id	sid	tid	token	lemma	pos
ejpam-4521	1	1	european	european	PROPN
ejpam-4521	1	2	journal	journal	PROPN
ejpam-4521	1	3	of	of	ADP
ejpam-4521	1	4	pure	pure	ADJ
ejpam-4521	1	5	and	and	CCONJ
ejpam-4521	1	6	applied	apply	VERB
ejpam-4521	1	7	mathematics	mathematic	NOUN
ejpam-4521	1	8	vol	vol	NOUN
ejpam-4521	1	9	.	.	PROPN
ejpam-4521	2	1	15	15	NUM
ejpam-4521	2	2	,	,	PUNCT
ejpam-4521	2	3	no	no	INTJ
ejpam-4521	2	4	.	.	NOUN
ejpam-4521	2	5	4	4	NUM
ejpam-4521	2	6	,	,	PUNCT
ejpam-4521	2	7	2022	2022	NUM
ejpam-4521	2	8	,	,	PUNCT
ejpam-4521	2	9	1597	1597	NUM
ejpam-4521	2	10	-	-	SYM
ejpam-4521	2	11	1612	1612	NUM
ejpam-4521	2	12	issn	issn	PROPN
ejpam-4521	2	13	1307	1307	NUM
ejpam-4521	2	14	-	-	SYM
ejpam-4521	2	15	5543	5543	NUM
ejpam-4521	2	16	–	–	PUNCT
ejpam-4521	2	17	ejpam.com	ejpam.com	X
ejpam-4521	2	18	published	publish	VERB
ejpam-4521	2	19	by	by	ADP
ejpam-4521	2	20	new	new	PROPN
ejpam-4521	2	21	york	york	PROPN
ejpam-4521	2	22	business	business	PROPN
ejpam-4521	2	23	global	global	ADJ
ejpam-4521	2	24	forcing	force	VERB
ejpam-4521	2	25	subsets	subset	NOUN
ejpam-4521	2	26	of	of	ADP
ejpam-4521	2	27	connected	connected	ADJ
ejpam-4521	2	28	co	co	ADJ
ejpam-4521	2	29	-	-	ADJ
ejpam-4521	2	30	independent	independent	ADJ
ejpam-4521	2	31	hop	hop	NOUN
ejpam-4521	2	32	domination	domination	NOUN
ejpam-4521	2	33	in	in	ADP
ejpam-4521	2	34	the	the	DET
ejpam-4521	2	35	edge	edge	NOUN
ejpam-4521	2	36	corona	corona	NOUN
ejpam-4521	2	37	and	and	CCONJ
ejpam-4521	2	38	lexicographic	lexicographic	ADJ
ejpam-4521	2	39	product	product	NOUN
ejpam-4521	2	40	of	of	ADP
ejpam-4521	2	41	graphs	graph	NOUN
ejpam-4521	2	42	yves	yves	PROPN
ejpam-4521	2	43	dave	dave	PROPN
ejpam-4521	2	44	l.	l.	PROPN
ejpam-4521	2	45	calanza1,∗	calanza1,∗	PROPN
ejpam-4521	2	46	,	,	PUNCT
ejpam-4521	2	47	helen	helen	PROPN
ejpam-4521	2	48	m.	m.	PROPN
ejpam-4521	2	49	rara2	rara2	PROPN
ejpam-4521	3	1	1	1	NUM
ejpam-4521	3	2	department	department	NOUN
ejpam-4521	3	3	of	of	ADP
ejpam-4521	3	4	mathematics	mathematic	NOUN
ejpam-4521	3	5	and	and	CCONJ
ejpam-4521	3	6	statistics	statistic	NOUN
ejpam-4521	3	7	,	,	PUNCT
ejpam-4521	3	8	college	college	NOUN
ejpam-4521	3	9	of	of	ADP
ejpam-4521	3	10	science	science	NOUN
ejpam-4521	3	11	and	and	CCONJ
ejpam-4521	3	12	mathematics	mathematic	NOUN
ejpam-4521	3	13	,	,	PUNCT
ejpam-4521	3	14	mindanao	mindanao	PROPN
ejpam-4521	3	15	state	state	PROPN
ejpam-4521	3	16	university	university	PROPN
ejpam-4521	3	17	-	-	PUNCT
ejpam-4521	3	18	iligan	iligan	PROPN
ejpam-4521	3	19	institute	institute	PROPN
ejpam-4521	3	20	of	of	ADP
ejpam-4521	3	21	technology	technology	PROPN
ejpam-4521	3	22	,	,	PUNCT
ejpam-4521	3	23	9200	9200	NUM
ejpam-4521	3	24	iligan	iligan	ADJ
ejpam-4521	3	25	city	city	NOUN
ejpam-4521	3	26	,	,	PUNCT
ejpam-4521	3	27	philippines	philippines	PROPN
ejpam-4521	3	28	2	2	NUM
ejpam-4521	3	29	department	department	NOUN
ejpam-4521	3	30	of	of	ADP
ejpam-4521	3	31	mathematics	mathematic	NOUN
ejpam-4521	3	32	and	and	CCONJ
ejpam-4521	3	33	statistics	statistic	NOUN
ejpam-4521	3	34	,	,	PUNCT
ejpam-4521	3	35	college	college	NOUN
ejpam-4521	3	36	of	of	ADP
ejpam-4521	3	37	science	science	NOUN
ejpam-4521	3	38	and	and	CCONJ
ejpam-4521	3	39	mathematics	mathematic	NOUN
ejpam-4521	3	40	,	,	PUNCT
ejpam-4521	3	41	center	center	NOUN
ejpam-4521	3	42	of	of	ADP
ejpam-4521	3	43	graph	graph	NOUN
ejpam-4521	3	44	theory	theory	NOUN
ejpam-4521	3	45	,	,	PUNCT
ejpam-4521	3	46	algebra	algebra	NOUN
ejpam-4521	3	47	,	,	PUNCT
ejpam-4521	3	48	and	and	CCONJ
ejpam-4521	3	49	analysis	analysis	NOUN
ejpam-4521	3	50	-	-	PUNCT
ejpam-4521	3	51	premier	premier	NOUN
ejpam-4521	3	52	research	research	NOUN
ejpam-4521	3	53	institute	institute	PROPN
ejpam-4521	3	54	of	of	ADP
ejpam-4521	3	55	science	science	NOUN
ejpam-4521	3	56	and	and	CCONJ
ejpam-4521	3	57	mathematics	mathematic	NOUN
ejpam-4521	3	58	,	,	PUNCT
ejpam-4521	3	59	mindanao	mindanao	PROPN
ejpam-4521	3	60	state	state	PROPN
ejpam-4521	3	61	university	university	PROPN
ejpam-4521	3	62	-	-	PUNCT
ejpam-4521	3	63	iligan	iligan	PROPN
ejpam-4521	3	64	institute	institute	PROPN
ejpam-4521	3	65	of	of	ADP
ejpam-4521	3	66	technology	technology	PROPN
ejpam-4521	3	67	,	,	PUNCT
ejpam-4521	3	68	9200	9200	NUM
ejpam-4521	3	69	iligan	iligan	ADJ
ejpam-4521	3	70	city	city	NOUN
ejpam-4521	3	71	,	,	PUNCT
ejpam-4521	3	72	philippines	philippine	NOUN
ejpam-4521	3	73	abstract	abstract	ADJ
ejpam-4521	3	74	.	.	PUNCT
ejpam-4521	4	1	this	this	DET
ejpam-4521	4	2	study	study	NOUN
ejpam-4521	4	3	deals	deal	VERB
ejpam-4521	4	4	with	with	ADP
ejpam-4521	4	5	the	the	DET
ejpam-4521	4	6	forcing	force	VERB
ejpam-4521	4	7	subsets	subset	NOUN
ejpam-4521	4	8	of	of	ADP
ejpam-4521	4	9	a	a	DET
ejpam-4521	4	10	minimum	minimum	ADJ
ejpam-4521	4	11	connected	connected	ADJ
ejpam-4521	4	12	co	co	NOUN
ejpam-4521	4	13	-	-	ADJ
ejpam-4521	4	14	independent	independent	ADJ
ejpam-4521	4	15	hop	hop	NOUN
ejpam-4521	4	16	dominating	dominating	NOUN
ejpam-4521	4	17	sets	set	NOUN
ejpam-4521	4	18	in	in	ADP
ejpam-4521	4	19	graphs	graph	NOUN
ejpam-4521	4	20	.	.	PUNCT
ejpam-4521	5	1	bounds	bound	NOUN
ejpam-4521	5	2	or	or	CCONJ
ejpam-4521	5	3	exact	exact	ADJ
ejpam-4521	5	4	values	value	NOUN
ejpam-4521	5	5	of	of	ADP
ejpam-4521	5	6	the	the	DET
ejpam-4521	5	7	forcing	force	VERB
ejpam-4521	5	8	connected	connect	VERB
ejpam-4521	5	9	co	co	ADJ
ejpam-4521	5	10	-	-	ADJ
ejpam-4521	5	11	independent	independent	ADJ
ejpam-4521	5	12	hop	hop	NOUN
ejpam-4521	5	13	domination	domination	NOUN
ejpam-4521	5	14	numbers	number	NOUN
ejpam-4521	5	15	of	of	ADP
ejpam-4521	5	16	graphs	graph	NOUN
ejpam-4521	5	17	resulting	result	VERB
ejpam-4521	5	18	from	from	ADP
ejpam-4521	5	19	some	some	DET
ejpam-4521	5	20	binary	binary	ADJ
ejpam-4521	5	21	operations	operation	NOUN
ejpam-4521	5	22	such	such	ADJ
ejpam-4521	5	23	as	as	ADP
ejpam-4521	5	24	edge	edge	NOUN
ejpam-4521	5	25	corona	corona	NOUN
ejpam-4521	5	26	and	and	CCONJ
ejpam-4521	5	27	lexicographic	lexicographic	ADJ
ejpam-4521	5	28	product	product	NOUN
ejpam-4521	5	29	of	of	ADP
ejpam-4521	5	30	graphs	graph	NOUN
ejpam-4521	5	31	are	be	AUX
ejpam-4521	5	32	determined	determine	VERB
ejpam-4521	5	33	.	.	PUNCT
ejpam-4521	6	1	some	some	DET
ejpam-4521	6	2	main	main	ADJ
ejpam-4521	6	3	results	result	NOUN
ejpam-4521	6	4	generated	generate	VERB
ejpam-4521	6	5	in	in	ADP
ejpam-4521	6	6	this	this	DET
ejpam-4521	6	7	study	study	NOUN
ejpam-4521	6	8	include	include	VERB
ejpam-4521	6	9	:	:	PUNCT
ejpam-4521	6	10	(	(	PUNCT
ejpam-4521	6	11	a	a	X
ejpam-4521	6	12	)	)	PUNCT
ejpam-4521	6	13	characterization	characterization	NOUN
ejpam-4521	6	14	of	of	ADP
ejpam-4521	6	15	the	the	DET
ejpam-4521	6	16	minimum	minimum	ADJ
ejpam-4521	6	17	connected	connect	VERB
ejpam-4521	6	18	co	co	NOUN
ejpam-4521	6	19	-	-	ADJ
ejpam-4521	6	20	independent	independent	ADJ
ejpam-4521	6	21	hop	hop	NOUN
ejpam-4521	6	22	dominating	dominating	NOUN
ejpam-4521	6	23	sets	set	NOUN
ejpam-4521	6	24	;	;	PUNCT
ejpam-4521	6	25	and	and	CCONJ
ejpam-4521	6	26	(	(	PUNCT
ejpam-4521	6	27	b	b	NOUN
ejpam-4521	6	28	)	)	PUNCT
ejpam-4521	6	29	characterization	characterization	NOUN
ejpam-4521	6	30	of	of	ADP
ejpam-4521	6	31	the	the	DET
ejpam-4521	6	32	forcing	force	VERB
ejpam-4521	6	33	subsets	subset	NOUN
ejpam-4521	6	34	for	for	ADP
ejpam-4521	6	35	these	these	DET
ejpam-4521	6	36	types	type	NOUN
ejpam-4521	6	37	of	of	ADP
ejpam-4521	6	38	sets	set	NOUN
ejpam-4521	6	39	.	.	PUNCT
ejpam-4521	7	1	2020	2020	NUM
ejpam-4521	7	2	mathematics	mathematic	NOUN
ejpam-4521	7	3	subject	subject	NOUN
ejpam-4521	7	4	classifications	classification	NOUN
ejpam-4521	7	5	:	:	PUNCT
ejpam-4521	7	6	05c69	05c69	X
ejpam-4521	7	7	key	key	ADJ
ejpam-4521	7	8	words	word	NOUN
ejpam-4521	7	9	and	and	CCONJ
ejpam-4521	7	10	phrases	phrase	NOUN
ejpam-4521	7	11	:	:	PUNCT
ejpam-4521	7	12	forcing	force	VERB
ejpam-4521	7	13	subsets	subset	NOUN
ejpam-4521	7	14	,	,	PUNCT
ejpam-4521	7	15	connected	connected	ADJ
ejpam-4521	7	16	co	co	ADJ
ejpam-4521	7	17	-	-	ADJ
ejpam-4521	7	18	independent	independent	ADJ
ejpam-4521	7	19	hop	hop	NOUN
ejpam-4521	7	20	,	,	PUNCT
ejpam-4521	7	21	domination	domination	NOUN
ejpam-4521	7	22	,	,	PUNCT
ejpam-4521	7	23	coindependent	coindependent	NOUN
ejpam-4521	7	24	set	set	NOUN
ejpam-4521	7	25	,	,	PUNCT
ejpam-4521	7	26	edge	edge	NOUN
ejpam-4521	7	27	corona	corona	NOUN
ejpam-4521	7	28	,	,	PUNCT
ejpam-4521	7	29	lexicographic	lexicographic	ADJ
ejpam-4521	7	30	product	product	NOUN
ejpam-4521	7	31	1	1	NUM
ejpam-4521	7	32	.	.	PUNCT
ejpam-4521	8	1	introduction	introduction	NOUN
ejpam-4521	8	2	beginning	begin	VERB
ejpam-4521	8	3	with	with	ADP
ejpam-4521	8	4	c.	c.	PROPN
ejpam-4521	8	5	berge	berge	NOUN
ejpam-4521	9	1	[	[	X
ejpam-4521	9	2	4	4	X
ejpam-4521	9	3	]	]	PUNCT
ejpam-4521	9	4	in	in	ADP
ejpam-4521	9	5	1958	1958	NUM
ejpam-4521	9	6	,	,	PUNCT
ejpam-4521	9	7	the	the	DET
ejpam-4521	9	8	study	study	NOUN
ejpam-4521	9	9	on	on	ADP
ejpam-4521	9	10	domination	domination	NOUN
ejpam-4521	9	11	in	in	ADP
ejpam-4521	9	12	graphs	graph	NOUN
ejpam-4521	9	13	was	be	AUX
ejpam-4521	9	14	developed	develop	VERB
ejpam-4521	9	15	.	.	PUNCT
ejpam-4521	10	1	there	there	PRON
ejpam-4521	10	2	are	be	VERB
ejpam-4521	10	3	now	now	ADV
ejpam-4521	10	4	a	a	DET
ejpam-4521	10	5	lot	lot	NOUN
ejpam-4521	10	6	of	of	ADP
ejpam-4521	10	7	studies	study	NOUN
ejpam-4521	10	8	involving	involve	VERB
ejpam-4521	10	9	domination	domination	NOUN
ejpam-4521	10	10	and	and	CCONJ
ejpam-4521	10	11	its	its	PRON
ejpam-4521	10	12	variations	variation	NOUN
ejpam-4521	10	13	.	.	PUNCT
ejpam-4521	11	1	one	one	NUM
ejpam-4521	11	2	of	of	ADP
ejpam-4521	11	3	its	its	PRON
ejpam-4521	11	4	variations	variation	NOUN
ejpam-4521	11	5	is	be	AUX
ejpam-4521	11	6	the	the	DET
ejpam-4521	11	7	connected	connected	ADJ
ejpam-4521	11	8	co	co	ADJ
ejpam-4521	11	9	-	-	ADJ
ejpam-4521	11	10	independent	independent	ADJ
ejpam-4521	11	11	domination	domination	NOUN
ejpam-4521	11	12	number	number	NOUN
ejpam-4521	11	13	of	of	ADP
ejpam-4521	11	14	graphs	graph	NOUN
ejpam-4521	11	15	that	that	PRON
ejpam-4521	11	16	was	be	AUX
ejpam-4521	11	17	studied	study	VERB
ejpam-4521	11	18	in	in	ADP
ejpam-4521	11	19	[	[	X
ejpam-4521	11	20	7	7	NUM
ejpam-4521	11	21	]	]	PUNCT
ejpam-4521	11	22	.	.	PUNCT
ejpam-4521	12	1	years	year	NOUN
ejpam-4521	12	2	later	later	ADV
ejpam-4521	12	3	,	,	PUNCT
ejpam-4521	12	4	a	a	DET
ejpam-4521	12	5	new	new	ADJ
ejpam-4521	12	6	domination	domination	NOUN
ejpam-4521	12	7	parameter	parameter	NOUN
ejpam-4521	12	8	called	call	VERB
ejpam-4521	12	9	hop	hop	NOUN
ejpam-4521	12	10	domination	domination	NOUN
ejpam-4521	12	11	in	in	ADP
ejpam-4521	12	12	graph	graph	NOUN
ejpam-4521	12	13	was	be	AUX
ejpam-4521	12	14	introduced	introduce	VERB
ejpam-4521	12	15	in	in	ADP
ejpam-4521	12	16	[	[	X
ejpam-4521	12	17	12	12	NUM
ejpam-4521	12	18	]	]	PUNCT
ejpam-4521	12	19	by	by	ADP
ejpam-4521	12	20	natarajan	natarajan	PROPN
ejpam-4521	12	21	and	and	CCONJ
ejpam-4521	12	22	ayyaswamy	ayyaswamy	PROPN
ejpam-4521	12	23	and	and	CCONJ
ejpam-4521	12	24	was	be	AUX
ejpam-4521	12	25	also	also	ADV
ejpam-4521	12	26	studied	study	VERB
ejpam-4521	12	27	in	in	ADP
ejpam-4521	12	28	[	[	X
ejpam-4521	12	29	3	3	NUM
ejpam-4521	12	30	,	,	PUNCT
ejpam-4521	12	31	13–15	13–15	NUM
ejpam-4521	12	32	]	]	PUNCT
ejpam-4521	12	33	.	.	PUNCT
ejpam-4521	13	1	a	a	DET
ejpam-4521	13	2	study	study	NOUN
ejpam-4521	13	3	in	in	ADP
ejpam-4521	13	4	2021	2021	NUM
ejpam-4521	13	5	by	by	ADP
ejpam-4521	13	6	s.	s.	PROPN
ejpam-4521	13	7	nanding	nanding	PROPN
ejpam-4521	13	8	and	and	CCONJ
ejpam-4521	13	9	h.	h.	PROPN
ejpam-4521	13	10	rara	rara	NOUN
ejpam-4521	14	1	[	[	X
ejpam-4521	14	2	11	11	NUM
ejpam-4521	14	3	]	]	PUNCT
ejpam-4521	14	4	introduced	introduce	VERB
ejpam-4521	14	5	a	a	DET
ejpam-4521	14	6	new	new	ADJ
ejpam-4521	14	7	concept	concept	NOUN
ejpam-4521	14	8	of	of	ADP
ejpam-4521	14	9	hop	hop	NOUN
ejpam-4521	14	10	domination	domination	NOUN
ejpam-4521	14	11	called	call	VERB
ejpam-4521	14	12	the	the	DET
ejpam-4521	14	13	connected	connected	ADJ
ejpam-4521	14	14	co	co	NOUN
ejpam-4521	14	15	-	-	ADJ
ejpam-4521	14	16	independent	independent	ADJ
ejpam-4521	14	17	hop	hop	NOUN
ejpam-4521	14	18	domination	domination	NOUN
ejpam-4521	14	19	and	and	CCONJ
ejpam-4521	14	20	generated	generate	VERB
ejpam-4521	14	21	some	some	DET
ejpam-4521	14	22	characterizations	characterization	NOUN
ejpam-4521	14	23	of	of	ADP
ejpam-4521	14	24	connected	connected	ADJ
ejpam-4521	14	25	co	co	ADJ
ejpam-4521	14	26	-	-	ADJ
ejpam-4521	14	27	independent	independent	ADJ
ejpam-4521	14	28	hop	hop	NOUN
ejpam-4521	14	29	domination	domination	NOUN
ejpam-4521	14	30	in	in	ADP
ejpam-4521	14	31	graphs	graph	NOUN
ejpam-4521	14	32	.	.	PUNCT
ejpam-4521	15	1	∗corresponding	∗corresponde	VERB
ejpam-4521	15	2	author	author	NOUN
ejpam-4521	15	3	.	.	PUNCT
ejpam-4521	16	1	doi	doi	NOUN
ejpam-4521	16	2	:	:	PUNCT
ejpam-4521	16	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4521	https://doi.org/10.29020/nybg.ejpam.v15i4.4521	NUM
ejpam-4521	16	4	email	email	NOUN
ejpam-4521	16	5	addresses	address	NOUN
ejpam-4521	16	6	:	:	PUNCT
ejpam-4521	16	7	yvesdave.calanza@g.msuiit.edu.ph	yvesdave.calanza@g.msuiit.edu.ph	PROPN
ejpam-4521	16	8	(	(	PUNCT
ejpam-4521	16	9	y.d	y.d	PROPN
ejpam-4521	16	10	.	.	PROPN
ejpam-4521	16	11	calanza	calanza	PROPN
ejpam-4521	16	12	)	)	PUNCT
ejpam-4521	16	13	,	,	PUNCT
ejpam-4521	16	14	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4521	16	15	(	(	PUNCT
ejpam-4521	16	16	h.	h.	PROPN
ejpam-4521	16	17	rara	rara	PROPN
ejpam-4521	16	18	)	)	PUNCT
ejpam-4521	16	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4521	16	20	1597	1597	NUM
ejpam-4521	17	1	©	©	PROPN
ejpam-4521	17	2	2022	2022	NUM
ejpam-4521	17	3	ejpam	ejpam	VERB
ejpam-4521	17	4	all	all	DET
ejpam-4521	17	5	rights	right	NOUN
ejpam-4521	17	6	reserved	reserve	VERB
ejpam-4521	17	7	.	.	PUNCT
ejpam-4521	18	1	y.d	y.d	PROPN
ejpam-4521	18	2	.	.	PROPN
ejpam-4521	18	3	calanza	calanza	PROPN
ejpam-4521	18	4	,	,	PUNCT
ejpam-4521	18	5	h.	h.	PROPN
ejpam-4521	18	6	rara	rara	PROPN
ejpam-4521	18	7	/	/	SYM
ejpam-4521	18	8	eur	eur	PROPN
ejpam-4521	18	9	.	.	PUNCT
ejpam-4521	19	1	j.	j.	PROPN
ejpam-4521	19	2	pure	pure	PROPN
ejpam-4521	19	3	appl	appl	PROPN
ejpam-4521	19	4	.	.	PROPN
ejpam-4521	19	5	math	math	PROPN
ejpam-4521	19	6	,	,	PUNCT
ejpam-4521	19	7	15	15	NUM
ejpam-4521	19	8	(	(	PUNCT
ejpam-4521	19	9	4	4	NUM
ejpam-4521	19	10	)	)	PUNCT
ejpam-4521	19	11	(	(	PUNCT
ejpam-4521	19	12	2022	2022	NUM
ejpam-4521	19	13	)	)	PUNCT
ejpam-4521	19	14	,	,	PUNCT
ejpam-4521	19	15	1597	1597	NUM
ejpam-4521	19	16	-	-	SYM
ejpam-4521	19	17	1612	1612	NUM
ejpam-4521	19	18	1598	1598	NUM
ejpam-4521	19	19	on	on	ADP
ejpam-4521	19	20	the	the	DET
ejpam-4521	19	21	other	other	ADJ
ejpam-4521	19	22	hand	hand	NOUN
ejpam-4521	19	23	,	,	PUNCT
ejpam-4521	19	24	the	the	DET
ejpam-4521	19	25	concept	concept	NOUN
ejpam-4521	19	26	of	of	ADP
ejpam-4521	19	27	forcing	force	VERB
ejpam-4521	19	28	numbers	number	NOUN
ejpam-4521	19	29	started	start	VERB
ejpam-4521	19	30	from	from	ADP
ejpam-4521	19	31	the	the	DET
ejpam-4521	19	32	study	study	NOUN
ejpam-4521	19	33	of	of	ADP
ejpam-4521	19	34	molecular	molecular	ADJ
ejpam-4521	19	35	resonance	resonance	NOUN
ejpam-4521	19	36	structure	structure	NOUN
ejpam-4521	19	37	which	which	PRON
ejpam-4521	19	38	was	be	AUX
ejpam-4521	19	39	introduced	introduce	VERB
ejpam-4521	19	40	by	by	ADP
ejpam-4521	19	41	klein	klein	PROPN
ejpam-4521	19	42	and	and	CCONJ
ejpam-4521	19	43	randic	randic	ADJ
ejpam-4521	19	44	[	[	X
ejpam-4521	19	45	10	10	NUM
ejpam-4521	19	46	]	]	PUNCT
ejpam-4521	19	47	in	in	ADP
ejpam-4521	19	48	1987	1987	NUM
ejpam-4521	19	49	.	.	PUNCT
ejpam-4521	20	1	harary	harary	PROPN
ejpam-4521	20	2	et	et	PROPN
ejpam-4521	20	3	.	.	PUNCT
ejpam-4521	21	1	al	al	PROPN
ejpam-4521	22	1	[	[	X
ejpam-4521	22	2	16	16	NUM
ejpam-4521	22	3	]	]	PUNCT
ejpam-4521	22	4	first	first	ADV
ejpam-4521	22	5	used	use	VERB
ejpam-4521	22	6	the	the	DET
ejpam-4521	22	7	name	name	NOUN
ejpam-4521	22	8	“	"	PUNCT
ejpam-4521	22	9	forcing	force	VERB
ejpam-4521	22	10	number	number	NOUN
ejpam-4521	22	11	”	"	PUNCT
ejpam-4521	22	12	and	and	CCONJ
ejpam-4521	22	13	introduced	introduce	VERB
ejpam-4521	22	14	the	the	DET
ejpam-4521	22	15	concept	concept	NOUN
ejpam-4521	22	16	of	of	ADP
ejpam-4521	22	17	the	the	DET
ejpam-4521	22	18	forcing	forcing	NOUN
ejpam-4521	22	19	of	of	ADP
ejpam-4521	22	20	a	a	DET
ejpam-4521	22	21	perfect	perfect	ADJ
ejpam-4521	22	22	match	match	NOUN
ejpam-4521	22	23	in	in	ADP
ejpam-4521	22	24	1991	1991	NUM
ejpam-4521	22	25	.	.	PUNCT
ejpam-4521	23	1	chartrand	chartrand	PROPN
ejpam-4521	23	2	et	et	PROPN
ejpam-4521	23	3	.	.	PUNCT
ejpam-4521	24	1	al	al	PROPN
ejpam-4521	25	1	[	[	X
ejpam-4521	25	2	5	5	NUM
ejpam-4521	25	3	]	]	PUNCT
ejpam-4521	25	4	initiated	initiate	VERB
ejpam-4521	25	5	the	the	DET
ejpam-4521	25	6	investigation	investigation	NOUN
ejpam-4521	25	7	on	on	ADP
ejpam-4521	25	8	the	the	DET
ejpam-4521	25	9	relation	relation	NOUN
ejpam-4521	25	10	between	between	ADP
ejpam-4521	25	11	forcing	force	VERB
ejpam-4521	25	12	and	and	CCONJ
ejpam-4521	25	13	domination	domination	NOUN
ejpam-4521	25	14	concepts	concept	NOUN
ejpam-4521	25	15	in	in	ADP
ejpam-4521	25	16	1997	1997	NUM
ejpam-4521	25	17	and	and	CCONJ
ejpam-4521	25	18	defined	define	VERB
ejpam-4521	25	19	the	the	DET
ejpam-4521	25	20	term	term	NOUN
ejpam-4521	25	21	“	"	PUNCT
ejpam-4521	25	22	forcing	force	VERB
ejpam-4521	25	23	domination	domination	NOUN
ejpam-4521	25	24	number	number	NOUN
ejpam-4521	25	25	”	"	PUNCT
ejpam-4521	25	26	.	.	PUNCT
ejpam-4521	26	1	in	in	ADP
ejpam-4521	26	2	2017	2017	NUM
ejpam-4521	26	3	,	,	PUNCT
ejpam-4521	26	4	john	john	PROPN
ejpam-4521	26	5	et	et	PROPN
ejpam-4521	26	6	.	.	PUNCT
ejpam-4521	27	1	al	al	PROPN
ejpam-4521	28	1	[	[	X
ejpam-4521	28	2	9	9	NUM
ejpam-4521	28	3	]	]	PUNCT
ejpam-4521	28	4	investigated	investigate	VERB
ejpam-4521	28	5	the	the	DET
ejpam-4521	28	6	forcing	force	VERB
ejpam-4521	28	7	connected	connect	VERB
ejpam-4521	28	8	domination	domination	NOUN
ejpam-4521	28	9	number	number	NOUN
ejpam-4521	28	10	of	of	ADP
ejpam-4521	28	11	a	a	DET
ejpam-4521	28	12	graph	graph	NOUN
ejpam-4521	28	13	,	,	PUNCT
ejpam-4521	28	14	and	and	CCONJ
ejpam-4521	28	15	c.	c.	PROPN
ejpam-4521	28	16	armada	armada	PROPN
ejpam-4521	28	17	and	and	CCONJ
ejpam-4521	28	18	s.	s.	PROPN
ejpam-4521	28	19	canoy	canoy	PROPN
ejpam-4521	28	20	jr	jr	PROPN
ejpam-4521	28	21	.	.	PUNCT
ejpam-4521	29	1	[	[	X
ejpam-4521	29	2	1	1	NUM
ejpam-4521	29	3	]	]	PUNCT
ejpam-4521	29	4	investigated	investigate	VERB
ejpam-4521	29	5	the	the	DET
ejpam-4521	29	6	forcing	force	VERB
ejpam-4521	29	7	independent	independent	ADJ
ejpam-4521	29	8	domination	domination	NOUN
ejpam-4521	29	9	number	number	NOUN
ejpam-4521	29	10	of	of	ADP
ejpam-4521	29	11	a	a	DET
ejpam-4521	29	12	graph	graph	NOUN
ejpam-4521	29	13	in	in	ADP
ejpam-4521	29	14	2019	2019	NUM
ejpam-4521	29	15	.	.	PUNCT
ejpam-4521	30	1	furthermore	furthermore	ADV
ejpam-4521	30	2	,	,	PUNCT
ejpam-4521	30	3	in	in	ADP
ejpam-4521	30	4	2018	2018	NUM
ejpam-4521	30	5	,	,	PUNCT
ejpam-4521	30	6	canoy	canoy	ADJ
ejpam-4521	30	7	et	et	PROPN
ejpam-4521	30	8	.	.	PUNCT
ejpam-4521	31	1	al	al	PROPN
ejpam-4521	32	1	[	[	X
ejpam-4521	32	2	2	2	NUM
ejpam-4521	32	3	]	]	PUNCT
ejpam-4521	32	4	investigated	investigate	VERB
ejpam-4521	32	5	the	the	DET
ejpam-4521	32	6	forcing	force	VERB
ejpam-4521	32	7	domination	domination	NOUN
ejpam-4521	32	8	number	number	NOUN
ejpam-4521	32	9	of	of	ADP
ejpam-4521	32	10	graphs	graph	NOUN
ejpam-4521	32	11	under	under	ADP
ejpam-4521	32	12	some	some	DET
ejpam-4521	32	13	binary	binary	ADJ
ejpam-4521	32	14	operations	operation	NOUN
ejpam-4521	32	15	.	.	PUNCT
ejpam-4521	33	1	in	in	ADP
ejpam-4521	33	2	this	this	DET
ejpam-4521	33	3	study	study	NOUN
ejpam-4521	33	4	,	,	PUNCT
ejpam-4521	33	5	the	the	DET
ejpam-4521	33	6	forcing	force	VERB
ejpam-4521	33	7	subsets	subset	NOUN
ejpam-4521	33	8	of	of	ADP
ejpam-4521	33	9	minimum	minimum	ADJ
ejpam-4521	33	10	connected	connected	ADJ
ejpam-4521	33	11	co	co	NOUN
ejpam-4521	33	12	-	-	ADJ
ejpam-4521	33	13	independent	independent	ADJ
ejpam-4521	33	14	hop	hop	NOUN
ejpam-4521	33	15	dominating	dominating	NOUN
ejpam-4521	33	16	sets	set	NOUN
ejpam-4521	33	17	in	in	ADP
ejpam-4521	33	18	graphs	graph	NOUN
ejpam-4521	33	19	are	be	AUX
ejpam-4521	33	20	defined	define	VERB
ejpam-4521	33	21	and	and	CCONJ
ejpam-4521	33	22	established	establish	VERB
ejpam-4521	33	23	and	and	CCONJ
ejpam-4521	33	24	some	some	DET
ejpam-4521	33	25	characterizations	characterization	NOUN
ejpam-4521	33	26	of	of	ADP
ejpam-4521	33	27	forcing	force	VERB
ejpam-4521	33	28	subsets	subset	NOUN
ejpam-4521	33	29	of	of	ADP
ejpam-4521	33	30	minimum	minimum	ADJ
ejpam-4521	33	31	connected	connected	ADJ
ejpam-4521	33	32	co	co	NOUN
ejpam-4521	33	33	-	-	ADJ
ejpam-4521	33	34	independent	independent	ADJ
ejpam-4521	33	35	hop	hop	NOUN
ejpam-4521	33	36	dominating	dominating	NOUN
ejpam-4521	33	37	sets	set	NOUN
ejpam-4521	33	38	of	of	ADP
ejpam-4521	33	39	graphs	graph	NOUN
ejpam-4521	33	40	resulting	result	VERB
ejpam-4521	33	41	from	from	ADP
ejpam-4521	33	42	the	the	DET
ejpam-4521	33	43	edge	edge	NOUN
ejpam-4521	33	44	corona	corona	NOUN
ejpam-4521	33	45	and	and	CCONJ
ejpam-4521	33	46	lexicographic	lexicographic	ADJ
ejpam-4521	33	47	product	product	NOUN
ejpam-4521	33	48	of	of	ADP
ejpam-4521	33	49	two	two	NUM
ejpam-4521	33	50	graphs	graph	NOUN
ejpam-4521	33	51	are	be	AUX
ejpam-4521	33	52	generated	generate	VERB
ejpam-4521	33	53	.	.	PUNCT
ejpam-4521	34	1	also	also	ADV
ejpam-4521	34	2	,	,	PUNCT
ejpam-4521	34	3	the	the	DET
ejpam-4521	34	4	values	value	NOUN
ejpam-4521	34	5	or	or	CCONJ
ejpam-4521	34	6	bounds	bound	NOUN
ejpam-4521	34	7	of	of	ADP
ejpam-4521	34	8	their	their	PRON
ejpam-4521	34	9	corresponding	correspond	VERB
ejpam-4521	34	10	forcing	force	VERB
ejpam-4521	34	11	connected	connect	VERB
ejpam-4521	34	12	co	co	NOUN
ejpam-4521	34	13	-	-	ADJ
ejpam-4521	34	14	independent	independent	ADJ
ejpam-4521	34	15	hop	hop	NOUN
ejpam-4521	34	16	domination	domination	NOUN
ejpam-4521	34	17	numbers	number	NOUN
ejpam-4521	34	18	are	be	AUX
ejpam-4521	34	19	determined	determine	VERB
ejpam-4521	34	20	.	.	PUNCT
ejpam-4521	35	1	connected	connect	VERB
ejpam-4521	35	2	co	co	ADJ
ejpam-4521	35	3	-	-	ADJ
ejpam-4521	35	4	independent	independent	ADJ
ejpam-4521	35	5	hop	hop	NOUN
ejpam-4521	35	6	domination	domination	NOUN
ejpam-4521	35	7	in	in	ADP
ejpam-4521	35	8	graphs	graph	NOUN
ejpam-4521	35	9	can	can	AUX
ejpam-4521	35	10	have	have	VERB
ejpam-4521	35	11	real	real	ADJ
ejpam-4521	35	12	world	world	NOUN
ejpam-4521	35	13	applications	application	NOUN
ejpam-4521	35	14	.	.	PUNCT
ejpam-4521	36	1	for	for	ADP
ejpam-4521	36	2	an	an	DET
ejpam-4521	36	3	application	application	NOUN
ejpam-4521	36	4	,	,	PUNCT
ejpam-4521	36	5	in	in	ADP
ejpam-4521	36	6	[	[	PUNCT
ejpam-4521	36	7	6	6	NUM
ejpam-4521	36	8	]	]	PUNCT
ejpam-4521	36	9	,	,	PUNCT
ejpam-4521	36	10	desormeaux	desormeaux	ADJ
ejpam-4521	36	11	,	,	PUNCT
ejpam-4521	36	12	haynes	hayne	NOUN
ejpam-4521	36	13	,	,	PUNCT
ejpam-4521	36	14	and	and	CCONJ
ejpam-4521	36	15	henning	henning	NOUN
ejpam-4521	36	16	inspired	inspire	VERB
ejpam-4521	36	17	their	their	PRON
ejpam-4521	36	18	research	research	NOUN
ejpam-4521	36	19	on	on	ADP
ejpam-4521	36	20	these	these	DET
ejpam-4521	36	21	concepts	concept	NOUN
ejpam-4521	36	22	through	through	ADP
ejpam-4521	36	23	social	social	ADJ
ejpam-4521	36	24	networking	network	VERB
ejpam-4521	36	25	applications	application	NOUN
ejpam-4521	36	26	.	.	PUNCT
ejpam-4521	37	1	they	they	PRON
ejpam-4521	37	2	considered	consider	VERB
ejpam-4521	37	3	a	a	DET
ejpam-4521	37	4	factory	factory	NOUN
ejpam-4521	37	5	with	with	ADP
ejpam-4521	37	6	a	a	DET
ejpam-4521	37	7	large	large	ADJ
ejpam-4521	37	8	number	number	NOUN
ejpam-4521	37	9	of	of	ADP
ejpam-4521	37	10	employees	employee	NOUN
ejpam-4521	37	11	and	and	CCONJ
ejpam-4521	37	12	needed	need	VERB
ejpam-4521	37	13	to	to	PART
ejpam-4521	37	14	implement	implement	VERB
ejpam-4521	37	15	a	a	DET
ejpam-4521	37	16	quality	quality	NOUN
ejpam-4521	37	17	assurance	assurance	NOUN
ejpam-4521	37	18	checking	check	VERB
ejpam-4521	37	19	system	system	NOUN
ejpam-4521	37	20	of	of	ADP
ejpam-4521	37	21	their	their	PRON
ejpam-4521	37	22	workers	worker	NOUN
ejpam-4521	37	23	.	.	PUNCT
ejpam-4521	38	1	the	the	DET
ejpam-4521	38	2	factory	factory	NOUN
ejpam-4521	38	3	manager	manager	NOUN
ejpam-4521	38	4	decides	decide	VERB
ejpam-4521	38	5	to	to	PART
ejpam-4521	38	6	designate	designate	VERB
ejpam-4521	38	7	an	an	DET
ejpam-4521	38	8	internal	internal	ADJ
ejpam-4521	38	9	committee	committee	NOUN
ejpam-4521	38	10	to	to	PART
ejpam-4521	38	11	do	do	VERB
ejpam-4521	38	12	this	this	PRON
ejpam-4521	38	13	.	.	PUNCT
ejpam-4521	39	1	in	in	ADP
ejpam-4521	39	2	other	other	ADJ
ejpam-4521	39	3	words	word	NOUN
ejpam-4521	39	4	,	,	PUNCT
ejpam-4521	39	5	the	the	DET
ejpam-4521	39	6	manager	manager	NOUN
ejpam-4521	39	7	will	will	AUX
ejpam-4521	39	8	select	select	VERB
ejpam-4521	39	9	some	some	DET
ejpam-4521	39	10	workers	worker	NOUN
ejpam-4521	39	11	to	to	PART
ejpam-4521	39	12	form	form	VERB
ejpam-4521	39	13	a	a	DET
ejpam-4521	39	14	quality	quality	NOUN
ejpam-4521	39	15	assurance	assurance	NOUN
ejpam-4521	39	16	team	team	NOUN
ejpam-4521	39	17	to	to	PART
ejpam-4521	39	18	inspect	inspect	VERB
ejpam-4521	39	19	the	the	DET
ejpam-4521	39	20	work	work	NOUN
ejpam-4521	39	21	of	of	ADP
ejpam-4521	39	22	their	their	PRON
ejpam-4521	39	23	co	co	NOUN
ejpam-4521	39	24	-	-	NOUN
ejpam-4521	39	25	workers	worker	NOUN
ejpam-4521	39	26	.	.	PUNCT
ejpam-4521	40	1	the	the	DET
ejpam-4521	40	2	manager	manager	NOUN
ejpam-4521	40	3	wants	want	VERB
ejpam-4521	40	4	to	to	PART
ejpam-4521	40	5	keep	keep	VERB
ejpam-4521	40	6	this	this	DET
ejpam-4521	40	7	team	team	NOUN
ejpam-4521	40	8	as	as	ADV
ejpam-4521	40	9	small	small	ADJ
ejpam-4521	40	10	as	as	ADP
ejpam-4521	40	11	possible	possible	ADJ
ejpam-4521	40	12	to	to	PART
ejpam-4521	40	13	minimize	minimize	VERB
ejpam-4521	40	14	costs	cost	NOUN
ejpam-4521	40	15	(	(	PUNCT
ejpam-4521	40	16	extra	extra	ADJ
ejpam-4521	40	17	costs	cost	NOUN
ejpam-4521	40	18	for	for	ADP
ejpam-4521	40	19	inspectors	inspector	NOUN
ejpam-4521	40	20	)	)	PUNCT
ejpam-4521	40	21	and	and	CCONJ
ejpam-4521	40	22	protect	protect	VERB
ejpam-4521	40	23	privacy	privacy	NOUN
ejpam-4521	40	24	(	(	PUNCT
ejpam-4521	40	25	keep	keep	VERB
ejpam-4521	40	26	the	the	DET
ejpam-4521	40	27	inspectors	inspector	NOUN
ejpam-4521	40	28	’	’	PART
ejpam-4521	40	29	identity	identity	NOUN
ejpam-4521	40	30	confidential	confidential	ADJ
ejpam-4521	40	31	)	)	PUNCT
ejpam-4521	40	32	.	.	PUNCT
ejpam-4521	41	1	to	to	PART
ejpam-4521	41	2	avoid	avoid	VERB
ejpam-4521	41	3	bias	bias	NOUN
ejpam-4521	41	4	,	,	PUNCT
ejpam-4521	41	5	an	an	DET
ejpam-4521	41	6	inspector	inspector	NOUN
ejpam-4521	41	7	should	should	AUX
ejpam-4521	41	8	neither	neither	CCONJ
ejpam-4521	41	9	be	be	AUX
ejpam-4521	41	10	close	close	ADJ
ejpam-4521	41	11	friends	friend	NOUN
ejpam-4521	41	12	nor	nor	CCONJ
ejpam-4521	41	13	enemies	enemy	NOUN
ejpam-4521	41	14	with	with	ADP
ejpam-4521	41	15	any	any	PRON
ejpam-4521	41	16	of	of	ADP
ejpam-4521	41	17	the	the	DET
ejpam-4521	41	18	workers	worker	NOUN
ejpam-4521	42	1	he	he	PRON
ejpam-4521	42	2	/	/	PUNCT
ejpam-4521	43	1	she	she	PRON
ejpam-4521	43	2	is	be	AUX
ejpam-4521	43	3	responsible	responsible	ADJ
ejpam-4521	43	4	for	for	ADP
ejpam-4521	43	5	inspecting	inspect	VERB
ejpam-4521	43	6	.	.	PUNCT
ejpam-4521	44	1	to	to	PART
ejpam-4521	44	2	model	model	VERB
ejpam-4521	44	3	this	this	DET
ejpam-4521	44	4	situation	situation	NOUN
ejpam-4521	44	5	,	,	PUNCT
ejpam-4521	44	6	a	a	DET
ejpam-4521	44	7	social	social	ADJ
ejpam-4521	44	8	network	network	NOUN
ejpam-4521	44	9	graph	graph	NOUN
ejpam-4521	44	10	can	can	AUX
ejpam-4521	44	11	be	be	AUX
ejpam-4521	44	12	constructed	construct	VERB
ejpam-4521	44	13	in	in	ADP
ejpam-4521	44	14	which	which	PRON
ejpam-4521	44	15	each	each	DET
ejpam-4521	44	16	worker	worker	NOUN
ejpam-4521	44	17	is	be	AUX
ejpam-4521	44	18	represented	represent	VERB
ejpam-4521	44	19	by	by	ADP
ejpam-4521	44	20	a	a	DET
ejpam-4521	44	21	vertex	vertex	NOUN
ejpam-4521	44	22	and	and	CCONJ
ejpam-4521	44	23	an	an	DET
ejpam-4521	44	24	edge	edge	NOUN
ejpam-4521	44	25	between	between	ADP
ejpam-4521	44	26	two	two	NUM
ejpam-4521	44	27	workers	worker	NOUN
ejpam-4521	44	28	represents	represent	VERB
ejpam-4521	44	29	possible	possible	ADJ
ejpam-4521	44	30	bias	bias	NOUN
ejpam-4521	44	31	,	,	PUNCT
ejpam-4521	44	32	that	that	ADV
ejpam-4521	44	33	is	is	ADV
ejpam-4521	44	34	,	,	PUNCT
ejpam-4521	44	35	whether	whether	SCONJ
ejpam-4521	44	36	the	the	DET
ejpam-4521	44	37	two	two	NUM
ejpam-4521	44	38	workers	worker	NOUN
ejpam-4521	44	39	are	be	AUX
ejpam-4521	44	40	close	close	ADJ
ejpam-4521	44	41	friends	friend	NOUN
ejpam-4521	44	42	or	or	CCONJ
ejpam-4521	44	43	enemies	enemy	NOUN
ejpam-4521	44	44	.	.	PUNCT
ejpam-4521	45	1	ideally	ideally	ADV
ejpam-4521	45	2	,	,	PUNCT
ejpam-4521	45	3	an	an	DET
ejpam-4521	45	4	inspector	inspector	NOUN
ejpam-4521	45	5	should	should	AUX
ejpam-4521	45	6	not	not	PART
ejpam-4521	45	7	be	be	AUX
ejpam-4521	45	8	adjacent	adjacent	ADJ
ejpam-4521	45	9	to	to	ADP
ejpam-4521	45	10	any	any	DET
ejpam-4521	45	11	worker	worker	NOUN
ejpam-4521	45	12	who	who	PRON
ejpam-4521	45	13	is	be	AUX
ejpam-4521	45	14	being	be	AUX
ejpam-4521	45	15	inspected	inspect	VERB
ejpam-4521	45	16	.	.	PUNCT
ejpam-4521	46	1	in	in	ADP
ejpam-4521	46	2	connected	connected	ADJ
ejpam-4521	46	3	co	co	ADJ
ejpam-4521	46	4	-	-	ADJ
ejpam-4521	46	5	independent	independent	ADJ
ejpam-4521	46	6	hop	hop	NOUN
ejpam-4521	46	7	domination	domination	NOUN
ejpam-4521	46	8	[	[	X
ejpam-4521	46	9	11	11	NUM
ejpam-4521	46	10	]	]	PUNCT
ejpam-4521	46	11	,	,	PUNCT
ejpam-4521	46	12	every	every	DET
ejpam-4521	46	13	worker	worker	NOUN
ejpam-4521	46	14	will	will	AUX
ejpam-4521	46	15	be	be	AUX
ejpam-4521	46	16	inspected	inspect	VERB
ejpam-4521	46	17	by	by	ADP
ejpam-4521	46	18	the	the	DET
ejpam-4521	46	19	nearest	near	ADJ
ejpam-4521	46	20	non	non	ADJ
ejpam-4521	46	21	-	-	ADJ
ejpam-4521	46	22	biased	biased	ADJ
ejpam-4521	46	23	inspector	inspector	NOUN
ejpam-4521	46	24	.	.	PUNCT
ejpam-4521	47	1	that	that	PRON
ejpam-4521	47	2	is	is	ADV
ejpam-4521	47	3	,	,	PUNCT
ejpam-4521	47	4	an	an	DET
ejpam-4521	47	5	inspector	inspector	NOUN
ejpam-4521	47	6	who	who	PRON
ejpam-4521	47	7	is	be	AUX
ejpam-4521	47	8	a	a	DET
ejpam-4521	47	9	close	close	ADJ
ejpam-4521	47	10	friend	friend	NOUN
ejpam-4521	47	11	(	(	PUNCT
ejpam-4521	47	12	or	or	CCONJ
ejpam-4521	47	13	an	an	DET
ejpam-4521	47	14	enemy	enemy	NOUN
ejpam-4521	47	15	)	)	PUNCT
ejpam-4521	47	16	of	of	ADP
ejpam-4521	47	17	a	a	DET
ejpam-4521	47	18	close	close	ADJ
ejpam-4521	47	19	friend	friend	NOUN
ejpam-4521	47	20	(	(	PUNCT
ejpam-4521	47	21	or	or	CCONJ
ejpam-4521	47	22	enemy	enemy	NOUN
ejpam-4521	47	23	)	)	PUNCT
ejpam-4521	47	24	of	of	ADP
ejpam-4521	47	25	a	a	DET
ejpam-4521	47	26	worker	worker	NOUN
ejpam-4521	47	27	.	.	PUNCT
ejpam-4521	48	1	this	this	PRON
ejpam-4521	48	2	is	be	AUX
ejpam-4521	48	3	to	to	PART
ejpam-4521	48	4	save	save	VERB
ejpam-4521	48	5	time	time	NOUN
ejpam-4521	48	6	and	and	CCONJ
ejpam-4521	48	7	effort	effort	NOUN
ejpam-4521	48	8	of	of	ADP
ejpam-4521	48	9	locating	locate	VERB
ejpam-4521	48	10	a	a	DET
ejpam-4521	48	11	particular	particular	ADJ
ejpam-4521	48	12	worker	worker	NOUN
ejpam-4521	48	13	.	.	PUNCT
ejpam-4521	49	1	also	also	ADV
ejpam-4521	49	2	,	,	PUNCT
ejpam-4521	49	3	the	the	DET
ejpam-4521	49	4	inspectors	inspector	NOUN
ejpam-4521	49	5	should	should	AUX
ejpam-4521	49	6	be	be	AUX
ejpam-4521	49	7	acquainted	acquaint	VERB
ejpam-4521	49	8	with	with	ADP
ejpam-4521	49	9	each	each	DET
ejpam-4521	49	10	other	other	ADJ
ejpam-4521	49	11	and	and	CCONJ
ejpam-4521	49	12	all	all	DET
ejpam-4521	49	13	non	non	ADJ
ejpam-4521	49	14	-	-	ADJ
ejpam-4521	49	15	inspector	inspector	ADJ
ejpam-4521	49	16	workers	worker	NOUN
ejpam-4521	49	17	are	be	AUX
ejpam-4521	49	18	neither	neither	CCONJ
ejpam-4521	49	19	friends	friend	NOUN
ejpam-4521	49	20	nor	nor	CCONJ
ejpam-4521	49	21	enemies	enemy	NOUN
ejpam-4521	49	22	,	,	PUNCT
ejpam-4521	49	23	that	that	ADV
ejpam-4521	49	24	is	is	ADV
ejpam-4521	49	25	,	,	PUNCT
ejpam-4521	49	26	they	they	PRON
ejpam-4521	49	27	are	be	AUX
ejpam-4521	49	28	not	not	PART
ejpam-4521	49	29	adjacent	adjacent	ADJ
ejpam-4521	49	30	or	or	CCONJ
ejpam-4521	49	31	there	there	PRON
ejpam-4521	49	32	is	be	VERB
ejpam-4521	49	33	no	no	DET
ejpam-4521	49	34	edge	edge	NOUN
ejpam-4521	49	35	between	between	ADP
ejpam-4521	49	36	them	they	PRON
ejpam-4521	49	37	.	.	PUNCT
ejpam-4521	50	1	the	the	DET
ejpam-4521	50	2	connected	connected	ADJ
ejpam-4521	50	3	co	co	NOUN
ejpam-4521	50	4	-	-	ADJ
ejpam-4521	50	5	independent	independent	ADJ
ejpam-4521	50	6	hop	hop	NOUN
ejpam-4521	50	7	domination	domination	NOUN
ejpam-4521	50	8	number	number	NOUN
ejpam-4521	50	9	will	will	AUX
ejpam-4521	50	10	give	give	VERB
ejpam-4521	50	11	the	the	DET
ejpam-4521	50	12	minimum	minimum	ADJ
ejpam-4521	50	13	number	number	NOUN
ejpam-4521	50	14	of	of	ADP
ejpam-4521	50	15	inspectors	inspector	NOUN
ejpam-4521	50	16	needed	need	VERB
ejpam-4521	50	17	.	.	PUNCT
ejpam-4521	51	1	in	in	ADP
ejpam-4521	51	2	forcing	force	VERB
ejpam-4521	51	3	subsets	subset	NOUN
ejpam-4521	51	4	of	of	ADP
ejpam-4521	51	5	connected	connected	ADJ
ejpam-4521	51	6	co	co	ADJ
ejpam-4521	51	7	-	-	ADJ
ejpam-4521	51	8	independent	independent	ADJ
ejpam-4521	51	9	hop	hop	NOUN
ejpam-4521	51	10	domination	domination	NOUN
ejpam-4521	51	11	,	,	PUNCT
ejpam-4521	51	12	in	in	ADP
ejpam-4521	51	13	each	each	DET
ejpam-4521	51	14	respective	respective	ADJ
ejpam-4521	51	15	group	group	NOUN
ejpam-4521	51	16	of	of	ADP
ejpam-4521	51	17	minimum	minimum	ADJ
ejpam-4521	51	18	number	number	NOUN
ejpam-4521	51	19	of	of	ADP
ejpam-4521	51	20	inspectors	inspector	NOUN
ejpam-4521	51	21	that	that	PRON
ejpam-4521	51	22	will	will	AUX
ejpam-4521	51	23	inspect	inspect	VERB
ejpam-4521	51	24	the	the	DET
ejpam-4521	51	25	workers	worker	NOUN
ejpam-4521	51	26	in	in	ADP
ejpam-4521	51	27	the	the	DET
ejpam-4521	51	28	designated	designate	VERB
ejpam-4521	51	29	areas	area	NOUN
ejpam-4521	51	30	of	of	ADP
ejpam-4521	51	31	the	the	DET
ejpam-4521	51	32	factory	factory	NOUN
ejpam-4521	51	33	,	,	PUNCT
ejpam-4521	51	34	the	the	DET
ejpam-4521	51	35	members	member	NOUN
ejpam-4521	51	36	of	of	ADP
ejpam-4521	51	37	that	that	DET
ejpam-4521	51	38	particular	particular	ADJ
ejpam-4521	51	39	group	group	NOUN
ejpam-4521	51	40	of	of	ADP
ejpam-4521	51	41	minimum	minimum	ADJ
ejpam-4521	51	42	number	number	NOUN
ejpam-4521	51	43	of	of	ADP
ejpam-4521	51	44	inspectors	inspector	NOUN
ejpam-4521	51	45	will	will	AUX
ejpam-4521	51	46	be	be	AUX
ejpam-4521	51	47	assigned	assign	VERB
ejpam-4521	51	48	only	only	ADV
ejpam-4521	51	49	to	to	ADP
ejpam-4521	51	50	that	that	DET
ejpam-4521	51	51	distinct	distinct	ADJ
ejpam-4521	51	52	group	group	NOUN
ejpam-4521	51	53	of	of	ADP
ejpam-4521	51	54	minimum	minimum	ADJ
ejpam-4521	51	55	number	number	NOUN
ejpam-4521	51	56	of	of	ADP
ejpam-4521	51	57	inspectors	inspector	NOUN
ejpam-4521	51	58	,	,	PUNCT
ejpam-4521	51	59	that	that	ADV
ejpam-4521	51	60	is	is	ADV
ejpam-4521	51	61	,	,	PUNCT
ejpam-4521	51	62	it	it	PRON
ejpam-4521	51	63	will	will	AUX
ejpam-4521	51	64	strengthen	strengthen	VERB
ejpam-4521	51	65	the	the	DET
ejpam-4521	51	66	bond	bond	NOUN
ejpam-4521	51	67	of	of	ADP
ejpam-4521	51	68	the	the	DET
ejpam-4521	51	69	respective	respective	ADJ
ejpam-4521	51	70	group	group	NOUN
ejpam-4521	51	71	of	of	ADP
ejpam-4521	51	72	minimum	minimum	ADJ
ejpam-4521	51	73	number	number	NOUN
ejpam-4521	51	74	of	of	ADP
ejpam-4521	51	75	non	non	ADJ
ejpam-4521	51	76	-	-	ADJ
ejpam-4521	51	77	biased	biased	ADJ
ejpam-4521	51	78	inspectors	inspector	NOUN
ejpam-4521	51	79	with	with	ADP
ejpam-4521	51	80	each	each	DET
ejpam-4521	51	81	other	other	ADJ
ejpam-4521	51	82	,	,	PUNCT
ejpam-4521	51	83	since	since	SCONJ
ejpam-4521	51	84	they	they	PRON
ejpam-4521	51	85	are	be	AUX
ejpam-4521	51	86	uniquely	uniquely	ADV
ejpam-4521	51	87	assigned	assign	VERB
ejpam-4521	51	88	to	to	ADP
ejpam-4521	51	89	particular	particular	ADJ
ejpam-4521	51	90	groups	group	NOUN
ejpam-4521	51	91	,	,	PUNCT
ejpam-4521	51	92	and	and	CCONJ
ejpam-4521	51	93	they	they	PRON
ejpam-4521	51	94	will	will	AUX
ejpam-4521	51	95	trust	trust	VERB
ejpam-4521	51	96	each	each	DET
ejpam-4521	51	97	other	other	ADJ
ejpam-4521	51	98	more	more	ADV
ejpam-4521	51	99	doing	do	VERB
ejpam-4521	51	100	their	their	PRON
ejpam-4521	51	101	duties	duty	NOUN
ejpam-4521	51	102	and	and	CCONJ
ejpam-4521	51	103	will	will	AUX
ejpam-4521	51	104	have	have	VERB
ejpam-4521	51	105	a	a	DET
ejpam-4521	51	106	much	much	ADV
ejpam-4521	51	107	easier	easy	ADJ
ejpam-4521	51	108	time	time	NOUN
ejpam-4521	51	109	doing	do	VERB
ejpam-4521	51	110	y.d	y.d	PROPN
ejpam-4521	51	111	.	.	PROPN
ejpam-4521	51	112	calanza	calanza	PROPN
ejpam-4521	51	113	,	,	PUNCT
ejpam-4521	51	114	h.	h.	PROPN
ejpam-4521	51	115	rara	rara	PROPN
ejpam-4521	51	116	/	/	SYM
ejpam-4521	51	117	eur	eur	PROPN
ejpam-4521	51	118	.	.	PUNCT
ejpam-4521	52	1	j.	j.	PROPN
ejpam-4521	52	2	pure	pure	PROPN
ejpam-4521	52	3	appl	appl	PROPN
ejpam-4521	52	4	.	.	PROPN
ejpam-4521	52	5	math	math	PROPN
ejpam-4521	52	6	,	,	PUNCT
ejpam-4521	52	7	15	15	NUM
ejpam-4521	52	8	(	(	PUNCT
ejpam-4521	52	9	4	4	NUM
ejpam-4521	52	10	)	)	PUNCT
ejpam-4521	52	11	(	(	PUNCT
ejpam-4521	52	12	2022	2022	NUM
ejpam-4521	52	13	)	)	PUNCT
ejpam-4521	52	14	,	,	PUNCT
ejpam-4521	52	15	1597	1597	NUM
ejpam-4521	52	16	-	-	SYM
ejpam-4521	52	17	1612	1612	NUM
ejpam-4521	52	18	1599	1599	NUM
ejpam-4521	52	19	their	their	PRON
ejpam-4521	52	20	job	job	NOUN
ejpam-4521	52	21	regarding	regard	VERB
ejpam-4521	52	22	with	with	ADP
ejpam-4521	52	23	the	the	DET
ejpam-4521	52	24	respective	respective	ADJ
ejpam-4521	52	25	workers	worker	NOUN
ejpam-4521	52	26	that	that	SCONJ
ejpam-4521	52	27	they	they	PRON
ejpam-4521	52	28	are	be	AUX
ejpam-4521	52	29	assigned	assign	VERB
ejpam-4521	52	30	to	to	PART
ejpam-4521	52	31	inspect	inspect	VERB
ejpam-4521	52	32	.	.	PUNCT
ejpam-4521	53	1	the	the	DET
ejpam-4521	53	2	forcing	force	VERB
ejpam-4521	53	3	connected	connect	VERB
ejpam-4521	53	4	co	co	ADJ
ejpam-4521	53	5	-	-	ADJ
ejpam-4521	53	6	independent	independent	ADJ
ejpam-4521	53	7	hop	hop	NOUN
ejpam-4521	53	8	domination	domination	NOUN
ejpam-4521	53	9	number	number	NOUN
ejpam-4521	53	10	will	will	AUX
ejpam-4521	53	11	determine	determine	VERB
ejpam-4521	53	12	the	the	DET
ejpam-4521	53	13	minimum	minimum	ADJ
ejpam-4521	53	14	number	number	NOUN
ejpam-4521	53	15	of	of	ADP
ejpam-4521	53	16	members	member	NOUN
ejpam-4521	53	17	from	from	ADP
ejpam-4521	53	18	the	the	DET
ejpam-4521	53	19	respective	respective	ADJ
ejpam-4521	53	20	group	group	NOUN
ejpam-4521	53	21	of	of	ADP
ejpam-4521	53	22	minimum	minimum	ADJ
ejpam-4521	53	23	number	number	NOUN
ejpam-4521	53	24	of	of	ADP
ejpam-4521	53	25	inspectors	inspector	NOUN
ejpam-4521	53	26	that	that	PRON
ejpam-4521	53	27	will	will	AUX
ejpam-4521	53	28	be	be	AUX
ejpam-4521	53	29	assigned	assign	VERB
ejpam-4521	53	30	only	only	ADV
ejpam-4521	53	31	to	to	ADP
ejpam-4521	53	32	that	that	DET
ejpam-4521	53	33	particular	particular	ADJ
ejpam-4521	53	34	group	group	NOUN
ejpam-4521	53	35	of	of	ADP
ejpam-4521	53	36	respective	respective	ADJ
ejpam-4521	53	37	minimum	minimum	ADJ
ejpam-4521	53	38	number	number	NOUN
ejpam-4521	53	39	of	of	ADP
ejpam-4521	53	40	inspectors	inspector	NOUN
ejpam-4521	53	41	.	.	PUNCT
ejpam-4521	54	1	in	in	ADP
ejpam-4521	54	2	this	this	DET
