id	sid	tid	token	lemma	pos
ejpam-6603	1	1	european	european	PROPN
ejpam-6603	1	2	journal	journal	PROPN
ejpam-6603	1	3	of	of	ADP
ejpam-6603	1	4	pure	pure	ADJ
ejpam-6603	1	5	and	and	CCONJ
ejpam-6603	1	6	applied	applied	ADJ
ejpam-6603	1	7	mathematics	mathematic	NOUN
ejpam-6603	1	8	2025	2025	NUM
ejpam-6603	1	9	,	,	PUNCT
ejpam-6603	1	10	vol	vol	NOUN
ejpam-6603	1	11	.	.	PROPN
ejpam-6603	1	12	18	18	NUM
ejpam-6603	1	13	,	,	PUNCT
ejpam-6603	1	14	issue	issue	NOUN
ejpam-6603	1	15	3	3	NUM
ejpam-6603	1	16	,	,	PUNCT
ejpam-6603	1	17	article	article	NOUN
ejpam-6603	1	18	number	number	NOUN
ejpam-6603	1	19	6603	6603	NUM
ejpam-6603	1	20	issn	issn	VERB
ejpam-6603	1	21	1307	1307	NUM
ejpam-6603	1	22	-	-	SYM
ejpam-6603	1	23	5543	5543	NUM
ejpam-6603	1	24	–	–	PUNCT
ejpam-6603	1	25	ejpam.com	ejpam.com	X
ejpam-6603	1	26	published	publish	VERB
ejpam-6603	1	27	by	by	ADP
ejpam-6603	1	28	new	new	PROPN
ejpam-6603	1	29	york	york	PROPN
ejpam-6603	1	30	business	business	PROPN
ejpam-6603	1	31	global	global	ADJ
ejpam-6603	1	32	perfect	perfect	ADJ
ejpam-6603	1	33	2	2	NUM
ejpam-6603	1	34	-	-	PUNCT
ejpam-6603	1	35	distance	distance	NOUN
ejpam-6603	1	36	zero	zero	NUM
ejpam-6603	1	37	forcing	force	VERB
ejpam-6603	1	38	in	in	ADP
ejpam-6603	1	39	graphs	graph	NOUN
ejpam-6603	1	40	javier	javier	PROPN
ejpam-6603	1	41	a.	a.	PROPN
ejpam-6603	1	42	hassan1,2,∗	hassan1,2,∗	PROPN
ejpam-6603	1	43	,	,	PUNCT
ejpam-6603	1	44	erwan	erwan	PROPN
ejpam-6603	1	45	d.	d.	PROPN
ejpam-6603	1	46	hajim1	hajim1	PROPN
ejpam-6603	1	47	,	,	PUNCT
ejpam-6603	1	48	angelica	angelica	PROPN
ejpam-6603	1	49	mae	mae	PROPN
ejpam-6603	1	50	l.	l.	PROPN
ejpam-6603	1	51	mahistrado3	mahistrado3	PROPN
ejpam-6603	1	52	,	,	PUNCT
ejpam-6603	2	1	akrimal	akrimal	ADJ
ejpam-6603	2	2	m.	m.	NOUN
ejpam-6603	2	3	alayka	alayka	NOUN
ejpam-6603	3	1	1department	1department	NUM
ejpam-6603	3	2	of	of	ADP
ejpam-6603	3	3	mathematics	mathematic	NOUN
ejpam-6603	3	4	,	,	PUNCT
ejpam-6603	3	5	college	college	NOUN
ejpam-6603	3	6	of	of	ADP
ejpam-6603	3	7	arts	art	NOUN
ejpam-6603	3	8	and	and	CCONJ
ejpam-6603	3	9	sciences	science	NOUN
ejpam-6603	3	10	,	,	PUNCT
ejpam-6603	3	11	msu	msu	PROPN
ejpam-6603	3	12	tawi	tawi	PROPN
ejpam-6603	3	13	-	-	PUNCT
ejpam-6603	3	14	tawi	tawi	PROPN
ejpam-6603	3	15	college	college	PROPN
ejpam-6603	3	16	of	of	ADP
ejpam-6603	3	17	technology	technology	NOUN
ejpam-6603	3	18	and	and	CCONJ
ejpam-6603	3	19	oceanography	oceanography	NOUN
ejpam-6603	3	20	,	,	PUNCT
ejpam-6603	3	21	bongao	bongao	NOUN
ejpam-6603	3	22	,	,	PUNCT
ejpam-6603	3	23	tawi	tawi	NOUN
ejpam-6603	3	24	-	-	PUNCT
ejpam-6603	3	25	tawi	tawi	NOUN
ejpam-6603	3	26	,	,	PUNCT
ejpam-6603	3	27	philippines	philippine	NOUN
ejpam-6603	3	28	2department	2department	NUM
ejpam-6603	3	29	of	of	ADP
ejpam-6603	3	30	mathematics	mathematic	NOUN
ejpam-6603	3	31	,	,	PUNCT
ejpam-6603	3	32	college	college	NOUN
ejpam-6603	3	33	of	of	ADP
ejpam-6603	3	34	science	science	PROPN
ejpam-6603	3	35	,	,	PUNCT
ejpam-6603	3	36	korea	korea	PROPN
ejpam-6603	3	37	university	university	PROPN
ejpam-6603	3	38	,	,	PUNCT
ejpam-6603	3	39	seoul	seoul	PROPN
ejpam-6603	3	40	,	,	PUNCT
ejpam-6603	3	41	south	south	PROPN
ejpam-6603	3	42	korea	korea	PROPN
ejpam-6603	4	1	3department	3department	NUM
ejpam-6603	4	2	of	of	ADP
ejpam-6603	4	3	mathematics	mathematic	NOUN
ejpam-6603	4	4	,	,	PUNCT
ejpam-6603	4	5	ateneo	ateneo	X
ejpam-6603	4	6	de	de	PROPN
ejpam-6603	4	7	davao	davao	PROPN
ejpam-6603	4	8	university	university	PROPN
ejpam-6603	4	9	,	,	PUNCT
ejpam-6603	4	10	davao	davao	PROPN
ejpam-6603	4	11	city	city	PROPN
ejpam-6603	4	12	,	,	PUNCT
ejpam-6603	4	13	philippines	philippine	NOUN
ejpam-6603	4	14	abstract	abstract	ADJ
ejpam-6603	4	15	.	.	PUNCT
ejpam-6603	5	1	let	let	VERB
ejpam-6603	5	2	g	g	PRON
ejpam-6603	5	3	be	be	AUX
ejpam-6603	5	4	a	a	DET
ejpam-6603	5	5	graph	graph	NOUN
ejpam-6603	5	6	.	.	PUNCT
ejpam-6603	6	1	then	then	ADV
ejpam-6603	6	2	a	a	DET
ejpam-6603	6	3	2	2	NUM
ejpam-6603	6	4	-	-	PUNCT
ejpam-6603	6	5	distance	distance	NOUN
ejpam-6603	6	6	color	color	NOUN
ejpam-6603	6	7	change	change	NOUN
ejpam-6603	6	8	rule	rule	NOUN
ejpam-6603	6	9	is	be	AUX
ejpam-6603	6	10	defined	define	VERB
ejpam-6603	6	11	as	as	SCONJ
ejpam-6603	6	12	follows	follow	VERB
ejpam-6603	6	13	:	:	PUNCT
ejpam-6603	6	14	if	if	SCONJ
ejpam-6603	6	15	a	a	DET
ejpam-6603	6	16	vertex	vertex	NOUN
ejpam-6603	6	17	x	x	SYM
ejpam-6603	6	18	∈	∈	NOUN
ejpam-6603	6	19	v	v	ADP
ejpam-6603	6	20	(	(	PUNCT
ejpam-6603	6	21	g	g	NOUN
ejpam-6603	6	22	)	)	PUNCT
ejpam-6603	6	23	is	be	AUX
ejpam-6603	6	24	colored	color	VERB
ejpam-6603	6	25	and	and	CCONJ
ejpam-6603	6	26	has	have	VERB
ejpam-6603	6	27	exactly	exactly	ADV
ejpam-6603	6	28	one	one	NUM
ejpam-6603	6	29	hop	hop	NOUN
ejpam-6603	6	30	neighbor	neighbor	NOUN
ejpam-6603	6	31	y	y	PROPN
ejpam-6603	6	32	is	be	AUX
ejpam-6603	6	33	uncolored	uncolored	ADJ
ejpam-6603	6	34	,	,	PUNCT
ejpam-6603	6	35	then	then	ADV
ejpam-6603	6	36	y	y	PROPN
ejpam-6603	6	37	will	will	AUX
ejpam-6603	6	38	become	become	VERB
ejpam-6603	6	39	colored	color	VERB
ejpam-6603	6	40	.	.	PUNCT
ejpam-6603	7	1	moreover	moreover	ADV
ejpam-6603	7	2	,	,	PUNCT
ejpam-6603	7	3	let	let	VERB
ejpam-6603	7	4	u	u	NOUN
ejpam-6603	7	5	,	,	PUNCT
ejpam-6603	7	6	v	v	NOUN
ejpam-6603	7	7	,	,	PUNCT
ejpam-6603	7	8	w	w	PROPN
ejpam-6603	7	9	∈	∈	PROPN
ejpam-6603	7	10	v	v	ADP
ejpam-6603	7	11	(	(	PUNCT
ejpam-6603	7	12	g	g	NOUN
ejpam-6603	7	13	)	)	PUNCT
ejpam-6603	7	14	.	.	PUNCT
ejpam-6603	8	1	if	if	SCONJ
ejpam-6603	8	2	u	u	NOUN
ejpam-6603	8	3	2	2	NUM
ejpam-6603	8	4	-	-	PUNCT
ejpam-6603	8	5	forces	force	NOUN
ejpam-6603	8	6	v	v	NOUN
ejpam-6603	8	7	and	and	CCONJ
ejpam-6603	8	8	v	v	ADP
ejpam-6603	8	9	2	2	NUM
ejpam-6603	8	10	-	-	PUNCT
ejpam-6603	8	11	forces	force	NOUN
ejpam-6603	8	12	w	w	NOUN
ejpam-6603	8	13	,	,	PUNCT
ejpam-6603	8	14	then	then	ADV
ejpam-6603	8	15	we	we	PRON
ejpam-6603	8	16	say	say	VERB
ejpam-6603	8	17	that	that	SCONJ
ejpam-6603	8	18	v	v	NOUN
ejpam-6603	8	19	and	and	CCONJ
ejpam-6603	8	20	w	w	NOUN
ejpam-6603	8	21	are	be	AUX
ejpam-6603	8	22	perfectly	perfectly	ADV
ejpam-6603	8	23	2	2	NUM
ejpam-6603	8	24	-	-	PUNCT
ejpam-6603	8	25	forced	force	VERB
ejpam-6603	8	26	by	by	ADP
ejpam-6603	8	27	u	u	NOUN
ejpam-6603	8	28	,	,	PUNCT
ejpam-6603	8	29	and	and	CCONJ
ejpam-6603	8	30	this	this	DET
ejpam-6603	8	31	process	process	NOUN
ejpam-6603	8	32	can	can	AUX
ejpam-6603	8	33	extend	extend	VERB
ejpam-6603	8	34	to	to	ADP
ejpam-6603	8	35	a	a	DET
ejpam-6603	8	36	chain	chain	NOUN
ejpam-6603	8	37	of	of	ADP
ejpam-6603	8	38	2	2	NUM
ejpam-6603	8	39	-	-	PUNCT
ejpam-6603	8	40	forcing	forcing	NOUN
ejpam-6603	8	41	initiated	initiate	VERB
ejpam-6603	8	42	by	by	ADP
ejpam-6603	8	43	a	a	DET
ejpam-6603	8	44	single	single	ADJ
ejpam-6603	8	45	vertex	vertex	NOUN
ejpam-6603	8	46	.	.	PUNCT
ejpam-6603	9	1	in	in	ADP
ejpam-6603	9	2	addition	addition	NOUN
ejpam-6603	9	3	,	,	PUNCT
ejpam-6603	9	4	a	a	DET
ejpam-6603	9	5	subset	subset	NOUN
ejpam-6603	9	6	s	s	NOUN
ejpam-6603	9	7	of	of	ADP
ejpam-6603	9	8	a	a	DET
ejpam-6603	9	9	vertex	vertex	NOUN
ejpam-6603	9	10	-	-	PUNCT
ejpam-6603	9	11	set	set	VERB
ejpam-6603	9	12	v	v	NOUN
ejpam-6603	9	13	(	(	PUNCT
ejpam-6603	9	14	g	g	NOUN
ejpam-6603	9	15	)	)	PUNCT
ejpam-6603	9	16	of	of	ADP
ejpam-6603	9	17	g	g	PROPN
ejpam-6603	9	18	is	be	AUX
ejpam-6603	9	19	called	call	VERB
ejpam-6603	9	20	a	a	DET
ejpam-6603	9	21	perfect	perfect	ADJ
ejpam-6603	9	22	2	2	NUM
ejpam-6603	9	23	-	-	PUNCT
ejpam-6603	9	24	distance	distance	NOUN
ejpam-6603	9	25	zero	zero	NUM
ejpam-6603	9	26	forcing	force	VERB
ejpam-6603	9	27	set	set	NOUN
ejpam-6603	9	28	of	of	ADP
ejpam-6603	9	29	g	g	NOUN
ejpam-6603	9	30	if	if	SCONJ
ejpam-6603	9	31	there	there	PRON
ejpam-6603	9	32	exists	exist	VERB
ejpam-6603	9	33	s	s	X
ejpam-6603	9	34	∈	∈	PROPN
ejpam-6603	9	35	s	s	VERB
ejpam-6603	9	36	such	such	ADJ
ejpam-6603	9	37	that	that	PRON
ejpam-6603	9	38	s	s	VERB
ejpam-6603	9	39	perfectly	perfectly	ADV
ejpam-6603	9	40	2	2	NUM
ejpam-6603	9	41	-	-	PUNCT
ejpam-6603	9	42	forces	force	NOUN
ejpam-6603	9	43	all	all	DET
ejpam-6603	9	44	other	other	ADJ
ejpam-6603	9	45	vertices	vertex	NOUN
ejpam-6603	9	46	outside	outside	ADP
ejpam-6603	9	47	s.	s.	PROPN
ejpam-6603	9	48	the	the	DET
ejpam-6603	9	49	minimum	minimum	ADJ
ejpam-6603	9	50	cardinality	cardinality	NOUN
ejpam-6603	9	51	of	of	ADP
ejpam-6603	9	52	a	a	DET
ejpam-6603	9	53	perfect	perfect	ADJ
ejpam-6603	9	54	2	2	NUM
ejpam-6603	9	55	-	-	PUNCT
ejpam-6603	9	56	distance	distance	NOUN
ejpam-6603	9	57	zero	zero	NUM
ejpam-6603	9	58	forcing	force	VERB
ejpam-6603	9	59	set	set	NOUN
ejpam-6603	9	60	of	of	ADP
ejpam-6603	9	61	g	g	NOUN
ejpam-6603	9	62	,	,	PUNCT
ejpam-6603	9	63	denoted	denote	VERB
ejpam-6603	9	64	by	by	ADP
ejpam-6603	9	65	z2	z2	PROPN
ejpam-6603	9	66	p(g	p(g	PROPN
ejpam-6603	9	67	)	)	PUNCT
ejpam-6603	9	68	,	,	PUNCT
ejpam-6603	9	69	is	be	AUX
ejpam-6603	9	70	called	call	VERB
ejpam-6603	9	71	the	the	DET
ejpam-6603	9	72	perfect	perfect	ADJ
ejpam-6603	9	73	2	2	NUM
ejpam-6603	9	74	-	-	PUNCT
ejpam-6603	9	75	distance	distance	NOUN
ejpam-6603	9	76	zero	zero	NUM
ejpam-6603	9	77	forcing	force	VERB
ejpam-6603	9	78	number	number	NOUN
ejpam-6603	9	79	of	of	ADP
ejpam-6603	9	80	g.	g.	PROPN
ejpam-6603	9	81	in	in	ADP
ejpam-6603	9	82	this	this	DET
ejpam-6603	9	83	paper	paper	NOUN
ejpam-6603	9	84	,	,	PUNCT
ejpam-6603	9	85	this	this	DET
ejpam-6603	9	86	new	new	ADJ
ejpam-6603	9	87	parameter	parameter	NOUN
ejpam-6603	9	88	is	be	AUX
ejpam-6603	9	89	introduced	introduce	VERB
ejpam-6603	9	90	and	and	CCONJ
ejpam-6603	9	91	initially	initially	ADV
ejpam-6603	9	92	investigated	investigate	VERB
ejpam-6603	9	93	on	on	ADP
ejpam-6603	9	94	some	some	DET
ejpam-6603	9	95	classes	class	NOUN
ejpam-6603	9	96	of	of	ADP
ejpam-6603	9	97	graphs	graph	NOUN
ejpam-6603	9	98	and	and	CCONJ
ejpam-6603	9	99	on	on	ADP
ejpam-6603	9	100	the	the	DET
ejpam-6603	9	101	join	join	NOUN
ejpam-6603	9	102	of	of	ADP
ejpam-6603	9	103	two	two	NUM
ejpam-6603	9	104	graphs	graph	NOUN
ejpam-6603	9	105	.	.	PUNCT
ejpam-6603	10	1	a	a	DET
ejpam-6603	10	2	particular	particular	ADJ
ejpam-6603	10	3	variant	variant	NOUN
ejpam-6603	10	4	of	of	ADP
ejpam-6603	10	5	zero	zero	NUM
ejpam-6603	10	6	forcing	force	VERB
ejpam-6603	10	7	called	call	VERB
ejpam-6603	10	8	perfect	perfect	ADJ
ejpam-6603	10	9	co	co	NOUN
ejpam-6603	10	10	-	-	ADJ
ejpam-6603	10	11	zero	zero	ADJ
ejpam-6603	10	12	forcing	forcing	NOUN
ejpam-6603	10	13	is	be	AUX
ejpam-6603	10	14	defined	define	VERB
ejpam-6603	10	15	to	to	PART
ejpam-6603	10	16	study	study	VERB
ejpam-6603	10	17	the	the	DET
ejpam-6603	10	18	behavior	behavior	NOUN
ejpam-6603	10	19	of	of	ADP
ejpam-6603	10	20	the	the	DET
ejpam-6603	10	21	perfect	perfect	ADJ
ejpam-6603	10	22	2	2	NUM
ejpam-6603	10	23	-	-	PUNCT
ejpam-6603	10	24	distance	distance	NOUN
ejpam-6603	10	25	zero	zero	NUM
ejpam-6603	10	26	forcing	force	VERB
ejpam-6603	10	27	sets	set	NOUN
ejpam-6603	10	28	in	in	ADP
ejpam-6603	10	29	the	the	DET
ejpam-6603	10	30	join	join	NOUN
ejpam-6603	10	31	of	of	ADP
ejpam-6603	10	32	graphs	graph	NOUN
ejpam-6603	10	33	.	.	PUNCT
ejpam-6603	11	1	characterizations	characterization	NOUN
ejpam-6603	11	2	of	of	ADP
ejpam-6603	11	3	perfect	perfect	ADJ
ejpam-6603	11	4	2	2	NUM
ejpam-6603	11	5	-	-	PUNCT
ejpam-6603	11	6	distance	distance	NOUN
ejpam-6603	11	7	zero	zero	NUM
ejpam-6603	11	8	forcing	forcing	NOUN
ejpam-6603	11	9	sets	set	NOUN
ejpam-6603	11	10	are	be	AUX
ejpam-6603	11	11	formulated	formulate	VERB
ejpam-6603	11	12	and	and	CCONJ
ejpam-6603	11	13	subsequently	subsequently	ADV
ejpam-6603	11	14	used	use	VERB
ejpam-6603	11	15	to	to	PART
ejpam-6603	11	16	obtain	obtain	VERB
ejpam-6603	11	17	some	some	DET
ejpam-6603	11	18	formulas	formula	NOUN
ejpam-6603	11	19	for	for	ADP
ejpam-6603	11	20	solving	solve	VERB
ejpam-6603	11	21	the	the	DET
ejpam-6603	11	22	perfect	perfect	ADJ
ejpam-6603	11	23	2	2	NUM
ejpam-6603	11	24	-	-	PUNCT
ejpam-6603	11	25	distance	distance	NOUN
ejpam-6603	11	26	zero	zero	NUM
ejpam-6603	11	27	forcing	force	VERB
ejpam-6603	11	28	numbers	number	NOUN
ejpam-6603	11	29	of	of	ADP
ejpam-6603	11	30	the	the	DET
ejpam-6603	11	31	join	join	NOUN
ejpam-6603	11	32	of	of	ADP
ejpam-6603	11	33	some	some	DET
ejpam-6603	11	34	graphs	graph	NOUN
ejpam-6603	11	35	.	.	PUNCT
ejpam-6603	12	1	2020	2020	NUM
ejpam-6603	12	2	mathematics	mathematic	NOUN
ejpam-6603	12	3	subject	subject	NOUN
ejpam-6603	12	4	classifications	classification	NOUN
ejpam-6603	12	5	:	:	PUNCT
ejpam-6603	12	6	05c69	05c69	X
ejpam-6603	12	7	key	key	ADJ
ejpam-6603	12	8	words	word	NOUN
ejpam-6603	12	9	and	and	CCONJ
ejpam-6603	12	10	phrases	phrase	NOUN
ejpam-6603	12	11	:	:	PUNCT
ejpam-6603	12	12	perfect	perfect	ADJ
ejpam-6603	12	13	2	2	NUM
ejpam-6603	12	14	-	-	PUNCT
ejpam-6603	12	15	distance	distance	NOUN
ejpam-6603	12	16	zero	zero	NUM
ejpam-6603	12	17	forcing	forcing	NOUN
ejpam-6603	12	18	set	set	NOUN
ejpam-6603	12	19	,	,	PUNCT
ejpam-6603	12	20	perfect	perfect	ADJ
ejpam-6603	12	21	2	2	NUM
ejpam-6603	12	22	-	-	PUNCT
ejpam-6603	12	23	distance	distance	NOUN
ejpam-6603	12	24	zero	zero	NUM
ejpam-6603	12	25	forcing	force	VERB
ejpam-6603	12	26	number	number	NOUN
ejpam-6603	12	27	,	,	PUNCT
ejpam-6603	12	28	perfect	perfect	ADJ
ejpam-6603	12	29	co	co	NOUN
ejpam-6603	12	30	-	-	ADJ
ejpam-6603	12	31	zero	zero	NUM
ejpam-6603	12	32	forcing	force	VERB
ejpam-6603	12	33	1	1	NUM
ejpam-6603	12	34	.	.	PUNCT
ejpam-6603	12	35	introduction	introduction	NOUN
ejpam-6603	12	36	the	the	DET
ejpam-6603	12	37	concept	concept	NOUN
ejpam-6603	12	38	of	of	ADP
ejpam-6603	12	39	zero	zero	NUM
ejpam-6603	12	40	forcing	force	VERB
ejpam-6603	12	41	set	set	NOUN
ejpam-6603	12	42	was	be	AUX
ejpam-6603	12	43	initially	initially	ADV
ejpam-6603	12	44	introduced	introduce	VERB
ejpam-6603	12	45	in	in	ADP
ejpam-6603	12	46	[	[	X
ejpam-6603	12	47	1	1	NUM
ejpam-6603	12	48	]	]	PUNCT
ejpam-6603	12	49	as	as	ADP
ejpam-6603	12	50	a	a	DET
ejpam-6603	12	51	bound	bind	VERB
ejpam-6603	12	52	for	for	ADP
ejpam-6603	12	53	the	the	DET
ejpam-6603	12	54	minimum	minimum	ADJ
ejpam-6603	12	55	rank	rank	NOUN
ejpam-6603	12	56	problem	problem	NOUN
ejpam-6603	12	57	.	.	PUNCT
ejpam-6603	13	1	a	a	DET
ejpam-6603	13	2	zero	zero	NUM
ejpam-6603	13	3	forcing	forcing	NOUN
ejpam-6603	13	4	set	set	NOUN
ejpam-6603	13	5	in	in	ADP
ejpam-6603	13	6	a	a	DET
ejpam-6603	13	7	graph	graph	NOUN
ejpam-6603	13	8	is	be	AUX
ejpam-6603	13	9	a	a	DET
ejpam-6603	13	10	subset	subset	NOUN
ejpam-6603	13	11	of	of	ADP
ejpam-6603	13	12	vertices	vertex	NOUN
ejpam-6603	13	13	with	with	ADP
ejpam-6603	13	14	a	a	DET
ejpam-6603	13	15	particular	particular	ADJ
ejpam-6603	13	16	dynamic	dynamic	ADJ
ejpam-6603	13	17	propagation	propagation	NOUN
ejpam-6603	13	18	property	property	NOUN
ejpam-6603	13	19	.	.	PUNCT
ejpam-6603	14	1	the	the	DET
ejpam-6603	14	2	zero	zero	NUM
ejpam-6603	14	3	forcing	forcing	NOUN
ejpam-6603	14	4	process	process	NOUN
ejpam-6603	14	5	starts	start	VERB
ejpam-6603	14	6	with	with	ADP
ejpam-6603	14	7	a	a	DET
ejpam-6603	14	8	set	set	NOUN
ejpam-6603	14	9	of	of	ADP
ejpam-6603	14	10	initially	initially	ADV
ejpam-6603	14	11	colored	color	VERB
ejpam-6603	14	12	vertices	vertex	NOUN
ejpam-6603	14	13	,	,	PUNCT
ejpam-6603	14	14	typically	typically	ADV
ejpam-6603	14	15	with	with	ADP
ejpam-6603	14	16	one	one	NUM
ejpam-6603	14	17	color	color	NOUN
ejpam-6603	14	18	representing	represent	VERB
ejpam-6603	14	19	”	"	PUNCT
ejpam-6603	14	20	active	active	ADJ
ejpam-6603	14	21	”	"	PUNCT
ejpam-6603	14	22	and	and	CCONJ
ejpam-6603	14	23	another	another	DET
ejpam-6603	14	24	”	"	PUNCT
ejpam-6603	14	25	inactive	inactive	ADJ
ejpam-6603	14	26	”	"	PUNCT
ejpam-6603	14	27	or	or	CCONJ
ejpam-6603	14	28	∗corresponding	∗corresponde	VERB
ejpam-6603	14	29	author	author	NOUN
ejpam-6603	14	30	.	.	PUNCT
ejpam-6603	15	1	doi	doi	NOUN
ejpam-6603	15	2	:	:	PUNCT
ejpam-6603	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6603	https://doi.org/10.29020/nybg.ejpam.v18i3.6603	PROPN
ejpam-6603	15	4	email	email	NOUN
ejpam-6603	15	5	addresses	address	NOUN
ejpam-6603	15	6	:	:	PUNCT
ejpam-6603	15	7	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-6603	15	8	(	(	PUNCT
ejpam-6603	15	9	j.	j.	PROPN
ejpam-6603	15	10	a.	a.	PROPN
ejpam-6603	15	11	hassan	hassan	PROPN
ejpam-6603	15	12	)	)	PUNCT
ejpam-6603	16	1	erwanhajim@msutawi-tawi.edu.ph	erwanhajim@msutawi-tawi.edu.ph	PROPN
ejpam-6603	16	2	(	(	PUNCT
ejpam-6603	16	3	e.	e.	PROPN
ejpam-6603	16	4	hajim	hajim	PROPN
ejpam-6603	16	5	)	)	PUNCT
ejpam-6603	16	6	amlmahistrado@addu.edu.ph(a.m	amlmahistrado@addu.edu.ph(a.m	PROPN
ejpam-6603	16	7	.	.	PUNCT
ejpam-6603	17	1	mahistrado	mahistrado	NOUN
ejpam-6603	17	2	)	)	PUNCT
ejpam-6603	18	1	akrimalalayka@msutawi-tawi.edu.ph	akrimalalayka@msutawi-tawi.edu.ph	PROPN
ejpam-6603	18	2	(	(	PUNCT
ejpam-6603	18	3	a.	a.	NOUN
ejpam-6603	18	4	alayka	alayka	PROPN
ejpam-6603	18	5	)	)	PUNCT
ejpam-6603	18	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6603	19	1	1	1	NUM
ejpam-6603	19	2	copyright	copyright	NOUN
ejpam-6603	19	3	:	:	PUNCT
ejpam-6603	19	4	©	©	PROPN
ejpam-6603	19	5	2025	2025	NUM
ejpam-6603	19	6	the	the	DET
ejpam-6603	19	7	author(s	author(s	NOUN
ejpam-6603	19	8	)	)	PUNCT
ejpam-6603	19	9	.	.	PUNCT
ejpam-6603	20	1	(	(	PUNCT
ejpam-6603	20	2	cc	cc	NOUN
ejpam-6603	20	3	by	by	ADP
ejpam-6603	20	4	-	-	PUNCT
ejpam-6603	20	5	nc	nc	PROPN
ejpam-6603	20	6	4.0	4.0	NUM
ejpam-6603	20	7	)	)	PUNCT
ejpam-6603	20	8	j.	j.	PROPN
ejpam-6603	20	9	a.	a.	PROPN
ejpam-6603	20	10	hassan	hassan	PROPN
ejpam-6603	20	11	et	et	PROPN
ejpam-6603	20	12	al	al	PROPN
ejpam-6603	20	13	.	.	PUNCT
ejpam-6603	20	14	/	/	SYM
ejpam-6603	20	15	eur	eur	PROPN
ejpam-6603	20	16	.	.	PUNCT
ejpam-6603	21	1	j.	j.	PROPN
ejpam-6603	21	2	pure	pure	PROPN
ejpam-6603	21	3	appl	appl	PROPN
ejpam-6603	21	4	.	.	PROPN
ejpam-6603	21	5	math	math	PROPN
ejpam-6603	21	6	,	,	PUNCT
ejpam-6603	21	7	18	18	NUM
ejpam-6603	21	8	(	(	PUNCT
ejpam-6603	21	9	3	3	NUM
ejpam-6603	21	10	)	)	PUNCT
ejpam-6603	21	11	(	(	PUNCT
ejpam-6603	21	12	2025	2025	NUM
ejpam-6603	21	13	)	)	PUNCT
ejpam-6603	21	14	,	,	PUNCT
ejpam-6603	21	15	6603	6603	NUM
ejpam-6603	21	16	2	2	NUM
ejpam-6603	21	17	of	of	ADP
ejpam-6603	21	18	9	9	NUM
ejpam-6603	21	19	”	"	PUNCT
ejpam-6603	21	20	unassigned	unassigned	ADJ
ejpam-6603	21	21	.	.	PUNCT
ejpam-6603	21	22	”	"	PUNCT
ejpam-6603	22	1	then	then	ADV
ejpam-6603	22	2	,	,	PUNCT
ejpam-6603	22	3	using	use	VERB
ejpam-6603	22	4	certain	certain	ADJ
ejpam-6603	22	5	propagation	propagation	NOUN
ejpam-6603	22	6	rules	rule	NOUN
ejpam-6603	22	7	,	,	PUNCT
ejpam-6603	22	8	the	the	DET
ejpam-6603	22	9	active	active	ADJ
ejpam-6603	22	10	vertices	vertex	NOUN
ejpam-6603	22	11	force	force	VERB
ejpam-6603	22	12	neighboring	neighboring	NOUN
ejpam-6603	22	13	inactive	inactive	ADJ
ejpam-6603	22	14	vertices	vertex	NOUN
ejpam-6603	22	15	to	to	PART
ejpam-6603	22	16	become	become	VERB
ejpam-6603	22	17	active	active	ADJ
ejpam-6603	22	18	.	.	PUNCT
ejpam-6603	23	1	the	the	DET
ejpam-6603	23	2	goal	goal	NOUN
ejpam-6603	23	3	is	be	AUX
ejpam-6603	23	4	to	to	PART
ejpam-6603	23	5	determine	determine	VERB
ejpam-6603	23	6	the	the	DET
ejpam-6603	23	7	minimum	minimum	ADJ
ejpam-6603	23	8	size	size	NOUN
ejpam-6603	23	9	of	of	ADP
ejpam-6603	23	10	a	a	DET
ejpam-6603	23	11	zero	zero	NUM
ejpam-6603	23	12	forcing	force	VERB
ejpam-6603	23	13	set	set	NOUN
ejpam-6603	23	14	required	require	VERB
ejpam-6603	23	15	to	to	PART
ejpam-6603	23	16	force	force	VERB
ejpam-6603	23	17	all	all	DET
ejpam-6603	23	18	vertices	vertex	NOUN
ejpam-6603	23	19	in	in	ADP
ejpam-6603	23	20	the	the	DET
ejpam-6603	23	21	graph	graph	NOUN
ejpam-6603	23	22	to	to	PART
ejpam-6603	23	23	become	become	VERB
ejpam-6603	23	24	active	active	ADJ
ejpam-6603	23	25	.	.	PUNCT
ejpam-6603	24	1	the	the	DET
ejpam-6603	24	2	concept	concept	NOUN
ejpam-6603	24	3	of	of	ADP
ejpam-6603	24	4	zero	zero	NUM
ejpam-6603	24	5	forcing	force	VERB
ejpam-6603	24	6	was	be	AUX
ejpam-6603	24	7	further	far	ADV
ejpam-6603	24	8	studied	study	VERB
ejpam-6603	24	9	by	by	ADP
ejpam-6603	24	10	many	many	ADJ
ejpam-6603	24	11	researchers	researcher	NOUN
ejpam-6603	24	12	,	,	PUNCT
ejpam-6603	24	13	and	and	CCONJ
ejpam-6603	24	14	these	these	DET
ejpam-6603	24	15	studies	study	NOUN
ejpam-6603	24	16	can	can	AUX
ejpam-6603	24	17	be	be	AUX
ejpam-6603	24	18	found	find	VERB
ejpam-6603	24	19	in	in	ADP
ejpam-6603	24	20	[	[	X
ejpam-6603	24	21	1–10	1–10	NOUN
ejpam-6603	24	22	]	]	PUNCT
ejpam-6603	24	23	.	.	PUNCT
ejpam-6603	25	1	in	in	ADP
ejpam-6603	25	2	2024	2024	NUM
ejpam-6603	25	3	,	,	PUNCT
ejpam-6603	25	4	j.	j.	PROPN
ejpam-6603	25	5	hassan	hassan	PROPN
ejpam-6603	25	6	et	et	PROPN
ejpam-6603	25	7	al	al	PROPN
ejpam-6603	25	8	.	.	PUNCT
ejpam-6603	26	1	[	[	X
ejpam-6603	26	2	11	11	NUM
ejpam-6603	26	3	]	]	PUNCT
ejpam-6603	26	4	,	,	PUNCT
ejpam-6603	26	5	introduced	introduce	VERB
ejpam-6603	26	6	another	another	DET
ejpam-6603	26	7	variant	variant	NOUN
ejpam-6603	26	8	of	of	ADP
ejpam-6603	26	9	zero	zero	NUM
ejpam-6603	26	10	forcing	force	VERB
ejpam-6603	26	11	by	by	ADP
ejpam-6603	26	12	changing	change	VERB
ejpam-6603	26	13	the	the	DET
ejpam-6603	26	14	distance	distance	NOUN
