id	sid	tid	token	lemma	pos
ejpam-4069	1	1	european	european	PROPN
ejpam-4069	1	2	journal	journal	PROPN
ejpam-4069	1	3	of	of	ADP
ejpam-4069	1	4	pure	pure	ADJ
ejpam-4069	1	5	and	and	CCONJ
ejpam-4069	1	6	applied	apply	VERB
ejpam-4069	1	7	mathematics	mathematic	NOUN
ejpam-4069	1	8	vol	vol	NOUN
ejpam-4069	1	9	.	.	PUNCT
ejpam-4069	2	1	14	14	NUM
ejpam-4069	2	2	,	,	PUNCT
ejpam-4069	2	3	no	no	INTJ
ejpam-4069	2	4	.	.	NOUN
ejpam-4069	2	5	4	4	NUM
ejpam-4069	2	6	,	,	PUNCT
ejpam-4069	2	7	2021	2021	NUM
ejpam-4069	2	8	,	,	PUNCT
ejpam-4069	2	9	1226	1226	NUM
ejpam-4069	2	10	-	-	SYM
ejpam-4069	2	11	1236	1236	NUM
ejpam-4069	2	12	issn	issn	PROPN
ejpam-4069	2	13	1307	1307	NUM
ejpam-4069	2	14	-	-	SYM
ejpam-4069	2	15	5543	5543	NUM
ejpam-4069	2	16	–	–	PUNCT
ejpam-4069	2	17	ejpam.com	ejpam.com	X
ejpam-4069	2	18	published	publish	VERB
ejpam-4069	2	19	by	by	ADP
ejpam-4069	2	20	new	new	PROPN
ejpam-4069	2	21	york	york	PROPN
ejpam-4069	2	22	business	business	PROPN
ejpam-4069	2	23	global	global	ADJ
ejpam-4069	2	24	on	on	ADP
ejpam-4069	2	25	connected	connected	ADJ
ejpam-4069	2	26	co	co	ADJ
ejpam-4069	2	27	-	-	ADJ
ejpam-4069	2	28	independent	independent	ADJ
ejpam-4069	2	29	hop	hop	NOUN
ejpam-4069	2	30	domination	domination	NOUN
ejpam-4069	2	31	in	in	ADP
ejpam-4069	2	32	graphs	graph	NOUN
ejpam-4069	2	33	sandra	sandra	PROPN
ejpam-4069	2	34	a.	a.	PROPN
ejpam-4069	2	35	nanding1,∗	nanding1,∗	PROPN
ejpam-4069	2	36	,	,	PUNCT
ejpam-4069	2	37	helen	helen	PROPN
ejpam-4069	2	38	m.	m.	PROPN
ejpam-4069	2	39	rara2	rara2	PROPN
ejpam-4069	3	1	1	1	NUM
ejpam-4069	3	2	department	department	NOUN
ejpam-4069	3	3	of	of	ADP
ejpam-4069	3	4	mathematics	mathematic	NOUN
ejpam-4069	3	5	and	and	CCONJ
ejpam-4069	3	6	statistics	statistic	NOUN
ejpam-4069	3	7	,	,	PUNCT
ejpam-4069	3	8	college	college	NOUN
ejpam-4069	3	9	of	of	ADP
ejpam-4069	3	10	science	science	NOUN
ejpam-4069	3	11	and	and	CCONJ
ejpam-4069	3	12	mathematics	mathematic	NOUN
ejpam-4069	3	13	,	,	PUNCT
ejpam-4069	3	14	mindanao	mindanao	PROPN
ejpam-4069	3	15	state	state	PROPN
ejpam-4069	3	16	university	university	PROPN
ejpam-4069	3	17	-	-	PUNCT
ejpam-4069	3	18	iligan	iligan	PROPN
ejpam-4069	3	19	institute	institute	PROPN
ejpam-4069	3	20	of	of	ADP
ejpam-4069	3	21	technology	technology	PROPN
ejpam-4069	3	22	,	,	PUNCT
ejpam-4069	3	23	9200	9200	NUM
ejpam-4069	3	24	iligan	iligan	ADJ
ejpam-4069	3	25	city	city	NOUN
ejpam-4069	3	26	,	,	PUNCT
ejpam-4069	3	27	philippines	philippines	PROPN
ejpam-4069	3	28	2	2	NUM
ejpam-4069	3	29	department	department	NOUN
ejpam-4069	3	30	of	of	ADP
ejpam-4069	3	31	mathematics	mathematic	NOUN
ejpam-4069	3	32	and	and	CCONJ
ejpam-4069	3	33	statistics	statistic	NOUN
ejpam-4069	3	34	,	,	PUNCT
ejpam-4069	3	35	college	college	NOUN
ejpam-4069	3	36	of	of	ADP
ejpam-4069	3	37	science	science	NOUN
ejpam-4069	3	38	and	and	CCONJ
ejpam-4069	3	39	mathematics	mathematic	NOUN
ejpam-4069	3	40	,	,	PUNCT
ejpam-4069	3	41	center	center	NOUN
ejpam-4069	3	42	of	of	ADP
ejpam-4069	3	43	graph	graph	NOUN
ejpam-4069	3	44	theory	theory	NOUN
ejpam-4069	3	45	,	,	PUNCT
ejpam-4069	3	46	algebra	algebra	NOUN
ejpam-4069	3	47	,	,	PUNCT
ejpam-4069	3	48	and	and	CCONJ
ejpam-4069	3	49	analysis	analysis	NOUN
ejpam-4069	3	50	-	-	PUNCT
ejpam-4069	3	51	premier	premier	NOUN
ejpam-4069	3	52	research	research	NOUN
ejpam-4069	3	53	institute	institute	PROPN
ejpam-4069	3	54	of	of	ADP
ejpam-4069	3	55	science	science	NOUN
ejpam-4069	3	56	and	and	CCONJ
ejpam-4069	3	57	mathematics	mathematic	NOUN
ejpam-4069	3	58	,	,	PUNCT
ejpam-4069	3	59	mindanao	mindanao	PROPN
ejpam-4069	3	60	state	state	PROPN
ejpam-4069	3	61	university	university	PROPN
ejpam-4069	3	62	-	-	PUNCT
ejpam-4069	3	63	iligan	iligan	PROPN
ejpam-4069	3	64	institute	institute	PROPN
ejpam-4069	3	65	of	of	ADP
ejpam-4069	3	66	technology	technology	PROPN
ejpam-4069	3	67	,	,	PUNCT
ejpam-4069	3	68	9200	9200	NUM
ejpam-4069	3	69	iligan	iligan	ADJ
ejpam-4069	3	70	city	city	NOUN
ejpam-4069	3	71	,	,	PUNCT
ejpam-4069	3	72	philippines	philippine	NOUN
ejpam-4069	3	73	abstract	abstract	ADJ
ejpam-4069	3	74	.	.	PUNCT
ejpam-4069	4	1	let	let	VERB
ejpam-4069	4	2	g	g	PRON
ejpam-4069	4	3	be	be	AUX
ejpam-4069	4	4	a	a	DET
ejpam-4069	4	5	connected	connected	ADJ
ejpam-4069	4	6	graph	graph	NOUN
ejpam-4069	4	7	.	.	PUNCT
ejpam-4069	5	1	a	a	DET
ejpam-4069	5	2	subset	subset	NOUN
ejpam-4069	5	3	s	s	NOUN
ejpam-4069	5	4	of	of	ADP
ejpam-4069	5	5	v	v	NOUN
ejpam-4069	5	6	(	(	PUNCT
ejpam-4069	5	7	g	g	NOUN
ejpam-4069	5	8	)	)	PUNCT
ejpam-4069	5	9	is	be	AUX
ejpam-4069	5	10	a	a	DET
ejpam-4069	5	11	connected	connected	ADJ
ejpam-4069	5	12	co	co	NOUN
ejpam-4069	5	13	-	-	ADJ
ejpam-4069	5	14	independent	independent	ADJ
ejpam-4069	5	15	hop	hop	NOUN
ejpam-4069	5	16	dominating	dominating	NOUN
ejpam-4069	5	17	set	set	VERB
ejpam-4069	5	18	in	in	ADP
ejpam-4069	5	19	g	g	PROPN
ejpam-4069	5	20	if	if	SCONJ
ejpam-4069	5	21	the	the	DET
ejpam-4069	5	22	subgraph	subgraph	NOUN
ejpam-4069	5	23	induced	induce	VERB
ejpam-4069	5	24	by	by	ADP
ejpam-4069	5	25	s	s	PROPN
ejpam-4069	5	26	is	be	AUX
ejpam-4069	5	27	connected	connect	VERB
ejpam-4069	5	28	and	and	CCONJ
ejpam-4069	5	29	v	v	NOUN
ejpam-4069	5	30	(	(	PUNCT
ejpam-4069	5	31	g)\s	g)\s	NOUN
ejpam-4069	5	32	is	be	AUX
ejpam-4069	5	33	an	an	DET
ejpam-4069	5	34	independent	independent	ADJ
ejpam-4069	5	35	set	set	NOUN
ejpam-4069	5	36	where	where	SCONJ
ejpam-4069	5	37	for	for	ADP
ejpam-4069	5	38	each	each	DET
ejpam-4069	5	39	v	v	NUM
ejpam-4069	5	40	∈	∈	NOUN
ejpam-4069	5	41	v	v	NOUN
ejpam-4069	5	42	(	(	PUNCT
ejpam-4069	5	43	g)\s	g)\s	NOUN
ejpam-4069	5	44	,	,	PUNCT
ejpam-4069	5	45	there	there	PRON
ejpam-4069	5	46	exists	exist	VERB
ejpam-4069	5	47	a	a	DET
ejpam-4069	5	48	vertex	vertex	NOUN
ejpam-4069	5	49	u	u	NOUN
ejpam-4069	5	50	∈	∈	NOUN
ejpam-4069	5	51	s	s	VERB
ejpam-4069	5	52	such	such	ADJ
ejpam-4069	5	53	that	that	DET
ejpam-4069	5	54	dg(u	dg(u	ADJ
ejpam-4069	5	55	,	,	PUNCT
ejpam-4069	5	56	v	v	NOUN
ejpam-4069	5	57	)	)	PUNCT
ejpam-4069	6	1	=	=	SYM
ejpam-4069	6	2	2	2	X
ejpam-4069	6	3	.	.	X
ejpam-4069	6	4	the	the	DET
ejpam-4069	6	5	smallest	small	ADJ
ejpam-4069	6	6	cardinality	cardinality	NOUN
ejpam-4069	6	7	of	of	ADP
ejpam-4069	6	8	such	such	DET
ejpam-4069	6	9	an	an	DET
ejpam-4069	6	10	s	s	NOUN
ejpam-4069	6	11	is	be	AUX
ejpam-4069	6	12	called	call	VERB
ejpam-4069	6	13	the	the	DET
ejpam-4069	6	14	connected	connected	ADJ
ejpam-4069	6	15	co	co	NOUN
ejpam-4069	6	16	-	-	ADJ
ejpam-4069	6	17	independent	independent	ADJ
ejpam-4069	6	18	hop	hop	NOUN
ejpam-4069	6	19	domination	domination	NOUN
ejpam-4069	6	20	number	number	NOUN
ejpam-4069	6	21	of	of	ADP
ejpam-4069	6	22	g.	g.	PROPN
ejpam-4069	6	23	this	this	DET
ejpam-4069	6	24	paper	paper	NOUN
ejpam-4069	6	25	presents	present	VERB
ejpam-4069	6	26	the	the	DET
ejpam-4069	6	27	characterizations	characterization	NOUN
ejpam-4069	6	28	of	of	ADP
ejpam-4069	6	29	the	the	DET
ejpam-4069	6	30	connected	connected	ADJ
ejpam-4069	6	31	co	co	NOUN
ejpam-4069	6	32	-	-	ADJ
ejpam-4069	6	33	independent	independent	ADJ
ejpam-4069	6	34	hop	hop	NOUN
ejpam-4069	6	35	dominating	dominating	NOUN
ejpam-4069	6	36	sets	set	NOUN
ejpam-4069	6	37	in	in	ADP
ejpam-4069	6	38	the	the	DET
ejpam-4069	6	39	join	join	NOUN
ejpam-4069	6	40	,	,	PUNCT
ejpam-4069	6	41	corona	corona	NOUN
ejpam-4069	6	42	and	and	CCONJ
ejpam-4069	6	43	lexicographic	lexicographic	ADJ
ejpam-4069	6	44	product	product	NOUN
ejpam-4069	6	45	of	of	ADP
ejpam-4069	6	46	two	two	NUM
ejpam-4069	6	47	graphs	graph	NOUN
ejpam-4069	6	48	.	.	PUNCT
ejpam-4069	7	1	it	it	PRON
ejpam-4069	7	2	also	also	ADV
ejpam-4069	7	3	discusses	discuss	VERB
ejpam-4069	7	4	the	the	DET
ejpam-4069	7	5	corresponding	corresponding	ADJ
ejpam-4069	7	6	connected	connect	VERB
ejpam-4069	7	7	co	co	ADJ
ejpam-4069	7	8	-	-	ADJ
ejpam-4069	7	9	independent	independent	ADJ
ejpam-4069	7	10	hop	hop	NOUN
ejpam-4069	7	11	domination	domination	NOUN
ejpam-4069	7	12	numbers	number	NOUN
ejpam-4069	7	13	of	of	ADP
ejpam-4069	7	14	the	the	DET
ejpam-4069	7	15	aforementioned	aforementioned	ADJ
ejpam-4069	7	16	graphs	graph	NOUN
ejpam-4069	7	17	.	.	PUNCT
ejpam-4069	8	1	2020	2020	NUM
ejpam-4069	8	2	mathematics	mathematic	NOUN
ejpam-4069	8	3	subject	subject	NOUN
ejpam-4069	8	4	classifications	classification	NOUN
ejpam-4069	8	5	:	:	PUNCT
ejpam-4069	8	6	05c69	05c69	X
ejpam-4069	8	7	key	key	ADJ
ejpam-4069	8	8	words	word	NOUN
ejpam-4069	8	9	and	and	CCONJ
ejpam-4069	8	10	phrases	phrase	NOUN
ejpam-4069	8	11	:	:	PUNCT
ejpam-4069	8	12	connected	connected	ADJ
ejpam-4069	8	13	co	co	ADJ
ejpam-4069	8	14	-	-	ADJ
ejpam-4069	8	15	independent	independent	ADJ
ejpam-4069	8	16	hop	hop	NOUN
ejpam-4069	8	17	dominating	dominating	NOUN
ejpam-4069	8	18	set	set	NOUN
ejpam-4069	8	19	,	,	PUNCT
ejpam-4069	8	20	connected	connected	ADJ
ejpam-4069	8	21	co	co	ADJ
ejpam-4069	8	22	-	-	ADJ
ejpam-4069	8	23	independent	independent	ADJ
ejpam-4069	8	24	hop	hop	NOUN
ejpam-4069	8	25	domination	domination	NOUN
ejpam-4069	8	26	number	number	NOUN
ejpam-4069	8	27	,	,	PUNCT
ejpam-4069	8	28	strictly	strictly	ADV
ejpam-4069	8	29	co	co	ADJ
ejpam-4069	8	30	-	-	ADJ
ejpam-4069	8	31	independent	independent	ADJ
ejpam-4069	8	32	set	set	NOUN
ejpam-4069	8	33	,	,	PUNCT
ejpam-4069	8	34	strictly	strictly	ADV
ejpam-4069	8	35	co	co	ADJ
ejpam-4069	8	36	-	-	ADJ
ejpam-4069	8	37	independent	independent	ADJ
ejpam-4069	8	38	number	number	NOUN
ejpam-4069	8	39	,	,	PUNCT
ejpam-4069	8	40	join	join	NOUN
ejpam-4069	8	41	,	,	PUNCT
ejpam-4069	8	42	corona	corona	PROPN
ejpam-4069	8	43	,	,	PUNCT
ejpam-4069	8	44	lexicographic	lexicographic	ADJ
ejpam-4069	8	45	product	product	NOUN
ejpam-4069	8	46	1	1	NUM
ejpam-4069	8	47	.	.	PUNCT
ejpam-4069	8	48	introduction	introduction	NOUN
ejpam-4069	8	49	in	in	ADP
ejpam-4069	8	50	the	the	DET
ejpam-4069	8	51	late	late	ADJ
ejpam-4069	8	52	1950	1950	NUM
ejpam-4069	8	53	’s	’s	NOUN
ejpam-4069	8	54	and	and	CCONJ
ejpam-4069	8	55	1960	1960	NUM
ejpam-4069	8	56	’s	’s	NOUN
ejpam-4069	8	57	,	,	PUNCT
ejpam-4069	8	58	the	the	DET
ejpam-4069	8	59	study	study	NOUN
ejpam-4069	8	60	on	on	ADP
ejpam-4069	8	61	domination	domination	NOUN
ejpam-4069	8	62	in	in	ADP
ejpam-4069	8	63	graphs	graph	NOUN
ejpam-4069	8	64	was	be	AUX
ejpam-4069	8	65	developed	develop	VERB
ejpam-4069	8	66	,	,	PUNCT
ejpam-4069	8	67	beginning	begin	VERB
ejpam-4069	8	68	with	with	ADP
ejpam-4069	8	69	c.	c.	PROPN
ejpam-4069	8	70	berge	berge	NOUN
ejpam-4069	9	1	[	[	X
ejpam-4069	9	2	1	1	X
ejpam-4069	9	3	]	]	PUNCT
ejpam-4069	9	4	in	in	ADP
ejpam-4069	9	5	1958	1958	NUM
ejpam-4069	9	6	.	.	PUNCT
ejpam-4069	10	1	there	there	PRON
ejpam-4069	10	2	are	be	VERB
ejpam-4069	10	3	now	now	ADV
ejpam-4069	10	4	many	many	ADJ
ejpam-4069	10	5	studies	study	NOUN
ejpam-4069	10	6	involving	involve	VERB
ejpam-4069	10	7	domination	domination	NOUN
ejpam-4069	10	8	and	and	CCONJ
ejpam-4069	10	9	its	its	PRON
ejpam-4069	10	10	variations	variation	NOUN
ejpam-4069	10	11	.	.	PUNCT
ejpam-4069	11	1	one	one	NUM
ejpam-4069	11	2	of	of	ADP
ejpam-4069	11	3	its	its	PRON
ejpam-4069	11	4	variation	variation	NOUN
ejpam-4069	11	5	is	be	AUX
ejpam-4069	11	6	the	the	DET
ejpam-4069	11	7	connected	connected	ADJ
ejpam-4069	11	8	co	co	ADJ
ejpam-4069	11	9	-	-	ADJ
ejpam-4069	11	10	independent	independent	ADJ
ejpam-4069	11	11	domination	domination	NOUN
ejpam-4069	11	12	number	number	NOUN
ejpam-4069	11	13	of	of	ADP
ejpam-4069	11	14	graphs	graph	NOUN
ejpam-4069	11	15	introduced	introduce	VERB
ejpam-4069	11	16	by	by	ADP
ejpam-4069	11	17	b.	b.	PROPN
ejpam-4069	11	18	gayathri	gayathri	PROPN
ejpam-4069	11	19	and	and	CCONJ
ejpam-4069	11	20	s.	s.	PROPN
ejpam-4069	11	21	kaspar	kaspar	PROPN
ejpam-4069	11	22	in	in	ADP
ejpam-4069	11	23	2010	2010	NUM
ejpam-4069	11	24	[	[	X
ejpam-4069	11	25	3	3	NUM
ejpam-4069	11	26	]	]	PUNCT
ejpam-4069	11	27	.	.	PUNCT
ejpam-4069	12	1	also	also	ADV
ejpam-4069	12	2	,	,	PUNCT
ejpam-4069	12	3	connected	connected	ADJ
ejpam-4069	12	4	co	co	ADJ
ejpam-4069	12	5	-	-	ADJ
ejpam-4069	12	6	independent	independent	ADJ
ejpam-4069	12	7	domination	domination	NOUN
ejpam-4069	12	8	number	number	NOUN
ejpam-4069	12	9	in	in	ADP
ejpam-4069	12	10	graphs	graph	NOUN
ejpam-4069	12	11	were	be	AUX
ejpam-4069	12	12	studied	study	VERB
ejpam-4069	12	13	in	in	ADP
ejpam-4069	12	14	[	[	X
ejpam-4069	12	15	2	2	NUM
ejpam-4069	12	16	,	,	PUNCT
ejpam-4069	12	17	6	6	NUM
ejpam-4069	12	18	,	,	PUNCT
ejpam-4069	12	19	12	12	NUM
ejpam-4069	12	20	]	]	PUNCT
ejpam-4069	12	21	.	.	PUNCT
ejpam-4069	13	1	years	year	NOUN
ejpam-4069	13	2	later	later	ADV
ejpam-4069	13	3	,	,	PUNCT
ejpam-4069	13	4	new	new	ADJ
ejpam-4069	13	5	domination	domination	NOUN
ejpam-4069	13	6	parameter	parameter	NOUN
ejpam-4069	13	7	called	call	VERB
ejpam-4069	13	8	hop	hop	NOUN
ejpam-4069	13	9	domination	domination	NOUN
ejpam-4069	13	10	in	in	ADP
ejpam-4069	13	11	graph	graph	NOUN
ejpam-4069	13	12	is	be	AUX
ejpam-4069	13	13	introduced	introduce	VERB
ejpam-4069	13	14	by	by	ADP
ejpam-4069	13	15	natarajan	natarajan	PROPN
ejpam-4069	13	16	and	and	CCONJ
ejpam-4069	13	17	ayyaswamy	ayyaswamy	ADJ
ejpam-4069	13	18	[	[	X
ejpam-4069	13	19	8	8	NUM
ejpam-4069	13	20	]	]	PUNCT
ejpam-4069	13	21	.	.	PUNCT
ejpam-4069	14	1	hop	hop	PROPN
ejpam-4069	14	2	domination	domination	NOUN
ejpam-4069	14	3	in	in	ADP
ejpam-4069	14	4	graphs	graph	NOUN
ejpam-4069	14	5	were	be	AUX
ejpam-4069	14	6	also	also	ADV
ejpam-4069	14	7	studied	study	VERB
ejpam-4069	14	8	in	in	ADP
ejpam-4069	14	9	[	[	X
ejpam-4069	14	10	7	7	NUM
ejpam-4069	14	11	,	,	PUNCT
ejpam-4069	14	12	9–11	9–11	NOUN
ejpam-4069	14	13	,	,	PUNCT
ejpam-4069	14	14	13	13	NUM
ejpam-4069	14	15	]	]	PUNCT
ejpam-4069	14	16	.	.	PUNCT
ejpam-4069	15	1	in	in	ADP
ejpam-4069	15	2	this	this	DET
ejpam-4069	15	3	study	study	NOUN
ejpam-4069	15	4	,	,	PUNCT
ejpam-4069	15	5	the	the	DET
ejpam-4069	15	6	researcher	researcher	NOUN
ejpam-4069	15	7	defines	define	VERB
ejpam-4069	15	8	and	and	CCONJ
ejpam-4069	15	9	establishes	establish	VERB
ejpam-4069	15	10	a	a	DET
ejpam-4069	15	11	new	new	ADJ
ejpam-4069	15	12	concept	concept	NOUN
ejpam-4069	15	13	of	of	ADP
ejpam-4069	15	14	hop	hop	NOUN
ejpam-4069	15	15	domination	domination	NOUN
ejpam-4069	15	16	called	call	VERB
ejpam-4069	15	17	a	a	DET
ejpam-4069	15	18	connected	connected	ADJ
ejpam-4069	15	19	co	co	ADJ
ejpam-4069	15	20	-	-	ADJ
ejpam-4069	15	21	independent	independent	ADJ
ejpam-4069	15	22	hop	hop	NOUN
ejpam-4069	15	23	domination	domination	NOUN
ejpam-4069	15	24	and	and	CCONJ
ejpam-4069	15	25	generates	generate	VERB
ejpam-4069	15	26	some	some	DET
ejpam-4069	15	27	characterizations	characterization	NOUN
ejpam-4069	15	28	∗corresponding	∗corresponde	VERB
ejpam-4069	15	29	author	author	NOUN
ejpam-4069	15	30	.	.	PUNCT
ejpam-4069	16	1	doi	doi	NOUN
ejpam-4069	16	2	:	:	PUNCT
ejpam-4069	16	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4069	https://doi.org/10.29020/nybg.ejpam.v14i4.4069	X
ejpam-4069	16	4	email	email	NOUN
ejpam-4069	16	5	addresses	address	NOUN
ejpam-4069	16	6	:	:	PUNCT
ejpam-4069	16	7	sandra.nanding@g.msuiit.edu.ph	sandra.nanding@g.msuiit.edu.ph	PROPN
ejpam-4069	16	8	(	(	PUNCT
ejpam-4069	16	9	s.	s.	PROPN
ejpam-4069	16	10	nanding	nanding	PROPN
ejpam-4069	16	11	)	)	PUNCT
ejpam-4069	16	12	,	,	PUNCT
ejpam-4069	16	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4069	16	14	(	(	PUNCT
ejpam-4069	16	15	h.	h.	PROPN
ejpam-4069	16	16	rara	rara	PROPN
ejpam-4069	16	17	)	)	PUNCT
ejpam-4069	16	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4069	16	19	1226	1226	NUM
ejpam-4069	16	20	©	©	PROPN
ejpam-4069	16	21	2021	2021	NUM
ejpam-4069	16	22	ejpam	ejpam	VERB
ejpam-4069	16	23	all	all	DET
ejpam-4069	16	24	rights	right	NOUN
ejpam-4069	16	25	reserved	reserve	VERB
ejpam-4069	16	26	.	.	PUNCT
ejpam-4069	17	1	s.	s.	PROPN
ejpam-4069	17	2	nanding	nanding	PROPN
ejpam-4069	17	3	,	,	PUNCT
ejpam-4069	17	4	h.	h.	PROPN
ejpam-4069	17	5	rara	rara	PROPN
ejpam-4069	17	6	/	/	SYM
ejpam-4069	17	7	eur	eur	PROPN
ejpam-4069	17	8	.	.	PUNCT
ejpam-4069	18	1	j.	j.	PROPN
ejpam-4069	18	2	pure	pure	PROPN
ejpam-4069	18	3	appl	appl	PROPN
ejpam-4069	18	4	.	.	PROPN
ejpam-4069	18	5	math	math	PROPN
ejpam-4069	18	6	,	,	PUNCT
ejpam-4069	18	7	14	14	NUM
ejpam-4069	18	8	(	(	PUNCT
ejpam-4069	18	9	4	4	NUM
ejpam-4069	18	10	)	)	PUNCT
ejpam-4069	18	11	(	(	PUNCT
ejpam-4069	18	12	2021	2021	NUM
ejpam-4069	18	13	)	)	PUNCT
ejpam-4069	18	14	,	,	PUNCT
ejpam-4069	18	15	1226	1226	NUM
ejpam-4069	18	16	-	-	SYM
ejpam-4069	18	17	1236	1236	NUM
ejpam-4069	18	18	1227	1227	NUM
ejpam-4069	18	19	of	of	ADP
ejpam-4069	18	20	connected	connected	ADJ
ejpam-4069	18	21	co	co	ADJ
ejpam-4069	18	22	-	-	ADJ
ejpam-4069	18	23	independent	independent	ADJ
ejpam-4069	18	24	hop	hop	NOUN
ejpam-4069	18	25	domination	domination	NOUN
ejpam-4069	18	26	in	in	ADP
ejpam-4069	18	27	graphs	graph	NOUN
ejpam-4069	18	28	.	.	PUNCT
ejpam-4069	19	1	connected	connect	VERB
ejpam-4069	19	2	co	co	ADJ
ejpam-4069	19	3	-	-	ADJ
ejpam-4069	19	4	independent	independent	ADJ
ejpam-4069	19	5	hop	hop	NOUN
ejpam-4069	19	6	domination	domination	NOUN
ejpam-4069	19	7	in	in	ADP
ejpam-4069	19	8	graphs	graph	NOUN
ejpam-4069	19	9	can	can	AUX
ejpam-4069	19	10	have	have	VERB
ejpam-4069	19	11	real	real	ADJ
ejpam-4069	19	12	world	world	NOUN
ejpam-4069	19	13	applications	application	NOUN
ejpam-4069	19	14	.	.	PUNCT
ejpam-4069	20	1	for	for	ADP
ejpam-4069	20	2	an	an	DET
ejpam-4069	20	3	application	application	NOUN
ejpam-4069	20	4	,	,	PUNCT
ejpam-4069	20	5	in	in	ADP
ejpam-4069	20	6	[	[	PUNCT
ejpam-4069	20	7	5	5	NUM
ejpam-4069	20	8	]	]	PUNCT
ejpam-4069	20	9	,	,	PUNCT
ejpam-4069	20	10	desormeaux	desormeaux	ADJ
ejpam-4069	20	11	,	,	PUNCT
ejpam-4069	20	12	haynes	hayne	NOUN
ejpam-4069	20	13	,	,	PUNCT
ejpam-4069	20	14	and	and	CCONJ
ejpam-4069	20	15	henning	henning	NOUN
ejpam-4069	20	16	inspired	inspire	VERB
ejpam-4069	20	17	their	their	PRON
ejpam-4069	20	18	research	research	NOUN
ejpam-4069	20	19	on	on	ADP
ejpam-4069	20	20	these	these	DET
ejpam-4069	20	21	concepts	concept	NOUN
ejpam-4069	20	22	through	through	ADP
ejpam-4069	20	23	social	social	ADJ
ejpam-4069	20	24	networking	network	VERB
ejpam-4069	20	25	applications	application	NOUN
ejpam-4069	20	26	.	.	PUNCT
ejpam-4069	21	1	they	they	PRON
ejpam-4069	21	2	considered	consider	VERB
ejpam-4069	21	3	a	a	DET
ejpam-4069	21	4	factory	factory	NOUN
ejpam-4069	21	5	with	with	ADP
ejpam-4069	21	6	a	a	DET
ejpam-4069	21	7	large	large	ADJ
ejpam-4069	21	8	number	number	NOUN
ejpam-4069	21	9	of	of	ADP
ejpam-4069	21	10	employees	employee	NOUN
ejpam-4069	21	11	and	and	CCONJ
ejpam-4069	21	12	needed	need	VERB
ejpam-4069	21	13	to	to	PART
ejpam-4069	21	14	implement	implement	VERB
ejpam-4069	21	15	a	a	DET
ejpam-4069	21	16	quality	quality	NOUN
ejpam-4069	21	17	assurance	assurance	NOUN
ejpam-4069	21	18	checking	check	VERB
ejpam-4069	21	19	system	system	NOUN
ejpam-4069	21	20	of	of	ADP
ejpam-4069	21	21	their	their	PRON
ejpam-4069	21	22	workers	worker	NOUN
ejpam-4069	21	23	.	.	PUNCT
ejpam-4069	22	1	the	the	DET
ejpam-4069	22	2	factory	factory	NOUN
ejpam-4069	22	3	manager	manager	NOUN
ejpam-4069	22	4	decides	decide	VERB
ejpam-4069	22	5	to	to	PART
ejpam-4069	22	6	designate	designate	VERB
ejpam-4069	22	7	an	an	DET
ejpam-4069	22	8	internal	internal	ADJ
ejpam-4069	22	9	committee	committee	NOUN
ejpam-4069	22	10	to	to	PART
ejpam-4069	22	11	do	do	VERB
ejpam-4069	22	12	this	this	PRON
ejpam-4069	22	13	.	.	PUNCT
ejpam-4069	23	1	in	in	ADP
ejpam-4069	23	2	other	other	ADJ
ejpam-4069	23	3	words	word	NOUN
ejpam-4069	23	4	,	,	PUNCT
ejpam-4069	23	5	the	the	DET
ejpam-4069	23	6	manager	manager	NOUN
ejpam-4069	23	7	will	will	AUX
ejpam-4069	23	8	select	select	VERB
ejpam-4069	23	9	some	some	DET
ejpam-4069	23	10	workers	worker	NOUN
ejpam-4069	23	11	to	to	PART
ejpam-4069	23	12	form	form	VERB
ejpam-4069	23	13	a	a	DET
ejpam-4069	23	14	quality	quality	NOUN
ejpam-4069	23	15	assurance	assurance	NOUN
ejpam-4069	23	16	team	team	NOUN
ejpam-4069	23	17	to	to	PART
ejpam-4069	23	18	inspect	inspect	VERB
ejpam-4069	23	19	the	the	DET
ejpam-4069	23	20	work	work	NOUN
ejpam-4069	23	21	of	of	ADP
ejpam-4069	23	22	their	their	PRON
ejpam-4069	23	23	co	co	NOUN
ejpam-4069	23	24	-	-	NOUN
ejpam-4069	23	25	workers	worker	NOUN
ejpam-4069	23	26	.	.	PUNCT
ejpam-4069	24	1	the	the	DET
ejpam-4069	24	2	manager	manager	NOUN
ejpam-4069	24	3	wants	want	VERB
ejpam-4069	24	4	to	to	PART
ejpam-4069	24	5	keep	keep	VERB
ejpam-4069	24	6	this	this	DET
ejpam-4069	24	7	team	team	NOUN
ejpam-4069	24	8	as	as	ADV
ejpam-4069	24	9	small	small	ADJ
ejpam-4069	24	10	as	as	ADP
ejpam-4069	24	11	possible	possible	ADJ
ejpam-4069	24	12	to	to	PART
ejpam-4069	24	13	minimize	minimize	VERB
ejpam-4069	24	14	costs	cost	NOUN
ejpam-4069	24	15	(	(	PUNCT
ejpam-4069	24	16	extra	extra	ADJ
ejpam-4069	24	17	costs	cost	NOUN
ejpam-4069	24	18	for	for	ADP
ejpam-4069	24	19	inspectors	inspector	NOUN
ejpam-4069	24	20	)	)	PUNCT
ejpam-4069	24	21	and	and	CCONJ
ejpam-4069	24	22	protect	protect	VERB
ejpam-4069	24	23	privacy	privacy	NOUN
ejpam-4069	24	24	(	(	PUNCT
ejpam-4069	24	25	keep	keep	VERB
ejpam-4069	24	26	the	the	DET
ejpam-4069	24	27	inspectors	inspector	NOUN
ejpam-4069	24	28	’	’	PART
ejpam-4069	24	29	identity	identity	NOUN
ejpam-4069	24	30	confidential	confidential	ADJ
ejpam-4069	24	31	)	)	PUNCT
ejpam-4069	24	32	.	.	PUNCT
ejpam-4069	25	1	to	to	PART
ejpam-4069	25	2	avoid	avoid	VERB
ejpam-4069	25	3	bias	bias	NOUN
ejpam-4069	25	4	,	,	PUNCT
ejpam-4069	25	5	an	an	DET
ejpam-4069	25	6	inspector	inspector	NOUN
ejpam-4069	25	7	should	should	AUX
ejpam-4069	25	8	neither	neither	CCONJ
ejpam-4069	25	9	be	be	AUX
ejpam-4069	25	10	close	close	ADJ
ejpam-4069	25	11	friends	friend	NOUN
ejpam-4069	25	12	nor	nor	CCONJ
ejpam-4069	25	13	enemies	enemy	NOUN
ejpam-4069	25	14	with	with	ADP
ejpam-4069	25	15	any	any	PRON
ejpam-4069	25	16	of	of	ADP
ejpam-4069	25	17	the	the	DET
ejpam-4069	25	18	workers	worker	NOUN
ejpam-4069	26	1	he	he	PRON
ejpam-4069	26	2	/	/	PUNCT
ejpam-4069	27	1	she	she	PRON
ejpam-4069	27	2	is	be	AUX
ejpam-4069	27	3	responsible	responsible	ADJ
ejpam-4069	27	4	for	for	ADP
ejpam-4069	27	5	inspecting	inspect	VERB
ejpam-4069	27	6	.	.	PUNCT
ejpam-4069	28	1	to	to	PART
ejpam-4069	28	2	model	model	VERB
ejpam-4069	28	3	this	this	DET
ejpam-4069	28	4	situation	situation	NOUN
ejpam-4069	28	5	,	,	PUNCT
ejpam-4069	28	6	a	a	DET
ejpam-4069	28	7	social	social	ADJ
ejpam-4069	28	8	network	network	NOUN
ejpam-4069	28	9	graph	graph	NOUN
ejpam-4069	28	10	can	can	AUX
ejpam-4069	28	11	be	be	AUX
ejpam-4069	28	12	constructed	construct	VERB
ejpam-4069	28	13	in	in	ADP
ejpam-4069	28	14	which	which	PRON
ejpam-4069	28	15	each	each	DET
ejpam-4069	28	16	worker	worker	NOUN
ejpam-4069	28	17	is	be	AUX
ejpam-4069	28	18	represented	represent	VERB
ejpam-4069	28	19	by	by	ADP
ejpam-4069	28	20	a	a	DET
ejpam-4069	28	21	vertex	vertex	NOUN
ejpam-4069	28	22	and	and	CCONJ
ejpam-4069	28	23	an	an	DET
ejpam-4069	28	24	edge	edge	NOUN
ejpam-4069	28	25	between	between	ADP
ejpam-4069	28	26	two	two	NUM
ejpam-4069	28	27	workers	worker	NOUN
ejpam-4069	28	28	represents	represent	VERB
ejpam-4069	28	29	possible	possible	ADJ
ejpam-4069	28	30	bias	bias	NOUN
ejpam-4069	28	31	,	,	PUNCT
ejpam-4069	28	32	that	that	ADV
ejpam-4069	28	33	is	is	ADV
ejpam-4069	28	34	,	,	PUNCT
ejpam-4069	28	35	whether	whether	SCONJ
ejpam-4069	28	36	the	the	DET
ejpam-4069	28	37	two	two	NUM
ejpam-4069	28	38	workers	worker	NOUN
ejpam-4069	28	39	are	be	AUX
ejpam-4069	28	40	close	close	ADJ
ejpam-4069	28	41	friends	friend	NOUN
ejpam-4069	28	42	or	or	CCONJ
ejpam-4069	28	43	enemies	enemy	NOUN
ejpam-4069	28	44	.	.	PUNCT
ejpam-4069	29	1	ideally	ideally	ADV
ejpam-4069	29	2	,	,	PUNCT
ejpam-4069	29	3	an	an	DET
ejpam-4069	29	4	inspector	inspector	NOUN
ejpam-4069	29	5	should	should	AUX
ejpam-4069	29	6	not	not	PART
ejpam-4069	29	7	be	be	AUX
ejpam-4069	29	8	adjacent	adjacent	ADJ
ejpam-4069	29	9	to	to	ADP
ejpam-4069	29	10	any	any	DET
ejpam-4069	29	11	worker	worker	NOUN
ejpam-4069	29	12	who	who	PRON
ejpam-4069	29	13	is	be	AUX
ejpam-4069	29	14	being	be	AUX
ejpam-4069	29	15	inspected	inspect	VERB
ejpam-4069	29	16	.	.	PUNCT
ejpam-4069	30	1	in	in	ADP
ejpam-4069	30	2	connected	connected	ADJ
ejpam-4069	30	3	co	co	ADJ
ejpam-4069	30	4	-	-	ADJ
ejpam-4069	30	5	independent	independent	ADJ
ejpam-4069	30	6	hop	hop	NOUN
ejpam-4069	30	7	domination	domination	NOUN
ejpam-4069	30	8	,	,	PUNCT
ejpam-4069	30	9	every	every	DET
ejpam-4069	30	10	worker	worker	NOUN
ejpam-4069	30	11	will	will	AUX
ejpam-4069	30	12	be	be	AUX
ejpam-4069	30	13	inspected	inspect	VERB
ejpam-4069	30	14	by	by	ADP
ejpam-4069	30	15	the	the	DET
ejpam-4069	30	16	nearest	near	ADJ
ejpam-4069	30	17	non	non	ADJ
ejpam-4069	30	18	-	-	ADJ
ejpam-4069	30	19	biased	biased	ADJ
ejpam-4069	30	20	inspector	inspector	NOUN
ejpam-4069	30	21	.	.	PUNCT
ejpam-4069	31	1	that	that	PRON
ejpam-4069	31	2	is	is	ADV
ejpam-4069	31	3	,	,	PUNCT
ejpam-4069	31	4	an	an	DET
