id	sid	tid	token	lemma	pos
ejpam-5046	1	1	european	european	PROPN
ejpam-5046	1	2	journal	journal	PROPN
ejpam-5046	1	3	of	of	ADP
ejpam-5046	1	4	pure	pure	ADJ
ejpam-5046	1	5	and	and	CCONJ
ejpam-5046	1	6	applied	apply	VERB
ejpam-5046	1	7	mathematics	mathematic	NOUN
ejpam-5046	1	8	vol	vol	NOUN
ejpam-5046	1	9	.	.	PROPN
ejpam-5046	2	1	17	17	NUM
ejpam-5046	2	2	,	,	PUNCT
ejpam-5046	2	3	no	no	INTJ
ejpam-5046	2	4	.	.	NOUN
ejpam-5046	2	5	2	2	NUM
ejpam-5046	2	6	,	,	PUNCT
ejpam-5046	2	7	2024	2024	NUM
ejpam-5046	2	8	,	,	PUNCT
ejpam-5046	2	9	1283	1283	NUM
ejpam-5046	2	10	-	-	SYM
ejpam-5046	2	11	1293	1293	NUM
ejpam-5046	2	12	issn	issn	PROPN
ejpam-5046	2	13	1307	1307	NUM
ejpam-5046	2	14	-	-	SYM
ejpam-5046	2	15	5543	5543	NUM
ejpam-5046	2	16	–	–	PUNCT
ejpam-5046	2	17	ejpam.com	ejpam.com	X
ejpam-5046	2	18	published	publish	VERB
ejpam-5046	2	19	by	by	ADP
ejpam-5046	2	20	new	new	PROPN
ejpam-5046	2	21	york	york	PROPN
ejpam-5046	2	22	business	business	PROPN
ejpam-5046	2	23	global	global	ADJ
ejpam-5046	2	24	2	2	NUM
ejpam-5046	2	25	-	-	PUNCT
ejpam-5046	2	26	distance	distance	NOUN
ejpam-5046	2	27	zero	zero	NUM
ejpam-5046	2	28	forcing	force	VERB
ejpam-5046	2	29	sets	set	NOUN
ejpam-5046	2	30	in	in	ADP
ejpam-5046	2	31	graphs	graph	NOUN
ejpam-5046	2	32	javier	javier	PROPN
ejpam-5046	2	33	a.	a.	PROPN
ejpam-5046	2	34	hassan∗	hassan∗	PROPN
ejpam-5046	2	35	,	,	PUNCT
ejpam-5046	2	36	lestlene	lestlene	ADJ
ejpam-5046	2	37	t.	t.	NOUN
ejpam-5046	2	38	udtohan	udtohan	PROPN
ejpam-5046	2	39	,	,	PUNCT
ejpam-5046	2	40	ladznar	ladznar	ADJ
ejpam-5046	2	41	s.	s.	PROPN
ejpam-5046	2	42	laja	laja	PROPN
ejpam-5046	2	43	mathematics	mathematics	PROPN
ejpam-5046	2	44	and	and	CCONJ
ejpam-5046	2	45	sciences	sciences	PROPN
ejpam-5046	2	46	department	department	PROPN
ejpam-5046	2	47	,	,	PUNCT
ejpam-5046	2	48	college	college	NOUN
ejpam-5046	2	49	of	of	ADP
ejpam-5046	2	50	arts	art	NOUN
ejpam-5046	2	51	and	and	CCONJ
ejpam-5046	2	52	sciences	science	NOUN
ejpam-5046	2	53	,	,	PUNCT
ejpam-5046	2	54	msu	msu	PROPN
ejpam-5046	2	55	tawi	tawi	PROPN
ejpam-5046	2	56	-	-	PUNCT
ejpam-5046	2	57	tawi	tawi	PROPN
ejpam-5046	2	58	college	college	PROPN
ejpam-5046	2	59	of	of	ADP
ejpam-5046	2	60	technology	technology	NOUN
ejpam-5046	2	61	and	and	CCONJ
ejpam-5046	2	62	oceanography	oceanography	NOUN
ejpam-5046	2	63	,	,	PUNCT
ejpam-5046	2	64	bongao	bongao	NOUN
ejpam-5046	2	65	,	,	PUNCT
ejpam-5046	2	66	tawi	tawi	NOUN
ejpam-5046	2	67	-	-	PUNCT
ejpam-5046	2	68	tawi	tawi	NOUN
ejpam-5046	2	69	,	,	PUNCT
ejpam-5046	2	70	philippines	philippine	NOUN
ejpam-5046	2	71	abstract	abstract	ADJ
ejpam-5046	2	72	.	.	PUNCT
ejpam-5046	3	1	in	in	ADP
ejpam-5046	3	2	this	this	DET
ejpam-5046	3	3	paper	paper	NOUN
ejpam-5046	3	4	,	,	PUNCT
ejpam-5046	3	5	we	we	PRON
ejpam-5046	3	6	introduce	introduce	VERB
ejpam-5046	3	7	new	new	ADJ
ejpam-5046	3	8	concept	concept	NOUN
ejpam-5046	3	9	in	in	ADP
ejpam-5046	3	10	graph	graph	NOUN
ejpam-5046	3	11	theory	theory	NOUN
ejpam-5046	3	12	called	call	VERB
ejpam-5046	3	13	2	2	NUM
ejpam-5046	3	14	-	-	PUNCT
ejpam-5046	3	15	distance	distance	NOUN
ejpam-5046	3	16	zero	zero	NUM
ejpam-5046	3	17	forcing	forcing	NOUN
ejpam-5046	3	18	.	.	PUNCT
ejpam-5046	4	1	we	we	PRON
ejpam-5046	4	2	give	give	VERB
ejpam-5046	4	3	some	some	DET
ejpam-5046	4	4	properties	property	NOUN
ejpam-5046	4	5	of	of	ADP
ejpam-5046	4	6	this	this	DET
ejpam-5046	4	7	new	new	ADJ
ejpam-5046	4	8	parameter	parameter	NOUN
ejpam-5046	4	9	and	and	CCONJ
ejpam-5046	4	10	investigate	investigate	VERB
ejpam-5046	4	11	its	its	PRON
ejpam-5046	4	12	connections	connection	NOUN
ejpam-5046	4	13	with	with	ADP
ejpam-5046	4	14	other	other	ADJ
ejpam-5046	4	15	parameters	parameter	NOUN
ejpam-5046	4	16	such	such	ADJ
ejpam-5046	4	17	as	as	ADP
ejpam-5046	4	18	zero	zero	NUM
ejpam-5046	4	19	forcing	forcing	NOUN
ejpam-5046	4	20	and	and	CCONJ
ejpam-5046	4	21	hop	hop	NOUN
ejpam-5046	4	22	domination	domination	NOUN
ejpam-5046	4	23	.	.	PUNCT
ejpam-5046	5	1	we	we	PRON
ejpam-5046	5	2	show	show	VERB
ejpam-5046	5	3	that	that	SCONJ
ejpam-5046	5	4	2	2	NUM
ejpam-5046	5	5	-	-	PUNCT
ejpam-5046	5	6	distance	distance	NOUN
ejpam-5046	5	7	zero	zero	NUM
ejpam-5046	5	8	forcing	forcing	NOUN
ejpam-5046	5	9	and	and	CCONJ
ejpam-5046	5	10	hop	hop	NOUN
ejpam-5046	5	11	domination(respectively	domination(respectively	ADV
ejpam-5046	5	12	,	,	PUNCT
ejpam-5046	5	13	zero	zero	NUM
ejpam-5046	5	14	forcing	forcing	NOUN
ejpam-5046	5	15	parameter	parameter	NOUN
ejpam-5046	5	16	)	)	PUNCT
ejpam-5046	5	17	are	be	AUX
ejpam-5046	5	18	incomparable	incomparable	ADJ
ejpam-5046	5	19	.	.	PUNCT
ejpam-5046	6	1	moreover	moreover	ADV
ejpam-5046	6	2	,	,	PUNCT
ejpam-5046	6	3	we	we	PRON
ejpam-5046	6	4	characterize	characterize	VERB
ejpam-5046	6	5	2	2	NUM
ejpam-5046	6	6	-	-	PUNCT
ejpam-5046	6	7	distance	distance	NOUN
ejpam-5046	6	8	zero	zero	NUM
ejpam-5046	6	9	forcing	force	VERB
ejpam-5046	6	10	sets	set	NOUN
ejpam-5046	6	11	in	in	ADP
ejpam-5046	6	12	some	some	DET
ejpam-5046	6	13	special	special	ADJ
ejpam-5046	6	14	graphs	graph	NOUN
ejpam-5046	6	15	,	,	PUNCT
ejpam-5046	6	16	and	and	CCONJ
ejpam-5046	6	17	finally	finally	ADV
ejpam-5046	6	18	derive	derive	VERB
ejpam-5046	6	19	the	the	DET
ejpam-5046	6	20	exact	exact	ADJ
ejpam-5046	6	21	values	value	NOUN
ejpam-5046	6	22	or	or	CCONJ
ejpam-5046	6	23	bounds	bound	NOUN
ejpam-5046	6	24	of	of	ADP
ejpam-5046	6	25	the	the	DET
ejpam-5046	6	26	parameter	parameter	NOUN
ejpam-5046	6	27	using	use	VERB
ejpam-5046	6	28	these	these	DET
ejpam-5046	6	29	results	result	NOUN
ejpam-5046	6	30	.	.	PUNCT
ejpam-5046	7	1	2020	2020	NUM
ejpam-5046	7	2	mathematics	mathematic	NOUN
ejpam-5046	7	3	subject	subject	NOUN
ejpam-5046	7	4	classifications	classification	NOUN
ejpam-5046	7	5	:	:	PUNCT
ejpam-5046	7	6	05c69	05c69	X
ejpam-5046	7	7	key	key	ADJ
ejpam-5046	7	8	words	word	NOUN
ejpam-5046	7	9	and	and	CCONJ
ejpam-5046	7	10	phrases	phrase	NOUN
ejpam-5046	7	11	:	:	PUNCT
ejpam-5046	7	12	zero	zero	NUM
ejpam-5046	7	13	forcing	forcing	NOUN
ejpam-5046	7	14	,	,	PUNCT
ejpam-5046	7	15	2	2	NUM
ejpam-5046	7	16	-	-	PUNCT
ejpam-5046	7	17	distance	distance	NOUN
ejpam-5046	7	18	zero	zero	NUM
ejpam-5046	7	19	forcing	forcing	NOUN
ejpam-5046	7	20	,	,	PUNCT
ejpam-5046	7	21	2	2	NUM
ejpam-5046	7	22	-	-	PUNCT
ejpam-5046	7	23	distance	distance	NOUN
ejpam-5046	7	24	zero	zero	NUM
ejpam-5046	7	25	forcing	force	VERB
ejpam-5046	7	26	number	number	NOUN
ejpam-5046	7	27	1	1	NUM
ejpam-5046	7	28	.	.	PUNCT
ejpam-5046	8	1	introduction	introduction	NOUN
ejpam-5046	8	2	zero	zero	NUM
ejpam-5046	8	3	forcing	force	VERB
ejpam-5046	8	4	is	be	AUX
ejpam-5046	8	5	a	a	DET
ejpam-5046	8	6	propagation	propagation	NOUN
ejpam-5046	8	7	process	process	NOUN
ejpam-5046	8	8	in	in	ADP
ejpam-5046	8	9	a	a	DET
ejpam-5046	8	10	graph	graph	NOUN
ejpam-5046	8	11	that	that	PRON
ejpam-5046	8	12	increases	increase	VERB
ejpam-5046	8	13	the	the	DET
ejpam-5046	8	14	number	number	NOUN
ejpam-5046	8	15	of	of	ADP
ejpam-5046	8	16	blue	blue	ADJ
ejpam-5046	8	17	vertices	vertex	NOUN
ejpam-5046	8	18	given	give	VERB
ejpam-5046	8	19	on	on	ADP
ejpam-5046	8	20	initial	initial	ADJ
ejpam-5046	8	21	set	set	NOUN
ejpam-5046	8	22	of	of	ADP
ejpam-5046	8	23	blue	blue	ADJ
ejpam-5046	8	24	vertices	vertex	NOUN
ejpam-5046	8	25	,	,	PUNCT
ejpam-5046	8	26	with	with	ADP
ejpam-5046	8	27	all	all	DET
ejpam-5046	8	28	other	other	ADJ
ejpam-5046	8	29	vertices	vertex	NOUN
ejpam-5046	8	30	white	white	ADJ
ejpam-5046	8	31	,	,	PUNCT
ejpam-5046	8	32	and	and	CCONJ
ejpam-5046	8	33	a	a	DET
ejpam-5046	8	34	colorchange	colorchange	NOUN
ejpam-5046	8	35	rule	rule	NOUN
ejpam-5046	8	36	.	.	PUNCT
ejpam-5046	9	1	the	the	DET
ejpam-5046	9	2	color	color	NOUN
ejpam-5046	9	3	-	-	PUNCT
ejpam-5046	9	4	change	change	NOUN
ejpam-5046	9	5	rule	rule	NOUN
ejpam-5046	9	6	states	state	NOUN
ejpam-5046	9	7	that	that	SCONJ
ejpam-5046	9	8	a	a	DET
ejpam-5046	9	9	blue	blue	ADJ
ejpam-5046	9	10	vertex	vertex	NOUN
ejpam-5046	9	11	adjacent	adjacent	ADJ
ejpam-5046	9	12	to	to	ADP
ejpam-5046	9	13	a	a	DET
ejpam-5046	9	14	single	single	ADJ
ejpam-5046	9	15	white	white	ADJ
ejpam-5046	9	16	neighbor	neighbor	NOUN
ejpam-5046	9	17	can	can	AUX
ejpam-5046	9	18	force	force	VERB
ejpam-5046	9	19	its	its	PRON
ejpam-5046	9	20	neighbor	neighbor	NOUN
ejpam-5046	9	21	to	to	PART
ejpam-5046	9	22	blue	blue	VERB
ejpam-5046	9	23	.	.	PUNCT
ejpam-5046	10	1	formally	formally	ADV
ejpam-5046	10	2	,	,	PUNCT
ejpam-5046	10	3	if	if	SCONJ
ejpam-5046	10	4	u	u	NOUN
ejpam-5046	10	5	is	be	AUX
ejpam-5046	10	6	a	a	DET
ejpam-5046	10	7	blue	blue	ADJ
ejpam-5046	10	8	vertex	vertex	NOUN
ejpam-5046	10	9	and	and	CCONJ
ejpam-5046	10	10	w	w	NOUN
ejpam-5046	10	11	is	be	AUX
ejpam-5046	10	12	the	the	DET
ejpam-5046	10	13	only	only	ADJ
ejpam-5046	10	14	white	white	ADJ
ejpam-5046	10	15	vertex	vertex	NOUN
ejpam-5046	10	16	in	in	ADP
ejpam-5046	10	17	n(u	n(u	PROPN
ejpam-5046	10	18	)	)	PUNCT
ejpam-5046	10	19	,	,	PUNCT
ejpam-5046	10	20	then	then	ADV
ejpam-5046	10	21	u−→w	u−→w	PROPN
ejpam-5046	10	22	will	will	AUX
ejpam-5046	10	23	be	be	AUX
ejpam-5046	10	24	used	use	VERB
ejpam-5046	10	25	to	to	PART
ejpam-5046	10	26	denote	denote	VERB
ejpam-5046	10	27	that	that	SCONJ
ejpam-5046	10	28	u	u	PROPN
ejpam-5046	10	29	forces	force	VERB
ejpam-5046	10	30	w	w	VERB
ejpam-5046	10	31	to	to	PART
ejpam-5046	10	32	blue	blue	VERB
ejpam-5046	10	33	.	.	PUNCT
ejpam-5046	11	1	given	give	VERB
ejpam-5046	11	2	a	a	DET
ejpam-5046	11	3	graph	graph	NOUN
ejpam-5046	11	4	g	g	NOUN
ejpam-5046	11	5	,	,	PUNCT
ejpam-5046	11	6	a	a	DET
ejpam-5046	11	7	zero	zero	NUM
ejpam-5046	11	8	forcing	force	VERB
ejpam-5046	11	9	set	set	NOUN
ejpam-5046	11	10	b	b	PROPN
ejpam-5046	11	11	of	of	ADP
ejpam-5046	11	12	g	g	PROPN
ejpam-5046	11	13	is	be	AUX
ejpam-5046	11	14	a	a	DET
ejpam-5046	11	15	subset	subset	NOUN
ejpam-5046	11	16	of	of	ADP
ejpam-5046	11	17	vertices	vertex	NOUN
ejpam-5046	11	18	of	of	ADP
ejpam-5046	11	19	v	v	NOUN
ejpam-5046	11	20	(	(	PUNCT
ejpam-5046	11	21	g	g	NOUN
ejpam-5046	11	22	)	)	PUNCT
ejpam-5046	11	23	such	such	ADJ
ejpam-5046	11	24	that	that	SCONJ
ejpam-5046	11	25	b	b	NOUN
ejpam-5046	11	26	is	be	AUX
ejpam-5046	11	27	initially	initially	ADV
ejpam-5046	11	28	colored	color	VERB
ejpam-5046	11	29	blue	blue	ADJ
ejpam-5046	11	30	,	,	PUNCT
ejpam-5046	11	31	and	and	CCONJ
ejpam-5046	11	32	the	the	DET
ejpam-5046	11	33	remaining	remain	VERB
ejpam-5046	11	34	vertices	vertex	NOUN
ejpam-5046	11	35	in	in	ADP
ejpam-5046	11	36	g	g	PROPN
ejpam-5046	11	37	are	be	AUX
ejpam-5046	11	38	white	white	ADJ
ejpam-5046	11	39	,	,	PUNCT
ejpam-5046	11	40	then	then	ADV
ejpam-5046	11	41	iteratively	iteratively	ADV
ejpam-5046	11	42	applying	apply	VERB
ejpam-5046	11	43	applying	apply	VERB
ejpam-5046	11	44	the	the	DET
ejpam-5046	11	45	color	color	NOUN
ejpam-5046	11	46	-	-	PUNCT
ejpam-5046	11	47	change	change	NOUN
ejpam-5046	11	48	rule	rule	NOUN
ejpam-5046	11	49	given	give	VERB
ejpam-5046	11	50	b	b	NOUN
ejpam-5046	11	51	results	result	NOUN
ejpam-5046	11	52	in	in	ADP
ejpam-5046	11	53	every	every	DET
ejpam-5046	11	54	vertex	vertex	NOUN
ejpam-5046	11	55	in	in	ADP
ejpam-5046	11	56	g	g	NOUN
ejpam-5046	11	57	becoming	become	VERB
ejpam-5046	11	58	blue	blue	ADJ
ejpam-5046	11	59	.	.	PUNCT
ejpam-5046	12	1	zero	zero	NUM
ejpam-5046	12	2	forcing	force	VERB
ejpam-5046	12	3	sets	set	NOUN
ejpam-5046	12	4	have	have	VERB
ejpam-5046	12	5	applications	application	NOUN
ejpam-5046	12	6	in	in	ADP
ejpam-5046	12	7	control	control	NOUN
ejpam-5046	12	8	theory	theory	NOUN
ejpam-5046	12	9	,	,	PUNCT
ejpam-5046	12	10	network	network	NOUN
ejpam-5046	12	11	coding	coding	NOUN
ejpam-5046	12	12	,	,	PUNCT
ejpam-5046	12	13	and	and	CCONJ
ejpam-5046	12	14	determining	determine	VERB
ejpam-5046	12	15	structural	structural	ADJ
ejpam-5046	12	16	properties	property	NOUN
ejpam-5046	12	17	of	of	ADP
ejpam-5046	12	18	graphs	graph	NOUN
ejpam-5046	12	19	.	.	PUNCT
ejpam-5046	13	1	some	some	DET
ejpam-5046	13	2	studies	study	NOUN
ejpam-5046	13	3	related	relate	VERB
ejpam-5046	13	4	to	to	ADP
ejpam-5046	13	5	zero	zero	NUM
ejpam-5046	13	6	forcing	force	VERB
ejpam-5046	13	7	sets	set	NOUN
ejpam-5046	13	8	and	and	CCONJ
ejpam-5046	13	9	its	its	PRON
ejpam-5046	13	10	variants	variant	NOUN
ejpam-5046	13	11	can	can	AUX
ejpam-5046	13	12	be	be	AUX
ejpam-5046	13	13	found	find	VERB
ejpam-5046	13	14	in	in	ADP
ejpam-5046	13	15	[	[	X
ejpam-5046	13	16	1–6	1–6	NUM
ejpam-5046	13	17	]	]	X
ejpam-5046	13	18	.	.	PUNCT
ejpam-5046	14	1	recently	recently	ADV
ejpam-5046	14	2	,	,	PUNCT
ejpam-5046	14	3	j.	j.	PROPN
ejpam-5046	14	4	manditong	manditong	PROPN
ejpam-5046	14	5	et	et	PROPN
ejpam-5046	14	6	al.[16	al.[16	PROPN
ejpam-5046	14	7	]	]	PUNCT
ejpam-5046	14	8	,	,	PUNCT
ejpam-5046	14	9	introduced	introduce	VERB
ejpam-5046	14	10	new	new	ADJ
ejpam-5046	14	11	variant	variant	NOUN
ejpam-5046	14	12	of	of	ADP
ejpam-5046	14	13	zero	zero	NUM
ejpam-5046	14	14	forcing	force	VERB
ejpam-5046	14	15	in	in	ADP
ejpam-5046	14	16	a	a	DET
ejpam-5046	14	17	graph	graph	NOUN
ejpam-5046	14	18	called	call	VERB
ejpam-5046	14	19	zero	zero	NUM
ejpam-5046	14	20	forcing	force	VERB
ejpam-5046	14	21	hop	hop	NOUN
ejpam-5046	14	22	domination	domination	NOUN
ejpam-5046	14	23	.	.	PUNCT
ejpam-5046	15	1	they	they	PRON
ejpam-5046	15	2	have	have	AUX
ejpam-5046	15	3	established	establish	VERB
ejpam-5046	15	4	some	some	DET
ejpam-5046	15	5	properties	property	NOUN
ejpam-5046	15	6	of	of	ADP
ejpam-5046	15	7	this	this	DET
ejpam-5046	15	8	parameter	parameter	NOUN
ejpam-5046	15	9	and	and	CCONJ
ejpam-5046	15	10	determined	determine	VERB
ejpam-5046	15	11	its	its	PRON
ejpam-5046	15	12	connections	connection	NOUN
ejpam-5046	15	13	with	with	ADP
ejpam-5046	15	14	other	other	ADJ
ejpam-5046	15	15	known	know	VERB
ejpam-5046	15	16	parameters	parameter	NOUN
ejpam-5046	15	17	in	in	ADP
ejpam-5046	15	18	graph	graph	NOUN
ejpam-5046	15	19	theory	theory	NOUN
ejpam-5046	15	20	.	.	PUNCT
ejpam-5046	16	1	moreover	moreover	ADV
ejpam-5046	16	2	,	,	PUNCT
ejpam-5046	16	3	they	they	PRON
ejpam-5046	16	4	have	have	AUX
ejpam-5046	16	5	obtained	obtain	VERB
ejpam-5046	16	6	some	some	DET
ejpam-5046	16	7	exact	exact	ADJ
ejpam-5046	16	8	values	value	NOUN
ejpam-5046	16	9	or	or	CCONJ
ejpam-5046	16	10	bounds	bound	NOUN
ejpam-5046	16	11	of	of	ADP
ejpam-5046	16	12	the	the	DET
ejpam-5046	16	13	parameter	parameter	NOUN
ejpam-5046	16	14	on	on	ADP
ejpam-5046	16	15	the	the	DET
ejpam-5046	16	16	generalized	generalized	ADJ
ejpam-5046	16	17	graph	graph	NOUN
ejpam-5046	16	18	,	,	PUNCT
ejpam-5046	16	19	some	some	DET
ejpam-5046	16	20	families	family	NOUN
ejpam-5046	16	21	of	of	ADP
ejpam-5046	16	22	graphs	graph	NOUN
ejpam-5046	16	23	,	,	PUNCT
ejpam-5046	16	24	and	and	CCONJ
ejpam-5046	16	25	graphs	graph	NOUN
ejpam-5046	16	26	under	under	ADP
ejpam-5046	16	27	some	some	DET
ejpam-5046	16	28	operations	operation	NOUN
ejpam-5046	16	29	via	via	ADP
ejpam-5046	16	30	characterizations	characterization	NOUN
ejpam-5046	16	31	.	.	PUNCT
ejpam-5046	17	1	some	some	DET
ejpam-5046	17	2	interesting	interesting	ADJ
ejpam-5046	17	3	studies	study	NOUN
ejpam-5046	17	4	related	relate	VERB
ejpam-5046	17	5	to	to	ADP
ejpam-5046	17	6	zero	zero	NUM
ejpam-5046	17	7	forcing	force	VERB
ejpam-5046	17	8	hop	hop	NOUN
ejpam-5046	17	9	domination	domination	NOUN
ejpam-5046	17	10	can	can	AUX
ejpam-5046	17	11	be	be	AUX
ejpam-5046	17	12	found	find	VERB
ejpam-5046	17	13	in	in	ADP
ejpam-5046	17	14	[	[	X
ejpam-5046	17	15	7–15	7–15	PROPN
ejpam-5046	17	16	]	]	PUNCT
ejpam-5046	17	17	.	.	PUNCT
ejpam-5046	18	1	doi	doi	PROPN
ejpam-5046	18	2	:	:	PUNCT
ejpam-5046	18	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5046	https://doi.org/10.29020/nybg.ejpam.v17i2.5046	PROPN
ejpam-5046	18	4	email	email	NOUN
ejpam-5046	18	5	addresses	address	VERB
ejpam-5046	18	6	:	:	PUNCT
ejpam-5046	18	7	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-5046	18	8	(	(	PUNCT
ejpam-5046	18	9	j.	j.	PROPN
ejpam-5046	18	10	a.	a.	PROPN
ejpam-5046	18	11	hassan	hassan	PROPN
ejpam-5046	18	12	)	)	PUNCT
ejpam-5046	19	1	lestleneudtohan@msutawi-tawi.edu.ph	lestleneudtohan@msutawi-tawi.edu.ph	PROPN
ejpam-5046	19	2	(	(	PUNCT
ejpam-5046	19	3	l.	l.	PROPN
ejpam-5046	19	4	t.udtohan	t.udtohan	NOUN
ejpam-5046	19	5	)	)	PUNCT
ejpam-5046	19	6	ladznarlaja@msutawi-tawi.edu.ph	ladznarlaja@msutawi-tawi.edu.ph	PROPN
ejpam-5046	19	7	(	(	PUNCT
ejpam-5046	19	8	l.s	l.s	NOUN
ejpam-5046	19	9	.	.	PROPN
ejpam-5046	19	10	laja	laja	PROPN
ejpam-5046	19	11	)	)	PUNCT
ejpam-5046	19	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5046	19	13	1283	1283	NUM
ejpam-5046	20	1	©	©	ADP
ejpam-5046	20	2	2024	2024	NUM
ejpam-5046	20	3	ejpam	ejpam	NOUN
ejpam-5046	20	4	all	all	DET
ejpam-5046	20	5	rights	right	NOUN
ejpam-5046	20	6	reserved	reserve	VERB
ejpam-5046	20	7	.	.	PUNCT
ejpam-5046	21	1	j.	j.	PROPN
ejpam-5046	21	2	a.	a.	PROPN
ejpam-5046	21	3	hassan	hassan	PROPN
ejpam-5046	21	4	,	,	PUNCT
ejpam-5046	21	5	l.	l.	PROPN
ejpam-5046	21	6	t.	t.	PROPN
ejpam-5046	21	7	udtohan	udtohan	PROPN
ejpam-5046	21	8	,	,	PUNCT
ejpam-5046	21	9	l.	l.	PROPN
ejpam-5046	21	10	s.	s.	PROPN
ejpam-5046	21	11	laja	laja	PROPN
ejpam-5046	21	12	/	/	SYM
ejpam-5046	21	13	eur	eur	PROPN
ejpam-5046	21	14	.	.	PUNCT
ejpam-5046	22	1	j.	j.	PROPN
ejpam-5046	22	2	pure	pure	PROPN
ejpam-5046	22	3	appl	appl	PROPN
ejpam-5046	22	4	.	.	PROPN
ejpam-5046	22	5	math	math	PROPN
ejpam-5046	22	6	,	,	PUNCT
ejpam-5046	22	7	17	17	NUM
ejpam-5046	22	8	(	(	PUNCT
ejpam-5046	22	9	2	2	NUM
ejpam-5046	22	10	)	)	PUNCT
ejpam-5046	22	11	(	(	PUNCT
ejpam-5046	22	12	2024	2024	NUM
ejpam-5046	22	13	)	)	PUNCT
ejpam-5046	22	14	,	,	PUNCT
ejpam-5046	22	15	1283	1283	NUM
ejpam-5046	22	16	-	-	SYM
ejpam-5046	22	17	1293	1293	NUM
ejpam-5046	22	18	1284	1284	NUM
ejpam-5046	22	19	in	in	ADP
ejpam-5046	22	20	this	this	DET
ejpam-5046	22	21	paper	paper	NOUN
ejpam-5046	22	22	,	,	PUNCT
ejpam-5046	22	23	we	we	PRON
ejpam-5046	22	24	introduce	introduce	VERB
ejpam-5046	22	25	the	the	DET
ejpam-5046	22	26	concept	concept	NOUN
ejpam-5046	22	27	of	of	ADP
ejpam-5046	22	28	2	2	NUM
ejpam-5046	22	29	-	-	PUNCT
ejpam-5046	22	30	distance	distance	NOUN
ejpam-5046	22	31	zero	zero	NUM
ejpam-5046	22	32	forcing	force	VERB
ejpam-5046	22	33	sets	set	NOUN
ejpam-5046	22	34	in	in	ADP
ejpam-5046	22	35	a	a	DET
ejpam-5046	22	36	graph	graph	NOUN
ejpam-5046	22	37	.	.	PUNCT
ejpam-5046	23	1	let	let	VERB
ejpam-5046	23	2	g	g	PRON
ejpam-5046	23	3	be	be	AUX
ejpam-5046	23	4	a	a	DET
ejpam-5046	23	5	graph	graph	NOUN
ejpam-5046	23	6	and	and	CCONJ
ejpam-5046	23	7	let	let	VERB
ejpam-5046	23	8	x	x	PRON
ejpam-5046	23	9	,	,	PUNCT
ejpam-5046	23	10	y	y	PROPN
ejpam-5046	23	11	∈	∈	PROPN
ejpam-5046	23	12	v	v	NOUN
ejpam-5046	23	13	(	(	PUNCT
ejpam-5046	23	14	g	g	NOUN
ejpam-5046	23	15	)	)	PUNCT
ejpam-5046	23	16	.	.	PUNCT
ejpam-5046	24	1	then	then	ADV
ejpam-5046	24	2	the	the	DET
ejpam-5046	24	3	2	2	NUM
ejpam-5046	24	4	-	-	PUNCT
ejpam-5046	24	5	distance	distance	NOUN
ejpam-5046	24	6	color	color	NOUN
ejpam-5046	24	7	change	change	NOUN
ejpam-5046	24	8	rule	rule	NOUN
ejpam-5046	24	9	is	be	AUX
ejpam-5046	24	10	if	if	SCONJ
ejpam-5046	24	11	x	x	PRON
ejpam-5046	24	12	is	be	AUX
ejpam-5046	24	13	colored	color	VERB
ejpam-5046	24	14	(	(	PUNCT
ejpam-5046	24	15	active	active	ADJ
ejpam-5046	24	16	)	)	PUNCT
ejpam-5046	24	17	vertex	vertex	NOUN
ejpam-5046	24	18	and	and	CCONJ
ejpam-5046	24	19	exactly	exactly	ADV
ejpam-5046	24	20	one	one	NUM
ejpam-5046	24	21	hop	hop	NOUN
ejpam-5046	24	22	neighbor	neighbor	NOUN
ejpam-5046	24	23	y	y	PROPN