ejpam-4521	54	3	study	study	NOUN
ejpam-4521	54	4	,	,	PUNCT
ejpam-4521	54	5	we	we	PRON
ejpam-4521	54	6	only	only	ADV
ejpam-4521	54	7	consider	consider	VERB
ejpam-4521	54	8	graphs	graph	NOUN
ejpam-4521	54	9	that	that	PRON
ejpam-4521	54	10	are	be	AUX
ejpam-4521	54	11	finite	finite	ADJ
ejpam-4521	54	12	,	,	PUNCT
ejpam-4521	54	13	simple	simple	ADJ
ejpam-4521	54	14	,	,	PUNCT
ejpam-4521	54	15	undirected	undirected	ADJ
ejpam-4521	54	16	and	and	CCONJ
ejpam-4521	54	17	connected	connected	ADJ
ejpam-4521	54	18	.	.	PUNCT
ejpam-4521	55	1	readers	reader	NOUN
ejpam-4521	55	2	are	be	AUX
ejpam-4521	55	3	referred	refer	VERB
ejpam-4521	55	4	to	to	ADP
ejpam-4521	55	5	[	[	X
ejpam-4521	55	6	8	8	NUM
ejpam-4521	55	7	]	]	PUNCT
ejpam-4521	55	8	for	for	ADP
ejpam-4521	55	9	elementary	elementary	ADJ
ejpam-4521	55	10	graph	graph	NOUN
ejpam-4521	55	11	theoretic	theoretic	ADJ
ejpam-4521	55	12	concepts	concept	NOUN
ejpam-4521	55	13	.	.	PUNCT
ejpam-4521	56	1	an	an	DET
ejpam-4521	56	2	independent	independent	ADJ
ejpam-4521	56	3	set	set	NOUN
ejpam-4521	56	4	s	s	NOUN
ejpam-4521	56	5	in	in	ADP
ejpam-4521	56	6	a	a	DET
ejpam-4521	56	7	graph	graph	NOUN
ejpam-4521	56	8	g	g	NOUN
ejpam-4521	56	9	is	be	AUX
ejpam-4521	56	10	a	a	DET
ejpam-4521	56	11	subset	subset	NOUN
ejpam-4521	56	12	of	of	ADP
ejpam-4521	56	13	the	the	DET
ejpam-4521	56	14	vertex	vertex	NOUN
ejpam-4521	56	15	-	-	PUNCT
ejpam-4521	56	16	set	set	NOUN
ejpam-4521	56	17	of	of	ADP
ejpam-4521	56	18	g	g	NOUN
ejpam-4521	56	19	such	such	ADJ
ejpam-4521	56	20	that	that	SCONJ
ejpam-4521	56	21	no	no	DET
ejpam-4521	56	22	two	two	NUM
ejpam-4521	56	23	vertices	vertex	NOUN
ejpam-4521	56	24	in	in	ADP
ejpam-4521	56	25	s	s	NOUN
ejpam-4521	56	26	are	be	AUX
ejpam-4521	56	27	adjacent	adjacent	ADJ
ejpam-4521	56	28	in	in	ADP
ejpam-4521	56	29	g.	g.	PROPN
ejpam-4521	56	30	the	the	DET
ejpam-4521	56	31	cardinality	cardinality	NOUN
ejpam-4521	56	32	of	of	ADP
ejpam-4521	56	33	a	a	DET
ejpam-4521	56	34	maximum	maximum	ADJ
ejpam-4521	56	35	independent	independent	ADJ
ejpam-4521	56	36	set	set	NOUN
ejpam-4521	56	37	is	be	AUX
ejpam-4521	56	38	called	call	VERB
ejpam-4521	56	39	the	the	DET
ejpam-4521	56	40	independence	independence	NOUN
ejpam-4521	56	41	number	number	NOUN
ejpam-4521	56	42	of	of	ADP
ejpam-4521	56	43	g	g	NOUN
ejpam-4521	56	44	and	and	CCONJ
ejpam-4521	56	45	is	be	AUX
ejpam-4521	56	46	denoted	denote	VERB
ejpam-4521	56	47	by	by	ADP
ejpam-4521	56	48	β(g	β(g	PROPN
ejpam-4521	56	49	)	)	PUNCT
ejpam-4521	56	50	.	.	PUNCT
ejpam-4521	57	1	an	an	DET
ejpam-4521	57	2	independent	independent	ADJ
ejpam-4521	57	3	set	set	NOUN
ejpam-4521	57	4	s	s	PROPN
ejpam-4521	57	5	⊆	⊆	NUM
ejpam-4521	57	6	v	v	NOUN
ejpam-4521	57	7	(	(	PUNCT
ejpam-4521	57	8	g	g	NOUN
ejpam-4521	57	9	)	)	PUNCT
ejpam-4521	57	10	with	with	ADP
ejpam-4521	57	11	|s|	|s|	PROPN
ejpam-4521	57	12	=	=	SYM
ejpam-4521	57	13	β(g	β(g	PROPN
ejpam-4521	57	14	)	)	PUNCT
ejpam-4521	57	15	is	be	AUX
ejpam-4521	57	16	called	call	VERB
ejpam-4521	57	17	a	a	DET
ejpam-4521	57	18	β	β	NOUN
ejpam-4521	57	19	-	-	NOUN
ejpam-4521	57	20	set	set	NOUN
ejpam-4521	57	21	of	of	ADP
ejpam-4521	57	22	g.	g.	PROPN
ejpam-4521	57	23	a	a	DET
ejpam-4521	57	24	set	set	NOUN
ejpam-4521	57	25	s	s	PROPN
ejpam-4521	57	26	⊆	⊆	NUM
ejpam-4521	57	27	v	v	NOUN
ejpam-4521	57	28	(	(	PUNCT
ejpam-4521	57	29	g	g	NOUN
ejpam-4521	57	30	)	)	PUNCT
ejpam-4521	57	31	is	be	AUX
ejpam-4521	57	32	a	a	DET
ejpam-4521	57	33	co	co	ADJ
ejpam-4521	57	34	-	-	ADJ
ejpam-4521	57	35	independent	independent	ADJ
ejpam-4521	57	36	set	set	NOUN
ejpam-4521	57	37	of	of	ADP
ejpam-4521	57	38	g	g	PROPN
ejpam-4521	57	39	if	if	SCONJ
ejpam-4521	57	40	v	v	X
ejpam-4521	57	41	(	(	PUNCT
ejpam-4521	57	42	g)\s	g)\s	NOUN
ejpam-4521	57	43	is	be	AUX
ejpam-4521	57	44	independent	independent	ADJ
ejpam-4521	57	45	.	.	PUNCT
ejpam-4521	58	1	the	the	DET
ejpam-4521	58	2	minimum	minimum	ADJ
ejpam-4521	58	3	cardinality	cardinality	NOUN
ejpam-4521	58	4	of	of	ADP
ejpam-4521	58	5	a	a	DET
ejpam-4521	58	6	co	co	ADJ
ejpam-4521	58	7	-	-	ADJ
ejpam-4521	58	8	independent	independent	ADJ
ejpam-4521	58	9	set	set	NOUN
ejpam-4521	58	10	in	in	ADP
ejpam-4521	58	11	g	g	NOUN
ejpam-4521	58	12	,	,	PUNCT
ejpam-4521	58	13	denoted	denote	VERB
ejpam-4521	58	14	by	by	ADP
ejpam-4521	58	15	coi(g	coi(g	NOUN
ejpam-4521	58	16	)	)	PUNCT
ejpam-4521	58	17	is	be	AUX
ejpam-4521	58	18	called	call	VERB
ejpam-4521	58	19	the	the	DET
ejpam-4521	58	20	co	co	ADJ
ejpam-4521	58	21	-	-	ADJ
ejpam-4521	58	22	independent	independent	ADJ
ejpam-4521	58	23	number	number	NOUN
ejpam-4521	58	24	of	of	ADP
ejpam-4521	58	25	g.	g.	PROPN
ejpam-4521	58	26	a	a	DET
ejpam-4521	58	27	co	co	ADJ
ejpam-4521	58	28	-	-	ADJ
ejpam-4521	58	29	independent	independent	ADJ
ejpam-4521	58	30	set	set	NOUN
ejpam-4521	58	31	s	s	NOUN
ejpam-4521	58	32	with	with	ADP
ejpam-4521	58	33	|s|	|s|	NOUN
ejpam-4521	58	34	=	=	SYM
ejpam-4521	58	35	coi(g	coi(g	PROPN
ejpam-4521	58	36	)	)	PUNCT
ejpam-4521	58	37	is	be	AUX
ejpam-4521	58	38	called	call	VERB
ejpam-4521	58	39	a	a	DET
ejpam-4521	58	40	coi	coi	NOUN
ejpam-4521	58	41	-set	-set	PUNCT
ejpam-4521	58	42	of	of	ADP
ejpam-4521	58	43	g.	g.	PROPN
ejpam-4521	58	44	a	a	DET
ejpam-4521	58	45	dominating	dominating	NOUN
ejpam-4521	58	46	set	set	NOUN
ejpam-4521	58	47	d	d	PROPN
ejpam-4521	58	48	⊆	⊆	NUM
ejpam-4521	58	49	v	v	ADP
ejpam-4521	58	50	(	(	PUNCT
ejpam-4521	58	51	g	g	NOUN
ejpam-4521	58	52	)	)	PUNCT
ejpam-4521	58	53	is	be	AUX
ejpam-4521	58	54	called	call	VERB
ejpam-4521	58	55	a	a	DET
ejpam-4521	58	56	connected	connected	ADJ
ejpam-4521	58	57	co	co	ADJ
ejpam-4521	58	58	-	-	ADJ
ejpam-4521	58	59	independent	independent	ADJ
ejpam-4521	58	60	dominating	dominating	NOUN
ejpam-4521	58	61	set	set	NOUN
ejpam-4521	58	62	of	of	ADP
ejpam-4521	58	63	g	g	PROPN
ejpam-4521	58	64	if	if	SCONJ
ejpam-4521	58	65	the	the	DET
ejpam-4521	58	66	subgraph	subgraph	NOUN
ejpam-4521	58	67	⟨d⟩	⟨d⟩	PROPN
ejpam-4521	58	68	is	be	AUX
ejpam-4521	58	69	connected	connect	VERB
ejpam-4521	58	70	and	and	CCONJ
ejpam-4521	58	71	v	v	ADJ
ejpam-4521	58	72	(	(	PUNCT
ejpam-4521	58	73	g	g	NOUN
ejpam-4521	58	74	)	)	PUNCT
ejpam-4521	58	75	\d	\d	NOUN
ejpam-4521	58	76	is	be	AUX
ejpam-4521	58	77	an	an	DET
ejpam-4521	58	78	independent	independent	ADJ
ejpam-4521	58	79	set	set	NOUN
ejpam-4521	58	80	.	.	PUNCT
ejpam-4521	59	1	the	the	DET
ejpam-4521	59	2	cardinality	cardinality	NOUN
ejpam-4521	59	3	of	of	ADP
ejpam-4521	59	4	such	such	DET
ejpam-4521	59	5	a	a	DET
ejpam-4521	59	6	minimum	minimum	NOUN
ejpam-4521	59	7	set	set	NOUN
ejpam-4521	59	8	d	d	NOUN
ejpam-4521	59	9	is	be	AUX
ejpam-4521	59	10	called	call	VERB
ejpam-4521	59	11	connected	connected	ADJ
ejpam-4521	59	12	co	co	ADJ
ejpam-4521	59	13	-	-	ADJ
ejpam-4521	59	14	independent	independent	ADJ
ejpam-4521	59	15	domination	domination	NOUN
ejpam-4521	59	16	number	number	NOUN
ejpam-4521	59	17	of	of	ADP
ejpam-4521	59	18	g	g	PROPN
ejpam-4521	59	19	denoted	denote	VERB
ejpam-4521	59	20	by	by	ADP
ejpam-4521	59	21	γc	γc	PROPN
ejpam-4521	59	22	,	,	PUNCT
ejpam-4521	59	23	coi(g	coi(g	PROPN
ejpam-4521	59	24	)	)	PUNCT
ejpam-4521	59	25	.	.	PUNCT
ejpam-4521	60	1	a	a	DET
ejpam-4521	60	2	connected	connected	ADJ
ejpam-4521	60	3	co	co	ADJ
ejpam-4521	60	4	-	-	ADJ
ejpam-4521	60	5	independent	independent	ADJ
ejpam-4521	60	6	dominating	dominating	NOUN
ejpam-4521	60	7	set	set	NOUN
ejpam-4521	60	8	d	d	NOUN
ejpam-4521	60	9	with	with	ADP
ejpam-4521	60	10	|d|	|d|	PROPN
ejpam-4521	60	11	=	=	SYM
ejpam-4521	60	12	γc	γc	PROPN
ejpam-4521	60	13	,	,	PUNCT
ejpam-4521	60	14	coi(g	coi(g	PROPN
ejpam-4521	60	15	)	)	PUNCT
ejpam-4521	60	16	is	be	AUX
ejpam-4521	60	17	called	call	VERB
ejpam-4521	60	18	a	a	DET
ejpam-4521	60	19	γc	γc	PROPN
ejpam-4521	60	20	,	,	PUNCT
ejpam-4521	60	21	coi	coi	NOUN
ejpam-4521	60	22	-	-	PUNCT
ejpam-4521	60	23	set	set	NOUN
ejpam-4521	60	24	of	of	ADP
ejpam-4521	60	25	g.	g.	PROPN
ejpam-4521	60	26	let	let	VERB
ejpam-4521	60	27	g	g	NOUN
ejpam-4521	60	28	be	be	AUX
ejpam-4521	60	29	a	a	DET
ejpam-4521	60	30	connected	connected	ADJ
ejpam-4521	60	31	graph	graph	NOUN
ejpam-4521	60	32	.	.	PUNCT
ejpam-4521	61	1	a	a	DET
ejpam-4521	61	2	set	set	NOUN
ejpam-4521	61	3	s	s	NOUN
ejpam-4521	61	4	⊆	⊆	NUM
ejpam-4521	61	5	v	v	NOUN
ejpam-4521	61	6	(	(	PUNCT
ejpam-4521	61	7	g	g	NOUN
ejpam-4521	61	8	)	)	PUNCT
ejpam-4521	61	9	is	be	AUX
ejpam-4521	61	10	a	a	DET
ejpam-4521	61	11	hop	hop	NOUN
ejpam-4521	61	12	dominating	dominating	NOUN
ejpam-4521	61	13	set	set	NOUN
ejpam-4521	61	14	of	of	ADP
ejpam-4521	61	15	g	g	PROPN
ejpam-4521	61	16	if	if	SCONJ
ejpam-4521	61	17	for	for	ADP
ejpam-4521	61	18	every	every	DET
ejpam-4521	61	19	v	v	NUM
ejpam-4521	61	20	∈	∈	NOUN
ejpam-4521	61	21	v	v	NOUN
ejpam-4521	61	22	(	(	PUNCT
ejpam-4521	61	23	g)\s	g)\s	NOUN
ejpam-4521	61	24	,	,	PUNCT
ejpam-4521	61	25	there	there	PRON
ejpam-4521	61	26	exists	exist	VERB
ejpam-4521	61	27	u	u	PROPN
ejpam-4521	61	28	∈	∈	PROPN
ejpam-4521	61	29	s	s	VERB
ejpam-4521	61	30	such	such	ADJ
ejpam-4521	61	31	that	that	DET
ejpam-4521	61	32	dg(u	dg(u	ADJ
ejpam-4521	61	33	,	,	PUNCT
ejpam-4521	61	34	v	v	NOUN
ejpam-4521	61	35	)	)	PUNCT
ejpam-4521	62	1	=	=	SYM
ejpam-4521	62	2	2	2	X
ejpam-4521	62	3	.	.	PUNCT
ejpam-4521	63	1	the	the	DET
ejpam-4521	63	2	minimum	minimum	ADJ
ejpam-4521	63	3	cardinality	cardinality	NOUN
ejpam-4521	63	4	of	of	ADP
ejpam-4521	63	5	a	a	DET
ejpam-4521	63	6	hop	hop	NOUN
ejpam-4521	63	7	dominating	dominating	NOUN
ejpam-4521	63	8	set	set	NOUN
ejpam-4521	63	9	of	of	ADP
ejpam-4521	63	10	g	g	NOUN
ejpam-4521	63	11	,	,	PUNCT
ejpam-4521	63	12	denoted	denote	VERB
ejpam-4521	63	13	by	by	ADP
ejpam-4521	63	14	γh(g	γh(g	NOUN
ejpam-4521	63	15	)	)	PUNCT
ejpam-4521	63	16	,	,	PUNCT
ejpam-4521	63	17	is	be	AUX
ejpam-4521	63	18	called	call	VERB
ejpam-4521	63	19	the	the	DET
ejpam-4521	63	20	hop	hop	NOUN
ejpam-4521	63	21	domination	domination	NOUN
ejpam-4521	63	22	number	number	NOUN
ejpam-4521	63	23	of	of	ADP
ejpam-4521	63	24	g.	g.	PROPN
ejpam-4521	63	25	any	any	DET
ejpam-4521	63	26	hop	hop	NOUN
ejpam-4521	63	27	dominating	dominating	NOUN
ejpam-4521	63	28	set	set	VERB
ejpam-4521	63	29	with	with	ADP
ejpam-4521	63	30	cardinality	cardinality	NOUN
ejpam-4521	63	31	equal	equal	ADJ
ejpam-4521	63	32	to	to	ADP
ejpam-4521	63	33	γh(g	γh(g	NOUN
ejpam-4521	63	34	)	)	PUNCT
ejpam-4521	63	35	is	be	AUX
ejpam-4521	63	36	called	call	VERB
ejpam-4521	63	37	a	a	DET
ejpam-4521	63	38	γh	γh	ADV
ejpam-4521	63	39	-	-	PUNCT
ejpam-4521	63	40	set	set	NOUN
ejpam-4521	63	41	.	.	PUNCT
ejpam-4521	64	1	a	a	DET
ejpam-4521	64	2	vertex	vertex	NOUN
ejpam-4521	64	3	v	v	NOUN
ejpam-4521	64	4	in	in	ADP
ejpam-4521	64	5	g	g	PROPN
ejpam-4521	64	6	is	be	AUX
ejpam-4521	64	7	a	a	DET
ejpam-4521	64	8	hop	hop	NOUN
ejpam-4521	64	9	neighbor	neighbor	NOUN
ejpam-4521	64	10	of	of	ADP
ejpam-4521	64	11	vertex	vertex	NOUN
ejpam-4521	64	12	u	u	NOUN
ejpam-4521	64	13	in	in	ADP
ejpam-4521	64	14	g	g	PROPN
ejpam-4521	64	15	if	if	SCONJ
ejpam-4521	64	16	dg(u	dg(u	NOUN
ejpam-4521	64	17	,	,	PUNCT
ejpam-4521	64	18	v	v	NOUN
ejpam-4521	64	19	)	)	PUNCT
ejpam-4521	64	20	=	=	SYM
ejpam-4521	64	21	2	2	X
ejpam-4521	64	22	.	.	X
ejpam-4521	65	1	the	the	DET
ejpam-4521	65	2	set	set	NOUN
ejpam-4521	65	3	ng(u	ng(u	NOUN
ejpam-4521	65	4	,	,	PUNCT
ejpam-4521	65	5	2	2	NUM
ejpam-4521	65	6	)	)	PUNCT
ejpam-4521	65	7	=	=	PRON
ejpam-4521	65	8	{	{	PUNCT
ejpam-4521	65	9	v	v	NUM
ejpam-4521	65	10	∈	∈	NOUN
ejpam-4521	65	11	v	v	NOUN
ejpam-4521	65	12	(	(	PUNCT
ejpam-4521	65	13	g	g	NOUN
ejpam-4521	65	14	)	)	PUNCT
ejpam-4521	65	15	:	:	PUNCT
ejpam-4521	65	16	dg(v	dg(v	X
ejpam-4521	65	17	,	,	PUNCT
ejpam-4521	65	18	u	u	NOUN
ejpam-4521	65	19	)	)	PUNCT
ejpam-4521	65	20	=	=	SYM
ejpam-4521	65	21	2	2	X
ejpam-4521	65	22	}	}	PUNCT
ejpam-4521	65	23	is	be	AUX
ejpam-4521	65	24	called	call	VERB
ejpam-4521	65	25	the	the	DET
ejpam-4521	65	26	open	open	ADJ
ejpam-4521	65	27	hop	hop	NOUN
ejpam-4521	65	28	neighborhood	neighborhood	NOUN
ejpam-4521	65	29	of	of	ADP
ejpam-4521	65	30	u.	u.	PROPN
ejpam-4521	65	31	the	the	DET
ejpam-4521	65	32	closed	closed	ADJ
ejpam-4521	65	33	hop	hop	NOUN
ejpam-4521	65	34	neighborhood	neighborhood	NOUN
ejpam-4521	65	35	of	of	ADP
ejpam-4521	65	36	u	u	PROPN
ejpam-4521	65	37	in	in	ADP
ejpam-4521	65	38	g	g	PROPN
ejpam-4521	65	39	is	be	AUX
ejpam-4521	65	40	given	give	VERB
ejpam-4521	65	41	by	by	ADP
ejpam-4521	65	42	ng[u	ng[u	PROPN
ejpam-4521	65	43	,	,	PUNCT
ejpam-4521	65	44	2	2	NUM
ejpam-4521	65	45	]	]	PUNCT
ejpam-4521	65	46	=	=	PUNCT
ejpam-4521	65	47	ng(u	ng(u	NOUN
ejpam-4521	65	48	,	,	PUNCT
ejpam-4521	65	49	2	2	X
ejpam-4521	65	50	)	)	PUNCT
ejpam-4521	65	51	∪	∪	NOUN
ejpam-4521	65	52	{	{	PUNCT
ejpam-4521	65	53	u	u	NOUN
ejpam-4521	65	54	}	}	PUNCT
ejpam-4521	65	55	.	.	PUNCT
ejpam-4521	66	1	the	the	DET
ejpam-4521	66	2	open	open	ADJ
ejpam-4521	66	3	hop	hop	NOUN
ejpam-4521	66	4	neighborhood	neighborhood	NOUN
ejpam-4521	66	5	of	of	ADP
ejpam-4521	66	6	x	x	PROPN
ejpam-4521	66	7	⊆	⊆	NUM
ejpam-4521	66	8	v	v	ADP
ejpam-4521	66	9	(	(	PUNCT
ejpam-4521	66	10	g	g	NOUN
ejpam-4521	66	11	)	)	PUNCT
ejpam-4521	66	12	is	be	AUX
ejpam-4521	66	13	the	the	DET
ejpam-4521	66	14	set	set	NOUN
ejpam-4521	66	15	ng(x	ng(x	NUM
ejpam-4521	66	16	,	,	PUNCT
ejpam-4521	66	17	2	2	X
ejpam-4521	66	18	)	)	PUNCT
ejpam-4521	66	19	=	=	NOUN
ejpam-4521	66	20	⋃	⋃	NOUN
ejpam-4521	66	21	u∈x	u∈x	ADJ
ejpam-4521	66	22	ng(u	ng(u	NOUN
ejpam-4521	66	23	,	,	PUNCT
ejpam-4521	66	24	2	2	NUM
ejpam-4521	66	25	)	)	PUNCT
ejpam-4521	66	26	.	.	PUNCT
ejpam-4521	67	1	the	the	DET
ejpam-4521	67	2	closed	closed	ADJ
ejpam-4521	67	3	hop	hop	NOUN
ejpam-4521	67	4	neighborhood	neighborhood	NOUN
ejpam-4521	67	5	of	of	ADP
ejpam-4521	67	6	x	x	PUNCT
ejpam-4521	67	7	in	in	ADP
ejpam-4521	67	8	g	g	PROPN
ejpam-4521	67	9	is	be	AUX
ejpam-4521	67	10	the	the	DET
ejpam-4521	67	11	set	set	PROPN
ejpam-4521	67	12	ng[x	ng[x	PROPN
ejpam-4521	67	13	,	,	PUNCT
ejpam-4521	67	14	2	2	NUM
ejpam-4521	67	15	]	]	PUNCT
ejpam-4521	67	16	=	=	SYM
ejpam-4521	67	17	ng(x	ng(x	X
ejpam-4521	67	18	,	,	PUNCT
ejpam-4521	67	19	2	2	NUM
ejpam-4521	67	20	)	)	PUNCT
ejpam-4521	67	21	∪x	∪x	AUX
ejpam-4521	67	22	.	.	PUNCT
ejpam-4521	68	1	let	let	VERB
ejpam-4521	68	2	g	g	PRON
ejpam-4521	68	3	be	be	AUX
ejpam-4521	68	4	a	a	DET
ejpam-4521	68	5	connected	connected	ADJ
ejpam-4521	68	6	graph	graph	NOUN
ejpam-4521	68	7	.	.	PUNCT
ejpam-4521	69	1	a	a	DET
ejpam-4521	69	2	hop	hop	NOUN
ejpam-4521	69	3	dominating	dominating	NOUN
ejpam-4521	69	4	set	set	NOUN
ejpam-4521	69	5	s	s	PROPN
ejpam-4521	69	6	⊆	⊆	NUM
ejpam-4521	69	7	v	v	NOUN
ejpam-4521	69	8	(	(	PUNCT
ejpam-4521	69	9	g	g	NOUN
ejpam-4521	69	10	)	)	PUNCT
ejpam-4521	69	11	is	be	AUX
ejpam-4521	69	12	a	a	DET
ejpam-4521	69	13	connected	connected	ADJ
ejpam-4521	69	14	co	co	NOUN
ejpam-4521	69	15	-	-	ADJ
ejpam-4521	69	16	independent	independent	ADJ
ejpam-4521	69	17	hop	hop	NOUN
ejpam-4521	69	18	dominating	dominating	NOUN
ejpam-4521	69	19	set	set	NOUN
ejpam-4521	69	20	of	of	ADP
ejpam-4521	69	21	g	g	PROPN
ejpam-4521	69	22	if	if	SCONJ
ejpam-4521	69	23	⟨s⟩	⟨s⟩	PROPN
ejpam-4521	69	24	is	be	AUX
ejpam-4521	69	25	connected	connect	VERB
ejpam-4521	69	26	and	and	CCONJ
ejpam-4521	69	27	v	v	NOUN
ejpam-4521	69	28	(	(	PUNCT
ejpam-4521	69	29	g)\s	g)\s	NOUN
ejpam-4521	69	30	is	be	AUX
ejpam-4521	69	31	an	an	DET
ejpam-4521	69	32	independent	independent	ADJ
ejpam-4521	69	33	set	set	NOUN
ejpam-4521	69	34	.	.	PUNCT
ejpam-4521	70	1	the	the	DET
ejpam-4521	70	2	minimum	minimum	ADJ
ejpam-4521	70	3	cardinality	cardinality	NOUN
ejpam-4521	70	4	of	of	ADP
ejpam-4521	70	5	a	a	DET
ejpam-4521	70	6	connected	connected	ADJ
ejpam-4521	70	7	co	co	NOUN
ejpam-4521	70	8	-	-	ADJ
ejpam-4521	70	9	independent	independent	ADJ
ejpam-4521	70	10	hop	hop	NOUN
ejpam-4521	70	11	dominating	dominating	NOUN
ejpam-4521	70	12	set	set	NOUN
ejpam-4521	70	13	of	of	ADP
ejpam-4521	70	14	g	g	NOUN
ejpam-4521	70	15	,	,	PUNCT
ejpam-4521	70	16	denoted	denote	VERB
ejpam-4521	70	17	by	by	ADP
ejpam-4521	70	18	γch	γch	NOUN
ejpam-4521	70	19	,	,	PUNCT
ejpam-4521	70	20	coi(g	coi(g	PROPN
ejpam-4521	70	21	)	)	PUNCT
ejpam-4521	70	22	,	,	PUNCT
ejpam-4521	70	23	is	be	AUX
ejpam-4521	70	24	called	call	VERB
ejpam-4521	70	25	the	the	DET
ejpam-4521	70	26	connected	connected	ADJ
ejpam-4521	70	27	co	co	NOUN
ejpam-4521	70	28	-	-	ADJ
ejpam-4521	70	29	independent	independent	ADJ
ejpam-4521	70	30	hop	hop	NOUN
ejpam-4521	70	31	domination	domination	NOUN
ejpam-4521	70	32	number	number	NOUN
ejpam-4521	70	33	of	of	ADP
ejpam-4521	70	34	g.	g.	PROPN
ejpam-4521	70	35	a	a	DET
ejpam-4521	70	36	connected	connected	ADJ
ejpam-4521	70	37	co	co	NOUN
ejpam-4521	70	38	-	-	ADJ
ejpam-4521	70	39	independent	independent	ADJ
ejpam-4521	70	40	hop	hop	NOUN
ejpam-4521	70	41	dominating	dominating	NOUN
ejpam-4521	70	42	set	set	NOUN
ejpam-4521	70	43	s	s	NOUN
ejpam-4521	70	44	with	with	ADP
ejpam-4521	70	45	|s|	|s|	NOUN
ejpam-4521	70	46	=	=	SYM
ejpam-4521	70	47	γch	γch	NOUN
ejpam-4521	70	48	,	,	PUNCT
ejpam-4521	70	49	coi(g	coi(g	PROPN
ejpam-4521	70	50	)	)	PUNCT
ejpam-4521	70	51	is	be	AUX
ejpam-4521	70	52	called	call	VERB
ejpam-4521	70	53	a	a	DET
ejpam-4521	70	54	γch	γch	NOUN
ejpam-4521	70	55	,	,	PUNCT
ejpam-4521	70	56	coi	coi	NOUN
ejpam-4521	70	57	-	-	PUNCT
ejpam-4521	70	58	set	set	NOUN
ejpam-4521	70	59	of	of	ADP
ejpam-4521	70	60	g.	g.	PROPN
ejpam-4521	70	61	let	let	VERB
ejpam-4521	70	62	w	w	NOUN
ejpam-4521	70	63	be	be	AUX
ejpam-4521	70	64	a	a	DET
ejpam-4521	70	65	γch	γch	NOUN
ejpam-4521	70	66	,	,	PUNCT
ejpam-4521	70	67	coi	coi	NOUN
ejpam-4521	70	68	-	-	PUNCT
ejpam-4521	70	69	set	set	NOUN
ejpam-4521	70	70	of	of	ADP
ejpam-4521	70	71	a	a	DET
ejpam-4521	70	72	graph	graph	NOUN
ejpam-4521	70	73	g.	g.	NOUN
ejpam-4521	70	74	a	a	DET
ejpam-4521	70	75	subset	subset	NOUN
ejpam-4521	70	76	s	s	NOUN
ejpam-4521	70	77	of	of	ADP
ejpam-4521	70	78	w	w	NOUN
ejpam-4521	70	79	is	be	AUX
ejpam-4521	70	80	said	say	VERB
ejpam-4521	70	81	to	to	PART
ejpam-4521	70	82	be	be	AUX
ejpam-4521	70	83	a	a	DET
ejpam-4521	70	84	forcing	forcing	NOUN
ejpam-4521	70	85	subset	subset	NOUN
ejpam-4521	70	86	for	for	ADP
ejpam-4521	70	87	w	w	PROPN
ejpam-4521	70	88	if	if	SCONJ
ejpam-4521	70	89	w	w	PROPN
ejpam-4521	70	90	is	be	AUX
ejpam-4521	70	91	the	the	DET
ejpam-4521	70	92	unique	unique	ADJ
ejpam-4521	70	93	γch	γch	NOUN
ejpam-4521	70	94	,	,	PUNCT
ejpam-4521	70	95	coi	coi	NOUN
ejpam-4521	70	96	-	-	PUNCT
ejpam-4521	70	97	set	set	NOUN
ejpam-4521	70	98	containing	contain	VERB
ejpam-4521	70	99	s.	s.	PROPN
ejpam-4521	70	100	the	the	DET
ejpam-4521	70	101	forcing	force	VERB
ejpam-4521	70	102	connected	connect	VERB
ejpam-4521	70	103	co	co	ADJ
ejpam-4521	70	104	-	-	ADJ
ejpam-4521	70	105	independent	independent	ADJ
ejpam-4521	70	106	hop	hop	NOUN
ejpam-4521	70	107	domination	domination	NOUN
ejpam-4521	70	108	number	number	NOUN
ejpam-4521	70	109	of	of	ADP
ejpam-4521	70	110	w	w	PROPN
ejpam-4521	70	111	is	be	AUX
ejpam-4521	70	112	given	give	VERB
ejpam-4521	70	113	by	by	ADP
ejpam-4521	70	114	fγch	fγch	NOUN
ejpam-4521	70	115	,	,	PUNCT
ejpam-4521	70	116	coi(w	coi(w	PROPN
ejpam-4521	70	117	)	)	PUNCT
ejpam-4521	71	1	=	=	NOUN
ejpam-4521	71	2	min{|s|	min{|s|	NOUN
ejpam-4521	71	3	:	:	PUNCT
ejpam-4521	71	4	s	s	VERB
ejpam-4521	71	5	is	be	AUX
ejpam-4521	71	6	a	a	DET
ejpam-4521	71	7	forcing	forcing	NOUN
ejpam-4521	71	8	subset	subset	NOUN
ejpam-4521	71	9	for	for	ADP
ejpam-4521	71	10	w	w	NOUN
ejpam-4521	71	11	}	}	PUNCT
ejpam-4521	71	12	.	.	PUNCT
ejpam-4521	72	1	the	the	DET
ejpam-4521	72	2	forcing	force	VERB
ejpam-4521	72	3	connected	connect	VERB
ejpam-4521	72	4	co	co	ADJ
ejpam-4521	72	5	-	-	ADJ
ejpam-4521	72	6	independent	independent	ADJ
ejpam-4521	72	7	hop	hop	NOUN
ejpam-4521	72	8	domination	domination	NOUN
ejpam-4521	72	9	number	number	NOUN
ejpam-4521	72	10	of	of	ADP
ejpam-4521	72	11	g	g	PROPN
ejpam-4521	72	12	is	be	AUX
ejpam-4521	72	13	given	give	VERB
ejpam-4521	72	14	by	by	ADP
ejpam-4521	72	15	fγch	fγch	NOUN
ejpam-4521	72	16	,	,	PUNCT
ejpam-4521	72	17	coi(g	coi(g	PROPN
ejpam-4521	72	18	)	)	PUNCT
ejpam-4521	73	1	=	=	SYM
ejpam-4521	73	2	min{fγch	min{fγch	NOUN
ejpam-4521	73	3	,	,	PUNCT
ejpam-4521	73	4	coi(w	coi(w	PROPN
ejpam-4521	73	5	)	)	PUNCT
ejpam-4521	73	6	:	:	PUNCT
ejpam-4521	74	1	w	w	NOUN
ejpam-4521	74	2	is	be	AUX
ejpam-4521	74	3	a	a	DET
ejpam-4521	74	4	γch	γch	NOUN
ejpam-4521	74	5	,	,	PUNCT
ejpam-4521	74	6	coi	coi	NOUN
ejpam-4521	74	7	-	-	PUNCT
ejpam-4521	74	8	set	set	NOUN
ejpam-4521	74	9	of	of	ADP
ejpam-4521	74	10	g	g	NOUN
ejpam-4521	74	11	}	}	PUNCT
ejpam-4521	74	12	.	.	PUNCT
ejpam-4521	75	1	let	let	VERB
ejpam-4521	75	2	w	w	NOUN
ejpam-4521	75	3	be	be	AUX
ejpam-4521	75	4	a	a	DET
ejpam-4521	75	5	coi	coi	NOUN
ejpam-4521	75	6	-	-	PUNCT
ejpam-4521	75	7	set	set	NOUN
ejpam-4521	75	8	of	of	ADP
ejpam-4521	75	9	a	a	DET
ejpam-4521	75	10	graph	graph	NOUN
ejpam-4521	75	11	g.	g.	NOUN
ejpam-4521	75	12	a	a	DET
ejpam-4521	75	13	subset	subset	NOUN
ejpam-4521	75	14	s	s	NOUN
ejpam-4521	75	15	of	of	ADP
ejpam-4521	75	16	w	w	NOUN
ejpam-4521	75	17	is	be	AUX
ejpam-4521	75	18	said	say	VERB
ejpam-4521	75	19	to	to	PART
ejpam-4521	75	20	be	be	AUX
ejpam-4521	75	21	a	a	DET
ejpam-4521	75	22	forcing	forcing	NOUN
ejpam-4521	75	23	subset	subset	NOUN
ejpam-4521	75	24	for	for	ADP
ejpam-4521	75	25	w	w	PROPN
ejpam-4521	75	26	if	if	SCONJ
ejpam-4521	75	27	w	w	PROPN
ejpam-4521	75	28	is	be	AUX
ejpam-4521	75	29	the	the	DET
ejpam-4521	75	30	unique	unique	ADJ
ejpam-4521	75	31	coi	coi	NOUN
ejpam-4521	75	32	-	-	PUNCT
ejpam-4521	75	33	set	set	NOUN
ejpam-4521	75	34	containing	contain	VERB
ejpam-4521	75	35	s.	s.	PROPN
ejpam-4521	75	36	the	the	DET
ejpam-4521	75	37	forcing	force	VERB
ejpam-4521	75	38	co	co	ADJ
ejpam-4521	75	39	-	-	ADJ
ejpam-4521	75	40	independent	independent	ADJ
ejpam-4521	75	41	number	number	NOUN
ejpam-4521	75	42	of	of	ADP
ejpam-4521	75	43	w	w	NOUN
ejpam-4521	75	44	is	be	AUX
ejpam-4521	75	45	given	give	VERB
ejpam-4521	75	46	by	by	ADP
ejpam-4521	75	47	fcoi(w	fcoi(w	NOUN
ejpam-4521	75	48	)	)	PUNCT
ejpam-4521	76	1	=	=	PUNCT
ejpam-4521	76	2	min{|s|	min{|s|	NOUN
ejpam-4521	76	3	:	:	PUNCT
ejpam-4521	76	4	s	s	VERB
ejpam-4521	76	5	is	be	AUX
ejpam-4521	76	6	a	a	DET
ejpam-4521	76	7	forcing	forcing	NOUN
ejpam-4521	76	8	subset	subset	NOUN
ejpam-4521	76	9	for	for	ADP
ejpam-4521	76	10	w	w	NOUN
ejpam-4521	76	11	}	}	PUNCT
ejpam-4521	76	12	.	.	PUNCT
ejpam-4521	77	1	the	the	DET
ejpam-4521	77	2	forcing	force	VERB
ejpam-4521	77	3	co	co	NOUN
ejpam-4521	77	4	-	-	ADJ
ejpam-4521	77	5	independent	independent	ADJ
ejpam-4521	77	6	number	number	NOUN
ejpam-4521	77	7	y.d	y.d	PROPN
ejpam-4521	77	8	.	.	PROPN
ejpam-4521	77	9	calanza	calanza	PROPN
ejpam-4521	77	10	,	,	PUNCT
ejpam-4521	77	11	h.	h.	PROPN
ejpam-4521	77	12	rara	rara	PROPN
ejpam-4521	77	13	/	/	SYM
ejpam-4521	77	14	eur	eur	PROPN
ejpam-4521	77	15	.	.	PUNCT
ejpam-4521	78	1	j.	j.	PROPN
ejpam-4521	78	2	pure	pure	PROPN
ejpam-4521	78	3	appl	appl	PROPN
ejpam-4521	78	4	.	.	PROPN
ejpam-4521	78	5	math	math	PROPN
ejpam-4521	78	6	,	,	PUNCT
ejpam-4521	78	7	15	15	NUM
ejpam-4521	78	8	(	(	PUNCT
ejpam-4521	78	9	4	4	NUM
ejpam-4521	78	10	)	)	PUNCT
ejpam-4521	78	11	(	(	PUNCT
ejpam-4521	78	12	2022	2022	NUM
ejpam-4521	78	13	)	)	PUNCT
ejpam-4521	78	14	,	,	PUNCT
ejpam-4521	78	15	1597	1597	NUM
ejpam-4521	78	16	-	-	SYM
ejpam-4521	78	17	1612	1612	NUM
ejpam-4521	78	18	1600	1600	NUM
ejpam-4521	78	19	of	of	ADP
ejpam-4521	78	20	g	g	PROPN
ejpam-4521	78	21	is	be	AUX
ejpam-4521	78	22	given	give	VERB
ejpam-4521	78	23	by	by	ADP
ejpam-4521	78	24	fcoi(g	fcoi(g	PROPN
ejpam-4521	78	25	)	)	PUNCT
ejpam-4521	79	1	=	=	SYM
ejpam-4521	79	2	min{fcoi(w	min{fcoi(w	PROPN
ejpam-4521	79	3	)	)	PUNCT
ejpam-4521	79	4	:	:	PUNCT
ejpam-4521	80	1	w	w	NOUN
ejpam-4521	80	2	is	be	AUX
ejpam-4521	80	3	a	a	DET
ejpam-4521	80	4	coi	coi	NOUN
ejpam-4521	80	5	-	-	PUNCT
ejpam-4521	80	6	set	set	NOUN
ejpam-4521	80	7	of	of	ADP
ejpam-4521	80	8	g	g	NOUN
ejpam-4521	80	9	}	}	PUNCT
ejpam-4521	80	10	.	.	PUNCT
ejpam-4521	81	1	let	let	VERB
ejpam-4521	81	2	g	g	PRON
ejpam-4521	81	3	be	be	AUX
ejpam-4521	81	4	a	a	DET
ejpam-4521	81	5	connected	connected	ADJ
ejpam-4521	81	6	graph	graph	NOUN
ejpam-4521	81	7	and	and	CCONJ
ejpam-4521	81	8	let	let	VERB
ejpam-4521	81	9	m	m	PRON
ejpam-4521	81	10	be	be	AUX
ejpam-4521	81	11	a	a	DET
ejpam-4521	81	12	β	β	NOUN
ejpam-4521	81	13	-	-	VERB
ejpam-4521	81	14	set	set	ADJ
ejpam-4521	81	15	(	(	PUNCT
ejpam-4521	81	16	maximum	maximum	ADJ
ejpam-4521	81	17	independent	independent	ADJ
ejpam-4521	81	18	set	set	NOUN
ejpam-4521	81	19	)	)	PUNCT
ejpam-4521	81	20	of	of	ADP
ejpam-4521	81	21	g.	g.	PROPN
ejpam-4521	81	22	a	a	DET
ejpam-4521	81	23	set	set	NOUN
ejpam-4521	81	24	d	d	PROPN
ejpam-4521	81	25	⊆	⊆	NUM
ejpam-4521	81	26	m	m	NOUN
ejpam-4521	81	27	c	c	NOUN
ejpam-4521	81	28	is	be	AUX
ejpam-4521	81	29	a	a	DET
ejpam-4521	81	30	forcing	forcing	NOUN
ejpam-4521	81	31	subset	subset	NOUN
ejpam-4521	81	32	for	for	ADP
ejpam-4521	81	33	the	the	DET
ejpam-4521	81	34	complement	complement	NOUN
ejpam-4521	81	35	m	m	NOUN
ejpam-4521	81	36	c	c	NOUN
ejpam-4521	81	37	of	of	ADP
ejpam-4521	81	38	m	m	PROPN
ejpam-4521	81	39	if	if	SCONJ
ejpam-4521	81	40	m	m	ADJ
ejpam-4521	81	41	is	be	AUX
ejpam-4521	81	42	the	the	DET
ejpam-4521	81	43	unique	unique	ADJ
ejpam-4521	81	44	β	β	NOUN
ejpam-4521	81	45	-	-	PUNCT
ejpam-4521	81	46	set	set	VERB
ejpam-4521	81	47	such	such	ADJ
ejpam-4521	81	48	that	that	SCONJ
ejpam-4521	81	49	m	m	VERB
ejpam-4521	81	50	c	c	NOUN
ejpam-4521	81	51	contains	contain	VERB
ejpam-4521	81	52	d.	d.	PROPN
ejpam-4521	81	53	the	the	DET
ejpam-4521	81	54	number	number	NOUN
ejpam-4521	81	55	fβc(m	fβc(m	PROPN
ejpam-4521	81	56	)	)	PUNCT
ejpam-4521	82	1	=	=	X
ejpam-4521	82	2	min{|d|	min{|d|	NOUN
ejpam-4521	82	3	:	:	PUNCT
ejpam-4521	83	1	d	d	X
ejpam-4521	83	2	is	be	AUX
ejpam-4521	83	3	a	a	DET
ejpam-4521	83	4	forcing	forcing	NOUN
ejpam-4521	83	5	subset	subset	NOUN
ejpam-4521	83	6	for	for	SCONJ
ejpam-4521	83	7	m	m	PROPN
ejpam-4521	83	8	c	c	AUX
ejpam-4521	83	9	}	}	PUNCT
ejpam-4521	83	10	is	be	AUX
ejpam-4521	83	11	defined	define	VERB
ejpam-4521	83	12	as	as	ADP
ejpam-4521	83	13	the	the	DET
ejpam-4521	83	14	forcing	force	VERB
ejpam-4521	83	15	complement	complement	NOUN
ejpam-4521	83	16	of	of	ADP
ejpam-4521	83	17	the	the	DET
ejpam-4521	83	18	independence	independence	NOUN
ejpam-4521	83	19	number	number	NOUN
ejpam-4521	83	20	m	m	PROPN
ejpam-4521	83	21	.	.	PUNCT
ejpam-4521	84	1	the	the	DET
ejpam-4521	84	2	forcing	force	VERB
ejpam-4521	84	3	complement	complement	NOUN
ejpam-4521	84	4	of	of	ADP
ejpam-4521	84	5	the	the	DET
ejpam-4521	84	6	independence	independence	NOUN
ejpam-4521	84	7	number	number	NOUN
ejpam-4521	84	8	of	of	ADP
ejpam-4521	84	9	g	g	PROPN
ejpam-4521	84	10	is	be	AUX
ejpam-4521	84	11	given	give	VERB
ejpam-4521	84	12	by	by	ADP
ejpam-4521	84	13	fβc(g	fβc(g	NUM
ejpam-4521	84	14	)	)	PUNCT
ejpam-4521	84	15	=	=	SYM
ejpam-4521	84	16	min{fβc(m	min{fβc(m	PROPN
ejpam-4521	84	17	)	)	PUNCT
ejpam-4521	84	18	:	:	PUNCT
ejpam-4521	85	1	m	m	VERB
ejpam-4521	85	2	is	be	AUX
ejpam-4521	85	3	a	a	DET
ejpam-4521	85	4	β	β	NOUN
ejpam-4521	85	5	-	-	NOUN
ejpam-4521	85	6	set	set	NOUN
ejpam-4521	85	7	of	of	ADP
ejpam-4521	85	8	g	g	NOUN
ejpam-4521	85	9	}	}	PUNCT
ejpam-4521	85	10	.	.	PUNCT
ejpam-4521	86	1	the	the	DET
ejpam-4521	86	2	edge	edge	NOUN
ejpam-4521	86	3	corona	corona	NOUN
ejpam-4521	86	4	g	g	PROPN
ejpam-4521	86	5	⋄h	⋄h	NOUN
ejpam-4521	86	6	of	of	ADP
ejpam-4521	86	7	g	g	PROPN
ejpam-4521	86	8	and	and	CCONJ
ejpam-4521	86	9	h	h	NOUN
ejpam-4521	86	10	is	be	AUX
ejpam-4521	86	11	the	the	DET
ejpam-4521	86	12	graph	graph	NOUN
ejpam-4521	86	13	obtained	obtain	VERB
ejpam-4521	86	14	by	by	ADP
ejpam-4521	86	15	taking	take	VERB
ejpam-4521	86	16	one	one	NUM
ejpam-4521	86	17	copy	copy	NOUN
ejpam-4521	86	18	of	of	ADP
ejpam-4521	86	19	g	g	PROPN
ejpam-4521	86	20	and	and	CCONJ
ejpam-4521	86	21	|e(g)|	|e(g)|	ADJ
ejpam-4521	86	22	copies	copy	NOUN
ejpam-4521	86	23	of	of	ADP
ejpam-4521	86	24	h	h	NOUN
ejpam-4521	86	25	and	and	CCONJ
ejpam-4521	86	26	joining	join	VERB
ejpam-4521	86	27	each	each	PRON
ejpam-4521	86	28	of	of	ADP
ejpam-4521	86	29	the	the	DET
ejpam-4521	86	30	end	end	NOUN
ejpam-4521	86	31	vertices	vertice	VERB
ejpam-4521	86	32	u	u	NOUN
ejpam-4521	86	33	and	and	CCONJ
ejpam-4521	86	34	v	v	NOUN
ejpam-4521	86	35	of	of	ADP
ejpam-4521	86	36	each	each	DET
ejpam-4521	86	37	edge	edge	NOUN
ejpam-4521	86	38	uv	uv	NOUN
ejpam-4521	86	39	of	of	ADP
ejpam-4521	86	40	g	g	NOUN
ejpam-4521	86	41	to	to	ADP
ejpam-4521	86	42	every	every	DET
ejpam-4521	86	43	vertex	vertex	NOUN
ejpam-4521	86	44	of	of	ADP
ejpam-4521	86	45	the	the	DET
ejpam-4521	86	46	copy	copy	NOUN
ejpam-4521	86	47	huv	huv	PROPN
ejpam-4521	86	48	of	of	ADP
ejpam-4521	86	49	h.	h.	PROPN
ejpam-4521	86	50	the	the	DET
ejpam-4521	86	51	lexicographic	lexicographic	ADJ
ejpam-4521	86	52	product	product	NOUN
ejpam-4521	86	53	of	of	ADP
ejpam-4521	86	54	two	two	NUM
ejpam-4521	86	55	graphs	graph	NOUN
ejpam-4521	86	56	g	g	NOUN
ejpam-4521	86	57	and	and	CCONJ
ejpam-4521	86	58	h	h	NOUN
ejpam-4521	86	59	,	,	PUNCT
ejpam-4521	86	60	denoted	denote	VERB
ejpam-4521	86	61	by	by	ADP
ejpam-4521	86	62	g[h	g[h	NOUN
ejpam-4521	86	63	]	]	PUNCT
ejpam-4521	86	64	,	,	PUNCT
ejpam-4521	86	65	is	be	AUX
ejpam-4521	86	66	the	the	DET
ejpam-4521	86	67	graph	graph	NOUN
ejpam-4521	86	68	with	with	ADP
ejpam-4521	86	69	vertex	vertex	NOUN
ejpam-4521	86	70	-	-	PUNCT
ejpam-4521	86	71	set	set	VERB
ejpam-4521	86	72	v	v	NOUN
ejpam-4521	86	73	(	(	PUNCT
ejpam-4521	86	74	g[h	g[h	PROPN
ejpam-4521	86	75	]	]	PUNCT
ejpam-4521	86	76	)	)	PUNCT
ejpam-4521	87	1	=	=	SYM
ejpam-4521	87	2	v	v	X
ejpam-4521	87	3	(	(	PUNCT
ejpam-4521	87	4	g	g	NOUN
ejpam-4521	87	5	)	)	PUNCT
ejpam-4521	87	6	×	×	NOUN
ejpam-4521	87	7	v	v	NOUN
ejpam-4521	87	8	(	(	PUNCT
ejpam-4521	87	9	h	h	NOUN
ejpam-4521	87	10	)	)	PUNCT
ejpam-4521	87	11	such	such	ADJ
ejpam-4521	87	12	that	that	SCONJ
ejpam-4521	87	13	(	(	PUNCT
ejpam-4521	87	14	u1	u1	NOUN
ejpam-4521	87	15	,	,	PUNCT
ejpam-4521	87	16	u2)(v1	u2)(v1	NOUN
ejpam-4521	87	17	,	,	PUNCT
ejpam-4521	87	18	v2	v2	NOUN
ejpam-4521	87	19	)	)	PUNCT
ejpam-4521	87	20	∈	∈	NOUN
ejpam-4521	87	21	e(g[h	e(g[h	NOUN
ejpam-4521	87	22	]	]	PUNCT
ejpam-4521	87	23	)	)	PUNCT
ejpam-4521	87	24	if	if	SCONJ
ejpam-4521	87	25	either	either	CCONJ
ejpam-4521	87	26	u1v1	u1v1	PROPN
ejpam-4521	87	27	∈	∈	PROPN
ejpam-4521	87	28	e(g	e(g	PROPN
ejpam-4521	87	29	)	)	PUNCT
ejpam-4521	87	30	or	or	CCONJ
ejpam-4521	87	31	u1	u1	NOUN
ejpam-4521	87	32	=	=	SYM
ejpam-4521	87	33	v1	v1	NOUN
ejpam-4521	87	34	and	and	CCONJ
ejpam-4521	87	35	u2v2	u2v2	ADJ
ejpam-4521	87	36	∈	∈	PROPN
ejpam-4521	87	37	e(h	e(h	PROPN
ejpam-4521	87	38	)	)	PUNCT
ejpam-4521	87	39	.	.	PUNCT
ejpam-4521	88	1	2	2	X
ejpam-4521	88	2	.	.	X
ejpam-4521	88	3	known	know	VERB
ejpam-4521	88	4	results	result	VERB
ejpam-4521	88	5	the	the	DET
ejpam-4521	88	6	following	follow	VERB
ejpam-4521	88	7	known	know	VERB
ejpam-4521	88	8	results	result	NOUN
ejpam-4521	88	9	are	be	AUX
ejpam-4521	88	10	taken	take	VERB
ejpam-4521	88	11	from	from	ADP
ejpam-4521	88	12	[	[	X
ejpam-4521	88	13	11	11	NUM
ejpam-4521	88	14	]	]	PUNCT
ejpam-4521	88	15	.	.	PUNCT
ejpam-4521	89	1	remark	remark	PROPN
ejpam-4521	89	2	1	1	NUM
ejpam-4521	89	3	.	.	PUNCT
ejpam-4521	90	1	let	let	VERB
ejpam-4521	90	2	g	g	PRON
ejpam-4521	90	3	be	be	AUX
ejpam-4521	90	4	a	a	DET
ejpam-4521	90	5	connected	connected	ADJ
ejpam-4521	90	6	graph	graph	NOUN
ejpam-4521	90	7	of	of	ADP
ejpam-4521	90	8	order	order	NOUN
ejpam-4521	90	9	n.	n.	NOUN
ejpam-4521	90	10	then	then	ADV
ejpam-4521	90	11	1	1	NUM
ejpam-4521	90	12	≤	≤	NOUN
ejpam-4521	90	13	γch	γch	NOUN
ejpam-4521	90	14	,	,	PUNCT
ejpam-4521	90	15	coi(g	coi(g	PROPN
ejpam-4521	90	16	)	)	PUNCT
ejpam-4521	90	17	≤	≤	PUNCT
ejpam-4521	90	18	n.	n.	NOUN
ejpam-4521	90	19	moreover	moreover	ADV
ejpam-4521	90	20	,	,	PUNCT
ejpam-4521	90	21	γch	γch	NOUN
ejpam-4521	90	22	,	,	PUNCT
ejpam-4521	90	23	coi(g	coi(g	PROPN
ejpam-4521	90	24	)	)	PUNCT
ejpam-4521	91	1	=	=	PUNCT
ejpam-4521	91	2	1	1	NUM
ejpam-4521	91	3	if	if	SCONJ
ejpam-4521	91	4	and	and	CCONJ
ejpam-4521	91	5	only	only	ADV
ejpam-4521	91	6	if	if	SCONJ
ejpam-4521	91	7	g	g	PROPN
ejpam-4521	91	8	=	=	PROPN
ejpam-4521	91	9	k1	k1	PROPN
ejpam-4521	91	10	.	.	PUNCT
ejpam-4521	91	11	example	example	NOUN
ejpam-4521	92	1	1	1	NUM
ejpam-4521	92	2	.	.	PUNCT
ejpam-4521	93	1	the	the	DET
ejpam-4521	93	2	equations	equation	NOUN
ejpam-4521	93	3	below	below	ADP
ejpam-4521	93	4	give	give	VERB
ejpam-4521	93	5	the	the	DET
ejpam-4521	93	6	connected	connected	ADJ
ejpam-4521	93	7	co	co	NOUN
ejpam-4521	93	8	-	-	ADJ
ejpam-4521	93	9	independent	independent	ADJ
ejpam-4521	93	10	hop	hop	NOUN
ejpam-4521	93	11	domination	domination	NOUN
ejpam-4521	93	12	number	number	NOUN
ejpam-4521	93	13	of	of	ADP
ejpam-4521	93	14	the	the	DET
ejpam-4521	93	15	path	path	NOUN
ejpam-4521	93	16	pn	pn	NOUN
ejpam-4521	93	17	and	and	CCONJ
ejpam-4521	93	18	cycle	cycle	NOUN
ejpam-4521	93	19	cn	cn	PROPN
ejpam-4521	93	20	.	.	PUNCT
ejpam-4521	93	21	γch	γch	NOUN
ejpam-4521	93	22	,	,	PUNCT
ejpam-4521	93	23	coi(pn	coi(pn	NOUN
ejpam-4521	93	24	)	)	PUNCT
ejpam-4521	93	25	=	=	SYM
ejpam-4521	94	1			NOUN
ejpam-4521	94	2	1	1	NUM
ejpam-4521	94	3	if	if	SCONJ
ejpam-4521	94	4	n	n	NOUN
ejpam-4521	94	5	=	=	SYM
ejpam-4521	94	6	1	1	NUM
ejpam-4521	94	7	,	,	PUNCT
ejpam-4521	94	8	2	2	NUM
ejpam-4521	94	9	if	if	SCONJ
ejpam-4521	94	10	n	n	NOUN
ejpam-4521	94	11	=	=	SYM
ejpam-4521	94	12	2	2	NUM
ejpam-4521	94	13	,	,	PUNCT
ejpam-4521	94	14	3	3	NUM
ejpam-4521	94	15	,	,	PUNCT
ejpam-4521	94	16	n−	n−	NOUN
ejpam-4521	94	17	2	2	NUM
ejpam-4521	94	18	if	if	SCONJ
ejpam-4521	94	19	n	n	PRON
ejpam-4521	94	20	≥	≥	NOUN
ejpam-4521	94	21	4	4	NUM
ejpam-4521	94	22	.	.	PUNCT
ejpam-4521	95	1	γch	γch	VERB
ejpam-4521	95	2	,	,	PUNCT
ejpam-4521	95	3	coi(cn	coi(cn	NUM
ejpam-4521	95	4	)	)	PUNCT
ejpam-4521	96	1	=	=	PRON
ejpam-4521	96	2	{	{	PUNCT
ejpam-4521	96	3	3	3	NUM
ejpam-4521	96	4	if	if	SCONJ
ejpam-4521	96	5	n	n	X
ejpam-4521	96	6	=	=	SYM
ejpam-4521	96	7	3	3	NUM
ejpam-4521	96	8	,	,	PUNCT
ejpam-4521	96	9	n−	n−	NOUN
ejpam-4521	96	10	1	1	NUM
ejpam-4521	96	11	if	if	SCONJ
ejpam-4521	96	12	n	n	PRON
ejpam-4521	96	13	≥	≥	NOUN
ejpam-4521	96	14	4	4	NUM
ejpam-4521	96	15	.	.	PUNCT
ejpam-4521	96	16	remark	remark	NOUN
ejpam-4521	96	17	2	2	NUM
ejpam-4521	96	18	.	.	PUNCT
ejpam-4521	97	1	if	if	SCONJ
ejpam-4521	97	2	g	g	PROPN
ejpam-4521	97	3	is	be	AUX
ejpam-4521	97	4	a	a	DET
ejpam-4521	97	5	complete	complete	ADJ
ejpam-4521	97	6	graph	graph	NOUN
ejpam-4521	97	7	,	,	PUNCT
ejpam-4521	97	8	then	then	ADV
ejpam-4521	97	9	γch	γch	VERB
ejpam-4521	97	10	,	,	PUNCT
ejpam-4521	97	11	coi(g	coi(g	PROPN
ejpam-4521	97	12	)	)	PUNCT
ejpam-4521	97	13	=	=	SYM
ejpam-4521	97	14	n.	n.	NOUN
ejpam-4521	97	15	theorem	theorem	NOUN
ejpam-4521	97	16	1	1	X
ejpam-4521	97	17	.	.	PUNCT
ejpam-4521	98	1	let	let	VERB
ejpam-4521	98	2	g	g	NOUN
ejpam-4521	98	3	and	and	CCONJ
ejpam-4521	98	4	h	h	NOUN
ejpam-4521	98	5	be	be	AUX
ejpam-4521	98	6	nontrivial	nontrivial	ADJ
ejpam-4521	98	7	connected	connect	VERB
ejpam-4521	98	8	graphs	graph	NOUN
ejpam-4521	98	9	with	with	ADP
ejpam-4521	98	10	|v	|v	PROPN
ejpam-4521	98	11	(	(	PUNCT
ejpam-4521	98	12	g)|	g)|	NOUN
ejpam-4521	98	13	=	=	PUNCT
ejpam-4521	98	14	n.	n.	NOUN
ejpam-4521	98	15	a	a	DET
ejpam-4521	98	16	subset	subset	NOUN
ejpam-4521	98	17	c	c	NOUN
ejpam-4521	99	1	=	=	PUNCT
ejpam-4521	99	2	⋃	⋃	PROPN
ejpam-4521	99	3	x∈s	x∈s	NOUN
ejpam-4521	99	4	(	(	PUNCT
ejpam-4521	99	5	{	{	PUNCT
ejpam-4521	99	6	x	x	NOUN
ejpam-4521	99	7	}	}	PUNCT
ejpam-4521	99	8	×	×	PROPN
ejpam-4521	99	9	tx	tx	PROPN
ejpam-4521	99	10	)	)	PUNCT
ejpam-4521	99	11	where	where	SCONJ
ejpam-4521	99	12	s	s	VERB
ejpam-4521	99	13	⊆	⊆	NUM
ejpam-4521	99	14	v	v	NOUN
ejpam-4521	99	15	(	(	PUNCT
ejpam-4521	99	16	g	g	NOUN
ejpam-4521	99	17	)	)	PUNCT
ejpam-4521	99	18	and	and	CCONJ
ejpam-4521	99	19	tx	tx	VERB
ejpam-4521	99	20	⊆	⊆	NUM
ejpam-4521	99	21	v	v	NOUN
ejpam-4521	99	22	(	(	PUNCT
ejpam-4521	99	23	h	h	NOUN
ejpam-4521	99	24	)	)	PUNCT
ejpam-4521	99	25	of	of	ADP
ejpam-4521	99	26	v	v	NOUN
ejpam-4521	99	27	(	(	PUNCT
ejpam-4521	99	28	g[h	g[h	PROPN
ejpam-4521	99	29	]	]	PUNCT
ejpam-4521	99	30	)	)	PUNCT
ejpam-4521	99	31	is	be	AUX
ejpam-4521	99	32	a	a	DET
ejpam-4521	99	33	connected	connected	ADJ
ejpam-4521	99	34	coindependent	coindependent	NOUN
ejpam-4521	99	35	hop	hop	NOUN
ejpam-4521	99	36	dominating	dominating	NOUN
ejpam-4521	99	37	set	set	VERB
ejpam-4521	99	38	if	if	SCONJ
ejpam-4521	99	39	and	and	CCONJ
ejpam-4521	99	40	only	only	ADV
ejpam-4521	99	41	if	if	SCONJ
ejpam-4521	99	42	(	(	PUNCT
ejpam-4521	99	43	i	i	NOUN
ejpam-4521	99	44	)	)	PUNCT
ejpam-4521	99	45	s	s	PART
ejpam-4521	99	46	=	=	SYM
ejpam-4521	99	47	v	v	NOUN
ejpam-4521	99	48	(	(	PUNCT
ejpam-4521	99	49	g	g	NOUN
ejpam-4521	99	50	)	)	PUNCT
ejpam-4521	99	51	.	.	PUNCT
ejpam-4521	100	1	(	(	PUNCT
ejpam-4521	100	2	ii	ii	NOUN
ejpam-4521	100	3	)	)	PUNCT
ejpam-4521	100	4	for	for	ADP
ejpam-4521	100	5	every	every	DET
ejpam-4521	100	6	x	x	SYM
ejpam-4521	100	7	∈	∈	PROPN
ejpam-4521	100	8	v	v	ADP
ejpam-4521	100	9	(	(	PUNCT
ejpam-4521	100	10	g	g	NOUN
ejpam-4521	100	11	)	)	PUNCT
ejpam-4521	100	12	such	such	ADJ
ejpam-4521	100	13	that	that	SCONJ
ejpam-4521	100	14	tx	tx	PROPN
ejpam-4521	100	15	̸=	̸=	PROPN
ejpam-4521	100	16	v	v	PROPN
ejpam-4521	100	17	(	(	PUNCT
ejpam-4521	100	18	h	h	NOUN
ejpam-4521	100	19	)	)	PUNCT
ejpam-4521	100	20	,	,	PUNCT
ejpam-4521	100	21	v	v	X
ejpam-4521	100	22	(	(	PUNCT
ejpam-4521	100	23	h)\tx	h)\tx	PROPN
ejpam-4521	100	24	is	be	AUX
ejpam-4521	100	25	an	an	DET
ejpam-4521	100	26	independent	independent	ADJ
ejpam-4521	100	27	set	set	NOUN
ejpam-4521	100	28	and	and	CCONJ
ejpam-4521	100	29	ty	ty	NOUN
ejpam-4521	100	30	=	=	NOUN
ejpam-4521	100	31	v	v	NOUN
ejpam-4521	100	32	(	(	PUNCT
ejpam-4521	100	33	h	h	NOUN
ejpam-4521	100	34	)	)	PUNCT
ejpam-4521	100	35	for	for	ADP
ejpam-4521	100	36	every	every	DET
ejpam-4521	100	37	y	y	PROPN
ejpam-4521	100	38	∈	∈	PROPN
ejpam-4521	100	39	ng(x	ng(x	NUM
ejpam-4521	100	40	)	)	PUNCT
ejpam-4521	100	41	where	where	SCONJ
ejpam-4521	100	42	tx	tx	PROPN
ejpam-4521	100	43	is	be	AUX
ejpam-4521	100	44	a	a	DET
ejpam-4521	100	45	hop	hop	NOUN
ejpam-4521	100	46	dominating	dominating	NOUN
ejpam-4521	100	47	set	set	NOUN
ejpam-4521	100	48	of	of	ADP
ejpam-4521	100	49	h	h	NOUN
ejpam-4521	100	50	if	if	SCONJ
ejpam-4521	100	51	degg(x	degg(x	NOUN
ejpam-4521	100	52	)	)	PUNCT
ejpam-4521	100	53	=	=	SYM
ejpam-4521	101	1	n−1	n−1	PROPN
ejpam-4521	101	2	.	.	PUNCT
ejpam-4521	101	3	y.d	y.d	PROPN
ejpam-4521	101	4	.	.	PROPN
ejpam-4521	101	5	calanza	calanza	PROPN
ejpam-4521	101	6	,	,	PUNCT
ejpam-4521	101	7	h.	h.	PROPN
ejpam-4521	101	8	rara	rara	PROPN
ejpam-4521	101	9	/	/	SYM
ejpam-4521	101	10	eur	eur	PROPN
ejpam-4521	101	11	.	.	PUNCT
ejpam-4521	102	1	j.	j.	PROPN
ejpam-4521	102	2	pure	pure	PROPN
ejpam-4521	102	3	appl	appl	PROPN
ejpam-4521	102	4	.	.	PROPN
ejpam-4521	102	5	math	math	PROPN
ejpam-4521	102	6	,	,	PUNCT
ejpam-4521	102	7	15	15	NUM
ejpam-4521	102	8	(	(	PUNCT
ejpam-4521	102	9	4	4	NUM
ejpam-4521	102	10	)	)	PUNCT
ejpam-4521	102	11	(	(	PUNCT
ejpam-4521	102	12	2022	2022	NUM
ejpam-4521	102	13	)	)	PUNCT
ejpam-4521	102	14	,	,	PUNCT
ejpam-4521	102	15	1597	1597	NUM
ejpam-4521	102	16	-	-	SYM
ejpam-4521	102	17	1612	1612	NUM
ejpam-4521	102	18	1601	1601	NUM
ejpam-4521	102	19	corollary	corollary	NOUN
ejpam-4521	102	20	1	1	NUM
ejpam-4521	102	21	.	.	PUNCT
ejpam-4521	103	1	let	let	VERB
ejpam-4521	103	2	g	g	NOUN
ejpam-4521	103	3	be	be	AUX
ejpam-4521	103	4	any	any	DET
ejpam-4521	103	5	connected	connected	ADJ
ejpam-4521	103	6	noncomplete	noncomplete	ADJ
ejpam-4521	103	7	graph	graph	NOUN
ejpam-4521	103	8	of	of	ADP
ejpam-4521	103	9	order	order	NOUN
ejpam-4521	103	10	m	m	VERB
