id	sid	tid	token	lemma	pos
ejpam-3904	1	1	european	european	PROPN
ejpam-3904	1	2	journal	journal	PROPN
ejpam-3904	1	3	of	of	ADP
ejpam-3904	1	4	pure	pure	ADJ
ejpam-3904	1	5	and	and	CCONJ
ejpam-3904	1	6	applied	apply	VERB
ejpam-3904	1	7	mathematics	mathematic	NOUN
ejpam-3904	1	8	vol	vol	NOUN
ejpam-3904	1	9	.	.	PUNCT
ejpam-3904	2	1	14	14	NUM
ejpam-3904	2	2	,	,	PUNCT
ejpam-3904	2	3	no	no	INTJ
ejpam-3904	2	4	.	.	NOUN
ejpam-3904	2	5	1	1	NUM
ejpam-3904	2	6	,	,	PUNCT
ejpam-3904	2	7	2021	2021	NUM
ejpam-3904	2	8	,	,	PUNCT
ejpam-3904	2	9	149	149	NUM
ejpam-3904	2	10	-	-	SYM
ejpam-3904	2	11	163	163	NUM
ejpam-3904	2	12	issn	issn	PROPN
ejpam-3904	2	13	1307	1307	NUM
ejpam-3904	2	14	-	-	SYM
ejpam-3904	2	15	5543	5543	NUM
ejpam-3904	2	16	–	–	PUNCT
ejpam-3904	2	17	ejpam.com	ejpam.com	X
ejpam-3904	2	18	published	publish	VERB
ejpam-3904	2	19	by	by	ADP
ejpam-3904	2	20	new	new	PROPN
ejpam-3904	2	21	york	york	PROPN
ejpam-3904	2	22	business	business	PROPN
ejpam-3904	2	23	global	global	PROPN
ejpam-3904	2	24	on	on	ADP
ejpam-3904	2	25	independent	independent	ADJ
ejpam-3904	2	26	transversal	transversal	ADJ
ejpam-3904	2	27	dominating	dominating	NOUN
ejpam-3904	2	28	sets	set	NOUN
ejpam-3904	2	29	in	in	ADP
ejpam-3904	2	30	graphs	graph	NOUN
ejpam-3904	2	31	daven	daven	PROPN
ejpam-3904	2	32	s.	s.	PROPN
ejpam-3904	2	33	sevilleno1,∗	sevilleno1,∗	PROPN
ejpam-3904	2	34	,	,	PUNCT
ejpam-3904	3	1	ferdinand	ferdinand	PROPN
ejpam-3904	3	2	p.	p.	PROPN
ejpam-3904	3	3	jamil2	jamil2	PROPN
ejpam-3904	4	1	1	1	NUM
ejpam-3904	4	2	department	department	NOUN
ejpam-3904	4	3	of	of	ADP
ejpam-3904	4	4	mathematics	mathematic	NOUN
ejpam-3904	4	5	and	and	CCONJ
ejpam-3904	4	6	statistics	statistic	NOUN
ejpam-3904	4	7	,	,	PUNCT
ejpam-3904	4	8	college	college	NOUN
ejpam-3904	4	9	of	of	ADP
ejpam-3904	4	10	liberal	liberal	ADJ
ejpam-3904	4	11	arts	art	NOUN
ejpam-3904	4	12	,	,	PUNCT
ejpam-3904	4	13	sciences	science	NOUN
ejpam-3904	4	14	and	and	CCONJ
ejpam-3904	4	15	education	education	NOUN
ejpam-3904	4	16	,	,	PUNCT
ejpam-3904	4	17	university	university	PROPN
ejpam-3904	4	18	of	of	ADP
ejpam-3904	4	19	san	san	PROPN
ejpam-3904	4	20	agustin	agustin	PROPN
ejpam-3904	4	21	,	,	PUNCT
ejpam-3904	4	22	5000	5000	NUM
ejpam-3904	4	23	iloilo	iloilo	PROPN
ejpam-3904	4	24	city	city	NOUN
ejpam-3904	4	25	philippines	philippines	PROPN
ejpam-3904	4	26	2	2	NUM
ejpam-3904	4	27	department	department	NOUN
ejpam-3904	4	28	of	of	ADP
ejpam-3904	4	29	mathematics	mathematic	NOUN
ejpam-3904	4	30	and	and	CCONJ
ejpam-3904	4	31	statistics	statistic	NOUN
ejpam-3904	4	32	,	,	PUNCT
ejpam-3904	4	33	college	college	NOUN
ejpam-3904	4	34	of	of	ADP
ejpam-3904	4	35	science	science	NOUN
ejpam-3904	4	36	and	and	CCONJ
ejpam-3904	4	37	mathematics	mathematic	NOUN
ejpam-3904	4	38	,	,	PUNCT
ejpam-3904	4	39	center	center	NOUN
ejpam-3904	4	40	of	of	ADP
ejpam-3904	4	41	graph	graph	NOUN
ejpam-3904	4	42	theory	theory	NOUN
ejpam-3904	4	43	,	,	PUNCT
ejpam-3904	4	44	algebra	algebra	NOUN
ejpam-3904	4	45	and	and	CCONJ
ejpam-3904	4	46	analysis	analysis	NOUN
ejpam-3904	4	47	,	,	PUNCT
ejpam-3904	4	48	premier	premier	PROPN
ejpam-3904	4	49	research	research	PROPN
ejpam-3904	4	50	institute	institute	PROPN
ejpam-3904	4	51	of	of	ADP
ejpam-3904	4	52	science	science	NOUN
ejpam-3904	4	53	and	and	CCONJ
ejpam-3904	4	54	mathematics	mathematic	NOUN
ejpam-3904	4	55	,	,	PUNCT
ejpam-3904	4	56	mindanao	mindanao	PROPN
ejpam-3904	4	57	state	state	PROPN
ejpam-3904	4	58	university	university	PROPN
ejpam-3904	4	59	-	-	PUNCT
ejpam-3904	4	60	iligan	iligan	PROPN
ejpam-3904	4	61	institute	institute	PROPN
ejpam-3904	4	62	of	of	ADP
ejpam-3904	4	63	technology	technology	PROPN
ejpam-3904	4	64	,	,	PUNCT
ejpam-3904	4	65	9200	9200	NUM
ejpam-3904	4	66	iligan	iligan	ADJ
ejpam-3904	4	67	city	city	NOUN
ejpam-3904	4	68	,	,	PUNCT
ejpam-3904	4	69	philippines	philippine	NOUN
ejpam-3904	4	70	abstract	abstract	ADJ
ejpam-3904	4	71	.	.	PUNCT
ejpam-3904	5	1	a	a	DET
ejpam-3904	5	2	set	set	NOUN
ejpam-3904	5	3	s	s	NOUN
ejpam-3904	5	4	⊆	⊆	NUM
ejpam-3904	5	5	v	v	NOUN
ejpam-3904	5	6	(	(	PUNCT
ejpam-3904	5	7	g	g	NOUN
ejpam-3904	5	8	)	)	PUNCT
ejpam-3904	5	9	is	be	AUX
ejpam-3904	5	10	an	an	DET
ejpam-3904	5	11	independent	independent	ADJ
ejpam-3904	5	12	transversal	transversal	NOUN
ejpam-3904	5	13	dominating	dominating	NOUN
ejpam-3904	5	14	set	set	NOUN
ejpam-3904	5	15	of	of	ADP
ejpam-3904	5	16	a	a	DET
ejpam-3904	5	17	graph	graph	NOUN
ejpam-3904	5	18	g	g	NOUN
ejpam-3904	5	19	if	if	SCONJ
ejpam-3904	5	20	s	s	VERB
ejpam-3904	5	21	is	be	AUX
ejpam-3904	5	22	a	a	DET
ejpam-3904	5	23	dominating	dominating	NOUN
ejpam-3904	5	24	set	set	NOUN
ejpam-3904	5	25	of	of	ADP
ejpam-3904	5	26	g	g	NOUN
ejpam-3904	5	27	and	and	CCONJ
ejpam-3904	5	28	intersects	intersect	VERB
ejpam-3904	5	29	every	every	DET
ejpam-3904	5	30	maximum	maximum	ADJ
ejpam-3904	5	31	independent	independent	ADJ
ejpam-3904	5	32	set	set	NOUN
ejpam-3904	5	33	of	of	ADP
ejpam-3904	5	34	g.	g.	PROPN
ejpam-3904	5	35	an	an	DET
ejpam-3904	5	36	independent	independent	ADJ
ejpam-3904	5	37	transversal	transversal	NOUN
ejpam-3904	5	38	dominating	dominating	NOUN
ejpam-3904	5	39	set	set	NOUN
ejpam-3904	5	40	which	which	PRON
ejpam-3904	5	41	is	be	AUX
ejpam-3904	5	42	a	a	DET
ejpam-3904	5	43	total	total	ADJ
ejpam-3904	5	44	dominating	dominating	NOUN
ejpam-3904	5	45	set	set	NOUN
ejpam-3904	5	46	is	be	AUX
ejpam-3904	5	47	an	an	DET
ejpam-3904	5	48	independent	independent	ADJ
ejpam-3904	5	49	transversal	transversal	ADJ
ejpam-3904	5	50	total	total	NOUN
ejpam-3904	5	51	dominating	dominating	NOUN
ejpam-3904	5	52	set	set	NOUN
ejpam-3904	5	53	.	.	PUNCT
ejpam-3904	6	1	the	the	DET
ejpam-3904	6	2	minimum	minimum	ADJ
ejpam-3904	6	3	cardinality	cardinality	PROPN
ejpam-3904	6	4	γit(g	γit(g	PROPN
ejpam-3904	6	5	)	)	PUNCT
ejpam-3904	6	6	(	(	PUNCT
ejpam-3904	6	7	resp	resp	NOUN
ejpam-3904	6	8	.	.	PUNCT
ejpam-3904	7	1	γitt(g	γitt(g	NOUN
ejpam-3904	7	2	)	)	PUNCT
ejpam-3904	7	3	)	)	PUNCT
ejpam-3904	7	4	of	of	ADP
ejpam-3904	7	5	an	an	DET
ejpam-3904	7	6	independent	independent	ADJ
ejpam-3904	7	7	transversal	transversal	NOUN
ejpam-3904	7	8	dominating	dominating	NOUN
ejpam-3904	7	9	set	set	NOUN
ejpam-3904	7	10	(	(	PUNCT
ejpam-3904	7	11	resp	resp	NOUN
ejpam-3904	7	12	.	.	PUNCT
ejpam-3904	8	1	independent	independent	ADJ
ejpam-3904	8	2	transversal	transversal	ADJ
ejpam-3904	8	3	total	total	NOUN
ejpam-3904	8	4	dominating	dominating	NOUN
ejpam-3904	8	5	set	set	NOUN
ejpam-3904	8	6	)	)	PUNCT
ejpam-3904	8	7	of	of	ADP
ejpam-3904	8	8	g	g	PROPN
ejpam-3904	8	9	is	be	AUX
ejpam-3904	8	10	the	the	DET
ejpam-3904	8	11	independent	independent	ADJ
ejpam-3904	8	12	transversal	transversal	ADJ
ejpam-3904	8	13	domination	domination	NOUN
ejpam-3904	8	14	number	number	NOUN
ejpam-3904	8	15	(	(	PUNCT
ejpam-3904	8	16	resp	resp	NOUN
ejpam-3904	8	17	.	.	PUNCT
ejpam-3904	9	1	independent	independent	ADJ
ejpam-3904	9	2	transversal	transversal	ADJ
ejpam-3904	9	3	total	total	ADJ
ejpam-3904	9	4	domination	domination	NOUN
ejpam-3904	9	5	number	number	NOUN
ejpam-3904	9	6	)	)	PUNCT
ejpam-3904	9	7	of	of	ADP
ejpam-3904	9	8	g.	g.	PROPN
ejpam-3904	9	9	in	in	ADP
ejpam-3904	9	10	this	this	DET
ejpam-3904	9	11	paper	paper	NOUN
ejpam-3904	9	12	,	,	PUNCT
ejpam-3904	9	13	we	we	PRON
ejpam-3904	9	14	show	show	VERB
ejpam-3904	9	15	that	that	SCONJ
ejpam-3904	9	16	for	for	ADP
ejpam-3904	9	17	every	every	DET
ejpam-3904	9	18	positive	positive	ADJ
ejpam-3904	9	19	integers	integer	NOUN
ejpam-3904	9	20	a	a	PRON
ejpam-3904	9	21	and	and	CCONJ
ejpam-3904	9	22	b	b	NOUN
ejpam-3904	9	23	with	with	ADP
ejpam-3904	9	24	5	5	NUM
ejpam-3904	9	25	≤	≤	NOUN
ejpam-3904	9	26	a	a	DET
ejpam-3904	9	27	≤	≤	NUM
ejpam-3904	9	28	b	b	NOUN
ejpam-3904	9	29	≤	≤	NOUN
ejpam-3904	9	30	2a−	2a−	NUM
ejpam-3904	9	31	2	2	NUM
ejpam-3904	9	32	,	,	PUNCT
ejpam-3904	9	33	there	there	PRON
ejpam-3904	9	34	exists	exist	VERB
ejpam-3904	9	35	a	a	DET
ejpam-3904	9	36	connected	connected	ADJ
ejpam-3904	9	37	graph	graph	NOUN
ejpam-3904	9	38	g	g	NOUN
ejpam-3904	9	39	for	for	ADP
ejpam-3904	9	40	which	which	PRON
ejpam-3904	9	41	γit(g	γit(g	NOUN
ejpam-3904	9	42	)	)	PUNCT
ejpam-3904	9	43	=	=	SYM
ejpam-3904	9	44	a	a	PRON
ejpam-3904	9	45	and	and	CCONJ
ejpam-3904	9	46	γitt(g	γitt(g	NOUN
ejpam-3904	9	47	)	)	PUNCT
ejpam-3904	10	1	=	=	SYM
ejpam-3904	10	2	b.	b.	NOUN
ejpam-3904	10	3	we	we	PRON
ejpam-3904	10	4	also	also	ADV
ejpam-3904	10	5	study	study	VERB
ejpam-3904	10	6	these	these	DET
ejpam-3904	10	7	two	two	NUM
ejpam-3904	10	8	concepts	concept	NOUN
ejpam-3904	10	9	in	in	ADP
ejpam-3904	10	10	graphs	graph	NOUN
ejpam-3904	10	11	which	which	PRON
ejpam-3904	10	12	are	be	AUX
ejpam-3904	10	13	the	the	DET
ejpam-3904	10	14	join	join	NOUN
ejpam-3904	10	15	,	,	PUNCT
ejpam-3904	10	16	corona	corona	NOUN
ejpam-3904	10	17	or	or	CCONJ
ejpam-3904	10	18	composition	composition	NOUN
ejpam-3904	10	19	of	of	ADP
ejpam-3904	10	20	graphs	graph	NOUN
ejpam-3904	10	21	.	.	PUNCT
ejpam-3904	11	1	2020	2020	NUM
ejpam-3904	11	2	mathematics	mathematic	NOUN
ejpam-3904	11	3	subject	subject	NOUN
ejpam-3904	11	4	classifications	classification	NOUN
ejpam-3904	11	5	:	:	PUNCT
ejpam-3904	11	6	05c22	05c22	NOUN
ejpam-3904	11	7	,	,	PUNCT
ejpam-3904	11	8	05c69	05c69	NUM
ejpam-3904	11	9	,	,	PUNCT
ejpam-3904	11	10	05c776	05c776	NOUN
ejpam-3904	11	11	key	key	ADJ
ejpam-3904	11	12	words	word	NOUN
ejpam-3904	11	13	and	and	CCONJ
ejpam-3904	11	14	phrases	phrase	NOUN
ejpam-3904	11	15	:	:	PUNCT
ejpam-3904	11	16	independent	independent	ADJ
ejpam-3904	11	17	transversal	transversal	ADJ
ejpam-3904	11	18	dominating	dominating	NOUN
ejpam-3904	11	19	set	set	NOUN
ejpam-3904	11	20	,	,	PUNCT
ejpam-3904	11	21	independent	independent	ADJ
ejpam-3904	11	22	transversal	transversal	ADJ
ejpam-3904	11	23	total	total	NOUN
ejpam-3904	11	24	dominating	dominating	NOUN
ejpam-3904	11	25	set	set	NOUN
ejpam-3904	11	26	,	,	PUNCT
ejpam-3904	11	27	independent	independent	ADJ
ejpam-3904	11	28	transversal	transversal	ADJ
ejpam-3904	11	29	domination	domination	NOUN
ejpam-3904	11	30	number	number	NOUN
ejpam-3904	11	31	,	,	PUNCT
ejpam-3904	11	32	independent	independent	ADJ
ejpam-3904	11	33	transversal	transversal	ADJ
ejpam-3904	11	34	total	total	NOUN
ejpam-3904	11	35	domination	domination	NOUN
ejpam-3904	11	36	number	number	NOUN
ejpam-3904	11	37	1	1	NUM
ejpam-3904	11	38	.	.	PUNCT
ejpam-3904	11	39	introduction	introduction	NOUN
ejpam-3904	11	40	throughout	throughout	ADP
ejpam-3904	11	41	this	this	DET
ejpam-3904	11	42	paper	paper	NOUN
ejpam-3904	11	43	,	,	PUNCT
ejpam-3904	11	44	by	by	ADP
ejpam-3904	11	45	a	a	DET
ejpam-3904	11	46	graph	graph	NOUN
ejpam-3904	11	47	g	g	NOUN
ejpam-3904	11	48	=	=	PUNCT
ejpam-3904	11	49	(	(	PUNCT
ejpam-3904	11	50	v	v	NOUN
ejpam-3904	11	51	(	(	PUNCT
ejpam-3904	11	52	g	g	NOUN
ejpam-3904	11	53	)	)	PUNCT
ejpam-3904	11	54	,	,	PUNCT
ejpam-3904	11	55	e(g	e(g	PROPN
ejpam-3904	11	56	)	)	PUNCT
ejpam-3904	11	57	)	)	PUNCT
ejpam-3904	11	58	is	be	AUX
ejpam-3904	11	59	meant	mean	VERB
ejpam-3904	11	60	a	a	DET
ejpam-3904	11	61	finite	finite	NOUN
ejpam-3904	11	62	,	,	PUNCT
ejpam-3904	11	63	simple	simple	ADJ
ejpam-3904	11	64	and	and	CCONJ
ejpam-3904	11	65	connected	connected	ADJ
ejpam-3904	11	66	graph	graph	NOUN
ejpam-3904	11	67	with	with	ADP
ejpam-3904	11	68	v	v	NOUN
ejpam-3904	11	69	(	(	PUNCT
ejpam-3904	11	70	g	g	NOUN
ejpam-3904	11	71	)	)	PUNCT
ejpam-3904	11	72	and	and	CCONJ
ejpam-3904	11	73	e(g	e(g	PROPN
ejpam-3904	11	74	)	)	PUNCT
ejpam-3904	11	75	being	be	AUX
ejpam-3904	11	76	the	the	DET
ejpam-3904	11	77	vertex	vertex	NOUN
ejpam-3904	11	78	set	set	NOUN
ejpam-3904	11	79	and	and	CCONJ
ejpam-3904	11	80	edge	edge	NOUN
ejpam-3904	11	81	set	set	NOUN
ejpam-3904	11	82	,	,	PUNCT
ejpam-3904	11	83	respectively	respectively	ADV
ejpam-3904	11	84	.	.	PUNCT
ejpam-3904	12	1	for	for	ADP
ejpam-3904	12	2	s	s	PROPN
ejpam-3904	12	3	⊆	⊆	NUM
ejpam-3904	12	4	v	v	NOUN
ejpam-3904	12	5	(	(	PUNCT
ejpam-3904	12	6	g	g	NOUN
ejpam-3904	12	7	)	)	PUNCT
ejpam-3904	12	8	,	,	PUNCT
ejpam-3904	12	9	|s|	|s|	PROPN
ejpam-3904	12	10	is	be	AUX
ejpam-3904	12	11	the	the	DET
ejpam-3904	12	12	cardinality	cardinality	NOUN
ejpam-3904	12	13	of	of	ADP
ejpam-3904	12	14	s.	s.	PROPN
ejpam-3904	12	15	in	in	ADP
ejpam-3904	12	16	particular	particular	ADJ
ejpam-3904	12	17	,	,	PUNCT
ejpam-3904	12	18	|v	|v	PROPN
ejpam-3904	12	19	(	(	PUNCT
ejpam-3904	12	20	g)|	g)|	PROPN
ejpam-3904	12	21	is	be	AUX
ejpam-3904	12	22	called	call	VERB
ejpam-3904	12	23	the	the	DET
ejpam-3904	12	24	order	order	NOUN
ejpam-3904	12	25	of	of	ADP
ejpam-3904	12	26	g.	g.	PROPN
ejpam-3904	12	27	all	all	DET
ejpam-3904	12	28	basic	basic	ADJ
ejpam-3904	12	29	terminologies	terminology	NOUN
ejpam-3904	12	30	used	use	VERB
ejpam-3904	12	31	here	here	ADV
ejpam-3904	12	32	are	be	AUX
ejpam-3904	12	33	adapted	adapt	VERB
ejpam-3904	12	34	from	from	ADP
ejpam-3904	12	35	[	[	X
ejpam-3904	12	36	4	4	NUM
ejpam-3904	12	37	]	]	PUNCT
ejpam-3904	12	38	.	.	PUNCT
ejpam-3904	13	1	given	give	VERB
ejpam-3904	13	2	two	two	NUM
ejpam-3904	13	3	graphs	graph	NOUN
ejpam-3904	13	4	g	g	NOUN
ejpam-3904	13	5	and	and	CCONJ
ejpam-3904	13	6	h	h	NOUN
ejpam-3904	13	7	with	with	ADP
ejpam-3904	13	8	disjoint	disjoint	ADJ
ejpam-3904	13	9	vertex	vertex	NOUN
ejpam-3904	13	10	sets	set	NOUN
ejpam-3904	13	11	,	,	PUNCT
ejpam-3904	13	12	•	•	ADP
ejpam-3904	13	13	the	the	DET
ejpam-3904	13	14	union	union	NOUN
ejpam-3904	13	15	of	of	ADP
ejpam-3904	13	16	g	g	PROPN
ejpam-3904	13	17	and	and	CCONJ
ejpam-3904	13	18	h	h	NOUN
ejpam-3904	13	19	,	,	PUNCT
ejpam-3904	13	20	denoted	denote	VERB
ejpam-3904	13	21	g	g	PROPN
ejpam-3904	13	22	∪h	∪h	NUM
ejpam-3904	13	23	,	,	PUNCT
ejpam-3904	13	24	is	be	AUX
ejpam-3904	13	25	the	the	DET
ejpam-3904	13	26	graph	graph	NOUN
ejpam-3904	13	27	with	with	ADP
ejpam-3904	13	28	vertex	vertex	NOUN
ejpam-3904	13	29	set	set	VERB
ejpam-3904	13	30	v	v	NOUN
ejpam-3904	13	31	(	(	PUNCT
ejpam-3904	13	32	g	g	NOUN
ejpam-3904	13	33	)	)	PUNCT
ejpam-3904	13	34	∪	∪	NOUN
ejpam-3904	13	35	v	v	NOUN
ejpam-3904	13	36	(	(	PUNCT
ejpam-3904	13	37	h	h	NOUN
ejpam-3904	13	38	)	)	PUNCT
ejpam-3904	13	39	and	and	CCONJ
ejpam-3904	13	40	edge	edge	VERB
ejpam-3904	13	41	set	set	VERB
ejpam-3904	13	42	e(g	e(g	NOUN
ejpam-3904	13	43	)	)	PUNCT
ejpam-3904	13	44	∪	∪	ADP
ejpam-3904	13	45	e(h	e(h	PROPN
ejpam-3904	13	46	)	)	PUNCT
ejpam-3904	13	47	;	;	PUNCT
ejpam-3904	13	48	∗corresponding	∗corresponde	VERB
ejpam-3904	13	49	author	author	NOUN
ejpam-3904	13	50	.	.	PUNCT
ejpam-3904	14	1	doi	doi	NOUN
ejpam-3904	14	2	:	:	PUNCT
ejpam-3904	14	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3904	https://doi.org/10.29020/nybg.ejpam.v14i1.3904	NUM
ejpam-3904	14	4	email	email	NOUN
ejpam-3904	14	5	addresses	address	NOUN
ejpam-3904	14	6	:	:	PUNCT
ejpam-3904	15	1	daven.sevilleno@g.msuiit.edu.ph	daven.sevilleno@g.msuiit.edu.ph	PROPN
ejpam-3904	15	2	(	(	PUNCT
ejpam-3904	15	3	d.	d.	PROPN
ejpam-3904	15	4	sevilleno	sevilleno	PROPN
ejpam-3904	15	5	)	)	PUNCT
ejpam-3904	15	6	,	,	PUNCT
ejpam-3904	15	7	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-3904	15	8	(	(	PUNCT
ejpam-3904	15	9	f.	f.	PROPN
ejpam-3904	15	10	jamil	jamil	PROPN
ejpam-3904	15	11	)	)	PUNCT
ejpam-3904	15	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3904	16	1	149	149	NUM
ejpam-3904	16	2	c	c	X
ejpam-3904	16	3	©	©	PROPN
ejpam-3904	16	4	2021	2021	NUM
ejpam-3904	16	5	ejpam	ejpam	VERB
ejpam-3904	16	6	all	all	DET
ejpam-3904	16	7	rights	right	NOUN
ejpam-3904	16	8	reserved	reserve	VERB
ejpam-3904	16	9	.	.	PUNCT
ejpam-3904	17	1	d.	d.	PROPN
ejpam-3904	17	2	sevilleno	sevilleno	PROPN
ejpam-3904	17	3	,	,	PUNCT
ejpam-3904	17	4	f.	f.	PROPN
ejpam-3904	17	5	jamil	jamil	PROPN
ejpam-3904	17	6	/	/	SYM
ejpam-3904	17	7	eur	eur	PROPN
ejpam-3904	17	8	.	.	PUNCT
ejpam-3904	18	1	j.	j.	PROPN
ejpam-3904	18	2	pure	pure	PROPN
ejpam-3904	18	3	appl	appl	PROPN
ejpam-3904	18	4	.	.	PUNCT
ejpam-3904	18	5	math	math	PROPN
ejpam-3904	18	6	,	,	PUNCT
ejpam-3904	18	7	149	149	NUM
ejpam-3904	18	8	-	-	SYM
ejpam-3904	18	9	163	163	NUM
ejpam-3904	18	10	150	150	NUM
ejpam-3904	18	11	•	•	NOUN
ejpam-3904	18	12	the	the	DET
ejpam-3904	18	13	join	join	NOUN
ejpam-3904	18	14	of	of	ADP
ejpam-3904	18	15	g	g	PROPN
ejpam-3904	18	16	and	and	CCONJ
ejpam-3904	18	17	h	h	NOUN
ejpam-3904	18	18	is	be	AUX
ejpam-3904	18	19	the	the	DET
ejpam-3904	18	20	graph	graph	NOUN
ejpam-3904	18	21	g+h	g+h	PROPN
ejpam-3904	18	22	with	with	ADP
ejpam-3904	18	23	vertex	vertex	NOUN
ejpam-3904	18	24	set	set	VERB
ejpam-3904	18	25	v	v	NOUN
ejpam-3904	18	26	(	(	PUNCT
ejpam-3904	18	27	g	g	NOUN
ejpam-3904	18	28	)	)	PUNCT
ejpam-3904	18	29	∪	∪	NOUN
ejpam-3904	18	30	v	v	NOUN
ejpam-3904	18	31	(	(	PUNCT
ejpam-3904	18	32	h	h	NOUN
ejpam-3904	18	33	)	)	PUNCT
ejpam-3904	18	34	and	and	CCONJ
ejpam-3904	18	35	edge	edge	VERB
ejpam-3904	18	36	set	set	VERB
ejpam-3904	18	37	e(g	e(g	NOUN
ejpam-3904	18	38	)	)	PUNCT
ejpam-3904	18	39	∪	∪	ADP
ejpam-3904	18	40	e(h	e(h	PROPN
ejpam-3904	18	41	)	)	PUNCT
ejpam-3904	18	42	∪	∪	NOUN
ejpam-3904	18	43	{	{	PUNCT
ejpam-3904	18	44	uv	uv	NOUN
ejpam-3904	18	45	:	:	PUNCT
ejpam-3904	18	46	u	u	PROPN
ejpam-3904	18	47	∈	∈	PROPN
ejpam-3904	18	48	v	v	ADP
ejpam-3904	18	49	(	(	PUNCT
ejpam-3904	18	50	g	g	NOUN
ejpam-3904	18	51	)	)	PUNCT
ejpam-3904	18	52	,	,	PUNCT
ejpam-3904	18	53	v	v	X
ejpam-3904	18	54	∈	∈	PROPN
ejpam-3904	18	55	v	v	NOUN
ejpam-3904	18	56	(	(	PUNCT
ejpam-3904	18	57	h	h	NOUN
ejpam-3904	18	58	)	)	PUNCT
ejpam-3904	18	59	}	}	PUNCT
ejpam-3904	18	60	;	;	PUNCT
ejpam-3904	18	61	•	•	X
ejpam-3904	18	62	the	the	DET
ejpam-3904	18	63	corona	corona	NOUN
ejpam-3904	18	64	of	of	ADP
ejpam-3904	18	65	g	g	PROPN
ejpam-3904	18	66	and	and	CCONJ
ejpam-3904	18	67	h	h	NOUN
ejpam-3904	18	68	is	be	AUX
ejpam-3904	18	69	the	the	DET
ejpam-3904	18	70	graph	graph	NOUN
ejpam-3904	18	71	g	g	PROPN
ejpam-3904	18	72	◦	◦	NOUN
ejpam-3904	18	73	h	h	NOUN
ejpam-3904	18	74	obtained	obtain	VERB
ejpam-3904	18	75	by	by	ADP
ejpam-3904	18	76	taking	take	VERB
ejpam-3904	18	77	one	one	NUM
ejpam-3904	18	78	copy	copy	NOUN
ejpam-3904	18	79	of	of	ADP
ejpam-3904	18	80	g	g	PROPN
ejpam-3904	18	81	and	and	CCONJ
ejpam-3904	18	82	|v	|v	PROPN
ejpam-3904	18	83	(	(	PUNCT
ejpam-3904	18	84	g)|	g)|	NOUN
ejpam-3904	18	85	copies	copy	NOUN
ejpam-3904	18	86	of	of	ADP
ejpam-3904	18	87	h	h	NOUN
ejpam-3904	18	88	,	,	PUNCT
ejpam-3904	18	89	and	and	CCONJ
ejpam-3904	18	90	then	then	ADV
ejpam-3904	18	91	joining	join	VERB
ejpam-3904	18	92	the	the	DET
ejpam-3904	18	93	ith	ith	PROPN
ejpam-3904	18	94	vertex	vertex	NOUN
ejpam-3904	18	95	of	of	ADP
ejpam-3904	18	96	g	g	NOUN
ejpam-3904	18	97	to	to	ADP
ejpam-3904	18	98	every	every	DET
ejpam-3904	18	99	vertex	vertex	NOUN
ejpam-3904	18	100	in	in	ADP
ejpam-3904	18	101	the	the	DET
ejpam-3904	18	102	ith	ith	PROPN
ejpam-3904	18	103	copy	copy	NOUN
ejpam-3904	18	104	of	of	ADP
ejpam-3904	18	105	h	h	NOUN
ejpam-3904	18	106	;	;	PUNCT
ejpam-3904	18	107	and	and	CCONJ
ejpam-3904	18	108	•	•	NUM
ejpam-3904	18	109	the	the	DET
ejpam-3904	18	110	composition	composition	NOUN
ejpam-3904	18	111	g[h	g[h	NOUN
ejpam-3904	18	112	]	]	PUNCT
ejpam-3904	18	113	of	of	ADP
ejpam-3904	18	114	g	g	PROPN
ejpam-3904	18	115	and	and	CCONJ
ejpam-3904	18	116	h	h	NOUN
ejpam-3904	18	117	is	be	AUX
ejpam-3904	18	118	the	the	DET
ejpam-3904	18	119	graph	graph	NOUN
ejpam-3904	18	120	with	with	ADP
ejpam-3904	18	121	v	v	NOUN
ejpam-3904	18	122	(	(	PUNCT
ejpam-3904	18	123	g[h	g[h	PROPN
ejpam-3904	18	124	]	]	PUNCT
ejpam-3904	18	125	)	)	PUNCT
ejpam-3904	18	126	=	=	SYM
ejpam-3904	18	127	v	v	X
ejpam-3904	18	128	(	(	PUNCT
ejpam-3904	18	129	g)×	g)×	NOUN
ejpam-3904	18	130	v	v	NOUN
ejpam-3904	18	131	(	(	PUNCT
ejpam-3904	18	132	h	h	NOUN
ejpam-3904	18	133	)	)	PUNCT
ejpam-3904	18	134	and	and	CCONJ
ejpam-3904	18	135	(	(	PUNCT
ejpam-3904	18	136	u	u	NOUN
ejpam-3904	18	137	,	,	PUNCT
ejpam-3904	18	138	v)(u′	v)(u′	NOUN
ejpam-3904	18	139	,	,	PUNCT
ejpam-3904	18	140	v′	v′	NOUN
ejpam-3904	18	141	)	)	PUNCT
ejpam-3904	18	142	∈	∈	NOUN
ejpam-3904	18	143	e(g[h	e(g[h	NOUN
ejpam-3904	18	144	]	]	PUNCT
ejpam-3904	18	145	)	)	PUNCT
ejpam-3904	19	1	if	if	SCONJ
ejpam-3904	19	2	and	and	CCONJ
ejpam-3904	19	3	only	only	ADV
ejpam-3904	19	4	if	if	SCONJ
ejpam-3904	19	5	either	either	CCONJ
ejpam-3904	19	6	uu′	uu′	PROPN
ejpam-3904	19	7	∈	∈	PROPN
ejpam-3904	19	8	e(g	e(g	PROPN
ejpam-3904	19	9	)	)	PUNCT
ejpam-3904	19	10	or	or	CCONJ
ejpam-3904	19	11	u	u	X
ejpam-3904	19	12	=	=	PUNCT
ejpam-3904	19	13	u′	u′	PROPN
ejpam-3904	19	14	and	and	CCONJ
ejpam-3904	19	15	vv′	vv′	NOUN
ejpam-3904	19	16	∈	∈	PROPN
ejpam-3904	19	17	e(h	e(h	PROPN
ejpam-3904	19	18	)	)	PUNCT
ejpam-3904	19	19	.	.	PUNCT
ejpam-3904	20	1	for	for	ADP
ejpam-3904	20	2	corona	corona	NOUN
ejpam-3904	20	3	of	of	ADP
ejpam-3904	20	4	graphs	graph	NOUN
ejpam-3904	20	5	g	g	PROPN
ejpam-3904	20	6	◦	◦	NOUN
ejpam-3904	20	7	h	h	NOUN
ejpam-3904	20	8	,	,	PUNCT
ejpam-3904	20	9	if	if	SCONJ
ejpam-3904	20	10	h	h	NOUN
ejpam-3904	20	11	=	=	SYM
ejpam-3904	20	12	k1	k1	PROPN
ejpam-3904	20	13	,	,	PUNCT
ejpam-3904	20	14	we	we	PRON
ejpam-3904	20	15	write	write	VERB
ejpam-3904	20	16	g	g	PROPN
ejpam-3904	20	17	◦	◦	NOUN
ejpam-3904	20	18	h	h	NOUN
ejpam-3904	20	19	=	=	SYM
ejpam-3904	20	20	cor(g	cor(g	PROPN
ejpam-3904	20	21	)	)	PUNCT
ejpam-3904	20	22	.	.	PUNCT
ejpam-3904	21	1	it	it	PRON
ejpam-3904	21	2	is	be	AUX
ejpam-3904	21	3	customary	customary	ADJ
ejpam-3904	21	4	to	to	PART
ejpam-3904	21	5	denote	denote	VERB
ejpam-3904	21	6	by	by	ADP
ejpam-3904	21	7	hv	hv	PROPN
ejpam-3904	21	8	that	that	DET
ejpam-3904	21	9	copy	copy	NOUN
ejpam-3904	21	10	of	of	ADP
ejpam-3904	21	11	h	h	NOUN
ejpam-3904	21	12	whose	whose	DET
ejpam-3904	21	13	vertices	vertex	NOUN
ejpam-3904	21	14	are	be	AUX
ejpam-3904	21	15	joined	join	VERB
ejpam-3904	21	16	with	with	ADP
ejpam-3904	21	17	the	the	DET
ejpam-3904	21	18	vertex	vertex	NOUN
ejpam-3904	21	19	v	v	NOUN
ejpam-3904	21	20	of	of	ADP
ejpam-3904	21	21	g.	g.	NOUN
ejpam-3904	21	22	similarly	similarly	ADV
ejpam-3904	21	23	,	,	PUNCT
ejpam-3904	21	24	we	we	PRON
ejpam-3904	21	25	also	also	ADV
ejpam-3904	21	26	write	write	VERB
ejpam-3904	21	27	uv	uv	NOUN
ejpam-3904	21	28	to	to	PART
ejpam-3904	21	29	denote	denote	VERB
ejpam-3904	21	30	that	that	DET
ejpam-3904	21	31	copy	copy	NOUN
ejpam-3904	21	32	of	of	ADP
ejpam-3904	21	33	u	u	PROPN
ejpam-3904	21	34	∈	∈	PROPN
ejpam-3904	21	35	v	v	ADP
ejpam-3904	21	36	(	(	PUNCT
ejpam-3904	21	37	h	h	NOUN
ejpam-3904	21	38	)	)	PUNCT
ejpam-3904	21	39	in	in	ADP
ejpam-3904	21	40	hv	hv	PROPN
ejpam-3904	21	41	.	.	PUNCT
ejpam-3904	22	1	for	for	ADP
ejpam-3904	22	2	vertices	vertex	NOUN
ejpam-3904	22	3	u	u	NOUN
ejpam-3904	22	4	and	and	CCONJ
ejpam-3904	22	5	v	v	NOUN
ejpam-3904	22	6	of	of	ADP
ejpam-3904	22	7	g	g	NOUN
ejpam-3904	22	8	,	,	PUNCT
ejpam-3904	22	9	a	a	DET
ejpam-3904	22	10	u	u	NOUN
ejpam-3904	22	11	-	-	NOUN
ejpam-3904	22	12	v	v	ADJ
ejpam-3904	22	13	geodesic	geodesic	NOUN
ejpam-3904	22	14	is	be	AUX
ejpam-3904	22	15	any	any	DET
ejpam-3904	22	16	shortest	short	ADJ
ejpam-3904	22	17	u	u	NOUN
ejpam-3904	22	18	-	-	NOUN
ejpam-3904	22	19	v	v	ADJ
ejpam-3904	22	20	path	path	NOUN
ejpam-3904	22	21	.	.	PUNCT
ejpam-3904	23	1	the	the	DET
ejpam-3904	23	2	distance	distance	NOUN
ejpam-3904	23	3	between	between	ADP
ejpam-3904	23	4	u	u	NOUN
ejpam-3904	23	5	and	and	CCONJ
ejpam-3904	23	6	v	v	NOUN
ejpam-3904	23	7	is	be	AUX
ejpam-3904	23	8	the	the	DET
ejpam-3904	23	9	length	length	NOUN
ejpam-3904	23	10	of	of	ADP
ejpam-3904	23	11	a	a	DET
ejpam-3904	23	12	u	u	NOUN
ejpam-3904	23	13	-	-	NOUN
ejpam-3904	23	14	v	v	NOUN
ejpam-3904	23	15	geodesic	geodesic	NOUN
ejpam-3904	23	16	,	,	PUNCT
ejpam-3904	23	17	and	and	CCONJ
ejpam-3904	23	18	is	be	AUX
ejpam-3904	23	19	denoted	denote	VERB
ejpam-3904	23	20	by	by	ADP
ejpam-3904	23	21	dg(u	dg(u	NOUN
ejpam-3904	23	22	,	,	PUNCT
ejpam-3904	23	23	v	v	NOUN
ejpam-3904	23	24	)	)	PUNCT
ejpam-3904	23	25	.	.	PUNCT
ejpam-3904	24	1	the	the	DET
ejpam-3904	24	2	eccentricity	eccentricity	NOUN
ejpam-3904	24	3	of	of	ADP
ejpam-3904	24	4	v	v	NOUN
ejpam-3904	24	5	,	,	PUNCT
ejpam-3904	24	6	denoted	denote	VERB
ejpam-3904	24	7	by	by	ADP
ejpam-3904	24	8	e(v	e(v	NOUN
ejpam-3904	24	9	)	)	PUNCT
ejpam-3904	24	10	,	,	PUNCT
ejpam-3904	24	11	is	be	AUX
ejpam-3904	24	12	given	give	VERB
ejpam-3904	24	13	by	by	ADP
ejpam-3904	24	14	e(v	e(v	NOUN
ejpam-3904	24	15	)	)	PUNCT
ejpam-3904	24	16	=	=	SYM
ejpam-3904	24	17	max{dg(u	max{dg(u	X
ejpam-3904	24	18	,	,	PUNCT
ejpam-3904	24	19	v	v	NOUN
ejpam-3904	24	20	)	)	PUNCT
ejpam-3904	24	21	:	:	PUNCT
ejpam-3904	24	22	u	u	PROPN
ejpam-3904	24	23	∈	∈	PROPN
ejpam-3904	24	24	v	v	ADP
ejpam-3904	24	25	(	(	PUNCT
ejpam-3904	24	26	g	g	NOUN
ejpam-3904	24	27	)	)	PUNCT
ejpam-3904	24	28	}	}	PUNCT
ejpam-3904	24	29	.	.	PUNCT
ejpam-3904	25	1	the	the	DET
ejpam-3904	25	2	diameter	diameter	NOUN
ejpam-3904	25	3	of	of	ADP
ejpam-3904	25	4	g	g	PROPN
ejpam-3904	25	5	,	,	PUNCT
ejpam-3904	25	6	denoted	denote	VERB
ejpam-3904	25	7	by	by	ADP
ejpam-3904	25	8	diam(g	diam(g	PROPN
ejpam-3904	25	9	)	)	PUNCT
ejpam-3904	25	10	,	,	PUNCT
ejpam-3904	25	11	is	be	AUX
ejpam-3904	25	12	defined	define	VERB
ejpam-3904	25	13	by	by	ADP
ejpam-3904	25	14	diam(g	diam(g	NOUN
ejpam-3904	25	15	)	)	PUNCT
ejpam-3904	25	16	=	=	SYM
ejpam-3904	25	17	max{dg(u	max{dg(u	X
ejpam-3904	25	18	,	,	PUNCT
ejpam-3904	25	19	v	v	NOUN
ejpam-3904	25	20	)	)	PUNCT
ejpam-3904	25	21	:	:	PUNCT
ejpam-3904	25	22	u	u	NOUN
ejpam-3904	25	23	,	,	PUNCT
ejpam-3904	25	24	v	v	PROPN
ejpam-3904	25	25	∈	∈	PROPN
ejpam-3904	25	26	v	v	NOUN
ejpam-3904	25	27	(	(	PUNCT
ejpam-3904	25	28	g	g	NOUN
ejpam-3904	25	29	)	)	PUNCT
ejpam-3904	25	30	}	}	PUNCT
ejpam-3904	25	31	.	.	PUNCT
ejpam-3904	26	1	any	any	DET
ejpam-3904	26	2	geodesic	geodesic	NOUN
ejpam-3904	26	3	of	of	ADP
ejpam-3904	26	4	length	length	NOUN
ejpam-3904	26	5	diam(g	diam(g	NOUN
ejpam-3904	26	6	)	)	PUNCT
ejpam-3904	26	7	is	be	AUX
ejpam-3904	26	8	called	call	VERB
ejpam-3904	26	9	diametral	diametral	ADJ
ejpam-3904	26	10	path	path	NOUN
ejpam-3904	26	11	of	of	ADP
ejpam-3904	26	12	g.	g.	PROPN
ejpam-3904	26	13	vertices	vertice	VERB
ejpam-3904	26	14	u	u	NOUN
ejpam-3904	26	15	and	and	CCONJ
ejpam-3904	26	16	v	v	NOUN
ejpam-3904	26	17	of	of	ADP
ejpam-3904	26	18	a	a	DET
ejpam-3904	26	19	graph	graph	NOUN
ejpam-3904	26	20	g	g	NOUN
ejpam-3904	26	21	are	be	AUX
ejpam-3904	26	22	neighbors	neighbor	NOUN
ejpam-3904	26	23	if	if	SCONJ
ejpam-3904	26	24	uv	uv	PROPN
ejpam-3904	26	25	∈	∈	PROPN
ejpam-3904	26	26	e(g	e(g	PROPN
ejpam-3904	26	27	)	)	PUNCT
ejpam-3904	26	28	.	.	PUNCT
ejpam-3904	27	1	the	the	DET
ejpam-3904	27	2	open	open	ADJ
ejpam-3904	27	3	neighborhood	neighborhood	NOUN
ejpam-3904	27	4	of	of	ADP
ejpam-3904	27	5	v	v	NOUN
ejpam-3904	27	6	refers	refer	VERB
ejpam-3904	27	7	to	to	ADP
ejpam-3904	27	8	the	the	DET
ejpam-3904	27	9	set	set	NOUN
ejpam-3904	27	10	ng(v	ng(v	PUNCT
ejpam-3904	27	11	)	)	PUNCT
ejpam-3904	27	12	consisting	consist	VERB
ejpam-3904	27	13	of	of	ADP
ejpam-3904	27	14	all	all	DET
ejpam-3904	27	15	neighbors	neighbor	NOUN
ejpam-3904	27	16	of	of	ADP
ejpam-3904	27	17	v.	v.	ADP
ejpam-3904	27	18	the	the	DET
ejpam-3904	27	19	closed	closed	ADJ
ejpam-3904	27	20	neighborhood	neighborhood	NOUN
ejpam-3904	27	21	of	of	ADP
ejpam-3904	27	22	v	v	NOUN
ejpam-3904	27	23	is	be	AUX
ejpam-3904	27	24	the	the	DET
ejpam-3904	27	25	set	set	NOUN
ejpam-3904	27	26	ng[v	ng[v	NOUN
ejpam-3904	27	27	]	]	X
ejpam-3904	27	28	=	=	SYM
ejpam-3904	27	29	ng(v	ng(v	X
ejpam-3904	27	30	)	)	PUNCT
ejpam-3904	27	31	∪	∪	ADP
ejpam-3904	27	32	{	{	PUNCT
ejpam-3904	27	33	v	v	NOUN
ejpam-3904	27	34	}	}	PUNCT
ejpam-3904	27	35	.	.	PUNCT
ejpam-3904	28	1	for	for	ADP
ejpam-3904	28	2	s	s	PROPN
ejpam-3904	28	3	⊆	⊆	NUM
ejpam-3904	28	4	v	v	NOUN
ejpam-3904	28	5	(	(	PUNCT
ejpam-3904	28	6	g	g	NOUN
ejpam-3904	28	7	)	)	PUNCT
ejpam-3904	28	8	,	,	PUNCT
ejpam-3904	28	9	ng(s	ng(s	NUM
ejpam-3904	28	10	)	)	PUNCT
ejpam-3904	28	11	=	=	SYM
ejpam-3904	28	12	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-3904	28	13	)	)	PUNCT
ejpam-3904	28	14	and	and	CCONJ
ejpam-3904	28	15	ng[s	ng[s	PROPN
ejpam-3904	28	16	]	]	PUNCT
ejpam-3904	28	17	=	=	SYM
ejpam-3904	28	18	∪v∈sng[v	∪v∈sng[v	X
ejpam-3904	28	19	]	]	PUNCT
ejpam-3904	28	20	.	.	PUNCT
ejpam-3904	28	21	a	a	DET
ejpam-3904	28	22	subset	subset	NOUN
ejpam-3904	28	23	s	s	VERB
ejpam-3904	28	24	⊆	⊆	NUM
ejpam-3904	28	25	v	v	NOUN
ejpam-3904	28	26	(	(	PUNCT
ejpam-3904	28	27	g	g	NOUN
ejpam-3904	28	28	)	)	PUNCT
ejpam-3904	28	29	is	be	AUX
ejpam-3904	28	30	a	a	DET
ejpam-3904	28	31	dominating	dominating	NOUN
ejpam-3904	28	32	set	set	NOUN
ejpam-3904	28	33	of	of	ADP
ejpam-3904	28	34	g	g	PROPN
ejpam-3904	28	35	if	if	SCONJ
ejpam-3904	28	36	ng[s	ng[	NOUN
ejpam-3904	28	37	]	]	PUNCT
ejpam-3904	28	38	=	=	SYM
ejpam-3904	28	39	v	v	NOUN
ejpam-3904	28	40	(	(	PUNCT
ejpam-3904	28	41	g	g	NOUN
ejpam-3904	28	42	)	)	PUNCT
ejpam-3904	28	43	.	.	PUNCT
ejpam-3904	29	1	the	the	DET
ejpam-3904	29	2	minimum	minimum	PROPN
ejpam-3904	29	3	cardinality	cardinality	PROPN
ejpam-3904	29	4	γ(g	γ(g	PROPN
ejpam-3904	29	5	)	)	PUNCT
ejpam-3904	29	6	of	of	ADP
ejpam-3904	29	7	a	a	DET
ejpam-3904	29	8	dominating	dominating	NOUN
ejpam-3904	29	9	set	set	NOUN
ejpam-3904	29	10	in	in	ADP
ejpam-3904	29	11	g	g	PROPN
ejpam-3904	29	12	is	be	AUX
ejpam-3904	29	13	the	the	DET
ejpam-3904	29	14	domination	domination	NOUN
ejpam-3904	29	15	number	number	NOUN
ejpam-3904	29	16	of	of	ADP
ejpam-3904	29	17	g.	g.	NOUN
ejpam-3904	29	18	we	we	PRON
ejpam-3904	29	19	refer	refer	VERB
ejpam-3904	29	20	to	to	ADP
ejpam-3904	29	21	[	[	X
ejpam-3904	29	22	1	1	NUM
ejpam-3904	29	23	,	,	PUNCT
ejpam-3904	29	24	2	2	NUM
ejpam-3904	29	25	,	,	PUNCT
ejpam-3904	29	26	5	5	NUM
ejpam-3904	29	27	,	,	PUNCT
ejpam-3904	29	28	7	7	NUM
ejpam-3904	29	29	,	,	PUNCT
ejpam-3904	29	30	9	9	NUM
ejpam-3904	29	31	,	,	PUNCT
ejpam-3904	29	32	11	11	NUM
ejpam-3904	29	33	,	,	PUNCT
ejpam-3904	29	34	14	14	NUM
ejpam-3904	29	35	,	,	PUNCT
ejpam-3904	29	36	16	16	NUM
ejpam-3904	29	37	,	,	PUNCT
ejpam-3904	29	38	19	19	NUM
ejpam-3904	29	39	]	]	PUNCT
ejpam-3904	29	40	for	for	ADP
ejpam-3904	29	41	the	the	DET
ejpam-3904	29	42	history	history	NOUN
ejpam-3904	29	43	,	,	PUNCT
ejpam-3904	29	44	fundamental	fundamental	ADJ
ejpam-3904	29	45	concepts	concept	NOUN
ejpam-3904	29	46	and	and	CCONJ
ejpam-3904	29	47	the	the	DET
ejpam-3904	29	48	subsequent	subsequent	ADJ
ejpam-3904	29	49	developments	development	NOUN
ejpam-3904	29	50	of	of	ADP
ejpam-3904	29	51	domination	domination	NOUN
ejpam-3904	29	52	in	in	ADP
ejpam-3904	29	53	graphs	graph	NOUN
ejpam-3904	29	54	as	as	ADV
ejpam-3904	29	55	well	well	ADV
ejpam-3904	29	56	as	as	ADP
ejpam-3904	29	57	its	its	PRON
ejpam-3904	29	58	various	various	ADJ
ejpam-3904	29	59	applications	application	NOUN
ejpam-3904	29	60	.	.	PUNCT
ejpam-3904	30	1	provided	provide	VERB
ejpam-3904	30	2	g	g	PROPN
ejpam-3904	30	3	has	have	AUX
ejpam-3904	30	4	no	no	DET
ejpam-3904	30	5	isolated	isolated	ADJ
ejpam-3904	30	6	vertices	vertex	NOUN
ejpam-3904	30	7	,	,	PUNCT
ejpam-3904	30	8	a	a	DET
ejpam-3904	30	9	dominating	dominating	NOUN
ejpam-3904	30	10	set	set	NOUN
ejpam-3904	30	11	s	s	VERB
ejpam-3904	30	12	is	be	AUX
ejpam-3904	30	13	a	a	DET
ejpam-3904	30	14	total	total	ADJ
ejpam-3904	30	15	dominating	dominating	NOUN
ejpam-3904	30	16	set	set	NOUN
ejpam-3904	30	17	of	of	ADP
ejpam-3904	30	18	g	g	PROPN
ejpam-3904	30	19	if	if	SCONJ
ejpam-3904	30	20	every	every	DET
ejpam-3904	30	21	vertex	vertex	NOUN
ejpam-3904	30	22	in	in	ADP
ejpam-3904	30	23	s	s	PROPN
ejpam-3904	30	24	is	be	AUX
ejpam-3904	30	25	adjacent	adjacent	ADJ
ejpam-3904	30	26	to	to	ADP
ejpam-3904	30	27	another	another	DET
ejpam-3904	30	28	vertex	vertex	NOUN
ejpam-3904	30	29	in	in	ADP
ejpam-3904	30	30	s.	s.	PROPN
ejpam-3904	30	31	the	the	DET
ejpam-3904	30	32	minimum	minimum	ADJ
ejpam-3904	30	33	cardinality	cardinality	NOUN
ejpam-3904	30	34	of	of	ADP
ejpam-3904	30	35	a	a	DET
ejpam-3904	30	36	total	total	ADJ
ejpam-3904	30	37	dominating	dominating	NOUN
ejpam-3904	30	38	set	set	NOUN
ejpam-3904	30	39	of	of	ADP
ejpam-3904	30	40	g	g	PROPN
ejpam-3904	30	41	is	be	AUX
ejpam-3904	30	42	the	the	DET
ejpam-3904	30	43	total	total	ADJ
ejpam-3904	30	44	domination	domination	NOUN
ejpam-3904	30	45	number	number	NOUN
ejpam-3904	30	46	of	of	ADP
ejpam-3904	30	47	g	g	NOUN
ejpam-3904	30	48	denoted	denote	VERB
ejpam-3904	30	49	by	by	ADP
ejpam-3904	30	50	γt(g	γt(g	NOUN
ejpam-3904	30	51	)	)	PUNCT
ejpam-3904	30	52	.	.	PUNCT
ejpam-3904	31	1	references	reference	NOUN
ejpam-3904	31	2	[	[	X
ejpam-3904	31	3	6	6	NUM
ejpam-3904	31	4	,	,	PUNCT
ejpam-3904	31	5	8	8	NUM
ejpam-3904	31	6	,	,	PUNCT
ejpam-3904	31	7	12	12	NUM
ejpam-3904	31	8	]	]	PUNCT
ejpam-3904	31	9	are	be	AUX
ejpam-3904	31	10	excellent	excellent	ADJ
ejpam-3904	31	11	studies	study	NOUN
ejpam-3904	31	12	on	on	ADP
ejpam-3904	31	13	total	total	ADJ
ejpam-3904	31	14	domination	domination	NOUN
ejpam-3904	31	15	in	in	ADP
ejpam-3904	31	16	graphs	graph	NOUN
ejpam-3904	31	17	.	.	PUNCT
ejpam-3904	32	1	a	a	DET