ejpam-5046	24	24	of	of	ADP
ejpam-5046	24	25	x	x	PRON
ejpam-5046	24	26	is	be	AUX
ejpam-5046	24	27	uncolored	uncolored	ADJ
ejpam-5046	24	28	(	(	PUNCT
ejpam-5046	24	29	inactive	inactive	ADJ
ejpam-5046	24	30	)	)	PUNCT
ejpam-5046	24	31	,	,	PUNCT
ejpam-5046	24	32	then	then	ADV
ejpam-5046	24	33	y	y	PROPN
ejpam-5046	24	34	will	will	AUX
ejpam-5046	24	35	become	become	VERB
ejpam-5046	24	36	colored	colored	ADJ
ejpam-5046	24	37	(	(	PUNCT
ejpam-5046	24	38	active	active	ADJ
ejpam-5046	24	39	)	)	PUNCT
ejpam-5046	24	40	.	.	PUNCT
ejpam-5046	25	1	a	a	DET
ejpam-5046	25	2	2	2	NUM
ejpam-5046	25	3	-	-	PUNCT
ejpam-5046	25	4	distance	distance	NOUN
ejpam-5046	25	5	zero	zero	NUM
ejpam-5046	25	6	forcing	force	VERB
ejpam-5046	25	7	set	set	NOUN
ejpam-5046	25	8	n	n	PROPN
ejpam-5046	25	9	of	of	ADP
ejpam-5046	25	10	g	g	PROPN
ejpam-5046	25	11	is	be	AUX
ejpam-5046	25	12	a	a	DET
ejpam-5046	25	13	subset	subset	NOUN
ejpam-5046	25	14	of	of	ADP
ejpam-5046	25	15	vertices	vertex	NOUN
ejpam-5046	25	16	of	of	ADP
ejpam-5046	25	17	g	g	NOUN
ejpam-5046	25	18	such	such	ADJ
ejpam-5046	25	19	that	that	SCONJ
ejpam-5046	25	20	when	when	SCONJ
ejpam-5046	25	21	the	the	DET
ejpam-5046	25	22	vertices	vertex	NOUN
ejpam-5046	25	23	in	in	ADP
ejpam-5046	25	24	n	n	CCONJ
ejpam-5046	25	25	are	be	AUX
ejpam-5046	25	26	colored	color	VERB
ejpam-5046	25	27	(	(	PUNCT
ejpam-5046	25	28	active	active	ADJ
ejpam-5046	25	29	)	)	PUNCT
ejpam-5046	25	30	and	and	CCONJ
ejpam-5046	25	31	the	the	DET
ejpam-5046	25	32	remaining	remain	VERB
ejpam-5046	25	33	vertices	vertex	NOUN
ejpam-5046	25	34	are	be	AUX
ejpam-5046	25	35	uncolored(inactive	uncolored(inactive	ADJ
ejpam-5046	25	36	)	)	PUNCT
ejpam-5046	25	37	initially	initially	ADV
ejpam-5046	25	38	,	,	PUNCT
ejpam-5046	25	39	repeated	repeat	VERB
ejpam-5046	25	40	application	application	NOUN
ejpam-5046	25	41	of	of	ADP
ejpam-5046	25	42	the	the	DET
ejpam-5046	25	43	2	2	NUM
ejpam-5046	25	44	-	-	PUNCT
ejpam-5046	25	45	distance	distance	NOUN
ejpam-5046	25	46	color	color	NOUN
ejpam-5046	25	47	change	change	NOUN
ejpam-5046	25	48	rule	rule	NOUN
ejpam-5046	25	49	all	all	DET
ejpam-5046	25	50	vertices	vertex	NOUN
ejpam-5046	25	51	of	of	ADP
ejpam-5046	25	52	g	g	NOUN
ejpam-5046	25	53	will	will	AUX
ejpam-5046	25	54	become	become	VERB
ejpam-5046	25	55	colored	colored	ADJ
ejpam-5046	25	56	(	(	PUNCT
ejpam-5046	25	57	active	active	ADJ
ejpam-5046	25	58	)	)	PUNCT
ejpam-5046	25	59	.	.	PUNCT
ejpam-5046	26	1	the	the	DET
ejpam-5046	26	2	minimum	minimum	ADJ
ejpam-5046	26	3	cardinality	cardinality	NOUN
ejpam-5046	26	4	of	of	ADP
ejpam-5046	26	5	a	a	DET
ejpam-5046	26	6	2	2	NUM
ejpam-5046	26	7	-	-	PUNCT
ejpam-5046	26	8	distance	distance	NOUN
ejpam-5046	26	9	zero	zero	NUM
ejpam-5046	26	10	forcing	force	VERB
ejpam-5046	26	11	set	set	NOUN
ejpam-5046	26	12	of	of	ADP
ejpam-5046	26	13	g	g	NOUN
ejpam-5046	26	14	,	,	PUNCT
ejpam-5046	26	15	denoted	denote	VERB
ejpam-5046	26	16	by	by	ADP
ejpam-5046	26	17	z2(g	z2(g	NOUN
ejpam-5046	26	18	)	)	PUNCT
ejpam-5046	26	19	,	,	PUNCT
ejpam-5046	26	20	is	be	AUX
ejpam-5046	26	21	called	call	VERB
ejpam-5046	26	22	the	the	DET
ejpam-5046	26	23	2	2	NUM
ejpam-5046	26	24	-	-	PUNCT
ejpam-5046	26	25	distance	distance	NOUN
ejpam-5046	26	26	zero	zero	NUM
ejpam-5046	26	27	forcing	force	VERB
ejpam-5046	26	28	number	number	NOUN
ejpam-5046	26	29	of	of	ADP
ejpam-5046	26	30	g.	g.	NOUN
ejpam-5046	26	31	we	we	PRON
ejpam-5046	26	32	study	study	VERB
ejpam-5046	26	33	its	its	PRON
ejpam-5046	26	34	connections	connection	NOUN
ejpam-5046	26	35	with	with	ADP
ejpam-5046	26	36	the	the	DET
ejpam-5046	26	37	standard	standard	ADJ
ejpam-5046	26	38	zero	zero	NUM
ejpam-5046	26	39	forcing	forcing	NOUN
ejpam-5046	26	40	and	and	CCONJ
ejpam-5046	26	41	hop	hop	NOUN
ejpam-5046	26	42	domination	domination	NOUN
ejpam-5046	26	43	parameter	parameter	NOUN
ejpam-5046	26	44	,	,	PUNCT
ejpam-5046	26	45	respectively	respectively	ADV
ejpam-5046	26	46	.	.	PUNCT
ejpam-5046	27	1	moreover	moreover	ADV
ejpam-5046	27	2	,	,	PUNCT
ejpam-5046	27	3	we	we	PRON
ejpam-5046	27	4	investigate	investigate	VERB
ejpam-5046	27	5	this	this	DET
ejpam-5046	27	6	parameter	parameter	NOUN
ejpam-5046	27	7	on	on	ADP
ejpam-5046	27	8	some	some	DET
ejpam-5046	27	9	families	family	NOUN
ejpam-5046	27	10	of	of	ADP
ejpam-5046	27	11	graphs	graph	NOUN
ejpam-5046	27	12	such	such	ADJ
ejpam-5046	27	13	as	as	ADP
ejpam-5046	27	14	complete	complete	ADJ
ejpam-5046	27	15	,	,	PUNCT
ejpam-5046	27	16	path	path	NOUN
ejpam-5046	27	17	,	,	PUNCT
ejpam-5046	27	18	cycle	cycle	NOUN
ejpam-5046	27	19	,	,	PUNCT
ejpam-5046	27	20	star	star	NOUN
ejpam-5046	27	21	,	,	PUNCT
ejpam-5046	27	22	and	and	CCONJ
ejpam-5046	27	23	complete	complete	ADJ
ejpam-5046	27	24	bipartite	bipartite	NOUN
ejpam-5046	27	25	graph	graph	NOUN
ejpam-5046	27	26	.	.	PUNCT
ejpam-5046	28	1	we	we	PRON
ejpam-5046	28	2	believe	believe	VERB
ejpam-5046	28	3	,	,	PUNCT
ejpam-5046	28	4	this	this	DET
ejpam-5046	28	5	new	new	ADJ
ejpam-5046	28	6	parameter	parameter	NOUN
ejpam-5046	28	7	and	and	CCONJ
ejpam-5046	28	8	its	its	PRON
ejpam-5046	28	9	results	result	NOUN
ejpam-5046	28	10	would	would	AUX
ejpam-5046	28	11	serve	serve	VERB
ejpam-5046	28	12	as	as	ADP
ejpam-5046	28	13	reference	reference	NOUN
ejpam-5046	28	14	to	to	ADP
ejpam-5046	28	15	future	future	ADJ
ejpam-5046	28	16	researchers	researcher	NOUN
ejpam-5046	28	17	who	who	PRON
ejpam-5046	28	18	will	will	AUX
ejpam-5046	28	19	study	study	VERB
ejpam-5046	28	20	on	on	ADP
ejpam-5046	28	21	variants	variant	NOUN
ejpam-5046	28	22	of	of	ADP
ejpam-5046	28	23	zero	zero	NUM
ejpam-5046	28	24	forcing	forcing	NOUN
ejpam-5046	28	25	,	,	PUNCT
ejpam-5046	28	26	and	and	CCONJ
ejpam-5046	28	27	would	would	AUX
ejpam-5046	28	28	lead	lead	VERB
ejpam-5046	28	29	to	to	ADP
ejpam-5046	28	30	an	an	DET
ejpam-5046	28	31	interesting	interesting	ADJ
ejpam-5046	28	32	topics	topic	NOUN
ejpam-5046	28	33	of	of	ADP
ejpam-5046	28	34	research	research	NOUN
ejpam-5046	28	35	in	in	ADP
ejpam-5046	28	36	the	the	DET
ejpam-5046	28	37	future	future	NOUN
ejpam-5046	28	38	.	.	PUNCT
ejpam-5046	29	1	2	2	X
ejpam-5046	29	2	.	.	X
ejpam-5046	29	3	terminology	terminology	NOUN
ejpam-5046	29	4	and	and	CCONJ
ejpam-5046	29	5	notation	notation	NOUN
ejpam-5046	29	6	a	a	DET
ejpam-5046	29	7	path	path	NOUN
ejpam-5046	29	8	graph	graph	NOUN
ejpam-5046	29	9	is	be	AUX
ejpam-5046	29	10	a	a	DET
ejpam-5046	29	11	non	non	ADJ
ejpam-5046	29	12	-	-	ADJ
ejpam-5046	29	13	empty	empty	ADJ
ejpam-5046	29	14	graph	graph	NOUN
ejpam-5046	29	15	with	with	ADP
ejpam-5046	29	16	vertex	vertex	NOUN
ejpam-5046	29	17	-	-	PUNCT
ejpam-5046	29	18	set	set	VERB
ejpam-5046	29	19	{	{	PUNCT
ejpam-5046	29	20	x1	x1	PROPN
ejpam-5046	29	21	,	,	PUNCT
ejpam-5046	29	22	x2	x2	PROPN
ejpam-5046	29	23	,	,	PUNCT
ejpam-5046	29	24	.	.	PUNCT
ejpam-5046	29	25	.	.	PUNCT
ejpam-5046	30	1	.	.	PUNCT
ejpam-5046	31	1	,	,	PUNCT
ejpam-5046	31	2	xn	xn	X
ejpam-5046	31	3	}	}	PUNCT
ejpam-5046	31	4	and	and	CCONJ
ejpam-5046	31	5	edge	edge	NOUN
ejpam-5046	31	6	-	-	PUNCT
ejpam-5046	31	7	set	set	NOUN
ejpam-5046	31	8	{	{	PUNCT
ejpam-5046	31	9	x1x2	x1x2	NOUN
ejpam-5046	31	10	,	,	PUNCT
ejpam-5046	31	11	x2x3	x2x3	PROPN
ejpam-5046	31	12	,	,	PUNCT
ejpam-5046	31	13	.	.	PUNCT
ejpam-5046	31	14	.	.	PUNCT
ejpam-5046	32	1	.	.	PUNCT
ejpam-5046	33	1	,	,	PUNCT
ejpam-5046	33	2	xn−1xn	xn−1xn	PROPN
ejpam-5046	33	3	}	}	PUNCT
ejpam-5046	33	4	,	,	PUNCT
ejpam-5046	33	5	where	where	SCONJ
ejpam-5046	33	6	the	the	DET
ejpam-5046	33	7	x	x	NOUN
ejpam-5046	33	8	′	′	NOUN
ejpam-5046	33	9	is	be	AUX
ejpam-5046	33	10	are	be	AUX
ejpam-5046	33	11	all	all	ADV
ejpam-5046	33	12	distinct	distinct	ADJ
ejpam-5046	33	13	.	.	PUNCT
ejpam-5046	34	1	the	the	DET
ejpam-5046	34	2	path	path	NOUN
ejpam-5046	34	3	of	of	ADP
ejpam-5046	34	4	order	order	NOUN
ejpam-5046	34	5	n	n	NOUN
ejpam-5046	34	6	is	be	AUX
ejpam-5046	34	7	denoted	denote	VERB
ejpam-5046	34	8	by	by	ADP
ejpam-5046	34	9	pn	pn	PROPN
ejpam-5046	34	10	.	.	PUNCT
ejpam-5046	35	1	if	if	SCONJ
ejpam-5046	35	2	g	g	PROPN
ejpam-5046	35	3	is	be	AUX
ejpam-5046	35	4	a	a	DET
ejpam-5046	35	5	graph	graph	NOUN
ejpam-5046	35	6	and	and	CCONJ
ejpam-5046	35	7	u	u	NOUN
ejpam-5046	35	8	and	and	CCONJ
ejpam-5046	35	9	v	v	NOUN
ejpam-5046	35	10	are	be	AUX
ejpam-5046	35	11	vertices	vertex	NOUN
ejpam-5046	35	12	of	of	ADP
ejpam-5046	35	13	g	g	NOUN
ejpam-5046	35	14	,	,	PUNCT
ejpam-5046	35	15	then	then	ADV
ejpam-5046	35	16	a	a	DET
ejpam-5046	35	17	path	path	NOUN
ejpam-5046	35	18	from	from	ADP
ejpam-5046	35	19	vertex	vertex	NOUN
ejpam-5046	35	20	u	u	NOUN
ejpam-5046	35	21	to	to	PART
ejpam-5046	35	22	vertex	vertex	NOUN
ejpam-5046	35	23	v	v	NOUN
ejpam-5046	35	24	is	be	AUX
ejpam-5046	35	25	sometimes	sometimes	ADV
ejpam-5046	35	26	called	call	VERB
ejpam-5046	35	27	a	a	DET
ejpam-5046	35	28	u	u	NOUN
ejpam-5046	35	29	-	-	NOUN
ejpam-5046	35	30	v	v	ADJ
ejpam-5046	35	31	path	path	NOUN
ejpam-5046	35	32	.	.	PUNCT
ejpam-5046	36	1	the	the	DET
ejpam-5046	36	2	cycle	cycle	NOUN
ejpam-5046	36	3	graph	graph	NOUN
ejpam-5046	36	4	cn	cn	PROPN
ejpam-5046	36	5	is	be	AUX
ejpam-5046	36	6	the	the	DET
ejpam-5046	36	7	graph	graph	NOUN
ejpam-5046	36	8	of	of	ADP
ejpam-5046	36	9	order	order	NOUN
ejpam-5046	36	10	n	n	PRON
ejpam-5046	36	11	≥	≥	NOUN
ejpam-5046	36	12	3	3	NUM
ejpam-5046	36	13	with	with	ADP
ejpam-5046	36	14	vertex	vertex	NOUN
ejpam-5046	36	15	-	-	PUNCT
ejpam-5046	36	16	set	set	VERB
ejpam-5046	36	17	{	{	PUNCT
ejpam-5046	36	18	x1	x1	PROPN
ejpam-5046	36	19	,	,	PUNCT
ejpam-5046	36	20	x2	x2	PROPN
ejpam-5046	36	21	,	,	PUNCT
ejpam-5046	36	22	.	.	PUNCT
ejpam-5046	36	23	.	.	PUNCT
ejpam-5046	36	24	.	.	PUNCT
ejpam-5046	37	1	,	,	PUNCT
ejpam-5046	37	2	xn	xn	X
ejpam-5046	37	3	}	}	PUNCT
ejpam-5046	37	4	and	and	CCONJ
ejpam-5046	37	5	edge	edge	NOUN
ejpam-5046	37	6	-	-	PUNCT
ejpam-5046	37	7	set	set	NOUN
ejpam-5046	37	8	{	{	PUNCT
ejpam-5046	37	9	x1x2	x1x2	NOUN
ejpam-5046	37	10	,	,	PUNCT
ejpam-5046	37	11	x2x3	x2x3	PROPN
ejpam-5046	37	12	,	,	PUNCT
ejpam-5046	37	13	.	.	PUNCT
ejpam-5046	37	14	.	.	PUNCT
ejpam-5046	38	1	.	.	PUNCT
ejpam-5046	39	1	,	,	PUNCT
ejpam-5046	39	2	xn−1xn	xn−1xn	PROPN
ejpam-5046	39	3	,	,	PUNCT
ejpam-5046	39	4	xnx1	xnx1	PROPN
ejpam-5046	39	5	}	}	PUNCT
ejpam-5046	39	6	.	.	PUNCT
ejpam-5046	40	1	let	let	VERB
ejpam-5046	40	2	g	g	PROPN
ejpam-5046	40	3	=	=	SYM
ejpam-5046	40	4	(	(	PUNCT
ejpam-5046	40	5	v	v	NOUN
ejpam-5046	40	6	(	(	PUNCT
ejpam-5046	40	7	g	g	NOUN
ejpam-5046	40	8	)	)	PUNCT
ejpam-5046	40	9	,	,	PUNCT
ejpam-5046	40	10	e(g	e(g	PROPN
ejpam-5046	40	11	)	)	PUNCT
ejpam-5046	40	12	)	)	PUNCT
ejpam-5046	41	1	be	be	AUX
ejpam-5046	41	2	a	a	DET
ejpam-5046	41	3	simple	simple	ADJ
ejpam-5046	41	4	and	and	CCONJ
ejpam-5046	41	5	undirected	undirected	ADJ
ejpam-5046	41	6	graph	graph	NOUN
ejpam-5046	41	7	.	.	PUNCT
ejpam-5046	42	1	the	the	DET
ejpam-5046	42	2	distance	distance	NOUN
ejpam-5046	42	3	dg(u	dg(u	NOUN
ejpam-5046	42	4	,	,	PUNCT
ejpam-5046	42	5	v	v	NOUN
ejpam-5046	42	6	)	)	PUNCT
ejpam-5046	42	7	in	in	ADP
ejpam-5046	42	8	g	g	NOUN
ejpam-5046	42	9	of	of	ADP
ejpam-5046	42	10	two	two	NUM
ejpam-5046	42	11	vertices	vertex	NOUN
ejpam-5046	42	12	u	u	NOUN
ejpam-5046	42	13	,	,	PUNCT
ejpam-5046	42	14	v	v	PROPN
ejpam-5046	42	15	is	be	AUX
ejpam-5046	42	16	the	the	DET
ejpam-5046	42	17	length	length	NOUN
ejpam-5046	42	18	of	of	ADP
ejpam-5046	42	19	a	a	DET
ejpam-5046	42	20	shortest	short	ADJ
ejpam-5046	42	21	u	u	NOUN
ejpam-5046	42	22	-	-	NOUN
ejpam-5046	42	23	v	v	ADJ
ejpam-5046	42	24	path	path	NOUN
ejpam-5046	42	25	in	in	ADP
ejpam-5046	42	26	g.	g.	PROPN
ejpam-5046	42	27	the	the	DET
ejpam-5046	42	28	greatest	great	ADJ
ejpam-5046	42	29	distance	distance	NOUN
ejpam-5046	42	30	between	between	ADP
ejpam-5046	42	31	any	any	DET
ejpam-5046	42	32	two	two	NUM
ejpam-5046	42	33	vertices	vertex	NOUN
ejpam-5046	42	34	in	in	ADP
ejpam-5046	42	35	g	g	NOUN
ejpam-5046	42	36	,	,	PUNCT
ejpam-5046	42	37	denoted	denote	VERB
ejpam-5046	42	38	by	by	ADP
ejpam-5046	42	39	diam(g	diam(g	PROPN
ejpam-5046	42	40	)	)	PUNCT
ejpam-5046	42	41	,	,	PUNCT
ejpam-5046	42	42	is	be	AUX
ejpam-5046	42	43	called	call	VERB
ejpam-5046	42	44	the	the	DET
ejpam-5046	42	45	diameter	diameter	NOUN
ejpam-5046	42	46	of	of	ADP
ejpam-5046	42	47	g.	g.	PROPN
ejpam-5046	42	48	two	two	NUM
ejpam-5046	42	49	vertices	vertice	VERB
ejpam-5046	42	50	x	x	X
ejpam-5046	42	51	,	,	PUNCT
ejpam-5046	42	52	y	y	PROPN
ejpam-5046	42	53	of	of	ADP
ejpam-5046	42	54	g	g	PROPN
ejpam-5046	42	55	are	be	AUX
ejpam-5046	42	56	adjacent	adjacent	ADJ
ejpam-5046	42	57	,	,	PUNCT
ejpam-5046	42	58	or	or	CCONJ
ejpam-5046	42	59	neighbors	neighbor	NOUN
ejpam-5046	42	60	,	,	PUNCT
ejpam-5046	42	61	if	if	SCONJ
ejpam-5046	42	62	xy	xy	PROPN
ejpam-5046	42	63	is	be	AUX
ejpam-5046	42	64	an	an	DET
ejpam-5046	42	65	edge	edge	NOUN
ejpam-5046	42	66	of	of	ADP
ejpam-5046	42	67	g.	g.	PROPN
ejpam-5046	42	68	the	the	DET
ejpam-5046	42	69	open	open	ADJ
ejpam-5046	42	70	neighborhood	neighborhood	NOUN
ejpam-5046	42	71	of	of	ADP
ejpam-5046	42	72	x	x	PUNCT
ejpam-5046	42	73	in	in	ADP
ejpam-5046	42	74	g	g	PROPN
ejpam-5046	42	75	is	be	AUX
ejpam-5046	42	76	the	the	DET
ejpam-5046	42	77	set	set	NOUN
ejpam-5046	42	78	ng(x	ng(x	NUM
ejpam-5046	42	79	)	)	PUNCT
ejpam-5046	42	80	=	=	PRON
ejpam-5046	42	81	{	{	PUNCT
ejpam-5046	42	82	y	y	PROPN
ejpam-5046	42	83	∈	∈	PROPN
ejpam-5046	42	84	v	v	NOUN
ejpam-5046	42	85	(	(	PUNCT
ejpam-5046	42	86	g	g	NOUN
ejpam-5046	42	87	)	)	PUNCT
ejpam-5046	42	88	:	:	PUNCT
ejpam-5046	42	89	xy	xy	PROPN
ejpam-5046	42	90	∈	∈	PROPN
ejpam-5046	42	91	e(g	e(g	PROPN
ejpam-5046	42	92	)	)	PUNCT
ejpam-5046	42	93	}	}	PUNCT
ejpam-5046	42	94	.	.	PUNCT
ejpam-5046	43	1	the	the	DET
ejpam-5046	43	2	closed	closed	ADJ
ejpam-5046	43	3	neighborhood	neighborhood	NOUN
ejpam-5046	43	4	of	of	ADP
ejpam-5046	43	5	x	x	SYM
ejpam-5046	43	6	ing	ing	NOUN
ejpam-5046	43	7	is	be	AUX
ejpam-5046	43	8	the	the	DET
ejpam-5046	43	9	setng[x	setng[x	NOUN
ejpam-5046	43	10	]	]	X
ejpam-5046	43	11	=	=	SYM
ejpam-5046	43	12	ng(x)∪{x	ng(x)∪{x	NOUN
ejpam-5046	43	13	}	}	PUNCT
ejpam-5046	43	14	.	.	PUNCT
ejpam-5046	44	1	ifx	ifx	PROPN
ejpam-5046	44	2	⊆	⊆	NUM
ejpam-5046	44	3	v	v	NOUN
ejpam-5046	44	4	(	(	PUNCT
ejpam-5046	44	5	g	g	NOUN
ejpam-5046	44	6	)	)	PUNCT
ejpam-5046	44	7	,	,	PUNCT
ejpam-5046	44	8	the	the	DET
ejpam-5046	44	9	open	open	ADJ
ejpam-5046	44	10	neighborhood	neighborhood	NOUN
ejpam-5046	44	11	of	of	ADP
ejpam-5046	44	12	x	x	PUNCT
ejpam-5046	44	13	in	in	ADP
ejpam-5046	44	14	g	g	PROPN
ejpam-5046	44	15	is	be	AUX
ejpam-5046	44	16	the	the	DET
ejpam-5046	44	17	set	set	NOUN
ejpam-5046	44	18	ng(x	ng(x	NUM
ejpam-5046	44	19	)	)	PUNCT
ejpam-5046	45	1	=	=	SYM
ejpam-5046	45	2	⋃	⋃	NOUN
ejpam-5046	45	3	x∈x	x∈x	NOUN
ejpam-5046	45	4	ng(x	ng(x	NUM
ejpam-5046	45	5	)	)	PUNCT
ejpam-5046	45	6	.	.	PUNCT
ejpam-5046	46	1	the	the	DET
ejpam-5046	46	2	closed	closed	ADJ
ejpam-5046	46	3	neighborhood	neighborhood	NOUN
ejpam-5046	46	4	of	of	ADP
ejpam-5046	46	5	x	x	PUNCT
ejpam-5046	46	6	in	in	ADP
ejpam-5046	46	7	g	g	PROPN
ejpam-5046	46	8	is	be	AUX
ejpam-5046	46	9	the	the	DET
ejpam-5046	46	10	set	set	NOUN
ejpam-5046	46	11	ng[x	ng[x	PROPN
ejpam-5046	46	12	]	]	X
ejpam-5046	46	13	=	=	PUNCT
ejpam-5046	46	14	ng(x	ng(x	X
ejpam-5046	46	15	)	)	PUNCT
ejpam-5046	47	1	∪x	∪x	ADP
ejpam-5046	47	2	.	.	PUNCT
ejpam-5046	48	1	a	a	DET
ejpam-5046	48	2	vertex	vertex	NOUN
ejpam-5046	48	3	of	of	ADP
ejpam-5046	48	4	a	a	PRON
ejpam-5046	48	5	in	in	ADP
ejpam-5046	48	6	g	g	PROPN
ejpam-5046	48	7	is	be	AUX
ejpam-5046	48	8	a	a	DET
ejpam-5046	48	9	hop	hop	NOUN
ejpam-5046	48	10	neighbor	neighbor	NOUN
ejpam-5046	48	11	of	of	ADP
ejpam-5046	48	12	a	a	DET
ejpam-5046	48	13	vertex	vertex	NOUN
ejpam-5046	48	14	b	b	NOUN
ejpam-5046	48	15	in	in	ADP
ejpam-5046	48	16	g	g	PROPN
ejpam-5046	48	17	if	if	SCONJ
ejpam-5046	48	18	dg(a	dg(a	X
ejpam-5046	48	19	,	,	PUNCT
ejpam-5046	48	20	b	b	X
ejpam-5046	48	21	)	)	PUNCT
ejpam-5046	48	22	=	=	SYM
ejpam-5046	48	23	2	2	X
ejpam-5046	48	24	.	.	X
ejpam-5046	48	25	the	the	DET
ejpam-5046	48	26	set	set	ADJ
ejpam-5046	48	27	n2	n2	PROPN
ejpam-5046	48	28	g(a	g(a	PROPN
ejpam-5046	48	29	)	)	PUNCT
ejpam-5046	48	30	=	=	PRON
ejpam-5046	49	1	{	{	PUNCT
ejpam-5046	49	2	b	b	PROPN
ejpam-5046	49	3	∈	∈	ADJ
ejpam-5046	49	4	v	v	NOUN
ejpam-5046	49	5	(	(	PUNCT
ejpam-5046	49	6	g	g	NOUN
ejpam-5046	49	7	)	)	PUNCT
ejpam-5046	49	8	:	:	PUNCT
ejpam-5046	50	1	dg(a	dg(a	X
ejpam-5046	50	2	,	,	PUNCT
ejpam-5046	50	3	b	b	X
ejpam-5046	50	4	)	)	PUNCT
ejpam-5046	50	5	=	=	SYM
ejpam-5046	50	6	2	2	X
ejpam-5046	50	7	}	}	PUNCT
ejpam-5046	50	8	is	be	AUX
ejpam-5046	50	9	called	call	VERB
ejpam-5046	50	10	the	the	DET
ejpam-5046	50	11	open	open	ADJ
ejpam-5046	50	12	hop	hop	NOUN
ejpam-5046	50	13	neighborhood	neighborhood	NOUN
ejpam-5046	50	14	of	of	ADP
ejpam-5046	50	15	a.	a.	NOUN
ejpam-5046	50	16	the	the	DET
ejpam-5046	50	17	closed	closed	ADJ
ejpam-5046	50	18	hop	hop	NOUN
ejpam-5046	50	19	neighborhood	neighborhood	NOUN
ejpam-5046	50	20	of	of	ADP
ejpam-5046	50	21	a	a	PRON
ejpam-5046	50	22	in	in	ADP
ejpam-5046	50	23	g	g	PROPN
ejpam-5046	50	24	is	be	AUX
ejpam-5046	50	25	given	give	VERB
ejpam-5046	50	26	by	by	ADP
ejpam-5046	50	27	n2	n2	ADJ
ejpam-5046	50	28	g[a	g[a	PROPN
ejpam-5046	50	29	]	]	X
ejpam-5046	50	30	=	=	SYM
ejpam-5046	50	31	n2	n2	PROPN
ejpam-5046	50	32	g(a	g(a	PROPN
ejpam-5046	50	33	)	)	PUNCT
ejpam-5046	50	34	∪	∪	ADP
ejpam-5046	50	35	{	{	PUNCT
ejpam-5046	50	36	a	a	NOUN
ejpam-5046	50	37	}	}	PUNCT
ejpam-5046	50	38	.	.	PUNCT
ejpam-5046	51	1	the	the	DET
ejpam-5046	51	2	open	open	ADJ
ejpam-5046	51	3	hop	hop	NOUN
ejpam-5046	51	4	neighborhood	neighborhood	NOUN
ejpam-5046	51	5	of	of	ADP
ejpam-5046	51	6	s	s	NOUN
ejpam-5046	51	7	⊆	⊆	NUM
ejpam-5046	51	8	v	v	NOUN
ejpam-5046	51	9	(	(	PUNCT
ejpam-5046	51	10	g	g	NOUN
ejpam-5046	51	11	)	)	PUNCT
ejpam-5046	51	12	is	be	AUX
ejpam-5046	51	13	the	the	DET
ejpam-5046	51	14	set	set	ADJ
ejpam-5046	51	15	n2	n2	ADJ
ejpam-5046	51	16	g(s	g(s	PROPN
ejpam-5046	51	17	)	)	PUNCT
ejpam-5046	51	18	=	=	SYM
ejpam-5046	52	1	⋃	⋃	ADP
ejpam-5046	52	2	a∈s	a∈s	ADJ
ejpam-5046	52	3	n2	n2	NOUN
ejpam-5046	52	4	g(a	g(a	PROPN
ejpam-5046	52	5	)	)	PUNCT
ejpam-5046	52	6	.	.	PUNCT
ejpam-5046	53	1	the	the	DET
ejpam-5046	53	2	closed	closed	ADJ
ejpam-5046	53	3	hop	hop	NOUN
ejpam-5046	53	4	neighborhood	neighborhood	NOUN
ejpam-5046	53	5	of	of	ADP
ejpam-5046	53	6	s	s	PRON
ejpam-5046	53	7	in	in	ADP
ejpam-5046	53	8	g	g	PROPN
ejpam-5046	53	9	is	be	AUX
ejpam-5046	53	10	the	the	DET
ejpam-5046	53	11	set	set	ADJ
ejpam-5046	53	12	n2	n2	ADJ
ejpam-5046	53	13	g[s	g[s	PROPN
ejpam-5046	53	14	]	]	PUNCT
ejpam-5046	53	15	=	=	SYM
ejpam-5046	53	16	n2	n2	ADJ
ejpam-5046	53	17	g(s	g(s	PROPN
ejpam-5046	53	18	)	)	PUNCT
ejpam-5046	53	19	∪	∪	ADP
ejpam-5046	53	20	s.	s.	PROPN
ejpam-5046	53	21	a	a	DET
ejpam-5046	53	22	subset	subset	NOUN
ejpam-5046	53	23	s	s	X
ejpam-5046	53	24	of	of	ADP
ejpam-5046	53	25	v	v	NOUN
ejpam-5046	53	26	(	(	PUNCT
ejpam-5046	53	27	g	g	NOUN
ejpam-5046	53	28	)	)	PUNCT
ejpam-5046	53	29	is	be	AUX
ejpam-5046	53	30	a	a	DET
ejpam-5046	53	31	hop	hop	NOUN
ejpam-5046	53	32	dominating	dominating	NOUN
ejpam-5046	53	33	of	of	ADP
ejpam-5046	53	34	g	g	PROPN
ejpam-5046	53	35	if	if	SCONJ
ejpam-5046	53	36	for	for	ADP
ejpam-5046	53	37	every	every	DET
ejpam-5046	53	38	a	a	DET
ejpam-5046	53	39	∈	∈	PROPN
ejpam-5046	53	40	v	v	NOUN
ejpam-5046	53	41	(	(	PUNCT
ejpam-5046	53	42	g)\s	g)\s	NOUN
ejpam-5046	53	43	,	,	PUNCT
ejpam-5046	53	44	there	there	PRON
ejpam-5046	53	45	exists	exist	VERB
ejpam-5046	53	46	b	b	PROPN
