id	sid	tid	token	lemma	pos
ejpam-4493	1	1	european	european	PROPN
ejpam-4493	1	2	journal	journal	PROPN
ejpam-4493	1	3	of	of	ADP
ejpam-4493	1	4	pure	pure	ADJ
ejpam-4493	1	5	and	and	CCONJ
ejpam-4493	1	6	applied	apply	VERB
ejpam-4493	1	7	mathematics	mathematic	NOUN
ejpam-4493	1	8	vol	vol	NOUN
ejpam-4493	1	9	.	.	PROPN
ejpam-4493	2	1	15	15	NUM
ejpam-4493	2	2	,	,	PUNCT
ejpam-4493	2	3	no	no	INTJ
ejpam-4493	2	4	.	.	NOUN
ejpam-4493	2	5	4	4	NUM
ejpam-4493	2	6	,	,	PUNCT
ejpam-4493	2	7	2022	2022	NUM
ejpam-4493	2	8	,	,	PUNCT
ejpam-4493	2	9	1649	1649	NUM
ejpam-4493	2	10	-	-	SYM
ejpam-4493	2	11	1661	1661	NUM
ejpam-4493	2	12	issn	issn	PROPN
ejpam-4493	2	13	1307	1307	NUM
ejpam-4493	2	14	-	-	SYM
ejpam-4493	2	15	5543	5543	NUM
ejpam-4493	2	16	–	–	PUNCT
ejpam-4493	2	17	ejpam.com	ejpam.com	X
ejpam-4493	2	18	published	publish	VERB
ejpam-4493	2	19	by	by	ADP
ejpam-4493	2	20	new	new	PROPN
ejpam-4493	2	21	york	york	PROPN
ejpam-4493	2	22	business	business	PROPN
ejpam-4493	2	23	global	global	ADJ
ejpam-4493	2	24	forcing	force	VERB
ejpam-4493	2	25	connected	connect	VERB
ejpam-4493	2	26	co	co	ADJ
ejpam-4493	2	27	-	-	ADJ
ejpam-4493	2	28	independent	independent	ADJ
ejpam-4493	2	29	hop	hop	NOUN
ejpam-4493	2	30	domination	domination	NOUN
ejpam-4493	2	31	numbers	number	NOUN
ejpam-4493	2	32	in	in	ADP
ejpam-4493	2	33	the	the	DET
ejpam-4493	2	34	join	join	NOUN
ejpam-4493	2	35	and	and	CCONJ
ejpam-4493	2	36	corona	corona	NOUN
ejpam-4493	2	37	of	of	ADP
ejpam-4493	2	38	graphs	graph	NOUN
ejpam-4493	2	39	yves	yves	PROPN
ejpam-4493	2	40	dave	dave	PROPN
ejpam-4493	2	41	l.	l.	PROPN
ejpam-4493	2	42	calanza1,∗	calanza1,∗	PROPN
ejpam-4493	2	43	,	,	PUNCT
ejpam-4493	2	44	helen	helen	PROPN
ejpam-4493	2	45	m.	m.	PROPN
ejpam-4493	2	46	rara2	rara2	PROPN
ejpam-4493	3	1	1	1	NUM
ejpam-4493	3	2	department	department	NOUN
ejpam-4493	3	3	of	of	ADP
ejpam-4493	3	4	mathematics	mathematic	NOUN
ejpam-4493	3	5	and	and	CCONJ
ejpam-4493	3	6	statistics	statistic	NOUN
ejpam-4493	3	7	,	,	PUNCT
ejpam-4493	3	8	college	college	NOUN
ejpam-4493	3	9	of	of	ADP
ejpam-4493	3	10	science	science	NOUN
ejpam-4493	3	11	and	and	CCONJ
ejpam-4493	3	12	mathematics	mathematic	NOUN
ejpam-4493	3	13	,	,	PUNCT
ejpam-4493	3	14	mindanao	mindanao	PROPN
ejpam-4493	3	15	state	state	PROPN
ejpam-4493	3	16	university	university	PROPN
ejpam-4493	3	17	-	-	PUNCT
ejpam-4493	3	18	iligan	iligan	PROPN
ejpam-4493	3	19	institute	institute	PROPN
ejpam-4493	3	20	of	of	ADP
ejpam-4493	3	21	technology	technology	PROPN
ejpam-4493	3	22	,	,	PUNCT
ejpam-4493	3	23	9200	9200	NUM
ejpam-4493	3	24	iligan	iligan	ADJ
ejpam-4493	3	25	city	city	NOUN
ejpam-4493	3	26	,	,	PUNCT
ejpam-4493	3	27	philippines	philippines	PROPN
ejpam-4493	3	28	2	2	NUM
ejpam-4493	3	29	department	department	NOUN
ejpam-4493	3	30	of	of	ADP
ejpam-4493	3	31	mathematics	mathematic	NOUN
ejpam-4493	3	32	and	and	CCONJ
ejpam-4493	3	33	statistics	statistic	NOUN
ejpam-4493	3	34	,	,	PUNCT
ejpam-4493	3	35	college	college	NOUN
ejpam-4493	3	36	of	of	ADP
ejpam-4493	3	37	science	science	NOUN
ejpam-4493	3	38	and	and	CCONJ
ejpam-4493	3	39	mathematics	mathematic	NOUN
ejpam-4493	3	40	,	,	PUNCT
ejpam-4493	3	41	center	center	NOUN
ejpam-4493	3	42	of	of	ADP
ejpam-4493	3	43	graph	graph	NOUN
ejpam-4493	3	44	theory	theory	NOUN
ejpam-4493	3	45	,	,	PUNCT
ejpam-4493	3	46	algebra	algebra	NOUN
ejpam-4493	3	47	,	,	PUNCT
ejpam-4493	3	48	and	and	CCONJ
ejpam-4493	3	49	analysis	analysis	NOUN
ejpam-4493	3	50	-	-	PUNCT
ejpam-4493	3	51	premier	premier	NOUN
ejpam-4493	3	52	research	research	NOUN
ejpam-4493	3	53	institute	institute	PROPN
ejpam-4493	3	54	of	of	ADP
ejpam-4493	3	55	science	science	NOUN
ejpam-4493	3	56	and	and	CCONJ
ejpam-4493	3	57	mathematics	mathematic	NOUN
ejpam-4493	3	58	,	,	PUNCT
ejpam-4493	3	59	mindanao	mindanao	PROPN
ejpam-4493	3	60	state	state	PROPN
ejpam-4493	3	61	university	university	PROPN
ejpam-4493	3	62	-	-	PUNCT
ejpam-4493	3	63	iligan	iligan	PROPN
ejpam-4493	3	64	institute	institute	PROPN
ejpam-4493	3	65	of	of	ADP
ejpam-4493	3	66	technology	technology	PROPN
ejpam-4493	3	67	,	,	PUNCT
ejpam-4493	3	68	9200	9200	NUM
ejpam-4493	3	69	iligan	iligan	ADJ
ejpam-4493	3	70	city	city	NOUN
ejpam-4493	3	71	,	,	PUNCT
ejpam-4493	3	72	philippines	philippine	NOUN
ejpam-4493	3	73	abstract	abstract	ADJ
ejpam-4493	3	74	.	.	PUNCT
ejpam-4493	4	1	this	this	DET
ejpam-4493	4	2	study	study	NOUN
ejpam-4493	4	3	deals	deal	VERB
ejpam-4493	4	4	with	with	ADP
ejpam-4493	4	5	the	the	DET
ejpam-4493	4	6	forcing	force	VERB
ejpam-4493	4	7	subsets	subset	NOUN
ejpam-4493	4	8	of	of	ADP
ejpam-4493	4	9	a	a	DET
ejpam-4493	4	10	minimum	minimum	ADJ
ejpam-4493	4	11	connected	connected	ADJ
ejpam-4493	4	12	co	co	NOUN
ejpam-4493	4	13	-	-	ADJ
ejpam-4493	4	14	independent	independent	ADJ
ejpam-4493	4	15	hop	hop	NOUN
ejpam-4493	4	16	dominating	dominating	NOUN
ejpam-4493	4	17	sets	set	NOUN
ejpam-4493	4	18	in	in	ADP
ejpam-4493	4	19	graphs	graph	NOUN
ejpam-4493	4	20	.	.	PUNCT
ejpam-4493	5	1	bounds	bound	NOUN
ejpam-4493	5	2	or	or	CCONJ
ejpam-4493	5	3	exact	exact	ADJ
ejpam-4493	5	4	values	value	NOUN
ejpam-4493	5	5	of	of	ADP
ejpam-4493	5	6	the	the	DET
ejpam-4493	5	7	forcing	force	VERB
ejpam-4493	5	8	connected	connect	VERB
ejpam-4493	5	9	co	co	ADJ
ejpam-4493	5	10	-	-	ADJ
ejpam-4493	5	11	independent	independent	ADJ
ejpam-4493	5	12	hop	hop	NOUN
ejpam-4493	5	13	domination	domination	NOUN
ejpam-4493	5	14	numbers	number	NOUN
ejpam-4493	5	15	of	of	ADP
ejpam-4493	5	16	graphs	graph	NOUN
ejpam-4493	5	17	resulting	result	VERB
ejpam-4493	5	18	from	from	ADP
ejpam-4493	5	19	some	some	DET
ejpam-4493	5	20	binary	binary	ADJ
ejpam-4493	5	21	operations	operation	NOUN
ejpam-4493	5	22	such	such	ADJ
ejpam-4493	5	23	as	as	ADP
ejpam-4493	5	24	join	join	NOUN
ejpam-4493	5	25	and	and	CCONJ
ejpam-4493	5	26	corona	corona	NOUN
ejpam-4493	5	27	of	of	ADP
ejpam-4493	5	28	graphs	graph	NOUN
ejpam-4493	5	29	are	be	AUX
ejpam-4493	5	30	determined	determine	VERB
ejpam-4493	5	31	.	.	PUNCT
ejpam-4493	6	1	some	some	DET
ejpam-4493	6	2	main	main	ADJ
ejpam-4493	6	3	results	result	NOUN
ejpam-4493	6	4	generated	generate	VERB
ejpam-4493	6	5	in	in	ADP
ejpam-4493	6	6	this	this	DET
ejpam-4493	6	7	study	study	NOUN
ejpam-4493	6	8	include	include	VERB
ejpam-4493	6	9	characterization	characterization	NOUN
ejpam-4493	6	10	of	of	ADP
ejpam-4493	6	11	the	the	DET
ejpam-4493	6	12	minimum	minimum	ADJ
ejpam-4493	6	13	connected	connect	VERB
ejpam-4493	6	14	co	co	NOUN
ejpam-4493	6	15	-	-	ADJ
ejpam-4493	6	16	independent	independent	ADJ
ejpam-4493	6	17	hop	hop	NOUN
ejpam-4493	6	18	dominating	dominating	NOUN
ejpam-4493	6	19	sets	set	NOUN
ejpam-4493	6	20	,	,	PUNCT
ejpam-4493	6	21	characterization	characterization	NOUN
ejpam-4493	6	22	of	of	ADP
ejpam-4493	6	23	the	the	DET
ejpam-4493	6	24	forcing	force	VERB
ejpam-4493	6	25	subsets	subset	NOUN
ejpam-4493	6	26	for	for	ADP
ejpam-4493	6	27	these	these	DET
ejpam-4493	6	28	types	type	NOUN
ejpam-4493	6	29	of	of	ADP
ejpam-4493	6	30	sets	set	NOUN
ejpam-4493	6	31	,	,	PUNCT
ejpam-4493	6	32	and	and	CCONJ
ejpam-4493	6	33	bounds	bound	NOUN
ejpam-4493	6	34	or	or	CCONJ
ejpam-4493	6	35	exact	exact	ADJ
ejpam-4493	6	36	values	value	NOUN
ejpam-4493	6	37	of	of	ADP
ejpam-4493	6	38	the	the	DET
ejpam-4493	6	39	forcing	force	VERB
ejpam-4493	6	40	connected	connect	VERB
ejpam-4493	6	41	co	co	ADJ
ejpam-4493	6	42	-	-	ADJ
ejpam-4493	6	43	independent	independent	ADJ
ejpam-4493	6	44	hop	hop	NOUN
ejpam-4493	6	45	domination	domination	NOUN
ejpam-4493	6	46	numbers	number	NOUN
ejpam-4493	6	47	of	of	ADP
ejpam-4493	6	48	the	the	DET
ejpam-4493	6	49	join	join	NOUN
ejpam-4493	6	50	and	and	CCONJ
ejpam-4493	6	51	corona	corona	NOUN
ejpam-4493	6	52	of	of	ADP
ejpam-4493	6	53	graphs	graph	NOUN
ejpam-4493	6	54	.	.	PUNCT
ejpam-4493	7	1	2020	2020	NUM
ejpam-4493	7	2	mathematics	mathematic	NOUN
ejpam-4493	7	3	subject	subject	NOUN
ejpam-4493	7	4	classifications	classification	NOUN
ejpam-4493	7	5	:	:	PUNCT
ejpam-4493	7	6	05c69	05c69	X
ejpam-4493	7	7	key	key	ADJ
ejpam-4493	7	8	words	word	NOUN
ejpam-4493	7	9	and	and	CCONJ
ejpam-4493	7	10	phrases	phrase	NOUN
ejpam-4493	7	11	:	:	PUNCT
ejpam-4493	7	12	forcing	force	VERB
ejpam-4493	7	13	subsets	subset	NOUN
ejpam-4493	7	14	,	,	PUNCT
ejpam-4493	7	15	connected	connected	ADJ
ejpam-4493	7	16	co	co	ADJ
ejpam-4493	7	17	-	-	ADJ
ejpam-4493	7	18	independent	independent	ADJ
ejpam-4493	7	19	hop	hop	NOUN
ejpam-4493	7	20	domination	domination	NOUN
ejpam-4493	7	21	,	,	PUNCT
ejpam-4493	7	22	strictly	strictly	ADV
ejpam-4493	7	23	co	co	ADJ
ejpam-4493	7	24	-	-	ADJ
ejpam-4493	7	25	independent	independent	ADJ
ejpam-4493	7	26	set	set	NOUN
ejpam-4493	7	27	,	,	PUNCT
ejpam-4493	7	28	co	co	ADJ
ejpam-4493	7	29	-	-	ADJ
ejpam-4493	7	30	independent	independent	ADJ
ejpam-4493	7	31	set	set	NOUN
ejpam-4493	7	32	,	,	PUNCT
ejpam-4493	7	33	join	join	NOUN
ejpam-4493	7	34	,	,	PUNCT
ejpam-4493	7	35	corona	corona	PROPN
ejpam-4493	7	36	1	1	NUM
ejpam-4493	7	37	.	.	PUNCT
ejpam-4493	8	1	introduction	introduction	NOUN
ejpam-4493	8	2	beginning	begin	VERB
ejpam-4493	8	3	with	with	ADP
ejpam-4493	8	4	c.	c.	PROPN
ejpam-4493	8	5	berge	berge	NOUN
ejpam-4493	9	1	[	[	X
ejpam-4493	9	2	4	4	X
ejpam-4493	9	3	]	]	PUNCT
ejpam-4493	9	4	in	in	ADP
ejpam-4493	9	5	1958	1958	NUM
ejpam-4493	9	6	,	,	PUNCT
ejpam-4493	9	7	the	the	DET
ejpam-4493	9	8	study	study	NOUN
ejpam-4493	9	9	on	on	ADP
ejpam-4493	9	10	domination	domination	NOUN
ejpam-4493	9	11	in	in	ADP
ejpam-4493	9	12	graphs	graph	NOUN
ejpam-4493	9	13	was	be	AUX
ejpam-4493	9	14	developed	develop	VERB
ejpam-4493	9	15	.	.	PUNCT
ejpam-4493	10	1	there	there	PRON
ejpam-4493	10	2	are	be	VERB
ejpam-4493	10	3	now	now	ADV
ejpam-4493	10	4	a	a	DET
ejpam-4493	10	5	lot	lot	NOUN
ejpam-4493	10	6	of	of	ADP
ejpam-4493	10	7	studies	study	NOUN
ejpam-4493	10	8	involving	involve	VERB
ejpam-4493	10	9	domination	domination	NOUN
ejpam-4493	10	10	and	and	CCONJ
ejpam-4493	10	11	its	its	PRON
ejpam-4493	10	12	variations	variation	NOUN
ejpam-4493	10	13	.	.	PUNCT
ejpam-4493	11	1	one	one	NUM
ejpam-4493	11	2	of	of	ADP
ejpam-4493	11	3	its	its	PRON
ejpam-4493	11	4	variation	variation	NOUN
ejpam-4493	11	5	is	be	AUX
ejpam-4493	11	6	the	the	DET
ejpam-4493	11	7	connected	connected	ADJ
ejpam-4493	11	8	co	co	ADJ
ejpam-4493	11	9	-	-	ADJ
ejpam-4493	11	10	independent	independent	ADJ
ejpam-4493	11	11	domination	domination	NOUN
ejpam-4493	11	12	number	number	NOUN
ejpam-4493	11	13	of	of	ADP
ejpam-4493	11	14	graphs	graph	NOUN
ejpam-4493	11	15	that	that	PRON
ejpam-4493	11	16	was	be	AUX
ejpam-4493	11	17	studied	study	VERB
ejpam-4493	11	18	in	in	ADP
ejpam-4493	11	19	[	[	X
ejpam-4493	11	20	7	7	NUM
ejpam-4493	11	21	]	]	PUNCT
ejpam-4493	11	22	.	.	PUNCT
ejpam-4493	12	1	years	year	NOUN
ejpam-4493	12	2	later	later	ADV
ejpam-4493	12	3	,	,	PUNCT
ejpam-4493	12	4	a	a	DET
ejpam-4493	12	5	new	new	ADJ
ejpam-4493	12	6	domination	domination	NOUN
ejpam-4493	12	7	parameter	parameter	NOUN
ejpam-4493	12	8	called	call	VERB
ejpam-4493	12	9	hop	hop	NOUN
ejpam-4493	12	10	domination	domination	NOUN
ejpam-4493	12	11	was	be	AUX
ejpam-4493	12	12	introduced	introduce	VERB
ejpam-4493	12	13	in	in	ADP
ejpam-4493	12	14	[	[	X
ejpam-4493	12	15	12	12	NUM
ejpam-4493	12	16	]	]	PUNCT
ejpam-4493	12	17	by	by	ADP
ejpam-4493	12	18	natarajan	natarajan	PROPN
ejpam-4493	12	19	and	and	CCONJ
ejpam-4493	12	20	ayyaswamy	ayyaswamy	PROPN
ejpam-4493	12	21	and	and	CCONJ
ejpam-4493	12	22	were	be	AUX
ejpam-4493	12	23	also	also	ADV
ejpam-4493	12	24	studied	study	VERB
ejpam-4493	12	25	in	in	ADP
ejpam-4493	12	26	[	[	X
ejpam-4493	12	27	3	3	NUM
ejpam-4493	12	28	,	,	PUNCT
ejpam-4493	12	29	13–15	13–15	NUM
ejpam-4493	12	30	]	]	PUNCT
ejpam-4493	12	31	.	.	PUNCT
ejpam-4493	13	1	a	a	DET
ejpam-4493	13	2	study	study	NOUN
ejpam-4493	13	3	in	in	ADP
ejpam-4493	13	4	2021	2021	NUM
ejpam-4493	13	5	by	by	ADP
ejpam-4493	13	6	nanding	nande	VERB
ejpam-4493	13	7	and	and	CCONJ
ejpam-4493	13	8	rara	rara	NOUN
ejpam-4493	13	9	[	[	X
ejpam-4493	13	10	11	11	NUM
ejpam-4493	13	11	]	]	PUNCT
ejpam-4493	13	12	introduced	introduce	VERB
ejpam-4493	13	13	a	a	DET
ejpam-4493	13	14	new	new	ADJ
ejpam-4493	13	15	concept	concept	NOUN
ejpam-4493	13	16	of	of	ADP
ejpam-4493	13	17	hop	hop	NOUN
ejpam-4493	13	18	domination	domination	NOUN
ejpam-4493	13	19	called	call	VERB
ejpam-4493	13	20	the	the	DET
ejpam-4493	13	21	connected	connected	ADJ
ejpam-4493	13	22	co	co	NOUN
ejpam-4493	13	23	-	-	ADJ
ejpam-4493	13	24	independent	independent	ADJ
ejpam-4493	13	25	hop	hop	NOUN
ejpam-4493	13	26	domination	domination	NOUN
ejpam-4493	13	27	and	and	CCONJ
ejpam-4493	13	28	generated	generate	VERB
ejpam-4493	13	29	some	some	DET
ejpam-4493	13	30	characterizations	characterization	NOUN
ejpam-4493	13	31	of	of	ADP
ejpam-4493	13	32	connected	connected	ADJ
ejpam-4493	13	33	coindependent	coindependent	NOUN
ejpam-4493	13	34	hop	hop	NOUN
ejpam-4493	13	35	domination	domination	NOUN
ejpam-4493	13	36	in	in	ADP
ejpam-4493	13	37	graphs	graph	NOUN
ejpam-4493	13	38	.	.	PUNCT
ejpam-4493	14	1	∗corresponding	∗corresponde	VERB
ejpam-4493	14	2	author	author	NOUN
ejpam-4493	14	3	.	.	PUNCT
ejpam-4493	15	1	doi	doi	NOUN
ejpam-4493	15	2	:	:	PUNCT
ejpam-4493	15	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4493	https://doi.org/10.29020/nybg.ejpam.v15i4.4493	PROPN
ejpam-4493	15	4	email	email	NOUN
ejpam-4493	15	5	addresses	address	NOUN
ejpam-4493	15	6	:	:	PUNCT
ejpam-4493	15	7	yvesdave.calanza@g.msuiit.edu.ph	yvesdave.calanza@g.msuiit.edu.ph	PROPN
ejpam-4493	15	8	(	(	PUNCT
ejpam-4493	15	9	y.d	y.d	PROPN
ejpam-4493	15	10	.	.	PROPN
ejpam-4493	15	11	calanza	calanza	PROPN
ejpam-4493	15	12	)	)	PUNCT
ejpam-4493	15	13	,	,	PUNCT
ejpam-4493	15	14	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4493	15	15	(	(	PUNCT
ejpam-4493	15	16	h.	h.	PROPN
ejpam-4493	15	17	rara	rara	PROPN
ejpam-4493	15	18	)	)	PUNCT
ejpam-4493	15	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4493	15	20	1649	1649	NUM
ejpam-4493	15	21	©	©	PROPN
ejpam-4493	15	22	2022	2022	NUM
ejpam-4493	15	23	ejpam	ejpam	VERB
ejpam-4493	15	24	all	all	DET
ejpam-4493	15	25	rights	right	NOUN
ejpam-4493	15	26	reserved	reserve	VERB
ejpam-4493	15	27	.	.	PUNCT
ejpam-4493	16	1	y.d	y.d	PROPN
ejpam-4493	16	2	.	.	PROPN
ejpam-4493	16	3	calanza	calanza	PROPN
ejpam-4493	16	4	,	,	PUNCT
ejpam-4493	16	5	h.	h.	PROPN
ejpam-4493	16	6	rara	rara	PROPN
ejpam-4493	16	7	/	/	SYM
ejpam-4493	16	8	eur	eur	PROPN
ejpam-4493	16	9	.	.	PUNCT
ejpam-4493	17	1	j.	j.	PROPN
ejpam-4493	17	2	pure	pure	PROPN
ejpam-4493	17	3	appl	appl	PROPN
ejpam-4493	17	4	.	.	PROPN
ejpam-4493	17	5	math	math	PROPN
ejpam-4493	17	6	,	,	PUNCT
ejpam-4493	17	7	15	15	NUM
ejpam-4493	17	8	(	(	PUNCT
ejpam-4493	17	9	4	4	NUM
ejpam-4493	17	10	)	)	PUNCT
ejpam-4493	17	11	(	(	PUNCT
ejpam-4493	17	12	2022	2022	NUM
ejpam-4493	17	13	)	)	PUNCT
ejpam-4493	17	14	,	,	PUNCT
ejpam-4493	17	15	1649	1649	NUM
ejpam-4493	17	16	-	-	SYM
ejpam-4493	17	17	1661	1661	NUM
ejpam-4493	17	18	1650	1650	NUM
ejpam-4493	17	19	on	on	ADP
ejpam-4493	17	20	the	the	DET
ejpam-4493	17	21	other	other	ADJ
ejpam-4493	17	22	hand	hand	NOUN
ejpam-4493	17	23	,	,	PUNCT
ejpam-4493	17	24	the	the	DET
ejpam-4493	17	25	concept	concept	NOUN
ejpam-4493	17	26	of	of	ADP
ejpam-4493	17	27	forcing	force	VERB
ejpam-4493	17	28	numbers	number	NOUN
ejpam-4493	17	29	started	start	VERB
ejpam-4493	17	30	from	from	ADP
ejpam-4493	17	31	the	the	DET
ejpam-4493	17	32	study	study	NOUN
ejpam-4493	17	33	of	of	ADP
ejpam-4493	17	34	molecular	molecular	ADJ
ejpam-4493	17	35	resonance	resonance	NOUN
ejpam-4493	17	36	structure	structure	NOUN
ejpam-4493	17	37	which	which	PRON
ejpam-4493	17	38	was	be	AUX
ejpam-4493	17	39	introduced	introduce	VERB
ejpam-4493	17	40	by	by	ADP
ejpam-4493	17	41	klein	klein	PROPN
ejpam-4493	17	42	and	and	CCONJ
ejpam-4493	17	43	randic	randic	ADJ
ejpam-4493	17	44	[	[	X
ejpam-4493	17	45	10	10	NUM
ejpam-4493	17	46	]	]	PUNCT
ejpam-4493	17	47	in	in	ADP
ejpam-4493	17	48	1987	1987	NUM
ejpam-4493	17	49	.	.	PUNCT
ejpam-4493	18	1	harary	harary	PROPN
ejpam-4493	18	2	et	et	PROPN
ejpam-4493	18	3	al	al	PROPN
ejpam-4493	18	4	.	.	PUNCT
ejpam-4493	19	1	[	[	X
ejpam-4493	19	2	16	16	NUM
ejpam-4493	19	3	]	]	PUNCT
ejpam-4493	19	4	first	first	ADV
ejpam-4493	19	5	used	use	VERB
ejpam-4493	19	6	the	the	DET
ejpam-4493	19	7	name	name	NOUN
ejpam-4493	19	8	“	"	PUNCT
ejpam-4493	19	9	forcing	force	VERB
ejpam-4493	19	10	number	number	NOUN
ejpam-4493	19	11	”	"	PUNCT
ejpam-4493	19	12	and	and	CCONJ
ejpam-4493	19	13	introduced	introduce	VERB
ejpam-4493	19	14	the	the	DET
ejpam-4493	19	15	concept	concept	NOUN
ejpam-4493	19	16	of	of	ADP
ejpam-4493	19	17	the	the	DET
ejpam-4493	19	18	forcing	forcing	NOUN
ejpam-4493	19	19	of	of	ADP
ejpam-4493	19	20	a	a	DET
ejpam-4493	19	21	perfect	perfect	ADJ
ejpam-4493	19	22	match	match	NOUN
ejpam-4493	19	23	in	in	ADP
ejpam-4493	19	24	1991	1991	NUM
ejpam-4493	19	25	.	.	PUNCT
ejpam-4493	20	1	chartrand	chartrand	NOUN
ejpam-4493	20	2	et	et	PROPN
ejpam-4493	20	3	al	al	PROPN
ejpam-4493	20	4	.	.	PUNCT
ejpam-4493	21	1	[	[	X
ejpam-4493	21	2	5	5	NUM
ejpam-4493	21	3	]	]	PUNCT
ejpam-4493	21	4	initiated	initiate	VERB
ejpam-4493	21	5	the	the	DET
ejpam-4493	21	6	investigation	investigation	NOUN
ejpam-4493	21	7	on	on	ADP
ejpam-4493	21	8	the	the	DET
ejpam-4493	21	9	relation	relation	NOUN
ejpam-4493	21	10	between	between	ADP
ejpam-4493	21	11	forcing	force	VERB
ejpam-4493	21	12	and	and	CCONJ
ejpam-4493	21	13	domination	domination	NOUN
ejpam-4493	21	14	concepts	concept	NOUN
ejpam-4493	21	15	in	in	ADP
ejpam-4493	21	16	1997	1997	NUM
ejpam-4493	21	17	and	and	CCONJ
ejpam-4493	21	18	defined	define	VERB
ejpam-4493	21	19	the	the	DET
ejpam-4493	21	20	term	term	NOUN
ejpam-4493	21	21	”	"	PUNCT
ejpam-4493	21	22	forcing	force	VERB
ejpam-4493	21	23	domination	domination	NOUN
ejpam-4493	21	24	number	number	NOUN
ejpam-4493	21	25	”	"	PUNCT
ejpam-4493	21	26	.	.	PUNCT
ejpam-4493	22	1	in	in	ADP
ejpam-4493	22	2	2017	2017	NUM
ejpam-4493	22	3	,	,	PUNCT
ejpam-4493	22	4	john	john	PROPN
ejpam-4493	22	5	et	et	PROPN
ejpam-4493	22	6	al	al	PROPN
ejpam-4493	22	7	.	.	PUNCT
ejpam-4493	23	1	[	[	X
ejpam-4493	23	2	9	9	NUM
ejpam-4493	23	3	]	]	PUNCT
ejpam-4493	23	4	investigated	investigate	VERB
ejpam-4493	23	5	the	the	DET
ejpam-4493	23	6	forcing	force	VERB
ejpam-4493	23	7	connected	connect	VERB
ejpam-4493	23	8	domination	domination	NOUN
ejpam-4493	23	9	number	number	NOUN
ejpam-4493	23	10	of	of	ADP
ejpam-4493	23	11	a	a	DET
ejpam-4493	23	12	graph	graph	NOUN
ejpam-4493	23	13	,	,	PUNCT
ejpam-4493	23	14	and	and	CCONJ
ejpam-4493	23	15	armada	armada	PROPN
ejpam-4493	23	16	and	and	CCONJ
ejpam-4493	23	17	canoy	canoy	ADJ
ejpam-4493	24	1	[	[	X
ejpam-4493	24	2	1	1	X
ejpam-4493	24	3	]	]	PUNCT
ejpam-4493	24	4	investigated	investigate	VERB
ejpam-4493	24	5	the	the	DET
ejpam-4493	24	6	forcing	force	VERB
ejpam-4493	24	7	independent	independent	ADJ
ejpam-4493	24	8	domination	domination	NOUN
ejpam-4493	24	9	number	number	NOUN
ejpam-4493	24	10	of	of	ADP
ejpam-4493	24	11	a	a	DET
ejpam-4493	24	12	graph	graph	NOUN
ejpam-4493	24	13	in	in	ADP
ejpam-4493	24	14	2019	2019	NUM
ejpam-4493	24	15	.	.	PUNCT
ejpam-4493	25	1	furthermore	furthermore	ADV
ejpam-4493	25	2	,	,	PUNCT
ejpam-4493	25	3	in	in	ADP
ejpam-4493	25	4	2018	2018	NUM
ejpam-4493	25	5	,	,	PUNCT
ejpam-4493	25	6	canoy	canoy	PROPN
ejpam-4493	25	7	et	et	PROPN
ejpam-4493	25	8	al	al	PROPN
ejpam-4493	25	9	.	.	PUNCT
ejpam-4493	26	1	[	[	X
ejpam-4493	26	2	2	2	NUM
ejpam-4493	26	3	]	]	PUNCT
ejpam-4493	26	4	investigated	investigate	VERB
ejpam-4493	26	5	the	the	DET
ejpam-4493	26	6	forcing	force	VERB
ejpam-4493	26	7	domination	domination	NOUN
ejpam-4493	26	8	number	number	NOUN
ejpam-4493	26	9	of	of	ADP
ejpam-4493	26	10	graphs	graph	NOUN
ejpam-4493	26	11	under	under	ADP
ejpam-4493	26	12	some	some	DET
ejpam-4493	26	13	binary	binary	ADJ
ejpam-4493	26	14	operations	operation	NOUN
ejpam-4493	26	15	.	.	PUNCT
ejpam-4493	27	1	in	in	ADP
ejpam-4493	27	2	this	this	DET
ejpam-4493	27	3	study	study	NOUN
ejpam-4493	27	4	,	,	PUNCT
ejpam-4493	27	5	the	the	DET
ejpam-4493	27	6	researchers	researcher	NOUN
ejpam-4493	27	7	define	define	VERB
ejpam-4493	27	8	and	and	CCONJ
ejpam-4493	27	9	establish	establish	VERB
ejpam-4493	27	10	the	the	DET
ejpam-4493	27	11	forcing	force	VERB
ejpam-4493	27	12	subsets	subset	NOUN
ejpam-4493	27	13	of	of	ADP
ejpam-4493	27	14	minimum	minimum	ADJ
ejpam-4493	27	15	connected	connected	ADJ
ejpam-4493	27	16	co	co	NOUN
ejpam-4493	27	17	-	-	ADJ
ejpam-4493	27	18	independent	independent	ADJ
ejpam-4493	27	19	hop	hop	NOUN
ejpam-4493	27	20	dominating	dominating	NOUN
ejpam-4493	27	21	sets	set	NOUN
ejpam-4493	27	22	in	in	ADP
ejpam-4493	27	23	graphs	graph	NOUN
ejpam-4493	27	24	and	and	CCONJ
ejpam-4493	27	25	generate	generate	VERB
ejpam-4493	27	26	some	some	DET
ejpam-4493	27	27	characterizations	characterization	NOUN
ejpam-4493	27	28	of	of	ADP
ejpam-4493	27	29	forcing	force	VERB
ejpam-4493	27	30	subsets	subset	NOUN
ejpam-4493	27	31	of	of	ADP
ejpam-4493	27	32	minimum	minimum	ADJ
ejpam-4493	27	33	connected	connected	ADJ
ejpam-4493	27	34	co	co	NOUN
ejpam-4493	27	35	-	-	ADJ
ejpam-4493	27	36	independent	independent	ADJ
ejpam-4493	27	37	hop	hop	NOUN
ejpam-4493	27	38	dominating	dominating	NOUN
ejpam-4493	27	39	sets	set	NOUN
ejpam-4493	27	40	of	of	ADP
ejpam-4493	27	41	graphs	graph	NOUN
ejpam-4493	27	42	resulting	result	VERB
ejpam-4493	27	43	from	from	ADP
ejpam-4493	27	44	the	the	DET
ejpam-4493	27	45	join	join	NOUN
ejpam-4493	27	46	and	and	CCONJ
ejpam-4493	27	47	corona	corona	NOUN
ejpam-4493	27	48	of	of	ADP
ejpam-4493	27	49	two	two	NUM
ejpam-4493	27	50	graphs	graph	NOUN
ejpam-4493	27	51	and	and	CCONJ
ejpam-4493	27	52	determine	determine	VERB
ejpam-4493	27	53	the	the	DET
ejpam-4493	27	54	values	value	NOUN
ejpam-4493	27	55	or	or	CCONJ
ejpam-4493	27	56	bounds	bound	NOUN
ejpam-4493	27	57	of	of	ADP
ejpam-4493	27	58	their	their	PRON
ejpam-4493	27	59	corresponding	correspond	VERB
ejpam-4493	27	60	forcing	force	VERB
ejpam-4493	27	61	connected	connect	VERB
ejpam-4493	27	62	co	co	NOUN
ejpam-4493	27	63	-	-	ADJ
ejpam-4493	27	64	independent	independent	ADJ
ejpam-4493	27	65	hop	hop	NOUN
ejpam-4493	27	66	domination	domination	NOUN
ejpam-4493	27	67	numbers	number	NOUN
ejpam-4493	27	68	.	.	PUNCT
ejpam-4493	28	1	connected	connect	VERB
ejpam-4493	28	2	co	co	ADJ
ejpam-4493	28	3	-	-	ADJ
ejpam-4493	28	4	independent	independent	ADJ
ejpam-4493	28	5	hop	hop	NOUN
ejpam-4493	28	6	domination	domination	NOUN
ejpam-4493	28	7	in	in	ADP
ejpam-4493	28	8	graphs	graph	NOUN
ejpam-4493	28	9	can	can	AUX
ejpam-4493	28	10	have	have	VERB
ejpam-4493	28	11	real	real	ADJ
ejpam-4493	28	12	world	world	NOUN
ejpam-4493	28	13	applications	application	NOUN
ejpam-4493	28	14	.	.	PUNCT
ejpam-4493	29	1	for	for	ADP
ejpam-4493	29	2	an	an	DET
ejpam-4493	29	3	application	application	NOUN
ejpam-4493	29	4	,	,	PUNCT
ejpam-4493	29	5	in	in	ADP
ejpam-4493	29	6	[	[	PUNCT
ejpam-4493	29	7	6	6	NUM
ejpam-4493	29	8	]	]	PUNCT
ejpam-4493	29	9	,	,	PUNCT
ejpam-4493	29	10	desormeaux	desormeaux	ADJ
ejpam-4493	29	11	,	,	PUNCT
ejpam-4493	29	12	haynes	hayne	NOUN
ejpam-4493	29	13	,	,	PUNCT
ejpam-4493	29	14	and	and	CCONJ
ejpam-4493	29	15	henning	henning	NOUN
ejpam-4493	29	16	inspired	inspire	VERB
ejpam-4493	29	17	their	their	PRON
ejpam-4493	29	18	research	research	NOUN
ejpam-4493	29	19	on	on	ADP
ejpam-4493	29	20	these	these	DET
ejpam-4493	29	21	concepts	concept	NOUN
ejpam-4493	29	22	through	through	ADP
ejpam-4493	29	23	social	social	ADJ
ejpam-4493	29	24	networking	network	VERB
ejpam-4493	29	25	applications	application	NOUN
ejpam-4493	29	26	.	.	PUNCT
ejpam-4493	30	1	they	they	PRON
ejpam-4493	30	2	considered	consider	VERB
ejpam-4493	30	3	a	a	DET
ejpam-4493	30	4	factory	factory	NOUN
ejpam-4493	30	5	with	with	ADP
ejpam-4493	30	6	a	a	DET
ejpam-4493	30	7	large	large	ADJ
ejpam-4493	30	8	number	number	NOUN
ejpam-4493	30	9	of	of	ADP
ejpam-4493	30	10	employees	employee	NOUN
ejpam-4493	30	11	and	and	CCONJ
ejpam-4493	30	12	needed	need	VERB
ejpam-4493	30	13	to	to	PART
ejpam-4493	30	14	implement	implement	VERB
ejpam-4493	30	15	a	a	DET
ejpam-4493	30	16	quality	quality	NOUN
ejpam-4493	30	17	assurance	assurance	NOUN
ejpam-4493	30	18	checking	check	VERB
ejpam-4493	30	19	system	system	NOUN
ejpam-4493	30	20	of	of	ADP
ejpam-4493	30	21	their	their	PRON
ejpam-4493	30	22	workers	worker	NOUN
ejpam-4493	30	23	.	.	PUNCT
ejpam-4493	31	1	the	the	DET
ejpam-4493	31	2	factory	factory	NOUN
ejpam-4493	31	3	manager	manager	NOUN
ejpam-4493	31	4	decides	decide	VERB
ejpam-4493	31	5	to	to	PART
ejpam-4493	31	6	designate	designate	VERB
ejpam-4493	31	7	an	an	DET
ejpam-4493	31	8	internal	internal	ADJ
ejpam-4493	31	9	committee	committee	NOUN
ejpam-4493	31	10	to	to	PART
ejpam-4493	31	11	do	do	VERB
ejpam-4493	31	12	this	this	PRON
ejpam-4493	31	13	.	.	PUNCT
ejpam-4493	32	1	in	in	ADP
ejpam-4493	32	2	other	other	ADJ
ejpam-4493	32	3	words	word	NOUN
ejpam-4493	32	4	,	,	PUNCT
ejpam-4493	32	5	the	the	DET
ejpam-4493	32	6	manager	manager	NOUN
ejpam-4493	32	7	will	will	AUX
ejpam-4493	32	8	select	select	VERB
ejpam-4493	32	9	some	some	DET
ejpam-4493	32	10	workers	worker	NOUN
ejpam-4493	32	11	to	to	PART
ejpam-4493	32	12	form	form	VERB
ejpam-4493	32	13	a	a	DET
ejpam-4493	32	14	quality	quality	NOUN
ejpam-4493	32	15	assurance	assurance	NOUN
ejpam-4493	32	16	team	team	NOUN
ejpam-4493	32	17	to	to	PART
ejpam-4493	32	18	inspect	inspect	VERB
ejpam-4493	32	19	the	the	DET
ejpam-4493	32	20	work	work	NOUN
ejpam-4493	32	21	of	of	ADP
ejpam-4493	32	22	their	their	PRON
ejpam-4493	32	23	co	co	NOUN
ejpam-4493	32	24	-	-	NOUN
ejpam-4493	32	25	workers	worker	NOUN
ejpam-4493	32	26	.	.	PUNCT
ejpam-4493	33	1	the	the	DET
ejpam-4493	33	2	manager	manager	NOUN
ejpam-4493	33	3	wants	want	VERB
ejpam-4493	33	4	to	to	PART
ejpam-4493	33	5	keep	keep	VERB
ejpam-4493	33	6	this	this	DET
ejpam-4493	33	7	team	team	NOUN
ejpam-4493	33	8	as	as	ADV
ejpam-4493	33	9	small	small	ADJ
ejpam-4493	33	10	as	as	ADP
ejpam-4493	33	11	possible	possible	ADJ
ejpam-4493	33	12	to	to	PART
ejpam-4493	33	13	minimize	minimize	VERB
ejpam-4493	33	14	costs	cost	NOUN
ejpam-4493	33	15	(	(	PUNCT
ejpam-4493	33	16	extra	extra	ADJ
ejpam-4493	33	17	costs	cost	NOUN
ejpam-4493	33	18	for	for	ADP
ejpam-4493	33	19	inspectors	inspector	NOUN
ejpam-4493	33	20	)	)	PUNCT
ejpam-4493	33	21	and	and	CCONJ
ejpam-4493	33	22	protect	protect	VERB
ejpam-4493	33	23	privacy	privacy	NOUN
ejpam-4493	33	24	(	(	PUNCT
ejpam-4493	33	25	keep	keep	VERB
ejpam-4493	33	26	the	the	DET
ejpam-4493	33	27	inspectors	inspector	NOUN
ejpam-4493	33	28	’	’	PART
ejpam-4493	33	29	identity	identity	NOUN
ejpam-4493	33	30	confidential	confidential	ADJ
ejpam-4493	33	31	)	)	PUNCT
ejpam-4493	33	32	.	.	PUNCT
ejpam-4493	34	1	to	to	PART
ejpam-4493	34	2	avoid	avoid	VERB
ejpam-4493	34	3	bias	bias	NOUN
ejpam-4493	34	4	,	,	PUNCT
ejpam-4493	34	5	an	an	DET
ejpam-4493	34	6	inspector	inspector	NOUN
ejpam-4493	34	7	should	should	AUX
ejpam-4493	34	8	neither	neither	CCONJ
ejpam-4493	34	9	be	be	AUX
ejpam-4493	34	10	close	close	ADJ
ejpam-4493	34	11	friends	friend	NOUN
ejpam-4493	34	12	nor	nor	CCONJ
ejpam-4493	34	13	enemies	enemy	NOUN
ejpam-4493	34	14	with	with	ADP
ejpam-4493	34	15	any	any	PRON
ejpam-4493	34	16	of	of	ADP
ejpam-4493	34	17	the	the	DET
ejpam-4493	34	18	workers	worker	NOUN
ejpam-4493	35	1	he	he	PRON
ejpam-4493	35	2	/	/	PUNCT
ejpam-4493	36	1	she	she	PRON
ejpam-4493	36	2	is	be	AUX
ejpam-4493	36	3	responsible	responsible	ADJ
ejpam-4493	36	4	for	for	ADP
ejpam-4493	36	5	inspecting	inspect	VERB
ejpam-4493	36	6	.	.	PUNCT
ejpam-4493	37	1	to	to	PART
ejpam-4493	37	2	model	model	VERB
ejpam-4493	37	3	this	this	DET
ejpam-4493	37	4	situation	situation	NOUN
ejpam-4493	37	5	,	,	PUNCT
ejpam-4493	37	6	a	a	DET
ejpam-4493	37	7	social	social	ADJ
ejpam-4493	37	8	network	network	NOUN
ejpam-4493	37	9	graph	graph	NOUN
ejpam-4493	37	10	can	can	AUX
ejpam-4493	37	11	be	be	AUX
ejpam-4493	37	12	constructed	construct	VERB
ejpam-4493	37	13	in	in	ADP
ejpam-4493	37	14	which	which	PRON
ejpam-4493	37	15	each	each	DET
ejpam-4493	37	16	worker	worker	NOUN
ejpam-4493	37	17	is	be	AUX
ejpam-4493	37	18	represented	represent	VERB
ejpam-4493	37	19	by	by	ADP
ejpam-4493	37	20	a	a	DET
ejpam-4493	37	21	vertex	vertex	NOUN
ejpam-4493	37	22	and	and	CCONJ
ejpam-4493	37	23	an	an	DET
ejpam-4493	37	24	edge	edge	NOUN
ejpam-4493	37	25	between	between	ADP
ejpam-4493	37	26	two	two	NUM
ejpam-4493	37	27	workers	worker	NOUN
ejpam-4493	37	28	represents	represent	VERB
ejpam-4493	37	29	possible	possible	ADJ
ejpam-4493	37	30	bias	bias	NOUN
ejpam-4493	37	31	,	,	PUNCT
ejpam-4493	37	32	that	that	ADV
ejpam-4493	37	33	is	is	ADV
ejpam-4493	37	34	,	,	PUNCT
ejpam-4493	37	35	whether	whether	SCONJ
ejpam-4493	37	36	the	the	DET
ejpam-4493	37	37	two	two	NUM
ejpam-4493	37	38	workers	worker	NOUN
ejpam-4493	37	39	are	be	AUX
ejpam-4493	37	40	close	close	ADJ
ejpam-4493	37	41	friends	friend	NOUN
ejpam-4493	37	42	or	or	CCONJ
ejpam-4493	37	43	enemies	enemy	NOUN
ejpam-4493	37	44	.	.	PUNCT
ejpam-4493	38	1	ideally	ideally	ADV
ejpam-4493	38	2	,	,	PUNCT
ejpam-4493	38	3	an	an	DET
ejpam-4493	38	4	inspector	inspector	NOUN
ejpam-4493	38	5	should	should	AUX
ejpam-4493	38	6	not	not	PART
ejpam-4493	38	7	be	be	AUX
ejpam-4493	38	8	adjacent	adjacent	ADJ
ejpam-4493	38	9	to	to	ADP
ejpam-4493	38	10	any	any	DET
ejpam-4493	38	11	worker	worker	NOUN
ejpam-4493	38	12	who	who	PRON
ejpam-4493	38	13	is	be	AUX
ejpam-4493	38	14	being	be	AUX
ejpam-4493	38	15	inspected	inspect	VERB
ejpam-4493	38	16	.	.	PUNCT
ejpam-4493	39	1	in	in	ADP
ejpam-4493	39	2	connected	connected	ADJ
ejpam-4493	39	3	co	co	ADJ
ejpam-4493	39	4	-	-	ADJ
ejpam-4493	39	5	independent	independent	ADJ
ejpam-4493	39	6	hop	hop	NOUN
ejpam-4493	39	7	domination	domination	NOUN
ejpam-4493	39	8	[	[	X
ejpam-4493	39	9	11	11	NUM
ejpam-4493	39	10	]	]	PUNCT
ejpam-4493	39	11	,	,	PUNCT
ejpam-4493	39	12	every	every	DET
ejpam-4493	39	13	worker	worker	NOUN
ejpam-4493	39	14	will	will	AUX
ejpam-4493	39	15	be	be	AUX
ejpam-4493	39	16	inspected	inspect	VERB
ejpam-4493	39	17	by	by	ADP
ejpam-4493	39	18	the	the	DET
ejpam-4493	39	19	nearest	near	ADJ
ejpam-4493	39	20	non	non	ADJ
ejpam-4493	39	21	-	-	ADJ
ejpam-4493	39	22	biased	biased	ADJ
ejpam-4493	39	23	inspector	inspector	NOUN
ejpam-4493	39	24	.	.	PUNCT
ejpam-4493	40	1	that	that	PRON
ejpam-4493	40	2	is	is	ADV
ejpam-4493	40	3	,	,	PUNCT
ejpam-4493	40	4	an	an	DET
ejpam-4493	40	5	inspector	inspector	NOUN
ejpam-4493	40	6	who	who	PRON
ejpam-4493	40	7	is	be	AUX
ejpam-4493	40	8	a	a	DET
ejpam-4493	40	9	close	close	ADJ
ejpam-4493	40	10	friend	friend	NOUN
ejpam-4493	40	11	(	(	PUNCT
ejpam-4493	40	12	or	or	CCONJ
ejpam-4493	40	13	an	an	DET
ejpam-4493	40	14	enemy	enemy	NOUN
ejpam-4493	40	15	)	)	PUNCT
ejpam-4493	40	16	of	of	ADP
ejpam-4493	40	17	a	a	DET
ejpam-4493	40	18	close	close	ADJ
ejpam-4493	40	19	friend	friend	NOUN
ejpam-4493	40	20	(	(	PUNCT
ejpam-4493	40	21	or	or	CCONJ
ejpam-4493	40	22	enemy	enemy	NOUN
ejpam-4493	40	23	)	)	PUNCT
ejpam-4493	40	24	of	of	ADP
ejpam-4493	40	25	a	a	DET
ejpam-4493	40	26	worker	worker	NOUN
ejpam-4493	40	27	.	.	PUNCT
ejpam-4493	41	1	this	this	PRON
ejpam-4493	41	2	is	be	AUX
ejpam-4493	41	3	to	to	PART
ejpam-4493	41	4	save	save	VERB
ejpam-4493	41	5	time	time	NOUN
ejpam-4493	41	6	and	and	CCONJ
ejpam-4493	41	7	effort	effort	NOUN
ejpam-4493	41	8	of	of	ADP
ejpam-4493	41	9	locating	locate	VERB
ejpam-4493	41	10	a	a	DET
ejpam-4493	41	11	particular	particular	ADJ
ejpam-4493	41	12	worker	worker	NOUN
ejpam-4493	41	13	.	.	PUNCT
ejpam-4493	42	1	also	also	ADV
ejpam-4493	42	2	,	,	PUNCT
ejpam-4493	42	3	the	the	DET
ejpam-4493	42	4	inspectors	inspector	NOUN
ejpam-4493	42	5	should	should	AUX
ejpam-4493	42	6	be	be	AUX
ejpam-4493	42	7	acquainted	acquaint	VERB
ejpam-4493	42	8	with	with	ADP
ejpam-4493	42	9	each	each	DET
ejpam-4493	42	10	other	other	ADJ
ejpam-4493	42	11	and	and	CCONJ
ejpam-4493	42	12	all	all	DET
ejpam-4493	42	13	noninspector	noninspector	NOUN
ejpam-4493	42	14	workers	worker	NOUN
ejpam-4493	42	15	are	be	AUX
ejpam-4493	42	16	neither	neither	CCONJ
ejpam-4493	42	17	friends	friend	NOUN
ejpam-4493	42	18	nor	nor	CCONJ
ejpam-4493	42	19	enemies	enemy	NOUN
ejpam-4493	42	20	,	,	PUNCT
ejpam-4493	42	21	that	that	ADV
ejpam-4493	42	22	is	is	ADV
ejpam-4493	42	23	,	,	PUNCT
ejpam-4493	42	24	they	they	PRON
ejpam-4493	42	25	are	be	AUX
ejpam-4493	42	26	not	not	PART
ejpam-4493	42	27	adjacent	adjacent	ADJ
ejpam-4493	42	28	or	or	CCONJ
ejpam-4493	42	29	there	there	PRON
ejpam-4493	42	30	is	be	VERB
ejpam-4493	42	31	no	no	DET
ejpam-4493	42	32	edge	edge	NOUN
ejpam-4493	42	33	between	between	ADP
ejpam-4493	42	34	them	they	PRON
ejpam-4493	42	35	.	.	PUNCT
ejpam-4493	43	1	the	the	DET
ejpam-4493	43	2	connected	connected	ADJ
ejpam-4493	43	3	co	co	NOUN
ejpam-4493	43	4	-	-	ADJ
ejpam-4493	43	5	independent	independent	ADJ
ejpam-4493	43	6	hop	hop	NOUN
ejpam-4493	43	7	domination	domination	NOUN
ejpam-4493	43	8	number	number	NOUN
ejpam-4493	43	9	will	will	AUX
ejpam-4493	43	10	give	give	VERB
ejpam-4493	43	11	the	the	DET
ejpam-4493	43	12	minimum	minimum	ADJ
ejpam-4493	43	13	number	number	NOUN
ejpam-4493	43	14	of	of	ADP
ejpam-4493	43	15	inspectors	inspector	NOUN
ejpam-4493	43	16	needed	need	VERB
ejpam-4493	43	17	.	.	PUNCT
ejpam-4493	44	1	in	in	ADP
ejpam-4493	44	2	forcing	force	VERB
ejpam-4493	44	3	subsets	subset	NOUN
ejpam-4493	44	4	of	of	ADP
ejpam-4493	44	5	connected	connected	ADJ
ejpam-4493	44	6	co	co	ADJ
ejpam-4493	44	7	-	-	ADJ
ejpam-4493	44	8	independent	independent	ADJ
ejpam-4493	44	9	hop	hop	NOUN
ejpam-4493	44	10	domination	domination	NOUN
ejpam-4493	44	11	,	,	PUNCT
ejpam-4493	44	12	in	in	ADP
ejpam-4493	44	13	each	each	DET
ejpam-4493	44	14	respective	respective	ADJ
ejpam-4493	44	15	group	group	NOUN
ejpam-4493	44	16	of	of	ADP
ejpam-4493	44	17	minimum	minimum	ADJ
ejpam-4493	44	18	number	number	NOUN
ejpam-4493	44	19	of	of	ADP
ejpam-4493	44	20	inspectors	inspector	NOUN
ejpam-4493	44	21	that	that	PRON
ejpam-4493	44	22	will	will	AUX
ejpam-4493	44	23	inspect	inspect	VERB
ejpam-4493	44	24	the	the	DET