ejpam-6603	26	15	to	to	ADP
ejpam-6603	26	16	two	two	NUM
ejpam-6603	26	17	(	(	PUNCT
ejpam-6603	26	18	2	2	NUM
ejpam-6603	26	19	)	)	PUNCT
ejpam-6603	26	20	for	for	ADP
ejpam-6603	26	21	a	a	DET
ejpam-6603	26	22	certain	certain	ADJ
ejpam-6603	26	23	vertex	vertex	NOUN
ejpam-6603	26	24	to	to	PART
ejpam-6603	26	25	force	force	VERB
ejpam-6603	26	26	another	another	DET
ejpam-6603	26	27	vertex	vertex	NOUN
ejpam-6603	26	28	in	in	ADP
ejpam-6603	26	29	a	a	DET
ejpam-6603	26	30	graph	graph	NOUN
ejpam-6603	26	31	.	.	PUNCT
ejpam-6603	27	1	the	the	DET
ejpam-6603	27	2	said	say	VERB
ejpam-6603	27	3	parameter	parameter	NOUN
ejpam-6603	27	4	was	be	AUX
ejpam-6603	27	5	investigated	investigate	VERB
ejpam-6603	27	6	on	on	ADP
ejpam-6603	27	7	some	some	DET
ejpam-6603	27	8	classes	class	NOUN
ejpam-6603	27	9	of	of	ADP
ejpam-6603	27	10	graphs	graph	NOUN
ejpam-6603	27	11	as	as	ADV
ejpam-6603	27	12	well	well	ADV
ejpam-6603	27	13	as	as	ADP
ejpam-6603	27	14	examined	examine	VERB
ejpam-6603	27	15	its	its	PRON
ejpam-6603	27	16	relationships	relationship	NOUN
ejpam-6603	27	17	with	with	ADP
ejpam-6603	27	18	other	other	ADJ
ejpam-6603	27	19	parameters	parameter	NOUN
ejpam-6603	27	20	such	such	ADJ
ejpam-6603	27	21	as	as	ADP
ejpam-6603	27	22	standard	standard	ADJ
ejpam-6603	27	23	zero	zero	NUM
ejpam-6603	27	24	forcing	forcing	NOUN
ejpam-6603	27	25	and	and	CCONJ
ejpam-6603	27	26	hop	hop	NOUN
ejpam-6603	27	27	domination	domination	NOUN
ejpam-6603	27	28	.	.	PUNCT
ejpam-6603	28	1	in	in	ADP
ejpam-6603	28	2	this	this	DET
ejpam-6603	28	3	paper	paper	NOUN
ejpam-6603	28	4	,	,	PUNCT
ejpam-6603	28	5	we	we	PRON
ejpam-6603	28	6	introduce	introduce	VERB
ejpam-6603	28	7	another	another	DET
ejpam-6603	28	8	variant	variant	NOUN
ejpam-6603	28	9	of	of	ADP
ejpam-6603	28	10	2	2	NUM
ejpam-6603	28	11	-	-	PUNCT
ejpam-6603	28	12	distance	distance	NOUN
ejpam-6603	28	13	zero	zero	NUM
ejpam-6603	28	14	forcing	force	VERB
ejpam-6603	28	15	by	by	ADP
ejpam-6603	28	16	adding	add	VERB
ejpam-6603	28	17	a	a	DET
ejpam-6603	28	18	certain	certain	ADJ
ejpam-6603	28	19	property	property	NOUN
ejpam-6603	28	20	wherein	wherein	SCONJ
ejpam-6603	28	21	the	the	DET
ejpam-6603	28	22	reinforcement	reinforcement	NOUN
ejpam-6603	28	23	is	be	AUX
ejpam-6603	28	24	not	not	PART
ejpam-6603	28	25	allowed	allow	VERB
ejpam-6603	28	26	,	,	PUNCT
ejpam-6603	28	27	and	and	CCONJ
ejpam-6603	28	28	we	we	PRON
ejpam-6603	28	29	call	call	VERB
ejpam-6603	28	30	it	it	PRON
ejpam-6603	28	31	a	a	DET
ejpam-6603	28	32	perfect	perfect	ADJ
ejpam-6603	28	33	2distance	2distance	NUM
ejpam-6603	28	34	zero	zero	NUM
ejpam-6603	28	35	forcing	forcing	NOUN
ejpam-6603	28	36	.	.	PUNCT
ejpam-6603	29	1	that	that	PRON
ejpam-6603	29	2	is	be	AUX
ejpam-6603	29	3	,	,	PUNCT
ejpam-6603	29	4	only	only	ADV
ejpam-6603	29	5	one	one	NUM
ejpam-6603	29	6	vertex	vertex	NOUN
ejpam-6603	29	7	in	in	ADP
ejpam-6603	29	8	a	a	DET
ejpam-6603	29	9	set	set	NOUN
ejpam-6603	29	10	is	be	AUX
ejpam-6603	29	11	needed	need	VERB
ejpam-6603	29	12	to	to	PART
ejpam-6603	29	13	force	force	VERB
ejpam-6603	29	14	all	all	DET
ejpam-6603	29	15	other	other	ADJ
ejpam-6603	29	16	vertices	vertex	NOUN
ejpam-6603	29	17	outside	outside	ADP
ejpam-6603	29	18	the	the	DET
ejpam-6603	29	19	considered	consider	VERB
ejpam-6603	29	20	set	set	NOUN
ejpam-6603	29	21	,	,	PUNCT
ejpam-6603	29	22	if	if	SCONJ
ejpam-6603	29	23	any	any	PRON
ejpam-6603	29	24	.	.	PUNCT
ejpam-6603	30	1	this	this	PRON
ejpam-6603	30	2	is	be	AUX
ejpam-6603	30	3	far	far	ADV
ejpam-6603	30	4	different	different	ADJ
ejpam-6603	30	5	compared	compare	VERB
ejpam-6603	30	6	to	to	ADP
ejpam-6603	30	7	the	the	DET
ejpam-6603	30	8	standard	standard	ADJ
ejpam-6603	30	9	2	2	NUM
ejpam-6603	30	10	-	-	PUNCT
ejpam-6603	30	11	distance	distance	NOUN
ejpam-6603	30	12	zero	zero	NUM
ejpam-6603	30	13	forcing	forcing	NOUN
ejpam-6603	30	14	wherein	wherein	SCONJ
ejpam-6603	30	15	the	the	DET
ejpam-6603	30	16	reinforcement	reinforcement	NOUN
ejpam-6603	30	17	is	be	AUX
ejpam-6603	30	18	allowed	allow	VERB
ejpam-6603	30	19	.	.	PUNCT
ejpam-6603	31	1	we	we	PRON
ejpam-6603	31	2	believe	believe	VERB
ejpam-6603	31	3	,	,	PUNCT
ejpam-6603	31	4	this	this	DET
ejpam-6603	31	5	new	new	ADJ
ejpam-6603	31	6	parameter	parameter	NOUN
ejpam-6603	31	7	and	and	CCONJ
ejpam-6603	31	8	its	its	PRON
ejpam-6603	31	9	results	result	NOUN
ejpam-6603	31	10	would	would	AUX
ejpam-6603	31	11	serve	serve	VERB
ejpam-6603	31	12	as	as	ADP
ejpam-6603	31	13	reference	reference	NOUN
ejpam-6603	31	14	to	to	ADP
ejpam-6603	31	15	future	future	ADJ
ejpam-6603	31	16	researchers	researcher	NOUN
ejpam-6603	31	17	who	who	PRON
ejpam-6603	31	18	will	will	AUX
ejpam-6603	31	19	study	study	VERB
ejpam-6603	31	20	on	on	ADP
ejpam-6603	31	21	variants	variant	NOUN
ejpam-6603	31	22	of	of	ADP
ejpam-6603	31	23	zero	zero	NUM
ejpam-6603	31	24	forcing	forcing	NOUN
ejpam-6603	31	25	,	,	PUNCT
ejpam-6603	31	26	and	and	CCONJ
ejpam-6603	31	27	would	would	AUX
ejpam-6603	31	28	lead	lead	VERB
ejpam-6603	31	29	to	to	ADP
ejpam-6603	31	30	an	an	DET
ejpam-6603	31	31	interesting	interesting	ADJ
ejpam-6603	31	32	topics	topic	NOUN
ejpam-6603	31	33	of	of	ADP
ejpam-6603	31	34	research	research	NOUN
ejpam-6603	31	35	in	in	ADP
ejpam-6603	31	36	the	the	DET
ejpam-6603	31	37	future	future	NOUN
ejpam-6603	31	38	.	.	PUNCT
ejpam-6603	32	1	2	2	X
ejpam-6603	32	2	.	.	X
ejpam-6603	32	3	terminology	terminology	NOUN
ejpam-6603	32	4	and	and	CCONJ
ejpam-6603	32	5	notation	notation	NOUN
ejpam-6603	32	6	let	let	VERB
ejpam-6603	32	7	g	g	NOUN
ejpam-6603	32	8	=	=	SYM
ejpam-6603	32	9	(	(	PUNCT
ejpam-6603	32	10	v	v	NOUN
ejpam-6603	32	11	(	(	PUNCT
ejpam-6603	32	12	g	g	NOUN
ejpam-6603	32	13	)	)	PUNCT
ejpam-6603	32	14	,	,	PUNCT
ejpam-6603	32	15	e(g	e(g	PROPN
ejpam-6603	32	16	)	)	PUNCT
ejpam-6603	32	17	)	)	PUNCT
ejpam-6603	32	18	be	be	AUX
ejpam-6603	32	19	a	a	DET
ejpam-6603	32	20	simple	simple	ADJ
ejpam-6603	32	21	and	and	CCONJ
ejpam-6603	32	22	undirected	undirected	ADJ
ejpam-6603	32	23	graph	graph	NOUN
ejpam-6603	32	24	.	.	PUNCT
ejpam-6603	33	1	the	the	DET
ejpam-6603	33	2	distance	distance	NOUN
ejpam-6603	33	3	dg(u	dg(u	NOUN
ejpam-6603	33	4	,	,	PUNCT
ejpam-6603	33	5	v	v	NOUN
ejpam-6603	33	6	)	)	PUNCT
ejpam-6603	33	7	in	in	ADP
ejpam-6603	33	8	g	g	NOUN
ejpam-6603	33	9	of	of	ADP
ejpam-6603	33	10	two	two	NUM
ejpam-6603	33	11	vertices	vertex	NOUN
ejpam-6603	33	12	u	u	NOUN
ejpam-6603	33	13	,	,	PUNCT
ejpam-6603	33	14	v	v	PROPN
ejpam-6603	33	15	is	be	AUX
ejpam-6603	33	16	the	the	DET
ejpam-6603	33	17	length	length	NOUN
ejpam-6603	33	18	of	of	ADP
ejpam-6603	33	19	a	a	DET
ejpam-6603	33	20	shortest	short	ADJ
ejpam-6603	33	21	u	u	NOUN
ejpam-6603	33	22	-	-	NOUN
ejpam-6603	33	23	v	v	ADJ
ejpam-6603	33	24	path	path	NOUN
ejpam-6603	33	25	in	in	ADP
ejpam-6603	33	26	g.	g.	PROPN
ejpam-6603	33	27	the	the	DET
ejpam-6603	33	28	greatest	great	ADJ
ejpam-6603	33	29	distance	distance	NOUN
ejpam-6603	33	30	between	between	ADP
ejpam-6603	33	31	any	any	DET
ejpam-6603	33	32	two	two	NUM
ejpam-6603	33	33	vertices	vertex	NOUN
ejpam-6603	33	34	in	in	ADP
ejpam-6603	33	35	g	g	NOUN
ejpam-6603	33	36	,	,	PUNCT
ejpam-6603	33	37	denoted	denote	VERB
ejpam-6603	33	38	by	by	ADP
ejpam-6603	33	39	diam(g	diam(g	PROPN
ejpam-6603	33	40	)	)	PUNCT
ejpam-6603	33	41	,	,	PUNCT
ejpam-6603	33	42	is	be	AUX
ejpam-6603	33	43	called	call	VERB
ejpam-6603	33	44	the	the	DET
ejpam-6603	33	45	diameter	diameter	NOUN
ejpam-6603	33	46	of	of	ADP
ejpam-6603	33	47	g.	g.	PROPN
ejpam-6603	33	48	a	a	DET
ejpam-6603	33	49	vertex	vertex	NOUN
ejpam-6603	33	50	of	of	ADP
ejpam-6603	33	51	a	a	PRON
ejpam-6603	33	52	in	in	ADP
ejpam-6603	33	53	g	g	PROPN
ejpam-6603	33	54	is	be	AUX
ejpam-6603	33	55	a	a	DET
ejpam-6603	33	56	hop	hop	NOUN
ejpam-6603	33	57	neighbor	neighbor	NOUN
ejpam-6603	33	58	of	of	ADP
ejpam-6603	33	59	a	a	DET
ejpam-6603	33	60	vertex	vertex	NOUN
ejpam-6603	33	61	b	b	NOUN
ejpam-6603	33	62	in	in	ADP
ejpam-6603	33	63	g	g	PROPN
ejpam-6603	33	64	if	if	SCONJ
ejpam-6603	33	65	dg(a	dg(a	X
ejpam-6603	33	66	,	,	PUNCT
ejpam-6603	33	67	b	b	X
ejpam-6603	33	68	)	)	PUNCT
ejpam-6603	34	1	=	=	SYM
ejpam-6603	34	2	2	2	X
ejpam-6603	34	3	.	.	X
ejpam-6603	34	4	let	let	VERB
ejpam-6603	34	5	g	g	PRON
ejpam-6603	34	6	be	be	AUX
ejpam-6603	34	7	a	a	DET
ejpam-6603	34	8	graph	graph	NOUN
ejpam-6603	34	9	and	and	CCONJ
ejpam-6603	34	10	let	let	VERB
ejpam-6603	34	11	x	x	PRON
ejpam-6603	34	12	,	,	PUNCT
ejpam-6603	34	13	y	y	PROPN
ejpam-6603	34	14	∈	∈	PROPN
ejpam-6603	34	15	v	v	NOUN
ejpam-6603	34	16	(	(	PUNCT
ejpam-6603	34	17	g	g	NOUN
ejpam-6603	34	18	)	)	PUNCT
ejpam-6603	34	19	.	.	PUNCT
ejpam-6603	35	1	then	then	ADV
ejpam-6603	35	2	the	the	DET
ejpam-6603	35	3	2	2	NUM
ejpam-6603	35	4	-	-	PUNCT
ejpam-6603	35	5	distance	distance	NOUN
ejpam-6603	35	6	color	color	NOUN
ejpam-6603	35	7	change	change	NOUN
ejpam-6603	35	8	rule	rule	NOUN
ejpam-6603	35	9	is	be	AUX
ejpam-6603	35	10	if	if	SCONJ
ejpam-6603	35	11	x	x	PRON
ejpam-6603	35	12	is	be	AUX
ejpam-6603	35	13	colored	color	VERB
ejpam-6603	35	14	(	(	PUNCT
ejpam-6603	35	15	active	active	ADJ
ejpam-6603	35	16	)	)	PUNCT
ejpam-6603	35	17	vertex	vertex	NOUN
ejpam-6603	35	18	and	and	CCONJ
ejpam-6603	35	19	exactly	exactly	ADV
ejpam-6603	35	20	one	one	NUM
ejpam-6603	35	21	hop	hop	NOUN
ejpam-6603	35	22	neighbor	neighbor	NOUN
ejpam-6603	35	23	y	y	PROPN
ejpam-6603	35	24	of	of	ADP
ejpam-6603	35	25	x	x	PRON
ejpam-6603	35	26	is	be	AUX
ejpam-6603	35	27	uncolored	uncolored	ADJ
ejpam-6603	35	28	(	(	PUNCT
ejpam-6603	35	29	inactive	inactive	ADJ
ejpam-6603	35	30	)	)	PUNCT
ejpam-6603	35	31	,	,	PUNCT
ejpam-6603	35	32	then	then	ADV
ejpam-6603	35	33	y	y	PROPN
ejpam-6603	35	34	will	will	AUX
ejpam-6603	35	35	become	become	VERB
ejpam-6603	35	36	colored	colored	ADJ
ejpam-6603	35	37	(	(	PUNCT
ejpam-6603	35	38	active	active	ADJ
ejpam-6603	35	39	)	)	PUNCT
ejpam-6603	35	40	.	.	PUNCT
ejpam-6603	36	1	a	a	DET
ejpam-6603	36	2	2	2	NUM
ejpam-6603	36	3	-	-	PUNCT
ejpam-6603	36	4	distance	distance	NOUN
ejpam-6603	36	5	zero	zero	NUM
ejpam-6603	36	6	forcing	force	VERB
ejpam-6603	36	7	set	set	NOUN
ejpam-6603	36	8	n	n	PROPN
ejpam-6603	36	9	of	of	ADP
ejpam-6603	36	10	g	g	PROPN
ejpam-6603	36	11	is	be	AUX
ejpam-6603	36	12	a	a	DET
ejpam-6603	36	13	subset	subset	NOUN
ejpam-6603	36	14	of	of	ADP
ejpam-6603	36	15	vertices	vertex	NOUN
ejpam-6603	36	16	of	of	ADP
ejpam-6603	36	17	g	g	NOUN
ejpam-6603	36	18	such	such	ADJ
ejpam-6603	36	19	that	that	SCONJ
ejpam-6603	36	20	when	when	SCONJ
ejpam-6603	36	21	the	the	DET
ejpam-6603	36	22	vertices	vertex	NOUN
ejpam-6603	36	23	in	in	ADP
ejpam-6603	36	24	n	n	CCONJ
ejpam-6603	36	25	are	be	AUX
ejpam-6603	36	26	colored	color	VERB
ejpam-6603	36	27	(	(	PUNCT
ejpam-6603	36	28	active	active	ADJ
ejpam-6603	36	29	)	)	PUNCT
ejpam-6603	36	30	and	and	CCONJ
ejpam-6603	36	31	the	the	DET
ejpam-6603	36	32	remaining	remain	VERB
ejpam-6603	36	33	vertices	vertex	NOUN
ejpam-6603	36	34	are	be	AUX
ejpam-6603	36	35	uncolored(inactive	uncolored(inactive	ADJ
ejpam-6603	36	36	)	)	PUNCT
ejpam-6603	36	37	initially	initially	ADV
ejpam-6603	36	38	,	,	PUNCT
ejpam-6603	36	39	repeated	repeat	VERB
ejpam-6603	36	40	application	application	NOUN
ejpam-6603	36	41	of	of	ADP
ejpam-6603	36	42	the	the	DET
ejpam-6603	36	43	2	2	NUM
ejpam-6603	36	44	-	-	PUNCT
ejpam-6603	36	45	distance	distance	NOUN
ejpam-6603	36	46	color	color	NOUN
ejpam-6603	36	47	change	change	NOUN
ejpam-6603	36	48	rule	rule	NOUN
ejpam-6603	36	49	all	all	DET
ejpam-6603	36	50	vertices	vertex	NOUN
ejpam-6603	36	51	of	of	ADP
ejpam-6603	36	52	g	g	NOUN
ejpam-6603	36	53	will	will	AUX
ejpam-6603	36	54	become	become	VERB
ejpam-6603	36	55	colored	colored	ADJ
ejpam-6603	36	56	(	(	PUNCT
ejpam-6603	36	57	active	active	ADJ
ejpam-6603	36	58	)	)	PUNCT
ejpam-6603	36	59	.	.	PUNCT
ejpam-6603	37	1	the	the	DET
ejpam-6603	37	2	minimum	minimum	ADJ
ejpam-6603	37	3	cardinality	cardinality	NOUN
ejpam-6603	37	4	of	of	ADP
ejpam-6603	37	5	a	a	DET
ejpam-6603	37	6	2	2	NUM
ejpam-6603	37	7	-	-	PUNCT
ejpam-6603	37	8	distance	distance	NOUN
ejpam-6603	37	9	zero	zero	NUM
ejpam-6603	37	10	forcing	force	VERB
ejpam-6603	37	11	set	set	NOUN
ejpam-6603	37	12	of	of	ADP
ejpam-6603	37	13	g	g	NOUN
ejpam-6603	37	14	,	,	PUNCT
ejpam-6603	37	15	denoted	denote	VERB
ejpam-6603	37	16	by	by	ADP
ejpam-6603	37	17	z2(g	z2(g	NOUN
ejpam-6603	37	18	)	)	PUNCT
ejpam-6603	37	19	,	,	PUNCT
ejpam-6603	37	20	is	be	AUX
ejpam-6603	37	21	called	call	VERB
ejpam-6603	37	22	the	the	DET
ejpam-6603	37	23	2	2	NUM
ejpam-6603	37	24	-	-	PUNCT
ejpam-6603	37	25	distance	distance	NOUN
ejpam-6603	37	26	zero	zero	NUM
ejpam-6603	37	27	forcing	force	VERB
ejpam-6603	37	28	number	number	NOUN
ejpam-6603	37	29	of	of	ADP
ejpam-6603	37	30	g.	g.	PROPN
ejpam-6603	37	31	let	let	VERB
ejpam-6603	37	32	g	g	NOUN
ejpam-6603	37	33	and	and	CCONJ
ejpam-6603	37	34	h	h	NOUN
ejpam-6603	37	35	be	be	VERB
ejpam-6603	37	36	any	any	DET
ejpam-6603	37	37	two	two	NUM
ejpam-6603	37	38	graphs	graph	NOUN
ejpam-6603	37	39	.	.	PUNCT
ejpam-6603	38	1	the	the	DET
ejpam-6603	38	2	join	join	NOUN
ejpam-6603	38	3	of	of	ADP
ejpam-6603	38	4	g	g	PROPN
ejpam-6603	38	5	and	and	CCONJ
ejpam-6603	38	6	h	h	NOUN
ejpam-6603	38	7	,	,	PUNCT
ejpam-6603	38	8	denoted	denote	VERB
ejpam-6603	38	9	by	by	ADP
ejpam-6603	38	10	g+h	g+h	PROPN
ejpam-6603	38	11	is	be	AUX
ejpam-6603	38	12	the	the	DET
ejpam-6603	38	13	graph	graph	NOUN
ejpam-6603	38	14	with	with	ADP
ejpam-6603	38	15	vertex	vertex	NOUN
ejpam-6603	38	16	set	set	VERB
ejpam-6603	38	17	v	v	NOUN
ejpam-6603	38	18	(	(	PUNCT
ejpam-6603	38	19	g+h	g+h	NOUN
ejpam-6603	38	20	)	)	PUNCT
ejpam-6603	39	1	=	=	SYM
ejpam-6603	39	2	v	v	X
ejpam-6603	39	3	(	(	PUNCT
ejpam-6603	39	4	g	g	NOUN
ejpam-6603	39	5	)	)	PUNCT
ejpam-6603	39	6	∪	∪	NOUN
ejpam-6603	39	7	v	v	NOUN
ejpam-6603	39	8	(	(	PUNCT
ejpam-6603	39	9	h	h	NOUN
ejpam-6603	39	10	)	)	PUNCT
ejpam-6603	39	11	and	and	CCONJ
ejpam-6603	39	12	edge	edge	NOUN
ejpam-6603	39	13	set	set	VERB
ejpam-6603	39	14	e(g+h	e(g+h	NUM
ejpam-6603	39	15	)	)	PUNCT
ejpam-6603	39	16	=	=	SYM
ejpam-6603	39	17	e(g	e(g	NOUN
ejpam-6603	39	18	)	)	PUNCT
ejpam-6603	39	19	∪	∪	ADP
ejpam-6603	39	20	e(h	e(h	PROPN
ejpam-6603	39	21	)	)	PUNCT
ejpam-6603	39	22	∪	∪	NOUN
ejpam-6603	39	23	{	{	PUNCT
ejpam-6603	39	24	uv	uv	NOUN
ejpam-6603	39	25	:	:	PUNCT
ejpam-6603	39	26	u	u	PROPN
ejpam-6603	39	27	∈	∈	PROPN
ejpam-6603	39	28	v	v	ADP
ejpam-6603	39	29	(	(	PUNCT
ejpam-6603	39	30	g	g	NOUN
ejpam-6603	39	31	)	)	PUNCT
ejpam-6603	39	32	,	,	PUNCT
ejpam-6603	39	33	v	v	X
ejpam-6603	39	34	∈	∈	PROPN
ejpam-6603	39	35	v	v	NOUN
ejpam-6603	39	36	(	(	PUNCT
ejpam-6603	39	37	h	h	NOUN
ejpam-6603	39	38	)	)	PUNCT
ejpam-6603	39	39	}	}	PUNCT
ejpam-6603	39	40	.	.	PUNCT
ejpam-6603	40	1	3	3	X
ejpam-6603	40	2	.	.	X
ejpam-6603	40	3	results	result	NOUN
ejpam-6603	40	4	we	we	PRON
ejpam-6603	40	5	begin	begin	VERB
ejpam-6603	40	6	this	this	DET
ejpam-6603	40	7	section	section	NOUN
ejpam-6603	40	8	by	by	ADP
ejpam-6603	40	9	introducing	introduce	VERB
ejpam-6603	40	10	the	the	DET
ejpam-6603	40	11	concept	concept	NOUN
ejpam-6603	40	12	of	of	ADP
ejpam-6603	40	13	perfect	perfect	ADJ
ejpam-6603	40	14	2	2	NUM
ejpam-6603	40	15	-	-	PUNCT
ejpam-6603	40	16	distance	distance	NOUN
ejpam-6603	40	17	zero	zero	NUM
ejpam-6603	40	18	forcing	force	VERB
ejpam-6603	40	19	in	in	ADP
ejpam-6603	40	20	a	a	DET
ejpam-6603	40	21	graph	graph	NOUN
ejpam-6603	40	22	.	.	PUNCT
ejpam-6603	41	1	definition	definition	NOUN
ejpam-6603	41	2	1	1	NUM
ejpam-6603	41	3	.	.	PUNCT
ejpam-6603	42	1	let	let	VERB
ejpam-6603	42	2	g	g	PRON
ejpam-6603	42	3	be	be	AUX
ejpam-6603	42	4	a	a	DET
ejpam-6603	42	5	graph	graph	NOUN
ejpam-6603	42	6	.	.	PUNCT
ejpam-6603	43	1	then	then	ADV
ejpam-6603	43	2	a	a	DET
ejpam-6603	43	3	2	2	NUM
ejpam-6603	43	4	-	-	PUNCT
ejpam-6603	43	5	distance	distance	NOUN
ejpam-6603	43	6	color	color	NOUN
ejpam-6603	43	7	change	change	NOUN
ejpam-6603	43	8	rule	rule	NOUN
ejpam-6603	43	9	is	be	AUX
ejpam-6603	43	10	defined	define	VERB
ejpam-6603	43	11	as	as	SCONJ
ejpam-6603	43	12	follows	follow	VERB
ejpam-6603	43	13	:	:	PUNCT
ejpam-6603	43	14	if	if	SCONJ
ejpam-6603	43	15	a	a	DET
ejpam-6603	43	16	vertex	vertex	NOUN
ejpam-6603	43	17	x	x	SYM
ejpam-6603	43	18	∈	∈	NOUN
ejpam-6603	43	19	v	v	ADP
ejpam-6603	43	20	(	(	PUNCT
ejpam-6603	43	21	g	g	NOUN
ejpam-6603	43	22	)	)	PUNCT
ejpam-6603	43	23	is	be	AUX
ejpam-6603	43	24	colored	color	VERB
ejpam-6603	43	25	and	and	CCONJ
ejpam-6603	43	26	has	have	VERB
ejpam-6603	43	27	exactly	exactly	ADV
ejpam-6603	43	28	one	one	NUM
ejpam-6603	43	29	hop	hop	NOUN
ejpam-6603	43	30	neighbor	neighbor	NOUN
ejpam-6603	43	31	y	y	PROPN
ejpam-6603	43	32	that	that	PRON
ejpam-6603	43	33	is	be	AUX
ejpam-6603	43	34	uncolored	uncolored	ADJ
ejpam-6603	43	35	,	,	PUNCT
ejpam-6603	43	36	then	then	ADV
ejpam-6603	43	37	y	y	PROPN
ejpam-6603	43	38	will	will	AUX
ejpam-6603	43	39	become	become	VERB
ejpam-6603	43	40	colored	color	VERB
ejpam-6603	43	41	.	.	PUNCT
ejpam-6603	44	1	in	in	ADP
ejpam-6603	44	2	this	this	DET
ejpam-6603	44	3	case	case	NOUN
ejpam-6603	44	4	,	,	PUNCT
ejpam-6603	44	5	we	we	PRON
ejpam-6603	44	6	say	say	VERB
ejpam-6603	44	7	that	that	SCONJ
ejpam-6603	44	8	a	a	DET
ejpam-6603	44	9	vertex	vertex	NOUN
ejpam-6603	44	10	y	y	PROPN
ejpam-6603	44	11	is	be	AUX
ejpam-6603	44	12	2	2	NUM
ejpam-6603	44	13	-	-	PUNCT
ejpam-6603	44	14	forced	force	VERB
ejpam-6603	44	15	by	by	ADP
ejpam-6603	44	16	a	a	DET
ejpam-6603	44	17	vertex	vertex	NOUN
ejpam-6603	44	18	x	x	PUNCT
ejpam-6603	44	19	in	in	ADP
ejpam-6603	44	20	g.	g.	PROPN
ejpam-6603	44	21	j.	j.	PROPN
ejpam-6603	44	22	a.	a.	PROPN
ejpam-6603	44	23	hassan	hassan	PROPN
ejpam-6603	44	24	et	et	PROPN
ejpam-6603	44	25	al	al	PROPN
ejpam-6603	44	26	.	.	PUNCT
ejpam-6603	44	27	/	/	SYM
ejpam-6603	44	28	eur	eur	PROPN
ejpam-6603	44	29	.	.	PUNCT
ejpam-6603	45	1	j.	j.	PROPN
ejpam-6603	45	2	pure	pure	PROPN
ejpam-6603	45	3	appl	appl	PROPN
ejpam-6603	45	4	.	.	PROPN
ejpam-6603	45	5	math	math	PROPN
ejpam-6603	45	6	,	,	PUNCT
ejpam-6603	45	7	18	18	NUM
ejpam-6603	45	8	(	(	PUNCT
ejpam-6603	45	9	3	3	NUM
ejpam-6603	45	10	)	)	PUNCT
ejpam-6603	45	11	(	(	PUNCT
ejpam-6603	45	12	2025	2025	NUM
ejpam-6603	45	13	)	)	PUNCT
ejpam-6603	45	14	,	,	PUNCT
ejpam-6603	45	15	6603	6603	NUM
ejpam-6603	45	16	3	3	NUM
ejpam-6603	45	17	of	of	ADP
ejpam-6603	45	18	9	9	NUM
ejpam-6603	45	19	moreover	moreover	ADV
ejpam-6603	45	20	,	,	PUNCT
ejpam-6603	45	21	let	let	VERB
ejpam-6603	45	22	u	u	NOUN
ejpam-6603	45	23	,	,	PUNCT
ejpam-6603	45	24	v	v	NOUN
ejpam-6603	45	25	,	,	PUNCT
ejpam-6603	45	26	w	w	PROPN
ejpam-6603	45	27	∈	∈	PROPN
ejpam-6603	45	28	v	v	ADP
ejpam-6603	45	29	(	(	PUNCT
ejpam-6603	45	30	g	g	NOUN
ejpam-6603	45	31	)	)	PUNCT
ejpam-6603	45	32	.	.	PUNCT
ejpam-6603	46	1	if	if	SCONJ
ejpam-6603	46	2	u	u	NOUN
ejpam-6603	46	3	2	2	NUM
ejpam-6603	46	4	-	-	PUNCT
ejpam-6603	46	5	forces	force	NOUN
ejpam-6603	46	6	v	v	NOUN
ejpam-6603	46	7	and	and	CCONJ
ejpam-6603	46	8	v	v	ADP
ejpam-6603	46	9	2	2	NUM
ejpam-6603	46	10	-	-	PUNCT
ejpam-6603	46	11	forces	force	NOUN
ejpam-6603	46	12	w	w	NOUN
ejpam-6603	46	13	,	,	PUNCT
ejpam-6603	46	14	then	then	ADV
ejpam-6603	46	15	we	we	PRON
ejpam-6603	46	16	say	say	VERB
ejpam-6603	46	17	that	that	SCONJ
ejpam-6603	46	18	v	v	NOUN
ejpam-6603	46	19	and	and	CCONJ
ejpam-6603	46	20	w	w	NOUN
ejpam-6603	46	21	are	be	AUX
ejpam-6603	46	22	perfectly	perfectly	ADV
ejpam-6603	46	23	2	2	NUM
ejpam-6603	46	24	-	-	PUNCT
ejpam-6603	46	25	forced	force	VERB
ejpam-6603	46	26	by	by	ADP
ejpam-6603	46	27	u	u	NOUN
ejpam-6603	46	28	,	,	PUNCT
ejpam-6603	46	29	and	and	CCONJ
ejpam-6603	46	30	this	this	DET
ejpam-6603	46	31	process	process	NOUN
ejpam-6603	46	32	can	can	AUX
ejpam-6603	46	33	extend	extend	VERB
ejpam-6603	46	34	to	to	ADP
ejpam-6603	46	35	a	a	DET
ejpam-6603	46	36	chain	chain	NOUN
ejpam-6603	46	37	of	of	ADP
ejpam-6603	46	38	2	2	NUM
ejpam-6603	46	39	-	-	PUNCT
ejpam-6603	46	40	forcing	forcing	NOUN
ejpam-6603	46	41	initiated	initiate	VERB
ejpam-6603	46	42	by	by	ADP
ejpam-6603	46	43	a	a	DET
ejpam-6603	46	44	single	single	ADJ
ejpam-6603	46	45	vertex	vertex	NOUN
ejpam-6603	46	46	.	.	PUNCT
ejpam-6603	47	1	in	in	ADP
ejpam-6603	47	2	addition	addition	NOUN
ejpam-6603	47	3	,	,	PUNCT
ejpam-6603	47	4	a	a	DET
ejpam-6603	47	5	subset	subset	NOUN
ejpam-6603	47	6	s	s	NOUN
ejpam-6603	47	7	of	of	ADP
ejpam-6603	47	8	a	a	DET
ejpam-6603	47	9	vertex	vertex	NOUN
ejpam-6603	47	10	-	-	PUNCT
ejpam-6603	47	11	set	set	VERB
ejpam-6603	47	12	v	v	NOUN
ejpam-6603	47	13	(	(	PUNCT
ejpam-6603	47	14	g	g	NOUN
ejpam-6603	47	15	)	)	PUNCT
ejpam-6603	47	16	of	of	ADP
ejpam-6603	47	17	g	g	PROPN
ejpam-6603	47	18	is	be	AUX
ejpam-6603	47	19	called	call	VERB
ejpam-6603	47	20	a	a	DET
ejpam-6603	47	21	perfect	perfect	ADJ
ejpam-6603	47	22	2	2	NUM
ejpam-6603	47	23	-	-	PUNCT
ejpam-6603	47	24	distance	distance	NOUN
ejpam-6603	47	25	zero	zero	NUM
ejpam-6603	47	26	forcing	force	VERB
ejpam-6603	47	27	set	set	NOUN
ejpam-6603	47	28	of	of	ADP
ejpam-6603	47	29	g	g	NOUN
ejpam-6603	47	30	if	if	SCONJ
ejpam-6603	47	31	there	there	PRON
ejpam-6603	47	32	exists	exist	VERB
ejpam-6603	47	33	s	s	X
ejpam-6603	47	34	∈	∈	PROPN
ejpam-6603	47	35	s	s	VERB
ejpam-6603	47	36	such	such	ADJ
