id	sid	tid	token	lemma	pos
ejpam-6544	1	1	european	european	PROPN
ejpam-6544	1	2	journal	journal	PROPN
ejpam-6544	1	3	of	of	ADP
ejpam-6544	1	4	pure	pure	ADJ
ejpam-6544	1	5	and	and	CCONJ
ejpam-6544	1	6	applied	applied	ADJ
ejpam-6544	1	7	mathematics	mathematic	NOUN
ejpam-6544	1	8	2025	2025	NUM
ejpam-6544	1	9	,	,	PUNCT
ejpam-6544	1	10	vol	vol	NOUN
ejpam-6544	1	11	.	.	PROPN
ejpam-6544	1	12	18	18	NUM
ejpam-6544	1	13	,	,	PUNCT
ejpam-6544	1	14	issue	issue	NOUN
ejpam-6544	1	15	3	3	NUM
ejpam-6544	1	16	,	,	PUNCT
ejpam-6544	1	17	article	article	NOUN
ejpam-6544	1	18	number	number	NOUN
ejpam-6544	1	19	6544	6544	NUM
ejpam-6544	1	20	issn	issn	PROPN
ejpam-6544	1	21	1307	1307	NUM
ejpam-6544	1	22	-	-	SYM
ejpam-6544	1	23	5543	5543	NUM
ejpam-6544	1	24	–	–	PUNCT
ejpam-6544	1	25	ejpam.com	ejpam.com	X
ejpam-6544	1	26	published	publish	VERB
ejpam-6544	1	27	by	by	ADP
ejpam-6544	1	28	new	new	PROPN
ejpam-6544	1	29	york	york	PROPN
ejpam-6544	1	30	business	business	PROPN
ejpam-6544	1	31	global	global	PROPN
ejpam-6544	1	32	failed	fail	VERB
ejpam-6544	1	33	2	2	NUM
ejpam-6544	1	34	-	-	PUNCT
ejpam-6544	1	35	distance	distance	NOUN
ejpam-6544	1	36	zero	zero	NUM
ejpam-6544	1	37	forcing	force	VERB
ejpam-6544	1	38	numbers	number	NOUN
ejpam-6544	1	39	of	of	ADP
ejpam-6544	1	40	some	some	DET
ejpam-6544	1	41	graphs	graph	NOUN
ejpam-6544	1	42	al	al	PROPN
ejpam-6544	1	43	-	-	PUNCT
ejpam-6544	1	44	fadzri	fadzri	PROPN
ejpam-6544	1	45	p.	p.	PROPN
ejpam-6544	1	46	madjatul1	madjatul1	PROPN
ejpam-6544	1	47	,	,	PUNCT
ejpam-6544	1	48	javier	javier	PROPN
ejpam-6544	1	49	a.	a.	PROPN
ejpam-6544	1	50	hassan1,2,∗	hassan1,2,∗	PROPN
ejpam-6544	1	51	,	,	PUNCT
ejpam-6544	1	52	maria	maria	PROPN
ejpam-6544	1	53	andrea	andrea	PROPN
ejpam-6544	1	54	o.	o.	PROPN
ejpam-6544	1	55	bonsocan3	bonsocan3	PROPN
ejpam-6544	1	56	,	,	PUNCT
ejpam-6544	1	57	vergel	vergel	NOUN
ejpam-6544	1	58	t.	t.	NOUN
ejpam-6544	1	59	bilar3	bilar3	NOUN
ejpam-6544	1	60	1department	1department	NUM
ejpam-6544	1	61	of	of	ADP
ejpam-6544	1	62	mathematics	mathematic	NOUN
ejpam-6544	1	63	,	,	PUNCT
ejpam-6544	1	64	college	college	NOUN
ejpam-6544	1	65	of	of	ADP
ejpam-6544	1	66	arts	art	NOUN
ejpam-6544	1	67	and	and	CCONJ
ejpam-6544	1	68	sciences	science	NOUN
ejpam-6544	1	69	,	,	PUNCT
ejpam-6544	1	70	msu	msu	PROPN
ejpam-6544	1	71	tawi	tawi	PROPN
ejpam-6544	1	72	-	-	PUNCT
ejpam-6544	1	73	tawi	tawi	PROPN
ejpam-6544	1	74	college	college	PROPN
ejpam-6544	1	75	of	of	ADP
ejpam-6544	1	76	technology	technology	NOUN
ejpam-6544	1	77	and	and	CCONJ
ejpam-6544	1	78	oceanography	oceanography	NOUN
ejpam-6544	1	79	,	,	PUNCT
ejpam-6544	1	80	bongao	bongao	NOUN
ejpam-6544	1	81	,	,	PUNCT
ejpam-6544	1	82	tawi	tawi	NOUN
ejpam-6544	1	83	-	-	PUNCT
ejpam-6544	1	84	tawi	tawi	NOUN
ejpam-6544	1	85	,	,	PUNCT
ejpam-6544	1	86	philippines	philippine	NOUN
ejpam-6544	1	87	2department	2department	NUM
ejpam-6544	1	88	of	of	ADP
ejpam-6544	1	89	mathematics	mathematic	NOUN
ejpam-6544	1	90	,	,	PUNCT
ejpam-6544	1	91	college	college	NOUN
ejpam-6544	1	92	of	of	ADP
ejpam-6544	1	93	science	science	PROPN
ejpam-6544	1	94	,	,	PUNCT
ejpam-6544	1	95	korea	korea	PROPN
ejpam-6544	1	96	university	university	PROPN
ejpam-6544	1	97	,	,	PUNCT
ejpam-6544	1	98	seoul	seoul	PROPN
ejpam-6544	1	99	,	,	PUNCT
ejpam-6544	1	100	south	south	PROPN
ejpam-6544	1	101	korea	korea	PROPN
ejpam-6544	2	1	3department	3department	NUM
ejpam-6544	2	2	of	of	ADP
ejpam-6544	2	3	mathematics	mathematic	NOUN
ejpam-6544	2	4	,	,	PUNCT
ejpam-6544	2	5	ateneo	ateneo	X
ejpam-6544	2	6	de	de	PROPN
ejpam-6544	2	7	davao	davao	PROPN
ejpam-6544	2	8	university	university	PROPN
ejpam-6544	2	9	,	,	PUNCT
ejpam-6544	2	10	davao	davao	PROPN
ejpam-6544	2	11	city	city	PROPN
ejpam-6544	2	12	,	,	PUNCT
ejpam-6544	2	13	philippines	philippine	NOUN
ejpam-6544	2	14	abstract	abstract	ADJ
ejpam-6544	2	15	.	.	PUNCT
ejpam-6544	3	1	let	let	VERB
ejpam-6544	3	2	g	g	PROPN
ejpam-6544	3	3	=	=	SYM
ejpam-6544	3	4	(	(	PUNCT
ejpam-6544	3	5	v	v	NOUN
ejpam-6544	3	6	(	(	PUNCT
ejpam-6544	3	7	g	g	NOUN
ejpam-6544	3	8	)	)	PUNCT
ejpam-6544	3	9	,	,	PUNCT
ejpam-6544	3	10	e(g	e(g	PROPN
ejpam-6544	3	11	)	)	PUNCT
ejpam-6544	3	12	)	)	PUNCT
ejpam-6544	4	1	be	be	AUX
ejpam-6544	4	2	a	a	DET
ejpam-6544	4	3	simple	simple	ADJ
ejpam-6544	4	4	and	and	CCONJ
ejpam-6544	4	5	undirected	undirected	ADJ
ejpam-6544	4	6	graph	graph	NOUN
ejpam-6544	4	7	and	and	CCONJ
ejpam-6544	4	8	let	let	VERB
ejpam-6544	4	9	x	x	PRON
ejpam-6544	4	10	,	,	PUNCT
ejpam-6544	4	11	y	y	PROPN
ejpam-6544	4	12	∈	∈	PROPN
ejpam-6544	4	13	v	v	NOUN
ejpam-6544	4	14	(	(	PUNCT
ejpam-6544	4	15	g	g	NOUN
ejpam-6544	4	16	)	)	PUNCT
ejpam-6544	4	17	.	.	PUNCT
ejpam-6544	5	1	if	if	SCONJ
ejpam-6544	5	2	x	x	PRON
ejpam-6544	5	3	is	be	AUX
ejpam-6544	5	4	a	a	DET
ejpam-6544	5	5	colored	colored	ADJ
ejpam-6544	5	6	(	(	PUNCT
ejpam-6544	5	7	active	active	ADJ
ejpam-6544	5	8	)	)	PUNCT
ejpam-6544	5	9	vertex	vertex	NOUN
ejpam-6544	5	10	and	and	CCONJ
ejpam-6544	5	11	exactly	exactly	ADV
ejpam-6544	5	12	one	one	NUM
ejpam-6544	5	13	hop	hop	NOUN
ejpam-6544	5	14	neighbor	neighbor	NOUN
ejpam-6544	5	15	y	y	PROPN
ejpam-6544	5	16	of	of	ADP
ejpam-6544	5	17	x	x	PRON
ejpam-6544	5	18	is	be	AUX
ejpam-6544	5	19	uncolored	uncolored	ADJ
ejpam-6544	5	20	(	(	PUNCT
ejpam-6544	5	21	inactive	inactive	ADJ
ejpam-6544	5	22	)	)	PUNCT
ejpam-6544	5	23	,	,	PUNCT
ejpam-6544	5	24	then	then	ADV
ejpam-6544	5	25	y	y	PROPN
ejpam-6544	5	26	will	will	AUX
ejpam-6544	5	27	become	become	VERB
ejpam-6544	5	28	colored	colored	ADJ
ejpam-6544	5	29	(	(	PUNCT
ejpam-6544	5	30	active	active	ADJ
ejpam-6544	5	31	)	)	PUNCT
ejpam-6544	5	32	,	,	PUNCT
ejpam-6544	5	33	and	and	CCONJ
ejpam-6544	5	34	we	we	PRON
ejpam-6544	5	35	call	call	VERB
ejpam-6544	5	36	this	this	DET
ejpam-6544	5	37	process	process	NOUN
ejpam-6544	5	38	a	a	DET
ejpam-6544	5	39	2	2	NUM
ejpam-6544	5	40	-	-	PUNCT
ejpam-6544	5	41	distance	distance	NOUN
ejpam-6544	5	42	color	color	NOUN
ejpam-6544	5	43	change	change	NOUN
ejpam-6544	5	44	rule	rule	NOUN
ejpam-6544	5	45	.	.	PUNCT
ejpam-6544	6	1	a	a	DET
ejpam-6544	6	2	2	2	NUM
ejpam-6544	6	3	-	-	PUNCT
ejpam-6544	6	4	distance	distance	NOUN
ejpam-6544	6	5	zero	zero	NUM
ejpam-6544	6	6	forcing	forcing	NOUN
ejpam-6544	6	7	set	set	NOUN
ejpam-6544	6	8	n	n	NUM
ejpam-6544	6	9	is	be	AUX
ejpam-6544	6	10	a	a	DET
ejpam-6544	6	11	subset	subset	NOUN
ejpam-6544	6	12	of	of	ADP
ejpam-6544	6	13	v	v	NOUN
ejpam-6544	6	14	(	(	PUNCT
ejpam-6544	6	15	g	g	NOUN
ejpam-6544	6	16	)	)	PUNCT
ejpam-6544	6	17	such	such	ADJ
ejpam-6544	6	18	that	that	SCONJ
ejpam-6544	6	19	when	when	SCONJ
ejpam-6544	6	20	the	the	DET
ejpam-6544	6	21	vertices	vertex	NOUN
ejpam-6544	6	22	in	in	ADP
ejpam-6544	6	23	n	n	CCONJ
ejpam-6544	6	24	are	be	AUX
ejpam-6544	6	25	colored	color	VERB
ejpam-6544	6	26	(	(	PUNCT
ejpam-6544	6	27	active	active	ADJ
ejpam-6544	6	28	)	)	PUNCT
ejpam-6544	6	29	and	and	CCONJ
ejpam-6544	6	30	the	the	DET
ejpam-6544	6	31	remaining	remain	VERB
ejpam-6544	6	32	vertices	vertex	NOUN
ejpam-6544	6	33	outside	outside	ADP
ejpam-6544	6	34	n	n	CCONJ
ejpam-6544	6	35	are	be	AUX
ejpam-6544	6	36	uncolored	uncolored	ADJ
ejpam-6544	6	37	(	(	PUNCT
ejpam-6544	6	38	inactive	inactive	ADJ
ejpam-6544	6	39	)	)	PUNCT
ejpam-6544	6	40	initially	initially	ADV
ejpam-6544	6	41	,	,	PUNCT
ejpam-6544	6	42	then	then	ADV
ejpam-6544	6	43	repeated	repeat	VERB
ejpam-6544	6	44	application	application	NOUN
ejpam-6544	6	45	of	of	ADP
ejpam-6544	6	46	a	a	DET
ejpam-6544	6	47	2	2	NUM
ejpam-6544	6	48	-	-	PUNCT
ejpam-6544	6	49	distance	distance	NOUN
ejpam-6544	6	50	color	color	NOUN
ejpam-6544	6	51	change	change	NOUN
ejpam-6544	6	52	rule	rule	NOUN
ejpam-6544	6	53	,	,	PUNCT
ejpam-6544	6	54	all	all	DET
ejpam-6544	6	55	vertices	vertex	NOUN
ejpam-6544	6	56	of	of	ADP
ejpam-6544	6	57	g	g	NOUN
ejpam-6544	6	58	will	will	AUX
ejpam-6544	6	59	become	become	VERB
ejpam-6544	6	60	colored	colored	ADJ
ejpam-6544	6	61	(	(	PUNCT
ejpam-6544	6	62	active	active	ADJ
ejpam-6544	6	63	)	)	PUNCT
ejpam-6544	6	64	.	.	PUNCT
ejpam-6544	7	1	now	now	ADV
ejpam-6544	7	2	,	,	PUNCT
ejpam-6544	7	3	a	a	DET
ejpam-6544	7	4	set	set	NOUN
ejpam-6544	7	5	m	m	NOUN
ejpam-6544	7	6	⊂	⊂	NOUN
ejpam-6544	7	7	v	v	ADJ
ejpam-6544	7	8	(	(	PUNCT
ejpam-6544	7	9	g	g	NOUN
ejpam-6544	7	10	)	)	PUNCT
ejpam-6544	7	11	is	be	AUX
ejpam-6544	7	12	called	call	VERB
ejpam-6544	7	13	a	a	DET
ejpam-6544	7	14	failed	fail	VERB
ejpam-6544	7	15	2	2	NUM
ejpam-6544	7	16	-	-	PUNCT
ejpam-6544	7	17	distance	distance	NOUN
ejpam-6544	7	18	zero	zero	NUM
ejpam-6544	7	19	forcing	force	VERB
ejpam-6544	7	20	set	set	NOUN
ejpam-6544	7	21	of	of	ADP
ejpam-6544	7	22	g	g	PROPN
ejpam-6544	7	23	if	if	SCONJ
ejpam-6544	7	24	m	m	PROPN
ejpam-6544	7	25	fails	fail	VERB
ejpam-6544	7	26	to	to	PART
ejpam-6544	7	27	be	be	AUX
ejpam-6544	7	28	a	a	DET
ejpam-6544	7	29	2	2	NUM
ejpam-6544	7	30	-	-	PUNCT
ejpam-6544	7	31	distance	distance	NOUN
ejpam-6544	7	32	zero	zero	NUM
ejpam-6544	7	33	forcing	force	VERB
ejpam-6544	7	34	set	set	NOUN
ejpam-6544	7	35	of	of	ADP
ejpam-6544	7	36	g.	g.	PROPN
ejpam-6544	7	37	the	the	DET
ejpam-6544	7	38	failed	fail	VERB
ejpam-6544	7	39	2	2	NUM
ejpam-6544	7	40	-	-	PUNCT
ejpam-6544	7	41	distance	distance	NOUN
ejpam-6544	7	42	zero	zero	NUM
ejpam-6544	7	43	forcing	force	VERB
ejpam-6544	7	44	number	number	NOUN
ejpam-6544	7	45	of	of	ADP
ejpam-6544	7	46	a	a	DET
ejpam-6544	7	47	graph	graph	NOUN
ejpam-6544	7	48	g	g	NOUN
ejpam-6544	7	49	,	,	PUNCT
ejpam-6544	7	50	denoted	denote	VERB
ejpam-6544	7	51	by	by	ADP
ejpam-6544	7	52	f	f	PROPN
ejpam-6544	7	53	2(g	2(g	NUM
ejpam-6544	7	54	)	)	PUNCT
ejpam-6544	7	55	,	,	PUNCT
ejpam-6544	7	56	is	be	AUX
ejpam-6544	7	57	the	the	DET
ejpam-6544	7	58	maximum	maximum	ADJ
ejpam-6544	7	59	cardinality	cardinality	NOUN
ejpam-6544	7	60	of	of	ADP
ejpam-6544	7	61	a	a	DET
ejpam-6544	7	62	failed	fail	VERB
ejpam-6544	7	63	2	2	NUM
ejpam-6544	7	64	-	-	PUNCT
ejpam-6544	7	65	distance	distance	NOUN
ejpam-6544	7	66	zero	zero	NUM
ejpam-6544	7	67	forcing	force	VERB
ejpam-6544	7	68	set	set	NOUN
ejpam-6544	7	69	of	of	ADP
ejpam-6544	7	70	g.	g.	PROPN
ejpam-6544	7	71	in	in	ADP
ejpam-6544	7	72	this	this	DET
ejpam-6544	7	73	paper	paper	NOUN
ejpam-6544	7	74	,	,	PUNCT
ejpam-6544	7	75	we	we	PRON
ejpam-6544	7	76	introduce	introduce	VERB
ejpam-6544	7	77	the	the	DET
ejpam-6544	7	78	said	say	VERB
ejpam-6544	7	79	parameter	parameter	NOUN
ejpam-6544	7	80	and	and	CCONJ
ejpam-6544	7	81	study	study	VERB
ejpam-6544	7	82	this	this	PRON
ejpam-6544	7	83	on	on	ADP
ejpam-6544	7	84	some	some	DET
ejpam-6544	7	85	special	special	ADJ
ejpam-6544	7	86	graphs	graph	NOUN
ejpam-6544	7	87	and	and	CCONJ
ejpam-6544	7	88	on	on	ADP
ejpam-6544	7	89	the	the	DET
ejpam-6544	7	90	join	join	NOUN
ejpam-6544	7	91	of	of	ADP
ejpam-6544	7	92	two	two	NUM
ejpam-6544	7	93	graphs	graph	NOUN
ejpam-6544	7	94	.	.	PUNCT
ejpam-6544	8	1	moreover	moreover	ADV
ejpam-6544	8	2	,	,	PUNCT
ejpam-6544	8	3	we	we	PRON
ejpam-6544	8	4	characterize	characterize	VERB
ejpam-6544	8	5	failed	fail	VERB
ejpam-6544	8	6	2	2	NUM
ejpam-6544	8	7	-	-	PUNCT
ejpam-6544	8	8	distance	distance	NOUN
ejpam-6544	8	9	zero	zero	NUM
ejpam-6544	8	10	forcing	force	VERB
ejpam-6544	8	11	sets	set	NOUN
ejpam-6544	8	12	in	in	ADP
ejpam-6544	8	13	the	the	DET
ejpam-6544	8	14	join	join	NOUN
ejpam-6544	8	15	of	of	ADP
ejpam-6544	8	16	two	two	NUM
ejpam-6544	8	17	graphs	graph	NOUN
ejpam-6544	8	18	using	use	VERB
ejpam-6544	8	19	a	a	DET
ejpam-6544	8	20	failed	failed	ADJ
ejpam-6544	8	21	co	co	ADJ
ejpam-6544	8	22	-	-	ADJ
ejpam-6544	8	23	zero	zero	ADJ
ejpam-6544	8	24	forcing	force	VERB
ejpam-6544	8	25	concept	concept	NOUN
ejpam-6544	8	26	.	.	PUNCT
ejpam-6544	9	1	finally	finally	ADV
ejpam-6544	9	2	,	,	PUNCT
ejpam-6544	9	3	we	we	PRON
ejpam-6544	9	4	derive	derive	VERB
ejpam-6544	9	5	some	some	DET
ejpam-6544	9	6	nice	nice	ADJ
ejpam-6544	9	7	formulas	formula	NOUN
ejpam-6544	9	8	for	for	ADP
ejpam-6544	9	9	computing	compute	VERB
ejpam-6544	9	10	the	the	DET
ejpam-6544	9	11	said	say	VERB
ejpam-6544	9	12	parameter	parameter	NOUN
ejpam-6544	9	13	on	on	ADP
ejpam-6544	9	14	the	the	DET
ejpam-6544	9	15	join	join	NOUN
ejpam-6544	9	16	of	of	ADP
ejpam-6544	9	17	any	any	DET
ejpam-6544	9	18	two	two	NUM
ejpam-6544	9	19	graphs	graph	NOUN
ejpam-6544	9	20	.	.	PUNCT
ejpam-6544	10	1	2020	2020	NUM
ejpam-6544	10	2	mathematics	mathematic	NOUN
ejpam-6544	10	3	subject	subject	NOUN
ejpam-6544	10	4	classifications	classification	NOUN
ejpam-6544	10	5	:	:	PUNCT
ejpam-6544	10	6	05c69	05c69	X
ejpam-6544	10	7	key	key	ADJ
ejpam-6544	10	8	words	word	NOUN
ejpam-6544	10	9	and	and	CCONJ
ejpam-6544	10	10	phrases	phrase	NOUN
ejpam-6544	10	11	:	:	PUNCT
ejpam-6544	10	12	failed	fail	VERB
ejpam-6544	10	13	2	2	NUM
ejpam-6544	10	14	-	-	PUNCT
ejpam-6544	10	15	distance	distance	NOUN
ejpam-6544	10	16	zero	zero	NUM
ejpam-6544	10	17	forcing	forcing	NOUN
ejpam-6544	10	18	set	set	NOUN
ejpam-6544	10	19	,	,	PUNCT
ejpam-6544	10	20	failed	fail	VERB
ejpam-6544	10	21	2	2	NUM
ejpam-6544	10	22	-	-	PUNCT
ejpam-6544	10	23	distance	distance	NOUN
ejpam-6544	10	24	zero	zero	NUM
ejpam-6544	10	25	forcing	force	VERB
ejpam-6544	10	26	number	number	NOUN
ejpam-6544	10	27	,	,	PUNCT
ejpam-6544	10	28	co	co	ADJ
ejpam-6544	10	29	-	-	ADJ
ejpam-6544	10	30	zero	zero	NUM
ejpam-6544	10	31	forcing	forcing	NOUN
ejpam-6544	10	32	,	,	PUNCT
ejpam-6544	10	33	failed	fail	VERB
ejpam-6544	10	34	co	co	ADJ
ejpam-6544	10	35	-	-	ADJ
ejpam-6544	10	36	zero	zero	ADJ
ejpam-6544	10	37	forcing	forcing	NOUN
ejpam-6544	10	38	set	set	NOUN
ejpam-6544	10	39	,	,	PUNCT
ejpam-6544	10	40	failed	fail	VERB
ejpam-6544	10	41	co	co	ADJ
ejpam-6544	10	42	-	-	ADJ
ejpam-6544	10	43	zero	zero	ADJ
ejpam-6544	10	44	forcing	force	VERB
ejpam-6544	10	45	number	number	NOUN
ejpam-6544	10	46	1	1	NUM
ejpam-6544	10	47	.	.	PUNCT
ejpam-6544	11	1	introduction	introduction	NOUN
ejpam-6544	11	2	the	the	DET
ejpam-6544	11	3	concept	concept	NOUN
ejpam-6544	11	4	of	of	ADP
ejpam-6544	11	5	zero	zero	NUM
ejpam-6544	11	6	forcing	forcing	NOUN
ejpam-6544	11	7	has	have	AUX
ejpam-6544	11	8	been	be	AUX
ejpam-6544	11	9	explored	explore	VERB
ejpam-6544	11	10	over	over	ADP
ejpam-6544	11	11	the	the	DET
ejpam-6544	11	12	past	past	ADJ
ejpam-6544	11	13	few	few	ADJ
ejpam-6544	11	14	years	year	NOUN
ejpam-6544	11	15	because	because	SCONJ
ejpam-6544	11	16	of	of	ADP
ejpam-6544	11	17	its	its	PRON
ejpam-6544	11	18	application	application	NOUN
ejpam-6544	11	19	to	to	ADP
ejpam-6544	11	20	minimum	minimum	ADJ
ejpam-6544	11	21	rank	rank	NOUN
ejpam-6544	11	22	problems	problem	NOUN
ejpam-6544	12	1	[	[	X
ejpam-6544	12	2	1	1	NUM
ejpam-6544	12	3	,	,	PUNCT
ejpam-6544	12	4	2	2	NUM
ejpam-6544	12	5	]	]	PUNCT
ejpam-6544	12	6	.	.	PUNCT
ejpam-6544	13	1	the	the	DET
ejpam-6544	13	2	zero	zero	NUM
ejpam-6544	13	3	forcing	forcing	NOUN
ejpam-6544	13	4	process	process	NOUN
ejpam-6544	13	5	was	be	AUX
ejpam-6544	13	6	initially	initially	ADV
ejpam-6544	13	7	∗corresponding	∗corresponde	VERB
ejpam-6544	13	8	author	author	NOUN
ejpam-6544	13	9	.	.	PUNCT
ejpam-6544	14	1	doi	doi	NOUN
ejpam-6544	14	2	:	:	PUNCT
ejpam-6544	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6544	https://doi.org/10.29020/nybg.ejpam.v18i3.6544	PROPN
ejpam-6544	14	4	email	email	NOUN
ejpam-6544	14	5	addresses	address	VERB
ejpam-6544	14	6	:	:	PUNCT
ejpam-6544	14	7	alfadzrimadjatul@msutawi-tawi.edu.ph	alfadzrimadjatul@msutawi-tawi.edu.ph	PROPN
ejpam-6544	14	8	(	(	PUNCT
ejpam-6544	14	9	a.	a.	NOUN
ejpam-6544	14	10	madjatul	madjatul	PROPN
ejpam-6544	14	11	)	)	PUNCT
ejpam-6544	14	12	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-6544	14	13	(	(	PUNCT
ejpam-6544	14	14	j.	j.	PROPN
ejpam-6544	14	15	hassan	hassan	PROPN
ejpam-6544	14	16	)	)	PUNCT
ejpam-6544	15	1	maobonsocan@addu.edu.ph	maobonsocan@addu.edu.ph	PROPN
ejpam-6544	15	2	(	(	PUNCT
ejpam-6544	15	3	m.a	m.a	PROPN
ejpam-6544	15	4	.	.	PROPN
ejpam-6544	15	5	bonsocan	bonsocan	PROPN
ejpam-6544	15	6	)	)	PUNCT
ejpam-6544	16	1	vtbilar@addu.edu.ph	vtbilar@addu.edu.ph	NOUN
ejpam-6544	16	2	(	(	PUNCT
ejpam-6544	16	3	v.	v.	X
ejpam-6544	16	4	bilar	bilar	PROPN
ejpam-6544	16	5	)	)	PUNCT
ejpam-6544	16	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6544	17	1	1	1	NUM
ejpam-6544	17	2	copyright	copyright	NOUN
ejpam-6544	17	3	:	:	PUNCT
ejpam-6544	17	4	©	©	PROPN
ejpam-6544	17	5	2025	2025	NUM
ejpam-6544	17	6	the	the	DET
ejpam-6544	17	7	author(s	author(s	NOUN
ejpam-6544	17	8	)	)	PUNCT
ejpam-6544	17	9	.	.	PUNCT
ejpam-6544	18	1	(	(	PUNCT
ejpam-6544	18	2	cc	cc	NOUN
ejpam-6544	18	3	by	by	ADP
ejpam-6544	18	4	-	-	PUNCT
ejpam-6544	18	5	nc	nc	PROPN
ejpam-6544	18	6	4.0	4.0	NUM
ejpam-6544	18	7	)	)	PUNCT
ejpam-6544	18	8	a.	a.	NOUN
ejpam-6544	18	9	madjatul	madjatul	NOUN
ejpam-6544	18	10	et	et	PROPN
ejpam-6544	18	11	al	al	PROPN
ejpam-6544	18	12	.	.	PUNCT
ejpam-6544	18	13	/	/	SYM
ejpam-6544	18	14	eur	eur	PROPN
ejpam-6544	18	15	.	.	PUNCT
ejpam-6544	19	1	j.	j.	PROPN
ejpam-6544	19	2	pure	pure	PROPN
ejpam-6544	19	3	appl	appl	PROPN
ejpam-6544	19	4	.	.	PROPN
ejpam-6544	19	5	math	math	PROPN
ejpam-6544	19	6	,	,	PUNCT
ejpam-6544	19	7	18	18	NUM
ejpam-6544	19	8	(	(	PUNCT
ejpam-6544	19	9	3	3	NUM
ejpam-6544	19	10	)	)	PUNCT
ejpam-6544	19	11	(	(	PUNCT
ejpam-6544	19	12	2025	2025	NUM
ejpam-6544	19	13	)	)	PUNCT
ejpam-6544	19	14	,	,	PUNCT
ejpam-6544	19	15	6544	6544	NUM
ejpam-6544	19	16	2	2	NUM
ejpam-6544	19	17	of	of	ADP
ejpam-6544	19	18	8	8	NUM
ejpam-6544	19	19	proposed	propose	VERB
ejpam-6544	19	20	in	in	ADP
ejpam-6544	19	21	[	[	X
ejpam-6544	19	22	3	3	NUM
ejpam-6544	19	23	]	]	PUNCT
ejpam-6544	19	24	,	,	PUNCT
ejpam-6544	19	25	and	and	CCONJ
ejpam-6544	19	26	has	have	AUX
ejpam-6544	19	27	been	be	AUX
ejpam-6544	19	28	further	far	ADV
ejpam-6544	19	29	studied	study	VERB
ejpam-6544	19	30	on	on	ADP
ejpam-6544	19	31	different	different	ADJ
ejpam-6544	19	32	types	type	NOUN
ejpam-6544	19	33	of	of	ADP
ejpam-6544	19	34	graphs	graph	NOUN
ejpam-6544	19	35	.	.	PUNCT
ejpam-6544	20	1	some	some	DET
ejpam-6544	20	2	studies	study	NOUN