ejpam-4069	31	5	inspector	inspector	NOUN
ejpam-4069	31	6	who	who	PRON
ejpam-4069	31	7	is	be	AUX
ejpam-4069	31	8	a	a	DET
ejpam-4069	31	9	close	close	ADJ
ejpam-4069	31	10	friend	friend	NOUN
ejpam-4069	31	11	(	(	PUNCT
ejpam-4069	31	12	or	or	CCONJ
ejpam-4069	31	13	an	an	DET
ejpam-4069	31	14	enemy	enemy	NOUN
ejpam-4069	31	15	)	)	PUNCT
ejpam-4069	31	16	of	of	ADP
ejpam-4069	31	17	a	a	DET
ejpam-4069	31	18	close	close	ADJ
ejpam-4069	31	19	friend	friend	NOUN
ejpam-4069	31	20	(	(	PUNCT
ejpam-4069	31	21	or	or	CCONJ
ejpam-4069	31	22	enemy	enemy	NOUN
ejpam-4069	31	23	)	)	PUNCT
ejpam-4069	31	24	of	of	ADP
ejpam-4069	31	25	a	a	DET
ejpam-4069	31	26	worker	worker	NOUN
ejpam-4069	31	27	.	.	PUNCT
ejpam-4069	32	1	this	this	PRON
ejpam-4069	32	2	is	be	AUX
ejpam-4069	32	3	to	to	PART
ejpam-4069	32	4	save	save	VERB
ejpam-4069	32	5	time	time	NOUN
ejpam-4069	32	6	and	and	CCONJ
ejpam-4069	32	7	effort	effort	NOUN
ejpam-4069	32	8	of	of	ADP
ejpam-4069	32	9	locating	locate	VERB
ejpam-4069	32	10	a	a	DET
ejpam-4069	32	11	particular	particular	ADJ
ejpam-4069	32	12	worker	worker	NOUN
ejpam-4069	32	13	.	.	PUNCT
ejpam-4069	33	1	also	also	ADV
ejpam-4069	33	2	,	,	PUNCT
ejpam-4069	33	3	the	the	DET
ejpam-4069	33	4	inspectors	inspector	NOUN
ejpam-4069	33	5	should	should	AUX
ejpam-4069	33	6	be	be	AUX
ejpam-4069	33	7	acquainted	acquaint	VERB
ejpam-4069	33	8	with	with	ADP
ejpam-4069	33	9	each	each	DET
ejpam-4069	33	10	other	other	ADJ
ejpam-4069	33	11	and	and	CCONJ
ejpam-4069	33	12	all	all	DET
ejpam-4069	33	13	noninspector	noninspector	NOUN
ejpam-4069	33	14	workers	worker	NOUN
ejpam-4069	33	15	are	be	AUX
ejpam-4069	33	16	neither	neither	CCONJ
ejpam-4069	33	17	friends	friend	NOUN
ejpam-4069	33	18	nor	nor	CCONJ
ejpam-4069	33	19	enemies	enemy	NOUN
ejpam-4069	33	20	,	,	PUNCT
ejpam-4069	33	21	that	that	ADV
ejpam-4069	33	22	is	is	ADV
ejpam-4069	33	23	,	,	PUNCT
ejpam-4069	33	24	they	they	PRON
ejpam-4069	33	25	are	be	AUX
ejpam-4069	33	26	not	not	PART
ejpam-4069	33	27	adjacent	adjacent	ADJ
ejpam-4069	33	28	or	or	CCONJ
ejpam-4069	33	29	there	there	PRON
ejpam-4069	33	30	is	be	VERB
ejpam-4069	33	31	no	no	DET
ejpam-4069	33	32	edge	edge	NOUN
ejpam-4069	33	33	between	between	ADP
ejpam-4069	33	34	them	they	PRON
ejpam-4069	33	35	.	.	PUNCT
ejpam-4069	34	1	the	the	DET
ejpam-4069	34	2	connected	connected	ADJ
ejpam-4069	34	3	co	co	NOUN
ejpam-4069	34	4	-	-	ADJ
ejpam-4069	34	5	independent	independent	ADJ
ejpam-4069	34	6	hop	hop	NOUN
ejpam-4069	34	7	domination	domination	NOUN
ejpam-4069	34	8	number	number	NOUN
ejpam-4069	34	9	will	will	AUX
ejpam-4069	34	10	give	give	VERB
ejpam-4069	34	11	the	the	DET
ejpam-4069	34	12	minimum	minimum	ADJ
ejpam-4069	34	13	number	number	NOUN
ejpam-4069	34	14	of	of	ADP
ejpam-4069	34	15	inspectors	inspector	NOUN
ejpam-4069	34	16	needed	need	VERB
ejpam-4069	34	17	.	.	PUNCT
ejpam-4069	35	1	in	in	ADP
ejpam-4069	35	2	this	this	DET
ejpam-4069	35	3	study	study	NOUN
ejpam-4069	35	4	,	,	PUNCT
ejpam-4069	35	5	we	we	PRON
ejpam-4069	35	6	only	only	ADV
ejpam-4069	35	7	consider	consider	VERB
ejpam-4069	35	8	graphs	graph	NOUN
ejpam-4069	35	9	that	that	PRON
ejpam-4069	35	10	are	be	AUX
ejpam-4069	35	11	finite	finite	ADJ
ejpam-4069	35	12	,	,	PUNCT
ejpam-4069	35	13	simple	simple	ADJ
ejpam-4069	35	14	,	,	PUNCT
ejpam-4069	35	15	undirected	undirected	ADJ
ejpam-4069	35	16	and	and	CCONJ
ejpam-4069	35	17	connected	connected	ADJ
ejpam-4069	35	18	.	.	PUNCT
ejpam-4069	36	1	readers	reader	NOUN
ejpam-4069	36	2	are	be	AUX
ejpam-4069	36	3	referred	refer	VERB
ejpam-4069	36	4	to	to	ADP
ejpam-4069	36	5	[	[	X
ejpam-4069	36	6	4	4	X
ejpam-4069	36	7	]	]	PUNCT
ejpam-4069	36	8	for	for	ADP
ejpam-4069	36	9	elementary	elementary	ADJ
ejpam-4069	36	10	graph	graph	NOUN
ejpam-4069	36	11	theoretic	theoretic	ADJ
ejpam-4069	36	12	concepts	concept	NOUN
ejpam-4069	36	13	.	.	PUNCT
ejpam-4069	37	1	an	an	DET
ejpam-4069	37	2	independent	independent	ADJ
ejpam-4069	37	3	set	set	NOUN
ejpam-4069	37	4	s	s	NOUN
ejpam-4069	37	5	in	in	ADP
ejpam-4069	37	6	a	a	DET
ejpam-4069	37	7	graph	graph	NOUN
ejpam-4069	37	8	g	g	NOUN
ejpam-4069	37	9	is	be	AUX
ejpam-4069	37	10	a	a	DET
ejpam-4069	37	11	subset	subset	NOUN
ejpam-4069	37	12	of	of	ADP
ejpam-4069	37	13	the	the	DET
ejpam-4069	37	14	vertex	vertex	NOUN
ejpam-4069	37	15	-	-	PUNCT
ejpam-4069	37	16	set	set	NOUN
ejpam-4069	37	17	of	of	ADP
ejpam-4069	37	18	g	g	NOUN
ejpam-4069	37	19	such	such	ADJ
ejpam-4069	37	20	that	that	SCONJ
ejpam-4069	37	21	no	no	DET
ejpam-4069	37	22	two	two	NUM
ejpam-4069	37	23	vertices	vertex	NOUN
ejpam-4069	37	24	in	in	ADP
ejpam-4069	37	25	s	s	NOUN
ejpam-4069	37	26	are	be	AUX
ejpam-4069	37	27	adjacent	adjacent	ADJ
ejpam-4069	37	28	in	in	ADP
ejpam-4069	37	29	g.	g.	PROPN
ejpam-4069	37	30	the	the	DET
ejpam-4069	37	31	cardinality	cardinality	NOUN
ejpam-4069	37	32	of	of	ADP
ejpam-4069	37	33	a	a	DET
ejpam-4069	37	34	maximum	maximum	ADJ
ejpam-4069	37	35	independent	independent	ADJ
ejpam-4069	37	36	set	set	NOUN
ejpam-4069	37	37	is	be	AUX
ejpam-4069	37	38	called	call	VERB
ejpam-4069	37	39	the	the	DET
ejpam-4069	37	40	independence	independence	NOUN
ejpam-4069	37	41	number	number	NOUN
ejpam-4069	37	42	of	of	ADP
ejpam-4069	37	43	g	g	NOUN
ejpam-4069	37	44	and	and	CCONJ
ejpam-4069	37	45	is	be	AUX
ejpam-4069	37	46	denoted	denote	VERB
ejpam-4069	37	47	by	by	ADP
ejpam-4069	37	48	β(g	β(g	PROPN
ejpam-4069	37	49	)	)	PUNCT
ejpam-4069	37	50	.	.	PUNCT
ejpam-4069	38	1	an	an	DET
ejpam-4069	38	2	independent	independent	ADJ
ejpam-4069	38	3	set	set	NOUN
ejpam-4069	38	4	s	s	PROPN
ejpam-4069	38	5	⊆	⊆	NUM
ejpam-4069	38	6	v	v	NOUN
ejpam-4069	38	7	(	(	PUNCT
ejpam-4069	38	8	g	g	NOUN
ejpam-4069	38	9	)	)	PUNCT
ejpam-4069	38	10	with	with	ADP
ejpam-4069	38	11	|s|	|s|	PROPN
ejpam-4069	38	12	=	=	SYM
ejpam-4069	38	13	β(g	β(g	PROPN
ejpam-4069	38	14	)	)	PUNCT
ejpam-4069	38	15	is	be	AUX
ejpam-4069	38	16	called	call	VERB
ejpam-4069	38	17	a	a	DET
ejpam-4069	38	18	β	β	NOUN
ejpam-4069	38	19	-	-	NOUN
ejpam-4069	38	20	set	set	NOUN
ejpam-4069	38	21	of	of	ADP
ejpam-4069	38	22	g.	g.	PROPN
ejpam-4069	38	23	a	a	DET
ejpam-4069	38	24	dominating	dominating	NOUN
ejpam-4069	38	25	set	set	NOUN
ejpam-4069	38	26	d	d	PROPN
ejpam-4069	38	27	⊆	⊆	NUM
ejpam-4069	38	28	v	v	ADP
ejpam-4069	38	29	(	(	PUNCT
ejpam-4069	38	30	g	g	NOUN
ejpam-4069	38	31	)	)	PUNCT
ejpam-4069	38	32	is	be	AUX
ejpam-4069	38	33	called	call	VERB
ejpam-4069	38	34	a	a	DET
ejpam-4069	38	35	connected	connected	ADJ
ejpam-4069	38	36	co	co	ADJ
ejpam-4069	38	37	-	-	ADJ
ejpam-4069	38	38	independent	independent	ADJ
ejpam-4069	38	39	dominating	dominating	NOUN
ejpam-4069	38	40	set	set	NOUN
ejpam-4069	38	41	of	of	ADP
ejpam-4069	38	42	g	g	PROPN
ejpam-4069	38	43	if	if	SCONJ
ejpam-4069	38	44	d	d	PROPN
ejpam-4069	38	45	is	be	AUX
ejpam-4069	38	46	a	a	DET
ejpam-4069	38	47	connected	connected	ADJ
ejpam-4069	38	48	dominating	dominating	NOUN
ejpam-4069	38	49	set	set	NOUN
ejpam-4069	38	50	of	of	ADP
ejpam-4069	38	51	g	g	PROPN
ejpam-4069	38	52	and	and	CCONJ
ejpam-4069	38	53	v	v	NOUN
ejpam-4069	38	54	(	(	PUNCT
ejpam-4069	38	55	g	g	NOUN
ejpam-4069	38	56	)	)	PUNCT
ejpam-4069	38	57	\	\	PUNCT
ejpam-4069	39	1	d	d	NOUN
ejpam-4069	39	2	is	be	AUX
ejpam-4069	39	3	an	an	DET
ejpam-4069	39	4	independent	independent	ADJ
ejpam-4069	39	5	set	set	NOUN
ejpam-4069	39	6	.	.	PUNCT
ejpam-4069	40	1	the	the	DET
ejpam-4069	40	2	cardinality	cardinality	NOUN
ejpam-4069	40	3	of	of	ADP
ejpam-4069	40	4	such	such	DET
ejpam-4069	40	5	a	a	DET
ejpam-4069	40	6	minimum	minimum	NOUN
ejpam-4069	40	7	set	set	NOUN
ejpam-4069	40	8	d	d	NOUN
ejpam-4069	40	9	is	be	AUX
ejpam-4069	40	10	called	call	VERB
ejpam-4069	40	11	a	a	DET
ejpam-4069	40	12	connected	connected	ADJ
ejpam-4069	40	13	co	co	ADJ
ejpam-4069	40	14	-	-	ADJ
ejpam-4069	40	15	independent	independent	ADJ
ejpam-4069	40	16	domination	domination	NOUN
ejpam-4069	40	17	number	number	NOUN
ejpam-4069	40	18	of	of	ADP
ejpam-4069	40	19	g	g	PROPN
ejpam-4069	40	20	denoted	denote	VERB
ejpam-4069	40	21	by	by	ADP
ejpam-4069	40	22	γc	γc	PROPN
ejpam-4069	40	23	,	,	PUNCT
ejpam-4069	40	24	coi(g	coi(g	PROPN
ejpam-4069	40	25	)	)	PUNCT
ejpam-4069	40	26	.	.	PUNCT
ejpam-4069	41	1	a	a	DET
ejpam-4069	41	2	connected	connected	ADJ
ejpam-4069	41	3	co	co	ADJ
ejpam-4069	41	4	-	-	ADJ
ejpam-4069	41	5	independent	independent	ADJ
ejpam-4069	41	6	dominating	dominating	NOUN
ejpam-4069	41	7	set	set	NOUN
ejpam-4069	41	8	d	d	NOUN
ejpam-4069	41	9	with	with	ADP
ejpam-4069	41	10	|d|	|d|	PROPN
ejpam-4069	41	11	=	=	SYM
ejpam-4069	41	12	γc	γc	PROPN
ejpam-4069	41	13	,	,	PUNCT
ejpam-4069	41	14	coi(g	coi(g	PROPN
ejpam-4069	41	15	)	)	PUNCT
ejpam-4069	41	16	is	be	AUX
ejpam-4069	41	17	called	call	VERB
ejpam-4069	41	18	a	a	DET
ejpam-4069	41	19	γc	γc	PROPN
ejpam-4069	41	20	,	,	PUNCT
ejpam-4069	41	21	coi	coi	NOUN
ejpam-4069	41	22	-	-	PUNCT
ejpam-4069	41	23	set	set	NOUN
ejpam-4069	41	24	of	of	ADP
ejpam-4069	41	25	g.	g.	PROPN
ejpam-4069	41	26	let	let	VERB
ejpam-4069	41	27	g	g	NOUN
ejpam-4069	41	28	be	be	AUX
ejpam-4069	41	29	a	a	DET
ejpam-4069	41	30	connected	connected	ADJ
ejpam-4069	41	31	graph	graph	NOUN
ejpam-4069	41	32	.	.	PUNCT
ejpam-4069	42	1	a	a	DET
ejpam-4069	42	2	set	set	NOUN
ejpam-4069	42	3	s	s	NOUN
ejpam-4069	42	4	⊆	⊆	NUM
ejpam-4069	42	5	v	v	NOUN
ejpam-4069	42	6	(	(	PUNCT
ejpam-4069	42	7	g	g	NOUN
ejpam-4069	42	8	)	)	PUNCT
ejpam-4069	42	9	is	be	AUX
ejpam-4069	42	10	a	a	DET
ejpam-4069	42	11	hop	hop	NOUN
ejpam-4069	42	12	dominating	dominating	NOUN
ejpam-4069	42	13	set	set	NOUN
ejpam-4069	42	14	of	of	ADP
ejpam-4069	42	15	g	g	PROPN
ejpam-4069	42	16	if	if	SCONJ
ejpam-4069	42	17	for	for	ADP
ejpam-4069	42	18	every	every	DET
ejpam-4069	42	19	v	v	NUM
ejpam-4069	42	20	∈	∈	NOUN
ejpam-4069	42	21	v	v	NOUN
ejpam-4069	42	22	(	(	PUNCT
ejpam-4069	42	23	g)\s	g)\s	NOUN
ejpam-4069	42	24	,	,	PUNCT
ejpam-4069	42	25	there	there	PRON
ejpam-4069	42	26	exists	exist	VERB
ejpam-4069	42	27	u	u	PROPN
ejpam-4069	42	28	∈	∈	PROPN
ejpam-4069	42	29	s	s	VERB
ejpam-4069	42	30	such	such	ADJ
ejpam-4069	42	31	that	that	DET
ejpam-4069	42	32	dg(u	dg(u	ADJ
ejpam-4069	42	33	,	,	PUNCT
ejpam-4069	42	34	v	v	NOUN
ejpam-4069	42	35	)	)	PUNCT
ejpam-4069	43	1	=	=	SYM
ejpam-4069	43	2	2	2	X
ejpam-4069	43	3	.	.	PUNCT
ejpam-4069	44	1	the	the	DET
ejpam-4069	44	2	minimum	minimum	ADJ
ejpam-4069	44	3	cardinality	cardinality	NOUN
ejpam-4069	44	4	of	of	ADP
ejpam-4069	44	5	a	a	DET
ejpam-4069	44	6	hop	hop	NOUN
ejpam-4069	44	7	dominating	dominating	NOUN
ejpam-4069	44	8	set	set	NOUN
ejpam-4069	44	9	of	of	ADP
ejpam-4069	44	10	g	g	NOUN
ejpam-4069	44	11	,	,	PUNCT
ejpam-4069	44	12	denoted	denote	VERB
ejpam-4069	44	13	by	by	ADP
ejpam-4069	44	14	γh(g	γh(g	NOUN
ejpam-4069	44	15	)	)	PUNCT
ejpam-4069	44	16	,	,	PUNCT
ejpam-4069	44	17	is	be	AUX
ejpam-4069	44	18	called	call	VERB
ejpam-4069	44	19	the	the	DET
ejpam-4069	44	20	hop	hop	NOUN
ejpam-4069	44	21	domination	domination	NOUN
ejpam-4069	44	22	number	number	NOUN
ejpam-4069	44	23	of	of	ADP
ejpam-4069	44	24	g.	g.	PROPN
ejpam-4069	44	25	any	any	DET
ejpam-4069	44	26	hop	hop	NOUN
ejpam-4069	44	27	dominating	dominating	NOUN
ejpam-4069	44	28	set	set	VERB
ejpam-4069	44	29	with	with	ADP
ejpam-4069	44	30	cardinality	cardinality	NOUN
ejpam-4069	44	31	equal	equal	ADJ
ejpam-4069	44	32	to	to	ADP
ejpam-4069	44	33	γh(g	γh(g	NOUN
ejpam-4069	44	34	)	)	PUNCT
ejpam-4069	44	35	is	be	AUX
ejpam-4069	44	36	called	call	VERB
ejpam-4069	44	37	a	a	DET
ejpam-4069	44	38	γh	γh	ADV
ejpam-4069	44	39	-	-	PUNCT
ejpam-4069	44	40	set	set	NOUN
ejpam-4069	44	41	.	.	PUNCT
ejpam-4069	45	1	a	a	DET
ejpam-4069	45	2	vertex	vertex	NOUN
ejpam-4069	45	3	v	v	NOUN
ejpam-4069	45	4	in	in	ADP
ejpam-4069	45	5	g	g	PROPN
ejpam-4069	45	6	is	be	AUX
ejpam-4069	45	7	a	a	DET
ejpam-4069	45	8	hop	hop	NOUN
ejpam-4069	45	9	neighbor	neighbor	NOUN
ejpam-4069	45	10	of	of	ADP
ejpam-4069	45	11	vertex	vertex	NOUN
ejpam-4069	45	12	u	u	NOUN
ejpam-4069	45	13	in	in	ADP
ejpam-4069	45	14	g	g	PROPN
ejpam-4069	45	15	if	if	SCONJ
ejpam-4069	45	16	dg(u	dg(u	NOUN
ejpam-4069	45	17	,	,	PUNCT
ejpam-4069	45	18	v	v	NOUN
ejpam-4069	45	19	)	)	PUNCT
ejpam-4069	45	20	=	=	SYM
ejpam-4069	45	21	2	2	X
ejpam-4069	45	22	.	.	X
ejpam-4069	46	1	the	the	DET
ejpam-4069	46	2	set	set	NOUN
ejpam-4069	46	3	ng(u	ng(u	NOUN
ejpam-4069	46	4	,	,	PUNCT
ejpam-4069	46	5	2	2	NUM
ejpam-4069	46	6	)	)	PUNCT
ejpam-4069	46	7	=	=	PRON
ejpam-4069	46	8	{	{	PUNCT
ejpam-4069	46	9	v	v	NUM
ejpam-4069	46	10	∈	∈	NOUN
ejpam-4069	46	11	v	v	NOUN
ejpam-4069	46	12	(	(	PUNCT
ejpam-4069	46	13	g	g	NOUN
ejpam-4069	46	14	)	)	PUNCT
ejpam-4069	46	15	:	:	PUNCT
ejpam-4069	46	16	dg(v	dg(v	X
ejpam-4069	46	17	,	,	PUNCT
ejpam-4069	46	18	u	u	NOUN
ejpam-4069	46	19	)	)	PUNCT
ejpam-4069	46	20	=	=	SYM
ejpam-4069	46	21	2	2	X
ejpam-4069	46	22	}	}	PUNCT
ejpam-4069	46	23	is	be	AUX
ejpam-4069	46	24	called	call	VERB
ejpam-4069	46	25	the	the	DET
ejpam-4069	46	26	open	open	ADJ
ejpam-4069	46	27	hop	hop	NOUN
ejpam-4069	46	28	neighborhood	neighborhood	NOUN
ejpam-4069	46	29	of	of	ADP
ejpam-4069	46	30	u.	u.	PROPN
ejpam-4069	46	31	the	the	DET
ejpam-4069	46	32	closed	closed	ADJ
ejpam-4069	46	33	hop	hop	NOUN
ejpam-4069	46	34	neighborhood	neighborhood	NOUN
ejpam-4069	46	35	of	of	ADP
ejpam-4069	46	36	u	u	PROPN
ejpam-4069	46	37	in	in	ADP
ejpam-4069	46	38	g	g	PROPN
ejpam-4069	46	39	is	be	AUX
ejpam-4069	46	40	given	give	VERB
ejpam-4069	46	41	by	by	ADP
ejpam-4069	46	42	ng[u	ng[u	PROPN
ejpam-4069	46	43	,	,	PUNCT
ejpam-4069	46	44	2	2	NUM
ejpam-4069	46	45	]	]	PUNCT
ejpam-4069	46	46	=	=	PUNCT
ejpam-4069	46	47	ng(u	ng(u	NOUN
ejpam-4069	46	48	,	,	PUNCT
ejpam-4069	46	49	2	2	X
ejpam-4069	46	50	)	)	PUNCT
ejpam-4069	46	51	∪	∪	NOUN
ejpam-4069	46	52	{	{	PUNCT
ejpam-4069	46	53	u	u	NOUN
ejpam-4069	46	54	}	}	PUNCT
ejpam-4069	46	55	.	.	PUNCT
ejpam-4069	47	1	the	the	DET
ejpam-4069	47	2	open	open	ADJ
ejpam-4069	47	3	hop	hop	NOUN
ejpam-4069	47	4	neighborhood	neighborhood	NOUN
ejpam-4069	47	5	of	of	ADP
ejpam-4069	47	6	x	x	PROPN
ejpam-4069	47	7	⊆	⊆	NUM
ejpam-4069	47	8	v	v	ADP
ejpam-4069	47	9	(	(	PUNCT
ejpam-4069	47	10	g	g	NOUN
ejpam-4069	47	11	)	)	PUNCT
ejpam-4069	47	12	is	be	AUX
ejpam-4069	47	13	the	the	DET
ejpam-4069	47	14	set	set	NOUN
ejpam-4069	47	15	ng(x	ng(x	NUM
ejpam-4069	47	16	,	,	PUNCT
ejpam-4069	47	17	2	2	X
ejpam-4069	47	18	)	)	PUNCT
ejpam-4069	47	19	=	=	NOUN
ejpam-4069	47	20	⋃	⋃	NOUN
ejpam-4069	47	21	u∈x	u∈x	ADJ
ejpam-4069	47	22	ng(u	ng(u	NOUN
ejpam-4069	47	23	,	,	PUNCT
ejpam-4069	47	24	2	2	NUM
ejpam-4069	47	25	)	)	PUNCT
ejpam-4069	47	26	.	.	PUNCT
ejpam-4069	48	1	the	the	DET
ejpam-4069	48	2	closed	closed	ADJ
ejpam-4069	48	3	hop	hop	NOUN
ejpam-4069	48	4	neighborhood	neighborhood	NOUN
ejpam-4069	48	5	of	of	ADP
ejpam-4069	48	6	x	x	PUNCT
ejpam-4069	48	7	in	in	ADP
ejpam-4069	48	8	g	g	PROPN
ejpam-4069	48	9	is	be	AUX
ejpam-4069	48	10	the	the	DET
ejpam-4069	48	11	set	set	PROPN
ejpam-4069	48	12	ng[x	ng[x	PROPN
ejpam-4069	48	13	,	,	PUNCT
ejpam-4069	48	14	2	2	NUM
ejpam-4069	48	15	]	]	PUNCT
ejpam-4069	48	16	=	=	SYM
ejpam-4069	48	17	ng(x	ng(x	X
ejpam-4069	48	18	,	,	PUNCT
ejpam-4069	48	19	2	2	X
ejpam-4069	48	20	)	)	PUNCT
ejpam-4069	48	21	∪	∪	NOUN
ejpam-4069	48	22	x.	x.	NOUN
ejpam-4069	48	23	let	let	VERB
ejpam-4069	48	24	g	g	NOUN
ejpam-4069	48	25	be	be	AUX
ejpam-4069	48	26	a	a	DET
ejpam-4069	48	27	graph	graph	NOUN
ejpam-4069	48	28	.	.	PUNCT
ejpam-4069	49	1	a	a	DET
ejpam-4069	49	2	subset	subset	NOUN
ejpam-4069	49	3	s	s	NOUN
ejpam-4069	49	4	of	of	ADP
ejpam-4069	49	5	v	v	NOUN
ejpam-4069	49	6	(	(	PUNCT
ejpam-4069	49	7	g	g	NOUN
ejpam-4069	49	8	)	)	PUNCT
ejpam-4069	49	9	is	be	AUX
ejpam-4069	49	10	a	a	DET
ejpam-4069	49	11	strictly	strictly	ADV
ejpam-4069	49	12	co	co	ADJ
ejpam-4069	49	13	-	-	ADJ
ejpam-4069	49	14	independent	independent	ADJ
ejpam-4069	49	15	set	set	NOUN
ejpam-4069	49	16	of	of	ADP
ejpam-4069	49	17	g	g	PROPN
ejpam-4069	49	18	if	if	SCONJ
ejpam-4069	49	19	v	v	X
ejpam-4069	49	20	(	(	PUNCT
ejpam-4069	49	21	g)\s	g)\s	NOUN
ejpam-4069	49	22	is	be	AUX
ejpam-4069	49	23	an	an	DET
ejpam-4069	49	24	independent	independent	ADJ
ejpam-4069	49	25	set	set	NOUN
ejpam-4069	49	26	and	and	CCONJ
ejpam-4069	49	27	ng(v)∩s	ng(v)∩s	PROPN
ejpam-4069	49	28	̸=	̸=	PROPN
ejpam-4069	49	29	s	s	VERB
ejpam-4069	49	30	for	for	ADP
ejpam-4069	49	31	all	all	PRON
ejpam-4069	49	32	v	v	ADP
ejpam-4069	49	33	∈	∈	NOUN
ejpam-4069	49	34	v	v	NOUN
ejpam-4069	49	35	(	(	PUNCT
ejpam-4069	49	36	g)\s	g)\s	NOUN
ejpam-4069	49	37	.	.	PUNCT
ejpam-4069	50	1	the	the	DET
ejpam-4069	50	2	minimum	minimum	ADJ
ejpam-4069	50	3	cardinality	cardinality	NOUN
ejpam-4069	50	4	of	of	ADP
ejpam-4069	50	5	a	a	DET
ejpam-4069	50	6	strictly	strictly	ADV
ejpam-4069	50	7	co	co	ADJ
ejpam-4069	50	8	-	-	ADJ
ejpam-4069	50	9	independent	independent	ADJ
ejpam-4069	50	10	s.	s.	PROPN
ejpam-4069	50	11	nanding	nanding	PROPN
ejpam-4069	50	12	,	,	PUNCT
ejpam-4069	50	13	h.	h.	PROPN
ejpam-4069	50	14	rara	rara	PROPN
ejpam-4069	50	15	/	/	SYM
ejpam-4069	50	16	eur	eur	PROPN
ejpam-4069	50	17	.	.	PUNCT
ejpam-4069	51	1	j.	j.	PROPN
ejpam-4069	51	2	pure	pure	PROPN
ejpam-4069	51	3	appl	appl	PROPN
ejpam-4069	51	4	.	.	PROPN
ejpam-4069	51	5	math	math	PROPN
ejpam-4069	51	6	,	,	PUNCT
ejpam-4069	51	7	14	14	NUM
ejpam-4069	51	8	(	(	PUNCT
ejpam-4069	51	9	4	4	NUM
ejpam-4069	51	10	)	)	PUNCT
ejpam-4069	51	11	(	(	PUNCT
ejpam-4069	51	12	2021	2021	NUM
ejpam-4069	51	13	)	)	PUNCT
ejpam-4069	51	14	,	,	PUNCT
ejpam-4069	51	15	1226	1226	NUM
ejpam-4069	51	16	-	-	SYM
ejpam-4069	51	17	1236	1236	NUM
ejpam-4069	51	18	1228	1228	NUM
ejpam-4069	51	19	set	set	VERB
ejpam-4069	51	20	in	in	ADP
ejpam-4069	51	21	g	g	NOUN
ejpam-4069	51	22	,	,	PUNCT
ejpam-4069	51	23	denoted	denote	VERB
ejpam-4069	51	24	by	by	ADP
ejpam-4069	51	25	sci(g	sci(g	PROPN
ejpam-4069	51	26	)	)	PUNCT
ejpam-4069	51	27	is	be	AUX
ejpam-4069	51	28	called	call	VERB
ejpam-4069	51	29	the	the	DET
ejpam-4069	51	30	strictly	strictly	ADV
ejpam-4069	51	31	co	co	ADJ
ejpam-4069	51	32	-	-	ADJ
ejpam-4069	51	33	independent	independent	ADJ
ejpam-4069	51	34	number	number	NOUN
ejpam-4069	51	35	of	of	ADP
ejpam-4069	51	36	g.	g.	PROPN
ejpam-4069	51	37	a	a	DET
ejpam-4069	51	38	strictly	strictly	ADV
ejpam-4069	51	39	co	co	ADJ
ejpam-4069	51	40	-	-	ADJ
ejpam-4069	51	41	independent	independent	ADJ
ejpam-4069	51	42	set	set	NOUN
ejpam-4069	51	43	s	s	NOUN
ejpam-4069	51	44	with	with	ADP
ejpam-4069	51	45	|s|	|s|	NOUN
ejpam-4069	51	46	=	=	PUNCT
ejpam-4069	51	47	sci(g	sci(g	PROPN
ejpam-4069	51	48	)	)	PUNCT
ejpam-4069	51	49	is	be	AUX
ejpam-4069	51	50	called	call	VERB
ejpam-4069	51	51	an	an	DET
ejpam-4069	51	52	sci	sci	PROPN
ejpam-4069	51	53	-	-	PUNCT
ejpam-4069	51	54	set	set	NOUN
ejpam-4069	51	55	of	of	ADP
ejpam-4069	51	56	g.	g.	PROPN
ejpam-4069	51	57	let	let	VERB
ejpam-4069	51	58	g	g	NOUN
ejpam-4069	51	59	be	be	AUX
ejpam-4069	51	60	a	a	DET
ejpam-4069	51	61	connected	connected	ADJ
ejpam-4069	51	62	graph	graph	NOUN
ejpam-4069	51	63	.	.	PUNCT
ejpam-4069	52	1	a	a	DET
ejpam-4069	52	2	hop	hop	NOUN
ejpam-4069	52	3	dominating	dominating	NOUN
ejpam-4069	52	4	set	set	NOUN
ejpam-4069	52	5	s	s	PROPN
ejpam-4069	52	6	⊆	⊆	NUM
ejpam-4069	52	7	v	v	NOUN
ejpam-4069	52	8	(	(	PUNCT
ejpam-4069	52	9	g	g	NOUN
ejpam-4069	52	10	)	)	PUNCT
ejpam-4069	52	11	is	be	AUX
ejpam-4069	52	12	a	a	DET
ejpam-4069	52	13	connected	connected	ADJ
ejpam-4069	52	14	co	co	NOUN
ejpam-4069	52	15	-	-	ADJ
ejpam-4069	52	16	independent	independent	ADJ
ejpam-4069	52	17	hop	hop	NOUN
ejpam-4069	52	18	dominating	dominating	NOUN
ejpam-4069	52	19	set	set	NOUN
ejpam-4069	52	20	of	of	ADP
ejpam-4069	52	21	g	g	PROPN
ejpam-4069	52	22	if	if	SCONJ
ejpam-4069	52	23	⟨s⟩	⟨s⟩	PROPN
ejpam-4069	52	24	is	be	AUX
ejpam-4069	52	25	connected	connect	VERB
ejpam-4069	52	26	and	and	CCONJ
ejpam-4069	52	27	v	v	NOUN
ejpam-4069	52	28	(	(	PUNCT
ejpam-4069	52	29	g)\s	g)\s	NOUN
ejpam-4069	52	30	is	be	AUX
ejpam-4069	52	31	an	an	DET
ejpam-4069	52	32	independent	independent	ADJ
ejpam-4069	52	33	set	set	NOUN
ejpam-4069	52	34	.	.	PUNCT
ejpam-4069	53	1	the	the	DET
ejpam-4069	53	2	minimum	minimum	ADJ
ejpam-4069	53	3	cardinality	cardinality	NOUN
ejpam-4069	53	4	of	of	ADP
ejpam-4069	53	5	a	a	DET
ejpam-4069	53	6	connected	connected	ADJ
ejpam-4069	53	7	co	co	NOUN
ejpam-4069	53	8	-	-	ADJ
ejpam-4069	53	9	independent	independent	ADJ
ejpam-4069	53	10	hop	hop	NOUN
ejpam-4069	53	11	dominating	dominating	NOUN
ejpam-4069	53	12	set	set	NOUN
ejpam-4069	53	13	of	of	ADP
ejpam-4069	53	14	g	g	NOUN
ejpam-4069	53	15	,	,	PUNCT
ejpam-4069	53	16	denoted	denote	VERB
ejpam-4069	53	17	by	by	ADP
ejpam-4069	53	18	γch	γch	NOUN
ejpam-4069	53	19	,	,	PUNCT
ejpam-4069	53	20	coi(g	coi(g	PROPN
ejpam-4069	53	21	)	)	PUNCT
ejpam-4069	53	22	,	,	PUNCT
ejpam-4069	53	23	is	be	AUX
ejpam-4069	53	24	called	call	VERB
ejpam-4069	53	25	the	the	DET
ejpam-4069	53	26	connected	connected	ADJ
ejpam-4069	53	27	co	co	NOUN
ejpam-4069	53	28	-	-	ADJ
ejpam-4069	53	29	independent	independent	ADJ
ejpam-4069	53	30	hop	hop	NOUN
ejpam-4069	53	31	domination	domination	NOUN
ejpam-4069	53	32	number	number	NOUN
ejpam-4069	53	33	of	of	ADP
ejpam-4069	53	34	g.	g.	PROPN
ejpam-4069	53	35	a	a	DET
ejpam-4069	53	36	connected	connected	ADJ
ejpam-4069	53	37	co	co	NOUN
ejpam-4069	53	38	-	-	ADJ
ejpam-4069	53	39	independent	independent	ADJ
ejpam-4069	53	40	hop	hop	NOUN
ejpam-4069	53	41	dominating	dominating	NOUN
ejpam-4069	53	42	set	set	NOUN
ejpam-4069	53	43	s	s	NOUN
ejpam-4069	53	44	with	with	ADP
ejpam-4069	53	45	|s|	|s|	NOUN
ejpam-4069	53	46	=	=	SYM
ejpam-4069	53	47	γch	γch	NOUN
ejpam-4069	53	48	,	,	PUNCT
ejpam-4069	53	49	coi(g	coi(g	PROPN
ejpam-4069	53	50	)	)	PUNCT
ejpam-4069	53	51	is	be	AUX
ejpam-4069	53	52	called	call	VERB
ejpam-4069	53	53	a	a	DET
ejpam-4069	53	54	γch	γch	NOUN
ejpam-4069	53	55	,	,	PUNCT
ejpam-4069	53	56	coi	coi	NOUN
ejpam-4069	53	57	-	-	PUNCT
ejpam-4069	53	58	set	set	NOUN
ejpam-4069	53	59	of	of	ADP
ejpam-4069	53	60	g.	g.	PROPN
ejpam-4069	53	61	2	2	NUM
ejpam-4069	53	62	.	.	PUNCT
ejpam-4069	54	1	preliminary	preliminary	ADJ
ejpam-4069	54	2	results	result	NOUN
ejpam-4069	54	3	remark	remark	VERB
ejpam-4069	54	4	1	1	NUM
ejpam-4069	54	5	.	.	PUNCT
ejpam-4069	55	1	every	every	DET
ejpam-4069	55	2	connected	connected	ADJ
ejpam-4069	55	3	co	co	NOUN
ejpam-4069	55	4	-	-	ADJ
ejpam-4069	55	5	independent	independent	ADJ
ejpam-4069	55	6	hop	hop	NOUN
ejpam-4069	55	7	dominating	dominating	NOUN
ejpam-4069	55	8	set	set	VERB
ejpam-4069	55	9	in	in	ADP
ejpam-4069	55	10	a	a	DET
ejpam-4069	55	11	connected	connected	ADJ
ejpam-4069	55	12	graph	graph	NOUN
ejpam-4069	55	13	g	g	PROPN
ejpam-4069	55	14	is	be	AUX
ejpam-4069	55	15	hop	hop	NOUN
ejpam-4069	55	16	dominating	dominating	NOUN
ejpam-4069	55	17	.	.	PUNCT
ejpam-4069	56	1	hence	hence	ADV
ejpam-4069	56	2	,	,	PUNCT
ejpam-4069	56	3	γh(g	γh(g	NOUN
ejpam-4069	56	4	)	)	PUNCT
ejpam-4069	56	5	≤	≤	NUM
ejpam-4069	56	6	γch	γch	NOUN
ejpam-4069	56	7	,	,	PUNCT
ejpam-4069	56	8	coi(g	coi(g	PROPN
ejpam-4069	56	9	)	)	PUNCT
ejpam-4069	56	10	.	.	PUNCT
ejpam-4069	57	1	remark	remark	NOUN
ejpam-4069	57	2	2	2	NUM
ejpam-4069	57	3	.	.	PUNCT
ejpam-4069	58	1	let	let	VERB
ejpam-4069	58	2	g	g	PRON
ejpam-4069	58	3	be	be	AUX
ejpam-4069	58	4	a	a	DET
ejpam-4069	58	5	connected	connected	ADJ
ejpam-4069	58	6	graph	graph	NOUN
ejpam-4069	58	7	of	of	ADP
ejpam-4069	58	8	order	order	NOUN
ejpam-4069	58	9	n.	n.	NOUN
ejpam-4069	58	10	then	then	ADV
ejpam-4069	59	1	1	1	NUM
ejpam-4069	59	2	≤	≤	NOUN
ejpam-4069	59	3	γch	γch	NOUN
ejpam-4069	59	4	,	,	PUNCT
ejpam-4069	59	5	coi(g	coi(g	PROPN
ejpam-4069	59	6	)	)	PUNCT
ejpam-4069	59	7	≤	≤	PUNCT
ejpam-4069	59	8	|v	|v	X
ejpam-4069	59	9	(	(	PUNCT
ejpam-4069	59	10	g)|	g)|	PROPN
ejpam-4069	59	11	.	.	PUNCT
ejpam-4069	60	1	moreover	moreover	ADV
ejpam-4069	60	2	,	,	PUNCT
ejpam-4069	60	3	γch	γch	NOUN
ejpam-4069	60	4	,	,	PUNCT
ejpam-4069	60	5	coi(g	coi(g	PROPN
ejpam-4069	60	6	)	)	PUNCT
ejpam-4069	60	7	=	=	PUNCT
ejpam-4069	60	8	1	1	NUM
ejpam-4069	60	9	if	if	SCONJ
ejpam-4069	60	10	and	and	CCONJ
ejpam-4069	60	11	only	only	ADV
ejpam-4069	60	12	if	if	SCONJ
ejpam-4069	60	13	g	g	PROPN
ejpam-4069	60	14	=	=	PROPN
ejpam-4069	60	15	k1	k1	PROPN
ejpam-4069	60	16	.	.	PUNCT
ejpam-4069	60	17	example	example	NOUN
ejpam-4069	61	1	1	1	NUM
ejpam-4069	61	2	.	.	PUNCT
ejpam-4069	62	1	the	the	DET
ejpam-4069	62	2	equations	equation	NOUN
ejpam-4069	62	3	below	below	ADP
ejpam-4069	62	4	give	give	VERB
ejpam-4069	62	5	the	the	DET
ejpam-4069	62	6	connected	connected	ADJ
ejpam-4069	62	7	co	co	NOUN
ejpam-4069	62	8	-	-	ADJ
ejpam-4069	62	9	independent	independent	ADJ
ejpam-4069	62	10	hop	hop	NOUN
ejpam-4069	62	11	domination	domination	NOUN
ejpam-4069	62	12	number	number	NOUN
ejpam-4069	62	13	of	of	ADP
ejpam-4069	62	14	the	the	DET
ejpam-4069	62	15	path	path	NOUN
ejpam-4069	62	16	pn	pn	NOUN
ejpam-4069	62	17	and	and	CCONJ
ejpam-4069	62	18	cycle	cycle	NOUN
ejpam-4069	62	19	cn	cn	PROPN
ejpam-4069	62	20	.	.	PUNCT
ejpam-4069	62	21	γch	γch	NOUN
ejpam-4069	62	22	,	,	PUNCT
ejpam-4069	62	23	coi(pn	coi(pn	NOUN