ejpam-6603	47	37	that	that	PRON
ejpam-6603	47	38	s	s	VERB
ejpam-6603	47	39	perfectly	perfectly	ADV
ejpam-6603	47	40	2	2	NUM
ejpam-6603	47	41	-	-	PUNCT
ejpam-6603	47	42	forces	force	NOUN
ejpam-6603	47	43	all	all	DET
ejpam-6603	47	44	other	other	ADJ
ejpam-6603	47	45	vertices	vertex	NOUN
ejpam-6603	47	46	outside	outside	ADP
ejpam-6603	47	47	s.	s.	PROPN
ejpam-6603	47	48	the	the	DET
ejpam-6603	47	49	minimum	minimum	ADJ
ejpam-6603	47	50	cardinality	cardinality	NOUN
ejpam-6603	47	51	of	of	ADP
ejpam-6603	47	52	a	a	DET
ejpam-6603	47	53	perfect	perfect	ADJ
ejpam-6603	47	54	2	2	NUM
ejpam-6603	47	55	-	-	PUNCT
ejpam-6603	47	56	distance	distance	NOUN
ejpam-6603	47	57	zero	zero	NUM
ejpam-6603	47	58	forcing	force	VERB
ejpam-6603	47	59	set	set	NOUN
ejpam-6603	47	60	of	of	ADP
ejpam-6603	47	61	g	g	NOUN
ejpam-6603	47	62	,	,	PUNCT
ejpam-6603	47	63	denoted	denote	VERB
ejpam-6603	47	64	by	by	ADP
ejpam-6603	47	65	z2	z2	PROPN
ejpam-6603	47	66	p(g	p(g	PROPN
ejpam-6603	47	67	)	)	PUNCT
ejpam-6603	47	68	,	,	PUNCT
ejpam-6603	47	69	is	be	AUX
ejpam-6603	47	70	called	call	VERB
ejpam-6603	47	71	the	the	DET
ejpam-6603	47	72	perfect	perfect	ADJ
ejpam-6603	47	73	2	2	NUM
ejpam-6603	47	74	-	-	PUNCT
ejpam-6603	47	75	distance	distance	NOUN
ejpam-6603	47	76	zero	zero	NUM
ejpam-6603	47	77	forcing	force	VERB
ejpam-6603	47	78	number	number	NOUN
ejpam-6603	47	79	of	of	ADP
ejpam-6603	47	80	g.	g.	PROPN
ejpam-6603	47	81	example	example	NOUN
ejpam-6603	48	1	1	1	X
ejpam-6603	48	2	.	.	X
ejpam-6603	48	3	consider	consider	VERB
ejpam-6603	48	4	the	the	DET
ejpam-6603	48	5	graph	graph	NOUN
ejpam-6603	48	6	p3	p3	NOUN
ejpam-6603	48	7	+	+	CCONJ
ejpam-6603	48	8	p4	p4	ADJ
ejpam-6603	48	9	below	below	ADV
ejpam-6603	48	10	.	.	PUNCT
ejpam-6603	49	1	let	let	VERB
ejpam-6603	49	2	s	s	PRON
ejpam-6603	49	3	=	=	NOUN
ejpam-6603	49	4	{	{	PUNCT
ejpam-6603	49	5	v1	v1	PROPN
ejpam-6603	49	6	,	,	PUNCT
ejpam-6603	49	7	v2	v2	PROPN
ejpam-6603	49	8	,	,	PUNCT
ejpam-6603	49	9	v3	v3	PROPN
ejpam-6603	49	10	,	,	PUNCT
ejpam-6603	49	11	v5	v5	PROPN
ejpam-6603	49	12	}	}	PUNCT
ejpam-6603	49	13	.	.	PUNCT
ejpam-6603	50	1	then	then	ADV
ejpam-6603	50	2	vertex	vertex	NOUN
ejpam-6603	50	3	v7	v7	NOUN
ejpam-6603	50	4	is	be	AUX
ejpam-6603	50	5	2	2	NUM
ejpam-6603	50	6	-	-	PUNCT
ejpam-6603	50	7	forced	force	VERB
ejpam-6603	50	8	by	by	ADP
ejpam-6603	50	9	vertex	vertex	NOUN
ejpam-6603	50	10	v5	v5	PROPN
ejpam-6603	50	11	,	,	PUNCT
ejpam-6603	50	12	vertex	vertex	NOUN
ejpam-6603	50	13	v4	v4	NOUN
ejpam-6603	50	14	is	be	AUX
ejpam-6603	50	15	2	2	NUM
ejpam-6603	50	16	-	-	PUNCT
ejpam-6603	50	17	forced	force	VERB
ejpam-6603	50	18	by	by	ADP
ejpam-6603	50	19	vertex	vertex	NOUN
ejpam-6603	50	20	v7	v7	NOUN
ejpam-6603	50	21	,	,	PUNCT
ejpam-6603	50	22	and	and	CCONJ
ejpam-6603	50	23	v6	v6	NOUN
ejpam-6603	50	24	is	be	AUX
ejpam-6603	50	25	2	2	NUM
ejpam-6603	50	26	-	-	PUNCT
ejpam-6603	50	27	forced	force	VERB
ejpam-6603	50	28	by	by	ADP
ejpam-6603	50	29	vertex	vertex	NOUN
ejpam-6603	50	30	v4	v4	NOUN
ejpam-6603	50	31	.	.	PUNCT
ejpam-6603	51	1	it	it	PRON
ejpam-6603	51	2	follows	follow	VERB
ejpam-6603	51	3	that	that	SCONJ
ejpam-6603	51	4	vertices	vertice	VERB
ejpam-6603	51	5	v4	v4	PROPN
ejpam-6603	51	6	,	,	PUNCT
ejpam-6603	51	7	v6	v6	NOUN
ejpam-6603	51	8	and	and	CCONJ
ejpam-6603	51	9	v7	v7	NOUN
ejpam-6603	51	10	are	be	AUX
ejpam-6603	51	11	perfectly	perfectly	ADV
ejpam-6603	51	12	2	2	NUM
ejpam-6603	51	13	-	-	PUNCT
ejpam-6603	51	14	forced	force	VERB
ejpam-6603	51	15	by	by	ADP
ejpam-6603	51	16	vertex	vertex	NOUN
ejpam-6603	51	17	v5	v5	PROPN
ejpam-6603	51	18	.	.	PUNCT
ejpam-6603	52	1	therefore	therefore	ADV
ejpam-6603	52	2	,	,	PUNCT
ejpam-6603	52	3	s	s	VERB
ejpam-6603	52	4	is	be	AUX
ejpam-6603	52	5	a	a	DET
ejpam-6603	52	6	perfect	perfect	ADJ
ejpam-6603	52	7	2	2	NUM
ejpam-6603	52	8	-	-	PUNCT
ejpam-6603	52	9	distance	distance	NOUN
ejpam-6603	52	10	zero	zero	NUM
ejpam-6603	52	11	forcing	force	VERB
ejpam-6603	52	12	set	set	NOUN
ejpam-6603	52	13	of	of	ADP
ejpam-6603	52	14	p3	p3	PROPN
ejpam-6603	52	15	+	+	CCONJ
ejpam-6603	52	16	p4	p4	ADJ
ejpam-6603	52	17	.	.	PUNCT
ejpam-6603	53	1	it	it	PRON
ejpam-6603	53	2	can	can	AUX
ejpam-6603	53	3	easily	easily	ADV
ejpam-6603	53	4	be	be	AUX
ejpam-6603	53	5	verified	verify	VERB
ejpam-6603	53	6	that	that	SCONJ
ejpam-6603	53	7	a	a	DET
ejpam-6603	53	8	perfect	perfect	ADJ
ejpam-6603	53	9	2	2	NUM
ejpam-6603	53	10	-	-	PUNCT
ejpam-6603	53	11	distance	distance	NOUN
ejpam-6603	53	12	zero	zero	NUM
ejpam-6603	53	13	forcing	force	VERB
ejpam-6603	53	14	number	number	NOUN
ejpam-6603	53	15	of	of	ADP
ejpam-6603	53	16	p3	p3	PROPN
ejpam-6603	53	17	+	+	CCONJ
ejpam-6603	53	18	p4	p4	ADJ
ejpam-6603	53	19	is	be	AUX
ejpam-6603	53	20	4	4	NUM
ejpam-6603	53	21	,	,	PUNCT
ejpam-6603	53	22	that	that	ADV
ejpam-6603	53	23	is	is	ADV
ejpam-6603	53	24	,	,	PUNCT
ejpam-6603	53	25	z2	z2	PROPN
ejpam-6603	53	26	p(p3	p(p3	NOUN
ejpam-6603	53	27	+	+	CCONJ
ejpam-6603	53	28	p4	p4	ADJ
ejpam-6603	53	29	)	)	PUNCT
ejpam-6603	53	30	=	=	SYM
ejpam-6603	53	31	4	4	X
ejpam-6603	53	32	.	.	X
ejpam-6603	53	33	v1	v1	VERB
ejpam-6603	53	34	v4	v4	NOUN
ejpam-6603	53	35	v2	v2	NOUN
ejpam-6603	53	36	v5	v5	PROPN
ejpam-6603	53	37	v6	v6	NOUN
ejpam-6603	53	38	v7	v7	PROPN
ejpam-6603	53	39	v3	v3	PROPN
ejpam-6603	53	40	p3	p3	PROPN
ejpam-6603	53	41	+	+	CCONJ
ejpam-6603	53	42	p4	p4	ADJ
ejpam-6603	53	43	:	:	PUNCT
ejpam-6603	53	44	theorem	theorem	NOUN
ejpam-6603	53	45	1	1	X
ejpam-6603	53	46	.	.	PUNCT
ejpam-6603	54	1	let	let	VERB
ejpam-6603	54	2	g	g	PRON
ejpam-6603	54	3	be	be	AUX
ejpam-6603	54	4	a	a	DET
ejpam-6603	54	5	graph	graph	NOUN
ejpam-6603	54	6	.	.	PUNCT
ejpam-6603	55	1	then	then	ADV
ejpam-6603	55	2	each	each	PRON
ejpam-6603	55	3	of	of	ADP
ejpam-6603	55	4	the	the	DET
ejpam-6603	55	5	following	follow	VERB
ejpam-6603	55	6	holds	hold	VERB
ejpam-6603	55	7	:	:	PUNCT
ejpam-6603	55	8	(	(	PUNCT
ejpam-6603	55	9	i	i	NOUN
ejpam-6603	55	10	)	)	PUNCT
ejpam-6603	55	11	z2(g	z2(g	X
ejpam-6603	55	12	)	)	PUNCT
ejpam-6603	55	13	≤	≤	NOUN
ejpam-6603	55	14	z2	z2	NOUN
ejpam-6603	55	15	p	p	X
ejpam-6603	55	16	(	(	PUNCT
ejpam-6603	55	17	g	g	NOUN
ejpam-6603	55	18	)	)	PUNCT
ejpam-6603	55	19	≤	≤	NOUN
ejpam-6603	55	20	|v	|v	X
ejpam-6603	55	21	(	(	PUNCT
ejpam-6603	55	22	g)|	g)|	PROPN
ejpam-6603	55	23	.	.	PUNCT
ejpam-6603	56	1	(	(	PUNCT
ejpam-6603	56	2	ii	ii	NOUN
ejpam-6603	56	3	)	)	PUNCT
ejpam-6603	56	4	let	let	VERB
ejpam-6603	56	5	g	g	NOUN
ejpam-6603	56	6	be	be	AUX
ejpam-6603	56	7	a	a	DET
ejpam-6603	56	8	non	non	ADJ
ejpam-6603	56	9	-	-	ADJ
ejpam-6603	56	10	trivial	trivial	ADJ
ejpam-6603	56	11	graph	graph	NOUN
ejpam-6603	56	12	.	.	PUNCT
ejpam-6603	57	1	if	if	SCONJ
ejpam-6603	57	2	g	g	PROPN
ejpam-6603	57	3	has	have	VERB
ejpam-6603	57	4	a	a	DET
ejpam-6603	57	5	dominating	dominating	NOUN
ejpam-6603	57	6	vertex	vertex	NOUN
ejpam-6603	57	7	,	,	PUNCT
ejpam-6603	57	8	then	then	ADV
ejpam-6603	57	9	z2	z2	PROPN
ejpam-6603	57	10	p(g	p(g	PROPN
ejpam-6603	57	11	)	)	PUNCT
ejpam-6603	57	12	≥	≥	NOUN
ejpam-6603	57	13	2	2	NUM
ejpam-6603	57	14	.	.	PUNCT
ejpam-6603	57	15	(	(	PUNCT
ejpam-6603	57	16	iii	iii	X
ejpam-6603	57	17	)	)	PUNCT
ejpam-6603	57	18	if	if	SCONJ
ejpam-6603	57	19	every	every	DET
ejpam-6603	57	20	vertex	vertex	NOUN
ejpam-6603	57	21	of	of	ADP
ejpam-6603	57	22	g	g	PROPN
ejpam-6603	57	23	is	be	AUX
ejpam-6603	57	24	a	a	DET
ejpam-6603	57	25	dominating	dominating	NOUN
ejpam-6603	57	26	vertex	vertex	NOUN
ejpam-6603	57	27	,	,	PUNCT
ejpam-6603	57	28	then	then	ADV
ejpam-6603	57	29	z2	z2	PROPN
ejpam-6603	57	30	p	p	X
ejpam-6603	57	31	(	(	PUNCT
ejpam-6603	57	32	g	g	NOUN
ejpam-6603	57	33	)	)	PUNCT
ejpam-6603	58	1	=	=	SYM
ejpam-6603	58	2	|v	|v	PROPN
ejpam-6603	58	3	(	(	PUNCT
ejpam-6603	58	4	g)|	g)|	NOUN
ejpam-6603	58	5	.	.	PUNCT
ejpam-6603	59	1	proof	proof	NOUN
ejpam-6603	59	2	.	.	PUNCT
ejpam-6603	60	1	(	(	PUNCT
ejpam-6603	60	2	i	i	NOUN
ejpam-6603	60	3	)	)	PUNCT
ejpam-6603	60	4	.	.	PUNCT
ejpam-6603	61	1	let	let	VERB
ejpam-6603	61	2	g	g	PRON
ejpam-6603	61	3	be	be	AUX
ejpam-6603	61	4	a	a	DET
ejpam-6603	61	5	graph	graph	NOUN
ejpam-6603	61	6	,	,	PUNCT
ejpam-6603	61	7	and	and	CCONJ
ejpam-6603	61	8	r	r	NOUN
ejpam-6603	61	9	be	be	VERB
ejpam-6603	61	10	a	a	DET
ejpam-6603	61	11	minimum	minimum	NOUN
ejpam-6603	61	12	perfect	perfect	ADJ
ejpam-6603	61	13	2	2	NUM
ejpam-6603	61	14	-	-	PUNCT
ejpam-6603	61	15	distance	distance	NOUN
ejpam-6603	61	16	zero	zero	NUM
ejpam-6603	61	17	forcing	force	VERB
ejpam-6603	61	18	set	set	NOUN
ejpam-6603	61	19	of	of	ADP
ejpam-6603	61	20	g.	g.	PROPN
ejpam-6603	61	21	then	then	ADV
ejpam-6603	61	22	|r|	|r|	PROPN
ejpam-6603	61	23	=	=	PROPN
ejpam-6603	61	24	z2	z2	PROPN
ejpam-6603	61	25	p	p	NOUN
ejpam-6603	61	26	(	(	PUNCT
ejpam-6603	61	27	g	g	NOUN
ejpam-6603	61	28	)	)	PUNCT
ejpam-6603	61	29	and	and	CCONJ
ejpam-6603	61	30	r	r	NOUN
ejpam-6603	61	31	is	be	AUX
ejpam-6603	61	32	a	a	DET
ejpam-6603	61	33	2	2	NUM
ejpam-6603	61	34	-	-	PUNCT
ejpam-6603	61	35	distance	distance	NOUN
ejpam-6603	61	36	zero	zero	NUM
ejpam-6603	61	37	forcing	force	VERB
ejpam-6603	61	38	set	set	NOUN
ejpam-6603	61	39	of	of	ADP
ejpam-6603	61	40	g.	g.	PROPN
ejpam-6603	61	41	thus	thus	ADV
ejpam-6603	61	42	,	,	PUNCT
ejpam-6603	61	43	z2(g	z2(g	NUM
ejpam-6603	61	44	)	)	PUNCT
ejpam-6603	61	45	≤	≤	NUM
ejpam-6603	61	46	|r|	|r|	NOUN
ejpam-6603	61	47	=	=	PROPN
ejpam-6603	61	48	z2	z2	PROPN
ejpam-6603	61	49	p	p	NOUN
ejpam-6603	61	50	(	(	PUNCT
ejpam-6603	61	51	g	g	NOUN
ejpam-6603	61	52	)	)	PUNCT
ejpam-6603	61	53	.	.	PUNCT
ejpam-6603	62	1	the	the	DET
ejpam-6603	62	2	upper	upper	ADJ
ejpam-6603	62	3	bound	bind	VERB
ejpam-6603	62	4	is	be	AUX
ejpam-6603	62	5	clear	clear	ADJ
ejpam-6603	62	6	since	since	SCONJ
ejpam-6603	62	7	every	every	DET
ejpam-6603	62	8	perfect	perfect	ADJ
ejpam-6603	62	9	2	2	NUM
ejpam-6603	62	10	-	-	PUNCT
ejpam-6603	62	11	distance	distance	NOUN
ejpam-6603	62	12	zero	zero	NUM
ejpam-6603	62	13	forcing	force	VERB
ejpam-6603	62	14	set	set	NOUN
ejpam-6603	62	15	of	of	ADP
ejpam-6603	62	16	g	g	PROPN
ejpam-6603	62	17	is	be	AUX
ejpam-6603	62	18	always	always	ADV
ejpam-6603	62	19	a	a	DET
ejpam-6603	62	20	subset	subset	NOUN
ejpam-6603	62	21	of	of	ADP
ejpam-6603	62	22	v	v	NOUN
ejpam-6603	62	23	(	(	PUNCT
ejpam-6603	62	24	g	g	NOUN
ejpam-6603	62	25	)	)	PUNCT
ejpam-6603	62	26	.	.	PUNCT
ejpam-6603	63	1	(	(	PUNCT
ejpam-6603	63	2	ii	ii	NOUN
ejpam-6603	63	3	)	)	PUNCT
ejpam-6603	63	4	.	.	PUNCT
ejpam-6603	64	1	let	let	VERB
ejpam-6603	64	2	x	x	SYM
ejpam-6603	64	3	∈	∈	PROPN
ejpam-6603	64	4	v	v	X
ejpam-6603	64	5	(	(	PUNCT
ejpam-6603	64	6	g	g	NOUN
ejpam-6603	64	7	)	)	PUNCT
ejpam-6603	64	8	be	be	AUX
ejpam-6603	64	9	a	a	DET
ejpam-6603	64	10	dominating	dominating	NOUN
ejpam-6603	64	11	vertex	vertex	NOUN
ejpam-6603	64	12	of	of	ADP
ejpam-6603	64	13	g.	g.	PROPN
ejpam-6603	64	14	then	then	ADV
ejpam-6603	64	15	dg(x	dg(x	NUM
ejpam-6603	64	16	,	,	PUNCT
ejpam-6603	64	17	u	u	NOUN
ejpam-6603	64	18	)	)	PUNCT
ejpam-6603	64	19	=	=	SYM
ejpam-6603	64	20	1	1	NUM
ejpam-6603	64	21	for	for	ADP
ejpam-6603	64	22	all	all	DET
ejpam-6603	64	23	u	u	NOUN
ejpam-6603	64	24	∈	∈	PROPN
ejpam-6603	64	25	v	v	NOUN
ejpam-6603	64	26	(	(	PUNCT
ejpam-6603	64	27	g	g	NOUN
ejpam-6603	64	28	)	)	PUNCT
ejpam-6603	64	29	\	\	NOUN
ejpam-6603	64	30	{	{	PUNCT
ejpam-6603	64	31	x	x	NOUN
ejpam-6603	64	32	}	}	PUNCT
ejpam-6603	64	33	.	.	PUNCT
ejpam-6603	65	1	suppose	suppose	VERB
ejpam-6603	65	2	that	that	SCONJ
ejpam-6603	65	3	x	x	X
ejpam-6603	65	4	/∈	/∈	PROPN
ejpam-6603	66	1	s	s	X
ejpam-6603	66	2	,	,	PUNCT
ejpam-6603	66	3	where	where	SCONJ
ejpam-6603	66	4	s	s	NOUN
ejpam-6603	66	5	is	be	AUX
ejpam-6603	66	6	a	a	DET
ejpam-6603	66	7	minimum	minimum	ADJ
ejpam-6603	66	8	perfect	perfect	ADJ
ejpam-6603	66	9	2	2	NUM
ejpam-6603	66	10	-	-	PUNCT
ejpam-6603	66	11	distance	distance	NOUN
ejpam-6603	66	12	zero	zero	NUM
ejpam-6603	66	13	forcing	force	VERB
ejpam-6603	66	14	set	set	NOUN
ejpam-6603	66	15	of	of	ADP
ejpam-6603	66	16	g.	g.	PROPN
ejpam-6603	66	17	then	then	ADV
ejpam-6603	66	18	there	there	PRON
ejpam-6603	66	19	must	must	AUX
ejpam-6603	66	20	be	be	AUX
ejpam-6603	66	21	a	a	DET
ejpam-6603	66	22	vertex	vertex	NOUN
ejpam-6603	66	23	w	w	NOUN
ejpam-6603	66	24	∈	∈	PROPN
ejpam-6603	66	25	v	v	ADP
ejpam-6603	66	26	(	(	PUNCT
ejpam-6603	66	27	g	g	NOUN
ejpam-6603	66	28	)	)	PUNCT
ejpam-6603	66	29	\	\	NOUN
ejpam-6603	67	1	{	{	PUNCT
ejpam-6603	67	2	x	x	X
ejpam-6603	67	3	}	}	PUNCT
ejpam-6603	67	4	such	such	ADJ
ejpam-6603	67	5	that	that	SCONJ
ejpam-6603	67	6	dg(w	dg(w	NUM
ejpam-6603	67	7	,	,	PUNCT
ejpam-6603	67	8	x	x	X
ejpam-6603	67	9	)	)	PUNCT
ejpam-6603	67	10	=	=	SYM
ejpam-6603	67	11	2	2	NUM
ejpam-6603	67	12	,	,	PUNCT
ejpam-6603	67	13	which	which	PRON
ejpam-6603	67	14	is	be	AUX
ejpam-6603	67	15	a	a	DET
ejpam-6603	67	16	contradiction	contradiction	NOUN
ejpam-6603	67	17	.	.	PUNCT
ejpam-6603	68	1	thus	thus	ADV
ejpam-6603	68	2	,	,	PUNCT
ejpam-6603	68	3	x	x	PROPN
ejpam-6603	68	4	∈	∈	PROPN
ejpam-6603	68	5	s.	s.	PROPN
ejpam-6603	68	6	since	since	SCONJ
ejpam-6603	68	7	g	g	PROPN
ejpam-6603	68	8	is	be	AUX
ejpam-6603	68	9	a	a	DET
ejpam-6603	68	10	non	non	ADJ
ejpam-6603	68	11	-	-	ADJ
ejpam-6603	68	12	trivial	trivial	ADJ
ejpam-6603	68	13	and	and	CCONJ
ejpam-6603	68	14	x	x	NOUN
ejpam-6603	68	15	is	be	AUX
ejpam-6603	68	16	a	a	DET
ejpam-6603	68	17	dominating	dominating	NOUN
ejpam-6603	68	18	vertex	vertex	NOUN
ejpam-6603	68	19	of	of	ADP
ejpam-6603	68	20	g	g	NOUN
ejpam-6603	68	21	,	,	PUNCT
ejpam-6603	68	22	there	there	PRON
ejpam-6603	68	23	exists	exist	VERB
ejpam-6603	68	24	y	y	PROPN
ejpam-6603	68	25	∈	∈	PROPN
ejpam-6603	68	26	v	v	ADP
ejpam-6603	68	27	(	(	PUNCT
ejpam-6603	68	28	g	g	NOUN
ejpam-6603	68	29	)	)	PUNCT
ejpam-6603	68	30	\	\	NOUN
ejpam-6603	68	31	{	{	PUNCT
ejpam-6603	68	32	x	x	X
ejpam-6603	68	33	}	}	PUNCT
ejpam-6603	68	34	such	such	ADJ
ejpam-6603	68	35	that	that	SCONJ
ejpam-6603	68	36	y	y	PROPN
ejpam-6603	68	37	∈	∈	PROPN
ejpam-6603	68	38	s.	s.	PROPN
ejpam-6603	68	39	therefore	therefore	ADV
ejpam-6603	68	40	,	,	PUNCT
ejpam-6603	68	41	z2	z2	PROPN
ejpam-6603	68	42	p	p	X
ejpam-6603	68	43	(	(	PUNCT
ejpam-6603	68	44	g	g	NOUN
ejpam-6603	68	45	)	)	PUNCT
ejpam-6603	68	46	≥	≥	NOUN
ejpam-6603	68	47	2	2	NUM
ejpam-6603	68	48	.	.	PUNCT
ejpam-6603	68	49	(	(	PUNCT
ejpam-6603	68	50	iii	iii	NOUN
ejpam-6603	68	51	)	)	PUNCT
ejpam-6603	68	52	.	.	PUNCT
ejpam-6603	69	1	let	let	VERB
ejpam-6603	69	2	v	v	X
ejpam-6603	69	3	(	(	PUNCT
ejpam-6603	69	4	g	g	NOUN
ejpam-6603	69	5	)	)	PUNCT
ejpam-6603	69	6	=	=	SYM
ejpam-6603	69	7	{	{	PUNCT
ejpam-6603	69	8	v1	v1	PROPN
ejpam-6603	69	9	,	,	PUNCT
ejpam-6603	69	10	v2	v2	PROPN
ejpam-6603	69	11	,	,	PUNCT
ejpam-6603	69	12	·	·	PUNCT
ejpam-6603	69	13	·	·	PUNCT
ejpam-6603	69	14	·	·	PUNCT
ejpam-6603	69	15	,	,	PUNCT
ejpam-6603	69	16	vk	vk	ADP
ejpam-6603	69	17	}	}	PUNCT
ejpam-6603	69	18	.	.	PUNCT
ejpam-6603	70	1	since	since	SCONJ
ejpam-6603	70	2	v1	v1	NOUN
ejpam-6603	70	3	is	be	AUX
ejpam-6603	70	4	a	a	DET
ejpam-6603	70	5	dominating	dominating	NOUN
ejpam-6603	70	6	vertex	vertex	NOUN
ejpam-6603	70	7	of	of	ADP
ejpam-6603	70	8	g	g	PROPN
ejpam-6603	70	9	,	,	PUNCT
ejpam-6603	70	10	dg(v1	dg(v1	NOUN
ejpam-6603	70	11	,	,	PUNCT
ejpam-6603	70	12	vi	vi	NOUN
ejpam-6603	70	13	)	)	PUNCT
ejpam-6603	70	14	=	=	SYM
ejpam-6603	70	15	1	1	NUM
ejpam-6603	70	16	for	for	ADP
ejpam-6603	70	17	all	all	PRON
ejpam-6603	70	18	i	i	PRON
ejpam-6603	70	19	∈	∈	PROPN
ejpam-6603	70	20	{	{	PUNCT
ejpam-6603	70	21	2	2	NUM
ejpam-6603	70	22	,	,	PUNCT
ejpam-6603	70	23	3	3	NUM
ejpam-6603	70	24	,	,	PUNCT
ejpam-6603	70	25	·	·	PUNCT
ejpam-6603	70	26	·	·	PUNCT
ejpam-6603	70	27	·	·	PUNCT
ejpam-6603	70	28	,	,	PUNCT
ejpam-6603	70	29	k	k	NOUN
ejpam-6603	70	30	}	}	PUNCT
ejpam-6603	70	31	.	.	PUNCT
ejpam-6603	71	1	applying	apply	VERB
ejpam-6603	71	2	the	the	DET
ejpam-6603	71	3	same	same	ADJ
ejpam-6603	71	4	argument	argument	NOUN
ejpam-6603	71	5	in	in	ADP
ejpam-6603	71	6	the	the	DET
ejpam-6603	71	7	proof	proof	NOUN
ejpam-6603	71	8	of	of	ADP
ejpam-6603	71	9	(	(	PUNCT
ejpam-6603	71	10	ii	ii	NOUN
ejpam-6603	71	11	)	)	PUNCT
ejpam-6603	71	12	,	,	PUNCT
ejpam-6603	71	13	v1	v1	PROPN
ejpam-6603	71	14	∈	∈	PROPN
ejpam-6603	71	15	q	q	NOUN
ejpam-6603	71	16	,	,	PUNCT
ejpam-6603	71	17	where	where	SCONJ
ejpam-6603	71	18	q	q	NOUN
ejpam-6603	71	19	is	be	AUX
ejpam-6603	71	20	a	a	DET
ejpam-6603	71	21	minimum	minimum	NOUN
ejpam-6603	71	22	perfect	perfect	ADJ
ejpam-6603	71	23	2	2	NUM
ejpam-6603	71	24	-	-	PUNCT
ejpam-6603	71	25	distance	distance	NOUN
ejpam-6603	71	26	zero	zero	NUM
ejpam-6603	71	27	forcing	force	VERB
ejpam-6603	71	28	set	set	NOUN
ejpam-6603	71	29	of	of	ADP
ejpam-6603	71	30	g.	g.	PROPN
ejpam-6603	71	31	now	now	ADV
ejpam-6603	71	32	,	,	PUNCT
ejpam-6603	71	33	since	since	SCONJ
ejpam-6603	71	34	v2	v2	PROPN
ejpam-6603	71	35	∈	∈	PROPN
ejpam-6603	71	36	v	v	NOUN
ejpam-6603	71	37	(	(	PUNCT
ejpam-6603	71	38	g	g	NOUN
ejpam-6603	71	39	)	)	PUNCT
ejpam-6603	71	40	\	\	NOUN
ejpam-6603	71	41	{	{	PUNCT
ejpam-6603	71	42	v1	v1	NOUN
ejpam-6603	71	43	}	}	PUNCT
ejpam-6603	71	44	is	be	AUX
ejpam-6603	71	45	a	a	DET
ejpam-6603	71	46	dominating	dominating	NOUN
ejpam-6603	71	47	vertex	vertex	NOUN
ejpam-6603	71	48	,	,	PUNCT
ejpam-6603	71	49	v2	v2	PROPN
ejpam-6603	71	50	must	must	AUX
ejpam-6603	71	51	be	be	AUX
ejpam-6603	71	52	also	also	ADV
ejpam-6603	71	53	in	in	ADP
ejpam-6603	71	54	q.	q.	PROPN
ejpam-6603	71	55	continuing	continue	VERB
ejpam-6603	71	56	in	in	ADP
ejpam-6603	71	57	this	this	DET
ejpam-6603	71	58	manner	manner	NOUN
ejpam-6603	71	59	,	,	PUNCT
ejpam-6603	71	60	v	v	NOUN
ejpam-6603	71	61	(	(	PUNCT
ejpam-6603	71	62	g	g	NOUN
ejpam-6603	71	63	)	)	PUNCT
ejpam-6603	71	64	⊆	⊆	NUM
ejpam-6603	71	65	q	q	NOUN
ejpam-6603	71	66	,	,	PUNCT
ejpam-6603	71	67	that	that	ADV
ejpam-6603	71	68	is	is	ADV
ejpam-6603	71	69	,	,	PUNCT
ejpam-6603	71	70	q	q	PROPN
ejpam-6603	71	71	=	=	SYM
ejpam-6603	71	72	v	v	X
ejpam-6603	71	73	(	(	PUNCT
ejpam-6603	71	74	g	g	NOUN
ejpam-6603	71	75	)	)	PUNCT
ejpam-6603	71	76	.	.	PUNCT
ejpam-6603	72	1	hence	hence	ADV
ejpam-6603	72	2	,	,	PUNCT
ejpam-6603	72	3	z2	z2	PROPN
ejpam-6603	72	4	p(g	p(g	NOUN
ejpam-6603	72	5	)	)	PUNCT
ejpam-6603	73	1	=	=	SYM
ejpam-6603	73	2	|v	|v	PROPN
ejpam-6603	73	3	(	(	PUNCT
ejpam-6603	73	4	g)|	g)|	PROPN
ejpam-6603	73	5	.	.	PUNCT
ejpam-6603	74	1	j.	j.	PROPN
ejpam-6603	74	2	a.	a.	PROPN
ejpam-6603	74	3	hassan	hassan	PROPN
ejpam-6603	74	4	et	et	PROPN
ejpam-6603	74	5	al	al	PROPN
ejpam-6603	74	6	.	.	PUNCT
ejpam-6603	74	7	/	/	SYM
ejpam-6603	74	8	eur	eur	PROPN
ejpam-6603	74	9	.	.	PUNCT
ejpam-6603	75	1	j.	j.	PROPN
ejpam-6603	75	2	pure	pure	PROPN
ejpam-6603	75	3	appl	appl	PROPN
ejpam-6603	75	4	.	.	PROPN
ejpam-6603	75	5	math	math	PROPN
ejpam-6603	75	6	,	,	PUNCT
ejpam-6603	75	7	18	18	NUM
ejpam-6603	75	8	(	(	PUNCT
ejpam-6603	75	9	3	3	NUM
ejpam-6603	75	10	)	)	PUNCT
ejpam-6603	75	11	(	(	PUNCT
ejpam-6603	75	12	2025	2025	NUM
ejpam-6603	75	13	)	)	PUNCT
ejpam-6603	75	14	,	,	PUNCT
ejpam-6603	75	15	6603	6603	NUM
ejpam-6603	75	16	4	4	NUM
ejpam-6603	75	17	of	of	ADP
ejpam-6603	75	18	9	9	NUM
ejpam-6603	75	19	theorem	theorem	NOUN
ejpam-6603	75	20	2	2	NUM
ejpam-6603	75	21	.	.	PUNCT
ejpam-6603	76	1	let	let	VERB
ejpam-6603	76	2	n	n	PRON
ejpam-6603	76	3	be	be	AUX
ejpam-6603	76	4	a	a	DET
ejpam-6603	76	5	positive	positive	ADJ
ejpam-6603	76	6	integer	integer	NOUN
ejpam-6603	76	7	.	.	PUNCT
ejpam-6603	77	1	z2	z2	NOUN
ejpam-6603	77	2	p(pn	p(pn	PROPN
ejpam-6603	77	3	)	)	PUNCT
ejpam-6603	77	4	=	=	PRON
ejpam-6603	77	5	{	{	PUNCT
ejpam-6603	77	6	n	n	ADV
ejpam-6603	77	7	2	2	NUM
ejpam-6603	77	8	+	+	NUM
ejpam-6603	77	9	1	1	NUM
ejpam-6603	77	10	,	,	PUNCT
ejpam-6603	77	11	if	if	SCONJ
ejpam-6603	77	12	n	n	PRON
ejpam-6603	77	13	is	be	AUX
ejpam-6603	77	14	even	even	ADV
ejpam-6603	77	15	n+1	n+1	ADV
ejpam-6603	77	16	2	2	NUM
ejpam-6603	77	17	,	,	PUNCT
ejpam-6603	77	18	if	if	SCONJ
ejpam-6603	77	19	n	n	PRON
ejpam-6603	77	20	is	be	AUX
ejpam-6603	77	21	odd	odd	ADJ
ejpam-6603	77	22	proof	proof	NOUN
ejpam-6603	77	23	.	.	PUNCT
ejpam-6603	78	1	clearly	clearly	ADV
ejpam-6603	78	2	,	,	PUNCT
ejpam-6603	78	3	z2	z2	PROPN
ejpam-6603	78	4	p(p1	p(p1	NOUN
ejpam-6603	78	5	)	)	PUNCT
ejpam-6603	78	6	=	=	SYM
ejpam-6603	78	7	1	1	NUM
ejpam-6603	78	8	and	and	CCONJ
ejpam-6603	78	9	z2	z2	NOUN
ejpam-6603	78	10	p(p2	p(p2	ADJ
ejpam-6603	78	11	)	)	PUNCT
ejpam-6603	78	12	=	=	SYM
ejpam-6603	78	13	2	2	NUM
ejpam-6603	78	14	=	=	SYM
ejpam-6603	78	15	z2	z2	PROPN
ejpam-6603	78	16	p(p3	p(p3	PROPN
ejpam-6603	78	17	)	)	PUNCT
ejpam-6603	78	18	.	.	PUNCT
ejpam-6603	79	1	suppose	suppose	VERB
ejpam-6603	79	2	that	that	SCONJ
ejpam-6603	79	3	n	n	PROPN
ejpam-6603	79	4	≥	≥	NOUN
ejpam-6603	79	5	4	4	NUM
ejpam-6603	79	6	and	and	CCONJ
ejpam-6603	79	7	even	even	ADV
ejpam-6603	79	8	,	,	PUNCT
ejpam-6603	79	9	let	let	VERB
ejpam-6603	79	10	pn	pn	VERB
ejpam-6603	79	11	=	=	PUNCT
ejpam-6603	80	1	[	[	X
ejpam-6603	80	2	v1	v1	NOUN
ejpam-6603	80	3	,	,	PUNCT
ejpam-6603	80	4	v2	v2	PROPN
ejpam-6603	80	5	,	,	PUNCT
ejpam-6603	80	6	...	...	PUNCT
ejpam-6603	80	7	,	,	PUNCT
ejpam-6603	80	8	vn	vn	X
ejpam-6603	80	9	]	]	X
ejpam-6603	80	10	,	,	PUNCT
ejpam-6603	80	11	and	and	CCONJ
ejpam-6603	80	12	consider	consider	VERB