ejpam-4521	103	11	and	and	CCONJ
ejpam-4521	103	12	h	h	NOUN
ejpam-4521	103	13	be	be	VERB
ejpam-4521	103	14	any	any	DET
ejpam-4521	103	15	nontrivial	nontrivial	ADJ
ejpam-4521	103	16	connected	connect	VERB
ejpam-4521	103	17	graph	graph	NOUN
ejpam-4521	103	18	of	of	ADP
ejpam-4521	103	19	order	order	NOUN
ejpam-4521	103	20	n.	n.	NOUN
ejpam-4521	103	21	then	then	ADV
ejpam-4521	103	22	γch	γch	VERB
ejpam-4521	103	23	,	,	PUNCT
ejpam-4521	103	24	coi(g[h	coi(g[h	NUM
ejpam-4521	103	25	]	]	PUNCT
ejpam-4521	103	26	)	)	PUNCT
ejpam-4521	103	27	=	=	SYM
ejpam-4521	103	28	m(n−	m(n−	NOUN
ejpam-4521	103	29	β(h	β(h	NOUN
ejpam-4521	103	30	)	)	PUNCT
ejpam-4521	103	31	)	)	PUNCT
ejpam-4521	104	1	+	+	CCONJ
ejpam-4521	105	1	r(g)β(h	r(g)β(h	X
ejpam-4521	105	2	)	)	PUNCT
ejpam-4521	105	3	,	,	PUNCT
ejpam-4521	105	4	where	where	SCONJ
ejpam-4521	105	5	r(g	r(g	ADJ
ejpam-4521	105	6	)	)	PUNCT
ejpam-4521	105	7	=	=	SYM
ejpam-4521	106	1	min{|d|	min{|d|	NOUN
ejpam-4521	106	2	:	:	PUNCT
ejpam-4521	106	3	v	v	X
ejpam-4521	106	4	(	(	PUNCT
ejpam-4521	106	5	g)\d	g)\d	NOUN
ejpam-4521	106	6	is	be	AUX
ejpam-4521	106	7	an	an	DET
ejpam-4521	106	8	independent	independent	ADJ
ejpam-4521	106	9	set	set	NOUN
ejpam-4521	106	10	}	}	PUNCT
ejpam-4521	106	11	and	and	CCONJ
ejpam-4521	106	12	β(h	β(h	NUM
ejpam-4521	106	13	)	)	PUNCT
ejpam-4521	106	14	is	be	AUX
ejpam-4521	106	15	the	the	DET
ejpam-4521	106	16	independence	independence	NOUN
ejpam-4521	106	17	number	number	NOUN
ejpam-4521	106	18	of	of	ADP
ejpam-4521	106	19	h.	h.	PROPN
ejpam-4521	106	20	3	3	NUM
ejpam-4521	106	21	.	.	PUNCT
ejpam-4521	107	1	forcing	force	VERB
ejpam-4521	107	2	connected	connected	ADJ
ejpam-4521	107	3	co	co	ADJ
ejpam-4521	107	4	-	-	ADJ
ejpam-4521	107	5	independent	independent	ADJ
ejpam-4521	107	6	hop	hop	NOUN
ejpam-4521	107	7	domination	domination	NOUN
ejpam-4521	107	8	number	number	NOUN
ejpam-4521	107	9	of	of	ADP
ejpam-4521	107	10	some	some	DET
ejpam-4521	107	11	special	special	ADJ
ejpam-4521	107	12	graphs	graph	NOUN
ejpam-4521	107	13	remark	remark	VERB
ejpam-4521	107	14	3	3	NUM
ejpam-4521	107	15	.	.	PUNCT
ejpam-4521	108	1	let	let	VERB
ejpam-4521	108	2	g	g	PRON
ejpam-4521	108	3	be	be	AUX
ejpam-4521	108	4	a	a	DET
ejpam-4521	108	5	connected	connected	ADJ
ejpam-4521	108	6	graph	graph	NOUN
ejpam-4521	108	7	.	.	PUNCT
ejpam-4521	109	1	then	then	ADV
ejpam-4521	109	2	(	(	PUNCT
ejpam-4521	109	3	i	i	NOUN
ejpam-4521	109	4	)	)	PUNCT
ejpam-4521	109	5	fγch	fγch	PROPN
ejpam-4521	109	6	,	,	PUNCT
ejpam-4521	109	7	coi(g	coi(g	PROPN
ejpam-4521	109	8	)	)	PUNCT
ejpam-4521	109	9	=	=	SYM
ejpam-4521	109	10	0	0	PUNCT
ejpam-4521	110	1	if	if	SCONJ
ejpam-4521	110	2	and	and	CCONJ
ejpam-4521	110	3	only	only	ADV
ejpam-4521	110	4	if	if	SCONJ
ejpam-4521	110	5	g	g	PROPN
ejpam-4521	110	6	has	have	VERB
ejpam-4521	110	7	a	a	DET
ejpam-4521	110	8	unique	unique	ADJ
ejpam-4521	110	9	γch	γch	NOUN
ejpam-4521	110	10	,	,	PUNCT
ejpam-4521	110	11	coi	coi	NOUN
ejpam-4521	110	12	-	-	PUNCT
ejpam-4521	110	13	set	set	NOUN
ejpam-4521	110	14	,	,	PUNCT
ejpam-4521	110	15	and	and	CCONJ
ejpam-4521	110	16	(	(	PUNCT
ejpam-4521	110	17	ii	ii	NOUN
ejpam-4521	110	18	)	)	PUNCT
ejpam-4521	110	19	fγch	fγch	PROPN
ejpam-4521	110	20	,	,	PUNCT
ejpam-4521	110	21	coi(g	coi(g	PROPN
ejpam-4521	110	22	)	)	PUNCT
ejpam-4521	110	23	=	=	PUNCT
ejpam-4521	110	24	1	1	NUM
ejpam-4521	110	25	if	if	SCONJ
ejpam-4521	110	26	and	and	CCONJ
ejpam-4521	110	27	only	only	ADV
ejpam-4521	110	28	if	if	SCONJ
ejpam-4521	110	29	g	g	PROPN
ejpam-4521	110	30	has	have	VERB
ejpam-4521	110	31	at	at	ADV
ejpam-4521	110	32	least	least	ADV
ejpam-4521	110	33	two	two	NUM
ejpam-4521	110	34	γch	γch	NOUN
ejpam-4521	110	35	,	,	PUNCT
ejpam-4521	110	36	coi	coi	NOUN
ejpam-4521	110	37	-	-	PUNCT
ejpam-4521	110	38	sets	set	NOUN
ejpam-4521	110	39	,	,	PUNCT
ejpam-4521	110	40	one	one	NUM
ejpam-4521	110	41	of	of	ADP
ejpam-4521	110	42	which	which	PRON
ejpam-4521	110	43	,	,	PUNCT
ejpam-4521	110	44	say	say	VERB
ejpam-4521	110	45	b	b	NOUN
ejpam-4521	110	46	,	,	PUNCT
ejpam-4521	110	47	contains	contain	VERB
ejpam-4521	110	48	an	an	DET
ejpam-4521	110	49	element	element	NOUN
ejpam-4521	110	50	which	which	PRON
ejpam-4521	110	51	is	be	AUX
ejpam-4521	110	52	not	not	PART
ejpam-4521	110	53	found	find	VERB
ejpam-4521	110	54	in	in	ADP
ejpam-4521	110	55	any	any	DET
ejpam-4521	110	56	γch	γch	NOUN
ejpam-4521	110	57	,	,	PUNCT
ejpam-4521	110	58	coi	coi	NOUN
ejpam-4521	110	59	-	-	PUNCT
ejpam-4521	110	60	set	set	NOUN
ejpam-4521	110	61	of	of	ADP
ejpam-4521	110	62	g.	g.	PROPN
ejpam-4521	110	63	theorem	theorem	PROPN
ejpam-4521	110	64	2	2	X
ejpam-4521	110	65	.	.	PUNCT
ejpam-4521	110	66	let	let	VERB
ejpam-4521	110	67	g	g	PRON
ejpam-4521	110	68	be	be	AUX
ejpam-4521	110	69	a	a	DET
ejpam-4521	110	70	connected	connected	ADJ
ejpam-4521	110	71	graph	graph	NOUN
ejpam-4521	110	72	.	.	PUNCT
ejpam-4521	111	1	then	then	ADV
ejpam-4521	111	2	fγch	fγch	ADJ
ejpam-4521	111	3	,	,	PUNCT
ejpam-4521	111	4	coi(g	coi(g	PROPN
ejpam-4521	111	5	)	)	PUNCT
ejpam-4521	111	6	=	=	PUNCT
ejpam-4521	112	1	γch	γch	X
ejpam-4521	112	2	,	,	PUNCT
ejpam-4521	112	3	coi(g	coi(g	PROPN
ejpam-4521	112	4	)	)	PUNCT
ejpam-4521	112	5	if	if	SCONJ
ejpam-4521	112	6	and	and	CCONJ
ejpam-4521	112	7	only	only	ADV
ejpam-4521	112	8	if	if	SCONJ
ejpam-4521	112	9	for	for	ADP
ejpam-4521	112	10	all	all	DET
ejpam-4521	112	11	γch	γch	NOUN
ejpam-4521	112	12	,	,	PUNCT
ejpam-4521	112	13	coi	coi	NOUN
ejpam-4521	112	14	-	-	PUNCT
ejpam-4521	112	15	set	set	VERB
ejpam-4521	112	16	b	b	NOUN
ejpam-4521	112	17	of	of	ADP
ejpam-4521	112	18	g	g	PROPN
ejpam-4521	112	19	and	and	CCONJ
ejpam-4521	112	20	for	for	ADP
ejpam-4521	112	21	each	each	DET
ejpam-4521	112	22	v	v	NUM
ejpam-4521	112	23	∈	∈	PROPN
ejpam-4521	112	24	b	b	NOUN
ejpam-4521	112	25	,	,	PUNCT
ejpam-4521	112	26	there	there	PRON
ejpam-4521	112	27	exists	exist	VERB
ejpam-4521	112	28	uv	uv	PROPN
ejpam-4521	112	29	∈	∈	PROPN
ejpam-4521	112	30	v	v	ADP
ejpam-4521	112	31	(	(	PUNCT
ejpam-4521	112	32	g	g	NOUN
ejpam-4521	112	33	)	)	PUNCT
ejpam-4521	112	34	\	\	PROPN
ejpam-4521	113	1	b	b	X
ejpam-4521	113	2	such	such	ADJ
ejpam-4521	113	3	that	that	SCONJ
ejpam-4521	113	4	[	[	PUNCT
ejpam-4521	113	5	b	b	X
ejpam-4521	113	6	\	\	X
ejpam-4521	113	7	{	{	PUNCT
ejpam-4521	113	8	v	v	NOUN
ejpam-4521	113	9	}	}	PUNCT
ejpam-4521	113	10	]	]	PUNCT
ejpam-4521	113	11	∪	∪	X
ejpam-4521	113	12	{	{	PUNCT
ejpam-4521	113	13	uv	uv	NOUN
ejpam-4521	113	14	}	}	PUNCT
ejpam-4521	113	15	is	be	AUX
ejpam-4521	113	16	a	a	DET
ejpam-4521	113	17	γch	γch	NOUN
ejpam-4521	113	18	,	,	PUNCT
ejpam-4521	113	19	coi	coi	NOUN
ejpam-4521	113	20	-	-	PUNCT
ejpam-4521	113	21	set	set	NOUN
ejpam-4521	113	22	of	of	ADP
ejpam-4521	113	23	g.	g.	PROPN
ejpam-4521	113	24	proof	proof	PROPN
ejpam-4521	113	25	:	:	PUNCT
ejpam-4521	113	26	suppose	suppose	VERB
ejpam-4521	113	27	that	that	SCONJ
ejpam-4521	113	28	fγch	fγch	NOUN
ejpam-4521	113	29	,	,	PUNCT
ejpam-4521	113	30	coi(g	coi(g	PROPN
ejpam-4521	113	31	)	)	PUNCT
ejpam-4521	113	32	=	=	PUNCT
ejpam-4521	114	1	γch	γch	X
ejpam-4521	114	2	,	,	PUNCT
ejpam-4521	114	3	coi(g	coi(g	PROPN
ejpam-4521	114	4	)	)	PUNCT
ejpam-4521	114	5	.	.	PUNCT
ejpam-4521	115	1	let	let	VERB
ejpam-4521	115	2	b	b	X
ejpam-4521	115	3	be	be	AUX
ejpam-4521	115	4	a	a	DET
ejpam-4521	115	5	γch	γch	NOUN
ejpam-4521	115	6	,	,	PUNCT
ejpam-4521	115	7	coi	coi	NOUN
ejpam-4521	115	8	-	-	PUNCT
ejpam-4521	115	9	set	set	NOUN
ejpam-4521	115	10	of	of	ADP
ejpam-4521	115	11	g	g	NOUN
ejpam-4521	115	12	such	such	ADJ
ejpam-4521	115	13	that	that	DET
ejpam-4521	115	14	fγch	fγch	NOUN
ejpam-4521	115	15	,	,	PUNCT
ejpam-4521	115	16	coi(g	coi(g	PROPN
ejpam-4521	115	17	)	)	PUNCT
ejpam-4521	116	1	=	=	SYM
ejpam-4521	116	2	|b|	|b|	PROPN
ejpam-4521	116	3	=	=	PUNCT
ejpam-4521	116	4	γch	γch	X
ejpam-4521	116	5	,	,	PUNCT
ejpam-4521	116	6	coi(g	coi(g	PROPN
ejpam-4521	116	7	)	)	PUNCT
ejpam-4521	116	8	,	,	PUNCT
ejpam-4521	116	9	that	that	ADV
ejpam-4521	116	10	is	is	ADV
ejpam-4521	116	11	,	,	PUNCT
ejpam-4521	116	12	b	b	PROPN
ejpam-4521	116	13	is	be	AUX
ejpam-4521	116	14	the	the	DET
ejpam-4521	116	15	only	only	ADJ
ejpam-4521	116	16	forcing	forcing	NOUN
ejpam-4521	116	17	subset	subset	NOUN
ejpam-4521	116	18	for	for	ADP
ejpam-4521	116	19	itself	itself	PRON
ejpam-4521	116	20	.	.	PUNCT
ejpam-4521	117	1	let	let	VERB
ejpam-4521	117	2	v	v	NUM
ejpam-4521	117	3	∈	∈	PROPN
ejpam-4521	117	4	b.	b.	PROPN
ejpam-4521	117	5	since	since	SCONJ
ejpam-4521	117	6	b	b	PROPN
ejpam-4521	117	7	\	\	PROPN
ejpam-4521	117	8	{	{	PUNCT
ejpam-4521	117	9	v	v	NOUN
ejpam-4521	117	10	}	}	PUNCT
ejpam-4521	117	11	is	be	AUX
ejpam-4521	117	12	not	not	PART
ejpam-4521	117	13	a	a	DET
ejpam-4521	117	14	forcing	forcing	NOUN
ejpam-4521	117	15	subset	subset	NOUN
ejpam-4521	117	16	for	for	ADP
ejpam-4521	117	17	b	b	NOUN
ejpam-4521	117	18	,	,	PUNCT
ejpam-4521	117	19	there	there	PRON
ejpam-4521	117	20	exists	exist	VERB
ejpam-4521	117	21	a	a	DET
ejpam-4521	117	22	uv	uv	NOUN
ejpam-4521	117	23	∈	∈	PROPN
ejpam-4521	117	24	v	v	NOUN
ejpam-4521	117	25	(	(	PUNCT
ejpam-4521	117	26	g	g	NOUN
ejpam-4521	117	27	)	)	PUNCT
ejpam-4521	117	28	\	\	PROPN
ejpam-4521	118	1	b	b	X
ejpam-4521	118	2	such	such	ADJ
ejpam-4521	118	3	that	that	SCONJ
ejpam-4521	118	4	[	[	PUNCT
ejpam-4521	118	5	b	b	X
ejpam-4521	118	6	\	\	X
ejpam-4521	118	7	{	{	PUNCT
ejpam-4521	118	8	v	v	NOUN
ejpam-4521	118	9	}	}	PUNCT
ejpam-4521	118	10	]	]	PUNCT
ejpam-4521	118	11	∪	∪	X
ejpam-4521	118	12	{	{	PUNCT
ejpam-4521	118	13	uv	uv	NOUN
ejpam-4521	118	14	}	}	PUNCT
ejpam-4521	118	15	is	be	AUX
ejpam-4521	118	16	a	a	DET
ejpam-4521	118	17	γch	γch	NOUN
ejpam-4521	118	18	,	,	PUNCT
ejpam-4521	118	19	coi	coi	NOUN
ejpam-4521	118	20	-	-	PUNCT
ejpam-4521	118	21	set	set	NOUN
ejpam-4521	118	22	of	of	ADP
ejpam-4521	118	23	g.	g.	NOUN
ejpam-4521	118	24	conversely	conversely	ADV
ejpam-4521	118	25	,	,	PUNCT
ejpam-4521	118	26	suppose	suppose	VERB
ejpam-4521	118	27	that	that	SCONJ
ejpam-4521	118	28	every	every	DET
ejpam-4521	118	29	γch	γch	NOUN
ejpam-4521	118	30	,	,	PUNCT
ejpam-4521	118	31	coi	coi	NOUN
ejpam-4521	118	32	-	-	PUNCT
ejpam-4521	118	33	set	set	VERB
ejpam-4521	118	34	b	b	NOUN
ejpam-4521	118	35	′	′	NUM
ejpam-4521	118	36	ofg	ofg	PROPN
ejpam-4521	118	37	satisfies	satisfy	VERB
ejpam-4521	118	38	the	the	DET
ejpam-4521	118	39	given	give	VERB
ejpam-4521	118	40	condition	condition	NOUN
ejpam-4521	118	41	.	.	PUNCT
ejpam-4521	119	1	let	let	VERB
ejpam-4521	119	2	b	b	X
ejpam-4521	119	3	be	be	AUX
ejpam-4521	119	4	a	a	DET
ejpam-4521	119	5	γch	γch	NOUN
ejpam-4521	119	6	,	,	PUNCT
ejpam-4521	119	7	coi	coi	NOUN
ejpam-4521	119	8	-	-	PUNCT
ejpam-4521	119	9	set	set	NOUN
ejpam-4521	119	10	of	of	ADP
ejpam-4521	119	11	g	g	NOUN
ejpam-4521	119	12	such	such	ADJ
ejpam-4521	119	13	that	that	DET
ejpam-4521	119	14	fγch	fγch	NOUN
ejpam-4521	119	15	,	,	PUNCT
ejpam-4521	119	16	coi(g	coi(g	PROPN
ejpam-4521	119	17	)	)	PUNCT
ejpam-4521	120	1	=	=	SYM
ejpam-4521	120	2	fγch	fγch	PROPN
ejpam-4521	120	3	,	,	PUNCT
ejpam-4521	120	4	coi(b	coi(b	PROPN
ejpam-4521	120	5	)	)	PUNCT
ejpam-4521	120	6	.	.	PUNCT
ejpam-4521	121	1	suppose	suppose	VERB
ejpam-4521	121	2	further	far	ADV
ejpam-4521	121	3	that	that	SCONJ
ejpam-4521	121	4	b	b	PROPN
ejpam-4521	121	5	has	have	VERB
ejpam-4521	121	6	a	a	DET
ejpam-4521	121	7	forcing	forcing	NOUN
ejpam-4521	121	8	subset	subset	NOUN
ejpam-4521	121	9	q	q	NOUN
ejpam-4521	121	10	with	with	ADP
ejpam-4521	121	11	|q|	|q|	PROPN
ejpam-4521	121	12	<	<	X
ejpam-4521	121	13	|b|	|b|	PROPN
ejpam-4521	121	14	,	,	PUNCT
ejpam-4521	121	15	that	that	ADV
ejpam-4521	121	16	is	be	AUX
ejpam-4521	121	17	,	,	PUNCT
ejpam-4521	121	18	b	b	X
ejpam-4521	121	19	=	=	SYM
ejpam-4521	121	20	q	q	X
ejpam-4521	121	21	∪	∪	ADP
ejpam-4521	121	22	p	p	NOUN
ejpam-4521	121	23	where	where	SCONJ
ejpam-4521	121	24	p	p	NOUN
ejpam-4521	121	25	=	=	X
ejpam-4521	121	26	{	{	PUNCT
ejpam-4521	121	27	z	z	PROPN
ejpam-4521	121	28	∈	∈	PROPN
ejpam-4521	121	29	b	b	PROPN
ejpam-4521	121	30	:	:	PUNCT
ejpam-4521	122	1	z	z	AUX
ejpam-4521	122	2	/∈	/∈	PUNCT
ejpam-4521	122	3	q	q	ADJ
ejpam-4521	122	4	}	}	PUNCT
ejpam-4521	122	5	.	.	PUNCT
ejpam-4521	123	1	pick	pick	VERB
ejpam-4521	123	2	z	z	PROPN
ejpam-4521	123	3	∈	∈	PROPN
ejpam-4521	123	4	p.	p.	NOUN
ejpam-4521	123	5	by	by	ADP
ejpam-4521	123	6	assumption	assumption	NOUN
ejpam-4521	123	7	,	,	PUNCT
ejpam-4521	123	8	there	there	PRON
ejpam-4521	123	9	exists	exist	VERB
ejpam-4521	123	10	uz	uz	PROPN
ejpam-4521	123	11	∈	∈	PROPN
ejpam-4521	123	12	v	v	PROPN
ejpam-4521	123	13	(	(	PUNCT
ejpam-4521	123	14	g)\b	g)\b	PROPN
ejpam-4521	123	15	such	such	ADJ
ejpam-4521	123	16	that	that	SCONJ
ejpam-4521	123	17	[	[	PUNCT
ejpam-4521	123	18	b	b	X
ejpam-4521	123	19	\{z	\{z	NOUN
ejpam-4521	123	20	}	}	PUNCT
ejpam-4521	123	21	]	]	PUNCT
ejpam-4521	123	22	∪{uz	∪{uz	X
ejpam-4521	123	23	}	}	PUNCT
ejpam-4521	123	24	=	=	SYM
ejpam-4521	123	25	t	t	NOUN
ejpam-4521	123	26	is	be	AUX
ejpam-4521	123	27	a	a	DET
ejpam-4521	123	28	γch	γch	NOUN
ejpam-4521	123	29	,	,	PUNCT
ejpam-4521	123	30	coi	coi	NOUN
ejpam-4521	123	31	-	-	PUNCT
ejpam-4521	123	32	set	set	NOUN
ejpam-4521	123	33	of	of	ADP
ejpam-4521	123	34	g.	g.	PROPN
ejpam-4521	123	35	thus	thus	ADV
ejpam-4521	123	36	,	,	PUNCT
ejpam-4521	123	37	t	t	PROPN
ejpam-4521	123	38	=	=	PUNCT
ejpam-4521	123	39	q∪r	q∪r	PROPN
ejpam-4521	123	40	,	,	PUNCT
ejpam-4521	123	41	where	where	SCONJ
ejpam-4521	123	42	r	r	NOUN
ejpam-4521	123	43	=	=	PUNCT
ejpam-4521	123	44	[	[	PUNCT
ejpam-4521	123	45	p	p	NOUN
ejpam-4521	123	46	\{z	\{z	NOUN
ejpam-4521	123	47	}	}	PUNCT
ejpam-4521	123	48	]	]	PUNCT
ejpam-4521	123	49	∪{uz	∪{uz	NUM
ejpam-4521	123	50	}	}	PUNCT
ejpam-4521	123	51	,	,	PUNCT
ejpam-4521	123	52	is	be	AUX
ejpam-4521	123	53	a	a	DET
ejpam-4521	123	54	γch	γch	NOUN
ejpam-4521	123	55	,	,	PUNCT
ejpam-4521	123	56	coi	coi	NOUN
ejpam-4521	123	57	-	-	PUNCT
ejpam-4521	123	58	set	set	NOUN
ejpam-4521	123	59	containing	contain	VERB
ejpam-4521	123	60	q	q	NOUN
ejpam-4521	123	61	,	,	PUNCT
ejpam-4521	123	62	a	a	DET
ejpam-4521	123	63	contradiction	contradiction	NOUN
ejpam-4521	123	64	.	.	PUNCT
ejpam-4521	124	1	hence	hence	ADV
ejpam-4521	124	2	,	,	PUNCT
ejpam-4521	124	3	b	b	PROPN
ejpam-4521	124	4	is	be	AUX
ejpam-4521	124	5	the	the	DET
ejpam-4521	124	6	only	only	ADJ
ejpam-4521	124	7	forcing	forcing	NOUN
ejpam-4521	124	8	subset	subset	NOUN
ejpam-4521	124	9	for	for	ADP
ejpam-4521	124	10	b.	b.	PROPN
ejpam-4521	124	11	therefore	therefore	ADV
ejpam-4521	124	12	,	,	PUNCT
ejpam-4521	124	13	fγch	fγch	ADJ
ejpam-4521	124	14	,	,	PUNCT
ejpam-4521	124	15	coi(g	coi(g	PROPN
ejpam-4521	124	16	)	)	PUNCT
ejpam-4521	125	1	=	=	PUNCT
ejpam-4521	125	2	γch	γch	X
ejpam-4521	125	3	,	,	PUNCT
ejpam-4521	125	4	coi(g	coi(g	PROPN
ejpam-4521	125	5	)	)	PUNCT
ejpam-4521	125	6	.	.	PUNCT
ejpam-4521	126	1	proposition	proposition	NOUN
ejpam-4521	126	2	1	1	NUM
ejpam-4521	126	3	.	.	PUNCT
ejpam-4521	127	1	for	for	ADP
ejpam-4521	127	2	any	any	DET
ejpam-4521	127	3	complete	complete	ADJ
ejpam-4521	127	4	graph	graph	NOUN
ejpam-4521	127	5	kn	kn	PROPN
ejpam-4521	127	6	with	with	ADP
ejpam-4521	127	7	n	n	PRON
ejpam-4521	127	8	≥	≥	NUM
ejpam-4521	127	9	1	1	NUM
ejpam-4521	127	10	vertices	vertex	NOUN
ejpam-4521	127	11	,	,	PUNCT
ejpam-4521	127	12	fγch	fγch	ADJ
ejpam-4521	127	13	,	,	PUNCT
ejpam-4521	127	14	coi(kn	coi(kn	NUM
ejpam-4521	127	15	)	)	PUNCT
ejpam-4521	127	16	=	=	SYM
ejpam-4521	127	17	0	0	X
ejpam-4521	127	18	.	.	X
ejpam-4521	128	1	proof	proof	NOUN
ejpam-4521	128	2	:	:	PUNCT
ejpam-4521	128	3	by	by	ADP
ejpam-4521	128	4	definition	definition	NOUN
ejpam-4521	128	5	of	of	ADP
ejpam-4521	128	6	kn	kn	PROPN
ejpam-4521	128	7	,	,	PUNCT
ejpam-4521	128	8	v	v	PROPN
ejpam-4521	128	9	(	(	PUNCT
ejpam-4521	128	10	kn	kn	PROPN
ejpam-4521	128	11	)	)	PUNCT
ejpam-4521	128	12	is	be	AUX
ejpam-4521	128	13	the	the	DET
ejpam-4521	128	14	only	only	ADJ
ejpam-4521	128	15	γch	γch	NOUN
ejpam-4521	128	16	,	,	PUNCT
ejpam-4521	128	17	coi	coi	NOUN
ejpam-4521	128	18	-	-	PUNCT
ejpam-4521	128	19	set	set	NOUN
ejpam-4521	128	20	of	of	ADP
ejpam-4521	128	21	kn	kn	PROPN
ejpam-4521	128	22	.	.	PUNCT
ejpam-4521	129	1	by	by	ADP
ejpam-4521	129	2	remark	remark	NOUN
ejpam-4521	129	3	3(i	3(i	NUM
ejpam-4521	129	4	)	)	PUNCT
ejpam-4521	129	5	,	,	PUNCT
ejpam-4521	129	6	fγch	fγch	NOUN
ejpam-4521	129	7	,	,	PUNCT
ejpam-4521	129	8	coi(kn	coi(kn	NUM
ejpam-4521	129	9	)	)	PUNCT
ejpam-4521	129	10	=	=	SYM
ejpam-4521	129	11	0	0	X
ejpam-4521	129	12	.	.	PUNCT
ejpam-4521	129	13	proposition	proposition	NOUN
ejpam-4521	129	14	2	2	NUM
ejpam-4521	129	15	.	.	X
ejpam-4521	130	1	for	for	ADP
ejpam-4521	130	2	any	any	DET
ejpam-4521	130	3	path	path	NOUN
ejpam-4521	130	4	pn	pn	NOUN
ejpam-4521	130	5	with	with	ADP
ejpam-4521	130	6	n	n	PRON
ejpam-4521	130	7	≥	≥	NUM
ejpam-4521	130	8	1	1	NUM
ejpam-4521	130	9	vertices	vertex	NOUN
ejpam-4521	130	10	,	,	PUNCT
ejpam-4521	130	11	fγch	fγch	ADJ
ejpam-4521	130	12	,	,	PUNCT
ejpam-4521	130	13	coi(pn	coi(pn	NOUN
ejpam-4521	130	14	)	)	PUNCT
ejpam-4521	130	15	=	=	NOUN
ejpam-4521	130	16	{	{	PUNCT
ejpam-4521	130	17	0	0	NUM
ejpam-4521	130	18	,	,	PUNCT
ejpam-4521	130	19	if	if	SCONJ
ejpam-4521	130	20	n	n	PRON
ejpam-4521	130	21	̸=	̸=	PROPN
ejpam-4521	130	22	3	3	NUM
ejpam-4521	130	23	,	,	PUNCT
ejpam-4521	130	24	1	1	NUM
ejpam-4521	130	25	,	,	PUNCT
ejpam-4521	130	26	if	if	SCONJ
ejpam-4521	130	27	n	n	NOUN
ejpam-4521	130	28	=	=	SYM
ejpam-4521	130	29	3	3	X
ejpam-4521	130	30	.	.	X
ejpam-4521	130	31	proof	proof	NOUN
ejpam-4521	130	32	:	:	PUNCT
ejpam-4521	130	33	suppose	suppose	VERB
ejpam-4521	130	34	that	that	SCONJ
ejpam-4521	130	35	pn	pn	PROPN
ejpam-4521	130	36	=	=	PUNCT
ejpam-4521	131	1	[	[	X
ejpam-4521	131	2	v1	v1	NOUN
ejpam-4521	131	3	,	,	PUNCT
ejpam-4521	131	4	v2	v2	NOUN
ejpam-4521	131	5	,	,	PUNCT
ejpam-4521	131	6	.	.	PUNCT
ejpam-4521	131	7	.	.	PUNCT
ejpam-4521	131	8	.	.	PUNCT
ejpam-4521	132	1	,	,	PUNCT
ejpam-4521	132	2	vn	vn	X
ejpam-4521	132	3	]	]	PUNCT
ejpam-4521	132	4	.	.	PUNCT
ejpam-4521	133	1	it	it	PRON
ejpam-4521	133	2	can	can	AUX
ejpam-4521	133	3	be	be	AUX
ejpam-4521	133	4	seen	see	VERB
ejpam-4521	133	5	that	that	SCONJ
ejpam-4521	133	6	fγch	fγch	NOUN
ejpam-4521	133	7	,	,	PUNCT
ejpam-4521	133	8	coi(p1	coi(p1	NOUN
ejpam-4521	133	9	)	)	PUNCT
ejpam-4521	133	10	=	=	SYM
ejpam-4521	134	1	fγch	fγch	ADJ
ejpam-4521	134	2	,	,	PUNCT
ejpam-4521	134	3	coi(p2	coi(p2	ADJ
ejpam-4521	134	4	)	)	PUNCT
ejpam-4521	134	5	=	=	SYM
ejpam-4521	134	6	0	0	X
ejpam-4521	134	7	.	.	PUNCT
ejpam-4521	135	1	moreover	moreover	ADV
ejpam-4521	135	2	,	,	PUNCT
ejpam-4521	135	3	if	if	SCONJ
ejpam-4521	135	4	n	n	CCONJ
ejpam-4521	135	5	=	=	SYM
ejpam-4521	135	6	4	4	NUM
ejpam-4521	135	7	,	,	PUNCT
ejpam-4521	135	8	then	then	ADV
ejpam-4521	135	9	p4	p4	ADJ
ejpam-4521	135	10	has	have	AUX
ejpam-4521	135	11	γch	γch	VERB
ejpam-4521	135	12	,	,	PUNCT
ejpam-4521	135	13	coi	coi	NOUN
ejpam-4521	135	14	-	-	PUNCT
ejpam-4521	135	15	set	set	VERB
ejpam-4521	135	16	b1	b1	NOUN
ejpam-4521	135	17	=	=	SYM
ejpam-4521	135	18	{	{	PUNCT
ejpam-4521	135	19	v2	v2	PROPN
ejpam-4521	135	20	,	,	PUNCT
ejpam-4521	135	21	v3	v3	PROPN
ejpam-4521	135	22	}	}	PUNCT
ejpam-4521	135	23	which	which	PRON
ejpam-4521	135	24	is	be	AUX
ejpam-4521	135	25	the	the	DET
ejpam-4521	135	26	only	only	ADJ
ejpam-4521	135	27	γch	γch	NOUN
ejpam-4521	135	28	,	,	PUNCT
ejpam-4521	135	29	coi	coi	NOUN
ejpam-4521	135	30	-	-	PUNCT
ejpam-4521	135	31	set	set	NOUN
ejpam-4521	135	32	of	of	ADP
ejpam-4521	135	33	p4	p4	NOUN
ejpam-4521	135	34	.	.	PUNCT
ejpam-4521	136	1	by	by	ADP
ejpam-4521	136	2	remark	remark	NOUN
ejpam-4521	136	3	3(i	3(i	NUM
ejpam-4521	136	4	)	)	PUNCT
ejpam-4521	136	5	,	,	PUNCT
ejpam-4521	136	6	fγch	fγch	NOUN
ejpam-4521	136	7	,	,	PUNCT
ejpam-4521	136	8	coi(p4	coi(p4	NOUN
ejpam-4521	136	9	)	)	PUNCT
ejpam-4521	136	10	=	=	SYM
ejpam-4521	136	11	0	0	X
ejpam-4521	136	12	.	.	PUNCT
ejpam-4521	136	13	suppose	suppose	VERB
ejpam-4521	136	14	that	that	SCONJ
ejpam-4521	136	15	n	n	PROPN
ejpam-4521	136	16	>	>	X
ejpam-4521	136	17	4	4	NUM
ejpam-4521	136	18	,	,	PUNCT
ejpam-4521	136	19	then	then	ADV
ejpam-4521	136	20	clearly	clearly	ADV
ejpam-4521	136	21	b2	b2	VERB
ejpam-4521	136	22	=	=	SYM
ejpam-4521	136	23	{	{	PUNCT
ejpam-4521	136	24	v2	v2	PROPN
ejpam-4521	136	25	,	,	PUNCT
ejpam-4521	136	26	v3	v3	PROPN
ejpam-4521	136	27	,	,	PUNCT
ejpam-4521	136	28	v4	v4	PROPN
ejpam-4521	136	29	,	,	PUNCT
ejpam-4521	136	30	.	.	PUNCT
ejpam-4521	136	31	.	.	PUNCT
ejpam-4521	137	1	.	.	PUNCT
ejpam-4521	138	1	,	,	PUNCT
ejpam-4521	138	2	vn−1	vn−1	PROPN
ejpam-4521	138	3	}	}	PUNCT
ejpam-4521	138	4	is	be	AUX
ejpam-4521	138	5	the	the	DET
ejpam-4521	138	6	only	only	ADJ
ejpam-4521	138	7	γch	γch	NOUN
ejpam-4521	138	8	,	,	PUNCT
ejpam-4521	138	9	coi	coi	NOUN
ejpam-4521	138	10	-	-	PUNCT
ejpam-4521	138	11	set	set	NOUN
ejpam-4521	138	12	of	of	ADP
ejpam-4521	138	13	pn	pn	PROPN
ejpam-4521	138	14	.	.	PUNCT
ejpam-4521	139	1	thus	thus	ADV
ejpam-4521	139	2	,	,	PUNCT
ejpam-4521	139	3	by	by	ADP
ejpam-4521	139	4	remark	remark	NOUN
ejpam-4521	139	5	3(i	3(i	NUM
ejpam-4521	139	6	)	)	PUNCT
ejpam-4521	139	7	,	,	PUNCT
ejpam-4521	139	8	y.d	y.d	PROPN
ejpam-4521	139	9	.	.	PROPN
ejpam-4521	139	10	calanza	calanza	PROPN
ejpam-4521	139	11	,	,	PUNCT
ejpam-4521	139	12	h.	h.	PROPN
ejpam-4521	139	13	rara	rara	PROPN
ejpam-4521	139	14	/	/	SYM
ejpam-4521	139	15	eur	eur	PROPN
ejpam-4521	139	16	.	.	PUNCT
ejpam-4521	140	1	j.	j.	PROPN
ejpam-4521	140	2	pure	pure	PROPN
ejpam-4521	140	3	appl	appl	PROPN
ejpam-4521	140	4	.	.	PROPN
ejpam-4521	140	5	math	math	PROPN
ejpam-4521	140	6	,	,	PUNCT
ejpam-4521	140	7	15	15	NUM
ejpam-4521	140	8	(	(	PUNCT
ejpam-4521	140	9	4	4	NUM
ejpam-4521	140	10	)	)	PUNCT
ejpam-4521	140	11	(	(	PUNCT
ejpam-4521	140	12	2022	2022	NUM
ejpam-4521	140	13	)	)	PUNCT
ejpam-4521	140	14	,	,	PUNCT
ejpam-4521	140	15	1597	1597	NUM
ejpam-4521	140	16	-	-	SYM
ejpam-4521	140	17	1612	1612	NUM
ejpam-4521	140	18	1602	1602	NUM
ejpam-4521	140	19	fγch	fγch	PROPN
ejpam-4521	140	20	,	,	PUNCT
ejpam-4521	140	21	coi(b2	coi(b2	NOUN
ejpam-4521	140	22	)	)	PUNCT
ejpam-4521	140	23	=	=	SYM
ejpam-4521	140	24	0	0	PUNCT
ejpam-4521	141	1	=	=	SYM
ejpam-4521	141	2	fγch	fγch	ADJ
ejpam-4521	141	3	,	,	PUNCT
ejpam-4521	141	4	coi(pn	coi(pn	NOUN
ejpam-4521	141	5	)	)	PUNCT
ejpam-4521	141	6	.	.	PUNCT
ejpam-4521	142	1	suppose	suppose	VERB
ejpam-4521	142	2	that	that	SCONJ
ejpam-4521	142	3	n	n	PROPN
ejpam-4521	142	4	=	=	SYM
ejpam-4521	142	5	3	3	X
ejpam-4521	142	6	.	.	X
ejpam-4521	142	7	then	then	ADV
ejpam-4521	142	8	p3	p3	PROPN
ejpam-4521	142	9	has	have	AUX
ejpam-4521	142	10	γch	γch	VERB
ejpam-4521	142	11	,	,	PUNCT
ejpam-4521	142	12	coi	coi	NOUN
ejpam-4521	142	13	-	-	PUNCT
ejpam-4521	142	14	sets	set	NOUN
ejpam-4521	142	15	b3	b3	NOUN
ejpam-4521	142	16	=	=	SYM
ejpam-4521	142	17	{	{	PUNCT
ejpam-4521	142	18	v1	v1	PROPN
ejpam-4521	142	19	,	,	PUNCT
ejpam-4521	142	20	v2	v2	NOUN
ejpam-4521	142	21	}	}	PUNCT
ejpam-4521	142	22	and	and	CCONJ
ejpam-4521	142	23	b4	b4	NOUN
ejpam-4521	142	24	=	=	SYM
ejpam-4521	143	1	{	{	PUNCT
ejpam-4521	143	2	v2	v2	PROPN
ejpam-4521	143	3	,	,	PUNCT
ejpam-4521	143	4	v3	v3	PROPN
ejpam-4521	143	5	}	}	PUNCT
ejpam-4521	143	6	which	which	PRON
ejpam-4521	143	7	are	be	AUX
ejpam-4521	143	8	the	the	DET
ejpam-4521	143	9	only	only	ADJ
ejpam-4521	143	10	γch	γch	NOUN
ejpam-4521	143	11	,	,	PUNCT
ejpam-4521	143	12	coi	coi	NOUN
ejpam-4521	143	13	-	-	PUNCT
ejpam-4521	143	14	sets	set	NOUN
ejpam-4521	143	15	of	of	ADP
ejpam-4521	143	16	p3	p3	PROPN
ejpam-4521	143	17	with	with	ADP
ejpam-4521	143	18	v1	v1	PROPN
ejpam-4521	143	19	∈	∈	PROPN
ejpam-4521	143	20	b3	b3	PROPN
ejpam-4521	143	21	and	and	CCONJ
ejpam-4521	143	22	v1	v1	NOUN
ejpam-4521	143	23	/∈	/∈	PUNCT
ejpam-4521	143	24	b4	b4	NOUN
ejpam-4521	143	25	.	.	PUNCT
ejpam-4521	144	1	hence	hence	ADV
ejpam-4521	144	2	,	,	PUNCT
ejpam-4521	144	3	by	by	ADP
ejpam-4521	144	4	remark	remark	NOUN
ejpam-4521	144	5	3(ii	3(ii	NUM
ejpam-4521	144	6	)	)	PUNCT
ejpam-4521	144	7	,	,	PUNCT
ejpam-4521	144	8	fγch	fγch	NOUN
ejpam-4521	144	9	,	,	PUNCT
ejpam-4521	144	10	coi(b3	coi(b3	NOUN
ejpam-4521	144	11	)	)	PUNCT
ejpam-4521	144	12	=	=	SYM
ejpam-4521	144	13	1	1	NUM
ejpam-4521	144	14	=	=	SYM
ejpam-4521	144	15	fγch	fγch	NOUN
ejpam-4521	144	16	,	,	PUNCT
ejpam-4521	144	17	coi(p3	coi(p3	PROPN
ejpam-4521	144	18	)	)	PUNCT
ejpam-4521	144	19	.	.	PUNCT
ejpam-4521	145	1	proposition	proposition	NOUN
ejpam-4521	145	2	3	3	NUM
ejpam-4521	145	3	.	.	X
ejpam-4521	146	1	for	for	ADP
ejpam-4521	146	2	any	any	DET
ejpam-4521	146	3	cycle	cycle	NOUN
ejpam-4521	146	4	cn	cn	NOUN
ejpam-4521	146	5	with	with	ADP
ejpam-4521	146	6	n	n	NUM
ejpam-4521	146	7	≥	≥	NUM
ejpam-4521	146	8	3	3	NUM
ejpam-4521	146	9	vertices	vertex	NOUN
ejpam-4521	146	10	,	,	PUNCT
ejpam-4521	146	11	fγch	fγch	NOUN
ejpam-4521	146	12	,	,	PUNCT
ejpam-4521	146	13	coi(cn	coi(cn	NUM
ejpam-4521	146	14	)	)	PUNCT
ejpam-4521	146	15	=	=	PRON
ejpam-4521	146	16	{	{	PUNCT
ejpam-4521	146	17	0	0	NUM
ejpam-4521	146	18	,	,	PUNCT
ejpam-4521	146	19	if	if	SCONJ
ejpam-4521	146	20	n	n	NOUN
ejpam-4521	146	21	=	=	SYM
ejpam-4521	146	22	3	3	NUM
ejpam-4521	146	23	,	,	PUNCT
ejpam-4521	146	24	n−	n−	NOUN
ejpam-4521	146	25	1	1	NUM
ejpam-4521	146	26	,	,	PUNCT
ejpam-4521	146	27	if	if	SCONJ
ejpam-4521	146	28	n	n	PRON
ejpam-4521	146	29	≥	≥	NOUN
ejpam-4521	146	30	4	4	NUM
ejpam-4521	146	31	.	.	PUNCT
ejpam-4521	146	32	proof	proof	NOUN
ejpam-4521	146	33	:	:	PUNCT
ejpam-4521	146	34	suppose	suppose	VERB
ejpam-4521	146	35	that	that	SCONJ
ejpam-4521	146	36	cn	cn	PROPN
ejpam-4521	146	37	=	=	PUNCT
ejpam-4521	146	38	[	[	X
ejpam-4521	146	39	v1	v1	NOUN
ejpam-4521	146	40	,	,	PUNCT
ejpam-4521	146	41	v2	v2	NOUN
ejpam-4521	146	42	,	,	PUNCT
ejpam-4521	146	43	.	.	PUNCT
ejpam-4521	146	44	.	.	PUNCT
ejpam-4521	147	1	.	.	PUNCT
ejpam-4521	148	1	,	,	PUNCT
ejpam-4521	148	2	vn	vn	X
ejpam-4521	148	3	,	,	PUNCT
ejpam-4521	148	4	v1	v1	PROPN
ejpam-4521	148	5	]	]	PUNCT
ejpam-4521	148	6	.	.	PUNCT
ejpam-4521	149	1	since	since	SCONJ
ejpam-4521	149	2	c3	c3	PROPN
ejpam-4521	149	3	=	=	SYM
ejpam-4521	149	4	k3	k3	PROPN
ejpam-4521	149	5	,	,	PUNCT
ejpam-4521	149	6	by	by	ADP
ejpam-4521	149	7	proposition	proposition	NOUN
ejpam-4521	149	8	1	1	NUM
ejpam-4521	149	9	,	,	PUNCT
ejpam-4521	149	10	fγch	fγch	NOUN
ejpam-4521	149	11	,	,	PUNCT
ejpam-4521	149	12	coi(c3	coi(c3	NOUN
ejpam-4521	149	13	)	)	PUNCT
ejpam-4521	149	14	=	=	SYM
ejpam-4521	149	15	0	0	X
ejpam-4521	149	16	.	.	PUNCT
ejpam-4521	149	17	suppose	suppose	VERB
ejpam-4521	149	18	that	that	SCONJ
ejpam-4521	149	19	n	n	PROPN
ejpam-4521	149	20	≥	≥	NUM
ejpam-4521	149	21	4	4	NUM
ejpam-4521	149	22	.	.	PUNCT
ejpam-4521	150	1	then	then	ADV
ejpam-4521	150	2	the	the	DET
ejpam-4521	150	3	γch	γch	NOUN
ejpam-4521	150	4	,	,	PUNCT
ejpam-4521	150	5	coi	coi	NOUN
ejpam-4521	150	6	-	-	PUNCT
ejpam-4521	150	7	sets	set	NOUN
ejpam-4521	150	8	of	of	ADP
ejpam-4521	150	9	cn	cn	PROPN
ejpam-4521	150	10	areb1	areb1	PROPN
ejpam-4521	151	1	=	=	NUM
ejpam-4521	151	2	{	{	PUNCT
ejpam-4521	151	3	v1	v1	PROPN
ejpam-4521	151	4	,	,	PUNCT
ejpam-4521	151	5	v2	v2	PROPN
ejpam-4521	151	6	,	,	PUNCT
ejpam-4521	151	7	.	.	PUNCT
ejpam-4521	151	8	.	.	PUNCT
ejpam-4521	151	9	.	.	PUNCT
ejpam-4521	152	1	,	,	PUNCT
ejpam-4521	152	2	vn−1	vn−1	ADJ
ejpam-4521	152	3	}	}	PUNCT
ejpam-4521	152	4	,	,	PUNCT
ejpam-4521	152	5	b2	b2	NOUN
ejpam-4521	152	6	=	=	SYM
ejpam-4521	152	7	{	{	PUNCT
ejpam-4521	152	8	v2	v2	PROPN
ejpam-4521	152	9	,	,	PUNCT
ejpam-4521	152	10	v3	v3	PROPN
ejpam-4521	152	11	,	,	PUNCT
ejpam-4521	152	12	.	.	PUNCT
ejpam-4521	152	13	.	.	PUNCT
ejpam-4521	152	14	.	.	PUNCT
ejpam-4521	153	1	,	,	PUNCT
ejpam-4521	153	2	vn	vn	PROPN
ejpam-4521	153	3	}	}	PUNCT
ejpam-4521	153	4	,	,	PUNCT
ejpam-4521	153	5	b3	b3	PROPN
ejpam-4521	153	6	=	=	SYM
ejpam-4521	153	7	{	{	PUNCT
ejpam-4521	153	8	v3	v3	PROPN
ejpam-4521	153	9	,	,	PUNCT
ejpam-4521	153	10	v4	v4	PROPN
ejpam-4521	153	11	,	,	PUNCT
ejpam-4521	153	12	.	.	PUNCT
ejpam-4521	153	13	.	.	PUNCT
ejpam-4521	154	1	.	.	PUNCT
ejpam-4521	155	1	,	,	PUNCT
ejpam-4521	155	2	vn	vn	X
ejpam-4521	155	3	,	,	PUNCT
ejpam-4521	155	4	v1	v1	PROPN
ejpam-4521	155	5	}	}	PUNCT
ejpam-4521	155	6	,	,	PUNCT
ejpam-4521	155	7	.	.	PUNCT
ejpam-4521	155	8	.	.	PUNCT
ejpam-4521	155	9	.	.	PUNCT
ejpam-4521	156	1	,	,	PUNCT
ejpam-4521	156	2	bn	bn	NOUN
ejpam-4521	156	3	=	=	SYM
ejpam-4521	156	4	{	{	PUNCT
ejpam-4521	156	5	vn	vn	PROPN
ejpam-4521	156	6	,	,	PUNCT
ejpam-4521	156	7	v1	v1	NOUN
ejpam-4521	156	8	,	,	PUNCT
ejpam-4521	156	9	v2	v2	NOUN
ejpam-4521	156	10	,	,	PUNCT
ejpam-4521	156	11	.	.	PUNCT
ejpam-4521	156	12	.	.	PUNCT
ejpam-4521	157	1	.	.	PUNCT
ejpam-4521	158	1	,	,	PUNCT
ejpam-4521	158	2	vn−2	vn−2	PROPN
ejpam-4521	158	3	}	}	PUNCT
ejpam-4521	158	4	.	.	PUNCT
ejpam-4521	159	1	clearly	clearly	ADV
ejpam-4521	159	2	,	,	PUNCT
ejpam-4521	159	3	for	for	ADP
ejpam-4521	159	4	each	each	DET
ejpam-4521	159	5	vi	vi	PROPN
ejpam-4521	159	6	∈	∈	NOUN
ejpam-4521	159	7	bj	bj	VERB
ejpam-4521	159	8	where	where	SCONJ
ejpam-4521	159	9	i	i	PRON
ejpam-4521	159	10	,	,	PUNCT
ejpam-4521	159	11	j	j	PROPN
ejpam-4521	159	12	∈	∈	PROPN
ejpam-4521	159	13	{	{	PUNCT
ejpam-4521	159	14	1	1	NUM
ejpam-4521	159	15	,	,	PUNCT
ejpam-4521	159	16	2	2	NUM
ejpam-4521	159	17	,	,	PUNCT
ejpam-4521	159	18	3	3	NUM
ejpam-4521	159	19	,	,	PUNCT
ejpam-4521	159	20	.	.	PUNCT
ejpam-4521	159	21	.	.	PUNCT
ejpam-4521	159	22	.	.	PUNCT
ejpam-4521	159	23	,	,	PUNCT
ejpam-4521	159	24	n	n	CCONJ
ejpam-4521	159	25	}	}	PUNCT
ejpam-4521	159	26	,	,	PUNCT
ejpam-4521	159	27	there	there	PRON
ejpam-4521	159	28	exists	exist	VERB
ejpam-4521	159	29	vk	vk	ADP
ejpam-4521	159	30	∈	∈	PROPN
ejpam-4521	159	31	v	v	PROPN
ejpam-4521	159	32	(	(	PUNCT
ejpam-4521	159	33	cn	cn	PROPN
ejpam-4521	159	34	)	)	PUNCT
ejpam-4521	159	35	\	\	NOUN
ejpam-4521	159	36	bj	bj	ADP
ejpam-4521	159	37	such	such	ADJ
ejpam-4521	159	38	that	that	SCONJ
ejpam-4521	159	39	[	[	PUNCT
ejpam-4521	159	40	bj	bj	ADP
ejpam-4521	159	41	\	\	NOUN
ejpam-4521	159	42	{	{	PUNCT
ejpam-4521	159	43	vi	vi	NOUN
ejpam-4521	159	44	}	}	PUNCT
ejpam-4521	159	45	]	]	PUNCT
ejpam-4521	159	46	∪	∪	X
ejpam-4521	159	47	{	{	PUNCT
ejpam-4521	159	48	vk	vk	INTJ
ejpam-4521	159	49	}	}	PUNCT
ejpam-4521	159	50	is	be	AUX
ejpam-4521	159	51	a	a	DET
ejpam-4521	159	52	γch	γch	NOUN
ejpam-4521	159	53	,	,	PUNCT
ejpam-4521	159	54	coi	coi	NOUN
ejpam-4521	159	55	-	-	PUNCT
ejpam-4521	159	56	set	set	NOUN
ejpam-4521	159	57	of	of	ADP
ejpam-4521	159	58	g.	g.	PROPN
ejpam-4521	159	59	hence	hence	ADV
ejpam-4521	159	60	,	,	PUNCT
ejpam-4521	159	61	by	by	ADP
ejpam-4521	159	62	theorem	theorem	NOUN
ejpam-4521	159	63	2	2	NUM
ejpam-4521	159	64	,	,	PUNCT
ejpam-4521	159	65	fγch	fγch	ADJ
ejpam-4521	159	66	,	,	PUNCT
ejpam-4521	159	67	coi(cn	coi(cn	NUM
ejpam-4521	159	68	)	)	PUNCT
ejpam-4521	160	1	=	=	PUNCT
ejpam-4521	160	2	n−	n−	NOUN
ejpam-4521	160	3	1	1	NUM
ejpam-4521	160	4	.	.	NOUN
ejpam-4521	160	5	4	4	X
ejpam-4521	160	6	.	.	X
ejpam-4521	160	7	forcing	force	VERB
ejpam-4521	160	8	connected	connected	ADJ
ejpam-4521	160	9	co	co	ADJ
ejpam-4521	160	10	-	-	ADJ
ejpam-4521	160	11	independent	independent	ADJ
ejpam-4521	160	12	hop	hop	NOUN
ejpam-4521	160	13	domination	domination	NOUN
ejpam-4521	160	14	in	in	ADP
ejpam-4521	160	15	the	the	DET
ejpam-4521	160	16	edge	edge	NOUN
ejpam-4521	160	17	corona	corona	NOUN
ejpam-4521	160	18	of	of	ADP
ejpam-4521	160	19	graphs	graph	NOUN
ejpam-4521	160	20	the	the	DET
ejpam-4521	160	21	following	follow	VERB
ejpam-4521	160	22	two	two	NUM
ejpam-4521	160	23	results	result	NOUN
ejpam-4521	160	24	are	be	AUX
ejpam-4521	160	25	taken	take	VERB
ejpam-4521	160	26	from	from	ADP
ejpam-4521	160	27	the	the	DET
ejpam-4521	160	28	masteral	masteral	ADJ
ejpam-4521	160	29	’s	’s	NOUN
ejpam-4521	160	30	thesis	thesis	NOUN
ejpam-4521	160	31	of	of	ADP
ejpam-4521	160	32	sandra	sandra	PROPN
ejpam-4521	160	33	a.	a.	PROPN
ejpam-4521	160	34	nanding	nanding	PROPN
ejpam-4521	160	35	.	.	PUNCT
ejpam-4521	161	1	to	to	PART
ejpam-4521	161	2	verify	verify	VERB
ejpam-4521	161	3	the	the	DET
ejpam-4521	161	4	result	result	NOUN
ejpam-4521	161	5	,	,	PUNCT
ejpam-4521	161	6	the	the	DET
ejpam-4521	161	7	proof	proof	NOUN
ejpam-4521	161	8	is	be	AUX
ejpam-4521	161	9	provided	provide	VERB
ejpam-4521	161	10	.	.	PUNCT
ejpam-4521	162	1	theorem	theorem	NOUN
ejpam-4521	162	2	3	3	X
ejpam-4521	162	3	.	.	PUNCT
ejpam-4521	163	1	let	let	VERB
ejpam-4521	163	2	g	g	PRON
ejpam-4521	163	3	be	be	AUX
ejpam-4521	163	4	a	a	DET
ejpam-4521	163	5	connected	connected	ADJ
ejpam-4521	163	6	graph	graph	NOUN
ejpam-4521	163	7	of	of	ADP
ejpam-4521	163	8	order	order	NOUN
ejpam-4521	163	9	n	n	PRON
ejpam-4521	163	10	≥	≥	NOUN
ejpam-4521	163	11	3	3	NUM
ejpam-4521	163	12	and	and	CCONJ
ejpam-4521	163	13	h	h	NOUN
ejpam-4521	163	14	be	be	VERB
ejpam-4521	163	15	any	any	DET
ejpam-4521	163	16	graph	graph	NOUN
ejpam-4521	163	17	.	.	PUNCT
ejpam-4521	164	1	then	then	ADV
ejpam-4521	164	2	c	c	PROPN
ejpam-4521	164	3	⊆	⊆	NUM
ejpam-4521	164	4	v	v	NOUN
ejpam-4521	164	5	(	(	PUNCT
ejpam-4521	164	6	g	g	PROPN
ejpam-4521	164	7	⋄h	⋄h	PROPN
ejpam-4521	164	8	)	)	PUNCT
ejpam-4521	164	9	is	be	AUX
ejpam-4521	164	10	a	a	DET
ejpam-4521	164	11	connected	connected	ADJ
ejpam-4521	164	12	co	co	NOUN
ejpam-4521	164	13	-	-	ADJ
ejpam-4521	164	14	independent	independent	ADJ
ejpam-4521	164	15	hop	hop	NOUN
ejpam-4521	164	16	dominating	dominating	NOUN
ejpam-4521	164	17	set	set	NOUN
ejpam-4521	164	18	of	of	ADP
ejpam-4521	164	19	g	g	PROPN
ejpam-4521	164	20	⋄h	⋄h	X
ejpam-4521	164	21	if	if	SCONJ
ejpam-4521	165	1	and	and	CCONJ
ejpam-4521	165	2	only	only	ADV
ejpam-4521	165	3	if	if	SCONJ
ejpam-4521	165	4	c	c	X
ejpam-4521	165	5	=	=	PUNCT
ejpam-4521	165	6	a	a	DET
ejpam-4521	165	7	∪	∪	X
ejpam-4521	165	8	(	(	PUNCT
ejpam-4521	165	9	⋃	⋃	NOUN
ejpam-4521	165	10	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	165	11	)	)	PUNCT
ejpam-4521	165	12	suv	suv	NOUN
ejpam-4521	165	13	)	)	PUNCT
ejpam-4521	165	14	where	where	SCONJ
ejpam-4521	165	15	(	(	PUNCT
ejpam-4521	165	16	i	i	NOUN
ejpam-4521	165	17	)	)	PUNCT
ejpam-4521	165	18	a	a	DET
ejpam-4521	165	19	⊆	⊆	NUM
ejpam-4521	165	20	v	v	NOUN
ejpam-4521	165	21	(	(	PUNCT
ejpam-4521	165	22	g	g	NOUN
ejpam-4521	165	23	)	)	PUNCT
ejpam-4521	165	24	is	be	AUX
ejpam-4521	165	25	a	a	DET
ejpam-4521	165	26	connected	connected	ADJ
ejpam-4521	165	27	co	co	ADJ
ejpam-4521	165	28	-	-	ADJ
ejpam-4521	165	29	independent	independent	ADJ
ejpam-4521	165	30	set	set	NOUN
ejpam-4521	165	31	of	of	ADP
ejpam-4521	165	32	g	g	NOUN
ejpam-4521	165	33	containing	contain	VERB
ejpam-4521	165	34	all	all	DET
ejpam-4521	165	35	vertices	vertex	NOUN
ejpam-4521	165	36	incident	incident	NOUN
ejpam-4521	165	37	to	to	ADP
ejpam-4521	165	38	all	all	DET
ejpam-4521	165	39	the	the	DET
ejpam-4521	165	40	edges	edge	NOUN
ejpam-4521	165	41	of	of	ADP
ejpam-4521	165	42	g.	g.	PROPN
ejpam-4521	165	43	(	(	PUNCT
ejpam-4521	165	44	ii	ii	PROPN
ejpam-4521	165	45	)	)	PUNCT
ejpam-4521	165	46	suv	suv	NOUN
ejpam-4521	166	1	=	=	SYM
ejpam-4521	166	2	v	v	PROPN
ejpam-4521	166	3	(	(	PUNCT
ejpam-4521	166	4	huv	huv	PROPN
ejpam-4521	166	5	)	)	PUNCT
ejpam-4521	166	6	if	if	SCONJ
ejpam-4521	166	7	uv	uv	PROPN
ejpam-4521	166	8	∈	∈	PROPN
ejpam-4521	166	9	e(g	e(g	PROPN
ejpam-4521	166	10	)	)	PUNCT
ejpam-4521	166	11	such	such	ADJ
ejpam-4521	166	12	that	that	SCONJ
ejpam-4521	166	13	u	u	PROPN
ejpam-4521	166	14	∈	∈	PROPN
ejpam-4521	166	15	v	v	NOUN
ejpam-4521	166	16	(	(	PUNCT
ejpam-4521	166	17	g)\a	g)\a	NOUN
ejpam-4521	166	18	or	or	CCONJ
ejpam-4521	166	19	v	v	ADP
ejpam-4521	166	20	∈	∈	PROPN
ejpam-4521	166	21	v	v	NOUN
ejpam-4521	166	22	(	(	PUNCT
ejpam-4521	166	23	g)\a	g)\a	NOUN
ejpam-4521	166	24	.	.	PUNCT
ejpam-4521	166	25	(	(	PUNCT
ejpam-4521	166	26	iii	iii	NOUN
ejpam-4521	166	27	)	)	PUNCT
ejpam-4521	166	28	for	for	ADP
ejpam-4521	166	29	every	every	DET
ejpam-4521	166	30	a	a	PROPN
ejpam-4521	166	31	,	,	PUNCT
ejpam-4521	166	32	b	b	PROPN
ejpam-4521	166	33	∈	∈	PROPN
ejpam-4521	166	34	a	a	PRON
ejpam-4521	166	35	such	such	ADJ
ejpam-4521	166	36	that	that	SCONJ
ejpam-4521	166	37	ab	ab	PROPN
ejpam-4521	166	38	∈	∈	PROPN
ejpam-4521	166	39	e(g	e(g	PROPN
ejpam-4521	166	40	)	)	PUNCT
ejpam-4521	166	41	and	and	CCONJ
ejpam-4521	166	42	sab	sab	VERB
ejpam-4521	166	43	̸=	̸=	PROPN
ejpam-4521	166	44	v	v	PROPN
ejpam-4521	166	45	(	(	PUNCT
ejpam-4521	166	46	hab	hab	NOUN
ejpam-4521	166	47	)	)	PUNCT
ejpam-4521	166	48	,	,	PUNCT
ejpam-4521	166	49	v	v	X
ejpam-4521	166	50	(	(	PUNCT
ejpam-4521	166	51	hab)\sab	hab)\sab	PROPN
ejpam-4521	166	52	is	be	AUX
ejpam-4521	166	53	an	an	DET
ejpam-4521	166	54	independent	independent	ADJ
ejpam-4521	166	55	set	set	NOUN
ejpam-4521	166	56	in	in	ADP
ejpam-4521	166	57	hab	hab	NOUN
ejpam-4521	166	58	.	.	PUNCT
ejpam-4521	167	1	proof	proof	NOUN
ejpam-4521	167	2	:	:	PUNCT
ejpam-4521	167	3	suppose	suppose	VERB
ejpam-4521	167	4	that	that	SCONJ
ejpam-4521	167	5	c	c	PROPN
ejpam-4521	167	6	is	be	AUX
ejpam-4521	167	7	a	a	DET
ejpam-4521	167	8	connected	connected	ADJ
ejpam-4521	167	9	co	co	NOUN
ejpam-4521	167	10	-	-	ADJ
ejpam-4521	167	11	independent	independent	ADJ
ejpam-4521	167	12	hop	hop	NOUN
ejpam-4521	167	13	dominating	dominating	NOUN
ejpam-4521	167	14	set	set	NOUN
ejpam-4521	167	15	of	of	ADP
ejpam-4521	167	16	g⋄h	g⋄h	PROPN
ejpam-4521	167	17	.	.	PUNCT
ejpam-4521	168	1	let	let	VERB
ejpam-4521	168	2	a	a	DET
ejpam-4521	168	3	=	=	SYM
ejpam-4521	168	4	c∩v	c∩v	NOUN
ejpam-4521	168	5	(	(	PUNCT
ejpam-4521	168	6	g	g	NOUN
ejpam-4521	168	7	)	)	PUNCT
ejpam-4521	168	8	and	and	CCONJ
ejpam-4521	168	9	let	let	VERB
ejpam-4521	168	10	suv	suv	PROPN
ejpam-4521	168	11	=	=	PROPN
ejpam-4521	168	12	c∩v	c∩v	NOUN
ejpam-4521	168	13	(	(	PUNCT
ejpam-4521	168	14	huv	huv	PROPN
ejpam-4521	168	15	)	)	PUNCT
ejpam-4521	168	16	for	for	ADP
ejpam-4521	168	17	each	each	DET
ejpam-4521	168	18	uv	uv	PROPN
ejpam-4521	168	19	∈	∈	PROPN
ejpam-4521	168	20	e(g	e(g	PROPN
ejpam-4521	168	21	)	)	PUNCT
ejpam-4521	168	22	.	.	PUNCT
ejpam-4521	169	1	then	then	ADV
ejpam-4521	169	2	c	c	X
ejpam-4521	169	3	=	=	SYM
ejpam-4521	169	4	a∪	a∪	PROPN
ejpam-4521	169	5	(	(	PUNCT
ejpam-4521	169	6	⋃	⋃	ADP
ejpam-4521	169	7	uv∈v	uv∈v	NOUN
ejpam-4521	169	8	(	(	PUNCT
ejpam-4521	169	9	g	g	NOUN
ejpam-4521	169	10	)	)	PUNCT
ejpam-4521	169	11	suv	suv	NOUN
ejpam-4521	169	12	)	)	PUNCT
ejpam-4521	169	13	where	where	SCONJ
ejpam-4521	169	14	a	a	DET
ejpam-4521	169	15	⊆	⊆	NUM
ejpam-4521	169	16	v	v	NOUN
ejpam-4521	169	17	(	(	PUNCT
ejpam-4521	169	18	g	g	NOUN
ejpam-4521	169	19	)	)	PUNCT
ejpam-4521	169	20	.	.	PUNCT
ejpam-4521	170	1	first	first	ADV
ejpam-4521	170	2	,	,	PUNCT
ejpam-4521	170	3	we	we	PRON
ejpam-4521	170	4	show	show	VERB
ejpam-4521	170	5	that	that	SCONJ
ejpam-4521	170	6	⟨a⟩	⟨a⟩	PROPN
ejpam-4521	170	7	is	be	AUX
ejpam-4521	170	8	connected	connect	VERB
ejpam-4521	170	9	.	.	PUNCT
ejpam-4521	171	1	let	let	VERB
ejpam-4521	171	2	x	x	PRON
ejpam-4521	171	3	,	,	PUNCT
ejpam-4521	171	4	y	y	PROPN
ejpam-4521	171	5	∈	∈	PROPN
ejpam-4521	172	1	a	a	DET
ejpam-4521	172	2	with	with	ADP
ejpam-4521	172	3	x	x	PUNCT
ejpam-4521	172	4	̸=	̸=	PROPN
ejpam-4521	172	5	y.	y.	NOUN
ejpam-4521	172	6	if	if	SCONJ
ejpam-4521	172	7	xy	xy	PROPN
ejpam-4521	172	8	∈	∈	PROPN
ejpam-4521	172	9	e(g	e(g	PROPN
ejpam-4521	172	10	)	)	PUNCT
ejpam-4521	172	11	,	,	PUNCT
ejpam-4521	172	12	then	then	ADV
ejpam-4521	172	13	we	we	PRON
ejpam-4521	172	14	are	be	AUX
ejpam-4521	172	15	done	do	VERB
ejpam-4521	172	16	.	.	PUNCT
ejpam-4521	173	1	suppose	suppose	VERB
ejpam-4521	173	2	that	that	SCONJ
ejpam-4521	173	3	xy	xy	PROPN
ejpam-4521	173	4	/∈	/∈	PUNCT
ejpam-4521	173	5	e(g	e(g	PROPN
ejpam-4521	173	6	)	)	PUNCT
ejpam-4521	173	7	.	.	PUNCT
ejpam-4521	174	1	since	since	SCONJ
ejpam-4521	174	2	⟨c⟩	⟨c⟩	PROPN
ejpam-4521	174	3	is	be	AUX
ejpam-4521	174	4	connected	connect	VERB
ejpam-4521	174	5	and	and	CCONJ
ejpam-4521	174	6	x	x	X
ejpam-4521	174	7	,	,	PUNCT
