v	v	X
ejpam-4920	290	6	(	(	PUNCT
ejpam-4920	290	7	t	t	PROPN
ejpam-4920	290	8	)	)	PUNCT
ejpam-4920	290	9	=	=	PRON
ejpam-4920	290	10	{	{	PUNCT
ejpam-4920	290	11	u1	u1	NOUN
ejpam-4920	290	12	,	,	PUNCT
ejpam-4920	290	13	u2	u2	NOUN
ejpam-4920	290	14	,	,	PUNCT
ejpam-4920	290	15	.	.	PUNCT
ejpam-4920	290	16	.	.	PUNCT
ejpam-4920	291	1	.	.	PUNCT
ejpam-4920	292	1	,	,	PUNCT
ejpam-4920	292	2	un	un	PROPN
ejpam-4920	292	3	}	}	PUNCT
ejpam-4920	292	4	and	and	CCONJ
ejpam-4920	292	5	let	let	VERB
ejpam-4920	292	6	zs	zs	PROPN
ejpam-4920	292	7	=	=	SYM
ejpam-4920	292	8	v	v	PROPN
ejpam-4920	292	9	(	(	PUNCT
ejpam-4920	292	10	s	s	NOUN
ejpam-4920	292	11	)	)	PUNCT
ejpam-4920	292	12	\	\	NOUN
ejpam-4920	292	13	{	{	PUNCT
ejpam-4920	292	14	vi	vi	NOUN
ejpam-4920	292	15	}	}	PUNCT
ejpam-4920	292	16	and	and	CCONJ
ejpam-4920	292	17	zt	zt	PROPN
ejpam-4920	292	18	=	=	SYM
ejpam-4920	292	19	v	v	PROPN
ejpam-4920	292	20	(	(	PUNCT
ejpam-4920	292	21	t	t	PROPN
ejpam-4920	292	22	)	)	PUNCT
ejpam-4920	292	23	\	\	PROPN
ejpam-4920	293	1	{	{	PUNCT
ejpam-4920	293	2	uj	uj	PROPN
ejpam-4920	293	3	}	}	PUNCT
ejpam-4920	293	4	for	for	ADP
ejpam-4920	293	5	some	some	DET
ejpam-4920	293	6	i	i	PRON
ejpam-4920	293	7	∈	∈	PROPN
ejpam-4920	293	8	{	{	PUNCT
ejpam-4920	293	9	1	1	NUM
ejpam-4920	293	10	,	,	PUNCT
ejpam-4920	293	11	2	2	NUM
ejpam-4920	293	12	,	,	PUNCT
ejpam-4920	293	13	.	.	PUNCT
ejpam-4920	293	14	.	.	PUNCT
ejpam-4920	293	15	.	.	PUNCT
ejpam-4920	294	1	,	,	PUNCT
ejpam-4920	294	2	m	m	VERB
ejpam-4920	294	3	}	}	PUNCT
ejpam-4920	294	4	,	,	PUNCT
ejpam-4920	294	5	j	j	PROPN
ejpam-4920	294	6	∈	∈	PROPN
ejpam-4920	294	7	{	{	PUNCT
ejpam-4920	294	8	1	1	NUM
ejpam-4920	294	9	,	,	PUNCT
ejpam-4920	294	10	2	2	NUM
ejpam-4920	294	11	,	,	PUNCT
ejpam-4920	294	12	.	.	PUNCT
ejpam-4920	294	13	.	.	PUNCT
ejpam-4920	294	14	.	.	PUNCT
ejpam-4920	294	15	,	,	PUNCT
ejpam-4920	294	16	n	n	CCONJ
ejpam-4920	294	17	}	}	PUNCT
ejpam-4920	294	18	.	.	PUNCT
ejpam-4920	295	1	clearly	clearly	ADV
ejpam-4920	295	2	,	,	PUNCT
ejpam-4920	295	3	zs	zs	PROPN
ejpam-4920	295	4	and	and	CCONJ
ejpam-4920	295	5	zt	zt	PROPN
ejpam-4920	295	6	are	be	AUX
ejpam-4920	295	7	zero	zero	NUM
ejpam-4920	295	8	forcing	force	VERB
ejpam-4920	295	9	sets	set	NOUN
ejpam-4920	295	10	in	in	ADP
ejpam-4920	295	11	s	s	PRON
ejpam-4920	295	12	and	and	CCONJ
ejpam-4920	295	13	t	t	NOUN
ejpam-4920	295	14	,	,	PUNCT
ejpam-4920	295	15	respectively	respectively	ADV
ejpam-4920	295	16	.	.	PUNCT
ejpam-4920	296	1	since	since	SCONJ
ejpam-4920	296	2	z	z	NOUN
ejpam-4920	296	3	=	=	SYM
ejpam-4920	296	4	zs	zs	PROPN
ejpam-4920	296	5	∪zt	∪zt	NOUN
ejpam-4920	296	6	is	be	AUX
ejpam-4920	296	7	a	a	DET
ejpam-4920	296	8	hop	hop	NOUN
ejpam-4920	296	9	dominating	dominating	NOUN
ejpam-4920	296	10	set	set	VERB
ejpam-4920	296	11	in	in	ADP
ejpam-4920	296	12	s	s	PROPN
ejpam-4920	296	13	+	+	X
ejpam-4920	296	14	t	t	NOUN
ejpam-4920	296	15	,	,	PUNCT
ejpam-4920	296	16	it	it	PRON
ejpam-4920	296	17	follows	follow	VERB
ejpam-4920	296	18	that	that	SCONJ
ejpam-4920	296	19	zs	zs	PROPN
ejpam-4920	296	20	and	and	CCONJ
ejpam-4920	296	21	zt	zt	PROPN
ejpam-4920	296	22	are	be	AUX
ejpam-4920	296	23	pnd	pnd	NOUN
ejpam-4920	296	24	sets	set	NOUN
ejpam-4920	296	25	in	in	ADP
ejpam-4920	296	26	s	s	PRON
ejpam-4920	296	27	and	and	CCONJ
ejpam-4920	296	28	t	t	PROPN
ejpam-4920	296	29	,	,	PUNCT
ejpam-4920	296	30	respectively	respectively	ADV
ejpam-4920	296	31	,	,	PUNCT
ejpam-4920	296	32	by	by	ADP
ejpam-4920	296	33	theorem	theorem	NOUN
ejpam-4920	296	34	5	5	NUM
ejpam-4920	296	35	.	.	PUNCT
ejpam-4920	297	1	therefore	therefore	ADV
ejpam-4920	297	2	,	,	PUNCT
ejpam-4920	297	3	zs	zs	PROPN
ejpam-4920	297	4	and	and	CCONJ
ejpam-4920	297	5	zt	zt	PROPN
ejpam-4920	297	6	are	be	AUX
ejpam-4920	297	7	zfpnd	zfpnd	NOUN
ejpam-4920	297	8	sets	set	NOUN
ejpam-4920	297	9	in	in	ADP
ejpam-4920	297	10	s	s	PRON
ejpam-4920	297	11	and	and	CCONJ
ejpam-4920	297	12	t	t	PROPN
ejpam-4920	297	13	,	,	PUNCT
ejpam-4920	297	14	respectively	respectively	ADV
ejpam-4920	297	15	,	,	PUNCT
ejpam-4920	297	16	showing	show	VERB
ejpam-4920	297	17	that	that	SCONJ
ejpam-4920	297	18	(	(	PUNCT
ejpam-4920	297	19	iii	iii	NOUN
ejpam-4920	297	20	)	)	PUNCT
ejpam-4920	297	21	holds	hold	VERB
ejpam-4920	297	22	.	.	PUNCT
ejpam-4920	298	1	conversely	conversely	ADV
ejpam-4920	298	2	,	,	PUNCT
ejpam-4920	298	3	suppose	suppose	VERB
ejpam-4920	298	4	that	that	SCONJ
ejpam-4920	298	5	(	(	PUNCT
ejpam-4920	298	6	i	i	NOUN
ejpam-4920	298	7	)	)	PUNCT
ejpam-4920	298	8	holds	hold	VERB
ejpam-4920	298	9	.	.	PUNCT
ejpam-4920	299	1	since	since	SCONJ
ejpam-4920	299	2	zt	zt	PROPN
ejpam-4920	299	3	is	be	AUX
ejpam-4920	299	4	a	a	DET
ejpam-4920	299	5	pnd	pnd	NOUN
ejpam-4920	299	6	set	set	VERB
ejpam-4920	299	7	in	in	ADP
ejpam-4920	299	8	t	t	PROPN
ejpam-4920	299	9	,	,	PUNCT
ejpam-4920	299	10	it	it	PRON
ejpam-4920	299	11	follows	follow	VERB
ejpam-4920	299	12	that	that	SCONJ
ejpam-4920	299	13	z	z	NOUN
ejpam-4920	299	14	=	=	SYM
ejpam-4920	299	15	v	v	X
ejpam-4920	299	16	(	(	PUNCT
ejpam-4920	299	17	s	s	NOUN
ejpam-4920	299	18	)	)	PUNCT
ejpam-4920	299	19	∪	∪	NOUN
ejpam-4920	299	20	zt	zt	PROPN
ejpam-4920	299	21	is	be	AUX
ejpam-4920	299	22	a	a	DET
ejpam-4920	299	23	hop	hop	NOUN
ejpam-4920	299	24	dominating	dominating	NOUN
ejpam-4920	299	25	set	set	NOUN
ejpam-4920	299	26	s	s	PART
ejpam-4920	299	27	+	+	X
ejpam-4920	299	28	t	t	NOUN
ejpam-4920	299	29	by	by	ADP
ejpam-4920	299	30	theorem	theorem	NOUN
ejpam-4920	299	31	5	5	NUM
ejpam-4920	299	32	.	.	PUNCT
ejpam-4920	299	33	since	since	SCONJ
ejpam-4920	299	34	zt	zt	PROPN
ejpam-4920	299	35	is	be	AUX
ejpam-4920	299	36	also	also	ADV
ejpam-4920	299	37	a	a	DET
ejpam-4920	299	38	zero	zero	NUM
ejpam-4920	299	39	forcing	forcing	NOUN
ejpam-4920	299	40	set	set	NOUN
ejpam-4920	299	41	in	in	ADP
ejpam-4920	299	42	t	t	PROPN
ejpam-4920	299	43	,	,	PUNCT
ejpam-4920	299	44	z	z	PROPN
ejpam-4920	299	45	=	=	SYM
ejpam-4920	299	46	v	v	X
ejpam-4920	299	47	(	(	PUNCT
ejpam-4920	299	48	s	s	NOUN
ejpam-4920	299	49	)	)	PUNCT
ejpam-4920	299	50	∪	∪	NOUN
ejpam-4920	300	1	zt	zt	PROPN
ejpam-4920	300	2	is	be	AUX
ejpam-4920	300	3	a	a	DET
ejpam-4920	300	4	zero	zero	NUM
ejpam-4920	300	5	forcing	forcing	NOUN
ejpam-4920	300	6	set	set	NOUN
ejpam-4920	300	7	in	in	ADP
ejpam-4920	300	8	s	s	PROPN
ejpam-4920	300	9	+	+	X
ejpam-4920	300	10	t	t	NOUN
ejpam-4920	300	11	.	.	PUNCT
ejpam-4920	301	1	hence	hence	ADV
ejpam-4920	301	2	,	,	PUNCT
ejpam-4920	301	3	z	z	NOUN
ejpam-4920	301	4	=	=	SYM
ejpam-4920	301	5	v	v	X
ejpam-4920	301	6	(	(	PUNCT
ejpam-4920	301	7	s	s	NOUN
ejpam-4920	301	8	)	)	PUNCT
ejpam-4920	301	9	∪	∪	NOUN
ejpam-4920	301	10	zt	zt	PROPN
ejpam-4920	301	11	is	be	AUX
ejpam-4920	301	12	a	a	DET
ejpam-4920	301	13	zero	zero	NUM
ejpam-4920	301	14	forcing	force	VERB
ejpam-4920	301	15	hop	hop	NOUN
ejpam-4920	301	16	dominating	dominating	NOUN
ejpam-4920	301	17	set	set	VERB
ejpam-4920	301	18	in	in	ADP
ejpam-4920	301	19	s	s	PROPN
ejpam-4920	301	20	+	+	X
ejpam-4920	301	21	t	t	PROPN
ejpam-4920	301	22	.	.	PUNCT
ejpam-4920	302	1	similarly	similarly	ADV
ejpam-4920	302	2	,	,	PUNCT
ejpam-4920	302	3	if	if	SCONJ
ejpam-4920	302	4	(	(	PUNCT
ejpam-4920	302	5	ii	ii	NOUN
ejpam-4920	302	6	)	)	PUNCT
ejpam-4920	302	7	holds	hold	VERB
ejpam-4920	302	8	,	,	PUNCT
ejpam-4920	302	9	then	then	ADV
ejpam-4920	302	10	the	the	DET
ejpam-4920	302	11	assertion	assertion	NOUN
ejpam-4920	302	12	follows	follow	VERB
ejpam-4920	302	13	.	.	PUNCT
ejpam-4920	303	1	now	now	ADV
ejpam-4920	303	2	,	,	PUNCT
ejpam-4920	303	3	suppose	suppose	VERB
ejpam-4920	303	4	that	that	SCONJ
ejpam-4920	303	5	(	(	PUNCT
ejpam-4920	303	6	iii	iii	NOUN
ejpam-4920	303	7	)	)	PUNCT
ejpam-4920	303	8	holds	hold	VERB
ejpam-4920	303	9	.	.	PUNCT
ejpam-4920	304	1	then	then	ADV
ejpam-4920	304	2	z	z	PROPN
ejpam-4920	304	3	is	be	AUX
ejpam-4920	304	4	a	a	DET
ejpam-4920	304	5	hop	hop	NOUN
ejpam-4920	304	6	dominating	dominating	NOUN
ejpam-4920	304	7	set	set	VERB
ejpam-4920	304	8	in	in	ADP
ejpam-4920	304	9	s	s	PROPN
ejpam-4920	304	10	+	+	X
ejpam-4920	304	11	t	t	NOUN
