id	sid	tid	token	lemma	pos
ejpam-5154	1	1	european	european	PROPN
ejpam-5154	1	2	journal	journal	PROPN
ejpam-5154	1	3	of	of	ADP
ejpam-5154	1	4	pure	pure	ADJ
ejpam-5154	1	5	and	and	CCONJ
ejpam-5154	1	6	applied	apply	VERB
ejpam-5154	1	7	mathematics	mathematic	NOUN
ejpam-5154	1	8	vol	vol	NOUN
ejpam-5154	1	9	.	.	PROPN
ejpam-5154	2	1	17	17	NUM
ejpam-5154	2	2	,	,	PUNCT
ejpam-5154	2	3	no	no	INTJ
ejpam-5154	2	4	.	.	NOUN
ejpam-5154	2	5	4	4	NUM
ejpam-5154	2	6	,	,	PUNCT
ejpam-5154	2	7	2024	2024	NUM
ejpam-5154	2	8	,	,	PUNCT
ejpam-5154	2	9	3772	3772	NUM
ejpam-5154	2	10	-	-	SYM
ejpam-5154	2	11	3780	3780	NUM
ejpam-5154	2	12	issn	issn	PROPN
ejpam-5154	2	13	1307	1307	NUM
ejpam-5154	2	14	-	-	SYM
ejpam-5154	2	15	5543	5543	NUM
ejpam-5154	2	16	–	–	PUNCT
ejpam-5154	2	17	ejpam.com	ejpam.com	X
ejpam-5154	2	18	published	publish	VERB
ejpam-5154	2	19	by	by	ADP
ejpam-5154	2	20	new	new	PROPN
ejpam-5154	2	21	york	york	PROPN
ejpam-5154	2	22	business	business	PROPN
ejpam-5154	2	23	global	global	ADJ
ejpam-5154	2	24	zero	zero	NUM
ejpam-5154	2	25	forcing	force	VERB
ejpam-5154	2	26	domination	domination	NOUN
ejpam-5154	2	27	in	in	ADP
ejpam-5154	2	28	some	some	DET
ejpam-5154	2	29	graphs	graph	NOUN
ejpam-5154	2	30	:	:	PUNCT
ejpam-5154	2	31	characterizations	characterization	NOUN
ejpam-5154	2	32	and	and	CCONJ
ejpam-5154	2	33	derived	derive	VERB
ejpam-5154	2	34	formulas	formula	NOUN
ejpam-5154	2	35	javier	javier	PROPN
ejpam-5154	2	36	a.	a.	PROPN
ejpam-5154	2	37	hassan1,2,∗	hassan1,2,∗	PROPN
ejpam-5154	2	38	,	,	PUNCT
ejpam-5154	2	39	maria	maria	PROPN
ejpam-5154	2	40	andrea	andrea	PROPN
ejpam-5154	2	41	o.	o.	PROPN
ejpam-5154	2	42	bonsocan3	bonsocan3	PROPN
ejpam-5154	2	43	,	,	PUNCT
ejpam-5154	2	44	mercedita	mercedita	PROPN
ejpam-5154	2	45	a.	a.	NOUN
ejpam-5154	2	46	langamin1	langamin1	PROPN
ejpam-5154	2	47	,	,	PUNCT
ejpam-5154	2	48	vergel	vergel	NOUN
ejpam-5154	2	49	t.	t.	PROPN
ejpam-5154	2	50	bilar3	bilar3	PROPN
ejpam-5154	2	51	,	,	PUNCT
ejpam-5154	2	52	sharifa	sharifa	PROPN
ejpam-5154	2	53	dianne	dianne	PROPN
ejpam-5154	2	54	a.	a.	PROPN
ejpam-5154	2	55	aming4	aming4	PROPN
ejpam-5154	2	56	,	,	PUNCT
ejpam-5154	2	57	bayah	bayah	PROPN
ejpam-5154	2	58	j.	j.	PROPN
ejpam-5154	2	59	amiruddin	amiruddin	PROPN
ejpam-5154	2	60	-	-	PUNCT
ejpam-5154	2	61	rajik1	rajik1	PROPN
ejpam-5154	2	62	1mathematics	1mathematics	NUM
ejpam-5154	2	63	and	and	CCONJ
ejpam-5154	2	64	statistics	statistics	PROPN
ejpam-5154	2	65	department	department	PROPN
ejpam-5154	2	66	,	,	PUNCT
ejpam-5154	2	67	college	college	NOUN
ejpam-5154	2	68	of	of	ADP
ejpam-5154	2	69	arts	art	NOUN
ejpam-5154	2	70	and	and	CCONJ
ejpam-5154	2	71	sciences	science	NOUN
ejpam-5154	2	72	,	,	PUNCT
ejpam-5154	2	73	msu	msu	PROPN
ejpam-5154	2	74	-	-	PUNCT
ejpam-5154	2	75	tawi	tawi	NOUN
ejpam-5154	2	76	-	-	PUNCT
ejpam-5154	2	77	tawi	tawi	NOUN
ejpam-5154	2	78	college	college	PROPN
ejpam-5154	2	79	of	of	ADP
ejpam-5154	2	80	technology	technology	NOUN
ejpam-5154	2	81	and	and	CCONJ
ejpam-5154	2	82	oceanography	oceanography	NOUN
ejpam-5154	2	83	,	,	PUNCT
ejpam-5154	2	84	bongao	bongao	NOUN
ejpam-5154	2	85	,	,	PUNCT
ejpam-5154	2	86	tawi	tawi	NOUN
ejpam-5154	2	87	-	-	PUNCT
ejpam-5154	2	88	tawi	tawi	NOUN
ejpam-5154	2	89	,	,	PUNCT
ejpam-5154	2	90	philippines	philippine	NOUN
ejpam-5154	2	91	2department	2department	NUM
ejpam-5154	2	92	of	of	ADP
ejpam-5154	2	93	mathematics	mathematic	NOUN
ejpam-5154	2	94	,	,	PUNCT
ejpam-5154	2	95	college	college	NOUN
ejpam-5154	2	96	of	of	ADP
ejpam-5154	2	97	science	science	PROPN
ejpam-5154	2	98	,	,	PUNCT
ejpam-5154	2	99	korea	korea	PROPN
ejpam-5154	2	100	university	university	PROPN
ejpam-5154	2	101	,	,	PUNCT
ejpam-5154	2	102	seoul	seoul	PROPN
ejpam-5154	2	103	02841	02841	PROPN
ejpam-5154	2	104	,	,	PUNCT
ejpam-5154	2	105	south	south	PROPN
ejpam-5154	2	106	korea	korea	PROPN
ejpam-5154	3	1	3department	3department	NUM
ejpam-5154	3	2	of	of	ADP
ejpam-5154	3	3	mathematics	mathematic	NOUN
ejpam-5154	3	4	,	,	PUNCT
ejpam-5154	3	5	ateneo	ateneo	X
ejpam-5154	3	6	de	de	PROPN
ejpam-5154	3	7	davao	davao	PROPN
ejpam-5154	3	8	university	university	PROPN
ejpam-5154	3	9	,	,	PUNCT
ejpam-5154	3	10	e.	e.	PROPN
ejpam-5154	3	11	jacinto	jacinto	PROPN
ejpam-5154	3	12	street	street	PROPN
ejpam-5154	3	13	,	,	PUNCT
ejpam-5154	3	14	8016	8016	NUM
ejpam-5154	3	15	davao	davao	PROPN
ejpam-5154	3	16	city	city	NOUN
ejpam-5154	3	17	,	,	PUNCT
ejpam-5154	3	18	philippines	philippine	VERB
ejpam-5154	3	19	4office	4office	NUM
ejpam-5154	3	20	of	of	ADP
ejpam-5154	3	21	the	the	DET
ejpam-5154	3	22	chancellor	chancellor	NOUN
ejpam-5154	3	23	,	,	PUNCT
ejpam-5154	3	24	msu	msu	PROPN
ejpam-5154	3	25	-	-	PUNCT
ejpam-5154	3	26	tawi	tawi	NOUN
ejpam-5154	3	27	-	-	PUNCT
ejpam-5154	3	28	tawi	tawi	NOUN
ejpam-5154	3	29	college	college	PROPN
ejpam-5154	3	30	of	of	ADP
ejpam-5154	3	31	technology	technology	NOUN
ejpam-5154	3	32	and	and	CCONJ
ejpam-5154	3	33	oceanography	oceanography	NOUN
ejpam-5154	3	34	,	,	PUNCT
ejpam-5154	3	35	bongao	bongao	NOUN
ejpam-5154	3	36	,	,	PUNCT
ejpam-5154	3	37	tawi	tawi	NOUN
ejpam-5154	3	38	-	-	PUNCT
ejpam-5154	3	39	tawi	tawi	NOUN
ejpam-5154	3	40	,	,	PUNCT
ejpam-5154	3	41	philippines	philippine	NOUN
ejpam-5154	3	42	abstract	abstract	ADJ
ejpam-5154	3	43	.	.	PUNCT
ejpam-5154	4	1	in	in	ADP
ejpam-5154	4	2	this	this	DET
ejpam-5154	4	3	paper	paper	NOUN
ejpam-5154	4	4	,	,	PUNCT
ejpam-5154	4	5	we	we	PRON
ejpam-5154	4	6	initiate	initiate	VERB
ejpam-5154	4	7	the	the	DET
ejpam-5154	4	8	study	study	NOUN
ejpam-5154	4	9	on	on	ADP
ejpam-5154	4	10	zero	zero	NUM
ejpam-5154	4	11	forcing	force	VERB
ejpam-5154	4	12	domination	domination	NOUN
ejpam-5154	4	13	in	in	ADP
ejpam-5154	4	14	a	a	DET
ejpam-5154	4	15	graph	graph	NOUN
ejpam-5154	4	16	.	.	PUNCT
ejpam-5154	5	1	we	we	PRON
ejpam-5154	5	2	characterize	characterize	VERB
ejpam-5154	5	3	zero	zero	NUM
ejpam-5154	5	4	forcing	force	VERB
ejpam-5154	5	5	dominating	dominating	NOUN
ejpam-5154	5	6	sets	set	NOUN
ejpam-5154	5	7	in	in	ADP
ejpam-5154	5	8	some	some	DET
ejpam-5154	5	9	special	special	ADJ
ejpam-5154	5	10	graphs	graph	NOUN
ejpam-5154	5	11	and	and	CCONJ
ejpam-5154	5	12	the	the	DET
ejpam-5154	5	13	join	join	NOUN
ejpam-5154	5	14	of	of	ADP
ejpam-5154	5	15	two	two	NUM
ejpam-5154	5	16	graphs	graph	NOUN
ejpam-5154	5	17	,	,	PUNCT
ejpam-5154	5	18	and	and	CCONJ
ejpam-5154	5	19	we	we	PRON
ejpam-5154	5	20	derive	derive	VERB
ejpam-5154	5	21	some	some	DET
ejpam-5154	5	22	formulas	formula	NOUN
ejpam-5154	5	23	of	of	ADP
ejpam-5154	5	24	the	the	DET
ejpam-5154	5	25	zero	zero	NUM
ejpam-5154	5	26	forcing	force	VERB
ejpam-5154	5	27	domination	domination	NOUN
ejpam-5154	5	28	using	use	VERB
ejpam-5154	5	29	characterization	characterization	NOUN
ejpam-5154	5	30	results	result	NOUN
ejpam-5154	5	31	.	.	PUNCT
ejpam-5154	6	1	moreover	moreover	ADV
ejpam-5154	6	2	,	,	PUNCT
ejpam-5154	6	3	we	we	PRON
ejpam-5154	6	4	present	present	VERB
ejpam-5154	6	5	some	some	DET
ejpam-5154	6	6	relationships	relationship	NOUN
ejpam-5154	6	7	of	of	ADP
ejpam-5154	6	8	this	this	DET
ejpam-5154	6	9	parameter	parameter	NOUN
ejpam-5154	6	10	with	with	ADP
ejpam-5154	6	11	other	other	ADJ
ejpam-5154	6	12	known	know	VERB
ejpam-5154	6	13	parameters	parameter	NOUN
ejpam-5154	6	14	in	in	ADP
ejpam-5154	6	15	graph	graph	NOUN
ejpam-5154	6	16	theory	theory	NOUN
ejpam-5154	6	17	.	.	PUNCT
ejpam-5154	7	1	2020	2020	NUM
ejpam-5154	7	2	mathematics	mathematic	NOUN
ejpam-5154	7	3	subject	subject	NOUN
ejpam-5154	7	4	classifications	classification	NOUN
ejpam-5154	7	5	:	:	PUNCT
ejpam-5154	7	6	05c69	05c69	X
ejpam-5154	7	7	key	key	ADJ
ejpam-5154	7	8	words	word	NOUN
ejpam-5154	7	9	and	and	CCONJ
ejpam-5154	7	10	phrases	phrase	NOUN
ejpam-5154	7	11	:	:	PUNCT
ejpam-5154	7	12	zero	zero	NUM
ejpam-5154	7	13	forcing	force	VERB
ejpam-5154	7	14	set	set	NOUN
ejpam-5154	7	15	,	,	PUNCT
ejpam-5154	7	16	zero	zero	NUM
ejpam-5154	7	17	forcing	force	VERB
ejpam-5154	7	18	dominating	dominating	NOUN
ejpam-5154	7	19	set	set	NOUN
ejpam-5154	7	20	,	,	PUNCT
ejpam-5154	7	21	zero	zero	NUM
ejpam-5154	7	22	forcing	force	VERB
ejpam-5154	7	23	domination	domination	NOUN
ejpam-5154	7	24	number	number	NOUN
ejpam-5154	7	25	1	1	NUM
ejpam-5154	7	26	.	.	PUNCT
ejpam-5154	7	27	introduction	introduction	NOUN
ejpam-5154	7	28	the	the	DET
ejpam-5154	7	29	concept	concept	NOUN
ejpam-5154	7	30	of	of	ADP
ejpam-5154	7	31	zero	zero	NUM
ejpam-5154	7	32	forcing	force	VERB
ejpam-5154	7	33	set	set	NOUN
ejpam-5154	7	34	was	be	AUX
ejpam-5154	7	35	initially	initially	ADV
ejpam-5154	7	36	introduced	introduce	VERB
ejpam-5154	7	37	in	in	ADP
ejpam-5154	7	38	[	[	X
ejpam-5154	7	39	4	4	NUM
ejpam-5154	7	40	]	]	PUNCT
ejpam-5154	7	41	as	as	ADP
ejpam-5154	7	42	a	a	DET
ejpam-5154	7	43	bound	bind	VERB
ejpam-5154	7	44	for	for	ADP
ejpam-5154	7	45	the	the	DET
ejpam-5154	7	46	minimum	minimum	ADJ
ejpam-5154	7	47	rank	rank	NOUN
ejpam-5154	7	48	problem	problem	NOUN
ejpam-5154	7	49	.	.	PUNCT
ejpam-5154	8	1	given	give	VERB
ejpam-5154	8	2	a	a	DET
ejpam-5154	8	3	starting	starting	NOUN
ejpam-5154	8	4	set	set	NOUN
ejpam-5154	8	5	of	of	ADP
ejpam-5154	8	6	blue	blue	ADJ
ejpam-5154	8	7	vertices	vertex	NOUN
ejpam-5154	8	8	,	,	PUNCT
ejpam-5154	8	9	with	with	ADP
ejpam-5154	8	10	all	all	DET
ejpam-5154	8	11	other	other	ADJ
ejpam-5154	8	12	vertices	vertex	NOUN
ejpam-5154	8	13	white	white	ADJ
ejpam-5154	8	14	,	,	PUNCT
ejpam-5154	8	15	and	and	CCONJ
ejpam-5154	8	16	a	a	DET
ejpam-5154	8	17	color	color	NOUN
ejpam-5154	8	18	-	-	PUNCT
ejpam-5154	8	19	change	change	NOUN
ejpam-5154	8	20	rule	rule	NOUN
ejpam-5154	8	21	,	,	PUNCT
ejpam-5154	8	22	zero	zero	NUM
ejpam-5154	8	23	forcing	force	VERB
ejpam-5154	8	24	is	be	AUX
ejpam-5154	8	25	a	a	DET
ejpam-5154	8	26	graph	graph	NOUN
ejpam-5154	8	27	propagation	propagation	NOUN
ejpam-5154	8	28	mechanism	mechanism	NOUN
ejpam-5154	8	29	that	that	PRON
ejpam-5154	8	30	increases	increase	VERB
ejpam-5154	8	31	the	the	DET
ejpam-5154	8	32	number	number	NOUN
ejpam-5154	8	33	of	of	ADP
ejpam-5154	8	34	blue	blue	ADJ
ejpam-5154	8	35	vertices	vertex	NOUN
ejpam-5154	8	36	.	.	PUNCT
ejpam-5154	9	1	according	accord	VERB
ejpam-5154	9	2	to	to	ADP
ejpam-5154	9	3	the	the	DET
ejpam-5154	9	4	zero	zero	NUM
ejpam-5154	9	5	forcing	force	VERB
ejpam-5154	9	6	color	color	NOUN
ejpam-5154	9	7	-	-	PUNCT
ejpam-5154	9	8	change	change	NOUN
ejpam-5154	9	9	rule	rule	NOUN
ejpam-5154	9	10	,	,	PUNCT
ejpam-5154	9	11	a	a	DET
ejpam-5154	9	12	blue	blue	ADJ
ejpam-5154	9	13	vertex	vertex	NOUN
ejpam-5154	9	14	next	next	ADV
ejpam-5154	9	15	to	to	ADP
ejpam-5154	9	16	a	a	DET
ejpam-5154	9	17	single	single	ADJ
ejpam-5154	9	18	white	white	ADJ
ejpam-5154	9	19	neighbor	neighbor	NOUN
ejpam-5154	9	20	can	can	AUX
ejpam-5154	9	21	force	force	VERB
ejpam-5154	9	22	that	that	DET
ejpam-5154	9	23	neighbor	neighbor	NOUN
ejpam-5154	9	24	to	to	PART
ejpam-5154	9	25	also	also	ADV
ejpam-5154	9	26	be	be	AUX
ejpam-5154	9	27	blue	blue	ADJ
ejpam-5154	9	28	.	.	PUNCT
ejpam-5154	10	1	the	the	DET
ejpam-5154	10	2	notation	notation	NOUN
ejpam-5154	10	3	u	u	PROPN
ejpam-5154	10	4	→	→	SYM
ejpam-5154	10	5	w	w	NOUN
ejpam-5154	10	6	means	mean	VERB
ejpam-5154	10	7	that	that	SCONJ
ejpam-5154	10	8	if	if	SCONJ
ejpam-5154	10	9	u	u	NOUN
ejpam-5154	10	10	is	be	AUX
ejpam-5154	10	11	a	a	DET
ejpam-5154	10	12	blue	blue	ADJ
ejpam-5154	10	13	vertex	vertex	NOUN
ejpam-5154	10	14	and	and	CCONJ
ejpam-5154	10	15	w	w	NOUN
ejpam-5154	10	16	is	be	AUX
ejpam-5154	10	17	the	the	DET
ejpam-5154	10	18	solitary	solitary	ADJ
ejpam-5154	10	19	white	white	ADJ
ejpam-5154	10	20	vertex	vertex	NOUN
ejpam-5154	10	21	in	in	ADP
ejpam-5154	10	22	n(u	n(u	PROPN
ejpam-5154	10	23	)	)	PUNCT
ejpam-5154	10	24	,	,	PUNCT
ejpam-5154	10	25	then	then	ADV
ejpam-5154	10	26	u	u	NOUN
ejpam-5154	10	27	∗corresponding	∗corresponde	VERB
ejpam-5154	10	28	author	author	NOUN
ejpam-5154	10	29	.	.	PUNCT
ejpam-5154	11	1	doi	doi	NOUN
ejpam-5154	11	2	:	:	PUNCT
ejpam-5154	11	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5154	https://doi.org/10.29020/nybg.ejpam.v17i4.5154	PROPN
ejpam-5154	11	4	email	email	NOUN
ejpam-5154	11	5	address	address	NOUN
ejpam-5154	11	6	:	:	PUNCT
ejpam-5154	11	7	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-5154	11	8	(	(	PUNCT
ejpam-5154	11	9	j.	j.	PROPN
ejpam-5154	11	10	a.	a.	PROPN
ejpam-5154	11	11	hassan	hassan	PROPN
ejpam-5154	11	12	)	)	PUNCT
ejpam-5154	11	13	,	,	PUNCT
ejpam-5154	11	14	mariaandrea.bonsocan@g.msuiit.edu.ph	mariaandrea.bonsocan@g.msuiit.edu.ph	PROPN
ejpam-5154	11	15	(	(	PUNCT
ejpam-5154	11	16	m.	m.	NOUN
ejpam-5154	11	17	a.	a.	PROPN
ejpam-5154	11	18	bonsocan	bonsocan	PROPN
ejpam-5154	11	19	)	)	PUNCT
ejpam-5154	11	20	merceditalangamin@msutawi-tawi.edu.ph	merceditalangamin@msutawi-tawi.edu.ph	PROPN
ejpam-5154	11	21	(	(	PUNCT
ejpam-5154	11	22	m.	m.	NOUN
ejpam-5154	11	23	langamin	langamin	PROPN
ejpam-5154	11	24	)	)	PUNCT
ejpam-5154	11	25	vtbilar@addu.edu.ph	vtbilar@addu.edu.ph	NOUN
ejpam-5154	11	26	(	(	PUNCT
ejpam-5154	11	27	v.	v.	X
ejpam-5154	11	28	bilar	bilar	PROPN
ejpam-5154	11	29	)	)	PUNCT
ejpam-5154	11	30	sharifadianneaming@msutawi-tawi.edu.ph	sharifadianneaming@msutawi-tawi.edu.ph	PROPN
ejpam-5154	11	31	(	(	PUNCT
ejpam-5154	11	32	s.	s.	PROPN
ejpam-5154	11	33	d.	d.	PROPN
ejpam-5154	11	34	aming	aming	PROPN
ejpam-5154	11	35	)	)	PUNCT
ejpam-5154	11	36	bayahamiruddin@msutawi-tawi.edu.ph	bayahamiruddin@msutawi-tawi.edu.ph	PROPN
ejpam-5154	11	37	(	(	PUNCT
ejpam-5154	11	38	b.	b.	PROPN
ejpam-5154	11	39	amiruddin	amiruddin	PROPN
ejpam-5154	11	40	)	)	PUNCT
ejpam-5154	11	41	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5154	11	42	3772	3772	NUM
ejpam-5154	11	43	copyright	copyright	NOUN
ejpam-5154	11	44	:	:	PUNCT
ejpam-5154	11	45	©	©	PROPN
ejpam-5154	11	46	2024	2024	NUM
ejpam-5154	11	47	the	the	DET
ejpam-5154	11	48	author(s	author(s	NOUN
ejpam-5154	11	49	)	)	PUNCT
ejpam-5154	11	50	.	.	PUNCT
ejpam-5154	12	1	(	(	PUNCT
ejpam-5154	12	2	cc	cc	NOUN
ejpam-5154	12	3	by	by	ADP
ejpam-5154	12	4	-	-	PUNCT
ejpam-5154	12	5	nc	nc	PROPN
ejpam-5154	12	6	4.0	4.0	NUM
ejpam-5154	12	7	)	)	PUNCT
ejpam-5154	12	8	j.	j.	PROPN
ejpam-5154	12	9	a.	a.	PROPN
ejpam-5154	12	10	hassan	hassan	PROPN
ejpam-5154	12	11	et	et	PROPN
ejpam-5154	12	12	al	al	PROPN
ejpam-5154	12	13	.	.	PUNCT
ejpam-5154	12	14	/	/	SYM
ejpam-5154	12	15	eur	eur	PROPN
ejpam-5154	12	16	.	.	PUNCT
ejpam-5154	13	1	j.	j.	PROPN
ejpam-5154	13	2	pure	pure	PROPN
ejpam-5154	13	3	appl	appl	PROPN
ejpam-5154	13	4	.	.	PROPN
ejpam-5154	13	5	math	math	PROPN
ejpam-5154	13	6	,	,	PUNCT
ejpam-5154	13	7	17	17	NUM
ejpam-5154	13	8	(	(	PUNCT
ejpam-5154	13	9	4	4	NUM
ejpam-5154	13	10	)	)	PUNCT
ejpam-5154	13	11	(	(	PUNCT
ejpam-5154	13	12	2024	2024	NUM
ejpam-5154	13	13	)	)	PUNCT
ejpam-5154	13	14	,	,	PUNCT
ejpam-5154	13	15	3772	3772	NUM
ejpam-5154	13	16	-	-	SYM
ejpam-5154	13	17	3780	3780	NUM
ejpam-5154	13	18	3773	3773	NUM
ejpam-5154	13	19	compels	compel	VERB
ejpam-5154	13	20	w	w	NOUN
ejpam-5154	13	21	to	to	PART
ejpam-5154	13	22	be	be	AUX
ejpam-5154	13	23	blue	blue	ADJ
ejpam-5154	13	24	.	.	PUNCT
ejpam-5154	14	1	with	with	ADP
ejpam-5154	14	2	graph	graph	NOUN
ejpam-5154	14	3	g	g	PROPN
ejpam-5154	14	4	as	as	ADP
ejpam-5154	14	5	input	input	NOUN
ejpam-5154	14	6	,	,	PUNCT
ejpam-5154	14	7	a	a	DET
ejpam-5154	14	8	zero	zero	NUM
ejpam-5154	14	9	forcing	force	VERB
ejpam-5154	14	10	set	set	NOUN
ejpam-5154	14	11	of	of	ADP
ejpam-5154	14	12	g	g	PROPN
ejpam-5154	14	13	is	be	AUX
ejpam-5154	14	14	a	a	DET
ejpam-5154	14	15	subset	subset	NOUN
ejpam-5154	14	16	of	of	ADP
ejpam-5154	14	17	vertices	vertex	NOUN
ejpam-5154	14	18	from	from	ADP
ejpam-5154	14	19	v(g	v(g	NOUN
ejpam-5154	14	20	)	)	PUNCT
ejpam-5154	14	21	such	such	ADJ
ejpam-5154	14	22	that	that	SCONJ
ejpam-5154	14	23	the	the	DET
ejpam-5154	14	24	color	color	NOUN
ejpam-5154	14	25	-	-	PUNCT
ejpam-5154	14	26	change	change	NOUN
ejpam-5154	14	27	rule	rule	NOUN
ejpam-5154	14	28	given	give	VERB
ejpam-5154	14	29	b	b	PROPN
ejpam-5154	14	30	is	be	AUX
ejpam-5154	14	31	applied	apply	VERB
ejpam-5154	14	32	iteratively	iteratively	ADV
ejpam-5154	14	33	if	if	SCONJ
ejpam-5154	14	34	b	b	NOUN
ejpam-5154	14	35	is	be	AUX
ejpam-5154	14	36	originally	originally	ADV
ejpam-5154	14	37	colored	color	VERB
ejpam-5154	14	38	blue	blue	ADJ
ejpam-5154	14	39	and	and	CCONJ
ejpam-5154	14	40	the	the	DET
ejpam-5154	14	41	remaining	remain	VERB
ejpam-5154	14	42	vertices	vertex	NOUN
ejpam-5154	14	43	in	in	ADP
ejpam-5154	14	44	g	g	PROPN
ejpam-5154	14	45	are	be	AUX
ejpam-5154	14	46	white	white	ADJ
ejpam-5154	14	47	.	.	PUNCT
ejpam-5154	15	1	apart	apart	ADV
ejpam-5154	15	2	from	from	ADP
ejpam-5154	15	3	its	its	PRON
ejpam-5154	15	4	use	use	NOUN
ejpam-5154	15	5	in	in	ADP
ejpam-5154	15	6	the	the	DET
ejpam-5154	15	7	minimal	minimal	ADJ
ejpam-5154	15	8	rank	rank	NOUN
ejpam-5154	15	9	problem	problem	NOUN
ejpam-5154	15	10	,	,	PUNCT
ejpam-5154	15	11	zero	zero	NUM
ejpam-5154	15	12	forcing	forcing	NOUN
ejpam-5154	15	13	sets	set	NOUN
ejpam-5154	15	14	have	have	AUX
ejpam-5154	15	15	also	also	ADV
ejpam-5154	15	16	proved	prove	VERB
ejpam-5154	15	17	interesting	interesting	ADJ
ejpam-5154	15	18	on	on	ADP
ejpam-5154	15	19	their	their	PRON
ejpam-5154	15	20	own	own	ADJ
ejpam-5154	15	21	.	.	PUNCT
ejpam-5154	16	1	numerous	numerous	ADJ
ejpam-5154	16	2	aspects	aspect	NOUN
ejpam-5154	16	3	and	and	CCONJ
ejpam-5154	16	4	extensions	extension	NOUN
ejpam-5154	16	5	of	of	ADP
ejpam-5154	16	6	zero	zero	NUM
ejpam-5154	16	7	forcing	force	VERB
ejpam-5154	16	8	have	have	AUX
ejpam-5154	16	9	been	be	AUX
ejpam-5154	16	10	examined	examine	VERB
ejpam-5154	16	11	.	.	PUNCT
ejpam-5154	17	1	among	among	ADP
ejpam-5154	17	2	these	these	PRON
ejpam-5154	17	3	are	be	AUX
ejpam-5154	17	4	positive	positive	ADJ
ejpam-5154	17	5	semi	semi	ADJ
ejpam-5154	17	6	-	-	ADJ
ejpam-5154	17	7	definite	definite	ADJ
ejpam-5154	17	8	zero	zero	NUM
ejpam-5154	17	9	forcing	forcing	NOUN
ejpam-5154	17	10	,	,	PUNCT
ejpam-5154	17	11	a	a	DET