ejpam-3904	32	2	subset	subset	NOUN
ejpam-3904	32	3	s	s	VERB
ejpam-3904	32	4	⊆	⊆	NUM
ejpam-3904	32	5	v	v	NOUN
ejpam-3904	32	6	(	(	PUNCT
ejpam-3904	32	7	g	g	NOUN
ejpam-3904	32	8	)	)	PUNCT
ejpam-3904	32	9	is	be	AUX
ejpam-3904	32	10	an	an	DET
ejpam-3904	32	11	independent	independent	ADJ
ejpam-3904	32	12	set	set	NOUN
ejpam-3904	32	13	of	of	ADP
ejpam-3904	32	14	g	g	PROPN
ejpam-3904	32	15	if	if	SCONJ
ejpam-3904	32	16	for	for	ADP
ejpam-3904	32	17	every	every	DET
ejpam-3904	32	18	distinct	distinct	ADJ
ejpam-3904	32	19	vertices	vertex	NOUN
ejpam-3904	32	20	u	u	NOUN
ejpam-3904	32	21	and	and	CCONJ
ejpam-3904	32	22	v	v	NOUN
ejpam-3904	32	23	in	in	ADP
ejpam-3904	32	24	s	s	PROPN
ejpam-3904	32	25	,	,	PUNCT
ejpam-3904	32	26	uv	uv	PROPN
ejpam-3904	32	27	/∈	/∈	PUNCT
ejpam-3904	32	28	e(g	e(g	PROPN
ejpam-3904	32	29	)	)	PUNCT
ejpam-3904	32	30	.	.	PUNCT
ejpam-3904	33	1	the	the	DET
ejpam-3904	33	2	maximum	maximum	ADJ
ejpam-3904	33	3	cardinality	cardinality	NOUN
ejpam-3904	33	4	of	of	ADP
ejpam-3904	33	5	an	an	DET
ejpam-3904	33	6	independent	independent	ADJ
ejpam-3904	33	7	set	set	NOUN
ejpam-3904	33	8	is	be	AUX
ejpam-3904	33	9	called	call	VERB
ejpam-3904	33	10	the	the	DET
ejpam-3904	33	11	independence	independence	NOUN
ejpam-3904	33	12	number	number	NOUN
ejpam-3904	33	13	of	of	ADP
ejpam-3904	33	14	g	g	NOUN
ejpam-3904	33	15	,	,	PUNCT
ejpam-3904	33	16	and	and	CCONJ
ejpam-3904	33	17	is	be	AUX
ejpam-3904	33	18	denoted	denote	VERB
ejpam-3904	33	19	by	by	ADP
ejpam-3904	33	20	β0(g	β0(g	NOUN
ejpam-3904	33	21	)	)	PUNCT
ejpam-3904	33	22	.	.	PUNCT
ejpam-3904	34	1	any	any	DET
ejpam-3904	34	2	independent	independent	ADJ
ejpam-3904	34	3	set	set	NOUN
ejpam-3904	34	4	of	of	ADP
ejpam-3904	34	5	cardinality	cardinality	PROPN
ejpam-3904	34	6	β0(g	β0(g	NOUN
ejpam-3904	34	7	)	)	PUNCT
ejpam-3904	34	8	is	be	AUX
ejpam-3904	34	9	referred	refer	VERB
ejpam-3904	34	10	to	to	ADP
ejpam-3904	34	11	as	as	ADP
ejpam-3904	34	12	a	a	DET
ejpam-3904	34	13	β0	β0	NOUN
ejpam-3904	34	14	-	-	PUNCT
ejpam-3904	34	15	set	set	NOUN
ejpam-3904	34	16	of	of	ADP
ejpam-3904	34	17	g.	g.	PROPN
ejpam-3904	34	18	in	in	ADP
ejpam-3904	34	19	[	[	X
ejpam-3904	34	20	13	13	NUM
ejpam-3904	34	21	]	]	PUNCT
ejpam-3904	34	22	,	,	PUNCT
ejpam-3904	34	23	it	it	PRON
ejpam-3904	34	24	is	be	AUX
ejpam-3904	34	25	called	call	VERB
ejpam-3904	34	26	a	a	DET
ejpam-3904	34	27	maximum	maximum	ADJ
ejpam-3904	34	28	independent	independent	ADJ
ejpam-3904	34	29	set	set	NOUN
ejpam-3904	34	30	.	.	PUNCT
ejpam-3904	35	1	it	it	PRON
ejpam-3904	35	2	is	be	AUX
ejpam-3904	35	3	worth	worth	ADJ
ejpam-3904	35	4	noting	note	VERB
ejpam-3904	35	5	that	that	SCONJ
ejpam-3904	35	6	if	if	SCONJ
ejpam-3904	35	7	g	g	PROPN
ejpam-3904	35	8	is	be	AUX
ejpam-3904	35	9	complete	complete	ADJ
ejpam-3904	35	10	,	,	PUNCT
ejpam-3904	35	11	then	then	ADV
ejpam-3904	35	12	{	{	PUNCT
ejpam-3904	35	13	v	v	NOUN
ejpam-3904	35	14	}	}	PUNCT
ejpam-3904	35	15	is	be	AUX
ejpam-3904	35	16	a	a	DET
ejpam-3904	35	17	β0	β0	NOUN
ejpam-3904	35	18	-	-	PUNCT
ejpam-3904	35	19	set	set	NOUN
ejpam-3904	35	20	for	for	ADP
ejpam-3904	35	21	all	all	DET
ejpam-3904	35	22	v	v	ADP
ejpam-3904	35	23	∈	∈	NOUN
ejpam-3904	35	24	v	v	NOUN
ejpam-3904	35	25	(	(	PUNCT
ejpam-3904	35	26	g	g	NOUN
ejpam-3904	35	27	)	)	PUNCT
ejpam-3904	35	28	.	.	PUNCT
ejpam-3904	36	1	the	the	DET
ejpam-3904	36	2	symbol	symbol	NOUN
ejpam-3904	36	3	xi(g	xi(g	PUNCT
ejpam-3904	36	4	)	)	PUNCT
ejpam-3904	36	5	denotes	denote	VERB
ejpam-3904	36	6	the	the	DET
ejpam-3904	36	7	family	family	NOUN
ejpam-3904	36	8	of	of	ADP
ejpam-3904	36	9	all	all	DET
ejpam-3904	36	10	β0	β0	NOUN
ejpam-3904	36	11	-	-	PUNCT
ejpam-3904	36	12	sets	set	NOUN
ejpam-3904	36	13	of	of	ADP
ejpam-3904	36	14	g	g	NOUN
ejpam-3904	36	15	,	,	PUNCT
ejpam-3904	36	16	and	and	CCONJ
ejpam-3904	36	17	xi(g	xi(g	NUM
ejpam-3904	36	18	)	)	PUNCT
ejpam-3904	37	1	=	=	NOUN
ejpam-3904	37	2	|xi(g)|	|xi(g)|	NOUN
ejpam-3904	37	3	.	.	PUNCT
ejpam-3904	38	1	a	a	DET
ejpam-3904	38	2	subset	subset	NOUN
ejpam-3904	38	3	s	s	VERB
ejpam-3904	38	4	⊆	⊆	NUM
ejpam-3904	38	5	v	v	NOUN
ejpam-3904	38	6	(	(	PUNCT
ejpam-3904	38	7	g	g	NOUN
ejpam-3904	38	8	)	)	PUNCT
ejpam-3904	38	9	of	of	ADP
ejpam-3904	38	10	g	g	PROPN
ejpam-3904	38	11	is	be	AUX
ejpam-3904	38	12	said	say	VERB
ejpam-3904	38	13	to	to	PART
ejpam-3904	38	14	be	be	AUX
ejpam-3904	38	15	an	an	DET
ejpam-3904	38	16	independent	independent	ADJ
ejpam-3904	38	17	transversal	transversal	NOUN
ejpam-3904	38	18	set	set	NOUN
ejpam-3904	38	19	of	of	ADP
ejpam-3904	38	20	g	g	PROPN
ejpam-3904	38	21	if	if	SCONJ
ejpam-3904	38	22	s	s	PRON
ejpam-3904	38	23	intersects	intersect	VERB
ejpam-3904	38	24	every	every	DET
ejpam-3904	38	25	β0	β0	NOUN
ejpam-3904	38	26	-	-	PUNCT
ejpam-3904	38	27	set	set	NOUN
ejpam-3904	38	28	of	of	ADP
ejpam-3904	38	29	g.	g.	PROPN
ejpam-3904	38	30	the	the	DET
ejpam-3904	38	31	minimum	minimum	ADJ
ejpam-3904	38	32	cardinality	cardinality	NOUN
ejpam-3904	38	33	of	of	ADP
ejpam-3904	38	34	an	an	DET
ejpam-3904	38	35	independent	independent	ADJ
ejpam-3904	38	36	transversal	transversal	NOUN
ejpam-3904	38	37	set	set	NOUN
ejpam-3904	38	38	of	of	ADP
ejpam-3904	38	39	g	g	PROPN
ejpam-3904	38	40	is	be	AUX
ejpam-3904	38	41	called	call	VERB
ejpam-3904	38	42	the	the	DET
ejpam-3904	38	43	independent	independent	ADJ
ejpam-3904	38	44	transversal	transversal	ADJ
ejpam-3904	38	45	number	number	NOUN
ejpam-3904	38	46	,	,	PUNCT
ejpam-3904	38	47	denoted	denote	VERB
ejpam-3904	38	48	by	by	ADP
ejpam-3904	38	49	β0t(g	β0t(g	PROPN
ejpam-3904	38	50	)	)	PUNCT
ejpam-3904	38	51	.	.	PUNCT
ejpam-3904	39	1	in	in	ADP
ejpam-3904	39	2	particular	particular	ADJ
ejpam-3904	39	3	,	,	PUNCT
ejpam-3904	39	4	β0t(kn	β0t(kn	NUM
ejpam-3904	39	5	)	)	PUNCT
ejpam-3904	39	6	=	=	SYM
ejpam-3904	40	1	n	n	CCONJ
ejpam-3904	40	2	;	;	PUNCT
ejpam-3904	40	3	for	for	ADP
ejpam-3904	40	4	path	path	NOUN
ejpam-3904	40	5	pn	pn	PROPN
ejpam-3904	40	6	,	,	PUNCT
ejpam-3904	40	7	β0t(pn	β0t(pn	NUM
ejpam-3904	40	8	)	)	PUNCT
ejpam-3904	40	9	=	=	SYM
ejpam-3904	40	10	1	1	NUM
ejpam-3904	40	11	when	when	SCONJ
ejpam-3904	40	12	n	n	X
ejpam-3904	40	13	is	be	AUX
ejpam-3904	40	14	odd	odd	ADJ
ejpam-3904	40	15	and	and	CCONJ
ejpam-3904	40	16	β0t(pn	β0t(pn	NUM
ejpam-3904	40	17	)	)	PUNCT
ejpam-3904	40	18	=	=	SYM
ejpam-3904	40	19	2	2	NUM
ejpam-3904	40	20	otherwise	otherwise	ADV
ejpam-3904	40	21	;	;	PUNCT
ejpam-3904	40	22	for	for	ADP
ejpam-3904	40	23	cycle	cycle	NOUN
ejpam-3904	40	24	cn	cn	PROPN
ejpam-3904	40	25	on	on	ADP
ejpam-3904	40	26	n	n	NUM
ejpam-3904	40	27	≥	≥	NUM
ejpam-3904	40	28	3	3	NUM
ejpam-3904	40	29	vertices	vertex	NOUN
ejpam-3904	40	30	,	,	PUNCT
ejpam-3904	40	31	β0t(cn	β0t(cn	NUM
ejpam-3904	40	32	)	)	PUNCT
ejpam-3904	40	33	=	=	SYM
ejpam-3904	40	34	2	2	NUM
ejpam-3904	40	35	when	when	SCONJ
ejpam-3904	40	36	n	n	X
ejpam-3904	40	37	is	be	AUX
ejpam-3904	40	38	even	even	ADV
ejpam-3904	40	39	and	and	CCONJ
ejpam-3904	40	40	β0t(cn	β0t(cn	NUM
ejpam-3904	40	41	)	)	PUNCT
ejpam-3904	40	42	=	=	SYM
ejpam-3904	41	1	3	3	NUM
ejpam-3904	41	2	otherwise	otherwise	ADV
ejpam-3904	41	3	;	;	PUNCT
ejpam-3904	41	4	and	and	CCONJ
ejpam-3904	41	5	for	for	ADP
ejpam-3904	41	6	the	the	DET
ejpam-3904	41	7	complete	complete	ADJ
ejpam-3904	41	8	bipartite	bipartite	PROPN
ejpam-3904	41	9	km	km	PROPN
ejpam-3904	41	10	,	,	PUNCT
ejpam-3904	41	11	n	n	CCONJ
ejpam-3904	41	12	,	,	PUNCT
ejpam-3904	41	13	β0t(km	β0t(km	ADJ
ejpam-3904	41	14	,	,	PUNCT
ejpam-3904	41	15	n	n	CCONJ
ejpam-3904	41	16	)	)	PUNCT
ejpam-3904	41	17	=	=	SYM
ejpam-3904	41	18	1	1	NUM
ejpam-3904	41	19	if	if	SCONJ
ejpam-3904	41	20	m	m	PROPN
ejpam-3904	41	21	6=	6=	NUM
ejpam-3904	41	22	n	n	CCONJ
ejpam-3904	41	23	,	,	PUNCT
ejpam-3904	41	24	and	and	CCONJ
ejpam-3904	41	25	β0t(km	β0t(km	ADJ
ejpam-3904	41	26	,	,	PUNCT
ejpam-3904	41	27	n	n	CCONJ
ejpam-3904	41	28	)	)	PUNCT
ejpam-3904	41	29	=	=	SYM
ejpam-3904	41	30	2	2	NUM
ejpam-3904	41	31	otherwise	otherwise	ADV
ejpam-3904	41	32	..	..	PUNCT
ejpam-3904	42	1	an	an	DET
ejpam-3904	42	2	independent	independent	ADJ
ejpam-3904	42	3	transversal	transversal	NOUN
ejpam-3904	42	4	set	set	NOUN
ejpam-3904	42	5	of	of	ADP
ejpam-3904	42	6	g	g	PROPN
ejpam-3904	42	7	is	be	AUX
ejpam-3904	42	8	an	an	DET
ejpam-3904	42	9	independent	independent	ADJ
ejpam-3904	42	10	transversal	transversal	NOUN
ejpam-3904	42	11	dominating	dominating	NOUN
ejpam-3904	42	12	set	set	NOUN
ejpam-3904	42	13	or	or	CCONJ
ejpam-3904	42	14	(	(	PUNCT
ejpam-3904	42	15	itd	itd	NOUN
ejpam-3904	42	16	-	-	PUNCT
ejpam-3904	42	17	set	set	NOUN
ejpam-3904	42	18	)	)	PUNCT
ejpam-3904	42	19	if	if	SCONJ
ejpam-3904	42	20	s	s	NOUN
ejpam-3904	42	21	is	be	AUX
ejpam-3904	42	22	a	a	DET
ejpam-3904	42	23	dominating	dominating	NOUN
ejpam-3904	42	24	set	set	NOUN
ejpam-3904	42	25	of	of	ADP
ejpam-3904	42	26	g.	g.	PROPN
ejpam-3904	42	27	the	the	DET
ejpam-3904	42	28	minimum	minimum	ADJ
ejpam-3904	42	29	cardinality	cardinality	NOUN
ejpam-3904	42	30	of	of	ADP
ejpam-3904	42	31	an	an	DET
ejpam-3904	42	32	itd	itd	NOUN
ejpam-3904	42	33	-	-	PUNCT
ejpam-3904	42	34	set	set	NOUN
ejpam-3904	42	35	of	of	ADP
ejpam-3904	42	36	g	g	PROPN
ejpam-3904	42	37	is	be	AUX
ejpam-3904	42	38	called	call	VERB
ejpam-3904	42	39	the	the	DET
ejpam-3904	42	40	independent	independent	ADJ
ejpam-3904	42	41	transversal	transversal	ADJ
ejpam-3904	42	42	domination	domination	NOUN
ejpam-3904	42	43	number	number	NOUN
ejpam-3904	42	44	of	of	ADP
ejpam-3904	42	45	g	g	NOUN
ejpam-3904	42	46	and	and	CCONJ
ejpam-3904	42	47	is	be	AUX
ejpam-3904	42	48	denoted	denote	VERB
ejpam-3904	42	49	by	by	ADP
ejpam-3904	42	50	γit(g	γit(g	PROPN
ejpam-3904	42	51	)	)	PUNCT
ejpam-3904	42	52	.	.	PUNCT
ejpam-3904	43	1	an	an	DET
ejpam-3904	43	2	d.	d.	PROPN
ejpam-3904	43	3	sevilleno	sevilleno	PROPN
ejpam-3904	43	4	,	,	PUNCT
ejpam-3904	43	5	f.	f.	PROPN
ejpam-3904	43	6	jamil	jamil	PROPN
ejpam-3904	43	7	/	/	SYM
ejpam-3904	43	8	eur	eur	PROPN
ejpam-3904	43	9	.	.	PUNCT
ejpam-3904	44	1	j.	j.	PROPN
ejpam-3904	44	2	pure	pure	PROPN
ejpam-3904	44	3	appl	appl	PROPN
ejpam-3904	44	4	.	.	PUNCT
ejpam-3904	44	5	math	math	PROPN
ejpam-3904	44	6	,	,	PUNCT
ejpam-3904	44	7	149	149	NUM
ejpam-3904	44	8	-	-	SYM
ejpam-3904	44	9	163	163	NUM
ejpam-3904	44	10	151	151	NUM
ejpam-3904	44	11	itd	itd	NOUN
ejpam-3904	44	12	-	-	PUNCT
ejpam-3904	44	13	set	set	NOUN
ejpam-3904	44	14	s	s	NOUN
ejpam-3904	44	15	of	of	ADP
ejpam-3904	44	16	g	g	NOUN
ejpam-3904	44	17	with	with	ADP
ejpam-3904	44	18	|s|	|s|	NOUN
ejpam-3904	44	19	=	=	PUNCT
ejpam-3904	44	20	γit(g	γit(g	PROPN
ejpam-3904	44	21	)	)	PUNCT
ejpam-3904	44	22	is	be	AUX
ejpam-3904	44	23	called	call	VERB
ejpam-3904	44	24	a	a	DET
ejpam-3904	44	25	γit	γit	ADV
ejpam-3904	44	26	-	-	PUNCT
ejpam-3904	44	27	set	set	NOUN
ejpam-3904	44	28	.	.	PUNCT
ejpam-3904	45	1	the	the	DET
ejpam-3904	45	2	study	study	NOUN
ejpam-3904	45	3	on	on	ADP
ejpam-3904	45	4	independent	independent	ADJ
ejpam-3904	45	5	transversal	transversal	ADJ
ejpam-3904	45	6	domination	domination	NOUN
ejpam-3904	45	7	in	in	ADP
ejpam-3904	45	8	graphs	graph	NOUN
ejpam-3904	45	9	was	be	AUX
ejpam-3904	45	10	initiated	initiate	VERB
ejpam-3904	45	11	by	by	ADP
ejpam-3904	45	12	i.	i.	PROPN
ejpam-3904	45	13	hamid	hamid	PROPN
ejpam-3904	46	1	[	[	X
ejpam-3904	46	2	10	10	NUM
ejpam-3904	46	3	]	]	PUNCT
ejpam-3904	46	4	in	in	ADP
ejpam-3904	46	5	2012	2012	NUM
ejpam-3904	46	6	.	.	PUNCT
ejpam-3904	47	1	it	it	PRON
ejpam-3904	47	2	was	be	AUX
ejpam-3904	47	3	studied	study	VERB
ejpam-3904	47	4	further	far	ADV
ejpam-3904	47	5	by	by	ADP
ejpam-3904	47	6	yero	yero	PROPN
ejpam-3904	47	7	et	et	PROPN
ejpam-3904	47	8	al	al	PROPN
ejpam-3904	47	9	.	.	PUNCT
ejpam-3904	48	1	[	[	X
ejpam-3904	48	2	17	17	NUM
ejpam-3904	48	3	,	,	PUNCT
ejpam-3904	48	4	18	18	NUM
ejpam-3904	48	5	,	,	PUNCT
ejpam-3904	48	6	20	20	NUM
ejpam-3904	48	7	]	]	PUNCT
ejpam-3904	48	8	in	in	ADP
ejpam-3904	48	9	2016	2016	NUM
ejpam-3904	48	10	,	,	PUNCT
ejpam-3904	48	11	2017	2017	NUM
ejpam-3904	48	12	and	and	CCONJ
ejpam-3904	48	13	2021	2021	NUM
ejpam-3904	48	14	,	,	PUNCT
ejpam-3904	48	15	and	and	CCONJ
ejpam-3904	48	16	by	by	ADP
ejpam-3904	48	17	ozeki	ozeki	PROPN
ejpam-3904	48	18	et	et	PROPN
ejpam-3904	48	19	al	al	PROPN
ejpam-3904	48	20	.	.	PUNCT
ejpam-3904	49	1	[	[	X
ejpam-3904	49	2	3	3	X
ejpam-3904	49	3	]	]	PUNCT
ejpam-3904	49	4	in	in	ADP
ejpam-3904	49	5	2018	2018	NUM
ejpam-3904	49	6	.	.	PUNCT
ejpam-3904	49	7	provided	provide	VERB
ejpam-3904	49	8	g	g	PROPN
ejpam-3904	49	9	has	have	AUX
ejpam-3904	49	10	no	no	DET
ejpam-3904	49	11	isolated	isolated	ADJ
ejpam-3904	49	12	vertex	vertex	NOUN
ejpam-3904	49	13	,	,	PUNCT
ejpam-3904	49	14	a	a	DET
ejpam-3904	49	15	subset	subset	NOUN
ejpam-3904	49	16	s	s	VERB
ejpam-3904	49	17	⊆	⊆	NUM
ejpam-3904	49	18	v	v	NOUN
ejpam-3904	49	19	(	(	PUNCT
ejpam-3904	49	20	g	g	NOUN
ejpam-3904	49	21	)	)	PUNCT
ejpam-3904	49	22	is	be	AUX
ejpam-3904	49	23	an	an	DET
ejpam-3904	49	24	independent	independent	ADJ
ejpam-3904	49	25	transversal	transversal	ADJ
ejpam-3904	49	26	total	total	NOUN
ejpam-3904	49	27	dominating	dominating	NOUN
ejpam-3904	49	28	set	set	NOUN
ejpam-3904	49	29	or	or	CCONJ
ejpam-3904	49	30	(	(	PUNCT
ejpam-3904	49	31	ittd	ittd	NOUN
ejpam-3904	49	32	-	-	PUNCT
ejpam-3904	49	33	set	set	NOUN
ejpam-3904	49	34	)	)	PUNCT
ejpam-3904	49	35	if	if	SCONJ
ejpam-3904	49	36	s	s	VERB
ejpam-3904	49	37	is	be	AUX
ejpam-3904	49	38	both	both	PRON
ejpam-3904	49	39	an	an	DET
ejpam-3904	49	40	itd	itd	NOUN
ejpam-3904	49	41	-	-	PUNCT
ejpam-3904	49	42	set	set	NOUN
ejpam-3904	49	43	and	and	CCONJ
ejpam-3904	49	44	a	a	DET
ejpam-3904	49	45	total	total	ADJ
ejpam-3904	49	46	dominating	dominating	NOUN
ejpam-3904	49	47	set	set	NOUN
ejpam-3904	49	48	of	of	ADP
ejpam-3904	49	49	g.	g.	PROPN
ejpam-3904	49	50	we	we	PRON
ejpam-3904	49	51	denote	denote	VERB
ejpam-3904	49	52	by	by	ADP
ejpam-3904	49	53	γitt(g	γitt(g	NOUN
ejpam-3904	49	54	)	)	PUNCT
ejpam-3904	49	55	the	the	DET
ejpam-3904	49	56	minimum	minimum	ADJ
ejpam-3904	49	57	cardinality	cardinality	NOUN
ejpam-3904	49	58	of	of	ADP
ejpam-3904	49	59	an	an	DET
ejpam-3904	49	60	ittd	ittd	NOUN
ejpam-3904	49	61	-	-	PUNCT
ejpam-3904	49	62	set	set	NOUN
ejpam-3904	49	63	of	of	ADP
ejpam-3904	49	64	g	g	NOUN
ejpam-3904	49	65	,	,	PUNCT
ejpam-3904	49	66	and	and	CCONJ
ejpam-3904	49	67	is	be	AUX
ejpam-3904	49	68	called	call	VERB
ejpam-3904	49	69	the	the	DET
ejpam-3904	49	70	independent	independent	ADJ
ejpam-3904	49	71	transversal	transversal	ADJ
ejpam-3904	49	72	total	total	NOUN
ejpam-3904	49	73	domination	domination	NOUN
ejpam-3904	49	74	number	number	NOUN
ejpam-3904	49	75	of	of	ADP
ejpam-3904	49	76	g.	g.	PROPN
ejpam-3904	49	77	in	in	ADP
ejpam-3904	49	78	[	[	X
ejpam-3904	49	79	17	17	NUM
ejpam-3904	49	80	]	]	PUNCT
ejpam-3904	49	81	,	,	PUNCT
ejpam-3904	49	82	cabrera	cabrera	PROPN
ejpam-3904	49	83	martinez	martinez	PROPN
ejpam-3904	49	84	et	et	PROPN
ejpam-3904	49	85	al	al	PROPN
ejpam-3904	49	86	.	.	PROPN
ejpam-3904	49	87	made	make	VERB
ejpam-3904	49	88	a	a	DET
ejpam-3904	49	89	good	good	ADJ
ejpam-3904	49	90	introduction	introduction	NOUN
ejpam-3904	49	91	of	of	ADP
ejpam-3904	49	92	this	this	DET
ejpam-3904	49	93	concept	concept	NOUN
ejpam-3904	49	94	.	.	PUNCT
ejpam-3904	50	1	the	the	DET
ejpam-3904	50	2	authors	author	NOUN
ejpam-3904	50	3	prove	prove	VERB
ejpam-3904	50	4	that	that	SCONJ
ejpam-3904	50	5	the	the	DET
ejpam-3904	50	6	complexity	complexity	NOUN
ejpam-3904	50	7	of	of	ADP
ejpam-3904	50	8	the	the	DET
ejpam-3904	50	9	decision	decision	NOUN
ejpam-3904	50	10	problem	problem	NOUN
ejpam-3904	50	11	associated	associate	VERB
ejpam-3904	50	12	to	to	ADP
ejpam-3904	50	13	the	the	DET
ejpam-3904	50	14	computation	computation	NOUN
ejpam-3904	50	15	of	of	ADP
ejpam-3904	50	16	the	the	DET
ejpam-3904	50	17	value	value	NOUN
ejpam-3904	50	18	of	of	ADP
ejpam-3904	50	19	γitt(g	γitt(g	NOUN
ejpam-3904	50	20	)	)	PUNCT
ejpam-3904	50	21	is	be	AUX
ejpam-3904	50	22	np	np	NOUN
ejpam-3904	50	23	-	-	PUNCT
ejpam-3904	50	24	complete	complete	ADJ
ejpam-3904	50	25	,	,	PUNCT
ejpam-3904	50	26	under	under	ADP
ejpam-3904	50	27	the	the	DET
ejpam-3904	50	28	assumption	assumption	NOUN
ejpam-3904	50	29	that	that	SCONJ
ejpam-3904	50	30	the	the	DET
ejpam-3904	50	31	independence	independence	NOUN
ejpam-3904	50	32	number	number	NOUN
ejpam-3904	50	33	is	be	AUX
ejpam-3904	50	34	known	know	VERB
ejpam-3904	50	35	.	.	PUNCT
ejpam-3904	51	1	henceforth	henceforth	ADV
ejpam-3904	51	2	,	,	PUNCT
ejpam-3904	51	3	all	all	DET
ejpam-3904	51	4	discussions	discussion	NOUN
ejpam-3904	51	5	of	of	ADP
ejpam-3904	51	6	total	total	ADJ
ejpam-3904	51	7	domination	domination	NOUN
ejpam-3904	51	8	or	or	CCONJ
ejpam-3904	51	9	independent	independent	ADJ
ejpam-3904	51	10	transversal	transversal	ADJ
ejpam-3904	51	11	total	total	NOUN
ejpam-3904	51	12	domination	domination	NOUN
ejpam-3904	51	13	are	be	AUX
ejpam-3904	51	14	always	always	ADV
ejpam-3904	51	15	with	with	ADP
ejpam-3904	51	16	respect	respect	NOUN
ejpam-3904	51	17	to	to	ADP
ejpam-3904	51	18	graphs	graph	NOUN
ejpam-3904	51	19	without	without	ADP
ejpam-3904	51	20	isolated	isolated	ADJ
ejpam-3904	51	21	vertices	vertex	NOUN
ejpam-3904	51	22	.	.	PUNCT
ejpam-3904	52	1	for	for	ADP
ejpam-3904	52	2	graphs	graph	NOUN
ejpam-3904	52	3	g	g	ADP
ejpam-3904	52	4	of	of	ADP
ejpam-3904	52	5	order	order	NOUN
ejpam-3904	52	6	n	n	PRON
ejpam-3904	52	7	≥	≥	NOUN
ejpam-3904	52	8	2	2	NUM
ejpam-3904	52	9	,	,	PUNCT
ejpam-3904	52	10	γit(g	γit(g	PROPN
ejpam-3904	52	11	)	)	PUNCT
ejpam-3904	52	12	≤	≤	NOUN
ejpam-3904	52	13	γitt(g	γitt(g	NOUN
ejpam-3904	52	14	)	)	PUNCT
ejpam-3904	52	15	.	.	PUNCT
ejpam-3904	53	1	2	2	X
ejpam-3904	53	2	.	.	NUM
ejpam-3904	53	3	preliminaries	preliminary	NOUN
ejpam-3904	53	4	and	and	CCONJ
ejpam-3904	53	5	known	know	VERB
ejpam-3904	53	6	results	result	NOUN
ejpam-3904	53	7	observation	observation	NOUN
ejpam-3904	53	8	1	1	NUM
ejpam-3904	53	9	.	.	PUNCT
ejpam-3904	54	1	(	(	PUNCT
ejpam-3904	54	2	i	i	NOUN
ejpam-3904	54	3	)	)	PUNCT
ejpam-3904	54	4	for	for	ADP
ejpam-3904	54	5	the	the	DET
ejpam-3904	54	6	complete	complete	ADJ
ejpam-3904	54	7	bipartite	bipartite	PROPN
ejpam-3904	54	8	km	km	PROPN
ejpam-3904	54	9	,	,	PUNCT
ejpam-3904	54	10	n	n	CCONJ
ejpam-3904	54	11	,	,	PUNCT
ejpam-3904	54	12	γit(km	γit(km	NOUN
ejpam-3904	54	13	,	,	PUNCT
ejpam-3904	54	14	n	n	CCONJ
ejpam-3904	54	15	)	)	PUNCT
ejpam-3904	54	16	=	=	SYM
ejpam-3904	54	17	γitt(km	γitt(km	NOUN
ejpam-3904	54	18	,	,	PUNCT
ejpam-3904	54	19	n	n	CCONJ
ejpam-3904	54	20	)	)	PUNCT
ejpam-3904	54	21	=	=	SYM
ejpam-3904	55	1	2	2	X
ejpam-3904	55	2	.	.	PUNCT
ejpam-3904	55	3	(	(	PUNCT
ejpam-3904	55	4	ii	ii	NOUN
ejpam-3904	55	5	)	)	PUNCT
ejpam-3904	55	6	for	for	ADP
ejpam-3904	55	7	any	any	DET
ejpam-3904	55	8	path	path	NOUN
ejpam-3904	55	9	pn	pn	NOUN
ejpam-3904	55	10	of	of	ADP
ejpam-3904	55	11	order	order	NOUN
ejpam-3904	55	12	n	n	PRON
ejpam-3904	55	13	≥	≥	NOUN
ejpam-3904	55	14	2	2	NUM
ejpam-3904	55	15	,	,	PUNCT
ejpam-3904	55	16	we	we	PRON
ejpam-3904	55	17	have	have	VERB
ejpam-3904	55	18	(	(	PUNCT
ejpam-3904	55	19	a	a	X
ejpam-3904	55	20	)	)	PUNCT
ejpam-3904	56	1	[	[	X
ejpam-3904	56	2	10	10	NUM
ejpam-3904	56	3	]	]	PUNCT
ejpam-3904	56	4	γit(pn	γit(pn	NOUN
ejpam-3904	56	5	)	)	PUNCT
ejpam-3904	56	6	=	=	SYM
ejpam-3904	57	1			NOUN
ejpam-3904	57	2	2	2	NUM
ejpam-3904	57	3	if	if	SCONJ
ejpam-3904	57	4	n	n	NOUN
ejpam-3904	57	5	=	=	SYM
ejpam-3904	57	6	2	2	NUM
ejpam-3904	57	7	,	,	PUNCT
ejpam-3904	57	8	3	3	NUM
ejpam-3904	57	9	,	,	PUNCT
ejpam-3904	57	10	3	3	NUM
ejpam-3904	57	11	if	if	SCONJ
ejpam-3904	57	12	n	n	X
ejpam-3904	57	13	=	=	SYM
ejpam-3904	57	14	6	6	NUM
ejpam-3904	57	15	,	,	PUNCT
ejpam-3904	57	16	dn3	dn3	NOUN
ejpam-3904	57	17	e	e	NOUN
ejpam-3904	57	18	otherwise	otherwise	ADV
ejpam-3904	57	19	,	,	PUNCT
ejpam-3904	57	20	and	and	CCONJ
ejpam-3904	57	21	(	(	PUNCT
ejpam-3904	57	22	b	b	X
ejpam-3904	57	23	)	)	PUNCT
ejpam-3904	57	24	γitt(pn	γitt(pn	NOUN
ejpam-3904	57	25	)	)	PUNCT
ejpam-3904	57	26	=	=	PUNCT
ejpam-3904	58	1			NOUN
ejpam-3904	58	2	3	3	NUM
ejpam-3904	58	3	if	if	SCONJ
ejpam-3904	58	4	n	n	NOUN
ejpam-3904	58	5	=	=	SYM
ejpam-3904	58	6	4	4	NUM
ejpam-3904	58	7	,	,	PUNCT
ejpam-3904	58	8	n	n	PRON
ejpam-3904	58	9	2	2	NUM
ejpam-3904	59	1	+	+	CCONJ
ejpam-3904	59	2	1	1	NUM
ejpam-3904	59	3	if	if	SCONJ
ejpam-3904	59	4	n	n	PRON
ejpam-3904	59	5	≡	≡	PROPN
ejpam-3904	59	6	2(mod	2(mod	NUM
ejpam-3904	59	7	4	4	NUM
ejpam-3904	59	8	)	)	PUNCT
ejpam-3904	59	9	,	,	PUNCT
ejpam-3904	59	10	dn2	dn2	NOUN
ejpam-3904	59	11	e	e	NOUN
ejpam-3904	59	12	,	,	PUNCT
ejpam-3904	59	13	otherwise	otherwise	ADV
ejpam-3904	59	14	(	(	PUNCT
ejpam-3904	59	15	iii	iii	NOUN
ejpam-3904	59	16	)	)	PUNCT
ejpam-3904	59	17	for	for	ADP
ejpam-3904	59	18	any	any	DET
ejpam-3904	59	19	cycle	cycle	NOUN
ejpam-3904	60	1	cn	cn	NOUN
ejpam-3904	60	2	of	of	ADP
ejpam-3904	60	3	order	order	NOUN
ejpam-3904	60	4	n	n	PRON
ejpam-3904	60	5	≥	≥	NOUN
ejpam-3904	60	6	3	3	NUM
ejpam-3904	60	7	,	,	PUNCT
ejpam-3904	60	8	we	we	PRON
ejpam-3904	60	9	have	have	VERB
ejpam-3904	60	10	(	(	PUNCT
ejpam-3904	60	11	a	a	X
ejpam-3904	60	12	)	)	PUNCT
ejpam-3904	61	1	[	[	X
ejpam-3904	61	2	10]γit(cn	10]γit(cn	NUM
ejpam-3904	61	3	)	)	PUNCT
ejpam-3904	61	4	=	=	NOUN
ejpam-3904	61	5	{	{	PUNCT
ejpam-3904	61	6	3	3	NUM
ejpam-3904	61	7	if	if	SCONJ
ejpam-3904	61	8	n	n	X
ejpam-3904	61	9	=	=	SYM
ejpam-3904	61	10	3	3	NUM
ejpam-3904	61	11	,	,	PUNCT
ejpam-3904	61	12	5	5	NUM
ejpam-3904	61	13	,	,	PUNCT
ejpam-3904	61	14	dn3	dn3	NOUN
ejpam-3904	61	15	e	e	NOUN
ejpam-3904	61	16	otherwise	otherwise	ADV
ejpam-3904	61	17	,	,	PUNCT
ejpam-3904	61	18	and	and	CCONJ
ejpam-3904	61	19	(	(	PUNCT
ejpam-3904	61	20	b	b	X
ejpam-3904	61	21	)	)	PUNCT
ejpam-3904	61	22	γitt(cn	γitt(cn	NOUN
ejpam-3904	61	23	)	)	PUNCT
ejpam-3904	61	24	=	=	PUNCT
ejpam-3904	62	1			NOUN
ejpam-3904	62	2	3	3	NUM
ejpam-3904	62	3	if	if	SCONJ
ejpam-3904	62	4	n	n	NOUN
ejpam-3904	62	5	=	=	SYM
ejpam-3904	62	6	3	3	NUM
ejpam-3904	62	7	,	,	PUNCT
ejpam-3904	62	8	n	n	PRON
ejpam-3904	62	9	2	2	NUM
ejpam-3904	63	1	+	+	CCONJ
ejpam-3904	63	2	1	1	NUM
ejpam-3904	63	3	if	if	SCONJ
ejpam-3904	63	4	n	n	PRON
ejpam-3904	63	5	≡	≡	PROPN
ejpam-3904	63	6	2(mod	2(mod	NUM
ejpam-3904	63	7	4	4	NUM
ejpam-3904	63	8	)	)	PUNCT
ejpam-3904	63	9	,	,	PUNCT
ejpam-3904	63	10	dn2	dn2	NOUN
ejpam-3904	63	11	e	e	NOUN
ejpam-3904	63	12	,	,	PUNCT
ejpam-3904	63	13	otherwise	otherwise	ADV
ejpam-3904	63	14	.	.	PUNCT
ejpam-3904	64	1	theorem	theorem	NOUN
ejpam-3904	64	2	1	1	NUM
ejpam-3904	64	3	.	.	X
ejpam-3904	64	4	for	for	ADP
ejpam-3904	64	5	any	any	DET
ejpam-3904	64	6	graph	graph	NOUN
ejpam-3904	64	7	g	g	NOUN
ejpam-3904	64	8	,	,	PUNCT
ejpam-3904	64	9	we	we	PRON
ejpam-3904	64	10	have	have	VERB
ejpam-3904	64	11	(	(	PUNCT
ejpam-3904	64	12	i	i	NOUN
ejpam-3904	64	13	)	)	PUNCT
ejpam-3904	65	1	[	[	X
ejpam-3904	65	2	10	10	NUM
ejpam-3904	65	3	]	]	X
ejpam-3904	65	4	γ(g	γ(g	PROPN
ejpam-3904	65	5	)	)	PUNCT
ejpam-3904	65	6	≤	≤	NUM
ejpam-3904	65	7	γit(g	γit(g	PROPN
ejpam-3904	65	8	)	)	PUNCT
ejpam-3904	65	9	≤	≤	PROPN
ejpam-3904	65	10	γ(g	γ(g	PROPN
ejpam-3904	65	11	)	)	PUNCT
ejpam-3904	65	12	+	+	CCONJ
ejpam-3904	65	13	δ(g	δ(g	NOUN
ejpam-3904	65	14	)	)	PUNCT
ejpam-3904	65	15	;	;	PUNCT
ejpam-3904	65	16	and	and	CCONJ
ejpam-3904	65	17	(	(	PUNCT
ejpam-3904	65	18	ii	ii	NOUN
ejpam-3904	65	19	)	)	PUNCT
ejpam-3904	66	1	[	[	X
ejpam-3904	66	2	17	17	NUM
ejpam-3904	66	3	]	]	PUNCT
ejpam-3904	66	4	γt(g	γt(g	NUM
ejpam-3904	66	5	)	)	PUNCT
ejpam-3904	66	6	≤	≤	NOUN
ejpam-3904	66	7	γitt(g	γitt(g	NOUN
ejpam-3904	66	8	)	)	PUNCT
ejpam-3904	66	9	≤	≤	NOUN
ejpam-3904	66	10	γt(g	γt(g	PUNCT
ejpam-3904	66	11	)	)	PUNCT
ejpam-3904	66	12	+	+	CCONJ
ejpam-3904	66	13	δ(g	δ(g	NOUN
ejpam-3904	66	14	)	)	PUNCT
ejpam-3904	66	15	.	.	PUNCT
ejpam-3904	67	1	corollary	corollary	ADJ
ejpam-3904	67	2	1	1	NUM
ejpam-3904	67	3	.	.	PUNCT
ejpam-3904	68	1	let	let	VERB
ejpam-3904	68	2	g	g	PRON
ejpam-3904	68	3	be	be	AUX
ejpam-3904	68	4	a	a	DET
ejpam-3904	68	5	graph	graph	NOUN
ejpam-3904	68	6	.	.	PUNCT
ejpam-3904	69	1	d.	d.	PROPN
ejpam-3904	69	2	sevilleno	sevilleno	PROPN
ejpam-3904	69	3	,	,	PUNCT
ejpam-3904	69	4	f.	f.	PROPN
ejpam-3904	69	5	jamil	jamil	PROPN
ejpam-3904	69	6	/	/	SYM
ejpam-3904	69	7	eur	eur	PROPN
ejpam-3904	69	8	.	.	PUNCT
ejpam-3904	70	1	j.	j.	PROPN
ejpam-3904	70	2	pure	pure	PROPN
ejpam-3904	70	3	appl	appl	PROPN
ejpam-3904	70	4	.	.	PUNCT
ejpam-3904	70	5	math	math	PROPN
ejpam-3904	70	6	,	,	PUNCT
ejpam-3904	70	7	149	149	NUM
ejpam-3904	70	8	-	-	SYM
ejpam-3904	70	9	163	163	NUM
ejpam-3904	70	10	152	152	NUM
ejpam-3904	70	11	(	(	PUNCT
ejpam-3904	70	12	i	i	NOUN
ejpam-3904	70	13	)	)	PUNCT
ejpam-3904	71	1	[	[	X
ejpam-3904	71	2	10	10	NUM
ejpam-3904	71	3	]	]	X
ejpam-3904	71	4	if	if	SCONJ
ejpam-3904	71	5	g	g	PROPN
ejpam-3904	71	6	has	have	VERB
ejpam-3904	71	7	an	an	DET
ejpam-3904	71	8	isolated	isolated	ADJ
ejpam-3904	71	9	vertex	vertex	NOUN
ejpam-3904	71	10	,	,	PUNCT
ejpam-3904	71	11	then	then	ADV
ejpam-3904	71	12	γit(g	γit(g	PROPN
ejpam-3904	71	13	)	)	PUNCT
ejpam-3904	71	14	=	=	PUNCT
ejpam-3904	71	15	γ(g	γ(g	PROPN
ejpam-3904	71	16	)	)	PUNCT
ejpam-3904	71	17	.	.	PUNCT
ejpam-3904	72	1	(	(	PUNCT
ejpam-3904	72	2	ii	ii	NOUN
ejpam-3904	72	3	)	)	PUNCT
ejpam-3904	72	4	if	if	SCONJ
ejpam-3904	72	5	g	g	PROPN
ejpam-3904	72	6	has	have	VERB
ejpam-3904	72	7	k2	k2	NOUN
ejpam-3904	72	8	as	as	ADP
ejpam-3904	72	9	a	a	DET
ejpam-3904	72	10	component	component	NOUN
ejpam-3904	72	11	,	,	PUNCT
ejpam-3904	72	12	then	then	ADV
ejpam-3904	72	13	γitt(g	γitt(g	NOUN
ejpam-3904	72	14	)	)	PUNCT
ejpam-3904	72	15	=	=	PUNCT
ejpam-3904	72	16	γt(g	γt(g	NUM
ejpam-3904	72	17	)	)	PUNCT
ejpam-3904	72	18	.	.	PUNCT
ejpam-3904	73	1	if	if	SCONJ
ejpam-3904	73	2	follows	follow	VERB
ejpam-3904	73	3	from	from	ADP
ejpam-3904	73	4	observation	observation	NOUN
ejpam-3904	73	5	1	1	NUM
ejpam-3904	73	6	that	that	SCONJ
ejpam-3904	73	7	if	if	SCONJ
ejpam-3904	73	8	g	g	PROPN
ejpam-3904	73	9	=	=	SYM
ejpam-3904	73	10	p3n−2	p3n−2	PROPN
ejpam-3904	73	11	,	,	PUNCT
ejpam-3904	73	12	then	then	ADV
ejpam-3904	73	13	γit(g	γit(g	PROPN
ejpam-3904	73	14	)	)	PUNCT
ejpam-3904	73	15	=	=	PUNCT
ejpam-3904	73	16	γ(g	γ(g	PROPN
ejpam-3904	73	17	)	)	PUNCT
ejpam-3904	73	18	=	=	SYM
ejpam-3904	73	19	n.	n.	PROPN
ejpam-3904	73	20	thus	thus	ADV
ejpam-3904	73	21	,	,	PUNCT
ejpam-3904	73	22	the	the	DET
ejpam-3904	73	23	following	follow	VERB
ejpam-3904	73	24	corollary	corollary	NOUN
ejpam-3904	73	25	is	be	AUX
ejpam-3904	73	26	clear	clear	ADJ
ejpam-3904	73	27	.	.	PUNCT
ejpam-3904	74	1	corollary	corollary	ADJ
ejpam-3904	74	2	2	2	NUM
ejpam-3904	74	3	.	.	PUNCT
ejpam-3904	75	1	for	for	ADP
ejpam-3904	75	2	all	all	DET
ejpam-3904	75	3	positive	positive	ADJ
ejpam-3904	75	4	integers	integer	NOUN
ejpam-3904	75	5	n	n	CCONJ
ejpam-3904	75	6	,	,	PUNCT
ejpam-3904	75	7	there	there	PRON
ejpam-3904	75	8	exists	exist	VERB
ejpam-3904	75	9	a	a	DET
ejpam-3904	75	10	connected	connected	ADJ
ejpam-3904	75	11	graph	graph	NOUN
ejpam-3904	75	12	g	g	NOUN
ejpam-3904	75	13	for	for	ADP
ejpam-3904	75	14	which	which	PRON
ejpam-3904	75	15	γ(g	γ(g	PROPN
ejpam-3904	75	16	)	)	PUNCT
ejpam-3904	76	1	=	=	SYM
ejpam-3904	76	2	γit(g	γit(g	PROPN
ejpam-3904	76	3	)	)	PUNCT
ejpam-3904	76	4	=	=	SYM
ejpam-3904	76	5	n.	n.	NOUN
ejpam-3904	76	6	observation	observation	NOUN
ejpam-3904	76	7	2	2	NUM
ejpam-3904	76	8	.	.	PUNCT
ejpam-3904	77	1	let	let	VERB
ejpam-3904	77	2	g	g	PRON
ejpam-3904	77	3	be	be	AUX
ejpam-3904	77	4	a	a	DET
ejpam-3904	77	5	connected	connected	ADJ
ejpam-3904	77	6	graph	graph	NOUN
ejpam-3904	77	7	of	of	ADP
ejpam-3904	77	8	order	order	NOUN
ejpam-3904	77	9	n.	n.	NOUN
ejpam-3904	78	1	then	then	ADV
ejpam-3904	78	2	(	(	PUNCT
ejpam-3904	78	3	i	i	NOUN
ejpam-3904	78	4	)	)	PUNCT
ejpam-3904	78	5	γit(g	γit(g	PROPN
ejpam-3904	78	6	)	)	PUNCT
ejpam-3904	78	7	=	=	SYM
ejpam-3904	79	1	n	n	NOUN
ejpam-3904	79	2	if	if	SCONJ
ejpam-3904	80	1	and	and	CCONJ
ejpam-3904	80	2	only	only	ADV
ejpam-3904	80	3	if	if	SCONJ
ejpam-3904	80	4	g	g	PROPN
ejpam-3904	80	5	=	=	PROPN
ejpam-3904	80	6	kn	kn	PROPN
ejpam-3904	80	7	.	.	PROPN
ejpam-3904	80	8	provided	provide	VERB
ejpam-3904	80	9	n	n	CCONJ
ejpam-3904	80	10	≥	≥	NUM
ejpam-3904	80	11	2	2	NUM
ejpam-3904	80	12	,	,	PUNCT
ejpam-3904	80	13	γitt(g	γitt(g	NOUN
ejpam-3904	80	14	)	)	PUNCT
ejpam-3904	80	15	=	=	SYM
ejpam-3904	81	1	n	n	NOUN
ejpam-3904	81	2	if	if	SCONJ
ejpam-3904	81	3	and	and	CCONJ
ejpam-3904	81	4	only	only	ADV
ejpam-3904	81	5	if	if	SCONJ
ejpam-3904	81	6	g	g	PROPN
ejpam-3904	81	7	=	=	PROPN
ejpam-3904	81	8	kn	kn	PROPN
ejpam-3904	81	9	.	.	PUNCT
ejpam-3904	81	10	(	(	PUNCT
ejpam-3904	81	11	ii	ii	NOUN
ejpam-3904	81	12	)	)	PUNCT
ejpam-3904	81	13	for	for	ADP
ejpam-3904	81	14	n	n	X
ejpam-3904	81	15	≥	≥	NUM
ejpam-3904	81	16	3	3	NUM
ejpam-3904	81	17	,	,	PUNCT
ejpam-3904	81	18	(	(	PUNCT
ejpam-3904	81	19	a	a	X
ejpam-3904	81	20	)	)	PUNCT
ejpam-3904	81	21	γit(g	γit(g	NOUN
ejpam-3904	81	22	)	)	PUNCT
ejpam-3904	82	1	=	=	PUNCT
ejpam-3904	82	2	n−	n−	NOUN
ejpam-3904	82	3	1	1	NUM
ejpam-3904	82	4	if	if	SCONJ
ejpam-3904	83	1	and	and	CCONJ
ejpam-3904	83	2	only	only	ADV
ejpam-3904	83	3	if	if	SCONJ
ejpam-3904	83	4	g	g	PROPN
ejpam-3904	83	5	=	=	PROPN
ejpam-3904	83	6	p3	p3	PROPN
ejpam-3904	83	7	.	.	PUNCT
ejpam-3904	84	1	(	(	PUNCT
ejpam-3904	84	2	b	b	X
ejpam-3904	84	3	)	)	PUNCT
ejpam-3904	84	4	γitt(g	γitt(g	NOUN
ejpam-3904	84	5	)	)	PUNCT
ejpam-3904	85	1	=	=	PUNCT
ejpam-3904	85	2	n−	n−	NOUN
ejpam-3904	85	3	1	1	NUM
ejpam-3904	85	4	if	if	SCONJ
ejpam-3904	85	5	and	and	CCONJ
ejpam-3904	85	6	only	only	ADV
ejpam-3904	85	7	if	if	SCONJ
ejpam-3904	85	8	g	g	PROPN
ejpam-3904	85	9	=	=	PROPN
ejpam-3904	85	10	p3	p3	PROPN
ejpam-3904	85	11	or	or	CCONJ
ejpam-3904	85	12	g	g	NOUN
ejpam-3904	85	13	=	=	SYM
ejpam-3904	85	14	p4	p4	ADJ
ejpam-3904	85	15	.	.	PUNCT
ejpam-3904	86	1	(	(	PUNCT
ejpam-3904	86	2	iii	iii	NOUN
ejpam-3904	86	3	)	)	PUNCT
ejpam-3904	86	4	γit(g	γit(g	PROPN
ejpam-3904	86	5	)	)	PUNCT
ejpam-3904	86	6	=	=	SYM
ejpam-3904	86	7	2	2	NUM
ejpam-3904	86	8	if	if	SCONJ
ejpam-3904	86	9	and	and	CCONJ
ejpam-3904	86	10	only	only	ADV
ejpam-3904	86	11	if	if	SCONJ
ejpam-3904	86	12	either	either	CCONJ
ejpam-3904	86	13	g	g	PROPN
ejpam-3904	86	14	=	=	SYM
ejpam-3904	86	15	k2	k2	PROPN
ejpam-3904	86	16	or	or	CCONJ
ejpam-3904	86	17	g	g	PROPN
ejpam-3904	86	18	has	have	VERB
ejpam-3904	86	19	a	a	DET
ejpam-3904	86	20	dominating	dominating	NOUN
ejpam-3904	86	21	set	set	NOUN
ejpam-3904	86	22	{	{	PUNCT
ejpam-3904	86	23	u	u	NOUN
ejpam-3904	86	24	,	,	PUNCT
ejpam-3904	86	25	v	v	NOUN
ejpam-3904	86	26	}	}	PUNCT
ejpam-3904	86	27	such	such	ADJ
ejpam-3904	86	28	that	that	SCONJ
ejpam-3904	86	29	every	every	DET
ejpam-3904	86	30	β0	β0	NOUN
ejpam-3904	86	31	-	-	PUNCT
ejpam-3904	86	32	set	set	NOUN
ejpam-3904	86	33	contains	contain	VERB
ejpam-3904	86	34	u	u	NOUN
ejpam-3904	86	35	or	or	CCONJ
ejpam-3904	86	36	v.	v.	CCONJ
ejpam-3904	86	37	(	(	PUNCT
ejpam-3904	86	38	iv	iv	X
ejpam-3904	86	39	)	)	PUNCT
ejpam-3904	86	40	γitt(g	γitt(g	NOUN
ejpam-3904	86	41	)	)	PUNCT
ejpam-3904	86	42	=	=	SYM
ejpam-3904	86	43	2	2	NUM
ejpam-3904	86	44	if	if	SCONJ
ejpam-3904	86	45	and	and	CCONJ
ejpam-3904	86	46	only	only	ADV
ejpam-3904	86	47	if	if	SCONJ
ejpam-3904	86	48	either	either	CCONJ
ejpam-3904	86	49	g	g	PROPN
ejpam-3904	86	50	=	=	SYM
ejpam-3904	86	51	k2	k2	PROPN
ejpam-3904	86	52	or	or	CCONJ
ejpam-3904	86	53	g	g	PROPN
ejpam-3904	86	54	has	have	VERB
ejpam-3904	86	55	a	a	DET
ejpam-3904	86	56	total	total	ADJ
ejpam-3904	86	57	dominating	dominating	NOUN
ejpam-3904	86	58	set	set	NOUN
ejpam-3904	86	59	{	{	PUNCT
ejpam-3904	86	60	u	u	NOUN
ejpam-3904	86	61	,	,	PUNCT
ejpam-3904	86	62	v	v	NOUN
ejpam-3904	86	63	}	}	PUNCT
ejpam-3904	86	64	such	such	ADJ
ejpam-3904	86	65	that	that	SCONJ
ejpam-3904	86	66	every	every	DET
ejpam-3904	86	67	β0	β0	NOUN
ejpam-3904	86	68	-	-	PUNCT
ejpam-3904	86	69	set	set	NOUN
ejpam-3904	86	70	contains	contain	VERB
ejpam-3904	86	71	either	either	CCONJ
ejpam-3904	86	72	u	u	NOUN
ejpam-3904	86	73	or	or	CCONJ
ejpam-3904	86	74	v.	v.	CCONJ
ejpam-3904	86	75	(	(	PUNCT
ejpam-3904	86	76	v	v	NOUN
ejpam-3904	86	77	)	)	PUNCT
ejpam-3904	86	78	γit(g	γit(g	PROPN
ejpam-3904	86	79	)	)	PUNCT
ejpam-3904	86	80	=	=	SYM
ejpam-3904	86	81	1	1	NUM
ejpam-3904	86	82	if	if	SCONJ
ejpam-3904	86	83	and	and	CCONJ
ejpam-3904	86	84	only	only	ADV
ejpam-3904	86	85	if	if	SCONJ
ejpam-3904	86	86	n	n	PROPN
ejpam-3904	86	87	=	=	SYM
ejpam-3904	86	88	1	1	X
ejpam-3904	86	89	.	.	PUNCT
ejpam-3904	87	1	in	in	ADP
ejpam-3904	87	2	observation	observation	NOUN
ejpam-3904	87	3	2(iii	2(iii	NUM
ejpam-3904	87	4	)	)	PUNCT
ejpam-3904	87	5	,	,	PUNCT
ejpam-3904	87	6	a	a	DET
ejpam-3904	87	7	β0	β0	NOUN
ejpam-3904	87	8	-	-	PUNCT
ejpam-3904	87	9	set	set	NOUN
ejpam-3904	87	10	may	may	AUX
ejpam-3904	87	11	contain	contain	VERB
ejpam-3904	87	12	both	both	DET
ejpam-3904	87	13	u	u	NOUN
ejpam-3904	87	14	and	and	CCONJ
ejpam-3904	87	15	v.	v.	ADP
ejpam-3904	87	16	consider	consider	VERB
ejpam-3904	87	17	,	,	PUNCT
ejpam-3904	87	18	for	for	ADP
ejpam-3904	87	19	example	example	NOUN
ejpam-3904	87	20	,	,	PUNCT
ejpam-3904	87	21	the	the	DET
