id	sid	tid	token	lemma	pos
ejpam-3812	1	1	european	european	PROPN
ejpam-3812	1	2	journal	journal	PROPN
ejpam-3812	1	3	of	of	ADP
ejpam-3812	1	4	pure	pure	ADJ
ejpam-3812	1	5	and	and	CCONJ
ejpam-3812	1	6	applied	apply	VERB
ejpam-3812	1	7	mathematics	mathematic	NOUN
ejpam-3812	1	8	vol	vol	NOUN
ejpam-3812	1	9	.	.	PROPN
ejpam-3812	2	1	13	13	NUM
ejpam-3812	2	2	,	,	PUNCT
ejpam-3812	2	3	no	no	INTJ
ejpam-3812	2	4	.	.	NOUN
ejpam-3812	2	5	4	4	NUM
ejpam-3812	2	6	,	,	PUNCT
ejpam-3812	2	7	2020	2020	NUM
ejpam-3812	2	8	,	,	PUNCT
ejpam-3812	2	9	779	779	NUM
ejpam-3812	2	10	-	-	SYM
ejpam-3812	2	11	793	793	NUM
ejpam-3812	2	12	issn	issn	PROPN
ejpam-3812	2	13	1307	1307	NUM
ejpam-3812	2	14	-	-	SYM
ejpam-3812	2	15	5543	5543	NUM
ejpam-3812	2	16	–	–	PUNCT
ejpam-3812	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3812	2	18	published	publish	VERB
ejpam-3812	2	19	by	by	ADP
ejpam-3812	2	20	new	new	PROPN
ejpam-3812	2	21	york	york	PROPN
ejpam-3812	2	22	business	business	PROPN
ejpam-3812	2	23	global	global	PROPN
ejpam-3812	2	24	on	on	ADP
ejpam-3812	2	25	semitotal	semitotal	ADJ
ejpam-3812	2	26	k	k	ADJ
ejpam-3812	2	27	-	-	ADJ
ejpam-3812	2	28	fair	fair	ADJ
ejpam-3812	2	29	and	and	CCONJ
ejpam-3812	2	30	independent	independent	ADJ
ejpam-3812	2	31	k	k	ADJ
ejpam-3812	2	32	-	-	PUNCT
ejpam-3812	2	33	fair	fair	ADJ
ejpam-3812	2	34	domination	domination	NOUN
ejpam-3812	2	35	in	in	ADP
ejpam-3812	2	36	graphs	graph	NOUN
ejpam-3812	2	37	marivir	marivir	PROPN
ejpam-3812	2	38	m.	m.	PROPN
ejpam-3812	2	39	ortega1,∗	ortega1,∗	PROPN
ejpam-3812	2	40	,	,	PUNCT
ejpam-3812	2	41	rowena	rowena	PROPN
ejpam-3812	2	42	t.	t.	PROPN
ejpam-3812	2	43	isla1,2	isla1,2	PROPN
ejpam-3812	2	44	1	1	NUM
ejpam-3812	2	45	department	department	NOUN
ejpam-3812	2	46	of	of	ADP
ejpam-3812	2	47	mathematics	mathematic	NOUN
ejpam-3812	2	48	and	and	CCONJ
ejpam-3812	2	49	statistics	statistic	NOUN
ejpam-3812	2	50	,	,	PUNCT
ejpam-3812	2	51	college	college	NOUN
ejpam-3812	2	52	of	of	ADP
ejpam-3812	2	53	science	science	NOUN
ejpam-3812	2	54	and	and	CCONJ
ejpam-3812	2	55	mathematics	mathematic	NOUN
ejpam-3812	2	56	,	,	PUNCT
ejpam-3812	2	57	mindanao	mindanao	PROPN
ejpam-3812	2	58	state	state	PROPN
ejpam-3812	2	59	university	university	PROPN
ejpam-3812	2	60	-	-	PUNCT
ejpam-3812	2	61	iligan	iligan	PROPN
ejpam-3812	2	62	institute	institute	PROPN
ejpam-3812	2	63	of	of	ADP
ejpam-3812	2	64	technology	technology	PROPN
ejpam-3812	2	65	,	,	PUNCT
ejpam-3812	2	66	9200	9200	NUM
ejpam-3812	2	67	iligan	iligan	ADJ
ejpam-3812	2	68	city	city	NOUN
ejpam-3812	2	69	,	,	PUNCT
ejpam-3812	2	70	philippines	philippine	NOUN
ejpam-3812	2	71	2	2	NUM
ejpam-3812	2	72	center	center	NOUN
ejpam-3812	2	73	for	for	ADP
ejpam-3812	2	74	graph	graph	NOUN
ejpam-3812	2	75	theory	theory	NOUN
ejpam-3812	2	76	,	,	PUNCT
ejpam-3812	2	77	algebra	algebra	NOUN
ejpam-3812	2	78	,	,	PUNCT
ejpam-3812	2	79	and	and	CCONJ
ejpam-3812	2	80	analysis	analysis	NOUN
ejpam-3812	2	81	,	,	PUNCT
ejpam-3812	2	82	premier	premier	PROPN
ejpam-3812	2	83	research	research	PROPN
ejpam-3812	2	84	institute	institute	PROPN
ejpam-3812	2	85	of	of	ADP
ejpam-3812	2	86	science	science	NOUN
ejpam-3812	2	87	and	and	CCONJ
ejpam-3812	2	88	mathematics	mathematic	NOUN
ejpam-3812	2	89	,	,	PUNCT
ejpam-3812	2	90	mindanao	mindanao	PROPN
ejpam-3812	2	91	state	state	PROPN
ejpam-3812	2	92	university	university	PROPN
ejpam-3812	2	93	-	-	PUNCT
ejpam-3812	2	94	iligan	iligan	PROPN
ejpam-3812	2	95	institute	institute	PROPN
ejpam-3812	2	96	of	of	ADP
ejpam-3812	2	97	technology	technology	PROPN
ejpam-3812	2	98	,	,	PUNCT
ejpam-3812	2	99	9200	9200	NUM
ejpam-3812	2	100	iligan	iligan	ADJ
ejpam-3812	2	101	city	city	NOUN
ejpam-3812	2	102	,	,	PUNCT
ejpam-3812	2	103	philippines	philippine	NOUN
ejpam-3812	2	104	abstract	abstract	ADJ
ejpam-3812	2	105	.	.	PUNCT
ejpam-3812	3	1	in	in	ADP
ejpam-3812	3	2	this	this	DET
ejpam-3812	3	3	paper	paper	NOUN
ejpam-3812	3	4	,	,	PUNCT
ejpam-3812	3	5	we	we	PRON
ejpam-3812	3	6	introduce	introduce	VERB
ejpam-3812	3	7	and	and	CCONJ
ejpam-3812	3	8	investigate	investigate	VERB
ejpam-3812	3	9	the	the	DET
ejpam-3812	3	10	concepts	concept	NOUN
ejpam-3812	3	11	of	of	ADP
ejpam-3812	3	12	semitotal	semitotal	ADJ
ejpam-3812	3	13	k	k	ADJ
ejpam-3812	3	14	-	-	PUNCT
ejpam-3812	3	15	fair	fair	ADJ
ejpam-3812	3	16	domination	domination	NOUN
ejpam-3812	3	17	and	and	CCONJ
ejpam-3812	3	18	independent	independent	ADJ
ejpam-3812	3	19	k	k	ADJ
ejpam-3812	3	20	-	-	PUNCT
ejpam-3812	3	21	fair	fair	ADJ
ejpam-3812	3	22	domination	domination	NOUN
ejpam-3812	3	23	,	,	PUNCT
ejpam-3812	3	24	where	where	SCONJ
ejpam-3812	3	25	k	k	PROPN
ejpam-3812	3	26	is	be	AUX
ejpam-3812	3	27	a	a	DET
ejpam-3812	3	28	positive	positive	ADJ
ejpam-3812	3	29	integer	integer	NOUN
ejpam-3812	3	30	.	.	PUNCT
ejpam-3812	4	1	we	we	PRON
ejpam-3812	4	2	also	also	ADV
ejpam-3812	4	3	characterize	characterize	VERB
ejpam-3812	4	4	the	the	DET
ejpam-3812	4	5	semitotal	semitotal	ADJ
ejpam-3812	4	6	1	1	NUM
ejpam-3812	4	7	-	-	PUNCT
ejpam-3812	4	8	fair	fair	ADJ
ejpam-3812	4	9	dominating	dominating	NOUN
ejpam-3812	4	10	sets	set	NOUN
ejpam-3812	4	11	and	and	CCONJ
ejpam-3812	4	12	independent	independent	ADJ
ejpam-3812	4	13	k	k	ADJ
ejpam-3812	4	14	-	-	ADJ
ejpam-3812	4	15	fair	fair	ADJ
ejpam-3812	4	16	dominating	dominating	NOUN
ejpam-3812	4	17	sets	set	NOUN
ejpam-3812	4	18	in	in	ADP
ejpam-3812	4	19	the	the	DET
ejpam-3812	4	20	join	join	NOUN
ejpam-3812	4	21	,	,	PUNCT
ejpam-3812	4	22	corona	corona	PROPN
ejpam-3812	4	23	,	,	PUNCT
ejpam-3812	4	24	lexicographic	lexicographic	ADJ
ejpam-3812	4	25	product	product	NOUN
ejpam-3812	4	26	,	,	PUNCT
ejpam-3812	4	27	and	and	CCONJ
ejpam-3812	4	28	cartesian	cartesian	ADJ
ejpam-3812	4	29	product	product	NOUN
ejpam-3812	4	30	of	of	ADP
ejpam-3812	4	31	graphs	graph	NOUN
ejpam-3812	4	32	and	and	CCONJ
ejpam-3812	4	33	determine	determine	VERB
ejpam-3812	4	34	the	the	DET
ejpam-3812	4	35	exact	exact	ADJ
ejpam-3812	4	36	value	value	NOUN
ejpam-3812	4	37	or	or	CCONJ
ejpam-3812	4	38	sharp	sharp	ADJ
ejpam-3812	4	39	bounds	bound	NOUN
ejpam-3812	4	40	of	of	ADP
ejpam-3812	4	41	the	the	DET
ejpam-3812	4	42	corresponding	corresponding	ADJ
ejpam-3812	4	43	semitotal	semitotal	ADJ
ejpam-3812	4	44	1	1	NUM
ejpam-3812	4	45	-	-	PUNCT
ejpam-3812	4	46	fair	fair	ADJ
ejpam-3812	4	47	domination	domination	NOUN
ejpam-3812	4	48	number	number	NOUN
ejpam-3812	4	49	and	and	CCONJ
ejpam-3812	4	50	independent	independent	ADJ
ejpam-3812	4	51	k	k	ADJ
ejpam-3812	4	52	-	-	PUNCT
ejpam-3812	4	53	fair	fair	ADJ
ejpam-3812	4	54	domination	domination	NOUN
ejpam-3812	4	55	number	number	NOUN
ejpam-3812	4	56	.	.	PUNCT
ejpam-3812	5	1	2020	2020	NUM
ejpam-3812	5	2	mathematics	mathematic	NOUN
ejpam-3812	5	3	subject	subject	NOUN
ejpam-3812	5	4	classifications	classification	NOUN
ejpam-3812	5	5	:	:	PUNCT
ejpam-3812	5	6	05c69	05c69	NUM
ejpam-3812	5	7	,	,	PUNCT
ejpam-3812	5	8	05c76	05c76	DET
ejpam-3812	5	9	key	key	ADJ
ejpam-3812	5	10	words	word	NOUN
ejpam-3812	5	11	and	and	CCONJ
ejpam-3812	5	12	phrases	phrase	NOUN
ejpam-3812	5	13	:	:	PUNCT
ejpam-3812	5	14	semitotal	semitotal	ADJ
ejpam-3812	5	15	domination	domination	NOUN
ejpam-3812	5	16	,	,	PUNCT
ejpam-3812	5	17	independent	independent	ADJ
ejpam-3812	5	18	domination	domination	NOUN
ejpam-3812	5	19	,	,	PUNCT
ejpam-3812	5	20	k	k	ADJ
ejpam-3812	5	21	-	-	PUNCT
ejpam-3812	5	22	fair	fair	ADJ
ejpam-3812	5	23	domination	domination	NOUN
ejpam-3812	5	24	,	,	PUNCT
ejpam-3812	5	25	join	join	NOUN
ejpam-3812	5	26	,	,	PUNCT
ejpam-3812	5	27	corona	corona	PROPN
ejpam-3812	5	28	,	,	PUNCT
ejpam-3812	5	29	lexicographic	lexicographic	ADJ
ejpam-3812	5	30	product	product	NOUN
ejpam-3812	5	31	,	,	PUNCT
ejpam-3812	5	32	cartesian	cartesian	ADJ
ejpam-3812	5	33	product	product	NOUN
ejpam-3812	5	34	1	1	NUM
ejpam-3812	5	35	.	.	PUNCT
ejpam-3812	6	1	introduction	introduction	NOUN
ejpam-3812	6	2	let	let	VERB
ejpam-3812	6	3	g	g	NOUN
ejpam-3812	6	4	=	=	SYM
ejpam-3812	6	5	(	(	PUNCT
ejpam-3812	6	6	v	v	NOUN
ejpam-3812	6	7	(	(	PUNCT
ejpam-3812	6	8	g	g	NOUN
ejpam-3812	6	9	)	)	PUNCT
ejpam-3812	6	10	,	,	PUNCT
ejpam-3812	6	11	e(g	e(g	PROPN
ejpam-3812	6	12	)	)	PUNCT
ejpam-3812	6	13	)	)	PUNCT
ejpam-3812	6	14	be	be	AUX
ejpam-3812	6	15	a	a	DET
ejpam-3812	6	16	simple	simple	ADJ
ejpam-3812	6	17	graph	graph	NOUN
ejpam-3812	6	18	and	and	CCONJ
ejpam-3812	6	19	v	v	ADP
ejpam-3812	6	20	∈	∈	PROPN
ejpam-3812	6	21	v	v	NOUN
ejpam-3812	6	22	(	(	PUNCT
ejpam-3812	6	23	g	g	NOUN
ejpam-3812	6	24	)	)	PUNCT
ejpam-3812	6	25	.	.	PUNCT
ejpam-3812	7	1	the	the	DET
ejpam-3812	7	2	open	open	ADJ
ejpam-3812	7	3	neighborhood	neighborhood	NOUN
ejpam-3812	7	4	of	of	ADP
ejpam-3812	7	5	v	v	NOUN
ejpam-3812	7	6	in	in	ADP
ejpam-3812	7	7	g	g	PROPN
ejpam-3812	7	8	is	be	AUX
ejpam-3812	7	9	the	the	DET
ejpam-3812	7	10	set	set	NOUN
ejpam-3812	7	11	ng(v	ng(v	PUNCT
ejpam-3812	7	12	)	)	PUNCT
ejpam-3812	7	13	=	=	SYM
ejpam-3812	8	1	{	{	PUNCT
ejpam-3812	8	2	u	u	NOUN
ejpam-3812	8	3	∈	∈	PROPN
ejpam-3812	8	4	v	v	NOUN
ejpam-3812	8	5	(	(	PUNCT
ejpam-3812	8	6	g	g	NOUN
ejpam-3812	8	7	)	)	PUNCT
ejpam-3812	8	8	:	:	PUNCT
ejpam-3812	8	9	uv	uv	PROPN
ejpam-3812	8	10	∈	∈	PROPN
ejpam-3812	8	11	e(g	e(g	PROPN
ejpam-3812	8	12	)	)	PUNCT
ejpam-3812	8	13	}	}	PUNCT
ejpam-3812	8	14	and	and	CCONJ
ejpam-3812	8	15	the	the	DET
ejpam-3812	8	16	closed	closed	ADJ
ejpam-3812	8	17	neighborhood	neighborhood	NOUN
ejpam-3812	8	18	of	of	ADP
ejpam-3812	8	19	v	v	NOUN
ejpam-3812	8	20	is	be	AUX
ejpam-3812	8	21	the	the	DET
ejpam-3812	8	22	set	set	NOUN
ejpam-3812	8	23	ng[v	ng[v	NOUN
ejpam-3812	8	24	]	]	X
ejpam-3812	8	25	=	=	SYM
ejpam-3812	8	26	ng(v	ng(v	X
ejpam-3812	8	27	)	)	PUNCT
ejpam-3812	8	28	∪	∪	ADP
ejpam-3812	8	29	{	{	PUNCT
ejpam-3812	8	30	v	v	NOUN
ejpam-3812	8	31	}	}	PUNCT
ejpam-3812	8	32	.	.	PUNCT
ejpam-3812	9	1	for	for	ADP
ejpam-3812	9	2	x	x	SYM
ejpam-3812	9	3	⊆	⊆	NUM
ejpam-3812	9	4	v	v	ADP
ejpam-3812	9	5	(	(	PUNCT
ejpam-3812	9	6	g	g	NOUN
ejpam-3812	9	7	)	)	PUNCT
ejpam-3812	9	8	,	,	PUNCT
ejpam-3812	9	9	the	the	DET
ejpam-3812	9	10	open	open	ADJ
ejpam-3812	9	11	neighborhood	neighborhood	NOUN
ejpam-3812	9	12	of	of	ADP
ejpam-3812	9	13	x	x	PUNCT
ejpam-3812	9	14	in	in	ADP
ejpam-3812	9	15	g	g	PROPN
ejpam-3812	9	16	is	be	AUX
ejpam-3812	9	17	the	the	DET
ejpam-3812	9	18	set	set	NOUN
ejpam-3812	9	19	ng(x	ng(x	NUM
ejpam-3812	9	20	)	)	PUNCT
ejpam-3812	9	21	=	=	SYM
ejpam-3812	9	22	n(x	n(x	X
ejpam-3812	9	23	)	)	PUNCT
ejpam-3812	9	24	=	=	SYM
ejpam-3812	10	1	⋃	⋃	NOUN
ejpam-3812	10	2	v∈x	v∈x	NOUN
ejpam-3812	10	3	ng(v	ng(v	PUNCT
ejpam-3812	10	4	)	)	PUNCT
ejpam-3812	10	5	and	and	CCONJ
ejpam-3812	10	6	its	its	PRON
ejpam-3812	10	7	closed	closed	ADJ
ejpam-3812	10	8	neighborhood	neighborhood	NOUN
ejpam-3812	10	9	is	be	AUX
ejpam-3812	10	10	the	the	DET
ejpam-3812	10	11	the	the	DET
ejpam-3812	10	12	set	set	NOUN
ejpam-3812	10	13	ng[x	ng[x	PROPN
ejpam-3812	10	14	]	]	X
ejpam-3812	10	15	=	=	SYM
ejpam-3812	11	1	n	n	PROPN
ejpam-3812	11	2	[	[	X
ejpam-3812	11	3	x	x	X
ejpam-3812	11	4	]	]	X
ejpam-3812	11	5	=	=	SYM
ejpam-3812	11	6	n(x	n(x	X
ejpam-3812	11	7	)	)	PUNCT
ejpam-3812	11	8	∪	∪	ADP
ejpam-3812	11	9	x.	x.	NOUN
ejpam-3812	11	10	a	a	DET
ejpam-3812	11	11	set	set	NOUN
ejpam-3812	12	1	d	d	NOUN
ejpam-3812	12	2	⊆	⊆	NUM
ejpam-3812	12	3	v	v	ADP
ejpam-3812	12	4	(	(	PUNCT
ejpam-3812	12	5	g	g	NOUN
ejpam-3812	12	6	)	)	PUNCT
ejpam-3812	12	7	is	be	AUX
ejpam-3812	12	8	a	a	DET
ejpam-3812	12	9	dominating	dominating	NOUN
ejpam-3812	12	10	set	set	VERB
ejpam-3812	12	11	in	in	ADP
ejpam-3812	12	12	g	g	PROPN
ejpam-3812	12	13	if	if	SCONJ
ejpam-3812	12	14	for	for	ADP
ejpam-3812	12	15	every	every	PRON
ejpam-3812	12	16	v	v	NUM
ejpam-3812	12	17	∈	∈	NOUN
ejpam-3812	12	18	v	v	NOUN
ejpam-3812	12	19	(	(	PUNCT
ejpam-3812	12	20	g	g	NOUN
ejpam-3812	12	21	)	)	PUNCT
ejpam-3812	12	22	\	\	PUNCT
ejpam-3812	13	1	d	d	X
ejpam-3812	13	2	,	,	PUNCT
ejpam-3812	13	3	there	there	PRON
ejpam-3812	13	4	exists	exist	VERB
ejpam-3812	13	5	u	u	NOUN
ejpam-3812	13	6	∈	∈	PROPN
ejpam-3812	13	7	d	d	ADP
ejpam-3812	13	8	such	such	ADJ
ejpam-3812	13	9	that	that	DET
ejpam-3812	13	10	uv	uv	PROPN
ejpam-3812	13	11	∈	∈	PROPN
ejpam-3812	13	12	e(g	e(g	PROPN
ejpam-3812	13	13	)	)	PUNCT
ejpam-3812	13	14	,	,	PUNCT
ejpam-3812	13	15	that	that	ADV
ejpam-3812	13	16	is	is	ADV
ejpam-3812	13	17	,	,	PUNCT
ejpam-3812	13	18	n	n	PROPN
ejpam-3812	13	19	[	[	X
ejpam-3812	13	20	d	d	X
ejpam-3812	13	21	]	]	X
ejpam-3812	13	22	=	=	SYM
ejpam-3812	13	23	v	v	NOUN
ejpam-3812	13	24	(	(	PUNCT
ejpam-3812	13	25	g	g	NOUN
ejpam-3812	13	26	)	)	PUNCT
ejpam-3812	13	27	.	.	PUNCT
ejpam-3812	14	1	the	the	DET
ejpam-3812	14	2	minimum	minimum	ADJ
ejpam-3812	14	3	cardinality	cardinality	NOUN
ejpam-3812	14	4	of	of	ADP
ejpam-3812	14	5	a	a	DET
ejpam-3812	14	6	dominating	dominating	NOUN
ejpam-3812	14	7	set	set	NOUN
ejpam-3812	14	8	in	in	ADP
ejpam-3812	14	9	g	g	NOUN
ejpam-3812	14	10	,	,	PUNCT
ejpam-3812	14	11	denoted	denote	VERB
ejpam-3812	14	12	by	by	ADP
ejpam-3812	14	13	γ(g	γ(g	PROPN
ejpam-3812	14	14	)	)	PUNCT
ejpam-3812	14	15	,	,	PUNCT
ejpam-3812	14	16	is	be	AUX
ejpam-3812	14	17	the	the	DET
ejpam-3812	14	18	domination	domination	NOUN
ejpam-3812	14	19	number	number	NOUN
ejpam-3812	14	20	of	of	ADP
ejpam-3812	14	21	g.	g.	PROPN
ejpam-3812	14	22	any	any	DET
ejpam-3812	14	23	dominating	dominating	NOUN
ejpam-3812	14	24	set	set	VERB
ejpam-3812	14	25	in	in	ADP
ejpam-3812	14	26	g	g	PROPN
ejpam-3812	14	27	of	of	ADP
ejpam-3812	14	28	cardinality	cardinality	PROPN
ejpam-3812	14	29	γ(g	γ(g	PROPN
ejpam-3812	14	30	)	)	PUNCT
ejpam-3812	14	31	is	be	AUX
ejpam-3812	14	32	referred	refer	VERB
ejpam-3812	14	33	to	to	ADP
ejpam-3812	14	34	as	as	SCONJ
ejpam-3812	14	35	γ	γ	NOUN
ejpam-3812	14	36	-	-	PUNCT
ejpam-3812	14	37	set	set	NOUN
ejpam-3812	14	38	in	in	ADP
ejpam-3812	14	39	g.	g.	PROPN
ejpam-3812	14	40	the	the	DET
ejpam-3812	14	41	theory	theory	NOUN
ejpam-3812	14	42	of	of	ADP
ejpam-3812	14	43	independent	independent	ADJ
ejpam-3812	14	44	domination	domination	NOUN
ejpam-3812	14	45	was	be	AUX
ejpam-3812	14	46	formalized	formalize	VERB
ejpam-3812	14	47	by	by	ADP
ejpam-3812	14	48	berge	berge	NOUN
ejpam-3812	14	49	[	[	X
ejpam-3812	14	50	1	1	X
ejpam-3812	14	51	]	]	PUNCT
ejpam-3812	14	52	and	and	CCONJ
ejpam-3812	14	53	ore	ore	NOUN
ejpam-3812	14	54	[	[	X
ejpam-3812	14	55	9	9	NUM
ejpam-3812	14	56	]	]	PUNCT
ejpam-3812	14	57	in	in	ADP
ejpam-3812	14	58	1962	1962	NUM
ejpam-3812	14	59	.	.	PUNCT
ejpam-3812	15	1	the	the	DET
ejpam-3812	15	2	independent	independent	ADJ
ejpam-3812	15	3	domination	domination	NOUN
ejpam-3812	15	4	number	number	NOUN
ejpam-3812	15	5	and	and	CCONJ
ejpam-3812	15	6	the	the	DET
ejpam-3812	15	7	notation	notation	NOUN
ejpam-3812	15	8	i(g	i(g	ADV
ejpam-3812	15	9	)	)	PUNCT
ejpam-3812	15	10	were	be	AUX
ejpam-3812	15	11	introduced	introduce	VERB
ejpam-3812	15	12	by	by	ADP
ejpam-3812	15	13	cockayne	cockayne	NOUN
ejpam-3812	15	14	and	and	CCONJ
ejpam-3812	15	15	hedetnieme	hedetnieme	NOUN
ejpam-3812	15	16	[	[	X
ejpam-3812	15	17	2	2	NUM
ejpam-3812	15	18	]	]	PUNCT
ejpam-3812	15	19	.	.	PUNCT
ejpam-3812	16	1	let	let	VERB
ejpam-3812	16	2	g	g	PRON
ejpam-3812	16	3	be	be	AUX
ejpam-3812	16	4	a	a	DET
ejpam-3812	16	5	connected	connected	ADJ
ejpam-3812	16	6	graph	graph	NOUN
ejpam-3812	16	7	.	.	PUNCT
ejpam-3812	17	1	a	a	DET
ejpam-3812	17	2	dominating	dominating	NOUN
ejpam-3812	17	3	set	set	NOUN
ejpam-3812	17	4	s	s	NOUN
ejpam-3812	17	5	in	in	ADP
ejpam-3812	17	6	g	g	PROPN
ejpam-3812	17	7	is	be	AUX
ejpam-3812	17	8	∗corresponding	∗corresponde	VERB
ejpam-3812	17	9	author	author	NOUN
ejpam-3812	17	10	.	.	PUNCT
ejpam-3812	18	1	doi	doi	NOUN
ejpam-3812	18	2	:	:	PUNCT
ejpam-3812	18	3	https://doi.org/10.29020/nybg.ejpam.v13i4.3812	https://doi.org/10.29020/nybg.ejpam.v13i4.3812	ADJ
ejpam-3812	18	4	email	email	NOUN
ejpam-3812	18	5	addresses	address	NOUN
ejpam-3812	18	6	:	:	PUNCT
ejpam-3812	18	7	marivir.ortega@g.msuiit.edu.ph	marivir.ortega@g.msuiit.edu.ph	PROPN
ejpam-3812	18	8	(	(	PUNCT
ejpam-3812	18	9	m.	m.	NOUN
ejpam-3812	18	10	ortega	ortega	PROPN
ejpam-3812	18	11	)	)	PUNCT
ejpam-3812	18	12	,	,	PUNCT
ejpam-3812	18	13	rowena.isla@g.msuiit.edu.ph	rowena.isla@g.msuiit.edu.ph	PROPN
ejpam-3812	18	14	(	(	PUNCT
ejpam-3812	18	15	r.isla	r.isla	NOUN
ejpam-3812	18	16	)	)	PUNCT
ejpam-3812	18	17	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-3812	19	1	779	779	NUM
ejpam-3812	19	2	c	c	AUX
ejpam-3812	19	3	©	©	PROPN
ejpam-3812	19	4	2020	2020	NUM
ejpam-3812	19	5	ejpam	ejpam	VERB
ejpam-3812	19	6	all	all	DET
ejpam-3812	19	7	rights	right	NOUN
ejpam-3812	19	8	reserved	reserve	VERB
ejpam-3812	19	9	.	.	PUNCT
ejpam-3812	20	1	m.	m.	PROPN
ejpam-3812	20	2	ortega	ortega	PROPN
ejpam-3812	20	3	,	,	PUNCT
ejpam-3812	20	4	r.	r.	PROPN
ejpam-3812	20	5	isla	isla	PROPN
ejpam-3812	20	6	/	/	SYM
ejpam-3812	20	7	eur	eur	PROPN
ejpam-3812	20	8	.	.	PUNCT
ejpam-3812	21	1	j.	j.	PROPN
ejpam-3812	21	2	pure	pure	PROPN
ejpam-3812	21	3	appl	appl	PROPN
ejpam-3812	21	4	.	.	PROPN
ejpam-3812	21	5	math	math	PROPN
ejpam-3812	21	6	,	,	PUNCT
ejpam-3812	21	7	13	13	NUM
ejpam-3812	21	8	(	(	PUNCT
ejpam-3812	21	9	4	4	NUM
ejpam-3812	21	10	)	)	PUNCT
ejpam-3812	21	11	(	(	PUNCT
ejpam-3812	21	12	2020	2020	NUM
ejpam-3812	21	13	)	)	PUNCT
ejpam-3812	21	14	,	,	PUNCT
ejpam-3812	21	15	779	779	NUM
ejpam-3812	21	16	-	-	SYM
ejpam-3812	21	17	793	793	NUM
ejpam-3812	21	18	780	780	NUM
ejpam-3812	21	19	an	an	DET
ejpam-3812	21	20	independent	independent	ADJ
ejpam-3812	21	21	dominating	dominating	NOUN
ejpam-3812	21	22	set	set	NOUN
ejpam-3812	21	23	of	of	ADP
ejpam-3812	21	24	g	g	PROPN
ejpam-3812	21	25	if	if	SCONJ
ejpam-3812	21	26	no	no	DET
ejpam-3812	21	27	two	two	NUM
ejpam-3812	21	28	vertices	vertex	NOUN
ejpam-3812	21	29	in	in	ADP
ejpam-3812	21	30	s	s	NOUN
ejpam-3812	21	31	are	be	AUX
ejpam-3812	21	32	adjacent	adjacent	ADJ
ejpam-3812	21	33	,	,	PUNCT
ejpam-3812	21	34	that	that	ADV
ejpam-3812	21	35	is	is	ADV
ejpam-3812	21	36	,	,	PUNCT
ejpam-3812	21	37	s	s	VERB
ejpam-3812	21	38	is	be	AUX
ejpam-3812	21	39	an	an	DET
ejpam-3812	21	40	independent	independent	ADJ
ejpam-3812	21	41	set	set	NOUN
ejpam-3812	21	42	.	.	PUNCT
ejpam-3812	22	1	the	the	DET
ejpam-3812	22	2	independent	independent	ADJ
ejpam-3812	22	3	domination	domination	NOUN
ejpam-3812	22	4	number	number	NOUN
ejpam-3812	22	5	i(g	i(g	PROPN
ejpam-3812	22	6	)	)	PUNCT
ejpam-3812	22	7	of	of	ADP
ejpam-3812	22	8	a	a	DET
ejpam-3812	22	9	graph	graph	NOUN
ejpam-3812	22	10	g	g	NOUN
ejpam-3812	22	11	is	be	AUX
ejpam-3812	22	12	the	the	DET
ejpam-3812	22	13	minimum	minimum	ADJ
ejpam-3812	22	14	cardinality	cardinality	NOUN
ejpam-3812	22	15	of	of	ADP
ejpam-3812	22	16	an	an	DET
ejpam-3812	22	17	independent	independent	ADJ
ejpam-3812	22	18	dominating	dominating	NOUN
ejpam-3812	22	19	set	set	NOUN
ejpam-3812	22	20	.	.	PUNCT
ejpam-3812	23	1	a	a	DET
ejpam-3812	23	2	domination	domination	NOUN
ejpam-3812	23	3	parameter	parameter	NOUN
ejpam-3812	23	4	called	call	VERB
ejpam-3812	23	5	fair	fair	ADJ
ejpam-3812	23	6	domination	domination	NOUN
ejpam-3812	23	7	was	be	AUX
ejpam-3812	23	8	introduced	introduce	VERB
ejpam-3812	23	9	by	by	ADP
ejpam-3812	23	10	caro	caro	NOUN
ejpam-3812	23	11	,	,	PUNCT
ejpam-3812	23	12	hansberg	hansberg	PROPN
ejpam-3812	23	13	,	,	PUNCT
ejpam-3812	23	14	and	and	CCONJ
ejpam-3812	23	15	henning	henne	VERB
ejpam-3812	24	1	[	[	X
ejpam-3812	24	2	4	4	X
ejpam-3812	24	3	]	]	PUNCT
ejpam-3812	24	4	in	in	ADP
ejpam-3812	24	5	2012	2012	NUM
ejpam-3812	24	6	.	.	PUNCT
ejpam-3812	25	1	for	for	ADP
ejpam-3812	25	2	an	an	DET
ejpam-3812	25	3	integer	integer	NOUN
ejpam-3812	25	4	k	k	PROPN
ejpam-3812	25	5	≥	≥	NUM
ejpam-3812	25	6	1	1	NUM
ejpam-3812	25	7	,	,	PUNCT
ejpam-3812	25	8	a	a	DET
ejpam-3812	25	9	k	k	ADJ
ejpam-3812	25	10	-	-	ADJ
ejpam-3812	25	11	fair	fair	ADJ
ejpam-3812	25	12	dominating	dominating	NOUN
ejpam-3812	25	13	set	set	NOUN
ejpam-3812	25	14	(	(	PUNCT
ejpam-3812	25	15	kfd	kfd	NOUN
ejpam-3812	25	16	-	-	PUNCT
ejpam-3812	25	17	set	set	NOUN
ejpam-3812	25	18	)	)	PUNCT
ejpam-3812	25	19	is	be	AUX
ejpam-3812	25	20	a	a	DET
ejpam-3812	25	21	dominating	dominating	NOUN
ejpam-3812	25	22	set	set	NOUN
ejpam-3812	25	23	s	s	PROPN
ejpam-3812	25	24	⊆	⊆	NUM
ejpam-3812	25	25	v	v	NOUN
ejpam-3812	25	26	(	(	PUNCT
ejpam-3812	25	27	g	g	NOUN
ejpam-3812	25	28	)	)	PUNCT
ejpam-3812	25	29	such	such	ADJ
ejpam-3812	25	30	that	that	SCONJ
ejpam-3812	25	31	|n(u	|n(u	NOUN
ejpam-3812	25	32	)	)	PUNCT
ejpam-3812	25	33	∩	∩	NOUN
ejpam-3812	25	34	s|	s|	VERB
ejpam-3812	25	35	=	=	SYM
ejpam-3812	25	36	k	k	NOUN
ejpam-3812	25	37	for	for	ADP
ejpam-3812	25	38	every	every	DET
ejpam-3812	25	39	u	u	PROPN
ejpam-3812	25	40	∈	∈	PROPN
ejpam-3812	25	41	v	v	NOUN
ejpam-3812	25	42	(	(	PUNCT
ejpam-3812	25	43	g)\s	g)\s	NOUN
ejpam-3812	25	44	.	.	PUNCT
ejpam-3812	26	1	the	the	DET
ejpam-3812	26	2	k	k	ADJ
ejpam-3812	26	3	-	-	PUNCT
ejpam-3812	26	4	fair	fair	ADJ
ejpam-3812	26	5	domination	domination	NOUN
ejpam-3812	26	6	number	number	NOUN
ejpam-3812	26	7	of	of	ADP
ejpam-3812	26	8	g	g	NOUN
ejpam-3812	26	9	,	,	PUNCT
ejpam-3812	26	10	denoted	denote	VERB
ejpam-3812	26	11	by	by	ADP
ejpam-3812	26	12	γkfd(g	γkfd(g	PROPN
ejpam-3812	26	13	)	)	PUNCT
ejpam-3812	26	14	,	,	PUNCT
ejpam-3812	26	15	is	be	AUX
ejpam-3812	26	16	the	the	DET
ejpam-3812	26	17	minimum	minimum	ADJ
ejpam-3812	26	18	cardinality	cardinality	NOUN
ejpam-3812	26	19	of	of	ADP
ejpam-3812	26	20	a	a	DET
ejpam-3812	26	21	kfd	kfd	NOUN
ejpam-3812	26	22	-	-	PUNCT
ejpam-3812	26	23	set	set	NOUN
ejpam-3812	26	24	.	.	PUNCT
ejpam-3812	27	1	clearly	clearly	ADV
ejpam-3812	27	2	,	,	PUNCT
ejpam-3812	27	3	k	k	PROPN
ejpam-3812	27	4	≤	≤	PROPN
ejpam-3812	27	5	γkfd(g	γkfd(g	PROPN
ejpam-3812	27	6	)	)	PUNCT
ejpam-3812	27	7	≤	≤	NOUN
ejpam-3812	27	8	|v	|v	X
ejpam-3812	27	9	(	(	PUNCT
ejpam-3812	27	10	g)|	g)|	NOUN
ejpam-3812	27	11	.	.	PUNCT
ejpam-3812	28	1	in	in	ADP
ejpam-3812	28	2	2014	2014	NUM
ejpam-3812	28	3	,	,	PUNCT
ejpam-3812	28	4	maravilla	maravilla	PROPN
ejpam-3812	28	5	,	,	PUNCT
ejpam-3812	28	6	isla	isla	PROPN
ejpam-3812	28	7	,	,	PUNCT
ejpam-3812	28	8	and	and	CCONJ
ejpam-3812	28	9	canoy	canoy	ADJ
ejpam-3812	28	10	[	[	X
ejpam-3812	28	11	6	6	NUM
ejpam-3812	28	12	]	]	PUNCT
ejpam-3812	28	13	characterized	characterize	VERB
ejpam-3812	28	14	the	the	DET
ejpam-3812	28	15	k	k	ADJ
ejpam-3812	28	16	-	-	ADJ
ejpam-3812	28	17	fair	fair	ADJ
ejpam-3812	28	18	dominating	dominating	NOUN
ejpam-3812	28	19	sets	set	NOUN
ejpam-3812	28	20	in	in	ADP
ejpam-3812	28	21	the	the	DET
ejpam-3812	28	22	join	join	NOUN
ejpam-3812	28	23	,	,	PUNCT
ejpam-3812	28	24	corona	corona	PROPN
ejpam-3812	28	25	,	,	PUNCT
ejpam-3812	28	26	lexicographic	lexicographic	ADJ
ejpam-3812	28	27	product	product	NOUN
ejpam-3812	28	28	,	,	PUNCT
ejpam-3812	28	29	and	and	CCONJ
ejpam-3812	28	30	cartesian	cartesian	ADJ
ejpam-3812	28	31	product	product	NOUN
ejpam-3812	28	32	of	of	ADP
ejpam-3812	28	33	graphs	graph	NOUN
ejpam-3812	28	34	and	and	CCONJ
ejpam-3812	28	35	determined	determine	VERB
ejpam-3812	28	36	the	the	DET
ejpam-3812	28	37	bounds	bound	NOUN
ejpam-3812	28	38	or	or	CCONJ
ejpam-3812	28	39	exact	exact	ADJ
ejpam-3812	28	40	values	value	NOUN
ejpam-3812	28	41	of	of	ADP
ejpam-3812	28	42	the	the	DET
ejpam-3812	28	43	k	k	ADJ
ejpam-3812	28	44	-	-	PUNCT
ejpam-3812	28	45	fair	fair	ADJ
ejpam-3812	28	46	domination	domination	NOUN
ejpam-3812	28	47	numbers	number	NOUN
ejpam-3812	28	48	of	of	ADP
ejpam-3812	28	49	these	these	DET
ejpam-3812	28	50	graphs	graph	NOUN
ejpam-3812	28	51	.	.	PUNCT
ejpam-3812	29	1	two	two	NUM
ejpam-3812	29	2	variants	variant	NOUN
ejpam-3812	29	3	of	of	ADP
ejpam-3812	29	4	k	k	ADJ
ejpam-3812	29	5	-	-	PUNCT
ejpam-3812	29	6	fair	fair	ADJ
ejpam-3812	29	7	domination	domination	NOUN
ejpam-3812	29	8	,	,	PUNCT
ejpam-3812	29	9	namely	namely	ADV
ejpam-3812	29	10	connected	connected	ADJ
ejpam-3812	29	11	k	k	ADJ
ejpam-3812	29	12	-	-	PUNCT
ejpam-3812	29	13	fair	fair	ADJ
ejpam-3812	29	14	domination	domination	NOUN
ejpam-3812	29	15	and	and	CCONJ
ejpam-3812	29	16	neighborhood	neighborhood	NOUN
ejpam-3812	29	17	connected	connect	VERB
ejpam-3812	29	18	k	k	ADJ
ejpam-3812	29	19	-	-	PUNCT
ejpam-3812	29	20	fair	fair	ADJ
ejpam-3812	29	21	domination	domination	NOUN
ejpam-3812	29	22	,	,	PUNCT
ejpam-3812	29	23	were	be	AUX
ejpam-3812	29	24	studied	study	VERB
ejpam-3812	29	25	by	by	ADP
ejpam-3812	29	26	bent	bent	ADJ
ejpam-3812	29	27	-	-	PUNCT
ejpam-3812	29	28	usman	usman	ADJ
ejpam-3812	29	29	,	,	PUNCT
ejpam-3812	29	30	gomisong	gomisong	PROPN
ejpam-3812	29	31	,	,	PUNCT
ejpam-3812	29	32	and	and	CCONJ
ejpam-3812	29	33	isla	isla	PROPN
ejpam-3812	30	1	[	[	X
ejpam-3812	30	2	3	3	X
ejpam-3812	30	3	]	]	PUNCT
ejpam-3812	30	4	in	in	ADP
ejpam-3812	30	5	2018	2018	NUM
ejpam-3812	30	6	and	and	CCONJ
ejpam-3812	30	7	by	by	ADP
ejpam-3812	30	8	bent	bent	ADJ
ejpam-3812	30	9	-	-	PUNCT
ejpam-3812	30	10	usman	usman	PROPN
ejpam-3812	30	11	,	,	PUNCT
ejpam-3812	30	12	isla	isla	PROPN
ejpam-3812	30	13	,	,	PUNCT
ejpam-3812	30	14	and	and	CCONJ
ejpam-3812	30	15	canoy	canoy	ADJ
ejpam-3812	31	1	[	[	X
ejpam-3812	31	2	7	7	X
ejpam-3812	31	3	]	]	PUNCT
ejpam-3812	31	4	in	in	ADP
ejpam-3812	31	5	2019	2019	NUM
ejpam-3812	31	6	,	,	PUNCT
ejpam-3812	31	7	respectively	respectively	ADV
ejpam-3812	31	8	.	.	PUNCT
ejpam-3812	32	1	another	another	DET
ejpam-3812	32	2	domination	domination	NOUN
ejpam-3812	32	3	parameter	parameter	NOUN
ejpam-3812	32	4	is	be	AUX
ejpam-3812	32	5	the	the	DET
ejpam-3812	32	6	semitotal	semitotal	ADJ
ejpam-3812	32	7	domination	domination	NOUN
ejpam-3812	32	8	of	of	ADP
ejpam-3812	32	9	graphs	graph	NOUN
ejpam-3812	32	10	introduced	introduce	VERB
ejpam-3812	32	11	by	by	ADP
ejpam-3812	32	12	goddard	goddard	PROPN
ejpam-3812	32	13	,	,	PUNCT
ejpam-3812	32	14	henning	henning	NOUN
ejpam-3812	32	15	,	,	PUNCT
ejpam-3812	32	16	and	and	CCONJ
ejpam-3812	32	17	mcpillan	mcpillan	NOUN
ejpam-3812	32	18	[	[	X
ejpam-3812	32	19	5	5	NUM
ejpam-3812	32	20	]	]	PUNCT
ejpam-3812	32	21	in	in	ADP
ejpam-3812	32	22	2014	2014	NUM
ejpam-3812	32	23	.	.	PUNCT
ejpam-3812	33	1	for	for	ADP
ejpam-3812	33	2	a	a	DET
ejpam-3812	33	3	graph	graph	NOUN
ejpam-3812	33	4	g	g	NOUN
ejpam-3812	33	5	with	with	ADP
ejpam-3812	33	6	no	no	DET
ejpam-3812	33	7	isolated	isolated	ADJ
ejpam-3812	33	8	vertices	vertex	NOUN
ejpam-3812	33	9	,	,	PUNCT
ejpam-3812	33	10	a	a	DET
ejpam-3812	33	11	set	set	NOUN
ejpam-3812	33	12	s	s	NOUN
ejpam-3812	33	13	⊆	⊆	NUM
ejpam-3812	33	14	v	v	NOUN
ejpam-3812	33	15	(	(	PUNCT
ejpam-3812	33	16	g	g	NOUN
ejpam-3812	33	17	)	)	PUNCT
ejpam-3812	33	18	is	be	AUX
ejpam-3812	33	19	a	a	DET
ejpam-3812	33	20	semitotal	semitotal	ADJ
ejpam-3812	33	21	dominating	dominating	NOUN
ejpam-3812	33	22	set	set	NOUN
ejpam-3812	33	23	in	in	ADP
ejpam-3812	33	24	g	g	PROPN
ejpam-3812	33	25	if	if	SCONJ
ejpam-3812	33	26	s	s	VERB
ejpam-3812	33	27	is	be	AUX
ejpam-3812	33	28	a	a	DET
ejpam-3812	33	29	dominating	dominating	NOUN
ejpam-3812	33	30	set	set	VERB
ejpam-3812	33	31	in	in	ADP
ejpam-3812	33	32	g	g	PROPN
ejpam-3812	33	33	such	such	ADJ
ejpam-3812	33	34	that	that	PRON
ejpam-3812	33	35	for	for	ADP
ejpam-3812	33	36	every	every	DET
ejpam-3812	33	37	x	x	SYM
ejpam-3812	33	38	∈	∈	PROPN
ejpam-3812	33	39	s	s	VERB
ejpam-3812	33	40	there	there	PRON
ejpam-3812	33	41	exists	exist	VERB
ejpam-3812	33	42	y	y	PROPN
ejpam-3812	33	43	∈	∈	PROPN
ejpam-3812	33	44	s	s	PART
ejpam-3812	33	45	\	\	X
ejpam-3812	33	46	{	{	PUNCT
ejpam-3812	33	47	x	x	X
ejpam-3812	33	48	}	}	PUNCT
ejpam-3812	33	49	such	such	ADJ
ejpam-3812	33	50	that	that	DET
ejpam-3812	33	51	dg(x	dg(x	PROPN
ejpam-3812	33	52	,	,	PUNCT
ejpam-3812	33	53	y	y	NOUN
ejpam-3812	33	54	)	)	PUNCT
ejpam-3812	33	55	≤	≤	NOUN
ejpam-3812	33	56	2	2	NUM
ejpam-3812	33	57	.	.	PUNCT
ejpam-3812	33	58	in	in	ADP
ejpam-3812	33	59	2019	2019	NUM
ejpam-3812	33	60	,	,	PUNCT
ejpam-3812	33	61	aniversario	aniversario	NOUN
ejpam-3812	33	62	,	,	PUNCT
ejpam-3812	33	63	canoy	canoy	ADJ
ejpam-3812	33	64	,	,	PUNCT
ejpam-3812	33	65	and	and	CCONJ
ejpam-3812	33	66	jamil	jamil	PROPN
ejpam-3812	34	1	[	[	X
ejpam-3812	34	2	8	8	NUM
ejpam-3812	34	3	]	]	PUNCT
ejpam-3812	34	4	characterized	characterize	VERB
ejpam-3812	34	5	the	the	DET
ejpam-3812	34	6	semitotal	semitotal	ADJ
ejpam-3812	34	7	dominating	dominating	NOUN
ejpam-3812	34	8	sets	set	NOUN
ejpam-3812	34	9	in	in	ADP
ejpam-3812	34	10	the	the	DET
ejpam-3812	34	11	join	join	NOUN
ejpam-3812	34	12	,	,	PUNCT
ejpam-3812	34	13	corona	corona	PROPN
ejpam-3812	34	14	,	,	PUNCT
ejpam-3812	34	15	and	and	CCONJ
ejpam-3812	34	16	lexicographic	lexicographic	ADJ
ejpam-3812	34	17	product	product	NOUN
ejpam-3812	34	18	of	of	ADP
ejpam-3812	34	19	graphs	graph	NOUN
ejpam-3812	34	20	.	.	PUNCT
ejpam-3812	35	1	let	let	VERB
ejpam-3812	35	2	g	g	PRON
ejpam-3812	35	3	be	be	AUX
ejpam-3812	35	4	a	a	DET
ejpam-3812	35	5	graph	graph	NOUN
ejpam-3812	35	6	without	without	ADP
ejpam-3812	35	7	isolated	isolated	ADJ
ejpam-3812	35	8	vertices	vertex	NOUN
ejpam-3812	35	9	.	.	PUNCT
ejpam-3812	36	1	a	a	DET
ejpam-3812	36	2	set	set	NOUN
ejpam-3812	36	3	s	s	NOUN
ejpam-3812	36	4	⊆	⊆	NUM
ejpam-3812	36	5	v	v	NOUN
ejpam-3812	36	6	(	(	PUNCT
ejpam-3812	36	7	g	g	NOUN
ejpam-3812	36	8	)	)	PUNCT
ejpam-3812	36	9	is	be	AUX
ejpam-3812	36	10	a	a	DET
ejpam-3812	36	11	semitotal	semitotal	ADJ
ejpam-3812	36	12	k	k	ADJ
ejpam-3812	36	13	-	-	PUNCT
ejpam-3812	36	14	fair	fair	ADJ
ejpam-3812	36	15	dominating	dominating	NOUN
ejpam-3812	36	16	set	set	NOUN
ejpam-3812	36	17	in	in	ADP
ejpam-3812	36	18	g	g	PROPN
ejpam-3812	36	19	,	,	PUNCT
ejpam-3812	36	20	if	if	SCONJ
ejpam-3812	36	21	s	s	VERB
ejpam-3812	36	22	is	be	AUX
ejpam-3812	36	23	a	a	DET
ejpam-3812	36	24	k	k	ADJ
ejpam-3812	36	25	-	-	ADJ
ejpam-3812	36	26	fair	fair	ADJ
ejpam-3812	36	27	dominating	dominating	NOUN
ejpam-3812	36	28	set	set	NOUN
ejpam-3812	36	29	in	in	ADP
ejpam-3812	36	30	g	g	PROPN
ejpam-3812	36	31	and	and	CCONJ
ejpam-3812	36	32	for	for	ADP
ejpam-3812	36	33	every	every	DET
ejpam-3812	36	34	x	x	SYM
ejpam-3812	36	35	∈	∈	PROPN
ejpam-3812	36	36	s	s	NOUN
ejpam-3812	36	37	,	,	PUNCT
ejpam-3812	36	38	there	there	PRON
ejpam-3812	36	39	exists	exist	VERB
ejpam-3812	36	40	y	y	PROPN
ejpam-3812	36	41	∈	∈	PROPN
ejpam-3812	36	42	s	s	PART
ejpam-3812	36	43	\	\	X
ejpam-3812	36	44	{	{	PUNCT
ejpam-3812	36	45	x	x	X
ejpam-3812	36	46	}	}	PUNCT
ejpam-3812	36	47	such	such	ADJ
ejpam-3812	36	48	that	that	SCONJ
ejpam-3812	36	49	d(x	d(x	PROPN
ejpam-3812	36	50	,	,	PUNCT
ejpam-3812	36	51	y	y	NOUN
ejpam-3812	36	52	)	)	PUNCT
ejpam-3812	36	53	≤	≤	NOUN
ejpam-3812	36	54	2	2	NUM
ejpam-3812	36	55	.	.	PUNCT
ejpam-3812	37	1	the	the	DET
ejpam-3812	37	2	semitotal	semitotal	ADJ
ejpam-3812	37	3	k	k	ADJ
ejpam-3812	37	4	-	-	PUNCT
ejpam-3812	37	5	fair	fair	ADJ
ejpam-3812	37	6	domination	domination	NOUN
ejpam-3812	37	7	number	number	NOUN
ejpam-3812	37	8	of	of	ADP
ejpam-3812	37	9	g	g	NOUN
ejpam-3812	37	10	,	,	PUNCT
ejpam-3812	37	11	denoted	denote	VERB
ejpam-3812	37	12	by	by	ADP
ejpam-3812	37	13	γt2kf	γt2kf	NUM
ejpam-3812	37	14	(	(	PUNCT
ejpam-3812	37	15	g	g	NOUN
ejpam-3812	37	16	)	)	PUNCT
ejpam-3812	37	17	,	,	PUNCT
ejpam-3812	37	18	is	be	AUX
ejpam-3812	37	19	the	the	DET
ejpam-3812	37	20	minimum	minimum	ADJ
ejpam-3812	37	21	cardinality	cardinality	NOUN
ejpam-3812	37	22	of	of	ADP
ejpam-3812	37	23	a	a	DET
ejpam-3812	37	24	semitotal	semitotal	ADJ
ejpam-3812	37	25	k	k	ADJ
ejpam-3812	37	26	-	-	PUNCT
ejpam-3812	37	27	fair	fair	ADJ
ejpam-3812	37	28	dominating	dominating	NOUN
ejpam-3812	37	29	set	set	NOUN
ejpam-3812	37	30	.	.	PUNCT
ejpam-3812	38	1	a	a	DET
ejpam-3812	38	2	semitotal	semitotal	ADJ
ejpam-3812	38	3	k	k	ADJ
ejpam-3812	38	4	-	-	PUNCT
ejpam-3812	38	5	fair	fair	ADJ
ejpam-3812	38	6	dominating	dominating	NOUN
ejpam-3812	38	7	set	set	NOUN
ejpam-3812	38	8	of	of	ADP
ejpam-3812	38	9	cardinality	cardinality	NOUN
ejpam-3812	38	10	γt2kf	γt2kf	NUM
ejpam-3812	38	11	(	(	PUNCT
ejpam-3812	38	12	g	g	NOUN
ejpam-3812	38	13	)	)	PUNCT
ejpam-3812	38	14	is	be	AUX
ejpam-3812	38	15	called	call	VERB
ejpam-3812	38	16	a	a	DET
ejpam-3812	38	17	minimum	minimum	ADJ
ejpam-3812	38	18	semitotal	semitotal	ADJ
ejpam-3812	38	19	k	k	ADJ
ejpam-3812	38	20	-	-	PUNCT
ejpam-3812	38	21	fair	fair	ADJ
ejpam-3812	38	22	dominating	dominating	NOUN
ejpam-3812	38	23	set	set	NOUN
ejpam-3812	38	24	or	or	CCONJ
ejpam-3812	38	25	a	a	DET
ejpam-3812	38	26	γt2kf	γt2kf	NUM
ejpam-3812	38	27	-set	-set	ADJ
ejpam-3812	38	28	.	.	PUNCT
ejpam-3812	39	1	let	let	VERB
ejpam-3812	39	2	g	g	PRON
ejpam-3812	39	3	be	be	AUX
ejpam-3812	39	4	a	a	DET
ejpam-3812	39	5	connected	connected	ADJ
ejpam-3812	39	6	graph	graph	NOUN
ejpam-3812	39	7	.	.	PUNCT
ejpam-3812	40	1	a	a	DET
ejpam-3812	40	2	set	set	NOUN
ejpam-3812	40	3	s	s	NOUN
ejpam-3812	40	4	⊆	⊆	NUM
ejpam-3812	40	5	v	v	NOUN
ejpam-3812	40	6	(	(	PUNCT
ejpam-3812	40	7	g	g	NOUN
ejpam-3812	40	8	)	)	PUNCT
ejpam-3812	40	9	is	be	AUX
ejpam-3812	40	10	an	an	DET
ejpam-3812	40	11	independent	independent	ADJ
ejpam-3812	40	12	k	k	ADJ
ejpam-3812	40	13	-	-	ADJ
ejpam-3812	40	14	fair	fair	ADJ
ejpam-3812	40	15	dominating	dominating	NOUN
ejpam-3812	40	16	set	set	NOUN
ejpam-3812	40	17	in	in	ADP
ejpam-3812	40	18	g	g	PROPN
ejpam-3812	40	19	if	if	SCONJ
ejpam-3812	40	20	s	s	VERB
ejpam-3812	40	21	is	be	AUX
ejpam-3812	40	22	a	a	DET
ejpam-3812	40	23	k	k	ADJ
ejpam-3812	40	24	-	-	ADJ
ejpam-3812	40	25	fair	fair	ADJ
ejpam-3812	40	26	dominating	dominating	NOUN
ejpam-3812	40	27	set	set	NOUN
ejpam-3812	40	28	in	in	ADP
ejpam-3812	40	29	g	g	PROPN
ejpam-3812	40	30	and	and	CCONJ
ejpam-3812	40	31	if	if	SCONJ
ejpam-3812	40	32	no	no	DET
ejpam-3812	40	33	two	two	NUM
ejpam-3812	40	34	vertices	vertex	NOUN
ejpam-3812	40	35	in	in	ADP
ejpam-3812	40	36	s	s	NOUN
ejpam-3812	40	37	are	be	AUX
ejpam-3812	40	38	adjacent	adjacent	ADJ
ejpam-3812	40	39	.	.	PUNCT
ejpam-3812	41	1	the	the	DET
ejpam-3812	41	2	independent	independent	ADJ
ejpam-3812	41	3	k	k	ADJ
ejpam-3812	41	4	-	-	PUNCT
ejpam-3812	41	5	fair	fair	ADJ
ejpam-3812	41	6	domination	domination	NOUN
ejpam-3812	41	7	number	number	NOUN
ejpam-3812	41	8	of	of	ADP
ejpam-3812	41	9	g	g	NOUN
ejpam-3812	41	10	,	,	PUNCT
ejpam-3812	41	11	denoted	denote	VERB
ejpam-3812	41	12	by	by	ADP
ejpam-3812	41	13	γikf	γikf	NOUN
ejpam-3812	41	14	(	(	PUNCT
ejpam-3812	41	15	g	g	NOUN
ejpam-3812	41	16	)	)	PUNCT
ejpam-3812	41	17	,	,	PUNCT
ejpam-3812	41	18	is	be	AUX
ejpam-3812	41	19	the	the	DET
ejpam-3812	41	20	minimum	minimum	ADJ
ejpam-3812	41	21	cardinality	cardinality	NOUN
ejpam-3812	41	22	of	of	ADP
ejpam-3812	41	23	an	an	DET
ejpam-3812	41	24	independent	independent	ADJ
ejpam-3812	41	25	k	k	ADJ
ejpam-3812	41	26	-	-	ADJ
ejpam-3812	41	27	fair	fair	ADJ
ejpam-3812	41	28	dominating	dominating	NOUN
ejpam-3812	41	29	set	set	NOUN
ejpam-3812	41	30	.	.	PUNCT
ejpam-3812	42	1	an	an	DET
ejpam-3812	42	2	independent	independent	ADJ
ejpam-3812	42	3	k	k	ADJ
ejpam-3812	42	4	-	-	ADJ
ejpam-3812	42	5	fair	fair	ADJ
ejpam-3812	42	6	dominating	dominating	NOUN
ejpam-3812	42	7	set	set	NOUN
ejpam-3812	42	8	of	of	ADP
ejpam-3812	42	9	cardinality	cardinality	PROPN
ejpam-3812	42	10	γikf	γikf	NOUN
ejpam-3812	42	11	(	(	PUNCT
ejpam-3812	42	12	g	g	NOUN
ejpam-3812	42	13	)	)	PUNCT
ejpam-3812	42	14	is	be	AUX
ejpam-3812	42	15	called	call	VERB
ejpam-3812	42	16	a	a	DET
ejpam-3812	42	17	minimum	minimum	ADJ
ejpam-3812	42	18	independent	independent	ADJ
ejpam-3812	42	19	k	k	ADJ
ejpam-3812	42	20	-	-	ADJ
ejpam-3812	42	21	fair	fair	ADJ
ejpam-3812	42	22	dominating	dominating	NOUN
ejpam-3812	42	23	set	set	NOUN
ejpam-3812	42	24	or	or	CCONJ
ejpam-3812	42	25	a	a	DET
ejpam-3812	42	26	γikf	γikf	NOUN
ejpam-3812	42	27	-set	-set	ADJ
ejpam-3812	42	28	.	.	PUNCT
ejpam-3812	43	1	the	the	DET
ejpam-3812	43	2	join	join	NOUN
ejpam-3812	43	3	g	g	PROPN
ejpam-3812	43	4	+	+	CCONJ
ejpam-3812	43	5	h	h	NOUN
ejpam-3812	43	6	of	of	ADP
ejpam-3812	43	7	two	two	NUM
ejpam-3812	43	8	graphs	graph	NOUN
ejpam-3812	43	9	g	g	NOUN
ejpam-3812	43	10	and	and	CCONJ
ejpam-3812	43	11	h	h	NOUN
ejpam-3812	43	12	is	be	AUX
ejpam-3812	43	13	the	the	DET
ejpam-3812	43	14	graph	graph	NOUN
ejpam-3812	43	15	with	with	ADP
ejpam-3812	43	16	vertex	vertex	NOUN
ejpam-3812	43	17	-	-	PUNCT
ejpam-3812	43	18	set	set	VERB
ejpam-3812	43	19	v	v	NOUN
ejpam-3812	43	20	(	(	PUNCT
ejpam-3812	43	21	g	g	PROPN
ejpam-3812	43	22	+	+	NOUN
ejpam-3812	43	23	h	h	NOUN
ejpam-3812	43	24	)	)	PUNCT
ejpam-3812	43	25	=	=	NOUN
ejpam-3812	43	26	v	v	X
ejpam-3812	43	27	(	(	PUNCT
ejpam-3812	43	28	g)∪v	g)∪v	NOUN
ejpam-3812	43	29	(	(	PUNCT
ejpam-3812	43	30	h	h	NOUN
ejpam-3812	43	31	)	)	PUNCT
ejpam-3812	43	32	and	and	CCONJ
ejpam-3812	43	33	edge	edge	NOUN
ejpam-3812	43	34	-	-	PUNCT
ejpam-3812	43	35	set	set	VERB
ejpam-3812	43	36	e(g	e(g	NOUN
ejpam-3812	43	37	+	+	CCONJ
ejpam-3812	43	38	h	h	NOUN
ejpam-3812	43	39	)	)	PUNCT
ejpam-3812	43	40	=	=	SYM
ejpam-3812	44	1	e(g)∪e(h	e(g)∪e(h	ADJ
ejpam-3812	44	2	)	)	PUNCT
ejpam-3812	44	3	∪	∪	NOUN
ejpam-3812	44	4	{	{	PUNCT
ejpam-3812	44	5	uv	uv	NOUN
ejpam-3812	44	6	:	:	PUNCT
ejpam-3812	44	7	u	u	PROPN
ejpam-3812	44	8	∈	∈	PROPN
ejpam-3812	44	9	v	v	ADP
ejpam-3812	44	10	(	(	PUNCT
ejpam-3812	44	11	g	g	NOUN
ejpam-3812	44	12	)	)	PUNCT
ejpam-3812	44	13	,	,	PUNCT
ejpam-3812	44	14	v	v	X
ejpam-3812	44	15	∈	∈	PROPN
ejpam-3812	44	16	v	v	NOUN
ejpam-3812	44	17	(	(	PUNCT
ejpam-3812	44	18	h	h	NOUN
ejpam-3812	44	19	)	)	PUNCT
ejpam-3812	44	20	}	}	PUNCT
ejpam-3812	44	21	.	.	PUNCT
ejpam-3812	45	1	the	the	DET
ejpam-3812	45	2	corona	corona	NOUN
ejpam-3812	45	3	of	of	ADP
ejpam-3812	45	4	two	two	NUM
ejpam-3812	45	5	graphs	graph	NOUN
ejpam-3812	45	6	g	g	NOUN
ejpam-3812	45	7	and	and	CCONJ
ejpam-3812	45	8	h	h	NOUN
ejpam-3812	45	9	,	,	PUNCT
ejpam-3812	45	10	denoted	denote	VERB
ejpam-3812	45	11	by	by	ADP
ejpam-3812	45	12	g	g	PROPN
ejpam-3812	45	13	◦	◦	NOUN
ejpam-3812	45	14	h	h	NOUN
ejpam-3812	45	15	,	,	PUNCT
ejpam-3812	45	16	is	be	AUX
ejpam-3812	45	17	the	the	DET
ejpam-3812	45	18	graph	graph	NOUN
ejpam-3812	45	19	obtained	obtain	VERB
ejpam-3812	45	20	by	by	ADP
ejpam-3812	45	21	taking	take	VERB
ejpam-3812	45	22	one	one	NUM
ejpam-3812	45	23	copy	copy	NOUN
ejpam-3812	45	24	of	of	ADP
ejpam-3812	45	25	g	g	NOUN
ejpam-3812	45	26	of	of	ADP
ejpam-3812	45	27	order	order	NOUN
ejpam-3812	45	28	n	n	NOUN
ejpam-3812	45	29	and	and	CCONJ
ejpam-3812	45	30	n	n	PRON
ejpam-3812	45	31	copies	copy	NOUN
ejpam-3812	45	32	of	of	ADP
ejpam-3812	45	33	h	h	NOUN
ejpam-3812	45	34	,	,	PUNCT
ejpam-3812	45	35	and	and	CCONJ
ejpam-3812	45	36	then	then	ADV
ejpam-3812	45	37	joining	join	VERB
ejpam-3812	45	38	the	the	DET
ejpam-3812	45	39	i	i	PROPN
ejpam-3812	45	40	-	-	PUNCT
ejpam-3812	45	41	th	th	X
ejpam-3812	45	42	vertex	vertex	NOUN
ejpam-3812	45	43	of	of	ADP
ejpam-3812	45	44	g	g	NOUN
ejpam-3812	45	45	to	to	ADP
ejpam-3812	45	46	every	every	DET
ejpam-3812	45	47	vertex	vertex	NOUN
ejpam-3812	45	48	in	in	ADP
ejpam-3812	45	49	the	the	DET
ejpam-3812	45	50	i	i	PROPN
ejpam-3812	45	51	-	-	PUNCT
ejpam-3812	45	52	th	th	PROPN
ejpam-3812	45	53	copy	copy	NOUN
ejpam-3812	45	54	of	of	ADP
ejpam-3812	45	55	h.	h.	PROPN
ejpam-3812	45	56	for	for	ADP
ejpam-3812	45	57	every	every	DET
ejpam-3812	45	58	v	v	NUM
ejpam-3812	45	59	∈	∈	PROPN
ejpam-3812	45	60	v	v	NOUN
ejpam-3812	45	61	(	(	PUNCT
ejpam-3812	45	62	g	g	NOUN
ejpam-3812	45	63	)	)	PUNCT
ejpam-3812	45	64	,	,	PUNCT