ejpam-4920	304	12	by	by	ADP
ejpam-4920	304	13	theorem	theorem	NOUN
ejpam-4920	304	14	5	5	NUM
ejpam-4920	304	15	.	.	PUNCT
ejpam-4920	305	1	since	since	SCONJ
ejpam-4920	305	2	s	s	PROPN
ejpam-4920	305	3	is	be	AUX
ejpam-4920	305	4	non	non	ADJ
ejpam-4920	305	5	-	-	ADJ
ejpam-4920	305	6	complete	complete	ADJ
ejpam-4920	305	7	,	,	PUNCT
ejpam-4920	305	8	there	there	PRON
ejpam-4920	305	9	exist	exist	VERB
ejpam-4920	305	10	x	x	NOUN
ejpam-4920	305	11	,	,	PUNCT
ejpam-4920	305	12	y	y	PROPN
ejpam-4920	305	13	∈	∈	PROPN
ejpam-4920	305	14	v	v	ADP
ejpam-4920	305	15	(	(	PUNCT
ejpam-4920	305	16	s	s	NOUN
ejpam-4920	305	17	)	)	PUNCT
ejpam-4920	305	18	such	such	ADJ
ejpam-4920	305	19	that	that	DET
ejpam-4920	305	20	ds(x	ds(x	PROPN
ejpam-4920	305	21	,	,	PUNCT
ejpam-4920	305	22	y	y	NOUN
ejpam-4920	305	23	)	)	PUNCT
ejpam-4920	305	24	=	=	SYM
ejpam-4920	306	1	2	2	X
ejpam-4920	306	2	.	.	PUNCT
ejpam-4920	306	3	since	since	SCONJ
ejpam-4920	306	4	zs	zs	PROPN
ejpam-4920	306	5	=	=	SYM
ejpam-4920	306	6	v	v	PROPN
ejpam-4920	306	7	(	(	PUNCT
ejpam-4920	306	8	s	s	NOUN
ejpam-4920	306	9	)	)	PUNCT
ejpam-4920	306	10	\	\	NOUN
ejpam-4920	306	11	{	{	PUNCT
ejpam-4920	306	12	a	a	NOUN
ejpam-4920	306	13	}	}	PUNCT
ejpam-4920	306	14	for	for	ADP
ejpam-4920	306	15	some	some	PRON
ejpam-4920	306	16	a	a	DET
ejpam-4920	306	17	∈	∈	PROPN
ejpam-4920	306	18	v	v	ADP
ejpam-4920	306	19	(	(	PUNCT
ejpam-4920	306	20	s	s	NOUN
ejpam-4920	306	21	)	)	PUNCT
ejpam-4920	306	22	,	,	PUNCT
ejpam-4920	306	23	we	we	PRON
ejpam-4920	306	24	let	let	VERB
ejpam-4920	306	25	y	y	PROPN
ejpam-4920	306	26	=	=	PUNCT
ejpam-4920	306	27	a	a	PROPN
ejpam-4920	306	28	and	and	CCONJ
ejpam-4920	306	29	so	so	ADV
ejpam-4920	306	30	x	x	SYM
ejpam-4920	306	31	∈	∈	PROPN
ejpam-4920	306	32	zs	zs	X
ejpam-4920	306	33	.	.	PUNCT
ejpam-4920	307	1	then	then	ADV
ejpam-4920	307	2	x	x	PUNCT
ejpam-4920	307	3	forces	force	VERB
ejpam-4920	307	4	all	all	DET
ejpam-4920	307	5	the	the	DET
ejpam-4920	307	6	vertices	vertex	NOUN
ejpam-4920	307	7	in	in	ADP
ejpam-4920	307	8	v	v	NOUN
ejpam-4920	307	9	(	(	PUNCT
ejpam-4920	307	10	s	s	NOUN
ejpam-4920	307	11	+	+	X
ejpam-4920	307	12	t	t	NOUN
ejpam-4920	307	13	)	)	PUNCT
ejpam-4920	307	14	\	\	PROPN
ejpam-4920	308	1	z	z	X
ejpam-4920	308	2	,	,	PUNCT
ejpam-4920	308	3	that	that	ADV
ejpam-4920	308	4	is	is	ADV
ejpam-4920	308	5	,	,	PUNCT
ejpam-4920	308	6	z	z	PROPN
ejpam-4920	308	7	is	be	AUX
ejpam-4920	308	8	a	a	DET
ejpam-4920	308	9	zero	zero	NUM
ejpam-4920	308	10	forcing	forcing	NOUN
ejpam-4920	308	11	set	set	NOUN
ejpam-4920	308	12	in	in	ADP
ejpam-4920	308	13	s	s	PROPN
ejpam-4920	308	14	+	+	X
ejpam-4920	308	15	t	t	PROPN
ejpam-4920	308	16	.	.	PUNCT
ejpam-4920	309	1	therefore	therefore	ADV
ejpam-4920	309	2	,	,	PUNCT
ejpam-4920	309	3	z	z	PROPN
ejpam-4920	309	4	is	be	AUX
ejpam-4920	309	5	a	a	DET
ejpam-4920	309	6	zero	zero	NUM
ejpam-4920	309	7	forcing	force	VERB
ejpam-4920	309	8	hop	hop	NOUN
ejpam-4920	309	9	dominating	dominating	NOUN
ejpam-4920	309	10	set	set	VERB
ejpam-4920	309	11	in	in	ADP
ejpam-4920	309	12	s	s	PROPN
ejpam-4920	309	13	+	+	X
ejpam-4920	309	14	t	t	NOUN
ejpam-4920	309	15	.	.	PUNCT
ejpam-4920	310	1	the	the	DET
ejpam-4920	310	2	following	following	ADJ
ejpam-4920	310	3	result	result	NOUN
ejpam-4920	310	4	follows	follow	VERB
ejpam-4920	310	5	from	from	ADP
ejpam-4920	310	6	theorem	theorem	ADJ
ejpam-4920	310	7	6	6	NUM
ejpam-4920	310	8	.	.	PUNCT
ejpam-4920	310	9	corollary	corollary	ADJ
ejpam-4920	310	10	3	3	X
ejpam-4920	310	11	.	.	PUNCT
ejpam-4920	311	1	let	let	VERB
ejpam-4920	311	2	s	s	PRON
ejpam-4920	311	3	and	and	CCONJ
ejpam-4920	311	4	t	t	PROPN
ejpam-4920	311	5	be	be	AUX
ejpam-4920	311	6	two	two	NUM
ejpam-4920	311	7	non	non	ADJ
ejpam-4920	311	8	-	-	ADJ
ejpam-4920	311	9	complete	complete	ADJ
ejpam-4920	311	10	graphs	graph	NOUN
ejpam-4920	311	11	.	.	PUNCT
ejpam-4920	312	1	then	then	ADV
ejpam-4920	312	2	γzh(s	γzh(s	PROPN
ejpam-4920	312	3	+	+	NUM
ejpam-4920	312	4	t	t	NOUN
ejpam-4920	312	5	)	)	PUNCT
ejpam-4920	313	1	=	=	PUNCT
ejpam-4920	313	2	min{|v	min{|v	PROPN
ejpam-4920	313	3	(	(	PUNCT
ejpam-4920	313	4	s)|+	s)|+	ADJ
ejpam-4920	313	5	|v	|v	PROPN
ejpam-4920	313	6	(	(	PUNCT
ejpam-4920	313	7	t	t	NOUN
ejpam-4920	313	8	)	)	PUNCT
ejpam-4920	313	9	|	|	ADV
ejpam-4920	313	10	−	−	PROPN
ejpam-4920	313	11	2	2	NUM
ejpam-4920	313	12	,	,	PUNCT
ejpam-4920	313	13	|v	|v	X
ejpam-4920	313	14	(	(	PUNCT
ejpam-4920	313	15	s)|+	s)|+	ADV
ejpam-4920	313	16	zfpnd(t	zfpnd(t	ADV
ejpam-4920	313	17	)	)	PUNCT
ejpam-4920	313	18	,	,	PUNCT
ejpam-4920	313	19	|v	|v	PROPN
ejpam-4920	313	20	(	(	PUNCT
ejpam-4920	313	21	t	t	NOUN
ejpam-4920	313	22	)	)	PUNCT
ejpam-4920	313	23	|+	|+	NOUN
ejpam-4920	313	24	zfpnd(s	zfpnd(s	NUM
ejpam-4920	313	25	)	)	PUNCT
ejpam-4920	313	26	}	}	PUNCT
ejpam-4920	313	27	.	.	PUNCT
ejpam-4920	314	1	theorem	theorem	VERB
ejpam-4920	314	2	7	7	NUM
ejpam-4920	314	3	.	.	PUNCT
ejpam-4920	315	1	let	let	VERB
ejpam-4920	315	2	j	j	PROPN
ejpam-4920	315	3	and	and	CCONJ
ejpam-4920	315	4	k	k	PROPN
ejpam-4920	315	5	be	be	AUX
ejpam-4920	315	6	complete	complete	ADJ
ejpam-4920	315	7	and	and	CCONJ
ejpam-4920	315	8	non	non	ADJ
ejpam-4920	315	9	-	-	ADJ
ejpam-4920	315	10	complete	complete	ADJ
ejpam-4920	315	11	graphs	graph	NOUN
ejpam-4920	315	12	,	,	PUNCT
ejpam-4920	315	13	respectively	respectively	ADV
ejpam-4920	315	14	.	.	PUNCT
ejpam-4920	316	1	a	a	DET
ejpam-4920	316	2	subset	subset	NOUN
ejpam-4920	316	3	z	z	NOUN
ejpam-4920	316	4	of	of	ADP
ejpam-4920	316	5	v	v	NOUN
ejpam-4920	316	6	(	(	PUNCT
ejpam-4920	316	7	j	j	PROPN
ejpam-4920	316	8	+	+	PROPN
ejpam-4920	316	9	k	k	NOUN
ejpam-4920	316	10	)	)	PUNCT
ejpam-4920	316	11	is	be	AUX
ejpam-4920	316	12	a	a	DET
ejpam-4920	316	13	zero	zero	NUM
ejpam-4920	316	14	forcing	force	VERB
ejpam-4920	316	15	hop	hop	NOUN
ejpam-4920	316	16	dominating	dominating	NOUN
ejpam-4920	316	17	set	set	VERB
ejpam-4920	316	18	in	in	ADP
ejpam-4920	316	19	j	j	PROPN
ejpam-4920	317	1	+	+	PROPN
ejpam-4920	317	2	k	k	PROPN
ejpam-4920	317	3	if	if	SCONJ
ejpam-4920	317	4	and	and	CCONJ
ejpam-4920	317	5	only	only	ADV
ejpam-4920	317	6	if	if	SCONJ
ejpam-4920	317	7	z	z	NOUN
ejpam-4920	317	8	=	=	SYM
ejpam-4920	317	9	v	v	PROPN
ejpam-4920	317	10	(	(	PUNCT
ejpam-4920	317	11	j)∪zk	j)∪zk	INTJ
ejpam-4920	317	12	,	,	PUNCT
ejpam-4920	317	13	where	where	SCONJ
ejpam-4920	317	14	zk	zk	PROPN
ejpam-4920	317	15	is	be	AUX
ejpam-4920	317	16	a	a	DET
ejpam-4920	317	17	zfpnd	zfpnd	NOUN
ejpam-4920	317	18	set	set	VERB
ejpam-4920	317	19	in	in	ADP
ejpam-4920	317	20	k.	k.	PROPN
ejpam-4920	317	21	proof	proof	PROPN
ejpam-4920	317	22	.	.	PUNCT
ejpam-4920	318	1	let	let	VERB
ejpam-4920	318	2	z	z	PRON
ejpam-4920	318	3	be	be	AUX
ejpam-4920	318	4	a	a	DET
ejpam-4920	318	5	zero	zero	NUM
ejpam-4920	318	6	forcing	force	VERB
ejpam-4920	318	7	hop	hop	NOUN
ejpam-4920	318	8	dominating	dominating	NOUN
ejpam-4920	318	9	set	set	VERB
ejpam-4920	318	10	in	in	ADP
ejpam-4920	318	11	j	j	PROPN
ejpam-4920	318	12	+	+	CCONJ
ejpam-4920	318	13	k.	k.	PROPN
ejpam-4920	318	14	since	since	SCONJ
ejpam-4920	318	15	j	j	PROPN
ejpam-4920	318	16	is	be	AUX
ejpam-4920	318	17	complete	complete	ADJ
ejpam-4920	318	18	,	,	PUNCT
ejpam-4920	318	19	z	z	NOUN
ejpam-4920	318	20	=	=	SYM
ejpam-4920	318	21	v	v	PROPN
ejpam-4920	318	22	(	(	PUNCT
ejpam-4920	318	23	j	j	NOUN
ejpam-4920	318	24	)	)	PUNCT
ejpam-4920	318	25	∪	∪	VERB
ejpam-4920	318	26	zk	zk	PROPN
ejpam-4920	318	27	,	,	PUNCT
ejpam-4920	318	28	zk	zk	PROPN
ejpam-4920	318	29	̸=	̸=	PROPN
ejpam-4920	318	30	∅.	∅.	ADV
ejpam-4920	318	31	thus	thus	ADV
ejpam-4920	318	32	,	,	PUNCT
ejpam-4920	318	33	by	by	ADP
ejpam-4920	318	34	theorem	theorem	NOUN
ejpam-4920	318	35	6(i	6(i	NUM
ejpam-4920	318	36	)	)	PUNCT
ejpam-4920	318	37	,	,	PUNCT
ejpam-4920	318	38	zk	zk	PROPN
ejpam-4920	318	39	is	be	AUX
ejpam-4920	318	40	a	a	DET
ejpam-4920	318	41	zfpnd	zfpnd	NOUN
ejpam-4920	318	42	set	set	VERB
ejpam-4920	318	43	in	in	ADP
ejpam-4920	318	44	k.	k.	PROPN
ejpam-4920	318	45	conversely	conversely	ADV
ejpam-4920	318	46	,	,	PUNCT
ejpam-4920	318	47	suppose	suppose	VERB