ejpam-3904	87	22	graph	graph	NOUN
ejpam-3904	87	23	g	g	PROPN
ejpam-3904	87	24	=	=	SYM
ejpam-3904	87	25	kn−1	kn−1	PROPN
ejpam-3904	88	1	+	+	PROPN
ejpam-3904	88	2	v	v	NOUN
ejpam-3904	88	3	for	for	ADP
ejpam-3904	88	4	n	n	X
ejpam-3904	88	5	≥	≥	NOUN
ejpam-3904	88	6	2	2	NUM
ejpam-3904	88	7	.	.	NOUN
ejpam-3904	88	8	3	3	NUM
ejpam-3904	88	9	.	.	X
ejpam-3904	88	10	realization	realization	NOUN
ejpam-3904	88	11	problems	problem	NOUN
ejpam-3904	88	12	theorem	theorem	VERB
ejpam-3904	88	13	2	2	NUM
ejpam-3904	88	14	.	.	PUNCT
ejpam-3904	89	1	[	[	X
ejpam-3904	89	2	20	20	NUM
ejpam-3904	89	3	]	]	PUNCT
ejpam-3904	89	4	for	for	ADP
ejpam-3904	89	5	every	every	DET
ejpam-3904	89	6	positive	positive	ADJ
ejpam-3904	89	7	integers	integer	NOUN
ejpam-3904	89	8	a	a	DET
ejpam-3904	89	9	,	,	PUNCT
ejpam-3904	89	10	b	b	NOUN
ejpam-3904	89	11	,	,	PUNCT
ejpam-3904	89	12	c	c	X
ejpam-3904	89	13	such	such	ADJ
ejpam-3904	89	14	that	that	SCONJ
ejpam-3904	89	15	c	c	PROPN
ejpam-3904	89	16	≥	≥	NUM
ejpam-3904	89	17	2	2	NUM
ejpam-3904	89	18	and	and	CCONJ
ejpam-3904	89	19	a	a	DET
ejpam-3904	89	20	≤	≤	NUM
ejpam-3904	89	21	b	b	NOUN
ejpam-3904	89	22	≤	≤	NOUN
ejpam-3904	89	23	a	a	DET
ejpam-3904	89	24	+	+	NOUN
ejpam-3904	89	25	c	c	X
ejpam-3904	89	26	,	,	PUNCT
ejpam-3904	89	27	there	there	PRON
ejpam-3904	89	28	exists	exist	VERB
ejpam-3904	89	29	a	a	DET
ejpam-3904	89	30	graph	graph	NOUN
ejpam-3904	89	31	g	g	ADP
ejpam-3904	89	32	such	such	ADJ
ejpam-3904	89	33	that	that	PRON
ejpam-3904	89	34	δ(g	δ(g	PROPN
ejpam-3904	89	35	)	)	PUNCT
ejpam-3904	89	36	=	=	SYM
ejpam-3904	89	37	c	c	X
ejpam-3904	89	38	,	,	PUNCT
ejpam-3904	89	39	γ(g	γ(g	PROPN
ejpam-3904	89	40	)	)	PUNCT
ejpam-3904	89	41	=	=	SYM
ejpam-3904	89	42	a	a	PRON
ejpam-3904	89	43	and	and	CCONJ
ejpam-3904	89	44	γit(g	γit(g	NOUN
ejpam-3904	89	45	)	)	PUNCT
ejpam-3904	89	46	=	=	SYM
ejpam-3904	89	47	b.	b.	PROPN
ejpam-3904	89	48	theorem	theorem	VERB
ejpam-3904	89	49	3	3	NUM
ejpam-3904	89	50	.	.	PUNCT
ejpam-3904	90	1	[	[	X
ejpam-3904	90	2	17	17	NUM
ejpam-3904	90	3	]	]	PUNCT
ejpam-3904	90	4	for	for	ADP
ejpam-3904	90	5	any	any	DET
ejpam-3904	90	6	two	two	NUM
ejpam-3904	90	7	positive	positive	ADJ
ejpam-3904	90	8	integers	integer	NOUN
ejpam-3904	90	9	a	a	PRON
ejpam-3904	90	10	and	and	CCONJ
ejpam-3904	90	11	b	b	NOUN
ejpam-3904	90	12	such	such	ADJ
ejpam-3904	90	13	that	that	SCONJ
ejpam-3904	90	14	2	2	NUM
ejpam-3904	90	15	≤	≤	NOUN
ejpam-3904	90	16	a	a	DET
ejpam-3904	90	17	≤	≤	NUM
ejpam-3904	90	18	2b	2b	NUM
ejpam-3904	90	19	3	3	NUM
ejpam-3904	90	20	,	,	PUNCT
ejpam-3904	90	21	there	there	PRON
ejpam-3904	90	22	is	be	VERB
ejpam-3904	90	23	a	a	DET
ejpam-3904	90	24	graph	graph	NOUN
ejpam-3904	90	25	of	of	ADP
ejpam-3904	90	26	order	order	NOUN
ejpam-3904	90	27	b	b	NOUN
ejpam-3904	90	28	such	such	ADJ
ejpam-3904	90	29	that	that	DET
ejpam-3904	90	30	γitt(g	γitt(g	NOUN
ejpam-3904	90	31	)	)	PUNCT
ejpam-3904	90	32	=	=	SYM
ejpam-3904	90	33	a.	a.	NOUN
ejpam-3904	90	34	theorem	theorem	NOUN
ejpam-3904	90	35	4	4	NUM
ejpam-3904	90	36	.	.	X
ejpam-3904	91	1	for	for	ADP
ejpam-3904	91	2	any	any	DET
ejpam-3904	91	3	positive	positive	ADJ
ejpam-3904	91	4	integers	integer	NOUN
ejpam-3904	91	5	a	a	PRON
ejpam-3904	91	6	and	and	CCONJ
ejpam-3904	91	7	b	b	NOUN
ejpam-3904	91	8	with	with	ADP
ejpam-3904	91	9	3	3	NUM
ejpam-3904	91	10	≤	≤	NOUN
ejpam-3904	91	11	a	a	DET
ejpam-3904	91	12	≤	≤	PROPN
ejpam-3904	91	13	b	b	NOUN
ejpam-3904	91	14	there	there	PRON
ejpam-3904	91	15	exists	exist	VERB
ejpam-3904	91	16	a	a	DET
ejpam-3904	91	17	connected	connected	ADJ
ejpam-3904	91	18	graph	graph	NOUN
ejpam-3904	91	19	g	g	NOUN
ejpam-3904	91	20	for	for	ADP
ejpam-3904	91	21	which	which	PRON
ejpam-3904	91	22	γt(g	γt(g	PUNCT
ejpam-3904	91	23	)	)	PUNCT
ejpam-3904	91	24	=	=	SYM
ejpam-3904	91	25	a	a	NOUN
ejpam-3904	91	26	and	and	CCONJ
ejpam-3904	91	27	γitt(g	γitt(g	NOUN
ejpam-3904	91	28	)	)	PUNCT
ejpam-3904	91	29	=	=	SYM
ejpam-3904	91	30	b.	b.	NOUN
ejpam-3904	91	31	proof	proof	NOUN
ejpam-3904	91	32	.	.	PUNCT
ejpam-3904	92	1	we	we	PRON
ejpam-3904	92	2	consider	consider	VERB
ejpam-3904	92	3	the	the	DET
ejpam-3904	92	4	following	follow	VERB
ejpam-3904	92	5	cases	case	NOUN
ejpam-3904	92	6	:	:	PUNCT
ejpam-3904	92	7	case	case	NOUN
ejpam-3904	92	8	1	1	NUM
ejpam-3904	92	9	:	:	PUNCT
ejpam-3904	92	10	suppose	suppose	VERB
ejpam-3904	92	11	that	that	SCONJ
ejpam-3904	92	12	a	a	DET
ejpam-3904	92	13	=	=	X
ejpam-3904	92	14	b.	b.	NOUN
ejpam-3904	92	15	if	if	SCONJ
ejpam-3904	92	16	a	a	DET
ejpam-3904	92	17	=	=	SYM
ejpam-3904	92	18	b	b	NOUN
ejpam-3904	92	19	=	=	SYM
ejpam-3904	92	20	3	3	NUM
ejpam-3904	92	21	,	,	PUNCT
ejpam-3904	92	22	then	then	ADV
ejpam-3904	92	23	we	we	PRON
ejpam-3904	92	24	choose	choose	VERB
ejpam-3904	92	25	g	g	PROPN
ejpam-3904	92	26	=	=	SYM
ejpam-3904	92	27	c5	c5	PROPN
ejpam-3904	92	28	.	.	PUNCT
ejpam-3904	92	29	suppose	suppose	VERB
ejpam-3904	92	30	that	that	SCONJ
ejpam-3904	92	31	a	a	DET
ejpam-3904	92	32	=	=	SYM
ejpam-3904	92	33	b	b	NOUN
ejpam-3904	92	34	≥	≥	NUM
ejpam-3904	92	35	4	4	NUM
ejpam-3904	92	36	.	.	PUNCT
ejpam-3904	93	1	if	if	SCONJ
ejpam-3904	93	2	a	a	DET
ejpam-3904	93	3	≡	≡	PROPN
ejpam-3904	93	4	0	0	NUM
ejpam-3904	93	5	,	,	PUNCT
ejpam-3904	93	6	2(mod	2(mod	NUM
ejpam-3904	93	7	4	4	NUM
ejpam-3904	93	8	)	)	PUNCT
ejpam-3904	93	9	,	,	PUNCT
ejpam-3904	93	10	then	then	ADV
ejpam-3904	93	11	choose	choose	VERB
ejpam-3904	93	12	g	g	NOUN
ejpam-3904	93	13	=	=	SYM
ejpam-3904	93	14	p2a	p2a	ADJ
ejpam-3904	93	15	.	.	PUNCT
ejpam-3904	94	1	if	if	SCONJ
ejpam-3904	94	2	a	a	DET
ejpam-3904	94	3	≡	≡	PROPN
ejpam-3904	94	4	1	1	NUM
ejpam-3904	94	5	,	,	PUNCT
ejpam-3904	94	6	3(mod	3(mod	NUM
ejpam-3904	94	7	4	4	NUM
ejpam-3904	94	8	)	)	PUNCT
ejpam-3904	94	9	,	,	PUNCT
ejpam-3904	94	10	then	then	ADV
ejpam-3904	94	11	choose	choose	VERB
ejpam-3904	94	12	g	g	PROPN
ejpam-3904	94	13	=	=	SYM
ejpam-3904	94	14	p2a−1	p2a−1	PROPN
ejpam-3904	94	15	.	.	PUNCT
ejpam-3904	95	1	in	in	ADP
ejpam-3904	95	2	any	any	DET
ejpam-3904	95	3	case	case	NOUN
ejpam-3904	95	4	,	,	PUNCT
ejpam-3904	95	5	γt(g	γt(g	PUNCT
ejpam-3904	95	6	)	)	PUNCT
ejpam-3904	95	7	=	=	SYM
ejpam-3904	95	8	γitt(g	γitt(g	NOUN
ejpam-3904	95	9	)	)	PUNCT
ejpam-3904	95	10	=	=	SYM
ejpam-3904	95	11	a.	a.	NOUN
ejpam-3904	95	12	d.	d.	PROPN
ejpam-3904	95	13	sevilleno	sevilleno	PROPN
ejpam-3904	95	14	,	,	PUNCT
ejpam-3904	95	15	f.	f.	PROPN
ejpam-3904	95	16	jamil	jamil	PROPN
ejpam-3904	95	17	/	/	SYM
ejpam-3904	95	18	eur	eur	PROPN
ejpam-3904	95	19	.	.	PUNCT
ejpam-3904	96	1	j.	j.	PROPN
ejpam-3904	96	2	pure	pure	PROPN
ejpam-3904	96	3	appl	appl	PROPN
ejpam-3904	96	4	.	.	PUNCT
ejpam-3904	96	5	math	math	PROPN
ejpam-3904	96	6	,	,	PUNCT
ejpam-3904	96	7	149	149	NUM
ejpam-3904	96	8	-	-	SYM
ejpam-3904	96	9	163	163	NUM
ejpam-3904	96	10	153	153	NUM
ejpam-3904	96	11	·	·	PUNCT
ejpam-3904	96	12	·	·	PUNCT
ejpam-3904	96	13	·	·	PUNCT
ejpam-3904	96	14	·	·	PUNCT
ejpam-3904	96	15	·	·	PUNCT
ejpam-3904	96	16	·	·	PUNCT
ejpam-3904	96	17	·	·	PUNCT
ejpam-3904	96	18	·	·	PUNCT
ejpam-3904	96	19	·	·	PUNCT
ejpam-3904	96	20	·	·	PUNCT
ejpam-3904	96	21	·	·	PUNCT
ejpam-3904	96	22	·	·	PUNCT
ejpam-3904	96	23	·	·	PUNCT
ejpam-3904	96	24	·	·	PUNCT
ejpam-3904	96	25	·	·	PUNCT
ejpam-3904	96	26	·	·	PUNCT
ejpam-3904	96	27	·	·	PUNCT
ejpam-3904	96	28	·	·	PUNCT
ejpam-3904	96	29	·	·	PUNCT
ejpam-3904	96	30	·	·	PUNCT
ejpam-3904	97	1	·	·	PUNCT
ejpam-3904	97	2	figure	figure	NOUN
ejpam-3904	97	3	1	1	NUM
ejpam-3904	97	4	:	:	PUNCT
ejpam-3904	97	5	graph	graph	NOUN
ejpam-3904	97	6	g	g	PROPN
ejpam-3904	97	7	=	=	PUNCT
ejpam-3904	97	8	ca	can	AUX
ejpam-3904	97	9	◦	◦	VERB
ejpam-3904	97	10	{	{	PUNCT
ejpam-3904	97	11	kn	kn	PROPN
ejpam-3904	97	12	∪kn	∪kn	PROPN
ejpam-3904	97	13	}	}	PUNCT
ejpam-3904	97	14	with	with	ADP
ejpam-3904	97	15	a	a	DET
ejpam-3904	97	16	≥	≥	NUM
ejpam-3904	97	17	3	3	NUM
ejpam-3904	97	18	case	case	NOUN
ejpam-3904	97	19	2	2	NUM
ejpam-3904	97	20	:	:	PUNCT
ejpam-3904	97	21	suppose	suppose	VERB
ejpam-3904	97	22	that	that	SCONJ
ejpam-3904	97	23	a	a	DET
ejpam-3904	97	24	<	<	X
ejpam-3904	97	25	b.	b.	PROPN
ejpam-3904	97	26	the	the	DET
ejpam-3904	97	27	b	b	PROPN
ejpam-3904	97	28	=	=	PUNCT
ejpam-3904	97	29	a	a	PROPN
ejpam-3904	97	30	+	+	X
ejpam-3904	97	31	n	n	NOUN
ejpam-3904	97	32	for	for	ADP
ejpam-3904	97	33	some	some	DET
ejpam-3904	97	34	positive	positive	ADJ
ejpam-3904	97	35	integer	integer	NOUN
ejpam-3904	97	36	n.	n.	NOUN
ejpam-3904	97	37	consider	consider	VERB
ejpam-3904	97	38	the	the	DET
ejpam-3904	97	39	corona	corona	NOUN
ejpam-3904	97	40	g	g	NOUN
ejpam-3904	97	41	=	=	PUNCT
ejpam-3904	97	42	ca	can	AUX
ejpam-3904	97	43	◦	◦	VERB
ejpam-3904	97	44	{	{	PUNCT
ejpam-3904	97	45	kn	kn	PROPN
ejpam-3904	97	46	∪kn	∪kn	PROPN
ejpam-3904	97	47	}	}	PUNCT
ejpam-3904	97	48	as	as	SCONJ
ejpam-3904	97	49	shown	show	VERB
ejpam-3904	97	50	in	in	ADP
ejpam-3904	97	51	figure	figure	NOUN
ejpam-3904	97	52	1	1	NUM
ejpam-3904	97	53	.	.	PUNCT
ejpam-3904	97	54	for	for	ADP
ejpam-3904	97	55	convenience	convenience	NOUN
ejpam-3904	97	56	,	,	PUNCT
ejpam-3904	97	57	write	write	VERB
ejpam-3904	97	58	(	(	PUNCT
ejpam-3904	97	59	kn	kn	PROPN
ejpam-3904	97	60	∪kn)v	∪kn)v	PROPN
ejpam-3904	97	61	=	=	SYM
ejpam-3904	97	62	kv	kv	PROPN
ejpam-3904	97	63	n	n	PART
ejpam-3904	97	64	∪	∪	PROPN
ejpam-3904	97	65	kv	kv	PROPN
ejpam-3904	97	66	n.	n.	PROPN
ejpam-3904	97	67	clearly	clearly	ADV
ejpam-3904	97	68	,	,	PUNCT
ejpam-3904	97	69	v	v	X
ejpam-3904	97	70	(	(	PUNCT
ejpam-3904	97	71	ca	ca	NOUN
ejpam-3904	97	72	)	)	PUNCT
ejpam-3904	97	73	is	be	AUX
ejpam-3904	97	74	a	a	DET
ejpam-3904	97	75	γt	γt	NOUN
ejpam-3904	97	76	-	-	NOUN
ejpam-3904	97	77	set	set	NOUN
ejpam-3904	97	78	of	of	ADP
ejpam-3904	97	79	g	g	NOUN
ejpam-3904	97	80	so	so	SCONJ
ejpam-3904	97	81	that	that	PRON
ejpam-3904	97	82	γt(g	γt(g	PUNCT
ejpam-3904	97	83	)	)	PUNCT
ejpam-3904	97	84	=	=	SYM
ejpam-3904	97	85	a.	a.	NOUN
ejpam-3904	97	86	let	let	VERB
ejpam-3904	97	87	v	v	ADP
ejpam-3904	97	88	∈	∈	PROPN
ejpam-3904	97	89	v	v	NOUN
ejpam-3904	97	90	(	(	PUNCT
ejpam-3904	97	91	ca	ca	NOUN
ejpam-3904	97	92	)	)	PUNCT
ejpam-3904	97	93	and	and	CCONJ
ejpam-3904	97	94	define	define	VERB
ejpam-3904	97	95	s	s	PART
ejpam-3904	97	96	=	=	X
ejpam-3904	97	97	v	v	NOUN
ejpam-3904	97	98	(	(	PUNCT
ejpam-3904	97	99	ca)∪v	ca)∪v	PROPN
ejpam-3904	97	100	(	(	PUNCT
ejpam-3904	97	101	kv	kv	PROPN
ejpam-3904	97	102	n	n	CCONJ
ejpam-3904	97	103	)	)	PUNCT
ejpam-3904	97	104	.	.	PUNCT
ejpam-3904	98	1	then	then	ADV
ejpam-3904	98	2	,	,	PUNCT
ejpam-3904	98	3	s	s	VERB
ejpam-3904	98	4	is	be	AUX
ejpam-3904	98	5	a	a	DET
ejpam-3904	98	6	total	total	ADJ
ejpam-3904	98	7	dominating	dominating	NOUN
ejpam-3904	98	8	set	set	NOUN
ejpam-3904	98	9	of	of	ADP
ejpam-3904	98	10	g.	g.	PROPN
ejpam-3904	98	11	now	now	ADV
ejpam-3904	98	12	a	a	DET
ejpam-3904	98	13	β0	β0	NOUN
ejpam-3904	98	14	-	-	PUNCT
ejpam-3904	98	15	set	set	VERB
ejpam-3904	98	16	m	m	NOUN
ejpam-3904	98	17	of	of	ADP
ejpam-3904	98	18	g	g	PROPN
ejpam-3904	98	19	is	be	AUX
ejpam-3904	98	20	of	of	ADP
ejpam-3904	98	21	the	the	DET
ejpam-3904	98	22	form	form	NOUN
ejpam-3904	98	23	m	m	NOUN
ejpam-3904	98	24	=	=	VERB
ejpam-3904	98	25	∪v∈v	∪v∈v	X
ejpam-3904	98	26	(	(	PUNCT
ejpam-3904	98	27	ca){av	ca){av	PROPN
ejpam-3904	98	28	,	,	PUNCT
ejpam-3904	98	29	bv	bv	NOUN
ejpam-3904	98	30	}	}	PUNCT
ejpam-3904	98	31	,	,	PUNCT
ejpam-3904	98	32	where	where	SCONJ
ejpam-3904	98	33	av	av	PROPN
ejpam-3904	98	34	and	and	CCONJ
ejpam-3904	98	35	bv	bv	PROPN
ejpam-3904	98	36	belong	belong	VERB
ejpam-3904	98	37	to	to	ADP
ejpam-3904	98	38	different	different	ADJ
ejpam-3904	98	39	components	component	NOUN
ejpam-3904	98	40	of	of	ADP
ejpam-3904	98	41	kv	kv	PROPN
ejpam-3904	98	42	n	n	CCONJ
ejpam-3904	98	43	∪kv	∪kv	PROPN
ejpam-3904	98	44	n.	n.	PROPN
ejpam-3904	98	45	then	then	ADV
ejpam-3904	98	46	m	m	VERB
ejpam-3904	98	47	∩	∩	PROPN
ejpam-3904	98	48	s	s	PART
ejpam-3904	98	49	6=	6=	NUM
ejpam-3904	98	50	∅.	∅.	ADP
ejpam-3904	98	51	thus	thus	ADV
ejpam-3904	98	52	,	,	PUNCT
ejpam-3904	98	53	s	s	VERB
ejpam-3904	98	54	is	be	AUX
ejpam-3904	98	55	an	an	DET
ejpam-3904	98	56	ittd	ittd	NOUN
ejpam-3904	98	57	-	-	PUNCT
ejpam-3904	98	58	set	set	NOUN
ejpam-3904	98	59	of	of	ADP
ejpam-3904	98	60	g.	g.	PROPN
ejpam-3904	98	61	thus	thus	ADV
ejpam-3904	98	62	,	,	PUNCT
ejpam-3904	98	63	γitt(g	γitt(g	NOUN
ejpam-3904	98	64	)	)	PUNCT
ejpam-3904	98	65	≤	≤	NUM
ejpam-3904	98	66	|s|	|s|	PROPN
ejpam-3904	98	67	=	=	SYM
ejpam-3904	98	68	a	a	DET
ejpam-3904	98	69	+	+	NUM
ejpam-3904	98	70	n	n	PROPN
ejpam-3904	98	71	=	=	PROPN
ejpam-3904	98	72	b.	b.	PROPN
ejpam-3904	98	73	let	let	VERB
ejpam-3904	98	74	t	t	PROPN
ejpam-3904	98	75	⊆	⊆	NUM
ejpam-3904	98	76	v	v	NOUN
ejpam-3904	98	77	(	(	PUNCT
ejpam-3904	98	78	g	g	NOUN
ejpam-3904	98	79	)	)	PUNCT
ejpam-3904	98	80	be	be	AUX
ejpam-3904	98	81	a	a	DET
ejpam-3904	98	82	total	total	ADJ
ejpam-3904	98	83	dominating	dominating	NOUN
ejpam-3904	98	84	set	set	VERB
ejpam-3904	98	85	with	with	ADP
ejpam-3904	98	86	|t	|t	PROPN
ejpam-3904	99	1	|	|	ADV
ejpam-3904	99	2	<	<	X
ejpam-3904	99	3	b.	b.	PROPN
ejpam-3904	99	4	then	then	ADV
ejpam-3904	99	5	v	v	X
ejpam-3904	99	6	(	(	PUNCT
ejpam-3904	99	7	kv	kv	PROPN
ejpam-3904	99	8	n)\t	n)\t	PROPN
ejpam-3904	99	9	6=	6=	PROPN
ejpam-3904	99	10	∅	∅	NOUN
ejpam-3904	99	11	for	for	ADP
ejpam-3904	99	12	all	all	PRON
ejpam-3904	99	13	v	v	ADP
ejpam-3904	99	14	∈	∈	NOUN
ejpam-3904	99	15	v	v	NOUN
ejpam-3904	99	16	(	(	PUNCT
ejpam-3904	99	17	ca	ca	NOUN
ejpam-3904	99	18	)	)	PUNCT
ejpam-3904	99	19	.	.	PUNCT
ejpam-3904	100	1	for	for	ADP
ejpam-3904	100	2	each	each	DET
ejpam-3904	100	3	v	v	NUM
ejpam-3904	100	4	∈	∈	PROPN
ejpam-3904	100	5	v	v	NOUN
ejpam-3904	100	6	(	(	PUNCT
ejpam-3904	100	7	ca	ca	NOUN
ejpam-3904	100	8	)	)	PUNCT
ejpam-3904	100	9	,	,	PUNCT
ejpam-3904	100	10	pick	pick	VERB
ejpam-3904	100	11	av	av	PROPN
ejpam-3904	100	12	,	,	PUNCT
ejpam-3904	100	13	bv	bv	PROPN
ejpam-3904	100	14	∈	∈	PROPN
ejpam-3904	100	15	v	v	PROPN
ejpam-3904	100	16	(	(	PUNCT
ejpam-3904	100	17	kv	kv	PROPN
ejpam-3904	100	18	n	n	CCONJ
ejpam-3904	100	19	∪kv	∪kv	NOUN
ejpam-3904	100	20	n	n	CCONJ
ejpam-3904	100	21	)	)	PUNCT
ejpam-3904	100	22	\	\	PROPN
ejpam-3904	101	1	t	t	PROPN
ejpam-3904	101	2	such	such	ADJ
ejpam-3904	101	3	tha	tha	INTJ
ejpam-3904	101	4	av	av	PROPN
ejpam-3904	101	5	and	and	CCONJ
ejpam-3904	101	6	bv	bv	PROPN
ejpam-3904	101	7	are	be	AUX
ejpam-3904	101	8	from	from	ADP
ejpam-3904	101	9	different	different	ADJ
ejpam-3904	101	10	components	component	NOUN
ejpam-3904	101	11	.	.	PUNCT
ejpam-3904	102	1	then	then	ADV
ejpam-3904	102	2	m	m	VERB
ejpam-3904	102	3	=	=	SYM
ejpam-3904	102	4	{	{	PUNCT
ejpam-3904	102	5	av	av	PROPN
ejpam-3904	102	6	,	,	PUNCT
ejpam-3904	102	7	bv	bv	PROPN
ejpam-3904	102	8	:	:	PUNCT
ejpam-3904	102	9	v	v	NUM
ejpam-3904	102	10	∈	∈	PROPN
ejpam-3904	102	11	v	v	NOUN
ejpam-3904	102	12	(	(	PUNCT
ejpam-3904	102	13	g	g	NOUN
ejpam-3904	102	14	)	)	PUNCT
ejpam-3904	102	15	}	}	PUNCT
ejpam-3904	102	16	is	be	AUX
ejpam-3904	102	17	a	a	DET
ejpam-3904	102	18	maximum	maximum	ADJ
ejpam-3904	102	19	independent	independent	ADJ
ejpam-3904	102	20	set	set	NOUN
ejpam-3904	102	21	of	of	ADP
ejpam-3904	102	22	g.	g.	PROPN
ejpam-3904	102	23	since	since	SCONJ
ejpam-3904	102	24	m	m	PROPN
ejpam-3904	102	25	∩	∩	PROPN
ejpam-3904	102	26	t	t	NOUN
ejpam-3904	102	27	=	=	SYM
ejpam-3904	102	28	∅	∅	NOUN
ejpam-3904	102	29	,	,	PUNCT
ejpam-3904	102	30	t	t	PROPN
ejpam-3904	102	31	is	be	AUX
ejpam-3904	102	32	not	not	PART
ejpam-3904	102	33	an	an	DET
ejpam-3904	102	34	ittd	ittd	NOUN
ejpam-3904	102	35	-	-	PUNCT
ejpam-3904	102	36	set	set	NOUN
ejpam-3904	102	37	of	of	ADP
ejpam-3904	102	38	g.	g.	PROPN
ejpam-3904	102	39	since	since	SCONJ
ejpam-3904	102	40	t	t	PROPN
ejpam-3904	102	41	is	be	AUX
ejpam-3904	102	42	arbitrary	arbitrary	ADJ
ejpam-3904	102	43	,	,	PUNCT
ejpam-3904	102	44	γitt(g	γitt(g	NOUN
ejpam-3904	102	45	)	)	PUNCT
ejpam-3904	102	46	=	=	SYM
ejpam-3904	102	47	b.	b.	PROPN
ejpam-3904	102	48	theorem	theorem	VERB
ejpam-3904	102	49	5	5	NUM
ejpam-3904	102	50	.	.	PUNCT
ejpam-3904	103	1	for	for	ADP
ejpam-3904	103	2	every	every	DET
ejpam-3904	103	3	positive	positive	ADJ
ejpam-3904	103	4	integers	integer	NOUN
ejpam-3904	103	5	n	n	CCONJ
ejpam-3904	103	6	,	,	PUNCT
ejpam-3904	103	7	a	a	PRON
ejpam-3904	103	8	and	and	CCONJ
ejpam-3904	103	9	b	b	NOUN
ejpam-3904	103	10	with	with	ADP
ejpam-3904	103	11	5	5	NUM
ejpam-3904	103	12	≤	≤	NOUN
ejpam-3904	103	13	a	a	DET
ejpam-3904	103	14	≤	≤	NUM
ejpam-3904	103	15	b	b	NOUN
ejpam-3904	103	16	≤	≤	NOUN
ejpam-3904	103	17	2a−	2a−	NUM
ejpam-3904	103	18	2	2	NUM
ejpam-3904	103	19	,	,	PUNCT
ejpam-3904	103	20	there	there	PRON
ejpam-3904	103	21	exists	exist	VERB
ejpam-3904	103	22	a	a	DET
ejpam-3904	103	23	connected	connected	ADJ
ejpam-3904	103	24	graph	graph	NOUN
ejpam-3904	103	25	g	g	NOUN
ejpam-3904	103	26	for	for	ADP
ejpam-3904	103	27	which	which	PRON
ejpam-3904	103	28	γit(g	γit(g	NOUN
ejpam-3904	103	29	)	)	PUNCT
ejpam-3904	103	30	=	=	SYM
ejpam-3904	103	31	a	a	PRON
ejpam-3904	103	32	and	and	CCONJ
ejpam-3904	103	33	γitt(g	γitt(g	NOUN
ejpam-3904	103	34	)	)	PUNCT
ejpam-3904	104	1	=	=	SYM
ejpam-3904	104	2	b.	b.	NOUN
ejpam-3904	104	3	proof	proof	NOUN
ejpam-3904	104	4	.	.	PUNCT
ejpam-3904	105	1	for	for	SCONJ
ejpam-3904	105	2	k	k	PROPN
ejpam-3904	105	3	≥	≥	PROPN
ejpam-3904	105	4	2	2	NUM
ejpam-3904	105	5	,	,	PUNCT
ejpam-3904	105	6	denote	denote	VERB
ejpam-3904	105	7	by	by	ADP
ejpam-3904	105	8	g(k	g(k	NOUN
ejpam-3904	105	9	)	)	PUNCT
ejpam-3904	105	10	the	the	DET
ejpam-3904	105	11	graph	graph	NOUN
ejpam-3904	105	12	given	give	VERB
ejpam-3904	105	13	in	in	ADP
ejpam-3904	105	14	figure	figure	NOUN
ejpam-3904	105	15	2	2	NUM
ejpam-3904	105	16	.	.	PUNCT
ejpam-3904	106	1	x1	x1	NUM
ejpam-3904	107	1	x2	x2	PROPN
ejpam-3904	107	2	x3	x3	PROPN
ejpam-3904	107	3	x4	x4	PROPN
ejpam-3904	107	4	xk	xk	X
ejpam-3904	107	5	·	·	PUNCT
ejpam-3904	107	6	·	·	PUNCT
ejpam-3904	107	7	·	·	PUNCT
ejpam-3904	108	1	x2	x2	INTJ
ejpam-3904	108	2	x3	x3	PROPN
ejpam-3904	108	3	x4	x4	PROPN
ejpam-3904	108	4	xk	xk	PROPN
ejpam-3904	108	5	figure	figure	NOUN
ejpam-3904	108	6	2	2	NUM
ejpam-3904	108	7	:	:	PUNCT
ejpam-3904	108	8	graph	graph	NOUN
ejpam-3904	108	9	g(k	g(k	NOUN
ejpam-3904	108	10	)	)	PUNCT
ejpam-3904	108	11	suppose	suppose	VERB
ejpam-3904	108	12	that	that	SCONJ
ejpam-3904	108	13	a	a	DET
ejpam-3904	108	14	=	=	X
ejpam-3904	108	15	b.	b.	NOUN
ejpam-3904	108	16	take	take	VERB
ejpam-3904	108	17	the	the	DET
ejpam-3904	108	18	graph	graph	NOUN
ejpam-3904	108	19	g	g	NOUN
ejpam-3904	108	20	as	as	ADP
ejpam-3904	108	21	in	in	ADP
ejpam-3904	108	22	figure	figure	NOUN
ejpam-3904	108	23	3	3	NUM
ejpam-3904	108	24	obtained	obtain	VERB
ejpam-3904	108	25	from	from	ADP
ejpam-3904	108	26	the	the	DET
ejpam-3904	108	27	graph	graph	NOUN
ejpam-3904	108	28	g(a−1	g(a−1	NOUN
ejpam-3904	108	29	)	)	PUNCT
ejpam-3904	108	30	by	by	ADP
ejpam-3904	108	31	adding	add	VERB
ejpam-3904	108	32	the	the	DET
ejpam-3904	108	33	path	path	NOUN
ejpam-3904	109	1	[	[	X
ejpam-3904	109	2	xa−1	xa−1	PROPN
ejpam-3904	109	3	,	,	PUNCT
ejpam-3904	109	4	xa	xa	PROPN
ejpam-3904	109	5	,	,	PUNCT
ejpam-3904	109	6	xa+1	xa+1	PROPN
ejpam-3904	109	7	,	,	PUNCT
ejpam-3904	109	8	xa+2	xa+2	PROPN
ejpam-3904	109	9	,	,	PUNCT
ejpam-3904	109	10	x	x	PUNCT
ejpam-3904	109	11	a+2	a+2	PROPN
ejpam-3904	109	12	]	]	PUNCT
ejpam-3904	109	13	.	.	PUNCT
ejpam-3904	110	1	observe	observe	VERB
ejpam-3904	110	2	that	that	SCONJ
ejpam-3904	110	3	{	{	PUNCT
ejpam-3904	110	4	x2	x2	ADJ
ejpam-3904	110	5	,	,	PUNCT
ejpam-3904	110	6	x3	x3	ADJ
ejpam-3904	110	7	,	,	PUNCT
ejpam-3904	110	8	...	...	PUNCT
ejpam-3904	110	9	,	,	PUNCT
ejpam-3904	110	10	xa−1	xa−1	PROPN
ejpam-3904	110	11	,	,	PUNCT
ejpam-3904	110	12	xa+2	xa+2	PROPN
ejpam-3904	110	13	}	}	PUNCT
ejpam-3904	110	14	is	be	AUX
ejpam-3904	110	15	a	a	DET
ejpam-3904	110	16	xa+1	xa+1	PROPN
ejpam-3904	110	17	xa+2	xa+2	PROPN
ejpam-3904	110	18	xa+2	xa+2	PROPN
ejpam-3904	110	19	x1	x1	PROPN
ejpam-3904	111	1	x2	x2	PROPN
ejpam-3904	111	2	x3	x3	PROPN
ejpam-3904	112	1	x4	x4	PROPN
ejpam-3904	112	2	xa−1	xa−1	PROPN
ejpam-3904	112	3	xa	xa	PROPN
ejpam-3904	112	4	·	·	PUNCT
ejpam-3904	112	5	·	·	PUNCT
ejpam-3904	112	6	·	·	PUNCT
ejpam-3904	113	1	x2	x2	INTJ
ejpam-3904	113	2	x3	x3	PROPN
ejpam-3904	113	3	x4	x4	PROPN
ejpam-3904	113	4	xa−1	xa−1	PROPN
ejpam-3904	113	5	figure	figure	NOUN
ejpam-3904	113	6	3	3	NUM
ejpam-3904	113	7	:	:	PUNCT
ejpam-3904	113	8	graph	graph	VERB
ejpam-3904	113	9	g	g	NOUN
ejpam-3904	113	10	with	with	ADP
ejpam-3904	113	11	γit(g	γit(g	NOUN
ejpam-3904	113	12	)	)	PUNCT
ejpam-3904	114	1	=	=	SYM
ejpam-3904	114	2	γitt(g	γitt(g	NOUN
ejpam-3904	114	3	)	)	PUNCT
ejpam-3904	114	4	γ	γ	PROPN
ejpam-3904	114	5	-	-	PUNCT
ejpam-3904	114	6	set	set	NOUN
ejpam-3904	114	7	of	of	ADP
ejpam-3904	114	8	g	g	PROPN
ejpam-3904	114	9	and	and	CCONJ
ejpam-3904	114	10	every	every	DET
ejpam-3904	114	11	maximum	maximum	ADJ
ejpam-3904	114	12	independent	independent	ADJ
ejpam-3904	114	13	set	set	NOUN
ejpam-3904	114	14	of	of	ADP
ejpam-3904	114	15	g	g	PROPN
ejpam-3904	114	16	contains	contain	VERB
ejpam-3904	114	17	either	either	CCONJ
ejpam-3904	114	18	xa+2	xa+2	PROPN
ejpam-3904	114	19	or	or	CCONJ
ejpam-3904	114	20	xa+2	xa+2	PROPN
ejpam-3904	114	21	.	.	PUNCT
ejpam-3904	115	1	thus	thus	ADV
ejpam-3904	115	2	,	,	PUNCT
ejpam-3904	115	3	d.	d.	PROPN
ejpam-3904	115	4	sevilleno	sevilleno	PROPN
ejpam-3904	115	5	,	,	PUNCT
ejpam-3904	115	6	f.	f.	PROPN
ejpam-3904	115	7	jamil	jamil	PROPN
ejpam-3904	115	8	/	/	SYM
ejpam-3904	115	9	eur	eur	PROPN
ejpam-3904	115	10	.	.	PUNCT
ejpam-3904	116	1	j.	j.	PROPN
ejpam-3904	116	2	pure	pure	PROPN
ejpam-3904	116	3	appl	appl	PROPN
ejpam-3904	116	4	.	.	PUNCT
ejpam-3904	116	5	math	math	PROPN
ejpam-3904	116	6	,	,	PUNCT
ejpam-3904	116	7	149	149	NUM
ejpam-3904	116	8	-	-	SYM
ejpam-3904	116	9	163	163	NUM
ejpam-3904	116	10	154	154	NUM
ejpam-3904	116	11	the	the	DET
ejpam-3904	116	12	set	set	NOUN
ejpam-3904	117	1	d	d	X
ejpam-3904	117	2	=	=	SYM
ejpam-3904	117	3	{	{	PUNCT
ejpam-3904	117	4	x2	x2	PROPN
ejpam-3904	117	5	,	,	PUNCT
ejpam-3904	117	6	x3	x3	ADJ
ejpam-3904	117	7	,	,	PUNCT
ejpam-3904	117	8	...	...	PUNCT
ejpam-3904	117	9	,	,	PUNCT
ejpam-3904	117	10	xa−1	xa−1	PROPN
ejpam-3904	117	11	,	,	PUNCT
ejpam-3904	117	12	xa+2	xa+2	PROPN
ejpam-3904	117	13	,	,	PUNCT
ejpam-3904	117	14	x	x	PUNCT
ejpam-3904	117	15	a+2	a+2	NOUN
ejpam-3904	117	16	}	}	PUNCT
ejpam-3904	117	17	is	be	AUX
ejpam-3904	117	18	a	a	DET
ejpam-3904	117	19	γit	γit	ADV
ejpam-3904	117	20	-	-	PUNCT
ejpam-3904	117	21	set	set	NOUN
ejpam-3904	117	22	of	of	ADP
ejpam-3904	117	23	g.	g.	PROPN
ejpam-3904	117	24	note	note	VERB
ejpam-3904	117	25	that	that	SCONJ
ejpam-3904	117	26	[	[	X
ejpam-3904	117	27	x2	x2	X
ejpam-3904	117	28	,	,	PUNCT
ejpam-3904	117	29	x3	x3	ADJ
ejpam-3904	117	30	,	,	PUNCT
ejpam-3904	117	31	...	...	PUNCT
ejpam-3904	117	32	,	,	PUNCT
ejpam-3904	117	33	xa−1	xa−1	PROPN
ejpam-3904	117	34	]	]	PUNCT
ejpam-3904	117	35	is	be	AUX
ejpam-3904	117	36	a	a	DET
ejpam-3904	117	37	path	path	NOUN
ejpam-3904	117	38	of	of	ADP
ejpam-3904	117	39	length	length	NOUN
ejpam-3904	117	40	at	at	ADV
ejpam-3904	117	41	least	least	ADV
ejpam-3904	117	42	2	2	NUM
ejpam-3904	117	43	.	.	PUNCT
ejpam-3904	118	1	hence	hence	ADV
ejpam-3904	118	2	d	d	PROPN
ejpam-3904	118	3	is	be	AUX
ejpam-3904	118	4	also	also	ADV
ejpam-3904	118	5	a	a	DET
ejpam-3904	118	6	γitt	γitt	VERB
ejpam-3904	118	7	-	-	PUNCT
ejpam-3904	118	8	set	set	NOUN
ejpam-3904	118	9	of	of	ADP
ejpam-3904	118	10	g.	g.	PROPN
ejpam-3904	118	11	therefore	therefore	ADV
ejpam-3904	118	12	γit(g	γit(g	PROPN
ejpam-3904	118	13	)	)	PUNCT
ejpam-3904	119	1	=	=	SYM
ejpam-3904	119	2	γitt(g	γitt(g	NOUN
ejpam-3904	119	3	)	)	PUNCT
ejpam-3904	119	4	=	=	SYM
ejpam-3904	119	5	(	(	PUNCT
ejpam-3904	119	6	a−	a−	PROPN
ejpam-3904	119	7	2	2	NUM
ejpam-3904	119	8	)	)	PUNCT
ejpam-3904	119	9	+	+	CCONJ
ejpam-3904	119	10	2	2	NUM
ejpam-3904	119	11	=	=	SYM
ejpam-3904	119	12	a.	a.	NOUN
ejpam-3904	119	13	suppose	suppose	VERB
ejpam-3904	119	14	now	now	ADV
ejpam-3904	119	15	that	that	SCONJ
ejpam-3904	119	16	a	a	DET
ejpam-3904	119	17	<	<	X
ejpam-3904	119	18	b.	b.	PROPN
ejpam-3904	119	19	then	then	ADV
ejpam-3904	119	20	b	b	X
ejpam-3904	119	21	=	=	PUNCT
ejpam-3904	119	22	a	a	PROPN
ejpam-3904	119	23	+	+	X
ejpam-3904	119	24	k	k	NOUN
ejpam-3904	119	25	for	for	ADP
ejpam-3904	119	26	some	some	DET
ejpam-3904	119	27	positive	positive	ADJ
ejpam-3904	119	28	integer	integer	NOUN
ejpam-3904	119	29	1	1	NUM
ejpam-3904	119	30	≤	≤	NUM
ejpam-3904	119	31	k	k	NOUN
ejpam-3904	119	32	≤	≤	NOUN
ejpam-3904	119	33	a	a	DET
ejpam-3904	119	34	−	−	PROPN
ejpam-3904	119	35	2	2	NUM
ejpam-3904	119	36	.	.	PUNCT
ejpam-3904	120	1	for	for	ADP
ejpam-3904	120	2	k	k	PROPN
ejpam-3904	120	3	=	=	SYM
ejpam-3904	120	4	1	1	NUM
ejpam-3904	120	5	,	,	PUNCT
ejpam-3904	120	6	consider	consider	VERB
ejpam-3904	120	7	the	the	DET
ejpam-3904	120	8	graph	graph	NOUN
ejpam-3904	120	9	g	g	NOUN
ejpam-3904	120	10	in	in	ADP
ejpam-3904	120	11	figure	figure	NOUN
ejpam-3904	120	12	4	4	NUM
ejpam-3904	120	13	obtained	obtain	VERB
ejpam-3904	120	14	from	from	ADP
ejpam-3904	120	15	g(a	g(a	PROPN
ejpam-3904	120	16	−	−	PROPN
ejpam-3904	120	17	2	2	NUM
ejpam-3904	120	18	)	)	PUNCT
ejpam-3904	120	19	by	by	ADP
ejpam-3904	120	20	adding	add	VERB
ejpam-3904	120	21	the	the	DET
ejpam-3904	120	22	paths	path	NOUN
ejpam-3904	120	23	[	[	X
ejpam-3904	120	24	xa−2	xa−2	PROPN
ejpam-3904	120	25	+	+	PROPN
ejpam-3904	120	26	3j	3j	NOUN
ejpam-3904	120	27	,	,	PUNCT
ejpam-3904	120	28	xa−1	xa−1	PROPN
ejpam-3904	120	29	+	+	PROPN
ejpam-3904	120	30	3j	3j	PROPN
ejpam-3904	120	31	,	,	PUNCT
ejpam-3904	120	32	xa+3j	xa+3j	PROPN
ejpam-3904	120	33	,	,	PUNCT
ejpam-3904	120	34	xa+1	xa+1	PROPN
ejpam-3904	120	35	+	+	PROPN
ejpam-3904	120	36	3j	3j	NOUN
ejpam-3904	120	37	,	,	PUNCT
ejpam-3904	120	38	x	x	PROPN
ejpam-3904	121	1	a+1	a+1	PROPN
ejpam-3904	121	2	+	+	PROPN
ejpam-3904	121	3	3j	3j	NOUN
ejpam-3904	121	4	]	]	PUNCT
ejpam-3904	122	1	where	where	SCONJ
ejpam-3904	122	2	j	j	PROPN
ejpam-3904	122	3	=	=	SYM
ejpam-3904	122	4	0	0	PROPN
ejpam-3904	122	5	,	,	PUNCT
ejpam-3904	122	6	1	1	NUM
ejpam-3904	122	7	.	.	PUNCT
ejpam-3904	122	8	by	by	ADP
ejpam-3904	122	9	a	a	DET
ejpam-3904	122	10	similar	similar	ADJ
ejpam-3904	122	11	argument	argument	NOUN
ejpam-3904	122	12	xa	xa	PROPN
ejpam-3904	122	13	xa+1	xa+1	PROPN
ejpam-3904	122	14	xa+1	xa+1	PROPN
ejpam-3904	122	15	x1	x1	PROPN
ejpam-3904	123	1	x2	x2	PROPN
ejpam-3904	123	2	x3	x3	PROPN
ejpam-3904	124	1	x4	x4	PROPN
ejpam-3904	124	2	xa−2	xa−2	PROPN
ejpam-3904	124	3	xa−1	xa−1	PROPN
ejpam-3904	124	4	xa+2	xa+2	PROPN
ejpam-3904	124	5	xa+3	xa+3	PROPN
ejpam-3904	124	6	xa+4	xa+4	PROPN
ejpam-3904	124	7	xa+4	xa+4	X
ejpam-3904	124	8	·	·	PUNCT
ejpam-3904	124	9	·	·	PUNCT
ejpam-3904	124	10	·	·	PUNCT
ejpam-3904	125	1	x2	x2	NOUN
ejpam-3904	125	2	x3	x3	PROPN
ejpam-3904	125	3	x4	x4	PROPN
ejpam-3904	126	1	xa−2	xa−2	PROPN
ejpam-3904	126	2	figure	figure	VERB
ejpam-3904	126	3	4	4	NUM
ejpam-3904	126	4	:	:	PUNCT
ejpam-3904	126	5	graph	graph	VERB
ejpam-3904	126	6	g	g	NOUN
ejpam-3904	126	7	with	with	ADP
ejpam-3904	126	8	γitt(g	γitt(g	NOUN
ejpam-3904	126	9	)	)	PUNCT
ejpam-3904	126	10	=	=	SYM
ejpam-3904	126	11	γit(g	γit(g	PROPN
ejpam-3904	126	12	)	)	PUNCT
ejpam-3904	127	1	+	+	CCONJ
ejpam-3904	127	2	1	1	NUM
ejpam-3904	127	3	d	d	NOUN
ejpam-3904	127	4	=	=	PUNCT
ejpam-3904	127	5	{	{	PUNCT
ejpam-3904	127	6	x2	x2	PROPN
ejpam-3904	127	7	,	,	PUNCT
ejpam-3904	127	8	x3	x3	ADJ
ejpam-3904	127	9	,	,	PUNCT
ejpam-3904	127	10	...	...	PUNCT
ejpam-3904	127	11	,	,	PUNCT
ejpam-3904	127	12	xa−2	xa−2	PROPN
ejpam-3904	127	13	,	,	PUNCT
ejpam-3904	127	14	xa+1	xa+1	PROPN
ejpam-3904	127	15	,	,	PUNCT
ejpam-3904	127	16	xa+4	xa+4	PRON
ejpam-3904	127	17	,	,	PUNCT
ejpam-3904	127	18	x	x	PUNCT
ejpam-3904	127	19	a+4	a+4	ADP
ejpam-3904	127	20	}	}	PUNCT
ejpam-3904	127	21	is	be	AUX
ejpam-3904	127	22	a	a	DET
ejpam-3904	127	23	γit	γit	ADV
ejpam-3904	127	24	-	-	PUNCT
ejpam-3904	127	25	set	set	NOUN
ejpam-3904	127	26	of	of	ADP
ejpam-3904	127	27	g.	g.	PROPN
ejpam-3904	127	28	this	this	PRON
ejpam-3904	127	29	implies	imply	VERB
ejpam-3904	127	30	that	that	SCONJ
ejpam-3904	127	31	γit(g	γit(g	NOUN
ejpam-3904	127	32	)	)	PUNCT
ejpam-3904	128	1	=	=	NOUN
ejpam-3904	128	2	(	(	PUNCT
ejpam-3904	128	3	a	a	DET
ejpam-3904	128	4	−	−	PROPN
ejpam-3904	128	5	3	3	NUM
ejpam-3904	128	6	)	)	PUNCT
ejpam-3904	128	7	+	+	CCONJ
ejpam-3904	128	8	3	3	NUM
ejpam-3904	128	9	=	=	SYM
ejpam-3904	128	10	a.	a.	NOUN
ejpam-3904	128	11	it	it	PRON
ejpam-3904	128	12	also	also	ADV
ejpam-3904	128	13	follows	follow	VERB
ejpam-3904	128	14	that	that	SCONJ
ejpam-3904	128	15	d	d	PROPN
ejpam-3904	128	16	∪	∪	X
ejpam-3904	128	17	{	{	PUNCT
ejpam-3904	128	18	xa+1	xa+1	PROPN
ejpam-3904	128	19	}	}	PUNCT
ejpam-3904	128	20	is	be	AUX
ejpam-3904	128	21	a	a	DET
ejpam-3904	128	22	γitt	γitt	VERB
ejpam-3904	128	23	-	-	PUNCT
ejpam-3904	128	24	set	set	NOUN
ejpam-3904	128	25	of	of	ADP
ejpam-3904	128	26	g.	g.	PROPN
ejpam-3904	128	27	thus	thus	ADV
ejpam-3904	128	28	,	,	PUNCT
ejpam-3904	128	29	γitt(g	γitt(g	NOUN
ejpam-3904	128	30	)	)	PUNCT
ejpam-3904	128	31	=	=	SYM
ejpam-3904	128	32	a+	a+	PUNCT
ejpam-3904	128	33	1	1	NUM
ejpam-3904	128	34	=	=	SYM
ejpam-3904	128	35	b.	b.	PROPN
ejpam-3904	128	36	for	for	ADP
ejpam-3904	128	37	2	2	NUM
ejpam-3904	128	38	≤	≤	NUM
ejpam-3904	128	39	k	k	PROPN
ejpam-3904	128	40	≤	≤	PROPN
ejpam-3904	128	41	a−4	a−4	PROPN
ejpam-3904	128	42	,	,	PUNCT
ejpam-3904	128	43	consider	consider	VERB
ejpam-3904	128	44	the	the	DET
ejpam-3904	128	45	graph	graph	NOUN
ejpam-3904	128	46	g	g	NOUN
ejpam-3904	128	47	in	in	ADP
ejpam-3904	128	48	figure	figure	NOUN
ejpam-3904	128	49	5	5	NUM
ejpam-3904	128	50	obtained	obtain	VERB
ejpam-3904	128	51	from	from	ADP
ejpam-3904	128	52	g(a−k−1	g(a−k−1	PROPN
ejpam-3904	128	53	)	)	PUNCT
ejpam-3904	128	54	by	by	ADP
ejpam-3904	128	55	adding	add	VERB
ejpam-3904	128	56	(	(	PUNCT
ejpam-3904	128	57	k	k	PROPN
ejpam-3904	128	58	+	+	PROPN
ejpam-3904	128	59	1	1	X
ejpam-3904	128	60	)	)	PUNCT
ejpam-3904	128	61	paths	path	NOUN
ejpam-3904	128	62	[	[	X
ejpam-3904	128	63	xa−k−1	xa−k−1	PROPN
ejpam-3904	128	64	+	+	NOUN
ejpam-3904	128	65	3j	3j	NOUN
ejpam-3904	128	66	,	,	PUNCT
ejpam-3904	128	67	xa−k+3j	xa−k+3j	PROPN
ejpam-3904	128	68	,	,	PUNCT
ejpam-3904	128	69	xa−k+1	xa−k+1	PROPN
ejpam-3904	128	70	+	+	PROPN
ejpam-3904	128	71	3j	3j	NOUN
ejpam-3904	128	72	,	,	PUNCT
ejpam-3904	128	73	xa−k+2	xa−k+2	PROPN
ejpam-3904	128	74	+	+	PROPN
ejpam-3904	128	75	3j	3j	NOUN
ejpam-3904	128	76	,	,	PUNCT
ejpam-3904	128	77	x	x	X
ejpam-3904	128	78	a−k+2	a−k+2	NOUN
ejpam-3904	128	79	+	+	NOUN
ejpam-3904	128	80	3j	3j	NOUN
ejpam-3904	128	81	]	]	PUNCT
ejpam-3904	128	82	(	(	PUNCT
ejpam-3904	128	83	j	j	NOUN
ejpam-3904	128	84	=	=	SYM
ejpam-3904	128	85	0	0	NUM
ejpam-3904	128	86	,	,	PUNCT
ejpam-3904	128	87	1	1	NUM
ejpam-3904	128	88	,	,	PUNCT
ejpam-3904	128	89	·	·	PUNCT
ejpam-3904	128	90	·	·	PUNCT
ejpam-3904	128	91	·	·	PUNCT
ejpam-3904	129	1	,	,	PUNCT
ejpam-3904	129	2	k	k	PROPN
ejpam-3904	129	3	−	−	NOUN
ejpam-3904	130	1	1	1	NUM
ejpam-3904	130	2	)	)	PUNCT
ejpam-3904	130	3	and	and	CCONJ
ejpam-3904	130	4	[	[	X
ejpam-3904	130	5	xa+2k	xa+2k	NOUN
ejpam-3904	130	6	,	,	PUNCT
ejpam-3904	130	7	xa+2k+1	xa+2k+1	PROPN
ejpam-3904	130	8	,	,	PUNCT
ejpam-3904	130	9	xa+2k+2	xa+2k+2	PROPN
ejpam-3904	130	10	,	,	PUNCT
ejpam-3904	130	11	xa+2k+3	xa+2k+3	PROPN
ejpam-3904	130	12	,	,	PUNCT
ejpam-3904	130	13	xa+2k+4	xa+2k+4	PROPN
ejpam-3904	130	14	,	,	PUNCT
ejpam-3904	130	15	xa+2k+5	xa+2k+5	PROPN
ejpam-3904	130	16	]	]	PUNCT
ejpam-3904	130	17	.	.	PUNCT
ejpam-3904	131	1	thend	thend	VERB
ejpam-3904	131	2	=	=	PUNCT
ejpam-3904	131	3	{	{	PUNCT
ejpam-3904	131	4	x2	x2	PROPN
ejpam-3904	131	5	,	,	PUNCT
ejpam-3904	131	6	x3	x3	ADJ
ejpam-3904	131	7	,	,	PUNCT
ejpam-3904	131	8	.	.	PUNCT
ejpam-3904	131	9	.	.	PUNCT
ejpam-3904	132	1	.	.	PUNCT
ejpam-3904	133	1	,	,	PUNCT
ejpam-3904	134	1	xa−k−1}∪	xa−k−1}∪	PROPN
ejpam-3904	134	2	xa−k+2	xa−k+2	PROPN
ejpam-3904	134	3	xa−k+2	xa−k+2	PROPN
ejpam-3904	134	4	x1	x1	PROPN
ejpam-3904	134	5	x2	x2	PROPN
ejpam-3904	134	6	x3	x3	PROPN
ejpam-3904	134	7	x4	x4	PROPN
ejpam-3904	134	8	xa−k−1	xa−k−1	PROPN
ejpam-3904	135	1	xa−k+5	xa−k+5	PROPN
ejpam-3904	135	2	xa−k+5	xa−k+5	PROPN
ejpam-3904	135	3	·	·	PUNCT
ejpam-3904	135	4	·	·	PUNCT
ejpam-3904	135	5	·	·	PUNCT
ejpam-3904	136	1	x2	x2	INTJ
ejpam-3904	136	2	x3	x3	PROPN
ejpam-3904	136	3	x4	x4	PROPN
ejpam-3904	136	4	xa−k−1	xa−k−1	PROPN
ejpam-3904	136	5	·	·	PUNCT
ejpam-3904	136	6	·	·	PUNCT
ejpam-3904	136	7	·	·	PUNCT
ejpam-3904	137	1	xa+2k−4	xa+2k−4	PUNCT
ejpam-3904	137	2	xa+2k−4	xa+2k−4	PUNCT
ejpam-3904	137	3	xa+2k−1	xa+2k−1	PUNCT
ejpam-3904	137	4	xa+2k−1	xa+2k−1	X
ejpam-3904	137	5	xa+2k+2	xa+2k+2	PUNCT
ejpam-3904	137	6	xa+2k+3	xa+2k+3	PROPN
ejpam-3904	138	1	xa+2k+4	xa+2k+4	PROPN
ejpam-3904	138	2	figure	figure	NOUN
ejpam-3904	138	3	5	5	NUM
ejpam-3904	138	4	:	:	PUNCT
ejpam-3904	138	5	graph	graph	VERB
ejpam-3904	138	6	g	g	NOUN
ejpam-3904	138	7	with	with	ADP