ejpam-5046	53	47	∈	∈	PROPN
ejpam-5046	53	48	s	s	VERB
ejpam-5046	53	49	such	such	ADJ
ejpam-5046	53	50	that	that	SCONJ
ejpam-5046	53	51	dg(a	dg(a	PROPN
ejpam-5046	53	52	,	,	PUNCT
ejpam-5046	53	53	b	b	X
ejpam-5046	53	54	)	)	PUNCT
ejpam-5046	53	55	=	=	SYM
ejpam-5046	53	56	2	2	X
ejpam-5046	53	57	.	.	PUNCT
ejpam-5046	53	58	the	the	DET
ejpam-5046	53	59	minimum	minimum	ADJ
ejpam-5046	53	60	cardinality	cardinality	NOUN
ejpam-5046	53	61	among	among	ADP
ejpam-5046	53	62	all	all	DET
ejpam-5046	53	63	hop	hop	NOUN
ejpam-5046	53	64	dominating	dominating	NOUN
ejpam-5046	53	65	sets	set	NOUN
ejpam-5046	53	66	of	of	ADP
ejpam-5046	53	67	g	g	NOUN
ejpam-5046	53	68	,	,	PUNCT
ejpam-5046	53	69	denoted	denote	VERB
ejpam-5046	53	70	by	by	ADP
ejpam-5046	53	71	γh(g	γh(g	NOUN
ejpam-5046	53	72	)	)	PUNCT
ejpam-5046	53	73	,	,	PUNCT
ejpam-5046	53	74	is	be	AUX
ejpam-5046	53	75	called	call	VERB
ejpam-5046	53	76	the	the	DET
ejpam-5046	53	77	hop	hop	NOUN
ejpam-5046	53	78	domination	domination	NOUN
ejpam-5046	53	79	number	number	NOUN
ejpam-5046	53	80	of	of	ADP
ejpam-5046	53	81	g.	g.	PROPN
ejpam-5046	53	82	let	let	VERB
ejpam-5046	53	83	g	g	NOUN
ejpam-5046	54	1	and	and	CCONJ
ejpam-5046	54	2	h	h	NOUN
ejpam-5046	54	3	be	be	VERB
ejpam-5046	54	4	any	any	DET
ejpam-5046	54	5	two	two	NUM
ejpam-5046	54	6	graphs	graph	NOUN
ejpam-5046	54	7	.	.	PUNCT
ejpam-5046	55	1	the	the	DET
ejpam-5046	55	2	join	join	NOUN
ejpam-5046	55	3	of	of	ADP
ejpam-5046	55	4	g	g	PROPN
ejpam-5046	55	5	and	and	CCONJ
ejpam-5046	55	6	h	h	NOUN
ejpam-5046	55	7	,	,	PUNCT
ejpam-5046	55	8	denoted	denote	VERB
ejpam-5046	55	9	by	by	ADP
ejpam-5046	55	10	g+h	g+h	PROPN
ejpam-5046	55	11	is	be	AUX
ejpam-5046	55	12	the	the	DET
ejpam-5046	55	13	graph	graph	NOUN
ejpam-5046	55	14	with	with	ADP
ejpam-5046	55	15	vertex	vertex	NOUN
ejpam-5046	55	16	set	set	VERB
ejpam-5046	55	17	v	v	NOUN
ejpam-5046	55	18	(	(	PUNCT
ejpam-5046	55	19	g+h	g+h	NOUN
ejpam-5046	55	20	)	)	PUNCT
ejpam-5046	56	1	=	=	SYM
ejpam-5046	56	2	v	v	X
ejpam-5046	56	3	(	(	PUNCT
ejpam-5046	56	4	g	g	NOUN
ejpam-5046	56	5	)	)	PUNCT
ejpam-5046	56	6	∪	∪	NOUN
ejpam-5046	56	7	v	v	NOUN
ejpam-5046	56	8	(	(	PUNCT
ejpam-5046	56	9	h	h	NOUN
ejpam-5046	56	10	)	)	PUNCT
ejpam-5046	56	11	and	and	CCONJ
ejpam-5046	56	12	edge	edge	NOUN
ejpam-5046	56	13	set	set	VERB
ejpam-5046	56	14	e(g+h	e(g+h	NUM
ejpam-5046	56	15	)	)	PUNCT
ejpam-5046	56	16	=	=	SYM
ejpam-5046	56	17	e(g	e(g	NOUN
ejpam-5046	56	18	)	)	PUNCT
ejpam-5046	56	19	∪	∪	ADP
ejpam-5046	56	20	e(h	e(h	PROPN
ejpam-5046	56	21	)	)	PUNCT
ejpam-5046	56	22	∪	∪	NOUN
ejpam-5046	56	23	{	{	PUNCT
ejpam-5046	56	24	uv	uv	NOUN
ejpam-5046	56	25	:	:	PUNCT
ejpam-5046	56	26	u	u	PROPN
ejpam-5046	56	27	∈	∈	PROPN
ejpam-5046	56	28	v	v	ADP
ejpam-5046	56	29	(	(	PUNCT
ejpam-5046	56	30	g	g	NOUN
ejpam-5046	56	31	)	)	PUNCT
ejpam-5046	56	32	,	,	PUNCT
ejpam-5046	56	33	v	v	X
ejpam-5046	56	34	∈	∈	PROPN
ejpam-5046	56	35	v	v	NOUN
ejpam-5046	56	36	(	(	PUNCT
ejpam-5046	56	37	h	h	NOUN
ejpam-5046	56	38	)	)	PUNCT
ejpam-5046	56	39	}	}	PUNCT
ejpam-5046	56	40	.	.	PUNCT
ejpam-5046	57	1	j.	j.	PROPN
ejpam-5046	57	2	a.	a.	PROPN
ejpam-5046	57	3	hassan	hassan	PROPN
ejpam-5046	57	4	,	,	PUNCT
ejpam-5046	57	5	l.	l.	PROPN
ejpam-5046	57	6	t.	t.	PROPN
ejpam-5046	57	7	udtohan	udtohan	PROPN
ejpam-5046	57	8	,	,	PUNCT
ejpam-5046	57	9	l.	l.	PROPN
ejpam-5046	57	10	s.	s.	PROPN
ejpam-5046	57	11	laja	laja	PROPN
ejpam-5046	57	12	/	/	SYM
ejpam-5046	57	13	eur	eur	PROPN
ejpam-5046	57	14	.	.	PUNCT
ejpam-5046	58	1	j.	j.	PROPN
ejpam-5046	58	2	pure	pure	PROPN
ejpam-5046	58	3	appl	appl	PROPN
ejpam-5046	58	4	.	.	PROPN
ejpam-5046	58	5	math	math	PROPN
ejpam-5046	58	6	,	,	PUNCT
ejpam-5046	58	7	17	17	NUM
ejpam-5046	58	8	(	(	PUNCT
ejpam-5046	58	9	2	2	NUM
ejpam-5046	58	10	)	)	PUNCT
ejpam-5046	58	11	(	(	PUNCT
ejpam-5046	58	12	2024	2024	NUM
ejpam-5046	58	13	)	)	PUNCT
ejpam-5046	58	14	,	,	PUNCT
ejpam-5046	58	15	1283	1283	NUM
ejpam-5046	58	16	-	-	SYM
ejpam-5046	58	17	1293	1293	NUM
ejpam-5046	58	18	1285	1285	NUM
ejpam-5046	58	19	the	the	DET
ejpam-5046	58	20	color	color	NOUN
ejpam-5046	58	21	change	change	NOUN
ejpam-5046	58	22	rule	rule	NOUN
ejpam-5046	58	23	states	state	NOUN
ejpam-5046	58	24	that	that	SCONJ
ejpam-5046	58	25	a	a	DET
ejpam-5046	58	26	blue	blue	ADJ
ejpam-5046	58	27	vertex	vertex	NOUN
ejpam-5046	58	28	adjacent	adjacent	ADJ
ejpam-5046	58	29	to	to	ADP
ejpam-5046	58	30	a	a	DET
ejpam-5046	58	31	single	single	ADJ
ejpam-5046	58	32	white	white	ADJ
ejpam-5046	58	33	neighbor	neighbor	NOUN
ejpam-5046	58	34	can	can	AUX
ejpam-5046	58	35	force	force	VERB
ejpam-5046	58	36	its	its	PRON
ejpam-5046	58	37	neighbor	neighbor	NOUN
ejpam-5046	58	38	to	to	PART
ejpam-5046	58	39	blue	blue	VERB
ejpam-5046	58	40	.	.	PUNCT
ejpam-5046	59	1	formally	formally	ADV
ejpam-5046	59	2	,	,	PUNCT
ejpam-5046	59	3	if	if	SCONJ
ejpam-5046	59	4	u	u	NOUN
ejpam-5046	59	5	is	be	AUX
ejpam-5046	59	6	a	a	DET
ejpam-5046	59	7	blue	blue	ADJ
ejpam-5046	59	8	vertex	vertex	NOUN
ejpam-5046	59	9	and	and	CCONJ
ejpam-5046	59	10	w	w	NOUN
ejpam-5046	59	11	is	be	AUX
ejpam-5046	59	12	the	the	DET
ejpam-5046	59	13	only	only	ADJ
ejpam-5046	59	14	white	white	ADJ
ejpam-5046	59	15	vertex	vertex	NOUN
ejpam-5046	59	16	in	in	ADP
ejpam-5046	59	17	ng(u	ng(u	NOUN
ejpam-5046	59	18	)	)	PUNCT
ejpam-5046	59	19	,	,	PUNCT
ejpam-5046	59	20	then	then	ADV
ejpam-5046	59	21	u−→w	u−→w	PROPN
ejpam-5046	59	22	will	will	AUX
ejpam-5046	59	23	be	be	AUX
ejpam-5046	59	24	used	use	VERB
ejpam-5046	59	25	to	to	PART
ejpam-5046	59	26	denote	denote	VERB
ejpam-5046	59	27	that	that	SCONJ
ejpam-5046	59	28	u	u	PROPN
ejpam-5046	59	29	forces	force	NOUN
ejpam-5046	59	30	w	w	NOUN
ejpam-5046	59	31	blue	blue	ADJ
ejpam-5046	59	32	.	.	PUNCT
ejpam-5046	60	1	a	a	DET
ejpam-5046	60	2	zero	zero	NUM
ejpam-5046	60	3	forcing	force	VERB
ejpam-5046	60	4	set	set	NOUN
ejpam-5046	60	5	for	for	ADP
ejpam-5046	60	6	a	a	DET
ejpam-5046	60	7	graph	graph	NOUN
ejpam-5046	60	8	g	g	NOUN
ejpam-5046	60	9	is	be	AUX
ejpam-5046	60	10	a	a	DET
ejpam-5046	60	11	subset	subset	NOUN
ejpam-5046	60	12	of	of	ADP
ejpam-5046	60	13	vertices	vertex	NOUN
ejpam-5046	60	14	in	in	ADP
ejpam-5046	60	15	z	z	NOUN
ejpam-5046	60	16	such	such	ADJ
ejpam-5046	60	17	that	that	SCONJ
ejpam-5046	60	18	if	if	SCONJ
ejpam-5046	60	19	initially	initially	ADV
ejpam-5046	60	20	the	the	DET
ejpam-5046	60	21	vertices	vertex	NOUN
ejpam-5046	60	22	in	in	ADP
ejpam-5046	60	23	z	z	NOUN
ejpam-5046	60	24	are	be	AUX
ejpam-5046	60	25	colored	color	VERB
ejpam-5046	60	26	blue	blue	ADJ
ejpam-5046	60	27	and	and	CCONJ
ejpam-5046	60	28	the	the	DET
ejpam-5046	60	29	remaining	remain	VERB
ejpam-5046	60	30	vertices	vertex	NOUN
ejpam-5046	60	31	are	be	AUX
ejpam-5046	60	32	colored	color	VERB
ejpam-5046	60	33	white	white	ADJ
ejpam-5046	60	34	,	,	PUNCT
ejpam-5046	60	35	the	the	DET
ejpam-5046	60	36	entire	entire	ADJ
ejpam-5046	60	37	graph	graph	NOUN
ejpam-5046	60	38	g	g	NOUN
ejpam-5046	60	39	may	may	AUX
ejpam-5046	60	40	be	be	AUX
ejpam-5046	60	41	colored	color	VERB
ejpam-5046	60	42	blue	blue	ADJ
ejpam-5046	60	43	by	by	ADP
ejpam-5046	60	44	repeatedly	repeatedly	ADV
ejpam-5046	60	45	applying	apply	VERB
ejpam-5046	60	46	the	the	DET
ejpam-5046	60	47	color	color	NOUN
ejpam-5046	60	48	-	-	PUNCT
ejpam-5046	60	49	change	change	NOUN
ejpam-5046	60	50	rule	rule	NOUN
ejpam-5046	60	51	.	.	PUNCT
ejpam-5046	61	1	furthermore	furthermore	ADV
ejpam-5046	61	2	,	,	PUNCT
ejpam-5046	61	3	the	the	DET
ejpam-5046	61	4	zero	zero	NUM
ejpam-5046	61	5	forcing	force	VERB
ejpam-5046	61	6	number	number	NOUN
ejpam-5046	61	7	,	,	PUNCT
ejpam-5046	61	8	z(g	z(g	NOUN
ejpam-5046	61	9	)	)	PUNCT
ejpam-5046	61	10	,	,	PUNCT
ejpam-5046	61	11	of	of	ADP
ejpam-5046	61	12	a	a	DET
ejpam-5046	61	13	graph	graph	NOUN
ejpam-5046	61	14	g	g	NOUN
ejpam-5046	61	15	is	be	AUX
ejpam-5046	61	16	the	the	DET
ejpam-5046	61	17	minimum	minimum	ADJ
ejpam-5046	61	18	cardinality	cardinality	NOUN
ejpam-5046	61	19	of	of	ADP
ejpam-5046	61	20	a	a	DET
ejpam-5046	61	21	set	set	NOUN
ejpam-5046	61	22	of	of	ADP
ejpam-5046	61	23	blue	blue	ADJ
ejpam-5046	61	24	vertices(whereas	vertices(whereas	PROPN
ejpam-5046	61	25	vertices	vertice	VERB
ejpam-5046	61	26	in	in	ADP
ejpam-5046	61	27	v	v	NOUN
ejpam-5046	61	28	(	(	PUNCT
ejpam-5046	61	29	g)\s	g)\s	NOUN
ejpam-5046	61	30	are	be	AUX
ejpam-5046	61	31	colored	color	VERB
ejpam-5046	61	32	white	white	ADJ
ejpam-5046	61	33	)	)	PUNCT
ejpam-5046	61	34	such	such	ADJ
ejpam-5046	61	35	that	that	PRON
ejpam-5046	61	36	v	v	NOUN
ejpam-5046	61	37	(	(	PUNCT
ejpam-5046	61	38	g	g	NOUN
ejpam-5046	61	39	)	)	PUNCT
ejpam-5046	61	40	is	be	AUX
ejpam-5046	61	41	turned	turn	VERB
ejpam-5046	61	42	blue	blue	ADJ
ejpam-5046	61	43	after	after	ADP
ejpam-5046	61	44	finitely	finitely	ADV
ejpam-5046	61	45	many	many	ADJ
ejpam-5046	61	46	applications	application	NOUN
ejpam-5046	61	47	of	of	ADP
ejpam-5046	61	48	”	"	PUNCT
ejpam-5046	61	49	the	the	DET
ejpam-5046	61	50	color	color	NOUN
ejpam-5046	61	51	change	change	NOUN
ejpam-5046	61	52	rule	rule	NOUN
ejpam-5046	61	53	”	"	PUNCT
ejpam-5046	61	54	:	:	PUNCT
ejpam-5046	61	55	a	a	DET
ejpam-5046	61	56	white	white	ADJ
ejpam-5046	61	57	vertex	vertex	NOUN
ejpam-5046	61	58	is	be	AUX
ejpam-5046	61	59	converted	convert	VERB
ejpam-5046	61	60	to	to	ADP
ejpam-5046	61	61	a	a	DET
ejpam-5046	61	62	blue	blue	ADJ
ejpam-5046	61	63	vertices	vertex	NOUN
ejpam-5046	61	64	if	if	SCONJ
ejpam-5046	61	65	it	it	PRON
ejpam-5046	61	66	is	be	AUX
ejpam-5046	61	67	the	the	DET
ejpam-5046	61	68	only	only	ADJ
ejpam-5046	61	69	white	white	ADJ
ejpam-5046	61	70	neighbor	neighbor	NOUN
ejpam-5046	61	71	of	of	ADP
ejpam-5046	61	72	a	a	DET
ejpam-5046	61	73	blue	blue	ADJ
ejpam-5046	61	74	vertex	vertex	NOUN
ejpam-5046	61	75	.	.	PUNCT
ejpam-5046	62	1	3	3	X
ejpam-5046	62	2	.	.	X
ejpam-5046	62	3	results	result	NOUN
ejpam-5046	62	4	we	we	PRON
ejpam-5046	62	5	begin	begin	VERB
ejpam-5046	62	6	this	this	DET
ejpam-5046	62	7	section	section	NOUN
ejpam-5046	62	8	by	by	ADP
ejpam-5046	62	9	introducing	introduce	VERB
ejpam-5046	62	10	the	the	DET
ejpam-5046	62	11	concepts	concept	NOUN
ejpam-5046	62	12	of	of	ADP
ejpam-5046	62	13	2	2	NUM
ejpam-5046	62	14	-	-	PUNCT
ejpam-5046	62	15	distance	distance	NOUN
ejpam-5046	62	16	zero	zero	NUM
ejpam-5046	62	17	forcing	forcing	NOUN
ejpam-5046	62	18	set	set	NOUN
ejpam-5046	62	19	and	and	CCONJ
ejpam-5046	62	20	2	2	NUM
ejpam-5046	62	21	-	-	PUNCT
ejpam-5046	62	22	distance	distance	NOUN
ejpam-5046	62	23	zero	zero	NUM
ejpam-5046	62	24	forcing	force	VERB
ejpam-5046	62	25	number	number	NOUN
ejpam-5046	62	26	of	of	ADP
ejpam-5046	62	27	a	a	DET
ejpam-5046	62	28	graph	graph	NOUN
ejpam-5046	62	29	.	.	PUNCT
ejpam-5046	63	1	definition	definition	NOUN
ejpam-5046	63	2	1	1	NUM
ejpam-5046	63	3	.	.	PUNCT
ejpam-5046	64	1	letg	letg	PROPN
ejpam-5046	64	2	be	be	AUX
ejpam-5046	64	3	a	a	DET
ejpam-5046	64	4	graph	graph	NOUN
ejpam-5046	64	5	and	and	CCONJ
ejpam-5046	64	6	let	let	VERB
ejpam-5046	64	7	x	x	PRON
ejpam-5046	64	8	,	,	PUNCT
ejpam-5046	64	9	y	y	PROPN
ejpam-5046	64	10	∈	∈	PROPN
ejpam-5046	64	11	v	v	NOUN
ejpam-5046	64	12	(	(	PUNCT
ejpam-5046	64	13	g	g	NOUN
ejpam-5046	64	14	)	)	PUNCT
ejpam-5046	64	15	.	.	PUNCT
ejpam-5046	65	1	then	then	ADV
ejpam-5046	65	2	the	the	DET
ejpam-5046	65	3	2	2	NUM
ejpam-5046	65	4	-	-	PUNCT
ejpam-5046	65	5	distance	distance	NOUN
ejpam-5046	65	6	color	color	NOUN
ejpam-5046	65	7	change	change	NOUN
ejpam-5046	65	8	rule	rule	NOUN
ejpam-5046	65	9	is	be	AUX
ejpam-5046	65	10	if	if	SCONJ
ejpam-5046	65	11	x	x	PRON
ejpam-5046	65	12	is	be	AUX
ejpam-5046	65	13	colored	color	VERB
ejpam-5046	65	14	(	(	PUNCT
ejpam-5046	65	15	active	active	ADJ
ejpam-5046	65	16	)	)	PUNCT
ejpam-5046	65	17	vertex	vertex	NOUN
ejpam-5046	65	18	and	and	CCONJ
ejpam-5046	65	19	exactly	exactly	ADV
ejpam-5046	65	20	one	one	NUM
ejpam-5046	65	21	hop	hop	NOUN
ejpam-5046	65	22	neighbor	neighbor	NOUN
ejpam-5046	65	23	y	y	PROPN
ejpam-5046	65	24	of	of	ADP
ejpam-5046	65	25	x	x	PRON
ejpam-5046	65	26	is	be	AUX
ejpam-5046	65	27	uncolored	uncolored	ADJ
ejpam-5046	65	28	(	(	PUNCT
ejpam-5046	65	29	inactive	inactive	ADJ
ejpam-5046	65	30	)	)	PUNCT
ejpam-5046	65	31	,	,	PUNCT
ejpam-5046	65	32	then	then	ADV
ejpam-5046	65	33	y	y	PROPN
ejpam-5046	65	34	will	will	AUX
ejpam-5046	65	35	become	become	VERB
ejpam-5046	65	36	colored	colored	ADJ
ejpam-5046	65	37	(	(	PUNCT
ejpam-5046	65	38	active	active	ADJ
ejpam-5046	65	39	)	)	PUNCT
ejpam-5046	65	40	.	.	PUNCT
ejpam-5046	66	1	formally	formally	ADV
ejpam-5046	66	2	,	,	PUNCT
ejpam-5046	66	3	if	if	SCONJ
ejpam-5046	66	4	x	x	PRON
ejpam-5046	66	5	is	be	AUX
ejpam-5046	66	6	a	a	DET
ejpam-5046	66	7	colored(active	colored(active	ADJ
ejpam-5046	66	8	)	)	PUNCT
ejpam-5046	66	9	vertex	vertex	NOUN
ejpam-5046	66	10	and	and	CCONJ
ejpam-5046	66	11	y	y	PROPN
ejpam-5046	66	12	is	be	AUX
ejpam-5046	66	13	the	the	DET
ejpam-5046	66	14	only	only	ADJ
ejpam-5046	66	15	uncolored	uncolored	ADJ
ejpam-5046	66	16	(	(	PUNCT
ejpam-5046	66	17	inactive	inactive	ADJ
ejpam-5046	66	18	)	)	PUNCT
ejpam-5046	66	19	vertex	vertex	NOUN
ejpam-5046	66	20	in	in	ADP
ejpam-5046	66	21	n2	n2	ADJ
ejpam-5046	66	22	g(x	g(x	PROPN
ejpam-5046	66	23	)	)	PUNCT
ejpam-5046	66	24	,	,	PUNCT
ejpam-5046	66	25	then	then	ADV
ejpam-5046	66	26	x−→y	x−→y	PROPN
ejpam-5046	66	27	will	will	AUX
ejpam-5046	66	28	be	be	AUX
ejpam-5046	66	29	used	use	VERB
ejpam-5046	66	30	to	to	PART
ejpam-5046	66	31	denote	denote	VERB
ejpam-5046	66	32	that	that	SCONJ
ejpam-5046	66	33	x	x	PROPN
ejpam-5046	66	34	2forces	2forces	NUM
ejpam-5046	66	35	y	y	NOUN
ejpam-5046	66	36	to	to	PART
ejpam-5046	66	37	be	be	AUX
ejpam-5046	66	38	colored	color	VERB
ejpam-5046	66	39	(	(	PUNCT
ejpam-5046	66	40	active	active	ADJ
ejpam-5046	66	41	)	)	PUNCT
ejpam-5046	66	42	.	.	PUNCT
ejpam-5046	67	1	a	a	DET
ejpam-5046	67	2	2	2	NUM
ejpam-5046	67	3	-	-	PUNCT
ejpam-5046	67	4	distance	distance	NOUN
ejpam-5046	67	5	zero	zero	NUM
ejpam-5046	67	6	forcing	force	VERB
ejpam-5046	67	7	set	set	NOUN
ejpam-5046	67	8	n	n	PROPN
ejpam-5046	67	9	of	of	ADP
ejpam-5046	67	10	g	g	PROPN
ejpam-5046	67	11	is	be	AUX
ejpam-5046	67	12	a	a	DET
ejpam-5046	67	13	subset	subset	NOUN
ejpam-5046	67	14	of	of	ADP
ejpam-5046	67	15	vertices	vertex	NOUN
ejpam-5046	67	16	of	of	ADP
ejpam-5046	67	17	g	g	NOUN
ejpam-5046	67	18	such	such	ADJ
ejpam-5046	67	19	that	that	SCONJ
ejpam-5046	67	20	when	when	SCONJ
ejpam-5046	67	21	the	the	DET
ejpam-5046	67	22	vertices	vertex	NOUN
ejpam-5046	67	23	in	in	ADP
ejpam-5046	67	24	n	n	CCONJ
ejpam-5046	67	25	are	be	AUX
ejpam-5046	67	26	colored	color	VERB
ejpam-5046	67	27	(	(	PUNCT
ejpam-5046	67	28	active	active	ADJ
ejpam-5046	67	29	)	)	PUNCT
ejpam-5046	67	30	and	and	CCONJ
ejpam-5046	67	31	the	the	DET
ejpam-5046	67	32	remaining	remain	VERB
ejpam-5046	67	33	vertices	vertex	NOUN
ejpam-5046	67	34	are	be	AUX
ejpam-5046	67	35	uncolored(inactive	uncolored(inactive	ADJ
ejpam-5046	67	36	)	)	PUNCT
ejpam-5046	67	37	initially	initially	ADV
ejpam-5046	67	38	,	,	PUNCT
ejpam-5046	67	39	repeated	repeat	VERB
ejpam-5046	67	40	application	application	NOUN
ejpam-5046	67	41	of	of	ADP
ejpam-5046	67	42	the	the	DET
ejpam-5046	67	43	2	2	NUM
ejpam-5046	67	44	-	-	PUNCT
ejpam-5046	67	45	distance	distance	NOUN
ejpam-5046	67	46	color	color	NOUN
ejpam-5046	67	47	change	change	NOUN
ejpam-5046	67	48	rule	rule	NOUN
ejpam-5046	67	49	all	all	DET
ejpam-5046	67	50	vertices	vertex	NOUN
ejpam-5046	67	51	of	of	ADP
ejpam-5046	67	52	g	g	NOUN
ejpam-5046	67	53	will	will	AUX
ejpam-5046	67	54	become	become	VERB
ejpam-5046	67	55	colored	colored	ADJ
ejpam-5046	67	56	(	(	PUNCT
ejpam-5046	67	57	active	active	ADJ
ejpam-5046	67	58	)	)	PUNCT
ejpam-5046	67	59	.	.	PUNCT
ejpam-5046	68	1	the	the	DET
ejpam-5046	68	2	minimum	minimum	ADJ
ejpam-5046	68	3	cardinality	cardinality	NOUN
ejpam-5046	68	4	of	of	ADP
ejpam-5046	68	5	a	a	DET
ejpam-5046	68	6	2	2	NUM
ejpam-5046	68	7	-	-	PUNCT
ejpam-5046	68	8	distance	distance	NOUN
ejpam-5046	68	9	zero	zero	NUM
ejpam-5046	68	10	forcing	force	VERB
ejpam-5046	68	11	set	set	NOUN
ejpam-5046	68	12	of	of	ADP
ejpam-5046	68	13	g	g	NOUN
ejpam-5046	68	14	,	,	PUNCT
ejpam-5046	68	15	denoted	denote	VERB
ejpam-5046	68	16	by	by	ADP
ejpam-5046	68	17	z2(g	z2(g	NOUN
ejpam-5046	68	18	)	)	PUNCT
ejpam-5046	68	19	,	,	PUNCT
ejpam-5046	68	20	is	be	AUX
ejpam-5046	68	21	called	call	VERB
ejpam-5046	68	22	the	the	DET
ejpam-5046	68	23	2	2	NUM
ejpam-5046	68	24	-	-	PUNCT
ejpam-5046	68	25	distance	distance	NOUN
ejpam-5046	68	26	zero	zero	NUM
ejpam-5046	68	27	forcing	force	VERB
ejpam-5046	68	28	number	number	NOUN
ejpam-5046	68	29	of	of	ADP
ejpam-5046	68	30	g.	g.	PROPN
ejpam-5046	68	31	example	example	NOUN
ejpam-5046	68	32	1	1	X
ejpam-5046	68	33	.	.	X
ejpam-5046	68	34	consider	consider	VERB
ejpam-5046	68	35	the	the	DET
ejpam-5046	68	36	graph	graph	NOUN
ejpam-5046	68	37	g	g	NOUN
ejpam-5046	68	38	in	in	ADP
ejpam-5046	68	39	figure	figure	NOUN
ejpam-5046	68	40	1	1	NUM
ejpam-5046	68	41	and	and	CCONJ
ejpam-5046	68	42	let	let	VERB
ejpam-5046	68	43	n	n	X
ejpam-5046	68	44	=	=	X
ejpam-5046	68	45	{	{	PUNCT
ejpam-5046	68	46	a	a	DET
ejpam-5046	68	47	,	,	PUNCT
ejpam-5046	68	48	b	b	NOUN
ejpam-5046	68	49	,	,	PUNCT
ejpam-5046	68	50	d	d	NOUN
ejpam-5046	68	51	}	}	PUNCT
ejpam-5046	68	52	.	.	PUNCT
ejpam-5046	69	1	then	then	ADV
ejpam-5046	69	2	vertex	vertex	PROPN
ejpam-5046	69	3	c	c	PROPN
ejpam-5046	69	4	is	be	AUX
ejpam-5046	69	5	2	2	NUM
ejpam-5046	69	6	-	-	PUNCT
ejpam-5046	69	7	forced	force	VERB
ejpam-5046	69	8	by	by	ADP
ejpam-5046	69	9	vertex	vertex	NOUN
ejpam-5046	69	10	a	a	PRON
ejpam-5046	69	11	and	and	CCONJ
ejpam-5046	69	12	vertex	vertex	NOUN
ejpam-5046	69	13	e	e	NOUN
ejpam-5046	69	14	is	be	AUX
ejpam-5046	69	15	2	2	NUM
ejpam-5046	69	16	-	-	PUNCT
ejpam-5046	69	17	forced	force	VERB
ejpam-5046	69	18	by	by	ADP
ejpam-5046	69	19	either	either	PRON
ejpam-5046	69	20	vertex	vertex	NOUN
ejpam-5046	69	21	d	d	NOUN
ejpam-5046	69	22	or	or	CCONJ
ejpam-5046	69	23	b.	b.	PROPN
ejpam-5046	69	24	thus	thus	ADV
ejpam-5046	69	25	,	,	PUNCT
ejpam-5046	69	26	n	n	PRON
ejpam-5046	69	27	is	be	AUX
ejpam-5046	69	28	a	a	DET
ejpam-5046	69	29	2	2	NUM
ejpam-5046	69	30	-	-	PUNCT
ejpam-5046	69	31	distance	distance	NOUN
ejpam-5046	69	32	zero	zero	NUM
ejpam-5046	69	33	forcing	force	VERB
ejpam-5046	69	34	set	set	NOUN
ejpam-5046	69	35	of	of	ADP
ejpam-5046	69	36	g.	g.	PROPN
ejpam-5046	69	37	moreover	moreover	ADV
ejpam-5046	69	38	,	,	PUNCT
ejpam-5046	69	39	z2(g	z2(g	NUM
ejpam-5046	69	40	)	)	PUNCT
ejpam-5046	69	41	=	=	SYM
ejpam-5046	70	1	3	3	X
ejpam-5046	70	2	.	.	PUNCT
ejpam-5046	70	3	a	a	DET
ejpam-5046	70	4	b	b	NOUN
ejpam-5046	70	5	d	d	X
ejpam-5046	70	6	c	c	NOUN
ejpam-5046	70	7	e	e	X
ejpam-5046	70	8	g	g	NOUN
ejpam-5046	70	9	:	:	PUNCT
ejpam-5046	70	10	figure	figure	NOUN
ejpam-5046	70	11	1	1	NUM
ejpam-5046	70	12	:	:	PUNCT
ejpam-5046	70	13	graph	graph	VERB
ejpam-5046	70	14	g	g	NOUN
ejpam-5046	70	15	with	with	ADP
ejpam-5046	70	16	z2(g	z2(g	NUM
ejpam-5046	70	17	)	)	PUNCT
ejpam-5046	70	18	=	=	SYM
ejpam-5046	70	19	3	3	NUM
ejpam-5046	70	20	proposition	proposition	NOUN
ejpam-5046	70	21	1	1	NUM
ejpam-5046	70	22	.	.	PUNCT
ejpam-5046	71	1	let	let	VERB
ejpam-5046	71	2	n	n	PRON
ejpam-5046	71	3	be	be	AUX
ejpam-5046	71	4	a	a	DET
ejpam-5046	71	5	positive	positive	ADJ
ejpam-5046	71	6	integer	integer	NOUN
ejpam-5046	71	7	.	.	PUNCT
ejpam-5046	72	1	then	then	ADV
ejpam-5046	72	2	s	s	VERB
ejpam-5046	72	3	is	be	AUX
ejpam-5046	72	4	a	a	DET
ejpam-5046	72	5	2	2	NUM
ejpam-5046	72	6	-	-	PUNCT