ejpam-6603	80	13	b	b	NOUN
ejpam-6603	80	14	=	=	SYM
ejpam-6603	80	15	{	{	PUNCT
ejpam-6603	80	16	v1	v1	PROPN
ejpam-6603	80	17	,	,	PUNCT
ejpam-6603	80	18	v2	v2	PROPN
ejpam-6603	80	19	,	,	PUNCT
ejpam-6603	80	20	v4	v4	PROPN
ejpam-6603	80	21	,	,	PUNCT
ejpam-6603	80	22	v6	v6	NOUN
ejpam-6603	80	23	,	,	PUNCT
ejpam-6603	80	24	.	.	PUNCT
ejpam-6603	80	25	.	.	PUNCT
ejpam-6603	80	26	.	.	PUNCT
ejpam-6603	81	1	,	,	PUNCT
ejpam-6603	81	2	vn	vn	PROPN
ejpam-6603	81	3	}	}	PUNCT
ejpam-6603	81	4	.	.	PUNCT
ejpam-6603	82	1	then	then	ADV
ejpam-6603	82	2	vertices	vertice	VERB
ejpam-6603	82	3	v3	v3	PROPN
ejpam-6603	82	4	,	,	PUNCT
ejpam-6603	82	5	v5	v5	PROPN
ejpam-6603	82	6	,	,	PUNCT
ejpam-6603	82	7	.	.	PUNCT
ejpam-6603	82	8	.	.	PUNCT
ejpam-6603	83	1	.	.	PUNCT
ejpam-6603	84	1	,	,	PUNCT
ejpam-6603	84	2	vn−1	vn−1	PROPN
ejpam-6603	84	3	are	be	AUX
ejpam-6603	84	4	perfectly	perfectly	ADV
ejpam-6603	84	5	2	2	NUM
ejpam-6603	84	6	-	-	PUNCT
ejpam-6603	84	7	forced	force	VERB
ejpam-6603	84	8	by	by	ADP
ejpam-6603	84	9	v1	v1	NOUN
ejpam-6603	84	10	.	.	PUNCT
ejpam-6603	85	1	it	it	PRON
ejpam-6603	85	2	follows	follow	VERB
ejpam-6603	85	3	that	that	SCONJ
ejpam-6603	85	4	b	b	NOUN
ejpam-6603	85	5	is	be	AUX
ejpam-6603	85	6	perfect	perfect	ADJ
ejpam-6603	85	7	2	2	NUM
ejpam-6603	85	8	-	-	PUNCT
ejpam-6603	85	9	distance	distance	NOUN
ejpam-6603	85	10	zero	zero	NUM
ejpam-6603	85	11	forcing	force	VERB
ejpam-6603	85	12	set	set	NOUN
ejpam-6603	85	13	of	of	ADP
ejpam-6603	85	14	pn	pn	PROPN
ejpam-6603	85	15	.	.	PROPN
ejpam-6603	85	16	notice	notice	VERB
ejpam-6603	85	17	that	that	SCONJ
ejpam-6603	85	18	,	,	PUNCT
ejpam-6603	85	19	if	if	SCONJ
ejpam-6603	85	20	we	we	PRON
ejpam-6603	85	21	remove	remove	VERB
ejpam-6603	85	22	vi	vi	PROPN
ejpam-6603	85	23	from	from	ADP
ejpam-6603	85	24	b	b	NOUN
ejpam-6603	85	25	for	for	ADP
ejpam-6603	85	26	some	some	DET
ejpam-6603	85	27	i	i	PRON
ejpam-6603	85	28	∈	∈	PROPN
ejpam-6603	85	29	{	{	PUNCT
ejpam-6603	85	30	2	2	NUM
ejpam-6603	85	31	,	,	PUNCT
ejpam-6603	85	32	4	4	NUM
ejpam-6603	85	33	,	,	PUNCT
ejpam-6603	85	34	.	.	PUNCT
ejpam-6603	85	35	.	.	PUNCT
ejpam-6603	86	1	.	.	PUNCT
ejpam-6603	87	1	,	,	PUNCT
ejpam-6603	87	2	n	n	CCONJ
ejpam-6603	87	3	}	}	PUNCT
ejpam-6603	87	4	,	,	PUNCT
ejpam-6603	87	5	then	then	ADV
ejpam-6603	87	6	vi	vi	PROPN
ejpam-6603	87	7	will	will	AUX
ejpam-6603	87	8	not	not	PART
ejpam-6603	87	9	be	be	AUX
ejpam-6603	87	10	perfectly	perfectly	ADV
ejpam-6603	87	11	2	2	NUM
ejpam-6603	87	12	-	-	PUNCT
ejpam-6603	87	13	forced	force	VERB
ejpam-6603	87	14	by	by	ADP
ejpam-6603	87	15	v1	v1	NOUN
ejpam-6603	87	16	.	.	PUNCT
ejpam-6603	88	1	thus	thus	ADV
ejpam-6603	88	2	,	,	PUNCT
ejpam-6603	88	3	b	b	PROPN
ejpam-6603	88	4	is	be	AUX
ejpam-6603	88	5	a	a	DET
ejpam-6603	88	6	minimum	minimum	NOUN
ejpam-6603	88	7	perfect	perfect	ADJ
ejpam-6603	88	8	2	2	NUM
ejpam-6603	88	9	-	-	PUNCT
ejpam-6603	88	10	distance	distance	NOUN
ejpam-6603	88	11	zero	zero	NUM
ejpam-6603	88	12	forcing	force	VERB
ejpam-6603	88	13	set	set	NOUN
ejpam-6603	88	14	of	of	ADP
ejpam-6603	88	15	pn	pn	PROPN
ejpam-6603	88	16	.	.	PROPN
ejpam-6603	89	1	hence	hence	ADV
ejpam-6603	89	2	,	,	PUNCT
ejpam-6603	89	3	z	z	NOUN
ejpam-6603	89	4	2	2	NUM
ejpam-6603	89	5	p(pn	p(pn	PROPN
ejpam-6603	89	6	)	)	PUNCT
ejpam-6603	89	7	=	=	SYM
ejpam-6603	89	8	n	n	PRON
ejpam-6603	89	9	2	2	NUM
ejpam-6603	89	10	+	+	CCONJ
ejpam-6603	89	11	1	1	NUM
ejpam-6603	89	12	for	for	ADP
ejpam-6603	89	13	all	all	DET
ejpam-6603	89	14	even	even	ADV
ejpam-6603	89	15	integers	integer	NOUN
ejpam-6603	89	16	n	n	PRON
ejpam-6603	89	17	≥	≥	NOUN
ejpam-6603	89	18	2	2	NUM
ejpam-6603	89	19	.	.	PUNCT
ejpam-6603	90	1	now	now	ADV
ejpam-6603	90	2	,	,	PUNCT
ejpam-6603	90	3	assume	assume	VERB
ejpam-6603	90	4	that	that	SCONJ
ejpam-6603	90	5	n	n	PRON
ejpam-6603	90	6	≥	≥	NOUN
ejpam-6603	90	7	5	5	NUM
ejpam-6603	90	8	and	and	CCONJ
ejpam-6603	90	9	odd	odd	ADJ
ejpam-6603	90	10	.	.	PUNCT
ejpam-6603	91	1	let	let	VERB
ejpam-6603	91	2	a	a	DET
ejpam-6603	91	3	=	=	X
ejpam-6603	91	4	{	{	PUNCT
ejpam-6603	91	5	v1	v1	PROPN
ejpam-6603	91	6	,	,	PUNCT
ejpam-6603	91	7	v2	v2	PROPN
ejpam-6603	91	8	,	,	PUNCT
ejpam-6603	91	9	v4	v4	PROPN
ejpam-6603	91	10	,	,	PUNCT
ejpam-6603	91	11	v6	v6	NOUN
ejpam-6603	91	12	,	,	PUNCT
ejpam-6603	91	13	.	.	PUNCT
ejpam-6603	91	14	.	.	PUNCT
ejpam-6603	92	1	.	.	PUNCT
ejpam-6603	93	1	,	,	PUNCT
ejpam-6603	93	2	vn−1	vn−1	ADJ
ejpam-6603	93	3	}	}	PUNCT
ejpam-6603	93	4	.	.	PUNCT
ejpam-6603	94	1	then	then	ADV
ejpam-6603	94	2	vertices	vertice	VERB
ejpam-6603	94	3	v3	v3	PROPN
ejpam-6603	94	4	,	,	PUNCT
ejpam-6603	94	5	v5	v5	PROPN
ejpam-6603	94	6	,	,	PUNCT
ejpam-6603	94	7	.	.	PUNCT
ejpam-6603	94	8	.	.	PUNCT
ejpam-6603	95	1	.	.	PUNCT
ejpam-6603	96	1	,	,	PUNCT
ejpam-6603	96	2	vn	vn	PROPN
ejpam-6603	96	3	are	be	AUX
ejpam-6603	96	4	perfectly	perfectly	ADV
ejpam-6603	96	5	2	2	NUM
ejpam-6603	96	6	-	-	PUNCT
ejpam-6603	96	7	forced	force	VERB
ejpam-6603	96	8	by	by	ADP
ejpam-6603	96	9	v1	v1	NOUN
ejpam-6603	96	10	.	.	PUNCT
ejpam-6603	97	1	thus	thus	ADV
ejpam-6603	97	2	,	,	PUNCT
ejpam-6603	97	3	a	a	PRON
ejpam-6603	97	4	is	be	AUX
ejpam-6603	97	5	a	a	DET
ejpam-6603	97	6	perfect	perfect	ADJ
ejpam-6603	97	7	2	2	NUM
ejpam-6603	97	8	-	-	PUNCT
ejpam-6603	97	9	distance	distance	NOUN
ejpam-6603	97	10	zero	zero	NUM
ejpam-6603	97	11	forcing	force	VERB
ejpam-6603	97	12	set	set	NOUN
ejpam-6603	97	13	of	of	ADP
ejpam-6603	97	14	pn	pn	PROPN
ejpam-6603	97	15	.	.	PUNCT
ejpam-6603	98	1	moreover	moreover	ADV
ejpam-6603	98	2	,	,	PUNCT
ejpam-6603	98	3	if	if	SCONJ
ejpam-6603	98	4	we	we	PRON
ejpam-6603	98	5	remove	remove	VERB
ejpam-6603	98	6	vj	vj	NOUN
ejpam-6603	98	7	from	from	ADP
ejpam-6603	98	8	a	a	PRON
ejpam-6603	98	9	for	for	ADP
ejpam-6603	98	10	some	some	DET
ejpam-6603	98	11	j	j	PROPN
ejpam-6603	98	12	∈	∈	PROPN
ejpam-6603	98	13	{	{	PUNCT
ejpam-6603	98	14	2	2	NUM
ejpam-6603	98	15	,	,	PUNCT
ejpam-6603	98	16	4	4	NUM
ejpam-6603	98	17	,	,	PUNCT
ejpam-6603	98	18	.	.	PUNCT
ejpam-6603	98	19	.	.	PUNCT
ejpam-6603	99	1	.	.	PUNCT
ejpam-6603	100	1	,	,	PUNCT
ejpam-6603	100	2	n−1	n−1	PROPN
ejpam-6603	100	3	}	}	PUNCT
ejpam-6603	100	4	,	,	PUNCT
ejpam-6603	100	5	then	then	ADV
ejpam-6603	100	6	vj	vj	INTJ
ejpam-6603	100	7	will	will	AUX
ejpam-6603	100	8	not	not	PART
ejpam-6603	100	9	be	be	AUX
ejpam-6603	100	10	perfectly	perfectly	ADV
ejpam-6603	100	11	2forced	2force	VERB
ejpam-6603	100	12	by	by	ADP
ejpam-6603	100	13	v1	v1	PROPN
ejpam-6603	100	14	.	.	PUNCT
ejpam-6603	101	1	this	this	PRON
ejpam-6603	101	2	means	mean	VERB
ejpam-6603	101	3	that	that	SCONJ
ejpam-6603	101	4	a	a	PRON
ejpam-6603	101	5	is	be	AUX
ejpam-6603	101	6	a	a	DET
ejpam-6603	101	7	minimum	minimum	ADJ
ejpam-6603	101	8	perfect	perfect	ADJ
ejpam-6603	101	9	2	2	NUM
ejpam-6603	101	10	-	-	PUNCT
ejpam-6603	101	11	distance	distance	NOUN
ejpam-6603	101	12	zero	zero	NUM
ejpam-6603	101	13	forcing	force	VERB
ejpam-6603	101	14	set	set	NOUN
ejpam-6603	101	15	of	of	ADP
ejpam-6603	101	16	pn	pn	PROPN
ejpam-6603	101	17	.	.	PROPN
ejpam-6603	102	1	hence	hence	ADV
ejpam-6603	102	2	,	,	PUNCT
ejpam-6603	102	3	z	z	NOUN
ejpam-6603	102	4	2	2	NUM
ejpam-6603	102	5	p(pn	p(pn	PROPN
ejpam-6603	102	6	)	)	PUNCT
ejpam-6603	102	7	=	=	SYM
ejpam-6603	102	8	n+1	n+1	PROPN
ejpam-6603	102	9	2	2	NUM
ejpam-6603	102	10	for	for	ADP
ejpam-6603	102	11	all	all	DET
ejpam-6603	102	12	odd	odd	ADJ
ejpam-6603	102	13	integers	integer	NOUN
ejpam-6603	102	14	n	n	PRON
ejpam-6603	102	15	≥	≥	NUM
ejpam-6603	102	16	5	5	NUM
ejpam-6603	102	17	.	.	PUNCT
ejpam-6603	102	18	to	to	PART
ejpam-6603	102	19	study	study	VERB
ejpam-6603	102	20	the	the	DET
ejpam-6603	102	21	behavior	behavior	NOUN
ejpam-6603	102	22	of	of	ADP
ejpam-6603	102	23	perfect	perfect	ADJ
ejpam-6603	102	24	2	2	NUM
ejpam-6603	102	25	-	-	PUNCT
ejpam-6603	102	26	distance	distance	NOUN
ejpam-6603	102	27	zero	zero	NUM
ejpam-6603	102	28	forcing	force	VERB
ejpam-6603	102	29	sets	set	NOUN
ejpam-6603	102	30	in	in	ADP
ejpam-6603	102	31	the	the	DET
ejpam-6603	102	32	join	join	NOUN
ejpam-6603	102	33	of	of	ADP
ejpam-6603	102	34	any	any	DET
ejpam-6603	102	35	two	two	NUM
ejpam-6603	102	36	graphs	graph	NOUN
ejpam-6603	102	37	,	,	PUNCT
ejpam-6603	102	38	the	the	DET
ejpam-6603	102	39	following	follow	VERB
ejpam-6603	102	40	concept	concept	NOUN
ejpam-6603	102	41	shall	shall	AUX
ejpam-6603	102	42	be	be	AUX
ejpam-6603	102	43	defined	define	VERB
ejpam-6603	102	44	:	:	PUNCT
ejpam-6603	102	45	definition	definition	NOUN
ejpam-6603	102	46	2	2	NUM
ejpam-6603	102	47	.	.	PUNCT
ejpam-6603	103	1	let	let	VERB
ejpam-6603	103	2	g	g	PRON
ejpam-6603	103	3	be	be	AUX
ejpam-6603	103	4	a	a	DET
ejpam-6603	103	5	graph	graph	NOUN
ejpam-6603	103	6	.	.	PUNCT
ejpam-6603	104	1	then	then	ADV
ejpam-6603	104	2	a	a	DET
ejpam-6603	104	3	co	co	ADJ
ejpam-6603	104	4	-	-	ADJ
ejpam-6603	104	5	color	color	ADJ
ejpam-6603	104	6	change	change	NOUN
ejpam-6603	104	7	rule	rule	NOUN
ejpam-6603	104	8	is	be	AUX
ejpam-6603	104	9	defined	define	VERB
ejpam-6603	104	10	as	as	SCONJ
ejpam-6603	104	11	follows	follow	VERB
ejpam-6603	104	12	:	:	PUNCT
ejpam-6603	104	13	if	if	SCONJ
ejpam-6603	104	14	a	a	DET
ejpam-6603	104	15	vertex	vertex	NOUN
ejpam-6603	104	16	x	x	SYM
ejpam-6603	104	17	∈	∈	NOUN
ejpam-6603	104	18	v	v	ADP
ejpam-6603	104	19	(	(	PUNCT
ejpam-6603	104	20	g	g	NOUN
ejpam-6603	104	21	)	)	PUNCT
ejpam-6603	104	22	is	be	AUX
ejpam-6603	104	23	colored	color	VERB
ejpam-6603	104	24	black	black	ADJ
ejpam-6603	104	25	and	and	CCONJ
ejpam-6603	104	26	has	have	VERB
ejpam-6603	104	27	exactly	exactly	ADV
ejpam-6603	104	28	one	one	NUM
ejpam-6603	104	29	non	non	ADJ
ejpam-6603	104	30	-	-	NOUN
ejpam-6603	104	31	neighbor	neighbor	ADJ
ejpam-6603	104	32	y	y	PROPN
ejpam-6603	104	33	that	that	PRON
ejpam-6603	104	34	is	be	AUX
ejpam-6603	104	35	colored	color	VERB
ejpam-6603	104	36	white	white	ADJ
ejpam-6603	104	37	,	,	PUNCT
ejpam-6603	104	38	then	then	ADV
ejpam-6603	104	39	y	y	PROPN
ejpam-6603	104	40	will	will	AUX
ejpam-6603	104	41	become	become	VERB
ejpam-6603	104	42	black	black	ADJ
ejpam-6603	104	43	.	.	PUNCT
ejpam-6603	105	1	in	in	ADP
ejpam-6603	105	2	this	this	DET
ejpam-6603	105	3	case	case	NOUN
ejpam-6603	105	4	,	,	PUNCT
ejpam-6603	105	5	we	we	PRON
ejpam-6603	105	6	say	say	VERB
ejpam-6603	105	7	that	that	SCONJ
ejpam-6603	105	8	a	a	DET
ejpam-6603	105	9	vertex	vertex	NOUN
ejpam-6603	105	10	y	y	PROPN
ejpam-6603	105	11	is	be	AUX
ejpam-6603	105	12	co	co	VERB
ejpam-6603	105	13	-	-	VERB
ejpam-6603	105	14	forced	force	VERB
ejpam-6603	105	15	by	by	ADP
ejpam-6603	105	16	a	a	DET
ejpam-6603	105	17	vertex	vertex	NOUN
ejpam-6603	105	18	x	x	PUNCT
ejpam-6603	105	19	in	in	ADP
ejpam-6603	105	20	g.	g.	PROPN
ejpam-6603	105	21	moreover	moreover	ADV
ejpam-6603	105	22	,	,	PUNCT
ejpam-6603	105	23	let	let	VERB
ejpam-6603	105	24	u	u	NOUN
ejpam-6603	105	25	,	,	PUNCT
ejpam-6603	105	26	v	v	NOUN
ejpam-6603	105	27	,	,	PUNCT
ejpam-6603	105	28	w	w	PROPN
ejpam-6603	105	29	∈	∈	PROPN
ejpam-6603	105	30	v	v	ADP
ejpam-6603	105	31	(	(	PUNCT
ejpam-6603	105	32	g	g	NOUN
ejpam-6603	105	33	)	)	PUNCT
ejpam-6603	105	34	.	.	PUNCT
ejpam-6603	106	1	if	if	SCONJ
ejpam-6603	106	2	u	u	PRON
ejpam-6603	106	3	co	co	NOUN
ejpam-6603	106	4	-	-	NOUN
ejpam-6603	106	5	forces	force	NOUN
ejpam-6603	106	6	v	v	NOUN
ejpam-6603	106	7	and	and	CCONJ
ejpam-6603	106	8	v	v	ADP
ejpam-6603	106	9	co	co	NOUN
ejpam-6603	106	10	-	-	NOUN
ejpam-6603	106	11	forces	force	NOUN
ejpam-6603	106	12	w	w	NOUN
ejpam-6603	106	13	,	,	PUNCT
ejpam-6603	106	14	then	then	ADV
ejpam-6603	106	15	we	we	PRON
ejpam-6603	106	16	say	say	VERB
ejpam-6603	106	17	that	that	SCONJ
ejpam-6603	106	18	v	v	NOUN
ejpam-6603	106	19	and	and	CCONJ
ejpam-6603	106	20	w	w	NOUN
ejpam-6603	106	21	are	be	AUX
ejpam-6603	106	22	perfectly	perfectly	ADV
ejpam-6603	106	23	co	co	VERB
ejpam-6603	106	24	-	-	VERB
ejpam-6603	106	25	forced	force	VERB
ejpam-6603	106	26	by	by	ADP
ejpam-6603	106	27	u	u	NOUN
ejpam-6603	106	28	,	,	PUNCT
ejpam-6603	106	29	and	and	CCONJ
ejpam-6603	106	30	this	this	DET
ejpam-6603	106	31	process	process	NOUN
ejpam-6603	106	32	can	can	AUX
ejpam-6603	106	33	extend	extend	VERB
ejpam-6603	106	34	to	to	ADP
ejpam-6603	106	35	a	a	DET
ejpam-6603	106	36	chain	chain	NOUN
ejpam-6603	106	37	of	of	ADP
ejpam-6603	106	38	co	co	VERB
ejpam-6603	106	39	-	-	ADJ
ejpam-6603	106	40	forcing	forcing	ADJ
ejpam-6603	106	41	initiated	initiate	VERB
ejpam-6603	106	42	by	by	ADP
ejpam-6603	106	43	a	a	DET
ejpam-6603	106	44	single	single	ADJ
ejpam-6603	106	45	vertex	vertex	NOUN
ejpam-6603	106	46	.	.	PUNCT
ejpam-6603	107	1	in	in	ADP
ejpam-6603	107	2	addition	addition	NOUN
ejpam-6603	107	3	,	,	PUNCT
ejpam-6603	107	4	a	a	DET
ejpam-6603	107	5	subset	subset	NOUN
ejpam-6603	107	6	b	b	NOUN
ejpam-6603	107	7	of	of	ADP
ejpam-6603	107	8	a	a	DET
ejpam-6603	107	9	vertex	vertex	NOUN
ejpam-6603	107	10	-	-	PUNCT
ejpam-6603	107	11	set	set	VERB
ejpam-6603	107	12	v	v	NOUN
ejpam-6603	107	13	(	(	PUNCT
ejpam-6603	107	14	g	g	NOUN
ejpam-6603	107	15	)	)	PUNCT
ejpam-6603	107	16	of	of	ADP
ejpam-6603	107	17	g	g	PROPN
ejpam-6603	107	18	is	be	AUX
ejpam-6603	107	19	called	call	VERB
ejpam-6603	107	20	a	a	DET
ejpam-6603	107	21	perfect	perfect	ADJ
ejpam-6603	107	22	co	co	NOUN
ejpam-6603	107	23	-	-	ADJ
ejpam-6603	107	24	zero	zero	ADJ
ejpam-6603	107	25	forcing	force	VERB
ejpam-6603	107	26	set	set	NOUN
ejpam-6603	107	27	of	of	ADP
ejpam-6603	107	28	g	g	NOUN
ejpam-6603	107	29	if	if	SCONJ
ejpam-6603	107	30	there	there	PRON
ejpam-6603	107	31	exists	exist	VERB
ejpam-6603	107	32	u	u	PROPN
ejpam-6603	107	33	∈	∈	PROPN
ejpam-6603	107	34	b	b	PROPN
ejpam-6603	107	35	such	such	ADJ
ejpam-6603	107	36	that	that	SCONJ
ejpam-6603	107	37	u	u	NOUN
ejpam-6603	107	38	perfectly	perfectly	ADV
ejpam-6603	107	39	co	co	NOUN
ejpam-6603	107	40	-	-	NOUN
ejpam-6603	107	41	forces	force	NOUN
ejpam-6603	107	42	all	all	DET
ejpam-6603	107	43	vertices	vertex	NOUN
ejpam-6603	107	44	outside	outside	ADP
ejpam-6603	107	45	b.	b.	PROPN
ejpam-6603	108	1	the	the	DET
ejpam-6603	108	2	minimum	minimum	ADJ
ejpam-6603	108	3	cardinality	cardinality	NOUN
ejpam-6603	108	4	of	of	ADP
ejpam-6603	108	5	a	a	DET
ejpam-6603	108	6	perfect	perfect	ADJ
ejpam-6603	108	7	co	co	NOUN
ejpam-6603	108	8	-	-	ADJ
ejpam-6603	108	9	zero	zero	ADJ
ejpam-6603	108	10	forcing	force	VERB
ejpam-6603	108	11	set	set	NOUN
ejpam-6603	108	12	of	of	ADP
ejpam-6603	108	13	g	g	NOUN
ejpam-6603	108	14	,	,	PUNCT
ejpam-6603	108	15	denoted	denote	VERB
ejpam-6603	108	16	by	by	ADP
ejpam-6603	108	17	zpco(g	zpco(g	NOUN
ejpam-6603	108	18	)	)	PUNCT
ejpam-6603	108	19	,	,	PUNCT
ejpam-6603	108	20	is	be	AUX
ejpam-6603	108	21	called	call	VERB
ejpam-6603	108	22	the	the	DET
ejpam-6603	108	23	perfect	perfect	ADJ
ejpam-6603	108	24	co	co	NOUN
ejpam-6603	108	25	-	-	ADJ
ejpam-6603	108	26	zero	zero	ADJ
ejpam-6603	108	27	forcing	force	VERB
ejpam-6603	108	28	number	number	NOUN
ejpam-6603	108	29	of	of	ADP
ejpam-6603	108	30	g.	g.	PROPN
ejpam-6603	108	31	lemma	lemma	PROPN
ejpam-6603	109	1	1	1	X
ejpam-6603	109	2	.	.	PUNCT
ejpam-6603	110	1	let	let	VERB
ejpam-6603	110	2	g	g	PRON
ejpam-6603	110	3	be	be	AUX
ejpam-6603	110	4	a	a	DET
ejpam-6603	110	5	non	non	ADJ
ejpam-6603	110	6	-	-	ADJ
ejpam-6603	110	7	trivial	trivial	ADJ
ejpam-6603	110	8	graph	graph	NOUN
ejpam-6603	110	9	.	.	PUNCT
ejpam-6603	111	1	if	if	SCONJ
ejpam-6603	111	2	g	g	PROPN
ejpam-6603	111	3	has	have	VERB
ejpam-6603	111	4	a	a	DET
ejpam-6603	111	5	dominating	dominating	NOUN
ejpam-6603	111	6	vertex	vertex	NOUN
ejpam-6603	111	7	,	,	PUNCT
ejpam-6603	111	8	then	then	ADV
ejpam-6603	111	9	zpco(g	zpco(g	VERB
ejpam-6603	111	10	)	)	PUNCT
ejpam-6603	111	11	≥	≥	NOUN
ejpam-6603	111	12	2	2	NUM
ejpam-6603	111	13	.	.	PUNCT
ejpam-6603	112	1	proof	proof	NOUN
ejpam-6603	112	2	.	.	PUNCT
ejpam-6603	113	1	let	let	VERB
ejpam-6603	113	2	v	v	NUM
ejpam-6603	113	3	∈	∈	PROPN
ejpam-6603	113	4	v	v	NOUN
ejpam-6603	113	5	(	(	PUNCT
ejpam-6603	113	6	g	g	NOUN
ejpam-6603	113	7	)	)	PUNCT
ejpam-6603	113	8	be	be	AUX
ejpam-6603	113	9	a	a	DET
ejpam-6603	113	10	dominating	dominating	NOUN
ejpam-6603	113	11	vertex	vertex	NOUN
ejpam-6603	113	12	of	of	ADP
ejpam-6603	113	13	g	g	NOUN
ejpam-6603	113	14	,	,	PUNCT
ejpam-6603	113	15	and	and	CCONJ
ejpam-6603	113	16	let	let	VERB
ejpam-6603	113	17	t	t	PROPN
ejpam-6603	113	18	be	be	AUX
ejpam-6603	113	19	a	a	DET
ejpam-6603	113	20	minimum	minimum	ADJ
ejpam-6603	113	21	perfect	perfect	ADJ
ejpam-6603	113	22	co	co	NOUN
ejpam-6603	113	23	-	-	ADJ
ejpam-6603	113	24	zero	zero	ADJ
ejpam-6603	113	25	forcing	force	VERB
ejpam-6603	113	26	set	set	NOUN
ejpam-6603	113	27	of	of	ADP
ejpam-6603	113	28	g.	g.	PROPN
ejpam-6603	113	29	assume	assume	VERB
ejpam-6603	113	30	that	that	SCONJ
ejpam-6603	113	31	v	v	X
ejpam-6603	113	32	/∈	/∈	PROPN
ejpam-6603	113	33	t	t	PROPN
ejpam-6603	113	34	.	.	PUNCT
ejpam-6603	114	1	then	then	ADV
ejpam-6603	114	2	there	there	PRON
ejpam-6603	114	3	must	must	AUX
ejpam-6603	114	4	be	be	AUX
ejpam-6603	114	5	a	a	DET
ejpam-6603	114	6	vertex	vertex	NOUN
ejpam-6603	114	7	w	w	PROPN
ejpam-6603	114	8	∈	∈	PROPN
ejpam-6603	114	9	t	t	PROPN
ejpam-6603	114	10	\	\	PROPN
ejpam-6603	114	11	{	{	PUNCT
ejpam-6603	114	12	v	v	NOUN
ejpam-6603	114	13	}	}	PUNCT
ejpam-6603	114	14	such	such	ADJ
ejpam-6603	114	15	that	that	SCONJ
ejpam-6603	114	16	w	w	PROPN
ejpam-6603	114	17	co	co	NOUN
ejpam-6603	114	18	-	-	NOUN
ejpam-6603	114	19	forces	force	NOUN
ejpam-6603	114	20	v	v	NOUN
ejpam-6603	114	21	,	,	PUNCT
ejpam-6603	114	22	that	that	ADV
ejpam-6603	114	23	is	is	ADV
ejpam-6603	114	24	,	,	PUNCT
ejpam-6603	114	25	dg(v	dg(v	X
ejpam-6603	114	26	,	,	PUNCT
ejpam-6603	114	27	w	w	NOUN
ejpam-6603	114	28	)	)	PUNCT
ejpam-6603	114	29	≥	≥	NOUN
ejpam-6603	114	30	2	2	NUM
ejpam-6603	114	31	.	.	PUNCT
ejpam-6603	115	1	since	since	SCONJ
ejpam-6603	115	2	v	v	NOUN
ejpam-6603	115	3	is	be	AUX
ejpam-6603	115	4	a	a	DET
ejpam-6603	115	5	dominating	dominating	NOUN
ejpam-6603	115	6	vertex	vertex	NOUN
ejpam-6603	115	7	of	of	ADP
ejpam-6603	115	8	g	g	PROPN
ejpam-6603	115	9	,	,	PUNCT
ejpam-6603	115	10	it	it	PRON
ejpam-6603	115	11	follows	follow	VERB
ejpam-6603	115	12	that	that	DET
ejpam-6603	115	13	dg(v	dg(v	PUNCT
ejpam-6603	115	14	,	,	PUNCT
ejpam-6603	115	15	u	u	NOUN
ejpam-6603	115	16	)	)	PUNCT
ejpam-6603	115	17	=	=	SYM
ejpam-6603	115	18	1	1	NUM
ejpam-6603	115	19	for	for	ADP
ejpam-6603	115	20	all	all	PRON
ejpam-6603	115	21	u	u	NOUN
ejpam-6603	115	22	∈	∈	PROPN
ejpam-6603	115	23	v	v	NOUN
ejpam-6603	115	24	(	(	PUNCT
ejpam-6603	115	25	g)\{v	g)\{v	PROPN
ejpam-6603	115	26	}	}	PUNCT
ejpam-6603	115	27	.	.	PUNCT
ejpam-6603	116	1	note	note	VERB
ejpam-6603	116	2	that	that	SCONJ
ejpam-6603	116	3	w	w	PROPN
ejpam-6603	116	4	∈	∈	PROPN
ejpam-6603	116	5	v	v	NOUN
ejpam-6603	116	6	(	(	PUNCT
ejpam-6603	116	7	g)\{v	g)\{v	PROPN
ejpam-6603	116	8	}	}	PUNCT
ejpam-6603	116	9	,	,	PUNCT
ejpam-6603	116	10	a	a	DET
ejpam-6603	116	11	contradiction	contradiction	NOUN
ejpam-6603	116	12	.	.	PUNCT
ejpam-6603	117	1	therefore	therefore	ADV
ejpam-6603	117	2	,	,	PUNCT
ejpam-6603	117	3	v	v	PROPN
ejpam-6603	117	4	∈	∈	PROPN
ejpam-6603	117	5	t	t	NOUN
ejpam-6603	117	6	.	.	PUNCT
ejpam-6603	118	1	moreover	moreover	ADV
ejpam-6603	118	2	,	,	PUNCT
ejpam-6603	118	3	since	since	SCONJ
ejpam-6603	118	4	dg(v	dg(v	NOUN
ejpam-6603	118	5	,	,	PUNCT
ejpam-6603	118	6	u	u	NOUN
ejpam-6603	118	7	)	)	PUNCT
ejpam-6603	118	8	=	=	SYM
ejpam-6603	118	9	1	1	NUM
ejpam-6603	118	10	for	for	ADP
ejpam-6603	118	11	all	all	DET
ejpam-6603	118	12	u	u	NOUN
ejpam-6603	118	13	∈	∈	PROPN
ejpam-6603	118	14	v	v	NOUN
ejpam-6603	118	15	(	(	PUNCT
ejpam-6603	118	16	g	g	NOUN
ejpam-6603	118	17	)	)	PUNCT
ejpam-6603	118	18	\	\	NOUN
ejpam-6603	118	19	{	{	PUNCT
ejpam-6603	118	20	v	v	NOUN
ejpam-6603	118	21	}	}	PUNCT
ejpam-6603	118	22	,	,	PUNCT
ejpam-6603	118	23	it	it	PRON
ejpam-6603	118	24	follows	follow	VERB
ejpam-6603	118	25	that	that	SCONJ
ejpam-6603	118	26	v	v	NOUN
ejpam-6603	118	27	can	can	AUX
ejpam-6603	118	28	not	not	PART
ejpam-6603	118	29	co	co	VERB
ejpam-6603	118	30	-	-	NOUN
ejpam-6603	118	31	force	force	VERB
ejpam-6603	118	32	any	any	DET
ejpam-6603	118	33	vertex	vertex	NOUN
ejpam-6603	118	34	u	u	NOUN
ejpam-6603	118	35	∈	∈	PROPN
ejpam-6603	118	36	v	v	NOUN
ejpam-6603	118	37	(	(	PUNCT
ejpam-6603	118	38	g)\{v	g)\{v	PROPN
ejpam-6603	118	39	}	}	PUNCT
ejpam-6603	118	40	.	.	PUNCT
ejpam-6603	119	1	thus	thus	ADV
ejpam-6603	119	2	,	,	PUNCT
ejpam-6603	119	3	there	there	PRON
ejpam-6603	119	4	must	must	AUX
ejpam-6603	119	5	be	be	AUX
ejpam-6603	119	6	another	another	DET
ejpam-6603	119	7	vertex	vertex	NOUN
ejpam-6603	119	8	t	t	PROPN
ejpam-6603	119	9	∈	∈	PROPN
ejpam-6603	119	10	t	t	PROPN
ejpam-6603	119	11	such	such	ADJ
ejpam-6603	119	12	that	that	SCONJ
ejpam-6603	119	13	t	t	PROPN
ejpam-6603	119	14	co	co	NOUN
ejpam-6603	119	15	-	-	NOUN
ejpam-6603	119	16	forces	force	NOUN
ejpam-6603	119	17	u	u	NOUN
ejpam-6603	119	18	(	(	PUNCT
ejpam-6603	119	19	possible	possible	ADJ
ejpam-6603	119	20	t	t	PROPN
ejpam-6603	119	21	=	=	SYM
ejpam-6603	119	22	u	u	NOUN
ejpam-6603	119	23	)	)	PUNCT
ejpam-6603	119	24	.	.	PUNCT
ejpam-6603	120	1	thus	thus	ADV
ejpam-6603	120	2	,	,	PUNCT
ejpam-6603	120	3	t	t	PROPN
ejpam-6603	120	4	has	have	VERB