ejpam-5154	17	12	variant	variant	NOUN
ejpam-5154	17	13	that	that	PRON
ejpam-5154	17	14	bounds	bound	VERB
ejpam-5154	17	15	the	the	DET
ejpam-5154	17	16	minimum	minimum	ADJ
ejpam-5154	17	17	rank	rank	NOUN
ejpam-5154	17	18	problem	problem	NOUN
ejpam-5154	17	19	when	when	SCONJ
ejpam-5154	17	20	the	the	DET
ejpam-5154	17	21	minimum	minimum	NOUN
ejpam-5154	17	22	is	be	AUX
ejpam-5154	17	23	taken	take	VERB
ejpam-5154	17	24	only	only	ADV
ejpam-5154	17	25	over	over	ADP
ejpam-5154	17	26	positive	positive	ADJ
ejpam-5154	17	27	semi	semi	ADJ
ejpam-5154	17	28	-	-	ADJ
ejpam-5154	17	29	definite	definite	ADJ
ejpam-5154	17	30	matrices	matrix	NOUN
ejpam-5154	17	31	with	with	ADP
ejpam-5154	17	32	graph	graph	NOUN
ejpam-5154	17	33	g	g	PROPN
ejpam-5154	17	34	[	[	X
ejpam-5154	17	35	3	3	NUM
ejpam-5154	17	36	]	]	PUNCT
ejpam-5154	17	37	.	.	PUNCT
ejpam-5154	18	1	on	on	ADP
ejpam-5154	18	2	the	the	DET
ejpam-5154	18	3	other	other	ADJ
ejpam-5154	18	4	hand	hand	NOUN
ejpam-5154	18	5	,	,	PUNCT
ejpam-5154	18	6	in	in	ADP
ejpam-5154	18	7	the	the	DET
ejpam-5154	18	8	late	late	ADJ
ejpam-5154	18	9	1950	1950	NUM
ejpam-5154	18	10	’s	’s	NOUN
ejpam-5154	18	11	and	and	CCONJ
ejpam-5154	18	12	1960	1960	NUM
ejpam-5154	18	13	’s	’s	NOUN
ejpam-5154	18	14	,	,	PUNCT
ejpam-5154	18	15	the	the	DET
ejpam-5154	18	16	study	study	NOUN
ejpam-5154	18	17	on	on	ADP
ejpam-5154	18	18	domination	domination	NOUN
ejpam-5154	18	19	in	in	ADP
ejpam-5154	18	20	graphs	graph	NOUN
ejpam-5154	18	21	was	be	AUX
ejpam-5154	18	22	developed	develop	VERB
ejpam-5154	18	23	.	.	PUNCT
ejpam-5154	19	1	beginning	begin	VERB
ejpam-5154	19	2	with	with	ADP
ejpam-5154	19	3	c.	c.	PROPN
ejpam-5154	19	4	berge	berge	NOUN
ejpam-5154	19	5	[	[	X
ejpam-5154	19	6	1	1	X
ejpam-5154	19	7	]	]	PUNCT
ejpam-5154	19	8	in	in	ADP
ejpam-5154	19	9	1958	1958	NUM
ejpam-5154	19	10	,	,	PUNCT
ejpam-5154	19	11	he	he	PRON
ejpam-5154	19	12	referred	refer	VERB
ejpam-5154	19	13	to	to	ADP
ejpam-5154	19	14	the	the	DET
ejpam-5154	19	15	domination	domination	NOUN
ejpam-5154	19	16	number	number	NOUN
ejpam-5154	19	17	as	as	ADP
ejpam-5154	19	18	the	the	DET
ejpam-5154	19	19	“	"	PUNCT
ejpam-5154	19	20	coefficient	coefficient	NOUN
ejpam-5154	19	21	of	of	ADP
ejpam-5154	19	22	external	external	ADJ
ejpam-5154	19	23	stability	stability	NOUN
ejpam-5154	19	24	”	"	PUNCT
ejpam-5154	19	25	[	[	X
ejpam-5154	19	26	13	13	NUM
ejpam-5154	19	27	]	]	PUNCT
ejpam-5154	19	28	.	.	PUNCT
ejpam-5154	20	1	in	in	ADP
ejpam-5154	20	2	1962	1962	NUM
ejpam-5154	20	3	,	,	PUNCT
ejpam-5154	20	4	o.	o.	NOUN
ejpam-5154	20	5	ore	ore	NOUN
ejpam-5154	20	6	introduced	introduce	VERB
ejpam-5154	20	7	the	the	DET
ejpam-5154	20	8	terms	term	NOUN
ejpam-5154	20	9	“	"	PUNCT
ejpam-5154	20	10	dominating	dominating	NOUN
ejpam-5154	20	11	set	set	NOUN
ejpam-5154	20	12	”	"	PUNCT
ejpam-5154	20	13	and	and	CCONJ
ejpam-5154	20	14	“	"	PUNCT
ejpam-5154	20	15	domination	domination	NOUN
ejpam-5154	20	16	number	number	NOUN
ejpam-5154	20	17	”	"	PUNCT
ejpam-5154	20	18	.	.	PUNCT
ejpam-5154	21	1	domination	domination	NOUN
ejpam-5154	21	2	in	in	ADP
ejpam-5154	21	3	a	a	DET
ejpam-5154	21	4	graph	graph	NOUN
ejpam-5154	21	5	has	have	AUX
ejpam-5154	21	6	been	be	AUX
ejpam-5154	21	7	on	on	ADP
ejpam-5154	21	8	the	the	DET
ejpam-5154	21	9	topics	topic	NOUN
ejpam-5154	21	10	studied	study	VERB
ejpam-5154	21	11	by	by	ADP
ejpam-5154	21	12	researchers	researcher	NOUN
ejpam-5154	21	13	recently	recently	ADV
ejpam-5154	21	14	.	.	PUNCT
ejpam-5154	22	1	different	different	ADJ
ejpam-5154	22	2	variants	variant	NOUN
ejpam-5154	22	3	of	of	ADP
ejpam-5154	22	4	this	this	DET
ejpam-5154	22	5	parameter	parameter	NOUN
ejpam-5154	22	6	have	have	AUX
ejpam-5154	22	7	been	be	AUX
ejpam-5154	22	8	established	establish	VERB
ejpam-5154	22	9	and	and	CCONJ
ejpam-5154	22	10	some	some	PRON
ejpam-5154	22	11	of	of	ADP
ejpam-5154	22	12	these	these	DET
ejpam-5154	22	13	studies	study	NOUN
ejpam-5154	22	14	can	can	AUX
ejpam-5154	22	15	be	be	AUX
ejpam-5154	22	16	found	find	VERB
ejpam-5154	22	17	in	in	ADP
ejpam-5154	22	18	[	[	X
ejpam-5154	22	19	2	2	NUM
ejpam-5154	22	20	,	,	PUNCT
ejpam-5154	22	21	5–12	5–12	NUM
ejpam-5154	22	22	,	,	PUNCT
ejpam-5154	22	23	14	14	NUM
ejpam-5154	22	24	,	,	PUNCT
ejpam-5154	22	25	15	15	NUM
ejpam-5154	22	26	]	]	PUNCT
ejpam-5154	22	27	.	.	PUNCT
ejpam-5154	23	1	in	in	ADP
ejpam-5154	23	2	this	this	DET
ejpam-5154	23	3	study	study	NOUN
ejpam-5154	23	4	,	,	PUNCT
ejpam-5154	23	5	we	we	PRON
ejpam-5154	23	6	initiate	initiate	VERB
ejpam-5154	23	7	the	the	DET
ejpam-5154	23	8	study	study	NOUN
ejpam-5154	23	9	of	of	ADP
ejpam-5154	23	10	zero	zero	NUM
ejpam-5154	23	11	forcing	force	VERB
ejpam-5154	23	12	domination	domination	NOUN
ejpam-5154	23	13	in	in	ADP
ejpam-5154	23	14	graphs	graph	NOUN
ejpam-5154	23	15	.	.	PUNCT
ejpam-5154	24	1	we	we	PRON
ejpam-5154	24	2	believe	believe	VERB
ejpam-5154	24	3	this	this	DET
ejpam-5154	24	4	parameter	parameter	NOUN
ejpam-5154	24	5	and	and	CCONJ
ejpam-5154	24	6	its	its	PRON
ejpam-5154	24	7	results	result	NOUN
ejpam-5154	24	8	would	would	AUX
ejpam-5154	24	9	serve	serve	VERB
ejpam-5154	24	10	as	as	ADP
ejpam-5154	24	11	reference	reference	NOUN
ejpam-5154	24	12	for	for	ADP
ejpam-5154	24	13	future	future	ADJ
ejpam-5154	24	14	researchers	researcher	NOUN
ejpam-5154	24	15	who	who	PRON
ejpam-5154	24	16	will	will	AUX
ejpam-5154	24	17	study	study	VERB
ejpam-5154	24	18	on	on	ADP
ejpam-5154	24	19	concept	concept	NOUN
ejpam-5154	24	20	related	relate	VERB
ejpam-5154	24	21	to	to	ADP
ejpam-5154	24	22	zero	zero	NUM
ejpam-5154	24	23	forcing	force	VERB
ejpam-5154	24	24	domination	domination	NOUN
ejpam-5154	24	25	in	in	ADP
ejpam-5154	24	26	a	a	DET
ejpam-5154	24	27	graph	graph	NOUN
ejpam-5154	24	28	.	.	PUNCT
ejpam-5154	25	1	2	2	X
ejpam-5154	25	2	.	.	X
ejpam-5154	25	3	terminology	terminology	NOUN
ejpam-5154	25	4	and	and	CCONJ
ejpam-5154	25	5	notation	notation	NOUN
ejpam-5154	25	6	let	let	VERB
ejpam-5154	25	7	g	g	NOUN
ejpam-5154	25	8	=	=	SYM
ejpam-5154	25	9	(	(	PUNCT
ejpam-5154	25	10	v	v	NOUN
ejpam-5154	25	11	(	(	PUNCT
ejpam-5154	25	12	g	g	NOUN
ejpam-5154	25	13	)	)	PUNCT
ejpam-5154	25	14	,	,	PUNCT
ejpam-5154	25	15	e(g	e(g	PROPN
ejpam-5154	25	16	)	)	PUNCT
ejpam-5154	25	17	)	)	PUNCT
ejpam-5154	25	18	be	be	AUX
ejpam-5154	25	19	a	a	DET
ejpam-5154	25	20	simple	simple	ADJ
ejpam-5154	25	21	and	and	CCONJ
ejpam-5154	25	22	undirected	undirected	ADJ
ejpam-5154	25	23	graph	graph	NOUN
ejpam-5154	25	24	.	.	PUNCT
ejpam-5154	26	1	the	the	DET
ejpam-5154	26	2	distance	distance	NOUN
ejpam-5154	26	3	dg(u	dg(u	NOUN
ejpam-5154	26	4	,	,	PUNCT
ejpam-5154	26	5	v	v	NOUN
ejpam-5154	26	6	)	)	PUNCT
ejpam-5154	26	7	in	in	ADP
ejpam-5154	26	8	g	g	NOUN
ejpam-5154	26	9	of	of	ADP
ejpam-5154	26	10	two	two	NUM
ejpam-5154	26	11	vertices	vertex	NOUN
ejpam-5154	26	12	u	u	NOUN
ejpam-5154	26	13	,	,	PUNCT
ejpam-5154	26	14	v	v	PROPN
ejpam-5154	26	15	is	be	AUX
ejpam-5154	26	16	the	the	DET
ejpam-5154	26	17	length	length	NOUN
ejpam-5154	26	18	of	of	ADP
ejpam-5154	26	19	a	a	DET
ejpam-5154	26	20	shortest	short	ADJ
ejpam-5154	26	21	u	u	NOUN
ejpam-5154	26	22	-	-	NOUN
ejpam-5154	26	23	v	v	ADJ
ejpam-5154	26	24	path	path	NOUN
ejpam-5154	26	25	in	in	ADP
ejpam-5154	26	26	g.	g.	PROPN
ejpam-5154	26	27	the	the	DET
ejpam-5154	26	28	greatest	great	ADJ
ejpam-5154	26	29	distance	distance	NOUN
ejpam-5154	26	30	between	between	ADP
ejpam-5154	26	31	any	any	DET
ejpam-5154	26	32	two	two	NUM
ejpam-5154	26	33	vertices	vertex	NOUN
ejpam-5154	26	34	in	in	ADP
ejpam-5154	26	35	g	g	NOUN
ejpam-5154	26	36	,	,	PUNCT
ejpam-5154	26	37	denoted	denote	VERB
ejpam-5154	26	38	by	by	ADP
ejpam-5154	26	39	diam(g	diam(g	PROPN
ejpam-5154	26	40	)	)	PUNCT
ejpam-5154	26	41	,	,	PUNCT
ejpam-5154	26	42	is	be	AUX
ejpam-5154	26	43	called	call	VERB
ejpam-5154	26	44	the	the	DET
ejpam-5154	26	45	diameter	diameter	NOUN
ejpam-5154	26	46	of	of	ADP
ejpam-5154	26	47	g.	g.	PROPN
ejpam-5154	26	48	two	two	NUM
ejpam-5154	26	49	vertices	vertice	VERB
ejpam-5154	26	50	x	x	X
ejpam-5154	26	51	,	,	PUNCT
ejpam-5154	26	52	y	y	PROPN
ejpam-5154	26	53	of	of	ADP
ejpam-5154	26	54	g	g	PROPN
ejpam-5154	26	55	are	be	AUX
ejpam-5154	26	56	adjacent	adjacent	ADJ
ejpam-5154	26	57	,	,	PUNCT
ejpam-5154	26	58	or	or	CCONJ
ejpam-5154	26	59	neighbors	neighbor	NOUN
ejpam-5154	26	60	,	,	PUNCT
ejpam-5154	26	61	if	if	SCONJ
ejpam-5154	26	62	xy	xy	PROPN
ejpam-5154	26	63	is	be	AUX
ejpam-5154	26	64	an	an	DET
ejpam-5154	26	65	edge	edge	NOUN
ejpam-5154	26	66	of	of	ADP
ejpam-5154	26	67	g.	g.	PROPN
ejpam-5154	26	68	the	the	DET
ejpam-5154	26	69	open	open	ADJ
ejpam-5154	26	70	neighborhood	neighborhood	NOUN
ejpam-5154	26	71	of	of	ADP
ejpam-5154	26	72	x	x	PUNCT
ejpam-5154	26	73	in	in	ADP
ejpam-5154	26	74	g	g	PROPN
ejpam-5154	26	75	is	be	AUX
ejpam-5154	26	76	the	the	DET
ejpam-5154	26	77	set	set	NOUN
ejpam-5154	26	78	ng(x	ng(x	NUM
ejpam-5154	26	79	)	)	PUNCT
ejpam-5154	26	80	=	=	PRON
ejpam-5154	26	81	{	{	PUNCT
ejpam-5154	26	82	y	y	PROPN
ejpam-5154	26	83	∈	∈	PROPN
ejpam-5154	26	84	v	v	NOUN
ejpam-5154	26	85	(	(	PUNCT
ejpam-5154	26	86	g	g	NOUN
ejpam-5154	26	87	)	)	PUNCT
ejpam-5154	26	88	:	:	PUNCT
ejpam-5154	26	89	xy	xy	PROPN
ejpam-5154	26	90	∈	∈	PROPN
ejpam-5154	26	91	e(g	e(g	PROPN
ejpam-5154	26	92	)	)	PUNCT
ejpam-5154	26	93	}	}	PUNCT
ejpam-5154	26	94	.	.	PUNCT
ejpam-5154	27	1	the	the	DET
ejpam-5154	27	2	closed	closed	ADJ
ejpam-5154	27	3	neighborhood	neighborhood	NOUN
ejpam-5154	27	4	of	of	ADP
ejpam-5154	27	5	x	x	SYM
ejpam-5154	27	6	ing	ing	NOUN
ejpam-5154	27	7	is	be	AUX
ejpam-5154	27	8	the	the	DET
ejpam-5154	27	9	setng[x	setng[x	NOUN
ejpam-5154	27	10	]	]	X
ejpam-5154	27	11	=	=	SYM
ejpam-5154	27	12	ng(x)∪{x	ng(x)∪{x	NOUN
ejpam-5154	27	13	}	}	PUNCT
ejpam-5154	27	14	.	.	PUNCT
ejpam-5154	28	1	ifx	ifx	PROPN
ejpam-5154	28	2	⊆	⊆	NUM
ejpam-5154	28	3	v	v	NOUN
ejpam-5154	28	4	(	(	PUNCT
ejpam-5154	28	5	g	g	NOUN
ejpam-5154	28	6	)	)	PUNCT
ejpam-5154	28	7	,	,	PUNCT
ejpam-5154	28	8	the	the	DET
ejpam-5154	28	9	open	open	ADJ
ejpam-5154	28	10	neighborhood	neighborhood	NOUN
ejpam-5154	28	11	of	of	ADP
ejpam-5154	28	12	x	x	PUNCT
ejpam-5154	28	13	in	in	ADP
ejpam-5154	28	14	g	g	PROPN
ejpam-5154	28	15	is	be	AUX
ejpam-5154	28	16	the	the	DET
ejpam-5154	28	17	set	set	NOUN
ejpam-5154	28	18	ng(x	ng(x	NUM
ejpam-5154	28	19	)	)	PUNCT
ejpam-5154	29	1	=	=	SYM
ejpam-5154	29	2	⋃	⋃	NOUN
ejpam-5154	29	3	x∈x	x∈x	NOUN
ejpam-5154	29	4	ng(x	ng(x	NUM
ejpam-5154	29	5	)	)	PUNCT
ejpam-5154	29	6	.	.	PUNCT
ejpam-5154	30	1	the	the	DET
ejpam-5154	30	2	closed	closed	ADJ
ejpam-5154	30	3	neighborhood	neighborhood	NOUN
ejpam-5154	30	4	of	of	ADP
ejpam-5154	30	5	x	x	PUNCT
ejpam-5154	30	6	in	in	ADP
ejpam-5154	30	7	g	g	PROPN
ejpam-5154	30	8	is	be	AUX
ejpam-5154	30	9	the	the	DET
ejpam-5154	30	10	set	set	NOUN
ejpam-5154	30	11	ng[x	ng[x	PROPN
ejpam-5154	30	12	]	]	X
ejpam-5154	30	13	=	=	PUNCT
ejpam-5154	30	14	ng(x	ng(x	X
ejpam-5154	30	15	)	)	PUNCT
ejpam-5154	31	1	∪x	∪x	PROPN
ejpam-5154	31	2	.	.	PUNCT
ejpam-5154	32	1	a	a	DET
ejpam-5154	32	2	subset	subset	NOUN
ejpam-5154	32	3	s	s	X
ejpam-5154	32	4	of	of	ADP
ejpam-5154	32	5	v	v	NOUN
ejpam-5154	32	6	(	(	PUNCT
ejpam-5154	32	7	g	g	NOUN
ejpam-5154	32	8	)	)	PUNCT
ejpam-5154	32	9	is	be	AUX
ejpam-5154	32	10	a	a	DET
ejpam-5154	32	11	dominating	dominating	NOUN
ejpam-5154	32	12	of	of	ADP
ejpam-5154	32	13	g	g	PROPN
ejpam-5154	32	14	if	if	SCONJ
ejpam-5154	32	15	for	for	ADP
ejpam-5154	32	16	every	every	DET
ejpam-5154	32	17	a	a	DET
ejpam-5154	32	18	∈	∈	PROPN
ejpam-5154	32	19	v	v	NOUN
ejpam-5154	32	20	(	(	PUNCT
ejpam-5154	32	21	g)\s	g)\s	NOUN
ejpam-5154	32	22	,	,	PUNCT
ejpam-5154	32	23	there	there	PRON
ejpam-5154	32	24	exists	exist	VERB
ejpam-5154	32	25	b	b	PROPN
ejpam-5154	32	26	∈	∈	PROPN
ejpam-5154	32	27	s	s	VERB
ejpam-5154	32	28	such	such	ADJ
ejpam-5154	32	29	that	that	SCONJ
ejpam-5154	32	30	dg(a	dg(a	PROPN
ejpam-5154	32	31	,	,	PUNCT
ejpam-5154	32	32	b	b	X
ejpam-5154	32	33	)	)	PUNCT
ejpam-5154	32	34	=	=	SYM
ejpam-5154	32	35	1	1	X
ejpam-5154	32	36	.	.	PUNCT
ejpam-5154	33	1	the	the	DET
ejpam-5154	33	2	minimum	minimum	ADJ
ejpam-5154	33	3	cardinality	cardinality	NOUN
ejpam-5154	33	4	among	among	ADP
ejpam-5154	33	5	all	all	DET
ejpam-5154	33	6	dominating	dominating	NOUN
ejpam-5154	33	7	sets	set	NOUN
ejpam-5154	33	8	of	of	ADP
ejpam-5154	33	9	g	g	NOUN
ejpam-5154	33	10	,	,	PUNCT
ejpam-5154	33	11	denoted	denote	VERB
ejpam-5154	33	12	by	by	ADP
ejpam-5154	33	13	γ(g	γ(g	PROPN
ejpam-5154	33	14	)	)	PUNCT
ejpam-5154	33	15	,	,	PUNCT
ejpam-5154	33	16	is	be	AUX
ejpam-5154	33	17	called	call	VERB
ejpam-5154	33	18	the	the	DET
ejpam-5154	33	19	domination	domination	NOUN
ejpam-5154	33	20	number	number	NOUN
ejpam-5154	33	21	of	of	ADP
ejpam-5154	33	22	g.	g.	PROPN
ejpam-5154	33	23	any	any	DET
ejpam-5154	33	24	dominating	dominating	NOUN
ejpam-5154	33	25	set	set	VERB
ejpam-5154	33	26	with	with	ADP
ejpam-5154	33	27	cardinality	cardinality	NOUN
ejpam-5154	33	28	equal	equal	ADJ
ejpam-5154	33	29	to	to	ADP
ejpam-5154	33	30	γh(g	γh(g	NOUN
ejpam-5154	33	31	)	)	PUNCT
ejpam-5154	33	32	is	be	AUX
ejpam-5154	33	33	called	call	VERB
ejpam-5154	33	34	a	a	DET
ejpam-5154	33	35	γ	γ	NOUN
ejpam-5154	33	36	-	-	PUNCT
ejpam-5154	33	37	set	set	NOUN
ejpam-5154	33	38	of	of	ADP
ejpam-5154	33	39	g.	g.	PROPN
ejpam-5154	33	40	the	the	DET
ejpam-5154	33	41	color	color	NOUN
ejpam-5154	33	42	change	change	NOUN
ejpam-5154	33	43	rule	rule	NOUN
ejpam-5154	33	44	states	state	NOUN
ejpam-5154	33	45	that	that	SCONJ
ejpam-5154	33	46	a	a	DET
ejpam-5154	33	47	blue	blue	ADJ
ejpam-5154	33	48	vertex	vertex	NOUN
ejpam-5154	33	49	adjacent	adjacent	ADJ
ejpam-5154	33	50	to	to	ADP
ejpam-5154	33	51	a	a	DET
ejpam-5154	33	52	single	single	ADJ
ejpam-5154	33	53	white	white	ADJ
ejpam-5154	33	54	neighbor	neighbor	NOUN
ejpam-5154	33	55	can	can	AUX
ejpam-5154	33	56	force	force	VERB
ejpam-5154	33	57	its	its	PRON
ejpam-5154	33	58	neighbor	neighbor	NOUN
ejpam-5154	33	59	to	to	PART
ejpam-5154	33	60	blue	blue	VERB
ejpam-5154	33	61	.	.	PUNCT
ejpam-5154	34	1	a	a	DET
ejpam-5154	34	2	zero	zero	NUM
ejpam-5154	34	3	forcing	force	VERB
ejpam-5154	34	4	set	set	NOUN
ejpam-5154	34	5	for	for	ADP
ejpam-5154	34	6	a	a	DET
ejpam-5154	34	7	graph	graph	NOUN
ejpam-5154	34	8	g	g	NOUN
ejpam-5154	34	9	is	be	AUX
ejpam-5154	34	10	a	a	DET
ejpam-5154	34	11	subset	subset	NOUN
ejpam-5154	34	12	z	z	NOUN
ejpam-5154	34	13	of	of	ADP
ejpam-5154	34	14	v(g	v(g	NUM
ejpam-5154	34	15	)	)	PUNCT
ejpam-5154	34	16	such	such	ADJ
ejpam-5154	34	17	that	that	SCONJ
ejpam-5154	34	18	if	if	SCONJ
ejpam-5154	34	19	initially	initially	ADV
ejpam-5154	34	20	the	the	DET
ejpam-5154	34	21	vertices	vertex	NOUN
ejpam-5154	34	22	in	in	ADP
ejpam-5154	34	23	z	z	NOUN
ejpam-5154	34	24	are	be	AUX
ejpam-5154	34	25	colored	color	VERB
ejpam-5154	34	26	blue	blue	ADJ
ejpam-5154	34	27	and	and	CCONJ
ejpam-5154	34	28	the	the	DET
ejpam-5154	34	29	remaining	remain	VERB
ejpam-5154	34	30	vertices	vertex	NOUN
ejpam-5154	34	31	are	be	AUX
ejpam-5154	34	32	colored	color	VERB
ejpam-5154	34	33	white	white	ADJ
ejpam-5154	34	34	,	,	PUNCT
ejpam-5154	34	35	the	the	DET
ejpam-5154	34	36	entire	entire	ADJ
ejpam-5154	34	37	graph	graph	NOUN
ejpam-5154	34	38	g	g	NOUN
ejpam-5154	34	39	may	may	AUX
ejpam-5154	34	40	be	be	AUX
ejpam-5154	34	41	colored	color	VERB
ejpam-5154	34	42	blue	blue	ADJ
ejpam-5154	34	43	by	by	ADP
ejpam-5154	34	44	repeatedly	repeatedly	ADV
ejpam-5154	34	45	applying	apply	VERB
ejpam-5154	34	46	the	the	DET
ejpam-5154	34	47	color	color	NOUN
ejpam-5154	34	48	-	-	PUNCT
ejpam-5154	34	49	change	change	NOUN
ejpam-5154	34	50	rule	rule	NOUN
ejpam-5154	34	51	.	.	PUNCT
ejpam-5154	35	1	furthermore	furthermore	ADV
ejpam-5154	35	2	,	,	PUNCT
ejpam-5154	35	3	the	the	DET
ejpam-5154	35	4	zero	zero	NUM
ejpam-5154	35	5	forcing	force	VERB
ejpam-5154	35	6	number	number	NOUN
ejpam-5154	35	7	of	of	ADP
ejpam-5154	35	8	g	g	NOUN
ejpam-5154	35	9	,	,	PUNCT
ejpam-5154	35	10	denoted	denote	VERB
ejpam-5154	35	11	by	by	ADP
ejpam-5154	35	12	z(g	z(g	NOUN
ejpam-5154	35	13	)	)	PUNCT
ejpam-5154	35	14	,	,	PUNCT
ejpam-5154	35	15	is	be	AUX
ejpam-5154	35	16	the	the	DET
ejpam-5154	35	17	minimum	minimum	ADJ
ejpam-5154	35	18	cardinality	cardinality	NOUN
ejpam-5154	35	19	of	of	ADP
ejpam-5154	35	20	zero	zero	NUM
ejpam-5154	35	21	forcing	force	VERB
ejpam-5154	35	22	set	set	NOUN
ejpam-5154	35	23	of	of	ADP
ejpam-5154	35	24	g.	g.	PROPN
ejpam-5154	35	25	a	a	DET
ejpam-5154	35	26	subset	subset	NOUN
ejpam-5154	35	27	z	z	NOUN
ejpam-5154	35	28	of	of	ADP
ejpam-5154	35	29	v	v	PROPN
ejpam-5154	35	30	(	(	PUNCT
ejpam-5154	35	31	g	g	NOUN
ejpam-5154	35	32	)	)	PUNCT
ejpam-5154	35	33	is	be	AUX
ejpam-5154	35	34	said	say	VERB
ejpam-5154	35	35	to	to	PART
ejpam-5154	35	36	be	be	AUX
ejpam-5154	35	37	a	a	DET
ejpam-5154	35	38	zero	zero	NUM
ejpam-5154	35	39	forcing	force	VERB
ejpam-5154	35	40	hop	hop	NOUN
ejpam-5154	35	41	dominating	dominating	NOUN
ejpam-5154	35	42	if	if	SCONJ
ejpam-5154	35	43	z	z	NOUN
ejpam-5154	35	44	is	be	AUX
ejpam-5154	35	45	both	both	PRON
ejpam-5154	35	46	a	a	DET
ejpam-5154	35	47	zero	zero	NUM
ejpam-5154	35	48	forcing	forcing	NOUN
ejpam-5154	35	49	and	and	CCONJ
ejpam-5154	35	50	a	a	DET
ejpam-5154	35	51	hop	hop	NOUN
ejpam-5154	35	52	dominating	dominating	NOUN
ejpam-5154	35	53	in	in	ADP
ejpam-5154	35	54	g.	g.	PROPN
ejpam-5154	35	55	the	the	DET
ejpam-5154	35	56	minimum	minimum	ADJ
ejpam-5154	35	57	cardinality	cardinality	NOUN
ejpam-5154	35	58	among	among	ADP
ejpam-5154	35	59	all	all	DET
ejpam-5154	35	60	zero	zero	NUM
ejpam-5154	35	61	forcing	force	VERB
ejpam-5154	35	62	hop	hop	NOUN
ejpam-5154	35	63	dominating	dominating	NOUN
ejpam-5154	35	64	sets	set	NOUN
ejpam-5154	35	65	in	in	ADP
ejpam-5154	35	66	g	g	NOUN
ejpam-5154	35	67	,	,	PUNCT
ejpam-5154	35	68	denoted	denote	VERB
ejpam-5154	35	69	by	by	ADP
ejpam-5154	35	70	γzh(g	γzh(g	NOUN
ejpam-5154	35	71	)	)	PUNCT
ejpam-5154	35	72	,	,	PUNCT
ejpam-5154	35	73	is	be	AUX
ejpam-5154	35	74	called	call	VERB
ejpam-5154	35	75	the	the	DET