ejpam-4521	174	8	y	y	PROPN
ejpam-4521	174	9	∈	∈	PROPN
ejpam-4521	174	10	c	c	X
ejpam-4521	174	11	,	,	PUNCT
ejpam-4521	174	12	there	there	PRON
ejpam-4521	174	13	exists	exist	VERB
ejpam-4521	174	14	an	an	DET
ejpam-4521	174	15	x	x	NOUN
ejpam-4521	174	16	-	-	NOUN
ejpam-4521	174	17	y	y	ADJ
ejpam-4521	174	18	path	path	NOUN
ejpam-4521	175	1	[	[	X
ejpam-4521	175	2	x1	x1	PROPN
ejpam-4521	175	3	,	,	PUNCT
ejpam-4521	175	4	x2	x2	PROPN
ejpam-4521	175	5	,	,	PUNCT
ejpam-4521	175	6	...	...	PUNCT
ejpam-4521	175	7	,	,	PUNCT
ejpam-4521	175	8	xn	xn	PROPN
ejpam-4521	175	9	]	]	X
ejpam-4521	175	10	in	in	ADP
ejpam-4521	175	11	⟨c⟩	⟨c⟩	PROPN
ejpam-4521	175	12	where	where	SCONJ
ejpam-4521	175	13	x	x	X
ejpam-4521	175	14	=	=	SYM
ejpam-4521	175	15	x1	x1	PROPN
ejpam-4521	175	16	,	,	PUNCT
ejpam-4521	175	17	y	y	PROPN
ejpam-4521	175	18	=	=	SYM
ejpam-4521	175	19	xn	xn	PROPN
ejpam-4521	175	20	and	and	CCONJ
ejpam-4521	175	21	n	n	CCONJ
ejpam-4521	175	22	>	>	X
ejpam-4521	175	23	2	2	X
ejpam-4521	175	24	.	.	PUNCT
ejpam-4521	176	1	if	if	SCONJ
ejpam-4521	176	2	xi	xi	PROPN
ejpam-4521	176	3	∈	∈	PROPN
ejpam-4521	176	4	a	a	PRON
ejpam-4521	176	5	for	for	ADP
ejpam-4521	176	6	all	all	PRON
ejpam-4521	176	7	i	i	PRON
ejpam-4521	176	8	∈	∈	PROPN
ejpam-4521	176	9	{	{	PUNCT
ejpam-4521	176	10	1	1	NUM
ejpam-4521	176	11	,	,	PUNCT
ejpam-4521	176	12	2	2	NUM
ejpam-4521	176	13	,	,	PUNCT
ejpam-4521	176	14	...	...	PUNCT
ejpam-4521	176	15	,	,	PUNCT
ejpam-4521	176	16	n	n	CCONJ
ejpam-4521	176	17	}	}	PUNCT
ejpam-4521	176	18	,	,	PUNCT
ejpam-4521	176	19	then	then	ADV
ejpam-4521	176	20	the	the	DET
ejpam-4521	176	21	path	path	NOUN
ejpam-4521	177	1	[	[	X
ejpam-4521	177	2	x1	x1	PROPN
ejpam-4521	177	3	,	,	PUNCT
ejpam-4521	177	4	x2	x2	PROPN
ejpam-4521	177	5	,	,	PUNCT
ejpam-4521	177	6	...	...	PUNCT
ejpam-4521	177	7	,	,	PUNCT
ejpam-4521	177	8	xn	xn	PROPN
ejpam-4521	177	9	]	]	X
ejpam-4521	177	10	is	be	AUX
ejpam-4521	177	11	in	in	ADP
ejpam-4521	177	12	a.	a.	NOUN
ejpam-4521	177	13	suppose	suppose	VERB
ejpam-4521	177	14	there	there	PRON
ejpam-4521	177	15	exists	exist	VERB
ejpam-4521	178	1	xi	xi	X
ejpam-4521	178	2	/∈	/∈	PUNCT
ejpam-4521	178	3	a.	a.	NOUN
ejpam-4521	178	4	then	then	ADV
ejpam-4521	178	5	xi	xi	PROPN
ejpam-4521	178	6	∈	∈	PROPN
ejpam-4521	178	7	suv	suv	PROPN
ejpam-4521	178	8	for	for	ADP
ejpam-4521	178	9	some	some	DET
ejpam-4521	178	10	edge	edge	NOUN
ejpam-4521	178	11	uv	uv	PROPN
ejpam-4521	178	12	∈	∈	PROPN
ejpam-4521	178	13	e(g	e(g	PROPN
ejpam-4521	178	14	)	)	PUNCT
ejpam-4521	178	15	.	.	PUNCT
ejpam-4521	179	1	by	by	ADP
ejpam-4521	179	2	definition	definition	NOUN
ejpam-4521	179	3	of	of	ADP
ejpam-4521	179	4	g	g	PROPN
ejpam-4521	179	5	⋄h	⋄h	PROPN
ejpam-4521	179	6	,	,	PUNCT
ejpam-4521	179	7	u	u	NOUN
ejpam-4521	179	8	,	,	PUNCT
ejpam-4521	179	9	v	v	NOUN
ejpam-4521	179	10	∈	∈	NOUN
ejpam-4521	179	11	a.	a.	NOUN
ejpam-4521	179	12	hence	hence	ADV
ejpam-4521	179	13	,	,	PUNCT
ejpam-4521	179	14	[	[	X
ejpam-4521	179	15	x1	x1	ADJ
ejpam-4521	179	16	,	,	PUNCT
ejpam-4521	179	17	...	...	PUNCT
ejpam-4521	179	18	,	,	PUNCT
ejpam-4521	179	19	u	u	NOUN
ejpam-4521	179	20	,	,	PUNCT
ejpam-4521	179	21	v	v	NOUN
ejpam-4521	179	22	,	,	PUNCT
ejpam-4521	179	23	...	...	PUNCT
ejpam-4521	179	24	,	,	PUNCT
ejpam-4521	179	25	xn	xn	PROPN
ejpam-4521	179	26	]	]	X
ejpam-4521	179	27	is	be	AUX
ejpam-4521	179	28	a	a	DET
ejpam-4521	179	29	path	path	NOUN
ejpam-4521	179	30	in	in	ADP
ejpam-4521	179	31	a	a	PRON
ejpam-4521	179	32	,	,	PUNCT
ejpam-4521	179	33	showing	show	VERB
ejpam-4521	179	34	that	that	SCONJ
ejpam-4521	179	35	⟨a⟩	⟨a⟩	PROPN
ejpam-4521	179	36	is	be	AUX
ejpam-4521	179	37	connected	connect	VERB
ejpam-4521	179	38	.	.	PUNCT
ejpam-4521	180	1	next	next	ADV
ejpam-4521	180	2	,	,	PUNCT
ejpam-4521	180	3	let	let	VERB
ejpam-4521	180	4	u	u	NOUN
ejpam-4521	180	5	,	,	PUNCT
ejpam-4521	180	6	v	v	PROPN
ejpam-4521	180	7	∈	∈	PROPN
ejpam-4521	180	8	v	v	NOUN
ejpam-4521	180	9	(	(	PUNCT
ejpam-4521	180	10	g)\a	g)\a	NOUN
ejpam-4521	180	11	with	with	ADP
ejpam-4521	180	12	u	u	NOUN
ejpam-4521	180	13	̸=	̸=	PROPN
ejpam-4521	180	14	v.	v.	ADP
ejpam-4521	180	15	then	then	ADV
ejpam-4521	180	16	u	u	PROPN
ejpam-4521	180	17	,	,	PUNCT
ejpam-4521	180	18	v	v	PROPN
ejpam-4521	180	19	∈	∈	PROPN
ejpam-4521	180	20	v	v	NOUN
ejpam-4521	180	21	(	(	PUNCT
ejpam-4521	180	22	g	g	NOUN
ejpam-4521	180	23	⋄h)\c	⋄h)\c	PROPN
ejpam-4521	180	24	.	.	PUNCT
ejpam-4521	181	1	since	since	SCONJ
ejpam-4521	181	2	v	v	NOUN
ejpam-4521	181	3	(	(	PUNCT
ejpam-4521	181	4	g	g	NOUN
ejpam-4521	181	5	⋄h)\c	⋄h)\c	PROPN
ejpam-4521	181	6	is	be	AUX
ejpam-4521	181	7	independent	independent	ADJ
ejpam-4521	181	8	,	,	PUNCT
ejpam-4521	181	9	uv	uv	NOUN
ejpam-4521	181	10	/∈	/∈	PUNCT
ejpam-4521	181	11	e(g	e(g	PROPN
ejpam-4521	181	12	⋄h	⋄h	PROPN
ejpam-4521	181	13	)	)	PUNCT
ejpam-4521	181	14	.	.	PUNCT
ejpam-4521	182	1	since	since	SCONJ
ejpam-4521	182	2	u	u	NOUN
ejpam-4521	182	3	,	,	PUNCT
ejpam-4521	182	4	v	v	PROPN
ejpam-4521	182	5	∈	∈	PROPN
ejpam-4521	182	6	v	v	NOUN
ejpam-4521	182	7	(	(	PUNCT
ejpam-4521	182	8	g	g	NOUN
ejpam-4521	182	9	)	)	PUNCT
ejpam-4521	182	10	,	,	PUNCT
ejpam-4521	182	11	uv	uv	NOUN
ejpam-4521	182	12	/∈	/∈	PUNCT
ejpam-4521	182	13	e(g	e(g	PROPN
ejpam-4521	182	14	)	)	PUNCT
ejpam-4521	182	15	implying	imply	VERB
ejpam-4521	182	16	that	that	PRON
ejpam-4521	182	17	v	v	NOUN
ejpam-4521	182	18	(	(	PUNCT
ejpam-4521	182	19	g)\a	g)\a	NOUN
ejpam-4521	182	20	is	be	AUX
ejpam-4521	182	21	independent	independent	ADJ
ejpam-4521	182	22	.	.	PUNCT
ejpam-4521	183	1	now	now	ADV
ejpam-4521	183	2	,	,	PUNCT
ejpam-4521	183	3	suppose	suppose	VERB
ejpam-4521	183	4	v	v	PRON
ejpam-4521	183	5	is	be	AUX
ejpam-4521	183	6	a	a	DET
ejpam-4521	183	7	vertex	vertex	NOUN
ejpam-4521	183	8	incident	incident	NOUN
ejpam-4521	183	9	to	to	ADP
ejpam-4521	183	10	all	all	DET
ejpam-4521	183	11	the	the	DET
ejpam-4521	183	12	edges	edge	NOUN
ejpam-4521	183	13	of	of	ADP
ejpam-4521	183	14	g	g	NOUN
ejpam-4521	183	15	and	and	CCONJ
ejpam-4521	183	16	v	v	NOUN
ejpam-4521	183	17	/∈	/∈	PUNCT
ejpam-4521	184	1	a.	a.	NOUN
ejpam-4521	184	2	then	then	ADV
ejpam-4521	184	3	v	v	ADP
ejpam-4521	184	4	∈	∈	PROPN
ejpam-4521	184	5	ng(w	ng(w	NOUN
ejpam-4521	184	6	)	)	PUNCT
ejpam-4521	184	7	∩	∩	NOUN
ejpam-4521	184	8	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4521	184	9	)	)	PUNCT
ejpam-4521	184	10	for	for	ADP
ejpam-4521	184	11	all	all	DET
ejpam-4521	184	12	w	w	PROPN
ejpam-4521	184	13	∈	∈	PROPN
ejpam-4521	184	14	v	v	ADP
ejpam-4521	184	15	(	(	PUNCT
ejpam-4521	184	16	g	g	NOUN
ejpam-4521	184	17	)	)	PUNCT
ejpam-4521	184	18	and	and	CCONJ
ejpam-4521	184	19	for	for	ADP
ejpam-4521	184	20	all	all	DET
ejpam-4521	184	21	p	p	NOUN
ejpam-4521	184	22	∈	∈	PROPN
ejpam-4521	184	23	v	v	ADP
ejpam-4521	184	24	(	(	PUNCT
ejpam-4521	184	25	hvw	hvw	NOUN
ejpam-4521	184	26	)	)	PUNCT
ejpam-4521	184	27	.	.	PUNCT
ejpam-4521	185	1	thus	thus	ADV
ejpam-4521	185	2	,	,	PUNCT
ejpam-4521	185	3	ng⋄h(v	ng⋄h(v	NOUN
ejpam-4521	185	4	,	,	PUNCT
ejpam-4521	185	5	2	2	NUM
ejpam-4521	185	6	)	)	PUNCT
ejpam-4521	185	7	∩	∩	NOUN
ejpam-4521	185	8	c	c	NOUN
ejpam-4521	185	9	=	=	SYM
ejpam-4521	185	10	∅	∅	NOUN
ejpam-4521	185	11	,	,	PUNCT
ejpam-4521	185	12	a	a	DET
ejpam-4521	185	13	contradiction	contradiction	NOUN
ejpam-4521	185	14	since	since	SCONJ
ejpam-4521	185	15	c	c	PROPN
ejpam-4521	185	16	y.d	y.d	PROPN
ejpam-4521	185	17	.	.	PROPN
ejpam-4521	185	18	calanza	calanza	PROPN
ejpam-4521	185	19	,	,	PUNCT
ejpam-4521	185	20	h.	h.	PROPN
ejpam-4521	185	21	rara	rara	PROPN
ejpam-4521	185	22	/	/	SYM
ejpam-4521	185	23	eur	eur	PROPN
ejpam-4521	185	24	.	.	PUNCT
ejpam-4521	186	1	j.	j.	PROPN
ejpam-4521	186	2	pure	pure	PROPN
ejpam-4521	186	3	appl	appl	PROPN
ejpam-4521	186	4	.	.	PROPN
ejpam-4521	186	5	math	math	PROPN
ejpam-4521	186	6	,	,	PUNCT
ejpam-4521	186	7	15	15	NUM
ejpam-4521	186	8	(	(	PUNCT
ejpam-4521	186	9	4	4	NUM
ejpam-4521	186	10	)	)	PUNCT
ejpam-4521	186	11	(	(	PUNCT
ejpam-4521	186	12	2022	2022	NUM
ejpam-4521	186	13	)	)	PUNCT
ejpam-4521	186	14	,	,	PUNCT
ejpam-4521	186	15	1597	1597	NUM
ejpam-4521	186	16	-	-	SYM
ejpam-4521	186	17	1612	1612	NUM
ejpam-4521	186	18	1603	1603	NUM
ejpam-4521	186	19	is	be	AUX
ejpam-4521	186	20	a	a	DET
ejpam-4521	186	21	hop	hop	NOUN
ejpam-4521	186	22	dominating	dominating	NOUN
ejpam-4521	186	23	set	set	NOUN
ejpam-4521	186	24	.	.	PUNCT
ejpam-4521	187	1	hence	hence	ADV
ejpam-4521	187	2	,	,	PUNCT
ejpam-4521	187	3	a	a	PRON
ejpam-4521	187	4	is	be	AUX
ejpam-4521	187	5	a	a	DET
ejpam-4521	187	6	connected	connected	ADJ
ejpam-4521	187	7	co	co	ADJ
ejpam-4521	187	8	-	-	ADJ
ejpam-4521	187	9	independent	independent	ADJ
ejpam-4521	187	10	set	set	NOUN
ejpam-4521	187	11	of	of	ADP
ejpam-4521	187	12	g	g	NOUN
ejpam-4521	187	13	containing	contain	VERB
ejpam-4521	187	14	all	all	DET
ejpam-4521	187	15	vertices	vertex	NOUN
ejpam-4521	187	16	incident	incident	NOUN
ejpam-4521	187	17	to	to	ADP
ejpam-4521	187	18	all	all	DET
ejpam-4521	187	19	edges	edge	NOUN
ejpam-4521	187	20	of	of	ADP
ejpam-4521	187	21	g	g	NOUN
ejpam-4521	187	22	,	,	PUNCT
ejpam-4521	187	23	showing	show	VERB
ejpam-4521	187	24	that	that	SCONJ
ejpam-4521	187	25	(	(	PUNCT
ejpam-4521	187	26	i	i	NOUN
ejpam-4521	187	27	)	)	PUNCT
ejpam-4521	187	28	holds	hold	VERB
ejpam-4521	187	29	.	.	PUNCT
ejpam-4521	188	1	let	let	VERB
ejpam-4521	188	2	uv	uv	PRON
ejpam-4521	188	3	∈	∈	PROPN
ejpam-4521	188	4	e(g	e(g	PROPN
ejpam-4521	188	5	)	)	PUNCT
ejpam-4521	188	6	with	with	ADP
ejpam-4521	188	7	u	u	PROPN
ejpam-4521	188	8	/∈	/∈	PROPN
ejpam-4521	188	9	a.	a.	PROPN
ejpam-4521	188	10	suppose	suppose	VERB
ejpam-4521	188	11	suv	suv	PROPN
ejpam-4521	188	12	̸=	̸=	PROPN
ejpam-4521	188	13	v	v	PROPN
ejpam-4521	188	14	(	(	PUNCT
ejpam-4521	188	15	huv	huv	PROPN
ejpam-4521	188	16	)	)	PUNCT
ejpam-4521	188	17	.	.	PUNCT
ejpam-4521	189	1	then	then	ADV
ejpam-4521	189	2	there	there	PRON
ejpam-4521	189	3	exists	exist	VERB
ejpam-4521	189	4	x	x	X
ejpam-4521	189	5	∈	∈	PROPN
ejpam-4521	189	6	v	v	NOUN
ejpam-4521	189	7	(	(	PUNCT
ejpam-4521	189	8	huv)\suv	huv)\suv	PROPN
ejpam-4521	189	9	.	.	PUNCT
ejpam-4521	190	1	hence	hence	ADV
ejpam-4521	190	2	,	,	PUNCT
ejpam-4521	190	3	x	x	X
ejpam-4521	190	4	,	,	PUNCT
ejpam-4521	190	5	u	u	PROPN
ejpam-4521	190	6	∈	∈	PROPN
ejpam-4521	190	7	v	v	NOUN
ejpam-4521	190	8	(	(	PUNCT
ejpam-4521	190	9	g	g	PROPN
ejpam-4521	190	10	⋄	⋄	PROPN
ejpam-4521	190	11	h)\c	h)\c	NOUN
ejpam-4521	190	12	and	and	CCONJ
ejpam-4521	190	13	xu	xu	PROPN
ejpam-4521	190	14	∈	∈	PROPN
ejpam-4521	191	1	e(g	e(g	PROPN
ejpam-4521	191	2	⋄	⋄	PROPN
ejpam-4521	191	3	h	h	NOUN
ejpam-4521	191	4	)	)	PUNCT
ejpam-4521	191	5	,	,	PUNCT
ejpam-4521	191	6	a	a	DET
ejpam-4521	191	7	contradiction	contradiction	NOUN
ejpam-4521	191	8	to	to	ADP
ejpam-4521	191	9	the	the	DET
ejpam-4521	191	10	independence	independence	NOUN
ejpam-4521	191	11	of	of	ADP
ejpam-4521	191	12	v	v	NOUN
ejpam-4521	191	13	(	(	PUNCT
ejpam-4521	191	14	g	g	NOUN
ejpam-4521	191	15	⋄h)\c	⋄h)\c	PROPN
ejpam-4521	191	16	.	.	PUNCT
ejpam-4521	192	1	thus	thus	ADV
ejpam-4521	192	2	,	,	PUNCT
ejpam-4521	192	3	suv	suv	PROPN
ejpam-4521	192	4	=	=	SYM
ejpam-4521	192	5	v	v	PROPN
ejpam-4521	192	6	(	(	PUNCT
ejpam-4521	192	7	huv	huv	PROPN
ejpam-4521	192	8	)	)	PUNCT
ejpam-4521	192	9	and	and	CCONJ
ejpam-4521	192	10	(	(	PUNCT
ejpam-4521	192	11	ii	ii	NOUN
ejpam-4521	192	12	)	)	PUNCT
ejpam-4521	192	13	holds	hold	VERB
ejpam-4521	192	14	.	.	PUNCT
ejpam-4521	193	1	lastly	lastly	ADV
ejpam-4521	193	2	,	,	PUNCT
ejpam-4521	193	3	let	let	VERB
ejpam-4521	193	4	a	a	DET
ejpam-4521	193	5	,	,	PUNCT
ejpam-4521	193	6	b	b	PROPN
ejpam-4521	193	7	∈	∈	PROPN
ejpam-4521	193	8	a	a	DET
ejpam-4521	193	9	such	such	ADJ
ejpam-4521	193	10	that	that	SCONJ
ejpam-4521	193	11	ab	ab	PROPN
ejpam-4521	193	12	∈	∈	PROPN
ejpam-4521	193	13	e(g	e(g	PROPN
ejpam-4521	193	14	)	)	PUNCT
ejpam-4521	193	15	and	and	CCONJ
ejpam-4521	193	16	sab	sab	VERB
ejpam-4521	193	17	̸=	̸=	PROPN
ejpam-4521	193	18	v	v	PROPN
ejpam-4521	193	19	(	(	PUNCT
ejpam-4521	193	20	hab	hab	NOUN
ejpam-4521	193	21	)	)	PUNCT
ejpam-4521	193	22	.	.	PUNCT
ejpam-4521	194	1	since	since	SCONJ
ejpam-4521	194	2	v	v	NOUN
ejpam-4521	194	3	(	(	PUNCT
ejpam-4521	194	4	g	g	PROPN
ejpam-4521	194	5	⋄	⋄	PROPN
ejpam-4521	194	6	h)\c	h)\c	NOUN
ejpam-4521	194	7	is	be	AUX
ejpam-4521	194	8	independent	independent	ADJ
ejpam-4521	194	9	and	and	CCONJ
ejpam-4521	194	10	(	(	PUNCT
ejpam-4521	194	11	v	v	NOUN
ejpam-4521	194	12	(	(	PUNCT
ejpam-4521	194	13	hab)\sab	hab)\sab	PROPN
ejpam-4521	194	14	)	)	PUNCT
ejpam-4521	194	15	⊆	⊆	NUM
ejpam-4521	194	16	v	v	NOUN
ejpam-4521	194	17	(	(	PUNCT
ejpam-4521	194	18	g	g	NOUN
ejpam-4521	194	19	⋄h)\c	⋄h)\c	PROPN
ejpam-4521	194	20	,	,	PUNCT
ejpam-4521	194	21	v	v	NUM
ejpam-4521	194	22	(	(	PUNCT
ejpam-4521	194	23	hab)\sab	hab)\sab	PROPN
ejpam-4521	194	24	is	be	AUX
ejpam-4521	194	25	an	an	DET
ejpam-4521	194	26	independent	independent	ADJ
ejpam-4521	194	27	set	set	NOUN
ejpam-4521	194	28	in	in	ADP
ejpam-4521	194	29	hab	hab	NOUN
ejpam-4521	194	30	.	.	PUNCT
ejpam-4521	195	1	hence	hence	ADV
ejpam-4521	195	2	,	,	PUNCT
ejpam-4521	195	3	(	(	PUNCT
ejpam-4521	195	4	iii	iii	NOUN
ejpam-4521	195	5	)	)	PUNCT
ejpam-4521	195	6	holds	hold	VERB
ejpam-4521	195	7	.	.	PUNCT
ejpam-4521	196	1	for	for	ADP
ejpam-4521	196	2	the	the	DET
ejpam-4521	196	3	converse	converse	NOUN
ejpam-4521	196	4	,	,	PUNCT
ejpam-4521	196	5	suppose	suppose	VERB
ejpam-4521	196	6	c	c	NOUN
ejpam-4521	196	7	=	=	PUNCT
ejpam-4521	196	8	a	a	DET
ejpam-4521	196	9	∪	∪	X
ejpam-4521	196	10	(	(	PUNCT
ejpam-4521	196	11	⋃	⋃	NOUN
ejpam-4521	196	12	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	196	13	)	)	PUNCT
ejpam-4521	196	14	suv	suv	NOUN
ejpam-4521	196	15	)	)	PUNCT
ejpam-4521	196	16	where	where	SCONJ
ejpam-4521	196	17	(	(	PUNCT
ejpam-4521	196	18	i	i	NOUN
ejpam-4521	196	19	)	)	PUNCT
ejpam-4521	196	20	,	,	PUNCT
ejpam-4521	196	21	(	(	PUNCT
ejpam-4521	196	22	ii	ii	NOUN
ejpam-4521	196	23	)	)	PUNCT
ejpam-4521	196	24	and	and	CCONJ
ejpam-4521	196	25	(	(	PUNCT
ejpam-4521	196	26	iii	iii	NOUN
ejpam-4521	196	27	)	)	PUNCT
ejpam-4521	196	28	hold	hold	NOUN
ejpam-4521	196	29	.	.	PUNCT
ejpam-4521	197	1	first	first	ADV
ejpam-4521	197	2	,	,	PUNCT
ejpam-4521	197	3	we	we	PRON
ejpam-4521	197	4	show	show	VERB
ejpam-4521	197	5	that	that	SCONJ
ejpam-4521	197	6	c	c	PROPN
ejpam-4521	197	7	is	be	AUX
ejpam-4521	197	8	connected	connect	VERB
ejpam-4521	197	9	.	.	PUNCT
ejpam-4521	198	1	let	let	VERB
ejpam-4521	198	2	u	u	NOUN
ejpam-4521	198	3	,	,	PUNCT
ejpam-4521	198	4	v	v	PROPN
ejpam-4521	198	5	∈	∈	NOUN
ejpam-4521	198	6	c	c	NOUN
ejpam-4521	198	7	with	with	ADP
ejpam-4521	198	8	u	u	NOUN
ejpam-4521	198	9	̸=	̸=	PROPN
ejpam-4521	198	10	v.	v.	ADV
ejpam-4521	198	11	if	if	SCONJ
ejpam-4521	198	12	uv	uv	PROPN
ejpam-4521	198	13	∈	∈	PROPN
ejpam-4521	198	14	e(g	e(g	PROPN
ejpam-4521	198	15	⋄	⋄	PROPN
ejpam-4521	198	16	h	h	NOUN
ejpam-4521	198	17	)	)	PUNCT
ejpam-4521	198	18	,	,	PUNCT
ejpam-4521	198	19	then	then	ADV
ejpam-4521	198	20	we	we	PRON
ejpam-4521	198	21	are	be	AUX
ejpam-4521	198	22	done	do	VERB
ejpam-4521	198	23	.	.	PUNCT
ejpam-4521	199	1	so	so	ADV
ejpam-4521	199	2	,	,	PUNCT
ejpam-4521	199	3	suppose	suppose	VERB
ejpam-4521	199	4	that	that	SCONJ
ejpam-4521	199	5	uv	uv	NOUN
ejpam-4521	199	6	/∈	/∈	PUNCT
ejpam-4521	199	7	e(g	e(g	PROPN
ejpam-4521	199	8	⋄h	⋄h	PROPN
ejpam-4521	199	9	)	)	PUNCT
ejpam-4521	199	10	.	.	PUNCT
ejpam-4521	200	1	consider	consider	VERB
ejpam-4521	200	2	the	the	DET
ejpam-4521	200	3	following	follow	VERB
ejpam-4521	200	4	cases	case	NOUN
ejpam-4521	200	5	.	.	PUNCT
ejpam-4521	201	1	case	case	NOUN
ejpam-4521	201	2	1	1	NUM
ejpam-4521	201	3	.	.	X
ejpam-4521	201	4	u	u	NOUN
ejpam-4521	201	5	,	,	PUNCT
ejpam-4521	201	6	v	v	PROPN
ejpam-4521	201	7	∈	∈	PRON
ejpam-4521	201	8	a	a	PRON
ejpam-4521	201	9	by	by	X
ejpam-4521	201	10	(	(	PUNCT
ejpam-4521	201	11	i	i	NOUN
ejpam-4521	201	12	)	)	PUNCT
ejpam-4521	201	13	,	,	PUNCT
ejpam-4521	201	14	⟨a⟩	⟨a⟩	PROPN
ejpam-4521	201	15	is	be	AUX
ejpam-4521	201	16	connected	connect	VERB
ejpam-4521	201	17	.	.	PUNCT
ejpam-4521	202	1	hence	hence	ADV
ejpam-4521	202	2	,	,	PUNCT
ejpam-4521	202	3	there	there	PRON
ejpam-4521	202	4	exists	exist	VERB
ejpam-4521	202	5	a	a	DET
ejpam-4521	202	6	u	u	NOUN
ejpam-4521	202	7	-	-	NOUN
ejpam-4521	202	8	v	v	ADJ
ejpam-4521	202	9	path	path	NOUN
ejpam-4521	202	10	p	p	X
ejpam-4521	203	1	[	[	X
ejpam-4521	203	2	u	u	NOUN
ejpam-4521	203	3	,	,	PUNCT
ejpam-4521	203	4	v	v	ADP
ejpam-4521	203	5	]	]	PUNCT
ejpam-4521	203	6	in	in	ADP
ejpam-4521	203	7	a.	a.	NOUN
ejpam-4521	203	8	since	since	SCONJ
ejpam-4521	203	9	a	a	DET
ejpam-4521	203	10	⊆	⊆	NUM
ejpam-4521	203	11	c	c	NOUN
ejpam-4521	203	12	,	,	PUNCT
ejpam-4521	203	13	the	the	DET
ejpam-4521	203	14	path	path	NOUN
ejpam-4521	203	15	p	p	X
ejpam-4521	204	1	[	[	X
ejpam-4521	204	2	u	u	NOUN
ejpam-4521	204	3	,	,	PUNCT
ejpam-4521	204	4	v	v	NOUN
ejpam-4521	204	5	]	]	PUNCT
ejpam-4521	204	6	is	be	AUX
ejpam-4521	204	7	in	in	ADP
ejpam-4521	204	8	c.	c.	NOUN
ejpam-4521	204	9	case	case	NOUN
ejpam-4521	204	10	2	2	NUM
ejpam-4521	204	11	.	.	X
ejpam-4521	204	12	u	u	PROPN
ejpam-4521	204	13	∈	∈	PROPN
ejpam-4521	204	14	a	a	PRON
ejpam-4521	204	15	and	and	CCONJ
ejpam-4521	204	16	v	v	NOUN
ejpam-4521	204	17	∈	∈	PROPN
ejpam-4521	204	18	sxy	sxy	PROPN
ejpam-4521	204	19	for	for	ADP
ejpam-4521	204	20	some	some	DET
ejpam-4521	204	21	xy	xy	PROPN
ejpam-4521	204	22	∈	∈	PROPN
ejpam-4521	204	23	e(g	e(g	PROPN
ejpam-4521	204	24	)	)	PUNCT
ejpam-4521	204	25	since	since	SCONJ
ejpam-4521	204	26	uv	uv	PROPN
ejpam-4521	204	27	/∈	/∈	PUNCT
ejpam-4521	204	28	e(g	e(g	PROPN
ejpam-4521	204	29	⋄	⋄	PROPN
ejpam-4521	204	30	h	h	NOUN
ejpam-4521	204	31	)	)	PUNCT
ejpam-4521	204	32	,	,	PUNCT
ejpam-4521	204	33	u	u	NOUN
ejpam-4521	204	34	̸=	̸=	PROPN
ejpam-4521	204	35	x	x	X
ejpam-4521	204	36	and	and	CCONJ
ejpam-4521	204	37	u	u	PROPN
ejpam-4521	204	38	̸=	̸=	PROPN
ejpam-4521	204	39	y.	y.	NOUN
ejpam-4521	204	40	since	since	SCONJ
ejpam-4521	204	41	v	v	NOUN
ejpam-4521	204	42	(	(	PUNCT
ejpam-4521	204	43	g)\a	g)\a	NOUN
ejpam-4521	204	44	is	be	AUX
ejpam-4521	204	45	independent	independent	ADJ
ejpam-4521	204	46	by	by	ADP
ejpam-4521	204	47	(	(	PUNCT
ejpam-4521	204	48	i	i	NOUN
ejpam-4521	204	49	)	)	PUNCT
ejpam-4521	204	50	,	,	PUNCT
ejpam-4521	204	51	x	x	PUNCT
ejpam-4521	204	52	∈	∈	PROPN
ejpam-4521	204	53	a	a	PRON
ejpam-4521	204	54	or	or	CCONJ
ejpam-4521	204	55	y	y	PROPN
ejpam-4521	204	56	∈	∈	PROPN
ejpam-4521	204	57	a	a	PRON
ejpam-4521	204	58	,	,	PUNCT
ejpam-4521	204	59	say	say	VERB
ejpam-4521	204	60	x	x	X
ejpam-4521	204	61	∈	∈	NOUN
ejpam-4521	204	62	a.	a.	NOUN
ejpam-4521	205	1	if	if	SCONJ
ejpam-4521	205	2	ux	ux	PROPN
ejpam-4521	205	3	∈	∈	PROPN
ejpam-4521	205	4	e(g	e(g	PROPN
ejpam-4521	205	5	)	)	PUNCT
ejpam-4521	205	6	,	,	PUNCT
ejpam-4521	205	7	then	then	ADV
ejpam-4521	205	8	the	the	DET
ejpam-4521	205	9	path	path	NOUN
ejpam-4521	206	1	[	[	X
ejpam-4521	206	2	u	u	NOUN
ejpam-4521	206	3	,	,	PUNCT
ejpam-4521	206	4	x	x	X
ejpam-4521	206	5	,	,	PUNCT
ejpam-4521	206	6	v	v	NOUN
ejpam-4521	206	7	]	]	PUNCT
ejpam-4521	206	8	is	be	AUX
ejpam-4521	206	9	a	a	DET
ejpam-4521	206	10	u	u	NOUN
ejpam-4521	206	11	-	-	NOUN
ejpam-4521	206	12	v	v	ADJ
ejpam-4521	206	13	path	path	NOUN
ejpam-4521	206	14	in	in	ADP
ejpam-4521	206	15	c.	c.	PROPN
ejpam-4521	206	16	suppose	suppose	VERB
ejpam-4521	206	17	ux	ux	PROPN
ejpam-4521	206	18	/∈	/∈	PUNCT
ejpam-4521	206	19	e(g	e(g	PROPN
ejpam-4521	206	20	)	)	PUNCT
ejpam-4521	206	21	.	.	PUNCT
ejpam-4521	207	1	since	since	SCONJ
ejpam-4521	207	2	⟨a⟩	⟨a⟩	PROPN
ejpam-4521	207	3	is	be	AUX
ejpam-4521	207	4	connected	connect	VERB
ejpam-4521	207	5	by	by	ADP
ejpam-4521	207	6	(	(	PUNCT
ejpam-4521	207	7	i	i	NOUN
ejpam-4521	207	8	)	)	PUNCT
ejpam-4521	207	9	and	and	CCONJ
ejpam-4521	207	10	u	u	NOUN
ejpam-4521	207	11	,	,	PUNCT
ejpam-4521	207	12	x	x	PROPN
ejpam-4521	207	13	∈	∈	PROPN
ejpam-4521	207	14	a	a	PRON
ejpam-4521	207	15	,	,	PUNCT
ejpam-4521	207	16	there	there	PRON
ejpam-4521	207	17	exists	exist	VERB
ejpam-4521	207	18	u	u	NOUN
ejpam-4521	207	19	-	-	ADJ
ejpam-4521	207	20	x	x	ADJ
ejpam-4521	207	21	path	path	NOUN
ejpam-4521	207	22	[	[	X
ejpam-4521	207	23	y1	y1	INTJ
ejpam-4521	207	24	,	,	PUNCT
ejpam-4521	207	25	y2	y2	PROPN
ejpam-4521	207	26	,	,	PUNCT
ejpam-4521	207	27	...	...	PUNCT
ejpam-4521	207	28	,	,	PUNCT
ejpam-4521	207	29	yk	yk	PROPN
ejpam-4521	207	30	]	]	PUNCT
ejpam-4521	207	31	in	in	ADP
ejpam-4521	207	32	a	a	DET
ejpam-4521	207	33	where	where	SCONJ
ejpam-4521	207	34	u	u	NOUN
ejpam-4521	207	35	=	=	PROPN
ejpam-4521	207	36	y1	y1	PROPN
ejpam-4521	207	37	,	,	PUNCT
ejpam-4521	207	38	x	x	X
ejpam-4521	207	39	=	=	SYM
ejpam-4521	207	40	yk	yk	PROPN
ejpam-4521	207	41	and	and	CCONJ
ejpam-4521	207	42	k	k	X
ejpam-4521	208	1	>	>	X
ejpam-4521	208	2	2	2	X
ejpam-4521	208	3	.	.	PUNCT
ejpam-4521	209	1	hence	hence	ADV
ejpam-4521	209	2	,	,	PUNCT
ejpam-4521	209	3	the	the	DET
ejpam-4521	209	4	path	path	NOUN
ejpam-4521	209	5	[	[	X
ejpam-4521	209	6	y1	y1	INTJ
ejpam-4521	209	7	,	,	PUNCT
ejpam-4521	209	8	y2	y2	PROPN
ejpam-4521	209	9	,	,	PUNCT
ejpam-4521	209	10	...	...	PUNCT
ejpam-4521	209	11	,	,	PUNCT
ejpam-4521	209	12	yk	yk	PROPN
ejpam-4521	209	13	,	,	PUNCT
ejpam-4521	209	14	v	v	NOUN
ejpam-4521	209	15	]	]	X
ejpam-4521	209	16	is	be	AUX
ejpam-4521	209	17	a	a	DET
ejpam-4521	209	18	u	u	NOUN
ejpam-4521	209	19	-	-	NOUN
ejpam-4521	209	20	v	v	ADJ
ejpam-4521	209	21	path	path	NOUN
ejpam-4521	209	22	in	in	ADP
ejpam-4521	209	23	c.	c.	PROPN
ejpam-4521	209	24	case	case	NOUN
ejpam-4521	209	25	3	3	NUM
ejpam-4521	209	26	.	.	X
ejpam-4521	209	27	u	u	NOUN
ejpam-4521	209	28	,	,	PUNCT
ejpam-4521	209	29	v	v	NOUN
ejpam-4521	209	30	∈	∈	NOUN
ejpam-4521	209	31	spq	spq	NOUN
ejpam-4521	209	32	for	for	ADP
ejpam-4521	209	33	some	some	DET
ejpam-4521	209	34	edge	edge	NOUN
ejpam-4521	209	35	pq	pq	PROPN
ejpam-4521	209	36	∈	∈	PROPN
ejpam-4521	209	37	e(g	e(g	PROPN
ejpam-4521	209	38	)	)	PUNCT
ejpam-4521	209	39	.	.	PUNCT
ejpam-4521	210	1	since	since	SCONJ
ejpam-4521	210	2	v	v	NOUN
ejpam-4521	210	3	(	(	PUNCT
ejpam-4521	210	4	g)\a	g)\a	NOUN
ejpam-4521	210	5	is	be	AUX
ejpam-4521	210	6	independent	independent	ADJ
ejpam-4521	210	7	by	by	ADP
ejpam-4521	210	8	(	(	PUNCT
ejpam-4521	210	9	i	i	NOUN
ejpam-4521	210	10	)	)	PUNCT
ejpam-4521	210	11	,	,	PUNCT
ejpam-4521	210	12	p	p	PROPN
ejpam-4521	210	13	∈	∈	PROPN
ejpam-4521	210	14	a	a	PRON
ejpam-4521	210	15	or	or	CCONJ
ejpam-4521	210	16	q	q	PROPN
ejpam-4521	210	17	∈	∈	PROPN
ejpam-4521	210	18	a.	a.	NOUN
ejpam-4521	210	19	hence	hence	ADV
ejpam-4521	210	20	,	,	PUNCT
ejpam-4521	210	21	the	the	DET
ejpam-4521	210	22	path	path	NOUN
ejpam-4521	211	1	[	[	X
ejpam-4521	211	2	u	u	NOUN
ejpam-4521	211	3	,	,	PUNCT
ejpam-4521	211	4	p	p	X
ejpam-4521	211	5	,	,	PUNCT
ejpam-4521	211	6	v	v	NOUN
ejpam-4521	211	7	]	]	PUNCT
ejpam-4521	211	8	or	or	CCONJ
ejpam-4521	211	9	[	[	X
ejpam-4521	211	10	u	u	NOUN
ejpam-4521	211	11	,	,	PUNCT
ejpam-4521	211	12	q	q	INTJ
ejpam-4521	211	13	,	,	PUNCT
ejpam-4521	211	14	v	v	NOUN
ejpam-4521	211	15	]	]	PUNCT
ejpam-4521	211	16	is	be	AUX
ejpam-4521	211	17	in	in	ADP
ejpam-4521	211	18	c.	c.	NOUN
ejpam-4521	211	19	in	in	ADP
ejpam-4521	211	20	any	any	DET
ejpam-4521	211	21	case	case	NOUN
ejpam-4521	211	22	,	,	PUNCT
ejpam-4521	211	23	⟨c⟩	⟨c⟩	PROPN
ejpam-4521	211	24	is	be	AUX
ejpam-4521	211	25	connected	connect	VERB
ejpam-4521	211	26	.	.	PUNCT
ejpam-4521	212	1	next	next	ADV
ejpam-4521	212	2	,	,	PUNCT
ejpam-4521	212	3	we	we	PRON
ejpam-4521	212	4	show	show	VERB
ejpam-4521	212	5	that	that	SCONJ
ejpam-4521	212	6	v	v	NOUN
ejpam-4521	212	7	(	(	PUNCT
ejpam-4521	212	8	g	g	NOUN
ejpam-4521	212	9	⋄h)\c	⋄h)\c	PROPN
ejpam-4521	212	10	is	be	AUX
ejpam-4521	212	11	independent	independent	ADJ
ejpam-4521	212	12	.	.	PUNCT
ejpam-4521	213	1	let	let	VERB
ejpam-4521	213	2	p	p	PRON
ejpam-4521	213	3	,	,	PUNCT
ejpam-4521	213	4	q	q	PROPN
ejpam-4521	213	5	∈	∈	PROPN
ejpam-4521	213	6	v	v	NOUN
ejpam-4521	213	7	(	(	PUNCT
ejpam-4521	213	8	g	g	NOUN
ejpam-4521	213	9	⋄h)\c	⋄h)\c	VERB
ejpam-4521	213	10	with	with	ADP
ejpam-4521	213	11	p	p	PROPN
ejpam-4521	213	12	̸=	̸=	PROPN
ejpam-4521	213	13	q.	q.	NOUN
ejpam-4521	213	14	consider	consider	VERB
ejpam-4521	213	15	the	the	DET
ejpam-4521	213	16	following	follow	VERB
ejpam-4521	213	17	cases	case	NOUN
ejpam-4521	213	18	.	.	PUNCT
ejpam-4521	214	1	case	case	NOUN
ejpam-4521	214	2	1	1	NUM
ejpam-4521	214	3	.	.	PUNCT
ejpam-4521	215	1	p	p	PROPN
ejpam-4521	215	2	∈	∈	PROPN
ejpam-4521	215	3	v	v	NOUN
ejpam-4521	215	4	(	(	PUNCT
ejpam-4521	215	5	g)\a	g)\a	NOUN
ejpam-4521	215	6	and	and	CCONJ
ejpam-4521	215	7	q	q	NOUN
ejpam-4521	215	8	∈	∈	PROPN
ejpam-4521	215	9	v	v	NOUN
ejpam-4521	215	10	(	(	PUNCT
ejpam-4521	215	11	g)\a	g)\a	NOUN
ejpam-4521	215	12	since	since	SCONJ
ejpam-4521	215	13	v	v	NOUN
ejpam-4521	215	14	(	(	PUNCT
ejpam-4521	215	15	g)\a	g)\a	NOUN
ejpam-4521	215	16	is	be	AUX
ejpam-4521	215	17	independent	independent	ADJ
ejpam-4521	215	18	by	by	ADP
ejpam-4521	215	19	(	(	PUNCT
ejpam-4521	215	20	i	i	NOUN
ejpam-4521	215	21	)	)	PUNCT
ejpam-4521	215	22	,	,	PUNCT
ejpam-4521	215	23	pq	pq	PROPN
ejpam-4521	215	24	/∈	/∈	PUNCT
ejpam-4521	215	25	e(g	e(g	PROPN
ejpam-4521	215	26	)	)	PUNCT
ejpam-4521	215	27	.	.	PUNCT
ejpam-4521	216	1	thus	thus	ADV
ejpam-4521	216	2	,	,	PUNCT
ejpam-4521	216	3	pq	pq	INTJ
ejpam-4521	216	4	/∈	/∈	PUNCT
ejpam-4521	216	5	e(g	e(g	PROPN
ejpam-4521	216	6	⋄h	⋄h	PROPN
ejpam-4521	216	7	)	)	PUNCT
ejpam-4521	216	8	.	.	PUNCT
ejpam-4521	217	1	case	case	NOUN
ejpam-4521	217	2	2	2	NUM
ejpam-4521	217	3	.	.	PUNCT
ejpam-4521	218	1	p	p	PROPN
ejpam-4521	218	2	∈	∈	PROPN
ejpam-4521	218	3	v	v	NOUN
ejpam-4521	218	4	(	(	PUNCT
ejpam-4521	218	5	g)\a	g)\a	NOUN
ejpam-4521	218	6	,	,	PUNCT
ejpam-4521	218	7	q	q	PROPN
ejpam-4521	218	8	∈	∈	PROPN
ejpam-4521	218	9	v	v	NOUN
ejpam-4521	218	10	(	(	PUNCT
ejpam-4521	218	11	hxy)\sxy	hxy)\sxy	PROPN
ejpam-4521	218	12	for	for	ADP
ejpam-4521	218	13	some	some	DET
ejpam-4521	218	14	xy	xy	PROPN
ejpam-4521	218	15	∈	∈	PROPN
ejpam-4521	218	16	e(g	e(g	PROPN
ejpam-4521	218	17	)	)	PUNCT
ejpam-4521	218	18	since	since	SCONJ
ejpam-4521	218	19	sxy	sxy	PROPN
ejpam-4521	218	20	̸=	̸=	PROPN
ejpam-4521	218	21	v	v	ADP
ejpam-4521	218	22	(	(	PUNCT
ejpam-4521	218	23	hxy	hxy	NOUN
ejpam-4521	218	24	)	)	PUNCT
ejpam-4521	218	25	,	,	PUNCT
ejpam-4521	218	26	x	x	X
ejpam-4521	218	27	,	,	PUNCT
ejpam-4521	218	28	y	y	PROPN
ejpam-4521	218	29	∈	∈	PROPN
ejpam-4521	218	30	a	a	DET
ejpam-4521	218	31	by	by	ADP
ejpam-4521	218	32	(	(	PUNCT
ejpam-4521	218	33	ii	ii	NOUN
ejpam-4521	218	34	)	)	PUNCT
ejpam-4521	218	35	.	.	PUNCT
ejpam-4521	219	1	hence	hence	ADV
ejpam-4521	219	2	,	,	PUNCT
ejpam-4521	219	3	p	p	PROPN
ejpam-4521	219	4	̸=	̸=	PROPN
ejpam-4521	219	5	x	x	PUNCT
ejpam-4521	219	6	and	and	CCONJ
ejpam-4521	219	7	p	p	PROPN
ejpam-4521	219	8	̸=	̸=	PROPN
ejpam-4521	219	9	y.	y.	NOUN
ejpam-4521	219	10	by	by	ADP
ejpam-4521	219	11	definition	definition	NOUN
ejpam-4521	219	12	of	of	ADP
ejpam-4521	219	13	g	g	PROPN
ejpam-4521	219	14	⋄h	⋄h	PROPN
ejpam-4521	219	15	,	,	PUNCT
ejpam-4521	219	16	pq	pq	NOUN
ejpam-4521	219	17	/∈	/∈	PUNCT
ejpam-4521	219	18	e(g	e(g	PROPN
ejpam-4521	219	19	⋄h	⋄h	PROPN
ejpam-4521	219	20	)	)	PUNCT
ejpam-4521	219	21	.	.	PUNCT
ejpam-4521	220	1	case	case	NOUN
ejpam-4521	220	2	3	3	X
ejpam-4521	220	3	.	.	PUNCT
ejpam-4521	221	1	p	p	PROPN
ejpam-4521	221	2	∈	∈	PROPN
ejpam-4521	221	3	v	v	NOUN
ejpam-4521	221	4	(	(	PUNCT
ejpam-4521	221	5	hxy)\sxy	hxy)\sxy	PROPN
ejpam-4521	221	6	and	and	CCONJ
ejpam-4521	221	7	q	q	NOUN
ejpam-4521	221	8	∈	∈	PROPN
ejpam-4521	221	9	v	v	NOUN
ejpam-4521	221	10	(	(	PUNCT
ejpam-4521	221	11	hrs)\srs	hrs)\srs	NOUN
ejpam-4521	221	12	for	for	ADP
ejpam-4521	221	13	some	some	DET
ejpam-4521	221	14	distinct	distinct	ADJ
ejpam-4521	221	15	edges	edge	NOUN
ejpam-4521	221	16	xy	xy	NOUN
ejpam-4521	221	17	,	,	PUNCT
ejpam-4521	221	18	rs	rs	PROPN
ejpam-4521	221	19	∈	∈	PROPN
ejpam-4521	221	20	e(g	e(g	PROPN
ejpam-4521	221	21	)	)	PUNCT
ejpam-4521	221	22	then	then	ADV
ejpam-4521	221	23	,	,	PUNCT
ejpam-4521	221	24	by	by	ADP
ejpam-4521	221	25	definition	definition	NOUN
ejpam-4521	221	26	of	of	ADP
ejpam-4521	221	27	g	g	PROPN
ejpam-4521	221	28	⋄h	⋄h	PROPN
ejpam-4521	221	29	,	,	PUNCT
ejpam-4521	221	30	pq	pq	NOUN
ejpam-4521	221	31	/∈	/∈	PUNCT
ejpam-4521	221	32	e(g	e(g	PROPN
ejpam-4521	221	33	⋄h	⋄h	PROPN
ejpam-4521	221	34	)	)	PUNCT
ejpam-4521	221	35	.	.	PUNCT
ejpam-4521	222	1	case	case	NOUN
ejpam-4521	222	2	4	4	NUM
ejpam-4521	222	3	.	.	X
ejpam-4521	223	1	p	p	X
ejpam-4521	223	2	,	,	PUNCT
ejpam-4521	223	3	q	q	PROPN
ejpam-4521	223	4	∈	∈	PROPN
ejpam-4521	223	5	v	v	NOUN
ejpam-4521	223	6	(	(	PUNCT
ejpam-4521	223	7	hzt)\szt	hzt)\szt	NOUN
ejpam-4521	223	8	for	for	ADP
ejpam-4521	223	9	some	some	DET
ejpam-4521	223	10	edge	edge	NOUN
ejpam-4521	223	11	zt	zt	PROPN
ejpam-4521	223	12	∈	∈	PROPN
ejpam-4521	223	13	e(g	e(g	PROPN
ejpam-4521	223	14	)	)	PUNCT
ejpam-4521	223	15	since	since	SCONJ
ejpam-4521	223	16	v	v	NUM
ejpam-4521	223	17	(	(	PUNCT
ejpam-4521	223	18	hzt)\szt	hzt)\szt	PROPN
ejpam-4521	223	19	is	be	AUX
ejpam-4521	223	20	independent	independent	ADJ
ejpam-4521	223	21	by	by	ADP
ejpam-4521	223	22	(	(	PUNCT
ejpam-4521	223	23	iii	iii	NOUN
ejpam-4521	223	24	)	)	PUNCT
ejpam-4521	223	25	,	,	PUNCT
ejpam-4521	223	26	pq	pq	INTJ
ejpam-4521	223	27	/∈	/∈	PUNCT
ejpam-4521	223	28	e(g	e(g	PROPN
ejpam-4521	223	29	⋄h	⋄h	PROPN
ejpam-4521	223	30	)	)	PUNCT
ejpam-4521	223	31	.	.	PUNCT
ejpam-4521	224	1	therefore	therefore	ADV
ejpam-4521	224	2	,	,	PUNCT
ejpam-4521	224	3	in	in	ADP
ejpam-4521	224	4	any	any	DET
ejpam-4521	224	5	case	case	NOUN
ejpam-4521	224	6	,	,	PUNCT
ejpam-4521	224	7	v	v	NOUN
ejpam-4521	224	8	(	(	PUNCT
ejpam-4521	224	9	g	g	NOUN
ejpam-4521	224	10	⋄h)\c	⋄h)\c	PROPN
ejpam-4521	224	11	is	be	AUX
ejpam-4521	224	12	an	an	DET
ejpam-4521	224	13	independent	independent	ADJ
ejpam-4521	224	14	set	set	NOUN
ejpam-4521	224	15	in	in	ADP
ejpam-4521	224	16	g	g	PROPN
ejpam-4521	224	17	⋄h	⋄h	PROPN
ejpam-4521	224	18	.	.	PUNCT
ejpam-4521	225	1	lastly	lastly	ADV
ejpam-4521	225	2	,	,	PUNCT
ejpam-4521	225	3	we	we	PRON
ejpam-4521	225	4	show	show	VERB
ejpam-4521	225	5	that	that	SCONJ
ejpam-4521	225	6	c	c	PROPN
ejpam-4521	225	7	is	be	AUX
ejpam-4521	225	8	a	a	DET
ejpam-4521	225	9	hop	hop	NOUN
ejpam-4521	225	10	dominating	dominating	NOUN
ejpam-4521	225	11	set	set	NOUN
ejpam-4521	225	12	of	of	ADP
ejpam-4521	225	13	g	g	PROPN
ejpam-4521	225	14	⋄	⋄	PROPN
ejpam-4521	225	15	h.	h.	PROPN
ejpam-4521	225	16	let	let	VERB
ejpam-4521	225	17	u	u	PRON
ejpam-4521	225	18	∈	∈	PROPN
ejpam-4521	225	19	v	v	NOUN
ejpam-4521	225	20	(	(	PUNCT
ejpam-4521	225	21	g	g	PROPN
ejpam-4521	225	22	⋄	⋄	PROPN
ejpam-4521	225	23	h)\c	h)\c	NOUN
ejpam-4521	225	24	.	.	PUNCT
ejpam-4521	226	1	consider	consider	VERB
ejpam-4521	226	2	the	the	DET
ejpam-4521	226	3	following	follow	VERB
ejpam-4521	226	4	cases	case	NOUN
ejpam-4521	226	5	.	.	PUNCT
ejpam-4521	227	1	case	case	NOUN
ejpam-4521	227	2	1	1	NUM
ejpam-4521	227	3	.	.	PUNCT
ejpam-4521	228	1	u	u	PROPN
ejpam-4521	228	2	∈	∈	PROPN
ejpam-4521	228	3	v	v	NOUN
ejpam-4521	228	4	(	(	PUNCT
ejpam-4521	228	5	g)\a	g)\a	NOUN
ejpam-4521	228	6	let	let	VERB
ejpam-4521	228	7	degg(u	degg(u	NUM
ejpam-4521	228	8	)	)	PUNCT
ejpam-4521	228	9	=	=	SYM
ejpam-4521	229	1	1	1	X
ejpam-4521	229	2	.	.	PUNCT
ejpam-4521	229	3	since	since	SCONJ
ejpam-4521	229	4	|v	|v	PROPN
ejpam-4521	229	5	(	(	PUNCT
ejpam-4521	229	6	g)|	g)|	X
ejpam-4521	229	7	≥	≥	NOUN
ejpam-4521	229	8	3	3	NUM
ejpam-4521	229	9	,	,	PUNCT
ejpam-4521	229	10	there	there	PRON
ejpam-4521	229	11	exists	exist	VERB
ejpam-4521	229	12	vw	vw	PROPN
ejpam-4521	229	13	∈	∈	PROPN
ejpam-4521	229	14	e(g	e(g	PROPN
ejpam-4521	229	15	)	)	PUNCT
ejpam-4521	229	16	with	with	ADP
ejpam-4521	229	17	u	u	PROPN
ejpam-4521	229	18	∈	∈	PROPN
ejpam-4521	229	19	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-4521	229	20	)	)	PUNCT
ejpam-4521	229	21	or	or	CCONJ
ejpam-4521	229	22	u	u	PROPN
ejpam-4521	229	23	∈	∈	PROPN
ejpam-4521	229	24	ng(w)\ng(v	ng(w)\ng(v	NOUN
ejpam-4521	229	25	)	)	PUNCT
ejpam-4521	229	26	.	.	PUNCT
ejpam-4521	230	1	if	if	SCONJ
ejpam-4521	230	2	w	w	PROPN
ejpam-4521	230	3	∈	∈	PROPN
ejpam-4521	230	4	a	a	PRON
ejpam-4521	230	5	,	,	PUNCT
ejpam-4521	230	6	then	then	ADV
ejpam-4521	230	7	w	w	PROPN
ejpam-4521	230	8	∈	∈	PROPN
ejpam-4521	230	9	ng(u	ng(u	NOUN
ejpam-4521	230	10	,	,	PUNCT
ejpam-4521	230	11	2	2	NUM
ejpam-4521	230	12	)	)	PUNCT
ejpam-4521	230	13	∩	∩	ADJ
ejpam-4521	230	14	a.	a.	NOUN
ejpam-4521	230	15	if	if	SCONJ
ejpam-4521	230	16	w	w	PROPN
ejpam-4521	230	17	/∈	/∈	PROPN
ejpam-4521	230	18	a	a	PRON
ejpam-4521	230	19	,	,	PUNCT
ejpam-4521	230	20	then	then	ADV
ejpam-4521	230	21	svw	svw	VERB
ejpam-4521	230	22	=	=	SYM
ejpam-4521	230	23	v	v	ADJ
ejpam-4521	230	24	(	(	PUNCT
ejpam-4521	230	25	hvw	hvw	NOUN
ejpam-4521	230	26	)	)	PUNCT
ejpam-4521	230	27	by	by	ADP
ejpam-4521	230	28	(	(	PUNCT
ejpam-4521	230	29	ii	ii	NOUN
ejpam-4521	230	30	)	)	PUNCT
ejpam-4521	230	31	.	.	PUNCT
ejpam-4521	231	1	thus	thus	ADV
ejpam-4521	231	2	,	,	PUNCT
ejpam-4521	231	3	a	a	DET
ejpam-4521	231	4	vertex	vertex	NOUN
ejpam-4521	231	5	p	p	X
ejpam-4521	231	6	∈	∈	PROPN
ejpam-4521	231	7	ng⋄h(u	ng⋄h(u	PROPN
ejpam-4521	231	8	,	,	PUNCT
ejpam-4521	231	9	2	2	X
ejpam-4521	231	10	)	)	PUNCT
ejpam-4521	231	11	∩	∩	NOUN
ejpam-4521	231	12	svw	svw	NOUN
ejpam-4521	231	13	exists	exist	VERB
ejpam-4521	231	14	.	.	PUNCT
ejpam-4521	232	1	hence	hence	ADV
ejpam-4521	232	2	,	,	PUNCT
ejpam-4521	232	3	p	p	PROPN
ejpam-4521	232	4	∈	∈	PROPN
ejpam-4521	232	5	ng⋄h(u	ng⋄h(u	PROPN
ejpam-4521	232	6	,	,	PUNCT
ejpam-4521	232	7	2	2	X
ejpam-4521	232	8	)	)	PUNCT
ejpam-4521	232	9	∩	∩	PROPN
ejpam-4521	232	10	c.	c.	PROPN
ejpam-4521	232	11	y.d	y.d	PROPN
ejpam-4521	232	12	.	.	PROPN
ejpam-4521	232	13	calanza	calanza	PROPN
ejpam-4521	232	14	,	,	PUNCT
ejpam-4521	232	15	h.	h.	PROPN
ejpam-4521	232	16	rara	rara	PROPN
ejpam-4521	232	17	/	/	SYM
ejpam-4521	232	18	eur	eur	PROPN
ejpam-4521	232	19	.	.	PUNCT
ejpam-4521	233	1	j.	j.	PROPN
ejpam-4521	233	2	pure	pure	PROPN
ejpam-4521	233	3	appl	appl	PROPN
ejpam-4521	233	4	.	.	PROPN
ejpam-4521	233	5	math	math	PROPN
ejpam-4521	233	6	,	,	PUNCT
ejpam-4521	233	7	15	15	NUM
ejpam-4521	233	8	(	(	PUNCT
ejpam-4521	233	9	4	4	NUM
ejpam-4521	233	10	)	)	PUNCT
ejpam-4521	233	11	(	(	PUNCT
ejpam-4521	233	12	2022	2022	NUM
ejpam-4521	233	13	)	)	PUNCT
ejpam-4521	233	14	,	,	PUNCT
ejpam-4521	233	15	1597	1597	NUM
ejpam-4521	233	16	-	-	SYM
ejpam-4521	233	17	1612	1612	NUM
ejpam-4521	233	18	1604	1604	NUM
ejpam-4521	233	19	case	case	NOUN
ejpam-4521	233	20	2	2	NUM
ejpam-4521	233	21	.	.	PUNCT
ejpam-4521	233	22	u	u	PROPN
ejpam-4521	233	23	∈	∈	PROPN
ejpam-4521	233	24	v	v	NOUN
ejpam-4521	233	25	(	(	PUNCT
ejpam-4521	233	26	hxy)\sxy	hxy)\sxy	PROPN
ejpam-4521	233	27	for	for	ADP
ejpam-4521	233	28	some	some	DET
ejpam-4521	233	29	xy	xy	PROPN
ejpam-4521	233	30	∈	∈	PROPN
ejpam-4521	233	31	e(g	e(g	PROPN
ejpam-4521	233	32	)	)	PUNCT
ejpam-4521	233	33	by	by	ADP
ejpam-4521	233	34	(	(	PUNCT
ejpam-4521	233	35	ii	ii	NOUN
ejpam-4521	233	36	)	)	PUNCT
ejpam-4521	233	37	,	,	PUNCT
ejpam-4521	233	38	x	x	X
ejpam-4521	233	39	,	,	PUNCT
ejpam-4521	233	40	y	y	PROPN
ejpam-4521	233	41	∈	∈	PROPN
ejpam-4521	233	42	a.	a.	NOUN
ejpam-4521	233	43	since	since	SCONJ
ejpam-4521	233	44	|v	|v	PROPN
ejpam-4521	233	45	(	(	PUNCT
ejpam-4521	233	46	g)|	g)|	X
ejpam-4521	233	47	≥	≥	NOUN
ejpam-4521	233	48	3	3	NUM
ejpam-4521	233	49	,	,	PUNCT
ejpam-4521	233	50	there	there	PRON
ejpam-4521	233	51	exist	exist	VERB
ejpam-4521	233	52	z	z	PROPN
ejpam-4521	233	53	∈	∈	PROPN
ejpam-4521	233	54	v	v	ADP
ejpam-4521	233	55	(	(	PUNCT
ejpam-4521	233	56	g	g	NOUN
ejpam-4521	233	57	)	)	PUNCT
ejpam-4521	233	58	∩ng(x	∩ng(x	NOUN
ejpam-4521	233	59	)	)	PUNCT
ejpam-4521	233	60	or	or	CCONJ
ejpam-4521	233	61	z	z	NOUN
ejpam-4521	233	62	∈	∈	PROPN
ejpam-4521	233	63	v	v	ADP
ejpam-4521	233	64	(	(	PUNCT
ejpam-4521	233	65	g	g	NOUN
ejpam-4521	233	66	)	)	PUNCT
ejpam-4521	233	67	∩ng(y	∩ng(y	PROPN
ejpam-4521	233	68	)	)	PUNCT
ejpam-4521	233	69	.	.	PUNCT
ejpam-4521	234	1	if	if	SCONJ
ejpam-4521	234	2	z	z	PROPN
ejpam-4521	234	3	∈	∈	PROPN
ejpam-4521	234	4	a	a	PRON
ejpam-4521	234	5	,	,	PUNCT
ejpam-4521	234	6	then	then	ADV
ejpam-4521	234	7	z	z	PROPN
ejpam-4521	234	8	∈	∈	PROPN
ejpam-4521	234	9	ng⋄h(u	ng⋄h(u	PROPN
ejpam-4521	234	10	,	,	PUNCT
ejpam-4521	234	11	2	2	X
ejpam-4521	234	12	)	)	PUNCT
ejpam-4521	234	13	∩	∩	ADJ
ejpam-4521	234	14	c.	c.	NOUN
ejpam-4521	234	15	if	if	SCONJ
ejpam-4521	234	16	z	z	PROPN
ejpam-4521	234	17	/∈	/∈	VERB
ejpam-4521	235	1	a	a	PRON
ejpam-4521	235	2	,	,	PUNCT
ejpam-4521	235	3	then	then	ADV
ejpam-4521	235	4	syz	syz	VERB
ejpam-4521	235	5	=	=	SYM
ejpam-4521	235	6	v	v	X
ejpam-4521	235	7	(	(	PUNCT
ejpam-4521	235	8	hyz	hyz	PROPN
ejpam-4521	235	9	)	)	PUNCT
ejpam-4521	235	10	.	.	PUNCT
ejpam-4521	236	1	hence	hence	ADV
ejpam-4521	236	2	,	,	PUNCT
ejpam-4521	236	3	a	a	DET
ejpam-4521	236	4	vertex	vertex	NOUN
ejpam-4521	236	5	w	w	PROPN
ejpam-4521	236	6	∈	∈	PROPN
ejpam-4521	236	7	ng⋄h(u	ng⋄h(u	PROPN
ejpam-4521	236	8	,	,	PUNCT
ejpam-4521	236	9	2	2	X
ejpam-4521	236	10	)	)	PUNCT
ejpam-4521	236	11	∩	∩	NOUN
ejpam-4521	236	12	syz	syz	VERB
ejpam-4521	236	13	or	or	CCONJ
ejpam-4521	236	14	w	w	PROPN
ejpam-4521	236	15	∈	∈	PROPN
ejpam-4521	236	16	ng⋄h(u	ng⋄h(u	PROPN
ejpam-4521	236	17	,	,	PUNCT
ejpam-4521	236	18	2	2	X
ejpam-4521	236	19	)	)	PUNCT
ejpam-4521	236	20	∩	∩	NOUN
ejpam-4521	236	21	sxz	sxz	PROPN
ejpam-4521	236	22	.	.	PUNCT
ejpam-4521	237	1	therefore	therefore	ADV
ejpam-4521	237	2	,	,	PUNCT
ejpam-4521	237	3	in	in	ADP
ejpam-4521	237	4	any	any	DET
ejpam-4521	237	5	case	case	NOUN
ejpam-4521	237	6	,	,	PUNCT
ejpam-4521	237	7	c	c	PROPN
ejpam-4521	237	8	is	be	AUX
ejpam-4521	237	9	a	a	DET
ejpam-4521	237	10	hop	hop	NOUN
ejpam-4521	237	11	dominating	dominating	NOUN
ejpam-4521	237	12	set	set	NOUN
ejpam-4521	237	13	of	of	ADP
ejpam-4521	237	14	g	g	PROPN
ejpam-4521	237	15	⋄h	⋄h	PROPN
ejpam-4521	237	16	.	.	PUNCT
ejpam-4521	238	1	accordingly	accordingly	ADV
ejpam-4521	238	2	,	,	PUNCT
ejpam-4521	238	3	c	c	PROPN
ejpam-4521	238	4	is	be	AUX
ejpam-4521	238	5	a	a	DET
ejpam-4521	238	6	connected	connected	ADJ
ejpam-4521	238	7	co	co	NOUN
ejpam-4521	238	8	-	-	ADJ
ejpam-4521	238	9	independent	independent	ADJ
ejpam-4521	238	10	hop	hop	NOUN
ejpam-4521	238	11	dominating	dominating	NOUN
ejpam-4521	238	12	set	set	NOUN
ejpam-4521	238	13	of	of	ADP
ejpam-4521	238	14	g	g	PROPN
ejpam-4521	238	15	⋄h	⋄h	PROPN
ejpam-4521	238	16	.	.	PUNCT
ejpam-4521	239	1	corollary	corollary	ADJ
ejpam-4521	239	2	2	2	NUM
ejpam-4521	239	3	.	.	PUNCT
ejpam-4521	240	1	let	let	VERB
ejpam-4521	240	2	g	g	PRON
ejpam-4521	240	3	be	be	AUX
ejpam-4521	240	4	a	a	DET
ejpam-4521	240	5	connected	connected	ADJ
ejpam-4521	240	6	graph	graph	NOUN
ejpam-4521	240	7	of	of	ADP
ejpam-4521	240	8	order	order	NOUN
ejpam-4521	240	9	n	n	PRON
ejpam-4521	240	10	≥	≥	NOUN
ejpam-4521	240	11	3	3	NUM
ejpam-4521	240	12	of	of	ADP
ejpam-4521	240	13	size	size	NOUN
ejpam-4521	240	14	p	p	NOUN
ejpam-4521	240	15	and	and	CCONJ
ejpam-4521	240	16	h	h	NOUN
ejpam-4521	240	17	be	be	VERB
ejpam-4521	240	18	any	any	DET
ejpam-4521	240	19	graph	graph	NOUN
ejpam-4521	240	20	of	of	ADP
ejpam-4521	240	21	order	order	NOUN
ejpam-4521	240	22	m.	m.	NOUN
ejpam-4521	240	23	then	then	ADV
ejpam-4521	240	24	γch	γch	VERB
ejpam-4521	240	25	,	,	PUNCT
ejpam-4521	240	26	coi(g	coi(g	PROPN
ejpam-4521	240	27	⋄h	⋄h	PROPN
ejpam-4521	240	28	)	)	PUNCT
ejpam-4521	240	29	=	=	PRON
ejpam-4521	240	30	n+	n+	X
ejpam-4521	240	31	p(m−	p(m−	NOUN
ejpam-4521	240	32	β(h	β(h	PROPN
ejpam-4521	240	33	)	)	PUNCT
ejpam-4521	240	34	)	)	PUNCT
ejpam-4521	240	35	.	.	PUNCT
ejpam-4521	241	1	proof	proof	NOUN
ejpam-4521	241	2	:	:	PUNCT
ejpam-4521	241	3	let	let	VERB
ejpam-4521	241	4	co	co	VERB