ejpam-6603	120	5	at	at	ADV
ejpam-6603	120	6	least	least	ADV
ejpam-6603	120	7	two	two	NUM
ejpam-6603	120	8	elements	element	NOUN
ejpam-6603	120	9	,	,	PUNCT
ejpam-6603	120	10	that	that	ADV
ejpam-6603	120	11	is	is	ADV
ejpam-6603	120	12	,	,	PUNCT
ejpam-6603	120	13	zpco(g	zpco(g	PROPN
ejpam-6603	120	14	)	)	PUNCT
ejpam-6603	120	15	≥	≥	NOUN
ejpam-6603	120	16	2	2	NUM
ejpam-6603	120	17	.	.	PUNCT
ejpam-6603	120	18	j.	j.	PROPN
ejpam-6603	120	19	a.	a.	PROPN
ejpam-6603	120	20	hassan	hassan	PROPN
ejpam-6603	120	21	et	et	PROPN
ejpam-6603	120	22	al	al	PROPN
ejpam-6603	120	23	.	.	PUNCT
ejpam-6603	120	24	/	/	SYM
ejpam-6603	120	25	eur	eur	PROPN
ejpam-6603	120	26	.	.	PUNCT
ejpam-6603	121	1	j.	j.	PROPN
ejpam-6603	121	2	pure	pure	PROPN
ejpam-6603	121	3	appl	appl	PROPN
ejpam-6603	121	4	.	.	PROPN
ejpam-6603	121	5	math	math	PROPN
ejpam-6603	121	6	,	,	PUNCT
ejpam-6603	121	7	18	18	NUM
ejpam-6603	121	8	(	(	PUNCT
ejpam-6603	121	9	3	3	NUM
ejpam-6603	121	10	)	)	PUNCT
ejpam-6603	121	11	(	(	PUNCT
ejpam-6603	121	12	2025	2025	NUM
ejpam-6603	121	13	)	)	PUNCT
ejpam-6603	121	14	,	,	PUNCT
ejpam-6603	121	15	6603	6603	NUM
ejpam-6603	121	16	5	5	NUM
ejpam-6603	121	17	of	of	ADP
ejpam-6603	121	18	9	9	NUM
ejpam-6603	121	19	theorem	theorem	NOUN
ejpam-6603	121	20	3	3	NUM
ejpam-6603	121	21	.	.	PUNCT
ejpam-6603	122	1	let	let	VERB
ejpam-6603	122	2	m	m	PRON
ejpam-6603	122	3	be	be	AUX
ejpam-6603	122	4	a	a	DET
ejpam-6603	122	5	positive	positive	ADJ
ejpam-6603	122	6	integer	integer	NOUN
ejpam-6603	122	7	.	.	PUNCT
ejpam-6603	123	1	then	then	ADV
ejpam-6603	123	2	zpco(cm	zpco(cm	NOUN
ejpam-6603	123	3	)	)	PUNCT
ejpam-6603	123	4	=	=	PUNCT
ejpam-6603	123	5	{	{	PUNCT
ejpam-6603	123	6	3	3	NUM
ejpam-6603	123	7	,	,	PUNCT
ejpam-6603	123	8	if	if	SCONJ
ejpam-6603	123	9	m	m	VERB
ejpam-6603	123	10	=	=	SYM
ejpam-6603	123	11	3	3	NUM
ejpam-6603	123	12	,	,	PUNCT
ejpam-6603	123	13	4	4	NUM
ejpam-6603	123	14	m-3	m-3	NOUN
ejpam-6603	123	15	,	,	PUNCT
ejpam-6603	123	16	if	if	SCONJ
ejpam-6603	123	17	m	m	PROPN
ejpam-6603	123	18	≥	≥	NOUN
ejpam-6603	123	19	5	5	NUM
ejpam-6603	123	20	.	.	PUNCT
ejpam-6603	124	1	proof	proof	NOUN
ejpam-6603	124	2	.	.	PUNCT
ejpam-6603	125	1	since	since	SCONJ
ejpam-6603	125	2	c3	c3	PROPN
ejpam-6603	125	3	has	have	AUX
ejpam-6603	125	4	dominating	dominate	VERB
ejpam-6603	125	5	vertex	vertex	NOUN
ejpam-6603	125	6	,	,	PUNCT
ejpam-6603	125	7	it	it	PRON
ejpam-6603	125	8	follows	follow	VERB
ejpam-6603	125	9	that	that	SCONJ
ejpam-6603	125	10	zpco(c3	zpco(c3	NOUN
ejpam-6603	125	11	)	)	PUNCT
ejpam-6603	125	12	≥	≥	PROPN
ejpam-6603	125	13	2	2	NUM
ejpam-6603	125	14	by	by	ADP
ejpam-6603	125	15	lemma	lemma	PROPN
ejpam-6603	125	16	1	1	NUM
ejpam-6603	125	17	.	.	PUNCT
ejpam-6603	125	18	assume	assume	VERB
ejpam-6603	125	19	that	that	SCONJ
ejpam-6603	125	20	zpco(c3	zpco(c3	NOUN
ejpam-6603	125	21	)	)	PUNCT
ejpam-6603	125	22	=	=	SYM
ejpam-6603	125	23	2	2	NUM
ejpam-6603	125	24	,	,	PUNCT
ejpam-6603	125	25	say	say	VERB
ejpam-6603	125	26	,	,	PUNCT
ejpam-6603	125	27	q	q	X
ejpam-6603	125	28	=	=	X
ejpam-6603	125	29	{	{	PUNCT
ejpam-6603	125	30	a	a	DET
ejpam-6603	125	31	,	,	PUNCT
ejpam-6603	125	32	b	b	NOUN
ejpam-6603	125	33	}	}	PUNCT
ejpam-6603	125	34	is	be	AUX
ejpam-6603	125	35	a	a	DET
ejpam-6603	125	36	minimum	minimum	ADJ
ejpam-6603	125	37	perfect	perfect	ADJ
ejpam-6603	125	38	co	co	NOUN
ejpam-6603	125	39	-	-	ADJ
ejpam-6603	125	40	zero	zero	ADJ
ejpam-6603	125	41	forcing	force	VERB
ejpam-6603	125	42	set	set	NOUN
ejpam-6603	125	43	of	of	ADP
ejpam-6603	125	44	c3	c3	PROPN
ejpam-6603	125	45	,	,	PUNCT
ejpam-6603	125	46	where	where	SCONJ
ejpam-6603	125	47	c3	c3	PROPN
ejpam-6603	125	48	=	=	PUNCT
ejpam-6603	126	1	[	[	X
ejpam-6603	126	2	a	a	PRON
ejpam-6603	126	3	,	,	PUNCT
ejpam-6603	126	4	b	b	NOUN
ejpam-6603	126	5	,	,	PUNCT
ejpam-6603	126	6	c	c	NOUN
ejpam-6603	126	7	,	,	PUNCT
ejpam-6603	126	8	a	a	PRON
ejpam-6603	126	9	]	]	X
ejpam-6603	126	10	.	.	PUNCT
ejpam-6603	127	1	then	then	ADV
ejpam-6603	127	2	either	either	CCONJ
ejpam-6603	127	3	vertex	vertex	NOUN
ejpam-6603	127	4	a	a	PRON
ejpam-6603	127	5	or	or	CCONJ
ejpam-6603	127	6	b	b	NOUN
ejpam-6603	127	7	must	must	AUX
ejpam-6603	127	8	co	co	VERB
ejpam-6603	127	9	-	-	VERB
ejpam-6603	127	10	forced	force	VERB
ejpam-6603	127	11	vertex	vertex	NOUN
ejpam-6603	127	12	c.	c.	NOUN
ejpam-6603	127	13	that	that	PRON
ejpam-6603	127	14	is	be	AUX
ejpam-6603	127	15	,	,	PUNCT
ejpam-6603	127	16	dc3(a	dc3(a	PROPN
ejpam-6603	127	17	,	,	PUNCT
ejpam-6603	127	18	c	c	NOUN
ejpam-6603	127	19	)	)	PUNCT
ejpam-6603	127	20	≥	≥	NOUN
ejpam-6603	127	21	2	2	NUM
ejpam-6603	127	22	or	or	CCONJ
ejpam-6603	127	23	dc3(b	dc3(b	ADJ
ejpam-6603	127	24	,	,	PUNCT
ejpam-6603	127	25	c	c	NOUN
ejpam-6603	127	26	)	)	PUNCT
ejpam-6603	127	27	≥	≥	NOUN
ejpam-6603	127	28	2	2	NUM
ejpam-6603	127	29	.	.	PUNCT
ejpam-6603	128	1	however	however	ADV
ejpam-6603	128	2	,	,	PUNCT
ejpam-6603	128	3	this	this	PRON
ejpam-6603	128	4	is	be	AUX
ejpam-6603	128	5	a	a	DET
ejpam-6603	128	6	contradiction	contradiction	NOUN
ejpam-6603	128	7	to	to	ADP
ejpam-6603	128	8	the	the	DET
ejpam-6603	128	9	fact	fact	NOUN
ejpam-6603	128	10	that	that	SCONJ
ejpam-6603	128	11	each	each	DET
ejpam-6603	128	12	pair	pair	NOUN
ejpam-6603	128	13	of	of	ADP
ejpam-6603	128	14	vertices	vertex	NOUN
ejpam-6603	128	15	in	in	ADP
ejpam-6603	128	16	c3	c3	PROPN
ejpam-6603	128	17	are	be	AUX
ejpam-6603	128	18	adjacent	adjacent	ADJ
ejpam-6603	128	19	.	.	PUNCT
ejpam-6603	129	1	therefore	therefore	ADV
ejpam-6603	129	2	,	,	PUNCT
ejpam-6603	129	3	zpco(c3	zpco(c3	NOUN
ejpam-6603	129	4	)	)	PUNCT
ejpam-6603	129	5	=	=	SYM
ejpam-6603	129	6	2	2	NUM
ejpam-6603	129	7	is	be	AUX
ejpam-6603	129	8	not	not	PART
ejpam-6603	129	9	possible	possible	ADJ
ejpam-6603	129	10	.	.	PUNCT
ejpam-6603	130	1	since	since	SCONJ
ejpam-6603	130	2	v	v	PROPN
ejpam-6603	130	3	(	(	PUNCT
ejpam-6603	130	4	c3	c3	PROPN
ejpam-6603	130	5	)	)	PUNCT
ejpam-6603	130	6	is	be	AUX
ejpam-6603	130	7	a	a	DET
ejpam-6603	130	8	perfect	perfect	ADJ
ejpam-6603	130	9	co	co	NOUN
ejpam-6603	130	10	-	-	ADJ
ejpam-6603	130	11	zero	zero	ADJ
ejpam-6603	130	12	forcing	force	VERB
ejpam-6603	130	13	set	set	NOUN
ejpam-6603	130	14	of	of	ADP
ejpam-6603	130	15	c3	c3	PROPN
ejpam-6603	130	16	,	,	PUNCT
ejpam-6603	130	17	it	it	PRON
ejpam-6603	130	18	follows	follow	VERB
ejpam-6603	130	19	that	that	SCONJ
ejpam-6603	130	20	zpco(c3	zpco(c3	NOUN
ejpam-6603	130	21	)	)	PUNCT
ejpam-6603	130	22	=	=	SYM
ejpam-6603	130	23	3	3	X
ejpam-6603	130	24	.	.	X
ejpam-6603	130	25	for	for	ADP
ejpam-6603	130	26	m	m	PROPN
ejpam-6603	130	27	=	=	SYM
ejpam-6603	130	28	4	4	NUM
ejpam-6603	130	29	,	,	PUNCT
ejpam-6603	130	30	let	let	VERB
ejpam-6603	130	31	c4	c4	NOUN
ejpam-6603	130	32	=	=	PUNCT
ejpam-6603	131	1	[	[	X
ejpam-6603	131	2	v1	v1	NOUN
ejpam-6603	131	3	,	,	PUNCT
ejpam-6603	131	4	v2	v2	PROPN
ejpam-6603	131	5	,	,	PUNCT
ejpam-6603	131	6	v3	v3	PROPN
ejpam-6603	131	7	,	,	PUNCT
ejpam-6603	131	8	v4	v4	NOUN
ejpam-6603	131	9	,	,	PUNCT
ejpam-6603	131	10	v1	v1	NOUN
ejpam-6603	131	11	]	]	PUNCT
ejpam-6603	131	12	,	,	PUNCT
ejpam-6603	131	13	and	and	CCONJ
ejpam-6603	131	14	consider	consider	VERB
ejpam-6603	131	15	q′	q′	NOUN
ejpam-6603	131	16	=	=	SYM
ejpam-6603	131	17	{	{	PUNCT
ejpam-6603	131	18	v1	v1	PROPN
ejpam-6603	131	19	,	,	PUNCT
ejpam-6603	131	20	v2	v2	PROPN
ejpam-6603	131	21	,	,	PUNCT
ejpam-6603	131	22	v3	v3	PROPN
ejpam-6603	131	23	}	}	PUNCT
ejpam-6603	131	24	.	.	PUNCT
ejpam-6603	132	1	then	then	ADV
ejpam-6603	132	2	q′	q′	NOUN
ejpam-6603	132	3	is	be	AUX
ejpam-6603	132	4	a	a	DET
ejpam-6603	132	5	perfect	perfect	ADJ
ejpam-6603	132	6	co	co	NOUN
ejpam-6603	132	7	-	-	ADJ
ejpam-6603	132	8	zero	zero	ADJ
ejpam-6603	132	9	forcing	force	VERB
ejpam-6603	132	10	set	set	NOUN
ejpam-6603	132	11	of	of	ADP
ejpam-6603	132	12	c4	c4	NOUN
ejpam-6603	132	13	.	.	PUNCT
ejpam-6603	133	1	hence	hence	ADV
ejpam-6603	133	2	,	,	PUNCT
ejpam-6603	133	3	zpco(c4	zpco(c4	NOUN
ejpam-6603	133	4	)	)	PUNCT
ejpam-6603	133	5	≤	≤	NUM
ejpam-6603	133	6	3	3	NUM
ejpam-6603	133	7	.	.	X
ejpam-6603	133	8	assume	assume	VERB
ejpam-6603	133	9	that	that	SCONJ
ejpam-6603	133	10	zpco(c4	zpco(c4	NOUN
ejpam-6603	133	11	)	)	PUNCT
ejpam-6603	133	12	=	=	SYM
ejpam-6603	133	13	2	2	NUM
ejpam-6603	133	14	,	,	PUNCT
ejpam-6603	133	15	say	say	INTJ
ejpam-6603	133	16	,	,	PUNCT
ejpam-6603	133	17	a	a	DET
ejpam-6603	133	18	minimum	minimum	NOUN
ejpam-6603	133	19	perfect	perfect	ADJ
ejpam-6603	133	20	co	co	NOUN
ejpam-6603	133	21	zero	zero	NUM
ejpam-6603	133	22	forcing	force	VERB
ejpam-6603	133	23	set	set	NOUN
ejpam-6603	133	24	of	of	ADP
ejpam-6603	133	25	c4	c4	NOUN
ejpam-6603	133	26	is	be	AUX
ejpam-6603	133	27	r	r	NOUN
ejpam-6603	133	28	=	=	PUNCT
ejpam-6603	133	29	{	{	PUNCT
ejpam-6603	133	30	vi	vi	PROPN
ejpam-6603	133	31	,	,	PUNCT
ejpam-6603	133	32	vj	vj	ADJ
ejpam-6603	133	33	}	}	PUNCT
ejpam-6603	133	34	,	,	PUNCT
ejpam-6603	133	35	where	where	SCONJ
ejpam-6603	133	36	i	i	PRON
ejpam-6603	133	37	,	,	PUNCT
ejpam-6603	133	38	j	j	PROPN
ejpam-6603	133	39	∈	∈	PROPN
ejpam-6603	133	40	{	{	PUNCT
ejpam-6603	133	41	1	1	NUM
ejpam-6603	133	42	,	,	PUNCT
ejpam-6603	133	43	2	2	NUM
ejpam-6603	133	44	,	,	PUNCT
ejpam-6603	133	45	3	3	NUM
ejpam-6603	133	46	,	,	PUNCT
ejpam-6603	133	47	4	4	NUM
ejpam-6603	133	48	}	}	PUNCT
ejpam-6603	133	49	.	.	PUNCT
ejpam-6603	134	1	if	if	SCONJ
ejpam-6603	134	2	vi	vi	PROPN
ejpam-6603	134	3	and	and	CCONJ
ejpam-6603	134	4	vj	vj	PROPN
ejpam-6603	134	5	are	be	AUX
ejpam-6603	134	6	adjacent	adjacent	ADJ
ejpam-6603	134	7	,	,	PUNCT
ejpam-6603	134	8	then	then	ADV
ejpam-6603	134	9	neither	neither	CCONJ
ejpam-6603	134	10	vi	vi	NOUN
ejpam-6603	134	11	nor	nor	CCONJ
ejpam-6603	134	12	vj	vj	PROPN
ejpam-6603	134	13	can	can	AUX
ejpam-6603	134	14	co	co	VERB
ejpam-6603	134	15	-	-	VERB
ejpam-6603	134	16	force	force	VERB
ejpam-6603	134	17	all	all	DET
ejpam-6603	134	18	the	the	DET
ejpam-6603	134	19	remaining	remain	VERB
ejpam-6603	134	20	vertices	vertex	NOUN
ejpam-6603	134	21	outside	outside	ADP
ejpam-6603	134	22	r	r	NOUN
ejpam-6603	134	23	,	,	PUNCT
ejpam-6603	134	24	a	a	DET
ejpam-6603	134	25	contradiction	contradiction	NOUN
ejpam-6603	134	26	.	.	PUNCT
ejpam-6603	135	1	if	if	SCONJ
ejpam-6603	135	2	vi	vi	PROPN
ejpam-6603	135	3	and	and	CCONJ
ejpam-6603	135	4	vj	vj	PROPN
ejpam-6603	135	5	are	be	AUX
ejpam-6603	135	6	non	non	ADJ
ejpam-6603	135	7	-	-	ADJ
ejpam-6603	135	8	adjacent	adjacent	ADJ
ejpam-6603	135	9	,	,	PUNCT
ejpam-6603	135	10	then	then	ADV
ejpam-6603	135	11	the	the	DET
ejpam-6603	135	12	remaining	remain	VERB
ejpam-6603	135	13	two	two	NUM
ejpam-6603	135	14	vertices	vertex	NOUN
ejpam-6603	135	15	outside	outside	ADP
ejpam-6603	135	16	r	r	NOUN
ejpam-6603	135	17	are	be	AUX
ejpam-6603	135	18	both	both	ADV
ejpam-6603	135	19	adjacent	adjacent	ADJ
ejpam-6603	135	20	to	to	ADP
ejpam-6603	135	21	vi	vi	PROPN
ejpam-6603	135	22	and	and	CCONJ
ejpam-6603	135	23	vj	vj	INTJ
ejpam-6603	135	24	.	.	PUNCT
ejpam-6603	136	1	that	that	PRON
ejpam-6603	136	2	is	is	ADV
ejpam-6603	136	3	,	,	PUNCT
ejpam-6603	136	4	neither	neither	CCONJ
ejpam-6603	136	5	vi	vi	NOUN
ejpam-6603	136	6	nor	nor	CCONJ
ejpam-6603	136	7	vj	vj	PROPN
ejpam-6603	136	8	can	can	AUX
ejpam-6603	136	9	co	co	VERB
ejpam-6603	136	10	-	-	NOUN
ejpam-6603	136	11	force	force	VERB
ejpam-6603	136	12	these	these	DET
ejpam-6603	136	13	two	two	NUM
ejpam-6603	136	14	vertices	vertex	NOUN
ejpam-6603	136	15	.	.	PUNCT
ejpam-6603	137	1	hence	hence	ADV
ejpam-6603	137	2	,	,	PUNCT
ejpam-6603	137	3	zpco(c4	zpco(c4	NOUN
ejpam-6603	137	4	)	)	PUNCT
ejpam-6603	137	5	=	=	SYM
ejpam-6603	137	6	2	2	NUM
ejpam-6603	137	7	is	be	AUX
ejpam-6603	137	8	not	not	PART
ejpam-6603	137	9	possible	possible	ADJ
ejpam-6603	137	10	.	.	PUNCT
ejpam-6603	138	1	since	since	SCONJ
ejpam-6603	138	2	{	{	PUNCT
ejpam-6603	138	3	v1	v1	NOUN
ejpam-6603	138	4	,	,	PUNCT
ejpam-6603	138	5	v2	v2	PROPN
ejpam-6603	138	6	,	,	PUNCT
ejpam-6603	138	7	v3	v3	PROPN
ejpam-6603	138	8	}	}	PUNCT
ejpam-6603	138	9	is	be	AUX
ejpam-6603	138	10	a	a	DET
ejpam-6603	138	11	perfect	perfect	ADJ
ejpam-6603	138	12	co	co	NOUN
ejpam-6603	138	13	-	-	ADJ
ejpam-6603	138	14	zero	zero	ADJ
ejpam-6603	138	15	forcing	force	VERB
ejpam-6603	138	16	set	set	NOUN
ejpam-6603	138	17	of	of	ADP
ejpam-6603	138	18	c4	c4	NOUN
ejpam-6603	138	19	,	,	PUNCT
ejpam-6603	138	20	we	we	PRON
ejpam-6603	138	21	have	have	VERB
ejpam-6603	138	22	zpco(c4	zpco(c4	NOUN
ejpam-6603	138	23	)	)	PUNCT
ejpam-6603	138	24	=	=	SYM
ejpam-6603	139	1	3	3	X
ejpam-6603	139	2	.	.	PUNCT
ejpam-6603	139	3	now	now	ADV
ejpam-6603	139	4	,	,	PUNCT
ejpam-6603	139	5	let	let	VERB
ejpam-6603	139	6	n	n	PRON
ejpam-6603	139	7	≥	≥	X
ejpam-6603	139	8	5	5	NUM
ejpam-6603	139	9	and	and	CCONJ
ejpam-6603	139	10	cn	cn	NOUN
ejpam-6603	139	11	=	=	PUNCT
ejpam-6603	140	1	[	[	X
ejpam-6603	140	2	x1	x1	PROPN
ejpam-6603	140	3	,	,	PUNCT
ejpam-6603	140	4	x2	x2	PROPN
ejpam-6603	140	5	,	,	PUNCT
ejpam-6603	140	6	·	·	PUNCT
ejpam-6603	140	7	·	·	PUNCT
ejpam-6603	140	8	·	·	PUNCT
ejpam-6603	140	9	,	,	PUNCT
ejpam-6603	140	10	xm	xm	PROPN
ejpam-6603	140	11	,	,	PUNCT
ejpam-6603	140	12	x1	x1	PROPN
ejpam-6603	140	13	]	]	PUNCT
ejpam-6603	140	14	.	.	PUNCT
ejpam-6603	141	1	consider	consider	VERB
ejpam-6603	141	2	x	x	NOUN
ejpam-6603	141	3	=	=	PRON
ejpam-6603	141	4	{	{	PUNCT
ejpam-6603	141	5	x1	x1	PROPN
ejpam-6603	141	6	,	,	PUNCT
ejpam-6603	141	7	x3	x3	ADJ
ejpam-6603	141	8	,	,	PUNCT
ejpam-6603	141	9	x4	x4	PROPN
ejpam-6603	141	10	,	,	PUNCT
ejpam-6603	141	11	·	·	PUNCT
ejpam-6603	141	12	·	·	PUNCT
ejpam-6603	141	13	·	·	PUNCT
ejpam-6603	141	14	,	,	PUNCT
ejpam-6603	141	15	xm−2	xm−2	PROPN
ejpam-6603	141	16	}	}	PUNCT
ejpam-6603	141	17	.	.	PUNCT
ejpam-6603	142	1	then	then	ADV
ejpam-6603	142	2	vertices	vertice	VERB
ejpam-6603	142	3	xm−1	xm−1	PROPN
ejpam-6603	142	4	,	,	PUNCT
ejpam-6603	142	5	x2	x2	PROPN
ejpam-6603	142	6	and	and	CCONJ
ejpam-6603	142	7	xm	xm	PROPN
ejpam-6603	142	8	are	be	AUX
ejpam-6603	142	9	perfectly	perfectly	ADV
ejpam-6603	142	10	co	co	VERB
ejpam-6603	142	11	-	-	VERB
ejpam-6603	142	12	forced	force	VERB
ejpam-6603	142	13	by	by	ADP
ejpam-6603	142	14	vertices	vertex	NOUN
ejpam-6603	142	15	x1	x1	PROPN
ejpam-6603	142	16	.	.	PUNCT
ejpam-6603	143	1	it	it	PRON
ejpam-6603	143	2	follows	follow	VERB
ejpam-6603	143	3	that	that	SCONJ
ejpam-6603	143	4	x	x	PRON
ejpam-6603	143	5	is	be	AUX
ejpam-6603	143	6	a	a	DET
ejpam-6603	143	7	perfect	perfect	ADJ
ejpam-6603	143	8	co	co	NOUN
ejpam-6603	143	9	-	-	ADJ
ejpam-6603	143	10	zero	zero	ADJ
ejpam-6603	143	11	forcing	force	VERB
ejpam-6603	143	12	set	set	NOUN
ejpam-6603	143	13	of	of	ADP
ejpam-6603	143	14	cm	cm	PROPN
ejpam-6603	143	15	.	.	PUNCT
ejpam-6603	144	1	thus	thus	ADV
ejpam-6603	144	2	,	,	PUNCT
ejpam-6603	144	3	zpco(cm	zpco(cm	NOUN
ejpam-6603	144	4	)	)	PUNCT
ejpam-6603	144	5	≤	≤	NOUN
ejpam-6603	144	6	m−	m−	PROPN
ejpam-6603	144	7	3	3	NUM
ejpam-6603	144	8	for	for	ADP
ejpam-6603	144	9	all	all	DET
ejpam-6603	144	10	m	m	NOUN
ejpam-6603	144	11	≥	≥	NOUN
ejpam-6603	144	12	5	5	NUM
ejpam-6603	144	13	.	.	PUNCT
ejpam-6603	144	14	assume	assume	VERB
ejpam-6603	144	15	that	that	SCONJ
ejpam-6603	144	16	zpco(cm	zpco(cm	NOUN
ejpam-6603	144	17	)	)	PUNCT
ejpam-6603	144	18	≤	≤	NOUN
ejpam-6603	144	19	m−	m−	PROPN
ejpam-6603	144	20	4	4	NUM
ejpam-6603	144	21	.	.	PUNCT
ejpam-6603	145	1	then	then	ADV
ejpam-6603	145	2	there	there	PRON
ejpam-6603	145	3	are	be	VERB
ejpam-6603	145	4	at	at	ADV
ejpam-6603	145	5	least	least	ADJ
ejpam-6603	145	6	four	four	NUM
ejpam-6603	145	7	vertices	vertex	NOUN
ejpam-6603	145	8	xi	xi	PROPN
ejpam-6603	145	9	,	,	PUNCT
ejpam-6603	145	10	xj	xj	PROPN
ejpam-6603	145	11	,	,	PUNCT
ejpam-6603	145	12	xk	xk	PROPN
ejpam-6603	145	13	,	,	PUNCT
ejpam-6603	145	14	xl	xl	PROPN
ejpam-6603	145	15	∈	∈	PROPN
ejpam-6603	145	16	v	v	PROPN
ejpam-6603	145	17	(	(	PUNCT
ejpam-6603	145	18	cm	cm	NOUN
ejpam-6603	145	19	)	)	PUNCT
ejpam-6603	145	20	\n	\n	PUNCT
ejpam-6603	145	21	,	,	PUNCT
ejpam-6603	145	22	where	where	SCONJ
ejpam-6603	145	23	n	n	PRON
ejpam-6603	145	24	is	be	AUX
ejpam-6603	145	25	a	a	DET
ejpam-6603	145	26	minimum	minimum	ADJ
ejpam-6603	145	27	perfect	perfect	ADJ
ejpam-6603	145	28	co	co	NOUN
ejpam-6603	145	29	-	-	ADJ
ejpam-6603	145	30	zero	zero	NUM
ejpam-6603	145	31	forcing	force	VERB
ejpam-6603	145	32	set	set	NOUN
ejpam-6603	145	33	of	of	ADP
ejpam-6603	145	34	cm	cm	PROPN
ejpam-6603	145	35	.	.	PUNCT
ejpam-6603	146	1	since	since	SCONJ
ejpam-6603	146	2	the	the	DET
ejpam-6603	146	3	graph	graph	NOUN
ejpam-6603	146	4	is	be	AUX
ejpam-6603	146	5	cycle	cycle	NOUN
ejpam-6603	146	6	,	,	PUNCT
ejpam-6603	146	7	at	at	ADP
ejpam-6603	146	8	least	least	ADV
ejpam-6603	146	9	two	two	NUM
ejpam-6603	146	10	vertices	vertex	NOUN
ejpam-6603	146	11	in	in	ADP
ejpam-6603	146	12	{	{	PUNCT
ejpam-6603	146	13	xi	xi	PROPN
ejpam-6603	146	14	,	,	PUNCT
ejpam-6603	146	15	xj	xj	PROPN
ejpam-6603	146	16	,	,	PUNCT
ejpam-6603	146	17	xk	xk	PROPN
ejpam-6603	146	18	,	,	PUNCT
ejpam-6603	146	19	xl	xl	PROPN
ejpam-6603	146	20	}	}	PUNCT
ejpam-6603	146	21	have	have	VERB
ejpam-6603	146	22	distance	distance	NOUN
ejpam-6603	146	23	of	of	ADP
ejpam-6603	146	24	at	at	ADV
ejpam-6603	146	25	least	least	ADV
ejpam-6603	146	26	two	two	NUM
ejpam-6603	146	27	to	to	ADP
ejpam-6603	146	28	any	any	DET
ejpam-6603	146	29	vertex	vertex	NOUN
ejpam-6603	146	30	in	in	ADP
ejpam-6603	146	31	n	n	PROPN
ejpam-6603	146	32	.	.	PUNCT
ejpam-6603	147	1	that	that	PRON
ejpam-6603	147	2	is	be	AUX
ejpam-6603	147	3	,	,	PUNCT
ejpam-6603	147	4	none	none	NOUN
ejpam-6603	147	5	of	of	ADP
ejpam-6603	147	6	the	the	DET
ejpam-6603	147	7	vertices	vertex	NOUN
ejpam-6603	147	8	in	in	ADP
ejpam-6603	147	9	n	n	CCONJ
ejpam-6603	147	10	can	can	AUX
ejpam-6603	147	11	perfectly	perfectly	ADV
ejpam-6603	147	12	co	co	VERB
ejpam-6603	147	13	-	-	NOUN
ejpam-6603	147	14	forces	force	NOUN
ejpam-6603	147	15	these	these	DET
ejpam-6603	147	16	vertices	vertex	NOUN
ejpam-6603	147	17	,	,	PUNCT
ejpam-6603	147	18	which	which	PRON
ejpam-6603	147	19	is	be	AUX
ejpam-6603	147	20	a	a	DET
ejpam-6603	147	21	contradiction	contradiction	NOUN
ejpam-6603	147	22	.	.	PUNCT
ejpam-6603	148	1	in	in	ADP
ejpam-6603	148	2	this	this	DET
ejpam-6603	148	3	case	case	NOUN
ejpam-6603	148	4	,	,	PUNCT
ejpam-6603	148	5	zpco(cm	zpco(cm	NOUN
ejpam-6603	148	6	)	)	PUNCT
ejpam-6603	148	7	≤	≤	NOUN
ejpam-6603	148	8	m−	m−	PROPN
ejpam-6603	148	9	4	4	NUM
ejpam-6603	148	10	is	be	AUX
ejpam-6603	148	11	not	not	PART
ejpam-6603	148	12	possible	possible	ADJ
ejpam-6603	148	13	.	.	PUNCT
ejpam-6603	149	1	therefore	therefore	ADV
ejpam-6603	149	2	,	,	PUNCT
ejpam-6603	149	3	zpco(cm	zpco(cm	NOUN
ejpam-6603	149	4	)	)	PUNCT
ejpam-6603	149	5	=	=	PUNCT
ejpam-6603	150	1	m−	m−	PROPN
ejpam-6603	150	2	3	3	NUM
ejpam-6603	150	3	for	for	ADP
ejpam-6603	150	4	all	all	DET
ejpam-6603	150	5	m	m	NOUN
ejpam-6603	150	6	≥	≥	NOUN
ejpam-6603	150	7	5	5	NUM
ejpam-6603	150	8	.	.	PUNCT
ejpam-6603	150	9	theorem	theorem	VERB
ejpam-6603	150	10	4	4	NUM
ejpam-6603	150	11	.	.	PUNCT
ejpam-6603	151	1	let	let	VERB
ejpam-6603	151	2	n	n	PRON
ejpam-6603	151	3	be	be	AUX
ejpam-6603	151	4	a	a	DET
ejpam-6603	151	5	natural	natural	ADJ
ejpam-6603	151	6	number	number	NOUN
ejpam-6603	151	7	.	.	PUNCT
ejpam-6603	152	1	then	then	ADV
ejpam-6603	152	2	zpco(pn	zpco(pn	NUM
ejpam-6603	152	3	)	)	PUNCT
ejpam-6603	152	4	=	=	SYM
ejpam-6603	153	1			PROPN
ejpam-6603	153	2	n	n	ADV
ejpam-6603	153	3	,	,	PUNCT
ejpam-6603	153	4	if	if	SCONJ
ejpam-6603	153	5	n	n	CCONJ
ejpam-6603	153	6	=	=	SYM
ejpam-6603	153	7	1	1	NUM
ejpam-6603	153	8	,	,	PUNCT
ejpam-6603	153	9	2	2	NUM
ejpam-6603	153	10	2	2	NUM
ejpam-6603	153	11	,	,	PUNCT
ejpam-6603	153	12	if	if	SCONJ
ejpam-6603	153	13	n	n	NOUN
ejpam-6603	153	14	=	=	SYM
ejpam-6603	153	15	3	3	X
ejpam-6603	153	16	.	.	X
ejpam-6603	154	1	n-3	n-3	ADJ
ejpam-6603	154	2	,	,	PUNCT
ejpam-6603	154	3	if	if	SCONJ
ejpam-6603	154	4	n	n	PRON
ejpam-6603	154	5	≥	≥	NOUN
ejpam-6603	154	6	4	4	NUM
ejpam-6603	154	7	.	.	PUNCT
ejpam-6603	155	1	proof	proof	NOUN
ejpam-6603	155	2	.	.	PUNCT
ejpam-6603	156	1	clearly	clearly	ADV
ejpam-6603	156	2	zpco(p1	zpco(p1	X
ejpam-6603	156	3	)	)	PUNCT
ejpam-6603	156	4	=	=	SYM
ejpam-6603	156	5	1	1	NUM
ejpam-6603	156	6	and	and	CCONJ
ejpam-6603	156	7	zpco(p2	zpco(p2	ADJ
ejpam-6603	156	8	)	)	PUNCT
ejpam-6603	156	9	=	=	SYM
ejpam-6603	157	1	2	2	X
ejpam-6603	157	2	.	.	X
ejpam-6603	157	3	for	for	ADP
ejpam-6603	157	4	n	n	NOUN
ejpam-6603	157	5	=	=	SYM
ejpam-6603	157	6	3	3	NUM
ejpam-6603	157	7	,	,	PUNCT
ejpam-6603	157	8	let	let	VERB
ejpam-6603	157	9	p3	p3	PROPN
ejpam-6603	157	10	=	=	PUNCT
ejpam-6603	158	1	[	[	X
ejpam-6603	158	2	a1	a1	NOUN
ejpam-6603	158	3	,	,	PUNCT
ejpam-6603	158	4	a2	a2	PROPN
ejpam-6603	158	5	,	,	PUNCT
ejpam-6603	158	6	a3	a3	NOUN
ejpam-6603	158	7	]	]	PUNCT
ejpam-6603	158	8	.	.	PUNCT
ejpam-6603	159	1	consider	consider	VERB
ejpam-6603	159	2	s	s	PRON
ejpam-6603	159	3	=	=	NOUN
ejpam-6603	159	4	{	{	PUNCT
ejpam-6603	159	5	a1	a1	PROPN
ejpam-6603	159	6	,	,	PUNCT
ejpam-6603	159	7	a2	a2	PROPN
ejpam-6603	159	8	}	}	PUNCT
ejpam-6603	159	9	.	.	PUNCT
ejpam-6603	160	1	then	then	ADV
ejpam-6603	160	2	a3	a3	PROPN
ejpam-6603	160	3	is	be	AUX
ejpam-6603	160	4	co	co	VERB
ejpam-6603	160	5	-	-	VERB