ejpam-3812	45	65	we	we	PRON
ejpam-3812	45	66	denote	denote	VERB
ejpam-3812	45	67	by	by	ADP
ejpam-3812	45	68	hv	hv	PROPN
ejpam-3812	45	69	the	the	DET
ejpam-3812	45	70	copy	copy	NOUN
ejpam-3812	45	71	of	of	ADP
ejpam-3812	45	72	h	h	NOUN
ejpam-3812	45	73	whose	whose	DET
ejpam-3812	45	74	vertices	vertex	NOUN
ejpam-3812	45	75	are	be	AUX
ejpam-3812	45	76	joined	join	VERB
ejpam-3812	45	77	or	or	CCONJ
ejpam-3812	45	78	attached	attach	VERB
ejpam-3812	45	79	to	to	ADP
ejpam-3812	45	80	the	the	DET
ejpam-3812	45	81	vertex	vertex	NOUN
ejpam-3812	45	82	v.	v.	CCONJ
ejpam-3812	45	83	for	for	ADP
ejpam-3812	45	84	each	each	DET
ejpam-3812	45	85	v	v	NUM
ejpam-3812	45	86	∈	∈	PROPN
ejpam-3812	45	87	v	v	NOUN
ejpam-3812	45	88	(	(	PUNCT
ejpam-3812	45	89	g	g	NOUN
ejpam-3812	45	90	)	)	PUNCT
ejpam-3812	45	91	,	,	PUNCT
ejpam-3812	45	92	the	the	DET
ejpam-3812	45	93	subgraph	subgraph	PROPN
ejpam-3812	45	94	〈	〈	PROPN
ejpam-3812	45	95	v〉+hv	v〉+hv	NOUN
ejpam-3812	45	96	of	of	ADP
ejpam-3812	45	97	g	g	NOUN
ejpam-3812	45	98	◦	◦	NOUN
ejpam-3812	45	99	h	h	NOUN
ejpam-3812	45	100	will	will	AUX
ejpam-3812	45	101	be	be	AUX
ejpam-3812	45	102	denoted	denote	VERB
ejpam-3812	45	103	by	by	ADP
ejpam-3812	45	104	v	v	PRON
ejpam-3812	45	105	+	+	X
ejpam-3812	45	106	hv	hv	PROPN
ejpam-3812	45	107	.	.	PUNCT
ejpam-3812	46	1	the	the	DET
ejpam-3812	46	2	lexicographic	lexicographic	ADJ
ejpam-3812	46	3	product	product	NOUN
ejpam-3812	46	4	of	of	ADP
ejpam-3812	46	5	two	two	NUM
ejpam-3812	46	6	graphs	graph	NOUN
ejpam-3812	46	7	g	g	NOUN
ejpam-3812	46	8	and	and	CCONJ
ejpam-3812	46	9	h	h	NOUN
ejpam-3812	46	10	,	,	PUNCT
ejpam-3812	46	11	denoted	denote	VERB
ejpam-3812	46	12	by	by	ADP
ejpam-3812	46	13	g[h	g[h	NOUN
ejpam-3812	46	14	]	]	PUNCT
ejpam-3812	46	15	,	,	PUNCT
ejpam-3812	46	16	is	be	AUX
ejpam-3812	46	17	the	the	DET
ejpam-3812	46	18	graph	graph	NOUN
ejpam-3812	46	19	with	with	ADP
ejpam-3812	46	20	vertex	vertex	NOUN
ejpam-3812	46	21	set	set	VERB
ejpam-3812	46	22	v	v	NOUN
ejpam-3812	46	23	(	(	PUNCT
ejpam-3812	46	24	g[h	g[h	PROPN
ejpam-3812	46	25	]	]	PUNCT
ejpam-3812	46	26	)	)	PUNCT
ejpam-3812	46	27	=	=	SYM
ejpam-3812	46	28	v	v	X
ejpam-3812	46	29	(	(	PUNCT
ejpam-3812	46	30	g	g	NOUN
ejpam-3812	46	31	)	)	PUNCT
ejpam-3812	46	32	×	×	NOUN
ejpam-3812	46	33	v	v	NOUN
ejpam-3812	46	34	(	(	PUNCT
ejpam-3812	46	35	h	h	NOUN
ejpam-3812	46	36	)	)	PUNCT
ejpam-3812	46	37	and	and	CCONJ
ejpam-3812	46	38	edge	edge	VERB
ejpam-3812	46	39	set	set	VERB
ejpam-3812	46	40	e(g[h	e(g[h	NOUN
ejpam-3812	46	41	]	]	PUNCT
ejpam-3812	46	42	)	)	PUNCT
ejpam-3812	46	43	satisfying	satisfy	VERB
ejpam-3812	46	44	the	the	DET
ejpam-3812	46	45	following	follow	VERB
ejpam-3812	46	46	conditions	condition	NOUN
ejpam-3812	46	47	:	:	PUNCT
ejpam-3812	46	48	(	(	PUNCT
ejpam-3812	46	49	u1	u1	PROPN
ejpam-3812	46	50	,	,	PUNCT
ejpam-3812	46	51	v1)(u2	v1)(u2	PROPN
ejpam-3812	46	52	,	,	PUNCT
ejpam-3812	46	53	v2	v2	PROPN
ejpam-3812	46	54	)	)	PUNCT
ejpam-3812	46	55	∈	∈	NOUN
ejpam-3812	46	56	e(g[h	e(g[h	NOUN
ejpam-3812	46	57	]	]	PUNCT
ejpam-3812	46	58	)	)	PUNCT
ejpam-3812	46	59	if	if	SCONJ
ejpam-3812	46	60	and	and	CCONJ
ejpam-3812	46	61	only	only	ADV
ejpam-3812	46	62	if	if	SCONJ
ejpam-3812	46	63	either	either	PRON
ejpam-3812	46	64	u1u2	u1u2	PROPN
ejpam-3812	46	65	∈	∈	PROPN
ejpam-3812	46	66	e(g	e(g	PROPN
ejpam-3812	46	67	)	)	PUNCT
ejpam-3812	46	68	or	or	CCONJ
ejpam-3812	46	69	u1	u1	NOUN
ejpam-3812	46	70	=	=	SYM
ejpam-3812	46	71	u2	u2	PROPN
ejpam-3812	46	72	and	and	CCONJ
ejpam-3812	46	73	v1v2	v1v2	PUNCT
ejpam-3812	46	74	∈	∈	PROPN
ejpam-3812	46	75	e(h	e(h	PROPN
ejpam-3812	46	76	)	)	PUNCT
ejpam-3812	46	77	.	.	PUNCT
ejpam-3812	47	1	the	the	DET
ejpam-3812	47	2	cartesian	cartesian	ADJ
ejpam-3812	47	3	product	product	NOUN
ejpam-3812	47	4	of	of	ADP
ejpam-3812	47	5	two	two	NUM
ejpam-3812	47	6	graphs	graph	NOUN
ejpam-3812	47	7	m.	m.	PROPN
ejpam-3812	47	8	ortega	ortega	PROPN
ejpam-3812	47	9	,	,	PUNCT
ejpam-3812	47	10	r.	r.	PROPN
ejpam-3812	47	11	isla	isla	PROPN
ejpam-3812	47	12	/	/	SYM
ejpam-3812	47	13	eur	eur	PROPN
ejpam-3812	47	14	.	.	PUNCT
ejpam-3812	48	1	j.	j.	PROPN
ejpam-3812	48	2	pure	pure	PROPN
ejpam-3812	48	3	appl	appl	PROPN
ejpam-3812	48	4	.	.	PROPN
ejpam-3812	48	5	math	math	PROPN
ejpam-3812	48	6	,	,	PUNCT
ejpam-3812	48	7	13	13	NUM
ejpam-3812	48	8	(	(	PUNCT
ejpam-3812	48	9	4	4	NUM
ejpam-3812	48	10	)	)	PUNCT
ejpam-3812	48	11	(	(	PUNCT
ejpam-3812	48	12	2020	2020	NUM
ejpam-3812	48	13	)	)	PUNCT
ejpam-3812	48	14	,	,	PUNCT
ejpam-3812	48	15	779	779	NUM
ejpam-3812	48	16	-	-	SYM
ejpam-3812	48	17	793	793	NUM
ejpam-3812	48	18	781	781	NUM
ejpam-3812	48	19	g	g	NOUN
ejpam-3812	48	20	and	and	CCONJ
ejpam-3812	48	21	h	h	NOUN
ejpam-3812	48	22	,	,	PUNCT
ejpam-3812	48	23	denoted	denote	VERB
ejpam-3812	48	24	by	by	ADP
ejpam-3812	48	25	g	g	PROPN
ejpam-3812	48	26	�	�	PROPN
ejpam-3812	48	27	h	h	NOUN
ejpam-3812	48	28	,	,	PUNCT
ejpam-3812	48	29	is	be	AUX
ejpam-3812	48	30	the	the	DET
ejpam-3812	48	31	graph	graph	NOUN
ejpam-3812	48	32	with	with	ADP
ejpam-3812	48	33	vertex	vertex	NOUN
ejpam-3812	48	34	-	-	PUNCT
ejpam-3812	48	35	set	set	VERB
ejpam-3812	48	36	v	v	NOUN
ejpam-3812	48	37	(	(	PUNCT
ejpam-3812	48	38	g	g	PROPN
ejpam-3812	48	39	�	�	NOUN
ejpam-3812	48	40	h	h	NOUN
ejpam-3812	48	41	)	)	PUNCT
ejpam-3812	48	42	=	=	NOUN
ejpam-3812	48	43	v	v	X
ejpam-3812	48	44	(	(	PUNCT
ejpam-3812	48	45	g)×	g)×	NOUN
ejpam-3812	48	46	v	v	NOUN
ejpam-3812	48	47	(	(	PUNCT
ejpam-3812	48	48	h	h	NOUN
ejpam-3812	48	49	)	)	PUNCT
ejpam-3812	48	50	and	and	CCONJ
ejpam-3812	48	51	edge	edge	NOUN
ejpam-3812	48	52	-	-	PUNCT
ejpam-3812	48	53	set	set	VERB
ejpam-3812	48	54	e(g	e(g	PROPN
ejpam-3812	48	55	�	�	PROPN
ejpam-3812	48	56	h	h	NOUN
ejpam-3812	48	57	)	)	PUNCT
ejpam-3812	48	58	satisfying	satisfy	VERB
ejpam-3812	48	59	the	the	DET
ejpam-3812	48	60	following	follow	VERB
ejpam-3812	48	61	conditions	condition	NOUN
ejpam-3812	48	62	:	:	PUNCT
ejpam-3812	48	63	(	(	PUNCT
ejpam-3812	48	64	u1	u1	PROPN
ejpam-3812	48	65	,	,	PUNCT
ejpam-3812	48	66	v1)(u2	v1)(u2	PROPN
ejpam-3812	48	67	,	,	PUNCT
ejpam-3812	48	68	v2	v2	PROPN
ejpam-3812	48	69	)	)	PUNCT
ejpam-3812	48	70	∈	∈	PROPN
ejpam-3812	48	71	e(g	e(g	PROPN
ejpam-3812	48	72	�	�	PROPN
ejpam-3812	48	73	h	h	PROPN
ejpam-3812	48	74	)	)	PUNCT
ejpam-3812	48	75	if	if	SCONJ
ejpam-3812	48	76	and	and	CCONJ
ejpam-3812	48	77	only	only	ADV
ejpam-3812	48	78	if	if	SCONJ
ejpam-3812	48	79	either	either	DET
ejpam-3812	48	80	u1u2	u1u2	PROPN
ejpam-3812	48	81	∈	∈	PROPN
ejpam-3812	48	82	e(g	e(g	PROPN
ejpam-3812	48	83	)	)	PUNCT
ejpam-3812	48	84	and	and	CCONJ
ejpam-3812	48	85	v1	v1	NOUN
ejpam-3812	48	86	=	=	SYM
ejpam-3812	48	87	v2	v2	NOUN
ejpam-3812	48	88	or	or	CCONJ
ejpam-3812	48	89	u1	u1	NOUN
ejpam-3812	48	90	=	=	SYM
ejpam-3812	48	91	u2	u2	PROPN
ejpam-3812	48	92	and	and	CCONJ
ejpam-3812	48	93	v1v2	v1v2	PUNCT
ejpam-3812	48	94	∈	∈	PROPN
ejpam-3812	48	95	e(h	e(h	PROPN
ejpam-3812	48	96	)	)	PUNCT
ejpam-3812	48	97	.	.	PUNCT
ejpam-3812	49	1	2	2	X
ejpam-3812	49	2	.	.	X
ejpam-3812	49	3	preliminary	preliminary	ADJ
ejpam-3812	49	4	results	result	NOUN
ejpam-3812	49	5	remark	remark	VERB
ejpam-3812	49	6	1	1	NUM
ejpam-3812	49	7	.	.	PUNCT
ejpam-3812	50	1	any	any	DET
ejpam-3812	50	2	semitotal	semitotal	ADJ
ejpam-3812	50	3	kfd	kfd	NOUN
ejpam-3812	50	4	-	-	PUNCT
ejpam-3812	50	5	set	set	NOUN
ejpam-3812	50	6	is	be	AUX
ejpam-3812	50	7	a	a	DET
ejpam-3812	50	8	kfd	kfd	NOUN
ejpam-3812	50	9	-	-	PUNCT
ejpam-3812	50	10	set	set	NOUN
ejpam-3812	50	11	,	,	PUNCT
ejpam-3812	50	12	where	where	SCONJ
ejpam-3812	50	13	k	k	PROPN
ejpam-3812	50	14	is	be	AUX
ejpam-3812	50	15	a	a	DET
ejpam-3812	50	16	positive	positive	ADJ
ejpam-3812	50	17	integer	integer	NOUN
ejpam-3812	50	18	.	.	PUNCT
ejpam-3812	51	1	theorem	theorem	NOUN
ejpam-3812	51	2	1	1	NUM
ejpam-3812	51	3	.	.	PUNCT
ejpam-3812	52	1	let	let	VERB
ejpam-3812	52	2	g	g	PRON
ejpam-3812	52	3	be	be	AUX
ejpam-3812	52	4	a	a	DET
ejpam-3812	52	5	nontrivial	nontrivial	ADJ
ejpam-3812	52	6	connected	connect	VERB
ejpam-3812	52	7	graph	graph	NOUN
ejpam-3812	52	8	.	.	PUNCT
ejpam-3812	53	1	then	then	ADV
ejpam-3812	53	2	γt21f	γt21f	VERB
ejpam-3812	53	3	(	(	PUNCT
ejpam-3812	53	4	g	g	NOUN
ejpam-3812	53	5	)	)	PUNCT
ejpam-3812	53	6	=	=	SYM
ejpam-3812	53	7	2	2	NUM
ejpam-3812	53	8	if	if	SCONJ
ejpam-3812	53	9	and	and	CCONJ
ejpam-3812	53	10	only	only	ADV
ejpam-3812	53	11	if	if	SCONJ
ejpam-3812	53	12	there	there	PRON
ejpam-3812	53	13	exist	exist	VERB
ejpam-3812	53	14	adjacent	adjacent	ADJ
ejpam-3812	53	15	vertices	vertex	NOUN
ejpam-3812	53	16	a	a	PRON
ejpam-3812	53	17	and	and	CCONJ
ejpam-3812	53	18	b	b	NOUN
ejpam-3812	53	19	such	such	ADJ
ejpam-3812	53	20	that	that	DET
ejpam-3812	53	21	ng(a	ng(a	NOUN
ejpam-3812	53	22	)	)	PUNCT
ejpam-3812	53	23	∩	∩	NOUN
ejpam-3812	53	24	ng(b	ng(b	CCONJ
ejpam-3812	53	25	)	)	PUNCT
ejpam-3812	53	26	=	=	NOUN
ejpam-3812	53	27	∅	∅	NOUN
ejpam-3812	53	28	and	and	CCONJ
ejpam-3812	53	29	v	v	NOUN
ejpam-3812	53	30	(	(	PUNCT
ejpam-3812	53	31	g	g	NOUN
ejpam-3812	53	32	)	)	PUNCT
ejpam-3812	53	33	\	\	PUNCT
ejpam-3812	54	1	ng[a	ng[a	NOUN
ejpam-3812	54	2	]	]	X
ejpam-3812	54	3	=	=	SYM
ejpam-3812	54	4	ng(b	ng(b	X
ejpam-3812	54	5	)	)	PUNCT
ejpam-3812	54	6	\	\	NOUN
ejpam-3812	54	7	{	{	PUNCT
ejpam-3812	54	8	a	a	X
ejpam-3812	54	9	}	}	PUNCT
ejpam-3812	54	10	.	.	PUNCT
ejpam-3812	55	1	proof	proof	NOUN
ejpam-3812	55	2	.	.	PUNCT
ejpam-3812	56	1	suppose	suppose	VERB
ejpam-3812	56	2	γt21f	γt21f	NOUN
ejpam-3812	56	3	(	(	PUNCT
ejpam-3812	56	4	g	g	NOUN
ejpam-3812	56	5	)	)	PUNCT
ejpam-3812	56	6	=	=	SYM
ejpam-3812	57	1	2	2	X
ejpam-3812	57	2	.	.	X
ejpam-3812	57	3	let	let	VERB
ejpam-3812	57	4	s	s	VERB
ejpam-3812	57	5	=	=	X
ejpam-3812	57	6	{	{	PUNCT
ejpam-3812	57	7	a	a	PRON
ejpam-3812	57	8	,	,	PUNCT
ejpam-3812	57	9	b	b	AUX
ejpam-3812	57	10	}	}	PUNCT
ejpam-3812	57	11	be	be	AUX
ejpam-3812	57	12	a	a	DET
ejpam-3812	57	13	γt21f	γt21f	NOUN
ejpam-3812	57	14	-set	-set	ADJ
ejpam-3812	57	15	of	of	ADP
ejpam-3812	57	16	g.	g.	PROPN
ejpam-3812	57	17	since	since	SCONJ
ejpam-3812	57	18	s	s	PROPN
ejpam-3812	57	19	is	be	AUX
ejpam-3812	57	20	a	a	DET
ejpam-3812	57	21	1fd	1fd	NOUN
ejpam-3812	57	22	-	-	PUNCT
ejpam-3812	57	23	set	set	NOUN
ejpam-3812	57	24	,	,	PUNCT
ejpam-3812	57	25	no	no	DET
ejpam-3812	57	26	vertex	vertex	NOUN
ejpam-3812	57	27	v	v	ADP
ejpam-3812	57	28	∈	∈	NOUN
ejpam-3812	57	29	v	v	NOUN
ejpam-3812	57	30	(	(	PUNCT
ejpam-3812	57	31	g	g	NOUN
ejpam-3812	57	32	)	)	PUNCT
ejpam-3812	57	33	\s	\s	NOUN
ejpam-3812	57	34	with	with	ADP
ejpam-3812	57	35	v	v	PRON
ejpam-3812	57	36	∈	∈	PROPN
ejpam-3812	57	37	ng(a)∩ng(b	ng(a)∩ng(b	PROPN
ejpam-3812	57	38	)	)	PUNCT
ejpam-3812	57	39	exists	exist	VERB
ejpam-3812	57	40	,	,	PUNCT
ejpam-3812	57	41	i.e.	i.e.	X
ejpam-3812	57	42	,	,	PUNCT
ejpam-3812	57	43	ng(a)∩ng(b	ng(a)∩ng(b	PROPN
ejpam-3812	57	44	)	)	PUNCT
ejpam-3812	57	45	=	=	PUNCT
ejpam-3812	57	46	∅.	∅.	ADP
ejpam-3812	57	47	this	this	PRON
ejpam-3812	57	48	implies	imply	VERB
ejpam-3812	57	49	that	that	SCONJ
ejpam-3812	57	50	ab	ab	PROPN
ejpam-3812	57	51	∈	∈	PROPN
ejpam-3812	57	52	e(g	e(g	PROPN
ejpam-3812	57	53	)	)	PUNCT
ejpam-3812	57	54	because	because	SCONJ
ejpam-3812	57	55	s	s	VERB
ejpam-3812	57	56	is	be	AUX
ejpam-3812	57	57	a	a	DET
ejpam-3812	57	58	semitotal	semitotal	ADJ
ejpam-3812	57	59	dominating	dominating	NOUN
ejpam-3812	57	60	set	set	NOUN
ejpam-3812	57	61	.	.	PUNCT
ejpam-3812	58	1	moreover	moreover	ADV
ejpam-3812	58	2	,	,	PUNCT
ejpam-3812	58	3	v	v	INTJ
ejpam-3812	58	4	(	(	PUNCT
ejpam-3812	58	5	g	g	NOUN
ejpam-3812	58	6	)	)	PUNCT
ejpam-3812	58	7	\	\	PUNCT
ejpam-3812	59	1	ng[a	ng[a	NOUN
ejpam-3812	59	2	]	]	X
ejpam-3812	59	3	=	=	SYM
ejpam-3812	59	4	ng(b	ng(b	X
ejpam-3812	59	5	)	)	PUNCT
ejpam-3812	59	6	\	\	NOUN
ejpam-3812	60	1	{	{	PUNCT
ejpam-3812	60	2	a	a	NOUN
ejpam-3812	60	3	}	}	PUNCT
ejpam-3812	60	4	(	(	PUNCT
ejpam-3812	60	5	or	or	CCONJ
ejpam-3812	60	6	v	v	NOUN
ejpam-3812	60	7	(	(	PUNCT
ejpam-3812	60	8	g	g	NOUN
ejpam-3812	60	9	)	)	PUNCT
ejpam-3812	60	10	\ng[b	\ng[b	NOUN
ejpam-3812	60	11	]	]	PUNCT
ejpam-3812	60	12	=	=	SYM
ejpam-3812	60	13	ng(a	ng(a	X
ejpam-3812	60	14	)	)	PUNCT
ejpam-3812	60	15	\	\	PUNCT
ejpam-3812	60	16	{	{	PUNCT
ejpam-3812	60	17	b	b	NOUN
ejpam-3812	60	18	}	}	PUNCT
ejpam-3812	60	19	)	)	PUNCT
ejpam-3812	60	20	because	because	SCONJ
ejpam-3812	60	21	s	s	NOUN
ejpam-3812	60	22	is	be	AUX
ejpam-3812	60	23	a	a	DET
ejpam-3812	60	24	dominating	dominating	NOUN
ejpam-3812	60	25	set	set	NOUN
ejpam-3812	60	26	.	.	PUNCT
ejpam-3812	61	1	the	the	DET
ejpam-3812	61	2	converse	converse	NOUN
ejpam-3812	61	3	is	be	AUX
ejpam-3812	61	4	clear	clear	ADJ
ejpam-3812	61	5	.	.	PUNCT
ejpam-3812	62	1	�	�	PROPN
ejpam-3812	62	2	corollary	corollary	ADJ
ejpam-3812	62	3	1	1	PROPN
ejpam-3812	62	4	.	.	NUM
ejpam-3812	62	5	γt21f	γt21f	PUNCT
ejpam-3812	63	1	(	(	PUNCT
ejpam-3812	63	2	k2	k2	NOUN
ejpam-3812	63	3	)	)	PUNCT
ejpam-3812	63	4	=	=	PRON
ejpam-3812	63	5	γt21f	γt21f	NOUN
ejpam-3812	63	6	(	(	PUNCT
ejpam-3812	63	7	k1	k1	NOUN
ejpam-3812	63	8	+	+	CCONJ
ejpam-3812	63	9	(	(	PUNCT
ejpam-3812	63	10	k1	k1	PROPN
ejpam-3812	63	11	∪h	∪h	NUM
ejpam-3812	63	12	)	)	PUNCT
ejpam-3812	63	13	)	)	PUNCT
ejpam-3812	64	1	=	=	PRON
ejpam-3812	65	1	γt21f	γt21f	NOUN
ejpam-3812	66	1	(	(	PUNCT
ejpam-3812	66	2	k2	k2	PROPN
ejpam-3812	66	3	◦	◦	NOUN
ejpam-3812	66	4	h	h	NOUN
ejpam-3812	66	5	)	)	PUNCT
ejpam-3812	66	6	=	=	SYM
ejpam-3812	66	7	2	2	NUM
ejpam-3812	66	8	for	for	ADP
ejpam-3812	66	9	any	any	DET
ejpam-3812	66	10	graph	graph	NOUN
ejpam-3812	66	11	h.	h.	PROPN
ejpam-3812	66	12	lemma	lemma	PROPN
ejpam-3812	67	1	1	1	X
ejpam-3812	67	2	.	.	PUNCT
ejpam-3812	68	1	[	[	X
ejpam-3812	68	2	6	6	NUM
ejpam-3812	68	3	]	]	PUNCT
ejpam-3812	68	4	let	let	VERB
ejpam-3812	68	5	g	g	PRON
ejpam-3812	68	6	be	be	AUX
ejpam-3812	68	7	a	a	DET
ejpam-3812	68	8	connected	connected	ADJ
ejpam-3812	68	9	graph	graph	NOUN
ejpam-3812	68	10	of	of	ADP
ejpam-3812	68	11	order	order	NOUN
ejpam-3812	68	12	n	n	PRON
ejpam-3812	68	13	≥	≥	NOUN
ejpam-3812	68	14	1	1	NUM
ejpam-3812	68	15	and	and	CCONJ
ejpam-3812	68	16	let	let	VERB
ejpam-3812	68	17	k	k	PRON
ejpam-3812	68	18	be	be	AUX
ejpam-3812	68	19	a	a	DET
ejpam-3812	68	20	positive	positive	ADJ
ejpam-3812	68	21	integer	integer	NOUN
ejpam-3812	68	22	such	such	ADJ
ejpam-3812	68	23	that	that	SCONJ
ejpam-3812	68	24	k	k	PROPN
ejpam-3812	68	25	≤	≤	PROPN
ejpam-3812	68	26	n.	n.	NOUN
ejpam-3812	68	27	then	then	ADV
ejpam-3812	68	28	:	:	PUNCT
ejpam-3812	68	29	(	(	PUNCT
ejpam-3812	68	30	i	i	NOUN
ejpam-3812	68	31	)	)	PUNCT
ejpam-3812	69	1	k	k	PROPN
ejpam-3812	69	2	≤	≤	PROPN
ejpam-3812	69	3	γkfd(g	γkfd(g	PROPN
ejpam-3812	69	4	)	)	PUNCT
ejpam-3812	69	5	≤	≤	NOUN
ejpam-3812	69	6	n.	n.	NOUN
ejpam-3812	69	7	(	(	PUNCT
ejpam-3812	69	8	ii	ii	PROPN
ejpam-3812	69	9	)	)	PUNCT
ejpam-3812	69	10	γkfd(g	γkfd(g	PROPN
ejpam-3812	69	11	)	)	PUNCT
ejpam-3812	69	12	=	=	SYM
ejpam-3812	70	1	k	k	NOUN
ejpam-3812	70	2	if	if	SCONJ
ejpam-3812	70	3	and	and	CCONJ
ejpam-3812	70	4	only	only	ADV
ejpam-3812	70	5	if	if	SCONJ
ejpam-3812	70	6	g	g	PROPN
ejpam-3812	70	7	has	have	VERB
ejpam-3812	70	8	a	a	DET
ejpam-3812	70	9	kfd	kfd	NOUN
ejpam-3812	70	10	-	-	PUNCT
ejpam-3812	70	11	set	set	NOUN
ejpam-3812	70	12	s	s	NOUN
ejpam-3812	70	13	with	with	ADP
ejpam-3812	70	14	|s|	|s|	PROPN
ejpam-3812	70	15	=	=	SYM
ejpam-3812	70	16	k.	k.	PROPN
ejpam-3812	70	17	(	(	PUNCT
ejpam-3812	70	18	iii	iii	NOUN
ejpam-3812	70	19	)	)	PUNCT
ejpam-3812	70	20	if	if	SCONJ
ejpam-3812	70	21	γkfd(g	γkfd(g	PROPN
ejpam-3812	70	22	)	)	PUNCT
ejpam-3812	70	23	=	=	SYM
ejpam-3812	70	24	n	n	CCONJ
ejpam-3812	70	25	,	,	PUNCT
ejpam-3812	70	26	then	then	ADV
ejpam-3812	70	27	g	g	PROPN
ejpam-3812	70	28	has	have	VERB
ejpam-3812	70	29	no	no	DET
ejpam-3812	70	30	vertex	vertex	NOUN
ejpam-3812	70	31	of	of	ADP
ejpam-3812	70	32	degree	degree	NOUN
ejpam-3812	70	33	k.	k.	PROPN
ejpam-3812	70	34	theorem	theorem	PROPN
ejpam-3812	70	35	2	2	X
ejpam-3812	70	36	.	.	PUNCT
ejpam-3812	71	1	let	let	VERB
ejpam-3812	71	2	g	g	PRON
ejpam-3812	71	3	be	be	AUX
ejpam-3812	71	4	a	a	DET
ejpam-3812	71	5	connected	connected	ADJ
ejpam-3812	71	6	graph	graph	NOUN
ejpam-3812	71	7	of	of	ADP
ejpam-3812	71	8	order	order	NOUN
ejpam-3812	71	9	n	n	PRON
ejpam-3812	71	10	≥	≥	NOUN
ejpam-3812	71	11	2	2	NUM
ejpam-3812	71	12	and	and	CCONJ
ejpam-3812	71	13	let	let	VERB
ejpam-3812	71	14	k	k	PRON
ejpam-3812	71	15	be	be	AUX
ejpam-3812	71	16	a	a	DET
ejpam-3812	71	17	positive	positive	ADJ
ejpam-3812	71	18	integer	integer	NOUN
ejpam-3812	71	19	with	with	ADP
ejpam-3812	71	20	2	2	NUM
ejpam-3812	71	21	≤	≤	NUM
ejpam-3812	71	22	k	k	PROPN
ejpam-3812	71	23	≤	≤	PROPN
ejpam-3812	71	24	n.	n.	NOUN
ejpam-3812	71	25	then	then	ADV
ejpam-3812	71	26	γt2kf	γt2kf	NUM
ejpam-3812	71	27	(	(	PUNCT
ejpam-3812	71	28	g	g	NOUN
ejpam-3812	71	29	)	)	PUNCT
ejpam-3812	71	30	=	=	SYM
ejpam-3812	72	1	k	k	NOUN
ejpam-3812	72	2	if	if	SCONJ
ejpam-3812	72	3	and	and	CCONJ
ejpam-3812	72	4	only	only	ADV
ejpam-3812	72	5	if	if	SCONJ
ejpam-3812	72	6	n	n	PROPN
ejpam-3812	72	7	=	=	SYM
ejpam-3812	72	8	k	k	PROPN
ejpam-3812	72	9	or	or	CCONJ
ejpam-3812	72	10	g	g	PROPN
ejpam-3812	72	11	=	=	PUNCT
ejpam-3812	72	12	h1	h1	PROPN
ejpam-3812	72	13	+	+	CCONJ
ejpam-3812	72	14	h2	h2	NOUN
ejpam-3812	72	15	for	for	ADP
ejpam-3812	72	16	some	some	DET
ejpam-3812	72	17	graphs	graph	NOUN
ejpam-3812	72	18	h1	h1	ADJ
ejpam-3812	72	19	and	and	CCONJ
ejpam-3812	72	20	h2	h2	NOUN
ejpam-3812	72	21	with	with	ADP
ejpam-3812	72	22	|v	|v	PROPN
ejpam-3812	72	23	(	(	PUNCT
ejpam-3812	72	24	h1)|	h1)|	PROPN
ejpam-3812	72	25	=	=	SYM
ejpam-3812	72	26	k.	k.	NOUN
ejpam-3812	72	27	proof	proof	NOUN
ejpam-3812	72	28	.	.	PUNCT
ejpam-3812	73	1	suppose	suppose	VERB
ejpam-3812	73	2	γt2kf	γt2kf	NUM
ejpam-3812	73	3	(	(	PUNCT
ejpam-3812	73	4	g	g	NOUN
ejpam-3812	73	5	)	)	PUNCT
ejpam-3812	73	6	=	=	VERB
ejpam-3812	73	7	k.	k.	PROPN
ejpam-3812	73	8	suppose	suppose	VERB
ejpam-3812	73	9	further	far	ADV
ejpam-3812	73	10	that	that	SCONJ
ejpam-3812	73	11	k	k	PROPN
ejpam-3812	73	12	<	<	X
ejpam-3812	73	13	n.	n.	PROPN
ejpam-3812	73	14	let	let	VERB
ejpam-3812	73	15	s	s	PRON
ejpam-3812	73	16	be	be	AUX
ejpam-3812	73	17	a	a	DET
ejpam-3812	73	18	γt2kf	γt2kf	NUM
ejpam-3812	73	19	-set	-set	ADJ
ejpam-3812	73	20	of	of	ADP
ejpam-3812	73	21	g.	g.	PROPN
ejpam-3812	73	22	then	then	ADV
ejpam-3812	73	23	|s|	|s|	PROPN
ejpam-3812	73	24	=	=	SYM
ejpam-3812	73	25	k.	k.	PROPN
ejpam-3812	73	26	set	set	VERB
ejpam-3812	73	27	h1	h1	PROPN
ejpam-3812	73	28	=	=	PUNCT
ejpam-3812	74	1	〈	〈	PROPN
ejpam-3812	74	2	s	s	PROPN
ejpam-3812	74	3	〉	〉	NOUN
ejpam-3812	74	4	and	and	CCONJ
ejpam-3812	74	5	h2	h2	NOUN
ejpam-3812	74	6	=	=	PUNCT
ejpam-3812	75	1	〈	〈	PROPN
ejpam-3812	75	2	v	v	X
ejpam-3812	75	3	(	(	PUNCT
ejpam-3812	75	4	g	g	NOUN
ejpam-3812	75	5	)	)	PUNCT
ejpam-3812	75	6	\	\	PUNCT
ejpam-3812	76	1	s	s	PROPN
ejpam-3812	76	2	〉	〉	PROPN
ejpam-3812	76	3	.	.	PUNCT
ejpam-3812	77	1	since	since	SCONJ
ejpam-3812	77	2	s	s	PROPN
ejpam-3812	77	3	is	be	AUX
ejpam-3812	77	4	a	a	DET
ejpam-3812	77	5	k	k	ADJ
ejpam-3812	77	6	-	-	ADJ
ejpam-3812	77	7	fair	fair	ADJ
ejpam-3812	77	8	dominating	dominating	NOUN
ejpam-3812	77	9	set	set	NOUN
ejpam-3812	77	10	of	of	ADP
ejpam-3812	77	11	g	g	PROPN
ejpam-3812	77	12	,	,	PUNCT
ejpam-3812	77	13	it	it	PRON
ejpam-3812	77	14	follows	follow	VERB
ejpam-3812	77	15	that	that	SCONJ
ejpam-3812	77	16	v	v	X
ejpam-3812	77	17	(	(	PUNCT
ejpam-3812	77	18	g	g	NOUN
ejpam-3812	77	19	)	)	PUNCT
ejpam-3812	77	20	\	\	PUNCT
ejpam-3812	77	21	s	s	PART
ejpam-3812	77	22	⊆	⊆	NUM
ejpam-3812	77	23	ng(v	ng(v	PUNCT
ejpam-3812	77	24	)	)	PUNCT
ejpam-3812	77	25	for	for	ADP
ejpam-3812	77	26	each	each	DET
ejpam-3812	77	27	v	v	NOUN
ejpam-3812	77	28	∈	∈	PROPN
ejpam-3812	77	29	s.	s.	PROPN
ejpam-3812	77	30	hence	hence	ADV
ejpam-3812	77	31	,	,	PUNCT
ejpam-3812	77	32	g	g	PROPN
ejpam-3812	77	33	=	=	PUNCT
ejpam-3812	77	34	h1	h1	PROPN
ejpam-3812	77	35	+	+	PROPN
ejpam-3812	77	36	h2	h2	NOUN
ejpam-3812	77	37	.	.	PUNCT
ejpam-3812	78	1	for	for	ADP
ejpam-3812	78	2	the	the	DET
ejpam-3812	78	3	converse	converse	NOUN
ejpam-3812	78	4	,	,	PUNCT
ejpam-3812	78	5	suppose	suppose	VERB
ejpam-3812	78	6	that	that	SCONJ
ejpam-3812	78	7	g	g	PROPN
ejpam-3812	78	8	=	=	PUNCT
ejpam-3812	78	9	h1	h1	PROPN
ejpam-3812	78	10	+	+	CCONJ
ejpam-3812	78	11	h2	h2	NOUN
ejpam-3812	78	12	where	where	SCONJ
ejpam-3812	78	13	|v	|v	PROPN
ejpam-3812	78	14	(	(	PUNCT
ejpam-3812	78	15	h1)|	h1)|	PROPN
ejpam-3812	78	16	=	=	SYM
ejpam-3812	78	17	k.	k.	PROPN
ejpam-3812	78	18	then	then	ADV
ejpam-3812	78	19	clearly	clearly	ADV
ejpam-3812	78	20	,	,	PUNCT
ejpam-3812	78	21	s	s	VERB
ejpam-3812	78	22	=	=	SYM
ejpam-3812	78	23	v	v	PROPN
ejpam-3812	78	24	(	(	PUNCT
ejpam-3812	78	25	h1	h1	PROPN
ejpam-3812	78	26	)	)	PUNCT
ejpam-3812	78	27	is	be	AUX
ejpam-3812	78	28	a	a	DET
ejpam-3812	78	29	k	k	ADJ
ejpam-3812	78	30	-	-	ADJ
ejpam-3812	78	31	fair	fair	ADJ
ejpam-3812	78	32	dominating	dominating	NOUN
ejpam-3812	78	33	set	set	NOUN
ejpam-3812	78	34	of	of	ADP
ejpam-3812	78	35	g.	g.	PROPN
ejpam-3812	78	36	let	let	VERB
ejpam-3812	78	37	x	x	PRON
ejpam-3812	78	38	,	,	PUNCT
ejpam-3812	78	39	y	y	PROPN
ejpam-3812	78	40	∈	∈	PROPN
ejpam-3812	78	41	s	s	PART
ejpam-3812	78	42	with	with	ADP
ejpam-3812	78	43	x	x	SYM
ejpam-3812	78	44	6=	6=	PROPN
ejpam-3812	78	45	y.	y.	NOUN
ejpam-3812	78	46	suppose	suppose	VERB
ejpam-3812	79	1	xy	xy	PROPN
ejpam-3812	79	2	/∈	/∈	PUNCT
ejpam-3812	79	3	e(g	e(g	PROPN
ejpam-3812	79	4	)	)	PUNCT
ejpam-3812	79	5	.	.	PUNCT
ejpam-3812	80	1	pick	pick	VERB
ejpam-3812	80	2	any	any	DET
ejpam-3812	80	3	z	z	NOUN
ejpam-3812	80	4	∈	∈	PROPN
ejpam-3812	80	5	v	v	NOUN
ejpam-3812	80	6	(	(	PUNCT
ejpam-3812	80	7	h2	h2	NOUN
ejpam-3812	80	8	)	)	PUNCT
ejpam-3812	80	9	.	.	PUNCT
ejpam-3812	81	1	then	then	ADV
ejpam-3812	81	2	z	z	PROPN
ejpam-3812	81	3	∈	∈	PROPN
ejpam-3812	81	4	ng(x	ng(x	NUM
ejpam-3812	81	5	)	)	PUNCT
ejpam-3812	81	6	∩	∩	NOUN
ejpam-3812	81	7	ng(y	ng(y	NOUN
ejpam-3812	81	8	)	)	PUNCT
ejpam-3812	81	9	.	.	PUNCT
ejpam-3812	82	1	this	this	PRON
ejpam-3812	82	2	implies	imply	VERB
ejpam-3812	82	3	that	that	SCONJ
ejpam-3812	82	4	dg(x	dg(x	PROPN
ejpam-3812	82	5	,	,	PUNCT
ejpam-3812	82	6	y	y	NOUN
ejpam-3812	82	7	)	)	PUNCT
ejpam-3812	82	8	=	=	SYM
ejpam-3812	83	1	2	2	X
ejpam-3812	83	2	.	.	X
ejpam-3812	83	3	therefore	therefore	ADV
ejpam-3812	83	4	,	,	PUNCT
ejpam-3812	83	5	s	s	VERB
ejpam-3812	83	6	is	be	AUX
ejpam-3812	83	7	a	a	DET
ejpam-3812	83	8	semitotal	semitotal	ADJ
ejpam-3812	83	9	kfd	kfd	NOUN
ejpam-3812	83	10	-	-	PUNCT
ejpam-3812	83	11	set	set	NOUN
ejpam-3812	83	12	of	of	ADP
ejpam-3812	83	13	g.	g.	PROPN
ejpam-3812	83	14	by	by	ADP
ejpam-3812	83	15	lemma	lemma	PROPN
ejpam-3812	83	16	1	1	NUM
ejpam-3812	83	17	(	(	PUNCT
ejpam-3812	83	18	ii	ii	NOUN
ejpam-3812	83	19	)	)	PUNCT
ejpam-3812	83	20	,	,	PUNCT
ejpam-3812	83	21	s	s	VERB
ejpam-3812	83	22	is	be	AUX
ejpam-3812	83	23	a	a	DET
ejpam-3812	83	24	γt2kf	γt2kf	NUM
ejpam-3812	83	25	-set	-set	ADJ
ejpam-3812	83	26	of	of	ADP
ejpam-3812	83	27	g	g	NOUN
ejpam-3812	83	28	,	,	PUNCT
ejpam-3812	83	29	that	that	ADV
ejpam-3812	83	30	is	is	ADV
ejpam-3812	83	31	,	,	PUNCT
ejpam-3812	83	32	γt2kf	γt2kf	NUM
ejpam-3812	83	33	(	(	PUNCT
ejpam-3812	83	34	g	g	NOUN
ejpam-3812	83	35	)	)	PUNCT
ejpam-3812	83	36	=	=	PUNCT
ejpam-3812	83	37	|s|	|s|	PROPN
ejpam-3812	83	38	=	=	PUNCT
ejpam-3812	83	39	k.	k.	PROPN
ejpam-3812	83	40	�	�	PROPN
ejpam-3812	83	41	corollary	corollary	NOUN
ejpam-3812	83	42	2	2	PROPN
ejpam-3812	83	43	.	.	PUNCT
ejpam-3812	84	1	let	let	VERB
ejpam-3812	84	2	g	g	PRON
ejpam-3812	84	3	be	be	AUX
ejpam-3812	84	4	a	a	DET
ejpam-3812	84	5	connected	connected	ADJ
ejpam-3812	84	6	graph	graph	NOUN
ejpam-3812	84	7	of	of	ADP
ejpam-3812	84	8	order	order	NOUN
ejpam-3812	84	9	n	n	PRON
ejpam-3812	84	10	≥	≥	NOUN
ejpam-3812	84	11	3	3	NUM
ejpam-3812	84	12	.	.	PUNCT
ejpam-3812	85	1	then	then	ADV
ejpam-3812	85	2	γt22f	γt22f	ADV
ejpam-3812	85	3	(	(	PUNCT
ejpam-3812	85	4	g	g	NOUN
ejpam-3812	85	5	)	)	PUNCT
ejpam-3812	85	6	=	=	SYM
ejpam-3812	85	7	2	2	NUM
ejpam-3812	85	8	if	if	SCONJ
ejpam-3812	85	9	and	and	CCONJ
ejpam-3812	85	10	only	only	ADV
ejpam-3812	85	11	if	if	SCONJ
ejpam-3812	85	12	g	g	PROPN
ejpam-3812	85	13	=	=	SYM
ejpam-3812	85	14	k2	k2	PROPN
ejpam-3812	85	15	+	+	PROPN
ejpam-3812	85	16	h	h	NOUN
ejpam-3812	85	17	or	or	CCONJ
ejpam-3812	85	18	g	g	PROPN
ejpam-3812	85	19	=	=	PROPN
ejpam-3812	85	20	k2	k2	PROPN
ejpam-3812	85	21	+	+	PROPN
ejpam-3812	85	22	h	h	NOUN
ejpam-3812	85	23	for	for	ADP
ejpam-3812	85	24	some	some	DET
ejpam-3812	85	25	graph	graph	NOUN
ejpam-3812	85	26	h.	h.	PROPN
ejpam-3812	85	27	m.	m.	PROPN
ejpam-3812	85	28	ortega	ortega	PROPN
ejpam-3812	85	29	,	,	PUNCT
ejpam-3812	85	30	r.	r.	PROPN
ejpam-3812	85	31	isla	isla	PROPN
ejpam-3812	85	32	/	/	SYM
ejpam-3812	85	33	eur	eur	PROPN
ejpam-3812	85	34	.	.	PUNCT
ejpam-3812	86	1	j.	j.	PROPN
ejpam-3812	86	2	pure	pure	PROPN
ejpam-3812	86	3	appl	appl	PROPN
ejpam-3812	86	4	.	.	PROPN
ejpam-3812	86	5	math	math	PROPN
ejpam-3812	86	6	,	,	PUNCT
ejpam-3812	86	7	13	13	NUM
ejpam-3812	86	8	(	(	PUNCT
ejpam-3812	86	9	4	4	NUM
ejpam-3812	86	10	)	)	PUNCT
ejpam-3812	86	11	(	(	PUNCT
ejpam-3812	86	12	2020	2020	NUM
ejpam-3812	86	13	)	)	PUNCT
ejpam-3812	86	14	,	,	PUNCT
ejpam-3812	86	15	779	779	NUM
ejpam-3812	86	16	-	-	SYM
ejpam-3812	86	17	793	793	NUM
ejpam-3812	86	18	782	782	NUM
ejpam-3812	86	19	proof	proof	NOUN
ejpam-3812	86	20	.	.	PUNCT
ejpam-3812	87	1	suppose	suppose	VERB
ejpam-3812	87	2	γt22f	γt22f	X
ejpam-3812	87	3	(	(	PUNCT
ejpam-3812	87	4	g	g	NOUN
ejpam-3812	87	5	)	)	PUNCT
ejpam-3812	87	6	=	=	SYM
ejpam-3812	87	7	2	2	NUM
ejpam-3812	87	8	,	,	PUNCT
ejpam-3812	87	9	say	say	VERB
ejpam-3812	87	10	s	s	X
ejpam-3812	87	11	=	=	PUNCT
ejpam-3812	87	12	{	{	PUNCT
ejpam-3812	87	13	a	a	DET
ejpam-3812	87	14	,	,	PUNCT
ejpam-3812	87	15	b	b	NOUN
ejpam-3812	87	16	}	}	PUNCT
ejpam-3812	87	17	is	be	AUX
ejpam-3812	87	18	a	a	DET
ejpam-3812	87	19	γt22f	γt22f	ADJ
ejpam-3812	87	20	-set	-set	ADJ
ejpam-3812	87	21	ofg	ofg	PROPN
ejpam-3812	87	22	.	.	PUNCT
ejpam-3812	88	1	leth	leth	PROPN
ejpam-3812	88	2	=	=	SYM
ejpam-3812	88	3	〈	〈	PROPN
ejpam-3812	88	4	v	v	X
ejpam-3812	88	5	(	(	PUNCT
ejpam-3812	88	6	g	g	NOUN
ejpam-3812	88	7	)	)	PUNCT
ejpam-3812	88	8	\	\	PUNCT
ejpam-3812	89	1	s	s	PROPN
ejpam-3812	89	2	〉	〉	PROPN
ejpam-3812	89	3	.	.	PUNCT
ejpam-3812	90	1	since	since	SCONJ
ejpam-3812	90	2	s	s	PROPN
ejpam-3812	90	3	is	be	AUX
ejpam-3812	90	4	a	a	DET
ejpam-3812	90	5	2	2	NUM
ejpam-3812	90	6	-	-	PUNCT
ejpam-3812	90	7	fair	fair	ADJ
ejpam-3812	90	8	dominating	dominating	NOUN
ejpam-3812	90	9	set	set	NOUN
ejpam-3812	90	10	,	,	PUNCT
ejpam-3812	90	11	v	v	PROPN
ejpam-3812	90	12	(	(	PUNCT
ejpam-3812	90	13	h	h	NOUN
ejpam-3812	90	14	)	)	PUNCT
ejpam-3812	91	1	=	=	NOUN
ejpam-3812	91	2	v	v	X
ejpam-3812	91	3	(	(	PUNCT
ejpam-3812	91	4	g	g	NOUN
ejpam-3812	91	5	)	)	PUNCT
ejpam-3812	91	6	\	\	PUNCT
ejpam-3812	91	7	s	s	PART
ejpam-3812	91	8	⊆	⊆	NUM
ejpam-3812	91	9	ng(a	ng(a	SYM
ejpam-3812	91	10	)	)	PUNCT
ejpam-3812	91	11	∩ng(b	∩ng(b	NOUN
ejpam-3812	91	12	)	)	PUNCT
ejpam-3812	91	13	.	.	PUNCT
ejpam-3812	92	1	since	since	SCONJ
ejpam-3812	92	2	s	s	PROPN
ejpam-3812	92	3	is	be	AUX
ejpam-3812	92	4	a	a	DET
ejpam-3812	92	5	semitotal	semitotal	ADJ
ejpam-3812	92	6	2	2	NUM
ejpam-3812	92	7	-	-	PUNCT
ejpam-3812	92	8	fair	fair	ADJ
ejpam-3812	92	9	dominating	dominating	NOUN
ejpam-3812	92	10	set	set	NOUN
ejpam-3812	92	11	,	,	PUNCT
ejpam-3812	92	12	either	either	CCONJ
ejpam-3812	92	13	ab	ab	PROPN
ejpam-3812	92	14	∈	∈	PROPN
ejpam-3812	92	15	e(g	e(g	PROPN
ejpam-3812	92	16	)	)	PUNCT
ejpam-3812	92	17	or	or	CCONJ
ejpam-3812	92	18	dg(a	dg(a	X
ejpam-3812	92	19	,	,	PUNCT
ejpam-3812	92	20	b	b	X
ejpam-3812	92	21	)	)	PUNCT
ejpam-3812	92	22	=	=	SYM
ejpam-3812	92	23	2	2	X
ejpam-3812	92	24	.	.	PUNCT
ejpam-3812	93	1	thus	thus	ADV
ejpam-3812	93	2	,	,	PUNCT
ejpam-3812	93	3	g	g	PROPN
ejpam-3812	93	4	=	=	PUNCT
ejpam-3812	93	5	k2+h	k2+h	X
ejpam-3812	93	6	or	or	CCONJ
ejpam-3812	93	7	g	g	PROPN
ejpam-3812	93	8	=	=	SYM
ejpam-3812	93	9	k2+h	k2+h	PROPN
ejpam-3812	93	10	.	.	PROPN
ejpam-3812	94	1	for	for	ADP
ejpam-3812	94	2	the	the	DET
ejpam-3812	94	3	converse	converse	NOUN
ejpam-3812	94	4	,	,	PUNCT
ejpam-3812	94	5	suppose	suppose	VERB
ejpam-3812	94	6	g	g	PROPN
ejpam-3812	94	7	=	=	PROPN
ejpam-3812	94	8	k2	k2	PROPN
ejpam-3812	95	1	+	+	PROPN
ejpam-3812	95	2	h	h	NOUN
ejpam-3812	95	3	or	or	CCONJ
ejpam-3812	95	4	g	g	PROPN
ejpam-3812	95	5	=	=	PROPN
ejpam-3812	95	6	k2	k2	PROPN
ejpam-3812	95	7	+	+	PROPN
ejpam-3812	95	8	h.	h.	PROPN
ejpam-3812	95	9	then	then	ADV
ejpam-3812	95	10	clearly	clearly	ADV
ejpam-3812	95	11	,	,	PUNCT
ejpam-3812	95	12	γt22f	γt22f	X
ejpam-3812	95	13	(	(	PUNCT
ejpam-3812	95	14	g	g	NOUN
ejpam-3812	95	15	)	)	PUNCT
ejpam-3812	95	16	=	=	SYM
ejpam-3812	95	17	2	2	X
ejpam-3812	95	18	.	.	X
ejpam-3812	95	19	�	�	PROPN
ejpam-3812	95	20	theorem	theorem	VERB
ejpam-3812	95	21	3	3	X
ejpam-3812	95	22	.	.	PUNCT
ejpam-3812	96	1	let	let	VERB
ejpam-3812	96	2	g	g	PRON
ejpam-3812	96	3	be	be	AUX
ejpam-3812	96	4	a	a	DET
ejpam-3812	96	5	connected	connected	ADJ
ejpam-3812	96	6	graph	graph	NOUN
ejpam-3812	96	7	of	of	ADP
ejpam-3812	96	8	order	order	NOUN
ejpam-3812	96	9	n	n	PRON
ejpam-3812	96	10	≥	≥	NOUN
ejpam-3812	96	11	2	2	NUM
ejpam-3812	96	12	and	and	CCONJ
ejpam-3812	96	13	let	let	VERB
ejpam-3812	96	14	k	k	PROPN
ejpam-3812	96	15	≥	≥	NUM
ejpam-3812	96	16	2	2	NUM
ejpam-3812	96	17	.	.	PUNCT
ejpam-3812	97	1	then	then	ADV
ejpam-3812	97	2	s	s	VERB
ejpam-3812	97	3	⊆	⊆	NUM
ejpam-3812	97	4	v	v	NOUN
ejpam-3812	97	5	(	(	PUNCT
ejpam-3812	97	6	g	g	NOUN
ejpam-3812	97	7	)	)	PUNCT
ejpam-3812	97	8	is	be	AUX
ejpam-3812	97	9	a	a	DET
ejpam-3812	97	10	semitotal	semitotal	ADJ
ejpam-3812	97	11	kfd	kfd	NOUN
ejpam-3812	97	12	-	-	PUNCT
ejpam-3812	97	13	set	set	NOUN
ejpam-3812	97	14	if	if	SCONJ
ejpam-3812	97	15	and	and	CCONJ
ejpam-3812	97	16	only	only	ADV
ejpam-3812	97	17	if	if	SCONJ
ejpam-3812	97	18	it	it	PRON
ejpam-3812	97	19	is	be	AUX
ejpam-3812	97	20	a	a	DET
ejpam-3812	97	21	kfd	kfd	NOUN
ejpam-3812	97	22	-	-	PUNCT
ejpam-3812	97	23	set	set	NOUN
ejpam-3812	97	24	.	.	PUNCT
ejpam-3812	98	1	in	in	ADP
ejpam-3812	98	2	particular	particular	ADJ
ejpam-3812	98	3	,	,	PUNCT
ejpam-3812	98	4	γt2kf	γt2kf	NUM
ejpam-3812	98	5	(	(	PUNCT
ejpam-3812	98	6	g	g	NOUN
ejpam-3812	98	7	)	)	PUNCT
ejpam-3812	98	8	=	=	SYM
ejpam-3812	98	9	γkfd(g	γkfd(g	PROPN
ejpam-3812	98	10	)	)	PUNCT
ejpam-3812	98	11	.	.	PUNCT
ejpam-3812	99	1	proof	proof	NOUN
ejpam-3812	99	2	.	.	PUNCT
ejpam-3812	100	1	suppose	suppose	VERB
ejpam-3812	100	2	s	s	PRON
ejpam-3812	100	3	is	be	AUX
ejpam-3812	100	4	a	a	DET
ejpam-3812	100	5	semitotal	semitotal	ADJ
ejpam-3812	100	6	kfd	kfd	NOUN
ejpam-3812	100	7	-	-	PUNCT
ejpam-3812	100	8	set	set	NOUN
ejpam-3812	100	9	.	.	PUNCT
ejpam-3812	101	1	then	then	ADV
ejpam-3812	101	2	s	s	VERB
ejpam-3812	101	3	is	be	AUX
ejpam-3812	101	4	a	a	DET
ejpam-3812	101	5	kfd	kfd	NOUN
ejpam-3812	101	6	-	-	PUNCT
ejpam-3812	101	7	set	set	NOUN
ejpam-3812	101	8	by	by	ADP
ejpam-3812	101	9	remark	remark	NOUN
ejpam-3812	101	10	1	1	NUM
ejpam-3812	101	11	.	.	PUNCT
ejpam-3812	102	1	for	for	ADP
ejpam-3812	102	2	the	the	DET
ejpam-3812	102	3	converse	converse	NOUN
ejpam-3812	102	4	,	,	PUNCT
ejpam-3812	102	5	suppose	suppose	VERB
ejpam-3812	102	6	s	s	NOUN
ejpam-3812	102	7	is	be	AUX
ejpam-3812	102	8	a	a	DET
ejpam-3812	102	9	kfd	kfd	NOUN
ejpam-3812	102	10	-	-	PUNCT
ejpam-3812	102	11	set	set	NOUN
ejpam-3812	102	12	.	.	PUNCT
ejpam-3812	103	1	let	let	VERB
ejpam-3812	103	2	x	x	SYM
ejpam-3812	103	3	∈	∈	PROPN
ejpam-3812	103	4	s.	s.	PROPN
ejpam-3812	103	5	if	if	SCONJ
ejpam-3812	103	6	ng(x	ng(x	NOUN
ejpam-3812	103	7	)	)	PUNCT
ejpam-3812	103	8	∩	∩	PROPN
ejpam-3812	103	9	s	s	PART
ejpam-3812	103	10	6=	6=	NUM
ejpam-3812	103	11	∅	∅	NOUN
ejpam-3812	103	12	,	,	PUNCT
ejpam-3812	103	13	then	then	ADV
ejpam-3812	103	14	there	there	PRON
ejpam-3812	103	15	exists	exist	VERB
ejpam-3812	103	16	w	w	PROPN
ejpam-3812	103	17	∈	∈	PROPN
ejpam-3812	103	18	s	s	VERB
ejpam-3812	103	19	such	such	ADJ
ejpam-3812	103	20	that	that	PRON
ejpam-3812	103	21	dg(x	dg(x	ADJ
ejpam-3812	103	22	,	,	PUNCT
ejpam-3812	103	23	w	w	NOUN
ejpam-3812	103	24	)	)	PUNCT
ejpam-3812	103	25	=	=	SYM
ejpam-3812	103	26	1	1	X
ejpam-3812	103	27	.	.	PUNCT
ejpam-3812	103	28	suppose	suppose	VERB
ejpam-3812	103	29	ng(x	ng(x	NOUN
ejpam-3812	103	30	)	)	PUNCT
ejpam-3812	103	31	∩	∩	NOUN
ejpam-3812	103	32	s	s	PART
ejpam-3812	103	33	=	=	X
ejpam-3812	103	34	∅.	∅.	VERB
ejpam-3812	103	35	let	let	VERB
ejpam-3812	103	36	v	v	ADP
ejpam-3812	103	37	∈	∈	PROPN
ejpam-3812	103	38	ng(x	ng(x	NUM
ejpam-3812	103	39	)	)	PUNCT
ejpam-3812	103	40	.	.	PUNCT
ejpam-3812	104	1	then	then	ADV
ejpam-3812	104	2	v	v	X
ejpam-3812	104	3	∈	∈	PROPN
ejpam-3812	104	4	v	v	NOUN
ejpam-3812	104	5	(	(	PUNCT
ejpam-3812	104	6	g	g	NOUN
ejpam-3812	104	7	)	)	PUNCT
ejpam-3812	104	8	\	\	PUNCT
ejpam-3812	105	1	s.	s.	PROPN
ejpam-3812	105	2	since	since	SCONJ
ejpam-3812	105	3	s	s	PROPN
ejpam-3812	105	4	is	be	AUX
ejpam-3812	105	5	a	a	DET
ejpam-3812	105	6	kfd	kfd	NOUN
ejpam-3812	105	7	-	-	PUNCT
ejpam-3812	105	8	set	set	NOUN
ejpam-3812	105	9	and	and	CCONJ
ejpam-3812	105	10	k	k	PROPN
ejpam-3812	105	11	≥	≥	NUM
ejpam-3812	105	12	2	2	NUM
ejpam-3812	105	13	,	,	PUNCT
ejpam-3812	105	14	there	there	PRON
ejpam-3812	105	15	exists	exist	VERB
ejpam-3812	105	16	u	u	PROPN
ejpam-3812	105	17	∈	∈	PROPN
ejpam-3812	105	18	s	s	PART
ejpam-3812	105	19	\	\	X
ejpam-3812	105	20	{	{	PUNCT
ejpam-3812	105	21	x	x	X
ejpam-3812	105	22	}	}	PUNCT
ejpam-3812	105	23	such	such	ADJ
ejpam-3812	105	24	that	that	SCONJ
ejpam-3812	105	25	uv	uv	PROPN
ejpam-3812	105	26	∈	∈	PROPN
ejpam-3812	105	27	e(g	e(g	PROPN
ejpam-3812	105	28	)	)	PUNCT
ejpam-3812	105	29	.	.	PUNCT
ejpam-3812	106	1	hence	hence	ADV
ejpam-3812	106	2	,	,	PUNCT
ejpam-3812	106	3	dg(x	dg(x	X
ejpam-3812	106	4	,	,	PUNCT
ejpam-3812	106	5	u	u	NOUN
ejpam-3812	106	6	)	)	PUNCT
ejpam-3812	106	7	=	=	SYM
ejpam-3812	106	8	2	2	X
ejpam-3812	106	9	.	.	PUNCT
ejpam-3812	107	1	thus	thus	ADV
ejpam-3812	107	2	,	,	PUNCT
ejpam-3812	107	3	dg(x	dg(x	X
ejpam-3812	107	4	,	,	PUNCT
ejpam-3812	107	5	z	z	NOUN
ejpam-3812	107	6	)	)	PUNCT
ejpam-3812	107	7	≤	≤	NUM
ejpam-3812	107	8	2	2	NUM
ejpam-3812	107	9	for	for	ADP
ejpam-3812	107	10	some	some	DET
ejpam-3812	107	11	z	z	PROPN
ejpam-3812	107	12	∈	∈	PROPN
ejpam-3812	107	13	s.	s.	PROPN
ejpam-3812	107	14	therefore	therefore	ADV
ejpam-3812	107	15	,	,	PUNCT
ejpam-3812	107	16	s	s	VERB
ejpam-3812	107	17	is	be	AUX
ejpam-3812	107	18	a	a	DET
ejpam-3812	107	19	semitotal	semitotal	ADJ
ejpam-3812	107	20	kfd	kfd	NOUN
ejpam-3812	107	21	-	-	PUNCT
ejpam-3812	107	22	set	set	NOUN
ejpam-3812	107	23	of	of	ADP
ejpam-3812	107	24	g.	g.	PROPN
ejpam-3812	107	25	accordingly	accordingly	ADV
ejpam-3812	107	26	,	,	PUNCT
ejpam-3812	107	27	γt2kf	γt2kf	NUM
ejpam-3812	107	28	(	(	PUNCT
ejpam-3812	107	29	g	g	NOUN
ejpam-3812	107	30	)	)	PUNCT
ejpam-3812	107	31	=	=	SYM
ejpam-3812	107	32	γkfd(g	γkfd(g	PROPN
ejpam-3812	107	33	)	)	PUNCT
ejpam-3812	107	34	.	.	PUNCT
ejpam-3812	108	1	�	�	PROPN
ejpam-3812	108	2	remark	remark	VERB
ejpam-3812	108	3	2	2	NUM
ejpam-3812	108	4	.	.	PUNCT
ejpam-3812	108	5	not	not	PART
ejpam-3812	108	6	every	every	DET
ejpam-3812	108	7	connected	connected	ADJ
ejpam-3812	108	8	graph	graph	NOUN
ejpam-3812	108	9	of	of	ADP
ejpam-3812	108	10	order	order	NOUN
ejpam-3812	108	11	n	n	PRON
ejpam-3812	108	12	admits	admit	VERB
ejpam-3812	108	13	an	an	DET
ejpam-3812	108	14	independent	independent	ADJ
ejpam-3812	108	15	kfd	kfd	NOUN
ejpam-3812	108	16	-	-	PUNCT
ejpam-3812	108	17	set	set	NOUN
ejpam-3812	108	18	,	,	PUNCT
ejpam-3812	108	19	where	where	SCONJ
ejpam-3812	108	20	k	k	PROPN
ejpam-3812	108	21	is	be	AUX
ejpam-3812	108	22	a	a	DET
ejpam-3812	108	23	positive	positive	ADJ
ejpam-3812	108	24	integer	integer	NOUN
ejpam-3812	108	25	and	and	CCONJ
ejpam-3812	108	26	1	1	NUM
ejpam-3812	108	27	≤	≤	NUM
ejpam-3812	108	28	k	k	X
ejpam-3812	108	29	≤	≤	PROPN
ejpam-3812	108	30	α(g	α(g	NUM
ejpam-3812	108	31	)	)	PUNCT
ejpam-3812	108	32	,	,	PUNCT
ejpam-3812	108	33	where	where	SCONJ
ejpam-3812	108	34	α(g	α(g	NUM
ejpam-3812	108	35	)	)	PUNCT
ejpam-3812	108	36	is	be	AUX
ejpam-3812	108	37	the	the	DET
ejpam-3812	108	38	independence	independence	NOUN
ejpam-3812	108	39	number	number	NOUN
ejpam-3812	108	40	of	of	ADP
ejpam-3812	108	41	g.	g.	PROPN
ejpam-3812	108	42	to	to	PART
ejpam-3812	108	43	see	see	VERB
ejpam-3812	108	44	this	this	PRON
ejpam-3812	108	45	,	,	PUNCT
ejpam-3812	108	46	consider	consider	VERB
ejpam-3812	108	47	c4	c4	NOUN
ejpam-3812	108	48	.	.	PUNCT
ejpam-3812	108	49	γ1fd(c4	γ1fd(c4	PROPN
ejpam-3812	108	50	)	)	PUNCT
ejpam-3812	109	1	=	=	SYM
ejpam-3812	109	2	2	2	NUM
ejpam-3812	109	3	but	but	CCONJ
ejpam-3812	109	4	c4	c4	NOUN
ejpam-3812	109	5	has	have	VERB
ejpam-3812	109	6	no	no	DET
ejpam-3812	109	7	independent	independent	ADJ
ejpam-3812	109	8	1fd	1fd	NOUN
ejpam-3812	109	9	-	-	PUNCT
ejpam-3812	109	10	set	set	NOUN
ejpam-3812	109	11	.	.	PUNCT
ejpam-3812	110	1	theorem	theorem	ADJ
ejpam-3812	110	2	4	4	NUM
ejpam-3812	110	3	.	.	PUNCT
ejpam-3812	111	1	let	let	VERB
ejpam-3812	111	2	g	g	PRON
ejpam-3812	111	3	be	be	AUX
ejpam-3812	111	4	a	a	DET
ejpam-3812	111	5	connected	connected	ADJ
ejpam-3812	111	6	graph	graph	NOUN
ejpam-3812	111	7	of	of	ADP
ejpam-3812	111	8	order	order	NOUN
ejpam-3812	111	9	n	n	NOUN
ejpam-3812	111	10	and	and	CCONJ
ejpam-3812	111	11	let	let	VERB
ejpam-3812	111	12	k	k	PRON
ejpam-3812	111	13	be	be	AUX
ejpam-3812	111	14	a	a	DET
ejpam-3812	111	15	positive	positive	ADJ
ejpam-3812	111	16	integer	integer	NOUN
ejpam-3812	111	17	with	with	ADP
ejpam-3812	111	18	1	1	NUM
ejpam-3812	111	19	≤	≤	NUM
ejpam-3812	111	20	k	k	X
ejpam-3812	111	21	≤	≤	PROPN
ejpam-3812	111	22	α(g	α(g	NUM
ejpam-3812	111	23	)	)	PUNCT
ejpam-3812	111	24	.	.	PUNCT
ejpam-3812	112	1	then	then	ADV
ejpam-3812	112	2	g	g	PROPN
ejpam-3812	112	3	admits	admit	VERB
ejpam-3812	112	4	an	an	DET
ejpam-3812	112	5	independent	independent	ADJ
ejpam-3812	112	6	kfd	kfd	NOUN
ejpam-3812	112	7	-	-	PUNCT
ejpam-3812	112	8	set	set	NOUN
ejpam-3812	112	9	(	(	PUNCT
ejpam-3812	112	10	and	and	CCONJ
ejpam-3812	112	11	hence	hence	ADV
ejpam-3812	112	12	,	,	PUNCT
ejpam-3812	112	13	γikf	γikf	NOUN
ejpam-3812	112	14	(	(	PUNCT
ejpam-3812	112	15	g	g	NOUN
ejpam-3812	112	16	)	)	PUNCT
ejpam-3812	112	17	=	=	SYM
ejpam-3812	113	1	k	k	X
ejpam-3812	113	2	)	)	PUNCT
ejpam-3812	113	3	if	if	SCONJ
ejpam-3812	113	4	and	and	CCONJ
ejpam-3812	113	5	only	only	ADV
ejpam-3812	113	6	if	if	SCONJ
ejpam-3812	113	7	g	g	PROPN
ejpam-3812	113	8	=	=	PUNCT
ejpam-3812	113	9	kk	kk	PROPN
ejpam-3812	114	1	+	+	NOUN
ejpam-3812	114	2	h	h	NOUN
ejpam-3812	114	3	for	for	ADP
ejpam-3812	114	4	some	some	DET
ejpam-3812	114	5	graph	graph	NOUN
ejpam-3812	114	6	h.	h.	NOUN
ejpam-3812	114	7	proof	proof	NOUN
ejpam-3812	114	8	.	.	PUNCT
ejpam-3812	115	1	suppose	suppose	VERB
ejpam-3812	115	2	g	g	PROPN
ejpam-3812	115	3	admits	admit	VERB
ejpam-3812	115	4	an	an	DET
ejpam-3812	115	5	independent	independent	ADJ
ejpam-3812	115	6	kfd	kfd	NOUN
ejpam-3812	115	7	-	-	PUNCT
ejpam-3812	115	8	set	set	NOUN
ejpam-3812	115	9	,	,	PUNCT
ejpam-3812	115	10	say	say	VERB
ejpam-3812	115	11	s	s	X
ejpam-3812	115	12	=	=	PUNCT
ejpam-3812	115	13	{	{	PUNCT