ejpam-4920	318	48	that	that	SCONJ
ejpam-4920	318	49	z	z	NOUN
ejpam-4920	318	50	=	=	SYM
ejpam-4920	318	51	v	v	PROPN
ejpam-4920	318	52	(	(	PUNCT
ejpam-4920	318	53	j	j	NOUN
ejpam-4920	318	54	)	)	PUNCT
ejpam-4920	318	55	∪	∪	VERB
ejpam-4920	318	56	zk	zk	PROPN
ejpam-4920	318	57	,	,	PUNCT
ejpam-4920	318	58	where	where	SCONJ
ejpam-4920	318	59	zk	zk	PROPN
ejpam-4920	318	60	is	be	AUX
ejpam-4920	318	61	a	a	DET
ejpam-4920	318	62	zfpnd	zfpnd	NOUN
ejpam-4920	318	63	set	set	VERB
ejpam-4920	318	64	in	in	ADP
ejpam-4920	318	65	k.	k.	PROPN
ejpam-4920	318	66	since	since	SCONJ
ejpam-4920	318	67	zk	zk	PROPN
ejpam-4920	318	68	is	be	AUX
ejpam-4920	318	69	a	a	DET
ejpam-4920	318	70	zero	zero	NUM
ejpam-4920	318	71	forcing	forcing	NOUN
ejpam-4920	318	72	in	in	ADP
ejpam-4920	318	73	k	k	PROPN
ejpam-4920	318	74	,	,	PUNCT
ejpam-4920	318	75	z	z	PROPN
ejpam-4920	318	76	=	=	SYM
ejpam-4920	318	77	v	v	PROPN
ejpam-4920	318	78	(	(	PUNCT
ejpam-4920	318	79	j	j	NOUN
ejpam-4920	318	80	)	)	PUNCT
ejpam-4920	318	81	∪	∪	ADP
ejpam-4920	318	82	zk	zk	PROPN
ejpam-4920	318	83	is	be	AUX
ejpam-4920	318	84	a	a	DET
ejpam-4920	318	85	zero	zero	NUM
ejpam-4920	318	86	forcing	forcing	NOUN
ejpam-4920	318	87	in	in	ADP
ejpam-4920	318	88	j	j	PROPN
ejpam-4920	319	1	+	+	CCONJ
ejpam-4920	319	2	k.	k.	PROPN
ejpam-4920	320	1	moreover	moreover	ADV
ejpam-4920	320	2	,	,	PUNCT
ejpam-4920	320	3	since	since	SCONJ
ejpam-4920	320	4	zk	zk	PROPN
ejpam-4920	320	5	is	be	AUX
ejpam-4920	320	6	pnd	pnd	NOUN
ejpam-4920	320	7	set	set	NOUN
ejpam-4920	320	8	in	in	ADP
ejpam-4920	320	9	k	k	PROPN
ejpam-4920	320	10	,	,	PUNCT
ejpam-4920	320	11	it	it	PRON
ejpam-4920	320	12	follows	follow	VERB
ejpam-4920	320	13	that	that	SCONJ
ejpam-4920	320	14	z	z	NOUN
ejpam-4920	320	15	=	=	SYM
ejpam-4920	320	16	v	v	PROPN
ejpam-4920	320	17	(	(	PUNCT
ejpam-4920	320	18	j	j	NOUN
ejpam-4920	320	19	)	)	PUNCT
ejpam-4920	320	20	∪	∪	ADP
ejpam-4920	320	21	zk	zk	PROPN
ejpam-4920	320	22	is	be	AUX
ejpam-4920	320	23	a	a	DET
ejpam-4920	320	24	hop	hop	NOUN
ejpam-4920	320	25	dominating	dominating	NOUN
ejpam-4920	320	26	set	set	VERB
ejpam-4920	320	27	in	in	ADP
ejpam-4920	320	28	j	j	PROPN
ejpam-4920	321	1	+	+	CCONJ
ejpam-4920	321	2	k	k	PROPN
ejpam-4920	321	3	by	by	ADP
ejpam-4920	321	4	theorem	theorem	NOUN
ejpam-4920	321	5	5	5	NUM
ejpam-4920	321	6	.	.	PUNCT
ejpam-4920	321	7	therefore	therefore	ADV
ejpam-4920	321	8	,	,	PUNCT
ejpam-4920	321	9	z	z	PROPN
ejpam-4920	321	10	is	be	AUX
ejpam-4920	321	11	a	a	PRON
ejpam-4920	321	12	zero	zero	NUM
ejpam-4920	321	13	forcing	force	VERB
ejpam-4920	321	14	hop	hop	NOUN
ejpam-4920	321	15	dominating	dominating	NOUN
ejpam-4920	321	16	set	set	NOUN
ejpam-4920	321	17	of	of	ADP
ejpam-4920	321	18	j	j	PROPN
ejpam-4920	321	19	+	+	PROPN
ejpam-4920	321	20	k.	k.	PROPN
ejpam-4920	321	21	j.	j.	PROPN
ejpam-4920	321	22	u.	u.	PROPN
ejpam-4920	321	23	manditong	manditong	PROPN
ejpam-4920	321	24	et	et	PROPN
ejpam-4920	321	25	al	al	PROPN
ejpam-4920	321	26	.	.	PUNCT
ejpam-4920	321	27	/	/	SYM
ejpam-4920	321	28	eur	eur	PROPN
ejpam-4920	321	29	.	.	PUNCT
ejpam-4920	322	1	j.	j.	PROPN
ejpam-4920	322	2	pure	pure	PROPN
ejpam-4920	322	3	appl	appl	PROPN
ejpam-4920	322	4	.	.	PROPN
ejpam-4920	322	5	math	math	PROPN
ejpam-4920	322	6	,	,	PUNCT
ejpam-4920	322	7	17	17	NUM
ejpam-4920	322	8	(	(	PUNCT
ejpam-4920	322	9	1	1	NUM
ejpam-4920	322	10	)	)	PUNCT
ejpam-4920	322	11	(	(	PUNCT
ejpam-4920	322	12	2024	2024	NUM
ejpam-4920	322	13	)	)	PUNCT
ejpam-4920	322	14	,	,	PUNCT
ejpam-4920	322	15	324	324	NUM
ejpam-4920	322	16	-	-	SYM
ejpam-4920	322	17	337	337	NUM
ejpam-4920	322	18	334	334	NUM
ejpam-4920	322	19	corollary	corollary	ADJ
ejpam-4920	322	20	4	4	NUM
ejpam-4920	322	21	.	.	PUNCT
ejpam-4920	323	1	let	let	VERB
ejpam-4920	323	2	j	j	PROPN
ejpam-4920	323	3	and	and	CCONJ
ejpam-4920	323	4	k	k	PROPN
ejpam-4920	323	5	be	be	AUX
ejpam-4920	323	6	complete	complete	ADJ
ejpam-4920	323	7	and	and	CCONJ
ejpam-4920	323	8	non	non	ADJ
ejpam-4920	323	9	-	-	ADJ
ejpam-4920	323	10	complete	complete	ADJ
ejpam-4920	323	11	graphs	graph	NOUN
ejpam-4920	323	12	,	,	PUNCT
ejpam-4920	323	13	respectively	respectively	ADV
ejpam-4920	323	14	.	.	PUNCT
ejpam-4920	324	1	then	then	ADV
ejpam-4920	324	2	γzh(j	γzh(j	PROPN
ejpam-4920	324	3	+	+	PROPN
ejpam-4920	324	4	k	k	NOUN
ejpam-4920	324	5	)	)	PUNCT
ejpam-4920	324	6	=	=	SYM
ejpam-4920	324	7	|v	|v	PROPN
ejpam-4920	324	8	(	(	PUNCT
ejpam-4920	324	9	j)|+	j)|+	PROPN
ejpam-4920	324	10	zfpnd(k	zfpnd(k	PROPN
ejpam-4920	324	11	)	)	PUNCT
ejpam-4920	324	12	.	.	PUNCT
ejpam-4920	325	1	in	in	ADP
ejpam-4920	325	2	particular	particular	ADJ
ejpam-4920	325	3	,	,	PUNCT
ejpam-4920	325	4	for	for	ADP
ejpam-4920	325	5	any	any	DET
ejpam-4920	325	6	positive	positive	ADJ
ejpam-4920	325	7	integers	integer	NOUN
ejpam-4920	325	8	m	m	PRON
ejpam-4920	325	9	,	,	PUNCT
ejpam-4920	325	10	n	n	PRON
ejpam-4920	325	11	≥	≥	NOUN
ejpam-4920	325	12	1	1	NUM
ejpam-4920	325	13	,	,	PUNCT
ejpam-4920	325	14	we	we	PRON
ejpam-4920	325	15	have	have	VERB
ejpam-4920	325	16	(	(	PUNCT
ejpam-4920	325	17	i	i	NOUN
ejpam-4920	325	18	)	)	PUNCT
ejpam-4920	325	19	γzh(km	γzh(km	NOUN
ejpam-4920	325	20	+	+	CCONJ
ejpam-4920	325	21	pn	pn	NOUN
ejpam-4920	325	22	)	)	PUNCT
ejpam-4920	325	23	=	=	PRON
ejpam-4920	325	24	{	{	PUNCT
ejpam-4920	326	1	m+	m+	NUM
ejpam-4920	326	2	n	n	NOUN
ejpam-4920	326	3	if	if	SCONJ
ejpam-4920	326	4	n	n	NOUN
ejpam-4920	326	5	=	=	SYM
ejpam-4920	326	6	1	1	NUM
ejpam-4920	326	7	,	,	PUNCT
ejpam-4920	326	8	2	2	NUM
ejpam-4920	326	9	m+	m+	NUM
ejpam-4920	326	10	2	2	NUM
ejpam-4920	326	11	if	if	SCONJ
ejpam-4920	326	12	n	n	PRON
ejpam-4920	326	13	≥	≥	NOUN
ejpam-4920	326	14	3	3	NUM
ejpam-4920	326	15	,	,	PUNCT
ejpam-4920	326	16	and	and	CCONJ
ejpam-4920	326	17	(	(	PUNCT
ejpam-4920	326	18	ii	ii	NOUN
ejpam-4920	326	19	)	)	PUNCT
ejpam-4920	326	20	γzh(km	γzh(km	NOUN
ejpam-4920	326	21	+	+	CCONJ
ejpam-4920	326	22	cn	cn	PROPN
ejpam-4920	326	23	)	)	PUNCT
ejpam-4920	326	24	=	=	PRON
ejpam-4920	326	25	{	{	PUNCT
ejpam-4920	326	26	m+	m+	NUM
ejpam-4920	326	27	3	3	NUM
ejpam-4920	326	28	if	if	SCONJ
ejpam-4920	326	29	n	n	NOUN
ejpam-4920	326	30	=	=	SYM
ejpam-4920	326	31	3	3	NUM
ejpam-4920	326	32	m+	m+	NUM
ejpam-4920	326	33	2	2	NUM
ejpam-4920	326	34	if	if	SCONJ
ejpam-4920	326	35	n	n	NUM
ejpam-4920	326	36	≥	≥	VERB
ejpam-4920	326	37	4	4	NUM
ejpam-4920	326	38	proof	proof	NOUN
ejpam-4920	326	39	.	.	PUNCT
ejpam-4920	327	1	let	let	VERB
ejpam-4920	327	2	z	z	PRON
ejpam-4920	327	3	be	be	AUX
ejpam-4920	327	4	a	a	DET
ejpam-4920	327	5	minimum	minimum	ADJ
ejpam-4920	327	6	zero	zero	NUM
ejpam-4920	327	7	forcing	force	VERB
ejpam-4920	327	8	hop	hop	NOUN
ejpam-4920	327	9	dominating	dominating	NOUN
ejpam-4920	327	10	set	set	VERB
ejpam-4920	327	11	in	in	ADP
ejpam-4920	327	12	j	j	PROPN
ejpam-4920	328	1	+	+	CCONJ
ejpam-4920	328	2	k.	k.	PROPN
ejpam-4920	328	3	then	then	ADV
ejpam-4920	328	4	by	by	ADP
ejpam-4920	328	5	theorem	theorem	NOUN
ejpam-4920	328	6	7	7	NUM
ejpam-4920	328	7	,	,	PUNCT
ejpam-4920	328	8	z	z	NOUN
ejpam-4920	328	9	=	=	SYM
ejpam-4920	328	10	v	v	PROPN
ejpam-4920	328	11	(	(	PUNCT
ejpam-4920	328	12	j	j	NOUN
ejpam-4920	328	13	)	)	PUNCT
ejpam-4920	328	14	∪	∪	VERB
ejpam-4920	328	15	zk	zk	PROPN
ejpam-4920	328	16	,	,	PUNCT
ejpam-4920	328	17	where	where	SCONJ
ejpam-4920	328	18	zk	zk	PROPN
ejpam-4920	328	19	is	be	AUX
ejpam-4920	328	20	a	a	DET
ejpam-4920	328	21	zfpnd	zfpnd	NOUN
ejpam-4920	328	22	set	set	VERB
ejpam-4920	328	23	in	in	ADP
ejpam-4920	328	24	k.	k.	PROPN
ejpam-4920	328	25	hence	hence	PROPN
ejpam-4920	328	26	,	,	PUNCT
ejpam-4920	328	27	γzh(j	γzh(j	PROPN
ejpam-4920	328	28	+	+	PROPN
ejpam-4920	328	29	k	k	NOUN
ejpam-4920	328	30	)	)	PUNCT
ejpam-4920	328	31	=	=	SYM
ejpam-4920	328	32	|z|	|z|	PROPN
ejpam-4920	328	33	=	=	SYM
ejpam-4920	328	34	|v	|v	X
ejpam-4920	328	35	(	(	PUNCT
ejpam-4920	328	36	j)|+	j)|+	PROPN
ejpam-4920	328	37	|zk	|zk	PUNCT
ejpam-4920	328	38	|	|	ADV
ejpam-4920	328	39	≥	≥	X
ejpam-4920	328	40	|v	|v	X
ejpam-4920	328	41	(	(	PUNCT
ejpam-4920	328	42	j)|+	j)|+	PROPN
ejpam-4920	328	43	zfpnd(k	zfpnd(k	PROPN