ejpam-5046	72	7	distance	distance	NOUN
ejpam-5046	72	8	zero	zero	NUM
ejpam-5046	72	9	forcing	force	VERB
ejpam-5046	72	10	set	set	NOUN
ejpam-5046	72	11	of	of	ADP
ejpam-5046	72	12	kn	kn	PROPN
ejpam-5046	72	13	if	if	SCONJ
ejpam-5046	72	14	and	and	CCONJ
ejpam-5046	72	15	only	only	ADV
ejpam-5046	72	16	if	if	SCONJ
ejpam-5046	72	17	s	s	VERB
ejpam-5046	72	18	=	=	SYM
ejpam-5046	72	19	v	v	PROPN
ejpam-5046	72	20	(	(	PUNCT
ejpam-5046	72	21	kn	kn	PROPN
ejpam-5046	72	22	)	)	PUNCT
ejpam-5046	72	23	.	.	PUNCT
ejpam-5046	73	1	proof	proof	NOUN
ejpam-5046	73	2	.	.	PUNCT
ejpam-5046	74	1	let	let	VERB
ejpam-5046	74	2	s	s	PRON
ejpam-5046	74	3	be	be	AUX
ejpam-5046	74	4	a	a	DET
ejpam-5046	74	5	2	2	NUM
ejpam-5046	74	6	-	-	PUNCT
ejpam-5046	74	7	distance	distance	NOUN
ejpam-5046	74	8	zero	zero	NUM
ejpam-5046	74	9	forcing	force	VERB
ejpam-5046	74	10	set	set	NOUN
ejpam-5046	74	11	of	of	ADP
ejpam-5046	74	12	kn	kn	PROPN
ejpam-5046	74	13	.	.	PUNCT
ejpam-5046	74	14	suppose	suppose	VERB
ejpam-5046	74	15	that	that	SCONJ
ejpam-5046	74	16	s	s	VERB
ejpam-5046	74	17	̸=	̸=	PROPN
ejpam-5046	74	18	v	v	NOUN
ejpam-5046	74	19	(	(	PUNCT
ejpam-5046	74	20	kn	kn	PROPN
ejpam-5046	74	21	)	)	PUNCT
ejpam-5046	74	22	.	.	PUNCT
ejpam-5046	75	1	then	then	ADV
ejpam-5046	75	2	there	there	PRON
ejpam-5046	75	3	exists	exist	VERB
ejpam-5046	75	4	x	x	X
ejpam-5046	75	5	∈	∈	PROPN
ejpam-5046	75	6	v	v	X
ejpam-5046	75	7	(	(	PUNCT
ejpam-5046	75	8	kn	kn	PROPN
ejpam-5046	75	9	)	)	PUNCT
ejpam-5046	75	10	such	such	ADJ
ejpam-5046	75	11	that	that	SCONJ
ejpam-5046	75	12	x	x	PROPN
ejpam-5046	75	13	/∈	/∈	PROPN
ejpam-5046	75	14	s.	s.	PROPN
ejpam-5046	75	15	however	however	ADV
ejpam-5046	75	16	,	,	PUNCT
ejpam-5046	75	17	dkn(x	dkn(x	X
ejpam-5046	75	18	,	,	PUNCT
ejpam-5046	75	19	y	y	NOUN
ejpam-5046	75	20	)	)	PUNCT
ejpam-5046	75	21	=	=	SYM
ejpam-5046	75	22	1	1	NUM
ejpam-5046	75	23	for	for	ADP
ejpam-5046	75	24	all	all	DET
ejpam-5046	75	25	y	y	PROPN
ejpam-5046	75	26	∈	∈	PROPN
ejpam-5046	75	27	s.	s.	PROPN
ejpam-5046	76	1	it	it	PRON
ejpam-5046	76	2	follows	follow	VERB
ejpam-5046	76	3	j.	j.	PROPN
ejpam-5046	76	4	a.	a.	PROPN
ejpam-5046	76	5	hassan	hassan	PROPN
ejpam-5046	76	6	,	,	PUNCT
ejpam-5046	76	7	l.	l.	PROPN
ejpam-5046	76	8	t.	t.	PROPN
ejpam-5046	76	9	udtohan	udtohan	PROPN
ejpam-5046	76	10	,	,	PUNCT
ejpam-5046	76	11	l.	l.	PROPN
ejpam-5046	76	12	s.	s.	PROPN
ejpam-5046	76	13	laja	laja	PROPN
ejpam-5046	76	14	/	/	SYM
ejpam-5046	76	15	eur	eur	PROPN
ejpam-5046	76	16	.	.	PUNCT
ejpam-5046	77	1	j.	j.	PROPN
ejpam-5046	77	2	pure	pure	PROPN
ejpam-5046	77	3	appl	appl	PROPN
ejpam-5046	77	4	.	.	PROPN
ejpam-5046	77	5	math	math	PROPN
ejpam-5046	77	6	,	,	PUNCT
ejpam-5046	77	7	17	17	NUM
ejpam-5046	77	8	(	(	PUNCT
ejpam-5046	77	9	2	2	NUM
ejpam-5046	77	10	)	)	PUNCT
ejpam-5046	77	11	(	(	PUNCT
ejpam-5046	77	12	2024	2024	NUM
ejpam-5046	77	13	)	)	PUNCT
ejpam-5046	77	14	,	,	PUNCT
ejpam-5046	77	15	1283	1283	NUM
ejpam-5046	77	16	-	-	SYM
ejpam-5046	77	17	1293	1293	NUM
ejpam-5046	77	18	1286	1286	NUM
ejpam-5046	77	19	that	that	PRON
ejpam-5046	77	20	s	s	VERB
ejpam-5046	77	21	can	can	AUX
ejpam-5046	77	22	not	not	PART
ejpam-5046	77	23	2	2	NUM
ejpam-5046	77	24	-	-	PUNCT
ejpam-5046	77	25	forced	forced	ADJ
ejpam-5046	77	26	x	x	NOUN
ejpam-5046	77	27	,	,	PUNCT
ejpam-5046	77	28	a	a	DET
ejpam-5046	77	29	contradiction	contradiction	NOUN
ejpam-5046	77	30	.	.	PUNCT
ejpam-5046	78	1	therefore	therefore	ADV
ejpam-5046	78	2	,	,	PUNCT
ejpam-5046	78	3	s	s	NOUN
ejpam-5046	78	4	=	=	SYM
ejpam-5046	78	5	v	v	PROPN
ejpam-5046	78	6	(	(	PUNCT
ejpam-5046	78	7	kn	kn	PROPN
ejpam-5046	78	8	)	)	PUNCT
ejpam-5046	78	9	.	.	PUNCT
ejpam-5046	79	1	the	the	DET
ejpam-5046	79	2	converse	converse	NOUN
ejpam-5046	79	3	is	be	AUX
ejpam-5046	79	4	clear	clear	ADJ
ejpam-5046	79	5	.	.	PUNCT
ejpam-5046	80	1	corollary	corollary	ADJ
ejpam-5046	80	2	1	1	NUM
ejpam-5046	80	3	.	.	PUNCT
ejpam-5046	81	1	let	let	VERB
ejpam-5046	81	2	n	n	PRON
ejpam-5046	81	3	be	be	AUX
ejpam-5046	81	4	a	a	DET
ejpam-5046	81	5	positive	positive	ADJ
ejpam-5046	81	6	integer	integer	NOUN
ejpam-5046	81	7	.	.	PUNCT
ejpam-5046	82	1	then	then	ADV
ejpam-5046	82	2	z2(kn	z2(kn	NUM
ejpam-5046	82	3	)	)	PUNCT
ejpam-5046	82	4	=	=	SYM
ejpam-5046	82	5	n.	n.	NOUN
ejpam-5046	82	6	theorem	theorem	NOUN
ejpam-5046	82	7	1	1	NUM
ejpam-5046	82	8	.	.	PUNCT
ejpam-5046	82	9	z2(g	z2(g	NUM
ejpam-5046	82	10	)	)	PUNCT
ejpam-5046	82	11	=	=	SYM
ejpam-5046	82	12	|v	|v	PROPN
ejpam-5046	82	13	(	(	PUNCT
ejpam-5046	82	14	g)|	g)|	VERB
ejpam-5046	82	15	if	if	SCONJ
ejpam-5046	82	16	and	and	CCONJ
ejpam-5046	82	17	only	only	ADV
ejpam-5046	82	18	if	if	SCONJ
ejpam-5046	82	19	diam(h	diam(h	ADJ
ejpam-5046	82	20	)	)	PUNCT
ejpam-5046	82	21	≤	≤	NOUN
ejpam-5046	82	22	1	1	NUM
ejpam-5046	82	23	for	for	ADP
ejpam-5046	82	24	each	each	DET
ejpam-5046	82	25	component	component	NOUN
ejpam-5046	82	26	h	h	NOUN
ejpam-5046	82	27	of	of	ADP
ejpam-5046	82	28	g.	g.	PROPN
ejpam-5046	82	29	proof	proof	PROPN
ejpam-5046	82	30	.	.	PUNCT
ejpam-5046	83	1	suppose	suppose	VERB
ejpam-5046	83	2	that	that	SCONJ
ejpam-5046	83	3	z2(g	z2(g	X
ejpam-5046	83	4	)	)	PUNCT
ejpam-5046	83	5	=	=	SYM
ejpam-5046	83	6	|v	|v	PROPN
ejpam-5046	83	7	(	(	PUNCT
ejpam-5046	83	8	g)|	g)|	PROPN
ejpam-5046	83	9	.	.	PUNCT
ejpam-5046	83	10	suppose	suppose	VERB
ejpam-5046	83	11	further	far	ADV
ejpam-5046	83	12	that	that	DET
ejpam-5046	83	13	diam(h	diam(h	NOUN
ejpam-5046	83	14	)	)	PUNCT
ejpam-5046	83	15	≥	≥	NOUN
ejpam-5046	83	16	2	2	NUM
ejpam-5046	83	17	for	for	ADP
ejpam-5046	83	18	some	some	DET
ejpam-5046	83	19	component	component	NOUN
ejpam-5046	83	20	h	h	NOUN
ejpam-5046	83	21	of	of	ADP
ejpam-5046	83	22	g.	g.	PROPN
ejpam-5046	83	23	then	then	ADV
ejpam-5046	83	24	there	there	PRON
ejpam-5046	83	25	exist	exist	VERB
ejpam-5046	83	26	a	a	DET
ejpam-5046	83	27	,	,	PUNCT
ejpam-5046	83	28	b	b	PROPN
ejpam-5046	83	29	∈	∈	PROPN
ejpam-5046	83	30	v	v	ADP
ejpam-5046	83	31	(	(	PUNCT
ejpam-5046	83	32	h	h	NOUN
ejpam-5046	83	33	)	)	PUNCT
ejpam-5046	83	34	such	such	ADJ
ejpam-5046	83	35	that	that	PRON
ejpam-5046	83	36	dh(a	dh(a	ADJ
ejpam-5046	83	37	,	,	PUNCT
ejpam-5046	83	38	b	b	NOUN
ejpam-5046	83	39	)	)	PUNCT
ejpam-5046	83	40	=	=	SYM
ejpam-5046	83	41	2	2	NUM
ejpam-5046	83	42	=	=	SYM
ejpam-5046	83	43	dg(a	dg(a	X
ejpam-5046	83	44	,	,	PUNCT
ejpam-5046	83	45	b	b	NOUN
ejpam-5046	83	46	)	)	PUNCT
ejpam-5046	83	47	.	.	PUNCT
ejpam-5046	84	1	let	let	VERB
ejpam-5046	84	2	n	n	NOUN
ejpam-5046	84	3	=	=	SYM
ejpam-5046	84	4	v	v	PROPN
ejpam-5046	84	5	(	(	PUNCT
ejpam-5046	84	6	g	g	NOUN
ejpam-5046	84	7	)	)	PUNCT
ejpam-5046	84	8	\	\	NOUN
ejpam-5046	85	1	{	{	PUNCT
ejpam-5046	85	2	b	b	NOUN
ejpam-5046	85	3	}	}	PUNCT
ejpam-5046	85	4	.	.	PUNCT
ejpam-5046	86	1	then	then	ADV
ejpam-5046	86	2	n	n	PRON
ejpam-5046	86	3	is	be	AUX
ejpam-5046	86	4	a	a	DET
ejpam-5046	86	5	2	2	NUM
ejpam-5046	86	6	-	-	PUNCT
ejpam-5046	86	7	distance	distance	NOUN
ejpam-5046	86	8	zero	zero	NUM
ejpam-5046	86	9	forcing	force	VERB
ejpam-5046	86	10	set	set	NOUN
ejpam-5046	86	11	of	of	ADP
ejpam-5046	86	12	g.	g.	PROPN
ejpam-5046	86	13	thus	thus	ADV
ejpam-5046	86	14	,	,	PUNCT
ejpam-5046	86	15	z2(g	z2(g	NUM
ejpam-5046	86	16	)	)	PUNCT
ejpam-5046	86	17	≤	≤	NOUN
ejpam-5046	86	18	|v	|v	X
ejpam-5046	86	19	(	(	PUNCT
ejpam-5046	86	20	g)|−	g)|−	PRON
ejpam-5046	86	21	1	1	NUM
ejpam-5046	86	22	,	,	PUNCT
ejpam-5046	86	23	a	a	DET
ejpam-5046	86	24	contradiction	contradiction	NOUN
ejpam-5046	86	25	.	.	PUNCT
ejpam-5046	87	1	therefore	therefore	ADV
ejpam-5046	87	2	,	,	PUNCT
ejpam-5046	87	3	diam(h	diam(h	INTJ
ejpam-5046	87	4	)	)	PUNCT
ejpam-5046	87	5	≤	≤	NOUN
ejpam-5046	87	6	1	1	NUM
ejpam-5046	87	7	for	for	ADP
ejpam-5046	87	8	each	each	DET
ejpam-5046	87	9	component	component	NOUN
ejpam-5046	87	10	h	h	NOUN
ejpam-5046	87	11	of	of	ADP
ejpam-5046	87	12	g.	g.	PROPN
ejpam-5046	87	13	conversely	conversely	ADV
ejpam-5046	87	14	,	,	PUNCT
ejpam-5046	87	15	suppose	suppose	VERB
ejpam-5046	87	16	that	that	SCONJ
ejpam-5046	87	17	diam(h	diam(h	NOUN
ejpam-5046	87	18	)	)	PUNCT
ejpam-5046	87	19	≤	≤	NOUN
ejpam-5046	87	20	1	1	NUM
ejpam-5046	87	21	for	for	ADP
ejpam-5046	87	22	each	each	DET
ejpam-5046	87	23	component	component	NOUN
ejpam-5046	87	24	h	h	NOUN
ejpam-5046	87	25	of	of	ADP
ejpam-5046	87	26	g.	g.	PROPN
ejpam-5046	87	27	if	if	SCONJ
ejpam-5046	87	28	g	g	PROPN
ejpam-5046	87	29	is	be	AUX
ejpam-5046	87	30	connected	connect	VERB
ejpam-5046	87	31	,	,	PUNCT
ejpam-5046	87	32	then	then	ADV
ejpam-5046	87	33	g	g	PROPN
ejpam-5046	87	34	=	=	PROPN
ejpam-5046	87	35	kn	kn	PROPN
ejpam-5046	87	36	.	.	PUNCT
ejpam-5046	88	1	thus	thus	ADV
ejpam-5046	88	2	,	,	PUNCT
ejpam-5046	88	3	z	z	NOUN
ejpam-5046	88	4	2(g	2(g	NUM
ejpam-5046	88	5	)	)	PUNCT
ejpam-5046	88	6	=	=	SYM
ejpam-5046	88	7	|v	|v	X
ejpam-5046	88	8	(	(	PUNCT
ejpam-5046	88	9	g)|	g)|	NOUN
ejpam-5046	88	10	=	=	PUNCT
ejpam-5046	88	11	n	n	X
ejpam-5046	88	12	by	by	ADP
ejpam-5046	88	13	corollary	corollary	ADJ
ejpam-5046	88	14	1	1	NUM
ejpam-5046	88	15	.	.	PUNCT
ejpam-5046	88	16	suppose	suppose	VERB
ejpam-5046	88	17	that	that	SCONJ
ejpam-5046	88	18	g	g	PROPN
ejpam-5046	88	19	is	be	AUX
ejpam-5046	88	20	disconnected	disconnect	VERB
ejpam-5046	88	21	.	.	PUNCT
ejpam-5046	89	1	let	let	VERB
ejpam-5046	89	2	h1	h1	VERB
ejpam-5046	89	3	,	,	PUNCT
ejpam-5046	89	4	.	.	PUNCT
ejpam-5046	89	5	.	.	PUNCT
ejpam-5046	90	1	.	.	PUNCT
ejpam-5046	91	1	,	,	PUNCT
ejpam-5046	91	2	hk	hk	PROPN
ejpam-5046	91	3	,	,	PUNCT
ejpam-5046	91	4	k	k	PROPN
ejpam-5046	91	5	≥	≥	NUM
ejpam-5046	91	6	2	2	NUM
ejpam-5046	91	7	be	be	AUX
ejpam-5046	91	8	components	component	NOUN
ejpam-5046	91	9	of	of	ADP
ejpam-5046	91	10	g.	g.	PROPN
ejpam-5046	91	11	since	since	SCONJ
ejpam-5046	91	12	diam(hi	diam(hi	PROPN
ejpam-5046	91	13	)	)	PUNCT
ejpam-5046	91	14	≤	≤	NOUN
ejpam-5046	91	15	1	1	NUM
ejpam-5046	91	16	,	,	PUNCT
ejpam-5046	91	17	z2(hi	z2(hi	NUM
ejpam-5046	91	18	)	)	PUNCT
ejpam-5046	92	1	=	=	SYM
ejpam-5046	92	2	|v	|v	PROPN
ejpam-5046	92	3	(	(	PUNCT
ejpam-5046	92	4	hi)|	hi)|	PROPN
ejpam-5046	92	5	for	for	ADP
ejpam-5046	92	6	each	each	DET
ejpam-5046	92	7	i	i	PRON
ejpam-5046	92	8	∈	∈	PROPN
ejpam-5046	92	9	{	{	PUNCT
ejpam-5046	92	10	1	1	NUM
ejpam-5046	92	11	,	,	PUNCT
ejpam-5046	92	12	.	.	PUNCT
ejpam-5046	92	13	.	.	PUNCT
ejpam-5046	92	14	.	.	PUNCT
ejpam-5046	92	15	,	,	PUNCT
ejpam-5046	92	16	k	k	X
ejpam-5046	92	17	}	}	PUNCT
ejpam-5046	92	18	.	.	PUNCT
ejpam-5046	93	1	thus	thus	ADV
ejpam-5046	93	2	,	,	PUNCT
ejpam-5046	93	3	z2(g	z2(g	NUM
ejpam-5046	93	4	)	)	PUNCT
ejpam-5046	93	5	=	=	SYM
ejpam-5046	93	6	z2(h1	z2(h1	PROPN
ejpam-5046	93	7	)	)	PUNCT
ejpam-5046	93	8	+	+	CCONJ
ejpam-5046	93	9	·	·	PUNCT
ejpam-5046	93	10	·	·	PUNCT
ejpam-5046	93	11	·	·	PUNCT
ejpam-5046	93	12	+	+	NUM
ejpam-5046	93	13	z2(hk	z2(hk	NOUN
ejpam-5046	93	14	)	)	PUNCT
ejpam-5046	93	15	=	=	SYM
ejpam-5046	93	16	|v	|v	PROPN
ejpam-5046	93	17	(	(	PUNCT
ejpam-5046	93	18	h1)|+	h1)|+	X
ejpam-5046	93	19	·	·	PUNCT
ejpam-5046	93	20	·	·	PUNCT
ejpam-5046	93	21	·	·	PUNCT
ejpam-5046	94	1	+	+	CCONJ
ejpam-5046	94	2	|v	|v	X
ejpam-5046	94	3	(	(	PUNCT
ejpam-5046	94	4	hk)|	hk)|	X
ejpam-5046	94	5	=	=	SYM
ejpam-5046	94	6	|v	|v	PROPN
ejpam-5046	94	7	(	(	PUNCT
ejpam-5046	94	8	g)|	g)|	PROPN
ejpam-5046	94	9	.	.	PUNCT
ejpam-5046	94	10	corollary	corollary	ADJ
ejpam-5046	94	11	2	2	NUM
ejpam-5046	94	12	.	.	PUNCT
ejpam-5046	94	13	let	let	VERB
ejpam-5046	94	14	n	n	PRON
ejpam-5046	94	15	be	be	AUX
ejpam-5046	94	16	a	a	DET
ejpam-5046	94	17	positive	positive	ADJ
ejpam-5046	94	18	integer	integer	NOUN
ejpam-5046	94	19	.	.	PUNCT
ejpam-5046	95	1	then	then	ADV
ejpam-5046	95	2	,	,	PUNCT
ejpam-5046	95	3	z2(kn	z2(kn	NUM
ejpam-5046	95	4	)	)	PUNCT
ejpam-5046	95	5	=	=	PUNCT
ejpam-5046	95	6	n.	n.	NOUN
ejpam-5046	95	7	proposition	proposition	NOUN
ejpam-5046	95	8	2	2	X
ejpam-5046	95	9	.	.	PUNCT
ejpam-5046	96	1	let	let	VERB
ejpam-5046	96	2	g	g	PRON
ejpam-5046	96	3	be	be	AUX
ejpam-5046	96	4	a	a	DET
ejpam-5046	96	5	graph	graph	NOUN
ejpam-5046	96	6	and	and	CCONJ
ejpam-5046	96	7	let	let	VERB
ejpam-5046	96	8	n	n	PRON
ejpam-5046	96	9	be	be	AUX
ejpam-5046	96	10	a	a	DET
ejpam-5046	96	11	2	2	NUM
ejpam-5046	96	12	-	-	PUNCT
ejpam-5046	96	13	distance	distance	NOUN
ejpam-5046	96	14	zero	zero	NUM
ejpam-5046	96	15	forcing	force	VERB
ejpam-5046	96	16	set	set	NOUN
ejpam-5046	96	17	of	of	ADP
ejpam-5046	96	18	g.	g.	PROPN
ejpam-5046	96	19	then	then	ADV
ejpam-5046	96	20	every	every	DET
ejpam-5046	96	21	dominating	dominating	NOUN
ejpam-5046	96	22	vertex	vertex	NOUN
ejpam-5046	96	23	v	v	ADP
ejpam-5046	96	24	∈	∈	PROPN
ejpam-5046	96	25	v	v	NOUN
ejpam-5046	96	26	(	(	PUNCT
ejpam-5046	96	27	g	g	NOUN
ejpam-5046	96	28	)	)	PUNCT
ejpam-5046	96	29	,	,	PUNCT
ejpam-5046	96	30	v	v	X
ejpam-5046	96	31	∈	∈	PROPN
ejpam-5046	96	32	n	n	X
ejpam-5046	96	33	.	.	PUNCT
ejpam-5046	97	1	proof	proof	NOUN
ejpam-5046	97	2	.	.	PUNCT
ejpam-5046	98	1	let	let	VERB
ejpam-5046	98	2	v	v	NUM
ejpam-5046	98	3	∈	∈	PROPN
ejpam-5046	98	4	v	v	NOUN
ejpam-5046	98	5	(	(	PUNCT
ejpam-5046	98	6	g	g	NOUN
ejpam-5046	98	7	)	)	PUNCT
ejpam-5046	98	8	be	be	AUX
ejpam-5046	98	9	a	a	DET
ejpam-5046	98	10	dominating	dominating	NOUN
ejpam-5046	98	11	vertex	vertex	NOUN
ejpam-5046	98	12	of	of	ADP
ejpam-5046	98	13	g.	g.	PROPN
ejpam-5046	98	14	then	then	ADV
ejpam-5046	98	15	ng[v	ng[v	X
ejpam-5046	98	16	]	]	X
ejpam-5046	98	17	=	=	SYM
ejpam-5046	98	18	v	v	X
ejpam-5046	98	19	(	(	PUNCT
ejpam-5046	98	20	g	g	NOUN
ejpam-5046	98	21	)	)	PUNCT
ejpam-5046	98	22	,	,	PUNCT
ejpam-5046	98	23	that	that	ADV
ejpam-5046	98	24	is	is	ADV
ejpam-5046	98	25	,	,	PUNCT
ejpam-5046	98	26	v	v	NOUN
ejpam-5046	98	27	is	be	AUX
ejpam-5046	98	28	adjacent	adjacent	ADJ
ejpam-5046	98	29	to	to	ADP
ejpam-5046	98	30	every	every	DET
ejpam-5046	98	31	vertex	vertex	NOUN
ejpam-5046	98	32	u	u	NOUN
ejpam-5046	98	33	∈	∈	PROPN
ejpam-5046	98	34	v	v	ADP
ejpam-5046	98	35	(	(	PUNCT
ejpam-5046	98	36	g	g	NOUN
ejpam-5046	98	37	)	)	PUNCT
ejpam-5046	98	38	\	\	NOUN
ejpam-5046	99	1	{	{	PUNCT
ejpam-5046	99	2	v	v	NOUN
ejpam-5046	99	3	}	}	PUNCT
ejpam-5046	99	4	.	.	PUNCT
ejpam-5046	100	1	suppose	suppose	VERB
ejpam-5046	100	2	that	that	SCONJ
ejpam-5046	100	3	v	v	NOUN
ejpam-5046	100	4	/∈	/∈	PUNCT
ejpam-5046	101	1	n	n	INTJ
ejpam-5046	101	2	.	.	PUNCT
ejpam-5046	102	1	then	then	ADV
ejpam-5046	102	2	dg(v	dg(v	PUNCT
ejpam-5046	102	3	,	,	PUNCT
ejpam-5046	102	4	w	w	NOUN
ejpam-5046	102	5	)	)	PUNCT
ejpam-5046	102	6	=	=	SYM
ejpam-5046	102	7	2	2	NUM
ejpam-5046	102	8	for	for	ADP
ejpam-5046	102	9	some	some	DET
ejpam-5046	102	10	w	w	PROPN
ejpam-5046	102	11	∈	∈	PROPN
ejpam-5046	102	12	n	n	PRON
ejpam-5046	102	13	,	,	PUNCT
ejpam-5046	102	14	a	a	DET
ejpam-5046	102	15	contradiction	contradiction	NOUN
ejpam-5046	102	16	.	.	PUNCT
ejpam-5046	103	1	therefore	therefore	ADV
ejpam-5046	103	2	,	,	PUNCT
ejpam-5046	103	3	v	v	PROPN
ejpam-5046	103	4	∈	∈	PROPN
ejpam-5046	103	5	n	n	X
ejpam-5046	103	6	.	.	PUNCT
ejpam-5046	104	1	proposition	proposition	NOUN
ejpam-5046	104	2	3	3	X
ejpam-5046	104	3	.	.	PUNCT
ejpam-5046	105	1	let	let	VERB
ejpam-5046	105	2	n	n	PRON
ejpam-5046	105	3	be	be	AUX
ejpam-5046	105	4	a	a	DET
ejpam-5046	105	5	positive	positive	ADJ
ejpam-5046	105	6	integer	integer	NOUN
ejpam-5046	105	7	.	.	PUNCT
ejpam-5046	106	1	then	then	ADV
ejpam-5046	106	2	,	,	PUNCT
ejpam-5046	106	3	z2(pn	z2(pn	NUM
ejpam-5046	106	4	)	)	PUNCT
ejpam-5046	106	5	=	=	NOUN
ejpam-5046	106	6	{	{	PUNCT
ejpam-5046	106	7	1	1	NUM
ejpam-5046	106	8	,	,	PUNCT
ejpam-5046	106	9	n	n	NOUN
ejpam-5046	106	10	=	=	SYM
ejpam-5046	106	11	1	1	NUM
ejpam-5046	106	12	2	2	NUM
ejpam-5046	106	13	,	,	PUNCT
ejpam-5046	106	14	n	n	PRON
ejpam-5046	106	15	≥	≥	NOUN
ejpam-5046	106	16	2	2	NUM
ejpam-5046	106	17	proof	proof	NOUN
ejpam-5046	106	18	.	.	PUNCT
ejpam-5046	107	1	by	by	ADP
ejpam-5046	107	2	theorem	theorem	NOUN
ejpam-5046	107	3	1	1	NUM
ejpam-5046	107	4	,	,	PUNCT
ejpam-5046	107	5	z2(p1	z2(p1	NOUN
ejpam-5046	107	6	)	)	PUNCT
ejpam-5046	107	7	=	=	SYM
ejpam-5046	107	8	1	1	NUM
ejpam-5046	107	9	and	and	CCONJ
ejpam-5046	107	10	z2(p2	z2(p2	NUM
ejpam-5046	107	11	)	)	PUNCT
ejpam-5046	107	12	=	=	SYM
ejpam-5046	107	13	2	2	X
ejpam-5046	107	14	.	.	PUNCT
ejpam-5046	107	15	clearly	clearly	ADV
ejpam-5046	107	16	,	,	PUNCT
ejpam-5046	107	17	z2(pn	z2(pn	NUM
ejpam-5046	107	18	)	)	PUNCT
ejpam-5046	107	19	=	=	SYM
ejpam-5046	107	20	2	2	NUM
ejpam-5046	107	21	for	for	ADP
ejpam-5046	107	22	n	n	NOUN
ejpam-5046	107	23	=	=	SYM
ejpam-5046	107	24	3	3	NUM
ejpam-5046	107	25	,	,	PUNCT
ejpam-5046	107	26	4	4	NUM
ejpam-5046	107	27	,	,	PUNCT
ejpam-5046	107	28	5	5	NUM
ejpam-5046	107	29	suppose	suppose	VERB
ejpam-5046	107	30	that	that	SCONJ
ejpam-5046	107	31	n	n	PRON
ejpam-5046	107	32	≥	≥	NUM
ejpam-5046	107	33	6	6	NUM
ejpam-5046	107	34	let	let	VERB
ejpam-5046	107	35	v	v	NOUN
ejpam-5046	107	36	(	(	PUNCT
ejpam-5046	107	37	pn	pn	NOUN
ejpam-5046	107	38	)	)	PUNCT
ejpam-5046	107	39	=	=	SYM
ejpam-5046	107	40	{	{	PUNCT
ejpam-5046	107	41	v1	v1	PROPN
ejpam-5046	107	42	,	,	PUNCT
ejpam-5046	107	43	v2	v2	PROPN
ejpam-5046	107	44	,	,	PUNCT
ejpam-5046	107	45	...	...	PUNCT
ejpam-5046	107	46	,	,	PUNCT
ejpam-5046	107	47	vn	vn	INTJ
ejpam-5046	107	48	}	}	PUNCT
ejpam-5046	107	49	and	and	CCONJ
ejpam-5046	107	50	n	n	CCONJ
ejpam-5046	107	51	=	=	NOUN
ejpam-5046	107	52	{	{	PUNCT
ejpam-5046	107	53	v1	v1	PROPN
ejpam-5046	107	54	,	,	PUNCT
ejpam-5046	107	55	v2	v2	PROPN
ejpam-5046	107	56	}	}	PUNCT
ejpam-5046	107	57	.	.	PUNCT
ejpam-5046	108	1	if	if	SCONJ
ejpam-5046	108	2	n	n	NOUN
ejpam-5046	108	3	is	be	AUX
ejpam-5046	108	4	odd	odd	ADJ
ejpam-5046	108	5	,	,	PUNCT
ejpam-5046	108	6	then	then	ADV
ejpam-5046	108	7	vertices	vertice	VERB
ejpam-5046	108	8	v3	v3	PROPN
ejpam-5046	108	9	,	,	PUNCT
ejpam-5046	108	10	v5	v5	PROPN
ejpam-5046	108	11	,	,	PUNCT
ejpam-5046	108	12	.	.	PUNCT
ejpam-5046	108	13	.	.	PUNCT
ejpam-5046	108	14	.	.	PUNCT
ejpam-5046	109	1	,	,	PUNCT
ejpam-5046	109	2	vn	vn	PROPN
ejpam-5046	109	3	are	be	AUX
ejpam-5046	109	4	2	2	NUM
ejpam-5046	109	5	-	-	PUNCT
ejpam-5046	109	6	forced	force	VERB
ejpam-5046	109	7	by	by	ADP
ejpam-5046	109	8	vertices	vertex	NOUN
ejpam-5046	109	9	v1	v1	PROPN
ejpam-5046	109	10	,	,	PUNCT
ejpam-5046	109	11	v3	v3	PROPN
ejpam-5046	109	12	,	,	PUNCT
ejpam-5046	109	13	.	.	PUNCT
ejpam-5046	109	14	.	.	PUNCT
ejpam-5046	110	1	.	.	PUNCT
ejpam-5046	111	1	,	,	PUNCT
ejpam-5046	111	2	vn−2	vn−2	PROPN
ejpam-5046	111	3	,	,	PUNCT
ejpam-5046	111	4	respectively	respectively	ADV
ejpam-5046	111	5	,	,	PUNCT
ejpam-5046	111	6	and	and	CCONJ
ejpam-5046	111	7	vertices	vertice	VERB
ejpam-5046	111	8	v4	v4	PROPN
ejpam-5046	111	9	,	,	PUNCT
ejpam-5046	111	10	v6	v6	NOUN
ejpam-5046	111	11	,	,	PUNCT
ejpam-5046	111	12	.	.	PUNCT
ejpam-5046	111	13	.	.	PUNCT
ejpam-5046	112	1	.	.	PUNCT
ejpam-5046	113	1	,	,	PUNCT
ejpam-5046	113	2	vn−1	vn−1	PROPN
ejpam-5046	113	3	are	be	AUX
ejpam-5046	113	4	2	2	NUM
ejpam-5046	113	5	-	-	PUNCT
ejpam-5046	113	6	forced	force	VERB
ejpam-5046	113	7	by	by	ADP
ejpam-5046	113	8	vertices	vertex	NOUN
ejpam-5046	113	9	v2	v2	PROPN
ejpam-5046	113	10	,	,	PUNCT
ejpam-5046	113	11	v4	v4	NOUN
ejpam-5046	113	12	,	,	PUNCT
ejpam-5046	113	13	.	.	PUNCT
ejpam-5046	113	14	.	.	PUNCT
ejpam-5046	114	1	.	.	PUNCT
ejpam-5046	115	1	,	,	PUNCT
ejpam-5046	115	2	vn−3	vn−3	PROPN
ejpam-5046	115	3	,	,	PUNCT
ejpam-5046	115	4	respectively	respectively	ADV
ejpam-5046	115	5	.	.	PUNCT
ejpam-5046	116	1	if	if	SCONJ
ejpam-5046	116	2	n	n	PRON
ejpam-5046	116	3	is	be	AUX
ejpam-5046	116	4	even	even	ADV
ejpam-5046	116	5	,	,	PUNCT
ejpam-5046	116	6	then	then	ADV
ejpam-5046	116	7	vertices	vertice	VERB