ejpam-6544	20	3	on	on	ADP
ejpam-6544	20	4	this	this	DET
ejpam-6544	20	5	parameter	parameter	NOUN
ejpam-6544	20	6	can	can	AUX
ejpam-6544	20	7	be	be	AUX
ejpam-6544	20	8	found	find	VERB
ejpam-6544	20	9	in	in	ADP
ejpam-6544	20	10	[	[	X
ejpam-6544	20	11	4–13	4–13	X
ejpam-6544	20	12	]	]	PUNCT
ejpam-6544	20	13	.	.	PUNCT
ejpam-6544	21	1	in	in	ADP
ejpam-6544	21	2	2015	2015	NUM
ejpam-6544	21	3	,	,	PUNCT
ejpam-6544	21	4	k.	k.	PROPN
ejpam-6544	21	5	fetcie	fetcie	PROPN
ejpam-6544	21	6	,	,	PUNCT
ejpam-6544	21	7	b.	b.	PROPN
ejpam-6544	21	8	jacob	jacob	PROPN
ejpam-6544	21	9	and	and	CCONJ
ejpam-6544	21	10	d.	d.	PROPN
ejpam-6544	21	11	saavedra	saavedra	PROPN
ejpam-6544	21	12	introduced	introduce	VERB
ejpam-6544	21	13	a	a	DET
ejpam-6544	21	14	new	new	ADJ
ejpam-6544	21	15	graph	graph	NOUN
ejpam-6544	21	16	parameter	parameter	NOUN
ejpam-6544	21	17	,	,	PUNCT
ejpam-6544	21	18	the	the	DET
ejpam-6544	21	19	failed	fail	VERB
ejpam-6544	21	20	zero	zero	NUM
ejpam-6544	21	21	forcing	force	VERB
ejpam-6544	21	22	number	number	NOUN
ejpam-6544	21	23	of	of	ADP
ejpam-6544	21	24	a	a	DET
ejpam-6544	21	25	graph	graph	NOUN
ejpam-6544	21	26	.	.	PUNCT
ejpam-6544	22	1	they	they	PRON
ejpam-6544	22	2	established	establish	VERB
ejpam-6544	22	3	bounds	bound	NOUN
ejpam-6544	22	4	on	on	ADP
ejpam-6544	22	5	the	the	DET
ejpam-6544	22	6	failed	failed	ADJ
ejpam-6544	22	7	zero	zero	NUM
ejpam-6544	22	8	forcing	force	VERB
ejpam-6544	22	9	number	number	NOUN
ejpam-6544	22	10	of	of	ADP
ejpam-6544	22	11	a	a	DET
ejpam-6544	22	12	graph	graph	NOUN
ejpam-6544	22	13	,	,	PUNCT
ejpam-6544	22	14	both	both	CCONJ
ejpam-6544	22	15	in	in	ADP
ejpam-6544	22	16	general	general	ADJ
ejpam-6544	22	17	and	and	CCONJ
ejpam-6544	22	18	for	for	ADP
ejpam-6544	22	19	connected	connected	ADJ
ejpam-6544	22	20	graph	graph	NOUN
ejpam-6544	22	21	.	.	PUNCT
ejpam-6544	23	1	some	some	DET
ejpam-6544	23	2	studies	study	NOUN
ejpam-6544	23	3	on	on	ADP
ejpam-6544	23	4	this	this	DET
ejpam-6544	23	5	parameter	parameter	NOUN
ejpam-6544	23	6	can	can	AUX
ejpam-6544	23	7	be	be	AUX
ejpam-6544	23	8	found	find	VERB
ejpam-6544	23	9	in	in	ADP
ejpam-6544	23	10	[	[	NOUN
ejpam-6544	23	11	14–17	14–17	NUM
ejpam-6544	23	12	]	]	PUNCT
ejpam-6544	23	13	.	.	PUNCT
ejpam-6544	24	1	in	in	ADP
ejpam-6544	24	2	a	a	DET
ejpam-6544	24	3	recent	recent	ADJ
ejpam-6544	24	4	year	year	NOUN
ejpam-6544	24	5	,	,	PUNCT
ejpam-6544	24	6	j.	j.	PROPN
ejpam-6544	24	7	hassan	hassan	PROPN
ejpam-6544	24	8	et	et	PROPN
ejpam-6544	24	9	al	al	PROPN
ejpam-6544	24	10	.	.	PROPN
ejpam-6544	24	11	introduced	introduce	VERB
ejpam-6544	24	12	the	the	DET
ejpam-6544	24	13	concept	concept	NOUN
ejpam-6544	24	14	of	of	ADP
ejpam-6544	24	15	2	2	NUM
ejpam-6544	24	16	-	-	PUNCT
ejpam-6544	24	17	distance	distance	NOUN
ejpam-6544	24	18	zero	zero	NUM
ejpam-6544	24	19	forcing	force	VERB
ejpam-6544	24	20	sets	set	NOUN
ejpam-6544	24	21	in	in	ADP
ejpam-6544	24	22	a	a	DET
ejpam-6544	24	23	graph	graph	NOUN
ejpam-6544	24	24	[	[	X
ejpam-6544	24	25	18	18	NUM
ejpam-6544	24	26	]	]	PUNCT
ejpam-6544	24	27	.	.	PUNCT
ejpam-6544	25	1	the	the	DET
ejpam-6544	25	2	said	say	VERB
ejpam-6544	25	3	concept	concept	NOUN
ejpam-6544	25	4	is	be	AUX
ejpam-6544	25	5	another	another	DET
ejpam-6544	25	6	variant	variant	NOUN
ejpam-6544	25	7	of	of	ADP
ejpam-6544	25	8	zero	zero	NUM
ejpam-6544	25	9	forcing	forcing	NOUN
ejpam-6544	25	10	wherein	wherein	SCONJ
ejpam-6544	25	11	its	its	PRON
ejpam-6544	25	12	color	color	NOUN
ejpam-6544	25	13	change	change	NOUN
ejpam-6544	25	14	property	property	NOUN
ejpam-6544	25	15	differs	differ	NOUN
ejpam-6544	25	16	from	from	ADP
ejpam-6544	25	17	the	the	DET
ejpam-6544	25	18	standard	standard	ADJ
ejpam-6544	25	19	color	color	NOUN
ejpam-6544	25	20	change	change	NOUN
ejpam-6544	25	21	rule	rule	NOUN
ejpam-6544	25	22	.	.	PUNCT
ejpam-6544	26	1	particularly	particularly	ADV
ejpam-6544	26	2	,	,	PUNCT
ejpam-6544	26	3	the	the	DET
ejpam-6544	26	4	distance	distance	NOUN
ejpam-6544	26	5	condition	condition	NOUN
ejpam-6544	26	6	has	have	AUX
ejpam-6544	26	7	extended	extend	VERB
ejpam-6544	26	8	to	to	ADP
ejpam-6544	26	9	two	two	NUM
ejpam-6544	26	10	.	.	PUNCT
ejpam-6544	27	1	they	they	PRON
ejpam-6544	27	2	had	have	AUX
ejpam-6544	27	3	initially	initially	ADV
ejpam-6544	27	4	investigated	investigate	VERB
ejpam-6544	27	5	the	the	DET
ejpam-6544	27	6	said	say	VERB
ejpam-6544	27	7	concept	concept	NOUN
ejpam-6544	27	8	on	on	ADP
ejpam-6544	27	9	some	some	DET
ejpam-6544	27	10	special	special	ADJ
ejpam-6544	27	11	types	type	NOUN
ejpam-6544	27	12	of	of	ADP
ejpam-6544	27	13	graphs	graph	NOUN
ejpam-6544	27	14	,	,	PUNCT
ejpam-6544	27	15	and	and	CCONJ
ejpam-6544	27	16	presented	present	VERB
ejpam-6544	27	17	some	some	DET
ejpam-6544	27	18	relationships	relationship	NOUN
ejpam-6544	27	19	with	with	ADP
ejpam-6544	27	20	other	other	ADJ
ejpam-6544	27	21	parameters	parameter	NOUN
ejpam-6544	27	22	.	.	PUNCT
ejpam-6544	28	1	in	in	ADP
ejpam-6544	28	2	particular	particular	ADJ
ejpam-6544	28	3	,	,	PUNCT
ejpam-6544	28	4	they	they	PRON
ejpam-6544	28	5	have	have	AUX
ejpam-6544	28	6	shown	show	VERB
ejpam-6544	28	7	that	that	SCONJ
ejpam-6544	28	8	this	this	DET
ejpam-6544	28	9	new	new	ADJ
ejpam-6544	28	10	variant	variant	NOUN
ejpam-6544	28	11	is	be	AUX
ejpam-6544	28	12	incomparable	incomparable	ADJ
ejpam-6544	28	13	with	with	ADP
ejpam-6544	28	14	the	the	DET
ejpam-6544	28	15	usual	usual	ADJ
ejpam-6544	28	16	zero	zero	NUM
ejpam-6544	28	17	forcing	forcing	NOUN
ejpam-6544	28	18	.	.	PUNCT
ejpam-6544	29	1	in	in	ADP
ejpam-6544	29	2	this	this	DET
ejpam-6544	29	3	study	study	NOUN
ejpam-6544	29	4	,	,	PUNCT
ejpam-6544	29	5	a	a	DET
ejpam-6544	29	6	new	new	ADJ
ejpam-6544	29	7	concept	concept	NOUN
ejpam-6544	29	8	related	relate	VERB
ejpam-6544	29	9	to	to	ADP
ejpam-6544	29	10	a	a	DET
ejpam-6544	29	11	2	2	NUM
ejpam-6544	29	12	-	-	PUNCT
ejpam-6544	29	13	distance	distance	NOUN
ejpam-6544	29	14	zero	zero	NUM
ejpam-6544	29	15	forcing	force	VERB
ejpam-6544	29	16	in	in	ADP
ejpam-6544	29	17	a	a	DET
ejpam-6544	29	18	graph	graph	NOUN
ejpam-6544	29	19	is	be	AUX
ejpam-6544	29	20	introduced	introduce	VERB
ejpam-6544	29	21	and	and	CCONJ
ejpam-6544	29	22	initially	initially	ADV
ejpam-6544	29	23	investigated	investigate	VERB
ejpam-6544	29	24	on	on	ADP
ejpam-6544	29	25	some	some	DET
ejpam-6544	29	26	families	family	NOUN
ejpam-6544	29	27	of	of	ADP
ejpam-6544	29	28	graphs	graph	NOUN
ejpam-6544	29	29	and	and	CCONJ
ejpam-6544	29	30	on	on	ADP
ejpam-6544	29	31	the	the	DET
ejpam-6544	29	32	join	join	NOUN
ejpam-6544	29	33	of	of	ADP
ejpam-6544	29	34	any	any	DET
ejpam-6544	29	35	two	two	NUM
ejpam-6544	29	36	graphs	graph	NOUN
ejpam-6544	29	37	,	,	PUNCT
ejpam-6544	29	38	and	and	CCONJ
ejpam-6544	29	39	we	we	PRON
ejpam-6544	29	40	call	call	VERB
ejpam-6544	29	41	it	it	PRON
ejpam-6544	29	42	a	a	DET
ejpam-6544	29	43	failed	failed	ADJ
ejpam-6544	29	44	2	2	NUM
ejpam-6544	29	45	-	-	PUNCT
ejpam-6544	29	46	distance	distance	NOUN
ejpam-6544	29	47	zero	zero	NUM
ejpam-6544	29	48	forcing	forcing	NOUN
ejpam-6544	29	49	.	.	PUNCT
ejpam-6544	30	1	this	this	DET
ejpam-6544	30	2	paper	paper	NOUN
ejpam-6544	30	3	may	may	AUX
ejpam-6544	30	4	give	give	VERB
ejpam-6544	30	5	further	further	ADJ
ejpam-6544	30	6	insights	insight	NOUN
ejpam-6544	30	7	and	and	CCONJ
ejpam-6544	30	8	may	may	AUX
ejpam-6544	30	9	develop	develop	VERB
ejpam-6544	30	10	new	new	ADJ
ejpam-6544	30	11	concepts	concept	NOUN
ejpam-6544	30	12	that	that	PRON
ejpam-6544	30	13	would	would	AUX
ejpam-6544	30	14	benefit	benefit	VERB
ejpam-6544	30	15	other	other	ADJ
ejpam-6544	30	16	researchers	researcher	NOUN
ejpam-6544	30	17	who	who	PRON
ejpam-6544	30	18	are	be	AUX
ejpam-6544	30	19	interested	interested	ADJ
ejpam-6544	30	20	in	in	ADP
ejpam-6544	30	21	the	the	DET
ejpam-6544	30	22	field	field	NOUN
ejpam-6544	30	23	of	of	ADP
ejpam-6544	30	24	graph	graph	NOUN
ejpam-6544	30	25	theory	theory	NOUN
ejpam-6544	30	26	.	.	PUNCT
ejpam-6544	31	1	moreover	moreover	ADV
ejpam-6544	31	2	,	,	PUNCT
ejpam-6544	31	3	this	this	DET
ejpam-6544	31	4	parameter	parameter	NOUN
ejpam-6544	31	5	may	may	AUX
ejpam-6544	31	6	offer	offer	VERB
ejpam-6544	31	7	interesting	interesting	ADJ
ejpam-6544	31	8	research	research	NOUN
ejpam-6544	31	9	topics	topic	NOUN
ejpam-6544	31	10	in	in	ADP
ejpam-6544	31	11	the	the	DET
ejpam-6544	31	12	future	future	NOUN
ejpam-6544	31	13	and	and	CCONJ
ejpam-6544	31	14	may	may	AUX
ejpam-6544	31	15	be	be	AUX
ejpam-6544	31	16	applied	apply	VERB
ejpam-6544	31	17	to	to	PART
ejpam-6544	31	18	model	model	VERB
ejpam-6544	31	19	a	a	DET
ejpam-6544	31	20	certain	certain	ADJ
ejpam-6544	31	21	real	real	ADJ
ejpam-6544	31	22	-	-	PUNCT
ejpam-6544	31	23	life	life	NOUN
ejpam-6544	31	24	scenarios	scenario	NOUN
ejpam-6544	31	25	.	.	PUNCT
ejpam-6544	32	1	2	2	X
ejpam-6544	32	2	.	.	X
ejpam-6544	32	3	terminology	terminology	NOUN
ejpam-6544	32	4	and	and	CCONJ
ejpam-6544	32	5	notation	notation	NOUN
ejpam-6544	32	6	let	let	VERB
ejpam-6544	32	7	g	g	NOUN
ejpam-6544	32	8	=	=	SYM
ejpam-6544	32	9	(	(	PUNCT
ejpam-6544	32	10	v	v	NOUN
ejpam-6544	32	11	(	(	PUNCT
ejpam-6544	32	12	g	g	NOUN
ejpam-6544	32	13	)	)	PUNCT
ejpam-6544	32	14	,	,	PUNCT
ejpam-6544	32	15	e(g	e(g	PROPN
ejpam-6544	32	16	)	)	PUNCT
ejpam-6544	32	17	)	)	PUNCT
ejpam-6544	32	18	be	be	AUX
ejpam-6544	32	19	a	a	DET
ejpam-6544	32	20	simple	simple	ADJ
ejpam-6544	32	21	and	and	CCONJ
ejpam-6544	32	22	undirected	undirected	ADJ
ejpam-6544	32	23	graph	graph	NOUN
ejpam-6544	32	24	.	.	PUNCT
ejpam-6544	33	1	the	the	DET
ejpam-6544	33	2	distance	distance	NOUN
ejpam-6544	33	3	dg(u	dg(u	NOUN
ejpam-6544	33	4	,	,	PUNCT
ejpam-6544	33	5	v	v	NOUN
ejpam-6544	33	6	)	)	PUNCT
ejpam-6544	33	7	in	in	ADP
ejpam-6544	33	8	g	g	NOUN
ejpam-6544	33	9	of	of	ADP
ejpam-6544	33	10	two	two	NUM
ejpam-6544	33	11	vertices	vertex	NOUN
ejpam-6544	33	12	u	u	NOUN
ejpam-6544	33	13	,	,	PUNCT
ejpam-6544	33	14	v	v	PROPN
ejpam-6544	33	15	is	be	AUX
ejpam-6544	33	16	the	the	DET
ejpam-6544	33	17	length	length	NOUN
ejpam-6544	33	18	of	of	ADP
ejpam-6544	33	19	a	a	DET
ejpam-6544	33	20	shortest	short	ADJ
ejpam-6544	33	21	u	u	NOUN
ejpam-6544	33	22	-	-	NOUN
ejpam-6544	33	23	v	v	ADJ
ejpam-6544	33	24	path	path	NOUN
ejpam-6544	33	25	in	in	ADP
ejpam-6544	33	26	g.	g.	PROPN
ejpam-6544	33	27	a	a	DET
ejpam-6544	33	28	vertex	vertex	NOUN
ejpam-6544	33	29	of	of	ADP
ejpam-6544	33	30	a	a	PRON
ejpam-6544	33	31	in	in	ADP
ejpam-6544	33	32	g	g	PROPN
ejpam-6544	33	33	is	be	AUX
ejpam-6544	33	34	a	a	DET
ejpam-6544	33	35	hop	hop	NOUN
ejpam-6544	33	36	neighbor	neighbor	NOUN
ejpam-6544	33	37	of	of	ADP
ejpam-6544	33	38	a	a	DET
ejpam-6544	33	39	vertex	vertex	NOUN
ejpam-6544	33	40	b	b	NOUN
ejpam-6544	33	41	in	in	ADP
ejpam-6544	33	42	g	g	PROPN
ejpam-6544	33	43	if	if	SCONJ
ejpam-6544	33	44	dg(a	dg(a	X
ejpam-6544	33	45	,	,	PUNCT
ejpam-6544	33	46	b	b	X
ejpam-6544	33	47	)	)	PUNCT
ejpam-6544	34	1	=	=	SYM
ejpam-6544	34	2	2	2	X
ejpam-6544	34	3	.	.	X
ejpam-6544	34	4	let	let	VERB
ejpam-6544	34	5	g	g	PROPN
ejpam-6544	34	6	=	=	SYM
ejpam-6544	34	7	(	(	PUNCT
ejpam-6544	34	8	v	v	NOUN
ejpam-6544	34	9	(	(	PUNCT
ejpam-6544	34	10	g	g	NOUN
ejpam-6544	34	11	)	)	PUNCT
ejpam-6544	34	12	,	,	PUNCT
ejpam-6544	34	13	e(g	e(g	PROPN
ejpam-6544	34	14	)	)	PUNCT
ejpam-6544	34	15	)	)	PUNCT
ejpam-6544	34	16	be	be	AUX
ejpam-6544	34	17	a	a	DET
ejpam-6544	34	18	simple	simple	ADJ
ejpam-6544	34	19	and	and	CCONJ
ejpam-6544	34	20	undirected	undirected	ADJ
ejpam-6544	34	21	graph	graph	NOUN
ejpam-6544	34	22	and	and	CCONJ
ejpam-6544	34	23	let	let	VERB
ejpam-6544	34	24	x	x	PRON
ejpam-6544	34	25	,	,	PUNCT
ejpam-6544	34	26	y	y	PROPN
ejpam-6544	34	27	∈	∈	PROPN
ejpam-6544	34	28	v	v	NOUN
ejpam-6544	34	29	(	(	PUNCT
ejpam-6544	34	30	g	g	NOUN
ejpam-6544	34	31	)	)	PUNCT
ejpam-6544	34	32	.	.	PUNCT
ejpam-6544	35	1	if	if	SCONJ
ejpam-6544	35	2	x	x	PRON
ejpam-6544	35	3	is	be	AUX
ejpam-6544	35	4	a	a	DET
ejpam-6544	35	5	colored	colored	ADJ
ejpam-6544	35	6	(	(	PUNCT
ejpam-6544	35	7	active	active	ADJ
ejpam-6544	35	8	)	)	PUNCT
ejpam-6544	35	9	vertex	vertex	NOUN
ejpam-6544	35	10	and	and	CCONJ
ejpam-6544	35	11	exactly	exactly	ADV
ejpam-6544	35	12	one	one	NUM
ejpam-6544	35	13	hop	hop	NOUN
ejpam-6544	35	14	neighbor	neighbor	NOUN
ejpam-6544	35	15	y	y	PROPN
ejpam-6544	35	16	of	of	ADP
ejpam-6544	35	17	x	x	PRON
ejpam-6544	35	18	is	be	AUX
ejpam-6544	35	19	uncolored	uncolored	ADJ
ejpam-6544	35	20	(	(	PUNCT
ejpam-6544	35	21	inactive	inactive	ADJ
ejpam-6544	35	22	)	)	PUNCT
ejpam-6544	35	23	,	,	PUNCT
ejpam-6544	35	24	then	then	ADV
ejpam-6544	35	25	y	y	PROPN
ejpam-6544	35	26	will	will	AUX
ejpam-6544	35	27	become	become	VERB
ejpam-6544	35	28	colored	colored	ADJ
ejpam-6544	35	29	(	(	PUNCT
ejpam-6544	35	30	active	active	ADJ
ejpam-6544	35	31	)	)	PUNCT
ejpam-6544	35	32	,	,	PUNCT
ejpam-6544	35	33	and	and	CCONJ
ejpam-6544	35	34	we	we	PRON
ejpam-6544	35	35	call	call	VERB
ejpam-6544	35	36	this	this	DET
ejpam-6544	35	37	process	process	NOUN
ejpam-6544	35	38	a	a	DET
ejpam-6544	35	39	2	2	NUM
ejpam-6544	35	40	-	-	PUNCT
ejpam-6544	35	41	distance	distance	NOUN
ejpam-6544	35	42	color	color	NOUN
ejpam-6544	35	43	change	change	NOUN
ejpam-6544	35	44	rule	rule	NOUN
ejpam-6544	35	45	.	.	PUNCT
ejpam-6544	36	1	a	a	DET
ejpam-6544	36	2	2	2	NUM
ejpam-6544	36	3	-	-	PUNCT
ejpam-6544	36	4	distance	distance	NOUN
ejpam-6544	36	5	zero	zero	NUM
ejpam-6544	36	6	forcing	forcing	NOUN
ejpam-6544	36	7	set	set	NOUN
ejpam-6544	36	8	n	n	NUM
ejpam-6544	36	9	is	be	AUX
ejpam-6544	36	10	a	a	DET
ejpam-6544	36	11	subset	subset	NOUN
ejpam-6544	36	12	of	of	ADP
ejpam-6544	36	13	vertices	vertex	NOUN
ejpam-6544	36	14	of	of	ADP
ejpam-6544	36	15	g	g	NOUN
ejpam-6544	36	16	such	such	ADJ
ejpam-6544	36	17	that	that	SCONJ
ejpam-6544	36	18	when	when	SCONJ
ejpam-6544	36	19	the	the	DET
ejpam-6544	36	20	vertices	vertex	NOUN
ejpam-6544	36	21	in	in	ADP
ejpam-6544	36	22	n	n	CCONJ
ejpam-6544	36	23	are	be	AUX
ejpam-6544	36	24	colored	color	VERB
ejpam-6544	36	25	(	(	PUNCT
ejpam-6544	36	26	active	active	ADJ
ejpam-6544	36	27	)	)	PUNCT
ejpam-6544	36	28	and	and	CCONJ
ejpam-6544	36	29	the	the	DET
ejpam-6544	36	30	remaining	remain	VERB
ejpam-6544	36	31	vertices	vertex	NOUN
ejpam-6544	36	32	outside	outside	ADP
ejpam-6544	36	33	n	n	CCONJ
ejpam-6544	36	34	are	be	AUX
ejpam-6544	36	35	uncolored	uncolored	ADJ
ejpam-6544	36	36	(	(	PUNCT
ejpam-6544	36	37	inactive	inactive	ADJ
ejpam-6544	36	38	)	)	PUNCT
ejpam-6544	36	39	initially	initially	ADV
ejpam-6544	36	40	,	,	PUNCT
ejpam-6544	36	41	then	then	ADV
ejpam-6544	36	42	repeated	repeat	VERB
ejpam-6544	36	43	application	application	NOUN
ejpam-6544	36	44	of	of	ADP
ejpam-6544	36	45	a	a	DET
ejpam-6544	36	46	2	2	NUM
ejpam-6544	36	47	-	-	PUNCT
ejpam-6544	36	48	distance	distance	NOUN
ejpam-6544	36	49	color	color	NOUN
ejpam-6544	36	50	change	change	NOUN
ejpam-6544	36	51	rule	rule	NOUN
ejpam-6544	36	52	,	,	PUNCT
ejpam-6544	36	53	all	all	DET
ejpam-6544	36	54	vertices	vertex	NOUN
ejpam-6544	36	55	of	of	ADP
ejpam-6544	36	56	g	g	NOUN
ejpam-6544	36	57	will	will	AUX
ejpam-6544	36	58	become	become	VERB
ejpam-6544	36	59	colored	colored	ADJ
ejpam-6544	36	60	(	(	PUNCT
ejpam-6544	36	61	active	active	ADJ
ejpam-6544	36	62	)	)	PUNCT
ejpam-6544	36	63	.	.	PUNCT
ejpam-6544	37	1	the	the	DET
ejpam-6544	37	2	minimum	minimum	ADJ
ejpam-6544	37	3	cardinality	cardinality	NOUN
ejpam-6544	37	4	of	of	ADP
ejpam-6544	37	5	a	a	DET
ejpam-6544	37	6	2	2	NUM
ejpam-6544	37	7	-	-	PUNCT
ejpam-6544	37	8	distance	distance	NOUN
ejpam-6544	37	9	zero	zero	NUM
ejpam-6544	37	10	forcing	force	VERB
ejpam-6544	37	11	set	set	NOUN
ejpam-6544	37	12	of	of	ADP
ejpam-6544	37	13	g	g	NOUN
ejpam-6544	37	14	,	,	PUNCT
ejpam-6544	37	15	denoted	denote	VERB
ejpam-6544	37	16	by	by	ADP
ejpam-6544	37	17	z2(g	z2(g	NOUN
ejpam-6544	37	18	)	)	PUNCT
ejpam-6544	37	19	,	,	PUNCT
ejpam-6544	37	20	is	be	AUX
ejpam-6544	37	21	called	call	VERB
ejpam-6544	37	22	the	the	DET
ejpam-6544	37	23	2	2	NUM
ejpam-6544	37	24	-	-	PUNCT
ejpam-6544	37	25	distance	distance	NOUN
ejpam-6544	37	26	zero	zero	NUM
ejpam-6544	37	27	forcing	force	VERB
ejpam-6544	37	28	number	number	NOUN
ejpam-6544	37	29	of	of	ADP
ejpam-6544	37	30	g.	g.	PROPN
ejpam-6544	37	31	let	let	VERB
ejpam-6544	37	32	g	g	NOUN
ejpam-6544	37	33	and	and	CCONJ
ejpam-6544	37	34	h	h	NOUN
ejpam-6544	37	35	be	be	VERB
ejpam-6544	37	36	any	any	DET
ejpam-6544	37	37	two	two	NUM
ejpam-6544	37	38	graphs	graph	NOUN
ejpam-6544	37	39	.	.	PUNCT
ejpam-6544	38	1	the	the	DET
ejpam-6544	38	2	join	join	NOUN
ejpam-6544	38	3	of	of	ADP
ejpam-6544	38	4	g	g	PROPN
ejpam-6544	38	5	and	and	CCONJ
ejpam-6544	38	6	h	h	NOUN
ejpam-6544	38	7	,	,	PUNCT
ejpam-6544	38	8	denoted	denote	VERB
ejpam-6544	38	9	by	by	ADP
ejpam-6544	38	10	g+h	g+h	PROPN
ejpam-6544	38	11	is	be	AUX
ejpam-6544	38	12	the	the	DET
ejpam-6544	38	13	graph	graph	NOUN
ejpam-6544	38	14	with	with	ADP
ejpam-6544	38	15	vertex	vertex	NOUN
ejpam-6544	38	16	set	set	VERB
ejpam-6544	38	17	v	v	NOUN
ejpam-6544	38	18	(	(	PUNCT
ejpam-6544	38	19	g+h	g+h	NOUN
ejpam-6544	38	20	)	)	PUNCT
ejpam-6544	39	1	=	=	SYM
ejpam-6544	39	2	v	v	X
ejpam-6544	39	3	(	(	PUNCT
ejpam-6544	39	4	g	g	NOUN
ejpam-6544	39	5	)	)	PUNCT
ejpam-6544	39	6	∪	∪	NOUN
ejpam-6544	39	7	v	v	NOUN
ejpam-6544	39	8	(	(	PUNCT
ejpam-6544	39	9	h	h	NOUN
ejpam-6544	39	10	)	)	PUNCT
ejpam-6544	39	11	and	and	CCONJ
ejpam-6544	39	12	edge	edge	NOUN
ejpam-6544	39	13	set	set	VERB
ejpam-6544	39	14	e(g+h	e(g+h	NUM
ejpam-6544	39	15	)	)	PUNCT
ejpam-6544	39	16	=	=	SYM
ejpam-6544	39	17	e(g	e(g	NOUN
ejpam-6544	39	18	)	)	PUNCT
ejpam-6544	39	19	∪	∪	ADP
ejpam-6544	39	20	e(h	e(h	PROPN
ejpam-6544	39	21	)	)	PUNCT
ejpam-6544	39	22	∪	∪	NOUN
ejpam-6544	39	23	{	{	PUNCT
ejpam-6544	39	24	uv	uv	NOUN
ejpam-6544	39	25	:	:	PUNCT
ejpam-6544	39	26	u	u	PROPN
ejpam-6544	39	27	∈	∈	PROPN
ejpam-6544	39	28	v	v	ADP
ejpam-6544	39	29	(	(	PUNCT
ejpam-6544	39	30	g	g	NOUN
ejpam-6544	39	31	)	)	PUNCT
ejpam-6544	39	32	,	,	PUNCT
ejpam-6544	39	33	v	v	X