ejpam-4493	44	25	workers	worker	NOUN
ejpam-4493	44	26	in	in	ADP
ejpam-4493	44	27	the	the	DET
ejpam-4493	44	28	designated	designate	VERB
ejpam-4493	44	29	areas	area	NOUN
ejpam-4493	44	30	of	of	ADP
ejpam-4493	44	31	the	the	DET
ejpam-4493	44	32	factory	factory	NOUN
ejpam-4493	44	33	,	,	PUNCT
ejpam-4493	44	34	the	the	DET
ejpam-4493	44	35	members	member	NOUN
ejpam-4493	44	36	of	of	ADP
ejpam-4493	44	37	that	that	DET
ejpam-4493	44	38	particular	particular	ADJ
ejpam-4493	44	39	group	group	NOUN
ejpam-4493	44	40	of	of	ADP
ejpam-4493	44	41	minimum	minimum	ADJ
ejpam-4493	44	42	number	number	NOUN
ejpam-4493	44	43	of	of	ADP
ejpam-4493	44	44	inspectors	inspector	NOUN
ejpam-4493	44	45	will	will	AUX
ejpam-4493	44	46	be	be	AUX
ejpam-4493	44	47	assigned	assign	VERB
ejpam-4493	44	48	only	only	ADV
ejpam-4493	44	49	to	to	ADP
ejpam-4493	44	50	that	that	DET
ejpam-4493	44	51	distinct	distinct	ADJ
ejpam-4493	44	52	group	group	NOUN
ejpam-4493	44	53	of	of	ADP
ejpam-4493	44	54	minimum	minimum	ADJ
ejpam-4493	44	55	number	number	NOUN
ejpam-4493	44	56	of	of	ADP
ejpam-4493	44	57	inspectors	inspector	NOUN
ejpam-4493	44	58	,	,	PUNCT
ejpam-4493	44	59	that	that	ADV
ejpam-4493	44	60	is	is	ADV
ejpam-4493	44	61	,	,	PUNCT
ejpam-4493	44	62	it	it	PRON
ejpam-4493	44	63	will	will	AUX
ejpam-4493	44	64	strengthen	strengthen	VERB
ejpam-4493	44	65	the	the	DET
ejpam-4493	44	66	bond	bond	NOUN
ejpam-4493	44	67	of	of	ADP
ejpam-4493	44	68	the	the	DET
ejpam-4493	44	69	respective	respective	ADJ
ejpam-4493	44	70	group	group	NOUN
ejpam-4493	44	71	of	of	ADP
ejpam-4493	44	72	minimum	minimum	ADJ
ejpam-4493	44	73	number	number	NOUN
ejpam-4493	44	74	of	of	ADP
ejpam-4493	44	75	non	non	ADJ
ejpam-4493	44	76	-	-	ADJ
ejpam-4493	44	77	biased	biased	ADJ
ejpam-4493	44	78	inspectors	inspector	NOUN
ejpam-4493	44	79	with	with	ADP
ejpam-4493	44	80	each	each	DET
ejpam-4493	44	81	other	other	ADJ
ejpam-4493	44	82	,	,	PUNCT
ejpam-4493	44	83	since	since	SCONJ
ejpam-4493	44	84	they	they	PRON
ejpam-4493	44	85	are	be	AUX
ejpam-4493	44	86	uniquely	uniquely	ADV
ejpam-4493	44	87	assigned	assign	VERB
ejpam-4493	44	88	to	to	ADP
ejpam-4493	44	89	particular	particular	ADJ
ejpam-4493	44	90	groups	group	NOUN
ejpam-4493	44	91	,	,	PUNCT
ejpam-4493	44	92	and	and	CCONJ
ejpam-4493	44	93	they	they	PRON
ejpam-4493	44	94	will	will	AUX
ejpam-4493	44	95	trust	trust	VERB
ejpam-4493	44	96	each	each	DET
ejpam-4493	44	97	other	other	ADJ
ejpam-4493	44	98	more	more	ADV
ejpam-4493	44	99	doing	do	VERB
ejpam-4493	44	100	their	their	PRON
ejpam-4493	44	101	duties	duty	NOUN
ejpam-4493	44	102	and	and	CCONJ
ejpam-4493	44	103	will	will	AUX
ejpam-4493	44	104	have	have	VERB
ejpam-4493	44	105	a	a	DET
ejpam-4493	44	106	much	much	ADV
ejpam-4493	44	107	easier	easy	ADJ
ejpam-4493	44	108	time	time	NOUN
ejpam-4493	44	109	doing	do	VERB
ejpam-4493	44	110	their	their	PRON
ejpam-4493	44	111	job	job	NOUN
ejpam-4493	44	112	regarding	regard	VERB
ejpam-4493	44	113	with	with	ADP
ejpam-4493	44	114	the	the	DET
ejpam-4493	44	115	respective	respective	ADJ
ejpam-4493	44	116	workers	worker	NOUN
ejpam-4493	44	117	that	that	SCONJ
ejpam-4493	44	118	they	they	PRON
ejpam-4493	44	119	are	be	AUX
ejpam-4493	44	120	assigned	assign	VERB
ejpam-4493	44	121	to	to	PART
ejpam-4493	44	122	inspect	inspect	VERB
ejpam-4493	44	123	.	.	PUNCT
ejpam-4493	45	1	the	the	DET
ejpam-4493	45	2	y.d	y.d	PROPN
ejpam-4493	45	3	.	.	PROPN
ejpam-4493	45	4	calanza	calanza	PROPN
ejpam-4493	45	5	,	,	PUNCT
ejpam-4493	45	6	h.	h.	PROPN
ejpam-4493	45	7	rara	rara	PROPN
ejpam-4493	45	8	/	/	SYM
ejpam-4493	45	9	eur	eur	PROPN
ejpam-4493	45	10	.	.	PUNCT
ejpam-4493	46	1	j.	j.	PROPN
ejpam-4493	46	2	pure	pure	PROPN
ejpam-4493	46	3	appl	appl	PROPN
ejpam-4493	46	4	.	.	PROPN
ejpam-4493	46	5	math	math	PROPN
ejpam-4493	46	6	,	,	PUNCT
ejpam-4493	46	7	15	15	NUM
ejpam-4493	46	8	(	(	PUNCT
ejpam-4493	46	9	4	4	NUM
ejpam-4493	46	10	)	)	PUNCT
ejpam-4493	46	11	(	(	PUNCT
ejpam-4493	46	12	2022	2022	NUM
ejpam-4493	46	13	)	)	PUNCT
ejpam-4493	46	14	,	,	PUNCT
ejpam-4493	46	15	1649	1649	NUM
ejpam-4493	46	16	-	-	SYM
ejpam-4493	46	17	1661	1661	NUM
ejpam-4493	46	18	1651	1651	NUM
ejpam-4493	46	19	forcing	force	VERB
ejpam-4493	46	20	connected	connect	VERB
ejpam-4493	46	21	co	co	ADJ
ejpam-4493	46	22	-	-	ADJ
ejpam-4493	46	23	independent	independent	ADJ
ejpam-4493	46	24	hop	hop	NOUN
ejpam-4493	46	25	domination	domination	NOUN
ejpam-4493	46	26	number	number	NOUN
ejpam-4493	46	27	will	will	AUX
ejpam-4493	46	28	determine	determine	VERB
ejpam-4493	46	29	the	the	DET
ejpam-4493	46	30	minimum	minimum	ADJ
ejpam-4493	46	31	number	number	NOUN
ejpam-4493	46	32	of	of	ADP
ejpam-4493	46	33	members	member	NOUN
ejpam-4493	46	34	from	from	ADP
ejpam-4493	46	35	the	the	DET
ejpam-4493	46	36	respective	respective	ADJ
ejpam-4493	46	37	group	group	NOUN
ejpam-4493	46	38	of	of	ADP
ejpam-4493	46	39	minimum	minimum	ADJ
ejpam-4493	46	40	number	number	NOUN
ejpam-4493	46	41	of	of	ADP
ejpam-4493	46	42	inspectors	inspector	NOUN
ejpam-4493	46	43	that	that	PRON
ejpam-4493	46	44	will	will	AUX
ejpam-4493	46	45	be	be	AUX
ejpam-4493	46	46	assigned	assign	VERB
ejpam-4493	46	47	only	only	ADV
ejpam-4493	46	48	to	to	ADP
ejpam-4493	46	49	that	that	DET
ejpam-4493	46	50	particular	particular	ADJ
ejpam-4493	46	51	group	group	NOUN
ejpam-4493	46	52	of	of	ADP
ejpam-4493	46	53	respective	respective	ADJ
ejpam-4493	46	54	minimum	minimum	ADJ
ejpam-4493	46	55	number	number	NOUN
ejpam-4493	46	56	of	of	ADP
ejpam-4493	46	57	inspectors	inspector	NOUN
ejpam-4493	46	58	.	.	PUNCT
ejpam-4493	47	1	in	in	ADP
ejpam-4493	47	2	this	this	DET
ejpam-4493	47	3	study	study	NOUN
ejpam-4493	47	4	,	,	PUNCT
ejpam-4493	47	5	we	we	PRON
ejpam-4493	47	6	only	only	ADV
ejpam-4493	47	7	consider	consider	VERB
ejpam-4493	47	8	graphs	graph	NOUN
ejpam-4493	47	9	that	that	PRON
ejpam-4493	47	10	are	be	AUX
ejpam-4493	47	11	finite	finite	ADJ
ejpam-4493	47	12	,	,	PUNCT
ejpam-4493	47	13	simple	simple	ADJ
ejpam-4493	47	14	,	,	PUNCT
ejpam-4493	47	15	undirected	undirected	ADJ
ejpam-4493	47	16	and	and	CCONJ
ejpam-4493	47	17	connected	connected	ADJ
ejpam-4493	47	18	.	.	PUNCT
ejpam-4493	48	1	readers	reader	NOUN
ejpam-4493	48	2	are	be	AUX
ejpam-4493	48	3	referred	refer	VERB
ejpam-4493	48	4	to	to	ADP
ejpam-4493	48	5	[	[	X
ejpam-4493	48	6	8	8	NUM
ejpam-4493	48	7	]	]	PUNCT
ejpam-4493	48	8	for	for	ADP
ejpam-4493	48	9	elementary	elementary	ADJ
ejpam-4493	48	10	graph	graph	NOUN
ejpam-4493	48	11	theoretic	theoretic	ADJ
ejpam-4493	48	12	concepts	concept	NOUN
ejpam-4493	48	13	.	.	PUNCT
ejpam-4493	49	1	an	an	DET
ejpam-4493	49	2	independent	independent	ADJ
ejpam-4493	49	3	set	set	NOUN
ejpam-4493	49	4	s	s	NOUN
ejpam-4493	49	5	in	in	ADP
ejpam-4493	49	6	a	a	DET
ejpam-4493	49	7	graph	graph	NOUN
ejpam-4493	49	8	g	g	NOUN
ejpam-4493	49	9	is	be	AUX
ejpam-4493	49	10	a	a	DET
ejpam-4493	49	11	subset	subset	NOUN
ejpam-4493	49	12	of	of	ADP
ejpam-4493	49	13	the	the	DET
ejpam-4493	49	14	vertex	vertex	NOUN
ejpam-4493	49	15	-	-	PUNCT
ejpam-4493	49	16	set	set	NOUN
ejpam-4493	49	17	of	of	ADP
ejpam-4493	49	18	g	g	NOUN
ejpam-4493	49	19	such	such	ADJ
ejpam-4493	49	20	that	that	SCONJ
ejpam-4493	49	21	no	no	DET
ejpam-4493	49	22	two	two	NUM
ejpam-4493	49	23	vertices	vertex	NOUN
ejpam-4493	49	24	in	in	ADP
ejpam-4493	49	25	s	s	NOUN
ejpam-4493	49	26	are	be	AUX
ejpam-4493	49	27	adjacent	adjacent	ADJ
ejpam-4493	49	28	in	in	ADP
ejpam-4493	49	29	g.	g.	PROPN
ejpam-4493	49	30	the	the	DET
ejpam-4493	49	31	cardinality	cardinality	NOUN
ejpam-4493	49	32	of	of	ADP
ejpam-4493	49	33	a	a	DET
ejpam-4493	49	34	maximum	maximum	ADJ
ejpam-4493	49	35	independent	independent	ADJ
ejpam-4493	49	36	set	set	NOUN
ejpam-4493	49	37	is	be	AUX
ejpam-4493	49	38	called	call	VERB
ejpam-4493	49	39	the	the	DET
ejpam-4493	49	40	independence	independence	NOUN
ejpam-4493	49	41	number	number	NOUN
ejpam-4493	49	42	of	of	ADP
ejpam-4493	49	43	g	g	NOUN
ejpam-4493	49	44	and	and	CCONJ
ejpam-4493	49	45	is	be	AUX
ejpam-4493	49	46	denoted	denote	VERB
ejpam-4493	49	47	by	by	ADP
ejpam-4493	49	48	β(g	β(g	PROPN
ejpam-4493	49	49	)	)	PUNCT
ejpam-4493	49	50	.	.	PUNCT
ejpam-4493	50	1	an	an	DET
ejpam-4493	50	2	independent	independent	ADJ
ejpam-4493	50	3	set	set	NOUN
ejpam-4493	50	4	s	s	PROPN
ejpam-4493	50	5	⊆	⊆	NUM
ejpam-4493	50	6	v	v	NOUN
ejpam-4493	50	7	(	(	PUNCT
ejpam-4493	50	8	g	g	NOUN
ejpam-4493	50	9	)	)	PUNCT
ejpam-4493	50	10	with	with	ADP
ejpam-4493	50	11	|s|	|s|	PROPN
ejpam-4493	50	12	=	=	SYM
ejpam-4493	50	13	β(g	β(g	PROPN
ejpam-4493	50	14	)	)	PUNCT
ejpam-4493	50	15	is	be	AUX
ejpam-4493	50	16	called	call	VERB
ejpam-4493	50	17	a	a	DET
ejpam-4493	50	18	β	β	NOUN
ejpam-4493	50	19	-	-	NOUN
ejpam-4493	50	20	set	set	NOUN
ejpam-4493	50	21	of	of	ADP
ejpam-4493	50	22	g.	g.	PROPN
ejpam-4493	50	23	a	a	DET
ejpam-4493	50	24	dominating	dominating	NOUN
ejpam-4493	50	25	set	set	NOUN
ejpam-4493	50	26	d	d	PROPN
ejpam-4493	50	27	⊆	⊆	NUM
ejpam-4493	50	28	v	v	ADP
ejpam-4493	50	29	(	(	PUNCT
ejpam-4493	50	30	g	g	NOUN
ejpam-4493	50	31	)	)	PUNCT
ejpam-4493	50	32	is	be	AUX
ejpam-4493	50	33	called	call	VERB
ejpam-4493	50	34	a	a	DET
ejpam-4493	50	35	connected	connected	ADJ
ejpam-4493	50	36	co	co	ADJ
ejpam-4493	50	37	-	-	ADJ
ejpam-4493	50	38	independent	independent	ADJ
ejpam-4493	50	39	dominating	dominating	NOUN
ejpam-4493	50	40	set	set	NOUN
ejpam-4493	50	41	of	of	ADP
ejpam-4493	50	42	g	g	PROPN
ejpam-4493	50	43	if	if	SCONJ
ejpam-4493	50	44	the	the	DET
ejpam-4493	50	45	subgraph	subgraph	NOUN
ejpam-4493	50	46	⟨d⟩	⟨d⟩	PROPN
ejpam-4493	50	47	induced	induce	VERB
ejpam-4493	50	48	by	by	ADP
ejpam-4493	50	49	d	d	PROPN
ejpam-4493	50	50	is	be	AUX
ejpam-4493	50	51	connected	connect	VERB
ejpam-4493	50	52	and	and	CCONJ
ejpam-4493	50	53	v	v	ADJ
ejpam-4493	50	54	(	(	PUNCT
ejpam-4493	50	55	g	g	NOUN
ejpam-4493	50	56	)	)	PUNCT
ejpam-4493	50	57	\	\	PUNCT
ejpam-4493	51	1	d	d	NOUN
ejpam-4493	51	2	is	be	AUX
ejpam-4493	51	3	an	an	DET
ejpam-4493	51	4	independent	independent	ADJ
ejpam-4493	51	5	set	set	NOUN
ejpam-4493	51	6	.	.	PUNCT
ejpam-4493	52	1	the	the	DET
ejpam-4493	52	2	cardinality	cardinality	NOUN
ejpam-4493	52	3	of	of	ADP
ejpam-4493	52	4	such	such	DET
ejpam-4493	52	5	a	a	DET
ejpam-4493	52	6	minimum	minimum	NOUN
ejpam-4493	52	7	set	set	NOUN
ejpam-4493	52	8	d	d	NOUN
ejpam-4493	52	9	is	be	AUX
ejpam-4493	52	10	called	call	VERB
ejpam-4493	52	11	connected	connected	ADJ
ejpam-4493	52	12	co	co	ADJ
ejpam-4493	52	13	-	-	ADJ
ejpam-4493	52	14	independent	independent	ADJ
ejpam-4493	52	15	domination	domination	NOUN
ejpam-4493	52	16	number	number	NOUN
ejpam-4493	52	17	of	of	ADP
ejpam-4493	52	18	g	g	PROPN
ejpam-4493	52	19	denoted	denote	VERB
ejpam-4493	52	20	by	by	ADP
ejpam-4493	52	21	γc	γc	PROPN
ejpam-4493	52	22	,	,	PUNCT
ejpam-4493	52	23	coi(g	coi(g	PROPN
ejpam-4493	52	24	)	)	PUNCT
ejpam-4493	52	25	.	.	PUNCT
ejpam-4493	53	1	a	a	DET
ejpam-4493	53	2	connected	connected	ADJ
ejpam-4493	53	3	co	co	ADJ
ejpam-4493	53	4	-	-	ADJ
ejpam-4493	53	5	independent	independent	ADJ
ejpam-4493	53	6	dominating	dominating	NOUN
ejpam-4493	53	7	set	set	NOUN
ejpam-4493	53	8	d	d	NOUN
ejpam-4493	53	9	with	with	ADP
ejpam-4493	53	10	|d|	|d|	PROPN
ejpam-4493	53	11	=	=	SYM
ejpam-4493	53	12	γc	γc	PROPN
ejpam-4493	53	13	,	,	PUNCT
ejpam-4493	53	14	coi(g	coi(g	PROPN
ejpam-4493	53	15	)	)	PUNCT
ejpam-4493	53	16	is	be	AUX
ejpam-4493	53	17	called	call	VERB
ejpam-4493	53	18	a	a	DET
ejpam-4493	53	19	γc	γc	PROPN
ejpam-4493	53	20	,	,	PUNCT
ejpam-4493	53	21	coi	coi	NOUN
ejpam-4493	53	22	-	-	PUNCT
ejpam-4493	53	23	set	set	NOUN
ejpam-4493	53	24	of	of	ADP
ejpam-4493	53	25	g.	g.	PROPN
ejpam-4493	53	26	let	let	VERB
ejpam-4493	53	27	g	g	NOUN
ejpam-4493	53	28	be	be	AUX
ejpam-4493	53	29	a	a	DET
ejpam-4493	53	30	connected	connected	ADJ
ejpam-4493	53	31	graph	graph	NOUN
ejpam-4493	53	32	.	.	PUNCT
ejpam-4493	54	1	a	a	DET
ejpam-4493	54	2	set	set	NOUN
ejpam-4493	54	3	s	s	NOUN
ejpam-4493	54	4	⊆	⊆	NUM
ejpam-4493	54	5	v	v	NOUN
ejpam-4493	54	6	(	(	PUNCT
ejpam-4493	54	7	g	g	NOUN
ejpam-4493	54	8	)	)	PUNCT
ejpam-4493	54	9	is	be	AUX
ejpam-4493	54	10	a	a	DET
ejpam-4493	54	11	hop	hop	NOUN
ejpam-4493	54	12	dominating	dominating	NOUN
ejpam-4493	54	13	set	set	NOUN
ejpam-4493	54	14	of	of	ADP
ejpam-4493	54	15	g	g	PROPN
ejpam-4493	54	16	if	if	SCONJ
ejpam-4493	54	17	for	for	ADP
ejpam-4493	54	18	every	every	DET
ejpam-4493	54	19	v	v	NUM
ejpam-4493	54	20	∈	∈	NOUN
ejpam-4493	54	21	v	v	NOUN
ejpam-4493	54	22	(	(	PUNCT
ejpam-4493	54	23	g)\s	g)\s	NOUN
ejpam-4493	54	24	,	,	PUNCT
ejpam-4493	54	25	there	there	PRON
ejpam-4493	54	26	exists	exist	VERB
ejpam-4493	54	27	u	u	PROPN
ejpam-4493	54	28	∈	∈	PROPN
ejpam-4493	54	29	s	s	VERB
ejpam-4493	54	30	such	such	ADJ
ejpam-4493	54	31	that	that	DET
ejpam-4493	54	32	dg(u	dg(u	ADJ
ejpam-4493	54	33	,	,	PUNCT
ejpam-4493	54	34	v	v	NOUN
ejpam-4493	54	35	)	)	PUNCT
ejpam-4493	55	1	=	=	SYM
ejpam-4493	55	2	2	2	X
ejpam-4493	55	3	.	.	PUNCT
ejpam-4493	56	1	the	the	DET
ejpam-4493	56	2	minimum	minimum	ADJ
ejpam-4493	56	3	cardinality	cardinality	NOUN
ejpam-4493	56	4	of	of	ADP
ejpam-4493	56	5	a	a	DET
ejpam-4493	56	6	hop	hop	NOUN
ejpam-4493	56	7	dominating	dominating	NOUN
ejpam-4493	56	8	set	set	NOUN
ejpam-4493	56	9	of	of	ADP
ejpam-4493	56	10	g	g	NOUN
ejpam-4493	56	11	,	,	PUNCT
ejpam-4493	56	12	denoted	denote	VERB
ejpam-4493	56	13	by	by	ADP
ejpam-4493	56	14	γh(g	γh(g	NOUN
ejpam-4493	56	15	)	)	PUNCT
ejpam-4493	56	16	,	,	PUNCT
ejpam-4493	56	17	is	be	AUX
ejpam-4493	56	18	called	call	VERB
ejpam-4493	56	19	the	the	DET
ejpam-4493	56	20	hop	hop	NOUN
ejpam-4493	56	21	domination	domination	NOUN
ejpam-4493	56	22	number	number	NOUN
ejpam-4493	56	23	of	of	ADP
ejpam-4493	56	24	g.	g.	PROPN
ejpam-4493	56	25	any	any	DET
ejpam-4493	56	26	hop	hop	NOUN
ejpam-4493	56	27	dominating	dominating	NOUN
ejpam-4493	56	28	set	set	VERB
ejpam-4493	56	29	with	with	ADP
ejpam-4493	56	30	cardinality	cardinality	NOUN
ejpam-4493	56	31	equal	equal	ADJ
ejpam-4493	56	32	to	to	ADP
ejpam-4493	56	33	γh(g	γh(g	NOUN
ejpam-4493	56	34	)	)	PUNCT
ejpam-4493	56	35	is	be	AUX
ejpam-4493	56	36	called	call	VERB
ejpam-4493	56	37	a	a	DET
ejpam-4493	56	38	γh	γh	ADV
ejpam-4493	56	39	-	-	PUNCT
ejpam-4493	56	40	set	set	NOUN
ejpam-4493	56	41	.	.	PUNCT
ejpam-4493	57	1	a	a	DET
ejpam-4493	57	2	vertex	vertex	NOUN
ejpam-4493	57	3	v	v	NOUN
ejpam-4493	57	4	in	in	ADP
ejpam-4493	57	5	g	g	PROPN
ejpam-4493	57	6	is	be	AUX
ejpam-4493	57	7	a	a	DET
ejpam-4493	57	8	hop	hop	NOUN
ejpam-4493	57	9	neighbor	neighbor	NOUN
ejpam-4493	57	10	of	of	ADP
ejpam-4493	57	11	vertex	vertex	NOUN
ejpam-4493	57	12	u	u	NOUN
ejpam-4493	57	13	in	in	ADP
ejpam-4493	57	14	g	g	PROPN
ejpam-4493	57	15	if	if	SCONJ
ejpam-4493	57	16	dg(u	dg(u	NOUN
ejpam-4493	57	17	,	,	PUNCT
ejpam-4493	57	18	v	v	NOUN
ejpam-4493	57	19	)	)	PUNCT
ejpam-4493	57	20	=	=	SYM
ejpam-4493	57	21	2	2	X
ejpam-4493	57	22	.	.	X
ejpam-4493	58	1	the	the	DET
ejpam-4493	58	2	set	set	NOUN
ejpam-4493	58	3	ng(u	ng(u	NOUN
ejpam-4493	58	4	,	,	PUNCT
ejpam-4493	58	5	2	2	NUM
ejpam-4493	58	6	)	)	PUNCT
ejpam-4493	58	7	=	=	PRON
ejpam-4493	58	8	{	{	PUNCT
ejpam-4493	58	9	v	v	NUM
ejpam-4493	58	10	∈	∈	NOUN
ejpam-4493	58	11	v	v	NOUN
ejpam-4493	58	12	(	(	PUNCT
ejpam-4493	58	13	g	g	NOUN
ejpam-4493	58	14	)	)	PUNCT
ejpam-4493	58	15	:	:	PUNCT
ejpam-4493	58	16	dg(v	dg(v	X
ejpam-4493	58	17	,	,	PUNCT
ejpam-4493	58	18	u	u	NOUN
ejpam-4493	58	19	)	)	PUNCT
ejpam-4493	58	20	=	=	SYM
ejpam-4493	58	21	2	2	X
ejpam-4493	58	22	}	}	PUNCT
ejpam-4493	58	23	is	be	AUX
ejpam-4493	58	24	called	call	VERB
ejpam-4493	58	25	the	the	DET
ejpam-4493	58	26	open	open	ADJ
ejpam-4493	58	27	hop	hop	NOUN
ejpam-4493	58	28	neighborhood	neighborhood	NOUN
ejpam-4493	58	29	of	of	ADP
ejpam-4493	58	30	u.	u.	PROPN
ejpam-4493	58	31	the	the	DET
ejpam-4493	58	32	closed	closed	ADJ
ejpam-4493	58	33	hop	hop	NOUN
ejpam-4493	58	34	neighborhood	neighborhood	NOUN
ejpam-4493	58	35	of	of	ADP
ejpam-4493	58	36	u	u	PROPN
ejpam-4493	58	37	in	in	ADP
ejpam-4493	58	38	g	g	PROPN
ejpam-4493	58	39	is	be	AUX
ejpam-4493	58	40	given	give	VERB
ejpam-4493	58	41	by	by	ADP
ejpam-4493	58	42	ng[u	ng[u	PROPN
ejpam-4493	58	43	,	,	PUNCT
ejpam-4493	58	44	2	2	NUM
ejpam-4493	58	45	]	]	PUNCT
ejpam-4493	58	46	=	=	PUNCT
ejpam-4493	58	47	ng(u	ng(u	NOUN
ejpam-4493	58	48	,	,	PUNCT
ejpam-4493	58	49	2	2	X
ejpam-4493	58	50	)	)	PUNCT
ejpam-4493	58	51	∪	∪	NOUN
ejpam-4493	58	52	{	{	PUNCT
ejpam-4493	58	53	u	u	NOUN
ejpam-4493	58	54	}	}	PUNCT
ejpam-4493	58	55	.	.	PUNCT
ejpam-4493	59	1	the	the	DET
ejpam-4493	59	2	open	open	ADJ
ejpam-4493	59	3	hop	hop	NOUN
ejpam-4493	59	4	neighborhood	neighborhood	NOUN
ejpam-4493	59	5	of	of	ADP
ejpam-4493	59	6	x	x	PROPN
ejpam-4493	59	7	⊆	⊆	NUM
ejpam-4493	59	8	v	v	ADP
ejpam-4493	59	9	(	(	PUNCT
ejpam-4493	59	10	g	g	NOUN
ejpam-4493	59	11	)	)	PUNCT
ejpam-4493	59	12	is	be	AUX
ejpam-4493	59	13	the	the	DET
ejpam-4493	59	14	set	set	NOUN
ejpam-4493	59	15	ng(x	ng(x	NUM
ejpam-4493	59	16	,	,	PUNCT
ejpam-4493	59	17	2	2	X
ejpam-4493	59	18	)	)	PUNCT
ejpam-4493	59	19	=	=	NOUN
ejpam-4493	59	20	⋃	⋃	NOUN
ejpam-4493	59	21	u∈x	u∈x	ADJ
ejpam-4493	59	22	ng(u	ng(u	NOUN
ejpam-4493	59	23	,	,	PUNCT
ejpam-4493	59	24	2	2	NUM
ejpam-4493	59	25	)	)	PUNCT
ejpam-4493	59	26	.	.	PUNCT
ejpam-4493	60	1	the	the	DET
ejpam-4493	60	2	closed	closed	ADJ
ejpam-4493	60	3	hop	hop	NOUN
ejpam-4493	60	4	neighborhood	neighborhood	NOUN
ejpam-4493	60	5	of	of	ADP
ejpam-4493	60	6	x	x	PUNCT
ejpam-4493	60	7	in	in	ADP
ejpam-4493	60	8	g	g	PROPN
ejpam-4493	60	9	is	be	AUX
ejpam-4493	60	10	the	the	DET
ejpam-4493	60	11	set	set	PROPN
ejpam-4493	60	12	ng[x	ng[x	PROPN
ejpam-4493	60	13	,	,	PUNCT
ejpam-4493	60	14	2	2	NUM
ejpam-4493	60	15	]	]	PUNCT
ejpam-4493	60	16	=	=	SYM
ejpam-4493	60	17	ng(x	ng(x	X
ejpam-4493	60	18	,	,	PUNCT
ejpam-4493	60	19	2	2	NUM
ejpam-4493	60	20	)	)	PUNCT
ejpam-4493	60	21	∪x	∪x	AUX
ejpam-4493	60	22	.	.	PUNCT
ejpam-4493	61	1	let	let	VERB
ejpam-4493	61	2	g	g	PRON
ejpam-4493	61	3	be	be	AUX
ejpam-4493	61	4	a	a	DET
ejpam-4493	61	5	graph	graph	NOUN
ejpam-4493	61	6	.	.	PUNCT
ejpam-4493	62	1	a	a	DET
ejpam-4493	62	2	subset	subset	NOUN
ejpam-4493	62	3	s	s	NOUN
ejpam-4493	62	4	of	of	ADP
ejpam-4493	62	5	v	v	NOUN
ejpam-4493	62	6	(	(	PUNCT
ejpam-4493	62	7	g	g	NOUN
ejpam-4493	62	8	)	)	PUNCT
ejpam-4493	62	9	is	be	AUX
ejpam-4493	62	10	a	a	DET
ejpam-4493	62	11	strictly	strictly	ADV
ejpam-4493	62	12	co	co	ADJ
ejpam-4493	62	13	-	-	ADJ
ejpam-4493	62	14	independent	independent	ADJ
ejpam-4493	62	15	set	set	NOUN
ejpam-4493	62	16	of	of	ADP
ejpam-4493	62	17	g	g	PROPN
ejpam-4493	62	18	if	if	SCONJ
ejpam-4493	62	19	v	v	X
ejpam-4493	62	20	(	(	PUNCT
ejpam-4493	62	21	g)\s	g)\s	NOUN
ejpam-4493	62	22	is	be	AUX
ejpam-4493	62	23	an	an	DET
ejpam-4493	62	24	independent	independent	ADJ
ejpam-4493	62	25	set	set	NOUN
ejpam-4493	62	26	and	and	CCONJ
ejpam-4493	62	27	ng(v)∩s	ng(v)∩s	PROPN
ejpam-4493	62	28	̸=	̸=	PROPN
ejpam-4493	62	29	s	s	VERB
ejpam-4493	62	30	for	for	ADP
ejpam-4493	62	31	all	all	PRON
ejpam-4493	62	32	v	v	ADP
ejpam-4493	62	33	∈	∈	NOUN
ejpam-4493	62	34	v	v	NOUN
ejpam-4493	62	35	(	(	PUNCT
ejpam-4493	62	36	g)\s	g)\s	NOUN
ejpam-4493	62	37	.	.	PUNCT
ejpam-4493	63	1	the	the	DET
ejpam-4493	63	2	minimum	minimum	ADJ
ejpam-4493	63	3	cardinality	cardinality	NOUN
ejpam-4493	63	4	of	of	ADP
ejpam-4493	63	5	a	a	DET
ejpam-4493	63	6	strictly	strictly	ADV
ejpam-4493	63	7	co	co	ADJ
ejpam-4493	63	8	-	-	ADJ
ejpam-4493	63	9	independent	independent	ADJ
ejpam-4493	63	10	set	set	NOUN
ejpam-4493	63	11	in	in	ADP
ejpam-4493	63	12	g	g	NOUN
ejpam-4493	63	13	,	,	PUNCT
ejpam-4493	63	14	denoted	denote	VERB
ejpam-4493	63	15	by	by	ADP
ejpam-4493	63	16	sci(g	sci(g	PROPN
ejpam-4493	63	17	)	)	PUNCT
ejpam-4493	63	18	is	be	AUX
ejpam-4493	63	19	called	call	VERB
ejpam-4493	63	20	the	the	DET
ejpam-4493	63	21	strictly	strictly	ADV
ejpam-4493	63	22	co	co	ADJ
ejpam-4493	63	23	-	-	ADJ
ejpam-4493	63	24	independent	independent	ADJ
ejpam-4493	63	25	number	number	NOUN
ejpam-4493	63	26	of	of	ADP
ejpam-4493	63	27	g.	g.	PROPN
ejpam-4493	63	28	a	a	DET
ejpam-4493	63	29	strictly	strictly	ADV
ejpam-4493	63	30	co	co	ADJ
ejpam-4493	63	31	-	-	ADJ
ejpam-4493	63	32	independent	independent	ADJ
ejpam-4493	63	33	set	set	NOUN
ejpam-4493	63	34	s	s	NOUN
ejpam-4493	63	35	with	with	ADP
ejpam-4493	63	36	|s|	|s|	NOUN
ejpam-4493	63	37	=	=	PUNCT
ejpam-4493	63	38	sci(g	sci(g	PROPN
ejpam-4493	63	39	)	)	PUNCT
ejpam-4493	63	40	is	be	AUX
ejpam-4493	63	41	called	call	VERB
ejpam-4493	63	42	an	an	DET
ejpam-4493	63	43	sci	sci	PROPN
ejpam-4493	63	44	-	-	PUNCT
ejpam-4493	63	45	set	set	NOUN
ejpam-4493	63	46	of	of	ADP
ejpam-4493	63	47	g.	g.	PROPN
ejpam-4493	63	48	a	a	DET
ejpam-4493	63	49	set	set	NOUN
ejpam-4493	63	50	s	s	PROPN
ejpam-4493	63	51	⊆	⊆	NUM
ejpam-4493	63	52	v	v	NOUN
ejpam-4493	63	53	(	(	PUNCT
ejpam-4493	63	54	g	g	NOUN
ejpam-4493	63	55	)	)	PUNCT
ejpam-4493	63	56	is	be	AUX
ejpam-4493	63	57	a	a	DET
ejpam-4493	63	58	co	co	ADJ
ejpam-4493	63	59	-	-	ADJ
ejpam-4493	63	60	independent	independent	ADJ
ejpam-4493	63	61	set	set	NOUN
ejpam-4493	63	62	of	of	ADP
ejpam-4493	63	63	g	g	PROPN
ejpam-4493	63	64	if	if	SCONJ
ejpam-4493	63	65	⟨v	⟨v	PROPN
ejpam-4493	63	66	(	(	PUNCT
ejpam-4493	63	67	g	g	NOUN
ejpam-4493	63	68	)	)	PUNCT
ejpam-4493	63	69	\	\	PROPN
ejpam-4493	63	70	s⟩	s⟩	PROPN
ejpam-4493	63	71	is	be	AUX
ejpam-4493	63	72	independent	independent	ADJ
ejpam-4493	63	73	.	.	PUNCT
ejpam-4493	64	1	the	the	DET
ejpam-4493	64	2	minimum	minimum	ADJ
ejpam-4493	64	3	cardinality	cardinality	NOUN
ejpam-4493	64	4	of	of	ADP
ejpam-4493	64	5	a	a	DET
ejpam-4493	64	6	co	co	ADJ
ejpam-4493	64	7	-	-	ADJ
ejpam-4493	64	8	independent	independent	ADJ
ejpam-4493	64	9	set	set	NOUN
ejpam-4493	64	10	in	in	ADP
ejpam-4493	64	11	g	g	NOUN
ejpam-4493	64	12	,	,	PUNCT
ejpam-4493	64	13	denoted	denote	VERB
ejpam-4493	64	14	by	by	ADP
ejpam-4493	64	15	coi(g	coi(g	NOUN
ejpam-4493	64	16	)	)	PUNCT
ejpam-4493	64	17	is	be	AUX
ejpam-4493	64	18	called	call	VERB
ejpam-4493	64	19	the	the	DET
ejpam-4493	64	20	co	co	ADJ
ejpam-4493	64	21	-	-	ADJ
ejpam-4493	64	22	independent	independent	ADJ
ejpam-4493	64	23	number	number	NOUN
ejpam-4493	64	24	of	of	ADP
ejpam-4493	64	25	g.	g.	PROPN
ejpam-4493	64	26	a	a	DET
ejpam-4493	64	27	co	co	ADJ
ejpam-4493	64	28	-	-	ADJ
ejpam-4493	64	29	independent	independent	ADJ
ejpam-4493	64	30	set	set	NOUN
ejpam-4493	64	31	s	s	NOUN
ejpam-4493	64	32	with	with	ADP
ejpam-4493	64	33	|s|	|s|	NOUN
ejpam-4493	64	34	=	=	SYM
ejpam-4493	64	35	coi(g	coi(g	PROPN
ejpam-4493	64	36	)	)	PUNCT
ejpam-4493	64	37	is	be	AUX
ejpam-4493	64	38	called	call	VERB
ejpam-4493	64	39	a	a	DET
ejpam-4493	64	40	coi	coi	NOUN
ejpam-4493	64	41	-set	-set	PUNCT
ejpam-4493	64	42	of	of	ADP
ejpam-4493	64	43	g.	g.	PROPN
ejpam-4493	64	44	let	let	VERB
ejpam-4493	64	45	g	g	NOUN
ejpam-4493	64	46	be	be	AUX
ejpam-4493	64	47	a	a	DET
ejpam-4493	64	48	connected	connected	ADJ
ejpam-4493	64	49	graph	graph	NOUN
ejpam-4493	64	50	.	.	PUNCT
ejpam-4493	65	1	a	a	DET
ejpam-4493	65	2	hop	hop	NOUN
ejpam-4493	65	3	dominating	dominating	NOUN
ejpam-4493	65	4	set	set	NOUN
ejpam-4493	65	5	s	s	PROPN
ejpam-4493	65	6	⊆	⊆	NUM
ejpam-4493	65	7	v	v	NOUN
ejpam-4493	65	8	(	(	PUNCT
ejpam-4493	65	9	g	g	NOUN
ejpam-4493	65	10	)	)	PUNCT
ejpam-4493	65	11	is	be	AUX
ejpam-4493	65	12	a	a	DET
ejpam-4493	65	13	connected	connected	ADJ
ejpam-4493	65	14	co	co	NOUN
ejpam-4493	65	15	-	-	ADJ
ejpam-4493	65	16	independent	independent	ADJ
ejpam-4493	65	17	hop	hop	NOUN
ejpam-4493	65	18	dominating	dominating	NOUN
ejpam-4493	65	19	set	set	NOUN
ejpam-4493	65	20	of	of	ADP
ejpam-4493	65	21	g	g	PROPN
ejpam-4493	65	22	if	if	SCONJ
ejpam-4493	65	23	⟨s⟩	⟨s⟩	PROPN
ejpam-4493	65	24	is	be	AUX
ejpam-4493	65	25	connected	connect	VERB
ejpam-4493	65	26	and	and	CCONJ
ejpam-4493	65	27	v	v	NOUN
ejpam-4493	65	28	(	(	PUNCT
ejpam-4493	65	29	g)\s	g)\s	NOUN
ejpam-4493	65	30	is	be	AUX
ejpam-4493	65	31	an	an	DET
ejpam-4493	65	32	independent	independent	ADJ
ejpam-4493	65	33	set	set	NOUN
ejpam-4493	65	34	.	.	PUNCT
ejpam-4493	66	1	the	the	DET
ejpam-4493	66	2	minimum	minimum	ADJ
ejpam-4493	66	3	cardinality	cardinality	NOUN
ejpam-4493	66	4	of	of	ADP
ejpam-4493	66	5	a	a	DET
ejpam-4493	66	6	connected	connected	ADJ
ejpam-4493	66	7	co	co	NOUN
ejpam-4493	66	8	-	-	ADJ
ejpam-4493	66	9	independent	independent	ADJ
ejpam-4493	66	10	hop	hop	NOUN
ejpam-4493	66	11	dominating	dominating	NOUN
ejpam-4493	66	12	set	set	NOUN
ejpam-4493	66	13	of	of	ADP
ejpam-4493	66	14	g	g	NOUN
ejpam-4493	66	15	,	,	PUNCT
ejpam-4493	66	16	denoted	denote	VERB
ejpam-4493	66	17	by	by	ADP
ejpam-4493	66	18	γch	γch	NOUN
ejpam-4493	66	19	,	,	PUNCT
ejpam-4493	66	20	coi(g	coi(g	PROPN
ejpam-4493	66	21	)	)	PUNCT
ejpam-4493	66	22	,	,	PUNCT
ejpam-4493	66	23	is	be	AUX
ejpam-4493	66	24	called	call	VERB
ejpam-4493	66	25	the	the	DET
ejpam-4493	66	26	connected	connected	ADJ
ejpam-4493	66	27	co	co	NOUN
ejpam-4493	66	28	-	-	ADJ
ejpam-4493	66	29	independent	independent	ADJ
ejpam-4493	66	30	hop	hop	NOUN
ejpam-4493	66	31	domination	domination	NOUN
ejpam-4493	66	32	number	number	NOUN
ejpam-4493	66	33	of	of	ADP
ejpam-4493	66	34	g.	g.	PROPN
ejpam-4493	66	35	a	a	DET
ejpam-4493	66	36	connected	connected	ADJ
ejpam-4493	66	37	co	co	NOUN
ejpam-4493	66	38	-	-	ADJ
ejpam-4493	66	39	independent	independent	ADJ
ejpam-4493	66	40	hop	hop	NOUN
ejpam-4493	66	41	dominating	dominating	NOUN
ejpam-4493	66	42	set	set	NOUN
ejpam-4493	66	43	s	s	NOUN
ejpam-4493	66	44	with	with	ADP
ejpam-4493	66	45	|s|	|s|	NOUN
ejpam-4493	66	46	=	=	SYM
ejpam-4493	66	47	γch	γch	NOUN
ejpam-4493	66	48	,	,	PUNCT
ejpam-4493	66	49	coi(g	coi(g	PROPN
ejpam-4493	66	50	)	)	PUNCT
ejpam-4493	66	51	is	be	AUX
ejpam-4493	66	52	called	call	VERB
ejpam-4493	66	53	a	a	DET
ejpam-4493	66	54	γch	γch	NOUN
ejpam-4493	66	55	,	,	PUNCT
ejpam-4493	66	56	coi	coi	NOUN
ejpam-4493	66	57	-	-	PUNCT
ejpam-4493	66	58	set	set	NOUN
ejpam-4493	66	59	of	of	ADP
ejpam-4493	66	60	g.	g.	PROPN
ejpam-4493	66	61	let	let	VERB
ejpam-4493	66	62	w	w	NOUN
ejpam-4493	66	63	be	be	AUX
ejpam-4493	66	64	a	a	DET
ejpam-4493	66	65	γch	γch	NOUN
ejpam-4493	66	66	,	,	PUNCT
ejpam-4493	66	67	coi	coi	NOUN
ejpam-4493	66	68	-	-	PUNCT
ejpam-4493	66	69	set	set	NOUN
ejpam-4493	66	70	of	of	ADP
ejpam-4493	66	71	a	a	DET
ejpam-4493	66	72	graph	graph	NOUN
ejpam-4493	66	73	g.	g.	NOUN
ejpam-4493	66	74	a	a	DET
ejpam-4493	66	75	subset	subset	NOUN
ejpam-4493	66	76	s	s	NOUN
ejpam-4493	66	77	of	of	ADP
ejpam-4493	66	78	w	w	NOUN
ejpam-4493	66	79	is	be	AUX
ejpam-4493	66	80	said	say	VERB
ejpam-4493	66	81	to	to	PART
ejpam-4493	66	82	be	be	AUX
ejpam-4493	66	83	a	a	DET
ejpam-4493	66	84	forcing	forcing	NOUN
ejpam-4493	66	85	subset	subset	NOUN
ejpam-4493	66	86	for	for	ADP
ejpam-4493	66	87	w	w	PROPN
ejpam-4493	66	88	if	if	SCONJ
ejpam-4493	66	89	w	w	PROPN
ejpam-4493	66	90	is	be	AUX
ejpam-4493	66	91	the	the	DET
ejpam-4493	66	92	unique	unique	ADJ
ejpam-4493	66	93	γch	γch	NOUN
ejpam-4493	66	94	,	,	PUNCT
ejpam-4493	66	95	coi	coi	NOUN
ejpam-4493	66	96	-	-	PUNCT
ejpam-4493	66	97	set	set	NOUN
ejpam-4493	66	98	containing	contain	VERB
ejpam-4493	66	99	s.	s.	PROPN
ejpam-4493	66	100	the	the	DET
ejpam-4493	66	101	forcing	force	VERB
ejpam-4493	66	102	connected	connect	VERB
ejpam-4493	66	103	co	co	ADJ
ejpam-4493	66	104	-	-	ADJ
ejpam-4493	66	105	independent	independent	ADJ
ejpam-4493	66	106	hop	hop	NOUN
ejpam-4493	66	107	domination	domination	NOUN
ejpam-4493	66	108	number	number	NOUN
ejpam-4493	66	109	of	of	ADP
ejpam-4493	66	110	w	w	PROPN
ejpam-4493	66	111	is	be	AUX
ejpam-4493	66	112	given	give	VERB
ejpam-4493	66	113	by	by	ADP
ejpam-4493	66	114	fγch	fγch	NOUN
ejpam-4493	66	115	,	,	PUNCT
ejpam-4493	66	116	coi(w	coi(w	PROPN
ejpam-4493	66	117	)	)	PUNCT
ejpam-4493	67	1	=	=	NOUN
ejpam-4493	67	2	min{|s|	min{|s|	NOUN
ejpam-4493	67	3	:	:	PUNCT
ejpam-4493	67	4	s	s	VERB
ejpam-4493	67	5	is	be	AUX
ejpam-4493	67	6	a	a	DET
ejpam-4493	67	7	forcing	forcing	NOUN
ejpam-4493	67	8	subset	subset	NOUN
ejpam-4493	67	9	for	for	ADP
ejpam-4493	67	10	w	w	NOUN
ejpam-4493	67	11	}	}	PUNCT
ejpam-4493	67	12	.	.	PUNCT
ejpam-4493	68	1	the	the	DET
ejpam-4493	68	2	forcing	force	VERB
ejpam-4493	68	3	connected	connect	VERB
ejpam-4493	68	4	co	co	ADJ
ejpam-4493	68	5	-	-	ADJ
ejpam-4493	68	6	independent	independent	ADJ
ejpam-4493	68	7	hop	hop	NOUN
ejpam-4493	68	8	domination	domination	NOUN
ejpam-4493	68	9	number	number	NOUN
ejpam-4493	68	10	of	of	ADP
ejpam-4493	68	11	g	g	PROPN
ejpam-4493	68	12	is	be	AUX
ejpam-4493	68	13	given	give	VERB
ejpam-4493	68	14	by	by	ADP
ejpam-4493	68	15	fγch	fγch	NOUN
ejpam-4493	68	16	,	,	PUNCT
ejpam-4493	68	17	coi(g	coi(g	PROPN
ejpam-4493	68	18	)	)	PUNCT
ejpam-4493	69	1	=	=	SYM
ejpam-4493	69	2	min{fγch	min{fγch	NOUN
ejpam-4493	69	3	,	,	PUNCT
ejpam-4493	69	4	coi(w	coi(w	PROPN
ejpam-4493	69	5	)	)	PUNCT
ejpam-4493	69	6	:	:	PUNCT
ejpam-4493	70	1	w	w	NOUN
ejpam-4493	70	2	is	be	AUX
ejpam-4493	70	3	a	a	DET
ejpam-4493	70	4	γch	γch	NOUN
ejpam-4493	70	5	,	,	PUNCT
ejpam-4493	70	6	coi	coi	NOUN
ejpam-4493	70	7	-	-	PUNCT
ejpam-4493	70	8	set	set	NOUN
ejpam-4493	70	9	of	of	ADP
ejpam-4493	70	10	g	g	NOUN
ejpam-4493	70	11	}	}	PUNCT
ejpam-4493	70	12	.	.	PUNCT
ejpam-4493	71	1	y.d	y.d	PROPN
ejpam-4493	71	2	.	.	PROPN
ejpam-4493	71	3	calanza	calanza	PROPN
ejpam-4493	71	4	,	,	PUNCT
ejpam-4493	71	5	h.	h.	PROPN
ejpam-4493	71	6	rara	rara	PROPN
ejpam-4493	71	7	/	/	SYM
ejpam-4493	71	8	eur	eur	PROPN
ejpam-4493	71	9	.	.	PUNCT
ejpam-4493	72	1	j.	j.	PROPN
ejpam-4493	72	2	pure	pure	PROPN
ejpam-4493	72	3	appl	appl	PROPN
ejpam-4493	72	4	.	.	PROPN
ejpam-4493	72	5	math	math	PROPN
ejpam-4493	72	6	,	,	PUNCT
ejpam-4493	72	7	15	15	NUM
ejpam-4493	72	8	(	(	PUNCT
ejpam-4493	72	9	4	4	NUM
ejpam-4493	72	10	)	)	PUNCT
ejpam-4493	72	11	(	(	PUNCT
ejpam-4493	72	12	2022	2022	NUM
ejpam-4493	72	13	)	)	PUNCT
ejpam-4493	72	14	,	,	PUNCT
ejpam-4493	72	15	1649	1649	NUM
ejpam-4493	72	16	-	-	SYM
ejpam-4493	72	17	1661	1661	NUM
ejpam-4493	72	18	1652	1652	NUM
ejpam-4493	72	19	let	let	VERB
ejpam-4493	72	20	w	w	NOUN
ejpam-4493	72	21	be	be	AUX
ejpam-4493	72	22	an	an	DET
ejpam-4493	72	23	sci	sci	PROPN
ejpam-4493	72	24	-	-	PUNCT
ejpam-4493	72	25	set	set	NOUN
ejpam-4493	72	26	of	of	ADP
ejpam-4493	72	27	a	a	DET
ejpam-4493	72	28	graph	graph	NOUN
ejpam-4493	72	29	g.	g.	NOUN
ejpam-4493	72	30	a	a	DET
ejpam-4493	72	31	subset	subset	NOUN
ejpam-4493	72	32	s	s	NOUN
ejpam-4493	72	33	of	of	ADP
ejpam-4493	72	34	w	w	NOUN
ejpam-4493	72	35	is	be	AUX
ejpam-4493	72	36	said	say	VERB
ejpam-4493	72	37	to	to	PART
ejpam-4493	72	38	be	be	AUX
ejpam-4493	72	39	a	a	DET
ejpam-4493	72	40	forcing	forcing	NOUN
ejpam-4493	72	41	subset	subset	NOUN
ejpam-4493	72	42	for	for	ADP
ejpam-4493	72	43	w	w	PROPN
ejpam-4493	72	44	if	if	SCONJ
ejpam-4493	72	45	w	w	PROPN
ejpam-4493	72	46	is	be	AUX
ejpam-4493	72	47	the	the	DET
ejpam-4493	72	48	unique	unique	ADJ
ejpam-4493	72	49	sci	sci	PROPN
ejpam-4493	72	50	-	-	PUNCT
ejpam-4493	72	51	set	set	NOUN
ejpam-4493	72	52	containing	contain	VERB
ejpam-4493	72	53	s.	s.	PROPN
ejpam-4493	72	54	the	the	DET
ejpam-4493	72	55	forcing	force	VERB
ejpam-4493	72	56	strictly	strictly	ADV
ejpam-4493	72	57	co	co	ADJ
ejpam-4493	72	58	-	-	ADJ
ejpam-4493	72	59	independent	independent	ADJ
ejpam-4493	72	60	number	number	NOUN
ejpam-4493	72	61	of	of	ADP
ejpam-4493	72	62	w	w	NOUN
ejpam-4493	72	63	is	be	AUX
ejpam-4493	72	64	given	give	VERB
ejpam-4493	72	65	by	by	ADP
ejpam-4493	72	66	fsci(w	fsci(w	NOUN
ejpam-4493	72	67	)	)	PUNCT
ejpam-4493	73	1	=	=	PUNCT
ejpam-4493	73	2	min{|s|	min{|s|	NOUN
ejpam-4493	73	3	:	:	PUNCT
ejpam-4493	73	4	s	s	VERB
ejpam-4493	73	5	is	be	AUX
ejpam-4493	73	6	a	a	DET
ejpam-4493	73	7	forcing	forcing	NOUN
ejpam-4493	73	8	subset	subset	NOUN
ejpam-4493	73	9	for	for	ADP
ejpam-4493	73	10	w	w	NOUN
ejpam-4493	73	11	}	}	PUNCT
ejpam-4493	73	12	.	.	PUNCT
ejpam-4493	74	1	the	the	DET
ejpam-4493	74	2	forcing	force	VERB
ejpam-4493	74	3	strictly	strictly	ADV
ejpam-4493	74	4	co	co	ADJ
ejpam-4493	74	5	-	-	ADJ
ejpam-4493	74	6	independent	independent	ADJ
ejpam-4493	74	7	number	number	NOUN
ejpam-4493	74	8	of	of	ADP
ejpam-4493	74	9	g	g	PROPN
ejpam-4493	74	10	is	be	AUX
ejpam-4493	74	11	given	give	VERB
ejpam-4493	74	12	by	by	ADP
ejpam-4493	74	13	fsci(g	fsci(g	PROPN
ejpam-4493	74	14	)	)	PUNCT
ejpam-4493	74	15	=	=	SYM
ejpam-4493	74	16	min{fsci(w	min{fsci(w	PROPN
ejpam-4493	74	17	)	)	PUNCT
ejpam-4493	74	18	:	:	PUNCT
ejpam-4493	75	1	w	w	NOUN
ejpam-4493	75	2	is	be	AUX
ejpam-4493	75	3	an	an	DET
ejpam-4493	75	4	sci	sci	PROPN
ejpam-4493	75	5	-	-	PUNCT
ejpam-4493	75	6	set	set	NOUN
ejpam-4493	75	7	of	of	ADP
ejpam-4493	75	8	g	g	NOUN
ejpam-4493	75	9	}	}	PUNCT
ejpam-4493	75	10	.	.	PUNCT
ejpam-4493	76	1	let	let	VERB
ejpam-4493	76	2	w	w	NOUN
ejpam-4493	76	3	be	be	AUX
ejpam-4493	76	4	a	a	DET
ejpam-4493	76	5	coi	coi	NOUN
ejpam-4493	76	6	-	-	PUNCT
ejpam-4493	76	7	set	set	NOUN
ejpam-4493	76	8	of	of	ADP
ejpam-4493	76	9	a	a	DET
ejpam-4493	76	10	graph	graph	NOUN
ejpam-4493	76	11	g.	g.	NOUN
ejpam-4493	76	12	a	a	DET
ejpam-4493	76	13	subset	subset	NOUN
ejpam-4493	76	14	s	s	NOUN
ejpam-4493	76	15	of	of	ADP
ejpam-4493	76	16	w	w	NOUN
ejpam-4493	76	17	is	be	AUX
ejpam-4493	76	18	said	say	VERB
ejpam-4493	76	19	to	to	PART
ejpam-4493	76	20	be	be	AUX
ejpam-4493	76	21	a	a	DET
ejpam-4493	76	22	forcing	forcing	NOUN
ejpam-4493	76	23	subset	subset	NOUN
ejpam-4493	76	24	for	for	ADP
ejpam-4493	76	25	w	w	PROPN
ejpam-4493	76	26	if	if	SCONJ
ejpam-4493	76	27	w	w	PROPN
ejpam-4493	76	28	is	be	AUX
ejpam-4493	76	29	the	the	DET
ejpam-4493	76	30	unique	unique	ADJ
ejpam-4493	76	31	coi	coi	NOUN
ejpam-4493	76	32	-	-	PUNCT
ejpam-4493	76	33	set	set	NOUN
ejpam-4493	76	34	containing	contain	VERB
ejpam-4493	76	35	s.	s.	PROPN
ejpam-4493	76	36	the	the	DET
ejpam-4493	76	37	forcing	force	VERB
ejpam-4493	76	38	co	co	ADJ
ejpam-4493	76	39	-	-	ADJ
ejpam-4493	76	40	independent	independent	ADJ
ejpam-4493	76	41	number	number	NOUN
ejpam-4493	76	42	of	of	ADP
ejpam-4493	76	43	w	w	NOUN
ejpam-4493	76	44	is	be	AUX
ejpam-4493	76	45	given	give	VERB
ejpam-4493	76	46	by	by	ADP
ejpam-4493	76	47	fcoi(w	fcoi(w	NOUN
ejpam-4493	76	48	)	)	PUNCT
ejpam-4493	77	1	=	=	PUNCT
ejpam-4493	77	2	min{|s|	min{|s|	NOUN
ejpam-4493	77	3	:	:	PUNCT