ejpam-6603	160	6	forced	force	VERB
ejpam-6603	160	7	by	by	ADP
ejpam-6603	160	8	a	a	DET
ejpam-6603	160	9	vertex	vertex	NOUN
ejpam-6603	160	10	a1	a1	NOUN
ejpam-6603	160	11	.	.	PUNCT
ejpam-6603	161	1	thus	thus	ADV
ejpam-6603	161	2	,	,	PUNCT
ejpam-6603	161	3	s	s	VERB
ejpam-6603	161	4	is	be	AUX
ejpam-6603	161	5	a	a	DET
ejpam-6603	161	6	perfect	perfect	ADJ
ejpam-6603	161	7	co	co	NOUN
ejpam-6603	161	8	-	-	ADJ
ejpam-6603	161	9	zero	zero	ADJ
ejpam-6603	161	10	forcing	force	VERB
ejpam-6603	161	11	set	set	NOUN
ejpam-6603	161	12	of	of	ADP
ejpam-6603	161	13	p3	p3	PROPN
ejpam-6603	161	14	,	,	PUNCT
ejpam-6603	161	15	and	and	CCONJ
ejpam-6603	161	16	so	so	ADV
ejpam-6603	161	17	zpco(p3	zpco(p3	X
ejpam-6603	161	18	)	)	PUNCT
ejpam-6603	161	19	≤	≤	NUM
ejpam-6603	161	20	2	2	NUM
ejpam-6603	161	21	.	.	PUNCT
ejpam-6603	162	1	since	since	SCONJ
ejpam-6603	162	2	a2	a2	PROPN
ejpam-6603	162	3	is	be	AUX
ejpam-6603	162	4	a	a	DET
ejpam-6603	162	5	dominating	dominating	NOUN
ejpam-6603	162	6	vertex	vertex	NOUN
ejpam-6603	162	7	,	,	PUNCT
ejpam-6603	162	8	if	if	SCONJ
ejpam-6603	162	9	follows	follow	VERB
ejpam-6603	162	10	that	that	PRON
ejpam-6603	162	11	zpco(p3	zpco(p3	NOUN
ejpam-6603	162	12	)	)	PUNCT
ejpam-6603	162	13	=	=	SYM
ejpam-6603	162	14	2	2	NUM
ejpam-6603	162	15	by	by	ADP
ejpam-6603	162	16	lemma	lemma	PROPN
ejpam-6603	162	17	1	1	NUM
ejpam-6603	162	18	.	.	PUNCT
ejpam-6603	163	1	let	let	VERB
ejpam-6603	163	2	n	n	NOUN
ejpam-6603	163	3	=	=	SYM
ejpam-6603	163	4	4	4	NUM
ejpam-6603	163	5	,	,	PUNCT
ejpam-6603	163	6	and	and	CCONJ
ejpam-6603	163	7	suppose	suppose	VERB
ejpam-6603	163	8	that	that	SCONJ
ejpam-6603	163	9	p4	p4	ADJ
ejpam-6603	163	10	=	=	PUNCT
ejpam-6603	164	1	[	[	X
ejpam-6603	164	2	a1	a1	NOUN
ejpam-6603	164	3	,	,	PUNCT
ejpam-6603	164	4	a2	a2	PROPN
ejpam-6603	164	5	,	,	PUNCT
ejpam-6603	164	6	a3	a3	NOUN
ejpam-6603	164	7	,	,	PUNCT
ejpam-6603	164	8	a4	a4	PROPN
ejpam-6603	164	9	]	]	PUNCT
ejpam-6603	164	10	.	.	PUNCT
ejpam-6603	165	1	consider	consider	VERB
ejpam-6603	165	2	b	b	NOUN
ejpam-6603	165	3	=	=	SYM
ejpam-6603	165	4	{	{	PUNCT
ejpam-6603	165	5	a2	a2	PROPN
ejpam-6603	165	6	}	}	PUNCT
ejpam-6603	165	7	.	.	PUNCT
ejpam-6603	166	1	then	then	ADV
ejpam-6603	166	2	a4	a4	NUM
ejpam-6603	166	3	,	,	PUNCT
ejpam-6603	166	4	a1	a1	NOUN
ejpam-6603	166	5	and	and	CCONJ
ejpam-6603	166	6	a3	a3	NOUN
ejpam-6603	166	7	are	be	AUX
ejpam-6603	166	8	perfectly	perfectly	ADV
ejpam-6603	166	9	co	co	ADJ
ejpam-6603	166	10	-	-	VERB
ejpam-6603	166	11	forced	force	VERB
ejpam-6603	166	12	by	by	ADP
ejpam-6603	166	13	vertex	vertex	NOUN
ejpam-6603	166	14	a2	a2	PROPN
ejpam-6603	166	15	.	.	PUNCT
ejpam-6603	167	1	thus	thus	ADV
ejpam-6603	167	2	,	,	PUNCT
ejpam-6603	167	3	b	b	PROPN
ejpam-6603	167	4	is	be	AUX
ejpam-6603	167	5	a	a	DET
ejpam-6603	167	6	perfect	perfect	ADJ
ejpam-6603	167	7	co	co	NOUN
ejpam-6603	167	8	-	-	ADJ
ejpam-6603	167	9	zero	zero	ADJ
ejpam-6603	167	10	forcing	force	VERB
ejpam-6603	167	11	set	set	NOUN
ejpam-6603	167	12	of	of	ADP
ejpam-6603	167	13	p4	p4	NOUN
ejpam-6603	167	14	.	.	PUNCT
ejpam-6603	168	1	j.	j.	PROPN
ejpam-6603	168	2	a.	a.	PROPN
ejpam-6603	168	3	hassan	hassan	PROPN
ejpam-6603	168	4	et	et	PROPN
ejpam-6603	168	5	al	al	PROPN
ejpam-6603	168	6	.	.	PUNCT
ejpam-6603	168	7	/	/	SYM
ejpam-6603	168	8	eur	eur	PROPN
ejpam-6603	168	9	.	.	PUNCT
ejpam-6603	169	1	j.	j.	PROPN
ejpam-6603	169	2	pure	pure	PROPN
ejpam-6603	169	3	appl	appl	PROPN
ejpam-6603	169	4	.	.	PROPN
ejpam-6603	169	5	math	math	PROPN
ejpam-6603	169	6	,	,	PUNCT
ejpam-6603	169	7	18	18	NUM
ejpam-6603	169	8	(	(	PUNCT
ejpam-6603	169	9	3	3	NUM
ejpam-6603	169	10	)	)	PUNCT
ejpam-6603	169	11	(	(	PUNCT
ejpam-6603	169	12	2025	2025	NUM
ejpam-6603	169	13	)	)	PUNCT
ejpam-6603	169	14	,	,	PUNCT
ejpam-6603	169	15	6603	6603	NUM
ejpam-6603	169	16	6	6	NUM
ejpam-6603	169	17	of	of	ADP
ejpam-6603	169	18	9	9	NUM
ejpam-6603	169	19	hence	hence	ADV
ejpam-6603	169	20	,	,	PUNCT
ejpam-6603	169	21	zpco(p4	zpco(p4	NOUN
ejpam-6603	169	22	)	)	PUNCT
ejpam-6603	169	23	=	=	SYM
ejpam-6603	170	1	1	1	X
ejpam-6603	170	2	.	.	PUNCT
ejpam-6603	170	3	now	now	ADV
ejpam-6603	170	4	,	,	PUNCT
ejpam-6603	170	5	for	for	ADP
ejpam-6603	170	6	n	n	X
ejpam-6603	170	7	≥	≥	NUM
ejpam-6603	170	8	5	5	NUM
ejpam-6603	170	9	,	,	PUNCT
ejpam-6603	170	10	let	let	VERB
ejpam-6603	170	11	pn	pn	VERB
ejpam-6603	170	12	=	=	PUNCT
ejpam-6603	171	1	[	[	X
ejpam-6603	171	2	a1	a1	NOUN
ejpam-6603	171	3	,	,	PUNCT
ejpam-6603	171	4	a2	a2	PROPN
ejpam-6603	171	5	,	,	PUNCT
ejpam-6603	171	6	.	.	PUNCT
ejpam-6603	171	7	.	.	PUNCT
ejpam-6603	172	1	.	.	PUNCT
ejpam-6603	173	1	,	,	PUNCT
ejpam-6603	173	2	an	an	PRON
ejpam-6603	173	3	]	]	X
ejpam-6603	173	4	.	.	PUNCT
ejpam-6603	174	1	let	let	VERB
ejpam-6603	174	2	b′	b′	NOUN
ejpam-6603	174	3	=	=	SYM
ejpam-6603	174	4	{	{	PUNCT
ejpam-6603	174	5	a2	a2	PROPN
ejpam-6603	174	6	,	,	PUNCT
ejpam-6603	174	7	a5	a5	NOUN
ejpam-6603	174	8	,	,	PUNCT
ejpam-6603	174	9	a6	a6	NOUN
ejpam-6603	174	10	,	,	PUNCT
ejpam-6603	174	11	.	.	PUNCT
ejpam-6603	174	12	.	.	PUNCT
ejpam-6603	175	1	.	.	PUNCT
ejpam-6603	176	1	,	,	PUNCT
ejpam-6603	176	2	an	an	PRON
ejpam-6603	176	3	}	}	PUNCT
ejpam-6603	176	4	.	.	PUNCT
ejpam-6603	177	1	then	then	ADV
ejpam-6603	177	2	vertices	vertice	VERB
ejpam-6603	177	3	a4	a4	NOUN
ejpam-6603	177	4	,	,	PUNCT
ejpam-6603	177	5	a1	a1	NOUN
ejpam-6603	177	6	and	and	CCONJ
ejpam-6603	177	7	a3	a3	NOUN
ejpam-6603	177	8	are	be	AUX
ejpam-6603	177	9	perfectly	perfectly	ADV
ejpam-6603	177	10	co	co	ADJ
ejpam-6603	177	11	-	-	VERB
ejpam-6603	177	12	forced	force	VERB
ejpam-6603	177	13	by	by	ADP
ejpam-6603	177	14	vertex	vertex	NOUN
ejpam-6603	177	15	a2	a2	PROPN
ejpam-6603	177	16	.	.	PUNCT
ejpam-6603	178	1	thus	thus	ADV
ejpam-6603	178	2	,	,	PUNCT
ejpam-6603	178	3	b	b	X
ejpam-6603	178	4	′	′	NOUN
ejpam-6603	178	5	is	be	AUX
ejpam-6603	178	6	a	a	DET
ejpam-6603	178	7	perfect	perfect	ADJ
ejpam-6603	178	8	co	co	NOUN
ejpam-6603	178	9	-	-	ADJ
ejpam-6603	178	10	zero	zero	ADJ
ejpam-6603	178	11	forcing	force	VERB
ejpam-6603	178	12	set	set	NOUN
ejpam-6603	178	13	of	of	ADP
ejpam-6603	178	14	pn	pn	PROPN
ejpam-6603	178	15	,	,	PUNCT
ejpam-6603	178	16	and	and	CCONJ
ejpam-6603	178	17	so	so	ADV
ejpam-6603	178	18	zpco(pn	zpco(pn	ADJ
ejpam-6603	178	19	)	)	PUNCT
ejpam-6603	178	20	≤	≤	NUM
ejpam-6603	178	21	n−	n−	NOUN
ejpam-6603	178	22	3	3	NUM
ejpam-6603	178	23	.	.	PUNCT
ejpam-6603	178	24	suppose	suppose	VERB
ejpam-6603	178	25	that	that	SCONJ
ejpam-6603	178	26	zpco(pn	zpco(pn	NOUN
ejpam-6603	178	27	)	)	PUNCT
ejpam-6603	178	28	≤	≤	NUM
ejpam-6603	178	29	n−	n−	NOUN
ejpam-6603	178	30	4	4	NUM
ejpam-6603	178	31	.	.	PUNCT
ejpam-6603	179	1	then	then	ADV
ejpam-6603	179	2	there	there	PRON
ejpam-6603	179	3	exist	exist	VERB
ejpam-6603	179	4	at	at	ADV
ejpam-6603	179	5	least	least	ADJ
ejpam-6603	179	6	four	four	NUM
ejpam-6603	179	7	vertices	vertex	NOUN
ejpam-6603	179	8	ai	ai	VERB
ejpam-6603	179	9	,	,	PUNCT
ejpam-6603	179	10	aj	aj	PROPN
ejpam-6603	179	11	,	,	PUNCT
ejpam-6603	179	12	ak	ak	PROPN
ejpam-6603	179	13	and	and	CCONJ
ejpam-6603	179	14	al	al	PROPN
ejpam-6603	179	15	in	in	ADP
ejpam-6603	179	16	v	v	NUM
ejpam-6603	179	17	(	(	PUNCT
ejpam-6603	179	18	g	g	NOUN
ejpam-6603	179	19	)	)	PUNCT
ejpam-6603	179	20	such	such	ADJ
ejpam-6603	179	21	that	that	PRON
ejpam-6603	179	22	ai	ai	VERB
ejpam-6603	179	23	,	,	PUNCT
ejpam-6603	179	24	aj	aj	PROPN
ejpam-6603	179	25	,	,	PUNCT
ejpam-6603	179	26	ak	ak	PROPN
ejpam-6603	179	27	,	,	PUNCT
ejpam-6603	179	28	al	al	PROPN
ejpam-6603	179	29	/∈	/∈	PUNCT
ejpam-6603	180	1	q	q	INTJ
ejpam-6603	180	2	,	,	PUNCT
ejpam-6603	180	3	where	where	SCONJ
ejpam-6603	180	4	q	q	NOUN
ejpam-6603	180	5	is	be	AUX
ejpam-6603	180	6	minimum	minimum	ADJ
ejpam-6603	180	7	perfect	perfect	ADJ
ejpam-6603	180	8	co	co	NOUN
ejpam-6603	180	9	-	-	ADJ
ejpam-6603	180	10	zero	zero	ADJ
ejpam-6603	180	11	forcing	force	VERB
ejpam-6603	180	12	set	set	NOUN
ejpam-6603	180	13	of	of	ADP
ejpam-6603	180	14	pn	pn	PROPN
ejpam-6603	180	15	.	.	PUNCT
ejpam-6603	181	1	since	since	SCONJ
ejpam-6603	181	2	the	the	DET
ejpam-6603	181	3	graph	graph	NOUN
ejpam-6603	181	4	is	be	AUX
ejpam-6603	181	5	a	a	DET
ejpam-6603	181	6	path	path	NOUN
ejpam-6603	181	7	graph	graph	NOUN
ejpam-6603	181	8	,	,	PUNCT
ejpam-6603	181	9	at	at	ADP
ejpam-6603	181	10	least	least	ADV
ejpam-6603	181	11	two	two	NUM
ejpam-6603	181	12	vertices	vertex	NOUN
ejpam-6603	181	13	in	in	ADP
ejpam-6603	181	14	{	{	PUNCT
ejpam-6603	181	15	ai	ai	PROPN
ejpam-6603	181	16	,	,	PUNCT
ejpam-6603	181	17	aj	aj	PROPN
ejpam-6603	181	18	,	,	PUNCT
ejpam-6603	181	19	ak	ak	PROPN
ejpam-6603	181	20	,	,	PUNCT
ejpam-6603	181	21	al	al	PROPN
ejpam-6603	181	22	}	}	PUNCT
ejpam-6603	181	23	have	have	VERB
ejpam-6603	181	24	distance	distance	NOUN
ejpam-6603	181	25	two	two	NUM
ejpam-6603	181	26	to	to	ADP
ejpam-6603	181	27	every	every	DET
ejpam-6603	181	28	vertex	vertex	NOUN
ejpam-6603	181	29	in	in	ADP
ejpam-6603	181	30	q.	q.	PROPN
ejpam-6603	181	31	thus	thus	ADV
ejpam-6603	181	32	,	,	PUNCT
ejpam-6603	181	33	none	none	NOUN
ejpam-6603	181	34	of	of	ADP
ejpam-6603	181	35	the	the	DET
ejpam-6603	181	36	vertices	vertex	NOUN
ejpam-6603	181	37	in	in	ADP
ejpam-6603	181	38	q	q	PROPN
ejpam-6603	181	39	can	can	AUX
ejpam-6603	181	40	perfectly	perfectly	ADV
ejpam-6603	181	41	co	co	VERB
ejpam-6603	181	42	-	-	NOUN
ejpam-6603	181	43	forces	force	NOUN
ejpam-6603	181	44	vertices	vertice	VERB
ejpam-6603	181	45	outside	outside	ADP
ejpam-6603	181	46	q	q	NOUN
ejpam-6603	181	47	,	,	PUNCT
ejpam-6603	181	48	a	a	DET
ejpam-6603	181	49	contradiction	contradiction	NOUN
ejpam-6603	181	50	to	to	ADP
ejpam-6603	181	51	the	the	DET
ejpam-6603	181	52	fact	fact	NOUN
ejpam-6603	181	53	that	that	SCONJ
ejpam-6603	181	54	q	q	NOUN
ejpam-6603	181	55	is	be	AUX
ejpam-6603	181	56	a	a	DET
ejpam-6603	181	57	perfect	perfect	ADJ
ejpam-6603	181	58	co	co	NOUN
ejpam-6603	181	59	-	-	ADJ
ejpam-6603	181	60	zero	zero	ADJ
ejpam-6603	181	61	forcing	force	VERB
ejpam-6603	181	62	set	set	NOUN
ejpam-6603	181	63	of	of	ADP
ejpam-6603	181	64	pn	pn	PROPN
ejpam-6603	181	65	.	.	PUNCT
ejpam-6603	182	1	in	in	ADP
ejpam-6603	182	2	this	this	DET
ejpam-6603	182	3	case	case	NOUN
ejpam-6603	182	4	,	,	PUNCT
ejpam-6603	182	5	zpco(pn	zpco(pn	NUM
ejpam-6603	182	6	)	)	PUNCT
ejpam-6603	182	7	≤	≤	NUM
ejpam-6603	182	8	n−	n−	NOUN
ejpam-6603	182	9	4	4	NUM
ejpam-6603	182	10	is	be	AUX
ejpam-6603	182	11	not	not	PART
ejpam-6603	182	12	possible	possible	ADJ
ejpam-6603	182	13	.	.	PUNCT
ejpam-6603	183	1	hence	hence	ADV
ejpam-6603	183	2	,	,	PUNCT
ejpam-6603	183	3	zpco(pn	zpco(pn	NUM
ejpam-6603	183	4	)	)	PUNCT
ejpam-6603	183	5	=	=	PUNCT
ejpam-6603	183	6	n−	n−	NOUN
ejpam-6603	183	7	3	3	NUM
ejpam-6603	183	8	for	for	ADP
ejpam-6603	183	9	all	all	DET
ejpam-6603	183	10	n	n	PRON
ejpam-6603	183	11	≥	≥	NOUN
ejpam-6603	183	12	5	5	NUM
ejpam-6603	183	13	.	.	PUNCT
ejpam-6603	184	1	we	we	PRON
ejpam-6603	184	2	shall	shall	AUX
ejpam-6603	184	3	now	now	ADV
ejpam-6603	184	4	characterize	characterize	VERB
ejpam-6603	184	5	the	the	DET
ejpam-6603	184	6	perfect	perfect	ADJ
ejpam-6603	184	7	2	2	NUM
ejpam-6603	184	8	-	-	PUNCT
ejpam-6603	184	9	distance	distance	NOUN
ejpam-6603	184	10	zero	zero	NUM
ejpam-6603	184	11	forcing	force	VERB
ejpam-6603	184	12	sets	set	NOUN
ejpam-6603	184	13	in	in	ADP
ejpam-6603	184	14	the	the	DET
ejpam-6603	184	15	join	join	NOUN
ejpam-6603	184	16	of	of	ADP
ejpam-6603	184	17	two	two	NUM
ejpam-6603	184	18	graphs	graph	NOUN
ejpam-6603	184	19	as	as	SCONJ
ejpam-6603	184	20	follows	follow	VERB
ejpam-6603	184	21	:	:	PUNCT
ejpam-6603	184	22	theorem	theorem	NOUN
ejpam-6603	184	23	5	5	NUM
ejpam-6603	184	24	.	.	PUNCT
ejpam-6603	185	1	let	let	VERB
ejpam-6603	185	2	g	g	NOUN
ejpam-6603	185	3	and	and	CCONJ
ejpam-6603	185	4	h	h	NOUN
ejpam-6603	185	5	be	be	VERB
ejpam-6603	185	6	any	any	DET
ejpam-6603	185	7	two	two	NUM
ejpam-6603	185	8	graphs	graph	NOUN
ejpam-6603	185	9	.	.	PUNCT
ejpam-6603	186	1	then	then	ADV
ejpam-6603	186	2	p	p	X
ejpam-6603	186	3	⊆	⊆	NUM
ejpam-6603	186	4	v	v	NOUN
ejpam-6603	186	5	(	(	PUNCT
ejpam-6603	186	6	g+h	g+h	NOUN
ejpam-6603	186	7	)	)	PUNCT
ejpam-6603	186	8	is	be	AUX
ejpam-6603	186	9	a	a	DET
ejpam-6603	186	10	perfect	perfect	ADJ
ejpam-6603	186	11	2	2	NUM
ejpam-6603	186	12	-	-	PUNCT
ejpam-6603	186	13	distance	distance	NOUN
ejpam-6603	186	14	zero	zero	NUM
ejpam-6603	186	15	forcing	force	VERB
ejpam-6603	186	16	if	if	SCONJ
ejpam-6603	186	17	and	and	CCONJ
ejpam-6603	186	18	only	only	ADV
ejpam-6603	186	19	if	if	SCONJ
ejpam-6603	186	20	one	one	NUM
ejpam-6603	186	21	of	of	ADP
ejpam-6603	186	22	the	the	DET
ejpam-6603	186	23	following	follow	VERB
ejpam-6603	186	24	conditions	condition	NOUN
ejpam-6603	186	25	hold	hold	VERB
ejpam-6603	186	26	:	:	PUNCT
ejpam-6603	186	27	(	(	PUNCT
ejpam-6603	186	28	i	i	NOUN
ejpam-6603	186	29	)	)	PUNCT
ejpam-6603	186	30	p	p	NOUN
ejpam-6603	187	1	=	=	PUNCT
ejpam-6603	187	2	pg	pg	X
ejpam-6603	187	3	∪	∪	NOUN
ejpam-6603	187	4	v	v	PROPN
ejpam-6603	187	5	(	(	PUNCT
ejpam-6603	187	6	h	h	NOUN
ejpam-6603	187	7	)	)	PUNCT
ejpam-6603	187	8	,	,	PUNCT
ejpam-6603	187	9	where	where	SCONJ
ejpam-6603	187	10	pg	pg	PROPN
ejpam-6603	187	11	is	be	AUX
ejpam-6603	187	12	a	a	DET
ejpam-6603	187	13	perfect	perfect	ADJ
ejpam-6603	187	14	co	co	NOUN
ejpam-6603	187	15	-	-	ADJ
ejpam-6603	187	16	zero	zero	ADJ
ejpam-6603	187	17	forcing	force	VERB
ejpam-6603	187	18	set	set	NOUN
ejpam-6603	187	19	of	of	ADP
ejpam-6603	187	20	g.	g.	PROPN
ejpam-6603	187	21	(	(	PUNCT
ejpam-6603	187	22	ii	ii	PROPN
ejpam-6603	187	23	)	)	PUNCT
ejpam-6603	187	24	p	p	NOUN
ejpam-6603	187	25	=	=	SYM
ejpam-6603	187	26	v	v	X
ejpam-6603	187	27	(	(	PUNCT
ejpam-6603	187	28	g	g	NOUN
ejpam-6603	187	29	)	)	PUNCT
ejpam-6603	187	30	∪	∪	ADP
ejpam-6603	187	31	ph	ph	NOUN
ejpam-6603	187	32	such	such	ADJ
ejpam-6603	187	33	that	that	SCONJ
ejpam-6603	187	34	ph	ph	NOUN
ejpam-6603	187	35	is	be	AUX
ejpam-6603	187	36	a	a	DET
ejpam-6603	187	37	perfect	perfect	ADJ
ejpam-6603	187	38	co	co	NOUN
ejpam-6603	187	39	-	-	ADJ
ejpam-6603	187	40	zero	zero	ADJ
ejpam-6603	187	41	forcing	force	VERB
ejpam-6603	187	42	set	set	NOUN
ejpam-6603	187	43	of	of	ADP
ejpam-6603	187	44	h.	h.	NOUN
ejpam-6603	187	45	proof	proof	NOUN
ejpam-6603	187	46	.	.	PUNCT
ejpam-6603	188	1	suppose	suppose	VERB
ejpam-6603	188	2	that	that	SCONJ
ejpam-6603	188	3	p	p	PROPN
ejpam-6603	188	4	is	be	AUX
ejpam-6603	188	5	a	a	DET
ejpam-6603	188	6	perfect	perfect	ADJ
ejpam-6603	188	7	2	2	NUM
ejpam-6603	188	8	-	-	PUNCT
ejpam-6603	188	9	distance	distance	NOUN
ejpam-6603	188	10	zero	zero	NUM
ejpam-6603	188	11	forcing	force	VERB
ejpam-6603	188	12	set	set	NOUN
ejpam-6603	188	13	of	of	ADP
ejpam-6603	188	14	g	g	PROPN
ejpam-6603	188	15	+	+	CCONJ
ejpam-6603	188	16	h.	h.	PROPN
ejpam-6603	189	1	then	then	ADV
ejpam-6603	189	2	p	p	X
ejpam-6603	189	3	=	=	PUNCT
ejpam-6603	189	4	pg	pg	X
ejpam-6603	189	5	∪	∪	ADJ
ejpam-6603	189	6	ph	ph	NOUN
ejpam-6603	189	7	,	,	PUNCT
ejpam-6603	189	8	where	where	SCONJ
ejpam-6603	189	9	pg	pg	PROPN
ejpam-6603	189	10	⊆	⊆	NUM
ejpam-6603	189	11	v	v	NOUN
ejpam-6603	189	12	(	(	PUNCT
ejpam-6603	189	13	g	g	NOUN
ejpam-6603	189	14	)	)	PUNCT
ejpam-6603	189	15	and	and	CCONJ
ejpam-6603	189	16	ph	ph	VERB
ejpam-6603	189	17	⊆	⊆	NUM
ejpam-6603	189	18	v	v	NOUN
ejpam-6603	189	19	(	(	PUNCT
ejpam-6603	189	20	h	h	NOUN
ejpam-6603	189	21	)	)	PUNCT
ejpam-6603	189	22	.	.	PUNCT
ejpam-6603	190	1	if	if	SCONJ
ejpam-6603	190	2	pg	pg	NOUN
ejpam-6603	190	3	=	=	NOUN
ejpam-6603	190	4	∅	∅	NOUN
ejpam-6603	190	5	,	,	PUNCT
ejpam-6603	190	6	then	then	ADV
ejpam-6603	190	7	p	p	NOUN
ejpam-6603	190	8	=	=	NOUN
ejpam-6603	190	9	ph	ph	PROPN
ejpam-6603	190	10	.	.	PUNCT
ejpam-6603	191	1	however	however	ADV
ejpam-6603	191	2	,	,	PUNCT
ejpam-6603	191	3	ph	ph	PROPN
ejpam-6603	191	4	can	can	AUX
ejpam-6603	191	5	not	not	PART
ejpam-6603	191	6	2	2	NUM
ejpam-6603	191	7	-	-	PUNCT
ejpam-6603	191	8	force	force	NOUN
ejpam-6603	191	9	any	any	DET
ejpam-6603	191	10	vertex	vertex	NOUN
ejpam-6603	191	11	in	in	ADP
ejpam-6603	191	12	v	v	NOUN
ejpam-6603	191	13	(	(	PUNCT
ejpam-6603	191	14	g	g	NOUN
ejpam-6603	191	15	)	)	PUNCT
ejpam-6603	191	16	,	,	PUNCT
ejpam-6603	191	17	a	a	DET
ejpam-6603	191	18	contradiction	contradiction	NOUN
ejpam-6603	191	19	.	.	PUNCT
ejpam-6603	192	1	the	the	DET
ejpam-6603	192	2	same	same	ADJ
ejpam-6603	192	3	assertion	assertion	NOUN
ejpam-6603	192	4	follows	follow	VERB
ejpam-6603	192	5	when	when	SCONJ
ejpam-6603	192	6	we	we	PRON
ejpam-6603	192	7	let	let	VERB
ejpam-6603	192	8	ph	ph	NOUN
ejpam-6603	192	9	=	=	VERB
ejpam-6603	192	10	∅.	∅.	VERB
ejpam-6603	192	11	thus	thus	ADV
ejpam-6603	192	12	,	,	PUNCT
ejpam-6603	192	13	pg	pg	PROPN
ejpam-6603	192	14	̸=	̸=	PROPN
ejpam-6603	192	15	∅	∅	NOUN
ejpam-6603	192	16	and	and	CCONJ
ejpam-6603	192	17	ph	ph	PROPN
ejpam-6603	192	18	̸=	̸=	PROPN
ejpam-6603	192	19	∅.	∅.	ADV
ejpam-6603	192	20	now	now	ADV
ejpam-6603	192	21	,	,	PUNCT
ejpam-6603	192	22	if	if	SCONJ
ejpam-6603	192	23	pg	pg	VERB
ejpam-6603	192	24	⊂	⊂	PROPN
ejpam-6603	192	25	v	v	X
ejpam-6603	192	26	(	(	PUNCT
ejpam-6603	192	27	g	g	NOUN
ejpam-6603	192	28	)	)	PUNCT
ejpam-6603	192	29	and	and	CCONJ
ejpam-6603	192	30	ph	ph	PROPN
ejpam-6603	192	31	⊂	⊂	PROPN
ejpam-6603	192	32	v	v	X
ejpam-6603	192	33	(	(	PUNCT
ejpam-6603	192	34	h	h	NOUN
ejpam-6603	192	35	)	)	PUNCT
ejpam-6603	192	36	,	,	PUNCT
ejpam-6603	192	37	that	that	ADV
ejpam-6603	192	38	is	is	ADV
ejpam-6603	192	39	,	,	PUNCT
ejpam-6603	192	40	pg	pg	PROPN
ejpam-6603	192	41	and	and	CCONJ
ejpam-6603	192	42	ph	ph	NOUN
ejpam-6603	192	43	are	be	AUX
ejpam-6603	192	44	proper	proper	ADJ
ejpam-6603	192	45	subsets	subset	NOUN
ejpam-6603	192	46	of	of	ADP
ejpam-6603	192	47	v	v	NOUN
ejpam-6603	192	48	(	(	PUNCT
ejpam-6603	192	49	g	g	NOUN
ejpam-6603	192	50	)	)	PUNCT
ejpam-6603	192	51	and	and	CCONJ
ejpam-6603	192	52	v	v	NOUN
ejpam-6603	192	53	(	(	PUNCT
ejpam-6603	192	54	h	h	NOUN
ejpam-6603	192	55	)	)	PUNCT
ejpam-6603	192	56	,	,	PUNCT
ejpam-6603	192	57	respectively	respectively	ADV
ejpam-6603	192	58	.	.	PUNCT
ejpam-6603	193	1	then	then	ADV
ejpam-6603	193	2	there	there	PRON
ejpam-6603	193	3	exist	exist	VERB
ejpam-6603	193	4	x	x	SYM
ejpam-6603	193	5	∈	∈	PROPN
ejpam-6603	193	6	v	v	ADP
ejpam-6603	193	7	(	(	PUNCT
ejpam-6603	193	8	g	g	NOUN
ejpam-6603	193	9	)	)	PUNCT
ejpam-6603	193	10	\	\	NOUN
ejpam-6603	193	11	pg	pg	NOUN
ejpam-6603	193	12	and	and	CCONJ
ejpam-6603	193	13	y	y	PROPN
ejpam-6603	193	14	∈	∈	PROPN
ejpam-6603	193	15	v	v	ADP
ejpam-6603	193	16	(	(	PUNCT
ejpam-6603	193	17	h	h	NOUN
ejpam-6603	193	18	)	)	PUNCT
ejpam-6603	193	19	\	\	PROPN
ejpam-6603	193	20	ph	ph	PROPN
ejpam-6603	193	21	.	.	PUNCT
ejpam-6603	194	1	notice	notice	VERB
ejpam-6603	194	2	that	that	SCONJ
ejpam-6603	194	3	,	,	PUNCT
ejpam-6603	194	4	vertex	vertex	NOUN
ejpam-6603	194	5	x	x	PUNCT
ejpam-6603	194	6	can	can	AUX
ejpam-6603	194	7	only	only	ADV
ejpam-6603	194	8	be	be	AUX
ejpam-6603	194	9	2	2	NUM
ejpam-6603	194	10	-	-	PUNCT
ejpam-6603	194	11	forced	force	VERB
ejpam-6603	194	12	by	by	ADP
ejpam-6603	194	13	a	a	DET
ejpam-6603	194	14	vertex	vertex	NOUN
ejpam-6603	194	15	in	in	ADP
ejpam-6603	194	16	pg	pg	PROPN
ejpam-6603	195	1	⊆	⊆	NUM
ejpam-6603	195	2	v	v	NOUN
ejpam-6603	195	3	(	(	PUNCT
ejpam-6603	195	4	g	g	NOUN
ejpam-6603	195	5	)	)	PUNCT
ejpam-6603	195	6	,	,	PUNCT
ejpam-6603	195	7	and	and	CCONJ
ejpam-6603	195	8	vertex	vertex	NOUN
ejpam-6603	195	9	y	y	PROPN
ejpam-6603	195	10	can	can	AUX
ejpam-6603	195	11	only	only	ADV
ejpam-6603	195	12	be	be	AUX
ejpam-6603	195	13	2	2	NUM
ejpam-6603	195	14	-	-	PUNCT
ejpam-6603	195	15	forced	force	VERB
ejpam-6603	195	16	by	by	ADP
ejpam-6603	195	17	a	a	DET
ejpam-6603	195	18	vertex	vertex	NOUN
ejpam-6603	195	19	in	in	ADP
ejpam-6603	195	20	ph	ph	PROPN
ejpam-6603	195	21	⊆	⊆	NUM
ejpam-6603	195	22	v	v	NOUN
ejpam-6603	195	23	(	(	PUNCT
ejpam-6603	195	24	h	h	NOUN
ejpam-6603	195	25	)	)	PUNCT
ejpam-6603	195	26	.	.	PUNCT
ejpam-6603	196	1	thus	thus	ADV
ejpam-6603	196	2	,	,	PUNCT
ejpam-6603	196	3	none	none	NOUN
ejpam-6603	196	4	of	of	ADP
ejpam-6603	196	5	the	the	DET
ejpam-6603	196	6	vertices	vertex	NOUN
ejpam-6603	196	7	in	in	ADP
ejpam-6603	196	8	p	p	PROPN
ejpam-6603	196	9	can	can	AUX
ejpam-6603	196	10	perfectly	perfectly	ADV
ejpam-6603	196	11	2	2	NUM
ejpam-6603	196	12	-	-	PUNCT
ejpam-6603	196	13	forces	force	NOUN
ejpam-6603	196	14	both	both	CCONJ
ejpam-6603	196	15	x	x	NOUN
ejpam-6603	196	16	and	and	CCONJ
ejpam-6603	196	17	y	y	PROPN
ejpam-6603	196	18	,	,	PUNCT
ejpam-6603	196	19	a	a	DET
ejpam-6603	196	20	contradiction	contradiction	NOUN
ejpam-6603	196	21	to	to	ADP
ejpam-6603	196	22	our	our	PRON
ejpam-6603	196	23	assumption	assumption	NOUN
ejpam-6603	196	24	that	that	SCONJ
ejpam-6603	196	25	p	p	NOUN
ejpam-6603	196	26	is	be	AUX
ejpam-6603	196	27	a	a	DET
ejpam-6603	196	28	perfect	perfect	ADJ
ejpam-6603	196	29	2	2	NUM
ejpam-6603	196	30	-	-	PUNCT
ejpam-6603	196	31	distance	distance	NOUN
ejpam-6603	196	32	zero	zero	NUM
ejpam-6603	196	33	forcing	force	VERB
ejpam-6603	196	34	set	set	NOUN
ejpam-6603	196	35	of	of	ADP
ejpam-6603	196	36	g	g	PROPN
ejpam-6603	196	37	+	+	PROPN
ejpam-6603	196	38	h.	h.	PROPN
ejpam-6603	196	39	hence	hence	ADV
ejpam-6603	196	40	,	,	PUNCT