ejpam-6544	39	34	∈	∈	PROPN
ejpam-6544	39	35	v	v	NOUN
ejpam-6544	39	36	(	(	PUNCT
ejpam-6544	39	37	h	h	NOUN
ejpam-6544	39	38	)	)	PUNCT
ejpam-6544	39	39	}	}	PUNCT
ejpam-6544	39	40	.	.	PUNCT
ejpam-6544	40	1	3	3	X
ejpam-6544	40	2	.	.	X
ejpam-6544	40	3	results	result	NOUN
ejpam-6544	40	4	we	we	PRON
ejpam-6544	40	5	shall	shall	AUX
ejpam-6544	40	6	now	now	ADV
ejpam-6544	40	7	define	define	VERB
ejpam-6544	40	8	the	the	DET
ejpam-6544	40	9	failed	fail	VERB
ejpam-6544	40	10	2	2	NUM
ejpam-6544	40	11	-	-	PUNCT
ejpam-6544	40	12	distance	distance	NOUN
ejpam-6544	40	13	zero	zero	NUM
ejpam-6544	40	14	forcing	force	VERB
ejpam-6544	40	15	in	in	ADP
ejpam-6544	40	16	a	a	DET
ejpam-6544	40	17	graph	graph	NOUN
ejpam-6544	40	18	and	and	CCONJ
ejpam-6544	40	19	investigate	investigate	VERB
ejpam-6544	40	20	this	this	PRON
ejpam-6544	40	21	on	on	ADP
ejpam-6544	40	22	some	some	DET
ejpam-6544	40	23	families	family	NOUN
ejpam-6544	40	24	of	of	ADP
ejpam-6544	40	25	graphs	graph	NOUN
ejpam-6544	40	26	and	and	CCONJ
ejpam-6544	40	27	on	on	ADP
ejpam-6544	40	28	the	the	DET
ejpam-6544	40	29	join	join	NOUN
ejpam-6544	40	30	of	of	ADP
ejpam-6544	40	31	two	two	NUM
ejpam-6544	40	32	graphs	graph	NOUN
ejpam-6544	40	33	.	.	PUNCT
ejpam-6544	41	1	definition	definition	NOUN
ejpam-6544	41	2	1	1	NUM
ejpam-6544	41	3	.	.	PUNCT
ejpam-6544	42	1	let	let	VERB
ejpam-6544	42	2	g	g	PROPN
ejpam-6544	42	3	=	=	SYM
ejpam-6544	42	4	(	(	PUNCT
ejpam-6544	42	5	v	v	NOUN
ejpam-6544	42	6	(	(	PUNCT
ejpam-6544	42	7	g	g	NOUN
ejpam-6544	42	8	)	)	PUNCT
ejpam-6544	42	9	,	,	PUNCT
ejpam-6544	42	10	e(g	e(g	PROPN
ejpam-6544	42	11	)	)	PUNCT
ejpam-6544	42	12	)	)	PUNCT
ejpam-6544	43	1	be	be	AUX
ejpam-6544	43	2	a	a	DET
ejpam-6544	43	3	simple	simple	ADJ
ejpam-6544	43	4	and	and	CCONJ
ejpam-6544	43	5	undirected	undirected	ADJ
ejpam-6544	43	6	graph	graph	NOUN
ejpam-6544	43	7	.	.	PUNCT
ejpam-6544	44	1	then	then	ADV
ejpam-6544	44	2	m	m	PROPN
ejpam-6544	44	3	⊂	⊂	PROPN
ejpam-6544	44	4	v	v	ADJ
ejpam-6544	44	5	(	(	PUNCT
ejpam-6544	44	6	g	g	NOUN
ejpam-6544	44	7	)	)	PUNCT
ejpam-6544	44	8	is	be	AUX
ejpam-6544	44	9	called	call	VERB
ejpam-6544	44	10	a	a	DET
ejpam-6544	44	11	failed	fail	VERB
ejpam-6544	44	12	2	2	NUM
ejpam-6544	44	13	-	-	PUNCT
ejpam-6544	44	14	distance	distance	NOUN
ejpam-6544	44	15	zero	zero	NUM
ejpam-6544	44	16	forcing	force	VERB
ejpam-6544	44	17	set	set	NOUN
ejpam-6544	44	18	of	of	ADP
ejpam-6544	44	19	g	g	PROPN
ejpam-6544	44	20	if	if	SCONJ
ejpam-6544	44	21	m	m	PROPN
ejpam-6544	44	22	fails	fail	VERB
ejpam-6544	44	23	to	to	PART
ejpam-6544	44	24	be	be	AUX
ejpam-6544	44	25	a	a	DET
ejpam-6544	44	26	2	2	NUM
ejpam-6544	44	27	-	-	PUNCT
ejpam-6544	44	28	distance	distance	NOUN
ejpam-6544	44	29	zero	zero	NUM
ejpam-6544	44	30	forcing	force	VERB
ejpam-6544	44	31	set	set	NOUN
ejpam-6544	44	32	a.	a.	NOUN
ejpam-6544	44	33	madjatul	madjatul	NOUN
ejpam-6544	44	34	et	et	PROPN
ejpam-6544	44	35	al	al	PROPN
ejpam-6544	44	36	.	.	PUNCT
ejpam-6544	44	37	/	/	SYM
ejpam-6544	44	38	eur	eur	PROPN
ejpam-6544	44	39	.	.	PUNCT
ejpam-6544	45	1	j.	j.	PROPN
ejpam-6544	45	2	pure	pure	PROPN
ejpam-6544	45	3	appl	appl	PROPN
ejpam-6544	45	4	.	.	PROPN
ejpam-6544	45	5	math	math	PROPN
ejpam-6544	45	6	,	,	PUNCT
ejpam-6544	45	7	18	18	NUM
ejpam-6544	45	8	(	(	PUNCT
ejpam-6544	45	9	3	3	NUM
ejpam-6544	45	10	)	)	PUNCT
ejpam-6544	45	11	(	(	PUNCT
ejpam-6544	45	12	2025	2025	NUM
ejpam-6544	45	13	)	)	PUNCT
ejpam-6544	45	14	,	,	PUNCT
ejpam-6544	45	15	6544	6544	NUM
ejpam-6544	45	16	3	3	NUM
ejpam-6544	45	17	of	of	ADP
ejpam-6544	45	18	8	8	NUM
ejpam-6544	45	19	of	of	ADP
ejpam-6544	45	20	g.	g.	PROPN
ejpam-6544	45	21	the	the	DET
ejpam-6544	45	22	failed	fail	VERB
ejpam-6544	45	23	2	2	NUM
ejpam-6544	45	24	-	-	PUNCT
ejpam-6544	45	25	distance	distance	NOUN
ejpam-6544	45	26	zero	zero	NUM
ejpam-6544	45	27	forcing	force	VERB
ejpam-6544	45	28	number	number	NOUN
ejpam-6544	45	29	of	of	ADP
ejpam-6544	45	30	g	g	NOUN
ejpam-6544	45	31	,	,	PUNCT
ejpam-6544	45	32	denoted	denote	VERB
ejpam-6544	45	33	by	by	ADP
ejpam-6544	45	34	f	f	PROPN
ejpam-6544	45	35	2(g	2(g	NUM
ejpam-6544	45	36	)	)	PUNCT
ejpam-6544	45	37	,	,	PUNCT
ejpam-6544	45	38	is	be	AUX
ejpam-6544	45	39	the	the	DET
ejpam-6544	45	40	maximum	maximum	ADJ
ejpam-6544	45	41	cardinality	cardinality	NOUN
ejpam-6544	45	42	of	of	ADP
ejpam-6544	45	43	a	a	DET
ejpam-6544	45	44	failed	fail	VERB
ejpam-6544	45	45	2	2	NUM
ejpam-6544	45	46	-	-	PUNCT
ejpam-6544	45	47	distance	distance	NOUN
ejpam-6544	45	48	zero	zero	NUM
ejpam-6544	45	49	forcing	force	VERB
ejpam-6544	45	50	set	set	NOUN
ejpam-6544	45	51	in	in	ADP
ejpam-6544	45	52	g.	g.	PROPN
ejpam-6544	45	53	4	4	NUM
ejpam-6544	45	54	.	.	PUNCT
ejpam-6544	46	1	some	some	DET
ejpam-6544	46	2	properties	property	NOUN
ejpam-6544	46	3	of	of	ADP
ejpam-6544	46	4	failed	fail	VERB
ejpam-6544	46	5	2	2	NUM
ejpam-6544	46	6	-	-	PUNCT
ejpam-6544	46	7	distance	distance	NOUN
ejpam-6544	46	8	zero	zero	NUM
ejpam-6544	46	9	forcing	force	VERB
ejpam-6544	46	10	in	in	ADP
ejpam-6544	46	11	some	some	DET
ejpam-6544	46	12	special	special	ADJ
ejpam-6544	46	13	graphs	graph	NOUN
ejpam-6544	46	14	let	let	VERB
ejpam-6544	46	15	’s	’s	PRON
ejpam-6544	46	16	begin	begin	VERB
ejpam-6544	46	17	with	with	ADP
ejpam-6544	46	18	the	the	DET
ejpam-6544	46	19	characterization	characterization	NOUN
ejpam-6544	46	20	of	of	ADP
ejpam-6544	46	21	a	a	DET
ejpam-6544	46	22	failed	fail	VERB
ejpam-6544	46	23	2	2	NUM
ejpam-6544	46	24	-	-	PUNCT
ejpam-6544	46	25	distance	distance	NOUN
ejpam-6544	46	26	zero	zero	NUM
ejpam-6544	46	27	forcing	force	VERB
ejpam-6544	46	28	sets	set	NOUN
ejpam-6544	46	29	in	in	ADP
ejpam-6544	46	30	a	a	DET
ejpam-6544	46	31	complete	complete	ADJ
ejpam-6544	46	32	graph	graph	NOUN
ejpam-6544	46	33	as	as	SCONJ
ejpam-6544	46	34	follows	follow	VERB
ejpam-6544	46	35	:	:	PUNCT
ejpam-6544	46	36	theorem	theorem	NOUN
ejpam-6544	46	37	1	1	X
ejpam-6544	46	38	.	.	PUNCT
ejpam-6544	47	1	let	let	VERB
ejpam-6544	47	2	n	n	PRON
ejpam-6544	47	3	be	be	AUX
ejpam-6544	47	4	a	a	DET
ejpam-6544	47	5	positive	positive	ADJ
ejpam-6544	47	6	integer	integer	NOUN
ejpam-6544	47	7	.	.	PUNCT
ejpam-6544	48	1	then	then	ADV
ejpam-6544	48	2	r	r	PROPN
ejpam-6544	48	3	⊂	⊂	PROPN
ejpam-6544	48	4	v	v	X
ejpam-6544	48	5	(	(	PUNCT
ejpam-6544	48	6	kn	kn	PROPN
ejpam-6544	48	7	)	)	PUNCT
ejpam-6544	48	8	is	be	AUX
ejpam-6544	48	9	a	a	DET
ejpam-6544	48	10	failed	failed	ADJ
ejpam-6544	48	11	2	2	NUM
ejpam-6544	48	12	-	-	PUNCT
ejpam-6544	48	13	distance	distance	NOUN
ejpam-6544	48	14	zero	zero	NUM
ejpam-6544	48	15	forcing	force	VERB
ejpam-6544	48	16	set	set	NOUN
ejpam-6544	48	17	in	in	ADP
ejpam-6544	48	18	kn	kn	PROPN
ejpam-6544	48	19	if	if	SCONJ
ejpam-6544	48	20	and	and	CCONJ
ejpam-6544	48	21	only	only	ADV
ejpam-6544	48	22	if	if	SCONJ
ejpam-6544	48	23	|r|	|r|	PRON
ejpam-6544	48	24	≤	≤	ADJ
ejpam-6544	48	25	n−	n−	PROPN
ejpam-6544	48	26	1	1	NUM
ejpam-6544	48	27	.	.	PUNCT
ejpam-6544	49	1	proof	proof	NOUN
ejpam-6544	49	2	.	.	PUNCT
ejpam-6544	50	1	suppose	suppose	VERB
ejpam-6544	50	2	that	that	SCONJ
ejpam-6544	50	3	r	r	PROPN
ejpam-6544	50	4	⊂	⊂	PRON
ejpam-6544	50	5	v	v	X
ejpam-6544	50	6	(	(	PUNCT
ejpam-6544	50	7	kn	kn	PROPN
ejpam-6544	50	8	)	)	PUNCT
ejpam-6544	50	9	is	be	AUX
ejpam-6544	50	10	a	a	DET
ejpam-6544	50	11	failed	failed	ADJ
ejpam-6544	50	12	2	2	NUM
ejpam-6544	50	13	-	-	PUNCT
ejpam-6544	50	14	distance	distance	NOUN
ejpam-6544	50	15	zero	zero	NUM
ejpam-6544	50	16	forcing	force	VERB
ejpam-6544	50	17	set	set	NOUN
ejpam-6544	50	18	of	of	ADP
ejpam-6544	50	19	kn	kn	PROPN
ejpam-6544	50	20	.	.	PUNCT
ejpam-6544	51	1	then	then	ADV
ejpam-6544	51	2	r	r	NOUN
ejpam-6544	51	3	is	be	AUX
ejpam-6544	51	4	not	not	PART
ejpam-6544	51	5	a	a	DET
ejpam-6544	51	6	2	2	NUM
ejpam-6544	51	7	-	-	PUNCT
ejpam-6544	51	8	distance	distance	NOUN
ejpam-6544	51	9	zero	zero	NUM
ejpam-6544	51	10	forcing	force	VERB
ejpam-6544	51	11	set	set	NOUN
ejpam-6544	51	12	of	of	ADP
ejpam-6544	51	13	kn	kn	PROPN
ejpam-6544	51	14	.	.	PUNCT
ejpam-6544	52	1	thus	thus	ADV
ejpam-6544	52	2	,	,	PUNCT
ejpam-6544	52	3	there	there	PRON
ejpam-6544	52	4	exist	exist	VERB
ejpam-6544	52	5	y	y	PROPN
ejpam-6544	52	6	∈	∈	PROPN
ejpam-6544	52	7	v	v	PROPN
ejpam-6544	52	8	(	(	PUNCT
ejpam-6544	52	9	kn	kn	PROPN
ejpam-6544	52	10	)	)	PUNCT
ejpam-6544	52	11	\	\	PUNCT
ejpam-6544	53	1	r	r	NOUN
ejpam-6544	53	2	such	such	ADJ
ejpam-6544	53	3	that	that	SCONJ
ejpam-6544	53	4	y	y	PROPN
ejpam-6544	53	5	can	can	AUX
ejpam-6544	53	6	not	not	PART
ejpam-6544	53	7	be	be	AUX
ejpam-6544	53	8	2	2	NUM
ejpam-6544	53	9	-	-	PUNCT
ejpam-6544	53	10	forced	forced	ADJ
ejpam-6544	53	11	.	.	PUNCT
ejpam-6544	54	1	that	that	PRON
ejpam-6544	54	2	is	be	AUX
ejpam-6544	54	3	,	,	PUNCT
ejpam-6544	54	4	r	r	PROPN
ejpam-6544	54	5	̸=	̸=	PROPN
ejpam-6544	54	6	v	v	NOUN
ejpam-6544	54	7	(	(	PUNCT
ejpam-6544	54	8	kn	kn	PROPN
ejpam-6544	54	9	)	)	PUNCT
ejpam-6544	54	10	.	.	PUNCT
ejpam-6544	55	1	therefore	therefore	ADV
ejpam-6544	55	2	,	,	PUNCT
ejpam-6544	55	3	|r|	|r|	NOUN
ejpam-6544	55	4	=	=	NOUN
ejpam-6544	55	5	̸	̸	NUM
ejpam-6544	55	6	n	n	CCONJ
ejpam-6544	55	7	,	,	PUNCT
ejpam-6544	55	8	and	and	CCONJ
ejpam-6544	55	9	so	so	ADV
ejpam-6544	55	10	|r|	|r|	NOUN
ejpam-6544	55	11	≤	≤	PROPN
ejpam-6544	55	12	n−	n−	PROPN
ejpam-6544	55	13	1	1	NUM
ejpam-6544	55	14	.	.	PUNCT
ejpam-6544	55	15	conversely	conversely	ADV
ejpam-6544	55	16	,	,	PUNCT
ejpam-6544	55	17	suppose	suppose	VERB
ejpam-6544	55	18	that	that	SCONJ
ejpam-6544	55	19	|r|	|r|	PROPN
ejpam-6544	55	20	≤	≤	PROPN
ejpam-6544	55	21	n−1	n−1	PROPN
ejpam-6544	55	22	.	.	PUNCT
ejpam-6544	56	1	then	then	ADV
ejpam-6544	56	2	there	there	PRON
ejpam-6544	56	3	is	be	VERB
ejpam-6544	56	4	exist	exist	VERB
ejpam-6544	56	5	at	at	ADV
ejpam-6544	56	6	least	least	ADV
ejpam-6544	56	7	one	one	NUM
ejpam-6544	56	8	vertex	vertex	NOUN
ejpam-6544	56	9	u	u	NOUN
ejpam-6544	56	10	∈	∈	PROPN
ejpam-6544	56	11	v	v	NOUN
ejpam-6544	56	12	(	(	PUNCT
ejpam-6544	56	13	kn	kn	PROPN
ejpam-6544	56	14	)	)	PUNCT
ejpam-6544	56	15	such	such	ADJ
ejpam-6544	56	16	that	that	SCONJ
ejpam-6544	56	17	u	u	PROPN
ejpam-6544	56	18	/∈	/∈	PROPN
ejpam-6544	56	19	r.	r.	PROPN
ejpam-6544	56	20	suppose	suppose	VERB
ejpam-6544	56	21	on	on	ADP
ejpam-6544	56	22	the	the	DET
ejpam-6544	56	23	contrary	contrary	NOUN
ejpam-6544	56	24	that	that	SCONJ
ejpam-6544	56	25	r	r	NOUN
ejpam-6544	56	26	is	be	AUX
ejpam-6544	56	27	a	a	DET
ejpam-6544	56	28	2	2	NUM
ejpam-6544	56	29	-	-	PUNCT
ejpam-6544	56	30	distance	distance	NOUN
ejpam-6544	56	31	zero	zero	NUM
ejpam-6544	56	32	forcing	force	VERB
ejpam-6544	56	33	set	set	NOUN
ejpam-6544	56	34	on	on	ADP
ejpam-6544	56	35	kn	kn	PROPN
ejpam-6544	56	36	.	.	PUNCT
ejpam-6544	57	1	then	then	ADV
ejpam-6544	57	2	there	there	PRON
ejpam-6544	57	3	exist	exist	VERB
ejpam-6544	57	4	y	y	PROPN
ejpam-6544	57	5	∈	∈	PROPN
ejpam-6544	57	6	r	r	NOUN
ejpam-6544	57	7	such	such	DET
ejpam-6544	57	8	that	that	DET
ejpam-6544	57	9	dkn	dkn	NOUN
ejpam-6544	57	10	(	(	PUNCT
ejpam-6544	57	11	u	u	NOUN
ejpam-6544	57	12	,	,	PUNCT
ejpam-6544	57	13	y	y	NOUN
ejpam-6544	57	14	)	)	PUNCT
ejpam-6544	57	15	=	=	SYM
ejpam-6544	58	1	2	2	X
ejpam-6544	58	2	.	.	PUNCT
ejpam-6544	58	3	however	however	ADV
ejpam-6544	58	4	,	,	PUNCT
ejpam-6544	58	5	this	this	PRON
ejpam-6544	58	6	is	be	AUX
ejpam-6544	58	7	a	a	DET
ejpam-6544	58	8	contradiction	contradiction	NOUN
ejpam-6544	58	9	since	since	SCONJ
ejpam-6544	58	10	the	the	DET
ejpam-6544	58	11	graph	graph	NOUN
ejpam-6544	58	12	is	be	AUX
ejpam-6544	58	13	complete	complete	ADJ
ejpam-6544	58	14	.	.	PUNCT
ejpam-6544	59	1	thus	thus	ADV
ejpam-6544	59	2	,	,	PUNCT
ejpam-6544	59	3	r	r	NOUN
ejpam-6544	59	4	is	be	AUX
ejpam-6544	59	5	a	a	DET
ejpam-6544	59	6	failed	failed	ADJ
ejpam-6544	59	7	2	2	NUM
ejpam-6544	59	8	-	-	PUNCT
ejpam-6544	59	9	distance	distance	NOUN
ejpam-6544	59	10	zero	zero	NUM
ejpam-6544	59	11	forcing	force	VERB
ejpam-6544	59	12	set	set	NOUN
ejpam-6544	59	13	of	of	ADP
ejpam-6544	59	14	kn	kn	PROPN
ejpam-6544	59	15	.	.	PUNCT
ejpam-6544	60	1	the	the	DET
ejpam-6544	60	2	following	following	ADJ
ejpam-6544	60	3	result	result	NOUN
ejpam-6544	60	4	follows	follow	VERB
ejpam-6544	60	5	directly	directly	ADV
ejpam-6544	60	6	from	from	ADP
ejpam-6544	60	7	theorem	theorem	ADJ
ejpam-6544	60	8	1	1	NUM
ejpam-6544	60	9	.	.	PUNCT
ejpam-6544	60	10	corollary	corollary	ADJ
ejpam-6544	60	11	1	1	NUM
ejpam-6544	60	12	.	.	PUNCT
ejpam-6544	61	1	let	let	VERB
ejpam-6544	61	2	n	n	PRON
ejpam-6544	61	3	be	be	AUX
ejpam-6544	61	4	a	a	DET
ejpam-6544	61	5	positive	positive	ADJ
ejpam-6544	61	6	integer	integer	NOUN
ejpam-6544	61	7	.	.	PUNCT
ejpam-6544	62	1	then	then	ADV
ejpam-6544	62	2	f	f	PROPN
ejpam-6544	62	3	2(kn	2(kn	PROPN
ejpam-6544	62	4	)	)	PUNCT
ejpam-6544	63	1	=	=	PUNCT
ejpam-6544	63	2	n−	n−	NOUN
ejpam-6544	63	3	1	1	NUM
ejpam-6544	63	4	for	for	ADP
ejpam-6544	63	5	all	all	DET
ejpam-6544	63	6	n	n	PRON
ejpam-6544	63	7	≥	≥	NOUN
ejpam-6544	63	8	1	1	NUM
ejpam-6544	63	9	now	now	ADV
ejpam-6544	63	10	,	,	PUNCT
ejpam-6544	63	11	let	let	VERB
ejpam-6544	63	12	’s	’s	PRON
ejpam-6544	63	13	study	study	VERB
ejpam-6544	63	14	the	the	DET
ejpam-6544	63	15	behavior	behavior	NOUN
ejpam-6544	63	16	of	of	ADP
ejpam-6544	63	17	a	a	DET
ejpam-6544	63	18	failed	fail	VERB
ejpam-6544	63	19	2	2	NUM
ejpam-6544	63	20	-	-	PUNCT
ejpam-6544	63	21	distance	distance	NOUN
ejpam-6544	63	22	zero	zero	NUM
ejpam-6544	63	23	forcing	force	VERB
ejpam-6544	63	24	number	number	NOUN
ejpam-6544	63	25	in	in	ADP
ejpam-6544	63	26	a	a	DET
ejpam-6544	63	27	path	path	NOUN
ejpam-6544	63	28	graph	graph	NOUN
ejpam-6544	63	29	with	with	ADP
ejpam-6544	63	30	order	order	NOUN
ejpam-6544	63	31	n	n	CCONJ
ejpam-6544	63	32	,	,	PUNCT
ejpam-6544	63	33	which	which	PRON
ejpam-6544	63	34	is	be	AUX
ejpam-6544	63	35	any	any	DET
ejpam-6544	63	36	positive	positive	ADJ
ejpam-6544	63	37	integer	integer	NOUN
ejpam-6544	63	38	.	.	PUNCT
ejpam-6544	64	1	theorem	theorem	NOUN
ejpam-6544	64	2	2	2	NUM
ejpam-6544	64	3	.	.	PUNCT
ejpam-6544	65	1	let	let	VERB
ejpam-6544	65	2	n	n	PRON
ejpam-6544	65	3	be	be	AUX
ejpam-6544	65	4	any	any	DET
ejpam-6544	65	5	positive	positive	ADJ
ejpam-6544	65	6	integer	integer	NOUN
ejpam-6544	65	7	.	.	PUNCT
ejpam-6544	66	1	then	then	ADV
ejpam-6544	66	2	f	f	PROPN
ejpam-6544	66	3	2(pn	2(pn	NUM
ejpam-6544	66	4	)	)	PUNCT
ejpam-6544	66	5	=	=	PUNCT
ejpam-6544	67	1			PRON
ejpam-6544	67	2	n−	n−	NOUN
ejpam-6544	67	3	1	1	NUM
ejpam-6544	67	4	,	,	PUNCT
ejpam-6544	67	5	if	if	SCONJ
ejpam-6544	67	6	n	n	CCONJ
ejpam-6544	67	7	=	=	SYM
ejpam-6544	67	8	1	1	NUM
ejpam-6544	67	9	,	,	PUNCT
ejpam-6544	67	10	2	2	NUM
ejpam-6544	67	11	,	,	PUNCT
ejpam-6544	67	12	3	3	NUM
ejpam-6544	67	13	,	,	PUNCT
ejpam-6544	67	14	⌊n4	⌊n4	NUM
ejpam-6544	67	15	⌋	⌋	NOUN
ejpam-6544	67	16	−	−	PROPN
ejpam-6544	67	17	1	1	NUM
ejpam-6544	67	18	,	,	PUNCT
ejpam-6544	67	19	if	if	SCONJ
ejpam-6544	67	20	n	n	PRON
ejpam-6544	67	21	is	be	AUX
ejpam-6544	67	22	odd	odd	ADJ
ejpam-6544	67	23	n	n	PRON
ejpam-6544	67	24	2	2	NUM
ejpam-6544	67	25	,	,	PUNCT
ejpam-6544	67	26	if	if	SCONJ
ejpam-6544	67	27	n	n	PRON
ejpam-6544	67	28	is	be	AUX
ejpam-6544	67	29	even	even	ADV
ejpam-6544	67	30	.	.	PUNCT
ejpam-6544	68	1	proof	proof	NOUN
ejpam-6544	68	2	.	.	PUNCT
ejpam-6544	69	1	by	by	ADP
ejpam-6544	69	2	theorem	theorem	ADJ
ejpam-6544	69	3	3.1.1	3.1.1	NUM
ejpam-6544	69	4	,	,	PUNCT
ejpam-6544	69	5	f	f	PROPN
ejpam-6544	69	6	2(p1	2(p1	NUM
ejpam-6544	69	7	)	)	PUNCT
ejpam-6544	69	8	=	=	SYM
ejpam-6544	69	9	0	0	NUM
ejpam-6544	69	10	and	and	CCONJ
ejpam-6544	69	11	f	f	PROPN
ejpam-6544	69	12	2(p2	2(p2	NUM
ejpam-6544	69	13	)	)	PUNCT
ejpam-6544	69	14	=	=	SYM
ejpam-6544	69	15	1	1	X
ejpam-6544	69	16	.	.	X
ejpam-6544	69	17	for	for	ADP
ejpam-6544	69	18	n	n	NOUN
ejpam-6544	69	19	=	=	SYM
ejpam-6544	69	20	3	3	NUM
ejpam-6544	69	21	,	,	PUNCT
ejpam-6544	69	22	let	let	VERB
ejpam-6544	69	23	p3	p3	PROPN
ejpam-6544	69	24	=	=	PUNCT
ejpam-6544	70	1	[	[	X
ejpam-6544	70	2	v1	v1	NOUN
ejpam-6544	70	3	,	,	PUNCT
ejpam-6544	70	4	v2	v2	PROPN
ejpam-6544	70	5	,	,	PUNCT
ejpam-6544	70	6	v3	v3	PROPN
ejpam-6544	70	7	]	]	PUNCT
ejpam-6544	70	8	,	,	PUNCT
ejpam-6544	70	9	and	and	CCONJ
ejpam-6544	70	10	consider	consider	VERB
ejpam-6544	70	11	s	s	PRON
ejpam-6544	70	12	=	=	NOUN
ejpam-6544	70	13	{	{	PUNCT
ejpam-6544	70	14	v1	v1	PROPN
ejpam-6544	70	15	,	,	PUNCT
ejpam-6544	70	16	v3	v3	PROPN
ejpam-6544	70	17	}	}	PUNCT
ejpam-6544	70	18	.	.	PUNCT
ejpam-6544	71	1	then	then	ADV
ejpam-6544	71	2	v2	v2	PROPN
ejpam-6544	71	3	can	can	AUX
ejpam-6544	71	4	not	not	PART
ejpam-6544	71	5	be	be	AUX
ejpam-6544	71	6	2	2	NUM
ejpam-6544	71	7	-	-	PUNCT
ejpam-6544	71	8	forced	force	VERB
ejpam-6544	71	9	by	by	ADP
ejpam-6544	71	10	any	any	DET
ejpam-6544	71	11	vertex	vertex	NOUN
ejpam-6544	71	12	in	in	ADP
ejpam-6544	71	13	s.	s.	PROPN
ejpam-6544	71	14	thus	thus	ADV
ejpam-6544	71	15	,	,	PUNCT
ejpam-6544	71	16	s	s	VERB
ejpam-6544	71	17	is	be	AUX
ejpam-6544	71	18	a	a	DET
ejpam-6544	71	19	failed	failed	ADJ
ejpam-6544	71	20	2	2	NUM
ejpam-6544	71	21	-	-	PUNCT
ejpam-6544	71	22	distance	distance	NOUN
ejpam-6544	71	23	zero	zero	NUM
ejpam-6544	71	24	forcing	force	VERB
ejpam-6544	71	25	set	set	NOUN
ejpam-6544	71	26	of	of	ADP
ejpam-6544	71	27	p3	p3	PROPN
ejpam-6544	71	28	.	.	PUNCT
ejpam-6544	72	1	obviously	obviously	ADV
ejpam-6544	72	2	s	s	VERB
ejpam-6544	72	3	is	be	AUX
ejpam-6544	72	4	a	a	DET
ejpam-6544	72	5	maximum	maximum	ADV
ejpam-6544	72	6	failed	fail	VERB
ejpam-6544	72	7	2	2	NUM
ejpam-6544	72	8	-	-	PUNCT
ejpam-6544	72	9	distance	distance	NOUN
ejpam-6544	72	10	zero	zero	NUM
ejpam-6544	72	11	forcing	force	VERB
ejpam-6544	72	12	set	set	NOUN
ejpam-6544	72	13	of	of	ADP
ejpam-6544	72	14	p3	p3	PROPN
ejpam-6544	72	15	since	since	SCONJ
ejpam-6544	72	16	v	v	PROPN
ejpam-6544	72	17	(	(	PUNCT
ejpam-6544	72	18	p3	p3	PROPN
ejpam-6544	72	19	)	)	PUNCT
ejpam-6544	72	20	is	be	AUX
ejpam-6544	72	21	a	a	DET
ejpam-6544	72	22	2	2	NUM
ejpam-6544	72	23	-	-	PUNCT
ejpam-6544	72	24	distance	distance	NOUN