ejpam-3904	138	8	γitt(g	γitt(g	NOUN
ejpam-3904	138	9	)	)	PUNCT
ejpam-3904	138	10	=	=	SYM
ejpam-3904	139	1	γit	γit	X
ejpam-3904	140	1	+	+	CCONJ
ejpam-3904	140	2	k	k	ADJ
ejpam-3904	140	3	,	,	PUNCT
ejpam-3904	140	4	where	where	SCONJ
ejpam-3904	140	5	2	2	NUM
ejpam-3904	140	6	≤	≤	NUM
ejpam-3904	140	7	k	k	X
ejpam-3904	140	8	≤	≤	ADJ
ejpam-3904	140	9	a−	a−	PROPN
ejpam-3904	140	10	4	4	NUM
ejpam-3904	140	11	{	{	PUNCT
ejpam-3904	140	12	xa−k+2	xa−k+2	PROPN
ejpam-3904	140	13	+	+	PROPN
ejpam-3904	140	14	3j	3j	NUM
ejpam-3904	140	15	:	:	PUNCT
ejpam-3904	140	16	j	j	PROPN
ejpam-3904	140	17	∈	∈	PROPN
ejpam-3904	140	18	{	{	PUNCT
ejpam-3904	140	19	0	0	NUM
ejpam-3904	140	20	,	,	PUNCT
ejpam-3904	140	21	1	1	NUM
ejpam-3904	140	22	,	,	PUNCT
ejpam-3904	140	23	2	2	NUM
ejpam-3904	140	24	,	,	PUNCT
ejpam-3904	140	25	.	.	PUNCT
ejpam-3904	140	26	.	.	PUNCT
ejpam-3904	140	27	.	.	PUNCT
ejpam-3904	141	1	,	,	PUNCT
ejpam-3904	142	1	k	k	PROPN
ejpam-3904	143	1	−	−	PROPN
ejpam-3904	144	1	1	1	NUM
ejpam-3904	144	2	}	}	PUNCT
ejpam-3904	144	3	}	}	PUNCT
ejpam-3904	144	4	∪	∪	X
ejpam-3904	144	5	{	{	PUNCT
ejpam-3904	144	6	xa+2k+2	xa+2k+2	PROPN
ejpam-3904	144	7	,	,	PUNCT
ejpam-3904	144	8	xa+2k+4	xa+2k+4	PROPN
ejpam-3904	144	9	}	}	PUNCT
ejpam-3904	144	10	is	be	AUX
ejpam-3904	144	11	a	a	DET
ejpam-3904	144	12	γit	γit	ADV
ejpam-3904	144	13	-	-	PUNCT
ejpam-3904	144	14	set	set	NOUN
ejpam-3904	144	15	of	of	ADP
ejpam-3904	144	16	g.	g.	PROPN
ejpam-3904	144	17	on	on	ADP
ejpam-3904	144	18	the	the	DET
ejpam-3904	144	19	other	other	ADJ
ejpam-3904	144	20	hand	hand	NOUN
ejpam-3904	144	21	,	,	PUNCT
ejpam-3904	144	22	d	d	X
ejpam-3904	144	23	∪	∪	X
ejpam-3904	144	24	{	{	PUNCT
ejpam-3904	144	25	xa−k+2	xa−k+2	PROPN
ejpam-3904	144	26	+	+	PROPN
ejpam-3904	144	27	3j	3j	NUM
ejpam-3904	144	28	:	:	PUNCT
ejpam-3904	144	29	j	j	PROPN
ejpam-3904	144	30	∈	∈	PROPN
ejpam-3904	144	31	{	{	PUNCT
ejpam-3904	144	32	0	0	NUM
ejpam-3904	144	33	,	,	PUNCT
ejpam-3904	144	34	1	1	NUM
ejpam-3904	144	35	,	,	PUNCT
ejpam-3904	144	36	2	2	NUM
ejpam-3904	144	37	,	,	PUNCT
ejpam-3904	144	38	.	.	PUNCT
ejpam-3904	144	39	.	.	PUNCT
ejpam-3904	144	40	.	.	PUNCT
ejpam-3904	145	1	,	,	PUNCT
ejpam-3904	146	1	k	k	PROPN
ejpam-3904	147	1	−	−	PROPN
ejpam-3904	148	1	1	1	NUM
ejpam-3904	148	2	}	}	PUNCT
ejpam-3904	148	3	}	}	PUNCT
ejpam-3904	148	4	∪	∪	X
ejpam-3904	148	5	{	{	PUNCT
ejpam-3904	148	6	xa+2k+3	xa+2k+3	PROPN
ejpam-3904	148	7	}	}	PUNCT
ejpam-3904	148	8	is	be	AUX
ejpam-3904	148	9	a	a	DET
ejpam-3904	148	10	γitt	γitt	VERB
ejpam-3904	148	11	-	-	PUNCT
ejpam-3904	148	12	set	set	NOUN
ejpam-3904	148	13	of	of	ADP
ejpam-3904	148	14	g.	g.	PROPN
ejpam-3904	148	15	thus	thus	ADV
ejpam-3904	148	16	,	,	PUNCT
ejpam-3904	148	17	γit(g	γit(g	PROPN
ejpam-3904	148	18	)	)	PUNCT
ejpam-3904	148	19	=	=	PUNCT
ejpam-3904	148	20	(	(	PUNCT
ejpam-3904	148	21	a−	a−	PROPN
ejpam-3904	148	22	k	k	PROPN
ejpam-3904	149	1	−	−	PROPN
ejpam-3904	149	2	2	2	NUM
ejpam-3904	149	3	)	)	PUNCT
ejpam-3904	149	4	+	+	NOUN
ejpam-3904	150	1	k	k	X
ejpam-3904	150	2	+	+	CCONJ
ejpam-3904	150	3	2	2	NUM
ejpam-3904	150	4	=	=	SYM
ejpam-3904	150	5	a	a	NOUN
ejpam-3904	150	6	and	and	CCONJ
ejpam-3904	150	7	γitt(g	γitt(g	NOUN
ejpam-3904	150	8	)	)	PUNCT
ejpam-3904	150	9	=	=	SYM
ejpam-3904	150	10	a+	a+	PUNCT
ejpam-3904	150	11	k	k	PROPN
ejpam-3904	150	12	=	=	PROPN
ejpam-3904	150	13	b.	b.	PROPN
ejpam-3904	150	14	for	for	ADP
ejpam-3904	150	15	k	k	PROPN
ejpam-3904	151	1	=	=	PUNCT
ejpam-3904	151	2	a	a	DET
ejpam-3904	151	3	−	−	PROPN
ejpam-3904	151	4	3	3	NUM
ejpam-3904	151	5	,	,	PUNCT
ejpam-3904	151	6	consider	consider	VERB
ejpam-3904	151	7	the	the	DET
ejpam-3904	151	8	graph	graph	NOUN
ejpam-3904	151	9	g	g	PROPN
ejpam-3904	151	10	in	in	ADP
ejpam-3904	151	11	figure	figure	NOUN
ejpam-3904	151	12	6	6	NUM
ejpam-3904	151	13	obtained	obtain	VERB
ejpam-3904	151	14	from	from	ADP
ejpam-3904	151	15	g(2	g(2	PROPN
ejpam-3904	151	16	)	)	PUNCT
ejpam-3904	151	17	,	,	PUNCT
ejpam-3904	151	18	by	by	ADP
ejpam-3904	151	19	adding	add	VERB
ejpam-3904	151	20	(	(	PUNCT
ejpam-3904	151	21	a	a	DET
ejpam-3904	151	22	−	−	PROPN
ejpam-3904	151	23	2	2	NUM
ejpam-3904	151	24	)	)	PUNCT
ejpam-3904	151	25	paths	path	NOUN
ejpam-3904	152	1	[	[	X
ejpam-3904	152	2	x2	x2	X
ejpam-3904	152	3	,	,	PUNCT
ejpam-3904	152	4	x3	x3	ADJ
ejpam-3904	152	5	,	,	PUNCT
ejpam-3904	152	6	x4	x4	PROPN
ejpam-3904	152	7	,	,	PUNCT
ejpam-3904	152	8	x	x	X
ejpam-3904	152	9	4	4	NUM
ejpam-3904	152	10	]	]	PUNCT
ejpam-3904	152	11	,	,	PUNCT
ejpam-3904	152	12	[	[	X
ejpam-3904	152	13	x4	x4	X
ejpam-3904	152	14	+	+	PROPN
ejpam-3904	152	15	3j	3j	NOUN
ejpam-3904	152	16	,	,	PUNCT
ejpam-3904	152	17	x5	x5	PROPN
ejpam-3904	152	18	+	+	PROPN
ejpam-3904	152	19	3j	3j	NOUN
ejpam-3904	152	20	,	,	PUNCT
ejpam-3904	152	21	x6	x6	PROPN
ejpam-3904	152	22	+	+	PROPN
ejpam-3904	152	23	3j	3j	NOUN
ejpam-3904	152	24	,	,	PUNCT
ejpam-3904	152	25	x7	x7	NOUN
ejpam-3904	152	26	+	+	NOUN
ejpam-3904	152	27	3j	3j	NOUN
ejpam-3904	152	28	,	,	PUNCT
ejpam-3904	152	29	x	x	X
ejpam-3904	152	30	7	7	NUM
ejpam-3904	152	31	+	+	NOUN
ejpam-3904	152	32	3j	3j	NOUN
ejpam-3904	152	33	]	]	X
ejpam-3904	152	34	,	,	PUNCT
ejpam-3904	152	35	j	j	PROPN
ejpam-3904	152	36	=	=	SYM
ejpam-3904	152	37	0	0	NUM
ejpam-3904	152	38	,	,	PUNCT
ejpam-3904	152	39	1	1	NUM
ejpam-3904	152	40	,	,	PUNCT
ejpam-3904	152	41	2	2	NUM
ejpam-3904	152	42	,	,	PUNCT
ejpam-3904	152	43	...	...	PUNCT
ejpam-3904	152	44	,	,	PUNCT
ejpam-3904	152	45	a	a	DET
ejpam-3904	152	46	−	−	PROPN
ejpam-3904	152	47	5	5	NUM
ejpam-3904	152	48	,	,	PUNCT
ejpam-3904	152	49	and	and	CCONJ
ejpam-3904	152	50	[	[	X
ejpam-3904	152	51	xa+2k−2	xa+2k−2	PROPN
ejpam-3904	152	52	,	,	PUNCT
ejpam-3904	152	53	xa+2k−1	xa+2k−1	PROPN
ejpam-3904	152	54	,	,	PUNCT
ejpam-3904	152	55	xa+2k	xa+2k	PROPN
ejpam-3904	152	56	,	,	PUNCT
ejpam-3904	152	57	xa+2k+1	xa+2k+1	PROPN
ejpam-3904	152	58	,	,	PUNCT
ejpam-3904	152	59	xa+2k+2	xa+2k+2	PROPN
ejpam-3904	152	60	,	,	PUNCT
ejpam-3904	152	61	xa+2k+3	xa+2k+3	PROPN
ejpam-3904	152	62	]	]	PUNCT
ejpam-3904	152	63	.	.	PUNCT
ejpam-3904	153	1	thend	thend	VERB
ejpam-3904	153	2	=	=	SYM
ejpam-3904	153	3	{	{	PUNCT
ejpam-3904	153	4	x2}∪{x4	x2}∪{x4	PROPN
ejpam-3904	153	5	+	+	PROPN
ejpam-3904	153	6	3j	3j	NOUN
ejpam-3904	153	7	|j	|j	NOUN
ejpam-3904	153	8	=	=	SYM
ejpam-3904	154	1	0	0	NUM
ejpam-3904	154	2	,	,	PUNCT
ejpam-3904	154	3	1	1	NUM
ejpam-3904	154	4	,	,	PUNCT
ejpam-3904	154	5	2	2	NUM
ejpam-3904	154	6	,	,	PUNCT
ejpam-3904	154	7	...	...	PUNCT
ejpam-3904	154	8	,	,	PUNCT
ejpam-3904	154	9	a	a	DET
ejpam-3904	154	10	−	−	NOUN
ejpam-3904	154	11	4	4	NUM
ejpam-3904	154	12	}	}	PUNCT
ejpam-3904	154	13	∪	∪	ADJ
ejpam-3904	154	14	{	{	PUNCT
ejpam-3904	154	15	xa+2k+1	xa+2k+1	PROPN
ejpam-3904	154	16	,	,	PUNCT
ejpam-3904	154	17	xa+2k+2	xa+2k+2	PRON
ejpam-3904	154	18	}	}	PUNCT
ejpam-3904	154	19	is	be	AUX
ejpam-3904	154	20	a	a	DET
ejpam-3904	154	21	γit	γit	ADV
ejpam-3904	154	22	-	-	PUNCT
ejpam-3904	154	23	set	set	NOUN
ejpam-3904	154	24	of	of	ADP
ejpam-3904	154	25	g.	g.	PROPN
ejpam-3904	154	26	on	on	ADP
ejpam-3904	154	27	the	the	DET
ejpam-3904	154	28	other	other	ADJ
ejpam-3904	154	29	hand	hand	NOUN
ejpam-3904	154	30	,	,	PUNCT
ejpam-3904	154	31	d	d	X
ejpam-3904	154	32	∪	∪	X
ejpam-3904	154	33	{	{	PUNCT
ejpam-3904	154	34	x3	x3	ADJ
ejpam-3904	154	35	}	}	PUNCT
ejpam-3904	154	36	∪	∪	X
ejpam-3904	154	37	{	{	PUNCT
ejpam-3904	154	38	x4	x4	PROPN
ejpam-3904	154	39	+	+	PROPN
ejpam-3904	154	40	3j	3j	NOUN
ejpam-3904	154	41	|j	|j	NOUN
ejpam-3904	155	1	=	=	SYM
ejpam-3904	155	2	0	0	NUM
ejpam-3904	155	3	,	,	PUNCT
ejpam-3904	155	4	1	1	NUM
ejpam-3904	155	5	,	,	PUNCT
ejpam-3904	155	6	2	2	NUM
ejpam-3904	155	7	,	,	PUNCT
ejpam-3904	155	8	...	...	PUNCT
ejpam-3904	155	9	,	,	PUNCT
ejpam-3904	155	10	a	a	DET
ejpam-3904	155	11	−	−	NOUN
ejpam-3904	155	12	4	4	NUM
ejpam-3904	155	13	}	}	PUNCT
ejpam-3904	155	14	is	be	AUX
ejpam-3904	155	15	a	a	DET
ejpam-3904	155	16	γitt	γitt	VERB
ejpam-3904	155	17	-	-	PUNCT
ejpam-3904	155	18	set	set	NOUN
ejpam-3904	155	19	of	of	ADP
ejpam-3904	155	20	g.	g.	PROPN
ejpam-3904	155	21	thus	thus	ADV
ejpam-3904	155	22	,	,	PUNCT
ejpam-3904	155	23	γit(g	γit(g	PROPN
ejpam-3904	155	24	)	)	PUNCT
ejpam-3904	155	25	=	=	SYM
ejpam-3904	156	1	1	1	NUM
ejpam-3904	156	2	+	+	CCONJ
ejpam-3904	156	3	a	a	DET
ejpam-3904	156	4	−	−	NOUN
ejpam-3904	156	5	3	3	NUM
ejpam-3904	156	6	+	+	SYM
ejpam-3904	156	7	2	2	NUM
ejpam-3904	156	8	=	=	SYM
ejpam-3904	156	9	a	a	NOUN
ejpam-3904	156	10	,	,	PUNCT
ejpam-3904	156	11	and	and	CCONJ
ejpam-3904	156	12	γitt(g	γitt(g	NOUN
ejpam-3904	156	13	)	)	PUNCT
ejpam-3904	156	14	=	=	SYM
ejpam-3904	156	15	a+	a+	PUNCT
ejpam-3904	156	16	(	(	PUNCT
ejpam-3904	156	17	a−	a−	PROPN
ejpam-3904	156	18	3	3	NUM
ejpam-3904	156	19	)	)	PUNCT
ejpam-3904	156	20	=	=	PRON
ejpam-3904	156	21	a+	a+	PUNCT
ejpam-3904	156	22	k.	k.	PROPN
ejpam-3904	157	1	now	now	ADV
ejpam-3904	157	2	,	,	PUNCT
ejpam-3904	157	3	for	for	ADP
ejpam-3904	157	4	k	k	PROPN
ejpam-3904	157	5	=	=	PUNCT
ejpam-3904	157	6	a	a	DET
ejpam-3904	157	7	−	−	PROPN
ejpam-3904	157	8	2	2	NUM
ejpam-3904	157	9	,	,	PUNCT
ejpam-3904	157	10	consider	consider	VERB
ejpam-3904	157	11	the	the	DET
ejpam-3904	157	12	graph	graph	NOUN
ejpam-3904	157	13	g	g	NOUN
ejpam-3904	157	14	as	as	ADP
ejpam-3904	157	15	in	in	ADP
ejpam-3904	157	16	figure	figure	NOUN
ejpam-3904	157	17	7	7	NUM
ejpam-3904	157	18	obtained	obtain	VERB
ejpam-3904	157	19	by	by	ADP
ejpam-3904	157	20	adding	add	VERB
ejpam-3904	157	21	(	(	PUNCT
ejpam-3904	157	22	a	a	DET
ejpam-3904	157	23	−	−	PROPN
ejpam-3904	157	24	2	2	NUM
ejpam-3904	157	25	)	)	PUNCT
ejpam-3904	157	26	p5	p5	ADJ
ejpam-3904	157	27	paths	path	NOUN
ejpam-3904	157	28	[	[	X
ejpam-3904	157	29	x2	x2	X
ejpam-3904	157	30	+	+	NOUN
ejpam-3904	157	31	3j	3j	NOUN
ejpam-3904	157	32	,	,	PUNCT
ejpam-3904	157	33	x3	x3	ADJ
ejpam-3904	157	34	+	+	NOUN
ejpam-3904	157	35	3j	3j	NOUN
ejpam-3904	157	36	,	,	PUNCT
ejpam-3904	158	1	x4	x4	PROPN
ejpam-3904	158	2	+	+	PROPN
ejpam-3904	158	3	3j	3j	NOUN
ejpam-3904	158	4	,	,	PUNCT
ejpam-3904	158	5	x5	x5	PROPN
ejpam-3904	158	6	+	+	PROPN
ejpam-3904	158	7	3j	3j	NOUN
ejpam-3904	158	8	,	,	PUNCT
ejpam-3904	158	9	x	x	X
ejpam-3904	158	10	5	5	NUM
ejpam-3904	158	11	+	+	NOUN
ejpam-3904	158	12	3j	3j	NOUN
ejpam-3904	158	13	]	]	X
ejpam-3904	158	14	,	,	PUNCT
ejpam-3904	158	15	j	j	PROPN
ejpam-3904	158	16	=	=	SYM
ejpam-3904	158	17	0	0	PROPN
ejpam-3904	158	18	,	,	PUNCT
ejpam-3904	158	19	1	1	NUM
ejpam-3904	158	20	,	,	PUNCT
ejpam-3904	158	21	.	.	PUNCT
ejpam-3904	158	22	.	.	PUNCT
ejpam-3904	159	1	.	.	PUNCT
ejpam-3904	160	1	,	,	PUNCT
ejpam-3904	160	2	a	a	DET
ejpam-3904	160	3	−	−	NOUN
ejpam-3904	160	4	3	3	NUM
ejpam-3904	160	5	,	,	PUNCT
ejpam-3904	160	6	to	to	ADP
ejpam-3904	160	7	the	the	DET
ejpam-3904	160	8	path	path	NOUN
ejpam-3904	160	9	g(2	g(2	PROPN
ejpam-3904	160	10	)	)	PUNCT
ejpam-3904	160	11	.	.	PUNCT
ejpam-3904	161	1	then	then	ADV
ejpam-3904	161	2	d	d	X
ejpam-3904	161	3	=	=	PUNCT
ejpam-3904	161	4	{	{	PUNCT
ejpam-3904	161	5	x3a−4	x3a−4	PROPN
ejpam-3904	161	6	,	,	PUNCT
ejpam-3904	161	7	x3a−4	x3a−4	PROPN
ejpam-3904	161	8	,	,	PUNCT
ejpam-3904	161	9	x2	x2	PROPN
ejpam-3904	161	10	+	+	PROPN
ejpam-3904	161	11	3j	3j	NUM
ejpam-3904	161	12	:	:	PUNCT
ejpam-3904	161	13	j	j	PROPN
ejpam-3904	161	14	∈	∈	PROPN
ejpam-3904	161	15	{	{	PUNCT
ejpam-3904	161	16	0	0	NUM
ejpam-3904	161	17	,	,	PUNCT
ejpam-3904	161	18	1	1	NUM
ejpam-3904	161	19	,	,	PUNCT
ejpam-3904	161	20	2	2	NUM
ejpam-3904	161	21	,	,	PUNCT
ejpam-3904	161	22	.	.	PUNCT
ejpam-3904	161	23	.	.	PUNCT
ejpam-3904	161	24	.	.	PUNCT
ejpam-3904	162	1	,	,	PUNCT
ejpam-3904	162	2	a	a	DET
ejpam-3904	162	3	−	−	NOUN
ejpam-3904	162	4	3	3	NUM
ejpam-3904	162	5	}	}	PUNCT
ejpam-3904	162	6	}	}	PUNCT
ejpam-3904	162	7	is	be	AUX
ejpam-3904	162	8	a	a	DET
ejpam-3904	162	9	γit	γit	ADV
ejpam-3904	162	10	-	-	PUNCT
ejpam-3904	162	11	set	set	NOUN
ejpam-3904	162	12	of	of	ADP
ejpam-3904	162	13	g	g	NOUN
ejpam-3904	162	14	,	,	PUNCT
ejpam-3904	162	15	and	and	CCONJ
ejpam-3904	162	16	d	d	X
ejpam-3904	162	17	∪	∪	X
ejpam-3904	162	18	{	{	PUNCT
ejpam-3904	162	19	x2	x2	PROPN
ejpam-3904	162	20	+	+	NOUN
ejpam-3904	162	21	3j	3j	NUM
ejpam-3904	162	22	:	:	PUNCT
ejpam-3904	162	23	j	j	PROPN
ejpam-3904	162	24	∈	∈	PROPN
ejpam-3904	162	25	{	{	PUNCT
ejpam-3904	162	26	0	0	NUM
ejpam-3904	162	27	,	,	PUNCT
ejpam-3904	162	28	1	1	NUM
ejpam-3904	162	29	,	,	PUNCT
ejpam-3904	162	30	2	2	NUM
ejpam-3904	162	31	,	,	PUNCT
ejpam-3904	162	32	.	.	PUNCT
ejpam-3904	162	33	.	.	PUNCT
ejpam-3904	163	1	.	.	PUNCT
ejpam-3904	164	1	,	,	PUNCT
ejpam-3904	164	2	a	a	DET
ejpam-3904	164	3	−	−	NOUN
ejpam-3904	164	4	3	3	NUM
ejpam-3904	164	5	}	}	PUNCT
ejpam-3904	164	6	}	}	PUNCT
ejpam-3904	164	7	forms	form	VERB
ejpam-3904	164	8	a	a	DET
ejpam-3904	164	9	γitt	γitt	VERB
ejpam-3904	164	10	-	-	PUNCT
ejpam-3904	164	11	set	set	NOUN
ejpam-3904	164	12	of	of	ADP
ejpam-3904	164	13	g.	g.	PROPN
ejpam-3904	164	14	therefore	therefore	ADV
ejpam-3904	164	15	,	,	PUNCT
ejpam-3904	164	16	γit(g	γit(g	PROPN
ejpam-3904	164	17	)	)	PUNCT
ejpam-3904	164	18	=	=	SYM
ejpam-3904	165	1	2	2	NUM
ejpam-3904	165	2	+	+	CCONJ
ejpam-3904	165	3	(	(	PUNCT
ejpam-3904	165	4	a	a	DET
ejpam-3904	165	5	−	−	PROPN
ejpam-3904	165	6	2	2	NUM
ejpam-3904	165	7	)	)	PUNCT
ejpam-3904	165	8	and	and	CCONJ
ejpam-3904	165	9	γitt(g	γitt(g	NUM
ejpam-3904	165	10	)	)	PUNCT
ejpam-3904	165	11	=	=	SYM
ejpam-3904	165	12	a+	a+	PUNCT
ejpam-3904	165	13	(	(	PUNCT
ejpam-3904	165	14	a−	a−	PROPN
ejpam-3904	165	15	2	2	NUM
ejpam-3904	165	16	)	)	PUNCT
ejpam-3904	165	17	=	=	SYM
ejpam-3904	165	18	b.	b.	PROPN
ejpam-3904	165	19	d.	d.	PROPN
ejpam-3904	165	20	sevilleno	sevilleno	PROPN
ejpam-3904	165	21	,	,	PUNCT
ejpam-3904	165	22	f.	f.	PROPN
ejpam-3904	165	23	jamil	jamil	PROPN
ejpam-3904	165	24	/	/	SYM
ejpam-3904	165	25	eur	eur	PROPN
ejpam-3904	165	26	.	.	PUNCT
ejpam-3904	166	1	j.	j.	PROPN
ejpam-3904	166	2	pure	pure	PROPN
ejpam-3904	166	3	appl	appl	PROPN
ejpam-3904	166	4	.	.	PUNCT
ejpam-3904	166	5	math	math	PROPN
ejpam-3904	166	6	,	,	PUNCT
ejpam-3904	166	7	149	149	NUM
ejpam-3904	166	8	-	-	SYM
ejpam-3904	166	9	163	163	NUM
ejpam-3904	166	10	155	155	NUM
ejpam-3904	166	11	x6	x6	NOUN
ejpam-3904	166	12	x7	x7	NOUN
ejpam-3904	166	13	x7	x7	NOUN
ejpam-3904	166	14	x1	x1	NOUN
ejpam-3904	166	15	x2	x2	PROPN
ejpam-3904	166	16	x4	x4	PROPN
ejpam-3904	166	17	x5	x5	PROPN
ejpam-3904	166	18	x8	x8	PROPN
ejpam-3904	166	19	x9	x9	PROPN
ejpam-3904	166	20	x10	x10	ADP
ejpam-3904	167	1	x10	x10	NOUN
ejpam-3904	168	1	x3	x3	PROPN
ejpam-3904	168	2	x2	x2	PROPN
ejpam-3904	169	1	x4	x4	PROPN
ejpam-3904	169	2	·	·	PUNCT
ejpam-3904	169	3	·	·	PUNCT
ejpam-3904	169	4	·	·	PUNCT
ejpam-3904	170	1	xa+2k−5	xa+2k−5	X
ejpam-3904	170	2	xa+2k−5	xa+2k−5	X
ejpam-3904	171	1	xa+2k−2	xa+2k−2	PROPN
ejpam-3904	171	2	xa+2k−2	xa+2k−2	PROPN
ejpam-3904	171	3	xa+2k+1	xa+2k+1	PROPN
ejpam-3904	171	4	xa+2k+2	xa+2k+2	PUNCT
ejpam-3904	172	1	xa+2k+3	xa+2k+3	PROPN
ejpam-3904	172	2	figure	figure	VERB
ejpam-3904	172	3	6	6	NUM
ejpam-3904	172	4	:	:	PUNCT
ejpam-3904	172	5	graph	graph	VERB
ejpam-3904	172	6	g	g	NOUN
ejpam-3904	172	7	with	with	ADP
ejpam-3904	172	8	γitt(g	γitt(g	NOUN
ejpam-3904	172	9	)	)	PUNCT
ejpam-3904	172	10	=	=	SYM
ejpam-3904	172	11	γit(g	γit(g	PROPN
ejpam-3904	172	12	)	)	PUNCT
ejpam-3904	173	1	+	+	NUM
ejpam-3904	173	2	a−	a−	PROPN
ejpam-3904	173	3	3	3	NUM
ejpam-3904	173	4	x7	x7	NOUN
ejpam-3904	173	5	x8	x8	NOUN
ejpam-3904	173	6	x8	x8	PROPN
ejpam-3904	173	7	x1	x1	PROPN
ejpam-3904	174	1	x2	x2	PROPN
ejpam-3904	174	2	x3	x3	PROPN
ejpam-3904	174	3	x4	x4	PROPN
ejpam-3904	174	4	x5	x5	PROPN
ejpam-3904	174	5	x6	x6	PROPN
ejpam-3904	174	6	x9	x9	NOUN
ejpam-3904	174	7	x10	x10	ADP
ejpam-3904	174	8	x11	x11	PROPN
ejpam-3904	174	9	x11x2	x11x2	PROPN
ejpam-3904	174	10	x5	x5	PROPN
ejpam-3904	174	11	x12	x12	NUM
ejpam-3904	174	12	·	·	PUNCT
ejpam-3904	174	13	·	·	PUNCT
ejpam-3904	175	1	·	·	PUNCT
ejpam-3904	175	2	x3k−5x3k−4	x3k−5x3k−4	PROPN
ejpam-3904	175	3	x3k−4	x3k−4	PROPN
ejpam-3904	175	4	figure	figure	VERB
ejpam-3904	175	5	7	7	NUM
ejpam-3904	175	6	:	:	PUNCT
ejpam-3904	175	7	graph	graph	VERB
ejpam-3904	175	8	g	g	NOUN
ejpam-3904	175	9	with	with	ADP
ejpam-3904	175	10	γitt(g	γitt(g	NOUN
ejpam-3904	175	11	)	)	PUNCT
ejpam-3904	175	12	=	=	SYM
ejpam-3904	175	13	γit(g	γit(g	PROPN
ejpam-3904	175	14	)	)	PUNCT
ejpam-3904	176	1	+	+	SYM
ejpam-3904	176	2	a−	a−	PROPN
ejpam-3904	176	3	2	2	NUM
ejpam-3904	176	4	4	4	NUM
ejpam-3904	176	5	.	.	PUNCT
ejpam-3904	177	1	on	on	ADP
ejpam-3904	177	2	join	join	NOUN
ejpam-3904	177	3	of	of	ADP
ejpam-3904	177	4	graphs	graph	NOUN
ejpam-3904	177	5	for	for	ADP
ejpam-3904	177	6	an	an	DET
ejpam-3904	177	7	independent	independent	ADJ
ejpam-3904	177	8	subset	subset	NOUN
ejpam-3904	177	9	d	d	X
ejpam-3904	177	10	⊆	⊆	NUM
ejpam-3904	177	11	v	v	NOUN
ejpam-3904	177	12	(	(	PUNCT
ejpam-3904	177	13	g	g	PROPN
ejpam-3904	177	14	+	+	NOUN
ejpam-3904	177	15	h	h	NOUN
ejpam-3904	177	16	)	)	PUNCT
ejpam-3904	177	17	,	,	PUNCT
ejpam-3904	177	18	either	either	CCONJ
ejpam-3904	177	19	d	d	PROPN
ejpam-3904	177	20	⊆	⊆	NUM
ejpam-3904	177	21	v	v	ADP
ejpam-3904	177	22	(	(	PUNCT
ejpam-3904	177	23	g	g	NOUN
ejpam-3904	177	24	)	)	PUNCT
ejpam-3904	177	25	or	or	CCONJ
ejpam-3904	177	26	d	d	PROPN
ejpam-3904	177	27	⊆	⊆	NUM
ejpam-3904	177	28	v	v	ADP
ejpam-3904	177	29	(	(	PUNCT
ejpam-3904	177	30	h	h	NOUN
ejpam-3904	177	31	)	)	PUNCT
ejpam-3904	177	32	.	.	PUNCT
ejpam-3904	178	1	in	in	ADP
ejpam-3904	178	2	particular	particular	ADJ
ejpam-3904	178	3	,	,	PUNCT
ejpam-3904	178	4	if	if	SCONJ
ejpam-3904	178	5	β0(h	β0(h	PRON
ejpam-3904	178	6	)	)	PUNCT
ejpam-3904	178	7	<	<	X
ejpam-3904	178	8	β0(g	β0(g	NOUN
ejpam-3904	178	9	)	)	PUNCT
ejpam-3904	178	10	,	,	PUNCT
ejpam-3904	178	11	then	then	ADV
ejpam-3904	178	12	d	d	PROPN
ejpam-3904	178	13	is	be	AUX
ejpam-3904	178	14	a	a	DET
ejpam-3904	178	15	β0	β0	NOUN
ejpam-3904	178	16	-	-	PUNCT
ejpam-3904	178	17	set	set	NOUN
ejpam-3904	178	18	of	of	ADP
ejpam-3904	178	19	g+h	g+h	PROPN
ejpam-3904	178	20	if	if	SCONJ
ejpam-3904	178	21	and	and	CCONJ
ejpam-3904	178	22	only	only	ADV
ejpam-3904	178	23	if	if	SCONJ
ejpam-3904	178	24	d	d	PROPN
ejpam-3904	178	25	⊆	⊆	NUM
ejpam-3904	178	26	v	v	ADP
ejpam-3904	178	27	(	(	PUNCT
ejpam-3904	178	28	g	g	NOUN
ejpam-3904	178	29	)	)	PUNCT
ejpam-3904	178	30	and	and	CCONJ
ejpam-3904	178	31	is	be	AUX
ejpam-3904	178	32	a	a	DET
ejpam-3904	178	33	β0	β0	NOUN
ejpam-3904	178	34	-	-	PUNCT
ejpam-3904	178	35	set	set	NOUN
ejpam-3904	178	36	of	of	ADP
ejpam-3904	178	37	g.	g.	PROPN
ejpam-3904	178	38	proposition	proposition	PROPN
ejpam-3904	178	39	1	1	NUM
ejpam-3904	178	40	.	.	PUNCT
ejpam-3904	179	1	let	let	VERB
ejpam-3904	179	2	g	g	NOUN
ejpam-3904	179	3	and	and	CCONJ
ejpam-3904	179	4	h	h	NOUN
ejpam-3904	179	5	be	be	AUX
ejpam-3904	179	6	connected	connect	VERB
ejpam-3904	179	7	graphs	graph	NOUN
ejpam-3904	179	8	with	with	ADP
ejpam-3904	179	9	β0(h	β0(h	NOUN
ejpam-3904	179	10	)	)	PUNCT
ejpam-3904	179	11	<	<	X
ejpam-3904	179	12	β0(g	β0(g	NOUN
ejpam-3904	179	13	)	)	PUNCT
ejpam-3904	179	14	.	.	PUNCT
ejpam-3904	180	1	then	then	ADV
ejpam-3904	180	2	d	d	PROPN
ejpam-3904	180	3	⊆	⊆	NUM
ejpam-3904	180	4	v	v	X
ejpam-3904	180	5	(	(	PUNCT
ejpam-3904	180	6	g	g	PROPN
ejpam-3904	180	7	+	+	NOUN
ejpam-3904	180	8	h	h	NOUN
ejpam-3904	180	9	)	)	PUNCT
ejpam-3904	180	10	is	be	AUX
ejpam-3904	180	11	an	an	DET
ejpam-3904	180	12	independent	independent	ADJ
ejpam-3904	180	13	transversal	transversal	NOUN
ejpam-3904	180	14	(	(	PUNCT
ejpam-3904	180	15	total	total	ADJ
ejpam-3904	180	16	)	)	PUNCT
ejpam-3904	180	17	dominating	dominating	NOUN
ejpam-3904	180	18	set	set	NOUN
ejpam-3904	180	19	of	of	ADP
ejpam-3904	180	20	g	g	PROPN
ejpam-3904	181	1	+	+	CCONJ
ejpam-3904	181	2	h	h	NOUN
ejpam-3904	181	3	if	if	SCONJ
ejpam-3904	181	4	and	and	CCONJ
ejpam-3904	181	5	only	only	ADV
ejpam-3904	181	6	if	if	SCONJ
ejpam-3904	181	7	one	one	NUM
ejpam-3904	181	8	of	of	ADP
ejpam-3904	181	9	the	the	DET
ejpam-3904	181	10	following	follow	VERB
ejpam-3904	181	11	holds	hold	VERB
ejpam-3904	181	12	:	:	PUNCT
ejpam-3904	181	13	(	(	PUNCT
ejpam-3904	181	14	i	i	NOUN
ejpam-3904	181	15	)	)	PUNCT
ejpam-3904	182	1	d	d	PROPN
ejpam-3904	182	2	⊆	⊆	NUM
ejpam-3904	182	3	v	v	ADP
ejpam-3904	182	4	(	(	PUNCT
ejpam-3904	182	5	g	g	NOUN
ejpam-3904	182	6	)	)	PUNCT
ejpam-3904	182	7	and	and	CCONJ
ejpam-3904	182	8	d	d	PROPN
ejpam-3904	182	9	is	be	AUX
ejpam-3904	182	10	an	an	DET
ejpam-3904	182	11	independent	independent	ADJ
ejpam-3904	182	12	transversal	transversal	NOUN
ejpam-3904	182	13	(	(	PUNCT
ejpam-3904	182	14	total	total	ADJ
ejpam-3904	182	15	)	)	PUNCT
ejpam-3904	182	16	dominating	dominating	NOUN
ejpam-3904	182	17	set	set	NOUN
ejpam-3904	182	18	of	of	ADP
ejpam-3904	182	19	g	g	NOUN
ejpam-3904	182	20	;	;	PUNCT
ejpam-3904	182	21	(	(	PUNCT
ejpam-3904	182	22	ii	ii	NOUN
ejpam-3904	182	23	)	)	PUNCT
ejpam-3904	182	24	d	d	NOUN
ejpam-3904	182	25	∩	∩	ADJ
ejpam-3904	182	26	v	v	X
ejpam-3904	182	27	(	(	PUNCT
ejpam-3904	182	28	g	g	NOUN
ejpam-3904	182	29	)	)	PUNCT
ejpam-3904	182	30	is	be	AUX
ejpam-3904	182	31	an	an	DET
ejpam-3904	182	32	independent	independent	ADJ
ejpam-3904	182	33	transversal	transversal	NOUN
ejpam-3904	182	34	set	set	NOUN
ejpam-3904	182	35	of	of	ADP
ejpam-3904	182	36	g	g	PROPN
ejpam-3904	182	37	and	and	CCONJ
ejpam-3904	182	38	d	d	PROPN
ejpam-3904	182	39	∩	∩	ADJ
ejpam-3904	182	40	v	v	X
ejpam-3904	182	41	(	(	PUNCT
ejpam-3904	182	42	h	h	NOUN
ejpam-3904	182	43	)	)	PUNCT
ejpam-3904	182	44	6=	6=	ADP
ejpam-3904	182	45	∅.	∅.	PRON
ejpam-3904	182	46	proof	proof	NOUN
ejpam-3904	182	47	.	.	PUNCT
ejpam-3904	183	1	let	let	VERB
ejpam-3904	183	2	d	d	NOUN
ejpam-3904	183	3	⊆	⊆	NUM
ejpam-3904	183	4	v	v	NOUN
ejpam-3904	183	5	(	(	PUNCT
ejpam-3904	183	6	g	g	PROPN
ejpam-3904	183	7	+	+	NOUN
ejpam-3904	183	8	h	h	NOUN
ejpam-3904	183	9	)	)	PUNCT
ejpam-3904	183	10	.	.	PUNCT
ejpam-3904	184	1	assume	assume	VERB
ejpam-3904	184	2	that	that	SCONJ
ejpam-3904	184	3	d	d	NOUN
ejpam-3904	184	4	is	be	AUX
ejpam-3904	184	5	an	an	DET
ejpam-3904	184	6	independent	independent	ADJ
ejpam-3904	184	7	transversal	transversal	NOUN
ejpam-3904	184	8	(	(	PUNCT
ejpam-3904	184	9	total	total	ADJ
ejpam-3904	184	10	)	)	PUNCT
ejpam-3904	184	11	dominating	dominating	NOUN
ejpam-3904	184	12	set	set	NOUN
ejpam-3904	184	13	of	of	ADP
ejpam-3904	184	14	g	g	PROPN
ejpam-3904	184	15	+	+	CCONJ
ejpam-3904	184	16	h.	h.	NOUN
ejpam-3904	184	17	in	in	ADP
ejpam-3904	184	18	view	view	NOUN
ejpam-3904	184	19	of	of	ADP
ejpam-3904	184	20	the	the	DET
ejpam-3904	184	21	preceding	precede	VERB
ejpam-3904	184	22	remark	remark	NOUN
ejpam-3904	184	23	,	,	PUNCT
ejpam-3904	184	24	d	d	ADP
ejpam-3904	184	25	∩	∩	ADJ
ejpam-3904	184	26	v	v	X
ejpam-3904	184	27	(	(	PUNCT
ejpam-3904	184	28	g	g	NOUN
ejpam-3904	184	29	)	)	PUNCT
ejpam-3904	184	30	6=	6=	ADP
ejpam-3904	184	31	∅.	∅.	AUX
ejpam-3904	184	32	suppose	suppose	VERB
ejpam-3904	184	33	that	that	SCONJ
ejpam-3904	184	34	d	d	PROPN
ejpam-3904	184	35	⊆	⊆	NUM
ejpam-3904	184	36	v	v	ADP
ejpam-3904	184	37	(	(	PUNCT
ejpam-3904	184	38	g	g	NOUN
ejpam-3904	184	39	)	)	PUNCT
ejpam-3904	184	40	.	.	PUNCT
ejpam-3904	185	1	then	then	ADV
ejpam-3904	185	2	d	d	X
ejpam-3904	185	3	is	be	AUX
ejpam-3904	185	4	a	a	DET
ejpam-3904	185	5	(	(	PUNCT
ejpam-3904	185	6	total	total	ADJ
ejpam-3904	185	7	)	)	PUNCT
ejpam-3904	185	8	dominating	dominating	NOUN
ejpam-3904	185	9	set	set	NOUN
ejpam-3904	185	10	of	of	ADP
ejpam-3904	185	11	g.	g.	PROPN
ejpam-3904	185	12	let	let	VERB
ejpam-3904	185	13	m	m	PRON
ejpam-3904	185	14	⊆	⊆	NUM
ejpam-3904	185	15	v	v	NOUN
ejpam-3904	185	16	(	(	PUNCT
ejpam-3904	185	17	g	g	NOUN
ejpam-3904	185	18	)	)	PUNCT
ejpam-3904	185	19	be	be	AUX
ejpam-3904	185	20	a	a	DET
ejpam-3904	185	21	β0set	β0set	NOUN
ejpam-3904	185	22	of	of	ADP
ejpam-3904	185	23	g.	g.	PROPN
ejpam-3904	186	1	then	then	ADV
ejpam-3904	186	2	m	m	PROPN
ejpam-3904	186	3	is	be	AUX
ejpam-3904	186	4	a	a	DET
ejpam-3904	186	5	β0	β0	NOUN
ejpam-3904	186	6	-	-	PUNCT
ejpam-3904	186	7	set	set	NOUN
ejpam-3904	186	8	of	of	ADP
ejpam-3904	186	9	g	g	PROPN
ejpam-3904	186	10	+	+	PROPN
ejpam-3904	186	11	h.	h.	PROPN
ejpam-3904	186	12	thus	thus	ADV
ejpam-3904	186	13	,	,	PUNCT
ejpam-3904	186	14	d	d	PROPN
ejpam-3904	186	15	∩	∩	X
ejpam-3904	186	16	m	m	VERB
ejpam-3904	186	17	6=	6=	NOUN
ejpam-3904	186	18	∅.	∅.	VERB
ejpam-3904	186	19	this	this	DET
ejpam-3904	186	20	shows	show	VERB
ejpam-3904	186	21	that	that	SCONJ
ejpam-3904	186	22	d	d	NOUN
ejpam-3904	186	23	is	be	AUX
ejpam-3904	186	24	an	an	DET
ejpam-3904	186	25	independent	independent	ADJ
ejpam-3904	186	26	transversal	transversal	NOUN
ejpam-3904	186	27	(	(	PUNCT
ejpam-3904	186	28	total	total	ADJ
ejpam-3904	186	29	)	)	PUNCT
ejpam-3904	186	30	dominating	dominating	NOUN
ejpam-3904	186	31	set	set	NOUN
ejpam-3904	186	32	of	of	ADP
ejpam-3904	186	33	g.	g.	PROPN
ejpam-3904	186	34	suppose	suppose	VERB
ejpam-3904	186	35	that	that	SCONJ
ejpam-3904	186	36	d	d	PROPN
ejpam-3904	186	37	intersects	intersect	VERB
ejpam-3904	186	38	both	both	PRON
ejpam-3904	186	39	v	v	NOUN
ejpam-3904	186	40	(	(	PUNCT
ejpam-3904	186	41	g	g	NOUN
ejpam-3904	186	42	)	)	PUNCT
ejpam-3904	186	43	and	and	CCONJ
ejpam-3904	186	44	v	v	NOUN
ejpam-3904	186	45	(	(	PUNCT
ejpam-3904	186	46	h	h	NOUN
ejpam-3904	186	47	)	)	PUNCT
ejpam-3904	186	48	,	,	PUNCT
ejpam-3904	186	49	and	and	CCONJ
ejpam-3904	186	50	let	let	VERB
ejpam-3904	186	51	m	m	PRON
ejpam-3904	186	52	⊆	⊆	NUM
ejpam-3904	186	53	v	v	NOUN
ejpam-3904	186	54	(	(	PUNCT
ejpam-3904	186	55	g	g	NOUN
ejpam-3904	186	56	)	)	PUNCT
ejpam-3904	186	57	be	be	AUX
ejpam-3904	186	58	a	a	DET
ejpam-3904	186	59	β0	β0	NOUN
ejpam-3904	186	60	-	-	PUNCT
ejpam-3904	186	61	set	set	NOUN
ejpam-3904	186	62	of	of	ADP
ejpam-3904	186	63	g.	g.	PROPN
ejpam-3904	186	64	since	since	SCONJ
ejpam-3904	186	65	m	m	PROPN
ejpam-3904	186	66	is	be	AUX
ejpam-3904	186	67	a	a	DET
ejpam-3904	186	68	β0	β0	NOUN
ejpam-3904	186	69	-	-	PUNCT
ejpam-3904	186	70	set	set	NOUN
ejpam-3904	186	71	of	of	ADP
ejpam-3904	186	72	g	g	PROPN
ejpam-3904	187	1	+	+	CCONJ
ejpam-3904	187	2	h	h	NOUN
ejpam-3904	187	3	,	,	PUNCT
ejpam-3904	187	4	m	m	VERB
ejpam-3904	187	5	∩	∩	NOUN
ejpam-3904	187	6	(	(	PUNCT
ejpam-3904	187	7	d	d	PROPN
ejpam-3904	187	8	∩	∩	ADJ
ejpam-3904	187	9	v	v	X
ejpam-3904	187	10	(	(	PUNCT
ejpam-3904	187	11	g	g	NOUN
ejpam-3904	187	12	)	)	PUNCT
ejpam-3904	187	13	)	)	PUNCT
ejpam-3904	188	1	=	=	PUNCT
ejpam-3904	189	1	m	m	NOUN
ejpam-3904	189	2	∩d	∩d	NOUN
ejpam-3904	189	3	6=	6=	ADP
ejpam-3904	189	4	∅.	∅.	ADP
ejpam-3904	189	5	thus	thus	ADV
ejpam-3904	189	6	,	,	PUNCT
ejpam-3904	189	7	d	d	ADP
ejpam-3904	189	8	∩	∩	ADJ
ejpam-3904	189	9	v	v	X
ejpam-3904	189	10	(	(	PUNCT
ejpam-3904	189	11	g	g	NOUN
ejpam-3904	189	12	)	)	PUNCT
ejpam-3904	189	13	is	be	AUX
ejpam-3904	189	14	an	an	DET
ejpam-3904	189	15	independent	independent	ADJ
ejpam-3904	189	16	transversal	transversal	NOUN
ejpam-3904	189	17	set	set	NOUN
ejpam-3904	189	18	of	of	ADP
ejpam-3904	189	19	g.	g.	PROPN
ejpam-3904	189	20	conversely	conversely	ADV
ejpam-3904	189	21	,	,	PUNCT
ejpam-3904	189	22	since	since	SCONJ
ejpam-3904	189	23	(	(	PUNCT
ejpam-3904	189	24	total	total	ADJ
ejpam-3904	189	25	)	)	PUNCT
ejpam-3904	189	26	dominating	dominating	NOUN
ejpam-3904	189	27	sets	set	NOUN
ejpam-3904	189	28	of	of	ADP
ejpam-3904	189	29	g	g	PROPN
ejpam-3904	189	30	are	be	AUX
ejpam-3904	189	31	(	(	PUNCT
ejpam-3904	189	32	total	total	ADJ
ejpam-3904	189	33	)	)	PUNCT
ejpam-3904	189	34	dominating	dominating	NOUN
ejpam-3904	189	35	sets	set	NOUN
ejpam-3904	189	36	of	of	ADP
ejpam-3904	189	37	g	g	PROPN
ejpam-3904	189	38	+	+	CCONJ
ejpam-3904	189	39	h	h	NOUN
ejpam-3904	189	40	,	,	PUNCT
ejpam-3904	189	41	in	in	ADP
ejpam-3904	189	42	view	view	NOUN
ejpam-3904	189	43	of	of	ADP
ejpam-3904	189	44	the	the	DET
ejpam-3904	189	45	preceding	precede	VERB
ejpam-3904	189	46	remark	remark	NOUN
ejpam-3904	189	47	,	,	PUNCT
ejpam-3904	189	48	if	if	SCONJ
ejpam-3904	189	49	(	(	PUNCT
ejpam-3904	189	50	i	i	NOUN
ejpam-3904	189	51	)	)	PUNCT
ejpam-3904	189	52	holds	hold	VERB
ejpam-3904	189	53	for	for	ADP
ejpam-3904	189	54	d	d	PROPN
ejpam-3904	189	55	⊆	⊆	PROPN
ejpam-3904	189	56	v	v	NOUN
ejpam-3904	189	57	(	(	PUNCT
ejpam-3904	189	58	g	g	NOUN
ejpam-3904	189	59	)	)	PUNCT
ejpam-3904	189	60	,	,	PUNCT
ejpam-3904	189	61	then	then	ADV
ejpam-3904	189	62	d	d	PROPN
ejpam-3904	189	63	is	be	AUX
ejpam-3904	189	64	an	an	DET
ejpam-3904	189	65	independent	independent	ADJ
ejpam-3904	189	66	transversal	transversal	NOUN
ejpam-3904	189	67	(	(	PUNCT
ejpam-3904	189	68	total	total	ADJ
ejpam-3904	189	69	)	)	PUNCT
ejpam-3904	189	70	dominating	dominating	NOUN
ejpam-3904	189	71	set	set	NOUN
ejpam-3904	189	72	of	of	ADP
ejpam-3904	189	73	g	g	PROPN
ejpam-3904	189	74	+	+	CCONJ
ejpam-3904	189	75	h.	h.	PROPN
ejpam-3904	189	76	suppose	suppose	VERB
ejpam-3904	189	77	that	that	SCONJ
ejpam-3904	189	78	(	(	PUNCT
ejpam-3904	189	79	ii	ii	NOUN
ejpam-3904	189	80	)	)	PUNCT
ejpam-3904	189	81	holds	hold	VERB
ejpam-3904	189	82	for	for	ADP
ejpam-3904	189	83	d.	d.	PROPN
ejpam-3904	189	84	then	then	ADV
ejpam-3904	189	85	d	d	PROPN
ejpam-3904	189	86	is	be	AUX
ejpam-3904	189	87	a	a	DET
ejpam-3904	189	88	(	(	PUNCT
ejpam-3904	189	89	total	total	ADJ
ejpam-3904	189	90	)	)	PUNCT
ejpam-3904	189	91	dominating	dominating	NOUN
ejpam-3904	189	92	set	set	NOUN
ejpam-3904	189	93	of	of	ADP
ejpam-3904	189	94	g	g	PROPN
ejpam-3904	189	95	+	+	CCONJ
ejpam-3904	189	96	h.	h.	PROPN
ejpam-3904	189	97	let	let	VERB
ejpam-3904	189	98	m	m	PRON
ejpam-3904	189	99	⊆	⊆	NUM
ejpam-3904	189	100	v	v	NOUN
ejpam-3904	189	101	(	(	PUNCT
ejpam-3904	189	102	g	g	PROPN
ejpam-3904	189	103	+	+	NOUN
ejpam-3904	189	104	h	h	NOUN
ejpam-3904	189	105	)	)	PUNCT
ejpam-3904	189	106	be	be	VERB
ejpam-3904	189	107	a	a	DET
ejpam-3904	189	108	β0	β0	NOUN
ejpam-3904	189	109	-	-	PUNCT
ejpam-3904	189	110	set	set	NOUN
ejpam-3904	189	111	of	of	ADP
ejpam-3904	189	112	g	g	PROPN
ejpam-3904	189	113	+	+	CCONJ
ejpam-3904	189	114	h.	h.	PROPN
ejpam-3904	189	115	then	then	ADV
ejpam-3904	189	116	m	m	VERB
ejpam-3904	189	117	⊆	⊆	NUM
ejpam-3904	189	118	v	v	ADP
ejpam-3904	189	119	(	(	PUNCT
ejpam-3904	189	120	g	g	NOUN
ejpam-3904	189	121	)	)	PUNCT
ejpam-3904	189	122	and	and	CCONJ
ejpam-3904	189	123	is	be	AUX
ejpam-3904	189	124	a	a	DET
ejpam-3904	189	125	β0	β0	NOUN
ejpam-3904	189	126	-	-	PUNCT
ejpam-3904	189	127	set	set	NOUN
ejpam-3904	189	128	of	of	ADP
ejpam-3904	189	129	g.	g.	PROPN
ejpam-3904	189	130	thus	thus	ADV
ejpam-3904	189	131	,	,	PUNCT
ejpam-3904	189	132	d	d	X
ejpam-3904	189	133	∩m	∩m	PROPN
ejpam-3904	189	134	=	=	PUNCT
ejpam-3904	189	135	(	(	PUNCT
ejpam-3904	189	136	d	d	X
ejpam-3904	189	137	∩	∩	ADJ
ejpam-3904	189	138	v	v	X
ejpam-3904	189	139	(	(	PUNCT
ejpam-3904	189	140	g	g	NOUN
ejpam-3904	189	141	)	)	PUNCT
ejpam-3904	189	142	)	)	PUNCT
ejpam-3904	190	1	∩m	∩m	PROPN
ejpam-3904	190	2	6=	6=	ADP
ejpam-3904	190	3	∅.	∅.	ADP
ejpam-3904	190	4	this	this	DET
ejpam-3904	190	5	shows	show	VERB
ejpam-3904	190	6	that	that	SCONJ
ejpam-3904	190	7	d	d	NOUN
ejpam-3904	190	8	is	be	AUX
ejpam-3904	190	9	an	an	DET
ejpam-3904	190	10	independent	independent	ADJ
ejpam-3904	190	11	transversal	transversal	NOUN
ejpam-3904	190	12	(	(	PUNCT
ejpam-3904	190	13	total	total	ADJ
ejpam-3904	190	14	)	)	PUNCT
ejpam-3904	190	15	dominating	dominating	NOUN
ejpam-3904	190	16	of	of	ADP
ejpam-3904	190	17	g+h	g+h	PROPN
ejpam-3904	190	18	.	.	PUNCT
ejpam-3904	191	1	proposition	proposition	NOUN
ejpam-3904	191	2	2	2	NUM
ejpam-3904	191	3	.	.	PUNCT
ejpam-3904	192	1	let	let	VERB
ejpam-3904	192	2	g	g	NOUN
ejpam-3904	192	3	and	and	CCONJ
ejpam-3904	192	4	h	h	NOUN
ejpam-3904	192	5	be	be	AUX
ejpam-3904	192	6	connected	connect	VERB
ejpam-3904	192	7	graphs	graph	NOUN
ejpam-3904	192	8	with	with	ADP
ejpam-3904	192	9	β0(g	β0(g	NOUN
ejpam-3904	192	10	)	)	PUNCT
ejpam-3904	192	11	=	=	SYM
ejpam-3904	192	12	β0(h	β0(h	PROPN
ejpam-3904	192	13	)	)	PUNCT
ejpam-3904	192	14	.	.	PUNCT
ejpam-3904	193	1	then	then	ADV
ejpam-3904	193	2	d	d	PROPN
ejpam-3904	193	3	⊆	⊆	NUM
ejpam-3904	193	4	v	v	X
ejpam-3904	193	5	(	(	PUNCT
ejpam-3904	193	6	g	g	PROPN
ejpam-3904	193	7	+	+	NOUN
ejpam-3904	193	8	h	h	NOUN
ejpam-3904	193	9	)	)	PUNCT
ejpam-3904	193	10	is	be	AUX
ejpam-3904	193	11	an	an	DET
ejpam-3904	193	12	independent	independent	ADJ
ejpam-3904	193	13	transversal	transversal	NOUN
ejpam-3904	193	14	(	(	PUNCT
ejpam-3904	193	15	total	total	ADJ
ejpam-3904	193	16	)	)	PUNCT
ejpam-3904	193	17	dominating	dominating	NOUN
ejpam-3904	193	18	set	set	NOUN
ejpam-3904	193	19	of	of	ADP
ejpam-3904	193	20	g	g	PROPN
ejpam-3904	194	1	+	+	CCONJ
ejpam-3904	194	2	h	h	NOUN
ejpam-3904	194	3	if	if	SCONJ
ejpam-3904	194	4	and	and	CCONJ
ejpam-3904	194	5	only	only	ADV
ejpam-3904	194	6	if	if	SCONJ
ejpam-3904	194	7	d	d	PROPN
ejpam-3904	194	8	∩	∩	X
ejpam-3904	194	9	v	v	X
ejpam-3904	194	10	(	(	PUNCT
ejpam-3904	194	11	g	g	NOUN
ejpam-3904	194	12	)	)	PUNCT
ejpam-3904	194	13	and	and	CCONJ
ejpam-3904	194	14	d	d	PROPN
ejpam-3904	194	15	∩	∩	ADJ
ejpam-3904	194	16	v	v	X
ejpam-3904	194	17	(	(	PUNCT