ejpam-5046	116	8	v3	v3	PROPN
ejpam-5046	116	9	,	,	PUNCT
ejpam-5046	116	10	v5	v5	PROPN
ejpam-5046	116	11	,	,	PUNCT
ejpam-5046	116	12	.	.	PUNCT
ejpam-5046	116	13	.	.	PUNCT
ejpam-5046	117	1	.	.	PUNCT
ejpam-5046	118	1	,	,	PUNCT
ejpam-5046	118	2	vn−1	vn−1	PROPN
ejpam-5046	118	3	are	be	AUX
ejpam-5046	118	4	2	2	NUM
ejpam-5046	118	5	-	-	PUNCT
ejpam-5046	118	6	forced	force	VERB
ejpam-5046	118	7	by	by	ADP
ejpam-5046	118	8	vertices	vertex	NOUN
ejpam-5046	118	9	v1	v1	PROPN
ejpam-5046	118	10	,	,	PUNCT
ejpam-5046	118	11	v3	v3	PROPN
ejpam-5046	118	12	,	,	PUNCT
ejpam-5046	118	13	.	.	PUNCT
ejpam-5046	118	14	.	.	PUNCT
ejpam-5046	119	1	.	.	PUNCT
ejpam-5046	120	1	,	,	PUNCT
ejpam-5046	120	2	vn−3	vn−3	PROPN
ejpam-5046	120	3	,	,	PUNCT
ejpam-5046	120	4	respectively	respectively	ADV
ejpam-5046	120	5	,	,	PUNCT
ejpam-5046	120	6	and	and	CCONJ
ejpam-5046	120	7	vertices	vertice	VERB
ejpam-5046	120	8	v4	v4	PROPN
ejpam-5046	120	9	,	,	PUNCT
ejpam-5046	120	10	v6	v6	NOUN
ejpam-5046	120	11	,	,	PUNCT
ejpam-5046	120	12	.	.	PUNCT
ejpam-5046	120	13	.	.	PUNCT
ejpam-5046	121	1	.	.	PUNCT
ejpam-5046	122	1	,	,	PUNCT
ejpam-5046	122	2	vn	vn	PROPN
ejpam-5046	122	3	are	be	AUX
ejpam-5046	122	4	2	2	NUM
ejpam-5046	122	5	-	-	PUNCT
ejpam-5046	122	6	forced	force	VERB
ejpam-5046	122	7	by	by	ADP
ejpam-5046	122	8	vertices	vertex	NOUN
ejpam-5046	122	9	v2	v2	PROPN
ejpam-5046	122	10	,	,	PUNCT
ejpam-5046	122	11	v4	v4	NOUN
ejpam-5046	122	12	,	,	PUNCT
ejpam-5046	122	13	.	.	PUNCT
ejpam-5046	122	14	.	.	PUNCT
ejpam-5046	123	1	.	.	PUNCT
ejpam-5046	124	1	,	,	PUNCT
ejpam-5046	124	2	vn−2	vn−2	PROPN
ejpam-5046	124	3	,	,	PUNCT
ejpam-5046	124	4	respectively	respectively	ADV
ejpam-5046	124	5	.	.	PUNCT
ejpam-5046	125	1	therefore	therefore	ADV
ejpam-5046	125	2	,	,	PUNCT
ejpam-5046	125	3	n	n	PRON
ejpam-5046	125	4	is	be	AUX
ejpam-5046	125	5	a	a	DET
ejpam-5046	125	6	2distance	2distance	NUM
ejpam-5046	125	7	zero	zero	NUM
ejpam-5046	125	8	forcing	force	VERB
ejpam-5046	125	9	set	set	NOUN
ejpam-5046	125	10	of	of	ADP
ejpam-5046	125	11	pn	pn	PROPN
ejpam-5046	125	12	.	.	PUNCT
ejpam-5046	126	1	since	since	SCONJ
ejpam-5046	126	2	any	any	DET
ejpam-5046	126	3	singleton	singleton	NOUN
ejpam-5046	126	4	subset	subset	NOUN
ejpam-5046	126	5	of	of	ADP
ejpam-5046	126	6	v	v	PROPN
ejpam-5046	126	7	(	(	PUNCT
ejpam-5046	126	8	pn	pn	NOUN
ejpam-5046	126	9	)	)	PUNCT
ejpam-5046	126	10	is	be	AUX
ejpam-5046	126	11	not	not	PART
ejpam-5046	126	12	a	a	DET
ejpam-5046	126	13	2	2	NUM
ejpam-5046	126	14	-	-	PUNCT
ejpam-5046	126	15	distance	distance	NOUN
ejpam-5046	126	16	zero	zero	NUM
ejpam-5046	126	17	forcing	force	VERB
ejpam-5046	126	18	set	set	NOUN
ejpam-5046	126	19	of	of	ADP
ejpam-5046	126	20	pn	pn	PROPN
ejpam-5046	126	21	,	,	PUNCT
ejpam-5046	126	22	it	it	PRON
ejpam-5046	126	23	follows	follow	VERB
ejpam-5046	126	24	that	that	SCONJ
ejpam-5046	126	25	n	n	PRON
ejpam-5046	126	26	is	be	AUX
ejpam-5046	126	27	a	a	DET
ejpam-5046	126	28	minimum	minimum	ADJ
ejpam-5046	126	29	2	2	NUM
ejpam-5046	126	30	-	-	PUNCT
ejpam-5046	126	31	distance	distance	NOUN
ejpam-5046	126	32	zero	zero	NUM
ejpam-5046	126	33	forcing	force	VERB
ejpam-5046	126	34	set	set	NOUN
ejpam-5046	126	35	of	of	ADP
ejpam-5046	126	36	pn	pn	PROPN
ejpam-5046	126	37	.	.	PUNCT
ejpam-5046	126	38	consequently	consequently	ADV
ejpam-5046	126	39	,	,	PUNCT
ejpam-5046	126	40	z2(pn	z2(pn	NUM
ejpam-5046	126	41	)	)	PUNCT
ejpam-5046	126	42	=	=	SYM
ejpam-5046	126	43	2	2	NUM
ejpam-5046	126	44	for	for	ADP
ejpam-5046	126	45	all	all	DET
ejpam-5046	126	46	n	n	PRON
ejpam-5046	126	47	≥	≥	NOUN
ejpam-5046	126	48	2	2	NUM
ejpam-5046	126	49	.	.	PUNCT
ejpam-5046	126	50	j.	j.	PROPN
ejpam-5046	126	51	a.	a.	PROPN
ejpam-5046	126	52	hassan	hassan	PROPN
ejpam-5046	126	53	,	,	PUNCT
ejpam-5046	126	54	l.	l.	PROPN
ejpam-5046	126	55	t.	t.	PROPN
ejpam-5046	126	56	udtohan	udtohan	PROPN
ejpam-5046	126	57	,	,	PUNCT
ejpam-5046	126	58	l.	l.	PROPN
ejpam-5046	126	59	s.	s.	PROPN
ejpam-5046	126	60	laja	laja	PROPN
ejpam-5046	126	61	/	/	SYM
ejpam-5046	126	62	eur	eur	PROPN
ejpam-5046	126	63	.	.	PUNCT
ejpam-5046	127	1	j.	j.	PROPN
ejpam-5046	127	2	pure	pure	PROPN
ejpam-5046	127	3	appl	appl	PROPN
ejpam-5046	127	4	.	.	PROPN
ejpam-5046	127	5	math	math	PROPN
ejpam-5046	127	6	,	,	PUNCT
ejpam-5046	127	7	17	17	NUM
ejpam-5046	127	8	(	(	PUNCT
ejpam-5046	127	9	2	2	NUM
ejpam-5046	127	10	)	)	PUNCT
ejpam-5046	127	11	(	(	PUNCT
ejpam-5046	127	12	2024	2024	NUM
ejpam-5046	127	13	)	)	PUNCT
ejpam-5046	127	14	,	,	PUNCT
ejpam-5046	127	15	1283	1283	NUM
ejpam-5046	127	16	-	-	SYM
ejpam-5046	127	17	1293	1293	NUM
ejpam-5046	127	18	1287	1287	NUM
ejpam-5046	127	19	proposition	proposition	NOUN
ejpam-5046	127	20	4	4	NUM
ejpam-5046	127	21	.	.	PUNCT
ejpam-5046	128	1	let	let	VERB
ejpam-5046	128	2	n	n	PRON
ejpam-5046	128	3	be	be	AUX
ejpam-5046	128	4	a	a	DET
ejpam-5046	128	5	positive	positive	ADJ
ejpam-5046	128	6	integer	integer	NOUN
ejpam-5046	128	7	.	.	PUNCT
ejpam-5046	129	1	then	then	ADV
ejpam-5046	129	2	,	,	PUNCT
ejpam-5046	129	3	(	(	PUNCT
ejpam-5046	129	4	i	i	NOUN
ejpam-5046	129	5	)	)	PUNCT
ejpam-5046	129	6	z2(cn	z2(cn	PROPN
ejpam-5046	129	7	)	)	PUNCT
ejpam-5046	129	8	=	=	SYM
ejpam-5046	130	1			NOUN
ejpam-5046	130	2	3	3	NUM
ejpam-5046	130	3	,	,	PUNCT
ejpam-5046	130	4	n	n	NOUN
ejpam-5046	130	5	=	=	SYM
ejpam-5046	130	6	3	3	NUM
ejpam-5046	130	7	2	2	NUM
ejpam-5046	130	8	,	,	PUNCT
ejpam-5046	130	9	n	n	NOUN
ejpam-5046	130	10	=	=	SYM
ejpam-5046	130	11	4	4	NUM
ejpam-5046	130	12	or	or	CCONJ
ejpam-5046	130	13	n	n	PRON
ejpam-5046	130	14	≥	≥	NOUN
ejpam-5046	130	15	5	5	NUM
ejpam-5046	130	16	and	and	CCONJ
ejpam-5046	130	17	odd	odd	ADJ
ejpam-5046	130	18	4	4	NUM
ejpam-5046	130	19	,	,	PUNCT
ejpam-5046	130	20	n	n	PRON
ejpam-5046	130	21	≥	≥	NOUN
ejpam-5046	130	22	6	6	NUM
ejpam-5046	130	23	and	and	CCONJ
ejpam-5046	130	24	even	even	ADV
ejpam-5046	130	25	(	(	PUNCT
ejpam-5046	130	26	ii	ii	NOUN
ejpam-5046	130	27	)	)	PUNCT
ejpam-5046	130	28	z2(sn	z2(sn	PROPN
ejpam-5046	130	29	)	)	PUNCT
ejpam-5046	130	30	=	=	PRON
ejpam-5046	130	31	{	{	PUNCT
ejpam-5046	130	32	2	2	NUM
ejpam-5046	130	33	,	,	PUNCT
ejpam-5046	130	34	n	n	NOUN
ejpam-5046	130	35	=	=	SYM
ejpam-5046	130	36	1	1	NUM
ejpam-5046	130	37	n	n	NOUN
ejpam-5046	130	38	,	,	PUNCT
ejpam-5046	130	39	n	n	CCONJ
ejpam-5046	130	40	≥	≥	NOUN
ejpam-5046	130	41	2	2	NUM
ejpam-5046	130	42	proof	proof	NOUN
ejpam-5046	130	43	.	.	PUNCT
ejpam-5046	131	1	(	(	PUNCT
ejpam-5046	131	2	i	i	NOUN
ejpam-5046	131	3	)	)	PUNCT
ejpam-5046	131	4	by	by	ADP
ejpam-5046	131	5	theorem	theorem	NOUN
ejpam-5046	131	6	1	1	NUM
ejpam-5046	131	7	,	,	PUNCT
ejpam-5046	131	8	z2(c3	z2(c3	NUM
ejpam-5046	131	9	)	)	PUNCT
ejpam-5046	131	10	=	=	SYM
ejpam-5046	131	11	3	3	X
ejpam-5046	131	12	.	.	PUNCT
ejpam-5046	131	13	clearly	clearly	ADV
ejpam-5046	131	14	,	,	PUNCT
ejpam-5046	131	15	z2(c4	z2(c4	NOUN
ejpam-5046	131	16	)	)	PUNCT
ejpam-5046	131	17	=	=	SYM
ejpam-5046	131	18	2	2	X
ejpam-5046	131	19	.	.	X
ejpam-5046	131	20	suppose	suppose	VERB
ejpam-5046	131	21	n	n	PRON
ejpam-5046	131	22	≥	≥	NUM
ejpam-5046	131	23	5	5	NUM
ejpam-5046	131	24	and	and	CCONJ
ejpam-5046	131	25	odd	odd	ADJ
ejpam-5046	131	26	.	.	PUNCT
ejpam-5046	132	1	let	let	VERB
ejpam-5046	132	2	v	v	X
ejpam-5046	132	3	(	(	PUNCT
ejpam-5046	132	4	cn	cn	PROPN
ejpam-5046	132	5	)	)	PUNCT
ejpam-5046	132	6	=	=	SYM
ejpam-5046	132	7	{	{	PUNCT
ejpam-5046	132	8	v1	v1	PROPN
ejpam-5046	132	9	,	,	PUNCT
ejpam-5046	132	10	v2	v2	PROPN
ejpam-5046	132	11	,	,	PUNCT
ejpam-5046	132	12	...	...	PUNCT
ejpam-5046	132	13	,	,	PUNCT
ejpam-5046	132	14	vn	vn	PROPN
ejpam-5046	132	15	}	}	PUNCT
ejpam-5046	132	16	and	and	CCONJ
ejpam-5046	132	17	let	let	VERB
ejpam-5046	132	18	n	n	X
ejpam-5046	132	19	=	=	SYM
ejpam-5046	132	20	{	{	PUNCT
ejpam-5046	132	21	v1	v1	PROPN
ejpam-5046	132	22	,	,	PUNCT
ejpam-5046	132	23	v3	v3	PROPN
ejpam-5046	132	24	}	}	PUNCT
ejpam-5046	132	25	.	.	PUNCT
ejpam-5046	133	1	then	then	ADV
ejpam-5046	133	2	n	n	PRON
ejpam-5046	133	3	is	be	AUX
ejpam-5046	133	4	a	a	DET
ejpam-5046	133	5	minimum	minimum	ADJ
ejpam-5046	133	6	2	2	NUM
ejpam-5046	133	7	-	-	PUNCT
ejpam-5046	133	8	distance	distance	NOUN
ejpam-5046	133	9	zero	zero	NUM
ejpam-5046	133	10	forcing	force	VERB
ejpam-5046	133	11	set	set	NOUN
ejpam-5046	133	12	of	of	ADP
ejpam-5046	133	13	cn	cn	PROPN
ejpam-5046	133	14	.	.	PUNCT
ejpam-5046	134	1	thus	thus	ADV
ejpam-5046	134	2	,	,	PUNCT
ejpam-5046	134	3	z2(cn	z2(cn	PROPN
ejpam-5046	134	4	)	)	PUNCT
ejpam-5046	134	5	=	=	SYM
ejpam-5046	134	6	2	2	NUM
ejpam-5046	134	7	for	for	ADP
ejpam-5046	134	8	all	all	DET
ejpam-5046	134	9	n	n	DET
ejpam-5046	134	10	≥	≥	NOUN
ejpam-5046	134	11	5	5	NUM
ejpam-5046	134	12	and	and	CCONJ
ejpam-5046	134	13	odd	odd	ADJ
ejpam-5046	134	14	.	.	PUNCT
ejpam-5046	135	1	next	next	ADV
ejpam-5046	135	2	,	,	PUNCT
ejpam-5046	135	3	suppose	suppose	VERB
ejpam-5046	135	4	that	that	SCONJ
ejpam-5046	135	5	n	n	PROPN
ejpam-5046	135	6	≥	≥	NOUN
ejpam-5046	135	7	6	6	NUM
ejpam-5046	135	8	and	and	CCONJ
ejpam-5046	135	9	even	even	ADV
ejpam-5046	135	10	.	.	PUNCT
ejpam-5046	136	1	let	let	VERB
ejpam-5046	136	2	n	n	PRON
ejpam-5046	136	3	′	′	VERB
ejpam-5046	137	1	=	=	PUNCT
ejpam-5046	137	2	{	{	PUNCT
ejpam-5046	137	3	v1	v1	NOUN
ejpam-5046	137	4	,	,	PUNCT
ejpam-5046	137	5	v2	v2	PROPN
ejpam-5046	137	6	,	,	PUNCT
ejpam-5046	137	7	v3	v3	PROPN
ejpam-5046	137	8	,	,	PUNCT
ejpam-5046	137	9	v4	v4	PROPN
ejpam-5046	137	10	}	}	PUNCT
ejpam-5046	137	11	.	.	PUNCT
ejpam-5046	138	1	then	then	ADV
ejpam-5046	138	2	n	n	DET
ejpam-5046	138	3	′	′	NOUN
ejpam-5046	138	4	is	be	AUX
ejpam-5046	138	5	a	a	DET
ejpam-5046	138	6	minimum	minimum	ADJ
ejpam-5046	138	7	2	2	NUM
ejpam-5046	138	8	-	-	PUNCT
ejpam-5046	138	9	distance	distance	NOUN
ejpam-5046	138	10	zero	zero	NUM
ejpam-5046	138	11	forcing	force	VERB
ejpam-5046	138	12	set	set	NOUN
ejpam-5046	138	13	cn	cn	PROPN
ejpam-5046	138	14	.	.	PUNCT
ejpam-5046	139	1	thus	thus	ADV
ejpam-5046	139	2	,	,	PUNCT
ejpam-5046	139	3	z2(cn	z2(cn	PROPN
ejpam-5046	139	4	)	)	PUNCT
ejpam-5046	139	5	=	=	SYM
ejpam-5046	139	6	4	4	NUM
ejpam-5046	139	7	for	for	ADP
ejpam-5046	139	8	all	all	DET
ejpam-5046	139	9	n	n	PRON
ejpam-5046	139	10	≥	≥	NOUN
ejpam-5046	139	11	6	6	NUM
ejpam-5046	139	12	and	and	CCONJ
ejpam-5046	139	13	even	even	ADV
ejpam-5046	139	14	.	.	PUNCT
ejpam-5046	140	1	(	(	PUNCT
ejpam-5046	140	2	ii	ii	NOUN
ejpam-5046	140	3	)	)	PUNCT
ejpam-5046	140	4	by	by	ADP
ejpam-5046	140	5	theorem	theorem	ADJ
ejpam-5046	140	6	1	1	NUM
ejpam-5046	140	7	,	,	PUNCT
ejpam-5046	140	8	z2(s1	z2(s1	NOUN
ejpam-5046	140	9	)	)	PUNCT
ejpam-5046	140	10	=	=	SYM
ejpam-5046	140	11	2	2	X
ejpam-5046	140	12	.	.	PUNCT
ejpam-5046	140	13	suppose	suppose	VERB
ejpam-5046	140	14	that	that	SCONJ
ejpam-5046	140	15	n	n	PROPN
ejpam-5046	140	16	≥	≥	NUM
ejpam-5046	140	17	2	2	NUM
ejpam-5046	140	18	.	.	PUNCT
ejpam-5046	141	1	let	let	VERB
ejpam-5046	141	2	v	v	NOUN
ejpam-5046	141	3	(	(	PUNCT
ejpam-5046	141	4	sn	sn	PROPN
ejpam-5046	141	5	)	)	PUNCT
ejpam-5046	141	6	=	=	SYM
ejpam-5046	141	7	{	{	PUNCT
ejpam-5046	141	8	d	d	NOUN
ejpam-5046	141	9	,	,	PUNCT
ejpam-5046	141	10	v1	v1	NOUN
ejpam-5046	141	11	,	,	PUNCT
ejpam-5046	141	12	...	...	PUNCT
ejpam-5046	141	13	,	,	PUNCT
ejpam-5046	141	14	vn	vn	PROPN
ejpam-5046	141	15	}	}	PUNCT
ejpam-5046	141	16	,	,	PUNCT
ejpam-5046	141	17	where	where	SCONJ
ejpam-5046	141	18	d	d	NOUN
ejpam-5046	141	19	is	be	AUX
ejpam-5046	141	20	the	the	DET
ejpam-5046	141	21	dominating	dominating	NOUN
ejpam-5046	141	22	vertex	vertex	NOUN
ejpam-5046	141	23	of	of	ADP
ejpam-5046	141	24	sn	sn	PROPN
ejpam-5046	141	25	.	.	PUNCT
ejpam-5046	142	1	consider	consider	VERB
ejpam-5046	142	2	m	m	VERB
ejpam-5046	142	3	=	=	PUNCT
ejpam-5046	142	4	{	{	PUNCT
ejpam-5046	142	5	d	d	PROPN
ejpam-5046	142	6	,	,	PUNCT
ejpam-5046	142	7	v1	v1	NOUN
ejpam-5046	142	8	,	,	PUNCT
ejpam-5046	142	9	...	...	PUNCT
ejpam-5046	142	10	,	,	PUNCT
ejpam-5046	142	11	vn−1	vn−1	ADJ
ejpam-5046	142	12	}	}	PUNCT
ejpam-5046	142	13	.	.	PUNCT
ejpam-5046	143	1	then	then	ADV
ejpam-5046	143	2	m	m	PROPN
ejpam-5046	143	3	is	be	AUX
ejpam-5046	143	4	a	a	DET
ejpam-5046	143	5	minimum	minimum	ADJ
ejpam-5046	143	6	2	2	NUM
ejpam-5046	143	7	-	-	PUNCT
ejpam-5046	143	8	distance	distance	NOUN
ejpam-5046	143	9	zero	zero	NUM
ejpam-5046	143	10	forcing	force	VERB
ejpam-5046	143	11	set	set	NOUN
ejpam-5046	143	12	of	of	ADP
ejpam-5046	143	13	sn	sn	PROPN
ejpam-5046	143	14	.	.	PUNCT
ejpam-5046	144	1	therefore	therefore	ADV
ejpam-5046	144	2	,	,	PUNCT
ejpam-5046	144	3	z	z	NOUN
ejpam-5046	144	4	2(sn	2(sn	NUM
ejpam-5046	144	5	)	)	PUNCT
ejpam-5046	144	6	=	=	SYM
ejpam-5046	144	7	n	n	PROPN
ejpam-5046	144	8	for	for	ADP
ejpam-5046	144	9	all	all	DET
ejpam-5046	144	10	n	n	PRON
ejpam-5046	144	11	≥	≥	NUM
ejpam-5046	144	12	2	2	NUM
ejpam-5046	144	13	.	.	PUNCT
ejpam-5046	144	14	theorem	theorem	NOUN
ejpam-5046	144	15	2	2	NUM
ejpam-5046	144	16	.	.	PUNCT
ejpam-5046	145	1	let	let	VERB
ejpam-5046	145	2	g	g	PRON
ejpam-5046	145	3	be	be	AUX
ejpam-5046	145	4	a	a	DET
ejpam-5046	145	5	graph	graph	NOUN
ejpam-5046	145	6	.	.	PUNCT
ejpam-5046	146	1	if	if	SCONJ
ejpam-5046	146	2	h	h	NOUN
ejpam-5046	146	3	is	be	AUX
ejpam-5046	146	4	a	a	DET
ejpam-5046	146	5	subgraph	subgraph	NOUN
ejpam-5046	146	6	of	of	ADP
ejpam-5046	146	7	g	g	NOUN
ejpam-5046	146	8	,	,	PUNCT
ejpam-5046	146	9	then	then	ADV
ejpam-5046	146	10	z2(h	z2(h	NUM
ejpam-5046	146	11	)	)	PUNCT
ejpam-5046	146	12	≤	≤	NOUN
ejpam-5046	146	13	z2(g	z2(g	NUM
ejpam-5046	146	14	)	)	PUNCT
ejpam-5046	146	15	is	be	AUX
ejpam-5046	146	16	not	not	PART
ejpam-5046	146	17	true	true	ADJ
ejpam-5046	146	18	in	in	ADP
ejpam-5046	146	19	general	general	ADJ
ejpam-5046	146	20	.	.	PUNCT
ejpam-5046	147	1	proof	proof	NOUN
ejpam-5046	147	2	.	.	PUNCT
ejpam-5046	148	1	consider	consider	VERB
ejpam-5046	148	2	the	the	DET
ejpam-5046	148	3	graph	graph	NOUN
ejpam-5046	148	4	k2	k2	PROPN
ejpam-5046	148	5	+	+	CCONJ
ejpam-5046	148	6	p3	p3	PROPN
ejpam-5046	148	7	below	below	ADV
ejpam-5046	148	8	.	.	PUNCT
ejpam-5046	149	1	a	a	DET
ejpam-5046	149	2	b	b	NOUN
ejpam-5046	149	3	c	c	NOUN
ejpam-5046	149	4	d	d	PROPN
ejpam-5046	149	5	e	e	PROPN
ejpam-5046	149	6	k2	k2	PROPN
ejpam-5046	149	7	+	+	CCONJ
ejpam-5046	149	8	p3	p3	PROPN
ejpam-5046	149	9	:	:	PUNCT
ejpam-5046	149	10	let	let	VERB
ejpam-5046	149	11	s1	s1	PROPN
ejpam-5046	149	12	=	=	PUNCT
ejpam-5046	149	13	{	{	PUNCT
ejpam-5046	149	14	a	a	PRON
ejpam-5046	149	15	,	,	PUNCT
ejpam-5046	149	16	b	b	NOUN
ejpam-5046	149	17	,	,	PUNCT
ejpam-5046	149	18	d	d	NOUN
ejpam-5046	149	19	,	,	PUNCT
ejpam-5046	149	20	e	e	NOUN
ejpam-5046	149	21	}	}	PUNCT
ejpam-5046	149	22	.	.	PUNCT
ejpam-5046	150	1	then	then	ADV
ejpam-5046	150	2	s1	s1	PROPN
ejpam-5046	150	3	is	be	AUX
ejpam-5046	150	4	a	a	DET
ejpam-5046	150	5	minimum	minimum	ADJ
ejpam-5046	150	6	2	2	NUM
ejpam-5046	150	7	-	-	PUNCT
ejpam-5046	150	8	distance	distance	NOUN
ejpam-5046	150	9	zero	zero	NUM
ejpam-5046	150	10	forcing	force	VERB
ejpam-5046	150	11	set	set	NOUN
ejpam-5046	150	12	of	of	ADP
ejpam-5046	150	13	k2+p3	k2+p3	PROPN
ejpam-5046	150	14	.	.	PUNCT
ejpam-5046	151	1	hence	hence	ADV
ejpam-5046	151	2	,	,	PUNCT
ejpam-5046	151	3	z2(k2	z2(k2	X
ejpam-5046	151	4	+	+	CCONJ
ejpam-5046	151	5	p3	p3	NOUN
ejpam-5046	151	6	)	)	PUNCT
ejpam-5046	151	7	=	=	SYM
ejpam-5046	152	1	4	4	X
ejpam-5046	152	2	.	.	PUNCT
ejpam-5046	152	3	now	now	ADV
ejpam-5046	152	4	,	,	PUNCT
ejpam-5046	152	5	consider	consider	VERB
ejpam-5046	152	6	the	the	DET
ejpam-5046	152	7	graph	graph	NOUN
ejpam-5046	152	8	p3	p3	NOUN
ejpam-5046	152	9	+	+	CCONJ
ejpam-5046	152	10	p4	p4	ADJ
ejpam-5046	152	11	below	below	ADV
ejpam-5046	152	12	.	.	PUNCT
ejpam-5046	153	1	u1	u1	PROPN
ejpam-5046	153	2	u2	u2	PROPN
ejpam-5046	153	3	u3	u3	PROPN
ejpam-5046	153	4	u4	u4	PROPN
ejpam-5046	153	5	u5	u5	PROPN
ejpam-5046	153	6	u6	u6	PROPN
ejpam-5046	153	7	u7	u7	PROPN
ejpam-5046	153	8	p3	p3	PROPN
ejpam-5046	153	9	+	+	CCONJ
ejpam-5046	153	10	p4	p4	ADJ
ejpam-5046	153	11	:	:	PUNCT
ejpam-5046	153	12	j.	j.	PROPN
ejpam-5046	153	13	a.	a.	PROPN
ejpam-5046	153	14	hassan	hassan	PROPN
ejpam-5046	153	15	,	,	PUNCT
ejpam-5046	153	16	l.	l.	PROPN
ejpam-5046	153	17	t.	t.	PROPN
ejpam-5046	153	18	udtohan	udtohan	PROPN
ejpam-5046	153	19	,	,	PUNCT
ejpam-5046	153	20	l.	l.	PROPN
ejpam-5046	153	21	s.	s.	PROPN
ejpam-5046	153	22	laja	laja	PROPN
ejpam-5046	153	23	/	/	SYM
ejpam-5046	153	24	eur	eur	PROPN
ejpam-5046	153	25	.	.	PUNCT
ejpam-5046	154	1	j.	j.	PROPN
ejpam-5046	154	2	pure	pure	PROPN
ejpam-5046	154	3	appl	appl	PROPN
ejpam-5046	154	4	.	.	PROPN
ejpam-5046	154	5	math	math	PROPN
ejpam-5046	154	6	,	,	PUNCT
ejpam-5046	154	7	17	17	NUM
ejpam-5046	154	8	(	(	PUNCT
ejpam-5046	154	9	2	2	NUM
ejpam-5046	154	10	)	)	PUNCT
ejpam-5046	154	11	(	(	PUNCT
ejpam-5046	154	12	2024	2024	NUM
ejpam-5046	154	13	)	)	PUNCT
ejpam-5046	154	14	,	,	PUNCT
ejpam-5046	154	15	1283	1283	NUM
ejpam-5046	154	16	-	-	SYM
ejpam-5046	154	17	1293	1293	NUM
ejpam-5046	154	18	1288	1288	NUM
ejpam-5046	154	19	let	let	VERB
ejpam-5046	154	20	s2	s2	VERB
ejpam-5046	154	21	=	=	SYM
ejpam-5046	154	22	{	{	PUNCT
ejpam-5046	154	23	u1	u1	NOUN
ejpam-5046	154	24	,	,	PUNCT
ejpam-5046	154	25	u2	u2	NOUN
ejpam-5046	154	26	,	,	PUNCT
ejpam-5046	154	27	u6	u6	NOUN
ejpam-5046	154	28	}	}	PUNCT
ejpam-5046	154	29	.	.	PUNCT
ejpam-5046	155	1	then	then	ADV
ejpam-5046	155	2	u3	u3	PROPN
ejpam-5046	155	3	,	,	PUNCT
ejpam-5046	155	4	u4	u4	PROPN
ejpam-5046	155	5	,	,	PUNCT
ejpam-5046	155	6	u7	u7	PROPN
ejpam-5046	155	7	and	and	CCONJ
ejpam-5046	155	8	u5	u5	PROPN
ejpam-5046	155	9	are	be	AUX
ejpam-5046	155	10	2	2	NUM
ejpam-5046	155	11	-	-	PUNCT
ejpam-5046	155	12	forced	force	VERB
ejpam-5046	155	13	by	by	ADP
ejpam-5046	155	14	u1	u1	NOUN
ejpam-5046	155	15	,	,	PUNCT
ejpam-5046	155	16	u6	u6	PROPN
ejpam-5046	155	17	,	,	PUNCT
ejpam-5046	155	18	u4	u4	PROPN
ejpam-5046	155	19	and	and	CCONJ
ejpam-5046	155	20	u7	u7	PROPN
ejpam-5046	155	21	,	,	PUNCT
ejpam-5046	155	22	respectively	respectively	ADV
ejpam-5046	155	23	.	.	PUNCT
ejpam-5046	156	1	thus	thus	ADV
ejpam-5046	156	2	,	,	PUNCT
ejpam-5046	156	3	s2	s2	PROPN
ejpam-5046	156	4	is	be	AUX
ejpam-5046	156	5	a	a	DET
ejpam-5046	156	6	2	2	NUM
ejpam-5046	156	7	-	-	PUNCT
ejpam-5046	156	8	distance	distance	NOUN
ejpam-5046	156	9	zero	zero	NUM
ejpam-5046	156	10	forcing	force	VERB
ejpam-5046	156	11	set	set	NOUN
ejpam-5046	156	12	of	of	ADP
ejpam-5046	156	13	p3+p4	p3+p4	PROPN
ejpam-5046	156	14	.	.	PUNCT
ejpam-5046	157	1	it	it	PRON
ejpam-5046	157	2	can	can	AUX
ejpam-5046	157	3	be	be	AUX
ejpam-5046	157	4	verified	verify	VERB
ejpam-5046	157	5	that	that	SCONJ
ejpam-5046	157	6	z2(p3+p4	z2(p3+p4	NOUN
ejpam-5046	157	7	)	)	PUNCT
ejpam-5046	157	8	=	=	SYM
ejpam-5046	158	1	3	3	X
ejpam-5046	158	2	.	.	PUNCT
ejpam-5046	158	3	consequently	consequently	ADV
ejpam-5046	158	4	,	,	PUNCT
ejpam-5046	158	5	the	the	DET
ejpam-5046	158	6	assertion	assertion	NOUN
ejpam-5046	158	7	follows	follow	VERB
ejpam-5046	158	8	.	.	PUNCT
ejpam-5046	159	1	theorem	theorem	NOUN
ejpam-5046	159	2	3	3	X
ejpam-5046	159	3	.	.	PUNCT
ejpam-5046	160	1	let	let	VERB
ejpam-5046	160	2	h	h	PRON
ejpam-5046	160	3	be	be	AUX
ejpam-5046	160	4	a	a	DET
ejpam-5046	160	5	graph	graph	NOUN
ejpam-5046	160	6	.	.	PUNCT
ejpam-5046	161	1	if	if	SCONJ
ejpam-5046	161	2	k	k	PROPN
ejpam-5046	161	3	is	be	AUX
ejpam-5046	161	4	a	a	DET
ejpam-5046	161	5	subgraph	subgraph	NOUN
ejpam-5046	161	6	of	of	ADP
ejpam-5046	161	7	h	h	NOUN
ejpam-5046	161	8	,	,	PUNCT
ejpam-5046	161	9	then	then	ADV
ejpam-5046	161	10	z2(k	z2(k	NOUN
ejpam-5046	161	11	)	)	PUNCT