ejpam-4920	328	44	)	)	PUNCT
ejpam-4920	328	45	.	.	PUNCT
ejpam-4920	329	1	conversely	conversely	ADV
ejpam-4920	329	2	,	,	PUNCT
ejpam-4920	329	3	suppose	suppose	VERB
ejpam-4920	329	4	that	that	SCONJ
ejpam-4920	329	5	z	z	NOUN
ejpam-4920	329	6	=	=	SYM
ejpam-4920	329	7	v	v	PROPN
ejpam-4920	329	8	(	(	PUNCT
ejpam-4920	329	9	j	j	NOUN
ejpam-4920	329	10	)	)	PUNCT
ejpam-4920	329	11	∪	∪	VERB
ejpam-4920	329	12	zk	zk	PROPN
ejpam-4920	329	13	,	,	PUNCT
ejpam-4920	329	14	where	where	SCONJ
ejpam-4920	329	15	zk	zk	PROPN
ejpam-4920	329	16	is	be	AUX
ejpam-4920	329	17	a	a	DET
ejpam-4920	329	18	minimum	minimum	ADJ
ejpam-4920	329	19	zfpnd	zfpnd	NOUN
ejpam-4920	329	20	set	set	VERB
ejpam-4920	329	21	in	in	ADP
ejpam-4920	329	22	k.	k.	PROPN
ejpam-4920	329	23	then	then	ADV
ejpam-4920	329	24	z	z	PROPN
ejpam-4920	329	25	is	be	AUX
ejpam-4920	329	26	a	a	DET
ejpam-4920	329	27	zero	zero	NUM
ejpam-4920	329	28	forcing	force	VERB
ejpam-4920	329	29	hop	hop	NOUN
ejpam-4920	329	30	dominating	dominating	NOUN
ejpam-4920	329	31	set	set	NOUN
ejpam-4920	329	32	of	of	ADP
ejpam-4920	329	33	j	j	PROPN
ejpam-4920	330	1	+	+	PROPN
ejpam-4920	330	2	k	k	X
ejpam-4920	330	3	by	by	ADP
ejpam-4920	330	4	theorem	theorem	NOUN
ejpam-4920	330	5	7	7	NUM
ejpam-4920	330	6	.	.	PUNCT
ejpam-4920	330	7	thus	thus	ADV
ejpam-4920	330	8	,	,	PUNCT
ejpam-4920	330	9	|v	|v	PROPN
ejpam-4920	330	10	(	(	PUNCT
ejpam-4920	330	11	j)|+	j)|+	PROPN
ejpam-4920	330	12	zfpnd(k	zfpnd(k	PROPN
ejpam-4920	330	13	)	)	PUNCT
ejpam-4920	330	14	=	=	PUNCT
ejpam-4920	330	15	|z|	|z|	NOUN
ejpam-4920	330	16	≥	≥	NOUN
ejpam-4920	330	17	γzh(j	γzh(j	PROPN
ejpam-4920	330	18	+	+	PROPN
ejpam-4920	330	19	k	k	NOUN
ejpam-4920	330	20	)	)	PUNCT
ejpam-4920	330	21	.	.	PUNCT
ejpam-4920	331	1	consequently	consequently	ADV
ejpam-4920	331	2	,	,	PUNCT
ejpam-4920	331	3	γzh(j	γzh(j	PROPN
ejpam-4920	331	4	+	+	PROPN
ejpam-4920	331	5	k	k	NOUN
ejpam-4920	331	6	)	)	PUNCT
ejpam-4920	331	7	=	=	SYM
ejpam-4920	331	8	|v	|v	PROPN
ejpam-4920	331	9	(	(	PUNCT
ejpam-4920	331	10	j)|+	j)|+	PROPN
ejpam-4920	331	11	zfpnd(k	zfpnd(k	PROPN
ejpam-4920	331	12	)	)	PUNCT
ejpam-4920	331	13	.	.	PUNCT
ejpam-4920	332	1	the	the	DET
ejpam-4920	332	2	particular	particular	ADJ
ejpam-4920	332	3	case	case	NOUN
ejpam-4920	332	4	,	,	PUNCT
ejpam-4920	332	5	follows	follow	VERB
ejpam-4920	332	6	from	from	ADP
ejpam-4920	332	7	proposition	proposition	NOUN
ejpam-4920	332	8	4	4	NUM
ejpam-4920	332	9	.	.	PUNCT
ejpam-4920	332	10	theorem	theorem	NOUN
ejpam-4920	332	11	8	8	NUM
ejpam-4920	332	12	.	.	PUNCT
ejpam-4920	333	1	let	let	VERB
ejpam-4920	333	2	j	j	PROPN
ejpam-4920	333	3	and	and	CCONJ
ejpam-4920	333	4	k	k	PROPN
ejpam-4920	333	5	be	be	AUX
ejpam-4920	333	6	any	any	DET
ejpam-4920	333	7	non	non	ADJ
ejpam-4920	333	8	-	-	ADJ
ejpam-4920	333	9	trivial	trivial	ADJ
ejpam-4920	333	10	connected	connect	VERB
ejpam-4920	333	11	and	and	CCONJ
ejpam-4920	333	12	any	any	DET
ejpam-4920	333	13	graph	graph	NOUN
ejpam-4920	333	14	,	,	PUNCT
ejpam-4920	333	15	respectively	respectively	ADV
ejpam-4920	333	16	.	.	PUNCT
ejpam-4920	334	1	then	then	ADV
ejpam-4920	334	2	,	,	PUNCT
ejpam-4920	334	3	m	m	VERB
ejpam-4920	334	4	=	=	ADJ
ejpam-4920	334	5	v	v	ADJ
ejpam-4920	334	6	(	(	PUNCT
ejpam-4920	334	7	j)∪	j)∪	PROPN
ejpam-4920	334	8	(	(	PUNCT
ejpam-4920	334	9	⋃	⋃	ADJ
ejpam-4920	334	10	v∈v	v∈v	NOUN
ejpam-4920	334	11	(	(	PUNCT
ejpam-4920	334	12	k	k	NOUN
ejpam-4920	334	13	)	)	PUNCT
ejpam-4920	334	14	mv	mv	NOUN
ejpam-4920	334	15	)	)	PUNCT
ejpam-4920	334	16	is	be	AUX
ejpam-4920	334	17	a	a	PRON
ejpam-4920	334	18	zero	zero	NUM
ejpam-4920	334	19	forcing	force	VERB
ejpam-4920	334	20	hop	hop	NOUN
ejpam-4920	334	21	dominating	dominating	NOUN
ejpam-4920	334	22	set	set	VERB
ejpam-4920	334	23	in	in	ADP
ejpam-4920	334	24	j	j	PROPN
ejpam-4920	334	25	◦	◦	PROPN
ejpam-4920	334	26	k	k	PROPN
ejpam-4920	334	27	if	if	SCONJ
ejpam-4920	334	28	mv	mv	PROPN
ejpam-4920	334	29	is	be	AUX
ejpam-4920	334	30	a	a	DET
ejpam-4920	334	31	zfpnd	zfpnd	NOUN
ejpam-4920	334	32	set	set	VERB
ejpam-4920	334	33	in	in	ADP
ejpam-4920	334	34	kv	kv	PROPN
ejpam-4920	334	35	for	for	ADP
ejpam-4920	334	36	each	each	DET
ejpam-4920	334	37	v	v	NUM
ejpam-4920	334	38	∈	∈	PROPN
ejpam-4920	334	39	v	v	NOUN
ejpam-4920	334	40	(	(	PUNCT
ejpam-4920	334	41	j	j	NOUN
ejpam-4920	334	42	)	)	PUNCT
ejpam-4920	334	43	.	.	PUNCT
ejpam-4920	335	1	moreover	moreover	ADV
ejpam-4920	335	2	,	,	PUNCT
ejpam-4920	335	3	γzh(j	γzh(j	PROPN
ejpam-4920	335	4	◦	◦	PROPN
ejpam-4920	335	5	k	k	NOUN
ejpam-4920	335	6	)	)	PUNCT
ejpam-4920	335	7	≤	≤	NOUN
ejpam-4920	335	8	|v	|v	X
ejpam-4920	335	9	(	(	PUNCT
ejpam-4920	335	10	j)|	j)|	PROPN
ejpam-4920	335	11	·	·	SYM
ejpam-4920	335	12	zfpnd(k	zfpnd(k	NOUN
ejpam-4920	335	13	)	)	PUNCT
ejpam-4920	336	1	+	+	CCONJ
ejpam-4920	336	2	|v	|v	X
ejpam-4920	336	3	(	(	PUNCT
ejpam-4920	336	4	j)|	j)|	NOUN
ejpam-4920	336	5	.	.	PUNCT
ejpam-4920	337	1	proof	proof	NOUN
ejpam-4920	337	2	.	.	PUNCT
ejpam-4920	338	1	let	let	VERB
ejpam-4920	338	2	m	m	PROPN
ejpam-4920	338	3	=	=	VERB
ejpam-4920	338	4	v	v	PROPN
ejpam-4920	338	5	(	(	PUNCT
ejpam-4920	338	6	j	j	NOUN
ejpam-4920	338	7	)	)	PUNCT
ejpam-4920	338	8	∪	∪	NOUN
ejpam-4920	338	9	(	(	PUNCT
ejpam-4920	338	10	⋃	⋃	NOUN
ejpam-4920	338	11	v∈v	v∈v	NOUN
ejpam-4920	338	12	(	(	PUNCT
ejpam-4920	338	13	k	k	NOUN
ejpam-4920	338	14	)	)	PUNCT
ejpam-4920	338	15	mv	mv	NOUN
ejpam-4920	338	16	)	)	PUNCT
ejpam-4920	338	17	,	,	PUNCT
ejpam-4920	338	18	where	where	SCONJ
ejpam-4920	338	19	mv	mv	PROPN
ejpam-4920	338	20	is	be	AUX
ejpam-4920	338	21	a	a	DET
ejpam-4920	338	22	zfpnd	zfpnd	NOUN
ejpam-4920	338	23	set	set	VERB
ejpam-4920	338	24	in	in	ADP
ejpam-4920	338	25	kv	kv	PROPN
ejpam-4920	338	26	for	for	ADP
ejpam-4920	338	27	each	each	DET
ejpam-4920	338	28	v	v	NUM
ejpam-4920	338	29	∈	∈	PROPN
ejpam-4920	338	30	v	v	NOUN
ejpam-4920	338	31	(	(	PUNCT
ejpam-4920	338	32	j	j	NOUN
ejpam-4920	338	33	)	)	PUNCT
ejpam-4920	338	34	.	.	PUNCT
ejpam-4920	339	1	let	let	VERB
ejpam-4920	339	2	u	u	PRON
ejpam-4920	339	3	∈	∈	PROPN
ejpam-4920	339	4	v	v	NOUN
ejpam-4920	339	5	(	(	PUNCT
ejpam-4920	339	6	j	j	PROPN
ejpam-4920	339	7	◦	◦	NOUN
ejpam-4920	339	8	k)\m	k)\m	PROPN
ejpam-4920	339	9	.	.	PUNCT
ejpam-4920	340	1	then	then	ADV
ejpam-4920	340	2	u	u	PROPN
ejpam-4920	340	3	∈	∈	PROPN
ejpam-4920	340	4	kw	kw	INTJ
ejpam-4920	340	5	for	for	ADP
ejpam-4920	340	6	some	some	DET
ejpam-4920	340	7	w	w	PROPN
ejpam-4920	340	8	∈	∈	PROPN
ejpam-4920	340	9	v	v	ADP
ejpam-4920	340	10	(	(	PUNCT
ejpam-4920	340	11	g	g	NOUN
ejpam-4920	340	12	)	)	PUNCT
ejpam-4920	340	13	.	.	PUNCT
ejpam-4920	341	1	since	since	SCONJ
ejpam-4920	341	2	mw	mw	PROPN
ejpam-4920	341	3	is	be	AUX
ejpam-4920	341	4	pnd	pnd	NOUN
ejpam-4920	341	5	set	set	VERB
ejpam-4920	341	6	in	in	ADP
ejpam-4920	341	7	kw	kw	PROPN
ejpam-4920	341	8	,	,	PUNCT
ejpam-4920	341	9	there	there	PRON
ejpam-4920	341	10	exists	exist	VERB
ejpam-4920	341	11	y	y	PROPN
ejpam-4920	341	12	∈	∈	PROPN
ejpam-4920	341	13	mw	mw	VERB
ejpam-4920	341	14	such	such	ADJ
ejpam-4920	341	15	that	that	PRON
ejpam-4920	341	16	dj	dj	NOUN
ejpam-4920	341	17	◦	◦	NOUN
ejpam-4920	341	18	k(u	k(u	X
ejpam-4920	341	19	,	,	PUNCT
ejpam-4920	341	20	y	y	NOUN
ejpam-4920	341	21	)	)	PUNCT
ejpam-4920	341	22	=	=	SYM
ejpam-4920	342	1	2	2	X
ejpam-4920	342	2	.	.	X
ejpam-4920	343	1	hence	hence	ADV
ejpam-4920	343	2	,	,	PUNCT
ejpam-4920	343	3	m	m	VERB
ejpam-4920	343	4	is	be	AUX
ejpam-4920	343	5	a	a	DET
ejpam-4920	343	6	hop	hop	NOUN
ejpam-4920	343	7	dominating	dominating	NOUN
ejpam-4920	343	8	set	set	NOUN
ejpam-4920	343	9	of	of	ADP
ejpam-4920	343	10	j	j	PROPN
ejpam-4920	343	11	◦	◦	PROPN
ejpam-4920	343	12	k.	k.	PROPN
ejpam-4920	343	13	now	now	ADV
ejpam-4920	343	14	,	,	PUNCT
ejpam-4920	343	15	since	since	SCONJ
ejpam-4920	343	16	mv	mv	PROPN
ejpam-4920	343	17	is	be	AUX
ejpam-4920	343	18	a	a	DET
ejpam-4920	343	19	zero	zero	NUM
ejpam-4920	343	20	forcing	forcing	NOUN
ejpam-4920	343	21	set	set	NOUN
ejpam-4920	343	22	in	in	ADP
ejpam-4920	343	23	kv	kv	PROPN
ejpam-4920	343	24	for	for	ADP