ejpam-3812	115	14	a1	a1	PROPN
ejpam-3812	115	15	,	,	PUNCT
ejpam-3812	115	16	a2	a2	PROPN
ejpam-3812	115	17	,	,	PUNCT
ejpam-3812	115	18	...	...	PUNCT
ejpam-3812	115	19	,	,	PUNCT
ejpam-3812	115	20	ak	ak	PROPN
ejpam-3812	115	21	}	}	PUNCT
ejpam-3812	115	22	.	.	PUNCT
ejpam-3812	116	1	let	let	VERB
ejpam-3812	116	2	h	h	NOUN
ejpam-3812	116	3	=	=	PUNCT
ejpam-3812	117	1	〈	〈	PROPN
ejpam-3812	117	2	v	v	X
ejpam-3812	117	3	(	(	PUNCT
ejpam-3812	117	4	g	g	NOUN
ejpam-3812	117	5	)	)	PUNCT
ejpam-3812	117	6	\	\	PUNCT
ejpam-3812	118	1	s	s	PROPN
ejpam-3812	118	2	〉	〉	PROPN
ejpam-3812	118	3	.	.	PUNCT
ejpam-3812	119	1	since	since	SCONJ
ejpam-3812	119	2	s	s	PROPN
ejpam-3812	119	3	is	be	AUX
ejpam-3812	119	4	a	a	DET
ejpam-3812	119	5	kfd	kfd	NOUN
ejpam-3812	119	6	-	-	PUNCT
ejpam-3812	119	7	set	set	NOUN
ejpam-3812	119	8	,	,	PUNCT
ejpam-3812	119	9	v	v	NOUN
ejpam-3812	119	10	(	(	PUNCT
ejpam-3812	119	11	h	h	NOUN
ejpam-3812	119	12	)	)	PUNCT
ejpam-3812	119	13	=	=	NOUN
ejpam-3812	119	14	v	v	X
ejpam-3812	119	15	(	(	PUNCT
ejpam-3812	119	16	g	g	NOUN
ejpam-3812	119	17	)	)	PUNCT
ejpam-3812	119	18	\	\	PUNCT
ejpam-3812	120	1	s	s	PART
ejpam-3812	120	2	⊆	⊆	NUM
ejpam-3812	120	3	ng(ai	ng(ai	ADJ
ejpam-3812	120	4	)	)	PUNCT
ejpam-3812	120	5	∩	∩	NOUN
ejpam-3812	120	6	ng(aj	ng(aj	PROPN
ejpam-3812	120	7	)	)	PUNCT
ejpam-3812	120	8	for	for	ADP
ejpam-3812	120	9	all	all	DET
ejpam-3812	120	10	i	i	PROPN
ejpam-3812	120	11	,	,	PUNCT
ejpam-3812	120	12	j	j	PROPN
ejpam-3812	120	13	=	=	SYM
ejpam-3812	120	14	1	1	NUM
ejpam-3812	120	15	,	,	PUNCT
ejpam-3812	120	16	2	2	NUM
ejpam-3812	120	17	,	,	PUNCT
ejpam-3812	120	18	...	...	PUNCT
ejpam-3812	120	19	,	,	PUNCT
ejpam-3812	120	20	k	k	PROPN
ejpam-3812	120	21	and	and	CCONJ
ejpam-3812	120	22	i	i	PROPN
ejpam-3812	120	23	6=	6=	PROPN
ejpam-3812	120	24	j.	j.	PROPN
ejpam-3812	120	25	since	since	SCONJ
ejpam-3812	120	26	s	s	PROPN
ejpam-3812	120	27	is	be	AUX
ejpam-3812	120	28	an	an	DET
ejpam-3812	120	29	independent	independent	ADJ
ejpam-3812	120	30	kfd	kfd	NOUN
ejpam-3812	120	31	-	-	PUNCT
ejpam-3812	120	32	set	set	NOUN
ejpam-3812	120	33	of	of	ADP
ejpam-3812	120	34	g	g	NOUN
ejpam-3812	120	35	,	,	PUNCT
ejpam-3812	120	36	|ng(s	|ng(s	NOUN
ejpam-3812	120	37	)	)	PUNCT
ejpam-3812	120	38	∩	∩	NOUN
ejpam-3812	120	39	s|	s|	NOUN
ejpam-3812	120	40	=	=	PUNCT
ejpam-3812	120	41	∅.	∅.	VERB
ejpam-3812	120	42	thus	thus	ADV
ejpam-3812	120	43	,	,	PUNCT
ejpam-3812	120	44	g	g	PROPN
ejpam-3812	120	45	=	=	PUNCT
ejpam-3812	120	46	kk	kk	PROPN
ejpam-3812	121	1	+	+	PROPN
ejpam-3812	121	2	h.	h.	PROPN
ejpam-3812	121	3	for	for	ADP
ejpam-3812	121	4	the	the	DET
ejpam-3812	121	5	converse	converse	NOUN
ejpam-3812	121	6	,	,	PUNCT
ejpam-3812	121	7	suppose	suppose	VERB
ejpam-3812	121	8	g	g	PROPN
ejpam-3812	121	9	=	=	SYM
ejpam-3812	121	10	kk	kk	PROPN
ejpam-3812	122	1	+	+	CCONJ
ejpam-3812	122	2	h	h	NOUN
ejpam-3812	122	3	for	for	ADP
ejpam-3812	122	4	some	some	DET
ejpam-3812	122	5	graph	graph	NOUN
ejpam-3812	122	6	h.	h.	PROPN
ejpam-3812	122	7	then	then	ADV
ejpam-3812	122	8	clearly	clearly	ADV
ejpam-3812	122	9	,	,	PUNCT
ejpam-3812	122	10	s	s	VERB
ejpam-3812	122	11	=	=	SYM
ejpam-3812	122	12	v	v	PROPN
ejpam-3812	122	13	(	(	PUNCT
ejpam-3812	122	14	kk	kk	PROPN
ejpam-3812	122	15	)	)	PUNCT
ejpam-3812	122	16	is	be	AUX
ejpam-3812	122	17	an	an	DET
ejpam-3812	122	18	independent	independent	ADJ
ejpam-3812	122	19	kfd	kfd	NOUN
ejpam-3812	122	20	-	-	PUNCT
ejpam-3812	122	21	set	set	NOUN
ejpam-3812	122	22	of	of	ADP
ejpam-3812	122	23	g	g	NOUN
ejpam-3812	122	24	and	and	CCONJ
ejpam-3812	122	25	γikf	γikf	NOUN
ejpam-3812	122	26	(	(	PUNCT
ejpam-3812	122	27	g	g	NOUN
ejpam-3812	122	28	)	)	PUNCT
ejpam-3812	122	29	=	=	PUNCT
ejpam-3812	122	30	k.	k.	PROPN
ejpam-3812	122	31	�	�	PROPN
ejpam-3812	122	32	theorem	theorem	VERB
ejpam-3812	122	33	5	5	NUM
ejpam-3812	122	34	.	.	PUNCT
ejpam-3812	123	1	let	let	VERB
ejpam-3812	123	2	g	g	PRON
ejpam-3812	123	3	be	be	AUX
ejpam-3812	123	4	a	a	DET
ejpam-3812	123	5	connected	connected	ADJ
ejpam-3812	123	6	graph	graph	NOUN
ejpam-3812	123	7	and	and	CCONJ
ejpam-3812	123	8	suppose	suppose	VERB
ejpam-3812	123	9	g	g	PROPN
ejpam-3812	123	10	admits	admit	VERB
ejpam-3812	123	11	an	an	DET
ejpam-3812	123	12	independent	independent	ADJ
ejpam-3812	123	13	1fd	1fd	NOUN
ejpam-3812	123	14	-	-	PUNCT
ejpam-3812	123	15	set	set	NOUN
ejpam-3812	123	16	.	.	PUNCT
ejpam-3812	124	1	then	then	ADV
ejpam-3812	124	2	1	1	NUM
ejpam-3812	124	3	≤	≤	NUM
ejpam-3812	124	4	γi1f	γi1f	X
ejpam-3812	124	5	(	(	PUNCT
ejpam-3812	124	6	g	g	NOUN
ejpam-3812	124	7	)	)	PUNCT
ejpam-3812	124	8	≤	≤	NOUN
ejpam-3812	124	9	α(g	α(g	NUM
ejpam-3812	124	10	)	)	PUNCT
ejpam-3812	124	11	.	.	PUNCT
ejpam-3812	125	1	moreover	moreover	ADV
ejpam-3812	125	2	,	,	PUNCT
ejpam-3812	125	3	(	(	PUNCT
ejpam-3812	125	4	i	i	NOUN
ejpam-3812	125	5	)	)	PUNCT
ejpam-3812	125	6	γi1f	γi1f	PROPN
ejpam-3812	125	7	(	(	PUNCT
ejpam-3812	125	8	g	g	NOUN
ejpam-3812	125	9	)	)	PUNCT
ejpam-3812	125	10	=	=	SYM
ejpam-3812	125	11	1	1	NUM
ejpam-3812	125	12	if	if	SCONJ
ejpam-3812	125	13	and	and	CCONJ
ejpam-3812	125	14	only	only	ADV
ejpam-3812	125	15	if	if	SCONJ
ejpam-3812	125	16	g	g	NOUN
ejpam-3812	125	17	=	=	PROPN
ejpam-3812	125	18	k1	k1	PROPN
ejpam-3812	126	1	+	+	NOUN
ejpam-3812	126	2	h	h	NOUN
ejpam-3812	126	3	for	for	ADP
ejpam-3812	126	4	some	some	DET
ejpam-3812	126	5	graph	graph	NOUN
ejpam-3812	126	6	h	h	NOUN
ejpam-3812	126	7	,	,	PUNCT
ejpam-3812	126	8	and	and	CCONJ
ejpam-3812	126	9	(	(	PUNCT
ejpam-3812	126	10	ii	ii	NOUN
ejpam-3812	126	11	)	)	PUNCT
ejpam-3812	126	12	γi1f	γi1f	PROPN
ejpam-3812	126	13	(	(	PUNCT
ejpam-3812	126	14	g	g	NOUN
ejpam-3812	126	15	)	)	PUNCT
ejpam-3812	126	16	=	=	SYM
ejpam-3812	126	17	α(g	α(g	NUM
ejpam-3812	126	18	)	)	PUNCT
ejpam-3812	126	19	≥	≥	NOUN
ejpam-3812	126	20	2	2	NUM
ejpam-3812	126	21	if	if	SCONJ
ejpam-3812	126	22	and	and	CCONJ
ejpam-3812	126	23	only	only	ADV
ejpam-3812	126	24	if	if	SCONJ
ejpam-3812	126	25	g	g	PROPN
ejpam-3812	126	26	has	have	VERB
ejpam-3812	126	27	a	a	DET
ejpam-3812	126	28	maximum	maximum	ADJ
ejpam-3812	126	29	independent	independent	ADJ
ejpam-3812	126	30	set	set	NOUN
ejpam-3812	126	31	such	such	ADJ
ejpam-3812	126	32	that	that	DET
ejpam-3812	126	33	dg(x	dg(x	NOUN
ejpam-3812	126	34	,	,	PUNCT
ejpam-3812	126	35	y	y	PROPN
ejpam-3812	126	36	)	)	PUNCT
ejpam-3812	126	37	≥	≥	NOUN
ejpam-3812	126	38	3	3	NUM
ejpam-3812	126	39	for	for	ADP
ejpam-3812	126	40	each	each	DET
ejpam-3812	126	41	pair	pair	NOUN
ejpam-3812	126	42	of	of	ADP
ejpam-3812	126	43	vertices	vertex	NOUN
ejpam-3812	126	44	x	x	X
ejpam-3812	126	45	,	,	PUNCT
ejpam-3812	126	46	y	y	PROPN
ejpam-3812	126	47	∈	∈	PROPN
ejpam-3812	126	48	s	s	PART
ejpam-3812	126	49	with	with	ADP
ejpam-3812	126	50	x	x	SYM
ejpam-3812	126	51	6=	6=	PROPN
ejpam-3812	126	52	y	y	PROPN
ejpam-3812	126	53	,	,	PUNCT
ejpam-3812	126	54	and	and	CCONJ
ejpam-3812	126	55	no	no	DET
ejpam-3812	126	56	other	other	ADJ
ejpam-3812	126	57	independent	independent	ADJ
ejpam-3812	126	58	set	set	NOUN
ejpam-3812	126	59	satisfies	satisfie	NOUN
ejpam-3812	126	60	this	this	DET
ejpam-3812	126	61	property	property	NOUN
ejpam-3812	126	62	.	.	PUNCT
ejpam-3812	127	1	proof	proof	NOUN
ejpam-3812	127	2	.	.	PUNCT
ejpam-3812	128	1	let	let	VERB
ejpam-3812	128	2	s	s	PRON
ejpam-3812	128	3	be	be	AUX
ejpam-3812	128	4	a	a	DET
ejpam-3812	128	5	γi1f	γi1f	PROPN
ejpam-3812	128	6	-set	-set	ADJ
ejpam-3812	128	7	.	.	PUNCT
ejpam-3812	129	1	since	since	SCONJ
ejpam-3812	129	2	s	s	PROPN
ejpam-3812	129	3	is	be	AUX
ejpam-3812	129	4	an	an	DET
ejpam-3812	129	5	independent	independent	ADJ
ejpam-3812	129	6	set	set	NOUN
ejpam-3812	129	7	,	,	PUNCT
ejpam-3812	129	8	1	1	NUM
ejpam-3812	129	9	≤	≤	NUM
ejpam-3812	129	10	|s|	|s|	PROPN
ejpam-3812	129	11	=	=	SYM
ejpam-3812	129	12	γi1f	γi1f	PROPN
ejpam-3812	129	13	(	(	PUNCT
ejpam-3812	129	14	g	g	NOUN
ejpam-3812	129	15	)	)	PUNCT
ejpam-3812	129	16	≤	≤	NOUN
ejpam-3812	129	17	α(g	α(g	NUM
ejpam-3812	129	18	)	)	PUNCT
ejpam-3812	129	19	.	.	PUNCT
ejpam-3812	130	1	(	(	PUNCT
ejpam-3812	130	2	i	i	NOUN
ejpam-3812	130	3	)	)	PUNCT
ejpam-3812	130	4	is	be	AUX
ejpam-3812	130	5	an	an	DET
ejpam-3812	130	6	immediate	immediate	ADJ
ejpam-3812	130	7	consequence	consequence	NOUN
ejpam-3812	130	8	of	of	ADP
ejpam-3812	130	9	theorem	theorem	NOUN
ejpam-3812	130	10	4	4	NUM
ejpam-3812	130	11	.	.	PUNCT
ejpam-3812	130	12	(	(	PUNCT
ejpam-3812	130	13	ii	ii	NOUN
ejpam-3812	130	14	)	)	PUNCT
ejpam-3812	130	15	suppose	suppose	VERB
ejpam-3812	130	16	γi1f	γi1f	X
ejpam-3812	130	17	(	(	PUNCT
ejpam-3812	130	18	g	g	NOUN
ejpam-3812	130	19	)	)	PUNCT
ejpam-3812	130	20	=	=	SYM
ejpam-3812	130	21	α(g	α(g	NUM
ejpam-3812	130	22	)	)	PUNCT
ejpam-3812	130	23	≥	≥	NOUN
ejpam-3812	130	24	2	2	NUM
ejpam-3812	130	25	.	.	PUNCT
ejpam-3812	131	1	let	let	VERB
ejpam-3812	131	2	s	s	PRON
ejpam-3812	131	3	be	be	AUX
ejpam-3812	131	4	a	a	DET
ejpam-3812	131	5	γi1f	γi1f	PROPN
ejpam-3812	131	6	-set	-set	PUNCT
ejpam-3812	131	7	of	of	ADP
ejpam-3812	131	8	g.	g.	PROPN
ejpam-3812	131	9	then	then	ADV
ejpam-3812	131	10	s	s	VERB
ejpam-3812	131	11	is	be	AUX
ejpam-3812	131	12	a	a	DET
ejpam-3812	131	13	maximum	maximum	ADJ
ejpam-3812	131	14	independent	independent	ADJ
ejpam-3812	131	15	set	set	NOUN
ejpam-3812	131	16	of	of	ADP
ejpam-3812	131	17	g.	g.	PROPN
ejpam-3812	131	18	let	let	VERB
ejpam-3812	131	19	x	x	PRON
ejpam-3812	131	20	,	,	PUNCT
ejpam-3812	131	21	y	y	PROPN
ejpam-3812	131	22	∈	∈	PROPN
ejpam-3812	131	23	s	s	PART
ejpam-3812	131	24	with	with	ADP
ejpam-3812	131	25	x	x	SYM
ejpam-3812	131	26	6=	6=	ADP
ejpam-3812	131	27	y.	y.	NOUN
ejpam-3812	131	28	since	since	SCONJ
ejpam-3812	131	29	s	s	PROPN
ejpam-3812	131	30	is	be	AUX
ejpam-3812	131	31	an	an	DET
ejpam-3812	131	32	independent	independent	ADJ
ejpam-3812	131	33	1fd	1fd	NOUN
ejpam-3812	131	34	-	-	PUNCT
ejpam-3812	131	35	set	set	VERB
ejpam-3812	131	36	,	,	PUNCT
ejpam-3812	131	37	dg(x	dg(x	NUM
ejpam-3812	131	38	,	,	PUNCT
ejpam-3812	131	39	y	y	PROPN
ejpam-3812	131	40	)	)	PUNCT
ejpam-3812	131	41	≥	≥	NOUN
ejpam-3812	131	42	3	3	NUM
ejpam-3812	131	43	.	.	PUNCT
ejpam-3812	131	44	m.	m.	PROPN
ejpam-3812	131	45	ortega	ortega	PROPN
ejpam-3812	131	46	,	,	PUNCT
ejpam-3812	131	47	r.	r.	PROPN
ejpam-3812	131	48	isla	isla	PROPN
ejpam-3812	131	49	/	/	SYM
ejpam-3812	131	50	eur	eur	PROPN
ejpam-3812	131	51	.	.	PUNCT
ejpam-3812	132	1	j.	j.	PROPN
ejpam-3812	132	2	pure	pure	PROPN
ejpam-3812	132	3	appl	appl	PROPN
ejpam-3812	132	4	.	.	PROPN
ejpam-3812	132	5	math	math	PROPN
ejpam-3812	132	6	,	,	PUNCT
ejpam-3812	132	7	13	13	NUM
ejpam-3812	132	8	(	(	PUNCT
ejpam-3812	132	9	4	4	NUM
ejpam-3812	132	10	)	)	PUNCT
ejpam-3812	132	11	(	(	PUNCT
ejpam-3812	132	12	2020	2020	NUM
ejpam-3812	132	13	)	)	PUNCT
ejpam-3812	132	14	,	,	PUNCT
ejpam-3812	132	15	779	779	NUM
ejpam-3812	132	16	-	-	SYM
ejpam-3812	132	17	793	793	NUM
ejpam-3812	132	18	783	783	NUM
ejpam-3812	132	19	for	for	ADP
ejpam-3812	132	20	the	the	DET
ejpam-3812	132	21	converse	converse	NOUN
ejpam-3812	132	22	,	,	PUNCT
ejpam-3812	132	23	suppose	suppose	VERB
ejpam-3812	132	24	thatg	thatg	PROPN
ejpam-3812	132	25	has	have	VERB
ejpam-3812	132	26	a	a	DET
ejpam-3812	132	27	maximum	maximum	ADJ
ejpam-3812	132	28	independent	independent	ADJ
ejpam-3812	132	29	set	set	NOUN
ejpam-3812	132	30	s	s	PRON
ejpam-3812	132	31	such	such	ADJ
ejpam-3812	132	32	that	that	DET
ejpam-3812	132	33	dg(x	dg(x	NOUN
ejpam-3812	132	34	,	,	PUNCT
ejpam-3812	132	35	y	y	PROPN
ejpam-3812	132	36	)	)	PUNCT
ejpam-3812	132	37	≥	≥	NOUN
ejpam-3812	132	38	3	3	NUM
ejpam-3812	132	39	for	for	ADP
ejpam-3812	132	40	all	all	DET
ejpam-3812	132	41	x	x	NOUN
ejpam-3812	132	42	,	,	PUNCT
ejpam-3812	132	43	y	y	PROPN
ejpam-3812	132	44	∈	∈	PROPN
ejpam-3812	132	45	s	s	PART
ejpam-3812	132	46	with	with	ADP
ejpam-3812	132	47	x	x	SYM
ejpam-3812	132	48	6=	6=	PROPN
ejpam-3812	132	49	y	y	PROPN
ejpam-3812	132	50	,	,	PUNCT
ejpam-3812	132	51	and	and	CCONJ
ejpam-3812	132	52	that	that	SCONJ
ejpam-3812	132	53	no	no	DET
ejpam-3812	132	54	other	other	ADJ
ejpam-3812	132	55	independent	independent	ADJ
ejpam-3812	132	56	set	set	NOUN
ejpam-3812	132	57	satisfies	satisfie	NOUN
ejpam-3812	132	58	this	this	DET
ejpam-3812	132	59	property	property	NOUN
ejpam-3812	132	60	.	.	PUNCT
ejpam-3812	133	1	then	then	ADV
ejpam-3812	133	2	s	s	VERB
ejpam-3812	133	3	is	be	AUX
ejpam-3812	133	4	a	a	DET
ejpam-3812	133	5	dominating	dominating	NOUN
ejpam-3812	133	6	set	set	NOUN
ejpam-3812	133	7	of	of	ADP
ejpam-3812	133	8	g.	g.	PROPN
ejpam-3812	133	9	let	let	VERB
ejpam-3812	133	10	z	z	PROPN
ejpam-3812	133	11	∈	∈	PROPN
ejpam-3812	133	12	v	v	ADP
ejpam-3812	133	13	(	(	PUNCT
ejpam-3812	133	14	g	g	NOUN
ejpam-3812	133	15	)	)	PUNCT
ejpam-3812	133	16	\	\	PUNCT
ejpam-3812	134	1	s.	s.	PROPN
ejpam-3812	134	2	then	then	ADV
ejpam-3812	134	3	there	there	PRON
ejpam-3812	134	4	exists	exist	VERB
ejpam-3812	134	5	v	v	ADP
ejpam-3812	134	6	∈	∈	PROPN
ejpam-3812	134	7	s	s	PART
ejpam-3812	134	8	∩	∩	NOUN
ejpam-3812	134	9	ng(z	ng(z	NUM
ejpam-3812	134	10	)	)	PUNCT
ejpam-3812	134	11	.	.	PUNCT
ejpam-3812	135	1	since	since	SCONJ
ejpam-3812	135	2	dg(v	dg(v	NOUN
ejpam-3812	135	3	,	,	PUNCT
ejpam-3812	135	4	y	y	PROPN
ejpam-3812	135	5	)	)	PUNCT
ejpam-3812	135	6	≥	≥	NOUN
ejpam-3812	135	7	3	3	NUM
ejpam-3812	135	8	for	for	ADP
ejpam-3812	135	9	all	all	DET
ejpam-3812	135	10	y	y	PROPN
ejpam-3812	135	11	∈	∈	PROPN
ejpam-3812	135	12	s	s	PART
ejpam-3812	135	13	\	\	X
ejpam-3812	135	14	{	{	PUNCT
ejpam-3812	135	15	v	v	NOUN
ejpam-3812	135	16	}	}	PUNCT
ejpam-3812	135	17	,	,	PUNCT
ejpam-3812	135	18	ng(z	ng(z	NUM
ejpam-3812	135	19	)	)	PUNCT
ejpam-3812	135	20	∩	∩	NOUN
ejpam-3812	135	21	s	s	PART
ejpam-3812	135	22	=	=	SYM
ejpam-3812	135	23	1	1	NUM
ejpam-3812	135	24	.	.	PUNCT
ejpam-3812	135	25	thus	thus	ADV
ejpam-3812	135	26	,	,	PUNCT
ejpam-3812	135	27	s	s	VERB
ejpam-3812	135	28	is	be	AUX
ejpam-3812	135	29	an	an	DET
ejpam-3812	135	30	independent	independent	ADJ
ejpam-3812	135	31	1fd	1fd	NOUN
ejpam-3812	135	32	-	-	PUNCT
ejpam-3812	135	33	set	set	NOUN
ejpam-3812	135	34	of	of	ADP
ejpam-3812	135	35	g.	g.	PROPN
ejpam-3812	135	36	hence	hence	ADV
ejpam-3812	135	37	,	,	PUNCT
ejpam-3812	135	38	γi1f	γi1f	X
ejpam-3812	135	39	(	(	PUNCT
ejpam-3812	135	40	g	g	NOUN
ejpam-3812	135	41	)	)	PUNCT
ejpam-3812	135	42	≤	≤	NUM
ejpam-3812	135	43	|s|	|s|	PROPN
ejpam-3812	135	44	=	=	SYM
ejpam-3812	135	45	α(g	α(g	PROPN
ejpam-3812	135	46	)	)	PUNCT
ejpam-3812	135	47	.	.	PUNCT
ejpam-3812	136	1	by	by	ADP
ejpam-3812	136	2	the	the	DET
ejpam-3812	136	3	additional	additional	ADJ
ejpam-3812	136	4	property	property	NOUN
ejpam-3812	136	5	,	,	PUNCT
ejpam-3812	136	6	γi1f	γi1f	X
ejpam-3812	136	7	(	(	PUNCT
ejpam-3812	136	8	g	g	NOUN
ejpam-3812	136	9	)	)	PUNCT
ejpam-3812	136	10	=	=	SYM
ejpam-3812	136	11	α(g	α(g	NUM
ejpam-3812	136	12	)	)	PUNCT
ejpam-3812	136	13	.	.	PUNCT
ejpam-3812	137	1	�	�	PROPN
ejpam-3812	137	2	since	since	SCONJ
ejpam-3812	137	3	kn	kn	PROPN
ejpam-3812	137	4	=	=	PROPN
ejpam-3812	137	5	k1	k1	PROPN
ejpam-3812	137	6	+	+	CCONJ
ejpam-3812	137	7	kn−1	kn−1	PROPN
ejpam-3812	137	8	and	and	CCONJ
ejpam-3812	137	9	α(kn	α(kn	NUM
ejpam-3812	137	10	)	)	PUNCT
ejpam-3812	137	11	=	=	SYM
ejpam-3812	138	1	1	1	NUM
ejpam-3812	138	2	,	,	PUNCT
ejpam-3812	138	3	the	the	DET
ejpam-3812	138	4	next	next	ADJ
ejpam-3812	138	5	result	result	NOUN
ejpam-3812	138	6	immediately	immediately	ADV
ejpam-3812	138	7	follows	follow	VERB
ejpam-3812	138	8	.	.	PUNCT
ejpam-3812	139	1	corollary	corollary	ADJ
ejpam-3812	139	2	3	3	NUM
ejpam-3812	139	3	.	.	PUNCT
ejpam-3812	140	1	for	for	ADP
ejpam-3812	140	2	any	any	DET
ejpam-3812	140	3	positive	positive	ADJ
ejpam-3812	140	4	integer	integer	NOUN
ejpam-3812	140	5	n	n	PRON
ejpam-3812	140	6	≥	≥	NOUN
ejpam-3812	140	7	1	1	NUM
ejpam-3812	140	8	,	,	PUNCT
ejpam-3812	140	9	γi1f	γi1f	PROPN
ejpam-3812	140	10	(	(	PUNCT
ejpam-3812	140	11	kn	kn	NOUN
ejpam-3812	140	12	)	)	PUNCT
ejpam-3812	140	13	=	=	SYM
ejpam-3812	140	14	1	1	X
ejpam-3812	140	15	.	.	NOUN
ejpam-3812	140	16	remark	remark	NOUN
ejpam-3812	140	17	3	3	NUM
ejpam-3812	140	18	.	.	PUNCT
ejpam-3812	141	1	any	any	DET
ejpam-3812	141	2	independent	independent	ADJ
ejpam-3812	141	3	kfd	kfd	NOUN
ejpam-3812	141	4	-	-	PUNCT
ejpam-3812	141	5	set	set	NOUN
ejpam-3812	141	6	is	be	AUX
ejpam-3812	141	7	a	a	DET
ejpam-3812	141	8	kfd	kfd	NOUN
ejpam-3812	141	9	-	-	PUNCT
ejpam-3812	141	10	set	set	NOUN
ejpam-3812	141	11	,	,	PUNCT
ejpam-3812	141	12	where	where	SCONJ
ejpam-3812	141	13	k	k	PROPN
ejpam-3812	141	14	is	be	AUX
ejpam-3812	141	15	a	a	DET
ejpam-3812	141	16	positive	positive	ADJ
ejpam-3812	141	17	integer	integer	NOUN
ejpam-3812	141	18	.	.	PUNCT
ejpam-3812	142	1	theorem	theorem	NOUN
ejpam-3812	142	2	6	6	NUM
ejpam-3812	142	3	.	.	PUNCT
ejpam-3812	143	1	let	let	VERB
ejpam-3812	143	2	g	g	PRON
ejpam-3812	143	3	be	be	AUX
ejpam-3812	143	4	a	a	DET
ejpam-3812	143	5	connected	connected	ADJ
ejpam-3812	143	6	graph	graph	NOUN
ejpam-3812	143	7	with	with	ADP
ejpam-3812	143	8	|v	|v	PROPN
ejpam-3812	143	9	(	(	PUNCT
ejpam-3812	143	10	g)|	g)|	X
ejpam-3812	143	11	≥	≥	NOUN
ejpam-3812	143	12	4	4	NUM
ejpam-3812	143	13	and	and	CCONJ
ejpam-3812	143	14	suppose	suppose	VERB
ejpam-3812	143	15	g	g	PROPN
ejpam-3812	143	16	admits	admit	VERB
ejpam-3812	143	17	an	an	DET
ejpam-3812	143	18	independent	independent	ADJ
ejpam-3812	143	19	1fd	1fd	NOUN
ejpam-3812	143	20	-	-	PUNCT
ejpam-3812	143	21	set	set	NOUN
ejpam-3812	143	22	.	.	PUNCT
ejpam-3812	144	1	then	then	ADV
ejpam-3812	144	2	γi1f	γi1f	PROPN
ejpam-3812	144	3	(	(	PUNCT
ejpam-3812	144	4	g	g	NOUN
ejpam-3812	144	5	)	)	PUNCT
ejpam-3812	144	6	=	=	SYM
ejpam-3812	144	7	2	2	NUM
ejpam-3812	144	8	if	if	SCONJ
ejpam-3812	144	9	and	and	CCONJ
ejpam-3812	144	10	only	only	ADV
ejpam-3812	144	11	if	if	SCONJ
ejpam-3812	144	12	there	there	PRON
ejpam-3812	144	13	exist	exist	VERB
ejpam-3812	144	14	non	non	ADJ
ejpam-3812	144	15	-	-	ADJ
ejpam-3812	144	16	adjacent	adjacent	ADJ
ejpam-3812	144	17	vertices	vertex	NOUN
ejpam-3812	144	18	a	a	PRON
ejpam-3812	144	19	and	and	CCONJ
ejpam-3812	144	20	b	b	NOUN
ejpam-3812	144	21	of	of	ADP
ejpam-3812	144	22	g	g	NOUN
ejpam-3812	144	23	satisfying	satisfy	VERB
ejpam-3812	144	24	the	the	DET
ejpam-3812	144	25	following	follow	VERB
ejpam-3812	144	26	conditions	condition	NOUN
ejpam-3812	144	27	:	:	PUNCT
ejpam-3812	144	28	(	(	PUNCT
ejpam-3812	144	29	i	i	NOUN
ejpam-3812	144	30	)	)	PUNCT
ejpam-3812	144	31	ng[a	ng[a	PROPN
ejpam-3812	144	32	]	]	X
ejpam-3812	144	33	∪ng[b	∪ng[b	X
ejpam-3812	144	34	]	]	X
ejpam-3812	144	35	=	=	SYM
ejpam-3812	144	36	v	v	X
ejpam-3812	144	37	(	(	PUNCT
ejpam-3812	144	38	g	g	NOUN
ejpam-3812	144	39	)	)	PUNCT
ejpam-3812	144	40	(	(	PUNCT
ejpam-3812	144	41	ii	ii	NOUN
ejpam-3812	144	42	)	)	PUNCT
ejpam-3812	144	43	ng[a	ng[a	NOUN
ejpam-3812	144	44	]	]	PUNCT
ejpam-3812	144	45	∩ng[b	∩ng[b	NOUN
ejpam-3812	144	46	]	]	X
ejpam-3812	144	47	=	=	SYM
ejpam-3812	144	48	∅	∅	NOUN
ejpam-3812	144	49	proof	proof	NOUN
ejpam-3812	144	50	.	.	PUNCT
ejpam-3812	145	1	suppose	suppose	VERB
ejpam-3812	145	2	s	s	VERB
ejpam-3812	145	3	=	=	X
ejpam-3812	145	4	{	{	PUNCT
ejpam-3812	145	5	a	a	DET
ejpam-3812	145	6	,	,	PUNCT
ejpam-3812	145	7	b	b	NOUN
ejpam-3812	145	8	}	}	PUNCT
ejpam-3812	145	9	is	be	AUX
ejpam-3812	145	10	a	a	DET
ejpam-3812	145	11	γi1f	γi1f	PROPN
ejpam-3812	145	12	-set	-set	PUNCT
ejpam-3812	145	13	of	of	ADP
ejpam-3812	145	14	g.	g.	PROPN
ejpam-3812	145	15	since	since	SCONJ
ejpam-3812	145	16	s	s	PROPN
ejpam-3812	145	17	is	be	AUX
ejpam-3812	145	18	a	a	DET
ejpam-3812	145	19	dominating	dominating	NOUN
ejpam-3812	145	20	set	set	NOUN
ejpam-3812	145	21	,	,	PUNCT
ejpam-3812	145	22	condition	condition	NOUN
ejpam-3812	145	23	(	(	PUNCT
ejpam-3812	145	24	i	i	NOUN
ejpam-3812	145	25	)	)	PUNCT
ejpam-3812	145	26	holds	hold	VERB
ejpam-3812	145	27	.	.	PUNCT
ejpam-3812	146	1	suppose	suppose	VERB
ejpam-3812	146	2	there	there	PRON
ejpam-3812	146	3	exists	exist	VERB
ejpam-3812	146	4	y	y	PROPN
ejpam-3812	146	5	∈	∈	PROPN
ejpam-3812	146	6	ng[a]∩ng[b	ng[a]∩ng[b	VERB
ejpam-3812	146	7	]	]	PUNCT
ejpam-3812	146	8	.	.	PUNCT
ejpam-3812	147	1	then	then	ADV
ejpam-3812	147	2	dg(a	dg(a	NUM
ejpam-3812	147	3	,	,	PUNCT
ejpam-3812	147	4	b	b	X
ejpam-3812	147	5	)	)	PUNCT
ejpam-3812	147	6	=	=	SYM
ejpam-3812	147	7	2	2	NUM
ejpam-3812	147	8	,	,	PUNCT
ejpam-3812	147	9	contrary	contrary	ADV
ejpam-3812	147	10	to	to	ADP
ejpam-3812	147	11	the	the	DET
ejpam-3812	147	12	fact	fact	NOUN
ejpam-3812	147	13	that	that	SCONJ
ejpam-3812	147	14	dg(a	dg(a	X
ejpam-3812	147	15	,	,	PUNCT
ejpam-3812	147	16	b	b	X
ejpam-3812	147	17	)	)	PUNCT
ejpam-3812	147	18	≥	≥	NOUN
ejpam-3812	147	19	3	3	NUM
ejpam-3812	147	20	since	since	SCONJ
ejpam-3812	147	21	s	s	NOUN
ejpam-3812	147	22	is	be	AUX
ejpam-3812	147	23	an	an	DET
ejpam-3812	147	24	independent	independent	ADJ
ejpam-3812	147	25	1fd	1fd	NOUN
ejpam-3812	147	26	-	-	PUNCT
ejpam-3812	147	27	set	set	NOUN
ejpam-3812	147	28	.	.	PUNCT
ejpam-3812	148	1	thus	thus	ADV
ejpam-3812	148	2	,	,	PUNCT
ejpam-3812	148	3	condition	condition	NOUN
ejpam-3812	148	4	(	(	PUNCT
ejpam-3812	148	5	ii	ii	NOUN
ejpam-3812	148	6	)	)	PUNCT
ejpam-3812	148	7	holds	hold	VERB
ejpam-3812	148	8	.	.	PUNCT
ejpam-3812	149	1	for	for	ADP
ejpam-3812	149	2	the	the	DET
ejpam-3812	149	3	converse	converse	NOUN
ejpam-3812	149	4	,	,	PUNCT
ejpam-3812	149	5	suppose	suppose	VERB
ejpam-3812	149	6	that	that	SCONJ
ejpam-3812	149	7	s	s	VERB
ejpam-3812	149	8	=	=	X
ejpam-3812	149	9	{	{	PUNCT
ejpam-3812	149	10	a	a	PRON
ejpam-3812	149	11	,	,	PUNCT
ejpam-3812	149	12	b	b	NOUN
ejpam-3812	149	13	}	}	PUNCT
ejpam-3812	149	14	satisfies	satisfy	VERB
ejpam-3812	149	15	conditions	condition	NOUN
ejpam-3812	149	16	(	(	PUNCT
ejpam-3812	149	17	i	i	NOUN
ejpam-3812	149	18	)	)	PUNCT
ejpam-3812	149	19	and	and	CCONJ
ejpam-3812	149	20	(	(	PUNCT
ejpam-3812	149	21	ii	ii	NOUN
ejpam-3812	149	22	)	)	PUNCT
ejpam-3812	149	23	.	.	PUNCT
ejpam-3812	150	1	then	then	ADV
ejpam-3812	150	2	clearly	clearly	ADV
ejpam-3812	150	3	,	,	PUNCT
ejpam-3812	150	4	γi1f	γi1f	PROPN
ejpam-3812	150	5	(	(	PUNCT
ejpam-3812	150	6	g	g	NOUN
ejpam-3812	150	7	)	)	PUNCT
ejpam-3812	150	8	=	=	SYM
ejpam-3812	150	9	2	2	X
ejpam-3812	150	10	.	.	X
ejpam-3812	150	11	�	�	PROPN
ejpam-3812	150	12	theorem	theorem	VERB
ejpam-3812	150	13	7	7	NUM
ejpam-3812	150	14	.	.	X
ejpam-3812	151	1	for	for	ADP
ejpam-3812	151	2	any	any	DET
ejpam-3812	151	3	positive	positive	ADJ
ejpam-3812	151	4	integer	integer	NOUN
ejpam-3812	151	5	n	n	PRON
ejpam-3812	151	6	≥	≥	NOUN
ejpam-3812	151	7	1	1	NUM
ejpam-3812	151	8	,	,	PUNCT
ejpam-3812	151	9	γi1f	γi1f	PROPN
ejpam-3812	151	10	(	(	PUNCT
ejpam-3812	151	11	pn	pn	NOUN
ejpam-3812	151	12	)	)	PUNCT
ejpam-3812	151	13	=	=	PUNCT
ejpam-3812	151	14	dn3	dn3	PROPN
ejpam-3812	151	15	e.	e.	PROPN
ejpam-3812	151	16	proof	proof	PROPN
ejpam-3812	151	17	.	.	PUNCT
ejpam-3812	152	1	let	let	VERB
ejpam-3812	152	2	pn	pn	VERB
ejpam-3812	152	3	=	=	PUNCT
ejpam-3812	152	4	{	{	PUNCT
ejpam-3812	152	5	v1	v1	PROPN
ejpam-3812	152	6	,	,	PUNCT
ejpam-3812	152	7	v2	v2	PROPN
ejpam-3812	152	8	,	,	PUNCT
ejpam-3812	152	9	v3	v3	PROPN
ejpam-3812	152	10	,	,	PUNCT
ejpam-3812	152	11	...	...	PUNCT
ejpam-3812	152	12	,	,	PUNCT
ejpam-3812	152	13	vn	vn	PROPN
ejpam-3812	152	14	}	}	PUNCT
ejpam-3812	152	15	.	.	PUNCT
ejpam-3812	153	1	clearly	clearly	ADV
ejpam-3812	153	2	,	,	PUNCT
ejpam-3812	153	3	γi1f	γi1f	PROPN
ejpam-3812	153	4	(	(	PUNCT
ejpam-3812	153	5	p1	p1	NOUN
ejpam-3812	153	6	)	)	PUNCT
ejpam-3812	153	7	=	=	SYM
ejpam-3812	153	8	γi1f	γi1f	PROPN
ejpam-3812	153	9	(	(	PUNCT
ejpam-3812	153	10	p2	p2	NOUN
ejpam-3812	153	11	)	)	PUNCT
ejpam-3812	153	12	=	=	SYM
ejpam-3812	153	13	γi1f	γi1f	X
ejpam-3812	153	14	(	(	PUNCT
ejpam-3812	153	15	p3	p3	NOUN
ejpam-3812	153	16	)	)	PUNCT
ejpam-3812	153	17	=	=	SYM
ejpam-3812	154	1	1	1	X
ejpam-3812	154	2	.	.	PUNCT
ejpam-3812	154	3	let	let	VERB
ejpam-3812	154	4	n	n	PRON
ejpam-3812	154	5	>	>	X
ejpam-3812	154	6	3	3	NUM
ejpam-3812	154	7	and	and	CCONJ
ejpam-3812	154	8	consider	consider	VERB
ejpam-3812	154	9	the	the	DET
ejpam-3812	154	10	following	follow	VERB
ejpam-3812	154	11	cases	case	NOUN
ejpam-3812	154	12	:	:	PUNCT
ejpam-3812	154	13	case	case	NOUN
ejpam-3812	154	14	1	1	NUM
ejpam-3812	154	15	:	:	PUNCT
ejpam-3812	154	16	n	n	PROPN
ejpam-3812	154	17	=	=	SYM
ejpam-3812	154	18	3r	3r	NUM
ejpam-3812	154	19	group	group	NOUN
ejpam-3812	154	20	the	the	DET
ejpam-3812	154	21	first	first	ADJ
ejpam-3812	154	22	3r	3r	NUM
ejpam-3812	154	23	vertices	vertex	NOUN
ejpam-3812	154	24	of	of	ADP
ejpam-3812	154	25	pn	pn	NOUN
ejpam-3812	154	26	into	into	ADP
ejpam-3812	154	27	r	r	NOUN
ejpam-3812	154	28	disjoint	disjoint	NOUN
ejpam-3812	154	29	subsets	subset	NOUN
ejpam-3812	154	30	s1	s1	NOUN
ejpam-3812	154	31	=	=	PUNCT
ejpam-3812	154	32	{	{	PUNCT
ejpam-3812	154	33	v1	v1	PROPN
ejpam-3812	154	34	,	,	PUNCT
ejpam-3812	154	35	v2	v2	PROPN
ejpam-3812	154	36	,	,	PUNCT
ejpam-3812	154	37	v3	v3	PROPN
ejpam-3812	154	38	,	,	PUNCT
ejpam-3812	154	39	}	}	PUNCT
ejpam-3812	154	40	s2	s2	NOUN
ejpam-3812	154	41	=	=	SYM
ejpam-3812	154	42	{	{	PUNCT
ejpam-3812	154	43	v4	v4	NOUN
ejpam-3812	154	44	,	,	PUNCT
ejpam-3812	154	45	v5	v5	PROPN
ejpam-3812	154	46	,	,	PUNCT
ejpam-3812	154	47	v6	v6	NOUN
ejpam-3812	154	48	}	}	PUNCT
ejpam-3812	154	49	...	...	PUNCT
ejpam-3812	155	1	sr−1	sr−1	PROPN
ejpam-3812	155	2	=	=	SYM
ejpam-3812	155	3	{	{	PUNCT
ejpam-3812	155	4	v3r−5	v3r−5	PROPN
ejpam-3812	155	5	,	,	PUNCT
ejpam-3812	155	6	v3r−4	v3r−4	PROPN
ejpam-3812	155	7	,	,	PUNCT
ejpam-3812	155	8	v3r−3	v3r−3	PROPN
ejpam-3812	155	9	}	}	PUNCT
ejpam-3812	155	10	sr	sr	NOUN
ejpam-3812	155	11	=	=	PRON
ejpam-3812	155	12	{	{	PUNCT
ejpam-3812	155	13	v3r−2	v3r−2	PROPN
ejpam-3812	155	14	,	,	PUNCT
ejpam-3812	155	15	v3r−1	v3r−1	PROPN
ejpam-3812	155	16	,	,	PUNCT
ejpam-3812	155	17	v3r	v3r	PROPN
ejpam-3812	155	18	}	}	PUNCT
ejpam-3812	155	19	.	.	PUNCT
ejpam-3812	156	1	for	for	ADP
ejpam-3812	156	2	every	every	DET
ejpam-3812	156	3	induced	induce	VERB
ejpam-3812	156	4	subgraph	subgraph	NOUN
ejpam-3812	156	5	〈	〈	PROPN
ejpam-3812	156	6	vi	vi	PROPN
ejpam-3812	156	7	,	,	PUNCT
ejpam-3812	156	8	vi+1	vi+1	NOUN
ejpam-3812	156	9	,	,	PUNCT
ejpam-3812	156	10	vi+2	vi+2	PROPN
ejpam-3812	156	11	〉	〉	NUM
ejpam-3812	156	12	of	of	ADP
ejpam-3812	156	13	pn	pn	PROPN
ejpam-3812	156	14	,	,	PUNCT
ejpam-3812	156	15	where	where	SCONJ
ejpam-3812	156	16	i	i	PRON
ejpam-3812	156	17	=	=	NOUN
ejpam-3812	156	18	1	1	NUM
ejpam-3812	156	19	,	,	PUNCT
ejpam-3812	156	20	4	4	NUM
ejpam-3812	156	21	,	,	PUNCT
ejpam-3812	156	22	...	...	PUNCT
ejpam-3812	156	23	,	,	PUNCT
ejpam-3812	156	24	3r−2	3r−2	X
ejpam-3812	156	25	,	,	PUNCT
ejpam-3812	156	26	the	the	DET
ejpam-3812	156	27	vertices	vertex	NOUN
ejpam-3812	156	28	vi+1	vi+1	ADP
ejpam-3812	156	29	form	form	VERB
ejpam-3812	156	30	an	an	DET
ejpam-3812	156	31	independent	independent	ADJ
ejpam-3812	156	32	1	1	NUM
ejpam-3812	156	33	-	-	PUNCT
ejpam-3812	156	34	fair	fair	ADJ
ejpam-3812	156	35	dominating	dominating	NOUN
ejpam-3812	156	36	set	set	NOUN
ejpam-3812	156	37	of	of	ADP
ejpam-3812	156	38	pn	pn	PROPN
ejpam-3812	156	39	.	.	PUNCT
ejpam-3812	157	1	thus	thus	ADV
ejpam-3812	157	2	,	,	PUNCT
ejpam-3812	157	3	the	the	DET
ejpam-3812	157	4	set	set	NOUN
ejpam-3812	157	5	t	t	NOUN
ejpam-3812	157	6	=	=	SYM
ejpam-3812	157	7	{	{	PUNCT
ejpam-3812	157	8	v2	v2	PROPN
ejpam-3812	157	9	,	,	PUNCT
ejpam-3812	157	10	v5	v5	PROPN
ejpam-3812	157	11	,	,	PUNCT
ejpam-3812	157	12	...	...	PUNCT
ejpam-3812	157	13	,	,	PUNCT
ejpam-3812	157	14	v3r−4	v3r−4	PROPN
ejpam-3812	157	15	,	,	PUNCT
ejpam-3812	157	16	v3r−1	v3r−1	PROPN
ejpam-3812	157	17	}	}	PUNCT
ejpam-3812	157	18	is	be	AUX
ejpam-3812	157	19	an	an	DET
ejpam-3812	157	20	independent	independent	ADJ
ejpam-3812	157	21	1	1	NUM
ejpam-3812	157	22	-	-	PUNCT
ejpam-3812	157	23	fair	fair	ADJ
ejpam-3812	157	24	dominating	dominating	NOUN
ejpam-3812	157	25	set	set	NOUN
ejpam-3812	157	26	of	of	ADP
ejpam-3812	157	27	pn	pn	PROPN
ejpam-3812	157	28	.	.	PUNCT
ejpam-3812	158	1	since	since	SCONJ
ejpam-3812	158	2	|t	|t	PROPN
ejpam-3812	158	3	|	|	ADV
ejpam-3812	158	4	=	=	SYM
ejpam-3812	158	5	r	r	NOUN
ejpam-3812	158	6	,	,	PUNCT
ejpam-3812	158	7	γi1f	γi1f	PROPN
ejpam-3812	158	8	(	(	PUNCT
ejpam-3812	158	9	pn	pn	NOUN
ejpam-3812	158	10	)	)	PUNCT
ejpam-3812	158	11	≤	≤	PROPN
ejpam-3812	158	12	r.	r.	PROPN
ejpam-3812	158	13	note	note	VERB
ejpam-3812	158	14	that	that	SCONJ
ejpam-3812	158	15	every	every	DET
ejpam-3812	158	16	three	three	NUM
ejpam-3812	158	17	adjacent	adjacent	ADJ
ejpam-3812	158	18	vertices	vertex	NOUN
ejpam-3812	158	19	in	in	ADP
ejpam-3812	158	20	pn	pn	PROPN
ejpam-3812	158	21	can	can	AUX
ejpam-3812	158	22	be	be	AUX
ejpam-3812	158	23	dominated	dominate	VERB
ejpam-3812	158	24	by	by	ADP
ejpam-3812	158	25	a	a	DET
ejpam-3812	158	26	single	single	ADJ
ejpam-3812	158	27	vertex	vertex	NOUN
ejpam-3812	158	28	.	.	PUNCT
ejpam-3812	159	1	thus	thus	ADV
ejpam-3812	159	2	,	,	PUNCT
ejpam-3812	159	3	every	every	DET
ejpam-3812	159	4	independent	independent	ADJ
ejpam-3812	159	5	1	1	NUM
ejpam-3812	159	6	-	-	PUNCT
ejpam-3812	159	7	fair	fair	ADJ
ejpam-3812	159	8	dominating	dominating	NOUN
ejpam-3812	159	9	set	set	NOUN
ejpam-3812	159	10	of	of	ADP
ejpam-3812	159	11	pn	pn	PROPN
ejpam-3812	159	12	contains	contain	VERB
ejpam-3812	159	13	at	at	ADP
ejpam-3812	159	14	least	least	ADJ
ejpam-3812	159	15	dn3	dn3	NOUN
ejpam-3812	159	16	e	e	NOUN
ejpam-3812	159	17	vertices	vertex	NOUN
ejpam-3812	159	18	.	.	PUNCT
ejpam-3812	160	1	hence	hence	ADV
ejpam-3812	160	2	,	,	PUNCT
ejpam-3812	160	3	γi1f	γi1f	PROPN
ejpam-3812	160	4	(	(	PUNCT
ejpam-3812	160	5	pn	pn	NOUN
ejpam-3812	160	6	)	)	PUNCT
ejpam-3812	160	7	≥	≥	NOUN
ejpam-3812	160	8	dn3	dn3	NOUN
ejpam-3812	160	9	e	e	PROPN
ejpam-3812	160	10	=	=	PROPN
ejpam-3812	160	11	r.	r.	PROPN
ejpam-3812	160	12	thus	thus	ADV
ejpam-3812	160	13	,	,	PUNCT
ejpam-3812	160	14	γi1f	γi1f	PROPN
ejpam-3812	160	15	(	(	PUNCT
ejpam-3812	160	16	pn	pn	NOUN
ejpam-3812	160	17	)	)	PUNCT
ejpam-3812	160	18	=	=	PUNCT
ejpam-3812	160	19	dn3	dn3	PROPN
ejpam-3812	160	20	e.	e.	PROPN
ejpam-3812	160	21	m.	m.	PROPN
ejpam-3812	160	22	ortega	ortega	PROPN
ejpam-3812	160	23	,	,	PUNCT
ejpam-3812	160	24	r.	r.	PROPN
ejpam-3812	160	25	isla	isla	PROPN
ejpam-3812	160	26	/	/	SYM
ejpam-3812	160	27	eur	eur	PROPN
ejpam-3812	160	28	.	.	PUNCT
ejpam-3812	161	1	j.	j.	PROPN
ejpam-3812	161	2	pure	pure	PROPN
ejpam-3812	161	3	appl	appl	PROPN
ejpam-3812	161	4	.	.	PROPN
ejpam-3812	161	5	math	math	PROPN
ejpam-3812	161	6	,	,	PUNCT
ejpam-3812	161	7	13	13	NUM
ejpam-3812	161	8	(	(	PUNCT
ejpam-3812	161	9	4	4	NUM
ejpam-3812	161	10	)	)	PUNCT
ejpam-3812	161	11	(	(	PUNCT
ejpam-3812	161	12	2020	2020	NUM
ejpam-3812	161	13	)	)	PUNCT
ejpam-3812	161	14	,	,	PUNCT
ejpam-3812	161	15	779	779	NUM
ejpam-3812	161	16	-	-	SYM
ejpam-3812	161	17	793	793	NUM
ejpam-3812	161	18	784	784	NUM
ejpam-3812	161	19	case	case	NOUN
ejpam-3812	161	20	2	2	NUM
ejpam-3812	161	21	:	:	PUNCT
ejpam-3812	161	22	n	n	NOUN
ejpam-3812	161	23	=	=	SYM
ejpam-3812	161	24	3r	3r	NUM
ejpam-3812	161	25	+	+	CCONJ
ejpam-3812	161	26	2	2	NUM
ejpam-3812	161	27	in	in	ADP
ejpam-3812	161	28	case	case	NOUN
ejpam-3812	161	29	1	1	NUM
ejpam-3812	161	30	,	,	PUNCT
ejpam-3812	161	31	the	the	DET
ejpam-3812	161	32	set	set	NOUN
ejpam-3812	161	33	t	t	PROPN
ejpam-3812	161	34	is	be	AUX
ejpam-3812	161	35	a	a	DET
ejpam-3812	161	36	γi1f	γi1f	PROPN
ejpam-3812	161	37	-set	-set	PUNCT
ejpam-3812	161	38	of	of	ADP
ejpam-3812	161	39	the	the	DET
ejpam-3812	161	40	induced	induced	ADJ
ejpam-3812	161	41	subgraph	subgraph	NOUN
ejpam-3812	161	42	〈	〈	PROPN
ejpam-3812	161	43	v1	v1	NOUN
ejpam-3812	161	44	,	,	PUNCT
ejpam-3812	161	45	v2	v2	PROPN
ejpam-3812	161	46	,	,	PUNCT
ejpam-3812	161	47	...	...	PUNCT
ejpam-3812	161	48	,	,	PUNCT
ejpam-3812	161	49	v3r	v3r	NOUN
ejpam-3812	161	50	〉	〉	NOUN
ejpam-3812	161	51	of	of	ADP
ejpam-3812	161	52	pn	pn	PROPN
ejpam-3812	161	53	.	.	PUNCT
ejpam-3812	162	1	since	since	SCONJ
ejpam-3812	162	2	n	n	NOUN
ejpam-3812	162	3	=	=	SYM
ejpam-3812	162	4	3r+	3r+	NUM
ejpam-3812	162	5	2	2	NUM
ejpam-3812	162	6	,	,	PUNCT
ejpam-3812	162	7	the	the	DET
ejpam-3812	162	8	set	set	NOUN
ejpam-3812	162	9	t	t	PROPN
ejpam-3812	162	10	∪	∪	X
ejpam-3812	162	11	{	{	PUNCT
ejpam-3812	162	12	v3r+2	v3r+2	ADJ
ejpam-3812	162	13	}	}	PUNCT
ejpam-3812	162	14	is	be	AUX
ejpam-3812	162	15	a	a	DET
ejpam-3812	162	16	γi1f	γi1f	PROPN
ejpam-3812	162	17	-set	-set	PUNCT
ejpam-3812	162	18	of	of	ADP
ejpam-3812	162	19	pn	pn	PROPN
ejpam-3812	162	20	.	.	PUNCT
ejpam-3812	163	1	thus	thus	ADV
ejpam-3812	163	2	,	,	PUNCT
ejpam-3812	163	3	γi1f	γi1f	PROPN
ejpam-3812	163	4	(	(	PUNCT
ejpam-3812	163	5	pn	pn	NOUN
ejpam-3812	163	6	)	)	PUNCT
ejpam-3812	163	7	=	=	NOUN
ejpam-3812	163	8	r+	r+	PUNCT
ejpam-3812	163	9	1	1	NUM
ejpam-3812	163	10	=	=	SYM
ejpam-3812	163	11	⌈	⌈	NOUN
ejpam-3812	163	12	3r+2	3r+2	NUM
ejpam-3812	163	13	3	3	NUM
ejpam-3812	163	14	⌉	⌉	NOUN
ejpam-3812	163	15	=	=	SYM
ejpam-3812	163	16	dn3	dn3	PROPN
ejpam-3812	163	17	e.	e.	PROPN
ejpam-3812	163	18	case	case	PROPN
ejpam-3812	163	19	3	3	NUM
ejpam-3812	163	20	:	:	PUNCT
ejpam-3812	163	21	n	n	NOUN
ejpam-3812	163	22	=	=	SYM
ejpam-3812	163	23	3r	3r	NUM
ejpam-3812	163	24	+	+	SYM
ejpam-3812	163	25	1	1	NUM
ejpam-3812	163	26	consider	consider	VERB
ejpam-3812	163	27	the	the	DET
ejpam-3812	163	28	grouping	grouping	NOUN
ejpam-3812	163	29	of	of	ADP
ejpam-3812	163	30	the	the	DET
ejpam-3812	163	31	first	first	ADJ
ejpam-3812	163	32	3r	3r	NUM
ejpam-3812	163	33	vertices	vertex	NOUN
ejpam-3812	163	34	of	of	ADP
ejpam-3812	163	35	pn	pn	NOUN
ejpam-3812	163	36	given	give	VERB
ejpam-3812	163	37	in	in	ADP
ejpam-3812	163	38	case	case	NOUN
ejpam-3812	163	39	1	1	NUM
ejpam-3812	163	40	.	.	PUNCT
ejpam-3812	164	1	the	the	DET
ejpam-3812	164	2	set	set	NOUN
ejpam-3812	164	3	s	s	PART
ejpam-3812	164	4	=	=	NOUN
ejpam-3812	164	5	{	{	PUNCT
ejpam-3812	164	6	v1	v1	PROPN
ejpam-3812	164	7	,	,	PUNCT
ejpam-3812	164	8	v4	v4	NOUN
ejpam-3812	164	9	,	,	PUNCT
ejpam-3812	164	10	...	...	PUNCT
ejpam-3812	164	11	,	,	PUNCT
ejpam-3812	164	12	v3r−2}∪{v3r+1	v3r−2}∪{v3r+1	NOUN
ejpam-3812	164	13	}	}	PUNCT
ejpam-3812	164	14	is	be	AUX
ejpam-3812	164	15	an	an	DET
ejpam-3812	164	16	independent	independent	ADJ
ejpam-3812	164	17	1	1	NUM
ejpam-3812	164	18	-	-	PUNCT
ejpam-3812	164	19	fair	fair	ADJ
ejpam-3812	164	20	dominating	dominating	NOUN
ejpam-3812	164	21	set	set	NOUN
ejpam-3812	164	22	of	of	ADP
ejpam-3812	164	23	pn	pn	PROPN
ejpam-3812	164	24	.	.	PUNCT
ejpam-3812	165	1	thus	thus	ADV
ejpam-3812	165	2	,	,	PUNCT
ejpam-3812	165	3	γi1f	γi1f	PROPN
ejpam-3812	165	4	(	(	PUNCT
ejpam-3812	165	5	pn	pn	NOUN
ejpam-3812	165	6	)	)	PUNCT
ejpam-3812	165	7	≤	≤	NOUN
ejpam-3812	165	8	|s|	|s|	VERB
ejpam-3812	165	9	+	+	CCONJ
ejpam-3812	165	10	1	1	NUM
ejpam-3812	165	11	=	=	SYM
ejpam-3812	165	12	r	r	NOUN
ejpam-3812	165	13	+	+	NOUN
ejpam-3812	165	14	1	1	NUM
ejpam-3812	165	15	=	=	SYM
ejpam-3812	165	16	⌈	⌈	SYM
ejpam-3812	165	17	3r+1	3r+1	NOUN
ejpam-3812	165	18	3	3	NUM
ejpam-3812	165	19	⌉	⌉	NOUN
ejpam-3812	165	20	=	=	SYM
ejpam-3812	165	21	dn3	dn3	PROPN
ejpam-3812	165	22	e.	e.	PROPN
ejpam-3812	165	23	note	note	VERB
ejpam-3812	165	24	that	that	SCONJ
ejpam-3812	165	25	each	each	PRON
ejpam-3812	165	26	of	of	ADP
ejpam-3812	165	27	the	the	DET
ejpam-3812	165	28	first	first	ADJ
ejpam-3812	165	29	r	r	NOUN
ejpam-3812	165	30	−	−	NOUN
ejpam-3812	165	31	1	1	NUM
ejpam-3812	165	32	induced	induced	ADJ
ejpam-3812	165	33	subgraph	subgraph	NOUN
ejpam-3812	165	34	〈	〈	PROPN
ejpam-3812	165	35	vi	vi	PROPN
ejpam-3812	165	36	,	,	PUNCT
ejpam-3812	165	37	vi+1	vi+1	NOUN
ejpam-3812	165	38	,	,	PUNCT
ejpam-3812	165	39	vi+2	vi+2	PROPN
ejpam-3812	165	40	〉	〉	PROPN
ejpam-3812	165	41	can	can	AUX
ejpam-3812	165	42	be	be	AUX
ejpam-3812	165	43	dominated	dominate	VERB
ejpam-3812	165	44	by	by	ADP
ejpam-3812	165	45	a	a	DET
ejpam-3812	165	46	single	single	ADJ
ejpam-3812	165	47	vertex	vertex	NOUN
ejpam-3812	165	48	,	,	PUNCT
ejpam-3812	165	49	while	while	SCONJ
ejpam-3812	165	50	the	the	DET
ejpam-3812	165	51	induced	induced	ADJ
ejpam-3812	165	52	subgraph	subgraph	NOUN
ejpam-3812	165	53	〈	〈	PROPN
ejpam-3812	165	54	v3r−2	v3r−2	PROPN
ejpam-3812	165	55	,	,	PUNCT
ejpam-3812	165	56	v3r−1	v3r−1	PROPN
ejpam-3812	165	57	,	,	PUNCT
ejpam-3812	165	58	v3r	v3r	PROPN
ejpam-3812	165	59	,	,	PUNCT
ejpam-3812	165	60	v3r+1	v3r+1	PUNCT
ejpam-3812	165	61	〉	〉	PROPN
ejpam-3812	165	62	can	can	AUX
ejpam-3812	165	63	be	be	AUX
ejpam-3812	165	64	dominated	dominate	VERB
ejpam-3812	165	65	by	by	ADP
ejpam-3812	165	66	the	the	DET
ejpam-3812	165	67	vertices	vertex	NOUN
ejpam-3812	165	68	v3r−2	v3r−2	PROPN
ejpam-3812	165	69	and	and	CCONJ
ejpam-3812	165	70	v3r+1	v3r+1	PROPN
ejpam-3812	165	71	.	.	PUNCT
ejpam-3812	166	1	thus	thus	ADV
ejpam-3812	166	2	,	,	PUNCT
ejpam-3812	166	3	every	every	DET
ejpam-3812	166	4	independent	independent	ADJ
ejpam-3812	166	5	1	1	NUM
ejpam-3812	166	6	-	-	PUNCT
ejpam-3812	166	7	fair	fair	ADJ
ejpam-3812	166	8	dominating	dominating	NOUN
ejpam-3812	166	9	set	set	NOUN
ejpam-3812	166	10	of	of	ADP
ejpam-3812	166	11	pn	pn	PROPN
ejpam-3812	166	12	contains	contain	VERB
ejpam-3812	166	13	at	at	ADP
ejpam-3812	166	14	least	least	ADJ
ejpam-3812	166	15	(	(	PUNCT
ejpam-3812	166	16	r	r	NOUN
ejpam-3812	166	17	−	−	PROPN
ejpam-3812	166	18	1	1	NUM
ejpam-3812	166	19	)	)	PUNCT
ejpam-3812	166	20	+	+	CCONJ
ejpam-3812	166	21	2	2	NUM
ejpam-3812	166	22	=	=	SYM
ejpam-3812	166	23	r	r	NOUN
ejpam-3812	166	24	+	+	NOUN
ejpam-3812	166	25	1	1	NUM
ejpam-3812	166	26	=	=	SYM
ejpam-3812	166	27	⌈	⌈	SYM
ejpam-3812	166	28	3r+1	3r+1	NOUN
ejpam-3812	166	29	3	3	NUM
ejpam-3812	166	30	⌉	⌉	NOUN
ejpam-3812	166	31	=	=	PUNCT
ejpam-3812	166	32	dn3	dn3	ADJ
ejpam-3812	166	33	e	e	NOUN
ejpam-3812	166	34	vertices	vertex	NOUN
ejpam-3812	166	35	.	.	PUNCT
ejpam-3812	167	1	hence	hence	ADV
ejpam-3812	167	2	,	,	PUNCT
ejpam-3812	167	3	γi1f	γi1f	PROPN
ejpam-3812	167	4	(	(	PUNCT
ejpam-3812	167	5	pn	pn	NOUN
ejpam-3812	167	6	)	)	PUNCT
ejpam-3812	167	7	≥	≥	PROPN
ejpam-3812	167	8	dn3	dn3	PROPN
ejpam-3812	167	9	e.	e.	PROPN
ejpam-3812	168	1	therefore	therefore	ADV
ejpam-3812	168	2	,	,	PUNCT
ejpam-3812	168	3	γi1f	γi1f	PROPN
ejpam-3812	168	4	(	(	PUNCT
ejpam-3812	168	5	pn	pn	NOUN
ejpam-3812	168	6	)	)	PUNCT
ejpam-3812	168	7	=	=	PUNCT
ejpam-3812	169	1	dn3	dn3	PROPN
ejpam-3812	169	2	e.	e.	PROPN
ejpam-3812	169	3	�	�	PROPN
ejpam-3812	169	4	corollary	corollary	PROPN
ejpam-3812	169	5	4	4	NUM
ejpam-3812	169	6	.	.	PUNCT
ejpam-3812	170	1	for	for	ADP
ejpam-3812	170	2	any	any	DET
ejpam-3812	170	3	positive	positive	ADJ
ejpam-3812	170	4	integer	integer	NOUN
ejpam-3812	170	5	n	n	PRON
ejpam-3812	170	6	≡	≡	PROPN
ejpam-3812	170	7	0	0	PUNCT
ejpam-3812	170	8	(	(	PUNCT
ejpam-3812	170	9	mod	mod	NOUN
ejpam-3812	170	10	3	3	NUM
ejpam-3812	170	11	)	)	PUNCT
ejpam-3812	170	12	,	,	PUNCT
ejpam-3812	170	13	γi1f	γi1f	X
ejpam-3812	170	14	(	(	PUNCT
ejpam-3812	170	15	cn	cn	NOUN
ejpam-3812	170	16	)	)	PUNCT
ejpam-3812	170	17	=	=	SYM
ejpam-3812	170	18	n	n	PRON
ejpam-3812	170	19	3	3	NUM
ejpam-3812	170	20	.	.	PUNCT
ejpam-3812	171	1	proof	proof	NOUN
ejpam-3812	171	2	.	.	PUNCT
ejpam-3812	172	1	immediately	immediately	ADV
ejpam-3812	172	2	follows	follow	VERB
ejpam-3812	172	3	from	from	ADP
ejpam-3812	172	4	case	case	NOUN
ejpam-3812	172	5	1	1	NUM