ejpam-5154	35	76	zero	zero	NUM
ejpam-5154	35	77	forcing	force	VERB
ejpam-5154	35	78	hop	hop	NOUN
ejpam-5154	35	79	domination	domination	NOUN
ejpam-5154	35	80	number	number	NOUN
ejpam-5154	35	81	of	of	ADP
ejpam-5154	35	82	g.	g.	PROPN
ejpam-5154	35	83	a	a	DET
ejpam-5154	35	84	zero	zero	NUM
ejpam-5154	35	85	forcing	force	VERB
ejpam-5154	35	86	hop	hop	NOUN
ejpam-5154	35	87	dominating	dominating	NOUN
ejpam-5154	35	88	set	set	NOUN
ejpam-5154	35	89	z	z	NOUN
ejpam-5154	35	90	with	with	ADP
ejpam-5154	35	91	|z|	|z|	NOUN
ejpam-5154	35	92	=	=	SYM
ejpam-5154	35	93	γzh(g	γzh(g	NOUN
ejpam-5154	35	94	)	)	PUNCT
ejpam-5154	35	95	,	,	PUNCT
ejpam-5154	35	96	is	be	AUX
ejpam-5154	35	97	called	call	VERB
ejpam-5154	35	98	the	the	DET
ejpam-5154	35	99	minimum	minimum	ADJ
ejpam-5154	35	100	zero	zero	NUM
ejpam-5154	35	101	j.	j.	PROPN
ejpam-5154	35	102	a.	a.	PROPN
ejpam-5154	35	103	hassan	hassan	PROPN
ejpam-5154	35	104	et	et	PROPN
ejpam-5154	35	105	al	al	PROPN
ejpam-5154	35	106	.	.	PUNCT
ejpam-5154	35	107	/	/	SYM
ejpam-5154	35	108	eur	eur	PROPN
ejpam-5154	35	109	.	.	PUNCT
ejpam-5154	36	1	j.	j.	PROPN
ejpam-5154	36	2	pure	pure	PROPN
ejpam-5154	36	3	appl	appl	PROPN
ejpam-5154	36	4	.	.	PROPN
ejpam-5154	36	5	math	math	PROPN
ejpam-5154	36	6	,	,	PUNCT
ejpam-5154	36	7	17	17	NUM
ejpam-5154	36	8	(	(	PUNCT
ejpam-5154	36	9	4	4	NUM
ejpam-5154	36	10	)	)	PUNCT
ejpam-5154	36	11	(	(	PUNCT
ejpam-5154	36	12	2024	2024	NUM
ejpam-5154	36	13	)	)	PUNCT
ejpam-5154	36	14	,	,	PUNCT
ejpam-5154	36	15	3772	3772	NUM
ejpam-5154	36	16	-	-	SYM
ejpam-5154	36	17	3780	3780	NUM
ejpam-5154	36	18	3774	3774	NUM
ejpam-5154	36	19	forcing	force	VERB
ejpam-5154	36	20	hop	hop	NOUN
ejpam-5154	36	21	dominating	dominating	NOUN
ejpam-5154	36	22	set	set	NOUN
ejpam-5154	36	23	of	of	ADP
ejpam-5154	36	24	g	g	PROPN
ejpam-5154	36	25	or	or	CCONJ
ejpam-5154	36	26	a	a	DET
ejpam-5154	36	27	γzh	γzh	NOUN
ejpam-5154	36	28	-	-	PUNCT
ejpam-5154	36	29	set	set	NOUN
ejpam-5154	36	30	of	of	ADP
ejpam-5154	36	31	g.	g.	PROPN
ejpam-5154	36	32	let	let	VERB
ejpam-5154	36	33	g	g	NOUN
ejpam-5154	36	34	and	and	CCONJ
ejpam-5154	36	35	h	h	NOUN
ejpam-5154	36	36	be	be	VERB
ejpam-5154	36	37	any	any	DET
ejpam-5154	36	38	two	two	NUM
ejpam-5154	36	39	graphs	graph	NOUN
ejpam-5154	36	40	.	.	PUNCT
ejpam-5154	37	1	the	the	DET
ejpam-5154	37	2	join	join	NOUN
ejpam-5154	37	3	of	of	ADP
ejpam-5154	37	4	g	g	PROPN
ejpam-5154	37	5	and	and	CCONJ
ejpam-5154	37	6	h	h	NOUN
ejpam-5154	37	7	,	,	PUNCT
ejpam-5154	37	8	denoted	denote	VERB
ejpam-5154	37	9	by	by	ADP
ejpam-5154	37	10	g+h	g+h	PROPN
ejpam-5154	37	11	is	be	AUX
ejpam-5154	37	12	the	the	DET
ejpam-5154	37	13	graph	graph	NOUN
ejpam-5154	37	14	with	with	ADP
ejpam-5154	37	15	vertex	vertex	NOUN
ejpam-5154	37	16	set	set	VERB
ejpam-5154	37	17	v	v	NOUN
ejpam-5154	37	18	(	(	PUNCT
ejpam-5154	37	19	g+h	g+h	NOUN
ejpam-5154	37	20	)	)	PUNCT
ejpam-5154	38	1	=	=	SYM
ejpam-5154	38	2	v	v	X
ejpam-5154	38	3	(	(	PUNCT
ejpam-5154	38	4	g	g	NOUN
ejpam-5154	38	5	)	)	PUNCT
ejpam-5154	38	6	∪	∪	NOUN
ejpam-5154	38	7	v	v	NOUN
ejpam-5154	38	8	(	(	PUNCT
ejpam-5154	38	9	h	h	NOUN
ejpam-5154	38	10	)	)	PUNCT
ejpam-5154	38	11	and	and	CCONJ
ejpam-5154	38	12	edge	edge	NOUN
ejpam-5154	38	13	set	set	VERB
ejpam-5154	38	14	e(g+h	e(g+h	NUM
ejpam-5154	38	15	)	)	PUNCT
ejpam-5154	38	16	=	=	SYM
ejpam-5154	38	17	e(g	e(g	NOUN
ejpam-5154	38	18	)	)	PUNCT
ejpam-5154	38	19	∪	∪	ADP
ejpam-5154	38	20	e(h	e(h	PROPN
ejpam-5154	38	21	)	)	PUNCT
ejpam-5154	38	22	∪	∪	NOUN
ejpam-5154	38	23	{	{	PUNCT
ejpam-5154	38	24	uv	uv	NOUN
ejpam-5154	38	25	:	:	PUNCT
ejpam-5154	38	26	u	u	PROPN
ejpam-5154	38	27	∈	∈	PROPN
ejpam-5154	38	28	v	v	ADP
ejpam-5154	38	29	(	(	PUNCT
ejpam-5154	38	30	g	g	NOUN
ejpam-5154	38	31	)	)	PUNCT
ejpam-5154	38	32	,	,	PUNCT
ejpam-5154	38	33	v	v	X
ejpam-5154	38	34	∈	∈	PROPN
ejpam-5154	38	35	v	v	NOUN
ejpam-5154	38	36	(	(	PUNCT
ejpam-5154	38	37	h	h	NOUN
ejpam-5154	38	38	)	)	PUNCT
ejpam-5154	38	39	}	}	PUNCT
ejpam-5154	38	40	.	.	PUNCT
ejpam-5154	39	1	3	3	X
ejpam-5154	39	2	.	.	X
ejpam-5154	39	3	results	result	NOUN
ejpam-5154	39	4	we	we	PRON
ejpam-5154	39	5	begin	begin	VERB
ejpam-5154	39	6	this	this	DET
ejpam-5154	39	7	section	section	NOUN
ejpam-5154	39	8	by	by	ADP
ejpam-5154	39	9	introducing	introduce	VERB
ejpam-5154	39	10	the	the	DET
ejpam-5154	39	11	concept	concept	NOUN
ejpam-5154	39	12	of	of	ADP
ejpam-5154	39	13	zero	zero	NUM
ejpam-5154	39	14	forcing	force	VERB
ejpam-5154	39	15	domination	domination	NOUN
ejpam-5154	39	16	in	in	ADP
ejpam-5154	39	17	a	a	DET
ejpam-5154	39	18	graph	graph	NOUN
ejpam-5154	39	19	.	.	PUNCT
ejpam-5154	40	1	definition	definition	NOUN
ejpam-5154	40	2	1	1	NUM
ejpam-5154	40	3	.	.	PUNCT
ejpam-5154	41	1	let	let	VERB
ejpam-5154	41	2	g	g	PRON
ejpam-5154	41	3	be	be	AUX
ejpam-5154	41	4	a	a	DET
ejpam-5154	41	5	graph	graph	NOUN
ejpam-5154	41	6	.	.	PUNCT
ejpam-5154	42	1	if	if	SCONJ
ejpam-5154	42	2	b	b	PROPN
ejpam-5154	42	3	is	be	AUX
ejpam-5154	42	4	zero	zero	NUM
ejpam-5154	42	5	forcing	force	VERB
ejpam-5154	42	6	set	set	NOUN
ejpam-5154	42	7	and	and	CCONJ
ejpam-5154	42	8	for	for	ADP
ejpam-5154	42	9	every	every	DET
ejpam-5154	42	10	u	u	PROPN
ejpam-5154	42	11	∈	∈	PROPN
ejpam-5154	42	12	v	v	ADP
ejpam-5154	42	13	(	(	PUNCT
ejpam-5154	42	14	g	g	NOUN
ejpam-5154	42	15	)	)	PUNCT
ejpam-5154	42	16	\	\	PROPN
ejpam-5154	42	17	b	b	X
ejpam-5154	42	18	,	,	PUNCT
ejpam-5154	42	19	there	there	PRON
ejpam-5154	42	20	exists	exist	VERB
ejpam-5154	42	21	v	v	ADP
ejpam-5154	42	22	∈	∈	PROPN
ejpam-5154	42	23	b	b	NOUN
ejpam-5154	42	24	such	such	ADJ
ejpam-5154	42	25	that	that	DET
ejpam-5154	42	26	uv	uv	PROPN
ejpam-5154	42	27	∈	∈	PROPN
ejpam-5154	42	28	e	e	X
ejpam-5154	42	29	(	(	PUNCT
ejpam-5154	42	30	g	g	NOUN
ejpam-5154	42	31	)	)	PUNCT
ejpam-5154	42	32	,	,	PUNCT
ejpam-5154	42	33	then	then	ADV
ejpam-5154	42	34	b	b	PROPN
ejpam-5154	42	35	is	be	AUX
ejpam-5154	42	36	called	call	VERB
ejpam-5154	42	37	a	a	DET
ejpam-5154	42	38	zero	zero	NUM
ejpam-5154	42	39	forcing	force	VERB
ejpam-5154	42	40	dominating	dominating	NOUN
ejpam-5154	42	41	set	set	NOUN
ejpam-5154	42	42	of	of	ADP
ejpam-5154	42	43	g.	g.	PROPN
ejpam-5154	42	44	the	the	DET
ejpam-5154	42	45	minimum	minimum	ADJ
ejpam-5154	42	46	cardinality	cardinality	NOUN
ejpam-5154	42	47	of	of	ADP
ejpam-5154	42	48	a	a	DET
ejpam-5154	42	49	zero	zero	NUM
ejpam-5154	42	50	forcing	force	VERB
ejpam-5154	42	51	dominating	dominating	NOUN
ejpam-5154	42	52	set	set	NOUN
ejpam-5154	42	53	of	of	ADP
ejpam-5154	42	54	g	g	NOUN
ejpam-5154	42	55	,	,	PUNCT
ejpam-5154	42	56	denoted	denote	VERB
ejpam-5154	42	57	by	by	ADP
ejpam-5154	42	58	γz(g	γz(g	NOUN
ejpam-5154	42	59	)	)	PUNCT
ejpam-5154	42	60	,	,	PUNCT
ejpam-5154	42	61	is	be	AUX
ejpam-5154	42	62	called	call	VERB
ejpam-5154	42	63	zero	zero	NUM
ejpam-5154	42	64	forcing	force	VERB
ejpam-5154	42	65	domination	domination	NOUN
ejpam-5154	42	66	number	number	NOUN
ejpam-5154	42	67	of	of	ADP
ejpam-5154	42	68	g.	g.	PROPN
ejpam-5154	42	69	example	example	NOUN
ejpam-5154	42	70	1	1	X
ejpam-5154	42	71	.	.	X
ejpam-5154	42	72	consider	consider	VERB
ejpam-5154	42	73	c5	c5	PROPN
ejpam-5154	42	74	below	below	ADV
ejpam-5154	42	75	:	:	PUNCT
ejpam-5154	42	76	a	a	DET
ejpam-5154	42	77	b	b	X
ejpam-5154	42	78	cd	cd	PROPN
ejpam-5154	42	79	e	e	PROPN
ejpam-5154	42	80	c5	c5	PROPN
ejpam-5154	42	81	:	:	PUNCT
ejpam-5154	42	82	let	let	VERB
ejpam-5154	42	83	b	b	X
ejpam-5154	42	84	=	=	PRON
ejpam-5154	42	85	{	{	PUNCT
ejpam-5154	42	86	a	a	X
ejpam-5154	42	87	,	,	PUNCT
ejpam-5154	42	88	c	c	NOUN
ejpam-5154	42	89	,	,	PUNCT
ejpam-5154	42	90	d	d	NOUN
ejpam-5154	42	91	}	}	PUNCT
ejpam-5154	42	92	.	.	PUNCT
ejpam-5154	43	1	then	then	ADV
ejpam-5154	43	2	nc5	nc5	VERB
ejpam-5154	43	3	[	[	X
ejpam-5154	43	4	b	b	X
ejpam-5154	43	5	]	]	X
ejpam-5154	43	6	=	=	SYM
ejpam-5154	43	7	v	v	X
ejpam-5154	43	8	(	(	PUNCT
ejpam-5154	43	9	c5	c5	PROPN
ejpam-5154	43	10	)	)	PUNCT
ejpam-5154	43	11	.	.	PUNCT
ejpam-5154	44	1	thus	thus	ADV
ejpam-5154	44	2	,	,	PUNCT
ejpam-5154	44	3	b	b	PROPN
ejpam-5154	44	4	is	be	AUX
ejpam-5154	44	5	a	a	DET
ejpam-5154	44	6	dominating	dominating	NOUN
ejpam-5154	44	7	set	set	NOUN
ejpam-5154	44	8	of	of	ADP
ejpam-5154	44	9	c5	c5	PROPN
ejpam-5154	44	10	.	.	PUNCT
ejpam-5154	45	1	observe	observe	VERB
ejpam-5154	45	2	that	that	SCONJ
ejpam-5154	45	3	vertices	vertice	VERB
ejpam-5154	45	4	b	b	NOUN
ejpam-5154	45	5	and	and	CCONJ
ejpam-5154	45	6	e	e	NOUN
ejpam-5154	45	7	can	can	AUX
ejpam-5154	45	8	be	be	AUX
ejpam-5154	45	9	forced	force	VERB
ejpam-5154	45	10	by	by	ADP
ejpam-5154	45	11	c	c	PROPN
ejpam-5154	45	12	and	and	CCONJ
ejpam-5154	45	13	d	d	NOUN
ejpam-5154	45	14	,	,	PUNCT
ejpam-5154	45	15	respectively	respectively	ADV
ejpam-5154	45	16	.	.	PUNCT
ejpam-5154	46	1	it	it	PRON
ejpam-5154	46	2	follows	follow	VERB
ejpam-5154	46	3	that	that	SCONJ
ejpam-5154	46	4	b	b	NOUN
ejpam-5154	46	5	is	be	AUX
ejpam-5154	46	6	a	a	DET
ejpam-5154	46	7	zero	zero	NUM
ejpam-5154	46	8	forcing	force	VERB
ejpam-5154	46	9	set	set	NOUN
ejpam-5154	46	10	of	of	ADP
ejpam-5154	46	11	c5	c5	PROPN
ejpam-5154	46	12	.	.	PUNCT
ejpam-5154	47	1	therefore	therefore	ADV
ejpam-5154	47	2	,	,	PUNCT
ejpam-5154	47	3	b	b	PROPN
ejpam-5154	47	4	is	be	AUX
ejpam-5154	47	5	a	a	DET
ejpam-5154	47	6	zero	zero	NUM
ejpam-5154	47	7	forcing	force	VERB
ejpam-5154	47	8	dominating	dominating	NOUN
ejpam-5154	47	9	set	set	NOUN
ejpam-5154	47	10	of	of	ADP
ejpam-5154	47	11	c5	c5	PROPN
ejpam-5154	47	12	.	.	PUNCT
ejpam-5154	48	1	moreover	moreover	ADV
ejpam-5154	48	2	,	,	PUNCT
ejpam-5154	48	3	it	it	PRON
ejpam-5154	48	4	can	can	AUX
ejpam-5154	48	5	be	be	AUX
ejpam-5154	48	6	verified	verify	VERB
ejpam-5154	48	7	that	that	SCONJ
ejpam-5154	48	8	γz	γz	PROPN
ejpam-5154	48	9	(	(	PUNCT
ejpam-5154	48	10	c5	c5	PROPN
ejpam-5154	48	11	)	)	PUNCT
ejpam-5154	48	12	=	=	SYM
ejpam-5154	48	13	3	3	X
ejpam-5154	48	14	.	.	NOUN
ejpam-5154	48	15	remark	remark	NOUN
ejpam-5154	48	16	1	1	NUM
ejpam-5154	48	17	.	.	PUNCT
ejpam-5154	49	1	let	let	VERB
ejpam-5154	49	2	g	g	PRON
ejpam-5154	49	3	be	be	AUX
ejpam-5154	49	4	a	a	DET
ejpam-5154	49	5	graph	graph	NOUN
ejpam-5154	49	6	.	.	PUNCT
ejpam-5154	50	1	then	then	ADV
ejpam-5154	50	2	the	the	DET
ejpam-5154	50	3	zero	zero	NUM
ejpam-5154	50	4	forcing	force	VERB
ejpam-5154	50	5	domination	domination	NOUN
ejpam-5154	50	6	and	and	CCONJ
ejpam-5154	50	7	zero	zero	NUM
ejpam-5154	50	8	forcing	force	VERB
ejpam-5154	50	9	hop	hop	NOUN
ejpam-5154	50	10	domination	domination	NOUN
ejpam-5154	50	11	parameter	parameter	NOUN
ejpam-5154	50	12	of	of	ADP
ejpam-5154	50	13	g	g	PROPN
ejpam-5154	50	14	are	be	AUX
ejpam-5154	50	15	incomparable	incomparable	ADJ
ejpam-5154	50	16	.	.	PUNCT
ejpam-5154	51	1	to	to	PART
ejpam-5154	51	2	see	see	VERB
ejpam-5154	51	3	this	this	PRON
ejpam-5154	51	4	,	,	PUNCT
ejpam-5154	51	5	consider	consider	VERB
ejpam-5154	51	6	the	the	DET
ejpam-5154	51	7	graph	graph	NOUN
ejpam-5154	51	8	g	g	NOUN
ejpam-5154	51	9	below	below	ADV
ejpam-5154	51	10	:	:	PUNCT
ejpam-5154	51	11	a	a	DET
ejpam-5154	51	12	b	b	X
ejpam-5154	51	13	c	c	NOUN
ejpam-5154	51	14	d	d	X
ejpam-5154	51	15	e	e	X
ejpam-5154	51	16	fg	fg	PROPN
ejpam-5154	51	17	:	:	PUNCT
ejpam-5154	51	18	let	let	VERB
ejpam-5154	51	19	q	q	NOUN
ejpam-5154	51	20	=	=	PUNCT
ejpam-5154	51	21	{	{	PUNCT
ejpam-5154	51	22	b	b	PROPN
ejpam-5154	51	23	,	,	PUNCT
ejpam-5154	51	24	c	c	X
ejpam-5154	51	25	,	,	PUNCT
ejpam-5154	51	26	e	e	NOUN
ejpam-5154	51	27	}	}	PUNCT
ejpam-5154	51	28	.	.	PUNCT
ejpam-5154	52	1	then	then	ADV
ejpam-5154	52	2	ng[q	ng[q	PROPN
ejpam-5154	52	3	]	]	X
ejpam-5154	52	4	=	=	SYM
ejpam-5154	52	5	v	v	NOUN
ejpam-5154	52	6	(	(	PUNCT
ejpam-5154	52	7	g	g	NOUN
ejpam-5154	52	8	)	)	PUNCT
ejpam-5154	52	9	.	.	PUNCT
ejpam-5154	53	1	thus	thus	ADV
ejpam-5154	53	2	,	,	PUNCT
ejpam-5154	53	3	q	q	X
ejpam-5154	53	4	is	be	AUX
ejpam-5154	53	5	a	a	DET
ejpam-5154	53	6	dominating	dominating	NOUN
ejpam-5154	53	7	set	set	NOUN
ejpam-5154	53	8	of	of	ADP
ejpam-5154	53	9	g.	g.	PROPN
ejpam-5154	53	10	moreover	moreover	ADV
ejpam-5154	53	11	,	,	PUNCT
ejpam-5154	53	12	observe	observe	VERB
ejpam-5154	53	13	that	that	SCONJ
ejpam-5154	53	14	vertices	vertice	VERB
ejpam-5154	53	15	a	a	PRON
ejpam-5154	53	16	,	,	PUNCT
ejpam-5154	54	1	d	d	NOUN
ejpam-5154	54	2	and	and	CCONJ
ejpam-5154	54	3	f	f	PROPN
ejpam-5154	54	4	are	be	AUX
ejpam-5154	54	5	forced	force	VERB
ejpam-5154	54	6	by	by	ADP
ejpam-5154	54	7	vertices	vertex	NOUN
ejpam-5154	54	8	b	b	NUM
ejpam-5154	54	9	,	,	PUNCT
ejpam-5154	54	10	c	c	PROPN
ejpam-5154	54	11	and	and	CCONJ
ejpam-5154	54	12	e.	e.	PROPN
ejpam-5154	54	13	it	it	PRON
ejpam-5154	54	14	follows	follow	VERB
ejpam-5154	54	15	that	that	SCONJ
ejpam-5154	54	16	q	q	NOUN
ejpam-5154	54	17	is	be	AUX
ejpam-5154	54	18	a	a	DET
ejpam-5154	54	19	zero	zero	NUM
ejpam-5154	54	20	j.	j.	PROPN
ejpam-5154	54	21	a.	a.	PROPN
ejpam-5154	54	22	hassan	hassan	PROPN
ejpam-5154	55	1	et	et	PROPN
ejpam-5154	55	2	al	al	PROPN
ejpam-5154	55	3	.	.	PUNCT
ejpam-5154	55	4	/	/	SYM
ejpam-5154	55	5	eur	eur	PROPN
ejpam-5154	55	6	.	.	PUNCT
ejpam-5154	56	1	j.	j.	PROPN
ejpam-5154	56	2	pure	pure	PROPN
ejpam-5154	56	3	appl	appl	PROPN
ejpam-5154	56	4	.	.	PROPN
ejpam-5154	56	5	math	math	PROPN
ejpam-5154	56	6	,	,	PUNCT
ejpam-5154	56	7	17	17	NUM
ejpam-5154	56	8	(	(	PUNCT
ejpam-5154	56	9	4	4	NUM
ejpam-5154	56	10	)	)	PUNCT
ejpam-5154	56	11	(	(	PUNCT
ejpam-5154	56	12	2024	2024	NUM
ejpam-5154	56	13	)	)	PUNCT
ejpam-5154	56	14	,	,	PUNCT
ejpam-5154	56	15	3772	3772	NUM
ejpam-5154	56	16	-	-	SYM
ejpam-5154	56	17	3780	3780	NUM
ejpam-5154	56	18	3775	3775	NUM
ejpam-5154	56	19	forcing	force	VERB
ejpam-5154	56	20	set	set	NOUN
ejpam-5154	56	21	of	of	ADP
ejpam-5154	56	22	g.	g.	PROPN
ejpam-5154	56	23	since	since	SCONJ
ejpam-5154	56	24	{	{	PUNCT
ejpam-5154	56	25	c	c	X
ejpam-5154	56	26	,	,	PUNCT
ejpam-5154	56	27	d	d	NOUN
ejpam-5154	56	28	}	}	PUNCT
ejpam-5154	56	29	is	be	AUX
ejpam-5154	56	30	not	not	PART
ejpam-5154	56	31	a	a	DET
ejpam-5154	56	32	zero	zero	NUM
ejpam-5154	56	33	forcing	force	VERB
ejpam-5154	56	34	set	set	NOUN
ejpam-5154	56	35	of	of	ADP
ejpam-5154	56	36	g	g	NOUN
ejpam-5154	56	37	,	,	PUNCT
ejpam-5154	56	38	it	it	PRON
ejpam-5154	56	39	follows	follow	VERB
ejpam-5154	56	40	that	that	PRON
ejpam-5154	56	41	q	q	PUNCT
ejpam-5154	57	1	=	=	PUNCT
ejpam-5154	57	2	{	{	PUNCT
ejpam-5154	57	3	b	b	PROPN
ejpam-5154	57	4	,	,	PUNCT
ejpam-5154	57	5	c	c	X
ejpam-5154	57	6	,	,	PUNCT
ejpam-5154	57	7	e	e	NOUN
ejpam-5154	57	8	}	}	PUNCT
ejpam-5154	57	9	is	be	AUX
ejpam-5154	57	10	a	a	DET
ejpam-5154	57	11	minimum	minimum	ADJ
ejpam-5154	57	12	zero	zero	NUM
ejpam-5154	57	13	forcing	force	VERB
ejpam-5154	57	14	dominating	dominating	NOUN
ejpam-5154	57	15	set	set	NOUN
ejpam-5154	57	16	of	of	ADP
ejpam-5154	57	17	g.	g.	PROPN
ejpam-5154	57	18	hence	hence	ADV
ejpam-5154	57	19	,	,	PUNCT
ejpam-5154	57	20	γz(g	γz(g	PUNCT
ejpam-5154	57	21	)	)	PUNCT
ejpam-5154	57	22	=	=	SYM
ejpam-5154	58	1	3	3	X
ejpam-5154	58	2	.	.	PUNCT
ejpam-5154	58	3	now	now	ADV
ejpam-5154	58	4	,	,	PUNCT
ejpam-5154	58	5	let	let	VERB
ejpam-5154	58	6	s	s	PRON
ejpam-5154	58	7	=	=	X
ejpam-5154	58	8	{	{	PUNCT
ejpam-5154	58	9	a	a	X
ejpam-5154	58	10	,	,	PUNCT
ejpam-5154	58	11	c	c	NOUN
ejpam-5154	58	12	,	,	PUNCT
ejpam-5154	58	13	d	d	NOUN
ejpam-5154	58	14	,	,	PUNCT
ejpam-5154	58	15	e	e	NOUN
ejpam-5154	58	16	}	}	PUNCT
ejpam-5154	58	17	.	.	PUNCT
ejpam-5154	59	1	then	then	ADV
ejpam-5154	59	2	s	s	VERB
ejpam-5154	59	3	is	be	AUX
ejpam-5154	59	4	a	a	DET
ejpam-5154	59	5	minimum	minimum	ADJ
ejpam-5154	59	6	zero	zero	NUM
ejpam-5154	59	7	forcing	force	VERB
ejpam-5154	59	8	hop	hop	NOUN
ejpam-5154	59	9	dominating	dominating	NOUN
ejpam-5154	59	10	set	set	NOUN
ejpam-5154	59	11	of	of	ADP
ejpam-5154	59	12	g.	g.	PROPN
ejpam-5154	59	13	therefore	therefore	ADV
ejpam-5154	59	14	,	,	PUNCT
ejpam-5154	59	15	γzh(g	γzh(g	PROPN
ejpam-5154	59	16	)	)	PUNCT
ejpam-5154	59	17	=	=	PUNCT
ejpam-5154	60	1	4	4	X
ejpam-5154	60	2	.	.	PUNCT
ejpam-5154	60	3	next	next	ADV
ejpam-5154	60	4	,	,	PUNCT
ejpam-5154	60	5	consider	consider	VERB
ejpam-5154	60	6	the	the	DET
ejpam-5154	60	7	graph	graph	NOUN
ejpam-5154	60	8	h	h	NOUN
ejpam-5154	60	9	below	below	ADV
ejpam-5154	60	10	:	:	PUNCT
ejpam-5154	60	11	a	a	DET
ejpam-5154	60	12	b	b	X
ejpam-5154	60	13	c	c	NOUN
ejpam-5154	60	14	h	h	NOUN
ejpam-5154	60	15	:	:	PUNCT
ejpam-5154	61	1	f	f	X
ejpam-5154	61	2	e	e	X
ejpam-5154	62	1	d	d	NOUN
ejpam-5154	62	2	i	i	PRON
ejpam-5154	62	3	h	h	VERB
ejpam-5154	62	4	g	g	NOUN
ejpam-5154	62	5	let	let	VERB
ejpam-5154	62	6	p	p	NOUN
ejpam-5154	62	7	=	=	X
ejpam-5154	62	8	{	{	PUNCT
ejpam-5154	62	9	c	c	NOUN
ejpam-5154	62	10	,	,	PUNCT
ejpam-5154	62	11	d	d	NOUN
ejpam-5154	62	12	,	,	PUNCT
ejpam-5154	62	13	g	g	NOUN
ejpam-5154	62	14	}	}	PUNCT
ejpam-5154	62	15	.	.	PUNCT
ejpam-5154	63	1	then	then	ADV
ejpam-5154	63	2	n2	n2	PROPN
ejpam-5154	63	3	g[p	g[p	PROPN
ejpam-5154	63	4	]	]	PUNCT
ejpam-5154	64	1	=	=	SYM
ejpam-5154	64	2	v	v	X
ejpam-5154	64	3	(	(	PUNCT
ejpam-5154	64	4	h	h	NOUN
ejpam-5154	64	5	)	)	PUNCT
ejpam-5154	64	6	,	,	PUNCT
ejpam-5154	64	7	and	and	CCONJ
ejpam-5154	64	8	so	so	ADV
ejpam-5154	64	9	p	p	PRON
ejpam-5154	64	10	is	be	AUX
ejpam-5154	64	11	a	a	DET
ejpam-5154	64	12	hop	hop	NOUN
ejpam-5154	64	13	dominating	dominating	NOUN
ejpam-5154	64	14	set	set	NOUN
ejpam-5154	64	15	of	of	ADP
ejpam-5154	64	16	h.	h.	PROPN
ejpam-5154	64	17	observe	observe	VERB
ejpam-5154	64	18	that	that	SCONJ
ejpam-5154	64	19	vertices	vertice	VERB
ejpam-5154	64	20	b	b	NOUN
ejpam-5154	64	21	and	and	CCONJ
ejpam-5154	64	22	a	a	PRON
ejpam-5154	64	23	are	be	AUX
ejpam-5154	64	24	forced	force	VERB
ejpam-5154	64	25	by	by	ADP
ejpam-5154	64	26	c	c	PROPN
ejpam-5154	64	27	and	and	CCONJ
ejpam-5154	64	28	b	b	NOUN
ejpam-5154	64	29	,	,	PUNCT
ejpam-5154	64	30	respectively	respectively	ADV
ejpam-5154	64	31	,	,	PUNCT
ejpam-5154	64	32	vertices	vertice	VERB
ejpam-5154	64	33	e	e	NOUN
ejpam-5154	64	34	and	and	CCONJ
ejpam-5154	64	35	f	f	PROPN
ejpam-5154	64	36	are	be	AUX
ejpam-5154	64	37	forced	force	VERB