ejpam-4069	62	24	)	)	PUNCT
ejpam-4069	62	25	=	=	SYM
ejpam-4069	63	1			NOUN
ejpam-4069	63	2	1	1	NUM
ejpam-4069	63	3	if	if	SCONJ
ejpam-4069	63	4	n	n	NOUN
ejpam-4069	63	5	=	=	SYM
ejpam-4069	63	6	1	1	NUM
ejpam-4069	63	7	2	2	NUM
ejpam-4069	63	8	if	if	SCONJ
ejpam-4069	63	9	n	n	NOUN
ejpam-4069	63	10	=	=	SYM
ejpam-4069	63	11	2	2	NUM
ejpam-4069	63	12	,	,	PUNCT
ejpam-4069	63	13	3	3	NUM
ejpam-4069	63	14	n−	n−	NOUN
ejpam-4069	63	15	2	2	NUM
ejpam-4069	63	16	if	if	SCONJ
ejpam-4069	63	17	n	n	PRON
ejpam-4069	63	18	≥	≥	NOUN
ejpam-4069	63	19	4	4	NUM
ejpam-4069	63	20	γch	γch	NOUN
ejpam-4069	63	21	,	,	PUNCT
ejpam-4069	63	22	coi(cn	coi(cn	NUM
ejpam-4069	63	23	)	)	PUNCT
ejpam-4069	63	24	=	=	PRON
ejpam-4069	63	25	{	{	PUNCT
ejpam-4069	63	26	3	3	NUM
ejpam-4069	63	27	if	if	SCONJ
ejpam-4069	63	28	n	n	NOUN
ejpam-4069	63	29	=	=	SYM
ejpam-4069	63	30	3	3	NUM
ejpam-4069	63	31	n−	n−	NOUN
ejpam-4069	63	32	1	1	NUM
ejpam-4069	63	33	if	if	SCONJ
ejpam-4069	63	34	n	n	PRON
ejpam-4069	63	35	≥	≥	VERB
ejpam-4069	63	36	4	4	NUM
ejpam-4069	63	37	remark	remark	NOUN
ejpam-4069	63	38	3	3	NUM
ejpam-4069	63	39	.	.	PUNCT
ejpam-4069	64	1	if	if	SCONJ
ejpam-4069	64	2	g	g	PROPN
ejpam-4069	64	3	is	be	AUX
ejpam-4069	64	4	a	a	DET
ejpam-4069	64	5	complete	complete	ADJ
ejpam-4069	64	6	graph	graph	NOUN
ejpam-4069	64	7	,	,	PUNCT
ejpam-4069	64	8	then	then	ADV
ejpam-4069	64	9	γch	γch	VERB
ejpam-4069	64	10	,	,	PUNCT
ejpam-4069	64	11	coi(g	coi(g	PROPN
ejpam-4069	64	12	)	)	PUNCT
ejpam-4069	64	13	=	=	SYM
ejpam-4069	64	14	n.	n.	NOUN
ejpam-4069	64	15	theorem	theorem	NOUN
ejpam-4069	64	16	1	1	X
ejpam-4069	64	17	.	.	PUNCT
ejpam-4069	65	1	let	let	VERB
ejpam-4069	65	2	g	g	PRON
ejpam-4069	65	3	be	be	AUX
ejpam-4069	65	4	a	a	DET
ejpam-4069	65	5	connected	connected	ADJ
ejpam-4069	65	6	graph	graph	NOUN
ejpam-4069	65	7	of	of	ADP
ejpam-4069	65	8	order	order	NOUN
ejpam-4069	65	9	n	n	PRON
ejpam-4069	65	10	≥	≥	NOUN
ejpam-4069	65	11	3	3	NUM
ejpam-4069	65	12	.	.	PUNCT
ejpam-4069	66	1	then	then	ADV
ejpam-4069	66	2	γch	γch	VERB
ejpam-4069	66	3	,	,	PUNCT
ejpam-4069	66	4	coi(g	coi(g	PROPN
ejpam-4069	66	5	)	)	PUNCT
ejpam-4069	66	6	=	=	SYM
ejpam-4069	66	7	2	2	NUM
ejpam-4069	66	8	if	if	SCONJ
ejpam-4069	66	9	and	and	CCONJ
ejpam-4069	66	10	only	only	ADV
ejpam-4069	66	11	if	if	SCONJ
ejpam-4069	66	12	there	there	PRON
ejpam-4069	66	13	exist	exist	VERB
ejpam-4069	66	14	adjacent	adjacent	ADJ
ejpam-4069	66	15	vertices	vertex	NOUN
ejpam-4069	66	16	x	x	PUNCT
ejpam-4069	66	17	and	and	CCONJ
ejpam-4069	66	18	y	y	PROPN
ejpam-4069	66	19	of	of	ADP
ejpam-4069	66	20	g	g	PROPN
ejpam-4069	66	21	such	such	ADJ
ejpam-4069	66	22	that	that	PRON
ejpam-4069	66	23	for	for	ADP
ejpam-4069	66	24	each	each	DET
ejpam-4069	66	25	z	z	NOUN
ejpam-4069	66	26	∈	∈	PROPN
ejpam-4069	66	27	v	v	NOUN
ejpam-4069	66	28	(	(	PUNCT
ejpam-4069	66	29	g)\{x	g)\{x	PROPN
ejpam-4069	66	30	,	,	PUNCT
ejpam-4069	66	31	y	y	NOUN
ejpam-4069	66	32	}	}	PUNCT
ejpam-4069	66	33	,	,	PUNCT
ejpam-4069	66	34	ng(z	ng(z	NUM
ejpam-4069	66	35	)	)	PUNCT
ejpam-4069	66	36	=	=	PRON
ejpam-4069	67	1	{	{	PUNCT
ejpam-4069	67	2	x	x	NOUN
ejpam-4069	67	3	}	}	PUNCT
ejpam-4069	67	4	or	or	CCONJ
ejpam-4069	67	5	ng(z	ng(z	NUM
ejpam-4069	67	6	)	)	PUNCT
ejpam-4069	68	1	=	=	PRON
ejpam-4069	68	2	{	{	PUNCT
ejpam-4069	68	3	y	y	NOUN
ejpam-4069	68	4	}	}	PUNCT
ejpam-4069	68	5	and	and	CCONJ
ejpam-4069	68	6	z	z	NOUN
ejpam-4069	68	7	/∈	/∈	PUNCT
ejpam-4069	68	8	ng(x	ng(x	NUM
ejpam-4069	68	9	)	)	PUNCT
ejpam-4069	68	10	∩ng(y	∩ng(y	PROPN
ejpam-4069	68	11	)	)	PUNCT
ejpam-4069	68	12	.	.	PUNCT
ejpam-4069	69	1	proof	proof	NOUN
ejpam-4069	69	2	:	:	PUNCT
ejpam-4069	69	3	suppose	suppose	VERB
ejpam-4069	69	4	γch	γch	NOUN
ejpam-4069	69	5	,	,	PUNCT
ejpam-4069	69	6	coi(g	coi(g	PROPN
ejpam-4069	69	7	)	)	PUNCT
ejpam-4069	69	8	=	=	SYM
ejpam-4069	70	1	2	2	X
ejpam-4069	70	2	.	.	X
ejpam-4069	70	3	let	let	VERB
ejpam-4069	70	4	s	s	VERB
ejpam-4069	70	5	=	=	PUNCT
ejpam-4069	70	6	{	{	PUNCT
ejpam-4069	70	7	x	x	PROPN
ejpam-4069	70	8	,	,	PUNCT
ejpam-4069	70	9	y	y	PROPN
ejpam-4069	70	10	}	}	PUNCT
ejpam-4069	70	11	be	be	AUX
ejpam-4069	70	12	a	a	DET
ejpam-4069	70	13	γch	γch	NOUN
ejpam-4069	70	14	,	,	PUNCT
ejpam-4069	70	15	coi	coi	NOUN
ejpam-4069	70	16	-	-	PUNCT
ejpam-4069	70	17	set	set	NOUN
ejpam-4069	70	18	of	of	ADP
ejpam-4069	70	19	g.	g.	PROPN
ejpam-4069	70	20	since	since	SCONJ
ejpam-4069	70	21	s	s	PRON
ejpam-4069	70	22	is	be	AUX
ejpam-4069	70	23	connected	connect	VERB
ejpam-4069	70	24	,	,	PUNCT
ejpam-4069	70	25	xy	xy	PROPN
ejpam-4069	70	26	∈	∈	PROPN
ejpam-4069	70	27	e(g	e(g	PROPN
ejpam-4069	70	28	)	)	PUNCT
ejpam-4069	70	29	.	.	PUNCT
ejpam-4069	71	1	let	let	VERB
ejpam-4069	71	2	z	z	NOUN
ejpam-4069	71	3	∈	∈	PROPN
ejpam-4069	71	4	v	v	PROPN
ejpam-4069	71	5	(	(	PUNCT
ejpam-4069	71	6	g)\{x	g)\{x	PROPN
ejpam-4069	71	7	,	,	PUNCT
ejpam-4069	71	8	y	y	NOUN
ejpam-4069	71	9	}	}	PUNCT
ejpam-4069	71	10	.	.	PUNCT
ejpam-4069	72	1	then	then	ADV
ejpam-4069	72	2	z	z	PROPN
ejpam-4069	72	3	/∈	/∈	PUNCT
ejpam-4069	72	4	s.	s.	PROPN
ejpam-4069	72	5	since	since	SCONJ
ejpam-4069	72	6	s	s	PROPN
ejpam-4069	72	7	is	be	AUX
ejpam-4069	72	8	a	a	DET
ejpam-4069	72	9	hop	hop	NOUN
ejpam-4069	72	10	dominating	dominating	NOUN
ejpam-4069	72	11	set	set	NOUN
ejpam-4069	72	12	of	of	ADP
ejpam-4069	72	13	g	g	PROPN
ejpam-4069	72	14	,	,	PUNCT
ejpam-4069	72	15	z	z	PROPN
ejpam-4069	72	16	∈	∈	PROPN
ejpam-4069	72	17	ng(x	ng(x	NUM
ejpam-4069	72	18	,	,	PUNCT
ejpam-4069	72	19	2)∪ng(y	2)∪ng(y	NUM
ejpam-4069	72	20	,	,	PUNCT
ejpam-4069	72	21	2	2	NUM
ejpam-4069	72	22	)	)	PUNCT
ejpam-4069	72	23	.	.	PUNCT
ejpam-4069	73	1	suppose	suppose	VERB
ejpam-4069	73	2	z	z	PROPN
ejpam-4069	73	3	∈	∈	PROPN
ejpam-4069	73	4	ng(x	ng(x	NUM
ejpam-4069	73	5	,	,	PUNCT
ejpam-4069	73	6	2	2	NUM
ejpam-4069	73	7	)	)	PUNCT
ejpam-4069	73	8	.	.	PUNCT
ejpam-4069	74	1	then	then	ADV
ejpam-4069	74	2	there	there	PRON
ejpam-4069	74	3	exist	exist	VERB
ejpam-4069	74	4	w	w	PROPN
ejpam-4069	74	5	∈	∈	PROPN
ejpam-4069	74	6	ng(z)∩ng(x	ng(z)∩ng(x	PROPN
ejpam-4069	74	7	)	)	PUNCT
ejpam-4069	74	8	.	.	PUNCT
ejpam-4069	75	1	since	since	SCONJ
ejpam-4069	75	2	v	v	NOUN
ejpam-4069	75	3	(	(	PUNCT
ejpam-4069	75	4	g)\s	g)\s	NOUN
ejpam-4069	75	5	is	be	AUX
ejpam-4069	75	6	an	an	DET
ejpam-4069	75	7	independent	independent	ADJ
ejpam-4069	75	8	set	set	NOUN
ejpam-4069	75	9	,	,	PUNCT
ejpam-4069	75	10	w	w	PROPN
ejpam-4069	75	11	∈	∈	PROPN
ejpam-4069	75	12	s.	s.	PROPN
ejpam-4069	75	13	thus	thus	ADV
ejpam-4069	75	14	,	,	PUNCT
ejpam-4069	75	15	w	w	PROPN
ejpam-4069	75	16	=	=	SYM
ejpam-4069	75	17	y	y	PROPN
ejpam-4069	75	18	,	,	PUNCT
ejpam-4069	75	19	that	that	ADV
ejpam-4069	75	20	is	is	ADV
ejpam-4069	75	21	,	,	PUNCT
ejpam-4069	75	22	ng(z	ng(z	PROPN
ejpam-4069	75	23	)	)	PUNCT
ejpam-4069	75	24	=	=	PRON
ejpam-4069	76	1	{	{	PUNCT
ejpam-4069	76	2	y	y	NOUN
ejpam-4069	76	3	}	}	PUNCT
ejpam-4069	76	4	.	.	PUNCT
ejpam-4069	77	1	similarly	similarly	ADV
ejpam-4069	77	2	,	,	PUNCT
ejpam-4069	77	3	if	if	SCONJ
ejpam-4069	77	4	z	z	PROPN
ejpam-4069	77	5	∈	∈	PROPN
ejpam-4069	77	6	ng(y	ng(y	NOUN
ejpam-4069	77	7	,	,	PUNCT
ejpam-4069	77	8	2	2	NUM
ejpam-4069	77	9	)	)	PUNCT
ejpam-4069	77	10	,	,	PUNCT
ejpam-4069	77	11	then	then	ADV
ejpam-4069	77	12	ng(z	ng(z	NUM
ejpam-4069	77	13	)	)	PUNCT
ejpam-4069	77	14	=	=	PRON
ejpam-4069	77	15	{	{	PUNCT
ejpam-4069	77	16	x	x	NOUN
ejpam-4069	77	17	}	}	PUNCT
ejpam-4069	77	18	.	.	PUNCT
ejpam-4069	78	1	since	since	SCONJ
ejpam-4069	78	2	z	z	PROPN
ejpam-4069	78	3	∈	∈	PROPN
ejpam-4069	78	4	ng(x	ng(x	NUM
ejpam-4069	78	5	,	,	PUNCT
ejpam-4069	78	6	2	2	X
ejpam-4069	78	7	)	)	PUNCT
ejpam-4069	78	8	∪ng(y	∪ng(y	PROPN
ejpam-4069	78	9	,	,	PUNCT
ejpam-4069	78	10	2	2	NUM
ejpam-4069	78	11	)	)	PUNCT
ejpam-4069	78	12	,	,	PUNCT
ejpam-4069	78	13	z	z	NOUN
ejpam-4069	78	14	/∈	/∈	PUNCT
ejpam-4069	78	15	ng(x	ng(x	NUM
ejpam-4069	78	16	)	)	PUNCT
ejpam-4069	78	17	∩ng(y	∩ng(y	PROPN
ejpam-4069	78	18	)	)	PUNCT
ejpam-4069	78	19	.	.	PUNCT
ejpam-4069	79	1	conversely	conversely	ADV
ejpam-4069	79	2	,	,	PUNCT
ejpam-4069	79	3	suppose	suppose	VERB
ejpam-4069	79	4	that	that	SCONJ
ejpam-4069	79	5	there	there	PRON
ejpam-4069	79	6	exist	exist	VERB
ejpam-4069	79	7	adjacent	adjacent	ADJ
ejpam-4069	79	8	vertices	vertex	NOUN
ejpam-4069	79	9	x	x	PUNCT
ejpam-4069	79	10	and	and	CCONJ
ejpam-4069	79	11	y	y	PROPN
ejpam-4069	79	12	of	of	ADP
ejpam-4069	79	13	g	g	PROPN
ejpam-4069	79	14	satisfying	satisfy	VERB
ejpam-4069	79	15	the	the	DET
ejpam-4069	79	16	given	give	VERB
ejpam-4069	79	17	condition	condition	NOUN
ejpam-4069	79	18	.	.	PUNCT
ejpam-4069	80	1	let	let	VERB
ejpam-4069	80	2	s	s	PRON
ejpam-4069	80	3	=	=	PUNCT
ejpam-4069	80	4	{	{	PUNCT
ejpam-4069	80	5	x	x	PROPN
ejpam-4069	80	6	,	,	PUNCT
ejpam-4069	80	7	y	y	PROPN
ejpam-4069	80	8	}	}	PUNCT
ejpam-4069	80	9	.	.	PUNCT
ejpam-4069	81	1	since	since	SCONJ
ejpam-4069	81	2	xy	xy	PROPN
ejpam-4069	81	3	∈	∈	PROPN
ejpam-4069	81	4	e(g	e(g	PROPN
ejpam-4069	81	5	)	)	PUNCT
ejpam-4069	81	6	,	,	PUNCT
ejpam-4069	81	7	s	s	VERB
ejpam-4069	81	8	is	be	AUX
ejpam-4069	81	9	connected	connect	VERB
ejpam-4069	81	10	.	.	PUNCT
ejpam-4069	82	1	let	let	VERB
ejpam-4069	82	2	z	z	NOUN
ejpam-4069	82	3	∈	∈	PROPN
ejpam-4069	82	4	v	v	NOUN
ejpam-4069	82	5	(	(	PUNCT
ejpam-4069	82	6	g)\s	g)\s	NOUN
ejpam-4069	82	7	.	.	PUNCT
ejpam-4069	83	1	if	if	SCONJ
ejpam-4069	83	2	ng(z	ng(z	NUM
ejpam-4069	83	3	)	)	PUNCT
ejpam-4069	84	1	=	=	PRON
ejpam-4069	84	2	{	{	PUNCT
ejpam-4069	84	3	x	x	NOUN
ejpam-4069	84	4	}	}	PUNCT
ejpam-4069	84	5	,	,	PUNCT
ejpam-4069	84	6	then	then	ADV
ejpam-4069	84	7	since	since	SCONJ
ejpam-4069	84	8	xy	xy	PROPN
ejpam-4069	84	9	∈	∈	PROPN
ejpam-4069	84	10	e(g	e(g	PROPN
ejpam-4069	84	11	)	)	PUNCT
ejpam-4069	84	12	,	,	PUNCT
ejpam-4069	84	13	dg(y	dg(y	ADJ
ejpam-4069	84	14	,	,	PUNCT
ejpam-4069	84	15	z	z	NOUN
ejpam-4069	84	16	)	)	PUNCT
ejpam-4069	84	17	=	=	SYM
ejpam-4069	84	18	2	2	X
ejpam-4069	84	19	.	.	PUNCT
ejpam-4069	84	20	while	while	SCONJ
ejpam-4069	84	21	on	on	ADP
ejpam-4069	84	22	the	the	DET
ejpam-4069	84	23	other	other	ADJ
ejpam-4069	84	24	hand	hand	NOUN
ejpam-4069	84	25	,	,	PUNCT
ejpam-4069	84	26	if	if	SCONJ
ejpam-4069	84	27	ng(z	ng(z	NUM
ejpam-4069	84	28	)	)	PUNCT
ejpam-4069	85	1	=	=	PRON
ejpam-4069	85	2	{	{	PUNCT
ejpam-4069	85	3	y	y	NOUN
ejpam-4069	85	4	}	}	PUNCT
ejpam-4069	85	5	,	,	PUNCT
ejpam-4069	85	6	then	then	ADV
ejpam-4069	85	7	dg(x	dg(x	NUM
ejpam-4069	85	8	,	,	PUNCT
ejpam-4069	85	9	z	z	X
ejpam-4069	85	10	)	)	PUNCT
ejpam-4069	85	11	=	=	SYM
ejpam-4069	85	12	2	2	X
ejpam-4069	85	13	.	.	PUNCT
ejpam-4069	85	14	thus	thus	ADV
ejpam-4069	85	15	,	,	PUNCT
ejpam-4069	85	16	s	s	VERB
ejpam-4069	85	17	is	be	AUX
ejpam-4069	85	18	a	a	DET
ejpam-4069	85	19	hop	hop	NOUN
ejpam-4069	85	20	dominating	dominating	NOUN
ejpam-4069	85	21	set	set	NOUN
ejpam-4069	85	22	of	of	ADP
ejpam-4069	85	23	g.	g.	PROPN
ejpam-4069	85	24	since	since	SCONJ
ejpam-4069	85	25	ng(z	ng(z	NUM
ejpam-4069	85	26	)	)	PUNCT
ejpam-4069	86	1	=	=	PRON
ejpam-4069	86	2	{	{	PUNCT
ejpam-4069	86	3	x	x	NOUN
ejpam-4069	86	4	}	}	PUNCT
ejpam-4069	86	5	or	or	CCONJ
ejpam-4069	86	6	ng(z	ng(z	NUM
ejpam-4069	86	7	)	)	PUNCT
ejpam-4069	87	1	=	=	PRON
ejpam-4069	87	2	{	{	PUNCT
ejpam-4069	87	3	y	y	NOUN
ejpam-4069	87	4	}	}	PUNCT
ejpam-4069	87	5	,	,	PUNCT
ejpam-4069	87	6	v	v	X
ejpam-4069	87	7	(	(	PUNCT
ejpam-4069	87	8	g)\s	g)\s	NOUN
ejpam-4069	87	9	is	be	AUX
ejpam-4069	87	10	an	an	DET
ejpam-4069	87	11	independent	independent	ADJ
ejpam-4069	87	12	set	set	NOUN
ejpam-4069	87	13	.	.	PUNCT
ejpam-4069	88	1	therefore	therefore	ADV
ejpam-4069	88	2	,	,	PUNCT
ejpam-4069	88	3	s	s	VERB
ejpam-4069	88	4	is	be	AUX
ejpam-4069	88	5	a	a	DET
ejpam-4069	88	6	connected	connected	ADJ
ejpam-4069	88	7	co	co	NOUN
ejpam-4069	88	8	-	-	ADJ
ejpam-4069	88	9	independent	independent	ADJ
ejpam-4069	88	10	hop	hop	NOUN
ejpam-4069	88	11	dominating	dominating	NOUN
ejpam-4069	88	12	set	set	NOUN
ejpam-4069	88	13	of	of	ADP
ejpam-4069	88	14	g.	g.	PROPN
ejpam-4069	89	1	so	so	ADV
ejpam-4069	89	2	,	,	PUNCT
ejpam-4069	89	3	γch	γch	NOUN
ejpam-4069	89	4	,	,	PUNCT
ejpam-4069	89	5	coi(g	coi(g	PROPN
ejpam-4069	89	6	)	)	PUNCT
ejpam-4069	89	7	≤	≤	NUM
ejpam-4069	89	8	|s|	|s|	PROPN
ejpam-4069	89	9	=	=	SYM
ejpam-4069	89	10	2	2	NUM
ejpam-4069	89	11	.	.	PUNCT
ejpam-4069	90	1	but	but	CCONJ
ejpam-4069	90	2	g	g	PROPN
ejpam-4069	90	3	is	be	AUX
ejpam-4069	90	4	nontrivial	nontrivial	ADJ
ejpam-4069	90	5	.	.	PUNCT
ejpam-4069	91	1	hence	hence	ADV
ejpam-4069	91	2	,	,	PUNCT
ejpam-4069	91	3	γch	γch	NOUN
ejpam-4069	91	4	,	,	PUNCT
ejpam-4069	91	5	coi(g	coi(g	PROPN
ejpam-4069	91	6	)	)	PUNCT
ejpam-4069	91	7	̸=	̸=	NOUN
ejpam-4069	91	8	1	1	NUM
ejpam-4069	91	9	and	and	CCONJ
ejpam-4069	91	10	so	so	ADV
ejpam-4069	91	11	γch	γch	ADV
ejpam-4069	91	12	,	,	PUNCT
ejpam-4069	91	13	coi(g	coi(g	PROPN
ejpam-4069	91	14	)	)	PUNCT
ejpam-4069	91	15	=	=	SYM
ejpam-4069	92	1	2	2	X
ejpam-4069	92	2	.	.	PUNCT
ejpam-4069	92	3	s.	s.	PROPN
ejpam-4069	92	4	nanding	nanding	PROPN
ejpam-4069	92	5	,	,	PUNCT
ejpam-4069	92	6	h.	h.	PROPN
ejpam-4069	92	7	rara	rara	PROPN
ejpam-4069	92	8	/	/	SYM
ejpam-4069	92	9	eur	eur	PROPN
ejpam-4069	92	10	.	.	PUNCT
ejpam-4069	93	1	j.	j.	PROPN
ejpam-4069	93	2	pure	pure	PROPN
ejpam-4069	93	3	appl	appl	PROPN
ejpam-4069	93	4	.	.	PROPN
ejpam-4069	93	5	math	math	PROPN
ejpam-4069	93	6	,	,	PUNCT
ejpam-4069	93	7	14	14	NUM
ejpam-4069	93	8	(	(	PUNCT
ejpam-4069	93	9	4	4	NUM
ejpam-4069	93	10	)	)	PUNCT
ejpam-4069	93	11	(	(	PUNCT
ejpam-4069	93	12	2021	2021	NUM
ejpam-4069	93	13	)	)	PUNCT
ejpam-4069	93	14	,	,	PUNCT
ejpam-4069	93	15	1226	1226	NUM
ejpam-4069	93	16	-	-	SYM
ejpam-4069	93	17	1236	1236	NUM
ejpam-4069	93	18	1229	1229	NUM
ejpam-4069	93	19	theorem	theorem	NOUN
ejpam-4069	93	20	2	2	NUM
ejpam-4069	93	21	.	.	PUNCT
ejpam-4069	94	1	let	let	VERB
ejpam-4069	94	2	g	g	PRON
ejpam-4069	94	3	be	be	AUX
ejpam-4069	94	4	a	a	DET
ejpam-4069	94	5	connected	connected	ADJ
ejpam-4069	94	6	graph	graph	NOUN
ejpam-4069	94	7	of	of	ADP
ejpam-4069	94	8	order	order	NOUN
ejpam-4069	94	9	n	n	PRON
ejpam-4069	94	10	≥	≥	NOUN
ejpam-4069	94	11	2	2	NUM
ejpam-4069	94	12	.	.	PUNCT
ejpam-4069	95	1	then	then	ADV
ejpam-4069	95	2	γch	γch	VERB
ejpam-4069	95	3	,	,	PUNCT
ejpam-4069	95	4	coi(g	coi(g	PROPN
ejpam-4069	95	5	)	)	PUNCT
ejpam-4069	96	1	=	=	SYM
ejpam-4069	97	1	n	n	NOUN
ejpam-4069	97	2	if	if	SCONJ
ejpam-4069	97	3	and	and	CCONJ
ejpam-4069	97	4	only	only	ADV
ejpam-4069	97	5	if	if	SCONJ
ejpam-4069	97	6	g	g	PROPN
ejpam-4069	97	7	is	be	AUX
ejpam-4069	97	8	complete	complete	ADJ
ejpam-4069	97	9	.	.	PUNCT
ejpam-4069	98	1	proof	proof	NOUN
ejpam-4069	98	2	:	:	PUNCT
ejpam-4069	98	3	suppose	suppose	VERB
ejpam-4069	98	4	γch	γch	NOUN
ejpam-4069	98	5	,	,	PUNCT
ejpam-4069	98	6	coi(g	coi(g	PROPN
ejpam-4069	98	7	)	)	PUNCT
ejpam-4069	99	1	=	=	SYM
ejpam-4069	99	2	n.	n.	NOUN
ejpam-4069	99	3	suppose	suppose	VERB
ejpam-4069	99	4	that	that	SCONJ
ejpam-4069	99	5	g	g	PROPN
ejpam-4069	99	6	is	be	AUX
ejpam-4069	99	7	not	not	PART
ejpam-4069	99	8	complete	complete	ADJ
ejpam-4069	99	9	.	.	PUNCT
ejpam-4069	100	1	then	then	ADV
ejpam-4069	100	2	there	there	PRON
ejpam-4069	100	3	exist	exist	VERB
ejpam-4069	100	4	distinct	distinct	ADJ
ejpam-4069	100	5	vertices	vertex	NOUN
ejpam-4069	100	6	u	u	NOUN
ejpam-4069	100	7	,	,	PUNCT
ejpam-4069	100	8	v	v	NOUN
ejpam-4069	100	9	∈	∈	PROPN
ejpam-4069	100	10	v	v	NOUN
ejpam-4069	100	11	(	(	PUNCT
ejpam-4069	100	12	g	g	NOUN
ejpam-4069	100	13	)	)	PUNCT
ejpam-4069	100	14	such	such	ADJ
ejpam-4069	100	15	that	that	SCONJ
ejpam-4069	100	16	dg(u	dg(u	ADJ
ejpam-4069	100	17	,	,	PUNCT
ejpam-4069	100	18	v	v	NOUN
ejpam-4069	100	19	)	)	PUNCT
ejpam-4069	100	20	=	=	SYM
ejpam-4069	100	21	2	2	X
ejpam-4069	100	22	.	.	X
ejpam-4069	100	23	let	let	VERB
ejpam-4069	100	24	s	s	NOUN
ejpam-4069	100	25	=	=	X
ejpam-4069	100	26	v	v	X
ejpam-4069	100	27	(	(	PUNCT
ejpam-4069	100	28	g)\{u	g)\{u	PROPN
ejpam-4069	100	29	}	}	PUNCT
ejpam-4069	100	30	.	.	PUNCT
ejpam-4069	101	1	then	then	ADV
ejpam-4069	101	2	s	s	VERB
ejpam-4069	101	3	is	be	AUX
ejpam-4069	101	4	a	a	DET
ejpam-4069	101	5	connected	connected	ADJ
ejpam-4069	101	6	co	co	NOUN
ejpam-4069	101	7	-	-	ADJ
ejpam-4069	101	8	independent	independent	ADJ
ejpam-4069	101	9	hop	hop	NOUN
ejpam-4069	101	10	dominating	dominating	NOUN
ejpam-4069	101	11	set	set	NOUN
ejpam-4069	101	12	of	of	ADP
ejpam-4069	101	13	g.	g.	PROPN
ejpam-4069	101	14	therefore	therefore	ADV
ejpam-4069	101	15	,	,	PUNCT
ejpam-4069	101	16	γch	γch	NOUN
ejpam-4069	101	17	,	,	PUNCT
ejpam-4069	101	18	coi(g	coi(g	PROPN
ejpam-4069	101	19	)	)	PUNCT
ejpam-4069	101	20	≤	≤	NUM
ejpam-4069	101	21	|s|	|s|	PROPN
ejpam-4069	101	22	=	=	SYM
ejpam-4069	101	23	n−	n−	NOUN
ejpam-4069	101	24	1	1	NUM
ejpam-4069	101	25	,	,	PUNCT
ejpam-4069	101	26	a	a	DET
ejpam-4069	101	27	contradiction	contradiction	NOUN
ejpam-4069	101	28	.	.	PUNCT
ejpam-4069	102	1	thus	thus	ADV
ejpam-4069	102	2	,	,	PUNCT
ejpam-4069	102	3	g	g	PROPN
ejpam-4069	102	4	is	be	AUX
ejpam-4069	102	5	a	a	DET
ejpam-4069	102	6	complete	complete	ADJ
ejpam-4069	102	7	graph	graph	NOUN
ejpam-4069	102	8	.	.	PUNCT
ejpam-4069	103	1	conversely	conversely	ADV
ejpam-4069	103	2	,	,	PUNCT
ejpam-4069	103	3	by	by	ADP
ejpam-4069	103	4	remark	remark	NOUN
ejpam-4069	103	5	3	3	NUM
ejpam-4069	103	6	,	,	PUNCT
ejpam-4069	103	7	γch	γch	NOUN
ejpam-4069	103	8	,	,	PUNCT
ejpam-4069	103	9	coi(kn	coi(kn	NUM
ejpam-4069	103	10	)	)	PUNCT
ejpam-4069	103	11	=	=	PUNCT
ejpam-4069	103	12	n.	n.	NOUN
ejpam-4069	103	13	3	3	X
ejpam-4069	103	14	.	.	PUNCT
ejpam-4069	104	1	on	on	ADP
ejpam-4069	104	2	connected	connected	ADJ
ejpam-4069	104	3	co	co	ADJ
ejpam-4069	104	4	-	-	ADJ
ejpam-4069	104	5	independent	independent	ADJ
ejpam-4069	104	6	hop	hop	NOUN
ejpam-4069	104	7	domination	domination	NOUN
ejpam-4069	104	8	in	in	ADP
ejpam-4069	104	9	the	the	DET
ejpam-4069	104	10	join	join	NOUN
ejpam-4069	104	11	of	of	ADP
ejpam-4069	104	12	graphs	graph	NOUN
ejpam-4069	104	13	the	the	DET
ejpam-4069	104	14	join	join	NOUN
ejpam-4069	104	15	of	of	ADP
ejpam-4069	104	16	two	two	NUM
ejpam-4069	104	17	graphs	graph	NOUN
ejpam-4069	104	18	g	g	NOUN
ejpam-4069	105	1	and	and	CCONJ
ejpam-4069	105	2	h	h	NOUN
ejpam-4069	105	3	is	be	AUX
ejpam-4069	105	4	the	the	DET
ejpam-4069	105	5	graph	graph	NOUN
ejpam-4069	105	6	g	g	NOUN
ejpam-4069	105	7	+	+	CCONJ
ejpam-4069	105	8	h	h	NOUN
ejpam-4069	105	9	with	with	ADP
ejpam-4069	105	10	vertex	vertex	NOUN
ejpam-4069	105	11	set	set	VERB
ejpam-4069	105	12	v	v	NOUN
ejpam-4069	105	13	(	(	PUNCT
ejpam-4069	105	14	g	g	PROPN
ejpam-4069	105	15	+	+	NOUN
ejpam-4069	105	16	h	h	NOUN
ejpam-4069	105	17	)	)	PUNCT
ejpam-4069	106	1	=	=	NOUN
ejpam-4069	106	2	v	v	X
ejpam-4069	106	3	(	(	PUNCT
ejpam-4069	106	4	g	g	NOUN
ejpam-4069	106	5	)	)	PUNCT
ejpam-4069	106	6	•	•	ADP
ejpam-4069	106	7	∪	∪	X
ejpam-4069	106	8	v	v	NOUN
ejpam-4069	106	9	(	(	PUNCT
ejpam-4069	106	10	h	h	NOUN
ejpam-4069	106	11	)	)	PUNCT
ejpam-4069	106	12	and	and	CCONJ
ejpam-4069	106	13	edge	edge	NOUN
ejpam-4069	106	14	set	set	VERB
ejpam-4069	106	15	e(g	e(g	PROPN
ejpam-4069	107	1	+	+	CCONJ
ejpam-4069	107	2	h	h	NOUN
ejpam-4069	107	3	)	)	PUNCT
ejpam-4069	107	4	=	=	SYM
ejpam-4069	107	5	e(g	e(g	PROPN
ejpam-4069	107	6	)	)	PUNCT
ejpam-4069	108	1	•	•	ADP
ejpam-4069	108	2	∪	∪	ADP
ejpam-4069	108	3	e(h	e(h	PROPN
ejpam-4069	108	4	)	)	PUNCT
ejpam-4069	108	5	∪	∪	NOUN
ejpam-4069	108	6	{	{	PUNCT
ejpam-4069	108	7	uv	uv	NOUN
ejpam-4069	108	8	:	:	PUNCT
ejpam-4069	108	9	u	u	PROPN
ejpam-4069	108	10	∈	∈	PROPN
ejpam-4069	108	11	v	v	ADP
ejpam-4069	108	12	(	(	PUNCT
ejpam-4069	108	13	g	g	NOUN
ejpam-4069	108	14	)	)	PUNCT
ejpam-4069	108	15	,	,	PUNCT
ejpam-4069	108	16	v	v	X
ejpam-4069	108	17	∈	∈	PROPN
ejpam-4069	108	18	v	v	NOUN
ejpam-4069	108	19	(	(	PUNCT
ejpam-4069	108	20	h	h	NOUN
ejpam-4069	108	21	)	)	PUNCT
ejpam-4069	108	22	}	}	PUNCT
ejpam-4069	108	23	.	.	PUNCT
ejpam-4069	109	1	theorem	theorem	NOUN
ejpam-4069	109	2	3	3	X
ejpam-4069	109	3	.	.	PUNCT
ejpam-4069	110	1	let	let	VERB
ejpam-4069	110	2	g	g	NOUN
ejpam-4069	111	1	and	and	CCONJ
ejpam-4069	111	2	h	h	NOUN
ejpam-4069	111	3	be	be	VERB
ejpam-4069	111	4	any	any	DET
ejpam-4069	111	5	two	two	NUM
ejpam-4069	111	6	graphs	graph	NOUN
ejpam-4069	111	7	.	.	PUNCT
ejpam-4069	112	1	then	then	ADV
ejpam-4069	112	2	s	s	VERB
ejpam-4069	112	3	⊆	⊆	NUM
ejpam-4069	112	4	v	v	NOUN
ejpam-4069	112	5	(	(	PUNCT
ejpam-4069	112	6	g	g	PROPN
ejpam-4069	112	7	+	+	NOUN
ejpam-4069	112	8	h	h	NOUN
ejpam-4069	112	9	)	)	PUNCT
ejpam-4069	112	10	is	be	AUX
ejpam-4069	112	11	a	a	DET
ejpam-4069	112	12	connected	connected	ADJ
ejpam-4069	112	13	co	co	NOUN
ejpam-4069	112	14	-	-	ADJ
ejpam-4069	112	15	independent	independent	ADJ
ejpam-4069	112	16	hop	hop	NOUN
ejpam-4069	112	17	dominating	dominating	NOUN
ejpam-4069	112	18	set	set	NOUN
ejpam-4069	112	19	of	of	ADP
ejpam-4069	112	20	g+h	g+h	PROPN
ejpam-4069	113	1	if	if	SCONJ
ejpam-4069	113	2	and	and	CCONJ
ejpam-4069	113	3	only	only	ADV
ejpam-4069	113	4	if	if	SCONJ
ejpam-4069	113	5	s	s	NOUN
ejpam-4069	113	6	=	=	PUNCT
ejpam-4069	113	7	sg	sg	ADP
ejpam-4069	113	8	∪sh	∪sh	NOUN
ejpam-4069	113	9	where	where	SCONJ
ejpam-4069	113	10	one	one	NUM
ejpam-4069	113	11	of	of	ADP
ejpam-4069	113	12	the	the	DET
ejpam-4069	113	13	following	follow	VERB
ejpam-4069	113	14	holds	hold	VERB
ejpam-4069	113	15	:	:	PUNCT
ejpam-4069	113	16	(	(	PUNCT
ejpam-4069	113	17	i	i	NOUN
ejpam-4069	113	18	)	)	PUNCT
ejpam-4069	113	19	sg	sg	PROPN
ejpam-4069	113	20	=	=	SYM
ejpam-4069	113	21	v	v	PROPN
ejpam-4069	113	22	(	(	PUNCT
ejpam-4069	113	23	g	g	NOUN
ejpam-4069	113	24	)	)	PUNCT
ejpam-4069	113	25	and	and	CCONJ
ejpam-4069	113	26	sh	sh	PROPN
ejpam-4069	113	27	is	be	AUX
ejpam-4069	113	28	a	a	DET
ejpam-4069	113	29	strictly	strictly	ADV
ejpam-4069	113	30	co	co	ADJ
ejpam-4069	113	31	-	-	ADJ
ejpam-4069	113	32	independent	independent	ADJ
ejpam-4069	113	33	set	set	NOUN
ejpam-4069	113	34	of	of	ADP
ejpam-4069	113	35	h.	h.	PROPN
ejpam-4069	113	36	(	(	PUNCT
ejpam-4069	113	37	ii	ii	PROPN
ejpam-4069	113	38	)	)	PUNCT
ejpam-4069	114	1	sh	sh	PROPN
ejpam-4069	114	2	=	=	SYM
ejpam-4069	114	3	v	v	PROPN
ejpam-4069	114	4	(	(	PUNCT
ejpam-4069	114	5	h	h	NOUN
ejpam-4069	114	6	)	)	PUNCT
ejpam-4069	114	7	and	and	CCONJ
ejpam-4069	114	8	sg	sg	PROPN
ejpam-4069	114	9	is	be	AUX
ejpam-4069	114	10	a	a	DET
ejpam-4069	114	11	strictly	strictly	ADV
ejpam-4069	114	12	co	co	ADJ
ejpam-4069	114	13	-	-	ADJ
ejpam-4069	114	14	independent	independent	ADJ
ejpam-4069	114	15	set	set	NOUN
ejpam-4069	114	16	of	of	ADP
ejpam-4069	114	17	g.	g.	PROPN
ejpam-4069	114	18	proof	proof	PROPN
ejpam-4069	114	19	:	:	PUNCT
ejpam-4069	114	20	suppose	suppose	VERB
ejpam-4069	114	21	s	s	NOUN
ejpam-4069	114	22	is	be	AUX
ejpam-4069	114	23	a	a	DET
ejpam-4069	114	24	connected	connected	ADJ
ejpam-4069	114	25	co	co	NOUN
ejpam-4069	114	26	-	-	ADJ
ejpam-4069	114	27	independent	independent	ADJ
ejpam-4069	114	28	hop	hop	NOUN
ejpam-4069	114	29	dominating	dominating	NOUN
ejpam-4069	114	30	set	set	NOUN
ejpam-4069	114	31	of	of	ADP
ejpam-4069	114	32	g	g	PROPN
ejpam-4069	114	33	+	+	CCONJ
ejpam-4069	114	34	h.	h.	PROPN
ejpam-4069	114	35	let	let	VERB
ejpam-4069	114	36	sg	sg	VERB
ejpam-4069	114	37	=	=	SYM
ejpam-4069	114	38	s	s	PART
ejpam-4069	114	39	∩	∩	ADJ
ejpam-4069	114	40	v	v	X
ejpam-4069	114	41	(	(	PUNCT
ejpam-4069	114	42	g	g	NOUN
ejpam-4069	114	43	)	)	PUNCT
ejpam-4069	114	44	and	and	CCONJ
ejpam-4069	114	45	sh	sh	INTJ
ejpam-4069	114	46	=	=	SYM
ejpam-4069	114	47	s	s	PROPN
ejpam-4069	114	48	∩	∩	ADJ
ejpam-4069	114	49	v	v	ADJ
ejpam-4069	114	50	(	(	PUNCT
ejpam-4069	114	51	h	h	NOUN
ejpam-4069	114	52	)	)	PUNCT
ejpam-4069	114	53	.	.	PUNCT
ejpam-4069	115	1	then	then	ADV
ejpam-4069	115	2	s	s	VERB
ejpam-4069	115	3	=	=	PUNCT
ejpam-4069	115	4	sg	sg	X
ejpam-4069	115	5	∪	∪	VERB
ejpam-4069	115	6	sh	sh	PROPN
ejpam-4069	115	7	.	.	PUNCT
ejpam-4069	116	1	since	since	SCONJ
ejpam-4069	116	2	s	s	PROPN
ejpam-4069	116	3	is	be	AUX
ejpam-4069	116	4	a	a	DET
ejpam-4069	116	5	hop	hop	NOUN
ejpam-4069	116	6	dominating	dominating	NOUN
ejpam-4069	116	7	set	set	NOUN
ejpam-4069	116	8	of	of	ADP
ejpam-4069	116	9	g+h	g+h	PROPN
ejpam-4069	116	10	,	,	PUNCT
ejpam-4069	116	11	sg	sg	ADP
ejpam-4069	116	12	̸=	̸=	PROPN
ejpam-4069	116	13	∅	∅	NOUN
ejpam-4069	116	14	and	and	CCONJ
ejpam-4069	116	15	sh	sh	PROPN
ejpam-4069	116	16	̸=	̸=	PROPN
ejpam-4069	116	17	∅.	∅.	NOUN
ejpam-4069	116	18	since	since	SCONJ
ejpam-4069	116	19	v	v	NOUN
ejpam-4069	116	20	(	(	PUNCT
ejpam-4069	116	21	g+h)\s	g+h)\s	PROPN
ejpam-4069	116	22	is	be	AUX
ejpam-4069	116	23	an	an	DET
ejpam-4069	116	24	independent	independent	ADJ
ejpam-4069	116	25	set	set	NOUN
ejpam-4069	116	26	,	,	PUNCT
ejpam-4069	116	27	sg	sg	ADP
ejpam-4069	116	28	=	=	SYM
ejpam-4069	116	29	v	v	PROPN
ejpam-4069	116	30	(	(	PUNCT
ejpam-4069	116	31	g	g	NOUN
ejpam-4069	116	32	)	)	PUNCT
ejpam-4069	116	33	or	or	CCONJ
ejpam-4069	116	34	sh	sh	INTJ
ejpam-4069	116	35	=	=	SYM
ejpam-4069	116	36	v	v	PROPN
ejpam-4069	116	37	(	(	PUNCT
ejpam-4069	116	38	h	h	NOUN