ejpam-4493	77	4	s	s	VERB
ejpam-4493	77	5	is	be	AUX
ejpam-4493	77	6	a	a	DET
ejpam-4493	77	7	forcing	forcing	NOUN
ejpam-4493	77	8	subset	subset	NOUN
ejpam-4493	77	9	for	for	ADP
ejpam-4493	77	10	w	w	NOUN
ejpam-4493	77	11	}	}	PUNCT
ejpam-4493	77	12	.	.	PUNCT
ejpam-4493	78	1	the	the	DET
ejpam-4493	78	2	forcing	force	VERB
ejpam-4493	78	3	co	co	ADJ
ejpam-4493	78	4	-	-	ADJ
ejpam-4493	78	5	independent	independent	ADJ
ejpam-4493	78	6	number	number	NOUN
ejpam-4493	78	7	of	of	ADP
ejpam-4493	78	8	g	g	PROPN
ejpam-4493	78	9	is	be	AUX
ejpam-4493	78	10	given	give	VERB
ejpam-4493	78	11	by	by	ADP
ejpam-4493	78	12	fcoi(g	fcoi(g	PROPN
ejpam-4493	78	13	)	)	PUNCT
ejpam-4493	79	1	=	=	SYM
ejpam-4493	79	2	min{fcoi(w	min{fcoi(w	PROPN
ejpam-4493	79	3	)	)	PUNCT
ejpam-4493	79	4	:	:	PUNCT
ejpam-4493	80	1	w	w	NOUN
ejpam-4493	80	2	is	be	AUX
ejpam-4493	80	3	a	a	DET
ejpam-4493	80	4	coi	coi	NOUN
ejpam-4493	80	5	-	-	PUNCT
ejpam-4493	80	6	set	set	NOUN
ejpam-4493	80	7	of	of	ADP
ejpam-4493	80	8	g	g	NOUN
ejpam-4493	80	9	}	}	PUNCT
ejpam-4493	80	10	.	.	PUNCT
ejpam-4493	81	1	2	2	X
ejpam-4493	81	2	.	.	X
ejpam-4493	81	3	known	know	VERB
ejpam-4493	81	4	results	result	VERB
ejpam-4493	81	5	the	the	DET
ejpam-4493	81	6	following	follow	VERB
ejpam-4493	81	7	known	know	VERB
ejpam-4493	81	8	results	result	NOUN
ejpam-4493	81	9	are	be	AUX
ejpam-4493	81	10	taken	take	VERB
ejpam-4493	81	11	from	from	ADP
ejpam-4493	81	12	[	[	X
ejpam-4493	81	13	11	11	NUM
ejpam-4493	81	14	]	]	PUNCT
ejpam-4493	81	15	.	.	PUNCT
ejpam-4493	82	1	theorem	theorem	NOUN
ejpam-4493	82	2	1	1	X
ejpam-4493	82	3	.	.	PUNCT
ejpam-4493	83	1	let	let	VERB
ejpam-4493	83	2	g	g	NOUN
ejpam-4493	84	1	and	and	CCONJ
ejpam-4493	84	2	h	h	NOUN
ejpam-4493	84	3	be	be	VERB
ejpam-4493	84	4	any	any	DET
ejpam-4493	84	5	two	two	NUM
ejpam-4493	84	6	graphs	graph	NOUN
ejpam-4493	84	7	.	.	PUNCT
ejpam-4493	85	1	then	then	ADV
ejpam-4493	85	2	s	s	VERB
ejpam-4493	85	3	⊆	⊆	NUM
ejpam-4493	85	4	v	v	NOUN
ejpam-4493	85	5	(	(	PUNCT
ejpam-4493	85	6	g	g	PROPN
ejpam-4493	85	7	+	+	NOUN
ejpam-4493	85	8	h	h	NOUN
ejpam-4493	85	9	)	)	PUNCT
ejpam-4493	85	10	is	be	AUX
ejpam-4493	85	11	a	a	DET
ejpam-4493	85	12	connected	connected	ADJ
ejpam-4493	85	13	co	co	NOUN
ejpam-4493	85	14	-	-	ADJ
ejpam-4493	85	15	independent	independent	ADJ
ejpam-4493	85	16	hop	hop	NOUN
ejpam-4493	85	17	dominating	dominating	NOUN
ejpam-4493	85	18	set	set	NOUN
ejpam-4493	85	19	of	of	ADP
ejpam-4493	85	20	g+h	g+h	PROPN
ejpam-4493	86	1	if	if	SCONJ
ejpam-4493	86	2	and	and	CCONJ
ejpam-4493	86	3	only	only	ADV
ejpam-4493	86	4	if	if	SCONJ
ejpam-4493	86	5	s	s	VERB
ejpam-4493	86	6	=	=	PUNCT
ejpam-4493	86	7	sg	sg	X
ejpam-4493	86	8	∪	∪	NOUN
ejpam-4493	86	9	sh	sh	PRON
ejpam-4493	86	10	where	where	SCONJ
ejpam-4493	86	11	one	one	NUM
ejpam-4493	86	12	of	of	ADP
ejpam-4493	86	13	the	the	DET
ejpam-4493	86	14	following	follow	VERB
ejpam-4493	86	15	holds	hold	VERB
ejpam-4493	86	16	:	:	PUNCT
ejpam-4493	86	17	(	(	PUNCT
ejpam-4493	86	18	i	i	NOUN
ejpam-4493	86	19	)	)	PUNCT
ejpam-4493	86	20	sg	sg	PROPN
ejpam-4493	86	21	=	=	SYM
ejpam-4493	86	22	v	v	PROPN
ejpam-4493	86	23	(	(	PUNCT
ejpam-4493	86	24	g	g	NOUN
ejpam-4493	86	25	)	)	PUNCT
ejpam-4493	86	26	and	and	CCONJ
ejpam-4493	86	27	sh	sh	PROPN
ejpam-4493	86	28	is	be	AUX
ejpam-4493	86	29	a	a	DET
ejpam-4493	86	30	strictly	strictly	ADV
ejpam-4493	86	31	co	co	ADJ
ejpam-4493	86	32	-	-	ADJ
ejpam-4493	86	33	independent	independent	ADJ
ejpam-4493	86	34	set	set	NOUN
ejpam-4493	86	35	of	of	ADP
ejpam-4493	86	36	h.	h.	PROPN
ejpam-4493	86	37	(	(	PUNCT
ejpam-4493	86	38	ii	ii	PROPN
ejpam-4493	86	39	)	)	PUNCT
ejpam-4493	87	1	sh	sh	PROPN
ejpam-4493	88	1	=	=	SYM
ejpam-4493	88	2	v	v	PROPN
ejpam-4493	88	3	(	(	PUNCT
ejpam-4493	88	4	h	h	NOUN
ejpam-4493	88	5	)	)	PUNCT
ejpam-4493	88	6	and	and	CCONJ
ejpam-4493	88	7	sg	sg	PROPN
ejpam-4493	88	8	is	be	AUX
ejpam-4493	88	9	a	a	DET
ejpam-4493	88	10	strictly	strictly	ADV
ejpam-4493	88	11	co	co	ADJ
ejpam-4493	88	12	-	-	ADJ
ejpam-4493	88	13	independent	independent	ADJ
ejpam-4493	88	14	set	set	NOUN
ejpam-4493	88	15	of	of	ADP
ejpam-4493	88	16	g.	g.	PROPN
ejpam-4493	88	17	corollary	corollary	PROPN
ejpam-4493	88	18	1	1	PROPN
ejpam-4493	88	19	.	.	PUNCT
ejpam-4493	89	1	let	let	VERB
ejpam-4493	89	2	g	g	NOUN
ejpam-4493	89	3	and	and	CCONJ
ejpam-4493	89	4	h	h	NOUN
ejpam-4493	89	5	be	be	VERB
ejpam-4493	89	6	any	any	DET
ejpam-4493	89	7	two	two	NUM
ejpam-4493	89	8	graphs	graph	NOUN
ejpam-4493	89	9	where	where	SCONJ
ejpam-4493	89	10	|v	|v	PROPN
ejpam-4493	89	11	(	(	PUNCT
ejpam-4493	89	12	g)|	g)|	NOUN
ejpam-4493	89	13	=	=	PUNCT
ejpam-4493	89	14	n	n	NOUN
ejpam-4493	89	15	and	and	CCONJ
ejpam-4493	89	16	|v	|v	PROPN
ejpam-4493	89	17	(	(	PUNCT
ejpam-4493	89	18	h)|	h)|	NOUN
ejpam-4493	89	19	=	=	PUNCT
ejpam-4493	89	20	m.	m.	NOUN
ejpam-4493	89	21	then	then	ADV
ejpam-4493	89	22	γch	γch	AUX
ejpam-4493	89	23	,	,	PUNCT
ejpam-4493	89	24	coi(g+h	coi(g+h	NOUN
ejpam-4493	89	25	)	)	PUNCT
ejpam-4493	89	26	=	=	PUNCT
ejpam-4493	90	1	min{n+	min{n+	VERB
ejpam-4493	90	2	sci(h),m+	sci(h),m+	NOUN
ejpam-4493	90	3	sci(g	sci(g	PROPN
ejpam-4493	90	4	)	)	PUNCT
ejpam-4493	90	5	}	}	PUNCT
ejpam-4493	90	6	.	.	PUNCT
ejpam-4493	91	1	theorem	theorem	NOUN
ejpam-4493	91	2	2	2	NUM
ejpam-4493	91	3	.	.	PUNCT
ejpam-4493	92	1	let	let	VERB
ejpam-4493	92	2	g	g	PRON
ejpam-4493	92	3	be	be	AUX
ejpam-4493	92	4	a	a	DET
ejpam-4493	92	5	nontrivial	nontrivial	ADJ
ejpam-4493	92	6	connected	connect	VERB
ejpam-4493	92	7	graph	graph	NOUN
ejpam-4493	92	8	and	and	CCONJ
ejpam-4493	92	9	h	h	NOUN
ejpam-4493	92	10	be	be	AUX
ejpam-4493	92	11	any	any	DET
ejpam-4493	92	12	graph	graph	NOUN
ejpam-4493	92	13	.	.	PUNCT
ejpam-4493	93	1	a	a	DET
ejpam-4493	93	2	set	set	NOUN
ejpam-4493	93	3	s	s	NOUN
ejpam-4493	93	4	⊆	⊆	NUM
ejpam-4493	93	5	v	v	NOUN
ejpam-4493	93	6	(	(	PUNCT
ejpam-4493	93	7	g	g	PROPN
ejpam-4493	93	8	◦	◦	NOUN
ejpam-4493	93	9	h	h	NOUN
ejpam-4493	93	10	)	)	PUNCT
ejpam-4493	93	11	is	be	AUX
ejpam-4493	93	12	a	a	DET
ejpam-4493	93	13	connected	connected	ADJ
ejpam-4493	93	14	co	co	NOUN
ejpam-4493	93	15	-	-	ADJ
ejpam-4493	93	16	independent	independent	ADJ
ejpam-4493	93	17	hop	hop	NOUN
ejpam-4493	93	18	dominating	dominating	NOUN
ejpam-4493	93	19	set	set	NOUN
ejpam-4493	93	20	of	of	ADP
ejpam-4493	93	21	g	g	PROPN
ejpam-4493	93	22	◦	◦	NOUN
ejpam-4493	93	23	h	h	NOUN
ejpam-4493	93	24	if	if	SCONJ
ejpam-4493	94	1	and	and	CCONJ
ejpam-4493	94	2	only	only	ADV
ejpam-4493	94	3	if	if	SCONJ
ejpam-4493	94	4	s	s	VERB
ejpam-4493	94	5	=	=	SYM
ejpam-4493	94	6	v	v	X
ejpam-4493	94	7	(	(	PUNCT
ejpam-4493	94	8	g	g	NOUN
ejpam-4493	94	9	)	)	PUNCT
ejpam-4493	94	10	∪	∪	NOUN
ejpam-4493	94	11	(	(	PUNCT
ejpam-4493	94	12	⋃	⋃	ADJ
ejpam-4493	94	13	v∈v	v∈v	NOUN
ejpam-4493	94	14	(	(	PUNCT
ejpam-4493	94	15	g	g	NOUN
ejpam-4493	94	16	)	)	PUNCT
ejpam-4493	94	17	sv	sv	NOUN
ejpam-4493	94	18	)	)	PUNCT
ejpam-4493	94	19	,	,	PUNCT
ejpam-4493	94	20	where	where	SCONJ
ejpam-4493	94	21	sv	sv	PROPN
ejpam-4493	94	22	⊆	⊆	NUM
ejpam-4493	94	23	v	v	X
ejpam-4493	94	24	(	(	PUNCT
ejpam-4493	94	25	hv	hv	NOUN
ejpam-4493	94	26	)	)	PUNCT
ejpam-4493	94	27	and	and	CCONJ
ejpam-4493	94	28	v	v	NOUN
ejpam-4493	94	29	(	(	PUNCT
ejpam-4493	94	30	hv)\sv	hv)\sv	PROPN
ejpam-4493	94	31	is	be	AUX
ejpam-4493	94	32	an	an	DET
ejpam-4493	94	33	independent	independent	ADJ
ejpam-4493	94	34	subset	subset	NOUN
ejpam-4493	94	35	of	of	ADP
ejpam-4493	94	36	v	v	PROPN
ejpam-4493	94	37	(	(	PUNCT
ejpam-4493	94	38	hv	hv	PROPN
ejpam-4493	94	39	)	)	PUNCT
ejpam-4493	94	40	for	for	ADP
ejpam-4493	94	41	each	each	DET
ejpam-4493	94	42	v	v	NUM
ejpam-4493	94	43	∈	∈	PROPN
ejpam-4493	94	44	v	v	NOUN
ejpam-4493	94	45	(	(	PUNCT
ejpam-4493	94	46	g	g	NOUN
ejpam-4493	94	47	)	)	PUNCT
ejpam-4493	94	48	.	.	PUNCT
ejpam-4493	95	1	corollary	corollary	ADJ
ejpam-4493	95	2	2	2	NUM
ejpam-4493	95	3	.	.	PUNCT
ejpam-4493	96	1	let	let	VERB
ejpam-4493	96	2	g	g	PRON
ejpam-4493	96	3	be	be	AUX
ejpam-4493	96	4	a	a	DET
ejpam-4493	96	5	nontrivial	nontrivial	ADJ
ejpam-4493	96	6	connected	connect	VERB
ejpam-4493	96	7	graph	graph	NOUN
ejpam-4493	96	8	of	of	ADP
ejpam-4493	96	9	order	order	NOUN
ejpam-4493	96	10	n	n	NOUN
ejpam-4493	97	1	and	and	CCONJ
ejpam-4493	97	2	h	h	NOUN
ejpam-4493	97	3	be	be	AUX
ejpam-4493	97	4	any	any	DET
ejpam-4493	97	5	graph	graph	NOUN
ejpam-4493	97	6	of	of	ADP
ejpam-4493	97	7	order	order	NOUN
ejpam-4493	97	8	m.	m.	NOUN
ejpam-4493	97	9	then	then	ADV
ejpam-4493	97	10	γch	γch	VERB
ejpam-4493	97	11	,	,	PUNCT
ejpam-4493	97	12	coi(g	coi(g	PROPN
ejpam-4493	97	13	◦	◦	NOUN
ejpam-4493	97	14	h	h	NOUN
ejpam-4493	97	15	)	)	PUNCT
ejpam-4493	97	16	=	=	PUNCT
ejpam-4493	98	1	n(1	n(1	PROPN
ejpam-4493	98	2	+	+	ADJ
ejpam-4493	98	3	m−	m−	PROPN
ejpam-4493	98	4	β(h	β(h	NOUN
ejpam-4493	98	5	)	)	PUNCT
ejpam-4493	98	6	)	)	PUNCT
ejpam-4493	98	7	.	.	PUNCT
ejpam-4493	99	1	3	3	X
ejpam-4493	99	2	.	.	X
ejpam-4493	99	3	forcing	force	VERB
ejpam-4493	99	4	connected	connected	ADJ
ejpam-4493	99	5	co	co	ADJ
ejpam-4493	99	6	-	-	ADJ
ejpam-4493	99	7	independent	independent	ADJ
ejpam-4493	99	8	hop	hop	NOUN
ejpam-4493	99	9	domination	domination	NOUN
ejpam-4493	99	10	number	number	NOUN
ejpam-4493	99	11	of	of	ADP
ejpam-4493	99	12	some	some	DET
ejpam-4493	99	13	special	special	ADJ
ejpam-4493	99	14	graphs	graph	NOUN
ejpam-4493	99	15	remark	remark	VERB
ejpam-4493	99	16	1	1	NUM
ejpam-4493	99	17	.	.	PUNCT
ejpam-4493	100	1	let	let	VERB
ejpam-4493	100	2	g	g	PRON
ejpam-4493	100	3	be	be	AUX
ejpam-4493	100	4	a	a	DET
ejpam-4493	100	5	connected	connected	ADJ
ejpam-4493	100	6	graph	graph	NOUN
ejpam-4493	100	7	.	.	PUNCT
ejpam-4493	101	1	then	then	ADV
ejpam-4493	101	2	(	(	PUNCT
ejpam-4493	101	3	i	i	NOUN
ejpam-4493	101	4	)	)	PUNCT
ejpam-4493	101	5	fγch	fγch	PROPN
ejpam-4493	101	6	,	,	PUNCT
ejpam-4493	101	7	coi(g	coi(g	PROPN
ejpam-4493	101	8	)	)	PUNCT
ejpam-4493	101	9	=	=	SYM
ejpam-4493	101	10	0	0	PUNCT
ejpam-4493	102	1	if	if	SCONJ
ejpam-4493	102	2	and	and	CCONJ
ejpam-4493	102	3	only	only	ADV
ejpam-4493	102	4	if	if	SCONJ
ejpam-4493	102	5	g	g	PROPN
ejpam-4493	102	6	has	have	VERB
ejpam-4493	102	7	a	a	DET
ejpam-4493	102	8	unique	unique	ADJ
ejpam-4493	102	9	γch	γch	NOUN
ejpam-4493	102	10	,	,	PUNCT
ejpam-4493	102	11	coi	coi	NOUN
ejpam-4493	102	12	-	-	PUNCT
ejpam-4493	102	13	set	set	NOUN
ejpam-4493	102	14	,	,	PUNCT
ejpam-4493	102	15	and	and	CCONJ
ejpam-4493	102	16	(	(	PUNCT
ejpam-4493	102	17	ii	ii	NOUN
ejpam-4493	102	18	)	)	PUNCT
ejpam-4493	102	19	fγch	fγch	PROPN
ejpam-4493	102	20	,	,	PUNCT
ejpam-4493	102	21	coi(g	coi(g	PROPN
ejpam-4493	102	22	)	)	PUNCT
ejpam-4493	102	23	=	=	PUNCT
ejpam-4493	102	24	1	1	NUM
ejpam-4493	102	25	if	if	SCONJ
ejpam-4493	102	26	and	and	CCONJ
ejpam-4493	102	27	only	only	ADV
ejpam-4493	102	28	if	if	SCONJ
ejpam-4493	102	29	g	g	PROPN
ejpam-4493	102	30	has	have	VERB
ejpam-4493	102	31	at	at	ADV
ejpam-4493	102	32	least	least	ADV
ejpam-4493	102	33	two	two	NUM
ejpam-4493	102	34	γch	γch	NOUN
ejpam-4493	102	35	,	,	PUNCT
ejpam-4493	102	36	coi	coi	NOUN
ejpam-4493	102	37	-	-	PUNCT
ejpam-4493	102	38	sets	set	NOUN
ejpam-4493	102	39	,	,	PUNCT
ejpam-4493	102	40	one	one	NUM
ejpam-4493	102	41	of	of	ADP
ejpam-4493	102	42	which	which	PRON
ejpam-4493	102	43	,	,	PUNCT
ejpam-4493	102	44	say	say	VERB
ejpam-4493	102	45	b	b	NOUN
ejpam-4493	102	46	,	,	PUNCT
ejpam-4493	102	47	contains	contain	VERB
ejpam-4493	102	48	an	an	DET
ejpam-4493	102	49	element	element	NOUN
ejpam-4493	102	50	which	which	PRON
ejpam-4493	102	51	is	be	AUX
ejpam-4493	102	52	not	not	PART
ejpam-4493	102	53	found	find	VERB
ejpam-4493	102	54	in	in	ADP
ejpam-4493	102	55	any	any	DET
ejpam-4493	102	56	γch	γch	NOUN
ejpam-4493	102	57	,	,	PUNCT
ejpam-4493	102	58	coi	coi	NOUN
ejpam-4493	102	59	-	-	PUNCT
ejpam-4493	102	60	set	set	NOUN
ejpam-4493	102	61	of	of	ADP
ejpam-4493	102	62	g.	g.	PROPN
ejpam-4493	102	63	theorem	theorem	VERB
ejpam-4493	102	64	3	3	X
ejpam-4493	102	65	.	.	PUNCT
ejpam-4493	102	66	let	let	VERB
ejpam-4493	102	67	g	g	PRON
ejpam-4493	102	68	be	be	AUX
ejpam-4493	102	69	a	a	DET
ejpam-4493	102	70	connected	connected	ADJ
ejpam-4493	102	71	graph	graph	NOUN
ejpam-4493	102	72	.	.	PUNCT
ejpam-4493	103	1	then	then	ADV
ejpam-4493	103	2	fγch	fγch	ADJ
ejpam-4493	103	3	,	,	PUNCT
ejpam-4493	103	4	coi(g	coi(g	PROPN
ejpam-4493	103	5	)	)	PUNCT
ejpam-4493	103	6	=	=	PUNCT
ejpam-4493	104	1	γch	γch	X
ejpam-4493	104	2	,	,	PUNCT
ejpam-4493	104	3	coi(g	coi(g	PROPN
ejpam-4493	104	4	)	)	PUNCT
ejpam-4493	104	5	if	if	SCONJ
ejpam-4493	104	6	and	and	CCONJ
ejpam-4493	104	7	only	only	ADV
ejpam-4493	104	8	if	if	SCONJ
ejpam-4493	104	9	for	for	ADP
ejpam-4493	104	10	all	all	DET
ejpam-4493	104	11	γch	γch	NOUN
ejpam-4493	104	12	,	,	PUNCT
ejpam-4493	104	13	coi	coi	NOUN
ejpam-4493	104	14	-	-	PUNCT
ejpam-4493	104	15	set	set	VERB
ejpam-4493	104	16	b	b	NOUN
ejpam-4493	104	17	of	of	ADP
ejpam-4493	104	18	g	g	PROPN
ejpam-4493	104	19	and	and	CCONJ
ejpam-4493	104	20	for	for	ADP
ejpam-4493	104	21	each	each	DET
ejpam-4493	104	22	v	v	NUM
ejpam-4493	104	23	∈	∈	PROPN
ejpam-4493	104	24	b	b	NOUN
ejpam-4493	104	25	,	,	PUNCT
ejpam-4493	104	26	there	there	PRON
ejpam-4493	104	27	exists	exist	VERB
ejpam-4493	104	28	uv	uv	PROPN
ejpam-4493	104	29	∈	∈	PROPN
ejpam-4493	104	30	v	v	ADP
ejpam-4493	104	31	(	(	PUNCT
ejpam-4493	104	32	g	g	NOUN
ejpam-4493	104	33	)	)	PUNCT
ejpam-4493	104	34	\	\	PROPN
ejpam-4493	105	1	b	b	X
ejpam-4493	105	2	such	such	ADJ
ejpam-4493	105	3	that	that	SCONJ
ejpam-4493	105	4	[	[	PUNCT
ejpam-4493	105	5	b	b	X
ejpam-4493	105	6	\	\	X
ejpam-4493	105	7	{	{	PUNCT
ejpam-4493	105	8	v	v	NOUN
ejpam-4493	105	9	}	}	PUNCT
ejpam-4493	105	10	]	]	PUNCT
ejpam-4493	105	11	∪	∪	X
ejpam-4493	105	12	{	{	PUNCT
ejpam-4493	105	13	uv	uv	NOUN
ejpam-4493	105	14	}	}	PUNCT
ejpam-4493	105	15	is	be	AUX
ejpam-4493	105	16	a	a	DET
ejpam-4493	105	17	γch	γch	NOUN
ejpam-4493	105	18	,	,	PUNCT
ejpam-4493	105	19	coi	coi	NOUN
ejpam-4493	105	20	-	-	PUNCT
ejpam-4493	105	21	set	set	NOUN
ejpam-4493	105	22	of	of	ADP
ejpam-4493	105	23	g.	g.	PROPN
ejpam-4493	105	24	y.d	y.d	PROPN
ejpam-4493	105	25	.	.	PROPN
ejpam-4493	105	26	calanza	calanza	PROPN
ejpam-4493	105	27	,	,	PUNCT
ejpam-4493	105	28	h.	h.	PROPN
ejpam-4493	105	29	rara	rara	PROPN
ejpam-4493	105	30	/	/	SYM
ejpam-4493	105	31	eur	eur	PROPN
ejpam-4493	105	32	.	.	PUNCT
ejpam-4493	106	1	j.	j.	PROPN
ejpam-4493	106	2	pure	pure	PROPN
ejpam-4493	106	3	appl	appl	PROPN
ejpam-4493	106	4	.	.	PROPN
ejpam-4493	106	5	math	math	PROPN
ejpam-4493	106	6	,	,	PUNCT
ejpam-4493	106	7	15	15	NUM
ejpam-4493	106	8	(	(	PUNCT
ejpam-4493	106	9	4	4	NUM
ejpam-4493	106	10	)	)	PUNCT
ejpam-4493	106	11	(	(	PUNCT
ejpam-4493	106	12	2022	2022	NUM
ejpam-4493	106	13	)	)	PUNCT
ejpam-4493	106	14	,	,	PUNCT
ejpam-4493	106	15	1649	1649	NUM
ejpam-4493	106	16	-	-	SYM
ejpam-4493	106	17	1661	1661	NUM
ejpam-4493	106	18	1653	1653	NUM
ejpam-4493	106	19	proof	proof	NOUN
ejpam-4493	106	20	:	:	PUNCT
ejpam-4493	106	21	suppose	suppose	VERB
ejpam-4493	106	22	that	that	SCONJ
ejpam-4493	106	23	fγch	fγch	NOUN
ejpam-4493	106	24	,	,	PUNCT
ejpam-4493	106	25	coi(g	coi(g	PROPN
ejpam-4493	106	26	)	)	PUNCT
ejpam-4493	106	27	=	=	PUNCT
ejpam-4493	107	1	γch	γch	X
ejpam-4493	107	2	,	,	PUNCT
ejpam-4493	107	3	coi(g	coi(g	PROPN
ejpam-4493	107	4	)	)	PUNCT
ejpam-4493	107	5	.	.	PUNCT
ejpam-4493	108	1	let	let	VERB
ejpam-4493	108	2	b	b	X
ejpam-4493	108	3	be	be	AUX
ejpam-4493	108	4	a	a	DET
ejpam-4493	108	5	γch	γch	NOUN
ejpam-4493	108	6	,	,	PUNCT
ejpam-4493	108	7	coi	coi	NOUN
ejpam-4493	108	8	-	-	PUNCT
ejpam-4493	108	9	set	set	NOUN
ejpam-4493	108	10	of	of	ADP
ejpam-4493	108	11	g	g	NOUN
ejpam-4493	108	12	such	such	ADJ
ejpam-4493	108	13	that	that	DET
ejpam-4493	108	14	fγch	fγch	NOUN
ejpam-4493	108	15	,	,	PUNCT
ejpam-4493	108	16	coi(g	coi(g	PROPN
ejpam-4493	108	17	)	)	PUNCT
ejpam-4493	109	1	=	=	SYM
ejpam-4493	109	2	|b|	|b|	PROPN
ejpam-4493	109	3	=	=	PUNCT
ejpam-4493	109	4	γch	γch	X
ejpam-4493	109	5	,	,	PUNCT
ejpam-4493	109	6	coi(g	coi(g	PROPN
ejpam-4493	109	7	)	)	PUNCT
ejpam-4493	109	8	,	,	PUNCT
ejpam-4493	109	9	that	that	ADV
ejpam-4493	109	10	is	is	ADV
ejpam-4493	109	11	,	,	PUNCT
ejpam-4493	109	12	b	b	PROPN
ejpam-4493	109	13	is	be	AUX
ejpam-4493	109	14	the	the	DET
ejpam-4493	109	15	only	only	ADJ
ejpam-4493	109	16	forcing	forcing	NOUN
ejpam-4493	109	17	subset	subset	NOUN
ejpam-4493	109	18	for	for	ADP
ejpam-4493	109	19	itself	itself	PRON
ejpam-4493	109	20	.	.	PUNCT
ejpam-4493	110	1	let	let	VERB
ejpam-4493	110	2	v	v	NUM
ejpam-4493	110	3	∈	∈	PROPN
ejpam-4493	110	4	b.	b.	PROPN
ejpam-4493	110	5	since	since	SCONJ
ejpam-4493	110	6	b	b	PROPN
ejpam-4493	110	7	\	\	PROPN
ejpam-4493	110	8	{	{	PUNCT
ejpam-4493	110	9	v	v	NOUN
ejpam-4493	110	10	}	}	PUNCT
ejpam-4493	110	11	is	be	AUX
ejpam-4493	110	12	not	not	PART
ejpam-4493	110	13	a	a	DET
ejpam-4493	110	14	forcing	forcing	NOUN
ejpam-4493	110	15	subset	subset	NOUN
ejpam-4493	110	16	for	for	ADP
ejpam-4493	110	17	b	b	NOUN
ejpam-4493	110	18	,	,	PUNCT
ejpam-4493	110	19	there	there	PRON
ejpam-4493	110	20	exists	exist	VERB
ejpam-4493	110	21	a	a	DET
ejpam-4493	110	22	uv	uv	NOUN
ejpam-4493	110	23	∈	∈	PROPN
ejpam-4493	110	24	v	v	NOUN
ejpam-4493	110	25	(	(	PUNCT
ejpam-4493	110	26	g	g	NOUN
ejpam-4493	110	27	)	)	PUNCT
ejpam-4493	110	28	\	\	PROPN
ejpam-4493	111	1	b	b	X
ejpam-4493	111	2	such	such	ADJ
ejpam-4493	111	3	that	that	SCONJ
ejpam-4493	111	4	[	[	PUNCT
ejpam-4493	111	5	b	b	X
ejpam-4493	111	6	\	\	X
ejpam-4493	111	7	{	{	PUNCT
ejpam-4493	111	8	v	v	NOUN
ejpam-4493	111	9	}	}	PUNCT
ejpam-4493	111	10	]	]	PUNCT
ejpam-4493	111	11	∪	∪	X
ejpam-4493	111	12	{	{	PUNCT
ejpam-4493	111	13	uv	uv	NOUN
ejpam-4493	111	14	}	}	PUNCT
ejpam-4493	111	15	is	be	AUX
ejpam-4493	111	16	a	a	DET
ejpam-4493	111	17	γch	γch	NOUN
ejpam-4493	111	18	,	,	PUNCT
ejpam-4493	111	19	coi	coi	NOUN
ejpam-4493	111	20	-	-	PUNCT
ejpam-4493	111	21	set	set	NOUN
ejpam-4493	111	22	of	of	ADP
ejpam-4493	111	23	g.	g.	NOUN
ejpam-4493	111	24	conversely	conversely	ADV
ejpam-4493	111	25	,	,	PUNCT
ejpam-4493	111	26	suppose	suppose	VERB
ejpam-4493	111	27	that	that	SCONJ
ejpam-4493	111	28	every	every	DET
ejpam-4493	111	29	γch	γch	NOUN
ejpam-4493	111	30	,	,	PUNCT
ejpam-4493	111	31	coi	coi	NOUN
ejpam-4493	111	32	-	-	PUNCT
ejpam-4493	111	33	set	set	VERB
ejpam-4493	111	34	b	b	NOUN
ejpam-4493	111	35	′	′	NUM
ejpam-4493	111	36	ofg	ofg	PROPN
ejpam-4493	111	37	satisfies	satisfy	VERB
ejpam-4493	111	38	the	the	DET
ejpam-4493	111	39	given	give	VERB
ejpam-4493	111	40	condition	condition	NOUN
ejpam-4493	111	41	.	.	PUNCT
ejpam-4493	112	1	let	let	VERB
ejpam-4493	112	2	b	b	X
ejpam-4493	112	3	be	be	AUX
ejpam-4493	112	4	a	a	DET
ejpam-4493	112	5	γch	γch	NOUN
ejpam-4493	112	6	,	,	PUNCT
ejpam-4493	112	7	coi	coi	NOUN
ejpam-4493	112	8	-	-	PUNCT
ejpam-4493	112	9	set	set	NOUN
ejpam-4493	112	10	of	of	ADP
ejpam-4493	112	11	g	g	NOUN
ejpam-4493	112	12	such	such	ADJ
ejpam-4493	112	13	that	that	DET
ejpam-4493	112	14	fγch	fγch	NOUN
ejpam-4493	112	15	,	,	PUNCT
ejpam-4493	112	16	coi(g	coi(g	PROPN
ejpam-4493	112	17	)	)	PUNCT
ejpam-4493	113	1	=	=	SYM
ejpam-4493	113	2	fγch	fγch	PROPN
ejpam-4493	113	3	,	,	PUNCT
ejpam-4493	113	4	coi(b	coi(b	PROPN
ejpam-4493	113	5	)	)	PUNCT
ejpam-4493	113	6	.	.	PUNCT
ejpam-4493	114	1	suppose	suppose	VERB
ejpam-4493	114	2	further	far	ADV
ejpam-4493	114	3	that	that	SCONJ
ejpam-4493	114	4	b	b	PROPN
ejpam-4493	114	5	has	have	VERB
ejpam-4493	114	6	a	a	DET
ejpam-4493	114	7	forcing	forcing	NOUN
ejpam-4493	114	8	subset	subset	NOUN
ejpam-4493	114	9	q	q	NOUN
ejpam-4493	114	10	with	with	ADP
ejpam-4493	114	11	|q|	|q|	PROPN
ejpam-4493	114	12	<	<	X
ejpam-4493	114	13	|b|	|b|	PROPN
ejpam-4493	114	14	,	,	PUNCT
ejpam-4493	114	15	that	that	ADV
ejpam-4493	114	16	is	be	AUX
ejpam-4493	114	17	,	,	PUNCT
ejpam-4493	114	18	b	b	X
ejpam-4493	114	19	=	=	SYM
ejpam-4493	114	20	q	q	X
ejpam-4493	114	21	∪	∪	ADP
ejpam-4493	114	22	p	p	NOUN
ejpam-4493	114	23	where	where	SCONJ
ejpam-4493	114	24	p	p	NOUN
ejpam-4493	114	25	=	=	X
ejpam-4493	114	26	{	{	PUNCT
ejpam-4493	114	27	z	z	PROPN
ejpam-4493	114	28	∈	∈	PROPN
ejpam-4493	114	29	b	b	PROPN
ejpam-4493	114	30	:	:	PUNCT
ejpam-4493	115	1	z	z	AUX
ejpam-4493	115	2	/∈	/∈	PUNCT
ejpam-4493	115	3	q	q	ADJ
ejpam-4493	115	4	}	}	PUNCT
ejpam-4493	115	5	.	.	PUNCT
ejpam-4493	116	1	pick	pick	VERB
ejpam-4493	116	2	z	z	PROPN
ejpam-4493	116	3	∈	∈	PROPN
ejpam-4493	116	4	p.	p.	NOUN
ejpam-4493	116	5	by	by	ADP
ejpam-4493	116	6	assumption	assumption	NOUN
ejpam-4493	116	7	,	,	PUNCT
ejpam-4493	116	8	there	there	PRON
ejpam-4493	116	9	exists	exist	VERB
ejpam-4493	116	10	uz	uz	PROPN
ejpam-4493	116	11	∈	∈	PROPN
ejpam-4493	116	12	v	v	PROPN
ejpam-4493	116	13	(	(	PUNCT
ejpam-4493	116	14	g)\b	g)\b	PROPN
ejpam-4493	116	15	such	such	ADJ
ejpam-4493	116	16	that	that	SCONJ
ejpam-4493	116	17	[	[	PUNCT
ejpam-4493	116	18	b	b	X
ejpam-4493	116	19	\{z	\{z	NOUN
ejpam-4493	116	20	}	}	PUNCT
ejpam-4493	116	21	]	]	PUNCT
ejpam-4493	116	22	∪{uz	∪{uz	X
ejpam-4493	116	23	}	}	PUNCT
ejpam-4493	116	24	=	=	SYM
ejpam-4493	116	25	t	t	NOUN
ejpam-4493	116	26	is	be	AUX
ejpam-4493	116	27	a	a	DET
ejpam-4493	116	28	γch	γch	NOUN
ejpam-4493	116	29	,	,	PUNCT
ejpam-4493	116	30	coi	coi	NOUN
ejpam-4493	116	31	-	-	PUNCT
ejpam-4493	116	32	set	set	NOUN
ejpam-4493	116	33	of	of	ADP
ejpam-4493	116	34	g.	g.	PROPN
ejpam-4493	116	35	hence	hence	ADV
ejpam-4493	116	36	,	,	PUNCT
ejpam-4493	116	37	t	t	PROPN
ejpam-4493	116	38	=	=	PUNCT
ejpam-4493	116	39	q∪r	q∪r	PROPN
ejpam-4493	116	40	,	,	PUNCT
ejpam-4493	116	41	where	where	SCONJ
ejpam-4493	116	42	r	r	NOUN
ejpam-4493	116	43	=	=	PUNCT
ejpam-4493	116	44	[	[	PUNCT
ejpam-4493	116	45	p	p	NOUN
ejpam-4493	116	46	\{z	\{z	NOUN
ejpam-4493	116	47	}	}	PUNCT
ejpam-4493	116	48	]	]	PUNCT
ejpam-4493	117	1	∪{uz	∪{uz	NUM
ejpam-4493	117	2	}	}	PUNCT
ejpam-4493	117	3	,	,	PUNCT
ejpam-4493	117	4	is	be	AUX
ejpam-4493	117	5	a	a	DET
ejpam-4493	117	6	γch	γch	NOUN
ejpam-4493	117	7	,	,	PUNCT
ejpam-4493	117	8	coi	coi	NOUN
ejpam-4493	117	9	-	-	PUNCT
ejpam-4493	117	10	set	set	NOUN
ejpam-4493	117	11	containing	contain	VERB
ejpam-4493	117	12	q	q	NOUN
ejpam-4493	117	13	,	,	PUNCT
ejpam-4493	117	14	a	a	DET
ejpam-4493	117	15	contradiction	contradiction	NOUN
ejpam-4493	117	16	.	.	PUNCT
ejpam-4493	118	1	hence	hence	ADV
ejpam-4493	118	2	,	,	PUNCT
ejpam-4493	118	3	b	b	PROPN
ejpam-4493	118	4	is	be	AUX
ejpam-4493	118	5	the	the	DET
ejpam-4493	118	6	only	only	ADJ
ejpam-4493	118	7	forcing	forcing	NOUN
ejpam-4493	118	8	subset	subset	NOUN
ejpam-4493	118	9	for	for	ADP
ejpam-4493	118	10	b.	b.	PROPN
ejpam-4493	118	11	therefore	therefore	ADV
ejpam-4493	118	12	,	,	PUNCT
ejpam-4493	118	13	fγch	fγch	ADJ
ejpam-4493	118	14	,	,	PUNCT
ejpam-4493	118	15	coi(g	coi(g	PROPN
ejpam-4493	118	16	)	)	PUNCT
ejpam-4493	119	1	=	=	PUNCT
ejpam-4493	119	2	γch	γch	X
ejpam-4493	119	3	,	,	PUNCT
ejpam-4493	119	4	coi(g	coi(g	PROPN
ejpam-4493	119	5	)	)	PUNCT
ejpam-4493	119	6	.	.	PUNCT
ejpam-4493	120	1	proposition	proposition	NOUN
ejpam-4493	120	2	1	1	NUM
ejpam-4493	120	3	.	.	PUNCT
ejpam-4493	121	1	for	for	ADP
ejpam-4493	121	2	any	any	DET
ejpam-4493	121	3	complete	complete	ADJ
ejpam-4493	121	4	graph	graph	NOUN
ejpam-4493	121	5	kn	kn	PROPN
ejpam-4493	121	6	with	with	ADP
ejpam-4493	121	7	n	n	PRON
ejpam-4493	121	8	≥	≥	NUM
ejpam-4493	121	9	1	1	NUM
ejpam-4493	121	10	vertices	vertex	NOUN
ejpam-4493	121	11	,	,	PUNCT
ejpam-4493	121	12	fγch	fγch	ADJ
ejpam-4493	121	13	,	,	PUNCT
ejpam-4493	121	14	coi(kn	coi(kn	NUM
ejpam-4493	121	15	)	)	PUNCT
ejpam-4493	121	16	=	=	SYM
ejpam-4493	121	17	0	0	X
ejpam-4493	121	18	.	.	X
ejpam-4493	122	1	proof	proof	NOUN
ejpam-4493	122	2	:	:	PUNCT
ejpam-4493	122	3	by	by	ADP
ejpam-4493	122	4	definition	definition	NOUN
ejpam-4493	122	5	of	of	ADP
ejpam-4493	122	6	kn	kn	PROPN
ejpam-4493	122	7	,	,	PUNCT
ejpam-4493	122	8	v	v	PROPN
ejpam-4493	122	9	(	(	PUNCT
ejpam-4493	122	10	kn	kn	PROPN
ejpam-4493	122	11	)	)	PUNCT
ejpam-4493	122	12	is	be	AUX
ejpam-4493	122	13	the	the	DET
ejpam-4493	122	14	only	only	ADJ
ejpam-4493	122	15	γch	γch	NOUN
ejpam-4493	122	16	,	,	PUNCT
ejpam-4493	122	17	coi	coi	NOUN
ejpam-4493	122	18	-	-	PUNCT
ejpam-4493	122	19	set	set	NOUN
ejpam-4493	122	20	of	of	ADP
ejpam-4493	122	21	kn	kn	PROPN
ejpam-4493	122	22	.	.	PUNCT
ejpam-4493	123	1	by	by	ADP
ejpam-4493	123	2	remark	remark	NOUN
ejpam-4493	123	3	1(i	1(i	NUM
ejpam-4493	123	4	)	)	PUNCT
ejpam-4493	123	5	,	,	PUNCT
ejpam-4493	123	6	fγch	fγch	NOUN
ejpam-4493	123	7	,	,	PUNCT
ejpam-4493	123	8	coi(kn	coi(kn	NUM
ejpam-4493	123	9	)	)	PUNCT
ejpam-4493	123	10	=	=	SYM
ejpam-4493	123	11	0	0	X
ejpam-4493	123	12	.	.	PUNCT
ejpam-4493	123	13	proposition	proposition	NOUN
ejpam-4493	123	14	2	2	NUM
ejpam-4493	123	15	.	.	X
ejpam-4493	124	1	for	for	ADP
ejpam-4493	124	2	any	any	DET
ejpam-4493	124	3	path	path	NOUN
ejpam-4493	124	4	pn	pn	NOUN
ejpam-4493	124	5	with	with	ADP
ejpam-4493	124	6	n	n	PRON
ejpam-4493	124	7	≥	≥	NUM
ejpam-4493	124	8	1	1	NUM
ejpam-4493	124	9	vertices	vertex	NOUN
ejpam-4493	124	10	,	,	PUNCT
ejpam-4493	124	11	fγch	fγch	ADJ
ejpam-4493	124	12	,	,	PUNCT
ejpam-4493	124	13	coi(pn	coi(pn	NOUN
ejpam-4493	124	14	)	)	PUNCT
ejpam-4493	124	15	=	=	NOUN
ejpam-4493	124	16	{	{	PUNCT
ejpam-4493	124	17	0	0	NUM
ejpam-4493	124	18	,	,	PUNCT
ejpam-4493	124	19	if	if	SCONJ
ejpam-4493	124	20	n	n	PRON
ejpam-4493	124	21	̸=	̸=	PROPN
ejpam-4493	124	22	3	3	NUM
ejpam-4493	124	23	,	,	PUNCT
ejpam-4493	124	24	1	1	NUM
ejpam-4493	124	25	,	,	PUNCT
ejpam-4493	124	26	if	if	SCONJ
ejpam-4493	124	27	n	n	NOUN
ejpam-4493	124	28	=	=	SYM
ejpam-4493	124	29	3	3	X
ejpam-4493	124	30	.	.	X
ejpam-4493	124	31	proof	proof	NOUN
ejpam-4493	124	32	:	:	PUNCT
ejpam-4493	124	33	suppose	suppose	VERB
ejpam-4493	124	34	that	that	SCONJ
ejpam-4493	124	35	pn	pn	PROPN
ejpam-4493	124	36	=	=	PUNCT
ejpam-4493	125	1	[	[	X
ejpam-4493	125	2	v1	v1	NOUN
ejpam-4493	125	3	,	,	PUNCT
ejpam-4493	125	4	v2	v2	NOUN
ejpam-4493	125	5	,	,	PUNCT
ejpam-4493	125	6	.	.	PUNCT
ejpam-4493	125	7	.	.	PUNCT
ejpam-4493	125	8	.	.	PUNCT
ejpam-4493	126	1	,	,	PUNCT
ejpam-4493	126	2	vn	vn	X
ejpam-4493	126	3	]	]	PUNCT
ejpam-4493	126	4	.	.	PUNCT
ejpam-4493	127	1	clearly	clearly	ADV
ejpam-4493	127	2	,	,	PUNCT
ejpam-4493	127	3	fγch	fγch	NOUN
ejpam-4493	127	4	,	,	PUNCT
ejpam-4493	127	5	coi(p1	coi(p1	NOUN
ejpam-4493	127	6	)	)	PUNCT
ejpam-4493	127	7	=	=	SYM
ejpam-4493	128	1	fγch	fγch	ADJ
ejpam-4493	128	2	,	,	PUNCT
ejpam-4493	128	3	coi(p2	coi(p2	ADJ
ejpam-4493	128	4	)	)	PUNCT
ejpam-4493	128	5	=	=	SYM
ejpam-4493	128	6	0	0	X
ejpam-4493	128	7	.	.	PUNCT
ejpam-4493	129	1	moreover	moreover	ADV
ejpam-4493	129	2	,	,	PUNCT
ejpam-4493	129	3	if	if	SCONJ
ejpam-4493	129	4	n	n	CCONJ
ejpam-4493	129	5	=	=	SYM
ejpam-4493	129	6	4	4	NUM
ejpam-4493	129	7	,	,	PUNCT
ejpam-4493	129	8	then	then	ADV
ejpam-4493	129	9	pn	pn	PROPN
ejpam-4493	129	10	has	have	AUX
ejpam-4493	129	11	γch	γch	VERB
ejpam-4493	129	12	,	,	PUNCT
ejpam-4493	129	13	coi	coi	NOUN
ejpam-4493	129	14	-	-	PUNCT
ejpam-4493	129	15	set	set	VERB
ejpam-4493	129	16	b1	b1	NOUN
ejpam-4493	129	17	=	=	SYM
ejpam-4493	129	18	{	{	PUNCT
ejpam-4493	129	19	v2	v2	PROPN
ejpam-4493	129	20	,	,	PUNCT
ejpam-4493	129	21	v3	v3	PROPN
ejpam-4493	129	22	}	}	PUNCT
ejpam-4493	129	23	which	which	PRON
ejpam-4493	129	24	is	be	AUX
ejpam-4493	129	25	the	the	DET
ejpam-4493	129	26	only	only	ADJ
ejpam-4493	129	27	γch	γch	NOUN
ejpam-4493	129	28	,	,	PUNCT
ejpam-4493	129	29	coi	coi	NOUN
ejpam-4493	129	30	-	-	PUNCT
ejpam-4493	129	31	set	set	NOUN
ejpam-4493	129	32	of	of	ADP
ejpam-4493	129	33	pn	pn	PROPN
ejpam-4493	129	34	.	.	PUNCT
ejpam-4493	130	1	by	by	ADP
ejpam-4493	130	2	remark	remark	NOUN
ejpam-4493	130	3	1(i	1(i	NUM
ejpam-4493	130	4	)	)	PUNCT
ejpam-4493	130	5	,	,	PUNCT
ejpam-4493	130	6	fγch	fγch	NOUN
ejpam-4493	130	7	,	,	PUNCT
ejpam-4493	130	8	coi(pn	coi(pn	NOUN
ejpam-4493	130	9	)	)	PUNCT
ejpam-4493	130	10	=	=	SYM
ejpam-4493	130	11	0	0	X
ejpam-4493	130	12	.	.	PUNCT
ejpam-4493	130	13	suppose	suppose	VERB
ejpam-4493	130	14	that	that	SCONJ
ejpam-4493	130	15	n	n	PROPN
ejpam-4493	130	16	>	>	X
ejpam-4493	130	17	4	4	NUM
ejpam-4493	130	18	,	,	PUNCT
ejpam-4493	130	19	then	then	ADV
ejpam-4493	130	20	clearly	clearly	ADV
ejpam-4493	130	21	b2	b2	VERB
ejpam-4493	130	22	=	=	SYM
ejpam-4493	130	23	{	{	PUNCT
ejpam-4493	130	24	v2	v2	PROPN
ejpam-4493	130	25	,	,	PUNCT
ejpam-4493	130	26	v3	v3	PROPN
ejpam-4493	130	27	,	,	PUNCT
ejpam-4493	130	28	v4	v4	PROPN
ejpam-4493	130	29	,	,	PUNCT
ejpam-4493	130	30	.	.	PUNCT
ejpam-4493	130	31	.	.	PUNCT
ejpam-4493	131	1	.	.	PUNCT
ejpam-4493	132	1	,	,	PUNCT
ejpam-4493	132	2	vn−1	vn−1	PROPN
ejpam-4493	132	3	}	}	PUNCT
ejpam-4493	132	4	is	be	AUX
ejpam-4493	132	5	the	the	DET
ejpam-4493	132	6	only	only	ADJ
ejpam-4493	132	7	γch	γch	NOUN
ejpam-4493	132	8	,	,	PUNCT
ejpam-4493	132	9	coi	coi	NOUN
ejpam-4493	132	10	-	-	PUNCT
ejpam-4493	132	11	set	set	NOUN
ejpam-4493	132	12	of	of	ADP
ejpam-4493	132	13	pn	pn	PROPN
ejpam-4493	132	14	.	.	PUNCT
ejpam-4493	133	1	thus	thus	ADV
ejpam-4493	133	2	,	,	PUNCT
ejpam-4493	133	3	by	by	ADP
ejpam-4493	133	4	remark	remark	NOUN
ejpam-4493	133	5	1(i	1(i	NUM
ejpam-4493	133	6	)	)	PUNCT
ejpam-4493	133	7	,	,	PUNCT
ejpam-4493	133	8	fγch	fγch	NOUN
ejpam-4493	133	9	,	,	PUNCT
ejpam-4493	133	10	coi(b2	coi(b2	NOUN
ejpam-4493	133	11	)	)	PUNCT
ejpam-4493	133	12	=	=	SYM
ejpam-4493	133	13	0	0	PUNCT
ejpam-4493	134	1	=	=	SYM
ejpam-4493	134	2	fγch	fγch	ADJ
ejpam-4493	134	3	,	,	PUNCT
ejpam-4493	134	4	coi(pn	coi(pn	NOUN
ejpam-4493	134	5	)	)	PUNCT
ejpam-4493	134	6	.	.	PUNCT
ejpam-4493	135	1	suppose	suppose	VERB
ejpam-4493	135	2	that	that	SCONJ
ejpam-4493	135	3	n	n	PROPN
ejpam-4493	135	4	=	=	SYM
ejpam-4493	135	5	3	3	X
ejpam-4493	135	6	.	.	PUNCT
ejpam-4493	135	7	then	then	ADV
ejpam-4493	135	8	pn	pn	PROPN
ejpam-4493	135	9	has	have	AUX
ejpam-4493	135	10	γch	γch	VERB
ejpam-4493	135	11	,	,	PUNCT
ejpam-4493	135	12	coi	coi	NOUN
ejpam-4493	135	13	-	-	PUNCT
ejpam-4493	135	14	sets	set	NOUN
ejpam-4493	135	15	b3	b3	NOUN
ejpam-4493	135	16	=	=	SYM
ejpam-4493	135	17	{	{	PUNCT
ejpam-4493	135	18	v1	v1	PROPN
ejpam-4493	135	19	,	,	PUNCT
ejpam-4493	135	20	v2	v2	NOUN
ejpam-4493	135	21	}	}	PUNCT
ejpam-4493	135	22	and	and	CCONJ
ejpam-4493	135	23	b4	b4	NOUN
ejpam-4493	135	24	=	=	SYM
ejpam-4493	135	25	{	{	PUNCT
ejpam-4493	135	26	v2	v2	PROPN
ejpam-4493	135	27	,	,	PUNCT
ejpam-4493	135	28	v3	v3	PROPN
ejpam-4493	135	29	}	}	PUNCT
ejpam-4493	135	30	which	which	PRON
ejpam-4493	135	31	are	be	AUX
ejpam-4493	135	32	the	the	DET
ejpam-4493	135	33	only	only	ADJ
ejpam-4493	135	34	γch	γch	NOUN
ejpam-4493	135	35	,	,	PUNCT
ejpam-4493	135	36	coi	coi	NOUN
ejpam-4493	135	37	-	-	PUNCT
ejpam-4493	135	38	sets	set	NOUN
ejpam-4493	135	39	of	of	ADP
ejpam-4493	135	40	pn	pn	PROPN
ejpam-4493	135	41	with	with	ADP
ejpam-4493	135	42	v1	v1	PROPN
ejpam-4493	135	43	∈	∈	PROPN
ejpam-4493	135	44	b3	b3	PROPN
ejpam-4493	135	45	and	and	CCONJ
ejpam-4493	135	46	v1	v1	NOUN
ejpam-4493	135	47	/∈	/∈	PUNCT
ejpam-4493	135	48	b4	b4	NOUN
ejpam-4493	135	49	.	.	PUNCT
ejpam-4493	136	1	hence	hence	ADV
ejpam-4493	136	2	,	,	PUNCT
ejpam-4493	136	3	by	by	ADP
ejpam-4493	136	4	remark	remark	NOUN
ejpam-4493	136	5	1(ii	1(ii	NUM
ejpam-4493	136	6	)	)	PUNCT
ejpam-4493	136	7	,	,	PUNCT
ejpam-4493	136	8	fγch	fγch	NOUN
ejpam-4493	136	9	,	,	PUNCT
ejpam-4493	136	10	coi(b3	coi(b3	NOUN
ejpam-4493	136	11	)	)	PUNCT
ejpam-4493	136	12	=	=	SYM
ejpam-4493	136	13	1	1	NUM
ejpam-4493	136	14	=	=	SYM
ejpam-4493	136	15	fγch	fγch	ADJ
ejpam-4493	136	16	,	,	PUNCT
ejpam-4493	136	17	coi(pn	coi(pn	NOUN
ejpam-4493	136	18	)	)	PUNCT
ejpam-4493	136	19	.	.	PUNCT
ejpam-4493	137	1	proposition	proposition	NOUN
ejpam-4493	137	2	3	3	NUM
ejpam-4493	137	3	.	.	X
ejpam-4493	138	1	for	for	ADP
ejpam-4493	138	2	any	any	DET
ejpam-4493	138	3	cycle	cycle	NOUN
ejpam-4493	138	4	cn	cn	NOUN
ejpam-4493	138	5	with	with	ADP
ejpam-4493	138	6	n	n	NUM
ejpam-4493	138	7	≥	≥	NUM
ejpam-4493	138	8	3	3	NUM
ejpam-4493	138	9	vertices	vertex	NOUN
ejpam-4493	138	10	,	,	PUNCT
ejpam-4493	138	11	fγch	fγch	NOUN
ejpam-4493	138	12	,	,	PUNCT
ejpam-4493	138	13	coi(cn	coi(cn	NUM
ejpam-4493	138	14	)	)	PUNCT
ejpam-4493	138	15	=	=	PRON
ejpam-4493	138	16	{	{	PUNCT
ejpam-4493	138	17	0	0	NUM
ejpam-4493	138	18	,	,	PUNCT
ejpam-4493	138	19	if	if	SCONJ
ejpam-4493	138	20	n	n	NOUN
ejpam-4493	138	21	=	=	SYM
ejpam-4493	138	22	3	3	NUM
ejpam-4493	138	23	,	,	PUNCT
ejpam-4493	138	24	n−	n−	NOUN
ejpam-4493	138	25	1	1	NUM
ejpam-4493	138	26	,	,	PUNCT
ejpam-4493	138	27	if	if	SCONJ
ejpam-4493	138	28	n	n	PRON
ejpam-4493	138	29	≥	≥	NOUN
ejpam-4493	138	30	4	4	NUM
ejpam-4493	138	31	.	.	PUNCT
ejpam-4493	138	32	proof	proof	NOUN
ejpam-4493	138	33	:	:	PUNCT
ejpam-4493	138	34	suppose	suppose	VERB
ejpam-4493	138	35	that	that	SCONJ
ejpam-4493	138	36	cn	cn	PROPN
ejpam-4493	138	37	=	=	PUNCT
ejpam-4493	138	38	[	[	X
ejpam-4493	138	39	v1	v1	NOUN
ejpam-4493	138	40	,	,	PUNCT
ejpam-4493	138	41	v2	v2	NOUN
ejpam-4493	138	42	,	,	PUNCT
ejpam-4493	138	43	.	.	PUNCT
ejpam-4493	138	44	.	.	PUNCT
ejpam-4493	139	1	.	.	PUNCT
ejpam-4493	140	1	,	,	PUNCT
ejpam-4493	140	2	vn	vn	X
ejpam-4493	140	3	,	,	PUNCT
ejpam-4493	140	4	v1	v1	PROPN
ejpam-4493	140	5	]	]	PUNCT
ejpam-4493	140	6	.	.	PUNCT
ejpam-4493	141	1	since	since	SCONJ
ejpam-4493	141	2	c3	c3	PROPN
ejpam-4493	141	3	=	=	SYM
ejpam-4493	141	4	k3	k3	PROPN
ejpam-4493	141	5	,	,	PUNCT
ejpam-4493	141	6	by	by	ADP
ejpam-4493	141	7	proposition	proposition	NOUN
ejpam-4493	141	8	1	1	NUM
ejpam-4493	141	9	,	,	PUNCT
ejpam-4493	141	10	fγch	fγch	NOUN
ejpam-4493	141	11	,	,	PUNCT
ejpam-4493	141	12	coi(c3	coi(c3	NOUN
ejpam-4493	141	13	)	)	PUNCT
ejpam-4493	141	14	=	=	SYM
ejpam-4493	141	15	0	0	X
ejpam-4493	141	16	.	.	PUNCT
ejpam-4493	141	17	suppose	suppose	VERB
ejpam-4493	141	18	that	that	SCONJ
ejpam-4493	141	19	n	n	PROPN
ejpam-4493	141	20	≥	≥	NUM
ejpam-4493	141	21	4	4	NUM
ejpam-4493	141	22	.	.	PUNCT
ejpam-4493	142	1	then	then	ADV
ejpam-4493	142	2	the	the	DET
ejpam-4493	142	3	γch	γch	NOUN
ejpam-4493	142	4	,	,	PUNCT
ejpam-4493	142	5	coi	coi	NOUN
ejpam-4493	142	6	-	-	PUNCT
ejpam-4493	142	7	sets	set	NOUN
ejpam-4493	142	8	of	of	ADP
ejpam-4493	142	9	cn	cn	PROPN
ejpam-4493	142	10	areb1	areb1	PROPN
ejpam-4493	143	1	=	=	NUM
ejpam-4493	143	2	{	{	PUNCT
ejpam-4493	143	3	v1	v1	PROPN