ejpam-4920	343	25	each	each	DET
ejpam-4920	343	26	v	v	NUM
ejpam-4920	343	27	∈	∈	PROPN
ejpam-4920	343	28	v	v	NOUN
ejpam-4920	343	29	(	(	PUNCT
ejpam-4920	343	30	j	j	NOUN
ejpam-4920	343	31	)	)	PUNCT
ejpam-4920	343	32	,	,	PUNCT
ejpam-4920	343	33	it	it	PRON
ejpam-4920	343	34	follows	follow	VERB
ejpam-4920	343	35	that	that	SCONJ
ejpam-4920	343	36	m	m	VERB
ejpam-4920	343	37	=	=	SYM
ejpam-4920	343	38	v	v	ADJ
ejpam-4920	343	39	(	(	PUNCT
ejpam-4920	343	40	j)∪	j)∪	PROPN
ejpam-4920	343	41	(	(	PUNCT
ejpam-4920	343	42	⋃	⋃	ADJ
ejpam-4920	343	43	v∈v	v∈v	NOUN
ejpam-4920	343	44	(	(	PUNCT
ejpam-4920	343	45	g	g	NOUN
ejpam-4920	343	46	)	)	PUNCT
ejpam-4920	343	47	mv	mv	NOUN
ejpam-4920	343	48	)	)	PUNCT
ejpam-4920	343	49	is	be	AUX
ejpam-4920	343	50	a	a	DET
ejpam-4920	343	51	zero	zero	NUM
ejpam-4920	343	52	forcing	forcing	NOUN
ejpam-4920	343	53	set	set	NOUN
ejpam-4920	343	54	in	in	ADP
ejpam-4920	343	55	j	j	PROPN
ejpam-4920	343	56	◦	◦	PROPN
ejpam-4920	343	57	k.	k.	PROPN
ejpam-4920	343	58	therefore	therefore	ADV
ejpam-4920	343	59	,	,	PUNCT
ejpam-4920	343	60	m	m	PROPN
ejpam-4920	343	61	is	be	AUX
ejpam-4920	343	62	a	a	DET
ejpam-4920	343	63	zero	zero	NUM
ejpam-4920	343	64	forcing	force	VERB
ejpam-4920	343	65	hop	hop	NOUN
ejpam-4920	343	66	dominating	dominating	NOUN
ejpam-4920	343	67	set	set	VERB
ejpam-4920	343	68	in	in	ADP
ejpam-4920	343	69	j	j	PROPN
ejpam-4920	343	70	◦	◦	PROPN
ejpam-4920	343	71	k.	k.	PROPN
ejpam-4920	343	72	since	since	SCONJ
ejpam-4920	343	73	γzh(j	γzh(j	PROPN
ejpam-4920	343	74	◦	◦	PROPN
ejpam-4920	343	75	k	k	NOUN
ejpam-4920	343	76	)	)	PUNCT
ejpam-4920	343	77	is	be	AUX
ejpam-4920	343	78	the	the	DET
ejpam-4920	343	79	minimum	minimum	ADJ
ejpam-4920	343	80	cardinality	cardinality	NOUN
ejpam-4920	343	81	among	among	ADP
ejpam-4920	343	82	all	all	DET
ejpam-4920	343	83	zero	zero	NUM
ejpam-4920	343	84	forcing	force	VERB
ejpam-4920	343	85	hop	hop	NOUN
ejpam-4920	343	86	dominating	dominating	NOUN
ejpam-4920	343	87	sets	set	NOUN
ejpam-4920	343	88	in	in	ADP
ejpam-4920	343	89	j	j	PROPN
ejpam-4920	343	90	◦	◦	PROPN
ejpam-4920	343	91	k	k	PROPN
ejpam-4920	343	92	,	,	PUNCT
ejpam-4920	343	93	we	we	PRON
ejpam-4920	343	94	have	have	VERB
ejpam-4920	343	95	γzh(j	γzh(j	PROPN
ejpam-4920	343	96	◦	◦	NOUN
ejpam-4920	343	97	k	k	NOUN
ejpam-4920	343	98	)	)	PUNCT
ejpam-4920	343	99	≤	≤	NUM
ejpam-4920	344	1	m	m	NOUN
ejpam-4920	344	2	=	=	NOUN
ejpam-4920	344	3	|v	|v	X
ejpam-4920	344	4	(	(	PUNCT
ejpam-4920	344	5	j)|	j)|	PROPN
ejpam-4920	344	6	·	·	SYM
ejpam-4920	344	7	zfpnd(k	zfpnd(k	NOUN
ejpam-4920	344	8	)	)	PUNCT
ejpam-4920	345	1	+	+	CCONJ
ejpam-4920	345	2	|v	|v	PROPN
ejpam-4920	345	3	(	(	PUNCT
ejpam-4920	345	4	j)|	j)|	PROPN
ejpam-4920	345	5	.	.	PUNCT
ejpam-4920	345	6	j.	j.	PROPN
ejpam-4920	345	7	u.	u.	PROPN
ejpam-4920	345	8	manditong	manditong	PROPN
ejpam-4920	345	9	et	et	PROPN
ejpam-4920	345	10	al	al	PROPN
ejpam-4920	345	11	.	.	PUNCT
ejpam-4920	345	12	/	/	SYM
ejpam-4920	345	13	eur	eur	PROPN
ejpam-4920	345	14	.	.	PUNCT
ejpam-4920	346	1	j.	j.	PROPN
ejpam-4920	346	2	pure	pure	PROPN
ejpam-4920	346	3	appl	appl	PROPN
ejpam-4920	346	4	.	.	PROPN
ejpam-4920	346	5	math	math	PROPN
ejpam-4920	346	6	,	,	PUNCT
ejpam-4920	346	7	17	17	NUM
ejpam-4920	346	8	(	(	PUNCT
ejpam-4920	346	9	1	1	NUM
ejpam-4920	346	10	)	)	PUNCT
ejpam-4920	346	11	(	(	PUNCT
ejpam-4920	346	12	2024	2024	NUM
ejpam-4920	346	13	)	)	PUNCT
ejpam-4920	346	14	,	,	PUNCT
ejpam-4920	346	15	324	324	NUM
ejpam-4920	346	16	-	-	SYM
ejpam-4920	346	17	337	337	NUM
ejpam-4920	346	18	335	335	NUM
ejpam-4920	346	19	remark	remark	NOUN
ejpam-4920	346	20	2	2	NUM
ejpam-4920	346	21	.	.	PUNCT
ejpam-4920	347	1	the	the	DET
ejpam-4920	347	2	sharpness	sharpness	NOUN
ejpam-4920	347	3	and	and	CCONJ
ejpam-4920	347	4	strict	strict	ADJ
ejpam-4920	347	5	inequality	inequality	NOUN
ejpam-4920	347	6	given	give	VERB
ejpam-4920	347	7	in	in	ADP
ejpam-4920	347	8	theorem	theorem	ADJ
ejpam-4920	347	9	8	8	NUM
ejpam-4920	347	10	are	be	AUX
ejpam-4920	347	11	attainable	attainable	ADJ
ejpam-4920	347	12	.	.	PUNCT
ejpam-4920	348	1	for	for	ADP
ejpam-4920	348	2	the	the	DET
ejpam-4920	348	3	sharpness	sharpness	NOUN
ejpam-4920	348	4	,	,	PUNCT
ejpam-4920	348	5	consider	consider	VERB
ejpam-4920	348	6	the	the	DET
ejpam-4920	348	7	graph	graph	NOUN
ejpam-4920	348	8	p3	p3	PROPN
ejpam-4920	348	9	◦	◦	PROPN
ejpam-4920	348	10	c4	c4	NOUN
ejpam-4920	348	11	below	below	ADV
ejpam-4920	348	12	.	.	PUNCT
ejpam-4920	349	1	u	u	PRON
ejpam-4920	349	2	v	v	PROPN
ejpam-4920	349	3	w	w	PROPN
ejpam-4920	349	4	u1	u1	PROPN
ejpam-4920	349	5	u2	u2	PROPN
ejpam-4920	349	6	u3	u3	PROPN
ejpam-4920	349	7	u4	u4	PROPN
ejpam-4920	349	8	v1	v1	PROPN
ejpam-4920	349	9	v2	v2	PROPN
ejpam-4920	349	10	v3	v3	PROPN
ejpam-4920	349	11	v4	v4	PROPN
ejpam-4920	349	12	w1	w1	PROPN
ejpam-4920	349	13	w2	w2	PROPN
ejpam-4920	349	14	w3	w3	PROPN
ejpam-4920	349	15	w4	w4	PROPN
ejpam-4920	349	16	p3	p3	PROPN
ejpam-4920	349	17	c4	c4	NOUN
ejpam-4920	349	18	:	:	PUNCT
ejpam-4920	349	19	figure	figure	VERB
ejpam-4920	349	20	4	4	NUM
ejpam-4920	349	21	:	:	PUNCT
ejpam-4920	349	22	graph	graph	NOUN
ejpam-4920	349	23	p3	p3	PROPN
ejpam-4920	349	24	◦	◦	PROPN
ejpam-4920	349	25	c4	c4	NOUN
ejpam-4920	349	26	with	with	ADP
ejpam-4920	349	27	γzh(p3	γzh(p3	PROPN
ejpam-4920	349	28	◦	◦	PROPN
ejpam-4920	349	29	c4	c4	NOUN
ejpam-4920	349	30	)	)	PUNCT
ejpam-4920	349	31	=	=	SYM
ejpam-4920	350	1	|v	|v	PROPN
ejpam-4920	350	2	(	(	PUNCT
ejpam-4920	350	3	p3)|	p3)|	NOUN
ejpam-4920	350	4	·	·	PUNCT
ejpam-4920	350	5	zfpnd(c4	zfpnd(c4	NUM
ejpam-4920	350	6	)	)	PUNCT
ejpam-4920	351	1	+	+	CCONJ
ejpam-4920	351	2	|v	|v	X
ejpam-4920	351	3	(	(	PUNCT
ejpam-4920	351	4	p3)|	p3)|	INTJ
ejpam-4920	351	5	.	.	PUNCT
ejpam-4920	352	1	let	let	VERB
ejpam-4920	352	2	m	m	VERB
ejpam-4920	352	3	=	=	PUNCT
ejpam-4920	352	4	{	{	PUNCT
ejpam-4920	352	5	u1	u1	NOUN
ejpam-4920	352	6	,	,	PUNCT
ejpam-4920	352	7	u2	u2	PROPN
ejpam-4920	352	8	,	,	PUNCT
ejpam-4920	352	9	u	u	NOUN
ejpam-4920	352	10	,	,	PUNCT
ejpam-4920	352	11	v1	v1	NOUN
ejpam-4920	352	12	,	,	PUNCT
ejpam-4920	352	13	v2	v2	PROPN
ejpam-4920	352	14	,	,	PUNCT
ejpam-4920	352	15	v	v	NOUN
ejpam-4920	352	16	,	,	PUNCT
ejpam-4920	352	17	w1	w1	NOUN
ejpam-4920	352	18	,	,	PUNCT
ejpam-4920	352	19	w2	w2	NOUN
ejpam-4920	352	20	,	,	PUNCT
ejpam-4920	352	21	w	w	PROPN
ejpam-4920	352	22	}	}	PUNCT
ejpam-4920	352	23	.	.	PUNCT
ejpam-4920	353	1	then	then	ADV
ejpam-4920	353	2	,	,	PUNCT
ejpam-4920	353	3	n2	n2	PROPN
ejpam-4920	353	4	p3	p3	PROPN
ejpam-4920	353	5	◦	◦	NOUN
ejpam-4920	353	6	c3	c3	X
ejpam-4920	353	7	[	[	X
ejpam-4920	353	8	m	m	X
ejpam-4920	353	9	]	]	X
ejpam-4920	353	10	=	=	SYM
ejpam-4920	353	11	v	v	X
ejpam-4920	353	12	(	(	PUNCT
ejpam-4920	353	13	p3	p3	PROPN
ejpam-4920	353	14	◦	◦	PROPN
ejpam-4920	353	15	c4	c4	NOUN
ejpam-4920	353	16	)	)	PUNCT
ejpam-4920	353	17	.	.	PUNCT
ejpam-4920	354	1	thus	thus	ADV
ejpam-4920	354	2	,	,	PUNCT
ejpam-4920	354	3	m	m	VERB
ejpam-4920	354	4	is	be	AUX
ejpam-4920	354	5	a	a	DET
ejpam-4920	354	6	hop	hop	NOUN
ejpam-4920	354	7	dominating	dominating	NOUN
ejpam-4920	354	8	set	set	NOUN
ejpam-4920	354	9	of	of	ADP
ejpam-4920	354	10	p3	p3	PROPN
ejpam-4920	354	11	◦	◦	NOUN
ejpam-4920	354	12	c4	c4	NOUN
ejpam-4920	354	13	.	.	PUNCT
ejpam-4920	355	1	observe	observe	VERB
ejpam-4920	355	2	that	that	SCONJ
ejpam-4920	355	3	{	{	PUNCT
ejpam-4920	355	4	u1	u1	NOUN
ejpam-4920	355	5	,	,	PUNCT
ejpam-4920	355	6	u2	u2	PROPN
ejpam-4920	355	7	}	}	PUNCT
ejpam-4920	355	8	,	,	PUNCT
ejpam-4920	355	9	{	{	PUNCT
ejpam-4920	355	10	v1	v1	NOUN
ejpam-4920	355	11	,	,	PUNCT
ejpam-4920	355	12	v2	v2	NOUN
ejpam-4920	355	13	}	}	PUNCT
ejpam-4920	355	14	and	and	CCONJ
ejpam-4920	355	15	{	{	PUNCT
ejpam-4920	355	16	w1	w1	NOUN
ejpam-4920	355	17	,	,	PUNCT
ejpam-4920	355	18	w2	w2	NOUN
ejpam-4920	355	19	}	}	PUNCT
ejpam-4920	355	20	are	be	AUX
ejpam-4920	355	21	zero	zero	NUM
ejpam-4920	355	22	forcing	force	VERB
ejpam-4920	355	23	sets	set	NOUN
ejpam-4920	355	24	in	in	ADP
ejpam-4920	355	25	cu	cu	PROPN
ejpam-4920	355	26	4	4	NUM
ejpam-4920	355	27	,	,	PUNCT