ejpam-4069	116	39	)	)	PUNCT
ejpam-4069	116	40	.	.	PUNCT
ejpam-4069	117	1	suppose	suppose	VERB
ejpam-4069	117	2	sg	sg	PROPN
ejpam-4069	117	3	=	=	SYM
ejpam-4069	117	4	v	v	PROPN
ejpam-4069	117	5	(	(	PUNCT
ejpam-4069	117	6	g	g	NOUN
ejpam-4069	117	7	)	)	PUNCT
ejpam-4069	117	8	.	.	PUNCT
ejpam-4069	118	1	then	then	ADV
ejpam-4069	118	2	v	v	X
ejpam-4069	118	3	(	(	PUNCT
ejpam-4069	118	4	h)\sh	h)\sh	PROPN
ejpam-4069	118	5	=	=	SYM
ejpam-4069	118	6	v	v	PROPN
ejpam-4069	118	7	(	(	PUNCT
ejpam-4069	118	8	g+h)\s	g+h)\s	PROPN
ejpam-4069	118	9	is	be	AUX
ejpam-4069	118	10	an	an	DET
ejpam-4069	118	11	independent	independent	ADJ
ejpam-4069	118	12	set	set	NOUN
ejpam-4069	118	13	.	.	PUNCT
ejpam-4069	119	1	let	let	VERB
ejpam-4069	119	2	v	v	NUM
ejpam-4069	119	3	∈	∈	NOUN
ejpam-4069	119	4	v	v	NOUN
ejpam-4069	119	5	(	(	PUNCT
ejpam-4069	119	6	h)\sh	h)\sh	PROPN
ejpam-4069	119	7	.	.	PUNCT
ejpam-4069	120	1	then	then	ADV
ejpam-4069	120	2	v	v	ADP
ejpam-4069	120	3	∈	∈	PROPN
ejpam-4069	120	4	v	v	NOUN
ejpam-4069	120	5	(	(	PUNCT
ejpam-4069	120	6	g	g	PROPN
ejpam-4069	120	7	+	+	PROPN
ejpam-4069	120	8	h)\s	h)\s	PROPN
ejpam-4069	120	9	.	.	PUNCT
ejpam-4069	121	1	since	since	SCONJ
ejpam-4069	121	2	s	s	PROPN
ejpam-4069	121	3	is	be	AUX
ejpam-4069	121	4	a	a	DET
ejpam-4069	121	5	hop	hop	NOUN
ejpam-4069	121	6	dominating	dominating	NOUN
ejpam-4069	121	7	set	set	NOUN
ejpam-4069	121	8	,	,	PUNCT
ejpam-4069	121	9	there	there	PRON
ejpam-4069	121	10	exists	exist	VERB
ejpam-4069	121	11	w	w	PROPN
ejpam-4069	121	12	∈	∈	PROPN
ejpam-4069	121	13	s	s	VERB
ejpam-4069	121	14	such	such	ADJ
ejpam-4069	121	15	that	that	SCONJ
ejpam-4069	121	16	dg+h(v	dg+h(v	PROPN
ejpam-4069	121	17	,	,	PUNCT
ejpam-4069	121	18	w	w	NOUN
ejpam-4069	121	19	)	)	PUNCT
ejpam-4069	121	20	=	=	SYM
ejpam-4069	121	21	2	2	X
ejpam-4069	121	22	.	.	X
ejpam-4069	122	1	hence	hence	ADV
ejpam-4069	122	2	,	,	PUNCT
ejpam-4069	122	3	w	w	PROPN
ejpam-4069	122	4	∈	∈	PROPN
ejpam-4069	122	5	sh\nh(v	sh\nh(v	PROPN
ejpam-4069	122	6	)	)	PUNCT
ejpam-4069	122	7	.	.	PUNCT
ejpam-4069	123	1	thus	thus	ADV
ejpam-4069	123	2	,	,	PUNCT
ejpam-4069	123	3	nh(v)∩sh	nh(v)∩sh	NUM
ejpam-4069	123	4	̸=	̸=	PROPN
ejpam-4069	123	5	sh	sh	INTJ
ejpam-4069	123	6	,	,	PUNCT
ejpam-4069	123	7	showing	show	VERB
ejpam-4069	123	8	that	that	SCONJ
ejpam-4069	123	9	sh	sh	PROPN
ejpam-4069	123	10	is	be	AUX
ejpam-4069	123	11	a	a	DET
ejpam-4069	123	12	strictly	strictly	ADV
ejpam-4069	123	13	co	co	ADJ
ejpam-4069	123	14	-	-	ADJ
ejpam-4069	123	15	independent	independent	ADJ
ejpam-4069	123	16	set	set	NOUN
ejpam-4069	123	17	of	of	ADP
ejpam-4069	123	18	h.	h.	PROPN
ejpam-4069	123	19	thus	thus	ADV
ejpam-4069	123	20	,	,	PUNCT
ejpam-4069	123	21	(	(	PUNCT
ejpam-4069	123	22	i	i	NOUN
ejpam-4069	123	23	)	)	PUNCT
ejpam-4069	123	24	holds	hold	VERB
ejpam-4069	123	25	.	.	PUNCT
ejpam-4069	124	1	similarly	similarly	ADV
ejpam-4069	124	2	,	,	PUNCT
ejpam-4069	124	3	if	if	SCONJ
ejpam-4069	124	4	sh	sh	PROPN
ejpam-4069	124	5	=	=	SYM
ejpam-4069	124	6	v	v	PROPN
ejpam-4069	124	7	(	(	PUNCT
ejpam-4069	124	8	h	h	NOUN
ejpam-4069	124	9	)	)	PUNCT
ejpam-4069	124	10	,	,	PUNCT
ejpam-4069	124	11	then	then	ADV
ejpam-4069	124	12	sg	sg	PROPN
ejpam-4069	124	13	is	be	AUX
ejpam-4069	124	14	a	a	DET
ejpam-4069	124	15	strictly	strictly	ADV
ejpam-4069	124	16	co	co	ADJ
ejpam-4069	124	17	-	-	ADJ
ejpam-4069	124	18	independent	independent	ADJ
ejpam-4069	124	19	set	set	NOUN
ejpam-4069	124	20	of	of	ADP
ejpam-4069	124	21	g	g	PROPN
ejpam-4069	124	22	and	and	CCONJ
ejpam-4069	124	23	(	(	PUNCT
ejpam-4069	124	24	ii	ii	NOUN
ejpam-4069	124	25	)	)	PUNCT
ejpam-4069	124	26	holds	hold	VERB
ejpam-4069	124	27	.	.	PUNCT
ejpam-4069	125	1	for	for	ADP
ejpam-4069	125	2	the	the	DET
ejpam-4069	125	3	converse	converse	NOUN
ejpam-4069	125	4	,	,	PUNCT
ejpam-4069	125	5	suppose	suppose	VERB
ejpam-4069	125	6	s	s	VERB
ejpam-4069	125	7	=	=	PUNCT
ejpam-4069	125	8	sg	sg	ADP
ejpam-4069	125	9	∪sh	∪sh	NOUN
ejpam-4069	125	10	where	where	SCONJ
ejpam-4069	125	11	sg	sg	PROPN
ejpam-4069	125	12	and	and	CCONJ
ejpam-4069	125	13	sh	sh	INTJ
ejpam-4069	125	14	satisfy	satisfy	VERB
ejpam-4069	125	15	the	the	DET
ejpam-4069	125	16	given	give	VERB
ejpam-4069	125	17	conditions	condition	NOUN
ejpam-4069	125	18	.	.	PUNCT
ejpam-4069	126	1	let	let	VERB
ejpam-4069	126	2	v	v	NUM
ejpam-4069	126	3	∈	∈	PROPN
ejpam-4069	126	4	v	v	NOUN
ejpam-4069	126	5	(	(	PUNCT
ejpam-4069	126	6	g+h)\s	g+h)\s	VERB
ejpam-4069	126	7	.	.	PUNCT
ejpam-4069	127	1	consider	consider	VERB
ejpam-4069	127	2	the	the	DET
ejpam-4069	127	3	following	follow	VERB
ejpam-4069	127	4	cases	case	NOUN
ejpam-4069	127	5	.	.	PUNCT
ejpam-4069	128	1	case	case	NOUN
ejpam-4069	128	2	1	1	NUM
ejpam-4069	128	3	.	.	PUNCT
ejpam-4069	129	1	sg	sg	PROPN
ejpam-4069	129	2	=	=	SYM
ejpam-4069	129	3	v	v	PROPN
ejpam-4069	129	4	(	(	PUNCT
ejpam-4069	129	5	g	g	NOUN
ejpam-4069	129	6	)	)	PUNCT
ejpam-4069	129	7	.	.	PUNCT
ejpam-4069	130	1	then	then	ADV
ejpam-4069	130	2	v	v	X
ejpam-4069	130	3	∈	∈	PROPN
ejpam-4069	130	4	v	v	NOUN
ejpam-4069	130	5	(	(	PUNCT
ejpam-4069	130	6	h)\sh	h)\sh	PROPN
ejpam-4069	130	7	.	.	PUNCT
ejpam-4069	131	1	by	by	ADP
ejpam-4069	131	2	(	(	PUNCT
ejpam-4069	131	3	i	i	NOUN
ejpam-4069	131	4	)	)	PUNCT
ejpam-4069	131	5	,	,	PUNCT
ejpam-4069	131	6	there	there	PRON
ejpam-4069	131	7	exists	exist	VERB
ejpam-4069	131	8	w	w	PROPN
ejpam-4069	131	9	∈	∈	PROPN
ejpam-4069	131	10	sh\nh(v	sh\nh(v	PROPN
ejpam-4069	131	11	)	)	PUNCT
ejpam-4069	131	12	.	.	PUNCT
ejpam-4069	132	1	hence	hence	ADV
ejpam-4069	132	2	,	,	PUNCT
ejpam-4069	132	3	w	w	PROPN
ejpam-4069	132	4	∈	∈	PROPN
ejpam-4069	132	5	s	s	X
ejpam-4069	132	6	and	and	CCONJ
ejpam-4069	132	7	dg+h(v	dg+h(v	PROPN
ejpam-4069	132	8	,	,	PUNCT
ejpam-4069	132	9	w	w	NOUN
ejpam-4069	132	10	)	)	PUNCT
ejpam-4069	132	11	=	=	SYM
ejpam-4069	132	12	2	2	X
ejpam-4069	132	13	.	.	X
ejpam-4069	132	14	case	case	NOUN
ejpam-4069	132	15	2	2	NUM
ejpam-4069	132	16	.	.	PUNCT
ejpam-4069	133	1	sh	sh	NOUN
ejpam-4069	133	2	=	=	SYM
ejpam-4069	133	3	v	v	PROPN
ejpam-4069	133	4	(	(	PUNCT
ejpam-4069	133	5	h	h	NOUN
ejpam-4069	133	6	)	)	PUNCT
ejpam-4069	133	7	then	then	ADV
ejpam-4069	133	8	v	v	ADP
ejpam-4069	133	9	∈	∈	PROPN
ejpam-4069	133	10	v	v	NOUN
ejpam-4069	133	11	(	(	PUNCT
ejpam-4069	133	12	g)\sg	g)\sg	PROPN
ejpam-4069	133	13	.	.	PUNCT
ejpam-4069	133	14	by	by	ADP
ejpam-4069	133	15	(	(	PUNCT
ejpam-4069	133	16	ii	ii	NOUN
ejpam-4069	133	17	)	)	PUNCT
ejpam-4069	134	1	,	,	PUNCT
ejpam-4069	134	2	there	there	PRON
ejpam-4069	134	3	exists	exist	VERB
ejpam-4069	134	4	u	u	PROPN
ejpam-4069	134	5	∈	∈	PROPN
ejpam-4069	134	6	sg\ng(v	sg\ng(v	NOUN
ejpam-4069	134	7	)	)	PUNCT
ejpam-4069	134	8	.	.	PUNCT
ejpam-4069	135	1	thus	thus	ADV
ejpam-4069	135	2	,	,	PUNCT
ejpam-4069	135	3	u	u	PROPN
ejpam-4069	135	4	∈	∈	PROPN
ejpam-4069	135	5	s	s	X
ejpam-4069	135	6	and	and	CCONJ
ejpam-4069	135	7	dg+h(u	dg+h(u	PROPN
ejpam-4069	135	8	,	,	PUNCT
ejpam-4069	135	9	v	v	NOUN
ejpam-4069	135	10	)	)	PUNCT
ejpam-4069	135	11	=	=	SYM
ejpam-4069	135	12	2	2	X
ejpam-4069	135	13	.	.	PUNCT
ejpam-4069	135	14	therefore	therefore	ADV
ejpam-4069	135	15	,	,	PUNCT
ejpam-4069	135	16	in	in	ADP
ejpam-4069	135	17	either	either	DET
ejpam-4069	135	18	case	case	NOUN
ejpam-4069	135	19	,	,	PUNCT
ejpam-4069	135	20	s	s	VERB
ejpam-4069	135	21	is	be	AUX
ejpam-4069	135	22	a	a	DET
ejpam-4069	135	23	hop	hop	NOUN
ejpam-4069	135	24	dominating	dominating	NOUN
ejpam-4069	135	25	set	set	NOUN
ejpam-4069	135	26	of	of	ADP
ejpam-4069	135	27	g+h	g+h	PROPN
ejpam-4069	135	28	.	.	PUNCT
ejpam-4069	136	1	since	since	SCONJ
ejpam-4069	136	2	v	v	NOUN
ejpam-4069	136	3	(	(	PUNCT
ejpam-4069	136	4	g+h)\s	g+h)\s	PROPN
ejpam-4069	136	5	=	=	SYM
ejpam-4069	136	6	v	v	NOUN
ejpam-4069	136	7	(	(	PUNCT
ejpam-4069	136	8	h)\sh	h)\sh	NOUN
ejpam-4069	136	9	if	if	SCONJ
ejpam-4069	136	10	(	(	PUNCT
ejpam-4069	136	11	i	i	NOUN
ejpam-4069	136	12	)	)	PUNCT
ejpam-4069	136	13	holds	hold	VERB
ejpam-4069	136	14	or	or	CCONJ
ejpam-4069	136	15	v	v	NOUN
ejpam-4069	136	16	(	(	PUNCT
ejpam-4069	136	17	g+h)\s	g+h)\s	PROPN
ejpam-4069	136	18	=	=	SYM
ejpam-4069	136	19	v	v	NOUN
ejpam-4069	136	20	(	(	PUNCT
ejpam-4069	136	21	g)\sg	g)\sg	PROPN
ejpam-4069	136	22	if	if	SCONJ
ejpam-4069	136	23	(	(	PUNCT
ejpam-4069	136	24	ii	ii	NOUN
ejpam-4069	136	25	)	)	PUNCT
ejpam-4069	136	26	holds	hold	VERB
ejpam-4069	136	27	,	,	PUNCT
ejpam-4069	136	28	v	v	X
ejpam-4069	136	29	(	(	PUNCT
ejpam-4069	136	30	g+h)\s	g+h)\s	PROPN
ejpam-4069	136	31	is	be	AUX
ejpam-4069	136	32	an	an	DET
ejpam-4069	136	33	independent	independent	ADJ
ejpam-4069	136	34	set	set	NOUN
ejpam-4069	136	35	.	.	PUNCT
ejpam-4069	137	1	it	it	PRON
ejpam-4069	137	2	is	be	AUX
ejpam-4069	137	3	clear	clear	ADJ
ejpam-4069	137	4	from	from	ADP
ejpam-4069	137	5	the	the	DET
ejpam-4069	137	6	definition	definition	NOUN
ejpam-4069	137	7	of	of	ADP
ejpam-4069	137	8	the	the	DET
ejpam-4069	137	9	join	join	NOUN
ejpam-4069	137	10	of	of	ADP
ejpam-4069	137	11	g	g	PROPN
ejpam-4069	137	12	and	and	CCONJ
ejpam-4069	137	13	h	h	NOUN
ejpam-4069	137	14	that	that	PRON
ejpam-4069	137	15	⟨s⟩	⟨s⟩	VERB
ejpam-4069	137	16	is	be	AUX
ejpam-4069	137	17	connected	connect	VERB
ejpam-4069	137	18	.	.	PUNCT
ejpam-4069	138	1	therefore	therefore	ADV
ejpam-4069	138	2	,	,	PUNCT
ejpam-4069	138	3	s	s	VERB
ejpam-4069	138	4	is	be	AUX
ejpam-4069	138	5	a	a	DET
ejpam-4069	138	6	connected	connected	ADJ
ejpam-4069	138	7	co	co	NOUN
ejpam-4069	138	8	-	-	ADJ
ejpam-4069	138	9	independent	independent	ADJ
ejpam-4069	138	10	hop	hop	NOUN
ejpam-4069	138	11	dominating	dominating	NOUN
ejpam-4069	138	12	set	set	NOUN
ejpam-4069	138	13	of	of	ADP
ejpam-4069	138	14	g+h	g+h	PROPN
ejpam-4069	138	15	.	.	PUNCT
ejpam-4069	139	1	s.	s.	PROPN
ejpam-4069	139	2	nanding	nanding	PROPN
ejpam-4069	139	3	,	,	PUNCT
ejpam-4069	139	4	h.	h.	PROPN
ejpam-4069	139	5	rara	rara	PROPN
ejpam-4069	139	6	/	/	SYM
ejpam-4069	139	7	eur	eur	PROPN
ejpam-4069	139	8	.	.	PUNCT
ejpam-4069	140	1	j.	j.	PROPN
ejpam-4069	140	2	pure	pure	PROPN
ejpam-4069	140	3	appl	appl	PROPN
ejpam-4069	140	4	.	.	PROPN
ejpam-4069	140	5	math	math	PROPN
ejpam-4069	140	6	,	,	PUNCT
ejpam-4069	140	7	14	14	NUM
ejpam-4069	140	8	(	(	PUNCT
ejpam-4069	140	9	4	4	NUM
ejpam-4069	140	10	)	)	PUNCT
ejpam-4069	140	11	(	(	PUNCT
ejpam-4069	140	12	2021	2021	NUM
ejpam-4069	140	13	)	)	PUNCT
ejpam-4069	140	14	,	,	PUNCT
ejpam-4069	140	15	1226	1226	NUM
ejpam-4069	140	16	-	-	SYM
ejpam-4069	140	17	1236	1236	NUM
ejpam-4069	140	18	1230	1230	NUM
ejpam-4069	140	19	corollary	corollary	NOUN
ejpam-4069	140	20	1	1	NUM
ejpam-4069	140	21	.	.	PUNCT
ejpam-4069	141	1	let	let	VERB
ejpam-4069	141	2	g	g	NOUN
ejpam-4069	141	3	and	and	CCONJ
ejpam-4069	141	4	h	h	NOUN
ejpam-4069	141	5	be	be	VERB
ejpam-4069	141	6	any	any	DET
ejpam-4069	141	7	two	two	NUM
ejpam-4069	141	8	graphs	graph	NOUN
ejpam-4069	141	9	where	where	SCONJ
ejpam-4069	141	10	|v	|v	PROPN
ejpam-4069	141	11	(	(	PUNCT
ejpam-4069	141	12	g)|	g)|	NOUN
ejpam-4069	141	13	=	=	PUNCT
ejpam-4069	141	14	n	n	NOUN
ejpam-4069	141	15	and	and	CCONJ
ejpam-4069	141	16	|v	|v	PROPN
ejpam-4069	141	17	(	(	PUNCT
ejpam-4069	141	18	h)|	h)|	NOUN
ejpam-4069	141	19	=	=	PUNCT
ejpam-4069	141	20	m.	m.	NOUN
ejpam-4069	141	21	then	then	ADV
ejpam-4069	141	22	γch	γch	AUX
ejpam-4069	141	23	,	,	PUNCT
ejpam-4069	141	24	coi(g+h	coi(g+h	NOUN
ejpam-4069	141	25	)	)	PUNCT
ejpam-4069	141	26	=	=	PUNCT
ejpam-4069	142	1	min{n+	min{n+	VERB
ejpam-4069	142	2	sci(h),m+	sci(h),m+	NOUN
ejpam-4069	142	3	sci(g	sci(g	PROPN
ejpam-4069	142	4	)	)	PUNCT
ejpam-4069	142	5	}	}	PUNCT
ejpam-4069	142	6	.	.	PUNCT
ejpam-4069	143	1	proof	proof	NOUN
ejpam-4069	143	2	:	:	PUNCT
ejpam-4069	143	3	let	let	VERB
ejpam-4069	143	4	s	s	PRON
ejpam-4069	143	5	be	be	AUX
ejpam-4069	143	6	a	a	DET
ejpam-4069	143	7	γch	γch	NOUN
ejpam-4069	143	8	,	,	PUNCT
ejpam-4069	143	9	coi	coi	NOUN
ejpam-4069	143	10	-	-	PUNCT
ejpam-4069	143	11	set	set	NOUN
ejpam-4069	143	12	of	of	ADP
ejpam-4069	143	13	g	g	PROPN
ejpam-4069	143	14	+	+	CCONJ
ejpam-4069	143	15	h.	h.	PROPN
ejpam-4069	144	1	then	then	ADV
ejpam-4069	144	2	s	s	VERB
ejpam-4069	144	3	is	be	AUX
ejpam-4069	144	4	a	a	DET
ejpam-4069	144	5	connected	connected	ADJ
ejpam-4069	144	6	co	co	NOUN
ejpam-4069	144	7	-	-	ADJ
ejpam-4069	144	8	independent	independent	ADJ
ejpam-4069	144	9	hop	hop	NOUN
ejpam-4069	144	10	dominating	dominating	NOUN
ejpam-4069	144	11	set	set	NOUN
ejpam-4069	144	12	of	of	ADP
ejpam-4069	144	13	g	g	PROPN
ejpam-4069	144	14	+	+	PROPN
ejpam-4069	144	15	h.	h.	PROPN
ejpam-4069	144	16	hence	hence	ADV
ejpam-4069	144	17	,	,	PUNCT
ejpam-4069	144	18	s	s	VERB
ejpam-4069	144	19	=	=	PUNCT
ejpam-4069	144	20	a	a	DET
ejpam-4069	144	21	∪	∪	X
ejpam-4069	144	22	b	b	PROPN
ejpam-4069	144	23	whre	whre	PROPN
ejpam-4069	144	24	a	a	DET
ejpam-4069	144	25	⊆	⊆	NUM
ejpam-4069	144	26	v	v	NOUN
ejpam-4069	144	27	(	(	PUNCT
ejpam-4069	144	28	g	g	NOUN
ejpam-4069	144	29	)	)	PUNCT
ejpam-4069	144	30	and	and	CCONJ
ejpam-4069	144	31	b	b	X
ejpam-4069	144	32	⊆	⊆	NUM
ejpam-4069	144	33	v	v	NOUN
ejpam-4069	144	34	(	(	PUNCT
ejpam-4069	144	35	h	h	NOUN
ejpam-4069	144	36	)	)	PUNCT
ejpam-4069	144	37	satisfying	satisfy	VERB
ejpam-4069	144	38	conditions	condition	NOUN
ejpam-4069	144	39	(	(	PUNCT
ejpam-4069	144	40	i	i	NOUN
ejpam-4069	144	41	)	)	PUNCT
ejpam-4069	144	42	or	or	CCONJ
ejpam-4069	144	43	(	(	PUNCT
ejpam-4069	144	44	ii	ii	NOUN
ejpam-4069	144	45	)	)	PUNCT
ejpam-4069	144	46	of	of	ADP
ejpam-4069	144	47	theorem	theorem	NOUN
ejpam-4069	144	48	3	3	NUM
ejpam-4069	144	49	.	.	PUNCT
ejpam-4069	144	50	thus	thus	ADV
ejpam-4069	144	51	,	,	PUNCT
ejpam-4069	144	52	γch	γch	NOUN
ejpam-4069	144	53	,	,	PUNCT
ejpam-4069	144	54	coi(g+h	coi(g+h	NOUN
ejpam-4069	144	55	)	)	PUNCT
ejpam-4069	144	56	=	=	SYM
ejpam-4069	144	57	|s|	|s|	NOUN
ejpam-4069	144	58	=	=	SYM
ejpam-4069	144	59	|a|+	|a|+	NOUN
ejpam-4069	144	60	|b|	|b|	PROPN
ejpam-4069	144	61	.	.	PUNCT
ejpam-4069	144	62	by	by	ADP
ejpam-4069	144	63	condition	condition	NOUN
ejpam-4069	144	64	(	(	PUNCT
ejpam-4069	144	65	i	i	NOUN
ejpam-4069	144	66	)	)	PUNCT
ejpam-4069	144	67	,	,	PUNCT
ejpam-4069	144	68	|s|	|s|	PROPN
ejpam-4069	144	69	=	=	SYM
ejpam-4069	144	70	|v	|v	PROPN
ejpam-4069	144	71	(	(	PUNCT
ejpam-4069	144	72	g)|+	g)|+	PROPN
ejpam-4069	144	73	|b|	|b|	PROPN
ejpam-4069	144	74	≥	≥	NUM
ejpam-4069	144	75	n+	n+	NUM
ejpam-4069	144	76	sci(h	sci(h	PROPN
ejpam-4069	144	77	)	)	PUNCT
ejpam-4069	144	78	.	.	PUNCT
ejpam-4069	145	1	by	by	ADP
ejpam-4069	145	2	condition	condition	NOUN
ejpam-4069	145	3	(	(	PUNCT
ejpam-4069	145	4	ii	ii	NOUN
ejpam-4069	145	5	)	)	PUNCT
ejpam-4069	145	6	,	,	PUNCT
ejpam-4069	145	7	|s|	|s|	PROPN
ejpam-4069	145	8	=	=	SYM
ejpam-4069	145	9	|v	|v	X
ejpam-4069	145	10	(	(	PUNCT
ejpam-4069	145	11	h)|+	h)|+	PROPN
ejpam-4069	145	12	|a|	|a|	NOUN
ejpam-4069	145	13	≥	≥	NUM
ejpam-4069	145	14	m+	m+	NUM
ejpam-4069	145	15	sci(g	sci(g	PROPN
ejpam-4069	145	16	)	)	PUNCT
ejpam-4069	145	17	.	.	PUNCT
ejpam-4069	146	1	hence	hence	ADV
ejpam-4069	146	2	,	,	PUNCT
ejpam-4069	146	3	γch	γch	NOUN
ejpam-4069	146	4	,	,	PUNCT
ejpam-4069	146	5	coi(g+h	coi(g+h	NOUN
ejpam-4069	146	6	)	)	PUNCT
ejpam-4069	146	7	=	=	SYM
ejpam-4069	146	8	|s|	|s|	NOUN
ejpam-4069	146	9	≥	≥	NOUN
ejpam-4069	146	10	min{n+	min{n+	PROPN
ejpam-4069	146	11	sci(h),m+	sci(h),m+	NOUN
ejpam-4069	146	12	sci(g	sci(g	PROPN
ejpam-4069	146	13	)	)	PUNCT
ejpam-4069	146	14	}	}	PUNCT
ejpam-4069	146	15	.	.	PUNCT
ejpam-4069	147	1	next	next	ADV
ejpam-4069	147	2	,	,	PUNCT
ejpam-4069	147	3	let	let	VERB
ejpam-4069	147	4	x	x	PRON
ejpam-4069	147	5	and	and	CCONJ
ejpam-4069	147	6	y	y	PROPN
ejpam-4069	147	7	be	be	AUX
ejpam-4069	147	8	the	the	DET
ejpam-4069	147	9	minimum	minimum	NOUN
ejpam-4069	147	10	strictly	strictly	ADV
ejpam-4069	147	11	co	co	ADJ
ejpam-4069	147	12	-	-	ADJ
ejpam-4069	147	13	independent	independent	ADJ
ejpam-4069	147	14	sets	set	NOUN
ejpam-4069	147	15	of	of	ADP
ejpam-4069	147	16	g	g	PROPN
ejpam-4069	147	17	and	and	CCONJ
ejpam-4069	147	18	h	h	NOUN
ejpam-4069	147	19	,	,	PUNCT
ejpam-4069	147	20	respectively	respectively	ADV
ejpam-4069	147	21	.	.	PUNCT
ejpam-4069	148	1	then	then	ADV
ejpam-4069	148	2	by	by	ADP
ejpam-4069	148	3	theorem	theorem	NOUN
ejpam-4069	148	4	3	3	NUM
ejpam-4069	148	5	,	,	PUNCT
ejpam-4069	148	6	s	s	PART
ejpam-4069	148	7	=	=	SYM
ejpam-4069	148	8	v	v	PROPN
ejpam-4069	148	9	(	(	PUNCT
ejpam-4069	148	10	g)∪y	g)∪y	PROPN
ejpam-4069	148	11	or	or	CCONJ
ejpam-4069	148	12	s	s	NOUN
ejpam-4069	148	13	=	=	SYM
ejpam-4069	148	14	v	v	PROPN
ejpam-4069	148	15	(	(	PUNCT
ejpam-4069	148	16	h)∪x	h)∪x	PROPN
ejpam-4069	148	17	is	be	AUX
ejpam-4069	148	18	a	a	DET
ejpam-4069	148	19	connected	connected	ADJ
ejpam-4069	148	20	co	co	NOUN
ejpam-4069	148	21	-	-	ADJ
ejpam-4069	148	22	independent	independent	ADJ
ejpam-4069	148	23	hop	hop	NOUN
ejpam-4069	148	24	dominating	dominating	NOUN
ejpam-4069	148	25	set	set	NOUN
ejpam-4069	148	26	of	of	ADP
ejpam-4069	148	27	g+h	g+h	PROPN
ejpam-4069	148	28	.	.	PUNCT
ejpam-4069	149	1	thus	thus	ADV
ejpam-4069	149	2	,	,	PUNCT
ejpam-4069	149	3	γch	γch	NOUN
ejpam-4069	149	4	,	,	PUNCT
ejpam-4069	149	5	coi(g+h	coi(g+h	NOUN
ejpam-4069	149	6	)	)	PUNCT
ejpam-4069	149	7	≤	≤	NUM
ejpam-4069	149	8	|s|	|s|	PROPN
ejpam-4069	149	9	=	=	SYM
ejpam-4069	149	10	|v	|v	X
ejpam-4069	149	11	(	(	PUNCT
ejpam-4069	149	12	g)|+	g)|+	NOUN
ejpam-4069	149	13	|y	|y	NOUN
ejpam-4069	149	14	|	|	ADV
ejpam-4069	149	15	=	=	SYM
ejpam-4069	149	16	n+	n+	NUM
ejpam-4069	149	17	sci(h	sci(h	PROPN
ejpam-4069	149	18	)	)	PUNCT
ejpam-4069	149	19	or	or	CCONJ
ejpam-4069	149	20	γch	γch	NOUN
ejpam-4069	149	21	,	,	PUNCT
ejpam-4069	149	22	coi(g+h	coi(g+h	NOUN
ejpam-4069	149	23	)	)	PUNCT
ejpam-4069	149	24	≤	≤	NUM
ejpam-4069	149	25	|s|	|s|	PROPN
ejpam-4069	149	26	=	=	SYM
ejpam-4069	149	27	|v	|v	X
ejpam-4069	149	28	(	(	PUNCT
ejpam-4069	149	29	h)|+	h)|+	NOUN
ejpam-4069	149	30	|x|	|x|	PROPN
ejpam-4069	149	31	=	=	SYM
ejpam-4069	149	32	m+	m+	NUM
ejpam-4069	149	33	sci(g	sci(g	PROPN
ejpam-4069	149	34	)	)	PUNCT
ejpam-4069	149	35	it	it	PRON
ejpam-4069	149	36	follows	follow	VERB
ejpam-4069	149	37	that	that	SCONJ
ejpam-4069	149	38	,	,	PUNCT
ejpam-4069	149	39	γch	γch	NOUN
ejpam-4069	149	40	,	,	PUNCT
ejpam-4069	149	41	coi(g+h	coi(g+h	NOUN
ejpam-4069	149	42	)	)	PUNCT
ejpam-4069	149	43	≤	≤	NUM
ejpam-4069	149	44	min{n+	min{n+	ADJ
ejpam-4069	149	45	sci(h),m+	sci(h),m+	NOUN
ejpam-4069	149	46	sci(g	sci(g	PROPN
ejpam-4069	149	47	)	)	PUNCT
ejpam-4069	149	48	}	}	PUNCT
ejpam-4069	149	49	.	.	PUNCT
ejpam-4069	150	1	therefore	therefore	ADV
ejpam-4069	150	2	,	,	PUNCT
ejpam-4069	150	3	γch	γch	NOUN
ejpam-4069	150	4	,	,	PUNCT
ejpam-4069	150	5	coi(g+h	coi(g+h	NOUN
ejpam-4069	150	6	)	)	PUNCT
ejpam-4069	150	7	=	=	PUNCT
ejpam-4069	150	8	min{n+	min{n+	VERB
ejpam-4069	150	9	sci(h),m+	sci(h),m+	NOUN
ejpam-4069	150	10	sci(g	sci(g	PROPN
ejpam-4069	150	11	)	)	PUNCT
ejpam-4069	150	12	}	}	PUNCT
ejpam-4069	150	13	.	.	PUNCT
ejpam-4069	151	1	4	4	X
ejpam-4069	151	2	.	.	X
ejpam-4069	151	3	on	on	ADP
ejpam-4069	151	4	connected	connected	ADJ
ejpam-4069	151	5	co	co	ADJ
ejpam-4069	151	6	-	-	ADJ
ejpam-4069	151	7	independent	independent	ADJ
ejpam-4069	151	8	hop	hop	NOUN
ejpam-4069	151	9	domination	domination	NOUN
ejpam-4069	151	10	in	in	ADP
ejpam-4069	151	11	the	the	DET
ejpam-4069	151	12	corona	corona	NOUN
ejpam-4069	151	13	of	of	ADP
ejpam-4069	151	14	graphs	graph	NOUN
ejpam-4069	151	15	the	the	DET
ejpam-4069	151	16	corona	corona	NOUN
ejpam-4069	151	17	of	of	ADP
ejpam-4069	151	18	two	two	NUM
ejpam-4069	151	19	graphs	graph	NOUN
ejpam-4069	151	20	g	g	NOUN
ejpam-4069	151	21	and	and	CCONJ
ejpam-4069	151	22	h	h	NOUN
ejpam-4069	151	23	,	,	PUNCT
ejpam-4069	151	24	denoted	denote	VERB
ejpam-4069	151	25	by	by	ADP
ejpam-4069	151	26	g	g	PROPN
ejpam-4069	151	27	◦	◦	NOUN
ejpam-4069	151	28	h	h	NOUN
ejpam-4069	151	29	,	,	PUNCT
ejpam-4069	151	30	is	be	AUX
ejpam-4069	151	31	the	the	DET
ejpam-4069	151	32	graph	graph	NOUN
ejpam-4069	151	33	obtained	obtain	VERB
ejpam-4069	151	34	by	by	ADP
ejpam-4069	151	35	taking	take	VERB
ejpam-4069	151	36	one	one	NUM
ejpam-4069	151	37	copy	copy	NOUN
ejpam-4069	151	38	of	of	ADP
ejpam-4069	151	39	g	g	NOUN
ejpam-4069	151	40	of	of	ADP
ejpam-4069	151	41	order	order	NOUN
ejpam-4069	151	42	n	n	NOUN
ejpam-4069	151	43	and	and	CCONJ
ejpam-4069	151	44	n	n	PRON
ejpam-4069	151	45	copies	copy	NOUN
ejpam-4069	151	46	of	of	ADP
ejpam-4069	151	47	h	h	NOUN
ejpam-4069	151	48	,	,	PUNCT
ejpam-4069	151	49	and	and	CCONJ
ejpam-4069	151	50	then	then	ADV
ejpam-4069	151	51	joining	join	VERB
ejpam-4069	151	52	every	every	DET
ejpam-4069	151	53	vertex	vertex	NOUN
ejpam-4069	151	54	of	of	ADP
ejpam-4069	151	55	the	the	DET
ejpam-4069	151	56	ith	ith	PROPN
ejpam-4069	151	57	copy	copy	NOUN
ejpam-4069	151	58	of	of	ADP
ejpam-4069	151	59	h	h	NOUN
ejpam-4069	151	60	to	to	ADP
ejpam-4069	151	61	the	the	DET
ejpam-4069	151	62	ith	ith	PROPN
ejpam-4069	151	63	vertex	vertex	NOUN
ejpam-4069	151	64	of	of	ADP
ejpam-4069	151	65	g.	g.	PROPN
ejpam-4069	151	66	for	for	ADP
ejpam-4069	151	67	v	v	NOUN
ejpam-4069	151	68	∈	∈	PROPN
ejpam-4069	151	69	v	v	NOUN
ejpam-4069	151	70	(	(	PUNCT
ejpam-4069	151	71	g	g	NOUN
ejpam-4069	151	72	)	)	PUNCT
ejpam-4069	151	73	,	,	PUNCT
ejpam-4069	151	74	denote	denote	VERB
ejpam-4069	151	75	by	by	ADP
ejpam-4069	151	76	hv	hv	PROPN
ejpam-4069	151	77	the	the	DET
ejpam-4069	151	78	copy	copy	NOUN
ejpam-4069	151	79	of	of	ADP
ejpam-4069	151	80	h	h	NOUN
ejpam-4069	151	81	whose	whose	DET
ejpam-4069	151	82	vertices	vertex	NOUN
ejpam-4069	151	83	are	be	AUX
ejpam-4069	151	84	attached	attach	VERB
ejpam-4069	151	85	one	one	NUM
ejpam-4069	151	86	by	by	ADP
ejpam-4069	151	87	one	one	NUM
ejpam-4069	151	88	to	to	ADP
ejpam-4069	151	89	the	the	DET
ejpam-4069	151	90	vertex	vertex	NOUN
ejpam-4069	151	91	v.	v.	ADP
ejpam-4069	151	92	subsequently	subsequently	ADV
ejpam-4069	151	93	,	,	PUNCT
ejpam-4069	151	94	denote	denote	VERB
ejpam-4069	151	95	by	by	ADP
ejpam-4069	151	96	v+hv	v+hv	NOUN
ejpam-4069	151	97	the	the	DET
ejpam-4069	151	98	subgraph	subgraph	NOUN
ejpam-4069	151	99	of	of	ADP
ejpam-4069	151	100	the	the	DET
ejpam-4069	151	101	corona	corona	NOUN
ejpam-4069	151	102	g	g	PROPN
ejpam-4069	151	103	◦	◦	NOUN
ejpam-4069	151	104	h	h	NOUN
ejpam-4069	151	105	corresponding	correspond	VERB
ejpam-4069	151	106	to	to	ADP
ejpam-4069	151	107	the	the	DET
ejpam-4069	151	108	join	join	NOUN
ejpam-4069	151	109	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4069	151	110	,	,	PUNCT
ejpam-4069	151	111	v	v	PROPN
ejpam-4069	151	112	∈	∈	PROPN
ejpam-4069	151	113	v	v	NOUN
ejpam-4069	151	114	(	(	PUNCT
ejpam-4069	151	115	g	g	NOUN
ejpam-4069	151	116	)	)	PUNCT
ejpam-4069	151	117	.	.	PUNCT
ejpam-4069	152	1	theorem	theorem	ADJ
ejpam-4069	152	2	4	4	NUM
ejpam-4069	152	3	.	.	PUNCT
ejpam-4069	153	1	let	let	VERB
ejpam-4069	153	2	g	g	PRON
ejpam-4069	153	3	be	be	AUX
ejpam-4069	153	4	a	a	DET
ejpam-4069	153	5	nontrivial	nontrivial	ADJ
ejpam-4069	153	6	connected	connect	VERB
ejpam-4069	153	7	graph	graph	NOUN
ejpam-4069	153	8	and	and	CCONJ
ejpam-4069	153	9	h	h	NOUN
ejpam-4069	153	10	be	be	AUX
ejpam-4069	153	11	any	any	DET
ejpam-4069	153	12	graph	graph	NOUN
ejpam-4069	153	13	.	.	PUNCT
ejpam-4069	154	1	a	a	DET
ejpam-4069	154	2	set	set	NOUN
ejpam-4069	154	3	s	s	NOUN
ejpam-4069	154	4	⊆	⊆	NUM
ejpam-4069	154	5	v	v	NOUN
ejpam-4069	154	6	(	(	PUNCT
ejpam-4069	154	7	g	g	PROPN
ejpam-4069	154	8	◦	◦	NOUN
ejpam-4069	154	9	h	h	NOUN
ejpam-4069	154	10	)	)	PUNCT
ejpam-4069	154	11	is	be	AUX
ejpam-4069	154	12	a	a	DET
ejpam-4069	154	13	connected	connected	ADJ
ejpam-4069	154	14	co	co	NOUN
ejpam-4069	154	15	-	-	ADJ
ejpam-4069	154	16	independent	independent	ADJ
ejpam-4069	154	17	hop	hop	NOUN
ejpam-4069	154	18	dominating	dominating	NOUN
ejpam-4069	154	19	set	set	NOUN
ejpam-4069	154	20	of	of	ADP
ejpam-4069	154	21	g	g	PROPN
ejpam-4069	154	22	◦	◦	NOUN
ejpam-4069	154	23	h	h	NOUN
ejpam-4069	154	24	if	if	SCONJ
ejpam-4069	155	1	and	and	CCONJ
ejpam-4069	155	2	only	only	ADV
ejpam-4069	155	3	if	if	SCONJ
ejpam-4069	155	4	s	s	VERB
ejpam-4069	155	5	=	=	SYM
ejpam-4069	155	6	v	v	X
ejpam-4069	155	7	(	(	PUNCT
ejpam-4069	155	8	g	g	NOUN
ejpam-4069	155	9	)	)	PUNCT
ejpam-4069	155	10	∪	∪	NOUN
ejpam-4069	155	11	(	(	PUNCT
ejpam-4069	155	12	⋃	⋃	ADJ
ejpam-4069	155	13	v∈v	v∈v	NOUN
ejpam-4069	155	14	(	(	PUNCT
ejpam-4069	155	15	g	g	NOUN
ejpam-4069	155	16	)	)	PUNCT
ejpam-4069	155	17	sv	sv	NOUN
ejpam-4069	155	18	)	)	PUNCT
ejpam-4069	155	19	,	,	PUNCT
ejpam-4069	155	20	where	where	SCONJ
ejpam-4069	155	21	sv	sv	PROPN
ejpam-4069	155	22	⊆	⊆	NUM
ejpam-4069	155	23	v	v	X
ejpam-4069	155	24	(	(	PUNCT
ejpam-4069	155	25	hv	hv	NOUN
ejpam-4069	155	26	)	)	PUNCT
ejpam-4069	155	27	and	and	CCONJ
ejpam-4069	155	28	v	v	NOUN
ejpam-4069	155	29	(	(	PUNCT
ejpam-4069	155	30	hv)\sv	hv)\sv	PROPN
ejpam-4069	155	31	is	be	AUX
ejpam-4069	155	32	an	an	DET
ejpam-4069	155	33	independent	independent	ADJ
ejpam-4069	155	34	subset	subset	NOUN
ejpam-4069	155	35	of	of	ADP