ejpam-3904	194	18	h	h	NOUN
ejpam-3904	194	19	)	)	PUNCT
ejpam-3904	194	20	are	be	AUX
ejpam-3904	194	21	independent	independent	ADJ
ejpam-3904	194	22	transversal	transversal	ADJ
ejpam-3904	194	23	sets	set	NOUN
ejpam-3904	194	24	of	of	ADP
ejpam-3904	194	25	g	g	PROPN
ejpam-3904	194	26	and	and	CCONJ
ejpam-3904	194	27	h	h	NOUN
ejpam-3904	194	28	,	,	PUNCT
ejpam-3904	194	29	respectively	respectively	ADV
ejpam-3904	194	30	.	.	PUNCT
ejpam-3904	195	1	d.	d.	PROPN
ejpam-3904	195	2	sevilleno	sevilleno	PROPN
ejpam-3904	195	3	,	,	PUNCT
ejpam-3904	195	4	f.	f.	PROPN
ejpam-3904	195	5	jamil	jamil	PROPN
ejpam-3904	195	6	/	/	SYM
ejpam-3904	195	7	eur	eur	PROPN
ejpam-3904	195	8	.	.	PUNCT
ejpam-3904	196	1	j.	j.	PROPN
ejpam-3904	196	2	pure	pure	PROPN
ejpam-3904	196	3	appl	appl	PROPN
ejpam-3904	196	4	.	.	PUNCT
ejpam-3904	196	5	math	math	PROPN
ejpam-3904	196	6	,	,	PUNCT
ejpam-3904	196	7	149	149	NUM
ejpam-3904	196	8	-	-	SYM
ejpam-3904	196	9	163	163	NUM
ejpam-3904	196	10	156	156	NUM
ejpam-3904	196	11	proof	proof	NOUN
ejpam-3904	196	12	.	.	PUNCT
ejpam-3904	197	1	let	let	VERB
ejpam-3904	197	2	d	d	NOUN
ejpam-3904	197	3	⊆	⊆	NUM
ejpam-3904	197	4	v	v	NOUN
ejpam-3904	197	5	(	(	PUNCT
ejpam-3904	197	6	g+h	g+h	PROPN
ejpam-3904	197	7	)	)	PUNCT
ejpam-3904	197	8	.	.	PUNCT
ejpam-3904	198	1	suppose	suppose	VERB
ejpam-3904	198	2	that	that	SCONJ
ejpam-3904	198	3	d	d	PROPN
ejpam-3904	198	4	is	be	AUX
ejpam-3904	198	5	an	an	DET
ejpam-3904	198	6	itd	itd	NOUN
ejpam-3904	198	7	-	-	PUNCT
ejpam-3904	198	8	set	set	NOUN
ejpam-3904	198	9	of	of	ADP
ejpam-3904	198	10	g+h	g+h	PROPN
ejpam-3904	198	11	.	.	PUNCT
ejpam-3904	199	1	we	we	PRON
ejpam-3904	199	2	claim	claim	VERB
ejpam-3904	199	3	that	that	SCONJ
ejpam-3904	199	4	d	d	NOUN
ejpam-3904	199	5	intersects	intersect	VERB
ejpam-3904	199	6	both	both	PRON
ejpam-3904	199	7	v	v	NOUN
ejpam-3904	199	8	(	(	PUNCT
ejpam-3904	199	9	g	g	NOUN
ejpam-3904	199	10	)	)	PUNCT
ejpam-3904	199	11	and	and	CCONJ
ejpam-3904	199	12	v	v	NOUN
ejpam-3904	199	13	(	(	PUNCT
ejpam-3904	199	14	h	h	NOUN
ejpam-3904	199	15	)	)	PUNCT
ejpam-3904	199	16	so	so	SCONJ
ejpam-3904	199	17	that	that	SCONJ
ejpam-3904	199	18	d	d	NOUN
ejpam-3904	199	19	is	be	AUX
ejpam-3904	199	20	in	in	ADP
ejpam-3904	199	21	fact	fact	NOUN
ejpam-3904	199	22	an	an	DET
ejpam-3904	199	23	ittd	ittd	NOUN
ejpam-3904	199	24	-	-	PUNCT
ejpam-3904	199	25	set	set	NOUN
ejpam-3904	199	26	of	of	ADP
ejpam-3904	199	27	g+h	g+h	PROPN
ejpam-3904	199	28	.	.	PUNCT
ejpam-3904	200	1	suppose	suppose	VERB
ejpam-3904	200	2	not	not	PART
ejpam-3904	200	3	,	,	PUNCT
ejpam-3904	200	4	say	say	VERB
ejpam-3904	200	5	d	d	PROPN
ejpam-3904	200	6	⊆	⊆	NUM
ejpam-3904	200	7	v	v	ADP
ejpam-3904	200	8	(	(	PUNCT
ejpam-3904	200	9	g	g	NOUN
ejpam-3904	200	10	)	)	PUNCT
ejpam-3904	200	11	.	.	PUNCT
ejpam-3904	201	1	pick	pick	VERB
ejpam-3904	201	2	a	a	DET
ejpam-3904	201	3	β0	β0	NOUN
ejpam-3904	201	4	-	-	PUNCT
ejpam-3904	201	5	set	set	VERB
ejpam-3904	201	6	m	m	PROPN
ejpam-3904	201	7	⊆	⊆	NUM
ejpam-3904	201	8	v	v	NOUN
ejpam-3904	201	9	(	(	PUNCT
ejpam-3904	201	10	h	h	NOUN
ejpam-3904	201	11	)	)	PUNCT
ejpam-3904	201	12	of	of	ADP
ejpam-3904	201	13	h.	h.	PROPN
ejpam-3904	201	14	since	since	SCONJ
ejpam-3904	201	15	m	m	PROPN
ejpam-3904	201	16	is	be	AUX
ejpam-3904	201	17	a	a	DET
ejpam-3904	201	18	β0	β0	NOUN
ejpam-3904	201	19	-	-	PUNCT
ejpam-3904	201	20	set	set	NOUN
ejpam-3904	201	21	of	of	ADP
ejpam-3904	201	22	g+h	g+h	PROPN
ejpam-3904	201	23	,	,	PUNCT
ejpam-3904	201	24	d∩m	d∩m	PROPN
ejpam-3904	201	25	6=	6=	PUNCT
ejpam-3904	201	26	∅	∅	NOUN
ejpam-3904	201	27	,	,	PUNCT
ejpam-3904	201	28	which	which	PRON
ejpam-3904	201	29	is	be	AUX
ejpam-3904	201	30	impossible	impossible	ADJ
ejpam-3904	201	31	.	.	PUNCT
ejpam-3904	202	1	now	now	ADV
ejpam-3904	202	2	,	,	PUNCT
ejpam-3904	202	3	for	for	ADP
ejpam-3904	202	4	all	all	DET
ejpam-3904	202	5	β0	β0	NOUN
ejpam-3904	202	6	-	-	PUNCT
ejpam-3904	202	7	sets	set	NOUN
ejpam-3904	202	8	m	m	VERB
ejpam-3904	202	9	⊆	⊆	NUM
ejpam-3904	202	10	v	v	NOUN
ejpam-3904	202	11	(	(	PUNCT
ejpam-3904	202	12	g	g	NOUN
ejpam-3904	202	13	)	)	PUNCT
ejpam-3904	202	14	of	of	ADP
ejpam-3904	202	15	g	g	PROPN
ejpam-3904	202	16	,	,	PUNCT
ejpam-3904	202	17	m	m	VERB
ejpam-3904	202	18	is	be	AUX
ejpam-3904	202	19	a	a	DET
ejpam-3904	202	20	β0	β0	NOUN
ejpam-3904	202	21	-	-	PUNCT
ejpam-3904	202	22	set	set	NOUN
ejpam-3904	202	23	of	of	ADP
ejpam-3904	202	24	g+h	g+h	NOUN
ejpam-3904	203	1	so	so	SCONJ
ejpam-3904	203	2	that	that	SCONJ
ejpam-3904	203	3	(	(	PUNCT
ejpam-3904	203	4	d	d	X
ejpam-3904	203	5	∩	∩	ADJ
ejpam-3904	203	6	v	v	NOUN
ejpam-3904	203	7	(	(	PUNCT
ejpam-3904	203	8	g))∩m	g))∩m	NOUN
ejpam-3904	203	9	=	=	SYM
ejpam-3904	203	10	d∩m	d∩m	PROPN
ejpam-3904	203	11	6=	6=	ADP
ejpam-3904	203	12	∅.	∅.	ADP
ejpam-3904	203	13	this	this	DET
ejpam-3904	203	14	means	mean	VERB
ejpam-3904	203	15	that	that	SCONJ
ejpam-3904	203	16	d∩v	d∩v	NOUN
ejpam-3904	203	17	(	(	PUNCT
ejpam-3904	203	18	g	g	NOUN
ejpam-3904	203	19	)	)	PUNCT
ejpam-3904	203	20	is	be	AUX
ejpam-3904	203	21	an	an	DET
ejpam-3904	203	22	independent	independent	ADJ
ejpam-3904	203	23	transversal	transversal	NOUN
ejpam-3904	203	24	set	set	NOUN
ejpam-3904	203	25	of	of	ADP
ejpam-3904	203	26	g.	g.	PROPN
ejpam-3904	203	27	similarly	similarly	ADV
ejpam-3904	203	28	,	,	PUNCT
ejpam-3904	203	29	d	d	PROPN
ejpam-3904	203	30	∩	∩	ADJ
ejpam-3904	203	31	v	v	X
ejpam-3904	203	32	(	(	PUNCT
ejpam-3904	203	33	h	h	NOUN
ejpam-3904	203	34	)	)	PUNCT
ejpam-3904	203	35	is	be	AUX
ejpam-3904	203	36	an	an	DET
ejpam-3904	203	37	independent	independent	ADJ
ejpam-3904	203	38	transversal	transversal	NOUN
ejpam-3904	203	39	set	set	NOUN
ejpam-3904	203	40	of	of	ADP
ejpam-3904	203	41	h.	h.	NOUN
ejpam-3904	203	42	conversely	conversely	ADV
ejpam-3904	203	43	,	,	PUNCT
ejpam-3904	203	44	suppose	suppose	VERB
ejpam-3904	203	45	that	that	SCONJ
ejpam-3904	203	46	d	d	PROPN
ejpam-3904	203	47	∩	∩	ADJ
ejpam-3904	203	48	v	v	X
ejpam-3904	203	49	(	(	PUNCT
ejpam-3904	203	50	g	g	NOUN
ejpam-3904	203	51	)	)	PUNCT
ejpam-3904	203	52	and	and	CCONJ
ejpam-3904	203	53	d	d	PROPN
ejpam-3904	203	54	∩	∩	ADJ
ejpam-3904	203	55	v	v	X
ejpam-3904	203	56	(	(	PUNCT
ejpam-3904	203	57	h	h	NOUN
ejpam-3904	203	58	)	)	PUNCT
ejpam-3904	203	59	are	be	AUX
ejpam-3904	203	60	independent	independent	ADJ
ejpam-3904	203	61	transversal	transversal	ADJ
ejpam-3904	203	62	sets	set	NOUN
ejpam-3904	203	63	of	of	ADP
ejpam-3904	203	64	g	g	PROPN
ejpam-3904	203	65	and	and	CCONJ
ejpam-3904	203	66	h	h	NOUN
ejpam-3904	203	67	,	,	PUNCT
ejpam-3904	203	68	respectively	respectively	ADV
ejpam-3904	203	69	.	.	PUNCT
ejpam-3904	204	1	then	then	ADV
ejpam-3904	204	2	d	d	PROPN
ejpam-3904	204	3	is	be	AUX
ejpam-3904	204	4	a	a	DET
ejpam-3904	204	5	total	total	ADJ
ejpam-3904	204	6	dominating	dominating	NOUN
ejpam-3904	204	7	set	set	NOUN
ejpam-3904	204	8	of	of	ADP
ejpam-3904	204	9	g+h	g+h	PROPN
ejpam-3904	204	10	.	.	PUNCT
ejpam-3904	205	1	let	let	AUX
ejpam-3904	205	2	m	m	PRON
ejpam-3904	205	3	⊆	⊆	NUM
ejpam-3904	205	4	v	v	NOUN
ejpam-3904	205	5	(	(	PUNCT
ejpam-3904	205	6	g+h	g+h	NOUN
ejpam-3904	205	7	)	)	PUNCT
ejpam-3904	205	8	be	be	AUX
ejpam-3904	205	9	a	a	DET
ejpam-3904	205	10	β0	β0	NOUN
ejpam-3904	205	11	-	-	PUNCT
ejpam-3904	205	12	set	set	NOUN
ejpam-3904	205	13	of	of	ADP
ejpam-3904	205	14	g	g	PROPN
ejpam-3904	205	15	+	+	CCONJ
ejpam-3904	205	16	h.	h.	PROPN
ejpam-3904	205	17	either	either	CCONJ
ejpam-3904	205	18	m	m	PROPN
ejpam-3904	205	19	⊆	⊆	NUM
ejpam-3904	205	20	v	v	NOUN
ejpam-3904	205	21	(	(	PUNCT
ejpam-3904	205	22	g	g	NOUN
ejpam-3904	205	23	)	)	PUNCT
ejpam-3904	205	24	and	and	CCONJ
ejpam-3904	205	25	is	be	AUX
ejpam-3904	205	26	a	a	DET
ejpam-3904	205	27	β0	β0	NOUN
ejpam-3904	205	28	-	-	PUNCT
ejpam-3904	205	29	set	set	NOUN
ejpam-3904	205	30	of	of	ADP
ejpam-3904	205	31	g	g	NOUN
ejpam-3904	205	32	or	or	CCONJ
ejpam-3904	205	33	m	m	PROPN
ejpam-3904	205	34	⊆	⊆	NUM
ejpam-3904	205	35	v	v	NOUN
ejpam-3904	205	36	(	(	PUNCT
ejpam-3904	205	37	h	h	NOUN
ejpam-3904	205	38	)	)	PUNCT
ejpam-3904	205	39	and	and	CCONJ
ejpam-3904	205	40	is	be	AUX
ejpam-3904	205	41	a	a	DET
ejpam-3904	205	42	β0	β0	NOUN
ejpam-3904	205	43	-	-	PUNCT
ejpam-3904	205	44	set	set	NOUN
ejpam-3904	205	45	of	of	ADP
ejpam-3904	205	46	h.	h.	NOUN
ejpam-3904	205	47	either	either	CCONJ
ejpam-3904	205	48	case	case	NOUN
ejpam-3904	205	49	yields	yield	VERB
ejpam-3904	205	50	d∩m	d∩m	PROPN
ejpam-3904	205	51	6=	6=	PUNCT
ejpam-3904	205	52	∅.	∅.	ADP
ejpam-3904	205	53	thus	thus	ADV
ejpam-3904	205	54	,	,	PUNCT
ejpam-3904	205	55	d	d	PRON
ejpam-3904	205	56	is	be	AUX
ejpam-3904	205	57	an	an	DET
ejpam-3904	205	58	independent	independent	ADJ
ejpam-3904	205	59	transversal	transversal	NOUN
ejpam-3904	205	60	(	(	PUNCT
ejpam-3904	205	61	total	total	ADJ
ejpam-3904	205	62	)	)	PUNCT
ejpam-3904	205	63	dominating	dominating	NOUN
ejpam-3904	205	64	set	set	NOUN
ejpam-3904	205	65	of	of	ADP
ejpam-3904	205	66	g+h	g+h	PROPN
ejpam-3904	205	67	.	.	PUNCT
ejpam-3904	206	1	corollary	corollary	ADJ
ejpam-3904	206	2	3	3	X
ejpam-3904	206	3	.	.	PUNCT
ejpam-3904	207	1	let	let	VERB
ejpam-3904	207	2	g	g	NOUN
ejpam-3904	207	3	and	and	CCONJ
ejpam-3904	207	4	h	h	NOUN
ejpam-3904	207	5	be	be	AUX
ejpam-3904	207	6	connected	connect	VERB
ejpam-3904	207	7	graphs	graph	NOUN
ejpam-3904	207	8	with	with	ADP
ejpam-3904	207	9	β0(h	β0(h	NOUN
ejpam-3904	207	10	)	)	PUNCT
ejpam-3904	207	11	≤	≤	NOUN
ejpam-3904	207	12	β0(g	β0(g	NOUN
ejpam-3904	207	13	)	)	PUNCT
ejpam-3904	207	14	.	.	PUNCT
ejpam-3904	208	1	then	then	ADV
ejpam-3904	208	2	the	the	DET
ejpam-3904	208	3	following	follow	VERB
ejpam-3904	208	4	hold	hold	NOUN
ejpam-3904	208	5	:	:	PUNCT
ejpam-3904	208	6	(	(	PUNCT
ejpam-3904	208	7	i	i	NOUN
ejpam-3904	208	8	)	)	PUNCT
ejpam-3904	208	9	if	if	SCONJ
ejpam-3904	208	10	β0(h	β0(h	PRON
ejpam-3904	208	11	)	)	PUNCT
ejpam-3904	208	12	=	=	SYM
ejpam-3904	208	13	β0(g	β0(g	NOUN
ejpam-3904	208	14	)	)	PUNCT
ejpam-3904	208	15	,	,	PUNCT
ejpam-3904	208	16	then	then	ADV
ejpam-3904	208	17	γit(g+h	γit(g+h	NUM
ejpam-3904	208	18	)	)	PUNCT
ejpam-3904	208	19	=	=	SYM
ejpam-3904	208	20	γitt(g+h	γitt(g+h	PROPN
ejpam-3904	208	21	)	)	PUNCT
ejpam-3904	208	22	=	=	SYM
ejpam-3904	208	23	β0t(g	β0t(g	PROPN
ejpam-3904	208	24	)	)	PUNCT
ejpam-3904	208	25	+	+	X
ejpam-3904	208	26	β0t(h	β0t(h	ADJ
ejpam-3904	208	27	)	)	PUNCT
ejpam-3904	208	28	.	.	PUNCT
ejpam-3904	209	1	(	(	PUNCT
ejpam-3904	209	2	ii	ii	NOUN
ejpam-3904	209	3	)	)	PUNCT
ejpam-3904	209	4	if	if	SCONJ
ejpam-3904	209	5	β0(h	β0(h	PRON
ejpam-3904	209	6	)	)	PUNCT
ejpam-3904	209	7	<	<	X
ejpam-3904	209	8	β0(g	β0(g	NOUN
ejpam-3904	209	9	)	)	PUNCT
ejpam-3904	209	10	and	and	CCONJ
ejpam-3904	209	11	β0t(g	β0t(g	PROPN
ejpam-3904	209	12	)	)	PUNCT
ejpam-3904	209	13	<	<	X
ejpam-3904	209	14	γit(g	γit(g	PROPN
ejpam-3904	209	15	)	)	PUNCT
ejpam-3904	209	16	,	,	PUNCT
ejpam-3904	209	17	then	then	ADV
ejpam-3904	209	18	γit(g+h	γit(g+h	NUM
ejpam-3904	209	19	)	)	PUNCT
ejpam-3904	209	20	=	=	SYM
ejpam-3904	209	21	γitt(g+h	γitt(g+h	PROPN
ejpam-3904	209	22	)	)	PUNCT
ejpam-3904	209	23	=	=	SYM
ejpam-3904	209	24	1	1	NUM
ejpam-3904	209	25	+	+	ADJ
ejpam-3904	209	26	β0t(g	β0t(g	NOUN
ejpam-3904	209	27	)	)	PUNCT
ejpam-3904	209	28	.	.	PUNCT
ejpam-3904	210	1	(	(	PUNCT
ejpam-3904	210	2	iii	iii	X
ejpam-3904	210	3	)	)	PUNCT
ejpam-3904	210	4	if	if	SCONJ
ejpam-3904	210	5	β0(h	β0(h	PRON
ejpam-3904	210	6	)	)	PUNCT
ejpam-3904	210	7	<	<	X
ejpam-3904	210	8	β0(g	β0(g	NOUN
ejpam-3904	210	9	)	)	PUNCT
ejpam-3904	210	10	and	and	CCONJ
ejpam-3904	210	11	β0t(g	β0t(g	PROPN
ejpam-3904	210	12	)	)	PUNCT
ejpam-3904	210	13	=	=	SYM
ejpam-3904	210	14	γit(g	γit(g	PROPN
ejpam-3904	210	15	)	)	PUNCT
ejpam-3904	210	16	=	=	SYM
ejpam-3904	211	1	γitt(g	γitt(g	NOUN
ejpam-3904	211	2	)	)	PUNCT
ejpam-3904	211	3	,	,	PUNCT
ejpam-3904	211	4	then	then	ADV
ejpam-3904	211	5	γit(g+h	γit(g+h	NUM
ejpam-3904	211	6	)	)	PUNCT
ejpam-3904	211	7	=	=	SYM
ejpam-3904	211	8	γitt(g+h	γitt(g+h	PROPN
ejpam-3904	211	9	)	)	PUNCT
ejpam-3904	211	10	=	=	SYM
ejpam-3904	212	1	γit(g	γit(g	PROPN
ejpam-3904	212	2	)	)	PUNCT
ejpam-3904	212	3	.	.	PUNCT
ejpam-3904	213	1	(	(	PUNCT
ejpam-3904	213	2	iv	iv	X
ejpam-3904	213	3	)	)	PUNCT
ejpam-3904	213	4	if	if	SCONJ
ejpam-3904	213	5	β0(h	β0(h	PRON
ejpam-3904	213	6	)	)	PUNCT
ejpam-3904	213	7	<	<	X
ejpam-3904	213	8	β0(g	β0(g	NOUN
ejpam-3904	213	9	)	)	PUNCT
ejpam-3904	213	10	and	and	CCONJ
ejpam-3904	213	11	β0t(g	β0t(g	PROPN
ejpam-3904	213	12	)	)	PUNCT
ejpam-3904	213	13	=	=	SYM
ejpam-3904	213	14	γit(g	γit(g	NOUN
ejpam-3904	213	15	)	)	PUNCT
ejpam-3904	213	16	<	<	X
ejpam-3904	214	1	γitt(g	γitt(g	NOUN
ejpam-3904	214	2	)	)	PUNCT
ejpam-3904	215	1	,	,	PUNCT
ejpam-3904	215	2	then	then	ADV
ejpam-3904	215	3	γit(g	γit(g	PROPN
ejpam-3904	215	4	+	+	CCONJ
ejpam-3904	215	5	h	h	NOUN
ejpam-3904	215	6	)	)	PUNCT
ejpam-3904	215	7	=	=	SYM
ejpam-3904	215	8	γit(g	γit(g	PROPN
ejpam-3904	215	9	)	)	PUNCT
ejpam-3904	215	10	and	and	CCONJ
ejpam-3904	215	11	γitt(g+h	γitt(g+h	PROPN
ejpam-3904	215	12	)	)	PUNCT
ejpam-3904	215	13	=	=	SYM
ejpam-3904	215	14	1	1	NUM
ejpam-3904	215	15	+	+	NUM
ejpam-3904	215	16	β0t(g	β0t(g	NOUN
ejpam-3904	215	17	)	)	PUNCT
ejpam-3904	215	18	.	.	PUNCT
ejpam-3904	216	1	proof	proof	NOUN
ejpam-3904	216	2	.	.	PUNCT
ejpam-3904	217	1	the	the	DET
ejpam-3904	217	2	case	case	NOUN
ejpam-3904	217	3	where	where	SCONJ
ejpam-3904	217	4	β0(g	β0(g	X
ejpam-3904	217	5	)	)	PUNCT
ejpam-3904	217	6	=	=	SYM
ejpam-3904	217	7	β0(h	β0(h	PROPN
ejpam-3904	217	8	)	)	PUNCT
ejpam-3904	217	9	is	be	AUX
ejpam-3904	217	10	immediate	immediate	ADJ
ejpam-3904	217	11	from	from	ADP
ejpam-3904	217	12	proposition	proposition	NOUN
ejpam-3904	217	13	2	2	NUM
ejpam-3904	217	14	.	.	PUNCT
ejpam-3904	217	15	assume	assume	VERB
ejpam-3904	217	16	that	that	SCONJ
ejpam-3904	217	17	β0(g	β0(g	VERB
ejpam-3904	217	18	)	)	PUNCT
ejpam-3904	217	19	>	>	PUNCT
ejpam-3904	217	20	β0(h	β0(h	PROPN
ejpam-3904	217	21	)	)	PUNCT
ejpam-3904	217	22	.	.	PUNCT
ejpam-3904	218	1	it	it	PRON
ejpam-3904	218	2	follows	follow	VERB
ejpam-3904	218	3	from	from	ADP
ejpam-3904	218	4	proposition	proposition	NOUN
ejpam-3904	218	5	1	1	NUM
ejpam-3904	218	6	that	that	SCONJ
ejpam-3904	218	7	γit(g+h	γit(g+h	NOUN
ejpam-3904	218	8	)	)	PUNCT
ejpam-3904	219	1	=	=	SYM
ejpam-3904	219	2	min{γit(g	min{γit(g	PROPN
ejpam-3904	219	3	)	)	PUNCT
ejpam-3904	219	4	,	,	PUNCT
ejpam-3904	219	5	1	1	NUM
ejpam-3904	219	6	+	+	CCONJ
ejpam-3904	219	7	β0t(g	β0t(g	NOUN
ejpam-3904	219	8	)	)	PUNCT
ejpam-3904	219	9	}	}	PUNCT
ejpam-3904	219	10	.	.	PUNCT
ejpam-3904	219	11	suppose	suppose	VERB
ejpam-3904	219	12	that	that	SCONJ
ejpam-3904	219	13	γit(g	γit(g	PROPN
ejpam-3904	219	14	)	)	PUNCT
ejpam-3904	219	15	>	>	PUNCT
ejpam-3904	220	1	β0t(g	β0t(g	PROPN
ejpam-3904	220	2	)	)	PUNCT
ejpam-3904	220	3	.	.	PUNCT
ejpam-3904	221	1	then	then	ADV
ejpam-3904	221	2	γit(g	γit(g	PROPN
ejpam-3904	221	3	+	+	CCONJ
ejpam-3904	221	4	h	h	NOUN
ejpam-3904	221	5	)	)	PUNCT
ejpam-3904	221	6	=	=	SYM
ejpam-3904	221	7	1	1	NUM
ejpam-3904	221	8	+	+	NUM
ejpam-3904	221	9	β0t(g	β0t(g	NOUN
ejpam-3904	221	10	)	)	PUNCT
ejpam-3904	221	11	and	and	CCONJ
ejpam-3904	221	12	any	any	DET
ejpam-3904	221	13	γit	γit	ADV
ejpam-3904	221	14	-	-	PUNCT
ejpam-3904	221	15	set	set	NOUN
ejpam-3904	221	16	of	of	ADP
ejpam-3904	221	17	g	g	PROPN
ejpam-3904	221	18	+	+	CCONJ
ejpam-3904	221	19	h	h	NOUN
ejpam-3904	221	20	is	be	AUX
ejpam-3904	221	21	a	a	DET
ejpam-3904	221	22	total	total	ADJ
ejpam-3904	221	23	dominating	dominating	NOUN
ejpam-3904	221	24	set	set	NOUN
ejpam-3904	221	25	of	of	ADP
ejpam-3904	221	26	g	g	PROPN
ejpam-3904	221	27	+	+	PROPN
ejpam-3904	221	28	h.	h.	PROPN
ejpam-3904	222	1	thus	thus	ADV
ejpam-3904	222	2	,	,	PUNCT
ejpam-3904	222	3	γitt(g	γitt(g	NOUN
ejpam-3904	222	4	+	+	CCONJ
ejpam-3904	222	5	h	h	NOUN
ejpam-3904	222	6	)	)	PUNCT
ejpam-3904	222	7	=	=	SYM
ejpam-3904	222	8	1	1	NUM
ejpam-3904	222	9	+	+	NUM
ejpam-3904	222	10	β0t(g	β0t(g	NOUN
ejpam-3904	222	11	)	)	PUNCT
ejpam-3904	222	12	.	.	PUNCT
ejpam-3904	222	13	suppose	suppose	VERB
ejpam-3904	222	14	that	that	SCONJ
ejpam-3904	222	15	γit(g	γit(g	NOUN
ejpam-3904	222	16	)	)	PUNCT
ejpam-3904	222	17	=	=	SYM
ejpam-3904	222	18	β0t(g	β0t(g	PROPN
ejpam-3904	222	19	)	)	PUNCT
ejpam-3904	222	20	.	.	PUNCT
ejpam-3904	223	1	if	if	SCONJ
ejpam-3904	223	2	γit(g	γit(g	NOUN
ejpam-3904	223	3	)	)	PUNCT
ejpam-3904	223	4	=	=	SYM
ejpam-3904	223	5	γitt(g	γitt(g	NOUN
ejpam-3904	223	6	)	)	PUNCT
ejpam-3904	223	7	,	,	PUNCT
ejpam-3904	223	8	then	then	ADV
ejpam-3904	223	9	γitt(g	γitt(g	NOUN
ejpam-3904	223	10	+	+	CCONJ
ejpam-3904	223	11	h	h	NOUN
ejpam-3904	223	12	)	)	PUNCT
ejpam-3904	223	13	=	=	PUNCT
ejpam-3904	224	1	γit(g	γit(g	PROPN
ejpam-3904	224	2	+	+	CCONJ
ejpam-3904	224	3	h	h	NOUN
ejpam-3904	224	4	)	)	PUNCT
ejpam-3904	224	5	=	=	SYM
ejpam-3904	224	6	γit(g	γit(g	PROPN
ejpam-3904	224	7	)	)	PUNCT
ejpam-3904	224	8	.	.	PUNCT
ejpam-3904	224	9	suppose	suppose	VERB
ejpam-3904	224	10	that	that	SCONJ
ejpam-3904	224	11	γit(g	γit(g	NOUN
ejpam-3904	224	12	)	)	PUNCT
ejpam-3904	224	13	<	<	X
ejpam-3904	225	1	γitt(g	γitt(g	NOUN
ejpam-3904	225	2	)	)	PUNCT
ejpam-3904	225	3	.	.	PUNCT
ejpam-3904	226	1	then	then	ADV
ejpam-3904	226	2	1	1	NUM
ejpam-3904	226	3	+	+	CCONJ
ejpam-3904	226	4	β0t(g	β0t(g	NOUN
ejpam-3904	226	5	)	)	PUNCT
ejpam-3904	226	6	≤	≤	NOUN
ejpam-3904	226	7	γitt(g	γitt(g	NOUN
ejpam-3904	226	8	)	)	PUNCT
ejpam-3904	226	9	.	.	PUNCT
ejpam-3904	227	1	in	in	ADP
ejpam-3904	227	2	view	view	NOUN
ejpam-3904	227	3	of	of	ADP
ejpam-3904	227	4	proposition	proposition	NOUN
ejpam-3904	227	5	1	1	NUM
ejpam-3904	227	6	,	,	PUNCT
ejpam-3904	227	7	γitt(g+h	γitt(g+h	PROPN
ejpam-3904	227	8	)	)	PUNCT
ejpam-3904	227	9	=	=	SYM
ejpam-3904	227	10	1	1	NUM
ejpam-3904	227	11	+	+	NUM
ejpam-3904	227	12	β0t(g	β0t(g	NOUN
ejpam-3904	227	13	)	)	PUNCT
ejpam-3904	227	14	.	.	PUNCT
ejpam-3904	227	15	example	example	NOUN
ejpam-3904	228	1	1	1	NUM
ejpam-3904	228	2	.	.	PUNCT
ejpam-3904	228	3	(	(	PUNCT
ejpam-3904	228	4	1	1	X
ejpam-3904	228	5	)	)	PUNCT
ejpam-3904	228	6	for	for	ADP
ejpam-3904	228	7	positive	positive	ADJ
ejpam-3904	228	8	integers	integer	NOUN
ejpam-3904	228	9	m	m	PRON
ejpam-3904	228	10	,	,	PUNCT
ejpam-3904	228	11	n	n	PROPN
ejpam-3904	228	12	and	and	CCONJ
ejpam-3904	228	13	p	p	NOUN
ejpam-3904	228	14	with	with	ADP
ejpam-3904	228	15	p	p	X
ejpam-3904	228	16	>	>	X
ejpam-3904	228	17	max{m	max{m	PROPN
ejpam-3904	228	18	,	,	PUNCT
ejpam-3904	228	19	n	n	CCONJ
ejpam-3904	228	20	}	}	PUNCT
ejpam-3904	228	21	,	,	PUNCT
ejpam-3904	228	22	γit(km	γit(km	NOUN
ejpam-3904	228	23	,	,	PUNCT
ejpam-3904	228	24	p	p	PROPN
ejpam-3904	228	25	+	+	PROPN
ejpam-3904	228	26	kn	kn	PROPN
ejpam-3904	228	27	,	,	PUNCT
ejpam-3904	228	28	p	p	NOUN
ejpam-3904	228	29	)	)	PUNCT
ejpam-3904	228	30	=	=	SYM
ejpam-3904	228	31	γitt(km	γitt(km	NOUN
ejpam-3904	228	32	,	,	PUNCT
ejpam-3904	228	33	p	p	PROPN
ejpam-3904	228	34	+	+	PROPN
ejpam-3904	228	35	kn	kn	PROPN
ejpam-3904	228	36	,	,	PUNCT
ejpam-3904	228	37	p	p	NOUN
ejpam-3904	228	38	)	)	PUNCT
ejpam-3904	228	39	=	=	SYM
ejpam-3904	228	40	2	2	X
ejpam-3904	228	41	.	.	PUNCT
ejpam-3904	228	42	(	(	PUNCT
ejpam-3904	228	43	2	2	NUM
ejpam-3904	228	44	)	)	PUNCT
ejpam-3904	228	45	for	for	ADP
ejpam-3904	228	46	the	the	DET
ejpam-3904	228	47	fan	fan	NOUN
ejpam-3904	228	48	fn	fn	PROPN
ejpam-3904	228	49	on	on	ADP
ejpam-3904	228	50	n+	n+	ADP
ejpam-3904	228	51	1	1	NUM
ejpam-3904	228	52	≥	≥	NOUN
ejpam-3904	228	53	3	3	NUM
ejpam-3904	228	54	vertices	vertex	NOUN
ejpam-3904	228	55	,	,	PUNCT
ejpam-3904	228	56	γit(fn	γit(fn	NOUN
ejpam-3904	228	57	)	)	PUNCT
ejpam-3904	228	58	=	=	SYM
ejpam-3904	228	59	{	{	PUNCT
ejpam-3904	228	60	2	2	NUM
ejpam-3904	228	61	,	,	PUNCT
ejpam-3904	228	62	if	if	SCONJ
ejpam-3904	228	63	n	n	NOUN
ejpam-3904	228	64	=	=	SYM
ejpam-3904	228	65	4	4	NUM
ejpam-3904	228	66	or	or	CCONJ
ejpam-3904	228	67	n	n	PROPN
ejpam-3904	228	68	is	be	AUX
ejpam-3904	228	69	odd	odd	ADJ
ejpam-3904	228	70	;	;	PUNCT
ejpam-3904	228	71	3	3	NUM
ejpam-3904	228	72	,	,	PUNCT
ejpam-3904	228	73	if	if	SCONJ
ejpam-3904	228	74	n	n	PRON
ejpam-3904	228	75	is	be	AUX
ejpam-3904	228	76	even	even	ADV
ejpam-3904	228	77	and	and	CCONJ
ejpam-3904	228	78	n	n	CCONJ
ejpam-3904	228	79	6=	6=	NUM
ejpam-3904	228	80	4	4	NUM
ejpam-3904	228	81	,	,	PUNCT
ejpam-3904	228	82	and	and	CCONJ
ejpam-3904	228	83	γitt(fn	γitt(fn	NOUN
ejpam-3904	228	84	)	)	PUNCT
ejpam-3904	228	85	=	=	PUNCT
ejpam-3904	228	86	{	{	PUNCT
ejpam-3904	228	87	2	2	NUM
ejpam-3904	228	88	,	,	PUNCT
ejpam-3904	228	89	if	if	SCONJ
ejpam-3904	228	90	n	n	PRON
ejpam-3904	228	91	is	be	AUX
ejpam-3904	228	92	odd	odd	ADJ
ejpam-3904	228	93	;	;	PUNCT
ejpam-3904	228	94	3	3	NUM
ejpam-3904	228	95	,	,	PUNCT
ejpam-3904	228	96	if	if	SCONJ
ejpam-3904	228	97	n	n	PRON
ejpam-3904	228	98	is	be	AUX
ejpam-3904	228	99	even	even	ADV
ejpam-3904	228	100	.	.	PUNCT
ejpam-3904	229	1	d.	d.	PROPN
ejpam-3904	229	2	sevilleno	sevilleno	PROPN
ejpam-3904	229	3	,	,	PUNCT
ejpam-3904	229	4	f.	f.	PROPN
ejpam-3904	229	5	jamil	jamil	PROPN
ejpam-3904	229	6	/	/	SYM
ejpam-3904	229	7	eur	eur	PROPN
ejpam-3904	229	8	.	.	PUNCT
ejpam-3904	230	1	j.	j.	PROPN
ejpam-3904	230	2	pure	pure	PROPN
ejpam-3904	230	3	appl	appl	PROPN
ejpam-3904	230	4	.	.	PUNCT
ejpam-3904	230	5	math	math	PROPN
ejpam-3904	230	6	,	,	PUNCT
ejpam-3904	230	7	149	149	NUM
ejpam-3904	230	8	-	-	SYM
ejpam-3904	230	9	163	163	NUM
ejpam-3904	230	10	157	157	NUM
ejpam-3904	230	11	(	(	PUNCT
ejpam-3904	230	12	3	3	NUM
ejpam-3904	230	13	)	)	PUNCT
ejpam-3904	230	14	for	for	ADP
ejpam-3904	230	15	the	the	DET
ejpam-3904	230	16	wheel	wheel	NOUN
ejpam-3904	230	17	wn	wn	NOUN
ejpam-3904	230	18	on	on	ADP
ejpam-3904	230	19	n+	n+	ADP
ejpam-3904	230	20	1	1	NUM
ejpam-3904	230	21	vertices	vertex	NOUN
ejpam-3904	230	22	,	,	PUNCT
ejpam-3904	230	23	γit(wn	γit(wn	NUM
ejpam-3904	230	24	)	)	PUNCT
ejpam-3904	230	25	=	=	SYM
ejpam-3904	231	1			NOUN
ejpam-3904	231	2	2	2	NUM
ejpam-3904	231	3	,	,	PUNCT
ejpam-3904	231	4	if	if	SCONJ
ejpam-3904	231	5	n	n	NOUN
ejpam-3904	231	6	=	=	SYM
ejpam-3904	231	7	4	4	NUM
ejpam-3904	231	8	;	;	PUNCT
ejpam-3904	231	9	3	3	NUM
ejpam-3904	231	10	,	,	PUNCT
ejpam-3904	231	11	if	if	SCONJ
ejpam-3904	231	12	n	n	ADV
ejpam-3904	231	13	∈	∈	PROPN
ejpam-3904	231	14	{	{	PUNCT
ejpam-3904	231	15	3	3	NUM
ejpam-3904	231	16	,	,	PUNCT
ejpam-3904	231	17	5	5	NUM
ejpam-3904	231	18	,	,	PUNCT
ejpam-3904	231	19	7	7	NUM
ejpam-3904	231	20	,	,	PUNCT
ejpam-3904	231	21	9	9	NUM
ejpam-3904	231	22	}	}	PUNCT
ejpam-3904	231	23	or	or	CCONJ
ejpam-3904	231	24	n	n	PRON
ejpam-3904	231	25	is	be	AUX
ejpam-3904	231	26	even	even	ADV
ejpam-3904	231	27	and	and	CCONJ
ejpam-3904	231	28	n	n	CCONJ
ejpam-3904	231	29	6=	6=	NUM
ejpam-3904	231	30	4	4	NUM
ejpam-3904	231	31	;	;	PUNCT
ejpam-3904	231	32	4	4	NUM
ejpam-3904	231	33	,	,	PUNCT
ejpam-3904	231	34	otherwise	otherwise	ADV
ejpam-3904	231	35	,	,	PUNCT
ejpam-3904	231	36	and	and	CCONJ
ejpam-3904	231	37	γitt(wn	γitt(wn	NOUN
ejpam-3904	231	38	)	)	PUNCT
ejpam-3904	231	39	=	=	PUNCT
ejpam-3904	232	1			NOUN
ejpam-3904	232	2	2	2	NUM
ejpam-3904	232	3	,	,	PUNCT
ejpam-3904	232	4	if	if	SCONJ
ejpam-3904	232	5	n	n	NOUN
ejpam-3904	232	6	=	=	SYM
ejpam-3904	232	7	4	4	NUM
ejpam-3904	232	8	;	;	PUNCT
ejpam-3904	232	9	3	3	NUM
ejpam-3904	232	10	,	,	PUNCT
ejpam-3904	232	11	if	if	SCONJ
ejpam-3904	232	12	n	n	ADV
ejpam-3904	232	13	∈	∈	PROPN
ejpam-3904	232	14	{	{	PUNCT
ejpam-3904	232	15	3	3	NUM
ejpam-3904	232	16	,	,	PUNCT
ejpam-3904	232	17	5	5	NUM
ejpam-3904	232	18	}	}	PUNCT
ejpam-3904	232	19	or	or	CCONJ
ejpam-3904	232	20	n	n	PRON
ejpam-3904	232	21	is	be	AUX
ejpam-3904	232	22	even	even	ADV
ejpam-3904	232	23	and	and	CCONJ
ejpam-3904	232	24	n	n	CCONJ
ejpam-3904	232	25	6=	6=	NUM
ejpam-3904	232	26	4	4	NUM
ejpam-3904	232	27	;	;	PUNCT
ejpam-3904	232	28	4	4	NUM
ejpam-3904	232	29	,	,	PUNCT
ejpam-3904	232	30	otherwise	otherwise	ADV
ejpam-3904	232	31	.	.	PUNCT
ejpam-3904	233	1	(	(	PUNCT
ejpam-3904	233	2	4	4	X
ejpam-3904	233	3	)	)	PUNCT
ejpam-3904	233	4	for	for	ADP
ejpam-3904	233	5	all	all	DET
ejpam-3904	233	6	positive	positive	ADJ
ejpam-3904	233	7	integers	integer	NOUN
ejpam-3904	233	8	n	n	PRON
ejpam-3904	233	9	≥	≥	NOUN
ejpam-3904	233	10	2	2	NUM
ejpam-3904	233	11	and	and	CCONJ
ejpam-3904	233	12	p	p	PRON
ejpam-3904	233	13	≥	≥	NUM
ejpam-3904	233	14	2	2	NUM
ejpam-3904	233	15	,	,	PUNCT
ejpam-3904	233	16	γit(kn	γit(kn	NOUN
ejpam-3904	233	17	,	,	PUNCT
ejpam-3904	233	18	n	n	X
ejpam-3904	233	19	+	+	ADJ
ejpam-3904	233	20	kp	kp	ADJ
ejpam-3904	233	21	)	)	PUNCT
ejpam-3904	233	22	=	=	SYM
ejpam-3904	233	23	γitt(kn	γitt(kn	NOUN
ejpam-3904	233	24	,	,	PUNCT
ejpam-3904	233	25	n	n	NOUN
ejpam-3904	233	26	+	+	NOUN
ejpam-3904	233	27	kp	kp	NOUN
ejpam-3904	233	28	)	)	PUNCT
ejpam-3904	233	29	=	=	SYM
ejpam-3904	233	30	2	2	NUM
ejpam-3904	233	31	.	.	NOUN
ejpam-3904	233	32	5	5	NUM
ejpam-3904	233	33	.	.	X
ejpam-3904	233	34	on	on	ADP
ejpam-3904	233	35	corona	corona	NOUN
ejpam-3904	233	36	of	of	ADP
ejpam-3904	233	37	graphs	graph	NOUN
ejpam-3904	233	38	it	it	PRON
ejpam-3904	233	39	is	be	AUX
ejpam-3904	233	40	worth	worth	ADJ
ejpam-3904	233	41	noting	note	VERB
ejpam-3904	233	42	that	that	SCONJ
ejpam-3904	233	43	g	g	PROPN
ejpam-3904	233	44	◦	◦	NOUN
ejpam-3904	233	45	h	h	NOUN
ejpam-3904	233	46	is	be	AUX
ejpam-3904	233	47	composed	compose	VERB
ejpam-3904	233	48	of	of	ADP
ejpam-3904	233	49	the	the	DET
ejpam-3904	233	50	joins	join	NOUN
ejpam-3904	233	51	hv	hv	PROPN
ejpam-3904	233	52	+	+	CCONJ
ejpam-3904	233	53	v	v	NOUN
ejpam-3904	233	54	=	=	SYM
ejpam-3904	233	55	hv	hv	PROPN
ejpam-3904	233	56	+	+	PROPN
ejpam-3904	233	57	〈	〈	PROPN
ejpam-3904	233	58	v	v	NOUN
ejpam-3904	233	59	〉	〉	NUM
ejpam-3904	233	60	,	,	PUNCT
ejpam-3904	233	61	v	v	ADP
ejpam-3904	233	62	∈	∈	PROPN
ejpam-3904	233	63	v	v	NOUN
ejpam-3904	233	64	(	(	PUNCT
ejpam-3904	233	65	g	g	NOUN
ejpam-3904	233	66	)	)	PUNCT
ejpam-3904	233	67	,	,	PUNCT
ejpam-3904	233	68	joined	join	VERB
ejpam-3904	233	69	together	together	ADV
ejpam-3904	233	70	by	by	ADP
ejpam-3904	233	71	the	the	DET
ejpam-3904	233	72	edges	edge	NOUN
ejpam-3904	233	73	of	of	ADP
ejpam-3904	233	74	g.	g.	PROPN
ejpam-3904	233	75	thus	thus	ADV
ejpam-3904	233	76	,	,	PUNCT
ejpam-3904	233	77	v	v	X
ejpam-3904	233	78	(	(	PUNCT
ejpam-3904	233	79	g	g	PROPN
ejpam-3904	233	80	◦	◦	NOUN
ejpam-3904	233	81	h	h	NOUN
ejpam-3904	233	82	)	)	PUNCT
ejpam-3904	234	1	=	=	NOUN
ejpam-3904	234	2	v	v	X
ejpam-3904	234	3	(	(	PUNCT
ejpam-3904	234	4	g	g	NOUN
ejpam-3904	234	5	)	)	PUNCT
ejpam-3904	234	6	∪	∪	NOUN
ejpam-3904	234	7	(	(	PUNCT
ejpam-3904	234	8	∪v∈v	∪v∈v	X
ejpam-3904	234	9	(	(	PUNCT
ejpam-3904	234	10	g)v	g)v	X
ejpam-3904	234	11	(	(	PUNCT
ejpam-3904	234	12	hv	hv	NOUN
ejpam-3904	234	13	)	)	PUNCT
ejpam-3904	234	14	)	)	PUNCT
ejpam-3904	235	1	=	=	PUNCT
ejpam-3904	236	1	∪v∈v	∪v∈v	X
ejpam-3904	236	2	(	(	PUNCT
ejpam-3904	236	3	g)v	g)v	X
ejpam-3904	236	4	(	(	PUNCT
ejpam-3904	236	5	hv	hv	PROPN
ejpam-3904	236	6	+	+	PROPN
ejpam-3904	236	7	v	v	NOUN
ejpam-3904	236	8	)	)	PUNCT
ejpam-3904	236	9	.	.	PUNCT
ejpam-3904	237	1	theorem	theorem	VERB
ejpam-3904	237	2	6	6	NUM
ejpam-3904	237	3	.	.	PUNCT
ejpam-3904	238	1	[	[	X
ejpam-3904	238	2	5	5	NUM
ejpam-3904	238	3	]	]	PUNCT
ejpam-3904	238	4	let	let	VERB
ejpam-3904	238	5	g	g	PRON
ejpam-3904	238	6	be	be	AUX
ejpam-3904	238	7	a	a	DET
ejpam-3904	238	8	connected	connected	ADJ
ejpam-3904	238	9	graph	graph	NOUN
ejpam-3904	238	10	and	and	CCONJ
ejpam-3904	238	11	h	h	NOUN
ejpam-3904	238	12	any	any	DET
ejpam-3904	238	13	graph	graph	NOUN
ejpam-3904	238	14	.	.	PUNCT
ejpam-3904	239	1	then	then	ADV
ejpam-3904	239	2	s	s	VERB
ejpam-3904	239	3	⊆	⊆	NUM
ejpam-3904	239	4	v	v	NOUN
ejpam-3904	239	5	(	(	PUNCT
ejpam-3904	239	6	g	g	PROPN
ejpam-3904	239	7	◦	◦	NOUN
ejpam-3904	239	8	h	h	NOUN
ejpam-3904	239	9	)	)	PUNCT
ejpam-3904	239	10	is	be	AUX
ejpam-3904	239	11	a	a	DET
ejpam-3904	239	12	dominating	dominating	NOUN
ejpam-3904	239	13	set	set	NOUN
ejpam-3904	239	14	of	of	ADP
ejpam-3904	239	15	g	g	PROPN
ejpam-3904	239	16	◦	◦	NOUN
ejpam-3904	239	17	h	h	NOUN
ejpam-3904	239	18	if	if	SCONJ
ejpam-3904	240	1	and	and	CCONJ
ejpam-3904	240	2	only	only	ADV
ejpam-3904	240	3	if	if	SCONJ
ejpam-3904	240	4	s	s	ADP
ejpam-3904	240	5	∩	∩	ADJ
ejpam-3904	240	6	v	v	X
ejpam-3904	240	7	(	(	PUNCT
ejpam-3904	240	8	hv	hv	PROPN
ejpam-3904	240	9	+	+	PROPN
ejpam-3904	240	10	v	v	NOUN
ejpam-3904	240	11	)	)	PUNCT
ejpam-3904	240	12	is	be	AUX
ejpam-3904	240	13	a	a	DET
ejpam-3904	240	14	dominating	dominating	NOUN
ejpam-3904	240	15	set	set	NOUN
ejpam-3904	240	16	of	of	ADP
ejpam-3904	240	17	hv	hv	PROPN
ejpam-3904	240	18	+	+	X
ejpam-3904	240	19	v	v	NOUN
ejpam-3904	240	20	for	for	ADP
ejpam-3904	240	21	each	each	DET
ejpam-3904	240	22	v	v	NUM
ejpam-3904	240	23	∈	∈	PROPN
ejpam-3904	240	24	v	v	NOUN
ejpam-3904	240	25	(	(	PUNCT
ejpam-3904	240	26	g	g	NOUN
ejpam-3904	240	27	)	)	PUNCT
ejpam-3904	240	28	.	.	PUNCT
ejpam-3904	241	1	observation	observation	NOUN
ejpam-3904	241	2	3	3	NUM
ejpam-3904	241	3	.	.	PUNCT
ejpam-3904	242	1	let	let	VERB
ejpam-3904	242	2	g	g	PRON
ejpam-3904	242	3	be	be	AUX
ejpam-3904	242	4	a	a	DET
ejpam-3904	242	5	nontrivial	nontrivial	ADJ
ejpam-3904	242	6	connected	connect	VERB
ejpam-3904	242	7	graph	graph	NOUN
ejpam-3904	242	8	of	of	ADP
ejpam-3904	242	9	order	order	NOUN
ejpam-3904	242	10	n	n	CCONJ
ejpam-3904	242	11	,	,	PUNCT
ejpam-3904	242	12	and	and	CCONJ
ejpam-3904	242	13	let	let	VERB
ejpam-3904	242	14	p	p	PRON
ejpam-3904	242	15	be	be	AUX
ejpam-3904	242	16	a	a	DET
ejpam-3904	242	17	positive	positive	ADJ
ejpam-3904	242	18	integer	integer	NOUN
ejpam-3904	242	19	.	.	PUNCT
ejpam-3904	243	1	then	then	ADV
ejpam-3904	243	2	γit(g	γit(g	PROPN
ejpam-3904	243	3	◦	◦	NOUN
ejpam-3904	243	4	kp	kp	NOUN
ejpam-3904	243	5	)	)	PUNCT
ejpam-3904	243	6	=	=	SYM
ejpam-3904	243	7	{	{	PUNCT
ejpam-3904	243	8	n	n	CCONJ
ejpam-3904	243	9	,	,	PUNCT
ejpam-3904	243	10	if	if	SCONJ
ejpam-3904	243	11	p	p	NOUN
ejpam-3904	243	12	=	=	NOUN
ejpam-3904	243	13	1	1	NUM
ejpam-3904	243	14	;	;	PUNCT
ejpam-3904	243	15	n+	n+	X
ejpam-3904	244	1	p	p	X
ejpam-3904	244	2	,	,	PUNCT
ejpam-3904	244	3	if	if	SCONJ
ejpam-3904	244	4	p	p	PRON
ejpam-3904	244	5	≥	≥	NOUN
ejpam-3904	244	6	2	2	NUM
ejpam-3904	244	7	,	,	PUNCT
ejpam-3904	244	8	and	and	CCONJ
ejpam-3904	244	9	γitt(g	γitt(g	NUM
ejpam-3904	244	10	◦	◦	NOUN
ejpam-3904	244	11	kp	kp	NOUN
ejpam-3904	244	12	)	)	PUNCT
ejpam-3904	244	13	=	=	PUNCT
ejpam-3904	244	14	n+	n+	PART
ejpam-3904	245	1	p.	p.	NOUN
ejpam-3904	245	2	a	a	DET
ejpam-3904	245	3	sharp	sharp	ADV
ejpam-3904	245	4	bound	bind	VERB
ejpam-3904	245	5	for	for	ADP
ejpam-3904	245	6	γit(g	γit(g	PROPN
ejpam-3904	245	7	◦	◦	NOUN
ejpam-3904	245	8	h	h	NOUN
ejpam-3904	245	9	)	)	PUNCT
ejpam-3904	245	10	is	be	AUX
ejpam-3904	245	11	provided	provide	VERB
ejpam-3904	245	12	in	in	ADP
ejpam-3904	245	13	[	[	PUNCT
ejpam-3904	245	14	20	20	NUM
ejpam-3904	245	15	]	]	PUNCT
ejpam-3904	245	16	theorem	theorem	VERB
ejpam-3904	245	17	7	7	NUM
ejpam-3904	245	18	.	.	PUNCT
ejpam-3904	246	1	[	[	X
ejpam-3904	246	2	20	20	NUM
ejpam-3904	246	3	]	]	PUNCT
ejpam-3904	246	4	let	let	VERB
ejpam-3904	246	5	g	g	PRON
ejpam-3904	246	6	be	be	AUX
ejpam-3904	246	7	a	a	DET
ejpam-3904	246	8	graph	graph	NOUN
ejpam-3904	246	9	of	of	ADP
ejpam-3904	246	10	order	order	NOUN
ejpam-3904	246	11	n	n	PRON
ejpam-3904	246	12	≥	≥	NOUN
ejpam-3904	246	13	2	2	NUM
ejpam-3904	246	14	.	.	PUNCT
ejpam-3904	247	1	then	then	ADV
ejpam-3904	247	2	for	for	ADP
ejpam-3904	247	3	any	any	DET
ejpam-3904	247	4	graph	graph	NOUN
ejpam-3904	247	5	h	h	NOUN
ejpam-3904	247	6	such	such	ADJ
ejpam-3904	247	7	that	that	SCONJ
ejpam-3904	247	8	β0(h	β0(h	PROPN
ejpam-3904	247	9	)	)	PUNCT
ejpam-3904	247	10	≥	≥	NOUN
ejpam-3904	247	11	2	2	NUM
ejpam-3904	247	12	,	,	PUNCT
ejpam-3904	247	13	n−	n−	NOUN
ejpam-3904	247	14	1	1	NUM
ejpam-3904	247	15	+	+	CCONJ
ejpam-3904	247	16	dβ(h	dβ(h	NOUN
ejpam-3904	247	17	)	)	PUNCT
ejpam-3904	247	18	≤	≤	NUM
ejpam-3904	247	19	γit(g	γit(g	PROPN
ejpam-3904	247	20	◦	◦	NOUN
ejpam-3904	247	21	h	h	NOUN
ejpam-3904	247	22	)	)	PUNCT
ejpam-3904	247	23	≤	≤	NOUN
ejpam-3904	247	24	n+	n+	NUM
ejpam-3904	247	25	dβ(h	dβ(h	NOUN
ejpam-3904	247	26	)	)	PUNCT
ejpam-3904	247	27	,	,	PUNCT
ejpam-3904	247	28	where	where	SCONJ
ejpam-3904	247	29	dβ(h	dβ(h	NOUN
ejpam-3904	247	30	)	)	PUNCT
ejpam-3904	247	31	is	be	AUX
ejpam-3904	247	32	the	the	DET
ejpam-3904	247	33	largest	large	ADJ
ejpam-3904	247	34	number	number	NOUN
ejpam-3904	247	35	of	of	ADP
ejpam-3904	247	36	pairwise	pairwise	PROPN
ejpam-3904	247	37	disjoint	disjoint	PROPN
ejpam-3904	247	38	β0	β0	NOUN
ejpam-3904	247	39	-	-	PUNCT
ejpam-3904	247	40	sets	set	NOUN
ejpam-3904	247	41	of	of	ADP
ejpam-3904	247	42	h.	h.	PROPN
ejpam-3904	247	43	moreover	moreover	ADV
ejpam-3904	247	44	,	,	PUNCT
ejpam-3904	247	45	if	if	SCONJ
ejpam-3904	247	46	there	there	PRON
ejpam-3904	247	47	is	be	VERB
ejpam-3904	247	48	a	a	DET
ejpam-3904	247	49	dβ(h)-set	dβ(h)-set	NOUN
ejpam-3904	247	50	which	which	PRON
ejpam-3904	247	51	is	be	AUX
ejpam-3904	247	52	a	a	DET
ejpam-3904	247	53	dominating	dominating	NOUN