ejpam-5046	161	12	≥	≥	NOUN
ejpam-5046	161	13	z2(h	z2(h	NUM
ejpam-5046	161	14	)	)	PUNCT
ejpam-5046	161	15	is	be	AUX
ejpam-5046	161	16	not	not	PART
ejpam-5046	161	17	true	true	ADJ
ejpam-5046	161	18	in	in	ADP
ejpam-5046	161	19	general	general	ADJ
ejpam-5046	161	20	.	.	PUNCT
ejpam-5046	162	1	proof	proof	NOUN
ejpam-5046	162	2	.	.	PUNCT
ejpam-5046	163	1	consider	consider	VERB
ejpam-5046	163	2	the	the	DET
ejpam-5046	163	3	graph	graph	NOUN
ejpam-5046	163	4	h	h	NOUN
ejpam-5046	163	5	below	below	ADV
ejpam-5046	163	6	.	.	PUNCT
ejpam-5046	164	1	a	a	DET
ejpam-5046	164	2	b	b	NOUN
ejpam-5046	164	3	c	c	NOUN
ejpam-5046	164	4	d	d	X
ejpam-5046	164	5	e	e	X
ejpam-5046	164	6	f	f	PROPN
ejpam-5046	164	7	gh	gh	PROPN
ejpam-5046	164	8	:	:	PUNCT
ejpam-5046	164	9	let	let	VERB
ejpam-5046	164	10	q1	q1	PROPN
ejpam-5046	164	11	=	=	PUNCT
ejpam-5046	164	12	{	{	PUNCT
ejpam-5046	164	13	a	a	PRON
ejpam-5046	164	14	,	,	PUNCT
ejpam-5046	164	15	b	b	NOUN
ejpam-5046	164	16	,	,	PUNCT
ejpam-5046	164	17	c	c	X
ejpam-5046	164	18	,	,	PUNCT
ejpam-5046	164	19	e	e	NOUN
ejpam-5046	164	20	,	,	PUNCT
ejpam-5046	164	21	f	f	NOUN
ejpam-5046	164	22	}	}	PUNCT
ejpam-5046	164	23	.	.	PUNCT
ejpam-5046	165	1	then	then	ADV
ejpam-5046	165	2	q1	q1	PROPN
ejpam-5046	165	3	is	be	AUX
ejpam-5046	165	4	a	a	DET
ejpam-5046	165	5	minimum	minimum	ADJ
ejpam-5046	165	6	2	2	NUM
ejpam-5046	165	7	-	-	PUNCT
ejpam-5046	165	8	distance	distance	NOUN
ejpam-5046	165	9	zero	zero	NUM
ejpam-5046	165	10	forcing	force	VERB
ejpam-5046	165	11	set	set	NOUN
ejpam-5046	165	12	of	of	ADP
ejpam-5046	165	13	h.	h.	PROPN
ejpam-5046	165	14	thus	thus	ADV
ejpam-5046	165	15	,	,	PUNCT
ejpam-5046	165	16	z2(h	z2(h	NOUN
ejpam-5046	165	17	)	)	PUNCT
ejpam-5046	165	18	=	=	SYM
ejpam-5046	165	19	5	5	X
ejpam-5046	165	20	.	.	PUNCT
ejpam-5046	165	21	now	now	ADV
ejpam-5046	165	22	,	,	PUNCT
ejpam-5046	165	23	consider	consider	VERB
ejpam-5046	165	24	the	the	DET
ejpam-5046	165	25	subgraph	subgraph	NOUN
ejpam-5046	165	26	k	k	PROPN
ejpam-5046	165	27	of	of	ADP
ejpam-5046	165	28	h	h	NOUN
ejpam-5046	165	29	below	below	ADV
ejpam-5046	165	30	.	.	PUNCT
ejpam-5046	166	1	a	a	DET
ejpam-5046	166	2	b	b	NOUN
ejpam-5046	166	3	c	c	NOUN
ejpam-5046	167	1	d	d	NOUN
ejpam-5046	167	2	g	g	PROPN
ejpam-5046	167	3	k	k	PROPN
ejpam-5046	167	4	:	:	PUNCT
ejpam-5046	167	5	let	let	VERB
ejpam-5046	167	6	q2	q2	NOUN
ejpam-5046	167	7	=	=	PUNCT
ejpam-5046	167	8	{	{	PUNCT
ejpam-5046	167	9	a	a	PRON
ejpam-5046	167	10	,	,	PUNCT
ejpam-5046	167	11	b	b	NOUN
ejpam-5046	167	12	,	,	PUNCT
ejpam-5046	167	13	c	c	NOUN
ejpam-5046	167	14	}	}	PUNCT
ejpam-5046	167	15	.	.	PUNCT
ejpam-5046	168	1	then	then	ADV
ejpam-5046	168	2	q2	q2	PROPN
ejpam-5046	168	3	is	be	AUX
ejpam-5046	168	4	a	a	DET
ejpam-5046	168	5	minimum	minimum	ADJ
ejpam-5046	168	6	2	2	NUM
ejpam-5046	168	7	-	-	PUNCT
ejpam-5046	168	8	distance	distance	NOUN
ejpam-5046	168	9	zero	zero	NUM
ejpam-5046	168	10	forcing	force	VERB
ejpam-5046	168	11	set	set	NOUN
ejpam-5046	168	12	of	of	ADP
ejpam-5046	168	13	k.	k.	PROPN
ejpam-5046	168	14	thus	thus	ADV
ejpam-5046	168	15	,	,	PUNCT
ejpam-5046	168	16	z2(k	z2(k	NOUN
ejpam-5046	168	17	)	)	PUNCT
ejpam-5046	168	18	=	=	SYM
ejpam-5046	169	1	3	3	X
ejpam-5046	169	2	.	.	X
ejpam-5046	169	3	therefore	therefore	ADV
ejpam-5046	169	4	,	,	PUNCT
ejpam-5046	169	5	the	the	DET
ejpam-5046	169	6	assertion	assertion	NOUN
ejpam-5046	169	7	follows	follow	VERB
ejpam-5046	169	8	.	.	PUNCT
ejpam-5046	170	1	j.	j.	PROPN
ejpam-5046	170	2	a.	a.	PROPN
ejpam-5046	170	3	hassan	hassan	PROPN
ejpam-5046	170	4	,	,	PUNCT
ejpam-5046	170	5	l.	l.	PROPN
ejpam-5046	170	6	t.	t.	PROPN
ejpam-5046	170	7	udtohan	udtohan	PROPN
ejpam-5046	170	8	,	,	PUNCT
ejpam-5046	170	9	l.	l.	PROPN
ejpam-5046	170	10	s.	s.	PROPN
ejpam-5046	170	11	laja	laja	PROPN
ejpam-5046	170	12	/	/	SYM
ejpam-5046	170	13	eur	eur	PROPN
ejpam-5046	170	14	.	.	PUNCT
ejpam-5046	171	1	j.	j.	PROPN
ejpam-5046	171	2	pure	pure	PROPN
ejpam-5046	171	3	appl	appl	PROPN
ejpam-5046	171	4	.	.	PROPN
ejpam-5046	171	5	math	math	PROPN
ejpam-5046	171	6	,	,	PUNCT
ejpam-5046	171	7	17	17	NUM
ejpam-5046	171	8	(	(	PUNCT
ejpam-5046	171	9	2	2	NUM
ejpam-5046	171	10	)	)	PUNCT
ejpam-5046	171	11	(	(	PUNCT
ejpam-5046	171	12	2024	2024	NUM
ejpam-5046	171	13	)	)	PUNCT
ejpam-5046	171	14	,	,	PUNCT
ejpam-5046	171	15	1283	1283	NUM
ejpam-5046	171	16	-	-	SYM
ejpam-5046	171	17	1293	1293	NUM
ejpam-5046	171	18	1289	1289	NUM
ejpam-5046	171	19	proposition	proposition	NOUN
ejpam-5046	171	20	5	5	NUM
ejpam-5046	171	21	.	.	PUNCT
ejpam-5046	172	1	let	let	VERB
ejpam-5046	172	2	g	g	PRON
ejpam-5046	172	3	be	be	AUX
ejpam-5046	172	4	a	a	DET
ejpam-5046	172	5	graph	graph	NOUN
ejpam-5046	172	6	.	.	PUNCT
ejpam-5046	173	1	then	then	ADV
ejpam-5046	173	2	the	the	DET
ejpam-5046	173	3	2	2	NUM
ejpam-5046	173	4	-	-	PUNCT
ejpam-5046	173	5	distance	distance	NOUN
ejpam-5046	173	6	zero	zero	NUM
ejpam-5046	173	7	forcing	force	VERB
ejpam-5046	173	8	z2(g	z2(g	NUM
ejpam-5046	173	9	)	)	PUNCT
ejpam-5046	173	10	and	and	CCONJ
ejpam-5046	173	11	hop	hop	NOUN
ejpam-5046	173	12	domination	domination	NOUN
ejpam-5046	173	13	parameters	parameter	NOUN
ejpam-5046	173	14	γh(g	γh(g	NOUN
ejpam-5046	173	15	)	)	PUNCT
ejpam-5046	173	16	of	of	ADP
ejpam-5046	173	17	g	g	PROPN
ejpam-5046	173	18	are	be	AUX
ejpam-5046	173	19	incomparable	incomparable	ADJ
ejpam-5046	173	20	.	.	PUNCT
ejpam-5046	174	1	proof	proof	NOUN
ejpam-5046	174	2	.	.	PUNCT
ejpam-5046	175	1	consider	consider	VERB
ejpam-5046	175	2	the	the	DET
ejpam-5046	175	3	graph	graph	NOUN
ejpam-5046	175	4	g	g	NOUN
ejpam-5046	175	5	below	below	ADV
ejpam-5046	175	6	.	.	PUNCT
ejpam-5046	176	1	a1	a1	NOUN
ejpam-5046	176	2	a2	a2	PROPN
ejpam-5046	176	3	a3	a3	PROPN
ejpam-5046	176	4	a4	a4	PROPN
ejpam-5046	176	5	a5	a5	PROPN
ejpam-5046	176	6	a6	a6	NOUN
ejpam-5046	176	7	a7	a7	PROPN
ejpam-5046	176	8	a8	a8	PROPN
ejpam-5046	176	9	g	g	PROPN
ejpam-5046	176	10	:	:	PUNCT
ejpam-5046	176	11	let	let	VERB
ejpam-5046	176	12	q	q	NOUN
ejpam-5046	176	13	=	=	PUNCT
ejpam-5046	176	14	{	{	PUNCT
ejpam-5046	176	15	a5	a5	NOUN
ejpam-5046	176	16	,	,	PUNCT
ejpam-5046	176	17	a6	a6	NOUN
ejpam-5046	176	18	}	}	PUNCT
ejpam-5046	176	19	.	.	PUNCT
ejpam-5046	177	1	then	then	ADV
ejpam-5046	177	2	q	q	X
ejpam-5046	177	3	is	be	AUX
ejpam-5046	177	4	a	a	DET
ejpam-5046	177	5	hop	hop	NOUN
ejpam-5046	177	6	dominating	dominating	NOUN
ejpam-5046	177	7	set	set	NOUN
ejpam-5046	177	8	of	of	ADP
ejpam-5046	177	9	g	g	PROPN
ejpam-5046	177	10	since	since	SCONJ
ejpam-5046	177	11	n2	n2	ADJ
ejpam-5046	177	12	g[q	g[q	NOUN
ejpam-5046	177	13	]	]	X
ejpam-5046	177	14	=	=	SYM
ejpam-5046	177	15	v	v	NOUN
ejpam-5046	177	16	(	(	PUNCT
ejpam-5046	177	17	g	g	NOUN
ejpam-5046	177	18	)	)	PUNCT
ejpam-5046	177	19	.	.	PUNCT
ejpam-5046	178	1	since	since	SCONJ
ejpam-5046	178	2	n2	n2	PROPN
ejpam-5046	178	3	g[ai	g[ai	PROPN
ejpam-5046	178	4	]	]	PUNCT
ejpam-5046	178	5	̸=	̸=	PROPN
ejpam-5046	178	6	v	v	NOUN
ejpam-5046	178	7	(	(	PUNCT
ejpam-5046	178	8	g	g	NOUN
ejpam-5046	178	9	)	)	PUNCT
ejpam-5046	178	10	for	for	ADP
ejpam-5046	178	11	every	every	DET
ejpam-5046	178	12	i	i	PROPN
ejpam-5046	178	13	∈	∈	PROPN
ejpam-5046	178	14	{	{	PUNCT
ejpam-5046	178	15	1	1	NUM
ejpam-5046	178	16	,	,	PUNCT
ejpam-5046	178	17	2	2	NUM
ejpam-5046	178	18	,	,	PUNCT
ejpam-5046	178	19	·	·	PUNCT
ejpam-5046	178	20	·	·	PUNCT
ejpam-5046	178	21	·	·	PUNCT
ejpam-5046	178	22	,	,	PUNCT
ejpam-5046	178	23	8	8	NUM
ejpam-5046	178	24	}	}	PUNCT
ejpam-5046	178	25	,	,	PUNCT
ejpam-5046	178	26	it	it	PRON
ejpam-5046	178	27	follows	follow	VERB
ejpam-5046	178	28	that	that	SCONJ
ejpam-5046	178	29	q	q	NOUN
ejpam-5046	178	30	is	be	AUX
ejpam-5046	178	31	a	a	DET
ejpam-5046	178	32	minimum	minimum	ADJ
ejpam-5046	178	33	hop	hop	NOUN
ejpam-5046	178	34	dominating	dominating	NOUN
ejpam-5046	178	35	set	set	NOUN
ejpam-5046	178	36	of	of	ADP
ejpam-5046	178	37	g.	g.	PROPN
ejpam-5046	178	38	thus	thus	ADV
ejpam-5046	178	39	,	,	PUNCT
ejpam-5046	178	40	γh(g	γh(g	NOUN
ejpam-5046	178	41	)	)	PUNCT
ejpam-5046	178	42	=	=	SYM
ejpam-5046	179	1	2	2	X
ejpam-5046	179	2	.	.	PUNCT
ejpam-5046	179	3	now	now	ADV
ejpam-5046	179	4	,	,	PUNCT
ejpam-5046	179	5	let	let	VERB
ejpam-5046	179	6	s	s	PRON
ejpam-5046	179	7	=	=	NOUN
ejpam-5046	179	8	{	{	PUNCT
ejpam-5046	179	9	a1	a1	PROPN
ejpam-5046	179	10	,	,	PUNCT
ejpam-5046	179	11	a2	a2	PROPN
ejpam-5046	179	12	,	,	PUNCT
ejpam-5046	179	13	a3	a3	NOUN
ejpam-5046	179	14	,	,	PUNCT
ejpam-5046	179	15	a6	a6	NOUN
ejpam-5046	179	16	,	,	PUNCT
ejpam-5046	179	17	a8	a8	PROPN
ejpam-5046	179	18	}	}	PUNCT
ejpam-5046	179	19	.	.	PUNCT
ejpam-5046	180	1	then	then	ADV
ejpam-5046	180	2	s	s	VERB
ejpam-5046	180	3	is	be	AUX
ejpam-5046	180	4	a	a	DET
ejpam-5046	180	5	minimum	minimum	ADJ
ejpam-5046	180	6	2	2	NUM
ejpam-5046	180	7	-	-	PUNCT
ejpam-5046	180	8	distance	distance	NOUN
ejpam-5046	180	9	zero	zero	NUM
ejpam-5046	180	10	forcing	force	VERB
ejpam-5046	180	11	set	set	NOUN
ejpam-5046	180	12	of	of	ADP
ejpam-5046	180	13	g.	g.	PROPN
ejpam-5046	180	14	therefore	therefore	ADV
ejpam-5046	180	15	,	,	PUNCT
ejpam-5046	180	16	z2(g	z2(g	NUM
ejpam-5046	180	17	)	)	PUNCT
ejpam-5046	180	18	=	=	SYM
ejpam-5046	180	19	5	5	X
ejpam-5046	180	20	.	.	PUNCT
ejpam-5046	180	21	on	on	ADP
ejpam-5046	180	22	the	the	DET
ejpam-5046	180	23	other	other	ADJ
ejpam-5046	180	24	hand	hand	NOUN
ejpam-5046	180	25	,	,	PUNCT
ejpam-5046	180	26	consider	consider	VERB
ejpam-5046	180	27	the	the	DET
ejpam-5046	180	28	graph	graph	NOUN
ejpam-5046	180	29	h	h	NOUN
ejpam-5046	180	30	below	below	ADV
ejpam-5046	180	31	.	.	PUNCT
ejpam-5046	181	1	h	h	NOUN
ejpam-5046	181	2	:	:	PUNCT
ejpam-5046	181	3	a1	a1	NOUN
ejpam-5046	181	4	a2	a2	PROPN
ejpam-5046	181	5	a3	a3	PROPN
ejpam-5046	181	6	a4	a4	PROPN
ejpam-5046	181	7	a5	a5	PROPN
ejpam-5046	181	8	a6	a6	NOUN
ejpam-5046	181	9	a7	a7	PROPN
ejpam-5046	181	10	a8	a8	PROPN
ejpam-5046	181	11	a9	a9	PROPN
ejpam-5046	181	12	let	let	VERB
ejpam-5046	181	13	d	d	NOUN
ejpam-5046	181	14	=	=	PUNCT
ejpam-5046	181	15	{	{	PUNCT
ejpam-5046	181	16	a1	a1	PROPN
ejpam-5046	181	17	,	,	PUNCT
ejpam-5046	181	18	a2	a2	PROPN
ejpam-5046	181	19	,	,	PUNCT
ejpam-5046	181	20	a8	a8	PROPN
ejpam-5046	181	21	}	}	PUNCT
ejpam-5046	181	22	.	.	PUNCT
ejpam-5046	182	1	then	then	ADV
ejpam-5046	182	2	vertices	vertice	VERB
ejpam-5046	182	3	a3	a3	NOUN
ejpam-5046	182	4	,	,	PUNCT
ejpam-5046	182	5	a5	a5	PROPN
ejpam-5046	182	6	and	and	CCONJ
ejpam-5046	182	7	a7	a7	PROPN
ejpam-5046	182	8	are	be	AUX
ejpam-5046	182	9	2	2	NUM
ejpam-5046	182	10	-	-	PUNCT
ejpam-5046	182	11	forced	force	VERB
ejpam-5046	182	12	by	by	ADP
ejpam-5046	182	13	the	the	DET
ejpam-5046	182	14	vertices	vertex	NOUN
ejpam-5046	182	15	a1	a1	NOUN
ejpam-5046	182	16	,	,	PUNCT
ejpam-5046	182	17	a3	a3	NOUN
ejpam-5046	182	18	and	and	CCONJ
ejpam-5046	182	19	a5	a5	NOUN
ejpam-5046	182	20	,	,	PUNCT
ejpam-5046	182	21	respectively	respectively	ADV
ejpam-5046	182	22	,	,	PUNCT
ejpam-5046	182	23	and	and	CCONJ
ejpam-5046	182	24	vertices	vertice	VERB
ejpam-5046	182	25	a4	a4	NUM
ejpam-5046	182	26	,	,	PUNCT
ejpam-5046	182	27	a6	a6	NOUN
ejpam-5046	182	28	and	and	CCONJ
ejpam-5046	182	29	a9	a9	NOUN
ejpam-5046	182	30	are	be	AUX
ejpam-5046	182	31	2	2	NUM
ejpam-5046	182	32	-	-	PUNCT
ejpam-5046	182	33	forced	force	VERB
ejpam-5046	182	34	by	by	ADP
ejpam-5046	182	35	the	the	DET
ejpam-5046	182	36	vertices	vertex	NOUN
ejpam-5046	182	37	a2	a2	PROPN
ejpam-5046	182	38	,	,	PUNCT
ejpam-5046	182	39	a4	a4	NOUN
ejpam-5046	182	40	and	and	CCONJ
ejpam-5046	182	41	a6	a6	NOUN
ejpam-5046	182	42	,	,	PUNCT
ejpam-5046	182	43	respectively	respectively	ADV
ejpam-5046	182	44	.	.	PUNCT
ejpam-5046	183	1	this	this	PRON
ejpam-5046	183	2	follows	follow	VERB
ejpam-5046	183	3	that	that	SCONJ
ejpam-5046	183	4	d	d	NOUN
ejpam-5046	183	5	is	be	AUX
ejpam-5046	183	6	a	a	DET
ejpam-5046	183	7	2	2	NUM
ejpam-5046	183	8	-	-	PUNCT
ejpam-5046	183	9	distance	distance	NOUN
ejpam-5046	183	10	zero	zero	NUM
ejpam-5046	183	11	forcing	force	VERB
ejpam-5046	183	12	set	set	NOUN
ejpam-5046	183	13	of	of	ADP
ejpam-5046	183	14	h.	h.	PROPN
ejpam-5046	183	15	moreover	moreover	ADV
ejpam-5046	183	16	,	,	PUNCT
ejpam-5046	183	17	z2(h	z2(h	NOUN
ejpam-5046	183	18	)	)	PUNCT
ejpam-5046	183	19	=	=	SYM
ejpam-5046	184	1	3	3	X
ejpam-5046	184	2	.	.	PUNCT
ejpam-5046	185	1	next	next	ADV
ejpam-5046	185	2	,	,	PUNCT
ejpam-5046	185	3	let	let	VERB
ejpam-5046	185	4	d′	d′	PRON
ejpam-5046	185	5	=	=	SYM
ejpam-5046	185	6	{	{	PUNCT
ejpam-5046	185	7	a3	a3	NOUN
ejpam-5046	185	8	,	,	PUNCT
ejpam-5046	185	9	a4	a4	PROPN
ejpam-5046	185	10	,	,	PUNCT
ejpam-5046	185	11	a5	a5	NOUN
ejpam-5046	185	12	,	,	PUNCT
ejpam-5046	185	13	a6	a6	NOUN
ejpam-5046	185	14	}	}	PUNCT
ejpam-5046	185	15	.	.	PUNCT
ejpam-5046	186	1	then	then	ADV
ejpam-5046	186	2	d′	d′	PRON
ejpam-5046	186	3	is	be	AUX
ejpam-5046	186	4	a	a	DET
ejpam-5046	186	5	minimum	minimum	ADJ
ejpam-5046	186	6	hop	hop	NOUN
ejpam-5046	186	7	dominating	dominating	NOUN
ejpam-5046	186	8	set	set	NOUN
ejpam-5046	186	9	of	of	ADP
ejpam-5046	186	10	h.	h.	PROPN
ejpam-5046	186	11	consequently	consequently	ADV
ejpam-5046	186	12	,	,	PUNCT
ejpam-5046	186	13	γh(h	γh(h	PUNCT
ejpam-5046	186	14	)	)	PUNCT
ejpam-5046	186	15	=	=	SYM
ejpam-5046	186	16	4	4	X
ejpam-5046	186	17	.	.	PUNCT
ejpam-5046	186	18	theorem	theorem	NOUN
ejpam-5046	186	19	4	4	NUM
ejpam-5046	186	20	.	.	PUNCT
ejpam-5046	187	1	let	let	VERB
ejpam-5046	187	2	g	g	PRON
ejpam-5046	187	3	be	be	AUX
ejpam-5046	187	4	a	a	DET
ejpam-5046	187	5	graph	graph	NOUN
ejpam-5046	187	6	.	.	PUNCT
ejpam-5046	188	1	then	then	ADV
ejpam-5046	188	2	z2(g	z2(g	NUM
ejpam-5046	188	3	)	)	PUNCT
ejpam-5046	188	4	=	=	NOUN
ejpam-5046	189	1	γh(g	γh(g	NOUN
ejpam-5046	189	2	)	)	PUNCT
ejpam-5046	190	1	=	=	SYM
ejpam-5046	190	2	|v	|v	PROPN
ejpam-5046	190	3	(	(	PUNCT
ejpam-5046	190	4	g)|	g)|	VERB
ejpam-5046	190	5	if	if	SCONJ
ejpam-5046	190	6	and	and	CCONJ
ejpam-5046	190	7	only	only	ADV
ejpam-5046	190	8	if	if	SCONJ
ejpam-5046	190	9	every	every	DET
ejpam-5046	190	10	component	component	NOUN
ejpam-5046	190	11	of	of	ADP
ejpam-5046	190	12	g	g	PROPN
ejpam-5046	190	13	is	be	AUX
ejpam-5046	190	14	complete	complete	ADJ
ejpam-5046	190	15	.	.	PUNCT
ejpam-5046	191	1	proof	proof	NOUN
ejpam-5046	191	2	.	.	PUNCT
ejpam-5046	192	1	suppose	suppose	VERB
ejpam-5046	192	2	that	that	SCONJ
ejpam-5046	192	3	z2(g	z2(g	X
ejpam-5046	192	4	)	)	PUNCT
ejpam-5046	192	5	=	=	SYM
ejpam-5046	192	6	|v	|v	X
ejpam-5046	192	7	(	(	PUNCT
ejpam-5046	192	8	g)|	g)|	NOUN
ejpam-5046	192	9	=	=	NOUN
ejpam-5046	192	10	γh(g	γh(g	NOUN
ejpam-5046	192	11	)	)	PUNCT
ejpam-5046	192	12	.	.	PUNCT
ejpam-5046	193	1	then	then	ADV
ejpam-5046	193	2	v	v	X
ejpam-5046	193	3	(	(	PUNCT
ejpam-5046	193	4	g	g	NOUN
ejpam-5046	193	5	)	)	PUNCT
ejpam-5046	193	6	is	be	AUX
ejpam-5046	193	7	both	both	CCONJ
ejpam-5046	193	8	the	the	DET
ejpam-5046	193	9	minimum	minimum	ADJ
ejpam-5046	193	10	2distance	2distance	NUM
ejpam-5046	193	11	zero	zero	NUM
ejpam-5046	193	12	forcing	forcing	NOUN
ejpam-5046	193	13	and	and	CCONJ
ejpam-5046	193	14	minimum	minimum	NOUN
ejpam-5046	193	15	hop	hop	NOUN
ejpam-5046	193	16	dominating	dominating	NOUN
ejpam-5046	193	17	set	set	NOUN
ejpam-5046	193	18	of	of	ADP
ejpam-5046	193	19	g.	g.	PROPN
ejpam-5046	193	20	suppose	suppose	VERB
ejpam-5046	193	21	there	there	PRON
ejpam-5046	193	22	is	be	VERB
ejpam-5046	193	23	a	a	DET
ejpam-5046	193	24	component	component	NOUN
ejpam-5046	193	25	of	of	ADP
ejpam-5046	193	26	g	g	NOUN
ejpam-5046	193	27	which	which	PRON
ejpam-5046	193	28	is	be	AUX
ejpam-5046	193	29	non	non	ADJ
ejpam-5046	193	30	-	-	ADJ
ejpam-5046	193	31	complete	complete	ADJ
ejpam-5046	193	32	.	.	PUNCT
ejpam-5046	194	1	then	then	ADV
ejpam-5046	194	2	there	there	PRON
ejpam-5046	194	3	exist	exist	VERB
ejpam-5046	194	4	a	a	DET
ejpam-5046	194	5	,	,	PUNCT
ejpam-5046	194	6	b	b	PROPN
ejpam-5046	194	7	∈	∈	PROPN
ejpam-5046	194	8	v	v	NOUN
ejpam-5046	194	9	(	(	PUNCT
ejpam-5046	194	10	q	q	NOUN
ejpam-5046	194	11	)	)	PUNCT
ejpam-5046	194	12	such	such	ADJ
ejpam-5046	194	13	that	that	SCONJ
ejpam-5046	194	14	dg(a	dg(a	PROPN
ejpam-5046	194	15	,	,	PUNCT
ejpam-5046	194	16	b	b	X
ejpam-5046	194	17	)	)	PUNCT
ejpam-5046	194	18	=	=	SYM
ejpam-5046	194	19	2	2	X
ejpam-5046	194	20	.	.	X
ejpam-5046	194	21	let	let	VERB
ejpam-5046	194	22	s	s	NOUN
ejpam-5046	194	23	=	=	X
ejpam-5046	194	24	v	v	ADJ
ejpam-5046	194	25	(	(	PUNCT
ejpam-5046	194	26	g	g	NOUN
ejpam-5046	194	27	)	)	PUNCT
ejpam-5046	194	28	\	\	NOUN
ejpam-5046	194	29	{	{	PUNCT
ejpam-5046	194	30	a	a	NOUN
ejpam-5046	194	31	}	}	PUNCT
ejpam-5046	194	32	.	.	PUNCT
ejpam-5046	195	1	then	then	ADV
ejpam-5046	195	2	s	s	VERB
ejpam-5046	195	3	is	be	AUX
ejpam-5046	195	4	both	both	PRON
ejpam-5046	195	5	a	a	DET
ejpam-5046	195	6	2	2	NUM
ejpam-5046	195	7	-	-	PUNCT
ejpam-5046	195	8	distance	distance	NOUN
ejpam-5046	195	9	zero	zero	NUM
ejpam-5046	195	10	forcing	forcing	NOUN
ejpam-5046	195	11	and	and	CCONJ
ejpam-5046	195	12	a	a	DET
ejpam-5046	195	13	hop	hop	NOUN
ejpam-5046	195	14	dominating	dominating	NOUN
ejpam-5046	195	15	set	set	NOUN
ejpam-5046	195	16	of	of	ADP
ejpam-5046	195	17	g.	g.	PROPN
ejpam-5046	195	18	a	a	DET
ejpam-5046	195	19	contradiction	contradiction	NOUN
ejpam-5046	195	20	.	.	PUNCT
ejpam-5046	196	1	therefore	therefore	ADV
ejpam-5046	196	2	,	,	PUNCT
ejpam-5046	196	3	every	every	DET
ejpam-5046	196	4	component	component	NOUN
ejpam-5046	196	5	of	of	ADP
ejpam-5046	196	6	g	g	PROPN
ejpam-5046	196	7	is	be	AUX
ejpam-5046	196	8	complete	complete	ADJ
ejpam-5046	196	9	.	.	PUNCT
ejpam-5046	197	1	j.	j.	PROPN
ejpam-5046	197	2	a.	a.	PROPN
ejpam-5046	197	3	hassan	hassan	PROPN
ejpam-5046	197	4	,	,	PUNCT
ejpam-5046	197	5	l.	l.	PROPN
ejpam-5046	197	6	t.	t.	PROPN
ejpam-5046	197	7	udtohan	udtohan	PROPN
ejpam-5046	197	8	,	,	PUNCT
ejpam-5046	197	9	l.	l.	PROPN
ejpam-5046	197	10	s.	s.	PROPN
ejpam-5046	197	11	laja	laja	PROPN
ejpam-5046	197	12	/	/	SYM
ejpam-5046	197	13	eur	eur	PROPN
ejpam-5046	197	14	.	.	PUNCT
ejpam-5046	198	1	j.	j.	PROPN
ejpam-5046	198	2	pure	pure	PROPN
ejpam-5046	198	3	appl	appl	PROPN
ejpam-5046	198	4	.	.	PROPN
ejpam-5046	198	5	math	math	PROPN
ejpam-5046	198	6	,	,	PUNCT
ejpam-5046	198	7	17	17	NUM
ejpam-5046	198	8	(	(	PUNCT
ejpam-5046	198	9	2	2	NUM
ejpam-5046	198	10	)	)	PUNCT
ejpam-5046	198	11	(	(	PUNCT
ejpam-5046	198	12	2024	2024	NUM
ejpam-5046	198	13	)	)	PUNCT
ejpam-5046	198	14	,	,	PUNCT
ejpam-5046	198	15	1283	1283	NUM
ejpam-5046	198	16	-	-	SYM
ejpam-5046	198	17	1293	1293	NUM
ejpam-5046	198	18	1290	1290	NUM
ejpam-5046	198	19	conversely	conversely	ADV
ejpam-5046	198	20	,	,	PUNCT
ejpam-5046	198	21	suppose	suppose	VERB
ejpam-5046	198	22	that	that	SCONJ
ejpam-5046	198	23	every	every	DET
ejpam-5046	198	24	component	component	NOUN
ejpam-5046	198	25	of	of	ADP
ejpam-5046	198	26	g	g	PROPN
ejpam-5046	198	27	is	be	AUX
ejpam-5046	198	28	complete	complete	ADJ
ejpam-5046	198	29	.	.	PUNCT
ejpam-5046	199	1	then	then	ADV
ejpam-5046	199	2	by	by	ADP
ejpam-5046	199	3	theorem	theorem	NOUN
ejpam-5046	199	4	1	1	NUM
ejpam-5046	199	5	,	,	PUNCT
ejpam-5046	199	6	z2(g	z2(g	NUM
ejpam-5046	199	7	)	)	PUNCT
ejpam-5046	199	8	=	=	SYM
ejpam-5046	199	9	|v	|v	PROPN
ejpam-5046	199	10	(	(	PUNCT
ejpam-5046	199	11	g)|	g)|	NOUN
ejpam-5046	199	12	.	.	PUNCT
ejpam-5046	200	1	moreover	moreover	ADV
ejpam-5046	200	2	,	,	PUNCT
ejpam-5046	200	3	γh(g	γh(g	NOUN
ejpam-5046	200	4	)	)	PUNCT
ejpam-5046	200	5	=	=	SYM
ejpam-5046	200	6	|v	|v	PROPN
ejpam-5046	200	7	(	(	PUNCT
ejpam-5046	200	8	g)|	g)|	NOUN
ejpam-5046	200	9	.	.	PUNCT
ejpam-5046	201	1	consequently	consequently	ADV