ejpam-3812	172	6	of	of	ADP
ejpam-3812	172	7	theorem	theorem	ADJ
ejpam-3812	172	8	7	7	NUM
ejpam-3812	172	9	.	.	PUNCT
ejpam-3812	172	10	�	�	PROPN
ejpam-3812	172	11	the	the	DET
ejpam-3812	172	12	following	follow	VERB
ejpam-3812	172	13	results	result	NOUN
ejpam-3812	172	14	are	be	AUX
ejpam-3812	172	15	used	use	VERB
ejpam-3812	172	16	in	in	ADP
ejpam-3812	172	17	the	the	DET
ejpam-3812	172	18	succeeding	succeed	VERB
ejpam-3812	172	19	sections	section	NOUN
ejpam-3812	172	20	.	.	PUNCT
ejpam-3812	173	1	theorem	theorem	VERB
ejpam-3812	173	2	8	8	NUM
ejpam-3812	173	3	.	.	PUNCT
ejpam-3812	174	1	[	[	X
ejpam-3812	174	2	6	6	NUM
ejpam-3812	174	3	]	]	PUNCT
ejpam-3812	174	4	let	let	VERB
ejpam-3812	174	5	g	g	NOUN
ejpam-3812	174	6	and	and	CCONJ
ejpam-3812	174	7	h	h	NOUN
ejpam-3812	174	8	be	be	AUX
ejpam-3812	174	9	nontrivial	nontrivial	ADJ
ejpam-3812	174	10	connected	connect	VERB
ejpam-3812	174	11	graphs	graph	NOUN
ejpam-3812	174	12	of	of	ADP
ejpam-3812	174	13	orders	order	NOUN
ejpam-3812	174	14	m	m	VERB
ejpam-3812	174	15	and	and	CCONJ
ejpam-3812	174	16	n	n	CCONJ
ejpam-3812	174	17	,	,	PUNCT
ejpam-3812	174	18	respectively	respectively	ADV
ejpam-3812	174	19	,	,	PUNCT
ejpam-3812	174	20	and	and	CCONJ
ejpam-3812	174	21	k	k	X
ejpam-3812	174	22	a	a	DET
ejpam-3812	174	23	positive	positive	ADJ
ejpam-3812	174	24	integer	integer	NOUN
ejpam-3812	174	25	with	with	ADP
ejpam-3812	174	26	1	1	NUM
ejpam-3812	174	27	≤	≤	NUM
ejpam-3812	174	28	k	k	NOUN
ejpam-3812	174	29	≤	≤	ADJ
ejpam-3812	174	30	max{m	max{m	NOUN
ejpam-3812	174	31	,	,	PUNCT
ejpam-3812	174	32	n	n	CCONJ
ejpam-3812	174	33	}	}	PUNCT
ejpam-3812	174	34	.	.	PUNCT
ejpam-3812	175	1	then	then	ADV
ejpam-3812	175	2	s	s	VERB
ejpam-3812	175	3	⊆	⊆	NUM
ejpam-3812	175	4	v	v	NOUN
ejpam-3812	175	5	(	(	PUNCT
ejpam-3812	175	6	g	g	PROPN
ejpam-3812	175	7	+	+	NOUN
ejpam-3812	175	8	h	h	NOUN
ejpam-3812	175	9	)	)	PUNCT
ejpam-3812	175	10	is	be	AUX
ejpam-3812	175	11	a	a	DET
ejpam-3812	175	12	kfd	kfd	NOUN
ejpam-3812	175	13	-	-	PUNCT
ejpam-3812	175	14	set	set	NOUN
ejpam-3812	175	15	in	in	ADP
ejpam-3812	175	16	g+h	g+h	PROPN
ejpam-3812	175	17	if	if	SCONJ
ejpam-3812	175	18	and	and	CCONJ
ejpam-3812	175	19	only	only	ADV
ejpam-3812	175	20	if	if	SCONJ
ejpam-3812	175	21	one	one	NUM
ejpam-3812	175	22	of	of	ADP
ejpam-3812	175	23	the	the	DET
ejpam-3812	175	24	following	following	NOUN
ejpam-3812	175	25	holds	hold	VERB
ejpam-3812	175	26	:	:	PUNCT
ejpam-3812	175	27	(	(	PUNCT
ejpam-3812	175	28	a	a	X
ejpam-3812	175	29	)	)	PUNCT
ejpam-3812	175	30	s	s	PART
ejpam-3812	175	31	=	=	SYM
ejpam-3812	175	32	v	v	PROPN
ejpam-3812	175	33	(	(	PUNCT
ejpam-3812	175	34	g+h	g+h	PROPN
ejpam-3812	175	35	)	)	PUNCT
ejpam-3812	175	36	.	.	PUNCT
ejpam-3812	176	1	(	(	PUNCT
ejpam-3812	176	2	b	b	X
ejpam-3812	176	3	)	)	PUNCT
ejpam-3812	176	4	s	s	PART
ejpam-3812	176	5	⊆	⊆	NUM
ejpam-3812	176	6	v	v	NOUN
ejpam-3812	176	7	(	(	PUNCT
ejpam-3812	176	8	g	g	NOUN
ejpam-3812	176	9	)	)	PUNCT
ejpam-3812	176	10	,	,	PUNCT
ejpam-3812	176	11	|s|	|s|	PROPN
ejpam-3812	176	12	=	=	SYM
ejpam-3812	176	13	k	k	PROPN
ejpam-3812	176	14	and	and	CCONJ
ejpam-3812	176	15	s	s	PROPN
ejpam-3812	176	16	is	be	AUX
ejpam-3812	176	17	a	a	DET
ejpam-3812	176	18	kfd	kfd	NOUN
ejpam-3812	176	19	-	-	PUNCT
ejpam-3812	176	20	set	set	NOUN
ejpam-3812	176	21	in	in	ADP
ejpam-3812	176	22	g.	g.	PROPN
ejpam-3812	176	23	(	(	PUNCT
ejpam-3812	176	24	c	c	X
ejpam-3812	176	25	)	)	PUNCT
ejpam-3812	176	26	s	s	PART
ejpam-3812	176	27	⊆	⊆	NUM
ejpam-3812	176	28	v	v	NOUN
ejpam-3812	176	29	(	(	PUNCT
ejpam-3812	176	30	h	h	NOUN
ejpam-3812	176	31	)	)	PUNCT
ejpam-3812	176	32	,	,	PUNCT
ejpam-3812	176	33	|s|	|s|	PROPN
ejpam-3812	176	34	=	=	SYM
ejpam-3812	176	35	k	k	PROPN
ejpam-3812	176	36	and	and	CCONJ
ejpam-3812	176	37	s	s	PROPN
ejpam-3812	176	38	is	be	AUX
ejpam-3812	176	39	a	a	DET
ejpam-3812	176	40	kfd	kfd	NOUN
ejpam-3812	176	41	-	-	PUNCT
ejpam-3812	176	42	set	set	NOUN
ejpam-3812	176	43	in	in	ADP
ejpam-3812	176	44	h.	h.	PROPN
ejpam-3812	176	45	(	(	PUNCT
ejpam-3812	176	46	d	d	X
ejpam-3812	176	47	)	)	PUNCT
ejpam-3812	176	48	s	s	PART
ejpam-3812	176	49	=	=	PUNCT
ejpam-3812	176	50	sg	sg	X
ejpam-3812	176	51	∪	∪	ADJ
ejpam-3812	176	52	sh	sh	PROPN
ejpam-3812	176	53	,	,	PUNCT
ejpam-3812	176	54	where	where	SCONJ
ejpam-3812	176	55	sg	sg	PROPN
ejpam-3812	176	56	is	be	AUX
ejpam-3812	176	57	a	a	DET
ejpam-3812	176	58	(	(	PUNCT
ejpam-3812	176	59	k	k	PROPN
ejpam-3812	176	60	−	−	PROPN
ejpam-3812	176	61	|sh	|sh	ADP
ejpam-3812	176	62	|)fd	|)fd	PROPN
ejpam-3812	176	63	-	-	PUNCT
ejpam-3812	176	64	set	set	VERB
ejpam-3812	176	65	in	in	ADP
ejpam-3812	176	66	g	g	PROPN
ejpam-3812	176	67	and	and	CCONJ
ejpam-3812	176	68	sh	sh	PROPN
ejpam-3812	176	69	is	be	AUX
ejpam-3812	176	70	a	a	DET
ejpam-3812	176	71	(	(	PUNCT
ejpam-3812	176	72	k	k	PROPN
ejpam-3812	176	73	−	−	PROPN
ejpam-3812	176	74	|sg|)fd	|sg|)fd	NOUN
ejpam-3812	176	75	-	-	PUNCT
ejpam-3812	176	76	set	set	NOUN
ejpam-3812	176	77	in	in	ADP
ejpam-3812	176	78	h.	h.	PROPN
ejpam-3812	176	79	(	(	PUNCT
ejpam-3812	176	80	e	e	X
ejpam-3812	176	81	)	)	PUNCT
ejpam-3812	176	82	s	s	PART
ejpam-3812	176	83	=	=	SYM
ejpam-3812	176	84	v	v	X
ejpam-3812	176	85	(	(	PUNCT
ejpam-3812	176	86	g	g	NOUN
ejpam-3812	176	87	)	)	PUNCT
ejpam-3812	176	88	∪	∪	ADP
ejpam-3812	176	89	t	t	PROPN
ejpam-3812	176	90	,	,	PUNCT
ejpam-3812	176	91	where	where	SCONJ
ejpam-3812	176	92	|v	|v	PROPN
ejpam-3812	176	93	(	(	PUNCT
ejpam-3812	176	94	g)|	g)|	NOUN
ejpam-3812	176	95	=	=	NOUN
ejpam-3812	176	96	m	m	PROPN
ejpam-3812	176	97	<	<	X
ejpam-3812	176	98	k	k	X
ejpam-3812	176	99	and	and	CCONJ
ejpam-3812	176	100	t	t	PROPN
ejpam-3812	176	101	is	be	AUX
ejpam-3812	176	102	a	a	DET
ejpam-3812	176	103	(	(	PUNCT
ejpam-3812	176	104	k	k	X
ejpam-3812	176	105	−m)fd	−m)fd	X
ejpam-3812	176	106	-	-	PUNCT
ejpam-3812	176	107	set	set	NOUN
ejpam-3812	176	108	in	in	ADP
ejpam-3812	176	109	h.	h.	PROPN
ejpam-3812	176	110	(	(	PUNCT
ejpam-3812	176	111	f	f	X
ejpam-3812	176	112	)	)	PUNCT
ejpam-3812	176	113	s	s	PART
ejpam-3812	177	1	=	=	X
ejpam-3812	177	2	d	d	X
ejpam-3812	177	3	∪	∪	X
ejpam-3812	177	4	v	v	NOUN
ejpam-3812	177	5	(	(	PUNCT
ejpam-3812	177	6	h	h	NOUN
ejpam-3812	177	7	)	)	PUNCT
ejpam-3812	177	8	,	,	PUNCT
ejpam-3812	178	1	where	where	SCONJ
ejpam-3812	178	2	|v	|v	PROPN
ejpam-3812	178	3	(	(	PUNCT
ejpam-3812	178	4	h)|	h)|	NOUN
ejpam-3812	178	5	=	=	SYM
ejpam-3812	178	6	n	n	CCONJ
ejpam-3812	178	7	<	<	X
ejpam-3812	178	8	k	k	PROPN
ejpam-3812	178	9	and	and	CCONJ
ejpam-3812	178	10	d	d	PROPN
ejpam-3812	178	11	is	be	AUX
ejpam-3812	178	12	a	a	DET
ejpam-3812	178	13	(	(	PUNCT
ejpam-3812	178	14	k	k	PROPN
ejpam-3812	178	15	−	−	PROPN
ejpam-3812	178	16	n)fd	n)fd	PROPN
ejpam-3812	178	17	-	-	PUNCT
ejpam-3812	178	18	set	set	NOUN
ejpam-3812	178	19	in	in	ADP
ejpam-3812	178	20	g.	g.	PROPN
ejpam-3812	178	21	theorem	theorem	VERB
ejpam-3812	178	22	9	9	NUM
ejpam-3812	178	23	.	.	PUNCT
ejpam-3812	179	1	[	[	X
ejpam-3812	179	2	6	6	NUM
ejpam-3812	179	3	]	]	PUNCT
ejpam-3812	179	4	let	let	VERB
ejpam-3812	179	5	g	g	NOUN
ejpam-3812	179	6	and	and	CCONJ
ejpam-3812	179	7	h	h	NOUN
ejpam-3812	179	8	be	be	AUX
ejpam-3812	179	9	nontrivial	nontrivial	ADJ
ejpam-3812	179	10	connected	connect	VERB
ejpam-3812	179	11	graphs	graph	NOUN
ejpam-3812	179	12	and	and	CCONJ
ejpam-3812	179	13	let	let	VERB
ejpam-3812	179	14	k	k	PRON
ejpam-3812	179	15	be	be	AUX
ejpam-3812	179	16	a	a	DET
ejpam-3812	179	17	positive	positive	ADJ
ejpam-3812	179	18	integer	integer	NOUN
ejpam-3812	179	19	with	with	ADP
ejpam-3812	179	20	k	k	PROPN
ejpam-3812	179	21	≤	≤	PROPN
ejpam-3812	179	22	|v	|v	PROPN
ejpam-3812	179	23	(	(	PUNCT
ejpam-3812	179	24	h)|	h)|	PROPN
ejpam-3812	179	25	.	.	PUNCT
ejpam-3812	180	1	then	then	ADV
ejpam-3812	180	2	c	c	PROPN
ejpam-3812	180	3	⊆	⊆	NUM
ejpam-3812	180	4	v	v	NOUN
ejpam-3812	180	5	(	(	PUNCT
ejpam-3812	180	6	g	g	PROPN
ejpam-3812	180	7	◦	◦	NOUN
ejpam-3812	180	8	h	h	NOUN
ejpam-3812	180	9	)	)	PUNCT
ejpam-3812	180	10	is	be	AUX
ejpam-3812	180	11	a	a	DET
ejpam-3812	180	12	kfd	kfd	NOUN
ejpam-3812	180	13	-	-	PUNCT
ejpam-3812	180	14	set	set	NOUN
ejpam-3812	180	15	in	in	ADP
ejpam-3812	180	16	g	g	PROPN
ejpam-3812	180	17	◦	◦	NOUN
ejpam-3812	180	18	h	h	NOUN
ejpam-3812	180	19	if	if	SCONJ
ejpam-3812	181	1	and	and	CCONJ
ejpam-3812	181	2	only	only	ADV
ejpam-3812	181	3	if	if	SCONJ
ejpam-3812	181	4	one	one	NUM
ejpam-3812	181	5	of	of	ADP
ejpam-3812	181	6	the	the	DET
ejpam-3812	181	7	following	following	NOUN
ejpam-3812	181	8	holds	hold	VERB
ejpam-3812	181	9	:	:	PUNCT
ejpam-3812	181	10	(	(	PUNCT
ejpam-3812	181	11	a	a	X
ejpam-3812	181	12	)	)	PUNCT
ejpam-3812	181	13	c	c	NOUN
ejpam-3812	181	14	=	=	SYM
ejpam-3812	181	15	v	v	PROPN
ejpam-3812	181	16	(	(	PUNCT
ejpam-3812	181	17	g	g	NOUN
ejpam-3812	181	18	)	)	PUNCT
ejpam-3812	181	19	∪b	∪b	VERB
ejpam-3812	181	20	,	,	PUNCT
ejpam-3812	181	21	where	where	SCONJ
ejpam-3812	181	22	b	b	NOUN
ejpam-3812	181	23	=	=	NOUN
ejpam-3812	181	24	∅	∅	NOUN
ejpam-3812	181	25	or	or	CCONJ
ejpam-3812	181	26	b	b	NOUN
ejpam-3812	181	27	=	=	SYM
ejpam-3812	181	28	⋃	⋃	NOUN
ejpam-3812	181	29	v∈v	v∈v	NOUN
ejpam-3812	181	30	(	(	PUNCT
ejpam-3812	181	31	g	g	NOUN
ejpam-3812	181	32	)	)	PUNCT
ejpam-3812	181	33	sv	sv	NOUN
ejpam-3812	181	34	,	,	PUNCT
ejpam-3812	181	35	where	where	SCONJ
ejpam-3812	181	36	each	each	PRON
ejpam-3812	181	37	sv	sv	PROPN
ejpam-3812	181	38	is	be	AUX
ejpam-3812	181	39	a	a	DET
ejpam-3812	181	40	(	(	PUNCT
ejpam-3812	181	41	k	k	PROPN
ejpam-3812	181	42	−	−	PROPN
ejpam-3812	182	1	1)fd	1)fd	PROPN
ejpam-3812	182	2	-	-	PUNCT
ejpam-3812	182	3	set	set	NOUN
ejpam-3812	182	4	in	in	ADP
ejpam-3812	182	5	hv	hv	PROPN
ejpam-3812	182	6	.	.	PUNCT
ejpam-3812	183	1	(	(	PUNCT
ejpam-3812	183	2	b	b	X
ejpam-3812	183	3	)	)	PUNCT
ejpam-3812	183	4	c	c	NOUN
ejpam-3812	184	1	=	=	PUNCT
ejpam-3812	184	2	⋃	⋃	NOUN
ejpam-3812	184	3	v∈v	v∈v	NOUN
ejpam-3812	184	4	(	(	PUNCT
ejpam-3812	184	5	g	g	NOUN
ejpam-3812	184	6	)	)	PUNCT
ejpam-3812	184	7	sv	sv	NOUN
ejpam-3812	184	8	,	,	PUNCT
ejpam-3812	184	9	where	where	SCONJ
ejpam-3812	184	10	each	each	PRON
ejpam-3812	184	11	sv	sv	PROPN
ejpam-3812	184	12	is	be	AUX
ejpam-3812	184	13	a	a	DET
ejpam-3812	184	14	kfd	kfd	NOUN
ejpam-3812	184	15	-	-	PUNCT
ejpam-3812	184	16	set	set	NOUN
ejpam-3812	184	17	in	in	ADP
ejpam-3812	184	18	hv	hv	PROPN
ejpam-3812	184	19	and	and	CCONJ
ejpam-3812	184	20	|sv|	|sv|	PROPN
ejpam-3812	184	21	=	=	SYM
ejpam-3812	184	22	k.	k.	PROPN
ejpam-3812	184	23	theorem	theorem	VERB
ejpam-3812	184	24	10	10	NUM
ejpam-3812	184	25	.	.	PUNCT
ejpam-3812	185	1	[	[	X
ejpam-3812	185	2	6	6	NUM
ejpam-3812	185	3	]	]	PUNCT
ejpam-3812	185	4	let	let	VERB
ejpam-3812	185	5	g	g	NOUN
ejpam-3812	185	6	and	and	CCONJ
ejpam-3812	185	7	h	h	NOUN
ejpam-3812	185	8	be	be	AUX
ejpam-3812	185	9	nontrivial	nontrivial	ADJ
ejpam-3812	185	10	connected	connected	ADJ
ejpam-3812	185	11	graphs	graph	NOUN
ejpam-3812	185	12	.	.	PUNCT
ejpam-3812	186	1	then	then	ADV
ejpam-3812	186	2	c	c	X
ejpam-3812	186	3	=	=	PUNCT
ejpam-3812	186	4	⋃	⋃	PROPN
ejpam-3812	186	5	x∈s	x∈s	NOUN
ejpam-3812	186	6	(	(	PUNCT
ejpam-3812	186	7	{	{	PUNCT
ejpam-3812	186	8	x}×tx	x}×tx	NUM
ejpam-3812	186	9	)	)	PUNCT
ejpam-3812	186	10	⊆	⊆	NUM
ejpam-3812	186	11	v	v	NOUN
ejpam-3812	186	12	(	(	PUNCT
ejpam-3812	186	13	g[h	g[h	PROPN
ejpam-3812	186	14	]	]	PUNCT
ejpam-3812	186	15	)	)	PUNCT
ejpam-3812	186	16	is	be	AUX
ejpam-3812	186	17	a	a	DET
ejpam-3812	186	18	kfd	kfd	NOUN
ejpam-3812	186	19	-	-	PUNCT
ejpam-3812	186	20	set	set	NOUN
ejpam-3812	186	21	in	in	ADP
ejpam-3812	186	22	g[h	g[h	PROPN
ejpam-3812	186	23	]	]	PUNCT
ejpam-3812	186	24	if	if	SCONJ
ejpam-3812	187	1	and	and	CCONJ
ejpam-3812	187	2	only	only	ADV
ejpam-3812	187	3	if	if	SCONJ
ejpam-3812	187	4	the	the	DET
ejpam-3812	187	5	following	follow	VERB
ejpam-3812	187	6	hold	hold	NOUN
ejpam-3812	187	7	:	:	PUNCT
ejpam-3812	187	8	m.	m.	PROPN
ejpam-3812	187	9	ortega	ortega	PROPN
ejpam-3812	187	10	,	,	PUNCT
ejpam-3812	187	11	r.	r.	PROPN
ejpam-3812	187	12	isla	isla	PROPN
ejpam-3812	187	13	/	/	SYM
ejpam-3812	187	14	eur	eur	PROPN
ejpam-3812	187	15	.	.	PUNCT
ejpam-3812	188	1	j.	j.	PROPN
ejpam-3812	188	2	pure	pure	PROPN
ejpam-3812	188	3	appl	appl	PROPN
ejpam-3812	188	4	.	.	PROPN
ejpam-3812	188	5	math	math	PROPN
ejpam-3812	188	6	,	,	PUNCT
ejpam-3812	188	7	13	13	NUM
ejpam-3812	188	8	(	(	PUNCT
ejpam-3812	188	9	4	4	NUM
ejpam-3812	188	10	)	)	PUNCT
ejpam-3812	188	11	(	(	PUNCT
ejpam-3812	188	12	2020	2020	NUM
ejpam-3812	188	13	)	)	PUNCT
ejpam-3812	188	14	,	,	PUNCT
ejpam-3812	188	15	779	779	NUM
ejpam-3812	188	16	-	-	SYM
ejpam-3812	188	17	793	793	NUM
ejpam-3812	188	18	785	785	NUM
ejpam-3812	188	19	(	(	PUNCT
ejpam-3812	188	20	i	i	NOUN
ejpam-3812	188	21	)	)	PUNCT
ejpam-3812	188	22	s	s	VERB
ejpam-3812	188	23	is	be	AUX
ejpam-3812	188	24	a	a	DET
ejpam-3812	188	25	dominating	dominating	NOUN
ejpam-3812	188	26	set	set	VERB
ejpam-3812	188	27	in	in	ADP
ejpam-3812	188	28	g.	g.	PROPN
ejpam-3812	188	29	(	(	PUNCT
ejpam-3812	188	30	ii	ii	PROPN
ejpam-3812	188	31	)	)	PUNCT
ejpam-3812	188	32	for	for	ADP
ejpam-3812	188	33	each	each	DET
ejpam-3812	188	34	x	x	SYM
ejpam-3812	188	35	∈	∈	PROPN
ejpam-3812	188	36	s	s	NOUN
ejpam-3812	188	37	∩ng(s	∩ng(s	NOUN
ejpam-3812	188	38	)	)	PUNCT
ejpam-3812	188	39	,	,	PUNCT
ejpam-3812	188	40	tx	tx	PROPN
ejpam-3812	189	1	=	=	SYM
ejpam-3812	189	2	v	v	PROPN
ejpam-3812	189	3	(	(	PUNCT
ejpam-3812	189	4	h	h	NOUN
ejpam-3812	189	5	)	)	PUNCT
ejpam-3812	189	6	and	and	CCONJ
ejpam-3812	189	7	|v	|v	PROPN
ejpam-3812	189	8	(	(	PUNCT
ejpam-3812	189	9	h)|	h)|	NOUN
ejpam-3812	189	10	=	=	NOUN
ejpam-3812	189	11	r	r	NOUN
ejpam-3812	189	12	≤	≤	NOUN
ejpam-3812	190	1	k	k	NOUN
ejpam-3812	190	2	whenever	whenever	SCONJ
ejpam-3812	190	3	c	c	PROPN
ejpam-3812	190	4	6=	6=	PROPN
ejpam-3812	190	5	v	v	PROPN
ejpam-3812	190	6	(	(	PUNCT
ejpam-3812	190	7	g[h	g[h	PROPN
ejpam-3812	190	8	]	]	PUNCT
ejpam-3812	190	9	)	)	PUNCT
ejpam-3812	190	10	or	or	CCONJ
ejpam-3812	190	11	tx	tx	PROPN
ejpam-3812	190	12	is	be	AUX
ejpam-3812	190	13	an	an	DET
ejpam-3812	190	14	rfd	rfd	NOUN
ejpam-3812	190	15	-	-	PUNCT
ejpam-3812	190	16	set	set	VERB
ejpam-3812	190	17	and	and	CCONJ
ejpam-3812	190	18	∑	∑	ADP
ejpam-3812	190	19	z∈ng(x)∩s	z∈ng(x)∩s	NUM
ejpam-3812	190	20	|tz|	|tz|	NOUN
ejpam-3812	191	1	=	=	SYM
ejpam-3812	191	2	k	k	PROPN
ejpam-3812	191	3	−	−	PROPN
ejpam-3812	191	4	r.	r.	PROPN
ejpam-3812	191	5	(	(	PUNCT
ejpam-3812	191	6	iii	iii	NOUN
ejpam-3812	191	7	)	)	PUNCT
ejpam-3812	191	8	for	for	ADP
ejpam-3812	191	9	each	each	DET
ejpam-3812	191	10	x	x	SYM
ejpam-3812	191	11	∈	∈	PROPN
ejpam-3812	191	12	s\ng(s	s\ng(s	NOUN
ejpam-3812	191	13	)	)	PUNCT
ejpam-3812	191	14	,	,	PUNCT
ejpam-3812	191	15	tx	tx	PROPN
ejpam-3812	191	16	=	=	SYM
ejpam-3812	191	17	v	v	PROPN
ejpam-3812	191	18	(	(	PUNCT
ejpam-3812	191	19	h	h	NOUN
ejpam-3812	191	20	)	)	PUNCT
ejpam-3812	191	21	and	and	CCONJ
ejpam-3812	191	22	|v	|v	PROPN
ejpam-3812	191	23	(	(	PUNCT
ejpam-3812	191	24	h)|	h)|	NOUN
ejpam-3812	191	25	≤	≤	PROPN
ejpam-3812	191	26	k	k	NOUN
ejpam-3812	191	27	or	or	CCONJ
ejpam-3812	191	28	|tx|	|tx|	NUM
ejpam-3812	191	29	=	=	SYM
ejpam-3812	191	30	k	k	PROPN
ejpam-3812	191	31	and	and	CCONJ
ejpam-3812	191	32	tx	tx	PROPN
ejpam-3812	191	33	is	be	AUX
ejpam-3812	191	34	a	a	DET
ejpam-3812	191	35	kfd	kfd	NOUN
ejpam-3812	191	36	-	-	PUNCT
ejpam-3812	191	37	set	set	NOUN
ejpam-3812	191	38	in	in	ADP
ejpam-3812	191	39	h.	h.	PROPN
ejpam-3812	191	40	(	(	PUNCT
ejpam-3812	191	41	iv	iv	X
ejpam-3812	191	42	)	)	PUNCT
ejpam-3812	191	43	for	for	ADP
ejpam-3812	191	44	each	each	DET
ejpam-3812	191	45	y	y	PROPN
ejpam-3812	191	46	∈	∈	PROPN
ejpam-3812	191	47	v	v	NOUN
ejpam-3812	191	48	(	(	PUNCT
ejpam-3812	191	49	g)\s	g)\s	NOUN
ejpam-3812	191	50	,	,	PUNCT
ejpam-3812	191	51	∑	∑	PUNCT
ejpam-3812	191	52	v∈ng(y)∩s	v∈ng(y)∩s	ADJ
ejpam-3812	191	53	|tv|	|tv|	PROPN
ejpam-3812	191	54	=	=	SYM
ejpam-3812	191	55	k.	k.	PROPN
ejpam-3812	191	56	corollary	corollary	NOUN
ejpam-3812	191	57	5	5	NUM
ejpam-3812	191	58	.	.	PUNCT
ejpam-3812	192	1	[	[	X
ejpam-3812	192	2	6	6	NUM
ejpam-3812	192	3	]	]	PUNCT
ejpam-3812	192	4	let	let	VERB
ejpam-3812	192	5	g	g	NOUN
ejpam-3812	192	6	and	and	CCONJ
ejpam-3812	192	7	h	h	NOUN
ejpam-3812	192	8	be	be	AUX
ejpam-3812	192	9	nontrivial	nontrivial	ADJ
ejpam-3812	192	10	connected	connected	ADJ
ejpam-3812	192	11	graphs	graph	NOUN
ejpam-3812	192	12	.	.	PUNCT
ejpam-3812	193	1	then	then	ADV
ejpam-3812	193	2	c	c	X
ejpam-3812	193	3	=	=	PUNCT
ejpam-3812	193	4	⋃	⋃	PROPN
ejpam-3812	193	5	x∈s	x∈s	NOUN
ejpam-3812	193	6	(	(	PUNCT
ejpam-3812	193	7	{	{	PUNCT
ejpam-3812	193	8	x}×tx	x}×tx	NUM
ejpam-3812	193	9	)	)	PUNCT
ejpam-3812	193	10	⊆	⊆	NUM
ejpam-3812	193	11	v	v	NOUN
ejpam-3812	193	12	(	(	PUNCT
ejpam-3812	193	13	g[h	g[h	PROPN
ejpam-3812	193	14	]	]	PUNCT
ejpam-3812	193	15	)	)	PUNCT
ejpam-3812	193	16	is	be	AUX
ejpam-3812	193	17	a	a	DET
ejpam-3812	193	18	1fd	1fd	NOUN
ejpam-3812	193	19	-	-	PUNCT
ejpam-3812	193	20	set	set	VERB
ejpam-3812	193	21	in	in	ADP
ejpam-3812	193	22	g[h	g[h	PROPN
ejpam-3812	193	23	]	]	PUNCT
ejpam-3812	193	24	if	if	SCONJ
ejpam-3812	194	1	and	and	CCONJ
ejpam-3812	194	2	only	only	ADV
ejpam-3812	194	3	if	if	SCONJ
ejpam-3812	194	4	s	s	NOUN
ejpam-3812	194	5	is	be	AUX
ejpam-3812	194	6	a	a	DET
ejpam-3812	194	7	1fd	1fd	NOUN
ejpam-3812	194	8	-	-	PUNCT
ejpam-3812	194	9	set	set	NOUN
ejpam-3812	194	10	in	in	ADP
ejpam-3812	194	11	g	g	PROPN
ejpam-3812	194	12	,	,	PUNCT
ejpam-3812	194	13	s	s	NOUN
ejpam-3812	194	14	∩ng(s	∩ng(s	ADJ
ejpam-3812	194	15	)	)	PUNCT
ejpam-3812	194	16	=	=	NOUN
ejpam-3812	194	17	∅	∅	NOUN
ejpam-3812	194	18	,	,	PUNCT
ejpam-3812	194	19	tx	tx	PROPN
ejpam-3812	194	20	is	be	AUX
ejpam-3812	194	21	a	a	DET
ejpam-3812	194	22	dominating	dominating	NOUN
ejpam-3812	194	23	set	set	NOUN
ejpam-3812	194	24	of	of	ADP
ejpam-3812	194	25	h	h	NOUN
ejpam-3812	194	26	,	,	PUNCT
ejpam-3812	194	27	and	and	CCONJ
ejpam-3812	194	28	|tx|	|tx|	X
ejpam-3812	194	29	=	=	SYM
ejpam-3812	194	30	1	1	NUM
ejpam-3812	194	31	for	for	ADP
ejpam-3812	194	32	each	each	PRON
ejpam-3812	194	33	x	x	PROPN
ejpam-3812	194	34	∈	∈	PROPN
ejpam-3812	194	35	s.	s.	PROPN
ejpam-3812	194	36	theorem	theorem	VERB
ejpam-3812	194	37	11	11	NUM
ejpam-3812	194	38	.	.	PUNCT
ejpam-3812	195	1	[	[	X
ejpam-3812	195	2	6	6	NUM
ejpam-3812	195	3	]	]	PUNCT
ejpam-3812	195	4	let	let	VERB
ejpam-3812	195	5	g	g	NOUN
ejpam-3812	195	6	and	and	CCONJ
ejpam-3812	195	7	h	h	NOUN
ejpam-3812	195	8	be	be	AUX
ejpam-3812	195	9	nontrivial	nontrivial	ADJ
ejpam-3812	195	10	connected	connect	VERB
ejpam-3812	195	11	graphs	graph	NOUN
ejpam-3812	195	12	of	of	ADP
ejpam-3812	195	13	orders	order	NOUN
ejpam-3812	195	14	m	m	VERB
ejpam-3812	195	15	and	and	CCONJ
ejpam-3812	195	16	n	n	CCONJ
ejpam-3812	195	17	,	,	PUNCT
ejpam-3812	195	18	respectively	respectively	ADV
ejpam-3812	195	19	,	,	PUNCT
ejpam-3812	195	20	and	and	CCONJ
ejpam-3812	195	21	k	k	X
ejpam-3812	195	22	a	a	DET
ejpam-3812	195	23	positive	positive	ADJ
ejpam-3812	195	24	integer	integer	NOUN
ejpam-3812	195	25	with	with	ADP
ejpam-3812	195	26	1	1	NUM
ejpam-3812	195	27	≤	≤	NUM
ejpam-3812	195	28	k	k	PROPN
ejpam-3812	195	29	≤	≤	ADJ
ejpam-3812	195	30	min{m	min{m	PROPN
ejpam-3812	195	31	,	,	PUNCT
ejpam-3812	195	32	n	n	CCONJ
ejpam-3812	195	33	}	}	PUNCT
ejpam-3812	195	34	.	.	PUNCT
ejpam-3812	196	1	then	then	ADV
ejpam-3812	196	2	c	c	X
ejpam-3812	196	3	=	=	PUNCT
ejpam-3812	196	4	⋃	⋃	PROPN
ejpam-3812	196	5	x∈v	x∈v	PROPN
ejpam-3812	196	6	(	(	PUNCT
ejpam-3812	196	7	g	g	NOUN
ejpam-3812	196	8	)	)	PUNCT
ejpam-3812	197	1	[	[	X
ejpam-3812	197	2	{	{	PUNCT
ejpam-3812	197	3	x	x	NOUN
ejpam-3812	197	4	}	}	PUNCT
ejpam-3812	197	5	×	×	PROPN
ejpam-3812	197	6	tx	tx	PROPN
ejpam-3812	197	7	]	]	X
ejpam-3812	197	8	⊆	⊆	NUM
ejpam-3812	197	9	v	v	NOUN
ejpam-3812	197	10	(	(	PUNCT
ejpam-3812	197	11	g	g	PROPN
ejpam-3812	197	12	�	�	NOUN
ejpam-3812	197	13	h	h	NOUN
ejpam-3812	197	14	)	)	PUNCT
ejpam-3812	197	15	is	be	AUX
ejpam-3812	197	16	a	a	DET
ejpam-3812	197	17	kfd	kfd	NOUN
ejpam-3812	197	18	-	-	PUNCT
ejpam-3812	197	19	set	set	NOUN
ejpam-3812	197	20	in	in	ADP
ejpam-3812	197	21	g	g	PROPN
ejpam-3812	197	22	�	�	NOUN
ejpam-3812	197	23	h	h	NOUN
ejpam-3812	197	24	if	if	SCONJ
ejpam-3812	197	25	and	and	CCONJ
ejpam-3812	197	26	only	only	ADV
ejpam-3812	197	27	if	if	SCONJ
ejpam-3812	197	28	(	(	PUNCT
ejpam-3812	197	29	i	i	NOUN
ejpam-3812	197	30	)	)	PUNCT
ejpam-3812	197	31	v	v	NOUN
ejpam-3812	197	32	(	(	PUNCT
ejpam-3812	197	33	h)\tx	h)\tx	NOUN
ejpam-3812	197	34	⊆	⊆	NUM
ejpam-3812	197	35	nh(tx	nh(tx	NOUN
ejpam-3812	197	36	)	)	PUNCT
ejpam-3812	197	37	∪	∪	NOUN
ejpam-3812	197	38	(	(	PUNCT
ejpam-3812	197	39	⋃	⋃	PROPN
ejpam-3812	197	40	z∈ng(x	z∈ng(x	NOUN
ejpam-3812	197	41	)	)	PUNCT
ejpam-3812	197	42	tz	tz	NOUN
ejpam-3812	197	43	)	)	PUNCT
ejpam-3812	197	44	for	for	ADP
ejpam-3812	197	45	each	each	DET
ejpam-3812	197	46	x	x	SYM
ejpam-3812	197	47	∈	∈	PROPN
ejpam-3812	197	48	v	v	NOUN
ejpam-3812	197	49	(	(	PUNCT
ejpam-3812	197	50	g	g	NOUN
ejpam-3812	197	51	)	)	PUNCT
ejpam-3812	197	52	,	,	PUNCT
ejpam-3812	197	53	and	and	CCONJ
ejpam-3812	197	54	(	(	PUNCT
ejpam-3812	197	55	ii	ii	NOUN
ejpam-3812	197	56	)	)	PUNCT
ejpam-3812	197	57	for	for	ADP
ejpam-3812	197	58	each	each	DET
ejpam-3812	197	59	x	x	SYM
ejpam-3812	197	60	∈	∈	PROPN
ejpam-3812	197	61	v	v	NOUN
ejpam-3812	197	62	(	(	PUNCT
ejpam-3812	197	63	g	g	NOUN
ejpam-3812	197	64	)	)	PUNCT
ejpam-3812	197	65	,	,	PUNCT
ejpam-3812	197	66	tx	tx	PROPN
ejpam-3812	197	67	=	=	SYM
ejpam-3812	197	68	v	v	PROPN
ejpam-3812	197	69	(	(	PUNCT
ejpam-3812	197	70	h	h	NOUN
ejpam-3812	197	71	)	)	PUNCT
ejpam-3812	197	72	or	or	CCONJ
ejpam-3812	197	73	for	for	ADP
ejpam-3812	197	74	each	each	PRON
ejpam-3812	197	75	a	a	DET
ejpam-3812	197	76	∈	∈	PROPN
ejpam-3812	197	77	v	v	NOUN
ejpam-3812	197	78	(	(	PUNCT
ejpam-3812	197	79	h)\tx	h)\tx	PROPN
ejpam-3812	197	80	,	,	PUNCT
ejpam-3812	197	81	either	either	PRON
ejpam-3812	197	82	|nh(a	|nh(a	NUM
ejpam-3812	197	83	)	)	PUNCT
ejpam-3812	197	84	∩	∩	NOUN
ejpam-3812	197	85	tx|	tx|	NOUN
ejpam-3812	197	86	=	=	SYM
ejpam-3812	197	87	k	k	PROPN
ejpam-3812	197	88	and	and	CCONJ
ejpam-3812	197	89	|{z	|{z	PROPN
ejpam-3812	197	90	:	:	PUNCT
ejpam-3812	197	91	z	z	PROPN
ejpam-3812	197	92	∈	∈	PROPN
ejpam-3812	197	93	ng(x	ng(x	NUM
ejpam-3812	197	94	)	)	PUNCT
ejpam-3812	197	95	,	,	PUNCT
ejpam-3812	197	96	a	a	DET
ejpam-3812	197	97	∈	∈	NOUN
ejpam-3812	197	98	tz}|	tz}|	NUM
ejpam-3812	197	99	=	=	SYM
ejpam-3812	197	100	0	0	NUM
ejpam-3812	197	101	or	or	CCONJ
ejpam-3812	197	102	|nh(a	|nh(a	NUM
ejpam-3812	197	103	)	)	PUNCT
ejpam-3812	197	104	∩	∩	NOUN
ejpam-3812	197	105	tx|	tx|	NOUN
ejpam-3812	197	106	=	=	PUNCT
ejpam-3812	197	107	r	r	NOUN
ejpam-3812	197	108	<	<	X
ejpam-3812	197	109	k	k	NOUN
ejpam-3812	197	110	and	and	CCONJ
ejpam-3812	197	111	a	a	DET
ejpam-3812	197	112	∈	∈	PROPN
ejpam-3812	197	113	⋂k−r	⋂k−r	PROPN
ejpam-3812	197	114	i=1	i=1	PROPN
ejpam-3812	197	115	txi	txi	PROPN
ejpam-3812	197	116	,	,	PUNCT
ejpam-3812	197	117	where	where	SCONJ
ejpam-3812	197	118	xi	xi	PROPN
ejpam-3812	197	119	∈	∈	PROPN
ejpam-3812	197	120	ng(x	ng(x	NUM
ejpam-3812	197	121	)	)	PUNCT
ejpam-3812	197	122	for	for	ADP
ejpam-3812	197	123	i	i	PROPN
ejpam-3812	197	124	=	=	SYM
ejpam-3812	197	125	1	1	NUM
ejpam-3812	197	126	,	,	PUNCT
ejpam-3812	197	127	2	2	NUM
ejpam-3812	197	128	,	,	PUNCT
ejpam-3812	197	129	...	...	PUNCT
ejpam-3812	197	130	,	,	PUNCT
ejpam-3812	198	1	k	k	PROPN
ejpam-3812	198	2	−	−	NOUN
ejpam-3812	198	3	r	r	NOUN
ejpam-3812	198	4	.	.	PUNCT
ejpam-3812	199	1	corollary	corollary	ADJ
ejpam-3812	199	2	6	6	NUM
ejpam-3812	199	3	.	.	PUNCT
ejpam-3812	200	1	[	[	X
ejpam-3812	200	2	6	6	NUM
ejpam-3812	200	3	]	]	PUNCT
ejpam-3812	200	4	let	let	VERB
ejpam-3812	200	5	g	g	NOUN
ejpam-3812	200	6	and	and	CCONJ
ejpam-3812	200	7	h	h	NOUN
ejpam-3812	200	8	be	be	AUX
ejpam-3812	200	9	nontrivial	nontrivial	ADJ
ejpam-3812	200	10	connected	connect	VERB
ejpam-3812	200	11	graphs	graph	NOUN
ejpam-3812	200	12	of	of	ADP
ejpam-3812	200	13	orders	order	NOUN
ejpam-3812	200	14	m	m	VERB
ejpam-3812	200	15	and	and	CCONJ
ejpam-3812	200	16	n	n	CCONJ
ejpam-3812	200	17	,	,	PUNCT
ejpam-3812	200	18	respectively	respectively	ADV
ejpam-3812	200	19	,	,	PUNCT
ejpam-3812	200	20	and	and	CCONJ
ejpam-3812	200	21	k	k	X
ejpam-3812	200	22	a	a	DET
ejpam-3812	200	23	positive	positive	ADJ
ejpam-3812	200	24	integer	integer	NOUN
ejpam-3812	200	25	with	with	ADP
ejpam-3812	200	26	k	k	PROPN
ejpam-3812	200	27	≤	≤	X
ejpam-3812	200	28	min{m	min{m	PROPN
ejpam-3812	200	29	,	,	PUNCT
ejpam-3812	200	30	n	n	CCONJ
ejpam-3812	200	31	}	}	PUNCT
ejpam-3812	200	32	.	.	PUNCT
ejpam-3812	201	1	then	then	ADV
ejpam-3812	201	2	γkfd(g	γkfd(g	PROPN
ejpam-3812	201	3	�	�	PROPN
ejpam-3812	201	4	h	h	NOUN
ejpam-3812	201	5	)	)	PUNCT
ejpam-3812	201	6	≤	≤	NOUN
ejpam-3812	201	7	min{n	min{n	NOUN
ejpam-3812	201	8	·	·	PUNCT
ejpam-3812	201	9	γkfd(g),m	γkfd(g),m	PROPN
ejpam-3812	201	10	·	·	PUNCT
ejpam-3812	201	11	γkfd(h	γkfd(h	NOUN
ejpam-3812	201	12	)	)	PUNCT
ejpam-3812	201	13	}	}	PUNCT
ejpam-3812	201	14	.	.	PUNCT
ejpam-3812	202	1	3	3	X
ejpam-3812	202	2	.	.	X
ejpam-3812	202	3	semitotal	semitotal	ADJ
ejpam-3812	202	4	1	1	NUM
ejpam-3812	202	5	-	-	PUNCT
ejpam-3812	202	6	fair	fair	ADJ
ejpam-3812	202	7	domination	domination	NOUN
ejpam-3812	202	8	in	in	ADP
ejpam-3812	202	9	view	view	NOUN
ejpam-3812	202	10	of	of	ADP
ejpam-3812	202	11	theorem	theorem	NOUN
ejpam-3812	202	12	3	3	NUM
ejpam-3812	202	13	,	,	PUNCT
ejpam-3812	202	14	which	which	PRON
ejpam-3812	202	15	shows	show	VERB
ejpam-3812	202	16	that	that	SCONJ
ejpam-3812	202	17	the	the	DET
ejpam-3812	202	18	concept	concept	NOUN
ejpam-3812	202	19	of	of	ADP
ejpam-3812	202	20	semitotal	semitotal	ADJ
ejpam-3812	202	21	k	k	ADJ
ejpam-3812	202	22	-	-	PUNCT
ejpam-3812	202	23	fair	fair	ADJ
ejpam-3812	202	24	dominatioin	dominatioin	NOUN
ejpam-3812	202	25	coincides	coincide	VERB
ejpam-3812	202	26	with	with	ADP
ejpam-3812	202	27	the	the	DET
ejpam-3812	202	28	notion	notion	NOUN
ejpam-3812	202	29	of	of	ADP
ejpam-3812	202	30	k	k	ADJ
ejpam-3812	202	31	-	-	PUNCT
ejpam-3812	202	32	fair	fair	ADJ
ejpam-3812	202	33	domination	domination	NOUN
ejpam-3812	202	34	when	when	SCONJ
ejpam-3812	202	35	k	k	PROPN
ejpam-3812	202	36	≥	≥	NUM
ejpam-3812	202	37	2	2	NUM
ejpam-3812	202	38	,	,	PUNCT
ejpam-3812	202	39	this	this	DET
ejpam-3812	202	40	section	section	NOUN
ejpam-3812	202	41	investigates	investigate	VERB
ejpam-3812	202	42	semitotal	semitotal	ADJ
ejpam-3812	202	43	k	k	ADJ
ejpam-3812	202	44	-	-	PUNCT
ejpam-3812	202	45	fair	fair	ADJ
ejpam-3812	202	46	domination	domination	NOUN
ejpam-3812	202	47	in	in	ADP
ejpam-3812	202	48	graphs	graph	NOUN
ejpam-3812	202	49	only	only	ADV
ejpam-3812	202	50	for	for	ADP
ejpam-3812	202	51	k	k	PROPN
ejpam-3812	202	52	=	=	SYM
ejpam-3812	202	53	1	1	X
ejpam-3812	202	54	.	.	PUNCT
ejpam-3812	203	1	the	the	DET
ejpam-3812	203	2	following	follow	VERB
ejpam-3812	203	3	remark	remark	NOUN
ejpam-3812	203	4	is	be	AUX
ejpam-3812	203	5	an	an	DET
ejpam-3812	203	6	immediate	immediate	ADJ
ejpam-3812	203	7	consequence	consequence	NOUN
ejpam-3812	203	8	of	of	ADP
ejpam-3812	203	9	remark	remark	NOUN
ejpam-3812	203	10	1	1	NUM
ejpam-3812	203	11	for	for	ADP
ejpam-3812	203	12	k	k	PROPN
ejpam-3812	203	13	=	=	SYM
ejpam-3812	203	14	1	1	X
ejpam-3812	203	15	.	.	PUNCT
ejpam-3812	203	16	remark	remark	NOUN
ejpam-3812	203	17	4	4	NUM
ejpam-3812	203	18	.	.	PUNCT
ejpam-3812	204	1	for	for	ADP
ejpam-3812	204	2	any	any	DET
ejpam-3812	204	3	connected	connected	ADJ
ejpam-3812	204	4	graph	graph	NOUN
ejpam-3812	204	5	g	g	NOUN
ejpam-3812	204	6	of	of	ADP
ejpam-3812	204	7	order	order	NOUN
ejpam-3812	204	8	n	n	PRON
ejpam-3812	204	9	≥	≥	NOUN
ejpam-3812	204	10	2	2	NUM
ejpam-3812	204	11	,	,	PUNCT
ejpam-3812	204	12	γ1fd(g	γ1fd(g	PROPN
ejpam-3812	204	13	)	)	PUNCT
ejpam-3812	204	14	≤	≤	NUM
ejpam-3812	204	15	γt21f	γt21f	PUNCT
ejpam-3812	204	16	(	(	PUNCT
ejpam-3812	204	17	g	g	NOUN
ejpam-3812	204	18	)	)	PUNCT
ejpam-3812	204	19	and	and	CCONJ
ejpam-3812	204	20	γt21f	γt21f	VERB
ejpam-3812	204	21	(	(	PUNCT
ejpam-3812	204	22	g	g	NOUN
ejpam-3812	204	23	)	)	PUNCT
ejpam-3812	204	24	≥	≥	NOUN
ejpam-3812	204	25	2	2	NUM
ejpam-3812	204	26	.	.	PUNCT
ejpam-3812	205	1	the	the	DET
ejpam-3812	205	2	succeeding	succeed	VERB
ejpam-3812	205	3	two	two	NUM
ejpam-3812	205	4	results	result	NOUN
ejpam-3812	205	5	are	be	AUX
ejpam-3812	205	6	easy	easy	ADJ
ejpam-3812	205	7	to	to	PART
ejpam-3812	205	8	verify	verify	VERB
ejpam-3812	205	9	.	.	PUNCT
ejpam-3812	206	1	m.	m.	PROPN
ejpam-3812	206	2	ortega	ortega	PROPN
ejpam-3812	206	3	,	,	PUNCT
ejpam-3812	206	4	r.	r.	PROPN
ejpam-3812	206	5	isla	isla	PROPN
ejpam-3812	206	6	/	/	SYM
ejpam-3812	206	7	eur	eur	PROPN
ejpam-3812	206	8	.	.	PUNCT
ejpam-3812	207	1	j.	j.	PROPN
ejpam-3812	207	2	pure	pure	PROPN
ejpam-3812	207	3	appl	appl	PROPN
ejpam-3812	207	4	.	.	PROPN
ejpam-3812	207	5	math	math	PROPN
ejpam-3812	207	6	,	,	PUNCT
ejpam-3812	207	7	13	13	NUM
ejpam-3812	207	8	(	(	PUNCT
ejpam-3812	207	9	4	4	NUM
ejpam-3812	207	10	)	)	PUNCT
ejpam-3812	207	11	(	(	PUNCT
ejpam-3812	207	12	2020	2020	NUM
ejpam-3812	207	13	)	)	PUNCT
ejpam-3812	207	14	,	,	PUNCT
ejpam-3812	207	15	779	779	NUM
ejpam-3812	207	16	-	-	SYM
ejpam-3812	207	17	793	793	NUM
ejpam-3812	207	18	786	786	NUM
ejpam-3812	207	19	proposition	proposition	NOUN
ejpam-3812	207	20	1	1	NUM
ejpam-3812	207	21	.	.	PUNCT
ejpam-3812	208	1	let	let	VERB
ejpam-3812	208	2	n	n	NOUN
ejpam-3812	208	3	and	and	CCONJ
ejpam-3812	208	4	r	r	NOUN
ejpam-3812	208	5	be	be	VERB
ejpam-3812	208	6	positive	positive	ADJ
ejpam-3812	208	7	integers	integer	NOUN
ejpam-3812	209	1	where	where	SCONJ
ejpam-3812	209	2	n	n	NUM
ejpam-3812	209	3	≥	≥	X
ejpam-3812	209	4	2	2	NUM
ejpam-3812	209	5	and	and	CCONJ
ejpam-3812	209	6	r	r	NOUN
ejpam-3812	209	7	≥	≥	NUM
ejpam-3812	209	8	1	1	NUM
ejpam-3812	209	9	.	.	PUNCT
ejpam-3812	209	10	then	then	ADV
ejpam-3812	209	11	γt21f	γt21f	VERB
ejpam-3812	209	12	(	(	PUNCT
ejpam-3812	209	13	pn	pn	NOUN
ejpam-3812	209	14	)	)	PUNCT
ejpam-3812	209	15	=	=	PUNCT
ejpam-3812	209	16			NOUN
ejpam-3812	209	17	2	2	NUM
ejpam-3812	209	18	,	,	PUNCT
ejpam-3812	209	19	2	2	NUM
ejpam-3812	209	20	≤	≤	NOUN
ejpam-3812	209	21	n	n	PRON
ejpam-3812	209	22	≤	≤	NUM
ejpam-3812	209	23	4	4	NUM
ejpam-3812	209	24	2r	2r	NUM
ejpam-3812	209	25	,	,	PUNCT
ejpam-3812	209	26	n	n	NOUN
ejpam-3812	209	27	=	=	NOUN
ejpam-3812	209	28	4r	4r	NUM
ejpam-3812	209	29	2r	2r	NUM
ejpam-3812	209	30	+	+	CCONJ
ejpam-3812	209	31	1	1	NUM
ejpam-3812	209	32	,	,	PUNCT
ejpam-3812	209	33	n	n	NOUN
ejpam-3812	209	34	=	=	NOUN
ejpam-3812	209	35	4r	4r	NOUN
ejpam-3812	209	36	+	+	CCONJ
ejpam-3812	209	37	1	1	NUM
ejpam-3812	209	38	2r	2r	NUM
ejpam-3812	209	39	+	+	CCONJ
ejpam-3812	209	40	2	2	NUM
ejpam-3812	209	41	,	,	PUNCT
ejpam-3812	209	42	n	n	NOUN
ejpam-3812	209	43	=	=	NOUN
ejpam-3812	209	44	4r	4r	NOUN
ejpam-3812	209	45	+	+	CCONJ
ejpam-3812	209	46	2	2	NUM
ejpam-3812	209	47	,	,	PUNCT
ejpam-3812	209	48	4r	4r	NOUN
ejpam-3812	209	49	+	+	CCONJ
ejpam-3812	209	50	3	3	X
ejpam-3812	209	51	.	.	X
ejpam-3812	209	52	proposition	proposition	NOUN
ejpam-3812	209	53	2	2	NUM
ejpam-3812	209	54	.	.	PUNCT
ejpam-3812	209	55	let	let	VERB
ejpam-3812	209	56	n	n	NOUN
ejpam-3812	209	57	and	and	CCONJ
ejpam-3812	209	58	r	r	NOUN
ejpam-3812	209	59	be	be	VERB
ejpam-3812	209	60	positive	positive	ADJ
ejpam-3812	209	61	integers	integer	NOUN
ejpam-3812	210	1	where	where	SCONJ
ejpam-3812	210	2	n	n	NUM
ejpam-3812	210	3	≥	≥	NOUN
ejpam-3812	210	4	3	3	NUM
ejpam-3812	210	5	and	and	CCONJ
ejpam-3812	210	6	r	r	NOUN
ejpam-3812	210	7	≥	≥	NUM
ejpam-3812	210	8	1	1	NUM
ejpam-3812	210	9	.	.	PUNCT
ejpam-3812	210	10	then	then	ADV
ejpam-3812	210	11	γt21f	γt21f	PUNCT
ejpam-3812	210	12	(	(	PUNCT
ejpam-3812	210	13	cn	cn	NOUN
ejpam-3812	210	14	)	)	PUNCT
ejpam-3812	210	15	=	=	PUNCT
ejpam-3812	210	16			NUM
ejpam-3812	210	17	3	3	NUM
ejpam-3812	210	18	,	,	PUNCT
ejpam-3812	210	19	n	n	NOUN
ejpam-3812	210	20	=	=	SYM
ejpam-3812	210	21	3	3	NUM
ejpam-3812	210	22	2r	2r	NUM
ejpam-3812	210	23	,	,	PUNCT
ejpam-3812	210	24	n	n	NOUN
ejpam-3812	210	25	=	=	NOUN
ejpam-3812	210	26	4r	4r	NUM
ejpam-3812	210	27	2r	2r	NUM
ejpam-3812	210	28	+	+	CCONJ
ejpam-3812	210	29	1	1	NUM
ejpam-3812	210	30	,	,	PUNCT
ejpam-3812	210	31	n	n	NOUN
ejpam-3812	210	32	=	=	NOUN
ejpam-3812	210	33	4r	4r	NOUN
ejpam-3812	210	34	+	+	CCONJ
ejpam-3812	210	35	1	1	NUM
ejpam-3812	210	36	2r	2r	NUM
ejpam-3812	210	37	+	+	CCONJ
ejpam-3812	210	38	2	2	NUM
ejpam-3812	210	39	,	,	PUNCT
ejpam-3812	210	40	n	n	NOUN
ejpam-3812	210	41	=	=	NOUN
ejpam-3812	210	42	4r	4r	NOUN
ejpam-3812	210	43	+	+	CCONJ
ejpam-3812	210	44	2	2	NUM
ejpam-3812	210	45	2r	2r	NUM
ejpam-3812	210	46	+	+	CCONJ
ejpam-3812	210	47	3	3	NUM
ejpam-3812	210	48	,	,	PUNCT
ejpam-3812	210	49	n	n	NOUN
ejpam-3812	210	50	=	=	NOUN
ejpam-3812	210	51	4r	4r	NOUN
ejpam-3812	210	52	+	+	CCONJ
ejpam-3812	210	53	3	3	X
ejpam-3812	210	54	.	.	X
ejpam-3812	210	55	theorem	theorem	NOUN
ejpam-3812	210	56	12	12	NUM
ejpam-3812	210	57	.	.	PUNCT
ejpam-3812	211	1	let	let	VERB
ejpam-3812	211	2	a	a	PRON
ejpam-3812	211	3	and	and	CCONJ
ejpam-3812	211	4	b	b	NOUN
ejpam-3812	211	5	be	be	AUX
ejpam-3812	211	6	positive	positive	ADJ
ejpam-3812	211	7	integers	integer	NOUN
ejpam-3812	211	8	such	such	ADJ
ejpam-3812	211	9	that	that	SCONJ
ejpam-3812	211	10	2	2	NUM
ejpam-3812	211	11	≤	≤	NUM
ejpam-3812	211	12	a	a	DET
ejpam-3812	211	13	≤	≤	PROPN
ejpam-3812	211	14	b.	b.	NOUN
ejpam-3812	212	1	then	then	ADV
ejpam-3812	212	2	there	there	PRON
ejpam-3812	212	3	exists	exist	VERB
ejpam-3812	212	4	a	a	DET
ejpam-3812	212	5	connected	connected	ADJ
ejpam-3812	212	6	graph	graph	NOUN
ejpam-3812	212	7	g	g	ADP
ejpam-3812	212	8	such	such	ADJ
ejpam-3812	212	9	that	that	DET
ejpam-3812	212	10	γ1fd(g	γ1fd(g	PROPN
ejpam-3812	212	11	)	)	PUNCT
ejpam-3812	212	12	=	=	SYM
ejpam-3812	213	1	a	a	PROPN
ejpam-3812	213	2	and	and	CCONJ
ejpam-3812	213	3	γt21f	γt21f	PUNCT
ejpam-3812	213	4	(	(	PUNCT
ejpam-3812	213	5	g	g	NOUN
ejpam-3812	213	6	)	)	PUNCT
ejpam-3812	213	7	=	=	SYM
ejpam-3812	213	8	b.	b.	NOUN
ejpam-3812	213	9	proof	proof	NOUN
ejpam-3812	213	10	.	.	PUNCT
ejpam-3812	214	1	consider	consider	VERB
ejpam-3812	214	2	the	the	DET
ejpam-3812	214	3	following	follow	VERB
ejpam-3812	214	4	cases	case	NOUN
ejpam-3812	214	5	:	:	PUNCT
ejpam-3812	214	6	case	case	NOUN
ejpam-3812	214	7	1	1	NUM
ejpam-3812	214	8	.	.	PUNCT
ejpam-3812	215	1	a	a	DET
ejpam-3812	215	2	=	=	X
ejpam-3812	215	3	b	b	NOUN
ejpam-3812	215	4	let	let	VERB
ejpam-3812	215	5	g	g	NOUN
ejpam-3812	215	6	=	=	PUNCT
ejpam-3812	215	7	g1	g1	PROPN
ejpam-3812	215	8	be	be	VERB
ejpam-3812	215	9	the	the	DET
ejpam-3812	215	10	graph	graph	NOUN
ejpam-3812	215	11	shown	show	VERB
ejpam-3812	215	12	in	in	ADP
ejpam-3812	215	13	figure	figure	NOUN
ejpam-3812	215	14	1	1	NUM
ejpam-3812	215	15	.	.	PUNCT
ejpam-3812	215	16	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	215	17	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	216	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	216	2	....................................	....................................	PUNCT
ejpam-3812	217	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	217	2	....................................	....................................	PUNCT
ejpam-3812	218	1	.........	.........	PUNCT
ejpam-3812	218	2	........	........	PUNCT
ejpam-3812	218	3	........	........	PUNCT
ejpam-3812	218	4	........	........	PUNCT
ejpam-3812	218	5	........	........	PUNCT
ejpam-3812	219	1	......	......	PUNCT
ejpam-3812	219	2	....................................	....................................	PUNCT
ejpam-3812	220	1	....................................	....................................	PUNCT
ejpam-3812	220	2	.........	.........	PUNCT
ejpam-3812	220	3	........	........	PUNCT
ejpam-3812	220	4	........	........	PUNCT
ejpam-3812	220	5	........	........	PUNCT
ejpam-3812	220	6	........	........	PUNCT
ejpam-3812	221	1	......	......	PUNCT
ejpam-3812	221	2	....................................	....................................	PUNCT
ejpam-3812	222	1	....................................	....................................	PUNCT
ejpam-3812	222	2	.........	.........	PUNCT
ejpam-3812	222	3	........	........	PUNCT
ejpam-3812	222	4	........	........	PUNCT
ejpam-3812	222	5	........	........	PUNCT
ejpam-3812	222	6	........	........	PUNCT
ejpam-3812	223	1	......	......	PUNCT
ejpam-3812	223	2	....................................	....................................	PUNCT
ejpam-3812	224	1	....................................	....................................	PUNCT
ejpam-3812	224	2	.........	.........	PUNCT
ejpam-3812	224	3	........	........	PUNCT
ejpam-3812	224	4	........	........	PUNCT
ejpam-3812	224	5	........	........	PUNCT
ejpam-3812	224	6	........	........	PUNCT
ejpam-3812	225	1	......	......	PUNCT
ejpam-3812	225	2	....................................	....................................	PUNCT
ejpam-3812	226	1	....................................	....................................	PUNCT
ejpam-3812	226	2	.........	.........	PUNCT
ejpam-3812	226	3	........	........	PUNCT
ejpam-3812	226	4	........	........	PUNCT
ejpam-3812	226	5	........	........	PUNCT
ejpam-3812	226	6	........	........	PUNCT
ejpam-3812	227	1	......	......	PUNCT
ejpam-3812	227	2	....................................	....................................	PUNCT
ejpam-3812	228	1	....................................	....................................	PUNCT
ejpam-3812	228	2	.........	.........	PUNCT
ejpam-3812	228	3	........	........	PUNCT
ejpam-3812	228	4	........	........	PUNCT
ejpam-3812	228	5	........	........	PUNCT
ejpam-3812	228	6	........	........	PUNCT
ejpam-3812	229	1	......	......	PUNCT
ejpam-3812	229	2	....................................	....................................	PUNCT
ejpam-3812	230	1	....................................	....................................	PUNCT
ejpam-3812	231	1	•	•	NUM
ejpam-3812	231	2	•	•	NUM
ejpam-3812	231	3	•	•	NUM
ejpam-3812	231	4	•	•	NOUN
ejpam-3812	231	5	•	•	NOUN
ejpam-3812	231	6	•	•	NUM
ejpam-3812	231	7	·	·	PUNCT
ejpam-3812	231	8	·	·	PUNCT
ejpam-3812	231	9	·	·	PUNCT
ejpam-3812	232	1	x1	x1	PUNCT
ejpam-3812	233	1	x2	x2	NOUN
ejpam-3812	233	2	x3	x3	PROPN
ejpam-3812	233	3	x4	x4	PROPN
ejpam-3812	233	4	xa−1	xa−1	PROPN
ejpam-3812	233	5	xa	xa	PROPN
ejpam-3812	233	6	figure	figure	VERB
ejpam-3812	233	7	1	1	NUM
ejpam-3812	233	8	:	:	PUNCT
ejpam-3812	233	9	a	a	DET
ejpam-3812	233	10	graph	graph	NOUN
ejpam-3812	233	11	g	g	NOUN
ejpam-3812	233	12	with	with	ADP
ejpam-3812	233	13	γ1fd(g	γ1fd(g	PROPN
ejpam-3812	233	14	)	)	PUNCT
ejpam-3812	233	15	=	=	PUNCT
ejpam-3812	234	1	a	a	PRON
ejpam-3812	234	2	=	=	X
ejpam-3812	234	3	γt2	γt2	NOUN
ejpam-3812	234	4	1f	1f	NUM
ejpam-3812	234	5	(	(	PUNCT
ejpam-3812	234	6	g	g	NOUN
ejpam-3812	234	7	)	)	PUNCT
ejpam-3812	234	8	=	=	SYM
ejpam-3812	235	1	b	b	X
ejpam-3812	235	2	it	it	PRON
ejpam-3812	235	3	is	be	AUX
ejpam-3812	235	4	clear	clear	ADJ
ejpam-3812	235	5	that	that	SCONJ
ejpam-3812	235	6	the	the	DET
ejpam-3812	235	7	set	set	NOUN
ejpam-3812	235	8	a	a	X
ejpam-3812	235	9	=	=	PUNCT
ejpam-3812	235	10	{	{	PUNCT
ejpam-3812	235	11	x1	x1	PROPN
ejpam-3812	235	12	,	,	PUNCT