ejpam-3904	247	54	set	set	NOUN
ejpam-3904	247	55	in	in	ADP
ejpam-3904	247	56	h	h	NOUN
ejpam-3904	247	57	,	,	PUNCT
ejpam-3904	247	58	then	then	ADV
ejpam-3904	247	59	γit(g	γit(g	PROPN
ejpam-3904	247	60	◦	◦	NOUN
ejpam-3904	247	61	h	h	NOUN
ejpam-3904	247	62	)	)	PUNCT
ejpam-3904	247	63	=	=	PUNCT
ejpam-3904	247	64	n−	n−	NOUN
ejpam-3904	247	65	1	1	NUM
ejpam-3904	247	66	+	+	CCONJ
ejpam-3904	247	67	dβ(h	dβ(h	NOUN
ejpam-3904	247	68	)	)	PUNCT
ejpam-3904	247	69	.	.	PUNCT
ejpam-3904	248	1	observe	observe	VERB
ejpam-3904	248	2	that	that	SCONJ
ejpam-3904	248	3	dβ(h	dβ(h	NOUN
ejpam-3904	248	4	)	)	PUNCT
ejpam-3904	248	5	≤	≤	NOUN
ejpam-3904	248	6	β0t(h	β0t(h	ADJ
ejpam-3904	248	7	)	)	PUNCT
ejpam-3904	248	8	for	for	ADP
ejpam-3904	248	9	any	any	DET
ejpam-3904	248	10	graph	graph	NOUN
ejpam-3904	248	11	h.	h.	NOUN
ejpam-3904	248	12	in	in	ADP
ejpam-3904	248	13	what	what	PRON
ejpam-3904	248	14	follows	follow	VERB
ejpam-3904	248	15	,	,	PUNCT
ejpam-3904	248	16	we	we	PRON
ejpam-3904	248	17	determine	determine	VERB
ejpam-3904	248	18	γit(g	γit(g	PROPN
ejpam-3904	248	19	◦	◦	NOUN
ejpam-3904	248	20	h	h	NOUN
ejpam-3904	248	21	)	)	PUNCT
ejpam-3904	248	22	in	in	ADP
ejpam-3904	248	23	terms	term	NOUN
ejpam-3904	248	24	of	of	ADP
ejpam-3904	248	25	β0t(h	β0t(h	PROPN
ejpam-3904	248	26	)	)	PUNCT
ejpam-3904	248	27	.	.	PUNCT
ejpam-3904	249	1	lemma	lemma	PROPN
ejpam-3904	249	2	1	1	X
ejpam-3904	249	3	.	.	PUNCT
ejpam-3904	250	1	let	let	VERB
ejpam-3904	250	2	g	g	PRON
ejpam-3904	250	3	be	be	AUX
ejpam-3904	250	4	a	a	DET
ejpam-3904	250	5	connected	connected	ADJ
ejpam-3904	250	6	graph	graph	NOUN
ejpam-3904	250	7	and	and	CCONJ
ejpam-3904	250	8	h	h	NOUN
ejpam-3904	250	9	a	a	DET
ejpam-3904	250	10	noncomplete	noncomplete	ADJ
ejpam-3904	250	11	graph	graph	NOUN
ejpam-3904	250	12	.	.	PUNCT
ejpam-3904	251	1	then	then	ADV
ejpam-3904	251	2	a	a	DET
ejpam-3904	251	3	subset	subset	NOUN
ejpam-3904	251	4	s	s	VERB
ejpam-3904	251	5	⊆	⊆	NUM
ejpam-3904	251	6	v	v	NOUN
ejpam-3904	251	7	(	(	PUNCT
ejpam-3904	251	8	g	g	PROPN
ejpam-3904	251	9	◦	◦	NOUN
ejpam-3904	251	10	h	h	NOUN
ejpam-3904	251	11	)	)	PUNCT
ejpam-3904	251	12	is	be	AUX
ejpam-3904	251	13	a	a	DET
ejpam-3904	251	14	β0	β0	NOUN
ejpam-3904	251	15	-	-	PUNCT
ejpam-3904	251	16	set	set	NOUN
ejpam-3904	251	17	of	of	ADP
ejpam-3904	251	18	g	g	PROPN
ejpam-3904	251	19	◦	◦	NOUN
ejpam-3904	251	20	h	h	NOUN
ejpam-3904	251	21	if	if	SCONJ
ejpam-3904	252	1	and	and	CCONJ
ejpam-3904	252	2	only	only	ADV
ejpam-3904	252	3	if	if	SCONJ
ejpam-3904	252	4	s	s	X
ejpam-3904	252	5	=	=	X
ejpam-3904	252	6	∪v∈v	∪v∈v	X
ejpam-3904	252	7	(	(	PUNCT
ejpam-3904	252	8	g)sv	g)sv	PROPN
ejpam-3904	252	9	,	,	PUNCT
ejpam-3904	252	10	where	where	SCONJ
ejpam-3904	252	11	sv	sv	PROPN
ejpam-3904	252	12	⊆	⊆	NUM
ejpam-3904	252	13	v	v	PROPN
ejpam-3904	252	14	(	(	PUNCT
ejpam-3904	252	15	hv	hv	X
ejpam-3904	252	16	)	)	PUNCT
ejpam-3904	252	17	is	be	AUX
ejpam-3904	252	18	a	a	DET
ejpam-3904	252	19	β0	β0	NOUN
ejpam-3904	252	20	-	-	PUNCT
ejpam-3904	252	21	set	set	NOUN
ejpam-3904	252	22	of	of	ADP
ejpam-3904	252	23	h	h	NOUN
ejpam-3904	252	24	v	v	NOUN
ejpam-3904	252	25	for	for	ADP
ejpam-3904	252	26	each	each	DET
ejpam-3904	252	27	v	v	NUM
ejpam-3904	252	28	∈	∈	PROPN
ejpam-3904	252	29	v	v	NOUN
ejpam-3904	252	30	(	(	PUNCT
ejpam-3904	252	31	g	g	NOUN
ejpam-3904	252	32	)	)	PUNCT
ejpam-3904	252	33	.	.	PUNCT
ejpam-3904	253	1	d.	d.	PROPN
ejpam-3904	253	2	sevilleno	sevilleno	PROPN
ejpam-3904	253	3	,	,	PUNCT
ejpam-3904	253	4	f.	f.	PROPN
ejpam-3904	253	5	jamil	jamil	PROPN
ejpam-3904	253	6	/	/	SYM
ejpam-3904	253	7	eur	eur	PROPN
ejpam-3904	253	8	.	.	PUNCT
ejpam-3904	254	1	j.	j.	PROPN
ejpam-3904	254	2	pure	pure	PROPN
ejpam-3904	254	3	appl	appl	PROPN
ejpam-3904	254	4	.	.	PUNCT
ejpam-3904	254	5	math	math	PROPN
ejpam-3904	254	6	,	,	PUNCT
ejpam-3904	254	7	149	149	NUM
ejpam-3904	254	8	-	-	SYM
ejpam-3904	254	9	163	163	NUM
ejpam-3904	254	10	158	158	NUM
ejpam-3904	254	11	proposition	proposition	NOUN
ejpam-3904	254	12	3	3	NUM
ejpam-3904	254	13	.	.	PUNCT
ejpam-3904	255	1	let	let	VERB
ejpam-3904	255	2	g	g	NOUN
ejpam-3904	255	3	and	and	CCONJ
ejpam-3904	255	4	h	h	NOUN
ejpam-3904	255	5	be	be	AUX
ejpam-3904	255	6	nontrivial	nontrivial	ADJ
ejpam-3904	255	7	connected	connect	VERB
ejpam-3904	255	8	graphs	graph	NOUN
ejpam-3904	255	9	with	with	ADP
ejpam-3904	255	10	h	h	PROPN
ejpam-3904	255	11	noncomplete	noncomplete	ADJ
ejpam-3904	255	12	.	.	PUNCT
ejpam-3904	256	1	then	then	ADV
ejpam-3904	256	2	s	s	VERB
ejpam-3904	256	3	⊆	⊆	NUM
ejpam-3904	256	4	v	v	NOUN
ejpam-3904	256	5	(	(	PUNCT
ejpam-3904	256	6	g	g	PROPN
ejpam-3904	256	7	◦	◦	NOUN
ejpam-3904	256	8	h	h	NOUN
ejpam-3904	256	9	)	)	PUNCT
ejpam-3904	256	10	is	be	AUX
ejpam-3904	256	11	an	an	DET
ejpam-3904	256	12	itd	itd	NOUN
ejpam-3904	256	13	-	-	PUNCT
ejpam-3904	256	14	set	set	NOUN
ejpam-3904	256	15	of	of	ADP
ejpam-3904	256	16	g	g	NOUN
ejpam-3904	256	17	◦	◦	NOUN
ejpam-3904	256	18	h	h	NOUN
ejpam-3904	256	19	if	if	SCONJ
ejpam-3904	257	1	and	and	CCONJ
ejpam-3904	257	2	only	only	ADV
ejpam-3904	257	3	if	if	SCONJ
ejpam-3904	257	4	s	s	X
ejpam-3904	257	5	=	=	VERB
ejpam-3904	257	6	a∪	a∪	PROPN
ejpam-3904	257	7	(	(	PUNCT
ejpam-3904	257	8	∪v∈v	∪v∈v	X
ejpam-3904	257	9	(	(	PUNCT
ejpam-3904	257	10	g)sv	g)sv	PROPN
ejpam-3904	257	11	)	)	PUNCT
ejpam-3904	257	12	,	,	PUNCT
ejpam-3904	257	13	where	where	SCONJ
ejpam-3904	257	14	a	a	DET
ejpam-3904	257	15	⊆	⊆	NUM
ejpam-3904	257	16	v	v	NOUN
ejpam-3904	257	17	(	(	PUNCT
ejpam-3904	257	18	g	g	NOUN
ejpam-3904	257	19	)	)	PUNCT
ejpam-3904	257	20	and	and	CCONJ
ejpam-3904	257	21	sv	sv	X
ejpam-3904	257	22	⊆	⊆	NUM
ejpam-3904	257	23	v	v	X
ejpam-3904	257	24	(	(	PUNCT
ejpam-3904	257	25	hv	hv	NOUN
ejpam-3904	257	26	)	)	PUNCT
ejpam-3904	257	27	for	for	ADP
ejpam-3904	257	28	all	all	PRON
ejpam-3904	257	29	v	v	ADP
ejpam-3904	257	30	∈	∈	NOUN
ejpam-3904	257	31	v	v	NOUN
ejpam-3904	257	32	(	(	PUNCT
ejpam-3904	257	33	g	g	NOUN
ejpam-3904	257	34	)	)	PUNCT
ejpam-3904	257	35	satisfying	satisfy	VERB
ejpam-3904	257	36	the	the	DET
ejpam-3904	257	37	following	following	NOUN
ejpam-3904	257	38	:	:	PUNCT
ejpam-3904	257	39	(	(	PUNCT
ejpam-3904	257	40	i	i	NOUN
ejpam-3904	257	41	)	)	PUNCT
ejpam-3904	257	42	for	for	ADP
ejpam-3904	257	43	each	each	DET
ejpam-3904	257	44	v	v	NUM
ejpam-3904	257	45	∈	∈	PROPN
ejpam-3904	257	46	v	v	NOUN
ejpam-3904	257	47	(	(	PUNCT
ejpam-3904	257	48	g	g	NOUN
ejpam-3904	257	49	)	)	PUNCT
ejpam-3904	257	50	\a	\a	ADJ
ejpam-3904	257	51	,	,	PUNCT
ejpam-3904	257	52	sv	sv	PROPN
ejpam-3904	257	53	is	be	AUX
ejpam-3904	257	54	a	a	DET
ejpam-3904	257	55	dominating	dominating	NOUN
ejpam-3904	257	56	set	set	NOUN
ejpam-3904	257	57	of	of	ADP
ejpam-3904	257	58	hv	hv	PROPN
ejpam-3904	257	59	.	.	PUNCT
ejpam-3904	257	60	(	(	PUNCT
ejpam-3904	257	61	ii	ii	NOUN
ejpam-3904	257	62	)	)	PUNCT
ejpam-3904	257	63	there	there	PRON
ejpam-3904	257	64	exists	exist	VERB
ejpam-3904	257	65	v	v	ADP
ejpam-3904	257	66	∈	∈	PROPN
ejpam-3904	257	67	v	v	NOUN
ejpam-3904	257	68	(	(	PUNCT
ejpam-3904	257	69	g	g	NOUN
ejpam-3904	257	70	)	)	PUNCT
ejpam-3904	257	71	for	for	ADP
ejpam-3904	257	72	which	which	PRON
ejpam-3904	257	73	sv	sv	PROPN
ejpam-3904	257	74	is	be	AUX
ejpam-3904	257	75	an	an	DET
ejpam-3904	257	76	independent	independent	ADJ
ejpam-3904	257	77	transversal	transversal	NOUN
ejpam-3904	257	78	set	set	NOUN
ejpam-3904	257	79	of	of	ADP
ejpam-3904	257	80	hv	hv	PROPN
ejpam-3904	257	81	.	.	PUNCT
ejpam-3904	258	1	proof	proof	NOUN
ejpam-3904	258	2	.	.	PUNCT
ejpam-3904	259	1	assume	assume	VERB
ejpam-3904	259	2	that	that	SCONJ
ejpam-3904	259	3	s	s	VERB
ejpam-3904	259	4	⊆	⊆	NUM
ejpam-3904	259	5	v	v	NOUN
ejpam-3904	259	6	(	(	PUNCT
ejpam-3904	259	7	g	g	PROPN
ejpam-3904	259	8	◦	◦	NOUN
ejpam-3904	259	9	h	h	NOUN
ejpam-3904	259	10	)	)	PUNCT
ejpam-3904	259	11	is	be	AUX
ejpam-3904	259	12	an	an	DET
ejpam-3904	259	13	itd	itd	NOUN
ejpam-3904	259	14	-	-	PUNCT
ejpam-3904	259	15	set	set	NOUN
ejpam-3904	259	16	of	of	ADP
ejpam-3904	259	17	g	g	PROPN
ejpam-3904	259	18	◦	◦	NOUN
ejpam-3904	259	19	h.	h.	NOUN
ejpam-3904	259	20	then	then	ADV
ejpam-3904	259	21	s	s	VERB
ejpam-3904	259	22	=	=	SYM
ejpam-3904	259	23	a∪	a∪	PROPN
ejpam-3904	259	24	(	(	PUNCT
ejpam-3904	259	25	∪v∈v	∪v∈v	X
ejpam-3904	259	26	(	(	PUNCT
ejpam-3904	259	27	g)sv	g)sv	PROPN
ejpam-3904	259	28	)	)	PUNCT
ejpam-3904	259	29	,	,	PUNCT
ejpam-3904	259	30	where	where	SCONJ
ejpam-3904	259	31	a	a	DET
ejpam-3904	259	32	=	=	SYM
ejpam-3904	259	33	s	s	NOUN
ejpam-3904	259	34	∩	∩	ADJ
ejpam-3904	259	35	v	v	X
ejpam-3904	259	36	(	(	PUNCT
ejpam-3904	259	37	g	g	NOUN
ejpam-3904	259	38	)	)	PUNCT
ejpam-3904	259	39	and	and	CCONJ
ejpam-3904	259	40	sv	sv	X
ejpam-3904	259	41	=	=	SYM
ejpam-3904	259	42	s	s	PROPN
ejpam-3904	259	43	∩	∩	ADJ
ejpam-3904	259	44	v	v	X
ejpam-3904	259	45	(	(	PUNCT
ejpam-3904	259	46	hv	hv	PROPN
ejpam-3904	259	47	)	)	PUNCT
ejpam-3904	259	48	for	for	ADP
ejpam-3904	259	49	all	all	PRON
ejpam-3904	259	50	v	v	ADP
ejpam-3904	259	51	∈	∈	NOUN
ejpam-3904	259	52	v	v	NOUN
ejpam-3904	259	53	(	(	PUNCT
ejpam-3904	259	54	g	g	NOUN
ejpam-3904	259	55	)	)	PUNCT
ejpam-3904	259	56	.	.	PUNCT
ejpam-3904	260	1	statement	statement	NOUN
ejpam-3904	260	2	(	(	PUNCT
ejpam-3904	260	3	i	i	NOUN
ejpam-3904	260	4	)	)	PUNCT
ejpam-3904	260	5	follows	follow	VERB
ejpam-3904	260	6	immediately	immediately	ADV
ejpam-3904	260	7	from	from	ADP
ejpam-3904	260	8	theorem	theorem	ADJ
ejpam-3904	260	9	6	6	NUM
ejpam-3904	260	10	.	.	PUNCT
ejpam-3904	260	11	to	to	PART
ejpam-3904	260	12	prove	prove	VERB
ejpam-3904	260	13	(	(	PUNCT
ejpam-3904	260	14	ii	ii	NOUN
ejpam-3904	260	15	)	)	PUNCT
ejpam-3904	260	16	,	,	PUNCT
ejpam-3904	260	17	suppose	suppose	VERB
ejpam-3904	260	18	that	that	SCONJ
ejpam-3904	260	19	for	for	ADP
ejpam-3904	260	20	each	each	DET
ejpam-3904	260	21	v	v	NUM
ejpam-3904	260	22	∈	∈	PROPN
ejpam-3904	260	23	v	v	NOUN
ejpam-3904	260	24	(	(	PUNCT
ejpam-3904	260	25	g	g	NOUN
ejpam-3904	260	26	)	)	PUNCT
ejpam-3904	260	27	there	there	PRON
ejpam-3904	260	28	exists	exist	VERB
ejpam-3904	260	29	a	a	DET
ejpam-3904	260	30	β0	β0	NOUN
ejpam-3904	260	31	-	-	PUNCT
ejpam-3904	260	32	set	set	VERB
ejpam-3904	260	33	mv	mv	PROPN
ejpam-3904	260	34	of	of	ADP
ejpam-3904	260	35	hv	hv	PROPN
ejpam-3904	260	36	for	for	ADP
ejpam-3904	260	37	which	which	PRON
ejpam-3904	260	38	sv	sv	AUX
ejpam-3904	260	39	∩mv	∩mv	VERB
ejpam-3904	260	40	=	=	PUNCT
ejpam-3904	260	41	∅.	∅.	NOUN
ejpam-3904	260	42	by	by	ADP
ejpam-3904	260	43	lemma	lemma	PROPN
ejpam-3904	260	44	1	1	NUM
ejpam-3904	260	45	,	,	PUNCT
ejpam-3904	260	46	m	m	VERB
ejpam-3904	260	47	=	=	SYM
ejpam-3904	260	48	∪v∈v	∪v∈v	X
ejpam-3904	260	49	(	(	PUNCT
ejpam-3904	260	50	g)mv	g)mv	PROPN
ejpam-3904	260	51	is	be	AUX
ejpam-3904	260	52	a	a	DET
ejpam-3904	260	53	β0	β0	NOUN
ejpam-3904	260	54	-	-	PUNCT
ejpam-3904	260	55	set	set	NOUN
ejpam-3904	260	56	of	of	ADP
ejpam-3904	260	57	g	g	PROPN
ejpam-3904	260	58	◦	◦	NOUN
ejpam-3904	260	59	h.	h.	NOUN
ejpam-3904	260	60	since	since	SCONJ
ejpam-3904	260	61	s	s	PROPN
ejpam-3904	260	62	is	be	AUX
ejpam-3904	260	63	an	an	DET
ejpam-3904	260	64	independent	independent	ADJ
ejpam-3904	260	65	transversal	transversal	NOUN
ejpam-3904	260	66	set	set	NOUN
ejpam-3904	260	67	of	of	ADP
ejpam-3904	260	68	g	g	NOUN
ejpam-3904	260	69	◦	◦	NOUN
ejpam-3904	260	70	h	h	NOUN
ejpam-3904	260	71	,	,	PUNCT
ejpam-3904	260	72	∪v∈v	∪v∈v	X
ejpam-3904	260	73	(	(	PUNCT
ejpam-3904	260	74	g	g	NOUN
ejpam-3904	260	75	)	)	PUNCT
ejpam-3904	260	76	(	(	PUNCT
ejpam-3904	260	77	sv	sv	INTJ
ejpam-3904	260	78	∩mv	∩mv	NOUN
ejpam-3904	260	79	)	)	PUNCT
ejpam-3904	260	80	=	=	SYM
ejpam-3904	260	81	s∩m	s∩m	PROPN
ejpam-3904	260	82	6=	6=	PUNCT
ejpam-3904	260	83	∅	∅	NOUN
ejpam-3904	260	84	,	,	PUNCT
ejpam-3904	260	85	which	which	PRON
ejpam-3904	260	86	is	be	AUX
ejpam-3904	260	87	impossible	impossible	ADJ
ejpam-3904	260	88	.	.	PUNCT
ejpam-3904	261	1	this	this	PRON
ejpam-3904	261	2	proves	prove	VERB
ejpam-3904	261	3	(	(	PUNCT
ejpam-3904	261	4	ii	ii	NOUN
ejpam-3904	261	5	)	)	PUNCT
ejpam-3904	261	6	.	.	PUNCT
ejpam-3904	262	1	conversely	conversely	ADV
ejpam-3904	262	2	,	,	PUNCT
ejpam-3904	262	3	assume	assume	VERB
ejpam-3904	262	4	that	that	SCONJ
ejpam-3904	262	5	(	(	PUNCT
ejpam-3904	262	6	i	i	NOUN
ejpam-3904	262	7	)	)	PUNCT
ejpam-3904	262	8	and	and	CCONJ
ejpam-3904	262	9	(	(	PUNCT
ejpam-3904	262	10	ii	ii	NOUN
ejpam-3904	262	11	)	)	PUNCT
ejpam-3904	262	12	hold	hold	VERB
ejpam-3904	262	13	for	for	ADP
ejpam-3904	262	14	s.	s.	PROPN
ejpam-3904	262	15	by	by	ADP
ejpam-3904	262	16	condition	condition	NOUN
ejpam-3904	262	17	(	(	PUNCT
ejpam-3904	262	18	i	i	NOUN
ejpam-3904	262	19	)	)	PUNCT
ejpam-3904	262	20	and	and	CCONJ
ejpam-3904	262	21	the	the	DET
ejpam-3904	262	22	fact	fact	NOUN
ejpam-3904	262	23	that	that	SCONJ
ejpam-3904	262	24	s	s	VERB
ejpam-3904	262	25	∩	∩	ADJ
ejpam-3904	262	26	v	v	X
ejpam-3904	262	27	(	(	PUNCT
ejpam-3904	262	28	hv	hv	PROPN
ejpam-3904	262	29	+	+	PROPN
ejpam-3904	262	30	v	v	NOUN
ejpam-3904	262	31	)	)	PUNCT
ejpam-3904	262	32	is	be	AUX
ejpam-3904	262	33	a	a	DET
ejpam-3904	262	34	dominating	dominating	NOUN
ejpam-3904	262	35	set	set	VERB
ejpam-3904	262	36	in	in	ADP
ejpam-3904	262	37	hv	hv	PROPN
ejpam-3904	262	38	+	+	CCONJ
ejpam-3904	262	39	v	v	ADP
ejpam-3904	262	40	whenever	whenever	SCONJ
ejpam-3904	262	41	v	v	VERB
ejpam-3904	262	42	∈	∈	PROPN
ejpam-3904	262	43	a	a	PRON
ejpam-3904	262	44	,	,	PUNCT
ejpam-3904	262	45	s	s	PART
ejpam-3904	262	46	is	be	AUX
ejpam-3904	262	47	a	a	DET
ejpam-3904	262	48	dominating	dominating	NOUN
ejpam-3904	262	49	set	set	NOUN
ejpam-3904	262	50	of	of	ADP
ejpam-3904	262	51	g	g	PROPN
ejpam-3904	262	52	◦	◦	NOUN
ejpam-3904	262	53	h.	h.	PROPN
ejpam-3904	262	54	let	let	VERB
ejpam-3904	262	55	m	m	PRON
ejpam-3904	262	56	⊆	⊆	NUM
ejpam-3904	262	57	v	v	NOUN
ejpam-3904	262	58	(	(	PUNCT
ejpam-3904	262	59	g	g	PROPN
ejpam-3904	262	60	◦	◦	NOUN
ejpam-3904	262	61	h	h	NOUN
ejpam-3904	262	62	)	)	PUNCT
ejpam-3904	262	63	be	be	VERB
ejpam-3904	262	64	a	a	DET
ejpam-3904	262	65	β0	β0	NOUN
ejpam-3904	262	66	-	-	PUNCT
ejpam-3904	262	67	set	set	NOUN
ejpam-3904	262	68	of	of	ADP
ejpam-3904	262	69	g	g	PROPN
ejpam-3904	262	70	◦	◦	NOUN
ejpam-3904	262	71	h.	h.	NOUN
ejpam-3904	262	72	by	by	ADP
ejpam-3904	262	73	(	(	PUNCT
ejpam-3904	262	74	ii	ii	NOUN
ejpam-3904	262	75	)	)	PUNCT
ejpam-3904	262	76	,	,	PUNCT
ejpam-3904	262	77	there	there	PRON
ejpam-3904	262	78	exists	exist	VERB
ejpam-3904	262	79	v	v	ADP
ejpam-3904	262	80	∈	∈	PROPN
ejpam-3904	262	81	v	v	NOUN
ejpam-3904	262	82	(	(	PUNCT
ejpam-3904	262	83	g	g	NOUN
ejpam-3904	262	84	)	)	PUNCT
ejpam-3904	262	85	for	for	ADP
ejpam-3904	262	86	which	which	PRON
ejpam-3904	262	87	sv	sv	PROPN
ejpam-3904	262	88	is	be	AUX
ejpam-3904	262	89	an	an	DET
ejpam-3904	262	90	independent	independent	ADJ
ejpam-3904	262	91	transversal	transversal	NOUN
ejpam-3904	262	92	set	set	NOUN
ejpam-3904	262	93	of	of	ADP
ejpam-3904	262	94	hv	hv	PROPN
ejpam-3904	262	95	.	.	PUNCT
ejpam-3904	263	1	since	since	SCONJ
ejpam-3904	263	2	mv	mv	PROPN
ejpam-3904	263	3	=	=	PROPN
ejpam-3904	263	4	m	m	PROPN
ejpam-3904	263	5	∩	∩	ADJ
ejpam-3904	263	6	v	v	ADJ
ejpam-3904	263	7	(	(	PUNCT
ejpam-3904	263	8	hv	hv	X
ejpam-3904	263	9	)	)	PUNCT
ejpam-3904	263	10	is	be	AUX
ejpam-3904	263	11	a	a	DET
ejpam-3904	263	12	β0	β0	NOUN
ejpam-3904	263	13	-	-	PUNCT
ejpam-3904	263	14	set	set	NOUN
ejpam-3904	263	15	of	of	ADP
ejpam-3904	263	16	hv	hv	PROPN
ejpam-3904	263	17	,	,	PUNCT
ejpam-3904	263	18	sv	sv	AUX
ejpam-3904	263	19	∩mv	∩mv	VERB
ejpam-3904	263	20	6=	6=	ADP
ejpam-3904	263	21	∅.	∅.	ADP
ejpam-3904	263	22	thus	thus	ADV
ejpam-3904	263	23	,	,	PUNCT
ejpam-3904	263	24	s	s	VERB
ejpam-3904	263	25	∩m	∩m	PROPN
ejpam-3904	263	26	6=	6=	ADP
ejpam-3904	263	27	∅.	∅.	VERB
ejpam-3904	263	28	therefore	therefore	ADV
ejpam-3904	263	29	,	,	PUNCT
ejpam-3904	263	30	s	s	PART
ejpam-3904	263	31	is	be	AUX
ejpam-3904	263	32	an	an	DET
ejpam-3904	263	33	itd	itd	NOUN
ejpam-3904	263	34	-	-	PUNCT
ejpam-3904	263	35	set	set	NOUN
ejpam-3904	263	36	of	of	ADP
ejpam-3904	263	37	g	g	PROPN
ejpam-3904	263	38	◦	◦	NOUN
ejpam-3904	263	39	h.	h.	NOUN
ejpam-3904	263	40	in	in	ADP
ejpam-3904	263	41	view	view	NOUN
ejpam-3904	263	42	of	of	ADP
ejpam-3904	263	43	proposition	proposition	NOUN
ejpam-3904	263	44	3	3	NUM
ejpam-3904	263	45	,	,	PUNCT
ejpam-3904	263	46	the	the	DET
ejpam-3904	263	47	following	follow	VERB
ejpam-3904	263	48	assertion	assertion	NOUN
ejpam-3904	263	49	is	be	AUX
ejpam-3904	263	50	clear	clear	ADJ
ejpam-3904	263	51	.	.	PUNCT
ejpam-3904	264	1	proposition	proposition	NOUN
ejpam-3904	264	2	4	4	NUM
ejpam-3904	264	3	.	.	PUNCT
ejpam-3904	265	1	let	let	VERB
ejpam-3904	265	2	g	g	NOUN
ejpam-3904	265	3	and	and	CCONJ
ejpam-3904	265	4	h	h	NOUN
ejpam-3904	265	5	be	be	AUX
ejpam-3904	265	6	nontrivial	nontrivial	ADJ
ejpam-3904	265	7	connected	connect	VERB
ejpam-3904	265	8	graphs	graph	NOUN
ejpam-3904	265	9	with	with	ADP
ejpam-3904	265	10	h	h	PROPN
ejpam-3904	265	11	noncomplete	noncomplete	ADJ
ejpam-3904	265	12	.	.	PUNCT
ejpam-3904	266	1	then	then	ADV
ejpam-3904	266	2	s	s	VERB
ejpam-3904	266	3	⊆	⊆	NUM
ejpam-3904	266	4	v	v	NOUN
ejpam-3904	266	5	(	(	PUNCT
ejpam-3904	266	6	g	g	PROPN
ejpam-3904	266	7	◦	◦	NOUN
ejpam-3904	266	8	h	h	NOUN
ejpam-3904	266	9	)	)	PUNCT
ejpam-3904	266	10	is	be	AUX
ejpam-3904	266	11	an	an	DET
ejpam-3904	266	12	independent	independent	ADJ
ejpam-3904	266	13	transversal	transversal	ADJ
ejpam-3904	266	14	total	total	NOUN
ejpam-3904	266	15	dominating	dominating	NOUN
ejpam-3904	266	16	set	set	NOUN
ejpam-3904	266	17	of	of	ADP
ejpam-3904	266	18	g	g	PROPN
ejpam-3904	266	19	◦	◦	NOUN
ejpam-3904	266	20	h	h	NOUN
ejpam-3904	267	1	if	if	SCONJ
ejpam-3904	267	2	and	and	CCONJ
ejpam-3904	267	3	only	only	ADV
ejpam-3904	267	4	if	if	SCONJ
ejpam-3904	267	5	s	s	VERB
ejpam-3904	267	6	=	=	PUNCT
ejpam-3904	267	7	a	a	DET
ejpam-3904	267	8	∪v∈v	∪v∈v	X
ejpam-3904	267	9	(	(	PUNCT
ejpam-3904	267	10	g	g	NOUN
ejpam-3904	267	11	)	)	PUNCT
ejpam-3904	267	12	sv	sv	NOUN
ejpam-3904	267	13	,	,	PUNCT
ejpam-3904	267	14	where	where	SCONJ
ejpam-3904	267	15	a	a	DET
ejpam-3904	267	16	⊆	⊆	NUM
ejpam-3904	267	17	v	v	NOUN
ejpam-3904	267	18	(	(	PUNCT
ejpam-3904	267	19	g	g	NOUN
ejpam-3904	267	20	)	)	PUNCT
ejpam-3904	267	21	and	and	CCONJ
ejpam-3904	267	22	sv	sv	X
ejpam-3904	267	23	⊆	⊆	NUM
ejpam-3904	267	24	v	v	X
ejpam-3904	267	25	(	(	PUNCT
ejpam-3904	267	26	hv	hv	NOUN
ejpam-3904	267	27	)	)	PUNCT
ejpam-3904	267	28	for	for	ADP
ejpam-3904	267	29	all	all	PRON
ejpam-3904	267	30	v	v	ADP
ejpam-3904	267	31	∈	∈	NOUN
ejpam-3904	267	32	v	v	NOUN
ejpam-3904	267	33	(	(	PUNCT
ejpam-3904	267	34	g	g	NOUN
ejpam-3904	267	35	)	)	PUNCT
ejpam-3904	267	36	satisfying	satisfy	VERB
ejpam-3904	267	37	the	the	DET
ejpam-3904	267	38	following	following	NOUN
ejpam-3904	267	39	:	:	PUNCT
ejpam-3904	267	40	(	(	PUNCT
ejpam-3904	267	41	i	i	NOUN
ejpam-3904	267	42	)	)	PUNCT
ejpam-3904	267	43	for	for	ADP
ejpam-3904	267	44	each	each	DET
ejpam-3904	267	45	v	v	NUM
ejpam-3904	267	46	∈	∈	PROPN
ejpam-3904	267	47	v	v	NOUN
ejpam-3904	267	48	(	(	PUNCT
ejpam-3904	267	49	g	g	NOUN
ejpam-3904	267	50	)	)	PUNCT
ejpam-3904	267	51	\a	\a	ADJ
ejpam-3904	267	52	,	,	PUNCT
ejpam-3904	267	53	sv	sv	PROPN
ejpam-3904	267	54	is	be	AUX
ejpam-3904	267	55	a	a	DET
ejpam-3904	267	56	total	total	ADJ
ejpam-3904	267	57	dominating	dominating	NOUN
ejpam-3904	267	58	set	set	NOUN
ejpam-3904	267	59	of	of	ADP
ejpam-3904	267	60	hv	hv	PROPN
ejpam-3904	267	61	.	.	PUNCT
ejpam-3904	268	1	(	(	PUNCT
ejpam-3904	268	2	ii	ii	NOUN
ejpam-3904	268	3	)	)	PUNCT
ejpam-3904	268	4	for	for	ADP
ejpam-3904	268	5	each	each	PRON
ejpam-3904	268	6	v	v	ADP
ejpam-3904	268	7	∈	∈	PROPN
ejpam-3904	268	8	a	a	PRON
ejpam-3904	268	9	,	,	PUNCT
ejpam-3904	268	10	sv	sv	PROPN
ejpam-3904	268	11	6=	6=	NOUN
ejpam-3904	268	12	∅	∅	NOUN
ejpam-3904	268	13	or	or	CCONJ
ejpam-3904	268	14	ng(v	ng(v	NUM
ejpam-3904	268	15	)	)	PUNCT
ejpam-3904	268	16	∩	∩	X
ejpam-3904	268	17	s	s	PART
ejpam-3904	268	18	6=	6=	NUM
ejpam-3904	268	19	∅.	∅.	X
ejpam-3904	268	20	(	(	PUNCT
ejpam-3904	268	21	iii	iii	X
ejpam-3904	268	22	)	)	PUNCT
ejpam-3904	268	23	there	there	PRON
ejpam-3904	268	24	exists	exist	VERB
ejpam-3904	268	25	v	v	ADP
ejpam-3904	268	26	∈	∈	PROPN
ejpam-3904	268	27	v	v	NOUN
ejpam-3904	268	28	(	(	PUNCT
ejpam-3904	268	29	g	g	NOUN
ejpam-3904	268	30	)	)	PUNCT
ejpam-3904	268	31	for	for	ADP
ejpam-3904	268	32	which	which	PRON
ejpam-3904	268	33	sv	sv	PROPN
ejpam-3904	268	34	is	be	AUX
ejpam-3904	268	35	an	an	DET
ejpam-3904	268	36	independent	independent	ADJ
ejpam-3904	268	37	transversal	transversal	NOUN
ejpam-3904	268	38	set	set	NOUN
ejpam-3904	268	39	of	of	ADP
ejpam-3904	268	40	hv	hv	PROPN
ejpam-3904	268	41	.	.	PROPN
ejpam-3904	269	1	corollary	corollary	ADJ
ejpam-3904	269	2	4	4	NUM
ejpam-3904	269	3	.	.	PUNCT
ejpam-3904	270	1	let	let	VERB
ejpam-3904	270	2	g	g	NOUN
ejpam-3904	270	3	and	and	CCONJ
ejpam-3904	270	4	h	h	NOUN
ejpam-3904	270	5	be	be	AUX
ejpam-3904	270	6	nontrivial	nontrivial	ADJ
ejpam-3904	270	7	connected	connected	ADJ
ejpam-3904	270	8	graphs	graph	NOUN
ejpam-3904	270	9	,	,	PUNCT
ejpam-3904	270	10	where	where	SCONJ
ejpam-3904	270	11	g	g	PROPN
ejpam-3904	270	12	is	be	AUX
ejpam-3904	270	13	of	of	ADP
ejpam-3904	270	14	order	order	NOUN
ejpam-3904	270	15	n	n	NOUN
ejpam-3904	270	16	and	and	CCONJ
ejpam-3904	270	17	h	h	PROPN
ejpam-3904	270	18	noncomplete.then	noncomplete.then	PROPN
ejpam-3904	270	19	γit(g	γit(g	PROPN
ejpam-3904	270	20	◦	◦	NOUN
ejpam-3904	270	21	h	h	NOUN
ejpam-3904	270	22	)	)	PUNCT
ejpam-3904	271	1	=	=	PUNCT
ejpam-3904	271	2	n−	n−	NOUN
ejpam-3904	271	3	1	1	NUM
ejpam-3904	271	4	+	+	CCONJ
ejpam-3904	271	5	min{γit(h	min{γit(h	PROPN
ejpam-3904	271	6	)	)	PUNCT
ejpam-3904	271	7	,	,	PUNCT
ejpam-3904	271	8	1	1	NUM
ejpam-3904	271	9	+	+	CCONJ
ejpam-3904	271	10	β0t(h	β0t(h	ADJ
ejpam-3904	271	11	)	)	PUNCT
ejpam-3904	271	12	}	}	PUNCT
ejpam-3904	271	13	,	,	PUNCT
ejpam-3904	271	14	(	(	PUNCT
ejpam-3904	271	15	1	1	X
ejpam-3904	271	16	)	)	PUNCT
ejpam-3904	271	17	and	and	CCONJ
ejpam-3904	271	18	γitt(g	γitt(g	NUM
ejpam-3904	271	19	◦	◦	NOUN
ejpam-3904	271	20	h	h	NOUN
ejpam-3904	271	21	)	)	PUNCT
ejpam-3904	272	1	=	=	PUNCT
ejpam-3904	272	2	n−	n−	NOUN
ejpam-3904	272	3	1	1	NUM
ejpam-3904	272	4	+	+	CCONJ
ejpam-3904	272	5	min{γitt(h	min{γitt(h	PROPN
ejpam-3904	272	6	)	)	PUNCT
ejpam-3904	272	7	,	,	PUNCT
ejpam-3904	272	8	1	1	NUM
ejpam-3904	272	9	+	+	CCONJ
ejpam-3904	272	10	β0t(h	β0t(h	ADJ
ejpam-3904	272	11	)	)	PUNCT
ejpam-3904	272	12	}	}	PUNCT
ejpam-3904	272	13	.	.	PUNCT
ejpam-3904	273	1	(	(	PUNCT
ejpam-3904	273	2	2	2	X
ejpam-3904	273	3	)	)	PUNCT
ejpam-3904	273	4	proof	proof	NOUN
ejpam-3904	273	5	.	.	PUNCT
ejpam-3904	274	1	let	let	VERB
ejpam-3904	274	2	v	v	NUM
ejpam-3904	274	3	∈	∈	PROPN
ejpam-3904	274	4	v	v	NOUN
ejpam-3904	274	5	(	(	PUNCT
ejpam-3904	274	6	g	g	NOUN
ejpam-3904	274	7	)	)	PUNCT
ejpam-3904	274	8	and	and	CCONJ
ejpam-3904	274	9	let	let	VERB
ejpam-3904	274	10	b1	b1	NOUN
ejpam-3904	274	11	,	,	PUNCT
ejpam-3904	274	12	b2	b2	NOUN
ejpam-3904	274	13	⊆	⊆	NUM
ejpam-3904	274	14	v	v	NOUN
ejpam-3904	274	15	(	(	PUNCT
ejpam-3904	274	16	hv	hv	NOUN
ejpam-3904	274	17	)	)	PUNCT
ejpam-3904	274	18	be	be	VERB
ejpam-3904	274	19	a	a	DET
ejpam-3904	274	20	γit	γit	ADV
ejpam-3904	274	21	-	-	PUNCT
ejpam-3904	274	22	set	set	VERB
ejpam-3904	274	23	and	and	CCONJ
ejpam-3904	274	24	a	a	DET
ejpam-3904	274	25	β0t	β0t	NOUN
ejpam-3904	274	26	-	-	PUNCT
ejpam-3904	274	27	set	set	NOUN
ejpam-3904	274	28	of	of	ADP
ejpam-3904	274	29	hv	hv	PROPN
ejpam-3904	274	30	,	,	PUNCT
ejpam-3904	274	31	respectively	respectively	ADV
ejpam-3904	274	32	.	.	PUNCT
ejpam-3904	275	1	put	put	VERB
ejpam-3904	275	2	s1	s1	NOUN
ejpam-3904	275	3	=	=	PUNCT
ejpam-3904	275	4	(	(	PUNCT
ejpam-3904	275	5	v	v	NOUN
ejpam-3904	275	6	(	(	PUNCT
ejpam-3904	275	7	g	g	NOUN
ejpam-3904	275	8	)	)	PUNCT
ejpam-3904	275	9	\	\	NOUN
ejpam-3904	275	10	{	{	PUNCT
ejpam-3904	275	11	v})∪b1	v})∪b1	NOUN
ejpam-3904	275	12	and	and	CCONJ
ejpam-3904	275	13	s2	s2	PROPN
ejpam-3904	275	14	=	=	SYM
ejpam-3904	275	15	v	v	PROPN
ejpam-3904	275	16	(	(	PUNCT
ejpam-3904	275	17	g)∪b2	g)∪b2	ADV
ejpam-3904	275	18	.	.	PUNCT
ejpam-3904	276	1	by	by	ADP
ejpam-3904	276	2	proposition	proposition	NOUN
ejpam-3904	276	3	3	3	NUM
ejpam-3904	276	4	,	,	PUNCT
ejpam-3904	276	5	both	both	PRON
ejpam-3904	276	6	s1	s1	NOUN
ejpam-3904	276	7	and	and	CCONJ
ejpam-3904	276	8	s2	s2	PROPN
ejpam-3904	276	9	are	be	AUX
ejpam-3904	276	10	itd	itd	NOUN
ejpam-3904	276	11	-	-	PUNCT
ejpam-3904	276	12	sets	set	NOUN
ejpam-3904	276	13	of	of	ADP
ejpam-3904	276	14	g	g	NOUN
ejpam-3904	276	15	◦	◦	NOUN
ejpam-3904	276	16	h.	h.	NOUN
ejpam-3904	276	17	thus	thus	ADV
ejpam-3904	276	18	,	,	PUNCT
ejpam-3904	276	19	γit(g	γit(g	PROPN
ejpam-3904	276	20	◦	◦	NOUN
ejpam-3904	276	21	h	h	NOUN
ejpam-3904	276	22	)	)	PUNCT
ejpam-3904	276	23	≤	≤	PROPN
ejpam-3904	276	24	min{|s1|	min{|s1|	PROPN
ejpam-3904	276	25	,	,	PUNCT
ejpam-3904	276	26	|s2|	|s2|	NOUN
ejpam-3904	276	27	}	}	PUNCT
ejpam-3904	276	28	=	=	SYM
ejpam-3904	276	29	n−1+min{γit(h	n−1+min{γit(h	NOUN
ejpam-3904	276	30	)	)	PUNCT
ejpam-3904	276	31	,	,	PUNCT
ejpam-3904	277	1	1	1	X
ejpam-3904	277	2	+	+	CCONJ
ejpam-3904	277	3	β0t(h	β0t(h	ADJ
ejpam-3904	277	4	)	)	PUNCT
ejpam-3904	277	5	}	}	PUNCT
ejpam-3904	277	6	.	.	PUNCT
ejpam-3904	278	1	d.	d.	PROPN
ejpam-3904	278	2	sevilleno	sevilleno	PROPN
ejpam-3904	278	3	,	,	PUNCT
ejpam-3904	278	4	f.	f.	PROPN
ejpam-3904	278	5	jamil	jamil	PROPN
ejpam-3904	278	6	/	/	SYM
ejpam-3904	278	7	eur	eur	PROPN
ejpam-3904	278	8	.	.	PUNCT
ejpam-3904	279	1	j.	j.	PROPN
ejpam-3904	279	2	pure	pure	PROPN
ejpam-3904	279	3	appl	appl	PROPN
ejpam-3904	279	4	.	.	PUNCT
ejpam-3904	279	5	math	math	PROPN
ejpam-3904	279	6	,	,	PUNCT
ejpam-3904	279	7	149	149	NUM
ejpam-3904	279	8	-	-	SYM
ejpam-3904	279	9	163	163	NUM
ejpam-3904	279	10	159	159	NUM
ejpam-3904	279	11	let	let	VERB
ejpam-3904	279	12	s	s	VERB
ejpam-3904	279	13	=	=	NOUN
ejpam-3904	279	14	a	a	DET
ejpam-3904	279	15	∪	∪	X
ejpam-3904	279	16	(	(	PUNCT
ejpam-3904	279	17	∪v∈v	∪v∈v	X
ejpam-3904	279	18	(	(	PUNCT
ejpam-3904	279	19	g)sv	g)sv	PROPN
ejpam-3904	279	20	)	)	PUNCT
ejpam-3904	279	21	⊆	⊆	NUM
ejpam-3904	279	22	v	v	NOUN
ejpam-3904	279	23	(	(	PUNCT
ejpam-3904	279	24	g	g	PROPN
ejpam-3904	279	25	◦	◦	NOUN
ejpam-3904	279	26	h	h	NOUN
ejpam-3904	279	27	)	)	PUNCT
ejpam-3904	279	28	where	where	SCONJ
ejpam-3904	279	29	a	a	DET
ejpam-3904	279	30	⊆	⊆	NUM
ejpam-3904	279	31	v	v	NOUN
ejpam-3904	279	32	(	(	PUNCT
ejpam-3904	279	33	g	g	NOUN
ejpam-3904	279	34	)	)	PUNCT
ejpam-3904	279	35	be	be	AUX
ejpam-3904	279	36	a	a	DET
ejpam-3904	279	37	γit	γit	ADV
ejpam-3904	279	38	-	-	PUNCT
ejpam-3904	279	39	set	set	NOUN
ejpam-3904	279	40	of	of	ADP
ejpam-3904	279	41	g	g	PROPN
ejpam-3904	279	42	◦	◦	PROPN
ejpam-3904	279	43	h.	h.	NOUN
ejpam-3904	279	44	by	by	ADP
ejpam-3904	279	45	proposition	proposition	NOUN
ejpam-3904	279	46	3	3	NUM
ejpam-3904	279	47	,	,	PUNCT
ejpam-3904	279	48	|sw|	|sw|	PROPN
ejpam-3904	279	49	≥	≥	NOUN
ejpam-3904	279	50	1	1	NUM
ejpam-3904	279	51	for	for	ADP
ejpam-3904	279	52	all	all	PRON
ejpam-3904	279	53	w	w	PROPN
ejpam-3904	279	54	∈	∈	PROPN
ejpam-3904	279	55	v	v	ADP
ejpam-3904	279	56	(	(	PUNCT
ejpam-3904	279	57	g	g	NOUN
ejpam-3904	279	58	)	)	PUNCT
ejpam-3904	279	59	\a	\a	VERB
ejpam-3904	280	1	and	and	CCONJ
ejpam-3904	280	2	there	there	PRON
ejpam-3904	280	3	exists	exist	VERB
ejpam-3904	280	4	v	v	ADP
ejpam-3904	280	5	∈	∈	PROPN
ejpam-3904	280	6	v	v	NOUN
ejpam-3904	280	7	(	(	PUNCT
ejpam-3904	280	8	g	g	NOUN
ejpam-3904	280	9	)	)	PUNCT
ejpam-3904	280	10	for	for	ADP
ejpam-3904	280	11	which	which	PRON
ejpam-3904	280	12	sv	sv	PROPN
ejpam-3904	280	13	is	be	AUX
ejpam-3904	280	14	an	an	DET
ejpam-3904	280	15	independent	independent	ADJ
ejpam-3904	280	16	transversal	transversal	NOUN
ejpam-3904	280	17	set	set	NOUN
ejpam-3904	280	18	of	of	ADP
ejpam-3904	280	19	hv	hv	PROPN
ejpam-3904	280	20	.	.	PUNCT
ejpam-3904	281	1	we	we	PRON
ejpam-3904	281	2	consider	consider	VERB
ejpam-3904	281	3	two	two	NUM
ejpam-3904	281	4	cases	case	NOUN
ejpam-3904	281	5	:	:	PUNCT
ejpam-3904	281	6	case	case	NOUN
ejpam-3904	281	7	1	1	NUM
ejpam-3904	281	8	:	:	PUNCT
ejpam-3904	281	9	suppose	suppose	VERB
ejpam-3904	281	10	that	that	SCONJ
ejpam-3904	281	11	v	v	X
ejpam-3904	281	12	∈	∈	PROPN
ejpam-3904	281	13	a.	a.	NOUN
ejpam-3904	281	14	then	then	ADV
ejpam-3904	281	15	γit(g	γit(g	PROPN
ejpam-3904	281	16	◦	◦	NOUN
ejpam-3904	281	17	h	h	NOUN
ejpam-3904	281	18	)	)	PUNCT
ejpam-3904	281	19	=	=	PUNCT
ejpam-3904	281	20	|s|	|s|	NOUN
ejpam-3904	281	21	=	=	PUNCT
ejpam-3904	281	22	|a|+	|a|+	NOUN
ejpam-3904	281	23	∑	∑	PUNCT
ejpam-3904	281	24	w∈v	w∈v	PROPN
ejpam-3904	281	25	(	(	PUNCT
ejpam-3904	281	26	g	g	NOUN
ejpam-3904	281	27	)	)	PUNCT
ejpam-3904	281	28	|sw|	|sw|	PROPN
ejpam-3904	281	29	≥	≥	NUM
ejpam-3904	281	30	n+	n+	PUNCT
ejpam-3904	281	31	|sv|	|sv|	PROPN
ejpam-3904	281	32	≥	≥	NUM
ejpam-3904	281	33	n−	n−	NOUN
ejpam-3904	281	34	1	1	NUM
ejpam-3904	281	35	+	+	CCONJ
ejpam-3904	281	36	min{γit(h	min{γit(h	PROPN
ejpam-3904	281	37	)	)	PUNCT
ejpam-3904	281	38	,	,	PUNCT
ejpam-3904	281	39	1	1	NUM
ejpam-3904	281	40	+	+	CCONJ
ejpam-3904	281	41	β0t(h	β0t(h	ADJ
ejpam-3904	281	42	)	)	PUNCT
ejpam-3904	281	43	}	}	PUNCT
ejpam-3904	281	44	.	.	PUNCT
ejpam-3904	282	1	case	case	NOUN
ejpam-3904	282	2	2	2	NUM
ejpam-3904	282	3	:	:	PUNCT
ejpam-3904	282	4	suppose	suppose	VERB
ejpam-3904	282	5	that	that	SCONJ
ejpam-3904	282	6	v	v	X
ejpam-3904	282	7	/∈	/∈	PUNCT
ejpam-3904	282	8	a.	a.	NOUN
ejpam-3904	283	1	then	then	ADV
ejpam-3904	283	2	sv	sv	PROPN
ejpam-3904	283	3	is	be	AUX
ejpam-3904	283	4	an	an	DET
ejpam-3904	283	5	itd	itd	NOUN
ejpam-3904	283	6	-	-	PUNCT
ejpam-3904	283	7	set	set	NOUN
ejpam-3904	283	8	of	of	ADP
ejpam-3904	283	9	hv	hv	PROPN
ejpam-3904	283	10	.	.	PUNCT
ejpam-3904	284	1	thus	thus	ADV
ejpam-3904	284	2	,	,	PUNCT
ejpam-3904	284	3	γit(g	γit(g	PROPN
ejpam-3904	284	4	◦	◦	NOUN
ejpam-3904	284	5	h	h	NOUN
ejpam-3904	284	6	)	)	PUNCT
ejpam-3904	284	7	=	=	PUNCT
ejpam-3904	284	8	|s|	|s|	NOUN
ejpam-3904	285	1	=	=	PUNCT
ejpam-3904	285	2	|a|+	|a|+	NOUN
ejpam-3904	285	3	∑	∑	PUNCT
ejpam-3904	285	4	w∈v	w∈v	PROPN
ejpam-3904	285	5	(	(	PUNCT
ejpam-3904	285	6	g	g	NOUN
ejpam-3904	285	7	)	)	PUNCT
ejpam-3904	285	8	|sw|	|sw|	PROPN
ejpam-3904	285	9	≥	≥	NOUN
ejpam-3904	285	10	n−	n−	NOUN
ejpam-3904	285	11	1	1	NUM
ejpam-3904	285	12	+	+	NUM
ejpam-3904	285	13	|sv|	|sv|	PROPN
ejpam-3904	285	14	≥	≥	NUM
ejpam-3904	285	15	n−	n−	NOUN
ejpam-3904	285	16	1	1	NUM
ejpam-3904	285	17	+	+	CCONJ
ejpam-3904	285	18	min{γit(h	min{γit(h	PROPN
ejpam-3904	285	19	)	)	PUNCT
ejpam-3904	285	20	,	,	PUNCT
ejpam-3904	285	21	1	1	NUM
ejpam-3904	285	22	+	+	CCONJ
ejpam-3904	285	23	β0t(h	β0t(h	ADJ
ejpam-3904	285	24	)	)	PUNCT
ejpam-3904	285	25	}	}	PUNCT
ejpam-3904	285	26	.	.	PUNCT
ejpam-3904	286	1	this	this	PRON
ejpam-3904	286	2	proves	prove	VERB
ejpam-3904	286	3	equation	equation	NOUN
ejpam-3904	286	4	1	1	NUM
ejpam-3904	286	5	.	.	PUNCT
ejpam-3904	286	6	similar	similar	ADJ
ejpam-3904	286	7	arguments	argument	NOUN
ejpam-3904	286	8	will	will	AUX
ejpam-3904	286	9	prove	prove	VERB
ejpam-3904	286	10	equation	equation	NOUN
ejpam-3904	286	11	2	2	NUM
ejpam-3904	286	12	.	.	NOUN
ejpam-3904	286	13	6	6	NUM
ejpam-3904	286	14	.	.	X
ejpam-3904	287	1	on	on	ADP
ejpam-3904	287	2	composition	composition	NOUN
ejpam-3904	287	3	of	of	ADP
ejpam-3904	287	4	graphs	graph	NOUN
ejpam-3904	287	5	for	for	ADP
ejpam-3904	287	6	a	a	DET
ejpam-3904	287	7	subset	subset	NOUN
ejpam-3904	287	8	c	c	NOUN
ejpam-3904	287	9	⊆	⊆	NUM
ejpam-3904	287	10	v	v	NOUN
ejpam-3904	287	11	(	(	PUNCT
ejpam-3904	287	12	g[h	g[h	PROPN
ejpam-3904	287	13	]	]	PUNCT
ejpam-3904	287	14	)	)	PUNCT
ejpam-3904	287	15	,	,	PUNCT
ejpam-3904	287	16	we	we	PRON
ejpam-3904	287	17	can	can	AUX
ejpam-3904	287	18	always	always	ADV
ejpam-3904	287	19	write	write	VERB
ejpam-3904	287	20	c	c	NOUN
ejpam-3904	287	21	=	=	SYM
ejpam-3904	287	22	∪x∈a({x	∪x∈a({x	PROPN
ejpam-3904	287	23	}	}	PUNCT
ejpam-3904	287	24	×	×	NOUN
ejpam-3904	287	25	ax	ax	NOUN
ejpam-3904	287	26	)	)	PUNCT
ejpam-3904	287	27	for	for	ADP
ejpam-3904	287	28	some	some	DET
ejpam-3904	287	29	a	a	DET
ejpam-3904	287	30	⊆	⊆	NUM
ejpam-3904	287	31	v	v	NOUN
ejpam-3904	287	32	(	(	PUNCT
ejpam-3904	287	33	g	g	NOUN
ejpam-3904	287	34	)	)	PUNCT
ejpam-3904	287	35	and	and	CCONJ
ejpam-3904	287	36	ax	ax	NOUN
ejpam-3904	287	37	=	=	SYM
ejpam-3904	287	38	{	{	PUNCT
ejpam-3904	287	39	y	y	PROPN
ejpam-3904	287	40	∈	∈	PROPN
ejpam-3904	287	41	v	v	PROPN
ejpam-3904	287	42	(	(	PUNCT
ejpam-3904	287	43	h	h	NOUN
ejpam-3904	287	44	)	)	PUNCT
ejpam-3904	287	45	:	:	PUNCT
ejpam-3904	287	46	(	(	PUNCT
ejpam-3904	287	47	x	x	X
ejpam-3904	287	48	,	,	PUNCT
ejpam-3904	287	49	y	y	PROPN
ejpam-3904	287	50	)	)	PUNCT
ejpam-3904	287	51	∈	∈	PROPN
ejpam-3904	287	52	a	a	PRON
ejpam-3904	287	53	}	}	PUNCT
ejpam-3904	287	54	.	.	PUNCT
ejpam-3904	288	1	theorem	theorem	ADJ
ejpam-3904	288	2	8	8	NUM
ejpam-3904	288	3	.	.	PUNCT
ejpam-3904	289	1	[	[	X