ejpam-4493	143	4	,	,	PUNCT
ejpam-4493	143	5	v2	v2	PROPN
ejpam-4493	143	6	,	,	PUNCT
ejpam-4493	143	7	.	.	PUNCT
ejpam-4493	143	8	.	.	PUNCT
ejpam-4493	143	9	.	.	PUNCT
ejpam-4493	144	1	,	,	PUNCT
ejpam-4493	144	2	vn−1	vn−1	ADJ
ejpam-4493	144	3	}	}	PUNCT
ejpam-4493	144	4	,	,	PUNCT
ejpam-4493	144	5	b2	b2	NOUN
ejpam-4493	144	6	=	=	SYM
ejpam-4493	144	7	{	{	PUNCT
ejpam-4493	144	8	v2	v2	PROPN
ejpam-4493	144	9	,	,	PUNCT
ejpam-4493	144	10	v3	v3	PROPN
ejpam-4493	144	11	,	,	PUNCT
ejpam-4493	144	12	.	.	PUNCT
ejpam-4493	144	13	.	.	PUNCT
ejpam-4493	144	14	.	.	PUNCT
ejpam-4493	145	1	,	,	PUNCT
ejpam-4493	145	2	vn	vn	PROPN
ejpam-4493	145	3	}	}	PUNCT
ejpam-4493	145	4	,	,	PUNCT
ejpam-4493	145	5	b3	b3	PROPN
ejpam-4493	145	6	=	=	SYM
ejpam-4493	145	7	{	{	PUNCT
ejpam-4493	145	8	v3	v3	PROPN
ejpam-4493	145	9	,	,	PUNCT
ejpam-4493	145	10	v4	v4	PROPN
ejpam-4493	145	11	,	,	PUNCT
ejpam-4493	145	12	.	.	PUNCT
ejpam-4493	145	13	.	.	PUNCT
ejpam-4493	146	1	.	.	PUNCT
ejpam-4493	147	1	,	,	PUNCT
ejpam-4493	147	2	vn	vn	X
ejpam-4493	147	3	,	,	PUNCT
ejpam-4493	147	4	v1	v1	PROPN
ejpam-4493	147	5	}	}	PUNCT
ejpam-4493	147	6	,	,	PUNCT
ejpam-4493	147	7	.	.	PUNCT
ejpam-4493	147	8	.	.	PUNCT
ejpam-4493	147	9	.	.	PUNCT
ejpam-4493	148	1	,	,	PUNCT
ejpam-4493	148	2	bn	bn	NOUN
ejpam-4493	148	3	=	=	SYM
ejpam-4493	148	4	{	{	PUNCT
ejpam-4493	148	5	vn	vn	PROPN
ejpam-4493	148	6	,	,	PUNCT
ejpam-4493	148	7	v1	v1	NOUN
ejpam-4493	148	8	,	,	PUNCT
ejpam-4493	148	9	v2	v2	NOUN
ejpam-4493	148	10	,	,	PUNCT
ejpam-4493	148	11	.	.	PUNCT
ejpam-4493	148	12	.	.	PUNCT
ejpam-4493	149	1	.	.	PUNCT
ejpam-4493	150	1	,	,	PUNCT
ejpam-4493	150	2	vn−2	vn−2	PROPN
ejpam-4493	150	3	}	}	PUNCT
ejpam-4493	150	4	.	.	PUNCT
ejpam-4493	151	1	clearly	clearly	ADV
ejpam-4493	151	2	,	,	PUNCT
ejpam-4493	151	3	for	for	ADP
ejpam-4493	151	4	each	each	DET
ejpam-4493	151	5	vi	vi	PROPN
ejpam-4493	151	6	∈	∈	NOUN
ejpam-4493	151	7	bj	bj	VERB
ejpam-4493	151	8	where	where	SCONJ
ejpam-4493	151	9	i	i	PRON
ejpam-4493	151	10	,	,	PUNCT
ejpam-4493	151	11	j	j	PROPN
ejpam-4493	151	12	∈	∈	PROPN
ejpam-4493	151	13	{	{	PUNCT
ejpam-4493	151	14	1	1	NUM
ejpam-4493	151	15	,	,	PUNCT
ejpam-4493	151	16	2	2	NUM
ejpam-4493	151	17	,	,	PUNCT
ejpam-4493	151	18	3	3	NUM
ejpam-4493	151	19	,	,	PUNCT
ejpam-4493	151	20	.	.	PUNCT
ejpam-4493	151	21	.	.	PUNCT
ejpam-4493	151	22	.	.	PUNCT
ejpam-4493	151	23	,	,	PUNCT
ejpam-4493	151	24	n	n	CCONJ
ejpam-4493	151	25	}	}	PUNCT
ejpam-4493	151	26	,	,	PUNCT
ejpam-4493	151	27	there	there	PRON
ejpam-4493	151	28	exists	exist	VERB
ejpam-4493	151	29	vk	vk	ADP
ejpam-4493	151	30	∈	∈	PROPN
ejpam-4493	151	31	v	v	PROPN
ejpam-4493	151	32	(	(	PUNCT
ejpam-4493	151	33	cn	cn	PROPN
ejpam-4493	151	34	)	)	PUNCT
ejpam-4493	151	35	\	\	NOUN
ejpam-4493	151	36	bj	bj	ADP
ejpam-4493	151	37	such	such	ADJ
ejpam-4493	151	38	that	that	SCONJ
ejpam-4493	151	39	[	[	PUNCT
ejpam-4493	151	40	bj	bj	ADP
ejpam-4493	151	41	\	\	NOUN
ejpam-4493	151	42	{	{	PUNCT
ejpam-4493	151	43	vi	vi	NOUN
ejpam-4493	151	44	}	}	PUNCT
ejpam-4493	151	45	]	]	PUNCT
ejpam-4493	151	46	∪	∪	X
ejpam-4493	151	47	{	{	PUNCT
ejpam-4493	151	48	vk	vk	INTJ
ejpam-4493	151	49	}	}	PUNCT
ejpam-4493	151	50	is	be	AUX
ejpam-4493	151	51	a	a	DET
ejpam-4493	151	52	γch	γch	NOUN
ejpam-4493	151	53	,	,	PUNCT
ejpam-4493	151	54	coi	coi	NOUN
ejpam-4493	151	55	-	-	PUNCT
ejpam-4493	151	56	set	set	NOUN
ejpam-4493	151	57	of	of	ADP
ejpam-4493	151	58	g.	g.	PROPN
ejpam-4493	151	59	hence	hence	ADV
ejpam-4493	151	60	,	,	PUNCT
ejpam-4493	151	61	by	by	ADP
ejpam-4493	151	62	theorem	theorem	NOUN
ejpam-4493	151	63	3	3	NUM
ejpam-4493	151	64	,	,	PUNCT
ejpam-4493	151	65	fγch	fγch	ADJ
ejpam-4493	151	66	,	,	PUNCT
ejpam-4493	151	67	coi(cn	coi(cn	NUM
ejpam-4493	151	68	)	)	PUNCT
ejpam-4493	152	1	=	=	PUNCT
ejpam-4493	152	2	n−	n−	NOUN
ejpam-4493	152	3	1	1	NUM
ejpam-4493	152	4	.	.	NOUN
ejpam-4493	152	5	4	4	X
ejpam-4493	152	6	.	.	X
ejpam-4493	152	7	forcing	force	VERB
ejpam-4493	152	8	connected	connected	ADJ
ejpam-4493	152	9	co	co	ADJ
ejpam-4493	152	10	-	-	ADJ
ejpam-4493	152	11	independent	independent	ADJ
ejpam-4493	152	12	hop	hop	NOUN
ejpam-4493	152	13	domination	domination	NOUN
ejpam-4493	152	14	in	in	ADP
ejpam-4493	152	15	the	the	DET
ejpam-4493	152	16	join	join	NOUN
ejpam-4493	152	17	of	of	ADP
ejpam-4493	152	18	graphs	graph	NOUN
ejpam-4493	152	19	the	the	DET
ejpam-4493	152	20	join	join	NOUN
ejpam-4493	152	21	of	of	ADP
ejpam-4493	152	22	two	two	NUM
ejpam-4493	152	23	graphs	graph	NOUN
ejpam-4493	152	24	g	g	NOUN
ejpam-4493	152	25	and	and	CCONJ
ejpam-4493	152	26	h	h	NOUN
ejpam-4493	152	27	is	be	AUX
ejpam-4493	152	28	the	the	DET
ejpam-4493	152	29	graph	graph	NOUN
ejpam-4493	152	30	g	g	NOUN
ejpam-4493	152	31	+	+	CCONJ
ejpam-4493	152	32	h	h	NOUN
ejpam-4493	152	33	with	with	ADP
ejpam-4493	152	34	vertex	vertex	NOUN
ejpam-4493	152	35	set	set	VERB
ejpam-4493	152	36	v	v	NOUN
ejpam-4493	152	37	(	(	PUNCT
ejpam-4493	152	38	g	g	PROPN
ejpam-4493	152	39	+	+	NOUN
ejpam-4493	152	40	h	h	NOUN
ejpam-4493	152	41	)	)	PUNCT
ejpam-4493	153	1	=	=	NOUN
ejpam-4493	153	2	v	v	X
ejpam-4493	153	3	(	(	PUNCT
ejpam-4493	153	4	g	g	NOUN
ejpam-4493	153	5	)	)	PUNCT
ejpam-4493	153	6	•	•	ADP
ejpam-4493	153	7	∪	∪	X
ejpam-4493	153	8	v	v	NOUN
ejpam-4493	153	9	(	(	PUNCT
ejpam-4493	153	10	h	h	NOUN
ejpam-4493	153	11	)	)	PUNCT
ejpam-4493	153	12	and	and	CCONJ
ejpam-4493	153	13	edge	edge	NOUN
ejpam-4493	153	14	set	set	VERB
ejpam-4493	153	15	e(g	e(g	PROPN
ejpam-4493	154	1	+	+	CCONJ
ejpam-4493	154	2	h	h	NOUN
ejpam-4493	154	3	)	)	PUNCT
ejpam-4493	154	4	=	=	SYM
ejpam-4493	154	5	e(g	e(g	PROPN
ejpam-4493	154	6	)	)	PUNCT
ejpam-4493	155	1	•	•	ADP
ejpam-4493	155	2	∪	∪	ADP
ejpam-4493	155	3	e(h	e(h	PROPN
ejpam-4493	155	4	)	)	PUNCT
ejpam-4493	155	5	∪	∪	NOUN
ejpam-4493	155	6	{	{	PUNCT
ejpam-4493	155	7	uv	uv	NOUN
ejpam-4493	155	8	:	:	PUNCT
ejpam-4493	155	9	u	u	PROPN
ejpam-4493	155	10	∈	∈	PROPN
ejpam-4493	155	11	v	v	ADP
ejpam-4493	155	12	(	(	PUNCT
ejpam-4493	155	13	g	g	NOUN
ejpam-4493	155	14	)	)	PUNCT
ejpam-4493	155	15	,	,	PUNCT
ejpam-4493	155	16	v	v	X
ejpam-4493	155	17	∈	∈	PROPN
ejpam-4493	155	18	v	v	NOUN
ejpam-4493	155	19	(	(	PUNCT
ejpam-4493	155	20	h	h	NOUN
ejpam-4493	155	21	)	)	PUNCT
ejpam-4493	155	22	}	}	PUNCT
ejpam-4493	155	23	.	.	PUNCT
ejpam-4493	156	1	y.d	y.d	PROPN
ejpam-4493	156	2	.	.	PROPN
ejpam-4493	156	3	calanza	calanza	PROPN
ejpam-4493	156	4	,	,	PUNCT
ejpam-4493	156	5	h.	h.	PROPN
ejpam-4493	156	6	rara	rara	PROPN
ejpam-4493	156	7	/	/	SYM
ejpam-4493	156	8	eur	eur	PROPN
ejpam-4493	156	9	.	.	PUNCT
ejpam-4493	157	1	j.	j.	PROPN
ejpam-4493	157	2	pure	pure	PROPN
ejpam-4493	157	3	appl	appl	PROPN
ejpam-4493	157	4	.	.	PROPN
ejpam-4493	157	5	math	math	PROPN
ejpam-4493	157	6	,	,	PUNCT
ejpam-4493	157	7	15	15	NUM
ejpam-4493	157	8	(	(	PUNCT
ejpam-4493	157	9	4	4	NUM
ejpam-4493	157	10	)	)	PUNCT
ejpam-4493	157	11	(	(	PUNCT
ejpam-4493	157	12	2022	2022	NUM
ejpam-4493	157	13	)	)	PUNCT
ejpam-4493	157	14	,	,	PUNCT
ejpam-4493	157	15	1649	1649	NUM
ejpam-4493	157	16	-	-	SYM
ejpam-4493	157	17	1661	1661	NUM
ejpam-4493	157	18	1654	1654	NUM
ejpam-4493	157	19	remark	remark	NOUN
ejpam-4493	157	20	2	2	NUM
ejpam-4493	157	21	.	.	PUNCT
ejpam-4493	158	1	let	let	VERB
ejpam-4493	158	2	g	g	PRON
ejpam-4493	158	3	be	be	AUX
ejpam-4493	158	4	a	a	DET
ejpam-4493	158	5	connected	connected	ADJ
ejpam-4493	158	6	graph	graph	NOUN
ejpam-4493	158	7	.	.	PUNCT
ejpam-4493	159	1	then	then	ADV
ejpam-4493	159	2	(	(	PUNCT
ejpam-4493	159	3	i	i	NOUN
ejpam-4493	159	4	)	)	PUNCT
ejpam-4493	159	5	fsci(g	fsci(g	NOUN
ejpam-4493	159	6	)	)	PUNCT
ejpam-4493	160	1	=	=	SYM
ejpam-4493	160	2	0	0	PUNCT
ejpam-4493	161	1	if	if	SCONJ
ejpam-4493	161	2	and	and	CCONJ
ejpam-4493	161	3	only	only	ADV
ejpam-4493	161	4	if	if	SCONJ
ejpam-4493	161	5	g	g	PROPN
ejpam-4493	161	6	has	have	VERB
ejpam-4493	161	7	a	a	DET
ejpam-4493	161	8	unique	unique	ADJ
ejpam-4493	161	9	sci	sci	NOUN
ejpam-4493	161	10	-	-	PUNCT
ejpam-4493	161	11	set	set	NOUN
ejpam-4493	161	12	,	,	PUNCT
ejpam-4493	161	13	and	and	CCONJ
ejpam-4493	161	14	(	(	PUNCT
ejpam-4493	161	15	ii	ii	NOUN
ejpam-4493	161	16	)	)	PUNCT
ejpam-4493	161	17	fsci(g	fsci(g	NOUN
ejpam-4493	161	18	)	)	PUNCT
ejpam-4493	162	1	=	=	SYM
ejpam-4493	162	2	1	1	NUM
ejpam-4493	162	3	if	if	SCONJ
ejpam-4493	162	4	and	and	CCONJ
ejpam-4493	162	5	only	only	ADV
ejpam-4493	162	6	if	if	SCONJ
ejpam-4493	162	7	g	g	PROPN
ejpam-4493	162	8	has	have	VERB
ejpam-4493	162	9	at	at	ADV
ejpam-4493	162	10	least	least	ADV
ejpam-4493	162	11	two	two	NUM
ejpam-4493	162	12	sci	sci	NOUN
ejpam-4493	162	13	-	-	PUNCT
ejpam-4493	162	14	sets	set	NOUN
ejpam-4493	162	15	,	,	PUNCT
ejpam-4493	162	16	one	one	NUM
ejpam-4493	162	17	of	of	ADP
ejpam-4493	162	18	which	which	PRON
ejpam-4493	162	19	,	,	PUNCT
ejpam-4493	162	20	say	say	VERB
ejpam-4493	162	21	b	b	NOUN
ejpam-4493	162	22	,	,	PUNCT
ejpam-4493	162	23	contains	contain	VERB
ejpam-4493	162	24	an	an	DET
ejpam-4493	162	25	element	element	NOUN
ejpam-4493	162	26	which	which	PRON
ejpam-4493	162	27	is	be	AUX
ejpam-4493	162	28	not	not	PART
ejpam-4493	162	29	found	find	VERB
ejpam-4493	162	30	in	in	ADP
ejpam-4493	162	31	any	any	DET
ejpam-4493	162	32	sci	sci	PROPN
ejpam-4493	162	33	-	-	PUNCT
ejpam-4493	162	34	set	set	NOUN
ejpam-4493	162	35	of	of	ADP
ejpam-4493	162	36	g.	g.	PROPN
ejpam-4493	162	37	theorem	theorem	VERB
ejpam-4493	162	38	4	4	X
ejpam-4493	162	39	.	.	PUNCT
ejpam-4493	163	1	let	let	VERB
ejpam-4493	163	2	g	g	PRON
ejpam-4493	163	3	be	be	AUX
ejpam-4493	163	4	a	a	DET
ejpam-4493	163	5	connected	connected	ADJ
ejpam-4493	163	6	graph	graph	NOUN
ejpam-4493	163	7	.	.	PUNCT
ejpam-4493	164	1	then	then	ADV
ejpam-4493	164	2	fsci(g	fsci(g	X
ejpam-4493	164	3	)	)	PUNCT
ejpam-4493	165	1	=	=	PUNCT
ejpam-4493	165	2	sci(g	sci(g	PROPN
ejpam-4493	165	3	)	)	PUNCT
ejpam-4493	166	1	if	if	SCONJ
ejpam-4493	166	2	and	and	CCONJ
ejpam-4493	166	3	only	only	ADV
ejpam-4493	166	4	if	if	SCONJ
ejpam-4493	166	5	for	for	ADP
ejpam-4493	166	6	all	all	DET
ejpam-4493	166	7	sci	sci	PROPN
ejpam-4493	166	8	-	-	PUNCT
ejpam-4493	166	9	set	set	VERB
ejpam-4493	166	10	b	b	PROPN
ejpam-4493	166	11	of	of	ADP
ejpam-4493	166	12	g	g	PROPN
ejpam-4493	166	13	and	and	CCONJ
ejpam-4493	166	14	for	for	ADP
ejpam-4493	166	15	each	each	DET
ejpam-4493	166	16	v	v	NUM
ejpam-4493	166	17	∈	∈	PROPN
ejpam-4493	166	18	b	b	NOUN
ejpam-4493	166	19	,	,	PUNCT
ejpam-4493	166	20	there	there	PRON
ejpam-4493	166	21	exists	exist	VERB
ejpam-4493	166	22	uv	uv	PROPN
ejpam-4493	166	23	∈	∈	PROPN
ejpam-4493	166	24	v	v	ADP
ejpam-4493	166	25	(	(	PUNCT
ejpam-4493	166	26	g	g	NOUN
ejpam-4493	166	27	)	)	PUNCT
ejpam-4493	166	28	\b	\b	NOUN
ejpam-4493	166	29	such	such	ADJ
ejpam-4493	166	30	that	that	SCONJ
ejpam-4493	166	31	[	[	PUNCT
ejpam-4493	166	32	b	b	X
ejpam-4493	166	33	\	\	X
ejpam-4493	166	34	{	{	PUNCT
ejpam-4493	166	35	v	v	NOUN
ejpam-4493	166	36	}	}	PUNCT
ejpam-4493	166	37	]	]	PUNCT
ejpam-4493	166	38	∪	∪	X
ejpam-4493	166	39	{	{	PUNCT
ejpam-4493	166	40	uv	uv	NOUN
ejpam-4493	166	41	}	}	PUNCT
ejpam-4493	166	42	is	be	AUX
ejpam-4493	166	43	an	an	DET
ejpam-4493	166	44	sci	sci	PROPN
ejpam-4493	166	45	-	-	PUNCT
ejpam-4493	166	46	set	set	NOUN
ejpam-4493	166	47	of	of	ADP
ejpam-4493	166	48	g.	g.	PROPN
ejpam-4493	166	49	proof	proof	PROPN
ejpam-4493	166	50	:	:	PUNCT
ejpam-4493	166	51	suppose	suppose	VERB
ejpam-4493	166	52	that	that	SCONJ
ejpam-4493	166	53	fsci(g	fsci(g	NOUN
ejpam-4493	166	54	)	)	PUNCT
ejpam-4493	166	55	=	=	PUNCT
ejpam-4493	166	56	sci(g	sci(g	PROPN
ejpam-4493	166	57	)	)	PUNCT
ejpam-4493	166	58	.	.	PUNCT
ejpam-4493	167	1	let	let	VERB
ejpam-4493	167	2	b	b	X
ejpam-4493	167	3	be	be	AUX
ejpam-4493	167	4	an	an	DET
ejpam-4493	167	5	sci	sci	PROPN
ejpam-4493	167	6	-	-	PUNCT
ejpam-4493	167	7	set	set	NOUN
ejpam-4493	167	8	of	of	ADP
ejpam-4493	167	9	g	g	NOUN
ejpam-4493	167	10	such	such	ADJ
ejpam-4493	167	11	that	that	DET
ejpam-4493	167	12	fsci(g	fsci(g	NOUN
ejpam-4493	167	13	)	)	PUNCT
ejpam-4493	168	1	=	=	PRON
ejpam-4493	168	2	|b|	|b|	PROPN
ejpam-4493	168	3	=	=	PUNCT
ejpam-4493	168	4	sci(g	sci(g	PROPN
ejpam-4493	168	5	)	)	PUNCT
ejpam-4493	168	6	,	,	PUNCT
ejpam-4493	168	7	that	that	ADV
ejpam-4493	168	8	is	is	ADV
ejpam-4493	168	9	,	,	PUNCT
ejpam-4493	168	10	b	b	PROPN
ejpam-4493	168	11	is	be	AUX
ejpam-4493	168	12	the	the	DET
ejpam-4493	168	13	only	only	ADJ
ejpam-4493	168	14	forcing	forcing	NOUN
ejpam-4493	168	15	subset	subset	NOUN
ejpam-4493	168	16	for	for	ADP
ejpam-4493	168	17	itself	itself	PRON
ejpam-4493	168	18	.	.	PUNCT
ejpam-4493	169	1	let	let	VERB
ejpam-4493	169	2	v	v	NUM
ejpam-4493	169	3	∈	∈	PROPN
ejpam-4493	169	4	b.	b.	PROPN
ejpam-4493	169	5	since	since	SCONJ
ejpam-4493	169	6	b	b	PROPN
ejpam-4493	169	7	\	\	PROPN
ejpam-4493	169	8	{	{	PUNCT
ejpam-4493	169	9	v	v	NOUN
ejpam-4493	169	10	}	}	PUNCT
ejpam-4493	169	11	is	be	AUX
ejpam-4493	169	12	not	not	PART
ejpam-4493	169	13	a	a	DET
ejpam-4493	169	14	forcing	forcing	NOUN
ejpam-4493	169	15	subset	subset	NOUN
ejpam-4493	169	16	for	for	ADP
ejpam-4493	169	17	b	b	NOUN
ejpam-4493	169	18	,	,	PUNCT
ejpam-4493	169	19	there	there	PRON
ejpam-4493	169	20	exists	exist	VERB
ejpam-4493	169	21	a	a	DET
ejpam-4493	169	22	uv	uv	NOUN
ejpam-4493	169	23	∈	∈	PROPN
ejpam-4493	169	24	v	v	NOUN
ejpam-4493	169	25	(	(	PUNCT
ejpam-4493	169	26	g	g	NOUN
ejpam-4493	169	27	)	)	PUNCT
ejpam-4493	169	28	\	\	PROPN
ejpam-4493	170	1	b	b	X
ejpam-4493	170	2	such	such	ADJ
ejpam-4493	170	3	that	that	SCONJ
ejpam-4493	170	4	[	[	PUNCT
ejpam-4493	170	5	b	b	X
ejpam-4493	170	6	\	\	X
ejpam-4493	170	7	{	{	PUNCT
ejpam-4493	170	8	v	v	NOUN
ejpam-4493	170	9	}	}	PUNCT
ejpam-4493	170	10	]	]	PUNCT
ejpam-4493	170	11	∪	∪	X
ejpam-4493	170	12	{	{	PUNCT
ejpam-4493	170	13	uv	uv	NOUN
ejpam-4493	170	14	}	}	PUNCT
ejpam-4493	170	15	is	be	AUX
ejpam-4493	170	16	an	an	DET
ejpam-4493	170	17	sci	sci	PROPN
ejpam-4493	170	18	-	-	PUNCT
ejpam-4493	170	19	set	set	NOUN
ejpam-4493	170	20	of	of	ADP
ejpam-4493	170	21	g.	g.	NOUN
ejpam-4493	170	22	conversely	conversely	ADV
ejpam-4493	170	23	,	,	PUNCT
ejpam-4493	170	24	suppose	suppose	VERB
ejpam-4493	170	25	that	that	SCONJ
ejpam-4493	170	26	every	every	DET
ejpam-4493	170	27	sci	sci	PROPN
ejpam-4493	170	28	-	-	PUNCT
ejpam-4493	170	29	set	set	VERB
ejpam-4493	170	30	b	b	NOUN
ejpam-4493	170	31	′	′	NOUN
ejpam-4493	170	32	of	of	ADP
ejpam-4493	170	33	g	g	PROPN
ejpam-4493	170	34	satisfies	satisfy	VERB
ejpam-4493	170	35	the	the	DET
ejpam-4493	170	36	given	give	VERB
ejpam-4493	170	37	condition	condition	NOUN
ejpam-4493	170	38	.	.	PUNCT
ejpam-4493	171	1	let	let	VERB
ejpam-4493	171	2	b	b	X
ejpam-4493	171	3	be	be	AUX
ejpam-4493	171	4	an	an	DET
ejpam-4493	171	5	sci	sci	PROPN
ejpam-4493	171	6	-	-	PUNCT
ejpam-4493	171	7	set	set	NOUN
ejpam-4493	171	8	of	of	ADP
ejpam-4493	171	9	g	g	NOUN
ejpam-4493	171	10	such	such	ADJ
ejpam-4493	171	11	that	that	DET
ejpam-4493	171	12	fsci(g	fsci(g	NOUN
ejpam-4493	171	13	)	)	PUNCT
ejpam-4493	172	1	=	=	SYM
ejpam-4493	172	2	fsci(b	fsci(b	PROPN
ejpam-4493	172	3	)	)	PUNCT
ejpam-4493	172	4	.	.	PUNCT
ejpam-4493	173	1	suppose	suppose	VERB
ejpam-4493	173	2	further	far	ADV
ejpam-4493	173	3	that	that	SCONJ
ejpam-4493	173	4	b	b	PROPN
ejpam-4493	173	5	has	have	VERB
ejpam-4493	173	6	a	a	DET
ejpam-4493	173	7	forcing	forcing	NOUN
ejpam-4493	173	8	subset	subset	NOUN
ejpam-4493	173	9	q	q	NOUN
ejpam-4493	173	10	with	with	ADP
ejpam-4493	173	11	|q|	|q|	PROPN
ejpam-4493	173	12	<	<	X
ejpam-4493	173	13	|b|	|b|	PROPN
ejpam-4493	173	14	,	,	PUNCT
ejpam-4493	173	15	that	that	ADV
ejpam-4493	173	16	is	be	AUX
ejpam-4493	173	17	,	,	PUNCT
ejpam-4493	173	18	b	b	X
ejpam-4493	173	19	=	=	SYM
ejpam-4493	173	20	q	q	X
ejpam-4493	173	21	∪	∪	ADP
ejpam-4493	173	22	p	p	NOUN
ejpam-4493	173	23	where	where	SCONJ
ejpam-4493	173	24	p	p	NOUN
ejpam-4493	173	25	=	=	X
ejpam-4493	173	26	{	{	PUNCT
ejpam-4493	173	27	z	z	PROPN
ejpam-4493	173	28	∈	∈	PROPN
ejpam-4493	173	29	b	b	PROPN
ejpam-4493	173	30	:	:	PUNCT
ejpam-4493	173	31	z	z	NOUN
ejpam-4493	173	32	/∈	/∈	PUNCT
ejpam-4493	174	1	q	q	ADJ
ejpam-4493	174	2	}	}	PUNCT
ejpam-4493	174	3	.	.	PUNCT
ejpam-4493	175	1	pick	pick	VERB
ejpam-4493	175	2	z	z	PROPN
ejpam-4493	175	3	∈	∈	PROPN
ejpam-4493	175	4	p.	p.	NOUN
ejpam-4493	175	5	by	by	ADP
ejpam-4493	175	6	assumption	assumption	NOUN
ejpam-4493	175	7	,	,	PUNCT
ejpam-4493	175	8	there	there	PRON
ejpam-4493	175	9	exists	exist	VERB
ejpam-4493	175	10	uz	uz	PROPN
ejpam-4493	175	11	∈	∈	PROPN
ejpam-4493	175	12	v	v	ADP
ejpam-4493	175	13	(	(	PUNCT
ejpam-4493	175	14	g	g	NOUN
ejpam-4493	175	15	)	)	PUNCT
ejpam-4493	175	16	\b	\b	NOUN
ejpam-4493	175	17	such	such	ADJ
ejpam-4493	175	18	that	that	SCONJ
ejpam-4493	175	19	[	[	PUNCT
ejpam-4493	175	20	b	b	X
ejpam-4493	175	21	\	\	X
ejpam-4493	175	22	{	{	PUNCT
ejpam-4493	175	23	z	z	NOUN
ejpam-4493	175	24	}	}	PUNCT
ejpam-4493	175	25	]	]	PUNCT
ejpam-4493	175	26	∪	∪	X
ejpam-4493	175	27	{	{	PUNCT
ejpam-4493	175	28	uz	uz	NOUN
ejpam-4493	175	29	}	}	PUNCT
ejpam-4493	175	30	=	=	SYM
ejpam-4493	175	31	t	t	NOUN
ejpam-4493	175	32	is	be	AUX
ejpam-4493	175	33	an	an	DET
ejpam-4493	175	34	sci	sci	PROPN
ejpam-4493	175	35	-	-	PUNCT
ejpam-4493	175	36	set	set	NOUN
ejpam-4493	175	37	of	of	ADP
ejpam-4493	175	38	g.	g.	PROPN
ejpam-4493	175	39	hence	hence	ADV
ejpam-4493	175	40	,	,	PUNCT
ejpam-4493	175	41	t	t	PROPN
ejpam-4493	175	42	=	=	PUNCT
ejpam-4493	175	43	q∪r	q∪r	PROPN
ejpam-4493	175	44	,	,	PUNCT
ejpam-4493	175	45	where	where	SCONJ
ejpam-4493	175	46	r	r	NOUN
ejpam-4493	175	47	=	=	PUNCT
ejpam-4493	175	48	[	[	PUNCT
ejpam-4493	175	49	p	p	NOUN
ejpam-4493	175	50	\{z	\{z	NOUN
ejpam-4493	175	51	}	}	PUNCT
ejpam-4493	175	52	]	]	PUNCT
ejpam-4493	176	1	∪{uz	∪{uz	NUM
ejpam-4493	176	2	}	}	PUNCT
ejpam-4493	176	3	,	,	PUNCT
ejpam-4493	176	4	is	be	AUX
ejpam-4493	176	5	an	an	DET
ejpam-4493	176	6	sci	sci	PROPN
ejpam-4493	176	7	-	-	PUNCT
ejpam-4493	176	8	set	set	NOUN
ejpam-4493	176	9	containing	contain	VERB
ejpam-4493	176	10	q	q	NOUN
ejpam-4493	176	11	,	,	PUNCT
ejpam-4493	176	12	a	a	DET
ejpam-4493	176	13	contradiction	contradiction	NOUN
ejpam-4493	176	14	.	.	PUNCT
ejpam-4493	177	1	hence	hence	ADV
ejpam-4493	177	2	,	,	PUNCT
ejpam-4493	177	3	b	b	PROPN
ejpam-4493	177	4	is	be	AUX
ejpam-4493	177	5	the	the	DET
ejpam-4493	177	6	only	only	ADJ
ejpam-4493	177	7	forcing	forcing	NOUN
ejpam-4493	177	8	subset	subset	NOUN
ejpam-4493	177	9	for	for	ADP
ejpam-4493	177	10	b.	b.	PROPN
ejpam-4493	177	11	therefore	therefore	ADV
ejpam-4493	177	12	,	,	PUNCT
ejpam-4493	177	13	fsci(g	fsci(g	NOUN
ejpam-4493	177	14	)	)	PUNCT
ejpam-4493	177	15	=	=	PUNCT
ejpam-4493	177	16	sci(g	sci(g	PROPN
ejpam-4493	177	17	)	)	PUNCT
ejpam-4493	177	18	.	.	PUNCT
ejpam-4493	178	1	proposition	proposition	NOUN
ejpam-4493	178	2	4	4	NUM
ejpam-4493	178	3	.	.	X
ejpam-4493	179	1	for	for	ADP
ejpam-4493	179	2	any	any	DET
ejpam-4493	179	3	complete	complete	ADJ
ejpam-4493	179	4	graph	graph	NOUN
ejpam-4493	179	5	kn	kn	PROPN
ejpam-4493	179	6	with	with	ADP
ejpam-4493	179	7	n	n	PRON
ejpam-4493	179	8	≥	≥	NUM
ejpam-4493	179	9	1	1	NUM
ejpam-4493	179	10	vertices	vertex	NOUN
ejpam-4493	179	11	,	,	PUNCT
ejpam-4493	179	12	fsci(kn	fsci(kn	NOUN
ejpam-4493	179	13	)	)	PUNCT
ejpam-4493	179	14	=	=	SYM
ejpam-4493	179	15	0	0	X
ejpam-4493	179	16	.	.	X
ejpam-4493	179	17	proof	proof	NOUN
ejpam-4493	179	18	:	:	PUNCT
ejpam-4493	179	19	by	by	ADP
ejpam-4493	179	20	definition	definition	NOUN
ejpam-4493	179	21	of	of	ADP
ejpam-4493	179	22	kn	kn	PROPN
ejpam-4493	179	23	,	,	PUNCT
ejpam-4493	179	24	v	v	PROPN
ejpam-4493	179	25	(	(	PUNCT
ejpam-4493	179	26	kn	kn	PROPN
ejpam-4493	179	27	)	)	PUNCT
ejpam-4493	179	28	is	be	AUX
ejpam-4493	179	29	the	the	DET
ejpam-4493	179	30	only	only	ADJ
ejpam-4493	179	31	sci	sci	PROPN
ejpam-4493	179	32	-	-	PUNCT
ejpam-4493	179	33	set	set	NOUN
ejpam-4493	179	34	of	of	ADP
ejpam-4493	179	35	kn	kn	PROPN
ejpam-4493	179	36	.	.	PUNCT
ejpam-4493	180	1	by	by	ADP
ejpam-4493	180	2	remark	remark	NOUN
ejpam-4493	180	3	2(i	2(i	NUM
ejpam-4493	180	4	)	)	PUNCT
ejpam-4493	180	5	,	,	PUNCT
ejpam-4493	180	6	fsci(kn	fsci(kn	NOUN
ejpam-4493	180	7	)	)	PUNCT
ejpam-4493	180	8	=	=	SYM
ejpam-4493	181	1	0	0	X
ejpam-4493	181	2	.	.	PUNCT
ejpam-4493	181	3	proposition	proposition	NOUN
ejpam-4493	181	4	5	5	NUM
ejpam-4493	181	5	.	.	PUNCT
ejpam-4493	182	1	for	for	ADP
ejpam-4493	182	2	any	any	DET
ejpam-4493	182	3	path	path	NOUN
ejpam-4493	182	4	pn	pn	NOUN
ejpam-4493	182	5	with	with	ADP
ejpam-4493	182	6	n	n	PRON
ejpam-4493	182	7	≥	≥	NUM
ejpam-4493	182	8	1	1	NUM
ejpam-4493	182	9	vertices	vertex	NOUN
ejpam-4493	182	10	,	,	PUNCT
ejpam-4493	182	11	fsci(pn	fsci(pn	NOUN
ejpam-4493	182	12	)	)	PUNCT
ejpam-4493	182	13	=	=	SYM
ejpam-4493	182	14			NOUN
ejpam-4493	182	15	0	0	NUM
ejpam-4493	182	16	,	,	PUNCT
ejpam-4493	182	17	if	if	SCONJ
ejpam-4493	182	18	n	n	NOUN
ejpam-4493	182	19	=	=	SYM
ejpam-4493	182	20	1	1	NUM
ejpam-4493	182	21	,	,	PUNCT
ejpam-4493	182	22	2	2	NUM
ejpam-4493	182	23	,	,	PUNCT
ejpam-4493	182	24	4	4	NUM
ejpam-4493	182	25	and	and	CCONJ
ejpam-4493	182	26	n	n	PRON
ejpam-4493	182	27	>	>	SYM
ejpam-4493	182	28	5	5	NUM
ejpam-4493	182	29	is	be	AUX
ejpam-4493	182	30	odd	odd	ADJ
ejpam-4493	182	31	,	,	PUNCT
ejpam-4493	182	32	1	1	NUM
ejpam-4493	182	33	,	,	PUNCT
ejpam-4493	182	34	if	if	SCONJ
ejpam-4493	182	35	n	n	CCONJ
ejpam-4493	182	36	=	=	SYM
ejpam-4493	182	37	3	3	NUM
ejpam-4493	182	38	and	and	CCONJ
ejpam-4493	182	39	n	n	PRON
ejpam-4493	182	40	≥	≥	NUM
ejpam-4493	182	41	6	6	NUM
ejpam-4493	182	42	is	be	AUX
ejpam-4493	182	43	even	even	ADV
ejpam-4493	182	44	,	,	PUNCT
ejpam-4493	182	45	2	2	NUM
ejpam-4493	182	46	,	,	PUNCT
ejpam-4493	182	47	if	if	SCONJ
ejpam-4493	182	48	n	n	NOUN
ejpam-4493	182	49	=	=	SYM
ejpam-4493	182	50	5	5	X
ejpam-4493	182	51	.	.	PUNCT
ejpam-4493	183	1	proof	proof	NOUN
ejpam-4493	183	2	:	:	PUNCT
ejpam-4493	183	3	suppose	suppose	VERB
ejpam-4493	183	4	that	that	SCONJ
ejpam-4493	183	5	pn	pn	PROPN
ejpam-4493	183	6	=	=	PUNCT
ejpam-4493	184	1	[	[	X
ejpam-4493	184	2	v1	v1	NOUN
ejpam-4493	184	3	,	,	PUNCT
ejpam-4493	184	4	v2	v2	NOUN
ejpam-4493	184	5	,	,	PUNCT
ejpam-4493	184	6	.	.	PUNCT
ejpam-4493	184	7	.	.	PUNCT
ejpam-4493	184	8	.	.	PUNCT
ejpam-4493	185	1	,	,	PUNCT
ejpam-4493	185	2	vn	vn	X
ejpam-4493	185	3	]	]	PUNCT
ejpam-4493	185	4	.	.	PUNCT
ejpam-4493	186	1	clearly	clearly	ADV
ejpam-4493	186	2	,	,	PUNCT
ejpam-4493	186	3	fsci(p1	fsci(p1	NOUN
ejpam-4493	186	4	)	)	PUNCT
ejpam-4493	187	1	=	=	SYM
ejpam-4493	187	2	fsci(p2	fsci(p2	X
ejpam-4493	187	3	)	)	PUNCT
ejpam-4493	187	4	=	=	SYM
ejpam-4493	187	5	fsci(p4	fsci(p4	NOUN
ejpam-4493	187	6	)	)	PUNCT
ejpam-4493	188	1	=	=	SYM
ejpam-4493	188	2	0	0	NUM
ejpam-4493	188	3	,	,	PUNCT
ejpam-4493	188	4	fsci(p3	fsci(p3	ADJ
ejpam-4493	188	5	)	)	PUNCT
ejpam-4493	188	6	=	=	SYM
ejpam-4493	188	7	1	1	NUM
ejpam-4493	188	8	and	and	CCONJ
ejpam-4493	188	9	fsci(p5	fsci(p5	ADJ
ejpam-4493	188	10	)	)	PUNCT
ejpam-4493	188	11	=	=	SYM
ejpam-4493	189	1	2	2	X
ejpam-4493	189	2	.	.	X
ejpam-4493	189	3	if	if	SCONJ
ejpam-4493	189	4	n	n	PROPN
ejpam-4493	189	5	>	>	X
ejpam-4493	189	6	5	5	NUM
ejpam-4493	189	7	and	and	CCONJ
ejpam-4493	189	8	n	n	PRON
ejpam-4493	189	9	is	be	AUX
ejpam-4493	189	10	odd	odd	ADJ
ejpam-4493	189	11	,	,	PUNCT
ejpam-4493	189	12	then	then	ADV
ejpam-4493	189	13	clearly	clearly	ADV
ejpam-4493	189	14	b	b	X
ejpam-4493	189	15	=	=	PRON
ejpam-4493	189	16	{	{	PUNCT
ejpam-4493	189	17	v2	v2	PROPN
ejpam-4493	189	18	,	,	PUNCT
ejpam-4493	189	19	v4	v4	PROPN
ejpam-4493	189	20	,	,	PUNCT
ejpam-4493	189	21	v6	v6	NOUN
ejpam-4493	189	22	,	,	PUNCT
ejpam-4493	189	23	.	.	PUNCT
ejpam-4493	189	24	.	.	PUNCT
ejpam-4493	189	25	.	.	PUNCT
ejpam-4493	190	1	,	,	PUNCT
ejpam-4493	190	2	vn−3	vn−3	PROPN
ejpam-4493	190	3	,	,	PUNCT
ejpam-4493	190	4	vn−1	vn−1	ADJ
ejpam-4493	190	5	}	}	PUNCT
ejpam-4493	190	6	is	be	AUX
ejpam-4493	190	7	the	the	DET
ejpam-4493	190	8	only	only	ADJ
ejpam-4493	190	9	sci	sci	PROPN
ejpam-4493	190	10	-	-	PUNCT
ejpam-4493	190	11	set	set	NOUN
ejpam-4493	190	12	of	of	ADP
ejpam-4493	190	13	pn	pn	PROPN
ejpam-4493	190	14	.	.	PUNCT
ejpam-4493	191	1	thus	thus	ADV
ejpam-4493	191	2	,	,	PUNCT
ejpam-4493	191	3	by	by	ADP
ejpam-4493	191	4	remark	remark	NOUN
ejpam-4493	191	5	2(i	2(i	NUM
ejpam-4493	191	6	)	)	PUNCT
ejpam-4493	191	7	,	,	PUNCT
ejpam-4493	191	8	fsci(b	fsci(b	PROPN
ejpam-4493	191	9	)	)	PUNCT
ejpam-4493	191	10	=	=	SYM
ejpam-4493	191	11	0	0	NUM
ejpam-4493	191	12	=	=	SYM
ejpam-4493	191	13	fsci(pn	fsci(pn	NOUN
ejpam-4493	191	14	)	)	PUNCT
ejpam-4493	191	15	.	.	PUNCT
ejpam-4493	192	1	suppose	suppose	VERB
ejpam-4493	192	2	that	that	SCONJ
ejpam-4493	192	3	n	n	PROPN
ejpam-4493	192	4	≥	≥	NUM
ejpam-4493	192	5	6	6	NUM
ejpam-4493	192	6	and	and	CCONJ
ejpam-4493	192	7	n	n	NUM
ejpam-4493	192	8	is	be	AUX
ejpam-4493	192	9	even	even	ADV
ejpam-4493	192	10	.	.	PUNCT
ejpam-4493	193	1	then	then	ADV
ejpam-4493	193	2	pn	pn	PROPN
ejpam-4493	193	3	has	have	VERB
ejpam-4493	193	4	sci	sci	PROPN
ejpam-4493	193	5	-	-	PUNCT
ejpam-4493	193	6	sets	set	NOUN
ejpam-4493	193	7	b1	b1	NOUN
ejpam-4493	193	8	=	=	SYM
ejpam-4493	193	9	{	{	PUNCT
ejpam-4493	193	10	v1	v1	PROPN
ejpam-4493	193	11	,	,	PUNCT
ejpam-4493	193	12	v3	v3	PROPN
ejpam-4493	193	13	,	,	PUNCT
ejpam-4493	193	14	v5	v5	PROPN
ejpam-4493	193	15	,	,	PUNCT
ejpam-4493	193	16	.	.	PUNCT
ejpam-4493	193	17	.	.	PUNCT
ejpam-4493	194	1	.	.	PUNCT
ejpam-4493	195	1	,	,	PUNCT
ejpam-4493	195	2	vn−1	vn−1	ADJ
ejpam-4493	195	3	}	}	PUNCT
ejpam-4493	195	4	and	and	CCONJ
ejpam-4493	195	5	b2	b2	NOUN
ejpam-4493	195	6	=	=	SYM
ejpam-4493	195	7	{	{	PUNCT
ejpam-4493	195	8	v2	v2	PROPN
ejpam-4493	195	9	,	,	PUNCT
ejpam-4493	195	10	v4	v4	PROPN
ejpam-4493	195	11	,	,	PUNCT
ejpam-4493	195	12	v6	v6	NOUN
ejpam-4493	195	13	,	,	PUNCT
ejpam-4493	195	14	.	.	PUNCT
ejpam-4493	195	15	.	.	PUNCT
ejpam-4493	195	16	.	.	PUNCT
ejpam-4493	196	1	,	,	PUNCT
ejpam-4493	196	2	vn	vn	PROPN
ejpam-4493	196	3	}	}	PUNCT
ejpam-4493	196	4	.	.	PUNCT
ejpam-4493	197	1	it	it	PRON
ejpam-4493	197	2	can	can	AUX
ejpam-4493	197	3	be	be	AUX
ejpam-4493	197	4	verified	verify	VERB
ejpam-4493	197	5	that	that	SCONJ
ejpam-4493	197	6	b1	b1	PROPN
ejpam-4493	197	7	is	be	AUX
ejpam-4493	197	8	the	the	DET
ejpam-4493	197	9	only	only	ADJ
ejpam-4493	197	10	sci	sci	PROPN
ejpam-4493	197	11	-	-	PUNCT
ejpam-4493	197	12	set	set	NOUN
ejpam-4493	197	13	of	of	ADP
ejpam-4493	197	14	pn	pn	PROPN
ejpam-4493	197	15	containing	contain	VERB
ejpam-4493	197	16	the	the	DET
ejpam-4493	197	17	vertex	vertex	NOUN
ejpam-4493	197	18	v1	v1	NOUN
ejpam-4493	197	19	.	.	PUNCT
ejpam-4493	198	1	hence	hence	ADV
ejpam-4493	198	2	,	,	PUNCT
ejpam-4493	198	3	by	by	ADP
ejpam-4493	198	4	remark	remark	NOUN
ejpam-4493	198	5	2(ii	2(ii	NUM
ejpam-4493	198	6	)	)	PUNCT
ejpam-4493	198	7	,	,	PUNCT
ejpam-4493	198	8	fsci(pn	fsci(pn	NOUN
ejpam-4493	198	9	)	)	PUNCT
ejpam-4493	198	10	=	=	SYM
ejpam-4493	198	11	1	1	X
ejpam-4493	198	12	.	.	X
ejpam-4493	198	13	proposition	proposition	NOUN
ejpam-4493	198	14	6	6	NUM
ejpam-4493	198	15	.	.	PUNCT
ejpam-4493	199	1	for	for	ADP
ejpam-4493	199	2	any	any	DET
ejpam-4493	199	3	cycle	cycle	NOUN
ejpam-4493	199	4	cn	cn	NOUN
ejpam-4493	199	5	with	with	ADP
ejpam-4493	199	6	n	n	NUM
ejpam-4493	199	7	≥	≥	NUM
ejpam-4493	199	8	3	3	NUM
ejpam-4493	199	9	vertices	vertex	NOUN
ejpam-4493	199	10	,	,	PUNCT
ejpam-4493	199	11	fsci(cn	fsci(cn	NOUN
ejpam-4493	199	12	)	)	PUNCT
ejpam-4493	199	13	=	=	PUNCT
ejpam-4493	199	14			NOUN
ejpam-4493	199	15	0	0	NUM
ejpam-4493	199	16	,	,	PUNCT
ejpam-4493	199	17	if	if	SCONJ
ejpam-4493	199	18	n	n	NOUN
ejpam-4493	199	19	=	=	SYM
ejpam-4493	199	20	3	3	NUM
ejpam-4493	199	21	,	,	PUNCT
ejpam-4493	199	22	1	1	NUM
ejpam-4493	199	23	,	,	PUNCT
ejpam-4493	199	24	if	if	SCONJ
ejpam-4493	199	25	n	n	PROPN
ejpam-4493	199	26	>	>	X
ejpam-4493	199	27	4	4	NUM
ejpam-4493	199	28	and	and	CCONJ
ejpam-4493	199	29	n	n	PRON
ejpam-4493	199	30	is	be	AUX
ejpam-4493	199	31	even	even	ADV
ejpam-4493	199	32	,	,	PUNCT
ejpam-4493	199	33	2	2	NUM
ejpam-4493	199	34	,	,	PUNCT
ejpam-4493	199	35	if	if	SCONJ
ejpam-4493	199	36	n	n	PROPN
ejpam-4493	199	37	>	>	X
ejpam-4493	199	38	3	3	NUM
ejpam-4493	199	39	and	and	CCONJ
ejpam-4493	199	40	n	n	PRON
ejpam-4493	199	41	is	be	AUX
ejpam-4493	199	42	odd	odd	ADJ
ejpam-4493	199	43	,	,	PUNCT
ejpam-4493	199	44	3	3	X
ejpam-4493	199	45	,	,	PUNCT
ejpam-4493	199	46	if	if	SCONJ
ejpam-4493	199	47	n	n	NOUN
ejpam-4493	199	48	=	=	SYM
ejpam-4493	199	49	4	4	X
ejpam-4493	199	50	.	.	X
ejpam-4493	199	51	y.d	y.d	PROPN
ejpam-4493	199	52	.	.	PROPN
ejpam-4493	199	53	calanza	calanza	PROPN
ejpam-4493	199	54	,	,	PUNCT
ejpam-4493	199	55	h.	h.	PROPN
ejpam-4493	199	56	rara	rara	PROPN
ejpam-4493	199	57	/	/	SYM
ejpam-4493	199	58	eur	eur	PROPN
ejpam-4493	199	59	.	.	PUNCT
ejpam-4493	200	1	j.	j.	PROPN
ejpam-4493	200	2	pure	pure	PROPN
ejpam-4493	200	3	appl	appl	PROPN
ejpam-4493	200	4	.	.	PROPN
ejpam-4493	200	5	math	math	PROPN
ejpam-4493	200	6	,	,	PUNCT
ejpam-4493	200	7	15	15	NUM
ejpam-4493	200	8	(	(	PUNCT
ejpam-4493	200	9	4	4	NUM
ejpam-4493	200	10	)	)	PUNCT
ejpam-4493	200	11	(	(	PUNCT
ejpam-4493	200	12	2022	2022	NUM
ejpam-4493	200	13	)	)	PUNCT
ejpam-4493	200	14	,	,	PUNCT
ejpam-4493	200	15	1649	1649	NUM
ejpam-4493	200	16	-	-	SYM
ejpam-4493	200	17	1661	1661	NUM
ejpam-4493	200	18	1655	1655	NUM
ejpam-4493	200	19	proof	proof	NOUN
ejpam-4493	200	20	:	:	PUNCT
ejpam-4493	200	21	suppose	suppose	VERB
ejpam-4493	200	22	that	that	SCONJ
ejpam-4493	200	23	cn	cn	PROPN
ejpam-4493	200	24	=	=	PUNCT
ejpam-4493	200	25	[	[	X
ejpam-4493	200	26	v1	v1	NOUN
ejpam-4493	200	27	,	,	PUNCT
ejpam-4493	200	28	v2	v2	NOUN
ejpam-4493	200	29	,	,	PUNCT
ejpam-4493	200	30	.	.	PUNCT
ejpam-4493	200	31	.	.	PUNCT
ejpam-4493	200	32	.	.	PUNCT
ejpam-4493	201	1	,	,	PUNCT
ejpam-4493	201	2	vn	vn	X
ejpam-4493	201	3	,	,	PUNCT
ejpam-4493	201	4	v1	v1	PROPN
ejpam-4493	201	5	]	]	PUNCT
ejpam-4493	201	6	.	.	PUNCT
ejpam-4493	202	1	since	since	SCONJ
ejpam-4493	202	2	c3	c3	PROPN
ejpam-4493	202	3	=	=	SYM
ejpam-4493	202	4	k3	k3	PROPN
ejpam-4493	202	5	,	,	PUNCT
ejpam-4493	202	6	by	by	ADP
ejpam-4493	202	7	proposition	proposition	NOUN
ejpam-4493	202	8	4	4	NUM
ejpam-4493	202	9	,	,	PUNCT
ejpam-4493	202	10	fsci(c3	fsci(c3	NOUN
ejpam-4493	202	11	)	)	PUNCT
ejpam-4493	202	12	=	=	SYM
ejpam-4493	202	13	0	0	X
ejpam-4493	202	14	.	.	PUNCT
ejpam-4493	202	15	suppose	suppose	VERB
ejpam-4493	202	16	that	that	SCONJ
ejpam-4493	202	17	n	n	PROPN
ejpam-4493	202	18	=	=	SYM
ejpam-4493	202	19	4	4	X
ejpam-4493	202	20	.	.	PUNCT
ejpam-4493	202	21	then	then	ADV
ejpam-4493	202	22	the	the	DET
ejpam-4493	202	23	sci	sci	PROPN
ejpam-4493	202	24	-	-	PUNCT
ejpam-4493	202	25	sets	set	NOUN
ejpam-4493	202	26	of	of	ADP
ejpam-4493	202	27	c4	c4	NOUN
ejpam-4493	202	28	are	be	AUX
ejpam-4493	202	29	r1	r1	NOUN
ejpam-4493	202	30	=	=	SYM
ejpam-4493	202	31	{	{	PUNCT
ejpam-4493	202	32	v1	v1	PROPN
ejpam-4493	202	33	,	,	PUNCT
ejpam-4493	202	34	v2	v2	PROPN
ejpam-4493	202	35	,	,	PUNCT
ejpam-4493	202	36	v3	v3	PROPN
ejpam-4493	202	37	}	}	PUNCT
ejpam-4493	202	38	,	,	PUNCT
ejpam-4493	202	39	r2	r2	PROPN
ejpam-4493	202	40	=	=	PUNCT
ejpam-4493	202	41	{	{	PUNCT
ejpam-4493	202	42	v2	v2	PROPN
ejpam-4493	202	43	,	,	PUNCT
ejpam-4493	202	44	v3	v3	PROPN
ejpam-4493	202	45	,	,	PUNCT
ejpam-4493	202	46	v4	v4	PROPN
ejpam-4493	202	47	}	}	PUNCT
ejpam-4493	202	48	,	,	PUNCT
ejpam-4493	202	49	r3	r3	PROPN
ejpam-4493	202	50	=	=	SYM
ejpam-4493	202	51	{	{	PUNCT
ejpam-4493	202	52	v1	v1	PROPN
ejpam-4493	202	53	,	,	PUNCT
ejpam-4493	202	54	v3	v3	PROPN
ejpam-4493	202	55	,	,	PUNCT
ejpam-4493	202	56	v4	v4	NOUN
ejpam-4493	202	57	}	}	PUNCT
ejpam-4493	202	58	and	and	CCONJ
ejpam-4493	202	59	r4	r4	VERB
ejpam-4493	202	60	=	=	SYM
ejpam-4493	202	61	{	{	PUNCT
ejpam-4493	202	62	v1	v1	PROPN
ejpam-4493	202	63	,	,	PUNCT
ejpam-4493	202	64	v2	v2	PROPN
ejpam-4493	202	65	,	,	PUNCT
ejpam-4493	202	66	v4	v4	PROPN
ejpam-4493	202	67	}	}	PUNCT
ejpam-4493	202	68	.	.	PUNCT
ejpam-4493	203	1	clearly	clearly	ADV
ejpam-4493	203	2	,	,	PUNCT
ejpam-4493	203	3	for	for	ADP
ejpam-4493	203	4	each	each	DET
ejpam-4493	203	5	vi	vi	PROPN
ejpam-4493	203	6	∈	∈	PROPN
ejpam-4493	203	7	rj	rj	X
ejpam-4493	203	8	where	where	SCONJ
ejpam-4493	203	9	i	i	PRON
ejpam-4493	203	10	,	,	PUNCT
ejpam-4493	203	11	j	j	PROPN
ejpam-4493	203	12	∈	∈	PROPN
ejpam-4493	203	13	{	{	PUNCT
ejpam-4493	203	14	1	1	NUM
ejpam-4493	203	15	,	,	PUNCT
ejpam-4493	203	16	2	2	NUM
ejpam-4493	203	17	,	,	PUNCT
ejpam-4493	203	18	3	3	NUM
ejpam-4493	203	19	,	,	PUNCT
ejpam-4493	203	20	4	4	NUM
ejpam-4493	203	21	}	}	PUNCT
ejpam-4493	203	22	,	,	PUNCT
ejpam-4493	203	23	there	there	PRON
ejpam-4493	203	24	exists	exist	VERB
ejpam-4493	203	25	vk	vk	ADP
ejpam-4493	203	26	∈	∈	PROPN
ejpam-4493	203	27	v	v	PROPN
ejpam-4493	203	28	(	(	PUNCT
ejpam-4493	203	29	c4	c4	NOUN
ejpam-4493	203	30	)	)	PUNCT
ejpam-4493	203	31	\	\	PROPN
ejpam-4493	204	1	rj	rj	PROPN
ejpam-4493	204	2	such	such	ADJ
ejpam-4493	204	3	that	that	SCONJ
ejpam-4493	205	1	[	[	X
ejpam-4493	205	2	rj	rj	X
ejpam-4493	205	3	\	\	PROPN
ejpam-4493	205	4	{	{	PUNCT
ejpam-4493	205	5	vi	vi	NOUN
ejpam-4493	205	6	}	}	PUNCT
ejpam-4493	205	7	]	]	PUNCT
ejpam-4493	205	8	∪	∪	X
ejpam-4493	205	9	{	{	PUNCT
ejpam-4493	205	10	vk	vk	INTJ
ejpam-4493	205	11	}	}	PUNCT
ejpam-4493	205	12	is	be	AUX
ejpam-4493	205	13	an	an	DET
ejpam-4493	205	14	sci	sci	PROPN
ejpam-4493	205	15	-	-	PUNCT
ejpam-4493	205	16	set	set	NOUN
ejpam-4493	205	17	of	of	ADP
ejpam-4493	205	18	g.	g.	PROPN
ejpam-4493	205	19	thus	thus	ADV
ejpam-4493	205	20	,	,	PUNCT
ejpam-4493	205	21	by	by	ADP
ejpam-4493	205	22	theorem	theorem	ADJ
ejpam-4493	205	23	4	4	NUM
ejpam-4493	205	24	,	,	PUNCT
ejpam-4493	205	25	fsci(c4	fsci(c4	NOUN
ejpam-4493	205	26	)	)	PUNCT
ejpam-4493	205	27	=	=	SYM
ejpam-4493	206	1	3	3	X
ejpam-4493	206	2	.	.	PUNCT
ejpam-4493	206	3	now	now	ADV
ejpam-4493	206	4	,	,	PUNCT
ejpam-4493	206	5	suppose	suppose	VERB
ejpam-4493	206	6	that	that	SCONJ
ejpam-4493	206	7	n	n	NOUN
ejpam-4493	206	8	>	>	X
ejpam-4493	206	9	4	4	NUM
ejpam-4493	206	10	and	and	CCONJ
ejpam-4493	206	11	n	n	PRON
ejpam-4493	206	12	is	be	AUX
ejpam-4493	206	13	even	even	ADV
ejpam-4493	206	14	.	.	PUNCT
ejpam-4493	207	1	then	then	ADV
ejpam-4493	207	2	b1	b1	NOUN
ejpam-4493	207	3	=	=	SYM
ejpam-4493	207	4	{	{	PUNCT
ejpam-4493	207	5	v1	v1	PROPN
ejpam-4493	207	6	,	,	PUNCT