ejpam-3812	235	13	x2	x2	PROPN
ejpam-3812	235	14	,	,	PUNCT
ejpam-3812	235	15	...	...	PUNCT
ejpam-3812	235	16	,	,	PUNCT
ejpam-3812	235	17	xa−1	xa−1	PROPN
ejpam-3812	235	18	,	,	PUNCT
ejpam-3812	235	19	xa	xa	PROPN
ejpam-3812	235	20	}	}	PUNCT
ejpam-3812	235	21	is	be	AUX
ejpam-3812	235	22	both	both	PRON
ejpam-3812	235	23	a	a	DET
ejpam-3812	235	24	γ1fd	γ1fd	NOUN
ejpam-3812	235	25	-	-	PUNCT
ejpam-3812	235	26	set	set	VERB
ejpam-3812	235	27	and	and	CCONJ
ejpam-3812	235	28	a	a	DET
ejpam-3812	235	29	γt21f	γt21f	NOUN
ejpam-3812	235	30	set	set	VERB
ejpam-3812	235	31	in	in	ADP
ejpam-3812	235	32	g1	g1	PROPN
ejpam-3812	235	33	.	.	PUNCT
ejpam-3812	236	1	it	it	PRON
ejpam-3812	236	2	follows	follow	VERB
ejpam-3812	236	3	that	that	PRON
ejpam-3812	236	4	γ1fd(g	γ1fd(g	PROPN
ejpam-3812	236	5	)	)	PUNCT
ejpam-3812	236	6	=	=	SYM
ejpam-3812	237	1	a	a	PRON
ejpam-3812	237	2	=	=	X
ejpam-3812	237	3	γt21f	γt21f	X
ejpam-3812	237	4	(	(	PUNCT
ejpam-3812	237	5	g	g	NOUN
ejpam-3812	237	6	)	)	PUNCT
ejpam-3812	237	7	=	=	SYM
ejpam-3812	237	8	b.	b.	NOUN
ejpam-3812	237	9	case	case	NOUN
ejpam-3812	237	10	2	2	NUM
ejpam-3812	237	11	.	.	PUNCT
ejpam-3812	237	12	a	a	DET
ejpam-3812	237	13	<	<	X
ejpam-3812	237	14	b	b	X
ejpam-3812	237	15	let	let	VERB
ejpam-3812	237	16	g	g	PROPN
ejpam-3812	237	17	=	=	PUNCT
ejpam-3812	237	18	g2	g2	PROPN
ejpam-3812	237	19	be	be	VERB
ejpam-3812	237	20	the	the	DET
ejpam-3812	237	21	graph	graph	NOUN
ejpam-3812	237	22	shown	show	VERB
ejpam-3812	237	23	in	in	ADP
ejpam-3812	237	24	figure	figure	NOUN
ejpam-3812	237	25	2	2	NUM
ejpam-3812	237	26	.	.	NOUN
ejpam-3812	237	27	•	•	NUM
ejpam-3812	237	28	•	•	NUM
ejpam-3812	237	29	•	•	NUM
ejpam-3812	237	30	•	•	NOUN
ejpam-3812	237	31	•	•	NOUN
ejpam-3812	237	32	xa−1	xa−1	PROPN
ejpam-3812	237	33	v	v	PROPN
ejpam-3812	237	34	xa	xa	PROPN
ejpam-3812	238	1	x1	x1	NUM
ejpam-3812	239	1	x2	x2	NOUN
ejpam-3812	239	2	x3	x3	PROPN
ejpam-3812	239	3	·	·	PUNCT
ejpam-3812	239	4	·	·	PUNCT
ejpam-3812	239	5	·	·	PUNCT
ejpam-3812	239	6	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	239	7	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	239	8	....................................	....................................	PUNCT
ejpam-3812	239	9	.........	.........	PUNCT
ejpam-3812	239	10	........	........	PUNCT
ejpam-3812	239	11	........	........	PUNCT
ejpam-3812	239	12	........	........	PUNCT
ejpam-3812	239	13	........	........	PUNCT
ejpam-3812	239	14	......	......	PUNCT
ejpam-3812	239	15	....................................	....................................	PUNCT
ejpam-3812	240	1	....................................	....................................	PUNCT
ejpam-3812	240	2	.........	.........	PUNCT
ejpam-3812	240	3	........	........	PUNCT
ejpam-3812	240	4	........	........	PUNCT
ejpam-3812	240	5	........	........	PUNCT
ejpam-3812	240	6	........	........	PUNCT
ejpam-3812	241	1	......	......	PUNCT
ejpam-3812	241	2	....................................	....................................	PUNCT
ejpam-3812	242	1	....................................	....................................	PUNCT
ejpam-3812	242	2	.........	.........	PUNCT
ejpam-3812	242	3	........	........	PUNCT
ejpam-3812	242	4	........	........	PUNCT
ejpam-3812	242	5	........	........	PUNCT
ejpam-3812	242	6	........	........	PUNCT
ejpam-3812	243	1	......	......	PUNCT
ejpam-3812	243	2	....................................	....................................	PUNCT
ejpam-3812	244	1	....................................	....................................	PUNCT
ejpam-3812	244	2	.........	.........	PUNCT
ejpam-3812	244	3	........	........	PUNCT
ejpam-3812	244	4	........	........	PUNCT
ejpam-3812	244	5	........	........	PUNCT
ejpam-3812	244	6	........	........	PUNCT
ejpam-3812	245	1	......	......	PUNCT
ejpam-3812	245	2	....................................	....................................	PUNCT
ejpam-3812	245	3	..........................................................................................	..........................................................................................	PUNCT
ejpam-3812	246	1	....................................	....................................	PUNCT
ejpam-3812	246	2	...................	...................	PUNCT
ejpam-3812	247	1	..................	..................	PUNCT
ejpam-3812	247	2	..................	..................	PUNCT
ejpam-3812	248	1	..................	..................	PUNCT
ejpam-3812	248	2	..................	..................	PUNCT
ejpam-3812	249	1	..................	..................	PUNCT
ejpam-3812	249	2	.........	.........	PUNCT
ejpam-3812	250	1	....................................	....................................	PUNCT
ejpam-3812	250	2	.........	.........	PUNCT
ejpam-3812	250	3	........	........	PUNCT
ejpam-3812	250	4	........	........	PUNCT
ejpam-3812	250	5	........	........	PUNCT
ejpam-3812	250	6	........	........	PUNCT
ejpam-3812	251	1	......	......	PUNCT
ejpam-3812	251	2	....................................	....................................	PUNCT
ejpam-3812	252	1	....................................	....................................	PUNCT
ejpam-3812	252	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-3812	253	1	....................................	....................................	PUNCT
ejpam-3812	253	2	............	............	PUNCT
ejpam-3812	253	3	...........	...........	PUNCT
ejpam-3812	253	4	...........	...........	PUNCT
ejpam-3812	253	5	...........	...........	PUNCT
ejpam-3812	253	6	...........	...........	PUNCT
ejpam-3812	253	7	...........	...........	PUNCT
ejpam-3812	253	8	....	....	PUNCT
ejpam-3812	253	9	....................................	....................................	PUNCT
ejpam-3812	253	10	....................................................................................................................................................................................	....................................................................................................................................................................................	PUNCT
ejpam-3812	253	11	....................................	....................................	PUNCT
ejpam-3812	253	12	.........	.........	PUNCT
ejpam-3812	253	13	........	........	PUNCT
ejpam-3812	253	14	........	........	PUNCT
ejpam-3812	253	15	........	........	PUNCT
ejpam-3812	253	16	........	........	PUNCT
ejpam-3812	254	1	......	......	PUNCT
ejpam-3812	254	2	....................................	....................................	PUNCT
ejpam-3812	255	1	..................................................................................................................................................................................................................................................................................................	..................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-3812	255	2	....................................	....................................	PUNCT
ejpam-3812	255	3	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-3812	256	1	....................................	....................................	PUNCT
ejpam-3812	256	2	....................................	....................................	PUNCT
ejpam-3812	257	1	·	·	PUNCT
ejpam-3812	257	2	·	·	PUNCT
ejpam-3812	257	3	·	·	PUNCT
ejpam-3812	257	4	•	•	NUM
ejpam-3812	257	5	•	•	NUM
ejpam-3812	257	6	•	•	NOUN
ejpam-3812	257	7	•	•	NOUN
ejpam-3812	257	8	y1	y1	NOUN
ejpam-3812	257	9	y2	y2	NOUN
ejpam-3812	257	10	y3	y3	NOUN
ejpam-3812	257	11	yb−a	yb−a	ADJ
ejpam-3812	257	12	figure	figure	NOUN
ejpam-3812	257	13	2	2	NUM
ejpam-3812	257	14	:	:	PUNCT
ejpam-3812	257	15	a	a	DET
ejpam-3812	257	16	graph	graph	NOUN
ejpam-3812	257	17	g	g	NOUN
ejpam-3812	257	18	with	with	ADP
ejpam-3812	257	19	γ1fd(g	γ1fd(g	PROPN
ejpam-3812	257	20	)	)	PUNCT
ejpam-3812	257	21	=	=	PUNCT
ejpam-3812	258	1	a	a	DET
ejpam-3812	258	2	<	<	X
ejpam-3812	258	3	γt2	γt2	NOUN
ejpam-3812	258	4	1f	1f	NUM
ejpam-3812	258	5	(	(	PUNCT
ejpam-3812	258	6	g	g	NOUN
ejpam-3812	258	7	)	)	PUNCT
ejpam-3812	258	8	=	=	SYM
ejpam-3812	259	1	b	b	X
ejpam-3812	259	2	let	let	VERB
ejpam-3812	259	3	a	a	PRON
ejpam-3812	259	4	=	=	PUNCT
ejpam-3812	259	5	{	{	PUNCT
ejpam-3812	259	6	x1	x1	PROPN
ejpam-3812	259	7	,	,	PUNCT
ejpam-3812	259	8	x2	x2	PROPN
ejpam-3812	259	9	,	,	PUNCT
ejpam-3812	259	10	...	...	PUNCT
ejpam-3812	259	11	,	,	PUNCT
ejpam-3812	259	12	xa	xa	PROPN
ejpam-3812	259	13	}	}	PUNCT
ejpam-3812	259	14	.	.	PUNCT
ejpam-3812	260	1	it	it	PRON
ejpam-3812	260	2	is	be	AUX
ejpam-3812	260	3	clear	clear	ADJ
ejpam-3812	260	4	that	that	SCONJ
ejpam-3812	260	5	the	the	DET
ejpam-3812	260	6	set	set	NOUN
ejpam-3812	260	7	a	a	PRON
ejpam-3812	260	8	is	be	AUX
ejpam-3812	260	9	a	a	DET
ejpam-3812	260	10	γ1fd	γ1fd	NOUN
ejpam-3812	260	11	-	-	PUNCT
ejpam-3812	260	12	set	set	VERB
ejpam-3812	260	13	and	and	CCONJ
ejpam-3812	260	14	the	the	DET
ejpam-3812	260	15	set	set	NOUN
ejpam-3812	260	16	b	b	PROPN
ejpam-3812	260	17	=	=	SYM
ejpam-3812	260	18	(	(	PUNCT
ejpam-3812	260	19	a	a	DET
ejpam-3812	260	20	\	\	PROPN
ejpam-3812	260	21	{	{	PUNCT
ejpam-3812	260	22	xa	xa	PROPN
ejpam-3812	260	23	}	}	PUNCT
ejpam-3812	260	24	)	)	PUNCT
ejpam-3812	260	25	∪	∪	ADP
ejpam-3812	260	26	{	{	PUNCT
ejpam-3812	260	27	v	v	NOUN
ejpam-3812	260	28	}	}	PUNCT
ejpam-3812	260	29	∪	∪	ADJ
ejpam-3812	260	30	{	{	PUNCT
ejpam-3812	260	31	y1	y1	NOUN
ejpam-3812	260	32	,	,	PUNCT
ejpam-3812	260	33	y2	y2	PROPN
ejpam-3812	260	34	,	,	PUNCT
ejpam-3812	260	35	y3	y3	PROPN
ejpam-3812	260	36	,	,	PUNCT
ejpam-3812	260	37	...	...	PUNCT
ejpam-3812	260	38	,	,	PUNCT
ejpam-3812	260	39	yb−a	yb−a	PRON
ejpam-3812	260	40	}	}	PUNCT
ejpam-3812	260	41	is	be	AUX
ejpam-3812	260	42	a	a	DET
ejpam-3812	260	43	γt21f	γt21f	NOUN
ejpam-3812	260	44	-set	-set	PROPN
ejpam-3812	260	45	in	in	ADP
ejpam-3812	260	46	g.	g.	PROPN
ejpam-3812	260	47	it	it	PRON
ejpam-3812	260	48	follows	follow	VERB
ejpam-3812	260	49	that	that	PRON
ejpam-3812	260	50	γ1fd(g	γ1fd(g	PROPN
ejpam-3812	260	51	)	)	PUNCT
ejpam-3812	261	1	=	=	SYM
ejpam-3812	261	2	|a|	|a|	PROPN
ejpam-3812	261	3	=	=	PROPN
ejpam-3812	261	4	a	a	PROPN
ejpam-3812	261	5	and	and	CCONJ
ejpam-3812	261	6	γt21f	γt21f	PUNCT
ejpam-3812	261	7	(	(	PUNCT
ejpam-3812	261	8	g	g	NOUN
ejpam-3812	261	9	)	)	PUNCT
ejpam-3812	261	10	=	=	SYM
ejpam-3812	262	1	|b|	|b|	PROPN
ejpam-3812	262	2	=	=	PUNCT
ejpam-3812	262	3	(	(	PUNCT
ejpam-3812	262	4	a−	a−	PROPN
ejpam-3812	262	5	1	1	NUM
ejpam-3812	262	6	)	)	PUNCT
ejpam-3812	262	7	+	+	CCONJ
ejpam-3812	262	8	1	1	NUM
ejpam-3812	262	9	+	+	CCONJ
ejpam-3812	262	10	(	(	PUNCT
ejpam-3812	262	11	b−	b−	PROPN
ejpam-3812	262	12	a	a	NOUN
ejpam-3812	262	13	)	)	PUNCT
ejpam-3812	262	14	=	=	SYM
ejpam-3812	262	15	b.	b.	PROPN
ejpam-3812	262	16	�	�	PROPN
ejpam-3812	262	17	m.	m.	PROPN
ejpam-3812	262	18	ortega	ortega	PROPN
ejpam-3812	262	19	,	,	PUNCT
ejpam-3812	262	20	r.	r.	PROPN
ejpam-3812	262	21	isla	isla	PROPN
ejpam-3812	262	22	/	/	SYM
ejpam-3812	262	23	eur	eur	PROPN
ejpam-3812	262	24	.	.	PUNCT
ejpam-3812	263	1	j.	j.	PROPN
ejpam-3812	263	2	pure	pure	PROPN
ejpam-3812	263	3	appl	appl	PROPN
ejpam-3812	263	4	.	.	PROPN
ejpam-3812	263	5	math	math	PROPN
ejpam-3812	263	6	,	,	PUNCT
ejpam-3812	263	7	13	13	NUM
ejpam-3812	263	8	(	(	PUNCT
ejpam-3812	263	9	4	4	NUM
ejpam-3812	263	10	)	)	PUNCT
ejpam-3812	263	11	(	(	PUNCT
ejpam-3812	263	12	2020	2020	NUM
ejpam-3812	263	13	)	)	PUNCT
ejpam-3812	263	14	,	,	PUNCT
ejpam-3812	263	15	779	779	NUM
ejpam-3812	263	16	-	-	SYM
ejpam-3812	263	17	793	793	NUM
ejpam-3812	263	18	787	787	NUM
ejpam-3812	263	19	corollary	corollary	ADJ
ejpam-3812	263	20	7	7	NUM
ejpam-3812	263	21	.	.	NOUN
ejpam-3812	263	22	γt21f	γt21f	NOUN
ejpam-3812	264	1	−	−	NOUN
ejpam-3812	264	2	γ1fd	γ1fd	PUNCT
ejpam-3812	264	3	can	can	AUX
ejpam-3812	264	4	be	be	AUX
ejpam-3812	264	5	made	make	VERB
ejpam-3812	264	6	arbitrarily	arbitrarily	ADV
ejpam-3812	264	7	large	large	ADJ
ejpam-3812	264	8	.	.	PUNCT
ejpam-3812	265	1	we	we	PRON
ejpam-3812	265	2	now	now	ADV
ejpam-3812	265	3	characterize	characterize	VERB
ejpam-3812	265	4	the	the	DET
ejpam-3812	265	5	semitotal	semitotal	ADJ
ejpam-3812	265	6	1	1	NUM
ejpam-3812	265	7	-	-	PUNCT
ejpam-3812	265	8	fair	fair	ADJ
ejpam-3812	265	9	dominating	dominating	NOUN
ejpam-3812	265	10	sets	set	NOUN
ejpam-3812	265	11	in	in	ADP
ejpam-3812	265	12	the	the	DET
ejpam-3812	265	13	join	join	NOUN
ejpam-3812	265	14	,	,	PUNCT
ejpam-3812	265	15	corona	corona	PROPN
ejpam-3812	265	16	,	,	PUNCT
ejpam-3812	265	17	lexicographic	lexicographic	ADJ
ejpam-3812	265	18	product	product	NOUN
ejpam-3812	265	19	,	,	PUNCT
ejpam-3812	265	20	and	and	CCONJ
ejpam-3812	265	21	cartesian	cartesian	ADJ
ejpam-3812	265	22	product	product	NOUN
ejpam-3812	265	23	of	of	ADP
ejpam-3812	265	24	graphs	graph	NOUN
ejpam-3812	265	25	in	in	ADP
ejpam-3812	265	26	this	this	DET
ejpam-3812	265	27	section	section	NOUN
ejpam-3812	265	28	.	.	PUNCT
ejpam-3812	266	1	we	we	PRON
ejpam-3812	266	2	also	also	ADV
ejpam-3812	266	3	establish	establish	VERB
ejpam-3812	266	4	the	the	DET
ejpam-3812	266	5	exact	exact	ADJ
ejpam-3812	266	6	value	value	NOUN
ejpam-3812	266	7	or	or	CCONJ
ejpam-3812	266	8	sharp	sharp	ADJ
ejpam-3812	266	9	bounds	bound	NOUN
ejpam-3812	266	10	of	of	ADP
ejpam-3812	266	11	the	the	DET
ejpam-3812	266	12	corresponding	corresponding	ADJ
ejpam-3812	266	13	semitotal	semitotal	ADJ
ejpam-3812	266	14	1	1	NUM
ejpam-3812	266	15	-	-	PUNCT
ejpam-3812	266	16	fair	fair	ADJ
ejpam-3812	266	17	domination	domination	NOUN
ejpam-3812	266	18	number	number	NOUN
ejpam-3812	266	19	.	.	PUNCT
ejpam-3812	267	1	theorem	theorem	VERB
ejpam-3812	267	2	13	13	NUM
ejpam-3812	267	3	.	.	PUNCT
ejpam-3812	268	1	let	let	VERB
ejpam-3812	268	2	g	g	NOUN
ejpam-3812	268	3	and	and	CCONJ
ejpam-3812	268	4	h	h	NOUN
ejpam-3812	268	5	be	be	VERB
ejpam-3812	268	6	any	any	DET
ejpam-3812	268	7	two	two	NUM
ejpam-3812	268	8	graphs	graph	NOUN
ejpam-3812	268	9	of	of	ADP
ejpam-3812	268	10	orders	order	NOUN
ejpam-3812	268	11	m	m	VERB
ejpam-3812	268	12	and	and	CCONJ
ejpam-3812	268	13	n	n	CCONJ
ejpam-3812	268	14	,	,	PUNCT
ejpam-3812	268	15	respectively	respectively	ADV
ejpam-3812	268	16	.	.	PUNCT
ejpam-3812	269	1	a	a	DET
ejpam-3812	269	2	set	set	NOUN
ejpam-3812	269	3	c	c	NOUN
ejpam-3812	269	4	⊆	⊆	NUM
ejpam-3812	269	5	v	v	NOUN
ejpam-3812	269	6	(	(	PUNCT
ejpam-3812	269	7	g+h	g+h	PROPN
ejpam-3812	269	8	)	)	PUNCT
ejpam-3812	269	9	is	be	AUX
ejpam-3812	269	10	a	a	DET
ejpam-3812	269	11	semitotal	semitotal	ADJ
ejpam-3812	269	12	1fd	1fd	NOUN
ejpam-3812	269	13	-	-	PUNCT
ejpam-3812	269	14	set	set	NOUN
ejpam-3812	269	15	of	of	ADP
ejpam-3812	269	16	g+h	g+h	PROPN
ejpam-3812	270	1	if	if	SCONJ
ejpam-3812	270	2	and	and	CCONJ
ejpam-3812	270	3	only	only	ADV
ejpam-3812	270	4	if	if	SCONJ
ejpam-3812	270	5	c	c	PROPN
ejpam-3812	270	6	=	=	SYM
ejpam-3812	270	7	v	v	PROPN
ejpam-3812	270	8	(	(	PUNCT
ejpam-3812	270	9	g+h	g+h	NOUN
ejpam-3812	270	10	)	)	PUNCT
ejpam-3812	270	11	or	or	CCONJ
ejpam-3812	270	12	c	c	X
ejpam-3812	270	13	=	=	SYM
ejpam-3812	270	14	{	{	PUNCT
ejpam-3812	270	15	v	v	NOUN
ejpam-3812	270	16	,	,	PUNCT
ejpam-3812	270	17	w	w	NOUN
ejpam-3812	270	18	}	}	PUNCT
ejpam-3812	270	19	for	for	ADP
ejpam-3812	270	20	some	some	DET
ejpam-3812	270	21	isolated	isolate	VERB
ejpam-3812	270	22	vertices	vertex	NOUN
ejpam-3812	270	23	v	v	NOUN
ejpam-3812	270	24	and	and	CCONJ
ejpam-3812	270	25	w	w	NOUN
ejpam-3812	270	26	of	of	ADP
ejpam-3812	270	27	g	g	PROPN
ejpam-3812	270	28	and	and	CCONJ
ejpam-3812	270	29	h	h	NOUN
ejpam-3812	270	30	,	,	PUNCT
ejpam-3812	270	31	respectively	respectively	ADV
ejpam-3812	270	32	.	.	PUNCT
ejpam-3812	271	1	proof	proof	NOUN
ejpam-3812	271	2	.	.	PUNCT
ejpam-3812	272	1	immediately	immediately	ADV
ejpam-3812	272	2	follows	follow	VERB
ejpam-3812	272	3	from	from	ADP
ejpam-3812	272	4	γt21f	γt21f	PUNCT
ejpam-3812	272	5	(	(	PUNCT
ejpam-3812	272	6	g+h	g+h	PROPN
ejpam-3812	272	7	)	)	PUNCT
ejpam-3812	272	8	≥	≥	NOUN
ejpam-3812	272	9	2	2	NUM
ejpam-3812	272	10	and	and	CCONJ
ejpam-3812	272	11	theorem	theorem	VERB
ejpam-3812	272	12	8	8	NUM
ejpam-3812	272	13	.	.	PUNCT
ejpam-3812	272	14	�	�	PROPN
ejpam-3812	272	15	corollary	corollary	ADJ
ejpam-3812	272	16	8	8	NUM
ejpam-3812	272	17	.	.	PUNCT
ejpam-3812	273	1	let	let	VERB
ejpam-3812	273	2	g	g	NOUN
ejpam-3812	273	3	and	and	CCONJ
ejpam-3812	273	4	h	h	NOUN
ejpam-3812	273	5	be	be	VERB
ejpam-3812	273	6	any	any	DET
ejpam-3812	273	7	graphs	graph	NOUN
ejpam-3812	273	8	of	of	ADP
ejpam-3812	273	9	orders	order	NOUN
ejpam-3812	273	10	m	m	VERB
ejpam-3812	273	11	and	and	CCONJ
ejpam-3812	273	12	n	n	CCONJ
ejpam-3812	273	13	,	,	PUNCT
ejpam-3812	273	14	respectively	respectively	ADV
ejpam-3812	273	15	.	.	PUNCT
ejpam-3812	274	1	then	then	ADV
ejpam-3812	274	2	γt21f	γt21f	VERB
ejpam-3812	274	3	(	(	PUNCT
ejpam-3812	274	4	g+	g+	NOUN
ejpam-3812	274	5	h	h	NOUN
ejpam-3812	274	6	)	)	PUNCT
ejpam-3812	274	7	=	=	SYM
ejpam-3812	274	8	2	2	NUM
ejpam-3812	274	9	if	if	SCONJ
ejpam-3812	274	10	g	g	PROPN
ejpam-3812	274	11	and	and	CCONJ
ejpam-3812	274	12	h	h	NOUN
ejpam-3812	274	13	both	both	PRON
ejpam-3812	274	14	contain	contain	VERB
ejpam-3812	274	15	isolated	isolated	ADJ
ejpam-3812	274	16	vertices	vertex	NOUN
ejpam-3812	274	17	and	and	CCONJ
ejpam-3812	274	18	γt21f	γt21f	PUNCT
ejpam-3812	274	19	(	(	PUNCT
ejpam-3812	274	20	g+h	g+h	NOUN
ejpam-3812	274	21	)	)	PUNCT
ejpam-3812	275	1	=	=	PUNCT
ejpam-3812	276	1	m+	m+	NOUN
ejpam-3812	276	2	n	n	CCONJ
ejpam-3812	276	3	otherwise	otherwise	ADV
ejpam-3812	276	4	.	.	PUNCT
ejpam-3812	277	1	theorem	theorem	VERB
ejpam-3812	277	2	14	14	NUM
ejpam-3812	277	3	.	.	PUNCT
ejpam-3812	278	1	let	let	VERB
ejpam-3812	278	2	g	g	PRON
ejpam-3812	278	3	be	be	AUX
ejpam-3812	278	4	a	a	DET
ejpam-3812	278	5	nontrivial	nontrivial	ADJ
ejpam-3812	278	6	connected	connect	VERB
ejpam-3812	278	7	graph	graph	NOUN
ejpam-3812	278	8	and	and	CCONJ
ejpam-3812	278	9	h	h	NOUN
ejpam-3812	278	10	be	be	AUX
ejpam-3812	278	11	any	any	DET
ejpam-3812	278	12	graph	graph	NOUN
ejpam-3812	278	13	.	.	PUNCT
ejpam-3812	279	1	then	then	ADV
ejpam-3812	279	2	c	c	PROPN
ejpam-3812	279	3	⊆	⊆	NUM
ejpam-3812	279	4	v	v	NOUN
ejpam-3812	279	5	(	(	PUNCT
ejpam-3812	279	6	g	g	PROPN
ejpam-3812	279	7	◦	◦	NOUN
ejpam-3812	279	8	h	h	NOUN
ejpam-3812	279	9	)	)	PUNCT
ejpam-3812	279	10	is	be	AUX
ejpam-3812	279	11	a	a	DET
ejpam-3812	279	12	semitotal	semitotal	ADJ
ejpam-3812	279	13	1fd	1fd	NOUN
ejpam-3812	279	14	-	-	PUNCT
ejpam-3812	279	15	set	set	NOUN
ejpam-3812	279	16	in	in	ADP
ejpam-3812	279	17	g	g	PROPN
ejpam-3812	279	18	◦	◦	NOUN
ejpam-3812	279	19	h	h	NOUN
ejpam-3812	279	20	if	if	SCONJ
ejpam-3812	280	1	and	and	CCONJ
ejpam-3812	280	2	only	only	ADV
ejpam-3812	280	3	if	if	SCONJ
ejpam-3812	280	4	c	c	PROPN
ejpam-3812	280	5	=	=	SYM
ejpam-3812	280	6	v	v	PROPN
ejpam-3812	280	7	(	(	PUNCT
ejpam-3812	280	8	g	g	NOUN
ejpam-3812	280	9	)	)	PUNCT
ejpam-3812	280	10	or	or	CCONJ
ejpam-3812	280	11	c	c	NOUN
ejpam-3812	280	12	=	=	SYM
ejpam-3812	280	13	v	v	PROPN
ejpam-3812	280	14	(	(	PUNCT
ejpam-3812	280	15	g	g	PROPN
ejpam-3812	280	16	◦	◦	NOUN
ejpam-3812	280	17	h	h	NOUN
ejpam-3812	280	18	)	)	PUNCT
ejpam-3812	280	19	.	.	PUNCT
ejpam-3812	281	1	proof	proof	NOUN
ejpam-3812	281	2	.	.	PUNCT
ejpam-3812	282	1	suppose	suppose	VERB
ejpam-3812	282	2	c	c	SYM
ejpam-3812	282	3	⊆	⊆	NUM
ejpam-3812	282	4	v	v	NOUN
ejpam-3812	282	5	(	(	PUNCT
ejpam-3812	282	6	g	g	PROPN
ejpam-3812	282	7	◦	◦	NOUN
ejpam-3812	282	8	h	h	NOUN
ejpam-3812	282	9	)	)	PUNCT
ejpam-3812	282	10	is	be	AUX
ejpam-3812	282	11	a	a	DET
ejpam-3812	282	12	semitotal	semitotal	ADJ
ejpam-3812	282	13	1fd	1fd	NOUN
ejpam-3812	282	14	-	-	PUNCT
ejpam-3812	282	15	set	set	NOUN
ejpam-3812	282	16	in	in	ADP
ejpam-3812	282	17	g	g	PROPN
ejpam-3812	282	18	◦	◦	NOUN
ejpam-3812	282	19	h.	h.	NOUN
ejpam-3812	283	1	then	then	ADV
ejpam-3812	283	2	c	c	PROPN
ejpam-3812	283	3	is	be	AUX
ejpam-3812	283	4	a	a	DET
ejpam-3812	283	5	1fd	1fd	NOUN
ejpam-3812	283	6	-	-	PUNCT
ejpam-3812	283	7	set	set	NOUN
ejpam-3812	283	8	in	in	ADP
ejpam-3812	283	9	g	g	PROPN
ejpam-3812	283	10	◦	◦	NOUN
ejpam-3812	283	11	h.	h.	NOUN
ejpam-3812	283	12	it	it	PRON
ejpam-3812	283	13	now	now	ADV
ejpam-3812	283	14	follows	follow	VERB
ejpam-3812	283	15	by	by	ADP
ejpam-3812	283	16	theorem	theorem	NOUN
ejpam-3812	283	17	9	9	NUM
ejpam-3812	283	18	that	that	PRON
ejpam-3812	283	19	c	c	NOUN
ejpam-3812	283	20	=	=	SYM
ejpam-3812	283	21	v	v	PROPN
ejpam-3812	283	22	(	(	PUNCT
ejpam-3812	283	23	g	g	NOUN
ejpam-3812	283	24	)	)	PUNCT
ejpam-3812	283	25	or	or	CCONJ
ejpam-3812	283	26	c	c	NOUN
ejpam-3812	283	27	=	=	SYM
ejpam-3812	283	28	v	v	PROPN
ejpam-3812	283	29	(	(	PUNCT
ejpam-3812	283	30	g	g	PROPN
ejpam-3812	283	31	◦	◦	NOUN
ejpam-3812	283	32	h	h	NOUN
ejpam-3812	283	33	)	)	PUNCT
ejpam-3812	283	34	.	.	PUNCT
ejpam-3812	284	1	the	the	DET
ejpam-3812	284	2	converse	converse	NOUN
ejpam-3812	284	3	is	be	AUX
ejpam-3812	284	4	obvious	obvious	ADJ
ejpam-3812	284	5	.	.	PUNCT
ejpam-3812	285	1	�	�	PROPN
ejpam-3812	285	2	corollary	corollary	NOUN
ejpam-3812	285	3	9	9	NUM
ejpam-3812	285	4	.	.	PUNCT
ejpam-3812	286	1	let	let	VERB
ejpam-3812	286	2	g	g	PRON
ejpam-3812	286	3	be	be	AUX
ejpam-3812	286	4	a	a	DET
ejpam-3812	286	5	nontrivial	nontrivial	ADJ
ejpam-3812	286	6	connected	connect	VERB
ejpam-3812	286	7	graph	graph	NOUN
ejpam-3812	286	8	and	and	CCONJ
ejpam-3812	286	9	h	h	NOUN
ejpam-3812	286	10	be	be	AUX
ejpam-3812	286	11	any	any	DET
ejpam-3812	286	12	graph	graph	NOUN
ejpam-3812	286	13	.	.	PUNCT
ejpam-3812	287	1	then	then	ADV
ejpam-3812	287	2	γt21f	γt21f	VERB
ejpam-3812	287	3	(	(	PUNCT
ejpam-3812	287	4	g	g	PROPN
ejpam-3812	287	5	◦	◦	NOUN
ejpam-3812	287	6	h	h	NOUN
ejpam-3812	287	7	)	)	PUNCT
ejpam-3812	288	1	=	=	SYM
ejpam-3812	288	2	|v	|v	PROPN
ejpam-3812	288	3	(	(	PUNCT
ejpam-3812	288	4	g)|	g)|	PROPN
ejpam-3812	288	5	.	.	PUNCT
ejpam-3812	288	6	theorem	theorem	PROPN
ejpam-3812	288	7	15	15	NUM
ejpam-3812	288	8	.	.	PUNCT
ejpam-3812	289	1	let	let	VERB
ejpam-3812	289	2	g	g	NOUN
ejpam-3812	289	3	and	and	CCONJ
ejpam-3812	289	4	h	h	NOUN
ejpam-3812	289	5	be	be	AUX
ejpam-3812	289	6	nontrivial	nontrivial	ADJ
ejpam-3812	289	7	connected	connected	ADJ
ejpam-3812	289	8	graphs	graph	NOUN
ejpam-3812	289	9	.	.	PUNCT
ejpam-3812	290	1	a	a	DET
ejpam-3812	290	2	set	set	NOUN
ejpam-3812	290	3	c	c	NOUN
ejpam-3812	290	4	⊆	⊆	NUM
ejpam-3812	290	5	v	v	NOUN
ejpam-3812	290	6	(	(	PUNCT
ejpam-3812	290	7	g[h	g[h	PROPN
ejpam-3812	290	8	]	]	PUNCT
ejpam-3812	290	9	)	)	PUNCT
ejpam-3812	290	10	is	be	AUX
ejpam-3812	290	11	a	a	DET
ejpam-3812	290	12	semitotal	semitotal	ADJ
ejpam-3812	290	13	1fd	1fd	NOUN
ejpam-3812	290	14	-	-	PUNCT
ejpam-3812	290	15	set	set	NOUN
ejpam-3812	290	16	of	of	ADP
ejpam-3812	290	17	g[h	g[h	NOUN
ejpam-3812	290	18	]	]	PUNCT
ejpam-3812	290	19	if	if	SCONJ
ejpam-3812	291	1	and	and	CCONJ
ejpam-3812	291	2	only	only	ADV
ejpam-3812	291	3	if	if	SCONJ
ejpam-3812	291	4	c	c	PROPN
ejpam-3812	291	5	=	=	SYM
ejpam-3812	291	6	v	v	PROPN
ejpam-3812	291	7	(	(	PUNCT
ejpam-3812	291	8	g[h	g[h	PROPN
ejpam-3812	291	9	]	]	PUNCT
ejpam-3812	291	10	)	)	PUNCT
ejpam-3812	291	11	.	.	PUNCT
ejpam-3812	292	1	proof	proof	NOUN
ejpam-3812	292	2	.	.	PUNCT
ejpam-3812	293	1	suppose	suppose	VERB
ejpam-3812	293	2	c	c	NOUN
ejpam-3812	293	3	=	=	SYM
ejpam-3812	293	4	⋃	⋃	PROPN
ejpam-3812	293	5	x∈s	x∈s	NOUN
ejpam-3812	293	6	(	(	PUNCT
ejpam-3812	293	7	{	{	PUNCT
ejpam-3812	293	8	x	x	NOUN
ejpam-3812	293	9	}	}	PUNCT
ejpam-3812	293	10	×	×	PROPN
ejpam-3812	293	11	tx	tx	PROPN
ejpam-3812	293	12	)	)	PUNCT
ejpam-3812	293	13	is	be	AUX
ejpam-3812	293	14	a	a	DET
ejpam-3812	293	15	semitotal	semitotal	ADJ
ejpam-3812	293	16	1fd	1fd	NOUN
ejpam-3812	293	17	-	-	PUNCT
ejpam-3812	293	18	set	set	NOUN
ejpam-3812	293	19	of	of	ADP
ejpam-3812	293	20	g[h	g[h	NOUN
ejpam-3812	293	21	]	]	PUNCT
ejpam-3812	293	22	.	.	PUNCT
ejpam-3812	294	1	then	then	ADV
ejpam-3812	294	2	s	s	VERB
ejpam-3812	294	3	is	be	AUX
ejpam-3812	294	4	a	a	DET
ejpam-3812	294	5	1fd	1fd	NOUN
ejpam-3812	294	6	-	-	PUNCT
ejpam-3812	294	7	set	set	NOUN
ejpam-3812	294	8	of	of	ADP
ejpam-3812	294	9	g	g	NOUN
ejpam-3812	294	10	,	,	PUNCT
ejpam-3812	294	11	s	s	PART
ejpam-3812	294	12	∩	∩	NOUN
ejpam-3812	294	13	ng(s	ng(s	NUM
ejpam-3812	294	14	)	)	PUNCT
ejpam-3812	295	1	=	=	NOUN
ejpam-3812	295	2	∅	∅	NOUN
ejpam-3812	295	3	,	,	PUNCT
ejpam-3812	295	4	tx	tx	PROPN
ejpam-3812	295	5	is	be	AUX
ejpam-3812	295	6	a	a	DET
ejpam-3812	295	7	dominating	dominating	NOUN
ejpam-3812	295	8	set	set	NOUN
ejpam-3812	295	9	of	of	ADP
ejpam-3812	295	10	h	h	NOUN
ejpam-3812	295	11	,	,	PUNCT
ejpam-3812	295	12	and	and	CCONJ
ejpam-3812	295	13	|tx|	|tx|	X
ejpam-3812	295	14	=	=	SYM
ejpam-3812	295	15	1	1	NUM
ejpam-3812	295	16	for	for	ADP
ejpam-3812	295	17	each	each	DET
ejpam-3812	295	18	x	x	SYM
ejpam-3812	295	19	∈	∈	PROPN
ejpam-3812	295	20	s	s	NOUN
ejpam-3812	295	21	,	,	PUNCT
ejpam-3812	295	22	by	by	ADP
ejpam-3812	295	23	corollary	corollary	ADJ
ejpam-3812	295	24	5	5	NUM
ejpam-3812	295	25	.	.	PUNCT
ejpam-3812	295	26	suppose	suppose	VERB
ejpam-3812	295	27	c	c	PROPN
ejpam-3812	295	28	6=	6=	ADP
ejpam-3812	295	29	v	v	PROPN
ejpam-3812	295	30	(	(	PUNCT
ejpam-3812	295	31	g[h	g[h	PROPN
ejpam-3812	295	32	]	]	PUNCT
ejpam-3812	295	33	)	)	PUNCT
ejpam-3812	295	34	,	,	PUNCT
ejpam-3812	295	35	say	say	VERB
ejpam-3812	295	36	there	there	PRON
ejpam-3812	295	37	exists	exist	VERB
ejpam-3812	295	38	(	(	PUNCT
ejpam-3812	295	39	y	y	NOUN
ejpam-3812	295	40	,	,	PUNCT
ejpam-3812	295	41	a	a	PRON
ejpam-3812	295	42	)	)	PUNCT
ejpam-3812	295	43	∈	∈	NOUN
ejpam-3812	295	44	v	v	NOUN
ejpam-3812	295	45	(	(	PUNCT
ejpam-3812	295	46	g[h	g[h	PROPN
ejpam-3812	295	47	]	]	PUNCT
ejpam-3812	295	48	)	)	PUNCT
ejpam-3812	295	49	\	\	PROPN
ejpam-3812	296	1	c.	c.	NOUN
ejpam-3812	296	2	if	if	SCONJ
ejpam-3812	296	3	y	y	PROPN
ejpam-3812	296	4	/∈	/∈	PUNCT
ejpam-3812	297	1	s	s	NOUN
ejpam-3812	297	2	,	,	PUNCT
ejpam-3812	297	3	then	then	ADV
ejpam-3812	297	4	|ng(y	|ng(y	NUM
ejpam-3812	297	5	)	)	PUNCT
ejpam-3812	298	1	∩	∩	NOUN
ejpam-3812	298	2	s|	s|	VERB
ejpam-3812	298	3	=	=	SYM
ejpam-3812	298	4	1	1	NUM
ejpam-3812	298	5	because	because	SCONJ
ejpam-3812	298	6	s	s	NOUN
ejpam-3812	298	7	is	be	AUX
ejpam-3812	298	8	a	a	DET
ejpam-3812	298	9	1fd	1fd	NOUN
ejpam-3812	298	10	-	-	PUNCT
ejpam-3812	298	11	set	set	NOUN
ejpam-3812	298	12	of	of	ADP
ejpam-3812	298	13	g.	g.	PROPN
ejpam-3812	298	14	let	let	VERB
ejpam-3812	298	15	ng(y	ng(y	NOUN
ejpam-3812	298	16	)	)	PUNCT
ejpam-3812	298	17	∩	∩	NOUN
ejpam-3812	298	18	s	s	PART
ejpam-3812	298	19	=	=	X
ejpam-3812	298	20	{	{	PUNCT
ejpam-3812	298	21	z	z	NOUN
ejpam-3812	298	22	}	}	PUNCT
ejpam-3812	298	23	and	and	CCONJ
ejpam-3812	298	24	let	let	VERB
ejpam-3812	298	25	tz	tz	NOUN
ejpam-3812	298	26	=	=	PUNCT
ejpam-3812	298	27	{	{	PUNCT
ejpam-3812	298	28	b	b	NOUN
ejpam-3812	298	29	}	}	PUNCT
ejpam-3812	298	30	.	.	PUNCT
ejpam-3812	299	1	since	since	SCONJ
ejpam-3812	299	2	c	c	PROPN
ejpam-3812	299	3	is	be	AUX
ejpam-3812	299	4	a	a	DET
ejpam-3812	299	5	semitotal	semitotal	ADJ
ejpam-3812	299	6	1fd	1fd	NOUN
ejpam-3812	299	7	-	-	PUNCT
ejpam-3812	299	8	set	set	NOUN
ejpam-3812	299	9	of	of	ADP
ejpam-3812	299	10	g[h	g[h	PROPN
ejpam-3812	299	11	]	]	PUNCT
ejpam-3812	299	12	,	,	PUNCT
ejpam-3812	299	13	there	there	PRON
ejpam-3812	299	14	exists	exist	VERB
ejpam-3812	299	15	(	(	PUNCT
ejpam-3812	299	16	w	w	NOUN
ejpam-3812	299	17	,	,	PUNCT
ejpam-3812	299	18	c	c	NOUN
ejpam-3812	299	19	)	)	PUNCT
ejpam-3812	299	20	∈	∈	PROPN
ejpam-3812	299	21	c	c	NOUN
ejpam-3812	299	22	such	such	ADJ
ejpam-3812	299	23	that	that	PRON
ejpam-3812	299	24	dg[h]((z	dg[h]((z	NOUN
ejpam-3812	299	25	,	,	PUNCT
ejpam-3812	299	26	b	b	NOUN
ejpam-3812	299	27	)	)	PUNCT
ejpam-3812	299	28	,	,	PUNCT
ejpam-3812	299	29	(	(	PUNCT
ejpam-3812	299	30	w	w	NOUN
ejpam-3812	299	31	,	,	PUNCT
ejpam-3812	299	32	c	c	NOUN
ejpam-3812	299	33	)	)	PUNCT
ejpam-3812	299	34	)	)	PUNCT
ejpam-3812	300	1	≤	≤	NUM
ejpam-3812	300	2	2	2	NUM
ejpam-3812	300	3	.	.	PUNCT
ejpam-3812	301	1	now	now	ADV
ejpam-3812	301	2	,	,	PUNCT
ejpam-3812	301	3	since	since	SCONJ
ejpam-3812	301	4	s	s	PART
ejpam-3812	301	5	∩	∩	NOUN
ejpam-3812	301	6	ng(s	ng(s	NUM
ejpam-3812	301	7	)	)	PUNCT
ejpam-3812	301	8	=	=	NOUN
ejpam-3812	301	9	∅	∅	NOUN
ejpam-3812	301	10	and	and	CCONJ
ejpam-3812	301	11	w	w	PROPN
ejpam-3812	301	12	∈	∈	PROPN
ejpam-3812	301	13	s	s	PART
ejpam-3812	301	14	\	\	X
ejpam-3812	301	15	{	{	PUNCT
ejpam-3812	301	16	z	z	NOUN
ejpam-3812	301	17	}	}	PUNCT
ejpam-3812	301	18	,	,	PUNCT
ejpam-3812	301	19	it	it	PRON
ejpam-3812	301	20	follows	follow	VERB
ejpam-3812	301	21	that	that	SCONJ
ejpam-3812	301	22	dg(z	dg(z	NOUN
ejpam-3812	301	23	,	,	PUNCT
ejpam-3812	301	24	w	w	NOUN
ejpam-3812	301	25	)	)	PUNCT
ejpam-3812	301	26	=	=	SYM
ejpam-3812	301	27	2	2	NUM
ejpam-3812	301	28	(	(	PUNCT
ejpam-3812	301	29	that	that	PRON
ejpam-3812	301	30	is	is	ADV
ejpam-3812	301	31	,	,	PUNCT
ejpam-3812	301	32	dg[h]((z	dg[h]((z	X
ejpam-3812	301	33	,	,	PUNCT
ejpam-3812	301	34	b	b	NOUN
ejpam-3812	301	35	)	)	PUNCT
ejpam-3812	301	36	,	,	PUNCT
ejpam-3812	301	37	(	(	PUNCT
ejpam-3812	301	38	w	w	NOUN
ejpam-3812	301	39	,	,	PUNCT
ejpam-3812	301	40	c	c	NOUN
ejpam-3812	301	41	)	)	PUNCT
ejpam-3812	301	42	)	)	PUNCT
ejpam-3812	301	43	=	=	SYM
ejpam-3812	302	1	2	2	NUM
ejpam-3812	302	2	)	)	PUNCT
ejpam-3812	302	3	.	.	PUNCT
ejpam-3812	303	1	let	let	VERB
ejpam-3812	303	2	u	u	PRON
ejpam-3812	303	3	∈	∈	PROPN
ejpam-3812	303	4	ng(z	ng(z	PROPN
ejpam-3812	303	5	)	)	PUNCT
ejpam-3812	303	6	∩	∩	NOUN
ejpam-3812	303	7	ng(w	ng(w	NOUN
ejpam-3812	303	8	)	)	PUNCT
ejpam-3812	303	9	.	.	PUNCT
ejpam-3812	304	1	then	then	ADV
ejpam-3812	304	2	u	u	PROPN
ejpam-3812	304	3	∈	∈	PROPN
ejpam-3812	304	4	v	v	ADP
ejpam-3812	304	5	(	(	PUNCT
ejpam-3812	304	6	g	g	NOUN
ejpam-3812	304	7	)	)	PUNCT
ejpam-3812	304	8	\	\	PUNCT
ejpam-3812	304	9	s.	s.	PROPN
ejpam-3812	304	10	since	since	SCONJ
ejpam-3812	304	11	z	z	PROPN
ejpam-3812	304	12	,	,	PUNCT
ejpam-3812	304	13	w	w	PROPN
ejpam-3812	304	14	∈	∈	PROPN
ejpam-3812	304	15	ng(u	ng(u	NOUN
ejpam-3812	304	16	)	)	PUNCT
ejpam-3812	304	17	∩	∩	NOUN
ejpam-3812	304	18	s	s	X
ejpam-3812	304	19	,	,	PUNCT
ejpam-3812	304	20	s	s	VERB
ejpam-3812	304	21	is	be	AUX
ejpam-3812	304	22	not	not	PART
ejpam-3812	304	23	a	a	DET
ejpam-3812	304	24	1fd	1fd	ADV
ejpam-3812	304	25	-	-	PUNCT
ejpam-3812	304	26	set	set	NOUN
ejpam-3812	304	27	,	,	PUNCT
ejpam-3812	304	28	a	a	DET
ejpam-3812	304	29	contradiction	contradiction	NOUN
ejpam-3812	304	30	.	.	PUNCT
ejpam-3812	305	1	suppose	suppose	VERB
ejpam-3812	305	2	y	y	PROPN
ejpam-3812	305	3	∈	∈	PROPN
ejpam-3812	305	4	s.	s.	PROPN
ejpam-3812	305	5	then	then	ADV
ejpam-3812	305	6	|ty|	|ty|	ADV
ejpam-3812	305	7	=	=	SYM
ejpam-3812	306	1	1	1	X
ejpam-3812	306	2	.	.	PUNCT
ejpam-3812	306	3	again	again	ADV
ejpam-3812	306	4	,	,	PUNCT
ejpam-3812	306	5	since	since	SCONJ
ejpam-3812	306	6	c	c	NOUN
ejpam-3812	306	7	is	be	AUX
ejpam-3812	306	8	a	a	DET
ejpam-3812	306	9	semitotal	semitotal	ADJ
ejpam-3812	306	10	1fd	1fd	NOUN
ejpam-3812	306	11	-	-	PUNCT
ejpam-3812	306	12	set	set	NOUN
ejpam-3812	306	13	of	of	ADP
ejpam-3812	306	14	g[h	g[h	NOUN
ejpam-3812	306	15	]	]	PUNCT
ejpam-3812	306	16	,	,	PUNCT
ejpam-3812	306	17	s	s	NOUN
ejpam-3812	306	18	∩ng(s	∩ng(s	ADJ
ejpam-3812	306	19	)	)	PUNCT
ejpam-3812	306	20	=	=	SYM
ejpam-3812	306	21	∅	∅	NOUN
ejpam-3812	306	22	,	,	PUNCT
ejpam-3812	306	23	and	and	CCONJ
ejpam-3812	306	24	|ty|	|ty|	ADV
ejpam-3812	307	1	=	=	SYM
ejpam-3812	307	2	1	1	NUM
ejpam-3812	307	3	,	,	PUNCT
ejpam-3812	307	4	there	there	PRON
ejpam-3812	307	5	exists	exist	VERB
ejpam-3812	307	6	p	p	PROPN
ejpam-3812	307	7	∈	∈	PROPN
ejpam-3812	307	8	ng(y)∩	ng(y)∩	PRON
ejpam-3812	307	9	s	s	VERB
ejpam-3812	307	10	such	such	ADJ
ejpam-3812	307	11	that	that	PRON
ejpam-3812	307	12	dg(y	dg(y	ADJ
ejpam-3812	307	13	,	,	PUNCT
ejpam-3812	307	14	p	p	NOUN
ejpam-3812	307	15	)	)	PUNCT
ejpam-3812	307	16	=	=	SYM
ejpam-3812	307	17	2	2	X
ejpam-3812	307	18	.	.	PUNCT
ejpam-3812	308	1	this	this	PRON
ejpam-3812	308	2	implies	imply	VERB
ejpam-3812	308	3	that	that	SCONJ
ejpam-3812	308	4	there	there	PRON
ejpam-3812	308	5	exists	exist	VERB
ejpam-3812	308	6	q	q	PROPN
ejpam-3812	308	7	∈	∈	PROPN
ejpam-3812	308	8	v	v	ADP
ejpam-3812	308	9	(	(	PUNCT
ejpam-3812	308	10	g	g	NOUN
ejpam-3812	308	11	)	)	PUNCT
ejpam-3812	308	12	\	\	PROPN
ejpam-3812	308	13	s	s	PART
ejpam-3812	308	14	(	(	PUNCT
ejpam-3812	308	15	q	q	NOUN
ejpam-3812	308	16	∈	∈	PROPN
ejpam-3812	308	17	ng(y	ng(y	NOUN
ejpam-3812	308	18	)	)	PUNCT
ejpam-3812	308	19	∩ng(p	∩ng(p	NOUN
ejpam-3812	308	20	)	)	PUNCT
ejpam-3812	308	21	)	)	PUNCT
ejpam-3812	308	22	such	such	ADJ
ejpam-3812	308	23	that	that	SCONJ
ejpam-3812	308	24	|ng(q	|ng(q	NOUN
ejpam-3812	308	25	)	)	PUNCT
ejpam-3812	308	26	∩	∩	NOUN
ejpam-3812	308	27	s|	s|	VERB
ejpam-3812	308	28	≥	≥	NOUN
ejpam-3812	308	29	2	2	NUM
ejpam-3812	308	30	,	,	PUNCT
ejpam-3812	308	31	contrary	contrary	ADV
ejpam-3812	308	32	to	to	ADP
ejpam-3812	308	33	the	the	DET
ejpam-3812	308	34	fact	fact	NOUN
ejpam-3812	308	35	that	that	SCONJ
ejpam-3812	308	36	s	s	VERB
ejpam-3812	308	37	is	be	AUX
ejpam-3812	308	38	a	a	DET
ejpam-3812	308	39	1fd	1fd	NOUN
ejpam-3812	308	40	-	-	PUNCT
ejpam-3812	308	41	set	set	NOUN
ejpam-3812	308	42	of	of	ADP
ejpam-3812	308	43	g.	g.	PROPN
ejpam-3812	308	44	thus	thus	ADV
ejpam-3812	308	45	,	,	PUNCT
ejpam-3812	308	46	c	c	PROPN
ejpam-3812	308	47	=	=	SYM
ejpam-3812	308	48	v	v	PROPN
ejpam-3812	308	49	(	(	PUNCT
ejpam-3812	308	50	g[h	g[h	PROPN
ejpam-3812	308	51	]	]	PUNCT
ejpam-3812	308	52	)	)	PUNCT
ejpam-3812	308	53	.	.	PUNCT
ejpam-3812	309	1	the	the	DET
ejpam-3812	309	2	converse	converse	NOUN
ejpam-3812	309	3	is	be	AUX
ejpam-3812	309	4	clear	clear	ADJ
ejpam-3812	309	5	.	.	PUNCT
ejpam-3812	310	1	�	�	PROPN
ejpam-3812	310	2	corollary	corollary	ADJ
ejpam-3812	310	3	10	10	NUM
ejpam-3812	310	4	.	.	PUNCT
ejpam-3812	311	1	let	let	VERB
ejpam-3812	311	2	g	g	NOUN
ejpam-3812	311	3	and	and	CCONJ
ejpam-3812	311	4	h	h	NOUN
ejpam-3812	311	5	be	be	AUX
ejpam-3812	311	6	nontrivial	nontrivial	ADJ
ejpam-3812	311	7	connected	connect	VERB
ejpam-3812	311	8	graphs	graph	NOUN
ejpam-3812	311	9	of	of	ADP
ejpam-3812	311	10	orders	order	NOUN
ejpam-3812	311	11	m	m	VERB
ejpam-3812	311	12	and	and	CCONJ
ejpam-3812	311	13	n	n	CCONJ
ejpam-3812	311	14	,	,	PUNCT
ejpam-3812	311	15	respectively	respectively	ADV
ejpam-3812	311	16	.	.	PUNCT
ejpam-3812	312	1	then	then	ADV
ejpam-3812	312	2	γt21f	γt21f	VERB
ejpam-3812	312	3	(	(	PUNCT
ejpam-3812	312	4	g[h	g[h	NOUN
ejpam-3812	312	5	]	]	PUNCT
ejpam-3812	312	6	)	)	PUNCT
ejpam-3812	312	7	=	=	PUNCT
ejpam-3812	312	8	m	m	PUNCT
ejpam-3812	312	9	·	·	PUNCT
ejpam-3812	312	10	n.	n.	PROPN
ejpam-3812	312	11	m.	m.	PROPN
ejpam-3812	312	12	ortega	ortega	PROPN
ejpam-3812	312	13	,	,	PUNCT
ejpam-3812	312	14	r.	r.	PROPN
ejpam-3812	312	15	isla	isla	PROPN
ejpam-3812	312	16	/	/	SYM
ejpam-3812	312	17	eur	eur	PROPN
ejpam-3812	312	18	.	.	PUNCT
ejpam-3812	313	1	j.	j.	PROPN
ejpam-3812	313	2	pure	pure	PROPN
ejpam-3812	313	3	appl	appl	PROPN
ejpam-3812	313	4	.	.	PROPN
ejpam-3812	313	5	math	math	PROPN
ejpam-3812	313	6	,	,	PUNCT
ejpam-3812	313	7	13	13	NUM
ejpam-3812	313	8	(	(	PUNCT
ejpam-3812	313	9	4	4	NUM
ejpam-3812	313	10	)	)	PUNCT
ejpam-3812	313	11	(	(	PUNCT
ejpam-3812	313	12	2020	2020	NUM
ejpam-3812	313	13	)	)	PUNCT
ejpam-3812	313	14	,	,	PUNCT
ejpam-3812	313	15	779	779	NUM
ejpam-3812	313	16	-	-	SYM
ejpam-3812	313	17	793	793	NUM
ejpam-3812	313	18	788	788	NUM
ejpam-3812	313	19	theorem	theorem	NOUN
ejpam-3812	313	20	16	16	NUM
ejpam-3812	313	21	.	.	PUNCT
ejpam-3812	314	1	let	let	VERB
ejpam-3812	314	2	g	g	NOUN
ejpam-3812	314	3	and	and	CCONJ
ejpam-3812	314	4	h	h	NOUN
ejpam-3812	314	5	be	be	AUX
ejpam-3812	314	6	nontrivial	nontrivial	ADJ
ejpam-3812	314	7	connected	connected	ADJ
ejpam-3812	314	8	graphs	graph	NOUN
ejpam-3812	314	9	.	.	PUNCT
ejpam-3812	315	1	then	then	ADV
ejpam-3812	315	2	c	c	X
ejpam-3812	315	3	=	=	PUNCT
ejpam-3812	315	4	⋃	⋃	PROPN
ejpam-3812	315	5	x∈v	x∈v	PROPN
ejpam-3812	315	6	(	(	PUNCT
ejpam-3812	315	7	g	g	NOUN
ejpam-3812	315	8	)	)	PUNCT
ejpam-3812	316	1	[	[	X
ejpam-3812	316	2	{	{	PUNCT
ejpam-3812	316	3	x}×tx	x}×tx	X
ejpam-3812	316	4	]	]	X
ejpam-3812	316	5	⊆	⊆	NUM
ejpam-3812	316	6	v	v	X
ejpam-3812	316	7	(	(	PUNCT
ejpam-3812	316	8	g	g	PROPN
ejpam-3812	316	9	�	�	NOUN
ejpam-3812	316	10	h	h	NOUN
ejpam-3812	316	11	)	)	PUNCT
ejpam-3812	316	12	is	be	AUX
ejpam-3812	316	13	a	a	DET
ejpam-3812	316	14	semitotal	semitotal	ADJ
ejpam-3812	316	15	1fd	1fd	NOUN
ejpam-3812	316	16	-	-	PUNCT
ejpam-3812	316	17	set	set	NOUN
ejpam-3812	316	18	of	of	ADP
ejpam-3812	316	19	g	g	PROPN
ejpam-3812	316	20	�	�	PROPN
ejpam-3812	316	21	h	h	NOUN
ejpam-3812	316	22	if	if	SCONJ
ejpam-3812	316	23	and	and	CCONJ
ejpam-3812	316	24	only	only	ADV
ejpam-3812	316	25	if	if	SCONJ
ejpam-3812	316	26	:	:	PUNCT
ejpam-3812	316	27	(	(	PUNCT
ejpam-3812	316	28	i	i	NOUN
ejpam-3812	316	29	)	)	PUNCT
ejpam-3812	316	30	v	v	NOUN
ejpam-3812	316	31	(	(	PUNCT
ejpam-3812	316	32	h)\tx	h)\tx	NOUN
ejpam-3812	316	33	⊆	⊆	NUM
ejpam-3812	316	34	nh(tx	nh(tx	NOUN
ejpam-3812	316	35	)	)	PUNCT
ejpam-3812	316	36	∪	∪	NOUN
ejpam-3812	316	37	(	(	PUNCT
ejpam-3812	316	38	⋃	⋃	PROPN
ejpam-3812	316	39	z∈ng(x	z∈ng(x	NOUN
ejpam-3812	316	40	)	)	PUNCT
ejpam-3812	316	41	tz	tz	NOUN
ejpam-3812	316	42	)	)	PUNCT
ejpam-3812	316	43	for	for	ADP
ejpam-3812	316	44	each	each	PRON
ejpam-3812	316	45	x	x	SYM
ejpam-3812	316	46	∈	∈	PROPN
ejpam-3812	316	47	v	v	NOUN
ejpam-3812	316	48	(	(	PUNCT
ejpam-3812	316	49	g	g	NOUN
ejpam-3812	316	50	)	)	PUNCT
ejpam-3812	316	51	;	;	PUNCT
ejpam-3812	316	52	(	(	PUNCT
ejpam-3812	316	53	ii	ii	NOUN
ejpam-3812	316	54	)	)	PUNCT
ejpam-3812	316	55	for	for	ADP
ejpam-3812	316	56	each	each	DET
ejpam-3812	316	57	x	x	SYM
ejpam-3812	316	58	∈	∈	PROPN
ejpam-3812	316	59	v	v	NOUN
ejpam-3812	316	60	(	(	PUNCT
ejpam-3812	316	61	g	g	NOUN
ejpam-3812	316	62	)	)	PUNCT
ejpam-3812	316	63	,	,	PUNCT
ejpam-3812	316	64	tx	tx	PROPN
ejpam-3812	316	65	=	=	SYM
ejpam-3812	316	66	v	v	PROPN
ejpam-3812	316	67	(	(	PUNCT
ejpam-3812	316	68	h	h	NOUN
ejpam-3812	316	69	)	)	PUNCT
ejpam-3812	316	70	or	or	CCONJ
ejpam-3812	316	71	for	for	ADP
ejpam-3812	316	72	each	each	PRON
ejpam-3812	316	73	a	a	DET
ejpam-3812	316	74	∈	∈	PROPN
ejpam-3812	316	75	v	v	NOUN
ejpam-3812	316	76	(	(	PUNCT
ejpam-3812	316	77	h)\tx	h)\tx	PROPN
ejpam-3812	316	78	,	,	PUNCT
ejpam-3812	316	79	either	either	CCONJ
ejpam-3812	316	80	|nh(a)∩tx|	|nh(a)∩tx|	NOUN
ejpam-3812	316	81	=	=	SYM
ejpam-3812	316	82	1	1	NUM
ejpam-3812	316	83	and	and	CCONJ
ejpam-3812	316	84	{	{	PUNCT
ejpam-3812	316	85	z	z	NOUN
ejpam-3812	316	86	:	:	PUNCT
ejpam-3812	316	87	z	z	PROPN
ejpam-3812	316	88	∈	∈	PROPN
ejpam-3812	316	89	ng(x	ng(x	NUM
ejpam-3812	316	90	)	)	PUNCT
ejpam-3812	316	91	,	,	PUNCT
ejpam-3812	316	92	a	a	DET
ejpam-3812	316	93	∈	∈	PROPN
ejpam-3812	316	94	tx	tx	PROPN
ejpam-3812	316	95	}	}	PUNCT
ejpam-3812	316	96	=	=	SYM
ejpam-3812	316	97	∅	∅	NOUN
ejpam-3812	316	98	,	,	PUNCT
ejpam-3812	316	99	or	or	CCONJ
ejpam-3812	316	100	nh(a	nh(a	NUM
ejpam-3812	316	101	)	)	PUNCT
ejpam-3812	316	102	∩	∩	NOUN
ejpam-3812	316	103	tx	tx	NOUN