ejpam-6603	196	41	the	the	DET
ejpam-6603	196	42	remaining	remain	VERB
ejpam-6603	196	43	cases	case	NOUN
ejpam-6603	196	44	are	be	AUX
ejpam-6603	196	45	either	either	CCONJ
ejpam-6603	196	46	p	p	X
ejpam-6603	196	47	=	=	X
ejpam-6603	196	48	pg	pg	X
ejpam-6603	196	49	∪	∪	NOUN
ejpam-6603	196	50	v	v	PROPN
ejpam-6603	196	51	(	(	PUNCT
ejpam-6603	196	52	h	h	NOUN
ejpam-6603	196	53	)	)	PUNCT
ejpam-6603	196	54	or	or	CCONJ
ejpam-6603	196	55	p	p	X
ejpam-6603	196	56	=	=	X
ejpam-6603	196	57	v	v	X
ejpam-6603	196	58	(	(	PUNCT
ejpam-6603	196	59	g	g	NOUN
ejpam-6603	196	60	)	)	PUNCT
ejpam-6603	196	61	∪	∪	NOUN
ejpam-6603	196	62	ph	ph	NOUN
ejpam-6603	196	63	where	where	SCONJ
ejpam-6603	196	64	pg	pg	PROPN
ejpam-6603	196	65	⊆	⊆	NUM
ejpam-6603	196	66	v	v	NOUN
ejpam-6603	196	67	(	(	PUNCT
ejpam-6603	196	68	g	g	NOUN
ejpam-6603	196	69	)	)	PUNCT
ejpam-6603	196	70	and	and	CCONJ
ejpam-6603	196	71	ph	ph	VERB
ejpam-6603	196	72	⊆	⊆	NUM
ejpam-6603	196	73	v	v	NOUN
ejpam-6603	196	74	(	(	PUNCT
ejpam-6603	196	75	h	h	NOUN
ejpam-6603	196	76	)	)	PUNCT
ejpam-6603	196	77	.	.	PUNCT
ejpam-6603	197	1	assume	assume	VERB
ejpam-6603	197	2	that	that	SCONJ
ejpam-6603	197	3	p	p	PRON
ejpam-6603	197	4	=	=	PUNCT
ejpam-6603	197	5	pg	pg	X
ejpam-6603	197	6	∪	∪	NOUN
ejpam-6603	197	7	v	v	PROPN
ejpam-6603	197	8	(	(	PUNCT
ejpam-6603	197	9	h	h	NOUN
ejpam-6603	197	10	)	)	PUNCT
ejpam-6603	197	11	.	.	PUNCT
ejpam-6603	198	1	suppose	suppose	VERB
ejpam-6603	198	2	on	on	ADP
ejpam-6603	198	3	the	the	DET
ejpam-6603	198	4	contrary	contrary	NOUN
ejpam-6603	198	5	that	that	PRON
ejpam-6603	198	6	pg	pg	VERB
ejpam-6603	198	7	is	be	AUX
ejpam-6603	198	8	not	not	PART
ejpam-6603	198	9	a	a	DET
ejpam-6603	198	10	perfect	perfect	ADJ
ejpam-6603	198	11	cozero	cozero	NOUN
ejpam-6603	198	12	forcing	force	VERB
ejpam-6603	198	13	set	set	NOUN
ejpam-6603	198	14	of	of	ADP
ejpam-6603	198	15	g.	g.	PROPN
ejpam-6603	198	16	then	then	ADV
ejpam-6603	198	17	there	there	PRON
ejpam-6603	198	18	exists	exist	VERB
ejpam-6603	198	19	y	y	PROPN
ejpam-6603	198	20	∈	∈	PROPN
ejpam-6603	198	21	v	v	ADP
ejpam-6603	198	22	(	(	PUNCT
ejpam-6603	198	23	g	g	NOUN
ejpam-6603	198	24	)	)	PUNCT
ejpam-6603	198	25	\	\	NOUN
ejpam-6603	199	1	pg	pg	AUX
ejpam-6603	199	2	such	such	ADJ
ejpam-6603	199	3	that	that	SCONJ
ejpam-6603	199	4	y	y	PROPN
ejpam-6603	199	5	can	can	AUX
ejpam-6603	199	6	not	not	PART
ejpam-6603	199	7	be	be	AUX
ejpam-6603	199	8	perfectly	perfectly	ADV
ejpam-6603	199	9	co	co	VERB
ejpam-6603	199	10	-	-	VERB
ejpam-6603	199	11	forced	force	VERB
ejpam-6603	199	12	by	by	ADP
ejpam-6603	199	13	any	any	DET
ejpam-6603	199	14	vertex	vertex	NOUN
ejpam-6603	199	15	in	in	ADP
ejpam-6603	199	16	pg	pg	NOUN
ejpam-6603	199	17	under	under	ADP
ejpam-6603	199	18	the	the	DET
ejpam-6603	199	19	graph	graph	NOUN
ejpam-6603	199	20	g.	g.	NOUN
ejpam-6603	200	1	this	this	PRON
ejpam-6603	200	2	means	mean	VERB
ejpam-6603	200	3	that	that	SCONJ
ejpam-6603	200	4	y	y	PROPN
ejpam-6603	200	5	can	can	AUX
ejpam-6603	200	6	not	not	PART
ejpam-6603	200	7	be	be	AUX
ejpam-6603	200	8	perfectly	perfectly	ADV
ejpam-6603	200	9	2forced	2force	VERB
ejpam-6603	200	10	by	by	ADP
ejpam-6603	200	11	any	any	DET
ejpam-6603	200	12	vertex	vertex	NOUN
ejpam-6603	200	13	in	in	ADP
ejpam-6603	200	14	pg	pg	NOUN
ejpam-6603	200	15	under	under	ADP
ejpam-6603	200	16	the	the	DET
ejpam-6603	200	17	graph	graph	NOUN
ejpam-6603	200	18	g+h	g+h	PROPN
ejpam-6603	200	19	.	.	PUNCT
ejpam-6603	201	1	however	however	ADV
ejpam-6603	201	2	,	,	PUNCT
ejpam-6603	201	3	this	this	PRON
ejpam-6603	201	4	is	be	AUX
ejpam-6603	201	5	a	a	DET
ejpam-6603	201	6	contradiction	contradiction	NOUN
ejpam-6603	201	7	to	to	ADP
ejpam-6603	201	8	our	our	PRON
ejpam-6603	201	9	assumption	assumption	NOUN
ejpam-6603	201	10	that	that	SCONJ
ejpam-6603	201	11	p	p	NOUN
ejpam-6603	201	12	is	be	AUX
ejpam-6603	201	13	a	a	DET
ejpam-6603	201	14	2	2	NUM
ejpam-6603	201	15	-	-	PUNCT
ejpam-6603	201	16	distance	distance	NOUN
ejpam-6603	201	17	zero	zero	NUM
ejpam-6603	201	18	forcing	force	VERB
ejpam-6603	201	19	set	set	NOUN
ejpam-6603	201	20	of	of	ADP
ejpam-6603	201	21	g	g	PROPN
ejpam-6603	201	22	+	+	PROPN
ejpam-6603	201	23	h.	h.	PROPN
ejpam-6603	201	24	hence	hence	ADV
ejpam-6603	201	25	,	,	PUNCT
ejpam-6603	201	26	pg	pg	PROPN
ejpam-6603	201	27	is	be	AUX
ejpam-6603	201	28	a	a	DET
ejpam-6603	201	29	perfect	perfect	ADJ
ejpam-6603	201	30	co	co	NOUN
ejpam-6603	201	31	-	-	ADJ
ejpam-6603	201	32	zero	zero	ADJ
ejpam-6603	201	33	forcing	forcing	NOUN
ejpam-6603	201	34	set	set	NOUN
ejpam-6603	201	35	in	in	ADP
ejpam-6603	201	36	g	g	NOUN
ejpam-6603	201	37	,	,	PUNCT
ejpam-6603	201	38	and	and	CCONJ
ejpam-6603	201	39	so	so	ADV
ejpam-6603	201	40	(	(	PUNCT
ejpam-6603	201	41	i	i	NOUN
ejpam-6603	201	42	)	)	PUNCT
ejpam-6603	201	43	holds	hold	VERB
ejpam-6603	201	44	.	.	PUNCT
ejpam-6603	202	1	j.	j.	PROPN
ejpam-6603	202	2	a.	a.	PROPN
ejpam-6603	202	3	hassan	hassan	PROPN
ejpam-6603	202	4	et	et	PROPN
ejpam-6603	202	5	al	al	PROPN
ejpam-6603	202	6	.	.	PUNCT
ejpam-6603	202	7	/	/	SYM
ejpam-6603	202	8	eur	eur	PROPN
ejpam-6603	202	9	.	.	PUNCT
ejpam-6603	203	1	j.	j.	PROPN
ejpam-6603	203	2	pure	pure	PROPN
ejpam-6603	203	3	appl	appl	PROPN
ejpam-6603	203	4	.	.	PROPN
ejpam-6603	203	5	math	math	PROPN
ejpam-6603	203	6	,	,	PUNCT
ejpam-6603	203	7	18	18	NUM
ejpam-6603	203	8	(	(	PUNCT
ejpam-6603	203	9	3	3	NUM
ejpam-6603	203	10	)	)	PUNCT
ejpam-6603	203	11	(	(	PUNCT
ejpam-6603	203	12	2025	2025	NUM
ejpam-6603	203	13	)	)	PUNCT
ejpam-6603	203	14	,	,	PUNCT
ejpam-6603	203	15	6603	6603	NUM
ejpam-6603	203	16	7	7	NUM
ejpam-6603	203	17	of	of	ADP
ejpam-6603	203	18	9	9	NUM
ejpam-6603	203	19	similarly	similarly	ADV
ejpam-6603	203	20	,	,	PUNCT
ejpam-6603	203	21	ph	ph	PROPN
ejpam-6603	203	22	is	be	AUX
ejpam-6603	203	23	a	a	DET
ejpam-6603	203	24	perfect	perfect	ADJ
ejpam-6603	203	25	co	co	NOUN
ejpam-6603	203	26	-	-	ADJ
ejpam-6603	203	27	zero	zero	ADJ
ejpam-6603	203	28	forcing	forcing	NOUN
ejpam-6603	203	29	set	set	NOUN
ejpam-6603	203	30	in	in	ADP
ejpam-6603	203	31	h	h	NOUN
ejpam-6603	203	32	when	when	SCONJ
ejpam-6603	203	33	p	p	PROPN
ejpam-6603	203	34	=	=	PROPN
ejpam-6603	203	35	v	v	X
ejpam-6603	203	36	(	(	PUNCT
ejpam-6603	203	37	g	g	NOUN
ejpam-6603	203	38	)	)	PUNCT
ejpam-6603	203	39	∪	∪	NOUN
ejpam-6603	203	40	ph	ph	NOUN
ejpam-6603	203	41	.	.	PUNCT
ejpam-6603	204	1	that	that	ADV
ejpam-6603	204	2	is	is	ADV
ejpam-6603	204	3	,	,	PUNCT
ejpam-6603	204	4	(	(	PUNCT
ejpam-6603	204	5	ii	ii	NOUN
ejpam-6603	204	6	)	)	PUNCT
ejpam-6603	204	7	holds	hold	VERB
ejpam-6603	204	8	.	.	PUNCT
ejpam-6603	205	1	conversely	conversely	ADV
ejpam-6603	205	2	,	,	PUNCT
ejpam-6603	205	3	suppose	suppose	VERB
ejpam-6603	205	4	that	that	SCONJ
ejpam-6603	205	5	p	p	PRON
ejpam-6603	205	6	=	=	PUNCT
ejpam-6603	205	7	pg	pg	X
ejpam-6603	205	8	∪	∪	NOUN
ejpam-6603	205	9	v	v	PROPN
ejpam-6603	205	10	(	(	PUNCT
ejpam-6603	205	11	h	h	NOUN
ejpam-6603	205	12	)	)	PUNCT
ejpam-6603	205	13	,	,	PUNCT
ejpam-6603	205	14	where	where	SCONJ
ejpam-6603	205	15	pg	pg	PROPN
ejpam-6603	205	16	is	be	AUX
ejpam-6603	205	17	a	a	DET
ejpam-6603	205	18	perfect	perfect	ADJ
ejpam-6603	205	19	co	co	NOUN
ejpam-6603	205	20	-	-	ADJ
ejpam-6603	205	21	zero	zero	ADJ
ejpam-6603	205	22	forcing	force	VERB
ejpam-6603	205	23	set	set	NOUN
ejpam-6603	205	24	of	of	ADP
ejpam-6603	205	25	g.	g.	PROPN
ejpam-6603	205	26	then	then	ADV
ejpam-6603	205	27	there	there	PRON
ejpam-6603	205	28	exists	exist	VERB
ejpam-6603	205	29	x	x	X
ejpam-6603	205	30	∈	∈	PROPN
ejpam-6603	205	31	pg	pg	VERB
ejpam-6603	205	32	such	such	ADJ
ejpam-6603	205	33	that	that	SCONJ
ejpam-6603	205	34	x	x	PUNCT
ejpam-6603	205	35	perfectly	perfectly	ADV
ejpam-6603	205	36	co	co	NOUN
ejpam-6603	205	37	-	-	NOUN
ejpam-6603	205	38	forces	force	NOUN
ejpam-6603	205	39	other	other	ADJ
ejpam-6603	205	40	vertices	vertex	NOUN
ejpam-6603	205	41	outside	outside	ADP
ejpam-6603	205	42	pg	pg	NOUN
ejpam-6603	205	43	in	in	ADP
ejpam-6603	205	44	g.	g.	PROPN
ejpam-6603	205	45	this	this	PRON
ejpam-6603	205	46	means	mean	VERB
ejpam-6603	205	47	that	that	SCONJ
ejpam-6603	205	48	x	x	PRON
ejpam-6603	205	49	can	can	AUX
ejpam-6603	205	50	perfectly	perfectly	ADV
ejpam-6603	205	51	2	2	NUM
ejpam-6603	205	52	-	-	PUNCT
ejpam-6603	205	53	forces	force	NOUN
ejpam-6603	205	54	other	other	ADJ
ejpam-6603	205	55	vertices	vertex	NOUN
ejpam-6603	205	56	outside	outside	ADP
ejpam-6603	205	57	p	p	NOUN
ejpam-6603	205	58	in	in	ADP
ejpam-6603	205	59	g+h	g+h	PROPN
ejpam-6603	205	60	.	.	PUNCT
ejpam-6603	206	1	it	it	PRON
ejpam-6603	206	2	follows	follow	VERB
ejpam-6603	206	3	that	that	SCONJ
ejpam-6603	206	4	p	p	PRON
ejpam-6603	206	5	=	=	PUNCT
ejpam-6603	206	6	pg	pg	NOUN
ejpam-6603	206	7	∪v	∪v	NOUN
ejpam-6603	206	8	(	(	PUNCT
ejpam-6603	206	9	h	h	NOUN
ejpam-6603	206	10	)	)	PUNCT
ejpam-6603	206	11	is	be	AUX
ejpam-6603	206	12	a	a	DET
ejpam-6603	206	13	perfect	perfect	ADJ
ejpam-6603	206	14	2	2	NUM
ejpam-6603	206	15	-	-	PUNCT
ejpam-6603	206	16	distance	distance	NOUN
ejpam-6603	206	17	zero	zero	NUM
ejpam-6603	206	18	forcing	force	VERB
ejpam-6603	206	19	set	set	NOUN
ejpam-6603	206	20	of	of	ADP
ejpam-6603	206	21	g+h	g+h	PROPN
ejpam-6603	206	22	.	.	PUNCT
ejpam-6603	207	1	similarly	similarly	ADV
ejpam-6603	207	2	,	,	PUNCT
ejpam-6603	207	3	the	the	DET
ejpam-6603	207	4	same	same	ADJ
ejpam-6603	207	5	assertion	assertion	NOUN
ejpam-6603	207	6	follows	follow	VERB
ejpam-6603	207	7	when	when	SCONJ
ejpam-6603	207	8	(	(	PUNCT
ejpam-6603	207	9	ii	ii	NOUN
ejpam-6603	207	10	)	)	PUNCT
ejpam-6603	207	11	holds	hold	VERB
ejpam-6603	207	12	.	.	PUNCT
ejpam-6603	208	1	theorem	theorem	NOUN
ejpam-6603	208	2	6	6	NUM
ejpam-6603	208	3	.	.	PUNCT
ejpam-6603	209	1	let	let	VERB
ejpam-6603	209	2	g	g	NOUN
ejpam-6603	210	1	and	and	CCONJ
ejpam-6603	210	2	h	h	NOUN
ejpam-6603	210	3	be	be	VERB
ejpam-6603	210	4	any	any	DET
ejpam-6603	210	5	graphs	graph	NOUN
ejpam-6603	210	6	.	.	PUNCT
ejpam-6603	211	1	then	then	ADV
ejpam-6603	211	2	z2	z2	PROPN
ejpam-6603	211	3	p(g+h	p(g+h	NOUN
ejpam-6603	211	4	)	)	PUNCT
ejpam-6603	211	5	=	=	SYM
ejpam-6603	211	6	min{zpco(g	min{zpco(g	PROPN
ejpam-6603	211	7	)	)	PUNCT
ejpam-6603	211	8	+	+	CCONJ
ejpam-6603	211	9	|v	|v	PROPN
ejpam-6603	211	10	(	(	PUNCT
ejpam-6603	211	11	h)|	h)|	PROPN
ejpam-6603	211	12	,	,	PUNCT
ejpam-6603	211	13	|v	|v	PROPN
ejpam-6603	211	14	(	(	PUNCT
ejpam-6603	211	15	g)|+	g)|+	NOUN
ejpam-6603	211	16	zpco(h	zpco(h	NOUN
ejpam-6603	211	17	)	)	PUNCT
ejpam-6603	211	18	}	}	PUNCT
ejpam-6603	211	19	.	.	PUNCT
ejpam-6603	212	1	proof	proof	NOUN
ejpam-6603	212	2	.	.	PUNCT
ejpam-6603	213	1	let	let	VERB
ejpam-6603	213	2	p	p	PRON
ejpam-6603	213	3	be	be	AUX
ejpam-6603	213	4	a	a	DET
ejpam-6603	213	5	minimum	minimum	NOUN
ejpam-6603	213	6	perfect	perfect	ADJ
ejpam-6603	213	7	2	2	NUM
ejpam-6603	213	8	-	-	PUNCT
ejpam-6603	213	9	distance	distance	NOUN
ejpam-6603	213	10	zero	zero	NUM
ejpam-6603	213	11	forcing	force	VERB
ejpam-6603	213	12	set	set	NOUN
ejpam-6603	213	13	of	of	ADP
ejpam-6603	213	14	g	g	PROPN
ejpam-6603	213	15	+	+	CCONJ
ejpam-6603	213	16	h.	h.	PROPN
ejpam-6603	213	17	then	then	ADV
ejpam-6603	213	18	by	by	ADP
ejpam-6603	213	19	theorem	theorem	NOUN
ejpam-6603	213	20	4	4	NUM
ejpam-6603	213	21	,	,	PUNCT
ejpam-6603	213	22	either	either	CCONJ
ejpam-6603	213	23	p	p	PROPN
ejpam-6603	213	24	=	=	PROPN
ejpam-6603	213	25	pg∪v	pg∪v	PROPN
ejpam-6603	213	26	(	(	PUNCT
ejpam-6603	213	27	h	h	NOUN
ejpam-6603	213	28	)	)	PUNCT
ejpam-6603	213	29	or	or	CCONJ
ejpam-6603	213	30	p	p	X
ejpam-6603	213	31	=	=	X
ejpam-6603	213	32	v	v	NOUN
ejpam-6603	213	33	(	(	PUNCT
ejpam-6603	213	34	g)∪ph	g)∪ph	NOUN
ejpam-6603	213	35	where	where	SCONJ
ejpam-6603	213	36	pg	pg	NOUN
ejpam-6603	213	37	and	and	CCONJ
ejpam-6603	213	38	ph	ph	NOUN
ejpam-6603	213	39	are	be	AUX
ejpam-6603	213	40	perfect	perfect	ADJ
ejpam-6603	213	41	co	co	ADJ
ejpam-6603	213	42	-	-	ADJ
ejpam-6603	213	43	zero	zero	ADJ
ejpam-6603	213	44	forcing	force	VERB
ejpam-6603	213	45	sets	set	NOUN
ejpam-6603	213	46	of	of	ADP
ejpam-6603	213	47	g	g	PROPN
ejpam-6603	213	48	and	and	CCONJ
ejpam-6603	213	49	h	h	NOUN
ejpam-6603	213	50	,	,	PUNCT
ejpam-6603	213	51	respectively	respectively	ADV
ejpam-6603	213	52	.	.	PUNCT
ejpam-6603	214	1	hence	hence	ADV
ejpam-6603	214	2	,	,	PUNCT
ejpam-6603	214	3	either	either	CCONJ
ejpam-6603	214	4	z2	z2	PROPN
ejpam-6603	214	5	p(g+h	p(g+h	NOUN
ejpam-6603	214	6	)	)	PUNCT
ejpam-6603	214	7	=	=	PRON
ejpam-6603	214	8	|p	|p	NOUN
ejpam-6603	214	9	|	|	ADV
ejpam-6603	214	10	≥	≥	X
ejpam-6603	214	11	zpco(g	zpco(g	VERB
ejpam-6603	214	12	)	)	PUNCT
ejpam-6603	214	13	+	+	CCONJ
ejpam-6603	214	14	|v	|v	X
ejpam-6603	214	15	(	(	PUNCT
ejpam-6603	214	16	h)|	h)|	NOUN
ejpam-6603	214	17	or	or	CCONJ
ejpam-6603	214	18	z2	z2	PROPN
ejpam-6603	214	19	p(g+h	p(g+h	NOUN
ejpam-6603	214	20	)	)	PUNCT
ejpam-6603	214	21	=	=	PRON
ejpam-6603	214	22	|p	|p	NOUN
ejpam-6603	214	23	|	|	ADV
ejpam-6603	214	24	≥	≥	NOUN
ejpam-6603	214	25	|v	|v	PROPN
ejpam-6603	214	26	(	(	PUNCT
ejpam-6603	214	27	g)|+	g)|+	NOUN
ejpam-6603	214	28	zpco(h	zpco(h	PROPN
ejpam-6603	214	29	)	)	PUNCT
ejpam-6603	214	30	.	.	PUNCT
ejpam-6603	215	1	now	now	ADV
ejpam-6603	215	2	,	,	PUNCT
ejpam-6603	215	3	suppose	suppose	VERB
ejpam-6603	215	4	that	that	SCONJ
ejpam-6603	215	5	either	either	CCONJ
ejpam-6603	215	6	p	p	X
ejpam-6603	215	7	=	=	X
ejpam-6603	215	8	pg	pg	X
ejpam-6603	215	9	∪	∪	NOUN
ejpam-6603	215	10	v	v	PROPN
ejpam-6603	215	11	(	(	PUNCT
ejpam-6603	215	12	h	h	NOUN
ejpam-6603	215	13	)	)	PUNCT
ejpam-6603	215	14	or	or	CCONJ
ejpam-6603	215	15	p	p	X
ejpam-6603	215	16	=	=	X
ejpam-6603	215	17	v	v	X
ejpam-6603	215	18	(	(	PUNCT
ejpam-6603	215	19	g	g	NOUN
ejpam-6603	215	20	)	)	PUNCT
ejpam-6603	215	21	∪	∪	NOUN
ejpam-6603	215	22	ph	ph	NOUN
ejpam-6603	215	23	,	,	PUNCT
ejpam-6603	215	24	where	where	SCONJ
ejpam-6603	215	25	pg	pg	NOUN
ejpam-6603	215	26	and	and	CCONJ
ejpam-6603	215	27	ph	ph	NOUN
ejpam-6603	215	28	are	be	AUX
ejpam-6603	215	29	minimum	minimum	ADJ
ejpam-6603	215	30	perfect	perfect	ADJ
ejpam-6603	215	31	co	co	ADJ
ejpam-6603	215	32	-	-	ADJ
ejpam-6603	215	33	zero	zero	ADJ
ejpam-6603	215	34	forcing	force	VERB
ejpam-6603	215	35	sets	set	NOUN
ejpam-6603	215	36	of	of	ADP
ejpam-6603	215	37	g	g	PROPN
ejpam-6603	215	38	and	and	CCONJ
ejpam-6603	215	39	h	h	NOUN
ejpam-6603	215	40	,	,	PUNCT
ejpam-6603	215	41	respectively	respectively	ADV
ejpam-6603	215	42	.	.	PUNCT
ejpam-6603	216	1	then	then	ADV
ejpam-6603	216	2	p	p	NOUN
ejpam-6603	216	3	is	be	AUX
ejpam-6603	216	4	a	a	DET
ejpam-6603	216	5	perfect	perfect	ADJ
ejpam-6603	216	6	2	2	NUM
ejpam-6603	216	7	-	-	PUNCT
ejpam-6603	216	8	distance	distance	NOUN
ejpam-6603	216	9	zero	zero	NUM
ejpam-6603	216	10	forcing	force	VERB
ejpam-6603	216	11	set	set	NOUN
ejpam-6603	216	12	of	of	ADP
ejpam-6603	216	13	g+h	g+h	PROPN
ejpam-6603	216	14	by	by	ADP
ejpam-6603	216	15	theorem	theorem	NOUN
ejpam-6603	216	16	4	4	NUM
ejpam-6603	216	17	.	.	PUNCT
ejpam-6603	217	1	thus	thus	ADV
ejpam-6603	217	2	,	,	PUNCT
ejpam-6603	217	3	either	either	CCONJ
ejpam-6603	217	4	z2	z2	PROPN
ejpam-6603	217	5	p(g+h	p(g+h	NOUN
ejpam-6603	217	6	)	)	PUNCT
ejpam-6603	217	7	≤	≤	NOUN
ejpam-6603	217	8	|p	|p	NOUN
ejpam-6603	217	9	|	|	NOUN
ejpam-6603	217	10	=	=	SYM
ejpam-6603	217	11	zpco(g	zpco(g	X
ejpam-6603	217	12	)	)	PUNCT
ejpam-6603	217	13	+	+	CCONJ
ejpam-6603	217	14	|v	|v	X
ejpam-6603	217	15	(	(	PUNCT
ejpam-6603	217	16	h)|	h)|	NOUN
ejpam-6603	217	17	or	or	CCONJ
ejpam-6603	217	18	z2	z2	PROPN
ejpam-6603	217	19	p(g+h	p(g+h	NOUN
ejpam-6603	217	20	)	)	PUNCT
ejpam-6603	217	21	≤	≤	NOUN
ejpam-6603	217	22	|p	|p	NOUN
ejpam-6603	217	23	|	|	NOUN
ejpam-6603	217	24	=	=	SYM
ejpam-6603	217	25	zpco(h	zpco(h	NUM
ejpam-6603	217	26	)	)	PUNCT
ejpam-6603	217	27	+	+	CCONJ
ejpam-6603	217	28	|v	|v	PROPN
ejpam-6603	217	29	(	(	PUNCT
ejpam-6603	217	30	g)|	g)|	NOUN
ejpam-6603	217	31	.	.	PUNCT
ejpam-6603	218	1	hence	hence	ADV
ejpam-6603	218	2	,	,	PUNCT
ejpam-6603	218	3	z2	z2	PROPN
ejpam-6603	218	4	p(g+h	p(g+h	NOUN
ejpam-6603	218	5	)	)	PUNCT
ejpam-6603	218	6	=	=	SYM
ejpam-6603	218	7	zpco(g	zpco(g	X
ejpam-6603	218	8	)	)	PUNCT
ejpam-6603	219	1	+	+	CCONJ
ejpam-6603	219	2	|v	|v	X
ejpam-6603	219	3	(	(	PUNCT
ejpam-6603	219	4	h)|	h)|	NOUN
ejpam-6603	219	5	or	or	CCONJ
ejpam-6603	219	6	z2	z2	PROPN
ejpam-6603	219	7	p(g+h	p(g+h	PROPN
ejpam-6603	219	8	)	)	PUNCT
ejpam-6603	219	9	=	=	SYM
ejpam-6603	219	10	zpco(h	zpco(h	NOUN
ejpam-6603	219	11	)	)	PUNCT
ejpam-6603	220	1	+	+	CCONJ
ejpam-6603	220	2	|v	|v	PROPN
ejpam-6603	220	3	(	(	PUNCT
ejpam-6603	220	4	g)|	g)|	NOUN
ejpam-6603	220	5	.	.	PUNCT
ejpam-6603	221	1	consequently	consequently	ADV
ejpam-6603	221	2	,	,	PUNCT
ejpam-6603	221	3	z2	z2	PROPN
ejpam-6603	221	4	p(g+h	p(g+h	NOUN
ejpam-6603	221	5	)	)	PUNCT
ejpam-6603	221	6	=	=	SYM
ejpam-6603	221	7	min{zpco(g	min{zpco(g	PROPN
ejpam-6603	221	8	)	)	PUNCT
ejpam-6603	222	1	+	+	CCONJ
ejpam-6603	222	2	|v	|v	PROPN
ejpam-6603	222	3	(	(	PUNCT
ejpam-6603	222	4	h)|	h)|	PROPN
ejpam-6603	222	5	,	,	PUNCT
ejpam-6603	222	6	|v	|v	PROPN
ejpam-6603	222	7	(	(	PUNCT
ejpam-6603	222	8	g)|+	g)|+	NOUN
ejpam-6603	222	9	zpco(h	zpco(h	NOUN
ejpam-6603	222	10	)	)	PUNCT
ejpam-6603	222	11	}	}	PUNCT
ejpam-6603	222	12	.	.	PUNCT
ejpam-6603	223	1	corollary	corollary	ADJ
ejpam-6603	223	2	1	1	NUM
ejpam-6603	223	3	.	.	PUNCT
ejpam-6603	224	1	let	let	VERB
ejpam-6603	224	2	n	n	PRON
ejpam-6603	224	3	and	and	CCONJ
ejpam-6603	224	4	m	m	AUX
ejpam-6603	224	5	be	be	AUX
ejpam-6603	224	6	a	a	DET
ejpam-6603	224	7	natural	natural	ADJ
ejpam-6603	224	8	numbers	number	NOUN
ejpam-6603	224	9	.	.	PUNCT
ejpam-6603	225	1	then	then	ADV
ejpam-6603	225	2	each	each	PRON
ejpam-6603	225	3	of	of	ADP
ejpam-6603	225	4	the	the	DET
ejpam-6603	225	5	following	follow	VERB
ejpam-6603	225	6	holds	hold	VERB
ejpam-6603	225	7	:	:	PUNCT
ejpam-6603	225	8	(	(	PUNCT
ejpam-6603	225	9	i	i	NOUN
ejpam-6603	225	10	)	)	PUNCT
ejpam-6603	225	11	z2	z2	PROPN
ejpam-6603	225	12	p(sn	p(sn	PROPN
ejpam-6603	225	13	)	)	PUNCT
ejpam-6603	225	14	=	=	SYM
ejpam-6603	225	15	z2	z2	NOUN
ejpam-6603	225	16	p(k1	p(k1	NOUN
ejpam-6603	225	17	+	+	X
ejpam-6603	225	18	k̄n	k̄n	PROPN
ejpam-6603	225	19	)	)	PUNCT
ejpam-6603	225	20	=	=	PRON
ejpam-6603	225	21	{	{	PUNCT
ejpam-6603	225	22	n+	n+	NOUN
ejpam-6603	225	23	1	1	NUM
ejpam-6603	225	24	,	,	PUNCT
ejpam-6603	225	25	if	if	SCONJ
ejpam-6603	225	26	n	n	CCONJ
ejpam-6603	225	27	=	=	SYM
ejpam-6603	225	28	1	1	NUM
ejpam-6603	225	29	n	n	CCONJ
ejpam-6603	225	30	,	,	PUNCT
ejpam-6603	225	31	if	if	SCONJ
ejpam-6603	225	32	n	n	PRON
ejpam-6603	225	33	≥	≥	NOUN
ejpam-6603	225	34	2	2	NUM
ejpam-6603	225	35	.	.	PUNCT
ejpam-6603	225	36	(	(	PUNCT
ejpam-6603	225	37	ii	ii	NOUN
ejpam-6603	225	38	)	)	PUNCT
ejpam-6603	225	39	z2	z2	PROPN
ejpam-6603	225	40	p(wn	p(wn	PROPN
ejpam-6603	225	41	)	)	PUNCT
ejpam-6603	225	42	=	=	SYM
ejpam-6603	225	43	z2	z2	NUM
ejpam-6603	225	44	p(k1	p(k1	NOUN
ejpam-6603	225	45	+	+	X
ejpam-6603	225	46	cn	cn	NOUN
ejpam-6603	225	47	)	)	PUNCT
ejpam-6603	225	48	=	=	PRON
ejpam-6603	225	49	{	{	PUNCT
ejpam-6603	225	50	4	4	NUM
ejpam-6603	225	51	,	,	PUNCT
ejpam-6603	225	52	if	if	SCONJ
ejpam-6603	225	53	n	n	CCONJ
ejpam-6603	225	54	=	=	SYM
ejpam-6603	225	55	3	3	NUM
ejpam-6603	225	56	,	,	PUNCT
ejpam-6603	225	57	4	4	NUM
ejpam-6603	225	58	n−	n−	NOUN
ejpam-6603	225	59	2	2	NUM
ejpam-6603	225	60	,	,	PUNCT
ejpam-6603	225	61	if	if	SCONJ
ejpam-6603	225	62	n	n	PRON
ejpam-6603	225	63	≥	≥	NOUN
ejpam-6603	225	64	5	5	NUM
ejpam-6603	225	65	.	.	PUNCT
ejpam-6603	225	66	j.	j.	PROPN
ejpam-6603	225	67	a.	a.	PROPN
ejpam-6603	225	68	hassan	hassan	PROPN
ejpam-6603	225	69	et	et	PROPN
ejpam-6603	225	70	al	al	PROPN
ejpam-6603	225	71	.	.	PUNCT
ejpam-6603	225	72	/	/	SYM
ejpam-6603	225	73	eur	eur	PROPN
ejpam-6603	225	74	.	.	PUNCT
ejpam-6603	226	1	j.	j.	PROPN
ejpam-6603	226	2	pure	pure	PROPN
ejpam-6603	226	3	appl	appl	PROPN
ejpam-6603	226	4	.	.	PROPN
ejpam-6603	226	5	math	math	PROPN
ejpam-6603	226	6	,	,	PUNCT
ejpam-6603	226	7	18	18	NUM
ejpam-6603	226	8	(	(	PUNCT
ejpam-6603	226	9	3	3	NUM
ejpam-6603	226	10	)	)	PUNCT
ejpam-6603	226	11	(	(	PUNCT
ejpam-6603	226	12	2025	2025	NUM
ejpam-6603	226	13	)	)	PUNCT
ejpam-6603	226	14	,	,	PUNCT
ejpam-6603	226	15	6603	6603	NUM
ejpam-6603	226	16	8	8	NUM
ejpam-6603	226	17	of	of	ADP
ejpam-6603	226	18	9	9	NUM
ejpam-6603	226	19	(	(	PUNCT
ejpam-6603	226	20	iii	iii	NOUN
ejpam-6603	226	21	)	)	PUNCT
ejpam-6603	226	22	z2	z2	NOUN
ejpam-6603	226	23	p(fn	p(fn	NOUN
ejpam-6603	226	24	)	)	PUNCT
ejpam-6603	226	25	=	=	SYM
ejpam-6603	226	26	z2	z2	NUM
ejpam-6603	226	27	p(k1	p(k1	NOUN
ejpam-6603	226	28	+	+	CCONJ
ejpam-6603	226	29	pn	pn	NOUN
ejpam-6603	226	30	)	)	PUNCT
ejpam-6603	226	31	=	=	PUNCT
ejpam-6603	227	1			PRON
ejpam-6603	227	2	n+	n+	ADP
ejpam-6603	227	3	1	1	NUM
ejpam-6603	227	4	,	,	PUNCT
ejpam-6603	227	5	if	if	SCONJ
ejpam-6603	227	6	n	n	CCONJ
ejpam-6603	227	7	=	=	SYM
ejpam-6603	227	8	1	1	NUM
ejpam-6603	227	9	,	,	PUNCT
ejpam-6603	227	10	2	2	NUM
ejpam-6603	227	11	3	3	NUM
ejpam-6603	227	12	,	,	PUNCT
ejpam-6603	227	13	if	if	SCONJ
ejpam-6603	227	14	n	n	NOUN
ejpam-6603	227	15	=	=	SYM
ejpam-6603	227	16	3	3	X
ejpam-6603	227	17	.	.	X
ejpam-6603	227	18	n−	n−	NOUN
ejpam-6603	227	19	2	2	NUM