ejpam-5154	64	38	by	by	ADP
ejpam-5154	64	39	vertices	vertex	NOUN
ejpam-5154	64	40	d	d	NOUN
ejpam-5154	64	41	and	and	CCONJ
ejpam-5154	64	42	e	e	NOUN
ejpam-5154	64	43	,	,	PUNCT
ejpam-5154	64	44	respectively	respectively	ADV
ejpam-5154	64	45	,	,	PUNCT
ejpam-5154	64	46	and	and	CCONJ
ejpam-5154	64	47	vertices	vertice	VERB
ejpam-5154	64	48	h	h	NOUN
ejpam-5154	65	1	and	and	CCONJ
ejpam-5154	65	2	i	i	PRON
ejpam-5154	65	3	are	be	AUX
ejpam-5154	65	4	forced	force	VERB
ejpam-5154	65	5	by	by	ADP
ejpam-5154	65	6	vertices	vertex	NOUN
ejpam-5154	65	7	g	g	PROPN
ejpam-5154	65	8	and	and	CCONJ
ejpam-5154	65	9	h	h	NOUN
ejpam-5154	65	10	,	,	PUNCT
ejpam-5154	65	11	respectively	respectively	ADV
ejpam-5154	65	12	.	.	PUNCT
ejpam-5154	66	1	thus	thus	ADV
ejpam-5154	66	2	,	,	PUNCT
ejpam-5154	66	3	p	p	PROPN
ejpam-5154	66	4	is	be	AUX
ejpam-5154	66	5	a	a	DET
ejpam-5154	66	6	zero	zero	NUM
ejpam-5154	66	7	forcing	force	VERB
ejpam-5154	66	8	hop	hop	NOUN
ejpam-5154	66	9	dominating	dominating	NOUN
ejpam-5154	66	10	set	set	NOUN
ejpam-5154	66	11	of	of	ADP
ejpam-5154	66	12	h.	h.	PROPN
ejpam-5154	66	13	since	since	SCONJ
ejpam-5154	66	14	p	p	PROPN
ejpam-5154	66	15	is	be	AUX
ejpam-5154	66	16	the	the	DET
ejpam-5154	66	17	minimum	minimum	ADJ
ejpam-5154	66	18	hop	hop	NOUN
ejpam-5154	66	19	domnating	domnating	NOUN
ejpam-5154	66	20	set	set	NOUN
ejpam-5154	66	21	of	of	ADP
ejpam-5154	66	22	h	h	NOUN
ejpam-5154	66	23	,	,	PUNCT
ejpam-5154	66	24	it	it	PRON
ejpam-5154	66	25	follows	follow	VERB
ejpam-5154	66	26	that	that	SCONJ
ejpam-5154	66	27	γzh(h	γzh(h	X
ejpam-5154	67	1	)	)	PUNCT
ejpam-5154	67	2	=	=	SYM
ejpam-5154	67	3	3	3	X
ejpam-5154	67	4	.	.	PUNCT
ejpam-5154	67	5	now	now	ADV
ejpam-5154	67	6	,	,	PUNCT
ejpam-5154	67	7	let	let	VERB
ejpam-5154	67	8	d	d	X
ejpam-5154	67	9	=	=	PUNCT
ejpam-5154	67	10	{	{	PUNCT
ejpam-5154	67	11	b	b	PROPN
ejpam-5154	67	12	,	,	PUNCT
ejpam-5154	67	13	e	e	NOUN
ejpam-5154	67	14	,	,	PUNCT
ejpam-5154	67	15	h	h	NOUN
ejpam-5154	67	16	,	,	PUNCT
ejpam-5154	67	17	g	g	NOUN
ejpam-5154	67	18	}	}	PUNCT
ejpam-5154	67	19	.	.	PUNCT
ejpam-5154	68	1	then	then	ADV
ejpam-5154	68	2	d	d	PROPN
ejpam-5154	68	3	is	be	AUX
ejpam-5154	68	4	a	a	DET
ejpam-5154	68	5	dominating	dominating	NOUN
ejpam-5154	68	6	set	set	NOUN
ejpam-5154	68	7	of	of	ADP
ejpam-5154	68	8	h.	h.	PROPN
ejpam-5154	68	9	observe	observe	VERB
ejpam-5154	68	10	that	that	SCONJ
ejpam-5154	68	11	vertices	vertice	VERB
ejpam-5154	68	12	d	d	NOUN
ejpam-5154	68	13	and	and	CCONJ
ejpam-5154	68	14	c	c	PROPN
ejpam-5154	68	15	are	be	AUX
ejpam-5154	68	16	forced	force	VERB
ejpam-5154	68	17	by	by	ADP
ejpam-5154	68	18	vertices	vertex	NOUN
ejpam-5154	68	19	g	g	PROPN
ejpam-5154	68	20	and	and	CCONJ
ejpam-5154	68	21	d	d	NOUN
ejpam-5154	68	22	,	,	PUNCT
ejpam-5154	68	23	respectively	respectively	ADV
ejpam-5154	68	24	,	,	PUNCT
ejpam-5154	68	25	and	and	CCONJ
ejpam-5154	68	26	vetices	vetice	NOUN
ejpam-5154	68	27	a	a	PRON
ejpam-5154	68	28	,	,	PUNCT
ejpam-5154	68	29	f	f	PROPN
ejpam-5154	69	1	and	and	CCONJ
ejpam-5154	69	2	i	i	PRON
ejpam-5154	69	3	are	be	AUX
ejpam-5154	69	4	forced	force	VERB
ejpam-5154	69	5	by	by	ADP
ejpam-5154	69	6	vertices	vertex	NOUN
ejpam-5154	69	7	b	b	NUM
ejpam-5154	69	8	,	,	PUNCT
ejpam-5154	69	9	e	e	NOUN
ejpam-5154	69	10	and	and	CCONJ
ejpam-5154	69	11	h	h	NOUN
ejpam-5154	69	12	,	,	PUNCT
ejpam-5154	69	13	respectively	respectively	ADV
ejpam-5154	69	14	.	.	PUNCT
ejpam-5154	70	1	thus	thus	ADV
ejpam-5154	70	2	,	,	PUNCT
ejpam-5154	70	3	d	d	PRON
ejpam-5154	70	4	is	be	AUX
ejpam-5154	70	5	a	a	DET
ejpam-5154	70	6	zero	zero	NUM
ejpam-5154	70	7	forcing	force	VERB
ejpam-5154	70	8	dominating	dominating	NOUN
ejpam-5154	70	9	set	set	NOUN
ejpam-5154	70	10	of	of	ADP
ejpam-5154	70	11	h.	h.	PROPN
ejpam-5154	70	12	since	since	SCONJ
ejpam-5154	70	13	{	{	PUNCT
ejpam-5154	70	14	b	b	NOUN
ejpam-5154	70	15	,	,	PUNCT
ejpam-5154	70	16	e	e	NOUN
ejpam-5154	70	17	,	,	PUNCT
ejpam-5154	70	18	h	h	NOUN
ejpam-5154	70	19	}	}	PUNCT
ejpam-5154	70	20	is	be	AUX
ejpam-5154	70	21	not	not	PART
ejpam-5154	70	22	a	a	DET
ejpam-5154	70	23	zero	zero	NUM
ejpam-5154	70	24	forcing	forcing	NOUN
ejpam-5154	70	25	set	set	NOUN
ejpam-5154	70	26	,	,	PUNCT
ejpam-5154	70	27	it	it	PRON
ejpam-5154	70	28	follows	follow	VERB
ejpam-5154	70	29	that	that	SCONJ
ejpam-5154	70	30	d	d	NOUN
ejpam-5154	70	31	is	be	AUX
ejpam-5154	70	32	a	a	DET
ejpam-5154	70	33	minimum	minimum	ADJ
ejpam-5154	70	34	zero	zero	NUM
ejpam-5154	70	35	forcing	force	VERB
ejpam-5154	70	36	dominating	dominating	NOUN
ejpam-5154	70	37	set	set	NOUN
ejpam-5154	70	38	of	of	ADP
ejpam-5154	70	39	h.	h.	PROPN
ejpam-5154	70	40	therefore	therefore	ADV
ejpam-5154	70	41	,	,	PUNCT
ejpam-5154	70	42	γzh(h	γzh(h	PROPN
ejpam-5154	70	43	)	)	PUNCT
ejpam-5154	70	44	=	=	SYM
ejpam-5154	70	45	4	4	X
ejpam-5154	70	46	.	.	X
ejpam-5154	70	47	proposition	proposition	NOUN
ejpam-5154	70	48	1	1	NUM
ejpam-5154	70	49	.	.	PUNCT
ejpam-5154	71	1	let	let	VERB
ejpam-5154	71	2	g	g	PRON
ejpam-5154	71	3	be	be	AUX
ejpam-5154	71	4	a	a	DET
ejpam-5154	71	5	graph	graph	NOUN
ejpam-5154	71	6	.	.	PUNCT
ejpam-5154	72	1	then	then	ADV
ejpam-5154	72	2	(	(	PUNCT
ejpam-5154	72	3	i	i	NOUN
ejpam-5154	72	4	)	)	PUNCT
ejpam-5154	72	5	a	a	DET
ejpam-5154	72	6	dominating	dominating	NOUN
ejpam-5154	72	7	set	set	NOUN
ejpam-5154	72	8	d	d	NOUN
ejpam-5154	72	9	of	of	ADP
ejpam-5154	72	10	g	g	NOUN
ejpam-5154	72	11	may	may	AUX
ejpam-5154	72	12	not	not	PART
ejpam-5154	72	13	be	be	AUX
ejpam-5154	72	14	a	a	DET
ejpam-5154	72	15	zero	zero	NUM
ejpam-5154	72	16	forcing	force	VERB
ejpam-5154	72	17	set	set	NOUN
ejpam-5154	72	18	of	of	ADP
ejpam-5154	72	19	g	g	NOUN
ejpam-5154	72	20	;	;	PUNCT
ejpam-5154	72	21	and	and	CCONJ
ejpam-5154	72	22	(	(	PUNCT
ejpam-5154	72	23	ii	ii	NOUN
ejpam-5154	72	24	)	)	PUNCT
ejpam-5154	72	25	a	a	DET
ejpam-5154	72	26	zero	zero	NUM
ejpam-5154	72	27	forcing	force	VERB
ejpam-5154	72	28	set	set	VERB
ejpam-5154	72	29	t	t	PROPN
ejpam-5154	72	30	of	of	ADP
ejpam-5154	72	31	g	g	PROPN
ejpam-5154	72	32	may	may	AUX
ejpam-5154	72	33	not	not	PART
ejpam-5154	72	34	be	be	AUX
ejpam-5154	72	35	a	a	DET
ejpam-5154	72	36	dominating	dominating	NOUN
ejpam-5154	72	37	set	set	NOUN
ejpam-5154	72	38	of	of	ADP
ejpam-5154	72	39	g	g	NOUN
ejpam-5154	72	40	;	;	PUNCT
ejpam-5154	72	41	proof	proof	NOUN
ejpam-5154	72	42	.	.	PUNCT
ejpam-5154	73	1	(	(	PUNCT
ejpam-5154	73	2	i	i	NOUN
ejpam-5154	73	3	)	)	PUNCT
ejpam-5154	73	4	consider	consider	VERB
ejpam-5154	73	5	the	the	DET
ejpam-5154	73	6	g	g	NOUN
ejpam-5154	73	7	below	below	ADV
ejpam-5154	73	8	:	:	PUNCT
ejpam-5154	73	9	a1	a1	VERB
ejpam-5154	73	10	a4a2	a4a2	PROPN
ejpam-5154	74	1	a5a3	a5a3	NOUN
ejpam-5154	74	2	g	g	NOUN
ejpam-5154	74	3	:	:	PUNCT
ejpam-5154	74	4	a6	a6	PROPN
ejpam-5154	74	5	a7	a7	PROPN
ejpam-5154	74	6	a8	a8	PROPN
ejpam-5154	74	7	letd	letd	NOUN
ejpam-5154	74	8	=	=	SYM
ejpam-5154	74	9	{	{	PUNCT
ejpam-5154	74	10	a4	a4	PROPN
ejpam-5154	74	11	,	,	PUNCT
ejpam-5154	74	12	a6	a6	NOUN
ejpam-5154	74	13	}	}	PUNCT
ejpam-5154	74	14	.	.	PUNCT
ejpam-5154	75	1	thenng	thenng	PROPN
ejpam-5154	76	1	[	[	X
ejpam-5154	76	2	a4	a4	X
ejpam-5154	76	3	]	]	X
ejpam-5154	76	4	=	=	SYM
ejpam-5154	76	5	{	{	PUNCT
ejpam-5154	76	6	a1	a1	PROPN
ejpam-5154	76	7	,	,	PUNCT
ejpam-5154	76	8	a2	a2	PROPN
ejpam-5154	76	9	,	,	PUNCT
ejpam-5154	76	10	a3	a3	NOUN
ejpam-5154	76	11	,	,	PUNCT
ejpam-5154	76	12	a4	a4	PROPN
ejpam-5154	76	13	,	,	PUNCT
ejpam-5154	76	14	a5	a5	NOUN
ejpam-5154	76	15	}	}	PUNCT
ejpam-5154	76	16	andng	andng	NOUN
ejpam-5154	77	1	[	[	X
ejpam-5154	77	2	a6	a6	X
ejpam-5154	77	3	]	]	X
ejpam-5154	77	4	=	=	SYM
ejpam-5154	77	5	{	{	PUNCT
ejpam-5154	77	6	a5	a5	PROPN
ejpam-5154	77	7	,	,	PUNCT
ejpam-5154	77	8	a6	a6	PROPN
ejpam-5154	77	9	,	,	PUNCT
ejpam-5154	77	10	a7	a7	PROPN
ejpam-5154	77	11	,	,	PUNCT
ejpam-5154	77	12	a8	a8	PROPN
ejpam-5154	77	13	}	}	PUNCT
ejpam-5154	77	14	.	.	PUNCT
ejpam-5154	78	1	thus	thus	ADV
ejpam-5154	78	2	,	,	PUNCT
ejpam-5154	78	3	ng	ng	PROPN
ejpam-5154	79	1	[	[	X
ejpam-5154	79	2	d	d	X
ejpam-5154	79	3	]	]	X
ejpam-5154	79	4	=	=	SYM
ejpam-5154	79	5	v	v	NOUN
ejpam-5154	79	6	(	(	PUNCT
ejpam-5154	79	7	g	g	NOUN
ejpam-5154	79	8	)	)	PUNCT
ejpam-5154	79	9	,	,	PUNCT
ejpam-5154	79	10	showing	show	VERB
ejpam-5154	79	11	that	that	SCONJ
ejpam-5154	79	12	d	d	NOUN
ejpam-5154	79	13	is	be	AUX
ejpam-5154	79	14	a	a	DET
ejpam-5154	79	15	dominating	dominating	NOUN
ejpam-5154	79	16	set	set	NOUN
ejpam-5154	79	17	of	of	ADP
ejpam-5154	79	18	g.	g.	PROPN
ejpam-5154	79	19	however	however	ADV
ejpam-5154	79	20	,	,	PUNCT
ejpam-5154	79	21	d	d	PROPN
ejpam-5154	79	22	is	be	AUX
ejpam-5154	79	23	not	not	PART
ejpam-5154	79	24	a	a	DET
ejpam-5154	79	25	j.	j.	PROPN
ejpam-5154	79	26	a.	a.	PROPN
ejpam-5154	79	27	hassan	hassan	PROPN
ejpam-5154	79	28	et	et	PROPN
ejpam-5154	79	29	al	al	PROPN
ejpam-5154	79	30	.	.	PUNCT
ejpam-5154	79	31	/	/	SYM
ejpam-5154	79	32	eur	eur	PROPN
ejpam-5154	79	33	.	.	PUNCT
ejpam-5154	80	1	j.	j.	PROPN
ejpam-5154	80	2	pure	pure	PROPN
ejpam-5154	80	3	appl	appl	PROPN
ejpam-5154	80	4	.	.	PROPN
ejpam-5154	80	5	math	math	PROPN
ejpam-5154	80	6	,	,	PUNCT
ejpam-5154	80	7	17	17	NUM
ejpam-5154	80	8	(	(	PUNCT
ejpam-5154	80	9	4	4	NUM
ejpam-5154	80	10	)	)	PUNCT
ejpam-5154	80	11	(	(	PUNCT
ejpam-5154	80	12	2024	2024	NUM
ejpam-5154	80	13	)	)	PUNCT
ejpam-5154	80	14	,	,	PUNCT
ejpam-5154	80	15	3772	3772	NUM
ejpam-5154	80	16	-	-	SYM
ejpam-5154	80	17	3780	3780	NUM
ejpam-5154	80	18	3776	3776	NUM
ejpam-5154	80	19	zero	zero	NUM
ejpam-5154	80	20	forcing	force	VERB
ejpam-5154	80	21	set	set	NOUN
ejpam-5154	80	22	of	of	ADP
ejpam-5154	80	23	g	g	PROPN
ejpam-5154	80	24	since	since	SCONJ
ejpam-5154	80	25	vertices	vertex	NOUN
ejpam-5154	80	26	a4	a4	NOUN
ejpam-5154	80	27	and	and	CCONJ
ejpam-5154	80	28	a6	a6	NOUN
ejpam-5154	80	29	can	can	AUX
ejpam-5154	80	30	not	not	PART
ejpam-5154	80	31	force	force	VERB
ejpam-5154	80	32	any	any	DET
ejpam-5154	80	33	other	other	ADJ
ejpam-5154	80	34	vertices	vertex	NOUN
ejpam-5154	80	35	in	in	ADP
ejpam-5154	80	36	v	v	ADP
ejpam-5154	80	37	(	(	PUNCT
ejpam-5154	80	38	g	g	NOUN
ejpam-5154	80	39	)	)	PUNCT
ejpam-5154	80	40	\d	\d	NOUN
ejpam-5154	80	41	.	.	PUNCT
ejpam-5154	81	1	(	(	PUNCT
ejpam-5154	81	2	ii	ii	NOUN
ejpam-5154	81	3	)	)	PUNCT
ejpam-5154	81	4	consider	consider	VERB
ejpam-5154	81	5	t	t	NOUN
ejpam-5154	81	6	=	=	SYM
ejpam-5154	81	7	{	{	PUNCT
ejpam-5154	81	8	a1	a1	PROPN
ejpam-5154	81	9	,	,	PUNCT
ejpam-5154	81	10	a2	a2	PROPN
ejpam-5154	81	11	,	,	PUNCT
ejpam-5154	81	12	,	,	PUNCT
ejpam-5154	81	13	a3	a3	NOUN
ejpam-5154	81	14	,	,	PUNCT
ejpam-5154	81	15	a7	a7	PROPN
ejpam-5154	81	16	,	,	PUNCT
ejpam-5154	81	17	a8	a8	PROPN
ejpam-5154	81	18	}	}	PUNCT
ejpam-5154	81	19	.	.	PUNCT
ejpam-5154	82	1	then	then	ADV
ejpam-5154	82	2	vertices	vertice	VERB
ejpam-5154	82	3	a4	a4	PROPN
ejpam-5154	82	4	,	,	PUNCT
ejpam-5154	82	5	a5	a5	PROPN
ejpam-5154	82	6	and	and	CCONJ
ejpam-5154	82	7	a6	a6	NOUN
ejpam-5154	82	8	are	be	AUX
ejpam-5154	82	9	forced	force	VERB
ejpam-5154	82	10	by	by	ADP
ejpam-5154	82	11	vertices	vertex	NOUN
ejpam-5154	82	12	a1	a1	NOUN
ejpam-5154	82	13	,	,	PUNCT
ejpam-5154	82	14	a4	a4	NOUN
ejpam-5154	82	15	and	and	CCONJ
ejpam-5154	82	16	a5	a5	NOUN
ejpam-5154	82	17	,	,	PUNCT
ejpam-5154	82	18	respectively	respectively	ADV
ejpam-5154	82	19	.	.	PUNCT
ejpam-5154	83	1	thus	thus	ADV
ejpam-5154	83	2	,	,	PUNCT
ejpam-5154	83	3	t	t	PROPN
ejpam-5154	83	4	is	be	AUX
ejpam-5154	83	5	a	a	DET
ejpam-5154	83	6	zero	zero	NUM
ejpam-5154	83	7	forcing	force	VERB
ejpam-5154	83	8	set	set	VERB
ejpam-5154	83	9	ofg	ofg	PROPN
ejpam-5154	83	10	.	.	PUNCT
ejpam-5154	84	1	however	however	ADV
ejpam-5154	84	2	,	,	PUNCT
ejpam-5154	84	3	t	t	PROPN
ejpam-5154	84	4	is	be	AUX
ejpam-5154	84	5	not	not	PART
ejpam-5154	84	6	dominating	dominate	VERB
ejpam-5154	84	7	set	set	NOUN
ejpam-5154	84	8	of	of	ADP
ejpam-5154	84	9	g	g	PROPN
ejpam-5154	84	10	since	since	SCONJ
ejpam-5154	84	11	a5	a5	PROPN
ejpam-5154	84	12	can	can	AUX
ejpam-5154	84	13	not	not	PART
ejpam-5154	84	14	be	be	AUX
ejpam-5154	84	15	dominated	dominate	VERB
ejpam-5154	84	16	by	by	ADP
ejpam-5154	84	17	any	any	DET
ejpam-5154	84	18	vertex	vertex	NOUN
ejpam-5154	84	19	in	in	ADP
ejpam-5154	84	20	t	t	PROPN
ejpam-5154	84	21	.	.	PUNCT
ejpam-5154	85	1	proposition	proposition	NOUN
ejpam-5154	85	2	2	2	NUM
ejpam-5154	85	3	.	.	PUNCT
ejpam-5154	86	1	let	let	VERB
ejpam-5154	86	2	g	g	PRON
ejpam-5154	86	3	be	be	AUX
ejpam-5154	86	4	a	a	DET
ejpam-5154	86	5	graph	graph	NOUN
ejpam-5154	86	6	.	.	PUNCT
ejpam-5154	87	1	then	then	ADV
ejpam-5154	87	2	(	(	PUNCT
ejpam-5154	87	3	i	i	NOUN
ejpam-5154	87	4	)	)	PUNCT
ejpam-5154	87	5	z	z	NOUN
ejpam-5154	87	6	(	(	PUNCT
ejpam-5154	87	7	g	g	NOUN
ejpam-5154	87	8	)	)	PUNCT
ejpam-5154	87	9	≤	≤	NOUN
ejpam-5154	87	10	γz(g	γz(g	PUNCT
ejpam-5154	87	11	)	)	PUNCT
ejpam-5154	87	12	;	;	PUNCT
ejpam-5154	87	13	(	(	PUNCT
ejpam-5154	87	14	ii	ii	NOUN
ejpam-5154	87	15	)	)	PUNCT
ejpam-5154	87	16	γ	γ	PROPN
ejpam-5154	87	17	(	(	PUNCT
ejpam-5154	87	18	g	g	NOUN
ejpam-5154	87	19	)	)	PUNCT
ejpam-5154	87	20	≤	≤	NOUN
ejpam-5154	87	21	γz(g	γz(g	PUNCT
ejpam-5154	87	22	)	)	PUNCT
ejpam-5154	87	23	;	;	PUNCT
ejpam-5154	87	24	and	and	CCONJ
ejpam-5154	87	25	(	(	PUNCT
ejpam-5154	87	26	iii	iii	X
ejpam-5154	87	27	)	)	PUNCT
ejpam-5154	87	28	1	1	NUM
ejpam-5154	87	29	≤	≤	NUM
ejpam-5154	87	30	γz	γz	ADP
ejpam-5154	87	31	(	(	PUNCT
ejpam-5154	87	32	g	g	NOUN
ejpam-5154	87	33	)	)	PUNCT
ejpam-5154	87	34	≤	≤	NOUN
ejpam-5154	87	35	|v	|v	X
ejpam-5154	87	36	(	(	PUNCT
ejpam-5154	87	37	g	g	NOUN
ejpam-5154	87	38	)	)	PUNCT
ejpam-5154	87	39	|	|	ADV
ejpam-5154	87	40	.	.	PUNCT
ejpam-5154	88	1	proof	proof	NOUN
ejpam-5154	88	2	.	.	PUNCT
ejpam-5154	89	1	(	(	PUNCT
ejpam-5154	89	2	i	i	NOUN
ejpam-5154	89	3	)	)	PUNCT
ejpam-5154	89	4	let	let	VERB
ejpam-5154	89	5	g	g	NOUN
ejpam-5154	89	6	be	be	AUX
ejpam-5154	89	7	a	a	DET
ejpam-5154	89	8	graph	graph	NOUN
ejpam-5154	89	9	and	and	CCONJ
ejpam-5154	89	10	let	let	VERB
ejpam-5154	89	11	q	q	PART
ejpam-5154	89	12	be	be	AUX
ejpam-5154	89	13	a	a	DET
ejpam-5154	89	14	minimum	minimum	ADJ
ejpam-5154	89	15	zero	zero	NUM
ejpam-5154	89	16	forcing	force	VERB
ejpam-5154	89	17	dominating	dominating	NOUN
ejpam-5154	89	18	set	set	NOUN
ejpam-5154	89	19	of	of	ADP
ejpam-5154	89	20	g.	g.	PROPN
ejpam-5154	90	1	then	then	ADV
ejpam-5154	90	2	q	q	X
ejpam-5154	90	3	is	be	AUX
ejpam-5154	90	4	a	a	DET
ejpam-5154	90	5	zero	zero	NUM
ejpam-5154	90	6	forcing	force	VERB
ejpam-5154	90	7	set	set	NOUN
ejpam-5154	90	8	of	of	ADP
ejpam-5154	90	9	g.	g.	PROPN
ejpam-5154	90	10	since	since	SCONJ
ejpam-5154	90	11	z(g	z(g	NOUN
ejpam-5154	90	12	)	)	PUNCT
ejpam-5154	90	13	is	be	AUX
ejpam-5154	90	14	the	the	DET
ejpam-5154	90	15	minimum	minimum	ADJ
ejpam-5154	90	16	cardinality	cardinality	NOUN
ejpam-5154	90	17	of	of	ADP
ejpam-5154	90	18	a	a	DET
ejpam-5154	90	19	zero	zero	NUM
ejpam-5154	90	20	forcing	force	VERB
ejpam-5154	90	21	set	set	NOUN
ejpam-5154	90	22	of	of	ADP
ejpam-5154	90	23	g	g	NOUN
ejpam-5154	90	24	,	,	PUNCT
ejpam-5154	90	25	it	it	PRON
ejpam-5154	90	26	follows	follow	VERB
ejpam-5154	90	27	that	that	SCONJ
ejpam-5154	90	28	γz	γz	INTJ
ejpam-5154	90	29	(	(	PUNCT
ejpam-5154	90	30	g	g	NOUN
ejpam-5154	90	31	)	)	PUNCT
ejpam-5154	90	32	=	=	SYM
ejpam-5154	91	1	|q|	|q|	VERB
ejpam-5154	91	2	≥	≥	NOUN
ejpam-5154	91	3	z(g	z(g	NOUN
ejpam-5154	91	4	)	)	PUNCT
ejpam-5154	91	5	.	.	PUNCT
ejpam-5154	92	1	(	(	PUNCT
ejpam-5154	92	2	ii	ii	NOUN
ejpam-5154	92	3	)	)	PUNCT
ejpam-5154	92	4	let	let	VERB
ejpam-5154	92	5	q1	q1	NOUN
ejpam-5154	92	6	be	be	AUX
ejpam-5154	92	7	minimum	minimum	ADJ
ejpam-5154	92	8	zero	zero	NUM
ejpam-5154	92	9	forcing	force	VERB
ejpam-5154	92	10	domination	domination	NOUN
ejpam-5154	92	11	of	of	ADP
ejpam-5154	92	12	g.	g.	PROPN
ejpam-5154	92	13	then	then	ADV
ejpam-5154	92	14	q1	q1	PROPN
ejpam-5154	92	15	is	be	AUX
ejpam-5154	92	16	a	a	DET
ejpam-5154	92	17	dominating	dominating	NOUN
ejpam-5154	92	18	set	set	NOUN
ejpam-5154	92	19	of	of	ADP
ejpam-5154	92	20	g.	g.	PROPN
ejpam-5154	92	21	since	since	SCONJ
ejpam-5154	92	22	γ	γ	X
ejpam-5154	92	23	(	(	PUNCT
ejpam-5154	92	24	g	g	NOUN
ejpam-5154	92	25	)	)	PUNCT
ejpam-5154	92	26	is	be	AUX
ejpam-5154	92	27	the	the	DET
ejpam-5154	92	28	minimum	minimum	ADJ
ejpam-5154	92	29	cardinality	cardinality	NOUN
ejpam-5154	92	30	of	of	ADP
ejpam-5154	92	31	a	a	DET
ejpam-5154	92	32	dominating	dominating	NOUN
ejpam-5154	92	33	set	set	NOUN
ejpam-5154	92	34	of	of	ADP
ejpam-5154	92	35	g	g	PROPN
ejpam-5154	92	36	,	,	PUNCT
ejpam-5154	92	37	we	we	PRON
ejpam-5154	92	38	have	have	AUX
ejpam-5154	92	39	γz	γz	NUM
ejpam-5154	92	40	(	(	PUNCT
ejpam-5154	92	41	g	g	NOUN
ejpam-5154	92	42	)	)	PUNCT
ejpam-5154	93	1	=	=	AUX
ejpam-5154	93	2	|q1|	|q1|	ADV
ejpam-5154	93	3	≥	≥	NUM
ejpam-5154	93	4	γ	γ	X
ejpam-5154	93	5	(	(	PUNCT
ejpam-5154	93	6	g	g	NOUN
ejpam-5154	93	7	)	)	PUNCT
ejpam-5154	93	8	.	.	PUNCT
ejpam-5154	94	1	(	(	PUNCT
ejpam-5154	94	2	iii	iii	X
ejpam-5154	94	3	)	)	PUNCT
ejpam-5154	94	4	since	since	SCONJ
ejpam-5154	94	5	γ	γ	X
ejpam-5154	94	6	(	(	PUNCT
ejpam-5154	94	7	g	g	NOUN
ejpam-5154	94	8	)	)	PUNCT
ejpam-5154	94	9	≥	≥	NOUN
ejpam-5154	94	10	1	1	NUM
ejpam-5154	94	11	for	for	ADP
ejpam-5154	94	12	any	any	DET
ejpam-5154	94	13	graph	graph	NOUN
ejpam-5154	94	14	g	g	NOUN
ejpam-5154	94	15	,	,	PUNCT
ejpam-5154	94	16	by	by	ADP
ejpam-5154	94	17	(	(	PUNCT
ejpam-5154	94	18	ii	ii	NOUN
ejpam-5154	94	19	)	)	PUNCT
ejpam-5154	94	20	,	,	PUNCT
ejpam-5154	94	21	γz	γz	PROPN
ejpam-5154	94	22	(	(	PUNCT
ejpam-5154	94	23	g	g	NOUN
ejpam-5154	94	24	)	)	PUNCT
ejpam-5154	94	25	≥	≥	NOUN
ejpam-5154	94	26	1	1	NUM
ejpam-5154	94	27	.	.	PUNCT
ejpam-5154	94	28	sine	sine	VERB
ejpam-5154	94	29	every	every	DET
ejpam-5154	94	30	zero	zero	NUM
ejpam-5154	94	31	forcing	force	VERB
ejpam-5154	94	32	dominating	dominating	NOUN
ejpam-5154	94	33	set	set	NOUN
ejpam-5154	94	34	p	p	NOUN
ejpam-5154	94	35	is	be	AUX
ejpam-5154	94	36	always	always	ADV
ejpam-5154	94	37	a	a	DET
ejpam-5154	94	38	subset	subset	NOUN