ejpam-3812	316	104	=	=	SYM
ejpam-3812	316	105	∅	∅	NOUN
ejpam-3812	316	106	and	and	CCONJ
ejpam-3812	316	107	a	a	DET
ejpam-3812	316	108	∈	∈	NOUN
ejpam-3812	316	109	ty	ty	NOUN
ejpam-3812	316	110	for	for	ADP
ejpam-3812	316	111	exactly	exactly	ADV
ejpam-3812	316	112	one	one	NUM
ejpam-3812	316	113	y	y	PROPN
ejpam-3812	316	114	∈	∈	PROPN
ejpam-3812	316	115	ng(x	ng(x	NUM
ejpam-3812	316	116	)	)	PUNCT
ejpam-3812	316	117	;	;	PUNCT
ejpam-3812	316	118	and	and	CCONJ
ejpam-3812	316	119	(	(	PUNCT
ejpam-3812	316	120	iii	iii	NOUN
ejpam-3812	316	121	)	)	PUNCT
ejpam-3812	316	122	for	for	ADP
ejpam-3812	316	123	each	each	DET
ejpam-3812	316	124	x	x	SYM
ejpam-3812	316	125	∈	∈	PROPN
ejpam-3812	316	126	v	v	ADP
ejpam-3812	316	127	(	(	PUNCT
ejpam-3812	316	128	g	g	NOUN
ejpam-3812	316	129	)	)	PUNCT
ejpam-3812	316	130	and	and	CCONJ
ejpam-3812	316	131	for	for	ADP
ejpam-3812	316	132	each	each	DET
ejpam-3812	316	133	a	a	DET
ejpam-3812	316	134	∈	∈	PROPN
ejpam-3812	316	135	tx	tx	PROPN
ejpam-3812	316	136	,	,	PUNCT
ejpam-3812	316	137	there	there	PRON
ejpam-3812	316	138	exists	exist	VERB
ejpam-3812	316	139	b	b	PROPN
ejpam-3812	316	140	∈	∈	PROPN
ejpam-3812	316	141	tx	tx	VERB
ejpam-3812	316	142	such	such	ADJ
ejpam-3812	316	143	that	that	SCONJ
ejpam-3812	316	144	ab	ab	PROPN
ejpam-3812	316	145	∈	∈	PROPN
ejpam-3812	316	146	e(h	e(h	PROPN
ejpam-3812	316	147	)	)	PUNCT
ejpam-3812	316	148	or	or	CCONJ
ejpam-3812	316	149	there	there	PRON
ejpam-3812	316	150	exists	exist	VERB
ejpam-3812	316	151	y	y	PROPN
ejpam-3812	316	152	∈	∈	PROPN
ejpam-3812	316	153	ng(x	ng(x	NUM
ejpam-3812	316	154	)	)	PUNCT
ejpam-3812	316	155	such	such	ADJ
ejpam-3812	316	156	that	that	SCONJ
ejpam-3812	316	157	a	a	DET
ejpam-3812	316	158	∈	∈	PROPN
ejpam-3812	316	159	ty	ty	NOUN
ejpam-3812	316	160	.	.	PUNCT
ejpam-3812	316	161	proof	proof	NOUN
ejpam-3812	316	162	.	.	PUNCT
ejpam-3812	317	1	suppose	suppose	VERB
ejpam-3812	317	2	c	c	NOUN
ejpam-3812	317	3	=	=	PUNCT
ejpam-3812	317	4	⋃	⋃	PROPN
ejpam-3812	317	5	x∈v	x∈v	PROPN
ejpam-3812	317	6	(	(	PUNCT
ejpam-3812	317	7	g	g	NOUN
ejpam-3812	317	8	)	)	PUNCT
ejpam-3812	317	9	[	[	X
ejpam-3812	317	10	{	{	PUNCT
ejpam-3812	317	11	x	x	NOUN
ejpam-3812	317	12	}	}	PUNCT
ejpam-3812	317	13	×	×	PROPN
ejpam-3812	317	14	tx	tx	PROPN
ejpam-3812	317	15	]	]	X
ejpam-3812	317	16	⊆	⊆	NUM
ejpam-3812	317	17	v	v	NOUN
ejpam-3812	317	18	(	(	PUNCT
ejpam-3812	317	19	g	g	PROPN
ejpam-3812	317	20	�	�	NOUN
ejpam-3812	317	21	h	h	NOUN
ejpam-3812	317	22	)	)	PUNCT
ejpam-3812	317	23	is	be	AUX
ejpam-3812	317	24	a	a	DET
ejpam-3812	317	25	semitotal	semitotal	ADJ
ejpam-3812	317	26	1fd	1fd	NOUN
ejpam-3812	317	27	-	-	PUNCT
ejpam-3812	317	28	set	set	NOUN
ejpam-3812	317	29	in	in	ADP
ejpam-3812	317	30	g	g	PROPN
ejpam-3812	317	31	�	�	PROPN
ejpam-3812	317	32	h.	h.	PROPN
ejpam-3812	317	33	since	since	SCONJ
ejpam-3812	317	34	c	c	PROPN
ejpam-3812	317	35	is	be	AUX
ejpam-3812	317	36	a	a	DET
ejpam-3812	317	37	1fd	1fd	NOUN
ejpam-3812	317	38	-	-	PUNCT
ejpam-3812	317	39	set	set	NOUN
ejpam-3812	317	40	in	in	ADP
ejpam-3812	317	41	g	g	PROPN
ejpam-3812	317	42	�	�	PROPN
ejpam-3812	317	43	h	h	NOUN
ejpam-3812	317	44	,	,	PUNCT
ejpam-3812	317	45	conditions	condition	NOUN
ejpam-3812	317	46	(	(	PUNCT
ejpam-3812	317	47	i	i	NOUN
ejpam-3812	317	48	)	)	PUNCT
ejpam-3812	317	49	and	and	CCONJ
ejpam-3812	317	50	(	(	PUNCT
ejpam-3812	317	51	ii	ii	NOUN
ejpam-3812	317	52	)	)	PUNCT
ejpam-3812	317	53	hold	hold	VERB
ejpam-3812	317	54	by	by	ADP
ejpam-3812	317	55	theorem	theorem	NOUN
ejpam-3812	317	56	11	11	NUM
ejpam-3812	317	57	.	.	PUNCT
ejpam-3812	318	1	let	let	VERB
ejpam-3812	318	2	x	x	SYM
ejpam-3812	318	3	∈	∈	PROPN
ejpam-3812	318	4	v	v	X
ejpam-3812	318	5	(	(	PUNCT
ejpam-3812	318	6	g	g	NOUN
ejpam-3812	318	7	)	)	PUNCT
ejpam-3812	318	8	.	.	PUNCT
ejpam-3812	319	1	suppose	suppose	VERB
ejpam-3812	319	2	there	there	PRON
ejpam-3812	319	3	exists	exist	VERB
ejpam-3812	319	4	a	a	DET
ejpam-3812	319	5	∈	∈	NOUN
ejpam-3812	319	6	tx	tx	ADP
ejpam-3812	319	7	such	such	ADJ
ejpam-3812	319	8	that	that	PRON
ejpam-3812	319	9	for	for	ADP
ejpam-3812	319	10	all	all	DET
ejpam-3812	319	11	b	b	PROPN
ejpam-3812	319	12	∈	∈	PROPN
ejpam-3812	319	13	tx	tx	PROPN
ejpam-3812	319	14	,	,	PUNCT
ejpam-3812	319	15	ab	ab	PROPN
ejpam-3812	319	16	/∈	/∈	PUNCT
ejpam-3812	319	17	e(h	e(h	PROPN
ejpam-3812	319	18	)	)	PUNCT
ejpam-3812	319	19	and	and	CCONJ
ejpam-3812	319	20	for	for	ADP
ejpam-3812	319	21	all	all	DET
ejpam-3812	319	22	y	y	PROPN
ejpam-3812	319	23	∈	∈	PROPN
ejpam-3812	319	24	ng(x	ng(x	NUM
ejpam-3812	319	25	)	)	PUNCT
ejpam-3812	320	1	,	,	PUNCT
ejpam-3812	320	2	a	a	DET
ejpam-3812	320	3	/∈	/∈	NOUN
ejpam-3812	320	4	ty	ty	INTJ
ejpam-3812	320	5	.	.	PUNCT
ejpam-3812	321	1	since	since	SCONJ
ejpam-3812	321	2	c	c	PROPN
ejpam-3812	321	3	is	be	AUX
ejpam-3812	321	4	a	a	DET
ejpam-3812	321	5	semitotal	semitotal	ADJ
ejpam-3812	321	6	dominating	dominating	NOUN
ejpam-3812	321	7	set	set	NOUN
ejpam-3812	321	8	,	,	PUNCT
ejpam-3812	321	9	there	there	PRON
ejpam-3812	321	10	exists	exist	VERB
ejpam-3812	321	11	(	(	PUNCT
ejpam-3812	321	12	x	x	X
ejpam-3812	321	13	,	,	PUNCT
ejpam-3812	321	14	c	c	NOUN
ejpam-3812	321	15	)	)	PUNCT
ejpam-3812	321	16	∈	∈	PROPN
ejpam-3812	321	17	c	c	NOUN
ejpam-3812	321	18	such	such	ADJ
ejpam-3812	321	19	that	that	SCONJ
ejpam-3812	321	20	dg	dg	PROPN
ejpam-3812	321	21	�	�	PROPN
ejpam-3812	321	22	h	h	PROPN
ejpam-3812	321	23	(	(	PUNCT
ejpam-3812	321	24	(	(	PUNCT
ejpam-3812	321	25	x	x	NOUN
ejpam-3812	321	26	,	,	PUNCT
ejpam-3812	321	27	a	a	PRON
ejpam-3812	321	28	)	)	PUNCT
ejpam-3812	321	29	,	,	PUNCT
ejpam-3812	321	30	(	(	PUNCT
ejpam-3812	321	31	x	x	NOUN
ejpam-3812	321	32	,	,	PUNCT
ejpam-3812	321	33	c	c	NOUN
ejpam-3812	321	34	)	)	PUNCT
ejpam-3812	321	35	)	)	PUNCT
ejpam-3812	322	1	=	=	SYM
ejpam-3812	322	2	2	2	NUM
ejpam-3812	322	3	or	or	CCONJ
ejpam-3812	322	4	there	there	PRON
ejpam-3812	322	5	exists	exist	VERB
ejpam-3812	322	6	(	(	PUNCT
ejpam-3812	322	7	z	z	NOUN
ejpam-3812	322	8	,	,	PUNCT
ejpam-3812	322	9	a	a	PRON
ejpam-3812	322	10	)	)	PUNCT
ejpam-3812	322	11	∈	∈	PROPN
ejpam-3812	322	12	c	c	NOUN
ejpam-3812	322	13	such	such	ADJ
ejpam-3812	322	14	that	that	SCONJ
ejpam-3812	322	15	dg	dg	PROPN
ejpam-3812	322	16	�	�	PROPN
ejpam-3812	322	17	h	h	PROPN
ejpam-3812	322	18	(	(	PUNCT
ejpam-3812	322	19	(	(	PUNCT
ejpam-3812	322	20	x	x	NOUN
ejpam-3812	322	21	,	,	PUNCT
ejpam-3812	322	22	a	a	PRON
ejpam-3812	322	23	)	)	PUNCT
ejpam-3812	322	24	,	,	PUNCT
ejpam-3812	322	25	(	(	PUNCT
ejpam-3812	322	26	z	z	X
ejpam-3812	322	27	,	,	PUNCT
ejpam-3812	322	28	a	a	NOUN
ejpam-3812	322	29	)	)	PUNCT
ejpam-3812	322	30	)	)	PUNCT
ejpam-3812	323	1	=	=	SYM
ejpam-3812	323	2	2	2	NUM
ejpam-3812	323	3	or	or	CCONJ
ejpam-3812	323	4	there	there	PRON
ejpam-3812	323	5	exist	exist	VERB
ejpam-3812	323	6	y	y	PROPN
ejpam-3812	323	7	∈	∈	PROPN
ejpam-3812	323	8	ng(x	ng(x	NUM
ejpam-3812	323	9	)	)	PUNCT
ejpam-3812	323	10	and	and	CCONJ
ejpam-3812	323	11	b	b	X
ejpam-3812	323	12	∈	∈	NOUN
ejpam-3812	323	13	ty	ty	INTJ
ejpam-3812	323	14	such	such	ADJ
ejpam-3812	323	15	that	that	SCONJ
ejpam-3812	323	16	dg	dg	PROPN
ejpam-3812	323	17	�	�	PROPN
ejpam-3812	323	18	h	h	PROPN
ejpam-3812	323	19	(	(	PUNCT
ejpam-3812	323	20	(	(	PUNCT
ejpam-3812	323	21	x	x	NOUN
ejpam-3812	323	22	,	,	PUNCT
ejpam-3812	323	23	a	a	PRON
ejpam-3812	323	24	)	)	PUNCT
ejpam-3812	323	25	,	,	PUNCT
ejpam-3812	323	26	(	(	PUNCT
ejpam-3812	323	27	y	y	PROPN
ejpam-3812	323	28	,	,	PUNCT
ejpam-3812	323	29	b	b	NOUN
ejpam-3812	323	30	)	)	PUNCT
ejpam-3812	323	31	)	)	PUNCT
ejpam-3812	324	1	=	=	SYM
ejpam-3812	324	2	2	2	NUM
ejpam-3812	324	3	,	,	PUNCT
ejpam-3812	324	4	where	where	SCONJ
ejpam-3812	324	5	(	(	PUNCT
ejpam-3812	324	6	y	y	NOUN
ejpam-3812	324	7	,	,	PUNCT
ejpam-3812	324	8	b	b	NOUN
ejpam-3812	324	9	)	)	PUNCT
ejpam-3812	324	10	∈	∈	PROPN
ejpam-3812	324	11	c.	c.	NOUN
ejpam-3812	324	12	however	however	ADV
ejpam-3812	324	13	,	,	PUNCT
ejpam-3812	324	14	in	in	ADP
ejpam-3812	324	15	each	each	PRON
ejpam-3812	324	16	of	of	ADP
ejpam-3812	324	17	these	these	DET
ejpam-3812	324	18	cases	case	NOUN
ejpam-3812	324	19	,	,	PUNCT
ejpam-3812	324	20	there	there	PRON
ejpam-3812	324	21	exists	exist	VERB
ejpam-3812	324	22	(	(	PUNCT
ejpam-3812	324	23	w	w	NOUN
ejpam-3812	324	24	,	,	PUNCT
ejpam-3812	324	25	d	d	NOUN
ejpam-3812	324	26	)	)	PUNCT
ejpam-3812	324	27	∈	∈	NOUN
ejpam-3812	324	28	v	v	NOUN
ejpam-3812	324	29	(	(	PUNCT
ejpam-3812	324	30	g	g	NOUN
ejpam-3812	324	31	�	�	NOUN
ejpam-3812	324	32	h)\c	h)\c	VERB
ejpam-3812	324	33	such	such	DET
ejpam-3812	324	34	that	that	SCONJ
ejpam-3812	324	35	|ng	|ng	NUM
ejpam-3812	324	36	�	�	PROPN
ejpam-3812	324	37	h(w	h(w	PROPN
ejpam-3812	324	38	,	,	PUNCT
ejpam-3812	324	39	d)∩	d)∩	PRON
ejpam-3812	324	40	c|	c|	VERB
ejpam-3812	324	41	≥	≥	NOUN
ejpam-3812	324	42	2	2	NUM
ejpam-3812	324	43	,	,	PUNCT
ejpam-3812	324	44	contrary	contrary	ADV
ejpam-3812	324	45	to	to	ADP
ejpam-3812	324	46	the	the	DET
ejpam-3812	324	47	assumption	assumption	NOUN
ejpam-3812	324	48	that	that	SCONJ
ejpam-3812	324	49	c	c	PROPN
ejpam-3812	324	50	is	be	AUX
ejpam-3812	324	51	a	a	DET
ejpam-3812	324	52	1fd	1fd	NOUN
ejpam-3812	324	53	-	-	PUNCT
ejpam-3812	324	54	set	set	NOUN
ejpam-3812	324	55	.	.	PUNCT
ejpam-3812	325	1	hence	hence	ADV
ejpam-3812	325	2	,	,	PUNCT
ejpam-3812	325	3	condition	condition	NOUN
ejpam-3812	325	4	(	(	PUNCT
ejpam-3812	325	5	iii	iii	NOUN
ejpam-3812	325	6	)	)	PUNCT
ejpam-3812	325	7	must	must	AUX
ejpam-3812	325	8	be	be	AUX
ejpam-3812	325	9	satisfied	satisfied	ADJ
ejpam-3812	325	10	.	.	PUNCT
ejpam-3812	326	1	for	for	ADP
ejpam-3812	326	2	the	the	DET
ejpam-3812	326	3	converse	converse	NOUN
ejpam-3812	326	4	,	,	PUNCT
ejpam-3812	326	5	suppose	suppose	VERB
ejpam-3812	326	6	conditions	condition	NOUN
ejpam-3812	326	7	(	(	PUNCT
ejpam-3812	326	8	i	i	NOUN
ejpam-3812	326	9	)	)	PUNCT
ejpam-3812	326	10	,	,	PUNCT
ejpam-3812	326	11	(	(	PUNCT
ejpam-3812	326	12	ii	ii	NOUN
ejpam-3812	326	13	)	)	PUNCT
ejpam-3812	326	14	,	,	PUNCT
ejpam-3812	326	15	and	and	CCONJ
ejpam-3812	326	16	(	(	PUNCT
ejpam-3812	326	17	iii	iii	NOUN
ejpam-3812	326	18	)	)	PUNCT
ejpam-3812	326	19	hold	hold	NOUN
ejpam-3812	326	20	.	.	PUNCT
ejpam-3812	327	1	by	by	ADP
ejpam-3812	327	2	theorem	theorem	NOUN
ejpam-3812	327	3	11	11	NUM
ejpam-3812	327	4	,	,	PUNCT
ejpam-3812	327	5	(	(	PUNCT
ejpam-3812	327	6	i	i	NOUN
ejpam-3812	327	7	)	)	PUNCT
ejpam-3812	327	8	and	and	CCONJ
ejpam-3812	327	9	(	(	PUNCT
ejpam-3812	327	10	ii	ii	NOUN
ejpam-3812	327	11	)	)	PUNCT
ejpam-3812	327	12	imply	imply	VERB
ejpam-3812	327	13	that	that	SCONJ
ejpam-3812	327	14	c	c	PROPN
ejpam-3812	327	15	is	be	AUX
ejpam-3812	327	16	a	a	DET
ejpam-3812	327	17	1fd	1fd	NOUN
ejpam-3812	327	18	-	-	PUNCT
ejpam-3812	327	19	set	set	NOUN
ejpam-3812	327	20	in	in	ADP
ejpam-3812	327	21	g	g	PROPN
ejpam-3812	327	22	�	�	PROPN
ejpam-3812	327	23	h	h	NOUN
ejpam-3812	327	24	,	,	PUNCT
ejpam-3812	327	25	while	while	SCONJ
ejpam-3812	327	26	(	(	PUNCT
ejpam-3812	327	27	iii	iii	NOUN
ejpam-3812	327	28	)	)	PUNCT
ejpam-3812	327	29	implies	imply	VERB
ejpam-3812	327	30	that	that	SCONJ
ejpam-3812	327	31	c	c	PROPN
ejpam-3812	327	32	is	be	AUX
ejpam-3812	327	33	a	a	DET
ejpam-3812	327	34	semitotal	semitotal	ADJ
ejpam-3812	327	35	dominating	dominating	NOUN
ejpam-3812	327	36	set	set	NOUN
ejpam-3812	327	37	.	.	PUNCT
ejpam-3812	328	1	thus	thus	ADV
ejpam-3812	328	2	,	,	PUNCT
ejpam-3812	328	3	c	c	PROPN
ejpam-3812	328	4	is	be	AUX
ejpam-3812	328	5	a	a	DET
ejpam-3812	328	6	semitotal	semitotal	ADJ
ejpam-3812	328	7	1fd	1fd	NOUN
ejpam-3812	328	8	-	-	PUNCT
ejpam-3812	328	9	set	set	NOUN
ejpam-3812	328	10	in	in	ADP
ejpam-3812	328	11	g	g	PROPN
ejpam-3812	328	12	�	�	PROPN
ejpam-3812	328	13	h.	h.	PROPN
ejpam-3812	328	14	�	�	PROPN
ejpam-3812	328	15	corollary	corollary	PROPN
ejpam-3812	328	16	11	11	NUM
ejpam-3812	328	17	.	.	PUNCT
ejpam-3812	329	1	let	let	VERB
ejpam-3812	329	2	g	g	NOUN
ejpam-3812	329	3	and	and	CCONJ
ejpam-3812	329	4	h	h	NOUN
ejpam-3812	329	5	be	be	AUX
ejpam-3812	329	6	nontrivial	nontrivial	ADJ
ejpam-3812	329	7	connected	connected	ADJ
ejpam-3812	329	8	graphs	graph	NOUN
ejpam-3812	329	9	.	.	PUNCT
ejpam-3812	330	1	then	then	ADV
ejpam-3812	330	2	c1	c1	PROPN
ejpam-3812	330	3	=	=	PROPN
ejpam-3812	331	1	s1	s1	PROPN
ejpam-3812	331	2	×	×	PROPN
ejpam-3812	331	3	v	v	NOUN
ejpam-3812	331	4	(	(	PUNCT
ejpam-3812	331	5	h	h	NOUN
ejpam-3812	331	6	)	)	PUNCT
ejpam-3812	331	7	and	and	CCONJ
ejpam-3812	331	8	c2	c2	PROPN
ejpam-3812	331	9	=	=	SYM
ejpam-3812	331	10	v	v	PROPN
ejpam-3812	331	11	(	(	PUNCT
ejpam-3812	331	12	g)×	g)×	NOUN
ejpam-3812	331	13	s2	s2	NOUN
ejpam-3812	331	14	are	be	AUX
ejpam-3812	331	15	semitotal	semitotal	ADJ
ejpam-3812	331	16	1fd	1fd	ADJ
ejpam-3812	331	17	-	-	PUNCT
ejpam-3812	331	18	sets	set	NOUN
ejpam-3812	331	19	in	in	ADP
ejpam-3812	331	20	g	g	PROPN
ejpam-3812	331	21	�	�	NOUN
ejpam-3812	331	22	h	h	NOUN
ejpam-3812	331	23	if	if	SCONJ
ejpam-3812	332	1	and	and	CCONJ
ejpam-3812	332	2	only	only	ADV
ejpam-3812	332	3	if	if	SCONJ
ejpam-3812	332	4	s1	s1	PROPN
ejpam-3812	332	5	and	and	CCONJ
ejpam-3812	332	6	s2	s2	NOUN
ejpam-3812	332	7	are	be	AUX
ejpam-3812	332	8	1fd	1fd	NOUN
ejpam-3812	332	9	-	-	PUNCT
ejpam-3812	332	10	sets	set	NOUN
ejpam-3812	332	11	in	in	ADP
ejpam-3812	332	12	g	g	PROPN
ejpam-3812	332	13	and	and	CCONJ
ejpam-3812	332	14	h	h	NOUN
ejpam-3812	332	15	,	,	PUNCT
ejpam-3812	332	16	respectively	respectively	ADV
ejpam-3812	332	17	.	.	PUNCT
ejpam-3812	333	1	the	the	DET
ejpam-3812	333	2	following	following	ADJ
ejpam-3812	333	3	result	result	NOUN
ejpam-3812	333	4	is	be	AUX
ejpam-3812	333	5	an	an	DET
ejpam-3812	333	6	immediate	immediate	ADJ
ejpam-3812	333	7	consequence	consequence	NOUN
ejpam-3812	333	8	of	of	ADP
ejpam-3812	333	9	corollary	corollary	ADJ
ejpam-3812	333	10	11	11	NUM
ejpam-3812	333	11	.	.	PUNCT
ejpam-3812	334	1	corollary	corollary	ADJ
ejpam-3812	334	2	12	12	NUM
ejpam-3812	334	3	.	.	PUNCT
ejpam-3812	335	1	let	let	VERB
ejpam-3812	335	2	g	g	NOUN
ejpam-3812	335	3	and	and	CCONJ
ejpam-3812	335	4	h	h	NOUN
ejpam-3812	335	5	be	be	AUX
ejpam-3812	335	6	nontrivial	nontrivial	ADJ
ejpam-3812	335	7	connected	connected	ADJ
ejpam-3812	335	8	graphs	graph	NOUN
ejpam-3812	335	9	.	.	PUNCT
ejpam-3812	336	1	then	then	ADV
ejpam-3812	336	2	γt21f	γt21f	VERB
ejpam-3812	336	3	(	(	PUNCT
ejpam-3812	336	4	g	g	PROPN
ejpam-3812	336	5	�	�	PROPN
ejpam-3812	336	6	h	h	NOUN
ejpam-3812	336	7	)	)	PUNCT
ejpam-3812	336	8	≤	≤	NUM
ejpam-3812	336	9	min{|v	min{|v	PROPN
ejpam-3812	336	10	(	(	PUNCT
ejpam-3812	336	11	h)|	h)|	PROPN
ejpam-3812	336	12	·	·	PUNCT
ejpam-3812	336	13	γ1fd(g	γ1fd(g	PROPN
ejpam-3812	336	14	)	)	PUNCT
ejpam-3812	336	15	,	,	PUNCT
ejpam-3812	336	16	|v	|v	PROPN
ejpam-3812	336	17	(	(	PUNCT
ejpam-3812	336	18	g)|	g)|	PROPN
ejpam-3812	336	19	·	·	PUNCT
ejpam-3812	336	20	γ1fd(h	γ1fd(h	PROPN
ejpam-3812	336	21	)	)	PUNCT
ejpam-3812	336	22	}	}	PUNCT
ejpam-3812	336	23	.	.	PUNCT
ejpam-3812	337	1	remark	remark	NOUN
ejpam-3812	337	2	5	5	NUM
ejpam-3812	337	3	.	.	PUNCT
ejpam-3812	338	1	the	the	DET
ejpam-3812	338	2	bound	bind	VERB
ejpam-3812	338	3	given	give	VERB
ejpam-3812	338	4	in	in	ADP
ejpam-3812	338	5	corollary	corollary	ADJ
ejpam-3812	338	6	12	12	NUM
ejpam-3812	338	7	is	be	AUX
ejpam-3812	338	8	sharp	sharp	ADJ
ejpam-3812	338	9	.	.	PUNCT
ejpam-3812	339	1	to	to	PART
ejpam-3812	339	2	see	see	VERB
ejpam-3812	339	3	this	this	PRON
ejpam-3812	339	4	,	,	PUNCT
ejpam-3812	339	5	consider	consider	VERB
ejpam-3812	339	6	the	the	DET
ejpam-3812	339	7	graph	graph	NOUN
ejpam-3812	339	8	shown	show	VERB
ejpam-3812	339	9	in	in	ADP
ejpam-3812	339	10	figure	figure	NOUN
ejpam-3812	339	11	3	3	NUM
ejpam-3812	339	12	.	.	PUNCT
ejpam-3812	340	1	the	the	DET
ejpam-3812	340	2	shaded	shade	VERB
ejpam-3812	340	3	vertices	vertex	NOUN
ejpam-3812	340	4	in	in	ADP
ejpam-3812	340	5	p4	p4	ADJ
ejpam-3812	340	6	�	�	PROPN
ejpam-3812	340	7	p6	p6	NOUN
ejpam-3812	340	8	form	form	NOUN
ejpam-3812	340	9	a	a	DET
ejpam-3812	340	10	γt21f	γt21f	NOUN
ejpam-3812	340	11	-set	-set	ADJ
ejpam-3812	340	12	.	.	PUNCT
ejpam-3812	341	1	thus	thus	ADV
ejpam-3812	341	2	,	,	PUNCT
ejpam-3812	341	3	γt21f	γt21f	PUNCT
ejpam-3812	341	4	(	(	PUNCT
ejpam-3812	341	5	p4	p4	ADJ
ejpam-3812	341	6	�	�	NOUN
ejpam-3812	341	7	p6	p6	PROPN
ejpam-3812	341	8	)	)	PUNCT
ejpam-3812	341	9	=	=	SYM
ejpam-3812	341	10	8	8	NUM
ejpam-3812	341	11	=	=	SYM
ejpam-3812	341	12	min{6	min{6	NOUN
ejpam-3812	341	13	·	·	SYM
ejpam-3812	341	14	2	2	NUM
ejpam-3812	341	15	,	,	PUNCT
ejpam-3812	341	16	4	4	NUM
ejpam-3812	341	17	·	·	SYM
ejpam-3812	341	18	2	2	NUM
ejpam-3812	341	19	}	}	PUNCT
ejpam-3812	341	20	=	=	SYM
ejpam-3812	341	21	min{|v	min{|v	PROPN
ejpam-3812	341	22	(	(	PUNCT
ejpam-3812	341	23	p6)|	p6)|	X
ejpam-3812	341	24	·	·	PUNCT
ejpam-3812	341	25	γ1fd(p4	γ1fd(p4	NUM
ejpam-3812	341	26	)	)	PUNCT
ejpam-3812	341	27	,	,	PUNCT
ejpam-3812	341	28	|v	|v	PROPN
ejpam-3812	341	29	(	(	PUNCT
ejpam-3812	341	30	p4)|	p4)|	PROPN
ejpam-3812	341	31	·	·	PUNCT
ejpam-3812	341	32	γ1fd(p6	γ1fd(p6	NUM
ejpam-3812	341	33	)	)	PUNCT
ejpam-3812	341	34	}	}	PUNCT
ejpam-3812	342	1	=	=	SYM
ejpam-3812	342	2	|v	|v	X
ejpam-3812	342	3	(	(	PUNCT
ejpam-3812	342	4	p4)|	p4)|	PROPN
ejpam-3812	342	5	·	·	PUNCT
ejpam-3812	342	6	γ1fd(p6	γ1fd(p6	NUM
ejpam-3812	342	7	)	)	PUNCT
ejpam-3812	342	8	.	.	PUNCT
ejpam-3812	343	1	m.	m.	PROPN
ejpam-3812	343	2	ortega	ortega	PROPN
ejpam-3812	343	3	,	,	PUNCT
ejpam-3812	343	4	r.	r.	PROPN
ejpam-3812	343	5	isla	isla	PROPN
ejpam-3812	343	6	/	/	SYM
ejpam-3812	343	7	eur	eur	PROPN
ejpam-3812	343	8	.	.	PUNCT
ejpam-3812	344	1	j.	j.	PROPN
ejpam-3812	344	2	pure	pure	PROPN
ejpam-3812	344	3	appl	appl	PROPN
ejpam-3812	344	4	.	.	PROPN
ejpam-3812	344	5	math	math	PROPN
ejpam-3812	344	6	,	,	PUNCT
ejpam-3812	344	7	13	13	NUM
ejpam-3812	344	8	(	(	PUNCT
ejpam-3812	344	9	4	4	NUM
ejpam-3812	344	10	)	)	PUNCT
ejpam-3812	344	11	(	(	PUNCT
ejpam-3812	344	12	2020	2020	NUM
ejpam-3812	344	13	)	)	PUNCT
ejpam-3812	344	14	,	,	PUNCT
ejpam-3812	344	15	779	779	NUM
ejpam-3812	344	16	-	-	SYM
ejpam-3812	344	17	793	793	NUM
ejpam-3812	344	18	789	789	NUM
ejpam-3812	344	19	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	20	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	21	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	22	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	23	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	24	....................................	....................................	PUNCT
ejpam-3812	344	25	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	26	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	27	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	28	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	29	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	30	....................................	....................................	PUNCT
ejpam-3812	344	31	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	32	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	33	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	34	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	35	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	36	....................................	....................................	PUNCT
ejpam-3812	344	37	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	38	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	39	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	40	...................................................................................	...................................................................................	PUNCT
ejpam-3812	344	41	...................................................................................	...................................................................................	PUNCT
ejpam-3812	345	1	....................................	....................................	PUNCT
ejpam-3812	345	2	.........	.........	PUNCT
ejpam-3812	345	3	........	........	PUNCT
ejpam-3812	345	4	........	........	PUNCT
ejpam-3812	345	5	........	........	PUNCT
ejpam-3812	345	6	........	........	PUNCT
ejpam-3812	346	1	......	......	PUNCT
ejpam-3812	346	2	.........	.........	PUNCT
ejpam-3812	346	3	........	........	PUNCT
ejpam-3812	346	4	........	........	PUNCT
ejpam-3812	346	5	........	........	PUNCT
ejpam-3812	346	6	........	........	PUNCT
ejpam-3812	347	1	......	......	PUNCT
ejpam-3812	347	2	.........	.........	PUNCT
ejpam-3812	347	3	........	........	PUNCT
ejpam-3812	347	4	........	........	PUNCT
ejpam-3812	347	5	........	........	PUNCT
ejpam-3812	347	6	........	........	PUNCT
ejpam-3812	348	1	......	......	PUNCT
ejpam-3812	348	2	.........	.........	PUNCT
ejpam-3812	348	3	........	........	PUNCT
ejpam-3812	348	4	........	........	PUNCT
ejpam-3812	348	5	........	........	PUNCT
ejpam-3812	348	6	........	........	PUNCT
ejpam-3812	349	1	......	......	PUNCT
ejpam-3812	349	2	.........	.........	PUNCT
ejpam-3812	349	3	........	........	PUNCT
ejpam-3812	349	4	........	........	PUNCT
ejpam-3812	349	5	........	........	PUNCT
ejpam-3812	349	6	........	........	PUNCT
ejpam-3812	350	1	......	......	PUNCT
ejpam-3812	350	2	.........	.........	PUNCT
ejpam-3812	350	3	........	........	PUNCT
ejpam-3812	350	4	........	........	PUNCT
ejpam-3812	350	5	........	........	PUNCT
ejpam-3812	350	6	........	........	PUNCT
ejpam-3812	351	1	......	......	PUNCT
ejpam-3812	351	2	.........	.........	PUNCT
ejpam-3812	351	3	........	........	PUNCT
ejpam-3812	351	4	........	........	PUNCT
ejpam-3812	351	5	........	........	PUNCT
ejpam-3812	351	6	........	........	PUNCT
ejpam-3812	352	1	......	......	PUNCT
ejpam-3812	352	2	.........	.........	PUNCT
ejpam-3812	352	3	........	........	PUNCT
ejpam-3812	352	4	........	........	PUNCT
ejpam-3812	352	5	........	........	PUNCT
ejpam-3812	352	6	........	........	PUNCT
ejpam-3812	353	1	......	......	PUNCT
ejpam-3812	353	2	.........	.........	PUNCT
ejpam-3812	353	3	........	........	PUNCT
ejpam-3812	353	4	........	........	PUNCT
ejpam-3812	353	5	........	........	PUNCT
ejpam-3812	353	6	........	........	PUNCT
ejpam-3812	354	1	......	......	PUNCT
ejpam-3812	354	2	.........	.........	PUNCT
ejpam-3812	354	3	........	........	PUNCT
ejpam-3812	354	4	........	........	PUNCT
ejpam-3812	354	5	........	........	PUNCT
ejpam-3812	354	6	........	........	PUNCT
ejpam-3812	355	1	......	......	PUNCT
ejpam-3812	355	2	.........	.........	PUNCT
ejpam-3812	355	3	........	........	PUNCT
ejpam-3812	355	4	........	........	PUNCT
ejpam-3812	355	5	........	........	PUNCT
ejpam-3812	355	6	........	........	PUNCT
ejpam-3812	356	1	......	......	PUNCT
ejpam-3812	356	2	.........	.........	PUNCT
ejpam-3812	356	3	........	........	PUNCT
ejpam-3812	356	4	........	........	PUNCT
ejpam-3812	356	5	........	........	PUNCT
ejpam-3812	356	6	........	........	PUNCT
ejpam-3812	357	1	......	......	PUNCT
ejpam-3812	357	2	.........	.........	PUNCT
ejpam-3812	357	3	........	........	PUNCT
ejpam-3812	357	4	........	........	PUNCT
ejpam-3812	357	5	........	........	PUNCT
ejpam-3812	357	6	........	........	PUNCT
ejpam-3812	358	1	......	......	PUNCT
ejpam-3812	358	2	.........	.........	PUNCT
ejpam-3812	358	3	........	........	PUNCT
ejpam-3812	358	4	........	........	PUNCT
ejpam-3812	358	5	........	........	PUNCT
ejpam-3812	358	6	........	........	PUNCT
ejpam-3812	359	1	......	......	PUNCT
ejpam-3812	359	2	.........	.........	PUNCT
ejpam-3812	359	3	........	........	PUNCT
ejpam-3812	359	4	........	........	PUNCT
ejpam-3812	359	5	........	........	PUNCT
ejpam-3812	359	6	........	........	PUNCT
ejpam-3812	360	1	......	......	PUNCT
ejpam-3812	360	2	.........	.........	PUNCT
ejpam-3812	360	3	........	........	PUNCT
ejpam-3812	360	4	........	........	PUNCT
ejpam-3812	360	5	........	........	PUNCT
ejpam-3812	360	6	........	........	PUNCT
ejpam-3812	361	1	......	......	PUNCT
ejpam-3812	361	2	.........	.........	PUNCT
ejpam-3812	361	3	........	........	PUNCT
ejpam-3812	361	4	........	........	PUNCT
ejpam-3812	361	5	........	........	PUNCT
ejpam-3812	361	6	........	........	PUNCT
ejpam-3812	362	1	......	......	PUNCT
ejpam-3812	362	2	.........	.........	PUNCT
ejpam-3812	362	3	........	........	PUNCT
ejpam-3812	362	4	........	........	PUNCT
ejpam-3812	362	5	........	........	PUNCT
ejpam-3812	363	1	........	........	PUNCT
ejpam-3812	364	1	......	......	PUNCT
ejpam-3812	365	1	•	•	NUM
ejpam-3812	365	2	•	•	NUM
ejpam-3812	365	3	•	•	NUM
ejpam-3812	365	4	•	•	NUM
ejpam-3812	365	5	•	•	NUM
ejpam-3812	365	6	•	•	NUM
ejpam-3812	365	7	•	•	NOUN
ejpam-3812	365	8	•	•	NUM
ejpam-3812	365	9	figure	figure	NOUN
ejpam-3812	365	10	3	3	NUM
ejpam-3812	365	11	:	:	PUNCT
ejpam-3812	365	12	the	the	DET
ejpam-3812	365	13	graph	graph	NOUN
ejpam-3812	365	14	p4	p4	PROPN
ejpam-3812	365	15	�	�	PROPN
ejpam-3812	365	16	p6	p6	PROPN
ejpam-3812	365	17	,	,	PUNCT
ejpam-3812	365	18	with	with	ADP
ejpam-3812	365	19	γ	γ	PROPN
ejpam-3812	365	20	t2	t2	PROPN
ejpam-3812	365	21	1f	1f	PROPN
ejpam-3812	365	22	(	(	PUNCT
ejpam-3812	365	23	p4	p4	PROPN
ejpam-3812	365	24	�	�	NOUN
ejpam-3812	365	25	p6	p6	PROPN
ejpam-3812	365	26	)	)	PUNCT
ejpam-3812	365	27	=	=	SYM
ejpam-3812	365	28	8	8	NUM
ejpam-3812	365	29	.	.	NOUN
ejpam-3812	365	30	4	4	NUM
ejpam-3812	365	31	.	.	X
ejpam-3812	366	1	independent	independent	ADJ
ejpam-3812	366	2	k	k	ADJ
ejpam-3812	366	3	-	-	PUNCT
ejpam-3812	366	4	fair	fair	ADJ
ejpam-3812	366	5	domination	domination	NOUN
ejpam-3812	366	6	we	we	PRON
ejpam-3812	366	7	characterize	characterize	VERB
ejpam-3812	366	8	the	the	DET
ejpam-3812	366	9	independent	independent	ADJ
ejpam-3812	366	10	k	k	ADJ
ejpam-3812	366	11	-	-	ADJ
ejpam-3812	366	12	fair	fair	ADJ
ejpam-3812	366	13	dominating	dominating	NOUN
ejpam-3812	366	14	sets	set	NOUN
ejpam-3812	366	15	in	in	ADP
ejpam-3812	366	16	the	the	DET
ejpam-3812	366	17	join	join	NOUN
ejpam-3812	366	18	,	,	PUNCT
ejpam-3812	366	19	corona	corona	PROPN
ejpam-3812	366	20	,	,	PUNCT
ejpam-3812	366	21	lexicographic	lexicographic	ADJ
ejpam-3812	366	22	product	product	NOUN
ejpam-3812	366	23	,	,	PUNCT
ejpam-3812	366	24	and	and	CCONJ
ejpam-3812	366	25	cartesian	cartesian	ADJ
ejpam-3812	366	26	product	product	NOUN
ejpam-3812	366	27	of	of	ADP
ejpam-3812	366	28	graphs	graph	NOUN
ejpam-3812	366	29	in	in	ADP
ejpam-3812	366	30	this	this	DET
ejpam-3812	366	31	section	section	NOUN
ejpam-3812	366	32	.	.	PUNCT
ejpam-3812	367	1	we	we	PRON
ejpam-3812	367	2	also	also	ADV
ejpam-3812	367	3	determine	determine	VERB
ejpam-3812	367	4	the	the	DET
ejpam-3812	367	5	exact	exact	ADJ
ejpam-3812	367	6	value	value	NOUN
ejpam-3812	367	7	or	or	CCONJ
ejpam-3812	367	8	sharp	sharp	ADJ
ejpam-3812	367	9	bounds	bound	NOUN
ejpam-3812	367	10	of	of	ADP
ejpam-3812	367	11	the	the	DET
ejpam-3812	367	12	corresponding	corresponding	ADJ
ejpam-3812	367	13	independent	independent	ADJ
ejpam-3812	367	14	k	k	ADJ
ejpam-3812	367	15	-	-	PUNCT
ejpam-3812	367	16	fair	fair	ADJ
ejpam-3812	367	17	domination	domination	NOUN
ejpam-3812	367	18	number	number	NOUN
ejpam-3812	367	19	.	.	PUNCT
ejpam-3812	368	1	theorem	theorem	VERB
ejpam-3812	368	2	17	17	NUM
ejpam-3812	368	3	.	.	PUNCT
ejpam-3812	369	1	let	let	VERB
ejpam-3812	369	2	g	g	NOUN
ejpam-3812	369	3	and	and	CCONJ
ejpam-3812	369	4	h	h	NOUN
ejpam-3812	369	5	be	be	AUX
ejpam-3812	369	6	nontrivial	nontrivial	ADJ
ejpam-3812	369	7	connected	connect	VERB
ejpam-3812	369	8	graphs	graph	NOUN
ejpam-3812	369	9	of	of	ADP
ejpam-3812	369	10	orders	order	NOUN
ejpam-3812	369	11	m	m	VERB
ejpam-3812	369	12	and	and	CCONJ
ejpam-3812	369	13	n	n	CCONJ
ejpam-3812	369	14	,	,	PUNCT
ejpam-3812	369	15	respectively	respectively	ADV
ejpam-3812	369	16	,	,	PUNCT
ejpam-3812	369	17	and	and	CCONJ
ejpam-3812	369	18	k	k	X
ejpam-3812	369	19	a	a	DET
ejpam-3812	369	20	positive	positive	ADJ
ejpam-3812	369	21	integer	integer	NOUN
ejpam-3812	369	22	with	with	ADP
ejpam-3812	369	23	1	1	NUM
ejpam-3812	369	24	≤	≤	NUM
ejpam-3812	369	25	k	k	PROPN
ejpam-3812	369	26	≤	≤	NUM
ejpam-3812	369	27	max{dm2	max{dm2	VERB
ejpam-3812	369	28	e	e	NOUN
ejpam-3812	369	29	,	,	PUNCT
ejpam-3812	369	30	d	d	NOUN
ejpam-3812	369	31	n	n	CCONJ
ejpam-3812	369	32	2	2	NUM
ejpam-3812	369	33	e	e	NOUN
ejpam-3812	369	34	}	}	PUNCT
ejpam-3812	369	35	.	.	PUNCT
ejpam-3812	370	1	then	then	ADV
ejpam-3812	370	2	g+h	g+h	PROPN
ejpam-3812	370	3	admits	admit	VERB
ejpam-3812	370	4	an	an	DET
ejpam-3812	370	5	independent	independent	ADJ
ejpam-3812	370	6	kfd	kfd	NOUN
ejpam-3812	370	7	-	-	PUNCT
ejpam-3812	370	8	set	set	NOUN
ejpam-3812	370	9	if	if	SCONJ
ejpam-3812	370	10	and	and	CCONJ
ejpam-3812	370	11	only	only	ADV
ejpam-3812	370	12	if	if	SCONJ
ejpam-3812	370	13	g	g	PROPN
ejpam-3812	370	14	or	or	CCONJ
ejpam-3812	370	15	h	h	PROPN
ejpam-3812	370	16	admits	admit	VERB
ejpam-3812	370	17	an	an	DET
ejpam-3812	370	18	independent	independent	ADJ
ejpam-3812	370	19	kfd	kfd	NOUN
ejpam-3812	370	20	-	-	PUNCT
ejpam-3812	370	21	set	set	NOUN
ejpam-3812	370	22	.	.	PUNCT
ejpam-3812	371	1	moreover	moreover	ADV
ejpam-3812	371	2	,	,	PUNCT
ejpam-3812	371	3	s	s	X
ejpam-3812	371	4	(	(	PUNCT
ejpam-3812	371	5	v	v	NOUN
ejpam-3812	371	6	(	(	PUNCT
ejpam-3812	371	7	g+h	g+h	PROPN
ejpam-3812	371	8	)	)	PUNCT
ejpam-3812	371	9	is	be	AUX
ejpam-3812	371	10	an	an	DET
ejpam-3812	371	11	independent	independent	ADJ
ejpam-3812	371	12	kfd	kfd	NOUN
ejpam-3812	371	13	-	-	PUNCT
ejpam-3812	371	14	set	set	NOUN
ejpam-3812	371	15	in	in	ADP
ejpam-3812	371	16	g+h	g+h	PROPN
ejpam-3812	371	17	if	if	SCONJ
ejpam-3812	371	18	and	and	CCONJ
ejpam-3812	371	19	only	only	ADV
ejpam-3812	371	20	if	if	SCONJ
ejpam-3812	371	21	one	one	NUM
ejpam-3812	371	22	of	of	ADP
ejpam-3812	371	23	the	the	DET
ejpam-3812	371	24	following	follow	VERB
ejpam-3812	371	25	holds	hold	VERB
ejpam-3812	371	26	:	:	PUNCT
ejpam-3812	371	27	(	(	PUNCT
ejpam-3812	371	28	i	i	NOUN
ejpam-3812	371	29	)	)	PUNCT
ejpam-3812	371	30	s	s	PROPN
ejpam-3812	371	31	(	(	PUNCT
ejpam-3812	371	32	v	v	NOUN
ejpam-3812	371	33	(	(	PUNCT
ejpam-3812	371	34	g	g	NOUN
ejpam-3812	371	35	)	)	PUNCT
ejpam-3812	371	36	,	,	PUNCT
ejpam-3812	371	37	|s|	|s|	PROPN
ejpam-3812	371	38	=	=	SYM
ejpam-3812	371	39	k	k	PROPN
ejpam-3812	371	40	and	and	CCONJ
ejpam-3812	371	41	s	s	PROPN
ejpam-3812	371	42	is	be	AUX
ejpam-3812	371	43	an	an	DET
ejpam-3812	371	44	independent	independent	ADJ
ejpam-3812	371	45	kfd	kfd	NOUN
ejpam-3812	371	46	-	-	PUNCT
ejpam-3812	371	47	set	set	NOUN
ejpam-3812	371	48	in	in	ADP
ejpam-3812	371	49	g.	g.	PROPN
ejpam-3812	371	50	(	(	PUNCT
ejpam-3812	371	51	ii	ii	PROPN
ejpam-3812	371	52	)	)	PUNCT
ejpam-3812	371	53	s	s	PART
ejpam-3812	371	54	(	(	PUNCT
ejpam-3812	371	55	v	v	NOUN
ejpam-3812	371	56	(	(	PUNCT
ejpam-3812	371	57	h	h	NOUN
ejpam-3812	371	58	)	)	PUNCT
ejpam-3812	371	59	,	,	PUNCT
ejpam-3812	371	60	|s|	|s|	PROPN
ejpam-3812	371	61	=	=	SYM
ejpam-3812	371	62	k	k	PROPN
ejpam-3812	371	63	and	and	CCONJ
ejpam-3812	371	64	s	s	PROPN
ejpam-3812	371	65	is	be	AUX
ejpam-3812	371	66	an	an	DET
ejpam-3812	371	67	independent	independent	ADJ
ejpam-3812	371	68	kfd	kfd	NOUN
ejpam-3812	371	69	-	-	PUNCT
ejpam-3812	371	70	set	set	NOUN
ejpam-3812	371	71	in	in	ADP
ejpam-3812	371	72	h.	h.	PROPN
ejpam-3812	371	73	proof	proof	NOUN
ejpam-3812	371	74	.	.	PUNCT
ejpam-3812	372	1	suppose	suppose	VERB
ejpam-3812	372	2	g+h	g+h	PROPN
ejpam-3812	372	3	admits	admit	VERB
ejpam-3812	372	4	an	an	DET
ejpam-3812	372	5	independent	independent	ADJ
ejpam-3812	372	6	kfd	kfd	NOUN
ejpam-3812	372	7	-	-	PUNCT
ejpam-3812	372	8	set	set	NOUN
ejpam-3812	372	9	,	,	PUNCT
ejpam-3812	372	10	where	where	SCONJ
ejpam-3812	372	11	1	1	NUM
ejpam-3812	372	12	≤	≤	NUM
ejpam-3812	372	13	k	k	PROPN
ejpam-3812	372	14	≤	≤	NUM
ejpam-3812	372	15	max{dm2	max{dm2	VERB
ejpam-3812	372	16	e	e	NOUN
ejpam-3812	372	17	,	,	PUNCT
ejpam-3812	372	18	d	d	NOUN
ejpam-3812	372	19	n	n	CCONJ
ejpam-3812	372	20	2	2	NUM
ejpam-3812	372	21	e	e	NOUN
ejpam-3812	372	22	}	}	PUNCT
ejpam-3812	372	23	.	.	PUNCT
ejpam-3812	373	1	suppose	suppose	VERB
ejpam-3812	373	2	further	far	ADV
ejpam-3812	373	3	that	that	PRON
ejpam-3812	373	4	s	s	X
ejpam-3812	373	5	(	(	PUNCT
ejpam-3812	373	6	v	v	NOUN
ejpam-3812	373	7	(	(	PUNCT
ejpam-3812	373	8	g	g	PROPN
ejpam-3812	373	9	+	+	NOUN
ejpam-3812	373	10	h	h	NOUN
ejpam-3812	373	11	)	)	PUNCT
ejpam-3812	373	12	is	be	AUX
ejpam-3812	373	13	an	an	DET
ejpam-3812	373	14	independent	independent	ADJ
ejpam-3812	373	15	kfd	kfd	NOUN
ejpam-3812	373	16	-	-	PUNCT
ejpam-3812	373	17	set	set	NOUN
ejpam-3812	373	18	in	in	ADP
ejpam-3812	373	19	g	g	PROPN
ejpam-3812	374	1	+	+	CCONJ
ejpam-3812	374	2	h.	h.	NOUN
ejpam-3812	374	3	if	if	SCONJ
ejpam-3812	374	4	there	there	PRON
ejpam-3812	374	5	exist	exist	VERB
ejpam-3812	374	6	u	u	NOUN
ejpam-3812	374	7	,	,	PUNCT
ejpam-3812	374	8	x	x	SYM
ejpam-3812	374	9	∈	∈	PROPN
ejpam-3812	374	10	s	s	VERB
ejpam-3812	374	11	such	such	ADJ
ejpam-3812	374	12	that	that	SCONJ
ejpam-3812	374	13	u	u	PROPN
ejpam-3812	374	14	∈	∈	PROPN
ejpam-3812	374	15	v	v	ADP
ejpam-3812	374	16	(	(	PUNCT
ejpam-3812	374	17	g	g	NOUN
ejpam-3812	374	18	)	)	PUNCT
ejpam-3812	374	19	and	and	CCONJ
ejpam-3812	374	20	x	x	PUNCT
ejpam-3812	374	21	∈	∈	NOUN
ejpam-3812	374	22	v	v	ADP
ejpam-3812	374	23	(	(	PUNCT
ejpam-3812	374	24	h	h	NOUN
ejpam-3812	374	25	)	)	PUNCT
ejpam-3812	374	26	,	,	PUNCT
ejpam-3812	374	27	then	then	ADV
ejpam-3812	374	28	ux	ux	PROPN
ejpam-3812	374	29	∈	∈	PROPN
ejpam-3812	374	30	e(g	e(g	PROPN
ejpam-3812	375	1	+	+	CCONJ
ejpam-3812	375	2	h	h	NOUN
ejpam-3812	375	3	)	)	PUNCT
ejpam-3812	375	4	,	,	PUNCT
ejpam-3812	375	5	contrary	contrary	ADV
ejpam-3812	375	6	to	to	ADP
ejpam-3812	375	7	the	the	DET
ejpam-3812	375	8	assumption	assumption	NOUN
ejpam-3812	375	9	that	that	SCONJ
ejpam-3812	375	10	s	s	VERB
ejpam-3812	375	11	is	be	AUX
ejpam-3812	375	12	an	an	DET
ejpam-3812	375	13	independent	independent	ADJ
ejpam-3812	375	14	set	set	NOUN
ejpam-3812	375	15	in	in	ADP
ejpam-3812	375	16	g+h	g+h	PROPN
ejpam-3812	375	17	.	.	PUNCT
ejpam-3812	376	1	hence	hence	ADV
ejpam-3812	376	2	,	,	PUNCT
ejpam-3812	376	3	either	either	CCONJ
ejpam-3812	376	4	s	s	VERB
ejpam-3812	376	5	(	(	PUNCT
ejpam-3812	376	6	v	v	NOUN
ejpam-3812	376	7	(	(	PUNCT
ejpam-3812	376	8	g	g	NOUN
ejpam-3812	376	9	)	)	PUNCT
ejpam-3812	376	10	or	or	CCONJ
ejpam-3812	376	11	s	s	X
ejpam-3812	376	12	(	(	PUNCT
ejpam-3812	376	13	v	v	NOUN
ejpam-3812	376	14	(	(	PUNCT
ejpam-3812	376	15	h	h	NOUN
ejpam-3812	376	16	)	)	PUNCT
ejpam-3812	376	17	.	.	PUNCT
ejpam-3812	376	18	assume	assume	VERB
ejpam-3812	376	19	that	that	SCONJ
ejpam-3812	376	20	s	s	VERB
ejpam-3812	376	21	(	(	PUNCT
ejpam-3812	376	22	v	v	NOUN
ejpam-3812	376	23	(	(	PUNCT
ejpam-3812	376	24	g	g	NOUN
ejpam-3812	376	25	)	)	PUNCT
ejpam-3812	376	26	.	.	PUNCT
ejpam-3812	377	1	let	let	VERB
ejpam-3812	377	2	x	x	SYM
ejpam-3812	377	3	∈	∈	PROPN
ejpam-3812	377	4	v	v	ADP
ejpam-3812	377	5	(	(	PUNCT
ejpam-3812	377	6	h	h	NOUN
ejpam-3812	377	7	)	)	PUNCT
ejpam-3812	377	8	.	.	PUNCT
ejpam-3812	378	1	then	then	ADV
ejpam-3812	378	2	|ng+h(x	|ng+h(x	NOUN
ejpam-3812	378	3	)	)	PUNCT
ejpam-3812	378	4	∩	∩	NOUN
ejpam-3812	378	5	s|	s|	NOUN
ejpam-3812	378	6	=	=	SYM
ejpam-3812	378	7	|s|	|s|	PROPN
ejpam-3812	378	8	=	=	SYM
ejpam-3812	378	9	k.	k.	PROPN
ejpam-3812	378	10	since	since	SCONJ
ejpam-3812	378	11	s	s	PROPN
ejpam-3812	378	12	is	be	AUX
ejpam-3812	378	13	a	a	DET
ejpam-3812	378	14	kfd	kfd	NOUN
ejpam-3812	378	15	-	-	PUNCT
ejpam-3812	378	16	set	set	NOUN
ejpam-3812	378	17	of	of	ADP
ejpam-3812	378	18	g	g	PROPN
ejpam-3812	378	19	+	+	CCONJ
ejpam-3812	378	20	h	h	NOUN
ejpam-3812	378	21	,	,	PUNCT
ejpam-3812	378	22	|ng(v	|ng(v	ADJ
ejpam-3812	378	23	)	)	PUNCT
ejpam-3812	378	24	∩	∩	NOUN
ejpam-3812	378	25	s|	s|	NOUN
ejpam-3812	378	26	=	=	SYM
ejpam-3812	378	27	|ng+h(v	|ng+h(v	X
ejpam-3812	378	28	)	)	PUNCT
ejpam-3812	378	29	∩	∩	NOUN
ejpam-3812	378	30	s|	s|	NOUN
ejpam-3812	378	31	=	=	SYM
ejpam-3812	378	32	k	k	NOUN
ejpam-3812	378	33	for	for	ADP
ejpam-3812	378	34	every	every	PRON
ejpam-3812	378	35	v	v	NUM
ejpam-3812	378	36	∈	∈	PROPN
ejpam-3812	378	37	v	v	NOUN
ejpam-3812	378	38	(	(	PUNCT
ejpam-3812	378	39	g	g	NOUN
ejpam-3812	378	40	)	)	PUNCT
ejpam-3812	378	41	\	\	NOUN
ejpam-3812	379	1	s.	s.	PROPN
ejpam-3812	379	2	hence	hence	ADV
ejpam-3812	379	3	,	,	PUNCT
ejpam-3812	379	4	s	s	VERB
ejpam-3812	379	5	is	be	AUX
ejpam-3812	379	6	a	a	DET
ejpam-3812	379	7	kfd	kfd	NOUN
ejpam-3812	379	8	-	-	PUNCT
ejpam-3812	379	9	set	set	NOUN
ejpam-3812	379	10	in	in	ADP
ejpam-3812	379	11	g.	g.	PROPN
ejpam-3812	379	12	since	since	SCONJ
ejpam-3812	379	13	s	s	PROPN
ejpam-3812	379	14	is	be	AUX
ejpam-3812	379	15	an	an	DET
ejpam-3812	379	16	independent	independent	ADJ
ejpam-3812	379	17	set	set	NOUN
ejpam-3812	379	18	by	by	ADP
ejpam-3812	379	19	assumption	assumption	NOUN
ejpam-3812	379	20	,	,	PUNCT
ejpam-3812	379	21	statement	statement	NOUN
ejpam-3812	379	22	(	(	PUNCT
ejpam-3812	379	23	i	i	NOUN
ejpam-3812	379	24	)	)	PUNCT
ejpam-3812	379	25	holds	hold	VERB
ejpam-3812	379	26	.	.	PUNCT
ejpam-3812	380	1	similarly	similarly	ADV
ejpam-3812	380	2	,	,	PUNCT
ejpam-3812	380	3	if	if	SCONJ
ejpam-3812	380	4	s	s	X
ejpam-3812	380	5	(	(	PUNCT
ejpam-3812	380	6	v	v	NOUN
ejpam-3812	380	7	(	(	PUNCT
ejpam-3812	380	8	h	h	NOUN
ejpam-3812	380	9	)	)	PUNCT
ejpam-3812	380	10	,	,	PUNCT
ejpam-3812	380	11	then	then	ADV
ejpam-3812	380	12	s	s	VERB
ejpam-3812	380	13	is	be	AUX
ejpam-3812	380	14	an	an	DET
ejpam-3812	380	15	independent	independent	ADJ
ejpam-3812	380	16	kfd	kfd	NOUN
ejpam-3812	380	17	-	-	PUNCT
ejpam-3812	380	18	set	set	NOUN
ejpam-3812	380	19	in	in	ADP
ejpam-3812	380	20	h	h	NOUN
ejpam-3812	380	21	,	,	PUNCT
ejpam-3812	380	22	showing	show	VERB
ejpam-3812	380	23	that	that	DET
ejpam-3812	380	24	statement	statement	NOUN
ejpam-3812	380	25	(	(	PUNCT
ejpam-3812	380	26	ii	ii	NOUN
ejpam-3812	380	27	)	)	PUNCT
ejpam-3812	380	28	holds	hold	VERB
ejpam-3812	380	29	.	.	PUNCT
ejpam-3812	381	1	therefore	therefore	ADV
ejpam-3812	381	2	,	,	PUNCT
ejpam-3812	381	3	g	g	PROPN
ejpam-3812	381	4	or	or	CCONJ
ejpam-3812	381	5	h	h	PROPN
ejpam-3812	381	6	admits	admit	VERB
ejpam-3812	381	7	an	an	DET
ejpam-3812	381	8	independent	independent	ADJ
ejpam-3812	381	9	kfd	kfd	NOUN
ejpam-3812	381	10	-	-	PUNCT
ejpam-3812	381	11	set	set	NOUN
ejpam-3812	381	12	.	.	PUNCT
ejpam-3812	382	1	conversely	conversely	ADV
ejpam-3812	382	2	,	,	PUNCT
ejpam-3812	382	3	suppose	suppose	VERB
ejpam-3812	382	4	that	that	SCONJ
ejpam-3812	382	5	statement	statement	NOUN
ejpam-3812	382	6	(	(	PUNCT
ejpam-3812	382	7	i	i	NOUN
ejpam-3812	382	8	)	)	PUNCT
ejpam-3812	382	9	or	or	CCONJ
ejpam-3812	382	10	(	(	PUNCT
ejpam-3812	382	11	ii	ii	NOUN
ejpam-3812	382	12	)	)	PUNCT
ejpam-3812	382	13	holds	hold	VERB
ejpam-3812	382	14	.	.	PUNCT
ejpam-3812	383	1	assume	assume	VERB
ejpam-3812	383	2	that	that	SCONJ
ejpam-3812	383	3	statement	statement	NOUN
ejpam-3812	383	4	(	(	PUNCT
ejpam-3812	383	5	i	i	NOUN
ejpam-3812	383	6	)	)	PUNCT
ejpam-3812	383	7	is	be	AUX
ejpam-3812	383	8	true	true	ADJ
ejpam-3812	383	9	.	.	PUNCT
ejpam-3812	384	1	then	then	ADV
ejpam-3812	384	2	|ng+h(v	|ng+h(v	X
ejpam-3812	384	3	)	)	PUNCT
ejpam-3812	384	4	∩	∩	NOUN
ejpam-3812	384	5	s|	s|	VERB
ejpam-3812	384	6	=	=	SYM
ejpam-3812	384	7	|ng(v	|ng(v	X