ejpam-4521	241	5	=	=	NOUN
ejpam-4521	241	6	a	a	DET
ejpam-4521	241	7	∪	∪	X
ejpam-4521	241	8	(	(	PUNCT
ejpam-4521	241	9	⋃	⋃	ADJ
ejpam-4521	241	10	uv∈v	uv∈v	NOUN
ejpam-4521	241	11	(	(	PUNCT
ejpam-4521	241	12	g	g	NOUN
ejpam-4521	241	13	)	)	PUNCT
ejpam-4521	241	14	suv	suv	PROPN
ejpam-4521	241	15	)	)	PUNCT
ejpam-4521	241	16	be	be	VERB
ejpam-4521	241	17	a	a	DET
ejpam-4521	241	18	γch	γch	NOUN
ejpam-4521	241	19	,	,	PUNCT
ejpam-4521	241	20	coi	coi	NOUN
ejpam-4521	241	21	-	-	PUNCT
ejpam-4521	241	22	set	set	NOUN
ejpam-4521	241	23	of	of	ADP
ejpam-4521	241	24	g	g	PROPN
ejpam-4521	241	25	⋄h	⋄h	PROPN
ejpam-4521	241	26	.	.	PUNCT
ejpam-4521	242	1	then	then	ADV
ejpam-4521	242	2	conditions	condition	NOUN
ejpam-4521	242	3	(	(	PUNCT
ejpam-4521	242	4	i	i	NOUN
ejpam-4521	242	5	)	)	PUNCT
ejpam-4521	242	6	,	,	PUNCT
ejpam-4521	242	7	(	(	PUNCT
ejpam-4521	242	8	ii	ii	NOUN
ejpam-4521	242	9	)	)	PUNCT
ejpam-4521	242	10	and	and	CCONJ
ejpam-4521	242	11	(	(	PUNCT
ejpam-4521	242	12	iii	iii	NOUN
ejpam-4521	242	13	)	)	PUNCT
ejpam-4521	242	14	of	of	ADP
ejpam-4521	242	15	theorem	theorem	ADJ
ejpam-4521	242	16	3	3	NUM
ejpam-4521	242	17	hold	hold	VERB
ejpam-4521	242	18	where	where	SCONJ
ejpam-4521	242	19	a	a	DET
ejpam-4521	242	20	=	=	SYM
ejpam-4521	242	21	v	v	NOUN
ejpam-4521	242	22	(	(	PUNCT
ejpam-4521	242	23	g	g	NOUN
ejpam-4521	242	24	)	)	PUNCT
ejpam-4521	242	25	and	and	CCONJ
ejpam-4521	242	26	suv	suv	PROPN
ejpam-4521	242	27	=	=	SYM
ejpam-4521	242	28	v	v	PROPN
ejpam-4521	242	29	(	(	PUNCT
ejpam-4521	242	30	huv)\s∗	huv)\s∗	PROPN
ejpam-4521	242	31	where	where	SCONJ
ejpam-4521	242	32	s∗	s∗	PROPN
ejpam-4521	242	33	is	be	AUX
ejpam-4521	242	34	any	any	DET
ejpam-4521	242	35	independent	independent	ADJ
ejpam-4521	242	36	set	set	NOUN
ejpam-4521	242	37	of	of	ADP
ejpam-4521	242	38	huv	huv	PROPN
ejpam-4521	242	39	.	.	PUNCT
ejpam-4521	243	1	thus	thus	ADV
ejpam-4521	243	2	,	,	PUNCT
ejpam-4521	243	3	γch	γch	NOUN
ejpam-4521	243	4	,	,	PUNCT
ejpam-4521	243	5	coi(g	coi(g	PROPN
ejpam-4521	243	6	⋄h	⋄h	PROPN
ejpam-4521	243	7	)	)	PUNCT
ejpam-4521	243	8	=	=	PUNCT
ejpam-4521	243	9	|a|+	|a|+	NOUN
ejpam-4521	243	10	p|suv|	p|suv|	NOUN
ejpam-4521	243	11	=	=	SYM
ejpam-4521	243	12	n+	n+	PROPN
ejpam-4521	243	13	p(|v	p(|v	PROPN
ejpam-4521	243	14	(	(	PUNCT
ejpam-4521	243	15	huv)|	huv)|	NOUN
ejpam-4521	243	16	−	−	NOUN
ejpam-4521	243	17	|s∗|	|s∗|	NUM
ejpam-4521	243	18	)	)	PUNCT
ejpam-4521	243	19	≥	≥	NOUN
ejpam-4521	243	20	n+	n+	PUNCT
ejpam-4521	243	21	p(m−	p(m−	NOUN
ejpam-4521	243	22	β(h	β(h	PROPN
ejpam-4521	243	23	)	)	PUNCT
ejpam-4521	243	24	)	)	PUNCT
ejpam-4521	243	25	.	.	PUNCT
ejpam-4521	244	1	let	let	VERB
ejpam-4521	244	2	t	t	NOUN
ejpam-4521	244	3	be	be	AUX
ejpam-4521	244	4	a	a	DET
ejpam-4521	244	5	β	β	NOUN
ejpam-4521	244	6	-	-	VERB
ejpam-4521	244	7	set	set	NOUN
ejpam-4521	244	8	of	of	ADP
ejpam-4521	244	9	h	h	NOUN
ejpam-4521	244	10	and	and	CCONJ
ejpam-4521	244	11	suv	suv	PROPN
ejpam-4521	244	12	=	=	SYM
ejpam-4521	244	13	v	v	PROPN
ejpam-4521	244	14	(	(	PUNCT
ejpam-4521	244	15	huv)\t	huv)\t	NOUN
ejpam-4521	244	16	for	for	ADP
ejpam-4521	244	17	each	each	DET
ejpam-4521	244	18	uv	uv	PROPN
ejpam-4521	244	19	∈	∈	PROPN
ejpam-4521	244	20	e(g	e(g	PROPN
ejpam-4521	244	21	)	)	PUNCT
ejpam-4521	244	22	.	.	PUNCT
ejpam-4521	245	1	then	then	ADV
ejpam-4521	245	2	c	c	X
ejpam-4521	245	3	=	=	SYM
ejpam-4521	245	4	v	v	PROPN
ejpam-4521	245	5	(	(	PUNCT
ejpam-4521	245	6	g	g	NOUN
ejpam-4521	245	7	)	)	PUNCT
ejpam-4521	245	8	∪	∪	NOUN
ejpam-4521	245	9	(	(	PUNCT
ejpam-4521	245	10	⋃	⋃	NOUN
ejpam-4521	245	11	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	245	12	)	)	PUNCT
ejpam-4521	245	13	suv	suv	PROPN
ejpam-4521	245	14	)	)	PUNCT
ejpam-4521	245	15	is	be	AUX
ejpam-4521	245	16	a	a	DET
ejpam-4521	245	17	connected	connected	ADJ
ejpam-4521	245	18	co	co	NOUN
ejpam-4521	245	19	-	-	ADJ
ejpam-4521	245	20	independent	independent	ADJ
ejpam-4521	245	21	hop	hop	NOUN
ejpam-4521	245	22	dominating	dominating	NOUN
ejpam-4521	245	23	set	set	NOUN
ejpam-4521	245	24	of	of	ADP
ejpam-4521	245	25	g	g	PROPN
ejpam-4521	245	26	⋄	⋄	PROPN
ejpam-4521	245	27	h	h	NOUN
ejpam-4521	245	28	by	by	ADP
ejpam-4521	245	29	theorem	theorem	NOUN
ejpam-4521	245	30	3	3	NUM
ejpam-4521	245	31	.	.	PUNCT
ejpam-4521	245	32	hence	hence	ADV
ejpam-4521	245	33	,	,	PUNCT
ejpam-4521	245	34	γch	γch	NOUN
ejpam-4521	245	35	,	,	PUNCT
ejpam-4521	245	36	coi(g	coi(g	PROPN
ejpam-4521	245	37	⋄h	⋄h	PROPN
ejpam-4521	245	38	)	)	PUNCT
ejpam-4521	245	39	≤	≤	PROPN
ejpam-4521	245	40	|c|	|c|	PROPN
ejpam-4521	245	41	=	=	SYM
ejpam-4521	245	42	|v	|v	PROPN
ejpam-4521	245	43	(	(	PUNCT
ejpam-4521	245	44	g)|+	g)|+	NOUN
ejpam-4521	245	45	p|suv|	p|suv|	NOUN
ejpam-4521	245	46	=	=	SYM
ejpam-4521	245	47	n+	n+	X
ejpam-4521	245	48	p|v	p|v	X
ejpam-4521	245	49	(	(	PUNCT
ejpam-4521	245	50	huv)\t	huv)\t	NOUN
ejpam-4521	245	51	|	|	NOUN
ejpam-4521	245	52	=	=	SYM
ejpam-4521	245	53	n+	n+	X
ejpam-4521	245	54	p(m−	p(m−	NOUN
ejpam-4521	245	55	β(h	β(h	PROPN
ejpam-4521	245	56	)	)	PUNCT
ejpam-4521	245	57	)	)	PUNCT
ejpam-4521	245	58	.	.	PUNCT
ejpam-4521	246	1	therefore	therefore	ADV
ejpam-4521	246	2	,	,	PUNCT
ejpam-4521	246	3	γch	γch	NOUN
ejpam-4521	246	4	,	,	PUNCT
ejpam-4521	246	5	coi(g	coi(g	PROPN
ejpam-4521	246	6	⋄h	⋄h	PROPN
ejpam-4521	246	7	)	)	PUNCT
ejpam-4521	246	8	=	=	PRON
ejpam-4521	246	9	n+	n+	X
ejpam-4521	246	10	p(m−	p(m−	NOUN
ejpam-4521	246	11	β(h	β(h	PROPN
ejpam-4521	246	12	)	)	PUNCT
ejpam-4521	246	13	)	)	PUNCT
ejpam-4521	246	14	.	.	PUNCT
ejpam-4521	247	1	remark	remark	PROPN
ejpam-4521	247	2	3	3	NUM
ejpam-4521	247	3	and	and	CCONJ
ejpam-4521	247	4	theorem	theorem	VERB
ejpam-4521	247	5	2	2	NUM
ejpam-4521	247	6	hold	hold	NOUN
ejpam-4521	247	7	if	if	SCONJ
ejpam-4521	247	8	the	the	DET
ejpam-4521	247	9	γch	γch	NOUN
ejpam-4521	247	10	,	,	PUNCT
ejpam-4521	247	11	coi	coi	NOUN
ejpam-4521	247	12	-	-	PUNCT
ejpam-4521	247	13	set	set	NOUN
ejpam-4521	247	14	is	be	AUX
ejpam-4521	247	15	replace	replace	NOUN
ejpam-4521	247	16	by	by	ADP
ejpam-4521	247	17	coi	coi	NOUN
ejpam-4521	247	18	-	-	PUNCT
ejpam-4521	247	19	set	set	NOUN
ejpam-4521	247	20	.	.	PUNCT
ejpam-4521	248	1	thus	thus	ADV
ejpam-4521	248	2	,	,	PUNCT
ejpam-4521	248	3	we	we	PRON
ejpam-4521	248	4	have	have	VERB
ejpam-4521	248	5	the	the	DET
ejpam-4521	248	6	following	follow	VERB
ejpam-4521	248	7	remark	remark	NOUN
ejpam-4521	248	8	and	and	CCONJ
ejpam-4521	248	9	theorem	theorem	ADJ
ejpam-4521	248	10	.	.	PROPN
ejpam-4521	248	11	remark	remark	PROPN
ejpam-4521	248	12	4	4	NUM
ejpam-4521	248	13	.	.	PUNCT
ejpam-4521	249	1	let	let	VERB
ejpam-4521	249	2	g	g	PRON
ejpam-4521	249	3	be	be	AUX
ejpam-4521	249	4	a	a	DET
ejpam-4521	249	5	connected	connected	ADJ
ejpam-4521	249	6	graph	graph	NOUN
ejpam-4521	249	7	.	.	PUNCT
ejpam-4521	250	1	then	then	ADV
ejpam-4521	250	2	(	(	PUNCT
ejpam-4521	250	3	i	i	NOUN
ejpam-4521	250	4	)	)	PUNCT
ejpam-4521	250	5	fcoi(g	fcoi(g	ADV
ejpam-4521	250	6	)	)	PUNCT
ejpam-4521	251	1	=	=	SYM
ejpam-4521	251	2	0	0	PUNCT
ejpam-4521	252	1	if	if	SCONJ
ejpam-4521	252	2	and	and	CCONJ
ejpam-4521	252	3	only	only	ADV
ejpam-4521	252	4	if	if	SCONJ
ejpam-4521	252	5	g	g	PROPN
ejpam-4521	252	6	has	have	VERB
ejpam-4521	252	7	a	a	DET
ejpam-4521	252	8	unique	unique	ADJ
ejpam-4521	252	9	coi	coi	NOUN
ejpam-4521	252	10	-	-	PUNCT
ejpam-4521	252	11	set	set	NOUN
ejpam-4521	252	12	,	,	PUNCT
ejpam-4521	252	13	and	and	CCONJ
ejpam-4521	252	14	(	(	PUNCT
ejpam-4521	252	15	ii	ii	NOUN
ejpam-4521	252	16	)	)	PUNCT
ejpam-4521	252	17	fcoi(g	fcoi(g	ADV
ejpam-4521	252	18	)	)	PUNCT
ejpam-4521	253	1	=	=	SYM
ejpam-4521	253	2	1	1	NUM
ejpam-4521	253	3	if	if	SCONJ
ejpam-4521	253	4	and	and	CCONJ
ejpam-4521	253	5	only	only	ADV
ejpam-4521	253	6	if	if	SCONJ
ejpam-4521	253	7	g	g	PROPN
ejpam-4521	253	8	has	have	VERB
ejpam-4521	253	9	at	at	ADV
ejpam-4521	253	10	least	least	ADV
ejpam-4521	253	11	two	two	NUM
ejpam-4521	253	12	coi	coi	NOUN
ejpam-4521	253	13	-	-	PUNCT
ejpam-4521	253	14	sets	set	NOUN
ejpam-4521	253	15	,	,	PUNCT
ejpam-4521	253	16	one	one	NUM
ejpam-4521	253	17	of	of	ADP
ejpam-4521	253	18	which	which	PRON
ejpam-4521	253	19	,	,	PUNCT
ejpam-4521	253	20	say	say	VERB
ejpam-4521	253	21	d	d	NOUN
ejpam-4521	253	22	,	,	PUNCT
ejpam-4521	253	23	contains	contain	VERB
ejpam-4521	253	24	an	an	DET
ejpam-4521	253	25	element	element	NOUN
ejpam-4521	253	26	which	which	PRON
ejpam-4521	253	27	is	be	AUX
ejpam-4521	253	28	not	not	PART
ejpam-4521	253	29	found	find	VERB
ejpam-4521	253	30	in	in	ADP
ejpam-4521	253	31	any	any	DET
ejpam-4521	253	32	coi	coi	NOUN
ejpam-4521	253	33	-	-	PUNCT
ejpam-4521	253	34	set	set	NOUN
ejpam-4521	253	35	of	of	ADP
ejpam-4521	253	36	g.	g.	PROPN
ejpam-4521	253	37	theorem	theorem	VERB
ejpam-4521	253	38	4	4	X
ejpam-4521	253	39	.	.	PUNCT
ejpam-4521	254	1	let	let	VERB
ejpam-4521	254	2	g	g	PRON
ejpam-4521	254	3	be	be	AUX
ejpam-4521	254	4	a	a	DET
ejpam-4521	254	5	connected	connected	ADJ
ejpam-4521	254	6	graph	graph	NOUN
ejpam-4521	254	7	.	.	PUNCT
ejpam-4521	255	1	then	then	ADV
ejpam-4521	255	2	fcoi(g	fcoi(g	ADV
ejpam-4521	255	3	)	)	PUNCT
ejpam-4521	256	1	=	=	PUNCT
ejpam-4521	256	2	coi(g	coi(g	PROPN
ejpam-4521	256	3	)	)	PUNCT
ejpam-4521	256	4	if	if	SCONJ
ejpam-4521	256	5	and	and	CCONJ
ejpam-4521	256	6	only	only	ADV
ejpam-4521	256	7	if	if	SCONJ
ejpam-4521	256	8	for	for	ADP
ejpam-4521	256	9	all	all	DET
ejpam-4521	256	10	coi	coi	NOUN
ejpam-4521	256	11	-	-	PUNCT
ejpam-4521	256	12	set	set	VERB
ejpam-4521	256	13	d	d	NOUN
ejpam-4521	256	14	of	of	ADP
ejpam-4521	256	15	g	g	PROPN
ejpam-4521	256	16	and	and	CCONJ
ejpam-4521	256	17	for	for	ADP
ejpam-4521	256	18	each	each	DET
ejpam-4521	256	19	z	z	NOUN
ejpam-4521	256	20	∈	∈	PROPN
ejpam-4521	256	21	d	d	NOUN
ejpam-4521	256	22	,	,	PUNCT
ejpam-4521	256	23	there	there	PRON
ejpam-4521	256	24	exists	exist	VERB
ejpam-4521	256	25	uz	uz	PROPN
ejpam-4521	256	26	∈	∈	PROPN
ejpam-4521	256	27	v	v	ADP
ejpam-4521	256	28	(	(	PUNCT
ejpam-4521	256	29	g	g	NOUN
ejpam-4521	256	30	)	)	PUNCT
ejpam-4521	256	31	\d	\d	NOUN
ejpam-4521	256	32	such	such	ADJ
ejpam-4521	256	33	that	that	SCONJ
ejpam-4521	256	34	[	[	PUNCT
ejpam-4521	256	35	d	d	X
ejpam-4521	256	36	\	\	X
ejpam-4521	256	37	{	{	PUNCT
ejpam-4521	256	38	z	z	NOUN
ejpam-4521	256	39	}	}	PUNCT
ejpam-4521	256	40	]	]	PUNCT
ejpam-4521	256	41	∪	∪	X
ejpam-4521	256	42	{	{	PUNCT
ejpam-4521	256	43	uz	uz	PROPN
ejpam-4521	256	44	}	}	PUNCT
ejpam-4521	256	45	is	be	AUX
ejpam-4521	256	46	a	a	DET
ejpam-4521	256	47	coi	coi	NOUN
ejpam-4521	256	48	-	-	PUNCT
ejpam-4521	256	49	set	set	NOUN
ejpam-4521	256	50	of	of	ADP
ejpam-4521	256	51	g.	g.	PROPN
ejpam-4521	256	52	proof	proof	PROPN
ejpam-4521	256	53	:	:	PUNCT
ejpam-4521	256	54	suppose	suppose	VERB
ejpam-4521	256	55	that	that	SCONJ
ejpam-4521	256	56	fcoi(g	fcoi(g	NOUN
ejpam-4521	256	57	)	)	PUNCT
ejpam-4521	256	58	=	=	PUNCT
ejpam-4521	256	59	coi(g	coi(g	PROPN
ejpam-4521	256	60	)	)	PUNCT
ejpam-4521	256	61	.	.	PUNCT
ejpam-4521	257	1	let	let	VERB
ejpam-4521	257	2	d	d	PRON
ejpam-4521	257	3	be	be	AUX
ejpam-4521	257	4	a	a	DET
ejpam-4521	257	5	coi	coi	NOUN
ejpam-4521	257	6	-	-	PUNCT
ejpam-4521	257	7	set	set	NOUN
ejpam-4521	257	8	of	of	ADP
ejpam-4521	257	9	g	g	NOUN
ejpam-4521	257	10	such	such	ADJ
ejpam-4521	257	11	that	that	DET
ejpam-4521	257	12	fcoi(g	fcoi(g	NOUN
ejpam-4521	257	13	)	)	PUNCT
ejpam-4521	258	1	=	=	SYM
ejpam-4521	258	2	|d|	|d|	PROPN
ejpam-4521	258	3	=	=	SYM
ejpam-4521	258	4	coi(g	coi(g	PROPN
ejpam-4521	258	5	)	)	PUNCT
ejpam-4521	258	6	,	,	PUNCT
ejpam-4521	258	7	that	that	ADV
ejpam-4521	258	8	is	is	ADV
ejpam-4521	258	9	,	,	PUNCT
ejpam-4521	258	10	d	d	PRON
ejpam-4521	258	11	is	be	AUX
ejpam-4521	258	12	the	the	DET
ejpam-4521	258	13	only	only	ADJ
ejpam-4521	258	14	forcing	forcing	NOUN
ejpam-4521	258	15	subset	subset	NOUN
ejpam-4521	258	16	for	for	ADP
ejpam-4521	258	17	itself	itself	PRON
ejpam-4521	258	18	.	.	PUNCT
ejpam-4521	259	1	let	let	VERB
ejpam-4521	259	2	z	z	PROPN
ejpam-4521	259	3	∈	∈	PROPN
ejpam-4521	259	4	d.	d.	PROPN
ejpam-4521	259	5	y.d	y.d	PROPN
ejpam-4521	259	6	.	.	PROPN
ejpam-4521	259	7	calanza	calanza	PROPN
ejpam-4521	259	8	,	,	PUNCT
ejpam-4521	259	9	h.	h.	PROPN
ejpam-4521	259	10	rara	rara	PROPN
ejpam-4521	259	11	/	/	SYM
ejpam-4521	259	12	eur	eur	PROPN
ejpam-4521	259	13	.	.	PUNCT
ejpam-4521	260	1	j.	j.	PROPN
ejpam-4521	260	2	pure	pure	PROPN
ejpam-4521	260	3	appl	appl	PROPN
ejpam-4521	260	4	.	.	PROPN
ejpam-4521	260	5	math	math	PROPN
ejpam-4521	260	6	,	,	PUNCT
ejpam-4521	260	7	15	15	NUM
ejpam-4521	260	8	(	(	PUNCT
ejpam-4521	260	9	4	4	NUM
ejpam-4521	260	10	)	)	PUNCT
ejpam-4521	260	11	(	(	PUNCT
ejpam-4521	260	12	2022	2022	NUM
ejpam-4521	260	13	)	)	PUNCT
ejpam-4521	260	14	,	,	PUNCT
ejpam-4521	260	15	1597	1597	NUM
ejpam-4521	260	16	-	-	SYM
ejpam-4521	260	17	1612	1612	NUM
ejpam-4521	260	18	1605	1605	NUM
ejpam-4521	260	19	since	since	SCONJ
ejpam-4521	260	20	d	d	PROPN
ejpam-4521	260	21	\	\	PROPN
ejpam-4521	260	22	{	{	PUNCT
ejpam-4521	260	23	z	z	NOUN
ejpam-4521	260	24	}	}	PUNCT
ejpam-4521	260	25	is	be	AUX
ejpam-4521	260	26	not	not	PART
ejpam-4521	260	27	a	a	DET
ejpam-4521	260	28	forcing	forcing	NOUN
ejpam-4521	260	29	subset	subset	NOUN
ejpam-4521	260	30	for	for	ADP
ejpam-4521	260	31	d	d	PROPN
ejpam-4521	260	32	,	,	PUNCT
ejpam-4521	260	33	there	there	PRON
ejpam-4521	260	34	exists	exist	VERB
ejpam-4521	260	35	a	a	DET
ejpam-4521	260	36	uz	uz	PROPN
ejpam-4521	260	37	∈	∈	PROPN
ejpam-4521	260	38	v	v	NOUN
ejpam-4521	260	39	(	(	PUNCT
ejpam-4521	260	40	g	g	NOUN
ejpam-4521	260	41	)	)	PUNCT
ejpam-4521	260	42	\	\	PUNCT
ejpam-4521	261	1	d	d	ADP
ejpam-4521	261	2	such	such	ADJ
ejpam-4521	261	3	that	that	SCONJ
ejpam-4521	261	4	[	[	PUNCT
ejpam-4521	261	5	d	d	NOUN
ejpam-4521	261	6	\	\	X
ejpam-4521	261	7	{	{	PUNCT
ejpam-4521	261	8	z	z	NOUN
ejpam-4521	261	9	}	}	PUNCT
ejpam-4521	261	10	]	]	PUNCT
ejpam-4521	261	11	∪	∪	X
ejpam-4521	261	12	{	{	PUNCT
ejpam-4521	261	13	uz	uz	PROPN
ejpam-4521	261	14	}	}	PUNCT
ejpam-4521	261	15	is	be	AUX
ejpam-4521	261	16	a	a	DET
ejpam-4521	261	17	coi	coi	NOUN
ejpam-4521	261	18	-	-	PUNCT
ejpam-4521	261	19	set	set	NOUN
ejpam-4521	261	20	of	of	ADP
ejpam-4521	261	21	g.	g.	NOUN
ejpam-4521	261	22	conversely	conversely	ADV
ejpam-4521	261	23	,	,	PUNCT
ejpam-4521	261	24	suppose	suppose	VERB
ejpam-4521	261	25	that	that	SCONJ
ejpam-4521	261	26	every	every	DET
ejpam-4521	261	27	coi	coi	NOUN
ejpam-4521	261	28	-	-	PUNCT
ejpam-4521	261	29	set	set	VERB
ejpam-4521	261	30	d	d	NOUN
ejpam-4521	261	31	′	′	NUM
ejpam-4521	261	32	of	of	ADP
ejpam-4521	261	33	g	g	PROPN
ejpam-4521	261	34	satisfies	satisfy	VERB
ejpam-4521	261	35	the	the	DET
ejpam-4521	261	36	given	give	VERB
ejpam-4521	261	37	condition	condition	NOUN
ejpam-4521	261	38	.	.	PUNCT
ejpam-4521	262	1	let	let	VERB
ejpam-4521	262	2	d	d	PRON
ejpam-4521	262	3	be	be	AUX
ejpam-4521	262	4	a	a	DET
ejpam-4521	262	5	coi	coi	NOUN
ejpam-4521	262	6	-	-	PUNCT
ejpam-4521	262	7	set	set	NOUN
ejpam-4521	262	8	of	of	ADP
ejpam-4521	262	9	g	g	NOUN
ejpam-4521	262	10	such	such	ADJ
ejpam-4521	262	11	that	that	DET
ejpam-4521	262	12	fcoi(g	fcoi(g	NOUN
ejpam-4521	262	13	)	)	PUNCT
ejpam-4521	263	1	=	=	SYM
ejpam-4521	263	2	fcoi(d	fcoi(d	PROPN
ejpam-4521	263	3	)	)	PUNCT
ejpam-4521	263	4	.	.	PUNCT
ejpam-4521	264	1	suppose	suppose	VERB
ejpam-4521	264	2	further	far	ADV
ejpam-4521	264	3	that	that	SCONJ
ejpam-4521	264	4	d	d	PROPN
ejpam-4521	264	5	has	have	VERB
ejpam-4521	264	6	a	a	DET
ejpam-4521	264	7	forcing	forcing	NOUN
ejpam-4521	264	8	subset	subset	NOUN
ejpam-4521	264	9	a	a	PRON
ejpam-4521	264	10	with	with	ADP
ejpam-4521	264	11	|a|	|a|	NOUN
ejpam-4521	264	12	<	<	X
ejpam-4521	264	13	|d|	|d|	PROPN
ejpam-4521	264	14	,	,	PUNCT
ejpam-4521	264	15	that	that	ADV
ejpam-4521	264	16	is	be	AUX
ejpam-4521	264	17	,	,	PUNCT
ejpam-4521	264	18	d	d	X
ejpam-4521	264	19	=	=	PUNCT
ejpam-4521	264	20	a	a	DET
ejpam-4521	264	21	∪	∪	NOUN
ejpam-4521	264	22	c	c	NOUN
ejpam-4521	264	23	where	where	SCONJ
ejpam-4521	264	24	c	c	NOUN
ejpam-4521	264	25	=	=	PRON
ejpam-4521	264	26	{	{	PUNCT
ejpam-4521	264	27	v	v	NUM
ejpam-4521	264	28	∈	∈	NOUN
ejpam-4521	264	29	d	d	NOUN
ejpam-4521	264	30	:	:	PUNCT
ejpam-4521	264	31	v	v	X
ejpam-4521	264	32	/∈	/∈	PUNCT
ejpam-4521	264	33	a	a	PRON
ejpam-4521	264	34	}	}	PUNCT
ejpam-4521	264	35	.	.	PUNCT
ejpam-4521	265	1	pick	pick	VERB
ejpam-4521	265	2	v	v	NUM
ejpam-4521	265	3	∈	∈	PROPN
ejpam-4521	265	4	c.	c.	NOUN
ejpam-4521	265	5	by	by	ADP
ejpam-4521	265	6	assumption	assumption	NOUN
ejpam-4521	265	7	,	,	PUNCT
ejpam-4521	265	8	there	there	PRON
ejpam-4521	265	9	exists	exist	VERB
ejpam-4521	265	10	uv	uv	PROPN
ejpam-4521	265	11	∈	∈	PROPN
ejpam-4521	265	12	v	v	ADP
ejpam-4521	265	13	(	(	PUNCT
ejpam-4521	265	14	g	g	NOUN
ejpam-4521	265	15	)	)	PUNCT
ejpam-4521	265	16	\d	\d	NOUN
ejpam-4521	265	17	such	such	ADJ
ejpam-4521	266	1	that	that	SCONJ
ejpam-4521	266	2	[	[	PUNCT
ejpam-4521	266	3	d	d	X
ejpam-4521	266	4	\	\	X
ejpam-4521	266	5	{	{	PUNCT
ejpam-4521	266	6	v	v	NOUN
ejpam-4521	266	7	}	}	PUNCT
ejpam-4521	266	8	]	]	PUNCT
ejpam-4521	266	9	∪	∪	X
ejpam-4521	266	10	{	{	PUNCT
ejpam-4521	266	11	uv	uv	NOUN
ejpam-4521	266	12	}	}	PUNCT
ejpam-4521	266	13	=	=	SYM
ejpam-4521	267	1	r	r	NOUN
ejpam-4521	267	2	is	be	AUX
ejpam-4521	267	3	a	a	DET
ejpam-4521	267	4	coi	coi	NOUN
ejpam-4521	267	5	-	-	PUNCT
ejpam-4521	267	6	set	set	NOUN
ejpam-4521	267	7	of	of	ADP
ejpam-4521	267	8	g.	g.	PROPN
ejpam-4521	267	9	thus	thus	ADV
ejpam-4521	267	10	,	,	PUNCT
ejpam-4521	267	11	r	r	NOUN
ejpam-4521	267	12	=	=	PUNCT
ejpam-4521	267	13	a	a	DET
ejpam-4521	267	14	∪	∪	ADJ
ejpam-4521	267	15	t	t	PROPN
ejpam-4521	267	16	,	,	PUNCT
ejpam-4521	267	17	where	where	SCONJ
ejpam-4521	267	18	t	t	NOUN
ejpam-4521	267	19	=	=	PUNCT
ejpam-4521	267	20	[	[	PUNCT
ejpam-4521	267	21	c	c	X
ejpam-4521	267	22	\	\	PROPN
ejpam-4521	267	23	{	{	PUNCT
ejpam-4521	267	24	v	v	NOUN
ejpam-4521	267	25	}	}	PUNCT
ejpam-4521	267	26	]	]	PUNCT
ejpam-4521	267	27	∪	∪	X
ejpam-4521	267	28	{	{	PUNCT
ejpam-4521	267	29	uv	uv	NOUN
ejpam-4521	267	30	}	}	PUNCT
ejpam-4521	267	31	,	,	PUNCT
ejpam-4521	267	32	is	be	AUX
ejpam-4521	267	33	a	a	DET
ejpam-4521	267	34	coi	coi	NOUN
ejpam-4521	267	35	-	-	PUNCT
ejpam-4521	267	36	set	set	NOUN
ejpam-4521	267	37	containing	contain	VERB
ejpam-4521	267	38	a	a	DET
ejpam-4521	267	39	,	,	PUNCT
ejpam-4521	267	40	a	a	DET
ejpam-4521	267	41	contradiction	contradiction	NOUN
ejpam-4521	267	42	.	.	PUNCT
ejpam-4521	268	1	hence	hence	ADV
ejpam-4521	268	2	,	,	PUNCT
ejpam-4521	268	3	d	d	PROPN
ejpam-4521	268	4	is	be	AUX
ejpam-4521	268	5	the	the	DET
ejpam-4521	268	6	only	only	ADJ
ejpam-4521	268	7	forcing	forcing	NOUN
ejpam-4521	268	8	subset	subset	NOUN
ejpam-4521	268	9	for	for	ADP
ejpam-4521	268	10	d.	d.	PROPN
ejpam-4521	268	11	therefore	therefore	ADV
ejpam-4521	268	12	,	,	PUNCT
ejpam-4521	268	13	fcoi(g	fcoi(g	ADV
ejpam-4521	268	14	)	)	PUNCT
ejpam-4521	268	15	=	=	PUNCT
ejpam-4521	268	16	coi(g	coi(g	PROPN
ejpam-4521	268	17	)	)	PUNCT
ejpam-4521	268	18	.	.	PUNCT
ejpam-4521	269	1	example	example	NOUN
ejpam-4521	270	1	2	2	NUM
ejpam-4521	270	2	.	.	PUNCT
ejpam-4521	270	3	the	the	DET
ejpam-4521	270	4	formulas	formula	NOUN
ejpam-4521	270	5	below	below	ADP
ejpam-4521	270	6	give	give	VERB
ejpam-4521	270	7	the	the	DET
ejpam-4521	270	8	co	co	NOUN
ejpam-4521	270	9	-	-	ADJ
ejpam-4521	270	10	independent	independent	ADJ
ejpam-4521	270	11	number	number	NOUN
ejpam-4521	270	12	of	of	ADP
ejpam-4521	270	13	the	the	DET
ejpam-4521	270	14	complete	complete	ADJ
ejpam-4521	270	15	graph	graph	NOUN
ejpam-4521	270	16	kn	kn	PROPN
ejpam-4521	270	17	,	,	PUNCT
ejpam-4521	270	18	path	path	NOUN
ejpam-4521	270	19	pn	pn	PROPN
ejpam-4521	270	20	and	and	CCONJ
ejpam-4521	270	21	cycle	cycle	NOUN
ejpam-4521	270	22	cn	cn	PROPN
ejpam-4521	270	23	.	.	PROPN
ejpam-4521	270	24	coi(kn	coi(kn	NUM
ejpam-4521	270	25	)	)	PUNCT
ejpam-4521	271	1	=	=	PRON
ejpam-4521	271	2	{	{	PUNCT
ejpam-4521	271	3	1	1	NUM
ejpam-4521	271	4	,	,	PUNCT
ejpam-4521	271	5	if	if	SCONJ
ejpam-4521	271	6	n	n	NOUN
ejpam-4521	271	7	=	=	SYM
ejpam-4521	271	8	1	1	NUM
ejpam-4521	271	9	,	,	PUNCT
ejpam-4521	271	10	n−	n−	NOUN
ejpam-4521	271	11	1	1	NUM
ejpam-4521	271	12	,	,	PUNCT
ejpam-4521	271	13	if	if	SCONJ
ejpam-4521	271	14	n	n	PRON
ejpam-4521	271	15	≥	≥	NOUN
ejpam-4521	271	16	2	2	NUM
ejpam-4521	271	17	.	.	PUNCT
ejpam-4521	271	18	coi(pn	coi(pn	NOUN
ejpam-4521	271	19	)	)	PUNCT
ejpam-4521	271	20	=	=	PUNCT
ejpam-4521	271	21			NOUN
ejpam-4521	271	22	1	1	NUM
ejpam-4521	271	23	,	,	PUNCT
ejpam-4521	271	24	if	if	SCONJ
ejpam-4521	271	25	n	n	NOUN
ejpam-4521	271	26	=	=	SYM
ejpam-4521	271	27	1	1	NUM
ejpam-4521	271	28	,	,	PUNCT
ejpam-4521	271	29	n	n	PRON
ejpam-4521	271	30	2	2	NUM
ejpam-4521	271	31	,	,	PUNCT
ejpam-4521	271	32	if	if	SCONJ
ejpam-4521	271	33	n	n	PRON
ejpam-4521	271	34	is	be	AUX
ejpam-4521	271	35	even	even	ADV
ejpam-4521	271	36	,	,	PUNCT
ejpam-4521	271	37	n−	n−	NOUN
ejpam-4521	271	38	1	1	NUM
ejpam-4521	271	39	2	2	NUM
ejpam-4521	271	40	,	,	PUNCT
ejpam-4521	271	41	if	if	SCONJ
ejpam-4521	271	42	n	n	PRON
ejpam-4521	271	43	is	be	AUX
ejpam-4521	271	44	odd	odd	ADJ
ejpam-4521	271	45	.	.	PUNCT
ejpam-4521	271	46	coi(cn	coi(cn	NUM
ejpam-4521	271	47	)	)	PUNCT
ejpam-4521	272	1	=	=	PUNCT
ejpam-4521	273	1			PROPN
ejpam-4521	273	2	n	n	PRON
ejpam-4521	273	3	2	2	NUM
ejpam-4521	273	4	,	,	PUNCT
ejpam-4521	273	5	if	if	SCONJ
ejpam-4521	273	6	n	n	PRON
ejpam-4521	273	7	≥	≥	NOUN
ejpam-4521	273	8	4	4	NUM
ejpam-4521	273	9	and	and	CCONJ
ejpam-4521	273	10	n	n	PRON
ejpam-4521	273	11	is	be	AUX
ejpam-4521	273	12	even	even	ADV
ejpam-4521	273	13	,	,	PUNCT
ejpam-4521	273	14	n+	n+	ADP
ejpam-4521	273	15	1	1	NUM
ejpam-4521	273	16	2	2	NUM
ejpam-4521	273	17	,	,	PUNCT
ejpam-4521	273	18	if	if	SCONJ
ejpam-4521	273	19	n	n	PRON
ejpam-4521	273	20	≥	≥	NOUN
ejpam-4521	273	21	3	3	NUM
ejpam-4521	273	22	and	and	CCONJ
ejpam-4521	273	23	n	n	PROPN
ejpam-4521	273	24	is	be	AUX
ejpam-4521	273	25	odd	odd	ADJ
ejpam-4521	273	26	.	.	PUNCT
ejpam-4521	274	1	proposition	proposition	NOUN
ejpam-4521	274	2	4	4	NUM
ejpam-4521	274	3	.	.	X
ejpam-4521	275	1	for	for	ADP
ejpam-4521	275	2	any	any	DET
ejpam-4521	275	3	complete	complete	ADJ
ejpam-4521	275	4	graph	graph	NOUN
ejpam-4521	275	5	kn	kn	PROPN
ejpam-4521	275	6	with	with	ADP
ejpam-4521	275	7	n	n	PRON
ejpam-4521	275	8	≥	≥	NUM
ejpam-4521	275	9	1	1	NUM
ejpam-4521	275	10	vertices	vertex	NOUN
ejpam-4521	275	11	,	,	PUNCT
ejpam-4521	275	12	fcoi(kn	fcoi(kn	NOUN
ejpam-4521	275	13	)	)	PUNCT
ejpam-4521	275	14	=	=	PUNCT
ejpam-4521	275	15	{	{	PUNCT
ejpam-4521	275	16	0	0	NUM
ejpam-4521	275	17	,	,	PUNCT
ejpam-4521	275	18	if	if	SCONJ
ejpam-4521	275	19	n	n	NOUN
ejpam-4521	275	20	=	=	SYM
ejpam-4521	275	21	1	1	NUM
ejpam-4521	275	22	,	,	PUNCT
ejpam-4521	275	23	n−	n−	NOUN
ejpam-4521	275	24	1	1	NUM
ejpam-4521	275	25	,	,	PUNCT
ejpam-4521	275	26	if	if	SCONJ
ejpam-4521	275	27	n	n	PRON
ejpam-4521	275	28	≥	≥	NOUN
ejpam-4521	275	29	2	2	NUM
ejpam-4521	275	30	.	.	PUNCT
ejpam-4521	275	31	proof	proof	NOUN
ejpam-4521	275	32	:	:	PUNCT
ejpam-4521	275	33	suppose	suppose	VERB
ejpam-4521	275	34	that	that	SCONJ
ejpam-4521	275	35	v	v	INTJ
ejpam-4521	275	36	(	(	PUNCT
ejpam-4521	275	37	kn	kn	PROPN
ejpam-4521	275	38	)	)	PUNCT
ejpam-4521	275	39	=	=	PRON
ejpam-4521	275	40	{	{	PUNCT
ejpam-4521	275	41	v1	v1	PROPN
ejpam-4521	275	42	,	,	PUNCT
ejpam-4521	275	43	v2	v2	PROPN
ejpam-4521	275	44	,	,	PUNCT
ejpam-4521	275	45	.	.	PUNCT
ejpam-4521	275	46	.	.	PUNCT
ejpam-4521	275	47	.	.	PUNCT
ejpam-4521	276	1	,	,	PUNCT
ejpam-4521	276	2	vn	vn	INTJ
ejpam-4521	276	3	}	}	PUNCT
ejpam-4521	276	4	.	.	PUNCT
ejpam-4521	277	1	it	it	PRON
ejpam-4521	277	2	can	can	AUX
ejpam-4521	277	3	be	be	AUX
ejpam-4521	277	4	seen	see	VERB
ejpam-4521	277	5	that	that	SCONJ
ejpam-4521	277	6	fcoi(k1	fcoi(k1	NOUN
ejpam-4521	277	7	)	)	PUNCT
ejpam-4521	277	8	=	=	SYM
ejpam-4521	278	1	0	0	X
ejpam-4521	278	2	.	.	PUNCT
ejpam-4521	279	1	if	if	SCONJ
ejpam-4521	279	2	n	n	NOUN
ejpam-4521	279	3	=	=	SYM
ejpam-4521	279	4	2	2	NUM
ejpam-4521	279	5	,	,	PUNCT
ejpam-4521	279	6	then	then	ADV
ejpam-4521	279	7	k2	k2	PROPN
ejpam-4521	279	8	has	have	VERB
ejpam-4521	279	9	only	only	ADV
ejpam-4521	279	10	two	two	NUM
ejpam-4521	279	11	coi	coi	NOUN
ejpam-4521	279	12	-	-	PUNCT
ejpam-4521	279	13	sets	set	NOUN
ejpam-4521	279	14	r1	r1	NOUN
ejpam-4521	279	15	=	=	SYM
ejpam-4521	279	16	{	{	PUNCT
ejpam-4521	279	17	v1	v1	NOUN
ejpam-4521	279	18	}	}	PUNCT
ejpam-4521	279	19	and	and	CCONJ
ejpam-4521	279	20	r2	r2	PROPN
ejpam-4521	279	21	=	=	PUNCT
ejpam-4521	279	22	{	{	PUNCT
ejpam-4521	279	23	v2	v2	NOUN
ejpam-4521	279	24	}	}	PUNCT
ejpam-4521	279	25	with	with	ADP
ejpam-4521	279	26	v1	v1	PROPN
ejpam-4521	279	27	∈	∈	PROPN
ejpam-4521	279	28	r1	r1	NOUN
ejpam-4521	279	29	and	and	CCONJ
ejpam-4521	279	30	v1	v1	NOUN
ejpam-4521	279	31	/∈	/∈	PUNCT
ejpam-4521	279	32	r2	r2	PROPN
ejpam-4521	279	33	.	.	PUNCT
ejpam-4521	280	1	by	by	ADP
ejpam-4521	280	2	remark	remark	NOUN
ejpam-4521	280	3	4(ii	4(ii	NUM
ejpam-4521	280	4	)	)	PUNCT
ejpam-4521	280	5	,	,	PUNCT
ejpam-4521	280	6	fcoi(k2	fcoi(k2	VERB
ejpam-4521	280	7	)	)	PUNCT
ejpam-4521	280	8	=	=	SYM
ejpam-4521	281	1	n−	n−	NOUN
ejpam-4521	281	2	1	1	NUM
ejpam-4521	281	3	=	=	SYM
ejpam-4521	281	4	1	1	X
ejpam-4521	281	5	.	.	PUNCT
ejpam-4521	281	6	suppose	suppose	VERB
ejpam-4521	281	7	that	that	SCONJ
ejpam-4521	281	8	n	n	PROPN
ejpam-4521	281	9	>	>	X
ejpam-4521	281	10	2	2	X
ejpam-4521	281	11	.	.	PUNCT
ejpam-4521	281	12	then	then	ADV
ejpam-4521	281	13	the	the	DET
ejpam-4521	281	14	coi	coi	NOUN
ejpam-4521	281	15	-	-	PUNCT
ejpam-4521	281	16	sets	set	NOUN
ejpam-4521	281	17	of	of	ADP
ejpam-4521	281	18	kn	kn	PROPN
ejpam-4521	281	19	are	be	AUX
ejpam-4521	281	20	b1	b1	NOUN
ejpam-4521	281	21	=	=	SYM
ejpam-4521	281	22	{	{	PUNCT
ejpam-4521	281	23	v1	v1	PROPN
ejpam-4521	281	24	,	,	PUNCT
ejpam-4521	281	25	v2	v2	PROPN
ejpam-4521	281	26	,	,	PUNCT
ejpam-4521	281	27	.	.	PUNCT
ejpam-4521	281	28	.	.	PUNCT
ejpam-4521	282	1	.	.	PUNCT
ejpam-4521	283	1	,	,	PUNCT
ejpam-4521	283	2	vn−1	vn−1	ADJ
ejpam-4521	283	3	}	}	PUNCT
ejpam-4521	283	4	,	,	PUNCT
ejpam-4521	283	5	b2	b2	NOUN
ejpam-4521	283	6	=	=	SYM
ejpam-4521	283	7	{	{	PUNCT
ejpam-4521	283	8	v2	v2	PROPN
ejpam-4521	283	9	,	,	PUNCT
ejpam-4521	283	10	v3	v3	PROPN
ejpam-4521	283	11	,	,	PUNCT
ejpam-4521	283	12	.	.	PUNCT
ejpam-4521	283	13	.	.	PUNCT
ejpam-4521	283	14	.	.	PUNCT
ejpam-4521	284	1	,	,	PUNCT
ejpam-4521	284	2	vn	vn	PROPN
ejpam-4521	284	3	}	}	PUNCT
ejpam-4521	284	4	,	,	PUNCT
ejpam-4521	284	5	b3	b3	PROPN
ejpam-4521	284	6	=	=	SYM
ejpam-4521	284	7	{	{	PUNCT
ejpam-4521	284	8	v3	v3	PROPN
ejpam-4521	284	9	,	,	PUNCT
ejpam-4521	284	10	v4	v4	PROPN
ejpam-4521	284	11	,	,	PUNCT
ejpam-4521	284	12	.	.	PUNCT
ejpam-4521	284	13	.	.	PUNCT
ejpam-4521	285	1	.	.	PUNCT
ejpam-4521	286	1	,	,	PUNCT
ejpam-4521	286	2	vn	vn	X
ejpam-4521	286	3	,	,	PUNCT
ejpam-4521	286	4	v1	v1	PROPN
ejpam-4521	286	5	}	}	PUNCT
ejpam-4521	286	6	,	,	PUNCT
ejpam-4521	286	7	.	.	PUNCT
ejpam-4521	286	8	.	.	PUNCT
ejpam-4521	286	9	.	.	PUNCT
ejpam-4521	287	1	,	,	PUNCT
ejpam-4521	287	2	bn	bn	NOUN
ejpam-4521	287	3	=	=	SYM
ejpam-4521	287	4	{	{	PUNCT
ejpam-4521	287	5	vn	vn	PROPN
ejpam-4521	287	6	,	,	PUNCT
ejpam-4521	287	7	v1	v1	NOUN
ejpam-4521	287	8	,	,	PUNCT
ejpam-4521	287	9	v2	v2	NOUN
ejpam-4521	287	10	,	,	PUNCT
ejpam-4521	287	11	.	.	PUNCT
ejpam-4521	287	12	.	.	PUNCT
ejpam-4521	288	1	.	.	PUNCT
ejpam-4521	289	1	,	,	PUNCT
ejpam-4521	289	2	vn−2	vn−2	PROPN
ejpam-4521	289	3	}	}	PUNCT
ejpam-4521	289	4	.	.	PUNCT
ejpam-4521	290	1	clearly	clearly	ADV
ejpam-4521	290	2	,	,	PUNCT
ejpam-4521	290	3	for	for	ADP
ejpam-4521	290	4	each	each	DET
ejpam-4521	290	5	vi	vi	PROPN
ejpam-4521	290	6	∈	∈	NOUN
ejpam-4521	290	7	bj	bj	VERB
ejpam-4521	290	8	where	where	SCONJ
ejpam-4521	290	9	i	i	PRON
ejpam-4521	290	10	,	,	PUNCT
ejpam-4521	290	11	j	j	PROPN
ejpam-4521	290	12	∈	∈	PROPN
ejpam-4521	290	13	{	{	PUNCT
ejpam-4521	290	14	1	1	NUM
ejpam-4521	290	15	,	,	PUNCT
ejpam-4521	290	16	2	2	NUM
ejpam-4521	290	17	,	,	PUNCT
ejpam-4521	290	18	3	3	NUM
ejpam-4521	290	19	,	,	PUNCT
ejpam-4521	290	20	.	.	PUNCT
ejpam-4521	290	21	.	.	PUNCT
ejpam-4521	290	22	.	.	PUNCT
ejpam-4521	290	23	,	,	PUNCT
ejpam-4521	290	24	n	n	CCONJ
ejpam-4521	290	25	}	}	PUNCT
ejpam-4521	290	26	,	,	PUNCT
ejpam-4521	290	27	there	there	PRON
ejpam-4521	290	28	exists	exist	VERB
ejpam-4521	290	29	vk	vk	ADP
ejpam-4521	290	30	∈	∈	PROPN
ejpam-4521	290	31	v	v	PROPN
ejpam-4521	290	32	(	(	PUNCT
ejpam-4521	290	33	kn	kn	PROPN
ejpam-4521	290	34	)	)	PUNCT
ejpam-4521	290	35	\	\	PUNCT
ejpam-4521	290	36	bj	bj	ADP
ejpam-4521	290	37	such	such	ADJ
ejpam-4521	290	38	that	that	SCONJ
ejpam-4521	290	39	[	[	PUNCT
ejpam-4521	290	40	bj	bj	ADP
ejpam-4521	290	41	\	\	NOUN
ejpam-4521	290	42	{	{	PUNCT
ejpam-4521	290	43	vi	vi	NOUN
ejpam-4521	290	44	}	}	PUNCT
ejpam-4521	290	45	]	]	PUNCT
ejpam-4521	290	46	∪	∪	X
ejpam-4521	290	47	{	{	PUNCT
ejpam-4521	290	48	vk	vk	INTJ
ejpam-4521	290	49	}	}	PUNCT
ejpam-4521	290	50	is	be	AUX
ejpam-4521	290	51	a	a	DET
ejpam-4521	290	52	coi	coi	NOUN
ejpam-4521	290	53	-	-	PUNCT
ejpam-4521	290	54	set	set	NOUN
ejpam-4521	290	55	of	of	ADP
ejpam-4521	290	56	g.	g.	PROPN
ejpam-4521	290	57	hence	hence	ADV
ejpam-4521	290	58	,	,	PUNCT
ejpam-4521	290	59	by	by	ADP
ejpam-4521	290	60	theorem	theorem	NOUN
ejpam-4521	290	61	4	4	NUM
ejpam-4521	290	62	,	,	PUNCT
ejpam-4521	290	63	fcoi(kn	fcoi(kn	NOUN
ejpam-4521	290	64	)	)	PUNCT
ejpam-4521	290	65	=	=	PUNCT
ejpam-4521	291	1	n−	n−	NOUN
ejpam-4521	291	2	1	1	NUM
ejpam-4521	291	3	.	.	PUNCT
ejpam-4521	291	4	proposition	proposition	NOUN
ejpam-4521	291	5	5	5	NUM
ejpam-4521	291	6	.	.	PUNCT
ejpam-4521	292	1	for	for	ADP
ejpam-4521	292	2	any	any	DET
ejpam-4521	292	3	path	path	NOUN
ejpam-4521	292	4	pn	pn	NOUN
ejpam-4521	292	5	with	with	ADP
ejpam-4521	292	6	n	n	PRON
ejpam-4521	292	7	≥	≥	NUM
ejpam-4521	292	8	1	1	NUM
ejpam-4521	292	9	vertices	vertex	NOUN
ejpam-4521	292	10	,	,	PUNCT
ejpam-4521	292	11	fcoi(pn	fcoi(pn	NOUN
ejpam-4521	292	12	)	)	PUNCT
ejpam-4521	292	13	=	=	SYM
ejpam-4521	292	14	{	{	PUNCT
ejpam-4521	292	15	0	0	NUM
ejpam-4521	292	16	,	,	PUNCT
ejpam-4521	292	17	if	if	SCONJ
ejpam-4521	292	18	n	n	NOUN
ejpam-4521	292	19	=	=	SYM
ejpam-4521	292	20	1	1	NUM
ejpam-4521	292	21	,	,	PUNCT
ejpam-4521	292	22	3	3	NUM
ejpam-4521	292	23	and	and	CCONJ
ejpam-4521	292	24	n	n	PRON
ejpam-4521	292	25	≥	≥	NOUN
ejpam-4521	292	26	5	5	NUM
ejpam-4521	292	27	is	be	AUX
ejpam-4521	292	28	odd	odd	ADJ
ejpam-4521	292	29	,	,	PUNCT
ejpam-4521	292	30	1	1	NUM
ejpam-4521	292	31	,	,	PUNCT
ejpam-4521	292	32	if	if	SCONJ
ejpam-4521	292	33	n	n	NOUN
ejpam-4521	292	34	=	=	SYM
ejpam-4521	292	35	2	2	NUM
ejpam-4521	292	36	,	,	PUNCT
ejpam-4521	292	37	4	4	NUM
ejpam-4521	292	38	and	and	CCONJ
ejpam-4521	292	39	n	n	PRON
ejpam-4521	292	40	≥	≥	NUM
ejpam-4521	292	41	6	6	NUM
ejpam-4521	292	42	is	be	AUX
ejpam-4521	292	43	even	even	ADV
ejpam-4521	292	44	.	.	PUNCT
ejpam-4521	293	1	y.d	y.d	PROPN
ejpam-4521	293	2	.	.	PROPN
ejpam-4521	293	3	calanza	calanza	PROPN
ejpam-4521	293	4	,	,	PUNCT
ejpam-4521	293	5	h.	h.	PROPN
ejpam-4521	293	6	rara	rara	PROPN
ejpam-4521	293	7	/	/	SYM
ejpam-4521	293	8	eur	eur	PROPN
ejpam-4521	293	9	.	.	PUNCT
ejpam-4521	294	1	j.	j.	PROPN
ejpam-4521	294	2	pure	pure	PROPN
ejpam-4521	294	3	appl	appl	PROPN
ejpam-4521	294	4	.	.	PROPN
ejpam-4521	294	5	math	math	PROPN
ejpam-4521	294	6	,	,	PUNCT
ejpam-4521	294	7	15	15	NUM
ejpam-4521	294	8	(	(	PUNCT
ejpam-4521	294	9	4	4	NUM
ejpam-4521	294	10	)	)	PUNCT
ejpam-4521	294	11	(	(	PUNCT
ejpam-4521	294	12	2022	2022	NUM
ejpam-4521	294	13	)	)	PUNCT
ejpam-4521	294	14	,	,	PUNCT
ejpam-4521	294	15	1597	1597	NUM
ejpam-4521	294	16	-	-	SYM
ejpam-4521	294	17	1612	1612	NUM
ejpam-4521	294	18	1606	1606	NUM
ejpam-4521	294	19	proof	proof	NOUN
ejpam-4521	294	20	:	:	PUNCT
ejpam-4521	294	21	suppose	suppose	VERB
ejpam-4521	294	22	that	that	SCONJ
ejpam-4521	294	23	pn	pn	PROPN
ejpam-4521	294	24	=	=	PUNCT
ejpam-4521	295	1	[	[	X
ejpam-4521	295	2	v1	v1	NOUN
ejpam-4521	295	3	,	,	PUNCT
ejpam-4521	295	4	v2	v2	NOUN
ejpam-4521	295	5	,	,	PUNCT
ejpam-4521	295	6	.	.	PUNCT
ejpam-4521	295	7	.	.	PUNCT
ejpam-4521	295	8	.	.	PUNCT
ejpam-4521	296	1	,	,	PUNCT
ejpam-4521	296	2	vn	vn	X
ejpam-4521	296	3	]	]	PUNCT
ejpam-4521	296	4	.	.	PUNCT
ejpam-4521	297	1	it	it	PRON
ejpam-4521	297	2	can	can	AUX
ejpam-4521	297	3	be	be	AUX
ejpam-4521	297	4	verified	verify	VERB
ejpam-4521	297	5	that	that	SCONJ
ejpam-4521	297	6	fcoi(p1	fcoi(p1	NOUN
ejpam-4521	297	7	)	)	PUNCT
ejpam-4521	298	1	=	=	SYM
ejpam-4521	298	2	fcoi(p3	fcoi(p3	PROPN
ejpam-4521	298	3	)	)	PUNCT
ejpam-4521	298	4	=	=	SYM
ejpam-4521	298	5	0	0	NUM
ejpam-4521	298	6	and	and	CCONJ
ejpam-4521	298	7	fcoi(p2	fcoi(p2	ADJ
ejpam-4521	298	8	)	)	PUNCT
ejpam-4521	298	9	=	=	SYM
ejpam-4521	299	1	1	1	X
ejpam-4521	299	2	.	.	PUNCT
ejpam-4521	300	1	if	if	SCONJ
ejpam-4521	300	2	n	n	NOUN
ejpam-4521	300	3	=	=	SYM
ejpam-4521	300	4	4	4	NUM
ejpam-4521	300	5	,	,	PUNCT
ejpam-4521	300	6	then	then	ADV
ejpam-4521	300	7	p4	p4	NOUN
ejpam-4521	300	8	has	have	VERB
ejpam-4521	300	9	coi	coi	NOUN
ejpam-4521	300	10	-	-	PUNCT
ejpam-4521	300	11	sets	set	NOUN
ejpam-4521	300	12	b1	b1	NOUN
ejpam-4521	300	13	=	=	SYM
ejpam-4521	300	14	{	{	PUNCT
ejpam-4521	300	15	v1	v1	PROPN
ejpam-4521	300	16	,	,	PUNCT
ejpam-4521	300	17	v3	v3	PROPN
ejpam-4521	300	18	}	}	PUNCT
ejpam-4521	300	19	,	,	PUNCT
ejpam-4521	300	20	b2	b2	NOUN
ejpam-4521	300	21	=	=	SYM
ejpam-4521	300	22	{	{	PUNCT
ejpam-4521	300	23	v2	v2	PROPN
ejpam-4521	300	24	,	,	PUNCT
ejpam-4521	300	25	v4	v4	NOUN
ejpam-4521	300	26	}	}	PUNCT
ejpam-4521	300	27	and	and	CCONJ
ejpam-4521	300	28	b3	b3	PROPN
ejpam-4521	300	29	=	=	SYM
ejpam-4521	300	30	{	{	PUNCT
ejpam-4521	300	31	v2	v2	PROPN
ejpam-4521	300	32	,	,	PUNCT
ejpam-4521	300	33	v3	v3	PROPN
ejpam-4521	300	34	}	}	PUNCT
ejpam-4521	300	35	which	which	PRON
ejpam-4521	300	36	are	be	AUX
ejpam-4521	300	37	the	the	DET
ejpam-4521	300	38	only	only	ADJ
ejpam-4521	300	39	coi	coi	NOUN
ejpam-4521	300	40	-	-	PUNCT
ejpam-4521	300	41	sets	set	NOUN
ejpam-4521	300	42	of	of	ADP
ejpam-4521	300	43	p4	p4	NOUN
ejpam-4521	300	44	with	with	ADP
ejpam-4521	300	45	v4	v4	PROPN
ejpam-4521	300	46	∈	∈	PROPN
ejpam-4521	300	47	b2	b2	NOUN
ejpam-4521	300	48	and	and	CCONJ
ejpam-4521	300	49	v4	v4	NOUN
ejpam-4521	300	50	/∈	/∈	PUNCT
ejpam-4521	301	1	b1	b1	PROPN
ejpam-4521	301	2	,	,	PUNCT
ejpam-4521	301	3	b3	b3	PROPN
ejpam-4521	301	4	.	.	PUNCT
ejpam-4521	302	1	thus	thus	ADV
ejpam-4521	302	2	,	,	PUNCT
ejpam-4521	302	3	by	by	ADP
ejpam-4521	302	4	remark	remark	NOUN
ejpam-4521	302	5	4(ii	4(ii	NUM
ejpam-4521	302	6	)	)	PUNCT
ejpam-4521	302	7	,	,	PUNCT
ejpam-4521	302	8	fcoi(p4	fcoi(p4	NOUN
ejpam-4521	302	9	)	)	PUNCT
ejpam-4521	302	10	=	=	SYM
ejpam-4521	303	1	1	1	X
ejpam-4521	303	2	.	.	PUNCT
ejpam-4521	303	3	now	now	ADV
ejpam-4521	303	4	,	,	PUNCT
ejpam-4521	303	5	suppose	suppose	VERB
ejpam-4521	303	6	that	that	SCONJ
ejpam-4521	303	7	n	n	PROPN
ejpam-4521	303	8	≥	≥	NUM
ejpam-4521	303	9	5	5	NUM
ejpam-4521	303	10	and	and	CCONJ
ejpam-4521	303	11	n	n	PRON
ejpam-4521	303	12	is	be	AUX
ejpam-4521	303	13	odd	odd	ADJ
ejpam-4521	303	14	,	,	PUNCT
ejpam-4521	303	15	then	then	ADV
ejpam-4521	303	16	clearly	clearly	ADV
ejpam-4521	303	17	b	b	X
ejpam-4521	303	18	=	=	PRON
ejpam-4521	303	19	{	{	PUNCT
ejpam-4521	303	20	v2	v2	PROPN
ejpam-4521	303	21	,	,	PUNCT
ejpam-4521	303	22	v4	v4	PROPN
ejpam-4521	303	23	,	,	PUNCT
ejpam-4521	303	24	v6	v6	NOUN
ejpam-4521	303	25	,	,	PUNCT
ejpam-4521	303	26	.	.	PUNCT
ejpam-4521	303	27	.	.	PUNCT
ejpam-4521	304	1	.	.	PUNCT
ejpam-4521	305	1	,	,	PUNCT
ejpam-4521	305	2	vn−3	vn−3	PROPN
ejpam-4521	305	3	,	,	PUNCT
ejpam-4521	305	4	vn−1	vn−1	ADJ
ejpam-4521	305	5	}	}	PUNCT
ejpam-4521	305	6	is	be	AUX
ejpam-4521	305	7	the	the	DET
ejpam-4521	305	8	only	only	ADJ
ejpam-4521	305	9	coi	coi	NOUN
ejpam-4521	305	10	-	-	PUNCT
ejpam-4521	305	11	set	set	NOUN
ejpam-4521	305	12	of	of	ADP
ejpam-4521	305	13	pn	pn	PROPN
ejpam-4521	305	14	.	.	PUNCT
ejpam-4521	306	1	thus	thus	ADV
ejpam-4521	306	2	,	,	PUNCT
ejpam-4521	306	3	by	by	ADP
ejpam-4521	306	4	remark	remark	NOUN
ejpam-4521	306	5	4(i	4(i	NUM
ejpam-4521	306	6	)	)	PUNCT
ejpam-4521	306	7	,	,	PUNCT
ejpam-4521	306	8	fcoi(b	fcoi(b	NOUN
ejpam-4521	306	9	)	)	PUNCT
ejpam-4521	306	10	=	=	SYM
ejpam-4521	306	11	0	0	NUM
ejpam-4521	307	1	=	=	SYM
ejpam-4521	307	2	fcoi(pn	fcoi(pn	NOUN
ejpam-4521	307	3	)	)	PUNCT
ejpam-4521	307	4	.	.	PUNCT
ejpam-4521	308	1	next	next	ADV
ejpam-4521	308	2	,	,	PUNCT
ejpam-4521	308	3	suppose	suppose	VERB
ejpam-4521	308	4	that	that	SCONJ
ejpam-4521	308	5	n	n	PROPN
ejpam-4521	308	6	≥	≥	NUM
ejpam-4521	308	7	6	6	NUM
ejpam-4521	308	8	and	and	CCONJ
ejpam-4521	308	9	n	n	NUM
ejpam-4521	308	10	is	be	AUX
ejpam-4521	308	11	even	even	ADV
ejpam-4521	308	12	.	.	PUNCT
ejpam-4521	309	1	then	then	ADV
ejpam-4521	309	2	pn	pn	PROPN
ejpam-4521	309	3	has	have	VERB
ejpam-4521	309	4	coi	coi	NOUN
ejpam-4521	309	5	-	-	PUNCT
ejpam-4521	309	6	sets	set	NOUN
ejpam-4521	309	7	s1	s1	NOUN
ejpam-4521	309	8	=	=	SYM
ejpam-4521	309	9	{	{	PUNCT
ejpam-4521	309	10	v1	v1	PROPN
ejpam-4521	309	11	,	,	PUNCT
ejpam-4521	309	12	v3	v3	PROPN
ejpam-4521	309	13	,	,	PUNCT
ejpam-4521	309	14	v5	v5	PROPN
ejpam-4521	309	15	,	,	PUNCT
ejpam-4521	309	16	.	.	PUNCT
ejpam-4521	309	17	.	.	PUNCT
ejpam-4521	310	1	.	.	PUNCT
ejpam-4521	311	1	,	,	PUNCT
ejpam-4521	311	2	vn−1	vn−1	ADJ
ejpam-4521	311	3	}	}	PUNCT
ejpam-4521	311	4	and	and	CCONJ
ejpam-4521	311	5	s2	s2	VERB
ejpam-4521	311	6	=	=	SYM
ejpam-4521	311	7	{	{	PUNCT
ejpam-4521	311	8	v2	v2	PROPN
ejpam-4521	311	9	,	,	PUNCT
ejpam-4521	311	10	v4	v4	PROPN
ejpam-4521	311	11	,	,	PUNCT
ejpam-4521	311	12	v6	v6	NOUN
ejpam-4521	311	13	,	,	PUNCT
ejpam-4521	311	14	.	.	PUNCT
ejpam-4521	311	15	.	.	PUNCT
ejpam-4521	311	16	.	.	PUNCT
ejpam-4521	312	1	,	,	PUNCT
ejpam-4521	312	2	vn	vn	PROPN
ejpam-4521	312	3	}	}	PUNCT
ejpam-4521	312	4	which	which	PRON
ejpam-4521	312	5	are	be	AUX
ejpam-4521	312	6	the	the	DET
ejpam-4521	312	7	only	only	ADJ
ejpam-4521	312	8	coi	coi	NOUN
ejpam-4521	312	9	-	-	PUNCT
ejpam-4521	312	10	set	set	NOUN
ejpam-4521	312	11	of	of	ADP
ejpam-4521	312	12	pn	pn	PROPN
ejpam-4521	312	13	with	with	ADP
ejpam-4521	312	14	v3	v3	PROPN
ejpam-4521	312	15	∈	∈	PROPN
ejpam-4521	312	16	s1	s1	PROPN
ejpam-4521	312	17	and	and	CCONJ
ejpam-4521	312	18	v3	v3	PROPN
ejpam-4521	312	19	/∈	/∈	PROPN
ejpam-4521	313	1	s2	s2	PROPN
ejpam-4521	313	2	.	.	PUNCT
ejpam-4521	314	1	hence	hence	ADV
ejpam-4521	314	2	,	,	PUNCT
ejpam-4521	314	3	by	by	ADP
ejpam-4521	314	4	remark	remark	NOUN
ejpam-4521	314	5	4(ii	4(ii	PROPN
ejpam-4521	314	6	)	)	PUNCT
ejpam-4521	314	7	,	,	PUNCT
ejpam-4521	314	8	fcoi(pn	fcoi(pn	NOUN
ejpam-4521	314	9	)	)	PUNCT
ejpam-4521	314	10	=	=	SYM
ejpam-4521	314	11	1	1	X
ejpam-4521	314	12	.	.	X
ejpam-4521	314	13	proposition	proposition	NOUN
ejpam-4521	314	14	6	6	NUM
ejpam-4521	314	15	.	.	PUNCT
ejpam-4521	315	1	for	for	ADP
ejpam-4521	315	2	any	any	DET
ejpam-4521	315	3	cycle	cycle	NOUN
ejpam-4521	315	4	cn	cn	NOUN
ejpam-4521	315	5	with	with	ADP
ejpam-4521	315	6	n	n	NUM
ejpam-4521	315	7	≥	≥	NUM
ejpam-4521	315	8	3	3	NUM
ejpam-4521	315	9	vertices	vertex	NOUN
ejpam-4521	315	10	,	,	PUNCT
ejpam-4521	315	11	fcoi(cn	fcoi(cn	NOUN
ejpam-4521	315	12	)	)	PUNCT
ejpam-4521	315	13	=	=	SYM
ejpam-4521	315	14	{	{	PUNCT
ejpam-4521	315	15	1	1	NUM
ejpam-4521	315	16	,	,	PUNCT
ejpam-4521	315	17	if	if	SCONJ
ejpam-4521	315	18	n	n	PRON
ejpam-4521	315	19	is	be	AUX
ejpam-4521	315	20	even	even	ADV
ejpam-4521	315	21	,	,	PUNCT
ejpam-4521	315	22	2	2	NUM
ejpam-4521	315	23	,	,	PUNCT
ejpam-4521	315	24	if	if	SCONJ
ejpam-4521	315	25	n	n	PRON
ejpam-4521	315	26	is	be	AUX
ejpam-4521	315	27	odd	odd	ADJ
ejpam-4521	315	28	.	.	PUNCT
ejpam-4521	316	1	proof	proof	NOUN
ejpam-4521	316	2	:	:	PUNCT
ejpam-4521	316	3	suppose	suppose	VERB
ejpam-4521	316	4	that	that	SCONJ