ejpam-4920	355	28	c	c	NOUN
ejpam-4920	355	29	v	v	NOUN
ejpam-4920	355	30	4	4	NUM
ejpam-4920	355	31	and	and	CCONJ
ejpam-4920	355	32	cw	cw	NOUN
ejpam-4920	355	33	4	4	NUM
ejpam-4920	355	34	,	,	PUNCT
ejpam-4920	355	35	respectively	respectively	ADV
ejpam-4920	355	36	.	.	PUNCT
ejpam-4920	356	1	hence	hence	ADV
ejpam-4920	356	2	,	,	PUNCT
ejpam-4920	356	3	m	m	VERB
ejpam-4920	356	4	is	be	AUX
ejpam-4920	356	5	a	a	DET
ejpam-4920	356	6	zero	zero	NUM
ejpam-4920	356	7	forcing	force	VERB
ejpam-4920	356	8	set	set	NOUN
ejpam-4920	356	9	in	in	ADP
ejpam-4920	356	10	p3	p3	PROPN
ejpam-4920	356	11	◦	◦	PROPN
ejpam-4920	356	12	c4	c4	NOUN
ejpam-4920	356	13	,	,	PUNCT
ejpam-4920	356	14	and	and	CCONJ
ejpam-4920	356	15	so	so	ADV
ejpam-4920	356	16	m	m	VERB
ejpam-4920	356	17	is	be	AUX
ejpam-4920	356	18	a	a	DET
ejpam-4920	356	19	zero	zero	NUM
ejpam-4920	356	20	forcing	force	VERB
ejpam-4920	356	21	hop	hop	NOUN
ejpam-4920	356	22	dominating	dominating	NOUN
ejpam-4920	356	23	set	set	VERB
ejpam-4920	356	24	in	in	ADP
ejpam-4920	356	25	p3	p3	PROPN
ejpam-4920	356	26	◦	◦	PROPN
ejpam-4920	356	27	c4	c4	NOUN
ejpam-4920	356	28	.	.	PUNCT
ejpam-4920	357	1	moreover	moreover	ADV
ejpam-4920	357	2	,	,	PUNCT
ejpam-4920	357	3	it	it	PRON
ejpam-4920	357	4	can	can	AUX
ejpam-4920	357	5	be	be	AUX
ejpam-4920	357	6	verified	verify	VERB
ejpam-4920	357	7	that	that	SCONJ
ejpam-4920	357	8	γzh(p3	γzh(p3	PROPN
ejpam-4920	357	9	◦	◦	PROPN
ejpam-4920	357	10	c4	c4	NOUN
ejpam-4920	357	11	)	)	PUNCT
ejpam-4920	357	12	=	=	SYM
ejpam-4920	357	13	|v	|v	PROPN
ejpam-4920	357	14	(	(	PUNCT
ejpam-4920	357	15	p3)|	p3)|	NOUN
ejpam-4920	357	16	·	·	PUNCT
ejpam-4920	357	17	zfpnd(c4	zfpnd(c4	NUM
ejpam-4920	357	18	)	)	PUNCT
ejpam-4920	358	1	+	+	CCONJ
ejpam-4920	358	2	|v	|v	X
ejpam-4920	358	3	(	(	PUNCT
ejpam-4920	358	4	p3)|	p3)|	NOUN
ejpam-4920	358	5	=	=	NOUN
ejpam-4920	358	6	3	3	NUM
ejpam-4920	358	7	·	·	SYM
ejpam-4920	358	8	2	2	NUM
ejpam-4920	358	9	+	+	CCONJ
ejpam-4920	358	10	3	3	NUM
ejpam-4920	358	11	=	=	SYM
ejpam-4920	358	12	9	9	NUM
ejpam-4920	358	13	.	.	X
ejpam-4920	358	14	for	for	ADP
ejpam-4920	358	15	strict	strict	ADJ
ejpam-4920	358	16	inequality	inequality	NOUN
ejpam-4920	358	17	,	,	PUNCT
ejpam-4920	358	18	consider	consider	VERB
ejpam-4920	358	19	the	the	DET
ejpam-4920	358	20	graph	graph	NOUN
ejpam-4920	358	21	c3	c3	PROPN
ejpam-4920	358	22	◦	◦	NOUN
ejpam-4920	358	23	k4	k4	NOUN
ejpam-4920	358	24	below	below	ADV
ejpam-4920	358	25	.	.	PUNCT
ejpam-4920	359	1	a4	a4	NOUN
ejpam-4920	359	2	a2	a2	PROPN
ejpam-4920	359	3	a3	a3	NOUN
ejpam-4920	359	4	a1	a1	NOUN
ejpam-4920	359	5	a	a	DET
ejpam-4920	359	6	b4	b4	NOUN
ejpam-4920	359	7	b2b1	b2b1	PROPN
ejpam-4920	359	8	b	b	PROPN
ejpam-4920	359	9	b3c3	b3c3	PROPN
ejpam-4920	359	10	c1	c1	PROPN
ejpam-4920	359	11	c2	c2	PROPN
ejpam-4920	359	12	c	c	PROPN
ejpam-4920	359	13	c4	c4	PROPN
ejpam-4920	359	14	c3	c3	PROPN
ejpam-4920	359	15	k4	k4	PROPN
ejpam-4920	359	16	:	:	PUNCT
ejpam-4920	359	17	figure	figure	NOUN
ejpam-4920	359	18	5	5	NUM
ejpam-4920	359	19	:	:	PUNCT
ejpam-4920	359	20	graph	graph	NOUN
ejpam-4920	359	21	c3	c3	PROPN
ejpam-4920	359	22	◦	◦	NOUN
ejpam-4920	359	23	k4	k4	PROPN
ejpam-4920	359	24	with	with	ADP
ejpam-4920	359	25	γzh(c3	γzh(c3	PROPN
ejpam-4920	359	26	◦	◦	NOUN
ejpam-4920	359	27	k4	k4	PROPN
ejpam-4920	359	28	)	)	PUNCT
ejpam-4920	359	29	<	<	X
ejpam-4920	359	30	|v	|v	X
ejpam-4920	359	31	(	(	PUNCT
ejpam-4920	359	32	c3)|	c3)|	NOUN
ejpam-4920	359	33	·	·	PUNCT
ejpam-4920	359	34	zfpnd(k4	zfpnd(k4	PROPN
ejpam-4920	359	35	)	)	PUNCT
ejpam-4920	360	1	+	+	CCONJ
ejpam-4920	360	2	|v	|v	X
ejpam-4920	360	3	(	(	PUNCT
ejpam-4920	360	4	c3)|	c3)|	NOUN
ejpam-4920	360	5	.	.	PUNCT
ejpam-4920	361	1	references	reference	NOUN
ejpam-4920	361	2	336	336	NUM
ejpam-4920	361	3	let	let	VERB
ejpam-4920	361	4	s	s	VERB
ejpam-4920	361	5	=	=	NOUN
ejpam-4920	361	6	{	{	PUNCT
ejpam-4920	361	7	a1	a1	PROPN
ejpam-4920	361	8	,	,	PUNCT
ejpam-4920	361	9	a2	a2	PROPN
ejpam-4920	361	10	,	,	PUNCT
ejpam-4920	361	11	a3	a3	NOUN
ejpam-4920	361	12	,	,	PUNCT
ejpam-4920	361	13	a4	a4	PROPN
ejpam-4920	361	14	,	,	PUNCT
ejpam-4920	361	15	b	b	NOUN
ejpam-4920	361	16	,	,	PUNCT
ejpam-4920	361	17	c	c	PROPN
ejpam-4920	361	18	,	,	PUNCT
ejpam-4920	361	19	c1	c1	PROPN
ejpam-4920	361	20	,	,	PUNCT
ejpam-4920	361	21	c2	c2	PROPN
ejpam-4920	361	22	,	,	PUNCT
ejpam-4920	361	23	c3	c3	PROPN
ejpam-4920	361	24	,	,	PUNCT
ejpam-4920	361	25	b1	b1	PROPN
ejpam-4920	361	26	,	,	PUNCT
ejpam-4920	361	27	b2	b2	NOUN
ejpam-4920	361	28	,	,	PUNCT
ejpam-4920	361	29	b3	b3	PROPN
ejpam-4920	361	30	}	}	PUNCT
ejpam-4920	361	31	.	.	PUNCT
ejpam-4920	362	1	clearly	clearly	ADV
ejpam-4920	362	2	,	,	PUNCT
ejpam-4920	362	3	s	s	VERB
ejpam-4920	362	4	is	be	AUX
ejpam-4920	362	5	a	a	DET
ejpam-4920	362	6	zero	zero	NUM
ejpam-4920	362	7	forcing	forcing	NOUN
ejpam-4920	362	8	set	set	NOUN
ejpam-4920	362	9	in	in	ADP
ejpam-4920	362	10	c3	c3	PROPN
ejpam-4920	362	11	◦	◦	NOUN
ejpam-4920	362	12	k4	k4	PROPN
ejpam-4920	362	13	.	.	PUNCT
ejpam-4920	363	1	notice	notice	VERB
ejpam-4920	363	2	that	that	SCONJ
ejpam-4920	363	3	n2	n2	PROPN
ejpam-4920	363	4	c3	c3	PROPN
ejpam-4920	363	5	◦	◦	NOUN
ejpam-4920	363	6	k4	k4	NOUN
ejpam-4920	363	7	[	[	X
ejpam-4920	363	8	s	s	X
ejpam-4920	363	9	]	]	X
ejpam-4920	363	10	=	=	SYM
ejpam-4920	363	11	v	v	X
ejpam-4920	363	12	(	(	PUNCT
ejpam-4920	363	13	c3	c3	PROPN
ejpam-4920	363	14	◦	◦	PROPN
ejpam-4920	363	15	k4	k4	PROPN
ejpam-4920	363	16	)	)	PUNCT
ejpam-4920	363	17	.	.	PUNCT
ejpam-4920	364	1	thus	thus	ADV
ejpam-4920	364	2	,	,	PUNCT
ejpam-4920	364	3	s	s	VERB
ejpam-4920	364	4	is	be	AUX
ejpam-4920	364	5	a	a	DET
ejpam-4920	364	6	zero	zero	NUM
ejpam-4920	364	7	forcing	force	VERB
ejpam-4920	364	8	hop	hop	NOUN
ejpam-4920	364	9	dominating	dominating	NOUN
ejpam-4920	364	10	set	set	VERB
ejpam-4920	364	11	in	in	ADP
ejpam-4920	364	12	c3	c3	PROPN
ejpam-4920	364	13	◦	◦	PROPN
ejpam-4920	364	14	k4	k4	PROPN
ejpam-4920	364	15	,	,	PUNCT
ejpam-4920	364	16	showing	show	VERB
ejpam-4920	364	17	that	that	DET
ejpam-4920	364	18	γzh(c3	γzh(c3	PROPN
ejpam-4920	364	19	◦	◦	NOUN
ejpam-4920	364	20	k4	k4	PROPN
ejpam-4920	364	21	)	)	PUNCT
ejpam-4920	364	22	≤	≤	NUM
ejpam-4920	364	23	|s|	|s|	PROPN
ejpam-4920	364	24	=	=	SYM
ejpam-4920	364	25	12	12	NUM
ejpam-4920	364	26	.	.	PUNCT
ejpam-4920	365	1	now	now	ADV
ejpam-4920	365	2	,	,	PUNCT
ejpam-4920	365	3	since	since	SCONJ
ejpam-4920	365	4	,	,	PUNCT
ejpam-4920	365	5	zfpnd(k4	zfpnd(k4	NOUN
ejpam-4920	365	6	)	)	PUNCT
ejpam-4920	365	7	=	=	SYM
ejpam-4920	365	8	4	4	NUM
ejpam-4920	365	9	,	,	PUNCT
ejpam-4920	365	10	it	it	PRON
ejpam-4920	365	11	follows	follow	VERB
ejpam-4920	365	12	that	that	SCONJ
ejpam-4920	365	13	|v	|v	PROPN
ejpam-4920	365	14	(	(	PUNCT
ejpam-4920	365	15	c3)|	c3)|	NOUN
ejpam-4920	365	16	·	·	PUNCT
ejpam-4920	365	17	zfpnd(k4	zfpnd(k4	PROPN
ejpam-4920	365	18	)	)	PUNCT
ejpam-4920	366	1	+	+	CCONJ
ejpam-4920	366	2	|v	|v	X
ejpam-4920	366	3	(	(	PUNCT
ejpam-4920	366	4	c3)|	c3)|	NOUN
ejpam-4920	366	5	=	=	NOUN
ejpam-4920	366	6	3	3	NUM
ejpam-4920	366	7	·	·	SYM
ejpam-4920	366	8	4	4	NUM
ejpam-4920	366	9	+	+	SYM
ejpam-4920	366	10	3	3	NUM
ejpam-4920	366	11	=	=	SYM
ejpam-4920	366	12	15	15	NUM
ejpam-4920	366	13	.	.	PUNCT
ejpam-4920	366	14	consequently	consequently	ADV
ejpam-4920	366	15	,	,	PUNCT
ejpam-4920	366	16	γzh(c3	γzh(c3	PROPN
ejpam-4920	366	17	◦	◦	NOUN
ejpam-4920	366	18	k4	k4	NOUN
ejpam-4920	366	19	)	)	PUNCT
ejpam-4920	366	20	≤	≤	NOUN
ejpam-4920	366	21	12	12	NUM
ejpam-4920	366	22	<	<	SYM
ejpam-4920	366	23	15	15	NUM
ejpam-4920	366	24	=	=	SYM
ejpam-4920	366	25	|v	|v	X
ejpam-4920	366	26	(	(	PUNCT
ejpam-4920	366	27	c3)|	c3)|	NOUN
ejpam-4920	366	28	·	·	PUNCT
ejpam-4920	366	29	zfpnd(k3	zfpnd(k3	NOUN
ejpam-4920	366	30	)	)	PUNCT
ejpam-4920	367	1	+	+	CCONJ
ejpam-4920	367	2	|v	|v	X
ejpam-4920	367	3	(	(	PUNCT
ejpam-4920	367	4	k4)|	k4)|	PROPN
ejpam-4920	367	5	.	.	PUNCT
ejpam-4920	368	1	acknowledgements	acknowledgement	NOUN
ejpam-4920	368	2	the	the	DET
ejpam-4920	368	3	authors	author	NOUN
ejpam-4920	368	4	would	would	AUX