ejpam-3812	384	8	)	)	PUNCT
ejpam-3812	384	9	∩	∩	NOUN
ejpam-3812	384	10	s|	s|	NOUN
ejpam-3812	384	11	=	=	SYM
ejpam-3812	384	12	k	k	PROPN
ejpam-3812	384	13	for	for	ADP
ejpam-3812	384	14	each	each	PRON
ejpam-3812	384	15	v	v	NUM
ejpam-3812	384	16	∈	∈	PROPN
ejpam-3812	384	17	v	v	NOUN
ejpam-3812	384	18	(	(	PUNCT
ejpam-3812	384	19	g	g	NOUN
ejpam-3812	384	20	)	)	PUNCT
ejpam-3812	384	21	\	\	PUNCT
ejpam-3812	385	1	s.	s.	PROPN
ejpam-3812	385	2	moreover	moreover	ADV
ejpam-3812	385	3	,	,	PUNCT
ejpam-3812	385	4	|ng+h(x	|ng+h(x	NOUN
ejpam-3812	385	5	)	)	PUNCT
ejpam-3812	385	6	∩	∩	NOUN
ejpam-3812	385	7	s|	s|	NOUN
ejpam-3812	385	8	=	=	SYM
ejpam-3812	385	9	|s|	|s|	PROPN
ejpam-3812	385	10	=	=	SYM
ejpam-3812	385	11	k	k	PROPN
ejpam-3812	385	12	for	for	ADP
ejpam-3812	385	13	every	every	DET
ejpam-3812	385	14	vertex	vertex	NOUN
ejpam-3812	385	15	x	x	SYM
ejpam-3812	385	16	∈	∈	NOUN
ejpam-3812	385	17	v	v	ADP
ejpam-3812	385	18	(	(	PUNCT
ejpam-3812	385	19	h	h	NOUN
ejpam-3812	385	20	)	)	PUNCT
ejpam-3812	385	21	.	.	PUNCT
ejpam-3812	386	1	thus	thus	ADV
ejpam-3812	386	2	.	.	PUNCT
ejpam-3812	387	1	s	s	VERB
ejpam-3812	387	2	is	be	AUX
ejpam-3812	387	3	a	a	DET
ejpam-3812	387	4	kfd	kfd	NOUN
ejpam-3812	387	5	-	-	PUNCT
ejpam-3812	387	6	set	set	NOUN
ejpam-3812	387	7	in	in	ADP
ejpam-3812	387	8	g	g	PROPN
ejpam-3812	387	9	+	+	CCONJ
ejpam-3812	387	10	h.	h.	PROPN
ejpam-3812	387	11	therefore	therefore	ADV
ejpam-3812	387	12	,	,	PUNCT
ejpam-3812	387	13	s	s	X
ejpam-3812	387	14	(	(	PUNCT
ejpam-3812	387	15	v	v	NOUN
ejpam-3812	387	16	(	(	PUNCT
ejpam-3812	387	17	g	g	PROPN
ejpam-3812	387	18	+	+	NOUN
ejpam-3812	387	19	h	h	NOUN
ejpam-3812	387	20	)	)	PUNCT
ejpam-3812	387	21	is	be	AUX
ejpam-3812	387	22	an	an	DET
ejpam-3812	387	23	independent	independent	ADJ
ejpam-3812	387	24	kfd	kfd	NOUN
ejpam-3812	387	25	-	-	PUNCT
ejpam-3812	387	26	set	set	NOUN
ejpam-3812	387	27	in	in	ADP
ejpam-3812	387	28	g	g	PROPN
ejpam-3812	387	29	+	+	CCONJ
ejpam-3812	387	30	h.	h.	NOUN
ejpam-3812	387	31	the	the	DET
ejpam-3812	387	32	same	same	ADJ
ejpam-3812	387	33	conclusion	conclusion	NOUN
ejpam-3812	387	34	similarly	similarly	ADV
ejpam-3812	387	35	follows	follow	VERB
ejpam-3812	387	36	if	if	SCONJ
ejpam-3812	387	37	statement	statement	NOUN
ejpam-3812	387	38	(	(	PUNCT
ejpam-3812	387	39	ii	ii	NOUN
ejpam-3812	387	40	)	)	PUNCT
ejpam-3812	387	41	holds	hold	VERB
ejpam-3812	387	42	.	.	PUNCT
ejpam-3812	388	1	�	�	PROPN
ejpam-3812	388	2	the	the	DET
ejpam-3812	388	3	next	next	ADJ
ejpam-3812	388	4	result	result	NOUN
ejpam-3812	388	5	is	be	AUX
ejpam-3812	388	6	an	an	DET
ejpam-3812	388	7	immediate	immediate	ADJ
ejpam-3812	388	8	consequence	consequence	NOUN
ejpam-3812	388	9	of	of	ADP
ejpam-3812	388	10	theorem	theorem	ADJ
ejpam-3812	388	11	17	17	NUM
ejpam-3812	388	12	.	.	PUNCT
ejpam-3812	388	13	corollary	corollary	ADJ
ejpam-3812	388	14	13	13	NUM
ejpam-3812	388	15	.	.	PUNCT
ejpam-3812	389	1	let	let	VERB
ejpam-3812	389	2	g	g	NOUN
ejpam-3812	389	3	and	and	CCONJ
ejpam-3812	389	4	h	h	NOUN
ejpam-3812	389	5	be	be	AUX
ejpam-3812	389	6	connected	connect	VERB
ejpam-3812	389	7	nontrivial	nontrivial	ADJ
ejpam-3812	389	8	graphs	graph	NOUN
ejpam-3812	389	9	of	of	ADP
ejpam-3812	389	10	orders	order	NOUN
ejpam-3812	389	11	m	m	VERB
ejpam-3812	389	12	and	and	CCONJ
ejpam-3812	389	13	n	n	CCONJ
ejpam-3812	389	14	,	,	PUNCT
ejpam-3812	389	15	respectively	respectively	ADV
ejpam-3812	389	16	,	,	PUNCT
ejpam-3812	389	17	and	and	CCONJ
ejpam-3812	389	18	k	k	X
ejpam-3812	389	19	a	a	DET
ejpam-3812	389	20	positive	positive	ADJ
ejpam-3812	389	21	integer	integer	NOUN
ejpam-3812	389	22	with	with	ADP
ejpam-3812	389	23	1	1	NUM
ejpam-3812	389	24	≤	≤	NUM
ejpam-3812	389	25	k	k	PROPN
ejpam-3812	389	26	≤	≤	NUM
ejpam-3812	389	27	max{dm2	max{dm2	VERB
ejpam-3812	389	28	e	e	NOUN
ejpam-3812	389	29	,	,	PUNCT
ejpam-3812	389	30	d	d	NOUN
ejpam-3812	389	31	n	n	CCONJ
ejpam-3812	389	32	2	2	NUM
ejpam-3812	389	33	e	e	NOUN
ejpam-3812	389	34	}	}	PUNCT
ejpam-3812	389	35	.	.	PUNCT
ejpam-3812	390	1	if	if	SCONJ
ejpam-3812	390	2	g	g	PROPN
ejpam-3812	390	3	or	or	CCONJ
ejpam-3812	390	4	h	h	NOUN
ejpam-3812	390	5	has	have	VERB
ejpam-3812	390	6	an	an	DET
ejpam-3812	390	7	independent	independent	ADJ
ejpam-3812	390	8	kfd	kfd	NOUN
ejpam-3812	390	9	-	-	PUNCT
ejpam-3812	390	10	set	set	NOUN
ejpam-3812	390	11	s	s	NOUN
ejpam-3812	390	12	with	with	ADP
ejpam-3812	390	13	|s|	|s|	PROPN
ejpam-3812	390	14	=	=	SYM
ejpam-3812	390	15	k	k	PROPN
ejpam-3812	390	16	,	,	PUNCT
ejpam-3812	390	17	then	then	ADV
ejpam-3812	390	18	γikf	γikf	NOUN
ejpam-3812	390	19	(	(	PUNCT
ejpam-3812	390	20	g+h	g+h	PROPN
ejpam-3812	390	21	)	)	PUNCT
ejpam-3812	390	22	=	=	SYM
ejpam-3812	390	23	k.	k.	PROPN
ejpam-3812	390	24	theorem	theorem	VERB
ejpam-3812	390	25	18	18	NUM
ejpam-3812	390	26	.	.	PUNCT
ejpam-3812	391	1	let	let	VERB
ejpam-3812	391	2	g	g	NOUN
ejpam-3812	391	3	and	and	CCONJ
ejpam-3812	391	4	h	h	NOUN
ejpam-3812	391	5	be	be	AUX
ejpam-3812	391	6	nontrivial	nontrivial	ADJ
ejpam-3812	391	7	connected	connected	ADJ
ejpam-3812	391	8	graphs	graph	NOUN
ejpam-3812	391	9	,	,	PUNCT
ejpam-3812	391	10	and	and	CCONJ
ejpam-3812	391	11	let	let	VERB
ejpam-3812	391	12	k	k	PRON
ejpam-3812	391	13	be	be	AUX
ejpam-3812	391	14	a	a	DET
ejpam-3812	391	15	positive	positive	ADJ
ejpam-3812	391	16	integer	integer	NOUN
ejpam-3812	391	17	with	with	ADP
ejpam-3812	391	18	k	k	PROPN
ejpam-3812	391	19	≤	≤	PROPN
ejpam-3812	392	1	⌈	⌈	X
ejpam-3812	392	2	|v	|v	PROPN
ejpam-3812	392	3	(	(	PUNCT
ejpam-3812	392	4	h)|	h)|	NOUN
ejpam-3812	392	5	2	2	NUM
ejpam-3812	392	6	⌉	⌉	X
ejpam-3812	392	7	.	.	PUNCT
ejpam-3812	393	1	then	then	ADV
ejpam-3812	393	2	g	g	PROPN
ejpam-3812	393	3	◦	◦	PROPN
ejpam-3812	393	4	h	h	NOUN
ejpam-3812	393	5	admits	admit	VERB
ejpam-3812	393	6	an	an	DET
ejpam-3812	393	7	independent	independent	ADJ
ejpam-3812	393	8	kfd	kfd	NOUN
ejpam-3812	393	9	-	-	PUNCT
ejpam-3812	393	10	set	set	NOUN
ejpam-3812	393	11	if	if	SCONJ
ejpam-3812	394	1	and	and	CCONJ
ejpam-3812	394	2	only	only	ADV
ejpam-3812	394	3	if	if	SCONJ
ejpam-3812	394	4	h	h	NOUN
ejpam-3812	394	5	admits	admit	VERB
ejpam-3812	394	6	an	an	DET
ejpam-3812	394	7	independent	independent	ADJ
ejpam-3812	394	8	kfd	kfd	NOUN
ejpam-3812	394	9	-	-	PUNCT
ejpam-3812	394	10	set	set	NOUN
ejpam-3812	394	11	consisting	consisting	NOUN
ejpam-3812	394	12	of	of	ADP
ejpam-3812	394	13	k	k	PROPN
ejpam-3812	394	14	vertices	vertex	NOUN
ejpam-3812	394	15	.	.	PUNCT
ejpam-3812	395	1	m.	m.	PROPN
ejpam-3812	395	2	ortega	ortega	PROPN
ejpam-3812	395	3	,	,	PUNCT
ejpam-3812	395	4	r.	r.	PROPN
ejpam-3812	395	5	isla	isla	PROPN
ejpam-3812	395	6	/	/	SYM
ejpam-3812	395	7	eur	eur	PROPN
ejpam-3812	395	8	.	.	PUNCT
ejpam-3812	396	1	j.	j.	PROPN
ejpam-3812	396	2	pure	pure	PROPN
ejpam-3812	396	3	appl	appl	PROPN
ejpam-3812	396	4	.	.	PROPN
ejpam-3812	396	5	math	math	PROPN
ejpam-3812	396	6	,	,	PUNCT
ejpam-3812	396	7	13	13	NUM
ejpam-3812	396	8	(	(	PUNCT
ejpam-3812	396	9	4	4	NUM
ejpam-3812	396	10	)	)	PUNCT
ejpam-3812	396	11	(	(	PUNCT
ejpam-3812	396	12	2020	2020	NUM
ejpam-3812	396	13	)	)	PUNCT
ejpam-3812	396	14	,	,	PUNCT
ejpam-3812	396	15	779	779	NUM
ejpam-3812	396	16	-	-	SYM
ejpam-3812	396	17	793	793	NUM
ejpam-3812	396	18	790	790	NUM
ejpam-3812	396	19	proof	proof	NOUN
ejpam-3812	396	20	.	.	PUNCT
ejpam-3812	397	1	suppose	suppose	VERB
ejpam-3812	397	2	g	g	PROPN
ejpam-3812	397	3	◦	◦	PROPN
ejpam-3812	397	4	h	h	PROPN
ejpam-3812	397	5	admits	admit	VERB
ejpam-3812	397	6	an	an	DET
ejpam-3812	397	7	independent	independent	ADJ
ejpam-3812	397	8	kfd	kfd	NOUN
ejpam-3812	397	9	-	-	PUNCT
ejpam-3812	397	10	set	set	NOUN
ejpam-3812	397	11	,	,	PUNCT
ejpam-3812	397	12	where	where	SCONJ
ejpam-3812	397	13	k	k	PROPN
ejpam-3812	397	14	≤	≤	X
ejpam-3812	397	15	⌈	⌈	X
ejpam-3812	397	16	|v	|v	PROPN
ejpam-3812	397	17	(	(	PUNCT
ejpam-3812	397	18	h)|	h)|	NOUN
ejpam-3812	397	19	2	2	NUM
ejpam-3812	397	20	⌉	⌉	X
ejpam-3812	397	21	.	.	PUNCT
ejpam-3812	398	1	suppose	suppose	VERB
ejpam-3812	398	2	further	far	ADV
ejpam-3812	398	3	that	that	SCONJ
ejpam-3812	398	4	c	c	PROPN
ejpam-3812	398	5	(	(	PUNCT
ejpam-3812	398	6	v	v	NOUN
ejpam-3812	398	7	(	(	PUNCT
ejpam-3812	398	8	g	g	PROPN
ejpam-3812	398	9	◦	◦	NOUN
ejpam-3812	398	10	h	h	NOUN
ejpam-3812	398	11	)	)	PUNCT
ejpam-3812	398	12	is	be	AUX
ejpam-3812	398	13	an	an	DET
ejpam-3812	398	14	independent	independent	ADJ
ejpam-3812	398	15	kfd	kfd	NOUN
ejpam-3812	398	16	-	-	PUNCT
ejpam-3812	398	17	set	set	NOUN
ejpam-3812	398	18	in	in	ADP
ejpam-3812	398	19	g	g	PROPN
ejpam-3812	398	20	◦	◦	NOUN
ejpam-3812	398	21	h.	h.	PROPN
ejpam-3812	398	22	suppose	suppose	VERB
ejpam-3812	398	23	c	c	NOUN
ejpam-3812	398	24	∩	∩	PROPN
ejpam-3812	398	25	v	v	X
ejpam-3812	398	26	(	(	PUNCT
ejpam-3812	398	27	g	g	NOUN
ejpam-3812	398	28	)	)	PUNCT
ejpam-3812	398	29	6=	6=	ADP
ejpam-3812	398	30	∅	∅	NOUN
ejpam-3812	398	31	,	,	PUNCT
ejpam-3812	398	32	say	say	VERB
ejpam-3812	398	33	v	v	NUM
ejpam-3812	398	34	∈	∈	PROPN
ejpam-3812	398	35	c	c	X
ejpam-3812	398	36	∩v	∩v	NOUN
ejpam-3812	398	37	(	(	PUNCT
ejpam-3812	398	38	g	g	NOUN
ejpam-3812	398	39	)	)	PUNCT
ejpam-3812	398	40	.	.	PUNCT
ejpam-3812	399	1	since	since	SCONJ
ejpam-3812	399	2	c	c	PROPN
ejpam-3812	399	3	is	be	AUX
ejpam-3812	399	4	an	an	DET
ejpam-3812	399	5	independent	independent	ADJ
ejpam-3812	399	6	set	set	NOUN
ejpam-3812	399	7	,	,	PUNCT
ejpam-3812	399	8	v	v	NOUN
ejpam-3812	399	9	(	(	PUNCT
ejpam-3812	399	10	hv)∩c	hv)∩c	ADJ
ejpam-3812	399	11	=	=	NOUN
ejpam-3812	399	12	∅	∅	NOUN
ejpam-3812	399	13	and	and	CCONJ
ejpam-3812	399	14	|ng	|ng	VERB
ejpam-3812	399	15	◦	◦	NOUN
ejpam-3812	399	16	h(x)∩c|	h(x)∩c|	ADJ
ejpam-3812	399	17	=	=	NOUN
ejpam-3812	399	18	1	1	NUM
ejpam-3812	399	19	for	for	ADP
ejpam-3812	399	20	all	all	PRON
ejpam-3812	399	21	x	x	SYM
ejpam-3812	399	22	∈	∈	PROPN
ejpam-3812	399	23	v	v	ADP
ejpam-3812	399	24	(	(	PUNCT
ejpam-3812	399	25	hv	hv	PROPN
ejpam-3812	399	26	)	)	PUNCT
ejpam-3812	399	27	.	.	PUNCT
ejpam-3812	400	1	this	this	PRON
ejpam-3812	400	2	implies	imply	VERB
ejpam-3812	400	3	that	that	SCONJ
ejpam-3812	400	4	k	k	PROPN
ejpam-3812	400	5	=	=	SYM
ejpam-3812	400	6	1	1	X
ejpam-3812	400	7	.	.	PUNCT
ejpam-3812	400	8	now	now	ADV
ejpam-3812	400	9	let	let	VERB
ejpam-3812	400	10	w	w	NOUN
ejpam-3812	400	11	∈	∈	PROPN
ejpam-3812	400	12	ng(v	ng(v	PRON
ejpam-3812	400	13	)	)	PUNCT
ejpam-3812	400	14	.	.	PUNCT
ejpam-3812	401	1	then	then	ADV
ejpam-3812	401	2	w	w	PROPN
ejpam-3812	401	3	/∈	/∈	PROPN
ejpam-3812	401	4	c.	c.	NOUN
ejpam-3812	401	5	since	since	SCONJ
ejpam-3812	401	6	|ng	|ng	VERB
ejpam-3812	401	7	◦	◦	NOUN
ejpam-3812	401	8	h(w	h(w	NOUN
ejpam-3812	401	9	)	)	PUNCT
ejpam-3812	401	10	∩	∩	NOUN
ejpam-3812	401	11	c|	c|	PROPN
ejpam-3812	401	12	=	=	SYM
ejpam-3812	401	13	1	1	NUM
ejpam-3812	401	14	,	,	PUNCT
ejpam-3812	401	15	v	v	PROPN
ejpam-3812	401	16	(	(	PUNCT
ejpam-3812	401	17	hw	hw	NOUN
ejpam-3812	401	18	)	)	PUNCT
ejpam-3812	401	19	∩	∩	NOUN
ejpam-3812	401	20	c	c	NOUN
ejpam-3812	401	21	=	=	PUNCT
ejpam-3812	401	22	∅.	∅.	PRON
ejpam-3812	401	23	hence	hence	ADV
ejpam-3812	401	24	,	,	PUNCT
ejpam-3812	401	25	v	v	PROPN
ejpam-3812	401	26	(	(	PUNCT
ejpam-3812	401	27	hw	hw	NOUN
ejpam-3812	401	28	)	)	PUNCT
ejpam-3812	401	29	∩	∩	PROPN
ejpam-3812	401	30	ng	ng	PROPN
ejpam-3812	401	31	◦	◦	NOUN
ejpam-3812	401	32	h	h	NOUN
ejpam-3812	402	1	[	[	X
ejpam-3812	402	2	c	c	X
ejpam-3812	402	3	]	]	X
ejpam-3812	402	4	=	=	SYM
ejpam-3812	402	5	∅	∅	NOUN
ejpam-3812	402	6	,	,	PUNCT
ejpam-3812	402	7	a	a	DET
ejpam-3812	402	8	contradiction	contradiction	NOUN
ejpam-3812	402	9	(	(	PUNCT
ejpam-3812	402	10	since	since	SCONJ
ejpam-3812	402	11	c	c	PROPN
ejpam-3812	402	12	is	be	AUX
ejpam-3812	402	13	a	a	DET
ejpam-3812	402	14	dominating	dominating	NOUN
ejpam-3812	402	15	set	set	NOUN
ejpam-3812	402	16	)	)	PUNCT
ejpam-3812	402	17	.	.	PUNCT
ejpam-3812	403	1	thus	thus	ADV
ejpam-3812	403	2	,	,	PUNCT
ejpam-3812	403	3	c	c	PROPN
ejpam-3812	403	4	∩	∩	PROPN
ejpam-3812	403	5	v	v	X
ejpam-3812	403	6	(	(	PUNCT
ejpam-3812	403	7	g	g	NOUN
ejpam-3812	403	8	)	)	PUNCT
ejpam-3812	403	9	=	=	VERB
ejpam-3812	403	10	∅.	∅.	NOUN
ejpam-3812	403	11	then	then	ADV
ejpam-3812	403	12	by	by	ADP
ejpam-3812	403	13	theorem	theorem	NOUN
ejpam-3812	403	14	9	9	NUM
ejpam-3812	403	15	,	,	PUNCT
ejpam-3812	403	16	c	c	NOUN
ejpam-3812	403	17	=	=	PUNCT
ejpam-3812	403	18	⋃	⋃	NOUN
ejpam-3812	403	19	v∈v	v∈v	NOUN
ejpam-3812	403	20	(	(	PUNCT
ejpam-3812	403	21	g	g	NOUN
ejpam-3812	403	22	)	)	PUNCT
ejpam-3812	403	23	sv	sv	NOUN
ejpam-3812	403	24	,	,	PUNCT
ejpam-3812	403	25	where	where	SCONJ
ejpam-3812	403	26	each	each	PRON
ejpam-3812	403	27	sv	sv	PROPN
ejpam-3812	403	28	is	be	AUX
ejpam-3812	403	29	an	an	DET
ejpam-3812	403	30	independent	independent	ADJ
ejpam-3812	403	31	kfd	kfd	NOUN
ejpam-3812	403	32	-	-	PUNCT
ejpam-3812	403	33	set	set	NOUN
ejpam-3812	403	34	in	in	ADP
ejpam-3812	403	35	hv	hv	PROPN
ejpam-3812	403	36	and	and	CCONJ
ejpam-3812	403	37	|sv|	|sv|	PROPN
ejpam-3812	403	38	=	=	SYM
ejpam-3812	403	39	k	k	PROPN
ejpam-3812	403	40	for	for	ADP
ejpam-3812	403	41	each	each	DET
ejpam-3812	403	42	v	v	NUM
ejpam-3812	403	43	∈	∈	PROPN
ejpam-3812	403	44	v	v	NOUN
ejpam-3812	403	45	(	(	PUNCT
ejpam-3812	403	46	g	g	NOUN
ejpam-3812	403	47	)	)	PUNCT
ejpam-3812	403	48	.	.	PUNCT
ejpam-3812	404	1	therefore	therefore	ADV
ejpam-3812	404	2	,	,	PUNCT
ejpam-3812	404	3	h	h	PROPN
ejpam-3812	404	4	admits	admit	VERB
ejpam-3812	404	5	an	an	DET
ejpam-3812	404	6	independent	independent	ADJ
ejpam-3812	404	7	kfd	kfd	NOUN
ejpam-3812	404	8	-	-	PUNCT
ejpam-3812	404	9	set	set	NOUN
ejpam-3812	404	10	consisting	consisting	NOUN
ejpam-3812	404	11	of	of	ADP
ejpam-3812	404	12	k	k	PROPN
ejpam-3812	404	13	vertices	vertex	NOUN
ejpam-3812	404	14	.	.	PUNCT
ejpam-3812	405	1	conversely	conversely	ADV
ejpam-3812	405	2	,	,	PUNCT
ejpam-3812	405	3	suppose	suppose	VERB
ejpam-3812	405	4	h	h	NOUN
ejpam-3812	405	5	admits	admit	VERB
ejpam-3812	405	6	an	an	DET
ejpam-3812	405	7	independent	independent	ADJ
ejpam-3812	405	8	kfd	kfd	NOUN
ejpam-3812	405	9	-	-	PUNCT
ejpam-3812	405	10	set	set	NOUN
ejpam-3812	405	11	consisting	consisting	NOUN
ejpam-3812	405	12	of	of	ADP
ejpam-3812	405	13	k	k	PROPN
ejpam-3812	405	14	vertices	vertex	NOUN
ejpam-3812	405	15	.	.	PUNCT
ejpam-3812	406	1	let	let	VERB
ejpam-3812	406	2	c	c	NOUN
ejpam-3812	406	3	=	=	PUNCT
ejpam-3812	407	1	⋃	⋃	NOUN
ejpam-3812	407	2	v∈v	v∈v	NOUN
ejpam-3812	407	3	(	(	PUNCT
ejpam-3812	407	4	g	g	NOUN
ejpam-3812	407	5	)	)	PUNCT
ejpam-3812	407	6	sv	sv	NOUN
ejpam-3812	407	7	,	,	PUNCT
ejpam-3812	407	8	where	where	SCONJ
ejpam-3812	407	9	each	each	PRON
ejpam-3812	407	10	sv	sv	PROPN
ejpam-3812	407	11	is	be	AUX
ejpam-3812	407	12	an	an	DET
ejpam-3812	407	13	independent	independent	ADJ
ejpam-3812	407	14	kfd	kfd	NOUN
ejpam-3812	407	15	-	-	PUNCT
ejpam-3812	407	16	set	set	NOUN
ejpam-3812	407	17	in	in	ADP
ejpam-3812	407	18	hv	hv	PROPN
ejpam-3812	407	19	and	and	CCONJ
ejpam-3812	407	20	|sv|	|sv|	PROPN
ejpam-3812	407	21	=	=	PUNCT
ejpam-3812	407	22	k.	k.	PROPN
ejpam-3812	407	23	then	then	ADV
ejpam-3812	407	24	c	c	PROPN
ejpam-3812	407	25	is	be	AUX
ejpam-3812	407	26	an	an	DET
ejpam-3812	407	27	independent	independent	ADJ
ejpam-3812	407	28	kfd	kfd	NOUN
ejpam-3812	407	29	-	-	PUNCT
ejpam-3812	407	30	set	set	NOUN
ejpam-3812	407	31	in	in	ADP
ejpam-3812	407	32	g	g	PROPN
ejpam-3812	407	33	◦	◦	NOUN
ejpam-3812	407	34	h	h	NOUN
ejpam-3812	407	35	by	by	ADP
ejpam-3812	407	36	theorem	theorem	NOUN
ejpam-3812	407	37	9	9	NUM
ejpam-3812	407	38	.	.	PUNCT
ejpam-3812	407	39	�	�	PROPN
ejpam-3812	408	1	the	the	DET
ejpam-3812	408	2	next	next	ADJ
ejpam-3812	408	3	result	result	NOUN
ejpam-3812	408	4	is	be	AUX
ejpam-3812	408	5	an	an	DET
ejpam-3812	408	6	immediate	immediate	ADJ
ejpam-3812	408	7	consequence	consequence	NOUN
ejpam-3812	408	8	of	of	ADP
ejpam-3812	408	9	theorem	theorem	ADJ
ejpam-3812	408	10	18	18	NUM
ejpam-3812	408	11	.	.	PUNCT
ejpam-3812	408	12	corollary	corollary	ADJ
ejpam-3812	408	13	14	14	NUM
ejpam-3812	408	14	.	.	PUNCT
ejpam-3812	409	1	let	let	VERB
ejpam-3812	409	2	g	g	NOUN
ejpam-3812	409	3	and	and	CCONJ
ejpam-3812	409	4	h	h	NOUN
ejpam-3812	409	5	be	be	AUX
ejpam-3812	409	6	nontrivial	nontrivial	ADJ
ejpam-3812	409	7	connected	connect	VERB
ejpam-3812	409	8	graphs	graph	NOUN
ejpam-3812	409	9	of	of	ADP
ejpam-3812	409	10	orders	order	NOUN
ejpam-3812	409	11	m	m	VERB
ejpam-3812	409	12	and	and	CCONJ
ejpam-3812	409	13	n	n	CCONJ
ejpam-3812	409	14	,	,	PUNCT
ejpam-3812	409	15	respectively	respectively	ADV
ejpam-3812	409	16	,	,	PUNCT
ejpam-3812	409	17	and	and	CCONJ
ejpam-3812	409	18	let	let	VERB
ejpam-3812	409	19	k	k	PRON
ejpam-3812	409	20	be	be	AUX
ejpam-3812	409	21	a	a	DET
ejpam-3812	409	22	positive	positive	ADJ
ejpam-3812	409	23	integer	integer	NOUN
ejpam-3812	409	24	with	with	ADP
ejpam-3812	409	25	k	k	PROPN
ejpam-3812	409	26	≤	≤	PROPN
ejpam-3812	409	27	⌈	⌈	NUM
ejpam-3812	409	28	n	n	CCONJ
ejpam-3812	409	29	2	2	NUM
ejpam-3812	409	30	⌉	⌉	X
ejpam-3812	409	31	.	.	PUNCT
ejpam-3812	410	1	if	if	SCONJ
ejpam-3812	410	2	h	h	NOUN
ejpam-3812	410	3	has	have	VERB
ejpam-3812	410	4	an	an	DET
ejpam-3812	410	5	independent	independent	ADJ
ejpam-3812	410	6	kfd	kfd	NOUN
ejpam-3812	410	7	-	-	PUNCT
ejpam-3812	410	8	set	set	NOUN
ejpam-3812	410	9	s	s	NOUN
ejpam-3812	410	10	with	with	ADP
ejpam-3812	410	11	|s|	|s|	PROPN
ejpam-3812	410	12	=	=	SYM
ejpam-3812	410	13	k	k	PROPN
ejpam-3812	410	14	,	,	PUNCT
ejpam-3812	410	15	then	then	ADV
ejpam-3812	410	16	γikf	γikf	NOUN
ejpam-3812	410	17	(	(	PUNCT
ejpam-3812	410	18	g	g	PROPN
ejpam-3812	410	19	◦	◦	NOUN
ejpam-3812	410	20	h	h	NOUN
ejpam-3812	410	21	)	)	PUNCT
ejpam-3812	410	22	=	=	SYM
ejpam-3812	410	23	mk	mk	PROPN
ejpam-3812	410	24	.	.	PUNCT
ejpam-3812	410	25	theorem	theorem	PROPN
ejpam-3812	410	26	19	19	NUM
ejpam-3812	410	27	.	.	PUNCT
ejpam-3812	411	1	let	let	VERB
ejpam-3812	411	2	g	g	NOUN
ejpam-3812	411	3	and	and	CCONJ
ejpam-3812	411	4	h	h	NOUN
ejpam-3812	411	5	be	be	AUX
ejpam-3812	411	6	nontrivial	nontrivial	ADJ
ejpam-3812	411	7	connected	connect	VERB
ejpam-3812	411	8	graphs	graph	NOUN
ejpam-3812	411	9	and	and	CCONJ
ejpam-3812	411	10	let	let	VERB
ejpam-3812	411	11	k	k	PRON
ejpam-3812	411	12	be	be	AUX
ejpam-3812	411	13	a	a	DET
ejpam-3812	411	14	positive	positive	ADJ
ejpam-3812	411	15	integer	integer	NOUN
ejpam-3812	411	16	with	with	ADP
ejpam-3812	411	17	1	1	NUM
ejpam-3812	411	18	≤	≤	NUM
ejpam-3812	411	19	k	k	X
ejpam-3812	411	20	≤	≤	PROPN
ejpam-3812	412	1	⌈	⌈	X
ejpam-3812	412	2	|v	|v	PROPN
ejpam-3812	412	3	(	(	PUNCT
ejpam-3812	412	4	h)|	h)|	NOUN
ejpam-3812	412	5	2	2	NUM
ejpam-3812	412	6	⌉	⌉	X
ejpam-3812	412	7	.	.	PUNCT
ejpam-3812	413	1	if	if	SCONJ
ejpam-3812	413	2	g[h	g[h	PROPN
ejpam-3812	413	3	]	]	PUNCT
ejpam-3812	413	4	admits	admit	VERB
ejpam-3812	413	5	an	an	DET
ejpam-3812	413	6	independent	independent	ADJ
ejpam-3812	413	7	kfd	kfd	NOUN
ejpam-3812	413	8	-	-	PUNCT
ejpam-3812	413	9	set	set	NOUN
ejpam-3812	413	10	,	,	PUNCT
ejpam-3812	413	11	then	then	ADV
ejpam-3812	413	12	c	c	NOUN
ejpam-3812	413	13	=	=	PUNCT
ejpam-3812	413	14	⋃	⋃	PROPN
ejpam-3812	413	15	x∈s	x∈s	NOUN
ejpam-3812	413	16	(	(	PUNCT
ejpam-3812	413	17	{	{	PUNCT
ejpam-3812	413	18	x}×tx	x}×tx	NUM
ejpam-3812	413	19	)	)	PUNCT
ejpam-3812	413	20	(	(	PUNCT
ejpam-3812	413	21	v	v	X
ejpam-3812	413	22	(	(	PUNCT
ejpam-3812	413	23	g[h	g[h	PROPN
ejpam-3812	413	24	]	]	PUNCT
ejpam-3812	413	25	)	)	PUNCT
ejpam-3812	413	26	is	be	AUX
ejpam-3812	413	27	an	an	DET
ejpam-3812	413	28	independent	independent	ADJ
ejpam-3812	413	29	kfd	kfd	NOUN
ejpam-3812	413	30	-	-	PUNCT
ejpam-3812	413	31	set	set	NOUN
ejpam-3812	413	32	in	in	ADP
ejpam-3812	413	33	g[h	g[h	PROPN
ejpam-3812	413	34	]	]	PUNCT
ejpam-3812	413	35	if	if	SCONJ
ejpam-3812	413	36	and	and	CCONJ
ejpam-3812	413	37	only	only	ADV
ejpam-3812	413	38	if	if	SCONJ
ejpam-3812	413	39	the	the	DET
ejpam-3812	413	40	following	follow	VERB
ejpam-3812	413	41	hold	hold	NOUN
ejpam-3812	413	42	:	:	PUNCT
ejpam-3812	413	43	(	(	PUNCT
ejpam-3812	413	44	i	i	NOUN
ejpam-3812	413	45	)	)	PUNCT
ejpam-3812	413	46	s	s	VERB
ejpam-3812	413	47	is	be	AUX
ejpam-3812	413	48	an	an	DET
ejpam-3812	413	49	independent	independent	ADJ
ejpam-3812	413	50	1fd	1fd	NOUN
ejpam-3812	413	51	-	-	PUNCT
ejpam-3812	413	52	set	set	NOUN
ejpam-3812	413	53	in	in	ADP
ejpam-3812	413	54	g	g	PROPN
ejpam-3812	413	55	,	,	PUNCT
ejpam-3812	413	56	(	(	PUNCT
ejpam-3812	413	57	ii	ii	NOUN
ejpam-3812	413	58	)	)	PUNCT
ejpam-3812	413	59	for	for	ADP
ejpam-3812	413	60	each	each	DET
ejpam-3812	413	61	x	x	SYM
ejpam-3812	413	62	∈	∈	PROPN
ejpam-3812	413	63	s	s	NOUN
ejpam-3812	413	64	,	,	PUNCT
ejpam-3812	413	65	|tx|	|tx|	X
ejpam-3812	413	66	=	=	SYM
ejpam-3812	414	1	k	k	PROPN
ejpam-3812	414	2	and	and	CCONJ
ejpam-3812	414	3	tx	tx	PROPN
ejpam-3812	414	4	is	be	AUX
ejpam-3812	414	5	an	an	DET
ejpam-3812	414	6	independent	independent	ADJ
ejpam-3812	414	7	kfd	kfd	NOUN
ejpam-3812	414	8	-	-	PUNCT
ejpam-3812	414	9	set	set	NOUN
ejpam-3812	414	10	in	in	ADP
ejpam-3812	414	11	h.	h.	PROPN
ejpam-3812	414	12	proof	proof	NOUN
ejpam-3812	414	13	.	.	PUNCT
ejpam-3812	415	1	suppose	suppose	VERB
ejpam-3812	415	2	c	c	NOUN
ejpam-3812	415	3	=	=	SYM
ejpam-3812	415	4	⋃	⋃	PROPN
ejpam-3812	415	5	x∈s	x∈s	NOUN
ejpam-3812	415	6	(	(	PUNCT
ejpam-3812	415	7	{	{	PUNCT
ejpam-3812	415	8	x	x	NOUN
ejpam-3812	415	9	}	}	PUNCT
ejpam-3812	415	10	×	×	PROPN
ejpam-3812	415	11	tx	tx	PROPN
ejpam-3812	415	12	)	)	PUNCT
ejpam-3812	415	13	(	(	PUNCT
ejpam-3812	415	14	v	v	X
ejpam-3812	415	15	(	(	PUNCT
ejpam-3812	415	16	g[h	g[h	PROPN
ejpam-3812	415	17	]	]	PUNCT
ejpam-3812	415	18	)	)	PUNCT
ejpam-3812	415	19	is	be	AUX
ejpam-3812	415	20	an	an	DET
ejpam-3812	415	21	independent	independent	ADJ
ejpam-3812	415	22	kfd	kfd	NOUN
ejpam-3812	415	23	-	-	PUNCT
ejpam-3812	415	24	set	set	NOUN
ejpam-3812	415	25	in	in	ADP
ejpam-3812	415	26	g[h	g[h	NOUN
ejpam-3812	415	27	]	]	PUNCT
ejpam-3812	415	28	.	.	PUNCT
ejpam-3812	416	1	then	then	ADV
ejpam-3812	416	2	c	c	PROPN
ejpam-3812	416	3	is	be	AUX
ejpam-3812	416	4	a	a	DET
ejpam-3812	416	5	kfd	kfd	NOUN
ejpam-3812	416	6	-	-	PUNCT
ejpam-3812	416	7	set	set	NOUN
ejpam-3812	416	8	in	in	ADP
ejpam-3812	416	9	g[h	g[h	NOUN
ejpam-3812	416	10	]	]	PUNCT
ejpam-3812	416	11	and	and	CCONJ
ejpam-3812	416	12	by	by	ADP
ejpam-3812	416	13	theorem	theorem	NOUN
ejpam-3812	416	14	10	10	NUM
ejpam-3812	416	15	,	,	PUNCT
ejpam-3812	416	16	s	s	VERB
ejpam-3812	416	17	is	be	AUX
ejpam-3812	416	18	a	a	DET
ejpam-3812	416	19	dominating	dominating	NOUN
ejpam-3812	416	20	set	set	VERB
ejpam-3812	416	21	in	in	ADP
ejpam-3812	416	22	g.	g.	PROPN
ejpam-3812	416	23	moreover	moreover	ADV
ejpam-3812	416	24	,	,	PUNCT
ejpam-3812	416	25	since	since	SCONJ
ejpam-3812	416	26	c	c	PROPN
ejpam-3812	416	27	is	be	AUX
ejpam-3812	416	28	an	an	DET
ejpam-3812	416	29	independent	independent	ADJ
ejpam-3812	416	30	set	set	NOUN
ejpam-3812	416	31	,	,	PUNCT
ejpam-3812	416	32	s∩ng(s	s∩ng(s	NOUN
ejpam-3812	416	33	)	)	PUNCT
ejpam-3812	416	34	=	=	PUNCT
ejpam-3812	416	35	∅.	∅.	VERB
ejpam-3812	416	36	finally	finally	ADV
ejpam-3812	416	37	,	,	PUNCT
ejpam-3812	416	38	from	from	ADP
ejpam-3812	416	39	statement	statement	NOUN
ejpam-3812	416	40	(	(	PUNCT
ejpam-3812	416	41	iv	iv	NOUN
ejpam-3812	416	42	)	)	PUNCT
ejpam-3812	416	43	of	of	ADP
ejpam-3812	416	44	theorem	theorem	ADJ
ejpam-3812	416	45	10	10	NUM
ejpam-3812	416	46	,	,	PUNCT
ejpam-3812	416	47	for	for	ADP
ejpam-3812	416	48	each	each	DET
ejpam-3812	416	49	y	y	PROPN
ejpam-3812	416	50	∈	∈	PROPN
ejpam-3812	416	51	v	v	NOUN
ejpam-3812	416	52	(	(	PUNCT
ejpam-3812	416	53	g)\s	g)\s	NOUN
ejpam-3812	416	54	,	,	PUNCT
ejpam-3812	416	55	∑	∑	PUNCT
ejpam-3812	416	56	v∈ng(y)∩s	v∈ng(y)∩s	ADJ
ejpam-3812	416	57	|tv|	|tv|	PROPN
ejpam-3812	416	58	=	=	SYM
ejpam-3812	416	59	k	k	NOUN
ejpam-3812	416	60	,	,	PUNCT
ejpam-3812	416	61	hence	hence	ADV
ejpam-3812	416	62	|ng(y)∩s|	|ng(y)∩s|	X
ejpam-3812	416	63	=	=	SYM
ejpam-3812	416	64	1	1	X
ejpam-3812	416	65	.	.	PUNCT
ejpam-3812	417	1	thus	thus	ADV
ejpam-3812	417	2	,	,	PUNCT
ejpam-3812	417	3	s	s	VERB
ejpam-3812	417	4	is	be	AUX
ejpam-3812	417	5	an	an	DET
ejpam-3812	417	6	independent	independent	ADJ
ejpam-3812	417	7	1fd	1fd	NOUN
ejpam-3812	417	8	-	-	PUNCT
ejpam-3812	417	9	set	set	VERB
ejpam-3812	417	10	in	in	ADP
ejpam-3812	417	11	g	g	NOUN
ejpam-3812	417	12	and	and	CCONJ
ejpam-3812	417	13	statement	statement	NOUN
ejpam-3812	417	14	(	(	PUNCT
ejpam-3812	417	15	i	i	NOUN
ejpam-3812	417	16	)	)	PUNCT
ejpam-3812	417	17	holds	hold	VERB
ejpam-3812	417	18	.	.	PUNCT
ejpam-3812	418	1	furthermore	furthermore	ADV
ejpam-3812	418	2	,	,	PUNCT
ejpam-3812	418	3	for	for	ADP
ejpam-3812	418	4	each	each	DET
ejpam-3812	418	5	x	x	SYM
ejpam-3812	418	6	∈	∈	PROPN
ejpam-3812	418	7	(	(	PUNCT
ejpam-3812	418	8	s\ng(s	s\ng(s	NOUN
ejpam-3812	418	9	)	)	PUNCT
ejpam-3812	418	10	)	)	PUNCT
ejpam-3812	418	11	=	=	SYM
ejpam-3812	418	12	s	s	X
ejpam-3812	418	13	,	,	PUNCT
ejpam-3812	418	14	|tx|	|tx|	X
ejpam-3812	418	15	=	=	SYM
ejpam-3812	418	16	k	k	PROPN
ejpam-3812	418	17	and	and	CCONJ
ejpam-3812	418	18	tx	tx	PROPN
ejpam-3812	418	19	is	be	AUX
ejpam-3812	418	20	a	a	DET
ejpam-3812	418	21	kfd	kfd	NOUN
ejpam-3812	418	22	-	-	PUNCT
ejpam-3812	418	23	set	set	NOUN
ejpam-3812	418	24	in	in	ADP
ejpam-3812	418	25	h	h	NOUN
ejpam-3812	418	26	by	by	ADP
ejpam-3812	418	27	statement	statement	NOUN
ejpam-3812	418	28	(	(	PUNCT
ejpam-3812	418	29	iii	iii	NOUN
ejpam-3812	418	30	)	)	PUNCT
ejpam-3812	418	31	of	of	ADP
ejpam-3812	418	32	theorem	theorem	ADJ
ejpam-3812	418	33	10	10	NUM
ejpam-3812	418	34	,	,	PUNCT
ejpam-3812	418	35	where	where	SCONJ
ejpam-3812	418	36	k	k	PROPN
ejpam-3812	418	37	≤	≤	X
ejpam-3812	418	38	⌈	⌈	X
ejpam-3812	418	39	|v	|v	PROPN
ejpam-3812	418	40	(	(	PUNCT
ejpam-3812	418	41	h)|	h)|	NOUN
ejpam-3812	418	42	2	2	NUM
ejpam-3812	418	43	⌉	⌉	PUNCT
ejpam-3812	418	44	since	since	SCONJ
ejpam-3812	418	45	c	c	PROPN
ejpam-3812	418	46	is	be	AUX
ejpam-3812	418	47	an	an	DET
ejpam-3812	418	48	independent	independent	ADJ
ejpam-3812	418	49	set	set	NOUN
ejpam-3812	418	50	.	.	PUNCT
ejpam-3812	419	1	suppose	suppose	VERB
ejpam-3812	419	2	there	there	PRON
ejpam-3812	419	3	is	be	VERB
ejpam-3812	419	4	a	a	DET
ejpam-3812	419	5	vertex	vertex	NOUN
ejpam-3812	419	6	a	a	DET
ejpam-3812	419	7	∈	∈	PROPN
ejpam-3812	419	8	tx	tx	PROPN
ejpam-3812	419	9	which	which	PRON
ejpam-3812	419	10	is	be	AUX
ejpam-3812	419	11	adjacent	adjacent	ADJ
ejpam-3812	419	12	to	to	ADP
ejpam-3812	419	13	a	a	DET
ejpam-3812	419	14	vertex	vertex	NOUN
ejpam-3812	419	15	b	b	PROPN
ejpam-3812	419	16	∈	∈	PROPN
ejpam-3812	419	17	tx	tx	PROPN
ejpam-3812	419	18	.	.	PUNCT
ejpam-3812	420	1	then	then	ADV
ejpam-3812	420	2	(	(	PUNCT
ejpam-3812	420	3	x	x	X
ejpam-3812	420	4	,	,	PUNCT
ejpam-3812	420	5	a	a	PRON
ejpam-3812	420	6	)	)	PUNCT
ejpam-3812	420	7	is	be	AUX
ejpam-3812	420	8	adjacent	adjacent	ADJ
ejpam-3812	420	9	to	to	ADP
ejpam-3812	420	10	(	(	PUNCT
ejpam-3812	420	11	x	x	NOUN
ejpam-3812	420	12	,	,	PUNCT
ejpam-3812	420	13	b	b	NOUN
ejpam-3812	420	14	)	)	PUNCT
ejpam-3812	420	15	in	in	ADP
ejpam-3812	420	16	c	c	PROPN
ejpam-3812	420	17	,	,	PUNCT
ejpam-3812	420	18	contrary	contrary	ADJ
ejpam-3812	420	19	to	to	ADP
ejpam-3812	420	20	assumption	assumption	NOUN
ejpam-3812	420	21	.	.	PUNCT
ejpam-3812	421	1	hence	hence	ADV
ejpam-3812	421	2	,	,	PUNCT
ejpam-3812	421	3	tx	tx	PROPN
ejpam-3812	421	4	is	be	AUX
ejpam-3812	421	5	an	an	DET
ejpam-3812	421	6	independent	independent	ADJ
ejpam-3812	421	7	kfd	kfd	NOUN
ejpam-3812	421	8	-	-	PUNCT
ejpam-3812	421	9	set	set	NOUN
ejpam-3812	421	10	in	in	ADP
ejpam-3812	421	11	h	h	NOUN
ejpam-3812	421	12	and	and	CCONJ
ejpam-3812	421	13	statement	statement	NOUN
ejpam-3812	421	14	(	(	PUNCT
ejpam-3812	421	15	ii	ii	NOUN
ejpam-3812	421	16	)	)	PUNCT
ejpam-3812	421	17	holds	hold	VERB
ejpam-3812	421	18	.	.	PUNCT
ejpam-3812	422	1	conversely	conversely	ADV
ejpam-3812	422	2	,	,	PUNCT
ejpam-3812	422	3	suppose	suppose	VERB
ejpam-3812	422	4	statements	statement	NOUN
ejpam-3812	422	5	(	(	PUNCT
ejpam-3812	422	6	i	i	NOUN
ejpam-3812	422	7	)	)	PUNCT
ejpam-3812	422	8	and	and	CCONJ
ejpam-3812	422	9	(	(	PUNCT
ejpam-3812	422	10	ii	ii	NOUN
ejpam-3812	422	11	)	)	PUNCT
ejpam-3812	422	12	hold	hold	NOUN
ejpam-3812	422	13	.	.	PUNCT
ejpam-3812	423	1	then	then	ADV
ejpam-3812	423	2	tx	tx	PROPN
ejpam-3812	423	3	is	be	AUX
ejpam-3812	423	4	a	a	DET
ejpam-3812	423	5	kfd	kfd	NOUN
ejpam-3812	423	6	-	-	PUNCT
ejpam-3812	423	7	set	set	NOUN
ejpam-3812	423	8	in	in	ADP
ejpam-3812	423	9	h	h	NOUN
ejpam-3812	423	10	for	for	ADP
ejpam-3812	423	11	each	each	DET
ejpam-3812	423	12	x	x	SYM
ejpam-3812	423	13	∈	∈	PROPN
ejpam-3812	423	14	s	s	NOUN
ejpam-3812	423	15	,	,	PUNCT
ejpam-3812	423	16	and	and	CCONJ
ejpam-3812	423	17	∑	∑	ADP
ejpam-3812	423	18	v∈ng(y)∩s	v∈ng(y)∩s	PROPN
ejpam-3812	423	19	|tv|	|tv|	PROPN
ejpam-3812	423	20	=	=	PUNCT
ejpam-3812	423	21	k	k	PROPN
ejpam-3812	423	22	for	for	ADP
ejpam-3812	423	23	each	each	DET
ejpam-3812	423	24	y	y	PROPN
ejpam-3812	423	25	∈	∈	PROPN
ejpam-3812	423	26	v	v	NOUN
ejpam-3812	423	27	(	(	PUNCT
ejpam-3812	423	28	g)\s	g)\s	NOUN
ejpam-3812	423	29	.	.	PUNCT
ejpam-3812	424	1	thus	thus	ADV
ejpam-3812	424	2	,	,	PUNCT
ejpam-3812	424	3	c	c	PROPN
ejpam-3812	424	4	is	be	AUX
ejpam-3812	424	5	a	a	DET
ejpam-3812	424	6	kfd	kfd	NOUN
ejpam-3812	424	7	-	-	PUNCT
ejpam-3812	424	8	set	set	NOUN
ejpam-3812	424	9	in	in	ADP
ejpam-3812	424	10	g[h	g[h	NOUN
ejpam-3812	424	11	]	]	PUNCT
ejpam-3812	424	12	by	by	ADP
ejpam-3812	424	13	theorem	theorem	NOUN
ejpam-3812	424	14	10	10	NUM
ejpam-3812	424	15	.	.	PUNCT
ejpam-3812	425	1	let	let	VERB
ejpam-3812	425	2	(	(	PUNCT
ejpam-3812	425	3	x	x	NOUN
ejpam-3812	425	4	,	,	PUNCT
ejpam-3812	425	5	a	a	DET
ejpam-3812	425	6	)	)	PUNCT
ejpam-3812	425	7	∈	∈	PROPN
ejpam-3812	425	8	c.	c.	NOUN
ejpam-3812	425	9	then	then	ADV
ejpam-3812	425	10	x	x	SYM
ejpam-3812	425	11	∈	∈	PROPN
ejpam-3812	425	12	s	s	X
ejpam-3812	425	13	and	and	CCONJ
ejpam-3812	425	14	a	a	DET
ejpam-3812	425	15	∈	∈	PROPN
ejpam-3812	425	16	tx	tx	PROPN
ejpam-3812	425	17	.	.	PUNCT
ejpam-3812	426	1	suppose	suppose	VERB
ejpam-3812	426	2	there	there	PRON
ejpam-3812	426	3	exists	exist	VERB
ejpam-3812	426	4	(	(	PUNCT
ejpam-3812	426	5	x	x	X
ejpam-3812	426	6	,	,	PUNCT
ejpam-3812	426	7	b	b	NOUN
ejpam-3812	426	8	)	)	PUNCT
ejpam-3812	426	9	∈	∈	PROPN
ejpam-3812	426	10	c	c	NOUN
ejpam-3812	426	11	such	such	ADJ
ejpam-3812	426	12	that	that	PRON
ejpam-3812	426	13	(	(	PUNCT
ejpam-3812	426	14	x	x	NOUN
ejpam-3812	426	15	,	,	PUNCT
ejpam-3812	426	16	a)(x	a)(x	PROPN
ejpam-3812	426	17	,	,	PUNCT
ejpam-3812	426	18	b	b	X
ejpam-3812	426	19	)	)	PUNCT
ejpam-3812	426	20	∈	∈	NOUN
ejpam-3812	426	21	e(g[h	e(g[h	NOUN
ejpam-3812	426	22	]	]	PUNCT
ejpam-3812	426	23	)	)	PUNCT
ejpam-3812	426	24	.	.	PUNCT
ejpam-3812	427	1	then	then	ADV
ejpam-3812	427	2	b	b	X
ejpam-3812	427	3	∈	∈	PROPN
ejpam-3812	427	4	tx	tx	PROPN
ejpam-3812	427	5	and	and	CCONJ
ejpam-3812	427	6	ab	ab	PROPN
ejpam-3812	427	7	∈	∈	PROPN
ejpam-3812	427	8	e(h	e(h	PROPN
ejpam-3812	427	9	)	)	PUNCT
ejpam-3812	427	10	,	,	PUNCT
ejpam-3812	427	11	contrary	contrary	ADV
ejpam-3812	427	12	to	to	ADP
ejpam-3812	427	13	statement	statement	NOUN
ejpam-3812	427	14	(	(	PUNCT
ejpam-3812	427	15	ii	ii	NOUN
ejpam-3812	427	16	)	)	PUNCT
ejpam-3812	427	17	that	that	PRON
ejpam-3812	427	18	m.	m.	PROPN
ejpam-3812	427	19	ortega	ortega	PROPN
ejpam-3812	427	20	,	,	PUNCT
ejpam-3812	427	21	r.	r.	PROPN
ejpam-3812	427	22	isla	isla	PROPN
ejpam-3812	427	23	/	/	SYM
ejpam-3812	427	24	eur	eur	PROPN
ejpam-3812	427	25	.	.	PUNCT
ejpam-3812	428	1	j.	j.	PROPN
ejpam-3812	428	2	pure	pure	PROPN
ejpam-3812	428	3	appl	appl	PROPN
ejpam-3812	428	4	.	.	PROPN
ejpam-3812	428	5	math	math	PROPN
ejpam-3812	428	6	,	,	PUNCT
ejpam-3812	428	7	13	13	NUM
ejpam-3812	428	8	(	(	PUNCT
ejpam-3812	428	9	4	4	NUM
ejpam-3812	428	10	)	)	PUNCT
ejpam-3812	428	11	(	(	PUNCT
ejpam-3812	428	12	2020	2020	NUM
ejpam-3812	428	13	)	)	PUNCT
ejpam-3812	428	14	,	,	PUNCT
ejpam-3812	428	15	779	779	NUM
ejpam-3812	428	16	-	-	SYM
ejpam-3812	428	17	793	793	NUM
ejpam-3812	428	18	791	791	NUM
ejpam-3812	428	19	tx	tx	NOUN
ejpam-3812	428	20	is	be	AUX
ejpam-3812	428	21	an	an	DET
ejpam-3812	428	22	independent	independent	ADJ
ejpam-3812	428	23	set	set	NOUN
ejpam-3812	428	24	.	.	PUNCT
ejpam-3812	429	1	hence	hence	ADV
ejpam-3812	429	2	,	,	PUNCT
ejpam-3812	429	3	(	(	PUNCT
ejpam-3812	429	4	x	x	X
ejpam-3812	429	5	,	,	PUNCT
ejpam-3812	429	6	a	a	PRON
ejpam-3812	429	7	)	)	PUNCT
ejpam-3812	429	8	is	be	AUX
ejpam-3812	429	9	not	not	PART
ejpam-3812	429	10	adjacent	adjacent	ADJ
ejpam-3812	429	11	to	to	ADP
ejpam-3812	429	12	any	any	DET
ejpam-3812	429	13	(	(	PUNCT
ejpam-3812	429	14	x	x	NOUN
ejpam-3812	429	15	,	,	PUNCT
ejpam-3812	429	16	b	b	NOUN
ejpam-3812	429	17	)	)	PUNCT
ejpam-3812	429	18	∈	∈	PROPN
ejpam-3812	429	19	c.	c.	NOUN
ejpam-3812	429	20	next	next	ADV
ejpam-3812	429	21	,	,	PUNCT
ejpam-3812	429	22	suppose	suppose	VERB
ejpam-3812	429	23	there	there	PRON
ejpam-3812	429	24	exists	exist	VERB
ejpam-3812	429	25	(	(	PUNCT
ejpam-3812	429	26	y	y	NOUN
ejpam-3812	429	27	,	,	PUNCT
ejpam-3812	429	28	d	d	NOUN
ejpam-3812	429	29	)	)	PUNCT
ejpam-3812	429	30	∈	∈	PROPN
ejpam-3812	429	31	c	c	X
ejpam-3812	429	32	,	,	PUNCT
ejpam-3812	429	33	y	y	PROPN
ejpam-3812	429	34	6=	6=	PROPN
ejpam-3812	429	35	x	x	PROPN
ejpam-3812	429	36	,	,	PUNCT
ejpam-3812	429	37	such	such	ADJ
ejpam-3812	429	38	that	that	SCONJ
ejpam-3812	429	39	(	(	PUNCT
ejpam-3812	429	40	x	x	NOUN
ejpam-3812	429	41	,	,	PUNCT
ejpam-3812	429	42	a)(y	a)(y	PROPN
ejpam-3812	429	43	,	,	PUNCT
ejpam-3812	429	44	d	d	X
ejpam-3812	429	45	)	)	PUNCT
ejpam-3812	429	46	∈	∈	NOUN
ejpam-3812	429	47	e(g[h	e(g[h	NOUN
ejpam-3812	429	48	]	]	PUNCT
ejpam-3812	429	49	)	)	PUNCT
ejpam-3812	429	50	.	.	PUNCT
ejpam-3812	430	1	then	then	ADV
ejpam-3812	430	2	y	y	PROPN
ejpam-3812	430	3	∈	∈	PROPN
ejpam-3812	430	4	ng(x	ng(x	NUM
ejpam-3812	430	5	)	)	PUNCT
ejpam-3812	430	6	∩	∩	PROPN
ejpam-3812	430	7	s	s	SYM
ejpam-3812	430	8	,	,	PUNCT
ejpam-3812	430	9	contrary	contrary	ADJ
ejpam-3812	430	10	to	to	ADP
ejpam-3812	430	11	the	the	DET
ejpam-3812	430	12	fact	fact	NOUN
ejpam-3812	430	13	that	that	SCONJ
ejpam-3812	430	14	s	s	VERB
ejpam-3812	430	15	∩ng(s	∩ng(s	NOUN
ejpam-3812	430	16	)	)	PUNCT
ejpam-3812	430	17	=	=	PUNCT
ejpam-3812	430	18	∅.	∅.	VERB
ejpam-3812	430	19	hence	hence	ADV
ejpam-3812	430	20	,	,	PUNCT
ejpam-3812	430	21	(	(	PUNCT
ejpam-3812	430	22	x	x	X
ejpam-3812	430	23	,	,	PUNCT
ejpam-3812	430	24	a	a	PRON
ejpam-3812	430	25	)	)	PUNCT
ejpam-3812	430	26	is	be	AUX
ejpam-3812	430	27	not	not	PART
ejpam-3812	430	28	adjacent	adjacent	ADJ
ejpam-3812	430	29	to	to	ADP
ejpam-3812	430	30	any	any	DET
ejpam-3812	430	31	(	(	PUNCT
ejpam-3812	430	32	y	y	PROPN
ejpam-3812	430	33	,	,	PUNCT
ejpam-3812	430	34	d	d	NOUN
ejpam-3812	430	35	)	)	PUNCT
ejpam-3812	430	36	∈	∈	PROPN
ejpam-3812	430	37	c.	c.	NOUN
ejpam-3812	430	38	therefore	therefore	ADV
ejpam-3812	430	39	,	,	PUNCT
ejpam-3812	430	40	c	c	PROPN
ejpam-3812	430	41	is	be	AUX
ejpam-3812	430	42	an	an	DET
ejpam-3812	430	43	independent	independent	ADJ
ejpam-3812	430	44	kfd	kfd	NOUN
ejpam-3812	430	45	-	-	PUNCT
ejpam-3812	430	46	set	set	NOUN
ejpam-3812	430	47	in	in	ADP
ejpam-3812	430	48	g[h	g[h	PROPN
ejpam-3812	430	49	]	]	PUNCT
ejpam-3812	430	50	.	.	PUNCT
ejpam-3812	431	1	�	�	PROPN
ejpam-3812	431	2	corollary	corollary	ADJ
ejpam-3812	431	3	15	15	NUM
ejpam-3812	431	4	.	.	PUNCT
ejpam-3812	432	1	let	let	VERB
ejpam-3812	432	2	g	g	NOUN
ejpam-3812	432	3	and	and	CCONJ
ejpam-3812	432	4	h	h	NOUN
ejpam-3812	432	5	be	be	AUX
ejpam-3812	432	6	nontrivial	nontrivial	ADJ
ejpam-3812	432	7	connected	connect	VERB
ejpam-3812	432	8	graphs	graph	NOUN
ejpam-3812	432	9	with	with	ADP
ejpam-3812	432	10	γikf	γikf	NOUN
ejpam-3812	432	11	(	(	PUNCT
ejpam-3812	432	12	h	h	NOUN
ejpam-3812	432	13	)	)	PUNCT
ejpam-3812	432	14	=	=	SYM
ejpam-3812	433	1	k	k	SYM
ejpam-3812	433	2	≤	≤	PROPN
ejpam-3812	433	3	⌈	⌈	X
ejpam-3812	433	4	|v	|v	PROPN
ejpam-3812	433	5	(	(	PUNCT
ejpam-3812	433	6	h)|	h)|	NOUN
ejpam-3812	433	7	2	2	NUM
ejpam-3812	433	8	⌉	⌉	X
ejpam-3812	433	9	.	.	PUNCT
ejpam-3812	434	1	if	if	SCONJ
ejpam-3812	434	2	g[h	g[h	PROPN
ejpam-3812	434	3	]	]	PUNCT
ejpam-3812	434	4	admits	admit	VERB
ejpam-3812	434	5	an	an	DET
ejpam-3812	434	6	independent	independent	ADJ
ejpam-3812	434	7	kfd	kfd	NOUN
ejpam-3812	434	8	-	-	PUNCT
ejpam-3812	434	9	set	set	NOUN
ejpam-3812	434	10	,	,	PUNCT
ejpam-3812	434	11	then	then	ADV
ejpam-3812	434	12	γikf	γikf	NOUN
ejpam-3812	434	13	(	(	PUNCT
ejpam-3812	434	14	g[h	g[h	PROPN
ejpam-3812	434	15	]	]	PUNCT
ejpam-3812	434	16	)	)	PUNCT
ejpam-3812	435	1	=	=	SYM
ejpam-3812	435	2	k	k	X
ejpam-3812	435	3	·	·	PUNCT
ejpam-3812	435	4	γi1f	γi1f	X
ejpam-3812	435	5	(	(	PUNCT
ejpam-3812	435	6	g	g	NOUN
ejpam-3812	435	7	)	)	PUNCT
ejpam-3812	435	8	.	.	PUNCT
ejpam-3812	436	1	proof	proof	NOUN
ejpam-3812	436	2	.	.	PUNCT
ejpam-3812	437	1	let	let	VERB
ejpam-3812	437	2	s	s	PRON
ejpam-3812	437	3	be	be	AUX
ejpam-3812	437	4	a	a	DET
ejpam-3812	437	5	γi1f	γi1f	PROPN
ejpam-3812	437	6	-set	-set	PUNCT
ejpam-3812	437	7	of	of	ADP
ejpam-3812	437	8	g	g	NOUN
ejpam-3812	437	9	and	and	CCONJ
ejpam-3812	437	10	let	let	VERB
ejpam-3812	437	11	{	{	PUNCT
ejpam-3812	437	12	a1	a1	VERB
ejpam-3812	437	13	,	,	PUNCT
ejpam-3812	437	14	...	...	PUNCT
ejpam-3812	437	15	,	,	PUNCT
ejpam-3812	437	16	ak	ak	AUX
ejpam-3812	437	17	}	}	PUNCT
ejpam-3812	437	18	be	be	AUX
ejpam-3812	437	19	a	a	DET
ejpam-3812	437	20	γikf	γikf	NOUN
ejpam-3812	437	21	-set	-set	PUNCT
ejpam-3812	437	22	of	of	ADP
ejpam-3812	437	23	h.	h.	PROPN
ejpam-3812	437	24	let	let	VERB
ejpam-3812	437	25	tx	tx	VERB
ejpam-3812	437	26	=	=	PUNCT
ejpam-3812	437	27	{	{	PUNCT
ejpam-3812	437	28	a1	a1	PROPN
ejpam-3812	437	29	,	,	PUNCT
ejpam-3812	437	30	...	...	PUNCT
ejpam-3812	437	31	,	,	PUNCT
ejpam-3812	437	32	ak	ak	PROPN
ejpam-3812	437	33	}	}	PUNCT
ejpam-3812	437	34	for	for	ADP
ejpam-3812	437	35	each	each	DET
ejpam-3812	437	36	x	x	SYM
ejpam-3812	437	37	∈	∈	PROPN
ejpam-3812	437	38	s.	s.	PROPN
ejpam-3812	437	39	then	then	ADV
ejpam-3812	437	40	c	c	PROPN
ejpam-3812	437	41	=	=	PUNCT
ejpam-3812	438	1	⋃	⋃	PROPN
ejpam-3812	438	2	x∈s	x∈s	NOUN
ejpam-3812	438	3	(	(	PUNCT
ejpam-3812	438	4	{	{	PUNCT
ejpam-3812	438	5	x	x	NOUN
ejpam-3812	438	6	}	}	PUNCT
ejpam-3812	438	7	×	×	PROPN
ejpam-3812	438	8	tx	tx	PROPN
ejpam-3812	438	9	)	)	PUNCT
ejpam-3812	438	10	is	be	AUX
ejpam-3812	438	11	an	an	DET
ejpam-3812	438	12	independent	independent	ADJ
ejpam-3812	438	13	kfd	kfd	NOUN
ejpam-3812	438	14	-	-	PUNCT
ejpam-3812	438	15	set	set	NOUN
ejpam-3812	438	16	in	in	ADP
ejpam-3812	438	17	g[h	g[h	NOUN
ejpam-3812	438	18	]	]	PUNCT
ejpam-3812	438	19	by	by	ADP
ejpam-3812	438	20	theorem	theorem	NOUN
ejpam-3812	438	21	19	19	NUM
ejpam-3812	438	22	.	.	PUNCT
ejpam-3812	439	1	hence	hence	ADV
ejpam-3812	439	2	,	,	PUNCT
ejpam-3812	439	3	γikf	γikf	NOUN
ejpam-3812	439	4	(	(	PUNCT
ejpam-3812	439	5	g[h	g[h	PROPN
ejpam-3812	439	6	]	]	PUNCT
ejpam-3812	439	7	)	)	PUNCT
ejpam-3812	439	8	≤	≤	NOUN
ejpam-3812	439	9	|c|	|c|	PROPN
ejpam-3812	439	10	=	=	SYM
ejpam-3812	439	11	k	k	X
ejpam-3812	439	12	·	·	PUNCT
ejpam-3812	439	13	γi1f	γi1f	X
ejpam-3812	439	14	(	(	PUNCT
ejpam-3812	439	15	g	g	NOUN
ejpam-3812	439	16	)	)	PUNCT
ejpam-3812	439	17	.	.	PUNCT