ejpam-4069	155	36	v	v	PROPN
ejpam-4069	155	37	(	(	PUNCT
ejpam-4069	155	38	hv	hv	PROPN
ejpam-4069	155	39	)	)	PUNCT
ejpam-4069	155	40	for	for	ADP
ejpam-4069	155	41	each	each	DET
ejpam-4069	155	42	v	v	NUM
ejpam-4069	155	43	∈	∈	PROPN
ejpam-4069	155	44	v	v	NOUN
ejpam-4069	155	45	(	(	PUNCT
ejpam-4069	155	46	g	g	NOUN
ejpam-4069	155	47	)	)	PUNCT
ejpam-4069	155	48	.	.	PUNCT
ejpam-4069	156	1	proof	proof	NOUN
ejpam-4069	156	2	:	:	PUNCT
ejpam-4069	156	3	suppose	suppose	VERB
ejpam-4069	156	4	s	s	NOUN
ejpam-4069	156	5	is	be	AUX
ejpam-4069	156	6	a	a	DET
ejpam-4069	156	7	connected	connected	ADJ
ejpam-4069	156	8	co	co	NOUN
ejpam-4069	156	9	-	-	ADJ
ejpam-4069	156	10	independent	independent	ADJ
ejpam-4069	156	11	hop	hop	NOUN
ejpam-4069	156	12	dominating	dominating	NOUN
ejpam-4069	156	13	set	set	NOUN
ejpam-4069	156	14	of	of	ADP
ejpam-4069	156	15	g	g	PROPN
ejpam-4069	156	16	◦	◦	NOUN
ejpam-4069	156	17	h	h	NOUN
ejpam-4069	156	18	and	and	CCONJ
ejpam-4069	156	19	let	let	VERB
ejpam-4069	156	20	sv	sv	INTJ
ejpam-4069	156	21	=	=	SYM
ejpam-4069	156	22	s∩v	s∩v	PROPN
ejpam-4069	156	23	(	(	PUNCT
ejpam-4069	156	24	hv	hv	PROPN
ejpam-4069	156	25	)	)	PUNCT
ejpam-4069	156	26	for	for	ADP
ejpam-4069	156	27	each	each	DET
ejpam-4069	156	28	v	v	NUM
ejpam-4069	156	29	∈	∈	PROPN
ejpam-4069	156	30	v	v	NOUN
ejpam-4069	156	31	(	(	PUNCT
ejpam-4069	156	32	g	g	NOUN
ejpam-4069	156	33	)	)	PUNCT
ejpam-4069	156	34	.	.	PUNCT
ejpam-4069	157	1	then	then	ADV
ejpam-4069	157	2	sv	sv	VERB
ejpam-4069	157	3	⊆	⊆	NUM
ejpam-4069	157	4	v	v	X
ejpam-4069	157	5	(	(	PUNCT
ejpam-4069	157	6	hv	hv	PROPN
ejpam-4069	157	7	)	)	PUNCT
ejpam-4069	157	8	.	.	PUNCT
ejpam-4069	158	1	since	since	SCONJ
ejpam-4069	158	2	⟨s⟩	⟨s⟩	PROPN
ejpam-4069	158	3	is	be	AUX
ejpam-4069	158	4	connected	connect	VERB
ejpam-4069	158	5	,	,	PUNCT
ejpam-4069	158	6	s	s	NOUN
ejpam-4069	158	7	=	=	SYM
ejpam-4069	158	8	v	v	NOUN
ejpam-4069	158	9	(	(	PUNCT
ejpam-4069	158	10	g)∪	g)∪	VERB
ejpam-4069	158	11	(	(	PUNCT
ejpam-4069	158	12	⋃	⋃	ADJ
ejpam-4069	158	13	v∈v	v∈v	NOUN
ejpam-4069	158	14	(	(	PUNCT
ejpam-4069	158	15	g	g	NOUN
ejpam-4069	158	16	)	)	PUNCT
ejpam-4069	158	17	sv	sv	NOUN
ejpam-4069	158	18	)	)	PUNCT
ejpam-4069	158	19	.	.	PUNCT
ejpam-4069	159	1	since	since	SCONJ
ejpam-4069	159	2	v	v	NOUN
ejpam-4069	159	3	(	(	PUNCT
ejpam-4069	159	4	g	g	NOUN
ejpam-4069	159	5	◦	◦	NOUN
ejpam-4069	159	6	h)\s	h)\s	PROPN
ejpam-4069	159	7	is	be	AUX
ejpam-4069	159	8	independent	independent	ADJ
ejpam-4069	159	9	and	and	CCONJ
ejpam-4069	159	10	v	v	ADJ
ejpam-4069	159	11	(	(	PUNCT
ejpam-4069	159	12	g	g	NOUN
ejpam-4069	159	13	◦	◦	NOUN
ejpam-4069	159	14	h)\s	h)\s	NOUN
ejpam-4069	159	15	=	=	PUNCT
ejpam-4069	160	1	⋃	⋃	NOUN
ejpam-4069	160	2	v∈v	v∈v	NOUN
ejpam-4069	160	3	(	(	PUNCT
ejpam-4069	160	4	g	g	NOUN
ejpam-4069	160	5	)	)	PUNCT
ejpam-4069	160	6	(	(	PUNCT
ejpam-4069	160	7	v	v	X
ejpam-4069	160	8	(	(	PUNCT
ejpam-4069	160	9	hv)\sv	hv)\sv	PROPN
ejpam-4069	160	10	)	)	PUNCT
ejpam-4069	160	11	,	,	PUNCT
ejpam-4069	160	12	s.	s.	PROPN
ejpam-4069	160	13	nanding	nanding	PROPN
ejpam-4069	160	14	,	,	PUNCT
ejpam-4069	160	15	h.	h.	PROPN
ejpam-4069	160	16	rara	rara	PROPN
ejpam-4069	160	17	/	/	SYM
ejpam-4069	160	18	eur	eur	PROPN
ejpam-4069	160	19	.	.	PUNCT
ejpam-4069	161	1	j.	j.	PROPN
ejpam-4069	161	2	pure	pure	PROPN
ejpam-4069	161	3	appl	appl	PROPN
ejpam-4069	161	4	.	.	PROPN
ejpam-4069	161	5	math	math	PROPN
ejpam-4069	161	6	,	,	PUNCT
ejpam-4069	161	7	14	14	NUM
ejpam-4069	161	8	(	(	PUNCT
ejpam-4069	161	9	4	4	NUM
ejpam-4069	161	10	)	)	PUNCT
ejpam-4069	161	11	(	(	PUNCT
ejpam-4069	161	12	2021	2021	NUM
ejpam-4069	161	13	)	)	PUNCT
ejpam-4069	161	14	,	,	PUNCT
ejpam-4069	161	15	1226	1226	NUM
ejpam-4069	161	16	-	-	SYM
ejpam-4069	161	17	1236	1236	NUM
ejpam-4069	161	18	1231	1231	NUM
ejpam-4069	161	19	v	v	NOUN
ejpam-4069	161	20	(	(	PUNCT
ejpam-4069	161	21	hv)\sv	hv)\sv	PROPN
ejpam-4069	161	22	is	be	AUX
ejpam-4069	161	23	an	an	DET
ejpam-4069	161	24	independent	independent	ADJ
ejpam-4069	161	25	subset	subset	NOUN
ejpam-4069	161	26	of	of	ADP
ejpam-4069	161	27	v	v	PROPN
ejpam-4069	161	28	(	(	PUNCT
ejpam-4069	161	29	hv	hv	PROPN
ejpam-4069	161	30	)	)	PUNCT
ejpam-4069	161	31	,	,	PUNCT
ejpam-4069	161	32	for	for	ADP
ejpam-4069	161	33	each	each	DET
ejpam-4069	161	34	v	v	NUM
ejpam-4069	161	35	∈	∈	PROPN
ejpam-4069	161	36	v	v	NOUN
ejpam-4069	161	37	(	(	PUNCT
ejpam-4069	161	38	g	g	NOUN
ejpam-4069	161	39	)	)	PUNCT
ejpam-4069	161	40	.	.	PUNCT
ejpam-4069	162	1	for	for	ADP
ejpam-4069	162	2	the	the	DET
ejpam-4069	162	3	converse	converse	NOUN
ejpam-4069	162	4	,	,	PUNCT
ejpam-4069	162	5	suppose	suppose	VERB
ejpam-4069	162	6	that	that	SCONJ
ejpam-4069	162	7	s	s	VERB
ejpam-4069	162	8	=	=	SYM
ejpam-4069	162	9	v	v	X
ejpam-4069	162	10	(	(	PUNCT
ejpam-4069	162	11	g	g	NOUN
ejpam-4069	162	12	)	)	PUNCT
ejpam-4069	162	13	∪	∪	NOUN
ejpam-4069	162	14	(	(	PUNCT
ejpam-4069	162	15	⋃	⋃	ADJ
ejpam-4069	162	16	v∈v	v∈v	NOUN
ejpam-4069	162	17	(	(	PUNCT
ejpam-4069	162	18	g	g	NOUN
ejpam-4069	162	19	)	)	PUNCT
ejpam-4069	162	20	sv	sv	NOUN
ejpam-4069	162	21	)	)	PUNCT
ejpam-4069	162	22	where	where	SCONJ
ejpam-4069	162	23	sv	sv	PROPN
ejpam-4069	162	24	⊆	⊆	NUM
ejpam-4069	162	25	v	v	X
ejpam-4069	162	26	(	(	PUNCT
ejpam-4069	162	27	hv	hv	NOUN
ejpam-4069	162	28	)	)	PUNCT
ejpam-4069	162	29	and	and	CCONJ
ejpam-4069	162	30	v	v	NOUN
ejpam-4069	162	31	(	(	PUNCT
ejpam-4069	162	32	hv)\sv	hv)\sv	PROPN
ejpam-4069	162	33	is	be	AUX
ejpam-4069	162	34	an	an	DET
ejpam-4069	162	35	independent	independent	ADJ
ejpam-4069	162	36	set	set	NOUN
ejpam-4069	162	37	.	.	PUNCT
ejpam-4069	163	1	clearly	clearly	ADV
ejpam-4069	163	2	,	,	PUNCT
ejpam-4069	163	3	⟨s⟩	⟨s⟩	PROPN
ejpam-4069	163	4	is	be	AUX
ejpam-4069	163	5	connected	connect	VERB
ejpam-4069	163	6	.	.	PUNCT
ejpam-4069	164	1	let	let	VERB
ejpam-4069	164	2	w	w	NOUN
ejpam-4069	164	3	∈	∈	PROPN
ejpam-4069	164	4	v	v	NOUN
ejpam-4069	164	5	(	(	PUNCT
ejpam-4069	164	6	g	g	PROPN
ejpam-4069	164	7	◦	◦	NOUN
ejpam-4069	164	8	h)\s	h)\s	NOUN
ejpam-4069	164	9	.	.	PUNCT
ejpam-4069	165	1	then	then	ADV
ejpam-4069	165	2	w	w	PROPN
ejpam-4069	165	3	∈	∈	PROPN
ejpam-4069	165	4	v	v	X
ejpam-4069	165	5	(	(	PUNCT
ejpam-4069	165	6	hv)\sv	hv)\sv	PROPN
ejpam-4069	165	7	for	for	ADP
ejpam-4069	165	8	some	some	DET
ejpam-4069	165	9	v	v	ADP
ejpam-4069	165	10	∈	∈	PROPN
ejpam-4069	165	11	v	v	NOUN
ejpam-4069	165	12	(	(	PUNCT
ejpam-4069	165	13	g	g	NOUN
ejpam-4069	165	14	)	)	PUNCT
ejpam-4069	165	15	.	.	PUNCT
ejpam-4069	166	1	since	since	SCONJ
ejpam-4069	166	2	g	g	PROPN
ejpam-4069	166	3	is	be	AUX
ejpam-4069	166	4	nontrivial	nontrivial	ADJ
ejpam-4069	166	5	connected	connect	VERB
ejpam-4069	166	6	graph	graph	NOUN
ejpam-4069	166	7	,	,	PUNCT
ejpam-4069	166	8	there	there	PRON
ejpam-4069	166	9	exists	exist	VERB
ejpam-4069	166	10	x	x	X
ejpam-4069	166	11	∈	∈	PROPN
ejpam-4069	166	12	v	v	X
ejpam-4069	166	13	(	(	PUNCT
ejpam-4069	166	14	g	g	NOUN
ejpam-4069	166	15	)	)	PUNCT
ejpam-4069	166	16	such	such	ADJ
ejpam-4069	166	17	that	that	SCONJ
ejpam-4069	166	18	vx	vx	PROPN
ejpam-4069	166	19	∈	∈	PROPN
ejpam-4069	166	20	e(g	e(g	PROPN
ejpam-4069	166	21	)	)	PUNCT
ejpam-4069	166	22	.	.	PUNCT
ejpam-4069	167	1	thus	thus	ADV
ejpam-4069	167	2	,	,	PUNCT
ejpam-4069	167	3	dg	dg	X
ejpam-4069	167	4	◦	◦	NOUN
ejpam-4069	167	5	h(w	h(w	PROPN
ejpam-4069	167	6	,	,	PUNCT
ejpam-4069	167	7	x	x	X
ejpam-4069	167	8	)	)	PUNCT
ejpam-4069	167	9	=	=	SYM
ejpam-4069	167	10	2	2	X
ejpam-4069	167	11	.	.	PUNCT
ejpam-4069	168	1	this	this	PRON
ejpam-4069	168	2	implies	imply	VERB
ejpam-4069	168	3	that	that	SCONJ
ejpam-4069	168	4	s	s	VERB
ejpam-4069	168	5	is	be	AUX
ejpam-4069	168	6	a	a	DET
ejpam-4069	168	7	hop	hop	NOUN
ejpam-4069	168	8	dominating	dominating	NOUN
ejpam-4069	168	9	set	set	NOUN
ejpam-4069	168	10	of	of	ADP
ejpam-4069	168	11	g	g	PROPN
ejpam-4069	168	12	◦	◦	NOUN
ejpam-4069	168	13	h.	h.	PROPN
ejpam-4069	168	14	since	since	SCONJ
ejpam-4069	168	15	v	v	PROPN
ejpam-4069	168	16	(	(	PUNCT
ejpam-4069	168	17	g	g	NOUN
ejpam-4069	168	18	◦	◦	NOUN
ejpam-4069	168	19	h)\s	h)\s	NOUN
ejpam-4069	168	20	=	=	PUNCT
ejpam-4069	168	21	⋃	⋃	NOUN
ejpam-4069	168	22	v∈v	v∈v	NOUN
ejpam-4069	168	23	(	(	PUNCT
ejpam-4069	168	24	g	g	NOUN
ejpam-4069	168	25	)	)	PUNCT
ejpam-4069	168	26	(	(	PUNCT
ejpam-4069	168	27	v	v	X
ejpam-4069	168	28	(	(	PUNCT
ejpam-4069	168	29	hv)\sv	hv)\sv	PROPN
ejpam-4069	168	30	)	)	PUNCT
ejpam-4069	168	31	and	and	CCONJ
ejpam-4069	168	32	v	v	NOUN
ejpam-4069	168	33	(	(	PUNCT
ejpam-4069	168	34	hv)\sv	hv)\sv	PROPN
ejpam-4069	168	35	is	be	AUX
ejpam-4069	168	36	an	an	DET
ejpam-4069	168	37	independent	independent	ADJ
ejpam-4069	168	38	set	set	NOUN
ejpam-4069	168	39	for	for	ADP
ejpam-4069	168	40	each	each	DET
ejpam-4069	168	41	v	v	NUM
ejpam-4069	168	42	∈	∈	PROPN
ejpam-4069	168	43	v	v	NOUN
ejpam-4069	168	44	(	(	PUNCT
ejpam-4069	168	45	g	g	NOUN
ejpam-4069	168	46	)	)	PUNCT
ejpam-4069	168	47	,	,	PUNCT
ejpam-4069	168	48	v	v	X
ejpam-4069	168	49	(	(	PUNCT
ejpam-4069	168	50	g	g	NOUN
ejpam-4069	168	51	◦	◦	NOUN
ejpam-4069	168	52	h)\s	h)\s	NOUN
ejpam-4069	168	53	is	be	AUX
ejpam-4069	168	54	independent	independent	ADJ
ejpam-4069	168	55	.	.	PUNCT
ejpam-4069	169	1	therefore	therefore	ADV
ejpam-4069	169	2	,	,	PUNCT
ejpam-4069	169	3	s	s	VERB
ejpam-4069	169	4	is	be	AUX
ejpam-4069	169	5	a	a	DET
ejpam-4069	169	6	connected	connected	ADJ
ejpam-4069	169	7	co	co	NOUN
ejpam-4069	169	8	-	-	ADJ
ejpam-4069	169	9	independent	independent	ADJ
ejpam-4069	169	10	hop	hop	NOUN
ejpam-4069	169	11	dominating	dominating	NOUN
ejpam-4069	169	12	set	set	NOUN
ejpam-4069	169	13	of	of	ADP
ejpam-4069	169	14	g	g	PROPN
ejpam-4069	169	15	◦	◦	NOUN
ejpam-4069	169	16	h.	h.	NOUN
ejpam-4069	169	17	corollary	corollary	ADJ
ejpam-4069	169	18	2	2	PROPN
ejpam-4069	169	19	.	.	PUNCT
ejpam-4069	170	1	let	let	VERB
ejpam-4069	170	2	g	g	PRON
ejpam-4069	170	3	be	be	AUX
ejpam-4069	170	4	a	a	DET
ejpam-4069	170	5	nontrivial	nontrivial	ADJ
ejpam-4069	170	6	connected	connect	VERB
ejpam-4069	170	7	graph	graph	NOUN
ejpam-4069	170	8	of	of	ADP
ejpam-4069	170	9	order	order	NOUN
ejpam-4069	170	10	n	n	NOUN
ejpam-4069	171	1	and	and	CCONJ
ejpam-4069	171	2	h	h	NOUN
ejpam-4069	171	3	be	be	AUX
ejpam-4069	171	4	any	any	DET
ejpam-4069	171	5	graph	graph	NOUN
ejpam-4069	171	6	of	of	ADP
ejpam-4069	171	7	order	order	NOUN
ejpam-4069	171	8	m.	m.	NOUN
ejpam-4069	171	9	then	then	ADV
ejpam-4069	171	10	γch	γch	VERB
ejpam-4069	171	11	,	,	PUNCT
ejpam-4069	171	12	coi(g	coi(g	PROPN
ejpam-4069	171	13	◦	◦	NOUN
ejpam-4069	171	14	h	h	NOUN
ejpam-4069	171	15	)	)	PUNCT
ejpam-4069	171	16	=	=	PUNCT
ejpam-4069	172	1	n(1	n(1	PROPN
ejpam-4069	172	2	+	+	ADJ
ejpam-4069	172	3	m−	m−	PROPN
ejpam-4069	172	4	β(h	β(h	NOUN
ejpam-4069	172	5	)	)	PUNCT
ejpam-4069	172	6	)	)	PUNCT
ejpam-4069	172	7	.	.	PUNCT
ejpam-4069	173	1	proof	proof	NOUN
ejpam-4069	173	2	:	:	PUNCT
ejpam-4069	173	3	let	let	VERB
ejpam-4069	173	4	c	c	PART
ejpam-4069	173	5	be	be	AUX
ejpam-4069	173	6	a	a	DET
ejpam-4069	173	7	γch	γch	NOUN
ejpam-4069	173	8	,	,	PUNCT
ejpam-4069	173	9	coi	coi	NOUN
ejpam-4069	173	10	-	-	PUNCT
ejpam-4069	173	11	set	set	NOUN
ejpam-4069	173	12	of	of	ADP
ejpam-4069	173	13	g	g	PROPN
ejpam-4069	173	14	◦	◦	PROPN
ejpam-4069	173	15	h.	h.	PROPN
ejpam-4069	174	1	then	then	ADV
ejpam-4069	174	2	c	c	PROPN
ejpam-4069	174	3	is	be	AUX
ejpam-4069	174	4	a	a	DET
ejpam-4069	174	5	connected	connected	ADJ
ejpam-4069	174	6	co	co	NOUN
ejpam-4069	174	7	-	-	ADJ
ejpam-4069	174	8	independent	independent	ADJ
ejpam-4069	174	9	hop	hop	NOUN
ejpam-4069	174	10	dominating	dominating	NOUN
ejpam-4069	174	11	set	set	NOUN
ejpam-4069	174	12	of	of	ADP
ejpam-4069	174	13	g	g	PROPN
ejpam-4069	174	14	◦	◦	NOUN
ejpam-4069	174	15	h.	h.	NOUN
ejpam-4069	174	16	by	by	ADP
ejpam-4069	174	17	theorem	theorem	NOUN
ejpam-4069	174	18	4	4	NUM
ejpam-4069	174	19	,	,	PUNCT
ejpam-4069	174	20	c	c	NOUN
ejpam-4069	174	21	=	=	SYM
ejpam-4069	174	22	v	v	PROPN
ejpam-4069	174	23	(	(	PUNCT
ejpam-4069	174	24	g	g	NOUN
ejpam-4069	174	25	)	)	PUNCT
ejpam-4069	174	26	⋃	⋃	NOUN
ejpam-4069	174	27	(	(	PUNCT
ejpam-4069	174	28	⋃	⋃	ADJ
ejpam-4069	174	29	v∈v	v∈v	NOUN
ejpam-4069	174	30	(	(	PUNCT
ejpam-4069	174	31	g	g	NOUN
ejpam-4069	174	32	)	)	PUNCT
ejpam-4069	174	33	sv	sv	NOUN
ejpam-4069	174	34	)	)	PUNCT
ejpam-4069	174	35	where	where	SCONJ
ejpam-4069	174	36	v	v	X
ejpam-4069	174	37	(	(	PUNCT
ejpam-4069	174	38	hv)\sv	hv)\sv	PROPN
ejpam-4069	174	39	is	be	AUX
ejpam-4069	174	40	an	an	DET
ejpam-4069	174	41	independent	independent	ADJ
ejpam-4069	174	42	set	set	NOUN
ejpam-4069	174	43	of	of	ADP
ejpam-4069	174	44	hv	hv	NOUN
ejpam-4069	174	45	for	for	ADP
ejpam-4069	174	46	every	every	DET
ejpam-4069	174	47	v	v	NUM
ejpam-4069	174	48	∈	∈	PROPN
ejpam-4069	174	49	v	v	NOUN
ejpam-4069	174	50	(	(	PUNCT
ejpam-4069	174	51	g	g	NOUN
ejpam-4069	174	52	)	)	PUNCT
ejpam-4069	174	53	.	.	PUNCT
ejpam-4069	175	1	then	then	ADV
ejpam-4069	175	2	γch	γch	VERB
ejpam-4069	175	3	,	,	PUNCT
ejpam-4069	175	4	coi(g	coi(g	PROPN
ejpam-4069	175	5	◦	◦	NOUN
ejpam-4069	175	6	h	h	NOUN
ejpam-4069	175	7	)	)	PUNCT
ejpam-4069	175	8	=	=	SYM
ejpam-4069	175	9	|c|	|c|	PROPN
ejpam-4069	175	10	=	=	SYM
ejpam-4069	175	11	|v	|v	PROPN
ejpam-4069	175	12	(	(	PUNCT
ejpam-4069	175	13	g)|+	g)|+	NOUN
ejpam-4069	175	14	|	|	ADV
ejpam-4069	175	15	⋃	⋃	PUNCT
ejpam-4069	175	16	v∈v	v∈v	NOUN
ejpam-4069	175	17	(	(	PUNCT
ejpam-4069	175	18	g	g	NOUN
ejpam-4069	175	19	)	)	PUNCT
ejpam-4069	175	20	sv|	sv|	NOUN
ejpam-4069	175	21	=	=	SYM
ejpam-4069	175	22	|v	|v	PROPN
ejpam-4069	175	23	(	(	PUNCT
ejpam-4069	175	24	g)|+	g)|+	PROPN
ejpam-4069	175	25	∑	∑	PUNCT
ejpam-4069	175	26	v∈v	v∈v	PROPN
ejpam-4069	175	27	(	(	PUNCT
ejpam-4069	175	28	g	g	NOUN
ejpam-4069	175	29	)	)	PUNCT
ejpam-4069	175	30	|sv|	|sv|	PROPN
ejpam-4069	176	1	=	=	SYM
ejpam-4069	176	2	|v	|v	PROPN
ejpam-4069	176	3	(	(	PUNCT
ejpam-4069	176	4	g)|+	g)|+	PROPN
ejpam-4069	176	5	∑	∑	PUNCT
ejpam-4069	176	6	v∈v	v∈v	PROPN
ejpam-4069	176	7	(	(	PUNCT
ejpam-4069	176	8	g	g	NOUN
ejpam-4069	176	9	)	)	PUNCT
ejpam-4069	176	10	(	(	PUNCT
ejpam-4069	176	11	|v	|v	X
ejpam-4069	176	12	(	(	PUNCT
ejpam-4069	176	13	hv)|	hv)|	PROPN
ejpam-4069	176	14	−	−	PROPN
ejpam-4069	176	15	|v	|v	PROPN
ejpam-4069	176	16	(	(	PUNCT
ejpam-4069	176	17	hv)\sv|	hv)\sv|	PROPN
ejpam-4069	176	18	)	)	PUNCT
ejpam-4069	176	19	≥	≥	NOUN
ejpam-4069	176	20	|v	|v	X
ejpam-4069	176	21	(	(	PUNCT
ejpam-4069	176	22	g)|+	g)|+	PROPN
ejpam-4069	176	23	|v	|v	PROPN
ejpam-4069	176	24	(	(	PUNCT
ejpam-4069	176	25	g)|(|v	g)|(|v	X
ejpam-4069	176	26	(	(	PUNCT
ejpam-4069	176	27	hv)|	hv)|	NOUN
ejpam-4069	176	28	−	−	NOUN
ejpam-4069	176	29	β(h	β(h	NUM
ejpam-4069	176	30	)	)	PUNCT
ejpam-4069	176	31	)	)	PUNCT
ejpam-4069	177	1	=	=	PRON
ejpam-4069	177	2	n+	n+	NUM
ejpam-4069	177	3	n(m−	n(m−	PROPN
ejpam-4069	177	4	β(h	β(h	NOUN
ejpam-4069	177	5	)	)	PUNCT
ejpam-4069	177	6	)	)	PUNCT
ejpam-4069	178	1	=	=	PUNCT
ejpam-4069	178	2	n(1	n(1	PROPN
ejpam-4069	179	1	+	+	ADJ
ejpam-4069	179	2	m−	m−	PROPN
ejpam-4069	179	3	β(h	β(h	NOUN
ejpam-4069	179	4	)	)	PUNCT
ejpam-4069	179	5	)	)	PUNCT
ejpam-4069	179	6	.	.	PUNCT
ejpam-4069	180	1	therefore	therefore	ADV
ejpam-4069	180	2	,	,	PUNCT
ejpam-4069	180	3	γch	γch	NOUN
ejpam-4069	180	4	,	,	PUNCT
ejpam-4069	180	5	coi(g	coi(g	PROPN
ejpam-4069	180	6	◦	◦	NOUN
ejpam-4069	180	7	h	h	NOUN
ejpam-4069	180	8	)	)	PUNCT
ejpam-4069	180	9	≥	≥	NOUN
ejpam-4069	180	10	n(1	n(1	NOUN
ejpam-4069	180	11	+	+	NOUN
ejpam-4069	180	12	m−	m−	PROPN
ejpam-4069	180	13	β(h	β(h	NOUN
ejpam-4069	180	14	)	)	PUNCT
ejpam-4069	180	15	)	)	PUNCT
ejpam-4069	180	16	.	.	PUNCT
ejpam-4069	181	1	let	let	VERB
ejpam-4069	181	2	d	d	PRON
ejpam-4069	181	3	be	be	AUX
ejpam-4069	181	4	a	a	DET
ejpam-4069	181	5	maximum	maximum	ADJ
ejpam-4069	181	6	independent	independent	ADJ
ejpam-4069	181	7	set	set	NOUN
ejpam-4069	181	8	of	of	ADP
ejpam-4069	181	9	h.	h.	PROPN
ejpam-4069	181	10	for	for	ADP
ejpam-4069	181	11	each	each	DET
ejpam-4069	181	12	v	v	NOUN
ejpam-4069	181	13	,	,	PUNCT
ejpam-4069	181	14	let	let	VERB
ejpam-4069	181	15	dv	dv	PROPN
ejpam-4069	181	16	⊆	⊆	NUM
ejpam-4069	181	17	v	v	PROPN
ejpam-4069	181	18	(	(	PUNCT
ejpam-4069	181	19	hv	hv	NOUN
ejpam-4069	181	20	)	)	PUNCT
ejpam-4069	181	21	such	such	ADJ
ejpam-4069	181	22	that	that	SCONJ
ejpam-4069	181	23	⟨dv⟩	⟨dv⟩	NOUN
ejpam-4069	181	24	∼=	∼=	PROPN
ejpam-4069	181	25	⟨d⟩.	⟨d⟩.	PROPN
ejpam-4069	181	26	let	let	VERB
ejpam-4069	181	27	sv	sv	VERB
ejpam-4069	181	28	=	=	SYM
ejpam-4069	181	29	v	v	PROPN
ejpam-4069	181	30	(	(	PUNCT
ejpam-4069	181	31	hv)\dv	hv)\dv	NOUN
ejpam-4069	181	32	.	.	PUNCT
ejpam-4069	182	1	then	then	ADV
ejpam-4069	182	2	c	c	X
ejpam-4069	182	3	=	=	SYM
ejpam-4069	182	4	v	v	PROPN
ejpam-4069	182	5	(	(	PUNCT
ejpam-4069	182	6	g	g	NOUN
ejpam-4069	182	7	)	)	PUNCT
ejpam-4069	182	8	⋃	⋃	NOUN
ejpam-4069	182	9	(	(	PUNCT
ejpam-4069	182	10	⋃	⋃	ADJ
ejpam-4069	182	11	v∈v	v∈v	NOUN
ejpam-4069	182	12	(	(	PUNCT
ejpam-4069	182	13	g	g	NOUN
ejpam-4069	182	14	)	)	PUNCT
ejpam-4069	182	15	sv	sv	NOUN
ejpam-4069	182	16	)	)	PUNCT
ejpam-4069	182	17	is	be	AUX
ejpam-4069	182	18	a	a	DET
ejpam-4069	182	19	connected	connected	ADJ
ejpam-4069	182	20	coindependent	coindependent	NOUN
ejpam-4069	182	21	hop	hop	NOUN
ejpam-4069	182	22	dominating	dominating	NOUN
ejpam-4069	182	23	set	set	NOUN
ejpam-4069	182	24	of	of	ADP
ejpam-4069	182	25	g	g	PROPN
ejpam-4069	182	26	◦	◦	NOUN
ejpam-4069	182	27	h	h	NOUN
ejpam-4069	182	28	by	by	ADP
ejpam-4069	182	29	theorem	theorem	NOUN
ejpam-4069	182	30	4	4	NUM
ejpam-4069	182	31	.	.	PUNCT
ejpam-4069	183	1	thus	thus	ADV
ejpam-4069	183	2	,	,	PUNCT
ejpam-4069	183	3	γch	γch	NOUN
ejpam-4069	183	4	,	,	PUNCT
ejpam-4069	183	5	coi(g	coi(g	PROPN
ejpam-4069	183	6	◦	◦	NOUN
ejpam-4069	183	7	h	h	NOUN
ejpam-4069	183	8	)	)	PUNCT
ejpam-4069	183	9	≤	≤	NOUN
ejpam-4069	183	10	|c|	|c|	PROPN
ejpam-4069	183	11	=	=	SYM
ejpam-4069	183	12	|v	|v	PROPN
ejpam-4069	183	13	(	(	PUNCT
ejpam-4069	183	14	g	g	NOUN
ejpam-4069	183	15	)	)	PUNCT
ejpam-4069	183	16	∪	∪	NOUN
ejpam-4069	183	17	(	(	PUNCT
ejpam-4069	183	18	⋃	⋃	ADJ
ejpam-4069	183	19	v∈v	v∈v	NOUN
ejpam-4069	183	20	(	(	PUNCT
ejpam-4069	183	21	g	g	NOUN
ejpam-4069	183	22	)	)	PUNCT
ejpam-4069	183	23	sv)|	sv)|	PROPN
ejpam-4069	184	1	=	=	PUNCT
ejpam-4069	184	2	|v	|v	X
ejpam-4069	184	3	(	(	PUNCT
ejpam-4069	184	4	g)|+	g)|+	PROPN
ejpam-4069	184	5	∑	∑	PUNCT
ejpam-4069	184	6	v∈v	v∈v	PROPN
ejpam-4069	184	7	(	(	PUNCT
ejpam-4069	184	8	g	g	NOUN
ejpam-4069	184	9	)	)	PUNCT
ejpam-4069	184	10	|sv|	|sv|	PROPN
ejpam-4069	185	1	=	=	SYM
ejpam-4069	185	2	|v	|v	PROPN
ejpam-4069	185	3	(	(	PUNCT
ejpam-4069	185	4	g)|+	g)|+	PROPN
ejpam-4069	185	5	|v	|v	PROPN
ejpam-4069	185	6	(	(	PUNCT
ejpam-4069	185	7	g)|(|v	g)|(|v	X
ejpam-4069	185	8	(	(	PUNCT
ejpam-4069	185	9	hv)|	hv)|	PROPN
ejpam-4069	185	10	−	−	NOUN
ejpam-4069	185	11	|dv|	|dv|	PROPN
ejpam-4069	185	12	)	)	PUNCT
ejpam-4069	185	13	=	=	SYM
ejpam-4069	185	14	|v	|v	PROPN
ejpam-4069	185	15	(	(	PUNCT
ejpam-4069	185	16	g)|+	g)|+	PROPN
ejpam-4069	185	17	|v	|v	PROPN
ejpam-4069	185	18	(	(	PUNCT
ejpam-4069	185	19	g)|(|v	g)|(|v	X
ejpam-4069	185	20	(	(	PUNCT
ejpam-4069	185	21	hv)|	hv)|	NOUN
ejpam-4069	185	22	−	−	NOUN
ejpam-4069	185	23	β(h	β(h	NUM
ejpam-4069	185	24	)	)	PUNCT
ejpam-4069	185	25	)	)	PUNCT
ejpam-4069	186	1	=	=	PRON
ejpam-4069	186	2	n+	n+	NUM
ejpam-4069	186	3	n(m−	n(m−	PROPN
ejpam-4069	186	4	β(h	β(h	NOUN
ejpam-4069	186	5	)	)	PUNCT
ejpam-4069	186	6	)	)	PUNCT
ejpam-4069	187	1	=	=	PUNCT
ejpam-4069	187	2	n(1	n(1	PROPN
ejpam-4069	188	1	+	+	ADJ
ejpam-4069	188	2	m−	m−	PROPN
ejpam-4069	188	3	β(h	β(h	NOUN
ejpam-4069	188	4	)	)	PUNCT
ejpam-4069	188	5	)	)	PUNCT
ejpam-4069	188	6	.	.	PUNCT
ejpam-4069	189	1	s.	s.	PROPN
ejpam-4069	189	2	nanding	nanding	PROPN
ejpam-4069	189	3	,	,	PUNCT
ejpam-4069	189	4	h.	h.	PROPN
ejpam-4069	189	5	rara	rara	PROPN
ejpam-4069	189	6	/	/	SYM
ejpam-4069	189	7	eur	eur	PROPN
ejpam-4069	189	8	.	.	PUNCT
ejpam-4069	190	1	j.	j.	PROPN
ejpam-4069	190	2	pure	pure	PROPN
ejpam-4069	190	3	appl	appl	PROPN
ejpam-4069	190	4	.	.	PROPN
ejpam-4069	190	5	math	math	PROPN
ejpam-4069	190	6	,	,	PUNCT
ejpam-4069	190	7	14	14	NUM
ejpam-4069	190	8	(	(	PUNCT
ejpam-4069	190	9	4	4	NUM
ejpam-4069	190	10	)	)	PUNCT
ejpam-4069	190	11	(	(	PUNCT
ejpam-4069	190	12	2021	2021	NUM
ejpam-4069	190	13	)	)	PUNCT
ejpam-4069	190	14	,	,	PUNCT
ejpam-4069	190	15	1226	1226	NUM
ejpam-4069	190	16	-	-	SYM
ejpam-4069	190	17	1236	1236	NUM
ejpam-4069	190	18	1232	1232	NUM
ejpam-4069	190	19	therefore	therefore	ADV
ejpam-4069	190	20	,	,	PUNCT
ejpam-4069	190	21	γch	γch	NOUN
ejpam-4069	190	22	,	,	PUNCT
ejpam-4069	190	23	coi(g	coi(g	PROPN
ejpam-4069	190	24	◦	◦	NOUN
ejpam-4069	190	25	h	h	NOUN
ejpam-4069	190	26	)	)	PUNCT
ejpam-4069	190	27	≤	≤	NUM
ejpam-4069	191	1	n(1	n(1	NOUN
ejpam-4069	192	1	+	+	NOUN
ejpam-4069	192	2	m−	m−	PROPN
ejpam-4069	192	3	β(h	β(h	NOUN
ejpam-4069	192	4	)	)	PUNCT
ejpam-4069	192	5	)	)	PUNCT
ejpam-4069	192	6	.	.	PUNCT
ejpam-4069	193	1	consequently	consequently	ADV
ejpam-4069	193	2	,	,	PUNCT
ejpam-4069	193	3	γch	γch	NOUN
ejpam-4069	193	4	,	,	PUNCT
ejpam-4069	193	5	coi(g	coi(g	PROPN
ejpam-4069	193	6	◦	◦	NOUN
ejpam-4069	193	7	h	h	NOUN
ejpam-4069	193	8	)	)	PUNCT
ejpam-4069	193	9	=	=	PUNCT
ejpam-4069	193	10	n(1	n(1	PROPN
ejpam-4069	193	11	+	+	ADJ
ejpam-4069	193	12	m−	m−	PROPN
ejpam-4069	193	13	β(h	β(h	NOUN
ejpam-4069	193	14	)	)	PUNCT
ejpam-4069	193	15	)	)	PUNCT
ejpam-4069	193	16	.	.	PUNCT
ejpam-4069	194	1	5	5	X
ejpam-4069	194	2	.	.	X
ejpam-4069	194	3	on	on	ADP
ejpam-4069	194	4	connected	connected	ADJ
ejpam-4069	194	5	co	co	ADJ
ejpam-4069	194	6	-	-	ADJ
ejpam-4069	194	7	independent	independent	ADJ
ejpam-4069	194	8	hop	hop	NOUN
ejpam-4069	194	9	domination	domination	NOUN
ejpam-4069	194	10	in	in	ADP
ejpam-4069	194	11	the	the	DET
ejpam-4069	194	12	lexicographic	lexicographic	ADJ
ejpam-4069	194	13	product	product	NOUN
ejpam-4069	194	14	of	of	ADP
ejpam-4069	194	15	graphs	graph	NOUN
ejpam-4069	194	16	the	the	DET
ejpam-4069	194	17	lexicographic	lexicographic	ADJ
ejpam-4069	194	18	product	product	NOUN
ejpam-4069	194	19	of	of	ADP
ejpam-4069	194	20	two	two	NUM
ejpam-4069	194	21	graphs	graph	NOUN
ejpam-4069	194	22	g	g	NOUN
ejpam-4069	194	23	and	and	CCONJ
ejpam-4069	194	24	h	h	NOUN
ejpam-4069	194	25	,	,	PUNCT
ejpam-4069	194	26	denoted	denote	VERB
ejpam-4069	194	27	by	by	ADP
ejpam-4069	194	28	g[h	g[h	NOUN
ejpam-4069	194	29	]	]	PUNCT
ejpam-4069	194	30	,	,	PUNCT
ejpam-4069	194	31	is	be	AUX
ejpam-4069	194	32	the	the	DET
ejpam-4069	194	33	graph	graph	NOUN
ejpam-4069	194	34	with	with	ADP
ejpam-4069	194	35	vertex	vertex	NOUN
ejpam-4069	194	36	-	-	PUNCT
ejpam-4069	194	37	set	set	VERB
ejpam-4069	194	38	v	v	NOUN
ejpam-4069	194	39	(	(	PUNCT
ejpam-4069	194	40	g[h	g[h	PROPN
ejpam-4069	194	41	]	]	PUNCT
ejpam-4069	194	42	)	)	PUNCT
ejpam-4069	194	43	=	=	SYM
ejpam-4069	194	44	v	v	X
ejpam-4069	194	45	(	(	PUNCT
ejpam-4069	194	46	g	g	NOUN
ejpam-4069	194	47	)	)	PUNCT
ejpam-4069	194	48	×	×	NOUN
ejpam-4069	194	49	v	v	NOUN
ejpam-4069	194	50	(	(	PUNCT
ejpam-4069	194	51	h	h	NOUN
ejpam-4069	194	52	)	)	PUNCT
ejpam-4069	194	53	such	such	ADJ
ejpam-4069	194	54	that	that	SCONJ
ejpam-4069	194	55	(	(	PUNCT
ejpam-4069	194	56	u1	u1	NOUN
ejpam-4069	194	57	,	,	PUNCT
ejpam-4069	194	58	u2)(v1	u2)(v1	NOUN
ejpam-4069	194	59	,	,	PUNCT
ejpam-4069	194	60	v2	v2	NOUN
ejpam-4069	194	61	)	)	PUNCT
ejpam-4069	194	62	∈	∈	NOUN
ejpam-4069	194	63	e(g[h	e(g[h	NOUN
ejpam-4069	194	64	]	]	PUNCT
ejpam-4069	194	65	)	)	PUNCT
ejpam-4069	194	66	if	if	SCONJ
ejpam-4069	194	67	either	either	CCONJ
ejpam-4069	194	68	u1v1	u1v1	PROPN
ejpam-4069	194	69	∈	∈	PROPN
ejpam-4069	194	70	e(g	e(g	PROPN
ejpam-4069	194	71	)	)	PUNCT
ejpam-4069	194	72	or	or	CCONJ
ejpam-4069	194	73	u1	u1	NOUN
ejpam-4069	194	74	=	=	SYM
ejpam-4069	194	75	v1	v1	NOUN
ejpam-4069	194	76	and	and	CCONJ
ejpam-4069	194	77	u2v2	u2v2	ADJ
ejpam-4069	194	78	∈	∈	PROPN
ejpam-4069	194	79	e(h	e(h	PROPN
ejpam-4069	194	80	)	)	PUNCT
ejpam-4069	194	81	.	.	PUNCT
ejpam-4069	195	1	theorem	theorem	NOUN
ejpam-4069	195	2	5	5	NUM
ejpam-4069	195	3	.	.	PUNCT
ejpam-4069	196	1	let	let	VERB
ejpam-4069	196	2	g	g	NOUN
ejpam-4069	196	3	and	and	CCONJ
ejpam-4069	196	4	h	h	NOUN
ejpam-4069	196	5	be	be	AUX
ejpam-4069	196	6	nontrivial	nontrivial	ADJ
ejpam-4069	196	7	connected	connect	VERB
ejpam-4069	196	8	graphs	graph	NOUN
ejpam-4069	196	9	with	with	ADP
ejpam-4069	196	10	|v	|v	PROPN
ejpam-4069	196	11	(	(	PUNCT
ejpam-4069	196	12	g)|	g)|	NOUN
ejpam-4069	196	13	=	=	PUNCT
ejpam-4069	196	14	n.	n.	NOUN
ejpam-4069	196	15	a	a	DET
ejpam-4069	196	16	subset	subset	NOUN
ejpam-4069	196	17	c	c	NOUN
ejpam-4069	197	1	=	=	PUNCT
ejpam-4069	197	2	⋃	⋃	PROPN
ejpam-4069	197	3	x∈s	x∈s	NOUN
ejpam-4069	197	4	(	(	PUNCT
ejpam-4069	197	5	{	{	PUNCT
ejpam-4069	197	6	x	x	NOUN
ejpam-4069	197	7	}	}	PUNCT
ejpam-4069	197	8	×	×	PROPN
ejpam-4069	197	9	tx	tx	PROPN
ejpam-4069	197	10	)	)	PUNCT
ejpam-4069	197	11	where	where	SCONJ
ejpam-4069	197	12	s	s	VERB
ejpam-4069	197	13	⊆	⊆	NUM