ejpam-4493	207	7	v3	v3	PROPN
ejpam-4493	207	8	,	,	PUNCT
ejpam-4493	207	9	v5	v5	PROPN
ejpam-4493	207	10	,	,	PUNCT
ejpam-4493	207	11	.	.	PUNCT
ejpam-4493	207	12	.	.	PUNCT
ejpam-4493	207	13	.	.	PUNCT
ejpam-4493	208	1	,	,	PUNCT
ejpam-4493	208	2	vn−1	vn−1	ADJ
ejpam-4493	208	3	}	}	PUNCT
ejpam-4493	208	4	and	and	CCONJ
ejpam-4493	208	5	b2	b2	NOUN
ejpam-4493	208	6	=	=	SYM
ejpam-4493	208	7	{	{	PUNCT
ejpam-4493	208	8	v2	v2	PROPN
ejpam-4493	208	9	,	,	PUNCT
ejpam-4493	208	10	v4	v4	PROPN
ejpam-4493	208	11	,	,	PUNCT
ejpam-4493	208	12	v6	v6	NOUN
ejpam-4493	208	13	,	,	PUNCT
ejpam-4493	208	14	.	.	PUNCT
ejpam-4493	208	15	.	.	PUNCT
ejpam-4493	208	16	.	.	PUNCT
ejpam-4493	209	1	,	,	PUNCT
ejpam-4493	209	2	vn	vn	PROPN
ejpam-4493	209	3	}	}	PUNCT
ejpam-4493	209	4	are	be	AUX
ejpam-4493	209	5	the	the	DET
ejpam-4493	209	6	only	only	ADJ
ejpam-4493	209	7	sci	sci	NOUN
ejpam-4493	209	8	-	-	PUNCT
ejpam-4493	209	9	sets	set	NOUN
ejpam-4493	209	10	of	of	ADP
ejpam-4493	209	11	cn	cn	PROPN
ejpam-4493	209	12	with	with	ADP
ejpam-4493	209	13	v1	v1	PROPN
ejpam-4493	209	14	∈	∈	PROPN
ejpam-4493	209	15	b1	b1	NOUN
ejpam-4493	209	16	and	and	CCONJ
ejpam-4493	209	17	v1	v1	PROPN
ejpam-4493	209	18	/∈	/∈	SYM
ejpam-4493	209	19	b2	b2	NOUN
ejpam-4493	209	20	.	.	PUNCT
ejpam-4493	210	1	hence	hence	ADV
ejpam-4493	210	2	,	,	PUNCT
ejpam-4493	210	3	by	by	ADP
ejpam-4493	210	4	remark	remark	NOUN
ejpam-4493	210	5	2(ii	2(ii	NUM
ejpam-4493	210	6	)	)	PUNCT
ejpam-4493	210	7	,	,	PUNCT
ejpam-4493	210	8	fsci(b1	fsci(b1	NOUN
ejpam-4493	210	9	)	)	PUNCT
ejpam-4493	210	10	=	=	SYM
ejpam-4493	210	11	1	1	NUM
ejpam-4493	210	12	=	=	SYM
ejpam-4493	210	13	fsci(cn	fsci(cn	NOUN
ejpam-4493	210	14	)	)	PUNCT
ejpam-4493	210	15	.	.	PUNCT
ejpam-4493	211	1	next	next	ADV
ejpam-4493	211	2	,	,	PUNCT
ejpam-4493	211	3	suppose	suppose	VERB
ejpam-4493	211	4	that	that	SCONJ
ejpam-4493	211	5	n	n	PROPN
ejpam-4493	211	6	>	>	X
ejpam-4493	211	7	3	3	NUM
ejpam-4493	211	8	and	and	CCONJ
ejpam-4493	211	9	n	n	PRON
ejpam-4493	211	10	is	be	AUX
ejpam-4493	211	11	odd	odd	ADJ
ejpam-4493	211	12	.	.	PUNCT
ejpam-4493	212	1	then	then	ADV
ejpam-4493	212	2	s1	s1	PROPN
ejpam-4493	212	3	=	=	SYM
ejpam-4493	212	4	{	{	PUNCT
ejpam-4493	212	5	v1	v1	PROPN
ejpam-4493	212	6	,	,	PUNCT
ejpam-4493	212	7	v3	v3	PROPN
ejpam-4493	212	8	,	,	PUNCT
ejpam-4493	212	9	v5	v5	PROPN
ejpam-4493	212	10	,	,	PUNCT
ejpam-4493	212	11	.	.	PUNCT
ejpam-4493	212	12	.	.	PUNCT
ejpam-4493	212	13	.	.	PUNCT
ejpam-4493	213	1	,	,	PUNCT
ejpam-4493	213	2	vn−2	vn−2	PROPN
ejpam-4493	213	3	,	,	PUNCT
ejpam-4493	213	4	vn	vn	NOUN
ejpam-4493	213	5	}	}	PUNCT
ejpam-4493	213	6	,	,	PUNCT
ejpam-4493	213	7	s2	s2	X
ejpam-4493	213	8	=	=	SYM
ejpam-4493	213	9	{	{	PUNCT
ejpam-4493	213	10	v1	v1	PROPN
ejpam-4493	213	11	,	,	PUNCT
ejpam-4493	213	12	v3	v3	PROPN
ejpam-4493	213	13	,	,	PUNCT
ejpam-4493	213	14	v5	v5	PROPN
ejpam-4493	213	15	,	,	PUNCT
ejpam-4493	213	16	.	.	PUNCT
ejpam-4493	213	17	.	.	PUNCT
ejpam-4493	213	18	.	.	PUNCT
ejpam-4493	214	1	,	,	PUNCT
ejpam-4493	214	2	vn−2	vn−2	PROPN
ejpam-4493	214	3	,	,	PUNCT
ejpam-4493	214	4	vn−1	vn−1	ADJ
ejpam-4493	214	5	}	}	PUNCT
ejpam-4493	214	6	,	,	PUNCT
ejpam-4493	214	7	s3	s3	PROPN
ejpam-4493	214	8	=	=	SYM
ejpam-4493	214	9	{	{	PUNCT
ejpam-4493	214	10	v2	v2	PROPN
ejpam-4493	214	11	,	,	PUNCT
ejpam-4493	214	12	v4	v4	PROPN
ejpam-4493	214	13	,	,	PUNCT
ejpam-4493	214	14	v6	v6	NOUN
ejpam-4493	214	15	,	,	PUNCT
ejpam-4493	214	16	.	.	PUNCT
ejpam-4493	214	17	.	.	PUNCT
ejpam-4493	214	18	.	.	PUNCT
ejpam-4493	215	1	,	,	PUNCT
ejpam-4493	215	2	vn−1	vn−1	PROPN
ejpam-4493	215	3	,	,	PUNCT
ejpam-4493	215	4	vn	vn	NOUN
ejpam-4493	215	5	}	}	PUNCT
ejpam-4493	215	6	and	and	CCONJ
ejpam-4493	215	7	,	,	PUNCT
ejpam-4493	215	8	s4	s4	PROPN
ejpam-4493	215	9	=	=	SYM
ejpam-4493	215	10	{	{	PUNCT
ejpam-4493	215	11	v2	v2	PROPN
ejpam-4493	215	12	,	,	PUNCT
ejpam-4493	215	13	v4	v4	PROPN
ejpam-4493	215	14	,	,	PUNCT
ejpam-4493	215	15	v6	v6	NOUN
ejpam-4493	215	16	,	,	PUNCT
ejpam-4493	215	17	.	.	PUNCT
ejpam-4493	215	18	.	.	PUNCT
ejpam-4493	216	1	.	.	PUNCT
ejpam-4493	217	1	,	,	PUNCT
ejpam-4493	217	2	vn−1	vn−1	ADJ
ejpam-4493	217	3	,	,	PUNCT
ejpam-4493	217	4	v1	v1	NOUN
ejpam-4493	217	5	}	}	PUNCT
ejpam-4493	217	6	are	be	AUX
ejpam-4493	217	7	the	the	DET
ejpam-4493	217	8	sci	sci	NOUN
ejpam-4493	217	9	-	-	PUNCT
ejpam-4493	217	10	sets	set	NOUN
ejpam-4493	217	11	of	of	ADP
ejpam-4493	217	12	cn	cn	PROPN
ejpam-4493	217	13	.	.	PUNCT
ejpam-4493	218	1	hence	hence	ADV
ejpam-4493	218	2	,	,	PUNCT
ejpam-4493	218	3	no	no	DET
ejpam-4493	218	4	vertex	vertex	NOUN
ejpam-4493	218	5	of	of	ADP
ejpam-4493	218	6	cn	cn	PROPN
ejpam-4493	218	7	is	be	AUX
ejpam-4493	218	8	contained	contain	VERB
ejpam-4493	218	9	in	in	ADP
ejpam-4493	218	10	a	a	DET
ejpam-4493	218	11	unique	unique	ADJ
ejpam-4493	218	12	sci	sci	NOUN
ejpam-4493	218	13	-	-	PUNCT
ejpam-4493	218	14	set	set	NOUN
ejpam-4493	218	15	.	.	PUNCT
ejpam-4493	219	1	thus	thus	ADV
ejpam-4493	219	2	,	,	PUNCT
ejpam-4493	219	3	fsci(cn	fsci(cn	ADJ
ejpam-4493	219	4	)	)	PUNCT
ejpam-4493	219	5	≥	≥	NOUN
ejpam-4493	219	6	2	2	NUM
ejpam-4493	219	7	.	.	PUNCT
ejpam-4493	220	1	clearly	clearly	ADV
ejpam-4493	220	2	,	,	PUNCT
ejpam-4493	220	3	{	{	PUNCT
ejpam-4493	220	4	v1	v1	NOUN
ejpam-4493	220	5	,	,	PUNCT
ejpam-4493	220	6	vn	vn	PROPN
ejpam-4493	220	7	}	}	PUNCT
ejpam-4493	220	8	is	be	AUX
ejpam-4493	220	9	uniquely	uniquely	ADV
ejpam-4493	220	10	contained	contain	VERB
ejpam-4493	220	11	in	in	ADP
ejpam-4493	220	12	s1	s1	NOUN
ejpam-4493	220	13	.	.	PUNCT
ejpam-4493	221	1	therefore	therefore	ADV
ejpam-4493	221	2	,	,	PUNCT
ejpam-4493	221	3	fsci(s1	fsci(s1	ADJ
ejpam-4493	221	4	)	)	PUNCT
ejpam-4493	221	5	=	=	SYM
ejpam-4493	221	6	2	2	NUM
ejpam-4493	221	7	=	=	SYM
ejpam-4493	221	8	fsci(cn	fsci(cn	NOUN
ejpam-4493	221	9	)	)	PUNCT
ejpam-4493	221	10	.	.	PUNCT
ejpam-4493	222	1	in	in	ADP
ejpam-4493	222	2	view	view	NOUN
ejpam-4493	222	3	of	of	ADP
ejpam-4493	222	4	theorem	theorem	NOUN
ejpam-4493	222	5	1	1	NUM
ejpam-4493	222	6	,	,	PUNCT
ejpam-4493	222	7	we	we	PRON
ejpam-4493	222	8	have	have	VERB
ejpam-4493	222	9	the	the	DET
ejpam-4493	222	10	following	follow	VERB
ejpam-4493	222	11	theorem	theorem	VERB
ejpam-4493	222	12	.	.	PUNCT
ejpam-4493	222	13	theorem	theorem	NOUN
ejpam-4493	222	14	5	5	NUM
ejpam-4493	222	15	.	.	PUNCT
ejpam-4493	223	1	let	let	VERB
ejpam-4493	223	2	g	g	NOUN
ejpam-4493	224	1	and	and	CCONJ
ejpam-4493	224	2	h	h	NOUN
ejpam-4493	224	3	be	be	VERB
ejpam-4493	224	4	any	any	DET
ejpam-4493	224	5	graphs	graph	NOUN
ejpam-4493	224	6	.	.	PUNCT
ejpam-4493	225	1	then	then	ADV
ejpam-4493	225	2	s	s	VERB
ejpam-4493	225	3	⊆	⊆	NUM
ejpam-4493	225	4	v	v	NOUN
ejpam-4493	225	5	(	(	PUNCT
ejpam-4493	225	6	g	g	PROPN
ejpam-4493	225	7	+	+	NOUN
ejpam-4493	225	8	h	h	NOUN
ejpam-4493	225	9	)	)	PUNCT
ejpam-4493	225	10	is	be	AUX
ejpam-4493	225	11	a	a	DET
ejpam-4493	225	12	connected	connected	ADJ
ejpam-4493	225	13	co	co	NOUN
ejpam-4493	225	14	-	-	ADJ
ejpam-4493	225	15	independent	independent	ADJ
ejpam-4493	225	16	hop	hop	NOUN
ejpam-4493	225	17	dominating	dominating	NOUN
ejpam-4493	225	18	set	set	NOUN
ejpam-4493	225	19	of	of	ADP
ejpam-4493	225	20	g+h	g+h	PROPN
ejpam-4493	226	1	if	if	SCONJ
ejpam-4493	226	2	and	and	CCONJ
ejpam-4493	226	3	only	only	ADV
ejpam-4493	226	4	if	if	SCONJ
ejpam-4493	226	5	one	one	NUM
ejpam-4493	226	6	of	of	ADP
ejpam-4493	226	7	the	the	DET
ejpam-4493	226	8	following	follow	VERB
ejpam-4493	226	9	holds	hold	VERB
ejpam-4493	226	10	:	:	PUNCT
ejpam-4493	226	11	(	(	PUNCT
ejpam-4493	226	12	i	i	NOUN
ejpam-4493	226	13	)	)	PUNCT
ejpam-4493	226	14	s	s	PART
ejpam-4493	226	15	=	=	SYM
ejpam-4493	226	16	v	v	X
ejpam-4493	226	17	(	(	PUNCT
ejpam-4493	226	18	g	g	NOUN
ejpam-4493	226	19	)	)	PUNCT
ejpam-4493	226	20	∪	∪	NOUN
ejpam-4493	226	21	sh	sh	PRON
ejpam-4493	226	22	where	where	SCONJ
ejpam-4493	226	23	sh	sh	PROPN
ejpam-4493	226	24	is	be	AUX
ejpam-4493	226	25	a	a	DET
ejpam-4493	226	26	strictly	strictly	ADV
ejpam-4493	226	27	co	co	ADJ
ejpam-4493	226	28	-	-	ADJ
ejpam-4493	226	29	independent	independent	ADJ
ejpam-4493	226	30	set	set	NOUN
ejpam-4493	226	31	of	of	ADP
ejpam-4493	226	32	h	h	NOUN
ejpam-4493	226	33	,	,	PUNCT
ejpam-4493	226	34	(	(	PUNCT
ejpam-4493	226	35	ii	ii	NOUN
ejpam-4493	226	36	)	)	PUNCT
ejpam-4493	226	37	s	s	PART
ejpam-4493	226	38	=	=	SYM
ejpam-4493	226	39	v	v	PROPN
ejpam-4493	226	40	(	(	PUNCT
ejpam-4493	226	41	h	h	NOUN
ejpam-4493	226	42	)	)	PUNCT
ejpam-4493	226	43	∪	∪	NOUN
ejpam-4493	226	44	sg	sg	ADP
ejpam-4493	226	45	where	where	SCONJ
ejpam-4493	226	46	sg	sg	PROPN
ejpam-4493	226	47	is	be	AUX
ejpam-4493	226	48	a	a	DET
ejpam-4493	226	49	strictly	strictly	ADV
ejpam-4493	226	50	co	co	ADJ
ejpam-4493	226	51	-	-	ADJ
ejpam-4493	226	52	independent	independent	ADJ
ejpam-4493	226	53	set	set	NOUN
ejpam-4493	226	54	of	of	ADP
ejpam-4493	226	55	g.	g.	PROPN
ejpam-4493	226	56	as	as	ADP
ejpam-4493	226	57	a	a	DET
ejpam-4493	226	58	consequence	consequence	NOUN
ejpam-4493	226	59	of	of	ADP
ejpam-4493	226	60	theorem	theorem	NOUN
ejpam-4493	226	61	5	5	NUM
ejpam-4493	226	62	,	,	PUNCT
ejpam-4493	226	63	the	the	DET
ejpam-4493	226	64	next	next	ADJ
ejpam-4493	226	65	results	result	NOUN
ejpam-4493	226	66	follow	follow	VERB
ejpam-4493	226	67	.	.	PUNCT
ejpam-4493	227	1	corollary	corollary	ADJ
ejpam-4493	227	2	3	3	X
ejpam-4493	227	3	.	.	PUNCT
ejpam-4493	228	1	let	let	VERB
ejpam-4493	228	2	g	g	NOUN
ejpam-4493	228	3	be	be	AUX
ejpam-4493	229	1	any	any	DET
ejpam-4493	229	2	graph	graph	NOUN
ejpam-4493	229	3	and	and	CCONJ
ejpam-4493	229	4	k1	k1	NOUN
ejpam-4493	229	5	=	=	SYM
ejpam-4493	229	6	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4493	229	7	then	then	ADV
ejpam-4493	229	8	s	s	VERB
ejpam-4493	229	9	⊆	⊆	NUM
ejpam-4493	229	10	v	v	NOUN
ejpam-4493	229	11	(	(	PUNCT
ejpam-4493	229	12	k1	k1	NOUN
ejpam-4493	229	13	+	+	NOUN
ejpam-4493	229	14	g	g	NOUN
ejpam-4493	229	15	)	)	PUNCT
ejpam-4493	229	16	is	be	AUX
ejpam-4493	229	17	a	a	DET
ejpam-4493	229	18	γch	γch	NOUN
ejpam-4493	229	19	,	,	PUNCT
ejpam-4493	229	20	coi	coi	NOUN
ejpam-4493	229	21	-	-	PUNCT
ejpam-4493	229	22	set	set	NOUN
ejpam-4493	229	23	of	of	ADP
ejpam-4493	229	24	k1	k1	NOUN
ejpam-4493	230	1	+	+	ADP
ejpam-4493	230	2	g	g	PROPN
ejpam-4493	230	3	if	if	SCONJ
ejpam-4493	230	4	and	and	CCONJ
ejpam-4493	230	5	only	only	ADV
ejpam-4493	230	6	if	if	SCONJ
ejpam-4493	230	7	s	s	VERB
ejpam-4493	230	8	=	=	NOUN
ejpam-4493	230	9	{	{	PUNCT
ejpam-4493	230	10	v	v	NOUN
ejpam-4493	230	11	}	}	PUNCT
ejpam-4493	230	12	∪	∪	ADP
ejpam-4493	230	13	t	t	PROPN
ejpam-4493	230	14	where	where	SCONJ
ejpam-4493	230	15	t	t	PROPN
ejpam-4493	230	16	is	be	AUX
ejpam-4493	230	17	an	an	DET
ejpam-4493	230	18	sci	sci	PROPN
ejpam-4493	230	19	-	-	PUNCT
ejpam-4493	230	20	set	set	NOUN
ejpam-4493	230	21	of	of	ADP
ejpam-4493	230	22	g.	g.	PROPN
ejpam-4493	230	23	corollary	corollary	PROPN
ejpam-4493	230	24	4	4	NUM
ejpam-4493	230	25	.	.	PUNCT
ejpam-4493	231	1	let	let	VERB
ejpam-4493	231	2	g	g	NOUN
ejpam-4493	231	3	be	be	AUX
ejpam-4493	231	4	any	any	DET
ejpam-4493	231	5	graph	graph	NOUN
ejpam-4493	231	6	.	.	PUNCT
ejpam-4493	232	1	then	then	ADV
ejpam-4493	232	2	fγch	fγch	PROPN
ejpam-4493	232	3	,	,	PUNCT
ejpam-4493	232	4	coi(k1	coi(k1	PROPN
ejpam-4493	232	5	+	+	NOUN
ejpam-4493	232	6	g	g	NOUN
ejpam-4493	232	7	)	)	PUNCT
ejpam-4493	232	8	=	=	NOUN
ejpam-4493	232	9	{	{	PUNCT
ejpam-4493	232	10	0	0	NUM
ejpam-4493	232	11	,	,	PUNCT
ejpam-4493	232	12	if	if	SCONJ
ejpam-4493	232	13	g	g	PROPN
ejpam-4493	232	14	has	have	VERB
ejpam-4493	232	15	a	a	DET
ejpam-4493	232	16	unique	unique	ADJ
ejpam-4493	232	17	sci	sci	NOUN
ejpam-4493	232	18	-	-	PUNCT
ejpam-4493	232	19	set	set	NOUN
ejpam-4493	232	20	,	,	PUNCT
ejpam-4493	232	21	fsci(g	fsci(g	PROPN
ejpam-4493	232	22	)	)	PUNCT
ejpam-4493	232	23	,	,	PUNCT
ejpam-4493	232	24	if	if	SCONJ
ejpam-4493	232	25	g	g	PROPN
ejpam-4493	232	26	has	have	VERB
ejpam-4493	232	27	no	no	DET
ejpam-4493	232	28	unique	unique	ADJ
ejpam-4493	232	29	sci	sci	NOUN
ejpam-4493	232	30	-	-	PUNCT
ejpam-4493	232	31	set	set	NOUN
ejpam-4493	232	32	.	.	PUNCT
ejpam-4493	233	1	proof	proof	NOUN
ejpam-4493	233	2	:	:	PUNCT
ejpam-4493	233	3	suppose	suppose	VERB
ejpam-4493	233	4	that	that	SCONJ
ejpam-4493	233	5	g	g	PROPN
ejpam-4493	233	6	has	have	VERB
ejpam-4493	233	7	a	a	DET
ejpam-4493	233	8	unique	unique	ADJ
ejpam-4493	233	9	sci	sci	PROPN
ejpam-4493	233	10	-set	-set	PROPN
ejpam-4493	233	11	,	,	PUNCT
ejpam-4493	233	12	say	say	VERB
ejpam-4493	233	13	sg	sg	PROPN
ejpam-4493	233	14	.	.	PUNCT
ejpam-4493	234	1	then	then	ADV
ejpam-4493	234	2	by	by	ADP
ejpam-4493	234	3	corollary	corollary	ADJ
ejpam-4493	234	4	3	3	NUM
ejpam-4493	234	5	,	,	PUNCT
ejpam-4493	234	6	{	{	PUNCT
ejpam-4493	234	7	v	v	AUX
ejpam-4493	234	8	}	}	PUNCT
ejpam-4493	234	9	∪	∪	NOUN
ejpam-4493	234	10	sg	sg	PROPN
ejpam-4493	234	11	is	be	AUX
ejpam-4493	234	12	a	a	DET
ejpam-4493	234	13	unique	unique	ADJ
ejpam-4493	234	14	γch	γch	NOUN
ejpam-4493	234	15	,	,	PUNCT
ejpam-4493	234	16	coi	coi	NOUN
ejpam-4493	234	17	-	-	PUNCT
ejpam-4493	234	18	set	set	NOUN
ejpam-4493	234	19	of	of	ADP
ejpam-4493	234	20	k1	k1	PROPN
ejpam-4493	234	21	+	+	CCONJ
ejpam-4493	234	22	g.	g.	NOUN
ejpam-4493	234	23	by	by	ADP
ejpam-4493	234	24	remark	remark	NOUN
ejpam-4493	234	25	1(i	1(i	NUM
ejpam-4493	234	26	)	)	PUNCT
ejpam-4493	234	27	,	,	PUNCT
ejpam-4493	234	28	fγch	fγch	PROPN
ejpam-4493	234	29	,	,	PUNCT
ejpam-4493	234	30	coi(k1	coi(k1	PROPN
ejpam-4493	235	1	+	+	NOUN
ejpam-4493	235	2	g	g	NOUN
ejpam-4493	235	3	)	)	PUNCT
ejpam-4493	236	1	=	=	SYM
ejpam-4493	236	2	0	0	X
ejpam-4493	236	3	.	.	PUNCT
ejpam-4493	237	1	now	now	ADV
ejpam-4493	237	2	,	,	PUNCT
ejpam-4493	237	3	suppose	suppose	VERB
ejpam-4493	237	4	that	that	SCONJ
ejpam-4493	237	5	g	g	PROPN
ejpam-4493	237	6	has	have	VERB
ejpam-4493	237	7	no	no	DET
ejpam-4493	237	8	unique	unique	ADJ
ejpam-4493	237	9	sci	sci	NOUN
ejpam-4493	237	10	-	-	PUNCT
ejpam-4493	237	11	set	set	NOUN
ejpam-4493	237	12	.	.	PUNCT
ejpam-4493	238	1	let	let	VERB
ejpam-4493	238	2	a	a	DET
ejpam-4493	238	3	be	be	AUX
ejpam-4493	238	4	an	an	DET
ejpam-4493	238	5	sci	sci	PROPN
ejpam-4493	238	6	-	-	PUNCT
ejpam-4493	238	7	set	set	NOUN
ejpam-4493	238	8	of	of	ADP
ejpam-4493	238	9	g	g	NOUN
ejpam-4493	238	10	and	and	CCONJ
ejpam-4493	238	11	let	let	VERB
ejpam-4493	238	12	f	f	PRON
ejpam-4493	238	13	be	be	AUX
ejpam-4493	238	14	a	a	DET
ejpam-4493	238	15	forcing	forcing	NOUN
ejpam-4493	238	16	subset	subset	NOUN
ejpam-4493	238	17	for	for	ADP
ejpam-4493	238	18	a	a	DET
ejpam-4493	238	19	such	such	ADJ
ejpam-4493	238	20	that	that	DET
ejpam-4493	238	21	fsci(g	fsci(g	NOUN
ejpam-4493	238	22	)	)	PUNCT
ejpam-4493	239	1	=	=	SYM
ejpam-4493	239	2	fsci(a	fsci(a	ADJ
ejpam-4493	239	3	)	)	PUNCT
ejpam-4493	239	4	=	=	SYM
ejpam-4493	239	5	|f	|f	PROPN
ejpam-4493	240	1	|	|	NOUN
ejpam-4493	240	2	.	.	PUNCT
ejpam-4493	241	1	by	by	ADP
ejpam-4493	241	2	corollary	corollary	ADJ
ejpam-4493	241	3	3	3	NUM
ejpam-4493	241	4	,	,	PUNCT
ejpam-4493	241	5	s	s	PART
ejpam-4493	241	6	=	=	PUNCT
ejpam-4493	241	7	{	{	PUNCT
ejpam-4493	241	8	v	v	NOUN
ejpam-4493	241	9	}	}	PUNCT
ejpam-4493	241	10	∪	∪	NOUN
ejpam-4493	241	11	a	a	PRON
ejpam-4493	241	12	is	be	AUX
ejpam-4493	241	13	a	a	DET
ejpam-4493	241	14	γch	γch	NOUN
ejpam-4493	241	15	,	,	PUNCT
ejpam-4493	241	16	coi	coi	NOUN
ejpam-4493	241	17	-	-	PUNCT
ejpam-4493	241	18	set	set	NOUN
ejpam-4493	241	19	of	of	ADP
ejpam-4493	241	20	k1	k1	PROPN
ejpam-4493	241	21	+	+	CCONJ
ejpam-4493	241	22	g.	g.	NOUN
ejpam-4493	242	1	then	then	ADV
ejpam-4493	242	2	it	it	PRON
ejpam-4493	242	3	can	can	AUX
ejpam-4493	242	4	be	be	AUX
ejpam-4493	242	5	seen	see	VERB
ejpam-4493	242	6	that	that	SCONJ
ejpam-4493	242	7	f	f	PROPN
ejpam-4493	242	8	is	be	AUX
ejpam-4493	242	9	also	also	ADV
ejpam-4493	242	10	a	a	DET
ejpam-4493	242	11	forcing	forcing	NOUN
ejpam-4493	242	12	subset	subset	NOUN
ejpam-4493	242	13	for	for	ADP
ejpam-4493	242	14	s.	s.	PROPN
ejpam-4493	242	15	thus	thus	ADV
ejpam-4493	242	16	,	,	PUNCT
ejpam-4493	242	17	fγch	fγch	PROPN
ejpam-4493	242	18	,	,	PUNCT
ejpam-4493	242	19	coi(k1	coi(k1	PROPN
ejpam-4493	243	1	+	+	NOUN
ejpam-4493	243	2	g	g	NOUN
ejpam-4493	243	3	)	)	PUNCT
ejpam-4493	243	4	≤	≤	NUM
ejpam-4493	243	5	fγch	fγch	NOUN
ejpam-4493	243	6	,	,	PUNCT
ejpam-4493	243	7	coi(s	coi(s	NUM
ejpam-4493	243	8	)	)	PUNCT
ejpam-4493	244	1	≤	≤	NOUN
ejpam-4493	244	2	|f	|f	PUNCT
ejpam-4493	245	1	|	|	NOUN
ejpam-4493	245	2	=	=	SYM
ejpam-4493	245	3	fsci(g	fsci(g	PROPN
ejpam-4493	245	4	)	)	PUNCT
ejpam-4493	245	5	.	.	PUNCT
ejpam-4493	246	1	let	let	VERB
ejpam-4493	246	2	s0	s0	PROPN
ejpam-4493	246	3	=	=	PUNCT
ejpam-4493	246	4	{	{	PUNCT
ejpam-4493	246	5	v	v	NOUN
ejpam-4493	246	6	}	}	PUNCT
ejpam-4493	246	7	∪a0	∪a0	NOUN
ejpam-4493	246	8	be	be	AUX
ejpam-4493	246	9	a	a	DET
ejpam-4493	246	10	γch	γch	NOUN
ejpam-4493	246	11	,	,	PUNCT
ejpam-4493	246	12	coi	coi	NOUN
ejpam-4493	246	13	-	-	PUNCT
ejpam-4493	246	14	set	set	NOUN
ejpam-4493	246	15	of	of	ADP
ejpam-4493	246	16	k1	k1	NOUN
ejpam-4493	247	1	+	+	ADP
ejpam-4493	247	2	g	g	NOUN
ejpam-4493	247	3	such	such	ADJ
ejpam-4493	247	4	that	that	DET
ejpam-4493	247	5	fγch	fγch	NOUN
ejpam-4493	247	6	,	,	PUNCT
ejpam-4493	247	7	coi(k1	coi(k1	PROPN
ejpam-4493	247	8	+	+	NOUN
ejpam-4493	247	9	g	g	NOUN
ejpam-4493	247	10	)	)	PUNCT
ejpam-4493	248	1	=	=	SYM
ejpam-4493	248	2	fγch	fγch	PROPN
ejpam-4493	248	3	,	,	PUNCT
ejpam-4493	248	4	coi(s0	coi(s0	PROPN
ejpam-4493	248	5	)	)	PUNCT
ejpam-4493	248	6	.	.	PUNCT
ejpam-4493	249	1	by	by	ADP
ejpam-4493	249	2	corollary	corollary	ADJ
ejpam-4493	249	3	3	3	NUM
ejpam-4493	249	4	,	,	PUNCT
ejpam-4493	249	5	a0	a0	PROPN
ejpam-4493	249	6	is	be	AUX
ejpam-4493	249	7	an	an	DET
ejpam-4493	249	8	sci	sci	PROPN
ejpam-4493	249	9	-	-	PUNCT
ejpam-4493	249	10	set	set	NOUN
ejpam-4493	249	11	of	of	ADP
ejpam-4493	249	12	g.	g.	PROPN
ejpam-4493	249	13	let	let	VERB
ejpam-4493	249	14	f0	f0	PROPN
ejpam-4493	249	15	be	be	AUX
ejpam-4493	249	16	a	a	DET
ejpam-4493	249	17	forcing	forcing	NOUN
ejpam-4493	249	18	subset	subset	NOUN
ejpam-4493	249	19	for	for	ADP
ejpam-4493	249	20	s0	s0	PROPN
ejpam-4493	249	21	with	with	ADP
ejpam-4493	249	22	fγch	fγch	PROPN
ejpam-4493	249	23	,	,	PUNCT
ejpam-4493	249	24	coi(s0	coi(s0	PROPN
ejpam-4493	249	25	)	)	PUNCT
ejpam-4493	249	26	=	=	SYM
ejpam-4493	250	1	|f0.|	|f0.|	PROPN
ejpam-4493	250	2	y.d	y.d	PROPN
ejpam-4493	250	3	.	.	PROPN
ejpam-4493	250	4	calanza	calanza	PROPN
ejpam-4493	250	5	,	,	PUNCT
ejpam-4493	250	6	h.	h.	PROPN
ejpam-4493	250	7	rara	rara	PROPN
ejpam-4493	250	8	/	/	SYM
ejpam-4493	250	9	eur	eur	PROPN
ejpam-4493	250	10	.	.	PUNCT
ejpam-4493	251	1	j.	j.	PROPN
ejpam-4493	251	2	pure	pure	PROPN
ejpam-4493	251	3	appl	appl	PROPN
ejpam-4493	251	4	.	.	PROPN
ejpam-4493	251	5	math	math	PROPN
ejpam-4493	251	6	,	,	PUNCT
ejpam-4493	251	7	15	15	NUM
ejpam-4493	251	8	(	(	PUNCT
ejpam-4493	251	9	4	4	NUM
ejpam-4493	251	10	)	)	PUNCT
ejpam-4493	251	11	(	(	PUNCT
ejpam-4493	251	12	2022	2022	NUM
ejpam-4493	251	13	)	)	PUNCT
ejpam-4493	251	14	,	,	PUNCT
ejpam-4493	251	15	1649	1649	NUM
ejpam-4493	251	16	-	-	SYM
ejpam-4493	251	17	1661	1661	NUM
ejpam-4493	251	18	1656	1656	NUM
ejpam-4493	251	19	suppose	suppose	VERB
ejpam-4493	251	20	f0	f0	PROPN
ejpam-4493	251	21	is	be	AUX
ejpam-4493	251	22	not	not	PART
ejpam-4493	251	23	a	a	DET
ejpam-4493	251	24	forcing	forcing	NOUN
ejpam-4493	251	25	subset	subset	NOUN
ejpam-4493	251	26	for	for	ADP
ejpam-4493	251	27	a0	a0	PROPN
ejpam-4493	251	28	.	.	PUNCT
ejpam-4493	252	1	then	then	ADV
ejpam-4493	252	2	there	there	PRON
ejpam-4493	252	3	exists	exist	VERB
ejpam-4493	252	4	an	an	DET
ejpam-4493	252	5	sci	sci	PROPN
ejpam-4493	252	6	-	-	PUNCT
ejpam-4493	252	7	set	set	VERB
ejpam-4493	252	8	a	a	DET
ejpam-4493	252	9	′	′	NUM
ejpam-4493	252	10	0	0	NUM
ejpam-4493	252	11	ofg	ofg	NOUN
ejpam-4493	252	12	with	with	ADP
ejpam-4493	252	13	a	a	DET
ejpam-4493	252	14	′	′	NOUN
ejpam-4493	252	15	0	0	NUM
ejpam-4493	252	16	̸=	̸=	PROPN
ejpam-4493	252	17	a0	a0	NOUN
ejpam-4493	252	18	and	and	CCONJ
ejpam-4493	252	19	f0	f0	VERB
ejpam-4493	252	20	⊆	⊆	NUM
ejpam-4493	252	21	a	a	DET
ejpam-4493	252	22	′	′	NUM
ejpam-4493	252	23	0	0	NUM
ejpam-4493	252	24	.	.	PUNCT
ejpam-4493	253	1	by	by	ADP
ejpam-4493	253	2	corollary	corollary	ADJ
ejpam-4493	253	3	3	3	NUM
ejpam-4493	253	4	,	,	PUNCT
ejpam-4493	253	5	s	s	VERB
ejpam-4493	253	6	′	′	NOUN
ejpam-4493	253	7	0	0	NUM
ejpam-4493	254	1	=	=	SYM
ejpam-4493	254	2	{	{	PUNCT
ejpam-4493	254	3	v	v	NOUN
ejpam-4493	254	4	}	}	PUNCT
ejpam-4493	254	5	∪	∪	ADP
ejpam-4493	254	6	a	a	DET
ejpam-4493	254	7	′	′	NUM
ejpam-4493	254	8	0	0	NUM
ejpam-4493	254	9	is	be	AUX
ejpam-4493	254	10	a	a	DET
ejpam-4493	254	11	γch	γch	NOUN
ejpam-4493	254	12	,	,	PUNCT
ejpam-4493	254	13	coi	coi	NOUN
ejpam-4493	254	14	-	-	PUNCT
ejpam-4493	254	15	set	set	NOUN
ejpam-4493	254	16	of	of	ADP
ejpam-4493	254	17	k1	k1	PROPN
ejpam-4493	254	18	+	+	CCONJ
ejpam-4493	254	19	g.	g.	NOUN
ejpam-4493	254	20	since	since	SCONJ
ejpam-4493	254	21	a	a	DET
ejpam-4493	254	22	′	′	NOUN
ejpam-4493	254	23	0	0	NUM
ejpam-4493	254	24	̸=	̸=	PROPN
ejpam-4493	254	25	a0	a0	NOUN
ejpam-4493	254	26	,	,	PUNCT
ejpam-4493	254	27	s	s	PART
ejpam-4493	254	28	′	′	NOUN
ejpam-4493	254	29	0	0	NUM
ejpam-4493	255	1	̸=	̸=	PROPN
ejpam-4493	255	2	s0	s0	PROPN
ejpam-4493	255	3	.	.	PUNCT
ejpam-4493	256	1	thus	thus	ADV
ejpam-4493	256	2	,	,	PUNCT
ejpam-4493	256	3	f0	f0	PROPN
ejpam-4493	256	4	⊆	⊆	NUM
ejpam-4493	256	5	s	s	PART
ejpam-4493	256	6	′	′	NOUN
ejpam-4493	256	7	0	0	NUM
ejpam-4493	256	8	,	,	PUNCT
ejpam-4493	256	9	a	a	DET
ejpam-4493	256	10	contradiction	contradiction	NOUN
ejpam-4493	256	11	since	since	SCONJ
ejpam-4493	256	12	f0	f0	PROPN
ejpam-4493	256	13	is	be	AUX
ejpam-4493	256	14	a	a	DET
ejpam-4493	256	15	forcing	forcing	NOUN
ejpam-4493	256	16	subset	subset	NOUN
ejpam-4493	256	17	for	for	ADP
ejpam-4493	256	18	s0	s0	PROPN
ejpam-4493	256	19	.	.	PUNCT
ejpam-4493	257	1	hence	hence	ADV
ejpam-4493	257	2	,	,	PUNCT
ejpam-4493	257	3	f0	f0	PROPN
ejpam-4493	257	4	is	be	AUX
ejpam-4493	257	5	a	a	DET
ejpam-4493	257	6	forcing	forcing	NOUN
ejpam-4493	257	7	subset	subset	NOUN
ejpam-4493	257	8	for	for	ADP
ejpam-4493	257	9	a0	a0	NOUN
ejpam-4493	257	10	.	.	PUNCT
ejpam-4493	258	1	thus	thus	ADV
ejpam-4493	258	2	,	,	PUNCT
ejpam-4493	258	3	fγch	fγch	PROPN
ejpam-4493	258	4	,	,	PUNCT
ejpam-4493	258	5	coi(k1	coi(k1	PROPN
ejpam-4493	259	1	+	+	NOUN
ejpam-4493	259	2	g	g	NOUN
ejpam-4493	259	3	)	)	PUNCT
ejpam-4493	260	1	=	=	SYM
ejpam-4493	260	2	fγch	fγch	PROPN
ejpam-4493	260	3	,	,	PUNCT
ejpam-4493	260	4	coi(s0	coi(s0	PROPN
ejpam-4493	260	5	)	)	PUNCT
ejpam-4493	260	6	=	=	PUNCT
ejpam-4493	260	7	|f0|	|f0|	NOUN
ejpam-4493	260	8	≥	≥	NOUN
ejpam-4493	260	9	fsci(a0	fsci(a0	PROPN
ejpam-4493	260	10	)	)	PUNCT
ejpam-4493	260	11	≥	≥	NUM
ejpam-4493	260	12	fsci(g	fsci(g	NOUN
ejpam-4493	260	13	)	)	PUNCT
ejpam-4493	260	14	.	.	PUNCT
ejpam-4493	261	1	therefore	therefore	ADV
ejpam-4493	261	2	,	,	PUNCT
ejpam-4493	261	3	fγch	fγch	PROPN
ejpam-4493	261	4	,	,	PUNCT
ejpam-4493	261	5	coi(k1	coi(k1	PROPN
ejpam-4493	261	6	+	+	NOUN
ejpam-4493	261	7	g	g	NOUN
ejpam-4493	261	8	)	)	PUNCT
ejpam-4493	261	9	=	=	SYM
ejpam-4493	261	10	fsci(g	fsci(g	PROPN
ejpam-4493	261	11	)	)	PUNCT
ejpam-4493	261	12	.	.	PUNCT
ejpam-4493	262	1	example	example	NOUN
ejpam-4493	263	1	1	1	NUM
ejpam-4493	263	2	.	.	PUNCT
ejpam-4493	263	3	(	(	PUNCT
ejpam-4493	263	4	1	1	NUM
ejpam-4493	263	5	.	.	PUNCT
ejpam-4493	263	6	)	)	PUNCT
ejpam-4493	263	7	for	for	ADP
ejpam-4493	263	8	the	the	DET
ejpam-4493	263	9	fan	fan	NOUN
ejpam-4493	263	10	fn	fn	PROPN
ejpam-4493	263	11	=	=	PROPN
ejpam-4493	263	12	k1	k1	PROPN
ejpam-4493	263	13	+	+	CCONJ
ejpam-4493	263	14	pn	pn	NOUN
ejpam-4493	263	15	,	,	PUNCT
ejpam-4493	263	16	where	where	SCONJ
ejpam-4493	263	17	n	n	PRON
ejpam-4493	263	18	≥	≥	NOUN
ejpam-4493	263	19	2	2	NUM
ejpam-4493	263	20	,	,	PUNCT
ejpam-4493	263	21	fγch	fγch	ADJ
ejpam-4493	263	22	,	,	PUNCT
ejpam-4493	263	23	coi(fn	coi(fn	NOUN
ejpam-4493	263	24	)	)	PUNCT
ejpam-4493	263	25	=	=	SYM
ejpam-4493	263	26	fsci(pn	fsci(pn	NOUN
ejpam-4493	263	27	)	)	PUNCT
ejpam-4493	263	28	=	=	SYM
ejpam-4493	264	1			NOUN
ejpam-4493	264	2	0	0	NUM
ejpam-4493	264	3	,	,	PUNCT
ejpam-4493	264	4	if	if	SCONJ
ejpam-4493	264	5	n	n	NOUN
ejpam-4493	264	6	=	=	SYM
ejpam-4493	264	7	2	2	NUM
ejpam-4493	264	8	,	,	PUNCT
ejpam-4493	264	9	4	4	NUM
ejpam-4493	264	10	and	and	CCONJ
ejpam-4493	264	11	n	n	PRON
ejpam-4493	264	12	>	>	SYM
ejpam-4493	264	13	5	5	NUM
ejpam-4493	264	14	is	be	AUX
ejpam-4493	264	15	odd	odd	ADJ
ejpam-4493	264	16	,	,	PUNCT
ejpam-4493	264	17	1	1	NUM
ejpam-4493	264	18	,	,	PUNCT
ejpam-4493	264	19	if	if	SCONJ
ejpam-4493	264	20	n	n	CCONJ
ejpam-4493	264	21	=	=	SYM
ejpam-4493	264	22	3	3	NUM
ejpam-4493	264	23	and	and	CCONJ
ejpam-4493	264	24	n	n	PRON
ejpam-4493	264	25	≥	≥	NUM
ejpam-4493	264	26	6	6	NUM
ejpam-4493	264	27	is	be	AUX
ejpam-4493	264	28	even	even	ADV
ejpam-4493	264	29	,	,	PUNCT
ejpam-4493	264	30	2	2	NUM
ejpam-4493	264	31	,	,	PUNCT
ejpam-4493	264	32	if	if	SCONJ
ejpam-4493	264	33	n	n	NOUN
ejpam-4493	264	34	=	=	SYM
ejpam-4493	264	35	5	5	X
ejpam-4493	264	36	.	.	PUNCT
ejpam-4493	265	1	(	(	PUNCT
ejpam-4493	265	2	2	2	NUM
ejpam-4493	265	3	.	.	PUNCT
ejpam-4493	265	4	)	)	PUNCT
ejpam-4493	266	1	for	for	ADP
ejpam-4493	266	2	the	the	DET
ejpam-4493	266	3	wheel	wheel	NOUN
ejpam-4493	266	4	wn	wn	PROPN
ejpam-4493	266	5	=	=	PROPN
ejpam-4493	266	6	k1	k1	PROPN
ejpam-4493	266	7	+	+	CCONJ
ejpam-4493	266	8	cn	cn	PROPN
ejpam-4493	266	9	,	,	PUNCT
ejpam-4493	266	10	where	where	SCONJ
ejpam-4493	266	11	n	n	PRON
ejpam-4493	266	12	≥	≥	NOUN
ejpam-4493	266	13	3	3	NUM
ejpam-4493	266	14	,	,	PUNCT
ejpam-4493	266	15	fγch	fγch	ADJ
ejpam-4493	266	16	,	,	PUNCT
ejpam-4493	266	17	coi(wn	coi(wn	NOUN
ejpam-4493	266	18	)	)	PUNCT
ejpam-4493	266	19	=	=	SYM
ejpam-4493	266	20	fsci(cn	fsci(cn	NOUN
ejpam-4493	266	21	)	)	PUNCT
ejpam-4493	266	22	=	=	PUNCT
ejpam-4493	266	23			NOUN
ejpam-4493	266	24	0	0	NUM
ejpam-4493	266	25	,	,	PUNCT
ejpam-4493	266	26	if	if	SCONJ
ejpam-4493	266	27	n	n	NOUN
ejpam-4493	266	28	=	=	SYM
ejpam-4493	266	29	3	3	NUM
ejpam-4493	266	30	,	,	PUNCT
ejpam-4493	266	31	1	1	NUM
ejpam-4493	266	32	,	,	PUNCT
ejpam-4493	266	33	if	if	SCONJ
ejpam-4493	266	34	n	n	PROPN
ejpam-4493	266	35	>	>	X
ejpam-4493	266	36	4	4	NUM
ejpam-4493	266	37	and	and	CCONJ
ejpam-4493	266	38	n	n	PRON
ejpam-4493	266	39	is	be	AUX
ejpam-4493	266	40	even	even	ADV
ejpam-4493	266	41	,	,	PUNCT
ejpam-4493	266	42	2	2	NUM
ejpam-4493	266	43	,	,	PUNCT
ejpam-4493	266	44	if	if	SCONJ
ejpam-4493	266	45	n	n	PROPN
ejpam-4493	266	46	>	>	X
ejpam-4493	266	47	3	3	NUM
ejpam-4493	266	48	and	and	CCONJ
ejpam-4493	266	49	n	n	PRON
ejpam-4493	266	50	is	be	AUX
ejpam-4493	266	51	odd	odd	ADJ
ejpam-4493	266	52	,	,	PUNCT
ejpam-4493	266	53	3	3	X
ejpam-4493	266	54	,	,	PUNCT
ejpam-4493	266	55	if	if	SCONJ
ejpam-4493	266	56	n	n	NOUN
ejpam-4493	266	57	=	=	SYM
ejpam-4493	266	58	4	4	X
ejpam-4493	266	59	.	.	PUNCT
ejpam-4493	267	1	(	(	PUNCT
ejpam-4493	267	2	3	3	NUM
ejpam-4493	267	3	.	.	PUNCT
ejpam-4493	267	4	)	)	PUNCT
ejpam-4493	268	1	for	for	ADP
ejpam-4493	268	2	the	the	DET
ejpam-4493	268	3	star	star	NOUN
ejpam-4493	268	4	sn	sn	PROPN
ejpam-4493	268	5	=	=	PUNCT
ejpam-4493	268	6	k1,n	k1,n	PROPN
ejpam-4493	268	7	of	of	ADP
ejpam-4493	268	8	order	order	NOUN
ejpam-4493	268	9	n+	n+	PUNCT
ejpam-4493	268	10	1	1	NUM
ejpam-4493	268	11	,	,	PUNCT
ejpam-4493	268	12	fγch	fγch	ADJ
ejpam-4493	268	13	,	,	PUNCT
ejpam-4493	268	14	coi(sn	coi(sn	ADJ
ejpam-4493	268	15	)	)	PUNCT
ejpam-4493	268	16	=	=	SYM
ejpam-4493	268	17	{	{	PUNCT
ejpam-4493	268	18	0	0	NUM
ejpam-4493	268	19	,	,	PUNCT
ejpam-4493	268	20	if	if	SCONJ
ejpam-4493	268	21	n	n	NOUN
ejpam-4493	268	22	=	=	SYM
ejpam-4493	268	23	1	1	NUM
ejpam-4493	268	24	,	,	PUNCT
ejpam-4493	268	25	1	1	NUM
ejpam-4493	268	26	,	,	PUNCT
ejpam-4493	268	27	if	if	SCONJ
ejpam-4493	268	28	n	n	PROPN
ejpam-4493	268	29	>	>	X
ejpam-4493	268	30	1	1	X
ejpam-4493	268	31	.	.	PUNCT
ejpam-4493	268	32	another	another	DET
ejpam-4493	268	33	consequence	consequence	NOUN
ejpam-4493	268	34	of	of	ADP
ejpam-4493	268	35	theorem	theorem	NOUN
ejpam-4493	268	36	5	5	NUM
ejpam-4493	268	37	is	be	AUX
ejpam-4493	268	38	the	the	DET
ejpam-4493	268	39	next	next	ADJ
ejpam-4493	268	40	corollary	corollary	NOUN
ejpam-4493	268	41	.	.	PUNCT
ejpam-4493	269	1	corollary	corollary	ADJ
ejpam-4493	269	2	5	5	NUM
ejpam-4493	269	3	.	.	PUNCT
ejpam-4493	270	1	let	let	VERB
ejpam-4493	270	2	g	g	NOUN
ejpam-4493	270	3	and	and	CCONJ
ejpam-4493	270	4	h	h	NOUN
ejpam-4493	270	5	be	be	VERB
ejpam-4493	270	6	any	any	DET
ejpam-4493	270	7	graphs	graph	NOUN
ejpam-4493	270	8	with	with	ADP
ejpam-4493	270	9	|v	|v	PROPN
ejpam-4493	270	10	(	(	PUNCT
ejpam-4493	270	11	g)|	g)|	PROPN
ejpam-4493	270	12	<	<	X
ejpam-4493	270	13	|v	|v	PROPN
ejpam-4493	270	14	(	(	PUNCT
ejpam-4493	270	15	h)|	h)|	PROPN
ejpam-4493	270	16	and	and	CCONJ
ejpam-4493	270	17	sci(h	sci(h	PROPN
ejpam-4493	270	18	)	)	PUNCT
ejpam-4493	271	1	=	=	PUNCT
ejpam-4493	271	2	sci(g	sci(g	PROPN
ejpam-4493	271	3	)	)	PUNCT
ejpam-4493	271	4	or	or	CCONJ
ejpam-4493	271	5	|v	|v	PROPN
ejpam-4493	271	6	(	(	PUNCT
ejpam-4493	271	7	g)|	g)|	NOUN
ejpam-4493	271	8	=	=	PUNCT
ejpam-4493	271	9	|v	|v	PROPN
ejpam-4493	271	10	(	(	PUNCT
ejpam-4493	271	11	h)|	h)|	PROPN
ejpam-4493	271	12	and	and	CCONJ
ejpam-4493	271	13	sci(h	sci(h	PROPN
ejpam-4493	271	14	)	)	PUNCT
ejpam-4493	271	15	<	<	X
ejpam-4493	271	16	sci(g	sci(g	PROPN
ejpam-4493	271	17	)	)	PUNCT
ejpam-4493	271	18	.	.	PUNCT
ejpam-4493	272	1	then	then	ADV
ejpam-4493	272	2	s	s	VERB
ejpam-4493	272	3	⊆	⊆	NUM
ejpam-4493	272	4	v	v	NOUN
ejpam-4493	272	5	(	(	PUNCT
ejpam-4493	272	6	g	g	PROPN
ejpam-4493	272	7	+	+	NOUN
ejpam-4493	272	8	h	h	NOUN
ejpam-4493	272	9	)	)	PUNCT
ejpam-4493	272	10	is	be	AUX
ejpam-4493	272	11	a	a	DET
ejpam-4493	272	12	γch	γch	NOUN
ejpam-4493	272	13	,	,	PUNCT
ejpam-4493	272	14	coi	coi	NOUN
ejpam-4493	272	15	-	-	PUNCT
ejpam-4493	272	16	set	set	NOUN
ejpam-4493	272	17	of	of	ADP
ejpam-4493	272	18	g	g	NOUN
ejpam-4493	272	19	+	+	CCONJ
ejpam-4493	272	20	h	h	NOUN
ejpam-4493	272	21	if	if	SCONJ
ejpam-4493	273	1	and	and	CCONJ
ejpam-4493	273	2	only	only	ADV
ejpam-4493	273	3	if	if	SCONJ
ejpam-4493	273	4	s	s	AUX
ejpam-4493	273	5	=	=	SYM
ejpam-4493	273	6	v	v	X
ejpam-4493	273	7	(	(	PUNCT
ejpam-4493	273	8	g	g	NOUN
ejpam-4493	273	9	)	)	PUNCT
ejpam-4493	273	10	∪	∪	NOUN
ejpam-4493	273	11	sh	sh	PROPN
ejpam-4493	273	12	for	for	ADP
ejpam-4493	273	13	some	some	DET
ejpam-4493	273	14	sci	sci	PROPN
ejpam-4493	273	15	-set	-set	PUNCT
ejpam-4493	274	1	sh	sh	PROPN
ejpam-4493	274	2	of	of	ADP
ejpam-4493	274	3	h.	h.	PROPN
ejpam-4493	274	4	theorem	theorem	PROPN
ejpam-4493	274	5	6	6	NUM
ejpam-4493	274	6	.	.	PUNCT
ejpam-4493	275	1	for	for	ADP
ejpam-4493	275	2	any	any	DET
ejpam-4493	275	3	graphs	graph	NOUN
ejpam-4493	275	4	g	g	NOUN
ejpam-4493	275	5	and	and	CCONJ
ejpam-4493	275	6	h	h	NOUN
ejpam-4493	275	7	with	with	ADP
ejpam-4493	275	8	|v	|v	PROPN
ejpam-4493	275	9	(	(	PUNCT
ejpam-4493	275	10	g)|	g)|	PROPN
ejpam-4493	275	11	<	<	X
ejpam-4493	275	12	|v	|v	PROPN
ejpam-4493	275	13	(	(	PUNCT
ejpam-4493	275	14	h)|	h)|	PROPN
ejpam-4493	275	15	and	and	CCONJ
ejpam-4493	275	16	sci(h	sci(h	PROPN
ejpam-4493	275	17	)	)	PUNCT
ejpam-4493	275	18	=	=	PUNCT
ejpam-4493	275	19	sci(g	sci(g	PROPN
ejpam-4493	275	20	)	)	PUNCT
ejpam-4493	275	21	,	,	PUNCT
ejpam-4493	275	22	or	or	CCONJ
ejpam-4493	275	23	|v	|v	PROPN
ejpam-4493	275	24	(	(	PUNCT
ejpam-4493	275	25	g)|	g)|	NOUN
ejpam-4493	275	26	=	=	PUNCT
ejpam-4493	275	27	|v	|v	PROPN
ejpam-4493	275	28	(	(	PUNCT
ejpam-4493	275	29	h)|	h)|	PROPN
ejpam-4493	275	30	and	and	CCONJ
ejpam-4493	275	31	sci(h	sci(h	PROPN
ejpam-4493	275	32	)	)	PUNCT
ejpam-4493	275	33	<	<	X
ejpam-4493	275	34	sci(g	sci(g	PROPN
ejpam-4493	275	35	)	)	PUNCT
ejpam-4493	275	36	.	.	PUNCT
ejpam-4493	276	1	then	then	ADV
ejpam-4493	276	2	fγch	fγch	PROPN
ejpam-4493	276	3	,	,	PUNCT
ejpam-4493	276	4	coi(g+h	coi(g+h	NOUN
ejpam-4493	276	5	)	)	PUNCT
ejpam-4493	276	6	=	=	PRON
ejpam-4493	276	7	{	{	PUNCT
ejpam-4493	276	8	0	0	NUM
ejpam-4493	276	9	,	,	PUNCT
ejpam-4493	276	10	if	if	SCONJ
ejpam-4493	276	11	h	h	NOUN
ejpam-4493	276	12	has	have	VERB
ejpam-4493	276	13	a	a	DET
ejpam-4493	276	14	unique	unique	ADJ
ejpam-4493	276	15	sci	sci	NOUN
ejpam-4493	276	16	-	-	PUNCT
ejpam-4493	276	17	set	set	NOUN
ejpam-4493	276	18	,	,	PUNCT
ejpam-4493	276	19	fsci(h	fsci(h	PROPN
ejpam-4493	276	20	)	)	PUNCT
ejpam-4493	276	21	,	,	PUNCT
ejpam-4493	276	22	if	if	SCONJ
ejpam-4493	276	23	h	h	NOUN
ejpam-4493	276	24	has	have	VERB
ejpam-4493	276	25	no	no	DET
ejpam-4493	276	26	unique	unique	ADJ
ejpam-4493	276	27	sci	sci	NOUN
ejpam-4493	276	28	-	-	PUNCT
ejpam-4493	276	29	set	set	NOUN
ejpam-4493	276	30	.	.	PUNCT
ejpam-4493	277	1	proof	proof	NOUN
ejpam-4493	277	2	:	:	PUNCT
ejpam-4493	277	3	suppose	suppose	VERB
ejpam-4493	277	4	that	that	SCONJ
ejpam-4493	277	5	h	h	NOUN
ejpam-4493	277	6	has	have	VERB
ejpam-4493	277	7	a	a	DET
ejpam-4493	277	8	unique	unique	ADJ
ejpam-4493	277	9	sci	sci	PROPN
ejpam-4493	277	10	-set	-set	NUM
ejpam-4493	277	11	,	,	PUNCT
ejpam-4493	277	12	say	say	VERB
ejpam-4493	277	13	sh	sh	INTJ
ejpam-4493	277	14	.	.	PUNCT
ejpam-4493	278	1	then	then	ADV
ejpam-4493	278	2	by	by	ADP
ejpam-4493	278	3	corollary	corollary	ADJ
ejpam-4493	278	4	5	5	NUM
ejpam-4493	278	5	,	,	PUNCT
ejpam-4493	278	6	v	v	NUM
ejpam-4493	278	7	(	(	PUNCT
ejpam-4493	278	8	g)∪sh	g)∪sh	PROPN
ejpam-4493	278	9	is	be	AUX
ejpam-4493	278	10	a	a	DET
ejpam-4493	278	11	unique	unique	ADJ
ejpam-4493	278	12	γch	γch	NOUN
ejpam-4493	278	13	,	,	PUNCT
ejpam-4493	278	14	coi	coi	NOUN
ejpam-4493	278	15	-	-	PUNCT
ejpam-4493	278	16	set	set	NOUN
ejpam-4493	278	17	of	of	ADP
ejpam-4493	278	18	g+h	g+h	PROPN
ejpam-4493	278	19	.	.	PUNCT
ejpam-4493	279	1	by	by	ADP
ejpam-4493	279	2	remark	remark	NOUN
ejpam-4493	279	3	1(i	1(i	NUM
ejpam-4493	279	4	)	)	PUNCT
ejpam-4493	279	5	,	,	PUNCT
ejpam-4493	279	6	fγch	fγch	NOUN
ejpam-4493	279	7	,	,	PUNCT
ejpam-4493	279	8	coi(g+h	coi(g+h	NOUN
ejpam-4493	279	9	)	)	PUNCT
ejpam-4493	279	10	=	=	SYM
ejpam-4493	279	11	0	0	X
ejpam-4493	279	12	.	.	PUNCT
ejpam-4493	280	1	now	now	ADV
ejpam-4493	280	2	,	,	PUNCT