ejpam-3812	440	1	now	now	ADV
ejpam-3812	440	2	,	,	PUNCT
ejpam-3812	440	3	let	let	VERB
ejpam-3812	440	4	c0	c0	NOUN
ejpam-3812	440	5	be	be	AUX
ejpam-3812	440	6	a	a	DET
ejpam-3812	440	7	γikf	γikf	NOUN
ejpam-3812	440	8	-set	-set	ADJ
ejpam-3812	440	9	of	of	ADP
ejpam-3812	440	10	g[h	g[h	NOUN
ejpam-3812	440	11	]	]	PUNCT
ejpam-3812	440	12	.	.	PUNCT
ejpam-3812	441	1	by	by	ADP
ejpam-3812	441	2	theorem	theorem	NOUN
ejpam-3812	441	3	19	19	NUM
ejpam-3812	441	4	,	,	PUNCT
ejpam-3812	441	5	c0	c0	NOUN
ejpam-3812	441	6	=	=	PUNCT
ejpam-3812	442	1	⋃	⋃	PROPN
ejpam-3812	442	2	x∈s0	x∈s0	NOUN
ejpam-3812	443	1	[	[	X
ejpam-3812	443	2	{	{	PUNCT
ejpam-3812	443	3	x}×qx	x}×qx	X
ejpam-3812	443	4	]	]	X
ejpam-3812	443	5	,	,	PUNCT
ejpam-3812	443	6	where	where	SCONJ
ejpam-3812	443	7	s0	s0	PROPN
ejpam-3812	443	8	is	be	AUX
ejpam-3812	443	9	an	an	DET
ejpam-3812	443	10	independent	independent	ADJ
ejpam-3812	443	11	1fd	1fd	NOUN
ejpam-3812	443	12	-	-	PUNCT
ejpam-3812	443	13	set	set	VERB
ejpam-3812	443	14	and	and	CCONJ
ejpam-3812	443	15	qx	qx	PROPN
ejpam-3812	443	16	is	be	AUX
ejpam-3812	443	17	an	an	DET
ejpam-3812	443	18	independent	independent	ADJ
ejpam-3812	443	19	kfd	kfd	NOUN
ejpam-3812	443	20	-	-	PUNCT
ejpam-3812	443	21	set	set	NOUN
ejpam-3812	443	22	of	of	ADP
ejpam-3812	443	23	h	h	NOUN
ejpam-3812	443	24	with	with	ADP
ejpam-3812	443	25	|qx|	|qx|	PROPN
ejpam-3812	443	26	=	=	SYM
ejpam-3812	443	27	k	k	PROPN
ejpam-3812	443	28	for	for	ADP
ejpam-3812	443	29	each	each	DET
ejpam-3812	443	30	x	x	SYM
ejpam-3812	443	31	∈	∈	PROPN
ejpam-3812	443	32	s0	s0	PROPN
ejpam-3812	443	33	.	.	PUNCT
ejpam-3812	444	1	hence	hence	ADV
ejpam-3812	444	2	,	,	PUNCT
ejpam-3812	444	3	γikf	γikf	NOUN
ejpam-3812	444	4	(	(	PUNCT
ejpam-3812	444	5	g[h	g[h	PROPN
ejpam-3812	444	6	]	]	PUNCT
ejpam-3812	444	7	)	)	PUNCT
ejpam-3812	444	8	=	=	SYM
ejpam-3812	444	9	|c0|	|c0|	NOUN
ejpam-3812	444	10	=	=	SYM
ejpam-3812	444	11	k|s0|	k|s0|	INTJ
ejpam-3812	444	12	≥	≥	NOUN
ejpam-3812	444	13	k	k	X
ejpam-3812	444	14	·	·	PUNCT
ejpam-3812	444	15	γi1f	γi1f	X
ejpam-3812	444	16	(	(	PUNCT
ejpam-3812	444	17	g	g	NOUN
ejpam-3812	444	18	)	)	PUNCT
ejpam-3812	444	19	.	.	PUNCT
ejpam-3812	445	1	this	this	PRON
ejpam-3812	445	2	establishes	establish	VERB
ejpam-3812	445	3	the	the	DET
ejpam-3812	445	4	desired	desire	VERB
ejpam-3812	445	5	equality	equality	NOUN
ejpam-3812	445	6	.	.	PUNCT
ejpam-3812	446	1	�	�	PROPN
ejpam-3812	446	2	theorem	theorem	VERB
ejpam-3812	446	3	20	20	NUM
ejpam-3812	446	4	.	.	PUNCT
ejpam-3812	447	1	let	let	VERB
ejpam-3812	447	2	g	g	NOUN
ejpam-3812	447	3	and	and	CCONJ
ejpam-3812	447	4	h	h	NOUN
ejpam-3812	447	5	be	be	AUX
ejpam-3812	447	6	nontrivial	nontrivial	ADJ
ejpam-3812	447	7	connected	connect	VERB
ejpam-3812	447	8	graphs	graph	NOUN
ejpam-3812	447	9	of	of	ADP
ejpam-3812	447	10	orders	order	NOUN
ejpam-3812	447	11	m	m	VERB
ejpam-3812	447	12	and	and	CCONJ
ejpam-3812	447	13	n	n	CCONJ
ejpam-3812	447	14	,	,	PUNCT
ejpam-3812	447	15	respectively	respectively	ADV
ejpam-3812	447	16	,	,	PUNCT
ejpam-3812	447	17	and	and	CCONJ
ejpam-3812	447	18	let	let	VERB
ejpam-3812	447	19	k	k	PRON
ejpam-3812	447	20	be	be	AUX
ejpam-3812	447	21	a	a	DET
ejpam-3812	447	22	positive	positive	ADJ
ejpam-3812	447	23	integer	integer	NOUN
ejpam-3812	447	24	with	with	ADP
ejpam-3812	447	25	1	1	NUM
ejpam-3812	447	26	≤	≤	NUM
ejpam-3812	447	27	k	k	PROPN
ejpam-3812	447	28	≤	≤	ADJ
ejpam-3812	447	29	min{m	min{m	PROPN
ejpam-3812	447	30	,	,	PUNCT
ejpam-3812	447	31	n	n	CCONJ
ejpam-3812	447	32	}	}	PUNCT
ejpam-3812	447	33	.	.	PUNCT
ejpam-3812	448	1	if	if	SCONJ
ejpam-3812	448	2	g	g	PROPN
ejpam-3812	448	3	�	�	PROPN
ejpam-3812	448	4	h	h	PROPN
ejpam-3812	448	5	admits	admit	VERB
ejpam-3812	448	6	an	an	DET
ejpam-3812	448	7	independent	independent	ADJ
ejpam-3812	448	8	kfd	kfd	NOUN
ejpam-3812	448	9	-	-	PUNCT
ejpam-3812	448	10	set	set	NOUN
ejpam-3812	448	11	,	,	PUNCT
ejpam-3812	448	12	then	then	ADV
ejpam-3812	448	13	c	c	NOUN
ejpam-3812	448	14	=	=	SYM
ejpam-3812	448	15	⋃	⋃	PROPN
ejpam-3812	448	16	x∈v	x∈v	PROPN
ejpam-3812	448	17	(	(	PUNCT
ejpam-3812	448	18	g	g	NOUN
ejpam-3812	448	19	)	)	PUNCT
ejpam-3812	448	20	(	(	PUNCT
ejpam-3812	448	21	{	{	PUNCT
ejpam-3812	448	22	x	x	NOUN
ejpam-3812	448	23	}	}	PUNCT
ejpam-3812	448	24	×	×	PROPN
ejpam-3812	448	25	tx	tx	PROPN
ejpam-3812	448	26	)	)	PUNCT
ejpam-3812	448	27	(	(	PUNCT
ejpam-3812	448	28	v	v	X
ejpam-3812	448	29	(	(	PUNCT
ejpam-3812	448	30	g	g	PROPN
ejpam-3812	448	31	�	�	NOUN
ejpam-3812	448	32	h	h	NOUN
ejpam-3812	448	33	)	)	PUNCT
ejpam-3812	448	34	is	be	AUX
ejpam-3812	448	35	an	an	DET
ejpam-3812	448	36	independent	independent	ADJ
ejpam-3812	448	37	kfd	kfd	NOUN
ejpam-3812	448	38	-	-	PUNCT
ejpam-3812	448	39	set	set	NOUN
ejpam-3812	448	40	in	in	ADP
ejpam-3812	448	41	g	g	PROPN
ejpam-3812	448	42	�	�	NOUN
ejpam-3812	448	43	h	h	NOUN
ejpam-3812	448	44	if	if	SCONJ
ejpam-3812	449	1	and	and	CCONJ
ejpam-3812	449	2	only	only	ADV
ejpam-3812	449	3	if	if	SCONJ
ejpam-3812	449	4	:	:	PUNCT
ejpam-3812	449	5	(	(	PUNCT
ejpam-3812	449	6	i	i	NOUN
ejpam-3812	449	7	)	)	PUNCT
ejpam-3812	449	8	tx	tx	PROPN
ejpam-3812	449	9	is	be	AUX
ejpam-3812	449	10	an	an	DET
ejpam-3812	449	11	independent	independent	ADJ
ejpam-3812	449	12	set	set	NOUN
ejpam-3812	449	13	in	in	ADP
ejpam-3812	449	14	h	h	NOUN
ejpam-3812	449	15	for	for	ADP
ejpam-3812	449	16	each	each	DET
ejpam-3812	449	17	x	x	SYM
ejpam-3812	449	18	∈	∈	PROPN
ejpam-3812	449	19	v	v	NOUN
ejpam-3812	449	20	(	(	PUNCT
ejpam-3812	449	21	g	g	NOUN
ejpam-3812	449	22	)	)	PUNCT
ejpam-3812	449	23	,	,	PUNCT
ejpam-3812	449	24	(	(	PUNCT
ejpam-3812	449	25	ii	ii	NOUN
ejpam-3812	449	26	)	)	PUNCT
ejpam-3812	449	27	for	for	ADP
ejpam-3812	449	28	each	each	DET
ejpam-3812	449	29	x	x	SYM
ejpam-3812	449	30	∈	∈	PROPN
ejpam-3812	449	31	v	v	ADP
ejpam-3812	449	32	(	(	PUNCT
ejpam-3812	449	33	g	g	NOUN
ejpam-3812	449	34	)	)	PUNCT
ejpam-3812	449	35	and	and	CCONJ
ejpam-3812	449	36	each	each	PRON
ejpam-3812	449	37	a	a	DET
ejpam-3812	449	38	∈	∈	PROPN
ejpam-3812	449	39	tx	tx	PROPN
ejpam-3812	449	40	,	,	PUNCT
ejpam-3812	449	41	|{z	|{z	PROPN
ejpam-3812	449	42	∈	∈	PROPN
ejpam-3812	449	43	v	v	ADP
ejpam-3812	449	44	(	(	PUNCT
ejpam-3812	449	45	g	g	NOUN
ejpam-3812	449	46	)	)	PUNCT
ejpam-3812	449	47	:	:	PUNCT
ejpam-3812	449	48	z	z	PROPN
ejpam-3812	449	49	∈	∈	PROPN
ejpam-3812	449	50	ng(x	ng(x	NUM
ejpam-3812	449	51	)	)	PUNCT
ejpam-3812	449	52	,	,	PUNCT
ejpam-3812	449	53	a	a	DET
ejpam-3812	449	54	∈	∈	NOUN
ejpam-3812	449	55	tz}|	tz}|	NUM
ejpam-3812	449	56	=	=	SYM
ejpam-3812	449	57	0	0	NUM
ejpam-3812	449	58	,	,	PUNCT
ejpam-3812	449	59	(	(	PUNCT
ejpam-3812	449	60	iii	iii	NOUN
ejpam-3812	449	61	)	)	PUNCT
ejpam-3812	449	62	v	v	NOUN
ejpam-3812	449	63	(	(	PUNCT
ejpam-3812	449	64	h)\tx	h)\tx	NOUN
ejpam-3812	449	65	⊆	⊆	NUM
ejpam-3812	449	66	nh(tx	nh(tx	NOUN
ejpam-3812	449	67	)	)	PUNCT
ejpam-3812	449	68	⋃	⋃	NOUN
ejpam-3812	449	69	(	(	PUNCT
ejpam-3812	449	70	⋃	⋃	PROPN
ejpam-3812	449	71	z∈ng(x	z∈ng(x	NOUN
ejpam-3812	449	72	)	)	PUNCT
ejpam-3812	449	73	tz	tz	NOUN
ejpam-3812	449	74	)	)	PUNCT
ejpam-3812	449	75	for	for	ADP
ejpam-3812	449	76	each	each	DET
ejpam-3812	449	77	x	x	SYM
ejpam-3812	449	78	∈	∈	PROPN
ejpam-3812	449	79	v	v	NOUN
ejpam-3812	449	80	(	(	PUNCT
ejpam-3812	449	81	g	g	NOUN
ejpam-3812	449	82	)	)	PUNCT
ejpam-3812	449	83	,	,	PUNCT
ejpam-3812	449	84	and	and	CCONJ
ejpam-3812	449	85	(	(	PUNCT
ejpam-3812	449	86	iv	iv	X
ejpam-3812	449	87	)	)	PUNCT
ejpam-3812	449	88	for	for	ADP
ejpam-3812	449	89	each	each	PRON
ejpam-3812	449	90	b	b	PROPN
ejpam-3812	449	91	∈	∈	PROPN
ejpam-3812	449	92	v	v	NOUN
ejpam-3812	449	93	(	(	PUNCT
ejpam-3812	449	94	h	h	NOUN
ejpam-3812	449	95	)	)	PUNCT
ejpam-3812	449	96	\tx	\tx	PROPN
ejpam-3812	449	97	,	,	PUNCT
ejpam-3812	449	98	either	either	CCONJ
ejpam-3812	449	99	|nh(b)∩tx|	|nh(b)∩tx|	NOUN
ejpam-3812	449	100	=	=	SYM
ejpam-3812	449	101	k	k	PROPN
ejpam-3812	449	102	and	and	CCONJ
ejpam-3812	449	103	|{z	|{z	PROPN
ejpam-3812	449	104	:	:	PUNCT
ejpam-3812	449	105	z	z	PROPN
ejpam-3812	449	106	∈	∈	PROPN
ejpam-3812	449	107	ng(x	ng(x	NUM
ejpam-3812	449	108	)	)	PUNCT
ejpam-3812	449	109	,	,	PUNCT
ejpam-3812	450	1	b	b	X
ejpam-3812	450	2	∈	∈	PROPN
ejpam-3812	450	3	tz}|	tz}|	X
ejpam-3812	450	4	=	=	SYM
ejpam-3812	450	5	0	0	NUM
ejpam-3812	450	6	or	or	CCONJ
ejpam-3812	450	7	|nh(b	|nh(b	NUM
ejpam-3812	450	8	)	)	PUNCT
ejpam-3812	450	9	∩	∩	NOUN
ejpam-3812	450	10	tx|	tx|	NOUN
ejpam-3812	450	11	=	=	PUNCT
ejpam-3812	450	12	r	r	NOUN
ejpam-3812	450	13	<	<	X
ejpam-3812	450	14	k	k	PROPN
ejpam-3812	450	15	and	and	CCONJ
ejpam-3812	450	16	b	b	PROPN
ejpam-3812	450	17	∈	∈	PROPN
ejpam-3812	450	18	k−r⋂	k−r⋂	PROPN
ejpam-3812	450	19	i=1	i=1	PROPN
ejpam-3812	450	20	txi	txi	PROPN
ejpam-3812	450	21	,	,	PUNCT
ejpam-3812	450	22	where	where	SCONJ
ejpam-3812	450	23	xi	xi	PROPN
ejpam-3812	450	24	∈	∈	PROPN
ejpam-3812	450	25	ng(x	ng(x	NUM
ejpam-3812	450	26	)	)	PUNCT
ejpam-3812	450	27	for	for	ADP
ejpam-3812	450	28	i	i	PROPN
ejpam-3812	450	29	=	=	SYM
ejpam-3812	450	30	1	1	NUM
ejpam-3812	450	31	,	,	PUNCT
ejpam-3812	450	32	2	2	NUM
ejpam-3812	450	33	,	,	PUNCT
ejpam-3812	450	34	...	...	PUNCT
ejpam-3812	450	35	,	,	PUNCT
ejpam-3812	450	36	k	k	PROPN
ejpam-3812	450	37	−	−	PROPN
ejpam-3812	450	38	r.	r.	PROPN
ejpam-3812	450	39	proof	proof	NOUN
ejpam-3812	450	40	.	.	PUNCT
ejpam-3812	451	1	suppose	suppose	VERB
ejpam-3812	451	2	c	c	NOUN
ejpam-3812	451	3	=	=	PUNCT
ejpam-3812	451	4	⋃	⋃	PROPN
ejpam-3812	451	5	x∈v	x∈v	PROPN
ejpam-3812	451	6	(	(	PUNCT
ejpam-3812	451	7	g	g	NOUN
ejpam-3812	451	8	)	)	PUNCT
ejpam-3812	451	9	(	(	PUNCT
ejpam-3812	451	10	{	{	PUNCT
ejpam-3812	451	11	x}×tx	x}×tx	NUM
ejpam-3812	451	12	)	)	PUNCT
ejpam-3812	451	13	(	(	PUNCT
ejpam-3812	451	14	v	v	X
ejpam-3812	451	15	(	(	PUNCT
ejpam-3812	451	16	g	g	PROPN
ejpam-3812	451	17	�	�	NOUN
ejpam-3812	451	18	h	h	NOUN
ejpam-3812	451	19	)	)	PUNCT
ejpam-3812	451	20	is	be	AUX
ejpam-3812	451	21	an	an	DET
ejpam-3812	451	22	independent	independent	ADJ
ejpam-3812	451	23	kfd	kfd	NOUN
ejpam-3812	451	24	-	-	PUNCT
ejpam-3812	451	25	set	set	NOUN
ejpam-3812	451	26	in	in	ADP
ejpam-3812	451	27	g	g	PROPN
ejpam-3812	451	28	�	�	PROPN
ejpam-3812	451	29	h.	h.	PROPN
ejpam-3812	451	30	then	then	ADV
ejpam-3812	451	31	by	by	ADP
ejpam-3812	451	32	theorem	theorem	NOUN
ejpam-3812	451	33	11	11	NUM
ejpam-3812	451	34	,	,	PUNCT
ejpam-3812	451	35	(	(	PUNCT
ejpam-3812	451	36	iii	iii	NOUN
ejpam-3812	451	37	)	)	PUNCT
ejpam-3812	451	38	and	and	CCONJ
ejpam-3812	451	39	(	(	PUNCT
ejpam-3812	451	40	iv	iv	X
ejpam-3812	451	41	)	)	PUNCT
ejpam-3812	451	42	hold	hold	NOUN
ejpam-3812	451	43	.	.	PUNCT
ejpam-3812	452	1	suppose	suppose	VERB
ejpam-3812	452	2	there	there	PRON
ejpam-3812	452	3	is	be	VERB
ejpam-3812	452	4	a	a	DET
ejpam-3812	452	5	vertex	vertex	NOUN
ejpam-3812	452	6	a	a	DET
ejpam-3812	452	7	∈	∈	PROPN
ejpam-3812	452	8	tx	tx	PROPN
ejpam-3812	452	9	which	which	PRON
ejpam-3812	452	10	is	be	AUX
ejpam-3812	452	11	adjacent	adjacent	ADJ
ejpam-3812	452	12	to	to	ADP
ejpam-3812	452	13	some	some	DET
ejpam-3812	452	14	vertex	vertex	NOUN
ejpam-3812	452	15	b	b	PROPN
ejpam-3812	452	16	in	in	ADP
ejpam-3812	452	17	tx	tx	PROPN
ejpam-3812	452	18	.	.	PUNCT
ejpam-3812	453	1	then	then	ADV
ejpam-3812	453	2	(	(	PUNCT
ejpam-3812	453	3	x	x	X
ejpam-3812	453	4	,	,	PUNCT
ejpam-3812	453	5	a	a	PRON
ejpam-3812	453	6	)	)	PUNCT
ejpam-3812	453	7	is	be	AUX
ejpam-3812	453	8	adjacent	adjacent	ADJ
ejpam-3812	453	9	to	to	ADP
ejpam-3812	453	10	(	(	PUNCT
ejpam-3812	453	11	x	x	NOUN
ejpam-3812	453	12	,	,	PUNCT
ejpam-3812	453	13	b	b	NOUN
ejpam-3812	453	14	)	)	PUNCT
ejpam-3812	453	15	in	in	ADP
ejpam-3812	453	16	c	c	PROPN
ejpam-3812	453	17	,	,	PUNCT
ejpam-3812	453	18	contrary	contrary	ADJ
ejpam-3812	453	19	to	to	ADP
ejpam-3812	453	20	assumption	assumption	NOUN
ejpam-3812	453	21	.	.	PUNCT
ejpam-3812	454	1	hence	hence	ADV
ejpam-3812	454	2	,	,	PUNCT
ejpam-3812	454	3	tx	tx	PROPN
ejpam-3812	454	4	is	be	AUX
ejpam-3812	454	5	an	an	DET
ejpam-3812	454	6	independent	independent	ADJ
ejpam-3812	454	7	set	set	NOUN
ejpam-3812	454	8	in	in	ADP
ejpam-3812	454	9	h	h	NOUN
ejpam-3812	454	10	and	and	CCONJ
ejpam-3812	454	11	(	(	PUNCT
ejpam-3812	454	12	i	i	NOUN
ejpam-3812	454	13	)	)	PUNCT
ejpam-3812	454	14	holds	hold	VERB
ejpam-3812	454	15	.	.	PUNCT
ejpam-3812	455	1	finally	finally	ADV
ejpam-3812	455	2	,	,	PUNCT
ejpam-3812	455	3	suppose	suppose	VERB
ejpam-3812	455	4	there	there	PRON
ejpam-3812	455	5	is	be	VERB
ejpam-3812	455	6	a	a	DET
ejpam-3812	455	7	vertex	vertex	NOUN
ejpam-3812	455	8	a	a	DET
ejpam-3812	455	9	∈	∈	NOUN
ejpam-3812	455	10	tx	tx	ADP
ejpam-3812	455	11	such	such	ADJ
ejpam-3812	455	12	that	that	PRON
ejpam-3812	455	13	for	for	ADP
ejpam-3812	455	14	some	some	DET
ejpam-3812	455	15	vertex	vertex	NOUN
ejpam-3812	455	16	z	z	NOUN
ejpam-3812	455	17	∈	∈	PROPN
ejpam-3812	455	18	ng(x	ng(x	NUM
ejpam-3812	455	19	)	)	PUNCT
ejpam-3812	455	20	,	,	PUNCT
ejpam-3812	455	21	a	a	DET
ejpam-3812	455	22	∈	∈	PROPN
ejpam-3812	455	23	tz	tz	NOUN
ejpam-3812	455	24	.	.	PUNCT
ejpam-3812	456	1	then	then	ADV
ejpam-3812	456	2	(	(	PUNCT
ejpam-3812	456	3	z	z	NOUN
ejpam-3812	456	4	,	,	PUNCT
ejpam-3812	456	5	a	a	PRON
ejpam-3812	456	6	)	)	PUNCT
ejpam-3812	456	7	∈	∈	PROPN
ejpam-3812	456	8	c	c	NOUN
ejpam-3812	456	9	and	and	CCONJ
ejpam-3812	456	10	(	(	PUNCT
ejpam-3812	456	11	x	x	NOUN
ejpam-3812	456	12	,	,	PUNCT
ejpam-3812	456	13	a	a	PRON
ejpam-3812	456	14	)	)	PUNCT
ejpam-3812	456	15	is	be	AUX
ejpam-3812	456	16	adjacent	adjacent	ADJ
ejpam-3812	456	17	to	to	ADP
ejpam-3812	456	18	(	(	PUNCT
ejpam-3812	456	19	z	z	NOUN
ejpam-3812	456	20	,	,	PUNCT
ejpam-3812	456	21	a	a	PRON
ejpam-3812	456	22	)	)	PUNCT
ejpam-3812	456	23	in	in	ADP
ejpam-3812	456	24	c	c	PROPN
ejpam-3812	456	25	,	,	PUNCT
ejpam-3812	456	26	contrary	contrary	ADJ
ejpam-3812	456	27	to	to	ADP
ejpam-3812	456	28	assumption	assumption	NOUN
ejpam-3812	456	29	.	.	PUNCT
ejpam-3812	457	1	hence	hence	ADV
ejpam-3812	457	2	,	,	PUNCT
ejpam-3812	457	3	(	(	PUNCT
ejpam-3812	457	4	ii	ii	NOUN
ejpam-3812	457	5	)	)	PUNCT
ejpam-3812	457	6	holds	hold	VERB
ejpam-3812	457	7	.	.	PUNCT
ejpam-3812	458	1	conversely	conversely	ADV
ejpam-3812	458	2	,	,	PUNCT
ejpam-3812	458	3	suppose	suppose	VERB
ejpam-3812	458	4	(	(	PUNCT
ejpam-3812	458	5	i	i	NOUN
ejpam-3812	458	6	)	)	PUNCT
ejpam-3812	458	7	to	to	PART
ejpam-3812	458	8	(	(	PUNCT
ejpam-3812	458	9	iv	iv	X
ejpam-3812	458	10	)	)	PUNCT
ejpam-3812	458	11	hold	hold	NOUN
ejpam-3812	458	12	.	.	PUNCT
ejpam-3812	459	1	from	from	ADP
ejpam-3812	459	2	(	(	PUNCT
ejpam-3812	459	3	iii	iii	NOUN
ejpam-3812	459	4	)	)	PUNCT
ejpam-3812	459	5	and	and	CCONJ
ejpam-3812	459	6	(	(	PUNCT
ejpam-3812	459	7	iv	iv	X
ejpam-3812	459	8	)	)	PUNCT
ejpam-3812	459	9	,	,	PUNCT
ejpam-3812	459	10	c	c	PROPN
ejpam-3812	459	11	is	be	AUX
ejpam-3812	459	12	a	a	DET
ejpam-3812	459	13	kfd	kfd	NOUN
ejpam-3812	459	14	-	-	PUNCT
ejpam-3812	459	15	set	set	NOUN
ejpam-3812	459	16	by	by	ADP
ejpam-3812	459	17	theorem	theorem	ADJ
ejpam-3812	459	18	references	reference	NOUN
ejpam-3812	459	19	792	792	NUM
ejpam-3812	459	20	11	11	NUM
ejpam-3812	459	21	.	.	PUNCT
ejpam-3812	460	1	by	by	ADP
ejpam-3812	460	2	(	(	PUNCT
ejpam-3812	460	3	i	i	NOUN
ejpam-3812	460	4	)	)	PUNCT
ejpam-3812	460	5	and	and	CCONJ
ejpam-3812	460	6	(	(	PUNCT
ejpam-3812	460	7	ii	ii	NOUN
ejpam-3812	460	8	)	)	PUNCT
ejpam-3812	460	9	,	,	PUNCT
ejpam-3812	460	10	c	c	PROPN
ejpam-3812	460	11	is	be	AUX
ejpam-3812	460	12	an	an	DET
ejpam-3812	460	13	independent	independent	ADJ
ejpam-3812	460	14	set	set	NOUN
ejpam-3812	460	15	in	in	ADP
ejpam-3812	460	16	g	g	PROPN
ejpam-3812	460	17	�	�	PROPN
ejpam-3812	460	18	h.	h.	PROPN
ejpam-3812	460	19	thus	thus	ADV
ejpam-3812	460	20	,	,	PUNCT
ejpam-3812	460	21	c	c	PROPN
ejpam-3812	460	22	is	be	AUX
ejpam-3812	460	23	an	an	DET
ejpam-3812	460	24	independent	independent	ADJ
ejpam-3812	460	25	kfd	kfd	NOUN
ejpam-3812	460	26	-	-	PUNCT
ejpam-3812	460	27	set	set	NOUN
ejpam-3812	460	28	in	in	ADP
ejpam-3812	460	29	g	g	PROPN
ejpam-3812	460	30	�	�	PROPN
ejpam-3812	460	31	h.	h.	PROPN
ejpam-3812	460	32	�	�	PROPN
ejpam-3812	460	33	the	the	DET
ejpam-3812	460	34	next	next	ADJ
ejpam-3812	460	35	result	result	NOUN
ejpam-3812	460	36	immediately	immediately	ADV
ejpam-3812	460	37	follows	follow	VERB
ejpam-3812	460	38	from	from	ADP
ejpam-3812	460	39	remark	remark	NOUN
ejpam-3812	460	40	3	3	NUM
ejpam-3812	460	41	and	and	CCONJ
ejpam-3812	460	42	corollary	corollary	ADJ
ejpam-3812	460	43	6	6	NUM
ejpam-3812	460	44	.	.	PUNCT
ejpam-3812	461	1	corollary	corollary	ADJ
ejpam-3812	461	2	16	16	NUM
ejpam-3812	461	3	.	.	PUNCT
ejpam-3812	462	1	let	let	VERB
ejpam-3812	462	2	g	g	NOUN
ejpam-3812	462	3	and	and	CCONJ
ejpam-3812	462	4	h	h	NOUN
ejpam-3812	462	5	be	be	AUX
ejpam-3812	462	6	nontrivial	nontrivial	ADJ
ejpam-3812	462	7	connected	connect	VERB
ejpam-3812	462	8	graphs	graph	NOUN
ejpam-3812	462	9	of	of	ADP
ejpam-3812	462	10	orders	order	NOUN
ejpam-3812	462	11	m	m	VERB
ejpam-3812	462	12	and	and	CCONJ
ejpam-3812	462	13	n	n	CCONJ
ejpam-3812	462	14	,	,	PUNCT
ejpam-3812	462	15	respectively	respectively	ADV
ejpam-3812	462	16	,	,	PUNCT
ejpam-3812	462	17	and	and	CCONJ
ejpam-3812	462	18	k	k	X
ejpam-3812	462	19	a	a	DET
ejpam-3812	462	20	positive	positive	ADJ
ejpam-3812	462	21	integer	integer	NOUN
ejpam-3812	462	22	with	with	ADP
ejpam-3812	462	23	1	1	NUM
ejpam-3812	462	24	≤	≤	NUM
ejpam-3812	462	25	k	k	PROPN
ejpam-3812	462	26	≤	≤	ADJ
ejpam-3812	462	27	min{m	min{m	PROPN
ejpam-3812	462	28	,	,	PUNCT
ejpam-3812	462	29	n	n	CCONJ
ejpam-3812	462	30	}	}	PUNCT
ejpam-3812	462	31	.	.	PUNCT
ejpam-3812	463	1	if	if	SCONJ
ejpam-3812	463	2	g	g	PROPN
ejpam-3812	463	3	�	�	PROPN
ejpam-3812	463	4	h	h	PROPN
ejpam-3812	463	5	admits	admit	VERB
ejpam-3812	463	6	an	an	DET
ejpam-3812	463	7	independent	independent	ADJ
ejpam-3812	463	8	kfd	kfd	NOUN
ejpam-3812	463	9	-	-	PUNCT
ejpam-3812	463	10	set	set	NOUN
ejpam-3812	463	11	,	,	PUNCT
ejpam-3812	463	12	then	then	ADV
ejpam-3812	463	13	γikf	γikf	NOUN
ejpam-3812	463	14	(	(	PUNCT
ejpam-3812	463	15	g	g	PROPN
ejpam-3812	463	16	�	�	PROPN
ejpam-3812	463	17	h	h	NOUN
ejpam-3812	463	18	)	)	PUNCT
ejpam-3812	463	19	≤	≤	NOUN
ejpam-3812	463	20	min{m	min{m	PROPN
ejpam-3812	463	21	·	·	SYM
ejpam-3812	463	22	γkfd(h	γkfd(h	PROPN
ejpam-3812	463	23	)	)	PUNCT
ejpam-3812	463	24	,	,	PUNCT
ejpam-3812	463	25	n	n	PROPN
ejpam-3812	463	26	·	·	PUNCT
ejpam-3812	463	27	γkfd(g	γkfd(g	NOUN
ejpam-3812	463	28	)	)	PUNCT
ejpam-3812	463	29	}	}	PUNCT
ejpam-3812	463	30	.	.	PUNCT
ejpam-3812	464	1	remark	remark	NOUN
ejpam-3812	464	2	6	6	NUM
ejpam-3812	464	3	.	.	PUNCT
ejpam-3812	465	1	the	the	DET
ejpam-3812	465	2	bound	bind	VERB
ejpam-3812	465	3	given	give	VERB
ejpam-3812	465	4	in	in	ADP
ejpam-3812	465	5	corollary	corollary	ADJ
ejpam-3812	465	6	16	16	NUM
ejpam-3812	465	7	is	be	AUX
ejpam-3812	465	8	sharp	sharp	ADJ
ejpam-3812	465	9	.	.	PUNCT
ejpam-3812	466	1	however	however	ADV
ejpam-3812	466	2	,	,	PUNCT
ejpam-3812	466	3	the	the	DET
ejpam-3812	466	4	strict	strict	ADJ
ejpam-3812	466	5	inequality	inequality	NOUN
ejpam-3812	466	6	can	can	AUX
ejpam-3812	466	7	be	be	AUX
ejpam-3812	466	8	attained	attain	VERB
ejpam-3812	466	9	.	.	PUNCT
ejpam-3812	467	1	to	to	PART
ejpam-3812	467	2	see	see	VERB
ejpam-3812	467	3	this	this	PRON
ejpam-3812	467	4	,	,	PUNCT
ejpam-3812	467	5	consider	consider	VERB
ejpam-3812	467	6	the	the	DET
ejpam-3812	467	7	graphs	graph	NOUN
ejpam-3812	467	8	shown	show	VERB
ejpam-3812	467	9	in	in	ADP
ejpam-3812	467	10	figure	figure	NOUN
ejpam-3812	467	11	4	4	NUM
ejpam-3812	467	12	.	.	PUNCT
ejpam-3812	468	1	the	the	DET
ejpam-3812	468	2	shaded	shade	VERB
ejpam-3812	468	3	vertices	vertex	NOUN
ejpam-3812	468	4	in	in	ADP
ejpam-3812	468	5	each	each	DET
ejpam-3812	468	6	graph	graph	NOUN
ejpam-3812	468	7	form	form	VERB
ejpam-3812	468	8	a	a	DET
ejpam-3812	468	9	γikf	γikf	NOUN
ejpam-3812	468	10	-set	-set	ADJ
ejpam-3812	468	11	.	.	PUNCT
ejpam-3812	469	1	thus	thus	ADV
ejpam-3812	469	2	,	,	PUNCT
ejpam-3812	469	3	γi1f	γi1f	PROPN
ejpam-3812	469	4	(	(	PUNCT
ejpam-3812	469	5	p2	p2	X
ejpam-3812	469	6	�	�	NOUN
ejpam-3812	469	7	p3	p3	NOUN
ejpam-3812	469	8	)	)	PUNCT
ejpam-3812	469	9	=	=	SYM
ejpam-3812	469	10	2	2	NUM
ejpam-3812	469	11	=	=	SYM
ejpam-3812	469	12	min{2	min{2	NUM
ejpam-3812	469	13	·	·	SYM
ejpam-3812	469	14	1	1	NUM
ejpam-3812	469	15	,	,	PUNCT
ejpam-3812	469	16	3	3	NUM
ejpam-3812	469	17	·	·	SYM
ejpam-3812	469	18	1	1	NUM
ejpam-3812	469	19	}	}	PUNCT
ejpam-3812	469	20	=	=	SYM
ejpam-3812	469	21	min{|v	min{|v	PROPN
ejpam-3812	469	22	(	(	PUNCT
ejpam-3812	469	23	p2)|	p2)|	PROPN
ejpam-3812	469	24	·	·	SYM
ejpam-3812	469	25	γ1fd(p3	γ1fd(p3	PROPN
ejpam-3812	469	26	)	)	PUNCT
ejpam-3812	469	27	,	,	PUNCT
ejpam-3812	469	28	|v	|v	PROPN
ejpam-3812	469	29	(	(	PUNCT
ejpam-3812	469	30	p3)|	p3)|	PROPN
ejpam-3812	469	31	·	·	PUNCT
ejpam-3812	469	32	γ1fd(p2	γ1fd(p2	ADJ
ejpam-3812	469	33	)	)	PUNCT
ejpam-3812	469	34	}	}	PUNCT
ejpam-3812	469	35	=	=	SYM
ejpam-3812	469	36	|v	|v	X
ejpam-3812	469	37	(	(	PUNCT
ejpam-3812	469	38	p2)|	p2)|	NOUN
ejpam-3812	469	39	·	·	PUNCT
ejpam-3812	469	40	γ1fd(p3	γ1fd(p3	PROPN
ejpam-3812	469	41	)	)	PUNCT
ejpam-3812	469	42	and	and	CCONJ
ejpam-3812	469	43	γi3f	γi3f	PROPN
ejpam-3812	469	44	(	(	PUNCT
ejpam-3812	469	45	p3	p3	PROPN
ejpam-3812	469	46	�	�	PROPN
ejpam-3812	469	47	p3	p3	PROPN
ejpam-3812	469	48	)	)	PUNCT
ejpam-3812	469	49	=	=	PUNCT
ejpam-3812	469	50	5	5	NUM
ejpam-3812	469	51	<	<	X
ejpam-3812	469	52	min{3	min{3	X
ejpam-3812	469	53	·	·	PUNCT
ejpam-3812	469	54	3	3	NUM
ejpam-3812	469	55	,	,	PUNCT
ejpam-3812	469	56	3	3	NUM
ejpam-3812	469	57	·	·	SYM
ejpam-3812	469	58	3	3	NUM
ejpam-3812	469	59	}	}	PUNCT
ejpam-3812	469	60	=	=	SYM
ejpam-3812	469	61	min{|v	min{|v	PROPN
ejpam-3812	469	62	(	(	PUNCT
ejpam-3812	469	63	p3)|	p3)|	NOUN
ejpam-3812	469	64	·	·	PUNCT
ejpam-3812	469	65	γ3fd(p3	γ3fd(p3	PROPN
ejpam-3812	469	66	)	)	PUNCT
ejpam-3812	469	67	,	,	PUNCT
ejpam-3812	469	68	|v	|v	PROPN
ejpam-3812	469	69	(	(	PUNCT
ejpam-3812	469	70	p3)|	p3)|	PROPN
ejpam-3812	469	71	·	·	PUNCT
ejpam-3812	469	72	γ3fd(p3	γ3fd(p3	NOUN
ejpam-3812	469	73	)	)	PUNCT
ejpam-3812	469	74	}	}	PUNCT
ejpam-3812	469	75	.	.	PUNCT
ejpam-3812	469	76	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	469	77	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	470	1	....................................	....................................	PUNCT
ejpam-3812	470	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	471	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	471	2	....................................	....................................	PUNCT
ejpam-3812	472	1	.........	.........	PUNCT
ejpam-3812	472	2	........	........	PUNCT
ejpam-3812	472	3	........	........	PUNCT
ejpam-3812	472	4	........	........	PUNCT
ejpam-3812	472	5	........	........	PUNCT
ejpam-3812	472	6	........	........	PUNCT
ejpam-3812	472	7	........	........	PUNCT
ejpam-3812	472	8	........	........	PUNCT
ejpam-3812	472	9	........	........	PUNCT
ejpam-3812	472	10	...	...	PUNCT
ejpam-3812	472	11	.........	.........	PUNCT
ejpam-3812	473	1	........	........	PUNCT
ejpam-3812	473	2	........	........	PUNCT
ejpam-3812	473	3	........	........	PUNCT
ejpam-3812	473	4	........	........	PUNCT
ejpam-3812	473	5	........	........	PUNCT
ejpam-3812	473	6	........	........	PUNCT
ejpam-3812	473	7	........	........	PUNCT
ejpam-3812	473	8	........	........	PUNCT
ejpam-3812	473	9	...	...	PUNCT
ejpam-3812	473	10	.........	.........	PUNCT
ejpam-3812	473	11	........	........	PUNCT
ejpam-3812	473	12	........	........	PUNCT
ejpam-3812	473	13	........	........	PUNCT
ejpam-3812	473	14	........	........	PUNCT
ejpam-3812	473	15	........	........	PUNCT
ejpam-3812	473	16	........	........	PUNCT
ejpam-3812	473	17	........	........	PUNCT
ejpam-3812	474	1	........	........	PUNCT
ejpam-3812	475	1	...	...	PUNCT
ejpam-3812	475	2	•	•	X
ejpam-3812	475	3	•	•	INTJ
ejpam-3812	475	4	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	475	5	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	475	6	....................................	....................................	PUNCT
ejpam-3812	475	7	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	475	8	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	475	9	....................................	....................................	PUNCT
ejpam-3812	475	10	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	475	11	................................................................................................................	................................................................................................................	PUNCT
ejpam-3812	475	12	....................................	....................................	PUNCT
ejpam-3812	475	13	.........	.........	PUNCT
ejpam-3812	475	14	........	........	PUNCT
ejpam-3812	475	15	........	........	PUNCT
ejpam-3812	475	16	........	........	PUNCT
ejpam-3812	475	17	........	........	PUNCT
ejpam-3812	475	18	........	........	PUNCT
ejpam-3812	475	19	........	........	PUNCT
ejpam-3812	475	20	........	........	PUNCT
ejpam-3812	475	21	........	........	PUNCT
ejpam-3812	475	22	...	...	PUNCT
ejpam-3812	475	23	.........	.........	PUNCT
ejpam-3812	475	24	........	........	PUNCT
ejpam-3812	475	25	........	........	PUNCT
ejpam-3812	475	26	........	........	PUNCT
ejpam-3812	475	27	........	........	PUNCT
ejpam-3812	475	28	........	........	PUNCT
ejpam-3812	475	29	........	........	PUNCT
ejpam-3812	475	30	........	........	PUNCT
ejpam-3812	475	31	........	........	PUNCT
ejpam-3812	475	32	...	...	PUNCT
ejpam-3812	475	33	.........	.........	PUNCT
ejpam-3812	475	34	........	........	PUNCT
ejpam-3812	475	35	........	........	PUNCT
ejpam-3812	475	36	........	........	PUNCT
ejpam-3812	475	37	........	........	PUNCT
ejpam-3812	475	38	........	........	PUNCT
ejpam-3812	475	39	........	........	PUNCT
ejpam-3812	475	40	........	........	PUNCT
ejpam-3812	475	41	........	........	PUNCT
ejpam-3812	475	42	...	...	PUNCT
ejpam-3812	475	43	.........	.........	PUNCT
ejpam-3812	475	44	........	........	PUNCT
ejpam-3812	475	45	........	........	PUNCT
ejpam-3812	475	46	........	........	PUNCT
ejpam-3812	475	47	........	........	PUNCT
ejpam-3812	475	48	........	........	PUNCT
ejpam-3812	475	49	........	........	PUNCT
ejpam-3812	475	50	........	........	PUNCT
ejpam-3812	475	51	........	........	PUNCT
ejpam-3812	475	52	...	...	PUNCT
ejpam-3812	475	53	.........	.........	PUNCT
ejpam-3812	475	54	........	........	PUNCT
ejpam-3812	475	55	........	........	PUNCT
ejpam-3812	475	56	........	........	PUNCT
ejpam-3812	475	57	........	........	PUNCT
ejpam-3812	475	58	........	........	PUNCT
ejpam-3812	475	59	........	........	PUNCT
ejpam-3812	475	60	........	........	PUNCT
ejpam-3812	475	61	........	........	PUNCT
ejpam-3812	475	62	...	...	PUNCT
ejpam-3812	475	63	.........	.........	PUNCT
ejpam-3812	475	64	........	........	PUNCT
ejpam-3812	475	65	........	........	PUNCT
ejpam-3812	475	66	........	........	PUNCT
ejpam-3812	475	67	........	........	PUNCT
ejpam-3812	475	68	........	........	PUNCT
ejpam-3812	475	69	........	........	PUNCT
ejpam-3812	475	70	........	........	PUNCT
ejpam-3812	475	71	........	........	PUNCT
ejpam-3812	475	72	...	...	PUNCT
ejpam-3812	476	1	••	••	NOUN
ejpam-3812	476	2	•	•	NUM
ejpam-3812	476	3	•	•	NOUN
ejpam-3812	476	4	•	•	NUM
ejpam-3812	476	5	figure	figure	NOUN
ejpam-3812	476	6	4	4	NUM
ejpam-3812	476	7	:	:	PUNCT
ejpam-3812	477	1	the	the	DET
ejpam-3812	477	2	graphs	graph	NOUN
ejpam-3812	477	3	p2	p2	VERB
ejpam-3812	477	4	�	�	PROPN
ejpam-3812	477	5	p3	p3	PROPN
ejpam-3812	477	6	and	and	CCONJ
ejpam-3812	477	7	p3	p3	PROPN
ejpam-3812	477	8	�	�	PROPN
ejpam-3812	477	9	p3	p3	PROPN
ejpam-3812	477	10	with	with	ADP
ejpam-3812	477	11	γi	γi	PROPN
ejpam-3812	477	12	1f	1f	PROPN
ejpam-3812	477	13	(	(	PUNCT
ejpam-3812	477	14	p2	p2	PROPN
ejpam-3812	477	15	�	�	NOUN
ejpam-3812	477	16	p3	p3	NOUN
ejpam-3812	477	17	)	)	PUNCT
ejpam-3812	477	18	=	=	SYM
ejpam-3812	477	19	2	2	NUM
ejpam-3812	477	20	and	and	CCONJ
ejpam-3812	477	21	γi	γi	PRON
ejpam-3812	477	22	3f	3f	PROPN
ejpam-3812	477	23	(	(	PUNCT
ejpam-3812	477	24	p3	p3	PROPN
ejpam-3812	477	25	�	�	PROPN
ejpam-3812	477	26	p3	p3	PROPN
ejpam-3812	477	27	)	)	PUNCT
ejpam-3812	477	28	=	=	SYM
ejpam-3812	477	29	5	5	NUM
ejpam-3812	477	30	acknowledgements	acknowledgement	NOUN
ejpam-3812	477	31	this	this	DET
ejpam-3812	477	32	research	research	NOUN
ejpam-3812	477	33	is	be	AUX
ejpam-3812	477	34	funded	fund	VERB
ejpam-3812	477	35	by	by	ADP
ejpam-3812	477	36	the	the	DET
ejpam-3812	477	37	department	department	PROPN
ejpam-3812	477	38	of	of	ADP
ejpam-3812	477	39	science	science	NOUN
ejpam-3812	477	40	and	and	CCONJ
ejpam-3812	477	41	technology	technology	NOUN
ejpam-3812	477	42	-	-	PUNCT
ejpam-3812	477	43	accelerated	accelerate	VERB
ejpam-3812	477	44	science	science	NOUN
ejpam-3812	477	45	and	and	CCONJ
ejpam-3812	477	46	technology	technology	NOUN
ejpam-3812	477	47	human	human	ADJ
ejpam-3812	477	48	resource	resource	NOUN
ejpam-3812	477	49	development	development	NOUN
ejpam-3812	477	50	program	program	NOUN
ejpam-3812	477	51	(	(	PUNCT
ejpam-3812	477	52	dost	dost	NOUN
ejpam-3812	477	53	-	-	PUNCT
ejpam-3812	477	54	asthrdp	asthrdp	NOUN
ejpam-3812	477	55	)	)	PUNCT
ejpam-3812	477	56	and	and	CCONJ
ejpam-3812	477	57	the	the	DET
ejpam-3812	477	58	mindanao	mindanao	PROPN
ejpam-3812	477	59	state	state	PROPN
ejpam-3812	477	60	university	university	PROPN
ejpam-3812	477	61	-	-	PUNCT
ejpam-3812	477	62	iligan	iligan	PROPN
ejpam-3812	477	63	institute	institute	PROPN
ejpam-3812	477	64	of	of	ADP
ejpam-3812	477	65	technology	technology	PROPN
ejpam-3812	477	66	.	.	PUNCT
ejpam-3812	478	1	the	the	DET
ejpam-3812	478	2	authors	author	NOUN
ejpam-3812	478	3	would	would	AUX
ejpam-3812	478	4	like	like	VERB
ejpam-3812	478	5	to	to	PART
ejpam-3812	478	6	thank	thank	VERB
ejpam-3812	478	7	the	the	DET
ejpam-3812	478	8	reviewers	reviewer	NOUN
ejpam-3812	478	9	for	for	ADP
ejpam-3812	478	10	their	their	PRON
ejpam-3812	478	11	invaluable	invaluable	ADJ
ejpam-3812	478	12	comments	comment	NOUN
ejpam-3812	478	13	and	and	CCONJ
ejpam-3812	478	14	suggestions	suggestion	NOUN
ejpam-3812	478	15	that	that	PRON
ejpam-3812	478	16	led	lead	VERB
ejpam-3812	478	17	to	to	ADP
ejpam-3812	478	18	this	this	DET
ejpam-3812	478	19	improved	improve	VERB
ejpam-3812	478	20	version	version	NOUN
ejpam-3812	478	21	of	of	ADP
ejpam-3812	478	22	the	the	DET
ejpam-3812	478	23	paper	paper	NOUN
ejpam-3812	478	24	.	.	PUNCT
ejpam-3812	479	1	references	reference	NOUN
ejpam-3812	479	2	[	[	X
ejpam-3812	479	3	1	1	NUM
ejpam-3812	479	4	]	]	PUNCT
ejpam-3812	479	5	c.	c.	PROPN
ejpam-3812	479	6	berge	berge	PROPN
ejpam-3812	479	7	.	.	PUNCT
ejpam-3812	480	1	the	the	DET
ejpam-3812	480	2	theory	theory	NOUN
ejpam-3812	480	3	of	of	ADP
ejpam-3812	480	4	graphs	graph	NOUN
ejpam-3812	480	5	and	and	CCONJ
ejpam-3812	480	6	applications	application	NOUN
ejpam-3812	480	7	.	.	PUNCT
ejpam-3812	481	1	methuen	methuen	PROPN
ejpam-3812	481	2	,	,	PUNCT
ejpam-3812	481	3	london	london	PROPN
ejpam-3812	481	4	,	,	PUNCT
ejpam-3812	481	5	1962	1962	NUM
ejpam-3812	481	6	.	.	PUNCT
ejpam-3812	482	1	[	[	X
ejpam-3812	482	2	2	2	X
ejpam-3812	482	3	]	]	PUNCT
ejpam-3812	482	4	e.	e.	PROPN
ejpam-3812	482	5	cockayne	cockayne	PROPN
ejpam-3812	482	6	and	and	CCONJ
ejpam-3812	482	7	s.	s.	PROPN
ejpam-3812	482	8	hedetniemi	hedetniemi	PROPN
ejpam-3812	482	9	.	.	PUNCT
ejpam-3812	483	1	independent	independent	ADJ
ejpam-3812	483	2	graphs	graph	NOUN
ejpam-3812	483	3	.	.	PUNCT
ejpam-3812	484	1	congr	congr	NOUN
ejpam-3812	484	2	.	.	PUNCT
ejpam-3812	485	1	numer	numer	PROPN
ejpam-3812	485	2	.	.	PROPN
ejpam-3812	485	3	,	,	PUNCT
ejpam-3812	485	4	x:471–491	x:471–491	PROPN
ejpam-3812	485	5	,	,	PUNCT
ejpam-3812	485	6	1974	1974	NUM
ejpam-3812	485	7	.	.	PUNCT
ejpam-3812	486	1	[	[	X
ejpam-3812	486	2	3	3	X
ejpam-3812	486	3	]	]	X
ejpam-3812	486	4	w.	w.	PROPN
ejpam-3812	486	5	bent	bent	PROPN
ejpam-3812	486	6	-	-	PUNCT
ejpam-3812	486	7	usman	usman	PROPN
ejpam-3812	486	8	.	.	PUNCT
ejpam-3812	487	1	d.	d.	PROPN
ejpam-3812	487	2	gomisong	gomisong	PROPN
ejpam-3812	487	3	and	and	CCONJ
ejpam-3812	487	4	r.	r.	PROPN
ejpam-3812	487	5	isla	isla	PROPN
ejpam-3812	487	6	.	.	PUNCT
ejpam-3812	488	1	connected	connect	VERB
ejpam-3812	488	2	k	k	ADJ
ejpam-3812	488	3	-	-	PUNCT
ejpam-3812	488	4	fair	fair	ADJ
ejpam-3812	488	5	domination	domination	NOUN
ejpam-3812	488	6	in	in	ADP
ejpam-3812	488	7	the	the	DET
ejpam-3812	488	8	join	join	NOUN
ejpam-3812	488	9	,	,	PUNCT
ejpam-3812	488	10	corona	corona	PROPN
ejpam-3812	488	11	,	,	PUNCT
ejpam-3812	488	12	lexicographic	lexicographic	ADJ
ejpam-3812	488	13	and	and	CCONJ
ejpam-3812	488	14	cartesian	cartesian	ADJ
ejpam-3812	488	15	product	product	NOUN
ejpam-3812	488	16	of	of	ADP
ejpam-3812	488	17	graphs	graph	NOUN
ejpam-3812	488	18	.	.	PUNCT
ejpam-3812	489	1	applied	apply	VERB
ejpam-3812	489	2	mathematical	mathematical	ADJ
ejpam-3812	489	3	sciences	science	NOUN
ejpam-3812	489	4	,	,	PUNCT
ejpam-3812	489	5	12(27):1341–1355	12(27):1341–1355	NUM
ejpam-3812	489	6	,	,	PUNCT
ejpam-3812	489	7	2018	2018	NUM
ejpam-3812	489	8	.	.	PUNCT
ejpam-3812	490	1	references	reference	NOUN
ejpam-3812	490	2	793	793	NUM
ejpam-3812	490	3	[	[	X
ejpam-3812	490	4	4	4	NUM
ejpam-3812	490	5	]	]	X
ejpam-3812	490	6	y.	y.	PROPN
ejpam-3812	490	7	caro	caro	PROPN
ejpam-3812	490	8	.	.	PUNCT
ejpam-3812	491	1	a.	a.	PROPN
ejpam-3812	491	2	hansberg	hansberg	PROPN
ejpam-3812	491	3	and	and	CCONJ
ejpam-3812	491	4	m.	m.	PROPN
ejpam-3812	491	5	henning	henning	PROPN
ejpam-3812	491	6	.	.	PUNCT
ejpam-3812	492	1	fair	fair	ADJ
ejpam-3812	492	2	domination	domination	NOUN
ejpam-3812	492	3	in	in	ADP
ejpam-3812	492	4	graphs	graph	NOUN
ejpam-3812	492	5	.	.	PUNCT
ejpam-3812	493	1	discrete	discrete	ADJ
ejpam-3812	493	2	mathematics	mathematic	NOUN
ejpam-3812	493	3	,	,	PUNCT
ejpam-3812	493	4	312(19):2905–2914	312(19):2905–2914	NUM
ejpam-3812	493	5	,	,	PUNCT
ejpam-3812	493	6	2012	2012	NUM
ejpam-3812	493	7	.	.	PUNCT
ejpam-3812	494	1	[	[	X
ejpam-3812	494	2	5	5	X
ejpam-3812	494	3	]	]	PUNCT
ejpam-3812	494	4	w.	w.	PROPN
ejpam-3812	494	5	goddard	goddard	PROPN
ejpam-3812	494	6	.	.	PUNCT
ejpam-3812	494	7	m.	m.	PROPN
ejpam-3812	494	8	henning	henning	PROPN
ejpam-3812	494	9	and	and	CCONJ
ejpam-3812	494	10	c.	c.	PROPN
ejpam-3812	494	11	mcpillan	mcpillan	PROPN
ejpam-3812	494	12	.	.	PUNCT
ejpam-3812	495	1	semitotal	semitotal	ADJ
ejpam-3812	495	2	domination	domination	NOUN
ejpam-3812	495	3	in	in	ADP
ejpam-3812	495	4	graphs	graph	NOUN
ejpam-3812	495	5	.	.	PUNCT
ejpam-3812	496	1	utilitas	utilitas	PROPN
ejpam-3812	496	2	mathematica	mathematica	PROPN
ejpam-3812	496	3	,	,	PUNCT
ejpam-3812	496	4	94:67–81	94:67–81	NUM
ejpam-3812	496	5	,	,	PUNCT
ejpam-3812	496	6	2014	2014	NUM
ejpam-3812	496	7	.	.	PUNCT
ejpam-3812	497	1	[	[	X
ejpam-3812	497	2	6	6	NUM
ejpam-3812	497	3	]	]	PUNCT
ejpam-3812	497	4	e.	e.	PROPN
ejpam-3812	497	5	maravilla	maravilla	PROPN
ejpam-3812	497	6	.	.	PUNCT
ejpam-3812	497	7	r.	r.	PROPN
ejpam-3812	497	8	isla	isla	PROPN
ejpam-3812	497	9	and	and	CCONJ
ejpam-3812	497	10	s.	s.	PROPN
ejpam-3812	497	11	canoy	canoy	PROPN
ejpam-3812	497	12	jr	jr	PROPN
ejpam-3812	497	13	.	.	PUNCT
ejpam-3812	498	1	k	k	ADJ
ejpam-3812	498	2	-	-	PUNCT
ejpam-3812	498	3	fair	fair	ADJ
ejpam-3812	498	4	domination	domination	NOUN
ejpam-3812	498	5	in	in	ADP
ejpam-3812	498	6	the	the	DET
ejpam-3812	498	7	join	join	NOUN
ejpam-3812	498	8	,	,	PUNCT
ejpam-3812	498	9	corona	corona	NOUN
ejpam-3812	498	10	,	,	PUNCT
ejpam-3812	498	11	composition	composition	NOUN
ejpam-3812	498	12	and	and	CCONJ
ejpam-3812	498	13	cartesian	cartesian	ADJ
ejpam-3812	498	14	product	product	NOUN
ejpam-3812	498	15	of	of	ADP
ejpam-3812	498	16	graphs	graph	NOUN
ejpam-3812	498	17	.	.	PUNCT
ejpam-3812	499	1	applied	apply	VERB
ejpam-3812	499	2	mathematical	mathematical	ADJ
ejpam-3812	499	3	sciences	science	NOUN
ejpam-3812	499	4	,	,	PUNCT
ejpam-3812	499	5	8(178):8863–8874	8(178):8863–8874	NOUN
ejpam-3812	499	6	,	,	PUNCT
ejpam-3812	499	7	2014	2014	NUM
ejpam-3812	499	8	.	.	PUNCT
ejpam-3812	500	1	[	[	X
ejpam-3812	500	2	7	7	X
ejpam-3812	500	3	]	]	X
ejpam-3812	500	4	w.	w.	PROPN
ejpam-3812	500	5	bent	bent	PROPN
ejpam-3812	500	6	-	-	PUNCT
ejpam-3812	500	7	usman	usman	PROPN
ejpam-3812	500	8	.	.	PUNCT
ejpam-3812	501	1	r.	r.	PROPN
ejpam-3812	501	2	isla	isla	PROPN
ejpam-3812	501	3	and	and	CCONJ
ejpam-3812	501	4	s.	s.	PROPN
ejpam-3812	501	5	canoy	canoy	PROPN
ejpam-3812	501	6	jr	jr	PROPN
ejpam-3812	501	7	.	.	PROPN
ejpam-3812	501	8	neighborhood	neighborhood	PROPN
ejpam-3812	501	9	connected	connect	VERB
ejpam-3812	501	10	k	k	ADJ
ejpam-3812	501	11	-	-	PUNCT
ejpam-3812	501	12	fair	fair	ADJ
ejpam-3812	501	13	domination	domination	NOUN
ejpam-3812	501	14	under	under	ADP
ejpam-3812	501	15	some	some	DET
ejpam-3812	501	16	binary	binary	ADJ
ejpam-3812	501	17	operations	operation	NOUN
ejpam-3812	501	18	.	.	PUNCT
ejpam-3812	502	1	european	european	ADJ
ejpam-3812	502	2	journal	journal	PROPN
ejpam-3812	502	3	of	of	ADP
ejpam-3812	502	4	pure	pure	ADJ
ejpam-3812	502	5	and	and	CCONJ
ejpam-3812	502	6	applied	applied	ADJ
ejpam-3812	502	7	mathematics	mathematic	NOUN
ejpam-3812	502	8	,	,	PUNCT
ejpam-3812	502	9	12(3):1337–1349	12(3):1337–1349	NUM
ejpam-3812	502	10	,	,	PUNCT
ejpam-3812	502	11	2019	2019	NUM
ejpam-3812	502	12	.	.	PUNCT
ejpam-3812	503	1	[	[	X
ejpam-3812	503	2	8	8	NUM
ejpam-3812	503	3	]	]	X
ejpam-3812	503	4	i.	i.	NOUN
ejpam-3812	503	5	aniversario	aniversario	PROPN
ejpam-3812	503	6	.	.	PUNCT
ejpam-3812	504	1	s.	s.	PROPN
ejpam-3812	504	2	canoy	canoy	PROPN
ejpam-3812	504	3	jr	jr	PROPN
ejpam-3812	504	4	and	and	CCONJ
ejpam-3812	504	5	f.	f.	PROPN
ejpam-3812	504	6	jamil	jamil	PROPN
ejpam-3812	504	7	.	.	PUNCT
ejpam-3812	505	1	on	on	ADP
ejpam-3812	505	2	semitotal	semitotal	ADJ
ejpam-3812	505	3	domination	domination	NOUN
ejpam-3812	505	4	in	in	ADP
ejpam-3812	505	5	graphs	graph	NOUN
ejpam-3812	505	6	.	.	PUNCT
ejpam-3812	506	1	european	european	ADJ
ejpam-3812	506	2	journal	journal	PROPN
ejpam-3812	506	3	of	of	ADP
ejpam-3812	506	4	pure	pure	ADJ
ejpam-3812	506	5	and	and	CCONJ
ejpam-3812	506	6	applied	applied	ADJ
ejpam-3812	506	7	mathematics	mathematic	NOUN
ejpam-3812	506	8	,	,	PUNCT
ejpam-3812	506	9	12(4):1410–1425	12(4):1410–1425	NUM
ejpam-3812	506	10	,	,	PUNCT
ejpam-3812	506	11	2019	2019	NUM
ejpam-3812	506	12	.	.	PUNCT
ejpam-3812	507	1	[	[	X
ejpam-3812	507	2	9	9	NUM
ejpam-3812	507	3	]	]	X
ejpam-3812	507	4	o.	o.	NOUN
ejpam-3812	507	5	ore	ore	PROPN
ejpam-3812	507	6	.	.	PUNCT
ejpam-3812	507	7	theory	theory	NOUN
ejpam-3812	507	8	of	of	ADP
ejpam-3812	507	9	graphs	graph	NOUN
ejpam-3812	507	10	.	.	PUNCT
ejpam-3812	508	1	amer	amer	PROPN
ejpam-3812	508	2	.	.	PUNCT
ejpam-3812	508	3	math	math	PROPN
ejpam-3812	508	4	.	.	PUNCT
ejpam-3812	509	1	colloq	colloq	PROPN
ejpam-3812	509	2	.	.	PUNCT
ejpam-3812	510	1	publ	publ	PROPN
ejpam-3812	510	2	.	.	PUNCT
ejpam-3812	510	3	,	,	PUNCT
ejpam-3812	511	1	38:206–212	38:206–212	NUM
ejpam-3812	511	2	,	,	PUNCT
ejpam-3812	511	3	1962	1962	NUM
ejpam-3812	511	4	.	.	PUNCT