ejpam-4069	197	14	v	v	NOUN
ejpam-4069	197	15	(	(	PUNCT
ejpam-4069	197	16	g	g	NOUN
ejpam-4069	197	17	)	)	PUNCT
ejpam-4069	197	18	and	and	CCONJ
ejpam-4069	197	19	tx	tx	VERB
ejpam-4069	197	20	⊆	⊆	NUM
ejpam-4069	197	21	v	v	NOUN
ejpam-4069	197	22	(	(	PUNCT
ejpam-4069	197	23	h	h	NOUN
ejpam-4069	197	24	)	)	PUNCT
ejpam-4069	197	25	of	of	ADP
ejpam-4069	197	26	v	v	NOUN
ejpam-4069	197	27	(	(	PUNCT
ejpam-4069	197	28	g[h	g[h	PROPN
ejpam-4069	197	29	]	]	PUNCT
ejpam-4069	197	30	)	)	PUNCT
ejpam-4069	197	31	is	be	AUX
ejpam-4069	197	32	a	a	DET
ejpam-4069	197	33	connected	connected	ADJ
ejpam-4069	197	34	coindependent	coindependent	NOUN
ejpam-4069	197	35	hop	hop	NOUN
ejpam-4069	197	36	dominating	dominating	NOUN
ejpam-4069	197	37	set	set	VERB
ejpam-4069	197	38	if	if	SCONJ
ejpam-4069	197	39	and	and	CCONJ
ejpam-4069	197	40	only	only	ADV
ejpam-4069	197	41	if	if	SCONJ
ejpam-4069	197	42	(	(	PUNCT
ejpam-4069	197	43	i	i	NOUN
ejpam-4069	197	44	)	)	PUNCT
ejpam-4069	197	45	s	s	PART
ejpam-4069	197	46	=	=	SYM
ejpam-4069	197	47	v	v	NOUN
ejpam-4069	197	48	(	(	PUNCT
ejpam-4069	197	49	g	g	NOUN
ejpam-4069	197	50	)	)	PUNCT
ejpam-4069	197	51	.	.	PUNCT
ejpam-4069	198	1	(	(	PUNCT
ejpam-4069	198	2	ii	ii	NOUN
ejpam-4069	198	3	)	)	PUNCT
ejpam-4069	198	4	for	for	ADP
ejpam-4069	198	5	every	every	DET
ejpam-4069	198	6	x	x	SYM
ejpam-4069	198	7	∈	∈	PROPN
ejpam-4069	198	8	v	v	ADP
ejpam-4069	198	9	(	(	PUNCT
ejpam-4069	198	10	g	g	NOUN
ejpam-4069	198	11	)	)	PUNCT
ejpam-4069	198	12	such	such	ADJ
ejpam-4069	198	13	that	that	SCONJ
ejpam-4069	198	14	tx	tx	PROPN
ejpam-4069	198	15	̸=	̸=	PROPN
ejpam-4069	198	16	v	v	PROPN
ejpam-4069	198	17	(	(	PUNCT
ejpam-4069	198	18	h	h	NOUN
ejpam-4069	198	19	)	)	PUNCT
ejpam-4069	198	20	,	,	PUNCT
ejpam-4069	198	21	v	v	X
ejpam-4069	198	22	(	(	PUNCT
ejpam-4069	198	23	h)\tx	h)\tx	PROPN
ejpam-4069	198	24	is	be	AUX
ejpam-4069	198	25	an	an	DET
ejpam-4069	198	26	independent	independent	ADJ
ejpam-4069	198	27	set	set	NOUN
ejpam-4069	198	28	and	and	CCONJ
ejpam-4069	198	29	ty	ty	NOUN
ejpam-4069	198	30	=	=	NOUN
ejpam-4069	198	31	v	v	NOUN
ejpam-4069	198	32	(	(	PUNCT
ejpam-4069	198	33	h	h	NOUN
ejpam-4069	198	34	)	)	PUNCT
ejpam-4069	198	35	for	for	ADP
ejpam-4069	198	36	every	every	DET
ejpam-4069	198	37	y	y	PROPN
ejpam-4069	198	38	∈	∈	PROPN
ejpam-4069	198	39	ng(x	ng(x	NUM
ejpam-4069	198	40	)	)	PUNCT
ejpam-4069	198	41	where	where	SCONJ
ejpam-4069	198	42	tx	tx	PROPN
ejpam-4069	198	43	is	be	AUX
ejpam-4069	198	44	a	a	DET
ejpam-4069	198	45	hop	hop	NOUN
ejpam-4069	198	46	dominating	dominating	NOUN
ejpam-4069	198	47	set	set	NOUN
ejpam-4069	198	48	of	of	ADP
ejpam-4069	198	49	h	h	NOUN
ejpam-4069	198	50	if	if	SCONJ
ejpam-4069	198	51	degg(x	degg(x	NOUN
ejpam-4069	198	52	)	)	PUNCT
ejpam-4069	198	53	=	=	SYM
ejpam-4069	198	54	n−1	n−1	PROPN
ejpam-4069	198	55	.	.	PUNCT
ejpam-4069	198	56	proof	proof	NOUN
ejpam-4069	198	57	:	:	PUNCT
ejpam-4069	198	58	suppose	suppose	VERB
ejpam-4069	198	59	c	c	NOUN
ejpam-4069	198	60	is	be	AUX
ejpam-4069	198	61	a	a	DET
ejpam-4069	198	62	connected	connected	ADJ
ejpam-4069	198	63	co	co	NOUN
ejpam-4069	198	64	-	-	ADJ
ejpam-4069	198	65	independent	independent	ADJ
ejpam-4069	198	66	hop	hop	NOUN
ejpam-4069	198	67	dominating	dominating	NOUN
ejpam-4069	198	68	set	set	NOUN
ejpam-4069	198	69	of	of	ADP
ejpam-4069	198	70	g[h	g[h	PROPN
ejpam-4069	198	71	]	]	PUNCT
ejpam-4069	198	72	and	and	CCONJ
ejpam-4069	198	73	s	s	VERB
ejpam-4069	198	74	̸=	̸=	PROPN
ejpam-4069	198	75	v	v	NOUN
ejpam-4069	198	76	(	(	PUNCT
ejpam-4069	198	77	g	g	NOUN
ejpam-4069	198	78	)	)	PUNCT
ejpam-4069	198	79	.	.	PUNCT
ejpam-4069	199	1	then	then	ADV
ejpam-4069	199	2	,	,	PUNCT
ejpam-4069	199	3	a	a	DET
ejpam-4069	199	4	vertex	vertex	NOUN
ejpam-4069	199	5	v	v	ADP
ejpam-4069	199	6	∈	∈	NOUN
ejpam-4069	199	7	v	v	NOUN
ejpam-4069	199	8	(	(	PUNCT
ejpam-4069	199	9	g)\s	g)\s	NOUN
ejpam-4069	199	10	exists	exist	VERB
ejpam-4069	199	11	.	.	PUNCT
ejpam-4069	200	1	thus	thus	ADV
ejpam-4069	200	2	,	,	PUNCT
ejpam-4069	200	3	(	(	PUNCT
ejpam-4069	200	4	v	v	NOUN
ejpam-4069	200	5	,	,	PUNCT
ejpam-4069	200	6	z	z	NOUN
ejpam-4069	200	7	)	)	PUNCT
ejpam-4069	200	8	∈	∈	NOUN
ejpam-4069	200	9	v	v	NOUN
ejpam-4069	200	10	(	(	PUNCT
ejpam-4069	200	11	g[h])\c	g[h])\c	VERB
ejpam-4069	200	12	for	for	ADP
ejpam-4069	200	13	all	all	DET
ejpam-4069	200	14	z	z	NOUN
ejpam-4069	200	15	∈	∈	PROPN
ejpam-4069	200	16	v	v	ADP
ejpam-4069	200	17	(	(	PUNCT
ejpam-4069	200	18	h	h	NOUN
ejpam-4069	200	19	)	)	PUNCT
ejpam-4069	200	20	.	.	PUNCT
ejpam-4069	201	1	since	since	SCONJ
ejpam-4069	201	2	h	h	NOUN
ejpam-4069	201	3	is	be	AUX
ejpam-4069	201	4	a	a	DET
ejpam-4069	201	5	nontrivial	nontrivial	ADJ
ejpam-4069	201	6	connected	connect	VERB
ejpam-4069	201	7	graph	graph	NOUN
ejpam-4069	201	8	,	,	PUNCT
ejpam-4069	201	9	an	an	DET
ejpam-4069	201	10	edge	edge	NOUN
ejpam-4069	201	11	pq	pq	NOUN
ejpam-4069	201	12	∈	∈	PROPN
ejpam-4069	201	13	e(h	e(h	PROPN
ejpam-4069	201	14	)	)	PUNCT
ejpam-4069	201	15	exists	exist	VERB
ejpam-4069	201	16	.	.	PUNCT
ejpam-4069	202	1	hence	hence	ADV
ejpam-4069	202	2	,	,	PUNCT
ejpam-4069	202	3	(	(	PUNCT
ejpam-4069	202	4	v	v	NOUN
ejpam-4069	202	5	,	,	PUNCT
ejpam-4069	202	6	p	p	NOUN
ejpam-4069	202	7	)	)	PUNCT
ejpam-4069	202	8	,	,	PUNCT
ejpam-4069	202	9	(	(	PUNCT
ejpam-4069	202	10	v	v	NOUN
ejpam-4069	202	11	,	,	PUNCT
ejpam-4069	202	12	q	q	NOUN
ejpam-4069	202	13	)	)	PUNCT
ejpam-4069	202	14	∈	∈	NOUN
ejpam-4069	202	15	v	v	NOUN
ejpam-4069	202	16	(	(	PUNCT
ejpam-4069	202	17	g[h])\c	g[h])\c	NOUN
ejpam-4069	202	18	and	and	CCONJ
ejpam-4069	202	19	(	(	PUNCT
ejpam-4069	202	20	v	v	NOUN
ejpam-4069	202	21	,	,	PUNCT
ejpam-4069	202	22	p)(v	p)(v	PROPN
ejpam-4069	202	23	,	,	PUNCT
ejpam-4069	202	24	q	q	X
ejpam-4069	202	25	)	)	PUNCT
ejpam-4069	202	26	∈	∈	NOUN
ejpam-4069	202	27	e(g[h	e(g[h	NOUN
ejpam-4069	202	28	]	]	PUNCT
ejpam-4069	202	29	)	)	PUNCT
ejpam-4069	202	30	.	.	PUNCT
ejpam-4069	203	1	this	this	PRON
ejpam-4069	203	2	contradicts	contradict	VERB
ejpam-4069	203	3	the	the	DET
ejpam-4069	203	4	independence	independence	NOUN
ejpam-4069	203	5	of	of	ADP
ejpam-4069	203	6	v	v	NOUN
ejpam-4069	203	7	(	(	PUNCT
ejpam-4069	203	8	g[h])\c	g[h])\c	NOUN
ejpam-4069	203	9	.	.	PUNCT
ejpam-4069	204	1	it	it	PRON
ejpam-4069	204	2	follows	follow	VERB
ejpam-4069	204	3	that	that	PRON
ejpam-4069	204	4	s	s	VERB
ejpam-4069	204	5	=	=	SYM
ejpam-4069	204	6	v	v	X
ejpam-4069	204	7	(	(	PUNCT
ejpam-4069	204	8	g	g	NOUN
ejpam-4069	204	9	)	)	PUNCT
ejpam-4069	204	10	and	and	CCONJ
ejpam-4069	204	11	(	(	PUNCT
ejpam-4069	204	12	i	i	NOUN
ejpam-4069	204	13	)	)	PUNCT
ejpam-4069	204	14	holds	hold	VERB
ejpam-4069	204	15	.	.	PUNCT
ejpam-4069	205	1	now	now	ADV
ejpam-4069	205	2	,	,	PUNCT
ejpam-4069	205	3	let	let	VERB
ejpam-4069	205	4	x	x	PUNCT
ejpam-4069	205	5	∈	∈	PROPN
ejpam-4069	205	6	v	v	X
ejpam-4069	205	7	(	(	PUNCT
ejpam-4069	205	8	g	g	NOUN
ejpam-4069	205	9	)	)	PUNCT
ejpam-4069	205	10	such	such	ADJ
ejpam-4069	205	11	that	that	SCONJ
ejpam-4069	205	12	tx	tx	PROPN
ejpam-4069	205	13	̸=	̸=	PROPN
ejpam-4069	205	14	v	v	PROPN
ejpam-4069	205	15	(	(	PUNCT
ejpam-4069	205	16	h	h	NOUN
ejpam-4069	205	17	)	)	PUNCT
ejpam-4069	205	18	.	.	PUNCT
ejpam-4069	206	1	we	we	PRON
ejpam-4069	206	2	claim	claim	VERB
ejpam-4069	206	3	that	that	SCONJ
ejpam-4069	206	4	v	v	INTJ
ejpam-4069	206	5	(	(	PUNCT
ejpam-4069	206	6	h)\tx	h)\tx	PROPN
ejpam-4069	206	7	is	be	AUX
ejpam-4069	206	8	an	an	DET
ejpam-4069	206	9	independent	independent	ADJ
ejpam-4069	206	10	set	set	NOUN
ejpam-4069	206	11	.	.	PUNCT
ejpam-4069	207	1	let	let	VERB
ejpam-4069	207	2	u	u	NOUN
ejpam-4069	207	3	,	,	PUNCT
ejpam-4069	207	4	w	w	PROPN
ejpam-4069	207	5	∈	∈	PROPN
ejpam-4069	207	6	v	v	NOUN
ejpam-4069	207	7	(	(	PUNCT
ejpam-4069	207	8	h)\tx	h)\tx	ADP
ejpam-4069	207	9	where	where	SCONJ
ejpam-4069	207	10	u	u	NOUN
ejpam-4069	207	11	̸=	̸=	PROPN
ejpam-4069	207	12	w.	w.	PROPN
ejpam-4069	207	13	then	then	ADV
ejpam-4069	207	14	(	(	PUNCT
ejpam-4069	207	15	x	x	X
ejpam-4069	207	16	,	,	PUNCT
ejpam-4069	207	17	u	u	NOUN
ejpam-4069	207	18	)	)	PUNCT
ejpam-4069	207	19	,	,	PUNCT
ejpam-4069	207	20	(	(	PUNCT
ejpam-4069	207	21	x	x	NOUN
ejpam-4069	207	22	,	,	PUNCT
ejpam-4069	207	23	w	w	NOUN
ejpam-4069	207	24	)	)	PUNCT
ejpam-4069	207	25	∈	∈	NOUN
ejpam-4069	207	26	v	v	NOUN
ejpam-4069	207	27	(	(	PUNCT
ejpam-4069	207	28	g[h])\c	g[h])\c	PROPN
ejpam-4069	207	29	.	.	NOUN
ejpam-4069	207	30	since	since	SCONJ
ejpam-4069	207	31	v	v	NOUN
ejpam-4069	207	32	(	(	PUNCT
ejpam-4069	207	33	g[h])\c	g[h])\c	PROPN
ejpam-4069	207	34	is	be	AUX
ejpam-4069	207	35	independent	independent	ADJ
ejpam-4069	207	36	,	,	PUNCT
ejpam-4069	207	37	(	(	PUNCT
ejpam-4069	207	38	x	x	NOUN
ejpam-4069	207	39	,	,	PUNCT
ejpam-4069	207	40	u)(x	u)(x	PROPN
ejpam-4069	207	41	,	,	PUNCT
ejpam-4069	207	42	w	w	NOUN
ejpam-4069	207	43	)	)	PUNCT
ejpam-4069	207	44	/∈	/∈	PUNCT
ejpam-4069	208	1	e(g[h	e(g[h	NOUN
ejpam-4069	208	2	]	]	PUNCT
ejpam-4069	208	3	)	)	PUNCT
ejpam-4069	208	4	.	.	PUNCT
ejpam-4069	209	1	thus	thus	ADV
ejpam-4069	209	2	,	,	PUNCT
ejpam-4069	209	3	uw	uw	PROPN
ejpam-4069	209	4	/∈	/∈	PUNCT
ejpam-4069	209	5	e(h	e(h	PROPN
ejpam-4069	209	6	)	)	PUNCT
ejpam-4069	209	7	.	.	PUNCT
ejpam-4069	210	1	hence	hence	ADV
ejpam-4069	210	2	,	,	PUNCT
ejpam-4069	210	3	v	v	INTJ
ejpam-4069	210	4	(	(	PUNCT
ejpam-4069	210	5	h)\tx	h)\tx	PROPN
ejpam-4069	210	6	is	be	AUX
ejpam-4069	210	7	an	an	DET
ejpam-4069	210	8	independent	independent	ADJ
ejpam-4069	210	9	set	set	NOUN
ejpam-4069	210	10	.	.	PUNCT
ejpam-4069	211	1	now	now	ADV
ejpam-4069	211	2	,	,	PUNCT
ejpam-4069	211	3	we	we	PRON
ejpam-4069	211	4	show	show	VERB
ejpam-4069	211	5	that	that	SCONJ
ejpam-4069	211	6	ty	ty	INTJ
ejpam-4069	211	7	=	=	SYM
ejpam-4069	211	8	v	v	NOUN
ejpam-4069	211	9	(	(	PUNCT
ejpam-4069	211	10	h	h	NOUN
ejpam-4069	211	11	)	)	PUNCT
ejpam-4069	211	12	for	for	ADP
ejpam-4069	211	13	every	every	DET
ejpam-4069	211	14	y	y	PROPN
ejpam-4069	211	15	∈	∈	PROPN
ejpam-4069	211	16	ng(x	ng(x	NUM
ejpam-4069	211	17	)	)	PUNCT
ejpam-4069	211	18	.	.	PUNCT
ejpam-4069	212	1	suppose	suppose	VERB
ejpam-4069	213	1	ty	ty	PRON
ejpam-4069	213	2	̸=	̸=	PROPN
ejpam-4069	213	3	v	v	NOUN
ejpam-4069	213	4	(	(	PUNCT
ejpam-4069	213	5	h	h	NOUN
ejpam-4069	213	6	)	)	PUNCT
ejpam-4069	213	7	.	.	PUNCT
ejpam-4069	214	1	then	then	ADV
ejpam-4069	214	2	there	there	PRON
ejpam-4069	214	3	exists	exist	VERB
ejpam-4069	214	4	p	p	PROPN
ejpam-4069	214	5	∈	∈	PROPN
ejpam-4069	214	6	v	v	NOUN
ejpam-4069	214	7	(	(	PUNCT
ejpam-4069	214	8	h)\ty	h)\ty	PROPN
ejpam-4069	214	9	.	.	PUNCT
ejpam-4069	215	1	thus	thus	ADV
ejpam-4069	215	2	,	,	PUNCT
ejpam-4069	215	3	(	(	PUNCT
ejpam-4069	215	4	y	y	NOUN
ejpam-4069	215	5	,	,	PUNCT
ejpam-4069	215	6	p	p	NOUN
ejpam-4069	215	7	)	)	PUNCT
ejpam-4069	215	8	∈	∈	PROPN
ejpam-4069	215	9	v	v	NOUN
ejpam-4069	215	10	(	(	PUNCT
ejpam-4069	215	11	g[h])\c	g[h])\c	PROPN
ejpam-4069	215	12	.	.	NOUN
ejpam-4069	215	13	since	since	SCONJ
ejpam-4069	215	14	y	y	PROPN
ejpam-4069	215	15	∈	∈	PROPN
ejpam-4069	215	16	ng(x	ng(x	NUM
ejpam-4069	215	17	)	)	PUNCT
ejpam-4069	215	18	,	,	PUNCT
ejpam-4069	215	19	(	(	PUNCT
ejpam-4069	215	20	y	y	NOUN
ejpam-4069	215	21	,	,	PUNCT
ejpam-4069	215	22	p)(x	p)(x	PROPN
ejpam-4069	215	23	,	,	PUNCT
ejpam-4069	215	24	q	q	X
ejpam-4069	215	25	)	)	PUNCT
ejpam-4069	215	26	∈	∈	NOUN
ejpam-4069	215	27	e(g[h	e(g[h	NOUN
ejpam-4069	215	28	]	]	PUNCT
ejpam-4069	215	29	)	)	PUNCT
ejpam-4069	215	30	for	for	ADP
ejpam-4069	215	31	all	all	DET
ejpam-4069	215	32	q	q	PROPN
ejpam-4069	215	33	∈	∈	PROPN
ejpam-4069	215	34	v	v	NOUN
ejpam-4069	215	35	(	(	PUNCT
ejpam-4069	215	36	h	h	NOUN
ejpam-4069	215	37	)	)	PUNCT
ejpam-4069	215	38	.	.	PUNCT
ejpam-4069	216	1	this	this	PRON
ejpam-4069	216	2	contradicts	contradict	VERB
ejpam-4069	216	3	the	the	DET
ejpam-4069	216	4	independence	independence	NOUN
ejpam-4069	216	5	of	of	ADP
ejpam-4069	216	6	v	v	NOUN
ejpam-4069	216	7	(	(	PUNCT
ejpam-4069	216	8	g[h])\c	g[h])\c	NOUN
ejpam-4069	216	9	.	.	PUNCT
ejpam-4069	216	10	hence	hence	ADV
ejpam-4069	216	11	,	,	PUNCT
ejpam-4069	216	12	ty	ty	INTJ
ejpam-4069	216	13	=	=	SYM
ejpam-4069	216	14	v	v	NOUN
ejpam-4069	216	15	(	(	PUNCT
ejpam-4069	216	16	h	h	NOUN
ejpam-4069	216	17	)	)	PUNCT
ejpam-4069	216	18	.	.	PUNCT
ejpam-4069	217	1	lastly	lastly	ADV
ejpam-4069	217	2	,	,	PUNCT
ejpam-4069	217	3	suppose	suppose	VERB
ejpam-4069	217	4	degg(x	degg(x	NOUN
ejpam-4069	217	5	)	)	PUNCT
ejpam-4069	217	6	=	=	SYM
ejpam-4069	217	7	n	n	CCONJ
ejpam-4069	217	8	−	−	PROPN
ejpam-4069	217	9	1	1	X
ejpam-4069	217	10	.	.	PUNCT
ejpam-4069	218	1	then	then	ADV
ejpam-4069	218	2	xa	xa	PROPN
ejpam-4069	218	3	∈	∈	PROPN
ejpam-4069	218	4	e(g	e(g	PROPN
ejpam-4069	218	5	)	)	PUNCT
ejpam-4069	219	1	for	for	ADP
ejpam-4069	219	2	all	all	DET
ejpam-4069	219	3	a	a	DET
ejpam-4069	219	4	∈	∈	PROPN
ejpam-4069	219	5	v	v	NOUN
ejpam-4069	219	6	(	(	PUNCT
ejpam-4069	219	7	g)\{x	g)\{x	PROPN
ejpam-4069	219	8	}	}	PUNCT
ejpam-4069	219	9	.	.	PUNCT
ejpam-4069	220	1	since	since	SCONJ
ejpam-4069	220	2	v	v	NOUN
ejpam-4069	220	3	(	(	PUNCT
ejpam-4069	220	4	g	g	NOUN
ejpam-4069	220	5	)	)	PUNCT
ejpam-4069	220	6	̸=	̸=	PROPN
ejpam-4069	220	7	tx	tx	PROPN
ejpam-4069	220	8	,	,	PUNCT
ejpam-4069	220	9	a	a	DET
ejpam-4069	220	10	vertex	vertex	NOUN
ejpam-4069	220	11	b	b	PROPN
ejpam-4069	220	12	∈	∈	NOUN
ejpam-4069	220	13	v	v	NOUN
ejpam-4069	220	14	(	(	PUNCT
ejpam-4069	220	15	h)\tx	h)\tx	NOUN
ejpam-4069	220	16	exists	exist	VERB
ejpam-4069	220	17	.	.	PUNCT
ejpam-4069	221	1	thus	thus	ADV
ejpam-4069	221	2	,	,	PUNCT
ejpam-4069	221	3	(	(	PUNCT
ejpam-4069	221	4	x	x	X
ejpam-4069	221	5	,	,	PUNCT
ejpam-4069	221	6	b	b	NOUN
ejpam-4069	221	7	)	)	PUNCT
ejpam-4069	221	8	∈	∈	NOUN
ejpam-4069	221	9	v	v	NOUN
ejpam-4069	221	10	(	(	PUNCT
ejpam-4069	221	11	g[h])\c	g[h])\c	PROPN
ejpam-4069	221	12	.	.	PUNCT
ejpam-4069	222	1	since	since	SCONJ
ejpam-4069	222	2	c	c	PROPN
ejpam-4069	222	3	is	be	AUX
ejpam-4069	222	4	a	a	DET
ejpam-4069	222	5	hop	hop	NOUN
ejpam-4069	222	6	dominating	dominating	NOUN
ejpam-4069	222	7	set	set	NOUN
ejpam-4069	222	8	and	and	CCONJ
ejpam-4069	222	9	(	(	PUNCT
ejpam-4069	222	10	x	x	NOUN
ejpam-4069	222	11	,	,	PUNCT
ejpam-4069	222	12	b)(a	b)(a	ADV
ejpam-4069	222	13	,	,	PUNCT
ejpam-4069	222	14	d	d	X
ejpam-4069	222	15	)	)	PUNCT
ejpam-4069	222	16	∈	∈	NOUN
ejpam-4069	222	17	e(g[h	e(g[h	NOUN
ejpam-4069	222	18	]	]	PUNCT
ejpam-4069	222	19	)	)	PUNCT
ejpam-4069	222	20	for	for	ADP
ejpam-4069	222	21	all	all	DET
ejpam-4069	222	22	a	a	DET
ejpam-4069	222	23	∈	∈	PROPN
ejpam-4069	222	24	v	v	NOUN
ejpam-4069	222	25	(	(	PUNCT
ejpam-4069	222	26	g)\{x	g)\{x	PROPN
ejpam-4069	222	27	}	}	PUNCT
ejpam-4069	222	28	and	and	CCONJ
ejpam-4069	222	29	d	d	PROPN
ejpam-4069	222	30	∈	∈	PROPN
ejpam-4069	222	31	ta	ta	X
ejpam-4069	222	32	,	,	PUNCT
ejpam-4069	222	33	there	there	PRON
ejpam-4069	222	34	exists	exist	VERB
ejpam-4069	222	35	z	z	PROPN
ejpam-4069	222	36	∈	∈	PROPN
ejpam-4069	222	37	tx	tx	ADP
ejpam-4069	222	38	such	such	ADJ
ejpam-4069	222	39	that	that	DET
ejpam-4069	222	40	dg[h]((x	dg[h]((x	NOUN
ejpam-4069	222	41	,	,	PUNCT
ejpam-4069	222	42	b	b	NOUN
ejpam-4069	222	43	)	)	PUNCT
ejpam-4069	222	44	,	,	PUNCT
ejpam-4069	222	45	(	(	PUNCT
ejpam-4069	222	46	x	x	X
ejpam-4069	222	47	,	,	PUNCT
ejpam-4069	222	48	z	z	NOUN
ejpam-4069	222	49	)	)	PUNCT
ejpam-4069	222	50	)	)	PUNCT
ejpam-4069	223	1	=	=	SYM
ejpam-4069	223	2	2	2	X
ejpam-4069	223	3	.	.	X
ejpam-4069	223	4	hence	hence	ADV
ejpam-4069	223	5	,	,	PUNCT
ejpam-4069	223	6	dh(b	dh(b	PROPN
ejpam-4069	223	7	,	,	PUNCT
ejpam-4069	223	8	z	z	NOUN
ejpam-4069	223	9	)	)	PUNCT
ejpam-4069	223	10	=	=	SYM
ejpam-4069	223	11	2	2	NUM
ejpam-4069	223	12	,	,	PUNCT
ejpam-4069	223	13	showing	show	VERB
ejpam-4069	223	14	that	that	SCONJ
ejpam-4069	223	15	z	z	PROPN
ejpam-4069	223	16	∈	∈	PROPN
ejpam-4069	223	17	tx\nh(b	tx\nh(b	PROPN
ejpam-4069	223	18	)	)	PUNCT
ejpam-4069	223	19	.	.	PUNCT
ejpam-4069	224	1	hence	hence	ADV
ejpam-4069	224	2	,	,	PUNCT
ejpam-4069	224	3	nh(b	nh(b	NOUN
ejpam-4069	224	4	)	)	PUNCT
ejpam-4069	224	5	∩	∩	NOUN
ejpam-4069	224	6	tx	tx	SCONJ
ejpam-4069	224	7	̸=	̸=	PROPN
ejpam-4069	224	8	tx	tx	VERB
ejpam-4069	224	9	implying	imply	VERB
ejpam-4069	224	10	that	that	SCONJ
ejpam-4069	224	11	tx	tx	PROPN
ejpam-4069	224	12	is	be	AUX
ejpam-4069	224	13	strictly	strictly	ADV
ejpam-4069	224	14	co	co	ADJ
ejpam-4069	224	15	-	-	ADJ
ejpam-4069	224	16	independent	independent	ADJ
ejpam-4069	224	17	set	set	NOUN
ejpam-4069	224	18	of	of	ADP
ejpam-4069	224	19	h.	h.	PROPN
ejpam-4069	224	20	thus	thus	ADV
ejpam-4069	224	21	,	,	PUNCT
ejpam-4069	224	22	(	(	PUNCT
ejpam-4069	224	23	ii	ii	NOUN
ejpam-4069	224	24	)	)	PUNCT
ejpam-4069	224	25	holds	hold	VERB
ejpam-4069	224	26	.	.	PUNCT
ejpam-4069	225	1	conversely	conversely	ADV
ejpam-4069	225	2	,	,	PUNCT
ejpam-4069	225	3	suppose	suppose	VERB
ejpam-4069	225	4	c	c	X
ejpam-4069	225	5	=	=	SYM
ejpam-4069	225	6	⋃	⋃	PROPN
ejpam-4069	225	7	x∈s	x∈s	NOUN
ejpam-4069	225	8	(	(	PUNCT
ejpam-4069	225	9	{	{	PUNCT
ejpam-4069	225	10	x	x	NOUN
ejpam-4069	225	11	}	}	PUNCT
ejpam-4069	225	12	×	×	PROPN
ejpam-4069	225	13	tx	tx	PROPN
ejpam-4069	225	14	)	)	PUNCT
ejpam-4069	225	15	satisfies	satisfy	VERB
ejpam-4069	225	16	conditions	condition	NOUN
ejpam-4069	225	17	(	(	PUNCT
ejpam-4069	225	18	i	i	NOUN
ejpam-4069	225	19	)	)	PUNCT
ejpam-4069	225	20	and	and	CCONJ
ejpam-4069	225	21	(	(	PUNCT
ejpam-4069	225	22	ii	ii	NOUN
ejpam-4069	225	23	)	)	PUNCT
ejpam-4069	225	24	.	.	PUNCT
ejpam-4069	226	1	first	first	ADV
ejpam-4069	226	2	,	,	PUNCT
ejpam-4069	226	3	we	we	PRON
ejpam-4069	226	4	claim	claim	VERB
ejpam-4069	226	5	that	that	SCONJ
ejpam-4069	226	6	c	c	PROPN
ejpam-4069	226	7	is	be	AUX
ejpam-4069	226	8	connected	connect	VERB
ejpam-4069	226	9	in	in	ADP
ejpam-4069	226	10	g[h	g[h	PROPN
ejpam-4069	226	11	]	]	PUNCT
ejpam-4069	226	12	.	.	PUNCT
ejpam-4069	227	1	let	let	VERB
ejpam-4069	227	2	(	(	PUNCT
ejpam-4069	227	3	x	x	X
ejpam-4069	227	4	,	,	PUNCT
ejpam-4069	227	5	a	a	PRON
ejpam-4069	227	6	)	)	PUNCT
ejpam-4069	227	7	and	and	CCONJ
ejpam-4069	227	8	(	(	PUNCT
ejpam-4069	227	9	y	y	PROPN
ejpam-4069	227	10	,	,	PUNCT
ejpam-4069	227	11	b	b	NOUN
ejpam-4069	227	12	)	)	PUNCT
ejpam-4069	227	13	be	be	AUX
ejpam-4069	227	14	two	two	NUM
ejpam-4069	227	15	distinct	distinct	ADJ
ejpam-4069	227	16	vertices	vertex	NOUN
ejpam-4069	227	17	in	in	ADP
ejpam-4069	227	18	c	c	PROPN
ejpam-4069	227	19	,	,	PUNCT
ejpam-4069	227	20	(	(	PUNCT
ejpam-4069	227	21	x	x	X
ejpam-4069	227	22	,	,	PUNCT
ejpam-4069	227	23	a)(y	a)(y	PROPN
ejpam-4069	227	24	,	,	PUNCT
ejpam-4069	227	25	b	b	NOUN
ejpam-4069	227	26	)	)	PUNCT
ejpam-4069	227	27	/∈	/∈	PUNCT
ejpam-4069	228	1	e(g[h	e(g[h	NOUN
ejpam-4069	228	2	]	]	PUNCT
ejpam-4069	228	3	)	)	PUNCT
ejpam-4069	228	4	.	.	PUNCT
ejpam-4069	229	1	consider	consider	VERB
ejpam-4069	229	2	the	the	DET
ejpam-4069	229	3	following	follow	VERB
ejpam-4069	229	4	cases	case	NOUN
ejpam-4069	229	5	.	.	PUNCT
ejpam-4069	230	1	case	case	NOUN
ejpam-4069	230	2	1	1	NUM
ejpam-4069	230	3	.	.	PUNCT
ejpam-4069	231	1	x	x	PUNCT
ejpam-4069	232	1	=	=	NOUN
ejpam-4069	232	2	y	y	PROPN
ejpam-4069	232	3	since	since	SCONJ
ejpam-4069	232	4	(	(	PUNCT
ejpam-4069	232	5	x	x	NOUN
ejpam-4069	232	6	,	,	PUNCT
ejpam-4069	232	7	a	a	PRON
ejpam-4069	232	8	)	)	PUNCT
ejpam-4069	232	9	̸=	̸=	PROPN
ejpam-4069	232	10	(	(	PUNCT
ejpam-4069	232	11	y	y	PROPN
ejpam-4069	232	12	,	,	PUNCT
ejpam-4069	232	13	b	b	NOUN
ejpam-4069	232	14	)	)	PUNCT
ejpam-4069	232	15	and	and	CCONJ
ejpam-4069	232	16	(	(	PUNCT
ejpam-4069	232	17	x	x	X
ejpam-4069	232	18	,	,	PUNCT
ejpam-4069	232	19	a)(y	a)(y	PROPN
ejpam-4069	232	20	,	,	PUNCT
ejpam-4069	232	21	b	b	NOUN
ejpam-4069	232	22	)	)	PUNCT
ejpam-4069	232	23	/∈	/∈	PUNCT
ejpam-4069	232	24	e(g[h	e(g[h	NOUN
ejpam-4069	232	25	]	]	PUNCT
ejpam-4069	232	26	)	)	PUNCT
ejpam-4069	232	27	,	,	PUNCT
ejpam-4069	232	28	a	a	DET
ejpam-4069	232	29	̸=	̸=	PROPN
ejpam-4069	232	30	b	b	PROPN
ejpam-4069	232	31	and	and	CCONJ
ejpam-4069	232	32	ab	ab	PROPN
ejpam-4069	232	33	/∈	/∈	PUNCT
ejpam-4069	232	34	e(h	e(h	PROPN
ejpam-4069	232	35	)	)	PUNCT
ejpam-4069	232	36	.	.	PUNCT
ejpam-4069	233	1	since	since	SCONJ
ejpam-4069	233	2	g	g	PROPN
ejpam-4069	233	3	is	be	AUX
ejpam-4069	233	4	a	a	DET
ejpam-4069	233	5	nontrivial	nontrivial	ADJ
ejpam-4069	233	6	connected	connect	VERB
ejpam-4069	233	7	graph	graph	NOUN
ejpam-4069	233	8	and	and	CCONJ
ejpam-4069	233	9	s	s	NOUN
ejpam-4069	233	10	=	=	SYM
ejpam-4069	233	11	v	v	X
ejpam-4069	233	12	(	(	PUNCT
ejpam-4069	233	13	g	g	NOUN
ejpam-4069	233	14	)	)	PUNCT
ejpam-4069	233	15	by	by	ADP
ejpam-4069	233	16	(	(	PUNCT
ejpam-4069	233	17	i	i	NOUN
ejpam-4069	233	18	)	)	PUNCT
ejpam-4069	233	19	,	,	PUNCT
ejpam-4069	233	20	there	there	PRON
ejpam-4069	233	21	exists	exist	VERB
ejpam-4069	233	22	z	z	PROPN
ejpam-4069	233	23	∈	∈	PROPN
ejpam-4069	233	24	s	s	PART
ejpam-4069	233	25	∩	∩	NOUN
ejpam-4069	233	26	ng(x	ng(x	NUM
ejpam-4069	233	27	)	)	PUNCT
ejpam-4069	233	28	.	.	PUNCT
ejpam-4069	234	1	thus	thus	ADV
ejpam-4069	234	2	,	,	PUNCT
ejpam-4069	234	3	(	(	PUNCT
ejpam-4069	234	4	z	z	X
ejpam-4069	234	5	,	,	PUNCT
ejpam-4069	234	6	w	w	NOUN
ejpam-4069	234	7	)	)	PUNCT
ejpam-4069	234	8	∈	∈	PROPN
ejpam-4069	234	9	c	c	NOUN
ejpam-4069	234	10	for	for	ADP
ejpam-4069	234	11	some	some	DET
ejpam-4069	234	12	w	w	PROPN
ejpam-4069	234	13	∈	∈	PROPN
ejpam-4069	234	14	v	v	ADP
ejpam-4069	234	15	(	(	PUNCT
ejpam-4069	234	16	h	h	NOUN
ejpam-4069	234	17	)	)	PUNCT
ejpam-4069	234	18	.	.	PUNCT
ejpam-4069	235	1	it	it	PRON
ejpam-4069	235	2	follows	follow	VERB
ejpam-4069	235	3	that	that	SCONJ
ejpam-4069	235	4	[	[	X
ejpam-4069	235	5	(	(	PUNCT
ejpam-4069	235	6	x	x	X
ejpam-4069	235	7	,	,	PUNCT
ejpam-4069	235	8	a	a	PRON
ejpam-4069	235	9	)	)	PUNCT
ejpam-4069	235	10	,	,	PUNCT
ejpam-4069	235	11	(	(	PUNCT
ejpam-4069	235	12	z	z	X
ejpam-4069	235	13	,	,	PUNCT
ejpam-4069	235	14	w	w	PROPN
ejpam-4069	235	15	)	)	PUNCT
ejpam-4069	235	16	,	,	PUNCT
ejpam-4069	235	17	(	(	PUNCT
ejpam-4069	235	18	y	y	PROPN
ejpam-4069	235	19	,	,	PUNCT
ejpam-4069	235	20	b	b	NOUN
ejpam-4069	235	21	)	)	PUNCT
ejpam-4069	235	22	]	]	PUNCT
ejpam-4069	235	23	is	be	AUX
ejpam-4069	235	24	a	a	DET
ejpam-4069	235	25	path	path	NOUN
ejpam-4069	235	26	in	in	ADP
ejpam-4069	235	27	c.	c.	PROPN
ejpam-4069	235	28	case	case	NOUN
ejpam-4069	235	29	2	2	NUM
ejpam-4069	235	30	.	.	PUNCT
ejpam-4069	235	31	x	x	X
ejpam-4069	236	1	̸=	̸=	PROPN
ejpam-4069	236	2	y	y	PROPN
ejpam-4069	236	3	since	since	SCONJ
ejpam-4069	236	4	g	g	PROPN
ejpam-4069	236	5	is	be	AUX
ejpam-4069	236	6	a	a	DET
ejpam-4069	236	7	nontrivial	nontrivial	ADJ
ejpam-4069	236	8	connected	connect	VERB
ejpam-4069	236	9	graph	graph	NOUN
ejpam-4069	236	10	,	,	PUNCT
ejpam-4069	236	11	there	there	PRON
ejpam-4069	236	12	exists	exist	VERB
ejpam-4069	236	13	an	an	DET
ejpam-4069	236	14	x	x	NOUN
ejpam-4069	236	15	-	-	NOUN
ejpam-4069	236	16	y	y	ADJ
ejpam-4069	236	17	path	path	NOUN
ejpam-4069	236	18	[	[	X
ejpam-4069	236	19	v1	v1	NOUN
ejpam-4069	236	20	,	,	PUNCT
ejpam-4069	236	21	v2	v2	PROPN
ejpam-4069	236	22	,	,	PUNCT
ejpam-4069	236	23	...	...	PUNCT
ejpam-4069	236	24	,	,	PUNCT
ejpam-4069	236	25	vn	vn	X
ejpam-4069	236	26	]	]	X
ejpam-4069	236	27	where	where	SCONJ
ejpam-4069	236	28	x	x	SYM
ejpam-4069	236	29	=	=	SYM
ejpam-4069	236	30	v1	v1	PROPN
ejpam-4069	236	31	and	and	CCONJ
ejpam-4069	236	32	y	y	PROPN
ejpam-4069	236	33	=	=	SYM
ejpam-4069	236	34	vn	vn	PROPN
ejpam-4069	236	35	,	,	PUNCT
ejpam-4069	236	36	n	n	PROPN
ejpam-4069	236	37	>	>	X
ejpam-4069	236	38	2	2	X
ejpam-4069	236	39	.	.	PUNCT
ejpam-4069	237	1	by	by	ADP
ejpam-4069	237	2	(	(	PUNCT
ejpam-4069	237	3	i	i	NOUN
ejpam-4069	237	4	)	)	PUNCT
ejpam-4069	237	5	vi	vi	PROPN
ejpam-4069	237	6	∈	∈	PROPN
ejpam-4069	237	7	s	s	NOUN
ejpam-4069	237	8	for	for	ADP
ejpam-4069	237	9	all	all	PRON
ejpam-4069	237	10	i	i	PRON
ejpam-4069	237	11	∈	∈	PROPN
ejpam-4069	237	12	{	{	PUNCT
ejpam-4069	237	13	1	1	NUM
ejpam-4069	237	14	,	,	PUNCT
ejpam-4069	237	15	2	2	NUM
ejpam-4069	237	16	,	,	PUNCT
ejpam-4069	237	17	...	...	PUNCT
ejpam-4069	237	18	,	,	PUNCT
ejpam-4069	237	19	n	n	CCONJ
ejpam-4069	237	20	}	}	PUNCT
ejpam-4069	237	21	.	.	PUNCT
ejpam-4069	238	1	let	let	VERB
ejpam-4069	238	2	ui	ui	PROPN
ejpam-4069	238	3	∈	∈	PROPN
ejpam-4069	238	4	tvi	tvi	PROPN
ejpam-4069	238	5	,	,	PUNCT
ejpam-4069	238	6	u1	u1	PROPN
ejpam-4069	238	7	=	=	SYM
ejpam-4069	238	8	a	a	PROPN
ejpam-4069	238	9	and	and	CCONJ
ejpam-4069	238	10	s.	s.	PROPN
ejpam-4069	238	11	nanding	nanding	PROPN
ejpam-4069	238	12	,	,	PUNCT
ejpam-4069	238	13	h.	h.	PROPN
ejpam-4069	238	14	rara	rara	PROPN
ejpam-4069	238	15	/	/	SYM
ejpam-4069	238	16	eur	eur	PROPN
ejpam-4069	238	17	.	.	PUNCT
ejpam-4069	239	1	j.	j.	PROPN
ejpam-4069	239	2	pure	pure	PROPN
ejpam-4069	239	3	appl	appl	PROPN
ejpam-4069	239	4	.	.	PROPN
ejpam-4069	239	5	math	math	PROPN
ejpam-4069	239	6	,	,	PUNCT
ejpam-4069	239	7	14	14	NUM
ejpam-4069	239	8	(	(	PUNCT
ejpam-4069	239	9	4	4	NUM
ejpam-4069	239	10	)	)	PUNCT
ejpam-4069	239	11	(	(	PUNCT
ejpam-4069	239	12	2021	2021	NUM