ejpam-5046	201	2	,	,	PUNCT
ejpam-5046	201	3	z2(g	z2(g	NUM
ejpam-5046	201	4	)	)	PUNCT
ejpam-5046	201	5	=	=	NOUN
ejpam-5046	201	6	γh(g	γh(g	NOUN
ejpam-5046	201	7	)	)	PUNCT
ejpam-5046	202	1	=	=	SYM
ejpam-5046	202	2	|v	|v	PROPN
ejpam-5046	202	3	(	(	PUNCT
ejpam-5046	202	4	g)|	g)|	NOUN
ejpam-5046	202	5	.	.	PUNCT
ejpam-5046	203	1	proposition	proposition	NOUN
ejpam-5046	203	2	6	6	NUM
ejpam-5046	203	3	.	.	PUNCT
ejpam-5046	204	1	let	let	VERB
ejpam-5046	204	2	g	g	PRON
ejpam-5046	204	3	be	be	AUX
ejpam-5046	204	4	a	a	DET
ejpam-5046	204	5	graph	graph	NOUN
ejpam-5046	204	6	.	.	PUNCT
ejpam-5046	205	1	then	then	ADV
ejpam-5046	205	2	zero	zero	NUM
ejpam-5046	205	3	forcing	force	VERB
ejpam-5046	205	4	z(g	z(g	NOUN
ejpam-5046	205	5	)	)	PUNCT
ejpam-5046	205	6	and	and	CCONJ
ejpam-5046	205	7	2	2	NUM
ejpam-5046	205	8	-	-	PUNCT
ejpam-5046	205	9	distance	distance	NOUN
ejpam-5046	205	10	zero	zero	NUM
ejpam-5046	205	11	forcing	force	VERB
ejpam-5046	205	12	z2(g	z2(g	NUM
ejpam-5046	205	13	)	)	PUNCT
ejpam-5046	205	14	parameter	parameter	NOUN
ejpam-5046	205	15	of	of	ADP
ejpam-5046	205	16	g	g	PROPN
ejpam-5046	205	17	are	be	AUX
ejpam-5046	205	18	incomparable	incomparable	ADJ
ejpam-5046	205	19	.	.	PUNCT
ejpam-5046	206	1	proof	proof	NOUN
ejpam-5046	206	2	.	.	PUNCT
ejpam-5046	207	1	consider	consider	VERB
ejpam-5046	207	2	the	the	DET
ejpam-5046	207	3	graph	graph	NOUN
ejpam-5046	207	4	p4	p4	ADJ
ejpam-5046	207	5	+	+	CCONJ
ejpam-5046	207	6	p4	p4	ADJ
ejpam-5046	207	7	below	below	ADV
ejpam-5046	207	8	.	.	PUNCT
ejpam-5046	208	1	a	a	DET
ejpam-5046	208	2	b	b	NOUN
ejpam-5046	208	3	c	c	NOUN
ejpam-5046	208	4	d	d	X
ejpam-5046	208	5	e	e	X
ejpam-5046	208	6	f	f	PROPN
ejpam-5046	208	7	g	g	PROPN
ejpam-5046	208	8	h	h	PROPN
ejpam-5046	208	9	p4	p4	ADJ
ejpam-5046	208	10	+	+	CCONJ
ejpam-5046	208	11	p4	p4	ADJ
ejpam-5046	208	12	:	:	PUNCT
ejpam-5046	208	13	let	let	VERB
ejpam-5046	208	14	s1	s1	PROPN
ejpam-5046	208	15	=	=	PUNCT
ejpam-5046	208	16	{	{	PUNCT
ejpam-5046	208	17	b	b	PROPN
ejpam-5046	208	18	,	,	PUNCT
ejpam-5046	208	19	f	f	NOUN
ejpam-5046	208	20	}	}	PUNCT
ejpam-5046	208	21	and	and	CCONJ
ejpam-5046	208	22	s2	s2	VERB
ejpam-5046	208	23	=	=	PUNCT
ejpam-5046	208	24	{	{	PUNCT
ejpam-5046	208	25	a	a	PRON
ejpam-5046	208	26	,	,	PUNCT
ejpam-5046	208	27	b	b	NOUN
ejpam-5046	208	28	,	,	PUNCT
ejpam-5046	208	29	c	c	NOUN
ejpam-5046	208	30	,	,	PUNCT
ejpam-5046	208	31	d	d	NOUN
ejpam-5046	208	32	,	,	PUNCT
ejpam-5046	208	33	e	e	NOUN
ejpam-5046	208	34	}	}	PUNCT
ejpam-5046	208	35	.	.	PUNCT
ejpam-5046	209	1	then	then	ADV
ejpam-5046	209	2	s1	s1	PROPN
ejpam-5046	209	3	and	and	CCONJ
ejpam-5046	209	4	s2	s2	PROPN
ejpam-5046	209	5	are	be	AUX
ejpam-5046	209	6	minimum	minimum	ADJ
ejpam-5046	209	7	2	2	NUM
ejpam-5046	209	8	-	-	PUNCT
ejpam-5046	209	9	distance	distance	NOUN
ejpam-5046	209	10	zero	zero	NUM
ejpam-5046	209	11	forcing	forcing	NOUN
ejpam-5046	209	12	and	and	CCONJ
ejpam-5046	209	13	zero	zero	NUM
ejpam-5046	209	14	forcing	force	VERB
ejpam-5046	209	15	sets	set	NOUN
ejpam-5046	209	16	of	of	ADP
ejpam-5046	209	17	p4	p4	ADJ
ejpam-5046	209	18	+	+	CCONJ
ejpam-5046	209	19	p4	p4	ADJ
ejpam-5046	209	20	,	,	PUNCT
ejpam-5046	209	21	respectively	respectively	ADV
ejpam-5046	209	22	.	.	PUNCT
ejpam-5046	210	1	thus	thus	ADV
ejpam-5046	210	2	,	,	PUNCT
ejpam-5046	210	3	z	z	NOUN
ejpam-5046	210	4	2(p4	2(p4	NUM
ejpam-5046	210	5	+	+	CCONJ
ejpam-5046	210	6	p4	p4	ADJ
ejpam-5046	210	7	)	)	PUNCT
ejpam-5046	210	8	=	=	SYM
ejpam-5046	210	9	2	2	NUM
ejpam-5046	210	10	and	and	CCONJ
ejpam-5046	210	11	z(p4	z(p4	NOUN
ejpam-5046	210	12	+	+	CCONJ
ejpam-5046	210	13	p4	p4	ADJ
ejpam-5046	210	14	)	)	PUNCT
ejpam-5046	210	15	=	=	SYM
ejpam-5046	211	1	5	5	X
ejpam-5046	211	2	.	.	PUNCT
ejpam-5046	212	1	next	next	ADV
ejpam-5046	212	2	,	,	PUNCT
ejpam-5046	212	3	consider	consider	VERB
ejpam-5046	212	4	the	the	DET
ejpam-5046	212	5	graph	graph	NOUN
ejpam-5046	212	6	g	g	NOUN
ejpam-5046	212	7	below	below	ADV
ejpam-5046	212	8	.	.	PUNCT
ejpam-5046	213	1	u1	u1	PROPN
ejpam-5046	213	2	u2	u2	PROPN
ejpam-5046	213	3	u3	u3	PROPN
ejpam-5046	213	4	u4	u4	PROPN
ejpam-5046	213	5	u5	u5	PROPN
ejpam-5046	213	6	u6	u6	PROPN
ejpam-5046	213	7	u7	u7	PROPN
ejpam-5046	213	8	u8	u8	PROPN
ejpam-5046	213	9	u9	u9	PROPN
ejpam-5046	213	10	u10	u10	PROPN
ejpam-5046	213	11	u11	u11	PROPN
ejpam-5046	213	12	u12	u12	PROPN
ejpam-5046	213	13	u13	u13	PROPN
ejpam-5046	213	14	g	g	NOUN
ejpam-5046	213	15	:	:	PUNCT
ejpam-5046	213	16	let	let	VERB
ejpam-5046	213	17	d1	d1	PROPN
ejpam-5046	213	18	=	=	SYM
ejpam-5046	213	19	{	{	PUNCT
ejpam-5046	213	20	u1	u1	PROPN
ejpam-5046	213	21	,	,	PUNCT
ejpam-5046	213	22	u11	u11	PROPN
ejpam-5046	213	23	,	,	PUNCT
ejpam-5046	213	24	u12	u12	PROPN
ejpam-5046	213	25	,	,	PUNCT
ejpam-5046	213	26	u13	u13	NOUN
ejpam-5046	213	27	}	}	PUNCT
ejpam-5046	213	28	and	and	CCONJ
ejpam-5046	213	29	d2	d2	PROPN
ejpam-5046	213	30	=	=	SYM
ejpam-5046	213	31	{	{	PUNCT
ejpam-5046	213	32	u1	u1	NOUN
ejpam-5046	213	33	,	,	PUNCT
ejpam-5046	213	34	u3	u3	PROPN
ejpam-5046	213	35	,	,	PUNCT
ejpam-5046	213	36	u11	u11	PROPN
ejpam-5046	213	37	,	,	PUNCT
ejpam-5046	213	38	u12	u12	PROPN
ejpam-5046	213	39	,	,	PUNCT
ejpam-5046	213	40	u13	u13	NOUN
ejpam-5046	213	41	}	}	PUNCT
ejpam-5046	213	42	.	.	PUNCT
ejpam-5046	214	1	then	then	ADV
ejpam-5046	214	2	d1	d1	PROPN
ejpam-5046	214	3	and	and	CCONJ
ejpam-5046	214	4	d2	d2	PROPN
ejpam-5046	214	5	are	be	AUX
ejpam-5046	214	6	minimum	minimum	NOUN
ejpam-5046	214	7	zero	zero	NUM
ejpam-5046	214	8	forcing	forcing	NOUN
ejpam-5046	214	9	and	and	CCONJ
ejpam-5046	214	10	2	2	NUM
ejpam-5046	214	11	-	-	PUNCT
ejpam-5046	214	12	distance	distance	NOUN
ejpam-5046	214	13	zero	zero	NUM
ejpam-5046	214	14	forcing	force	VERB
ejpam-5046	214	15	set	set	NOUN
ejpam-5046	214	16	of	of	ADP
ejpam-5046	214	17	g	g	NOUN
ejpam-5046	214	18	,	,	PUNCT
ejpam-5046	214	19	respectively	respectively	ADV
ejpam-5046	214	20	.	.	PUNCT
ejpam-5046	215	1	therefore	therefore	ADV
ejpam-5046	215	2	,	,	PUNCT
ejpam-5046	215	3	z(g	z(g	NOUN
ejpam-5046	215	4	)	)	PUNCT
ejpam-5046	215	5	=	=	SYM
ejpam-5046	215	6	4	4	NUM
ejpam-5046	215	7	and	and	CCONJ
ejpam-5046	215	8	z2(g	z2(g	NUM
ejpam-5046	215	9	)	)	PUNCT
ejpam-5046	215	10	=	=	SYM
ejpam-5046	215	11	5	5	X
ejpam-5046	215	12	.	.	PUNCT
ejpam-5046	215	13	j.	j.	PROPN
ejpam-5046	215	14	a.	a.	PROPN
ejpam-5046	215	15	hassan	hassan	PROPN
ejpam-5046	215	16	,	,	PUNCT
ejpam-5046	215	17	l.	l.	PROPN
ejpam-5046	215	18	t.	t.	PROPN
ejpam-5046	215	19	udtohan	udtohan	PROPN
ejpam-5046	215	20	,	,	PUNCT
ejpam-5046	215	21	l.	l.	PROPN
ejpam-5046	215	22	s.	s.	PROPN
ejpam-5046	215	23	laja	laja	PROPN
ejpam-5046	215	24	/	/	SYM
ejpam-5046	215	25	eur	eur	PROPN
ejpam-5046	215	26	.	.	PUNCT
ejpam-5046	216	1	j.	j.	PROPN
ejpam-5046	216	2	pure	pure	PROPN
ejpam-5046	216	3	appl	appl	PROPN
ejpam-5046	216	4	.	.	PROPN
ejpam-5046	216	5	math	math	PROPN
ejpam-5046	216	6	,	,	PUNCT
ejpam-5046	216	7	17	17	NUM
ejpam-5046	216	8	(	(	PUNCT
ejpam-5046	216	9	2	2	NUM
ejpam-5046	216	10	)	)	PUNCT
ejpam-5046	216	11	(	(	PUNCT
ejpam-5046	216	12	2024	2024	NUM
ejpam-5046	216	13	)	)	PUNCT
ejpam-5046	216	14	,	,	PUNCT
ejpam-5046	216	15	1283	1283	NUM
ejpam-5046	216	16	-	-	SYM
ejpam-5046	216	17	1293	1293	NUM
ejpam-5046	216	18	1291	1291	NUM
ejpam-5046	216	19	theorem	theorem	NOUN
ejpam-5046	216	20	5	5	NUM
ejpam-5046	216	21	.	.	PUNCT
ejpam-5046	217	1	there	there	PRON
ejpam-5046	217	2	exists	exist	VERB
ejpam-5046	217	3	a	a	DET
ejpam-5046	217	4	graph	graph	NOUN
ejpam-5046	217	5	g	g	ADP
ejpam-5046	217	6	such	such	ADJ
ejpam-5046	217	7	that	that	SCONJ
ejpam-5046	217	8	z2(g	z2(g	NUM
ejpam-5046	217	9	)	)	PUNCT
ejpam-5046	217	10	=	=	PUNCT
ejpam-5046	217	11	z(g	z(g	NOUN
ejpam-5046	217	12	)	)	PUNCT
ejpam-5046	217	13	.	.	PUNCT
ejpam-5046	218	1	proof	proof	NOUN
ejpam-5046	218	2	.	.	PUNCT
ejpam-5046	219	1	consider	consider	VERB
ejpam-5046	219	2	the	the	DET
ejpam-5046	219	3	graph	graph	NOUN
ejpam-5046	219	4	k2	k2	ADJ
ejpam-5046	219	5	+	+	CCONJ
ejpam-5046	219	6	p4	p4	ADJ
ejpam-5046	219	7	below	below	ADV
ejpam-5046	219	8	.	.	PUNCT
ejpam-5046	220	1	v1	v1	PROPN
ejpam-5046	220	2	v2	v2	PROPN
ejpam-5046	220	3	v3	v3	PROPN
ejpam-5046	220	4	v4	v4	PROPN
ejpam-5046	220	5	v5	v5	PROPN
ejpam-5046	220	6	v6	v6	PROPN
ejpam-5046	220	7	k2	k2	PROPN
ejpam-5046	220	8	+	+	CCONJ
ejpam-5046	220	9	p4	p4	ADJ
ejpam-5046	220	10	:	:	PUNCT
ejpam-5046	220	11	letd′	letd′	NOUN
ejpam-5046	220	12	=	=	SYM
ejpam-5046	220	13	{	{	PUNCT
ejpam-5046	220	14	v1	v1	PROPN
ejpam-5046	220	15	,	,	PUNCT
ejpam-5046	220	16	v5	v5	PROPN
ejpam-5046	220	17	,	,	PUNCT
ejpam-5046	220	18	v6	v6	NOUN
ejpam-5046	220	19	}	}	PUNCT
ejpam-5046	220	20	andd′′	andd′′	NOUN
ejpam-5046	220	21	=	=	SYM
ejpam-5046	220	22	{	{	PUNCT
ejpam-5046	220	23	v3	v3	PROPN
ejpam-5046	220	24	,	,	PUNCT
ejpam-5046	220	25	v5	v5	PROPN
ejpam-5046	220	26	,	,	PUNCT
ejpam-5046	220	27	v6	v6	NOUN
ejpam-5046	220	28	}	}	PUNCT
ejpam-5046	220	29	.	.	PUNCT
ejpam-5046	221	1	thend′	thend′	X
ejpam-5046	221	2	andd′′	andd′′	PROPN
ejpam-5046	221	3	are	be	AUX
ejpam-5046	221	4	minimum	minimum	NOUN
ejpam-5046	221	5	zero	zero	NUM
ejpam-5046	221	6	forcing	forcing	NOUN
ejpam-5046	221	7	and	and	CCONJ
ejpam-5046	221	8	2	2	NUM
ejpam-5046	221	9	-	-	PUNCT
ejpam-5046	221	10	distance	distance	NOUN
ejpam-5046	221	11	zero	zero	NUM
ejpam-5046	221	12	forcing	force	VERB
ejpam-5046	221	13	sets	set	NOUN
ejpam-5046	221	14	of	of	ADP
ejpam-5046	221	15	k2+p4	k2+p4	NOUN
ejpam-5046	221	16	,	,	PUNCT
ejpam-5046	221	17	respectively	respectively	ADV
ejpam-5046	221	18	.	.	PUNCT
ejpam-5046	222	1	hence	hence	ADV
ejpam-5046	222	2	,	,	PUNCT
ejpam-5046	222	3	z(k2+p4	z(k2+p4	NOUN
ejpam-5046	222	4	)	)	PUNCT
ejpam-5046	222	5	=	=	SYM
ejpam-5046	222	6	3	3	NUM
ejpam-5046	222	7	=	=	SYM
ejpam-5046	222	8	z2(k2+p4	z2(k2+p4	NOUN
ejpam-5046	222	9	)	)	PUNCT
ejpam-5046	222	10	.	.	PUNCT
ejpam-5046	223	1	let	let	VERB
ejpam-5046	223	2	g	g	PROPN
ejpam-5046	223	3	=	=	PROPN
ejpam-5046	223	4	k2	k2	PROPN
ejpam-5046	223	5	+	+	CCONJ
ejpam-5046	223	6	p4	p4	ADJ
ejpam-5046	223	7	.	.	PUNCT
ejpam-5046	224	1	then	then	ADV
ejpam-5046	224	2	the	the	DET
ejpam-5046	224	3	assertion	assertion	NOUN
ejpam-5046	224	4	follows	follow	VERB
ejpam-5046	224	5	.	.	PUNCT
ejpam-5046	225	1	theorem	theorem	ADJ
ejpam-5046	225	2	6	6	NUM
ejpam-5046	225	3	.	.	PUNCT
ejpam-5046	226	1	let	let	VERB
ejpam-5046	226	2	g	g	PRON
ejpam-5046	226	3	be	be	AUX
ejpam-5046	226	4	a	a	DET
ejpam-5046	226	5	graph	graph	NOUN
ejpam-5046	226	6	.	.	PUNCT
ejpam-5046	227	1	then	then	ADV
ejpam-5046	227	2	z2(g	z2(g	NUM
ejpam-5046	227	3	)	)	PUNCT
ejpam-5046	227	4	=	=	PUNCT
ejpam-5046	227	5	z(g	z(g	NOUN
ejpam-5046	227	6	)	)	PUNCT
ejpam-5046	227	7	=	=	SYM
ejpam-5046	227	8	|v	|v	X
ejpam-5046	227	9	(	(	PUNCT
ejpam-5046	227	10	g)|	g)|	VERB
ejpam-5046	227	11	if	if	SCONJ
ejpam-5046	228	1	and	and	CCONJ
ejpam-5046	228	2	only	only	ADV
ejpam-5046	228	3	if	if	SCONJ
ejpam-5046	228	4	every	every	DET
ejpam-5046	228	5	component	component	NOUN
ejpam-5046	228	6	of	of	ADP
ejpam-5046	228	7	g	g	PROPN
ejpam-5046	228	8	is	be	AUX
ejpam-5046	228	9	trivial	trivial	ADJ
ejpam-5046	228	10	.	.	PUNCT
ejpam-5046	229	1	proof	proof	NOUN
ejpam-5046	229	2	.	.	PUNCT
ejpam-5046	230	1	suppose	suppose	VERB
ejpam-5046	230	2	that	that	SCONJ
ejpam-5046	230	3	z2(g	z2(g	NUM
ejpam-5046	230	4	)	)	PUNCT
ejpam-5046	230	5	=	=	SYM
ejpam-5046	230	6	z(g	z(g	NOUN
ejpam-5046	230	7	)	)	PUNCT
ejpam-5046	230	8	=	=	SYM
ejpam-5046	230	9	|v	|v	PROPN
ejpam-5046	230	10	(	(	PUNCT
ejpam-5046	230	11	g)|	g)|	NOUN
ejpam-5046	230	12	.	.	PUNCT
ejpam-5046	230	13	suppose	suppose	VERB
ejpam-5046	230	14	there	there	PRON
ejpam-5046	230	15	is	be	VERB
ejpam-5046	230	16	component	component	NOUN
ejpam-5046	230	17	k	k	PROPN
ejpam-5046	230	18	of	of	ADP
ejpam-5046	230	19	g	g	PROPN
ejpam-5046	230	20	which	which	PRON
ejpam-5046	230	21	is	be	AUX
ejpam-5046	230	22	non	non	ADJ
ejpam-5046	230	23	-	-	ADJ
ejpam-5046	230	24	trivial	trivial	ADJ
ejpam-5046	230	25	.	.	PUNCT
ejpam-5046	231	1	let	let	VERB
ejpam-5046	231	2	v	v	X
ejpam-5046	231	3	(	(	PUNCT
ejpam-5046	231	4	k	k	NOUN
ejpam-5046	231	5	)	)	PUNCT
ejpam-5046	231	6	=	=	SYM
ejpam-5046	231	7	{	{	PUNCT
ejpam-5046	231	8	k1	k1	PROPN
ejpam-5046	231	9	,	,	PUNCT
ejpam-5046	231	10	...	...	PUNCT
ejpam-5046	231	11	,	,	PUNCT
ejpam-5046	231	12	kn	kn	PROPN
ejpam-5046	231	13	}	}	PUNCT
ejpam-5046	231	14	,	,	PUNCT
ejpam-5046	231	15	k	k	PROPN
ejpam-5046	231	16	≥	≥	NUM
ejpam-5046	231	17	2	2	X
ejpam-5046	231	18	.	.	X
ejpam-5046	231	19	consider	consider	VERB
ejpam-5046	231	20	q	q	NOUN
ejpam-5046	231	21	=	=	SYM
ejpam-5046	231	22	v	v	X
ejpam-5046	231	23	(	(	PUNCT
ejpam-5046	231	24	g	g	NOUN
ejpam-5046	231	25	)	)	PUNCT
ejpam-5046	231	26	\	\	NOUN
ejpam-5046	231	27	{	{	PUNCT
ejpam-5046	231	28	k1	k1	NOUN
ejpam-5046	231	29	}	}	PUNCT
ejpam-5046	231	30	.	.	PUNCT
ejpam-5046	232	1	then	then	ADV
ejpam-5046	232	2	q	q	X
ejpam-5046	232	3	is	be	AUX
ejpam-5046	232	4	a	a	DET
ejpam-5046	232	5	zero	zero	NUM
ejpam-5046	232	6	forcing	force	VERB
ejpam-5046	232	7	set	set	NOUN
ejpam-5046	232	8	of	of	ADP
ejpam-5046	232	9	g.	g.	PROPN
ejpam-5046	232	10	thus	thus	ADV
ejpam-5046	232	11	,	,	PUNCT
ejpam-5046	232	12	z(g	z(g	NOUN
ejpam-5046	232	13	)	)	PUNCT
ejpam-5046	232	14	≤	≤	NOUN
ejpam-5046	232	15	|v	|v	X
ejpam-5046	232	16	(	(	PUNCT
ejpam-5046	232	17	g)|	g)|	INTJ
ejpam-5046	232	18	−	−	PROPN
ejpam-5046	232	19	1	1	NUM
ejpam-5046	232	20	,	,	PUNCT
ejpam-5046	232	21	a	a	DET
ejpam-5046	232	22	contradiction	contradiction	NOUN
ejpam-5046	232	23	.	.	PUNCT
ejpam-5046	233	1	therefore	therefore	ADV
ejpam-5046	233	2	,	,	PUNCT
ejpam-5046	233	3	every	every	DET
ejpam-5046	233	4	component	component	NOUN
ejpam-5046	233	5	of	of	ADP
ejpam-5046	233	6	g	g	PROPN
ejpam-5046	233	7	is	be	AUX
ejpam-5046	233	8	trivial	trivial	ADJ
ejpam-5046	233	9	.	.	PUNCT
ejpam-5046	234	1	the	the	DET
ejpam-5046	234	2	converse	converse	NOUN
ejpam-5046	234	3	is	be	AUX
ejpam-5046	234	4	clear	clear	ADJ
ejpam-5046	234	5	.	.	PUNCT
ejpam-5046	235	1	4	4	X
ejpam-5046	235	2	.	.	X
ejpam-5046	235	3	conclusion	conclusion	VERB
ejpam-5046	235	4	the	the	DET
ejpam-5046	235	5	concept	concept	NOUN
ejpam-5046	235	6	of	of	ADP
ejpam-5046	235	7	2	2	NUM
ejpam-5046	235	8	-	-	PUNCT
ejpam-5046	235	9	distance	distance	NOUN
ejpam-5046	235	10	zero	zero	NUM
ejpam-5046	235	11	forcing	force	VERB
ejpam-5046	235	12	in	in	ADP
ejpam-5046	235	13	a	a	DET
ejpam-5046	235	14	graph	graph	NOUN
ejpam-5046	235	15	has	have	AUX
ejpam-5046	235	16	been	be	AUX
ejpam-5046	235	17	introduced	introduce	VERB
ejpam-5046	235	18	and	and	CCONJ
ejpam-5046	235	19	investigated	investigate	VERB
ejpam-5046	235	20	in	in	ADP
ejpam-5046	235	21	this	this	DET
ejpam-5046	235	22	paper	paper	NOUN
ejpam-5046	235	23	.	.	PUNCT
ejpam-5046	236	1	the	the	DET
ejpam-5046	236	2	2	2	NUM
ejpam-5046	236	3	-	-	PUNCT
ejpam-5046	236	4	distance	distance	NOUN
ejpam-5046	236	5	zero	zero	NUM
ejpam-5046	236	6	forcing	force	VERB
ejpam-5046	236	7	numbers	number	NOUN
ejpam-5046	236	8	of	of	ADP
ejpam-5046	236	9	some	some	DET
ejpam-5046	236	10	graphs	graph	NOUN
ejpam-5046	236	11	are	be	AUX
ejpam-5046	236	12	obtained	obtain	VERB
ejpam-5046	236	13	.	.	PUNCT
ejpam-5046	237	1	the	the	DET
ejpam-5046	237	2	connections	connection	NOUN
ejpam-5046	237	3	of	of	ADP
ejpam-5046	237	4	the	the	DET
ejpam-5046	237	5	2	2	NUM
ejpam-5046	237	6	-	-	PUNCT
ejpam-5046	237	7	distance	distance	NOUN
ejpam-5046	237	8	zero	zero	NUM
ejpam-5046	237	9	forcing	forcing	NOUN
ejpam-5046	237	10	parameter	parameter	NOUN
ejpam-5046	237	11	with	with	ADP
ejpam-5046	237	12	the	the	DET
ejpam-5046	237	13	standard	standard	ADJ
ejpam-5046	237	14	zero	zero	NUM
ejpam-5046	237	15	forcing	forcing	NOUN
ejpam-5046	237	16	and	and	CCONJ
ejpam-5046	237	17	hop	hop	NOUN
ejpam-5046	237	18	domination	domination	NOUN
ejpam-5046	237	19	parameter	parameter	NOUN
ejpam-5046	237	20	have	have	AUX
ejpam-5046	237	21	been	be	AUX
ejpam-5046	237	22	presented	present	VERB
ejpam-5046	237	23	.	.	PUNCT
ejpam-5046	238	1	interested	interested	ADJ
ejpam-5046	238	2	researchers	researcher	NOUN
ejpam-5046	238	3	may	may	AUX
ejpam-5046	238	4	study	study	VERB
ejpam-5046	238	5	this	this	DET
ejpam-5046	238	6	concept	concept	NOUN
ejpam-5046	238	7	on	on	ADP
ejpam-5046	238	8	graphs	graph	NOUN
ejpam-5046	238	9	that	that	PRON
ejpam-5046	238	10	were	be	AUX
ejpam-5046	238	11	not	not	PART
ejpam-5046	238	12	considered	consider	VERB
ejpam-5046	238	13	in	in	ADP
ejpam-5046	238	14	this	this	DET
ejpam-5046	238	15	study	study	NOUN
ejpam-5046	238	16	.	.	PUNCT
ejpam-5046	239	1	interested	interested	ADJ
ejpam-5046	239	2	researchers	researcher	NOUN
ejpam-5046	239	3	may	may	AUX
ejpam-5046	239	4	also	also	ADV
ejpam-5046	239	5	consider	consider	VERB
ejpam-5046	239	6	on	on	ADP
ejpam-5046	239	7	providing	provide	VERB
ejpam-5046	239	8	an	an	DET
ejpam-5046	239	9	application	application	NOUN
ejpam-5046	239	10	of	of	ADP
ejpam-5046	239	11	this	this	DET
ejpam-5046	239	12	parameter	parameter	NOUN
ejpam-5046	239	13	.	.	PUNCT
ejpam-5046	240	1	acknowledgements	acknowledgement	NOUN
ejpam-5046	240	2	the	the	DET
ejpam-5046	240	3	authors	author	NOUN
ejpam-5046	240	4	would	would	AUX
ejpam-5046	240	5	like	like	VERB
ejpam-5046	240	6	to	to	PART
ejpam-5046	240	7	thank	thank	VERB
ejpam-5046	240	8	mindanao	mindanao	PROPN
ejpam-5046	240	9	state	state	PROPN
ejpam-5046	240	10	universitytawi	universitytawi	PROPN
ejpam-5046	240	11	-	-	PUNCT
ejpam-5046	240	12	tawi	tawi	NOUN
ejpam-5046	240	13	college	college	PROPN
ejpam-5046	240	14	of	of	ADP
ejpam-5046	240	15	technology	technology	NOUN
ejpam-5046	240	16	and	and	CCONJ
ejpam-5046	240	17	oceanography	oceanography	NOUN
ejpam-5046	240	18	for	for	ADP
ejpam-5046	240	19	funding	fund	VERB
ejpam-5046	240	20	this	this	DET
ejpam-5046	240	21	research	research	NOUN
ejpam-5046	240	22	.	.	PUNCT
ejpam-5046	241	1	references	reference	NOUN
ejpam-5046	241	2	1292	1292	NUM
ejpam-5046	241	3	references	reference	NOUN
ejpam-5046	241	4	[	[	X
ejpam-5046	241	5	1	1	NUM
ejpam-5046	241	6	]	]	PUNCT
ejpam-5046	241	7	f.	f.	NOUN
ejpam-5046	241	8	barioli	barioli	PROPN
ejpam-5046	241	9	,	,	PUNCT
ejpam-5046	241	10	w.	w.	PROPN
ejpam-5046	241	11	barett	barett	PROPN
ejpam-5046	241	12	,	,	PUNCT
ejpam-5046	241	13	s.	s.	PROPN
ejpam-5046	241	14	fallat	fallat	PROPN
ejpam-5046	241	15	,	,	PUNCT
ejpam-5046	241	16	h.	h.	PROPN
ejpam-5046	241	17	hall	hall	PROPN
ejpam-5046	241	18	,	,	PUNCT
ejpam-5046	241	19	l.	l.	PROPN
ejpam-5046	241	20	hogben	hogben	PROPN
ejpam-5046	241	21	,	,	PUNCT
ejpam-5046	241	22	h.	h.	PROPN
ejpam-5046	241	23	van	van	PROPN
ejpam-5046	241	24	der	der	PROPN
ejpam-5046	241	25	holst	holst	NOUN
ejpam-5046	241	26	,	,	PUNCT
ejpam-5046	241	27	and	and	CCONJ
ejpam-5046	241	28	b.	b.	PROPN
ejpam-5046	241	29	shader	shader	NOUN
ejpam-5046	241	30	.	.	PUNCT
ejpam-5046	242	1	zero	zero	NUM
ejpam-5046	242	2	forcing	force	VERB
ejpam-5046	242	3	parameters	parameter	NOUN
ejpam-5046	242	4	and	and	CCONJ
ejpam-5046	242	5	minimum	minimum	ADJ
ejpam-5046	242	6	rank	rank	NOUN
ejpam-5046	242	7	problems	problem	NOUN
ejpam-5046	242	8	.	.	PUNCT
ejpam-5046	243	1	linear	linear	ADJ
ejpam-5046	243	2	algebra	algebra	PROPN
ejpam-5046	243	3	appl	appl	NOUN
ejpam-5046	243	4	.	.	PROPN
ejpam-5046	244	1	,	,	PUNCT
ejpam-5046	244	2	,	,	PUNCT
ejpam-5046	244	3	443:401	443:401	NOUN
ejpam-5046	244	4	–	–	PUNCT
ejpam-5046	244	5	411	411	NUM
ejpam-5046	244	6	,	,	PUNCT
ejpam-5046	244	7	2010	2010	NUM
ejpam-5046	244	8	.	.	PUNCT
ejpam-5046	245	1	[	[	X