ejpam-5154	94	39	of	of	ADP
ejpam-5154	94	40	a	a	DET
ejpam-5154	94	41	vertex	vertex	NOUN
ejpam-5154	94	42	-	-	PUNCT
ejpam-5154	94	43	set	set	VERB
ejpam-5154	94	44	v	v	NOUN
ejpam-5154	94	45	(	(	PUNCT
ejpam-5154	94	46	g	g	NOUN
ejpam-5154	94	47	)	)	PUNCT
ejpam-5154	94	48	,	,	PUNCT
ejpam-5154	94	49	we	we	PRON
ejpam-5154	94	50	have	have	VERB
ejpam-5154	94	51	γz	γz	NUM
ejpam-5154	94	52	(	(	PUNCT
ejpam-5154	94	53	g	g	NOUN
ejpam-5154	94	54	)	)	PUNCT
ejpam-5154	94	55	≤	≤	NOUN
ejpam-5154	95	1	|v	|v	X
ejpam-5154	95	2	(	(	PUNCT
ejpam-5154	95	3	g	g	NOUN
ejpam-5154	95	4	)	)	PUNCT
ejpam-5154	95	5	|	|	ADV
ejpam-5154	95	6	.	.	PUNCT
ejpam-5154	96	1	therefore	therefore	ADV
ejpam-5154	96	2	,	,	PUNCT
ejpam-5154	96	3	1	1	NUM
ejpam-5154	96	4	≤	≤	NUM
ejpam-5154	96	5	γz	γz	ADP
ejpam-5154	96	6	(	(	PUNCT
ejpam-5154	96	7	g	g	NOUN
ejpam-5154	96	8	)	)	PUNCT
ejpam-5154	96	9	≤	≤	NOUN
ejpam-5154	96	10	|v	|v	X
ejpam-5154	96	11	(	(	PUNCT
ejpam-5154	96	12	g	g	NOUN
ejpam-5154	96	13	)	)	PUNCT
ejpam-5154	96	14	|	|	ADV
ejpam-5154	96	15	.	.	PUNCT
ejpam-5154	97	1	lemma	lemma	PROPN
ejpam-5154	97	2	1	1	X
ejpam-5154	97	3	.	.	PUNCT
ejpam-5154	98	1	let	let	VERB
ejpam-5154	98	2	g	g	NOUN
ejpam-5154	98	3	be	be	AUX
ejpam-5154	98	4	graph	graph	NOUN
ejpam-5154	98	5	.	.	PUNCT
ejpam-5154	99	1	then	then	ADV
ejpam-5154	99	2	z	z	PROPN
ejpam-5154	99	3	(	(	PUNCT
ejpam-5154	99	4	g	g	NOUN
ejpam-5154	99	5	)	)	PUNCT
ejpam-5154	99	6	=	=	SYM
ejpam-5154	99	7	1	1	NUM
ejpam-5154	99	8	if	if	SCONJ
ejpam-5154	99	9	and	and	CCONJ
ejpam-5154	99	10	only	only	ADV
ejpam-5154	99	11	if	if	SCONJ
ejpam-5154	99	12	g	g	PROPN
ejpam-5154	99	13	=	=	PUNCT
ejpam-5154	99	14	pn	pn	PROPN
ejpam-5154	99	15	for	for	ADP
ejpam-5154	99	16	all	all	DET
ejpam-5154	99	17	n	n	PRON
ejpam-5154	99	18	≥	≥	NUM
ejpam-5154	99	19	1	1	NUM
ejpam-5154	99	20	.	.	PUNCT
ejpam-5154	99	21	theorem	theorem	NOUN
ejpam-5154	99	22	1	1	NUM
ejpam-5154	99	23	.	.	PUNCT
ejpam-5154	100	1	let	let	VERB
ejpam-5154	100	2	g	g	PRON
ejpam-5154	100	3	be	be	AUX
ejpam-5154	100	4	a	a	DET
ejpam-5154	100	5	graph	graph	NOUN
ejpam-5154	100	6	.	.	PUNCT
ejpam-5154	101	1	then	then	ADV
ejpam-5154	101	2	γz	γz	INTJ
ejpam-5154	101	3	(	(	PUNCT
ejpam-5154	101	4	g	g	NOUN
ejpam-5154	101	5	)	)	PUNCT
ejpam-5154	101	6	=	=	SYM
ejpam-5154	101	7	z	z	NOUN
ejpam-5154	101	8	(	(	PUNCT
ejpam-5154	101	9	g	g	NOUN
ejpam-5154	101	10	)	)	PUNCT
ejpam-5154	101	11	=	=	SYM
ejpam-5154	101	12	1	1	NUM
ejpam-5154	101	13	if	if	SCONJ
ejpam-5154	101	14	and	and	CCONJ
ejpam-5154	101	15	only	only	ADV
ejpam-5154	101	16	if	if	SCONJ
ejpam-5154	101	17	g	g	PROPN
ejpam-5154	101	18	=	=	PROPN
ejpam-5154	101	19	p1	p1	PROPN
ejpam-5154	101	20	or	or	CCONJ
ejpam-5154	101	21	g	g	NOUN
ejpam-5154	101	22	=	=	SYM
ejpam-5154	101	23	p	p	PROPN
ejpam-5154	101	24	2	2	NUM
ejpam-5154	101	25	.	.	PUNCT
ejpam-5154	101	26	proof	proof	NOUN
ejpam-5154	101	27	.	.	PUNCT
ejpam-5154	102	1	suppose	suppose	VERB
ejpam-5154	102	2	that	that	SCONJ
ejpam-5154	102	3	γz	γz	INTJ
ejpam-5154	102	4	(	(	PUNCT
ejpam-5154	102	5	g	g	NOUN
ejpam-5154	102	6	)	)	PUNCT
ejpam-5154	102	7	=	=	SYM
ejpam-5154	102	8	z	z	NOUN
ejpam-5154	102	9	(	(	PUNCT
ejpam-5154	102	10	g	g	NOUN
ejpam-5154	102	11	)	)	PUNCT
ejpam-5154	102	12	=	=	SYM
ejpam-5154	103	1	1	1	X
ejpam-5154	103	2	.	.	PUNCT
ejpam-5154	103	3	then	then	ADV
ejpam-5154	103	4	by	by	ADP
ejpam-5154	103	5	lemma	lemma	PROPN
ejpam-5154	103	6	1	1	NUM
ejpam-5154	103	7	,	,	PUNCT
ejpam-5154	103	8	g	g	PROPN
ejpam-5154	103	9	=	=	SYM
ejpam-5154	103	10	pn	pn	X
ejpam-5154	103	11	∀	∀	X
ejpam-5154	103	12	n	n	PRON
ejpam-5154	103	13	≥	≥	NOUN
ejpam-5154	103	14	1	1	NUM
ejpam-5154	103	15	.	.	PUNCT
ejpam-5154	104	1	if	if	SCONJ
ejpam-5154	104	2	n	n	NUM
ejpam-5154	104	3	≥	≥	NOUN
ejpam-5154	104	4	4	4	NUM
ejpam-5154	104	5	,	,	PUNCT
ejpam-5154	104	6	then	then	ADV
ejpam-5154	104	7	γ	γ	PROPN
ejpam-5154	104	8	(	(	PUNCT
ejpam-5154	104	9	pn	pn	PROPN
ejpam-5154	104	10	)	)	PUNCT
ejpam-5154	104	11	≥	≥	NOUN
ejpam-5154	104	12	2	2	NUM
ejpam-5154	104	13	.	.	PUNCT
ejpam-5154	105	1	since	since	SCONJ
ejpam-5154	105	2	γz	γz	PROPN
ejpam-5154	105	3	(	(	PUNCT
ejpam-5154	105	4	g	g	NOUN
ejpam-5154	105	5	)	)	PUNCT
ejpam-5154	105	6	≥	≥	PROPN
ejpam-5154	105	7	γ	γ	PROPN
ejpam-5154	105	8	(	(	PUNCT
ejpam-5154	105	9	g)for	g)for	ADP
ejpam-5154	105	10	any	any	DET
ejpam-5154	105	11	graph	graph	NOUN
ejpam-5154	105	12	g	g	NOUN
ejpam-5154	105	13	,	,	PUNCT
ejpam-5154	105	14	γz	γz	PROPN
ejpam-5154	105	15	(	(	PUNCT
ejpam-5154	105	16	g	g	NOUN
ejpam-5154	105	17	)	)	PUNCT
ejpam-5154	105	18	≥	≥	NOUN
ejpam-5154	105	19	2	2	NUM
ejpam-5154	105	20	,	,	PUNCT
ejpam-5154	105	21	a	a	DET
ejpam-5154	105	22	contradiction	contradiction	NOUN
ejpam-5154	105	23	.	.	PUNCT
ejpam-5154	106	1	assume	assume	VERB
ejpam-5154	106	2	that	that	SCONJ
ejpam-5154	106	3	n	n	NOUN
ejpam-5154	106	4	=	=	SYM
ejpam-5154	106	5	3	3	X
ejpam-5154	106	6	.	.	PUNCT
ejpam-5154	107	1	let	let	VERB
ejpam-5154	107	2	v	v	NOUN
ejpam-5154	107	3	(	(	PUNCT
ejpam-5154	107	4	p3	p3	PROPN
ejpam-5154	107	5	)	)	PUNCT
ejpam-5154	108	1	=	=	PRON
ejpam-5154	108	2	{	{	PUNCT
ejpam-5154	108	3	a1	a1	PROPN
ejpam-5154	108	4	,	,	PUNCT
ejpam-5154	108	5	a2	a2	PROPN
ejpam-5154	108	6	,	,	PUNCT
ejpam-5154	108	7	a3	a3	NOUN
ejpam-5154	108	8	}	}	PUNCT
ejpam-5154	108	9	.	.	PUNCT
ejpam-5154	109	1	note	note	VERB
ejpam-5154	109	2	that	that	SCONJ
ejpam-5154	109	3	{	{	PUNCT
ejpam-5154	109	4	a2	a2	PROPN
ejpam-5154	109	5	}	}	PUNCT
ejpam-5154	109	6	is	be	AUX
ejpam-5154	109	7	a	a	DET
ejpam-5154	109	8	dominating	dominating	NOUN
ejpam-5154	109	9	but	but	CCONJ
ejpam-5154	109	10	not	not	PART
ejpam-5154	109	11	a	a	DET
ejpam-5154	109	12	zero	zero	NUM
ejpam-5154	109	13	forcing	force	VERB
ejpam-5154	109	14	set	set	NOUN
ejpam-5154	109	15	in	in	ADP
ejpam-5154	109	16	p3	p3	PROPN
ejpam-5154	109	17	and	and	CCONJ
ejpam-5154	109	18	{	{	PUNCT
ejpam-5154	109	19	a1	a1	NOUN
ejpam-5154	109	20	}	}	PUNCT
ejpam-5154	109	21	or	or	CCONJ
ejpam-5154	109	22	{	{	PUNCT
ejpam-5154	109	23	a3	a3	NOUN
ejpam-5154	109	24	}	}	PUNCT
ejpam-5154	109	25	is	be	AUX
ejpam-5154	109	26	a	a	DET
ejpam-5154	109	27	zero	zero	NUM
ejpam-5154	109	28	forcing	forcing	NOUN
ejpam-5154	109	29	but	but	CCONJ
ejpam-5154	109	30	not	not	PART
ejpam-5154	109	31	a	a	DET
ejpam-5154	109	32	dominating	dominating	NOUN
ejpam-5154	109	33	set	set	NOUN
ejpam-5154	109	34	in	in	ADP
ejpam-5154	109	35	p3	p3	PROPN
ejpam-5154	109	36	.	.	PUNCT
ejpam-5154	110	1	let	let	VERB
ejpam-5154	110	2	n	n	NOUN
ejpam-5154	110	3	=	=	SYM
ejpam-5154	110	4	{	{	PUNCT
ejpam-5154	110	5	a1	a1	PROPN
ejpam-5154	110	6	,	,	PUNCT
ejpam-5154	110	7	a2	a2	PROPN
ejpam-5154	110	8	}	}	PUNCT
ejpam-5154	110	9	.	.	PUNCT
ejpam-5154	111	1	then	then	ADV
ejpam-5154	111	2	n	n	PRON
ejpam-5154	111	3	is	be	AUX
ejpam-5154	111	4	a	a	DET
ejpam-5154	111	5	minimum	minimum	ADJ
ejpam-5154	111	6	zero	zero	NUM
ejpam-5154	111	7	forcing	force	VERB
ejpam-5154	111	8	dominating	dominating	NOUN
ejpam-5154	111	9	set	set	NOUN
ejpam-5154	111	10	p3	p3	PROPN
ejpam-5154	111	11	.	.	PUNCT
ejpam-5154	112	1	thus	thus	ADV
ejpam-5154	112	2	,	,	PUNCT
ejpam-5154	112	3	γz	γz	PROPN
ejpam-5154	112	4	(	(	PUNCT
ejpam-5154	112	5	p3	p3	PROPN
ejpam-5154	112	6	)	)	PUNCT
ejpam-5154	112	7	=	=	SYM
ejpam-5154	112	8	2	2	NUM
ejpam-5154	112	9	,	,	PUNCT
ejpam-5154	112	10	which	which	PRON
ejpam-5154	112	11	is	be	AUX
ejpam-5154	112	12	a	a	DET
ejpam-5154	112	13	contradiction	contradiction	NOUN
ejpam-5154	112	14	.	.	PUNCT
ejpam-5154	113	1	therefore	therefore	ADV
ejpam-5154	113	2	,	,	PUNCT
ejpam-5154	113	3	either	either	CCONJ
ejpam-5154	113	4	n	n	CCONJ
ejpam-5154	113	5	=	=	SYM
ejpam-5154	113	6	1	1	NUM
ejpam-5154	113	7	or	or	CCONJ
ejpam-5154	113	8	n	n	NOUN
ejpam-5154	113	9	=	=	SYM
ejpam-5154	113	10	2	2	NUM
ejpam-5154	113	11	,	,	PUNCT
ejpam-5154	113	12	that	that	PRON
ejpam-5154	113	13	is	be	AUX
ejpam-5154	113	14	g	g	NOUN
ejpam-5154	113	15	=	=	SYM
ejpam-5154	113	16	p1	p1	PROPN
ejpam-5154	113	17	or	or	CCONJ
ejpam-5154	113	18	g	g	NOUN
ejpam-5154	113	19	=	=	NOUN
ejpam-5154	113	20	p2	p2	NOUN
ejpam-5154	113	21	.	.	PUNCT
ejpam-5154	114	1	conversely	conversely	ADV
ejpam-5154	114	2	,	,	PUNCT
ejpam-5154	114	3	suppose	suppose	VERB
ejpam-5154	114	4	that	that	SCONJ
ejpam-5154	114	5	g	g	PROPN
ejpam-5154	114	6	=	=	PROPN
ejpam-5154	114	7	p1	p1	PROPN
ejpam-5154	114	8	.	.	PUNCT
ejpam-5154	115	1	then	then	ADV
ejpam-5154	115	2	γz	γz	INTJ
ejpam-5154	115	3	(	(	PUNCT
ejpam-5154	115	4	g	g	NOUN
ejpam-5154	115	5	)	)	PUNCT
ejpam-5154	115	6	=	=	SYM
ejpam-5154	115	7	1	1	NUM
ejpam-5154	115	8	=	=	SYM
ejpam-5154	115	9	z(p1	z(p1	NOUN
ejpam-5154	115	10	)	)	PUNCT
ejpam-5154	115	11	.	.	PUNCT
ejpam-5154	116	1	similarly	similarly	ADV
ejpam-5154	116	2	,	,	PUNCT
ejpam-5154	116	3	when	when	SCONJ
ejpam-5154	116	4	g	g	NOUN
ejpam-5154	116	5	=	=	NOUN
ejpam-5154	116	6	p2	p2	NOUN
ejpam-5154	116	7	,	,	PUNCT
ejpam-5154	116	8	then	then	ADV
ejpam-5154	116	9	γz	γz	INTJ
ejpam-5154	116	10	(	(	PUNCT
ejpam-5154	116	11	g	g	NOUN
ejpam-5154	116	12	)	)	PUNCT
ejpam-5154	116	13	=	=	SYM
ejpam-5154	116	14	1	1	NUM
ejpam-5154	116	15	=	=	SYM
ejpam-5154	116	16	z(p2	z(p2	NUM
ejpam-5154	116	17	)	)	PUNCT
ejpam-5154	116	18	.	.	PUNCT
ejpam-5154	116	19	theorem	theorem	NOUN
ejpam-5154	116	20	2	2	NUM
ejpam-5154	116	21	.	.	PUNCT
ejpam-5154	117	1	let	let	VERB
ejpam-5154	117	2	g	g	PRON
ejpam-5154	117	3	be	be	AUX
ejpam-5154	117	4	a	a	DET
ejpam-5154	117	5	graph	graph	NOUN
ejpam-5154	117	6	.	.	PUNCT
ejpam-5154	118	1	then	then	ADV
ejpam-5154	118	2	γz	γz	INTJ
ejpam-5154	118	3	(	(	PUNCT
ejpam-5154	118	4	g	g	NOUN
ejpam-5154	118	5	)	)	PUNCT
ejpam-5154	118	6	=	=	SYM
ejpam-5154	118	7	|v	|v	PROPN
ejpam-5154	118	8	(	(	PUNCT
ejpam-5154	118	9	g)|	g)|	NOUN
ejpam-5154	118	10	=	=	SYM
ejpam-5154	118	11	z	z	PROPN
ejpam-5154	118	12	(	(	PUNCT
ejpam-5154	118	13	g	g	NOUN
ejpam-5154	118	14	)	)	PUNCT
ejpam-5154	118	15	if	if	SCONJ
ejpam-5154	119	1	and	and	CCONJ
ejpam-5154	119	2	only	only	ADV
ejpam-5154	119	3	if	if	SCONJ
ejpam-5154	119	4	g	g	PROPN
ejpam-5154	119	5	=	=	PROPN
ejpam-5154	119	6	kn	kn	PROPN
ejpam-5154	119	7	.	.	PUNCT
ejpam-5154	120	1	j.	j.	PROPN
ejpam-5154	120	2	a.	a.	PROPN
ejpam-5154	120	3	hassan	hassan	PROPN
ejpam-5154	120	4	et	et	PROPN
ejpam-5154	120	5	al	al	PROPN
ejpam-5154	120	6	.	.	PUNCT
ejpam-5154	120	7	/	/	SYM
ejpam-5154	120	8	eur	eur	PROPN
ejpam-5154	120	9	.	.	PUNCT
ejpam-5154	121	1	j.	j.	PROPN
ejpam-5154	121	2	pure	pure	PROPN
ejpam-5154	121	3	appl	appl	PROPN
ejpam-5154	121	4	.	.	PROPN
ejpam-5154	121	5	math	math	PROPN
ejpam-5154	121	6	,	,	PUNCT
ejpam-5154	121	7	17	17	NUM
ejpam-5154	121	8	(	(	PUNCT
ejpam-5154	121	9	4	4	NUM
ejpam-5154	121	10	)	)	PUNCT
ejpam-5154	121	11	(	(	PUNCT
ejpam-5154	121	12	2024	2024	NUM
ejpam-5154	121	13	)	)	PUNCT
ejpam-5154	121	14	,	,	PUNCT
ejpam-5154	121	15	3772	3772	NUM
ejpam-5154	121	16	-	-	SYM
ejpam-5154	121	17	3780	3780	NUM
ejpam-5154	121	18	3777	3777	NUM
ejpam-5154	121	19	proof	proof	NOUN
ejpam-5154	121	20	.	.	PUNCT
ejpam-5154	121	21	suppose	suppose	VERB
ejpam-5154	121	22	that	that	SCONJ
ejpam-5154	121	23	γz	γz	INTJ
ejpam-5154	121	24	(	(	PUNCT
ejpam-5154	121	25	g	g	NOUN
ejpam-5154	121	26	)	)	PUNCT
ejpam-5154	121	27	=	=	SYM
ejpam-5154	121	28	|v	|v	PROPN
ejpam-5154	121	29	(	(	PUNCT
ejpam-5154	121	30	g)|	g)|	NOUN
ejpam-5154	121	31	=	=	SYM
ejpam-5154	121	32	z	z	PROPN
ejpam-5154	121	33	(	(	PUNCT
ejpam-5154	121	34	g	g	NOUN
ejpam-5154	121	35	)	)	PUNCT
ejpam-5154	121	36	.	.	PUNCT
ejpam-5154	122	1	then	then	ADV
ejpam-5154	122	2	v	v	X
ejpam-5154	122	3	(	(	PUNCT
ejpam-5154	122	4	g	g	NOUN
ejpam-5154	122	5	)	)	PUNCT
ejpam-5154	122	6	is	be	AUX
ejpam-5154	122	7	the	the	DET
ejpam-5154	122	8	minimum	minimum	ADJ
ejpam-5154	122	9	zero	zero	NUM
ejpam-5154	122	10	forcing	force	VERB
ejpam-5154	122	11	set	set	NOUN
ejpam-5154	122	12	of	of	ADP
ejpam-5154	122	13	g.	g.	PROPN
ejpam-5154	122	14	suppose	suppose	VERB
ejpam-5154	122	15	there	there	PRON
ejpam-5154	122	16	is	be	VERB
ejpam-5154	122	17	a	a	DET
ejpam-5154	122	18	component	component	NOUN
ejpam-5154	122	19	h	h	NOUN
ejpam-5154	122	20	of	of	ADP
ejpam-5154	122	21	g	g	NOUN
ejpam-5154	122	22	which	which	PRON
ejpam-5154	122	23	is	be	AUX
ejpam-5154	122	24	non	non	ADJ
ejpam-5154	122	25	-	-	ADJ
ejpam-5154	122	26	trivial	trivial	ADJ
ejpam-5154	122	27	.	.	PUNCT
ejpam-5154	123	1	let	let	VERB
ejpam-5154	123	2	v	v	X
ejpam-5154	123	3	(	(	PUNCT
ejpam-5154	123	4	h	h	NOUN
ejpam-5154	123	5	)	)	PUNCT
ejpam-5154	123	6	=	=	PRON
ejpam-5154	123	7	{	{	PUNCT
ejpam-5154	123	8	x1	x1	PROPN
ejpam-5154	123	9	,	,	PUNCT
ejpam-5154	123	10	.	.	PUNCT
ejpam-5154	123	11	.	.	PUNCT
ejpam-5154	124	1	.	.	PUNCT
ejpam-5154	125	1	,	,	PUNCT
ejpam-5154	125	2	xk	xk	PROPN
ejpam-5154	125	3	}	}	PUNCT
ejpam-5154	125	4	,	,	PUNCT
ejpam-5154	125	5	where	where	SCONJ
ejpam-5154	125	6	k	k	PROPN
ejpam-5154	125	7	≥	≥	NUM
ejpam-5154	125	8	2	2	NUM
ejpam-5154	125	9	.	.	PUNCT
ejpam-5154	125	10	then	then	ADV
ejpam-5154	125	11	v	v	X
ejpam-5154	125	12	(	(	PUNCT
ejpam-5154	125	13	g	g	NOUN
ejpam-5154	125	14	)	)	PUNCT
ejpam-5154	125	15	\	\	NOUN
ejpam-5154	125	16	{	{	PUNCT
ejpam-5154	125	17	x1	x1	PROPN
ejpam-5154	125	18	}	}	PUNCT
ejpam-5154	125	19	is	be	AUX
ejpam-5154	125	20	a	a	DET
ejpam-5154	125	21	zero	zero	NUM
ejpam-5154	125	22	forcing	force	VERB
ejpam-5154	125	23	set	set	NOUN
ejpam-5154	125	24	of	of	ADP
ejpam-5154	125	25	g.	g.	PROPN
ejpam-5154	125	26	thus	thus	ADV
ejpam-5154	125	27	,	,	PUNCT
ejpam-5154	125	28	z	z	PROPN
ejpam-5154	125	29	(	(	PUNCT
ejpam-5154	125	30	g	g	NOUN
ejpam-5154	125	31	)	)	PUNCT
ejpam-5154	125	32	≤	≤	NOUN
ejpam-5154	125	33	|v	|v	X
ejpam-5154	125	34	(	(	PUNCT
ejpam-5154	125	35	g)|	g)|	INTJ
ejpam-5154	125	36	−	−	PROPN
ejpam-5154	125	37	1	1	NUM
ejpam-5154	125	38	,	,	PUNCT
ejpam-5154	125	39	a	a	DET
ejpam-5154	125	40	contradiction	contradiction	NOUN
ejpam-5154	125	41	.	.	PUNCT
ejpam-5154	126	1	therefore	therefore	ADV
ejpam-5154	126	2	,	,	PUNCT
ejpam-5154	126	3	every	every	DET
ejpam-5154	126	4	component	component	NOUN
ejpam-5154	126	5	of	of	ADP
ejpam-5154	126	6	g	g	PROPN
ejpam-5154	126	7	is	be	AUX
ejpam-5154	126	8	trivial	trivial	ADJ
ejpam-5154	126	9	,	,	PUNCT
ejpam-5154	126	10	that	that	ADV
ejpam-5154	126	11	is	is	ADV
ejpam-5154	126	12	,	,	PUNCT
ejpam-5154	126	13	g	g	PROPN
ejpam-5154	126	14	=	=	SYM
ejpam-5154	126	15	kn	kn	PROPN
ejpam-5154	126	16	.	.	PUNCT
ejpam-5154	126	17	conversely	conversely	ADV
ejpam-5154	126	18	,	,	PUNCT
ejpam-5154	126	19	suppose	suppose	VERB
ejpam-5154	126	20	that	that	SCONJ
ejpam-5154	126	21	g	g	PROPN
ejpam-5154	126	22	=	=	PROPN
ejpam-5154	126	23	kn	kn	PROPN
ejpam-5154	126	24	.	.	PUNCT
ejpam-5154	127	1	then	then	ADV
ejpam-5154	127	2	v	v	X
ejpam-5154	127	3	(	(	PUNCT
ejpam-5154	127	4	g	g	NOUN
ejpam-5154	127	5	)	)	PUNCT
ejpam-5154	127	6	is	be	AUX
ejpam-5154	127	7	the	the	DET
ejpam-5154	127	8	minimum	minimum	ADJ
ejpam-5154	127	9	dominating	dominating	NOUN
ejpam-5154	127	10	set	set	NOUN
ejpam-5154	127	11	of	of	ADP
ejpam-5154	127	12	g	g	NOUN
ejpam-5154	127	13	,	,	PUNCT
ejpam-5154	127	14	and	and	CCONJ
ejpam-5154	127	15	so	so	ADV
ejpam-5154	127	16	γ	γ	X
ejpam-5154	127	17	(	(	PUNCT
ejpam-5154	127	18	g	g	NOUN
ejpam-5154	127	19	)	)	PUNCT
ejpam-5154	127	20	=	=	SYM
ejpam-5154	127	21	|v	|v	X
ejpam-5154	127	22	(	(	PUNCT
ejpam-5154	127	23	g	g	NOUN
ejpam-5154	127	24	)	)	PUNCT
ejpam-5154	127	25	|	|	INTJ
ejpam-5154	127	26	.	.	PUNCT
ejpam-5154	128	1	since	since	SCONJ
ejpam-5154	128	2	γz	γz	PROPN
ejpam-5154	128	3	(	(	PUNCT
ejpam-5154	128	4	g	g	NOUN
ejpam-5154	128	5	)	)	PUNCT
ejpam-5154	128	6	≥	≥	PROPN
ejpam-5154	128	7	γ	γ	X
ejpam-5154	128	8	(	(	PUNCT
ejpam-5154	128	9	g	g	PROPN
ejpam-5154	128	10	)	)	PUNCT
ejpam-5154	128	11	,	,	PUNCT
ejpam-5154	128	12	it	it	PRON
ejpam-5154	128	13	follows	follow	VERB
ejpam-5154	128	14	that	that	SCONJ
ejpam-5154	128	15	γz	γz	INTJ
ejpam-5154	128	16	(	(	PUNCT
ejpam-5154	128	17	g	g	NOUN
ejpam-5154	128	18	)	)	PUNCT
ejpam-5154	129	1	=	=	SYM
ejpam-5154	129	2	|v	|v	X
ejpam-5154	129	3	(	(	PUNCT
ejpam-5154	129	4	g	g	NOUN
ejpam-5154	129	5	)	)	PUNCT
ejpam-5154	129	6	|	|	ADV
ejpam-5154	129	7	.	.	PUNCT
ejpam-5154	130	1	clearly	clearly	ADV
ejpam-5154	130	2	,	,	PUNCT
ejpam-5154	130	3	v	v	X
ejpam-5154	130	4	(	(	PUNCT
ejpam-5154	130	5	g	g	NOUN
ejpam-5154	130	6	)	)	PUNCT
ejpam-5154	130	7	is	be	AUX
ejpam-5154	130	8	the	the	DET
ejpam-5154	130	9	only	only	ADJ
ejpam-5154	130	10	zero	zero	NUM
ejpam-5154	130	11	forcing	force	VERB
ejpam-5154	130	12	set	set	NOUN
ejpam-5154	130	13	of	of	ADP
ejpam-5154	130	14	g.	g.	PROPN
ejpam-5154	130	15	consequently	consequently	ADV
ejpam-5154	130	16	,	,	PUNCT
ejpam-5154	130	17	z	z	PROPN
ejpam-5154	130	18	(	(	PUNCT
ejpam-5154	130	19	g	g	NOUN
ejpam-5154	130	20	)	)	PUNCT
ejpam-5154	130	21	=	=	SYM
ejpam-5154	130	22	|v	|v	PROPN
ejpam-5154	130	23	(	(	PUNCT
ejpam-5154	130	24	g)|	g)|	NOUN
ejpam-5154	130	25	=	=	SYM
ejpam-5154	130	26	γz	γz	PROPN
ejpam-5154	130	27	(	(	PUNCT
ejpam-5154	130	28	g	g	NOUN
ejpam-5154	130	29	)	)	PUNCT
ejpam-5154	130	30	.	.	PUNCT
ejpam-5154	131	1	corollary	corollary	ADJ
ejpam-5154	131	2	1	1	NUM
ejpam-5154	131	3	.	.	PUNCT
ejpam-5154	132	1	let	let	VERB
ejpam-5154	132	2	g	g	PRON
ejpam-5154	132	3	be	be	AUX
ejpam-5154	132	4	a	a	DET
ejpam-5154	132	5	graph	graph	NOUN
ejpam-5154	132	6	.	.	PUNCT
ejpam-5154	133	1	then	then	ADV
ejpam-5154	133	2	γz	γz	INTJ
ejpam-5154	133	3	(	(	PUNCT
ejpam-5154	133	4	g	g	NOUN
ejpam-5154	133	5	)	)	PUNCT
ejpam-5154	133	6	≤	≤	NOUN
ejpam-5154	133	7	|v	|v	PROPN
ejpam-5154	133	8	(	(	PUNCT
ejpam-5154	133	9	g)|−1	g)|−1	NOUN
ejpam-5154	133	10	if	if	SCONJ
ejpam-5154	133	11	and	and	CCONJ
ejpam-5154	133	12	only	only	ADV
ejpam-5154	133	13	if	if	SCONJ
ejpam-5154	133	14	g	g	PROPN
ejpam-5154	133	15	has	have	VERB
ejpam-5154	133	16	non	non	ADJ
ejpam-5154	133	17	-	-	ADJ
ejpam-5154	133	18	trivial	trivial	ADJ
ejpam-5154	133	19	component	component	NOUN
ejpam-5154	133	20	.	.	PUNCT
ejpam-5154	134	1	theorem	theorem	NOUN
ejpam-5154	134	2	3	3	X
ejpam-5154	134	3	.	.	PUNCT