ejpam-4069	239	13	)	)	PUNCT
ejpam-4069	239	14	,	,	PUNCT
ejpam-4069	239	15	1226	1226	NUM
ejpam-4069	239	16	-	-	SYM
ejpam-4069	239	17	1236	1236	NUM
ejpam-4069	239	18	1233	1233	NUM
ejpam-4069	239	19	un	un	PROPN
ejpam-4069	239	20	=	=	PROPN
ejpam-4069	239	21	b.	b.	PROPN
ejpam-4069	240	1	then	then	ADV
ejpam-4069	240	2	[	[	X
ejpam-4069	240	3	(	(	PUNCT
ejpam-4069	240	4	x	x	NOUN
ejpam-4069	240	5	,	,	PUNCT
ejpam-4069	240	6	a	a	PRON
ejpam-4069	240	7	)	)	PUNCT
ejpam-4069	240	8	,	,	PUNCT
ejpam-4069	240	9	(	(	PUNCT
ejpam-4069	240	10	v2	v2	NOUN
ejpam-4069	240	11	,	,	PUNCT
ejpam-4069	240	12	u2	u2	PROPN
ejpam-4069	240	13	)	)	PUNCT
ejpam-4069	240	14	,	,	PUNCT
ejpam-4069	240	15	(	(	PUNCT
ejpam-4069	240	16	v3	v3	PROPN
ejpam-4069	240	17	,	,	PUNCT
ejpam-4069	240	18	u3	u3	PROPN
ejpam-4069	240	19	)	)	PUNCT
ejpam-4069	240	20	,	,	PUNCT
ejpam-4069	240	21	...	...	PUNCT
ejpam-4069	240	22	,	,	PUNCT
ejpam-4069	240	23	(	(	PUNCT
ejpam-4069	240	24	y	y	NOUN
ejpam-4069	240	25	,	,	PUNCT
ejpam-4069	240	26	b	b	NOUN
ejpam-4069	240	27	)	)	PUNCT
ejpam-4069	240	28	]	]	PUNCT
ejpam-4069	240	29	is	be	AUX
ejpam-4069	240	30	an	an	DET
ejpam-4069	240	31	(	(	PUNCT
ejpam-4069	240	32	x	x	NOUN
ejpam-4069	240	33	,	,	PUNCT
ejpam-4069	240	34	a)-(y	a)-(y	PROPN
ejpam-4069	240	35	,	,	PUNCT
ejpam-4069	240	36	b	b	NOUN
ejpam-4069	240	37	)	)	PUNCT
ejpam-4069	240	38	path	path	NOUN
ejpam-4069	240	39	in	in	ADP
ejpam-4069	240	40	c.	c.	PROPN
ejpam-4069	240	41	therefore	therefore	ADV
ejpam-4069	240	42	in	in	ADP
ejpam-4069	240	43	either	either	DET
ejpam-4069	240	44	case	case	NOUN
ejpam-4069	240	45	,	,	PUNCT
ejpam-4069	240	46	c	c	PROPN
ejpam-4069	240	47	is	be	AUX
ejpam-4069	240	48	connected	connect	VERB
ejpam-4069	240	49	.	.	PUNCT
ejpam-4069	241	1	now	now	ADV
ejpam-4069	241	2	,	,	PUNCT
ejpam-4069	241	3	let	let	VERB
ejpam-4069	241	4	(	(	PUNCT
ejpam-4069	241	5	u	u	NOUN
ejpam-4069	241	6	,	,	PUNCT
ejpam-4069	241	7	v	v	NOUN
ejpam-4069	241	8	)	)	PUNCT
ejpam-4069	241	9	,	,	PUNCT
ejpam-4069	241	10	(	(	PUNCT
ejpam-4069	241	11	w	w	X
ejpam-4069	241	12	,	,	PUNCT
ejpam-4069	241	13	p	p	NOUN
ejpam-4069	241	14	)	)	PUNCT
ejpam-4069	241	15	∈	∈	PROPN
ejpam-4069	241	16	v	v	NOUN
ejpam-4069	241	17	(	(	PUNCT
ejpam-4069	241	18	g[h])\c	g[h])\c	X
ejpam-4069	241	19	where	where	SCONJ
ejpam-4069	241	20	(	(	PUNCT
ejpam-4069	241	21	u	u	NOUN
ejpam-4069	241	22	,	,	PUNCT
ejpam-4069	241	23	v	v	NOUN
ejpam-4069	241	24	)	)	PUNCT
ejpam-4069	241	25	̸=	̸=	PROPN
ejpam-4069	241	26	(	(	PUNCT
ejpam-4069	241	27	w	w	PROPN
ejpam-4069	241	28	,	,	PUNCT
ejpam-4069	241	29	p	p	NOUN
ejpam-4069	241	30	)	)	PUNCT
ejpam-4069	241	31	.	.	PUNCT
ejpam-4069	242	1	consider	consider	VERB
ejpam-4069	242	2	the	the	DET
ejpam-4069	242	3	following	follow	VERB
ejpam-4069	242	4	cases	case	NOUN
ejpam-4069	242	5	.	.	PUNCT
ejpam-4069	243	1	case	case	NOUN
ejpam-4069	243	2	1	1	NUM
ejpam-4069	243	3	.	.	X
ejpam-4069	243	4	u	u	X
ejpam-4069	243	5	=	=	NOUN
ejpam-4069	243	6	w	w	NOUN
ejpam-4069	243	7	since	since	SCONJ
ejpam-4069	243	8	(	(	PUNCT
ejpam-4069	243	9	u	u	NOUN
ejpam-4069	243	10	,	,	PUNCT
ejpam-4069	243	11	v	v	NOUN
ejpam-4069	243	12	)	)	PUNCT
ejpam-4069	243	13	,	,	PUNCT
ejpam-4069	243	14	(	(	PUNCT
ejpam-4069	243	15	w	w	X
ejpam-4069	243	16	,	,	PUNCT
ejpam-4069	243	17	p	p	NOUN
ejpam-4069	243	18	)	)	PUNCT
ejpam-4069	243	19	/∈	/∈	PUNCT
ejpam-4069	244	1	c	c	X
ejpam-4069	244	2	,	,	PUNCT
ejpam-4069	244	3	v	v	NOUN
ejpam-4069	244	4	,	,	PUNCT
ejpam-4069	244	5	p	p	NOUN
ejpam-4069	244	6	/∈	/∈	NOUN
ejpam-4069	245	1	tu	tu	PROPN
ejpam-4069	245	2	=	=	PUNCT
ejpam-4069	245	3	tw	tw	NOUN
ejpam-4069	245	4	and	and	CCONJ
ejpam-4069	245	5	v	v	ADP
ejpam-4069	245	6	̸=	̸=	PROPN
ejpam-4069	245	7	p.	p.	NOUN
ejpam-4069	245	8	hence	hence	ADV
ejpam-4069	245	9	,	,	PUNCT
ejpam-4069	245	10	v	v	ADP
ejpam-4069	245	11	,	,	PUNCT
ejpam-4069	245	12	p	p	PROPN
ejpam-4069	245	13	∈	∈	PROPN
ejpam-4069	245	14	v	v	NOUN
ejpam-4069	245	15	(	(	PUNCT
ejpam-4069	245	16	h)\tu	h)\tu	PROPN
ejpam-4069	245	17	.	.	PROPN
ejpam-4069	246	1	since	since	SCONJ
ejpam-4069	246	2	,	,	PUNCT
ejpam-4069	246	3	v	v	X
ejpam-4069	246	4	(	(	PUNCT
ejpam-4069	246	5	h)\tu	h)\tu	PROPN
ejpam-4069	246	6	is	be	AUX
ejpam-4069	246	7	independent	independent	ADJ
ejpam-4069	246	8	by	by	ADP
ejpam-4069	246	9	(	(	PUNCT
ejpam-4069	246	10	ii	ii	NOUN
ejpam-4069	246	11	)	)	PUNCT
ejpam-4069	246	12	,	,	PUNCT
ejpam-4069	246	13	vp	vp	PROPN
ejpam-4069	246	14	/∈	/∈	PUNCT
ejpam-4069	246	15	e(h	e(h	PROPN
ejpam-4069	246	16	)	)	PUNCT
ejpam-4069	246	17	.	.	PUNCT
ejpam-4069	247	1	thus	thus	ADV
ejpam-4069	247	2	,	,	PUNCT
ejpam-4069	247	3	(	(	PUNCT
ejpam-4069	247	4	u	u	NOUN
ejpam-4069	247	5	,	,	PUNCT
ejpam-4069	247	6	v)(w	v)(w	NOUN
ejpam-4069	247	7	,	,	PUNCT
ejpam-4069	247	8	p	p	NOUN
ejpam-4069	247	9	)	)	PUNCT
ejpam-4069	247	10	/∈	/∈	PUNCT
ejpam-4069	247	11	e(g[h	e(g[h	NOUN
ejpam-4069	247	12	]	]	PUNCT
ejpam-4069	247	13	)	)	PUNCT
ejpam-4069	247	14	.	.	PUNCT
ejpam-4069	248	1	case	case	NOUN
ejpam-4069	248	2	2	2	NUM
ejpam-4069	248	3	.	.	X
ejpam-4069	248	4	u	u	NOUN
ejpam-4069	248	5	̸=	̸=	PROPN
ejpam-4069	248	6	w	w	NOUN
ejpam-4069	248	7	since	since	SCONJ
ejpam-4069	248	8	v	v	NUM
ejpam-4069	248	9	/∈	/∈	PUNCT
ejpam-4069	248	10	tu	tu	PROPN
ejpam-4069	248	11	and	and	CCONJ
ejpam-4069	248	12	p	p	NOUN
ejpam-4069	248	13	/∈	/∈	PROPN
ejpam-4069	249	1	tw	tw	PROPN
ejpam-4069	249	2	,	,	PUNCT
ejpam-4069	249	3	tu	tu	PROPN
ejpam-4069	249	4	̸=	̸=	PROPN
ejpam-4069	249	5	v	v	PROPN
ejpam-4069	249	6	(	(	PUNCT
ejpam-4069	249	7	h	h	NOUN
ejpam-4069	249	8	)	)	PUNCT
ejpam-4069	249	9	and	and	CCONJ
ejpam-4069	249	10	tw	tw	VERB
ejpam-4069	249	11	̸=	̸=	PROPN
ejpam-4069	249	12	v	v	PROPN
ejpam-4069	249	13	(	(	PUNCT
ejpam-4069	249	14	h	h	NOUN
ejpam-4069	249	15	)	)	PUNCT
ejpam-4069	249	16	.	.	PUNCT
ejpam-4069	250	1	by	by	ADP
ejpam-4069	250	2	(	(	PUNCT
ejpam-4069	250	3	ii	ii	NOUN
ejpam-4069	250	4	)	)	PUNCT
ejpam-4069	250	5	,	,	PUNCT
ejpam-4069	250	6	u	u	NOUN
ejpam-4069	250	7	/∈	/∈	PROPN
ejpam-4069	250	8	ng(w	ng(w	NOUN
ejpam-4069	250	9	)	)	PUNCT
ejpam-4069	250	10	.	.	PUNCT
ejpam-4069	251	1	thus	thus	ADV
ejpam-4069	251	2	,	,	PUNCT
ejpam-4069	251	3	(	(	PUNCT
ejpam-4069	251	4	u	u	NOUN
ejpam-4069	251	5	,	,	PUNCT
ejpam-4069	251	6	v)(w	v)(w	NOUN
ejpam-4069	251	7	,	,	PUNCT
ejpam-4069	251	8	p	p	NOUN
ejpam-4069	251	9	)	)	PUNCT
ejpam-4069	251	10	/∈	/∈	PUNCT
ejpam-4069	251	11	e(g[h	e(g[h	NOUN
ejpam-4069	251	12	]	]	PUNCT
ejpam-4069	251	13	)	)	PUNCT
ejpam-4069	251	14	.	.	PUNCT
ejpam-4069	252	1	therefore	therefore	ADV
ejpam-4069	252	2	,	,	PUNCT
ejpam-4069	252	3	in	in	ADP
ejpam-4069	252	4	any	any	DET
ejpam-4069	252	5	case	case	NOUN
ejpam-4069	252	6	v	v	NOUN
ejpam-4069	252	7	(	(	PUNCT
ejpam-4069	252	8	g[h])\c	g[h])\c	VERB
ejpam-4069	252	9	is	be	AUX
ejpam-4069	252	10	an	an	DET
ejpam-4069	252	11	independent	independent	ADJ
ejpam-4069	252	12	set	set	NOUN
ejpam-4069	252	13	.	.	PUNCT
ejpam-4069	253	1	finally	finally	ADV
ejpam-4069	253	2	,	,	PUNCT
ejpam-4069	253	3	we	we	PRON
ejpam-4069	253	4	show	show	VERB
ejpam-4069	253	5	that	that	SCONJ
ejpam-4069	253	6	c	c	PROPN
ejpam-4069	253	7	is	be	AUX
ejpam-4069	253	8	a	a	DET
ejpam-4069	253	9	hop	hop	NOUN
ejpam-4069	253	10	dominating	dominating	NOUN
ejpam-4069	253	11	set	set	NOUN
ejpam-4069	253	12	.	.	PUNCT
ejpam-4069	254	1	let	let	VERB
ejpam-4069	254	2	(	(	PUNCT
ejpam-4069	254	3	x	x	NOUN
ejpam-4069	254	4	,	,	PUNCT
ejpam-4069	254	5	y	y	NOUN
ejpam-4069	254	6	)	)	PUNCT
ejpam-4069	254	7	∈	∈	NOUN
ejpam-4069	254	8	v	v	NOUN
ejpam-4069	254	9	(	(	PUNCT
ejpam-4069	254	10	g[h])\c	g[h])\c	PROPN
ejpam-4069	254	11	.	.	PUNCT
ejpam-4069	255	1	then	then	ADV
ejpam-4069	255	2	y	y	PROPN
ejpam-4069	255	3	/∈	/∈	PUNCT
ejpam-4069	256	1	tx	tx	PROPN
ejpam-4069	256	2	,	,	PUNCT
ejpam-4069	256	3	that	that	ADV
ejpam-4069	256	4	is	is	ADV
ejpam-4069	256	5	,	,	PUNCT
ejpam-4069	256	6	v	v	INTJ
ejpam-4069	256	7	(	(	PUNCT
ejpam-4069	256	8	h	h	NOUN
ejpam-4069	256	9	)	)	PUNCT
ejpam-4069	256	10	̸=	̸=	PROPN
ejpam-4069	256	11	tx	tx	PROPN
ejpam-4069	256	12	.	.	PUNCT
ejpam-4069	256	13	suppose	suppose	VERB
ejpam-4069	256	14	degg(x	degg(x	NOUN
ejpam-4069	256	15	)	)	PUNCT
ejpam-4069	256	16	=	=	PUNCT
ejpam-4069	256	17	n−	n−	NOUN
ejpam-4069	256	18	1	1	NUM
ejpam-4069	256	19	.	.	PUNCT
ejpam-4069	257	1	by	by	ADP
ejpam-4069	257	2	(	(	PUNCT
ejpam-4069	257	3	ii	ii	NOUN
ejpam-4069	257	4	)	)	PUNCT
ejpam-4069	257	5	,	,	PUNCT
ejpam-4069	257	6	tx	tx	PROPN
ejpam-4069	257	7	is	be	AUX
ejpam-4069	257	8	a	a	DET
ejpam-4069	257	9	strictly	strictly	ADV
ejpam-4069	257	10	co	co	ADJ
ejpam-4069	257	11	-	-	ADJ
ejpam-4069	257	12	independent	independent	ADJ
ejpam-4069	257	13	set	set	NOUN
ejpam-4069	257	14	of	of	ADP
ejpam-4069	257	15	h.	h.	PROPN
ejpam-4069	257	16	since	since	SCONJ
ejpam-4069	257	17	y	y	PROPN
ejpam-4069	257	18	/∈	/∈	PUNCT
ejpam-4069	258	1	tx	tx	PROPN
ejpam-4069	258	2	,	,	PUNCT
ejpam-4069	258	3	nh(y	nh(y	ADV
ejpam-4069	258	4	)	)	PUNCT
ejpam-4069	258	5	∩	∩	NOUN
ejpam-4069	258	6	tx	tx	PROPN
ejpam-4069	258	7	̸=	̸=	PROPN
ejpam-4069	258	8	tx	tx	PROPN
ejpam-4069	258	9	.	.	PUNCT
ejpam-4069	259	1	this	this	PRON
ejpam-4069	259	2	implies	imply	VERB
ejpam-4069	259	3	that	that	SCONJ
ejpam-4069	259	4	there	there	PRON
ejpam-4069	259	5	exists	exist	VERB
ejpam-4069	259	6	a	a	DET
ejpam-4069	259	7	∈	∈	NOUN
ejpam-4069	259	8	tx	tx	ADP
ejpam-4069	259	9	such	such	ADJ
ejpam-4069	259	10	that	that	DET
ejpam-4069	259	11	dh(a	dh(a	NOUN
ejpam-4069	259	12	,	,	PUNCT
ejpam-4069	259	13	y	y	NOUN
ejpam-4069	259	14	)	)	PUNCT
ejpam-4069	259	15	=	=	SYM
ejpam-4069	260	1	2	2	X
ejpam-4069	260	2	.	.	X
ejpam-4069	260	3	hence	hence	ADV
ejpam-4069	260	4	,	,	PUNCT
ejpam-4069	260	5	(	(	PUNCT
ejpam-4069	260	6	x	x	X
ejpam-4069	260	7	,	,	PUNCT
ejpam-4069	260	8	a	a	PRON
ejpam-4069	260	9	)	)	PUNCT
ejpam-4069	260	10	∈	∈	PROPN
ejpam-4069	260	11	c	c	PROPN
ejpam-4069	260	12	and	and	CCONJ
ejpam-4069	260	13	dg[h]((x	dg[h]((x	PROPN
ejpam-4069	260	14	,	,	PUNCT
ejpam-4069	260	15	y	y	PROPN
ejpam-4069	260	16	)	)	PUNCT
ejpam-4069	260	17	,	,	PUNCT
ejpam-4069	260	18	(	(	PUNCT
ejpam-4069	260	19	x	x	X
ejpam-4069	260	20	,	,	PUNCT
ejpam-4069	260	21	a	a	NOUN
ejpam-4069	260	22	)	)	PUNCT
ejpam-4069	260	23	)	)	PUNCT
ejpam-4069	261	1	=	=	SYM
ejpam-4069	261	2	2	2	X
ejpam-4069	261	3	.	.	PUNCT
ejpam-4069	261	4	suppose	suppose	VERB
ejpam-4069	261	5	degg(x	degg(x	NOUN
ejpam-4069	261	6	)	)	PUNCT
ejpam-4069	261	7	<	<	X
ejpam-4069	261	8	n	n	CCONJ
ejpam-4069	262	1	−	−	PROPN
ejpam-4069	262	2	1	1	NUM
ejpam-4069	262	3	.	.	PUNCT
ejpam-4069	263	1	then	then	ADV
ejpam-4069	263	2	a	a	DET
ejpam-4069	263	3	vertex	vertex	NOUN
ejpam-4069	263	4	z	z	NOUN
ejpam-4069	263	5	∈	∈	PROPN
ejpam-4069	263	6	v	v	ADP
ejpam-4069	263	7	(	(	PUNCT
ejpam-4069	263	8	g)\ng(x	g)\ng(x	NOUN
ejpam-4069	263	9	)	)	PUNCT
ejpam-4069	263	10	exists	exist	VERB
ejpam-4069	263	11	.	.	PUNCT
ejpam-4069	264	1	choose	choose	VERB
ejpam-4069	264	2	z	z	NOUN
ejpam-4069	264	3	such	such	ADJ
ejpam-4069	264	4	that	that	PRON
ejpam-4069	264	5	dg(x	dg(x	NOUN
ejpam-4069	264	6	,	,	PUNCT
ejpam-4069	264	7	z	z	NOUN
ejpam-4069	264	8	)	)	PUNCT
ejpam-4069	264	9	=	=	SYM
ejpam-4069	264	10	2	2	X
ejpam-4069	264	11	.	.	PUNCT
ejpam-4069	265	1	since	since	SCONJ
ejpam-4069	265	2	s	s	PART
ejpam-4069	265	3	=	=	SYM
ejpam-4069	265	4	v	v	PROPN
ejpam-4069	265	5	(	(	PUNCT
ejpam-4069	265	6	g	g	NOUN
ejpam-4069	265	7	)	)	PUNCT
ejpam-4069	265	8	by	by	ADP
ejpam-4069	265	9	(	(	PUNCT
ejpam-4069	265	10	i	i	NOUN
ejpam-4069	265	11	)	)	PUNCT
ejpam-4069	265	12	,	,	PUNCT
ejpam-4069	265	13	there	there	PRON
ejpam-4069	265	14	exists	exist	VERB
ejpam-4069	265	15	b	b	PROPN
ejpam-4069	265	16	∈	∈	PROPN
ejpam-4069	265	17	tz	tz	NOUN
ejpam-4069	265	18	,	,	PUNCT
ejpam-4069	265	19	that	that	ADV
ejpam-4069	265	20	is	is	ADV
ejpam-4069	265	21	,	,	PUNCT
ejpam-4069	265	22	(	(	PUNCT
ejpam-4069	265	23	z	z	X
ejpam-4069	265	24	,	,	PUNCT
ejpam-4069	265	25	b	b	NOUN
ejpam-4069	265	26	)	)	PUNCT
ejpam-4069	265	27	∈	∈	PROPN
ejpam-4069	265	28	c.	c.	NOUN
ejpam-4069	265	29	it	it	PRON
ejpam-4069	265	30	follows	follow	VERB
ejpam-4069	265	31	that	that	PRON
ejpam-4069	265	32	dg[h]((x	dg[h]((x	PROPN
ejpam-4069	265	33	,	,	PUNCT
ejpam-4069	265	34	y	y	PROPN
ejpam-4069	265	35	)	)	PUNCT
ejpam-4069	265	36	,	,	PUNCT
ejpam-4069	265	37	(	(	PUNCT
ejpam-4069	265	38	z	z	X
ejpam-4069	265	39	,	,	PUNCT
ejpam-4069	265	40	b	b	NOUN
ejpam-4069	265	41	)	)	PUNCT
ejpam-4069	265	42	)	)	PUNCT
ejpam-4069	266	1	=	=	SYM
ejpam-4069	266	2	2	2	X
ejpam-4069	266	3	.	.	X
ejpam-4069	266	4	therefore	therefore	ADV
ejpam-4069	266	5	,	,	PUNCT
ejpam-4069	266	6	c	c	PROPN
ejpam-4069	266	7	is	be	AUX
ejpam-4069	266	8	a	a	DET
ejpam-4069	266	9	hop	hop	NOUN
ejpam-4069	266	10	dominating	dominating	NOUN
ejpam-4069	266	11	set	set	NOUN
ejpam-4069	266	12	of	of	ADP
ejpam-4069	266	13	g[h	g[h	PROPN
ejpam-4069	266	14	]	]	PUNCT
ejpam-4069	266	15	.	.	PUNCT
ejpam-4069	267	1	accordingly	accordingly	ADV
ejpam-4069	267	2	,	,	PUNCT
ejpam-4069	267	3	c	c	PROPN
ejpam-4069	267	4	is	be	AUX
ejpam-4069	267	5	a	a	DET
ejpam-4069	267	6	connected	connected	ADJ
ejpam-4069	267	7	co	co	NOUN
ejpam-4069	267	8	-	-	ADJ
ejpam-4069	267	9	independent	independent	ADJ
ejpam-4069	267	10	hop	hop	NOUN
ejpam-4069	267	11	dominating	dominating	NOUN
ejpam-4069	267	12	set	set	NOUN
ejpam-4069	267	13	of	of	ADP
ejpam-4069	267	14	g[h	g[h	PROPN
ejpam-4069	267	15	]	]	PUNCT
ejpam-4069	267	16	.	.	PUNCT
ejpam-4069	268	1	corollary	corollary	ADJ
ejpam-4069	268	2	3	3	X
ejpam-4069	268	3	.	.	PUNCT
ejpam-4069	269	1	let	let	VERB
ejpam-4069	269	2	g	g	NOUN
ejpam-4069	269	3	be	be	AUX
ejpam-4069	269	4	any	any	DET
ejpam-4069	269	5	connected	connected	ADJ
ejpam-4069	269	6	noncomplete	noncomplete	ADJ
ejpam-4069	269	7	graph	graph	NOUN
ejpam-4069	269	8	of	of	ADP
ejpam-4069	269	9	order	order	NOUN
ejpam-4069	269	10	m	m	VERB
ejpam-4069	269	11	and	and	CCONJ
ejpam-4069	269	12	h	h	NOUN
ejpam-4069	269	13	be	be	VERB
ejpam-4069	269	14	any	any	DET
ejpam-4069	269	15	nontrivial	nontrivial	ADJ
ejpam-4069	269	16	connected	connect	VERB
ejpam-4069	269	17	graph	graph	NOUN
ejpam-4069	269	18	of	of	ADP
ejpam-4069	269	19	order	order	NOUN
ejpam-4069	269	20	n.	n.	NOUN
ejpam-4069	269	21	then	then	ADV
ejpam-4069	269	22	γch	γch	VERB
ejpam-4069	269	23	,	,	PUNCT
ejpam-4069	269	24	coi(g[h	coi(g[h	NUM
ejpam-4069	269	25	]	]	PUNCT
ejpam-4069	269	26	)	)	PUNCT
ejpam-4069	269	27	=	=	SYM
ejpam-4069	269	28	m(n−	m(n−	NOUN
ejpam-4069	269	29	β(h	β(h	NOUN
ejpam-4069	269	30	)	)	PUNCT
ejpam-4069	269	31	)	)	PUNCT
ejpam-4069	270	1	+	+	CCONJ
ejpam-4069	271	1	r(g)β(h	r(g)β(h	X
ejpam-4069	271	2	)	)	PUNCT
ejpam-4069	271	3	,	,	PUNCT
ejpam-4069	271	4	where	where	SCONJ
ejpam-4069	271	5	r(g	r(g	ADJ
ejpam-4069	271	6	)	)	PUNCT
ejpam-4069	271	7	=	=	SYM
ejpam-4069	272	1	min{|d|	min{|d|	NOUN
ejpam-4069	272	2	:	:	PUNCT
ejpam-4069	272	3	v	v	X
ejpam-4069	272	4	(	(	PUNCT
ejpam-4069	272	5	g)\d	g)\d	NOUN
ejpam-4069	272	6	is	be	AUX
ejpam-4069	272	7	an	an	DET
ejpam-4069	272	8	independent	independent	ADJ
ejpam-4069	272	9	set	set	NOUN
ejpam-4069	272	10	}	}	PUNCT
ejpam-4069	272	11	and	and	CCONJ
ejpam-4069	272	12	β(h	β(h	NUM
ejpam-4069	272	13	)	)	PUNCT
ejpam-4069	272	14	is	be	AUX
ejpam-4069	272	15	an	an	DET
ejpam-4069	272	16	independence	independence	NOUN
ejpam-4069	272	17	number	number	NOUN
ejpam-4069	272	18	of	of	ADP
ejpam-4069	272	19	h.	h.	NOUN
ejpam-4069	272	20	proof	proof	NOUN
ejpam-4069	272	21	:	:	PUNCT
ejpam-4069	272	22	let	let	VERB
ejpam-4069	272	23	r(g	r(g	NUM
ejpam-4069	272	24	)	)	PUNCT
ejpam-4069	273	1	=	=	SYM
ejpam-4069	273	2	min{|d|	min{|d|	NOUN
ejpam-4069	273	3	:	:	PUNCT
ejpam-4069	273	4	v	v	X
ejpam-4069	273	5	(	(	PUNCT
ejpam-4069	273	6	g)\d	g)\d	NOUN
ejpam-4069	273	7	is	be	AUX
ejpam-4069	273	8	an	an	DET
ejpam-4069	273	9	independent	independent	ADJ
ejpam-4069	273	10	set	set	NOUN
ejpam-4069	273	11	}	}	PUNCT
ejpam-4069	273	12	.	.	PUNCT
ejpam-4069	274	1	let	let	VERB
ejpam-4069	274	2	d0	d0	NOUN
ejpam-4069	274	3	⊆	⊆	NUM
ejpam-4069	274	4	v	v	NOUN
ejpam-4069	274	5	(	(	PUNCT
ejpam-4069	274	6	g	g	NOUN
ejpam-4069	274	7	)	)	PUNCT
ejpam-4069	274	8	such	such	ADJ
ejpam-4069	274	9	that	that	DET
ejpam-4069	274	10	v	v	NOUN
ejpam-4069	274	11	(	(	PUNCT
ejpam-4069	274	12	g)\d0	g)\d0	PROPN
ejpam-4069	274	13	is	be	AUX
ejpam-4069	274	14	an	an	DET
ejpam-4069	274	15	independent	independent	ADJ
ejpam-4069	274	16	set	set	NOUN
ejpam-4069	274	17	and	and	CCONJ
ejpam-4069	274	18	|d0|	|d0|	NOUN
ejpam-4069	274	19	=	=	SYM
ejpam-4069	274	20	r(g	r(g	NUM
ejpam-4069	274	21	)	)	PUNCT
ejpam-4069	274	22	.	.	PUNCT
ejpam-4069	275	1	let	let	VERB
ejpam-4069	275	2	t	t	NOUN
ejpam-4069	275	3	be	be	AUX
ejpam-4069	275	4	a	a	DET
ejpam-4069	275	5	β	β	NOUN
ejpam-4069	275	6	-	-	VERB
ejpam-4069	275	7	set	set	NOUN
ejpam-4069	275	8	of	of	ADP
ejpam-4069	275	9	h.	h.	NOUN
ejpam-4069	275	10	let	let	VERB
ejpam-4069	275	11	tx	tx	VERB
ejpam-4069	275	12	=	=	SYM
ejpam-4069	275	13	v	v	X
ejpam-4069	275	14	(	(	PUNCT
ejpam-4069	275	15	h)\t	h)\t	NOUN
ejpam-4069	275	16	for	for	ADP
ejpam-4069	275	17	each	each	DET
ejpam-4069	275	18	x	x	SYM
ejpam-4069	275	19	∈	∈	PROPN
ejpam-4069	275	20	v	v	NOUN
ejpam-4069	275	21	(	(	PUNCT
ejpam-4069	275	22	g)\d0	g)\d0	PROPN
ejpam-4069	275	23	and	and	CCONJ
ejpam-4069	275	24	let	let	VERB
ejpam-4069	275	25	ty	ty	INTJ
ejpam-4069	275	26	=	=	NOUN
ejpam-4069	275	27	v	v	ADJ
ejpam-4069	275	28	(	(	PUNCT
ejpam-4069	275	29	h	h	NOUN
ejpam-4069	275	30	)	)	PUNCT
ejpam-4069	275	31	for	for	ADP
ejpam-4069	275	32	each	each	DET
ejpam-4069	275	33	y	y	PROPN
ejpam-4069	275	34	∈	∈	PROPN
ejpam-4069	275	35	d0	d0	NOUN
ejpam-4069	275	36	.	.	PUNCT
ejpam-4069	276	1	then	then	ADV
ejpam-4069	276	2	c	c	X
ejpam-4069	277	1	=	=	PUNCT
ejpam-4069	277	2	⋃	⋃	PROPN
ejpam-4069	277	3	x∈v	x∈v	PROPN
ejpam-4069	277	4	(	(	PUNCT
ejpam-4069	277	5	g	g	NOUN
ejpam-4069	277	6	)	)	PUNCT
ejpam-4069	278	1	[	[	X
ejpam-4069	278	2	{	{	PUNCT
ejpam-4069	278	3	x	x	NOUN
ejpam-4069	278	4	}	}	PUNCT
ejpam-4069	278	5	×	×	NOUN
ejpam-4069	278	6	tx	tx	NOUN
ejpam-4069	278	7	]	]	X
ejpam-4069	278	8	=	=	PUNCT
ejpam-4069	278	9	⋃	⋃	NOUN
ejpam-4069	278	10	y∈d0	y∈d0	NOUN
ejpam-4069	278	11	(	(	PUNCT
ejpam-4069	278	12	{	{	PUNCT
ejpam-4069	278	13	y	y	NOUN
ejpam-4069	278	14	}	}	PUNCT
ejpam-4069	278	15	×	×	NOUN
ejpam-4069	278	16	ty	ty	INTJ
ejpam-4069	278	17	)	)	PUNCT
ejpam-4069	278	18	∪	∪	ADP
ejpam-4069	278	19			PROPN
ejpam-4069	278	20	⋃	⋃	PROPN
ejpam-4069	278	21	x∈v	x∈v	PROPN
ejpam-4069	278	22	(	(	PUNCT
ejpam-4069	278	23	g)\d0	g)\d0	PROPN
ejpam-4069	278	24	[	[	X
ejpam-4069	278	25	{	{	PUNCT
ejpam-4069	278	26	x	x	NOUN
ejpam-4069	278	27	}	}	PUNCT
ejpam-4069	278	28	×	×	PROPN
ejpam-4069	278	29	tx	tx	PROPN
ejpam-4069	278	30	]	]	X
ejpam-4069	278	31			PROPN
ejpam-4069	278	32	is	be	AUX
ejpam-4069	278	33	a	a	DET
ejpam-4069	278	34	connected	connected	ADJ
ejpam-4069	278	35	co	co	NOUN
ejpam-4069	278	36	-	-	ADJ
ejpam-4069	278	37	independent	independent	ADJ
ejpam-4069	278	38	hop	hop	NOUN
ejpam-4069	278	39	dominating	dominating	NOUN
ejpam-4069	278	40	set	set	NOUN
ejpam-4069	278	41	of	of	ADP
ejpam-4069	278	42	g[h	g[h	PROPN
ejpam-4069	278	43	]	]	PUNCT
ejpam-4069	278	44	,	,	PUNCT
ejpam-4069	278	45	by	by	ADP
ejpam-4069	278	46	theorem	theorem	NOUN
ejpam-4069	278	47	5	5	NUM
ejpam-4069	278	48	.	.	PUNCT
ejpam-4069	279	1	hence	hence	ADV
ejpam-4069	279	2	,	,	PUNCT
ejpam-4069	279	3	γch	γch	NOUN
ejpam-4069	279	4	,	,	PUNCT
ejpam-4069	279	5	coi(g[h	coi(g[h	NUM
ejpam-4069	279	6	]	]	PUNCT
ejpam-4069	279	7	)	)	PUNCT
ejpam-4069	279	8	≤	≤	NOUN
ejpam-4069	279	9	|c|	|c|	PROPN
ejpam-4069	279	10	=	=	SYM
ejpam-4069	279	11	nr(g	nr(g	X
ejpam-4069	279	12	)	)	PUNCT
ejpam-4069	280	1	+	+	CCONJ
ejpam-4069	280	2	(	(	PUNCT
ejpam-4069	280	3	m−	m−	PROPN
ejpam-4069	280	4	r(g))(n−	r(g))(n−	VERB
ejpam-4069	280	5	β(h	β(h	NOUN
ejpam-4069	280	6	)	)	PUNCT
ejpam-4069	280	7	)	)	PUNCT
ejpam-4069	281	1	=	=	SYM
ejpam-4069	281	2	nr(g	nr(g	X
ejpam-4069	281	3	)	)	PUNCT
ejpam-4069	282	1	+	+	NOUN
ejpam-4069	282	2	mn−mβ(h)−	mn−mβ(h)−	PROPN
ejpam-4069	282	3	nr(g	nr(g	PUNCT
ejpam-4069	282	4	)	)	PUNCT
ejpam-4069	282	5	+	+	CCONJ
ejpam-4069	282	6	r(g)β(h	r(g)β(h	X
ejpam-4069	282	7	)	)	PUNCT
ejpam-4069	282	8	=	=	SYM
ejpam-4069	282	9	mn−mβ(h	mn−mβ(h	PROPN
ejpam-4069	282	10	)	)	PUNCT
ejpam-4069	282	11	+	+	NUM
ejpam-4069	282	12	r(g)β(h	r(g)β(h	NOUN
ejpam-4069	282	13	)	)	PUNCT
ejpam-4069	282	14	=	=	SYM
ejpam-4069	282	15	m(n−	m(n−	NOUN
ejpam-4069	282	16	β(h	β(h	NOUN
ejpam-4069	282	17	)	)	PUNCT
ejpam-4069	282	18	)	)	PUNCT
ejpam-4069	283	1	+	+	CCONJ
ejpam-4069	283	2	r(g)β(h	r(g)β(h	X
ejpam-4069	283	3	)	)	PUNCT
ejpam-4069	283	4	γc	γc	PROPN
ejpam-4069	283	5	,	,	PUNCT
ejpam-4069	283	6	coi(g[h	coi(g[h	NUM
ejpam-4069	283	7	]	]	PUNCT
ejpam-4069	283	8	)	)	PUNCT
ejpam-4069	283	9	≤	≤	NUM
ejpam-4069	283	10	m(n−	m(n−	NOUN
ejpam-4069	283	11	β(h	β(h	NOUN
ejpam-4069	283	12	)	)	PUNCT
ejpam-4069	283	13	)	)	PUNCT
ejpam-4069	284	1	+	+	CCONJ
ejpam-4069	284	2	r(g)β(h	r(g)β(h	NOUN
ejpam-4069	284	3	)	)	PUNCT
ejpam-4069	284	4	.	.	PUNCT
ejpam-4069	285	1	s.	s.	PROPN
ejpam-4069	285	2	nanding	nanding	PROPN
ejpam-4069	285	3	,	,	PUNCT
ejpam-4069	285	4	h.	h.	PROPN
ejpam-4069	285	5	rara	rara	PROPN
ejpam-4069	285	6	/	/	SYM
ejpam-4069	285	7	eur	eur	PROPN
ejpam-4069	285	8	.	.	PUNCT
ejpam-4069	286	1	j.	j.	PROPN
ejpam-4069	286	2	pure	pure	PROPN
ejpam-4069	286	3	appl	appl	PROPN
ejpam-4069	286	4	.	.	PROPN
ejpam-4069	286	5	math	math	PROPN
ejpam-4069	286	6	,	,	PUNCT
ejpam-4069	286	7	14	14	NUM
ejpam-4069	286	8	(	(	PUNCT
ejpam-4069	286	9	4	4	NUM
ejpam-4069	286	10	)	)	PUNCT
ejpam-4069	286	11	(	(	PUNCT
ejpam-4069	286	12	2021	2021	NUM
ejpam-4069	286	13	)	)	PUNCT
ejpam-4069	286	14	,	,	PUNCT
ejpam-4069	286	15	1226	1226	NUM
ejpam-4069	286	16	-	-	SYM
ejpam-4069	286	17	1236	1236	NUM
ejpam-4069	286	18	1234	1234	NUM
ejpam-4069	286	19	let	let	VERB
ejpam-4069	286	20	c0	c0	PROPN
ejpam-4069	286	21	=	=	PUNCT
ejpam-4069	286	22	⋃	⋃	PROPN
ejpam-4069	286	23	x∈v	x∈v	PROPN
ejpam-4069	286	24	(	(	PUNCT
ejpam-4069	286	25	g	g	NOUN
ejpam-4069	286	26	)	)	PUNCT
ejpam-4069	287	1	[	[	X
ejpam-4069	287	2	{	{	PUNCT
ejpam-4069	287	3	x}×rx	x}×rx	X
ejpam-4069	287	4	]	]	X
ejpam-4069	287	5	be	be	VERB
ejpam-4069	287	6	a	a	DET
ejpam-4069	287	7	γch	γch	NOUN
ejpam-4069	287	8	,	,	PUNCT
ejpam-4069	287	9	coi	coi	NOUN
ejpam-4069	287	10	-	-	PUNCT
ejpam-4069	287	11	set	set	NOUN
ejpam-4069	287	12	of	of	ADP
ejpam-4069	287	13	g[h	g[h	NOUN
ejpam-4069	287	14	]	]	PUNCT
ejpam-4069	287	15	.	.	PUNCT
ejpam-4069	288	1	let	let	VERB
ejpam-4069	288	2	d	d	NOUN
ejpam-4069	288	3	=	=	PRON
ejpam-4069	288	4	{	{	PUNCT
ejpam-4069	288	5	x	x	PROPN
ejpam-4069	288	6	∈	∈	PROPN
ejpam-4069	288	7	v	v	NOUN
ejpam-4069	288	8	(	(	PUNCT
ejpam-4069	288	9	g	g	NOUN
ejpam-4069	288	10	)	)	PUNCT
ejpam-4069	288	11	:	:	PUNCT
ejpam-4069	288	12	rx	rx	VERB
ejpam-4069	288	13	=	=	SYM
ejpam-4069	288	14	v	v	ADJ
ejpam-4069	288	15	(	(	PUNCT
ejpam-4069	288	16	h	h	NOUN
ejpam-4069	288	17	)	)	PUNCT
ejpam-4069	288	18	}	}	PUNCT
ejpam-4069	288	19	.	.	PUNCT
ejpam-4069	289	1	then	then	ADV
ejpam-4069	289	2	v	v	X
ejpam-4069	289	3	(	(	PUNCT
ejpam-4069	289	4	g)\d	g)\d	NOUN
ejpam-4069	289	5	is	be	AUX
ejpam-4069	289	6	an	an	DET
ejpam-4069	289	7	independent	independent	ADJ
ejpam-4069	289	8	set	set	NOUN
ejpam-4069	289	9	of	of	ADP
ejpam-4069	289	10	g.	g.	PROPN
ejpam-4069	289	11	then	then	ADV
ejpam-4069	289	12	c0	c0	PROPN
ejpam-4069	289	13	=	=	PUNCT
ejpam-4069	289	14	(	(	PUNCT
ejpam-4069	289	15	⋃	⋃	PROPN
ejpam-4069	289	16	x∈d	x∈d	NOUN
ejpam-4069	289	17	rx	rx	VERB
ejpam-4069	289	18	)	)	PUNCT
ejpam-4069	289	19	∪	∪	ADP
ejpam-4069	289	20			PROPN
ejpam-4069	289	21	⋃	⋃	PROPN
ejpam-4069	289	22	x∈v	x∈v	PROPN
ejpam-4069	289	23	(	(	PUNCT
ejpam-4069	289	24	g)\d	g)\d	NOUN
ejpam-4069	289	25	tx	tx	PROPN
ejpam-4069	289	26			PROPN
ejpam-4069	289	27	.	.	PUNCT
ejpam-4069	290	1	moreover	moreover	ADV
ejpam-4069	290	2	,	,	PUNCT
ejpam-4069	290	3	γch	γch	NOUN
ejpam-4069	290	4	,	,	PUNCT
ejpam-4069	290	5	coi(g[h	coi(g[h	NUM
ejpam-4069	290	6	]	]	PUNCT
ejpam-4069	290	7	)	)	PUNCT
ejpam-4069	290	8	=	=	SYM
ejpam-4069	290	9	|c0|	|c0|	NOUN
ejpam-4069	290	10	=	=	NOUN
ejpam-4069	290	11	n|d|+	n|d|+	VERB
ejpam-4069	290	12	∑	∑	PROPN
ejpam-4069	290	13	x∈v	x∈v	PROPN
ejpam-4069	290	14	(	(	PUNCT
ejpam-4069	290	15	g)\d	g)\d	NOUN
ejpam-4069	290	16	|tx|	|tx|	NOUN
ejpam-4069	290	17	.	.	PUNCT
ejpam-4069	291	1	since	since	SCONJ
ejpam-4069	291	2	v	v	NOUN
ejpam-4069	291	3	(	(	PUNCT
ejpam-4069	291	4	h)\tx	h)\tx	PROPN
ejpam-4069	291	5	is	be	AUX
ejpam-4069	291	6	an	an	DET
ejpam-4069	291	7	independent	independent	ADJ
ejpam-4069	291	8	set	set	NOUN
ejpam-4069	291	9	of	of	ADP
ejpam-4069	291	10	h	h	NOUN
ejpam-4069	291	11	for	for	ADP
ejpam-4069	291	12	each	each	DET
ejpam-4069	291	13	x	x	SYM
ejpam-4069	291	14	∈	∈	PROPN
ejpam-4069	291	15	v	v	NOUN
ejpam-4069	291	16	(	(	PUNCT
ejpam-4069	291	17	g)\d	g)\d	NOUN
ejpam-4069	291	18	,	,	PUNCT
ejpam-4069	291	19	it	it	PRON
ejpam-4069	291	20	follows	follow	VERB