ejpam-4920	368	5	like	like	VERB
ejpam-4920	368	6	to	to	PART
ejpam-4920	368	7	thank	thank	VERB
ejpam-4920	368	8	mindanao	mindanao	PROPN
ejpam-4920	368	9	state	state	PROPN
ejpam-4920	368	10	university	university	PROPN
ejpam-4920	368	11	tawi	tawi	PROPN
ejpam-4920	368	12	-	-	PUNCT
ejpam-4920	368	13	tawi	tawi	PROPN
ejpam-4920	368	14	college	college	PROPN
ejpam-4920	368	15	of	of	ADP
ejpam-4920	368	16	technology	technology	NOUN
ejpam-4920	368	17	and	and	CCONJ
ejpam-4920	368	18	oceanography	oceanography	NOUN
ejpam-4920	368	19	for	for	ADP
ejpam-4920	368	20	funding	fund	VERB
ejpam-4920	368	21	this	this	DET
ejpam-4920	368	22	research	research	NOUN
ejpam-4920	368	23	.	.	PUNCT
ejpam-4920	369	1	moreover	moreover	ADV
ejpam-4920	369	2	,	,	PUNCT
ejpam-4920	369	3	the	the	DET
ejpam-4920	369	4	authors	author	NOUN
ejpam-4920	369	5	would	would	AUX
ejpam-4920	369	6	like	like	VERB
ejpam-4920	369	7	to	to	PART
ejpam-4920	369	8	thank	thank	VERB
ejpam-4920	369	9	the	the	DET
ejpam-4920	369	10	referees	referee	NOUN
ejpam-4920	369	11	for	for	ADP
ejpam-4920	369	12	their	their	PRON
ejpam-4920	369	13	invaluable	invaluable	ADJ
ejpam-4920	369	14	comments	comment	NOUN
ejpam-4920	369	15	and	and	CCONJ
ejpam-4920	369	16	suggestions	suggestion	NOUN
ejpam-4920	369	17	that	that	PRON
ejpam-4920	369	18	led	lead	VERB
ejpam-4920	369	19	to	to	ADP
ejpam-4920	369	20	the	the	DET
ejpam-4920	369	21	improvement	improvement	NOUN
ejpam-4920	369	22	of	of	ADP
ejpam-4920	369	23	the	the	DET
ejpam-4920	369	24	paper	paper	NOUN
ejpam-4920	369	25	.	.	PUNCT
ejpam-4920	370	1	references	reference	NOUN
ejpam-4920	370	2	[	[	X
ejpam-4920	370	3	1	1	NUM
ejpam-4920	370	4	]	]	PUNCT
ejpam-4920	370	5	s.	s.	PROPN
ejpam-4920	370	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4920	370	7	,	,	PUNCT
ejpam-4920	370	8	b.	b.	PROPN
ejpam-4920	370	9	krishnakumari	krishnakumari	PROPN
ejpam-4920	370	10	,	,	PUNCT
ejpam-4920	370	11	b.	b.	PROPN
ejpam-4920	370	12	natarjan	natarjan	PROPN
ejpam-4920	370	13	,	,	PUNCT
ejpam-4920	370	14	and	and	CCONJ
ejpam-4920	370	15	y.	y.	PROPN
ejpam-4920	370	16	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4920	370	17	.	.	PUNCT
ejpam-4920	371	1	bounds	bound	NOUN
ejpam-4920	371	2	on	on	ADP
ejpam-4920	371	3	the	the	DET
ejpam-4920	371	4	hop	hop	NOUN
ejpam-4920	371	5	domination	domination	NOUN
ejpam-4920	371	6	number	number	NOUN
ejpam-4920	371	7	of	of	ADP
ejpam-4920	371	8	a	a	DET
ejpam-4920	371	9	tree	tree	NOUN
ejpam-4920	371	10	.	.	PUNCT
ejpam-4920	372	1	proceedings	proceeding	NOUN
ejpam-4920	372	2	-	-	PUNCT
ejpam-4920	372	3	mathematical	mathematical	ADJ
ejpam-4920	372	4	sciences	science	NOUN
ejpam-4920	372	5	.	.	PUNCT
ejpam-4920	372	6	,	,	PUNCT
ejpam-4920	372	7	125(4):449–455	125(4):449–455	ADP
ejpam-4920	372	8	,	,	PUNCT
ejpam-4920	372	9	2015	2015	NUM
ejpam-4920	372	10	.	.	PUNCT
ejpam-4920	373	1	[	[	X
ejpam-4920	373	2	2	2	NUM
ejpam-4920	373	3	]	]	PUNCT
ejpam-4920	373	4	s.	s.	PROPN
ejpam-4920	373	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4920	373	6	,	,	PUNCT
ejpam-4920	373	7	c.	c.	PROPN
ejpam-4920	373	8	natarajan	natarajan	PROPN
ejpam-4920	373	9	,	,	PUNCT
ejpam-4920	373	10	and	and	CCONJ
ejpam-4920	373	11	g.	g.	PROPN
ejpam-4920	373	12	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4920	373	13	.	.	PUNCT
ejpam-4920	374	1	a	a	DET
ejpam-4920	374	2	note	note	NOUN
ejpam-4920	374	3	on	on	ADP
ejpam-4920	374	4	hop	hop	NOUN
ejpam-4920	374	5	domination	domination	NOUN
ejpam-4920	374	6	number	number	NOUN
ejpam-4920	374	7	of	of	ADP
ejpam-4920	374	8	some	some	DET
ejpam-4920	374	9	special	special	ADJ
ejpam-4920	374	10	families	family	NOUN
ejpam-4920	374	11	of	of	ADP
ejpam-4920	374	12	graphs	graph	NOUN
ejpam-4920	374	13	.	.	PUNCT
ejpam-4920	375	1	international	international	ADJ
ejpam-4920	375	2	journal	journal	NOUN
ejpam-4920	375	3	of	of	ADP
ejpam-4920	375	4	pure	pure	ADJ
ejpam-4920	375	5	and	and	CCONJ
ejpam-4920	375	6	applied	applied	ADJ
ejpam-4920	375	7	mathematics	mathematic	NOUN
ejpam-4920	375	8	.	.	PUNCT
ejpam-4920	375	9	,	,	PUNCT
ejpam-4920	375	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4920	375	11	,	,	PUNCT
ejpam-4920	375	12	2018	2018	NUM
ejpam-4920	375	13	.	.	PUNCT
ejpam-4920	376	1	[	[	X
ejpam-4920	376	2	3	3	X
ejpam-4920	376	3	]	]	PUNCT
ejpam-4920	376	4	j.	j.	PROPN
ejpam-4920	376	5	hassan	hassan	PROPN
ejpam-4920	376	6	,	,	PUNCT
ejpam-4920	376	7	ar	ar	PROPN
ejpam-4920	376	8	.	.	PROPN
ejpam-4920	376	9	bakkang	bakkang	PROPN
ejpam-4920	376	10	,	,	PUNCT
ejpam-4920	376	11	and	and	CCONJ
ejpam-4920	376	12	ass	ass	PROPN
ejpam-4920	376	13	.	.	PROPN
ejpam-4920	376	14	sappari	sappari	PROPN
ejpam-4920	376	15	.	.	PUNCT
ejpam-4920	377	1	j2	j2	PROPN
ejpam-4920	377	2	-	-	PUNCT
ejpam-4920	377	3	hop	hop	PROPN
ejpam-4920	377	4	domination	domination	NOUN
ejpam-4920	377	5	in	in	ADP
ejpam-4920	377	6	graphs	graph	NOUN
ejpam-4920	377	7	:	:	PUNCT
ejpam-4920	377	8	properties	property	NOUN
ejpam-4920	377	9	and	and	CCONJ
ejpam-4920	377	10	connections	connection	NOUN
ejpam-4920	377	11	with	with	ADP
ejpam-4920	377	12	other	other	ADJ
ejpam-4920	377	13	parameters	parameter	NOUN
ejpam-4920	377	14	.	.	PUNCT
ejpam-4920	378	1	eur	eur	PROPN
ejpam-4920	378	2	.	.	PUNCT
ejpam-4920	379	1	j.	j.	PROPN
ejpam-4920	379	2	pure	pure	PROPN
ejpam-4920	379	3	appl	appl	PROPN
ejpam-4920	379	4	.	.	PUNCT
ejpam-4920	379	5	math	math	PROPN
ejpam-4920	379	6	.	.	PUNCT
ejpam-4920	379	7	,	,	PUNCT
ejpam-4920	379	8	16(4):2118–2131	16(4):2118–2131	NUM
ejpam-4920	379	9	,	,	PUNCT
ejpam-4920	379	10	2023	2023	NUM
ejpam-4920	379	11	.	.	PUNCT
ejpam-4920	380	1	[	[	X
ejpam-4920	380	2	4	4	X
ejpam-4920	380	3	]	]	PUNCT
ejpam-4920	380	4	j.	j.	PROPN
ejpam-4920	380	5	hassan	hassan	PROPN
ejpam-4920	380	6	and	and	CCONJ
ejpam-4920	380	7	s.	s.	PROPN
ejpam-4920	380	8	canoy	canoy	PROPN
ejpam-4920	380	9	jr	jr	PROPN
ejpam-4920	380	10	.	.	PUNCT
ejpam-4920	381	1	grundy	grundy	PROPN
ejpam-4920	381	2	hop	hop	PROPN
ejpam-4920	381	3	domination	domination	PROPN
ejpam-4920	381	4	in	in	ADP
ejpam-4920	381	5	graphs	graph	NOUN
ejpam-4920	381	6	.	.	PUNCT
ejpam-4920	382	1	eur	eur	PROPN
ejpam-4920	382	2	.	.	PUNCT
ejpam-4920	383	1	j.	j.	PROPN
ejpam-4920	383	2	pure	pure	PROPN
ejpam-4920	383	3	appl	appl	PROPN
ejpam-4920	383	4	.	.	PUNCT
ejpam-4920	383	5	math	math	PROPN
ejpam-4920	383	6	.	.	PUNCT
ejpam-4920	383	7	,	,	PUNCT
ejpam-4920	383	8	15(4):1623–1636	15(4):1623–1636	NUM
ejpam-4920	383	9	,	,	PUNCT
ejpam-4920	383	10	2022	2022	NUM
ejpam-4920	383	11	.	.	PUNCT
ejpam-4920	384	1	[	[	X
ejpam-4920	384	2	5	5	X
ejpam-4920	384	3	]	]	PUNCT
ejpam-4920	384	4	j.	j.	PROPN
ejpam-4920	384	5	hassan	hassan	PROPN
ejpam-4920	384	6	and	and	CCONJ
ejpam-4920	384	7	s.	s.	PROPN
ejpam-4920	384	8	canoy	canoy	PROPN
ejpam-4920	384	9	jr	jr	PROPN
ejpam-4920	384	10	.	.	PUNCT
ejpam-4920	385	1	grundy	grundy	PROPN
ejpam-4920	385	2	total	total	PROPN
ejpam-4920	385	3	hop	hop	PROPN
ejpam-4920	385	4	dominating	dominate	VERB
ejpam-4920	385	5	sequences	sequence	NOUN
ejpam-4920	385	6	in	in	ADP
ejpam-4920	385	7	graphs	graph	NOUN
ejpam-4920	385	8	.	.	PUNCT
ejpam-4920	386	1	eur	eur	PROPN
ejpam-4920	386	2	.	.	PUNCT
ejpam-4920	387	1	j.	j.	PROPN
ejpam-4920	387	2	pure	pure	PROPN
ejpam-4920	387	3	appl	appl	PROPN
ejpam-4920	387	4	.	.	PUNCT
ejpam-4920	387	5	math	math	PROPN
ejpam-4920	387	6	.	.	PUNCT
ejpam-4920	387	7	,	,	PUNCT
ejpam-4920	387	8	16(4):2597–2612	16(4):2597–2612	NUM
ejpam-4920	387	9	,	,	PUNCT
ejpam-4920	387	10	2023	2023	NUM
ejpam-4920	387	11	.	.	PUNCT
ejpam-4920	388	1	[	[	X
ejpam-4920	388	2	6	6	NUM
ejpam-4920	388	3	]	]	PUNCT
ejpam-4920	388	4	j.	j.	PROPN
ejpam-4920	388	5	hassan	hassan	PROPN
ejpam-4920	388	6	,	,	PUNCT
ejpam-4920	388	7	a.	a.	PROPN
ejpam-4920	388	8	lintasan	lintasan	PROPN
ejpam-4920	388	9	,	,	PUNCT
ejpam-4920	388	10	and	and	CCONJ
ejpam-4920	388	11	n.h	n.h	PROPN
ejpam-4920	388	12	.	.	PUNCT
ejpam-4920	389	1	mohammad	mohammad	PROPN
ejpam-4920	389	2	.	.	PUNCT
ejpam-4920	390	1	some	some	DET
ejpam-4920	390	2	properties	property	NOUN
ejpam-4920	390	3	and	and	CCONJ