ejpam-6544	72	25	zero	zero	NUM
ejpam-6544	72	26	forcing	force	VERB
ejpam-6544	72	27	set	set	NOUN
ejpam-6544	72	28	of	of	ADP
ejpam-6544	72	29	p3	p3	PROPN
ejpam-6544	72	30	.	.	PUNCT
ejpam-6544	73	1	therefore	therefore	ADV
ejpam-6544	73	2	,	,	PUNCT
ejpam-6544	73	3	f	f	PROPN
ejpam-6544	73	4	2(p3	2(p3	NUM
ejpam-6544	73	5	)	)	PUNCT
ejpam-6544	73	6	=	=	SYM
ejpam-6544	74	1	2	2	X
ejpam-6544	74	2	.	.	X
ejpam-6544	74	3	let	let	VERB
ejpam-6544	74	4	pn	pn	VERB
ejpam-6544	75	1	=	=	PUNCT
ejpam-6544	76	1	[	[	X
ejpam-6544	76	2	a1	a1	NOUN
ejpam-6544	76	3	,	,	PUNCT
ejpam-6544	76	4	a2	a2	PROPN
ejpam-6544	76	5	,	,	PUNCT
ejpam-6544	76	6	...	...	PUNCT
ejpam-6544	76	7	,	,	PUNCT
ejpam-6544	76	8	an	an	PRON
ejpam-6544	76	9	]	]	X
ejpam-6544	76	10	.	.	PUNCT
ejpam-6544	77	1	for	for	ADP
ejpam-6544	77	2	n	n	NOUN
ejpam-6544	77	3	=	=	SYM
ejpam-6544	77	4	4	4	NUM
ejpam-6544	77	5	,	,	PUNCT
ejpam-6544	77	6	consider	consider	VERB
ejpam-6544	77	7	n	n	X
ejpam-6544	77	8	=	=	SYM
ejpam-6544	77	9	{	{	PUNCT
ejpam-6544	77	10	a1	a1	NOUN
ejpam-6544	77	11	,	,	PUNCT
ejpam-6544	77	12	a3	a3	NOUN
ejpam-6544	77	13	}	}	PUNCT
ejpam-6544	77	14	.	.	PUNCT
ejpam-6544	78	1	then	then	ADV
ejpam-6544	78	2	a2	a2	PROPN
ejpam-6544	78	3	and	and	CCONJ
ejpam-6544	78	4	a4	a4	NOUN
ejpam-6544	78	5	can	can	AUX
ejpam-6544	78	6	not	not	PART
ejpam-6544	78	7	be	be	AUX
ejpam-6544	78	8	2	2	NUM
ejpam-6544	78	9	-	-	PUNCT
ejpam-6544	78	10	forced	force	VERB
ejpam-6544	78	11	by	by	ADP
ejpam-6544	78	12	any	any	DET
ejpam-6544	78	13	vertex	vertex	NOUN
ejpam-6544	78	14	in	in	ADP
ejpam-6544	78	15	n	n	PROPN
ejpam-6544	78	16	.	.	PUNCT
ejpam-6544	79	1	it	it	PRON
ejpam-6544	79	2	follows	follow	VERB
ejpam-6544	79	3	that	that	SCONJ
ejpam-6544	79	4	n	n	PRON
ejpam-6544	79	5	is	be	AUX
ejpam-6544	79	6	a	a	DET
ejpam-6544	79	7	failed	failed	ADJ
ejpam-6544	79	8	2	2	NUM
ejpam-6544	79	9	-	-	PUNCT
ejpam-6544	79	10	distance	distance	NOUN
ejpam-6544	79	11	zero	zero	NUM
ejpam-6544	79	12	forcing	force	VERB
ejpam-6544	79	13	set	set	NOUN
ejpam-6544	79	14	of	of	ADP
ejpam-6544	79	15	p4	p4	NOUN
ejpam-6544	79	16	.	.	PUNCT
ejpam-6544	80	1	thus	thus	ADV
ejpam-6544	80	2	,	,	PUNCT
ejpam-6544	80	3	f	f	PROPN
ejpam-6544	80	4	2(p4	2(p4	NUM
ejpam-6544	80	5	)	)	PUNCT
ejpam-6544	80	6	≥	≥	NOUN
ejpam-6544	80	7	2	2	NUM
ejpam-6544	80	8	.	.	X
ejpam-6544	80	9	notice	notice	VERB
ejpam-6544	80	10	that	that	SCONJ
ejpam-6544	80	11	n	n	VERB
ejpam-6544	81	1	′	′	NOUN
ejpam-6544	81	2	=	=	PUNCT
ejpam-6544	81	3	t	t	PROPN
ejpam-6544	81	4	∪	∪	X
ejpam-6544	81	5	{	{	PUNCT
ejpam-6544	81	6	a1	a1	NOUN
ejpam-6544	81	7	,	,	PUNCT
ejpam-6544	81	8	a3	a3	NOUN
ejpam-6544	81	9	}	}	PUNCT
ejpam-6544	81	10	where	where	SCONJ
ejpam-6544	81	11	t	t	PROPN
ejpam-6544	81	12	⊆	⊆	NUM
ejpam-6544	81	13	{	{	PUNCT
ejpam-6544	81	14	a2	a2	PROPN
ejpam-6544	81	15	,	,	PUNCT
ejpam-6544	81	16	a4	a4	PROPN
ejpam-6544	81	17	}	}	PUNCT
ejpam-6544	81	18	,	,	PUNCT
ejpam-6544	81	19	is	be	AUX
ejpam-6544	81	20	a	a	DET
ejpam-6544	81	21	2	2	NUM
ejpam-6544	81	22	-	-	PUNCT
ejpam-6544	81	23	distance	distance	NOUN
ejpam-6544	81	24	zero	zero	NUM
ejpam-6544	81	25	forcing	force	VERB
ejpam-6544	81	26	set	set	NOUN
ejpam-6544	81	27	of	of	ADP
ejpam-6544	81	28	p4	p4	NOUN
ejpam-6544	81	29	.	.	PUNCT
ejpam-6544	82	1	therefore	therefore	ADV
ejpam-6544	82	2	,	,	PUNCT
ejpam-6544	82	3	f	f	PROPN
ejpam-6544	82	4	2(p4	2(p4	NUM
ejpam-6544	82	5	)	)	PUNCT
ejpam-6544	82	6	≥	≥	NOUN
ejpam-6544	82	7	3	3	NUM
ejpam-6544	82	8	is	be	AUX
ejpam-6544	82	9	impossible	impossible	ADJ
ejpam-6544	82	10	,	,	PUNCT
ejpam-6544	82	11	and	and	CCONJ
ejpam-6544	82	12	so	so	ADV
ejpam-6544	82	13	f	f	PROPN
ejpam-6544	82	14	2(p4	2(p4	NUM
ejpam-6544	82	15	)	)	PUNCT
ejpam-6544	82	16	=	=	SYM
ejpam-6544	83	1	2	2	X
ejpam-6544	83	2	.	.	PUNCT
ejpam-6544	83	3	a.	a.	NOUN
ejpam-6544	83	4	madjatul	madjatul	PROPN
ejpam-6544	83	5	et	et	PROPN
ejpam-6544	83	6	al	al	PROPN
ejpam-6544	83	7	.	.	PUNCT
ejpam-6544	83	8	/	/	SYM
ejpam-6544	83	9	eur	eur	PROPN
ejpam-6544	83	10	.	.	PUNCT
ejpam-6544	84	1	j.	j.	PROPN
ejpam-6544	84	2	pure	pure	PROPN
ejpam-6544	84	3	appl	appl	PROPN
ejpam-6544	84	4	.	.	PROPN
ejpam-6544	84	5	math	math	PROPN
ejpam-6544	84	6	,	,	PUNCT
ejpam-6544	84	7	18	18	NUM
ejpam-6544	84	8	(	(	PUNCT
ejpam-6544	84	9	3	3	NUM
ejpam-6544	84	10	)	)	PUNCT
ejpam-6544	84	11	(	(	PUNCT
ejpam-6544	84	12	2025	2025	NUM
ejpam-6544	84	13	)	)	PUNCT
ejpam-6544	84	14	,	,	PUNCT
ejpam-6544	84	15	6544	6544	NUM
ejpam-6544	84	16	4	4	NUM
ejpam-6544	84	17	of	of	ADP
ejpam-6544	84	18	8	8	NUM
ejpam-6544	84	19	now	now	ADV
ejpam-6544	84	20	,	,	PUNCT
ejpam-6544	84	21	for	for	ADP
ejpam-6544	84	22	n	n	NUM
ejpam-6544	84	23	≥	≥	NUM
ejpam-6544	84	24	6	6	NUM
ejpam-6544	84	25	and	and	CCONJ
ejpam-6544	84	26	even	even	ADV
ejpam-6544	84	27	,	,	PUNCT
ejpam-6544	84	28	consider	consider	VERB
ejpam-6544	84	29	r	r	NOUN
ejpam-6544	84	30	=	=	SYM
ejpam-6544	84	31	{	{	PUNCT
ejpam-6544	84	32	a1	a1	NOUN
ejpam-6544	84	33	,	,	PUNCT
ejpam-6544	84	34	a3	a3	NOUN
ejpam-6544	84	35	,	,	PUNCT
ejpam-6544	84	36	a4	a4	PROPN
ejpam-6544	84	37	,	,	PUNCT
ejpam-6544	84	38	a5	a5	PROPN
ejpam-6544	84	39	,	,	PUNCT
ejpam-6544	84	40	a7	a7	PROPN
ejpam-6544	84	41	,	,	PUNCT
ejpam-6544	84	42	a8	a8	PROPN
ejpam-6544	84	43	,	,	PUNCT
ejpam-6544	84	44	a9	a9	NOUN
ejpam-6544	84	45	,	,	PUNCT
ejpam-6544	84	46	.	.	PUNCT
ejpam-6544	84	47	.	.	PUNCT
ejpam-6544	85	1	.	.	PUNCT
ejpam-6544	86	1	,	,	PUNCT
ejpam-6544	86	2	an−1	an−1	ADJ
ejpam-6544	86	3	}	}	PUNCT
ejpam-6544	86	4	.	.	PUNCT
ejpam-6544	87	1	then	then	ADV
ejpam-6544	87	2	the	the	DET
ejpam-6544	87	3	vertices	vertex	NOUN
ejpam-6544	87	4	a2	a2	PROPN
ejpam-6544	87	5	,	,	PUNCT
ejpam-6544	87	6	a6	a6	NOUN
ejpam-6544	87	7	,	,	PUNCT
ejpam-6544	87	8	...	...	PUNCT
ejpam-6544	87	9	,	,	PUNCT
ejpam-6544	87	10	an	an	PRON
ejpam-6544	87	11	can	can	AUX
ejpam-6544	87	12	not	not	PART
ejpam-6544	87	13	be	be	AUX
ejpam-6544	87	14	2	2	NUM
ejpam-6544	87	15	-	-	PUNCT
ejpam-6544	87	16	forced	forced	ADJ
ejpam-6544	87	17	.	.	PUNCT
ejpam-6544	88	1	thus	thus	ADV
ejpam-6544	88	2	,	,	PUNCT
ejpam-6544	88	3	r	r	NOUN
ejpam-6544	88	4	is	be	AUX
ejpam-6544	88	5	a	a	DET
ejpam-6544	88	6	failed	failed	ADJ
ejpam-6544	88	7	2	2	NUM
ejpam-6544	88	8	-	-	PUNCT
ejpam-6544	88	9	distance	distance	NOUN
ejpam-6544	88	10	zero	zero	NUM
ejpam-6544	88	11	forcing	force	VERB
ejpam-6544	88	12	set	set	NOUN
ejpam-6544	88	13	of	of	ADP
ejpam-6544	88	14	pn	pn	PROPN
ejpam-6544	88	15	.	.	PUNCT
ejpam-6544	89	1	now	now	ADV
ejpam-6544	89	2	,	,	PUNCT
ejpam-6544	89	3	if	if	SCONJ
ejpam-6544	89	4	we	we	PRON
ejpam-6544	89	5	add	add	VERB
ejpam-6544	89	6	vertex	vertex	NOUN
ejpam-6544	89	7	a2	a2	PROPN
ejpam-6544	89	8	to	to	ADP
ejpam-6544	89	9	r	r	NOUN
ejpam-6544	89	10	,	,	PUNCT
ejpam-6544	89	11	then	then	ADV
ejpam-6544	89	12	repeatedly	repeatedly	ADV
ejpam-6544	89	13	applying	apply	VERB
ejpam-6544	89	14	the	the	DET
ejpam-6544	89	15	2	2	NUM
ejpam-6544	89	16	-	-	PUNCT
ejpam-6544	89	17	distance	distance	NOUN
ejpam-6544	89	18	color	color	NOUN
ejpam-6544	89	19	change	change	NOUN
ejpam-6544	89	20	rule	rule	NOUN
ejpam-6544	89	21	on	on	ADP
ejpam-6544	89	22	r	r	NOUN
ejpam-6544	89	23	,	,	PUNCT
ejpam-6544	89	24	all	all	DET
ejpam-6544	89	25	vertices	vertice	VERB
ejpam-6544	89	26	outside	outside	ADV
ejpam-6544	89	27	r	r	NOUN
ejpam-6544	89	28	can	can	AUX
ejpam-6544	89	29	now	now	ADV
ejpam-6544	89	30	be	be	AUX
ejpam-6544	89	31	2	2	NUM
ejpam-6544	89	32	-	-	PUNCT
ejpam-6544	89	33	forced	force	VERB
ejpam-6544	89	34	,	,	PUNCT
ejpam-6544	89	35	which	which	PRON
ejpam-6544	89	36	is	be	AUX
ejpam-6544	89	37	a	a	DET
ejpam-6544	89	38	contradiction	contradiction	NOUN
ejpam-6544	89	39	.	.	PUNCT
ejpam-6544	90	1	similarly	similarly	ADV
ejpam-6544	90	2	,	,	PUNCT
ejpam-6544	90	3	if	if	SCONJ
ejpam-6544	90	4	we	we	PRON
ejpam-6544	90	5	add	add	VERB
ejpam-6544	90	6	vertices	vertex	NOUN
ejpam-6544	90	7	from	from	ADP
ejpam-6544	90	8	{	{	PUNCT
ejpam-6544	90	9	a6	a6	NOUN
ejpam-6544	90	10	,	,	PUNCT
ejpam-6544	90	11	a10	a10	PROPN
ejpam-6544	90	12	,	,	PUNCT
ejpam-6544	90	13	...	...	PUNCT
ejpam-6544	90	14	,	,	PUNCT
ejpam-6544	90	15	an	an	PRON
ejpam-6544	90	16	}	}	PUNCT
ejpam-6544	90	17	to	to	ADP
ejpam-6544	90	18	r	r	NOUN
ejpam-6544	90	19	,	,	PUNCT
ejpam-6544	90	20	then	then	ADV
ejpam-6544	90	21	r	r	NOUN
ejpam-6544	90	22	is	be	AUX
ejpam-6544	90	23	a	a	DET
ejpam-6544	90	24	2	2	NUM
ejpam-6544	90	25	-	-	PUNCT
ejpam-6544	90	26	distance	distance	NOUN
ejpam-6544	90	27	zero	zero	NUM
ejpam-6544	90	28	forcing	force	VERB
ejpam-6544	90	29	set	set	NOUN
ejpam-6544	90	30	of	of	ADP
ejpam-6544	90	31	pn	pn	PROPN
ejpam-6544	90	32	,	,	PUNCT
ejpam-6544	90	33	a	a	DET
ejpam-6544	90	34	contradiction	contradiction	NOUN
ejpam-6544	90	35	.	.	PUNCT
ejpam-6544	91	1	therefore	therefore	ADV
ejpam-6544	91	2	,	,	PUNCT
ejpam-6544	91	3	r	r	NOUN
ejpam-6544	91	4	is	be	AUX
ejpam-6544	91	5	a	a	DET
ejpam-6544	91	6	maximum	maximum	ADV
ejpam-6544	91	7	failed	fail	VERB
ejpam-6544	91	8	2	2	NUM
ejpam-6544	91	9	-	-	PUNCT
ejpam-6544	91	10	distance	distance	NOUN
ejpam-6544	91	11	zero	zero	NUM
ejpam-6544	91	12	forcing	force	VERB
ejpam-6544	91	13	set	set	NOUN
ejpam-6544	91	14	of	of	ADP
ejpam-6544	91	15	pn	pn	PROPN
ejpam-6544	91	16	.	.	PROPN
ejpam-6544	91	17	for	for	ADP
ejpam-6544	91	18	n	n	NOUN
ejpam-6544	91	19	=	=	SYM
ejpam-6544	91	20	5	5	X
ejpam-6544	91	21	.	.	PUNCT
ejpam-6544	92	1	let	let	VERB
ejpam-6544	92	2	t	t	NOUN
ejpam-6544	92	3	=	=	SYM
ejpam-6544	92	4	{	{	PUNCT
ejpam-6544	92	5	a2	a2	PROPN
ejpam-6544	92	6	,	,	PUNCT
ejpam-6544	92	7	a3	a3	NOUN
ejpam-6544	92	8	,	,	PUNCT
ejpam-6544	92	9	a4	a4	PROPN
ejpam-6544	92	10	}	}	PUNCT
ejpam-6544	92	11	.	.	PUNCT
ejpam-6544	93	1	then	then	ADV
ejpam-6544	93	2	a1	a1	PROPN
ejpam-6544	93	3	and	and	CCONJ
ejpam-6544	93	4	a5	a5	PROPN
ejpam-6544	93	5	can	can	AUX
ejpam-6544	93	6	not	not	PART
ejpam-6544	93	7	be	be	AUX
ejpam-6544	93	8	2	2	NUM
ejpam-6544	93	9	-	-	PUNCT
ejpam-6544	93	10	forced	forced	ADJ
ejpam-6544	93	11	.	.	PUNCT
ejpam-6544	94	1	hence	hence	ADV
ejpam-6544	94	2	,	,	PUNCT
ejpam-6544	94	3	t	t	PROPN
ejpam-6544	94	4	is	be	AUX
ejpam-6544	94	5	a	a	DET
ejpam-6544	94	6	failed	failed	ADJ
ejpam-6544	94	7	2	2	NUM
ejpam-6544	94	8	-	-	PUNCT
ejpam-6544	94	9	distance	distance	NOUN
ejpam-6544	94	10	zero	zero	NUM
ejpam-6544	94	11	forcing	force	VERB
ejpam-6544	94	12	set	set	NOUN
ejpam-6544	94	13	of	of	ADP
ejpam-6544	94	14	p5	p5	PROPN
ejpam-6544	94	15	.	.	PUNCT
ejpam-6544	95	1	now	now	ADV
ejpam-6544	95	2	,	,	PUNCT
ejpam-6544	95	3	if	if	SCONJ
ejpam-6544	95	4	we	we	PRON
ejpam-6544	95	5	add	add	VERB
ejpam-6544	95	6	a1	a1	NOUN
ejpam-6544	95	7	to	to	ADP
ejpam-6544	95	8	t	t	PROPN
ejpam-6544	95	9	.	.	PUNCT
ejpam-6544	96	1	then	then	ADV
ejpam-6544	96	2	vertex	vertex	NOUN
ejpam-6544	96	3	a5	a5	PROPN
ejpam-6544	96	4	can	can	AUX
ejpam-6544	96	5	now	now	ADV
ejpam-6544	96	6	be	be	AUX
ejpam-6544	96	7	2	2	NUM
ejpam-6544	96	8	-	-	PUNCT
ejpam-6544	96	9	forced	force	VERB
ejpam-6544	96	10	by	by	ADP
ejpam-6544	96	11	a	a	DET
ejpam-6544	96	12	vertex	vertex	NOUN
ejpam-6544	96	13	a3	a3	NOUN
ejpam-6544	96	14	,	,	PUNCT
ejpam-6544	96	15	a	a	DET
ejpam-6544	96	16	contradiction	contradiction	NOUN
ejpam-6544	96	17	.	.	PUNCT
ejpam-6544	97	1	thus	thus	ADV
ejpam-6544	97	2	,	,	PUNCT
ejpam-6544	97	3	t	t	PROPN
ejpam-6544	97	4	is	be	AUX
ejpam-6544	97	5	the	the	DET
ejpam-6544	97	6	maximum	maximum	NOUN
ejpam-6544	97	7	failed	fail	VERB
ejpam-6544	97	8	2	2	NUM
ejpam-6544	97	9	-	-	PUNCT
ejpam-6544	97	10	distance	distance	NOUN
ejpam-6544	97	11	zero	zero	NUM
ejpam-6544	97	12	forcing	forcing	NOUN
ejpam-6544	97	13	of	of	ADP
ejpam-6544	97	14	p5	p5	ADJ
ejpam-6544	97	15	.	.	PUNCT
ejpam-6544	98	1	assume	assume	VERB
ejpam-6544	98	2	that	that	SCONJ
ejpam-6544	98	3	n	n	PRON
ejpam-6544	98	4	≥	≥	NOUN
ejpam-6544	98	5	7	7	NUM
ejpam-6544	98	6	and	and	CCONJ
ejpam-6544	98	7	odd	odd	ADJ
ejpam-6544	98	8	.	.	PUNCT
ejpam-6544	99	1	consider	consider	VERB
ejpam-6544	99	2	the	the	DET
ejpam-6544	99	3	following	follow	VERB
ejpam-6544	99	4	cases	case	NOUN
ejpam-6544	99	5	:	:	PUNCT
ejpam-6544	99	6	case	case	NOUN
ejpam-6544	99	7	1	1	NUM
ejpam-6544	99	8	:	:	PUNCT
ejpam-6544	99	9	for	for	ADP
ejpam-6544	99	10	n	n	PRON
ejpam-6544	99	11	∈	∈	PROPN
ejpam-6544	99	12	{	{	PUNCT
ejpam-6544	99	13	7	7	NUM
ejpam-6544	99	14	,	,	PUNCT
ejpam-6544	99	15	11	11	NUM
ejpam-6544	99	16	,	,	PUNCT
ejpam-6544	99	17	15	15	NUM
ejpam-6544	99	18	,	,	PUNCT
ejpam-6544	99	19	...	...	PUNCT
ejpam-6544	99	20	}	}	PUNCT
ejpam-6544	99	21	,	,	PUNCT
ejpam-6544	99	22	consider	consider	VERB
ejpam-6544	99	23	q	q	PUNCT
ejpam-6544	99	24	=	=	PUNCT
ejpam-6544	99	25	{	{	PUNCT
ejpam-6544	99	26	a1	a1	NOUN
ejpam-6544	99	27	,	,	PUNCT
ejpam-6544	99	28	a3	a3	NOUN
ejpam-6544	99	29	,	,	PUNCT
ejpam-6544	99	30	a4	a4	PROPN
ejpam-6544	99	31	,	,	PUNCT
ejpam-6544	99	32	a5	a5	PROPN
ejpam-6544	99	33	,	,	PUNCT
ejpam-6544	99	34	a7	a7	PROPN
ejpam-6544	99	35	,	,	PUNCT
ejpam-6544	99	36	a8	a8	PROPN
ejpam-6544	99	37	,	,	PUNCT
ejpam-6544	99	38	a9	a9	NOUN
ejpam-6544	99	39	,	,	PUNCT
ejpam-6544	99	40	.	.	PUNCT
ejpam-6544	99	41	.	.	PUNCT
ejpam-6544	100	1	.	.	PUNCT
ejpam-6544	101	1	,	,	PUNCT
ejpam-6544	101	2	an−4	an−4	PROPN
ejpam-6544	101	3	,	,	PUNCT
ejpam-6544	101	4	an−3	an−3	PROPN
ejpam-6544	101	5	,	,	PUNCT
ejpam-6544	101	6	an−2	an−2	PROPN
ejpam-6544	101	7	,	,	PUNCT
ejpam-6544	101	8	an	an	PRON
ejpam-6544	101	9	}	}	PUNCT
ejpam-6544	101	10	.	.	PUNCT
ejpam-6544	102	1	then	then	ADV
ejpam-6544	102	2	vertices	vertice	VERB
ejpam-6544	102	3	in	in	ADP
ejpam-6544	102	4	v	v	NOUN
ejpam-6544	102	5	(	(	PUNCT
ejpam-6544	102	6	pn	pn	NOUN
ejpam-6544	102	7	)	)	PUNCT
ejpam-6544	102	8	\	\	PROPN
ejpam-6544	103	1	q	q	PROPN
ejpam-6544	103	2	can	can	AUX
ejpam-6544	103	3	not	not	PART
ejpam-6544	103	4	be	be	AUX
ejpam-6544	103	5	2	2	NUM
ejpam-6544	103	6	-	-	PUNCT
ejpam-6544	103	7	forced	forced	ADJ
ejpam-6544	103	8	.	.	PUNCT
ejpam-6544	104	1	it	it	PRON
ejpam-6544	104	2	follows	follow	VERB
ejpam-6544	104	3	q	q	NOUN
ejpam-6544	104	4	is	be	AUX
ejpam-6544	104	5	a	a	DET
ejpam-6544	104	6	failed	failed	ADJ
ejpam-6544	104	7	2	2	NUM
ejpam-6544	104	8	-	-	PUNCT
ejpam-6544	104	9	distance	distance	NOUN
ejpam-6544	104	10	zero	zero	NUM
ejpam-6544	104	11	forcing	forcing	NOUN
ejpam-6544	104	12	set	set	NOUN
ejpam-6544	104	13	.	.	PUNCT
ejpam-6544	105	1	now	now	ADV
ejpam-6544	105	2	,	,	PUNCT
ejpam-6544	105	3	if	if	SCONJ
ejpam-6544	105	4	we	we	PRON
ejpam-6544	105	5	add	add	VERB
ejpam-6544	105	6	a2	a2	PROPN
ejpam-6544	105	7	to	to	ADP
ejpam-6544	105	8	q	q	PRON
ejpam-6544	105	9	,	,	PUNCT
ejpam-6544	105	10	then	then	ADV
ejpam-6544	105	11	repeatedly	repeatedly	ADV
ejpam-6544	105	12	applying	apply	VERB
ejpam-6544	105	13	the	the	DET
ejpam-6544	105	14	2	2	NUM
ejpam-6544	105	15	-	-	PUNCT
ejpam-6544	105	16	distance	distance	NOUN
ejpam-6544	105	17	color	color	NOUN
ejpam-6544	105	18	change	change	NOUN
ejpam-6544	105	19	rule	rule	NOUN
ejpam-6544	105	20	on	on	ADP
ejpam-6544	105	21	q	q	X
ejpam-6544	105	22	,	,	PUNCT
ejpam-6544	105	23	all	all	DET
ejpam-6544	105	24	vertices	vertice	VERB
ejpam-6544	105	25	outside	outside	ADV
ejpam-6544	105	26	q	q	PROPN
ejpam-6544	105	27	can	can	AUX
ejpam-6544	105	28	now	now	ADV
ejpam-6544	105	29	be	be	AUX
ejpam-6544	105	30	2	2	NUM
ejpam-6544	105	31	-	-	PUNCT
ejpam-6544	105	32	forced	force	VERB
ejpam-6544	105	33	,	,	PUNCT
ejpam-6544	105	34	which	which	PRON
ejpam-6544	105	35	is	be	AUX
ejpam-6544	105	36	also	also	ADV
ejpam-6544	105	37	a	a	DET
ejpam-6544	105	38	contradiction	contradiction	NOUN
ejpam-6544	105	39	.	.	PUNCT
ejpam-6544	106	1	similarly	similarly	ADV
ejpam-6544	106	2	,	,	PUNCT
ejpam-6544	106	3	if	if	SCONJ
ejpam-6544	106	4	we	we	PRON
ejpam-6544	106	5	add	add	VERB
ejpam-6544	106	6	vertices	vertex	NOUN
ejpam-6544	106	7	from	from	ADP
ejpam-6544	106	8	{	{	PUNCT
ejpam-6544	106	9	a6	a6	NOUN
ejpam-6544	106	10	,	,	PUNCT
ejpam-6544	106	11	a10	a10	PROPN
ejpam-6544	106	12	,	,	PUNCT
ejpam-6544	106	13	...	...	PUNCT
ejpam-6544	106	14	,	,	PUNCT
ejpam-6544	106	15	an−1	an−1	ADJ
ejpam-6544	106	16	}	}	PUNCT
ejpam-6544	106	17	to	to	ADP
ejpam-6544	106	18	q	q	PRON
ejpam-6544	106	19	,	,	PUNCT
ejpam-6544	106	20	then	then	ADV
ejpam-6544	106	21	q	q	X
ejpam-6544	106	22	is	be	AUX
ejpam-6544	106	23	a	a	DET
ejpam-6544	106	24	failed	failed	ADJ
ejpam-6544	106	25	2	2	NUM
ejpam-6544	106	26	-	-	PUNCT
ejpam-6544	106	27	distance	distance	NOUN
ejpam-6544	106	28	zero	zero	NUM
ejpam-6544	106	29	forcing	force	VERB
ejpam-6544	106	30	set	set	NOUN
ejpam-6544	106	31	of	of	ADP
ejpam-6544	106	32	pn	pn	PROPN
ejpam-6544	106	33	,	,	PUNCT
ejpam-6544	106	34	another	another	DET
ejpam-6544	106	35	contradiction	contradiction	NOUN
ejpam-6544	106	36	.	.	PUNCT
ejpam-6544	107	1	thus	thus	ADV
ejpam-6544	107	2	,	,	PUNCT
ejpam-6544	107	3	q	q	PROPN
ejpam-6544	107	4	is	be	AUX
ejpam-6544	107	5	a	a	DET
ejpam-6544	107	6	maximum	maximum	ADV
ejpam-6544	107	7	failed	fail	VERB
ejpam-6544	107	8	2	2	NUM
ejpam-6544	107	9	-	-	PUNCT
ejpam-6544	107	10	distance	distance	NOUN
ejpam-6544	107	11	zero	zero	NUM
ejpam-6544	107	12	forcing	force	VERB
ejpam-6544	107	13	set	set	NOUN
ejpam-6544	107	14	of	of	ADP
ejpam-6544	107	15	pn	pn	PROPN
ejpam-6544	107	16	.	.	PROPN
ejpam-6544	107	17	case	case	NOUN
ejpam-6544	107	18	2	2	NUM
ejpam-6544	107	19	:	:	PUNCT
ejpam-6544	107	20	for	for	ADP
ejpam-6544	107	21	n	n	PRON
ejpam-6544	107	22	∈	∈	NOUN
ejpam-6544	107	23	{	{	PUNCT
ejpam-6544	107	24	9	9	NUM
ejpam-6544	107	25	,	,	PUNCT
ejpam-6544	107	26	13	13	NUM
ejpam-6544	107	27	,	,	PUNCT
ejpam-6544	107	28	17	17	NUM
ejpam-6544	107	29	,	,	PUNCT
ejpam-6544	107	30	...	...	PUNCT
ejpam-6544	107	31	}	}	PUNCT
ejpam-6544	107	32	,	,	PUNCT
ejpam-6544	107	33	consider	consider	VERB
ejpam-6544	107	34	q′	q′	NOUN
ejpam-6544	107	35	=	=	SYM
ejpam-6544	107	36	{	{	PUNCT
ejpam-6544	107	37	a1	a1	PROPN
ejpam-6544	107	38	,	,	PUNCT
ejpam-6544	107	39	a3	a3	NOUN
ejpam-6544	107	40	,	,	PUNCT
ejpam-6544	107	41	a4	a4	PROPN
ejpam-6544	107	42	,	,	PUNCT
ejpam-6544	107	43	a5	a5	PROPN