ejpam-4069	291	21	that	that	SCONJ
ejpam-4069	291	22	|v	|v	PROPN
ejpam-4069	291	23	(	(	PUNCT
ejpam-4069	291	24	h)\tx|	h)\tx|	NOUN
ejpam-4069	291	25	≤	≤	ADJ
ejpam-4069	291	26	β(h	β(h	NOUN
ejpam-4069	291	27	)	)	PUNCT
ejpam-4069	291	28	for	for	ADP
ejpam-4069	291	29	each	each	DET
ejpam-4069	291	30	x	x	SYM
ejpam-4069	291	31	∈	∈	PROPN
ejpam-4069	291	32	v	v	NOUN
ejpam-4069	291	33	(	(	PUNCT
ejpam-4069	291	34	g)\d	g)\d	NOUN
ejpam-4069	291	35	.	.	PUNCT
ejpam-4069	292	1	thus	thus	ADV
ejpam-4069	292	2	,	,	PUNCT
ejpam-4069	292	3	|v	|v	PROPN
ejpam-4069	292	4	(	(	PUNCT
ejpam-4069	292	5	h)\tx|	h)\tx|	X
ejpam-4069	292	6	=	=	PUNCT
ejpam-4069	292	7	|v	|v	PROPN
ejpam-4069	292	8	(	(	PUNCT
ejpam-4069	292	9	h)|	h)|	NOUN
ejpam-4069	292	10	−	−	NOUN
ejpam-4069	292	11	|tx|	|tx|	NOUN
ejpam-4069	292	12	≤	≤	NOUN
ejpam-4069	292	13	β(h	β(h	NOUN
ejpam-4069	292	14	)	)	PUNCT
ejpam-4069	292	15	.	.	PUNCT
ejpam-4069	293	1	hence	hence	ADV
ejpam-4069	293	2	|tx|	|tx|	NOUN
ejpam-4069	293	3	≥	≥	NOUN
ejpam-4069	293	4	n−	n−	PROPN
ejpam-4069	293	5	β(h	β(h	NOUN
ejpam-4069	293	6	)	)	PUNCT
ejpam-4069	293	7	.	.	PUNCT
ejpam-4069	294	1	therefore	therefore	ADV
ejpam-4069	294	2	,	,	PUNCT
ejpam-4069	294	3	γch	γch	NOUN
ejpam-4069	294	4	,	,	PUNCT
ejpam-4069	294	5	coi(g[h	coi(g[h	NUM
ejpam-4069	294	6	]	]	PUNCT
ejpam-4069	294	7	)	)	PUNCT
ejpam-4069	294	8	=	=	SYM
ejpam-4069	294	9	|c0|	|c0|	NOUN
ejpam-4069	294	10	=	=	PUNCT
ejpam-4069	294	11	n|d|+	n|d|+	VERB
ejpam-4069	294	12	|v	|v	X
ejpam-4069	294	13	(	(	PUNCT
ejpam-4069	294	14	g)\d|	g)\d|	NOUN
ejpam-4069	294	15	|tx|	|tx|	NOUN
ejpam-4069	294	16	=	=	PUNCT
ejpam-4069	294	17	n|d|+	n|d|+	PROPN
ejpam-4069	294	18	(	(	PUNCT
ejpam-4069	294	19	|v	|v	X
ejpam-4069	294	20	(	(	PUNCT
ejpam-4069	294	21	g)−	g)−	PROPN
ejpam-4069	294	22	|d|	|d|	PROPN
ejpam-4069	294	23	)	)	PUNCT
ejpam-4069	294	24	|tx|	|tx|	NOUN
ejpam-4069	294	25	≥	≥	NOUN
ejpam-4069	294	26	n|d|+	n|d|+	PROPN
ejpam-4069	294	27	(	(	PUNCT
ejpam-4069	294	28	m−	m−	PROPN
ejpam-4069	294	29	|d|)(n−	|d|)(n−	PROPN
ejpam-4069	294	30	β(h	β(h	PROPN
ejpam-4069	294	31	)	)	PUNCT
ejpam-4069	294	32	)	)	PUNCT
ejpam-4069	295	1	=	=	PRON
ejpam-4069	295	2	n|d|+mn−mβ(h)−	n|d|+mn−mβ(h)−	NOUN
ejpam-4069	295	3	n|d|+	n|d|+	PROPN
ejpam-4069	295	4	|d|β(h	|d|β(h	PROPN
ejpam-4069	295	5	)	)	PUNCT
ejpam-4069	295	6	=	=	SYM
ejpam-4069	295	7	m(n−	m(n−	NOUN
ejpam-4069	295	8	β(h	β(h	NOUN
ejpam-4069	295	9	)	)	PUNCT
ejpam-4069	295	10	)	)	PUNCT
ejpam-4069	296	1	+	+	X
ejpam-4069	296	2	|d|β(h	|d|β(h	NUM
ejpam-4069	296	3	)	)	PUNCT
ejpam-4069	296	4	=	=	SYM
ejpam-4069	296	5	m(n−	m(n−	NOUN
ejpam-4069	296	6	β(h	β(h	NOUN
ejpam-4069	296	7	)	)	PUNCT
ejpam-4069	296	8	)	)	PUNCT
ejpam-4069	297	1	+	+	CCONJ
ejpam-4069	297	2	r(g)β(h	r(g)β(h	X
ejpam-4069	297	3	)	)	PUNCT
ejpam-4069	297	4	γc	γc	PROPN
ejpam-4069	297	5	,	,	PUNCT
ejpam-4069	297	6	coi(g[h	coi(g[h	NUM
ejpam-4069	297	7	]	]	PUNCT
ejpam-4069	297	8	)	)	PUNCT
ejpam-4069	297	9	≥	≥	NOUN
ejpam-4069	297	10	m(n−	m(n−	NOUN
ejpam-4069	297	11	β(h	β(h	NOUN
ejpam-4069	297	12	)	)	PUNCT
ejpam-4069	297	13	)	)	PUNCT
ejpam-4069	298	1	+	+	CCONJ
ejpam-4069	298	2	r(g)β(h	r(g)β(h	NOUN
ejpam-4069	298	3	)	)	PUNCT
ejpam-4069	298	4	,	,	PUNCT
ejpam-4069	298	5	therefore	therefore	ADV
ejpam-4069	298	6	,	,	PUNCT
ejpam-4069	298	7	γc	γc	NOUN
ejpam-4069	298	8	,	,	PUNCT
ejpam-4069	298	9	coi(g[h	coi(g[h	NUM
ejpam-4069	298	10	]	]	PUNCT
ejpam-4069	298	11	)	)	PUNCT
ejpam-4069	298	12	=	=	SYM
ejpam-4069	298	13	m(n−	m(n−	NOUN
ejpam-4069	298	14	β(h	β(h	NOUN
ejpam-4069	298	15	)	)	PUNCT
ejpam-4069	298	16	)	)	PUNCT
ejpam-4069	299	1	+	+	CCONJ
ejpam-4069	299	2	r(g)β(h	r(g)β(h	NOUN
ejpam-4069	299	3	)	)	PUNCT
ejpam-4069	299	4	.	.	PUNCT
ejpam-4069	300	1	corollary	corollary	ADJ
ejpam-4069	300	2	4	4	NUM
ejpam-4069	300	3	.	.	PUNCT
ejpam-4069	301	1	let	let	VERB
ejpam-4069	301	2	h	h	NOUN
ejpam-4069	301	3	be	be	AUX
ejpam-4069	301	4	any	any	DET
ejpam-4069	301	5	nontrivial	nontrivial	ADJ
ejpam-4069	301	6	connected	connect	VERB
ejpam-4069	301	7	graph	graph	NOUN
ejpam-4069	301	8	of	of	ADP
ejpam-4069	301	9	orderm	orderm	NOUN
ejpam-4069	301	10	.	.	PUNCT
ejpam-4069	302	1	then	then	ADV
ejpam-4069	302	2	γch	γch	VERB
ejpam-4069	302	3	,	,	PUNCT
ejpam-4069	302	4	coi(kn[h	coi(kn[h	PROPN
ejpam-4069	302	5	]	]	PUNCT
ejpam-4069	302	6	)	)	PUNCT
ejpam-4069	302	7	=	=	SYM
ejpam-4069	302	8	m(n−	m(n−	NOUN
ejpam-4069	302	9	1	1	NUM
ejpam-4069	302	10	)	)	PUNCT
ejpam-4069	302	11	+	+	NUM
ejpam-4069	302	12	sci(h	sci(h	NOUN
ejpam-4069	302	13	)	)	PUNCT
ejpam-4069	302	14	.	.	PUNCT
ejpam-4069	303	1	proof	proof	NOUN
ejpam-4069	303	2	:	:	PUNCT
ejpam-4069	303	3	let	let	VERB
ejpam-4069	303	4	t	t	NOUN
ejpam-4069	303	5	be	be	AUX
ejpam-4069	303	6	an	an	DET
ejpam-4069	303	7	sci	sci	PROPN
ejpam-4069	303	8	-	-	PUNCT
ejpam-4069	303	9	set	set	NOUN
ejpam-4069	303	10	of	of	ADP
ejpam-4069	303	11	h.	h.	PROPN
ejpam-4069	303	12	let	let	VERB
ejpam-4069	303	13	v	v	ADP
ejpam-4069	303	14	∈	∈	PROPN
ejpam-4069	303	15	v	v	NOUN
ejpam-4069	303	16	(	(	PUNCT
ejpam-4069	303	17	kn	kn	PROPN
ejpam-4069	303	18	)	)	PUNCT
ejpam-4069	303	19	and	and	CCONJ
ejpam-4069	303	20	tv	tv	NOUN
ejpam-4069	303	21	=	=	SYM
ejpam-4069	303	22	t	t	PROPN
ejpam-4069	303	23	.	.	PUNCT
ejpam-4069	304	1	by	by	ADP
ejpam-4069	304	2	theorem	theorem	NOUN
ejpam-4069	304	3	5	5	NUM
ejpam-4069	304	4	,	,	PUNCT
ejpam-4069	304	5	c	c	NOUN
ejpam-4069	304	6	=	=	SYM
ejpam-4069	304	7	⋃	⋃	VERB
ejpam-4069	304	8	y∈v	y∈v	NOUN
ejpam-4069	304	9	(	(	PUNCT
ejpam-4069	304	10	kn)\{v	kn)\{v	NOUN
ejpam-4069	304	11	}	}	PUNCT
ejpam-4069	304	12	(	(	PUNCT
ejpam-4069	304	13	{	{	PUNCT
ejpam-4069	304	14	y}×ty)∪	y}×ty)∪	X
ejpam-4069	304	15	(	(	PUNCT
ejpam-4069	304	16	{	{	PUNCT
ejpam-4069	304	17	v}×tv	v}×tv	NOUN
ejpam-4069	304	18	)	)	PUNCT
ejpam-4069	304	19	is	be	AUX
ejpam-4069	304	20	a	a	DET
ejpam-4069	304	21	connected	connected	ADJ
ejpam-4069	304	22	co	co	NOUN
ejpam-4069	304	23	-	-	ADJ
ejpam-4069	304	24	independent	independent	ADJ
ejpam-4069	304	25	hop	hop	NOUN
ejpam-4069	304	26	dominating	dominating	NOUN
ejpam-4069	304	27	set	set	NOUN
ejpam-4069	304	28	of	of	ADP
ejpam-4069	304	29	kn[h	kn[h	PROPN
ejpam-4069	304	30	]	]	PUNCT
ejpam-4069	304	31	.	.	PUNCT
ejpam-4069	305	1	since	since	SCONJ
ejpam-4069	305	2	y	y	PROPN
ejpam-4069	305	3	∈	∈	PROPN
ejpam-4069	305	4	nkn(v	nkn(v	PROPN
ejpam-4069	305	5	)	)	PUNCT
ejpam-4069	305	6	for	for	ADP
ejpam-4069	305	7	each	each	DET
ejpam-4069	305	8	y	y	PROPN
ejpam-4069	305	9	∈	∈	PROPN
ejpam-4069	305	10	v	v	PROPN
ejpam-4069	305	11	(	(	PUNCT
ejpam-4069	305	12	kn)\{v	kn)\{v	NOUN
ejpam-4069	305	13	}	}	PUNCT
ejpam-4069	305	14	,	,	PUNCT
ejpam-4069	305	15	ty	ty	INTJ
ejpam-4069	305	16	=	=	SYM
ejpam-4069	305	17	v	v	NOUN
ejpam-4069	305	18	(	(	PUNCT
ejpam-4069	305	19	h	h	NOUN
ejpam-4069	305	20	)	)	PUNCT
ejpam-4069	305	21	.	.	PUNCT
ejpam-4069	306	1	thus	thus	ADV
ejpam-4069	306	2	,	,	PUNCT
ejpam-4069	306	3	γch	γch	NOUN
ejpam-4069	306	4	,	,	PUNCT
ejpam-4069	306	5	coi(kn[h	coi(kn[h	PROPN
ejpam-4069	306	6	]	]	X
ejpam-4069	306	7	)	)	PUNCT
ejpam-4069	306	8	≤	≤	NUM
ejpam-4069	306	9	|c|	|c|	PROPN
ejpam-4069	306	10	=	=	PUNCT
ejpam-4069	306	11	(	(	PUNCT
ejpam-4069	306	12	n−	n−	NOUN
ejpam-4069	306	13	1)|ty|+	1)|ty|+	X
ejpam-4069	306	14	|tv|	|tv|	NUM
ejpam-4069	306	15	=	=	PUNCT
ejpam-4069	306	16	(	(	PUNCT
ejpam-4069	306	17	n−	n−	NOUN
ejpam-4069	306	18	1)m+	1)m+	NUM
ejpam-4069	306	19	|t	|t	VERB
ejpam-4069	306	20	|	|	ADV
ejpam-4069	306	21	=	=	PUNCT
ejpam-4069	306	22	(	(	PUNCT
ejpam-4069	306	23	n−	n−	NOUN
ejpam-4069	306	24	1)m+	1)m+	NUM
ejpam-4069	306	25	sci(h	sci(h	NOUN
ejpam-4069	306	26	)	)	PUNCT
ejpam-4069	306	27	.	.	PUNCT
ejpam-4069	307	1	let	let	VERB
ejpam-4069	307	2	co	co	VERB
ejpam-4069	307	3	=	=	VERB
ejpam-4069	307	4	⋃	⋃	PROPN
ejpam-4069	307	5	x∈v	x∈v	PROPN
ejpam-4069	307	6	(	(	PUNCT
ejpam-4069	307	7	kn	kn	PROPN
ejpam-4069	307	8	)	)	PUNCT
ejpam-4069	307	9	(	(	PUNCT
ejpam-4069	307	10	{	{	PUNCT
ejpam-4069	307	11	x	x	NOUN
ejpam-4069	307	12	}	}	PUNCT
ejpam-4069	307	13	×	×	NOUN
ejpam-4069	307	14	rx	rx	NOUN
ejpam-4069	307	15	)	)	PUNCT
ejpam-4069	307	16	be	be	AUX
ejpam-4069	307	17	a	a	DET
ejpam-4069	307	18	γch	γch	NOUN
ejpam-4069	307	19	,	,	PUNCT
ejpam-4069	307	20	coi	coi	NOUN
ejpam-4069	307	21	-	-	PUNCT
ejpam-4069	307	22	set	set	NOUN
ejpam-4069	307	23	of	of	ADP
ejpam-4069	307	24	kn[h	kn[h	PROPN
ejpam-4069	307	25	]	]	PUNCT
ejpam-4069	307	26	.	.	PUNCT
ejpam-4069	308	1	since	since	SCONJ
ejpam-4069	308	2	degkn(x	degkn(x	PROPN
ejpam-4069	308	3	)	)	PUNCT
ejpam-4069	308	4	=	=	SYM
ejpam-4069	308	5	n	n	CCONJ
ejpam-4069	308	6	−	−	NUM
ejpam-4069	308	7	1	1	NUM
ejpam-4069	308	8	for	for	ADP
ejpam-4069	308	9	each	each	DET
ejpam-4069	308	10	x	x	SYM
ejpam-4069	308	11	∈	∈	PROPN
ejpam-4069	308	12	v	v	X
ejpam-4069	308	13	(	(	PUNCT
ejpam-4069	308	14	kn	kn	PROPN
ejpam-4069	308	15	)	)	PUNCT
ejpam-4069	308	16	,	,	PUNCT
ejpam-4069	308	17	by	by	ADP
ejpam-4069	308	18	theorem	theorem	NOUN
ejpam-4069	308	19	5	5	NUM
ejpam-4069	308	20	,	,	PUNCT
ejpam-4069	308	21	ry	ry	NOUN
ejpam-4069	308	22	=	=	PROPN
ejpam-4069	308	23	t	t	PROPN
ejpam-4069	308	24	where	where	SCONJ
ejpam-4069	308	25	t	t	PROPN
ejpam-4069	308	26	is	be	AUX
ejpam-4069	308	27	a	a	DET
ejpam-4069	308	28	strictly	strictly	ADV
ejpam-4069	308	29	co	co	ADJ
ejpam-4069	308	30	-	-	ADJ
ejpam-4069	308	31	independent	independent	ADJ
ejpam-4069	308	32	set	set	NOUN
ejpam-4069	308	33	of	of	ADP
ejpam-4069	308	34	h	h	NOUN
ejpam-4069	308	35	for	for	ADP
ejpam-4069	308	36	a	a	DET
ejpam-4069	308	37	unique	unique	ADJ
ejpam-4069	308	38	y	y	PROPN
ejpam-4069	308	39	∈	∈	PROPN
ejpam-4069	308	40	v	v	PROPN
ejpam-4069	308	41	(	(	PUNCT
ejpam-4069	308	42	kn	kn	PROPN
ejpam-4069	308	43	)	)	PUNCT
ejpam-4069	308	44	and	and	CCONJ
ejpam-4069	308	45	rx	rx	VERB
ejpam-4069	308	46	=	=	NOUN
ejpam-4069	308	47	v	v	ADJ
ejpam-4069	308	48	(	(	PUNCT
ejpam-4069	308	49	h	h	NOUN
ejpam-4069	308	50	)	)	PUNCT
ejpam-4069	308	51	for	for	ADP
ejpam-4069	308	52	all	all	DET
ejpam-4069	308	53	x	x	SYM
ejpam-4069	308	54	∈	∈	PROPN
ejpam-4069	308	55	v	v	X
ejpam-4069	308	56	(	(	PUNCT
ejpam-4069	308	57	kn)\{y	kn)\{y	PROPN
ejpam-4069	308	58	}	}	PUNCT
ejpam-4069	308	59	.	.	PUNCT
ejpam-4069	309	1	hence	hence	ADV
ejpam-4069	309	2	,	,	PUNCT
ejpam-4069	309	3	co	co	X
ejpam-4069	309	4	=	=	PUNCT
ejpam-4069	309	5	(	(	PUNCT
ejpam-4069	309	6	{	{	PUNCT
ejpam-4069	309	7	y	y	NOUN
ejpam-4069	309	8	}	}	PUNCT
ejpam-4069	309	9	×ry	×ry	PROPN
ejpam-4069	309	10	)	)	PUNCT
ejpam-4069	309	11	∪	∪	NOUN
ejpam-4069	309	12	(	(	PUNCT
ejpam-4069	309	13	⋃	⋃	PROPN
ejpam-4069	309	14	x∈v	x∈v	PROPN
ejpam-4069	309	15	(	(	PUNCT
ejpam-4069	309	16	kn)\{y	kn)\{y	PROPN
ejpam-4069	309	17	}	}	PUNCT
ejpam-4069	309	18	(	(	PUNCT
ejpam-4069	309	19	{	{	PUNCT
ejpam-4069	309	20	x	x	NOUN
ejpam-4069	309	21	}	}	PUNCT
ejpam-4069	309	22	×rx	×rx	PROPN
ejpam-4069	309	23	)	)	PUNCT
ejpam-4069	309	24	and	and	CCONJ
ejpam-4069	309	25	γch	γch	NOUN
ejpam-4069	309	26	,	,	PUNCT
ejpam-4069	309	27	coi(kn[h	coi(kn[h	PROPN
ejpam-4069	309	28	]	]	PUNCT
ejpam-4069	309	29	)	)	PUNCT
ejpam-4069	309	30	=	=	SYM
ejpam-4069	309	31	|co|	|co|	PROPN
ejpam-4069	309	32	references	reference	NOUN
ejpam-4069	309	33	1235	1235	NUM
ejpam-4069	309	34	=	=	SYM
ejpam-4069	309	35	|ry|+	|ry|+	NOUN
ejpam-4069	309	36	(	(	PUNCT
ejpam-4069	309	37	n−	n−	NOUN
ejpam-4069	309	38	1)|rx|	1)|rx|	NUM
ejpam-4069	309	39	=	=	PUNCT
ejpam-4069	309	40	|t	|t	PROPN
ejpam-4069	309	41	|+	|+	NOUN
ejpam-4069	309	42	(	(	PUNCT
ejpam-4069	309	43	n−	n−	NOUN
ejpam-4069	309	44	1)|v	1)|v	NUM
ejpam-4069	309	45	(	(	PUNCT
ejpam-4069	309	46	h)|	h)|	PROPN
ejpam-4069	309	47	≥	≥	NUM
ejpam-4069	309	48	sci(h	sci(h	PROPN
ejpam-4069	309	49	)	)	PUNCT
ejpam-4069	310	1	+	+	CCONJ
ejpam-4069	310	2	(	(	PUNCT
ejpam-4069	310	3	n−	n−	NOUN
ejpam-4069	310	4	1)m	1)m	NUM
ejpam-4069	310	5	.	.	PUNCT
ejpam-4069	311	1	therefore	therefore	ADV
ejpam-4069	311	2	,	,	PUNCT
ejpam-4069	311	3	γch	γch	X
ejpam-4069	311	4	,	,	PUNCT
ejpam-4069	311	5	coi(kn[h	coi(kn[h	PROPN
ejpam-4069	311	6	]	]	PUNCT
ejpam-4069	311	7	)	)	PUNCT
ejpam-4069	311	8	=	=	SYM
ejpam-4069	311	9	m(n−	m(n−	NOUN
ejpam-4069	311	10	1	1	NUM
ejpam-4069	311	11	)	)	PUNCT
ejpam-4069	311	12	+	+	NUM
ejpam-4069	311	13	sci(h	sci(h	NOUN
ejpam-4069	311	14	)	)	PUNCT
ejpam-4069	311	15	.	.	PUNCT
ejpam-4069	312	1	acknowledgements	acknowledgement	NOUN
ejpam-4069	312	2	this	this	DET
ejpam-4069	312	3	research	research	NOUN
ejpam-4069	312	4	is	be	AUX
ejpam-4069	312	5	funded	fund	VERB
ejpam-4069	312	6	by	by	ADP
ejpam-4069	312	7	the	the	DET
ejpam-4069	312	8	department	department	PROPN
ejpam-4069	312	9	of	of	ADP
ejpam-4069	312	10	science	science	NOUN
ejpam-4069	312	11	and	and	CCONJ
ejpam-4069	312	12	technology	technology	NOUN
ejpam-4069	312	13	accelerated	accelerate	VERB
ejpam-4069	312	14	science	science	NOUN
ejpam-4069	312	15	and	and	CCONJ
ejpam-4069	312	16	technology	technology	NOUN
ejpam-4069	312	17	human	human	ADJ
ejpam-4069	312	18	resource	resource	NOUN
ejpam-4069	312	19	development	development	NOUN
ejpam-4069	312	20	program	program	NOUN
ejpam-4069	312	21	(	(	PUNCT
ejpam-4069	312	22	dost	dost	NOUN
ejpam-4069	312	23	-	-	PUNCT
ejpam-4069	312	24	asthrdp	asthrdp	NOUN
ejpam-4069	312	25	)	)	PUNCT
ejpam-4069	312	26	,	,	PUNCT
ejpam-4069	312	27	philippines	philippine	NOUN
ejpam-4069	312	28	.	.	PUNCT
ejpam-4069	313	1	references	reference	NOUN
ejpam-4069	313	2	[	[	X
ejpam-4069	313	3	1	1	NUM
ejpam-4069	313	4	]	]	PUNCT
ejpam-4069	313	5	c.	c.	PROPN
ejpam-4069	313	6	berge	berge	PROPN
ejpam-4069	313	7	.	.	PUNCT
ejpam-4069	314	1	theorie	theorie	PROPN
ejpam-4069	314	2	des	des	PROPN
ejpam-4069	314	3	graphes	graphes	PROPN
ejpam-4069	314	4	et	et	PROPN
ejpam-4069	314	5	ses	ses	PROPN
ejpam-4069	314	6	applications	application	NOUN
ejpam-4069	314	7	.	.	PUNCT
ejpam-4069	315	1	metheun	metheun	NOUN
ejpam-4069	315	2	and	and	CCONJ
ejpam-4069	315	3	wiley	wiley	PROPN
ejpam-4069	315	4	,	,	PUNCT
ejpam-4069	315	5	london	london	PROPN
ejpam-4069	315	6	and	and	CCONJ
ejpam-4069	315	7	new	new	PROPN
ejpam-4069	315	8	york	york	PROPN
ejpam-4069	315	9	,	,	PUNCT
ejpam-4069	315	10	1962	1962	NUM
ejpam-4069	315	11	.	.	PUNCT
ejpam-4069	316	1	[	[	X
ejpam-4069	316	2	2	2	NUM
ejpam-4069	316	3	]	]	X
ejpam-4069	316	4	r.	r.	NOUN
ejpam-4069	316	5	detalla	detalla	PROPN
ejpam-4069	316	6	and	and	CCONJ
ejpam-4069	316	7	h.	h.	PROPN
ejpam-4069	316	8	rara	rara	PROPN
ejpam-4069	316	9	.	.	PUNCT
ejpam-4069	317	1	on	on	ADP
ejpam-4069	317	2	connected	connected	ADJ
ejpam-4069	317	3	co	co	ADJ
ejpam-4069	317	4	-	-	ADJ
ejpam-4069	317	5	independent	independent	ADJ
ejpam-4069	317	6	domination	domination	NOUN
ejpam-4069	317	7	in	in	ADP
ejpam-4069	317	8	the	the	DET
ejpam-4069	317	9	join	join	NOUN
ejpam-4069	317	10	and	and	CCONJ
ejpam-4069	317	11	corona	corona	NOUN
ejpam-4069	317	12	of	of	ADP
ejpam-4069	317	13	graphs	graph	NOUN
ejpam-4069	317	14	.	.	PUNCT
ejpam-4069	318	1	undergraduate	undergraduate	ADJ
ejpam-4069	318	2	thesis	thesis	NOUN
ejpam-4069	318	3	,	,	PUNCT
ejpam-4069	318	4	2019	2019	NUM
ejpam-4069	318	5	.	.	PUNCT
ejpam-4069	319	1	[	[	X
ejpam-4069	319	2	3	3	X
ejpam-4069	319	3	]	]	X
ejpam-4069	319	4	b.	b.	PROPN
ejpam-4069	319	5	gayathri	gayathri	PROPN
ejpam-4069	319	6	and	and	CCONJ
ejpam-4069	319	7	s.	s.	PROPN
ejpam-4069	319	8	kaspar	kaspar	PROPN
ejpam-4069	319	9	.	.	PUNCT
ejpam-4069	320	1	connected	connect	VERB
ejpam-4069	320	2	co	co	ADJ
ejpam-4069	320	3	-	-	ADJ
ejpam-4069	320	4	independent	independent	ADJ
ejpam-4069	320	5	domination	domination	NOUN
ejpam-4069	320	6	of	of	ADP
ejpam-4069	320	7	a	a	DET
ejpam-4069	320	8	graph	graph	NOUN
ejpam-4069	320	9	.	.	PUNCT
ejpam-4069	321	1	international	international	ADJ
ejpam-4069	321	2	journal	journal	PROPN
ejpam-4069	321	3	contemp	contemp	NOUN
ejpam-4069	321	4	.	.	PUNCT
ejpam-4069	322	1	mathematics	mathematic	NOUN
ejpam-4069	322	2	and	and	CCONJ
ejpam-4069	322	3	sciences	science	NOUN
ejpam-4069	322	4	,	,	PUNCT
ejpam-4069	322	5	6:423–429	6:423–429	PROPN
ejpam-4069	322	6	,	,	PUNCT
ejpam-4069	322	7	2011	2011	NUM
ejpam-4069	322	8	.	.	PUNCT
ejpam-4069	323	1	[	[	X
ejpam-4069	323	2	4	4	NUM
ejpam-4069	323	3	]	]	PUNCT
ejpam-4069	323	4	f.	f.	PROPN
ejpam-4069	323	5	harary	harary	PROPN
ejpam-4069	323	6	.	.	PUNCT
ejpam-4069	324	1	graph	graph	NOUN
ejpam-4069	324	2	theory	theory	NOUN
ejpam-4069	324	3	.	.	PUNCT
ejpam-4069	325	1	addison	addison	PROPN
ejpam-4069	325	2	-	-	PUNCT
ejpam-4069	325	3	wesley	wesley	PROPN
ejpam-4069	325	4	publishing	publishing	PROPN
ejpam-4069	325	5	company	company	NOUN
ejpam-4069	325	6	,	,	PUNCT
ejpam-4069	325	7	usa	usa	PROPN
ejpam-4069	325	8	,	,	PUNCT
ejpam-4069	325	9	1969	1969	NUM
ejpam-4069	325	10	.	.	PUNCT
ejpam-4069	326	1	[	[	X
ejpam-4069	326	2	5	5	X
ejpam-4069	326	3	]	]	PUNCT
ejpam-4069	326	4	w.	w.	PROPN
ejpam-4069	326	5	desormeaux	desormeaux	PROPN
ejpam-4069	326	6	,	,	PUNCT
ejpam-4069	326	7	t.	t.	PROPN
ejpam-4069	326	8	haynes	haynes	PROPN
ejpam-4069	326	9	and	and	CCONJ
ejpam-4069	326	10	m.a	m.a	PROPN
ejpam-4069	326	11	.	.	PROPN
ejpam-4069	326	12	henning	henning	PROPN
ejpam-4069	326	13	.	.	PUNCT
ejpam-4069	327	1	a	a	DET
ejpam-4069	327	2	note	note	NOUN
ejpam-4069	327	3	on	on	ADP
ejpam-4069	327	4	non	non	ADJ
ejpam-4069	327	5	-	-	ADJ
ejpam-4069	327	6	dominating	dominating	ADJ
ejpam-4069	327	7	set	set	VERB
ejpam-4069	327	8	partitions	partition	NOUN
ejpam-4069	327	9	in	in	ADP
ejpam-4069	327	10	graphs	graph	NOUN
ejpam-4069	327	11	.	.	PUNCT
ejpam-4069	328	1	networks	network	NOUN
ejpam-4069	328	2	,	,	PUNCT
ejpam-4069	328	3	pages	page	NOUN
ejpam-4069	328	4	1–8	1–8	NUM
ejpam-4069	328	5	,	,	PUNCT
ejpam-4069	328	6	2016	2016	NUM
ejpam-4069	328	7	.	.	PUNCT
ejpam-4069	329	1	[	[	X
ejpam-4069	329	2	6	6	NUM
ejpam-4069	329	3	]	]	SYM
ejpam-4069	329	4	i.	i.	PROPN
ejpam-4069	329	5	aniversario	aniversario	PROPN
ejpam-4069	329	6	m.	m.	PROPN
ejpam-4069	329	7	bonsocan	bonsocan	PROPN
ejpam-4069	329	8	.	.	PUNCT
ejpam-4069	330	1	on	on	ADP
ejpam-4069	330	2	connected	connected	ADJ
ejpam-4069	330	3	co	co	ADJ
ejpam-4069	330	4	-	-	ADJ
ejpam-4069	330	5	independent	independent	ADJ
ejpam-4069	330	6	domination	domination	NOUN
ejpam-4069	330	7	of	of	ADP
ejpam-4069	330	8	some	some	DET
ejpam-4069	330	9	graphs	graph	NOUN
ejpam-4069	330	10	.	.	PUNCT
ejpam-4069	331	1	undergraduate	undergraduate	ADJ
ejpam-4069	331	2	thesis	thesis	NOUN
ejpam-4069	331	3	,	,	PUNCT
ejpam-4069	331	4	2018	2018	NUM
ejpam-4069	331	5	.	.	PUNCT
ejpam-4069	332	1	[	[	X
ejpam-4069	332	2	7	7	X
ejpam-4069	332	3	]	]	X
ejpam-4069	332	4	s.	s.	PROPN
ejpam-4069	332	5	canoy	canoy	PROPN
ejpam-4069	332	6	,	,	PUNCT
ejpam-4069	332	7	r.	r.	NOUN
ejpam-4069	332	8	mollejon	mollejon	NOUN
ejpam-4069	332	9	and	and	CCONJ
ejpam-4069	332	10	j.	j.	PROPN
ejpam-4069	332	11	canoy	canoy	PROPN
ejpam-4069	332	12	.	.	PUNCT
ejpam-4069	333	1	hop	hop	PROPN
ejpam-4069	333	2	dominating	dominating	NOUN
ejpam-4069	333	3	sets	set	NOUN
ejpam-4069	333	4	in	in	ADP
ejpam-4069	333	5	graphs	graph	NOUN
ejpam-4069	333	6	under	under	ADP
ejpam-4069	333	7	binary	binary	ADJ
ejpam-4069	333	8	operations	operation	NOUN
ejpam-4069	333	9	.	.	PUNCT
ejpam-4069	334	1	european	european	ADJ
ejpam-4069	334	2	journal	journal	PROPN
ejpam-4069	334	3	of	of	ADP
ejpam-4069	334	4	pure	pure	ADJ
ejpam-4069	334	5	and	and	CCONJ
ejpam-4069	334	6	applied	applied	ADJ
ejpam-4069	334	7	mathematics	mathematic	NOUN
ejpam-4069	334	8	,	,	PUNCT
ejpam-4069	334	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4069	334	10	,	,	PUNCT
ejpam-4069	334	11	2019	2019	NUM
ejpam-4069	334	12	.	.	PUNCT
ejpam-4069	335	1	[	[	X
ejpam-4069	335	2	8	8	NUM
ejpam-4069	335	3	]	]	X
ejpam-4069	335	4	c.	c.	PROPN
ejpam-4069	335	5	natarajan	natarajan	PROPN
ejpam-4069	335	6	and	and	CCONJ
ejpam-4069	335	7	s.	s.	PROPN
ejpam-4069	335	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4069	335	9	.	.	PUNCT
ejpam-4069	336	1	hop	hop	PROPN
ejpam-4069	336	2	domination	domination	NOUN
ejpam-4069	336	3	in	in	ADP
ejpam-4069	336	4	graphs	graph	NOUN
ejpam-4069	336	5	-	-	PUNCT
ejpam-4069	336	6	ii	ii	NOUN
ejpam-4069	336	7	.	.	PUNCT
ejpam-4069	336	8	versita	versita	PROPN
ejpam-4069	336	9	,	,	PUNCT
ejpam-4069	336	10	23(2):187	23(2):187	NUM
ejpam-4069	336	11	–	–	PUNCT
ejpam-4069	336	12	199	199	NUM
ejpam-4069	336	13	,	,	PUNCT
ejpam-4069	336	14	2015	2015	NUM
ejpam-4069	336	15	.	.	PUNCT
ejpam-4069	337	1	[	[	X
ejpam-4069	337	2	9	9	NUM
ejpam-4069	337	3	]	]	PUNCT
ejpam-4069	337	4	s.	s.	PROPN
ejpam-4069	337	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4069	337	6	,	,	PUNCT
ejpam-4069	337	7	c.	c.	PROPN
ejpam-4069	337	8	natarajan	natarajan	PROPN
ejpam-4069	337	9	and	and	CCONJ
ejpam-4069	337	10	g.	g.	PROPN
ejpam-4069	337	11	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4069	337	12	.	.	PUNCT
ejpam-4069	338	1	a	a	DET
ejpam-4069	338	2	note	note	NOUN
ejpam-4069	338	3	on	on	ADP
ejpam-4069	338	4	hop	hop	NOUN
ejpam-4069	338	5	domination	domination	NOUN
ejpam-4069	338	6	number	number	NOUN
ejpam-4069	338	7	of	of	ADP
ejpam-4069	338	8	some	some	DET
ejpam-4069	338	9	special	special	ADJ
ejpam-4069	338	10	families	family	NOUN
ejpam-4069	338	11	of	of	ADP
ejpam-4069	338	12	graphs	graph	NOUN
ejpam-4069	338	13	.	.	PUNCT
ejpam-4069	339	1	international	international	ADJ
ejpam-4069	339	2	journal	journal	NOUN
ejpam-4069	339	3	of	of	ADP
ejpam-4069	339	4	pure	pure	ADJ
ejpam-4069	339	5	and	and	CCONJ
ejpam-4069	339	6	applied	applied	ADJ
ejpam-4069	339	7	mathematics	mathematic	NOUN
ejpam-4069	339	8	,	,	PUNCT
ejpam-4069	339	9	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4069	339	10	,	,	PUNCT
ejpam-4069	339	11	2018	2018	NUM
ejpam-4069	339	12	.	.	PUNCT
ejpam-4069	340	1	[	[	X
ejpam-4069	340	2	10	10	NUM
ejpam-4069	340	3	]	]	X
ejpam-4069	340	4	y.	y.	PROPN
ejpam-4069	340	5	pabilona	pabilona	PROPN
ejpam-4069	340	6	and	and	CCONJ
ejpam-4069	340	7	h.	h.	PROPN
ejpam-4069	340	8	rara	rara	PROPN
ejpam-4069	340	9	.	.	PUNCT
ejpam-4069	341	1	some	some	DET
ejpam-4069	341	2	variants	variant	NOUN
ejpam-4069	341	3	of	of	ADP
ejpam-4069	341	4	hop	hop	NOUN
ejpam-4069	341	5	domination	domination	NOUN
ejpam-4069	341	6	in	in	ADP
ejpam-4069	341	7	graphs	graph	NOUN
ejpam-4069	341	8	.	.	PUNCT
ejpam-4069	342	1	dissertation	dissertation	NOUN
ejpam-4069	342	2	,	,	PUNCT
ejpam-4069	342	3	2017	2017	NUM
ejpam-4069	342	4	.	.	PUNCT
ejpam-4069	343	1	[	[	X
ejpam-4069	343	2	11	11	NUM
ejpam-4069	343	3	]	]	X
ejpam-4069	343	4	y.	y.	NOUN
ejpam-4069	343	5	pabilona	pabilona	PROPN
ejpam-4069	343	6	and	and	CCONJ
ejpam-4069	343	7	h.	h.	PROPN
ejpam-4069	343	8	rara	rara	PROPN
ejpam-4069	343	9	.	.	PUNCT
ejpam-4069	344	1	connected	connect	VERB
ejpam-4069	344	2	hop	hop	NOUN
ejpam-4069	344	3	domination	domination	NOUN
ejpam-4069	344	4	in	in	ADP
ejpam-4069	344	5	graphs	graph	NOUN
ejpam-4069	344	6	under	under	ADP
ejpam-4069	344	7	some	some	DET
ejpam-4069	344	8	binary	binary	ADJ
ejpam-4069	344	9	operations	operation	NOUN
ejpam-4069	344	10	.	.	PUNCT
ejpam-4069	345	1	asian	asian	ADJ
ejpam-4069	345	2	-	-	PUNCT
ejpam-4069	345	3	european	european	ADJ
ejpam-4069	345	4	journal	journal	NOUN
ejpam-4069	345	5	of	of	ADP
ejpam-4069	345	6	mathematics	mathematic	NOUN
ejpam-4069	345	7	,	,	PUNCT
ejpam-4069	345	8	2018	2018	NUM
ejpam-4069	345	9	.	.	PUNCT
ejpam-4069	346	1	references	reference	NOUN
ejpam-4069	346	2	1236	1236	NUM
ejpam-4069	346	3	[	[	X
ejpam-4069	346	4	12	12	NUM
ejpam-4069	346	5	]	]	PUNCT
ejpam-4069	346	6	m.	m.	NOUN
ejpam-4069	346	7	perocho	perocho	NOUN
ejpam-4069	346	8	and	and	CCONJ
ejpam-4069	346	9	h.	h.	PROPN
ejpam-4069	346	10	rara	rara	PROPN
ejpam-4069	346	11	.	.	PUNCT
ejpam-4069	347	1	on	on	ADP
ejpam-4069	347	2	connected	connected	ADJ
ejpam-4069	347	3	co	co	ADJ
ejpam-4069	347	4	-	-	ADJ
ejpam-4069	347	5	independent	independent	ADJ
ejpam-4069	347	6	domination	domination	NOUN
ejpam-4069	347	7	in	in	ADP
ejpam-4069	347	8	lexicographic	lexicographic	ADJ
ejpam-4069	347	9	product	product	NOUN
ejpam-4069	347	10	of	of	ADP
ejpam-4069	347	11	graphs	graph	NOUN
ejpam-4069	347	12	.	.	PUNCT
ejpam-4069	348	1	undergraduate	undergraduate	ADJ
ejpam-4069	348	2	thesis	thesis	NOUN
ejpam-4069	348	3	,	,	PUNCT
ejpam-4069	348	4	2020	2020	NUM
ejpam-4069	348	5	.	.	PUNCT
ejpam-4069	349	1	[	[	X
ejpam-4069	349	2	13	13	NUM
ejpam-4069	349	3	]	]	X
ejpam-4069	349	4	g.	g.	NOUN
ejpam-4069	349	5	salasalan	salasalan	NOUN
ejpam-4069	349	6	and	and	CCONJ
ejpam-4069	349	7	s.	s.	PROPN
ejpam-4069	349	8	canoy	canoy	PROPN
ejpam-4069	349	9	jr	jr	PROPN
ejpam-4069	349	10	.	.	PUNCT
ejpam-4069	350	1	some	some	DET
ejpam-4069	350	2	related	relate	VERB
ejpam-4069	350	3	concepts	concept	NOUN
ejpam-4069	350	4	of	of	ADP
ejpam-4069	350	5	hop	hop	NOUN
ejpam-4069	350	6	domination	domination	NOUN
ejpam-4069	350	7	in	in	ADP
ejpam-4069	350	8	a	a	DET
ejpam-4069	350	9	graph	graph	NOUN
ejpam-4069	350	10	.	.	PUNCT
ejpam-4069	351	1	dissertation	dissertation	NOUN
ejpam-4069	351	2	,	,	PUNCT
ejpam-4069	351	3	2021	2021	NUM
ejpam-4069	351	4	.	.	PUNCT