ejpam-3904	289	2	15	15	NUM
ejpam-3904	289	3	]	]	PUNCT
ejpam-3904	289	4	let	let	VERB
ejpam-3904	289	5	g	g	NOUN
ejpam-3904	289	6	and	and	CCONJ
ejpam-3904	289	7	h	h	NOUN
ejpam-3904	289	8	be	be	AUX
ejpam-3904	289	9	connected	connect	VERB
ejpam-3904	289	10	graphs	graph	NOUN
ejpam-3904	289	11	,	,	PUNCT
ejpam-3904	289	12	and	and	CCONJ
ejpam-3904	289	13	c	c	X
ejpam-3904	289	14	=	=	SYM
ejpam-3904	289	15	∪x∈s	∪x∈s	PROPN
ejpam-3904	289	16	(	(	PUNCT
ejpam-3904	289	17	{	{	PUNCT
ejpam-3904	289	18	x	x	NOUN
ejpam-3904	289	19	}	}	PUNCT
ejpam-3904	289	20	×	×	PROPN
ejpam-3904	289	21	sx	sx	PROPN
ejpam-3904	289	22	)	)	PUNCT
ejpam-3904	289	23	⊆	⊆	NUM
ejpam-3904	289	24	v	v	NOUN
ejpam-3904	289	25	(	(	PUNCT
ejpam-3904	289	26	g[h	g[h	PROPN
ejpam-3904	289	27	]	]	PUNCT
ejpam-3904	289	28	)	)	PUNCT
ejpam-3904	289	29	.	.	PUNCT
ejpam-3904	290	1	then	then	ADV
ejpam-3904	290	2	c	c	PROPN
ejpam-3904	290	3	is	be	AUX
ejpam-3904	290	4	a	a	DET
ejpam-3904	290	5	dominating	dominating	NOUN
ejpam-3904	290	6	set	set	NOUN
ejpam-3904	290	7	of	of	ADP
ejpam-3904	290	8	g[h	g[h	NOUN
ejpam-3904	290	9	]	]	PUNCT
ejpam-3904	290	10	if	if	SCONJ
ejpam-3904	290	11	and	and	CCONJ
ejpam-3904	290	12	only	only	ADV
ejpam-3904	290	13	if	if	SCONJ
ejpam-3904	290	14	one	one	NUM
ejpam-3904	290	15	of	of	ADP
ejpam-3904	290	16	the	the	DET
ejpam-3904	290	17	following	follow	VERB
ejpam-3904	290	18	holds	hold	VERB
ejpam-3904	290	19	:	:	PUNCT
ejpam-3904	290	20	(	(	PUNCT
ejpam-3904	290	21	i	i	NOUN
ejpam-3904	290	22	)	)	PUNCT
ejpam-3904	290	23	s	s	VERB
ejpam-3904	290	24	is	be	AUX
ejpam-3904	290	25	a	a	DET
ejpam-3904	290	26	total	total	ADJ
ejpam-3904	290	27	dominating	dominating	NOUN
ejpam-3904	290	28	set	set	NOUN
ejpam-3904	290	29	of	of	ADP
ejpam-3904	290	30	g	g	NOUN
ejpam-3904	290	31	;	;	PUNCT
ejpam-3904	290	32	(	(	PUNCT
ejpam-3904	290	33	ii	ii	NOUN
ejpam-3904	290	34	)	)	PUNCT
ejpam-3904	290	35	s	s	VERB
ejpam-3904	290	36	is	be	AUX
ejpam-3904	290	37	a	a	DET
ejpam-3904	290	38	dominating	dominating	NOUN
ejpam-3904	290	39	set	set	NOUN
ejpam-3904	290	40	of	of	ADP
ejpam-3904	290	41	g	g	PROPN
ejpam-3904	290	42	and	and	CCONJ
ejpam-3904	290	43	sx	sx	PROPN
ejpam-3904	290	44	is	be	AUX
ejpam-3904	290	45	a	a	DET
ejpam-3904	290	46	dominating	dominating	NOUN
ejpam-3904	290	47	set	set	NOUN
ejpam-3904	290	48	of	of	ADP
ejpam-3904	290	49	h	h	NOUN
ejpam-3904	290	50	for	for	ADP
ejpam-3904	290	51	each	each	DET
ejpam-3904	290	52	x	x	SYM
ejpam-3904	290	53	∈	∈	PROPN
ejpam-3904	290	54	s	s	PART
ejpam-3904	290	55	\ng(s	\ng(s	NOUN
ejpam-3904	290	56	)	)	PUNCT
ejpam-3904	290	57	.	.	PUNCT
ejpam-3904	291	1	lemma	lemma	PROPN
ejpam-3904	291	2	2	2	X
ejpam-3904	291	3	.	.	PUNCT
ejpam-3904	292	1	let	let	VERB
ejpam-3904	292	2	g	g	NOUN
ejpam-3904	292	3	and	and	CCONJ
ejpam-3904	292	4	h	h	NOUN
ejpam-3904	292	5	be	be	AUX
ejpam-3904	292	6	nontrivial	nontrivial	ADJ
ejpam-3904	292	7	connected	connected	ADJ
ejpam-3904	292	8	graphs	graph	NOUN
ejpam-3904	292	9	,	,	PUNCT
ejpam-3904	292	10	and	and	CCONJ
ejpam-3904	292	11	c	c	X
ejpam-3904	292	12	=	=	SYM
ejpam-3904	292	13	∪x∈s	∪x∈s	PROPN
ejpam-3904	292	14	(	(	PUNCT
ejpam-3904	292	15	{	{	PUNCT
ejpam-3904	292	16	x	x	NOUN
ejpam-3904	292	17	}	}	PUNCT
ejpam-3904	292	18	×	×	PROPN
ejpam-3904	292	19	sx	sx	PROPN
ejpam-3904	292	20	)	)	PUNCT
ejpam-3904	292	21	⊆	⊆	NUM
ejpam-3904	292	22	v	v	NOUN
ejpam-3904	292	23	(	(	PUNCT
ejpam-3904	292	24	g[h	g[h	PROPN
ejpam-3904	292	25	]	]	PUNCT
ejpam-3904	292	26	)	)	PUNCT
ejpam-3904	292	27	.	.	PUNCT
ejpam-3904	293	1	then	then	ADV
ejpam-3904	293	2	c	c	PROPN
ejpam-3904	293	3	is	be	AUX
ejpam-3904	293	4	an	an	DET
ejpam-3904	293	5	(	(	PUNCT
ejpam-3904	293	6	maximum	maximum	ADJ
ejpam-3904	293	7	)	)	PUNCT
ejpam-3904	293	8	independent	independent	ADJ
ejpam-3904	293	9	set	set	NOUN
ejpam-3904	293	10	of	of	ADP
ejpam-3904	293	11	g[h	g[h	NOUN
ejpam-3904	293	12	]	]	PUNCT
ejpam-3904	293	13	if	if	SCONJ
ejpam-3904	293	14	and	and	CCONJ
ejpam-3904	293	15	only	only	ADV
ejpam-3904	293	16	if	if	SCONJ
ejpam-3904	293	17	s	s	NOUN
ejpam-3904	293	18	is	be	AUX
ejpam-3904	293	19	an	an	DET
ejpam-3904	293	20	(	(	PUNCT
ejpam-3904	293	21	maximum	maximum	ADJ
ejpam-3904	293	22	)	)	PUNCT
ejpam-3904	293	23	independent	independent	ADJ
ejpam-3904	293	24	set	set	NOUN
ejpam-3904	293	25	of	of	ADP
ejpam-3904	293	26	g	g	PROPN
ejpam-3904	293	27	and	and	CCONJ
ejpam-3904	293	28	sx	sx	PROPN
ejpam-3904	293	29	is	be	AUX
ejpam-3904	293	30	an	an	DET
ejpam-3904	293	31	(	(	PUNCT
ejpam-3904	293	32	maximum	maximum	ADJ
ejpam-3904	293	33	)	)	PUNCT
ejpam-3904	293	34	independent	independent	ADJ
ejpam-3904	293	35	set	set	NOUN
ejpam-3904	293	36	of	of	ADP
ejpam-3904	293	37	h	h	NOUN
ejpam-3904	293	38	for	for	ADP
ejpam-3904	293	39	each	each	DET
ejpam-3904	293	40	x	x	SYM
ejpam-3904	293	41	∈	∈	PROPN
ejpam-3904	293	42	s.	s.	PROPN
ejpam-3904	293	43	proposition	proposition	NOUN
ejpam-3904	293	44	5	5	NUM
ejpam-3904	293	45	.	.	PUNCT
ejpam-3904	294	1	let	let	VERB
ejpam-3904	294	2	g	g	NOUN
ejpam-3904	294	3	and	and	CCONJ
ejpam-3904	294	4	h	h	NOUN
ejpam-3904	294	5	be	be	AUX
ejpam-3904	294	6	nontrivial	nontrivial	ADJ
ejpam-3904	294	7	connected	connected	ADJ
ejpam-3904	294	8	graphs	graph	NOUN
ejpam-3904	294	9	,	,	PUNCT
ejpam-3904	294	10	and	and	CCONJ
ejpam-3904	294	11	c	c	X
ejpam-3904	294	12	=	=	SYM
ejpam-3904	294	13	∪x∈s	∪x∈s	PROPN
ejpam-3904	294	14	(	(	PUNCT
ejpam-3904	294	15	{	{	PUNCT
ejpam-3904	294	16	x	x	NOUN
ejpam-3904	294	17	}	}	PUNCT
ejpam-3904	294	18	×	×	PROPN
ejpam-3904	294	19	sx	sx	PROPN
ejpam-3904	294	20	)	)	PUNCT
ejpam-3904	294	21	⊆	⊆	NUM
ejpam-3904	294	22	v	v	NOUN
ejpam-3904	294	23	(	(	PUNCT
ejpam-3904	294	24	g[h	g[h	PROPN
ejpam-3904	294	25	]	]	PUNCT
ejpam-3904	294	26	)	)	PUNCT
ejpam-3904	294	27	.	.	PUNCT
ejpam-3904	295	1	then	then	ADV
ejpam-3904	295	2	c	c	PROPN
ejpam-3904	295	3	is	be	AUX
ejpam-3904	295	4	an	an	DET
ejpam-3904	295	5	independent	independent	ADJ
ejpam-3904	295	6	transversal	transversal	NOUN
ejpam-3904	295	7	dominating	dominating	NOUN
ejpam-3904	295	8	set	set	NOUN
ejpam-3904	295	9	of	of	ADP
ejpam-3904	295	10	g[h	g[h	PROPN
ejpam-3904	295	11	]	]	PUNCT
ejpam-3904	295	12	if	if	SCONJ
ejpam-3904	295	13	and	and	CCONJ
ejpam-3904	295	14	only	only	ADV
ejpam-3904	295	15	if	if	SCONJ
ejpam-3904	295	16	each	each	PRON
ejpam-3904	295	17	of	of	ADP
ejpam-3904	295	18	the	the	DET
ejpam-3904	295	19	following	follow	VERB
ejpam-3904	295	20	holds	hold	VERB
ejpam-3904	295	21	:	:	PUNCT
ejpam-3904	295	22	(	(	PUNCT
ejpam-3904	295	23	i	i	NOUN
ejpam-3904	295	24	)	)	PUNCT
ejpam-3904	295	25	one	one	NUM
ejpam-3904	295	26	of	of	ADP
ejpam-3904	295	27	the	the	DET
ejpam-3904	295	28	following	following	NOUN
ejpam-3904	295	29	holds	hold	VERB
ejpam-3904	295	30	:	:	PUNCT
ejpam-3904	295	31	(	(	PUNCT
ejpam-3904	295	32	a	a	X
ejpam-3904	295	33	)	)	PUNCT
ejpam-3904	295	34	s	s	VERB
ejpam-3904	295	35	is	be	AUX
ejpam-3904	295	36	an	an	DET
ejpam-3904	295	37	ittd	ittd	NOUN
ejpam-3904	295	38	-	-	PUNCT
ejpam-3904	295	39	set	set	NOUN
ejpam-3904	295	40	of	of	ADP
ejpam-3904	295	41	g.	g.	PROPN
ejpam-3904	295	42	d.	d.	PROPN
ejpam-3904	295	43	sevilleno	sevilleno	PROPN
ejpam-3904	295	44	,	,	PUNCT
ejpam-3904	295	45	f.	f.	PROPN
ejpam-3904	295	46	jamil	jamil	PROPN
ejpam-3904	295	47	/	/	SYM
ejpam-3904	295	48	eur	eur	PROPN
ejpam-3904	295	49	.	.	PUNCT
ejpam-3904	296	1	j.	j.	PROPN
ejpam-3904	296	2	pure	pure	PROPN
ejpam-3904	296	3	appl	appl	PROPN
ejpam-3904	296	4	.	.	PUNCT
ejpam-3904	296	5	math	math	PROPN
ejpam-3904	296	6	,	,	PUNCT
ejpam-3904	296	7	149	149	NUM
ejpam-3904	296	8	-	-	SYM
ejpam-3904	296	9	163	163	NUM
ejpam-3904	296	10	160	160	NUM
ejpam-3904	296	11	(	(	PUNCT
ejpam-3904	296	12	b	b	NOUN
ejpam-3904	296	13	)	)	PUNCT
ejpam-3904	296	14	s	s	AUX
ejpam-3904	296	15	is	be	AUX
ejpam-3904	296	16	an	an	DET
ejpam-3904	296	17	itd	itd	NOUN
ejpam-3904	296	18	-	-	PUNCT
ejpam-3904	296	19	set	set	NOUN
ejpam-3904	296	20	of	of	ADP
ejpam-3904	296	21	g	g	PROPN
ejpam-3904	296	22	and	and	CCONJ
ejpam-3904	296	23	sx	sx	PROPN
ejpam-3904	296	24	is	be	AUX
ejpam-3904	296	25	a	a	DET
ejpam-3904	296	26	dominating	dominating	NOUN
ejpam-3904	296	27	set	set	NOUN
ejpam-3904	296	28	of	of	ADP
ejpam-3904	296	29	h	h	NOUN
ejpam-3904	296	30	for	for	ADP
ejpam-3904	296	31	each	each	DET
ejpam-3904	296	32	x	x	SYM
ejpam-3904	296	33	∈	∈	PROPN
ejpam-3904	296	34	s	s	PART
ejpam-3904	296	35	\ng(s	\ng(s	NOUN
ejpam-3904	296	36	)	)	PUNCT
ejpam-3904	296	37	.	.	PUNCT
ejpam-3904	297	1	(	(	PUNCT
ejpam-3904	297	2	ii	ii	NOUN
ejpam-3904	297	3	)	)	PUNCT
ejpam-3904	297	4	for	for	ADP
ejpam-3904	297	5	every	every	DET
ejpam-3904	297	6	pair	pair	NOUN
ejpam-3904	297	7	of	of	ADP
ejpam-3904	297	8	β0	β0	NOUN
ejpam-3904	297	9	-	-	PUNCT
ejpam-3904	297	10	sets	set	NOUN
ejpam-3904	297	11	a	a	PRON
ejpam-3904	297	12	and	and	CCONJ
ejpam-3904	297	13	b	b	NOUN
ejpam-3904	297	14	of	of	ADP
ejpam-3904	297	15	g	g	PROPN
ejpam-3904	297	16	and	and	CCONJ
ejpam-3904	297	17	h	h	NOUN
ejpam-3904	297	18	,	,	PUNCT
ejpam-3904	297	19	respectively	respectively	ADV
ejpam-3904	297	20	,	,	PUNCT
ejpam-3904	297	21	there	there	PRON
ejpam-3904	297	22	exists	exist	VERB
ejpam-3904	297	23	x	x	X
ejpam-3904	297	24	∈	∈	PROPN
ejpam-3904	297	25	s	s	PART
ejpam-3904	297	26	∩	∩	NOUN
ejpam-3904	297	27	a	a	PRON
ejpam-3904	297	28	for	for	ADP
ejpam-3904	297	29	which	which	PRON
ejpam-3904	297	30	b	b	NOUN
ejpam-3904	297	31	∩	∩	X
ejpam-3904	297	32	sx	sx	PROPN
ejpam-3904	297	33	6=	6=	ADP
ejpam-3904	297	34	∅.	∅.	NOUN
ejpam-3904	297	35	proof	proof	NOUN
ejpam-3904	297	36	.	.	PUNCT
ejpam-3904	298	1	suppose	suppose	VERB
ejpam-3904	298	2	that	that	SCONJ
ejpam-3904	298	3	conditions	condition	NOUN
ejpam-3904	298	4	(	(	PUNCT
ejpam-3904	298	5	i	i	NOUN
ejpam-3904	298	6	)	)	PUNCT
ejpam-3904	298	7	and	and	CCONJ
ejpam-3904	298	8	(	(	PUNCT
ejpam-3904	298	9	ii	ii	NOUN
ejpam-3904	298	10	)	)	PUNCT
ejpam-3904	298	11	hold	hold	VERB
ejpam-3904	298	12	for	for	ADP
ejpam-3904	298	13	s.	s.	PROPN
ejpam-3904	298	14	condition	condition	PROPN
ejpam-3904	298	15	(	(	PUNCT
ejpam-3904	298	16	i	i	NOUN
ejpam-3904	298	17	)	)	PUNCT
ejpam-3904	298	18	implies	imply	VERB
ejpam-3904	298	19	that	that	SCONJ
ejpam-3904	298	20	c	c	PROPN
ejpam-3904	298	21	is	be	AUX
ejpam-3904	298	22	a	a	DET
ejpam-3904	298	23	dominating	dominating	NOUN
ejpam-3904	298	24	set	set	NOUN
ejpam-3904	298	25	of	of	ADP
ejpam-3904	298	26	g[h	g[h	PROPN
ejpam-3904	298	27	]	]	PUNCT
ejpam-3904	298	28	by	by	ADP
ejpam-3904	298	29	theorem	theorem	NOUN
ejpam-3904	298	30	8	8	NUM
ejpam-3904	298	31	.	.	PUNCT
ejpam-3904	299	1	let	let	VERB
ejpam-3904	299	2	d	d	NOUN
ejpam-3904	299	3	=	=	PUNCT
ejpam-3904	299	4	∪x∈a	∪x∈a	PROPN
ejpam-3904	299	5	(	(	PUNCT
ejpam-3904	299	6	{	{	PUNCT
ejpam-3904	299	7	x	x	NOUN
ejpam-3904	299	8	}	}	PUNCT
ejpam-3904	299	9	×ax	×ax	ADJ
ejpam-3904	299	10	)	)	PUNCT
ejpam-3904	299	11	⊆	⊆	NUM
ejpam-3904	299	12	v	v	NOUN
ejpam-3904	299	13	(	(	PUNCT
ejpam-3904	299	14	g[h	g[h	PROPN
ejpam-3904	299	15	]	]	PUNCT
ejpam-3904	299	16	)	)	PUNCT
ejpam-3904	299	17	be	be	AUX
ejpam-3904	299	18	a	a	DET
ejpam-3904	299	19	β0	β0	NOUN
ejpam-3904	299	20	-	-	PUNCT
ejpam-3904	299	21	set	set	NOUN
ejpam-3904	299	22	of	of	ADP
ejpam-3904	299	23	g[h	g[h	NOUN
ejpam-3904	299	24	]	]	PUNCT
ejpam-3904	299	25	.	.	PUNCT
ejpam-3904	300	1	by	by	ADP
ejpam-3904	300	2	lemma	lemma	PROPN
ejpam-3904	300	3	2	2	NUM
ejpam-3904	300	4	,	,	PUNCT
ejpam-3904	300	5	a	a	PRON
ejpam-3904	300	6	is	be	AUX
ejpam-3904	300	7	a	a	DET
ejpam-3904	300	8	β0	β0	NOUN
ejpam-3904	300	9	-	-	PUNCT
ejpam-3904	300	10	set	set	NOUN
ejpam-3904	300	11	of	of	ADP
ejpam-3904	300	12	g	g	NOUN
ejpam-3904	300	13	and	and	CCONJ
ejpam-3904	300	14	ax	ax	NOUN
ejpam-3904	300	15	is	be	AUX
ejpam-3904	300	16	a	a	DET
ejpam-3904	300	17	β0	β0	NOUN
ejpam-3904	300	18	-	-	PUNCT
ejpam-3904	300	19	set	set	NOUN
ejpam-3904	300	20	of	of	ADP
ejpam-3904	300	21	h	h	NOUN
ejpam-3904	300	22	for	for	ADP
ejpam-3904	300	23	each	each	DET
ejpam-3904	300	24	x	x	SYM
ejpam-3904	300	25	∈	∈	PROPN
ejpam-3904	300	26	a.	a.	NOUN
ejpam-3904	300	27	since	since	SCONJ
ejpam-3904	300	28	s	s	PROPN
ejpam-3904	300	29	is	be	AUX
ejpam-3904	300	30	an	an	DET
ejpam-3904	300	31	itd	itd	NOUN
ejpam-3904	300	32	-	-	PUNCT
ejpam-3904	300	33	set	set	NOUN
ejpam-3904	300	34	of	of	ADP
ejpam-3904	300	35	g	g	NOUN
ejpam-3904	300	36	,	,	PUNCT
ejpam-3904	300	37	s	s	AUX
ejpam-3904	300	38	∩a	∩a	PROPN
ejpam-3904	300	39	6=	6=	ADP
ejpam-3904	300	40	∅.	∅.	ADP
ejpam-3904	300	41	by	by	ADP
ejpam-3904	300	42	condition(ii	condition(ii	PROPN
ejpam-3904	300	43	)	)	PUNCT
ejpam-3904	300	44	,	,	PUNCT
ejpam-3904	300	45	there	there	PRON
ejpam-3904	300	46	exists	exist	VERB
ejpam-3904	300	47	x	x	X
ejpam-3904	300	48	∈	∈	PROPN
ejpam-3904	300	49	s	s	VERB
ejpam-3904	300	50	∩a	∩a	NOUN
ejpam-3904	300	51	for	for	ADP
ejpam-3904	300	52	which	which	PRON
ejpam-3904	300	53	sx∩ax	sx∩ax	PROPN
ejpam-3904	300	54	6=	6=	ADP
ejpam-3904	300	55	∅.	∅.	AUX
ejpam-3904	300	56	let	let	VERB
ejpam-3904	300	57	y	y	PROPN
ejpam-3904	300	58	∈	∈	PROPN
ejpam-3904	300	59	sx∩ax	sx∩ax	PROPN
ejpam-3904	300	60	.	.	PUNCT
ejpam-3904	301	1	then	then	ADV
ejpam-3904	301	2	(	(	PUNCT
ejpam-3904	301	3	x	x	X
ejpam-3904	301	4	,	,	PUNCT
ejpam-3904	301	5	y	y	NOUN
ejpam-3904	301	6	)	)	PUNCT
ejpam-3904	301	7	∈	∈	NOUN
ejpam-3904	301	8	c∩d	c∩d	NOUN
ejpam-3904	301	9	.	.	PUNCT
ejpam-3904	302	1	since	since	SCONJ
ejpam-3904	302	2	d	d	PROPN
ejpam-3904	302	3	is	be	AUX
ejpam-3904	302	4	arbitrary	arbitrary	ADJ
ejpam-3904	302	5	,	,	PUNCT
ejpam-3904	302	6	c	c	PROPN
ejpam-3904	302	7	is	be	AUX
ejpam-3904	302	8	an	an	DET
ejpam-3904	302	9	itd	itd	NOUN
ejpam-3904	302	10	-	-	PUNCT
ejpam-3904	302	11	set	set	NOUN
ejpam-3904	302	12	of	of	ADP
ejpam-3904	302	13	g[h	g[h	NOUN
ejpam-3904	302	14	]	]	PUNCT
ejpam-3904	302	15	.	.	PUNCT
ejpam-3904	303	1	conversely	conversely	ADV
ejpam-3904	303	2	,	,	PUNCT
ejpam-3904	303	3	assume	assume	VERB
ejpam-3904	303	4	that	that	SCONJ
ejpam-3904	303	5	c	c	PROPN
ejpam-3904	303	6	is	be	AUX
ejpam-3904	303	7	an	an	DET
ejpam-3904	303	8	itd	itd	NOUN
ejpam-3904	303	9	-	-	PUNCT
ejpam-3904	303	10	set	set	NOUN
ejpam-3904	303	11	of	of	ADP
ejpam-3904	303	12	g[h	g[h	NOUN
ejpam-3904	303	13	]	]	PUNCT
ejpam-3904	303	14	.	.	PUNCT
ejpam-3904	304	1	by	by	ADP
ejpam-3904	304	2	theorem	theorem	NOUN
ejpam-3904	304	3	8	8	NUM
ejpam-3904	304	4	,	,	PUNCT
ejpam-3904	304	5	since	since	SCONJ
ejpam-3904	304	6	c	c	NOUN
ejpam-3904	304	7	is	be	AUX
ejpam-3904	304	8	a	a	DET
ejpam-3904	304	9	dominating	dominating	NOUN
ejpam-3904	304	10	set	set	NOUN
ejpam-3904	304	11	of	of	ADP
ejpam-3904	304	12	g[h	g[h	PROPN
ejpam-3904	304	13	]	]	PUNCT
ejpam-3904	304	14	,	,	PUNCT
ejpam-3904	304	15	s	s	VERB
ejpam-3904	304	16	is	be	AUX
ejpam-3904	304	17	a	a	DET
ejpam-3904	304	18	dominating	dominating	NOUN
ejpam-3904	304	19	set	set	NOUN
ejpam-3904	304	20	of	of	ADP
ejpam-3904	304	21	g	g	PROPN
ejpam-3904	304	22	and	and	CCONJ
ejpam-3904	304	23	sx	sx	PROPN
ejpam-3904	304	24	a	a	DET
ejpam-3904	304	25	dominating	dominating	NOUN
ejpam-3904	304	26	set	set	NOUN
ejpam-3904	304	27	of	of	ADP
ejpam-3904	304	28	h	h	NOUN
ejpam-3904	304	29	for	for	ADP
ejpam-3904	304	30	each	each	DET
ejpam-3904	304	31	x	x	SYM
ejpam-3904	304	32	∈	∈	PROPN
ejpam-3904	304	33	s	s	PART
ejpam-3904	304	34	\	\	NOUN
ejpam-3904	304	35	ng(s	ng(s	NUM
ejpam-3904	304	36	)	)	PUNCT
ejpam-3904	304	37	or	or	CCONJ
ejpam-3904	304	38	s	s	VERB
ejpam-3904	304	39	is	be	AUX
ejpam-3904	304	40	a	a	DET
ejpam-3904	304	41	total	total	ADJ
ejpam-3904	304	42	dominating	dominating	NOUN
ejpam-3904	304	43	set	set	NOUN
ejpam-3904	304	44	of	of	ADP
ejpam-3904	304	45	g.	g.	PROPN
ejpam-3904	304	46	let	let	VERB
ejpam-3904	304	47	a	a	DET
ejpam-3904	304	48	⊆	⊆	NUM
ejpam-3904	304	49	v	v	NOUN
ejpam-3904	304	50	(	(	PUNCT
ejpam-3904	304	51	g	g	NOUN
ejpam-3904	304	52	)	)	PUNCT
ejpam-3904	304	53	be	be	AUX
ejpam-3904	304	54	a	a	DET
ejpam-3904	304	55	β0	β0	NOUN
ejpam-3904	304	56	-	-	PUNCT
ejpam-3904	304	57	set	set	NOUN
ejpam-3904	304	58	of	of	ADP
ejpam-3904	304	59	g	g	PROPN
ejpam-3904	304	60	and	and	CCONJ
ejpam-3904	304	61	b	b	NOUN
ejpam-3904	304	62	⊆	⊆	NUM
ejpam-3904	304	63	v	v	NOUN
ejpam-3904	304	64	(	(	PUNCT
ejpam-3904	304	65	h	h	NOUN
ejpam-3904	304	66	)	)	PUNCT
ejpam-3904	304	67	a	a	DET
ejpam-3904	304	68	β0	β0	NOUN
ejpam-3904	304	69	-	-	PUNCT
ejpam-3904	304	70	set	set	NOUN
ejpam-3904	304	71	of	of	ADP
ejpam-3904	304	72	h.	h.	NOUN
ejpam-3904	304	73	since	since	SCONJ
ejpam-3904	304	74	c∗	c∗	PROPN
ejpam-3904	304	75	=	=	SYM
ejpam-3904	304	76	∪x∈a	∪x∈a	PROPN
ejpam-3904	304	77	(	(	PUNCT
ejpam-3904	304	78	{	{	PUNCT
ejpam-3904	304	79	x	x	NOUN
ejpam-3904	304	80	}	}	PUNCT
ejpam-3904	304	81	×b	×b	NOUN
ejpam-3904	304	82	)	)	PUNCT
ejpam-3904	304	83	is	be	AUX
ejpam-3904	304	84	a	a	DET
ejpam-3904	304	85	β0	β0	NOUN
ejpam-3904	304	86	-	-	PUNCT
ejpam-3904	304	87	set	set	NOUN
ejpam-3904	304	88	of	of	ADP
ejpam-3904	304	89	g[h	g[h	NOUN
ejpam-3904	304	90	]	]	PUNCT
ejpam-3904	304	91	,	,	PUNCT
ejpam-3904	304	92	c	c	PROPN
ejpam-3904	304	93	∩	∩	PROPN
ejpam-3904	304	94	c∗	c∗	PROPN
ejpam-3904	304	95	6=	6=	AUX
ejpam-3904	304	96	∅.	∅.	ADV
ejpam-3904	304	97	let	let	VERB
ejpam-3904	304	98	(	(	PUNCT
ejpam-3904	304	99	x	x	NOUN
ejpam-3904	304	100	,	,	PUNCT
ejpam-3904	304	101	y	y	NOUN
ejpam-3904	304	102	)	)	PUNCT
ejpam-3904	304	103	∈	∈	PROPN
ejpam-3904	304	104	c	c	NOUN
ejpam-3904	304	105	∩	∩	X
ejpam-3904	304	106	c∗.	c∗.	NOUN
ejpam-3904	305	1	then	then	ADV
ejpam-3904	305	2	x	x	PART
ejpam-3904	305	3	∈	∈	PROPN
ejpam-3904	305	4	s	s	PART
ejpam-3904	305	5	∩	∩	ADJ
ejpam-3904	305	6	a.	a.	NOUN
ejpam-3904	305	7	so	so	ADV
ejpam-3904	305	8	far	far	ADV
ejpam-3904	305	9	,	,	PUNCT
ejpam-3904	305	10	we	we	PRON
ejpam-3904	305	11	have	have	AUX
ejpam-3904	305	12	shown	show	VERB
ejpam-3904	305	13	that	that	SCONJ
ejpam-3904	305	14	s	s	NOUN
ejpam-3904	305	15	is	be	AUX
ejpam-3904	305	16	an	an	DET
ejpam-3904	305	17	itd	itd	NOUN
ejpam-3904	305	18	-	-	PUNCT
ejpam-3904	305	19	set	set	NOUN
ejpam-3904	305	20	of	of	ADP
ejpam-3904	305	21	g	g	NOUN
ejpam-3904	305	22	,	,	PUNCT
ejpam-3904	305	23	thus	thus	ADV
ejpam-3904	305	24	(	(	PUNCT
ejpam-3904	305	25	i	i	NOUN
ejpam-3904	305	26	)	)	PUNCT
ejpam-3904	305	27	holds	hold	VERB
ejpam-3904	305	28	.	.	PUNCT
ejpam-3904	306	1	moreover	moreover	ADV
ejpam-3904	306	2	,	,	PUNCT
ejpam-3904	306	3	y	y	PROPN
ejpam-3904	306	4	∈	∈	PROPN
ejpam-3904	306	5	sx	sx	NOUN
ejpam-3904	306	6	∩b	∩b	NOUN
ejpam-3904	306	7	so	so	SCONJ
ejpam-3904	306	8	that	that	SCONJ
ejpam-3904	306	9	sx	sx	PROPN
ejpam-3904	306	10	∩b	∩b	PROPN
ejpam-3904	306	11	6=	6=	ADP
ejpam-3904	306	12	∅.	∅.	ADP
ejpam-3904	306	13	this	this	DET
ejpam-3904	306	14	proves	prof	NOUN
ejpam-3904	306	15	(	(	PUNCT
ejpam-3904	306	16	ii	ii	NOUN
ejpam-3904	306	17	)	)	PUNCT
ejpam-3904	306	18	.	.	PUNCT
ejpam-3904	307	1	it	it	PRON
ejpam-3904	307	2	should	should	AUX
ejpam-3904	307	3	be	be	AUX
ejpam-3904	307	4	noted	note	VERB
ejpam-3904	307	5	that	that	SCONJ
ejpam-3904	307	6	if	if	SCONJ
ejpam-3904	307	7	s	s	VERB
ejpam-3904	307	8	∩	∩	NOUN
ejpam-3904	307	9	a	a	X
ejpam-3904	307	10	=	=	SYM
ejpam-3904	307	11	{	{	PUNCT
ejpam-3904	307	12	x	x	NOUN
ejpam-3904	307	13	}	}	PUNCT
ejpam-3904	307	14	(	(	PUNCT
ejpam-3904	307	15	singleton	singleton	PROPN
ejpam-3904	307	16	)	)	PUNCT
ejpam-3904	307	17	in	in	ADP
ejpam-3904	307	18	theorem	theorem	NOUN
ejpam-3904	307	19	5(ii	5(ii	NUM
ejpam-3904	307	20	)	)	PUNCT
ejpam-3904	307	21	,	,	PUNCT
ejpam-3904	307	22	then	then	ADV
ejpam-3904	307	23	sx	sx	PROPN
ejpam-3904	307	24	is	be	AUX
ejpam-3904	307	25	an	an	DET
ejpam-3904	307	26	independent	independent	ADJ
ejpam-3904	307	27	transversal	transversal	NOUN
ejpam-3904	307	28	set	set	NOUN
ejpam-3904	307	29	of	of	ADP
ejpam-3904	307	30	h.	h.	PROPN
ejpam-3904	307	31	consider	consider	VERB
ejpam-3904	307	32	g	g	NOUN
ejpam-3904	307	33	=	=	SYM
ejpam-3904	307	34	p5[p4	p5[p4	PROPN
ejpam-3904	307	35	]	]	PUNCT
ejpam-3904	307	36	.	.	PUNCT
ejpam-3904	308	1	write	write	VERB
ejpam-3904	308	2	p5	p5	ADJ
ejpam-3904	308	3	=	=	PUNCT
ejpam-3904	309	1	[	[	X
ejpam-3904	309	2	x1	x1	PROPN
ejpam-3904	309	3	,	,	PUNCT
ejpam-3904	309	4	x2	x2	PROPN
ejpam-3904	309	5	,	,	PUNCT
ejpam-3904	309	6	x3	x3	PROPN
ejpam-3904	309	7	,	,	PUNCT
ejpam-3904	309	8	x4	x4	PROPN
ejpam-3904	309	9	,	,	PUNCT
ejpam-3904	309	10	x5	x5	NOUN
ejpam-3904	309	11	]	]	X
ejpam-3904	309	12	and	and	CCONJ
ejpam-3904	309	13	p4	p4	ADJ
ejpam-3904	309	14	=	=	PUNCT
ejpam-3904	310	1	[	[	X
ejpam-3904	310	2	y1	y1	X
ejpam-3904	310	3	,	,	PUNCT
ejpam-3904	310	4	y2	y2	PROPN
ejpam-3904	310	5	,	,	PUNCT
ejpam-3904	310	6	y3	y3	PROPN
ejpam-3904	310	7	,	,	PUNCT
ejpam-3904	310	8	y4	y4	X
ejpam-3904	310	9	]	]	PUNCT
ejpam-3904	310	10	.	.	PUNCT
ejpam-3904	311	1	then	then	ADV
ejpam-3904	311	2	c	c	X
ejpam-3904	311	3	=	=	PRON
ejpam-3904	311	4	{	{	PUNCT
ejpam-3904	311	5	(	(	PUNCT
ejpam-3904	311	6	x2	x2	PROPN
ejpam-3904	311	7	,	,	PUNCT
ejpam-3904	311	8	y2	y2	PROPN
ejpam-3904	311	9	)	)	PUNCT
ejpam-3904	311	10	,	,	PUNCT
ejpam-3904	311	11	(	(	PUNCT
ejpam-3904	311	12	x3	x3	ADJ
ejpam-3904	311	13	,	,	PUNCT
ejpam-3904	311	14	y1	y1	PROPN
ejpam-3904	311	15	)	)	PUNCT
ejpam-3904	311	16	,	,	PUNCT
ejpam-3904	311	17	(	(	PUNCT
ejpam-3904	311	18	x3	x3	ADJ
ejpam-3904	311	19	,	,	PUNCT
ejpam-3904	311	20	y2	y2	PROPN
ejpam-3904	311	21	)	)	PUNCT
ejpam-3904	311	22	,	,	PUNCT
ejpam-3904	311	23	(	(	PUNCT
ejpam-3904	311	24	x4	x4	PROPN
ejpam-3904	311	25	,	,	PUNCT
ejpam-3904	311	26	y2	y2	PROPN
ejpam-3904	311	27	)	)	PUNCT
ejpam-3904	311	28	}	}	PUNCT
ejpam-3904	311	29	is	be	AUX
ejpam-3904	311	30	a	a	DET
ejpam-3904	311	31	γit	γit	ADV
ejpam-3904	311	32	-	-	PUNCT
ejpam-3904	311	33	set	set	NOUN
ejpam-3904	311	34	of	of	ADP
ejpam-3904	311	35	g.	g.	PROPN
ejpam-3904	311	36	put	put	VERB
ejpam-3904	311	37	s	s	PART
ejpam-3904	311	38	=	=	PUNCT
ejpam-3904	311	39	{	{	PUNCT
ejpam-3904	311	40	x2	x2	PROPN
ejpam-3904	311	41	,	,	PUNCT
ejpam-3904	311	42	x3	x3	ADJ
ejpam-3904	311	43	,	,	PUNCT
ejpam-3904	311	44	x4	x4	PROPN
ejpam-3904	311	45	}	}	PUNCT
ejpam-3904	311	46	and	and	CCONJ
ejpam-3904	311	47	a	a	PRON
ejpam-3904	311	48	=	=	X
ejpam-3904	311	49	{	{	PUNCT
ejpam-3904	311	50	x1	x1	PROPN
ejpam-3904	311	51	,	,	PUNCT
ejpam-3904	311	52	x3	x3	ADJ
ejpam-3904	311	53	,	,	PUNCT
ejpam-3904	311	54	x5	x5	NOUN
ejpam-3904	311	55	}	}	PUNCT
ejpam-3904	311	56	.	.	PUNCT
ejpam-3904	312	1	then	then	ADV
ejpam-3904	312	2	s	s	VERB
ejpam-3904	312	3	is	be	AUX
ejpam-3904	312	4	a	a	DET
ejpam-3904	312	5	γitt	γitt	VERB
ejpam-3904	312	6	-	-	PUNCT
ejpam-3904	312	7	set	set	NOUN
ejpam-3904	312	8	of	of	ADP
ejpam-3904	312	9	p5	p5	ADJ
ejpam-3904	312	10	and	and	CCONJ
ejpam-3904	312	11	a	a	PRON
ejpam-3904	312	12	is	be	AUX
ejpam-3904	312	13	the	the	DET
ejpam-3904	312	14	unique	unique	ADJ
ejpam-3904	312	15	β0	β0	NOUN
ejpam-3904	312	16	-	-	PUNCT
ejpam-3904	312	17	set	set	NOUN
ejpam-3904	312	18	of	of	ADP
ejpam-3904	312	19	p5	p5	NOUN
ejpam-3904	312	20	.	.	PUNCT
ejpam-3904	313	1	further	far	ADV
ejpam-3904	313	2	,	,	PUNCT
ejpam-3904	313	3	s	s	VERB
ejpam-3904	313	4	∩a	∩a	NOUN
ejpam-3904	313	5	=	=	PUNCT
ejpam-3904	313	6	{	{	PUNCT
ejpam-3904	313	7	x3	x3	ADJ
ejpam-3904	313	8	}	}	PUNCT
ejpam-3904	313	9	and	and	CCONJ
ejpam-3904	313	10	sx3	sx3	PROPN
ejpam-3904	313	11	=	=	SYM
ejpam-3904	313	12	{	{	PUNCT
ejpam-3904	313	13	y1	y1	PROPN
ejpam-3904	313	14	,	,	PUNCT
ejpam-3904	313	15	y2	y2	PROPN
ejpam-3904	313	16	}	}	PUNCT
ejpam-3904	313	17	is	be	AUX
ejpam-3904	313	18	an	an	DET
ejpam-3904	313	19	independent	independent	ADJ
ejpam-3904	313	20	transversal	transversal	NOUN
ejpam-3904	313	21	set	set	NOUN
ejpam-3904	313	22	of	of	ADP
ejpam-3904	313	23	p4	p4	NOUN
ejpam-3904	313	24	.	.	PUNCT
ejpam-3904	314	1	the	the	DET
ejpam-3904	314	2	following	follow	VERB
ejpam-3904	314	3	is	be	AUX
ejpam-3904	314	4	immediate	immediate	ADJ
ejpam-3904	314	5	from	from	ADP
ejpam-3904	314	6	proposition	proposition	NOUN
ejpam-3904	314	7	5	5	NUM
ejpam-3904	314	8	.	.	PUNCT
ejpam-3904	314	9	proposition	proposition	NOUN
ejpam-3904	314	10	6	6	NUM
ejpam-3904	314	11	.	.	PUNCT
ejpam-3904	315	1	let	let	VERB
ejpam-3904	315	2	g	g	NOUN
ejpam-3904	315	3	and	and	CCONJ
ejpam-3904	315	4	h	h	NOUN
ejpam-3904	315	5	be	be	AUX
ejpam-3904	315	6	nontrivial	nontrivial	ADJ
ejpam-3904	315	7	connected	connected	ADJ
ejpam-3904	315	8	graphs	graph	NOUN
ejpam-3904	315	9	,	,	PUNCT
ejpam-3904	315	10	and	and	CCONJ
ejpam-3904	315	11	c	c	X
ejpam-3904	315	12	=	=	SYM
ejpam-3904	315	13	∪x∈s	∪x∈s	PROPN
ejpam-3904	315	14	(	(	PUNCT
ejpam-3904	315	15	{	{	PUNCT
ejpam-3904	315	16	x	x	NOUN
ejpam-3904	315	17	}	}	PUNCT
ejpam-3904	315	18	×	×	PROPN
ejpam-3904	315	19	sx	sx	PROPN
ejpam-3904	315	20	)	)	PUNCT
ejpam-3904	315	21	⊆	⊆	NUM
ejpam-3904	315	22	v	v	NOUN
ejpam-3904	315	23	(	(	PUNCT
ejpam-3904	315	24	g[h	g[h	PROPN
ejpam-3904	315	25	]	]	PUNCT
ejpam-3904	315	26	)	)	PUNCT
ejpam-3904	315	27	.	.	PUNCT
ejpam-3904	316	1	then	then	ADV
ejpam-3904	316	2	c	c	PROPN
ejpam-3904	316	3	is	be	AUX
ejpam-3904	316	4	an	an	DET
ejpam-3904	316	5	independent	independent	ADJ
ejpam-3904	316	6	transversal	transversal	ADJ
ejpam-3904	316	7	total	total	NOUN
ejpam-3904	316	8	dominating	dominating	NOUN
ejpam-3904	316	9	set	set	NOUN
ejpam-3904	316	10	of	of	ADP
ejpam-3904	316	11	g[h	g[h	PROPN
ejpam-3904	316	12	]	]	PUNCT
ejpam-3904	316	13	if	if	SCONJ
ejpam-3904	316	14	and	and	CCONJ
ejpam-3904	316	15	only	only	ADV
ejpam-3904	316	16	if	if	SCONJ
ejpam-3904	316	17	each	each	PRON
ejpam-3904	316	18	of	of	ADP
ejpam-3904	316	19	the	the	DET
ejpam-3904	316	20	following	follow	VERB
ejpam-3904	316	21	holds	hold	VERB
ejpam-3904	316	22	:	:	PUNCT
ejpam-3904	316	23	(	(	PUNCT
ejpam-3904	316	24	i	i	NOUN
ejpam-3904	316	25	)	)	PUNCT
ejpam-3904	316	26	s	s	VERB
ejpam-3904	316	27	is	be	AUX
ejpam-3904	316	28	an	an	DET
ejpam-3904	316	29	independent	independent	ADJ
ejpam-3904	316	30	transversal	transversal	ADJ
ejpam-3904	316	31	total	total	NOUN
ejpam-3904	316	32	dominating	dominating	NOUN
ejpam-3904	316	33	set	set	NOUN
ejpam-3904	316	34	of	of	ADP
ejpam-3904	316	35	g.	g.	PROPN
ejpam-3904	316	36	(	(	PUNCT
ejpam-3904	316	37	ii	ii	PROPN
ejpam-3904	316	38	)	)	PUNCT
ejpam-3904	316	39	for	for	ADP
ejpam-3904	316	40	every	every	DET
ejpam-3904	316	41	pair	pair	NOUN
ejpam-3904	316	42	of	of	ADP
ejpam-3904	316	43	maximum	maximum	ADJ
ejpam-3904	316	44	independent	independent	ADJ
ejpam-3904	316	45	sets	set	NOUN
ejpam-3904	316	46	a	a	PRON
ejpam-3904	316	47	and	and	CCONJ
ejpam-3904	316	48	b	b	NOUN
ejpam-3904	316	49	of	of	ADP
ejpam-3904	316	50	g	g	PROPN
ejpam-3904	316	51	and	and	CCONJ
ejpam-3904	316	52	h	h	NOUN
ejpam-3904	316	53	,	,	PUNCT
ejpam-3904	316	54	respectively	respectively	ADV
ejpam-3904	316	55	,	,	PUNCT
ejpam-3904	316	56	there	there	PRON
ejpam-3904	316	57	exists	exist	VERB
ejpam-3904	316	58	x	x	X
ejpam-3904	316	59	∈	∈	PROPN
ejpam-3904	316	60	s	s	VERB
ejpam-3904	316	61	∩a	∩a	NOUN
ejpam-3904	316	62	for	for	ADP
ejpam-3904	316	63	which	which	PRON
ejpam-3904	316	64	b	b	NOUN
ejpam-3904	316	65	∩	∩	X
ejpam-3904	316	66	sx	sx	PROPN
ejpam-3904	317	1	6=	6=	PROPN
ejpam-3904	317	2	∅.	∅.	ADV
ejpam-3904	317	3	given	give	VERB
ejpam-3904	317	4	an	an	DET
ejpam-3904	317	5	itd	itd	NOUN
ejpam-3904	317	6	-	-	PUNCT
ejpam-3904	317	7	set	set	VERB
ejpam-3904	317	8	(	(	PUNCT
ejpam-3904	317	9	resp	resp	NOUN
ejpam-3904	317	10	.	.	PUNCT
ejpam-3904	318	1	ittd	ittd	PROPN
ejpam-3904	318	2	-	-	PUNCT
ejpam-3904	318	3	set	set	PROPN
ejpam-3904	318	4	)	)	PUNCT
ejpam-3904	318	5	s	s	PART
ejpam-3904	318	6	⊆	⊆	NUM
ejpam-3904	318	7	v	v	NOUN
ejpam-3904	318	8	(	(	PUNCT
ejpam-3904	318	9	g	g	NOUN
ejpam-3904	318	10	)	)	PUNCT
ejpam-3904	318	11	of	of	ADP
ejpam-3904	318	12	g	g	NOUN
ejpam-3904	318	13	,	,	PUNCT
ejpam-3904	318	14	define	define	VERB
ejpam-3904	318	15	mg(s	mg(s	NOUN
ejpam-3904	318	16	)	)	PUNCT
ejpam-3904	318	17	(	(	PUNCT
ejpam-3904	318	18	resp	resp	NOUN
ejpam-3904	318	19	.	.	PUNCT
ejpam-3904	319	1	m	m	PROPN
ejpam-3904	319	2	t	t	PRON
ejpam-3904	319	3	g(s	g(s	PROPN
ejpam-3904	319	4	)	)	PUNCT
ejpam-3904	319	5	)	)	PUNCT
ejpam-3904	320	1	to	to	PART
ejpam-3904	320	2	be	be	AUX
ejpam-3904	320	3	any	any	DET
ejpam-3904	320	4	subset	subset	NOUN
ejpam-3904	320	5	of	of	ADP
ejpam-3904	320	6	s	s	PRON
ejpam-3904	320	7	of	of	ADP
ejpam-3904	320	8	minimum	minimum	ADJ
ejpam-3904	320	9	cardinality	cardinality	NOUN
ejpam-3904	320	10	such	such	ADJ
ejpam-3904	320	11	that	that	PRON
ejpam-3904	320	12	for	for	ADP
ejpam-3904	320	13	each	each	DET
ejpam-3904	320	14	x	x	SYM
ejpam-3904	320	15	∈	∈	PROPN
ejpam-3904	320	16	mg(s	mg(s	NOUN
ejpam-3904	320	17	)	)	PUNCT
ejpam-3904	320	18	(	(	PUNCT
ejpam-3904	320	19	resp	resp	NOUN
ejpam-3904	320	20	.	.	PUNCT
ejpam-3904	321	1	x	x	X
ejpam-3904	321	2	∈m	∈m	ADP
ejpam-3904	321	3	t	t	PROPN
ejpam-3904	321	4	g(s	g(s	PROPN
ejpam-3904	321	5	)	)	PUNCT
ejpam-3904	321	6	)	)	PUNCT
ejpam-3904	321	7	,	,	PUNCT
ejpam-3904	321	8	x	x	PUNCT
ejpam-3904	321	9	∈m	∈m	NOUN
ejpam-3904	321	10	for	for	ADP
ejpam-3904	321	11	some	some	DET
ejpam-3904	321	12	m	m	NOUN
ejpam-3904	321	13	∈	∈	NOUN
ejpam-3904	321	14	xi(g	xi(g	NOUN
ejpam-3904	321	15	)	)	PUNCT
ejpam-3904	321	16	,	,	PUNCT
ejpam-3904	321	17	and	and	CCONJ
ejpam-3904	321	18	put	put	VERB
ejpam-3904	321	19	η(g	η(g	NUM
ejpam-3904	321	20	)	)	PUNCT
ejpam-3904	321	21	=	=	SYM
ejpam-3904	322	1	min{|mg(s)|	min{|mg(s)|	X
ejpam-3904	322	2	:	:	PUNCT
ejpam-3904	322	3	s	s	VERB
ejpam-3904	322	4	is	be	AUX
ejpam-3904	322	5	an	an	DET
ejpam-3904	322	6	γit	γit	ADV
ejpam-3904	322	7	-	-	PUNCT
ejpam-3904	322	8	set	set	NOUN
ejpam-3904	322	9	of	of	ADP
ejpam-3904	322	10	g	g	NOUN
ejpam-3904	322	11	}	}	PUNCT
ejpam-3904	322	12	,	,	PUNCT
ejpam-3904	322	13	and	and	CCONJ
ejpam-3904	322	14	ηt(g	ηt(g	X
ejpam-3904	322	15	)	)	PUNCT
ejpam-3904	322	16	=	=	SYM
ejpam-3904	322	17	min{|m	min{|m	PROPN
ejpam-3904	322	18	t	t	PROPN
ejpam-3904	322	19	g(s)|	g(s)|	PROPN
ejpam-3904	322	20	:	:	PUNCT
ejpam-3904	322	21	s	s	VERB
ejpam-3904	322	22	is	be	AUX
ejpam-3904	322	23	a	a	DET
ejpam-3904	322	24	γitt	γitt	VERB
ejpam-3904	322	25	-	-	PUNCT
ejpam-3904	322	26	set	set	NOUN
ejpam-3904	322	27	of	of	ADP
ejpam-3904	322	28	g	g	NOUN
ejpam-3904	322	29	}	}	PUNCT
ejpam-3904	322	30	.	.	PUNCT
ejpam-3904	323	1	d.	d.	PROPN
ejpam-3904	323	2	sevilleno	sevilleno	PROPN
ejpam-3904	323	3	,	,	PUNCT
ejpam-3904	323	4	f.	f.	PROPN
ejpam-3904	323	5	jamil	jamil	PROPN
ejpam-3904	323	6	/	/	SYM
ejpam-3904	323	7	eur	eur	PROPN
ejpam-3904	323	8	.	.	PUNCT
ejpam-3904	324	1	j.	j.	PROPN
ejpam-3904	324	2	pure	pure	PROPN
ejpam-3904	324	3	appl	appl	PROPN
ejpam-3904	324	4	.	.	PUNCT
ejpam-3904	324	5	math	math	PROPN
ejpam-3904	324	6	,	,	PUNCT
ejpam-3904	324	7	149	149	NUM
ejpam-3904	324	8	-	-	SYM
ejpam-3904	324	9	163	163	NUM
ejpam-3904	324	10	161	161	NUM
ejpam-3904	324	11	corollary	corollary	NOUN
ejpam-3904	324	12	5	5	NUM
ejpam-3904	324	13	.	.	PUNCT
ejpam-3904	325	1	for	for	ADP
ejpam-3904	325	2	all	all	DET
ejpam-3904	325	3	nontrivial	nontrivial	ADJ
ejpam-3904	325	4	connected	connect	VERB
ejpam-3904	325	5	graphs	graph	NOUN
ejpam-3904	325	6	g	g	NOUN
ejpam-3904	325	7	and	and	CCONJ
ejpam-3904	325	8	positive	positive	ADJ
ejpam-3904	325	9	integers	integer	NOUN
ejpam-3904	325	10	p	p	NOUN
ejpam-3904	325	11	≥	≥	NUM
ejpam-3904	325	12	2	2	NUM
ejpam-3904	325	13	,	,	PUNCT
ejpam-3904	325	14	γit(g[kp	γit(g[kp	PROPN
ejpam-3904	325	15	]	]	PUNCT
ejpam-3904	325	16	)	)	PUNCT
ejpam-3904	325	17	≤	≤	NOUN
ejpam-3904	325	18	(	(	PUNCT
ejpam-3904	325	19	p−	p−	NOUN
ejpam-3904	325	20	1)η(g	1)η(g	NUM
ejpam-3904	325	21	)	)	PUNCT
ejpam-3904	325	22	+	+	NUM
ejpam-3904	325	23	γit(g	γit(g	NOUN
ejpam-3904	325	24	)	)	PUNCT
ejpam-3904	325	25	,	,	PUNCT
ejpam-3904	325	26	and	and	CCONJ
ejpam-3904	325	27	γitt(g[kp	γitt(g[kp	NOUN
ejpam-3904	325	28	]	]	X
ejpam-3904	325	29	)	)	PUNCT
ejpam-3904	325	30	≤	≤	NOUN
ejpam-3904	325	31	(	(	PUNCT
ejpam-3904	325	32	p−	p−	NOUN
ejpam-3904	325	33	1)ηt(g	1)ηt(g	NUM
ejpam-3904	325	34	)	)	PUNCT
ejpam-3904	325	35	+	+	CCONJ
ejpam-3904	325	36	γitt(g	γitt(g	NOUN
ejpam-3904	325	37	)	)	PUNCT
ejpam-3904	325	38	.	.	PUNCT
ejpam-3904	326	1	equality	equality	NOUN
ejpam-3904	326	2	in	in	ADP
ejpam-3904	326	3	each	each	PRON
ejpam-3904	326	4	is	be	AUX
ejpam-3904	326	5	attained	attain	VERB
ejpam-3904	326	6	if	if	SCONJ
ejpam-3904	326	7	xi(g	xi(g	NOUN
ejpam-3904	326	8	)	)	PUNCT
ejpam-3904	326	9	consists	consist	VERB
ejpam-3904	326	10	of	of	ADP
ejpam-3904	326	11	pairwise	pairwise	PROPN
ejpam-3904	326	12	disjoint	disjoint	PROPN
ejpam-3904	326	13	β0	β0	NOUN
ejpam-3904	326	14	-	-	PUNCT
ejpam-3904	326	15	sets	set	NOUN
ejpam-3904	326	16	of	of	ADP
ejpam-3904	326	17	g.	g.	NOUN
ejpam-3904	326	18	proof	proof	NOUN
ejpam-3904	326	19	.	.	PUNCT
ejpam-3904	327	1	let	let	VERB
ejpam-3904	327	2	s	s	PRON
ejpam-3904	327	3	⊆	⊆	NUM
ejpam-3904	327	4	v	v	NOUN
ejpam-3904	327	5	(	(	PUNCT
ejpam-3904	327	6	g	g	NOUN
ejpam-3904	327	7	)	)	PUNCT
ejpam-3904	327	8	be	be	AUX
ejpam-3904	327	9	a	a	DET
ejpam-3904	327	10	γit	γit	ADV
ejpam-3904	327	11	-	-	PUNCT
ejpam-3904	327	12	set	set	NOUN
ejpam-3904	327	13	of	of	ADP