ejpam-6544	107	44	,	,	PUNCT
ejpam-6544	107	45	a7	a7	PROPN
ejpam-6544	107	46	,	,	PUNCT
ejpam-6544	107	47	a8	a8	PROPN
ejpam-6544	107	48	,	,	PUNCT
ejpam-6544	107	49	a9	a9	NOUN
ejpam-6544	107	50	,	,	PUNCT
ejpam-6544	107	51	.	.	PUNCT
ejpam-6544	107	52	.	.	PUNCT
ejpam-6544	108	1	.	.	PUNCT
ejpam-6544	109	1	,	,	PUNCT
ejpam-6544	109	2	an−6	an−6	NOUN
ejpam-6544	109	3	,	,	PUNCT
ejpam-6544	109	4	an−5	an−5	PROPN
ejpam-6544	109	5	,	,	PUNCT
ejpam-6544	109	6	an−4	an−4	PROPN
ejpam-6544	109	7	,	,	PUNCT
ejpam-6544	109	8	an−2	an−2	PROPN
ejpam-6544	109	9	,	,	PUNCT
ejpam-6544	109	10	an	an	PRON
ejpam-6544	109	11	}	}	PUNCT
ejpam-6544	109	12	.	.	PUNCT
ejpam-6544	110	1	then	then	ADV
ejpam-6544	110	2	vertices	vertice	VERB
ejpam-6544	110	3	in	in	ADP
ejpam-6544	110	4	v	v	NOUN
ejpam-6544	110	5	(	(	PUNCT
ejpam-6544	110	6	pn	pn	NOUN
ejpam-6544	110	7	)	)	PUNCT
ejpam-6544	110	8	\	\	NOUN
ejpam-6544	110	9	q′	q′	NOUN
ejpam-6544	110	10	can	can	AUX
ejpam-6544	110	11	not	not	PART
ejpam-6544	110	12	be	be	AUX
ejpam-6544	110	13	2	2	NUM
ejpam-6544	110	14	-	-	PUNCT
ejpam-6544	110	15	forced	forced	ADJ
ejpam-6544	110	16	.	.	PUNCT
ejpam-6544	111	1	it	it	PRON
ejpam-6544	111	2	follows	follow	VERB
ejpam-6544	111	3	q′	q′	NOUN
ejpam-6544	111	4	is	be	AUX
ejpam-6544	111	5	a	a	DET
ejpam-6544	111	6	failed	failed	ADJ
ejpam-6544	111	7	2	2	NUM
ejpam-6544	111	8	-	-	PUNCT
ejpam-6544	111	9	distance	distance	NOUN
ejpam-6544	111	10	zero	zero	NUM
ejpam-6544	111	11	forcing	forcing	NOUN
ejpam-6544	111	12	set	set	NOUN
ejpam-6544	111	13	.	.	PUNCT
ejpam-6544	112	1	now	now	ADV
ejpam-6544	112	2	,	,	PUNCT
ejpam-6544	112	3	if	if	SCONJ
ejpam-6544	112	4	we	we	PRON
ejpam-6544	112	5	add	add	VERB
ejpam-6544	112	6	a2	a2	PROPN
ejpam-6544	112	7	to	to	ADP
ejpam-6544	112	8	q′	q′	NOUN
ejpam-6544	112	9	,	,	PUNCT
ejpam-6544	112	10	then	then	ADV
ejpam-6544	112	11	repeatedly	repeatedly	ADV
ejpam-6544	112	12	applying	apply	VERB
ejpam-6544	112	13	the	the	DET
ejpam-6544	112	14	2	2	NUM
ejpam-6544	112	15	-	-	PUNCT
ejpam-6544	112	16	distance	distance	NOUN
ejpam-6544	112	17	color	color	NOUN
ejpam-6544	112	18	change	change	NOUN
ejpam-6544	112	19	rule	rule	NOUN
ejpam-6544	112	20	on	on	ADP
ejpam-6544	112	21	q′	q′	NOUN
ejpam-6544	112	22	,	,	PUNCT
ejpam-6544	112	23	all	all	DET
ejpam-6544	112	24	vertices	vertice	VERB
ejpam-6544	112	25	outside	outside	ADV
ejpam-6544	112	26	q′	q′	NOUN
ejpam-6544	112	27	can	can	AUX
ejpam-6544	112	28	now	now	ADV
ejpam-6544	112	29	be	be	AUX
ejpam-6544	112	30	2	2	NUM
ejpam-6544	112	31	-	-	PUNCT
ejpam-6544	112	32	forced	force	VERB
ejpam-6544	112	33	,	,	PUNCT
ejpam-6544	112	34	a	a	DET
ejpam-6544	112	35	contradiction	contradiction	NOUN
ejpam-6544	112	36	.	.	PUNCT
ejpam-6544	113	1	similarly	similarly	ADV
ejpam-6544	113	2	,	,	PUNCT
ejpam-6544	113	3	if	if	SCONJ
ejpam-6544	113	4	we	we	PRON
ejpam-6544	113	5	add	add	VERB
ejpam-6544	113	6	vertices	vertex	NOUN
ejpam-6544	113	7	from	from	ADP
ejpam-6544	113	8	{	{	PUNCT
ejpam-6544	113	9	a6	a6	NOUN
ejpam-6544	113	10	,	,	PUNCT
ejpam-6544	113	11	a10	a10	PROPN
ejpam-6544	113	12	,	,	PUNCT
ejpam-6544	113	13	...	...	PUNCT
ejpam-6544	113	14	,	,	PUNCT
ejpam-6544	113	15	an−3	an−3	PROPN
ejpam-6544	113	16	,	,	PUNCT
ejpam-6544	113	17	an−1	an−1	ADJ
ejpam-6544	113	18	}	}	PUNCT
ejpam-6544	113	19	to	to	ADP
ejpam-6544	113	20	q′	q′	NOUN
ejpam-6544	113	21	,	,	PUNCT
ejpam-6544	113	22	then	then	ADV
ejpam-6544	113	23	q′	q′	NOUN
ejpam-6544	113	24	is	be	AUX
ejpam-6544	113	25	a	a	DET
ejpam-6544	113	26	failed	failed	ADJ
ejpam-6544	113	27	2	2	NUM
ejpam-6544	113	28	-	-	PUNCT
ejpam-6544	113	29	distance	distance	NOUN
ejpam-6544	113	30	zero	zero	NUM
ejpam-6544	113	31	forcing	force	VERB
ejpam-6544	113	32	set	set	NOUN
ejpam-6544	113	33	of	of	ADP
ejpam-6544	113	34	pn	pn	PROPN
ejpam-6544	113	35	,	,	PUNCT
ejpam-6544	113	36	another	another	DET
ejpam-6544	113	37	contradiction	contradiction	NOUN
ejpam-6544	113	38	.	.	PUNCT
ejpam-6544	114	1	thus	thus	ADV
ejpam-6544	114	2	,	,	PUNCT
ejpam-6544	114	3	q	q	NOUN
ejpam-6544	114	4	′	′	NUM
ejpam-6544	114	5	is	be	AUX
ejpam-6544	114	6	a	a	DET
ejpam-6544	114	7	maximum	maximum	NOUN
ejpam-6544	114	8	failed	fail	VERB
ejpam-6544	114	9	2	2	NUM
ejpam-6544	114	10	-	-	PUNCT
ejpam-6544	114	11	distance	distance	NOUN
ejpam-6544	114	12	zero	zero	NUM
ejpam-6544	114	13	forcing	force	VERB
ejpam-6544	114	14	set	set	NOUN
ejpam-6544	114	15	of	of	ADP
ejpam-6544	114	16	pn	pn	PROPN
ejpam-6544	114	17	.	.	PUNCT
ejpam-6544	115	1	therefore	therefore	ADV
ejpam-6544	115	2	,	,	PUNCT
ejpam-6544	115	3	f	f	PROPN
ejpam-6544	115	4	2(pn	2(pn	NUM
ejpam-6544	115	5	)	)	PUNCT
ejpam-6544	115	6	=	=	SYM
ejpam-6544	116	1	n−	n−	NOUN
ejpam-6544	116	2	(	(	PUNCT
ejpam-6544	116	3	⌊n	⌊n	X
ejpam-6544	116	4	4	4	NUM
ejpam-6544	116	5	⌋+	⌋+	NOUN
ejpam-6544	116	6	1	1	NUM
ejpam-6544	116	7	)	)	PUNCT
ejpam-6544	116	8	for	for	ADP
ejpam-6544	116	9	n	n	X
ejpam-6544	116	10	≥	≥	NOUN
ejpam-6544	116	11	4	4	NUM
ejpam-6544	116	12	.	.	PUNCT
ejpam-6544	117	1	now	now	ADV
ejpam-6544	117	2	,	,	PUNCT
ejpam-6544	117	3	we	we	PRON
ejpam-6544	117	4	will	will	AUX
ejpam-6544	117	5	characterize	characterize	VERB
ejpam-6544	117	6	a	a	DET
ejpam-6544	117	7	failed	fail	VERB
ejpam-6544	117	8	2	2	NUM
ejpam-6544	117	9	-	-	PUNCT
ejpam-6544	117	10	distance	distance	NOUN
ejpam-6544	117	11	zero	zero	NUM
ejpam-6544	117	12	forcing	force	VERB
ejpam-6544	117	13	set	set	NOUN
ejpam-6544	117	14	in	in	ADP
ejpam-6544	117	15	star	star	NOUN
ejpam-6544	117	16	graph	graph	NOUN
ejpam-6544	117	17	to	to	PART
ejpam-6544	117	18	derive	derive	VERB
ejpam-6544	117	19	the	the	DET
ejpam-6544	117	20	parameter	parameter	NOUN
ejpam-6544	117	21	’s	’s	PART
ejpam-6544	117	22	formula	formula	NOUN
ejpam-6544	117	23	for	for	ADP
ejpam-6544	117	24	the	the	DET
ejpam-6544	117	25	said	say	VERB
ejpam-6544	117	26	graph	graph	NOUN
ejpam-6544	117	27	.	.	PUNCT
ejpam-6544	118	1	a.	a.	NOUN
ejpam-6544	118	2	madjatul	madjatul	PROPN
ejpam-6544	118	3	et	et	PROPN
ejpam-6544	118	4	al	al	PROPN
ejpam-6544	118	5	.	.	PUNCT
ejpam-6544	118	6	/	/	SYM
ejpam-6544	118	7	eur	eur	PROPN
ejpam-6544	118	8	.	.	PUNCT
ejpam-6544	119	1	j.	j.	PROPN
ejpam-6544	119	2	pure	pure	PROPN
ejpam-6544	119	3	appl	appl	PROPN
ejpam-6544	119	4	.	.	PROPN
ejpam-6544	119	5	math	math	PROPN
ejpam-6544	119	6	,	,	PUNCT
ejpam-6544	119	7	18	18	NUM
ejpam-6544	119	8	(	(	PUNCT
ejpam-6544	119	9	3	3	NUM
ejpam-6544	119	10	)	)	PUNCT
ejpam-6544	119	11	(	(	PUNCT
ejpam-6544	119	12	2025	2025	NUM
ejpam-6544	119	13	)	)	PUNCT
ejpam-6544	119	14	,	,	PUNCT
ejpam-6544	119	15	6544	6544	NUM
ejpam-6544	119	16	5	5	NUM
ejpam-6544	119	17	of	of	ADP
ejpam-6544	119	18	8	8	NUM
ejpam-6544	119	19	theorem	theorem	NOUN
ejpam-6544	119	20	3	3	X
ejpam-6544	119	21	.	.	PUNCT
ejpam-6544	120	1	let	let	VERB
ejpam-6544	120	2	n	n	PRON
ejpam-6544	120	3	be	be	AUX
ejpam-6544	120	4	a	a	DET
ejpam-6544	120	5	positive	positive	ADJ
ejpam-6544	120	6	integer	integer	NOUN
ejpam-6544	120	7	and	and	CCONJ
ejpam-6544	120	8	v	v	AUX
ejpam-6544	120	9	be	be	AUX
ejpam-6544	120	10	a	a	DET
ejpam-6544	120	11	dominating	dominating	NOUN
ejpam-6544	120	12	vertex	vertex	NOUN
ejpam-6544	120	13	of	of	ADP
ejpam-6544	120	14	sn	sn	PROPN
ejpam-6544	120	15	.	.	PUNCT
ejpam-6544	121	1	then	then	ADV
ejpam-6544	121	2	s	s	VERB
ejpam-6544	121	3	⊂	⊂	PROPN
ejpam-6544	121	4	v	v	X
ejpam-6544	121	5	(	(	PUNCT
ejpam-6544	121	6	sn	sn	PROPN
ejpam-6544	121	7	)	)	PUNCT
ejpam-6544	121	8	is	be	AUX
ejpam-6544	121	9	a	a	DET
ejpam-6544	121	10	failed	failed	ADJ
ejpam-6544	121	11	2	2	NUM
ejpam-6544	121	12	-	-	PUNCT
ejpam-6544	121	13	distance	distance	NOUN
ejpam-6544	121	14	zero	zero	NUM
ejpam-6544	121	15	forcing	force	VERB
ejpam-6544	121	16	set	set	NOUN
ejpam-6544	121	17	in	in	ADP
ejpam-6544	121	18	sn	sn	PROPN
ejpam-6544	121	19	if	if	SCONJ
ejpam-6544	121	20	and	and	CCONJ
ejpam-6544	121	21	only	only	ADV
ejpam-6544	121	22	if	if	SCONJ
ejpam-6544	121	23	one	one	NUM
ejpam-6544	121	24	of	of	ADP
ejpam-6544	121	25	the	the	DET
ejpam-6544	121	26	following	follow	VERB
ejpam-6544	121	27	conditions	condition	NOUN
ejpam-6544	121	28	holds	hold	VERB
ejpam-6544	121	29	:	:	PUNCT
ejpam-6544	121	30	(	(	PUNCT
ejpam-6544	121	31	i	i	NOUN
ejpam-6544	121	32	)	)	PUNCT
ejpam-6544	121	33	if	if	SCONJ
ejpam-6544	121	34	v	v	NUM
ejpam-6544	121	35	∈	∈	PROPN
ejpam-6544	121	36	s	s	NOUN
ejpam-6544	121	37	,	,	PUNCT
ejpam-6544	121	38	then	then	ADV
ejpam-6544	121	39	at	at	ADP
ejpam-6544	121	40	least	least	ADV
ejpam-6544	121	41	two	two	NUM
ejpam-6544	121	42	vertices	vertex	NOUN
ejpam-6544	121	43	in	in	ADP
ejpam-6544	121	44	kn	kn	PROPN
ejpam-6544	121	45	must	must	AUX
ejpam-6544	121	46	not	not	PART
ejpam-6544	121	47	be	be	AUX
ejpam-6544	121	48	in	in	ADP
ejpam-6544	121	49	s.	s.	PROPN
ejpam-6544	121	50	(	(	PUNCT
ejpam-6544	121	51	ii	ii	PROPN
ejpam-6544	121	52	)	)	PUNCT
ejpam-6544	121	53	v	v	NOUN
ejpam-6544	121	54	/∈	/∈	PUNCT
ejpam-6544	122	1	s	s	X
ejpam-6544	122	2	,	,	PUNCT
ejpam-6544	122	3	then	then	ADV
ejpam-6544	122	4	s	s	VERB
ejpam-6544	122	5	⊆	⊆	NUM
ejpam-6544	122	6	kn	kn	PROPN
ejpam-6544	122	7	.	.	PUNCT
ejpam-6544	123	1	proof	proof	PROPN
ejpam-6544	123	2	.	.	PUNCT
ejpam-6544	124	1	suppose	suppose	VERB
ejpam-6544	124	2	that	that	SCONJ
ejpam-6544	124	3	s	s	VERB
ejpam-6544	124	4	⊂	⊂	PROPN
ejpam-6544	124	5	v	v	X
ejpam-6544	124	6	(	(	PUNCT
ejpam-6544	124	7	sn	sn	PROPN
ejpam-6544	124	8	)	)	PUNCT
ejpam-6544	124	9	is	be	AUX
ejpam-6544	124	10	a	a	DET
ejpam-6544	124	11	failed2	failed2	NOUN
ejpam-6544	124	12	distance	distance	NOUN
ejpam-6544	124	13	zero	zero	NUM
ejpam-6544	124	14	forcing	force	VERB
ejpam-6544	124	15	set	set	NOUN
ejpam-6544	124	16	of	of	ADP
ejpam-6544	124	17	sn	sn	PROPN
ejpam-6544	124	18	.	.	PUNCT
ejpam-6544	125	1	let	let	VERB
ejpam-6544	125	2	v	v	PART
ejpam-6544	125	3	be	be	AUX
ejpam-6544	125	4	a	a	DET
ejpam-6544	125	5	dominating	dominating	NOUN
ejpam-6544	125	6	vertex	vertex	NOUN
ejpam-6544	125	7	of	of	ADP
ejpam-6544	125	8	sn	sn	PROPN
ejpam-6544	125	9	such	such	ADJ
ejpam-6544	125	10	that	that	PRON
ejpam-6544	125	11	v	v	NOUN
ejpam-6544	125	12	∈	∈	PROPN
ejpam-6544	125	13	s.	s.	PROPN
ejpam-6544	125	14	assume	assume	VERB
ejpam-6544	125	15	that	that	SCONJ
ejpam-6544	125	16	there	there	PRON
ejpam-6544	125	17	is	be	VERB
ejpam-6544	125	18	at	at	ADP
ejpam-6544	125	19	most	most	ADV
ejpam-6544	125	20	one	one	NUM
ejpam-6544	125	21	vertex	vertex	NOUN
ejpam-6544	125	22	w	w	NOUN
ejpam-6544	125	23	∈	∈	PROPN
ejpam-6544	125	24	v	v	ADP
ejpam-6544	125	25	(	(	PUNCT
ejpam-6544	125	26	kn	kn	PROPN
ejpam-6544	125	27	)	)	PUNCT
ejpam-6544	125	28	such	such	ADJ
ejpam-6544	125	29	that	that	PRON
ejpam-6544	125	30	w	w	PROPN
ejpam-6544	125	31	/∈	/∈	PUNCT
ejpam-6544	125	32	s.	s.	PROPN
ejpam-6544	126	1	then	then	ADV
ejpam-6544	126	2	s	s	VERB
ejpam-6544	126	3	=	=	SYM
ejpam-6544	126	4	v	v	PROPN
ejpam-6544	126	5	(	(	PUNCT
ejpam-6544	126	6	sn	sn	PROPN
ejpam-6544	126	7	)	)	PUNCT
ejpam-6544	126	8	\	\	NOUN
ejpam-6544	127	1	{	{	PUNCT
ejpam-6544	127	2	w}=	w}=	PROPN
ejpam-6544	127	3	v	v	PROPN
ejpam-6544	127	4	(	(	PUNCT
ejpam-6544	127	5	kn	kn	NOUN
ejpam-6544	127	6	+	+	NOUN
ejpam-6544	127	7	k1	k1	NOUN
ejpam-6544	127	8	)	)	PUNCT
ejpam-6544	127	9	\	\	NOUN
ejpam-6544	128	1	{	{	PUNCT
ejpam-6544	128	2	w	w	NOUN
ejpam-6544	128	3	}	}	PUNCT
ejpam-6544	128	4	is	be	AUX
ejpam-6544	128	5	a	a	DET
ejpam-6544	128	6	2distance	2distance	NUM
ejpam-6544	128	7	zero	zero	NUM
ejpam-6544	128	8	forcing	force	VERB
ejpam-6544	128	9	set	set	NOUN
ejpam-6544	128	10	of	of	ADP
ejpam-6544	128	11	sn	sn	PROPN
ejpam-6544	128	12	since	since	SCONJ
ejpam-6544	128	13	dsn(w	dsn(w	PROPN
ejpam-6544	128	14	,	,	PUNCT
ejpam-6544	128	15	y	y	NOUN
ejpam-6544	128	16	)	)	PUNCT
ejpam-6544	128	17	=	=	SYM
ejpam-6544	128	18	2	2	NUM
ejpam-6544	128	19	for	for	ADP
ejpam-6544	128	20	some	some	DET
ejpam-6544	128	21	vertex	vertex	NOUN
ejpam-6544	128	22	y	y	PROPN
ejpam-6544	128	23	∈	∈	PROPN
ejpam-6544	128	24	v	v	PROPN
ejpam-6544	128	25	(	(	PUNCT
ejpam-6544	128	26	sn	sn	NOUN
ejpam-6544	128	27	)	)	PUNCT
ejpam-6544	128	28	\	\	NOUN
ejpam-6544	128	29	{	{	PUNCT
ejpam-6544	128	30	w}=	w}=	PROPN
ejpam-6544	128	31	s.	s.	PROPN
ejpam-6544	128	32	that	that	PRON
ejpam-6544	128	33	is	be	AUX
ejpam-6544	128	34	,	,	PUNCT
ejpam-6544	128	35	w	w	PROPN
ejpam-6544	128	36	can	can	AUX
ejpam-6544	128	37	be	be	AUX
ejpam-6544	128	38	2	2	NUM
ejpam-6544	128	39	-	-	PUNCT
ejpam-6544	128	40	forced	force	VERB
ejpam-6544	128	41	by	by	ADP
ejpam-6544	128	42	y	y	PROPN
ejpam-6544	128	43	∈	∈	PROPN
ejpam-6544	128	44	v	v	PROPN
ejpam-6544	128	45	(	(	PUNCT
ejpam-6544	128	46	sn)\{w}=s	sn)\{w}=s	NOUN
ejpam-6544	128	47	.	.	PUNCT
ejpam-6544	129	1	however	however	ADV
ejpam-6544	129	2	,	,	PUNCT
ejpam-6544	129	3	this	this	PRON
ejpam-6544	129	4	is	be	AUX
ejpam-6544	129	5	a	a	DET
ejpam-6544	129	6	contradiction	contradiction	NOUN
ejpam-6544	129	7	to	to	ADP
ejpam-6544	129	8	our	our	PRON
ejpam-6544	129	9	assumption	assumption	NOUN
ejpam-6544	129	10	that	that	SCONJ
ejpam-6544	129	11	s	s	VERB
ejpam-6544	129	12	is	be	AUX
ejpam-6544	129	13	a	a	DET
ejpam-6544	129	14	failed	failed	ADJ
ejpam-6544	129	15	2	2	NUM
ejpam-6544	129	16	-	-	PUNCT
ejpam-6544	129	17	distance	distance	NOUN
ejpam-6544	129	18	zero	zero	NUM
ejpam-6544	129	19	forcing	force	VERB
ejpam-6544	129	20	hence,(a	hence,(a	NOUN
ejpam-6544	129	21	)	)	PUNCT
ejpam-6544	129	22	holds	hold	VERB
ejpam-6544	129	23	.	.	PUNCT
ejpam-6544	130	1	let	let	VERB
ejpam-6544	130	2	v	v	NOUN
ejpam-6544	130	3	/∈	/∈	PUNCT
ejpam-6544	131	1	s	s	X
ejpam-6544	131	2	,	,	PUNCT
ejpam-6544	131	3	then	then	ADV
ejpam-6544	131	4	it	it	PRON
ejpam-6544	131	5	is	be	AUX
ejpam-6544	131	6	clearly	clearly	ADV
ejpam-6544	131	7	that	that	SCONJ
ejpam-6544	131	8	s	s	VERB
ejpam-6544	131	9	⊆	⊆	NUM
ejpam-6544	131	10	v	v	NOUN
ejpam-6544	131	11	(	(	PUNCT
ejpam-6544	131	12	kn	kn	PROPN
ejpam-6544	131	13	)	)	PUNCT
ejpam-6544	131	14	.	.	PUNCT
ejpam-6544	132	1	thus	thus	ADV
ejpam-6544	132	2	,	,	PUNCT
ejpam-6544	132	3	(	(	PUNCT
ejpam-6544	132	4	b	b	X
ejpam-6544	132	5	)	)	PUNCT
ejpam-6544	132	6	also	also	ADV
ejpam-6544	132	7	holds	hold	VERB
ejpam-6544	132	8	.	.	PUNCT
ejpam-6544	133	1	conversely	conversely	ADV
ejpam-6544	133	2	,	,	PUNCT
ejpam-6544	133	3	if	if	SCONJ
ejpam-6544	133	4	(	(	PUNCT
ejpam-6544	133	5	a	a	PRON
ejpam-6544	133	6	)	)	PUNCT
ejpam-6544	133	7	holds	hold	NOUN
ejpam-6544	133	8	.	.	PUNCT
ejpam-6544	134	1	then	then	ADV
ejpam-6544	134	2	the	the	DET
ejpam-6544	134	3	remaining	remain	VERB
ejpam-6544	134	4	at	at	ADV
ejpam-6544	134	5	least	least	ADV
ejpam-6544	134	6	two	two	NUM
ejpam-6544	134	7	vertices	vertex	NOUN
ejpam-6544	134	8	in	in	ADP
ejpam-6544	134	9	v	v	PROPN
ejpam-6544	134	10	(	(	PUNCT
ejpam-6544	134	11	sn	sn	NOUN
ejpam-6544	134	12	)	)	PUNCT
ejpam-6544	134	13	\	\	PROPN
ejpam-6544	135	1	s	s	AUX
ejpam-6544	135	2	can	can	AUX
ejpam-6544	135	3	not	not	PART
ejpam-6544	135	4	be	be	AUX
ejpam-6544	135	5	2	2	NUM
ejpam-6544	135	6	-	-	PUNCT
ejpam-6544	135	7	forced	force	VERB
ejpam-6544	135	8	by	by	ADP
ejpam-6544	135	9	s.	s.	PROPN
ejpam-6544	135	10	thus	thus	ADV
ejpam-6544	135	11	,	,	PUNCT
ejpam-6544	135	12	s	s	VERB
ejpam-6544	135	13	is	be	AUX
ejpam-6544	135	14	a	a	DET
ejpam-6544	135	15	failed	failed	ADJ
ejpam-6544	135	16	2	2	NUM
ejpam-6544	135	17	-	-	PUNCT
ejpam-6544	135	18	distance	distance	NOUN
ejpam-6544	135	19	zero	zero	NUM
ejpam-6544	135	20	forcing	forcing	NOUN
ejpam-6544	135	21	.	.	PUNCT
ejpam-6544	136	1	similarly	similarly	ADV
ejpam-6544	136	2	,	,	PUNCT
ejpam-6544	136	3	the	the	DET
ejpam-6544	136	4	same	same	ADJ
ejpam-6544	136	5	assertion	assertion	NOUN
ejpam-6544	136	6	follows	follow	VERB
ejpam-6544	136	7	when	when	SCONJ
ejpam-6544	136	8	(	(	PUNCT
ejpam-6544	136	9	b	b	X
ejpam-6544	136	10	)	)	PUNCT
ejpam-6544	136	11	holds	hold	VERB
ejpam-6544	136	12	.	.	PUNCT
ejpam-6544	137	1	since	since	SCONJ
ejpam-6544	137	2	the	the	DET
ejpam-6544	137	3	failed	fail	VERB
ejpam-6544	137	4	2	2	NUM
ejpam-6544	137	5	-	-	PUNCT
ejpam-6544	137	6	distance	distance	NOUN
ejpam-6544	137	7	zero	zero	NUM
ejpam-6544	137	8	forcing	forcing	NOUN
ejpam-6544	137	9	number	number	NOUN
ejpam-6544	137	10	was	be	AUX
ejpam-6544	137	11	defined	define	VERB
ejpam-6544	137	12	with	with	ADP
ejpam-6544	137	13	respect	respect	NOUN
ejpam-6544	137	14	to	to	ADP
ejpam-6544	137	15	the	the	DET
ejpam-6544	137	16	maximality	maximality	NOUN
ejpam-6544	137	17	of	of	ADP
ejpam-6544	137	18	its	its	PRON
ejpam-6544	137	19	corresponding	corresponding	ADJ
ejpam-6544	137	20	set	set	NOUN
ejpam-6544	137	21	,	,	PUNCT
ejpam-6544	137	22	the	the	DET
ejpam-6544	137	23	following	following	ADJ
ejpam-6544	137	24	result	result	NOUN
ejpam-6544	137	25	follows	follow	VERB
ejpam-6544	137	26	immediately	immediately	ADV
ejpam-6544	137	27	from	from	ADP
ejpam-6544	137	28	theorem	theorem	ADJ
ejpam-6544	137	29	3	3	NUM
ejpam-6544	137	30	.	.	PUNCT
ejpam-6544	137	31	corollary	corollary	ADJ
ejpam-6544	137	32	2	2	NUM
ejpam-6544	137	33	.	.	PUNCT
ejpam-6544	138	1	let	let	VERB
ejpam-6544	138	2	n	n	PRON
ejpam-6544	138	3	be	be	AUX
ejpam-6544	138	4	a	a	DET
ejpam-6544	138	5	positive	positive	ADJ
ejpam-6544	138	6	integer	integer	NOUN
ejpam-6544	138	7	.	.	PUNCT
ejpam-6544	139	1	then	then	ADV
ejpam-6544	139	2	f	f	PROPN
ejpam-6544	139	3	2(sn	2(sn	NUM
ejpam-6544	139	4	)	)	PUNCT
ejpam-6544	139	5	=	=	SYM
ejpam-6544	139	6	n	n	PROPN
ejpam-6544	139	7	for	for	ADP
ejpam-6544	139	8	all	all	DET
ejpam-6544	139	9	n	n	PRON
ejpam-6544	139	10	≥	≥	NOUN
ejpam-6544	139	11	1	1	NUM
ejpam-6544	139	12	.	.	X
ejpam-6544	139	13	5	5	NUM
ejpam-6544	139	14	.	.	NUM
ejpam-6544	139	15	failed	fail	VERB
ejpam-6544	139	16	2	2	NUM
ejpam-6544	139	17	-	-	PUNCT
ejpam-6544	139	18	distance	distance	NOUN
ejpam-6544	139	19	zero	zero	NUM
ejpam-6544	139	20	forcing	force	VERB
ejpam-6544	139	21	in	in	ADP
ejpam-6544	139	22	the	the	DET
ejpam-6544	139	23	join	join	NOUN
ejpam-6544	139	24	of	of	ADP
ejpam-6544	139	25	two	two	NUM
ejpam-6544	139	26	graphs	graph	NOUN
ejpam-6544	139	27	we	we	PRON