ejpam-5046	245	2	2	2	X
ejpam-5046	245	3	]	]	PUNCT
ejpam-5046	245	4	k.	k.	PROPN
ejpam-5046	245	5	benson	benson	PROPN
ejpam-5046	245	6	,	,	PUNCT
ejpam-5046	245	7	d.	d.	PROPN
ejpam-5046	245	8	ferrero	ferrero	PROPN
ejpam-5046	245	9	,	,	PUNCT
ejpam-5046	245	10	m.	m.	PROPN
ejpam-5046	245	11	flagg	flagg	PROPN
ejpam-5046	245	12	,	,	PUNCT
ejpam-5046	245	13	v.	v.	PROPN
ejpam-5046	245	14	furst	furst	PROPN
ejpam-5046	245	15	,	,	PUNCT
ejpam-5046	245	16	l.	l.	PROPN
ejpam-5046	245	17	hogben	hogben	PROPN
ejpam-5046	245	18	,	,	PUNCT
ejpam-5046	245	19	v.	v.	ADP
ejpam-5046	245	20	vasilevska	vasilevska	NOUN
ejpam-5046	245	21	,	,	PUNCT
ejpam-5046	245	22	and	and	CCONJ
ejpam-5046	245	23	b.	b.	PROPN
ejpam-5046	245	24	wissman	wissman	NOUN
ejpam-5046	245	25	.	.	PUNCT
ejpam-5046	246	1	zero	zero	NUM
ejpam-5046	246	2	forcing	forcing	NOUN
ejpam-5046	246	3	and	and	CCONJ
ejpam-5046	246	4	power	power	NOUN
ejpam-5046	246	5	domination	domination	NOUN
ejpam-5046	246	6	for	for	ADP
ejpam-5046	246	7	graphs	graph	NOUN
ejpam-5046	246	8	products	product	NOUN
ejpam-5046	246	9	.	.	PUNCT
ejpam-5046	247	1	australas	australas	PROPN
ejpam-5046	247	2	.	.	PUNCT
ejpam-5046	248	1	j.	j.	PROPN
ejpam-5046	248	2	combin	combin	PROPN
ejpam-5046	248	3	,	,	PUNCT
ejpam-5046	248	4	70:221–235	70:221–235	PROPN
ejpam-5046	248	5	,	,	PUNCT
ejpam-5046	248	6	2018	2018	NUM
ejpam-5046	248	7	.	.	PUNCT
ejpam-5046	249	1	[	[	X
ejpam-5046	249	2	3	3	X
ejpam-5046	249	3	]	]	X
ejpam-5046	249	4	r.	r.	PROPN
ejpam-5046	249	5	davila	davila	PROPN
ejpam-5046	249	6	,	,	PUNCT
ejpam-5046	249	7	t.	t.	PROPN
ejpam-5046	249	8	kalinowski	kalinowski	PROPN
ejpam-5046	249	9	,	,	PUNCT
ejpam-5046	249	10	and	and	CCONJ
ejpam-5046	249	11	s.	s.	PROPN
ejpam-5046	249	12	sudeep	sudeep	PROPN
ejpam-5046	249	13	.	.	PUNCT
ejpam-5046	250	1	a	a	DET
ejpam-5046	250	2	lower	lower	ADV
ejpam-5046	250	3	bound	bind	VERB
ejpam-5046	250	4	on	on	ADP
ejpam-5046	250	5	the	the	DET
ejpam-5046	250	6	zero	zero	NUM
ejpam-5046	250	7	forcing	force	VERB
ejpam-5046	250	8	number	number	NOUN
ejpam-5046	250	9	.	.	PUNCT
ejpam-5046	251	1	discrete	discrete	ADJ
ejpam-5046	251	2	appl	appl	PROPN
ejpam-5046	251	3	.	.	PUNCT
ejpam-5046	251	4	math	math	PROPN
ejpam-5046	251	5	.	.	PUNCT
ejpam-5046	251	6	,	,	PUNCT
ejpam-5046	251	7	250:363–367	250:363–367	NUM
ejpam-5046	251	8	,	,	PUNCT
ejpam-5046	251	9	2018	2018	NUM
ejpam-5046	251	10	.	.	PUNCT
ejpam-5046	252	1	[	[	X
ejpam-5046	252	2	4	4	X
ejpam-5046	252	3	]	]	PUNCT
ejpam-5046	252	4	s.	s.	PROPN
ejpam-5046	252	5	m.	m.	PROPN
ejpam-5046	252	6	fallat	fallat	PROPN
ejpam-5046	252	7	and	and	CCONJ
ejpam-5046	252	8	l.	l.	PROPN
ejpam-5046	252	9	hogben	hogben	PROPN
ejpam-5046	252	10	.	.	PUNCT
ejpam-5046	253	1	minimum	minimum	ADJ
ejpam-5046	253	2	rank	rank	NOUN
ejpam-5046	253	3	,	,	PUNCT
ejpam-5046	253	4	maximum	maximum	ADJ
ejpam-5046	253	5	nullity	nullity	NOUN
ejpam-5046	253	6	,	,	PUNCT
ejpam-5046	253	7	and	and	CCONJ
ejpam-5046	253	8	zero	zero	NUM
ejpam-5046	253	9	forcing	force	VERB
ejpam-5046	253	10	number	number	NOUN
ejpam-5046	253	11	of	of	ADP
ejpam-5046	253	12	graphs	graph	NOUN
ejpam-5046	253	13	.	.	PUNCT
ejpam-5046	254	1	2nd	2nd	ADJ
ejpam-5046	254	2	ed	ed	NOUN
ejpam-5046	254	3	.	.	PROPN
ejpam-5046	254	4	,	,	PUNCT
ejpam-5046	254	5	in	in	ADP
ejpam-5046	254	6	handbook	handbook	NOUN
ejpam-5046	254	7	of	of	ADP
ejpam-5046	254	8	linear	linear	PROPN
ejpam-5046	254	9	algebra	algebra	PROPN
ejpam-5046	254	10	,	,	PUNCT
ejpam-5046	254	11	crc	crc	NOUN
ejpam-5046	254	12	press	press	PROPN
ejpam-5046	254	13	,	,	PUNCT
ejpam-5046	254	14	boca	boca	PROPN
ejpam-5046	254	15	raton	raton	PROPN
ejpam-5046	254	16	,	,	PUNCT
ejpam-5046	254	17	fl	fl	PROPN
ejpam-5046	254	18	,	,	PUNCT
ejpam-5046	254	19	pages	page	NOUN
ejpam-5046	254	20	775–810	775–810	NUM
ejpam-5046	254	21	,	,	PUNCT
ejpam-5046	254	22	2013	2013	NUM
ejpam-5046	254	23	.	.	PUNCT
ejpam-5046	255	1	[	[	X
ejpam-5046	255	2	5	5	NUM
ejpam-5046	255	3	]	]	PUNCT
ejpam-5046	255	4	m.	m.	NOUN
ejpam-5046	255	5	gentner	gentner	NOUN
ejpam-5046	255	6	,	,	PUNCT
ejpam-5046	255	7	l.	l.	PROPN
ejpam-5046	255	8	d.	d.	PROPN
ejpam-5046	255	9	penso	penso	PROPN
ejpam-5046	255	10	,	,	PUNCT
ejpam-5046	255	11	d.	d.	PROPN
ejpam-5046	255	12	rautenbach	rautenbach	PROPN
ejpam-5046	255	13	,	,	PUNCT
ejpam-5046	255	14	,	,	PUNCT
ejpam-5046	255	15	and	and	CCONJ
ejpam-5046	255	16	u.	u.	PROPN
ejpam-5046	255	17	s.	s.	PROPN
ejpam-5046	255	18	souza	souza	PROPN
ejpam-5046	255	19	.	.	PUNCT
ejpam-5046	256	1	extremal	extremal	ADJ
ejpam-5046	256	2	values	value	NOUN
ejpam-5046	256	3	and	and	CCONJ
ejpam-5046	256	4	bounds	bound	NOUN
ejpam-5046	256	5	for	for	ADP
ejpam-5046	256	6	the	the	DET
ejpam-5046	256	7	zero	zero	NUM
ejpam-5046	256	8	forcing	force	VERB
ejpam-5046	256	9	number	number	NOUN
ejpam-5046	256	10	.	.	PUNCT
ejpam-5046	257	1	discrete	discrete	ADJ
ejpam-5046	257	2	appl	appl	PROPN
ejpam-5046	257	3	.	.	PUNCT
ejpam-5046	257	4	math	math	PROPN
ejpam-5046	257	5	.	.	PUNCT
ejpam-5046	257	6	,	,	PUNCT
ejpam-5046	257	7	214:196–200	214:196–200	NUM
ejpam-5046	257	8	,	,	PUNCT
ejpam-5046	257	9	2016	2016	NUM
ejpam-5046	257	10	.	.	PUNCT
ejpam-5046	258	1	[	[	X
ejpam-5046	258	2	6	6	NUM
ejpam-5046	258	3	]	]	PUNCT
ejpam-5046	258	4	aim	aim	VERB
ejpam-5046	258	5	minimum	minimum	ADJ
ejpam-5046	258	6	rank	rank	NOUN
ejpam-5046	258	7	special	special	ADJ
ejpam-5046	258	8	graphs	graph	NOUN
ejpam-5046	258	9	work	work	NOUN
ejpam-5046	258	10	group	group	NOUN
ejpam-5046	258	11	.	.	PUNCT
ejpam-5046	259	1	zero	zero	NUM
ejpam-5046	259	2	forcing	force	VERB
ejpam-5046	259	3	sets	set	NOUN
ejpam-5046	259	4	and	and	CCONJ
ejpam-5046	259	5	the	the	DET
ejpam-5046	259	6	minimum	minimum	ADJ
ejpam-5046	259	7	rank	rank	NOUN
ejpam-5046	259	8	of	of	ADP
ejpam-5046	259	9	graphs	graph	NOUN
ejpam-5046	259	10	,	,	PUNCT
ejpam-5046	259	11	.	.	PUNCT
ejpam-5046	260	1	linear	linear	PROPN
ejpam-5046	260	2	algebra	algebra	PROPN
ejpam-5046	260	3	appl	appl	NOUN
ejpam-5046	260	4	.	.	PROPN
ejpam-5046	260	5	,	,	PUNCT
ejpam-5046	260	6	,	,	PUNCT
ejpam-5046	260	7	428:1628–1648	428:1628–1648	NOUN
ejpam-5046	260	8	,	,	PUNCT
ejpam-5046	260	9	2008	2008	NUM
ejpam-5046	260	10	.	.	PUNCT
ejpam-5046	261	1	[	[	X
ejpam-5046	261	2	7	7	X
ejpam-5046	261	3	]	]	PUNCT
ejpam-5046	261	4	j.	j.	PROPN
ejpam-5046	261	5	hassan	hassan	PROPN
ejpam-5046	261	6	,	,	PUNCT
ejpam-5046	261	7	ar	ar	PROPN
ejpam-5046	261	8	.	.	PROPN
ejpam-5046	261	9	bakkang	bakkang	PROPN
ejpam-5046	261	10	,	,	PUNCT
ejpam-5046	261	11	and	and	CCONJ
ejpam-5046	261	12	ass	ass	PROPN
ejpam-5046	261	13	.	.	PROPN
ejpam-5046	261	14	sappari	sappari	PROPN
ejpam-5046	261	15	.	.	PUNCT
ejpam-5046	262	1	j2	j2	PROPN
ejpam-5046	262	2	-	-	PUNCT
ejpam-5046	262	3	hop	hop	PROPN
ejpam-5046	262	4	domination	domination	NOUN
ejpam-5046	262	5	in	in	ADP
ejpam-5046	262	6	graphs	graph	NOUN
ejpam-5046	262	7	:	:	PUNCT
ejpam-5046	262	8	properties	property	NOUN
ejpam-5046	262	9	and	and	CCONJ
ejpam-5046	262	10	connections	connection	NOUN
ejpam-5046	262	11	with	with	ADP
ejpam-5046	262	12	other	other	ADJ
ejpam-5046	262	13	parameters	parameter	NOUN
ejpam-5046	262	14	.	.	PUNCT
ejpam-5046	263	1	eur	eur	PROPN
ejpam-5046	263	2	.	.	PUNCT
ejpam-5046	264	1	j.	j.	PROPN
ejpam-5046	264	2	pure	pure	PROPN
ejpam-5046	264	3	appl	appl	PROPN
ejpam-5046	264	4	.	.	PUNCT
ejpam-5046	264	5	math	math	PROPN
ejpam-5046	264	6	.	.	PUNCT
ejpam-5046	264	7	,	,	PUNCT
ejpam-5046	264	8	16(4):2118–2131	16(4):2118–2131	NUM
ejpam-5046	264	9	,	,	PUNCT
ejpam-5046	264	10	2023	2023	NUM
ejpam-5046	264	11	.	.	PUNCT
ejpam-5046	265	1	[	[	X
ejpam-5046	265	2	8	8	NUM
ejpam-5046	265	3	]	]	PUNCT
ejpam-5046	265	4	j.	j.	PROPN
ejpam-5046	265	5	hassan	hassan	PROPN
ejpam-5046	265	6	and	and	CCONJ
ejpam-5046	265	7	s.	s.	PROPN
ejpam-5046	265	8	canoy	canoy	PROPN
ejpam-5046	265	9	.	.	PUNCT
ejpam-5046	266	1	connected	connect	VERB
ejpam-5046	266	2	grundy	grundy	PROPN
ejpam-5046	266	3	hop	hop	NOUN
ejpam-5046	266	4	dominating	dominate	VERB
ejpam-5046	266	5	sequences	sequence	NOUN
ejpam-5046	266	6	in	in	ADP
ejpam-5046	266	7	graphs	graph	NOUN
ejpam-5046	266	8	.	.	PUNCT
ejpam-5046	267	1	eur	eur	PROPN
ejpam-5046	267	2	.	.	PUNCT
ejpam-5046	268	1	j.	j.	PROPN
ejpam-5046	268	2	pure	pure	PROPN
ejpam-5046	268	3	appl	appl	PROPN
ejpam-5046	268	4	.	.	PUNCT
ejpam-5046	268	5	math	math	PROPN
ejpam-5046	268	6	.	.	PUNCT
ejpam-5046	268	7	,	,	PUNCT
ejpam-5046	269	1	16(2):1212–1227	16(2):1212–1227	NUM
ejpam-5046	269	2	,	,	PUNCT
ejpam-5046	269	3	2023	2023	NUM
ejpam-5046	269	4	.	.	PUNCT
ejpam-5046	270	1	[	[	X
ejpam-5046	270	2	9	9	NUM
ejpam-5046	270	3	]	]	PUNCT
ejpam-5046	270	4	j.	j.	PROPN
ejpam-5046	270	5	hassan	hassan	PROPN
ejpam-5046	270	6	,	,	PUNCT
ejpam-5046	270	7	s.	s.	PROPN
ejpam-5046	270	8	canoy	canoy	PROPN
ejpam-5046	270	9	,	,	PUNCT
ejpam-5046	270	10	and	and	CCONJ
ejpam-5046	270	11	c.j	c.j	PROPN
ejpam-5046	270	12	.	.	PROPN
ejpam-5046	270	13	saromines	saromine	NOUN
ejpam-5046	270	14	.	.	PUNCT
ejpam-5046	271	1	convex	convex	VERB
ejpam-5046	271	2	hop	hop	NOUN
ejpam-5046	271	3	domination	domination	NOUN
ejpam-5046	271	4	in	in	ADP
ejpam-5046	271	5	graphs	graph	NOUN
ejpam-5046	271	6	.	.	PUNCT
ejpam-5046	272	1	eur	eur	PROPN
ejpam-5046	272	2	.	.	PUNCT
ejpam-5046	273	1	j.	j.	PROPN
ejpam-5046	273	2	pure	pure	PROPN
ejpam-5046	273	3	appl	appl	PROPN
ejpam-5046	273	4	.	.	PUNCT
ejpam-5046	273	5	math	math	PROPN
ejpam-5046	273	6	.	.	PUNCT
ejpam-5046	273	7	,	,	PUNCT
ejpam-5046	273	8	16(1):319–335	16(1):319–335	NOUN
ejpam-5046	273	9	,	,	PUNCT
ejpam-5046	273	10	2023	2023	NUM
ejpam-5046	273	11	.	.	PUNCT
ejpam-5046	274	1	[	[	X
ejpam-5046	274	2	10	10	NUM
ejpam-5046	274	3	]	]	PUNCT
ejpam-5046	274	4	j.	j.	PROPN
ejpam-5046	274	5	hassan	hassan	PROPN
ejpam-5046	274	6	and	and	CCONJ
ejpam-5046	274	7	s.	s.	PROPN
ejpam-5046	274	8	canoy	canoy	PROPN
ejpam-5046	274	9	jr	jr	PROPN
ejpam-5046	274	10	.	.	PUNCT
ejpam-5046	274	11	grundy	grundy	PROPN
ejpam-5046	274	12	dominating	dominating	PROPN
ejpam-5046	274	13	and	and	CCONJ
ejpam-5046	274	14	grundy	grundy	PROPN
ejpam-5046	274	15	hop	hop	NOUN
ejpam-5046	274	16	dominating	dominate	VERB
ejpam-5046	274	17	sequences	sequence	NOUN
ejpam-5046	274	18	in	in	ADP
ejpam-5046	274	19	graphs	graph	NOUN
ejpam-5046	274	20	:	:	PUNCT
ejpam-5046	274	21	relationships	relationship	NOUN
ejpam-5046	274	22	and	and	CCONJ
ejpam-5046	274	23	some	some	DET
ejpam-5046	274	24	structural	structural	ADJ
ejpam-5046	274	25	properties	property	NOUN
ejpam-5046	274	26	.	.	PUNCT
ejpam-5046	275	1	eur	eur	PROPN
ejpam-5046	275	2	.	.	PUNCT
ejpam-5046	276	1	j.	j.	PROPN
ejpam-5046	276	2	pure	pure	PROPN
ejpam-5046	276	3	appl	appl	PROPN
ejpam-5046	276	4	.	.	PUNCT
ejpam-5046	276	5	math	math	PROPN
ejpam-5046	276	6	.	.	PUNCT
ejpam-5046	276	7	,	,	PUNCT
ejpam-5046	277	1	16(2):1154–1166	16(2):1154–1166	NUM
ejpam-5046	277	2	,	,	PUNCT
ejpam-5046	277	3	2023	2023	NUM
ejpam-5046	277	4	.	.	PUNCT
ejpam-5046	278	1	[	[	X
ejpam-5046	278	2	11	11	NUM
ejpam-5046	278	3	]	]	PUNCT
ejpam-5046	278	4	j.	j.	PROPN
ejpam-5046	278	5	hassan	hassan	PROPN
ejpam-5046	278	6	and	and	CCONJ
ejpam-5046	278	7	s.	s.	PROPN
ejpam-5046	278	8	canoy	canoy	PROPN
ejpam-5046	278	9	jr	jr	PROPN
ejpam-5046	278	10	.	.	PUNCT
ejpam-5046	279	1	grundy	grundy	PROPN
ejpam-5046	279	2	total	total	PROPN
ejpam-5046	279	3	hop	hop	PROPN
ejpam-5046	279	4	dominating	dominate	VERB
ejpam-5046	279	5	sequences	sequence	NOUN
ejpam-5046	279	6	in	in	ADP
ejpam-5046	279	7	graphs	graph	NOUN
ejpam-5046	279	8	.	.	PUNCT
ejpam-5046	280	1	eur	eur	PROPN
ejpam-5046	280	2	.	.	PUNCT
ejpam-5046	281	1	j.	j.	PROPN
ejpam-5046	281	2	pure	pure	PROPN
ejpam-5046	281	3	appl	appl	PROPN
ejpam-5046	281	4	.	.	PUNCT
ejpam-5046	281	5	math	math	PROPN
ejpam-5046	281	6	.	.	PUNCT
ejpam-5046	281	7	,	,	PUNCT
ejpam-5046	281	8	16(4):2597–2612	16(4):2597–2612	NUM
ejpam-5046	281	9	,	,	PUNCT
ejpam-5046	281	10	2023	2023	NUM
ejpam-5046	281	11	.	.	PUNCT
ejpam-5046	282	1	[	[	X
ejpam-5046	282	2	12	12	NUM
ejpam-5046	282	3	]	]	PUNCT
ejpam-5046	282	4	j.	j.	PROPN
ejpam-5046	282	5	hassan	hassan	PROPN
ejpam-5046	282	6	,	,	PUNCT
ejpam-5046	282	7	a.	a.	PROPN
ejpam-5046	282	8	lintasan	lintasan	PROPN
ejpam-5046	282	9	,	,	PUNCT
ejpam-5046	282	10	and	and	CCONJ
ejpam-5046	282	11	n.h	n.h	PROPN
ejpam-5046	282	12	.	.	PUNCT
ejpam-5046	283	1	mohammad	mohammad	PROPN
ejpam-5046	283	2	.	.	PUNCT
ejpam-5046	284	1	some	some	DET
ejpam-5046	284	2	properties	property	NOUN
ejpam-5046	284	3	and	and	CCONJ
ejpam-5046	284	4	realization	realization	NOUN
ejpam-5046	284	5	problems	problem	NOUN
ejpam-5046	284	6	involving	involve	VERB
ejpam-5046	284	7	connected	connected	ADJ
ejpam-5046	284	8	outer	outer	ADJ
ejpam-5046	284	9	-	-	PUNCT
ejpam-5046	284	10	hop	hop	NOUN
ejpam-5046	284	11	independent	independent	ADJ
ejpam-5046	284	12	hop	hop	NOUN
ejpam-5046	284	13	domination	domination	NOUN
ejpam-5046	284	14	in	in	ADP
ejpam-5046	284	15	graphs	graph	NOUN
ejpam-5046	284	16	.	.	PUNCT
ejpam-5046	285	1	eur	eur	PROPN
ejpam-5046	285	2	.	.	PUNCT
ejpam-5046	286	1	j.	j.	PROPN
ejpam-5046	286	2	pure	pure	PROPN
ejpam-5046	286	3	appl	appl	PROPN
ejpam-5046	286	4	.	.	PUNCT
ejpam-5046	286	5	math	math	PROPN
ejpam-5046	286	6	.	.	PUNCT
ejpam-5046	286	7	,	,	PUNCT
ejpam-5046	286	8	16(3):1848–1861	16(3):1848–1861	NUM
ejpam-5046	286	9	,	,	PUNCT
ejpam-5046	286	10	2023	2023	NUM
ejpam-5046	286	11	.	.	PUNCT
ejpam-5046	287	1	[	[	X
ejpam-5046	287	2	13	13	NUM
ejpam-5046	287	3	]	]	PUNCT
ejpam-5046	287	4	s.	s.	PROPN
ejpam-5046	287	5	canoy	canoy	PROPN
ejpam-5046	287	6	jr	jr	PROPN
ejpam-5046	287	7	.	.	PROPN
ejpam-5046	287	8	and	and	CCONJ
ejpam-5046	287	9	j.	j.	PROPN
ejpam-5046	287	10	hassan	hassan	PROPN
ejpam-5046	287	11	.	.	PUNCT
ejpam-5046	288	1	weakly	weakly	ADJ
ejpam-5046	288	2	convex	convex	VERB
ejpam-5046	288	3	hop	hop	NOUN
ejpam-5046	288	4	dominating	dominating	NOUN
ejpam-5046	288	5	sets	set	NOUN
ejpam-5046	288	6	in	in	ADP
ejpam-5046	288	7	graphs	graph	NOUN
ejpam-5046	288	8	.	.	PUNCT
ejpam-5046	289	1	eur	eur	PROPN
ejpam-5046	289	2	.	.	PUNCT
ejpam-5046	290	1	j.	j.	PROPN
ejpam-5046	290	2	pure	pure	PROPN
ejpam-5046	290	3	appl	appl	PROPN
ejpam-5046	290	4	.	.	PUNCT
ejpam-5046	290	5	math	math	PROPN
ejpam-5046	290	6	.	.	PUNCT
ejpam-5046	290	7	,	,	PUNCT
ejpam-5046	290	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-5046	290	9	,	,	PUNCT
ejpam-5046	290	10	2022	2022	NUM
ejpam-5046	290	11	.	.	PUNCT
ejpam-5046	291	1	references	reference	NOUN
ejpam-5046	291	2	1293	1293	NUM
ejpam-5046	291	3	[	[	X
ejpam-5046	291	4	14	14	NUM
ejpam-5046	291	5	]	]	X
ejpam-5046	291	6	s.	s.	PROPN
ejpam-5046	291	7	kaida	kaida	PROPN
ejpam-5046	291	8	,	,	PUNCT
ejpam-5046	291	9	k.j	k.j	PROPN
ejpam-5046	291	10	.	.	PROPN
ejpam-5046	291	11	maharajul	maharajul	PROPN
ejpam-5046	291	12	,	,	PUNCT
ejpam-5046	291	13	j.	j.	PROPN
ejpam-5046	291	14	hassan	hassan	PROPN
ejpam-5046	291	15	,	,	PUNCT
ejpam-5046	291	16	l.	l.	PROPN
ejpam-5046	291	17	s.	s.	PROPN
ejpam-5046	291	18	laja	laja	PROPN
ejpam-5046	291	19	,	,	PUNCT
ejpam-5046	291	20	a.b	a.b	PROPN
ejpam-5046	291	21	.	.	PROPN
ejpam-5046	291	22	lintasan	lintasan	PROPN
ejpam-5046	291	23	,	,	PUNCT
ejpam-5046	291	24	and	and	CCONJ
ejpam-5046	291	25	a.a	a.a	PROPN
ejpam-5046	291	26	.	.	PROPN
ejpam-5046	291	27	pablo	pablo	PROPN
ejpam-5046	291	28	.	.	PUNCT
ejpam-5046	292	1	certified	certify	VERB
ejpam-5046	292	2	hop	hop	NOUN
ejpam-5046	292	3	independence	independence	NOUN
ejpam-5046	292	4	:	:	PUNCT
ejpam-5046	292	5	properties	property	NOUN
ejpam-5046	292	6	and	and	CCONJ
ejpam-5046	292	7	connections	connection	NOUN
ejpam-5046	292	8	with	with	ADP
ejpam-5046	292	9	other	other	ADJ
ejpam-5046	292	10	variants	variant	NOUN
ejpam-5046	292	11	of	of	ADP
ejpam-5046	292	12	independence	independence	NOUN
ejpam-5046	292	13	.	.	PUNCT
ejpam-5046	293	1	eur	eur	PROPN
ejpam-5046	293	2	.	.	PUNCT
ejpam-5046	294	1	j.	j.	PROPN
ejpam-5046	294	2	pure	pure	PROPN
ejpam-5046	294	3	appl	appl	PROPN
ejpam-5046	294	4	.	.	PUNCT
ejpam-5046	294	5	math	math	PROPN
ejpam-5046	294	6	.	.	PUNCT
ejpam-5046	294	7	,	,	PUNCT
ejpam-5046	294	8	17(1):435–444	17(1):435–444	NUM
ejpam-5046	294	9	,	,	PUNCT
ejpam-5046	294	10	2024	2024	NUM
ejpam-5046	294	11	.	.	PUNCT
ejpam-5046	295	1	[	[	X
ejpam-5046	295	2	15	15	NUM
ejpam-5046	295	3	]	]	X
ejpam-5046	295	4	j.	j.	PROPN
ejpam-5046	295	5	manditong	manditong	PROPN
ejpam-5046	295	6	,	,	PUNCT
ejpam-5046	295	7	j.	j.	PROPN
ejpam-5046	295	8	hassan	hassan	PROPN
ejpam-5046	295	9	,	,	PUNCT
ejpam-5046	295	10	ls	ls	PROPN
ejpam-5046	295	11	laja	laja	PROPN
ejpam-5046	295	12	,	,	PUNCT
ejpam-5046	295	13	aa	aa	INTJ
ejpam-5046	295	14	.	.	PUNCT
ejpam-5046	295	15	laja	laja	PROPN
ejpam-5046	295	16	,	,	PUNCT
ejpam-5046	295	17	nhm	nhm	PROPN
ejpam-5046	295	18	.	.	PUNCT
ejpam-5046	295	19	mohammad	mohammad	PROPN
ejpam-5046	295	20	,	,	PUNCT
ejpam-5046	295	21	and	and	CCONJ
ejpam-5046	295	22	su	su	PROPN
ejpam-5046	295	23	.	.	PROPN
ejpam-5046	295	24	kamdon	kamdon	PROPN
ejpam-5046	295	25	.	.	PUNCT
ejpam-5046	296	1	connected	connected	ADJ
ejpam-5046	296	2	outer	outer	ADJ
ejpam-5046	296	3	-	-	PUNCT
ejpam-5046	296	4	hop	hop	NOUN
ejpam-5046	296	5	independent	independent	ADJ
ejpam-5046	296	6	dominating	dominating	NOUN
ejpam-5046	296	7	sets	set	NOUN
ejpam-5046	296	8	in	in	ADP
ejpam-5046	296	9	graphs	graph	NOUN
ejpam-5046	296	10	under	under	ADP
ejpam-5046	296	11	some	some	DET
ejpam-5046	296	12	binary	binary	ADJ
ejpam-5046	296	13	operations	operation	NOUN
ejpam-5046	296	14	.	.	PUNCT
ejpam-5046	297	1	eur	eur	PROPN
ejpam-5046	297	2	.	.	PUNCT
ejpam-5046	298	1	j.	j.	PROPN
ejpam-5046	298	2	pure	pure	PROPN
ejpam-5046	298	3	appl	appl	PROPN
ejpam-5046	298	4	.	.	PUNCT
ejpam-5046	298	5	math	math	PROPN
ejpam-5046	298	6	.	.	PUNCT
ejpam-5046	298	7	,	,	PUNCT
ejpam-5046	299	1	16(3):1817–1829	16(3):1817–1829	NUM
ejpam-5046	299	2	,	,	PUNCT
ejpam-5046	299	3	2023	2023	NUM
ejpam-5046	299	4	.	.	PUNCT
ejpam-5046	300	1	[	[	X
ejpam-5046	300	2	16	16	NUM
ejpam-5046	300	3	]	]	X
ejpam-5046	300	4	j.	j.	PROPN
ejpam-5046	300	5	manditong	manditong	PROPN
ejpam-5046	300	6	,	,	PUNCT
ejpam-5046	300	7	a.	a.	NOUN
ejpam-5046	300	8	tapeing	tapeing	NOUN
ejpam-5046	300	9	,	,	PUNCT
ejpam-5046	300	10	j.	j.	PROPN
ejpam-5046	300	11	hassan	hassan	PROPN
ejpam-5046	300	12	,	,	PUNCT
ejpam-5046	300	13	a.r	a.r	PROPN
ejpam-5046	300	14	.	.	PROPN
ejpam-5046	300	15	bakkang	bakkang	PROPN
ejpam-5046	300	16	,	,	PUNCT
ejpam-5046	300	17	n.h	n.h	PROPN
ejpam-5046	300	18	.	.	PUNCT
ejpam-5046	300	19	mohammad	mohammad	PROPN
ejpam-5046	300	20	,	,	PUNCT
ejpam-5046	300	21	and	and	CCONJ
ejpam-5046	300	22	s.u	s.u	PROPN
ejpam-5046	300	23	.	.	PROPN
ejpam-5046	300	24	kamdon	kamdon	PROPN
ejpam-5046	300	25	.	.	PUNCT
ejpam-5046	301	1	some	some	DET
ejpam-5046	301	2	properties	property	NOUN
ejpam-5046	301	3	of	of	ADP
ejpam-5046	301	4	zero	zero	NUM
ejpam-5046	301	5	forcing	force	VERB
ejpam-5046	301	6	hop	hop	NOUN
ejpam-5046	301	7	dominating	dominating	NOUN
ejpam-5046	301	8	sets	set	NOUN
ejpam-5046	301	9	in	in	ADP
ejpam-5046	301	10	a	a	DET
ejpam-5046	301	11	graph	graph	NOUN
ejpam-5046	301	12	.	.	PUNCT
ejpam-5046	302	1	eur	eur	PROPN
ejpam-5046	302	2	.	.	PUNCT
ejpam-5046	303	1	j.	j.	PROPN
ejpam-5046	303	2	pure	pure	PROPN
ejpam-5046	303	3	appl	appl	PROPN
ejpam-5046	303	4	.	.	PUNCT
ejpam-5046	303	5	math	math	PROPN
ejpam-5046	303	6	.	.	PUNCT
ejpam-5046	304	1	,	,	PUNCT
ejpam-5046	304	2	17(1):324–337	17(1):324–337	PROPN
ejpam-5046	304	3	,	,	PUNCT
ejpam-5046	304	4	2024	2024	NUM
ejpam-5046	304	5	.	.	PUNCT