ejpam-3904	327	14	g	g	NOUN
ejpam-3904	327	15	for	for	ADP
ejpam-3904	327	16	which	which	PRON
ejpam-3904	327	17	|mg(s)|	|mg(s)|	PROPN
ejpam-3904	327	18	=	=	SYM
ejpam-3904	327	19	η(g	η(g	PROPN
ejpam-3904	327	20	)	)	PUNCT
ejpam-3904	327	21	,	,	PUNCT
ejpam-3904	327	22	and	and	CCONJ
ejpam-3904	327	23	let	let	VERB
ejpam-3904	327	24	y	y	PROPN
ejpam-3904	327	25	∈	∈	PROPN
ejpam-3904	327	26	v	v	PROPN
ejpam-3904	327	27	(	(	PUNCT
ejpam-3904	327	28	kp	kp	PROPN
ejpam-3904	327	29	)	)	PUNCT
ejpam-3904	327	30	.	.	PUNCT
ejpam-3904	328	1	define	define	VERB
ejpam-3904	328	2	c	c	NOUN
ejpam-3904	329	1	=	=	PUNCT
ejpam-3904	330	1	[	[	X
ejpam-3904	330	2	∪x∈mg(s	∪x∈mg(s	NOUN
ejpam-3904	330	3	)	)	PUNCT
ejpam-3904	330	4	(	(	PUNCT
ejpam-3904	330	5	{	{	PUNCT
ejpam-3904	330	6	x	x	NOUN
ejpam-3904	330	7	}	}	PUNCT
ejpam-3904	330	8	×	×	NOUN
ejpam-3904	330	9	v	v	NOUN
ejpam-3904	330	10	(	(	PUNCT
ejpam-3904	330	11	kp	kp	PROPN
ejpam-3904	330	12	)	)	PUNCT
ejpam-3904	330	13	)	)	PUNCT
ejpam-3904	330	14	]	]	PUNCT
ejpam-3904	330	15	∪	∪	ADP
ejpam-3904	330	16	[	[	PUNCT
ejpam-3904	330	17	∪x∈s\mg(s){(x	∪x∈s\mg(s){(x	NOUN
ejpam-3904	330	18	,	,	PUNCT
ejpam-3904	330	19	y	y	NOUN
ejpam-3904	330	20	)	)	PUNCT
ejpam-3904	330	21	}	}	PUNCT
ejpam-3904	330	22	]	]	PUNCT
ejpam-3904	330	23	.	.	PUNCT
ejpam-3904	331	1	by	by	ADP
ejpam-3904	331	2	proposition	proposition	NOUN
ejpam-3904	331	3	5	5	NUM
ejpam-3904	331	4	,	,	PUNCT
ejpam-3904	331	5	c	c	PROPN
ejpam-3904	331	6	is	be	AUX
ejpam-3904	331	7	an	an	DET
ejpam-3904	331	8	itd	itd	NOUN
ejpam-3904	331	9	-	-	PUNCT
ejpam-3904	331	10	set	set	NOUN
ejpam-3904	331	11	of	of	ADP
ejpam-3904	331	12	g[kp	g[kp	PROPN
ejpam-3904	331	13	]	]	PUNCT
ejpam-3904	331	14	.	.	PUNCT
ejpam-3904	332	1	consequently	consequently	ADV
ejpam-3904	332	2	,	,	PUNCT
ejpam-3904	332	3	γit(g[kp	γit(g[kp	PROPN
ejpam-3904	332	4	]	]	PUNCT
ejpam-3904	332	5	)	)	PUNCT
ejpam-3904	332	6	≤	≤	NOUN
ejpam-3904	332	7	|c|	|c|	PROPN
ejpam-3904	333	1	=	=	SYM
ejpam-3904	334	1	p	p	X
ejpam-3904	334	2	·	·	PUNCT
ejpam-3904	334	3	η(g	η(g	NUM
ejpam-3904	334	4	)	)	PUNCT
ejpam-3904	334	5	+	+	CCONJ
ejpam-3904	334	6	(	(	PUNCT
ejpam-3904	334	7	γit(g)−	γit(g)−	NOUN
ejpam-3904	334	8	η(g	η(g	NOUN
ejpam-3904	334	9	)	)	PUNCT
ejpam-3904	334	10	)	)	PUNCT
ejpam-3904	335	1	=	=	PRON
ejpam-3904	335	2	(	(	PUNCT
ejpam-3904	335	3	p−	p−	NOUN
ejpam-3904	335	4	1)η(g	1)η(g	NUM
ejpam-3904	335	5	)	)	PUNCT
ejpam-3904	335	6	+	+	NUM
ejpam-3904	335	7	γit(g	γit(g	NOUN
ejpam-3904	335	8	)	)	PUNCT
ejpam-3904	335	9	.	.	PUNCT
ejpam-3904	336	1	now	now	ADV
ejpam-3904	336	2	suppose	suppose	VERB
ejpam-3904	336	3	that	that	SCONJ
ejpam-3904	336	4	xi(g	xi(g	PROPN
ejpam-3904	336	5	)	)	PUNCT
ejpam-3904	336	6	consists	consist	VERB
ejpam-3904	336	7	of	of	ADP
ejpam-3904	336	8	pairwise	pairwise	PROPN
ejpam-3904	336	9	disjoint	disjoint	PROPN
ejpam-3904	336	10	β0	β0	NOUN
ejpam-3904	336	11	-	-	PUNCT
ejpam-3904	336	12	sets	set	NOUN
ejpam-3904	336	13	of	of	ADP
ejpam-3904	336	14	g.	g.	PROPN
ejpam-3904	336	15	then	then	ADV
ejpam-3904	336	16	|mg(s)|	|mg(s)|	X
ejpam-3904	336	17	=	=	SYM
ejpam-3904	336	18	η(g	η(g	PROPN
ejpam-3904	336	19	)	)	PUNCT
ejpam-3904	336	20	=	=	SYM
ejpam-3904	336	21	xi(g	xi(g	X
ejpam-3904	336	22	)	)	PUNCT
ejpam-3904	336	23	for	for	ADP
ejpam-3904	336	24	all	all	DET
ejpam-3904	336	25	itd	itd	NOUN
ejpam-3904	336	26	-	-	PUNCT
ejpam-3904	336	27	sets	set	NOUN
ejpam-3904	336	28	s	s	NOUN
ejpam-3904	336	29	of	of	ADP
ejpam-3904	336	30	g.	g.	NOUN
ejpam-3904	336	31	let	let	VERB
ejpam-3904	336	32	c	c	NOUN
ejpam-3904	336	33	=	=	SYM
ejpam-3904	336	34	∪x∈s	∪x∈s	PROPN
ejpam-3904	336	35	(	(	PUNCT
ejpam-3904	336	36	{	{	PUNCT
ejpam-3904	336	37	x	x	NOUN
ejpam-3904	336	38	}	}	PUNCT
ejpam-3904	336	39	×	×	PROPN
ejpam-3904	336	40	sx	sx	PROPN
ejpam-3904	336	41	}	}	PUNCT
ejpam-3904	336	42	)	)	PUNCT
ejpam-3904	336	43	be	be	AUX
ejpam-3904	336	44	a	a	DET
ejpam-3904	336	45	γit	γit	ADV
ejpam-3904	336	46	-	-	PUNCT
ejpam-3904	336	47	set	set	NOUN
ejpam-3904	336	48	of	of	ADP
ejpam-3904	336	49	g[kp	g[kp	PROPN
ejpam-3904	336	50	]	]	PUNCT
ejpam-3904	336	51	.	.	PUNCT
ejpam-3904	337	1	in	in	ADP
ejpam-3904	337	2	view	view	NOUN
ejpam-3904	337	3	of	of	ADP
ejpam-3904	337	4	proposition	proposition	NOUN
ejpam-3904	337	5	5	5	NUM
ejpam-3904	337	6	,	,	PUNCT
ejpam-3904	337	7	s	s	VERB
ejpam-3904	337	8	is	be	AUX
ejpam-3904	337	9	an	an	DET
ejpam-3904	337	10	itd	itd	NOUN
ejpam-3904	337	11	-	-	PUNCT
ejpam-3904	337	12	set	set	NOUN
ejpam-3904	337	13	of	of	ADP
ejpam-3904	337	14	g.	g.	PROPN
ejpam-3904	337	15	write	write	VERB
ejpam-3904	337	16	c	c	PROPN
ejpam-3904	337	17	=	=	SYM
ejpam-3904	337	18	(	(	PUNCT
ejpam-3904	337	19	∪x∈mg(s	∪x∈mg(s	NOUN
ejpam-3904	337	20	)	)	PUNCT
ejpam-3904	337	21	(	(	PUNCT
ejpam-3904	337	22	{	{	PUNCT
ejpam-3904	337	23	x	x	NOUN
ejpam-3904	337	24	}	}	PUNCT
ejpam-3904	337	25	×	×	PROPN
ejpam-3904	337	26	sx	sx	PROPN
ejpam-3904	337	27	)	)	PUNCT
ejpam-3904	337	28	)	)	PUNCT
ejpam-3904	337	29	∪	∪	ADP
ejpam-3904	337	30	(	(	PUNCT
ejpam-3904	337	31	∪x∈s\mg(s	∪x∈s\mg(s	PUNCT
ejpam-3904	337	32	)	)	PUNCT
ejpam-3904	337	33	(	(	PUNCT
ejpam-3904	337	34	{	{	PUNCT
ejpam-3904	337	35	x	x	NOUN
ejpam-3904	337	36	}	}	PUNCT
ejpam-3904	337	37	×	×	PROPN
ejpam-3904	337	38	sx	sx	PROPN
ejpam-3904	337	39	)	)	PUNCT
ejpam-3904	337	40	)	)	PUNCT
ejpam-3904	337	41	,	,	PUNCT
ejpam-3904	337	42	and	and	CCONJ
ejpam-3904	337	43	we	we	PRON
ejpam-3904	337	44	claim	claim	VERB
ejpam-3904	337	45	that	that	SCONJ
ejpam-3904	337	46	sx	sx	PROPN
ejpam-3904	337	47	=	=	PUNCT
ejpam-3904	337	48	v	v	PROPN
ejpam-3904	337	49	(	(	PUNCT
ejpam-3904	337	50	kp	kp	PROPN
ejpam-3904	337	51	)	)	PUNCT
ejpam-3904	337	52	for	for	ADP
ejpam-3904	337	53	all	all	DET
ejpam-3904	337	54	x	x	SYM
ejpam-3904	337	55	∈	∈	NOUN
ejpam-3904	337	56	mg(s	mg(s	NOUN
ejpam-3904	337	57	)	)	PUNCT
ejpam-3904	337	58	.	.	PUNCT
ejpam-3904	338	1	let	let	VERB
ejpam-3904	338	2	x	x	PUNCT
ejpam-3904	338	3	∈	∈	PROPN
ejpam-3904	338	4	mg(s	mg(s	NOUN
ejpam-3904	338	5	)	)	PUNCT
ejpam-3904	338	6	,	,	PUNCT
ejpam-3904	338	7	and	and	CCONJ
ejpam-3904	338	8	let	let	VERB
ejpam-3904	338	9	y	y	PROPN
ejpam-3904	338	10	∈	∈	PROPN
ejpam-3904	338	11	v	v	PROPN
ejpam-3904	338	12	(	(	PUNCT
ejpam-3904	338	13	kp	kp	PROPN
ejpam-3904	338	14	)	)	PUNCT
ejpam-3904	338	15	.	.	PUNCT
ejpam-3904	339	1	pick	pick	VERB
ejpam-3904	339	2	a	a	DET
ejpam-3904	339	3	β0	β0	NOUN
ejpam-3904	339	4	-	-	PUNCT
ejpam-3904	339	5	set	set	NOUN
ejpam-3904	339	6	a	a	DET
ejpam-3904	339	7	⊆	⊆	NUM
ejpam-3904	339	8	v	v	NOUN
ejpam-3904	339	9	(	(	PUNCT
ejpam-3904	339	10	g	g	NOUN
ejpam-3904	339	11	)	)	PUNCT
ejpam-3904	339	12	of	of	ADP
ejpam-3904	339	13	g	g	NOUN
ejpam-3904	339	14	for	for	ADP
ejpam-3904	339	15	which	which	PRON
ejpam-3904	339	16	x	x	SYM
ejpam-3904	339	17	∈	∈	NOUN
ejpam-3904	339	18	s	s	PART
ejpam-3904	339	19	∩	∩	ADJ
ejpam-3904	339	20	a.	a.	NOUN
ejpam-3904	339	21	by	by	ADP
ejpam-3904	339	22	proposition	proposition	NOUN
ejpam-3904	339	23	5(ii	5(ii	NUM
ejpam-3904	339	24	)	)	PUNCT
ejpam-3904	339	25	,	,	PUNCT
ejpam-3904	339	26	since	since	SCONJ
ejpam-3904	339	27	{	{	PUNCT
ejpam-3904	339	28	y	y	NOUN
ejpam-3904	339	29	}	}	PUNCT
ejpam-3904	339	30	is	be	AUX
ejpam-3904	339	31	a	a	DET
ejpam-3904	339	32	β0	β0	NOUN
ejpam-3904	339	33	-	-	PUNCT
ejpam-3904	339	34	set	set	NOUN
ejpam-3904	339	35	of	of	ADP
ejpam-3904	339	36	kp	kp	NOUN
ejpam-3904	339	37	,	,	PUNCT
ejpam-3904	339	38	there	there	PRON
ejpam-3904	339	39	exists	exist	VERB
ejpam-3904	339	40	u	u	PROPN
ejpam-3904	339	41	∈	∈	PROPN
ejpam-3904	339	42	s∩a	s∩a	PROPN
ejpam-3904	339	43	,	,	PUNCT
ejpam-3904	339	44	consequently	consequently	ADV
ejpam-3904	339	45	u	u	NOUN
ejpam-3904	339	46	∈mg(s	∈mg(s	NOUN
ejpam-3904	339	47	)	)	PUNCT
ejpam-3904	339	48	,	,	PUNCT
ejpam-3904	339	49	such	such	ADJ
ejpam-3904	339	50	that	that	DET
ejpam-3904	339	51	su	su	PROPN
ejpam-3904	340	1	=	=	PRON
ejpam-3904	340	2	{	{	PUNCT
ejpam-3904	340	3	y	y	NOUN
ejpam-3904	340	4	}	}	PUNCT
ejpam-3904	340	5	.	.	PUNCT
ejpam-3904	341	1	by	by	ADP
ejpam-3904	341	2	the	the	DET
ejpam-3904	341	3	minimality	minimality	NOUN
ejpam-3904	341	4	of	of	ADP
ejpam-3904	341	5	the	the	DET
ejpam-3904	341	6	cardinality	cardinality	NOUN
ejpam-3904	341	7	of	of	ADP
ejpam-3904	341	8	mg(s	mg(s	NOUN
ejpam-3904	341	9	)	)	PUNCT
ejpam-3904	341	10	,	,	PUNCT
ejpam-3904	341	11	x	x	X
ejpam-3904	341	12	=	=	PUNCT
ejpam-3904	341	13	u	u	NOUN
ejpam-3904	341	14	so	so	SCONJ
ejpam-3904	341	15	that	that	SCONJ
ejpam-3904	341	16	y	y	PROPN
ejpam-3904	341	17	∈	∈	PROPN
ejpam-3904	341	18	sx	sx	PROPN
ejpam-3904	341	19	.	.	PUNCT
ejpam-3904	341	20	accordingly	accordingly	ADV
ejpam-3904	341	21	,	,	PUNCT
ejpam-3904	341	22	sx	sx	PROPN
ejpam-3904	341	23	=	=	SYM
ejpam-3904	341	24	v	v	PROPN
ejpam-3904	341	25	(	(	PUNCT
ejpam-3904	341	26	kp	kp	PROPN
ejpam-3904	341	27	)	)	PUNCT
ejpam-3904	341	28	.	.	PUNCT
ejpam-3904	342	1	thus	thus	ADV
ejpam-3904	342	2	,	,	PUNCT
ejpam-3904	342	3	γit(g	γit(g	PROPN
ejpam-3904	342	4	◦	◦	NOUN
ejpam-3904	342	5	kp	kp	NOUN
ejpam-3904	342	6	)	)	PUNCT
ejpam-3904	342	7	=	=	SYM
ejpam-3904	342	8	|c|	|c|	PROPN
ejpam-3904	342	9	≥	≥	NOUN
ejpam-3904	342	10	p	p	X
ejpam-3904	342	11	·	·	PUNCT
ejpam-3904	342	12	η(g	η(g	NUM
ejpam-3904	342	13	)	)	PUNCT
ejpam-3904	342	14	+	+	CCONJ
ejpam-3904	342	15	(	(	PUNCT
ejpam-3904	342	16	|s|	|s|	NOUN
ejpam-3904	342	17	−	−	PROPN
ejpam-3904	342	18	η(g	η(g	PROPN
ejpam-3904	342	19	)	)	PUNCT
ejpam-3904	342	20	)	)	PUNCT
ejpam-3904	342	21	≥	≥	NOUN
ejpam-3904	342	22	(	(	PUNCT
ejpam-3904	342	23	p−	p−	NOUN
ejpam-3904	342	24	1)η(g	1)η(g	NUM
ejpam-3904	342	25	)	)	PUNCT
ejpam-3904	342	26	+	+	NUM
ejpam-3904	342	27	γit(g	γit(g	NOUN
ejpam-3904	342	28	)	)	PUNCT
ejpam-3904	342	29	.	.	PUNCT
ejpam-3904	343	1	similar	similar	ADJ
ejpam-3904	343	2	arguments	argument	NOUN
ejpam-3904	343	3	will	will	AUX
ejpam-3904	343	4	prove	prove	VERB
ejpam-3904	343	5	the	the	DET
ejpam-3904	343	6	desired	desire	VERB
ejpam-3904	343	7	results	result	NOUN
ejpam-3904	343	8	for	for	ADP
ejpam-3904	343	9	γitt(g	γitt(g	NOUN
ejpam-3904	343	10	◦	◦	NOUN
ejpam-3904	343	11	kp	kp	NOUN
ejpam-3904	343	12	)	)	PUNCT
ejpam-3904	343	13	.	.	PUNCT
ejpam-3904	344	1	if	if	SCONJ
ejpam-3904	344	2	,	,	PUNCT
ejpam-3904	344	3	in	in	ADP
ejpam-3904	344	4	particular	particular	ADJ
ejpam-3904	344	5	,	,	PUNCT
ejpam-3904	344	6	g	g	PROPN
ejpam-3904	344	7	=	=	SYM
ejpam-3904	344	8	k1,n	k1,n	PROPN
ejpam-3904	344	9	on	on	ADP
ejpam-3904	344	10	n+	n+	ADP
ejpam-3904	344	11	1	1	NUM
ejpam-3904	344	12	vertices	vertex	NOUN
ejpam-3904	344	13	,	,	PUNCT
ejpam-3904	344	14	then	then	ADV
ejpam-3904	344	15	η(g	η(g	NUM
ejpam-3904	344	16	)	)	PUNCT
ejpam-3904	344	17	=	=	SYM
ejpam-3904	344	18	1	1	NUM
ejpam-3904	344	19	,	,	PUNCT
ejpam-3904	344	20	γit(g	γit(g	PROPN
ejpam-3904	344	21	)	)	PUNCT
ejpam-3904	344	22	=	=	SYM
ejpam-3904	344	23	γitt(g	γitt(g	NOUN
ejpam-3904	344	24	)	)	PUNCT
ejpam-3904	344	25	=	=	SYM
ejpam-3904	344	26	2	2	NUM
ejpam-3904	344	27	,	,	PUNCT
ejpam-3904	344	28	and	and	CCONJ
ejpam-3904	344	29	γit(g[kp	γit(g[kp	PROPN
ejpam-3904	344	30	]	]	PUNCT
ejpam-3904	344	31	)	)	PUNCT
ejpam-3904	344	32	=	=	SYM
ejpam-3904	344	33	γitt(g[kp	γitt(g[kp	NOUN
ejpam-3904	344	34	]	]	X
ejpam-3904	344	35	)	)	PUNCT
ejpam-3904	344	36	=	=	SYM
ejpam-3904	344	37	p+	p+	ADJ
ejpam-3904	344	38	1	1	NUM
ejpam-3904	344	39	.	.	PUNCT
ejpam-3904	345	1	acknowledgements	acknowledgement	NOUN
ejpam-3904	345	2	the	the	DET
ejpam-3904	345	3	authors	author	NOUN
ejpam-3904	345	4	would	would	AUX
ejpam-3904	345	5	like	like	VERB
ejpam-3904	345	6	to	to	PART
ejpam-3904	345	7	thank	thank	VERB
ejpam-3904	345	8	the	the	DET
ejpam-3904	345	9	referees	referee	NOUN
ejpam-3904	345	10	for	for	ADP
ejpam-3904	345	11	reviewing	review	VERB
ejpam-3904	345	12	the	the	DET
ejpam-3904	345	13	initial	initial	ADJ
ejpam-3904	345	14	paper	paper	NOUN
ejpam-3904	345	15	and	and	CCONJ
ejpam-3904	345	16	for	for	ADP
ejpam-3904	345	17	the	the	DET
ejpam-3904	345	18	invaluable	invaluable	ADJ
ejpam-3904	345	19	comments	comment	NOUN
ejpam-3904	345	20	and	and	CCONJ
ejpam-3904	345	21	suggestions	suggestion	NOUN
ejpam-3904	345	22	that	that	PRON
ejpam-3904	345	23	eventually	eventually	ADV
ejpam-3904	345	24	led	lead	VERB
ejpam-3904	345	25	to	to	ADP
ejpam-3904	345	26	this	this	DET
ejpam-3904	345	27	much	much	ADV
ejpam-3904	345	28	improved	improved	ADJ
ejpam-3904	345	29	version	version	NOUN
ejpam-3904	345	30	of	of	ADP
ejpam-3904	345	31	the	the	DET
ejpam-3904	345	32	work	work	NOUN
ejpam-3904	345	33	.	.	PUNCT
ejpam-3904	346	1	this	this	DET
ejpam-3904	346	2	research	research	NOUN
ejpam-3904	346	3	is	be	AUX
ejpam-3904	346	4	funded	fund	VERB
ejpam-3904	346	5	by	by	ADP
ejpam-3904	346	6	the	the	DET
ejpam-3904	346	7	department	department	PROPN
ejpam-3904	346	8	of	of	ADP
ejpam-3904	346	9	science	science	NOUN
ejpam-3904	346	10	and	and	CCONJ
ejpam-3904	346	11	technology	technology	NOUN
ejpam-3904	346	12	accelerated	accelerate	VERB
ejpam-3904	346	13	science	science	NOUN
ejpam-3904	346	14	and	and	CCONJ
ejpam-3904	346	15	technology	technology	NOUN
ejpam-3904	346	16	human	human	ADJ
ejpam-3904	346	17	resource	resource	NOUN
ejpam-3904	346	18	development	development	NOUN
ejpam-3904	346	19	program	program	NOUN
ejpam-3904	346	20	(	(	PUNCT
ejpam-3904	346	21	dostasthrdp	dostasthrdp	PROPN
ejpam-3904	346	22	)	)	PUNCT
ejpam-3904	346	23	,	,	PUNCT
ejpam-3904	346	24	philippines	philippine	NOUN
ejpam-3904	346	25	.	.	PUNCT
ejpam-3904	347	1	references	reference	NOUN
ejpam-3904	347	2	162	162	NUM
ejpam-3904	347	3	references	reference	NOUN
ejpam-3904	347	4	[	[	X
ejpam-3904	347	5	1	1	NUM
ejpam-3904	347	6	]	]	PUNCT
ejpam-3904	347	7	c.	c.	PROPN
ejpam-3904	347	8	berge	berge	PROPN
ejpam-3904	347	9	.	.	PUNCT
ejpam-3904	348	1	theory	theory	NOUN
ejpam-3904	348	2	of	of	ADP
ejpam-3904	348	3	graphs	graph	NOUN
ejpam-3904	348	4	and	and	CCONJ
ejpam-3904	348	5	its	its	PRON
ejpam-3904	348	6	applications	application	NOUN
ejpam-3904	348	7	.	.	PUNCT
ejpam-3904	349	1	methuen	methuen	PROPN
ejpam-3904	349	2	,	,	PUNCT
ejpam-3904	349	3	london	london	PROPN
ejpam-3904	349	4	,	,	PUNCT
ejpam-3904	349	5	1962	1962	NUM
ejpam-3904	349	6	.	.	PUNCT
ejpam-3904	350	1	[	[	X
ejpam-3904	350	2	2	2	X
ejpam-3904	350	3	]	]	X
ejpam-3904	350	4	j.a	j.a	PROPN
ejpam-3904	350	5	.	.	PROPN
ejpam-3904	350	6	bondy	bondy	PROPN
ejpam-3904	350	7	and	and	CCONJ
ejpam-3904	350	8	geng	geng	PROPN
ejpam-3904	350	9	hau	hau	PROPN
ejpam-3904	350	10	fan	fan	PROPN
ejpam-3904	350	11	.	.	PUNCT
ejpam-3904	351	1	a	a	DET
ejpam-3904	351	2	sufficient	sufficient	ADJ
ejpam-3904	351	3	condition	condition	NOUN
ejpam-3904	351	4	for	for	ADP
ejpam-3904	351	5	dominating	dominating	NOUN
ejpam-3904	351	6	cycles	cycle	NOUN
ejpam-3904	351	7	.	.	PUNCT
ejpam-3904	352	1	discrete	discrete	ADJ
ejpam-3904	352	2	math	math	NOUN
ejpam-3904	352	3	,	,	PUNCT
ejpam-3904	352	4	67(2):205–208	67(2):205–208	NOUN
ejpam-3904	352	5	,	,	PUNCT
ejpam-3904	352	6	1987	1987	NUM
ejpam-3904	352	7	.	.	PUNCT
ejpam-3904	353	1	[	[	X
ejpam-3904	353	2	3	3	X
ejpam-3904	353	3	]	]	X
ejpam-3904	353	4	c.	c.	PROPN
ejpam-3904	353	5	brausee	brausee	PROPN
ejpam-3904	353	6	,	,	PUNCT
ejpam-3904	353	7	k.	k.	PROPN
ejpam-3904	353	8	ozekie	ozekie	PROPN
ejpam-3904	353	9	m.	m.	PROPN
ejpam-3904	353	10	a.	a.	PROPN
ejpam-3904	353	11	henning	henning	PROPN
ejpam-3904	353	12	,	,	PUNCT
ejpam-3904	353	13	i.	i.	PROPN
ejpam-3904	353	14	schiermeyere	schiermeyere	ADV
ejpam-3904	353	15	,	,	PUNCT
ejpam-3904	353	16	and	and	CCONJ
ejpam-3904	353	17	e.	e.	PROPN
ejpam-3904	353	18	vumar	vumar	PROPN
ejpam-3904	353	19	.	.	PUNCT
ejpam-3904	354	1	on	on	ADP
ejpam-3904	354	2	upper	upper	ADJ
ejpam-3904	354	3	bounds	bound	NOUN
ejpam-3904	354	4	for	for	ADP
ejpam-3904	354	5	the	the	DET
ejpam-3904	354	6	independent	independent	ADJ
ejpam-3904	354	7	transversal	transversal	ADJ
ejpam-3904	354	8	domination	domination	NOUN
ejpam-3904	354	9	number	number	NOUN
ejpam-3904	354	10	.	.	PUNCT
ejpam-3904	355	1	discrete	discrete	ADJ
ejpam-3904	355	2	applied	apply	VERB
ejpam-3904	355	3	mathematics	mathematic	NOUN
ejpam-3904	355	4	,	,	PUNCT
ejpam-3904	355	5	236:66–72	236:66–72	NUM
ejpam-3904	355	6	,	,	PUNCT
ejpam-3904	355	7	2018	2018	NUM
ejpam-3904	355	8	.	.	PUNCT
ejpam-3904	356	1	[	[	X
ejpam-3904	356	2	4	4	NUM
ejpam-3904	356	3	]	]	X
ejpam-3904	356	4	f.	f.	PROPN
ejpam-3904	356	5	buckley	buckley	PROPN
ejpam-3904	356	6	and	and	CCONJ
ejpam-3904	356	7	f.	f.	PROPN
ejpam-3904	356	8	harary	harary	PROPN
ejpam-3904	356	9	.	.	PUNCT
ejpam-3904	357	1	distance	distance	NOUN
ejpam-3904	357	2	in	in	ADP
ejpam-3904	357	3	graphs	graph	NOUN
ejpam-3904	357	4	.	.	PUNCT
ejpam-3904	358	1	addison	addison	PROPN
ejpam-3904	358	2	-	-	PUNCT
ejpam-3904	358	3	wesley	wesley	PROPN
ejpam-3904	358	4	,	,	PUNCT
ejpam-3904	358	5	redwood	redwood	NOUN
ejpam-3904	358	6	city	city	NOUN
ejpam-3904	358	7	,	,	PUNCT
ejpam-3904	358	8	ca	ca	NOUN
ejpam-3904	358	9	,	,	PUNCT
ejpam-3904	358	10	1990	1990	NUM
ejpam-3904	358	11	.	.	PUNCT
ejpam-3904	359	1	[	[	X
ejpam-3904	359	2	5	5	NUM
ejpam-3904	359	3	]	]	X
ejpam-3904	359	4	s.r	s.r	PROPN
ejpam-3904	359	5	.	.	PROPN
ejpam-3904	359	6	canoy	canoy	PROPN
ejpam-3904	359	7	and	and	CCONJ
ejpam-3904	359	8	c.e	c.e	PROPN
ejpam-3904	359	9	.	.	PROPN
ejpam-3904	359	10	go	go	VERB
ejpam-3904	359	11	.	.	PUNCT
ejpam-3904	360	1	domination	domination	NOUN
ejpam-3904	360	2	in	in	ADP
ejpam-3904	360	3	the	the	DET
ejpam-3904	360	4	corona	corona	NOUN
ejpam-3904	360	5	and	and	CCONJ
ejpam-3904	360	6	join	join	VERB
ejpam-3904	360	7	of	of	ADP
ejpam-3904	360	8	graphs	graph	NOUN
ejpam-3904	360	9	.	.	PUNCT
ejpam-3904	361	1	international	international	ADJ
ejpam-3904	361	2	mathematical	mathematical	PROPN
ejpam-3904	361	3	forum	forum	PROPN
ejpam-3904	361	4	,	,	PUNCT
ejpam-3904	361	5	6(16):763–771	6(16):763–771	NUM
ejpam-3904	361	6	,	,	PUNCT
ejpam-3904	361	7	2011	2011	NUM
ejpam-3904	361	8	.	.	PUNCT
ejpam-3904	362	1	[	[	X
ejpam-3904	362	2	6	6	NUM
ejpam-3904	362	3	]	]	PUNCT
ejpam-3904	362	4	e.	e.	PROPN
ejpam-3904	362	5	cockayne	cockayne	PROPN
ejpam-3904	362	6	,	,	PUNCT
ejpam-3904	362	7	r.m	r.m	PROPN
ejpam-3904	362	8	.	.	PROPN
ejpam-3904	362	9	dawes	dawes	PROPN
ejpam-3904	362	10	,	,	PUNCT
ejpam-3904	362	11	and	and	CCONJ
ejpam-3904	362	12	s.t	s.t	PROPN
ejpam-3904	362	13	.	.	PROPN
ejpam-3904	362	14	hedetniemi	hedetniemi	PROPN
ejpam-3904	362	15	.	.	PUNCT
ejpam-3904	363	1	total	total	ADJ
ejpam-3904	363	2	domination	domination	NOUN
ejpam-3904	363	3	in	in	ADP
ejpam-3904	363	4	graphs	graph	NOUN
ejpam-3904	363	5	.	.	PUNCT
ejpam-3904	364	1	networks	network	NOUN
ejpam-3904	364	2	,	,	PUNCT
ejpam-3904	364	3	10(3):211–219	10(3):211–219	NUM
ejpam-3904	364	4	,	,	PUNCT
ejpam-3904	364	5	2006	2006	NUM
ejpam-3904	364	6	.	.	PUNCT
ejpam-3904	365	1	[	[	X
ejpam-3904	365	2	7	7	NUM
ejpam-3904	365	3	]	]	X
ejpam-3904	365	4	e.j	e.j	PROPN
ejpam-3904	365	5	.	.	PROPN
ejpam-3904	365	6	cockayne	cockayne	PROPN
ejpam-3904	365	7	and	and	CCONJ
ejpam-3904	365	8	s.t	s.t	PROPN
ejpam-3904	365	9	.	.	PROPN
ejpam-3904	365	10	hedetniemi	hedetniemi	PROPN
ejpam-3904	365	11	.	.	PUNCT
ejpam-3904	366	1	towards	towards	ADP
ejpam-3904	366	2	a	a	DET
ejpam-3904	366	3	theory	theory	NOUN
ejpam-3904	366	4	of	of	ADP
ejpam-3904	366	5	domination	domination	NOUN
ejpam-3904	366	6	in	in	ADP
ejpam-3904	366	7	graphs	graph	NOUN
ejpam-3904	366	8	.	.	PUNCT
ejpam-3904	367	1	networks	network	NOUN
ejpam-3904	367	2	,	,	PUNCT
ejpam-3904	367	3	7(3):247–261	7(3):247–261	NUM
ejpam-3904	367	4	,	,	PUNCT
ejpam-3904	367	5	1997	1997	NUM
ejpam-3904	367	6	.	.	PUNCT
ejpam-3904	368	1	[	[	X
ejpam-3904	368	2	8	8	NUM
ejpam-3904	368	3	]	]	X
ejpam-3904	368	4	w.j	w.j	PROPN
ejpam-3904	368	5	.	.	PROPN
ejpam-3904	368	6	desormeauxe	desormeauxe	PROPN
ejpam-3904	368	7	,	,	PUNCT
ejpam-3904	368	8	t.w	t.w	PROPN
ejpam-3904	368	9	.	.	PROPN
ejpam-3904	368	10	haynes	haynes	PROPN
ejpam-3904	368	11	,	,	PUNCT
ejpam-3904	368	12	and	and	CCONJ
ejpam-3904	368	13	m.a	m.a	PROPN
ejpam-3904	368	14	.	.	PROPN
ejpam-3904	368	15	henning	henning	PROPN
ejpam-3904	368	16	.	.	PUNCT
ejpam-3904	369	1	an	an	DET
ejpam-3904	369	2	extremal	extremal	ADJ
ejpam-3904	369	3	problem	problem	NOUN
ejpam-3904	369	4	for	for	ADP
ejpam-3904	369	5	total	total	ADJ
ejpam-3904	369	6	domination	domination	NOUN
ejpam-3904	369	7	stable	stable	ADJ
ejpam-3904	369	8	graphs	graph	NOUN
ejpam-3904	369	9	upon	upon	SCONJ
ejpam-3904	369	10	edge	edge	NOUN
ejpam-3904	369	11	removal	removal	NOUN
ejpam-3904	369	12	.	.	PUNCT
ejpam-3904	370	1	discrete	discrete	ADJ
ejpam-3904	370	2	appl	appl	PROPN
ejpam-3904	370	3	.	.	PUNCT
ejpam-3904	370	4	math	math	PROPN
ejpam-3904	370	5	,	,	PUNCT
ejpam-3904	370	6	159:1048–1052	159:1048–1052	NUM
ejpam-3904	370	7	,	,	PUNCT
ejpam-3904	370	8	2011	2011	NUM
ejpam-3904	370	9	.	.	PUNCT
ejpam-3904	371	1	[	[	X
ejpam-3904	371	2	9	9	NUM
ejpam-3904	371	3	]	]	PUNCT
ejpam-3904	371	4	allan	allan	PROPN
ejpam-3904	371	5	frendrupe	frendrupe	PROPN
ejpam-3904	371	6	,	,	PUNCT
ejpam-3904	371	7	michael	michael	PROPN
ejpam-3904	371	8	a.	a.	PROPN
ejpam-3904	371	9	henningbe	henningbe	PROPN
ejpam-3904	371	10	,	,	PUNCT
ejpam-3904	371	11	bert	bert	PROPN
ejpam-3904	371	12	randerathe	randerathe	PROPN
ejpam-3904	371	13	,	,	PUNCT
ejpam-3904	371	14	and	and	CCONJ
ejpam-3904	371	15	preben	preben	PROPN
ejpam-3904	371	16	dahl	dahl	PROPN
ejpam-3904	371	17	vestergaard	vestergaard	PROPN
ejpam-3904	371	18	.	.	PUNCT
ejpam-3904	372	1	an	an	DET
ejpam-3904	372	2	upper	upper	ADJ
ejpam-3904	372	3	bound	bind	VERB
ejpam-3904	372	4	on	on	ADP
ejpam-3904	372	5	the	the	DET
ejpam-3904	372	6	domination	domination	NOUN
ejpam-3904	372	7	number	number	NOUN
ejpam-3904	372	8	of	of	ADP
ejpam-3904	372	9	a	a	DET
ejpam-3904	372	10	graph	graph	NOUN
ejpam-3904	372	11	with	with	ADP
ejpam-3904	372	12	minimum	minimum	NOUN
ejpam-3904	372	13	degree	degree	NOUN
ejpam-3904	372	14	2	2	NUM
ejpam-3904	372	15	.	.	PUNCT
ejpam-3904	372	16	discrete	discrete	ADJ
ejpam-3904	372	17	mathematics	mathematic	NOUN
ejpam-3904	372	18	,	,	PUNCT
ejpam-3904	372	19	309:639–646	309:639–646	NUM
ejpam-3904	372	20	,	,	PUNCT
ejpam-3904	372	21	2009	2009	NUM
ejpam-3904	372	22	.	.	PUNCT
ejpam-3904	373	1	[	[	X
ejpam-3904	373	2	10	10	NUM
ejpam-3904	373	3	]	]	X
ejpam-3904	373	4	i.s	i.s	PROPN
ejpam-3904	373	5	.	.	PROPN
ejpam-3904	373	6	hamid	hamid	PROPN
ejpam-3904	373	7	.	.	PUNCT
ejpam-3904	374	1	independent	independent	ADJ
ejpam-3904	374	2	transversal	transversal	ADJ
ejpam-3904	374	3	domination	domination	NOUN
ejpam-3904	374	4	in	in	ADP
ejpam-3904	374	5	graphs	graph	NOUN
ejpam-3904	374	6	.	.	PUNCT
ejpam-3904	375	1	discussiones	discussione	NOUN
ejpam-3904	375	2	mathematicae	mathematicae	VERB
ejpam-3904	375	3	,	,	PUNCT
ejpam-3904	375	4	graph	graph	NOUN
ejpam-3904	375	5	theory	theory	NOUN
ejpam-3904	375	6	,	,	PUNCT
ejpam-3904	375	7	32:5–17	32:5–17	NUM
ejpam-3904	375	8	,	,	PUNCT
ejpam-3904	375	9	2012	2012	NUM
ejpam-3904	375	10	.	.	PUNCT
ejpam-3904	376	1	[	[	X
ejpam-3904	376	2	11	11	NUM
ejpam-3904	376	3	]	]	X
ejpam-3904	376	4	t.w	t.w	PROPN
ejpam-3904	376	5	.	.	PROPN
ejpam-3904	376	6	haynese	haynese	PROPN
ejpam-3904	376	7	,	,	PUNCT
ejpam-3904	376	8	s.t	s.t	PROPN
ejpam-3904	376	9	.	.	PROPN
ejpam-3904	376	10	hedetniemi	hedetniemi	PROPN
ejpam-3904	376	11	,	,	PUNCT
ejpam-3904	376	12	and	and	CCONJ
ejpam-3904	376	13	p.j	p.j	PROPN
ejpam-3904	376	14	.	.	PROPN
ejpam-3904	376	15	slater	slater	PROPN
ejpam-3904	376	16	.	.	PUNCT
ejpam-3904	377	1	fundamentals	fundamental	NOUN
ejpam-3904	377	2	of	of	ADP
ejpam-3904	377	3	domination	domination	NOUN
ejpam-3904	377	4	in	in	ADP
ejpam-3904	377	5	graphs	graph	NOUN
ejpam-3904	377	6	.	.	PUNCT
ejpam-3904	378	1	marcel	marcel	PROPN
ejpam-3904	378	2	dekker	dekker	PROPN
ejpam-3904	378	3	,	,	PUNCT
ejpam-3904	378	4	inc	inc	PROPN
ejpam-3904	378	5	.	.	PROPN
ejpam-3904	378	6	,	,	PUNCT
ejpam-3904	378	7	new	new	PROPN
ejpam-3904	378	8	york	york	PROPN
ejpam-3904	378	9	,	,	PUNCT
ejpam-3904	378	10	1998	1998	NUM
ejpam-3904	378	11	.	.	PUNCT
ejpam-3904	379	1	[	[	X
ejpam-3904	379	2	12	12	NUM
ejpam-3904	379	3	]	]	PUNCT
ejpam-3904	379	4	m.	m.	NOUN
ejpam-3904	379	5	henning	henning	PROPN
ejpam-3904	379	6	and	and	CCONJ
ejpam-3904	379	7	a.	a.	PROPN
ejpam-3904	379	8	yeo	yeo	PROPN
ejpam-3904	379	9	.	.	PROPN
ejpam-3904	380	1	total	total	ADJ
ejpam-3904	380	2	domination	domination	NOUN
ejpam-3904	380	3	in	in	ADP
ejpam-3904	380	4	graphs	graph	NOUN
ejpam-3904	380	5	.	.	PUNCT
ejpam-3904	381	1	springer	springer	NOUN
ejpam-3904	381	2	,	,	PUNCT
ejpam-3904	381	3	new	new	PROPN
ejpam-3904	381	4	york	york	PROPN
ejpam-3904	381	5	,	,	PUNCT
ejpam-3904	381	6	2013	2013	NUM
ejpam-3904	381	7	.	.	PUNCT
ejpam-3904	382	1	[	[	X
ejpam-3904	382	2	13	13	NUM
ejpam-3904	382	3	]	]	SYM
ejpam-3904	382	4	min	min	PROPN
ejpam-3904	382	5	-	-	PROPN
ejpam-3904	382	6	jen	jen	PROPN
ejpam-3904	382	7	jou	jou	INTJ
ejpam-3904	382	8	and	and	CCONJ
ejpam-3904	382	9	g.	g.	PROPN
ejpam-3904	382	10	j.	j.	PROPN
ejpam-3904	382	11	chang	chang	PROPN
ejpam-3904	382	12	.	.	PUNCT
ejpam-3904	383	1	the	the	DET
ejpam-3904	383	2	number	number	NOUN
ejpam-3904	383	3	of	of	ADP
ejpam-3904	383	4	maximum	maximum	ADJ
ejpam-3904	383	5	independent	independent	ADJ
ejpam-3904	383	6	sets	set	NOUN
ejpam-3904	383	7	in	in	ADP
ejpam-3904	383	8	graphs	graph	NOUN
ejpam-3904	383	9	.	.	PUNCT
ejpam-3904	384	1	taiwanese	taiwanese	ADJ
ejpam-3904	384	2	journal	journal	NOUN
ejpam-3904	384	3	of	of	ADP
ejpam-3904	384	4	mathematics	mathematic	NOUN
ejpam-3904	384	5	,	,	PUNCT
ejpam-3904	384	6	4(4):685–695	4(4):685–695	NUM
ejpam-3904	384	7	,	,	PUNCT
ejpam-3904	384	8	2000	2000	NUM
ejpam-3904	384	9	.	.	PUNCT
ejpam-3904	385	1	[	[	X
ejpam-3904	385	2	14	14	NUM
ejpam-3904	385	3	]	]	X
ejpam-3904	385	4	r.p	r.p	PROPN
ejpam-3904	385	5	.	.	PROPN
ejpam-3904	385	6	malalay	malalay	PROPN
ejpam-3904	385	7	and	and	CCONJ
ejpam-3904	385	8	f.p	f.p	PROPN
ejpam-3904	385	9	.	.	PROPN
ejpam-3904	385	10	jamil	jamil	PROPN
ejpam-3904	385	11	.	.	PUNCT
ejpam-3904	386	1	on	on	ADP
ejpam-3904	386	2	disjunctive	disjunctive	ADJ
ejpam-3904	386	3	domination	domination	NOUN
ejpam-3904	386	4	in	in	ADP
ejpam-3904	386	5	graphs	graph	NOUN
ejpam-3904	386	6	.	.	PUNCT
ejpam-3904	387	1	quaestiones	quaestione	NOUN
ejpam-3904	387	2	mathematicae	mathematicae	PROPN
ejpam-3904	387	3	,	,	PUNCT
ejpam-3904	387	4	43(2):149–168	43(2):149–168	PROPN
ejpam-3904	387	5	,	,	PUNCT
ejpam-3904	387	6	2020	2020	NUM
ejpam-3904	387	7	.	.	PUNCT
ejpam-3904	388	1	[	[	X
ejpam-3904	388	2	15	15	NUM
ejpam-3904	388	3	]	]	X
ejpam-3904	388	4	e.	e.	PROPN
ejpam-3904	388	5	maravillae	maravillae	PROPN
ejpam-3904	388	6	,	,	PUNCT
ejpam-3904	388	7	r.t	r.t	PROPN
ejpam-3904	388	8	.	.	PROPN
ejpam-3904	388	9	isla	isla	PROPN
ejpam-3904	388	10	,	,	PUNCT
ejpam-3904	388	11	and	and	CCONJ
ejpam-3904	388	12	s.r	s.r	PROPN
ejpam-3904	388	13	.	.	PROPN
ejpam-3904	388	14	canoy	canoy	PROPN
ejpam-3904	388	15	jr	jr	PROPN
ejpam-3904	388	16	.	.	PROPN
ejpam-3904	388	17	fair	fair	ADJ
ejpam-3904	388	18	domination	domination	NOUN
ejpam-3904	388	19	in	in	ADP
ejpam-3904	388	20	the	the	DET
ejpam-3904	388	21	join	join	NOUN
ejpam-3904	388	22	,	,	PUNCT
ejpam-3904	388	23	corona	corona	NOUN
ejpam-3904	388	24	and	and	CCONJ
ejpam-3904	388	25	composition	composition	NOUN
ejpam-3904	388	26	of	of	ADP
ejpam-3904	388	27	graphs	graph	NOUN
ejpam-3904	388	28	.	.	PUNCT
ejpam-3904	389	1	applied	apply	VERB
ejpam-3904	389	2	mathematical	mathematical	ADJ
ejpam-3904	389	3	sciences	science	NOUN
ejpam-3904	389	4	,	,	PUNCT
ejpam-3904	389	5	8(93):4609–4620	8(93):4609–4620	NUM
ejpam-3904	389	6	.	.	PUNCT
ejpam-3904	390	1	references	reference	NOUN
ejpam-3904	390	2	163	163	NUM
ejpam-3904	390	3	[	[	X
ejpam-3904	390	4	16	16	NUM
ejpam-3904	390	5	]	]	X
ejpam-3904	390	6	s.l.n	s.l.n	NOUN
ejpam-3904	390	7	.	.	PUNCT
ejpam-3904	391	1	marohombsar	marohombsar	PROPN
ejpam-3904	391	2	and	and	CCONJ
ejpam-3904	391	3	f.p	f.p	PROPN
ejpam-3904	391	4	.	.	PROPN
ejpam-3904	391	5	jamil	jamil	PROPN
ejpam-3904	391	6	.	.	PUNCT
ejpam-3904	392	1	on	on	ADP
ejpam-3904	392	2	2	2	NUM
ejpam-3904	392	3	-	-	PUNCT
ejpam-3904	392	4	point	point	NOUN
ejpam-3904	392	5	set	set	VERB
ejpam-3904	392	6	dominating	dominating	NOUN
ejpam-3904	392	7	sets	set	NOUN
ejpam-3904	392	8	in	in	ADP
ejpam-3904	392	9	graphs	graph	NOUN
ejpam-3904	392	10	.	.	PUNCT
ejpam-3904	393	1	advances	advance	NOUN
ejpam-3904	393	2	and	and	CCONJ
ejpam-3904	393	3	applications	application	NOUN
ejpam-3904	393	4	in	in	ADP
ejpam-3904	393	5	discrete	discrete	ADJ
ejpam-3904	393	6	mathematics	mathematic	NOUN
ejpam-3904	393	7	,	,	PUNCT
ejpam-3904	393	8	21(2):139–162	21(2):139–162	PROPN
ejpam-3904	393	9	,	,	PUNCT
ejpam-3904	393	10	2019	2019	NUM
ejpam-3904	393	11	.	.	PUNCT
ejpam-3904	394	1	[	[	X
ejpam-3904	394	2	17	17	NUM
ejpam-3904	394	3	]	]	PUNCT
ejpam-3904	394	4	a.cabrera	a.cabrera	NOUN
ejpam-3904	394	5	martineze	martineze	NOUN
ejpam-3904	394	6	,	,	PUNCT
ejpam-3904	394	7	j.m	j.m	PROPN
ejpam-3904	394	8	.	.	PROPN
ejpam-3904	394	9	sigarreta	sigarreta	PROPN
ejpam-3904	394	10	almira	almira	PROPN
ejpam-3904	394	11	,	,	PUNCT
ejpam-3904	394	12	and	and	CCONJ
ejpam-3904	394	13	i.g	i.g	PROPN
ejpam-3904	394	14	.	.	PROPN
ejpam-3904	394	15	yero	yero	PROPN
ejpam-3904	394	16	.	.	PUNCT
ejpam-3904	395	1	on	on	ADP
ejpam-3904	395	2	the	the	DET
ejpam-3904	395	3	independence	independence	NOUN
ejpam-3904	395	4	transversal	transversal	NOUN
ejpam-3904	395	5	total	total	ADJ
ejpam-3904	395	6	domination	domination	NOUN
ejpam-3904	395	7	number	number	NOUN
ejpam-3904	395	8	of	of	ADP
ejpam-3904	395	9	graphs	graph	NOUN
ejpam-3904	395	10	.	.	PUNCT
ejpam-3904	396	1	discrete	discrete	ADJ
ejpam-3904	396	2	aplied	aplie	VERB
ejpam-3904	396	3	mathematics	mathematic	NOUN
ejpam-3904	396	4	,	,	PUNCT
ejpam-3904	396	5	219:65	219:65	NUM
ejpam-3904	396	6	–	–	PUNCT
ejpam-3904	396	7	73	73	NUM
ejpam-3904	396	8	,	,	PUNCT
ejpam-3904	396	9	2017	2017	NUM
ejpam-3904	396	10	.	.	PUNCT
ejpam-3904	397	1	[	[	X
ejpam-3904	397	2	18	18	NUM
ejpam-3904	397	3	]	]	PUNCT
ejpam-3904	397	4	a.cabrera	a.cabrera	NOUN
ejpam-3904	397	5	martineze	martineze	NOUN
ejpam-3904	397	6	,	,	PUNCT
ejpam-3904	397	7	i.	i.	NOUN
ejpam-3904	397	8	peterine	peterine	NOUN
ejpam-3904	397	9	,	,	PUNCT
ejpam-3904	397	10	and	and	CCONJ
ejpam-3904	397	11	i.g	i.g	PROPN
ejpam-3904	397	12	.	.	PROPN
ejpam-3904	397	13	yero	yero	PROPN
ejpam-3904	397	14	.	.	PUNCT
ejpam-3904	398	1	independent	independent	ADJ
ejpam-3904	398	2	transversal	transversal	ADJ
ejpam-3904	398	3	total	total	ADJ
ejpam-3904	398	4	domination	domination	NOUN
ejpam-3904	398	5	versus	versus	ADP
ejpam-3904	398	6	total	total	ADJ
ejpam-3904	398	7	domination	domination	NOUN
ejpam-3904	398	8	in	in	ADP
ejpam-3904	398	9	trees	tree	NOUN
ejpam-3904	398	10	.	.	PUNCT
ejpam-3904	399	1	discussiones	discussione	NOUN
ejpam-3904	399	2	mathematicae	mathematicae	PROPN
ejpam-3904	399	3	graph	graph	NOUN
ejpam-3904	399	4	theory	theory	NOUN
ejpam-3904	399	5	,	,	PUNCT
ejpam-3904	399	6	41:213–224	41:213–224	PROPN
ejpam-3904	399	7	,	,	PUNCT
ejpam-3904	399	8	2021	2021	NUM
ejpam-3904	399	9	.	.	PUNCT
ejpam-3904	400	1	[	[	X
ejpam-3904	400	2	19	19	NUM
ejpam-3904	400	3	]	]	X
ejpam-3904	400	4	o.	o.	PROPN
ejpam-3904	400	5	ore	ore	PROPN
ejpam-3904	400	6	.	.	PUNCT
ejpam-3904	401	1	theory	theory	NOUN
ejpam-3904	401	2	of	of	ADP
ejpam-3904	401	3	graphs	graph	NOUN
ejpam-3904	401	4	.	.	PUNCT
ejpam-3904	402	1	amer	amer	PROPN
ejpam-3904	402	2	.	.	PUNCT
ejpam-3904	402	3	math	math	PROPN
ejpam-3904	402	4	.	.	PUNCT
ejpam-3904	403	1	soc	soc	PROPN
ejpam-3904	403	2	.	.	PUNCT
ejpam-3904	403	3	,	,	PUNCT
ejpam-3904	403	4	prividence	prividence	NOUN
ejpam-3904	403	5	,	,	PUNCT
ejpam-3904	403	6	ri	ri	PROPN
ejpam-3904	403	7	,	,	PUNCT
ejpam-3904	403	8	38:206–212	38:206–212	NUM
ejpam-3904	403	9	,	,	PUNCT
ejpam-3904	403	10	1962	1962	NUM
ejpam-3904	403	11	.	.	PUNCT
ejpam-3904	404	1	[	[	X
ejpam-3904	404	2	20	20	NUM
ejpam-3904	404	3	]	]	X
ejpam-3904	404	4	v.	v.	PROPN
ejpam-3904	404	5	samodivkine	samodivkine	PROPN
ejpam-3904	404	6	,	,	PUNCT
ejpam-3904	404	7	h.a	h.a	PROPN
ejpam-3904	404	8	.	.	PROPN
ejpam-3904	404	9	ahanger	ahanger	PROPN
ejpam-3904	404	10	,	,	PUNCT
ejpam-3904	404	11	and	and	CCONJ
ejpam-3904	404	12	i.g	i.g	PROPN
ejpam-3904	404	13	.	.	PROPN
ejpam-3904	404	14	yero	yero	PROPN
ejpam-3904	404	15	.	.	PUNCT
ejpam-3904	405	1	independent	independent	ADJ
ejpam-3904	405	2	transversal	transversal	ADJ
ejpam-3904	405	3	dominating	dominating	NOUN
ejpam-3904	405	4	sets	set	NOUN
ejpam-3904	405	5	in	in	ADP
ejpam-3904	405	6	graphs	graph	NOUN
ejpam-3904	405	7	:	:	PUNCT
ejpam-3904	405	8	complexity	complexity	NOUN
ejpam-3904	405	9	and	and	CCONJ
ejpam-3904	405	10	structural	structural	ADJ
ejpam-3904	405	11	properties	property	NOUN
ejpam-3904	405	12	.	.	PUNCT
ejpam-3904	406	1	filomat	filomat	PROPN
ejpam-3904	406	2	,	,	PUNCT
ejpam-3904	406	3	30(2):293–303	30(2):293–303	PROPN
ejpam-3904	406	4	,	,	PUNCT
ejpam-3904	406	5	2016	2016	NUM
ejpam-3904	406	6	.	.	PUNCT