ejpam-6544	139	28	shall	shall	AUX
ejpam-6544	139	29	define	define	VERB
ejpam-6544	139	30	the	the	DET
ejpam-6544	139	31	following	follow	VERB
ejpam-6544	139	32	definition	definition	NOUN
ejpam-6544	139	33	to	to	PART
ejpam-6544	139	34	study	study	VERB
ejpam-6544	139	35	the	the	DET
ejpam-6544	139	36	behavior	behavior	NOUN
ejpam-6544	139	37	of	of	ADP
ejpam-6544	139	38	failed	fail	VERB
ejpam-6544	139	39	2	2	NUM
ejpam-6544	139	40	-	-	PUNCT
ejpam-6544	139	41	distance	distance	NOUN
ejpam-6544	139	42	zero	zero	NUM
ejpam-6544	139	43	forcing	force	VERB
ejpam-6544	139	44	sets	set	NOUN
ejpam-6544	139	45	in	in	ADP
ejpam-6544	139	46	the	the	DET
ejpam-6544	139	47	join	join	NOUN
ejpam-6544	139	48	of	of	ADP
ejpam-6544	139	49	two	two	NUM
ejpam-6544	139	50	graphs	graph	NOUN
ejpam-6544	139	51	.	.	PUNCT
ejpam-6544	140	1	definition	definition	NOUN
ejpam-6544	140	2	2	2	NUM
ejpam-6544	140	3	.	.	PUNCT
ejpam-6544	141	1	let	let	VERB
ejpam-6544	141	2	g	g	PRON
ejpam-6544	141	3	be	be	AUX
ejpam-6544	141	4	a	a	DET
ejpam-6544	141	5	simple	simple	ADJ
ejpam-6544	141	6	and	and	CCONJ
ejpam-6544	141	7	undirected	undirected	ADJ
ejpam-6544	141	8	graph	graph	NOUN
ejpam-6544	141	9	.	.	PUNCT
ejpam-6544	142	1	then	then	ADV
ejpam-6544	142	2	a	a	DET
ejpam-6544	142	3	co	co	ADJ
ejpam-6544	142	4	-	-	ADJ
ejpam-6544	142	5	color	color	ADJ
ejpam-6544	142	6	change	change	NOUN
ejpam-6544	142	7	rule	rule	NOUN
ejpam-6544	142	8	is	be	AUX
ejpam-6544	142	9	defined	define	VERB
ejpam-6544	142	10	as	as	SCONJ
ejpam-6544	142	11	follows	follow	VERB
ejpam-6544	142	12	:	:	PUNCT
ejpam-6544	142	13	if	if	SCONJ
ejpam-6544	142	14	a	a	DET
ejpam-6544	142	15	vertex	vertex	NOUN
ejpam-6544	142	16	x	x	SYM
ejpam-6544	142	17	∈	∈	NOUN
ejpam-6544	142	18	v	v	ADP
ejpam-6544	142	19	(	(	PUNCT
ejpam-6544	142	20	g	g	NOUN
ejpam-6544	142	21	)	)	PUNCT
ejpam-6544	142	22	is	be	AUX
ejpam-6544	142	23	colored	color	VERB
ejpam-6544	142	24	(	(	PUNCT
ejpam-6544	142	25	active	active	ADJ
ejpam-6544	142	26	)	)	PUNCT
ejpam-6544	142	27	and	and	CCONJ
ejpam-6544	142	28	has	have	VERB
ejpam-6544	142	29	exactly	exactly	ADV
ejpam-6544	142	30	one	one	NUM
ejpam-6544	142	31	nonneighbor	nonneighbor	NOUN
ejpam-6544	142	32	y	y	PROPN
ejpam-6544	142	33	is	be	AUX
ejpam-6544	142	34	uncolored	uncolored	ADJ
ejpam-6544	142	35	(	(	PUNCT
ejpam-6544	142	36	inactive	inactive	ADJ
ejpam-6544	142	37	)	)	PUNCT
ejpam-6544	142	38	,	,	PUNCT
ejpam-6544	142	39	then	then	ADV
ejpam-6544	142	40	y	y	PROPN
ejpam-6544	142	41	will	will	AUX
ejpam-6544	142	42	become	become	VERB
ejpam-6544	142	43	colored	colored	ADJ
ejpam-6544	142	44	(	(	PUNCT
ejpam-6544	142	45	active	active	ADJ
ejpam-6544	142	46	)	)	PUNCT
ejpam-6544	142	47	.	.	PUNCT
ejpam-6544	143	1	in	in	ADP
ejpam-6544	143	2	this	this	DET
ejpam-6544	143	3	case	case	NOUN
ejpam-6544	143	4	,	,	PUNCT
ejpam-6544	143	5	we	we	PRON
ejpam-6544	143	6	say	say	VERB
ejpam-6544	143	7	that	that	SCONJ
ejpam-6544	143	8	a	a	DET
ejpam-6544	143	9	vertex	vertex	NOUN
ejpam-6544	143	10	y	y	PROPN
ejpam-6544	143	11	is	be	AUX
ejpam-6544	143	12	co	co	VERB
ejpam-6544	143	13	-	-	VERB
ejpam-6544	143	14	forced	force	VERB
ejpam-6544	143	15	by	by	ADP
ejpam-6544	143	16	a	a	DET
ejpam-6544	143	17	vertex	vertex	NOUN
ejpam-6544	143	18	x	x	PUNCT
ejpam-6544	143	19	in	in	ADP
ejpam-6544	143	20	g.	g.	PROPN
ejpam-6544	143	21	a	a	DET
ejpam-6544	143	22	subset	subset	PROPN
ejpam-6544	143	23	b	b	NOUN
ejpam-6544	143	24	of	of	ADP
ejpam-6544	143	25	a	a	DET
ejpam-6544	143	26	vertex	vertex	NOUN
ejpam-6544	143	27	-	-	PUNCT
ejpam-6544	143	28	set	set	VERB
ejpam-6544	143	29	v	v	NOUN
ejpam-6544	143	30	(	(	PUNCT
ejpam-6544	143	31	g	g	NOUN
ejpam-6544	143	32	)	)	PUNCT
ejpam-6544	143	33	of	of	ADP
ejpam-6544	143	34	g	g	PROPN
ejpam-6544	143	35	is	be	AUX
ejpam-6544	143	36	called	call	VERB
ejpam-6544	143	37	a	a	DET
ejpam-6544	143	38	co	co	NOUN
ejpam-6544	143	39	-	-	ADJ
ejpam-6544	143	40	zero	zero	ADJ
ejpam-6544	143	41	forcing	force	VERB
ejpam-6544	143	42	set	set	NOUN
ejpam-6544	143	43	if	if	SCONJ
ejpam-6544	143	44	repeatedly	repeatedly	ADV
ejpam-6544	143	45	applying	apply	VERB
ejpam-6544	143	46	the	the	DET
ejpam-6544	143	47	co	co	ADJ
ejpam-6544	143	48	-	-	ADJ
ejpam-6544	143	49	color	color	ADJ
ejpam-6544	143	50	change	change	NOUN
ejpam-6544	143	51	rule	rule	NOUN
ejpam-6544	143	52	on	on	ADP
ejpam-6544	143	53	a	a	DET
ejpam-6544	143	54	set	set	NOUN
ejpam-6544	143	55	b	b	NOUN
ejpam-6544	143	56	,	,	PUNCT
ejpam-6544	143	57	the	the	DET
ejpam-6544	143	58	whole	whole	ADJ
ejpam-6544	143	59	vertex	vertex	NOUN
ejpam-6544	143	60	-	-	PUNCT
ejpam-6544	143	61	set	set	NOUN
ejpam-6544	143	62	of	of	ADP
ejpam-6544	143	63	g	g	NOUN
ejpam-6544	143	64	becomes	become	VERB
ejpam-6544	143	65	colored	colored	ADJ
ejpam-6544	143	66	(	(	PUNCT
ejpam-6544	143	67	active	active	ADJ
ejpam-6544	143	68	)	)	PUNCT
ejpam-6544	143	69	.	.	PUNCT
ejpam-6544	144	1	moreover	moreover	ADV
ejpam-6544	144	2	,	,	PUNCT
ejpam-6544	144	3	a	a	DET
ejpam-6544	144	4	subset	subset	NOUN
ejpam-6544	144	5	s	s	X
ejpam-6544	144	6	of	of	ADP
ejpam-6544	144	7	v	v	NOUN
ejpam-6544	144	8	(	(	PUNCT
ejpam-6544	144	9	g	g	NOUN
ejpam-6544	144	10	)	)	PUNCT
ejpam-6544	144	11	is	be	AUX
ejpam-6544	144	12	called	call	VERB
ejpam-6544	144	13	a	a	DET
ejpam-6544	144	14	failed	failed	ADJ
ejpam-6544	144	15	co	co	NOUN
ejpam-6544	144	16	-	-	ADJ
ejpam-6544	144	17	zero	zero	ADJ
ejpam-6544	144	18	forcing	force	VERB
ejpam-6544	144	19	set	set	NOUN
ejpam-6544	144	20	of	of	ADP
ejpam-6544	144	21	g	g	PROPN
ejpam-6544	144	22	if	if	SCONJ
ejpam-6544	144	23	s	s	VERB
ejpam-6544	144	24	is	be	AUX
ejpam-6544	144	25	not	not	PART
ejpam-6544	144	26	a	a	DET
ejpam-6544	144	27	co	co	NOUN
ejpam-6544	144	28	-	-	ADJ
ejpam-6544	144	29	zero	zero	ADJ
ejpam-6544	144	30	forcing	force	VERB
ejpam-6544	144	31	set	set	NOUN
ejpam-6544	144	32	of	of	ADP
ejpam-6544	144	33	g.	g.	PROPN
ejpam-6544	144	34	the	the	DET
ejpam-6544	144	35	maximum	maximum	ADJ
ejpam-6544	144	36	cardinality	cardinality	NOUN
ejpam-6544	144	37	of	of	ADP
ejpam-6544	144	38	a	a	DET
ejpam-6544	144	39	failed	failed	ADJ
ejpam-6544	144	40	co	co	NOUN
ejpam-6544	144	41	-	-	ADJ
ejpam-6544	144	42	zero	zero	ADJ
ejpam-6544	144	43	forcing	force	VERB
ejpam-6544	144	44	set	set	NOUN
ejpam-6544	144	45	of	of	ADP
ejpam-6544	144	46	g	g	NOUN
ejpam-6544	144	47	,	,	PUNCT
ejpam-6544	144	48	denoted	denote	VERB
ejpam-6544	144	49	by	by	ADP
ejpam-6544	144	50	fco(g	fco(g	NOUN
ejpam-6544	144	51	)	)	PUNCT
ejpam-6544	144	52	,	,	PUNCT
ejpam-6544	144	53	is	be	AUX
ejpam-6544	144	54	called	call	VERB
ejpam-6544	144	55	the	the	DET
ejpam-6544	144	56	failed	fail	VERB
ejpam-6544	144	57	co	co	NOUN
ejpam-6544	144	58	-	-	ADJ
ejpam-6544	144	59	zero	zero	ADJ
ejpam-6544	144	60	forcing	force	VERB
ejpam-6544	144	61	number	number	NOUN
ejpam-6544	144	62	of	of	ADP
ejpam-6544	144	63	g.	g.	NOUN
ejpam-6544	144	64	we	we	PRON
ejpam-6544	144	65	shall	shall	AUX
ejpam-6544	144	66	now	now	ADV
ejpam-6544	144	67	characterize	characterize	VERB
ejpam-6544	144	68	the	the	DET
ejpam-6544	144	69	failed	fail	VERB
ejpam-6544	144	70	2	2	NUM
ejpam-6544	144	71	-	-	PUNCT
ejpam-6544	144	72	distance	distance	NOUN
ejpam-6544	144	73	zero	zero	NUM
ejpam-6544	144	74	forcing	force	VERB
ejpam-6544	144	75	sets	set	NOUN
ejpam-6544	144	76	in	in	ADP
ejpam-6544	144	77	the	the	DET
ejpam-6544	144	78	join	join	NOUN
ejpam-6544	144	79	of	of	ADP
ejpam-6544	144	80	two	two	NUM
ejpam-6544	144	81	graphs	graph	NOUN
ejpam-6544	144	82	as	as	SCONJ
ejpam-6544	144	83	follows	follow	VERB
ejpam-6544	144	84	:	:	PUNCT
ejpam-6544	144	85	theorem	theorem	NOUN
ejpam-6544	144	86	4	4	NUM
ejpam-6544	144	87	.	.	PUNCT
ejpam-6544	145	1	let	let	VERB
ejpam-6544	145	2	g	g	NOUN
ejpam-6544	145	3	and	and	CCONJ
ejpam-6544	145	4	h	h	PROPN
ejpam-6544	145	5	be	be	AUX
ejpam-6544	145	6	graphs	graph	NOUN
ejpam-6544	145	7	.	.	PUNCT
ejpam-6544	146	1	then	then	ADV
ejpam-6544	146	2	q	q	X
ejpam-6544	146	3	is	be	AUX
ejpam-6544	146	4	a	a	DET
ejpam-6544	146	5	failed	failed	ADJ
ejpam-6544	146	6	2	2	NUM
ejpam-6544	146	7	-	-	PUNCT
ejpam-6544	146	8	distance	distance	NOUN
ejpam-6544	146	9	zero	zero	NUM
ejpam-6544	146	10	forcing	force	VERB
ejpam-6544	146	11	set	set	NOUN
ejpam-6544	146	12	of	of	ADP
ejpam-6544	146	13	g+h	g+h	PROPN
ejpam-6544	147	1	if	if	SCONJ
ejpam-6544	147	2	and	and	CCONJ
ejpam-6544	147	3	only	only	ADV
ejpam-6544	147	4	if	if	SCONJ
ejpam-6544	147	5	q	q	NOUN
ejpam-6544	147	6	satisfies	satisfy	VERB
ejpam-6544	147	7	one	one	NUM
ejpam-6544	147	8	of	of	ADP
ejpam-6544	147	9	the	the	DET
ejpam-6544	147	10	following	follow	VERB
ejpam-6544	147	11	conditions	condition	NOUN
ejpam-6544	147	12	.	.	PUNCT
ejpam-6544	148	1	a.	a.	NOUN
ejpam-6544	148	2	madjatul	madjatul	PROPN
ejpam-6544	148	3	et	et	PROPN
ejpam-6544	148	4	al	al	PROPN
ejpam-6544	148	5	.	.	PUNCT
ejpam-6544	148	6	/	/	SYM
ejpam-6544	148	7	eur	eur	PROPN
ejpam-6544	148	8	.	.	PUNCT
ejpam-6544	149	1	j.	j.	PROPN
ejpam-6544	149	2	pure	pure	PROPN
ejpam-6544	149	3	appl	appl	PROPN
ejpam-6544	149	4	.	.	PROPN
ejpam-6544	149	5	math	math	PROPN
ejpam-6544	149	6	,	,	PUNCT
ejpam-6544	149	7	18	18	NUM
ejpam-6544	149	8	(	(	PUNCT
ejpam-6544	149	9	3	3	NUM
ejpam-6544	149	10	)	)	PUNCT
ejpam-6544	149	11	(	(	PUNCT
ejpam-6544	149	12	2025	2025	NUM
ejpam-6544	149	13	)	)	PUNCT
ejpam-6544	149	14	,	,	PUNCT
ejpam-6544	149	15	6544	6544	NUM
ejpam-6544	149	16	6	6	NUM
ejpam-6544	149	17	of	of	ADP
ejpam-6544	149	18	8	8	NUM
ejpam-6544	149	19	(	(	PUNCT
ejpam-6544	149	20	i	i	NOUN
ejpam-6544	149	21	)	)	PUNCT
ejpam-6544	149	22	q	q	PROPN
ejpam-6544	150	1	⊆	⊆	NUM
ejpam-6544	150	2	v	v	NOUN
ejpam-6544	150	3	(	(	PUNCT
ejpam-6544	150	4	g	g	NOUN
ejpam-6544	150	5	)	)	PUNCT
ejpam-6544	150	6	.	.	PUNCT
ejpam-6544	151	1	(	(	PUNCT
ejpam-6544	151	2	ii	ii	NOUN
ejpam-6544	151	3	)	)	PUNCT
ejpam-6544	151	4	q	q	NOUN
ejpam-6544	152	1	⊆	⊆	NUM
ejpam-6544	152	2	v	v	NOUN
ejpam-6544	152	3	(	(	PUNCT
ejpam-6544	152	4	h	h	NOUN
ejpam-6544	152	5	)	)	PUNCT
ejpam-6544	152	6	.	.	PUNCT
ejpam-6544	153	1	(	(	PUNCT
ejpam-6544	153	2	iii	iii	X
ejpam-6544	153	3	)	)	PUNCT
ejpam-6544	153	4	q	q	NOUN
ejpam-6544	154	1	=	=	PUNCT
ejpam-6544	154	2	qg	qg	PROPN
ejpam-6544	154	3	∪	∪	PROPN
ejpam-6544	154	4	qh	qh	PROPN
ejpam-6544	154	5	such	such	ADJ
ejpam-6544	154	6	that	that	SCONJ
ejpam-6544	154	7	qg	qg	PROPN
ejpam-6544	154	8	or	or	CCONJ
ejpam-6544	154	9	qh	qh	NOUN
ejpam-6544	154	10	is	be	AUX
ejpam-6544	154	11	failed	fail	VERB
ejpam-6544	154	12	a	a	DET
ejpam-6544	154	13	co	co	NOUN
ejpam-6544	154	14	-	-	ADJ
ejpam-6544	154	15	zero	zero	ADJ
ejpam-6544	154	16	forcing	forcing	NOUN
ejpam-6544	154	17	set	set	NOUN
ejpam-6544	154	18	in	in	ADP
ejpam-6544	154	19	g	g	PROPN
ejpam-6544	154	20	and	and	CCONJ
ejpam-6544	154	21	h	h	NOUN
ejpam-6544	154	22	,	,	PUNCT
ejpam-6544	154	23	respectively	respectively	ADV
ejpam-6544	154	24	.	.	PUNCT
ejpam-6544	155	1	proof	proof	NOUN
ejpam-6544	155	2	.	.	PUNCT
ejpam-6544	156	1	suppose	suppose	VERB
ejpam-6544	156	2	that	that	PRON
ejpam-6544	156	3	q	q	NOUN
ejpam-6544	156	4	is	be	AUX
ejpam-6544	156	5	a	a	DET
ejpam-6544	156	6	failed	failed	ADJ
ejpam-6544	156	7	2distance	2distance	NUM
ejpam-6544	156	8	zero	zero	NUM
ejpam-6544	156	9	forcing	force	VERB
ejpam-6544	156	10	set	set	NOUN
ejpam-6544	156	11	of	of	ADP
ejpam-6544	156	12	g+h	g+h	PROPN
ejpam-6544	156	13	.	.	PUNCT
ejpam-6544	157	1	then	then	ADV
ejpam-6544	157	2	q	q	PROPN
ejpam-6544	157	3	̸=	̸=	PROPN
ejpam-6544	157	4	v	v	NOUN
ejpam-6544	157	5	(	(	PUNCT
ejpam-6544	157	6	g	g	PROPN
ejpam-6544	157	7	+	+	NOUN
ejpam-6544	157	8	h	h	NOUN
ejpam-6544	157	9	)	)	PUNCT
ejpam-6544	157	10	.	.	PUNCT
ejpam-6544	158	1	thus	thus	ADV
ejpam-6544	158	2	,	,	PUNCT
ejpam-6544	158	3	either	either	CCONJ
ejpam-6544	158	4	q	q	PROPN
ejpam-6544	158	5	⊆	⊆	NUM
ejpam-6544	158	6	v	v	NOUN
ejpam-6544	158	7	(	(	PUNCT
ejpam-6544	158	8	g	g	NOUN
ejpam-6544	158	9	)	)	PUNCT
ejpam-6544	158	10	,	,	PUNCT
ejpam-6544	158	11	q	q	PUNCT
ejpam-6544	158	12	⊆	⊆	NUM
ejpam-6544	158	13	v	v	NOUN
ejpam-6544	158	14	(	(	PUNCT
ejpam-6544	158	15	h	h	NOUN
ejpam-6544	158	16	)	)	PUNCT
ejpam-6544	158	17	or	or	CCONJ
ejpam-6544	158	18	q	q	NOUN
ejpam-6544	158	19	=	=	SYM
ejpam-6544	158	20	qg	qg	PROPN
ejpam-6544	158	21	∪	∪	PROPN
ejpam-6544	158	22	qh	qh	PROPN
ejpam-6544	158	23	,	,	PUNCT
ejpam-6544	158	24	where	where	SCONJ
ejpam-6544	158	25	qg	qg	PROPN
ejpam-6544	158	26	⊆	⊆	NUM
ejpam-6544	158	27	v	v	NOUN
ejpam-6544	158	28	(	(	PUNCT
ejpam-6544	158	29	g	g	NOUN
ejpam-6544	158	30	)	)	PUNCT
ejpam-6544	158	31	and	and	CCONJ
ejpam-6544	158	32	qh	qh	VERB
ejpam-6544	158	33	⊆	⊆	NUM
ejpam-6544	158	34	v	v	NOUN
ejpam-6544	158	35	(	(	PUNCT
ejpam-6544	158	36	h	h	NOUN
ejpam-6544	158	37	)	)	PUNCT
ejpam-6544	158	38	,	,	PUNCT
ejpam-6544	158	39	it	it	PRON
ejpam-6544	158	40	follows	follow	VERB
ejpam-6544	158	41	that	that	SCONJ
ejpam-6544	158	42	(	(	PUNCT
ejpam-6544	158	43	a	a	X
ejpam-6544	158	44	)	)	PUNCT
ejpam-6544	158	45	and	and	CCONJ
ejpam-6544	158	46	(	(	PUNCT
ejpam-6544	158	47	b	b	NOUN
ejpam-6544	158	48	)	)	PUNCT
ejpam-6544	158	49	hold	hold	NOUN
ejpam-6544	158	50	.	.	PUNCT
ejpam-6544	159	1	assume	assume	VERB
ejpam-6544	159	2	that	that	SCONJ
ejpam-6544	159	3	qg	qg	PROPN
ejpam-6544	159	4	is	be	AUX
ejpam-6544	159	5	a	a	DET
ejpam-6544	159	6	co	co	NOUN
ejpam-6544	159	7	-	-	ADJ
ejpam-6544	159	8	zero	zero	ADJ
ejpam-6544	159	9	forcing	force	VERB
ejpam-6544	159	10	set	set	NOUN
ejpam-6544	159	11	of	of	ADP
ejpam-6544	159	12	g.	g.	PROPN
ejpam-6544	159	13	then	then	ADV
ejpam-6544	159	14	by	by	ADP
ejpam-6544	159	15	repeatedly	repeatedly	ADV
ejpam-6544	159	16	applying	apply	VERB
ejpam-6544	159	17	the	the	DET
ejpam-6544	159	18	co	co	ADJ
ejpam-6544	159	19	-	-	ADJ
ejpam-6544	159	20	color	color	ADJ
ejpam-6544	159	21	change	change	NOUN
ejpam-6544	159	22	rule	rule	NOUN
ejpam-6544	159	23	on	on	ADP
ejpam-6544	159	24	qg	qg	PROPN
ejpam-6544	159	25	,	,	PUNCT
ejpam-6544	159	26	all	all	DET
ejpam-6544	159	27	other	other	ADJ
ejpam-6544	159	28	vertices	vertex	NOUN
ejpam-6544	159	29	in	in	ADP
ejpam-6544	159	30	v	v	ADP
ejpam-6544	159	31	(	(	PUNCT
ejpam-6544	159	32	g	g	NOUN
ejpam-6544	159	33	)	)	PUNCT
ejpam-6544	159	34	\qg	\qg	PROPN
ejpam-6544	159	35	will	will	AUX
ejpam-6544	159	36	become	become	VERB
ejpam-6544	159	37	colored	color	VERB
ejpam-6544	159	38	.	.	PUNCT
ejpam-6544	160	1	suppose	suppose	VERB
ejpam-6544	160	2	on	on	ADP
ejpam-6544	160	3	the	the	DET
ejpam-6544	160	4	contrary	contrary	NOUN
ejpam-6544	160	5	that	that	SCONJ
ejpam-6544	160	6	qh	qh	NOUN
ejpam-6544	160	7	is	be	AUX
ejpam-6544	160	8	a	a	DET
ejpam-6544	160	9	co	co	NOUN
ejpam-6544	160	10	-	-	ADJ
ejpam-6544	160	11	zero	zero	ADJ
ejpam-6544	160	12	forcing	force	VERB
ejpam-6544	160	13	set	set	NOUN
ejpam-6544	160	14	of	of	ADP
ejpam-6544	160	15	h.	h.	PROPN
ejpam-6544	160	16	then	then	ADV
ejpam-6544	160	17	by	by	ADP
ejpam-6544	160	18	repeatedly	repeatedly	ADV
ejpam-6544	160	19	applying	apply	VERB
ejpam-6544	160	20	the	the	DET
ejpam-6544	160	21	co	co	ADJ
ejpam-6544	160	22	-	-	ADJ
ejpam-6544	160	23	color	color	ADJ
ejpam-6544	160	24	change	change	NOUN
ejpam-6544	160	25	rule	rule	NOUN
ejpam-6544	160	26	on	on	ADP
ejpam-6544	160	27	qh	qh	PROPN
ejpam-6544	160	28	,	,	PUNCT
ejpam-6544	160	29	all	all	DET
ejpam-6544	160	30	other	other	ADJ
ejpam-6544	160	31	vertices	vertex	NOUN
ejpam-6544	160	32	in	in	ADP
ejpam-6544	160	33	v	v	ADP
ejpam-6544	160	34	(	(	PUNCT
ejpam-6544	160	35	h	h	NOUN
ejpam-6544	160	36	)	)	PUNCT
ejpam-6544	160	37	\qh	\qh	NOUN
ejpam-6544	160	38	will	will	AUX
ejpam-6544	160	39	be	be	AUX
ejpam-6544	160	40	2	2	NUM
ejpam-6544	160	41	-	-	PUNCT
ejpam-6544	160	42	forced	forced	ADJ
ejpam-6544	160	43	.	.	PUNCT
ejpam-6544	161	1	it	it	PRON
ejpam-6544	161	2	follows	follow	VERB
ejpam-6544	161	3	that	that	SCONJ
ejpam-6544	161	4	q	q	NOUN
ejpam-6544	161	5	is	be	AUX
ejpam-6544	161	6	a	a	DET
ejpam-6544	161	7	2	2	NUM
ejpam-6544	161	8	-	-	PUNCT
ejpam-6544	161	9	distance	distance	NOUN
ejpam-6544	161	10	zero	zero	NUM
ejpam-6544	161	11	forcing	force	VERB
ejpam-6544	161	12	set	set	NOUN
ejpam-6544	161	13	of	of	ADP
ejpam-6544	161	14	g+h	g+h	PROPN
ejpam-6544	161	15	,	,	PUNCT
ejpam-6544	161	16	which	which	PRON
ejpam-6544	161	17	is	be	AUX
ejpam-6544	161	18	a	a	DET
ejpam-6544	161	19	contradiction	contradiction	NOUN
ejpam-6544	161	20	.	.	PUNCT
ejpam-6544	162	1	similarly	similarly	ADV
ejpam-6544	162	2	,	,	PUNCT
ejpam-6544	162	3	when	when	SCONJ
ejpam-6544	162	4	qh	qh	NOUN
ejpam-6544	162	5	is	be	AUX
ejpam-6544	162	6	a	a	DET
ejpam-6544	162	7	cozero	cozero	NOUN
ejpam-6544	162	8	forcing	force	VERB
ejpam-6544	162	9	set	set	NOUN
ejpam-6544	162	10	of	of	ADP
ejpam-6544	162	11	h	h	NOUN
ejpam-6544	162	12	,	,	PUNCT
ejpam-6544	162	13	then	then	ADV
ejpam-6544	162	14	qg	qg	PROPN
ejpam-6544	162	15	must	must	AUX
ejpam-6544	162	16	be	be	AUX
ejpam-6544	162	17	a	a	DET
ejpam-6544	162	18	failed	failed	ADJ
ejpam-6544	162	19	co	co	NOUN
ejpam-6544	162	20	-	-	ADJ
ejpam-6544	162	21	zero	zero	ADJ
ejpam-6544	162	22	forcing	force	VERB
ejpam-6544	162	23	set	set	NOUN
ejpam-6544	162	24	of	of	ADP
ejpam-6544	162	25	g.	g.	PROPN
ejpam-6544	162	26	thus	thus	ADV
ejpam-6544	162	27	,	,	PUNCT
ejpam-6544	162	28	(	(	PUNCT
ejpam-6544	162	29	c	c	X
ejpam-6544	162	30	)	)	PUNCT
ejpam-6544	162	31	holds	hold	NOUN
ejpam-6544	162	32	.	.	PUNCT
ejpam-6544	163	1	conversely	conversely	ADV
ejpam-6544	163	2	,	,	PUNCT
ejpam-6544	163	3	if	if	SCONJ
ejpam-6544	163	4	(	(	PUNCT
ejpam-6544	163	5	a	a	PRON
ejpam-6544	163	6	)	)	PUNCT
ejpam-6544	163	7	holds	hold	NOUN
ejpam-6544	163	8	.	.	PUNCT
ejpam-6544	164	1	then	then	ADV
ejpam-6544	164	2	v	v	X
ejpam-6544	164	3	(	(	PUNCT
ejpam-6544	164	4	h	h	NOUN
ejpam-6544	164	5	)	)	PUNCT
ejpam-6544	164	6	can	can	AUX
ejpam-6544	164	7	not	not	PART
ejpam-6544	164	8	be	be	AUX
ejpam-6544	164	9	2	2	NUM
ejpam-6544	164	10	-	-	PUNCT
ejpam-6544	164	11	forced	forced	ADJ
ejpam-6544	164	12	.	.	PUNCT
ejpam-6544	165	1	hence	hence	ADV
ejpam-6544	165	2	,	,	PUNCT
ejpam-6544	165	3	q	q	NOUN