ejpam-6603	227	20	,	,	PUNCT
ejpam-6603	227	21	if	if	SCONJ
ejpam-6603	227	22	n	n	PRON
ejpam-6603	227	23	≥	≥	NOUN
ejpam-6603	227	24	4	4	NUM
ejpam-6603	227	25	.	.	PUNCT
ejpam-6603	227	26	(	(	PUNCT
ejpam-6603	227	27	iv	iv	X
ejpam-6603	227	28	)	)	PUNCT
ejpam-6603	227	29	z2	z2	PROPN
ejpam-6603	227	30	p(km	p(km	PROPN
ejpam-6603	227	31	,	,	PUNCT
ejpam-6603	227	32	n	n	CCONJ
ejpam-6603	227	33	)	)	PUNCT
ejpam-6603	227	34	=	=	SYM
ejpam-6603	227	35	z2	z2	PROPN
ejpam-6603	227	36	p(k̄m	p(k̄m	NOUN
ejpam-6603	227	37	+	+	CCONJ
ejpam-6603	227	38	k̄n	k̄n	PROPN
ejpam-6603	227	39	)	)	PUNCT
ejpam-6603	227	40	=	=	PUNCT
ejpam-6603	228	1			NOUN
ejpam-6603	228	2	2	2	NUM
ejpam-6603	228	3	,	,	PUNCT
ejpam-6603	228	4	if	if	SCONJ
ejpam-6603	228	5	m	m	VERB
ejpam-6603	228	6	=	=	SYM
ejpam-6603	228	7	n	n	NOUN
ejpam-6603	228	8	=	=	SYM
ejpam-6603	228	9	1	1	NUM
ejpam-6603	228	10	m+	m+	NUM
ejpam-6603	228	11	n−	n−	NOUN
ejpam-6603	228	12	1	1	NUM
ejpam-6603	228	13	,	,	PUNCT
ejpam-6603	228	14	if	if	SCONJ
ejpam-6603	228	15	2	2	NUM
ejpam-6603	228	16	≤	≤	NUM
ejpam-6603	228	17	m	m	VERB
ejpam-6603	228	18	≤	≤	NOUN
ejpam-6603	228	19	n	n	DET
ejpam-6603	228	20	or	or	CCONJ
ejpam-6603	228	21	2	2	NUM
ejpam-6603	228	22	≤	≤	NUM
ejpam-6603	228	23	n	n	PRON
ejpam-6603	228	24	≤	≤	NOUN
ejpam-6603	228	25	m.	m.	NOUN
ejpam-6603	228	26	n	n	CCONJ
ejpam-6603	228	27	,	,	PUNCT
ejpam-6603	228	28	if	if	SCONJ
ejpam-6603	228	29	m	m	VERB
ejpam-6603	228	30	=	=	SYM
ejpam-6603	228	31	1	1	NUM
ejpam-6603	228	32	and	and	CCONJ
ejpam-6603	228	33	n	n	PRON
ejpam-6603	228	34	≥	≥	NOUN
ejpam-6603	228	35	2	2	NUM
ejpam-6603	228	36	.	.	NOUN
ejpam-6603	228	37	4	4	NUM
ejpam-6603	228	38	.	.	X
ejpam-6603	228	39	conclusion	conclusion	NOUN
ejpam-6603	228	40	perfect	perfect	VERB
ejpam-6603	228	41	2	2	NUM
ejpam-6603	228	42	-	-	PUNCT
ejpam-6603	228	43	distance	distance	NOUN
ejpam-6603	228	44	zero	zero	NUM
ejpam-6603	228	45	forcing	forcing	NOUN
ejpam-6603	228	46	,	,	PUNCT
ejpam-6603	228	47	a	a	DET
ejpam-6603	228	48	new	new	ADJ
ejpam-6603	228	49	variant	variant	NOUN
ejpam-6603	228	50	of	of	ADP
ejpam-6603	228	51	zero	zero	NUM
ejpam-6603	228	52	forcing	forcing	NOUN
ejpam-6603	228	53	has	have	AUX
ejpam-6603	228	54	been	be	AUX
ejpam-6603	228	55	introduced	introduce	VERB
ejpam-6603	228	56	and	and	CCONJ
ejpam-6603	228	57	studied	study	VERB
ejpam-6603	228	58	in	in	ADP
ejpam-6603	228	59	this	this	DET
ejpam-6603	228	60	paper	paper	NOUN
ejpam-6603	228	61	.	.	PUNCT
ejpam-6603	229	1	it	it	PRON
ejpam-6603	229	2	is	be	AUX
ejpam-6603	229	3	observed	observe	VERB
ejpam-6603	229	4	that	that	SCONJ
ejpam-6603	229	5	every	every	DET
ejpam-6603	229	6	graph	graph	NOUN
ejpam-6603	229	7	admits	admit	VERB
ejpam-6603	229	8	perfect	perfect	ADJ
ejpam-6603	229	9	2	2	NUM
ejpam-6603	229	10	-	-	PUNCT
ejpam-6603	229	11	distance	distance	NOUN
ejpam-6603	229	12	zero	zero	NUM
ejpam-6603	229	13	forcing	forcing	NOUN
ejpam-6603	229	14	.	.	PUNCT
ejpam-6603	230	1	it	it	PRON
ejpam-6603	230	2	is	be	AUX
ejpam-6603	230	3	shown	show	VERB
ejpam-6603	230	4	that	that	SCONJ
ejpam-6603	230	5	the	the	DET
ejpam-6603	230	6	parameter	parameter	NOUN
ejpam-6603	230	7	for	for	ADP
ejpam-6603	230	8	a	a	DET
ejpam-6603	230	9	perfect	perfect	ADJ
ejpam-6603	230	10	2	2	NUM
ejpam-6603	230	11	-	-	PUNCT
ejpam-6603	230	12	distance	distance	NOUN
ejpam-6603	230	13	zero	zero	NUM
ejpam-6603	230	14	forcing	forcing	NOUN
ejpam-6603	230	15	is	be	AUX
ejpam-6603	230	16	always	always	ADV
ejpam-6603	230	17	greater	great	ADJ
ejpam-6603	230	18	than	than	ADP
ejpam-6603	230	19	the	the	DET
ejpam-6603	230	20	parameter	parameter	NOUN
ejpam-6603	230	21	for	for	ADP
ejpam-6603	230	22	standard	standard	ADJ
ejpam-6603	230	23	2	2	NUM
ejpam-6603	230	24	-	-	PUNCT
ejpam-6603	230	25	distance	distance	NOUN
ejpam-6603	230	26	zero	zero	NUM
ejpam-6603	230	27	forcing	force	VERB
ejpam-6603	230	28	on	on	ADP
ejpam-6603	230	29	any	any	DET
ejpam-6603	230	30	simple	simple	ADJ
ejpam-6603	230	31	and	and	CCONJ
ejpam-6603	230	32	undirected	undirected	ADJ
ejpam-6603	230	33	graph	graph	NOUN
ejpam-6603	230	34	.	.	PUNCT
ejpam-6603	231	1	moreover	moreover	ADV
ejpam-6603	231	2	,	,	PUNCT
ejpam-6603	231	3	a	a	DET
ejpam-6603	231	4	certain	certain	ADJ
ejpam-6603	231	5	variant	variant	NOUN
ejpam-6603	231	6	of	of	ADP
ejpam-6603	231	7	zero	zero	NUM
ejpam-6603	231	8	forcing	force	VERB
ejpam-6603	231	9	called	call	VERB
ejpam-6603	231	10	perfect	perfect	ADJ
ejpam-6603	231	11	co	co	NOUN
ejpam-6603	231	12	-	-	ADJ
ejpam-6603	231	13	zero	zero	ADJ
ejpam-6603	231	14	forcing	forcing	NOUN
ejpam-6603	231	15	was	be	AUX
ejpam-6603	231	16	defined	define	VERB
ejpam-6603	231	17	to	to	PART
ejpam-6603	231	18	solve	solve	VERB
ejpam-6603	231	19	the	the	DET
ejpam-6603	231	20	perfect	perfect	ADJ
ejpam-6603	231	21	2	2	NUM
ejpam-6603	231	22	-	-	PUNCT
ejpam-6603	231	23	distance	distance	NOUN
ejpam-6603	231	24	zero	zero	NUM
ejpam-6603	231	25	forcing	force	VERB
ejpam-6603	231	26	number	number	NOUN
ejpam-6603	231	27	of	of	ADP
ejpam-6603	231	28	the	the	DET
ejpam-6603	231	29	join	join	NOUN
ejpam-6603	231	30	of	of	ADP
ejpam-6603	231	31	any	any	DET
ejpam-6603	231	32	two	two	NUM
ejpam-6603	231	33	graphs	graph	NOUN
ejpam-6603	231	34	.	.	PUNCT
ejpam-6603	232	1	acknowledgements	acknowledgement	NOUN
ejpam-6603	232	2	the	the	DET
ejpam-6603	232	3	author	author	NOUN
ejpam-6603	232	4	would	would	AUX
ejpam-6603	232	5	like	like	VERB
ejpam-6603	232	6	to	to	PART
ejpam-6603	232	7	thank	thank	VERB
ejpam-6603	232	8	mindanao	mindanao	PROPN
ejpam-6603	232	9	state	state	PROPN
ejpam-6603	232	10	university	university	PROPN
ejpam-6603	232	11	tawi	tawi	PROPN
ejpam-6603	232	12	-	-	PUNCT
ejpam-6603	232	13	tawi	tawi	PROPN
ejpam-6603	232	14	college	college	PROPN
ejpam-6603	232	15	of	of	ADP
ejpam-6603	232	16	technology	technology	NOUN
ejpam-6603	232	17	and	and	CCONJ
ejpam-6603	232	18	oceanography	oceanography	NOUN
ejpam-6603	232	19	,	,	PUNCT
ejpam-6603	232	20	korea	korea	PROPN
ejpam-6603	232	21	university	university	PROPN
ejpam-6603	232	22	,	,	PUNCT
ejpam-6603	232	23	and	and	CCONJ
ejpam-6603	232	24	ateneo	ateneo	PROPN
ejpam-6603	232	25	de	de	PROPN
ejpam-6603	232	26	davao	davao	PROPN
ejpam-6603	232	27	university	university	PROPN
ejpam-6603	232	28	for	for	ADP
ejpam-6603	232	29	funding	fund	VERB
ejpam-6603	232	30	this	this	DET
ejpam-6603	232	31	research	research	NOUN
ejpam-6603	232	32	.	.	PUNCT
ejpam-6603	233	1	references	reference	NOUN
ejpam-6603	233	2	[	[	X
ejpam-6603	233	3	1	1	NUM
ejpam-6603	233	4	]	]	PUNCT
ejpam-6603	233	5	f.	f.	NOUN
ejpam-6603	233	6	barioli	barioli	PROPN
ejpam-6603	233	7	,	,	PUNCT
ejpam-6603	233	8	w.	w.	PROPN
ejpam-6603	233	9	barrett	barrett	PROPN
ejpam-6603	233	10	,	,	PUNCT
ejpam-6603	233	11	s.	s.	PROPN
ejpam-6603	233	12	fallat	fallat	PROPN
ejpam-6603	233	13	,	,	PUNCT
ejpam-6603	233	14	h.	h.	PROPN
ejpam-6603	233	15	hall	hall	PROPN
ejpam-6603	233	16	,	,	PUNCT
ejpam-6603	233	17	l.	l.	PROPN
ejpam-6603	233	18	hogben	hogben	PROPN
ejpam-6603	233	19	,	,	PUNCT
ejpam-6603	233	20	h.	h.	PROPN
ejpam-6603	233	21	van	van	PROPN
ejpam-6603	233	22	der	der	PROPN
ejpam-6603	233	23	holst	holst	NOUN
ejpam-6603	233	24	,	,	PUNCT
ejpam-6603	233	25	and	and	CCONJ
ejpam-6603	233	26	b.	b.	PROPN
ejpam-6603	233	27	shader	shader	NOUN
ejpam-6603	233	28	.	.	PUNCT
ejpam-6603	234	1	zero	zero	NUM
ejpam-6603	234	2	forcing	force	VERB
ejpam-6603	234	3	parameters	parameter	NOUN
ejpam-6603	234	4	and	and	CCONJ
ejpam-6603	234	5	minimum	minimum	ADJ
ejpam-6603	234	6	rank	rank	NOUN
ejpam-6603	234	7	problems	problem	NOUN
ejpam-6603	234	8	.	.	PUNCT
ejpam-6603	235	1	linear	linear	ADJ
ejpam-6603	235	2	algebra	algebra	NOUN
ejpam-6603	235	3	and	and	CCONJ
ejpam-6603	235	4	its	its	PRON
ejpam-6603	235	5	applications	application	NOUN
ejpam-6603	235	6	,	,	PUNCT
ejpam-6603	235	7	433:401–411	433:401–411	NUM
ejpam-6603	235	8	,	,	PUNCT
ejpam-6603	235	9	2010	2010	NUM
ejpam-6603	235	10	.	.	PUNCT
ejpam-6603	236	1	[	[	X
ejpam-6603	236	2	2	2	X
ejpam-6603	236	3	]	]	PUNCT
ejpam-6603	236	4	k.	k.	PROPN
ejpam-6603	236	5	benson	benson	PROPN
ejpam-6603	236	6	,	,	PUNCT
ejpam-6603	236	7	d.	d.	PROPN
ejpam-6603	236	8	ferrero	ferrero	PROPN
ejpam-6603	236	9	,	,	PUNCT
ejpam-6603	236	10	m.	m.	PROPN
ejpam-6603	236	11	flagg	flagg	PROPN
ejpam-6603	236	12	,	,	PUNCT
ejpam-6603	236	13	v.	v.	PROPN
ejpam-6603	236	14	furst	furst	PROPN
ejpam-6603	236	15	,	,	PUNCT
ejpam-6603	236	16	l.	l.	PROPN
ejpam-6603	236	17	hogben	hogben	PROPN
ejpam-6603	236	18	,	,	PUNCT
ejpam-6603	236	19	v.	v.	ADP
ejpam-6603	236	20	vasilevska	vasilevska	NOUN
ejpam-6603	236	21	,	,	PUNCT
ejpam-6603	236	22	and	and	CCONJ
ejpam-6603	236	23	b.	b.	PROPN
ejpam-6603	236	24	wissman	wissman	NOUN
ejpam-6603	236	25	.	.	PUNCT
ejpam-6603	237	1	zero	zero	NUM
ejpam-6603	237	2	forcing	forcing	NOUN
ejpam-6603	237	3	and	and	CCONJ
ejpam-6603	237	4	power	power	NOUN
ejpam-6603	237	5	domination	domination	NOUN
ejpam-6603	237	6	for	for	ADP
ejpam-6603	237	7	graph	graph	NOUN
ejpam-6603	237	8	products	product	NOUN
ejpam-6603	237	9	.	.	PUNCT
ejpam-6603	238	1	australasian	australasian	ADJ
ejpam-6603	238	2	journal	journal	NOUN
ejpam-6603	238	3	of	of	ADP
ejpam-6603	238	4	combinatorics	combinatoric	NOUN
ejpam-6603	238	5	,	,	PUNCT
ejpam-6603	238	6	70:221–235	70:221–235	PROPN
ejpam-6603	238	7	,	,	PUNCT
ejpam-6603	238	8	2018	2018	NUM
ejpam-6603	238	9	.	.	PUNCT
ejpam-6603	239	1	[	[	X
ejpam-6603	239	2	3	3	X
ejpam-6603	239	3	]	]	X
ejpam-6603	239	4	r.	r.	PROPN
ejpam-6603	239	5	davila	davila	PROPN
ejpam-6603	239	6	,	,	PUNCT
ejpam-6603	239	7	t.	t.	PROPN
ejpam-6603	239	8	kalinowski	kalinowski	PROPN
ejpam-6603	239	9	,	,	PUNCT
ejpam-6603	239	10	and	and	CCONJ
ejpam-6603	239	11	s.	s.	PROPN
ejpam-6603	239	12	stephen	stephen	PROPN
ejpam-6603	239	13	.	.	PUNCT
ejpam-6603	240	1	a	a	DET
ejpam-6603	240	2	lower	lower	ADV
ejpam-6603	240	3	bound	bind	VERB
ejpam-6603	240	4	on	on	ADP
ejpam-6603	240	5	the	the	DET
ejpam-6603	240	6	zero	zero	NUM
ejpam-6603	240	7	forcing	force	VERB
ejpam-6603	240	8	number	number	NOUN
ejpam-6603	240	9	.	.	PUNCT
ejpam-6603	241	1	discrete	discrete	ADJ
ejpam-6603	241	2	applied	apply	VERB
ejpam-6603	241	3	mathematics	mathematic	NOUN
ejpam-6603	241	4	,	,	PUNCT
ejpam-6603	241	5	250:363–367	250:363–367	NUM
ejpam-6603	241	6	,	,	PUNCT
ejpam-6603	241	7	2018	2018	NUM
ejpam-6603	241	8	.	.	PUNCT
ejpam-6603	242	1	[	[	X
ejpam-6603	242	2	4	4	X
ejpam-6603	242	3	]	]	PUNCT
ejpam-6603	242	4	s.	s.	PROPN
ejpam-6603	242	5	m.	m.	PROPN
ejpam-6603	242	6	fallat	fallat	PROPN
ejpam-6603	242	7	and	and	CCONJ
ejpam-6603	242	8	l.	l.	PROPN
ejpam-6603	242	9	hogben	hogben	PROPN
ejpam-6603	242	10	.	.	PUNCT
ejpam-6603	243	1	minimum	minimum	ADJ
ejpam-6603	243	2	rank	rank	NOUN
ejpam-6603	243	3	,	,	PUNCT
ejpam-6603	243	4	maximum	maximum	ADJ
ejpam-6603	243	5	nullity	nullity	NOUN
ejpam-6603	243	6	,	,	PUNCT
ejpam-6603	243	7	and	and	CCONJ
ejpam-6603	243	8	zero	zero	NUM
ejpam-6603	243	9	forcing	force	VERB
ejpam-6603	243	10	number	number	NOUN
ejpam-6603	243	11	of	of	ADP
ejpam-6603	243	12	graphs	graph	NOUN
ejpam-6603	243	13	.	.	PUNCT
ejpam-6603	244	1	in	in	ADP
ejpam-6603	244	2	handbook	handbook	NOUN
ejpam-6603	244	3	of	of	ADP
ejpam-6603	244	4	linear	linear	PROPN
ejpam-6603	244	5	algebra	algebra	PROPN
ejpam-6603	244	6	,	,	PUNCT
ejpam-6603	244	7	pages	page	NOUN
ejpam-6603	244	8	775–810	775–810	NUM
ejpam-6603	244	9	.	.	PUNCT
ejpam-6603	245	1	crc	crc	PROPN
ejpam-6603	245	2	press	press	PROPN
ejpam-6603	245	3	,	,	PUNCT
ejpam-6603	245	4	boca	boca	PROPN
ejpam-6603	245	5	raton	raton	PROPN
ejpam-6603	245	6	,	,	PUNCT
ejpam-6603	245	7	fl	fl	PROPN
ejpam-6603	245	8	,	,	PUNCT
ejpam-6603	245	9	2	2	NUM
ejpam-6603	245	10	edition	edition	NOUN
ejpam-6603	245	11	,	,	PUNCT
ejpam-6603	245	12	2013	2013	NUM
ejpam-6603	245	13	.	.	PUNCT
ejpam-6603	246	1	[	[	X
ejpam-6603	246	2	5	5	NUM
ejpam-6603	246	3	]	]	PUNCT
ejpam-6603	246	4	m.	m.	NOUN
ejpam-6603	246	5	gentner	gentner	NOUN
ejpam-6603	246	6	,	,	PUNCT
ejpam-6603	246	7	l.	l.	PROPN
ejpam-6603	246	8	d.	d.	PROPN
ejpam-6603	246	9	penso	penso	PROPN
ejpam-6603	246	10	,	,	PUNCT
ejpam-6603	246	11	d.	d.	PROPN
ejpam-6603	246	12	rautenbach	rautenbach	NOUN
ejpam-6603	246	13	,	,	PUNCT
ejpam-6603	246	14	and	and	CCONJ
ejpam-6603	246	15	u.	u.	PROPN
ejpam-6603	246	16	s.	s.	PROPN
ejpam-6603	246	17	souza	souza	PROPN
ejpam-6603	246	18	.	.	PUNCT
ejpam-6603	247	1	extremal	extremal	ADJ
ejpam-6603	247	2	values	value	NOUN
ejpam-6603	247	3	and	and	CCONJ
ejpam-6603	247	4	bounds	bound	NOUN
ejpam-6603	247	5	for	for	ADP
ejpam-6603	247	6	the	the	DET
ejpam-6603	247	7	zero	zero	NUM
ejpam-6603	247	8	forcing	force	VERB
ejpam-6603	247	9	number	number	NOUN
ejpam-6603	247	10	.	.	PUNCT
ejpam-6603	248	1	discrete	discrete	ADJ
ejpam-6603	248	2	applied	apply	VERB
ejpam-6603	248	3	mathematics	mathematic	NOUN
ejpam-6603	248	4	,	,	PUNCT
ejpam-6603	248	5	214:196–200	214:196–200	NUM
ejpam-6603	248	6	,	,	PUNCT
ejpam-6603	248	7	2016	2016	NUM
ejpam-6603	248	8	.	.	PUNCT
ejpam-6603	249	1	[	[	X
ejpam-6603	249	2	6	6	NUM
ejpam-6603	249	3	]	]	PUNCT
ejpam-6603	249	4	j.	j.	PROPN
ejpam-6603	249	5	hassan	hassan	PROPN
ejpam-6603	249	6	and	and	CCONJ
ejpam-6603	249	7	l.	l.	PROPN
ejpam-6603	249	8	laja	laja	PROPN
ejpam-6603	249	9	.	.	PUNCT
ejpam-6603	250	1	vertex	vertex	NOUN
ejpam-6603	250	2	cover	cover	NOUN
ejpam-6603	250	3	zero	zero	NUM
ejpam-6603	250	4	forcing	force	VERB
ejpam-6603	250	5	sets	set	NOUN
ejpam-6603	250	6	in	in	ADP
ejpam-6603	250	7	graphs	graph	NOUN
ejpam-6603	250	8	.	.	PUNCT
ejpam-6603	251	1	international	international	ADJ
ejpam-6603	251	2	journal	journal	NOUN
ejpam-6603	251	3	of	of	ADP
ejpam-6603	251	4	mathematics	mathematic	NOUN
ejpam-6603	251	5	and	and	CCONJ
ejpam-6603	251	6	computer	computer	NOUN
ejpam-6603	251	7	science	science	NOUN
ejpam-6603	251	8	,	,	PUNCT
ejpam-6603	251	9	19(4):999–1003	19(4):999–1003	NUM
ejpam-6603	251	10	,	,	PUNCT
ejpam-6603	251	11	2024	2024	NUM
ejpam-6603	251	12	.	.	PUNCT
ejpam-6603	252	1	j.	j.	PROPN
ejpam-6603	252	2	a.	a.	PROPN
ejpam-6603	252	3	hassan	hassan	PROPN
ejpam-6603	252	4	et	et	PROPN
ejpam-6603	252	5	al	al	PROPN
ejpam-6603	252	6	.	.	PUNCT
ejpam-6603	252	7	/	/	SYM
ejpam-6603	252	8	eur	eur	PROPN
ejpam-6603	252	9	.	.	PUNCT
ejpam-6603	253	1	j.	j.	PROPN
ejpam-6603	253	2	pure	pure	PROPN
ejpam-6603	253	3	appl	appl	PROPN
ejpam-6603	253	4	.	.	PROPN
ejpam-6603	253	5	math	math	PROPN
ejpam-6603	253	6	,	,	PUNCT
ejpam-6603	253	7	18	18	NUM
ejpam-6603	253	8	(	(	PUNCT
ejpam-6603	253	9	3	3	NUM
ejpam-6603	253	10	)	)	PUNCT
ejpam-6603	253	11	(	(	PUNCT
ejpam-6603	253	12	2025	2025	NUM
ejpam-6603	253	13	)	)	PUNCT
ejpam-6603	253	14	,	,	PUNCT
ejpam-6603	253	15	6603	6603	NUM
ejpam-6603	253	16	9	9	NUM
ejpam-6603	253	17	of	of	ADP
ejpam-6603	253	18	9	9	NUM
ejpam-6603	254	1	[	[	X
ejpam-6603	254	2	7	7	NUM
ejpam-6603	254	3	]	]	PUNCT
ejpam-6603	254	4	j.	j.	PROPN
ejpam-6603	254	5	hassan	hassan	PROPN
ejpam-6603	254	6	,	,	PUNCT
ejpam-6603	254	7	m.	m.	NOUN
ejpam-6603	254	8	a.	a.	PROPN
ejpam-6603	254	9	bonsocan	bonsocan	PROPN
ejpam-6603	254	10	,	,	PUNCT
ejpam-6603	254	11	m.	m.	NOUN
ejpam-6603	254	12	langamin	langamin	PROPN
ejpam-6603	254	13	,	,	PUNCT
ejpam-6603	254	14	v.	v.	PROPN
ejpam-6603	254	15	bilar	bilar	PROPN
ejpam-6603	254	16	,	,	PUNCT
ejpam-6603	254	17	s.	s.	PROPN
ejpam-6603	254	18	d.	d.	PROPN
ejpam-6603	254	19	aming	aming	PROPN
ejpam-6603	254	20	,	,	PUNCT
ejpam-6603	254	21	and	and	CCONJ
ejpam-6603	254	22	b.	b.	PROPN
ejpam-6603	254	23	amiruddin	amiruddin	PROPN
ejpam-6603	254	24	.	.	PUNCT
ejpam-6603	255	1	zero	zero	NUM
ejpam-6603	255	2	forcing	force	VERB
ejpam-6603	255	3	domination	domination	NOUN
ejpam-6603	255	4	in	in	ADP
ejpam-6603	255	5	some	some	DET
ejpam-6603	255	6	graphs	graph	NOUN
ejpam-6603	255	7	:	:	PUNCT
ejpam-6603	255	8	characterizations	characterization	NOUN
ejpam-6603	255	9	and	and	CCONJ
ejpam-6603	255	10	derived	derive	VERB
ejpam-6603	255	11	formulas	formula	NOUN
ejpam-6603	255	12	.	.	PUNCT
ejpam-6603	256	1	european	european	ADJ
ejpam-6603	256	2	journal	journal	PROPN
ejpam-6603	256	3	of	of	ADP
ejpam-6603	256	4	pure	pure	ADJ
ejpam-6603	256	5	and	and	CCONJ
ejpam-6603	256	6	applied	applied	ADJ
ejpam-6603	256	7	mathematics	mathematic	NOUN
ejpam-6603	256	8	,	,	PUNCT
ejpam-6603	256	9	17(4):3772–3780	17(4):3772–3780	NUM
ejpam-6603	256	10	,	,	PUNCT
ejpam-6603	256	11	2024	2024	NUM
ejpam-6603	256	12	.	.	PUNCT
ejpam-6603	257	1	[	[	X
ejpam-6603	257	2	8	8	X
ejpam-6603	257	3	]	]	X
ejpam-6603	257	4	j.	j.	PROPN
ejpam-6603	257	5	hassan	hassan	PROPN
ejpam-6603	257	6	,	,	PUNCT
ejpam-6603	257	7	l.	l.	PROPN
ejpam-6603	257	8	laja	laja	PROPN
ejpam-6603	257	9	,	,	PUNCT
ejpam-6603	257	10	and	and	CCONJ
ejpam-6603	257	11	h.	h.	PROPN
ejpam-6603	257	12	copel	copel	PROPN
ejpam-6603	257	13	.	.	PUNCT
ejpam-6603	258	1	2	2	NUM
ejpam-6603	258	2	-	-	PUNCT
ejpam-6603	258	3	domination	domination	NOUN
ejpam-6603	258	4	zero	zero	NUM
ejpam-6603	258	5	forcing	force	VERB
ejpam-6603	258	6	in	in	ADP
ejpam-6603	258	7	graphs	graph	NOUN
ejpam-6603	258	8	.	.	PUNCT
ejpam-6603	259	1	international	international	ADJ
ejpam-6603	259	2	journal	journal	NOUN
ejpam-6603	259	3	of	of	ADP
ejpam-6603	259	4	mathematics	mathematic	NOUN
ejpam-6603	259	5	and	and	CCONJ
ejpam-6603	259	6	computer	computer	NOUN
ejpam-6603	259	7	science	science	NOUN
ejpam-6603	259	8	,	,	PUNCT
ejpam-6603	259	9	19(4):1065–1070	19(4):1065–1070	NUM
ejpam-6603	259	10	,	,	PUNCT
ejpam-6603	259	11	2024	2024	NUM
ejpam-6603	259	12	.	.	PUNCT
ejpam-6603	260	1	[	[	X
ejpam-6603	260	2	9	9	NUM
ejpam-6603	260	3	]	]	PUNCT
ejpam-6603	260	4	t.	t.	PROPN
ejpam-6603	260	5	kalinowski	kalinowski	PROPN
ejpam-6603	260	6	,	,	PUNCT
ejpam-6603	260	7	n.	n.	NOUN
ejpam-6603	260	8	kamcev	kamcev	PROPN
ejpam-6603	260	9	,	,	PUNCT
ejpam-6603	260	10	and	and	CCONJ
ejpam-6603	260	11	b.	b.	PROPN
ejpam-6603	260	12	sudakov	sudakov	PROPN
ejpam-6603	260	13	.	.	PUNCT
ejpam-6603	261	1	the	the	DET
ejpam-6603	261	2	zero	zero	NUM
ejpam-6603	261	3	forcing	force	VERB
ejpam-6603	261	4	number	number	NOUN
ejpam-6603	261	5	of	of	ADP
ejpam-6603	261	6	graphs	graph	NOUN
ejpam-6603	261	7	.	.	PUNCT
ejpam-6603	262	1	siam	siam	PROPN
ejpam-6603	262	2	journal	journal	PROPN
ejpam-6603	262	3	on	on	ADP
ejpam-6603	262	4	discrete	discrete	ADJ
ejpam-6603	262	5	mathematics	mathematic	NOUN
ejpam-6603	262	6	,	,	PUNCT
ejpam-6603	262	7	33(1):95–115	33(1):95–115	NUM
ejpam-6603	262	8	,	,	PUNCT
ejpam-6603	262	9	2019	2019	NUM
ejpam-6603	262	10	.	.	PUNCT
ejpam-6603	263	1	[	[	X
ejpam-6603	263	2	10	10	NUM
ejpam-6603	263	3	]	]	X
ejpam-6603	263	4	j.	j.	PROPN
ejpam-6603	263	5	manditong	manditong	PROPN
ejpam-6603	263	6	,	,	PUNCT
ejpam-6603	263	7	a.	a.	NOUN
ejpam-6603	263	8	tapeing	tapeing	NOUN
ejpam-6603	263	9	,	,	PUNCT
ejpam-6603	263	10	j.	j.	PROPN
ejpam-6603	263	11	hassan	hassan	PROPN
ejpam-6603	263	12	,	,	PUNCT
ejpam-6603	263	13	a.	a.	PROPN
ejpam-6603	263	14	r.	r.	PROPN
ejpam-6603	263	15	bakkang	bakkang	PROPN
ejpam-6603	263	16	,	,	PUNCT
ejpam-6603	263	17	n.	n.	PROPN
ejpam-6603	263	18	h.	h.	PROPN
ejpam-6603	263	19	mohammad	mohammad	PROPN
ejpam-6603	263	20	,	,	PUNCT
ejpam-6603	263	21	and	and	CCONJ
ejpam-6603	263	22	s.	s.	PROPN
ejpam-6603	263	23	u.	u.	PROPN
ejpam-6603	263	24	kamdon	kamdon	PROPN
ejpam-6603	263	25	.	.	PUNCT
ejpam-6603	264	1	some	some	DET
ejpam-6603	264	2	properties	property	NOUN
ejpam-6603	264	3	of	of	ADP
ejpam-6603	264	4	zero	zero	NUM
ejpam-6603	264	5	forcing	force	VERB
ejpam-6603	264	6	hop	hop	NOUN
ejpam-6603	264	7	dominating	dominating	NOUN
ejpam-6603	264	8	sets	set	NOUN
ejpam-6603	264	9	in	in	ADP
ejpam-6603	264	10	a	a	DET
ejpam-6603	264	11	graph	graph	NOUN
ejpam-6603	264	12	.	.	PUNCT
ejpam-6603	265	1	european	european	ADJ
ejpam-6603	265	2	journal	journal	PROPN
ejpam-6603	265	3	of	of	ADP
ejpam-6603	265	4	pure	pure	ADJ
ejpam-6603	265	5	and	and	CCONJ
ejpam-6603	265	6	applied	applied	ADJ
ejpam-6603	265	7	mathematics	mathematic	NOUN
ejpam-6603	265	8	,	,	PUNCT
ejpam-6603	265	9	17(1):324–337	17(1):324–337	PROPN
ejpam-6603	265	10	,	,	PUNCT
ejpam-6603	265	11	2024	2024	NUM
ejpam-6603	265	12	.	.	PUNCT
ejpam-6603	266	1	[	[	X
ejpam-6603	266	2	11	11	NUM
ejpam-6603	266	3	]	]	PUNCT
ejpam-6603	266	4	j.	j.	PROPN
ejpam-6603	266	5	hassan	hassan	PROPN
ejpam-6603	266	6	,	,	PUNCT
ejpam-6603	266	7	l.	l.	PROPN
ejpam-6603	266	8	udtohan	udtohan	PROPN
ejpam-6603	266	9	,	,	PUNCT
ejpam-6603	266	10	and	and	CCONJ
ejpam-6603	266	11	l.	l.	PROPN
ejpam-6603	266	12	laja	laja	PROPN
ejpam-6603	266	13	.	.	PUNCT
ejpam-6603	267	1	2	2	NUM
ejpam-6603	267	2	-	-	PUNCT
ejpam-6603	267	3	distance	distance	NOUN
ejpam-6603	267	4	zero	zero	NUM
ejpam-6603	267	5	forcing	force	VERB
ejpam-6603	267	6	in	in	ADP
ejpam-6603	267	7	graphs	graph	NOUN
ejpam-6603	267	8	.	.	PUNCT
ejpam-6603	268	1	european	european	ADJ
ejpam-6603	268	2	journal	journal	PROPN
ejpam-6603	268	3	of	of	ADP
ejpam-6603	268	4	pure	pure	ADJ
ejpam-6603	268	5	and	and	CCONJ
ejpam-6603	268	6	applied	applied	ADJ
ejpam-6603	268	7	mathematics	mathematic	NOUN
ejpam-6603	268	8	,	,	PUNCT
ejpam-6603	268	9	17(2):1283–1293	17(2):1283–1293	NUM
ejpam-6603	268	10	,	,	PUNCT
ejpam-6603	268	11	2024	2024	NUM
ejpam-6603	268	12	.	.	PUNCT