ejpam-4493	280	3	suppose	suppose	VERB
ejpam-4493	280	4	that	that	SCONJ
ejpam-4493	280	5	h	h	NOUN
ejpam-4493	280	6	has	have	VERB
ejpam-4493	280	7	no	no	DET
ejpam-4493	280	8	unique	unique	ADJ
ejpam-4493	280	9	sci	sci	NOUN
ejpam-4493	280	10	-	-	PUNCT
ejpam-4493	280	11	set	set	NOUN
ejpam-4493	280	12	.	.	PUNCT
ejpam-4493	281	1	let	let	VERB
ejpam-4493	281	2	a	a	DET
ejpam-4493	281	3	be	be	AUX
ejpam-4493	281	4	an	an	DET
ejpam-4493	281	5	sci	sci	PROPN
ejpam-4493	281	6	-	-	PUNCT
ejpam-4493	281	7	set	set	NOUN
ejpam-4493	281	8	of	of	ADP
ejpam-4493	281	9	h	h	NOUN
ejpam-4493	281	10	and	and	CCONJ
ejpam-4493	281	11	let	let	VERB
ejpam-4493	281	12	f	f	PRON
ejpam-4493	281	13	be	be	AUX
ejpam-4493	281	14	a	a	DET
ejpam-4493	281	15	forcing	forcing	NOUN
ejpam-4493	281	16	subset	subset	NOUN
ejpam-4493	281	17	for	for	ADP
ejpam-4493	281	18	a	a	DET
ejpam-4493	281	19	such	such	ADJ
ejpam-4493	281	20	that	that	DET
ejpam-4493	281	21	fsci(h	fsci(h	PROPN
ejpam-4493	281	22	)	)	PUNCT
ejpam-4493	281	23	=	=	SYM
ejpam-4493	281	24	fsci(a	fsci(a	ADJ
ejpam-4493	281	25	)	)	PUNCT
ejpam-4493	281	26	=	=	SYM
ejpam-4493	281	27	|f	|f	PROPN
ejpam-4493	282	1	|	|	NOUN
ejpam-4493	282	2	.	.	PUNCT
ejpam-4493	283	1	by	by	ADP
ejpam-4493	283	2	corollary	corollary	ADJ
ejpam-4493	283	3	5	5	NUM
ejpam-4493	283	4	,	,	PUNCT
ejpam-4493	283	5	s	s	PART
ejpam-4493	283	6	=	=	SYM
ejpam-4493	283	7	v	v	X
ejpam-4493	283	8	(	(	PUNCT
ejpam-4493	283	9	g	g	NOUN
ejpam-4493	283	10	)	)	PUNCT
ejpam-4493	283	11	∪	∪	ADP
ejpam-4493	283	12	a	a	PRON
ejpam-4493	283	13	is	be	AUX
ejpam-4493	283	14	a	a	DET
ejpam-4493	283	15	γch	γch	NOUN
ejpam-4493	283	16	,	,	PUNCT
ejpam-4493	283	17	coi	coi	NOUN
ejpam-4493	283	18	-	-	PUNCT
ejpam-4493	283	19	set	set	NOUN
ejpam-4493	283	20	of	of	ADP
ejpam-4493	283	21	g	g	PROPN
ejpam-4493	283	22	+	+	CCONJ
ejpam-4493	283	23	h.	h.	PROPN
ejpam-4493	283	24	suppose	suppose	VERB
ejpam-4493	283	25	f	f	PROPN
ejpam-4493	283	26	is	be	AUX
ejpam-4493	283	27	not	not	PART
ejpam-4493	283	28	a	a	DET
ejpam-4493	283	29	forcing	forcing	NOUN
ejpam-4493	283	30	subset	subset	NOUN
ejpam-4493	283	31	for	for	ADP
ejpam-4493	283	32	s.	s.	PROPN
ejpam-4493	283	33	then	then	ADV
ejpam-4493	283	34	there	there	PRON
ejpam-4493	283	35	exists	exist	VERB
ejpam-4493	283	36	a	a	DET
ejpam-4493	283	37	γch	γch	NOUN
ejpam-4493	283	38	,	,	PUNCT
ejpam-4493	283	39	coi	coi	NOUN
ejpam-4493	283	40	-	-	PUNCT
ejpam-4493	283	41	set	set	NOUN
ejpam-4493	283	42	s	s	NOUN
ejpam-4493	283	43	′	′	NOUN
ejpam-4493	283	44	of	of	ADP
ejpam-4493	283	45	g	g	PROPN
ejpam-4493	283	46	+	+	PROPN
ejpam-4493	283	47	h	h	NOUN
ejpam-4493	283	48	such	such	ADJ
ejpam-4493	283	49	y.d	y.d	PROPN
ejpam-4493	283	50	.	.	PROPN
ejpam-4493	283	51	calanza	calanza	PROPN
ejpam-4493	283	52	,	,	PUNCT
ejpam-4493	283	53	h.	h.	PROPN
ejpam-4493	283	54	rara	rara	PROPN
ejpam-4493	283	55	/	/	SYM
ejpam-4493	283	56	eur	eur	PROPN
ejpam-4493	283	57	.	.	PUNCT
ejpam-4493	284	1	j.	j.	PROPN
ejpam-4493	284	2	pure	pure	PROPN
ejpam-4493	284	3	appl	appl	PROPN
ejpam-4493	284	4	.	.	PROPN
ejpam-4493	284	5	math	math	PROPN
ejpam-4493	284	6	,	,	PUNCT
ejpam-4493	284	7	15	15	NUM
ejpam-4493	284	8	(	(	PUNCT
ejpam-4493	284	9	4	4	NUM
ejpam-4493	284	10	)	)	PUNCT
ejpam-4493	284	11	(	(	PUNCT
ejpam-4493	284	12	2022	2022	NUM
ejpam-4493	284	13	)	)	PUNCT
ejpam-4493	284	14	,	,	PUNCT
ejpam-4493	284	15	1649	1649	NUM
ejpam-4493	284	16	-	-	SYM
ejpam-4493	284	17	1661	1661	NUM
ejpam-4493	284	18	1657	1657	NUM
ejpam-4493	284	19	that	that	PRON
ejpam-4493	284	20	s	s	AUX
ejpam-4493	284	21	′	′	VERB
ejpam-4493	284	22	̸=	̸=	PROPN
ejpam-4493	284	23	s	s	NOUN
ejpam-4493	284	24	and	and	CCONJ
ejpam-4493	284	25	f	f	PROPN
ejpam-4493	285	1	⊆	⊆	NUM
ejpam-4493	285	2	s	s	NOUN
ejpam-4493	285	3	′	′	NOUN
ejpam-4493	285	4	.	.	PUNCT
ejpam-4493	286	1	by	by	ADP
ejpam-4493	286	2	corollary	corollary	ADJ
ejpam-4493	286	3	5	5	NUM
ejpam-4493	286	4	,	,	PUNCT
ejpam-4493	286	5	s	s	PART
ejpam-4493	286	6	′	′	NOUN
ejpam-4493	286	7	=	=	SYM
ejpam-4493	286	8	v	v	NOUN
ejpam-4493	286	9	(	(	PUNCT
ejpam-4493	286	10	g)∪a	g)∪a	PROPN
ejpam-4493	287	1	′	′	VERB
ejpam-4493	287	2	where	where	SCONJ
ejpam-4493	287	3	a	a	DET
ejpam-4493	287	4	′	′	NOUN
ejpam-4493	287	5	is	be	AUX
ejpam-4493	287	6	an	an	DET
ejpam-4493	287	7	sci	sci	PROPN
ejpam-4493	287	8	-	-	PUNCT
ejpam-4493	287	9	set	set	NOUN
ejpam-4493	287	10	of	of	ADP
ejpam-4493	287	11	h.	h.	NOUN
ejpam-4493	287	12	since	since	SCONJ
ejpam-4493	287	13	s	s	PROPN
ejpam-4493	287	14	′	′	NUM
ejpam-4493	287	15	̸=	̸=	PROPN
ejpam-4493	287	16	s	s	PROPN
ejpam-4493	287	17	,	,	PUNCT
ejpam-4493	287	18	a	a	DET
ejpam-4493	287	19	′	′	NUM
ejpam-4493	287	20	̸=	̸=	PROPN
ejpam-4493	287	21	a.	a.	NOUN
ejpam-4493	287	22	on	on	ADP
ejpam-4493	287	23	the	the	DET
ejpam-4493	287	24	other	other	ADJ
ejpam-4493	287	25	hand	hand	NOUN
ejpam-4493	287	26	,	,	PUNCT
ejpam-4493	287	27	f	f	PUNCT
ejpam-4493	287	28	being	be	AUX
ejpam-4493	287	29	a	a	DET
ejpam-4493	287	30	forcing	forcing	NOUN
ejpam-4493	287	31	subset	subset	NOUN
ejpam-4493	287	32	for	for	ADP
ejpam-4493	287	33	a	a	PRON
ejpam-4493	287	34	which	which	PRON
ejpam-4493	287	35	is	be	AUX
ejpam-4493	287	36	an	an	DET
ejpam-4493	287	37	sci	sci	PROPN
ejpam-4493	287	38	-	-	PUNCT
ejpam-4493	287	39	set	set	NOUN
ejpam-4493	287	40	of	of	ADP
ejpam-4493	287	41	h	h	NOUN
ejpam-4493	287	42	implies	imply	VERB
ejpam-4493	287	43	that	that	SCONJ
ejpam-4493	287	44	f	f	PROPN
ejpam-4493	287	45	⊆	⊆	NUM
ejpam-4493	287	46	v	v	ADP
ejpam-4493	287	47	(	(	PUNCT
ejpam-4493	287	48	h	h	NOUN
ejpam-4493	287	49	)	)	PUNCT
ejpam-4493	287	50	.	.	PUNCT
ejpam-4493	288	1	thus	thus	ADV
ejpam-4493	288	2	,	,	PUNCT
ejpam-4493	288	3	f	f	PROPN
ejpam-4493	288	4	⊆	⊆	NUM
ejpam-4493	288	5	a	a	DET
ejpam-4493	288	6	′	′	NOUN
ejpam-4493	288	7	,	,	PUNCT
ejpam-4493	288	8	a	a	DET
ejpam-4493	288	9	contradiction	contradiction	NOUN
ejpam-4493	288	10	since	since	SCONJ
ejpam-4493	288	11	f	f	PROPN
ejpam-4493	288	12	is	be	AUX
ejpam-4493	288	13	a	a	DET
ejpam-4493	288	14	forcing	forcing	NOUN
ejpam-4493	288	15	subset	subset	NOUN
ejpam-4493	288	16	for	for	ADP
ejpam-4493	288	17	a.	a.	NOUN
ejpam-4493	288	18	hence	hence	ADV
ejpam-4493	288	19	,	,	PUNCT
ejpam-4493	288	20	f	f	PROPN
ejpam-4493	288	21	is	be	AUX
ejpam-4493	288	22	a	a	DET
ejpam-4493	288	23	forcing	forcing	NOUN
ejpam-4493	288	24	subset	subset	NOUN
ejpam-4493	288	25	for	for	ADP
ejpam-4493	288	26	s.	s.	PROPN
ejpam-4493	288	27	thus	thus	ADV
ejpam-4493	288	28	,	,	PUNCT
ejpam-4493	288	29	fγch	fγch	NOUN
ejpam-4493	288	30	,	,	PUNCT
ejpam-4493	288	31	coi(g+h	coi(g+h	NOUN
ejpam-4493	288	32	)	)	PUNCT
ejpam-4493	288	33	≤	≤	NOUN
ejpam-4493	288	34	fγch	fγch	NOUN
ejpam-4493	288	35	,	,	PUNCT
ejpam-4493	288	36	coi(s	coi(s	NUM
ejpam-4493	288	37	)	)	PUNCT
ejpam-4493	288	38	≤	≤	NOUN
ejpam-4493	288	39	|f	|f	PUNCT
ejpam-4493	289	1	|	|	ADV
ejpam-4493	289	2	=	=	SYM
ejpam-4493	289	3	fsci(h	fsci(h	PROPN
ejpam-4493	289	4	)	)	PUNCT
ejpam-4493	289	5	.	.	PUNCT
ejpam-4493	290	1	let	let	VERB
ejpam-4493	290	2	s0	s0	PROPN
ejpam-4493	290	3	=	=	SYM
ejpam-4493	290	4	v	v	PROPN
ejpam-4493	290	5	(	(	PUNCT
ejpam-4493	290	6	g)∪a0	g)∪a0	PROPN
ejpam-4493	290	7	be	be	AUX
ejpam-4493	290	8	a	a	DET
ejpam-4493	290	9	γch	γch	NOUN
ejpam-4493	290	10	,	,	PUNCT
ejpam-4493	290	11	coi	coi	NOUN
ejpam-4493	290	12	-	-	PUNCT
ejpam-4493	290	13	set	set	NOUN
ejpam-4493	290	14	of	of	ADP
ejpam-4493	290	15	g+h	g+h	PROPN
ejpam-4493	290	16	such	such	ADJ
ejpam-4493	290	17	that	that	DET
ejpam-4493	290	18	fγch	fγch	NOUN
ejpam-4493	290	19	,	,	PUNCT
ejpam-4493	290	20	coi(g+h	coi(g+h	NOUN
ejpam-4493	290	21	)	)	PUNCT
ejpam-4493	291	1	=	=	SYM
ejpam-4493	291	2	fγch	fγch	PROPN
ejpam-4493	291	3	,	,	PUNCT
ejpam-4493	291	4	coi(s0	coi(s0	PROPN
ejpam-4493	291	5	)	)	PUNCT
ejpam-4493	291	6	.	.	PUNCT
ejpam-4493	292	1	by	by	ADP
ejpam-4493	292	2	corollary	corollary	ADJ
ejpam-4493	292	3	5	5	NUM
ejpam-4493	292	4	,	,	PUNCT
ejpam-4493	292	5	a0	a0	PROPN
ejpam-4493	292	6	is	be	AUX
ejpam-4493	292	7	an	an	DET
ejpam-4493	292	8	sci	sci	PROPN
ejpam-4493	292	9	-	-	PUNCT
ejpam-4493	292	10	set	set	NOUN
ejpam-4493	292	11	of	of	ADP
ejpam-4493	292	12	h.	h.	PROPN
ejpam-4493	292	13	let	let	VERB
ejpam-4493	292	14	f0	f0	PROPN
ejpam-4493	292	15	be	be	AUX
ejpam-4493	292	16	a	a	DET
ejpam-4493	292	17	forcing	forcing	NOUN
ejpam-4493	292	18	subset	subset	NOUN
ejpam-4493	292	19	for	for	ADP
ejpam-4493	292	20	s0	s0	PROPN
ejpam-4493	292	21	with	with	ADP
ejpam-4493	292	22	fγch	fγch	PROPN
ejpam-4493	292	23	,	,	PUNCT
ejpam-4493	292	24	coi(s0	coi(s0	PROPN
ejpam-4493	292	25	)	)	PUNCT
ejpam-4493	292	26	=	=	PUNCT
ejpam-4493	293	1	|f0.|	|f0.|	PROPN
ejpam-4493	293	2	suppose	suppose	VERB
ejpam-4493	293	3	f0	f0	PROPN
ejpam-4493	293	4	is	be	AUX
ejpam-4493	293	5	not	not	PART
ejpam-4493	293	6	a	a	DET
ejpam-4493	293	7	forcing	forcing	NOUN
ejpam-4493	293	8	subset	subset	NOUN
ejpam-4493	293	9	for	for	ADP
ejpam-4493	293	10	a0	a0	PROPN
ejpam-4493	293	11	.	.	PUNCT
ejpam-4493	294	1	then	then	ADV
ejpam-4493	294	2	there	there	PRON
ejpam-4493	294	3	exists	exist	VERB
ejpam-4493	294	4	an	an	DET
ejpam-4493	294	5	sci	sci	PROPN
ejpam-4493	294	6	-	-	PUNCT
ejpam-4493	294	7	set	set	VERB
ejpam-4493	294	8	a	a	DET
ejpam-4493	294	9	′	′	NOUN
ejpam-4493	294	10	0	0	NUM
ejpam-4493	294	11	̸=	̸=	PROPN
ejpam-4493	294	12	a0	a0	NOUN
ejpam-4493	294	13	of	of	ADP
ejpam-4493	294	14	h	h	PROPN
ejpam-4493	294	15	such	such	ADJ
ejpam-4493	294	16	that	that	SCONJ
ejpam-4493	294	17	f0	f0	PROPN
ejpam-4493	294	18	⊆	⊆	NUM
ejpam-4493	294	19	a	a	DET
ejpam-4493	294	20	′	′	NUM
ejpam-4493	294	21	0	0	NUM
ejpam-4493	294	22	.	.	PUNCT
ejpam-4493	295	1	by	by	ADP
ejpam-4493	295	2	corollary	corollary	ADJ
ejpam-4493	295	3	5	5	NUM
ejpam-4493	295	4	,	,	PUNCT
ejpam-4493	295	5	s	s	VERB
ejpam-4493	295	6	′	′	NOUN
ejpam-4493	295	7	0	0	X
ejpam-4493	296	1	=	=	SYM
ejpam-4493	296	2	v	v	NOUN
ejpam-4493	296	3	(	(	PUNCT
ejpam-4493	296	4	g	g	NOUN
ejpam-4493	296	5	)	)	PUNCT
ejpam-4493	296	6	∪a	∪a	NUM
ejpam-4493	297	1	′	′	NOUN
ejpam-4493	297	2	0	0	NUM
ejpam-4493	297	3	is	be	AUX
ejpam-4493	297	4	a	a	DET
ejpam-4493	297	5	γch	γch	NOUN
ejpam-4493	297	6	,	,	PUNCT
ejpam-4493	297	7	coi	coi	NOUN
ejpam-4493	297	8	-	-	PUNCT
ejpam-4493	297	9	set	set	NOUN
ejpam-4493	297	10	of	of	ADP
ejpam-4493	297	11	g+h	g+h	PROPN
ejpam-4493	297	12	with	with	ADP
ejpam-4493	297	13	f0	f0	PROPN
ejpam-4493	297	14	⊆	⊆	NUM
ejpam-4493	297	15	s	s	PART
ejpam-4493	297	16	′	′	NOUN
ejpam-4493	297	17	0	0	PUNCT
ejpam-4493	298	1	and	and	CCONJ
ejpam-4493	298	2	s	s	VERB
ejpam-4493	298	3	′	′	NOUN
ejpam-4493	298	4	0	0	NUM
ejpam-4493	299	1	̸=	̸=	PROPN
ejpam-4493	299	2	s0	s0	NOUN
ejpam-4493	299	3	.	.	PUNCT
ejpam-4493	300	1	this	this	PRON
ejpam-4493	300	2	is	be	AUX
ejpam-4493	300	3	a	a	DET
ejpam-4493	300	4	contradiction	contradiction	NOUN
ejpam-4493	300	5	since	since	SCONJ
ejpam-4493	300	6	f0	f0	PROPN
ejpam-4493	300	7	is	be	AUX
ejpam-4493	300	8	a	a	DET
ejpam-4493	300	9	forcing	forcing	NOUN
ejpam-4493	300	10	subset	subset	NOUN
ejpam-4493	300	11	for	for	ADP
ejpam-4493	300	12	s0	s0	PROPN
ejpam-4493	300	13	.	.	PUNCT
ejpam-4493	301	1	thus	thus	ADV
ejpam-4493	301	2	,	,	PUNCT
ejpam-4493	301	3	f0	f0	PROPN
ejpam-4493	301	4	is	be	AUX
ejpam-4493	301	5	a	a	DET
ejpam-4493	301	6	forcing	forcing	NOUN
ejpam-4493	301	7	subset	subset	NOUN
ejpam-4493	301	8	for	for	ADP
ejpam-4493	301	9	a0	a0	NOUN
ejpam-4493	301	10	.	.	PUNCT
ejpam-4493	302	1	hence	hence	ADV
ejpam-4493	302	2	,	,	PUNCT
ejpam-4493	302	3	fγch	fγch	NOUN
ejpam-4493	302	4	,	,	PUNCT
ejpam-4493	302	5	coi(g+h	coi(g+h	NOUN
ejpam-4493	302	6	)	)	PUNCT
ejpam-4493	302	7	=	=	SYM
ejpam-4493	302	8	fγch	fγch	PROPN
ejpam-4493	302	9	,	,	PUNCT
ejpam-4493	302	10	coi(s0	coi(s0	PROPN
ejpam-4493	302	11	)	)	PUNCT
ejpam-4493	302	12	=	=	PUNCT
ejpam-4493	302	13	|f0|	|f0|	NOUN
ejpam-4493	302	14	≥	≥	NUM
ejpam-4493	302	15	fsci(a0	fsci(a0	PROPN
ejpam-4493	302	16	)	)	PUNCT
ejpam-4493	302	17	≥	≥	PROPN
ejpam-4493	302	18	fsci(h	fsci(h	PROPN
ejpam-4493	302	19	)	)	PUNCT
ejpam-4493	302	20	.	.	PUNCT
ejpam-4493	303	1	therefore	therefore	ADV
ejpam-4493	303	2	,	,	PUNCT
ejpam-4493	303	3	fγch	fγch	NOUN
ejpam-4493	303	4	,	,	PUNCT
ejpam-4493	303	5	coi(g+h	coi(g+h	NOUN
ejpam-4493	303	6	)	)	PUNCT
ejpam-4493	303	7	=	=	SYM
ejpam-4493	303	8	fsci(h	fsci(h	PROPN
ejpam-4493	303	9	)	)	PUNCT
ejpam-4493	303	10	.	.	PUNCT
ejpam-4493	304	1	example	example	NOUN
ejpam-4493	305	1	2	2	NUM
ejpam-4493	305	2	.	.	PUNCT
ejpam-4493	305	3	let	let	VERB
ejpam-4493	305	4	g	g	PROPN
ejpam-4493	305	5	=	=	PROPN
ejpam-4493	305	6	c3	c3	PROPN
ejpam-4493	305	7	and	and	CCONJ
ejpam-4493	305	8	h	h	NOUN
ejpam-4493	305	9	=	=	PUNCT
ejpam-4493	305	10	p7	p7	PROPN
ejpam-4493	305	11	.	.	PUNCT
ejpam-4493	306	1	then	then	ADV
ejpam-4493	306	2	|v	|v	PROPN
ejpam-4493	306	3	(	(	PUNCT
ejpam-4493	306	4	c3)|	c3)|	PROPN
ejpam-4493	306	5	<	<	X
ejpam-4493	306	6	|v	|v	PROPN
ejpam-4493	306	7	(	(	PUNCT
ejpam-4493	306	8	p7)|	p7)|	NOUN
ejpam-4493	306	9	and	and	CCONJ
ejpam-4493	306	10	sci(c3	sci(c3	NOUN
ejpam-4493	306	11	)	)	PUNCT
ejpam-4493	306	12	=	=	SYM
ejpam-4493	306	13	3	3	NUM
ejpam-4493	306	14	=	=	SYM
ejpam-4493	306	15	sci(p7	sci(p7	NOUN
ejpam-4493	306	16	)	)	PUNCT
ejpam-4493	306	17	.	.	PUNCT
ejpam-4493	307	1	since	since	SCONJ
ejpam-4493	307	2	p7	p7	PROPN
ejpam-4493	307	3	has	have	VERB
ejpam-4493	307	4	a	a	DET
ejpam-4493	307	5	unique	unique	ADJ
ejpam-4493	307	6	sci	sci	NOUN
ejpam-4493	307	7	-	-	PUNCT
ejpam-4493	307	8	set	set	NOUN
ejpam-4493	307	9	,	,	PUNCT
ejpam-4493	307	10	fγch	fγch	ADJ
ejpam-4493	307	11	,	,	PUNCT
ejpam-4493	307	12	coi(c3	coi(c3	PROPN
ejpam-4493	307	13	+	+	CCONJ
ejpam-4493	307	14	p7	p7	ADJ
ejpam-4493	307	15	)	)	PUNCT
ejpam-4493	307	16	=	=	SYM
ejpam-4493	307	17	0	0	X
ejpam-4493	307	18	.	.	NOUN
ejpam-4493	307	19	example	example	NOUN
ejpam-4493	308	1	3	3	X
ejpam-4493	308	2	.	.	PUNCT
ejpam-4493	309	1	let	let	VERB
ejpam-4493	309	2	g	g	PROPN
ejpam-4493	309	3	=	=	PROPN
ejpam-4493	309	4	c3	c3	PROPN
ejpam-4493	309	5	and	and	CCONJ
ejpam-4493	309	6	h	h	NOUN
ejpam-4493	309	7	=	=	PROPN
ejpam-4493	309	8	p3	p3	PROPN
ejpam-4493	309	9	.	.	PUNCT
ejpam-4493	310	1	then	then	ADV
ejpam-4493	310	2	|v	|v	PROPN
ejpam-4493	310	3	(	(	PUNCT
ejpam-4493	310	4	c3)|	c3)|	NOUN
ejpam-4493	310	5	=	=	SYM
ejpam-4493	310	6	|v	|v	PROPN
ejpam-4493	310	7	(	(	PUNCT
ejpam-4493	310	8	p3)|	p3)|	NOUN
ejpam-4493	310	9	and	and	CCONJ
ejpam-4493	310	10	sci(p3	sci(p3	NOUN
ejpam-4493	310	11	)	)	PUNCT
ejpam-4493	310	12	=	=	SYM
ejpam-4493	310	13	2	2	NUM
ejpam-4493	310	14	<	<	SYM
ejpam-4493	310	15	3	3	NUM
ejpam-4493	310	16	=	=	SYM
ejpam-4493	310	17	sci(c3	sci(c3	PROPN
ejpam-4493	310	18	)	)	PUNCT
ejpam-4493	310	19	.	.	PUNCT
ejpam-4493	311	1	since	since	SCONJ
ejpam-4493	311	2	p3	p3	PROPN
ejpam-4493	311	3	has	have	VERB
ejpam-4493	311	4	no	no	DET
ejpam-4493	311	5	unique	unique	ADJ
ejpam-4493	311	6	sci	sci	NOUN
ejpam-4493	311	7	-	-	PUNCT
ejpam-4493	311	8	sets	set	NOUN
ejpam-4493	311	9	,	,	PUNCT
ejpam-4493	311	10	fγch	fγch	ADJ
ejpam-4493	311	11	,	,	PUNCT
ejpam-4493	311	12	coi(c3+p3	coi(c3+p3	X
ejpam-4493	311	13	)	)	PUNCT
ejpam-4493	311	14	=	=	SYM
ejpam-4493	311	15	fsci(p3	fsci(p3	X
ejpam-4493	311	16	)	)	PUNCT
ejpam-4493	311	17	=	=	SYM
ejpam-4493	312	1	1	1	NUM
ejpam-4493	312	2	.	.	NOUN
ejpam-4493	312	3	5	5	NUM
ejpam-4493	312	4	.	.	X
ejpam-4493	312	5	forcing	force	VERB
ejpam-4493	312	6	connected	connected	ADJ
ejpam-4493	312	7	co	co	ADJ
ejpam-4493	312	8	-	-	ADJ
ejpam-4493	312	9	independent	independent	ADJ
ejpam-4493	312	10	hop	hop	NOUN
ejpam-4493	312	11	domination	domination	NOUN
ejpam-4493	312	12	in	in	ADP
ejpam-4493	312	13	the	the	DET
ejpam-4493	312	14	corona	corona	NOUN
ejpam-4493	312	15	of	of	ADP
ejpam-4493	312	16	graphs	graph	NOUN
ejpam-4493	312	17	the	the	DET
ejpam-4493	312	18	corona	corona	NOUN
ejpam-4493	312	19	of	of	ADP
ejpam-4493	312	20	two	two	NUM
ejpam-4493	312	21	graphs	graph	NOUN
ejpam-4493	312	22	g	g	NOUN
ejpam-4493	312	23	and	and	CCONJ
ejpam-4493	312	24	h	h	NOUN
ejpam-4493	312	25	,	,	PUNCT
ejpam-4493	312	26	denoted	denote	VERB
ejpam-4493	312	27	by	by	ADP
ejpam-4493	312	28	g	g	PROPN
ejpam-4493	312	29	◦	◦	NOUN
ejpam-4493	312	30	h	h	NOUN
ejpam-4493	312	31	,	,	PUNCT
ejpam-4493	312	32	is	be	AUX
ejpam-4493	312	33	the	the	DET
ejpam-4493	312	34	graph	graph	NOUN
ejpam-4493	312	35	obtained	obtain	VERB
ejpam-4493	312	36	by	by	ADP
ejpam-4493	312	37	taking	take	VERB
ejpam-4493	312	38	one	one	NUM
ejpam-4493	312	39	copy	copy	NOUN
ejpam-4493	312	40	of	of	ADP
ejpam-4493	312	41	g	g	NOUN
ejpam-4493	312	42	of	of	ADP
ejpam-4493	312	43	order	order	NOUN
ejpam-4493	312	44	n	n	NOUN
ejpam-4493	312	45	and	and	CCONJ
ejpam-4493	312	46	n	n	PRON
ejpam-4493	312	47	copies	copy	NOUN
ejpam-4493	312	48	of	of	ADP
ejpam-4493	312	49	h	h	NOUN
ejpam-4493	312	50	,	,	PUNCT
ejpam-4493	312	51	and	and	CCONJ
ejpam-4493	312	52	then	then	ADV
ejpam-4493	312	53	joining	join	VERB
ejpam-4493	312	54	every	every	DET
ejpam-4493	312	55	vertex	vertex	NOUN
ejpam-4493	312	56	of	of	ADP
ejpam-4493	312	57	the	the	DET
ejpam-4493	312	58	ith	ith	PROPN
ejpam-4493	312	59	copy	copy	NOUN
ejpam-4493	312	60	of	of	ADP
ejpam-4493	312	61	h	h	NOUN
ejpam-4493	312	62	to	to	ADP
ejpam-4493	312	63	the	the	DET
ejpam-4493	312	64	ith	ith	PROPN
ejpam-4493	312	65	vertex	vertex	NOUN
ejpam-4493	312	66	of	of	ADP
ejpam-4493	312	67	g.	g.	PROPN
ejpam-4493	312	68	for	for	ADP
ejpam-4493	312	69	v	v	NOUN
ejpam-4493	312	70	∈	∈	PROPN
ejpam-4493	312	71	v	v	NOUN
ejpam-4493	312	72	(	(	PUNCT
ejpam-4493	312	73	g	g	NOUN
ejpam-4493	312	74	)	)	PUNCT
ejpam-4493	312	75	,	,	PUNCT
ejpam-4493	312	76	denote	denote	VERB
ejpam-4493	312	77	by	by	ADP
ejpam-4493	312	78	hv	hv	PROPN
ejpam-4493	312	79	the	the	DET
ejpam-4493	312	80	copy	copy	NOUN
ejpam-4493	312	81	of	of	ADP
ejpam-4493	312	82	h	h	NOUN
ejpam-4493	312	83	whose	whose	DET
ejpam-4493	312	84	vertices	vertex	NOUN
ejpam-4493	312	85	are	be	AUX
ejpam-4493	312	86	attached	attach	VERB
ejpam-4493	312	87	one	one	NUM
ejpam-4493	312	88	by	by	ADP
ejpam-4493	312	89	one	one	NUM
ejpam-4493	312	90	to	to	ADP
ejpam-4493	312	91	the	the	DET
ejpam-4493	312	92	vertex	vertex	NOUN
ejpam-4493	312	93	v.	v.	ADP
ejpam-4493	312	94	subsequently	subsequently	ADV
ejpam-4493	312	95	,	,	PUNCT
ejpam-4493	312	96	denote	denote	VERB
ejpam-4493	312	97	by	by	ADP
ejpam-4493	312	98	v+hv	v+hv	NOUN
ejpam-4493	312	99	the	the	DET
ejpam-4493	312	100	subgraph	subgraph	NOUN
ejpam-4493	312	101	of	of	ADP
ejpam-4493	312	102	the	the	DET
ejpam-4493	312	103	corona	corona	NOUN
ejpam-4493	312	104	g	g	PROPN
ejpam-4493	312	105	◦	◦	NOUN
ejpam-4493	312	106	h	h	NOUN
ejpam-4493	312	107	corresponding	correspond	VERB
ejpam-4493	312	108	to	to	ADP
ejpam-4493	312	109	the	the	DET
ejpam-4493	312	110	join	join	NOUN
ejpam-4493	312	111	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4493	312	112	,	,	PUNCT
ejpam-4493	312	113	v	v	PROPN
ejpam-4493	312	114	∈	∈	PROPN
ejpam-4493	312	115	v	v	NOUN
ejpam-4493	312	116	(	(	PUNCT
ejpam-4493	312	117	g	g	NOUN
ejpam-4493	312	118	)	)	PUNCT
ejpam-4493	312	119	.	.	PUNCT
ejpam-4493	313	1	remark	remark	PROPN
ejpam-4493	313	2	3	3	NUM
ejpam-4493	313	3	.	.	PUNCT
ejpam-4493	314	1	let	let	VERB
ejpam-4493	314	2	g	g	PRON
ejpam-4493	314	3	be	be	AUX
ejpam-4493	314	4	a	a	DET
ejpam-4493	314	5	connected	connected	ADJ
ejpam-4493	314	6	graph	graph	NOUN
ejpam-4493	314	7	.	.	PUNCT
ejpam-4493	315	1	then	then	ADV
ejpam-4493	315	2	(	(	PUNCT
ejpam-4493	315	3	i	i	NOUN
ejpam-4493	315	4	)	)	PUNCT
ejpam-4493	315	5	fcoi(g	fcoi(g	ADV
ejpam-4493	315	6	)	)	PUNCT
ejpam-4493	316	1	=	=	SYM
ejpam-4493	316	2	0	0	PUNCT
ejpam-4493	317	1	if	if	SCONJ
ejpam-4493	317	2	and	and	CCONJ
ejpam-4493	317	3	only	only	ADV
ejpam-4493	317	4	if	if	SCONJ
ejpam-4493	317	5	g	g	PROPN
ejpam-4493	317	6	has	have	VERB
ejpam-4493	317	7	a	a	DET
ejpam-4493	317	8	unique	unique	ADJ
ejpam-4493	317	9	coi	coi	NOUN
ejpam-4493	317	10	-	-	PUNCT
ejpam-4493	317	11	set	set	NOUN
ejpam-4493	317	12	,	,	PUNCT
ejpam-4493	317	13	and	and	CCONJ
ejpam-4493	317	14	(	(	PUNCT
ejpam-4493	317	15	ii	ii	NOUN
ejpam-4493	317	16	)	)	PUNCT
ejpam-4493	317	17	fcoi(g	fcoi(g	ADV
ejpam-4493	317	18	)	)	PUNCT
ejpam-4493	318	1	=	=	SYM
ejpam-4493	318	2	1	1	NUM
ejpam-4493	318	3	if	if	SCONJ
ejpam-4493	318	4	and	and	CCONJ
ejpam-4493	318	5	only	only	ADV
ejpam-4493	318	6	if	if	SCONJ
ejpam-4493	318	7	g	g	PROPN
ejpam-4493	318	8	has	have	VERB
ejpam-4493	318	9	at	at	ADV
ejpam-4493	318	10	least	least	ADV
ejpam-4493	318	11	two	two	NUM
ejpam-4493	318	12	coi	coi	NOUN
ejpam-4493	318	13	-	-	PUNCT
ejpam-4493	318	14	sets	set	NOUN
ejpam-4493	318	15	,	,	PUNCT
ejpam-4493	318	16	one	one	NUM
ejpam-4493	318	17	of	of	ADP
ejpam-4493	318	18	which	which	PRON
ejpam-4493	318	19	,	,	PUNCT
ejpam-4493	318	20	say	say	VERB
ejpam-4493	318	21	b	b	NOUN
ejpam-4493	318	22	,	,	PUNCT
ejpam-4493	318	23	contains	contain	VERB
ejpam-4493	318	24	an	an	DET
ejpam-4493	318	25	element	element	NOUN
ejpam-4493	318	26	which	which	PRON
ejpam-4493	318	27	is	be	AUX
ejpam-4493	318	28	not	not	PART
ejpam-4493	318	29	found	find	VERB
ejpam-4493	318	30	in	in	ADP
ejpam-4493	318	31	any	any	DET
ejpam-4493	318	32	coi	coi	NOUN
ejpam-4493	318	33	-	-	PUNCT
ejpam-4493	318	34	set	set	NOUN
ejpam-4493	318	35	of	of	ADP
ejpam-4493	318	36	g.	g.	PROPN
ejpam-4493	318	37	theorem	theorem	VERB
ejpam-4493	318	38	7	7	NUM
ejpam-4493	318	39	.	.	PUNCT
ejpam-4493	319	1	let	let	VERB
ejpam-4493	319	2	g	g	PRON
ejpam-4493	319	3	be	be	AUX
ejpam-4493	319	4	a	a	DET
ejpam-4493	319	5	connected	connected	ADJ
ejpam-4493	319	6	graph	graph	NOUN
ejpam-4493	319	7	.	.	PUNCT
ejpam-4493	320	1	then	then	ADV
ejpam-4493	320	2	fcoi(g	fcoi(g	ADV
ejpam-4493	320	3	)	)	PUNCT
ejpam-4493	321	1	=	=	PUNCT
ejpam-4493	321	2	coi(g	coi(g	PROPN
ejpam-4493	321	3	)	)	PUNCT
ejpam-4493	321	4	if	if	SCONJ
ejpam-4493	321	5	and	and	CCONJ
ejpam-4493	321	6	only	only	ADV
ejpam-4493	321	7	if	if	SCONJ
ejpam-4493	321	8	for	for	ADP
ejpam-4493	321	9	all	all	DET
ejpam-4493	321	10	coi	coi	NOUN
ejpam-4493	321	11	-	-	PUNCT
ejpam-4493	321	12	set	set	VERB
ejpam-4493	321	13	b	b	NOUN
ejpam-4493	321	14	of	of	ADP
ejpam-4493	321	15	g	g	PROPN
ejpam-4493	321	16	and	and	CCONJ
ejpam-4493	321	17	for	for	ADP
ejpam-4493	321	18	each	each	DET
ejpam-4493	321	19	v	v	NUM
ejpam-4493	321	20	∈	∈	PROPN
ejpam-4493	321	21	b	b	NOUN
ejpam-4493	321	22	,	,	PUNCT
ejpam-4493	321	23	there	there	PRON
ejpam-4493	321	24	exists	exist	VERB
ejpam-4493	321	25	uv	uv	PROPN
ejpam-4493	321	26	∈	∈	PROPN
ejpam-4493	321	27	v	v	ADP
ejpam-4493	321	28	(	(	PUNCT
ejpam-4493	321	29	g	g	NOUN
ejpam-4493	321	30	)	)	PUNCT
ejpam-4493	321	31	\b	\b	NOUN
ejpam-4493	321	32	such	such	ADJ
ejpam-4493	321	33	that	that	SCONJ
ejpam-4493	321	34	[	[	PUNCT
ejpam-4493	321	35	b	b	X
ejpam-4493	321	36	\	\	X
ejpam-4493	321	37	{	{	PUNCT
ejpam-4493	321	38	v	v	NOUN
ejpam-4493	321	39	}	}	PUNCT
ejpam-4493	321	40	]	]	PUNCT
ejpam-4493	321	41	∪	∪	X
ejpam-4493	321	42	{	{	PUNCT
ejpam-4493	321	43	uv	uv	NOUN
ejpam-4493	321	44	}	}	PUNCT
ejpam-4493	321	45	is	be	AUX
ejpam-4493	321	46	a	a	DET
ejpam-4493	321	47	coi	coi	NOUN
ejpam-4493	321	48	-	-	PUNCT
ejpam-4493	321	49	set	set	NOUN
ejpam-4493	321	50	of	of	ADP
ejpam-4493	321	51	g.	g.	PROPN
ejpam-4493	321	52	proof	proof	PROPN
ejpam-4493	321	53	:	:	PUNCT
ejpam-4493	321	54	suppose	suppose	VERB
ejpam-4493	321	55	that	that	SCONJ
ejpam-4493	321	56	fcoi(g	fcoi(g	NOUN
ejpam-4493	321	57	)	)	PUNCT
ejpam-4493	321	58	=	=	PUNCT
ejpam-4493	321	59	coi(g	coi(g	PROPN
ejpam-4493	321	60	)	)	PUNCT
ejpam-4493	321	61	.	.	PUNCT
ejpam-4493	322	1	let	let	VERB
ejpam-4493	322	2	b	b	X
ejpam-4493	322	3	be	be	AUX
ejpam-4493	322	4	a	a	DET
ejpam-4493	322	5	coi	coi	NOUN
ejpam-4493	322	6	-	-	PUNCT
ejpam-4493	322	7	set	set	NOUN
ejpam-4493	322	8	of	of	ADP
ejpam-4493	322	9	g	g	NOUN
ejpam-4493	322	10	such	such	ADJ
ejpam-4493	322	11	that	that	DET
ejpam-4493	322	12	fcoi(g	fcoi(g	NOUN
ejpam-4493	322	13	)	)	PUNCT
ejpam-4493	323	1	=	=	PRON
ejpam-4493	323	2	|b|	|b|	X
ejpam-4493	323	3	=	=	PUNCT
ejpam-4493	323	4	coi(g	coi(g	PROPN
ejpam-4493	323	5	)	)	PUNCT
ejpam-4493	323	6	,	,	PUNCT
ejpam-4493	323	7	that	that	ADV
ejpam-4493	323	8	is	is	ADV
ejpam-4493	323	9	,	,	PUNCT
ejpam-4493	323	10	b	b	PROPN
ejpam-4493	323	11	is	be	AUX
ejpam-4493	323	12	the	the	DET
ejpam-4493	323	13	only	only	ADJ
ejpam-4493	323	14	forcing	forcing	NOUN
ejpam-4493	323	15	subset	subset	NOUN
ejpam-4493	323	16	for	for	ADP
ejpam-4493	323	17	itself	itself	PRON
ejpam-4493	323	18	.	.	PUNCT
ejpam-4493	324	1	let	let	VERB
ejpam-4493	324	2	v	v	NUM
ejpam-4493	324	3	∈	∈	PROPN
ejpam-4493	324	4	b.	b.	PROPN
ejpam-4493	324	5	since	since	SCONJ
ejpam-4493	324	6	b	b	PROPN
ejpam-4493	324	7	\	\	PROPN
ejpam-4493	324	8	{	{	PUNCT
ejpam-4493	324	9	v	v	NOUN
ejpam-4493	324	10	}	}	PUNCT
ejpam-4493	324	11	is	be	AUX
ejpam-4493	324	12	not	not	PART
ejpam-4493	324	13	a	a	DET
ejpam-4493	324	14	forcing	forcing	NOUN
ejpam-4493	324	15	subset	subset	NOUN
ejpam-4493	324	16	for	for	ADP
ejpam-4493	324	17	b	b	NOUN
ejpam-4493	324	18	,	,	PUNCT
ejpam-4493	324	19	there	there	PRON
ejpam-4493	324	20	exists	exist	VERB
ejpam-4493	325	1	a	a	DET
ejpam-4493	325	2	uv	uv	NOUN
ejpam-4493	325	3	∈	∈	PROPN
ejpam-4493	325	4	v	v	NOUN
ejpam-4493	325	5	(	(	PUNCT
ejpam-4493	325	6	g	g	NOUN
ejpam-4493	325	7	)	)	PUNCT
ejpam-4493	325	8	\	\	PROPN
ejpam-4493	325	9	b	b	X
ejpam-4493	325	10	such	such	ADJ
ejpam-4493	325	11	that	that	DET
ejpam-4493	325	12	y.d	y.d	PROPN
ejpam-4493	325	13	.	.	PROPN
ejpam-4493	325	14	calanza	calanza	PROPN
ejpam-4493	325	15	,	,	PUNCT
ejpam-4493	325	16	h.	h.	PROPN
ejpam-4493	325	17	rara	rara	PROPN
ejpam-4493	325	18	/	/	SYM
ejpam-4493	325	19	eur	eur	PROPN
ejpam-4493	325	20	.	.	PUNCT
ejpam-4493	326	1	j.	j.	PROPN
ejpam-4493	326	2	pure	pure	PROPN
ejpam-4493	326	3	appl	appl	PROPN
ejpam-4493	326	4	.	.	PROPN
ejpam-4493	326	5	math	math	PROPN
ejpam-4493	326	6	,	,	PUNCT
ejpam-4493	326	7	15	15	NUM
ejpam-4493	326	8	(	(	PUNCT
ejpam-4493	326	9	4	4	NUM
ejpam-4493	326	10	)	)	PUNCT
ejpam-4493	326	11	(	(	PUNCT
ejpam-4493	326	12	2022	2022	NUM
ejpam-4493	326	13	)	)	PUNCT
ejpam-4493	326	14	,	,	PUNCT
ejpam-4493	326	15	1649	1649	NUM
ejpam-4493	326	16	-	-	SYM
ejpam-4493	326	17	1661	1661	NUM
ejpam-4493	326	18	1658	1658	NUM
ejpam-4493	326	19	[	[	PUNCT
ejpam-4493	326	20	b	b	NOUN
ejpam-4493	326	21	\	\	X
ejpam-4493	326	22	{	{	PUNCT
ejpam-4493	326	23	v	v	NOUN
ejpam-4493	326	24	}	}	PUNCT
ejpam-4493	326	25	]	]	PUNCT
ejpam-4493	326	26	∪	∪	X
ejpam-4493	326	27	{	{	PUNCT
ejpam-4493	326	28	uv	uv	NOUN
ejpam-4493	326	29	}	}	PUNCT
ejpam-4493	326	30	is	be	AUX
ejpam-4493	326	31	a	a	DET
ejpam-4493	326	32	coi	coi	NOUN
ejpam-4493	326	33	-	-	PUNCT
ejpam-4493	326	34	set	set	NOUN
ejpam-4493	326	35	of	of	ADP
ejpam-4493	326	36	g.	g.	NOUN
ejpam-4493	326	37	conversely	conversely	ADV
ejpam-4493	326	38	,	,	PUNCT
ejpam-4493	326	39	suppose	suppose	VERB
ejpam-4493	326	40	that	that	SCONJ
ejpam-4493	326	41	every	every	DET
ejpam-4493	326	42	coi	coi	NOUN
ejpam-4493	326	43	-	-	PUNCT
ejpam-4493	326	44	set	set	VERB
ejpam-4493	326	45	b	b	NOUN
ejpam-4493	326	46	′	′	NUM
ejpam-4493	326	47	of	of	ADP
ejpam-4493	326	48	g	g	PROPN
ejpam-4493	326	49	satisfies	satisfy	VERB
ejpam-4493	326	50	the	the	DET
ejpam-4493	326	51	given	give	VERB
ejpam-4493	326	52	condition	condition	NOUN
ejpam-4493	326	53	.	.	PUNCT
ejpam-4493	327	1	let	let	VERB
ejpam-4493	327	2	b	b	X
ejpam-4493	327	3	be	be	AUX
ejpam-4493	327	4	a	a	DET
ejpam-4493	327	5	coi	coi	NOUN
ejpam-4493	327	6	-	-	PUNCT
ejpam-4493	327	7	set	set	NOUN
ejpam-4493	327	8	of	of	ADP
ejpam-4493	327	9	g	g	NOUN
ejpam-4493	327	10	such	such	ADJ
ejpam-4493	327	11	that	that	DET
ejpam-4493	327	12	fcoi(g	fcoi(g	NOUN
ejpam-4493	327	13	)	)	PUNCT
ejpam-4493	328	1	=	=	SYM
ejpam-4493	328	2	fcoi(b	fcoi(b	NOUN
ejpam-4493	328	3	)	)	PUNCT
ejpam-4493	328	4	.	.	PUNCT
ejpam-4493	329	1	suppose	suppose	VERB
ejpam-4493	329	2	further	far	ADV
ejpam-4493	329	3	that	that	SCONJ
ejpam-4493	329	4	b	b	PROPN
ejpam-4493	329	5	has	have	VERB
ejpam-4493	329	6	a	a	DET
ejpam-4493	329	7	forcing	forcing	NOUN
ejpam-4493	329	8	subset	subset	NOUN
ejpam-4493	329	9	q	q	NOUN
ejpam-4493	329	10	with	with	ADP
ejpam-4493	329	11	|q|	|q|	PROPN
ejpam-4493	329	12	<	<	X
ejpam-4493	329	13	|b|	|b|	PROPN
ejpam-4493	329	14	,	,	PUNCT
ejpam-4493	329	15	that	that	ADV
ejpam-4493	329	16	is	be	AUX
ejpam-4493	329	17	,	,	PUNCT
ejpam-4493	329	18	b	b	X
ejpam-4493	329	19	=	=	SYM
ejpam-4493	329	20	q	q	X
ejpam-4493	329	21	∪	∪	ADP
ejpam-4493	329	22	p	p	NOUN
ejpam-4493	329	23	where	where	SCONJ
ejpam-4493	329	24	p	p	NOUN
ejpam-4493	329	25	=	=	X
ejpam-4493	329	26	{	{	PUNCT
ejpam-4493	329	27	z	z	PROPN
ejpam-4493	329	28	∈	∈	PROPN
ejpam-4493	329	29	b	b	PROPN
ejpam-4493	329	30	:	:	PUNCT
ejpam-4493	330	1	z	z	AUX
ejpam-4493	330	2	/∈	/∈	PUNCT
ejpam-4493	330	3	q	q	ADJ
ejpam-4493	330	4	}	}	PUNCT
ejpam-4493	330	5	.	.	PUNCT
ejpam-4493	331	1	pick	pick	VERB
ejpam-4493	331	2	z	z	PROPN
ejpam-4493	331	3	∈	∈	PROPN
ejpam-4493	331	4	p.	p.	NOUN
ejpam-4493	331	5	by	by	ADP
ejpam-4493	331	6	assumption	assumption	NOUN
ejpam-4493	331	7	,	,	PUNCT
ejpam-4493	331	8	there	there	PRON
ejpam-4493	331	9	exists	exist	VERB
ejpam-4493	331	10	uz	uz	PROPN
ejpam-4493	331	11	∈	∈	PROPN
ejpam-4493	331	12	v	v	ADP
ejpam-4493	331	13	(	(	PUNCT
ejpam-4493	331	14	g	g	NOUN
ejpam-4493	331	15	)	)	PUNCT
ejpam-4493	331	16	\	\	PROPN
ejpam-4493	332	1	b	b	X
ejpam-4493	332	2	such	such	ADJ
ejpam-4493	332	3	that	that	SCONJ
ejpam-4493	332	4	[	[	PUNCT
ejpam-4493	332	5	b	b	X
ejpam-4493	332	6	\	\	X
ejpam-4493	332	7	{	{	PUNCT
ejpam-4493	332	8	z	z	NOUN
ejpam-4493	332	9	}	}	PUNCT
ejpam-4493	332	10	]	]	PUNCT
ejpam-4493	332	11	∪	∪	X
ejpam-4493	332	12	{	{	PUNCT
ejpam-4493	332	13	uz	uz	NOUN
ejpam-4493	332	14	}	}	PUNCT
ejpam-4493	332	15	=	=	SYM
ejpam-4493	332	16	t	t	NOUN
ejpam-4493	332	17	is	be	AUX
ejpam-4493	332	18	a	a	DET
ejpam-4493	332	19	coi	coi	NOUN
ejpam-4493	332	20	-	-	PUNCT
ejpam-4493	332	21	set	set	NOUN
ejpam-4493	332	22	of	of	ADP
ejpam-4493	332	23	g.	g.	PROPN
ejpam-4493	332	24	hence	hence	ADV
ejpam-4493	332	25	,	,	PUNCT
ejpam-4493	332	26	t	t	PROPN
ejpam-4493	332	27	=	=	PUNCT
ejpam-4493	332	28	q∪r	q∪r	PROPN
ejpam-4493	332	29	,	,	PUNCT
ejpam-4493	332	30	where	where	SCONJ
ejpam-4493	332	31	r	r	NOUN
ejpam-4493	332	32	=	=	PUNCT
ejpam-4493	332	33	[	[	PUNCT
ejpam-4493	332	34	p	p	X
ejpam-4493	332	35	\	\	X
ejpam-4493	332	36	{	{	PUNCT
ejpam-4493	332	37	z	z	NOUN
ejpam-4493	332	38	}	}	PUNCT
ejpam-4493	332	39	]	]	X
ejpam-4493	333	1	∪{uz	∪{uz	NUM
ejpam-4493	333	2	}	}	PUNCT
ejpam-4493	333	3	,	,	PUNCT
ejpam-4493	333	4	is	be	AUX
ejpam-4493	333	5	a	a	DET
ejpam-4493	333	6	coi	coi	NOUN
ejpam-4493	333	7	-	-	PUNCT
ejpam-4493	333	8	set	set	NOUN
ejpam-4493	333	9	containing	contain	VERB
ejpam-4493	333	10	q	q	NOUN
ejpam-4493	333	11	,	,	PUNCT
ejpam-4493	333	12	a	a	DET
ejpam-4493	333	13	contradiction	contradiction	NOUN
ejpam-4493	333	14	.	.	PUNCT
ejpam-4493	334	1	hence	hence	ADV
ejpam-4493	334	2	,	,	PUNCT
ejpam-4493	334	3	b	b	PROPN
ejpam-4493	334	4	is	be	AUX
ejpam-4493	334	5	the	the	DET
ejpam-4493	334	6	only	only	ADJ
ejpam-4493	334	7	forcing	forcing	NOUN
ejpam-4493	334	8	subset	subset	NOUN
ejpam-4493	334	9	for	for	ADP
ejpam-4493	334	10	b.	b.	PROPN
ejpam-4493	334	11	therefore	therefore	ADV
ejpam-4493	334	12	,	,	PUNCT
ejpam-4493	334	13	fcoi(g	fcoi(g	ADV
ejpam-4493	334	14	)	)	PUNCT
ejpam-4493	334	15	=	=	PUNCT
ejpam-4493	334	16	coi(g	coi(g	PROPN
ejpam-4493	334	17	)	)	PUNCT
ejpam-4493	334	18	.	.	PUNCT
ejpam-4493	335	1	proposition	proposition	NOUN
ejpam-4493	335	2	7	7	NUM
ejpam-4493	335	3	.	.	X
ejpam-4493	335	4	for	for	ADP
ejpam-4493	335	5	any	any	DET
ejpam-4493	335	6	complete	complete	ADJ
ejpam-4493	335	7	graph	graph	NOUN
ejpam-4493	335	8	kn	kn	PROPN
ejpam-4493	335	9	with	with	ADP
ejpam-4493	335	10	n	n	PRON
ejpam-4493	335	11	≥	≥	NUM
ejpam-4493	335	12	1	1	NUM
ejpam-4493	335	13	vertices	vertex	NOUN
ejpam-4493	335	14	,	,	PUNCT
ejpam-4493	335	15	fcoi(kn	fcoi(kn	NOUN
ejpam-4493	335	16	)	)	PUNCT
ejpam-4493	335	17	=	=	PUNCT
ejpam-4493	335	18	{	{	PUNCT
ejpam-4493	335	19	0	0	NUM
ejpam-4493	335	20	,	,	PUNCT
ejpam-4493	335	21	if	if	SCONJ
ejpam-4493	335	22	n	n	NOUN
ejpam-4493	335	23	=	=	SYM
ejpam-4493	335	24	1	1	NUM
ejpam-4493	335	25	,	,	PUNCT
ejpam-4493	335	26	n−	n−	NOUN
ejpam-4493	335	27	1	1	NUM
ejpam-4493	335	28	,	,	PUNCT
ejpam-4493	335	29	if	if	SCONJ
ejpam-4493	335	30	n	n	PRON
ejpam-4493	335	31	≥	≥	NOUN
ejpam-4493	335	32	2	2	NUM
ejpam-4493	335	33	.	.	PUNCT
ejpam-4493	336	1	proof	proof	NOUN
ejpam-4493	336	2	:	:	PUNCT
ejpam-4493	336	3	suppose	suppose	VERB
ejpam-4493	336	4	that	that	SCONJ
ejpam-4493	336	5	v	v	INTJ
ejpam-4493	336	6	(	(	PUNCT
ejpam-4493	336	7	kn	kn	PROPN
ejpam-4493	336	8	)	)	PUNCT
ejpam-4493	336	9	=	=	PRON
ejpam-4493	336	10	{	{	PUNCT
ejpam-4493	336	11	v1	v1	PROPN
ejpam-4493	336	12	,	,	PUNCT
ejpam-4493	336	13	v2	v2	PROPN
ejpam-4493	336	14	,	,	PUNCT
ejpam-4493	336	15	.	.	PUNCT
ejpam-4493	336	16	.	.	PUNCT
ejpam-4493	336	17	.	.	PUNCT
ejpam-4493	337	1	,	,	PUNCT
ejpam-4493	337	2	vn	vn	INTJ
ejpam-4493	337	3	}	}	PUNCT
ejpam-4493	337	4	.	.	PUNCT
ejpam-4493	338	1	clearly	clearly	ADV
ejpam-4493	338	2	,	,	PUNCT
ejpam-4493	338	3	fcoi(k1	fcoi(k1	NOUN
ejpam-4493	338	4	)	)	PUNCT
ejpam-4493	338	5	=	=	SYM
ejpam-4493	339	1	0	0	X
ejpam-4493	339	2	.	.	PUNCT
ejpam-4493	340	1	if	if	SCONJ
ejpam-4493	340	2	n	n	NOUN
ejpam-4493	340	3	=	=	SYM
ejpam-4493	340	4	2	2	NUM
ejpam-4493	340	5	,	,	PUNCT
ejpam-4493	340	6	then	then	ADV
ejpam-4493	340	7	kn	kn	PROPN
ejpam-4493	340	8	has	have	VERB
ejpam-4493	340	9	coi	coi	NOUN
ejpam-4493	340	10	-	-	PUNCT
ejpam-4493	340	11	set	set	VERB
ejpam-4493	340	12	r1	r1	NOUN
ejpam-4493	340	13	=	=	SYM
ejpam-4493	340	14	{	{	PUNCT
ejpam-4493	340	15	v1	v1	NOUN
ejpam-4493	340	16	}	}	PUNCT
ejpam-4493	340	17	and	and	CCONJ
ejpam-4493	340	18	r2	r2	PROPN
ejpam-4493	340	19	=	=	SYM
ejpam-4493	340	20	{	{	PUNCT
ejpam-4493	340	21	v2	v2	PROPN
ejpam-4493	340	22	}	}	PUNCT
ejpam-4493	340	23	which	which	PRON
ejpam-4493	340	24	are	be	AUX
ejpam-4493	340	25	the	the	DET
ejpam-4493	340	26	only	only	ADJ
ejpam-4493	340	27	coi	coi	NOUN
ejpam-4493	340	28	-	-	PUNCT
ejpam-4493	340	29	sets	set	NOUN
ejpam-4493	340	30	of	of	ADP