ejpam-4521	316	5	cn	cn	PROPN
ejpam-4521	316	6	=	=	PUNCT
ejpam-4521	316	7	[	[	X
ejpam-4521	316	8	v1	v1	NOUN
ejpam-4521	316	9	,	,	PUNCT
ejpam-4521	316	10	v2	v2	NOUN
ejpam-4521	316	11	,	,	PUNCT
ejpam-4521	316	12	.	.	PUNCT
ejpam-4521	316	13	.	.	PUNCT
ejpam-4521	316	14	.	.	PUNCT
ejpam-4521	317	1	,	,	PUNCT
ejpam-4521	317	2	vn	vn	X
ejpam-4521	317	3	,	,	PUNCT
ejpam-4521	317	4	v1	v1	PROPN
ejpam-4521	317	5	]	]	PUNCT
ejpam-4521	317	6	.	.	PUNCT
ejpam-4521	318	1	if	if	SCONJ
ejpam-4521	318	2	n	n	NUM
ejpam-4521	318	3	=	=	SYM
ejpam-4521	318	4	3	3	NUM
ejpam-4521	318	5	,	,	PUNCT
ejpam-4521	318	6	then	then	ADV
ejpam-4521	318	7	the	the	DET
ejpam-4521	318	8	coi	coi	NOUN
ejpam-4521	318	9	-	-	PUNCT
ejpam-4521	318	10	sets	set	NOUN
ejpam-4521	318	11	of	of	ADP
ejpam-4521	318	12	c3	c3	PROPN
ejpam-4521	318	13	are	be	AUX
ejpam-4521	318	14	q1	q1	NOUN
ejpam-4521	318	15	=	=	SYM
ejpam-4521	318	16	{	{	PUNCT
ejpam-4521	318	17	v1	v1	PROPN
ejpam-4521	318	18	,	,	PUNCT
ejpam-4521	318	19	v2	v2	PROPN
ejpam-4521	318	20	}	}	PUNCT
ejpam-4521	318	21	,	,	PUNCT
ejpam-4521	318	22	q2	q2	NOUN
ejpam-4521	318	23	=	=	SYM
ejpam-4521	318	24	{	{	PUNCT
ejpam-4521	318	25	v2	v2	PROPN
ejpam-4521	318	26	,	,	PUNCT
ejpam-4521	318	27	v3	v3	PROPN
ejpam-4521	318	28	}	}	PUNCT
ejpam-4521	318	29	and	and	CCONJ
ejpam-4521	318	30	q3	q3	NOUN
ejpam-4521	318	31	=	=	SYM
ejpam-4521	318	32	{	{	PUNCT
ejpam-4521	318	33	v1	v1	PROPN
ejpam-4521	318	34	,	,	PUNCT
ejpam-4521	318	35	v3	v3	PROPN
ejpam-4521	318	36	}	}	PUNCT
ejpam-4521	318	37	.	.	PUNCT
ejpam-4521	319	1	clearly	clearly	ADV
ejpam-4521	319	2	,	,	PUNCT
ejpam-4521	319	3	for	for	ADP
ejpam-4521	319	4	each	each	DET
ejpam-4521	319	5	vi	vi	PROPN
ejpam-4521	319	6	∈	∈	PROPN
ejpam-4521	319	7	qj	qj	PROPN
ejpam-4521	319	8	where	where	SCONJ
ejpam-4521	319	9	i	i	PRON
ejpam-4521	319	10	,	,	PUNCT
ejpam-4521	319	11	j	j	PROPN
ejpam-4521	319	12	∈	∈	PROPN
ejpam-4521	319	13	{	{	PUNCT
ejpam-4521	319	14	1	1	NUM
ejpam-4521	319	15	,	,	PUNCT
ejpam-4521	319	16	2	2	NUM
ejpam-4521	319	17	,	,	PUNCT
ejpam-4521	319	18	3	3	NUM
ejpam-4521	319	19	}	}	PUNCT
ejpam-4521	319	20	,	,	PUNCT
ejpam-4521	319	21	there	there	PRON
ejpam-4521	319	22	exists	exist	VERB
ejpam-4521	319	23	vk	vk	ADP
ejpam-4521	319	24	∈	∈	PROPN
ejpam-4521	319	25	v	v	PROPN
ejpam-4521	319	26	(	(	PUNCT
ejpam-4521	319	27	c3	c3	PROPN
ejpam-4521	319	28	)	)	PUNCT
ejpam-4521	319	29	\	\	PROPN
ejpam-4521	319	30	qj	qj	PROPN
ejpam-4521	319	31	,	,	PUNCT
ejpam-4521	319	32	where	where	SCONJ
ejpam-4521	319	33	k	k	PROPN
ejpam-4521	319	34	∈	∈	PROPN
ejpam-4521	319	35	{	{	PUNCT
ejpam-4521	319	36	1	1	NUM
ejpam-4521	319	37	,	,	PUNCT
ejpam-4521	319	38	2	2	NUM
ejpam-4521	319	39	,	,	PUNCT
ejpam-4521	319	40	3	3	NUM
ejpam-4521	319	41	}	}	PUNCT
ejpam-4521	319	42	and	and	CCONJ
ejpam-4521	319	43	i	i	PRON
ejpam-4521	319	44	̸=	̸=	PROPN
ejpam-4521	319	45	k	k	PROPN
ejpam-4521	319	46	such	such	ADJ
ejpam-4521	319	47	that	that	SCONJ
ejpam-4521	319	48	[	[	PUNCT
ejpam-4521	319	49	qj	qj	PROPN
ejpam-4521	319	50	\	\	PROPN
ejpam-4521	319	51	{	{	PUNCT
ejpam-4521	319	52	vi	vi	NOUN
ejpam-4521	319	53	}	}	PUNCT
ejpam-4521	319	54	]	]	PUNCT
ejpam-4521	319	55	∪	∪	X
ejpam-4521	319	56	{	{	PUNCT
ejpam-4521	319	57	vk	vk	INTJ
ejpam-4521	319	58	}	}	PUNCT
ejpam-4521	319	59	is	be	AUX
ejpam-4521	319	60	a	a	DET
ejpam-4521	319	61	coi	coi	NOUN
ejpam-4521	319	62	-	-	PUNCT
ejpam-4521	319	63	set	set	NOUN
ejpam-4521	319	64	of	of	ADP
ejpam-4521	319	65	g.	g.	PROPN
ejpam-4521	319	66	thus	thus	ADV
ejpam-4521	319	67	,	,	PUNCT
ejpam-4521	319	68	by	by	ADP
ejpam-4521	319	69	theorem	theorem	ADJ
ejpam-4521	319	70	4	4	NUM
ejpam-4521	319	71	,	,	PUNCT
ejpam-4521	319	72	fcoi(c3	fcoi(c3	NOUN
ejpam-4521	319	73	)	)	PUNCT
ejpam-4521	319	74	=	=	SYM
ejpam-4521	319	75	2	2	X
ejpam-4521	319	76	.	.	PUNCT
ejpam-4521	319	77	now	now	ADV
ejpam-4521	319	78	,	,	PUNCT
ejpam-4521	319	79	suppose	suppose	VERB
ejpam-4521	319	80	that	that	SCONJ
ejpam-4521	319	81	n	n	PRON
ejpam-4521	319	82	is	be	AUX
ejpam-4521	319	83	even	even	ADV
ejpam-4521	319	84	.	.	PUNCT
ejpam-4521	320	1	then	then	ADV
ejpam-4521	320	2	b1	b1	NOUN
ejpam-4521	320	3	=	=	SYM
ejpam-4521	320	4	{	{	PUNCT
ejpam-4521	320	5	v1	v1	PROPN
ejpam-4521	320	6	,	,	PUNCT
ejpam-4521	320	7	v3	v3	PROPN
ejpam-4521	320	8	,	,	PUNCT
ejpam-4521	320	9	v5	v5	PROPN
ejpam-4521	320	10	,	,	PUNCT
ejpam-4521	320	11	.	.	PUNCT
ejpam-4521	320	12	.	.	PUNCT
ejpam-4521	320	13	.	.	PUNCT
ejpam-4521	321	1	,	,	PUNCT
ejpam-4521	321	2	vn−1	vn−1	ADJ
ejpam-4521	321	3	}	}	PUNCT
ejpam-4521	321	4	and	and	CCONJ
ejpam-4521	321	5	b2	b2	NOUN
ejpam-4521	321	6	=	=	SYM
ejpam-4521	321	7	{	{	PUNCT
ejpam-4521	321	8	v2	v2	PROPN
ejpam-4521	321	9	,	,	PUNCT
ejpam-4521	321	10	v4	v4	PROPN
ejpam-4521	321	11	,	,	PUNCT
ejpam-4521	321	12	v6	v6	NOUN
ejpam-4521	321	13	,	,	PUNCT
ejpam-4521	321	14	.	.	PUNCT
ejpam-4521	321	15	.	.	PUNCT
ejpam-4521	321	16	.	.	PUNCT
ejpam-4521	322	1	,	,	PUNCT
ejpam-4521	322	2	vn	vn	PROPN
ejpam-4521	322	3	}	}	PUNCT
ejpam-4521	322	4	are	be	AUX
ejpam-4521	322	5	the	the	DET
ejpam-4521	322	6	only	only	ADJ
ejpam-4521	322	7	coi	coi	NOUN
ejpam-4521	322	8	-	-	PUNCT
ejpam-4521	322	9	sets	set	NOUN
ejpam-4521	322	10	of	of	ADP
ejpam-4521	322	11	cn	cn	PROPN
ejpam-4521	322	12	with	with	ADP
ejpam-4521	322	13	v3	v3	PROPN
ejpam-4521	322	14	∈	∈	PROPN
ejpam-4521	322	15	b1	b1	PROPN
ejpam-4521	322	16	and	and	CCONJ
ejpam-4521	322	17	v3	v3	PROPN
ejpam-4521	322	18	/∈	/∈	PROPN
ejpam-4521	322	19	b2	b2	PROPN
ejpam-4521	322	20	.	.	PUNCT
ejpam-4521	323	1	thus	thus	ADV
ejpam-4521	323	2	,	,	PUNCT
ejpam-4521	323	3	by	by	ADP
ejpam-4521	323	4	remark	remark	NOUN
ejpam-4521	323	5	4(ii	4(ii	NUM
ejpam-4521	323	6	)	)	PUNCT
ejpam-4521	323	7	,	,	PUNCT
ejpam-4521	323	8	fcoi(b1	fcoi(b1	VERB
ejpam-4521	323	9	)	)	PUNCT
ejpam-4521	323	10	=	=	SYM
ejpam-4521	323	11	1	1	NUM
ejpam-4521	323	12	=	=	SYM
ejpam-4521	323	13	fcoi(cn	fcoi(cn	NOUN
ejpam-4521	323	14	)	)	PUNCT
ejpam-4521	323	15	.	.	PUNCT
ejpam-4521	324	1	next	next	ADV
ejpam-4521	324	2	,	,	PUNCT
ejpam-4521	324	3	suppose	suppose	VERB
ejpam-4521	324	4	that	that	SCONJ
ejpam-4521	324	5	n	n	PROPN
ejpam-4521	324	6	>	>	X
ejpam-4521	324	7	3	3	NUM
ejpam-4521	324	8	and	and	CCONJ
ejpam-4521	324	9	n	n	PRON
ejpam-4521	324	10	is	be	AUX
ejpam-4521	324	11	odd	odd	ADJ
ejpam-4521	324	12	.	.	PUNCT
ejpam-4521	325	1	then	then	ADV
ejpam-4521	325	2	r1	r1	PROPN
ejpam-4521	325	3	=	=	SYM
ejpam-4521	325	4	{	{	PUNCT
ejpam-4521	325	5	v1	v1	PROPN
ejpam-4521	325	6	,	,	PUNCT
ejpam-4521	325	7	v3	v3	PROPN
ejpam-4521	325	8	,	,	PUNCT
ejpam-4521	325	9	v5	v5	PROPN
ejpam-4521	325	10	,	,	PUNCT
ejpam-4521	325	11	.	.	PUNCT
ejpam-4521	325	12	.	.	PUNCT
ejpam-4521	325	13	.	.	PUNCT
ejpam-4521	326	1	,	,	PUNCT
ejpam-4521	326	2	vn−2	vn−2	PROPN
ejpam-4521	326	3	,	,	PUNCT
ejpam-4521	326	4	vn	vn	NOUN
ejpam-4521	326	5	}	}	PUNCT
ejpam-4521	326	6	,	,	PUNCT
ejpam-4521	326	7	r2	r2	PROPN
ejpam-4521	326	8	=	=	SYM
ejpam-4521	326	9	{	{	PUNCT
ejpam-4521	326	10	v1	v1	PROPN
ejpam-4521	326	11	,	,	PUNCT
ejpam-4521	326	12	v3	v3	PROPN
ejpam-4521	326	13	,	,	PUNCT
ejpam-4521	326	14	v5	v5	PROPN
ejpam-4521	326	15	,	,	PUNCT
ejpam-4521	326	16	.	.	PUNCT
ejpam-4521	326	17	.	.	PUNCT
ejpam-4521	326	18	.	.	PUNCT
ejpam-4521	327	1	,	,	PUNCT
ejpam-4521	327	2	vn−2	vn−2	PROPN
ejpam-4521	327	3	,	,	PUNCT
ejpam-4521	327	4	vn−1	vn−1	ADJ
ejpam-4521	327	5	}	}	PUNCT
ejpam-4521	327	6	,	,	PUNCT
ejpam-4521	327	7	r3	r3	PROPN
ejpam-4521	327	8	=	=	SYM
ejpam-4521	327	9	{	{	PUNCT
ejpam-4521	327	10	v2	v2	PROPN
ejpam-4521	327	11	,	,	PUNCT
ejpam-4521	327	12	v4	v4	PROPN
ejpam-4521	327	13	,	,	PUNCT
ejpam-4521	327	14	v6	v6	NOUN
ejpam-4521	327	15	,	,	PUNCT
ejpam-4521	327	16	.	.	PUNCT
ejpam-4521	327	17	.	.	PUNCT
ejpam-4521	328	1	.	.	PUNCT
ejpam-4521	329	1	,	,	PUNCT
ejpam-4521	329	2	vn−1	vn−1	PROPN
ejpam-4521	329	3	,	,	PUNCT
ejpam-4521	329	4	vn	vn	NOUN
ejpam-4521	329	5	}	}	PUNCT
ejpam-4521	329	6	and	and	CCONJ
ejpam-4521	329	7	,	,	PUNCT
ejpam-4521	329	8	r4	r4	NOUN
ejpam-4521	329	9	=	=	PUNCT
ejpam-4521	329	10	{	{	PUNCT
ejpam-4521	329	11	v2	v2	PROPN
ejpam-4521	329	12	,	,	PUNCT
ejpam-4521	329	13	v4	v4	PROPN
ejpam-4521	329	14	,	,	PUNCT
ejpam-4521	329	15	v6	v6	NOUN
ejpam-4521	329	16	,	,	PUNCT
ejpam-4521	329	17	.	.	PUNCT
ejpam-4521	329	18	.	.	PUNCT
ejpam-4521	330	1	.	.	PUNCT
ejpam-4521	331	1	,	,	PUNCT
ejpam-4521	331	2	vn−1	vn−1	ADJ
ejpam-4521	331	3	,	,	PUNCT
ejpam-4521	331	4	v1	v1	NOUN
ejpam-4521	331	5	}	}	PUNCT
ejpam-4521	331	6	are	be	AUX
ejpam-4521	331	7	coi	coi	NOUN
ejpam-4521	331	8	-	-	PUNCT
ejpam-4521	331	9	sets	set	NOUN
ejpam-4521	331	10	of	of	ADP
ejpam-4521	331	11	cn	cn	PROPN
ejpam-4521	331	12	.	.	PUNCT
ejpam-4521	332	1	hence	hence	ADV
ejpam-4521	332	2	,	,	PUNCT
ejpam-4521	332	3	no	no	DET
ejpam-4521	332	4	vertex	vertex	NOUN
ejpam-4521	332	5	of	of	ADP
ejpam-4521	332	6	cn	cn	PROPN
ejpam-4521	332	7	is	be	AUX
ejpam-4521	332	8	contained	contain	VERB
ejpam-4521	332	9	in	in	ADP
ejpam-4521	332	10	a	a	DET
ejpam-4521	332	11	unique	unique	ADJ
ejpam-4521	332	12	coi	coi	NOUN
ejpam-4521	332	13	-	-	PUNCT
ejpam-4521	332	14	set	set	NOUN
ejpam-4521	332	15	.	.	PUNCT
ejpam-4521	333	1	thus	thus	ADV
ejpam-4521	333	2	,	,	PUNCT
ejpam-4521	333	3	fcoi(cn	fcoi(cn	NOUN
ejpam-4521	333	4	)	)	PUNCT
ejpam-4521	333	5	≥	≥	NOUN
ejpam-4521	333	6	2	2	NUM
ejpam-4521	333	7	.	.	PUNCT
ejpam-4521	334	1	clearly	clearly	ADV
ejpam-4521	334	2	,	,	PUNCT
ejpam-4521	334	3	{	{	PUNCT
ejpam-4521	334	4	v1	v1	NOUN
ejpam-4521	334	5	,	,	PUNCT
ejpam-4521	334	6	vn	vn	PROPN
ejpam-4521	334	7	}	}	PUNCT
ejpam-4521	334	8	is	be	AUX
ejpam-4521	334	9	uniquely	uniquely	ADV
ejpam-4521	334	10	contained	contain	VERB
ejpam-4521	334	11	in	in	ADP
ejpam-4521	334	12	r1	r1	PROPN
ejpam-4521	334	13	.	.	PUNCT
ejpam-4521	335	1	therefore	therefore	ADV
ejpam-4521	335	2	,	,	PUNCT
ejpam-4521	335	3	fcoi(r1	fcoi(r1	NOUN
ejpam-4521	335	4	)	)	PUNCT
ejpam-4521	335	5	=	=	SYM
ejpam-4521	335	6	2	2	NUM
ejpam-4521	335	7	=	=	SYM
ejpam-4521	335	8	fcoi(cn	fcoi(cn	NOUN
ejpam-4521	335	9	)	)	PUNCT
ejpam-4521	335	10	.	.	PUNCT
ejpam-4521	336	1	the	the	DET
ejpam-4521	336	2	next	next	ADJ
ejpam-4521	336	3	result	result	NOUN
ejpam-4521	336	4	is	be	AUX
ejpam-4521	336	5	a	a	DET
ejpam-4521	336	6	restatement	restatement	NOUN
ejpam-4521	336	7	of	of	ADP
ejpam-4521	336	8	corollary	corollary	ADJ
ejpam-4521	336	9	2	2	NUM
ejpam-4521	336	10	.	.	PUNCT
ejpam-4521	336	11	corollary	corollary	ADJ
ejpam-4521	336	12	3	3	X
ejpam-4521	336	13	.	.	PUNCT
ejpam-4521	337	1	let	let	VERB
ejpam-4521	337	2	g	g	PRON
ejpam-4521	337	3	be	be	AUX
ejpam-4521	337	4	a	a	DET
ejpam-4521	337	5	connected	connected	ADJ
ejpam-4521	337	6	graph	graph	NOUN
ejpam-4521	337	7	of	of	ADP
ejpam-4521	337	8	order	order	NOUN
ejpam-4521	337	9	n	n	PRON
ejpam-4521	337	10	≥	≥	NOUN
ejpam-4521	337	11	3	3	NUM
ejpam-4521	337	12	of	of	ADP
ejpam-4521	337	13	size	size	NOUN
ejpam-4521	337	14	p	p	NOUN
ejpam-4521	337	15	and	and	CCONJ
ejpam-4521	337	16	h	h	NOUN
ejpam-4521	337	17	be	be	AUX
ejpam-4521	337	18	any	any	DET
ejpam-4521	337	19	graph	graph	NOUN
ejpam-4521	337	20	.	.	PUNCT
ejpam-4521	338	1	then	then	ADV
ejpam-4521	338	2	c	c	PROPN
ejpam-4521	338	3	⊆	⊆	NUM
ejpam-4521	338	4	v	v	NOUN
ejpam-4521	338	5	(	(	PUNCT
ejpam-4521	338	6	g	g	PROPN
ejpam-4521	338	7	⋄	⋄	PROPN
ejpam-4521	338	8	h	h	NOUN
ejpam-4521	338	9	)	)	PUNCT
ejpam-4521	338	10	is	be	AUX
ejpam-4521	338	11	a	a	DET
ejpam-4521	338	12	γch	γch	NOUN
ejpam-4521	338	13	,	,	PUNCT
ejpam-4521	338	14	coi	coi	NOUN
ejpam-4521	338	15	-	-	PUNCT
ejpam-4521	338	16	set	set	NOUN
ejpam-4521	338	17	of	of	ADP
ejpam-4521	338	18	g	g	PROPN
ejpam-4521	338	19	⋄	⋄	PROPN
ejpam-4521	338	20	h	h	NOUN
ejpam-4521	339	1	if	if	SCONJ
ejpam-4521	339	2	and	and	CCONJ
ejpam-4521	339	3	only	only	ADV
ejpam-4521	339	4	if	if	SCONJ
ejpam-4521	339	5	c	c	PROPN
ejpam-4521	339	6	=	=	SYM
ejpam-4521	339	7	v	v	PROPN
ejpam-4521	339	8	(	(	PUNCT
ejpam-4521	339	9	g	g	NOUN
ejpam-4521	339	10	)	)	PUNCT
ejpam-4521	339	11	∪	∪	NOUN
ejpam-4521	339	12	(	(	PUNCT
ejpam-4521	339	13	⋃	⋃	NOUN
ejpam-4521	339	14	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	339	15	)	)	PUNCT
ejpam-4521	339	16	suv	suv	PROPN
ejpam-4521	339	17	)	)	PUNCT
ejpam-4521	339	18	where	where	SCONJ
ejpam-4521	339	19	suv	suv	PROPN
ejpam-4521	339	20	is	be	AUX
ejpam-4521	339	21	a	a	DET
ejpam-4521	339	22	co	co	ADJ
ejpam-4521	339	23	-	-	ADJ
ejpam-4521	339	24	independent	independent	ADJ
ejpam-4521	339	25	set	set	NOUN
ejpam-4521	339	26	of	of	ADP
ejpam-4521	339	27	huv	huv	PROPN
ejpam-4521	339	28	for	for	ADP
ejpam-4521	339	29	each	each	DET
ejpam-4521	339	30	u	u	NOUN
ejpam-4521	339	31	,	,	PUNCT
ejpam-4521	339	32	v	v	PROPN
ejpam-4521	339	33	∈	∈	PROPN
ejpam-4521	339	34	v	v	NOUN
ejpam-4521	339	35	(	(	PUNCT
ejpam-4521	339	36	g	g	NOUN
ejpam-4521	339	37	)	)	PUNCT
ejpam-4521	339	38	such	such	ADJ
ejpam-4521	339	39	that	that	SCONJ
ejpam-4521	339	40	uv	uv	PROPN
ejpam-4521	339	41	∈	∈	PROPN
ejpam-4521	339	42	e(g	e(g	PROPN
ejpam-4521	339	43	)	)	PUNCT
ejpam-4521	339	44	,	,	PUNCT
ejpam-4521	339	45	and	and	CCONJ
ejpam-4521	339	46	suv	suv	PROPN
ejpam-4521	339	47	̸=	̸=	PROPN
ejpam-4521	339	48	v	v	PROPN
ejpam-4521	339	49	(	(	PUNCT
ejpam-4521	339	50	huv	huv	PROPN
ejpam-4521	339	51	)	)	PUNCT
ejpam-4521	339	52	.	.	PUNCT
ejpam-4521	340	1	in	in	ADP
ejpam-4521	340	2	particular	particular	ADJ
ejpam-4521	340	3	,	,	PUNCT
ejpam-4521	340	4	γch	γch	NOUN
ejpam-4521	340	5	,	,	PUNCT
ejpam-4521	340	6	coi(g	coi(g	PROPN
ejpam-4521	340	7	⋄h	⋄h	PROPN
ejpam-4521	340	8	)	)	PUNCT
ejpam-4521	341	1	=	=	SYM
ejpam-4521	341	2	|v	|v	PROPN
ejpam-4521	341	3	(	(	PUNCT
ejpam-4521	341	4	g)|+	g)|+	NOUN
ejpam-4521	341	5	p	p	PROPN
ejpam-4521	341	6	(	(	PUNCT
ejpam-4521	341	7	coi(h	coi(h	NOUN
ejpam-4521	341	8	)	)	PUNCT
ejpam-4521	341	9	)	)	PUNCT
ejpam-4521	341	10	.	.	PUNCT
ejpam-4521	342	1	theorem	theorem	ADJ
ejpam-4521	342	2	5	5	NUM
ejpam-4521	342	3	.	.	PUNCT
ejpam-4521	343	1	let	let	VERB
ejpam-4521	343	2	g	g	PRON
ejpam-4521	343	3	be	be	AUX
ejpam-4521	343	4	a	a	DET
ejpam-4521	343	5	nontrivial	nontrivial	ADJ
ejpam-4521	343	6	connected	connect	VERB
ejpam-4521	343	7	graph	graph	NOUN
ejpam-4521	343	8	of	of	ADP
ejpam-4521	343	9	order	order	NOUN
ejpam-4521	343	10	n	n	PRON
ejpam-4521	343	11	≥	≥	NOUN
ejpam-4521	343	12	3	3	NUM
ejpam-4521	343	13	of	of	ADP
ejpam-4521	343	14	size	size	NOUN
ejpam-4521	343	15	p	p	NOUN
ejpam-4521	343	16	and	and	CCONJ
ejpam-4521	343	17	h	h	NOUN
ejpam-4521	343	18	be	be	AUX
ejpam-4521	343	19	any	any	DET
ejpam-4521	343	20	graph	graph	NOUN
ejpam-4521	343	21	.	.	PUNCT
ejpam-4521	344	1	then	then	ADV
ejpam-4521	344	2	fγch	fγch	NOUN
ejpam-4521	344	3	,	,	PUNCT
ejpam-4521	344	4	coi(g	coi(g	PROPN
ejpam-4521	344	5	⋄h	⋄h	PROPN
ejpam-4521	344	6	)	)	PUNCT
ejpam-4521	344	7	=	=	PRON
ejpam-4521	344	8	{	{	PUNCT
ejpam-4521	344	9	0	0	NUM
ejpam-4521	344	10	,	,	PUNCT
ejpam-4521	344	11	if	if	SCONJ
ejpam-4521	344	12	h	h	NOUN
ejpam-4521	344	13	has	have	VERB
ejpam-4521	344	14	a	a	DET
ejpam-4521	344	15	unique	unique	ADJ
ejpam-4521	344	16	coi	coi	NOUN
ejpam-4521	344	17	-	-	PUNCT
ejpam-4521	344	18	set	set	NOUN
ejpam-4521	344	19	,	,	PUNCT
ejpam-4521	344	20	p	p	X
ejpam-4521	344	21	[	[	PUNCT
ejpam-4521	344	22	fcoi(h	fcoi(h	PROPN
ejpam-4521	344	23	)	)	PUNCT
ejpam-4521	344	24	]	]	PUNCT
ejpam-4521	344	25	,	,	PUNCT
ejpam-4521	344	26	if	if	SCONJ
ejpam-4521	344	27	h	h	NOUN
ejpam-4521	344	28	has	have	VERB
ejpam-4521	344	29	no	no	DET
ejpam-4521	344	30	unique	unique	ADJ
ejpam-4521	344	31	coi	coi	NOUN
ejpam-4521	344	32	-	-	PUNCT
ejpam-4521	344	33	set	set	NOUN
ejpam-4521	344	34	.	.	PUNCT
ejpam-4521	345	1	y.d	y.d	PROPN
ejpam-4521	345	2	.	.	PROPN
ejpam-4521	345	3	calanza	calanza	PROPN
ejpam-4521	345	4	,	,	PUNCT
ejpam-4521	345	5	h.	h.	PROPN
ejpam-4521	345	6	rara	rara	PROPN
ejpam-4521	345	7	/	/	SYM
ejpam-4521	345	8	eur	eur	PROPN
ejpam-4521	345	9	.	.	PUNCT
ejpam-4521	346	1	j.	j.	PROPN
ejpam-4521	346	2	pure	pure	PROPN
ejpam-4521	346	3	appl	appl	PROPN
ejpam-4521	346	4	.	.	PROPN
ejpam-4521	346	5	math	math	PROPN
ejpam-4521	346	6	,	,	PUNCT
ejpam-4521	346	7	15	15	NUM
ejpam-4521	346	8	(	(	PUNCT
ejpam-4521	346	9	4	4	NUM
ejpam-4521	346	10	)	)	PUNCT
ejpam-4521	346	11	(	(	PUNCT
ejpam-4521	346	12	2022	2022	NUM
ejpam-4521	346	13	)	)	PUNCT
ejpam-4521	346	14	,	,	PUNCT
ejpam-4521	346	15	1597	1597	NUM
ejpam-4521	346	16	-	-	SYM
ejpam-4521	346	17	1612	1612	NUM
ejpam-4521	346	18	1607	1607	NUM
ejpam-4521	346	19	proof	proof	NOUN
ejpam-4521	346	20	:	:	PUNCT
ejpam-4521	346	21	suppose	suppose	VERB
ejpam-4521	346	22	h	h	NOUN
ejpam-4521	346	23	has	have	VERB
ejpam-4521	346	24	a	a	DET
ejpam-4521	346	25	unique	unique	ADJ
ejpam-4521	346	26	coi	coi	NOUN
ejpam-4521	346	27	-set	-set	NOUN
ejpam-4521	346	28	.	.	PUNCT
ejpam-4521	347	1	for	for	ADP
ejpam-4521	347	2	each	each	DET
ejpam-4521	347	3	uv	uv	PROPN
ejpam-4521	347	4	∈	∈	PROPN
ejpam-4521	347	5	e(g	e(g	PROPN
ejpam-4521	347	6	)	)	PUNCT
ejpam-4521	347	7	,	,	PUNCT
ejpam-4521	347	8	where	where	SCONJ
ejpam-4521	347	9	u	u	NOUN
ejpam-4521	347	10	,	,	PUNCT
ejpam-4521	347	11	v	v	PROPN
ejpam-4521	347	12	∈	∈	PROPN
ejpam-4521	347	13	v	v	NOUN
ejpam-4521	347	14	(	(	PUNCT
ejpam-4521	347	15	g	g	NOUN
ejpam-4521	347	16	)	)	PUNCT
ejpam-4521	347	17	,	,	PUNCT
ejpam-4521	347	18	let	let	VERB
ejpam-4521	347	19	ruv	ruv	PROPN
ejpam-4521	347	20	⊆	⊆	PROPN
ejpam-4521	347	21	v	v	NOUN
ejpam-4521	347	22	(	(	PUNCT
ejpam-4521	347	23	huv	huv	PROPN
ejpam-4521	347	24	)	)	PUNCT
ejpam-4521	347	25	be	be	AUX
ejpam-4521	347	26	the	the	DET
ejpam-4521	347	27	unique	unique	ADJ
ejpam-4521	347	28	coi	coi	NOUN
ejpam-4521	347	29	-set	-set	PUNCT
ejpam-4521	347	30	of	of	ADP
ejpam-4521	347	31	huv	huv	PROPN
ejpam-4521	347	32	.	.	PUNCT
ejpam-4521	348	1	by	by	ADP
ejpam-4521	348	2	corollary	corollary	ADJ
ejpam-4521	348	3	3	3	NUM
ejpam-4521	348	4	,	,	PUNCT
ejpam-4521	348	5	c	c	NOUN
ejpam-4521	348	6	=	=	SYM
ejpam-4521	348	7	v	v	PROPN
ejpam-4521	348	8	(	(	PUNCT
ejpam-4521	348	9	g	g	NOUN
ejpam-4521	348	10	)	)	PUNCT
ejpam-4521	348	11	∪	∪	NOUN
ejpam-4521	348	12	(	(	PUNCT
ejpam-4521	348	13	⋃	⋃	NOUN
ejpam-4521	348	14	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	348	15	)	)	PUNCT
ejpam-4521	348	16	ruv	ruv	PROPN
ejpam-4521	348	17	)	)	PUNCT
ejpam-4521	348	18	is	be	AUX
ejpam-4521	348	19	the	the	DET
ejpam-4521	348	20	unique	unique	ADJ
ejpam-4521	348	21	γch	γch	NOUN
ejpam-4521	348	22	,	,	PUNCT
ejpam-4521	348	23	coi	coi	NOUN
ejpam-4521	348	24	-	-	PUNCT
ejpam-4521	348	25	set	set	NOUN
ejpam-4521	348	26	of	of	ADP
ejpam-4521	348	27	g	g	PROPN
ejpam-4521	348	28	⋄	⋄	PROPN
ejpam-4521	348	29	h.	h.	PROPN
ejpam-4521	349	1	thus	thus	ADV
ejpam-4521	349	2	,	,	PUNCT
ejpam-4521	349	3	by	by	ADP
ejpam-4521	349	4	remark	remark	NOUN
ejpam-4521	349	5	3(i	3(i	NUM
ejpam-4521	349	6	)	)	PUNCT
ejpam-4521	349	7	,	,	PUNCT
ejpam-4521	349	8	fγch	fγch	PROPN
ejpam-4521	349	9	,	,	PUNCT
ejpam-4521	349	10	coi(g	coi(g	PROPN
ejpam-4521	349	11	⋄	⋄	PROPN
ejpam-4521	349	12	h	h	NOUN
ejpam-4521	349	13	)	)	PUNCT
ejpam-4521	349	14	=	=	NOUN
ejpam-4521	350	1	0	0	X
ejpam-4521	350	2	.	.	PUNCT
ejpam-4521	351	1	on	on	ADP
ejpam-4521	351	2	the	the	DET
ejpam-4521	351	3	other	other	ADJ
ejpam-4521	351	4	hand	hand	NOUN
ejpam-4521	351	5	,	,	PUNCT
ejpam-4521	351	6	suppose	suppose	VERB
ejpam-4521	351	7	that	that	SCONJ
ejpam-4521	351	8	h	h	NOUN
ejpam-4521	351	9	does	do	AUX
ejpam-4521	351	10	not	not	PART
ejpam-4521	351	11	have	have	VERB
ejpam-4521	351	12	a	a	DET
ejpam-4521	351	13	unique	unique	ADJ
ejpam-4521	351	14	coi	coi	NOUN
ejpam-4521	351	15	-set	-set	NOUN
ejpam-4521	351	16	.	.	PUNCT
ejpam-4521	352	1	for	for	ADP
ejpam-4521	352	2	every	every	DET
ejpam-4521	352	3	uv	uv	PROPN
ejpam-4521	352	4	∈	∈	PROPN
ejpam-4521	352	5	e(g	e(g	PROPN
ejpam-4521	352	6	)	)	PUNCT
ejpam-4521	352	7	,	,	PUNCT
ejpam-4521	352	8	where	where	SCONJ
ejpam-4521	352	9	u	u	NOUN
ejpam-4521	352	10	,	,	PUNCT
ejpam-4521	352	11	v	v	PROPN
ejpam-4521	352	12	∈	∈	PROPN
ejpam-4521	352	13	v	v	NOUN
ejpam-4521	352	14	(	(	PUNCT
ejpam-4521	352	15	g	g	NOUN
ejpam-4521	352	16	)	)	PUNCT
ejpam-4521	352	17	,	,	PUNCT
ejpam-4521	352	18	let	let	VERB
ejpam-4521	352	19	wuv	wuv	PROPN
ejpam-4521	352	20	⊆	⊆	NUM
ejpam-4521	352	21	v	v	NOUN
ejpam-4521	352	22	(	(	PUNCT
ejpam-4521	352	23	huv	huv	PROPN
ejpam-4521	352	24	)	)	PUNCT
ejpam-4521	352	25	be	be	AUX
ejpam-4521	352	26	a	a	DET
ejpam-4521	352	27	coi	coi	NOUN
ejpam-4521	352	28	-set	-set	PUNCT
ejpam-4521	352	29	of	of	ADP
ejpam-4521	352	30	huv	huv	PROPN
ejpam-4521	352	31	with	with	ADP
ejpam-4521	352	32	fcoi(huv	fcoi(huv	PROPN
ejpam-4521	352	33	)	)	PUNCT
ejpam-4521	353	1	=	=	SYM
ejpam-4521	353	2	fcoi(wuv	fcoi(wuv	PROPN
ejpam-4521	353	3	)	)	PUNCT
ejpam-4521	353	4	,	,	PUNCT
ejpam-4521	353	5	and	and	CCONJ
ejpam-4521	353	6	let	let	VERB
ejpam-4521	353	7	rwuv	rwuv	NOUN
ejpam-4521	353	8	⊆	⊆	NUM
ejpam-4521	353	9	wuv	wuv	NOUN
ejpam-4521	353	10	be	be	AUX
ejpam-4521	353	11	a	a	DET
ejpam-4521	353	12	forcing	forcing	NOUN
ejpam-4521	353	13	subset	subset	NOUN
ejpam-4521	353	14	for	for	ADP
ejpam-4521	353	15	wuv	wuv	NOUN
ejpam-4521	353	16	with	with	ADP
ejpam-4521	353	17	fcoi(wuv	fcoi(wuv	NOUN
ejpam-4521	353	18	)	)	PUNCT
ejpam-4521	354	1	=	=	PUNCT
ejpam-4521	355	1	|rwuv	|rwuv	NOUN
ejpam-4521	356	1	|	|	ADV
ejpam-4521	356	2	.	.	PUNCT
ejpam-4521	357	1	then	then	ADV
ejpam-4521	357	2	by	by	ADP
ejpam-4521	357	3	corollary	corollary	ADJ
ejpam-4521	357	4	3	3	NUM
ejpam-4521	357	5	,	,	PUNCT
ejpam-4521	357	6	sw	sw	PROPN
ejpam-4521	357	7	=	=	SYM
ejpam-4521	357	8	v	v	PROPN
ejpam-4521	357	9	(	(	PUNCT
ejpam-4521	357	10	g	g	NOUN
ejpam-4521	357	11	)	)	PUNCT
ejpam-4521	357	12	∪	∪	NOUN
ejpam-4521	357	13	(	(	PUNCT
ejpam-4521	357	14	⋃	⋃	NOUN
ejpam-4521	357	15	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	357	16	)	)	PUNCT
ejpam-4521	357	17	wuv	wuv	NOUN
ejpam-4521	357	18	)	)	PUNCT
ejpam-4521	357	19	is	be	AUX
ejpam-4521	357	20	a	a	DET
ejpam-4521	357	21	γch	γch	NOUN
ejpam-4521	357	22	,	,	PUNCT
ejpam-4521	357	23	coi	coi	NOUN
ejpam-4521	357	24	-	-	PUNCT
ejpam-4521	357	25	set	set	NOUN
ejpam-4521	357	26	of	of	ADP
ejpam-4521	357	27	g	g	PROPN
ejpam-4521	357	28	⋄h	⋄h	PROPN
ejpam-4521	357	29	.	.	PUNCT
ejpam-4521	358	1	let	let	VERB
ejpam-4521	358	2	d	d	NOUN
ejpam-4521	358	3	=	=	PUNCT
ejpam-4521	358	4	⋃	⋃	NOUN
ejpam-4521	358	5	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	358	6	)	)	PUNCT
ejpam-4521	358	7	rwuv	rwuv	NOUN
ejpam-4521	358	8	.	.	PUNCT
ejpam-4521	359	1	then	then	ADV
ejpam-4521	359	2	d	d	PROPN
ejpam-4521	359	3	is	be	AUX
ejpam-4521	359	4	a	a	DET
ejpam-4521	359	5	forcing	forcing	NOUN
ejpam-4521	359	6	subset	subset	NOUN
ejpam-4521	359	7	for	for	ADP
ejpam-4521	359	8	sw	sw	PROPN
ejpam-4521	359	9	.	.	PUNCT
ejpam-4521	360	1	thus	thus	ADV
ejpam-4521	360	2	,	,	PUNCT
ejpam-4521	360	3	fγch	fγch	NOUN
ejpam-4521	360	4	,	,	PUNCT
ejpam-4521	360	5	coi(g	coi(g	PROPN
ejpam-4521	360	6	⋄h	⋄h	PROPN
ejpam-4521	360	7	)	)	PUNCT
ejpam-4521	360	8	≤	≤	NOUN
ejpam-4521	361	1	fγch	fγch	NOUN
ejpam-4521	361	2	,	,	PUNCT
ejpam-4521	361	3	coi(sw	coi(sw	VERB
ejpam-4521	361	4	)	)	PUNCT
ejpam-4521	361	5	≤	≤	NUM
ejpam-4521	362	1	|d|	|d|	PROPN
ejpam-4521	362	2	=	=	SYM
ejpam-4521	363	1	p	p	X
ejpam-4521	363	2	[	[	PUNCT
ejpam-4521	363	3	fcoi(h	fcoi(h	PROPN
ejpam-4521	363	4	)	)	PUNCT
ejpam-4521	363	5	]	]	PUNCT
ejpam-4521	363	6	.	.	PUNCT
ejpam-4521	364	1	next	next	ADV
ejpam-4521	364	2	,	,	PUNCT
ejpam-4521	364	3	let	let	VERB
ejpam-4521	364	4	c	c	NOUN
ejpam-4521	364	5	′	′	VERB
ejpam-4521	364	6	be	be	AUX
ejpam-4521	364	7	a	a	DET
ejpam-4521	364	8	γch	γch	NOUN
ejpam-4521	364	9	,	,	PUNCT
ejpam-4521	364	10	coi	coi	NOUN
ejpam-4521	364	11	-	-	PUNCT
ejpam-4521	364	12	set	set	NOUN
ejpam-4521	364	13	of	of	ADP
ejpam-4521	364	14	g	g	PROPN
ejpam-4521	364	15	⋄	⋄	PROPN
ejpam-4521	364	16	h	h	NOUN
ejpam-4521	364	17	such	such	ADJ
ejpam-4521	364	18	that	that	DET
ejpam-4521	364	19	fγch	fγch	NOUN
ejpam-4521	364	20	,	,	PUNCT
ejpam-4521	364	21	coi(g	coi(g	PROPN
ejpam-4521	364	22	⋄	⋄	PROPN
ejpam-4521	364	23	h	h	NOUN
ejpam-4521	364	24	)	)	PUNCT
ejpam-4521	364	25	=	=	SYM
ejpam-4521	365	1	fγch	fγch	ADJ
ejpam-4521	365	2	,	,	PUNCT
ejpam-4521	365	3	coi(c	coi(c	PROPN
ejpam-4521	365	4	′	′	NUM
ejpam-4521	365	5	)	)	PUNCT
ejpam-4521	365	6	.	.	PUNCT
ejpam-4521	366	1	then	then	ADV
ejpam-4521	366	2	by	by	ADP
ejpam-4521	366	3	corollary	corollary	ADJ
ejpam-4521	366	4	3	3	NUM
ejpam-4521	366	5	,	,	PUNCT
ejpam-4521	366	6	let	let	VERB
ejpam-4521	366	7	c	c	NOUN
ejpam-4521	366	8	′	′	NOUN
ejpam-4521	366	9	=	=	SYM
ejpam-4521	366	10	v	v	NOUN
ejpam-4521	366	11	(	(	PUNCT
ejpam-4521	366	12	g	g	NOUN
ejpam-4521	366	13	)	)	PUNCT
ejpam-4521	366	14	∪	∪	NOUN
ejpam-4521	366	15	(	(	PUNCT
ejpam-4521	366	16	⋃	⋃	NOUN
ejpam-4521	366	17	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	366	18	)	)	PUNCT
ejpam-4521	366	19	quv	quv	PROPN
ejpam-4521	366	20	)	)	PUNCT
ejpam-4521	366	21	where	where	SCONJ
ejpam-4521	366	22	quv	quv	PROPN
ejpam-4521	366	23	is	be	AUX
ejpam-4521	366	24	a	a	DET
ejpam-4521	366	25	coi	coi	NOUN
ejpam-4521	366	26	-set	-set	PUNCT
ejpam-4521	366	27	of	of	ADP
ejpam-4521	366	28	huv	huv	PROPN
ejpam-4521	366	29	for	for	ADP
ejpam-4521	366	30	each	each	DET
ejpam-4521	366	31	uv	uv	PROPN
ejpam-4521	366	32	∈	∈	PROPN
ejpam-4521	366	33	e(g	e(g	PROPN
ejpam-4521	366	34	)	)	PUNCT
ejpam-4521	366	35	for	for	ADP
ejpam-4521	366	36	which	which	PRON
ejpam-4521	366	37	u	u	NOUN
ejpam-4521	366	38	,	,	PUNCT
ejpam-4521	366	39	v	v	PROPN
ejpam-4521	366	40	∈	∈	PROPN
ejpam-4521	366	41	v	v	NOUN
ejpam-4521	366	42	(	(	PUNCT
ejpam-4521	366	43	g	g	NOUN
ejpam-4521	366	44	)	)	PUNCT
ejpam-4521	366	45	.	.	PUNCT
ejpam-4521	367	1	now	now	ADV
ejpam-4521	367	2	,	,	PUNCT
ejpam-4521	367	3	we	we	PRON
ejpam-4521	367	4	let	let	VERB
ejpam-4521	367	5	d′	d′	PRON
ejpam-4521	367	6	be	be	AUX
ejpam-4521	367	7	a	a	DET
ejpam-4521	367	8	forcing	forcing	NOUN
ejpam-4521	367	9	subset	subset	NOUN
ejpam-4521	367	10	for	for	ADP
ejpam-4521	367	11	c	c	NOUN
ejpam-4521	367	12	′	′	NOUN
ejpam-4521	367	13	such	such	ADJ
ejpam-4521	367	14	that	that	DET
ejpam-4521	367	15	fγch	fγch	NOUN
ejpam-4521	367	16	,	,	PUNCT
ejpam-4521	367	17	coi(c	coi(c	PROPN
ejpam-4521	367	18	′	′	NOUN
ejpam-4521	367	19	)	)	PUNCT
ejpam-4521	368	1	=	=	VERB
ejpam-4521	368	2	|d′|	|d′|	PROPN
ejpam-4521	368	3	.	.	PROPN
ejpam-4521	368	4	suppose	suppose	VERB
ejpam-4521	368	5	that	that	SCONJ
ejpam-4521	368	6	there	there	PRON
ejpam-4521	368	7	exists	exist	VERB
ejpam-4521	368	8	ab	ab	PROPN
ejpam-4521	368	9	∈	∈	PROPN
ejpam-4521	368	10	e(g	e(g	PROPN
ejpam-4521	368	11	)	)	PUNCT
ejpam-4521	368	12	,	,	PUNCT
ejpam-4521	368	13	for	for	SCONJ
ejpam-4521	368	14	each	each	DET
ejpam-4521	368	15	a	a	NOUN
ejpam-4521	368	16	,	,	PUNCT
ejpam-4521	368	17	b	b	PROPN
ejpam-4521	368	18	∈	∈	PROPN
ejpam-4521	368	19	v	v	NOUN
ejpam-4521	368	20	(	(	PUNCT
ejpam-4521	368	21	g	g	NOUN
ejpam-4521	368	22	)	)	PUNCT
ejpam-4521	368	23	such	such	ADJ
ejpam-4521	368	24	that	that	DET
ejpam-4521	368	25	d′∩qab	d′∩qab	NOUN
ejpam-4521	368	26	=	=	SYM
ejpam-4521	368	27	dab	dab	NOUN
ejpam-4521	368	28	is	be	AUX
ejpam-4521	368	29	not	not	PART
ejpam-4521	368	30	a	a	DET
ejpam-4521	368	31	forcing	forcing	NOUN
ejpam-4521	368	32	subset	subset	NOUN
ejpam-4521	368	33	for	for	ADP
ejpam-4521	368	34	qab	qab	NOUN
ejpam-4521	368	35	.	.	PUNCT
ejpam-4521	369	1	let	let	VERB
ejpam-4521	369	2	q	q	NOUN
ejpam-4521	370	1	′	′	NOUN
ejpam-4521	370	2	ab	ab	PROPN
ejpam-4521	370	3	be	be	AUX
ejpam-4521	370	4	a	a	DET
ejpam-4521	370	5	coi	coi	NOUN
ejpam-4521	370	6	-set	-set	PUNCT
ejpam-4521	370	7	of	of	ADP
ejpam-4521	370	8	hab	hab	NOUN
ejpam-4521	370	9	with	with	ADP
ejpam-4521	370	10	q	q	PROPN
ejpam-4521	370	11	′	′	NUM
ejpam-4521	370	12	ab	ab	PROPN
ejpam-4521	370	13	̸=	̸=	PROPN
ejpam-4521	370	14	qab	qab	NOUN
ejpam-4521	370	15	.	.	PUNCT
ejpam-4521	371	1	then	then	ADV
ejpam-4521	371	2	c	c	X
ejpam-4521	372	1	′′	′′	PROPN
ejpam-4521	372	2	=	=	SYM
ejpam-4521	372	3	v	v	PROPN
ejpam-4521	372	4	(	(	PUNCT
ejpam-4521	372	5	g	g	NOUN
ejpam-4521	372	6	)	)	PUNCT
ejpam-4521	372	7	∪	∪	NOUN
ejpam-4521	372	8	(	(	PUNCT
ejpam-4521	372	9	⋃	⋃	PROPN
ejpam-4521	372	10	uv∈e(g)\{ab	uv∈e(g)\{ab	ADJ
ejpam-4521	372	11	}	}	PUNCT
ejpam-4521	372	12	quv	quv	PROPN
ejpam-4521	372	13	)	)	PUNCT
ejpam-4521	372	14	∪q	∪q	NUM
ejpam-4521	373	1	′	′	NUM
ejpam-4521	373	2	ab	ab	PROPN
ejpam-4521	373	3	is	be	AUX
ejpam-4521	373	4	a	a	DET
ejpam-4521	373	5	γch	γch	NOUN
ejpam-4521	373	6	,	,	PUNCT
ejpam-4521	373	7	coi	coi	NOUN
ejpam-4521	373	8	-	-	PUNCT
ejpam-4521	373	9	set	set	NOUN
ejpam-4521	373	10	of	of	ADP
ejpam-4521	373	11	g⋄h	g⋄h	PROPN
ejpam-4521	373	12	with	with	ADP
ejpam-4521	373	13	c	c	NOUN
ejpam-4521	373	14	′	′	NOUN
ejpam-4521	373	15	̸=	̸=	PROPN
ejpam-4521	373	16	c	c	NOUN
ejpam-4521	373	17	′′	′′	PROPN
ejpam-4521	373	18	and	and	CCONJ
ejpam-4521	373	19	d′	d′	NUM
ejpam-4521	373	20	⊆	⊆	NUM
ejpam-4521	373	21	c	c	PROPN
ejpam-4521	373	22	′′	′′	PROPN
ejpam-4521	373	23	,	,	PUNCT
ejpam-4521	373	24	a	a	DET
ejpam-4521	373	25	contradiction	contradiction	NOUN
ejpam-4521	373	26	.	.	PUNCT
ejpam-4521	374	1	thus	thus	ADV
ejpam-4521	374	2	,	,	PUNCT
ejpam-4521	374	3	cuv	cuv	PROPN
ejpam-4521	374	4	=	=	PROPN
ejpam-4521	374	5	d′∩quv	d′∩quv	PROPN
ejpam-4521	374	6	is	be	AUX
ejpam-4521	374	7	a	a	DET
ejpam-4521	374	8	forcing	forcing	NOUN
ejpam-4521	374	9	subset	subset	NOUN
ejpam-4521	374	10	for	for	ADP
ejpam-4521	374	11	quv	quv	PROPN
ejpam-4521	374	12	for	for	ADP
ejpam-4521	374	13	each	each	DET
ejpam-4521	374	14	uv	uv	PROPN
ejpam-4521	374	15	∈	∈	PROPN
ejpam-4521	374	16	e(g	e(g	PROPN
ejpam-4521	374	17	)	)	PUNCT
ejpam-4521	374	18	where	where	SCONJ
ejpam-4521	374	19	u	u	NOUN
ejpam-4521	374	20	,	,	PUNCT
ejpam-4521	374	21	v	v	PROPN
ejpam-4521	374	22	∈	∈	PROPN
ejpam-4521	374	23	v	v	NOUN
ejpam-4521	374	24	(	(	PUNCT
ejpam-4521	374	25	g	g	NOUN
ejpam-4521	374	26	)	)	PUNCT
ejpam-4521	374	27	.	.	PUNCT
ejpam-4521	375	1	let	let	VERB
ejpam-4521	375	2	c0	c0	PROPN
ejpam-4521	375	3	=	=	PUNCT
ejpam-4521	375	4	⋃	⋃	PROPN
ejpam-4521	375	5	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	375	6	)	)	PUNCT
ejpam-4521	375	7	cuv	cuv	PROPN
ejpam-4521	375	8	.	.	PUNCT
ejpam-4521	376	1	then	then	ADV
ejpam-4521	376	2	fγch	fγch	PROPN
ejpam-4521	376	3	,	,	PUNCT
ejpam-4521	376	4	coi(g	coi(g	PROPN
ejpam-4521	376	5	⋄h	⋄h	PROPN
ejpam-4521	376	6	)	)	PUNCT
ejpam-4521	376	7	=	=	PRON
ejpam-4521	377	1	|d′|	|d′|	PROPN
ejpam-4521	377	2	≥	≥	NUM
ejpam-4521	377	3	|c0|	|c0|	NOUN
ejpam-4521	377	4	=	=	SYM
ejpam-4521	377	5	∑	∑	NOUN
ejpam-4521	377	6	uv∈e(g	uv∈e(g	NUM
ejpam-4521	377	7	)	)	PUNCT
ejpam-4521	378	1	|cuv|	|cuv|	X
ejpam-4521	378	2	≥	≥	NUM
ejpam-4521	378	3	∑	∑	NOUN
ejpam-4521	378	4	uv∈e(g	uv∈e(g	NOUN
ejpam-4521	378	5	)	)	PUNCT
ejpam-4521	378	6	fcoi(huv	fcoi(huv	PROPN
ejpam-4521	378	7	)	)	PUNCT
ejpam-4521	378	8	=	=	SYM
ejpam-4521	378	9	|e(g)|fcoi(h	|e(g)|fcoi(h	NOUN
ejpam-4521	378	10	)	)	PUNCT
ejpam-4521	378	11	.	.	PUNCT
ejpam-4521	379	1	therefore	therefore	ADV
ejpam-4521	379	2	,	,	PUNCT
ejpam-4521	379	3	fγch	fγch	NOUN
ejpam-4521	379	4	,	,	PUNCT
ejpam-4521	379	5	coi(g	coi(g	PROPN
ejpam-4521	379	6	⋄h	⋄h	PROPN
ejpam-4521	379	7	)	)	PUNCT
ejpam-4521	380	1	=	=	PUNCT
ejpam-4521	381	1	p	p	X
ejpam-4521	381	2	[	[	PUNCT
ejpam-4521	381	3	fcoi(h	fcoi(h	PROPN
ejpam-4521	381	4	)	)	PUNCT
ejpam-4521	381	5	]	]	PUNCT
ejpam-4521	381	6	.	.	PUNCT
ejpam-4521	382	1	example	example	NOUN
ejpam-4521	383	1	3	3	NUM
ejpam-4521	383	2	.	.	X
ejpam-4521	384	1	for	for	ADP
ejpam-4521	384	2	complete	complete	ADJ
ejpam-4521	384	3	graph	graph	NOUN
ejpam-4521	384	4	k3	k3	ADJ
ejpam-4521	384	5	and	and	CCONJ
ejpam-4521	384	6	path	path	NOUN
ejpam-4521	384	7	p5	p5	PROPN
ejpam-4521	384	8	,	,	PUNCT
ejpam-4521	384	9	fγch	fγch	PROPN
ejpam-4521	384	10	,	,	PUNCT
ejpam-4521	384	11	coi(k3	coi(k3	PROPN
ejpam-4521	384	12	⋄	⋄	PROPN
ejpam-4521	384	13	p5	p5	PROPN
ejpam-4521	384	14	)	)	PUNCT
ejpam-4521	384	15	=	=	SYM
ejpam-4521	384	16	0	0	PUNCT
ejpam-4521	384	17	since	since	SCONJ
ejpam-4521	384	18	p5	p5	PROPN
ejpam-4521	384	19	has	have	VERB
ejpam-4521	384	20	a	a	DET
ejpam-4521	384	21	unique	unique	ADJ
ejpam-4521	384	22	coi	coi	NOUN
ejpam-4521	384	23	-	-	PUNCT
ejpam-4521	384	24	set	set	NOUN
ejpam-4521	384	25	.	.	PUNCT
ejpam-4521	384	26	example	example	NOUN
ejpam-4521	385	1	4	4	NUM
ejpam-4521	385	2	.	.	X
ejpam-4521	386	1	for	for	ADP
ejpam-4521	386	2	cycle	cycle	NOUN
ejpam-4521	386	3	c3	c3	NOUN
ejpam-4521	386	4	and	and	CCONJ
ejpam-4521	386	5	path	path	NOUN
ejpam-4521	386	6	p2	p2	NOUN
ejpam-4521	386	7	,	,	PUNCT
ejpam-4521	386	8	fγch	fγch	NOUN
ejpam-4521	386	9	,	,	PUNCT
ejpam-4521	386	10	coi(c3	coi(c3	PROPN
ejpam-4521	386	11	⋄	⋄	NOUN
ejpam-4521	386	12	p2	p2	NOUN
ejpam-4521	386	13	)	)	PUNCT
ejpam-4521	387	1	=	=	SYM
ejpam-4521	387	2	3	3	NUM
ejpam-4521	387	3	[	[	PUNCT
ejpam-4521	387	4	fcoi(p2	fcoi(p2	NOUN
ejpam-4521	387	5	)	)	PUNCT
ejpam-4521	387	6	]	]	PUNCT
ejpam-4521	388	1	=	=	SYM
ejpam-4521	388	2	3	3	X
ejpam-4521	388	3	·	·	SYM
ejpam-4521	388	4	1	1	NUM
ejpam-4521	388	5	=	=	SYM
ejpam-4521	388	6	3	3	NUM
ejpam-4521	388	7	since	since	SCONJ
ejpam-4521	388	8	p2	p2	PROPN
ejpam-4521	388	9	has	have	VERB
ejpam-4521	388	10	no	no	DET
ejpam-4521	388	11	unique	unique	ADJ
ejpam-4521	388	12	coi	coi	NOUN
ejpam-4521	388	13	-	-	PUNCT
ejpam-4521	388	14	sets	set	NOUN
ejpam-4521	388	15	.	.	PUNCT
ejpam-4521	389	1	5	5	X
ejpam-4521	389	2	.	.	X
ejpam-4521	389	3	forcing	force	VERB
ejpam-4521	389	4	connected	connected	ADJ
ejpam-4521	389	5	co	co	ADJ
ejpam-4521	389	6	-	-	ADJ
ejpam-4521	389	7	independent	independent	ADJ
ejpam-4521	389	8	hop	hop	NOUN
ejpam-4521	389	9	domination	domination	NOUN
ejpam-4521	389	10	in	in	ADP
ejpam-4521	389	11	the	the	DET
ejpam-4521	389	12	lexicographic	lexicographic	ADJ
ejpam-4521	389	13	product	product	NOUN
ejpam-4521	389	14	of	of	ADP
ejpam-4521	389	15	graphs	graph	NOUN
ejpam-4521	389	16	the	the	DET
ejpam-4521	389	17	following	follow	VERB
ejpam-4521	389	18	is	be	AUX
ejpam-4521	389	19	a	a	DET
ejpam-4521	389	20	restatement	restatement	NOUN
ejpam-4521	389	21	of	of	ADP
ejpam-4521	389	22	corollary	corollary	ADJ
ejpam-4521	389	23	1	1	NUM
ejpam-4521	389	24	.	.	PUNCT
ejpam-4521	389	25	theorem	theorem	NOUN
ejpam-4521	389	26	6	6	NUM
ejpam-4521	389	27	.	.	PUNCT
ejpam-4521	390	1	let	let	VERB
ejpam-4521	390	2	g	g	NOUN
ejpam-4521	391	1	and	and	CCONJ
ejpam-4521	391	2	h	h	NOUN
ejpam-4521	391	3	be	be	VERB
ejpam-4521	391	4	any	any	DET
ejpam-4521	391	5	nontrivial	nontrivial	ADJ
ejpam-4521	391	6	connected	connect	VERB
ejpam-4521	391	7	graphs	graph	NOUN
ejpam-4521	391	8	of	of	ADP
ejpam-4521	391	9	orders	order	NOUN
ejpam-4521	391	10	m	m	VERB
ejpam-4521	391	11	>	>	X
ejpam-4521	391	12	2	2	NUM
ejpam-4521	391	13	and	and	CCONJ
ejpam-4521	391	14	n	n	NOUN
ejpam-4521	391	15	>	>	X
ejpam-4521	391	16	2	2	NUM
ejpam-4521	391	17	,	,	PUNCT
ejpam-4521	391	18	respectively	respectively	ADV
ejpam-4521	391	19	with	with	ADP
ejpam-4521	391	20	γ(h	γ(h	NOUN
ejpam-4521	391	21	)	)	PUNCT
ejpam-4521	391	22	̸=	̸=	PROPN
ejpam-4521	391	23	1	1	NUM
ejpam-4521	391	24	.	.	PUNCT
ejpam-4521	392	1	then	then	ADV
ejpam-4521	392	2	γch	γch	VERB
ejpam-4521	392	3	,	,	PUNCT
ejpam-4521	392	4	coi(g[h	coi(g[h	NUM
ejpam-4521	392	5	]	]	PUNCT
ejpam-4521	392	6	)	)	PUNCT
ejpam-4521	393	1	=	=	SYM
ejpam-4521	393	2	mn−	mn−	NOUN
ejpam-4521	393	3	β(g)β(h	β(g)β(h	NUM
ejpam-4521	393	4	)	)	PUNCT
ejpam-4521	393	5	.	.	PUNCT
ejpam-4521	394	1	y.d	y.d	PROPN
ejpam-4521	394	2	.	.	PROPN
ejpam-4521	394	3	calanza	calanza	PROPN
ejpam-4521	394	4	,	,	PUNCT
ejpam-4521	394	5	h.	h.	PROPN
ejpam-4521	394	6	rara	rara	PROPN
ejpam-4521	394	7	/	/	SYM
ejpam-4521	394	8	eur	eur	PROPN
ejpam-4521	394	9	.	.	PUNCT
ejpam-4521	395	1	j.	j.	PROPN
ejpam-4521	395	2	pure	pure	PROPN
ejpam-4521	395	3	appl	appl	PROPN
ejpam-4521	395	4	.	.	PROPN
ejpam-4521	395	5	math	math	PROPN
ejpam-4521	395	6	,	,	PUNCT
ejpam-4521	395	7	15	15	NUM
ejpam-4521	395	8	(	(	PUNCT
ejpam-4521	395	9	4	4	NUM
ejpam-4521	395	10	)	)	PUNCT
ejpam-4521	395	11	(	(	PUNCT
ejpam-4521	395	12	2022	2022	NUM
ejpam-4521	395	13	)	)	PUNCT
ejpam-4521	395	14	,	,	PUNCT
ejpam-4521	395	15	1597	1597	NUM
ejpam-4521	395	16	-	-	SYM
ejpam-4521	395	17	1612	1612	NUM
ejpam-4521	395	18	1608	1608	NUM
ejpam-4521	395	19	proof	proof	NOUN
ejpam-4521	395	20	:	:	PUNCT
ejpam-4521	395	21	suppose	suppose	VERB
ejpam-4521	395	22	that	that	SCONJ
ejpam-4521	395	23	m	m	PROPN
ejpam-4521	395	24	is	be	AUX
ejpam-4521	395	25	a	a	DET
ejpam-4521	395	26	β	β	NOUN
ejpam-4521	395	27	-	-	PUNCT
ejpam-4521	395	28	set	set	NOUN
ejpam-4521	395	29	of	of	ADP
ejpam-4521	395	30	g	g	PROPN
ejpam-4521	395	31	and	and	CCONJ
ejpam-4521	395	32	n	n	PROPN
ejpam-4521	395	33	is	be	AUX
ejpam-4521	395	34	a	a	DET
ejpam-4521	395	35	β	β	NOUN
ejpam-4521	395	36	-	-	VERB
ejpam-4521	395	37	set	set	NOUN
ejpam-4521	395	38	of	of	ADP
ejpam-4521	395	39	h.	h.	PROPN
ejpam-4521	395	40	set	set	VERB
ejpam-4521	395	41	tx	tx	PROPN
ejpam-4521	395	42	=	=	SYM
ejpam-4521	395	43	v	v	PROPN
ejpam-4521	395	44	(	(	PUNCT
ejpam-4521	395	45	h	h	NOUN
ejpam-4521	395	46	)	)	PUNCT
ejpam-4521	395	47	\n	\n	PUNCT
ejpam-4521	396	1	if	if	SCONJ
ejpam-4521	396	2	x	x	PUNCT
ejpam-4521	396	3	∈	∈	PROPN
ejpam-4521	396	4	m	m	NOUN
ejpam-4521	396	5	and	and	CCONJ
ejpam-4521	396	6	else	else	ADV
ejpam-4521	396	7	set	set	VERB
ejpam-4521	396	8	tx	tx	PROPN
ejpam-4521	396	9	=	=	SYM
ejpam-4521	396	10	v	v	PROPN
ejpam-4521	396	11	(	(	PUNCT
ejpam-4521	396	12	h	h	NOUN
ejpam-4521	396	13	)	)	PUNCT
ejpam-4521	396	14	.	.	PUNCT
ejpam-4521	397	1	then	then	ADV
ejpam-4521	397	2	in	in	ADP
ejpam-4521	397	3	view	view	NOUN
ejpam-4521	397	4	of	of	ADP
ejpam-4521	397	5	theorem	theorem	NOUN
ejpam-4521	397	6	1	1	NUM
ejpam-4521	397	7	,	,	PUNCT
ejpam-4521	397	8	s	s	NOUN
ejpam-4521	397	9	=	=	PUNCT
ejpam-4521	397	10	⋃	⋃	PROPN
ejpam-4521	397	11	x∈v	x∈v	PROPN
ejpam-4521	397	12	(	(	PUNCT
ejpam-4521	397	13	g	g	NOUN
ejpam-4521	397	14	)	)	PUNCT
ejpam-4521	397	15	(	(	PUNCT
ejpam-4521	397	16	{	{	PUNCT
ejpam-4521	397	17	x	x	NOUN
ejpam-4521	397	18	}	}	PUNCT
ejpam-4521	397	19	×	×	PROPN
ejpam-4521	397	20	tx	tx	PROPN
ejpam-4521	397	21	)	)	PUNCT
ejpam-4521	397	22	is	be	AUX
ejpam-4521	397	23	a	a	DET
ejpam-4521	397	24	connected	connected	ADJ
ejpam-4521	397	25	co	co	NOUN
ejpam-4521	397	26	-	-	ADJ
ejpam-4521	397	27	independent	independent	ADJ
ejpam-4521	397	28	hop	hop	NOUN
ejpam-4521	397	29	dominating	dominating	NOUN
ejpam-4521	397	30	set	set	NOUN
ejpam-4521	397	31	of	of	ADP
ejpam-4521	397	32	g[h	g[h	NOUN
ejpam-4521	397	33	]	]	PUNCT
ejpam-4521	397	34	.	.	PUNCT
ejpam-4521	398	1	hence	hence	ADV
ejpam-4521	398	2	,	,	PUNCT
ejpam-4521	398	3	γch	γch	NOUN
ejpam-4521	398	4	,	,	PUNCT
ejpam-4521	398	5	coi(g[h	coi(g[h	NUM
ejpam-4521	398	6	]	]	PUNCT
ejpam-4521	398	7	)	)	PUNCT
ejpam-4521	398	8	≤	≤	NUM
ejpam-4521	398	9	|s|	|s|	PROPN
ejpam-4521	398	10	=	=	SYM
ejpam-4521	398	11	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4521	398	12	⋃	⋃	PROPN
ejpam-4521	398	13	x∈m	x∈m	NOUN
ejpam-4521	398	14	(	(	PUNCT
ejpam-4521	398	15	{	{	PUNCT
ejpam-4521	398	16	x	x	NOUN
ejpam-4521	398	17	}	}	PUNCT
ejpam-4521	398	18	×	×	NOUN
ejpam-4521	398	19	(	(	PUNCT
ejpam-4521	398	20	v	v	NOUN
ejpam-4521	398	21	(	(	PUNCT
ejpam-4521	398	22	h	h	NOUN
ejpam-4521	398	23	)	)	PUNCT
ejpam-4521	398	24	\n	\n	NUM
ejpam-4521	398	25	)	)	PUNCT
ejpam-4521	398	26	)	)	PUNCT
ejpam-4521	398	27	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ejpam-4521	398	28	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4521	398	29	⋃	⋃	PROPN
ejpam-4521	398	30	x∈v	x∈v	PROPN
ejpam-4521	398	31	(	(	PUNCT
ejpam-4521	398	32	g)\m	g)\m	PROPN
ejpam-4521	398	33	(	(	PUNCT
ejpam-4521	398	34	{	{	PUNCT
ejpam-4521	398	35	x	x	NOUN
ejpam-4521	398	36	}	}	PUNCT
ejpam-4521	398	37	×	×	NOUN
ejpam-4521	398	38	v	v	NOUN
ejpam-4521	398	39	(	(	PUNCT
ejpam-4521	398	40	h	h	NOUN
ejpam-4521	398	41	)	)	PUNCT
ejpam-4521	398	42	)	)	PUNCT