ejpam-5154	135	1	let	let	VERB
ejpam-5154	135	2	n	n	PRON
ejpam-5154	135	3	≥	≥	X
ejpam-5154	135	4	2	2	NUM
ejpam-5154	135	5	be	be	AUX
ejpam-5154	135	6	a	a	DET
ejpam-5154	135	7	positive	positive	ADJ
ejpam-5154	135	8	integer	integer	NOUN
ejpam-5154	135	9	and	and	CCONJ
ejpam-5154	135	10	let	let	VERB
ejpam-5154	135	11	s	s	PRON
ejpam-5154	135	12	be	be	AUX
ejpam-5154	135	13	a	a	DET
ejpam-5154	135	14	zero	zero	NUM
ejpam-5154	135	15	forcing	force	VERB
ejpam-5154	135	16	dominating	dominating	NOUN
ejpam-5154	135	17	set	set	NOUN
ejpam-5154	135	18	of	of	ADP
ejpam-5154	135	19	kn	kn	PROPN
ejpam-5154	135	20	.	.	PUNCT
ejpam-5154	136	1	then	then	ADV
ejpam-5154	136	2	s	s	VERB
ejpam-5154	136	3	is	be	AUX
ejpam-5154	136	4	a	a	DET
ejpam-5154	136	5	minimum	minimum	ADJ
ejpam-5154	136	6	zero	zero	NUM
ejpam-5154	136	7	forcing	force	VERB
ejpam-5154	136	8	dominating	dominating	NOUN
ejpam-5154	136	9	set	set	NOUN
ejpam-5154	136	10	of	of	ADP
ejpam-5154	136	11	kn	kn	PROPN
ejpam-5154	136	12	if	if	SCONJ
ejpam-5154	136	13	and	and	CCONJ
ejpam-5154	136	14	only	only	ADV
ejpam-5154	136	15	if	if	SCONJ
ejpam-5154	136	16	|s|	|s|	PROPN
ejpam-5154	136	17	=	=	SYM
ejpam-5154	136	18	n−	n−	NOUN
ejpam-5154	136	19	1	1	NUM
ejpam-5154	136	20	.	.	PUNCT
ejpam-5154	137	1	proof	proof	NOUN
ejpam-5154	137	2	.	.	PUNCT
ejpam-5154	138	1	let	let	VERB
ejpam-5154	138	2	s	s	PRON
ejpam-5154	138	3	be	be	AUX
ejpam-5154	138	4	a	a	DET
ejpam-5154	138	5	minimum	minimum	ADJ
ejpam-5154	138	6	zero	zero	NUM
ejpam-5154	138	7	forcing	force	VERB
ejpam-5154	138	8	dominating	dominating	NOUN
ejpam-5154	138	9	set	set	NOUN
ejpam-5154	138	10	of	of	ADP
ejpam-5154	138	11	kn	kn	PROPN
ejpam-5154	138	12	and	and	CCONJ
ejpam-5154	138	13	let	let	VERB
ejpam-5154	138	14	v	v	X
ejpam-5154	138	15	(	(	PUNCT
ejpam-5154	138	16	kn	kn	PROPN
ejpam-5154	138	17	)	)	PUNCT
ejpam-5154	138	18	=	=	SYM
ejpam-5154	138	19	{	{	PUNCT
ejpam-5154	138	20	v1	v1	PROPN
ejpam-5154	138	21	,	,	PUNCT
ejpam-5154	138	22	v2	v2	PROPN
ejpam-5154	138	23	,	,	PUNCT
ejpam-5154	138	24	.	.	PUNCT
ejpam-5154	138	25	.	.	PUNCT
ejpam-5154	139	1	.	.	PUNCT
ejpam-5154	140	1	,	,	PUNCT
ejpam-5154	140	2	vn	vn	PROPN
ejpam-5154	140	3	}	}	PUNCT
ejpam-5154	140	4	.	.	PUNCT
ejpam-5154	141	1	suppose	suppose	VERB
ejpam-5154	141	2	that	that	SCONJ
ejpam-5154	141	3	|s|	|s|	VERB
ejpam-5154	141	4	≤	≤	PROPN
ejpam-5154	141	5	n	n	CCONJ
ejpam-5154	141	6	−	−	PROPN
ejpam-5154	141	7	2	2	NUM
ejpam-5154	141	8	.	.	PUNCT
ejpam-5154	141	9	then	then	ADV
ejpam-5154	141	10	there	there	PRON
ejpam-5154	141	11	exist	exist	VERB
ejpam-5154	141	12	ui	ui	PROPN
ejpam-5154	141	13	,	,	PUNCT
ejpam-5154	141	14	uj	uj	PROPN
ejpam-5154	141	15	∈	∈	PROPN
ejpam-5154	141	16	v	v	PROPN
ejpam-5154	141	17	(	(	PUNCT
ejpam-5154	141	18	kn	kn	PROPN
ejpam-5154	141	19	)	)	PUNCT
ejpam-5154	141	20	such	such	ADJ
ejpam-5154	141	21	that	that	DET
ejpam-5154	141	22	ui	ui	PROPN
ejpam-5154	141	23	,	,	PUNCT
ejpam-5154	141	24	uj	uj	PROPN
ejpam-5154	141	25	/∈	/∈	PUNCT
ejpam-5154	141	26	s	s	PROPN
ejpam-5154	141	27	for	for	ADP
ejpam-5154	141	28	some	some	DET
ejpam-5154	141	29	i	i	PROPN
ejpam-5154	141	30	,	,	PUNCT
ejpam-5154	141	31	j	j	PROPN
ejpam-5154	141	32	∈	∈	PROPN
ejpam-5154	141	33	{	{	PUNCT
ejpam-5154	141	34	1	1	NUM
ejpam-5154	141	35	,	,	PUNCT
ejpam-5154	141	36	2	2	NUM
ejpam-5154	141	37	,	,	PUNCT
ejpam-5154	141	38	.	.	PUNCT
ejpam-5154	141	39	.	.	PUNCT
ejpam-5154	142	1	.	.	PUNCT
ejpam-5154	143	1	,	,	PUNCT
ejpam-5154	144	1	n	n	CCONJ
ejpam-5154	144	2	}	}	PUNCT
ejpam-5154	144	3	.	.	PUNCT
ejpam-5154	145	1	now	now	ADV
ejpam-5154	145	2	,	,	PUNCT
ejpam-5154	145	3	let	let	VERB
ejpam-5154	145	4	ut	ut	PROPN
ejpam-5154	145	5	∈	∈	PROPN
ejpam-5154	145	6	s	s	PROPN
ejpam-5154	145	7	,	,	PUNCT
ejpam-5154	145	8	where	where	SCONJ
ejpam-5154	145	9	t	t	PROPN
ejpam-5154	145	10	̸=	̸=	PROPN
ejpam-5154	145	11	i	i	PROPN
ejpam-5154	145	12	,	,	PUNCT
ejpam-5154	145	13	j.	j.	PROPN
ejpam-5154	145	14	since	since	SCONJ
ejpam-5154	145	15	the	the	DET
ejpam-5154	145	16	graph	graph	NOUN
ejpam-5154	145	17	is	be	AUX
ejpam-5154	145	18	complete	complete	ADJ
ejpam-5154	145	19	,	,	PUNCT
ejpam-5154	145	20	ut	ut	PROPN
ejpam-5154	145	21	is	be	AUX
ejpam-5154	145	22	adjacent	adjacent	ADJ
ejpam-5154	145	23	to	to	ADP
ejpam-5154	145	24	both	both	DET
ejpam-5154	145	25	ui	ui	PROPN
ejpam-5154	145	26	and	and	CCONJ
ejpam-5154	145	27	uj	uj	PROPN
ejpam-5154	145	28	.	.	PUNCT
ejpam-5154	146	1	thus	thus	ADV
ejpam-5154	146	2	,	,	PUNCT
ejpam-5154	146	3	ut	ut	PROPN
ejpam-5154	146	4	can	can	AUX
ejpam-5154	146	5	not	not	PART
ejpam-5154	146	6	force	force	VERB
ejpam-5154	146	7	either	either	CCONJ
ejpam-5154	146	8	ui	ui	PROPN
ejpam-5154	146	9	or	or	CCONJ
ejpam-5154	146	10	uj	uj	PROPN
ejpam-5154	146	11	.	.	PUNCT
ejpam-5154	147	1	since	since	SCONJ
ejpam-5154	147	2	ut	ut	PROPN
ejpam-5154	147	3	is	be	AUX
ejpam-5154	147	4	arbitrary	arbitrary	ADJ
ejpam-5154	147	5	,	,	PUNCT
ejpam-5154	147	6	it	it	PRON
ejpam-5154	147	7	follows	follow	VERB
ejpam-5154	147	8	that	that	SCONJ
ejpam-5154	147	9	s	s	VERB
ejpam-5154	147	10	is	be	AUX
ejpam-5154	147	11	not	not	PART
ejpam-5154	147	12	a	a	DET
ejpam-5154	147	13	zero	zero	NUM
ejpam-5154	147	14	forcing	force	VERB
ejpam-5154	147	15	set	set	NOUN
ejpam-5154	147	16	of	of	ADP
ejpam-5154	147	17	kn	kn	PROPN
ejpam-5154	147	18	,	,	PUNCT
ejpam-5154	147	19	which	which	PRON
ejpam-5154	147	20	is	be	AUX
ejpam-5154	147	21	a	a	DET
ejpam-5154	147	22	contradiction	contradiction	NOUN
ejpam-5154	147	23	.	.	PUNCT
ejpam-5154	148	1	therefore	therefore	ADV
ejpam-5154	148	2	,	,	PUNCT
ejpam-5154	148	3	|s|	|s|	X
ejpam-5154	148	4	≥	≥	NOUN
ejpam-5154	148	5	n−1	n−1	PROPN
ejpam-5154	148	6	.	.	PUNCT
ejpam-5154	149	1	since	since	SCONJ
ejpam-5154	149	2	s	s	PART
ejpam-5154	149	3	=	=	SYM
ejpam-5154	149	4	v	v	PROPN
ejpam-5154	149	5	(	(	PUNCT
ejpam-5154	149	6	kn)\{vk	kn)\{vk	NOUN
ejpam-5154	149	7	}	}	PUNCT
ejpam-5154	149	8	is	be	AUX
ejpam-5154	149	9	a	a	DET
ejpam-5154	149	10	zero	zero	NUM
ejpam-5154	149	11	forcing	force	VERB
ejpam-5154	149	12	dominating	dominating	NOUN
ejpam-5154	149	13	set	set	NOUN
ejpam-5154	149	14	of	of	ADP
ejpam-5154	149	15	kn	kn	PROPN
ejpam-5154	149	16	for	for	ADP
ejpam-5154	149	17	some	some	DET
ejpam-5154	149	18	k	k	PROPN
ejpam-5154	149	19	∈	∈	PROPN
ejpam-5154	149	20	{	{	PUNCT
ejpam-5154	149	21	1	1	NUM
ejpam-5154	149	22	,	,	PUNCT
ejpam-5154	149	23	2	2	NUM
ejpam-5154	149	24	,	,	PUNCT
ejpam-5154	149	25	.	.	PUNCT
ejpam-5154	149	26	.	.	PUNCT
ejpam-5154	150	1	.	.	PUNCT
ejpam-5154	151	1	,	,	PUNCT
ejpam-5154	151	2	n	n	CCONJ
ejpam-5154	151	3	}	}	PUNCT
ejpam-5154	151	4	,	,	PUNCT
ejpam-5154	151	5	the	the	DET
ejpam-5154	151	6	assertion	assertion	NOUN
ejpam-5154	151	7	follows	follow	VERB
ejpam-5154	151	8	.	.	PUNCT
ejpam-5154	152	1	conversely	conversely	ADV
ejpam-5154	152	2	,	,	PUNCT
ejpam-5154	152	3	suppose	suppose	VERB
ejpam-5154	152	4	that	that	SCONJ
ejpam-5154	152	5	|s|	|s|	PROPN
ejpam-5154	152	6	=	=	SYM
ejpam-5154	152	7	n−1	n−1	PROPN
ejpam-5154	152	8	,	,	PUNCT
ejpam-5154	152	9	say	say	VERB
ejpam-5154	152	10	s	s	VERB
ejpam-5154	152	11	=	=	SYM
ejpam-5154	152	12	v	v	PROPN
ejpam-5154	152	13	(	(	PUNCT
ejpam-5154	152	14	kn)\{vi	kn)\{vi	NOUN
ejpam-5154	152	15	}	}	PUNCT
ejpam-5154	152	16	for	for	ADP
ejpam-5154	152	17	some	some	DET
ejpam-5154	152	18	i	i	PRON
ejpam-5154	152	19	∈	∈	PROPN
ejpam-5154	152	20	{	{	PUNCT
ejpam-5154	152	21	1	1	NUM
ejpam-5154	152	22	,	,	PUNCT
ejpam-5154	152	23	2	2	NUM
ejpam-5154	152	24	,	,	PUNCT
ejpam-5154	152	25	.	.	PUNCT
ejpam-5154	152	26	.	.	PUNCT
ejpam-5154	153	1	.	.	PUNCT
ejpam-5154	153	2	,	,	PUNCT
ejpam-5154	153	3	n	n	CCONJ
ejpam-5154	153	4	}	}	PUNCT
ejpam-5154	153	5	.	.	PUNCT
ejpam-5154	154	1	then	then	ADV
ejpam-5154	154	2	s	s	VERB
ejpam-5154	154	3	is	be	AUX
ejpam-5154	154	4	a	a	DET
ejpam-5154	154	5	zero	zero	NUM
ejpam-5154	154	6	forcing	force	VERB
ejpam-5154	154	7	dominating	dominating	NOUN
ejpam-5154	154	8	set	set	NOUN
ejpam-5154	154	9	of	of	ADP
ejpam-5154	154	10	kn	kn	PROPN
ejpam-5154	154	11	.	.	PUNCT
ejpam-5154	155	1	if	if	SCONJ
ejpam-5154	155	2	s	s	VERB
ejpam-5154	155	3	is	be	AUX
ejpam-5154	155	4	not	not	PART
ejpam-5154	155	5	the	the	DET
ejpam-5154	155	6	minimum	minimum	NOUN
ejpam-5154	155	7	,	,	PUNCT
ejpam-5154	155	8	then	then	ADV
ejpam-5154	155	9	there	there	PRON
ejpam-5154	155	10	exists	exist	VERB
ejpam-5154	155	11	t	t	PROPN
ejpam-5154	155	12	⊂	⊂	PROPN
ejpam-5154	155	13	s	s	PART
ejpam-5154	155	14	⊂	⊂	X
ejpam-5154	155	15	v	v	X
ejpam-5154	155	16	(	(	PUNCT
ejpam-5154	155	17	kn	kn	PROPN
ejpam-5154	155	18	)	)	PUNCT
ejpam-5154	155	19	such	such	ADJ
ejpam-5154	155	20	that	that	SCONJ
ejpam-5154	155	21	t	t	PROPN
ejpam-5154	155	22	is	be	AUX
ejpam-5154	155	23	a	a	DET
ejpam-5154	155	24	zero	zero	NUM
ejpam-5154	155	25	forcing	force	VERB
ejpam-5154	155	26	dominating	dominating	NOUN
ejpam-5154	155	27	set	set	NOUN
ejpam-5154	155	28	of	of	ADP
ejpam-5154	155	29	kn	kn	PROPN
ejpam-5154	155	30	.	.	PUNCT
ejpam-5154	156	1	let	let	VERB
ejpam-5154	156	2	vs	vs	ADP
ejpam-5154	156	3	,	,	PUNCT
ejpam-5154	156	4	vt	vt	PROPN
ejpam-5154	156	5	∈	∈	PROPN
ejpam-5154	156	6	v	v	PROPN
ejpam-5154	156	7	(	(	PUNCT
ejpam-5154	156	8	kn	kn	PROPN
ejpam-5154	156	9	)	)	PUNCT
ejpam-5154	156	10	such	such	ADJ
ejpam-5154	156	11	that	that	PRON
ejpam-5154	156	12	vs	vs	ADP
ejpam-5154	156	13	,	,	PUNCT
ejpam-5154	156	14	vt	vt	PROPN
ejpam-5154	156	15	/∈	/∈	PROPN
ejpam-5154	156	16	t	t	PROPN
ejpam-5154	156	17	.	.	PUNCT
ejpam-5154	157	1	then	then	ADV
ejpam-5154	157	2	any	any	DET
ejpam-5154	157	3	element	element	NOUN
ejpam-5154	157	4	of	of	ADP
ejpam-5154	157	5	t	t	PROPN
ejpam-5154	157	6	can	can	AUX
ejpam-5154	157	7	not	not	PART
ejpam-5154	157	8	force	force	VERB
ejpam-5154	157	9	either	either	CCONJ
ejpam-5154	157	10	vs	vs	ADP
ejpam-5154	157	11	or	or	CCONJ
ejpam-5154	157	12	vt	vt	PROPN
ejpam-5154	157	13	,	,	PUNCT
ejpam-5154	157	14	a	a	DET
ejpam-5154	157	15	contradiction	contradiction	NOUN
ejpam-5154	157	16	.	.	PUNCT
ejpam-5154	158	1	hence	hence	ADV
ejpam-5154	158	2	,	,	PUNCT
ejpam-5154	158	3	s	s	VERB
ejpam-5154	158	4	must	must	AUX
ejpam-5154	158	5	be	be	AUX
ejpam-5154	158	6	a	a	DET
ejpam-5154	158	7	minimum	minimum	ADJ
ejpam-5154	158	8	zero	zero	NUM
ejpam-5154	158	9	forcing	force	VERB
ejpam-5154	158	10	dominating	dominating	NOUN
ejpam-5154	158	11	set	set	NOUN
ejpam-5154	158	12	of	of	ADP
ejpam-5154	158	13	kn	kn	PROPN
ejpam-5154	158	14	.	.	PUNCT
ejpam-5154	158	15	corollary	corollary	ADJ
ejpam-5154	159	1	2	2	NUM
ejpam-5154	159	2	.	.	PUNCT
ejpam-5154	160	1	let	let	VERB
ejpam-5154	160	2	m	m	PRON
ejpam-5154	160	3	be	be	AUX
ejpam-5154	160	4	a	a	DET
ejpam-5154	160	5	positive	positive	ADJ
ejpam-5154	160	6	integer	integer	NOUN
ejpam-5154	160	7	.	.	PUNCT
ejpam-5154	161	1	then	then	ADV
ejpam-5154	161	2	γz	γz	INTJ
ejpam-5154	161	3	(	(	PUNCT
ejpam-5154	161	4	km	km	PROPN
ejpam-5154	161	5	)	)	PUNCT
ejpam-5154	161	6	=	=	PRON
ejpam-5154	161	7	{	{	PUNCT
ejpam-5154	161	8	1	1	NUM
ejpam-5154	161	9	,	,	PUNCT
ejpam-5154	161	10	if	if	SCONJ
ejpam-5154	161	11	m	m	ADV
ejpam-5154	161	12	=	=	SYM
ejpam-5154	161	13	1	1	NUM
ejpam-5154	161	14	m−	m−	PROPN
ejpam-5154	161	15	1	1	NUM
ejpam-5154	161	16	,	,	PUNCT
ejpam-5154	161	17	if	if	SCONJ
ejpam-5154	161	18	m	m	PROPN
ejpam-5154	161	19	≥	≥	NOUN
ejpam-5154	161	20	2	2	NUM
ejpam-5154	161	21	.	.	PUNCT
ejpam-5154	161	22	theorem	theorem	NOUN
ejpam-5154	161	23	4	4	NUM
ejpam-5154	161	24	.	.	PUNCT
ejpam-5154	162	1	let	let	VERB
ejpam-5154	162	2	g	g	NOUN
ejpam-5154	162	3	and	and	CCONJ
ejpam-5154	162	4	h	h	NOUN
ejpam-5154	162	5	be	be	VERB
ejpam-5154	162	6	two	two	NUM
ejpam-5154	162	7	non	non	ADJ
ejpam-5154	162	8	-	-	ADJ
ejpam-5154	162	9	complete	complete	ADJ
ejpam-5154	162	10	graphs	graph	NOUN
ejpam-5154	162	11	.	.	PUNCT
ejpam-5154	163	1	then	then	ADV
ejpam-5154	163	2	q	q	X
ejpam-5154	163	3	⊆	⊆	NUM
ejpam-5154	163	4	v	v	NOUN
ejpam-5154	163	5	(	(	PUNCT
ejpam-5154	163	6	g	g	PROPN
ejpam-5154	163	7	+	+	NOUN
ejpam-5154	163	8	h	h	NOUN
ejpam-5154	163	9	)	)	PUNCT
ejpam-5154	163	10	is	be	AUX
ejpam-5154	163	11	a	a	DET
ejpam-5154	163	12	zero	zero	NUM
ejpam-5154	163	13	forcing	force	VERB
ejpam-5154	163	14	dominating	dominating	NOUN
ejpam-5154	163	15	set	set	VERB
ejpam-5154	163	16	in	in	ADP
ejpam-5154	163	17	g	g	PROPN
ejpam-5154	164	1	+	+	NOUN
ejpam-5154	164	2	h	h	NOUN
ejpam-5154	164	3	if	if	SCONJ
ejpam-5154	164	4	and	and	CCONJ
ejpam-5154	164	5	only	only	ADV
ejpam-5154	164	6	if	if	SCONJ
ejpam-5154	164	7	q	q	PROPN
ejpam-5154	164	8	=	=	SYM
ejpam-5154	164	9	qg	qg	PROPN
ejpam-5154	164	10	∪	∪	PROPN
ejpam-5154	164	11	qh	qh	PROPN
ejpam-5154	164	12	and	and	CCONJ
ejpam-5154	164	13	satisfies	satisfy	VERB
ejpam-5154	164	14	one	one	NUM
ejpam-5154	164	15	of	of	ADP
ejpam-5154	164	16	the	the	DET
ejpam-5154	164	17	following	following	NOUN
ejpam-5154	164	18	:	:	PUNCT
ejpam-5154	164	19	(	(	PUNCT
ejpam-5154	164	20	i	i	NOUN
ejpam-5154	164	21	)	)	PUNCT
ejpam-5154	164	22	qg	qg	PROPN
ejpam-5154	164	23	=	=	SYM
ejpam-5154	164	24	v	v	PROPN
ejpam-5154	164	25	(	(	PUNCT
ejpam-5154	164	26	g	g	NOUN
ejpam-5154	164	27	)	)	PUNCT
ejpam-5154	164	28	and	and	CCONJ
ejpam-5154	164	29	qh	qh	NOUN
ejpam-5154	164	30	is	be	AUX
ejpam-5154	164	31	a	a	DET
ejpam-5154	164	32	zero	zero	NUM
ejpam-5154	164	33	forcing	force	VERB
ejpam-5154	164	34	set	set	NOUN
ejpam-5154	164	35	of	of	ADP
ejpam-5154	164	36	h.	h.	PROPN
ejpam-5154	164	37	(	(	PUNCT
ejpam-5154	164	38	ii	ii	PROPN
ejpam-5154	164	39	)	)	PUNCT
ejpam-5154	164	40	qh	qh	NOUN
ejpam-5154	164	41	=	=	NOUN
ejpam-5154	164	42	v	v	PROPN
ejpam-5154	164	43	(	(	PUNCT
ejpam-5154	164	44	h	h	NOUN
ejpam-5154	164	45	)	)	PUNCT
ejpam-5154	165	1	and	and	CCONJ
ejpam-5154	165	2	qg	qg	PROPN
ejpam-5154	165	3	is	be	AUX
ejpam-5154	165	4	a	a	DET
ejpam-5154	165	5	zero	zero	NUM
ejpam-5154	165	6	forcing	force	VERB
ejpam-5154	165	7	set	set	NOUN
ejpam-5154	165	8	of	of	ADP
ejpam-5154	165	9	g.	g.	PROPN
ejpam-5154	165	10	(	(	PUNCT
ejpam-5154	165	11	iii	iii	PROPN
ejpam-5154	165	12	)	)	PUNCT
ejpam-5154	165	13	qg	qg	PROPN
ejpam-5154	165	14	=	=	SYM
ejpam-5154	165	15	v	v	PROPN
ejpam-5154	165	16	(	(	PUNCT
ejpam-5154	165	17	g)\{x	g)\{x	PROPN
ejpam-5154	165	18	}	}	PUNCT
ejpam-5154	165	19	and	and	CCONJ
ejpam-5154	165	20	qh	qh	NOUN
ejpam-5154	165	21	is	be	AUX
ejpam-5154	165	22	a	a	DET
ejpam-5154	165	23	zero	zero	NUM
ejpam-5154	165	24	forcing	force	VERB
ejpam-5154	165	25	set	set	NOUN
ejpam-5154	165	26	of	of	ADP
ejpam-5154	165	27	h	h	PROPN
ejpam-5154	165	28	with	with	ADP
ejpam-5154	165	29	nh	nh	PROPN
ejpam-5154	166	1	[	[	X
ejpam-5154	166	2	y]∩	y]∩	NOUN
ejpam-5154	166	3	(	(	PUNCT
ejpam-5154	166	4	v	v	NOUN
ejpam-5154	166	5	(	(	PUNCT
ejpam-5154	166	6	h	h	NOUN
ejpam-5154	166	7	)	)	PUNCT
ejpam-5154	166	8	\qh	\qh	NOUN
ejpam-5154	166	9	)	)	PUNCT
ejpam-5154	166	10	=	=	NOUN
ejpam-5154	166	11	∅	∅	NOUN
ejpam-5154	166	12	for	for	ADP
ejpam-5154	166	13	some	some	DET
ejpam-5154	166	14	y	y	PROPN
ejpam-5154	166	15	∈	∈	PROPN
ejpam-5154	166	16	qh	qh	PROPN
ejpam-5154	166	17	and	and	CCONJ
ejpam-5154	166	18	x	x	PROPN
ejpam-5154	166	19	∈	∈	PROPN
ejpam-5154	166	20	v	v	ADP
ejpam-5154	166	21	(	(	PUNCT
ejpam-5154	166	22	g	g	NOUN
ejpam-5154	166	23	)	)	PUNCT
ejpam-5154	166	24	.	.	PUNCT
ejpam-5154	167	1	j.	j.	PROPN
ejpam-5154	167	2	a.	a.	PROPN
ejpam-5154	167	3	hassan	hassan	PROPN
ejpam-5154	167	4	et	et	PROPN
ejpam-5154	167	5	al	al	PROPN
ejpam-5154	167	6	.	.	PUNCT
ejpam-5154	167	7	/	/	SYM
ejpam-5154	167	8	eur	eur	PROPN
ejpam-5154	167	9	.	.	PUNCT
ejpam-5154	168	1	j.	j.	PROPN
ejpam-5154	168	2	pure	pure	PROPN
ejpam-5154	168	3	appl	appl	PROPN
ejpam-5154	168	4	.	.	PROPN
ejpam-5154	168	5	math	math	PROPN
ejpam-5154	168	6	,	,	PUNCT
ejpam-5154	168	7	17	17	NUM
ejpam-5154	168	8	(	(	PUNCT
ejpam-5154	168	9	4	4	NUM
ejpam-5154	168	10	)	)	PUNCT
ejpam-5154	168	11	(	(	PUNCT
ejpam-5154	168	12	2024	2024	NUM
ejpam-5154	168	13	)	)	PUNCT
ejpam-5154	168	14	,	,	PUNCT
ejpam-5154	168	15	3772	3772	NUM
ejpam-5154	168	16	-	-	SYM
ejpam-5154	168	17	3780	3780	NUM
ejpam-5154	168	18	3778	3778	NUM
ejpam-5154	168	19	(	(	PUNCT
ejpam-5154	168	20	iv	iv	X
ejpam-5154	168	21	)	)	PUNCT
ejpam-5154	168	22	qh	qh	NOUN
ejpam-5154	168	23	=	=	NOUN
ejpam-5154	168	24	v	v	PROPN
ejpam-5154	168	25	(	(	PUNCT
ejpam-5154	168	26	h)\{u	h)\{u	PROPN
ejpam-5154	168	27	}	}	PUNCT
ejpam-5154	168	28	and	and	CCONJ
ejpam-5154	168	29	qg	qg	PROPN
ejpam-5154	168	30	is	be	AUX
ejpam-5154	168	31	a	a	DET
ejpam-5154	168	32	zero	zero	NUM
ejpam-5154	168	33	forcing	force	VERB
ejpam-5154	168	34	set	set	NOUN
ejpam-5154	168	35	of	of	ADP
ejpam-5154	168	36	g	g	PROPN
ejpam-5154	168	37	with	with	ADP
ejpam-5154	168	38	ng	ng	PROPN
ejpam-5154	169	1	[	[	X
ejpam-5154	169	2	v]∩	v]∩	X
ejpam-5154	169	3	(	(	PUNCT
ejpam-5154	169	4	v	v	NOUN
ejpam-5154	169	5	(	(	PUNCT
ejpam-5154	169	6	g	g	NOUN
ejpam-5154	169	7	)	)	PUNCT
ejpam-5154	169	8	\qg	\qg	PROPN
ejpam-5154	169	9	)	)	PUNCT
ejpam-5154	170	1	=	=	NOUN
ejpam-5154	170	2	∅	∅	NOUN
ejpam-5154	170	3	for	for	ADP
ejpam-5154	170	4	some	some	DET
ejpam-5154	170	5	v	v	NOUN
ejpam-5154	170	6	∈	∈	PROPN
ejpam-5154	170	7	qg	qg	PROPN
ejpam-5154	170	8	and	and	CCONJ
ejpam-5154	170	9	u	u	PROPN
ejpam-5154	170	10	∈	∈	PROPN
ejpam-5154	170	11	v	v	ADP
ejpam-5154	170	12	(	(	PUNCT
ejpam-5154	170	13	g	g	NOUN
ejpam-5154	170	14	)	)	PUNCT
ejpam-5154	170	15	.	.	PUNCT
ejpam-5154	171	1	proof	proof	NOUN
ejpam-5154	171	2	.	.	PUNCT
ejpam-5154	172	1	suppose	suppose	VERB
ejpam-5154	172	2	that	that	SCONJ
ejpam-5154	172	3	q	q	PROPN
ejpam-5154	172	4	=	=	SYM
ejpam-5154	172	5	qg	qg	PROPN
ejpam-5154	172	6	∪	∪	PROPN
ejpam-5154	172	7	qh	qh	PROPN
ejpam-5154	172	8	is	be	AUX
ejpam-5154	172	9	a	a	DET
ejpam-5154	172	10	zero	zero	NUM
ejpam-5154	172	11	forcing	force	VERB
ejpam-5154	172	12	dominating	dominating	NOUN
ejpam-5154	172	13	set	set	NOUN
ejpam-5154	172	14	of	of	ADP
ejpam-5154	172	15	g+h	g+h	PROPN
ejpam-5154	172	16	.	.	PUNCT
ejpam-5154	173	1	assume	assume	VERB
ejpam-5154	173	2	that	that	SCONJ
ejpam-5154	173	3	qg	qg	PROPN