ejpam-4493	340	31	kn	kn	PROPN
ejpam-4493	340	32	with	with	ADP
ejpam-4493	340	33	v1	v1	PROPN
ejpam-4493	340	34	∈	∈	PROPN
ejpam-4493	340	35	r1	r1	NOUN
ejpam-4493	340	36	and	and	CCONJ
ejpam-4493	340	37	v1	v1	NOUN
ejpam-4493	340	38	/∈	/∈	PUNCT
ejpam-4493	340	39	r2	r2	PROPN
ejpam-4493	340	40	.	.	PUNCT
ejpam-4493	341	1	by	by	ADP
ejpam-4493	341	2	remark	remark	NOUN
ejpam-4493	341	3	3(ii	3(ii	NUM
ejpam-4493	341	4	)	)	PUNCT
ejpam-4493	341	5	,	,	PUNCT
ejpam-4493	341	6	fcoi(kn	fcoi(kn	NOUN
ejpam-4493	341	7	)	)	PUNCT
ejpam-4493	342	1	=	=	PUNCT
ejpam-4493	342	2	n−	n−	NOUN
ejpam-4493	342	3	1	1	NUM
ejpam-4493	342	4	=	=	SYM
ejpam-4493	342	5	1	1	X
ejpam-4493	342	6	.	.	PUNCT
ejpam-4493	342	7	suppose	suppose	VERB
ejpam-4493	342	8	that	that	SCONJ
ejpam-4493	342	9	n	n	PROPN
ejpam-4493	342	10	>	>	X
ejpam-4493	342	11	2	2	X
ejpam-4493	342	12	.	.	PUNCT
ejpam-4493	342	13	then	then	ADV
ejpam-4493	342	14	the	the	DET
ejpam-4493	342	15	coi	coi	NOUN
ejpam-4493	342	16	-	-	PUNCT
ejpam-4493	342	17	sets	set	NOUN
ejpam-4493	342	18	of	of	ADP
ejpam-4493	342	19	kn	kn	PROPN
ejpam-4493	342	20	are	be	AUX
ejpam-4493	342	21	b1	b1	NOUN
ejpam-4493	342	22	=	=	SYM
ejpam-4493	342	23	{	{	PUNCT
ejpam-4493	342	24	v1	v1	PROPN
ejpam-4493	342	25	,	,	PUNCT
ejpam-4493	342	26	v2	v2	PROPN
ejpam-4493	342	27	,	,	PUNCT
ejpam-4493	342	28	.	.	PUNCT
ejpam-4493	342	29	.	.	PUNCT
ejpam-4493	343	1	.	.	PUNCT
ejpam-4493	344	1	,	,	PUNCT
ejpam-4493	344	2	vn−1	vn−1	ADJ
ejpam-4493	344	3	}	}	PUNCT
ejpam-4493	344	4	,	,	PUNCT
ejpam-4493	344	5	b2	b2	NOUN
ejpam-4493	344	6	=	=	SYM
ejpam-4493	344	7	{	{	PUNCT
ejpam-4493	344	8	v2	v2	PROPN
ejpam-4493	344	9	,	,	PUNCT
ejpam-4493	344	10	v3	v3	PROPN
ejpam-4493	344	11	,	,	PUNCT
ejpam-4493	344	12	.	.	PUNCT
ejpam-4493	344	13	.	.	PUNCT
ejpam-4493	344	14	.	.	PUNCT
ejpam-4493	345	1	,	,	PUNCT
ejpam-4493	345	2	vn	vn	PROPN
ejpam-4493	345	3	}	}	PUNCT
ejpam-4493	345	4	,	,	PUNCT
ejpam-4493	345	5	b3	b3	PROPN
ejpam-4493	345	6	=	=	SYM
ejpam-4493	345	7	{	{	PUNCT
ejpam-4493	345	8	v3	v3	PROPN
ejpam-4493	345	9	,	,	PUNCT
ejpam-4493	345	10	v4	v4	PROPN
ejpam-4493	345	11	,	,	PUNCT
ejpam-4493	345	12	.	.	PUNCT
ejpam-4493	345	13	.	.	PUNCT
ejpam-4493	346	1	.	.	PUNCT
ejpam-4493	347	1	,	,	PUNCT
ejpam-4493	347	2	vn	vn	X
ejpam-4493	347	3	,	,	PUNCT
ejpam-4493	347	4	v1	v1	PROPN
ejpam-4493	347	5	}	}	PUNCT
ejpam-4493	347	6	,	,	PUNCT
ejpam-4493	347	7	.	.	PUNCT
ejpam-4493	347	8	.	.	PUNCT
ejpam-4493	347	9	.	.	PUNCT
ejpam-4493	348	1	,	,	PUNCT
ejpam-4493	348	2	bn	bn	NOUN
ejpam-4493	348	3	=	=	SYM
ejpam-4493	348	4	{	{	PUNCT
ejpam-4493	348	5	vn	vn	PROPN
ejpam-4493	348	6	,	,	PUNCT
ejpam-4493	348	7	v1	v1	NOUN
ejpam-4493	348	8	,	,	PUNCT
ejpam-4493	348	9	v2	v2	NOUN
ejpam-4493	348	10	,	,	PUNCT
ejpam-4493	348	11	.	.	PUNCT
ejpam-4493	348	12	.	.	PUNCT
ejpam-4493	349	1	.	.	PUNCT
ejpam-4493	350	1	,	,	PUNCT
ejpam-4493	350	2	vn−2	vn−2	PROPN
ejpam-4493	350	3	}	}	PUNCT
ejpam-4493	350	4	.	.	PUNCT
ejpam-4493	351	1	clearly	clearly	ADV
ejpam-4493	351	2	,	,	PUNCT
ejpam-4493	351	3	for	for	ADP
ejpam-4493	351	4	each	each	DET
ejpam-4493	351	5	vi	vi	PROPN
ejpam-4493	351	6	∈	∈	NOUN
ejpam-4493	351	7	bj	bj	VERB
ejpam-4493	351	8	where	where	SCONJ
ejpam-4493	351	9	i	i	PRON
ejpam-4493	351	10	,	,	PUNCT
ejpam-4493	351	11	j	j	PROPN
ejpam-4493	351	12	∈	∈	PROPN
ejpam-4493	351	13	{	{	PUNCT
ejpam-4493	351	14	1	1	NUM
ejpam-4493	351	15	,	,	PUNCT
ejpam-4493	351	16	2	2	NUM
ejpam-4493	351	17	,	,	PUNCT
ejpam-4493	351	18	3	3	NUM
ejpam-4493	351	19	,	,	PUNCT
ejpam-4493	351	20	.	.	PUNCT
ejpam-4493	351	21	.	.	PUNCT
ejpam-4493	351	22	.	.	PUNCT
ejpam-4493	351	23	,	,	PUNCT
ejpam-4493	351	24	n	n	CCONJ
ejpam-4493	351	25	}	}	PUNCT
ejpam-4493	351	26	,	,	PUNCT
ejpam-4493	351	27	there	there	PRON
ejpam-4493	351	28	exists	exist	VERB
ejpam-4493	351	29	vk	vk	ADP
ejpam-4493	351	30	∈	∈	PROPN
ejpam-4493	351	31	v	v	PROPN
ejpam-4493	351	32	(	(	PUNCT
ejpam-4493	351	33	kn	kn	PROPN
ejpam-4493	351	34	)	)	PUNCT
ejpam-4493	351	35	\	\	PUNCT
ejpam-4493	351	36	bj	bj	ADP
ejpam-4493	351	37	such	such	ADJ
ejpam-4493	351	38	that	that	SCONJ
ejpam-4493	351	39	[	[	PUNCT
ejpam-4493	351	40	bj	bj	ADP
ejpam-4493	351	41	\	\	NOUN
ejpam-4493	351	42	{	{	PUNCT
ejpam-4493	351	43	vi	vi	NOUN
ejpam-4493	351	44	}	}	PUNCT
ejpam-4493	351	45	]	]	PUNCT
ejpam-4493	351	46	∪	∪	X
ejpam-4493	351	47	{	{	PUNCT
ejpam-4493	351	48	vk	vk	INTJ
ejpam-4493	351	49	}	}	PUNCT
ejpam-4493	351	50	is	be	AUX
ejpam-4493	351	51	a	a	DET
ejpam-4493	351	52	coi	coi	NOUN
ejpam-4493	351	53	-	-	PUNCT
ejpam-4493	351	54	set	set	NOUN
ejpam-4493	351	55	of	of	ADP
ejpam-4493	351	56	g.	g.	PROPN
ejpam-4493	351	57	hence	hence	ADV
ejpam-4493	351	58	,	,	PUNCT
ejpam-4493	351	59	by	by	ADP
ejpam-4493	351	60	theorem	theorem	NOUN
ejpam-4493	351	61	7	7	NUM
ejpam-4493	351	62	,	,	PUNCT
ejpam-4493	351	63	fcoi(kn	fcoi(kn	NOUN
ejpam-4493	351	64	)	)	PUNCT
ejpam-4493	352	1	=	=	PUNCT
ejpam-4493	352	2	n−	n−	NOUN
ejpam-4493	352	3	1	1	NUM
ejpam-4493	352	4	.	.	PUNCT
ejpam-4493	352	5	proposition	proposition	NOUN
ejpam-4493	352	6	8	8	NUM
ejpam-4493	352	7	.	.	PUNCT
ejpam-4493	353	1	for	for	ADP
ejpam-4493	353	2	any	any	DET
ejpam-4493	353	3	path	path	NOUN
ejpam-4493	353	4	pn	pn	NOUN
ejpam-4493	353	5	with	with	ADP
ejpam-4493	353	6	n	n	PRON
ejpam-4493	353	7	≥	≥	NUM
ejpam-4493	353	8	1	1	NUM
ejpam-4493	353	9	vertices	vertex	NOUN
ejpam-4493	353	10	,	,	PUNCT
ejpam-4493	353	11	fcoi(pn	fcoi(pn	NOUN
ejpam-4493	353	12	)	)	PUNCT
ejpam-4493	353	13	=	=	SYM
ejpam-4493	353	14	{	{	PUNCT
ejpam-4493	353	15	0	0	NUM
ejpam-4493	353	16	,	,	PUNCT
ejpam-4493	353	17	if	if	SCONJ
ejpam-4493	353	18	n	n	NOUN
ejpam-4493	353	19	=	=	SYM
ejpam-4493	353	20	1	1	NUM
ejpam-4493	353	21	,	,	PUNCT
ejpam-4493	353	22	3	3	NUM
ejpam-4493	353	23	and	and	CCONJ
ejpam-4493	353	24	n	n	PRON
ejpam-4493	353	25	≥	≥	NOUN
ejpam-4493	353	26	5	5	NUM
ejpam-4493	353	27	is	be	AUX
ejpam-4493	353	28	odd	odd	ADJ
ejpam-4493	353	29	,	,	PUNCT
ejpam-4493	353	30	1	1	NUM
ejpam-4493	353	31	,	,	PUNCT
ejpam-4493	353	32	if	if	SCONJ
ejpam-4493	353	33	n	n	NOUN
ejpam-4493	353	34	=	=	SYM
ejpam-4493	353	35	2	2	NUM
ejpam-4493	353	36	,	,	PUNCT
ejpam-4493	353	37	4	4	NUM
ejpam-4493	353	38	and	and	CCONJ
ejpam-4493	353	39	n	n	PRON
ejpam-4493	353	40	≥	≥	NUM
ejpam-4493	353	41	6	6	NUM
ejpam-4493	353	42	is	be	AUX
ejpam-4493	353	43	even	even	ADV
ejpam-4493	353	44	.	.	PUNCT
ejpam-4493	354	1	proof	proof	NOUN
ejpam-4493	354	2	:	:	PUNCT
ejpam-4493	354	3	suppose	suppose	VERB
ejpam-4493	354	4	that	that	SCONJ
ejpam-4493	354	5	pn	pn	PROPN
ejpam-4493	354	6	=	=	PUNCT
ejpam-4493	355	1	[	[	X
ejpam-4493	355	2	v1	v1	NOUN
ejpam-4493	355	3	,	,	PUNCT
ejpam-4493	355	4	v2	v2	NOUN
ejpam-4493	355	5	,	,	PUNCT
ejpam-4493	355	6	.	.	PUNCT
ejpam-4493	355	7	.	.	PUNCT
ejpam-4493	355	8	.	.	PUNCT
ejpam-4493	356	1	,	,	PUNCT
ejpam-4493	356	2	vn	vn	X
ejpam-4493	356	3	]	]	PUNCT
ejpam-4493	356	4	.	.	PUNCT
ejpam-4493	357	1	clearly	clearly	ADV
ejpam-4493	357	2	,	,	PUNCT
ejpam-4493	357	3	fcoi(p1	fcoi(p1	NOUN
ejpam-4493	357	4	)	)	PUNCT
ejpam-4493	357	5	=	=	SYM
ejpam-4493	357	6	fcoi(p3	fcoi(p3	PROPN
ejpam-4493	357	7	)	)	PUNCT
ejpam-4493	357	8	=	=	SYM
ejpam-4493	357	9	0	0	NUM
ejpam-4493	357	10	and	and	CCONJ
ejpam-4493	357	11	fcoi(p2	fcoi(p2	ADJ
ejpam-4493	357	12	)	)	PUNCT
ejpam-4493	357	13	=	=	SYM
ejpam-4493	358	1	1	1	X
ejpam-4493	358	2	.	.	PUNCT
ejpam-4493	359	1	if	if	SCONJ
ejpam-4493	359	2	n	n	NOUN
ejpam-4493	359	3	=	=	SYM
ejpam-4493	359	4	4	4	NUM
ejpam-4493	359	5	,	,	PUNCT
ejpam-4493	359	6	then	then	ADV
ejpam-4493	359	7	pn	pn	PROPN
ejpam-4493	359	8	has	have	VERB
ejpam-4493	359	9	coi	coi	NOUN
ejpam-4493	359	10	-	-	PUNCT
ejpam-4493	359	11	sets	set	NOUN
ejpam-4493	359	12	b1	b1	NOUN
ejpam-4493	359	13	=	=	SYM
ejpam-4493	359	14	{	{	PUNCT
ejpam-4493	359	15	v1	v1	PROPN
ejpam-4493	359	16	,	,	PUNCT
ejpam-4493	359	17	v3	v3	PROPN
ejpam-4493	359	18	}	}	PUNCT
ejpam-4493	359	19	,	,	PUNCT
ejpam-4493	359	20	b2	b2	NOUN
ejpam-4493	359	21	=	=	SYM
ejpam-4493	359	22	{	{	PUNCT
ejpam-4493	359	23	v2	v2	PROPN
ejpam-4493	359	24	,	,	PUNCT
ejpam-4493	359	25	v4	v4	NOUN
ejpam-4493	359	26	}	}	PUNCT
ejpam-4493	359	27	and	and	CCONJ
ejpam-4493	359	28	b3	b3	PROPN
ejpam-4493	359	29	=	=	SYM
ejpam-4493	359	30	{	{	PUNCT
ejpam-4493	359	31	v2	v2	PROPN
ejpam-4493	359	32	,	,	PUNCT
ejpam-4493	359	33	v3	v3	PROPN
ejpam-4493	359	34	}	}	PUNCT
ejpam-4493	359	35	which	which	PRON
ejpam-4493	359	36	are	be	AUX
ejpam-4493	359	37	the	the	DET
ejpam-4493	359	38	only	only	ADJ
ejpam-4493	359	39	coi	coi	NOUN
ejpam-4493	359	40	-	-	PUNCT
ejpam-4493	359	41	sets	set	NOUN
ejpam-4493	359	42	of	of	ADP
ejpam-4493	359	43	pn	pn	PROPN
ejpam-4493	359	44	with	with	ADP
ejpam-4493	359	45	v4	v4	PROPN
ejpam-4493	359	46	∈	∈	PROPN
ejpam-4493	359	47	b2	b2	NOUN
ejpam-4493	359	48	and	and	CCONJ
ejpam-4493	359	49	v4	v4	NOUN
ejpam-4493	359	50	/∈	/∈	PUNCT
ejpam-4493	360	1	b1	b1	PROPN
ejpam-4493	360	2	,	,	PUNCT
ejpam-4493	360	3	b3	b3	PROPN
ejpam-4493	360	4	.	.	PUNCT
ejpam-4493	361	1	thus	thus	ADV
ejpam-4493	361	2	,	,	PUNCT
ejpam-4493	361	3	by	by	ADP
ejpam-4493	361	4	remark	remark	NOUN
ejpam-4493	361	5	3(ii	3(ii	NUM
ejpam-4493	361	6	)	)	PUNCT
ejpam-4493	361	7	,	,	PUNCT
ejpam-4493	361	8	fcoi(pn	fcoi(pn	NOUN
ejpam-4493	361	9	)	)	PUNCT
ejpam-4493	361	10	=	=	SYM
ejpam-4493	362	1	1	1	X
ejpam-4493	362	2	.	.	PUNCT
ejpam-4493	362	3	now	now	ADV
ejpam-4493	362	4	,	,	PUNCT
ejpam-4493	362	5	suppose	suppose	VERB
ejpam-4493	362	6	that	that	SCONJ
ejpam-4493	362	7	n	n	PROPN
ejpam-4493	362	8	≥	≥	NUM
ejpam-4493	362	9	5	5	NUM
ejpam-4493	362	10	and	and	CCONJ
ejpam-4493	362	11	n	n	PRON
ejpam-4493	362	12	is	be	AUX
ejpam-4493	362	13	odd	odd	ADJ
ejpam-4493	362	14	,	,	PUNCT
ejpam-4493	362	15	then	then	ADV
ejpam-4493	362	16	clearly	clearly	ADV
ejpam-4493	362	17	b	b	X
ejpam-4493	362	18	=	=	PRON
ejpam-4493	362	19	{	{	PUNCT
ejpam-4493	362	20	v2	v2	PROPN
ejpam-4493	362	21	,	,	PUNCT
ejpam-4493	362	22	v4	v4	PROPN
ejpam-4493	362	23	,	,	PUNCT
ejpam-4493	362	24	v6	v6	NOUN
ejpam-4493	362	25	,	,	PUNCT
ejpam-4493	362	26	.	.	PUNCT
ejpam-4493	362	27	.	.	PUNCT
ejpam-4493	363	1	.	.	PUNCT
ejpam-4493	364	1	,	,	PUNCT
ejpam-4493	364	2	vn−3	vn−3	PROPN
ejpam-4493	364	3	,	,	PUNCT
ejpam-4493	364	4	vn−1	vn−1	ADJ
ejpam-4493	364	5	}	}	PUNCT
ejpam-4493	364	6	is	be	AUX
ejpam-4493	364	7	the	the	DET
ejpam-4493	364	8	only	only	ADJ
ejpam-4493	364	9	coi	coi	NOUN
ejpam-4493	364	10	-	-	PUNCT
ejpam-4493	364	11	set	set	NOUN
ejpam-4493	364	12	of	of	ADP
ejpam-4493	364	13	pn	pn	PROPN
ejpam-4493	364	14	.	.	PUNCT
ejpam-4493	365	1	thus	thus	ADV
ejpam-4493	365	2	,	,	PUNCT
ejpam-4493	365	3	by	by	ADP
ejpam-4493	365	4	remark	remark	NOUN
ejpam-4493	365	5	3(i	3(i	NUM
ejpam-4493	365	6	)	)	PUNCT
ejpam-4493	365	7	,	,	PUNCT
ejpam-4493	365	8	fcoi(b	fcoi(b	NOUN
ejpam-4493	365	9	)	)	PUNCT
ejpam-4493	365	10	=	=	SYM
ejpam-4493	365	11	0	0	NUM
ejpam-4493	366	1	=	=	SYM
ejpam-4493	366	2	fcoi(pn	fcoi(pn	NOUN
ejpam-4493	366	3	)	)	PUNCT
ejpam-4493	366	4	.	.	PUNCT
ejpam-4493	367	1	next	next	ADV
ejpam-4493	367	2	,	,	PUNCT
ejpam-4493	367	3	suppose	suppose	VERB
ejpam-4493	367	4	that	that	SCONJ
ejpam-4493	367	5	n	n	PROPN
ejpam-4493	367	6	≥	≥	NUM
ejpam-4493	367	7	6	6	NUM
ejpam-4493	367	8	and	and	CCONJ
ejpam-4493	367	9	n	n	NUM
ejpam-4493	367	10	is	be	AUX
ejpam-4493	367	11	even	even	ADV
ejpam-4493	367	12	.	.	PUNCT
ejpam-4493	368	1	then	then	ADV
ejpam-4493	368	2	pn	pn	PROPN
ejpam-4493	368	3	has	have	VERB
ejpam-4493	368	4	coi	coi	NOUN
ejpam-4493	368	5	-	-	PUNCT
ejpam-4493	368	6	sets	set	NOUN
ejpam-4493	368	7	s1	s1	NOUN
ejpam-4493	368	8	=	=	SYM
ejpam-4493	368	9	{	{	PUNCT
ejpam-4493	368	10	v1	v1	PROPN
ejpam-4493	368	11	,	,	PUNCT
ejpam-4493	368	12	v3	v3	PROPN
ejpam-4493	368	13	,	,	PUNCT
ejpam-4493	368	14	v5	v5	PROPN
ejpam-4493	368	15	,	,	PUNCT
ejpam-4493	368	16	.	.	PUNCT
ejpam-4493	368	17	.	.	PUNCT
ejpam-4493	369	1	.	.	PUNCT
ejpam-4493	370	1	,	,	PUNCT
ejpam-4493	370	2	vn−1	vn−1	ADJ
ejpam-4493	370	3	}	}	PUNCT
ejpam-4493	370	4	and	and	CCONJ
ejpam-4493	370	5	s2	s2	VERB
ejpam-4493	370	6	=	=	SYM
ejpam-4493	370	7	{	{	PUNCT
ejpam-4493	370	8	v2	v2	PROPN
ejpam-4493	370	9	,	,	PUNCT
ejpam-4493	370	10	v4	v4	PROPN
ejpam-4493	370	11	,	,	PUNCT
ejpam-4493	370	12	v6	v6	NOUN
ejpam-4493	370	13	,	,	PUNCT
ejpam-4493	370	14	.	.	PUNCT
ejpam-4493	370	15	.	.	PUNCT
ejpam-4493	370	16	.	.	PUNCT
ejpam-4493	371	1	,	,	PUNCT
ejpam-4493	371	2	vn	vn	PROPN
ejpam-4493	371	3	}	}	PUNCT
ejpam-4493	371	4	which	which	PRON
ejpam-4493	371	5	are	be	AUX
ejpam-4493	371	6	the	the	DET
ejpam-4493	371	7	only	only	ADJ
ejpam-4493	371	8	coi	coi	NOUN
ejpam-4493	371	9	-	-	PUNCT
ejpam-4493	371	10	set	set	NOUN
ejpam-4493	371	11	of	of	ADP
ejpam-4493	371	12	pn	pn	PROPN
ejpam-4493	371	13	with	with	ADP
ejpam-4493	371	14	v3	v3	PROPN
ejpam-4493	371	15	∈	∈	PROPN
ejpam-4493	371	16	s1	s1	PROPN
ejpam-4493	371	17	and	and	CCONJ
ejpam-4493	371	18	v3	v3	PROPN
ejpam-4493	371	19	/∈	/∈	PROPN
ejpam-4493	372	1	s2	s2	PROPN
ejpam-4493	372	2	.	.	PUNCT
ejpam-4493	373	1	hence	hence	ADV
ejpam-4493	373	2	,	,	PUNCT
ejpam-4493	373	3	by	by	ADP
ejpam-4493	373	4	remark	remark	NOUN
ejpam-4493	373	5	3(ii	3(ii	NUM
ejpam-4493	373	6	)	)	PUNCT
ejpam-4493	373	7	,	,	PUNCT
ejpam-4493	373	8	fcoi(pn	fcoi(pn	NOUN
ejpam-4493	373	9	)	)	PUNCT
ejpam-4493	373	10	=	=	SYM
ejpam-4493	373	11	1	1	X
ejpam-4493	373	12	.	.	X
ejpam-4493	373	13	proposition	proposition	NOUN
ejpam-4493	373	14	9	9	NUM
ejpam-4493	373	15	.	.	PUNCT
ejpam-4493	374	1	for	for	ADP
ejpam-4493	374	2	any	any	DET
ejpam-4493	374	3	cycle	cycle	NOUN
ejpam-4493	374	4	cn	cn	NOUN
ejpam-4493	374	5	with	with	ADP
ejpam-4493	374	6	n	n	NUM
ejpam-4493	374	7	≥	≥	NUM
ejpam-4493	374	8	3	3	NUM
ejpam-4493	374	9	vertices	vertex	NOUN
ejpam-4493	374	10	,	,	PUNCT
ejpam-4493	374	11	fcoi(cn	fcoi(cn	NOUN
ejpam-4493	374	12	)	)	PUNCT
ejpam-4493	374	13	=	=	SYM
ejpam-4493	374	14	{	{	PUNCT
ejpam-4493	374	15	1	1	NUM
ejpam-4493	374	16	,	,	PUNCT
ejpam-4493	374	17	if	if	SCONJ
ejpam-4493	374	18	n	n	NOUN
ejpam-4493	374	19	=	=	SYM
ejpam-4493	374	20	4	4	NUM
ejpam-4493	374	21	and	and	CCONJ
ejpam-4493	374	22	n	n	PRON
ejpam-4493	374	23	>	>	SYM
ejpam-4493	374	24	4	4	NUM
ejpam-4493	374	25	is	be	AUX
ejpam-4493	374	26	even	even	ADV
ejpam-4493	374	27	,	,	PUNCT
ejpam-4493	374	28	2	2	NUM
ejpam-4493	374	29	,	,	PUNCT
ejpam-4493	374	30	if	if	SCONJ
ejpam-4493	374	31	n	n	NOUN
ejpam-4493	374	32	=	=	SYM
ejpam-4493	374	33	3	3	NUM
ejpam-4493	374	34	and	and	CCONJ
ejpam-4493	374	35	n	n	PROPN
ejpam-4493	374	36	>	>	SYM
ejpam-4493	374	37	3	3	NUM
ejpam-4493	374	38	is	be	AUX
ejpam-4493	374	39	odd	odd	ADJ
ejpam-4493	374	40	.	.	PUNCT
ejpam-4493	375	1	proof	proof	NOUN
ejpam-4493	375	2	:	:	PUNCT
ejpam-4493	375	3	suppose	suppose	VERB
ejpam-4493	375	4	that	that	SCONJ
ejpam-4493	375	5	cn	cn	PROPN
ejpam-4493	375	6	=	=	PUNCT
ejpam-4493	375	7	[	[	X
ejpam-4493	375	8	v1	v1	NOUN
ejpam-4493	375	9	,	,	PUNCT
ejpam-4493	375	10	v2	v2	NOUN
ejpam-4493	375	11	,	,	PUNCT
ejpam-4493	375	12	.	.	PUNCT
ejpam-4493	375	13	.	.	PUNCT
ejpam-4493	375	14	.	.	PUNCT
ejpam-4493	376	1	,	,	PUNCT
ejpam-4493	376	2	vn	vn	X
ejpam-4493	376	3	,	,	PUNCT
ejpam-4493	376	4	v1	v1	PROPN
ejpam-4493	376	5	]	]	PUNCT
ejpam-4493	376	6	.	.	PUNCT
ejpam-4493	377	1	it	it	PRON
ejpam-4493	377	2	can	can	AUX
ejpam-4493	377	3	be	be	AUX
ejpam-4493	377	4	verified	verify	VERB
ejpam-4493	377	5	that	that	SCONJ
ejpam-4493	377	6	fcoi(c4	fcoi(c4	NOUN
ejpam-4493	377	7	)	)	PUNCT
ejpam-4493	377	8	=	=	SYM
ejpam-4493	378	1	1	1	X
ejpam-4493	378	2	.	.	PUNCT
ejpam-4493	378	3	suppose	suppose	VERB
ejpam-4493	378	4	that	that	SCONJ
ejpam-4493	378	5	n	n	PROPN
ejpam-4493	378	6	=	=	SYM
ejpam-4493	378	7	3	3	X
ejpam-4493	378	8	.	.	PUNCT
ejpam-4493	378	9	then	then	ADV
ejpam-4493	378	10	the	the	DET
ejpam-4493	378	11	coi	coi	NOUN
ejpam-4493	378	12	-	-	PUNCT
ejpam-4493	378	13	sets	set	NOUN
ejpam-4493	378	14	of	of	ADP
ejpam-4493	378	15	c3	c3	PROPN
ejpam-4493	378	16	are	be	AUX
ejpam-4493	378	17	q1	q1	NOUN
ejpam-4493	378	18	=	=	SYM
ejpam-4493	378	19	{	{	PUNCT
ejpam-4493	378	20	v1	v1	PROPN
ejpam-4493	378	21	,	,	PUNCT
ejpam-4493	378	22	v2	v2	PROPN
ejpam-4493	378	23	}	}	PUNCT
ejpam-4493	378	24	,	,	PUNCT
ejpam-4493	378	25	q2	q2	NOUN
ejpam-4493	378	26	=	=	SYM
ejpam-4493	378	27	{	{	PUNCT
ejpam-4493	378	28	v2	v2	PROPN
ejpam-4493	378	29	,	,	PUNCT
ejpam-4493	378	30	v3	v3	PROPN
ejpam-4493	378	31	}	}	PUNCT
ejpam-4493	378	32	and	and	CCONJ
ejpam-4493	378	33	q3	q3	NOUN
ejpam-4493	378	34	=	=	SYM
ejpam-4493	378	35	{	{	PUNCT
ejpam-4493	378	36	v1	v1	PROPN
ejpam-4493	378	37	,	,	PUNCT
ejpam-4493	378	38	v3	v3	PROPN
ejpam-4493	378	39	}	}	PUNCT
ejpam-4493	378	40	.	.	PUNCT
ejpam-4493	379	1	clearly	clearly	ADV
ejpam-4493	379	2	,	,	PUNCT
ejpam-4493	379	3	for	for	ADP
ejpam-4493	379	4	each	each	DET
ejpam-4493	379	5	vi	vi	PROPN
ejpam-4493	379	6	∈	∈	PROPN
ejpam-4493	379	7	qj	qj	PROPN
ejpam-4493	379	8	where	where	SCONJ
ejpam-4493	379	9	i	i	PRON
ejpam-4493	379	10	,	,	PUNCT
ejpam-4493	379	11	j	j	PROPN
ejpam-4493	379	12	∈	∈	PROPN
ejpam-4493	379	13	{	{	PUNCT
ejpam-4493	379	14	1	1	NUM
ejpam-4493	379	15	,	,	PUNCT
ejpam-4493	379	16	2	2	NUM
ejpam-4493	379	17	,	,	PUNCT
ejpam-4493	379	18	3	3	NUM
ejpam-4493	379	19	}	}	PUNCT
ejpam-4493	379	20	,	,	PUNCT
ejpam-4493	379	21	there	there	PRON
ejpam-4493	379	22	exists	exist	VERB
ejpam-4493	379	23	vk	vk	ADP
ejpam-4493	379	24	∈	∈	PROPN
ejpam-4493	379	25	v	v	PROPN
ejpam-4493	379	26	(	(	PUNCT
ejpam-4493	379	27	c3	c3	NOUN
ejpam-4493	379	28	)	)	PUNCT
ejpam-4493	379	29	\qj	\qj	PROPN
ejpam-4493	379	30	such	such	ADJ
ejpam-4493	379	31	y.d	y.d	PROPN
ejpam-4493	379	32	.	.	PROPN
ejpam-4493	379	33	calanza	calanza	PROPN
ejpam-4493	379	34	,	,	PUNCT
ejpam-4493	379	35	h.	h.	PROPN
ejpam-4493	379	36	rara	rara	PROPN
ejpam-4493	379	37	/	/	SYM
ejpam-4493	379	38	eur	eur	PROPN
ejpam-4493	379	39	.	.	PUNCT
ejpam-4493	380	1	j.	j.	PROPN
ejpam-4493	380	2	pure	pure	PROPN
ejpam-4493	380	3	appl	appl	PROPN
ejpam-4493	380	4	.	.	PROPN
ejpam-4493	380	5	math	math	PROPN
ejpam-4493	380	6	,	,	PUNCT
ejpam-4493	380	7	15	15	NUM
ejpam-4493	380	8	(	(	PUNCT
ejpam-4493	380	9	4	4	NUM
ejpam-4493	380	10	)	)	PUNCT
ejpam-4493	380	11	(	(	PUNCT
ejpam-4493	380	12	2022	2022	NUM
ejpam-4493	380	13	)	)	PUNCT
ejpam-4493	380	14	,	,	PUNCT
ejpam-4493	380	15	1649	1649	NUM
ejpam-4493	380	16	-	-	SYM
ejpam-4493	380	17	1661	1661	NUM
ejpam-4493	380	18	1659	1659	NUM
ejpam-4493	380	19	that	that	SCONJ
ejpam-4493	380	20	[	[	PUNCT
ejpam-4493	380	21	qj	qj	PROPN
ejpam-4493	380	22	\	\	PROPN
ejpam-4493	380	23	{	{	PUNCT
ejpam-4493	380	24	vi	vi	NOUN
ejpam-4493	380	25	}	}	PUNCT
ejpam-4493	380	26	]	]	PUNCT
ejpam-4493	380	27	∪{vk	∪{vk	NOUN
ejpam-4493	380	28	}	}	PUNCT
ejpam-4493	380	29	is	be	AUX
ejpam-4493	380	30	a	a	DET
ejpam-4493	380	31	coi	coi	NOUN
ejpam-4493	380	32	-	-	PUNCT
ejpam-4493	380	33	set	set	NOUN
ejpam-4493	380	34	of	of	ADP
ejpam-4493	380	35	g.	g.	PROPN
ejpam-4493	380	36	thus	thus	ADV
ejpam-4493	380	37	,	,	PUNCT
ejpam-4493	380	38	by	by	ADP
ejpam-4493	380	39	theorem	theorem	ADJ
ejpam-4493	380	40	7	7	NUM
ejpam-4493	380	41	,	,	PUNCT
ejpam-4493	380	42	fcoi(c3	fcoi(c3	NOUN
ejpam-4493	380	43	)	)	PUNCT
ejpam-4493	380	44	=	=	SYM
ejpam-4493	381	1	2	2	X
ejpam-4493	381	2	.	.	PUNCT
ejpam-4493	381	3	now	now	ADV
ejpam-4493	381	4	,	,	PUNCT
ejpam-4493	381	5	suppose	suppose	VERB
ejpam-4493	381	6	that	that	SCONJ
ejpam-4493	381	7	n	n	NOUN
ejpam-4493	381	8	>	>	X
ejpam-4493	381	9	4	4	NUM
ejpam-4493	381	10	and	and	CCONJ
ejpam-4493	381	11	n	n	PRON
ejpam-4493	381	12	is	be	AUX
ejpam-4493	381	13	even	even	ADV
ejpam-4493	381	14	.	.	PUNCT
ejpam-4493	382	1	then	then	ADV
ejpam-4493	382	2	b1	b1	NOUN
ejpam-4493	382	3	=	=	SYM
ejpam-4493	382	4	{	{	PUNCT
ejpam-4493	382	5	v1	v1	PROPN
ejpam-4493	382	6	,	,	PUNCT
ejpam-4493	382	7	v3	v3	PROPN
ejpam-4493	382	8	,	,	PUNCT
ejpam-4493	382	9	v5	v5	PROPN
ejpam-4493	382	10	,	,	PUNCT
ejpam-4493	382	11	.	.	PUNCT
ejpam-4493	382	12	.	.	PUNCT
ejpam-4493	382	13	.	.	PUNCT
ejpam-4493	383	1	,	,	PUNCT
ejpam-4493	383	2	vn−1	vn−1	ADJ
ejpam-4493	383	3	}	}	PUNCT
ejpam-4493	383	4	and	and	CCONJ
ejpam-4493	383	5	b2	b2	NOUN
ejpam-4493	383	6	=	=	SYM
ejpam-4493	383	7	{	{	PUNCT
ejpam-4493	383	8	v2	v2	PROPN
ejpam-4493	383	9	,	,	PUNCT
ejpam-4493	383	10	v4	v4	PROPN
ejpam-4493	383	11	,	,	PUNCT
ejpam-4493	383	12	v6	v6	NOUN
ejpam-4493	383	13	,	,	PUNCT
ejpam-4493	383	14	.	.	PUNCT
ejpam-4493	383	15	.	.	PUNCT
ejpam-4493	383	16	.	.	PUNCT
ejpam-4493	384	1	,	,	PUNCT
ejpam-4493	384	2	vn	vn	PROPN
ejpam-4493	384	3	}	}	PUNCT
ejpam-4493	384	4	are	be	AUX
ejpam-4493	384	5	the	the	DET
ejpam-4493	384	6	only	only	ADJ
ejpam-4493	384	7	coi	coi	NOUN
ejpam-4493	384	8	-	-	PUNCT
ejpam-4493	384	9	sets	set	NOUN
ejpam-4493	384	10	of	of	ADP
ejpam-4493	384	11	cn	cn	PROPN
ejpam-4493	384	12	with	with	ADP
ejpam-4493	384	13	v3	v3	PROPN
ejpam-4493	384	14	∈	∈	PROPN
ejpam-4493	384	15	b1	b1	PROPN
ejpam-4493	384	16	and	and	CCONJ
ejpam-4493	384	17	v3	v3	PROPN
ejpam-4493	384	18	/∈	/∈	PROPN
ejpam-4493	384	19	b2	b2	PROPN
ejpam-4493	384	20	.	.	PUNCT
ejpam-4493	385	1	thus	thus	ADV
ejpam-4493	385	2	,	,	PUNCT
ejpam-4493	385	3	by	by	ADP
ejpam-4493	385	4	remark	remark	NOUN
ejpam-4493	385	5	3(ii	3(ii	NUM
ejpam-4493	385	6	)	)	PUNCT
ejpam-4493	385	7	,	,	PUNCT
ejpam-4493	385	8	fcoi(b1	fcoi(b1	VERB
ejpam-4493	385	9	)	)	PUNCT
ejpam-4493	385	10	=	=	SYM
ejpam-4493	385	11	1	1	NUM
ejpam-4493	385	12	=	=	SYM
ejpam-4493	385	13	fcoi(cn	fcoi(cn	NOUN
ejpam-4493	385	14	)	)	PUNCT
ejpam-4493	385	15	.	.	PUNCT
ejpam-4493	386	1	next	next	ADV
ejpam-4493	386	2	,	,	PUNCT
ejpam-4493	386	3	suppose	suppose	VERB
ejpam-4493	386	4	that	that	SCONJ
ejpam-4493	386	5	n	n	PROPN
ejpam-4493	386	6	>	>	X
ejpam-4493	386	7	3	3	NUM
ejpam-4493	386	8	and	and	CCONJ
ejpam-4493	386	9	n	n	PRON
ejpam-4493	386	10	is	be	AUX
ejpam-4493	386	11	odd	odd	ADJ
ejpam-4493	386	12	.	.	PUNCT
ejpam-4493	387	1	then	then	ADV
ejpam-4493	387	2	q1	q1	VERB
ejpam-4493	387	3	=	=	SYM
ejpam-4493	387	4	{	{	PUNCT
ejpam-4493	387	5	v1	v1	PROPN
ejpam-4493	387	6	,	,	PUNCT
ejpam-4493	387	7	v3	v3	PROPN
ejpam-4493	387	8	,	,	PUNCT
ejpam-4493	387	9	v5	v5	PROPN
ejpam-4493	387	10	,	,	PUNCT
ejpam-4493	387	11	.	.	PUNCT
ejpam-4493	387	12	.	.	PUNCT
ejpam-4493	388	1	.	.	PUNCT
ejpam-4493	389	1	,	,	PUNCT
ejpam-4493	389	2	vn−2	vn−2	PROPN
ejpam-4493	389	3	,	,	PUNCT
ejpam-4493	389	4	vn	vn	NOUN
ejpam-4493	389	5	}	}	PUNCT
ejpam-4493	389	6	,	,	PUNCT
ejpam-4493	389	7	q2	q2	NOUN
ejpam-4493	389	8	=	=	SYM
ejpam-4493	389	9	{	{	PUNCT
ejpam-4493	389	10	v1	v1	PROPN
ejpam-4493	389	11	,	,	PUNCT
ejpam-4493	389	12	v3	v3	PROPN
ejpam-4493	389	13	,	,	PUNCT
ejpam-4493	389	14	v5	v5	PROPN
ejpam-4493	389	15	,	,	PUNCT
ejpam-4493	389	16	.	.	PUNCT
ejpam-4493	389	17	.	.	PUNCT
ejpam-4493	390	1	.	.	PUNCT
ejpam-4493	391	1	,	,	PUNCT
ejpam-4493	391	2	vn−2	vn−2	PROPN
ejpam-4493	391	3	,	,	PUNCT
ejpam-4493	391	4	vn−1	vn−1	ADJ
ejpam-4493	391	5	}	}	PUNCT
ejpam-4493	391	6	,	,	PUNCT
ejpam-4493	391	7	q3	q3	NOUN
ejpam-4493	391	8	=	=	PUNCT
ejpam-4493	391	9	{	{	PUNCT
ejpam-4493	391	10	v2	v2	PROPN
ejpam-4493	391	11	,	,	PUNCT
ejpam-4493	391	12	v4	v4	PROPN
ejpam-4493	391	13	,	,	PUNCT
ejpam-4493	391	14	v6	v6	NOUN
ejpam-4493	391	15	,	,	PUNCT
ejpam-4493	391	16	.	.	PUNCT
ejpam-4493	391	17	.	.	PUNCT
ejpam-4493	391	18	.	.	PUNCT
ejpam-4493	392	1	,	,	PUNCT
ejpam-4493	392	2	vn−1	vn−1	PROPN
ejpam-4493	392	3	,	,	PUNCT
ejpam-4493	392	4	vn	vn	NOUN
ejpam-4493	392	5	}	}	PUNCT
ejpam-4493	392	6	and	and	CCONJ
ejpam-4493	392	7	,	,	PUNCT
ejpam-4493	392	8	q4	q4	PROPN
ejpam-4493	392	9	=	=	PUNCT
ejpam-4493	392	10	{	{	PUNCT
ejpam-4493	392	11	v2	v2	PROPN
ejpam-4493	392	12	,	,	PUNCT
ejpam-4493	392	13	v4	v4	PROPN
ejpam-4493	392	14	,	,	PUNCT
ejpam-4493	392	15	v6	v6	NOUN
ejpam-4493	392	16	,	,	PUNCT
ejpam-4493	392	17	.	.	PUNCT
ejpam-4493	392	18	.	.	PUNCT
ejpam-4493	393	1	.	.	PUNCT
ejpam-4493	394	1	,	,	PUNCT
ejpam-4493	394	2	vn−1	vn−1	ADJ
ejpam-4493	394	3	,	,	PUNCT
ejpam-4493	394	4	v1	v1	NOUN
ejpam-4493	394	5	}	}	PUNCT
ejpam-4493	394	6	are	be	AUX
ejpam-4493	394	7	coi	coi	NOUN
ejpam-4493	394	8	-	-	PUNCT
ejpam-4493	394	9	sets	set	NOUN
ejpam-4493	394	10	of	of	ADP
ejpam-4493	394	11	cn	cn	PROPN
ejpam-4493	394	12	.	.	PUNCT
ejpam-4493	395	1	hence	hence	ADV
ejpam-4493	395	2	,	,	PUNCT
ejpam-4493	395	3	no	no	DET
ejpam-4493	395	4	vertex	vertex	NOUN
ejpam-4493	395	5	of	of	ADP
ejpam-4493	395	6	cn	cn	PROPN
ejpam-4493	395	7	is	be	AUX
ejpam-4493	395	8	contained	contain	VERB
ejpam-4493	395	9	in	in	ADP
ejpam-4493	395	10	a	a	DET
ejpam-4493	395	11	unique	unique	ADJ
ejpam-4493	395	12	coi	coi	NOUN
ejpam-4493	395	13	-	-	PUNCT
ejpam-4493	395	14	set	set	NOUN
ejpam-4493	395	15	.	.	PUNCT
ejpam-4493	396	1	thus	thus	ADV
ejpam-4493	396	2	,	,	PUNCT
ejpam-4493	396	3	fcoi(cn	fcoi(cn	NOUN
ejpam-4493	396	4	)	)	PUNCT
ejpam-4493	396	5	≥	≥	NOUN
ejpam-4493	396	6	2	2	NUM
ejpam-4493	396	7	.	.	PUNCT
ejpam-4493	397	1	clearly	clearly	ADV
ejpam-4493	397	2	,	,	PUNCT
ejpam-4493	397	3	{	{	PUNCT
ejpam-4493	397	4	v1	v1	NOUN
ejpam-4493	397	5	,	,	PUNCT
ejpam-4493	397	6	vn	vn	PROPN
ejpam-4493	397	7	}	}	PUNCT
ejpam-4493	397	8	is	be	AUX
ejpam-4493	397	9	uniquely	uniquely	ADV
ejpam-4493	397	10	contained	contain	VERB
ejpam-4493	397	11	in	in	ADP
ejpam-4493	397	12	q1	q1	PROPN
ejpam-4493	397	13	.	.	PUNCT
ejpam-4493	398	1	therefore	therefore	ADV
ejpam-4493	398	2	,	,	PUNCT
ejpam-4493	398	3	fcoi(q1	fcoi(q1	NOUN
ejpam-4493	398	4	)	)	PUNCT
ejpam-4493	398	5	=	=	SYM
ejpam-4493	398	6	2	2	NUM
ejpam-4493	398	7	=	=	SYM
ejpam-4493	398	8	fcoi(cn	fcoi(cn	NOUN
ejpam-4493	398	9	)	)	PUNCT
ejpam-4493	398	10	.	.	PUNCT
ejpam-4493	399	1	in	in	ADP
ejpam-4493	399	2	view	view	NOUN
ejpam-4493	399	3	of	of	ADP
ejpam-4493	399	4	theorem	theorem	NOUN
ejpam-4493	399	5	2	2	NUM
ejpam-4493	399	6	,	,	PUNCT
ejpam-4493	399	7	we	we	PRON
ejpam-4493	399	8	have	have	VERB
ejpam-4493	399	9	the	the	DET
ejpam-4493	399	10	following	follow	VERB
ejpam-4493	399	11	theorem	theorem	VERB
ejpam-4493	399	12	.	.	PUNCT
ejpam-4493	399	13	theorem	theorem	NOUN
ejpam-4493	399	14	8	8	NUM
ejpam-4493	399	15	.	.	PUNCT
ejpam-4493	400	1	let	let	VERB
ejpam-4493	400	2	g	g	PRON
ejpam-4493	400	3	be	be	AUX
ejpam-4493	400	4	a	a	DET
ejpam-4493	400	5	nontrivial	nontrivial	ADJ
ejpam-4493	400	6	connected	connect	VERB
ejpam-4493	400	7	graph	graph	NOUN
ejpam-4493	400	8	and	and	CCONJ
ejpam-4493	400	9	h	h	NOUN
ejpam-4493	400	10	be	be	AUX
ejpam-4493	400	11	any	any	DET
ejpam-4493	400	12	graph	graph	NOUN
ejpam-4493	400	13	.	.	PUNCT
ejpam-4493	401	1	a	a	DET
ejpam-4493	401	2	set	set	NOUN
ejpam-4493	401	3	s	s	NOUN
ejpam-4493	401	4	⊆	⊆	NUM
ejpam-4493	401	5	v	v	NOUN
ejpam-4493	401	6	(	(	PUNCT
ejpam-4493	401	7	g	g	PROPN
ejpam-4493	401	8	◦	◦	NOUN
ejpam-4493	401	9	h	h	NOUN
ejpam-4493	401	10	)	)	PUNCT
ejpam-4493	401	11	is	be	AUX
ejpam-4493	401	12	a	a	DET
ejpam-4493	401	13	connected	connected	ADJ
ejpam-4493	401	14	co	co	NOUN
ejpam-4493	401	15	-	-	ADJ
ejpam-4493	401	16	independent	independent	ADJ
ejpam-4493	401	17	hop	hop	NOUN
ejpam-4493	401	18	dominating	dominating	NOUN
ejpam-4493	401	19	set	set	NOUN
ejpam-4493	401	20	of	of	ADP
ejpam-4493	401	21	g	g	PROPN
ejpam-4493	401	22	◦	◦	NOUN
ejpam-4493	401	23	h	h	NOUN
ejpam-4493	401	24	if	if	SCONJ
ejpam-4493	402	1	and	and	CCONJ
ejpam-4493	402	2	only	only	ADV
ejpam-4493	402	3	if	if	SCONJ
ejpam-4493	402	4	s	s	VERB
ejpam-4493	402	5	=	=	SYM
ejpam-4493	402	6	v	v	X
ejpam-4493	402	7	(	(	PUNCT
ejpam-4493	402	8	g	g	NOUN
ejpam-4493	402	9	)	)	PUNCT
ejpam-4493	402	10	∪	∪	NOUN
ejpam-4493	402	11	(	(	PUNCT
ejpam-4493	402	12	⋃	⋃	ADJ
ejpam-4493	402	13	v∈v	v∈v	NOUN
ejpam-4493	402	14	(	(	PUNCT
ejpam-4493	402	15	g	g	NOUN
ejpam-4493	402	16	)	)	PUNCT
ejpam-4493	402	17	sv	sv	NOUN
ejpam-4493	402	18	)	)	PUNCT
ejpam-4493	402	19	where	where	SCONJ
ejpam-4493	402	20	sv	sv	PROPN
ejpam-4493	402	21	is	be	AUX
ejpam-4493	402	22	a	a	DET
ejpam-4493	402	23	co	co	ADJ
ejpam-4493	402	24	-	-	ADJ
ejpam-4493	402	25	independent	independent	ADJ
ejpam-4493	402	26	set	set	NOUN
ejpam-4493	402	27	of	of	ADP
ejpam-4493	402	28	hv	hv	PROPN
ejpam-4493	402	29	for	for	ADP
ejpam-4493	402	30	each	each	DET
ejpam-4493	402	31	v	v	NUM
ejpam-4493	402	32	∈	∈	PROPN
ejpam-4493	402	33	v	v	NOUN
ejpam-4493	402	34	(	(	PUNCT
ejpam-4493	402	35	g	g	NOUN
ejpam-4493	402	36	)	)	PUNCT
ejpam-4493	402	37	.	.	PUNCT
ejpam-4493	403	1	the	the	DET
ejpam-4493	403	2	next	next	ADJ
ejpam-4493	403	3	result	result	NOUN
ejpam-4493	403	4	is	be	AUX
ejpam-4493	403	5	a	a	DET
ejpam-4493	403	6	restatement	restatement	NOUN
ejpam-4493	403	7	of	of	ADP
ejpam-4493	403	8	corollary	corollary	ADJ
ejpam-4493	403	9	2	2	NUM
ejpam-4493	403	10	.	.	PUNCT
ejpam-4493	403	11	corollary	corollary	ADJ
ejpam-4493	403	12	6	6	NUM
ejpam-4493	403	13	.	.	PUNCT
ejpam-4493	404	1	let	let	VERB
ejpam-4493	404	2	g	g	PRON
ejpam-4493	404	3	be	be	AUX
ejpam-4493	404	4	a	a	DET
ejpam-4493	404	5	nontrivial	nontrivial	ADJ
ejpam-4493	404	6	connected	connect	VERB
ejpam-4493	404	7	graph	graph	NOUN
ejpam-4493	404	8	and	and	CCONJ
ejpam-4493	404	9	h	h	NOUN
ejpam-4493	404	10	be	be	AUX
ejpam-4493	404	11	any	any	DET
ejpam-4493	404	12	graph	graph	NOUN
ejpam-4493	404	13	.	.	PUNCT
ejpam-4493	405	1	a	a	DET
ejpam-4493	405	2	set	set	NOUN
ejpam-4493	405	3	s	s	NOUN
ejpam-4493	405	4	⊆	⊆	NUM
ejpam-4493	405	5	v	v	NOUN
ejpam-4493	405	6	(	(	PUNCT
ejpam-4493	405	7	g	g	PROPN
ejpam-4493	405	8	◦	◦	NOUN
ejpam-4493	405	9	h	h	NOUN
ejpam-4493	405	10	)	)	PUNCT
ejpam-4493	405	11	is	be	AUX
ejpam-4493	405	12	a	a	DET
ejpam-4493	405	13	γch	γch	NOUN
ejpam-4493	405	14	,	,	PUNCT
ejpam-4493	405	15	coi	coi	NOUN
ejpam-4493	405	16	-	-	PUNCT
ejpam-4493	405	17	set	set	NOUN
ejpam-4493	405	18	of	of	ADP
ejpam-4493	405	19	g	g	PROPN
ejpam-4493	405	20	◦	◦	NOUN
ejpam-4493	405	21	h	h	NOUN
ejpam-4493	405	22	if	if	SCONJ
ejpam-4493	406	1	and	and	CCONJ
ejpam-4493	406	2	only	only	ADV
ejpam-4493	406	3	if	if	SCONJ
ejpam-4493	406	4	s	s	VERB
ejpam-4493	406	5	=	=	SYM
ejpam-4493	406	6	v	v	X
ejpam-4493	406	7	(	(	PUNCT
ejpam-4493	406	8	g	g	NOUN
ejpam-4493	406	9	)	)	PUNCT
ejpam-4493	406	10	∪	∪	NOUN
ejpam-4493	406	11	(	(	PUNCT
ejpam-4493	406	12	⋃	⋃	ADJ
ejpam-4493	406	13	v∈v	v∈v	NOUN
ejpam-4493	406	14	(	(	PUNCT
ejpam-4493	406	15	g	g	NOUN
ejpam-4493	406	16	)	)	PUNCT
ejpam-4493	406	17	sv	sv	NOUN
ejpam-4493	406	18	)	)	PUNCT
ejpam-4493	406	19	where	where	SCONJ
ejpam-4493	406	20	sv	sv	PROPN
ejpam-4493	406	21	is	be	AUX
ejpam-4493	406	22	a	a	DET
ejpam-4493	406	23	coi	coi	NOUN
ejpam-4493	406	24	-	-	PUNCT
ejpam-4493	406	25	set	set	NOUN
ejpam-4493	406	26	of	of	ADP
ejpam-4493	406	27	hv	hv	PROPN
ejpam-4493	406	28	for	for	ADP
ejpam-4493	406	29	each	each	DET
ejpam-4493	406	30	v	v	NUM
ejpam-4493	406	31	∈	∈	PROPN
ejpam-4493	406	32	v	v	NOUN
ejpam-4493	406	33	(	(	PUNCT
ejpam-4493	406	34	g	g	NOUN
ejpam-4493	406	35	)	)	PUNCT
ejpam-4493	406	36	.	.	PUNCT
ejpam-4493	407	1	in	in	ADP
ejpam-4493	407	2	particular	particular	ADJ
ejpam-4493	407	3	,	,	PUNCT
ejpam-4493	407	4	γch	γch	NOUN
ejpam-4493	407	5	,	,	PUNCT
ejpam-4493	407	6	coi(g	coi(g	PROPN
ejpam-4493	407	7	◦	◦	NOUN
ejpam-4493	407	8	h	h	NOUN
ejpam-4493	407	9	)	)	PUNCT
ejpam-4493	407	10	=	=	SYM
ejpam-4493	407	11	|v	|v	PROPN
ejpam-4493	407	12	(	(	PUNCT
ejpam-4493	407	13	g)|	g)|	X
ejpam-4493	407	14	(	(	PUNCT
ejpam-4493	407	15	1	1	NUM
ejpam-4493	407	16	+	+	NUM
ejpam-4493	407	17	coi(h	coi(h	NOUN
ejpam-4493	407	18	)	)	PUNCT
ejpam-4493	407	19	)	)	PUNCT
ejpam-4493	407	20	.	.	PUNCT
ejpam-4493	408	1	theorem	theorem	ADJ
ejpam-4493	408	2	9	9	NUM
ejpam-4493	408	3	.	.	PUNCT
ejpam-4493	409	1	let	let	VERB
ejpam-4493	409	2	g	g	PRON
ejpam-4493	409	3	be	be	AUX
ejpam-4493	409	4	a	a	DET
ejpam-4493	409	5	nontrivial	nontrivial	ADJ
ejpam-4493	409	6	connected	connect	VERB
ejpam-4493	409	7	graph	graph	NOUN
ejpam-4493	409	8	of	of	ADP
ejpam-4493	409	9	order	order	NOUN
ejpam-4493	409	10	n	n	NOUN
ejpam-4493	410	1	and	and	CCONJ
ejpam-4493	410	2	h	h	NOUN
ejpam-4493	410	3	be	be	AUX
ejpam-4493	410	4	any	any	DET
ejpam-4493	410	5	graph	graph	NOUN
ejpam-4493	410	6	.	.	PUNCT
ejpam-4493	411	1	then	then	ADV
ejpam-4493	411	2	fγch	fγch	ADJ
ejpam-4493	411	3	,	,	PUNCT
ejpam-4493	411	4	coi(g	coi(g	PROPN
ejpam-4493	411	5	◦	◦	NOUN
ejpam-4493	411	6	h	h	NOUN
ejpam-4493	411	7	)	)	PUNCT
ejpam-4493	411	8	=	=	PRON
ejpam-4493	411	9	{	{	PUNCT
ejpam-4493	411	10	0	0	NUM
ejpam-4493	411	11	,	,	PUNCT
ejpam-4493	411	12	if	if	SCONJ
ejpam-4493	411	13	h	h	NOUN
ejpam-4493	411	14	has	have	VERB
ejpam-4493	411	15	a	a	DET
ejpam-4493	411	16	unique	unique	ADJ
ejpam-4493	411	17	coi	coi	NOUN
ejpam-4493	411	18	-	-	PUNCT
ejpam-4493	411	19	set	set	NOUN
ejpam-4493	411	20	,	,	PUNCT
ejpam-4493	411	21	n	n	CCONJ
ejpam-4493	411	22	[	[	PUNCT
ejpam-4493	411	23	fcoi(h	fcoi(h	PROPN
ejpam-4493	411	24	)	)	PUNCT
ejpam-4493	411	25	]	]	PUNCT
ejpam-4493	411	26	,	,	PUNCT
ejpam-4493	411	27	if	if	SCONJ
ejpam-4493	411	28	h	h	NOUN
ejpam-4493	411	29	has	have	VERB
ejpam-4493	411	30	no	no	DET
ejpam-4493	411	31	unique	unique	ADJ
ejpam-4493	411	32	coi	coi	NOUN
ejpam-4493	411	33	-	-	PUNCT
ejpam-4493	411	34	set	set	NOUN
ejpam-4493	411	35	.	.	PUNCT
ejpam-4493	412	1	proof	proof	NOUN
ejpam-4493	412	2	:	:	PUNCT
ejpam-4493	412	3	suppose	suppose	VERB
ejpam-4493	412	4	h	h	NOUN
ejpam-4493	412	5	has	have	VERB
ejpam-4493	412	6	a	a	DET
ejpam-4493	412	7	unique	unique	ADJ
ejpam-4493	412	8	coi	coi	NOUN
ejpam-4493	412	9	-set	-set	NOUN
ejpam-4493	412	10	.	.	PUNCT
ejpam-4493	413	1	for	for	ADP
ejpam-4493	413	2	each	each	DET
ejpam-4493	413	3	v	v	NUM
ejpam-4493	413	4	∈	∈	PROPN
ejpam-4493	413	5	v	v	NOUN
ejpam-4493	413	6	(	(	PUNCT
ejpam-4493	413	7	g	g	NOUN
ejpam-4493	413	8	)	)	PUNCT
ejpam-4493	413	9	,	,	PUNCT
ejpam-4493	413	10	let	let	VERB
ejpam-4493	413	11	pv	pv	PRON
ejpam-4493	413	12	⊆	⊆	NUM
ejpam-4493	413	13	v	v	NOUN
ejpam-4493	413	14	(	(	PUNCT
ejpam-4493	413	15	hv	hv	NOUN
ejpam-4493	413	16	)	)	PUNCT
ejpam-4493	413	17	be	be	VERB
ejpam-4493	413	18	the	the	DET
ejpam-4493	413	19	unique	unique	ADJ
ejpam-4493	413	20	coi	coi	NOUN
ejpam-4493	413	21	-set	-set	PUNCT
ejpam-4493	413	22	of	of	ADP
ejpam-4493	413	23	hv	hv	PROPN
ejpam-4493	413	24	.	.	PUNCT
ejpam-4493	414	1	by	by	ADP
ejpam-4493	414	2	corollary	corollary	ADJ
ejpam-4493	414	3	6	6	NUM
ejpam-4493	414	4	,	,	PUNCT
ejpam-4493	414	5	s	s	PART
ejpam-4493	414	6	=	=	SYM
ejpam-4493	414	7	v	v	X