ejpam-4521	398	43	∣∣∣∣∣∣	∣∣∣∣∣∣	NOUN
ejpam-4521	399	1	=	=	SYM
ejpam-4521	399	2	|m	|m	NOUN
ejpam-4521	400	1	|	|	ADV
ejpam-4521	400	2	(	(	PUNCT
ejpam-4521	400	3	|v	|v	PROPN
ejpam-4521	400	4	(	(	PUNCT
ejpam-4521	400	5	h)|	h)|	PROPN
ejpam-4521	400	6	−	−	PROPN
ejpam-4521	400	7	|n	|n	NOUN
ejpam-4521	400	8	|	|	ADV
ejpam-4521	400	9	)	)	PUNCT
ejpam-4521	401	1	+	+	CCONJ
ejpam-4521	401	2	(	(	PUNCT
ejpam-4521	401	3	|v	|v	X
ejpam-4521	401	4	(	(	PUNCT
ejpam-4521	401	5	g)|	g)|	NOUN
ejpam-4521	401	6	−	−	NOUN
ejpam-4521	401	7	|m	|m	NOUN
ejpam-4521	401	8	|	|	ADV
ejpam-4521	401	9	)	)	PUNCT
ejpam-4521	401	10	|v	|v	PROPN
ejpam-4521	401	11	(	(	PUNCT
ejpam-4521	401	12	h)|	h)|	NOUN
ejpam-4521	401	13	=	=	SYM
ejpam-4521	401	14	β(g	β(g	PROPN
ejpam-4521	401	15	)	)	PUNCT
ejpam-4521	401	16	(	(	PUNCT
ejpam-4521	401	17	n−	n−	NOUN
ejpam-4521	401	18	β(h	β(h	NOUN
ejpam-4521	401	19	)	)	PUNCT
ejpam-4521	401	20	)	)	PUNCT
ejpam-4521	402	1	+	+	CCONJ
ejpam-4521	402	2	(	(	PUNCT
ejpam-4521	402	3	m−	m−	PROPN
ejpam-4521	402	4	β(g	β(g	PROPN
ejpam-4521	402	5	)	)	PUNCT
ejpam-4521	402	6	)	)	PUNCT
ejpam-4521	403	1	n	n	NOUN
ejpam-4521	403	2	=	=	SYM
ejpam-4521	403	3	(	(	PUNCT
ejpam-4521	403	4	β(g	β(g	PROPN
ejpam-4521	403	5	)	)	PUNCT
ejpam-4521	403	6	)	)	PUNCT
ejpam-4521	404	1	n−	n−	NOUN
ejpam-4521	404	2	β(g)β(h	β(g)β(h	NUM
ejpam-4521	404	3	)	)	PUNCT
ejpam-4521	404	4	+	+	NUM
ejpam-4521	404	5	mn−	mn−	PROPN
ejpam-4521	404	6	(	(	PUNCT
ejpam-4521	404	7	β(g	β(g	PROPN
ejpam-4521	404	8	)	)	PUNCT
ejpam-4521	404	9	)	)	PUNCT
ejpam-4521	405	1	n	n	NOUN
ejpam-4521	405	2	=	=	SYM
ejpam-4521	405	3	mn−	mn−	NOUN
ejpam-4521	405	4	β(g)β(h	β(g)β(h	NUM
ejpam-4521	405	5	)	)	PUNCT
ejpam-4521	405	6	.	.	PUNCT
ejpam-4521	406	1	conversely	conversely	ADV
ejpam-4521	406	2	,	,	PUNCT
ejpam-4521	406	3	suppose	suppose	VERB
ejpam-4521	406	4	that	that	SCONJ
ejpam-4521	406	5	s0	s0	PROPN
ejpam-4521	406	6	=	=	PUNCT
ejpam-4521	406	7	⋃	⋃	PROPN
ejpam-4521	406	8	x∈v	x∈v	PROPN
ejpam-4521	406	9	(	(	PUNCT
ejpam-4521	406	10	g	g	NOUN
ejpam-4521	406	11	)	)	PUNCT
ejpam-4521	406	12	(	(	PUNCT
ejpam-4521	406	13	{	{	PUNCT
ejpam-4521	406	14	x	x	NOUN
ejpam-4521	406	15	}	}	PUNCT
ejpam-4521	406	16	×	×	NOUN
ejpam-4521	406	17	rx	rx	NOUN
ejpam-4521	406	18	)	)	PUNCT
ejpam-4521	406	19	is	be	AUX
ejpam-4521	406	20	a	a	DET
ejpam-4521	406	21	γch	γch	NOUN
ejpam-4521	406	22	,	,	PUNCT
ejpam-4521	406	23	coi	coi	NOUN
ejpam-4521	406	24	-	-	PUNCT
ejpam-4521	406	25	set	set	NOUN
ejpam-4521	406	26	of	of	ADP
ejpam-4521	406	27	g[h	g[h	NOUN
ejpam-4521	406	28	]	]	PUNCT
ejpam-4521	406	29	.	.	PUNCT
ejpam-4521	407	1	let	let	VERB
ejpam-4521	407	2	d	d	NOUN
ejpam-4521	407	3	=	=	PRON
ejpam-4521	407	4	{	{	PUNCT
ejpam-4521	407	5	x	x	PUNCT
ejpam-4521	407	6	∈	∈	PROPN
ejpam-4521	407	7	v	v	NOUN
ejpam-4521	407	8	(	(	PUNCT
ejpam-4521	407	9	g	g	NOUN
ejpam-4521	407	10	)	)	PUNCT
ejpam-4521	407	11	:	:	PUNCT
ejpam-4521	407	12	rx	rx	VERB
ejpam-4521	407	13	=	=	SYM
ejpam-4521	407	14	v	v	ADJ
ejpam-4521	407	15	(	(	PUNCT
ejpam-4521	407	16	h	h	NOUN
ejpam-4521	407	17	)	)	PUNCT
ejpam-4521	407	18	}	}	PUNCT
ejpam-4521	407	19	.	.	PUNCT
ejpam-4521	408	1	we	we	PRON
ejpam-4521	408	2	claim	claim	VERB
ejpam-4521	408	3	that	that	SCONJ
ejpam-4521	408	4	v	v	INTJ
ejpam-4521	408	5	(	(	PUNCT
ejpam-4521	408	6	g	g	NOUN
ejpam-4521	408	7	)	)	PUNCT
ejpam-4521	408	8	\	\	PUNCT
ejpam-4521	409	1	d	d	NOUN
ejpam-4521	409	2	is	be	AUX
ejpam-4521	409	3	an	an	DET
ejpam-4521	409	4	independent	independent	ADJ
ejpam-4521	409	5	set	set	NOUN
ejpam-4521	409	6	of	of	ADP
ejpam-4521	409	7	g.	g.	PROPN
ejpam-4521	409	8	suppose	suppose	VERB
ejpam-4521	409	9	on	on	ADP
ejpam-4521	409	10	the	the	DET
ejpam-4521	409	11	contrary	contrary	NOUN
ejpam-4521	409	12	.	.	PUNCT
ejpam-4521	410	1	then	then	ADV
ejpam-4521	410	2	there	there	PRON
ejpam-4521	410	3	exists	exist	VERB
ejpam-4521	410	4	vertices	vertex	NOUN
ejpam-4521	410	5	x	x	PRON
ejpam-4521	410	6	,	,	PUNCT
ejpam-4521	410	7	y	y	PROPN
ejpam-4521	410	8	∈	∈	PROPN
ejpam-4521	410	9	v	v	ADP
ejpam-4521	410	10	(	(	PUNCT
ejpam-4521	410	11	g	g	NOUN
ejpam-4521	410	12	)	)	PUNCT
ejpam-4521	410	13	\d	\d	NOUN
ejpam-4521	410	14	such	such	ADJ
ejpam-4521	410	15	that	that	AUX
ejpam-4521	410	16	xy	xy	PROPN
ejpam-4521	410	17	∈	∈	PROPN
ejpam-4521	410	18	e(g	e(g	PROPN
ejpam-4521	410	19	)	)	PUNCT
ejpam-4521	410	20	and	and	CCONJ
ejpam-4521	410	21	pick	pick	VERB
ejpam-4521	410	22	a	a	DET
ejpam-4521	410	23	,	,	PUNCT
ejpam-4521	410	24	b	b	PROPN
ejpam-4521	410	25	∈	∈	PROPN
ejpam-4521	410	26	v	v	ADP
ejpam-4521	410	27	(	(	PUNCT
ejpam-4521	410	28	h	h	NOUN
ejpam-4521	410	29	)	)	PUNCT
ejpam-4521	410	30	\	\	NOUN
ejpam-4521	410	31	rx	rx	VERB
ejpam-4521	410	32	for	for	ADP
ejpam-4521	410	33	which	which	PRON
ejpam-4521	410	34	ab	ab	PROPN
ejpam-4521	410	35	∈	∈	PROPN
ejpam-4521	410	36	e(h	e(h	PROPN
ejpam-4521	410	37	)	)	PUNCT
ejpam-4521	410	38	.	.	PUNCT
ejpam-4521	411	1	this	this	PRON
ejpam-4521	411	2	implies	imply	VERB
ejpam-4521	411	3	that	that	SCONJ
ejpam-4521	411	4	(	(	PUNCT
ejpam-4521	411	5	x	x	NOUN
ejpam-4521	411	6	,	,	PUNCT
ejpam-4521	411	7	a)(x	a)(x	PROPN
ejpam-4521	411	8	,	,	PUNCT
ejpam-4521	411	9	b	b	NOUN
ejpam-4521	411	10	)	)	PUNCT
ejpam-4521	411	11	,	,	PUNCT
ejpam-4521	411	12	(	(	PUNCT
ejpam-4521	411	13	y	y	NOUN
ejpam-4521	411	14	,	,	PUNCT
ejpam-4521	411	15	a)(y	a)(y	PROPN
ejpam-4521	411	16	,	,	PUNCT
ejpam-4521	411	17	b	b	X
ejpam-4521	411	18	)	)	PUNCT
ejpam-4521	411	19	∈	∈	NOUN
ejpam-4521	411	20	e(g[h	e(g[h	NOUN
ejpam-4521	411	21	]	]	PUNCT
ejpam-4521	411	22	)	)	PUNCT
ejpam-4521	411	23	,	,	PUNCT
ejpam-4521	411	24	a	a	DET
ejpam-4521	411	25	contradiction	contradiction	NOUN
ejpam-4521	411	26	to	to	ADP
ejpam-4521	411	27	the	the	DET
ejpam-4521	411	28	fact	fact	NOUN
ejpam-4521	411	29	that	that	SCONJ
ejpam-4521	411	30	s0	s0	PROPN
ejpam-4521	411	31	is	be	AUX
ejpam-4521	411	32	a	a	DET
ejpam-4521	411	33	γch	γch	NOUN
ejpam-4521	411	34	,	,	PUNCT
ejpam-4521	411	35	coi	coi	NOUN
ejpam-4521	411	36	-	-	PUNCT
ejpam-4521	411	37	set	set	NOUN
ejpam-4521	411	38	of	of	ADP
ejpam-4521	411	39	g[h	g[h	NOUN
ejpam-4521	411	40	]	]	PUNCT
ejpam-4521	411	41	.	.	PUNCT
ejpam-4521	412	1	thus	thus	ADV
ejpam-4521	412	2	,	,	PUNCT
ejpam-4521	412	3	v	v	INTJ
ejpam-4521	412	4	(	(	PUNCT
ejpam-4521	412	5	g	g	NOUN
ejpam-4521	412	6	)	)	PUNCT
ejpam-4521	412	7	\d	\d	NOUN
ejpam-4521	412	8	is	be	AUX
ejpam-4521	412	9	an	an	DET
ejpam-4521	412	10	independent	independent	ADJ
ejpam-4521	412	11	set	set	NOUN
ejpam-4521	412	12	of	of	ADP
ejpam-4521	412	13	g.	g.	PROPN
ejpam-4521	412	14	hence	hence	ADV
ejpam-4521	412	15	,	,	PUNCT
ejpam-4521	412	16	|v	|v	PROPN
ejpam-4521	412	17	(	(	PUNCT
ejpam-4521	412	18	g	g	NOUN
ejpam-4521	412	19	)	)	PUNCT
ejpam-4521	412	20	\d|	\d|	ADJ
ejpam-4521	412	21	≤	≤	NUM
ejpam-4521	412	22	β(g	β(g	PROPN
ejpam-4521	412	23	)	)	PUNCT
ejpam-4521	412	24	and	and	CCONJ
ejpam-4521	412	25	so	so	ADV
ejpam-4521	412	26	(	(	PUNCT
ejpam-4521	412	27	1	1	X
ejpam-4521	412	28	)	)	PUNCT
ejpam-4521	412	29	|d|	|d|	PROPN
ejpam-4521	412	30	≥	≥	NOUN
ejpam-4521	412	31	m−	m−	PROPN
ejpam-4521	412	32	β(g	β(g	PROPN
ejpam-4521	412	33	)	)	PUNCT
ejpam-4521	412	34	.	.	PUNCT
ejpam-4521	413	1	on	on	ADP
ejpam-4521	413	2	the	the	DET
ejpam-4521	413	3	other	other	ADJ
ejpam-4521	413	4	hand	hand	NOUN
ejpam-4521	413	5	,	,	PUNCT
ejpam-4521	413	6	by	by	ADP
ejpam-4521	413	7	condition	condition	NOUN
ejpam-4521	413	8	(	(	PUNCT
ejpam-4521	413	9	ii	ii	NOUN
ejpam-4521	413	10	)	)	PUNCT
ejpam-4521	413	11	in	in	ADP
ejpam-4521	413	12	theorem	theorem	NOUN
ejpam-4521	413	13	1	1	NUM
ejpam-4521	413	14	,	,	PUNCT
ejpam-4521	413	15	we	we	PRON
ejpam-4521	413	16	have	have	VERB
ejpam-4521	413	17	v	v	NUM
ejpam-4521	413	18	(	(	PUNCT
ejpam-4521	413	19	h	h	NOUN
ejpam-4521	413	20	)	)	PUNCT
ejpam-4521	413	21	\rx	\rx	NOUN
ejpam-4521	413	22	is	be	AUX
ejpam-4521	413	23	an	an	DET
ejpam-4521	413	24	independent	independent	ADJ
ejpam-4521	413	25	set	set	NOUN
ejpam-4521	413	26	of	of	ADP
ejpam-4521	413	27	h.	h.	PROPN
ejpam-4521	413	28	thus	thus	ADV
ejpam-4521	413	29	,	,	PUNCT
ejpam-4521	413	30	|v	|v	PROPN
ejpam-4521	413	31	(	(	PUNCT
ejpam-4521	413	32	h	h	NOUN
ejpam-4521	413	33	)	)	PUNCT
ejpam-4521	413	34	\rx|	\rx|	ADJ
ejpam-4521	413	35	≤	≤	NOUN
ejpam-4521	413	36	β(h	β(h	NUM
ejpam-4521	413	37	)	)	PUNCT
ejpam-4521	413	38	and	and	CCONJ
ejpam-4521	413	39	so	so	ADV
ejpam-4521	413	40	(	(	PUNCT
ejpam-4521	413	41	2	2	X
ejpam-4521	413	42	)	)	PUNCT
ejpam-4521	413	43	|rx|	|rx|	NOUN
ejpam-4521	413	44	≥	≥	NOUN
ejpam-4521	413	45	n−	n−	PROPN
ejpam-4521	413	46	β(h	β(h	NOUN
ejpam-4521	413	47	)	)	PUNCT
ejpam-4521	413	48	.	.	PUNCT
ejpam-4521	414	1	therefore	therefore	ADV
ejpam-4521	414	2	,	,	PUNCT
ejpam-4521	414	3	inequalities	inequality	NOUN
ejpam-4521	414	4	(	(	PUNCT
ejpam-4521	414	5	1	1	NUM
ejpam-4521	414	6	)	)	PUNCT
ejpam-4521	414	7	and	and	CCONJ
ejpam-4521	414	8	(	(	PUNCT
ejpam-4521	414	9	2	2	X
ejpam-4521	414	10	)	)	PUNCT
ejpam-4521	414	11	imply	imply	VERB
ejpam-4521	414	12	γch	γch	NOUN
ejpam-4521	414	13	,	,	PUNCT
ejpam-4521	414	14	coi(g[h	coi(g[h	NUM
ejpam-4521	414	15	]	]	PUNCT
ejpam-4521	414	16	)	)	PUNCT
ejpam-4521	414	17	=	=	SYM
ejpam-4521	414	18	|s0|	|s0|	NOUN
ejpam-4521	414	19	=	=	SYM
ejpam-4521	415	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4521	415	2	⋃	⋃	X
ejpam-4521	415	3	x∈d	x∈d	NOUN
ejpam-4521	415	4	(	(	PUNCT
ejpam-4521	415	5	{	{	PUNCT
ejpam-4521	415	6	x	x	NOUN
ejpam-4521	415	7	}	}	PUNCT
ejpam-4521	415	8	×	×	NOUN
ejpam-4521	415	9	v	v	NOUN
ejpam-4521	415	10	(	(	PUNCT
ejpam-4521	415	11	h	h	NOUN
ejpam-4521	415	12	)	)	PUNCT
ejpam-4521	415	13	)	)	PUNCT
ejpam-4521	415	14	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ejpam-4521	415	15	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4521	415	16	⋃	⋃	PROPN
ejpam-4521	415	17	x∈v	x∈v	PROPN
ejpam-4521	415	18	(	(	PUNCT
ejpam-4521	415	19	g)\d	g)\d	NOUN
ejpam-4521	415	20	(	(	PUNCT
ejpam-4521	415	21	{	{	PUNCT
ejpam-4521	415	22	x	x	NOUN
ejpam-4521	415	23	}	}	PUNCT
ejpam-4521	415	24	×rx	×rx	ADJ
ejpam-4521	415	25	)	)	PUNCT
ejpam-4521	415	26	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4521	415	27	=	=	SYM
ejpam-4521	415	28	|d||v	|d||v	PROPN
ejpam-4521	415	29	(	(	PUNCT
ejpam-4521	415	30	h)|+	h)|+	PROPN
ejpam-4521	415	31	(	(	PUNCT
ejpam-4521	415	32	|v	|v	X
ejpam-4521	415	33	(	(	PUNCT
ejpam-4521	415	34	g)|	g)|	PROPN
ejpam-4521	415	35	−	−	PROPN
ejpam-4521	415	36	|d|	|d|	PROPN
ejpam-4521	415	37	)	)	PUNCT
ejpam-4521	415	38	|rx|	|rx|	NOUN
ejpam-4521	415	39	≥	≥	NOUN
ejpam-4521	415	40	|d|n+	|d|n+	PROPN
ejpam-4521	415	41	(	(	PUNCT
ejpam-4521	415	42	m−	m−	PROPN
ejpam-4521	415	43	|d|	|d|	PROPN
ejpam-4521	415	44	)	)	PUNCT
ejpam-4521	415	45	(	(	PUNCT
ejpam-4521	415	46	n−	n−	NOUN
ejpam-4521	415	47	β(h	β(h	NOUN
ejpam-4521	415	48	)	)	PUNCT
ejpam-4521	415	49	)	)	PUNCT
ejpam-4521	416	1	=	=	PUNCT
ejpam-4521	416	2	|d|n+mn−mβ(h)−	|d|n+mn−mβ(h)−	X
ejpam-4521	416	3	|d|n+	|d|n+	ADJ
ejpam-4521	416	4	|d|β(h	|d|β(h	PROPN
ejpam-4521	416	5	)	)	PUNCT
ejpam-4521	416	6	≥	≥	NOUN
ejpam-4521	416	7	mn−mβ(h	mn−mβ(h	PROPN
ejpam-4521	416	8	)	)	PUNCT
ejpam-4521	417	1	+	+	CCONJ
ejpam-4521	417	2	(	(	PUNCT
ejpam-4521	417	3	m−	m−	PROPN
ejpam-4521	417	4	β(g	β(g	PROPN
ejpam-4521	417	5	)	)	PUNCT
ejpam-4521	417	6	)	)	PUNCT
ejpam-4521	418	1	β(h	β(h	SYM
ejpam-4521	418	2	)	)	PUNCT
ejpam-4521	418	3	=	=	SYM
ejpam-4521	418	4	mn−mβ(h	mn−mβ(h	PROPN
ejpam-4521	418	5	)	)	PUNCT
ejpam-4521	419	1	+	+	NUM
ejpam-4521	419	2	mβ(h)−	mβ(h)−	NOUN
ejpam-4521	419	3	β(g)β(h	β(g)β(h	NOUN
ejpam-4521	419	4	)	)	PUNCT
ejpam-4521	419	5	y.d	y.d	PROPN
ejpam-4521	419	6	.	.	PROPN
ejpam-4521	419	7	calanza	calanza	PROPN
ejpam-4521	419	8	,	,	PUNCT
ejpam-4521	419	9	h.	h.	PROPN
ejpam-4521	419	10	rara	rara	PROPN
ejpam-4521	419	11	/	/	SYM
ejpam-4521	419	12	eur	eur	PROPN
ejpam-4521	419	13	.	.	PUNCT
ejpam-4521	420	1	j.	j.	PROPN
ejpam-4521	420	2	pure	pure	PROPN
ejpam-4521	420	3	appl	appl	PROPN
ejpam-4521	420	4	.	.	PROPN
ejpam-4521	420	5	math	math	PROPN
ejpam-4521	420	6	,	,	PUNCT
ejpam-4521	420	7	15	15	NUM
ejpam-4521	420	8	(	(	PUNCT
ejpam-4521	420	9	4	4	NUM
ejpam-4521	420	10	)	)	PUNCT
ejpam-4521	420	11	(	(	PUNCT
ejpam-4521	420	12	2022	2022	NUM
ejpam-4521	420	13	)	)	PUNCT
ejpam-4521	420	14	,	,	PUNCT
ejpam-4521	420	15	1597	1597	NUM
ejpam-4521	420	16	-	-	SYM
ejpam-4521	420	17	1612	1612	NUM
ejpam-4521	420	18	1609	1609	NUM
ejpam-4521	420	19	=	=	SYM
ejpam-4521	420	20	mn−	mn−	NOUN
ejpam-4521	420	21	β(g)β(h	β(g)β(h	NUM
ejpam-4521	420	22	)	)	PUNCT
ejpam-4521	420	23	.	.	PUNCT
ejpam-4521	421	1	therefore	therefore	ADV
ejpam-4521	421	2	,	,	PUNCT
ejpam-4521	421	3	γch	γch	NOUN
ejpam-4521	421	4	,	,	PUNCT
ejpam-4521	421	5	coi(g[h	coi(g[h	NUM
ejpam-4521	421	6	]	]	PUNCT
ejpam-4521	421	7	)	)	PUNCT
ejpam-4521	421	8	=	=	SYM
ejpam-4521	421	9	mn−	mn−	NOUN
ejpam-4521	421	10	β(g)β(h	β(g)β(h	NUM
ejpam-4521	421	11	)	)	PUNCT
ejpam-4521	421	12	.	.	PUNCT
ejpam-4521	422	1	as	as	ADP
ejpam-4521	422	2	a	a	DET
ejpam-4521	422	3	consequence	consequence	NOUN
ejpam-4521	422	4	of	of	ADP
ejpam-4521	422	5	theorem	theorem	NOUN
ejpam-4521	422	6	6	6	NUM
ejpam-4521	422	7	,	,	PUNCT
ejpam-4521	422	8	the	the	DET
ejpam-4521	422	9	next	next	ADJ
ejpam-4521	422	10	result	result	NOUN
ejpam-4521	422	11	follows	follow	VERB
ejpam-4521	422	12	.	.	PUNCT
ejpam-4521	423	1	corollary	corollary	ADJ
ejpam-4521	423	2	4	4	NUM
ejpam-4521	423	3	.	.	PUNCT
ejpam-4521	424	1	let	let	VERB
ejpam-4521	424	2	g	g	NOUN
ejpam-4521	424	3	and	and	CCONJ
ejpam-4521	424	4	h	h	NOUN
ejpam-4521	424	5	be	be	AUX
ejpam-4521	424	6	nontrivial	nontrivial	ADJ
ejpam-4521	424	7	connected	connect	VERB
ejpam-4521	424	8	graphs	graph	NOUN
ejpam-4521	424	9	with	with	ADP
ejpam-4521	424	10	orders	order	NOUN
ejpam-4521	424	11	m	m	VERB
ejpam-4521	424	12	>	>	X
ejpam-4521	424	13	2	2	NUM
ejpam-4521	424	14	and	and	CCONJ
ejpam-4521	424	15	n	n	NOUN
ejpam-4521	424	16	>	>	X
ejpam-4521	424	17	2	2	NUM
ejpam-4521	424	18	,	,	PUNCT
ejpam-4521	424	19	respectively	respectively	ADV
ejpam-4521	424	20	,	,	PUNCT
ejpam-4521	424	21	and	and	CCONJ
ejpam-4521	424	22	γ(h	γ(h	NOUN
ejpam-4521	424	23	)	)	PUNCT
ejpam-4521	424	24	̸=	̸=	PROPN
ejpam-4521	424	25	1	1	NUM
ejpam-4521	424	26	.	.	PUNCT
ejpam-4521	425	1	then	then	ADV
ejpam-4521	425	2	s	s	VERB
ejpam-4521	425	3	⊆	⊆	NUM
ejpam-4521	425	4	v	v	NOUN
ejpam-4521	425	5	(	(	PUNCT
ejpam-4521	425	6	g[h	g[h	PROPN
ejpam-4521	425	7	]	]	PUNCT
ejpam-4521	425	8	)	)	PUNCT
ejpam-4521	425	9	is	be	AUX
ejpam-4521	425	10	a	a	DET
ejpam-4521	425	11	γch	γch	NOUN
ejpam-4521	425	12	,	,	PUNCT
ejpam-4521	425	13	coi	coi	NOUN
ejpam-4521	425	14	-	-	PUNCT
ejpam-4521	425	15	set	set	NOUN
ejpam-4521	425	16	of	of	ADP
ejpam-4521	425	17	g[h	g[h	NOUN
ejpam-4521	425	18	]	]	PUNCT
ejpam-4521	426	1	if	if	SCONJ
ejpam-4521	426	2	and	and	CCONJ
ejpam-4521	426	3	only	only	ADV
ejpam-4521	426	4	if	if	SCONJ
ejpam-4521	426	5	s	s	X
ejpam-4521	426	6	=	=	PUNCT
ejpam-4521	426	7	⋃	⋃	NOUN
ejpam-4521	426	8	x∈a	x∈a	NOUN
ejpam-4521	426	9	(	(	PUNCT
ejpam-4521	426	10	{	{	PUNCT
ejpam-4521	426	11	x	x	NOUN
ejpam-4521	426	12	}	}	PUNCT
ejpam-4521	426	13	×	×	PROPN
ejpam-4521	426	14	tx	tx	PROPN
ejpam-4521	426	15	)	)	PUNCT
ejpam-4521	426	16	∪	∪	VERB
ejpam-4521	426	17	[	[	X
ejpam-4521	426	18	(	(	PUNCT
ejpam-4521	426	19	v	v	NOUN
ejpam-4521	426	20	(	(	PUNCT
ejpam-4521	426	21	g	g	NOUN
ejpam-4521	426	22	)	)	PUNCT
ejpam-4521	426	23	\a	\a	NUM
ejpam-4521	426	24	)	)	PUNCT
ejpam-4521	427	1	×	×	NOUN
ejpam-4521	427	2	v	v	INTJ
ejpam-4521	427	3	(	(	PUNCT
ejpam-4521	427	4	h	h	NOUN
ejpam-4521	427	5	)	)	PUNCT
ejpam-4521	427	6	]	]	PUNCT
ejpam-4521	427	7	for	for	ADP
ejpam-4521	427	8	some	some	PRON
ejpam-4521	427	9	β	β	NOUN
ejpam-4521	427	10	-	-	PUNCT
ejpam-4521	427	11	set	set	VERB
ejpam-4521	427	12	a	a	PRON
ejpam-4521	427	13	of	of	ADP
ejpam-4521	427	14	g	g	NOUN
ejpam-4521	427	15	such	such	ADJ
ejpam-4521	427	16	that	that	PRON
ejpam-4521	427	17	v	v	NOUN
ejpam-4521	427	18	(	(	PUNCT
ejpam-4521	427	19	h	h	NOUN
ejpam-4521	427	20	)	)	PUNCT
ejpam-4521	427	21	\	\	PROPN
ejpam-4521	427	22	tx	tx	PROPN
ejpam-4521	427	23	is	be	AUX
ejpam-4521	427	24	a	a	DET
ejpam-4521	427	25	β	β	NOUN
ejpam-4521	427	26	-	-	VERB
ejpam-4521	427	27	set	set	NOUN
ejpam-4521	427	28	of	of	ADP
ejpam-4521	427	29	h	h	NOUN
ejpam-4521	427	30	for	for	ADP
ejpam-4521	427	31	all	all	DET
ejpam-4521	427	32	x	x	SYM
ejpam-4521	427	33	∈	∈	NOUN
ejpam-4521	427	34	a.	a.	NOUN
ejpam-4521	427	35	theorem	theorem	NOUN
ejpam-4521	427	36	7	7	NUM
ejpam-4521	427	37	.	.	PUNCT
ejpam-4521	428	1	let	let	VERB
ejpam-4521	428	2	g	g	NOUN
ejpam-4521	429	1	and	and	CCONJ
ejpam-4521	429	2	h	h	NOUN
ejpam-4521	429	3	be	be	AUX
ejpam-4521	429	4	connected	connect	VERB
ejpam-4521	429	5	graphs	graph	NOUN
ejpam-4521	429	6	of	of	ADP
ejpam-4521	429	7	orders	order	NOUN
ejpam-4521	429	8	m	m	VERB
ejpam-4521	429	9	>	>	X
ejpam-4521	429	10	2	2	NUM
ejpam-4521	429	11	and	and	CCONJ
ejpam-4521	429	12	n	n	NOUN
ejpam-4521	429	13	>	>	X
ejpam-4521	429	14	2	2	NUM
ejpam-4521	429	15	,	,	PUNCT
ejpam-4521	429	16	respectively	respectively	ADV
ejpam-4521	429	17	,	,	PUNCT
ejpam-4521	429	18	where	where	SCONJ
ejpam-4521	429	19	h	h	NOUN
ejpam-4521	429	20	has	have	VERB
ejpam-4521	429	21	a	a	DET
ejpam-4521	429	22	unique	unique	ADJ
ejpam-4521	429	23	β	β	NOUN
ejpam-4521	429	24	-	-	ADJ
ejpam-4521	429	25	set	set	VERB
ejpam-4521	429	26	and	and	CCONJ
ejpam-4521	429	27	γ(h	γ(h	NOUN
ejpam-4521	429	28	)	)	PUNCT
ejpam-4521	429	29	̸=	̸=	PROPN
ejpam-4521	429	30	1	1	NUM
ejpam-4521	429	31	.	.	PUNCT
ejpam-4521	430	1	then	then	ADV
ejpam-4521	430	2	fγch	fγch	NOUN
ejpam-4521	430	3	,	,	PUNCT
ejpam-4521	430	4	coi(g[h	coi(g[h	NUM
ejpam-4521	430	5	]	]	PUNCT
ejpam-4521	430	6	)	)	PUNCT
ejpam-4521	431	1	=	=	SYM
ejpam-4521	431	2	{	{	PUNCT
ejpam-4521	431	3	0	0	NUM
ejpam-4521	431	4	,	,	PUNCT
ejpam-4521	431	5	if	if	SCONJ
ejpam-4521	431	6	g	g	PROPN
ejpam-4521	431	7	has	have	VERB
ejpam-4521	431	8	a	a	DET
ejpam-4521	431	9	unique	unique	ADJ
ejpam-4521	431	10	β	β	NOUN
ejpam-4521	431	11	-	-	ADJ
ejpam-4521	431	12	set	set	ADJ
ejpam-4521	431	13	,	,	PUNCT
ejpam-4521	431	14	fβc(g	fβc(g	PROPN
ejpam-4521	431	15	)	)	PUNCT
ejpam-4521	431	16	,	,	PUNCT
ejpam-4521	431	17	if	if	SCONJ
ejpam-4521	431	18	g	g	PROPN
ejpam-4521	431	19	has	have	VERB
ejpam-4521	431	20	no	no	DET
ejpam-4521	431	21	unique	unique	ADJ
ejpam-4521	431	22	β	β	NOUN
ejpam-4521	431	23	-	-	NOUN
ejpam-4521	431	24	set	set	ADJ
ejpam-4521	431	25	.	.	PUNCT
ejpam-4521	432	1	proof	proof	NOUN
ejpam-4521	432	2	:	:	PUNCT
ejpam-4521	432	3	by	by	ADP
ejpam-4521	432	4	corollary	corollary	ADJ
ejpam-4521	432	5	4	4	NUM
ejpam-4521	432	6	,	,	PUNCT
ejpam-4521	432	7	s	s	PART
ejpam-4521	432	8	=	=	PUNCT
ejpam-4521	432	9	[	[	PUNCT
ejpam-4521	432	10	a	a	DET
ejpam-4521	432	11	×	×	PROPN
ejpam-4521	432	12	b	b	X
ejpam-4521	432	13	]	]	PUNCT
ejpam-4521	432	14	∪	∪	X
ejpam-4521	432	15	[	[	PUNCT
ejpam-4521	432	16	ac	ac	PROPN
ejpam-4521	432	17	×	×	PROPN
ejpam-4521	432	18	v	v	PROPN
ejpam-4521	432	19	(	(	PUNCT
ejpam-4521	432	20	h	h	NOUN
ejpam-4521	432	21	)	)	PUNCT
ejpam-4521	432	22	]	]	PUNCT
ejpam-4521	432	23	is	be	AUX
ejpam-4521	432	24	a	a	DET
ejpam-4521	432	25	γch	γch	NOUN
ejpam-4521	432	26	,	,	PUNCT
ejpam-4521	432	27	coi	coi	NOUN
ejpam-4521	432	28	-	-	PUNCT
ejpam-4521	432	29	set	set	NOUN
ejpam-4521	432	30	of	of	ADP
ejpam-4521	432	31	g[h	g[h	NOUN
ejpam-4521	432	32	]	]	PUNCT
ejpam-4521	432	33	for	for	ADP
ejpam-4521	432	34	some	some	PRON
ejpam-4521	432	35	β	β	NOUN
ejpam-4521	432	36	-	-	PUNCT
ejpam-4521	432	37	set	set	VERB
ejpam-4521	432	38	a	a	PRON
ejpam-4521	432	39	of	of	ADP
ejpam-4521	432	40	g	g	NOUN
ejpam-4521	433	1	such	such	ADJ
ejpam-4521	433	2	that	that	PRON
ejpam-4521	433	3	v	v	NOUN
ejpam-4521	433	4	(	(	PUNCT
ejpam-4521	433	5	h	h	NOUN
ejpam-4521	433	6	)	)	PUNCT
ejpam-4521	433	7	\	\	PROPN
ejpam-4521	434	1	b	b	PROPN
ejpam-4521	434	2	is	be	AUX
ejpam-4521	434	3	a	a	DET
ejpam-4521	434	4	β	β	NOUN
ejpam-4521	434	5	-	-	VERB
ejpam-4521	434	6	set	set	NOUN
ejpam-4521	434	7	of	of	ADP
ejpam-4521	434	8	h.	h.	PROPN
ejpam-4521	434	9	suppose	suppose	VERB
ejpam-4521	434	10	that	that	SCONJ
ejpam-4521	434	11	h	h	PROPN
ejpam-4521	434	12	has	have	AUX
ejpam-4521	434	13	unique	unique	ADJ
ejpam-4521	434	14	β	β	NOUN
ejpam-4521	434	15	-	-	NOUN
ejpam-4521	434	16	set	set	ADJ
ejpam-4521	434	17	,	,	PUNCT
ejpam-4521	434	18	say	say	VERB
ejpam-4521	434	19	r.	r.	PROPN
ejpam-4521	434	20	if	if	SCONJ
ejpam-4521	434	21	g	g	PROPN
ejpam-4521	434	22	has	have	VERB
ejpam-4521	434	23	a	a	DET
ejpam-4521	434	24	unique	unique	ADJ
ejpam-4521	434	25	β	β	NOUN
ejpam-4521	434	26	-	-	ADJ
ejpam-4521	434	27	set	set	VERB
ejpam-4521	434	28	m	m	NOUN
ejpam-4521	434	29	,	,	PUNCT
ejpam-4521	434	30	then	then	ADV
ejpam-4521	434	31	g[h	g[h	PROPN
ejpam-4521	434	32	]	]	PUNCT
ejpam-4521	434	33	has	have	VERB
ejpam-4521	434	34	a	a	DET
ejpam-4521	434	35	unique	unique	ADJ
ejpam-4521	434	36	γch	γch	NOUN
ejpam-4521	434	37	,	,	PUNCT
ejpam-4521	434	38	coi	coi	NOUN
ejpam-4521	434	39	-	-	PUNCT
ejpam-4521	434	40	set	set	NOUN
ejpam-4521	434	41	[	[	PUNCT
ejpam-4521	434	42	m	m	NOUN
ejpam-4521	434	43	×r	×r	NOUN
ejpam-4521	434	44	]	]	PUNCT
ejpam-4521	434	45	∪	∪	X
ejpam-4521	434	46	[	[	PUNCT
ejpam-4521	434	47	m	m	NOUN
ejpam-4521	434	48	c	c	NOUN
ejpam-4521	434	49	×	×	PROPN
ejpam-4521	434	50	v	v	NOUN
ejpam-4521	434	51	(	(	PUNCT
ejpam-4521	434	52	h	h	NOUN
ejpam-4521	434	53	)	)	PUNCT
ejpam-4521	434	54	]	]	PUNCT
ejpam-4521	434	55	.	.	PUNCT
ejpam-4521	435	1	by	by	ADP
ejpam-4521	435	2	remark	remark	NOUN
ejpam-4521	435	3	3(i	3(i	NUM
ejpam-4521	435	4	)	)	PUNCT
ejpam-4521	435	5	,	,	PUNCT
ejpam-4521	435	6	fγch	fγch	NOUN
ejpam-4521	435	7	,	,	PUNCT
ejpam-4521	435	8	coi(g[h	coi(g[h	NUM
ejpam-4521	435	9	]	]	PUNCT
ejpam-4521	435	10	)	)	PUNCT
ejpam-4521	435	11	=	=	SYM
ejpam-4521	435	12	0	0	X
ejpam-4521	435	13	.	.	PUNCT
ejpam-4521	436	1	now	now	ADV
ejpam-4521	436	2	,	,	PUNCT
ejpam-4521	436	3	suppose	suppose	VERB
ejpam-4521	436	4	that	that	SCONJ
ejpam-4521	436	5	g	g	PROPN
ejpam-4521	436	6	has	have	VERB
ejpam-4521	436	7	no	no	DET
ejpam-4521	436	8	unique	unique	ADJ
ejpam-4521	436	9	β	β	NOUN
ejpam-4521	436	10	-	-	NOUN
ejpam-4521	436	11	set	set	ADJ
ejpam-4521	436	12	.	.	PUNCT
ejpam-4521	437	1	let	let	VERB
ejpam-4521	437	2	a	a	DET
ejpam-4521	437	3	be	be	AUX
ejpam-4521	437	4	a	a	DET
ejpam-4521	437	5	β	β	NOUN
ejpam-4521	437	6	-	-	NOUN
ejpam-4521	437	7	set	set	NOUN
ejpam-4521	437	8	of	of	ADP
ejpam-4521	437	9	g	g	NOUN
ejpam-4521	437	10	and	and	CCONJ
ejpam-4521	437	11	let	let	VERB
ejpam-4521	437	12	dac	dac	PROPN
ejpam-4521	437	13	be	be	AUX
ejpam-4521	437	14	a	a	DET
ejpam-4521	437	15	forcing	forcing	NOUN
ejpam-4521	437	16	subset	subset	NOUN
ejpam-4521	437	17	for	for	ADP
ejpam-4521	437	18	the	the	DET
ejpam-4521	437	19	complement	complement	NOUN
ejpam-4521	437	20	ac	ac	ADV
ejpam-4521	437	21	of	of	ADP
ejpam-4521	437	22	a	a	DET
ejpam-4521	437	23	such	such	ADJ
ejpam-4521	437	24	that	that	DET
ejpam-4521	437	25	fβc(g	fβc(g	PROPN
ejpam-4521	437	26	)	)	PUNCT
ejpam-4521	437	27	=	=	SYM
ejpam-4521	437	28	fβc(a	fβc(a	PROPN
ejpam-4521	437	29	)	)	PUNCT
ejpam-4521	437	30	=	=	NOUN
ejpam-4521	437	31	|dac	|dac	PROPN
ejpam-4521	437	32	|	|	NOUN
ejpam-4521	437	33	.	.	PUNCT
ejpam-4521	438	1	by	by	ADP
ejpam-4521	438	2	corollary	corollary	ADJ
ejpam-4521	438	3	4	4	NUM
ejpam-4521	438	4	,	,	PUNCT
ejpam-4521	438	5	s	s	PART
ejpam-4521	438	6	=	=	X
ejpam-4521	438	7	[	[	PUNCT
ejpam-4521	438	8	a×r	a×r	X
ejpam-4521	438	9	]	]	PUNCT
ejpam-4521	438	10	∪	∪	X
ejpam-4521	438	11	[	[	PUNCT
ejpam-4521	438	12	ac	ac	PROPN
ejpam-4521	438	13	×	×	PROPN
ejpam-4521	438	14	v	v	PROPN
ejpam-4521	438	15	(	(	PUNCT
ejpam-4521	438	16	h	h	NOUN
ejpam-4521	438	17	)	)	PUNCT
ejpam-4521	438	18	]	]	PUNCT
ejpam-4521	438	19	is	be	AUX
ejpam-4521	438	20	a	a	DET
ejpam-4521	438	21	γch	γch	NOUN
ejpam-4521	438	22	,	,	PUNCT
ejpam-4521	438	23	coi	coi	NOUN
ejpam-4521	438	24	-	-	PUNCT
ejpam-4521	438	25	set	set	NOUN
ejpam-4521	438	26	of	of	ADP
ejpam-4521	438	27	g[h	g[h	NOUN
ejpam-4521	438	28	]	]	PUNCT
ejpam-4521	438	29	.	.	PUNCT
ejpam-4521	439	1	we	we	PRON
ejpam-4521	439	2	claim	claim	VERB
ejpam-4521	439	3	that	that	SCONJ
ejpam-4521	439	4	dac	dac	PROPN
ejpam-4521	439	5	×	×	PROPN
ejpam-4521	439	6	{	{	PUNCT
ejpam-4521	439	7	a	a	PRON
ejpam-4521	439	8	}	}	PUNCT
ejpam-4521	439	9	is	be	AUX
ejpam-4521	439	10	a	a	DET
ejpam-4521	439	11	forcing	forcing	NOUN
ejpam-4521	439	12	subset	subset	NOUN
ejpam-4521	439	13	for	for	ADP
ejpam-4521	439	14	s	s	PRON
ejpam-4521	439	15	for	for	ADP
ejpam-4521	439	16	every	every	PRON
ejpam-4521	439	17	a	a	DET
ejpam-4521	439	18	∈	∈	PROPN
ejpam-4521	439	19	v	v	ADP
ejpam-4521	439	20	(	(	PUNCT
ejpam-4521	439	21	h	h	NOUN
ejpam-4521	439	22	)	)	PUNCT
ejpam-4521	439	23	\	\	PROPN
ejpam-4521	439	24	r.	r.	PROPN
ejpam-4521	439	25	suppose	suppose	VERB
ejpam-4521	439	26	on	on	ADP
ejpam-4521	439	27	the	the	DET
ejpam-4521	439	28	contrary	contrary	NOUN
ejpam-4521	439	29	.	.	PUNCT
ejpam-4521	440	1	then	then	ADV
ejpam-4521	440	2	there	there	PRON
ejpam-4521	440	3	exists	exist	VERB
ejpam-4521	440	4	a	a	DET
ejpam-4521	440	5	γch	γch	NOUN
ejpam-4521	440	6	,	,	PUNCT
ejpam-4521	440	7	coi	coi	NOUN
ejpam-4521	440	8	-	-	PUNCT
ejpam-4521	440	9	set	set	NOUN
ejpam-4521	440	10	s	s	PART
ejpam-4521	440	11	′	′	NOUN
ejpam-4521	440	12	of	of	ADP
ejpam-4521	440	13	g[h	g[h	NOUN
ejpam-4521	440	14	]	]	PUNCT
ejpam-4521	440	15	with	with	ADP
ejpam-4521	440	16	s	s	PRON
ejpam-4521	440	17	′	′	NUM
ejpam-4521	440	18	̸=	̸=	PROPN
ejpam-4521	440	19	s	s	VERB
ejpam-4521	440	20	such	such	ADJ
ejpam-4521	440	21	that	that	PRON
ejpam-4521	440	22	dac	dac	PROPN
ejpam-4521	440	23	×	×	PROPN
ejpam-4521	440	24	{	{	PUNCT
ejpam-4521	440	25	a	a	NOUN
ejpam-4521	440	26	}	}	PUNCT
ejpam-4521	440	27	⊆	⊆	NUM
ejpam-4521	440	28	s	s	NOUN
ejpam-4521	440	29	′	′	NOUN
ejpam-4521	440	30	.	.	PUNCT
ejpam-4521	441	1	then	then	ADV
ejpam-4521	441	2	s	s	VERB
ejpam-4521	441	3	′	′	NOUN
ejpam-4521	441	4	=	=	PUNCT
ejpam-4521	442	1	[	[	PUNCT
ejpam-4521	442	2	a	a	DET
ejpam-4521	442	3	′	′	NUM
ejpam-4521	442	4	×	×	NOUN
ejpam-4521	442	5	r	r	NOUN
ejpam-4521	442	6	]	]	PUNCT
ejpam-4521	442	7	∪	∪	X
ejpam-4521	442	8	[	[	PUNCT
ejpam-4521	442	9	(	(	PUNCT
ejpam-4521	442	10	a	a	DET
ejpam-4521	442	11	′	′	NOUN
ejpam-4521	442	12	)	)	PUNCT
ejpam-4521	443	1	c	c	NOUN
ejpam-4521	443	2	×	×	PROPN
ejpam-4521	443	3	v	v	NOUN
ejpam-4521	443	4	(	(	PUNCT
ejpam-4521	443	5	h	h	NOUN
ejpam-4521	443	6	)	)	PUNCT
ejpam-4521	443	7	]	]	PUNCT
ejpam-4521	443	8	for	for	SCONJ
ejpam-4521	443	9	some	some	PRON
ejpam-4521	443	10	β	β	NOUN
ejpam-4521	443	11	-	-	VERB
ejpam-4521	443	12	set	set	VERB
ejpam-4521	443	13	a	a	DET
ejpam-4521	443	14	′	′	NOUN
ejpam-4521	443	15	of	of	ADP
ejpam-4521	443	16	g.	g.	PROPN
ejpam-4521	443	17	since	since	SCONJ
ejpam-4521	443	18	s	s	PROPN
ejpam-4521	443	19	′	′	NUM
ejpam-4521	443	20	̸=	̸=	PROPN
ejpam-4521	443	21	s	s	PROPN
ejpam-4521	443	22	,	,	PUNCT
ejpam-4521	443	23	a	a	DET
ejpam-4521	443	24	′	′	NUM
ejpam-4521	443	25	̸=	̸=	PROPN
ejpam-4521	443	26	a	a	PRON
ejpam-4521	443	27	and	and	CCONJ
ejpam-4521	443	28	dac	dac	PROPN
ejpam-4521	443	29	×	×	PROPN
ejpam-4521	443	30	{	{	PUNCT
ejpam-4521	443	31	a	a	NOUN
ejpam-4521	443	32	}	}	PUNCT
ejpam-4521	443	33	⊆	⊆	NUM
ejpam-4521	443	34	(	(	PUNCT
ejpam-4521	443	35	a	a	DET
ejpam-4521	443	36	′	′	NOUN
ejpam-4521	443	37	)	)	PUNCT
ejpam-4521	444	1	c	c	NOUN
ejpam-4521	444	2	×	×	PROPN
ejpam-4521	444	3	v	v	NOUN
ejpam-4521	444	4	(	(	PUNCT
ejpam-4521	444	5	h	h	NOUN
ejpam-4521	444	6	)	)	PUNCT
ejpam-4521	444	7	.	.	PUNCT
ejpam-4521	445	1	thus	thus	ADV
ejpam-4521	445	2	,	,	PUNCT
ejpam-4521	445	3	dac	dac	NOUN
ejpam-4521	445	4	⊆	⊆	NUM
ejpam-4521	445	5	(	(	PUNCT
ejpam-4521	445	6	a	a	DET
ejpam-4521	445	7	′	′	NOUN
ejpam-4521	445	8	)	)	PUNCT
ejpam-4521	445	9	c	c	NOUN
ejpam-4521	445	10	a	a	DET
ejpam-4521	445	11	contradiction	contradiction	NOUN
ejpam-4521	445	12	since	since	SCONJ
ejpam-4521	445	13	dac	dac	NOUN
ejpam-4521	445	14	is	be	AUX
ejpam-4521	445	15	a	a	DET
ejpam-4521	445	16	forcing	forcing	NOUN
ejpam-4521	445	17	subset	subset	NOUN
ejpam-4521	445	18	for	for	ADP
ejpam-4521	445	19	ac	ac	PROPN
ejpam-4521	445	20	.	.	PUNCT
ejpam-4521	446	1	hence	hence	ADV
ejpam-4521	446	2	,	,	PUNCT
ejpam-4521	446	3	dac	dac	PROPN
ejpam-4521	446	4	×	×	PROPN
ejpam-4521	446	5	{	{	PUNCT
ejpam-4521	446	6	a	a	PRON
ejpam-4521	446	7	}	}	PUNCT
ejpam-4521	446	8	is	be	AUX
ejpam-4521	446	9	a	a	DET
ejpam-4521	446	10	forcing	forcing	NOUN
ejpam-4521	446	11	subset	subset	NOUN
ejpam-4521	446	12	for	for	ADP
ejpam-4521	446	13	s.	s.	PROPN
ejpam-4521	446	14	thus	thus	ADV
ejpam-4521	446	15	,	,	PUNCT
ejpam-4521	446	16	fγch	fγch	NOUN
ejpam-4521	446	17	,	,	PUNCT
ejpam-4521	446	18	coi(g[h	coi(g[h	NUM
ejpam-4521	446	19	]	]	PUNCT
ejpam-4521	446	20	)	)	PUNCT
ejpam-4521	446	21	≤	≤	NUM
ejpam-4521	446	22	fγch	fγch	NOUN
ejpam-4521	446	23	,	,	PUNCT
ejpam-4521	446	24	coi(s	coi(s	NUM
ejpam-4521	446	25	)	)	PUNCT
ejpam-4521	446	26	≤	≤	NUM
ejpam-4521	446	27	|dac	|dac	PROPN
ejpam-4521	446	28	×	×	NOUN
ejpam-4521	446	29	{	{	PUNCT
ejpam-4521	446	30	a}|	a}|	PROPN
ejpam-4521	446	31	=	=	SYM
ejpam-4521	447	1	|dac	|dac	PROPN
ejpam-4521	447	2	|	|	NOUN
ejpam-4521	447	3	=	=	SYM
ejpam-4521	447	4	fβc(g	fβc(g	PROPN
ejpam-4521	447	5	)	)	PUNCT
ejpam-4521	447	6	.	.	PUNCT
ejpam-4521	448	1	let	let	VERB
ejpam-4521	448	2	s0	s0	PROPN
ejpam-4521	448	3	=	=	PUNCT
ejpam-4521	448	4	[	[	PUNCT
ejpam-4521	448	5	a0	a0	PROPN
ejpam-4521	448	6	×	×	NOUN
ejpam-4521	448	7	r	r	NOUN
ejpam-4521	448	8	]	]	PUNCT
ejpam-4521	448	9	∪	∪	X
ejpam-4521	448	10	[	[	PUNCT
ejpam-4521	448	11	ac	ac	PROPN
ejpam-4521	448	12	0	0	NUM
ejpam-4521	448	13	×	×	PROPN
ejpam-4521	448	14	v	v	NOUN
ejpam-4521	448	15	(	(	PUNCT
ejpam-4521	448	16	h	h	NOUN
ejpam-4521	448	17	)	)	PUNCT
ejpam-4521	448	18	]	]	PUNCT
ejpam-4521	448	19	be	be	AUX
ejpam-4521	448	20	a	a	DET
ejpam-4521	448	21	γch	γch	NOUN
ejpam-4521	448	22	,	,	PUNCT
ejpam-4521	448	23	coi	coi	NOUN
ejpam-4521	448	24	-	-	PUNCT
ejpam-4521	448	25	set	set	NOUN
ejpam-4521	448	26	of	of	ADP
ejpam-4521	448	27	g[h	g[h	NOUN
ejpam-4521	448	28	]	]	PUNCT
ejpam-4521	448	29	such	such	ADJ
ejpam-4521	448	30	that	that	DET
ejpam-4521	448	31	fγch	fγch	NOUN
ejpam-4521	448	32	,	,	PUNCT
ejpam-4521	448	33	coi(g[h	coi(g[h	NUM
ejpam-4521	448	34	]	]	PUNCT
ejpam-4521	448	35	)	)	PUNCT
ejpam-4521	449	1	=	=	SYM
ejpam-4521	449	2	fγch	fγch	PROPN
ejpam-4521	449	3	,	,	PUNCT
ejpam-4521	449	4	coi(s0	coi(s0	PROPN
ejpam-4521	449	5	)	)	PUNCT
ejpam-4521	449	6	.	.	PUNCT
ejpam-4521	450	1	by	by	ADP
ejpam-4521	450	2	corollary	corollary	ADJ
ejpam-4521	450	3	4	4	NUM
ejpam-4521	450	4	,	,	PUNCT
ejpam-4521	450	5	a0	a0	PROPN
ejpam-4521	450	6	is	be	AUX
ejpam-4521	450	7	β	β	NOUN
ejpam-4521	450	8	-	-	PUNCT
ejpam-4521	450	9	set	set	NOUN
ejpam-4521	450	10	of	of	ADP
ejpam-4521	450	11	g.	g.	PROPN
ejpam-4521	450	12	let	let	VERB
ejpam-4521	450	13	f0	f0	PROPN
ejpam-4521	450	14	be	be	AUX
ejpam-4521	450	15	a	a	DET
ejpam-4521	450	16	forcing	forcing	NOUN
ejpam-4521	450	17	subset	subset	NOUN
ejpam-4521	450	18	for	for	ADP
ejpam-4521	450	19	s0	s0	PROPN
ejpam-4521	450	20	with	with	ADP
ejpam-4521	450	21	fγch	fγch	PROPN
ejpam-4521	450	22	,	,	PUNCT
ejpam-4521	450	23	coi(s0	coi(s0	PROPN
ejpam-4521	450	24	)	)	PUNCT
ejpam-4521	450	25	=	=	NOUN
ejpam-4521	450	26	|f0|	|f0|	NOUN
ejpam-4521	450	27	.	.	PUNCT
ejpam-4521	451	1	let	let	VERB
ejpam-4521	451	2	f0	f0	VERB
ejpam-4521	451	3	=	=	PUNCT
ejpam-4521	451	4	⋃	⋃	PROPN
ejpam-4521	451	5	x∈k	x∈k	X
ejpam-4521	451	6	(	(	PUNCT
ejpam-4521	451	7	{	{	PUNCT
ejpam-4521	451	8	x	x	NOUN
ejpam-4521	451	9	}	}	PUNCT
ejpam-4521	451	10	×	×	PROPN
ejpam-4521	451	11	tx	tx	PROPN
ejpam-4521	451	12	)	)	PUNCT
ejpam-4521	451	13	.	.	PUNCT
ejpam-4521	452	1	we	we	PRON
ejpam-4521	452	2	claim	claim	VERB
ejpam-4521	452	3	that	that	SCONJ
ejpam-4521	452	4	k	k	PROPN
ejpam-4521	452	5	⊆	⊆	NUM
ejpam-4521	452	6	ac	ac	PROPN
ejpam-4521	452	7	0	0	NUM
ejpam-4521	452	8	y.d	y.d	PROPN
ejpam-4521	452	9	.	.	PROPN
ejpam-4521	452	10	calanza	calanza	PROPN
ejpam-4521	452	11	,	,	PUNCT
ejpam-4521	452	12	h.	h.	PROPN
ejpam-4521	452	13	rara	rara	PROPN
ejpam-4521	452	14	/	/	SYM
ejpam-4521	452	15	eur	eur	PROPN
ejpam-4521	452	16	.	.	PUNCT
ejpam-4521	453	1	j.	j.	PROPN
ejpam-4521	453	2	pure	pure	PROPN
ejpam-4521	453	3	appl	appl	PROPN
ejpam-4521	453	4	.	.	PROPN
ejpam-4521	453	5	math	math	PROPN
ejpam-4521	453	6	,	,	PUNCT
ejpam-4521	453	7	15	15	NUM
ejpam-4521	453	8	(	(	PUNCT
ejpam-4521	453	9	4	4	NUM
ejpam-4521	453	10	)	)	PUNCT
ejpam-4521	453	11	(	(	PUNCT
ejpam-4521	453	12	2022	2022	NUM
ejpam-4521	453	13	)	)	PUNCT
ejpam-4521	453	14	,	,	PUNCT
ejpam-4521	453	15	1597	1597	NUM
ejpam-4521	453	16	-	-	SYM
ejpam-4521	453	17	1612	1612	NUM
ejpam-4521	453	18	1610	1610	NUM
ejpam-4521	453	19	and	and	CCONJ
ejpam-4521	453	20	tx	tx	VERB
ejpam-4521	453	21	⊆	⊆	NUM
ejpam-4521	453	22	v	v	NOUN
ejpam-4521	453	23	(	(	PUNCT
ejpam-4521	453	24	h	h	NOUN
ejpam-4521	453	25	)	)	PUNCT
ejpam-4521	453	26	.	.	PUNCT
ejpam-4521	454	1	let	let	VERB
ejpam-4521	454	2	k	k	NOUN
ejpam-4521	454	3	=	=	PUNCT
ejpam-4521	454	4	k1∪k2	k1∪k2	X
ejpam-4521	454	5	where	where	SCONJ
ejpam-4521	454	6	k1∩k2	k1∩k2	NOUN
ejpam-4521	454	7	=	=	PUNCT
ejpam-4521	454	8	∅.	∅.	AUX
ejpam-4521	454	9	suppose	suppose	VERB
ejpam-4521	454	10	that	that	SCONJ
ejpam-4521	454	11	k	k	PROPN
ejpam-4521	454	12	⊆	⊆	NUM
ejpam-4521	454	13	a0	a0	NOUN
ejpam-4521	454	14	or	or	CCONJ
ejpam-4521	454	15	k1	k1	NOUN
ejpam-4521	454	16	⊆	⊆	NUM
ejpam-4521	454	17	a0	a0	NOUN
ejpam-4521	454	18	and	and	CCONJ
ejpam-4521	454	19	k2	k2	PROPN
ejpam-4521	454	20	⊆	⊆	NUM
ejpam-4521	454	21	ac	ac	PROPN
ejpam-4521	454	22	0	0	NUM
ejpam-4521	454	23	.	.	PUNCT
ejpam-4521	455	1	let	let	VERB
ejpam-4521	455	2	b0	b0	NOUN
ejpam-4521	455	3	be	be	AUX
ejpam-4521	455	4	a	a	DET
ejpam-4521	455	5	β	β	NOUN
ejpam-4521	455	6	-	-	NOUN
ejpam-4521	455	7	set	set	NOUN
ejpam-4521	455	8	of	of	ADP
ejpam-4521	455	9	g	g	NOUN
ejpam-4521	455	10	with	with	ADP
ejpam-4521	455	11	b0	b0	NOUN
ejpam-4521	455	12	̸=	̸=	PROPN
ejpam-4521	455	13	a0	a0	NOUN
ejpam-4521	455	14	.	.	PUNCT
ejpam-4521	456	1	consider	consider	VERB
ejpam-4521	456	2	the	the	DET
ejpam-4521	456	3	γch	γch	NOUN
ejpam-4521	456	4	,	,	PUNCT
ejpam-4521	456	5	coi	coi	NOUN
ejpam-4521	456	6	-	-	PUNCT
ejpam-4521	456	7	set	set	NOUN
ejpam-4521	456	8	s	s	PART
ejpam-4521	456	9	′	′	NOUN
ejpam-4521	456	10	0	0	NUM
ejpam-4521	457	1	=	=	PUNCT
ejpam-4521	457	2	[	[	PUNCT
ejpam-4521	457	3	b0	b0	NOUN
ejpam-4521	457	4	×r	×r	NUM
ejpam-4521	457	5	]	]	PUNCT
ejpam-4521	457	6	∪	∪	PROPN
ejpam-4521	457	7	[	[	PUNCT
ejpam-4521	457	8	bc	bc	PROPN
ejpam-4521	457	9	0	0	NUM
ejpam-4521	457	10	×	×	PROPN
ejpam-4521	457	11	v	v	NOUN
ejpam-4521	457	12	(	(	PUNCT
ejpam-4521	457	13	h	h	NOUN
ejpam-4521	457	14	)	)	PUNCT
ejpam-4521	457	15	]	]	PUNCT
ejpam-4521	457	16	.	.	PUNCT
ejpam-4521	458	1	then	then	ADV
ejpam-4521	458	2	s	s	VERB
ejpam-4521	458	3	′	′	NOUN
ejpam-4521	458	4	0	0	NUM
ejpam-4521	459	1	̸=	̸=	PROPN
ejpam-4521	459	2	s0	s0	NOUN
ejpam-4521	459	3	.	.	PUNCT
ejpam-4521	460	1	if	if	SCONJ
ejpam-4521	460	2	a0	a0	PROPN
ejpam-4521	460	3	∩b0	∩b0	PROPN
ejpam-4521	461	1	=	=	NOUN
ejpam-4521	461	2	∅	∅	NOUN
ejpam-4521	461	3	,	,	PUNCT
ejpam-4521	461	4	then	then	ADV
ejpam-4521	461	5	k	k	PROPN
ejpam-4521	461	6	⊆	⊆	NUM
ejpam-4521	461	7	bc	bc	PROPN
ejpam-4521	461	8	0	0	NUM
ejpam-4521	461	9	and	and	CCONJ
ejpam-4521	461	10	f0	f0	PROPN
ejpam-4521	461	11	⊆	⊆	NUM
ejpam-4521	461	12	k	k	PROPN
ejpam-4521	461	13	×r	×r	NUM
ejpam-4521	461	14	⊆	⊆	NUM
ejpam-4521	461	15	bc	bc	PROPN
ejpam-4521	461	16	0	0	NUM
ejpam-4521	461	17	×	×	PROPN
ejpam-4521	461	18	v	v	NOUN
ejpam-4521	461	19	(	(	PUNCT
ejpam-4521	461	20	h	h	NOUN
ejpam-4521	461	21	)	)	PUNCT
ejpam-4521	462	1	⊆	⊆	NUM
ejpam-4521	462	2	s	s	NOUN
ejpam-4521	462	3	′	′	NOUN
ejpam-4521	462	4	0	0	NUM
ejpam-4521	462	5	or	or	CCONJ
ejpam-4521	462	6	f0	f0	VERB
ejpam-4521	462	7	⊆	⊆	NUM
ejpam-4521	462	8	[	[	PUNCT
ejpam-4521	462	9	k1	k1	NOUN
ejpam-4521	462	10	×r	×r	X
ejpam-4521	462	11	]	]	PUNCT
ejpam-4521	462	12	∪	∪	PROPN
ejpam-4521	462	13	[	[	PUNCT
ejpam-4521	462	14	k2	k2	ADJ
ejpam-4521	462	15	×	×	PROPN
ejpam-4521	462	16	v	v	NOUN
ejpam-4521	462	17	(	(	PUNCT
ejpam-4521	462	18	h	h	NOUN
ejpam-4521	462	19	)	)	PUNCT
ejpam-4521	462	20	]	]	PUNCT
ejpam-4521	463	1	⊆	⊆	X
ejpam-4521	463	2	(	(	PUNCT
ejpam-4521	463	3	k1	k1	X
ejpam-4521	463	4	∪k2)×	∪k2)×	X
ejpam-4521	463	5	v	v	NOUN
ejpam-4521	463	6	(	(	PUNCT
ejpam-4521	463	7	h	h	NOUN
ejpam-4521	463	8	)	)	PUNCT
ejpam-4521	463	9	⊆	⊆	NUM
ejpam-4521	463	10	bc	bc	PROPN
ejpam-4521	463	11	0	0	NUM
ejpam-4521	463	12	×	×	PROPN
ejpam-4521	463	13	v	v	NOUN
ejpam-4521	463	14	(	(	PUNCT
ejpam-4521	463	15	h	h	NOUN
ejpam-4521	463	16	)	)	PUNCT
ejpam-4521	463	17	⊆	⊆	NUM
ejpam-4521	463	18	s	s	NOUN
ejpam-4521	463	19	′	′	NOUN
ejpam-4521	463	20	0	0	NUM
ejpam-4521	463	21	.	.	PUNCT
ejpam-4521	464	1	on	on	ADP
ejpam-4521	464	2	the	the	DET
ejpam-4521	464	3	other	other	ADJ
ejpam-4521	464	4	hand	hand	NOUN
ejpam-4521	464	5	,	,	PUNCT
ejpam-4521	464	6	if	if	SCONJ
ejpam-4521	464	7	a0	a0	PROPN
ejpam-4521	464	8	∩b0	∩b0	PROPN
ejpam-4521	464	9	̸=	̸=	PROPN
ejpam-4521	464	10	∅	∅	NOUN
ejpam-4521	464	11	and	and	CCONJ
ejpam-4521	464	12	k1	k1	VERB
ejpam-4521	464	13	⊆	⊆	NUM
ejpam-4521	464	14	b0	b0	NOUN
ejpam-4521	464	15	and	and	CCONJ
ejpam-4521	464	16	k2	k2	PROPN
ejpam-4521	464	17	⊆	⊆	NUM
ejpam-4521	464	18	bc	bc	PROPN
ejpam-4521	464	19	0	0	NUM
ejpam-4521	464	20	,	,	PUNCT
ejpam-4521	464	21	then	then	ADV
ejpam-4521	464	22	f0	f0	PROPN
ejpam-4521	464	23	⊆	⊆	NUM
ejpam-4521	464	24	[	[	PUNCT
ejpam-4521	464	25	k	k	X
ejpam-4521	464	26	×r	×r	X
ejpam-4521	464	27	]	]	PUNCT
ejpam-4521	464	28	⊆	⊆	NUM
ejpam-4521	464	29	[	[	PUNCT
ejpam-4521	464	30	k1	k1	NOUN
ejpam-4521	464	31	×r	×r	X
ejpam-4521	464	32	]	]	PUNCT
ejpam-4521	464	33	∪	∪	PROPN
ejpam-4521	464	34	[	[	PUNCT
ejpam-4521	464	35	k2	k2	ADJ
ejpam-4521	464	36	×	×	PROPN
ejpam-4521	464	37	v	v	NOUN
ejpam-4521	464	38	(	(	PUNCT
ejpam-4521	464	39	h	h	NOUN
ejpam-4521	464	40	)	)	PUNCT
ejpam-4521	464	41	]	]	PUNCT
ejpam-4521	465	1	⊆	⊆	NUM
ejpam-4521	465	2	[	[	PUNCT
ejpam-4521	465	3	b0	b0	NOUN
ejpam-4521	465	4	×r	×r	PUNCT
ejpam-4521	465	5	]	]	PUNCT
ejpam-4521	465	6	∪	∪	PROPN
ejpam-4521	465	7	[	[	PUNCT
ejpam-4521	465	8	bc	bc	PROPN
ejpam-4521	465	9	0	0	NUM
ejpam-4521	465	10	×	×	PROPN
ejpam-4521	465	11	v	v	NOUN
ejpam-4521	465	12	(	(	PUNCT
ejpam-4521	465	13	h	h	NOUN
ejpam-4521	465	14	)	)	PUNCT
ejpam-4521	465	15	]	]	PUNCT
ejpam-4521	466	1	=	=	PUNCT
ejpam-4521	466	2	s	s	VERB
ejpam-4521	466	3	′	′	NUM
ejpam-4521	466	4	0	0	NUM
ejpam-4521	466	5	.	.	PUNCT
ejpam-4521	467	1	in	in	ADP
ejpam-4521	467	2	either	either	DET
ejpam-4521	467	3	case	case	NOUN
ejpam-4521	467	4	,	,	PUNCT
ejpam-4521	467	5	we	we	PRON
ejpam-4521	467	6	have	have	VERB
ejpam-4521	467	7	a	a	DET
ejpam-4521	467	8	contradiction	contradiction	NOUN
ejpam-4521	467	9	since	since	SCONJ
ejpam-4521	467	10	f0	f0	PROPN
ejpam-4521	467	11	is	be	AUX
ejpam-4521	467	12	a	a	DET
ejpam-4521	467	13	forcing	forcing	NOUN
ejpam-4521	467	14	subset	subset	NOUN
ejpam-4521	467	15	for	for	ADP
ejpam-4521	467	16	s0	s0	PROPN
ejpam-4521	467	17	.	.	PUNCT
ejpam-4521	468	1	hence	hence	ADV
ejpam-4521	468	2	,	,	PUNCT
ejpam-4521	468	3	k	k	PROPN
ejpam-4521	468	4	⊆	⊆	NUM
ejpam-4521	468	5	ac	ac	PROPN
ejpam-4521	468	6	0	0	NUM
ejpam-4521	468	7	and	and	CCONJ
ejpam-4521	468	8	tx	tx	VERB
ejpam-4521	468	9	⊆	⊆	NUM
ejpam-4521	468	10	v	v	NOUN
ejpam-4521	468	11	(	(	PUNCT
ejpam-4521	468	12	h	h	NOUN
ejpam-4521	468	13	)	)	PUNCT
ejpam-4521	468	14	.	.	PUNCT
ejpam-4521	469	1	this	this	PRON
ejpam-4521	469	2	implies	imply	VERB
ejpam-4521	469	3	that	that	SCONJ
ejpam-4521	469	4	k	k	PROPN
ejpam-4521	469	5	is	be	AUX
ejpam-4521	469	6	a	a	DET
ejpam-4521	469	7	forcing	forcing	NOUN