ejpam-4920	390	4	realization	realization	NOUN
ejpam-4920	390	5	problems	problem	NOUN
ejpam-4920	390	6	involving	involve	VERB
ejpam-4920	390	7	connected	connected	ADJ
ejpam-4920	390	8	outer	outer	ADJ
ejpam-4920	390	9	-	-	PUNCT
ejpam-4920	390	10	hop	hop	NOUN
ejpam-4920	390	11	independent	independent	ADJ
ejpam-4920	390	12	hop	hop	NOUN
ejpam-4920	390	13	domination	domination	NOUN
ejpam-4920	390	14	in	in	ADP
ejpam-4920	390	15	graphs	graph	NOUN
ejpam-4920	390	16	.	.	PUNCT
ejpam-4920	391	1	eur	eur	PROPN
ejpam-4920	391	2	.	.	PUNCT
ejpam-4920	392	1	j.	j.	PROPN
ejpam-4920	392	2	pure	pure	PROPN
ejpam-4920	392	3	appl	appl	PROPN
ejpam-4920	392	4	.	.	PUNCT
ejpam-4920	392	5	math	math	PROPN
ejpam-4920	392	6	.	.	PUNCT
ejpam-4920	392	7	,	,	PUNCT
ejpam-4920	392	8	16(3):1848–1861	16(3):1848–1861	NUM
ejpam-4920	392	9	,	,	PUNCT
ejpam-4920	392	10	2023	2023	NUM
ejpam-4920	392	11	.	.	PUNCT
ejpam-4920	393	1	[	[	X
ejpam-4920	393	2	7	7	X
ejpam-4920	393	3	]	]	X
ejpam-4920	393	4	m.	m.	NOUN
ejpam-4920	393	5	henning	henning	PROPN
ejpam-4920	393	6	and	and	CCONJ
ejpam-4920	393	7	n.	n.	PROPN
ejpam-4920	393	8	rad	rad	PROPN
ejpam-4920	393	9	.	.	PROPN
ejpam-4920	394	1	on	on	ADP
ejpam-4920	394	2	2	2	NUM
ejpam-4920	394	3	-	-	PUNCT
ejpam-4920	394	4	step	step	NOUN
ejpam-4920	394	5	and	and	CCONJ
ejpam-4920	394	6	hop	hop	NOUN
ejpam-4920	394	7	dominating	dominating	NOUN
ejpam-4920	394	8	sets	set	NOUN
ejpam-4920	394	9	in	in	ADP
ejpam-4920	394	10	graphs	graph	NOUN
ejpam-4920	394	11	.	.	PUNCT
ejpam-4920	395	1	graphs	graph	NOUN
ejpam-4920	395	2	and	and	CCONJ
ejpam-4920	395	3	combinatorics	combinatoric	NOUN
ejpam-4920	395	4	.	.	PUNCT
ejpam-4920	395	5	,	,	PUNCT
ejpam-4920	395	6	33(4):913–927	33(4):913–927	PROPN
ejpam-4920	395	7	,	,	PUNCT
ejpam-4920	395	8	2017	2017	NUM
ejpam-4920	395	9	.	.	PUNCT
ejpam-4920	396	1	[	[	X
ejpam-4920	396	2	8	8	NUM
ejpam-4920	396	3	]	]	X
ejpam-4920	396	4	aay	aay	PROPN
ejpam-4920	396	5	.	.	PUNCT
ejpam-4920	396	6	isahac	isahac	PROPN
ejpam-4920	396	7	,	,	PUNCT
ejpam-4920	396	8	j.	j.	PROPN
ejpam-4920	396	9	hassan	hassan	PROPN
ejpam-4920	396	10	,	,	PUNCT
ejpam-4920	396	11	ls	ls	PROPN
ejpam-4920	396	12	.	.	PROPN
ejpam-4920	396	13	laja	laja	PROPN
ejpam-4920	396	14	,	,	PUNCT
ejpam-4920	396	15	and	and	CCONJ
ejpam-4920	396	16	hb	hb	PROPN
ejpam-4920	396	17	.	.	PUNCT
ejpam-4920	397	1	copel	copel	ADJ
ejpam-4920	397	2	.	.	PUNCT
ejpam-4920	398	1	outer	outer	ADJ
ejpam-4920	398	2	-	-	PUNCT
ejpam-4920	398	3	convex	convex	ADJ
ejpam-4920	398	4	hop	hop	NOUN
ejpam-4920	398	5	domination	domination	NOUN
ejpam-4920	398	6	in	in	ADP
ejpam-4920	398	7	graphs	graph	NOUN
ejpam-4920	398	8	under	under	ADP
ejpam-4920	398	9	some	some	DET
ejpam-4920	398	10	binary	binary	ADJ
ejpam-4920	398	11	operations	operation	NOUN
ejpam-4920	398	12	.	.	PUNCT
ejpam-4920	399	1	eur	eur	PROPN
ejpam-4920	399	2	.	.	PUNCT
ejpam-4920	400	1	j.	j.	PROPN
ejpam-4920	400	2	pure	pure	PROPN
ejpam-4920	400	3	appl	appl	PROPN
ejpam-4920	400	4	.	.	PUNCT
ejpam-4920	400	5	math	math	PROPN
ejpam-4920	400	6	.	.	PUNCT
ejpam-4920	400	7	,	,	PUNCT
ejpam-4920	400	8	16(4):2035–2048	16(4):2035–2048	NUM
ejpam-4920	400	9	,	,	PUNCT
ejpam-4920	400	10	2023	2023	NUM
ejpam-4920	400	11	.	.	PUNCT
ejpam-4920	401	1	references	reference	NOUN
ejpam-4920	401	2	337	337	NUM
ejpam-4920	402	1	[	[	X
ejpam-4920	402	2	9	9	NUM
ejpam-4920	402	3	]	]	PUNCT
ejpam-4920	402	4	s.	s.	PROPN
ejpam-4920	402	5	canoy	canoy	PROPN
ejpam-4920	402	6	jr	jr	PROPN
ejpam-4920	402	7	.	.	PROPN
ejpam-4920	402	8	and	and	CCONJ
ejpam-4920	402	9	j.	j.	PROPN
ejpam-4920	402	10	hassan	hassan	PROPN
ejpam-4920	402	11	.	.	PUNCT
ejpam-4920	403	1	weakly	weakly	ADJ
ejpam-4920	403	2	convex	convex	VERB
ejpam-4920	403	3	hop	hop	NOUN
ejpam-4920	403	4	dominating	dominating	NOUN
ejpam-4920	403	5	sets	set	NOUN
ejpam-4920	403	6	in	in	ADP
ejpam-4920	403	7	graphs	graph	NOUN
ejpam-4920	403	8	.	.	PUNCT
ejpam-4920	404	1	eur	eur	PROPN
ejpam-4920	404	2	.	.	PUNCT
ejpam-4920	405	1	j.	j.	PROPN
ejpam-4920	405	2	pure	pure	PROPN
ejpam-4920	405	3	appl	appl	PROPN
ejpam-4920	405	4	.	.	PUNCT
ejpam-4920	405	5	math	math	PROPN
ejpam-4920	405	6	.	.	PUNCT
ejpam-4920	405	7	,	,	PUNCT
ejpam-4920	405	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-4920	405	9	,	,	PUNCT
ejpam-4920	405	10	2022	2022	NUM
ejpam-4920	405	11	.	.	PUNCT
ejpam-4920	406	1	[	[	X
ejpam-4920	406	2	10	10	NUM
ejpam-4920	406	3	]	]	X
ejpam-4920	406	4	s.	s.	PROPN
ejpam-4920	406	5	canoy	canoy	PROPN
ejpam-4920	406	6	jr	jr	PROPN
ejpam-4920	406	7	.	.	PROPN
ejpam-4920	406	8	,	,	PUNCT
ejpam-4920	406	9	r.	r.	PROPN
ejpam-4920	406	10	mollejon	mollejon	NOUN
ejpam-4920	406	11	,	,	PUNCT
ejpam-4920	406	12	and	and	CCONJ
ejpam-4920	406	13	j.	j.	PROPN
ejpam-4920	406	14	g.	g.	PROPN
ejpam-4920	406	15	canoy	canoy	PROPN
ejpam-4920	406	16	.	.	PUNCT
ejpam-4920	407	1	hop	hop	PROPN
ejpam-4920	407	2	dominating	dominating	NOUN
ejpam-4920	407	3	sets	set	NOUN
ejpam-4920	407	4	in	in	ADP
ejpam-4920	407	5	graphs	graph	NOUN
ejpam-4920	407	6	under	under	ADP
ejpam-4920	407	7	binary	binary	ADJ
ejpam-4920	407	8	operations	operation	NOUN
ejpam-4920	407	9	.	.	PUNCT
ejpam-4920	408	1	eur	eur	PROPN
ejpam-4920	408	2	.	.	PUNCT
ejpam-4920	409	1	j.	j.	PROPN
ejpam-4920	409	2	pure	pure	PROPN
ejpam-4920	409	3	appl	appl	PROPN
ejpam-4920	409	4	.	.	PUNCT
ejpam-4920	409	5	math	math	PROPN
ejpam-4920	409	6	.	.	PUNCT
ejpam-4920	409	7	,	,	PUNCT
ejpam-4920	410	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4920	410	2	,	,	PUNCT
ejpam-4920	410	3	2019	2019	NUM
ejpam-4920	410	4	.	.	PUNCT
ejpam-4920	411	1	[	[	X
ejpam-4920	411	2	11	11	NUM
ejpam-4920	411	3	]	]	PUNCT
ejpam-4920	411	4	j.	j.	PROPN
ejpam-4920	411	5	manditong	manditong	PROPN
ejpam-4920	411	6	,	,	PUNCT
ejpam-4920	411	7	j.	j.	PROPN
ejpam-4920	411	8	hassan	hassan	PROPN
ejpam-4920	411	9	,	,	PUNCT
ejpam-4920	411	10	ls	ls	PROPN
ejpam-4920	411	11	laja	laja	PROPN
ejpam-4920	411	12	,	,	PUNCT
ejpam-4920	411	13	aa	aa	INTJ
ejpam-4920	411	14	.	.	PUNCT
ejpam-4920	411	15	laja	laja	PROPN
ejpam-4920	411	16	,	,	PUNCT
ejpam-4920	411	17	nhm	nhm	PROPN
ejpam-4920	411	18	.	.	PUNCT
ejpam-4920	411	19	mohammad	mohammad	PROPN
ejpam-4920	411	20	,	,	PUNCT
ejpam-4920	411	21	and	and	CCONJ
ejpam-4920	411	22	su	su	PROPN
ejpam-4920	411	23	.	.	PROPN
ejpam-4920	411	24	kamdon	kamdon	PROPN
ejpam-4920	411	25	.	.	PROPN
ejpam-4920	411	26	conneted	connete	VERB
ejpam-4920	411	27	outer	outer	ADJ
ejpam-4920	411	28	-	-	PUNCT
ejpam-4920	411	29	hop	hop	NOUN
ejpam-4920	411	30	independent	independent	ADJ
ejpam-4920	411	31	dominating	dominating	NOUN
ejpam-4920	411	32	sets	set	NOUN
ejpam-4920	411	33	in	in	ADP
ejpam-4920	411	34	graphs	graph	NOUN
ejpam-4920	411	35	under	under	ADP
ejpam-4920	411	36	some	some	DET
ejpam-4920	411	37	binary	binary	ADJ
ejpam-4920	411	38	operations	operation	NOUN
ejpam-4920	411	39	.	.	PUNCT
ejpam-4920	412	1	eur	eur	PROPN
ejpam-4920	412	2	.	.	PUNCT
ejpam-4920	413	1	j.	j.	PROPN
ejpam-4920	413	2	pure	pure	PROPN
ejpam-4920	413	3	appl	appl	PROPN
ejpam-4920	413	4	.	.	PUNCT
ejpam-4920	413	5	math	math	PROPN
ejpam-4920	413	6	.	.	PUNCT
ejpam-4920	413	7	,	,	PUNCT
ejpam-4920	414	1	16(3):1817–1829	16(3):1817–1829	NUM
ejpam-4920	414	2	,	,	PUNCT
ejpam-4920	414	3	2023	2023	NUM
ejpam-4920	414	4	.	.	PUNCT
ejpam-4920	415	1	[	[	X
ejpam-4920	415	2	12	12	NUM
ejpam-4920	415	3	]	]	X
ejpam-4920	415	4	c.	c.	PROPN
ejpam-4920	415	5	natarajan	natarajan	PROPN
ejpam-4920	415	6	and	and	CCONJ
ejpam-4920	415	7	s.	s.	PROPN
ejpam-4920	415	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4920	415	9	.	.	PUNCT
ejpam-4920	416	1	hop	hop	PROPN
ejpam-4920	416	2	domination	domination	NOUN
ejpam-4920	416	3	in	in	ADP
ejpam-4920	416	4	graphs	graphs	PROPN
ejpam-4920	416	5	ii	ii	PROPN
ejpam-4920	416	6	.	.	PUNCT
ejpam-4920	416	7	versita	versita	PROPN
ejpam-4920	416	8	,	,	PUNCT
ejpam-4920	416	9	23(2):187	23(2):187	NUM
ejpam-4920	416	10	–	–	PUNCT
ejpam-4920	416	11	199	199	NUM
ejpam-4920	416	12	,	,	PUNCT
ejpam-4920	416	13	2015	2015	NUM
ejpam-4920	416	14	.	.	PUNCT