ejpam-4493	414	8	(	(	PUNCT
ejpam-4493	414	9	g	g	NOUN
ejpam-4493	414	10	)	)	PUNCT
ejpam-4493	414	11	∪	∪	NOUN
ejpam-4493	414	12	(	(	PUNCT
ejpam-4493	414	13	⋃	⋃	ADJ
ejpam-4493	414	14	v∈v	v∈v	NOUN
ejpam-4493	414	15	(	(	PUNCT
ejpam-4493	414	16	g	g	NOUN
ejpam-4493	414	17	)	)	PUNCT
ejpam-4493	414	18	pv	pv	NOUN
ejpam-4493	414	19	)	)	PUNCT
ejpam-4493	414	20	is	be	AUX
ejpam-4493	414	21	the	the	DET
ejpam-4493	414	22	unique	unique	ADJ
ejpam-4493	414	23	γch	γch	NOUN
ejpam-4493	414	24	,	,	PUNCT
ejpam-4493	414	25	coi	coi	NOUN
ejpam-4493	414	26	-	-	PUNCT
ejpam-4493	414	27	set	set	NOUN
ejpam-4493	414	28	of	of	ADP
ejpam-4493	414	29	g	g	PROPN
ejpam-4493	414	30	◦	◦	PROPN
ejpam-4493	414	31	h.	h.	PROPN
ejpam-4493	414	32	thus	thus	ADV
ejpam-4493	414	33	,	,	PUNCT
ejpam-4493	414	34	by	by	ADP
ejpam-4493	414	35	remark	remark	NOUN
ejpam-4493	414	36	1(i	1(i	NUM
ejpam-4493	414	37	)	)	PUNCT
ejpam-4493	414	38	,	,	PUNCT
ejpam-4493	414	39	fγch	fγch	NOUN
ejpam-4493	414	40	,	,	PUNCT
ejpam-4493	414	41	coi(g	coi(g	PROPN
ejpam-4493	414	42	◦	◦	NOUN
ejpam-4493	414	43	h	h	NOUN
ejpam-4493	414	44	)	)	PUNCT
ejpam-4493	414	45	=	=	NOUN
ejpam-4493	415	1	0	0	X
ejpam-4493	415	2	.	.	PUNCT
ejpam-4493	416	1	on	on	ADP
ejpam-4493	416	2	the	the	DET
ejpam-4493	416	3	other	other	ADJ
ejpam-4493	416	4	hand	hand	NOUN
ejpam-4493	416	5	,	,	PUNCT
ejpam-4493	416	6	suppose	suppose	VERB
ejpam-4493	416	7	that	that	SCONJ
ejpam-4493	416	8	h	h	NOUN
ejpam-4493	416	9	does	do	AUX
ejpam-4493	416	10	not	not	PART
ejpam-4493	416	11	have	have	VERB
ejpam-4493	416	12	a	a	DET
ejpam-4493	416	13	unique	unique	ADJ
ejpam-4493	416	14	coi	coi	NOUN
ejpam-4493	416	15	-set	-set	NOUN
ejpam-4493	416	16	.	.	PUNCT
ejpam-4493	417	1	for	for	ADP
ejpam-4493	417	2	each	each	DET
ejpam-4493	417	3	v	v	NUM
ejpam-4493	417	4	∈	∈	PROPN
ejpam-4493	417	5	v	v	NOUN
ejpam-4493	417	6	(	(	PUNCT
ejpam-4493	417	7	g	g	NOUN
ejpam-4493	417	8	)	)	PUNCT
ejpam-4493	417	9	,	,	PUNCT
ejpam-4493	417	10	let	let	VERB
ejpam-4493	417	11	qv	qv	PRON
ejpam-4493	417	12	⊆	⊆	NUM
ejpam-4493	417	13	v	v	ADP
ejpam-4493	417	14	(	(	PUNCT
ejpam-4493	417	15	hv	hv	NOUN
ejpam-4493	417	16	)	)	PUNCT
ejpam-4493	417	17	be	be	VERB
ejpam-4493	417	18	a	a	DET
ejpam-4493	417	19	coi	coi	NOUN
ejpam-4493	417	20	-set	-set	PUNCT
ejpam-4493	417	21	of	of	ADP
ejpam-4493	417	22	hv	hv	PROPN
ejpam-4493	417	23	with	with	ADP
ejpam-4493	417	24	fcoi(hv	fcoi(hv	PROPN
ejpam-4493	417	25	)	)	PUNCT
ejpam-4493	417	26	=	=	SYM
ejpam-4493	417	27	fcoi(qv	fcoi(qv	NOUN
ejpam-4493	417	28	)	)	PUNCT
ejpam-4493	417	29	,	,	PUNCT
ejpam-4493	417	30	and	and	CCONJ
ejpam-4493	417	31	let	let	VERB
ejpam-4493	417	32	pqv	pqv	PROPN
ejpam-4493	417	33	⊆	⊆	NUM
ejpam-4493	417	34	qv	qv	INTJ
ejpam-4493	417	35	be	be	AUX
ejpam-4493	417	36	a	a	DET
ejpam-4493	417	37	forcing	forcing	NOUN
ejpam-4493	417	38	subset	subset	NOUN
ejpam-4493	417	39	for	for	ADP
ejpam-4493	417	40	qv	qv	INTJ
ejpam-4493	417	41	with	with	ADP
ejpam-4493	417	42	fcoi(qv	fcoi(qv	NOUN
ejpam-4493	417	43	)	)	PUNCT
ejpam-4493	417	44	=	=	SYM
ejpam-4493	418	1	|pqv	|pqv	PROPN
ejpam-4493	418	2	|	|	NOUN
ejpam-4493	418	3	.	.	PUNCT
ejpam-4493	419	1	then	then	ADV
ejpam-4493	419	2	by	by	ADP
ejpam-4493	419	3	corollary	corollary	ADJ
ejpam-4493	419	4	6	6	NUM
ejpam-4493	419	5	,	,	PUNCT
ejpam-4493	419	6	sq	sq	NOUN
ejpam-4493	419	7	=	=	PROPN
ejpam-4493	419	8	v	v	NOUN
ejpam-4493	419	9	(	(	PUNCT
ejpam-4493	419	10	g)∪	g)∪	VERB
ejpam-4493	419	11	(	(	PUNCT
ejpam-4493	419	12	⋃	⋃	ADJ
ejpam-4493	419	13	v∈v	v∈v	NOUN
ejpam-4493	419	14	(	(	PUNCT
ejpam-4493	419	15	g	g	NOUN
ejpam-4493	419	16	)	)	PUNCT
ejpam-4493	419	17	qv	qv	NOUN
ejpam-4493	419	18	)	)	PUNCT
ejpam-4493	419	19	is	be	AUX
ejpam-4493	419	20	a	a	DET
ejpam-4493	419	21	γch	γch	NOUN
ejpam-4493	419	22	,	,	PUNCT
ejpam-4493	419	23	coi	coi	NOUN
ejpam-4493	419	24	-	-	PUNCT
ejpam-4493	419	25	set	set	NOUN
ejpam-4493	419	26	of	of	ADP
ejpam-4493	419	27	g	g	PROPN
ejpam-4493	419	28	◦	◦	NOUN
ejpam-4493	419	29	h.	h.	NOUN
ejpam-4493	419	30	let	let	VERB
ejpam-4493	419	31	c	c	NOUN
ejpam-4493	419	32	=	=	PUNCT
ejpam-4493	419	33	⋃	⋃	NOUN
ejpam-4493	419	34	v∈v	v∈v	NOUN
ejpam-4493	419	35	(	(	PUNCT
ejpam-4493	419	36	g	g	NOUN
ejpam-4493	419	37	)	)	PUNCT
ejpam-4493	419	38	pqv	pqv	NOUN
ejpam-4493	419	39	.	.	PUNCT
ejpam-4493	420	1	then	then	ADV
ejpam-4493	420	2	c	c	PROPN
ejpam-4493	420	3	is	be	AUX
ejpam-4493	420	4	a	a	DET
ejpam-4493	420	5	forcing	forcing	NOUN
ejpam-4493	420	6	subset	subset	NOUN
ejpam-4493	420	7	for	for	ADP
ejpam-4493	420	8	sq	sq	PROPN
ejpam-4493	420	9	.	.	PROPN
ejpam-4493	420	10	thus	thus	ADV
ejpam-4493	420	11	,	,	PUNCT
ejpam-4493	420	12	fγch	fγch	ADJ
ejpam-4493	420	13	,	,	PUNCT
ejpam-4493	420	14	coi(g	coi(g	PROPN
ejpam-4493	420	15	◦	◦	NOUN
ejpam-4493	420	16	h	h	NOUN
ejpam-4493	420	17	)	)	PUNCT
ejpam-4493	420	18	≤	≤	NOUN
ejpam-4493	420	19	fγch	fγch	NOUN
ejpam-4493	420	20	,	,	PUNCT
ejpam-4493	420	21	coi(sq	coi(sq	NOUN
ejpam-4493	420	22	)	)	PUNCT
ejpam-4493	420	23	≤	≤	NOUN
ejpam-4493	420	24	|c|	|c|	PROPN
ejpam-4493	420	25	=	=	SYM
ejpam-4493	420	26	n	n	CCONJ
ejpam-4493	420	27	[	[	PUNCT
ejpam-4493	420	28	fcoi(h	fcoi(h	PROPN
ejpam-4493	420	29	)	)	PUNCT
ejpam-4493	420	30	]	]	PUNCT
ejpam-4493	420	31	.	.	PUNCT
ejpam-4493	421	1	references	reference	NOUN
ejpam-4493	421	2	1660	1660	NUM
ejpam-4493	421	3	next	next	ADV
ejpam-4493	421	4	,	,	PUNCT
ejpam-4493	421	5	let	let	VERB
ejpam-4493	421	6	s′	s′	NOUN
ejpam-4493	421	7	be	be	AUX
ejpam-4493	421	8	a	a	DET
ejpam-4493	421	9	γch	γch	NOUN
ejpam-4493	421	10	,	,	PUNCT
ejpam-4493	421	11	coi	coi	NOUN
ejpam-4493	421	12	-	-	PUNCT
ejpam-4493	421	13	set	set	NOUN
ejpam-4493	421	14	of	of	ADP
ejpam-4493	421	15	g	g	PROPN
ejpam-4493	421	16	◦	◦	NOUN
ejpam-4493	421	17	h	h	NOUN
ejpam-4493	421	18	such	such	ADJ
ejpam-4493	421	19	that	that	DET
ejpam-4493	421	20	fγch	fγch	NOUN
ejpam-4493	421	21	,	,	PUNCT
ejpam-4493	421	22	coi(g	coi(g	PROPN
ejpam-4493	421	23	◦	◦	NOUN
ejpam-4493	421	24	h	h	NOUN
ejpam-4493	421	25	)	)	PUNCT
ejpam-4493	422	1	=	=	SYM
ejpam-4493	422	2	fγch	fγch	PROPN
ejpam-4493	422	3	,	,	PUNCT
ejpam-4493	422	4	coi(s	coi(s	PROPN
ejpam-4493	422	5	′	′	NUM
ejpam-4493	422	6	)	)	PUNCT
ejpam-4493	422	7	.	.	PUNCT
ejpam-4493	423	1	then	then	ADV
ejpam-4493	423	2	by	by	ADP
ejpam-4493	423	3	corollary	corollary	ADJ
ejpam-4493	423	4	6	6	NUM
ejpam-4493	423	5	,	,	PUNCT
ejpam-4493	423	6	let	let	VERB
ejpam-4493	423	7	s′	s′	ADJ
ejpam-4493	423	8	=	=	SYM
ejpam-4493	423	9	v	v	ADJ
ejpam-4493	423	10	(	(	PUNCT
ejpam-4493	423	11	g	g	NOUN
ejpam-4493	423	12	)	)	PUNCT
ejpam-4493	423	13	∪	∪	NOUN
ejpam-4493	423	14	(	(	PUNCT
ejpam-4493	423	15	⋃	⋃	ADJ
ejpam-4493	423	16	v∈v	v∈v	NOUN
ejpam-4493	423	17	(	(	PUNCT
ejpam-4493	423	18	g	g	NOUN
ejpam-4493	423	19	)	)	PUNCT
ejpam-4493	423	20	rv	rv	PROPN
ejpam-4493	423	21	)	)	PUNCT
ejpam-4493	423	22	where	where	SCONJ
ejpam-4493	423	23	rv	rv	PROPN
ejpam-4493	423	24	is	be	AUX
ejpam-4493	423	25	a	a	DET
ejpam-4493	423	26	coi	coi	NOUN
ejpam-4493	423	27	-set	-set	PUNCT
ejpam-4493	423	28	of	of	ADP
ejpam-4493	423	29	hv	hv	PROPN
ejpam-4493	423	30	for	for	ADP
ejpam-4493	423	31	each	each	DET
ejpam-4493	423	32	v	v	NUM
ejpam-4493	423	33	∈	∈	PROPN
ejpam-4493	423	34	v	v	NOUN
ejpam-4493	423	35	(	(	PUNCT
ejpam-4493	423	36	g	g	NOUN
ejpam-4493	423	37	)	)	PUNCT
ejpam-4493	423	38	.	.	PUNCT
ejpam-4493	424	1	let	let	VERB
ejpam-4493	424	2	c	c	NOUN
ejpam-4493	424	3	′	′	VERB
ejpam-4493	424	4	be	be	AUX
ejpam-4493	424	5	a	a	DET
ejpam-4493	424	6	forcing	forcing	NOUN
ejpam-4493	424	7	subset	subset	NOUN
ejpam-4493	424	8	for	for	ADP
ejpam-4493	424	9	s′	s′	NUM
ejpam-4493	424	10	such	such	ADJ
ejpam-4493	424	11	that	that	DET
ejpam-4493	424	12	fγch	fγch	NOUN
ejpam-4493	424	13	,	,	PUNCT
ejpam-4493	424	14	coi(s	coi(s	PROPN
ejpam-4493	424	15	′	′	NUM
ejpam-4493	424	16	)	)	PUNCT
ejpam-4493	425	1	=	=	PRON
ejpam-4493	425	2	|c	|c	VERB
ejpam-4493	425	3	′|	′|	PROPN
ejpam-4493	425	4	.	.	PUNCT
ejpam-4493	425	5	suppose	suppose	VERB
ejpam-4493	425	6	that	that	SCONJ
ejpam-4493	425	7	there	there	PRON
ejpam-4493	425	8	exists	exist	VERB
ejpam-4493	425	9	w	w	PROPN
ejpam-4493	425	10	∈	∈	PROPN
ejpam-4493	425	11	v	v	ADP
ejpam-4493	425	12	(	(	PUNCT
ejpam-4493	425	13	g	g	NOUN
ejpam-4493	425	14	)	)	PUNCT
ejpam-4493	425	15	such	such	ADJ
ejpam-4493	425	16	that	that	SCONJ
ejpam-4493	425	17	c	c	NOUN
ejpam-4493	425	18	′	′	NUM
ejpam-4493	425	19	∩rw	∩rw	NOUN
ejpam-4493	425	20	=	=	SYM
ejpam-4493	425	21	cw	cw	NOUN
ejpam-4493	425	22	is	be	AUX
ejpam-4493	425	23	not	not	PART
ejpam-4493	425	24	a	a	DET
ejpam-4493	425	25	forcing	forcing	NOUN
ejpam-4493	425	26	subset	subset	NOUN
ejpam-4493	425	27	for	for	ADP
ejpam-4493	425	28	rw	rw	NOUN
ejpam-4493	425	29	.	.	PUNCT
ejpam-4493	426	1	let	let	VERB
ejpam-4493	426	2	r	r	PRON
ejpam-4493	426	3	′	′	AUX
ejpam-4493	426	4	w	w	AUX
ejpam-4493	426	5	be	be	AUX
ejpam-4493	426	6	a	a	DET
ejpam-4493	426	7	coi	coi	NOUN
ejpam-4493	426	8	-set	-set	PUNCT
ejpam-4493	426	9	of	of	ADP
ejpam-4493	426	10	hw	hw	PRON
ejpam-4493	426	11	with	with	ADP
ejpam-4493	426	12	r	r	NOUN
ejpam-4493	426	13	′	′	NUM
ejpam-4493	426	14	w	w	NOUN
ejpam-4493	426	15	̸=	̸=	PROPN
ejpam-4493	426	16	rw	rw	NOUN
ejpam-4493	426	17	.	.	PUNCT
ejpam-4493	427	1	then	then	ADV
ejpam-4493	427	2	s′′	s′′	PROPN
ejpam-4493	427	3	=	=	SYM
ejpam-4493	427	4	v	v	PROPN
ejpam-4493	427	5	(	(	PUNCT
ejpam-4493	427	6	g	g	NOUN
ejpam-4493	427	7	)	)	PUNCT
ejpam-4493	427	8	∪	∪	NOUN
ejpam-4493	427	9	(	(	PUNCT
ejpam-4493	427	10	⋃	⋃	NOUN
ejpam-4493	427	11	v∈v	v∈v	NOUN
ejpam-4493	427	12	(	(	PUNCT
ejpam-4493	427	13	g)\{w	g)\{w	NOUN
ejpam-4493	427	14	}	}	PUNCT
ejpam-4493	427	15	rv	rv	PROPN
ejpam-4493	427	16	)	)	PUNCT
ejpam-4493	427	17	∪r	∪r	PUNCT
ejpam-4493	428	1	′	′	NUM
ejpam-4493	429	1	w	w	NOUN
ejpam-4493	429	2	is	be	AUX
ejpam-4493	429	3	a	a	DET
ejpam-4493	429	4	γch	γch	NOUN
ejpam-4493	429	5	,	,	PUNCT
ejpam-4493	429	6	coi	coi	NOUN
ejpam-4493	429	7	-	-	PUNCT
ejpam-4493	429	8	set	set	NOUN
ejpam-4493	429	9	of	of	ADP
ejpam-4493	429	10	g	g	PROPN
ejpam-4493	429	11	◦	◦	NOUN
ejpam-4493	429	12	h	h	NOUN
ejpam-4493	429	13	with	with	ADP
ejpam-4493	429	14	s′	s′	ADJ
ejpam-4493	429	15	̸=	̸=	PROPN
ejpam-4493	429	16	s′′	s′′	PROPN
ejpam-4493	429	17	and	and	CCONJ
ejpam-4493	429	18	c	c	NOUN
ejpam-4493	429	19	′	′	NOUN
ejpam-4493	429	20	⊆	⊆	NUM
ejpam-4493	429	21	s′′	s′′	PROPN
ejpam-4493	429	22	,	,	PUNCT
ejpam-4493	429	23	a	a	DET
ejpam-4493	429	24	contradiction	contradiction	NOUN
ejpam-4493	429	25	.	.	PUNCT
ejpam-4493	430	1	thus	thus	ADV
ejpam-4493	430	2	,	,	PUNCT
ejpam-4493	430	3	sv	sv	PROPN
ejpam-4493	430	4	=	=	SYM
ejpam-4493	430	5	c	c	NOUN
ejpam-4493	430	6	′	′	NOUN
ejpam-4493	431	1	∩rv	∩rv	NOUN
ejpam-4493	431	2	is	be	AUX
ejpam-4493	431	3	a	a	DET
ejpam-4493	431	4	forcing	forcing	NOUN
ejpam-4493	431	5	subset	subset	NOUN
ejpam-4493	431	6	for	for	ADP
ejpam-4493	431	7	rv	rv	PROPN
ejpam-4493	431	8	for	for	ADP
ejpam-4493	431	9	each	each	DET
ejpam-4493	431	10	v	v	NUM
ejpam-4493	431	11	∈	∈	PROPN
ejpam-4493	431	12	v	v	NOUN
ejpam-4493	431	13	(	(	PUNCT
ejpam-4493	431	14	g	g	NOUN
ejpam-4493	431	15	)	)	PUNCT
ejpam-4493	431	16	.	.	PUNCT
ejpam-4493	432	1	let	let	VERB
ejpam-4493	432	2	s0	s0	PROPN
ejpam-4493	432	3	=	=	PUNCT
ejpam-4493	432	4	⋃	⋃	PROPN
ejpam-4493	432	5	v∈v	v∈v	NOUN
ejpam-4493	432	6	(	(	PUNCT
ejpam-4493	432	7	g	g	NOUN
ejpam-4493	432	8	)	)	PUNCT
ejpam-4493	432	9	sv	sv	PROPN
ejpam-4493	432	10	.	.	PUNCT
ejpam-4493	433	1	then	then	ADV
ejpam-4493	433	2	fγch	fγch	ADJ
ejpam-4493	433	3	,	,	PUNCT
ejpam-4493	433	4	coi(g	coi(g	PROPN
ejpam-4493	433	5	◦	◦	NOUN
ejpam-4493	433	6	h	h	NOUN
ejpam-4493	433	7	)	)	PUNCT
ejpam-4493	433	8	=	=	NOUN
ejpam-4493	433	9	|c	|c	VERB
ejpam-4493	433	10	′|	′|	NUM
ejpam-4493	433	11	≥	≥	NOUN
ejpam-4493	433	12	|s0|	|s0|	NOUN
ejpam-4493	433	13	=	=	SYM
ejpam-4493	433	14	∑	∑	PUNCT
ejpam-4493	433	15	v∈v	v∈v	PROPN
ejpam-4493	433	16	(	(	PUNCT
ejpam-4493	433	17	g	g	NOUN
ejpam-4493	433	18	)	)	PUNCT
ejpam-4493	433	19	|sv|	|sv|	PROPN
ejpam-4493	433	20	≥	≥	PROPN
ejpam-4493	433	21	∑	∑	PUNCT
ejpam-4493	433	22	v∈v	v∈v	PROPN
ejpam-4493	433	23	(	(	PUNCT
ejpam-4493	433	24	g	g	NOUN
ejpam-4493	433	25	)	)	PUNCT
ejpam-4493	433	26	fcoi(hv	fcoi(hv	ADJ
ejpam-4493	433	27	)	)	PUNCT
ejpam-4493	434	1	=	=	SYM
ejpam-4493	434	2	|v	|v	PROPN
ejpam-4493	434	3	(	(	PUNCT
ejpam-4493	434	4	g)|fcoi(h	g)|fcoi(h	PROPN
ejpam-4493	434	5	)	)	PUNCT
ejpam-4493	434	6	.	.	PUNCT
ejpam-4493	435	1	therefore	therefore	ADV
ejpam-4493	435	2	,	,	PUNCT
ejpam-4493	435	3	fγch	fγch	ADJ
ejpam-4493	435	4	,	,	PUNCT
ejpam-4493	435	5	coi(g	coi(g	PROPN
ejpam-4493	435	6	◦	◦	NOUN
ejpam-4493	435	7	h	h	NOUN
ejpam-4493	435	8	)	)	PUNCT
ejpam-4493	435	9	=	=	SYM
ejpam-4493	436	1	n	n	CCONJ
ejpam-4493	436	2	[	[	PUNCT
ejpam-4493	436	3	fcoi(h	fcoi(h	PROPN
ejpam-4493	436	4	)	)	PUNCT
ejpam-4493	436	5	]	]	PUNCT
ejpam-4493	436	6	.	.	PUNCT
ejpam-4493	437	1	example	example	NOUN
ejpam-4493	438	1	4	4	X
ejpam-4493	438	2	.	.	PUNCT
ejpam-4493	438	3	let	let	VERB
ejpam-4493	438	4	g	g	PROPN
ejpam-4493	438	5	=	=	SYM
ejpam-4493	438	6	k2	k2	ADJ
ejpam-4493	438	7	andh	andh	NOUN
ejpam-4493	438	8	=	=	SYM
ejpam-4493	438	9	p5	p5	PROPN
ejpam-4493	438	10	.	.	PUNCT
ejpam-4493	439	1	since	since	SCONJ
ejpam-4493	439	2	p5	p5	PROPN
ejpam-4493	439	3	has	have	VERB
ejpam-4493	439	4	a	a	DET
ejpam-4493	439	5	unique	unique	ADJ
ejpam-4493	439	6	coi	coi	NOUN
ejpam-4493	439	7	-	-	PUNCT
ejpam-4493	439	8	set	set	NOUN
ejpam-4493	439	9	,	,	PUNCT
ejpam-4493	439	10	fγch	fγch	NOUN
ejpam-4493	439	11	,	,	PUNCT
ejpam-4493	439	12	coi(k2	coi(k2	NOUN
ejpam-4493	439	13	◦	◦	NOUN
ejpam-4493	439	14	p5	p5	ADJ
ejpam-4493	439	15	)	)	PUNCT
ejpam-4493	439	16	=	=	SYM
ejpam-4493	439	17	0	0	X
ejpam-4493	439	18	.	.	NOUN
ejpam-4493	439	19	example	example	NOUN
ejpam-4493	440	1	5	5	NUM
ejpam-4493	440	2	.	.	PUNCT
ejpam-4493	441	1	let	let	VERB
ejpam-4493	441	2	g	g	PROPN
ejpam-4493	441	3	=	=	PROPN
ejpam-4493	441	4	c3	c3	PROPN
ejpam-4493	441	5	and	and	CCONJ
ejpam-4493	441	6	h	h	NOUN
ejpam-4493	441	7	=	=	NOUN
ejpam-4493	441	8	p4	p4	ADJ
ejpam-4493	441	9	.	.	PUNCT
ejpam-4493	442	1	since	since	SCONJ
ejpam-4493	442	2	p4	p4	NOUN
ejpam-4493	442	3	has	have	VERB
ejpam-4493	442	4	no	no	DET
ejpam-4493	442	5	unique	unique	ADJ
ejpam-4493	442	6	coi	coi	NOUN
ejpam-4493	442	7	-	-	PUNCT
ejpam-4493	442	8	sets	set	NOUN
ejpam-4493	442	9	,	,	PUNCT
ejpam-4493	442	10	fγch	fγch	ADJ
ejpam-4493	442	11	,	,	PUNCT
ejpam-4493	442	12	coi(c3	coi(c3	ADJ
ejpam-4493	442	13	◦	◦	NOUN
ejpam-4493	442	14	p4	p4	ADJ
ejpam-4493	442	15	)	)	PUNCT
ejpam-4493	442	16	=	=	SYM
ejpam-4493	442	17	3	3	NUM
ejpam-4493	442	18	[	[	PUNCT
ejpam-4493	442	19	fcoi(p4	fcoi(p4	NOUN
ejpam-4493	442	20	)	)	PUNCT
ejpam-4493	442	21	]	]	PUNCT
ejpam-4493	443	1	=	=	SYM
ejpam-4493	443	2	3	3	X
ejpam-4493	443	3	·	·	SYM
ejpam-4493	443	4	1	1	NUM
ejpam-4493	443	5	=	=	SYM
ejpam-4493	443	6	3	3	X
ejpam-4493	443	7	.	.	PUNCT
ejpam-4493	443	8	acknowledgements	acknowledgement	NOUN
ejpam-4493	443	9	the	the	DET
ejpam-4493	443	10	authors	author	NOUN
ejpam-4493	443	11	would	would	AUX
ejpam-4493	443	12	like	like	VERB
ejpam-4493	443	13	to	to	PART
ejpam-4493	443	14	express	express	VERB
ejpam-4493	443	15	their	their	PRON
ejpam-4493	443	16	gratitude	gratitude	NOUN
ejpam-4493	443	17	to	to	ADP
ejpam-4493	443	18	the	the	DET
ejpam-4493	443	19	referees	referee	NOUN
ejpam-4493	443	20	for	for	ADP
ejpam-4493	443	21	their	their	PRON
ejpam-4493	443	22	insightful	insightful	ADJ
ejpam-4493	443	23	comments	comment	NOUN
ejpam-4493	443	24	and	and	CCONJ
ejpam-4493	443	25	suggestions	suggestion	NOUN
ejpam-4493	443	26	,	,	PUNCT
ejpam-4493	443	27	which	which	PRON
ejpam-4493	443	28	significantly	significantly	ADV
ejpam-4493	443	29	improved	improve	VERB
ejpam-4493	443	30	the	the	DET
ejpam-4493	443	31	paper	paper	NOUN
ejpam-4493	443	32	.	.	PUNCT
ejpam-4493	444	1	the	the	DET
ejpam-4493	444	2	authors	author	NOUN
ejpam-4493	444	3	would	would	AUX
ejpam-4493	444	4	also	also	ADV
ejpam-4493	444	5	like	like	VERB
ejpam-4493	444	6	to	to	PART
ejpam-4493	444	7	thank	thank	VERB
ejpam-4493	444	8	the	the	DET
ejpam-4493	444	9	following	follow	VERB
ejpam-4493	444	10	funding	funding	NOUN
ejpam-4493	444	11	agencies	agency	NOUN
ejpam-4493	444	12	:	:	PUNCT
ejpam-4493	444	13	mindanao	mindanao	PROPN
ejpam-4493	444	14	state	state	PROPN
ejpam-4493	444	15	university	university	PROPN
ejpam-4493	444	16	iligan	iligan	PROPN
ejpam-4493	444	17	institute	institute	PROPN
ejpam-4493	444	18	of	of	ADP
ejpam-4493	444	19	technology	technology	PROPN
ejpam-4493	444	20	(	(	PUNCT
ejpam-4493	444	21	msu	msu	PROPN
ejpam-4493	444	22	-	-	PUNCT
ejpam-4493	444	23	iit	iit	NOUN
ejpam-4493	444	24	)	)	PUNCT
ejpam-4493	444	25	and	and	CCONJ
ejpam-4493	444	26	the	the	DET
ejpam-4493	444	27	department	department	NOUN
ejpam-4493	444	28	of	of	ADP
ejpam-4493	444	29	science	science	NOUN
ejpam-4493	444	30	and	and	CCONJ
ejpam-4493	444	31	technology	technology	NOUN
ejpam-4493	444	32	accelerated	accelerate	VERB
ejpam-4493	444	33	science	science	NOUN
ejpam-4493	444	34	and	and	CCONJ
ejpam-4493	444	35	technology	technology	NOUN
ejpam-4493	444	36	human	human	ADJ
ejpam-4493	444	37	resource	resource	NOUN
ejpam-4493	444	38	development	development	NOUN
ejpam-4493	444	39	program	program	NOUN
ejpam-4493	444	40	(	(	PUNCT
ejpam-4493	444	41	dostasthrdp	dostasthrdp	PROPN
ejpam-4493	444	42	)	)	PUNCT
ejpam-4493	444	43	,	,	PUNCT
ejpam-4493	444	44	philippines	philippine	NOUN
ejpam-4493	444	45	.	.	PUNCT
ejpam-4493	445	1	references	reference	NOUN
ejpam-4493	445	2	[	[	X
ejpam-4493	445	3	1	1	NUM
ejpam-4493	445	4	]	]	X
ejpam-4493	445	5	c.	c.	PROPN
ejpam-4493	445	6	armada	armada	PROPN
ejpam-4493	445	7	and	and	CCONJ
ejpam-4493	445	8	s.	s.	PROPN
ejpam-4493	445	9	canoy	canoy	PROPN
ejpam-4493	445	10	jr	jr	PROPN
ejpam-4493	445	11	.	.	PUNCT
ejpam-4493	446	1	forcing	force	VERB
ejpam-4493	446	2	independent	independent	ADJ
ejpam-4493	446	3	domination	domination	NOUN
ejpam-4493	446	4	number	number	NOUN
ejpam-4493	446	5	of	of	ADP
ejpam-4493	446	6	a	a	DET
ejpam-4493	446	7	graph	graph	NOUN
ejpam-4493	446	8	.	.	PUNCT
ejpam-4493	447	1	european	european	ADJ
ejpam-4493	447	2	journal	journal	PROPN
ejpam-4493	447	3	of	of	ADP
ejpam-4493	447	4	pure	pure	ADJ
ejpam-4493	447	5	and	and	CCONJ
ejpam-4493	447	6	applied	applied	ADJ
ejpam-4493	447	7	mathematics	mathematic	NOUN
ejpam-4493	447	8	,	,	PUNCT
ejpam-4493	447	9	12(4):1371–1381	12(4):1371–1381	NUM
ejpam-4493	447	10	,	,	PUNCT
ejpam-4493	447	11	2019	2019	NUM
ejpam-4493	447	12	.	.	PUNCT
ejpam-4493	448	1	[	[	X
ejpam-4493	448	2	2	2	NUM
ejpam-4493	448	3	]	]	PUNCT
ejpam-4493	448	4	c.	c.	PROPN
ejpam-4493	448	5	armadaa	armadaa	PROPN
ejpam-4493	448	6	,	,	PUNCT
ejpam-4493	448	7	s.	s.	PROPN
ejpam-4493	448	8	canoy	canoy	PROPN
ejpam-4493	448	9	jr	jr	PROPN
ejpam-4493	448	10	.	.	PROPN
ejpam-4493	448	11	,	,	PUNCT
ejpam-4493	448	12	and	and	CCONJ
ejpam-4493	448	13	c.	c.	PROPN
ejpam-4493	448	14	go	go	VERB
ejpam-4493	448	15	.	.	PUNCT
ejpam-4493	449	1	forcing	force	VERB
ejpam-4493	449	2	domination	domination	NOUN
ejpam-4493	449	3	numbers	number	NOUN
ejpam-4493	449	4	of	of	ADP
ejpam-4493	449	5	graphs	graph	NOUN
ejpam-4493	449	6	under	under	ADP
ejpam-4493	449	7	some	some	DET
ejpam-4493	449	8	binary	binary	ADJ
ejpam-4493	449	9	operations	operation	NOUN
ejpam-4493	449	10	.	.	PUNCT
ejpam-4493	450	1	advances	advance	NOUN
ejpam-4493	450	2	and	and	CCONJ
ejpam-4493	450	3	applications	application	NOUN
ejpam-4493	450	4	in	in	ADP
ejpam-4493	450	5	discrete	discrete	ADJ
ejpam-4493	450	6	mathematics	mathematic	NOUN
ejpam-4493	450	7	,	,	PUNCT
ejpam-4493	450	8	19(3):213–228	19(3):213–228	NUM
ejpam-4493	450	9	,	,	PUNCT
ejpam-4493	450	10	2018	2018	NUM
ejpam-4493	450	11	.	.	PUNCT
ejpam-4493	451	1	[	[	X
ejpam-4493	451	2	3	3	X
ejpam-4493	451	3	]	]	X
ejpam-4493	451	4	s.	s.	PROPN
ejpam-4493	451	5	ayyaswamya	ayyaswamya	PROPN
ejpam-4493	451	6	,	,	PUNCT
ejpam-4493	451	7	b.	b.	PROPN
ejpam-4493	451	8	krishnakumaria	krishnakumaria	PROPN
ejpam-4493	451	9	,	,	PUNCT
ejpam-4493	451	10	c.	c.	PROPN
ejpam-4493	451	11	natarajan	natarajan	PROPN
ejpam-4493	451	12	,	,	PUNCT
ejpam-4493	451	13	and	and	CCONJ
ejpam-4493	451	14	y.b	y.b	PROPN
ejpam-4493	451	15	.	.	PROPN
ejpam-4493	451	16	venkatakrishman	venkatakrishman	NOUN
ejpam-4493	451	17	.	.	PUNCT
ejpam-4493	452	1	bounds	bound	NOUN
ejpam-4493	452	2	on	on	ADP
ejpam-4493	452	3	the	the	DET
ejpam-4493	452	4	hop	hop	NOUN
ejpam-4493	452	5	domination	domination	NOUN
ejpam-4493	452	6	number	number	NOUN
ejpam-4493	452	7	of	of	ADP
ejpam-4493	452	8	a	a	DET
ejpam-4493	452	9	tree	tree	NOUN
ejpam-4493	452	10	.	.	PUNCT
ejpam-4493	453	1	proc	proc	NOUN
ejpam-4493	453	2	.	.	PUNCT
ejpam-4493	454	1	math	math	NOUN
ejpam-4493	454	2	.	.	PUNCT
ejpam-4493	455	1	sci	sci	PROPN
ejpam-4493	455	2	.	.	PROPN
ejpam-4493	455	3	,	,	PUNCT
ejpam-4493	455	4	125:449–455	125:449–455	NUM
ejpam-4493	455	5	,	,	PUNCT
ejpam-4493	455	6	2015	2015	NUM
ejpam-4493	455	7	.	.	PUNCT
ejpam-4493	456	1	references	reference	NOUN
ejpam-4493	456	2	1661	1661	NUM
ejpam-4493	456	3	[	[	X
ejpam-4493	456	4	4	4	NUM
ejpam-4493	456	5	]	]	PUNCT
ejpam-4493	456	6	c.	c.	PROPN
ejpam-4493	456	7	berge	berge	PROPN
ejpam-4493	456	8	.	.	PUNCT
ejpam-4493	457	1	theorie	theorie	PROPN
ejpam-4493	457	2	des	des	PROPN
ejpam-4493	457	3	graphes	graphes	PROPN
ejpam-4493	457	4	et	et	PROPN
ejpam-4493	457	5	ses	ses	PROPN
ejpam-4493	457	6	applications	application	NOUN
ejpam-4493	457	7	.	.	PUNCT
ejpam-4493	458	1	metheun	metheun	NOUN
ejpam-4493	458	2	and	and	CCONJ
ejpam-4493	458	3	wiley	wiley	PROPN
ejpam-4493	458	4	,	,	PUNCT
ejpam-4493	458	5	london	london	PROPN
ejpam-4493	458	6	and	and	CCONJ
ejpam-4493	458	7	new	new	PROPN
ejpam-4493	458	8	york	york	PROPN
ejpam-4493	458	9	,	,	PUNCT
ejpam-4493	458	10	1962	1962	NUM
ejpam-4493	458	11	.	.	PUNCT
ejpam-4493	459	1	[	[	X
ejpam-4493	459	2	5	5	X
ejpam-4493	459	3	]	]	PUNCT
ejpam-4493	459	4	g.	g.	PROPN
ejpam-4493	459	5	chartranda	chartranda	PROPN
ejpam-4493	459	6	,	,	PUNCT
ejpam-4493	459	7	h.	h.	PROPN
ejpam-4493	459	8	gavlasa	gavlasa	PROPN
ejpam-4493	459	9	,	,	PUNCT
ejpam-4493	459	10	k.c	k.c	PROPN
ejpam-4493	459	11	.	.	PROPN
ejpam-4493	459	12	vandell	vandell	PROPN
ejpam-4493	459	13	,	,	PUNCT
ejpam-4493	459	14	and	and	CCONJ
ejpam-4493	459	15	f.	f.	PROPN
ejpam-4493	459	16	harary	harary	PROPN
ejpam-4493	459	17	.	.	PUNCT
ejpam-4493	460	1	the	the	DET
ejpam-4493	460	2	forcing	force	VERB
ejpam-4493	460	3	domination	domination	NOUN
ejpam-4493	460	4	number	number	NOUN
ejpam-4493	460	5	of	of	ADP
ejpam-4493	460	6	a	a	DET
ejpam-4493	460	7	graph	graph	NOUN
ejpam-4493	460	8	.	.	PUNCT
ejpam-4493	461	1	j.combin	j.combin	NOUN
ejpam-4493	461	2	.	.	PUNCT
ejpam-4493	462	1	math	math	NOUN
ejpam-4493	462	2	.	.	PUNCT
ejpam-4493	463	1	combin	combin	NOUN
ejpam-4493	463	2	.	.	PUNCT
ejpam-4493	464	1	comput	comput	NOUN
ejpam-4493	464	2	.	.	PUNCT
ejpam-4493	464	3	,	,	PUNCT
ejpam-4493	465	1	25:161–174	25:161–174	NUM
ejpam-4493	465	2	,	,	PUNCT
ejpam-4493	465	3	1997	1997	NUM
ejpam-4493	465	4	.	.	PUNCT
ejpam-4493	466	1	[	[	X
ejpam-4493	466	2	6	6	NUM
ejpam-4493	466	3	]	]	PUNCT
ejpam-4493	466	4	w.	w.	NOUN
ejpam-4493	466	5	desormeauxa	desormeauxa	NOUN
ejpam-4493	466	6	,	,	PUNCT
ejpam-4493	466	7	t.	t.	PROPN
ejpam-4493	466	8	haynes	haynes	PROPN
ejpam-4493	466	9	,	,	PUNCT
ejpam-4493	466	10	and	and	CCONJ
ejpam-4493	466	11	m.a	m.a	PROPN
ejpam-4493	466	12	.	.	PROPN
ejpam-4493	466	13	henning	henning	PROPN
ejpam-4493	466	14	.	.	PUNCT
ejpam-4493	467	1	a	a	DET
ejpam-4493	467	2	note	note	NOUN
ejpam-4493	467	3	on	on	ADP
ejpam-4493	467	4	non	non	ADJ
ejpam-4493	467	5	-	-	ADJ
ejpam-4493	467	6	dominating	dominating	ADJ
ejpam-4493	467	7	set	set	VERB
ejpam-4493	467	8	partitions	partition	NOUN
ejpam-4493	467	9	in	in	ADP
ejpam-4493	467	10	graphs	graph	NOUN
ejpam-4493	467	11	.	.	PUNCT
ejpam-4493	468	1	networks	network	NOUN
ejpam-4493	468	2	,	,	PUNCT
ejpam-4493	468	3	pages	page	NOUN
ejpam-4493	468	4	1–8	1–8	NUM
ejpam-4493	468	5	,	,	PUNCT
ejpam-4493	468	6	2016	2016	NUM
ejpam-4493	468	7	.	.	PUNCT
ejpam-4493	469	1	[	[	X
ejpam-4493	469	2	7	7	X
ejpam-4493	469	3	]	]	X
ejpam-4493	469	4	b.	b.	PROPN
ejpam-4493	469	5	gayathri	gayathri	PROPN
ejpam-4493	469	6	and	and	CCONJ
ejpam-4493	469	7	s.	s.	PROPN
ejpam-4493	469	8	kaspar	kaspar	PROPN
ejpam-4493	469	9	.	.	PUNCT
ejpam-4493	470	1	connected	connect	VERB
ejpam-4493	470	2	co	co	ADJ
ejpam-4493	470	3	-	-	ADJ
ejpam-4493	470	4	independent	independent	ADJ
ejpam-4493	470	5	domination	domination	NOUN
ejpam-4493	470	6	of	of	ADP
ejpam-4493	470	7	a	a	DET
ejpam-4493	470	8	graph	graph	NOUN
ejpam-4493	470	9	.	.	PUNCT
ejpam-4493	471	1	international	international	ADJ
ejpam-4493	471	2	journal	journal	PROPN
ejpam-4493	471	3	contemp	contemp	NOUN
ejpam-4493	471	4	.	.	PUNCT
ejpam-4493	472	1	mathematics	mathematic	NOUN
ejpam-4493	472	2	and	and	CCONJ
ejpam-4493	472	3	sciences	science	NOUN
ejpam-4493	472	4	,	,	PUNCT
ejpam-4493	472	5	6:423–429	6:423–429	PROPN
ejpam-4493	472	6	,	,	PUNCT
ejpam-4493	472	7	2011	2011	NUM
ejpam-4493	472	8	.	.	PUNCT
ejpam-4493	473	1	[	[	X
ejpam-4493	473	2	8	8	NUM
ejpam-4493	473	3	]	]	X
ejpam-4493	473	4	f.	f.	PROPN
ejpam-4493	473	5	harary	harary	PROPN
ejpam-4493	473	6	.	.	PUNCT
ejpam-4493	474	1	graph	graph	NOUN
ejpam-4493	474	2	theory	theory	NOUN
ejpam-4493	474	3	.	.	PUNCT
ejpam-4493	475	1	addison	addison	PROPN
ejpam-4493	475	2	-	-	PUNCT
ejpam-4493	475	3	wesley	wesley	PROPN
ejpam-4493	475	4	publishing	publishing	PROPN
ejpam-4493	475	5	company	company	NOUN
ejpam-4493	475	6	,	,	PUNCT
ejpam-4493	475	7	usa	usa	PROPN
ejpam-4493	475	8	,	,	PUNCT
ejpam-4493	475	9	1969	1969	NUM
ejpam-4493	475	10	.	.	PUNCT
ejpam-4493	476	1	[	[	X
ejpam-4493	476	2	9	9	NUM
ejpam-4493	476	3	]	]	PUNCT
ejpam-4493	476	4	s.	s.	PROPN
ejpam-4493	476	5	kavithaa	kavithaa	PROPN
ejpam-4493	476	6	,	,	PUNCT
ejpam-4493	476	7	s.	s.	PROPN
ejpam-4493	476	8	robinson	robinson	PROPN
ejpam-4493	476	9	chellathurai	chellathurai	PROPN
ejpam-4493	476	10	,	,	PUNCT
ejpam-4493	476	11	and	and	CCONJ
ejpam-4493	476	12	j.	j.	PROPN
ejpam-4493	476	13	john	john	PROPN
ejpam-4493	476	14	.	.	PUNCT
ejpam-4493	477	1	on	on	ADP
ejpam-4493	477	2	the	the	DET
ejpam-4493	477	3	forcing	force	VERB
ejpam-4493	477	4	connected	connect	VERB
ejpam-4493	477	5	domination	domination	NOUN
ejpam-4493	477	6	number	number	NOUN
ejpam-4493	477	7	of	of	ADP
ejpam-4493	477	8	a	a	DET
ejpam-4493	477	9	graph	graph	NOUN
ejpam-4493	477	10	.	.	PUNCT
ejpam-4493	477	11	journal	journal	NOUN
ejpam-4493	477	12	of	of	ADP
ejpam-4493	477	13	discrete	discrete	ADJ
ejpam-4493	477	14	mathematical	mathematical	ADJ
ejpam-4493	477	15	sciences	science	NOUN
ejpam-4493	477	16	and	and	CCONJ
ejpam-4493	477	17	cryptography	cryptography	NOUN
ejpam-4493	477	18	,	,	PUNCT
ejpam-4493	477	19	20(3):611–624	20(3):611–624	PROPN
ejpam-4493	477	20	,	,	PUNCT
ejpam-4493	477	21	2017	2017	NUM
ejpam-4493	477	22	.	.	PUNCT
ejpam-4493	478	1	[	[	X
ejpam-4493	478	2	10	10	NUM
ejpam-4493	478	3	]	]	X
ejpam-4493	478	4	d.j	d.j	PROPN
ejpam-4493	478	5	.	.	PROPN
ejpam-4493	478	6	klein	klein	PROPN
ejpam-4493	478	7	and	and	CCONJ
ejpam-4493	478	8	m.	m.	PROPN
ejpam-4493	478	9	randic	randic	PROPN
ejpam-4493	478	10	.	.	PUNCT
ejpam-4493	478	11	innate	innate	ADJ
ejpam-4493	478	12	degree	degree	NOUN
ejpam-4493	478	13	of	of	ADP
ejpam-4493	478	14	freedom	freedom	NOUN
ejpam-4493	478	15	of	of	ADP
ejpam-4493	478	16	a	a	DET
ejpam-4493	478	17	graph	graph	NOUN
ejpam-4493	478	18	.	.	PUNCT
ejpam-4493	479	1	comput	comput	NOUN
ejpam-4493	479	2	.	.	PUNCT
ejpam-4493	480	1	chem	chem	NOUN
ejpam-4493	480	2	.	.	PUNCT
ejpam-4493	480	3	,	,	PUNCT
ejpam-4493	480	4	8:516–521	8:516–521	NOUN
ejpam-4493	480	5	,	,	PUNCT
ejpam-4493	480	6	1987	1987	NUM
ejpam-4493	480	7	.	.	PUNCT
ejpam-4493	481	1	[	[	X
ejpam-4493	481	2	11	11	NUM
ejpam-4493	481	3	]	]	PUNCT
ejpam-4493	481	4	s.	s.	PROPN
ejpam-4493	481	5	nanding	nanding	PROPN
ejpam-4493	481	6	and	and	CCONJ
ejpam-4493	481	7	h.	h.	PROPN
ejpam-4493	481	8	rara	rara	PROPN
ejpam-4493	481	9	.	.	PUNCT
ejpam-4493	482	1	on	on	ADP
ejpam-4493	482	2	connected	connected	ADJ
ejpam-4493	482	3	co	co	ADJ
ejpam-4493	482	4	-	-	ADJ
ejpam-4493	482	5	independent	independent	ADJ
ejpam-4493	482	6	hop	hop	NOUN
ejpam-4493	482	7	domination	domination	NOUN
ejpam-4493	482	8	in	in	ADP
ejpam-4493	482	9	graphs	graph	NOUN
ejpam-4493	482	10	.	.	PUNCT
ejpam-4493	483	1	european	european	ADJ
ejpam-4493	483	2	journal	journal	PROPN
ejpam-4493	483	3	of	of	ADP
ejpam-4493	483	4	pure	pure	ADJ
ejpam-4493	483	5	and	and	CCONJ
ejpam-4493	483	6	applied	applied	ADJ
ejpam-4493	483	7	mathematics	mathematic	NOUN
ejpam-4493	483	8	,	,	PUNCT
ejpam-4493	483	9	14(4):1226–1236	14(4):1226–1236	NUM
ejpam-4493	483	10	,	,	PUNCT
ejpam-4493	483	11	2021	2021	NUM
ejpam-4493	483	12	.	.	PUNCT
ejpam-4493	484	1	[	[	X
ejpam-4493	484	2	12	12	NUM
ejpam-4493	484	3	]	]	X
ejpam-4493	484	4	c.	c.	PROPN
ejpam-4493	484	5	natarajan	natarajan	PROPN
ejpam-4493	484	6	and	and	CCONJ
ejpam-4493	484	7	s.	s.	PROPN
ejpam-4493	484	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4493	484	9	.	.	PUNCT
ejpam-4493	485	1	hop	hop	PROPN
ejpam-4493	485	2	domination	domination	NOUN
ejpam-4493	485	3	in	in	ADP
ejpam-4493	485	4	graphs	graph	NOUN
ejpam-4493	485	5	-	-	PUNCT
ejpam-4493	485	6	ii	ii	NOUN
ejpam-4493	485	7	.	.	PUNCT
ejpam-4493	485	8	versita	versita	PROPN
ejpam-4493	485	9	,	,	PUNCT
ejpam-4493	485	10	23(2):187	23(2):187	NUM
ejpam-4493	485	11	–	–	PUNCT
ejpam-4493	485	12	199	199	NUM
ejpam-4493	485	13	,	,	PUNCT
ejpam-4493	485	14	2015	2015	NUM
ejpam-4493	485	15	.	.	PUNCT
ejpam-4493	486	1	[	[	X
ejpam-4493	486	2	13	13	NUM
ejpam-4493	486	3	]	]	SYM
ejpam-4493	486	4	salasalan	salasalan	NOUN
ejpam-4493	486	5	g.	g.	PROPN
ejpam-4493	486	6	p.	p.	NOUN
ejpam-4493	486	7	and	and	CCONJ
ejpam-4493	486	8	canoy	canoy	PROPN
ejpam-4493	486	9	jr	jr	PROPN
ejpam-4493	486	10	s.	s.	PROPN
ejpam-4493	486	11	r.	r.	PROPN
ejpam-4493	486	12	revisiting	revisiting	PROPN
ejpam-4493	486	13	domination	domination	NOUN
ejpam-4493	486	14	,	,	PUNCT
ejpam-4493	486	15	hop	hop	NOUN
ejpam-4493	486	16	domination	domination	NOUN
ejpam-4493	486	17	,	,	PUNCT
ejpam-4493	486	18	and	and	CCONJ
ejpam-4493	486	19	global	global	ADJ
ejpam-4493	486	20	hop	hop	NOUN
ejpam-4493	486	21	domination	domination	NOUN
ejpam-4493	486	22	in	in	ADP
ejpam-4493	486	23	graphs	graph	NOUN
ejpam-4493	486	24	.	.	PUNCT
ejpam-4493	487	1	european	european	ADJ
ejpam-4493	487	2	journal	journal	PROPN
ejpam-4493	487	3	of	of	ADP
ejpam-4493	487	4	pure	pure	ADJ
ejpam-4493	487	5	and	and	CCONJ
ejpam-4493	487	6	applied	applied	ADJ
ejpam-4493	487	7	mathematics	mathematic	NOUN
ejpam-4493	487	8	,	,	PUNCT
ejpam-4493	487	9	14(4	14(4	NUM
ejpam-4493	487	10	)	)	PUNCT
ejpam-4493	487	11	,	,	PUNCT
ejpam-4493	487	12	2021	2021	NUM
ejpam-4493	487	13	.	.	PUNCT
ejpam-4493	488	1	[	[	X
ejpam-4493	488	2	14	14	NUM
ejpam-4493	488	3	]	]	X
ejpam-4493	488	4	y.	y.	PROPN
ejpam-4493	488	5	pabilona	pabilona	PROPN
ejpam-4493	488	6	and	and	CCONJ
ejpam-4493	488	7	h.	h.	PROPN
ejpam-4493	488	8	rara	rara	PROPN
ejpam-4493	488	9	.	.	PUNCT
ejpam-4493	489	1	total	total	ADJ
ejpam-4493	489	2	hop	hop	NOUN
ejpam-4493	489	3	dominating	dominating	NOUN
ejpam-4493	489	4	sets	set	NOUN
ejpam-4493	489	5	in	in	ADP
ejpam-4493	489	6	the	the	DET
ejpam-4493	489	7	join	join	NOUN
ejpam-4493	489	8	,	,	PUNCT
ejpam-4493	489	9	corona	corona	PROPN
ejpam-4493	489	10	,	,	PUNCT
ejpam-4493	489	11	and	and	CCONJ
ejpam-4493	489	12	lexicographic	lexicographic	ADJ
ejpam-4493	489	13	product	product	NOUN
ejpam-4493	489	14	of	of	ADP
ejpam-4493	489	15	graph	graph	NOUN
ejpam-4493	489	16	.	.	PUNCT
ejpam-4493	490	1	journal	journal	PROPN
ejpam-4493	490	2	of	of	ADP
ejpam-4493	490	3	algebra	algebra	PROPN
ejpam-4493	490	4	and	and	CCONJ
ejpam-4493	490	5	applied	apply	VERB
ejpam-4493	490	6	mathematics	mathematic	NOUN
ejpam-4493	490	7	,	,	PUNCT
ejpam-4493	490	8	2017	2017	NUM
ejpam-4493	490	9	.	.	PUNCT
ejpam-4493	491	1	[	[	X
ejpam-4493	491	2	15	15	NUM
ejpam-4493	491	3	]	]	X
ejpam-4493	491	4	y.	y.	PROPN
ejpam-4493	491	5	m.	m.	NOUN
ejpam-4493	491	6	pabilona	pabilona	PROPN
ejpam-4493	491	7	and	and	CCONJ
ejpam-4493	491	8	h.	h.	PROPN
ejpam-4493	491	9	rara	rara	PROPN
ejpam-4493	491	10	.	.	PUNCT
ejpam-4493	492	1	connected	connect	VERB
ejpam-4493	492	2	hop	hop	NOUN
ejpam-4493	492	3	domination	domination	NOUN
ejpam-4493	492	4	in	in	ADP
ejpam-4493	492	5	graphs	graph	NOUN
ejpam-4493	492	6	under	under	ADP
ejpam-4493	492	7	some	some	DET
ejpam-4493	492	8	binary	binary	ADJ
ejpam-4493	492	9	operations	operation	NOUN
ejpam-4493	492	10	.	.	PUNCT
ejpam-4493	493	1	asian	asian	ADJ
ejpam-4493	493	2	-	-	PUNCT
ejpam-4493	493	3	european	european	ADJ
ejpam-4493	493	4	journal	journal	NOUN
ejpam-4493	493	5	of	of	ADP
ejpam-4493	493	6	mathematics	mathematic	NOUN
ejpam-4493	493	7	,	,	PUNCT
ejpam-4493	493	8	11(5	11(5	NUM
ejpam-4493	493	9	)	)	PUNCT
ejpam-4493	493	10	,	,	PUNCT
ejpam-4493	493	11	2018	2018	NUM
ejpam-4493	493	12	.	.	PUNCT
ejpam-4493	494	1	[	[	X
ejpam-4493	494	2	16	16	NUM
ejpam-4493	494	3	]	]	X
ejpam-4493	494	4	t.p	t.p	PROPN
ejpam-4493	494	5	.	.	PROPN
ejpam-4493	494	6	zivkovica	zivkovica	PROPN
ejpam-4493	494	7	,	,	PUNCT
ejpam-4493	494	8	f.	f.	PROPN
ejpam-4493	494	9	harary	harary	PROPN
ejpam-4493	494	10	,	,	PUNCT
ejpam-4493	494	11	and	and	CCONJ
ejpam-4493	494	12	klein	klein	PROPN
ejpam-4493	494	13	d.j	d.j	PROPN
ejpam-4493	494	14	.	.	PROPN
ejpam-4493	494	15	graphical	graphical	ADJ
ejpam-4493	494	16	properties	property	NOUN
ejpam-4493	494	17	of	of	ADP
ejpam-4493	494	18	polyhexes	polyhexe	NOUN
ejpam-4493	494	19	:	:	PUNCT
ejpam-4493	494	20	perfect	perfect	ADJ
ejpam-4493	494	21	matching	matching	NOUN
ejpam-4493	494	22	vector	vector	NOUN
ejpam-4493	494	23	and	and	CCONJ
ejpam-4493	494	24	forcing	forcing	NOUN
ejpam-4493	494	25	.	.	PUNCT
ejpam-4493	495	1	j.	j.	PROPN
ejpam-4493	495	2	math	math	PROPN
ejpam-4493	495	3	.	.	PUNCT
ejpam-4493	496	1	chem	chem	PROPN
ejpam-4493	496	2	.	.	PUNCT
ejpam-4493	496	3	,	,	PUNCT
ejpam-4493	497	1	6:295–306	6:295–306	NUM
ejpam-4493	497	2	,	,	PUNCT
ejpam-4493	497	3	1991	1991	NUM
ejpam-4493	497	4	.	.	PUNCT