ejpam-4521	469	8	subset	subset	NOUN
ejpam-4521	469	9	for	for	ADP
ejpam-4521	469	10	ac	ac	PROPN
ejpam-4521	469	11	0	0	NUM
ejpam-4521	469	12	.	.	PUNCT
ejpam-4521	470	1	choose	choose	VERB
ejpam-4521	470	2	any	any	DET
ejpam-4521	470	3	x	x	SYM
ejpam-4521	470	4	∈	∈	PROPN
ejpam-4521	470	5	k	k	PROPN
ejpam-4521	470	6	and	and	CCONJ
ejpam-4521	470	7	a	a	DET
ejpam-4521	470	8	∈	∈	PROPN
ejpam-4521	470	9	tx	tx	PROPN
ejpam-4521	470	10	.	.	PUNCT
ejpam-4521	471	1	then	then	ADV
ejpam-4521	471	2	fa	fa	PROPN
ejpam-4521	472	1	=	=	SYM
ejpam-4521	472	2	k	k	PROPN
ejpam-4521	472	3	×	×	PROPN
ejpam-4521	472	4	{	{	PUNCT
ejpam-4521	472	5	a	a	NOUN
ejpam-4521	472	6	}	}	PUNCT
ejpam-4521	472	7	⊆	⊆	NUM
ejpam-4521	472	8	f0	f0	NOUN
ejpam-4521	472	9	.	.	PUNCT
ejpam-4521	473	1	thus	thus	ADV
ejpam-4521	473	2	,	,	PUNCT
ejpam-4521	473	3	fγch	fγch	ADJ
ejpam-4521	473	4	,	,	PUNCT
ejpam-4521	473	5	coi(g[h	coi(g[h	NUM
ejpam-4521	473	6	]	]	PUNCT
ejpam-4521	473	7	)	)	PUNCT
ejpam-4521	474	1	=	=	SYM
ejpam-4521	474	2	fγch	fγch	PROPN
ejpam-4521	474	3	,	,	PUNCT
ejpam-4521	474	4	coi(s0	coi(s0	PROPN
ejpam-4521	474	5	)	)	PUNCT
ejpam-4521	474	6	=	=	PUNCT
ejpam-4521	474	7	|f0|	|f0|	NOUN
ejpam-4521	474	8	≥	≥	PRON
ejpam-4521	474	9	|fa|	|fa|	PROPN
ejpam-4521	474	10	=	=	PUNCT
ejpam-4521	474	11	|k|	|k|	PROPN
ejpam-4521	474	12	≥	≥	NOUN
ejpam-4521	474	13	fβc(a0	fβc(a0	VERB
ejpam-4521	474	14	)	)	PUNCT
ejpam-4521	474	15	=	=	SYM
ejpam-4521	474	16	fβc(g	fβc(g	PROPN
ejpam-4521	474	17	)	)	PUNCT
ejpam-4521	474	18	.	.	PUNCT
ejpam-4521	475	1	therefore	therefore	ADV
ejpam-4521	475	2	,	,	PUNCT
ejpam-4521	475	3	fγch	fγch	NOUN
ejpam-4521	475	4	,	,	PUNCT
ejpam-4521	475	5	coi(g[h	coi(g[h	NUM
ejpam-4521	475	6	]	]	PUNCT
ejpam-4521	475	7	)	)	PUNCT
ejpam-4521	475	8	=	=	SYM
ejpam-4521	475	9	fβc(g	fβc(g	PROPN
ejpam-4521	475	10	)	)	PUNCT
ejpam-4521	475	11	.	.	PUNCT
ejpam-4521	476	1	example	example	NOUN
ejpam-4521	477	1	5	5	NUM
ejpam-4521	477	2	.	.	X
ejpam-4521	478	1	for	for	ADP
ejpam-4521	478	2	paths	path	NOUN
ejpam-4521	478	3	p3	p3	NOUN
ejpam-4521	478	4	and	and	CCONJ
ejpam-4521	478	5	p5	p5	ADJ
ejpam-4521	478	6	,	,	PUNCT
ejpam-4521	478	7	fγch	fγch	ADJ
ejpam-4521	478	8	,	,	PUNCT
ejpam-4521	478	9	coi(p3[p5	coi(p3[p5	VERB
ejpam-4521	478	10	]	]	PUNCT
ejpam-4521	478	11	)	)	PUNCT
ejpam-4521	479	1	=	=	SYM
ejpam-4521	479	2	0	0	PUNCT
ejpam-4521	479	3	since	since	SCONJ
ejpam-4521	479	4	p5	p5	PROPN
ejpam-4521	479	5	has	have	VERB
ejpam-4521	479	6	a	a	DET
ejpam-4521	479	7	unique	unique	ADJ
ejpam-4521	479	8	β	β	NOUN
ejpam-4521	479	9	-	-	NOUN
ejpam-4521	479	10	set	set	VERB
ejpam-4521	479	11	.	.	PUNCT
ejpam-4521	480	1	example	example	NOUN
ejpam-4521	481	1	6	6	NUM
ejpam-4521	481	2	.	.	X
ejpam-4521	482	1	for	for	ADP
ejpam-4521	482	2	paths	path	NOUN
ejpam-4521	482	3	p4	p4	ADJ
ejpam-4521	482	4	and	and	CCONJ
ejpam-4521	482	5	p3	p3	PROPN
ejpam-4521	482	6	,	,	PUNCT
ejpam-4521	482	7	fγch	fγch	NOUN
ejpam-4521	482	8	,	,	PUNCT
ejpam-4521	482	9	coi(p4[p3	coi(p4[p3	NOUN
ejpam-4521	482	10	]	]	X
ejpam-4521	482	11	)	)	PUNCT
ejpam-4521	482	12	=	=	SYM
ejpam-4521	482	13	fβc(p4	fβc(p4	NOUN
ejpam-4521	482	14	)	)	PUNCT
ejpam-4521	482	15	=	=	SYM
ejpam-4521	482	16	2	2	NUM
ejpam-4521	482	17	since	since	SCONJ
ejpam-4521	482	18	p4	p4	ADJ
ejpam-4521	482	19	has	have	VERB
ejpam-4521	482	20	no	no	DET
ejpam-4521	482	21	unique	unique	ADJ
ejpam-4521	482	22	β	β	NOUN
ejpam-4521	482	23	-	-	NOUN
ejpam-4521	482	24	sets	set	NOUN
ejpam-4521	482	25	.	.	PUNCT
ejpam-4521	483	1	theorem	theorem	ADJ
ejpam-4521	483	2	8	8	NUM
ejpam-4521	483	3	.	.	PUNCT
ejpam-4521	484	1	let	let	VERB
ejpam-4521	484	2	g	g	NOUN
ejpam-4521	484	3	and	and	CCONJ
ejpam-4521	484	4	h	h	NOUN
ejpam-4521	484	5	be	be	AUX
ejpam-4521	484	6	connected	connect	VERB
ejpam-4521	484	7	graphs	graph	NOUN
ejpam-4521	484	8	of	of	ADP
ejpam-4521	484	9	orders	order	NOUN
ejpam-4521	484	10	m	m	VERB
ejpam-4521	484	11	>	>	X
ejpam-4521	484	12	2	2	NUM
ejpam-4521	484	13	and	and	CCONJ
ejpam-4521	484	14	n	n	NOUN
ejpam-4521	484	15	>	>	X
ejpam-4521	484	16	2	2	NUM
ejpam-4521	484	17	,	,	PUNCT
ejpam-4521	484	18	respectively	respectively	ADV
ejpam-4521	484	19	,	,	PUNCT
ejpam-4521	484	20	where	where	SCONJ
ejpam-4521	484	21	g	g	PROPN
ejpam-4521	484	22	and	and	CCONJ
ejpam-4521	484	23	h	h	NOUN
ejpam-4521	484	24	have	have	VERB
ejpam-4521	484	25	no	no	DET
ejpam-4521	484	26	unique	unique	ADJ
ejpam-4521	484	27	β	β	NOUN
ejpam-4521	484	28	-	-	NOUN
ejpam-4521	484	29	sets	set	NOUN
ejpam-4521	484	30	and	and	CCONJ
ejpam-4521	484	31	γ(h	γ(h	NOUN
ejpam-4521	484	32	)	)	PUNCT
ejpam-4521	484	33	̸=	̸=	PROPN
ejpam-4521	484	34	1	1	NUM
ejpam-4521	484	35	.	.	PUNCT
ejpam-4521	485	1	then	then	ADV
ejpam-4521	485	2	fγch	fγch	NOUN
ejpam-4521	485	3	,	,	PUNCT
ejpam-4521	485	4	coi(g[h	coi(g[h	NUM
ejpam-4521	485	5	]	]	PUNCT
ejpam-4521	485	6	)	)	PUNCT
ejpam-4521	485	7	≤	≤	NUM
ejpam-4521	485	8	fβc(h	fβc(h	PROPN
ejpam-4521	485	9	)	)	PUNCT
ejpam-4521	485	10	+	+	NUM
ejpam-4521	485	11	fβc(g	fβc(g	X
ejpam-4521	485	12	)	)	PUNCT
ejpam-4521	485	13	[	[	PUNCT
ejpam-4521	485	14	fβc(h	fβc(h	NOUN
ejpam-4521	485	15	)	)	PUNCT
ejpam-4521	485	16	+	+	NUM
ejpam-4521	485	17	1	1	NUM
ejpam-4521	485	18	]	]	PUNCT
ejpam-4521	485	19	.	.	PUNCT
ejpam-4521	486	1	proof	proof	NOUN
ejpam-4521	486	2	:	:	PUNCT
ejpam-4521	486	3	suppose	suppose	VERB
ejpam-4521	486	4	that	that	SCONJ
ejpam-4521	486	5	g	g	PROPN
ejpam-4521	486	6	and	and	CCONJ
ejpam-4521	486	7	h	h	NOUN
ejpam-4521	486	8	do	do	AUX
ejpam-4521	486	9	not	not	PART
ejpam-4521	486	10	have	have	VERB
ejpam-4521	486	11	unique	unique	ADJ
ejpam-4521	486	12	β	β	NOUN
ejpam-4521	486	13	-	-	NOUN
ejpam-4521	486	14	sets	set	NOUN
ejpam-4521	486	15	.	.	PUNCT
ejpam-4521	487	1	let	let	VERB
ejpam-4521	487	2	a	a	DET
ejpam-4521	487	3	be	be	AUX
ejpam-4521	487	4	a	a	DET
ejpam-4521	487	5	β	β	NOUN
ejpam-4521	487	6	-	-	NOUN
ejpam-4521	487	7	set	set	NOUN
ejpam-4521	487	8	of	of	ADP
ejpam-4521	487	9	g	g	PROPN
ejpam-4521	487	10	and	and	CCONJ
ejpam-4521	487	11	fac	fac	PROPN
ejpam-4521	487	12	be	be	AUX
ejpam-4521	487	13	a	a	DET
ejpam-4521	487	14	forcing	forcing	NOUN
ejpam-4521	487	15	subset	subset	NOUN
ejpam-4521	487	16	for	for	ADP
ejpam-4521	487	17	the	the	DET
ejpam-4521	487	18	complement	complement	NOUN
ejpam-4521	487	19	ac	ac	ADV
ejpam-4521	487	20	of	of	ADP
ejpam-4521	487	21	a	a	DET
ejpam-4521	487	22	such	such	ADJ
ejpam-4521	487	23	that	that	DET
ejpam-4521	487	24	fβc(g	fβc(g	PROPN
ejpam-4521	487	25	)	)	PUNCT
ejpam-4521	487	26	=	=	SYM
ejpam-4521	487	27	fβc(a	fβc(a	PROPN
ejpam-4521	487	28	)	)	PUNCT
ejpam-4521	487	29	=	=	PUNCT
ejpam-4521	487	30	|fac	|fac	ADJ
ejpam-4521	487	31	|	|	NOUN
ejpam-4521	487	32	.	.	PUNCT
ejpam-4521	488	1	then	then	ADV
ejpam-4521	488	2	for	for	SCONJ
ejpam-4521	488	3	all	all	DET
ejpam-4521	488	4	x	x	SYM
ejpam-4521	488	5	∈	∈	PROPN
ejpam-4521	488	6	a	a	PRON
ejpam-4521	488	7	,	,	PUNCT
ejpam-4521	488	8	let	let	AUX
ejpam-4521	488	9	b	b	X
ejpam-4521	488	10	=	=	SYM
ejpam-4521	488	11	v	v	PROPN
ejpam-4521	488	12	(	(	PUNCT
ejpam-4521	488	13	h	h	NOUN
ejpam-4521	488	14	)	)	PUNCT
ejpam-4521	488	15	\tx	\tx	VERB
ejpam-4521	488	16	be	be	AUX
ejpam-4521	488	17	a	a	DET
ejpam-4521	488	18	β	β	NOUN
ejpam-4521	488	19	-	-	VERB
ejpam-4521	488	20	set	set	NOUN
ejpam-4521	488	21	of	of	ADP
ejpam-4521	488	22	h	h	NOUN
ejpam-4521	488	23	and	and	CCONJ
ejpam-4521	488	24	fbc	fbc	PROPN
ejpam-4521	488	25	be	be	AUX
ejpam-4521	488	26	a	a	DET
ejpam-4521	488	27	forcing	forcing	NOUN
ejpam-4521	488	28	subset	subset	NOUN
ejpam-4521	488	29	for	for	ADP
ejpam-4521	488	30	the	the	DET
ejpam-4521	488	31	complement	complement	NOUN
ejpam-4521	488	32	bc	bc	PROPN
ejpam-4521	488	33	of	of	ADP
ejpam-4521	488	34	b	b	PROPN
ejpam-4521	488	35	such	such	ADJ
ejpam-4521	488	36	that	that	DET
ejpam-4521	488	37	fβc(h	fβc(h	NOUN
ejpam-4521	488	38	)	)	PUNCT
ejpam-4521	488	39	=	=	SYM
ejpam-4521	488	40	fβc(b	fβc(b	PROPN
ejpam-4521	488	41	)	)	PUNCT
ejpam-4521	489	1	=	=	PUNCT
ejpam-4521	490	1	|fbc	|fbc	PROPN
ejpam-4521	490	2	|	|	NOUN
ejpam-4521	490	3	.	.	PUNCT
ejpam-4521	491	1	by	by	ADP
ejpam-4521	491	2	corollary	corollary	ADJ
ejpam-4521	491	3	4	4	NUM
ejpam-4521	491	4	,	,	PUNCT
ejpam-4521	491	5	s	s	PART
ejpam-4521	491	6	=	=	PUNCT
ejpam-4521	491	7	⋃	⋃	NOUN
ejpam-4521	491	8	x∈a	x∈a	NOUN
ejpam-4521	491	9	(	(	PUNCT
ejpam-4521	491	10	{	{	PUNCT
ejpam-4521	491	11	x	x	NOUN
ejpam-4521	491	12	}	}	PUNCT
ejpam-4521	491	13	×	×	PROPN
ejpam-4521	491	14	tx	tx	PROPN
ejpam-4521	491	15	)	)	PUNCT
ejpam-4521	491	16	∪	∪	PROPN
ejpam-4521	491	17	[	[	PUNCT
ejpam-4521	491	18	ac	ac	ADJ
ejpam-4521	491	19	×	×	PROPN
ejpam-4521	491	20	v	v	PROPN
ejpam-4521	491	21	(	(	PUNCT
ejpam-4521	491	22	h	h	NOUN
ejpam-4521	491	23	)	)	PUNCT
ejpam-4521	491	24	]	]	PUNCT
ejpam-4521	491	25	references	reference	NOUN
ejpam-4521	491	26	1611	1611	NUM
ejpam-4521	491	27	is	be	AUX
ejpam-4521	491	28	a	a	DET
ejpam-4521	491	29	γch	γch	NOUN
ejpam-4521	491	30	,	,	PUNCT
ejpam-4521	491	31	coi	coi	NOUN
ejpam-4521	491	32	-	-	PUNCT
ejpam-4521	491	33	set	set	NOUN
ejpam-4521	491	34	of	of	ADP
ejpam-4521	491	35	g[h	g[h	NOUN
ejpam-4521	491	36	]	]	PUNCT
ejpam-4521	491	37	.	.	PUNCT
ejpam-4521	492	1	we	we	PRON
ejpam-4521	492	2	claim	claim	VERB
ejpam-4521	492	3	that	that	SCONJ
ejpam-4521	492	4	s0	s0	NOUN
ejpam-4521	492	5	=	=	PUNCT
ejpam-4521	492	6	(	(	PUNCT
ejpam-4521	492	7	{	{	PUNCT
ejpam-4521	492	8	x	x	NOUN
ejpam-4521	492	9	}	}	PUNCT
ejpam-4521	492	10	×	×	PROPN
ejpam-4521	492	11	fbc	fbc	PROPN
ejpam-4521	492	12	)	)	PUNCT
ejpam-4521	492	13	∪	∪	PROPN
ejpam-4521	492	14	(	(	PUNCT
ejpam-4521	492	15	fac	fac	PROPN
ejpam-4521	492	16	×	×	PROPN
ejpam-4521	493	1	[	[	X
ejpam-4521	493	2	fbc	fbc	PROPN
ejpam-4521	493	3	∪	∪	X
ejpam-4521	493	4	{	{	PUNCT
ejpam-4521	493	5	y	y	NOUN
ejpam-4521	493	6	}	}	PUNCT
ejpam-4521	493	7	]	]	PUNCT
ejpam-4521	493	8	)	)	PUNCT
ejpam-4521	493	9	for	for	ADP
ejpam-4521	493	10	each	each	DET
ejpam-4521	493	11	x	x	SYM
ejpam-4521	493	12	∈	∈	PROPN
ejpam-4521	493	13	a	a	PRON
ejpam-4521	493	14	and	and	CCONJ
ejpam-4521	493	15	y	y	PROPN
ejpam-4521	493	16	∈	∈	PROPN
ejpam-4521	493	17	b	b	PROPN
ejpam-4521	493	18	is	be	AUX
ejpam-4521	493	19	a	a	DET
ejpam-4521	493	20	forcing	forcing	NOUN
ejpam-4521	493	21	subset	subset	NOUN
ejpam-4521	493	22	for	for	ADP
ejpam-4521	493	23	s.	s.	PROPN
ejpam-4521	493	24	suppose	suppose	VERB
ejpam-4521	493	25	on	on	ADP
ejpam-4521	493	26	the	the	DET
ejpam-4521	493	27	contrary	contrary	NOUN
ejpam-4521	493	28	.	.	PUNCT
ejpam-4521	494	1	then	then	ADV
ejpam-4521	494	2	there	there	PRON
ejpam-4521	494	3	exists	exist	VERB
ejpam-4521	494	4	a	a	DET
ejpam-4521	494	5	γch.coi	γch.coi	NOUN
ejpam-4521	494	6	-	-	PUNCT
ejpam-4521	494	7	set	set	VERB
ejpam-4521	494	8	s	s	PART
ejpam-4521	494	9	′	′	NUM
ejpam-4521	494	10	̸=	̸=	PROPN
ejpam-4521	494	11	s	s	VERB
ejpam-4521	494	12	such	such	ADJ
ejpam-4521	494	13	that	that	SCONJ
ejpam-4521	494	14	s0	s0	PROPN
ejpam-4521	494	15	⊆	⊆	NUM
ejpam-4521	494	16	s	s	PART
ejpam-4521	494	17	′	′	NOUN
ejpam-4521	494	18	.	.	PUNCT
ejpam-4521	495	1	by	by	ADP
ejpam-4521	495	2	corollary	corollary	ADJ
ejpam-4521	495	3	4	4	NUM
ejpam-4521	495	4	,	,	PUNCT
ejpam-4521	495	5	s	s	VERB
ejpam-4521	495	6	′	′	NOUN
ejpam-4521	495	7	=	=	PUNCT
ejpam-4521	496	1	⋃	⋃	PROPN
ejpam-4521	496	2	x∈a′	x∈a′	PROPN
ejpam-4521	496	3	(	(	PUNCT
ejpam-4521	496	4	{	{	PUNCT
ejpam-4521	496	5	x	x	NOUN
ejpam-4521	496	6	}	}	PUNCT
ejpam-4521	496	7	×	×	NOUN
ejpam-4521	496	8	t	t	NOUN
ejpam-4521	496	9	′	′	NUM
ejpam-4521	496	10	x	x	X
ejpam-4521	496	11	)	)	PUNCT
ejpam-4521	496	12	∪	∪	ADP
ejpam-4521	496	13	[	[	PUNCT
ejpam-4521	496	14	(	(	PUNCT
ejpam-4521	496	15	a	a	DET
ejpam-4521	496	16	′	′	NOUN
ejpam-4521	496	17	)	)	PUNCT
ejpam-4521	496	18	c	c	NOUN
ejpam-4521	496	19	×	×	PROPN
ejpam-4521	496	20	v	v	NOUN
ejpam-4521	496	21	(	(	PUNCT
ejpam-4521	496	22	h	h	NOUN
ejpam-4521	496	23	)	)	PUNCT
ejpam-4521	496	24	]	]	PUNCT
ejpam-4521	496	25	for	for	SCONJ
ejpam-4521	496	26	some	some	PRON
ejpam-4521	496	27	β	β	NOUN
ejpam-4521	496	28	-	-	VERB
ejpam-4521	496	29	set	set	VERB
ejpam-4521	496	30	a	a	DET
ejpam-4521	496	31	′	′	NOUN
ejpam-4521	496	32	of	of	ADP
ejpam-4521	496	33	g	g	NOUN
ejpam-4521	496	34	such	such	ADJ
ejpam-4521	496	35	that	that	PRON
ejpam-4521	496	36	b	b	NOUN
ejpam-4521	496	37	′	′	NUM
ejpam-4521	496	38	=	=	SYM
ejpam-4521	496	39	v	v	NOUN
ejpam-4521	496	40	(	(	PUNCT
ejpam-4521	496	41	h	h	NOUN
ejpam-4521	496	42	)	)	PUNCT
ejpam-4521	496	43	\	\	PROPN
ejpam-4521	496	44	t	t	NOUN
ejpam-4521	496	45	′	′	NUM
ejpam-4521	496	46	x	x	PUNCT
ejpam-4521	496	47	is	be	AUX
ejpam-4521	496	48	a	a	DET
ejpam-4521	496	49	β	β	NOUN
ejpam-4521	496	50	-	-	PUNCT
ejpam-4521	496	51	set	set	NOUN
ejpam-4521	496	52	of	of	ADP
ejpam-4521	496	53	h	h	NOUN
ejpam-4521	496	54	for	for	ADP
ejpam-4521	496	55	all	all	DET
ejpam-4521	496	56	x	x	SYM
ejpam-4521	496	57	∈	∈	PROPN
ejpam-4521	496	58	a	a	DET
ejpam-4521	496	59	′	′	NOUN
ejpam-4521	496	60	.	.	PUNCT
ejpam-4521	497	1	since	since	SCONJ
ejpam-4521	497	2	s	s	PRON
ejpam-4521	497	3	′	′	NUM
ejpam-4521	497	4	̸=	̸=	PROPN
ejpam-4521	497	5	s	s	PROPN
ejpam-4521	497	6	,	,	PUNCT
ejpam-4521	497	7	either	either	CCONJ
ejpam-4521	497	8	one	one	NUM
ejpam-4521	497	9	of	of	ADP
ejpam-4521	497	10	the	the	DET
ejpam-4521	497	11	following	follow	VERB
ejpam-4521	497	12	holds	hold	VERB
ejpam-4521	497	13	:	:	PUNCT
ejpam-4521	497	14	(	(	PUNCT
ejpam-4521	497	15	i	i	NOUN
ejpam-4521	497	16	)	)	PUNCT
ejpam-4521	497	17	a	a	DET
ejpam-4521	497	18	′	′	NOUN
ejpam-4521	497	19	=	=	PUNCT
ejpam-4521	497	20	a	a	PRON
ejpam-4521	497	21	and	and	CCONJ
ejpam-4521	497	22	b	b	NOUN
ejpam-4521	497	23	′	′	NUM
ejpam-4521	497	24	̸=	̸=	PROPN
ejpam-4521	497	25	b	b	PROPN
ejpam-4521	497	26	(	(	PUNCT
ejpam-4521	497	27	ii	ii	PROPN
ejpam-4521	497	28	)	)	PUNCT
ejpam-4521	497	29	a	a	DET
ejpam-4521	497	30	′	′	NUM
ejpam-4521	497	31	̸=	̸=	PROPN
ejpam-4521	497	32	a	a	PRON
ejpam-4521	497	33	and	and	CCONJ
ejpam-4521	497	34	b	b	NOUN
ejpam-4521	497	35	′	′	NUM
ejpam-4521	497	36	=	=	SYM
ejpam-4521	497	37	b	b	PROPN
ejpam-4521	497	38	(	(	PUNCT
ejpam-4521	497	39	iii	iii	NOUN
ejpam-4521	497	40	)	)	PUNCT
ejpam-4521	497	41	a	a	DET
ejpam-4521	497	42	′	′	NUM
ejpam-4521	497	43	̸=	̸=	PROPN
ejpam-4521	497	44	a	a	PRON
ejpam-4521	497	45	and	and	CCONJ
ejpam-4521	497	46	b	b	NOUN
ejpam-4521	497	47	′	′	NUM
ejpam-4521	497	48	̸=	̸=	PROPN
ejpam-4521	497	49	b.	b.	PROPN
ejpam-4521	497	50	suppose	suppose	VERB
ejpam-4521	497	51	(	(	PUNCT
ejpam-4521	497	52	i	i	NOUN
ejpam-4521	497	53	)	)	PUNCT
ejpam-4521	497	54	holds	hold	VERB
ejpam-4521	497	55	.	.	PUNCT
ejpam-4521	498	1	then	then	ADV
ejpam-4521	498	2	s	s	VERB
ejpam-4521	498	3	′	′	NOUN
ejpam-4521	498	4	=	=	PUNCT
ejpam-4521	498	5	⋃	⋃	NOUN
ejpam-4521	498	6	x∈a	x∈a	NOUN
ejpam-4521	498	7	(	(	PUNCT
ejpam-4521	498	8	{	{	PUNCT
ejpam-4521	498	9	x	x	NOUN
ejpam-4521	498	10	}	}	PUNCT
ejpam-4521	498	11	×	×	NOUN
ejpam-4521	498	12	t	t	NOUN
ejpam-4521	498	13	′	′	NUM
ejpam-4521	498	14	x	x	X
ejpam-4521	498	15	)	)	PUNCT
ejpam-4521	498	16	∪	∪	ADP
ejpam-4521	498	17	[	[	PUNCT
ejpam-4521	498	18	ac	ac	ADJ
ejpam-4521	498	19	×	×	PROPN
ejpam-4521	498	20	v	v	PROPN
ejpam-4521	498	21	(	(	PUNCT
ejpam-4521	498	22	h	h	NOUN
ejpam-4521	498	23	)	)	PUNCT
ejpam-4521	498	24	]	]	PUNCT
ejpam-4521	498	25	.	.	PUNCT
ejpam-4521	499	1	since	since	SCONJ
ejpam-4521	499	2	s0	s0	PROPN
ejpam-4521	499	3	⊆	⊆	NUM
ejpam-4521	499	4	s	s	PART
ejpam-4521	499	5	′	′	NOUN
ejpam-4521	499	6	,	,	PUNCT
ejpam-4521	499	7	fbc	fbc	PROPN
ejpam-4521	499	8	⊆	⊆	NUM
ejpam-4521	499	9	t	t	NOUN
ejpam-4521	499	10	′	′	NUM
ejpam-4521	499	11	x	x	X
ejpam-4521	499	12	=	=	SYM
ejpam-4521	499	13	v	v	X
ejpam-4521	499	14	(	(	PUNCT
ejpam-4521	499	15	h	h	NOUN
ejpam-4521	499	16	)	)	PUNCT
ejpam-4521	499	17	\	\	NOUN
ejpam-4521	500	1	b	b	NOUN
ejpam-4521	500	2	′	′	NUM
ejpam-4521	501	1	=	=	SYM
ejpam-4521	501	2	(	(	PUNCT
ejpam-4521	501	3	b	b	NOUN
ejpam-4521	501	4	′	′	NUM
ejpam-4521	501	5	)	)	PUNCT
ejpam-4521	501	6	c	c	X
ejpam-4521	501	7	,	,	PUNCT
ejpam-4521	501	8	a	a	DET
ejpam-4521	501	9	contradiction	contradiction	NOUN
ejpam-4521	501	10	since	since	SCONJ
ejpam-4521	501	11	fbc	fbc	PROPN
ejpam-4521	501	12	is	be	AUX
ejpam-4521	501	13	a	a	DET
ejpam-4521	501	14	forcing	forcing	NOUN
ejpam-4521	501	15	subset	subset	NOUN
ejpam-4521	501	16	for	for	ADP
ejpam-4521	501	17	bc	bc	PROPN
ejpam-4521	501	18	.	.	PROPN
ejpam-4521	502	1	if	if	SCONJ
ejpam-4521	502	2	(	(	PUNCT
ejpam-4521	502	3	ii	ii	NOUN
ejpam-4521	502	4	)	)	PUNCT
ejpam-4521	502	5	holds	hold	VERB
ejpam-4521	502	6	,	,	PUNCT
ejpam-4521	502	7	then	then	ADV
ejpam-4521	502	8	fac	fac	PROPN
ejpam-4521	502	9	⊆	⊆	NUM
ejpam-4521	502	10	(	(	PUNCT
ejpam-4521	502	11	a	a	DET
ejpam-4521	502	12	′	′	NOUN
ejpam-4521	502	13	)	)	PUNCT
ejpam-4521	503	1	c.	c.	NOUN
ejpam-4521	503	2	this	this	PRON
ejpam-4521	503	3	is	be	AUX
ejpam-4521	503	4	again	again	ADV
ejpam-4521	503	5	a	a	DET
ejpam-4521	503	6	contradiction	contradiction	NOUN
ejpam-4521	503	7	since	since	SCONJ
ejpam-4521	503	8	fac	fac	PROPN
ejpam-4521	503	9	is	be	AUX
ejpam-4521	503	10	a	a	DET
ejpam-4521	503	11	forcing	forcing	NOUN
ejpam-4521	503	12	subset	subset	NOUN
ejpam-4521	503	13	for	for	ADP
ejpam-4521	503	14	ac	ac	PROPN
ejpam-4521	503	15	.	.	PUNCT
ejpam-4521	504	1	if	if	SCONJ
ejpam-4521	504	2	(	(	PUNCT
ejpam-4521	504	3	iii	iii	NOUN
ejpam-4521	504	4	)	)	PUNCT
ejpam-4521	504	5	holds	hold	VERB
ejpam-4521	504	6	,	,	PUNCT
ejpam-4521	504	7	then	then	ADV
ejpam-4521	504	8	fbc	fbc	PROPN
ejpam-4521	504	9	⊆	⊆	X
ejpam-4521	504	10	(	(	PUNCT
ejpam-4521	504	11	b	b	NOUN
ejpam-4521	504	12	′	′	NUM
ejpam-4521	504	13	)	)	PUNCT
ejpam-4521	504	14	c	c	NOUN
ejpam-4521	504	15	and	and	CCONJ
ejpam-4521	504	16	fac	fac	PROPN
ejpam-4521	504	17	⊆	⊆	NUM
ejpam-4521	504	18	(	(	PUNCT
ejpam-4521	504	19	a	a	DET
ejpam-4521	504	20	′	′	NOUN
ejpam-4521	504	21	)	)	PUNCT
ejpam-4521	504	22	c	c	X
ejpam-4521	504	23	,	,	PUNCT
ejpam-4521	504	24	a	a	DET
ejpam-4521	504	25	contradiction	contradiction	NOUN
ejpam-4521	504	26	.	.	PUNCT
ejpam-4521	505	1	therefore	therefore	ADV
ejpam-4521	505	2	,	,	PUNCT
ejpam-4521	505	3	s0	s0	PROPN
ejpam-4521	505	4	is	be	AUX
ejpam-4521	505	5	a	a	DET
ejpam-4521	505	6	forcing	forcing	NOUN
ejpam-4521	505	7	subset	subset	NOUN
ejpam-4521	505	8	for	for	ADP
ejpam-4521	505	9	s.	s.	PROPN
ejpam-4521	505	10	thus	thus	ADV
ejpam-4521	505	11	,	,	PUNCT
ejpam-4521	505	12	fγch	fγch	NOUN
ejpam-4521	505	13	,	,	PUNCT
ejpam-4521	505	14	coi(g[h	coi(g[h	NUM
ejpam-4521	505	15	]	]	PUNCT
ejpam-4521	505	16	)	)	PUNCT
ejpam-4521	505	17	≤	≤	NUM
ejpam-4521	505	18	fγch	fγch	NOUN
ejpam-4521	505	19	,	,	PUNCT
ejpam-4521	505	20	coi(s	coi(s	X
ejpam-4521	505	21	)	)	PUNCT
ejpam-4521	506	1	=	=	SYM
ejpam-4521	506	2	|s0|	|s0|	NOUN
ejpam-4521	506	3	=	=	SYM
ejpam-4521	506	4	fβc(h	fβc(h	PROPN
ejpam-4521	506	5	)	)	PUNCT
ejpam-4521	506	6	+	+	NUM
ejpam-4521	506	7	fβc(g	fβc(g	X
ejpam-4521	506	8	)	)	PUNCT
ejpam-4521	506	9	[	[	PUNCT
ejpam-4521	506	10	fβc(h	fβc(h	NOUN
ejpam-4521	506	11	)	)	PUNCT
ejpam-4521	506	12	+	+	NUM
ejpam-4521	506	13	1	1	NUM
ejpam-4521	506	14	]	]	PUNCT
ejpam-4521	506	15	.	.	PUNCT
ejpam-4521	507	1	example	example	NOUN
ejpam-4521	508	1	7	7	NUM
ejpam-4521	508	2	.	.	X
ejpam-4521	509	1	for	for	ADP
ejpam-4521	509	2	cycle	cycle	NOUN
ejpam-4521	509	3	c4	c4	NOUN
ejpam-4521	509	4	and	and	CCONJ
ejpam-4521	509	5	path	path	NOUN
ejpam-4521	509	6	p4	p4	ADJ
ejpam-4521	509	7	,	,	PUNCT
ejpam-4521	509	8	fγch	fγch	NOUN
ejpam-4521	509	9	,	,	PUNCT
ejpam-4521	509	10	coi(c4[p4	coi(c4[p4	NOUN
ejpam-4521	509	11	]	]	X
ejpam-4521	509	12	)	)	PUNCT
ejpam-4521	509	13	≤	≤	NUM
ejpam-4521	509	14	fβc(p4	fβc(p4	NOUN
ejpam-4521	509	15	)	)	PUNCT
ejpam-4521	509	16	+	+	SYM
ejpam-4521	509	17	fβc(c4	fβc(c4	NOUN
ejpam-4521	509	18	)	)	PUNCT
ejpam-4521	509	19	[	[	PUNCT
ejpam-4521	509	20	fβc(p4	fβc(p4	NOUN
ejpam-4521	509	21	)	)	PUNCT
ejpam-4521	509	22	+	+	NOUN
ejpam-4521	509	23	1	1	X
ejpam-4521	509	24	]	]	PUNCT
ejpam-4521	509	25	=	=	SYM
ejpam-4521	510	1	2	2	NUM
ejpam-4521	510	2	+	+	NUM
ejpam-4521	510	3	2[2	2[2	NUM
ejpam-4521	510	4	+	+	CCONJ
ejpam-4521	510	5	1	1	NUM
ejpam-4521	510	6	]	]	X
ejpam-4521	510	7	=	=	SYM
ejpam-4521	510	8	8	8	NUM
ejpam-4521	510	9	since	since	SCONJ
ejpam-4521	510	10	both	both	PRON
ejpam-4521	510	11	c4	c4	NOUN
ejpam-4521	510	12	and	and	CCONJ
ejpam-4521	510	13	p4	p4	ADJ
ejpam-4521	510	14	have	have	VERB
ejpam-4521	510	15	no	no	DET
ejpam-4521	510	16	unique	unique	ADJ
ejpam-4521	510	17	β	β	NOUN
ejpam-4521	510	18	-	-	NOUN
ejpam-4521	510	19	sets	set	NOUN
ejpam-4521	510	20	.	.	PUNCT
ejpam-4521	511	1	acknowledgements	acknowledgement	NOUN
ejpam-4521	511	2	the	the	DET
ejpam-4521	511	3	authors	author	NOUN
ejpam-4521	511	4	would	would	AUX
ejpam-4521	511	5	like	like	VERB
ejpam-4521	511	6	to	to	PART
ejpam-4521	511	7	express	express	VERB
ejpam-4521	511	8	their	their	PRON
ejpam-4521	511	9	gratitude	gratitude	NOUN
ejpam-4521	511	10	to	to	ADP
ejpam-4521	511	11	the	the	DET
ejpam-4521	511	12	referees	referee	NOUN
ejpam-4521	511	13	for	for	ADP
ejpam-4521	511	14	their	their	PRON
ejpam-4521	511	15	insightful	insightful	ADJ
ejpam-4521	511	16	comments	comment	NOUN
ejpam-4521	511	17	and	and	CCONJ
ejpam-4521	511	18	suggestions	suggestion	NOUN
ejpam-4521	511	19	,	,	PUNCT
ejpam-4521	511	20	which	which	PRON
ejpam-4521	511	21	significantly	significantly	ADV
ejpam-4521	511	22	improved	improve	VERB
ejpam-4521	511	23	the	the	DET
ejpam-4521	511	24	paper	paper	NOUN
ejpam-4521	511	25	.	.	PUNCT
ejpam-4521	512	1	the	the	DET
ejpam-4521	512	2	authors	author	NOUN
ejpam-4521	512	3	would	would	AUX
ejpam-4521	512	4	also	also	ADV
ejpam-4521	512	5	like	like	VERB
ejpam-4521	512	6	to	to	PART
ejpam-4521	512	7	thank	thank	VERB
ejpam-4521	512	8	the	the	DET
ejpam-4521	512	9	following	follow	VERB
ejpam-4521	512	10	funding	funding	NOUN
ejpam-4521	512	11	agencies	agency	NOUN
ejpam-4521	512	12	:	:	PUNCT
ejpam-4521	512	13	mindanao	mindanao	PROPN
ejpam-4521	512	14	state	state	PROPN
ejpam-4521	512	15	university	university	PROPN
ejpam-4521	512	16	iligan	iligan	PROPN
ejpam-4521	512	17	institute	institute	PROPN
ejpam-4521	512	18	of	of	ADP
ejpam-4521	512	19	technology	technology	PROPN
ejpam-4521	512	20	(	(	PUNCT
ejpam-4521	512	21	msu	msu	PROPN
ejpam-4521	512	22	-	-	PUNCT
ejpam-4521	512	23	iit	iit	NOUN
ejpam-4521	512	24	)	)	PUNCT
ejpam-4521	512	25	and	and	CCONJ
ejpam-4521	512	26	the	the	DET
ejpam-4521	512	27	department	department	NOUN
ejpam-4521	512	28	of	of	ADP
ejpam-4521	512	29	science	science	NOUN
ejpam-4521	512	30	and	and	CCONJ
ejpam-4521	512	31	technology	technology	NOUN
ejpam-4521	512	32	accelerated	accelerate	VERB
ejpam-4521	512	33	science	science	NOUN
ejpam-4521	512	34	and	and	CCONJ
ejpam-4521	512	35	technology	technology	NOUN
ejpam-4521	512	36	human	human	ADJ
ejpam-4521	512	37	resource	resource	NOUN
ejpam-4521	512	38	development	development	NOUN
ejpam-4521	512	39	program	program	NOUN
ejpam-4521	512	40	(	(	PUNCT
ejpam-4521	512	41	dostasthrdp	dostasthrdp	PROPN
ejpam-4521	512	42	)	)	PUNCT
ejpam-4521	512	43	,	,	PUNCT
ejpam-4521	512	44	philippines	philippine	NOUN
ejpam-4521	512	45	.	.	PUNCT
ejpam-4521	513	1	references	reference	NOUN
ejpam-4521	513	2	[	[	X
ejpam-4521	513	3	1	1	NUM
ejpam-4521	513	4	]	]	X
ejpam-4521	513	5	c.	c.	PROPN
ejpam-4521	513	6	armada	armada	PROPN
ejpam-4521	513	7	and	and	CCONJ
ejpam-4521	513	8	s.	s.	PROPN
ejpam-4521	513	9	canoy	canoy	PROPN
ejpam-4521	513	10	jr	jr	PROPN
ejpam-4521	513	11	.	.	PUNCT
ejpam-4521	514	1	forcing	force	VERB
ejpam-4521	514	2	independent	independent	ADJ
ejpam-4521	514	3	domination	domination	NOUN
ejpam-4521	514	4	number	number	NOUN
ejpam-4521	514	5	of	of	ADP
ejpam-4521	514	6	a	a	DET
ejpam-4521	514	7	graph	graph	NOUN
ejpam-4521	514	8	.	.	PUNCT
ejpam-4521	515	1	european	european	ADJ
ejpam-4521	515	2	journal	journal	PROPN
ejpam-4521	515	3	of	of	ADP
ejpam-4521	515	4	pure	pure	ADJ
ejpam-4521	515	5	and	and	CCONJ
ejpam-4521	515	6	applied	applied	ADJ
ejpam-4521	515	7	mathematics	mathematic	NOUN
ejpam-4521	515	8	,	,	PUNCT
ejpam-4521	515	9	12(4):1371–1381	12(4):1371–1381	NUM
ejpam-4521	515	10	,	,	PUNCT
ejpam-4521	515	11	2019	2019	NUM
ejpam-4521	515	12	.	.	PUNCT
ejpam-4521	516	1	[	[	X
ejpam-4521	516	2	2	2	NUM
ejpam-4521	516	3	]	]	X
ejpam-4521	516	4	c.	c.	PROPN
ejpam-4521	516	5	armada	armada	PROPN
ejpam-4521	516	6	,	,	PUNCT
ejpam-4521	516	7	s.	s.	PROPN
ejpam-4521	516	8	canoy	canoy	PROPN
ejpam-4521	516	9	jr	jr	PROPN
ejpam-4521	516	10	.	.	PROPN
ejpam-4521	516	11	,	,	PUNCT
ejpam-4521	516	12	and	and	CCONJ
ejpam-4521	516	13	c.	c.	PROPN
ejpam-4521	516	14	go	go	VERB
ejpam-4521	516	15	.	.	PUNCT
ejpam-4521	517	1	forcing	force	VERB
ejpam-4521	517	2	domination	domination	NOUN
ejpam-4521	517	3	numbers	number	NOUN
ejpam-4521	517	4	of	of	ADP
ejpam-4521	517	5	graphs	graph	NOUN
ejpam-4521	517	6	under	under	ADP
ejpam-4521	517	7	some	some	DET
ejpam-4521	517	8	binary	binary	ADJ
ejpam-4521	517	9	operations	operation	NOUN
ejpam-4521	517	10	.	.	PUNCT
ejpam-4521	518	1	advances	advance	NOUN
ejpam-4521	518	2	and	and	CCONJ
ejpam-4521	518	3	applications	application	NOUN
ejpam-4521	518	4	in	in	ADP
ejpam-4521	518	5	discrete	discrete	ADJ
ejpam-4521	518	6	mathematics	mathematic	NOUN
ejpam-4521	518	7	,	,	PUNCT
ejpam-4521	518	8	19(3):213–228	19(3):213–228	NUM
ejpam-4521	518	9	,	,	PUNCT
ejpam-4521	518	10	2018	2018	NUM
ejpam-4521	518	11	.	.	PUNCT
ejpam-4521	519	1	references	reference	NOUN
ejpam-4521	519	2	1612	1612	NUM
ejpam-4521	520	1	[	[	X
ejpam-4521	520	2	3	3	NUM
ejpam-4521	520	3	]	]	PUNCT
ejpam-4521	520	4	s.	s.	PROPN
ejpam-4521	520	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4521	520	6	,	,	PUNCT
ejpam-4521	520	7	b.	b.	PROPN
ejpam-4521	520	8	krishnakumari	krishnakumari	PROPN
ejpam-4521	520	9	,	,	PUNCT
ejpam-4521	520	10	c.	c.	PROPN
ejpam-4521	520	11	natarajan	natarajan	PROPN
ejpam-4521	520	12	,	,	PUNCT
ejpam-4521	520	13	and	and	CCONJ
ejpam-4521	520	14	y.b	y.b	PROPN
ejpam-4521	520	15	.	.	PROPN
ejpam-4521	520	16	venkatakrishman	venkatakrishman	NOUN
ejpam-4521	520	17	.	.	PUNCT
ejpam-4521	521	1	bounds	bound	NOUN
ejpam-4521	521	2	on	on	ADP
ejpam-4521	521	3	the	the	DET
ejpam-4521	521	4	hop	hop	NOUN
ejpam-4521	521	5	domination	domination	NOUN
ejpam-4521	521	6	number	number	NOUN
ejpam-4521	521	7	of	of	ADP
ejpam-4521	521	8	a	a	DET
ejpam-4521	521	9	tree	tree	NOUN
ejpam-4521	521	10	.	.	PUNCT
ejpam-4521	522	1	proc	proc	NOUN
ejpam-4521	522	2	.	.	PUNCT
ejpam-4521	523	1	math	math	NOUN
ejpam-4521	523	2	.	.	PUNCT
ejpam-4521	524	1	sci	sci	PROPN
ejpam-4521	524	2	.	.	PROPN
ejpam-4521	524	3	,	,	PUNCT
ejpam-4521	524	4	125:449–455	125:449–455	NUM
ejpam-4521	524	5	,	,	PUNCT
ejpam-4521	524	6	2015	2015	NUM
ejpam-4521	524	7	.	.	PUNCT
ejpam-4521	525	1	[	[	X
ejpam-4521	525	2	4	4	NUM
ejpam-4521	525	3	]	]	X
ejpam-4521	525	4	c.	c.	PROPN
ejpam-4521	525	5	berge	berge	PROPN
ejpam-4521	525	6	.	.	PUNCT
ejpam-4521	526	1	theorie	theorie	PROPN
ejpam-4521	526	2	des	des	PROPN
ejpam-4521	526	3	graphes	graphes	PROPN
ejpam-4521	526	4	et	et	PROPN
ejpam-4521	526	5	ses	ses	PROPN
ejpam-4521	526	6	applications	application	NOUN
ejpam-4521	526	7	.	.	PUNCT
ejpam-4521	527	1	metheun	metheun	NOUN
ejpam-4521	527	2	and	and	CCONJ
ejpam-4521	527	3	wiley	wiley	PROPN
ejpam-4521	527	4	,	,	PUNCT
ejpam-4521	527	5	london	london	PROPN
ejpam-4521	527	6	and	and	CCONJ
ejpam-4521	527	7	new	new	PROPN
ejpam-4521	527	8	york	york	PROPN
ejpam-4521	527	9	,	,	PUNCT
ejpam-4521	527	10	1962	1962	NUM
ejpam-4521	527	11	.	.	PUNCT
ejpam-4521	528	1	[	[	X
ejpam-4521	528	2	5	5	X
ejpam-4521	528	3	]	]	PUNCT
ejpam-4521	528	4	g.	g.	PROPN
ejpam-4521	528	5	chartrand	chartrand	PROPN
ejpam-4521	528	6	,	,	PUNCT
ejpam-4521	528	7	h.	h.	PROPN
ejpam-4521	528	8	gavlas	gavlas	PROPN
ejpam-4521	528	9	,	,	PUNCT
ejpam-4521	528	10	k.c	k.c	PROPN
ejpam-4521	528	11	.	.	PROPN
ejpam-4521	528	12	vandell	vandell	PROPN
ejpam-4521	528	13	,	,	PUNCT
ejpam-4521	528	14	and	and	CCONJ
ejpam-4521	528	15	f.	f.	PROPN
ejpam-4521	528	16	harary	harary	PROPN
ejpam-4521	528	17	.	.	PUNCT
ejpam-4521	529	1	the	the	DET
ejpam-4521	529	2	forcing	force	VERB
ejpam-4521	529	3	domination	domination	NOUN
ejpam-4521	529	4	number	number	NOUN
ejpam-4521	529	5	of	of	ADP
ejpam-4521	529	6	a	a	DET
ejpam-4521	529	7	graph	graph	NOUN
ejpam-4521	529	8	.	.	PUNCT
ejpam-4521	530	1	j.combin	j.combin	NOUN
ejpam-4521	530	2	.	.	PUNCT
ejpam-4521	531	1	math	math	NOUN
ejpam-4521	531	2	.	.	PUNCT
ejpam-4521	532	1	combin	combin	NOUN
ejpam-4521	532	2	.	.	PUNCT
ejpam-4521	533	1	comput	comput	NOUN
ejpam-4521	533	2	.	.	PUNCT
ejpam-4521	533	3	,	,	PUNCT
ejpam-4521	534	1	25:161–174	25:161–174	NUM
ejpam-4521	534	2	,	,	PUNCT
ejpam-4521	534	3	1997	1997	NUM
ejpam-4521	534	4	.	.	PUNCT
ejpam-4521	535	1	[	[	X
ejpam-4521	535	2	6	6	NUM
ejpam-4521	535	3	]	]	PUNCT
ejpam-4521	535	4	w.	w.	PROPN
ejpam-4521	535	5	desormeau	desormeau	PROPN
ejpam-4521	535	6	,	,	PUNCT
ejpam-4521	535	7	t.	t.	PROPN
ejpam-4521	535	8	haynes	haynes	PROPN
ejpam-4521	535	9	,	,	PUNCT
ejpam-4521	535	10	and	and	CCONJ
ejpam-4521	535	11	m.a	m.a	PROPN
ejpam-4521	535	12	.	.	PROPN
ejpam-4521	535	13	henning	henning	PROPN
ejpam-4521	535	14	.	.	PUNCT
ejpam-4521	536	1	a	a	DET
ejpam-4521	536	2	note	note	NOUN
ejpam-4521	536	3	on	on	ADP
ejpam-4521	536	4	non	non	ADJ
ejpam-4521	536	5	-	-	ADJ
ejpam-4521	536	6	dominating	dominating	ADJ
ejpam-4521	536	7	set	set	VERB
ejpam-4521	536	8	partitions	partition	NOUN
ejpam-4521	536	9	in	in	ADP
ejpam-4521	536	10	graphs	graph	NOUN
ejpam-4521	536	11	.	.	PUNCT
ejpam-4521	537	1	networks	network	NOUN
ejpam-4521	537	2	,	,	PUNCT
ejpam-4521	537	3	pages	page	NOUN
ejpam-4521	537	4	1–8	1–8	NUM
ejpam-4521	537	5	,	,	PUNCT
ejpam-4521	537	6	2016	2016	NUM
ejpam-4521	537	7	.	.	PUNCT
ejpam-4521	538	1	[	[	X
ejpam-4521	538	2	7	7	X
ejpam-4521	538	3	]	]	X
ejpam-4521	538	4	b.	b.	PROPN
ejpam-4521	538	5	gayathri	gayathri	PROPN
ejpam-4521	538	6	and	and	CCONJ
ejpam-4521	538	7	s.	s.	PROPN
ejpam-4521	538	8	kaspar	kaspar	PROPN
ejpam-4521	538	9	.	.	PUNCT
ejpam-4521	539	1	connected	connect	VERB
ejpam-4521	539	2	co	co	ADJ
ejpam-4521	539	3	-	-	ADJ
ejpam-4521	539	4	independent	independent	ADJ
ejpam-4521	539	5	domination	domination	NOUN
ejpam-4521	539	6	of	of	ADP
ejpam-4521	539	7	a	a	DET
ejpam-4521	539	8	graph	graph	NOUN
ejpam-4521	539	9	.	.	PUNCT
ejpam-4521	540	1	international	international	ADJ
ejpam-4521	540	2	journal	journal	PROPN
ejpam-4521	540	3	contemp	contemp	NOUN
ejpam-4521	540	4	.	.	PUNCT
ejpam-4521	541	1	mathematics	mathematic	NOUN
ejpam-4521	541	2	and	and	CCONJ
ejpam-4521	541	3	sciences	science	NOUN
ejpam-4521	541	4	,	,	PUNCT
ejpam-4521	541	5	6:423–429	6:423–429	PROPN
ejpam-4521	541	6	,	,	PUNCT
ejpam-4521	541	7	2011	2011	NUM
ejpam-4521	541	8	.	.	PUNCT
ejpam-4521	542	1	[	[	X
ejpam-4521	542	2	8	8	NUM
ejpam-4521	542	3	]	]	X
ejpam-4521	542	4	f.	f.	PROPN
ejpam-4521	542	5	harary	harary	PROPN
ejpam-4521	542	6	.	.	PUNCT
ejpam-4521	543	1	graph	graph	NOUN
ejpam-4521	543	2	theory	theory	NOUN
ejpam-4521	543	3	.	.	PUNCT
ejpam-4521	544	1	addison	addison	PROPN
ejpam-4521	544	2	-	-	PUNCT
ejpam-4521	544	3	wesley	wesley	PROPN
ejpam-4521	544	4	publishing	publishing	PROPN
ejpam-4521	544	5	company	company	NOUN
ejpam-4521	544	6	,	,	PUNCT
ejpam-4521	544	7	usa	usa	PROPN
ejpam-4521	544	8	,	,	PUNCT
ejpam-4521	544	9	1969	1969	NUM
ejpam-4521	544	10	.	.	PUNCT
ejpam-4521	545	1	[	[	X
ejpam-4521	545	2	9	9	NUM
ejpam-4521	545	3	]	]	PUNCT
ejpam-4521	545	4	s.	s.	PROPN
ejpam-4521	545	5	kavitha	kavitha	PROPN
ejpam-4521	545	6	,	,	PUNCT
ejpam-4521	545	7	s.	s.	PROPN
ejpam-4521	545	8	robinson	robinson	PROPN
ejpam-4521	545	9	chellathurai	chellathurai	PROPN
ejpam-4521	545	10	,	,	PUNCT
ejpam-4521	545	11	and	and	CCONJ
ejpam-4521	545	12	j.	j.	PROPN
ejpam-4521	545	13	john	john	PROPN
ejpam-4521	545	14	.	.	PUNCT
ejpam-4521	546	1	on	on	ADP
ejpam-4521	546	2	the	the	DET
ejpam-4521	546	3	forcing	force	VERB
ejpam-4521	546	4	connected	connect	VERB
ejpam-4521	546	5	domination	domination	NOUN
ejpam-4521	546	6	number	number	NOUN
ejpam-4521	546	7	of	of	ADP
ejpam-4521	546	8	a	a	DET
ejpam-4521	546	9	graph	graph	NOUN
ejpam-4521	546	10	.	.	PUNCT
ejpam-4521	546	11	journal	journal	NOUN
ejpam-4521	546	12	of	of	ADP
ejpam-4521	546	13	discrete	discrete	ADJ
ejpam-4521	546	14	mathematical	mathematical	ADJ
ejpam-4521	546	15	sciences	science	NOUN
ejpam-4521	546	16	and	and	CCONJ
ejpam-4521	546	17	cryptography	cryptography	NOUN
ejpam-4521	546	18	,	,	PUNCT
ejpam-4521	546	19	20(3):611–624	20(3):611–624	PROPN
ejpam-4521	546	20	,	,	PUNCT
ejpam-4521	546	21	2017	2017	NUM
ejpam-4521	546	22	.	.	PUNCT
ejpam-4521	547	1	[	[	X
ejpam-4521	547	2	10	10	NUM
ejpam-4521	547	3	]	]	X
ejpam-4521	547	4	d.j	d.j	PROPN
ejpam-4521	547	5	.	.	PROPN
ejpam-4521	547	6	klein	klein	PROPN
ejpam-4521	547	7	and	and	CCONJ
ejpam-4521	547	8	m.	m.	PROPN
ejpam-4521	547	9	randic	randic	PROPN
ejpam-4521	547	10	.	.	PUNCT
ejpam-4521	547	11	innate	innate	ADJ
ejpam-4521	547	12	degree	degree	NOUN
ejpam-4521	547	13	of	of	ADP
ejpam-4521	547	14	freedom	freedom	NOUN
ejpam-4521	547	15	of	of	ADP
ejpam-4521	547	16	a	a	DET
ejpam-4521	547	17	graph	graph	NOUN
ejpam-4521	547	18	.	.	PUNCT
ejpam-4521	548	1	comput	comput	NOUN
ejpam-4521	548	2	.	.	PUNCT
ejpam-4521	549	1	chem	chem	NOUN
ejpam-4521	549	2	.	.	PUNCT
ejpam-4521	549	3	,	,	PUNCT
ejpam-4521	549	4	8:516–521	8:516–521	NOUN
ejpam-4521	549	5	,	,	PUNCT
ejpam-4521	549	6	1987	1987	NUM
ejpam-4521	549	7	.	.	PUNCT
ejpam-4521	550	1	[	[	X
ejpam-4521	550	2	11	11	NUM
ejpam-4521	550	3	]	]	PUNCT
ejpam-4521	550	4	s.	s.	PROPN
ejpam-4521	550	5	nanding	nanding	PROPN
ejpam-4521	550	6	and	and	CCONJ
ejpam-4521	550	7	h.	h.	PROPN
ejpam-4521	550	8	rara	rara	PROPN
ejpam-4521	550	9	.	.	PUNCT
ejpam-4521	551	1	on	on	ADP
ejpam-4521	551	2	connected	connected	ADJ
ejpam-4521	551	3	co	co	ADJ
ejpam-4521	551	4	-	-	ADJ
ejpam-4521	551	5	independent	independent	ADJ
ejpam-4521	551	6	hop	hop	NOUN
ejpam-4521	551	7	domination	domination	NOUN
ejpam-4521	551	8	in	in	ADP
ejpam-4521	551	9	graphs	graph	NOUN
ejpam-4521	551	10	.	.	PUNCT
ejpam-4521	552	1	european	european	ADJ
ejpam-4521	552	2	journal	journal	PROPN
ejpam-4521	552	3	of	of	ADP
ejpam-4521	552	4	pure	pure	ADJ
ejpam-4521	552	5	and	and	CCONJ
ejpam-4521	552	6	applied	applied	ADJ
ejpam-4521	552	7	mathematics	mathematic	NOUN
ejpam-4521	552	8	,	,	PUNCT
ejpam-4521	552	9	14(4):1226–1236	14(4):1226–1236	NUM
ejpam-4521	552	10	,	,	PUNCT
ejpam-4521	552	11	2021	2021	NUM
ejpam-4521	552	12	.	.	PUNCT
ejpam-4521	553	1	[	[	X
ejpam-4521	553	2	12	12	NUM
ejpam-4521	553	3	]	]	X
ejpam-4521	553	4	c.	c.	PROPN
ejpam-4521	553	5	natarajan	natarajan	PROPN
ejpam-4521	553	6	and	and	CCONJ
ejpam-4521	553	7	s.	s.	PROPN
ejpam-4521	553	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4521	553	9	.	.	PUNCT
ejpam-4521	554	1	hop	hop	PROPN
ejpam-4521	554	2	domination	domination	NOUN
ejpam-4521	554	3	in	in	ADP
ejpam-4521	554	4	graphs	graph	NOUN
ejpam-4521	554	5	-	-	PUNCT
ejpam-4521	554	6	ii	ii	NOUN
ejpam-4521	554	7	.	.	PUNCT
ejpam-4521	554	8	versita	versita	PROPN
ejpam-4521	554	9	,	,	PUNCT
ejpam-4521	554	10	23(2):187	23(2):187	NUM
ejpam-4521	554	11	–	–	PUNCT
ejpam-4521	554	12	199	199	NUM
ejpam-4521	554	13	,	,	PUNCT
ejpam-4521	554	14	2015	2015	NUM
ejpam-4521	554	15	.	.	PUNCT
ejpam-4521	555	1	[	[	X
ejpam-4521	555	2	13	13	NUM
ejpam-4521	555	3	]	]	SYM
ejpam-4521	555	4	salasalan	salasalan	NOUN
ejpam-4521	555	5	g.	g.	PROPN
ejpam-4521	555	6	p.	p.	NOUN
ejpam-4521	555	7	and	and	CCONJ
ejpam-4521	555	8	canoy	canoy	PROPN
ejpam-4521	555	9	jr	jr	PROPN
ejpam-4521	555	10	s.	s.	PROPN
ejpam-4521	555	11	r.	r.	PROPN
ejpam-4521	555	12	revisiting	revisiting	PROPN
ejpam-4521	555	13	domination	domination	NOUN
ejpam-4521	555	14	,	,	PUNCT
ejpam-4521	555	15	hop	hop	NOUN
ejpam-4521	555	16	domination	domination	NOUN
ejpam-4521	555	17	,	,	PUNCT
ejpam-4521	555	18	and	and	CCONJ
ejpam-4521	555	19	global	global	ADJ
ejpam-4521	555	20	hop	hop	NOUN
ejpam-4521	555	21	domination	domination	NOUN
ejpam-4521	555	22	in	in	ADP
ejpam-4521	555	23	graphs	graph	NOUN
ejpam-4521	555	24	.	.	PUNCT
ejpam-4521	556	1	european	european	ADJ
ejpam-4521	556	2	journal	journal	PROPN
ejpam-4521	556	3	of	of	ADP
ejpam-4521	556	4	pure	pure	ADJ
ejpam-4521	556	5	and	and	CCONJ
ejpam-4521	556	6	applied	applied	ADJ
ejpam-4521	556	7	mathematics	mathematic	NOUN
ejpam-4521	556	8	,	,	PUNCT
ejpam-4521	556	9	14(4	14(4	NUM
ejpam-4521	556	10	)	)	PUNCT
ejpam-4521	556	11	,	,	PUNCT
ejpam-4521	556	12	2021	2021	NUM
ejpam-4521	556	13	.	.	PUNCT
ejpam-4521	557	1	[	[	X
ejpam-4521	557	2	14	14	NUM
ejpam-4521	557	3	]	]	X
ejpam-4521	557	4	y.	y.	PROPN
ejpam-4521	557	5	pabilona	pabilona	PROPN
ejpam-4521	557	6	and	and	CCONJ
ejpam-4521	557	7	h.	h.	PROPN
ejpam-4521	557	8	rara	rara	PROPN
ejpam-4521	557	9	.	.	PUNCT
ejpam-4521	558	1	total	total	ADJ
ejpam-4521	558	2	hop	hop	NOUN
ejpam-4521	558	3	dominating	dominating	NOUN
ejpam-4521	558	4	sets	set	NOUN
ejpam-4521	558	5	in	in	ADP
ejpam-4521	558	6	the	the	DET
ejpam-4521	558	7	join	join	NOUN
ejpam-4521	558	8	,	,	PUNCT
ejpam-4521	558	9	corona	corona	PROPN
ejpam-4521	558	10	,	,	PUNCT
ejpam-4521	558	11	and	and	CCONJ
ejpam-4521	558	12	lexicographic	lexicographic	ADJ
ejpam-4521	558	13	product	product	NOUN
ejpam-4521	558	14	of	of	ADP
ejpam-4521	558	15	graph	graph	NOUN
ejpam-4521	558	16	.	.	PUNCT
ejpam-4521	559	1	journal	journal	PROPN
ejpam-4521	559	2	of	of	ADP
ejpam-4521	559	3	algebra	algebra	PROPN
ejpam-4521	559	4	and	and	CCONJ
ejpam-4521	559	5	applied	apply	VERB
ejpam-4521	559	6	mathematics	mathematic	NOUN
ejpam-4521	559	7	,	,	PUNCT
ejpam-4521	559	8	2017	2017	NUM
ejpam-4521	559	9	.	.	PUNCT
ejpam-4521	560	1	[	[	X
ejpam-4521	560	2	15	15	NUM
ejpam-4521	560	3	]	]	X
ejpam-4521	560	4	y.	y.	PROPN
ejpam-4521	560	5	m.	m.	NOUN
ejpam-4521	560	6	pabilona	pabilona	PROPN
ejpam-4521	560	7	and	and	CCONJ
ejpam-4521	560	8	h.	h.	PROPN
ejpam-4521	560	9	rara	rara	PROPN
ejpam-4521	560	10	.	.	PUNCT
ejpam-4521	561	1	connected	connect	VERB
ejpam-4521	561	2	hop	hop	NOUN
ejpam-4521	561	3	domination	domination	NOUN
ejpam-4521	561	4	in	in	ADP
ejpam-4521	561	5	graphs	graph	NOUN
ejpam-4521	561	6	under	under	ADP
ejpam-4521	561	7	some	some	DET
ejpam-4521	561	8	binary	binary	ADJ
ejpam-4521	561	9	operations	operation	NOUN
ejpam-4521	561	10	.	.	PUNCT
ejpam-4521	562	1	asian	asian	ADJ
ejpam-4521	562	2	-	-	PUNCT
ejpam-4521	562	3	european	european	ADJ
ejpam-4521	562	4	journal	journal	NOUN
ejpam-4521	562	5	of	of	ADP
ejpam-4521	562	6	mathematics	mathematic	NOUN
ejpam-4521	562	7	,	,	PUNCT
ejpam-4521	562	8	11(5	11(5	NUM
ejpam-4521	562	9	)	)	PUNCT
ejpam-4521	562	10	,	,	PUNCT
ejpam-4521	562	11	2018	2018	NUM
ejpam-4521	562	12	.	.	PUNCT
ejpam-4521	563	1	[	[	X
ejpam-4521	563	2	16	16	NUM
ejpam-4521	563	3	]	]	X
ejpam-4521	563	4	t.p	t.p	PROPN
ejpam-4521	563	5	.	.	PROPN
ejpam-4521	563	6	zivkovic	zivkovic	PROPN
ejpam-4521	563	7	,	,	PUNCT
ejpam-4521	563	8	f.	f.	PROPN
ejpam-4521	563	9	harary	harary	PROPN
ejpam-4521	563	10	,	,	PUNCT
ejpam-4521	563	11	and	and	CCONJ
ejpam-4521	563	12	klein	klein	PROPN
ejpam-4521	563	13	d.j	d.j	PROPN
ejpam-4521	563	14	.	.	PROPN
ejpam-4521	563	15	graphical	graphical	ADJ
ejpam-4521	563	16	properties	property	NOUN
ejpam-4521	563	17	of	of	ADP
ejpam-4521	563	18	polyhexes	polyhexe	NOUN
ejpam-4521	563	19	:	:	PUNCT
ejpam-4521	563	20	perfect	perfect	ADJ
ejpam-4521	563	21	matching	matching	NOUN
ejpam-4521	563	22	vector	vector	NOUN
ejpam-4521	563	23	and	and	CCONJ
ejpam-4521	563	24	forcing	forcing	NOUN
ejpam-4521	563	25	.	.	PUNCT
ejpam-4521	564	1	j.	j.	PROPN
ejpam-4521	564	2	math	math	PROPN
ejpam-4521	564	3	.	.	PUNCT
ejpam-4521	565	1	chem	chem	PROPN
ejpam-4521	565	2	.	.	PUNCT
ejpam-4521	565	3	,	,	PUNCT
ejpam-4521	566	1	6:295–306	6:295–306	NUM
ejpam-4521	566	2	,	,	PUNCT
ejpam-4521	566	3	1991	1991	NUM
ejpam-4521	566	4	.	.	PUNCT