ejpam-5154	173	4	=	=	SYM
ejpam-5154	173	5	v	v	PROPN
ejpam-5154	173	6	(	(	PUNCT
ejpam-5154	173	7	g	g	NOUN
ejpam-5154	173	8	)	)	PUNCT
ejpam-5154	173	9	.	.	PUNCT
ejpam-5154	174	1	if	if	SCONJ
ejpam-5154	174	2	qh	qh	PROPN
ejpam-5154	174	3	=	=	NOUN
ejpam-5154	174	4	v	v	PROPN
ejpam-5154	174	5	(	(	PUNCT
ejpam-5154	174	6	h	h	NOUN
ejpam-5154	174	7	)	)	PUNCT
ejpam-5154	174	8	,	,	PUNCT
ejpam-5154	174	9	then	then	ADV
ejpam-5154	174	10	(	(	PUNCT
ejpam-5154	174	11	i	i	NOUN
ejpam-5154	174	12	)	)	PUNCT
ejpam-5154	174	13	and	and	CCONJ
ejpam-5154	174	14	(	(	PUNCT
ejpam-5154	174	15	ii	ii	NOUN
ejpam-5154	174	16	)	)	PUNCT
ejpam-5154	174	17	follows	follow	VERB
ejpam-5154	174	18	.	.	PUNCT
ejpam-5154	175	1	suppose	suppose	VERB
ejpam-5154	175	2	that	that	SCONJ
ejpam-5154	175	3	qh	qh	PROPN
ejpam-5154	175	4	̸=	̸=	PROPN
ejpam-5154	175	5	v	v	PROPN
ejpam-5154	175	6	(	(	PUNCT
ejpam-5154	175	7	h	h	NOUN
ejpam-5154	175	8	)	)	PUNCT
ejpam-5154	175	9	.	.	PUNCT
ejpam-5154	176	1	if	if	SCONJ
ejpam-5154	176	2	qh	qh	NOUN
ejpam-5154	176	3	is	be	AUX
ejpam-5154	176	4	not	not	PART
ejpam-5154	176	5	a	a	DET
ejpam-5154	176	6	zero	zero	NUM
ejpam-5154	176	7	forcing	forcing	NOUN
ejpam-5154	176	8	set	set	NOUN
ejpam-5154	176	9	,	,	PUNCT
ejpam-5154	176	10	then	then	ADV
ejpam-5154	176	11	there	there	PRON
ejpam-5154	176	12	exists	exist	VERB
ejpam-5154	176	13	two	two	NUM
ejpam-5154	176	14	vertices	vertex	NOUN
ejpam-5154	176	15	x	x	X
ejpam-5154	176	16	,	,	PUNCT
ejpam-5154	176	17	y	y	PROPN
ejpam-5154	176	18	∈	∈	PROPN
ejpam-5154	176	19	v	v	ADP
ejpam-5154	176	20	(	(	PUNCT
ejpam-5154	176	21	h	h	NOUN
ejpam-5154	176	22	)	)	PUNCT
ejpam-5154	176	23	\qh	\qh	NOUN
ejpam-5154	176	24	such	such	ADJ
ejpam-5154	176	25	that	that	SCONJ
ejpam-5154	176	26	x	x	PROPN
ejpam-5154	176	27	and	and	CCONJ
ejpam-5154	176	28	y	y	PROPN
ejpam-5154	176	29	can	can	AUX
ejpam-5154	176	30	not	not	PART
ejpam-5154	176	31	be	be	AUX
ejpam-5154	176	32	forced	force	VERB
ejpam-5154	176	33	by	by	ADP
ejpam-5154	176	34	any	any	DET
ejpam-5154	176	35	element	element	NOUN
ejpam-5154	176	36	in	in	ADP
ejpam-5154	176	37	qh	qh	PROPN
ejpam-5154	176	38	.	.	PUNCT
ejpam-5154	177	1	therefore	therefore	ADV
ejpam-5154	177	2	,	,	PUNCT
ejpam-5154	177	3	q	q	PROPN
ejpam-5154	177	4	=	=	SYM
ejpam-5154	177	5	qg	qg	PROPN
ejpam-5154	177	6	∪	∪	PROPN
ejpam-5154	177	7	qh	qh	PROPN
ejpam-5154	177	8	is	be	AUX
ejpam-5154	177	9	not	not	PART
ejpam-5154	177	10	a	a	DET
ejpam-5154	177	11	zero	zero	NUM
ejpam-5154	177	12	forcing	forcing	NOUN
ejpam-5154	177	13	set	set	NOUN
ejpam-5154	177	14	,	,	PUNCT
ejpam-5154	177	15	a	a	DET
ejpam-5154	177	16	contradiction	contradiction	NOUN
ejpam-5154	177	17	.	.	PUNCT
ejpam-5154	178	1	hence	hence	ADV
ejpam-5154	178	2	,	,	PUNCT
ejpam-5154	178	3	qh	qh	NOUN
ejpam-5154	178	4	must	must	AUX
ejpam-5154	178	5	be	be	AUX
ejpam-5154	178	6	a	a	DET
ejpam-5154	178	7	zero	zero	NUM
ejpam-5154	178	8	forcing	force	VERB
ejpam-5154	178	9	set	set	NOUN
ejpam-5154	178	10	of	of	ADP
ejpam-5154	178	11	h	h	NOUN
ejpam-5154	178	12	,	,	PUNCT
ejpam-5154	178	13	and	and	CCONJ
ejpam-5154	178	14	so	so	ADV
ejpam-5154	178	15	(	(	PUNCT
ejpam-5154	178	16	i	i	NOUN
ejpam-5154	178	17	)	)	PUNCT
ejpam-5154	178	18	holds	hold	VERB
ejpam-5154	178	19	.	.	PUNCT
ejpam-5154	179	1	similarly	similarly	ADV
ejpam-5154	179	2	,	,	PUNCT
ejpam-5154	179	3	(	(	PUNCT
ejpam-5154	179	4	ii	ii	NOUN
ejpam-5154	179	5	)	)	PUNCT
ejpam-5154	179	6	holds	hold	VERB
ejpam-5154	179	7	.	.	PUNCT
ejpam-5154	180	1	now	now	ADV
ejpam-5154	180	2	,	,	PUNCT
ejpam-5154	180	3	suppose	suppose	VERB
ejpam-5154	180	4	that	that	SCONJ
ejpam-5154	180	5	qg	qg	PROPN
ejpam-5154	180	6	̸=	̸=	PROPN
ejpam-5154	180	7	v	v	PROPN
ejpam-5154	180	8	(	(	PUNCT
ejpam-5154	180	9	g	g	NOUN
ejpam-5154	180	10	)	)	PUNCT
ejpam-5154	180	11	and	and	CCONJ
ejpam-5154	180	12	qh	qh	NOUN
ejpam-5154	180	13	̸=	̸=	PROPN
ejpam-5154	180	14	v	v	NOUN
ejpam-5154	180	15	(	(	PUNCT
ejpam-5154	180	16	h	h	NOUN
ejpam-5154	180	17	)	)	PUNCT
ejpam-5154	180	18	.	.	PUNCT
ejpam-5154	181	1	since	since	SCONJ
ejpam-5154	181	2	q	q	PROPN
ejpam-5154	181	3	is	be	AUX
ejpam-5154	181	4	zero	zero	NUM
ejpam-5154	181	5	forcing	forcing	NOUN
ejpam-5154	181	6	,	,	PUNCT
ejpam-5154	181	7	either	either	CCONJ
ejpam-5154	181	8	|qg|	|qg|	NOUN
ejpam-5154	181	9	=	=	SYM
ejpam-5154	181	10	|v	|v	PROPN
ejpam-5154	181	11	(	(	PUNCT
ejpam-5154	181	12	g)|	g)|	INTJ
ejpam-5154	181	13	−	−	NOUN
ejpam-5154	181	14	1	1	NUM
ejpam-5154	181	15	or	or	CCONJ
ejpam-5154	181	16	|qh	|qh	INTJ
ejpam-5154	181	17	|	|	ADV
ejpam-5154	181	18	=	=	SYM
ejpam-5154	181	19	|v	|v	PROPN
ejpam-5154	181	20	(	(	PUNCT
ejpam-5154	181	21	h)|	h)|	NOUN
ejpam-5154	181	22	−	−	PROPN
ejpam-5154	181	23	1	1	X
ejpam-5154	181	24	.	.	PUNCT
ejpam-5154	181	25	assume	assume	VERB
ejpam-5154	181	26	that	that	SCONJ
ejpam-5154	181	27	|qg|	|qg|	NOUN
ejpam-5154	181	28	=	=	SYM
ejpam-5154	181	29	|v	|v	PROPN
ejpam-5154	181	30	(	(	PUNCT
ejpam-5154	181	31	g)|	g)|	INTJ
ejpam-5154	181	32	−	−	NOUN
ejpam-5154	181	33	1	1	NUM
ejpam-5154	181	34	.	.	PUNCT
ejpam-5154	182	1	since	since	SCONJ
ejpam-5154	182	2	q	q	PROPN
ejpam-5154	182	3	is	be	AUX
ejpam-5154	182	4	a	a	DET
ejpam-5154	182	5	zero	zero	NUM
ejpam-5154	182	6	forcing	force	VERB
ejpam-5154	182	7	set	set	NOUN
ejpam-5154	182	8	of	of	ADP
ejpam-5154	182	9	g	g	PROPN
ejpam-5154	182	10	+	+	CCONJ
ejpam-5154	182	11	h	h	NOUN
ejpam-5154	182	12	,	,	PUNCT
ejpam-5154	182	13	qh	qh	NOUN
ejpam-5154	182	14	must	must	AUX
ejpam-5154	182	15	be	be	AUX
ejpam-5154	182	16	a	a	DET
ejpam-5154	182	17	zero	zero	NUM
ejpam-5154	182	18	forcing	forcing	NOUN
ejpam-5154	182	19	in	in	ADP
ejpam-5154	182	20	h.	h.	PROPN
ejpam-5154	182	21	now	now	ADV
ejpam-5154	182	22	,	,	PUNCT
ejpam-5154	182	23	suppose	suppose	VERB
ejpam-5154	182	24	that	that	SCONJ
ejpam-5154	182	25	for	for	ADP
ejpam-5154	182	26	every	every	DET
ejpam-5154	182	27	element	element	NOUN
ejpam-5154	182	28	w	w	PROPN
ejpam-5154	182	29	∈	∈	PROPN
ejpam-5154	182	30	qh	qh	PROPN
ejpam-5154	182	31	,	,	PUNCT
ejpam-5154	182	32	nh	nh	PROPN
ejpam-5154	183	1	[	[	X
ejpam-5154	183	2	w	w	X
ejpam-5154	183	3	]	]	X
ejpam-5154	183	4	∩	∩	NOUN
ejpam-5154	183	5	(	(	PUNCT
ejpam-5154	183	6	v	v	NOUN
ejpam-5154	183	7	(	(	PUNCT
ejpam-5154	183	8	g	g	NOUN
ejpam-5154	183	9	)	)	PUNCT
ejpam-5154	183	10	\qh	\qh	PROPN
ejpam-5154	183	11	)	)	PUNCT
ejpam-5154	183	12	̸=	̸=	PROPN
ejpam-5154	183	13	∅.	∅.	ADV
ejpam-5154	183	14	since	since	SCONJ
ejpam-5154	183	15	|qg|	|qg|	NOUN
ejpam-5154	183	16	=	=	SYM
ejpam-5154	183	17	|v	|v	PROPN
ejpam-5154	183	18	(	(	PUNCT
ejpam-5154	183	19	g)|	g)|	NOUN
ejpam-5154	183	20	−	−	PROPN
ejpam-5154	183	21	1	1	NUM
ejpam-5154	183	22	,	,	PUNCT
ejpam-5154	183	23	and	and	CCONJ
ejpam-5154	183	24	h	h	NOUN
ejpam-5154	183	25	is	be	AUX
ejpam-5154	183	26	non	non	ADJ
ejpam-5154	183	27	-	-	ADJ
ejpam-5154	183	28	complete	complete	ADJ
ejpam-5154	183	29	graph	graph	NOUN
ejpam-5154	183	30	,	,	PUNCT
ejpam-5154	183	31	it	it	PRON
ejpam-5154	183	32	follows	follow	VERB
ejpam-5154	183	33	that	that	SCONJ
ejpam-5154	183	34	any	any	DET
ejpam-5154	183	35	element	element	NOUN
ejpam-5154	183	36	w	w	PROPN
ejpam-5154	183	37	∈	∈	PROPN
ejpam-5154	183	38	qh	qh	NOUN
ejpam-5154	183	39	can	can	AUX
ejpam-5154	183	40	not	not	PART
ejpam-5154	183	41	force	force	VERB
ejpam-5154	183	42	any	any	DET
ejpam-5154	183	43	element	element	NOUN
ejpam-5154	183	44	in	in	ADP
ejpam-5154	183	45	v	v	NOUN
ejpam-5154	183	46	(	(	PUNCT
ejpam-5154	183	47	g	g	NOUN
ejpam-5154	183	48	)	)	PUNCT
ejpam-5154	183	49	\	\	NOUN
ejpam-5154	183	50	{	{	PUNCT
ejpam-5154	183	51	x	x	NOUN
ejpam-5154	183	52	}	}	PUNCT
ejpam-5154	183	53	and	and	CCONJ
ejpam-5154	183	54	in	in	ADP
ejpam-5154	183	55	v	v	NUM
ejpam-5154	183	56	(	(	PUNCT
ejpam-5154	183	57	h	h	NOUN
ejpam-5154	183	58	)	)	PUNCT
ejpam-5154	183	59	\qh	\qh	PROPN
ejpam-5154	183	60	,	,	PUNCT
ejpam-5154	183	61	respectively	respectively	ADV
ejpam-5154	183	62	,	,	PUNCT
ejpam-5154	183	63	a	a	DET
ejpam-5154	183	64	contradiction	contradiction	NOUN
ejpam-5154	183	65	.	.	PUNCT
ejpam-5154	184	1	hence	hence	ADV
ejpam-5154	184	2	(	(	PUNCT
ejpam-5154	184	3	iii	iii	NOUN
ejpam-5154	184	4	)	)	PUNCT
ejpam-5154	184	5	holds	hold	VERB
ejpam-5154	184	6	.	.	PUNCT
ejpam-5154	185	1	similarly	similarly	ADV
ejpam-5154	185	2	,	,	PUNCT
ejpam-5154	185	3	(	(	PUNCT
ejpam-5154	185	4	iv	iv	X
ejpam-5154	185	5	)	)	PUNCT
ejpam-5154	185	6	holds	hold	NOUN
ejpam-5154	185	7	.	.	PUNCT
ejpam-5154	186	1	conversely	conversely	ADV
ejpam-5154	186	2	,	,	PUNCT
ejpam-5154	186	3	suppose	suppose	VERB
ejpam-5154	186	4	that	that	SCONJ
ejpam-5154	186	5	(	(	PUNCT
ejpam-5154	186	6	i	i	NOUN
ejpam-5154	186	7	)	)	PUNCT
ejpam-5154	186	8	holds	hold	VERB
ejpam-5154	186	9	.	.	PUNCT
ejpam-5154	187	1	since	since	SCONJ
ejpam-5154	187	2	qh	qh	PROPN
ejpam-5154	187	3	is	be	AUX
ejpam-5154	187	4	a	a	DET
ejpam-5154	187	5	zero	zero	NUM
ejpam-5154	187	6	forcing	forcing	NOUN
ejpam-5154	187	7	set	set	NOUN
ejpam-5154	187	8	in	in	ADP
ejpam-5154	187	9	h	h	NOUN
ejpam-5154	187	10	,	,	PUNCT
ejpam-5154	187	11	q	q	PROPN
ejpam-5154	187	12	=	=	PUNCT
ejpam-5154	187	13	qg	qg	PROPN
ejpam-5154	187	14	∪	∪	PROPN
ejpam-5154	187	15	qh	qh	PROPN
ejpam-5154	187	16	is	be	AUX
ejpam-5154	187	17	a	a	DET
ejpam-5154	187	18	zero	zero	NUM
ejpam-5154	187	19	forcing	forcing	NOUN
ejpam-5154	187	20	set	set	NOUN
ejpam-5154	187	21	in	in	ADP
ejpam-5154	187	22	g+h	g+h	PROPN
ejpam-5154	187	23	.	.	PUNCT
ejpam-5154	188	1	thus	thus	ADV
ejpam-5154	188	2	,	,	PUNCT
ejpam-5154	188	3	q	q	X
ejpam-5154	188	4	is	be	AUX
ejpam-5154	188	5	a	a	DET
ejpam-5154	188	6	zero	zero	NUM
ejpam-5154	188	7	forcing	force	VERB
ejpam-5154	188	8	dominating	dominating	NOUN
ejpam-5154	188	9	set	set	NOUN
ejpam-5154	188	10	of	of	ADP
ejpam-5154	188	11	g+h	g+h	PROPN
ejpam-5154	188	12	.	.	PUNCT
ejpam-5154	189	1	similarly	similarly	ADV
ejpam-5154	189	2	,	,	PUNCT
ejpam-5154	189	3	the	the	DET
ejpam-5154	189	4	assertion	assertion	NOUN
ejpam-5154	189	5	follows	follow	VERB
ejpam-5154	189	6	when	when	SCONJ
ejpam-5154	189	7	(	(	PUNCT
ejpam-5154	189	8	ii	ii	NOUN
ejpam-5154	189	9	)	)	PUNCT
ejpam-5154	189	10	holds	hold	VERB
ejpam-5154	189	11	.	.	PUNCT
ejpam-5154	190	1	next	next	ADV
ejpam-5154	190	2	,	,	PUNCT
ejpam-5154	190	3	suppose	suppose	VERB
ejpam-5154	190	4	that	that	SCONJ
ejpam-5154	190	5	(	(	PUNCT
ejpam-5154	190	6	iii	iii	NOUN
ejpam-5154	190	7	)	)	PUNCT
ejpam-5154	190	8	holds	hold	VERB
ejpam-5154	190	9	.	.	PUNCT
ejpam-5154	191	1	then	then	ADV
ejpam-5154	191	2	q	q	X
ejpam-5154	191	3	is	be	AUX
ejpam-5154	191	4	a	a	DET
ejpam-5154	191	5	dominating	dominating	NOUN
ejpam-5154	191	6	set	set	NOUN
ejpam-5154	191	7	of	of	ADP
ejpam-5154	191	8	g+h	g+h	PROPN
ejpam-5154	191	9	.	.	PUNCT
ejpam-5154	192	1	let	let	VERB
ejpam-5154	192	2	y	y	PROPN
ejpam-5154	192	3	∈	∈	PROPN
ejpam-5154	192	4	q	q	NOUN
ejpam-5154	192	5	such	such	ADJ
ejpam-5154	192	6	that	that	PRON
ejpam-5154	192	7	nh	nh	PROPN
ejpam-5154	193	1	[	[	X
ejpam-5154	193	2	y	y	X
ejpam-5154	193	3	]	]	X
ejpam-5154	193	4	∩	∩	NOUN
ejpam-5154	193	5	(	(	PUNCT
ejpam-5154	193	6	v	v	NOUN
ejpam-5154	193	7	(	(	PUNCT
ejpam-5154	193	8	h	h	NOUN
ejpam-5154	193	9	)	)	PUNCT
ejpam-5154	193	10	\qh	\qh	PROPN
ejpam-5154	193	11	)	)	PUNCT
ejpam-5154	194	1	=	=	PUNCT
ejpam-5154	194	2	∅.	∅.	NOUN
ejpam-5154	194	3	then	then	ADV
ejpam-5154	194	4	y	y	PROPN
ejpam-5154	194	5	forces	force	VERB
ejpam-5154	194	6	vertex	vertex	NOUN
ejpam-5154	194	7	x	x	NOUN
ejpam-5154	194	8	in	in	ADP
ejpam-5154	194	9	g.	g.	PROPN
ejpam-5154	194	10	since	since	SCONJ
ejpam-5154	194	11	qh	qh	PROPN
ejpam-5154	194	12	is	be	AUX
ejpam-5154	194	13	a	a	DET
ejpam-5154	194	14	zero	zero	NUM
ejpam-5154	194	15	forcing	forcing	NOUN
ejpam-5154	194	16	set	set	NOUN
ejpam-5154	194	17	in	in	ADP
ejpam-5154	194	18	h	h	NOUN
ejpam-5154	194	19	,	,	PUNCT
ejpam-5154	194	20	it	it	PRON
ejpam-5154	194	21	follows	follow	VERB
ejpam-5154	194	22	that	that	DET
ejpam-5154	194	23	q	q	PROPN
ejpam-5154	194	24	=	=	SYM
ejpam-5154	194	25	qg	qg	PROPN
ejpam-5154	194	26	∪	∪	PROPN
ejpam-5154	194	27	qh	qh	PROPN
ejpam-5154	194	28	is	be	AUX
ejpam-5154	194	29	a	a	DET
ejpam-5154	194	30	zero	zero	NUM
ejpam-5154	194	31	forcing	force	VERB
ejpam-5154	194	32	set	set	NOUN
ejpam-5154	194	33	of	of	ADP
ejpam-5154	194	34	g	g	PROPN
ejpam-5154	194	35	+	+	PROPN
ejpam-5154	194	36	h.	h.	PROPN
ejpam-5154	194	37	therefore	therefore	ADV
ejpam-5154	194	38	,	,	PUNCT
ejpam-5154	194	39	q	q	PROPN
ejpam-5154	194	40	is	be	AUX
ejpam-5154	194	41	zero	zero	NUM
ejpam-5154	194	42	forcing	force	VERB
ejpam-5154	194	43	dominating	dominating	NOUN
ejpam-5154	194	44	set	set	NOUN
ejpam-5154	194	45	of	of	ADP
ejpam-5154	194	46	g+h	g+h	PROPN
ejpam-5154	194	47	.	.	PUNCT
ejpam-5154	195	1	similarly	similarly	ADV
ejpam-5154	195	2	,	,	PUNCT
ejpam-5154	195	3	the	the	DET
ejpam-5154	195	4	assertion	assertion	NOUN
ejpam-5154	195	5	holds	hold	VERB
ejpam-5154	195	6	,	,	PUNCT
ejpam-5154	195	7	when	when	SCONJ
ejpam-5154	195	8	(	(	PUNCT
ejpam-5154	195	9	iv	iv	X
ejpam-5154	195	10	)	)	PUNCT
ejpam-5154	195	11	is	be	AUX
ejpam-5154	195	12	true	true	ADJ
ejpam-5154	195	13	.	.	PUNCT
ejpam-5154	196	1	corollary	corollary	ADJ
ejpam-5154	196	2	3	3	X
ejpam-5154	196	3	.	.	PUNCT
ejpam-5154	197	1	let	let	VERB
ejpam-5154	197	2	g	g	NOUN
ejpam-5154	197	3	and	and	CCONJ
ejpam-5154	197	4	h	h	NOUN
ejpam-5154	197	5	be	be	VERB
ejpam-5154	197	6	two	two	NUM
ejpam-5154	197	7	non	non	ADJ
ejpam-5154	197	8	-	-	ADJ
ejpam-5154	197	9	complete	complete	ADJ
ejpam-5154	197	10	graphs	graph	NOUN
ejpam-5154	197	11	.	.	PUNCT
ejpam-5154	198	1	then	then	ADV
ejpam-5154	198	2	γz	γz	PROPN
ejpam-5154	198	3	(	(	PUNCT
ejpam-5154	198	4	g+h	g+h	PROPN
ejpam-5154	198	5	)	)	PUNCT
ejpam-5154	199	1	=	=	SYM
ejpam-5154	199	2	min{|v	min{|v	PROPN
ejpam-5154	199	3	(	(	PUNCT
ejpam-5154	199	4	g)|+	g)|+	NOUN
ejpam-5154	199	5	z	z	PROPN
ejpam-5154	199	6	(	(	PUNCT
ejpam-5154	199	7	h	h	NOUN
ejpam-5154	199	8	)	)	PUNCT
ejpam-5154	199	9	,	,	PUNCT
ejpam-5154	199	10	|v	|v	PROPN
ejpam-5154	199	11	(	(	PUNCT
ejpam-5154	199	12	h)|+	h)|+	NOUN
ejpam-5154	199	13	z	z	NOUN
ejpam-5154	199	14	(	(	PUNCT
ejpam-5154	199	15	g	g	NOUN
ejpam-5154	199	16	}	}	PUNCT
ejpam-5154	199	17	.	.	PUNCT
ejpam-5154	200	1	4	4	X
ejpam-5154	200	2	.	.	X
ejpam-5154	200	3	conclusion	conclusion	VERB
ejpam-5154	200	4	the	the	DET
ejpam-5154	200	5	concept	concept	NOUN
ejpam-5154	200	6	of	of	ADP
ejpam-5154	200	7	zero	zero	NUM
ejpam-5154	200	8	forcing	force	VERB
ejpam-5154	200	9	domination	domination	NOUN
ejpam-5154	200	10	has	have	AUX
ejpam-5154	200	11	been	be	AUX
ejpam-5154	200	12	introduced	introduce	VERB
ejpam-5154	200	13	and	and	CCONJ
ejpam-5154	200	14	initially	initially	ADV
ejpam-5154	200	15	investigated	investigate	VERB
ejpam-5154	200	16	in	in	ADP
ejpam-5154	200	17	this	this	DET
ejpam-5154	200	18	study	study	NOUN
ejpam-5154	200	19	.	.	PUNCT
ejpam-5154	201	1	its	its	PRON
ejpam-5154	201	2	bounds	bound	NOUN
ejpam-5154	201	3	concerning	concern	VERB
ejpam-5154	201	4	other	other	ADJ
ejpam-5154	201	5	known	know	VERB
ejpam-5154	201	6	parameters	parameter	NOUN
ejpam-5154	201	7	in	in	ADP
ejpam-5154	201	8	graph	graph	NOUN
ejpam-5154	201	9	theory	theory	NOUN
ejpam-5154	201	10	have	have	AUX
ejpam-5154	201	11	been	be	AUX
ejpam-5154	201	12	established	establish	VERB
ejpam-5154	201	13	.	.	PUNCT
ejpam-5154	202	1	moreover	moreover	ADV
ejpam-5154	202	2	,	,	PUNCT
ejpam-5154	202	3	the	the	DET
ejpam-5154	202	4	zero	zero	NUM
ejpam-5154	202	5	forcing	force	VERB
ejpam-5154	202	6	domination	domination	NOUN
ejpam-5154	202	7	number	number	NOUN
ejpam-5154	202	8	of	of	ADP
ejpam-5154	202	9	some	some	DET
ejpam-5154	202	10	graphs	graph	NOUN
ejpam-5154	202	11	has	have	AUX
ejpam-5154	202	12	been	be	AUX
ejpam-5154	202	13	determined	determine	VERB
ejpam-5154	202	14	.	.	PUNCT
ejpam-5154	203	1	in	in	ADP
ejpam-5154	203	2	addition	addition	NOUN
ejpam-5154	203	3	,	,	PUNCT
ejpam-5154	203	4	characterizations	characterization	NOUN
ejpam-5154	203	5	of	of	ADP
ejpam-5154	203	6	zero	zero	NUM
ejpam-5154	203	7	forcing	force	VERB
ejpam-5154	203	8	dominating	dominating	NOUN
ejpam-5154	203	9	sets	set	NOUN
ejpam-5154	203	10	in	in	ADP
ejpam-5154	203	11	some	some	DET
ejpam-5154	203	12	graphs	graph	NOUN
ejpam-5154	203	13	were	be	AUX
ejpam-5154	203	14	formulated	formulate	VERB
ejpam-5154	203	15	and	and	CCONJ
ejpam-5154	203	16	were	be	AUX
ejpam-5154	203	17	used	use	VERB
ejpam-5154	203	18	to	to	PART
ejpam-5154	203	19	solve	solve	VERB
ejpam-5154	203	20	the	the	DET
ejpam-5154	203	21	exact	exact	ADJ
ejpam-5154	203	22	value	value	NOUN
ejpam-5154	203	23	of	of	ADP
ejpam-5154	203	24	the	the	DET
ejpam-5154	203	25	parameter	parameter	NOUN
ejpam-5154	203	26	of	of	ADP
ejpam-5154	203	27	these	these	DET
ejpam-5154	203	28	graphs	graph	NOUN
ejpam-5154	203	29	.	.	PUNCT
ejpam-5154	204	1	analyzing	analyze	VERB
ejpam-5154	204	2	graphs	graph	NOUN
ejpam-5154	204	3	that	that	PRON
ejpam-5154	204	4	are	be	AUX
ejpam-5154	204	5	n’t	not	PART
ejpam-5154	204	6	covered	cover	VERB
ejpam-5154	204	7	in	in	ADP
ejpam-5154	204	8	this	this	DET
ejpam-5154	204	9	study	study	NOUN
ejpam-5154	204	10	may	may	AUX
ejpam-5154	204	11	be	be	AUX
ejpam-5154	204	12	intriguing	intriguing	ADJ
ejpam-5154	204	13	and	and	CCONJ
ejpam-5154	204	14	provide	provide	VERB
ejpam-5154	204	15	a	a	DET
ejpam-5154	204	16	different	different	ADJ
ejpam-5154	204	17	view	view	NOUN
ejpam-5154	204	18	references	reference	NOUN
ejpam-5154	204	19	3779	3779	NUM
ejpam-5154	204	20	acknowledgements	acknowledgement	NOUN
ejpam-5154	204	21	the	the	DET
ejpam-5154	204	22	authors	author	NOUN
ejpam-5154	204	23	would	would	AUX
ejpam-5154	204	24	like	like	VERB
ejpam-5154	204	25	to	to	PART
ejpam-5154	204	26	thank	thank	VERB
ejpam-5154	204	27	mindanao	mindanao	PROPN
ejpam-5154	204	28	state	state	PROPN
ejpam-5154	204	29	university	university	PROPN
ejpam-5154	204	30	tawi	tawi	PROPN
ejpam-5154	204	31	-	-	PUNCT
ejpam-5154	204	32	tawi	tawi	PROPN
ejpam-5154	204	33	college	college	PROPN