ejpam-6544	165	4	⊆	⊆	NUM
ejpam-6544	165	5	v	v	NOUN
ejpam-6544	165	6	(	(	PUNCT
ejpam-6544	165	7	g	g	NOUN
ejpam-6544	165	8	)	)	PUNCT
ejpam-6544	165	9	⊆	⊆	NUM
ejpam-6544	165	10	v	v	NOUN
ejpam-6544	165	11	(	(	PUNCT
ejpam-6544	165	12	g+h	g+h	NOUN
ejpam-6544	165	13	)	)	PUNCT
ejpam-6544	165	14	is	be	AUX
ejpam-6544	165	15	a	a	DET
ejpam-6544	165	16	failed	failed	ADJ
ejpam-6544	165	17	2	2	NUM
ejpam-6544	165	18	-	-	PUNCT
ejpam-6544	165	19	distance	distance	NOUN
ejpam-6544	165	20	zero	zero	NUM
ejpam-6544	165	21	forcing	forcing	NOUN
ejpam-6544	165	22	of	of	ADP
ejpam-6544	165	23	g+h	g+h	PROPN
ejpam-6544	165	24	.	.	PUNCT
ejpam-6544	166	1	similarly	similarly	ADV
ejpam-6544	166	2	,	,	PUNCT
ejpam-6544	166	3	when	when	SCONJ
ejpam-6544	166	4	(	(	PUNCT
ejpam-6544	166	5	b	b	NOUN
ejpam-6544	166	6	)	)	PUNCT
ejpam-6544	166	7	holds	hold	VERB
ejpam-6544	166	8	,	,	PUNCT
ejpam-6544	166	9	then	then	ADV
ejpam-6544	166	10	q	q	PROPN
ejpam-6544	166	11	⊆	⊆	NUM
ejpam-6544	166	12	v	v	ADP
ejpam-6544	166	13	(	(	PUNCT
ejpam-6544	166	14	h	h	NOUN
ejpam-6544	166	15	)	)	PUNCT
ejpam-6544	166	16	⊆	⊆	NUM
ejpam-6544	166	17	v	v	NOUN
ejpam-6544	166	18	(	(	PUNCT
ejpam-6544	166	19	g	g	PROPN
ejpam-6544	166	20	+	+	NOUN
ejpam-6544	166	21	h	h	NOUN
ejpam-6544	166	22	)	)	PUNCT
ejpam-6544	166	23	is	be	AUX
ejpam-6544	166	24	a	a	DET
ejpam-6544	166	25	failed	failed	ADJ
ejpam-6544	166	26	2	2	NUM
ejpam-6544	166	27	-	-	PUNCT
ejpam-6544	166	28	distance	distance	NOUN
ejpam-6544	166	29	zero	zero	NUM
ejpam-6544	166	30	forcing	forcing	NOUN
ejpam-6544	166	31	of	of	ADP
ejpam-6544	166	32	g	g	PROPN
ejpam-6544	166	33	+	+	CCONJ
ejpam-6544	166	34	h.	h.	PROPN
ejpam-6544	166	35	now	now	ADV
ejpam-6544	166	36	,	,	PUNCT
ejpam-6544	166	37	suppose	suppose	VERB
ejpam-6544	166	38	that	that	SCONJ
ejpam-6544	166	39	(	(	PUNCT
ejpam-6544	166	40	c	c	X
ejpam-6544	166	41	)	)	PUNCT
ejpam-6544	166	42	holds	hold	VERB
ejpam-6544	166	43	.	.	PUNCT
ejpam-6544	167	1	if	if	SCONJ
ejpam-6544	167	2	qg	qg	PROPN
ejpam-6544	167	3	is	be	AUX
ejpam-6544	167	4	failed	fail	VERB
ejpam-6544	167	5	a	a	DET
ejpam-6544	167	6	co	co	NOUN
ejpam-6544	167	7	-	-	ADJ
ejpam-6544	167	8	zero	zero	ADJ
ejpam-6544	167	9	forcing	force	VERB
ejpam-6544	167	10	set	set	NOUN
ejpam-6544	167	11	of	of	ADP
ejpam-6544	167	12	g	g	NOUN
ejpam-6544	167	13	,	,	PUNCT
ejpam-6544	167	14	then	then	ADV
ejpam-6544	167	15	there	there	PRON
ejpam-6544	167	16	exist	exist	VERB
ejpam-6544	167	17	y	y	PROPN
ejpam-6544	167	18	∈	∈	PROPN
ejpam-6544	167	19	v	v	ADP
ejpam-6544	167	20	(	(	PUNCT
ejpam-6544	167	21	g	g	NOUN
ejpam-6544	167	22	)	)	PUNCT
ejpam-6544	167	23	\qg	\qg	NOUN
ejpam-6544	167	24	such	such	ADJ
ejpam-6544	167	25	that	that	SCONJ
ejpam-6544	167	26	y	y	PROPN
ejpam-6544	167	27	can	can	AUX
ejpam-6544	167	28	not	not	PART
ejpam-6544	167	29	be	be	AUX
ejpam-6544	167	30	co	co	VERB
ejpam-6544	167	31	-	-	VERB
ejpam-6544	167	32	forced	forced	ADJ
ejpam-6544	167	33	.	.	PUNCT
ejpam-6544	168	1	it	it	PRON
ejpam-6544	168	2	follows	follow	VERB
ejpam-6544	168	3	that	that	SCONJ
ejpam-6544	168	4	y	y	PROPN
ejpam-6544	168	5	∈	∈	PROPN
ejpam-6544	168	6	v	v	ADP
ejpam-6544	168	7	(	(	PUNCT
ejpam-6544	168	8	g	g	PROPN
ejpam-6544	168	9	+	+	NOUN
ejpam-6544	168	10	h	h	NOUN
ejpam-6544	168	11	)	)	PUNCT
ejpam-6544	168	12	\	\	NOUN
ejpam-6544	169	1	q	q	PUNCT
ejpam-6544	169	2	can	can	AUX
ejpam-6544	169	3	not	not	PART
ejpam-6544	169	4	be	be	AUX
ejpam-6544	169	5	2	2	NUM
ejpam-6544	169	6	-	-	PUNCT
ejpam-6544	169	7	forced	forced	ADJ
ejpam-6544	169	8	.	.	PUNCT
ejpam-6544	170	1	thus	thus	ADV
ejpam-6544	170	2	,	,	PUNCT
ejpam-6544	170	3	q	q	X
ejpam-6544	170	4	is	be	AUX
ejpam-6544	170	5	a	a	DET
ejpam-6544	170	6	failed	failed	ADJ
ejpam-6544	170	7	2	2	NUM
ejpam-6544	170	8	-	-	PUNCT
ejpam-6544	170	9	distance	distance	NOUN
ejpam-6544	170	10	zero	zero	NUM
ejpam-6544	170	11	forcing	force	VERB
ejpam-6544	170	12	set	set	NOUN
ejpam-6544	170	13	of	of	ADP
ejpam-6544	170	14	g.	g.	PROPN
ejpam-6544	170	15	similarly	similarly	ADV
ejpam-6544	170	16	,	,	PUNCT
ejpam-6544	170	17	when	when	SCONJ
ejpam-6544	170	18	qh	qh	PROPN
ejpam-6544	170	19	is	be	AUX
ejpam-6544	170	20	failed	fail	VERB
ejpam-6544	170	21	a	a	DET
ejpam-6544	170	22	co	co	NOUN
ejpam-6544	170	23	-	-	ADJ
ejpam-6544	170	24	zero	zero	ADJ
ejpam-6544	170	25	forcing	force	VERB
ejpam-6544	170	26	set	set	NOUN
ejpam-6544	170	27	of	of	ADP
ejpam-6544	170	28	h	h	NOUN
ejpam-6544	170	29	,	,	PUNCT
ejpam-6544	170	30	then	then	ADV
ejpam-6544	170	31	q	q	X
ejpam-6544	170	32	is	be	AUX
ejpam-6544	170	33	a	a	DET
ejpam-6544	170	34	failed	failed	ADJ
ejpam-6544	170	35	2	2	NUM
ejpam-6544	170	36	-	-	PUNCT
ejpam-6544	170	37	distance	distance	NOUN
ejpam-6544	170	38	zero	zero	NUM
ejpam-6544	170	39	forcing	forcing	NOUN
ejpam-6544	170	40	of	of	ADP
ejpam-6544	170	41	g+h	g+h	PROPN
ejpam-6544	170	42	.	.	PUNCT
ejpam-6544	171	1	moreover	moreover	ADV
ejpam-6544	171	2	,	,	PUNCT
ejpam-6544	171	3	q	q	X
ejpam-6544	171	4	is	be	AUX
ejpam-6544	171	5	a	a	DET
ejpam-6544	171	6	failed	failed	ADJ
ejpam-6544	171	7	2	2	NUM
ejpam-6544	171	8	-	-	PUNCT
ejpam-6544	171	9	distance	distance	NOUN
ejpam-6544	171	10	zero	zero	NUM
ejpam-6544	171	11	forcing	force	VERB
ejpam-6544	171	12	set	set	NOUN
ejpam-6544	171	13	of	of	ADP
ejpam-6544	171	14	g	g	PROPN
ejpam-6544	171	15	+	+	PROPN
ejpam-6544	171	16	h	h	NOUN
ejpam-6544	171	17	whenever	whenever	SCONJ
ejpam-6544	171	18	qg	qg	PROPN
ejpam-6544	171	19	and	and	CCONJ
ejpam-6544	171	20	qh	qh	PROPN
ejpam-6544	171	21	are	be	AUX
ejpam-6544	171	22	both	both	PRON
ejpam-6544	171	23	failed	fail	VERB
ejpam-6544	171	24	co	co	ADJ
ejpam-6544	171	25	-	-	ADJ
ejpam-6544	171	26	zero	zero	ADJ
ejpam-6544	171	27	forcing	force	VERB
ejpam-6544	171	28	sets	set	NOUN
ejpam-6544	171	29	of	of	ADP
ejpam-6544	171	30	g	g	PROPN
ejpam-6544	171	31	and	and	CCONJ
ejpam-6544	171	32	h	h	NOUN
ejpam-6544	171	33	,	,	PUNCT
ejpam-6544	171	34	respectively	respectively	ADV
ejpam-6544	171	35	.	.	PUNCT
ejpam-6544	172	1	the	the	DET
ejpam-6544	172	2	following	following	ADJ
ejpam-6544	172	3	result	result	NOUN
ejpam-6544	172	4	follows	follow	VERB
ejpam-6544	172	5	from	from	ADP
ejpam-6544	172	6	theorem	theorem	ADJ
ejpam-6544	172	7	4	4	NUM
ejpam-6544	172	8	.	.	PUNCT
ejpam-6544	172	9	corollary	corollary	ADJ
ejpam-6544	172	10	3	3	X
ejpam-6544	172	11	.	.	PUNCT
ejpam-6544	173	1	let	let	VERB
ejpam-6544	173	2	g	g	NOUN
ejpam-6544	173	3	and	and	CCONJ
ejpam-6544	173	4	h	h	PROPN
ejpam-6544	173	5	be	be	AUX
ejpam-6544	173	6	graphs	graph	NOUN
ejpam-6544	173	7	.	.	PUNCT
ejpam-6544	174	1	then	then	ADV
ejpam-6544	174	2	f	f	PROPN
ejpam-6544	174	3	2(g+h	2(g+h	PROPN
ejpam-6544	174	4	)	)	PUNCT
ejpam-6544	175	1	=	=	SYM
ejpam-6544	175	2	max{|v	max{|v	PROPN
ejpam-6544	175	3	(	(	PUNCT
ejpam-6544	175	4	g)|+	g)|+	PROPN
ejpam-6544	175	5	fco(h	fco(h	PROPN
ejpam-6544	175	6	)	)	PUNCT
ejpam-6544	175	7	,	,	PUNCT
ejpam-6544	175	8	|v	|v	PROPN
ejpam-6544	175	9	(	(	PUNCT
ejpam-6544	175	10	h)|+	h)|+	ADJ
ejpam-6544	175	11	fco(g	fco(g	NOUN
ejpam-6544	175	12	)	)	PUNCT
ejpam-6544	175	13	}	}	PUNCT
ejpam-6544	175	14	.	.	PUNCT
ejpam-6544	176	1	6	6	X
ejpam-6544	176	2	.	.	X
ejpam-6544	176	3	conclusion	conclusion	NOUN
ejpam-6544	176	4	the	the	DET
ejpam-6544	176	5	concept	concept	NOUN
ejpam-6544	176	6	of	of	ADP
ejpam-6544	176	7	failed	fail	VERB
ejpam-6544	176	8	2	2	NUM
ejpam-6544	176	9	-	-	PUNCT
ejpam-6544	176	10	distance	distance	NOUN
ejpam-6544	176	11	zero	zero	NUM
ejpam-6544	176	12	forcing	force	VERB
ejpam-6544	176	13	in	in	ADP
ejpam-6544	176	14	a	a	DET
ejpam-6544	176	15	graph	graph	NOUN
ejpam-6544	176	16	has	have	AUX
ejpam-6544	176	17	been	be	AUX
ejpam-6544	176	18	introduced	introduce	VERB
ejpam-6544	176	19	and	and	CCONJ
ejpam-6544	176	20	investigated	investigate	VERB
ejpam-6544	176	21	in	in	ADP
ejpam-6544	176	22	this	this	DET
ejpam-6544	176	23	paper	paper	NOUN
ejpam-6544	176	24	.	.	PUNCT
ejpam-6544	177	1	characterizations	characterization	NOUN
ejpam-6544	177	2	of	of	ADP
ejpam-6544	177	3	failed	fail	VERB
ejpam-6544	177	4	2	2	NUM
ejpam-6544	177	5	-	-	PUNCT
ejpam-6544	177	6	failed	fail	VERB
ejpam-6544	177	7	zero	zero	NUM
ejpam-6544	177	8	forcing	force	VERB
ejpam-6544	177	9	sets	set	NOUN
ejpam-6544	177	10	in	in	ADP
ejpam-6544	177	11	some	some	DET
ejpam-6544	177	12	special	special	ADJ
ejpam-6544	177	13	graphs	graph	NOUN
ejpam-6544	177	14	and	and	CCONJ
ejpam-6544	177	15	the	the	DET
ejpam-6544	177	16	join	join	NOUN
ejpam-6544	177	17	of	of	ADP
ejpam-6544	177	18	any	any	DET
ejpam-6544	177	19	two	two	NUM
ejpam-6544	177	20	graphs	graph	NOUN
ejpam-6544	177	21	are	be	AUX
ejpam-6544	177	22	formulated	formulate	VERB
ejpam-6544	177	23	,	,	PUNCT
ejpam-6544	177	24	and	and	CCONJ
ejpam-6544	177	25	were	be	AUX
ejpam-6544	177	26	used	use	VERB
ejpam-6544	177	27	to	to	PART
ejpam-6544	177	28	derive	derive	VERB
ejpam-6544	177	29	some	some	DET
ejpam-6544	177	30	formulas	formula	NOUN
ejpam-6544	177	31	of	of	ADP
ejpam-6544	177	32	the	the	DET
ejpam-6544	177	33	parameter	parameter	NOUN
ejpam-6544	177	34	.	.	PUNCT
ejpam-6544	178	1	interested	interested	ADJ
ejpam-6544	178	2	researchers	researcher	NOUN
ejpam-6544	178	3	may	may	AUX
ejpam-6544	178	4	further	far	ADV
ejpam-6544	178	5	study	study	VERB
ejpam-6544	178	6	this	this	DET
ejpam-6544	178	7	concept	concept	NOUN
ejpam-6544	178	8	on	on	ADP
ejpam-6544	178	9	graphs	graph	NOUN
ejpam-6544	178	10	which	which	PRON
ejpam-6544	178	11	were	be	AUX
ejpam-6544	178	12	not	not	PART
ejpam-6544	178	13	considered	consider	VERB
ejpam-6544	178	14	in	in	ADP
ejpam-6544	178	15	this	this	DET
ejpam-6544	178	16	study	study	NOUN
ejpam-6544	178	17	.	.	PUNCT
ejpam-6544	179	1	providing	provide	VERB
ejpam-6544	179	2	real	real	ADJ
ejpam-6544	179	3	-	-	PUNCT
ejpam-6544	179	4	life	life	NOUN
ejpam-6544	179	5	applications	application	NOUN
ejpam-6544	179	6	of	of	ADP
ejpam-6544	179	7	the	the	DET
ejpam-6544	179	8	parameter	parameter	NOUN
ejpam-6544	179	9	and	and	CCONJ
ejpam-6544	179	10	studying	study	VERB
ejpam-6544	179	11	its	its	PRON
ejpam-6544	179	12	complexity	complexity	NOUN
ejpam-6544	179	13	could	could	AUX
ejpam-6544	179	14	also	also	ADV
ejpam-6544	179	15	be	be	AUX
ejpam-6544	179	16	an	an	DET
ejpam-6544	179	17	interesting	interesting	ADJ
ejpam-6544	179	18	cases	case	NOUN
ejpam-6544	179	19	to	to	PART
ejpam-6544	179	20	be	be	AUX
ejpam-6544	179	21	considered	consider	VERB
ejpam-6544	179	22	by	by	ADP
ejpam-6544	179	23	researchers	researcher	NOUN
ejpam-6544	179	24	.	.	PUNCT
ejpam-6544	180	1	a.	a.	NOUN
ejpam-6544	180	2	madjatul	madjatul	PROPN
ejpam-6544	180	3	et	et	PROPN
ejpam-6544	180	4	al	al	PROPN
ejpam-6544	180	5	.	.	PUNCT
ejpam-6544	180	6	/	/	SYM
ejpam-6544	180	7	eur	eur	PROPN
ejpam-6544	180	8	.	.	PUNCT
ejpam-6544	181	1	j.	j.	PROPN
ejpam-6544	181	2	pure	pure	PROPN
ejpam-6544	181	3	appl	appl	PROPN
ejpam-6544	181	4	.	.	PROPN
ejpam-6544	181	5	math	math	PROPN
ejpam-6544	181	6	,	,	PUNCT
ejpam-6544	181	7	18	18	NUM
ejpam-6544	181	8	(	(	PUNCT
ejpam-6544	181	9	3	3	NUM
ejpam-6544	181	10	)	)	PUNCT
ejpam-6544	181	11	(	(	PUNCT
ejpam-6544	181	12	2025	2025	NUM
ejpam-6544	181	13	)	)	PUNCT
ejpam-6544	181	14	,	,	PUNCT
ejpam-6544	181	15	6544	6544	NUM
ejpam-6544	181	16	7	7	NUM
ejpam-6544	181	17	of	of	ADP
ejpam-6544	181	18	8	8	NUM
ejpam-6544	181	19	7	7	NUM
ejpam-6544	181	20	.	.	PUNCT
ejpam-6544	182	1	acknowledgements	acknowledgement	NOUN
ejpam-6544	182	2	the	the	DET
ejpam-6544	182	3	authors	author	NOUN
ejpam-6544	182	4	would	would	AUX
ejpam-6544	182	5	like	like	VERB
ejpam-6544	182	6	to	to	PART
ejpam-6544	182	7	thank	thank	VERB
ejpam-6544	182	8	mindanao	mindanao	PROPN
ejpam-6544	182	9	state	state	PROPN
ejpam-6544	182	10	university	university	PROPN
ejpam-6544	182	11	tawi	tawi	PROPN
ejpam-6544	182	12	-	-	PUNCT
ejpam-6544	182	13	tawi	tawi	PROPN
ejpam-6544	182	14	college	college	PROPN
ejpam-6544	182	15	of	of	ADP
ejpam-6544	182	16	technology	technology	NOUN
ejpam-6544	182	17	and	and	CCONJ
ejpam-6544	182	18	oceanography	oceanography	NOUN
ejpam-6544	182	19	,	,	PUNCT
ejpam-6544	182	20	korea	korea	PROPN
ejpam-6544	182	21	university	university	PROPN
ejpam-6544	182	22	,	,	PUNCT
ejpam-6544	182	23	and	and	CCONJ
ejpam-6544	182	24	ateneo	ateneo	PROPN
ejpam-6544	182	25	de	de	PROPN
ejpam-6544	182	26	davao	davao	PROPN
ejpam-6544	182	27	university	university	PROPN
ejpam-6544	182	28	for	for	ADP
ejpam-6544	182	29	the	the	DET
ejpam-6544	182	30	support	support	NOUN
ejpam-6544	182	31	they	they	PRON
ejpam-6544	182	32	had	have	AUX
ejpam-6544	182	33	extended	extend	VERB
ejpam-6544	182	34	.	.	PUNCT
ejpam-6544	183	1	references	reference	NOUN
ejpam-6544	183	2	[	[	X
ejpam-6544	183	3	1	1	NUM
ejpam-6544	183	4	]	]	PUNCT
ejpam-6544	183	5	f.	f.	NOUN
ejpam-6544	183	6	barioli	barioli	PROPN
ejpam-6544	183	7	,	,	PUNCT
ejpam-6544	183	8	w.	w.	PROPN
ejpam-6544	183	9	barrett	barrett	PROPN
ejpam-6544	183	10	,	,	PUNCT
ejpam-6544	183	11	s.	s.	PROPN
ejpam-6544	183	12	m.	m.	PROPN
ejpam-6544	183	13	fallat	fallat	PROPN
ejpam-6544	183	14	,	,	PUNCT
ejpam-6544	183	15	h.	h.	PROPN
ejpam-6544	183	16	t.	t.	PROPN
ejpam-6544	183	17	hall	hall	PROPN
ejpam-6544	183	18	,	,	PUNCT
ejpam-6544	183	19	l.	l.	PROPN
ejpam-6544	183	20	hogben	hogben	PROPN
ejpam-6544	183	21	,	,	PUNCT
ejpam-6544	183	22	b.	b.	PROPN
ejpam-6544	183	23	shader	shader	PROPN
ejpam-6544	183	24	,	,	PUNCT
ejpam-6544	183	25	p.	p.	PROPN
ejpam-6544	183	26	van	van	PROPN
ejpam-6544	183	27	den	den	PROPN
ejpam-6544	183	28	driessche	driessche	PROPN
ejpam-6544	183	29	,	,	PUNCT
ejpam-6544	183	30	and	and	CCONJ
ejpam-6544	183	31	h.	h.	PROPN
ejpam-6544	183	32	van	van	PROPN
ejpam-6544	183	33	der	der	PROPN
ejpam-6544	183	34	holst	holst	NOUN
ejpam-6544	183	35	.	.	PUNCT
ejpam-6544	184	1	zero	zero	NUM
ejpam-6544	184	2	forcing	force	VERB
ejpam-6544	184	3	parameters	parameter	NOUN
ejpam-6544	184	4	and	and	CCONJ
ejpam-6544	184	5	minimum	minimum	ADJ
ejpam-6544	184	6	rank	rank	NOUN
ejpam-6544	184	7	problems	problem	NOUN
ejpam-6544	184	8	.	.	PUNCT
ejpam-6544	185	1	linear	linear	ADJ
ejpam-6544	185	2	algebra	algebra	NOUN
ejpam-6544	185	3	and	and	CCONJ
ejpam-6544	185	4	its	its	PRON
ejpam-6544	185	5	applications	application	NOUN
ejpam-6544	185	6	,	,	PUNCT
ejpam-6544	185	7	433:401–411	433:401–411	NUM
ejpam-6544	185	8	,	,	PUNCT
ejpam-6544	185	9	2010	2010	NUM
ejpam-6544	185	10	.	.	PUNCT
ejpam-6544	186	1	[	[	X
ejpam-6544	186	2	2	2	X
ejpam-6544	186	3	]	]	PUNCT
ejpam-6544	186	4	s.	s.	PROPN
ejpam-6544	186	5	m.	m.	PROPN
ejpam-6544	186	6	fallat	fallat	PROPN
ejpam-6544	186	7	and	and	CCONJ
ejpam-6544	186	8	l.	l.	PROPN
ejpam-6544	186	9	hogben	hogben	PROPN
ejpam-6544	186	10	.	.	PUNCT
ejpam-6544	187	1	minimum	minimum	ADJ
ejpam-6544	187	2	rank	rank	NOUN
ejpam-6544	187	3	,	,	PUNCT
ejpam-6544	187	4	maximum	maximum	ADJ
ejpam-6544	187	5	nullity	nullity	NOUN
ejpam-6544	187	6	,	,	PUNCT
ejpam-6544	187	7	and	and	CCONJ
ejpam-6544	187	8	zero	zero	NUM
ejpam-6544	187	9	forcing	force	VERB
ejpam-6544	187	10	number	number	NOUN
ejpam-6544	187	11	of	of	ADP
ejpam-6544	187	12	graphs	graph	NOUN
ejpam-6544	187	13	.	.	PUNCT
ejpam-6544	188	1	handbook	handbook	NOUN
ejpam-6544	188	2	of	of	ADP
ejpam-6544	188	3	linear	linear	PROPN
ejpam-6544	188	4	algebra	algebra	PROPN
ejpam-6544	188	5	.	.	PUNCT
ejpam-6544	189	1	crc	crc	PROPN
ejpam-6544	189	2	press	press	PROPN
ejpam-6544	189	3	,	,	PUNCT
ejpam-6544	189	4	boca	boca	PROPN
ejpam-6544	189	5	raton	raton	PROPN
ejpam-6544	189	6	,	,	PUNCT
ejpam-6544	189	7	fl	fl	PROPN
ejpam-6544	189	8	,	,	PUNCT
ejpam-6544	189	9	2nd	2nd	ADJ
ejpam-6544	189	10	edition	edition	NOUN
ejpam-6544	189	11	,	,	PUNCT
ejpam-6544	189	12	2013	2013	NUM
ejpam-6544	189	13	.	.	PUNCT
ejpam-6544	190	1	[	[	X
ejpam-6544	190	2	3	3	NUM
ejpam-6544	190	3	]	]	X
ejpam-6544	190	4	aimminimum	aimminimum	ADJ
ejpam-6544	190	5	rank	rank	NOUN
ejpam-6544	190	6	-	-	PUNCT
ejpam-6544	190	7	special	special	ADJ
ejpam-6544	190	8	graphs	graph	NOUN
ejpam-6544	190	9	work	work	NOUN
ejpam-6544	190	10	group	group	NOUN
ejpam-6544	190	11	.	.	PUNCT
ejpam-6544	191	1	zero	zero	NUM
ejpam-6544	191	2	forcing	force	VERB
ejpam-6544	191	3	sets	set	NOUN
ejpam-6544	191	4	and	and	CCONJ
ejpam-6544	191	5	the	the	DET
ejpam-6544	191	6	minimum	minimum	ADJ
ejpam-6544	191	7	rank	rank	NOUN
ejpam-6544	191	8	of	of	ADP
ejpam-6544	191	9	graphs	graph	NOUN
ejpam-6544	191	10	.	.	PUNCT
ejpam-6544	192	1	linear	linear	ADJ
ejpam-6544	192	2	algebra	algebra	NOUN
ejpam-6544	192	3	and	and	CCONJ
ejpam-6544	192	4	its	its	PRON
ejpam-6544	192	5	applications	application	NOUN
ejpam-6544	192	6	,	,	PUNCT
ejpam-6544	192	7	428:1628–1648	428:1628–1648	NOUN
ejpam-6544	192	8	,	,	PUNCT
ejpam-6544	192	9	2008	2008	NUM
ejpam-6544	192	10	.	.	PUNCT
ejpam-6544	193	1	[	[	X
ejpam-6544	193	2	4	4	X
ejpam-6544	193	3	]	]	PUNCT
ejpam-6544	193	4	k.	k.	PROPN
ejpam-6544	193	5	benson	benson	PROPN
ejpam-6544	193	6	,	,	PUNCT
ejpam-6544	193	7	d.	d.	PROPN
ejpam-6544	193	8	ferrero	ferrero	PROPN
ejpam-6544	193	9	,	,	PUNCT
ejpam-6544	193	10	m.	m.	PROPN
ejpam-6544	193	11	flagg	flagg	PROPN
ejpam-6544	193	12	,	,	PUNCT
ejpam-6544	193	13	v.	v.	PROPN
ejpam-6544	193	14	furst	furst	PROPN
ejpam-6544	193	15	,	,	PUNCT
ejpam-6544	193	16	l.	l.	PROPN
ejpam-6544	193	17	hogben	hogben	PROPN
ejpam-6544	193	18	,	,	PUNCT
ejpam-6544	193	19	v.	v.	ADP
ejpam-6544	193	20	vasilevska	vasilevska	NOUN
ejpam-6544	193	21	,	,	PUNCT
ejpam-6544	193	22	and	and	CCONJ
ejpam-6544	193	23	b.	b.	PROPN
ejpam-6544	193	24	wissman	wissman	NOUN
ejpam-6544	193	25	.	.	PUNCT
ejpam-6544	194	1	zero	zero	NUM
ejpam-6544	194	2	forcing	forcing	NOUN
ejpam-6544	194	3	and	and	CCONJ
ejpam-6544	194	4	power	power	NOUN
ejpam-6544	194	5	domination	domination	NOUN
ejpam-6544	194	6	for	for	ADP
ejpam-6544	194	7	graphs	graph	NOUN
ejpam-6544	194	8	products	product	NOUN
ejpam-6544	194	9	.	.	PUNCT
ejpam-6544	195	1	australasian	australasian	ADJ
ejpam-6544	195	2	journal	journal	NOUN
ejpam-6544	195	3	of	of	ADP
ejpam-6544	195	4	combinatorics	combinatoric	NOUN
ejpam-6544	195	5	,	,	PUNCT
ejpam-6544	195	6	70:221–235	70:221–235	PROPN
ejpam-6544	195	7	,	,	PUNCT
ejpam-6544	195	8	2018	2018	NUM
ejpam-6544	195	9	.	.	PUNCT
ejpam-6544	196	1	[	[	X
ejpam-6544	196	2	5	5	NUM
ejpam-6544	196	3	]	]	PUNCT
ejpam-6544	196	4	a.	a.	NOUN
ejpam-6544	196	5	berliner	berliner	PROPN
ejpam-6544	196	6	,	,	PUNCT
ejpam-6544	196	7	c.	c.	PROPN
ejpam-6544	196	8	bozeman	bozeman	PROPN
ejpam-6544	196	9	,	,	PUNCT
ejpam-6544	196	10	s.	s.	PROPN
ejpam-6544	196	11	butler	butler	PROPN
ejpam-6544	196	12	,	,	PUNCT
ejpam-6544	196	13	m.	m.	NOUN
ejpam-6544	196	14	catral	catral	PROPN
ejpam-6544	196	15	,	,	PUNCT
ejpam-6544	196	16	l.	l.	PROPN
ejpam-6544	196	17	hogben	hogben	PROPN
ejpam-6544	196	18	,	,	PUNCT
ejpam-6544	196	19	b.	b.	PROPN
ejpam-6544	196	20	kroschel	kroschel	PROPN
ejpam-6544	196	21	,	,	PUNCT
ejpam-6544	196	22	j.	j.	PROPN
ejpam-6544	196	23	c.	c.	PROPN
ejpam-6544	196	24	h.	h.	PROPN
ejpam-6544	196	25	lin	lin	PROPN
ejpam-6544	196	26	,	,	PUNCT
ejpam-6544	196	27	n.	n.	PROPN
ejpam-6544	196	28	warnberg	warnberg	PROPN
ejpam-6544	196	29	,	,	PUNCT
ejpam-6544	196	30	and	and	CCONJ
ejpam-6544	196	31	m.	m.	NOUN
ejpam-6544	196	32	young	young	ADJ
ejpam-6544	196	33	.	.	PUNCT
ejpam-6544	197	1	zero	zero	NUM
ejpam-6544	197	2	forcing	force	VERB
ejpam-6544	197	3	propagation	propagation	NOUN
ejpam-6544	197	4	time	time	NOUN
ejpam-6544	197	5	on	on	ADP
ejpam-6544	197	6	oriented	orient	VERB
ejpam-6544	197	7	graphs	graph	NOUN
ejpam-6544	197	8	.	.	PUNCT
ejpam-6544	198	1	discrete	discrete	ADJ
ejpam-6544	198	2	applied	apply	VERB
ejpam-6544	198	3	mathematics	mathematic	NOUN
ejpam-6544	198	4	,	,	PUNCT
ejpam-6544	198	5	224:45–59	224:45–59	PROPN
ejpam-6544	198	6	,	,	PUNCT
ejpam-6544	198	7	2017	2017	NUM
ejpam-6544	198	8	.	.	PUNCT
ejpam-6544	199	1	[	[	X
ejpam-6544	199	2	6	6	NUM
ejpam-6544	199	3	]	]	PUNCT
ejpam-6544	199	4	r.	r.	PROPN
ejpam-6544	199	5	davila	davila	PROPN
ejpam-6544	199	6	,	,	PUNCT
ejpam-6544	199	7	t.	t.	PROPN
ejpam-6544	199	8	kalinowski	kalinowski	PROPN
ejpam-6544	199	9	,	,	PUNCT
ejpam-6544	199	10	and	and	CCONJ
ejpam-6544	199	11	s.	s.	PROPN
ejpam-6544	199	12	stephen	stephen	PROPN
ejpam-6544	199	13	.	.	PUNCT
ejpam-6544	200	1	a	a	DET
ejpam-6544	200	2	lower	lower	ADV
ejpam-6544	200	3	bound	bind	VERB
ejpam-6544	200	4	on	on	ADP
ejpam-6544	200	5	the	the	DET
ejpam-6544	200	6	zero	zero	NUM
ejpam-6544	200	7	forcing	force	VERB
ejpam-6544	200	8	number	number	NOUN
ejpam-6544	200	9	.	.	PUNCT
ejpam-6544	201	1	discrete	discrete	ADJ
ejpam-6544	201	2	applied	apply	VERB
ejpam-6544	201	3	mathematics	mathematic	NOUN
ejpam-6544	201	4	,	,	PUNCT
ejpam-6544	201	5	250:363–367	250:363–367	NUM
ejpam-6544	201	6	,	,	PUNCT
ejpam-6544	201	7	2018	2018	NUM
ejpam-6544	201	8	.	.	PUNCT
ejpam-6544	202	1	[	[	X
ejpam-6544	202	2	7	7	X
ejpam-6544	202	3	]	]	X
ejpam-6544	202	4	j.	j.	PROPN
ejpam-6544	202	5	ekstrand	ekstrand	PROPN
ejpam-6544	202	6	,	,	PUNCT
ejpam-6544	202	7	c.	c.	PROPN
ejpam-6544	202	8	erickson	erickson	PROPN
ejpam-6544	202	9	,	,	PUNCT
ejpam-6544	202	10	h.	h.	PROPN
ejpam-6544	202	11	t.	t.	PROPN
ejpam-6544	202	12	hall	hall	PROPN
ejpam-6544	202	13	,	,	PUNCT
ejpam-6544	202	14	d.	d.	PROPN
ejpam-6544	202	15	hay	hay	PROPN
ejpam-6544	202	16	,	,	PUNCT
ejpam-6544	202	17	l.	l.	PROPN
ejpam-6544	202	18	hogben	hogben	PROPN
ejpam-6544	202	19	,	,	PUNCT
ejpam-6544	202	20	r.	r.	PROPN
ejpam-6544	202	21	johnson	johnson	PROPN
ejpam-6544	202	22	,	,	PUNCT
ejpam-6544	202	23	n.	n.	PROPN
ejpam-6544	202	24	kingsley	kingsley	PROPN
ejpam-6544	202	25	,	,	PUNCT
ejpam-6544	202	26	s.	s.	PROPN
ejpam-6544	202	27	osborne	osborne	PROPN
ejpam-6544	202	28	,	,	PUNCT
ejpam-6544	202	29	t.	t.	PROPN
ejpam-6544	202	30	peters	peters	PROPN
ejpam-6544	202	31	,	,	PUNCT
ejpam-6544	202	32	j.	j.	PROPN
ejpam-6544	202	33	roat	roat	PROPN
ejpam-6544	202	34	,	,	PUNCT
ejpam-6544	202	35	a.	a.	PROPN
ejpam-6544	202	36	ross	ross	PROPN
ejpam-6544	202	37	,	,	PUNCT
ejpam-6544	202	38	d.	d.	PROPN
ejpam-6544	202	39	d.	d.	PROPN
ejpam-6544	202	40	row	row	PROPN
ejpam-6544	202	41	,	,	PUNCT
ejpam-6544	202	42	n.	n.	PROPN
ejpam-6544	202	43	warnberg	warnberg	PROPN
ejpam-6544	202	44	,	,	PUNCT
ejpam-6544	202	45	and	and	CCONJ
ejpam-6544	202	46	m.	m.	NOUN
ejpam-6544	202	47	young	young	PROPN
ejpam-6544	202	48	.	.	PUNCT
ejpam-6544	203	1	positive	positive	ADJ
ejpam-6544	203	2	semidefinite	semidefinite	NOUN
ejpam-6544	203	3	zero	zero	NUM
ejpam-6544	203	4	forcing	forcing	NOUN
ejpam-6544	203	5	.	.	PUNCT
ejpam-6544	204	1	linear	linear	ADJ
ejpam-6544	204	2	algebra	algebra	NOUN
ejpam-6544	204	3	and	and	CCONJ
ejpam-6544	204	4	its	its	PRON
ejpam-6544	204	5	applications	application	NOUN
ejpam-6544	204	6	,	,	PUNCT
ejpam-6544	204	7	439:1862–1874	439:1862–1874	NUM
ejpam-6544	204	8	,	,	PUNCT
ejpam-6544	204	9	2013	2013	NUM
ejpam-6544	204	10	.	.	PUNCT
ejpam-6544	205	1	[	[	X
ejpam-6544	205	2	8	8	NUM
ejpam-6544	205	3	]	]	PUNCT
ejpam-6544	205	4	m.	m.	NOUN
ejpam-6544	205	5	gentner	gentner	NOUN
ejpam-6544	205	6	,	,	PUNCT
ejpam-6544	205	7	l.	l.	PROPN
ejpam-6544	205	8	d.	d.	PROPN
ejpam-6544	205	9	penso	penso	PROPN
ejpam-6544	205	10	,	,	PUNCT
ejpam-6544	205	11	d.	d.	PROPN
ejpam-6544	205	12	rautenbach	rautenbach	NOUN
ejpam-6544	205	13	,	,	PUNCT
ejpam-6544	205	14	and	and	CCONJ
ejpam-6544	205	15	u.	u.	PROPN
ejpam-6544	205	16	s.	s.	PROPN
ejpam-6544	205	17	souza	souza	PROPN
ejpam-6544	205	18	.	.	PUNCT
ejpam-6544	206	1	extremal	extremal	ADJ
ejpam-6544	206	2	values	value	NOUN
ejpam-6544	206	3	and	and	CCONJ
ejpam-6544	206	4	bounds	bound	NOUN
ejpam-6544	206	5	for	for	ADP
ejpam-6544	206	6	the	the	DET
ejpam-6544	206	7	zero	zero	NUM
ejpam-6544	206	8	forcing	force	VERB
ejpam-6544	206	9	number	number	NOUN
ejpam-6544	206	10	.	.	PUNCT
ejpam-6544	207	1	discrete	discrete	ADJ
ejpam-6544	207	2	applied	apply	VERB
ejpam-6544	207	3	mathematics	mathematic	NOUN
ejpam-6544	207	4	,	,	PUNCT
ejpam-6544	207	5	214:196–200	214:196–200	NUM
ejpam-6544	207	6	,	,	PUNCT
ejpam-6544	207	7	2016	2016	NUM
ejpam-6544	207	8	.	.	PUNCT
ejpam-6544	208	1	[	[	X
ejpam-6544	208	2	9	9	NUM
ejpam-6544	208	3	]	]	PUNCT
ejpam-6544	208	4	j.	j.	PROPN
ejpam-6544	208	5	hassan	hassan	PROPN
ejpam-6544	208	6	,	,	PUNCT
ejpam-6544	208	7	m.	m.	NOUN
ejpam-6544	208	8	a.	a.	PROPN
ejpam-6544	208	9	bonsocan	bonsocan	PROPN
ejpam-6544	208	10	,	,	PUNCT
ejpam-6544	208	11	m.	m.	NOUN
ejpam-6544	208	12	langamin	langamin	PROPN
ejpam-6544	208	13	,	,	PUNCT
ejpam-6544	208	14	v.	v.	PROPN
ejpam-6544	208	15	bilar	bilar	PROPN
ejpam-6544	208	16	,	,	PUNCT
ejpam-6544	208	17	s.	s.	PROPN
ejpam-6544	208	18	d.	d.	PROPN
ejpam-6544	208	19	aming	aming	PROPN
ejpam-6544	208	20	,	,	PUNCT
ejpam-6544	208	21	and	and	CCONJ
ejpam-6544	208	22	b.	b.	PROPN
ejpam-6544	208	23	amiruddin	amiruddin	PROPN
ejpam-6544	208	24	.	.	PUNCT
ejpam-6544	208	25	zero	zero	NUM
ejpam-6544	208	26	forcing	force	VERB
ejpam-6544	208	27	domination	domination	NOUN
ejpam-6544	208	28	in	in	ADP
ejpam-6544	208	29	some	some	DET
ejpam-6544	208	30	graphs	graph	NOUN
ejpam-6544	208	31	:	:	PUNCT
ejpam-6544	208	32	characterizations	characterization	NOUN
ejpam-6544	208	33	and	and	CCONJ
ejpam-6544	208	34	derived	derive	VERB
ejpam-6544	208	35	formulas	formula	NOUN
ejpam-6544	208	36	.	.	PUNCT
ejpam-6544	209	1	european	european	ADJ
ejpam-6544	209	2	journal	journal	PROPN
ejpam-6544	209	3	of	of	ADP
ejpam-6544	209	4	pure	pure	ADJ
ejpam-6544	209	5	and	and	CCONJ
ejpam-6544	209	6	applied	applied	ADJ
ejpam-6544	209	7	mathematics	mathematic	NOUN
ejpam-6544	209	8	,	,	PUNCT
ejpam-6544	209	9	17(4):3772–3780	17(4):3772–3780	NUM
ejpam-6544	209	10	,	,	PUNCT
ejpam-6544	209	11	2024	2024	NUM
ejpam-6544	209	12	.	.	PUNCT
ejpam-6544	210	1	[	[	X
ejpam-6544	210	2	10	10	NUM
ejpam-6544	210	3	]	]	X
ejpam-6544	210	4	j.	j.	PROPN
ejpam-6544	210	5	hassan	hassan	PROPN
ejpam-6544	210	6	and	and	CCONJ
ejpam-6544	210	7	l.	l.	PROPN
ejpam-6544	210	8	s.	s.	PROPN
ejpam-6544	210	9	laja	laja	PROPN
ejpam-6544	210	10	.	.	PUNCT
ejpam-6544	211	1	vertex	vertex	NOUN
ejpam-6544	211	2	cover	cover	NOUN
ejpam-6544	211	3	zero	zero	NUM
ejpam-6544	211	4	forcing	force	VERB
ejpam-6544	211	5	sets	set	NOUN
ejpam-6544	211	6	in	in	ADP
ejpam-6544	211	7	graphs	graph	NOUN
ejpam-6544	211	8	.	.	PUNCT
ejpam-6544	212	1	european	european	ADJ
ejpam-6544	212	2	journal	journal	PROPN
ejpam-6544	212	3	of	of	ADP
ejpam-6544	212	4	pure	pure	ADJ
ejpam-6544	212	5	and	and	CCONJ
ejpam-6544	212	6	applied	applied	ADJ
ejpam-6544	212	7	mathematics	mathematic	NOUN
ejpam-6544	212	8	,	,	PUNCT
ejpam-6544	212	9	19(4):999–1003	19(4):999–1003	NUM
ejpam-6544	212	10	,	,	PUNCT
ejpam-6544	212	11	2024	2024	NUM
ejpam-6544	212	12	.	.	PUNCT
ejpam-6544	213	1	[	[	X
ejpam-6544	213	2	11	11	NUM
ejpam-6544	213	3	]	]	PUNCT
ejpam-6544	213	4	j.	j.	PROPN
ejpam-6544	213	5	hassan	hassan	PROPN
ejpam-6544	213	6	,	,	PUNCT
ejpam-6544	213	7	l.	l.	PROPN
ejpam-6544	213	8	laja	laja	PROPN
ejpam-6544	213	9	,	,	PUNCT
ejpam-6544	213	10	and	and	CCONJ
ejpam-6544	213	11	hounam	hounam	PROPN
ejpam-6544	213	12	b.	b.	PROPN
ejpam-6544	213	13	copel	copel	PROPN
ejpam-6544	213	14	.	.	PUNCT
ejpam-6544	213	15	2	2	NUM
ejpam-6544	213	16	-	-	PUNCT
ejpam-6544	213	17	domination	domination	NOUN
ejpam-6544	213	18	zero	zero	NUM
ejpam-6544	213	19	forcing	force	VERB
ejpam-6544	213	20	in	in	ADP
ejpam-6544	213	21	graphs	graph	NOUN
ejpam-6544	213	22	.	.	PUNCT
ejpam-6544	214	1	international	international	ADJ
ejpam-6544	214	2	journal	journal	NOUN
ejpam-6544	214	3	of	of	ADP
ejpam-6544	214	4	mathematics	mathematic	NOUN
ejpam-6544	214	5	and	and	CCONJ
ejpam-6544	214	6	computer	computer	NOUN
ejpam-6544	214	7	science	science	NOUN
ejpam-6544	214	8	,	,	PUNCT
ejpam-6544	214	9	19(4):1065–1070	19(4):1065–1070	NUM
ejpam-6544	214	10	,	,	PUNCT
ejpam-6544	214	11	2024	2024	NUM
ejpam-6544	214	12	.	.	PUNCT
ejpam-6544	215	1	[	[	X
ejpam-6544	215	2	12	12	NUM
ejpam-6544	215	3	]	]	PUNCT
ejpam-6544	215	4	t.	t.	PROPN
ejpam-6544	215	5	kalinowski	kalinowski	PROPN
ejpam-6544	215	6	,	,	PUNCT
ejpam-6544	215	7	n.	n.	NOUN
ejpam-6544	215	8	kamcev	kamcev	PROPN
ejpam-6544	215	9	,	,	PUNCT
ejpam-6544	215	10	and	and	CCONJ
ejpam-6544	215	11	b.	b.	PROPN
ejpam-6544	215	12	sudakov	sudakov	PROPN
ejpam-6544	215	13	.	.	PUNCT
ejpam-6544	216	1	the	the	DET
ejpam-6544	216	2	zero	zero	NUM
ejpam-6544	216	3	forcing	force	VERB
ejpam-6544	216	4	number	number	NOUN
ejpam-6544	216	5	of	of	ADP
ejpam-6544	216	6	graphs	graph	NOUN
ejpam-6544	216	7	.	.	PUNCT
ejpam-6544	217	1	siam	siam	PROPN
ejpam-6544	217	2	journal	journal	PROPN
ejpam-6544	217	3	on	on	ADP
ejpam-6544	217	4	discrete	discrete	ADJ
ejpam-6544	217	5	mathematics	mathematic	NOUN
ejpam-6544	217	6	,	,	PUNCT
ejpam-6544	217	7	33(1):95–115	33(1):95–115	NUM
ejpam-6544	217	8	,	,	PUNCT
ejpam-6544	217	9	2019	2019	NUM
ejpam-6544	217	10	.	.	PUNCT
ejpam-6544	218	1	[	[	X
ejpam-6544	218	2	13	13	NUM
ejpam-6544	218	3	]	]	PUNCT
ejpam-6544	218	4	j.	j.	PROPN
ejpam-6544	218	5	manditong	manditong	PROPN
ejpam-6544	218	6	,	,	PUNCT
ejpam-6544	218	7	a.	a.	NOUN
ejpam-6544	218	8	tapeing	tapeing	NOUN
ejpam-6544	218	9	,	,	PUNCT
ejpam-6544	218	10	j.	j.	PROPN
ejpam-6544	218	11	hassan	hassan	PROPN
ejpam-6544	218	12	,	,	PUNCT
ejpam-6544	218	13	a.	a.	PROPN
ejpam-6544	218	14	r.	r.	PROPN
ejpam-6544	218	15	bakkang	bakkang	PROPN
ejpam-6544	218	16	,	,	PUNCT
ejpam-6544	218	17	n.	n.	PROPN
ejpam-6544	218	18	h.	h.	PROPN
ejpam-6544	218	19	mohammad	mohammad	PROPN
ejpam-6544	218	20	,	,	PUNCT
ejpam-6544	218	21	and	and	CCONJ
ejpam-6544	218	22	s.	s.	PROPN
ejpam-6544	218	23	u.	u.	PROPN
ejpam-6544	218	24	kamdon	kamdon	PROPN
ejpam-6544	218	25	.	.	PUNCT
ejpam-6544	219	1	some	some	DET
ejpam-6544	219	2	properties	property	NOUN
ejpam-6544	219	3	of	of	ADP
ejpam-6544	219	4	zero	zero	NUM
ejpam-6544	219	5	forcing	force	VERB
ejpam-6544	219	6	hop	hop	NOUN
ejpam-6544	219	7	dominating	dominating	NOUN
ejpam-6544	219	8	sets	set	NOUN
ejpam-6544	219	9	in	in	ADP
ejpam-6544	219	10	a	a	DET
ejpam-6544	219	11	graph	graph	NOUN
ejpam-6544	219	12	.	.	PUNCT
ejpam-6544	220	1	european	european	PROPN
ejpam-6544	220	2	journal	journal	PROPN
ejpam-6544	220	3	of	of	ADP
ejpam-6544	220	4	applied	apply	VERB
ejpam-6544	220	5	mathematics	mathematic	NOUN
ejpam-6544	220	6	,	,	PUNCT
ejpam-6544	220	7	17(1):324–337	17(1):324–337	PROPN
ejpam-6544	220	8	,	,	PUNCT
ejpam-6544	220	9	2014	2014	NUM
ejpam-6544	220	10	.	.	PUNCT
ejpam-6544	221	1	a.	a.	NOUN
ejpam-6544	221	2	madjatul	madjatul	PROPN
ejpam-6544	221	3	et	et	PROPN
ejpam-6544	221	4	al	al	PROPN
ejpam-6544	221	5	.	.	PUNCT
ejpam-6544	221	6	/	/	SYM
ejpam-6544	221	7	eur	eur	PROPN
ejpam-6544	221	8	.	.	PUNCT
ejpam-6544	222	1	j.	j.	PROPN
ejpam-6544	222	2	pure	pure	PROPN
ejpam-6544	222	3	appl	appl	PROPN
ejpam-6544	222	4	.	.	PROPN
ejpam-6544	222	5	math	math	PROPN
ejpam-6544	222	6	,	,	PUNCT
ejpam-6544	222	7	18	18	NUM
ejpam-6544	222	8	(	(	PUNCT
ejpam-6544	222	9	3	3	NUM
ejpam-6544	222	10	)	)	PUNCT
ejpam-6544	222	11	(	(	PUNCT
ejpam-6544	222	12	2025	2025	NUM
ejpam-6544	222	13	)	)	PUNCT
ejpam-6544	222	14	,	,	PUNCT
ejpam-6544	222	15	6544	6544	NUM
ejpam-6544	222	16	8	8	NUM
ejpam-6544	222	17	of	of	ADP
ejpam-6544	222	18	8	8	NUM
ejpam-6544	222	19	[	[	SYM
ejpam-6544	222	20	14	14	NUM
ejpam-6544	222	21	]	]	X
ejpam-6544	222	22	a.	a.	PROPN
ejpam-6544	222	23	adams	adams	PROPN
ejpam-6544	222	24	and	and	CCONJ
ejpam-6544	222	25	b.	b.	PROPN
ejpam-6544	222	26	jacob	jacob	PROPN
ejpam-6544	222	27	.	.	PROPN
ejpam-6544	222	28	failed	fail	VERB
ejpam-6544	222	29	zero	zero	NUM
ejpam-6544	222	30	forcing	forcing	NOUN
ejpam-6544	222	31	and	and	CCONJ
ejpam-6544	222	32	critical	critical	ADJ
ejpam-6544	222	33	sets	set	NOUN
ejpam-6544	222	34	on	on	ADP
ejpam-6544	222	35	directed	direct	VERB
ejpam-6544	222	36	graphs	graph	NOUN
ejpam-6544	222	37	.	.	PUNCT
ejpam-6544	223	1	australasian	australasian	ADJ
ejpam-6544	223	2	journal	journal	NOUN
ejpam-6544	223	3	of	of	ADP
ejpam-6544	223	4	combinatorics	combinatoric	NOUN
ejpam-6544	223	5	,	,	PUNCT
ejpam-6544	223	6	81(3):367–387	81(3):367–387	NUM
ejpam-6544	223	7	,	,	PUNCT
ejpam-6544	223	8	2021	2021	NUM
ejpam-6544	223	9	.	.	PUNCT
ejpam-6544	224	1	[	[	X
ejpam-6544	224	2	15	15	X
ejpam-6544	224	3	]	]	X
ejpam-6544	224	4	t.	t.	PROPN
ejpam-6544	224	5	ansill	ansill	PROPN
ejpam-6544	224	6	,	,	PUNCT
ejpam-6544	224	7	b.	b.	PROPN
ejpam-6544	224	8	jacob	jacob	PROPN
ejpam-6544	224	9	,	,	PUNCT
ejpam-6544	224	10	j.	j.	PROPN
ejpam-6544	224	11	penzellna	penzellna	PROPN
ejpam-6544	224	12	,	,	PUNCT
ejpam-6544	224	13	and	and	CCONJ
ejpam-6544	224	14	d.	d.	PROPN
ejpam-6544	224	15	saavedra	saavedra	PROPN
ejpam-6544	224	16	.	.	PUNCT
ejpam-6544	224	17	failed	fail	VERB
ejpam-6544	224	18	skew	skew	NOUN
ejpam-6544	224	19	zero	zero	NUM
ejpam-6544	224	20	forcing	force	VERB
ejpam-6544	224	21	on	on	ADP
ejpam-6544	224	22	a	a	DET
ejpam-6544	224	23	graph	graph	NOUN
ejpam-6544	224	24	.	.	PUNCT
ejpam-6544	225	1	linear	linear	ADJ
ejpam-6544	225	2	algebra	algebra	NOUN
ejpam-6544	225	3	and	and	CCONJ
ejpam-6544	225	4	its	its	PRON
ejpam-6544	225	5	applications	application	NOUN
ejpam-6544	225	6	,	,	PUNCT
ejpam-6544	225	7	509:40–63	509:40–63	NUM
ejpam-6544	225	8	,	,	PUNCT
ejpam-6544	225	9	2016	2016	NUM
ejpam-6544	225	10	.	.	PUNCT
ejpam-6544	226	1	[	[	X
ejpam-6544	226	2	16	16	NUM
ejpam-6544	226	3	]	]	PUNCT
ejpam-6544	226	4	k.	k.	PROPN
ejpam-6544	226	5	fetcie	fetcie	PROPN
ejpam-6544	226	6	,	,	PUNCT
ejpam-6544	226	7	b.	b.	PROPN
ejpam-6544	226	8	jacob	jacob	PROPN
ejpam-6544	226	9	,	,	PUNCT
ejpam-6544	226	10	and	and	CCONJ
ejpam-6544	226	11	d.	d.	PROPN
ejpam-6544	226	12	saavedra	saavedra	PROPN
ejpam-6544	226	13	.	.	PUNCT
ejpam-6544	227	1	the	the	DET
ejpam-6544	227	2	failed	fail	VERB
ejpam-6544	227	3	zero	zero	NUM
ejpam-6544	227	4	-	-	PUNCT
ejpam-6544	227	5	forcing	force	VERB
ejpam-6544	227	6	number	number	NOUN
ejpam-6544	227	7	of	of	ADP
ejpam-6544	227	8	a	a	DET
ejpam-6544	227	9	graph	graph	NOUN
ejpam-6544	227	10	.	.	PUNCT
ejpam-6544	227	11	involve	involve	NOUN
ejpam-6544	227	12	,	,	PUNCT
ejpam-6544	227	13	8:99–117	8:99–117	NUM
ejpam-6544	227	14	,	,	PUNCT
ejpam-6544	227	15	2015	2015	NUM
ejpam-6544	227	16	.	.	PUNCT
ejpam-6544	228	1	[	[	X
ejpam-6544	228	2	17	17	NUM
ejpam-6544	228	3	]	]	X
ejpam-6544	228	4	y.	y.	PROPN
ejpam-6544	228	5	shitov	shitov	PROPN
ejpam-6544	228	6	.	.	PUNCT
ejpam-6544	229	1	on	on	ADP
ejpam-6544	229	2	the	the	DET
ejpam-6544	229	3	complexity	complexity	NOUN
ejpam-6544	229	4	of	of	ADP
ejpam-6544	229	5	failed	fail	VERB
ejpam-6544	229	6	zero	zero	NUM
ejpam-6544	229	7	forcing	forcing	NOUN
ejpam-6544	229	8	.	.	PUNCT
ejpam-6544	230	1	theoretical	theoretical	ADJ
ejpam-6544	230	2	computer	computer	NOUN
ejpam-6544	230	3	science	science	NOUN
ejpam-6544	230	4	,	,	PUNCT
ejpam-6544	230	5	660:102–104	660:102–104	NOUN
ejpam-6544	230	6	,	,	PUNCT
ejpam-6544	230	7	2017	2017	NUM
ejpam-6544	230	8	.	.	PUNCT
ejpam-6544	231	1	[	[	X
ejpam-6544	231	2	18	18	NUM
ejpam-6544	231	3	]	]	PUNCT
ejpam-6544	231	4	j.	j.	PROPN
ejpam-6544	231	5	hassan	hassan	PROPN
ejpam-6544	231	6	,	,	PUNCT
ejpam-6544	231	7	l.	l.	PROPN
ejpam-6544	231	8	t.	t.	PROPN
ejpam-6544	231	9	udtohan	udtohan	PROPN
ejpam-6544	231	10	,	,	PUNCT
ejpam-6544	231	11	and	and	CCONJ
ejpam-6544	231	12	l.	l.	PROPN
ejpam-6544	231	13	s.	s.	PROPN
ejpam-6544	231	14	laja	laja	PROPN
ejpam-6544	231	15	.	.	PUNCT
ejpam-6544	232	1	2	2	NUM
ejpam-6544	232	2	-	-	PUNCT
ejpam-6544	232	3	distance	distance	NOUN
ejpam-6544	232	4	zero	zero	NUM
ejpam-6544	232	5	forcing	force	VERB
ejpam-6544	232	6	in	in	ADP
ejpam-6544	232	7	graphs	graph	NOUN
ejpam-6544	232	8	.	.	PUNCT
ejpam-6544	233	1	european	european	ADJ
ejpam-6544	233	2	journal	journal	PROPN
ejpam-6544	233	3	of	of	ADP
ejpam-6544	233	4	pure	pure	ADJ
ejpam-6544	233	5	and	and	CCONJ
ejpam-6544	233	6	applied	applied	ADJ
ejpam-6544	233	7	mathematics	mathematic	NOUN
ejpam-6544	233	8	,	,	PUNCT
ejpam-6544	233	9	17(2):1283–1293	17(2):1283–1293	NUM
ejpam-6544	233	10	,	,	PUNCT
ejpam-6544	233	11	2024	2024	NUM
ejpam-6544	233	12	.	.	PUNCT