ejpam-5154	204	34	of	of	ADP
ejpam-5154	204	35	technology	technology	NOUN
ejpam-5154	204	36	and	and	CCONJ
ejpam-5154	204	37	oceanography	oceanography	NOUN
ejpam-5154	204	38	,	,	PUNCT
ejpam-5154	204	39	korea	korea	PROPN
ejpam-5154	204	40	university	university	PROPN
ejpam-5154	204	41	,	,	PUNCT
ejpam-5154	204	42	and	and	CCONJ
ejpam-5154	204	43	ateneo	ateneo	PROPN
ejpam-5154	204	44	de	de	PROPN
ejpam-5154	204	45	davao	davao	PROPN
ejpam-5154	204	46	university	university	PROPN
ejpam-5154	204	47	for	for	ADP
ejpam-5154	204	48	funding	fund	VERB
ejpam-5154	204	49	this	this	DET
ejpam-5154	204	50	research	research	NOUN
ejpam-5154	204	51	.	.	PUNCT
ejpam-5154	205	1	references	reference	NOUN
ejpam-5154	205	2	[	[	X
ejpam-5154	205	3	1	1	NUM
ejpam-5154	205	4	]	]	PUNCT
ejpam-5154	205	5	c.	c.	PROPN
ejpam-5154	205	6	berge	berge	PROPN
ejpam-5154	205	7	.	.	PUNCT
ejpam-5154	206	1	theory	theory	NOUN
ejpam-5154	206	2	of	of	ADP
ejpam-5154	206	3	graphs	graph	NOUN
ejpam-5154	206	4	and	and	CCONJ
ejpam-5154	206	5	its	its	PRON
ejpam-5154	206	6	applications	application	NOUN
ejpam-5154	206	7	.	.	PUNCT
ejpam-5154	207	1	methuen	methuen	PROPN
ejpam-5154	207	2	,	,	PUNCT
ejpam-5154	207	3	london	london	PROPN
ejpam-5154	207	4	,	,	PUNCT
ejpam-5154	207	5	1962	1962	NUM
ejpam-5154	207	6	.	.	PUNCT
ejpam-5154	208	1	[	[	X
ejpam-5154	208	2	2	2	X
ejpam-5154	208	3	]	]	PUNCT
ejpam-5154	208	4	v.	v.	X
ejpam-5154	208	5	bilar	bilar	PROPN
ejpam-5154	208	6	,	,	PUNCT
ejpam-5154	208	7	m.	m.	NOUN
ejpam-5154	208	8	a.	a.	PROPN
ejpam-5154	208	9	bonsocan	bonsocan	PROPN
ejpam-5154	208	10	,	,	PUNCT
ejpam-5154	208	11	j.	j.	PROPN
ejpam-5154	208	12	hassan	hassan	PROPN
ejpam-5154	208	13	,	,	PUNCT
ejpam-5154	208	14	and	and	CCONJ
ejpam-5154	208	15	s.	s.	PROPN
ejpam-5154	208	16	dagondon	dagondon	PROPN
ejpam-5154	208	17	.	.	PUNCT
ejpam-5154	209	1	vertex	vertex	NOUN
ejpam-5154	209	2	cover	cover	VERB
ejpam-5154	209	3	hop	hop	NOUN
ejpam-5154	209	4	dominating	dominating	NOUN
ejpam-5154	209	5	sets	set	NOUN
ejpam-5154	209	6	in	in	ADP
ejpam-5154	209	7	graphs	graph	NOUN
ejpam-5154	209	8	.	.	PUNCT
ejpam-5154	210	1	eur	eur	PROPN
ejpam-5154	210	2	.	.	PUNCT
ejpam-5154	211	1	j.	j.	PROPN
ejpam-5154	211	2	appl	appl	PROPN
ejpam-5154	211	3	.	.	PROPN
ejpam-5154	211	4	math	math	PROPN
ejpam-5154	211	5	.	.	PUNCT
ejpam-5154	211	6	,	,	PUNCT
ejpam-5154	211	7	17(1):93–104	17(1):93–104	NUM
ejpam-5154	211	8	,	,	PUNCT
ejpam-5154	211	9	2024	2024	NUM
ejpam-5154	211	10	.	.	PUNCT
ejpam-5154	212	1	[	[	X
ejpam-5154	212	2	3	3	X
ejpam-5154	212	3	]	]	X
ejpam-5154	212	4	j.	j.	PROPN
ejpam-5154	212	5	ekstrand	ekstrand	PROPN
ejpam-5154	212	6	,	,	PUNCT
ejpam-5154	212	7	c.	c.	PROPN
ejpam-5154	212	8	erickson	erickson	PROPN
ejpam-5154	212	9	,	,	PUNCT
ejpam-5154	212	10	h.	h.	PROPN
ejpam-5154	212	11	t.	t.	PROPN
ejpam-5154	212	12	hall	hall	PROPN
ejpam-5154	212	13	,	,	PUNCT
ejpam-5154	212	14	d.	d.	PROPN
ejpam-5154	212	15	hay	hay	PROPN
ejpam-5154	212	16	,	,	PUNCT
ejpam-5154	212	17	l.	l.	PROPN
ejpam-5154	212	18	hogben	hogben	PROPN
ejpam-5154	212	19	,	,	PUNCT
ejpam-5154	212	20	r.	r.	PROPN
ejpam-5154	212	21	johnson	johnson	PROPN
ejpam-5154	212	22	,	,	PUNCT
ejpam-5154	212	23	n.	n.	PROPN
ejpam-5154	212	24	kingsley	kingsley	PROPN
ejpam-5154	212	25	,	,	PUNCT
ejpam-5154	212	26	s.	s.	PROPN
ejpam-5154	212	27	osborne	osborne	PROPN
ejpam-5154	212	28	,	,	PUNCT
ejpam-5154	212	29	t.	t.	PROPN
ejpam-5154	212	30	peters	peters	PROPN
ejpam-5154	212	31	,	,	PUNCT
ejpam-5154	212	32	j.	j.	PROPN
ejpam-5154	212	33	roat	roat	PROPN
ejpam-5154	212	34	,	,	PUNCT
ejpam-5154	212	35	a.	a.	PROPN
ejpam-5154	212	36	ross	ross	PROPN
ejpam-5154	212	37	,	,	PUNCT
ejpam-5154	212	38	d.	d.	PROPN
ejpam-5154	212	39	d.	d.	PROPN
ejpam-5154	212	40	row	row	PROPN
ejpam-5154	212	41	,	,	PUNCT
ejpam-5154	212	42	n.	n.	PROPN
ejpam-5154	212	43	warnberg	warnberg	PROPN
ejpam-5154	212	44	,	,	PUNCT
ejpam-5154	212	45	and	and	CCONJ
ejpam-5154	212	46	m.	m.	NOUN
ejpam-5154	212	47	young	young	PROPN
ejpam-5154	212	48	.	.	PUNCT
ejpam-5154	213	1	positive	positive	ADJ
ejpam-5154	213	2	semidefinite	semidefinite	NOUN
ejpam-5154	213	3	zero	zero	NUM
ejpam-5154	213	4	forcing	forcing	NOUN
ejpam-5154	213	5	.	.	PUNCT
ejpam-5154	214	1	linear	linear	ADJ
ejpam-5154	214	2	algebra	algebra	NOUN
ejpam-5154	214	3	and	and	CCONJ
ejpam-5154	214	4	its	its	PRON
ejpam-5154	214	5	applications	application	NOUN
ejpam-5154	214	6	,	,	PUNCT
ejpam-5154	214	7	439:1862–1874	439:1862–1874	NUM
ejpam-5154	214	8	,	,	PUNCT
ejpam-5154	214	9	2013	2013	NUM
ejpam-5154	214	10	.	.	PUNCT
ejpam-5154	215	1	[	[	X
ejpam-5154	215	2	4	4	X
ejpam-5154	215	3	]	]	PUNCT
ejpam-5154	215	4	aim	aim	VERB
ejpam-5154	215	5	minimum	minimum	ADJ
ejpam-5154	215	6	rank	rank	NOUN
ejpam-5154	215	7	–	–	PUNCT
ejpam-5154	215	8	special	special	ADJ
ejpam-5154	215	9	graphs	graph	NOUN
ejpam-5154	215	10	work	work	NOUN
ejpam-5154	215	11	group	group	NOUN
ejpam-5154	215	12	.	.	PUNCT
ejpam-5154	216	1	zero	zero	NUM
ejpam-5154	216	2	forcing	force	VERB
ejpam-5154	216	3	sets	set	NOUN
ejpam-5154	216	4	and	and	CCONJ
ejpam-5154	216	5	the	the	DET
ejpam-5154	216	6	minimum	minimum	ADJ
ejpam-5154	216	7	rank	rank	NOUN
ejpam-5154	216	8	of	of	ADP
ejpam-5154	216	9	graphs	graph	NOUN
ejpam-5154	216	10	.	.	PUNCT
ejpam-5154	217	1	linear	linear	ADJ
ejpam-5154	217	2	algebra	algebra	PROPN
ejpam-5154	217	3	appl	appl	NOUN
ejpam-5154	217	4	.	.	PUNCT
ejpam-5154	217	5	,	,	PUNCT
ejpam-5154	218	1	428(7):1628–1648	428(7):1628–1648	INTJ
ejpam-5154	218	2	,	,	PUNCT
ejpam-5154	218	3	2008	2008	NUM
ejpam-5154	218	4	.	.	PUNCT
ejpam-5154	219	1	[	[	X
ejpam-5154	219	2	5	5	X
ejpam-5154	219	3	]	]	PUNCT
ejpam-5154	219	4	j.	j.	PROPN
ejpam-5154	219	5	hassan	hassan	PROPN
ejpam-5154	219	6	,	,	PUNCT
ejpam-5154	219	7	a.	a.	PROPN
ejpam-5154	219	8	r.	r.	PROPN
ejpam-5154	219	9	bakkang	bakkang	PROPN
ejpam-5154	219	10	,	,	PUNCT
ejpam-5154	219	11	and	and	CCONJ
ejpam-5154	219	12	a.	a.	PROPN
ejpam-5154	219	13	s.	s.	PROPN
ejpam-5154	219	14	sappari	sappari	PROPN
ejpam-5154	219	15	.	.	PUNCT
ejpam-5154	220	1	j2	j2	PROPN
ejpam-5154	220	2	-	-	PUNCT
ejpam-5154	220	3	hop	hop	PROPN
ejpam-5154	220	4	domination	domination	NOUN
ejpam-5154	220	5	in	in	ADP
ejpam-5154	220	6	graphs	graph	NOUN
ejpam-5154	220	7	:	:	PUNCT
ejpam-5154	220	8	properties	property	NOUN
ejpam-5154	220	9	and	and	CCONJ
ejpam-5154	220	10	connection	connection	NOUN
ejpam-5154	220	11	with	with	ADP
ejpam-5154	220	12	other	other	ADJ
ejpam-5154	220	13	parameters	parameter	NOUN
ejpam-5154	220	14	.	.	PUNCT
ejpam-5154	221	1	eur	eur	PROPN
ejpam-5154	221	2	.	.	PUNCT
ejpam-5154	222	1	j.	j.	PROPN
ejpam-5154	222	2	pure	pure	PROPN
ejpam-5154	222	3	appl	appl	PROPN
ejpam-5154	222	4	.	.	PUNCT
ejpam-5154	222	5	math	math	PROPN
ejpam-5154	222	6	.	.	PUNCT
ejpam-5154	222	7	,	,	PUNCT
ejpam-5154	222	8	16(4):2118–2131	16(4):2118–2131	NUM
ejpam-5154	222	9	,	,	PUNCT
ejpam-5154	222	10	2023	2023	NUM
ejpam-5154	222	11	.	.	PUNCT
ejpam-5154	223	1	[	[	X
ejpam-5154	223	2	6	6	NUM
ejpam-5154	223	3	]	]	PUNCT
ejpam-5154	223	4	j.	j.	PROPN
ejpam-5154	223	5	hassan	hassan	PROPN
ejpam-5154	223	6	and	and	CCONJ
ejpam-5154	223	7	s.	s.	PROPN
ejpam-5154	223	8	canoy	canoy	PROPN
ejpam-5154	223	9	jr	jr	PROPN
ejpam-5154	223	10	.	.	PUNCT
ejpam-5154	224	1	grundy	grundy	PROPN
ejpam-5154	224	2	hop	hop	PROPN
ejpam-5154	224	3	domination	domination	PROPN
ejpam-5154	224	4	in	in	ADP
ejpam-5154	224	5	graphs	graph	NOUN
ejpam-5154	224	6	.	.	PUNCT
ejpam-5154	225	1	eur	eur	PROPN
ejpam-5154	225	2	.	.	PUNCT
ejpam-5154	226	1	j.	j.	PROPN
ejpam-5154	226	2	pure	pure	PROPN
ejpam-5154	226	3	appl	appl	PROPN
ejpam-5154	226	4	.	.	PUNCT
ejpam-5154	226	5	math	math	PROPN
ejpam-5154	226	6	.	.	PUNCT
ejpam-5154	226	7	,	,	PUNCT
ejpam-5154	226	8	15(4):1623–1636	15(4):1623–1636	NUM
ejpam-5154	226	9	,	,	PUNCT
ejpam-5154	226	10	2022	2022	NUM
ejpam-5154	226	11	.	.	PUNCT
ejpam-5154	227	1	[	[	X
ejpam-5154	227	2	7	7	X
ejpam-5154	227	3	]	]	PUNCT
ejpam-5154	227	4	j.	j.	PROPN
ejpam-5154	227	5	hassan	hassan	PROPN
ejpam-5154	227	6	and	and	CCONJ
ejpam-5154	227	7	s.	s.	PROPN
ejpam-5154	227	8	canoy	canoy	PROPN
ejpam-5154	227	9	jr	jr	PROPN
ejpam-5154	227	10	.	.	PUNCT
ejpam-5154	228	1	grundy	grundy	PROPN
ejpam-5154	228	2	dominating	dominating	PROPN
ejpam-5154	228	3	and	and	CCONJ
ejpam-5154	228	4	grundy	grundy	PROPN
ejpam-5154	228	5	hop	hop	NOUN
ejpam-5154	228	6	dominating	dominate	VERB
ejpam-5154	228	7	sequences	sequence	NOUN
ejpam-5154	228	8	in	in	ADP
ejpam-5154	228	9	graphs	graph	NOUN
ejpam-5154	228	10	:	:	PUNCT
ejpam-5154	228	11	relationships	relationship	NOUN
ejpam-5154	228	12	and	and	CCONJ
ejpam-5154	228	13	some	some	DET
ejpam-5154	228	14	structural	structural	ADJ
ejpam-5154	228	15	properties	property	NOUN
ejpam-5154	228	16	.	.	PUNCT
ejpam-5154	229	1	eur	eur	PROPN
ejpam-5154	229	2	.	.	PUNCT
ejpam-5154	230	1	j.	j.	PROPN
ejpam-5154	230	2	pure	pure	PROPN
ejpam-5154	230	3	appl	appl	PROPN
ejpam-5154	230	4	.	.	PUNCT
ejpam-5154	230	5	math	math	PROPN
ejpam-5154	230	6	.	.	PUNCT
ejpam-5154	230	7	,	,	PUNCT
ejpam-5154	231	1	16(2):1154–1166	16(2):1154–1166	NUM
ejpam-5154	231	2	,	,	PUNCT
ejpam-5154	231	3	2023	2023	NUM
ejpam-5154	231	4	.	.	PUNCT
ejpam-5154	232	1	[	[	X
ejpam-5154	232	2	8	8	NUM
ejpam-5154	232	3	]	]	PUNCT
ejpam-5154	232	4	j.	j.	PROPN
ejpam-5154	232	5	hassan	hassan	PROPN
ejpam-5154	232	6	and	and	CCONJ
ejpam-5154	232	7	s.	s.	PROPN
ejpam-5154	232	8	canoy	canoy	PROPN
ejpam-5154	232	9	jr	jr	PROPN
ejpam-5154	232	10	.	.	PUNCT
ejpam-5154	233	1	grundy	grundy	PROPN
ejpam-5154	233	2	total	total	PROPN
ejpam-5154	233	3	hop	hop	PROPN
ejpam-5154	233	4	dominating	dominate	VERB
ejpam-5154	233	5	sequences	sequence	NOUN
ejpam-5154	233	6	in	in	ADP
ejpam-5154	233	7	graphs	graph	NOUN
ejpam-5154	233	8	.	.	PUNCT
ejpam-5154	234	1	eur	eur	PROPN
ejpam-5154	234	2	.	.	PUNCT
ejpam-5154	235	1	j.	j.	PROPN
ejpam-5154	235	2	appl	appl	PROPN
ejpam-5154	235	3	.	.	PROPN
ejpam-5154	235	4	math	math	PROPN
ejpam-5154	235	5	.	.	PUNCT
ejpam-5154	235	6	,	,	PUNCT
ejpam-5154	235	7	16(4):2597–2612	16(4):2597–2612	NUM
ejpam-5154	235	8	,	,	PUNCT
ejpam-5154	235	9	2023	2023	NUM
ejpam-5154	235	10	.	.	PUNCT
ejpam-5154	236	1	[	[	X
ejpam-5154	236	2	9	9	NUM
ejpam-5154	236	3	]	]	PUNCT
ejpam-5154	236	4	j.	j.	PROPN
ejpam-5154	236	5	hassan	hassan	PROPN
ejpam-5154	236	6	and	and	CCONJ
ejpam-5154	236	7	j.	j.	PROPN
ejpam-5154	236	8	i.	i.	PROPN
ejpam-5154	236	9	salim	salim	PROPN
ejpam-5154	236	10	.	.	PUNCT
ejpam-5154	237	1	j	j	PROPN
ejpam-5154	237	2	-	-	PUNCT
ejpam-5154	237	3	domination	domination	NOUN
ejpam-5154	237	4	in	in	ADP
ejpam-5154	237	5	graphs	graph	NOUN
ejpam-5154	237	6	.	.	PUNCT
ejpam-5154	238	1	eur	eur	PROPN
ejpam-5154	238	2	.	.	PUNCT
ejpam-5154	239	1	j.	j.	PROPN
ejpam-5154	239	2	pure	pure	PROPN
ejpam-5154	239	3	appl	appl	PROPN
ejpam-5154	239	4	.	.	PUNCT
ejpam-5154	239	5	math	math	PROPN
ejpam-5154	239	6	.	.	PUNCT
ejpam-5154	239	7	,	,	PUNCT
ejpam-5154	239	8	16(4):2082–2095	16(4):2082–2095	NUM
ejpam-5154	239	9	,	,	PUNCT
ejpam-5154	239	10	2023	2023	NUM
ejpam-5154	239	11	.	.	PUNCT
ejpam-5154	240	1	[	[	X
ejpam-5154	240	2	10	10	NUM
ejpam-5154	240	3	]	]	X
ejpam-5154	240	4	s.	s.	PROPN
ejpam-5154	240	5	canoy	canoy	PROPN
ejpam-5154	240	6	jr	jr	PROPN
ejpam-5154	240	7	.	.	PROPN
ejpam-5154	240	8	and	and	CCONJ
ejpam-5154	240	9	g.	g.	PROPN
ejpam-5154	240	10	salasalan	salasalan	NOUN
ejpam-5154	240	11	.	.	PUNCT
ejpam-5154	241	1	revisiting	revisit	VERB
ejpam-5154	241	2	domination	domination	NOUN
ejpam-5154	241	3	,	,	PUNCT
ejpam-5154	241	4	hop	hop	NOUN
ejpam-5154	241	5	domination	domination	NOUN
ejpam-5154	241	6	,	,	PUNCT
ejpam-5154	241	7	and	and	CCONJ
ejpam-5154	241	8	global	global	ADJ
ejpam-5154	241	9	hop	hop	NOUN
ejpam-5154	241	10	domination	domination	NOUN
ejpam-5154	241	11	in	in	ADP
ejpam-5154	241	12	graphs	graph	NOUN
ejpam-5154	241	13	.	.	PUNCT
ejpam-5154	242	1	eur	eur	PROPN
ejpam-5154	242	2	.	.	PUNCT
ejpam-5154	243	1	j.	j.	PROPN
ejpam-5154	243	2	pure	pure	PROPN
ejpam-5154	243	3	appl	appl	PROPN
ejpam-5154	243	4	.	.	PUNCT
ejpam-5154	243	5	math	math	PROPN
ejpam-5154	243	6	.	.	PUNCT
ejpam-5154	243	7	,	,	PUNCT
ejpam-5154	243	8	14:1415–1428	14:1415–1428	NUM
ejpam-5154	243	9	,	,	PUNCT
ejpam-5154	243	10	2021	2021	NUM
ejpam-5154	243	11	.	.	PUNCT
ejpam-5154	244	1	[	[	X
ejpam-5154	244	2	11	11	NUM
ejpam-5154	244	3	]	]	PUNCT
ejpam-5154	244	4	j.	j.	PROPN
ejpam-5154	244	5	manditong	manditong	PROPN
ejpam-5154	244	6	,	,	PUNCT
ejpam-5154	244	7	a.	a.	NOUN
ejpam-5154	244	8	tapeing	tapeing	NOUN
ejpam-5154	244	9	,	,	PUNCT
ejpam-5154	244	10	j.	j.	PROPN
ejpam-5154	244	11	hassan	hassan	PROPN
ejpam-5154	244	12	,	,	PUNCT
ejpam-5154	244	13	a.	a.	PROPN
ejpam-5154	244	14	r.	r.	PROPN
ejpam-5154	244	15	bakkang	bakkang	PROPN
ejpam-5154	244	16	,	,	PUNCT
ejpam-5154	244	17	n.	n.	PROPN
ejpam-5154	244	18	h.	h.	PROPN
ejpam-5154	244	19	mohammad	mohammad	PROPN
ejpam-5154	244	20	,	,	PUNCT
ejpam-5154	244	21	and	and	CCONJ
ejpam-5154	244	22	s.	s.	PROPN
ejpam-5154	244	23	u.	u.	PROPN
ejpam-5154	244	24	kamdon	kamdon	PROPN
ejpam-5154	244	25	.	.	PUNCT
ejpam-5154	245	1	some	some	DET
ejpam-5154	245	2	properties	property	NOUN
ejpam-5154	245	3	of	of	ADP
ejpam-5154	245	4	zero	zero	NUM
ejpam-5154	245	5	forcing	force	VERB
ejpam-5154	245	6	hop	hop	NOUN
ejpam-5154	245	7	dominating	dominating	NOUN
ejpam-5154	245	8	sets	set	NOUN
ejpam-5154	245	9	in	in	ADP
ejpam-5154	245	10	a	a	DET
ejpam-5154	245	11	graph	graph	NOUN
ejpam-5154	245	12	.	.	PUNCT
ejpam-5154	246	1	eur	eur	PROPN
ejpam-5154	246	2	.	.	PUNCT
ejpam-5154	247	1	j.	j.	PROPN
ejpam-5154	247	2	appl	appl	PROPN
ejpam-5154	247	3	.	.	PROPN
ejpam-5154	247	4	math	math	PROPN
ejpam-5154	247	5	.	.	PUNCT
ejpam-5154	248	1	,	,	PUNCT
ejpam-5154	248	2	17(1):324–337	17(1):324–337	PROPN
ejpam-5154	248	3	,	,	PUNCT
ejpam-5154	248	4	2024	2024	NUM
ejpam-5154	248	5	.	.	PUNCT
ejpam-5154	249	1	[	[	X
ejpam-5154	249	2	12	12	NUM
ejpam-5154	249	3	]	]	X
ejpam-5154	249	4	c.	c.	PROPN
ejpam-5154	249	5	natarajan	natarajan	PROPN
ejpam-5154	249	6	and	and	CCONJ
ejpam-5154	249	7	s.	s.	PROPN
ejpam-5154	249	8	ayyaswamy	ayyaswamy	PROPN
ejpam-5154	249	9	.	.	PUNCT
ejpam-5154	250	1	hop	hop	PROPN
ejpam-5154	250	2	domination	domination	NOUN
ejpam-5154	250	3	in	in	ADP
ejpam-5154	250	4	graphs	graphs	PROPN
ejpam-5154	250	5	ii	ii	PROPN
ejpam-5154	250	6	.	.	PUNCT
ejpam-5154	250	7	versita	versita	PROPN
ejpam-5154	250	8	,	,	PUNCT
ejpam-5154	250	9	23(2):187	23(2):187	NUM
ejpam-5154	250	10	–	–	PUNCT
ejpam-5154	250	11	199	199	NUM
ejpam-5154	250	12	,	,	PUNCT
ejpam-5154	250	13	2015	2015	NUM
ejpam-5154	250	14	.	.	PUNCT
ejpam-5154	251	1	references	reference	NOUN
ejpam-5154	251	2	3780	3780	NUM
ejpam-5154	251	3	[	[	X
ejpam-5154	251	4	13	13	NUM
ejpam-5154	251	5	]	]	X
ejpam-5154	251	6	o.	o.	PROPN
ejpam-5154	251	7	ore	ore	PROPN
ejpam-5154	251	8	.	.	PUNCT
ejpam-5154	252	1	theory	theory	NOUN
ejpam-5154	252	2	of	of	ADP
ejpam-5154	252	3	graphs	graph	NOUN
ejpam-5154	252	4	.	.	PUNCT
ejpam-5154	253	1	amer	amer	PROPN
ejpam-5154	253	2	.	.	PUNCT
ejpam-5154	253	3	math	math	PROPN
ejpam-5154	253	4	.	.	PUNCT
ejpam-5154	254	1	soc	soc	PROPN
ejpam-5154	254	2	.	.	PUNCT
ejpam-5154	255	1	colloq	colloq	PROPN
ejpam-5154	255	2	.	.	PUNCT
ejpam-5154	256	1	publ	publ	PROPN
ejpam-5154	256	2	.	.	PUNCT
ejpam-5154	256	3	,	,	PUNCT
ejpam-5154	256	4	38	38	NUM
ejpam-5154	256	5	,	,	PUNCT
ejpam-5154	256	6	amer	amer	PROPN
ejpam-5154	256	7	.	.	PROPN
ejpam-5154	256	8	math	math	PROPN
ejpam-5154	256	9	.	.	PUNCT
ejpam-5154	257	1	soc	soc	PROPN
ejpam-5154	257	2	.	.	PUNCT
ejpam-5154	257	3	,	,	PUNCT
ejpam-5154	257	4	providence	providence	NOUN
ejpam-5154	257	5	,	,	PUNCT
ejpam-5154	257	6	ri	ri	PROPN
ejpam-5154	257	7	,	,	PUNCT
ejpam-5154	257	8	1962	1962	NUM
ejpam-5154	257	9	.	.	PUNCT
ejpam-5154	258	1	[	[	X
ejpam-5154	258	2	14	14	NUM
ejpam-5154	258	3	]	]	X
ejpam-5154	258	4	y.	y.	PROPN
ejpam-5154	258	5	pabilona	pabilona	PROPN
ejpam-5154	258	6	and	and	CCONJ
ejpam-5154	258	7	h.	h.	PROPN
ejpam-5154	258	8	rara	rara	PROPN
ejpam-5154	258	9	.	.	PUNCT
ejpam-5154	259	1	total	total	ADJ
ejpam-5154	259	2	hop	hop	NOUN
ejpam-5154	259	3	dominating	dominating	NOUN
ejpam-5154	259	4	sets	set	NOUN
ejpam-5154	259	5	in	in	ADP
ejpam-5154	259	6	the	the	DET
ejpam-5154	259	7	join	join	NOUN
ejpam-5154	259	8	,	,	PUNCT
ejpam-5154	259	9	corona	corona	NOUN
ejpam-5154	259	10	and	and	CCONJ
ejpam-5154	259	11	lexicographic	lexicographic	ADJ
ejpam-5154	259	12	product	product	NOUN
ejpam-5154	259	13	of	of	ADP
ejpam-5154	259	14	graphs	graph	NOUN
ejpam-5154	259	15	.	.	PUNCT
ejpam-5154	260	1	jour	jour	X
ejpam-5154	260	2	.	.	PROPN
ejpam-5154	260	3	of	of	ADP
ejpam-5154	260	4	algebra	algebra	NOUN
ejpam-5154	260	5	and	and	CCONJ
ejpam-5154	260	6	appl	appl	PROPN
ejpam-5154	260	7	.	.	PROPN
ejpam-5154	260	8	math	math	PROPN
ejpam-5154	260	9	.	.	PUNCT
ejpam-5154	260	10	,	,	PUNCT
ejpam-5154	260	11	2:103–115	2:103–115	PROPN
ejpam-5154	260	12	,	,	PUNCT
ejpam-5154	260	13	2017	2017	NUM
ejpam-5154	260	14	.	.	PUNCT
ejpam-5154	261	1	[	[	X
ejpam-5154	261	2	15	15	NUM
ejpam-5154	261	3	]	]	X
ejpam-5154	261	4	g.	g.	NOUN
ejpam-5154	261	5	salasalan	salasalan	NOUN
ejpam-5154	261	6	and	and	CCONJ
ejpam-5154	261	7	s.	s.	PROPN
ejpam-5154	261	8	canoy	canoy	PROPN
ejpam-5154	261	9	jr	jr	PROPN
ejpam-5154	261	10	.	.	PROPN
ejpam-5154	261	11	global	global	PROPN
ejpam-5154	261	12	hop	hop	PROPN
ejpam-5154	261	13	domination	domination	PROPN
ejpam-5154	261	14	numbers	number	NOUN
ejpam-5154	261	15	of	of	ADP
ejpam-5154	261	16	graphs	graph	NOUN
ejpam-5154	261	17	.	.	PUNCT
ejpam-5154	262	1	eur	eur	PROPN
ejpam-5154	262	2	.	.	PUNCT
ejpam-5154	263	1	j.	j.	PROPN
ejpam-5154	263	2	pure	pure	PROPN
ejpam-5154	263	3	appl	appl	PROPN
ejpam-5154	263	4	.	.	PUNCT
ejpam-5154	263	5	math	math	PROPN
ejpam-5154	263	6	.	.	PUNCT
ejpam-5154	263	7	,	,	PUNCT
ejpam-5154	263	8	14(1):112–125	14(1):112–125	NUM
ejpam-5154	263	9	,	,	PUNCT
ejpam-5154	263	10	2021	2021	NUM
ejpam-5154	263	11	.	.	PUNCT